LMFDB - Embedded newform 503.2.c.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(2,503)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(502))

chi = DirichletCharacter(H, H._module([202]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("503.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.c (of order $251$, degree $250$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$10250$
Relative dimension:	$41$ over $\Q(\zeta_{251})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{251}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.945803 - 1.16449i) q^{2} +(-0.790504 + 0.684188i) q^{3} +(-0.0513814 + 0.245250i) q^{4} +(-0.107766 - 0.340345i) q^{5} +(1.54439 + 0.273425i) q^{6} +(0.296825 - 0.861848i) q^{7} +(-2.33318 + 1.20172i) q^{8} +(-0.273541 + 1.88727i) q^{9} +O(q^{10})$	\(q+(-0.945803 - 1.16449i) q^{2} +(-0.790504 + 0.684188i) q^{3} +(-0.0513814 + 0.245250i) q^{4} +(-0.107766 - 0.340345i) q^{5} +(1.54439 + 0.273425i) q^{6} +(0.296825 - 0.861848i) q^{7} +(-2.33318 + 1.20172i) q^{8} +(-0.273541 + 1.88727i) q^{9} +(-0.294402 + 0.447391i) q^{10} +(2.44073 - 0.789665i) q^{11} +(-0.127180 - 0.229026i) q^{12} +(-5.63196 + 1.90033i) q^{13} +(-1.28435 + 0.469489i) q^{14} +(0.318049 + 0.195312i) q^{15} +(4.06512 + 1.78153i) q^{16} +(-3.07927 - 1.53754i) q^{17} +(2.45642 - 1.46645i) q^{18} +(-0.257697 - 0.578148i) q^{19} +(0.0890067 - 0.00894219i) q^{20} +(0.355025 + 0.884379i) q^{21} +(-3.22800 - 2.09533i) q^{22} +(-2.21825 + 7.66748i) q^{23} +(1.02219 - 2.54630i) q^{24} +(3.98455 - 2.80449i) q^{25} +(7.53963 + 4.76100i) q^{26} +(-2.76618 - 4.32046i) q^{27} +(0.196117 + 0.117079i) q^{28} +(-0.698058 + 5.84303i) q^{29} +(-0.0733736 - 0.555090i) q^{30} +(0.275139 + 3.37445i) q^{31} +(-0.374722 - 1.35872i) q^{32} +(-1.38913 + 2.29415i) q^{33} +(1.12193 + 5.03998i) q^{34} +(-0.325313 - 0.00814513i) q^{35} +(-0.448798 - 0.164056i) q^{36} +(0.501595 + 0.633615i) q^{37} +(-0.429516 + 0.846899i) q^{38} +(3.15190 - 5.35554i) q^{39} +(0.660435 + 0.664581i) q^{40} +(-2.08494 + 10.6118i) q^{41} +(0.694065 - 1.24987i) q^{42} +(-0.678624 + 3.69811i) q^{43} +(0.0682574 + 0.639164i) q^{44} +(0.671800 - 0.110285i) q^{45} +(11.0267 - 4.66880i) q^{46} +(-3.27607 + 0.123071i) q^{47} +(-4.43240 + 1.37300i) q^{48} +(4.86080 + 3.79876i) q^{49} +(-7.03439 - 1.98747i) q^{50} +(3.48614 - 0.891369i) q^{51} +(-0.176680 - 1.47888i) q^{52} +(1.71696 - 3.85204i) q^{53} +(-2.41486 + 7.30748i) q^{54} +(-0.531785 - 0.745590i) q^{55} +(0.343152 + 2.36755i) q^{56} +(0.599273 + 0.280715i) q^{57} +(7.46436 - 4.71347i) q^{58} +(-3.88952 + 9.34874i) q^{59} +(-0.0642420 + 0.0679662i) q^{60} +(-0.738171 - 1.21910i) q^{61} +(3.66928 - 3.51196i) q^{62} +(1.54535 + 0.795940i) q^{63} +(3.92669 - 5.50542i) q^{64} +(1.25370 + 1.71201i) q^{65} +(3.98535 - 0.552194i) q^{66} +(-2.15732 + 1.32480i) q^{67} +(0.535299 - 0.676191i) q^{68} +(-3.49247 - 7.57887i) q^{69} +(0.298197 + 0.386527i) q^{70} +(-1.46820 - 9.30755i) q^{71} +(-1.62975 - 4.73206i) q^{72} +(-0.798600 - 0.764360i) q^{73} +(0.263427 - 1.18338i) q^{74} +(-1.23100 + 4.94314i) q^{75} +(0.155032 - 0.0334942i) q^{76} +(0.0438985 - 2.33793i) q^{77} +(-9.21753 + 1.39494i) q^{78} +(-0.297294 - 5.27276i) q^{79} +(0.168254 - 1.57553i) q^{80} +(-0.342867 - 0.101523i) q^{81} +(14.3293 - 7.60878i) q^{82} +(6.45602 + 12.3442i) q^{83} +(-0.235136 + 0.0416294i) q^{84} +(-0.191454 + 1.21371i) q^{85} +(4.94825 - 2.70743i) q^{86} +(-3.44592 - 5.09654i) q^{87} +(-4.74571 + 4.77550i) q^{88} +(-3.50296 - 13.3513i) q^{89} +(-0.763816 - 0.677995i) q^{90} +(-0.0339068 + 5.41796i) q^{91} +(-1.76648 - 0.937992i) q^{92} +(-2.52626 - 2.47927i) q^{93} +(3.24183 + 3.69854i) q^{94} +(-0.168999 + 0.150010i) q^{95} +(1.22584 + 0.817694i) q^{96} +(-3.44695 - 14.6193i) q^{97} +(-0.173745 - 9.25322i) q^{98} +(0.822672 + 4.82232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9}+O(q^{10}) $ 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9} - 233 q^{10} - 239 q^{11} - 239 q^{12} - 245 q^{13} - 223 q^{14} - 231 q^{15} - 263 q^{16} - 243 q^{17} - 217 q^{18} - 229 q^{19} - 195 q^{20} - 215 q^{21} - 233 q^{22} - 241 q^{23} - 181 q^{24} - 280 q^{25} - 215 q^{26} - 237 q^{27} - 185 q^{28} - 217 q^{29} - 159 q^{30} - 219 q^{31} - 185 q^{32} - 209 q^{33} - 167 q^{34} - 187 q^{35} - 203 q^{36} - 237 q^{37} - 161 q^{38} - 197 q^{39} - 135 q^{40} - 209 q^{41} - 117 q^{42} - 221 q^{43} - 147 q^{44} - 167 q^{45} - 167 q^{46} - 195 q^{47} - 141 q^{48} - 234 q^{49} - 145 q^{50} - 177 q^{51} - 179 q^{52} - 211 q^{53} - 83 q^{54} - 165 q^{55} - 125 q^{56} - 177 q^{57} - 205 q^{58} - 189 q^{59} - 27 q^{60} - 193 q^{61} - 143 q^{62} - 159 q^{63} - 185 q^{64} - 155 q^{65} - 97 q^{66} - 201 q^{67} - 155 q^{68} - 113 q^{69} - 123 q^{70} - 153 q^{71} - 21 q^{72} - 213 q^{73} - 83 q^{74} - 161 q^{75} - 97 q^{76} - 139 q^{77} - 43 q^{78} - 191 q^{79} + 3 q^{80} - 188 q^{81} - 97 q^{82} - 161 q^{83} + 67 q^{84} - 159 q^{85} - 121 q^{86} - 121 q^{87} - 143 q^{88} - 155 q^{89} + 115 q^{90} - 137 q^{91} - 119 q^{92} - 123 q^{93} - 99 q^{94} - 181 q^{95} + 67 q^{96} - 229 q^{97} - 63 q^{98} - 85 q^{99}+O(q^{100}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9 - 233 * q^10 - 239 * q^11 - 239 * q^12 - 245 * q^13 - 223 * q^14 - 231 * q^15 - 263 * q^16 - 243 * q^17 - 217 * q^18 - 229 * q^19 - 195 * q^20 - 215 * q^21 - 233 * q^22 - 241 * q^23 - 181 * q^24 - 280 * q^25 - 215 * q^26 - 237 * q^27 - 185 * q^28 - 217 * q^29 - 159 * q^30 - 219 * q^31 - 185 * q^32 - 209 * q^33 - 167 * q^34 - 187 * q^35 - 203 * q^36 - 237 * q^37 - 161 * q^38 - 197 * q^39 - 135 * q^40 - 209 * q^41 - 117 * q^42 - 221 * q^43 - 147 * q^44 - 167 * q^45 - 167 * q^46 - 195 * q^47 - 141 * q^48 - 234 * q^49 - 145 * q^50 - 177 * q^51 - 179 * q^52 - 211 * q^53 - 83 * q^54 - 165 * q^55 - 125 * q^56 - 177 * q^57 - 205 * q^58 - 189 * q^59 - 27 * q^60 - 193 * q^61 - 143 * q^62 - 159 * q^63 - 185 * q^64 - 155 * q^65 - 97 * q^66 - 201 * q^67 - 155 * q^68 - 113 * q^69 - 123 * q^70 - 153 * q^71 - 21 * q^72 - 213 * q^73 - 83 * q^74 - 161 * q^75 - 97 * q^76 - 139 * q^77 - 43 * q^78 - 191 * q^79 + 3 * q^80 - 188 * q^81 - 97 * q^82 - 161 * q^83 + 67 * q^84 - 159 * q^85 - 121 * q^86 - 121 * q^87 - 143 * q^88 - 155 * q^89 + 115 * q^90 - 137 * q^91 - 119 * q^92 - 123 * q^93 - 99 * q^94 - 181 * q^95 + 67 * q^96 - 229 * q^97 - 63 * q^98 - 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/503\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{101}{251}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.945803	−	1.16449i	−0.668783	−	0.823417i	0.323653	−	0.946176i	$-0.395089\pi$
$2$	−0.945803	−	1.16449i	−0.668783	−	0.823417i	−0.992437	+	0.122758i	$0.960826\pi$
$3$	−0.790504	+	0.684188i	−0.456398	+	0.395016i	−0.852114	−	0.523356i	$-0.824680\pi$
$3$	−0.790504	+	0.684188i	−0.456398	+	0.395016i	0.395716	+	0.918373i	$0.370496\pi$
$4$	−0.0513814	+	0.245250i	−0.0256907	+	0.122625i
$5$	−0.107766	−	0.340345i	−0.0481943	−	0.152207i	0.926211	−	0.377006i	$-0.123046\pi$
$5$	−0.107766	−	0.340345i	−0.0481943	−	0.152207i	−0.974405	+	0.224799i	$0.927827\pi$
$6$	1.54439	+	0.273425i	0.630494	+	0.111625i
$7$	0.296825	−	0.861848i	0.112189	−	0.325748i	−0.875267	−	0.483640i	$-0.839314\pi$
$7$	0.296825	−	0.861848i	0.112189	−	0.325748i	0.987456	+	0.157892i	$0.0504698\pi$
$8$	−2.33318	+	1.20172i	−0.824904	+	0.424872i
$9$	−0.273541	+	1.88727i	−0.0911802	+	0.629090i
$10$	−0.294402	+	0.447391i	−0.0930981	+	0.141477i
$11$	2.44073	−	0.789665i	0.735908	−	0.238093i	0.0840788	−	0.996459i	$-0.473205\pi$
$11$	2.44073	−	0.789665i	0.735908	−	0.238093i	0.651829	+	0.758366i	$0.274002\pi$
$12$	−0.127180	−	0.229026i	−0.0367138	−	0.0661141i
$13$	−5.63196	+	1.90033i	−1.56202	+	0.527058i	−0.962029	−	0.272947i	$-0.912002\pi$
$13$	−5.63196	+	1.90033i	−1.56202	+	0.527058i	−0.599994	+	0.800004i	$0.704830\pi$
$14$	−1.28435	+	0.469489i	−0.343257	+	0.125476i
$15$	0.318049	+	0.195312i	0.0821199	+	0.0504292i
$16$	4.06512	+	1.78153i	1.01628	+	0.445383i
$17$	−3.07927	−	1.53754i	−0.746832	−	0.372908i	0.0325389	−	0.999470i	$-0.489641\pi$
$17$	−3.07927	−	1.53754i	−0.746832	−	0.372908i	−0.779371	+	0.626562i	$0.784461\pi$
$18$	2.45642	−	1.46645i	0.578983	−	0.345646i
$19$	−0.257697	−	0.578148i	−0.0591198	−	0.132636i	0.881405	−	0.472361i	$-0.156598\pi$
$19$	−0.257697	−	0.578148i	−0.0591198	−	0.132636i	−0.940525	+	0.339725i	$0.889666\pi$
$20$	0.0890067	−	0.00894219i	0.0199025	−	0.00199953i
$21$	0.355025	+	0.884379i	0.0774728	+	0.192987i
$22$	−3.22800	−	2.09533i	−0.688213	−	0.446726i
$23$	−2.21825	+	7.66748i	−0.462536	+	1.59878i	0.301406	+	0.953496i	$0.402544\pi$
$23$	−2.21825	+	7.66748i	−0.462536	+	1.59878i	−0.763942	+	0.645285i	$0.776739\pi$
$24$	1.02219	−	2.54630i	0.208653	−	0.519761i
$25$	3.98455	−	2.80449i	0.796910	−	0.560897i
$26$	7.53963	+	4.76100i	1.47864	+	0.933710i
$27$	−2.76618	−	4.32046i	−0.532352	−	0.831472i
$28$	0.196117	+	0.117079i	0.0370627	+	0.0221259i
$29$	−0.698058	+	5.84303i	−0.129626	+	1.08502i	0.766817	+	0.641865i	$0.221839\pi$
$29$	−0.698058	+	5.84303i	−0.129626	+	1.08502i	−0.896444	+	0.443158i	$0.853858\pi$
$30$	−0.0733736	−	0.555090i	−0.0133961	−	0.101345i
$31$	0.275139	+	3.37445i	0.0494164	+	0.606069i	0.974216	+	0.225615i	$0.0724393\pi$
$31$	0.275139	+	3.37445i	0.0494164	+	0.606069i	−0.924800	+	0.380454i	$0.875768\pi$
$32$	−0.374722	−	1.35872i	−0.0662421	−	0.240190i
$33$	−1.38913	+	2.29415i	−0.241816	+	0.399361i
$34$	1.12193	+	5.03998i	0.192410	+	0.864350i
$35$	−0.325313	−	0.00814513i	−0.0549879	−	0.00137678i
$36$	−0.448798	−	0.164056i	−0.0747997	−	0.0273427i
$37$	0.501595	+	0.633615i	0.0824617	+	0.104166i	0.823555	−	0.567236i	$-0.191987\pi$
$37$	0.501595	+	0.633615i	0.0824617	+	0.104166i	−0.741094	+	0.671402i	$0.765692\pi$
$38$	−0.429516	+	0.846899i	−0.0696767	+	0.137385i
$39$	3.15190	−	5.35554i	0.504707	−	0.857573i
$40$	0.660435	+	0.664581i	0.104424	+	0.105080i
$41$	−2.08494	+	10.6118i	−0.325613	+	1.65728i	0.362726	+	0.931896i	$0.381846\pi$
$41$	−2.08494	+	10.6118i	−0.325613	+	1.65728i	−0.688339	+	0.725389i	$0.741660\pi$
$42$	0.694065	−	1.24987i	0.107096	−	0.192859i
$43$	−0.678624	+	3.69811i	−0.103489	+	0.563956i	0.890546	+	0.454894i	$0.150323\pi$
$43$	−0.678624	+	3.69811i	−0.103489	+	0.563956i	−0.994035	+	0.109063i	$0.965215\pi$
