LMFDB - Embedded newform 525.2.bg.a.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.13
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.337888 - 0.150438i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.24672 + 1.38463i) q^{4} +(-1.99129 - 1.01724i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 - 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.337888 - 0.150438i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.24672 + 1.38463i) q^{4} +(-1.99129 - 1.01724i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 - 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.825864 - 0.0441485i) q^{10} +(0.316215 - 3.00858i) q^{11} +(-0.194757 - 1.85299i) q^{12} +(-0.201783 + 0.146604i) q^{13} +(0.281163 - 0.937309i) q^{14} +(2.08839 - 0.799150i) q^{15} +(-0.334273 - 3.18040i) q^{16} +(4.92226 - 1.04626i) q^{17} +(-0.184932 - 0.320312i) q^{18} +(3.43641 + 3.81652i) q^{19} +(3.89108 - 1.48898i) q^{20} +(0.336292 + 2.62429i) q^{21} +(-0.345759 - 1.06414i) q^{22} +(0.653248 - 0.290845i) q^{23} +(-0.714431 - 1.23743i) q^{24} +(2.93045 + 4.05123i) q^{25} +(-0.0461254 + 0.0798915i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.626580 + 4.88958i) q^{28} +(-2.58817 - 7.96556i) q^{29} +(0.585419 - 0.584195i) q^{30} +(8.07108 - 1.71556i) q^{31} +(-2.02026 - 3.49919i) q^{32} +(2.02422 + 2.24813i) q^{33} +(1.50578 - 1.09401i) q^{34} +(-5.47587 + 2.23939i) q^{35} +(1.50736 + 1.09516i) q^{36} +(-0.770953 - 7.33513i) q^{37} +(1.73527 + 0.772592i) q^{38} +(0.0260712 - 0.248051i) q^{39} +(2.26159 - 2.25686i) q^{40} +(2.64381 - 1.92084i) q^{41} +(0.508421 + 0.836127i) q^{42} -2.20428 q^{43} +(3.77153 + 4.18871i) q^{44} +(-0.803520 + 2.08671i) q^{45} +(0.176971 - 0.196546i) q^{46} +(0.570388 + 0.121240i) q^{47} +(2.58717 + 1.87969i) q^{48} +(-1.04733 - 6.92121i) q^{49} +(1.59962 + 0.928013i) q^{50} +(-2.51611 + 4.35804i) q^{51} +(0.0485759 - 0.462169i) q^{52} +(-0.887199 + 0.985335i) q^{53} +(0.361782 + 0.0768992i) q^{54} +(-3.69012 + 5.66929i) q^{55} +(1.96413 + 3.23012i) q^{56} -5.13563 q^{57} +(-2.07283 - 2.30211i) q^{58} +(-6.10950 - 2.72013i) q^{59} +(-1.49712 + 3.88796i) q^{60} +(-2.01885 + 0.898848i) q^{61} +(2.46904 - 1.79386i) q^{62} +(-2.17525 - 1.50608i) q^{63} +(3.96530 + 2.88096i) q^{64} +(0.550939 - 0.0866691i) q^{65} +(1.02216 + 0.455097i) q^{66} +(-13.4899 + 2.86737i) q^{67} +(-4.68802 + 8.11990i) q^{68} +(-0.220968 + 0.680071i) q^{69} +(-1.51334 + 1.58044i) q^{70} +(-3.27981 - 10.0942i) q^{71} +(1.39764 + 0.297077i) q^{72} +(-1.11133 + 10.5736i) q^{73} +(-1.36398 - 2.36247i) q^{74} +(-4.97150 - 0.533051i) q^{75} -9.56870 q^{76} +(-5.48941 - 5.82472i) q^{77} +(-0.0285071 - 0.0877357i) q^{78} +(15.2031 + 3.23153i) q^{79} +(-2.56959 + 6.67312i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.604345 - 1.04676i) q^{82} +(4.42407 - 13.6159i) q^{83} +(-4.05293 - 2.80613i) q^{84} +(-10.8659 - 2.92371i) q^{85} +(-0.744801 + 0.331607i) q^{86} +(7.65139 + 3.40662i) q^{87} +(3.94883 + 1.75813i) q^{88} +(3.48518 - 1.55170i) q^{89} +(0.0424196 + 0.825954i) q^{90} +(-0.0540432 + 0.657680i) q^{91} +(-0.411708 + 1.26711i) q^{92} +(-4.12570 + 7.14591i) q^{93} +(0.210966 - 0.0448423i) q^{94} +(-2.96057 - 11.0954i) q^{95} +(3.95222 + 0.840071i) q^{96} +(0.963569 + 2.96556i) q^{97} +(-1.39509 - 2.18104i) q^{98} -3.02516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.337888	−	0.150438i	0.238923	−	0.106375i	−0.283782	−	0.958889i	$-0.591589\pi$
$2$	0.337888	−	0.150438i	0.238923	−	0.106375i	0.522706	+	0.852513i	$0.324923\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−1.24672	+	1.38463i	−0.623362	+	0.692314i
$5$	−1.99129	−	1.01724i	−0.890531	−	0.454923i
$5$	−1.99129	−	1.01724i	−0.890531	−	0.454923i
$6$	−0.114295	+	0.351762i	−0.0466605	+	0.143606i
$7$	1.72521	−	2.00591i	0.652066	−	0.758162i
$7$	1.72521	−	2.00591i	0.652066	−	0.758162i
$8$	−0.441543	+	1.35893i	−0.156109	+	0.480454i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.825864	−	0.0441485i	−0.261161	−	0.0139610i
$11$	0.316215	−	3.00858i	0.0953424	−	0.907122i	−0.837403	−	0.546586i	$-0.815927\pi$
$11$	0.316215	−	3.00858i	0.0953424	−	0.907122i	0.932745	−	0.360536i	$-0.117406\pi$
$12$	−0.194757	−	1.85299i	−0.0562216	−	0.534913i
