LMFDB - Embedded newform 637.2.bl.b.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18557 - 1.49010i) q^{2} +(-1.35107 - 1.25361i) q^{3} +(1.82564 + 4.65166i) q^{4} +(2.14986 - 0.663145i) q^{5} +(1.08486 + 4.75308i) q^{6} +(-1.64665 + 2.07088i) q^{7} +(1.76413 - 7.72914i) q^{8} +(0.0296636 + 0.395833i) q^{9} +O(q^{10})$	\(q+(-2.18557 - 1.49010i) q^{2} +(-1.35107 - 1.25361i) q^{3} +(1.82564 + 4.65166i) q^{4} +(2.14986 - 0.663145i) q^{5} +(1.08486 + 4.75308i) q^{6} +(-1.64665 + 2.07088i) q^{7} +(1.76413 - 7.72914i) q^{8} +(0.0296636 + 0.395833i) q^{9} +(-5.68682 - 1.75415i) q^{10} +(0.0234531 - 0.312960i) q^{11} +(3.36481 - 8.57338i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(6.68467 - 2.07240i) q^{14} +(-3.73595 - 1.79914i) q^{15} +(-8.04652 + 7.46608i) q^{16} +(-1.34513 + 0.202746i) q^{17} +(0.524997 - 0.909321i) q^{18} +(1.01124 + 1.75153i) q^{19} +(7.00960 + 8.78977i) q^{20} +(4.82082 - 0.733659i) q^{21} +(-0.517598 + 0.649047i) q^{22} +(-2.29170 - 0.345418i) q^{23} +(-12.0728 + 8.23111i) q^{24} +(0.0509509 - 0.0347378i) q^{25} +(2.61566 + 0.394247i) q^{26} +(-2.99128 + 3.75095i) q^{27} +(-12.6392 - 3.87895i) q^{28} +(5.31274 + 6.66197i) q^{29} +(5.48428 + 9.49905i) q^{30} +(-4.50578 + 7.80424i) q^{31} +(13.0327 - 1.96436i) q^{32} +(-0.424017 + 0.393430i) q^{33} +(3.24199 + 1.56126i) q^{34} +(-2.16677 + 5.54408i) q^{35} +(-1.78712 + 0.860634i) q^{36} +(-0.000631250 + 0.00160840i) q^{37} +(0.399798 - 5.33493i) q^{38} +(1.76120 + 0.543257i) q^{39} +(-1.33291 - 17.7865i) q^{40} +(0.180553 - 0.791054i) q^{41} +(-11.6295 - 5.58003i) q^{42} +(1.59526 + 6.98928i) q^{43} +(1.49860 - 0.462257i) q^{44} +(0.326267 + 0.831314i) q^{45} +(4.49395 + 4.16978i) q^{46} +(2.90310 + 1.97930i) q^{47} +20.2310 q^{48} +(-1.57712 - 6.82002i) q^{49} -0.163119 q^{50} +(2.07154 + 1.41235i) q^{51} +(-3.66313 - 3.39889i) q^{52} +(-2.61029 - 6.65092i) q^{53} +(12.1269 - 3.74066i) q^{54} +(-0.157117 - 0.688373i) q^{55} +(13.1013 + 16.3805i) q^{56} +(0.829471 - 3.63415i) q^{57} +(-1.68439 - 22.4767i) q^{58} +(8.66862 + 2.67391i) q^{59} +(1.54847 - 20.6629i) q^{60} +(3.88983 - 9.91114i) q^{61} +(21.4767 - 10.3427i) q^{62} +(-0.868569 - 0.590366i) q^{63} +(-11.6315 - 5.60142i) q^{64} +(-1.64923 + 1.53026i) q^{65} +(1.51297 - 0.228043i) q^{66} +(-0.0328337 + 0.0568696i) q^{67} +(-3.39884 - 5.88696i) q^{68} +(2.66323 + 3.33958i) q^{69} +(12.9968 - 8.88827i) q^{70} +(-9.85435 + 12.3570i) q^{71} +(3.11178 + 0.469025i) q^{72} +(0.628113 - 0.428240i) q^{73} +(0.00377631 - 0.00257464i) q^{74} +(-0.112386 - 0.0169395i) q^{75} +(-6.30134 + 7.90163i) q^{76} +(0.609484 + 0.563902i) q^{77} +(-3.03971 - 3.81168i) q^{78} +(-3.00006 - 5.19626i) q^{79} +(-12.3478 + 21.3871i) q^{80} +(9.92120 - 1.49538i) q^{81} +(-1.57336 + 1.45986i) q^{82} +(6.91466 + 3.32993i) q^{83} +(12.2138 + 21.0854i) q^{84} +(-2.75740 + 1.32789i) q^{85} +(6.92815 - 17.6526i) q^{86} +(1.17362 - 15.6609i) q^{87} +(-2.37754 - 0.733373i) q^{88} +(1.23621 + 16.4961i) q^{89} +(0.525659 - 2.30306i) q^{90} +(0.585054 - 2.58025i) q^{91} +(-2.57705 - 11.2908i) q^{92} +(15.8711 - 4.89559i) q^{93} +(-3.39558 - 8.65179i) q^{94} +(3.33555 + 3.09494i) q^{95} +(-20.0706 - 13.6839i) q^{96} -1.65603 q^{97} +(-6.71559 + 17.2557i) q^{98} +0.124575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−2.18557	−	1.49010i	−1.54543	−	1.05366i	−0.972168	−	0.234284i	$-0.924725\pi$
$2$	−2.18557	−	1.49010i	−1.54543	−	1.05366i	−0.573262	−	0.819372i	$-0.694322\pi$
$3$	−1.35107	−	1.25361i	−0.780042	−	0.723774i	0.185889	−	0.982571i	$-0.440483\pi$
$3$	−1.35107	−	1.25361i	−0.780042	−	0.723774i	−0.965932	+	0.258797i	$0.916674\pi$
$4$	1.82564	+	4.65166i	0.912821	+	2.32583i
$5$	2.14986	−	0.663145i	0.961447	−	0.296567i	0.225983	−	0.974131i	$-0.427440\pi$
$5$	2.14986	−	0.663145i	0.961447	−	0.296567i	0.735464	+	0.677564i	$0.236964\pi$
$6$	1.08486	+	4.75308i	0.442892	+	1.94044i
$7$	−1.64665	+	2.07088i	−0.622374	+	0.782720i
$7$	−1.64665	+	2.07088i	−0.622374	+	0.782720i
$8$	1.76413	−	7.72914i	0.623713	−	2.73267i
$9$	0.0296636	+	0.395833i	0.00988785	+	0.131944i
$10$	−5.68682	−	1.75415i	−1.79833	−	0.554711i
$11$	0.0234531	−	0.312960i	0.00707137	−	0.0943609i	−0.992551	−	0.121827i	$-0.961125\pi$
$11$	0.0234531	−	0.312960i	0.00707137	−	0.0943609i	0.999623	+	0.0274660i	$0.00874379\pi$
$12$	3.36481	−	8.57338i	0.971336	−	2.47492i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	6.68467	−	2.07240i	1.78655	−	0.553872i
$15$	−3.73595	−	1.79914i	−0.964617	−	0.464535i
$16$	−8.04652	+	7.46608i	−2.01163	+	1.86652i
$17$	−1.34513	+	0.202746i	−0.326242	+	0.0491731i	−0.310121	−	0.950697i	$-0.600370\pi$
$17$	−1.34513	+	0.202746i	−0.326242	+	0.0491731i	−0.0161208	+	0.999870i	$0.505132\pi$
$18$	0.524997	−	0.909321i	0.123743	−	0.214329i
$19$	1.01124	+	1.75153i	0.231995	+	0.401828i	0.958395	−	0.285444i	$-0.0921412\pi$
$19$	1.01124	+	1.75153i	0.231995	+	0.401828i	−0.726400	+	0.687272i	$0.758808\pi$
$20$	7.00960	+	8.78977i	1.56740	+	1.96545i
$21$	4.82082	−	0.733659i	1.05199	−	0.160097i
$22$	−0.517598	+	0.649047i	−0.110352	+	0.138377i
$23$	−2.29170	−	0.345418i	−0.477852	−	0.0720246i	−0.0942997	−	0.995544i	$-0.530061\pi$
$23$	−2.29170	−	0.345418i	−0.477852	−	0.0720246i	−0.383552	+	0.923519i	$0.625299\pi$
$24$	−12.0728	+	8.23111i	−2.46435	+	1.68017i
$25$	0.0509509	−	0.0347378i	0.0101902	−	0.00694755i
$26$	2.61566	+	0.394247i	0.512973	+	0.0773182i
$27$	−2.99128	+	3.75095i	−0.575672	+	0.721870i
$28$	−12.6392	−	3.87895i	−2.38859	−	0.733052i
$29$	5.31274	+	6.66197i	0.986552	+	1.23710i	0.971458	+	0.237211i	$0.0762332\pi$
$29$	5.31274	+	6.66197i	0.986552	+	1.23710i	0.0150936	+	0.999886i	$0.495195\pi$
$30$	5.48428	+	9.49905i	1.00129	+	1.73428i
$31$	−4.50578	+	7.80424i	−0.809262	+	1.40168i	0.104114	+	0.994565i	$0.466799\pi$
$31$	−4.50578	+	7.80424i	−0.809262	+	1.40168i	−0.913376	+	0.407117i	$0.866534\pi$
$32$	13.0327	−	1.96436i	2.30387	−	0.347253i
$33$	−0.424017	+	0.393430i	−0.0738119	+	0.0684874i
$34$	3.24199	+	1.56126i	0.555996	+	0.267754i
$35$	−2.16677	+	5.54408i	−0.366250	+	0.937120i
$36$	−1.78712	+	0.860634i	−0.297854	+	0.143439i
$37$	−0.000631250		0.00160840i	−0.000103777		0.000264419i	−0.930926	−	0.365209i	$-0.880998\pi$
$37$	−0.000631250		0.00160840i	−0.000103777		0.000264419i	0.930822	+	0.365473i	$0.119093\pi$
$38$	0.399798	−	5.33493i	0.0648558	−	0.865441i
$39$	1.76120	+	0.543257i	0.282017	+	0.0869908i
$40$	−1.33291	−	17.7865i	−0.210752	−	2.81229i
$41$	0.180553	−	0.791054i	0.0281976	−	0.123542i	−0.958870	−	0.283845i	$-0.908390\pi$
$41$	0.180553	−	0.791054i	0.0281976	−	0.123542i	0.987068	+	0.160303i	$0.0512471\pi$
$42$	−11.6295	−	5.58003i	−1.79446	−	0.861017i
$43$	1.59526	+	6.98928i	0.243275	+	1.06586i	0.938015	+	0.346595i	$0.112662\pi$
$43$	1.59526	+	6.98928i	0.243275	+	1.06586i	−0.694740	+	0.719261i	$0.744481\pi$
$44$	1.49860	−	0.462257i	0.225922	−	0.0696878i
$45$	0.326267	+	0.831314i	0.0486370	+	0.123925i
$46$	4.49395	+	4.16978i	0.662597	+	0.614800i
$47$	2.90310	+	1.97930i	0.423461	+	0.288711i	0.756240	−	0.654294i	$-0.227034\pi$
$47$	2.90310	+	1.97930i	0.423461	+	0.288711i	−0.332780	+	0.943005i	$0.607987\pi$
$48$	20.2310			2.92010
$49$	−1.57712	−	6.82002i	−0.225302	−	0.974289i
$50$	−0.163119			−0.0230686
$51$	2.07154	+	1.41235i	0.290073	+	0.197768i
$52$	−3.66313	−	3.39889i	−0.507984	−	0.471341i
$53$	−2.61029	−	6.65092i	−0.358551	−	0.913574i	−0.990369	−	0.138456i	$-0.955786\pi$
$53$	−2.61029	−	6.65092i	−0.358551	−	0.913574i	0.631817	−	0.775117i	$-0.282309\pi$
$54$	12.1269	−	3.74066i	1.65026	−	0.509039i
$55$	−0.157117	−	0.688373i	−0.0211856	−	0.0928202i
$56$	13.1013	+	16.3805i	1.75073	+	2.18893i
$57$	0.829471	−	3.63415i	0.109866	−	0.481355i
$58$	−1.68439	−	22.4767i	−0.221172	−	2.95133i
$59$	8.66862	+	2.67391i	1.12856	+	0.348114i	0.802154	−	0.597117i	$-0.203687\pi$
$59$	8.66862	+	2.67391i	1.12856	+	0.348114i	0.326403	+	0.945231i	$0.394163\pi$
$60$	1.54847	−	20.6629i	0.199907	−	2.66757i
$61$	3.88983	−	9.91114i	0.498042	−	1.26899i	−0.432111	−	0.901820i	$-0.642231\pi$
$61$	3.88983	−	9.91114i	0.498042	−	1.26899i	0.930154	−	0.367171i	$-0.119674\pi$
$62$	21.4767	−	10.3427i	2.72755	−	1.31352i
$63$	−0.868569	−	0.590366i	−0.109429	−	0.0743792i
$64$	−11.6315	−	5.60142i	−1.45393	−	0.700177i
$65$	−1.64923	+	1.53026i	−0.204562	+	0.189806i
$66$	1.51297	−	0.228043i	0.186233	−	0.0280702i
$67$	−0.0328337	+	0.0568696i	−0.00401127	+	0.00694773i	−0.868024	−	0.496522i	$-0.834610\pi$
$67$	−0.0328337	+	0.0568696i	−0.00401127	+	0.00694773i	0.864013	+	0.503470i	$0.167943\pi$
$68$	−3.39884	−	5.88696i	−0.412169	−	0.713898i
$69$	2.66323	+	3.33958i	0.320615	+	0.402039i
$70$	12.9968	−	8.88827i	1.55342	−	1.06235i
$71$	−9.85435	+	12.3570i	−1.16950	+	1.46650i	−0.313447	+	0.949606i	$0.601484\pi$
$71$	−9.85435	+	12.3570i	−1.16950	+	1.46650i	−0.856049	+	0.516895i	$0.827088\pi$
$72$	3.11178	+	0.469025i	0.366727	+	0.0552751i
$73$	0.628113	−	0.428240i	0.0735150	−	0.0501217i	−0.526005	−	0.850482i	$-0.676311\pi$
$73$	0.628113	−	0.428240i	0.0735150	−	0.0501217i	0.599520	+	0.800360i	$0.295358\pi$
$74$	0.00377631	−	0.00257464i	0.000438987	−	0.000299296i
$75$	−0.112386	−	0.0169395i	−0.0129772	−	0.00195600i
$76$	−6.30134	+	7.90163i	−0.722813	+	0.906379i
$77$	0.609484	+	0.563902i	0.0694572	+	0.0642626i
$78$	−3.03971	−	3.81168i	−0.344179	−	0.431587i