$44$	0.0682574	+	0.639164i	0.0102902	+	0.0963575i
$45$	0.671800	−	0.110285i	0.100146	−	0.0164403i
$46$	11.0267	−	4.66880i	1.62580	−	0.688378i
$47$	−3.27607	+	0.123071i	−0.477864	+	0.0179517i	−0.275383	−	0.961335i	$-0.588805\pi$
$47$	−3.27607	+	0.123071i	−0.477864	+	0.0179517i	−0.202481	+	0.979286i	$0.564900\pi$
$48$	−4.43240	+	1.37300i	−0.639761	+	0.198176i
$49$	4.86080	+	3.79876i	0.694400	+	0.542680i
$50$	−7.03439	−	1.98747i	−0.994812	−	0.281070i
$51$	3.48614	−	0.891369i	0.488157	−	0.124817i
$52$	−0.176680	−	1.47888i	−0.0245010	−	0.205084i
$53$	1.71696	−	3.85204i	0.235843	−	0.529118i	−0.756300	−	0.654225i	$-0.772995\pi$
$53$	1.71696	−	3.85204i	0.235843	−	0.529118i	0.992143	+	0.125107i	$0.0399273\pi$
$54$	−2.41486	+	7.30748i	−0.328621	+	0.994422i
$55$	−0.531785	−	0.745590i	−0.0717059	−	0.100535i
$56$	0.343152	+	2.36755i	0.0458556	+	0.316377i
$57$	0.599273	+	0.280715i	0.0793756	+	0.0371816i
$58$	7.46436	−	4.71347i	0.980119	−	0.618909i
$59$	−3.88952	+	9.34874i	−0.506373	+	1.21710i	0.441156	+	0.897431i	$0.354569\pi$
$59$	−3.88952	+	9.34874i	−0.506373	+	1.21710i	−0.947528	+	0.319672i	$0.896427\pi$
$60$	−0.0642420	+	0.0679662i	−0.00829361	+	0.00877440i
$61$	−0.738171	−	1.21910i	−0.0945132	−	0.156089i	0.804583	−	0.593840i	$-0.202389\pi$
$61$	−0.738171	−	1.21910i	−0.0945132	−	0.156089i	−0.899096	+	0.437751i	$0.855775\pi$
$62$	3.66928	−	3.51196i	0.465999	−	0.446019i
$63$	1.54535	+	0.795940i	0.194695	+	0.100279i
$64$	3.92669	−	5.50542i	0.490836	−	0.688177i
$65$	1.25370	+	1.71201i	0.155502	+	0.212349i
$66$	3.98535	−	0.552194i	0.490563	−	0.0679704i
$67$	−2.15732	+	1.32480i	−0.263559	+	0.161850i	−0.648783	−	0.760973i	$-0.724722\pi$
$67$	−2.15732	+	1.32480i	−0.263559	+	0.161850i	0.385224	+	0.922823i	$0.374124\pi$
$68$	0.535299	−	0.676191i	0.0649146	−	0.0820001i
$69$	−3.49247	−	7.57887i	−0.420444	−	0.912389i
$70$	0.298197	+	0.386527i	0.0356413	+	0.0461988i
$71$	−1.46820	−	9.30755i	−0.174243	−	1.10460i	−0.906075	−	0.423117i	$-0.860936\pi$
$71$	−1.46820	−	9.30755i	−0.174243	−	1.10460i	0.731832	−	0.681485i	$-0.238666\pi$
$72$	−1.62975	−	4.73206i	−0.192068	−	0.557679i
$73$	−0.798600	−	0.764360i	−0.0934690	−	0.0894616i	0.643267	−	0.765642i	$-0.277578\pi$
$73$	−0.798600	−	0.764360i	−0.0934690	−	0.0894616i	−0.736736	+	0.676180i	$0.763634\pi$
$74$	0.263427	−	1.18338i	0.0306228	−	0.137565i
$75$	−1.23100	+	4.94314i	−0.142144	+	0.570784i
$76$	0.155032	−	0.0334942i	0.0177834	−	0.00384205i
$77$	0.0438985	−	2.33793i	0.00500270	−	0.266432i
$78$	−9.21753	+	1.39494i	−1.04368	+	0.157946i
$79$	−0.297294	−	5.27276i	−0.0334482	−	0.593232i	−0.970060	−	0.242864i	$-0.921913\pi$
$79$	−0.297294	−	5.27276i	−0.0334482	−	0.593232i	0.936612	−	0.350368i	$-0.113943\pi$
$80$	0.168254	−	1.57553i	0.0188113	−	0.176150i
$81$	−0.342867	−	0.101523i	−0.0380963	−	0.0112803i
$82$	14.3293	−	7.60878i	1.58240	−	0.840249i
$83$	6.45602	+	12.3442i	0.708640	+	1.35495i	0.925499	+	0.378749i	$0.123646\pi$
$83$	6.45602	+	12.3442i	0.708640	+	1.35495i	−0.216859	+	0.976203i	$0.569581\pi$
$84$	−0.235136	+	0.0416294i	−0.0256554	+	0.00454214i
$85$	−0.191454	+	1.21371i	−0.0207661	+	0.131645i
$86$	4.94825	−	2.70743i	0.533583	−	0.291950i
$87$	−3.44592	−	5.09654i	−0.369441	−	0.546406i
$88$	−4.74571	+	4.77550i	−0.505894	+	0.509070i
$89$	−3.50296	−	13.3513i	−0.371313	−	1.41524i	−0.845104	−	0.534602i	$-0.820461\pi$
$89$	−3.50296	−	13.3513i	−0.371313	−	1.41524i	0.473791	−	0.880637i	$-0.342885\pi$
$90$	−0.763816	−	0.677995i	−0.0805133	−	0.0714670i
$91$	−0.0339068	+	5.41796i	−0.00355440	+	0.567956i
$92$	−1.76648	−	0.937992i	−0.184168	−	0.0977924i
$93$	−2.52626	−	2.47927i	−0.261961	−	0.257088i
$94$	3.24183	+	3.69854i	0.334369	+	0.381476i
$95$	−0.168999	+	0.150010i	−0.0173389	+	0.0153907i
$96$	1.22584	+	0.817694i	0.125112	+	0.0834556i
$97$	−3.44695	−	14.6193i	−0.349985	−	1.48437i	−0.804674	−	0.593717i	$-0.797660\pi$
$97$	−3.44695	−	14.6193i	−0.349985	−	1.48437i	0.454689	−	0.890650i	$-0.349750\pi$
$98$	−0.173745	−	9.25322i	−0.0175509	−	0.934716i
$99$	0.822672	+	4.82232i	0.0826817	+	0.484661i
$100$	0.483069	+	1.12131i	0.0483069	+	0.112131i
$101$	−9.15810	+	3.61005i	−0.911265	+	0.359213i	−0.775368	−	0.631510i	$-0.782435\pi$
$101$	−9.15810	+	3.61005i	−0.911265	+	0.359213i	−0.135897	+	0.990723i	$0.543392\pi$
$102$	−4.33519	−	3.21651i	−0.429248	−	0.318482i
$103$	8.38195	−	1.70138i	0.825898	−	0.167642i	0.232546	−	0.972585i	$-0.425294\pi$
$103$	8.38195	−	1.70138i	0.825898	−	0.167642i	0.593352	+	0.804943i	$0.297804\pi$
$104$	10.8567	−	11.2018i	1.06459	−	1.09843i
$105$	0.262734	−	0.216137i	0.0256402	−	0.0210928i
$106$	−6.10956	+	1.64388i	−0.593413	+	0.159668i
$107$	−17.9971	−	0.676090i	−1.73985	−	0.0653601i	−0.851451	−	0.524435i	$-0.824277\pi$
$107$	−17.9971	−	0.676090i	−1.73985	−	0.0653601i	−0.888398	+	0.459075i	$0.848181\pi$
$108$	1.20172	−	0.456415i	0.115636	−	0.0439186i
$109$	−6.57910	−	6.96050i	−0.630163	−	0.666695i	0.330694	−	0.943738i	$-0.392717\pi$
$109$	−6.57910	−	6.96050i	−0.630163	−	0.666695i	−0.960857	+	0.277043i	$0.910645\pi$
$110$	−0.365267	+	1.32444i	−0.0348268	+	0.126280i
$111$	−0.830025	−	0.157690i	−0.0787825	−	0.0149673i
$112$	2.74204	−	2.97471i	0.259098	−	0.281084i
$113$	−0.783211	−	1.59343i	−0.0736783	−	0.149897i	0.857474	−	0.514527i	$-0.172032\pi$
$113$	−0.783211	−	1.59343i	−0.0736783	−	0.149897i	−0.931153	+	0.364629i	$0.881196\pi$
$114$	−0.239905	−	0.963347i	−0.0224691	−	0.0902257i
$115$	2.84864	−	0.0713237i	0.265637	−	0.00665097i
$116$	−1.39714	−	0.471422i	−0.129721	−	0.0437704i
$117$	−2.04587	−	11.1488i	−0.189141	−	1.03071i
$118$	14.5652	−	4.31276i	1.34084	−	0.397022i
$119$	−2.23913	+	2.19748i	−0.205261	+	0.201443i
$120$	−0.976775	−	0.0734919i	−0.0891670	−	0.00670886i
$121$	−3.58175	+	2.58862i	−0.325614	+	0.235329i
$122$	−0.721458	+	2.01262i	−0.0653177	+	0.182214i
$123$	−5.61232	−	9.81516i	−0.506046	−	0.885003i
$124$	−0.841722	−	0.105906i	−0.0755888	−	0.00951064i
$125$	−2.80398	−	2.13535i	−0.250795	−	0.190991i
$126$	−0.534730	−	2.55234i	−0.0476376	−	0.227380i
$127$	−5.34649	+	3.01289i	−0.474425	+	0.267351i	−0.709603	−	0.704602i	$-0.751126\pi$
$127$	−5.34649	+	3.01289i	−0.474425	+	0.267351i	0.235179	+	0.971952i	$0.424433\pi$
$128$	−12.9382	+	0.810753i	−1.14359	+	0.0716611i
$129$	−1.99375	−	3.38768i	−0.175540	−	0.298268i
$130$	0.807868	−	3.07915i	0.0708547	−	0.270059i
$131$	−15.0151	+	10.0158i	−1.31187	+	0.875082i	−0.997248	−	0.0741344i	$-0.976381\pi$
$131$	−15.0151	+	10.0158i	−1.31187	+	0.875082i	−0.314625	+	0.949216i	$0.601879\pi$
$132$	−0.491266	−	0.458560i	−0.0427592	−	0.0399125i
$133$	−0.574767	+	0.0504870i	−0.0498386	+	0.00437777i
$134$	3.58311	+	1.25918i	0.309534	+	0.108777i
$135$	−1.17234	+	1.40705i	−0.100899	+	0.121100i
$136$	9.03218	−	0.113055i	0.774503	−	0.00969442i
$137$	6.48398	+	16.7554i	0.553964	+	1.43151i	0.874851	+	0.484392i	$0.160959\pi$
$137$	6.48398	+	16.7554i	0.553964	+	1.43151i	−0.320887	+	0.947118i	$0.603981\pi$
$138$	−5.52232	+	11.2351i	−0.470091	+	0.956392i
$139$	0.955210	+	0.206371i	0.0810198	+	0.0175041i	0.251504	−	0.967856i	$-0.419075\pi$
$139$	0.955210	+	0.206371i	0.0810198	+	0.0175041i	−0.170484	+	0.985360i	$0.554533\pi$
$140$	0.0187126	−	0.0793646i	0.00158151	−	0.00670753i
$141$	2.50554	−	2.33874i	0.211005	−	0.196957i
$142$	−9.44990	+	10.5128i	−0.793018	+	0.882215i
$143$	−12.2455	+	9.08556i	−1.02402	+	0.759773i
$144$	−4.47420	+	7.18466i	−0.372850	+	0.598721i
$145$	2.06387	−	0.392098i	0.171395	−	0.0325620i
$146$	−0.134770	+	1.65289i	−0.0111537	+	0.136794i
$147$	−6.44155	+	0.322767i	−0.531290	+	0.0266214i
$148$	−0.181167	+	0.0904602i	−0.0148918	+	0.00743578i
$149$	1.29405	−	2.02116i	0.106013	−	0.165580i	−0.785089	−	0.619382i	$-0.787383\pi$
$149$	1.29405	−	2.02116i	0.106013	−	0.165580i	0.891102	+	0.453803i	$0.149933\pi$
$150$	6.92051	−	3.24175i	0.565057	−	0.264687i
$151$	−1.06631	−	1.62042i	−0.0867748	−	0.131868i	0.789367	−	0.613922i	$-0.210409\pi$
$151$	−1.06631	−	1.62042i	−0.0867748	−	0.131868i	−0.876142	+	0.482054i	$0.839891\pi$
$152$	1.29603	+	1.03924i	0.105122	+	0.0842939i
$153$	3.74406	−	5.39083i	0.302689	−	0.435823i
$154$	−2.76401	+	2.16010i	−0.222730	+	0.174066i
$155$	1.11882	−	0.457292i	0.0898662	−	0.0367306i
$156$	1.15150	+	1.04818i	0.0921937	+	0.0839214i
$157$	8.00400	−	16.8123i	0.638789	−	1.34177i	−0.284874	−	0.958565i	$-0.591952\pi$
$157$	8.00400	−	16.8123i	0.638789	−	1.34177i	0.923663	−	0.383205i	$-0.125180\pi$
$158$	−5.85889	+	5.33319i	−0.466108	+	0.424286i
$159$	1.27825	+	4.21978i	0.101372	+	0.334650i
$160$	−0.422051	+	0.273958i	−0.0333661	+	0.0216583i
$161$	5.94977	+	4.18769i	0.468908	+	0.330036i
$162$	0.206062	+	0.495284i	0.0161898	+	0.0389132i
$163$	1.71757	+	0.652334i	0.134530	+	0.0510948i	0.421400	−	0.906875i	$-0.361539\pi$
$163$	1.71757	+	0.652334i	0.134530	+	0.0510948i	−0.286869	+	0.957970i	$0.592615\pi$
$164$	−2.49542	−	1.05658i	−0.194860	−	0.0825052i
$165$	0.930502	+	0.225551i	0.0724395	+	0.0175591i
$166$	8.26856	−	19.1931i	0.641765	−	1.48968i
$167$	−0.606320	+	19.3706i	−0.0469184	+	1.49894i	0.637837	+	0.770171i	$0.279829\pi$
$167$	−0.606320	+	19.3706i	−0.0469184	+	1.49894i	−0.684755	+	0.728773i	$0.740091\pi$
$168$	−1.89111	−	1.63677i	−0.145902	−	0.126280i
$169$	17.7652	−	13.5290i	1.36656	−	1.04069i
$170$	1.59442	−	0.924981i	0.122287	−	0.0709428i
$171$	1.16161	−	0.328197i	0.0888307	−	0.0250979i
$172$	−0.872093	−	0.356447i	−0.0664965	−	0.0271788i
$173$	−10.1961	−	21.4168i	−0.775194	−	1.62829i	−0.777979	−	0.628290i	$-0.783755\pi$
$173$	−10.1961	−	21.4168i	−0.775194	−	1.62829i	0.00278573	−	0.999996i	$-0.499113\pi$
$174$	−2.67570	+	8.83305i	−0.202845	+	0.669632i
$175$	−1.23433	−	4.26652i	−0.0933064	−	0.322518i
$176$	11.3287	+	1.13815i	0.853931	+	0.0857914i
$177$	−3.32162	−	10.0514i	−0.249668	−	0.755508i
$178$	−12.2344	+	16.7069i	−0.917005	+	1.25223i
$179$	6.81519	−	12.6431i	0.509391	−	0.944987i	−0.488003	−	0.872842i	$-0.662275\pi$
$179$	6.81519	−	12.6431i	0.509391	−	0.944987i	0.997394	−	0.0721449i	$-0.0229844\pi$
$180$	−0.00747063	+	0.170426i	−0.000556828	+	0.0127028i
$181$	−1.11788	−	16.2132i	−0.0830911	−	1.20512i	−0.836651	−	0.547737i	$-0.815489\pi$
$181$	−1.11788	−	16.2132i	−0.0830911	−	1.20512i	0.753559	−	0.657380i	$-0.228335\pi$
$182$	6.34122	−	5.08483i	0.470042	−	0.376913i
$183$	1.41762	+	0.458651i	0.104793	+	0.0339045i