$13$	−0.201783	+	0.146604i	−0.0559645	+	0.0406606i	−0.615416	−	0.788203i	$-0.711012\pi$
$13$	−0.201783	+	0.146604i	−0.0559645	+	0.0406606i	0.559451	+	0.828863i	$0.311012\pi$
$14$	0.281163	−	0.937309i	0.0751439	−	0.250506i
$15$	2.08839	−	0.799150i	0.539219	−	0.206340i
$16$	−0.334273	−	3.18040i	−0.0835683	−	0.795099i
$17$	4.92226	−	1.04626i	1.19382	−	0.253755i	0.432202	−	0.901777i	$-0.357737\pi$
$17$	4.92226	−	1.04626i	1.19382	−	0.253755i	0.761622	+	0.648022i	$0.224403\pi$
$18$	−0.184932	−	0.320312i	−0.0435890	−	0.0754983i
$19$	3.43641	+	3.81652i	0.788366	+	0.875569i	0.994690	−	0.102915i	$-0.0328169\pi$
$19$	3.43641	+	3.81652i	0.788366	+	0.875569i	−0.206324	+	0.978484i	$0.566150\pi$
$20$	3.89108	−	1.48898i	0.870073	−	0.332945i
$21$	0.336292	+	2.62429i	0.0733850	+	0.572667i
$22$	−0.345759	−	1.06414i	−0.0737160	−	0.226875i
$23$	0.653248	−	0.290845i	0.136212	−	0.0606453i	−0.337499	−	0.941326i	$-0.609581\pi$
$23$	0.653248	−	0.290845i	0.136212	−	0.0606453i	0.473711	+	0.880681i	$0.342914\pi$
$24$	−0.714431	−	1.23743i	−0.145833	−	0.252589i
$25$	2.93045	+	4.05123i	0.586090	+	0.810246i
$26$	−0.0461254	+	0.0798915i	−0.00904593	+	0.0156680i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.626580	+	4.88958i	0.118412	+	0.924044i
$29$	−2.58817	−	7.96556i	−0.480611	−	1.47917i	−0.838238	−	0.545304i	$-0.816414\pi$
$29$	−2.58817	−	7.96556i	−0.480611	−	1.47917i	0.357628	−	0.933864i	$-0.383586\pi$
$30$	0.585419	−	0.584195i	0.106882	−	0.106659i
$31$	8.07108	−	1.71556i	1.44961	−	0.308124i	0.585190	−	0.810896i	$-0.301020\pi$
$31$	8.07108	−	1.71556i	1.44961	−	0.308124i	0.864419	+	0.502773i	$0.167687\pi$
$32$	−2.02026	−	3.49919i	−0.357135	−	0.618576i
$33$	2.02422	+	2.24813i	0.352372	+	0.391349i
$34$	1.50578	−	1.09401i	0.258239	−	0.187622i
$35$	−5.47587	+	2.23939i	−0.925590	+	0.378527i
$36$	1.50736	+	1.09516i	0.251227	+	0.182527i
$37$	−0.770953	−	7.33513i	−0.126744	−	1.20589i	−0.854278	−	0.519816i	$-0.826000\pi$
$37$	−0.770953	−	7.33513i	−0.126744	−	1.20589i	0.727534	−	0.686072i	$-0.240666\pi$
$38$	1.73527	+	0.772592i	0.281498	+	0.125331i
$39$	0.0260712	−	0.248051i	0.00417474	−	0.0397200i
$40$	2.26159	−	2.25686i	0.357589	−	0.356841i
$41$	2.64381	−	1.92084i	0.412893	−	0.299984i	−0.361879	−	0.932225i	$-0.617865\pi$
$41$	2.64381	−	1.92084i	0.412893	−	0.299984i	0.774772	+	0.632241i	$0.217865\pi$
$42$	0.508421	+	0.836127i	0.0784511	+	0.129017i
$43$	−2.20428			−0.336150			−0.168075	−	0.985774i	$-0.553755\pi$
$43$	−2.20428			−0.336150			−0.168075	+	0.985774i	$0.553755\pi$
$44$	3.77153	+	4.18871i	0.568580	+	0.631472i
$45$	−0.803520	+	2.08671i	−0.119782	+	0.311068i
$46$	0.176971	−	0.196546i	0.0260929	−	0.0289791i
$47$	0.570388	+	0.121240i	0.0831996	+	0.0176846i	0.249323	−	0.968420i	$-0.419792\pi$
$47$	0.570388	+	0.121240i	0.0831996	+	0.0176846i	−0.166124	+	0.986105i	$0.553125\pi$
$48$	2.58717	+	1.87969i	0.373425	+	0.271309i
$49$	−1.04733	−	6.92121i	−0.149619	−	0.988744i
$50$	1.59962	+	0.928013i	0.226221	+	0.131241i
$51$	−2.51611	+	4.35804i	−0.352326	+	0.610247i
$52$	0.0485759	−	0.462169i	0.00673627	−	0.0640913i
$53$	−0.887199	+	0.985335i	−0.121866	+	0.135346i	−0.800990	−	0.598677i	$-0.795693\pi$
$53$	−0.887199	+	0.985335i	−0.121866	+	0.135346i	0.679124	+	0.734024i	$0.262360\pi$
$54$	0.361782	+	0.0768992i	0.0492323	+	0.0104647i
$55$	−3.69012	+	5.66929i	−0.497576	+	0.764447i
$56$	1.96413	+	3.23012i	0.262468	+	0.431644i
$57$	−5.13563			−0.680231
$58$	−2.07283	−	2.30211i	−0.272176	−	0.302282i
$59$	−6.10950	−	2.72013i	−0.795389	−	0.354130i	−0.0315217	−	0.999503i	$-0.510035\pi$
$59$	−6.10950	−	2.72013i	−0.795389	−	0.354130i	−0.763868	+	0.645373i	$0.776702\pi$
$60$	−1.49712	+	3.88796i	−0.193277	+	0.501933i
$61$	−2.01885	+	0.898848i	−0.258487	+	0.115086i	−0.531889	−	0.846814i	$-0.678518\pi$
$61$	−2.01885	+	0.898848i	−0.258487	+	0.115086i	0.273402	+	0.961900i	$0.411851\pi$
$62$	2.46904	−	1.79386i	0.313568	−	0.227821i
$63$	−2.17525	−	1.50608i	−0.274056	−	0.189748i
$64$	3.96530	+	2.88096i	0.495663	+	0.360120i
$65$	0.550939	−	0.0866691i	0.0683356	−	0.0107500i
$66$	1.02216	+	0.455097i	0.125820	+	0.0560186i
$67$	−13.4899	+	2.86737i	−1.64805	+	0.350305i	−0.936049	−	0.351870i	$-0.885546\pi$