$79$	−3.00006	−	5.19626i	−0.337533	−	0.584625i	0.646435	−	0.762969i	$-0.276259\pi$
$79$	−3.00006	−	5.19626i	−0.337533	−	0.584625i	−0.983968	+	0.178344i	$0.942926\pi$
$80$	−12.3478	+	21.3871i	−1.38053	+	2.39115i
$81$	9.92120	−	1.49538i	1.10236	−	0.166153i
$82$	−1.57336	+	1.45986i	−0.173748	+	0.161215i
$83$	6.91466	+	3.32993i	0.758983	+	0.365507i	0.773009	−	0.634395i	$-0.218751\pi$
$83$	6.91466	+	3.32993i	0.758983	+	0.365507i	−0.0140263	+	0.999902i	$0.504465\pi$
$84$	12.2138	+	21.0854i	1.33264	+	2.30061i
$85$	−2.75740	+	1.32789i	−0.299082	+	0.144030i
$86$	6.92815	−	17.6526i	0.747081	−	1.90353i
$87$	1.17362	−	15.6609i	0.125826	−	1.67903i
$88$	−2.37754	−	0.733373i	−0.253446	−	0.0781778i
$89$	1.23621	+	16.4961i	0.131038	+	1.74859i	0.545130	+	0.838351i	$0.316480\pi$
$89$	1.23621	+	16.4961i	0.131038	+	1.74859i	−0.414092	+	0.910235i	$0.635901\pi$
$90$	0.525659	−	2.30306i	0.0554093	−	0.242764i
$91$	0.585054	−	2.58025i	0.0613303	−	0.270484i
$92$	−2.57705	−	11.2908i	−0.268676	−	1.17715i
$93$	15.8711	−	4.89559i	1.64576	−	0.507649i
$94$	−3.39558	−	8.65179i	−0.350227	−	0.892364i
$95$	3.33555	+	3.09494i	0.342220	+	0.317534i
$96$	−20.0706	−	13.6839i	−2.04845	−	1.39661i
$97$	−1.65603			−0.168145			−0.0840724	−	0.996460i	$-0.526793\pi$
$97$	−1.65603			−0.168145			−0.0840724	+	0.996460i	$0.526793\pi$
$98$	−6.71559	+	17.2557i	−0.678377	+	1.74309i
$99$	0.124575			0.0125203
$100$	0.254607	+	0.173588i	0.0254607	+	0.0173588i
$101$	12.5394	+	11.6348i	1.24772	+	1.15771i	0.981015	+	0.193931i	$0.0621239\pi$
$101$	12.5394	+	11.6348i	1.24772	+	1.15771i	0.266700	+	0.963779i	$0.414067\pi$
$102$	−2.42295	−	6.17357i	−0.239908	−	0.611275i
$103$	−0.798873	+	0.246420i	−0.0787153	+	0.0242805i	−0.333863	−	0.942622i	$-0.608352\pi$
$103$	−0.798873	+	0.246420i	−0.0787153	+	0.0242805i	0.255147	+	0.966902i	$0.417876\pi$
$104$	1.76413	+	7.72914i	0.172987	+	0.757905i
$105$	9.87758	−	4.77417i	0.963953	−	0.465911i
$106$	−4.20553	+	18.4256i	−0.408477	+	1.78965i
$107$	−0.682824	−	9.11165i	−0.0660111	−	0.880856i	−0.927678	−	0.373382i	$-0.878198\pi$
$107$	−0.682824	−	9.11165i	−0.0660111	−	0.880856i	0.861667	−	0.507475i	$-0.169421\pi$
$108$	−22.9092	−	7.06654i	−2.20443	−	0.679978i
$109$	−0.798908	+	10.6607i	−0.0765215	+	1.02111i	0.818331	+	0.574747i	$0.194900\pi$
$109$	−0.798908	+	10.6607i	−0.0765215	+	1.02111i	−0.894853	+	0.446362i	$0.852719\pi$
$110$	−0.682352	+	1.73860i	−0.0650597	+	0.165769i
$111$	0.00286917	−	0.00138172i	0.000272330	−	0.000131147i
$112$	−2.21161	−	28.9574i	−0.208978	−	2.73622i
$113$	−18.8554	−	9.08028i	−1.77377	−	0.854201i	−0.963305	−	0.268409i	$-0.913502\pi$
$113$	−18.8554	−	9.08028i	−1.77377	−	0.854201i	−0.810462	−	0.585792i	$-0.800784\pi$
$114$	−7.22810	+	6.70669i	−0.676973	+	0.628139i
$115$	−5.15589	+	0.777126i	−0.480789	+	0.0724673i
$116$	−21.2901	+	36.8755i	−1.97673	+	3.42380i
$117$	−0.198471	−	0.343762i	−0.0183487	−	0.0317808i
$118$	−14.9615	−	18.7611i	−1.37731	−	1.72710i
$119$	1.79509	−	3.11946i	0.164556	−	0.285961i
$120$	−20.4965	+	25.7018i	−1.87106	+	2.34624i
$121$	10.7797	+	1.62479i	0.979977	+	0.147708i
$122$	−23.2700	+	15.8652i	−2.10677	+	1.43637i
$123$	−1.23561	+	0.842428i	−0.111412	+	0.0759592i
$124$	−44.5286	−	6.71161i	−3.99879	−	0.602720i
$125$	−6.92718	+	8.68641i	−0.619586	+	0.776936i
$126$	1.01861	+	2.58454i	0.0907454	+	0.230249i
$127$	8.79032	+	11.0227i	0.780015	+	0.978108i	0.999997	+	0.00260390i	$0.000828847\pi$
$127$	8.79032	+	11.0227i	0.780015	+	0.978108i	−0.219982	+	0.975504i	$0.570600\pi$
$128$	3.89483	+	6.74605i	0.344258	+	0.596272i
$129$	6.60654	−	11.4429i	0.581673	−	1.00749i
$130$	5.88474	−	0.886982i	0.516126	−	0.0777935i
$131$	9.78445	−	9.07864i	0.854871	−	0.793205i	−0.125141	−	0.992139i	$-0.539938\pi$
$131$	9.78445	−	9.07864i	0.854871	−	0.793205i	0.980013	+	0.198934i	$0.0637480\pi$
$132$	−2.60421	−	1.25412i	−0.226667	−	0.109157i
$133$	−5.29237	−	0.789975i	−0.458907	−	0.0684995i
$134$	0.156501	−	0.0753671i	0.0135197	−	0.00651072i
$135$	−3.94342	+	10.0477i	−0.339396	+	0.864766i
$136$	−0.805930	+	10.7544i	−0.0691079	+	0.922181i
$137$	11.7321	+	3.61889i	1.00234	+	0.309182i	0.752135	−	0.659009i	$-0.229024\pi$
$137$	11.7321	+	3.61889i	1.00234	+	0.309182i	0.250210	+	0.968192i	$0.419500\pi$
$138$	−0.844371	−	11.2674i	−0.0718777	−	0.959141i
$139$	−1.89229	+	8.29066i	−0.160502	+	0.703205i	0.829068	+	0.559148i	$0.188872\pi$
$139$	−1.89229	+	8.29066i	−0.160502	+	0.703205i	−0.989569	+	0.144056i	$0.953985\pi$
$140$	−29.7449	+	0.0424425i	−2.51390	+	0.00358705i
$141$	−1.44102	−	6.31354i	−0.121356	−	0.531696i
$142$	39.9504	−	12.3231i	3.35256	−	1.03413i
$143$	0.114658	+	0.292143i	0.00958815	+	0.0244302i
$144$	−3.19401	−	2.96361i	−0.266167	−	0.246967i
$145$	15.8395	+	10.7992i	1.31540	+	0.896825i
$146$	−2.01090			−0.166423
$147$	−6.41887	+	11.1914i	−0.529419	+	0.923054i
$148$	−0.00863416			−0.000709724
$149$	−12.2658	−	8.36271i	−1.00486	−	0.685100i	−0.0552269	−	0.998474i	$-0.517588\pi$
$149$	−12.2658	−	8.36271i	−1.00486	−	0.685100i	−0.949630	+	0.313374i	$0.898541\pi$
$150$	0.220386	+	0.204488i	0.0179945	+	0.0166964i
$151$	−1.63733	−	4.17184i	−0.133244	−	0.339499i	0.848644	−	0.528965i	$-0.177420\pi$
$151$	−1.63733	−	4.17184i	−0.133244	−	0.339499i	−0.981887	+	0.189466i	$0.939324\pi$
$152$	15.3218	−	4.72614i	1.24276	−	0.383341i
$153$	−0.120155	−	0.526433i	−0.00971395	−	0.0425596i
$154$	−0.491801	−	2.14064i	−0.0396304	−	0.172497i
$155$	−4.51146	+	19.7660i	−0.362369	+	1.58764i
$156$	0.688267	+	9.18429i	0.0551055	+	0.735331i
$157$	19.1097	+	5.89456i	1.52512	+	0.470437i	0.940191	−	0.340648i	$-0.110646\pi$
$157$	19.1097	+	5.89456i	1.52512	+	0.470437i	0.584928	+	0.811085i	$0.301123\pi$
$158$	−1.18608	+	15.8272i	−0.0943596	+	1.25914i
$159$	−4.81098	+	12.2582i	−0.381535	+	0.972136i
$160$	26.7158	−	12.8656i	2.11207	−	1.01712i
$161$	4.48893	−	4.17706i	0.353777	−	0.329198i
$162$	−23.9117	−	11.5153i	−1.87868	−	0.904726i
$163$	−12.3571	+	11.4657i	−0.967882	+	0.898063i	−0.994828	−	0.101574i	$-0.967612\pi$
$163$	−12.3571	+	11.4657i	−0.967882	+	0.898063i	0.0269461	+	0.999637i	$0.491422\pi$
$164$	4.00934	−	0.604311i	0.313077	−	0.0471887i
$165$	−0.650677	+	1.12701i	−0.0506551	+	0.0877372i
$166$	−10.1506	−	17.5813i	−0.787836	−	1.36457i
$167$	3.70272	+	4.64307i	0.286525	+	0.359291i	0.904175	−	0.427162i	$-0.140487\pi$
$167$	3.70272	+	4.64307i	0.286525	+	0.359291i	−0.617650	+	0.786453i	$0.711915\pi$
$168$	2.83399	−	38.5551i	0.218647	−	2.97459i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	8.00516	+	1.20658i	0.613968	+	0.0925408i
$171$	−0.663315	+	0.452240i	−0.0507249	+	0.0345837i
$172$	−29.5994	+	20.1805i	−2.25693	+	1.53875i
$173$	−12.8922	−	1.94319i	−0.980176	−	0.147738i	−0.360639	−	0.932705i	$-0.617442\pi$
$173$	−12.8922	−	1.94319i	−0.980176	−	0.147738i	−0.619537	+	0.784967i	$0.712680\pi$
$174$	−25.9013	+	32.4792i	−1.96357	+	2.46224i
$175$	−0.0119603	+	0.162714i	−0.000904113	+	0.0123000i
$176$	2.14787	+	2.69334i	0.161902	+	0.203018i
$177$	−8.35988	−	14.4797i	−0.628367	−	1.08836i
$178$	21.8790	−	37.8955i	1.63990	−	2.84039i
$179$	11.0100	−	1.65950i	0.822929	−	0.124037i	0.275938	−	0.961175i	$-0.411011\pi$
$179$	11.0100	−	1.65950i	0.822929	−	0.124037i	0.546991	+	0.837139i	$0.315773\pi$
$180$	−3.27135	+	3.03537i	−0.243832	+	0.226243i
$181$	−3.94612	−	1.90035i	−0.293313	−	0.141252i	0.281440	−	0.959579i	$-0.409188\pi$
$181$	−3.94612	−	1.90035i	−0.293313	−	0.141252i	−0.574754	+	0.818327i	$0.694902\pi$
$182$	−5.12350	+	4.76754i	−0.379779	+	0.353393i
$183$	−17.6802	+	8.51432i	−1.30696	+	0.629397i
$184$	−6.71263	+	17.1035i	−0.494861	+	1.26089i
$185$	−0.000290499		0.00387644i	−2.13579e−5		0.000285002i
$186$	−41.9823	−	12.9498i	−3.07829	−	0.949528i
$187$	0.0319038	+	0.425727i	0.00233304	+	0.0311322i
$188$	−3.90701	+	17.1177i	−0.284948	+	1.24844i
$189$	−2.84220	−	12.3711i	−0.206739	−	0.899863i
$190$	−2.67832	−	11.7345i	−0.194306	−	0.851310i
$191$	2.06895	−	0.638188i	0.149704	−	0.0461777i	−0.218997	−	0.975725i	$-0.570279\pi$
$191$	2.06895	−	0.638188i	0.149704	−	0.0461777i	0.368702	+	0.929548i	$0.379802\pi$
$192$	8.69295	+	22.1493i	0.627360	+	1.59849i
$193$	3.56340	+	3.30635i	0.256499	+	0.237997i	0.797932	−	0.602748i	$-0.205927\pi$
$193$	3.56340	+	3.30635i	0.256499	+	0.237997i	−0.541433	+	0.840744i	$0.682118\pi$
$194$	3.61937	+	2.46765i	0.259856	+	0.177167i
$195$	4.14659			0.296943
$196$	28.8452	−	19.7871i	2.06037	−	1.41337i
$197$	14.5977			1.04004			0.520020	−	0.854154i	$-0.325924\pi$
$197$	14.5977			1.04004			0.520020	+	0.854154i	$0.325924\pi$
$198$	−0.272268	−	0.185629i	−0.0193492	−	0.0131921i
$199$	−7.94913	−	7.37571i	−0.563499	−	0.522850i	0.346177	−	0.938169i	$-0.387480\pi$
$199$	−7.94913	−	7.37571i	−0.563499	−	0.522850i	−0.909676	+	0.415319i	$0.863670\pi$
$200$	−0.178609	−	0.455089i	−0.0126296	−	0.0321797i
$201$	0.115653	−	0.0356743i	0.00815754	−	0.00251627i
$202$	−10.0686	−	44.1136i	−0.708428	−	3.10382i
$203$	−22.5444	+	0.0321682i	−1.58230	+	0.00225777i
$204$	−2.78789	+	12.2145i	−0.195191	+	0.855188i
$205$	−0.136419	−	1.82039i	−0.00952793	−	0.127141i
$206$	2.11318	+	0.651830i	0.147232	+	0.0454151i
$207$	0.0687477	−	0.917375i	0.00477830	−	0.0637619i
$208$	4.01026	−	10.2180i	0.278061	−	0.708488i
$209$	0.571874	−	0.275400i	0.0395574	−	0.0190498i
$210$	−28.7021	−	4.28427i	−1.98063	−	0.295643i
$211$	−15.2072	−	7.32338i	−1.04690	−	0.504162i	−0.170309	−	0.985391i	$-0.554476\pi$