$184$	−4.03858	−	20.5553i	−0.297728	−	1.51536i
$185$	0.161593	−	0.238997i	0.0118805	−	0.0175714i
$186$	−0.497737	+	5.28669i	−0.0364958	+	0.387639i
$187$	−8.72980	−	1.32113i	−0.638387	−	0.0966105i
$188$	0.138146	−	0.809781i	0.0100753	−	0.0590593i
$189$	−4.54465	+	1.10161i	−0.330575	+	0.0801302i
$190$	0.334525	+	0.0549167i	0.0242690	+	0.00398407i
$191$	−0.485049	+	8.60275i	−0.0350969	+	0.622473i	0.931115	+	0.364725i	$0.118837\pi$
$191$	−0.485049	+	8.60275i	−0.0350969	+	0.622473i	−0.966212	+	0.257748i	$0.917020\pi$
$192$	0.662681	+	7.03865i	0.0478249	+	0.507970i
$193$	2.95540	+	1.61704i	0.212734	+	0.116397i	0.582824	−	0.812599i	$-0.301948\pi$
$193$	2.95540	+	1.61704i	0.212734	+	0.116397i	−0.370089	+	0.928996i	$0.620673\pi$
$194$	−13.7639	+	17.8409i	−0.988189	+	1.28090i
$195$	−2.16239	−	0.495587i	−0.154852	−	0.0354897i
$196$	−1.18140	+	0.996926i	−0.0843858	+	0.0712090i
$197$	24.4846	−	1.84220i	1.74445	−	0.131252i	0.835863	−	0.548938i	$-0.184968\pi$
$197$	24.4846	−	1.84220i	1.74445	−	0.131252i	0.908591	+	0.417686i	$0.137159\pi$
$198$	4.83745	−	5.51895i	0.343782	−	0.392215i
$199$	0.129754	+	20.7333i	0.00919799	+	1.46974i	0.682777	+	0.730627i	$0.260772\pi$
$199$	0.129754	+	20.7333i	0.00919799	+	1.46974i	−0.673579	+	0.739115i	$0.735244\pi$
$200$	−5.92647	+	11.3317i	−0.419064	+	0.801271i
$201$	0.798962	−	2.52327i	0.0563544	−	0.177978i
$202$	12.8656	+	7.25010i	0.905221	+	0.510116i
$203$	4.82860	+	2.33598i	0.338901	+	0.163954i
$204$	0.0394856	+	0.900777i	0.00276455	+	0.0630670i
$205$	3.83635	−	0.433990i	0.267943	−	0.0303112i
$206$	−9.90891	−	8.15151i	−0.690386	−	0.567942i
$207$	−13.8638	−	6.28380i	−0.963603	−	0.436754i
$208$	−26.2801	−	2.30842i	−1.82220	−	0.160060i
$209$	−1.08551	−	1.20761i	−0.0750865	−	0.0835320i
$210$	−0.500183	−	0.101528i	−0.0345159	−	0.00700609i
$211$	17.6944	−	12.1258i	1.21814	−	0.834772i	0.227833	−	0.973700i	$-0.426836\pi$
$211$	17.6944	−	12.1258i	1.21814	−	0.834772i	0.990302	+	0.138929i	$0.0443658\pi$
$212$	0.856493	+	0.619009i	0.0588242	+	0.0425137i
$213$	7.52873	+	6.35312i	0.515860	+	0.435309i
$214$	16.2344	+	21.5969i	1.10976	+	1.47633i
$215$	1.33176	−	0.167563i	0.0908255	−	0.0114277i
$216$	11.6460	+	6.75623i	0.792408	+	0.459704i
$217$	2.98993	+	0.764493i	0.202970	+	0.0518972i
$218$	−1.88289	+	14.2445i	−0.127525	+	0.964762i
$219$	1.15426	+	0.0578367i	0.0779978	+	0.00390824i
$220$	0.210180	−	0.0921110i	0.0141703	−	0.00621012i
$221$	20.2641	+	2.80772i	1.36311	+	0.188868i
$222$	0.601412	+	1.11570i	0.0403641	+	0.0748807i
$223$	−13.8970	+	6.72306i	−0.930609	+	0.450209i	−0.838109	−	0.545503i	$-0.816338\pi$
$223$	−13.8970	+	6.72306i	−0.930609	+	0.450209i	−0.0925002	+	0.995713i	$0.529486\pi$
$224$	−1.28224	−	0.0803494i	−0.0856732	−	0.00536857i
$225$	4.20289	+	8.28706i	0.280192	+	0.552470i
$226$	−1.11477	+	2.41911i	−0.0741531	+	0.160917i
$227$	−2.66300	+	0.610318i	−0.176750	+	0.0405082i	−0.310847	−	0.950460i	$-0.600613\pi$
$227$	−2.66300	+	0.610318i	−0.176750	+	0.0405082i	0.134098	+	0.990968i	$0.457186\pi$
$228$	−0.0996369	+	0.132548i	−0.00659861	+	0.00877822i
$229$	−7.53651	+	13.1803i	−0.498027	+	0.870980i	0.501955	+	0.864894i	$0.332614\pi$
$229$	−7.53651	+	13.1803i	−0.498027	+	0.870980i	−0.999981	+	0.00608569i	$0.998063\pi$
$230$	−2.77730	−	3.24975i	−0.183130	−	0.214282i
$231$	1.56488	+	1.87818i	0.102962	+	0.123575i
$232$	−5.39298	−	14.4717i	−0.354067	−	0.950114i
$233$	19.8359	+	0.248285i	1.29949	+	0.0162657i	0.659261	−	0.751914i	$-0.270869\pi$
$233$	19.8359	+	0.248285i	1.29949	+	0.0162657i	0.640234	+	0.768180i	$0.278838\pi$
$234$	−11.0477	+	12.9270i	−0.722210	+	0.845064i
$235$	0.394934	+	1.10173i	0.0257627	+	0.0718689i
$236$	−2.09293	−	1.43426i	−0.136238	−	0.0933622i
$237$	3.84258	+	3.96473i	0.249602	+	0.257537i
$238$	4.67672	+	0.529057i	0.303147	+	0.0342936i
$239$	−0.912167	+	13.2297i	−0.0590032	+	0.855755i	0.871714	+	0.490015i	$0.163009\pi$
$239$	−0.912167	+	13.2297i	−0.0590032	+	0.855755i	−0.930717	+	0.365740i	$0.880816\pi$
$240$	0.944954	+	1.36058i	0.0609965	+	0.0878250i
$241$	27.0639	+	8.38345i	1.74334	+	0.540026i	0.992692	−	0.120677i	$-0.0385065\pi$
$241$	27.0639	+	8.38345i	1.74334	+	0.540026i	0.750648	+	0.660703i	$0.229742\pi$
$242$	6.40205	+	1.72258i	0.411540	+	0.110732i
$243$	14.3582	−	6.50786i	0.921078	−	0.417480i
$244$	0.336912	−	0.118398i	0.0215686	−	0.00757965i
$245$	0.769060	−	2.06372i	0.0491334	−	0.131846i
$246$	−6.12149	+	15.8187i	−0.390292	+	1.00856i
$247$	2.55001	+	2.76639i	0.162253	+	0.176021i
$248$	−4.69709	−	7.54256i	−0.298265	−	0.478953i
$249$	−13.5493	−	5.34101i	−0.858650	−	0.338473i
$250$	0.165420	+	5.28481i	0.0104621	+	0.334241i
$251$	1.21496	−	1.49588i	0.0766878	−	0.0944193i	−0.736445	−	0.676497i	$-0.763497\pi$
$251$	1.21496	−	1.49588i	0.0766878	−	0.0944193i	0.813133	+	0.582078i	$0.197760\pi$
$252$	−0.274606	+	0.338100i	−0.0172986	+	0.0212983i
$253$	0.640603	+	20.4659i	0.0402744	+	1.28668i
$254$	8.56520	+	3.37633i	0.537428	+	0.211850i
$255$	−0.679059	−	1.09043i	−0.0425243	−	0.0682854i
$256$	4.01464	+	4.35530i	0.250915	+	0.272206i
$257$	5.45067	−	14.0852i	0.340003	−	0.878609i	−0.652655	−	0.757655i	$-0.726345\pi$
$257$	5.45067	−	14.0852i	0.340003	−	0.878609i	0.992658	−	0.120954i	$-0.0385954\pi$
$258$	−2.05921	+	5.52577i	−0.128201	+	0.344019i
$259$	0.694966	−	0.244226i	0.0431831	−	0.0151754i
$260$	−0.484289	+	0.219505i	−0.0300343	+	0.0136131i
$261$	−10.8364	−	2.91573i	−0.670758	−	0.180479i
$262$	25.8645	+	8.01193i	1.59792	+	0.494979i
$263$	0.925476	+	1.33253i	0.0570673	+	0.0821676i	0.848845	−	0.528642i	$-0.177298\pi$
$263$	0.925476	+	1.33253i	0.0570673	+	0.0821676i	−0.791778	+	0.610809i	$0.790844\pi$
$264$	0.484158	−	7.02201i	0.0297979	−	0.432175i
$265$	−1.49605	−	0.169242i	−0.0919016	−	0.0103964i
$266$	0.602407	+	0.621558i	0.0369360	+	0.0381102i
$267$	11.9039	+	8.15761i	0.728509	+	0.499237i
$268$	−0.214060	−	0.597154i	−0.0130758	−	0.0364770i
$269$	−4.80942	+	5.62754i	−0.293235	+	0.343117i	−0.887209	−	0.461367i	$-0.847359\pi$
$269$	−4.80942	+	5.62754i	−0.293235	+	0.343117i	0.593974	+	0.804484i	$0.297558\pi$
$270$	2.74730	+	0.0343878i	0.167195	+	0.00209278i
$271$	6.01767	+	16.1480i	0.365547	+	0.980922i	0.981215	+	0.192916i	$0.0617946\pi$
$271$	6.01767	+	16.1480i	0.365547	+	0.980922i	−0.615668	+	0.788006i	$0.711114\pi$
$272$	−9.77842	−	11.7361i	−0.592904	−	0.711605i
$273$	−3.68010	−	4.30611i	−0.222730	−	0.260618i
$274$	13.3789	−	23.3978i	0.808248	−	1.41351i
$275$	7.51060	−	9.99145i	0.452906	−	0.602507i
$276$	2.03817	−	0.467116i	0.122683	−	0.0281171i
$277$	−6.14587	+	13.3369i	−0.369269	+	0.801337i	0.630416	+	0.776257i	$0.282884\pi$
$277$	−6.14587	+	13.3369i	−0.369269	+	0.801337i	−0.999685	+	0.0250794i	$0.992016\pi$
$278$	−0.663124	−	1.30752i	−0.0397715	−	0.0784196i
$279$	−6.44376	−	0.403787i	−0.385778	−	0.0241741i
$280$	0.768802	−	0.371930i	0.0459447	−	0.0222271i
$281$	−4.23859	−	7.86314i	−0.252853	−	0.469076i	0.722009	−	0.691883i	$-0.243219\pi$
$281$	−4.23859	−	7.86314i	−0.252853	−	0.469076i	−0.974862	+	0.222808i	$0.928478\pi$
$282$	−5.09318	−	0.705690i	−0.303294	−	0.0420232i
$283$	−17.7795	+	7.79185i	−1.05688	+	0.463177i	−0.856289	−	0.516497i	$-0.827236\pi$
$283$	−17.7795	+	7.79185i	−1.05688	+	0.463177i	−0.200595	+	0.979674i	$0.564288\pi$
$284$	2.35812	+	0.118158i	0.139928	+	0.00701141i
$285$	0.0309587	−	0.234211i	0.00183383	−	0.0138734i
$286$	22.1618	+	5.66654i	1.31046	+	0.335069i
$287$	8.52690	+	4.94675i	0.503327	+	0.291998i
$288$	2.66678	−	0.335536i	0.157141	−	0.0197716i
$289$	−3.09693	−	4.11989i	−0.182172	−	0.242346i
$290$	−2.40861	−	2.03250i	−0.141438	−	0.119353i
$291$	12.7272	+	9.19826i	0.746081	+	0.539212i
$292$	0.228493	−	0.156583i	0.0133715	−	0.00916332i
$293$	−25.5674	−	5.18970i	−1.49366	−	0.303186i	−0.618025	−	0.786158i	$-0.712067\pi$
$293$	−25.5674	−	5.18970i	−1.49366	−	0.303186i	−0.875636	+	0.482972i	$0.839557\pi$
$294$	6.46829	+	7.19583i	0.377238	+	0.419669i
$295$	3.60095	+	0.316304i	0.209655	+	0.0184159i
$296$	−1.93174	−	0.875563i	−0.112280	−	0.0508911i
$297$	−10.1632	−	8.36071i	−0.589729	−	0.485138i
$298$	−3.57753	+	0.404711i	−0.207241	+	0.0234443i
$299$	−2.07771	−	47.3983i	−0.120157	−	2.74112i
$300$	−1.14906	−	0.555889i	−0.0663407	−	0.0320943i
$301$	2.98578	+	1.68256i	0.172097	+	0.0969813i
$302$	−0.878447	+	2.77430i	−0.0505489	+	0.159643i
$303$	4.76956	−	9.11962i	0.274004	−	0.523908i
$304$	−0.0175815	−	2.80934i	−0.00100837	−	0.161127i
$305$	−0.335363	+	0.382609i	−0.0192028	+	0.0219081i
$306$	−9.81870	+	0.738752i	−0.561298	+	0.0422317i
$307$	1.55005	−	1.30801i	0.0884662	−	0.0746523i	−0.599602	−	0.800299i	$-0.704674\pi$
$307$	1.55005	−	1.30801i	0.0884662	−	0.0746523i	0.688068	+	0.725646i	$0.258459\pi$
$308$	0.571122	+	0.130892i	0.0325427	+	0.00745828i
$309$	−5.46190	+	7.07978i	−0.310716	+	0.402755i
$310$	−1.59070	−	0.870350i	−0.0903456	−	0.0494326i
$311$	−0.427044	−	4.53584i	−0.0242155	−	0.257204i	−0.999364	−	0.0356526i	$-0.988649\pi$
$311$	−0.427044	−	4.53584i	−0.0242155	−	0.257204i	0.975149	−	0.221551i	$-0.0711119\pi$
$312$	−0.918092	+	16.2831i	−0.0519767	+	0.921851i
$313$	15.8286	+	2.59848i	0.894688	+	0.146875i	0.591737	−	0.806131i	$-0.298443\pi$
$313$	15.8286	+	2.59848i	0.894688	+	0.146875i	0.302951	+	0.953006i	$0.402028\pi$
$314$	−27.1480	+	6.58057i	−1.53205	+	0.371363i
$315$	0.104358	−	0.611725i	0.00587993	−	0.0344668i
$316$	1.30842	+	0.198010i	0.0736045	+	0.0111390i
$317$	−0.477168	+	5.06823i	−0.0268004	+	0.284660i	0.971971	+	0.235102i	$0.0755423\pi$
$317$	−0.477168	+	5.06823i	−0.0268004	+	0.284660i	−0.998771	+	0.0495583i	$0.984219\pi$
$318$	3.70490	−	5.47958i	0.207761	−	0.307280i
$319$	2.91027	+	14.8125i	0.162944	+	0.829340i
$320$	−2.29690	−	0.743131i	−0.128401	−	0.0415423i
$321$	14.6894	−	11.7790i	0.819881	−	0.657438i
$322$	−0.750794	−	10.8892i	−0.0418401	−	0.606830i
$323$	−0.0954068	+	2.17649i	−0.00530858	+	0.121103i
$324$	0.0425155	−	0.0788717i	0.00236197	−	0.00438176i
$325$	−17.1113	+	23.3667i	−0.949166	+	1.29615i
$326$	−0.864847	−	2.61707i	−0.0478994	−	0.144946i
$327$	9.96309	+	1.00096i	0.550960	+	0.0553530i
$328$	−7.88785	−	27.2648i	−0.435534	−	1.50544i
$329$	−0.866352	+	2.86001i	−0.0477635	+	0.157677i
$330$	−0.617421	−	1.29688i	−0.0339879	−	0.0713912i
$331$	−9.34262	−	3.81856i	−0.513517	−	0.209887i	0.106739	−	0.994287i	$-0.465959\pi$