$67$	−13.4899	+	2.86737i	−1.64805	+	0.350305i	−0.712005	+	0.702175i	$0.752213\pi$
$68$	−4.68802	+	8.11990i	−0.568506	+	0.984682i
$69$	−0.220968	+	0.680071i	−0.0266015	+	0.0818709i
$70$	−1.51334	+	1.58044i	−0.180879	+	0.188899i
$71$	−3.27981	−	10.0942i	−0.389242	−	1.19796i	−0.933356	−	0.358952i	$-0.883134\pi$
$71$	−3.27981	−	10.0942i	−0.389242	−	1.19796i	0.544115	−	0.839011i	$-0.316866\pi$
$72$	1.39764	+	0.297077i	0.164713	+	0.0350109i
$73$	−1.11133	+	10.5736i	−0.130072	+	1.23755i	0.713546	+	0.700608i	$0.247088\pi$
$73$	−1.11133	+	10.5736i	−0.130072	+	1.23755i	−0.843618	+	0.536943i	$0.819579\pi$
$74$	−1.36398	−	2.36247i	−0.158559	−	0.274632i
$75$	−4.97150	−	0.533051i	−0.574060	−	0.0615514i
$76$	−9.56870			−1.09761
$77$	−5.48941	−	5.82472i	−0.625576	−	0.663789i
$78$	−0.0285071	−	0.0877357i	−0.00322779	−	0.00993411i
$79$	15.2031	+	3.23153i	1.71049	+	0.363575i	0.956142	−	0.292904i	$-0.0946216\pi$
$79$	15.2031	+	3.23153i	1.71049	+	0.363575i	0.754344	+	0.656479i	$0.227955\pi$
$80$	−2.56959	+	6.67312i	−0.287289	+	0.746077i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.604345	−	1.04676i	0.0667387	−	0.115595i
$83$	4.42407	−	13.6159i	0.485605	−	1.49454i	−0.345498	−	0.938420i	$-0.612290\pi$
$83$	4.42407	−	13.6159i	0.485605	−	1.49454i	0.831103	−	0.556119i	$-0.187710\pi$
$84$	−4.05293	−	2.80613i	−0.442211	−	0.306174i
$85$	−10.8659	−	2.92371i	−1.17858	−	0.317121i
$86$	−0.744801	+	0.331607i	−0.0803139	+	0.0357581i
$87$	7.65139	+	3.40662i	0.820315	+	0.365228i
$88$	3.94883	+	1.75813i	0.420946	+	0.187417i
$89$	3.48518	−	1.55170i	0.369429	−	0.164480i	−0.213621	−	0.976917i	$-0.568526\pi$
$89$	3.48518	−	1.55170i	0.369429	−	0.164480i	0.583050	+	0.812436i	$0.301859\pi$
$90$	0.0424196	+	0.825954i	0.00447142	+	0.0870632i
$91$	−0.0540432	+	0.657680i	−0.00566526	+	0.0689436i
$92$	−0.411708	+	1.26711i	−0.0429236	+	0.132105i
$93$	−4.12570	+	7.14591i	−0.427815	+	0.740997i
$94$	0.210966	−	0.0448423i	0.0217595	−	0.00462513i
$95$	−2.96057	−	11.0954i	−0.303748	−	1.13837i
$96$	3.95222	+	0.840071i	0.403372	+	0.0857394i
$97$	0.963569	+	2.96556i	0.0978356	+	0.301107i	0.987982	−	0.154567i	$-0.0493982\pi$
$97$	0.963569	+	2.96556i	0.0978356	+	0.301107i	−0.890147	+	0.455674i	$0.849398\pi$
$98$	−1.39509	−	2.18104i	−0.140925	−	0.220318i
$99$	−3.02516			−0.304040
$100$	−9.26291	−	0.993180i	−0.926291	−	0.0993180i
$101$	4.35514	+	7.54333i	0.433353	+	0.750589i	0.997160	−	0.0753174i	$-0.0239970\pi$
$101$	4.35514	+	7.54333i	0.433353	+	0.750589i	−0.563807	+	0.825907i	$0.690664\pi$
$102$	−0.194553	+	1.85105i	−0.0192636	+	0.183281i
$103$	−9.25231	−	1.96664i	−0.911657	−	0.193779i	−0.271873	−	0.962333i	$-0.587643\pi$
$103$	−9.25231	−	1.96664i	−0.911657	−	0.193779i	−0.639784	+	0.768554i	$0.720976\pi$
$104$	−0.110128	−	0.338940i	−0.0107990	−	0.0332358i
$105$	1.99988	−	5.56781i	0.195168	−	0.543363i
$106$	−0.151543	+	0.466401i	−0.0147192	+	0.0453009i
$107$	3.98626	−	6.90440i	0.385366	−	0.667473i	−0.606454	−	0.795119i	$-0.707409\pi$
$107$	3.98626	−	6.90440i	0.385366	−	0.667473i	0.991820	+	0.127645i	$0.0407419\pi$
$108$	−1.82248	+	0.387381i	−0.175369	+	0.0372758i
$109$	12.1180	+	5.39527i	1.16069	+	0.516773i	0.894465	−	0.447138i	$-0.147557\pi$
$109$	12.1180	+	5.39527i	1.16069	+	0.516773i	0.266226	+	0.963911i	$0.414223\pi$
$110$	−0.393975	+	2.47072i	−0.0375640	+	0.235574i
$111$	5.96693	+	4.33523i	0.566356	+	0.411482i
$112$	−6.95627	−	4.81632i	−0.657306	−	0.455099i
$113$	−10.3090	+	7.48995i	−0.969792	+	0.704595i	−0.955404	−	0.295301i	$-0.904580\pi$
$113$	−10.3090	+	7.48995i	−0.969792	+	0.704595i	−0.0143880	+	0.999896i	$0.504580\pi$
$114$	−1.73527	+	0.772592i	−0.162523	+	0.0723598i
$115$	−1.59666	−	0.0853535i	−0.148890	−	0.00795925i
$116$	14.2561	+	6.34721i	1.32364	+	0.589324i
$117$	0.166893	+	0.185353i	0.0154293	+	0.0171359i
$118$	−2.47354			−0.227708
$119$	6.39321	−	11.6786i	0.586065	−	1.07058i
$120$	0.163875	+	3.19083i	0.0149597	+	0.291281i
$121$	1.80804	+	0.384311i	0.164367	+	0.0349374i
$122$	−0.546924	+	0.607421i	−0.0495162	+	0.0549933i
$123$	−0.341591	+	3.25002i	−0.0308002	+	0.293045i
$124$	−7.68700	+	13.3143i	−0.690313	+	1.19566i
$125$	−1.71431	−	11.0481i	−0.153332	−	0.988175i
$126$	−0.961563	−	0.181647i	−0.0856629	−	0.0161824i