$211$	−15.2072	−	7.32338i	−1.04690	−	0.504162i	−0.876595	+	0.481228i	$0.840191\pi$
$212$	26.1724	−	24.2844i	1.79752	−	1.66786i
$213$	28.8048	−	4.34162i	1.97367	−	0.297483i
$214$	−12.0849	+	20.9316i	−0.826105	+	1.43086i
$215$	8.06449	+	13.9681i	0.549993	+	0.952617i
$216$	23.7146	+	29.7372i	1.61358	+	2.02336i
$217$	−8.74224	−	22.1818i	−0.593462	−	1.50580i
$218$	17.6315	−	22.1092i	1.19416	−	1.49743i
$219$	−1.38547	−	0.208826i	−0.0936216	−	0.0141112i
$220$	2.91524	−	1.98758i	0.196545	−	0.134002i
$221$	1.12395	−	0.766298i	0.0756053	−	0.0515468i
$222$	−0.00832967	−	0.00125550i	−0.000559051	−	8.42634e-5i
$223$	−7.23201	+	9.06865i	−0.484291	+	0.607282i	−0.962606	−	0.270907i	$-0.912676\pi$
$223$	−7.23201	+	9.06865i	−0.484291	+	0.607282i	0.478314	+	0.878189i	$0.341248\pi$
$224$	−17.3922	+	30.2237i	−1.16207	+	2.01941i
$225$	0.0152617	+	0.0191376i	0.00101745	+	0.00127584i
$226$	27.6793	+	47.9419i	1.84120	+	3.18905i
$227$	−7.85534	+	13.6059i	−0.521377	+	0.903052i	0.478313	+	0.878189i	$0.341248\pi$
$227$	−7.85534	+	13.6059i	−0.521377	+	0.903052i	−0.999691	+	0.0248631i	$0.992085\pi$
$228$	18.4192	−	2.77624i	1.21984	−	0.183861i
$229$	−16.1810	+	15.0138i	−1.06927	+	0.992139i	−0.999985	−	0.00545769i	$-0.998263\pi$
$229$	−16.1810	+	15.0138i	−1.06927	+	0.992139i	−0.0692866	+	0.997597i	$0.522072\pi$
$230$	12.4265	+	5.98431i	0.819382	+	0.394594i
$231$	−0.116542	−	1.52593i	−0.00766793	−	0.100399i
$232$	60.8637	−	29.3104i	3.99590	−	1.92432i
$233$	6.98698	−	17.8025i	0.457732	−	1.16628i	−0.496718	−	0.867912i	$-0.665462\pi$
$233$	6.98698	−	17.8025i	0.457732	−	1.16628i	0.954450	−	0.298371i	$-0.0964432\pi$
$234$	−0.0784661	+	1.04706i	−0.00512949	+	0.0684483i
$235$	7.55382	+	2.33005i	0.492757	+	0.151995i
$236$	3.38765	+	45.2051i	0.220517	+	2.94260i
$237$	−2.46079	+	10.7814i	−0.159846	+	0.700330i
$238$	−8.57159	+	4.14294i	−0.555614	+	0.268547i
$239$	−5.98866	−	26.2380i	−0.387374	−	1.69720i	−0.673650	−	0.739050i	$-0.735275\pi$
$239$	−5.98866	−	26.2380i	−0.387374	−	1.69720i	0.286276	−	0.958147i	$-0.407583\pi$
$240$	43.4939	−	13.4161i	2.80752	−	0.866005i
$241$	1.89979	+	4.84058i	0.122376	+	0.311809i	0.978913	−	0.204276i	$-0.0654840\pi$
$241$	1.89979	+	4.84058i	0.122376	+	0.311809i	−0.856537	+	0.516085i	$0.827389\pi$
$242$	−21.1388	−	19.6139i	−1.35885	−	1.26083i
$243$	−3.38690	−	2.30915i	−0.217270	−	0.148132i
$244$	53.2047			3.40608
$245$	−7.91324	−	13.6162i	−0.505558	−	0.869910i
$246$	3.95582			0.252214
$247$	−1.67106	−	1.13931i	−0.106327	−	0.0724925i
$248$	52.3713	+	48.5935i	3.32558	+	3.08569i
$249$	−5.16778	−	13.1673i	−0.327495	−	0.834443i
$250$	28.0834	−	8.66258i	1.77615	−	0.547870i
$251$	−2.37413	−	10.4018i	−0.149854	−	0.656553i	−0.992924	−	0.118750i	$-0.962111\pi$
$251$	−2.37413	−	10.4018i	−0.149854	−	0.656553i	0.843070	−	0.537803i	$-0.180746\pi$
$252$	1.16049	−	5.11809i	0.0731039	−	0.322409i
$253$	−0.161849	+	0.709107i	−0.0101754	+	0.0445812i
$254$	−2.78695	−	37.1893i	−0.174869	−	2.33347i
$255$	5.39011	+	1.66263i	0.337542	+	0.104118i
$256$	−0.389693	+	5.20009i	−0.0243558	+	0.325005i
$257$	−1.59771	+	4.07090i	−0.0996624	+	0.253936i	−0.972005	−	0.234959i	$-0.924504\pi$
$257$	−1.59771	+	4.07090i	−0.0996624	+	0.253936i	0.872343	+	0.488895i	$0.162600\pi$
$258$	−31.4900	+	15.1648i	−1.96048	+	0.944118i
$259$	−0.00229136	−	0.00395571i	−0.000142378	−	0.000245796i
$260$	−10.1292	−	4.87795i	−0.628185	−	0.302518i
$261$	−2.47943	+	2.30058i	−0.153473	+	0.142402i
$262$	−34.9126	+	5.26223i	−2.15691	+	0.325102i
$263$	−1.81797	+	3.14881i	−0.112101	+	0.194164i	−0.916617	−	0.399766i	$-0.869091\pi$
$263$	−1.81797	+	3.14881i	−0.112101	+	0.194164i	0.804516	+	0.593930i	$0.202425\pi$
$264$	2.29286	+	3.97135i	0.141116	+	0.244420i
$265$	−10.0223	−	12.5676i	−0.615664	−	0.772019i
$266$	10.3897	+	9.61268i	0.637033	+	0.589391i
$267$	19.0095	−	23.8372i	1.16337	−	1.45881i
$268$	−0.324481	−	0.0489076i	−0.0198208	−	0.00298751i
$269$	−23.4843	+	16.0113i	−1.43186	+	0.976226i	−0.434727	+	0.900562i	$0.643155\pi$
$269$	−23.4843	+	16.0113i	−1.43186	+	0.976226i	−0.997133	+	0.0756636i	$0.975892\pi$
$270$	23.5906	−	16.0838i	1.43568	−	0.978829i
$271$	−20.9748	−	3.16145i	−1.27413	−	0.192044i	−0.523076	−	0.852286i	$-0.675216\pi$
$271$	−20.9748	−	3.16145i	−1.27413	−	0.192044i	−0.751053	+	0.660242i	$0.770454\pi$
$272$	9.30991	−	11.6743i	0.564496	−	0.707856i
$273$	−4.02509	+	2.75268i	−0.243610	+	0.166600i
$274$	−20.2489	−	25.3913i	−1.22328	−	1.53395i
$275$	−0.00967656	−	0.0167603i	−0.000583519	−	0.00101068i
$276$	−10.6725	+	18.4853i	−0.642410	+	1.11269i
$277$	−1.13528	+	0.171117i	−0.0682126	+	0.0102814i	−0.183060	−	0.983102i	$-0.558600\pi$
$277$	−1.13528	+	0.171117i	−0.0682126	+	0.0102814i	0.114847	+	0.993383i	$0.463362\pi$
$278$	16.4896	−	15.3001i	0.988981	−	0.917640i
$279$	−3.22283	−	1.55203i	−0.192946	−	0.0929178i
$280$	39.0285	+	26.5277i	2.33240	+	1.58533i
$281$	22.2188	−	10.7000i	1.32546	−	0.638310i	0.368802	−	0.929508i	$-0.379768\pi$
$281$	22.2188	−	10.7000i	1.32546	−	0.638310i	0.956663	+	0.291198i	$0.0940537\pi$
$282$	−6.25832	+	15.9459i	−0.372678	+	0.949567i
$283$	−1.69773	+	22.6547i	−0.100920	+	1.34668i	0.685087	+	0.728461i	$0.259764\pi$
$283$	−1.69773	+	22.6547i	−0.100920	+	1.34668i	−0.786007	+	0.618218i	$0.787855\pi$
$284$	−75.4709	−	23.2797i	−4.47837	−	1.38140i
$285$	−0.626719	−	8.36298i	−0.0371236	−	0.495380i
$286$	0.184729	−	0.809349i	0.0109232	−	0.0478578i
$287$	1.34087	+	1.67649i	0.0791492	+	0.0989600i
$288$	1.16415	+	5.10049i	0.0685984	+	0.300549i
$289$	−14.4765	+	4.46540i	−0.851557	+	0.262670i
$290$	−18.5265	−	47.2048i	−1.08791	−	2.77196i
$291$	2.23742	+	2.07602i	0.131160	+	0.121699i
$292$	3.13874	+	2.13995i	0.183681	+	0.125231i
$293$	21.5041			1.25628			0.628141	−	0.778099i	$-0.283816\pi$
$293$	21.5041			1.25628			0.628141	+	0.778099i	$0.283816\pi$
$294$	30.7052	−	14.8949i	1.79076	−	0.868690i
$295$	20.4095			1.18829
$296$	0.0113179	+	0.00771644i	0.000657842	+	0.000448509i
$297$	1.10374	+	1.02412i	0.0640455	+	0.0594256i
$298$	14.3466	+	36.5545i	0.831076	+	2.11755i
$299$	2.21462	−	0.683119i	0.128075	−	0.0395058i
$300$	−0.126380	−	0.553708i	−0.00729656	−	0.0319683i
$301$	−17.1008	−	8.20528i	−0.985674	−	0.472944i
$302$	−2.63795	+	11.5576i	−0.151797	+	0.665066i
$303$	−2.35603	−	31.4391i	−0.135350	−	1.80613i
$304$	−21.2141	−	6.54367i	−1.21671	−	0.375305i
$305$	1.79009	−	23.8871i	0.102500	−	1.36777i
$306$	−0.521828	+	1.32960i	−0.0298309	+	0.0760080i
$307$	−19.6566	+	9.46611i	−1.12186	+	0.540260i	−0.900467	−	0.434925i	$-0.856775\pi$
$307$	−19.6566	+	9.46611i	−1.12186	+	0.540260i	−0.221394	+	0.975184i	$0.571061\pi$
$308$	−1.51038	+	3.86460i	−0.0860620	+	0.220206i
$309$	1.38825	+	0.668546i	0.0789748	+	0.0380323i
$310$	39.3133	−	36.4775i	2.23285	−	2.07178i
$311$	4.24243	−	0.639443i	0.240566	−	0.0362595i	−0.0276525	−	0.999618i	$-0.508803\pi$
$311$	4.24243	−	0.639443i	0.240566	−	0.0362595i	0.268218	+	0.963358i	$0.413565\pi$
$312$	7.30589	−	12.6542i	0.413614	−	0.716401i
$313$	−4.38058	−	7.58738i	−0.247605	−	0.428864i	0.715256	−	0.698863i	$-0.246310\pi$
$313$	−4.38058	−	7.58738i	−0.247605	−	0.428864i	−0.962861	+	0.269998i	$0.912977\pi$
$314$	−32.9821	−	41.3582i	−1.86129	−	2.33398i
$315$	−2.25880	−	0.693220i	−0.127269	−	0.0390585i
$316$	18.6942	−	23.4418i	1.05163	−	1.31870i
$317$	−23.3623	−	3.52131i	−1.31216	−	0.197776i	−0.544569	−	0.838716i	$-0.683307\pi$
$317$	−23.3623	−	3.52131i	−1.31216	−	0.197776i	−0.767591	+	0.640940i	$0.778545\pi$
$318$	28.7806	−	19.6223i	1.61393	−	1.10036i
$319$	2.20953	−	1.50643i	0.123710	−	0.0843439i
$320$	−28.7206	−	4.32893i	−1.60553	−	0.241995i
$321$	−10.4999	+	13.1665i	−0.586049	+	0.734882i
$322$	−16.0351	+	2.44030i	−0.893600	+	0.135993i
$323$	−1.71537	−	2.15101i	−0.0954459	−	0.119685i
$324$	25.0686	+	43.4200i	1.39270	+	2.41222i
$325$	−0.0308331	+	0.0534044i	−0.00171031	+	0.00296234i
$326$	44.0923	−	6.64584i	2.44204	−	0.368079i
$327$	14.4438	−	13.4019i	0.798742	−	0.741124i
$328$	−5.79565	−	2.79104i	−0.320011	−	0.154109i
$329$	−8.87928	+	2.75278i	−0.489530	+	0.151765i
$330$	3.10144	−	1.49358i	0.170729	−	0.0822187i
$331$	−0.769199	+	1.95989i	−0.0422790	+	0.107725i	−0.950454	−	0.310866i	$-0.899381\pi$
$331$	−0.769199	+	1.95989i	−0.0422790	+	0.107725i	0.908175	+	0.418592i	$0.137476\pi$
$332$	−2.86599	+	38.2439i	−0.157291	+	2.09891i
$333$	−0.000655382	0	0.000202159i	−3.59147e−5	0	1.10782e-5i
$334$	−1.17394	−	15.6652i	−0.0642352	−	0.857159i
$335$	−0.0328751	+	0.144035i	−0.00179616	+	0.00786948i
$336$	−33.3133	+	41.8961i	−1.81739	+	2.28562i
$337$	0.152516	+	0.668216i	0.00830807	+	0.0364000i	0.978912	−	0.204282i	$-0.0654860\pi$
$337$	0.152516	+	0.668216i	0.00830807	+	0.0364000i	−0.970604	+	0.240682i	$0.922629\pi$
$338$	−2.52768	+	0.779687i	−0.137488	+	0.0424094i
$339$	14.0919	+	35.9055i	0.765365	+	1.95012i
$340$	−11.2109	−	10.4022i	−0.607998	−	0.564140i
$341$	2.33674	+	1.59316i	0.126541	+	0.0862745i
$342$	2.12360			0.114831
$343$	16.7204	+	7.96414i	0.902818	+	0.430023i
$344$	56.8354			3.06436
$345$	7.94020	+	5.41354i	0.427486	+	0.291455i
$346$	25.2813	+	23.4576i	1.35913	+	1.26109i
$347$	−7.59523	−	19.3523i	−0.407733	−	1.03889i	−0.976333	−	0.216273i	$-0.930610\pi$
$347$	−7.59523	−	19.3523i	−0.407733	−	1.03889i	0.568600	−	0.822614i	$-0.307485\pi$
$348$	74.9920	−	23.1320i	4.01999	−	1.24000i