$331$	−9.34262	−	3.81856i	−0.513517	−	0.209887i	−0.620256	+	0.784400i	$0.712971\pi$
$332$	−3.35914	+	0.949077i	−0.184357	+	0.0520874i
$333$	−1.33301	+	0.773325i	−0.0730485	+	0.0423780i
$334$	23.1303	−	17.6147i	1.26564	−	0.963836i
$335$	0.683373	+	0.591466i	0.0373367	+	0.0323152i
$336$	−0.132328	+	4.22759i	−0.00721907	+	0.230634i
$337$	−10.2697	+	23.8382i	−0.559426	+	1.29855i	0.369825	+	0.929101i	$0.379418\pi$
$337$	−10.2697	+	23.8382i	−0.559426	+	1.29855i	−0.929251	+	0.369449i	$0.879547\pi$
$338$	−32.5568	−	7.89165i	−1.77085	−	0.429249i
$339$	1.70934	+	0.723748i	0.0928384	+	0.0393086i
$340$	−0.287825	−	0.109316i	−0.0156095	−	0.00592849i
$341$	3.33622	+	8.01885i	0.180667	+	0.434245i
$342$	−1.48084	−	1.04227i	−0.0800745	−	0.0563597i
$343$	10.0688	−	6.53577i	0.543664	−	0.352898i
$344$	−2.86073	−	9.44387i	−0.154240	−	0.509179i
$345$	−2.20306	+	2.00539i	−0.118609	+	0.107966i
$346$	−15.2961	+	32.1292i	−0.822322	+	1.72728i
$347$	18.0377	+	16.4193i	0.968316	+	0.881432i	0.992982	−	0.118264i	$-0.0377328\pi$
$347$	18.0377	+	16.4193i	0.968316	+	0.881432i	−0.0246663	+	0.999696i	$0.507852\pi$
$348$	1.42698	−	0.583244i	0.0764943	−	0.0312652i
$349$	−23.2573	+	18.1758i	−1.24493	+	0.972929i	−0.244941	+	0.969538i	$0.578768\pi$
$349$	−23.2573	+	18.1758i	−1.24493	+	0.972929i	−0.999994	+	0.00339055i	$0.998921\pi$
$350$	−3.80088	+	5.47264i	−0.203165	+	0.292525i
$351$	23.7893	+	19.0760i	1.26978	+	1.01820i
$352$	−1.98753	−	3.02037i	−0.105936	−	0.160986i
$353$	3.98481	−	1.86659i	0.212090	−	0.0993484i	−0.315230	−	0.949015i	$-0.602082\pi$
$353$	3.98481	−	1.86659i	0.212090	−	0.0993484i	0.527320	+	0.849667i	$0.323197\pi$
$354$	−8.56312	+	13.3746i	−0.455125	+	0.710852i
$355$	−3.00955	+	1.50273i	−0.159730	+	0.0797565i
$356$	3.45441	−	0.173090i	0.183083	−	0.00917377i
$357$	0.266550	−	3.26910i	0.0141073	−	0.173019i
$358$	−21.1685	+	4.02164i	−1.11879	+	0.212550i
$359$	4.38314	−	7.03843i	0.231334	−	0.371474i	−0.712621	−	0.701549i	$-0.752492\pi$
$359$	4.38314	−	7.03843i	0.231334	−	0.371474i	0.943955	+	0.330075i	$0.107074\pi$
$360$	−1.43490	+	1.06463i	−0.0756259	+	0.0561109i
$361$	12.4338	−	13.8324i	0.654413	−	0.728020i
$362$	−17.8228	+	16.6362i	−0.936744	+	0.874381i
$363$	1.06028	−	4.49691i	0.0556505	−	0.236027i
$364$	−1.32701	−	0.286698i	−0.0695544	−	0.0150271i
$365$	−0.174084	+	0.354171i	−0.00911198	+	0.0185382i
$366$	−0.806693	−	2.08459i	−0.0421665	−	0.108963i
$367$	−7.18906	+	0.0899852i	−0.375266	+	0.00469719i	−0.199927	−	0.979811i	$-0.564070\pi$
$367$	−7.18906	+	0.0899852i	−0.375266	+	0.00469719i	−0.175339	+	0.984508i	$0.556102\pi$
$368$	−22.6773	+	27.2174i	−1.18214	+	1.41880i
$369$	−19.4570	−	6.83760i	−1.01289	−	0.355951i
$370$	−0.431144	+	0.0378713i	−0.0224141	+	0.00196883i
$371$	−2.81023	−	2.62314i	−0.145900	−	0.136187i
$372$	0.737844	−	0.492177i	0.0382554	−	0.0255182i
$373$	−0.939237	+	3.57985i	−0.0486318	+	0.185358i	−0.987128	−	0.159932i	$-0.948873\pi$
$373$	−0.939237	+	3.57985i	−0.0486318	+	0.185358i	0.938496	+	0.345289i	$0.112219\pi$
$374$	6.71823	+	11.4153i	0.347392	+	0.590270i
$375$	3.67753	−	0.230447i	0.189907	−	0.0119002i
$376$	7.49577	−	4.22406i	0.386565	−	0.217839i
$377$	−7.17228	−	34.2342i	−0.369391	−	1.76315i
$378$	5.58115	+	4.25029i	0.287063	+	0.218611i
$379$	8.52656	+	1.07282i	0.437980	+	0.0551070i	0.340748	−	0.940155i	$-0.389320\pi$
$379$	8.52656	+	1.07282i	0.437980	+	0.0551070i	0.0972323	+	0.995262i	$0.469001\pi$
$380$	−0.0281067	−	0.0491547i	−0.00144184	−	0.00252158i
$381$	2.16504	−	6.03971i	0.110918	−	0.309424i
$382$	10.4766	−	7.57167i	0.536028	−	0.387400i
$383$	−37.7707	−	2.84184i	−1.92999	−	0.145211i	−0.946089	−	0.323908i	$-0.895003\pi$
$383$	−37.7707	−	2.84184i	−1.92999	−	0.145211i	−0.983904	+	0.178697i	$0.942812\pi$
$384$	9.67302	−	9.49310i	0.493624	−	0.484442i
$385$	−0.800433	+	0.237008i	−0.0407938	+	0.0120791i
$386$	−0.912193	−	4.97093i	−0.0464294	−	0.253014i
$387$	−6.79370	−	2.29233i	−0.345343	−	0.116526i
$388$	3.76250	−	0.0942049i	0.191012	−	0.00478253i
$389$	−5.54028	−	22.2472i	−0.280904	−	1.12798i	−0.930085	−	0.367345i	$-0.880267\pi$
$389$	−5.54028	−	22.2472i	−0.280904	−	1.12798i	0.649181	−	0.760634i	$-0.275112\pi$
$390$	1.46809	+	2.98681i	0.0743398	+	0.151243i
$391$	18.6196	−	20.1996i	0.941636	−	1.02154i
$392$	−15.9062	−	3.02188i	−0.803382	−	0.152628i
$393$	5.01680	−	18.1906i	0.253064	−	0.917596i
$394$	−25.3028	−	26.7696i	−1.27474	−	1.34864i
$395$	−1.76252	+	0.669406i	−0.0886819	+	0.0336814i
$396$	−1.22495	−	0.0460170i	−0.0615558	−	0.00231244i
$397$	12.4951	−	3.36203i	0.627112	−	0.168736i	0.0678087	−	0.997698i	$-0.478399\pi$
$397$	12.4951	−	3.36203i	0.627112	−	0.168736i	0.559304	+	0.828963i	$0.311069\pi$
$398$	24.0209	−	19.7607i	1.20406	−	0.990513i
$399$	0.419813	−	0.433159i	0.0210169	−	0.0216851i
$400$	21.1939	−	4.30198i	1.05970	−	0.215099i
$401$	20.1863	+	14.9773i	1.00806	+	0.747932i	0.967919	−	0.251262i	$-0.0808455\pi$
$401$	20.1863	+	14.9773i	1.00806	+	0.747932i	0.0401386	+	0.999194i	$0.487220\pi$
$402$	−3.69398	+	1.45614i	−0.184239	+	0.0726255i
$403$	−7.96215	−	18.4819i	−0.396623	−	0.920649i
$404$	−0.414809	−	2.43151i	−0.0206375	−	0.120972i
$405$	0.00239653	+	0.127633i	0.000119085	+	0.00634216i
$406$	−1.84669	−	7.83222i	−0.0916495	−	0.388707i
$407$	1.72460	+	1.15039i	0.0854853	+	0.0570228i
$408$	−7.06262	+	6.26908i	−0.349652	+	0.310366i
$409$	2.73131	+	3.11610i	0.135055	+	0.154081i	0.815582	−	0.578641i	$-0.196417\pi$
$409$	2.73131	+	3.11610i	0.135055	+	0.154081i	−0.680528	+	0.732722i	$0.738249\pi$
$410$	−4.13381	−	4.05692i	−0.204154	−	0.200357i
$411$	−16.5895	−	8.80894i	−0.818298	−	0.434513i
$412$	−0.0134120	+	2.14309i	−0.000660761	+	0.105583i
$413$	6.90269	+	6.12712i	0.339659	+	0.301496i
$414$	5.79504	+	22.0875i	0.284811	+	1.08554i
$415$	3.50554	−	3.52755i	0.172080	−	0.173161i
$416$	4.69244	+	6.94016i	0.230066	+	0.340270i
$417$	−0.896293	+	0.490407i	−0.0438917	+	0.0240153i
$418$	−0.379565	+	2.40623i	−0.0185651	+	0.117692i
$419$	18.7052	−	3.31165i	0.913810	−	0.161785i	0.302476	−	0.953157i	$-0.402187\pi$
$419$	18.7052	−	3.31165i	0.913810	−	0.161785i	0.611334	+	0.791372i	$0.290633\pi$
$420$	0.0395079	+	0.0755409i	0.00192779	+	0.00368602i
$421$	−18.7578	+	9.96030i	−0.914198	+	0.485436i	−0.858385	−	0.513006i	$-0.828532\pi$
$421$	−18.7578	+	9.96030i	−0.914198	+	0.485436i	−0.0558128	+	0.998441i	$0.517775\pi$
$422$	−30.8557	−	9.13639i	−1.50203	−	0.444752i
$423$	0.663870	−	6.21649i	0.0322785	−	0.302256i
$424$	0.623077	+	11.0508i	0.0302593	+	0.536674i
$425$	−16.5815	+	2.50937i	−0.804321	+	0.121722i
$426$	0.277442	−	14.7759i	0.0134421	−	0.715896i
$427$	−1.26978	+	0.274334i	−0.0614491	+	0.0132759i
$428$	1.09053	−	4.37906i	0.0527127	−	0.211670i
$429$	3.46384	−	15.5604i	0.167236	−	0.751262i
$430$	−1.45471	−	1.39234i	−0.0701524	−	0.0671446i
$431$	13.0370	+	37.8536i	0.627969	+	1.82334i	0.564620	+	0.825351i	$0.309023\pi$
$431$	13.0370	+	37.8536i	0.627969	+	1.82334i	0.0633494	+	0.997991i	$0.479822\pi$
$432$	−3.54783	−	22.4912i	−0.170695	−	1.08211i
$433$	−4.56151	−	5.91269i	−0.219212	−	0.284146i	0.669306	−	0.742987i	$-0.266591\pi$
$433$	−4.56151	−	5.91269i	−0.219212	−	0.284146i	−0.888518	+	0.458841i	$0.848265\pi$
$434$	−1.93764	−	4.20480i	−0.0930098	−	0.201837i
$435$	−1.36323	+	1.72203i	−0.0653618	+	0.0825651i
$436$	2.04511	−	1.25589i	0.0979428	−	0.0601460i
$437$	5.00458	−	0.693414i	0.239401	−	0.0331705i
$438$	−1.02435	−	1.39883i	−0.0489455	−	0.0668385i
$439$	−6.57809	+	9.22282i	−0.313955	+	0.440181i	−0.940800	−	0.338963i	$-0.889924\pi$
$439$	−6.57809	+	9.22282i	−0.313955	+	0.440181i	0.626845	+	0.779144i	$0.284346\pi$
$440$	2.13674	+	1.10054i	0.101865	+	0.0524662i
$441$	−8.49891	+	8.13452i	−0.404710	+	0.387358i
$442$	−15.8963	−	26.2529i	−0.756111	−	1.24872i
$443$	−6.50630	+	6.88348i	−0.309124	+	0.327044i	−0.862663	−	0.505779i	$-0.831205\pi$
$443$	−6.50630	+	6.88348i	−0.309124	+	0.327044i	0.553539	+	0.832823i	$0.313277\pi$
$444$	0.0813213	−	0.195461i	0.00385934	−	0.00927619i
$445$	−4.16656	+	2.63103i	−0.197514	+	0.124723i
$446$	20.9727	+	9.82415i	0.993086	+	0.465187i
$447$	0.359901	+	2.48311i	0.0170227	+	0.117447i
$448$	−3.57929	−	5.01835i	−0.169106	−	0.237095i
$449$	−2.28549	+	6.91601i	−0.107859	+	0.326386i	−0.989298	−	0.145912i	$-0.953388\pi$
$449$	−2.28549	+	6.91601i	−0.107859	+	0.326386i	0.881439	+	0.472299i	$0.156576\pi$
$450$	5.67508	−	12.7321i	0.267526	−	0.600198i
$451$	3.29099	+	27.5469i	0.154967	+	1.29713i
$452$	0.431031	−	0.110210i	0.0202740	−	0.00518385i
$453$	1.95159	+	0.551395i	0.0916939	+	0.0259068i
$454$	3.22938	+	2.52379i	0.151562	+	0.118447i
$455$	1.84763	−	0.572330i	0.0866180	−	0.0268312i
$456$	−1.73555	+	0.0651987i	−0.0812747	+	0.00305321i
$457$	30.3669	−	12.8576i	1.42050	−	0.601453i	0.462090	−	0.886833i	$-0.347100\pi$
$457$	30.3669	−	12.8576i	1.42050	−	0.601453i	0.958415	+	0.285380i	$0.0921197\pi$
$458$	22.4764	−	3.68979i	1.05025	−	0.172413i
$459$	1.87494	+	17.5570i	0.0875147	+	0.819489i
$460$	−0.128875	+	0.702294i	−0.00600882	+	0.0327446i
$461$	18.8513	−	33.9474i	0.877993	−	1.58109i	0.0656992	−	0.997839i	$-0.479072\pi$
$461$	18.8513	−	33.9474i	0.877993	−	1.58109i	0.812294	−	0.583248i	$-0.198219\pi$
$462$	0.707045	−	3.59867i	0.0328947	−	0.167425i
$463$	20.4879	+	20.6166i	0.952155	+	0.958133i	0.999169	−	0.0407615i	$-0.0129784\pi$
$463$	20.4879	+	20.6166i	0.952155	+	0.958133i	−0.0470136	+	0.998894i	$0.514970\pi$
$464$	−13.2472	+	22.5090i	−0.614987	+	1.04495i
$465$	−0.571561	+	1.12698i	−0.0265055	+	0.0522624i
$466$	−18.4717	−	23.3335i	−0.855687	−	1.08090i
$467$	−1.96628	−	0.718766i	−0.0909886	−	0.0332605i	0.297429	−	0.954744i	$-0.403871\pi$
$467$	−1.96628	−	0.718766i	−0.0909886	−	0.0332605i	−0.388418	+	0.921483i	$0.626978\pi$
$468$	2.83937	+	0.0710918i	0.131250	+	0.00328622i
$469$	0.501426	+	2.25252i	0.0231537	+	0.104012i
$470$	0.909421	−	1.50192i	0.0419485	−	0.0692782i
$471$	5.17560	+	18.7665i	0.238479	+	0.864712i
$472$	−2.15959	−	26.4864i	−0.0994034	−	1.21914i
$473$	1.26393	+	9.56197i	0.0581156	+	0.439660i
$474$	0.982567	−	8.22449i	0.0451308	−	0.377763i
$475$	−2.64822	−	1.58095i	−0.121508	−	0.0725390i
$476$	−0.423883	−	0.662057i	−0.0194287	−	0.0303453i
$477$	6.80017	+	4.29406i	0.311358	+	0.196612i
$478$	16.2685	−	11.4504i	0.744104	−	0.523731i
$479$	1.09280	−	2.72221i	0.0499315	−	0.124381i	−0.900963	−	0.433896i	$-0.857139\pi$