$127$	−7.69553	−	5.59113i	−0.682868	−	0.496133i	0.191440	−	0.981504i	$-0.438684\pi$
$127$	−7.69553	−	5.59113i	−0.682868	−	0.496133i	−0.874308	+	0.485372i	$0.838684\pi$
$128$	9.67768	+	2.05706i	0.855394	+	0.181820i
$129$	1.47495	−	1.63810i	0.129862	−	0.144227i
$130$	0.173118	−	0.112166i	0.0151834	−	0.00983765i
$131$	12.8150	+	14.2325i	1.11965	+	1.24350i	0.966878	+	0.255239i	$0.0821541\pi$
$131$	12.8150	+	14.2325i	1.11965	+	1.24350i	0.152774	+	0.988261i	$0.451179\pi$
$132$	−5.63647			−0.490592
$133$	13.5841	−	0.308840i	1.17789	−	0.0267798i
$134$	−4.12672	+	2.99824i	−0.356494	+	0.259008i
$135$	−1.01307	−	1.99341i	−0.0871910	−	0.171566i
$136$	−0.751597	+	7.15097i	−0.0644489	+	0.613191i
$137$	−6.74451	−	3.00285i	−0.576223	−	0.256551i	0.0978682	−	0.995199i	$-0.468798\pi$
$137$	−6.74451	−	3.00285i	−0.576223	−	0.256551i	−0.674091	+	0.738649i	$0.735464\pi$
$138$	0.0276456	+	0.263030i	0.00235335	+	0.0223906i
$139$	−0.635975	−	0.462063i	−0.0539427	−	0.0391917i	0.560487	−	0.828163i	$-0.310614\pi$
$139$	−0.635975	−	0.462063i	−0.0539427	−	0.0391917i	−0.614430	+	0.788971i	$0.710614\pi$
$140$	3.72617	−	10.3739i	0.314919	−	0.876758i
$141$	−0.471762	+	0.342755i	−0.0397296	+	0.0288652i
$142$	−2.62676	−	2.91731i	−0.220433	−	0.244815i
$143$	0.377263	+	0.653439i	0.0315483	+	0.0546433i
$144$	−3.12803	+	0.664884i	−0.260669	+	0.0554070i
$145$	−2.94909	+	18.4945i	−0.244909	+	1.53589i
$146$	1.21517	+	3.73990i	0.100568	+	0.309516i
$147$	5.84426	+	3.85287i	0.482026	+	0.317779i
$148$	11.1176	+	8.07740i	0.913860	+	0.663958i
$149$	4.40067	−	7.62218i	0.360517	−	0.624433i	−0.627529	−	0.778593i	$-0.715934\pi$
$149$	4.40067	−	7.62218i	0.360517	−	0.624433i	0.988046	+	0.154160i	$0.0492670\pi$
$150$	−1.76000	+	0.567789i	−0.143704	+	0.0463598i
$151$	2.45605	+	4.25400i	0.199870	+	0.346185i	0.948486	−	0.316819i	$-0.102615\pi$
$151$	2.45605	+	4.25400i	0.199870	+	0.346185i	−0.748616	+	0.663004i	$0.769281\pi$
$152$	−6.70369	+	2.98468i	−0.543741	+	0.242089i
$153$	−1.55504	−	4.78593i	−0.125718	−	0.386920i
$154$	−2.73106	−	1.14229i	−0.220075	−	0.0920486i
$155$	−17.8170	−	4.79404i	−1.43109	−	0.385066i
$156$	0.310955	+	0.345350i	0.0248963	+	0.0276502i
$157$	0.169557	+	0.293682i	0.0135321	+	0.0234383i	0.872712	−	0.488235i	$-0.162359\pi$
$157$	0.169557	+	0.293682i	0.0135321	+	0.0234383i	−0.859180	+	0.511673i	$0.829026\pi$
$158$	5.62310	−	1.19523i	0.447350	−	0.0950872i
$159$	−0.138594	−	1.31864i	−0.0109912	−	0.104575i
$160$	0.463405	+	9.02298i	0.0366354	+	0.713330i
$161$	0.543579	−	1.81212i	0.0428401	−	0.142815i
$162$	−0.299227	+	0.217401i	−0.0235095	+	0.0170806i
$163$	−0.666243	−	6.33888i	−0.0521842	−	0.496500i	−0.989132	−	0.147030i	$-0.953029\pi$
$163$	−0.666243	−	6.33888i	−0.0521842	−	0.496500i	0.936948	−	0.349469i	$-0.113638\pi$
$164$	−0.636452	+	6.05544i	−0.0496986	+	0.472850i
$165$	−1.74393	−	6.53579i	−0.135765	−	0.508810i
$166$	−0.553500	−	5.26620i	−0.0429599	−	0.408736i
$167$	−6.25583	+	19.2535i	−0.484090	+	1.48988i	0.349204	+	0.937047i	$0.386452\pi$
$167$	−6.25583	+	19.2535i	−0.484090	+	1.48988i	−0.833294	+	0.552830i	$0.813548\pi$
$168$	−3.71471	−	0.701740i	−0.286596	−	0.0541404i
$169$	−3.99800	+	12.3046i	−0.307538	+	0.946505i
$170$	−4.11131	+	0.646757i	−0.315323	+	0.0496040i
$171$	3.43641	−	3.81652i	0.262789	−	0.291856i
$172$	2.74813	−	3.05211i	0.209543	−	0.232721i
$173$	−10.9122	+	4.85842i	−0.829639	+	0.369379i	−0.777207	−	0.629246i	$-0.783364\pi$
$173$	−10.9122	+	4.85842i	−0.829639	+	0.369379i	−0.0524321	+	0.998624i	$0.516697\pi$
$174$	3.09780			0.234844
$175$	13.1820	+	1.11099i	0.996467	+	0.0839826i
$176$	−9.67419			−0.729219
$177$	6.10950	−	2.72013i	0.459218	−	0.204457i
$178$	0.944168	−	1.04860i	0.0707684	−	0.0785963i
$179$	7.89363	−	8.76676i	0.589998	−	0.655259i	−0.372027	−	0.928222i	$-0.621337\pi$
$179$	7.89363	−	8.76676i	0.589998	−	0.655259i	0.962024	+	0.272963i	$0.0880038\pi$
$180$	−1.88755	−	3.71413i	−0.140689	−	0.276835i
$181$	2.32295	−	7.14930i	0.172663	−	0.531403i	−0.826856	−	0.562414i	$-0.809873\pi$
$181$	2.32295	−	7.14930i	0.172663	−	0.531403i	0.999519	+	0.0310110i	$0.00987269\pi$
$182$	0.0806792	+	0.230353i	0.00598034	+	0.0170749i
$183$	0.682897	−	2.10174i	0.0504812	−	0.155365i
$184$	0.106800	+	1.01614i	0.00787343	+	0.0749107i