$349$	4.99581	+	21.8881i	0.267420	+	1.17164i	0.913003	+	0.407952i	$0.133757\pi$
$349$	4.99581	+	21.8881i	0.267420	+	1.17164i	−0.645583	+	0.763690i	$0.723386\pi$
$350$	0.268600	−	0.337801i	0.0143573	−	0.0180562i
$351$	1.06758	−	4.67736i	0.0569830	−	0.249659i
$352$	−0.309109	−	4.12477i	−0.0164756	−	0.219851i
$353$	14.1149	+	4.35388i	0.751263	+	0.231734i	0.646658	−	0.762780i	$-0.276166\pi$
$353$	14.1149	+	4.35388i	0.751263	+	0.231734i	0.104605	+	0.994514i	$0.466642\pi$
$354$	−3.30510	+	44.1035i	−0.175664	+	2.34407i
$355$	−12.9910	+	33.1006i	−0.689492	+	1.75680i
$356$	−74.4775	+	35.8665i	−3.94730	+	1.90092i
$357$	−6.33590	+	1.96427i	−0.335331	+	0.103960i
$358$	−26.5360	−	12.7791i	−1.40247	−	0.675395i
$359$	−13.5103	+	12.5357i	−0.713046	+	0.661610i	−0.950832	−	0.309708i	$-0.899769\pi$
$359$	−13.5103	+	12.5357i	−0.713046	+	0.661610i	0.237786	+	0.971318i	$0.423578\pi$
$360$	7.00092	−	1.05522i	0.368981	−	0.0556150i
$361$	7.45477	−	12.9120i	0.392356	−	0.679581i
$362$	5.79282	+	10.0335i	0.304464	+	0.527347i
$363$	−12.5274	−	15.7088i	−0.657516	−	0.824500i
$364$	13.0706	−	1.98915i	0.685084	−	0.104260i
$365$	1.06637	−	1.33719i	0.0558164	−	0.0699915i
$366$	51.3284	+	7.73651i	2.68298	+	0.404394i
$367$	−1.25608	+	0.856381i	−0.0655669	+	0.0447027i	−0.595660	−	0.803237i	$-0.703109\pi$
$367$	−1.25608	+	0.856381i	−0.0655669	+	0.0447027i	0.530093	+	0.847939i	$0.322157\pi$
$368$	21.0191	−	14.3306i	1.09570	−	0.747033i
$369$	0.318481	+	0.0480032i	0.0165794	+	0.00249895i
$370$	0.00641118	−	0.00803936i	0.000333301	−	0.000417947i
$371$	18.0715	+	5.54609i	0.938226	+	0.287939i
$372$	51.7476	+	64.8895i	2.68299	+	3.36436i
$373$	2.32817	+	4.03250i	0.120548	+	0.208795i	0.919984	−	0.391956i	$-0.128202\pi$
$373$	2.32817	+	4.03250i	0.120548	+	0.208795i	−0.799436	+	0.600751i	$0.794868\pi$
$374$	0.564646	−	0.977995i	0.0291971	−	0.0505709i
$375$	20.2485	−	3.05197i	1.04563	−	0.157603i
$376$	20.4197	−	18.9467i	1.05307	−	0.977104i
$377$	−7.67714	−	3.69711i	−0.395393	−	0.190411i
$378$	−12.2223	+	31.2730i	−0.628646	+	1.60851i
$379$	−29.1607	+	14.0431i	−1.49789	+	0.721344i	−0.990129	−	0.140157i	$-0.955239\pi$
$379$	−29.1607	+	14.0431i	−1.49789	+	0.721344i	−0.507756	+	0.861501i	$0.669525\pi$
$380$	−8.30709	+	21.1661i	−0.426145	+	1.08580i
$381$	1.94185	−	25.9122i	0.0994839	−	1.32752i
$382$	−5.47280	−	1.68814i	−0.280013	−	0.0863725i
$383$	0.974686	+	13.0063i	0.0498041	+	0.664590i	0.965112	+	0.261836i	$0.0843279\pi$
$383$	0.974686	+	13.0063i	0.0498041	+	0.664590i	−0.915308	+	0.402754i	$0.868053\pi$
$384$	3.19473	−	13.9970i	0.163030	−	0.714282i
$385$	1.68426	+	0.808136i	0.0858376	+	0.0411864i
$386$	−2.86128	−	12.5361i	−0.145635	−	0.638069i
$387$	−2.71926	+	0.838782i	−0.138228	+	0.0426377i
$388$	−3.02333	−	7.70331i	−0.153486	−	0.391076i
$389$	1.32268	+	1.22727i	0.0670625	+	0.0622249i	0.712992	−	0.701172i	$-0.247340\pi$
$389$	1.32268	+	1.22727i	0.0670625	+	0.0622249i	−0.645930	+	0.763397i	$0.723530\pi$
$390$	−9.06265	−	6.17881i	−0.458905	−	0.312876i
$391$	3.15266			0.159437
$392$	−55.4952	+	0.158371i	−2.80293	+	0.00799893i
$393$	−24.6006			−1.24094
$394$	−31.9042	−	21.7519i	−1.60731	−	1.09585i
$395$	−9.89559	−	9.18176i	−0.497901	−	0.461985i
$396$	0.227430	+	0.579483i	0.0114288	+	0.0291201i
$397$	−16.9712	+	5.23492i	−0.851761	+	0.262733i	−0.689743	−	0.724055i	$-0.742276\pi$
$397$	−16.9712	+	5.23492i	−0.851761	+	0.262733i	−0.162018	+	0.986788i	$0.551800\pi$
$398$	6.38285	+	27.9651i	0.319943	+	1.40176i
$399$	6.16006	+	7.70190i	0.308389	+	0.385577i
$400$	−0.150623	+	0.659922i	−0.00753115	+	0.0329961i
$401$	2.14458	+	28.6174i	0.107095	+	1.42908i	0.749138	+	0.662414i	$0.230468\pi$
$401$	2.14458	+	28.6174i	0.107095	+	1.42908i	−0.642043	+	0.766669i	$0.721913\pi$
$402$	−0.305926	−	0.0943656i	−0.0152582	−	0.00470653i
$403$	0.673434	−	8.98636i	0.0335462	−	0.447642i
$404$	−31.2289	+	79.5701i	−1.55370	+	3.95876i
$405$	20.3376	−	9.79405i	1.01058	−	0.486670i
$406$	49.3202	+	33.5230i	2.44772	+	1.66372i
$407$	0.000488559	0	0.000235278i	2.42170e−5	0	1.16623e-5i
$408$	14.5707	−	13.5196i	0.721357	−	0.669322i
$409$	−7.57322	+	1.14148i	−0.374471	+	0.0564425i	−0.333582	−	0.942721i	$-0.608257\pi$
$409$	−7.57322	+	1.14148i	−0.374471	+	0.0564425i	−0.0408897	+	0.999164i	$0.513019\pi$
$410$	−2.41440	+	4.18186i	−0.119239	+	0.206527i
$411$	−11.3143	−	19.5969i	−0.558093	−	0.966646i
$412$	−2.60472	−	3.26621i	−0.128325	−	0.160915i
$413$	−19.8115	+	13.5487i	−0.974860	+	0.666688i
$414$	−1.51723	+	1.90254i	−0.0745677	+	0.0935050i
$415$	17.0738	+	2.57346i	0.838120	+	0.126326i
$416$	−10.8897	+	7.42449i	−0.533913	+	0.364016i
$417$	12.9499	−	8.82909i	0.634159	−	0.432363i
$418$	−1.66024	−	0.250241i	−0.0812051	−	0.0122397i
$419$	18.9029	−	23.7035i	0.923469	−	1.15799i	−0.0636441	−	0.997973i	$-0.520272\pi$
$419$	18.9029	−	23.7035i	0.923469	−	1.15799i	0.987114	−	0.160021i	$-0.0511563\pi$
$420$	40.2408	+	37.2313i	1.96355	+	1.81670i
$421$	−20.7560	−	26.0272i	−1.01159	−	1.26849i	−0.962952	−	0.269672i	$-0.913085\pi$
$421$	−20.7560	−	26.0272i	−1.01159	−	1.26849i	−0.0486333	−	0.998817i	$-0.515487\pi$
$422$	22.3237	+	38.6659i	1.08670	+	1.88222i
$423$	−0.697355	+	1.20785i	−0.0339066	+	0.0587279i
$424$	−56.0108	+	8.44227i	−2.72012	+	0.409993i
$425$	−0.0614928	+	0.0570570i	−0.00298284	+	0.00276767i
$426$	−69.4242	−	33.4329i	−3.36362	−	1.61983i
$427$	14.1196	+	24.3755i	0.683297	+	1.17961i
$428$	41.1377	−	19.8109i	1.98847	−	0.957595i
$429$	0.211323	−	0.538443i	0.0102028	−	0.0259962i
$430$	3.18831	−	42.5451i	0.153754	−	2.05171i
$431$	29.9734	+	9.24557i	1.44377	+	0.445343i	0.915011	−	0.403430i	$-0.132182\pi$
$431$	29.9734	+	9.24557i	1.44377	+	0.445343i	0.528757	+	0.848773i	$0.322658\pi$
$432$	−3.93547	−	52.5152i	−0.189346	−	2.52664i
$433$	−5.94757	+	26.0580i	−0.285822	+	1.25227i	0.604377	+	0.796698i	$0.293422\pi$
$433$	−5.94757	+	26.0580i	−0.285822	+	1.25227i	−0.890200	+	0.455571i	$0.849435\pi$
$434$	−13.9462	+	61.5065i	−0.669437	+	2.95241i
$435$	−7.86233	−	34.4471i	−0.376970	−	1.65161i
$436$	−51.0485	+	15.7464i	−2.44478	+	0.754114i
$437$	−1.71246	−	4.36327i	−0.0819180	−	0.208724i
$438$	2.71687	+	2.52089i	0.129817	+	0.120453i
$439$	3.82824	+	2.61005i	0.182712	+	0.124571i	0.651222	−	0.758887i	$-0.274257\pi$
$439$	3.82824	+	2.61005i	0.182712	+	0.124571i	−0.468510	+	0.883458i	$0.655209\pi$
$440$	−5.59771			−0.266860
$441$	2.65281	−	0.826580i	0.126324	−	0.0393610i
$442$	−3.59833			−0.171155
$443$	−14.4491	−	9.85125i	−0.686499	−	0.468047i	0.169159	−	0.985589i	$-0.445895\pi$
$443$	−14.4491	−	9.85125i	−0.686499	−	0.468047i	−0.855658	+	0.517542i	$0.826847\pi$
$444$	0.0116654	+	0.0108239i	0.000553615	+	0.000513679i
$445$	13.5970	+	34.6446i	0.644560	+	1.64231i
$446$	29.3192	−	9.04378i	1.38830	−	0.428235i
$447$	6.08845	+	26.6752i	0.287974	+	1.26170i
$448$	30.7528	−	14.8639i	1.45293	−	0.702251i
$449$	5.39295	−	23.6281i	0.254509	−	1.11508i	−0.672517	−	0.740081i	$-0.734787\pi$
$449$	5.39295	−	23.6281i	0.254509	−	1.11508i	0.927027	−	0.374996i	$-0.122356\pi$
$450$	−0.00483870	−	0.0645680i	−0.000228099	−	0.00304376i
$451$	−0.243333	−	0.0750584i	−0.0114581	−	0.00353436i
$452$	7.81518	−	104.286i	0.367595	−	4.90521i
$453$	−3.01772	+	7.68903i	−0.141785	+	0.361262i
$454$	37.4424	−	18.0313i	1.75726	−	0.846251i
$455$	−0.453296	−	5.93517i	−0.0212509	−	0.278245i
$456$	−26.6256	−	12.8222i	−1.24686	−	0.600455i
$457$	22.0989	−	20.5048i	1.03374	−	0.959174i	0.0345535	−	0.999403i	$-0.488999\pi$
$457$	22.0989	−	20.5048i	1.03374	−	0.959174i	0.999191	+	0.0402286i	$0.0128086\pi$
$458$	57.7367	−	8.70241i	2.69786	−	0.406637i
$459$	3.26318	−	5.65199i	0.152312	−	0.263812i
$460$	−13.0277	−	22.5647i	−0.607422	−	1.05209i
$461$	−11.9031	−	14.9261i	−0.554384	−	0.695176i	0.423124	−	0.906072i	$-0.360933\pi$
$461$	−11.9031	−	14.9261i	−0.554384	−	0.695176i	−0.977509	+	0.210896i	$0.932362\pi$
$462$	−2.01907	+	3.50868i	−0.0939356	+	0.163239i
$463$	−13.9020	+	17.4326i	−0.646081	+	0.810160i	−0.991749	−	0.128197i	$-0.959081\pi$
$463$	−13.9020	+	17.4326i	−0.646081	+	0.810160i	0.345668	+	0.938357i	$0.387653\pi$
$464$	−92.4880	−	13.9403i	−4.29365	−	0.647163i
$465$	30.8742	−	21.0497i	1.43176	−	0.976156i
$466$	−41.7980	+	28.4974i	−1.93625	+	1.32012i
$467$	17.6826	+	2.66523i	0.818254	+	0.123332i	0.544814	−	0.838557i	$-0.316600\pi$
$467$	17.6826	+	2.66523i	0.818254	+	0.123332i	0.273440	+	0.961889i	$0.411838\pi$
$468$	1.23673	−	1.55081i	0.0571678	−	0.0716862i
$469$	−0.0637049	−	0.161639i	−0.00294162	−	0.00746378i
$470$	−13.0374	−	16.3484i	−0.601371	−	0.754095i
$471$	−18.4291	−	31.9201i	−0.849168	−	1.47080i
$472$	35.9596	−	62.2839i	1.65518	−	2.86685i
$473$	2.22478	−	0.335331i	0.102295	−	0.0154185i
$474$	21.4436	−	19.8968i	0.984937	−	0.913888i
$475$	0.112368	+	0.0541136i	0.00515580	+	0.00248290i
$476$	17.7879	+	2.65514i	0.815306	+	0.121698i
$477$	2.55522	−	1.23053i	0.116995	−	0.0563421i
$478$	−26.0085	+	66.2687i	−1.18960	+	3.03106i
$479$	1.60468	−	21.4130i	0.0733199	−	0.978386i	−0.832308	−	0.554313i	$-0.812981\pi$
$479$	1.60468	−	21.4130i	0.0733199	−	0.978386i	0.905628	−	0.424073i	$-0.139400\pi$
$480$	−52.2235	−	16.1088i	−2.38367	−	0.735264i
$481$	−0.000129121	−	0.00172301i	−5.88743e−6	−	7.85623e-5i
$482$	3.06081	−	13.4103i	0.139416	−	0.610822i
$483$	−11.3013	+	0.0161256i	−0.514226	+	0.000733741i
$484$	12.1220	+	53.1100i	0.551001	+	2.41409i
$485$	−3.56024	+	1.09819i	−0.161662	+	0.0498662i