$479$	1.09280	−	2.72221i	0.0499315	−	0.124381i	0.950895	+	0.309515i	$0.100167\pi$
$480$	0.146194	−	0.505328i	0.00667282	−	0.0230649i
$481$	−4.02904	−	2.61529i	−0.183708	−	0.119247i
$482$	−15.8347	−	39.4447i	−0.721250	−	1.79666i
$483$	−7.56849	+	0.760379i	−0.344378	+	0.0345985i
$484$	−0.450825	−	1.01143i	−0.0204920	−	0.0459742i
$485$	−4.60414	+	2.74861i	−0.209063	+	0.124808i
$486$	−21.1583	−	10.5648i	−0.959762	−	0.479228i
$487$	−27.7198	−	12.1482i	−1.25611	−	0.550486i	−0.335891	−	0.941901i	$-0.609037\pi$
$487$	−27.7198	−	12.1482i	−1.25611	−	0.550486i	−0.920214	+	0.391415i	$0.871986\pi$
$488$	3.18730	+	1.95730i	0.144282	+	0.0886026i
$489$	−1.80406	+	0.659469i	−0.0815826	+	0.0298222i
$490$	−3.13056	+	1.05631i	−0.141424	+	0.0477194i
$491$	−8.76988	−	15.7928i	−0.395779	−	0.712719i	0.600433	−	0.799675i	$-0.294995\pi$
$491$	−8.76988	−	15.7928i	−0.395779	−	0.712719i	−0.996212	+	0.0869566i	$0.972286\pi$
$492$	2.69554	−	0.872105i	0.121524	−	0.0393175i
$493$	11.1334	−	16.9190i	0.501423	−	0.761992i
$494$	0.809623	−	5.58592i	0.0364267	−	0.251323i
$495$	1.55259	−	0.799673i	0.0697839	−	0.0359426i
$496$	−4.89321	+	14.2077i	−0.219712	+	0.637945i
$497$	−8.45749	−	1.49735i	−0.379370	−	0.0671652i
$498$	6.59539	+	20.8295i	0.295547	+	0.933392i
$499$	3.26608	−	15.5895i	0.146210	−	0.697880i	−0.841331	−	0.540520i	$-0.818228\pi$
$499$	3.26608	−	15.5895i	0.146210	−	0.697880i	0.987541	−	0.157360i	$-0.0502983\pi$
$500$	0.667767	−	0.577959i	0.0298634	−	0.0258471i
$501$	−12.7739	−	15.7274i	−0.570694	−	0.702648i
$502$	−2.89105			−0.129034
$503$	12.8838	−	18.3578i	0.574461	−	0.818532i
$503$	12.8838	−	18.3578i	0.574461	−	0.818532i
$504$	−4.56207			−0.203211
$505$	2.21559	+	2.72787i	0.0985924	+	0.121389i
$506$	23.2264	−	20.1027i	1.03254	−	0.893674i
$507$	−4.78711	+	22.8495i	−0.212603	+	1.01478i
$508$	−0.464201	−	1.46604i	−0.0205956	−	0.0650448i
$509$	17.1982	+	3.04484i	0.762298	+	0.134960i	0.541892	−	0.840448i	$-0.317708\pi$
$509$	17.1982	+	3.04484i	0.762298	+	0.134960i	0.220406	+	0.975408i	$0.429262\pi$
$510$	−0.627537	+	1.82209i	−0.0277878	+	0.0806834i
$511$	−0.895807	+	0.461391i	−0.0396282	+	0.0204107i
$512$	−2.44439	+	16.8649i	−0.108028	+	0.745329i
$513$	−1.78503	+	2.71263i	−0.0788109	+	0.119766i
$514$	−21.5573	+	6.97457i	−0.950851	+	0.307635i
$515$	−1.48234	−	2.66940i	−0.0653198	−	0.117628i
$516$	0.933270	−	0.314904i	0.0410849	−	0.0138629i
$517$	−7.89882	+	2.88738i	−0.347390	+	0.126987i
$518$	−0.941699	−	0.578290i	−0.0413759	−	0.0254086i
$519$	22.7131	+	9.95399i	0.996996	+	0.436932i
$520$	−4.98247	−	2.48784i	−0.218496	−	0.109099i
$521$	21.5833	−	12.8849i	0.945581	−	0.564499i	0.0449050	−	0.998991i	$-0.485701\pi$
$521$	21.5833	−	12.8849i	0.945581	−	0.564499i	0.900676	+	0.434492i	$0.143072\pi$
$522$	6.85379	+	15.3766i	0.299982	+	0.673015i
$523$	1.68175	−	0.168960i	0.0735378	−	0.00738808i	−0.0631260	−	0.998006i	$-0.520107\pi$
$523$	1.68175	−	0.168960i	0.0735378	−	0.00738808i	0.136664	+	0.990617i	$0.456362\pi$
$524$	−1.68487	−	4.19707i	−0.0736041	−	0.183350i
$525$	3.89484	+	2.52819i	0.169985	+	0.110339i
$526$	0.676402	−	2.33802i	0.0294925	−	0.101942i
$527$	4.34112	−	10.8139i	0.189102	−	0.471060i
$528$	−9.73407	+	6.85123i	−0.423621	+	0.298162i
$529$	−34.4224	−	21.7365i	−1.49663	−	0.945065i
$530$	1.21789	+	1.90220i	0.0529017	+	0.0826263i
$531$	−16.5797	−	9.89784i	−0.719496	−	0.429530i
$532$	0.0171504	−	0.143556i	0.000743564	−	0.00622393i
$533$	−8.42367	−	63.7273i	−0.364870	−	2.76033i
$534$	−1.75934	−	21.5775i	−0.0761341	−	0.933749i
$535$	1.70937	+	6.19808i	0.0739025	+	0.267967i
$536$	3.44139	−	5.68349i	0.148646	−	0.245489i
$537$	3.26280	+	14.6573i	0.140800	+	0.632507i
$538$	11.1020	+	0.277969i	0.478639	+	0.0119841i
$539$	14.8636	+	5.43335i	0.640222	+	0.234031i
$540$	−0.284843	−	0.359814i	−0.0122577	−	0.0154839i
$541$	−15.1585	+	29.8887i	−0.651713	+	1.28502i	0.292684	+	0.956209i	$0.405452\pi$
$541$	−15.1585	+	29.8887i	−0.651713	+	1.28502i	−0.944397	+	0.328808i	$0.893353\pi$
$542$	13.1126	−	22.2803i	0.563236	−	0.957022i
$543$	11.9766	+	12.0517i	0.513963	+	0.517190i
$544$	−0.935219	+	4.76002i	−0.0400972	+	0.204084i
$545$	−1.65997	+	2.98926i	−0.0711051	+	0.128046i
$546$	−1.53377	+	8.35817i	−0.0656393	+	0.357697i
$547$	2.72842	+	25.5490i	0.116659	+	1.09240i	0.889228	+	0.457465i	$0.151242\pi$
$547$	2.72842	+	25.5490i	0.116659	+	1.09240i	−0.772569	+	0.634931i	$0.781029\pi$
$548$	−4.44242	+	0.729282i	−0.189771	+	0.0311534i
$549$	2.50268	−	1.05966i	0.106812	−	0.0452250i
$550$	−18.7385	+	0.703940i	−0.799011	+	0.0300161i
$551$	3.55802	−	1.10215i	0.151577	−	0.0469532i
$552$	17.2562	+	13.4859i	0.734474	+	0.573999i
$553$	−4.63257	−	1.30887i	−0.196997	−	0.0556587i
$554$	21.3434	−	5.45729i	0.906796	−	0.231858i
$555$	0.0357794	+	0.299488i	0.00151875	+	0.0127126i
$556$	−0.0996925	+	0.223662i	−0.00422790	+	0.00948537i
$557$	6.36550	−	19.2623i	0.269715	−	0.816171i	−0.722471	−	0.691401i	$-0.756994\pi$
$557$	6.36550	−	19.2623i	0.269715	−	0.816171i	0.992186	−	0.124770i	$-0.0398192\pi$
$558$	5.62432	+	7.88558i	0.238096	+	0.333823i
$559$	−3.20566	−	22.1172i	−0.135585	−	0.935458i
$560$	−1.30793	−	0.612666i	−0.0552699	−	0.0258899i
$561$	7.80484	−	4.92847i	0.329521	−	0.208080i
$562$	−5.14766	+	12.3728i	−0.217141	+	0.521914i
$563$	4.27650	−	4.52441i	0.180233	−	0.190681i	−0.630340	−	0.776319i	$-0.717084\pi$
$563$	4.27650	−	4.52441i	0.180233	−	0.190681i	0.810573	+	0.585638i	$0.199156\pi$
$564$	0.444838	+	0.734652i	0.0187310	+	0.0309344i
$565$	−0.457911	+	0.438279i	−0.0192645	+	0.0184385i
$566$	25.8895	+	13.3345i	1.08822	+	0.560492i
$567$	−0.189269	+	0.265364i	−0.00794854	+	0.0111443i
$568$	14.6106	+	19.9518i	0.613048	+	0.837160i
$569$	39.0091	−	5.40495i	1.63535	−	0.226587i	0.740210	−	0.672376i	$-0.234726\pi$
$569$	39.0091	−	5.40495i	1.63535	−	0.226587i	0.895138	+	0.445789i	$0.147077\pi$
$570$	−0.302016	+	0.185466i	−0.0126501	+	0.00776832i
$571$	−4.20324	+	5.30953i	−0.175900	+	0.222197i	−0.864095	−	0.503329i	$-0.832109\pi$
$571$	−4.20324	+	5.30953i	−0.175900	+	0.222197i	0.688195	+	0.725526i	$0.258403\pi$
$572$	−1.59905	−	3.47003i	−0.0668595	−	0.145089i
$573$	−5.50247	−	7.13237i	−0.229869	−	0.297959i
$574$	−2.30433	−	14.6081i	−0.0961808	−	0.609731i
$575$	12.6646	+	36.7725i	0.528152	+	1.53352i
$576$	9.31610	+	8.91667i	0.388171	+	0.371528i
$577$	−4.58424	+	20.5934i	−0.190844	+	0.857316i	0.781526	+	0.623873i	$0.214442\pi$
$577$	−4.58424	+	20.5934i	−0.190844	+	0.857316i	−0.972370	+	0.233443i	$0.925001\pi$
$578$	−1.86848	+	7.50294i	−0.0777184	+	0.312081i
$579$	−3.44262	+	0.743769i	−0.143070	+	0.0309100i
$580$	−0.00988237	+	0.526311i	−0.000410343	+	0.0218539i
$581$	12.5551	−	1.90004i	0.520875	−	0.0788268i
$582$	−1.32615	−	23.5204i	−0.0549707	−	0.974952i
$583$	1.14882	−	10.7576i	0.0475794	−	0.445534i
$584$	2.78182	+	0.823698i	0.115113	+	0.0340849i
$585$	−3.57397	+	1.89776i	−0.147765	+	0.0784629i
$586$	18.1383	+	34.6813i	0.749287	+	1.43267i
$587$	4.46293	−	0.790135i	0.184205	−	0.0326124i	−0.0814663	−	0.996676i	$-0.525960\pi$
$587$	4.46293	−	0.790135i	0.184205	−	0.0326124i	0.265671	+	0.964064i	$0.414407\pi$
$588$	0.251817	−	1.59638i	0.0103848	−	0.0658334i
$589$	1.88003	−	1.02866i	0.0774652	−	0.0423851i
$590$	−3.03746	−	4.49242i	−0.125050	−	0.184950i
$591$	−18.0947	+	18.2083i	−0.744318	+	0.748991i
$592$	0.910239	+	3.46933i	0.0374106	+	0.142589i
$593$	−1.67750	−	1.48902i	−0.0688866	−	0.0611467i	0.628695	−	0.777652i	$-0.283589\pi$
$593$	−1.67750	−	1.48902i	−0.0688866	−	0.0611467i	−0.697582	+	0.716505i	$0.745741\pi$
$594$	−0.123553	+	19.7425i	−0.00506945	+	0.810045i
$595$	0.989202	+	0.525263i	0.0405533	+	0.0215337i
$596$	0.429200	+	0.421216i	0.0175807	+	0.0172537i
$597$	−14.2880	−	16.3009i	−0.584770	−	0.667153i
$598$	−53.2297	+	47.2489i	−2.17672	+	1.93215i
$599$	−9.25757	−	6.17524i	−0.378254	−	0.252314i	0.351262	−	0.936277i	$-0.385753\pi$
$599$	−9.25757	−	6.17524i	−0.378254	−	0.252314i	−0.729516	+	0.683964i	$0.760255\pi$
$600$	−3.06811	−	13.0126i	−0.125255	−	0.531235i
$601$	−0.0318546	−	1.69650i	−0.00129937	−	0.0692016i	−0.999875	−	0.0158387i	$-0.994958\pi$
$601$	−0.0318546	−	1.69650i	−0.00129937	−	0.0692016i	0.998575	−	0.0533629i	$-0.0169940\pi$
$602$	−0.864631	−	5.06827i	−0.0352397	−	0.206567i
$603$	−1.91013	−	4.43384i	−0.0777867	−	0.180560i
$604$	0.452197	−	0.178252i	0.0183996	−	0.00725299i
$605$	1.26701	+	0.940066i	0.0515114	+	0.0382191i
$606$	−15.1307	+	3.07126i	−0.614645	+	0.124762i
$607$	22.7768	−	23.5009i	0.924484	−	0.953874i	−0.0745765	−	0.997215i	$-0.523761\pi$
$607$	22.7768	−	23.5009i	0.924484	−	0.953874i	0.999060	+	0.0433415i	$0.0138003\pi$
$608$	−0.688978	+	0.566784i	−0.0279417	+	0.0229861i
$609$	−5.41528	+	1.45707i	−0.219438	+	0.0590436i
$610$	0.762731	+	0.0286532i	0.0308821	+	0.00116013i
$611$	18.2168	−	6.91876i	0.736973	−	0.279903i
$612$	1.12973	+	1.19522i	0.0456665	+	0.0483139i
$613$	−5.86594	+	21.2696i	−0.236923	+	0.859071i	0.744565	+	0.667550i	$0.232657\pi$
$613$	−5.86594	+	21.2696i	−0.236923	+	0.859071i	−0.981489	+	0.191521i	$0.938658\pi$
$614$	−2.98921	−	0.567896i	−0.120635	−	0.0229184i
$615$	−2.73572	+	2.96786i	−0.110315	+	0.119676i
$616$	2.70711	+	5.50757i	0.109073	+	0.221906i
$617$	10.4868	+	42.1100i	0.422181	+	1.69528i	0.683433	+	0.730013i	$0.260486\pi$
$617$	10.4868	+	42.1100i	0.422181	+	1.69528i	−0.261252	+	0.965271i	$0.584135\pi$
$618$	13.4102	−	0.335762i	0.539437	−	0.0135063i
$619$	5.97517	+	2.01614i	0.240162	+	0.0810356i	0.437214	−	0.899358i	$-0.355965\pi$
$619$	5.97517	+	2.01614i	0.240162	+	0.0810356i	−0.197051	+	0.980393i	$0.563137\pi$
$620$	0.0546642	+	0.297888i	0.00219537	+	0.0119635i
$621$	39.2631	−	11.6258i	1.57557	−	0.466527i
$622$	−4.87803	+	4.78729i	−0.195591	+	0.191953i
$623$	−12.5466	−	0.943998i	−0.502669	−	0.0378205i
$624$	22.3539	−	16.1557i	0.894872	−	0.646746i
$625$	7.79644	−	21.7494i	0.311858	−	0.869974i
$626$	−11.9449	−	20.8899i	−0.477413	−	0.834929i
$627$	1.68433	+	0.211924i	0.0672658	+	0.00846344i
$628$	3.71197	+	2.82682i	0.148124	+	0.112803i
$629$	−0.570337	−	2.72229i	−0.0227408	−	0.108545i
$630$	−0.811049	+	0.457047i	−0.0323130	+	0.0182092i
$631$	2.54270	−	0.159334i	0.101223	−	0.00634299i	−0.0118486	−	0.999930i	$-0.503772\pi$
$631$	2.54270	−	0.159334i	0.101223	−	0.00634299i	0.113072	+	0.993587i	$0.463931\pi$
$632$	7.03002	+	11.9450i	0.279639	+	0.475148i