$185$	−5.92639	+	15.3906i	−0.435717	+	1.13154i
$186$	−0.319010	+	3.03518i	−0.0233910	+	0.222550i
$187$	−1.59127	−	15.1399i	−0.116365	−	1.10714i
$188$	−0.878988	+	0.638622i	−0.0641068	+	0.0465763i
$189$	2.57476	−	0.608763i	0.187286	−	0.0442810i
$190$	−2.66951	−	3.30363i	−0.193667	−	0.239671i
$191$	−1.75316	−	16.6802i	−0.126854	−	1.20694i	−0.853933	−	0.520383i	$-0.825789\pi$
$191$	−1.75316	−	16.6802i	−0.126854	−	1.20694i	0.727079	−	0.686554i	$-0.240878\pi$
$192$	−4.79428	+	1.01905i	−0.345997	+	0.0735439i
$193$	5.55806	+	9.62685i	0.400078	+	0.692956i	0.993735	−	0.111763i	$-0.0356496\pi$
$193$	5.55806	+	9.62685i	0.400078	+	0.692956i	−0.593657	+	0.804718i	$0.702316\pi$
$194$	0.771711	+	0.857071i	0.0554056	+	0.0615341i
$195$	−0.304242	+	0.467421i	−0.0217873	+	0.0334727i
$196$	10.8890	+	7.17867i	0.777788	+	0.512762i
$197$	5.51769	+	16.9817i	0.393119	+	1.20990i	0.930417	+	0.366504i	$0.119445\pi$
$197$	5.51769	+	16.9817i	0.393119	+	1.20990i	−0.537297	+	0.843393i	$0.680555\pi$
$198$	−1.02216	+	0.455097i	−0.0726421	+	0.0323423i
$199$	−7.10732	−	12.3102i	−0.503825	−	0.872650i	−0.999990	−	0.00442211i	$-0.998592\pi$
$199$	−7.10732	−	12.3102i	−0.503825	−	0.872650i	0.496165	−	0.868228i	$-0.334741\pi$
$200$	−6.79925	+	2.19348i	−0.480779	+	0.155103i
$201$	6.89564	−	11.9436i	0.486381	−	0.842436i
$202$	2.60635	+	1.89363i	0.183382	+	0.133235i
$203$	−20.4433	−	8.55061i	−1.43484	−	0.600135i
$204$	−2.89736	−	8.91715i	−0.202856	−	0.624326i
$205$	−7.21853	+	1.13556i	−0.504164	+	0.0793108i
$206$	−3.42210	+	0.727391i	−0.238429	+	0.0506797i
$207$	−0.357535	−	0.619268i	−0.0248504	−	0.0430421i
$208$	0.533709	+	0.592744i	0.0370061	+	0.0410994i
$209$	12.5689	−	9.13188i	0.869412	−	0.631665i
$210$	−0.161873	−	2.18215i	−0.0111703	−	0.150583i
$211$	−21.1961	−	15.3999i	−1.45920	−	1.06017i	−0.983570	−	0.180526i	$-0.942220\pi$
$211$	−21.1961	−	15.3999i	−1.45920	−	1.06017i	−0.475630	−	0.879645i	$-0.657780\pi$
$212$	−0.258229	−	2.45688i	−0.0177352	−	0.168739i
$213$	9.69608	+	4.31697i	0.664365	+	0.295794i
$214$	0.308229	−	2.93260i	0.0210701	−	0.200468i
$215$	4.38936	+	2.24228i	0.299352	+	0.152922i
$216$	−1.15597	+	0.839864i	−0.0786540	+	0.0571455i
$217$	10.4830	−	19.1495i	0.711633	−	1.29996i
$218$	4.90617			0.332288
$219$	−7.11412	−	7.90103i	−0.480728	−	0.533902i
$220$	−3.24929	−	12.1775i	−0.219067	−	0.821006i
$221$	−0.839843	+	0.932740i	−0.0564940	+	0.0627429i
$222$	2.66834	+	0.567173i	0.179087	+	0.0380661i
$223$	18.5531	+	13.4796i	1.24241	+	0.902661i	0.997756	−	0.0669509i	$-0.0213271\pi$
$223$	18.5531	+	13.4796i	1.24241	+	0.902661i	0.244650	+	0.969612i	$0.421327\pi$
$224$	−10.5044	−	1.98437i	−0.701856	−	0.132586i
$225$	3.72272	−	3.33787i	0.248181	−	0.222524i
$226$	−2.35653	+	4.08163i	−0.156754	+	0.271506i
$227$	−1.00512	+	9.56308i	−0.0667122	+	0.634724i	0.909170	+	0.416425i	$0.136717\pi$
$227$	−1.00512	+	9.56308i	−0.0667122	+	0.634724i	−0.975882	+	0.218299i	$0.929949\pi$
$228$	6.40271	−	7.11093i	0.424030	−	0.470933i
$229$	20.8456	+	4.43087i	1.37752	+	0.292800i	0.836387	−	0.548140i	$-0.184664\pi$
$229$	20.8456	+	4.43087i	1.37752	+	0.292800i	0.541129	+	0.840940i	$0.317997\pi$
$230$	−0.552334	+	0.211358i	−0.0364198	+	0.0139365i
$231$	8.00174	−	0.181923i	0.526476	−	0.0119697i
$232$	11.9674			0.785699
$233$	6.42337	+	7.13388i	0.420809	+	0.467356i	0.915854	−	0.401511i	$-0.131515\pi$
$233$	6.42337	+	7.13388i	0.420809	+	0.467356i	−0.495045	+	0.868867i	$0.664848\pi$
$234$	0.0842753	+	0.0375218i	0.00550925	+	0.00245287i
$235$	−1.01248	−	0.821643i	−0.0660467	−	0.0535981i
$236$	11.3832	−	5.06814i	0.740985	−	0.329908i
$237$	−12.5744	+	9.13582i	−0.816793	+	0.593435i
$238$	0.403290	−	4.90785i	0.0261414	−	0.318129i
$239$	8.59024	+	6.24118i	0.555657	+	0.403708i	0.829867	−	0.557962i	$-0.188416\pi$
$239$	8.59024	+	6.24118i	0.555657	+	0.403708i	−0.274210	+	0.961670i	$0.588416\pi$
$240$	−3.23970	−	6.37476i	−0.209122	−	0.411489i
$241$	11.7025	+	5.21029i	0.753824	+	0.335624i	0.747417	−	0.664356i	$-0.231294\pi$
$241$	11.7025	+	5.21029i	0.753824	+	0.335624i	0.00640704	+	0.999979i	$0.497961\pi$
$242$	0.668731	−	0.142143i	0.0429877	−	0.00913731i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.27237	−	3.91597i	0.0814554	−	0.250694i