$486$	3.96145	+	10.0936i	0.179695	+	0.457855i
$487$	−19.8828	−	18.4486i	−0.900977	−	0.835985i	0.0860905	−	0.996287i	$-0.472563\pi$
$487$	−19.8828	−	18.4486i	−0.900977	−	0.835985i	−0.987068	+	0.160302i	$0.948753\pi$
$488$	−69.7424	−	47.5496i	−3.15709	−	2.15247i
$489$	31.0689			1.40498
$490$	−2.99458	+	41.5507i	−0.135281	+	1.87707i
$491$	−34.0051			−1.53463			−0.767314	−	0.641272i	$-0.778407\pi$
$491$	−34.0051			−1.53463			−0.767314	+	0.641272i	$0.778407\pi$
$492$	−6.17448	−	4.20969i	−0.278367	−	0.189787i
$493$	−8.49703	−	7.88409i	−0.382687	−	0.355081i
$494$	1.95454	+	4.98008i	0.0879387	+	0.224064i
$495$	0.267820	−	0.0826115i	0.0120376	−	0.00371311i
$496$	−22.0112	−	96.4375i	−0.988333	−	4.33017i
$497$	−9.36320	−	40.7547i	−0.419997	−	1.82810i
$498$	−8.32598	+	36.4785i	−0.373096	+	1.63464i
$499$	−2.44088	−	32.5713i	−0.109269	−	1.45809i	−0.735008	−	0.678058i	$-0.762822\pi$
$499$	−2.44088	−	32.5713i	−0.109269	−	1.45809i	0.625739	−	0.780032i	$-0.284797\pi$
$500$	−53.0528	−	16.3646i	−2.37259	−	0.731848i
$501$	0.817959	−	10.9149i	0.0365437	−	0.487642i
$502$	−10.3108	+	26.2714i	−0.460192	+	1.17255i
$503$	−15.6709	+	7.54672i	−0.698732	+	0.336492i	−0.749302	−	0.662229i	$-0.769611\pi$
$503$	−15.6709	+	7.54672i	−0.698732	+	0.336492i	0.0505693	+	0.998721i	$0.483896\pi$
$504$	−6.09529	+	5.67181i	−0.271506	+	0.252643i
$505$	34.6735	+	16.6979i	1.54295	+	0.743046i
$506$	1.41037	−	1.30863i	0.0626986	−	0.0581758i
$507$	−1.82249	+	0.274697i	−0.0809398	+	0.0121997i
$508$	−35.2260	+	61.0132i	−1.56290	+	2.70702i
$509$	−11.2426	−	19.4728i	−0.498320	−	0.863115i	0.501678	−	0.865054i	$-0.332716\pi$
$509$	−11.2426	−	19.4728i	−0.498320	−	0.863115i	−0.999998	+	0.00193904i	$0.999383\pi$
$510$	−9.30297	−	11.6656i	−0.411943	−	0.516560i
$511$	−0.147444	+	2.00591i	−0.00652254	+	0.0887361i
$512$	18.3139	−	22.9649i	0.809367	−	1.01491i
$513$	−9.59480	−	1.44618i	−0.423621	−	0.0638506i
$514$	9.55793	−	6.51649i	0.421582	−	0.287430i
$515$	−1.55406	+	1.05954i	−0.0684799	+	0.0466888i
$516$	65.2895	+	9.84081i	2.87421	+	0.433218i
$517$	0.687528	−	0.862132i	0.0302374	−	0.0379165i
$518$	−0.000886455		0.0120598i	−3.89486e−5		0.000529878i
$519$	14.9823	+	18.7872i	0.657650	+	0.824668i
$520$	8.91817	+	15.4467i	0.391088	+	0.677384i
$521$	15.0875	−	26.1323i	0.660995	−	1.14488i	−0.319360	−	0.947634i	$-0.603468\pi$
$521$	15.0875	−	26.1323i	0.660995	−	1.14488i	0.980355	−	0.197243i	$-0.0631989\pi$
$522$	8.84704	−	1.33348i	0.387225	−	0.0583647i
$523$	−2.99793	+	2.78167i	−0.131090	+	0.121634i	−0.742993	−	0.669299i	$-0.766595\pi$
$523$	−2.99793	+	2.78167i	−0.131090	+	0.121634i	0.611903	+	0.790933i	$0.290404\pi$
$524$	60.0937	+	28.9396i	2.62520	+	1.26423i
$525$	0.220140	−	0.204845i	0.00960769	−	0.00894018i
$526$	8.66532	−	4.17300i	0.377826	−	0.181951i
$527$	4.47859	−	11.4113i	0.195090	−	0.497082i
$528$	0.474480	−	6.33149i	0.0206491	−	0.275543i
$529$	−16.8456	−	5.19618i	−0.732418	−	0.225921i
$530$	3.17755	+	42.4014i	0.138024	+	1.84180i
$531$	−0.801281	+	3.51064i	−0.0347726	+	0.152349i
$532$	−5.98728	−	26.0605i	−0.259582	−	1.12987i
$533$	0.180553	+	0.791054i	0.00782061	+	0.0342643i
$534$	−77.0664	+	23.7718i	−3.33499	+	1.02871i
$535$	−7.51032	−	19.1360i	−0.324699	−	0.827320i
$536$	0.381630	+	0.354101i	0.0164839	+	0.0152948i
$537$	−16.9557	−	11.5602i	−0.731694	−	0.498860i
$538$	75.1848			3.24145
$539$	−2.17138	+	0.333623i	−0.0935280	+	0.0143702i
$540$	−53.9376			−2.32111
$541$	−12.0663	−	8.22669i	−0.518773	−	0.353693i	0.275455	−	0.961314i	$-0.411172\pi$
$541$	−12.0663	−	8.22669i	−0.518773	−	0.353693i	−0.794227	+	0.607621i	$0.792124\pi$
$542$	41.1310	+	38.1640i	1.76673	+	1.63929i
$543$	2.94920	+	7.51443i	0.126562	+	0.322475i
$544$	−17.1324	+	5.28464i	−0.734545	+	0.226577i
$545$	5.35204	+	23.4488i	0.229256	+	1.00444i
$546$	12.8989	−	0.0184052i	0.552020	−	0.000787669i
$547$	4.87238	−	21.3473i	0.208328	−	0.912744i	−0.757352	−	0.653007i	$-0.773507\pi$
$547$	4.87238	−	21.3473i	0.208328	−	0.912744i	0.965680	−	0.259736i	$-0.0836357\pi$
$548$	4.58486	+	61.1807i	0.195856	+	2.61351i
$549$	4.03854	+	1.24572i	0.172361	+	0.0531662i
$550$	−0.00382565	+	0.0510498i	−0.000163126	+	0.00217677i
$551$	−6.29614	+	16.0423i	−0.268225	+	0.683425i
$552$	30.5104	−	14.6930i	1.29861	−	0.625377i
$553$	15.7009	+	2.34362i	0.667669	+	0.0996609i
$554$	2.73622	+	1.31769i	0.116251	+	0.0559835i
$555$	0.00525205	−	0.00487319i	0.000222937	−	0.000206855i
$556$	−42.0200	+	6.33350i	−1.78205	+	0.268600i
$557$	−2.09176	+	3.62304i	−0.0886308	+	0.153513i	−0.906933	−	0.421276i	$-0.861582\pi$
$557$	−2.09176	+	3.62304i	−0.0886308	+	0.153513i	0.818302	+	0.574789i	$0.194916\pi$
$558$	4.73104	+	8.19440i	0.200281	+	0.346896i
$559$	−4.46981	−	5.60497i	−0.189053	−	0.237065i
$560$	−23.9576	−	60.7878i	−1.01239	−	2.56875i
$561$	0.490592	−	0.615183i	0.0207128	−	0.0259731i
$562$	−64.5049	−	9.72254i	−2.72097	−	0.410121i
$563$	0.886332	−	0.604291i	0.0373544	−	0.0254678i	−0.544499	−	0.838762i	$-0.683280\pi$
$563$	0.886332	−	0.604291i	0.0373544	−	0.0254678i	0.581853	+	0.813294i	$0.302328\pi$
$564$	26.7377	−	18.2294i	1.12586	−	0.767597i
$565$	−46.5580	−	7.01749i	−1.95871	−	0.295228i
$566$	37.4681	−	46.9835i	1.57490	−	1.97486i
$567$	−13.2399	+	23.0080i	−0.556025	+	0.966246i
$568$	78.1244	+	97.9649i	3.27803	+	4.11052i
$569$	−2.87917	−	4.98686i	−0.120701	−	0.209060i	0.799343	−	0.600875i	$-0.205181\pi$
$569$	−2.87917	−	4.98686i	−0.120701	−	0.209060i	−0.920044	+	0.391814i	$0.871848\pi$
$570$	−11.0919	+	19.2117i	−0.464589	+	0.804691i
$571$	35.7788	−	5.39278i	1.49730	−	0.225681i	0.651279	−	0.758838i	$-0.274233\pi$
$571$	35.7788	−	5.39278i	1.49730	−	0.225681i	0.846016	+	0.533157i	$0.178995\pi$
$572$	−1.14963	+	1.06670i	−0.0480683	+	0.0446008i
$573$	−3.59535	−	1.73143i	−0.150198	−	0.0723315i
$574$	−0.432442	−	5.66211i	−0.0180498	−	0.236332i
$575$	−0.128763	+	0.0620091i	−0.00536979	+	0.00258596i
$576$	1.87219	−	4.77027i	0.0780081	−	0.198761i
$577$	−1.16857	+	15.5935i	−0.0486482	+	0.649165i	0.918576	+	0.395243i	$0.129340\pi$
$577$	−1.16857	+	15.5935i	−0.0486482	+	0.649165i	−0.967225	+	0.253922i	$0.918279\pi$
$578$	38.2932	+	11.8119i	1.59279	+	0.491309i
$579$	−0.669530	−	8.93425i	−0.0278247	−	0.371295i
$580$	−21.3169	+	93.3955i	−0.885137	+	3.87804i
$581$	−18.2819	+	8.83625i	−0.758461	+	0.366590i
$582$	−1.79657	−	7.87127i	−0.0744700	−	0.326274i
$583$	−2.14269	+	0.660932i	−0.0887411	+	0.0273730i
$584$	−2.20186	−	5.61024i	−0.0911135	−	0.232153i
$585$	−0.654650	−	0.607426i	−0.0270664	−	0.0251140i
$586$	−46.9986	−	32.0431i	−1.94150	−	1.32369i
$587$	39.3143			1.62267			0.811337	−	0.584579i	$-0.198740\pi$
$587$	39.3143			1.62267			0.811337	+	0.584579i	$0.198740\pi$
$588$	−63.7774	−	9.42683i	−2.63013	−	0.388756i
$589$	−18.2258			−0.750980
$590$	−44.6064	−	30.4121i	−1.83642	−	1.25205i
$591$	−19.7225	−	18.2998i	−0.811275	−	0.752754i
$592$	−0.00692907	−	0.0176550i	−0.000284783	−	0.000725615i
$593$	−5.86526	+	1.80919i	−0.240857	+	0.0742946i	−0.412834	−	0.910806i	$-0.635461\pi$
$593$	−5.86526	+	1.80919i	−0.240857	+	0.0742946i	0.171976	+	0.985101i	$0.444985\pi$
$594$	−0.886262	−	3.88297i	−0.0363638	−	0.159320i
$595$	1.79055	−	7.89682i	0.0734052	−	0.323738i
$596$	16.5074	−	72.3239i	0.676171	−	2.96250i
$597$	1.49357	+	19.9302i	0.0611276	+	0.815691i
$598$	−5.85811	−	1.80699i	−0.239556	−	0.0738932i
$599$	−0.0842559	+	1.12432i	−0.00344260	+	0.0459383i	−0.998661	−	0.0517411i	$-0.983523\pi$
$599$	−0.0842559	+	1.12432i	−0.00344260	+	0.0459383i	0.995218	+	0.0976794i	$0.0311420\pi$
$600$	−0.329191	+	0.838765i	−0.0134392	+	0.0342424i
$601$	24.7917	−	11.9391i	1.01128	−	0.487004i	0.146525	−	0.989207i	$-0.453191\pi$
$601$	24.7917	−	11.9391i	1.01128	−	0.487004i	0.864750	+	0.502203i	$0.167477\pi$
$602$	25.1483	+	43.4150i	1.02497	+	1.76946i
$603$	−0.0234848	−	0.0113097i	−0.000956375	−	0.000460566i
$604$	16.4168	−	15.2326i	0.667991	−	0.619805i
$605$	24.2524	−	3.65547i	0.986001	−	0.148616i
$606$	−41.6979	+	72.2229i	−1.69386	+	2.93386i
$607$	13.2844	+	23.0093i	0.539199	+	0.933920i	0.998947	+	0.0458708i	$0.0146063\pi$
$607$	13.2844	+	23.0093i	0.539199	+	0.933920i	−0.459748	+	0.888049i	$0.652060\pi$
$608$	16.6199	+	20.8406i	0.674024	+	0.845199i
$609$	30.4994	+	28.2184i	1.23590	+	1.14347i
$610$	−39.5064	+	49.5395i	−1.59957	+	2.00579i
$611$	−3.47439	−	0.523680i	−0.140559	−	0.0211858i
$612$	2.22943	−	1.52000i	0.0901193	−	0.0614423i
$613$	−9.32015	+	6.35437i	−0.376437	+	0.256651i	−0.736728	−	0.676190i	$-0.763630\pi$
$613$	−9.32015	+	6.35437i	−0.376437	+	0.256651i	0.360290	+	0.932840i	$0.382678\pi$
$614$	57.0662	+	8.60135i	2.30301	+	0.347122i
$615$	−2.09775	+	2.63049i	−0.0845894	+	0.106072i
$616$	5.43369	−	3.71599i	0.218930	−	0.149722i
$617$	28.4283	+	35.6480i	1.14448	+	1.43513i	0.882657	+	0.470017i	$0.155752\pi$
$617$	28.4283	+	35.6480i	1.14448	+	1.43513i	0.261823	+	0.965116i	$0.415676\pi$
$618$	−2.03792	−	3.52978i	−0.0819771	−	0.141989i
$619$	6.86380	−	11.8884i	0.275879	−	0.477837i	−0.694477	−	0.719515i	$-0.744364\pi$
$619$	6.86380	−	11.8884i	0.275879	−	0.477837i	0.970357	+	0.241678i	$0.0776977\pi$
$620$	−100.181	+	15.0999i	−4.02337	+	0.606426i
$621$	8.15075	−	7.56279i	0.327078	−	0.303484i
$622$	−10.2249	−	4.92407i	−0.409983	−	0.197437i
$623$	−36.1972	−	24.6032i	−1.45021	−	0.985708i
$624$	−18.2275	+	8.77791i	−0.729685	+	0.351398i
$625$	−9.24478	+	23.5553i	−0.369791	+	0.942213i