$633$	−5.69122	+	21.6918i	−0.226206	+	0.862171i
$634$	6.35320	−	4.23788i	0.252318	−	0.168308i
$635$	1.60159	+	1.49496i	0.0635571	+	0.0593258i
$636$	−1.10058	+	0.0966738i	−0.0436408	+	0.00383337i
$637$	−34.5947	−	12.1573i	−1.37069	−	0.481690i
$638$	14.4964	−	17.3987i	0.573919	−	0.688819i
$639$	17.9675	−	0.224898i	0.710782	−	0.00889683i
$640$	1.67023	+	4.31609i	0.0660218	+	0.170608i
$641$	−12.5846	+	25.6031i	−0.497061	+	1.01126i	0.492922	+	0.870073i	$0.335929\pi$
$641$	−12.5846	+	25.6031i	−0.497061	+	1.01126i	−0.989983	+	0.141188i	$0.954908\pi$
$642$	−27.6097	−	5.96501i	−1.08967	−	0.235420i
$643$	−4.14336	+	17.5729i	−0.163398	+	0.693009i	0.827845	+	0.560957i	$0.189567\pi$
$643$	−4.14336	+	17.5729i	−0.163398	+	0.693009i	−0.991243	+	0.132052i	$0.957844\pi$
$644$	−1.33274	+	1.24401i	−0.0525173	+	0.0490210i
$645$	−0.938119	+	1.04364i	−0.0369384	+	0.0410932i
$646$	2.62474	−	1.94743i	0.103269	−	0.0766207i
$647$	−15.2373	+	24.4680i	−0.599040	+	0.961936i	0.399929	+	0.916546i	$0.369035\pi$
$647$	−15.2373	+	24.4680i	−0.599040	+	0.961936i	−0.998969	+	0.0453897i	$0.985547\pi$
$648$	0.921971	−	0.175158i	0.0362185	−	0.00688085i
$649$	−2.11090	+	25.8892i	−0.0828600	+	1.01624i
$650$	43.3942	−	2.17436i	1.70206	−	0.0852853i
$651$	−2.88661	+	1.44134i	−0.113135	+	0.0564906i
$652$	−0.248236	+	0.387717i	−0.00972168	+	0.0151842i
$653$	9.40579	−	4.40592i	0.368077	−	0.172417i	−0.231302	−	0.972882i	$-0.574299\pi$
$653$	9.40579	−	4.40592i	0.368077	−	0.172417i	0.599379	+	0.800465i	$0.295414\pi$
$654$	−8.25752	−	12.5486i	−0.322894	−	0.490689i
$655$	5.02692	+	4.03094i	0.196418	+	0.157502i
$656$	−27.3808	+	39.4239i	−1.06904	+	1.53924i
$657$	1.66100	−	1.29809i	0.0648019	−	0.0506433i
$658$	4.14984	−	1.69614i	0.161778	−	0.0661226i
$659$	16.0669	+	14.6253i	0.625878	+	0.569720i	0.922847	−	0.385167i	$-0.125856\pi$
$659$	16.0669	+	14.6253i	0.625878	+	0.569720i	−0.296969	+	0.954887i	$0.595976\pi$
$660$	−0.103127	+	0.216617i	−0.00401421	+	0.00843180i
$661$	−6.34402	+	5.77479i	−0.246754	+	0.224613i	−0.787094	−	0.616833i	$-0.788415\pi$
$661$	−6.34402	+	5.77479i	−0.246754	+	0.224613i	0.540340	+	0.841447i	$0.318296\pi$
$662$	4.38960	+	14.4910i	0.170607	+	0.563208i
$663$	−17.9399	+	11.6450i	−0.696728	+	0.452254i
$664$	−29.8973	−	21.0429i	−1.16024	−	0.816624i
$665$	0.0791231	+	0.190178i	0.00306826	+	0.00737479i
$666$	2.16129	+	0.820860i	0.0837483	+	0.0318077i
$667$	−43.2529	−	18.3136i	−1.67476	−	0.709106i
$668$	−4.71950	−	1.14399i	−0.182603	−	0.0442623i
$669$	6.38576	−	14.8227i	0.246888	−	0.573080i
$670$	0.0424188	−	1.35519i	0.00163878	−	0.0523555i
$671$	−2.76435	−	2.39257i	−0.106717	−	0.0923643i
$672$	1.06859	−	0.813776i	0.0412217	−	0.0313921i
$673$	7.15237	−	4.14934i	0.275704	−	0.159945i	−0.357540	−	0.933898i	$-0.616384\pi$
$673$	7.15237	−	4.14934i	0.275704	−	0.159945i	0.633244	+	0.773952i	$0.281723\pi$
$674$	37.4724	−	10.5873i	1.44338	−	0.407808i
$675$	−23.1386	−	9.45735i	−0.890607	−	0.364013i
$676$	2.40519	+	5.05207i	0.0925072	+	0.194310i
$677$	−11.8451	+	39.1032i	−0.455246	+	1.50286i	0.365088	+	0.930973i	$0.381039\pi$
$677$	−11.8451	+	39.1032i	−0.455246	+	1.50286i	−0.820333	+	0.571886i	$0.806212\pi$
$678$	−0.773900	−	2.67502i	−0.0297214	−	0.102734i
$679$	−13.6228	−	1.36863i	−0.522794	−	0.0525233i
$680$	−1.01184	−	3.06187i	−0.0388022	−	0.117417i
$681$	1.68754	−	2.30445i	0.0646667	−	0.0883069i
$682$	6.18245	−	11.4692i	0.236738	−	0.439180i
$683$	−0.834539	+	19.0381i	−0.0319328	+	0.728474i	0.914310	+	0.405016i	$0.132734\pi$
$683$	−0.834539	+	19.0381i	−0.0319328	+	0.728474i	−0.946242	+	0.323458i	$0.895154\pi$
$684$	0.0208052	+	0.301749i	0.000795506	+	0.0115377i
$685$	5.00386	−	4.01244i	0.191187	−	0.153308i
$686$	−17.1339	−	5.54345i	−0.654176	−	0.211650i
$687$	−3.06017	−	15.5755i	−0.116753	−	0.594242i
$688$	−9.34698	+	13.8243i	−0.356350	+	0.527045i
$689$	−2.34970	+	24.9573i	−0.0895166	+	0.950797i
$690$	4.41891	+	0.668737i	0.168225	+	0.0254584i
$691$	4.98163	−	29.2012i	0.189510	−	1.11086i	−0.719625	−	0.694363i	$-0.755686\pi$
$691$	4.98163	−	29.2012i	0.189510	−	1.11086i	0.909135	−	0.416502i	$-0.136744\pi$
$692$	5.77635	−	1.40017i	0.219584	−	0.0532264i
$693$	4.40030	+	0.722367i	0.167153	+	0.0274405i
$694$	2.05990	−	36.5341i	0.0781928	−	1.38682i
$695$	−0.0327017	−	0.347340i	−0.00124045	−	0.0131754i
$696$	14.1645	+	7.75013i	0.536906	+	0.293768i
$697$	22.7362	−	29.4709i	0.861194	−	1.11629i
$698$	43.1623	+	9.89213i	1.63372	+	0.374422i
$699$	−15.8502	+	13.3752i	−0.599511	+	0.505898i
$700$	1.10979	−	0.0834995i	0.0419460	−	0.00315599i
$701$	−19.0869	+	21.7759i	−0.720903	+	0.822465i	−0.990062	−	0.140630i	$-0.955087\pi$
$701$	−19.0869	+	21.7759i	−0.720903	+	0.822465i	0.269159	+	0.963096i	$0.413254\pi$
$702$	−0.286280	−	45.7445i	−0.0108049	−	1.72651i
$703$	0.237064	−	0.453277i	0.00894103	−	0.0170957i
$704$	5.23654	−	16.5380i	0.197360	−	0.623299i
$705$	−1.06599	−	0.600712i	−0.0401474	−	0.0226241i
$706$	−5.94246	−	2.87484i	−0.223647	−	0.108196i
$707$	0.392957	+	8.96444i	0.0147787	+	0.337143i
$708$	2.63577	−	0.298174i	0.0990584	−	0.0112060i
$709$	−22.6703	−	18.6496i	−0.851401	−	0.700400i	0.104362	−	0.994539i	$-0.466720\pi$
$709$	−22.6703	−	18.6496i	−0.851401	−	0.700400i	−0.955763	+	0.294139i	$0.904967\pi$
$710$	4.59635	+	2.08330i	0.172498	+	0.0781849i
$711$	10.0324	+	0.881240i	0.376246	+	0.0330491i
$712$	24.2176	+	26.9415i	0.907593	+	1.00968i
$713$	−26.4839	−	5.37574i	−0.991828	−	0.201323i
$714$	−4.05894	+	2.78153i	−0.151902	+	0.104096i
$715$	4.41186	+	3.18856i	0.164994	+	0.119245i
$716$	2.75054	+	2.32104i	0.102792	+	0.0867415i
$717$	−8.33051	−	11.0822i	−0.311108	−	0.413872i
$718$	−12.3418	+	1.55285i	−0.460590	+	0.0579518i
$719$	−39.0491	−	22.6537i	−1.45628	−	0.844841i	−0.457274	−	0.889326i	$-0.651174\pi$
$719$	−39.0491	−	22.6537i	−1.45628	−	0.844841i	−0.999010	+	0.0444844i	$0.985835\pi$
$720$	2.92742	+	0.748511i	0.109099	+	0.0278954i
$721$	1.02164	−	7.72898i	0.0380479	−	0.287842i
$722$	−27.8676	−	1.39636i	−1.03712	−	0.0519673i
$723$	−27.1300	+	11.8897i	−1.00897	+	0.442181i
$724$	4.03373	+	0.558897i	0.149912	+	0.0207712i
$725$	13.6053	+	25.2395i	0.505286	+	0.937372i
$726$	−6.23942	+	3.01850i	−0.231567	+	0.112027i
$727$	21.4975	+	1.34710i	0.797297	+	0.0499613i	0.455983	−	0.889988i	$-0.349288\pi$
$727$	21.4975	+	1.34710i	0.797297	+	0.0499613i	0.341313	+	0.939950i	$0.389128\pi$
$728$	−6.43175	−	12.6818i	−0.238376	−	0.470020i
$729$	−6.44863	+	13.9939i	−0.238838	+	0.518293i
$730$	0.577077	−	0.132257i	0.0213586	−	0.00489505i
$731$	7.77565	−	10.3441i	0.287593	−	0.382589i
$732$	−0.185324	+	0.324105i	−0.00684976	+	0.0119793i
$733$	6.69147	+	7.82974i	0.247155	+	0.289198i	0.869901	−	0.493226i	$-0.164182\pi$
$733$	6.69147	+	7.82974i	0.247155	+	0.289198i	−0.622746	+	0.782424i	$0.713983\pi$
$734$	6.90422	+	8.28647i	0.254839	+	0.305859i
$735$	0.804030	+	2.15756i	0.0296571	+	0.0795829i
$736$	11.2492	+	0.140806i	0.414651	+	0.00519017i
$737$	−4.21930	+	4.93703i	−0.155420	+	0.181858i
$738$	10.4402	+	29.1245i	0.384309	+	1.07209i
$739$	21.1295	+	14.4797i	0.777260	+	0.532645i	0.887251	−	0.461287i	$-0.152612\pi$
$739$	21.1295	+	14.4797i	0.777260	+	0.532645i	−0.109991	+	0.993933i	$0.535082\pi$
$740$	0.0503112	+	0.0519107i	0.00184948	+	0.00190827i
$741$	−3.90853	−	0.442155i	−0.143583	−	0.0162430i
$742$	−0.396693	+	5.75346i	−0.0145631	+	0.211216i
$743$	−2.34894	−	3.38208i	−0.0861741	−	0.124077i	0.775906	−	0.630848i	$-0.217293\pi$
$743$	−2.34894	−	3.38208i	−0.0861741	−	0.124077i	−0.862080	+	0.506772i	$0.830839\pi$
$744$	8.87360	+	2.74873i	0.325322	+	0.100773i
$745$	−0.827345	−	0.222611i	−0.0303116	−	0.00815585i
$746$	5.05703	−	2.29211i	0.185151	−	0.0839199i
$747$	−25.0628	+	8.80760i	−0.917001	+	0.322253i
$748$	0.772557	−	2.07311i	0.0282475	−	0.0758002i
$749$	−5.92469	+	15.3101i	−0.216483	+	0.559419i
$750$	−3.74657	−	4.06449i	−0.136806	−	0.148414i
$751$	20.4532	+	32.8437i	0.746348	+	1.19848i	0.974397	+	0.224833i	$0.0721837\pi$
$751$	20.4532	+	32.8437i	0.746348	+	1.19848i	−0.228049	+	0.973650i	$0.573235\pi$
$752$	−13.5369	−	5.33612i	−0.493639	−	0.194588i
$753$	0.0630328	+	2.01376i	0.00229704	+	0.0733856i
$754$	−33.0818	+	40.7308i	−1.20477	+	1.48333i
$755$	−0.436591	+	0.537538i	−0.0158892	+	0.0195630i
$756$	−0.0366590	−	1.17118i	−0.00133328	−	0.0425953i
$757$	−20.4332	−	8.05459i	−0.742657	−	0.292749i	−0.0350792	−	0.999385i	$-0.511168\pi$
$757$	−20.4332	−	8.05459i	−0.742657	−	0.292749i	−0.707578	+	0.706635i	$0.750212\pi$
$758$	−6.81516	−	10.9438i	−0.247538	−	0.397495i
$759$	−14.5089	−	15.7401i	−0.526641	−	0.571329i
$760$	0.214034	−	0.553090i	0.00776383	−	0.0200627i
$761$	−1.17845	+	3.16230i	−0.0427188	+	0.114633i	−0.956654	−	0.291227i	$-0.905936\pi$
$761$	−1.17845	+	3.16230i	−0.0427188	+	0.114633i	0.913935	+	0.405860i	$0.133028\pi$
$762$	−9.08087	+	3.19121i	−0.328965	+	0.115605i
$763$	−7.95173	+	3.60413i	−0.287872	+	0.130478i
$764$	−2.08490	−	0.560980i	−0.0754292	−	0.0202955i
$765$	−2.23822	−	0.693323i	−0.0809230	−	0.0250671i
$766$	32.4143	+	46.6714i	1.17118	+	1.68630i
$767$	4.13989	−	60.0431i	0.149483	−	2.16803i
$768$	−6.15343	−	0.696111i	−0.222043	−	0.0251187i
$769$	−7.60090	−	7.84254i	−0.274095	−	0.282809i	0.566975	−	0.823735i	$-0.308114\pi$
$769$	−7.60090	−	7.84254i	−0.274095	−	0.282809i	−0.841070	+	0.540926i	$0.818074\pi$
$770$	1.03304	+	0.707931i	0.0372283	+	0.0255121i
$771$	5.32815	+	14.8637i	0.191888	+	0.535302i
$772$	−0.548433	+	0.641726i	−0.0197385	+	0.0230962i
$773$	4.62375	+	0.0578753i	0.166305	+	0.00208163i	0.0956250	−	0.995417i	$-0.469515\pi$
$773$	4.62375	+	0.0578753i	0.166305	+	0.00208163i	0.0706797	+	0.997499i	$0.477483\pi$
$774$	3.75611	+	10.0793i	0.135010	+	0.362292i
$775$	10.5599	+	12.6740i	0.379323	+	0.455265i
$776$	25.6107	+	29.9672i	0.919369	+	1.07576i
$777$	−0.382277	+	0.668549i	−0.0137141	+	0.0239841i
$778$	−20.6666	+	27.4931i	−0.740934	+	0.985675i
$779$	6.67248	−	1.52923i	0.239066	−	0.0547902i
$780$	0.232650	−	0.504864i	0.00833019	−	0.0180770i
$781$	−10.9333	−	21.5578i	−0.391225	−	0.771399i
$782$	−41.1327	−	2.57751i	−1.47090	−	0.0921717i
$783$	27.1755	−	13.1469i	0.971173	−	0.469833i
$784$	12.9921	+	24.1021i	0.464004	+	0.860789i
$785$	−6.58454	−	0.912327i	−0.235012	−	0.0325623i
$786$	−25.9277	+	11.3628i	−0.924810	+	0.405296i
$787$	25.4988	+	1.27767i	0.908933	+	0.0455440i	0.499030	−	0.866585i	$-0.333690\pi$