$245$	−4.95498	+	14.8475i	−0.316562	+	0.948572i
$246$	0.373506	+	1.14953i	0.0238139	+	0.0732915i
$247$	−1.25292	−	0.266317i	−0.0797217	−	0.0169454i
$248$	−1.23240	+	11.7255i	−0.0782575	+	0.744571i
$249$	7.15830	+	12.3985i	0.453639	+	0.785725i
$250$	−2.24130	−	3.47514i	−0.141752	−	0.219787i
$251$	10.9005			0.688035			0.344017	−	0.938963i	$-0.388212\pi$
$251$	10.9005			0.688035			0.344017	+	0.938963i	$0.388212\pi$
$252$	4.79730	−	1.13425i	0.302201	−	0.0714509i
$253$	−0.668464	−	2.05732i	−0.0420260	−	0.129343i
$254$	−3.44135	−	0.731481i	−0.215929	−	0.0458972i
$255$	9.44347	−	6.11862i	0.591373	−	0.383163i
$256$	−6.00912	+	1.27728i	−0.375570	+	0.0798298i
$257$	4.13610	−	7.16394i	0.258003	−	0.446874i	−0.707704	−	0.706509i	$-0.750269\pi$
$257$	4.13610	−	7.16394i	0.258003	−	0.446874i	0.965707	+	0.259635i	$0.0836022\pi$
$258$	0.251937	−	0.775383i	0.0156849	−	0.0482732i
$259$	−16.0436	−	11.1081i	−0.996904	−	0.690227i
$260$	−0.566865	+	0.870898i	−0.0351554	+	0.0540108i
$261$	−7.65139	+	3.40662i	−0.473609	+	0.210864i
$262$	6.47115	+	2.88114i	0.399789	+	0.177997i
$263$	−15.6239	−	6.95622i	−0.963413	−	0.428939i	−0.136109	−	0.990694i	$-0.543460\pi$
$263$	−15.6239	−	6.95622i	−0.963413	−	0.428939i	−0.827304	+	0.561755i	$0.810126\pi$
$264$	−3.94883	+	1.75813i	−0.243033	+	0.108205i
$265$	2.76899	−	1.05959i	0.170098	−	0.0650902i
$266$	4.54344	−	2.14791i	0.278576	−	0.131697i
$267$	−1.17890	+	3.62829i	−0.0721476	+	0.222048i
$268$	12.8480	−	22.2533i	0.784813	−	1.35934i
$269$	−12.8066	+	2.72212i	−0.780830	+	0.165971i	−0.581048	−	0.813870i	$-0.697357\pi$
$269$	−12.8066	+	2.72212i	−0.780830	+	0.165971i	−0.199783	+	0.979840i	$0.564024\pi$
$270$	−0.642188	−	0.521147i	−0.0390823	−	0.0317160i
$271$	−17.6644	−	3.75468i	−1.07304	−	0.228081i	−0.362673	−	0.931916i	$-0.618136\pi$
$271$	−17.6644	−	3.75468i	−1.07304	−	0.228081i	−0.710363	+	0.703836i	$0.751469\pi$
$272$	−4.97290	−	15.3050i	−0.301526	−	0.928002i
$273$	−0.452590	−	0.480236i	−0.0273920	−	0.0290652i
$274$	−2.73063			−0.164964
$275$	13.1151	−	7.53545i	0.790871	−	0.454405i
$276$	−0.666158	−	1.15382i	−0.0400980	−	0.0694518i
$277$	0.934919	−	8.89516i	0.0561738	−	0.534458i	−0.929860	−	0.367913i	$-0.880072\pi$
$277$	0.934919	−	8.89516i	0.0561738	−	0.534458i	0.986034	−	0.166545i	$-0.0532611\pi$
$278$	−0.284400	−	0.0604511i	−0.0170572	−	0.00362562i
$279$	−2.54982	−	7.84754i	−0.152654	−	0.469820i
$280$	−0.625347	−	8.43010i	−0.0373717	−	0.503795i
$281$	−8.31286	+	25.5844i	−0.495904	+	1.52623i	0.319640	+	0.947539i	$0.396438\pi$
$281$	−8.31286	+	25.5844i	−0.495904	+	1.52623i	−0.815544	+	0.578696i	$0.803562\pi$
$282$	−0.107840	+	0.186784i	−0.00642176	+	0.0111228i
$283$	1.84050	−	0.391210i	0.109406	−	0.0232550i	−0.152883	−	0.988244i	$-0.548856\pi$
$283$	1.84050	−	0.391210i	0.109406	−	0.0232550i	0.262289	+	0.964989i	$0.415522\pi$
$284$	18.0657	+	8.04338i	1.07200	+	0.477287i
$285$	10.2265	+	5.22416i	0.605766	+	0.309452i
$286$	0.225775	+	0.164035i	0.0133503	+	0.00969959i
$287$	0.708085	−	8.61707i	0.0417970	−	0.508649i
$288$	−3.26885	+	2.37496i	−0.192619	+	0.139946i
$289$	7.60374	−	3.38540i	0.447279	−	0.199141i
$290$	1.78581	+	6.69273i	0.104866	+	0.393011i
$291$	−2.84859	−	1.26828i	−0.166988	−	0.0743477i
$292$	−13.2550	−	14.7212i	−0.775692	−	0.861493i
$293$	−19.3698			−1.13159			−0.565797	−	0.824545i	$-0.691431\pi$
$293$	−19.3698			−1.13159			−0.565797	+	0.824545i	$0.691431\pi$
$294$	2.55432	+	0.422644i	0.148971	+	0.0246491i
$295$	9.39876	+	11.6314i	0.547217	+	0.677205i
$296$	10.3083	+	2.19110i	0.599159	+	0.127355i
$297$	2.02422	−	2.24813i	0.117457	−	0.130450i
$298$	0.340272	−	3.23747i	0.0197114	−	0.187542i
$299$	−0.0891754	+	0.154456i	−0.00515714	+	0.00893244i
$300$	6.93617	−	6.21911i	0.400460	−	0.359061i
$301$	−3.80284	+	4.42158i	−0.219192	+	0.254856i
$302$	1.46983	+	1.06789i	0.0845792	+	0.0614504i
$303$	−8.51995	−	1.81097i	−0.489458	−	0.104038i
$304$	10.9893	−	12.2049i	0.630282	−	0.699999i
$305$	4.93445	+	0.263783i	0.282546	+	0.0151042i
$306$	−1.24542	−	1.38317i	−0.0711957	−	0.0790708i
$307$	−9.12753			−0.520936			−0.260468	−	0.965483i	$-0.583877\pi$
$307$	−9.12753			−0.520936			−0.260468	+	0.965483i	$0.583877\pi$
$308$	14.9088	−	0.338959i	0.849510	−	0.0193140i