$626$	−1.73187	+	23.1102i	−0.0692195	+	0.923670i
$627$	−1.11789	−	0.344823i	−0.0446442	−	0.0137709i
$628$	7.46797	+	99.6532i	0.298005	+	3.97660i
$629$	0.000523018	−	0.00229149i	2.08541e−5	−	9.13677e-5i
$630$	3.90380	+	4.88091i	0.155531	+	0.194460i
$631$	4.65904	+	20.4126i	0.185473	+	0.812612i	0.978965	+	0.204031i	$0.0654042\pi$
$631$	4.65904	+	20.4126i	0.185473	+	0.812612i	−0.793491	+	0.608582i	$0.791739\pi$
$632$	−45.4551	+	14.0210i	−1.80811	+	0.557727i
$633$	11.3653	+	28.9583i	0.451730	+	1.15099i
$634$	45.8129	+	42.5082i	1.81946	+	1.68822i
$635$	26.2076	+	17.8681i	1.04002	+	0.709072i
$636$	−65.8040			−2.60930
$637$	4.38003	+	5.46034i	0.173543	+	0.216347i
$638$	−7.07380			−0.280054
$639$	−5.18360	−	3.53412i	−0.205060	−	0.139808i
$640$	12.8470	+	11.9202i	0.507821	+	0.471189i
$641$	−0.516214	−	1.31529i	−0.0203892	−	0.0519509i	0.920317	−	0.391174i	$-0.127931\pi$
$641$	−0.516214	−	1.31529i	−0.0203892	−	0.0519509i	−0.940706	+	0.339223i	$0.889836\pi$
$642$	42.5677	−	13.1304i	1.68001	−	0.518215i
$643$	3.20561	+	14.0447i	0.126417	+	0.553869i	0.997977	+	0.0635798i	$0.0202518\pi$
$643$	3.20561	+	14.0447i	0.126417	+	0.553869i	−0.871560	+	0.490289i	$0.836891\pi$
$644$	27.6254	+	13.2552i	1.08859	+	0.522327i
$645$	6.61488	−	28.9817i	0.260460	−	1.14115i
$646$	0.543855	+	7.25724i	0.0213977	+	0.285532i
$647$	−13.4835	−	4.15912i	−0.530093	−	0.163512i	0.0181437	−	0.999835i	$-0.494224\pi$
$647$	−13.4835	−	4.15912i	−0.530093	−	0.163512i	−0.548236	+	0.836323i	$0.684701\pi$
$648$	5.94424	−	79.3204i	0.233512	−	3.11600i
$649$	1.04013	−	2.65022i	0.0408288	−	0.104030i
$650$	0.146965	−	0.0707748i	0.00576446	−	0.00277602i
$651$	−15.9959	+	40.9286i	−0.626929	+	1.60412i
$652$	−75.8942	−	36.5487i	−2.97225	−	1.43136i
$653$	−23.2584	+	21.5806i	−0.910172	+	0.844516i	−0.988315	−	0.152426i	$-0.951291\pi$
$653$	−23.2584	+	21.5806i	−0.910172	+	0.844516i	0.0781431	+	0.996942i	$0.475101\pi$
$654$	−51.5379	+	7.76808i	−2.01529	+	0.303756i
$655$	15.0148	−	26.0063i	0.586675	−	1.01615i
$656$	4.45325	+	7.71325i	0.173870	+	0.301152i
$657$	0.188143	+	0.235924i	0.00734017	+	0.00920429i
$658$	23.5082	+	7.21459i	0.916444	+	0.281254i
$659$	−3.95364	+	4.95771i	−0.154012	+	0.193125i	−0.852851	−	0.522154i	$-0.825129\pi$
$659$	−3.95364	+	4.95771i	−0.154012	+	0.193125i	0.698839	+	0.715279i	$0.253700\pi$
$660$	−6.43035	−	0.969219i	−0.250301	−	0.0377268i
$661$	25.3613	−	17.2910i	0.986441	−	0.672544i	0.0412793	−	0.999148i	$-0.486857\pi$
$661$	25.3613	−	17.2910i	0.986441	−	0.672544i	0.945161	+	0.326604i	$0.105904\pi$
$662$	4.60156	−	3.13729i	0.178845	−	0.121934i
$663$	−2.47918	−	0.373677i	−0.0962835	−	0.0145124i
$664$	37.9358	−	47.5700i	1.47220	−	1.84608i
$665$	−11.9017	+	1.81127i	−0.461529	+	0.0702380i
$666$	0.00113115	+	0.00141841i	4.38310e−5	+	5.49624e-5i
$667$	−9.87403	−	17.1023i	−0.382324	−	0.662205i
$668$	−14.8381	+	25.7004i	−0.574105	+	0.994378i
$669$	21.1395	−	3.18627i	0.817302	−	0.123188i
$670$	0.286477	−	0.265812i	0.0110676	−	0.0102692i
$671$	−3.01056	−	1.44981i	−0.116221	−	0.0559692i
$672$	61.3871	−	19.0314i	2.36806	−	0.734151i
$673$	−17.3997	+	8.37928i	−0.670711	+	0.322997i	−0.738063	−	0.674732i	$-0.764259\pi$
$673$	−17.3997	+	8.37928i	−0.670711	+	0.322997i	0.0673519	+	0.997729i	$0.478545\pi$
$674$	0.662371	−	1.68769i	0.0255136	−	0.0650075i
$675$	−0.0221090	+	0.295025i	−0.000850978	+	0.0113555i
$676$	4.77509	+	1.47292i	0.183657	+	0.0566507i
$677$	1.55672	+	20.7730i	0.0598297	+	0.798371i	0.943734	+	0.330704i	$0.107286\pi$
$677$	1.55672	+	20.7730i	0.0598297	+	0.798371i	−0.883905	+	0.467667i	$0.845095\pi$
$678$	22.7039	−	99.4721i	0.871936	−	3.82020i
$679$	2.72690	−	3.42945i	0.104649	−	0.131610i
$680$	5.39907	+	23.6549i	0.207045	+	0.907124i
$681$	27.6696	−	8.53495i	1.06030	−	0.327060i
$682$	−2.73314	−	6.96392i	−0.104657	−	0.266662i
$683$	0.0249519	+	0.0231520i	0.000954757	+	0.000885885i	0.680650	−	0.732609i	$-0.261697\pi$
$683$	0.0249519	+	0.0231520i	0.000954757	+	0.000885885i	−0.679695	+	0.733495i	$0.737888\pi$
$684$	−3.31464	−	2.25989i	−0.126739	−	0.0864089i
$685$	27.6223			1.05539
$686$	−24.6763	−	42.3212i	−0.942145	−	1.61583i
$687$	40.6832			1.55216
$688$	−65.0188	−	44.3291i	−2.47882	−	1.69003i
$689$	5.23752	+	4.85971i	0.199534	+	0.185140i
$690$	−9.28717	−	23.6633i	−0.353556	−	0.900847i
$691$	18.5852	−	5.73278i	0.707015	−	0.218085i	0.0796640	−	0.996822i	$-0.474615\pi$
$691$	18.5852	−	5.73278i	0.707015	−	0.218085i	0.627351	+	0.778736i	$0.284139\pi$
$692$	−14.4975	−	63.5178i	−0.551113	−	2.41458i
$693$	−0.205132	+	0.257981i	−0.00779230	+	0.00979989i
$694$	−12.2369	+	53.6135i	−0.464507	+	2.03514i
$695$	1.42975	+	19.0786i	0.0542334	+	0.723694i
$696$	−118.975	−	36.6990i	−4.50974	−	1.39107i
$697$	−0.0824844	+	1.10068i	−0.00312432	+	0.0416911i
$698$	21.6966	−	55.2821i	0.821230	−	2.09246i
$699$	−31.7574	+	15.2936i	−1.20118	+	0.578456i
$700$	−0.778727	+	0.241423i	−0.0294331	+	0.00912493i
$701$	−23.4906	−	11.3125i	−0.887228	−	0.427267i	−0.0659688	−	0.997822i	$-0.521014\pi$
$701$	−23.4906	−	11.3125i	−0.887228	−	0.427267i	−0.821259	+	0.570555i	$0.806728\pi$
$702$	−9.30296	+	8.63189i	−0.351118	+	0.325790i
$703$	−0.00345550		0.000520833i	−0.000130327		1.96436e-5i
$704$	−2.02581	+	3.50881i	−0.0763507	+	0.132243i
$705$	−7.28479	−	12.6176i	−0.274361	−	0.475208i
$706$	−24.3615	−	30.5483i	−0.916856	−	1.14970i
$707$	−44.7423	+	6.80913i	−1.68271	+	0.256084i
$708$	52.0927	−	65.3222i	1.95776	−	2.45496i
$709$	41.7538	+	6.29338i	1.56810	+	0.236353i	0.874867	−	0.484363i	$-0.160949\pi$
$709$	41.7538	+	6.29338i	1.56810	+	0.236353i	0.693231	+	0.720716i	$0.256187\pi$
$710$	77.7158	−	52.9858i	2.91662	−	1.98852i
$711$	1.96786	−	1.34166i	0.0738004	−	0.0503163i
$712$	129.682	+	19.5464i	4.86003	+	0.732532i
$713$	13.0216	−	16.3286i	0.487663	−	0.611510i
$714$	16.7745	+	5.14804i	0.627769	+	0.192661i
$715$	0.440231	+	0.552032i	0.0164637	+	0.0206448i
$716$	27.8198	+	48.1853i	1.03968	+	1.80077i
$717$	−24.8012	+	42.9570i	−0.926218	+	1.60426i
$718$	48.2071	−	7.26605i	1.79907	−	0.271166i
$719$	−16.0954	+	14.9344i	−0.600258	+	0.556958i	−0.920681	−	0.390317i	$-0.872366\pi$
$719$	−16.0954	+	14.9344i	−0.600258	+	0.556958i	0.320423	+	0.947275i	$0.396175\pi$
$720$	−8.83198	−	4.25326i	−0.329148	−	0.158509i
$721$	0.805155	−	2.06014i	0.0299855	−	0.0767236i
$722$	−35.5331	+	17.1118i	−1.32240	+	0.636836i
$723$	3.50146	−	8.92158i	0.130221	−	0.331797i
$724$	1.63559	−	21.8254i	0.0607861	−	0.811135i
$725$	0.502111	+	0.154881i	0.0186479	+	0.00575213i
$726$	3.97178	+	52.9997i	0.147406	+	1.96700i
$727$	−1.58281	+	6.93475i	−0.0587032	+	0.257196i	−0.995761	−	0.0919788i	$-0.970681\pi$
$727$	−1.58281	+	6.93475i	−0.0587032	+	0.257196i	0.937058	+	0.349174i	$0.113538\pi$
$728$	−18.9110	−	9.07386i	−0.700890	−	0.336300i
$729$	−5.01666	−	21.9794i	−0.185802	−	0.814053i
$730$	−4.32316	+	1.33352i	−0.160007	+	0.0493557i
$731$	−3.56288	−	9.07807i	−0.131778	−	0.335765i
$732$	−71.8834	−	66.6981i	−2.65689	−	2.46523i
$733$	16.4489	+	11.2147i	0.607555	+	0.414224i	0.827642	−	0.561256i	$-0.189682\pi$
$733$	16.4489	+	11.2147i	0.607555	+	0.414224i	−0.220087	+	0.975480i	$0.570634\pi$
$734$	4.02134			0.148430
$735$	−6.37813	+	28.3167i	−0.235261	+	1.04448i
$736$	−30.5455			−1.12592
$737$	0.0170278	+	0.0116094i	0.000627228	+	0.000427637i
$738$	−0.624532	−	0.579481i	−0.0229893	−	0.0213310i
$739$	8.28365	+	21.1064i	0.304719	+	0.776411i	0.998422	+	0.0561505i	$0.0178827\pi$
$739$	8.28365	+	21.1064i	0.304719	+	0.776411i	−0.693703	+	0.720261i	$0.744022\pi$
$740$	−0.0185623	+	0.00572570i	−0.000682362	+	0.000210481i
$741$	0.829471	+	3.63415i	0.0304714	+	0.133504i
$742$	−31.2323	−	39.0496i	−1.14657	−	1.43356i
$743$	7.25531	−	31.7876i	0.266171	−	1.16617i	−0.648256	−	0.761423i	$-0.724501\pi$
$743$	7.25531	−	31.7876i	0.266171	−	1.16617i	0.914427	−	0.404751i	$-0.132642\pi$
$744$	−9.84007	−	131.307i	−0.360755	−	4.81394i
$745$	−31.9155	−	9.84464i	−1.16929	−	0.360680i
$746$	0.920446	−	12.2825i	0.0336999	−	0.449694i
$747$	−1.11298	+	2.83583i	−0.0407218	+	0.103758i
$748$	−1.92209	+	0.925631i	−0.0702787	+	0.0338444i
$749$	19.9935	+	13.5896i	0.730548	+	0.496554i
$750$	−48.8023	−	23.5019i	−1.78201	−	0.858169i
$751$	21.8925	−	20.3132i	0.798867	−	0.741241i	−0.170896	−	0.985289i	$-0.554666\pi$
$751$	21.8925	−	20.3132i	0.798867	−	0.741241i	0.969763	+	0.244048i	$0.0784756\pi$
$752$	−38.1375	+	5.74830i	−1.39073	+	0.209619i
$753$	−9.83214	+	17.0298i	−0.358303	+	0.620599i
$754$	11.2699	+	19.5200i	0.410424	+	0.710875i
$755$	−6.28656	−	7.88309i	−0.228791	−	0.286895i
$756$	52.3572	−	35.8061i	1.90421	−	1.30226i
$757$	−8.70741	+	10.9188i	−0.316476	+	0.396849i	−0.914471	−	0.404651i	$-0.867393\pi$
$757$	−8.70741	+	10.9188i	−0.316476	+	0.396849i	0.597995	+	0.801500i	$0.295964\pi$
$758$	84.6582	+	12.7602i	3.07493	+	0.463471i
$759$	1.10762	−	0.755160i	0.0402039	−	0.0274106i
$760$	29.8056	−	20.3211i	1.08116	−	0.737124i
$761$	34.2933	+	5.16888i	1.24313	+	0.187372i	0.737482	−	0.675367i	$-0.236015\pi$
$761$	34.2933	+	5.16888i	1.24313	+	0.187372i	0.505649	+	0.862739i	$0.331253\pi$
$762$	−42.8556	+	53.7392i	−1.55250	+	1.94677i
$763$	−20.7615	−	19.2088i	−0.751618	−	0.695406i
$764$	6.74581	+	8.45897i	0.244055	+	0.306035i
$765$	−0.607417	−	1.05208i	−0.0219612	−	0.0380380i
$766$	17.2504	−	29.8785i	0.623280	−	1.07955i
$767$	−8.97032	+	1.35206i	−0.323900	+	0.0488200i