$787$	25.4988	+	1.27767i	0.908933	+	0.0455440i	0.409904	+	0.912129i	$0.365562\pi$
$788$	−0.806251	+	6.09951i	−0.0287215	+	0.217286i
$789$	−1.64330	−	0.420173i	−0.0585029	−	0.0149586i
$790$	2.44651	+	1.41931i	0.0870429	+	0.0504966i
$791$	−1.60577	+	0.202039i	−0.0570946	+	0.00718369i
$792$	−7.71451	−	10.2627i	−0.274123	−	0.364670i
$793$	6.47404	+	5.46312i	0.229900	+	0.194001i
$794$	−15.7330	−	11.3706i	−0.558342	−	0.403528i
$795$	1.29843	−	0.889793i	0.0460504	−	0.0315577i
$796$	−5.09150	−	1.03348i	−0.180464	−	0.0366308i
$797$	−6.96741	−	7.75109i	−0.246798	−	0.274558i	0.607524	−	0.794301i	$-0.292163\pi$
$797$	−6.96741	−	7.75109i	−0.246798	−	0.274558i	−0.854322	+	0.519744i	$0.826027\pi$
$798$	−0.901468	−	0.0791841i	−0.0319116	−	0.00280309i
$799$	10.2771	+	4.65812i	0.363579	+	0.164792i
$800$	−5.30361	−	4.36299i	−0.187511	−	0.154255i
$801$	26.1558	−	2.95889i	0.924169	−	0.104547i
$802$	−1.65137	−	37.6724i	−0.0583120	−	1.33026i
$803$	−2.55275	−	1.23497i	−0.0900848	−	0.0435811i
$804$	0.577782	+	0.325595i	0.0203768	+	0.0114828i
$805$	0.784077	−	2.47626i	0.0276351	−	0.0872768i
$806$	−13.9913	+	26.7521i	−0.492823	+	0.942301i
$807$	−0.0484333	−	7.73913i	−0.00170493	−	0.272430i
$808$	17.0292	−	19.4283i	0.599086	−	0.683487i
$809$	13.4827	−	1.01443i	0.474028	−	0.0356655i	0.164137	−	0.986438i	$-0.447516\pi$
$809$	13.4827	−	1.01443i	0.474028	−	0.0356655i	0.309891	+	0.950772i	$0.399707\pi$
$810$	0.146361	−	0.123507i	0.00514260	−	0.00433958i
$811$	−36.4757	−	8.35965i	−1.28083	−	0.293547i	−0.472008	−	0.881594i	$-0.656471\pi$
$811$	−36.4757	−	8.35965i	−1.28083	−	0.293547i	−0.808826	+	0.588047i	$0.799897\pi$
$812$	−0.821000	+	1.06419i	−0.0288114	+	0.0373458i
$813$	−15.8053	−	8.64785i	−0.554315	−	0.303293i
$814$	−0.291515	−	3.09632i	−0.0102176	−	0.108526i
$815$	0.0369232	−	0.654865i	0.00129336	−	0.0229389i
$816$	15.7596	+	2.58714i	0.551696	+	0.0905682i
$817$	2.31293	−	0.560647i	0.0809193	−	0.0196146i
$818$	1.04538	−	6.12780i	0.0365510	−	0.214253i
$819$	−10.2159	−	1.54602i	−0.356971	−	0.0540224i
$820$	−0.0906811	+	0.963166i	−0.00316672	+	0.0336352i
$821$	22.7739	−	33.6828i	0.794814	−	1.17554i	−0.186374	−	0.982479i	$-0.559674\pi$
$821$	22.7739	−	33.6828i	0.794814	−	1.17554i	0.981187	−	0.193057i	$-0.0618404\pi$
$822$	5.43245	+	27.6497i	0.189478	+	0.964395i
$823$	5.87321	+	1.90020i	0.204727	+	0.0662367i	0.408403	−	0.912802i	$-0.366086\pi$
$823$	5.87321	+	1.90020i	0.204727	+	0.0662367i	−0.203676	+	0.979038i	$0.565289\pi$
$824$	−17.5120	+	14.0424i	−0.610060	+	0.489189i
$825$	0.898879	+	13.0369i	0.0312950	+	0.453888i
$826$	0.606377	−	13.8331i	0.0210986	−	0.481317i
$827$	7.58697	−	14.0748i	0.263825	−	0.489429i	−0.713644	−	0.700508i	$-0.752957\pi$
$827$	7.58697	−	14.0748i	0.263825	−	0.489429i	0.977469	+	0.211079i	$0.0676977\pi$
$828$	2.25345	−	3.07724i	0.0783126	−	0.106941i
$829$	11.1960	+	33.8798i	0.388854	+	1.17669i	0.939675	+	0.342069i	$0.111128\pi$
$829$	11.1960	+	33.8798i	0.388854	+	1.17669i	−0.550820	+	0.834624i	$0.685685\pi$
$830$	−7.42334	−	0.745797i	−0.257668	−	0.0258870i
$831$	−4.26662	−	14.7478i	−0.148007	−	0.511596i
$832$	−11.6528	+	38.4683i	−0.403988	+	1.33365i
$833$	−9.12696	−	19.1711i	−0.316230	−	0.664239i
$834$	1.41879	+	0.579895i	0.0491286	+	0.0200801i
$835$	6.65803	−	1.88113i	0.230411	−	0.0650993i
$836$	0.351941	−	0.204174i	0.0121722	−	0.00706149i
$837$	13.8181	−	10.5231i	0.477623	−	0.363730i
$838$	−21.5478	−	18.6498i	−0.744357	−	0.644248i
$839$	−0.222985	+	7.12391i	−0.00769831	+	0.245945i	0.988068	+	0.154020i	$0.0492221\pi$
$839$	−0.222985	+	7.12391i	−0.00769831	+	0.245945i	−0.995766	+	0.0919243i	$0.970698\pi$
$840$	−0.353270	+	0.820018i	−0.0121890	+	0.0282933i
$841$	−5.46987	−	1.32588i	−0.188616	−	0.0457200i
$842$	29.3398	+	12.4227i	1.01112	+	0.428115i
$843$	8.73049	+	3.31585i	0.300694	+	0.114204i
$844$	2.06468	+	4.96260i	0.0710692	+	0.170820i
$845$	−6.51900	−	4.58834i	−0.224261	−	0.157844i
$846$	−7.86692	+	5.10651i	−0.270470	+	0.175565i
$847$	1.16785	+	3.85530i	0.0401276	+	0.132470i
$848$	13.8422	−	12.6002i	0.475343	−	0.432692i
$849$	8.72371	−	18.3240i	0.299397	−	0.628880i
$850$	18.6050	+	16.9356i	0.638145	+	0.580886i
$851$	−5.97089	+	2.44046i	−0.204680	+	0.0836577i
$852$	−1.94494	+	1.51999i	−0.0666326	+	0.0520740i
$853$	−10.9731	+	15.7995i	−0.375711	+	0.540963i	−0.963380	−	0.268138i	$-0.913592\pi$
$853$	−10.9731	+	15.7995i	−0.375711	+	0.540963i	0.587669	+	0.809101i	$0.300046\pi$
$854$	1.52042	+	1.21918i	0.0520278	+	0.0417195i
$855$	−0.236882	−	0.359980i	−0.00810119	−	0.0123111i
$856$	42.8030	−	20.0500i	1.46298	−	0.685296i
$857$	−17.1577	+	26.7984i	−0.586096	+	0.915414i	0.413891	+	0.910326i	$0.364169\pi$
$857$	−17.1577	+	26.7984i	−0.586096	+	0.915414i	−0.999987	+	0.00508794i	$0.998380\pi$
$858$	−21.3960	+	10.6834i	−0.730446	+	0.364726i
$859$	−8.81275	+	0.441581i	−0.300687	+	0.0150666i	−0.199818	−	0.979833i	$-0.564035\pi$
$859$	−8.81275	+	0.441581i	−0.300687	+	0.0150666i	−0.100869	+	0.994900i	$0.532162\pi$
$860$	−0.0273329	+	0.335225i	−0.000932044	+	0.0114311i
$861$	−10.1251	+	1.92358i	−0.345061	+	0.0655554i
$862$	31.7496	−	50.9834i	1.08140	−	1.73650i
$863$	37.1002	−	27.5266i	1.26291	−	0.937017i	0.263289	−	0.964717i	$-0.415193\pi$
$863$	37.1002	−	27.5266i	1.26291	−	0.937017i	0.999616	+	0.0276997i	$0.00881820\pi$
$864$	−4.83375	+	5.37744i	−0.164447	+	0.182944i
$865$	−6.19029	+	5.77817i	−0.210476	+	0.196464i
$866$	−2.57097	+	10.9041i	−0.0873650	+	0.370535i
$867$	5.26692	+	1.13790i	0.178874	+	0.0386452i
$868$	−0.341119	+	0.694001i	−0.0115783	+	0.0235559i
$869$	−4.88933	−	12.6346i	−0.165859	−	0.428600i
$870$	3.29463	−	0.0412387i	0.111698	−	0.00139812i
$871$	9.63240	−	11.5608i	0.326381	−	0.391724i
$872$	23.7148	+	8.33387i	0.803084	+	0.282221i
$873$	28.5335	−	2.50635i	0.965712	−	0.0848272i
$874$	−5.54081	−	5.17194i	−0.187421	−	0.174943i
$875$	−2.67264	+	1.78278i	−0.0903516	+	0.0602688i
$876$	−0.0734921	+	0.280111i	−0.00248307	+	0.00946409i
$877$	−6.38982	−	10.8573i	−0.215769	−	0.366624i	0.734218	−	0.678914i	$-0.237549\pi$
$877$	−6.38982	−	10.8573i	−0.215769	−	0.366624i	−0.949987	+	0.312291i	$0.898904\pi$
$878$	16.9614	−	1.06286i	0.572421	−	0.0358698i
$879$	23.7618	−	13.3904i	0.801467	−	0.451647i
$880$	−0.833479	−	3.97831i	−0.0280966	−	0.134109i
$881$	−13.2202	−	10.0677i	−0.445399	−	0.339190i	0.358941	−	0.933360i	$-0.383138\pi$
$881$	−13.2202	−	10.0677i	−0.445399	−	0.339190i	−0.804339	+	0.594170i	$0.797481\pi$
$882$	17.5108	+	2.20323i	0.589621	+	0.0741866i
$883$	−22.3759	−	39.1323i	−0.753008	−	1.31691i	−0.942228	−	0.334971i	$-0.891273\pi$
$883$	−22.3759	−	39.1323i	−0.753008	−	1.31691i	0.189220	−	0.981935i	$-0.439404\pi$
$884$	−1.72979	+	4.82552i	−0.0581793	+	0.162300i
$885$	−3.06298	+	2.21369i	−0.102961	+	0.0744123i
$886$	14.1694	+	1.06610i	0.476030	+	0.0358162i
$887$	−0.970117	+	0.952073i	−0.0325734	+	0.0319675i	−0.716542	−	0.697544i	$-0.754276\pi$
$887$	−0.970117	+	0.952073i	−0.0325734	+	0.0319675i	0.683969	+	0.729511i	$0.260252\pi$
$888$	2.12610	−	0.629537i	0.0713471	−	0.0211259i
$889$	1.00968	+	5.50217i	0.0338635	+	0.184537i
$890$	7.00454	+	2.36347i	0.234793	+	0.0792238i
$891$	−0.917013	+	0.0229600i	−0.0307211	+	0.000769190i
$892$	−0.934786	−	3.75367i	−0.0312990	−	0.125682i
$893$	0.915387	+	1.86234i	0.0306323	+	0.0623208i
$894$	2.55115	−	2.76763i	0.0853234	−	0.0925634i
$895$	−5.03744	−	0.957023i	−0.168383	−	0.0319897i
$896$	−3.14165	+	11.3914i	−0.104955	+	0.380562i
$897$	34.0718	+	36.0470i	1.13763	+	1.20357i
$898$	10.2152	−	3.87975i	0.340887	−	0.129469i
$899$	−19.9091	−	0.747916i	−0.664005	−	0.0249444i
$900$	−2.24835	+	0.604958i	−0.0749451	+	0.0201653i
$901$	−11.2097	+	9.22156i	−0.373448	+	0.307215i
$902$	28.9655	−	29.8863i	0.964444	−	0.995105i
$903$	−3.51146	+	0.712761i	−0.116854	+	0.0237192i
$904$	3.74223	+	2.77656i	0.124465	+	0.0923469i
$905$	−5.39760	+	2.12769i	−0.179422	+	0.0707268i
$906$	−1.20373	−	2.79412i	−0.0399912	−	0.0928284i
$907$	8.09194	+	47.4331i	0.268688	+	1.57499i	0.727278	+	0.686343i	$0.240785\pi$
$907$	8.09194	+	47.4331i	0.268688	+	1.57499i	−0.458590	+	0.888648i	$0.651645\pi$
$908$	−0.0128519	−	0.684461i	−0.000426505	−	0.0227146i
$909$	−4.30802	−	18.2713i	−0.142888	−	0.606020i
$910$	−2.41396	−	1.61023i	−0.0800220	−	0.0533785i
$911$	−22.1219	+	19.6363i	−0.732931	+	0.650581i	−0.945148	−	0.326641i	$-0.894083\pi$
$911$	−22.1219	+	19.6363i	−0.732931	+	0.650581i	0.212217	+	0.977223i	$0.431932\pi$
$912$	1.93601	+	2.20876i	0.0641078	+	0.0731394i
$913$	25.5052	+	25.0308i	0.844098	+	0.828398i
$914$	−43.6936	−	23.2011i	−1.44526	−	0.767426i
$915$	0.00332879	−	0.531906i	0.000110046	−	0.0175843i
$916$	−2.84524	−	2.52555i	−0.0940093	−	0.0834467i
$917$	4.17522	+	15.9136i	0.137878	+	0.525515i
$918$	18.6715	−	18.7888i	0.616253	−	0.620122i
$919$	8.33311	+	12.3247i	0.274884	+	0.406556i	0.940529	−	0.339712i	$-0.110330\pi$
$919$	8.33311	+	12.3247i	0.274884	+	0.406556i	−0.665645	+	0.746268i	$0.731844\pi$
$920$	−6.56067	+	3.58967i	−0.216299	+	0.118348i
$921$	−0.330396	+	2.09452i	−0.0108869	+	0.0690167i
$922$	−57.3610	+	10.1554i	−1.88908	+	0.334451i
$923$	25.9563	+	49.6296i	0.854361	+	1.63358i
$924$	−0.541029	+	0.287285i	−0.0177986	+	0.00945097i
$925$	3.77559	+	1.11795i	0.124141	+	0.0367581i
$926$	4.63019	−	43.3572i	0.152157	−	1.42480i
$927$	0.918163	+	16.2844i	0.0301564	+	0.534850i
$928$	8.20063	−	1.24105i	0.269199	−	0.0407393i
$929$	−0.492084	+	26.2072i	−0.0161448	+	0.859831i	0.894602	+	0.446865i	$0.147459\pi$
$929$	−0.492084	+	26.2072i	−0.0161448	+	0.859831i	−0.910746	+	0.412966i	$0.864493\pi$
$930$	1.85294	−	0.400322i	0.0607602	−	0.0131271i
$931$	0.943632	−	3.78919i	0.0309263	−	0.124186i
$932$	−1.08009	+	4.85201i	−0.0353795	+	0.158933i
$933$	3.44095	+	3.29342i	0.112652	+	0.107822i
$934$	1.02272	+	2.96952i	0.0334644	+	0.0971657i
$935$	0.491135	+	3.11351i	0.0160618	+	0.101823i
$936$	18.1712	+	23.5537i	0.593943	+	0.769876i
$937$	−4.99753	−	10.8450i	−0.163262	−	0.354289i	0.809134	−	0.587624i	$-0.199937\pi$
$937$	−4.99753	−	10.8450i	−0.163262	−	0.354289i	−0.972396	+	0.233335i	$0.925036\pi$
$938$	2.14878	−	2.71434i	0.0701602	−	0.0886264i
$939$	−14.2904	+	8.77566i	−0.466351	+	0.286383i
$940$	−0.290492	+	0.0402494i	−0.00947480	+	0.00131279i
$941$	−9.95639	−	13.5961i	−0.324569	−	0.443222i	0.613487	−	0.789705i	$-0.289766\pi$