$309$	7.65250	−	5.55987i	0.435336	−	0.316290i
$310$	−6.74135	+	1.06049i	−0.382883	+	0.0602320i
$311$	0.475060	−	4.51989i	0.0269382	−	0.256300i	−0.972762	−	0.231807i	$-0.925536\pi$
$311$	0.475060	−	4.51989i	0.0269382	−	0.256300i	0.999700	−	0.0244928i	$-0.00779707\pi$
$312$	0.325572	+	0.144954i	0.0184319	+	0.00820641i
$313$	−0.311240	−	2.96125i	−0.0175923	−	0.167380i	0.982198	−	0.187848i	$-0.0601511\pi$
$313$	−0.311240	−	2.96125i	−0.0175923	−	0.167380i	−0.999791	+	0.0204679i	$0.993484\pi$
$314$	0.101472	+	0.0737238i	0.00572640	+	0.00416048i
$315$	2.79951	+	5.21179i	0.157735	+	0.293651i
$316$	−23.4286	+	17.0219i	−1.31796	+	0.957554i
$317$	21.0170	+	23.3418i	1.18044	+	1.31101i	0.940332	+	0.340259i	$0.110515\pi$
$317$	21.0170	+	23.3418i	1.18044	+	1.31101i	0.240103	+	0.970747i	$0.422819\pi$
$318$	−0.245202	−	0.424702i	−0.0137502	−	0.0238161i
$319$	−24.7835	+	5.26789i	−1.38761	+	0.294945i
$320$	−4.96543	−	9.77048i	−0.277576	−	0.546186i
$321$	2.46364	+	7.58231i	0.137507	+	0.423203i
$322$	−0.0889422	−	0.694070i	−0.00495655	−	0.0386790i
$323$	20.9080	+	15.1905i	1.16335	+	0.845223i
$324$	0.931600	−	1.61358i	0.0517556	−	0.0896433i
$325$	−1.18524	−	0.387853i	−0.0657454	−	0.0215142i
$326$	−1.17872	−	2.04161i	−0.0652834	−	0.113074i
$327$	−12.1180	+	5.39527i	−0.670125	+	0.298359i
$328$	1.44293	+	4.44087i	0.0796723	+	0.245206i
$329$	1.22723	−	0.934982i	0.0676594	−	0.0515472i
$330$	−1.57248	−	1.94601i	−0.0865623	−	0.107125i
$331$	−8.62703	−	9.58129i	−0.474184	−	0.526635i	0.457838	−	0.889036i	$-0.348624\pi$
$331$	−8.62703	−	9.58129i	−0.474184	−	0.526635i	−0.932022	+	0.362400i	$0.881957\pi$
$332$	13.3373	+	23.1010i	0.731982	+	1.26783i
$333$	−7.21436	+	1.53346i	−0.395345	+	0.0840331i
$334$	0.782672	+	7.44663i	0.0428259	+	0.407461i
$335$	29.7791	+	8.01269i	1.62700	+	0.437780i
$336$	8.23387	−	1.94677i	0.449195	−	0.106205i
$337$	3.29572	−	2.39448i	0.179529	−	0.130436i	−0.494391	−	0.869240i	$-0.664609\pi$
$337$	3.29572	−	2.39448i	0.179529	−	0.130436i	0.673921	+	0.738804i	$0.264609\pi$
$338$	0.500193	+	4.75902i	0.0272069	+	0.258857i
$339$	1.33197	−	12.6729i	0.0723427	−	0.688295i
$340$	17.5951	−	11.4002i	0.954227	−	0.618263i
$341$	−2.60921	−	24.8250i	−0.141297	−	1.34435i
$342$	0.586974	−	1.80652i	0.0317399	−	0.0976855i
$343$	−15.6902	−	9.83965i	−0.847189	−	0.531291i
$344$	0.973284	−	2.99546i	0.0524759	−	0.161504i
$345$	1.13181	−	1.12944i	0.0609344	−	0.0608070i
$346$	−2.95621	+	3.28321i	−0.158927	+	0.176506i
$347$	−11.1758	+	12.4120i	−0.599951	+	0.666313i	−0.964258	−	0.264966i	$-0.914639\pi$
$347$	−11.1758	+	12.4120i	−0.599951	+	0.666313i	0.364307	+	0.931279i	$0.381306\pi$
$348$	−14.2561	+	6.34721i	−0.764206	+	0.340246i
$349$	14.9074			0.797976			0.398988	−	0.916956i	$-0.369361\pi$
$349$	14.9074			0.797976			0.398988	+	0.916956i	$0.369361\pi$
$350$	4.62119	−	1.60768i	0.247013	−	0.0859342i
$351$	−0.249417			−0.0133129
$352$	−11.1664	+	4.97162i	−0.595174	+	0.264988i
$353$	−1.26418	+	1.40401i	−0.0672853	+	0.0747279i	−0.775848	−	0.630920i	$-0.782677\pi$
$353$	−1.26418	+	1.40401i	−0.0672853	+	0.0747279i	0.708562	+	0.705648i	$0.249344\pi$
$354$	1.65512	−	1.83820i	0.0879686	−	0.0976991i
$355$	−3.73718	+	23.4368i	−0.198349	+	1.24390i
$356$	−2.19653	+	6.76023i	−0.116416	+	0.358291i
$357$	4.40101	+	12.5656i	0.232926	+	0.665042i
$358$	1.34831	−	4.14969i	0.0712606	−	0.219318i
$359$	−2.29623	−	21.8471i	−0.121190	−	1.15305i	−0.870962	−	0.491351i	$-0.836503\pi$
$359$	−2.29623	−	21.8471i	−0.121190	−	1.15305i	0.749772	−	0.661697i	$-0.230163\pi$
$360$	−2.48090	−	2.01330i	−0.130755	−	0.106110i
$361$	−0.770865	+	7.33429i	−0.0405718	+	0.386015i
$362$	−0.290626	−	2.76512i	−0.0152750	−	0.145332i
$363$	−1.49541	+	1.08648i	−0.0784889	+	0.0570255i
$364$	−0.843265	−	0.894775i	−0.0441991	−	0.0468990i
$365$	12.9689	−	19.9247i	0.678823	−	1.04290i
$366$	−0.0854379	−	0.812888i	−0.00446591	−	0.0424903i
$367$	33.5497	−	7.13121i	1.75128	−	0.372246i	0.782983	−	0.622043i	$-0.213697\pi$
$367$	33.5497	−	7.13121i	1.75128	−	0.372246i	0.968298	+	0.249797i	$0.0803638\pi$
$368$	−1.14336	−	1.98037i	−0.0596020	−	0.103234i
$369$	−2.18667	−	2.42854i	−0.113833	−	0.126425i
$370$	0.312867	+	6.09185i	0.0162652	+	0.316700i
$371$	0.445889	+	3.47955i	0.0231494	+	0.180649i