$768$	7.04540	−	6.53717i	0.254229	−	0.235890i
$769$	44.5915	+	21.4741i	1.60801	+	0.774377i	0.999812	−	0.0194089i	$-0.00617842\pi$
$769$	44.5915	+	21.4741i	1.60801	+	0.774377i	0.608198	+	0.793785i	$0.291893\pi$
$770$	−2.47686	−	4.27594i	−0.0892597	−	0.154094i
$771$	7.26195	−	3.49717i	0.261533	−	0.125948i
$772$	−8.87454	+	22.6120i	−0.319402	+	0.813822i
$773$	2.18571	−	29.1663i	0.0786146	−	1.04904i	−0.808805	−	0.588077i	$-0.799885\pi$
$773$	2.18571	−	29.1663i	0.0786146	−	1.04904i	0.887420	−	0.460962i	$-0.152496\pi$
$774$	7.19300	+	2.21875i	0.258547	+	0.0797512i
$775$	0.0415281	+	0.554154i	0.00149173	+	0.0199058i
$776$	−2.92145	+	12.7997i	−0.104874	+	0.459483i
$777$	−0.00186313	+	0.00821693i	−6.68394e−5	+	0.000294781i
$778$	−1.06206	−	4.65319i	−0.0380767	−	0.166825i
$779$	1.56814	−	0.483706i	0.0561843	−	0.0173306i
$780$	7.57019	+	19.2885i	0.271056	+	0.690640i
$781$	3.63611	+	3.37382i	0.130110	+	0.120725i
$782$	−6.89036	−	4.69777i	−0.246399	−	0.167992i
$783$	−40.8806			−1.46095
$784$	63.6092	+	43.1026i	2.27176	+	1.53938i
$785$	44.9921			1.60584
$786$	53.7663	+	36.6572i	1.91778	+	1.30752i
$787$	24.8595	+	23.0663i	0.886147	+	0.822224i	0.984942	−	0.172884i	$-0.0553085\pi$
$787$	24.8595	+	23.0663i	0.886147	+	0.822224i	−0.0987956	+	0.995108i	$0.531499\pi$
$788$	26.6501	+	67.9034i	0.949371	+	2.41896i
$789$	6.40360	−	1.97525i	0.227974	−	0.0703207i
$790$	7.94578	+	34.8127i	0.282698	+	1.23858i
$791$	49.8524	−	24.0953i	1.77255	−	0.856731i
$792$	0.219767	−	0.962861i	0.00780907	−	0.0342138i
$793$	0.795661	+	10.6174i	0.0282548	+	0.377034i
$794$	44.8923	+	13.8474i	1.59317	+	0.491427i
$795$	−2.21400	+	29.5437i	−0.0785224	+	1.04781i
$796$	19.7971	−	50.4421i	0.701688	−	1.78787i
$797$	−12.4162	+	5.97932i	−0.439804	+	0.211798i	−0.640664	−	0.767822i	$-0.721341\pi$
$797$	−12.4162	+	5.97932i	−0.439804	+	0.211798i	0.200860	+	0.979620i	$0.435626\pi$
$798$	−1.98667	−	26.0121i	−0.0703272	−	0.920818i
$799$	−4.30635	−	2.07383i	−0.152348	−	0.0733667i
$800$	0.595790	−	0.552812i	0.0210643	−	0.0195449i
$801$	−6.49304	+	0.978668i	−0.229420	+	0.0345795i
$802$	37.9555	−	65.7408i	1.34025	−	2.32139i
$803$	−0.119291	−	0.206617i	−0.00420967	−	0.00729137i
$804$	0.377086	+	0.472851i	0.0132988	+	0.0166762i
$805$	6.88059	−	11.9569i	0.242509	−	0.421425i
$806$	−14.8624	+	18.6368i	−0.523504	+	0.656454i
$807$	51.8009	+	7.80773i	1.82348	+	0.274845i
$808$	112.048	−	76.3934i	3.94185	−	2.68751i
$809$	−15.2062	+	10.3674i	−0.534621	+	0.364499i	−0.800335	−	0.599553i	$-0.795345\pi$
$809$	−15.2062	+	10.3674i	−0.534621	+	0.364499i	0.265714	+	0.964052i	$0.414392\pi$
$810$	−59.0432	−	8.89933i	−2.07457	−	0.312691i
$811$	15.1818	−	19.0374i	0.533106	−	0.668494i	−0.440228	−	0.897886i	$-0.645102\pi$
$811$	15.1818	−	19.0374i	0.533106	−	0.668494i	0.973334	+	0.229392i	$0.0736738\pi$
$812$	−41.3076	−	104.810i	−1.44961	−	3.67811i
$813$	24.3753	+	30.5656i	0.854879	+	1.07198i
$814$	−0.000717193	−	0.00124222i	−2.51376e−5	−	4.35396e-5i
$815$	−18.9626	+	32.8442i	−0.664231	+	1.15048i
$816$	−27.2134	+	4.10176i	−0.952659	+	0.143590i
$817$	−10.6287	+	9.86201i	−0.371852	+	0.345028i
$818$	18.2527	+	8.79003i	0.638190	+	0.307336i
$819$	1.03870	+	0.155044i	0.0362952	+	0.00541767i
$820$	8.21878	−	3.95796i	0.287012	−	0.138218i
$821$	−7.41400	+	18.8906i	−0.258750	+	0.659285i	−0.999928	−	0.0120241i	$-0.996173\pi$
$821$	−7.41400	+	18.8906i	−0.258750	+	0.659285i	0.741177	+	0.671309i	$0.234268\pi$
$822$	−4.47313	+	59.6898i	−0.156018	+	2.08192i
$823$	33.0068	+	10.1813i	1.15055	+	0.354896i	0.810629	−	0.585560i	$-0.199125\pi$
$823$	33.0068	+	10.1813i	1.15055	+	0.354896i	0.339916	+	0.940456i	$0.389601\pi$
$824$	0.495300	+	6.60932i	0.0172546	+	0.230247i
$825$	−0.00793718	+	0.0347750i	−0.000276337	+	0.00121071i
$826$	63.4883	−	0.0905904i	2.20904	−	0.00315204i
$827$	−9.01320	−	39.4894i	−0.313420	−	1.37318i	−0.848864	−	0.528611i	$-0.822713\pi$
$827$	−9.01320	−	39.4894i	−0.313420	−	1.37318i	0.535445	−	0.844570i	$-0.320144\pi$
$828$	4.39283	−	1.35501i	0.152661	−	0.0470898i
$829$	7.77840	+	19.8190i	0.270155	+	0.688344i	0.999989	+	0.00471917i	$0.00150216\pi$
$829$	7.77840	+	19.8190i	0.270155	+	0.688344i	−0.729834	+	0.683625i	$0.760403\pi$
$830$	−33.4812	−	31.0661i	−1.16215	−	1.07832i
$831$	1.74837	+	1.19202i	0.0606501	+	0.0413506i
$832$	12.9100			0.447572
$833$	3.50416	+	8.85407i	0.121412	+	0.306775i
$834$	−41.4591			−1.43561
$835$	11.0394	+	7.52651i	0.382033	+	0.260466i
$836$	2.32511	+	2.15738i	0.0804155	+	0.0746147i
$837$	−15.7952	−	40.2456i	−0.545963	−	1.39109i
$838$	−76.6342	+	23.6385i	−2.64729	+	0.816579i
$839$	−7.91121	−	34.6613i	−0.273125	−	1.19664i	−0.906301	−	0.422633i	$-0.861106\pi$
$839$	−7.91121	−	34.6613i	−0.273125	−	1.19664i	0.633176	−	0.774008i	$-0.281751\pi$
$840$	−19.4749	−	84.7675i	−0.671949	−	2.92476i
$841$	−9.70349	+	42.5138i	−0.334603	+	1.46599i
$842$	6.58065	+	87.8127i	0.226784	+	3.02622i
$843$	−43.4330	−	13.3973i	−1.49591	−	0.461427i
$844$	6.30306	−	84.1084i	0.216960	−	2.89513i
$845$	0.821950	−	2.09429i	0.0282759	−	0.0720459i
$846$	3.32394	−	1.60072i	0.114279	−	0.0550340i
$847$	−21.1152	+	19.6481i	−0.725526	+	0.675118i
$848$	70.6601	+	34.0281i	2.42648	+	1.16853i
$849$	30.6939	−	28.4798i	1.05341	−	0.977424i
$850$	0.219417	−	0.0330718i	0.00752594	−	0.00113435i
$851$	0.00200220	−	0.00346792i	6.86346e−5	−	0.000118879i
$852$	72.7830	+	126.064i	2.49350	+	4.31888i
$853$	−8.04539	−	10.0886i	−0.275469	−	0.345427i	0.624782	−	0.780800i	$-0.285188\pi$
$853$	−8.04539	−	10.0886i	−0.275469	−	0.345427i	−0.900250	+	0.435373i	$0.856617\pi$
$854$	5.46244	−	74.3140i	0.186921	−	2.54297i
$855$	−1.12613	+	1.41213i	−0.0385130	+	0.0482937i
$856$	−71.6298	−	10.7965i	−2.44826	−	0.369015i
$857$	1.11718	−	0.761678i	0.0381620	−	0.0260184i	−0.544089	−	0.839028i	$-0.683125\pi$
$857$	1.11718	−	0.761678i	0.0381620	−	0.0260184i	0.582251	+	0.813009i	$0.302172\pi$
$858$	−1.26419	+	0.861911i	−0.0431588	+	0.0294252i
$859$	−18.0503	−	2.72064i	−0.615868	−	0.0928271i	−0.166303	−	0.986075i	$-0.553183\pi$
$859$	−18.0503	−	2.72064i	−0.615868	−	0.0928271i	−0.449565	+	0.893248i	$0.648421\pi$
$860$	−50.2520	+	63.0140i	−1.71358	+	2.14876i
$861$	0.290050	−	3.94599i	0.00988487	−	0.134479i
$862$	−51.7321	−	64.8701i	−1.76200	−	2.20948i
$863$	6.90263	+	11.9557i	0.234968	+	0.406977i	0.959263	−	0.282513i	$-0.0911681\pi$
$863$	6.90263	+	11.9557i	0.234968	+	0.406977i	−0.724295	+	0.689490i	$0.757835\pi$
$864$	−31.6162	+	54.7608i	−1.07560	+	1.86300i
$865$	−29.0051	+	4.37181i	−0.986202	+	0.148646i
$866$	51.8278	−	48.0891i	1.76118	−	1.63414i
$867$	25.1566	+	12.1148i	0.854364	+	0.411440i
$868$	87.2218	−	81.1619i	2.96050	−	2.75481i
$869$	−1.69658	+	0.817030i	−0.0575525	+	0.0277158i
$870$	−34.1458	+	87.0021i	−1.15765	+	2.94965i
$871$	0.00490733	−	0.0654837i	0.000166278	−	0.00221883i
$872$	80.9886	+	24.9817i	2.74262	+	0.845987i
$873$	−0.0491239	−	0.655512i	−0.00166259	−	0.0221857i
$874$	−2.75900	+	12.0880i	−0.0933244	+	0.408881i
$875$	−6.58193	−	28.6488i	−0.222510	−	0.968507i
$876$	−1.55799	−	6.82599i	−0.0526396	−	0.230629i
$877$	33.5932	−	10.3621i	1.13436	−	0.349904i	0.329962	−	0.943994i	$-0.392964\pi$
$877$	33.5932	−	10.3621i	1.13436	−	0.349904i	0.804399	+	0.594090i	$0.202488\pi$
$878$	−4.47765	−	11.4089i	−0.151113	−	0.385031i
$879$	−29.0536	−	26.9578i	−0.979953	−	0.909264i
$880$	6.40369	+	4.36596i	0.215868	+	0.147177i
$881$	−3.62904			−0.122266			−0.0611328	−	0.998130i	$-0.519471\pi$
$881$	−3.62904			−0.122266			−0.0611328	+	0.998130i	$0.519471\pi$
$882$	−7.02957	−	2.14638i	−0.236698	−	0.0722725i
$883$	1.64937			0.0555056			0.0277528	−	0.999615i	$-0.491165\pi$
$883$	1.64937			0.0555056			0.0277528	+	0.999615i	$0.491165\pi$
$884$	5.61650	+	3.82926i	0.188903	+	0.128792i
$885$	−27.5748	−	25.5856i	−0.926915	−	0.860052i
$886$	16.9003	+	43.0611i	0.567775	+	1.44667i
$887$	−18.1610	+	5.60193i	−0.609787	+	0.188094i	−0.584242	−	0.811579i	$-0.698608\pi$
$887$	−18.1610	+	5.60193i	−0.609787	+	0.188094i	−0.0255447	+	0.999674i	$0.508132\pi$
$888$	−0.00561794	−	0.0246138i	−0.000188526	−	0.000825985i
$889$	−37.3013	+	0.0532246i	−1.25105	+	0.00178510i
$890$	21.9066	−	95.9790i	0.734310	−	3.21722i
$891$	−0.235311	−	3.14001i	−0.00788322	−	0.105194i
$892$	−55.3874	−	17.0847i	−1.85451	−	0.572039i
$893$	−0.531053	+	7.08642i	−0.0177710	+	0.237138i
$894$	26.4419	−	67.3729i	0.884350	−	2.25329i
$895$	22.5696	−	10.8689i	0.754418	−	0.363308i
$896$	−20.3837	−	3.04261i	−0.680971	−	0.101646i
$897$	−3.84848	−	1.85333i	−0.128497	−	0.0618809i
$898$	−46.9947	+	43.6047i	−1.56823	+	1.45511i
$899$	−75.9296	+	11.4446i	−2.53240	+	0.381697i
$900$	−0.0611592	+	0.105931i	−0.00203864	+	0.00353103i
$901$	4.85963	+	8.41713i	0.161898	+	0.280415i
$902$	0.419977	+	0.526635i	0.0139837	+	0.0175350i
$903$	12.8182	+	32.5237i	0.426563	+	1.08232i
$904$	−103.446	+	129.717i	−3.44057	+	4.31433i
$905$	−9.74383	−	1.46865i	−0.323896	−	0.0488195i
$906$	18.0528	−	12.3082i	0.599765	−	0.408913i
$907$	3.33760	−	2.27553i	0.110823	−	0.0755579i	−0.506640	−	0.862158i	$-0.669113\pi$
$907$	3.33760	−	2.27553i	0.110823	−	0.0755579i	0.617463	+	0.786600i	$0.288160\pi$
$908$	−77.6309	−	11.7010i	−2.57627	−	0.388310i
$909$	−4.23349	+	5.30863i	−0.140416	+	0.176076i
$910$	−7.85325	+	13.6472i	−0.260333	+	0.452399i
$911$	22.3285	+	27.9990i	0.739775	+	0.927649i	0.999274	−	0.0380944i	$-0.0121287\pi$