$941$	−9.95639	−	13.5961i	−0.324569	−	0.443222i	−0.938056	+	0.346483i	$0.887376\pi$
$942$	16.9582	−	23.7763i	0.552528	−	0.774673i
$943$	−76.7409	−	39.5258i	−2.49903	−	1.28714i
$944$	−32.4664	+	31.0745i	−1.05669	+	1.01139i
$945$	0.864683	+	1.42803i	0.0281282	+	0.0464538i
$946$	9.93937	−	10.5156i	0.323157	−	0.341891i
$947$	10.9612	−	26.3460i	0.356191	−	0.856130i	−0.639954	−	0.768413i	$-0.721047\pi$
$947$	10.9612	−	26.3460i	0.356191	−	0.856130i	0.996145	−	0.0877172i	$-0.0279572\pi$
$948$	−1.16979	+	0.738679i	−0.0379930	+	0.0239912i
$949$	5.95022	+	2.78724i	0.193152	+	0.0904775i
$950$	0.663691	+	4.57908i	0.0215330	+	0.148565i
$951$	−3.09042	−	4.33292i	−0.100214	−	0.140505i
$952$	2.58354	−	7.81793i	0.0837331	−	0.253380i
$953$	15.9132	−	35.7014i	0.515478	−	1.15648i	−0.449291	−	0.893385i	$-0.648324\pi$
$953$	15.9132	−	35.7014i	0.515478	−	1.15648i	0.964769	−	0.263098i	$-0.0847442\pi$
$954$	−1.43124	−	11.9801i	−0.0463381	−	0.387869i
$955$	2.98017	−	0.761998i	0.0964361	−	0.0246577i
$956$	−3.19771	−	0.903467i	−0.103421	−	0.0292202i
$957$	−12.4351	−	9.71816i	−0.401970	−	0.314143i
$958$	−4.20355	+	1.30211i	−0.135811	+	0.0420694i
$959$	16.3652	−	0.614785i	0.528460	−	0.0198524i
$960$	2.32415	−	0.984065i	0.0750116	−	0.0317605i
$961$	19.2793	−	3.16496i	0.621914	−	0.102095i
$962$	0.765198	+	7.16532i	0.0246710	+	0.231019i
$963$	6.19891	−	33.7805i	0.199757	−	1.08856i
$964$	−3.44663	+	6.20668i	−0.111008	+	0.199904i
$965$	0.231862	−	1.18012i	0.00746390	−	0.0379893i
$966$	8.04375	+	8.09425i	0.258803	+	0.260428i
$967$	−27.1659	+	46.1589i	−0.873596	+	1.48437i	0.00126615	+	0.999999i	$0.499597\pi$
$967$	−27.1659	+	46.1589i	−0.873596	+	1.48437i	−0.874863	+	0.484371i	$0.839048\pi$
$968$	5.24608	−	10.3440i	0.168616	−	0.332468i
$969$	−1.41371	−	1.78580i	−0.0454150	−	0.0573682i
$970$	7.55533	+	2.76182i	0.242587	+	0.0886768i
$971$	22.3649	+	0.559970i	0.717725	+	0.0179703i	0.382224	−	0.924070i	$-0.375158\pi$
$971$	22.3649	+	0.559970i	0.717725	+	0.0179703i	0.335501	+	0.942040i	$0.391095\pi$
$972$	0.858312	+	3.85573i	0.0275304	+	0.123673i
$973$	0.461390	−	0.761990i	0.0147915	−	0.0244283i
$974$	12.0711	+	43.7692i	0.386783	+	1.40245i
$975$	−2.46066	−	30.1789i	−0.0788042	−	0.966497i
$976$	−0.828900	−	6.27085i	−0.0265324	−	0.200725i
$977$	−3.62898	+	30.3760i	−0.116101	+	0.971815i	0.807872	+	0.589358i	$0.200619\pi$
$977$	−3.62898	+	30.3760i	−0.116101	+	0.971815i	−0.923973	+	0.382457i	$0.875078\pi$
$978$	2.47423	+	1.47708i	0.0791172	+	0.0472320i
$979$	−19.0929	−	29.8209i	−0.610211	−	0.953079i
$980$	0.466613	+	0.294649i	0.0149054	+	0.00941222i
$981$	14.9360	−	10.5126i	0.476869	−	0.335640i
$982$	−10.0959	+	25.1493i	−0.322174	+	0.802546i
$983$	1.60160	−	5.53602i	0.0510832	−	0.176572i	−0.931000	−	0.365019i	$-0.881063\pi$
$983$	1.60160	−	5.53602i	0.0510832	−	0.176572i	0.982083	+	0.188447i	$0.0603454\pi$
$984$	24.8896	+	16.1561i	0.793452	+	0.515038i
$985$	−3.26558	−	8.13467i	−0.104050	−	0.259192i
$986$	−30.2319	+	3.03729i	−0.962781	+	0.0967272i
$987$	−1.27193	−	2.85359i	−0.0404859	−	0.0908309i
$988$	−0.809482	+	0.483250i	−0.0257531	+	0.0153742i
$989$	−26.8498	−	13.4067i	−0.853775	−	0.426307i
$990$	−2.39966	−	1.05164i	−0.0762661	−	0.0334235i
$991$	44.7867	+	27.5032i	1.42270	+	0.873668i	0.999476	−	0.0323579i	$-0.0103016\pi$
$991$	44.7867	+	27.5032i	1.42270	+	0.873668i	0.423221	+	0.906026i	$0.360899\pi$
$992$	4.48184	−	1.63832i	0.142298	−	0.0520166i
$993$	9.99799	−	3.37352i	0.317277	−	0.107055i
$994$	6.25547	+	11.2648i	0.198412	+	0.357299i
$995$	7.04247	−	2.27850i	0.223261	−	0.0722332i
$996$	2.00606	−	3.04853i	0.0635646	−	0.0965964i
$997$	0.520019	−	3.58782i	0.0164692	−	0.113627i	−0.979792	−	0.200018i	$-0.935900\pi$
$997$	0.520019	−	3.58782i	0.0164692	−	0.113627i	0.996261	+	0.0863907i	$0.0275333\pi$
$998$	−21.2428	+	10.9412i	−0.672429	+	0.346339i
$999$	1.35000	−	3.91981i	0.0427123	−	0.124017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.c.a.2.13	✓	10250
503.252	even	251	inner	503.2.c.a.252.13	yes	10250

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.c.a.2.13	✓	10250	1.1	even	1	trivial
503.2.c.a.252.13	yes	10250	503.252	even	251	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\), degree \(250\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.945803 - 1.16449i) q^{2} +(-0.790504 + 0.684188i) q^{3} +(-0.0513814 + 0.245250i) q^{4} +(-0.107766 - 0.340345i) q^{5} +(1.54439 + 0.273425i) q^{6} +(0.296825 - 0.861848i) q^{7} +(-2.33318 + 1.20172i) q^{8} +(-0.273541 + 1.88727i) q^{9} +O(q^{10})\)	\(q+(-0.945803 - 1.16449i) q^{2} +(-0.790504 + 0.684188i) q^{3} +(-0.0513814 + 0.245250i) q^{4} +(-0.107766 - 0.340345i) q^{5} +(1.54439 + 0.273425i) q^{6} +(0.296825 - 0.861848i) q^{7} +(-2.33318 + 1.20172i) q^{8} +(-0.273541 + 1.88727i) q^{9} +(-0.294402 + 0.447391i) q^{10} +(2.44073 - 0.789665i) q^{11} +(-0.127180 - 0.229026i) q^{12} +(-5.63196 + 1.90033i) q^{13} +(-1.28435 + 0.469489i) q^{14} +(0.318049 + 0.195312i) q^{15} +(4.06512 + 1.78153i) q^{16} +(-3.07927 - 1.53754i) q^{17} +(2.45642 - 1.46645i) q^{18} +(-0.257697 - 0.578148i) q^{19} +(0.0890067 - 0.00894219i) q^{20} +(0.355025 + 0.884379i) q^{21} +(-3.22800 - 2.09533i) q^{22} +(-2.21825 + 7.66748i) q^{23} +(1.02219 - 2.54630i) q^{24} +(3.98455 - 2.80449i) q^{25} +(7.53963 + 4.76100i) q^{26} +(-2.76618 - 4.32046i) q^{27} +(0.196117 + 0.117079i) q^{28} +(-0.698058 + 5.84303i) q^{29} +(-0.0733736 - 0.555090i) q^{30} +(0.275139 + 3.37445i) q^{31} +(-0.374722 - 1.35872i) q^{32} +(-1.38913 + 2.29415i) q^{33} +(1.12193 + 5.03998i) q^{34} +(-0.325313 - 0.00814513i) q^{35} +(-0.448798 - 0.164056i) q^{36} +(0.501595 + 0.633615i) q^{37} +(-0.429516 + 0.846899i) q^{38} +(3.15190 - 5.35554i) q^{39} +(0.660435 + 0.664581i) q^{40} +(-2.08494 + 10.6118i) q^{41} +(0.694065 - 1.24987i) q^{42} +(-0.678624 + 3.69811i) q^{43} +(0.0682574 + 0.639164i) q^{44} +(0.671800 - 0.110285i) q^{45} +(11.0267 - 4.66880i) q^{46} +(-3.27607 + 0.123071i) q^{47} +(-4.43240 + 1.37300i) q^{48} +(4.86080 + 3.79876i) q^{49} +(-7.03439 - 1.98747i) q^{50} +(3.48614 - 0.891369i) q^{51} +(-0.176680 - 1.47888i) q^{52} +(1.71696 - 3.85204i) q^{53} +(-2.41486 + 7.30748i) q^{54} +(-0.531785 - 0.745590i) q^{55} +(0.343152 + 2.36755i) q^{56} +(0.599273 + 0.280715i) q^{57} +(7.46436 - 4.71347i) q^{58} +(-3.88952 + 9.34874i) q^{59} +(-0.0642420 + 0.0679662i) q^{60} +(-0.738171 - 1.21910i) q^{61} +(3.66928 - 3.51196i) q^{62} +(1.54535 + 0.795940i) q^{63} +(3.92669 - 5.50542i) q^{64} +(1.25370 + 1.71201i) q^{65} +(3.98535 - 0.552194i) q^{66} +(-2.15732 + 1.32480i) q^{67} +(0.535299 - 0.676191i) q^{68} +(-3.49247 - 7.57887i) q^{69} +(0.298197 + 0.386527i) q^{70} +(-1.46820 - 9.30755i) q^{71} +(-1.62975 - 4.73206i) q^{72} +(-0.798600 - 0.764360i) q^{73} +(0.263427 - 1.18338i) q^{74} +(-1.23100 + 4.94314i) q^{75} +(0.155032 - 0.0334942i) q^{76} +(0.0438985 - 2.33793i) q^{77} +(-9.21753 + 1.39494i) q^{78} +(-0.297294 - 5.27276i) q^{79} +(0.168254 - 1.57553i) q^{80} +(-0.342867 - 0.101523i) q^{81} +(14.3293 - 7.60878i) q^{82} +(6.45602 + 12.3442i) q^{83} +(-0.235136 + 0.0416294i) q^{84} +(-0.191454 + 1.21371i) q^{85} +(4.94825 - 2.70743i) q^{86} +(-3.44592 - 5.09654i) q^{87} +(-4.74571 + 4.77550i) q^{88} +(-3.50296 - 13.3513i) q^{89} +(-0.763816 - 0.677995i) q^{90} +(-0.0339068 + 5.41796i) q^{91} +(-1.76648 - 0.937992i) q^{92} +(-2.52626 - 2.47927i) q^{93} +(3.24183 + 3.69854i) q^{94} +(-0.168999 + 0.150010i) q^{95} +(1.22584 + 0.817694i) q^{96} +(-3.44695 - 14.6193i) q^{97} +(-0.173745 - 9.25322i) q^{98} +(0.822672 + 4.82232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9}+O(q^{10}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9	\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9} - 233 q^{10} - 239 q^{11} - 239 q^{12} - 245 q^{13} - 223 q^{14} - 231 q^{15} - 263 q^{16} - 243 q^{17} - 217 q^{18} - 229 q^{19} - 195 q^{20} - 215 q^{21} - 233 q^{22} - 241 q^{23} - 181 q^{24} - 280 q^{25} - 215 q^{26} - 237 q^{27} - 185 q^{28} - 217 q^{29} - 159 q^{30} - 219 q^{31} - 185 q^{32} - 209 q^{33} - 167 q^{34} - 187 q^{35} - 203 q^{36} - 237 q^{37} - 161 q^{38} - 197 q^{39} - 135 q^{40} - 209 q^{41} - 117 q^{42} - 221 q^{43} - 147 q^{44} - 167 q^{45} - 167 q^{46} - 195 q^{47} - 141 q^{48} - 234 q^{49} - 145 q^{50} - 177 q^{51} - 179 q^{52} - 211 q^{53} - 83 q^{54} - 165 q^{55} - 125 q^{56} - 177 q^{57} - 205 q^{58} - 189 q^{59} - 27 q^{60} - 193 q^{61} - 143 q^{62} - 159 q^{63} - 185 q^{64} - 155 q^{65} - 97 q^{66} - 201 q^{67} - 155 q^{68} - 113 q^{69} - 123 q^{70} - 153 q^{71} - 21 q^{72} - 213 q^{73} - 83 q^{74} - 161 q^{75} - 97 q^{76} - 139 q^{77} - 43 q^{78} - 191 q^{79} + 3 q^{80} - 188 q^{81} - 97 q^{82} - 161 q^{83} + 67 q^{84} - 159 q^{85} - 121 q^{86} - 121 q^{87} - 143 q^{88} - 155 q^{89} + 115 q^{90} - 137 q^{91} - 119 q^{92} - 123 q^{93} - 99 q^{94} - 181 q^{95} + 67 q^{96} - 229 q^{97} - 63 q^{98} - 85 q^{99}+O(q^{100}) \) 10250 * q - 249 * q^2 - 249 * q^3 - 285 * q^4 - 245 * q^5 - 237 * q^6 - 247 * q^7 - 239 * q^8 - 280 * q^9 - 233 * q^10 - 239 * q^11 - 239 * q^12 - 245 * q^13 - 223 * q^14 - 231 * q^15 - 263 * q^16 - 243 * q^17 - 217 * q^18 - 229 * q^19 - 195 * q^20 - 215 * q^21 - 233 * q^22 - 241 * q^23 - 181 * q^24 - 280 * q^25 - 215 * q^26 - 237 * q^27 - 185 * q^28 - 217 * q^29 - 159 * q^30 - 219 * q^31 - 185 * q^32 - 209 * q^33 - 167 * q^34 - 187 * q^35 - 203 * q^36 - 237 * q^37 - 161 * q^38 - 197 * q^39 - 135 * q^40 - 209 * q^41 - 117 * q^42 - 221 * q^43 - 147 * q^44 - 167 * q^45 - 167 * q^46 - 195 * q^47 - 141 * q^48 - 234 * q^49 - 145 * q^50 - 177 * q^51 - 179 * q^52 - 211 * q^53 - 83 * q^54 - 165 * q^55 - 125 * q^56 - 177 * q^57 - 205 * q^58 - 189 * q^59 - 27 * q^60 - 193 * q^61 - 143 * q^62 - 159 * q^63 - 185 * q^64 - 155 * q^65 - 97 * q^66 - 201 * q^67 - 155 * q^68 - 113 * q^69 - 123 * q^70 - 153 * q^71 - 21 * q^72 - 213 * q^73 - 83 * q^74 - 161 * q^75 - 97 * q^76 - 139 * q^77 - 43 * q^78 - 191 * q^79 + 3 * q^80 - 188 * q^81 - 97 * q^82 - 161 * q^83 + 67 * q^84 - 159 * q^85 - 121 * q^86 - 121 * q^87 - 143 * q^88 - 155 * q^89 + 115 * q^90 - 137 * q^91 - 119 * q^92 - 123 * q^93 - 99 * q^94 - 181 * q^95 + 67 * q^96 - 229 * q^97 - 63 * q^98 - 85 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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