$911$	22.3285	+	27.9990i	0.739775	+	0.927649i	−0.259499	+	0.965743i	$0.583557\pi$
$912$	20.4585	+	35.4352i	0.677449	+	1.17338i
$913$	1.20430	−	2.08591i	0.0398566	−	0.0690337i
$914$	−78.8528	+	11.8851i	−2.60822	+	0.393126i
$915$	−32.3637	+	30.0291i	−1.06991	+	0.992732i
$916$	−99.3798	−	47.8588i	−3.28360	−	1.58130i
$917$	2.68929	+	35.2118i	0.0888081	+	1.16279i
$918$	−15.5539	+	7.49036i	−0.513355	+	0.247219i
$919$	10.2369	−	26.0831i	0.337683	−	0.860401i	−0.656661	−	0.754186i	$-0.728032\pi$
$919$	10.2369	−	26.0831i	0.337683	−	0.860401i	0.994343	−	0.106215i	$-0.0338731\pi$
$920$	−3.08913	+	41.2216i	−0.101846	+	1.35904i
$921$	38.4243	+	11.8523i	1.26612	+	0.390548i
$922$	3.77387	+	50.3587i	0.124286	+	1.65848i
$923$	3.51698	−	15.4089i	0.115763	−	0.507189i
$924$	6.88535	−	3.32792i	0.226511	−	0.109481i
$925$	2.37094e−5	0	0.000103878i	7.79560e−7	0	3.41548e-6i
$926$	56.3600	−	17.3848i	1.85210	−	0.571298i
$927$	−0.121238	−	0.308910i	−0.00398199	−	0.0101460i
$928$	82.3258	+	76.3871i	2.70248	+	2.50753i
$929$	31.5410	+	21.5043i	1.03483	+	0.705532i	0.956600	−	0.291403i	$-0.0941222\pi$
$929$	31.5410	+	21.5043i	1.03483	+	0.705532i	0.0782255	+	0.996936i	$0.475075\pi$
$930$	−98.8438			−3.24122
$931$	10.3506	−	9.65907i	0.339227	−	0.316563i
$932$	95.5671			3.13040
$933$	−6.53344	−	4.45443i	−0.213895	−	0.145831i
$934$	−34.6751	−	32.1738i	−1.13460	−	1.05276i
$935$	0.350907	+	0.894097i	0.0114759	+	0.0292401i
$936$	−3.00712	+	0.927573i	−0.0982907	+	0.0303187i
$937$	−1.79996	−	7.88613i	−0.0588020	−	0.257628i	0.936980	−	0.349384i	$-0.113609\pi$
$937$	−1.79996	−	7.88613i	−0.0588020	−	0.257628i	−0.995782	+	0.0917558i	$0.970752\pi$
$938$	−0.101626	+	0.448199i	−0.00331820	+	0.0146342i
$939$	−3.59316	+	15.7427i	−0.117258	+	0.513742i
$940$	2.95200	+	39.3917i	0.0962836	+	1.28481i
$941$	20.8429	+	6.42919i	0.679460	+	0.209586i	0.615228	−	0.788349i	$-0.289064\pi$
$941$	20.8429	+	6.42919i	0.679460	+	0.209586i	0.0642319	+	0.997935i	$0.479540\pi$
$942$	−7.28599	+	97.2247i	−0.237390	+	3.16775i
$943$	−0.687016	+	1.75049i	−0.0223723	+	0.0570037i
$944$	−89.7159	+	43.2049i	−2.92000	+	1.40620i
$945$	−14.3141	−	24.7113i	−0.465639	−	0.803859i
$946$	−5.36208	−	2.58224i	−0.174336	−	0.0839559i
$947$	23.2089	−	21.5347i	0.754187	−	0.699783i	−0.206183	−	0.978514i	$-0.566104\pi$
$947$	23.2089	−	21.5347i	0.754187	−	0.699783i	0.960369	+	0.278731i	$0.0899136\pi$
$948$	−54.6441	+	8.23628i	−1.77476	+	0.267502i
$949$	−0.380104	+	0.658359i	−0.0123387	+	0.0213712i
$950$	−0.164954	−	0.285708i	−0.00535180	−	0.00926959i
$951$	27.1499	+	34.0449i	0.880395	+	1.10398i
$952$	−20.9440	−	19.3776i	−0.678799	−	0.628033i
$953$	15.2986	−	19.1838i	0.495571	−	0.621426i	−0.469653	−	0.882851i	$-0.655621\pi$
$953$	15.2986	−	19.1838i	0.495571	−	0.621426i	0.965224	+	0.261425i	$0.0841925\pi$
$954$	−7.41821	−	1.11812i	−0.240174	−	0.0362003i
$955$	4.02476	−	2.74403i	0.130238	−	0.0887948i
$956$	111.117	−	75.7585i	3.59379	−	2.45021i
$957$	−4.87371	−	0.734594i	−0.157545	−	0.0237461i
$958$	−35.4146	+	44.4085i	−1.14419	+	1.43477i
$959$	−26.8130	+	18.3369i	−0.865836	+	0.592128i
$960$	33.3768	+	41.8532i	1.07723	+	1.35081i
$961$	−25.1041	−	43.4815i	−0.809809	−	1.40263i
$962$	−0.00228524	+	0.00395815i	−7.36791e−5	+	0.000127616i
$963$	3.58643	−	0.540568i	0.115571	−	0.0174196i
$964$	−19.0484	+	17.6743i	−0.613508	+	0.569252i
$965$	9.85341	+	4.74515i	0.317193	+	0.152752i
$966$	24.7238	+	16.8047i	0.795474	+	0.540684i
$967$	9.02074	−	4.34416i	0.290087	−	0.139699i	−0.283181	−	0.959067i	$-0.591390\pi$
$967$	9.02074	−	4.34416i	0.290087	−	0.139699i	0.573268	+	0.819368i	$0.305675\pi$
$968$	31.5750	−	80.4519i	1.01486	−	2.58582i
$969$	−0.378938	+	5.05658i	−0.0121733	+	0.162441i
$970$	9.41756	+	2.90493i	0.302380	+	0.0932718i
$971$	−0.846441	−	11.2950i	−0.0271636	−	0.362473i	−0.994178	−	0.107751i	$-0.965635\pi$
$971$	−0.846441	−	11.2950i	−0.0271636	−	0.362473i	0.967014	−	0.254722i	$-0.0819840\pi$
$972$	4.55811	−	19.9704i	0.146202	−	0.640551i
$973$	−14.0531	−	17.5705i	−0.450521	−	0.563284i
$974$	15.9652	+	69.9480i	0.511557	+	2.24128i
$975$	0.108606	−	0.0335006i	0.00347818	−	0.00107288i
$976$	42.6977	+	108.792i	1.36672	+	3.48235i
$977$	18.2794	+	16.9608i	0.584811	+	0.542625i	0.916124	−	0.400896i	$-0.131301\pi$
$977$	18.2794	+	16.9608i	0.584811	+	0.542625i	−0.331313	+	0.943521i	$0.607492\pi$
$978$	−67.9032	−	46.2956i	−2.17130	−	1.48037i
$979$	5.19162			0.165925
$980$	48.8914	−	61.6681i	1.56178	−	1.96992i
$981$	−4.24355			−0.135486
$982$	74.3204	+	50.6708i	2.37166	+	1.61697i
$983$	−34.5859	−	32.0911i	−1.10312	−	1.02355i	−0.999582	−	0.0289204i	$-0.990793\pi$
$983$	−34.5859	−	32.0911i	−1.10312	−	1.02355i	−0.103538	−	0.994625i	$-0.533016\pi$
$984$	4.33147	+	11.0364i	0.138082	+	0.351827i
$985$	31.3830	−	9.68036i	0.999944	−	0.308442i
$986$	6.82279	+	29.8926i	0.217282	+	0.951974i
$987$	15.4475	+	7.41197i	0.491698	+	0.235926i
$988$	2.24892	−	9.85317i	0.0715478	−	0.313471i
$989$	−1.24163	−	16.5683i	−0.0394814	−	0.526843i
$990$	−0.708437	−	0.218524i	−0.0225156	−	0.00694515i
$991$	0.747340	−	9.97256i	0.0237400	−	0.316789i	−0.972674	−	0.232176i	$-0.925416\pi$
$991$	0.747340	−	9.97256i	0.0237400	−	0.316789i	0.996414	−	0.0846130i	$-0.0269654\pi$
$992$	−43.3920	+	110.561i	−1.37770	+	3.51032i
$993$	3.49618	−	1.68367i	0.110948	−	0.0534298i
$994$	−40.2645	+	103.024i	−1.27711	+	3.26773i
$995$	−21.9807	−	10.5853i	−0.696835	−	0.335578i
$996$	51.8152	−	48.0775i	1.64183	−	1.52339i
$997$	29.2518	−	4.40900i	0.926413	−	0.139634i	0.331528	−	0.943445i	$-0.392436\pi$
$997$	29.2518	−	4.40900i	0.926413	−	0.139634i	0.594885	+	0.803811i	$0.297198\pi$
$998$	−43.1996	+	74.8239i	−1.36746	+	2.36851i
$999$	−0.00414477	−	0.00717896i	−0.000131135	−	0.000227132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.2	✓	348
49.37	even	21	inner	637.2.bl.b.625.2	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.2	✓	348	1.1	even	1	trivial
637.2.bl.b.625.2	yes	348	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18557 - 1.49010i) q^{2} +(-1.35107 - 1.25361i) q^{3} +(1.82564 + 4.65166i) q^{4} +(2.14986 - 0.663145i) q^{5} +(1.08486 + 4.75308i) q^{6} +(-1.64665 + 2.07088i) q^{7} +(1.76413 - 7.72914i) q^{8} +(0.0296636 + 0.395833i) q^{9} +O(q^{10})\)	\(q+(-2.18557 - 1.49010i) q^{2} +(-1.35107 - 1.25361i) q^{3} +(1.82564 + 4.65166i) q^{4} +(2.14986 - 0.663145i) q^{5} +(1.08486 + 4.75308i) q^{6} +(-1.64665 + 2.07088i) q^{7} +(1.76413 - 7.72914i) q^{8} +(0.0296636 + 0.395833i) q^{9} +(-5.68682 - 1.75415i) q^{10} +(0.0234531 - 0.312960i) q^{11} +(3.36481 - 8.57338i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(6.68467 - 2.07240i) q^{14} +(-3.73595 - 1.79914i) q^{15} +(-8.04652 + 7.46608i) q^{16} +(-1.34513 + 0.202746i) q^{17} +(0.524997 - 0.909321i) q^{18} +(1.01124 + 1.75153i) q^{19} +(7.00960 + 8.78977i) q^{20} +(4.82082 - 0.733659i) q^{21} +(-0.517598 + 0.649047i) q^{22} +(-2.29170 - 0.345418i) q^{23} +(-12.0728 + 8.23111i) q^{24} +(0.0509509 - 0.0347378i) q^{25} +(2.61566 + 0.394247i) q^{26} +(-2.99128 + 3.75095i) q^{27} +(-12.6392 - 3.87895i) q^{28} +(5.31274 + 6.66197i) q^{29} +(5.48428 + 9.49905i) q^{30} +(-4.50578 + 7.80424i) q^{31} +(13.0327 - 1.96436i) q^{32} +(-0.424017 + 0.393430i) q^{33} +(3.24199 + 1.56126i) q^{34} +(-2.16677 + 5.54408i) q^{35} +(-1.78712 + 0.860634i) q^{36} +(-0.000631250 + 0.00160840i) q^{37} +(0.399798 - 5.33493i) q^{38} +(1.76120 + 0.543257i) q^{39} +(-1.33291 - 17.7865i) q^{40} +(0.180553 - 0.791054i) q^{41} +(-11.6295 - 5.58003i) q^{42} +(1.59526 + 6.98928i) q^{43} +(1.49860 - 0.462257i) q^{44} +(0.326267 + 0.831314i) q^{45} +(4.49395 + 4.16978i) q^{46} +(2.90310 + 1.97930i) q^{47} +20.2310 q^{48} +(-1.57712 - 6.82002i) q^{49} -0.163119 q^{50} +(2.07154 + 1.41235i) q^{51} +(-3.66313 - 3.39889i) q^{52} +(-2.61029 - 6.65092i) q^{53} +(12.1269 - 3.74066i) q^{54} +(-0.157117 - 0.688373i) q^{55} +(13.1013 + 16.3805i) q^{56} +(0.829471 - 3.63415i) q^{57} +(-1.68439 - 22.4767i) q^{58} +(8.66862 + 2.67391i) q^{59} +(1.54847 - 20.6629i) q^{60} +(3.88983 - 9.91114i) q^{61} +(21.4767 - 10.3427i) q^{62} +(-0.868569 - 0.590366i) q^{63} +(-11.6315 - 5.60142i) q^{64} +(-1.64923 + 1.53026i) q^{65} +(1.51297 - 0.228043i) q^{66} +(-0.0328337 + 0.0568696i) q^{67} +(-3.39884 - 5.88696i) q^{68} +(2.66323 + 3.33958i) q^{69} +(12.9968 - 8.88827i) q^{70} +(-9.85435 + 12.3570i) q^{71} +(3.11178 + 0.469025i) q^{72} +(0.628113 - 0.428240i) q^{73} +(0.00377631 - 0.00257464i) q^{74} +(-0.112386 - 0.0169395i) q^{75} +(-6.30134 + 7.90163i) q^{76} +(0.609484 + 0.563902i) q^{77} +(-3.03971 - 3.81168i) q^{78} +(-3.00006 - 5.19626i) q^{79} +(-12.3478 + 21.3871i) q^{80} +(9.92120 - 1.49538i) q^{81} +(-1.57336 + 1.45986i) q^{82} +(6.91466 + 3.32993i) q^{83} +(12.2138 + 21.0854i) q^{84} +(-2.75740 + 1.32789i) q^{85} +(6.92815 - 17.6526i) q^{86} +(1.17362 - 15.6609i) q^{87} +(-2.37754 - 0.733373i) q^{88} +(1.23621 + 16.4961i) q^{89} +(0.525659 - 2.30306i) q^{90} +(0.585054 - 2.58025i) q^{91} +(-2.57705 - 11.2908i) q^{92} +(15.8711 - 4.89559i) q^{93} +(-3.39558 - 8.65179i) q^{94} +(3.33555 + 3.09494i) q^{95} +(-20.0706 - 13.6839i) q^{96} -1.65603 q^{97} +(-6.71559 + 17.2557i) q^{98} +0.124575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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Database

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