$372$	−4.75082	−	14.6215i	−0.246319	−	0.758091i
$373$	30.3248	−	13.5015i	1.57016	−	0.699080i	0.577098	−	0.816675i	$-0.304185\pi$
$373$	30.3248	−	13.5015i	1.57016	−	0.699080i	0.993062	+	0.117595i	$0.0375185\pi$
$374$	−2.81528	−	4.87620i	−0.145574	−	0.252142i
$375$	9.35745	+	6.11866i	0.483217	+	0.315966i
$376$	−0.416606	+	0.721583i	−0.0214848	+	0.0372128i
$377$	1.69003	+	1.22788i	0.0870410	+	0.0632390i
$378$	0.778402	−	0.593035i	0.0400367	−	0.0305024i
$379$	−6.12153	−	18.8401i	−0.314442	−	0.967752i	−0.975984	−	0.217844i	$-0.930098\pi$
$379$	−6.12153	−	18.8401i	−0.314442	−	0.967752i	0.661542	−	0.749908i	$-0.269902\pi$
$380$	19.0540	+	9.73365i	0.977452	+	0.499326i
$381$	9.30433	−	1.97770i	0.476676	−	0.101321i
$382$	−3.10170	−	5.37231i	−0.158697	−	0.274871i
$383$	−15.0650	−	16.7314i	−0.769788	−	0.854936i	0.223000	−	0.974818i	$-0.428415\pi$
$383$	−15.0650	−	16.7314i	−0.769788	−	0.854936i	−0.992788	+	0.119882i	$0.961748\pi$
$384$	−8.00432	+	5.81548i	−0.408469	+	0.296770i
$385$	5.00585	+	17.1827i	0.255122	+	0.875713i
$386$	3.32625	+	2.41666i	0.169301	+	0.123005i
$387$	0.230410	+	2.19220i	0.0117124	+	0.111436i
$388$	−5.30750	−	2.36305i	−0.269448	−	0.119966i
$389$	−2.87439	+	27.3480i	−0.145737	+	1.38660i	0.640160	+	0.768242i	$0.278868\pi$
$389$	−2.87439	+	27.3480i	−0.145737	+	1.38660i	−0.785897	+	0.618357i	$0.787799\pi$
$390$	−0.0324824	+	0.203705i	−0.00164481	+	0.0103150i
$391$	2.91116	−	2.11508i	0.147224	−	0.106964i
$392$	9.86786	+	1.63276i	0.498402	+	0.0824667i
$393$	−19.1517			−0.966077
$394$	4.41905	+	4.90785i	0.222629	+	0.247254i
$395$	−26.9866	−	21.9001i	−1.35784	−	1.10191i
$396$	3.77153	−	4.18871i	0.189527	−	0.210491i
$397$	−7.31544	−	1.55495i	−0.367152	−	0.0780405i	0.0206415	−	0.999787i	$-0.493429\pi$
$397$	−7.31544	−	1.55495i	−0.367152	−	0.0780405i	−0.387793	+	0.921746i	$0.626762\pi$
$398$	−4.25340	−	3.09028i	−0.213204	−	0.154902i
$399$	−8.86002	+	10.3016i	−0.443556	+	0.515725i
$400$	11.9049	−	10.6742i	0.595247	−	0.533711i
$401$	−4.68393	+	8.11280i	−0.233904	+	0.405134i	−0.958954	−	0.283563i	$-0.908484\pi$
$401$	−4.68393	+	8.11280i	−0.233904	+	0.405134i	0.725049	+	0.688697i	$0.241817\pi$
$402$	0.533190	−	5.07296i	0.0265931	−	0.253016i
$403$	−1.37710	+	1.52942i	−0.0685982	+	0.0761860i
$404$	−15.8744	−	3.37420i	−0.789779	−	0.167873i
$405$	2.15927	+	0.580997i	0.107295	+	0.0288700i
$406$	−8.19389	+	0.186292i	−0.406656	+	0.00924550i
$407$	−22.3121			−1.10597
$408$	−4.81129	−	5.34348i	−0.238194	−	0.264542i
$409$	28.7708	+	12.8096i	1.42263	+	0.633393i	0.966534	−	0.256539i	$-0.0825824\pi$
$409$	28.7708	+	12.8096i	1.42263	+	0.633393i	0.456091	+	0.889933i	$0.349249\pi$
$410$	−2.26822	+	1.46963i	−0.112020	+	0.0725798i
$411$	6.74451	−	3.00285i	0.332682	−	0.148120i
$412$	14.2581	−	10.3591i	0.702448	−	0.510358i
$413$	−15.9965	+	7.56232i	−0.787135	+	0.372117i
$414$	−0.213968	−	0.155457i	−0.0105159	−	0.00764028i
$415$	−22.6602	+	22.6128i	−1.11235	+	1.11002i
$416$	0.920649	+	0.409900i	0.0451386	+	0.0200970i
$417$	0.768930	−	0.163441i	0.0376547	−	0.00800375i
$418$	2.87312	−	4.97640i	0.140529	−	0.243404i
$419$	−6.22040	+	19.1444i	−0.303887	+	0.935267i	0.676204	+	0.736715i	$0.263624\pi$
$419$	−6.22040	+	19.1444i	−0.303887	+	0.935267i	−0.980090	+	0.198552i	$0.936376\pi$
$420$	5.21605	+	9.71061i	0.254517	+	0.473829i
$421$	−7.97680	−	24.5501i	−0.388765	−	1.19650i	−0.933712	−	0.358026i	$-0.883450\pi$
$421$	−7.97680	−	24.5501i	−0.388765	−	1.19650i	0.544947	−	0.838471i	$-0.316550\pi$
$422$	−9.47864	−	2.01475i	−0.461413	−	0.0980763i
$423$	0.0609537	−	0.579936i	0.00296367	−	0.0281974i
$424$	−0.947263	−	1.64071i	−0.0460032	−	0.0796798i
$425$	18.6631	+	16.8752i	0.905293	+	0.818567i
$426$	3.92563			0.190197
$427$	−1.67992	+	5.60032i	−0.0812969	+	0.271018i
$428$	4.59026	+	14.1274i	0.221878	+	0.682872i
$429$	−0.738038	−	0.156875i	−0.0356328	−	0.00757399i
$430$	1.82043	+	0.0973157i	0.0877892	+	0.00469298i
$431$	−12.5488	+	2.66732i	−0.604452	+	0.128480i	−0.499965	−	0.866046i	$-0.666654\pi$
$431$	−12.5488	+	2.66732i	−0.604452	+	0.128480i	−0.104488	+	0.994526i	$0.533320\pi$
$432$	1.59896	−	2.76948i	0.0769299	−	0.133246i
$433$	5.88280	−	18.1054i	0.282709	−	0.870090i	−0.704367	−	0.709836i	$-0.748769\pi$
$433$	5.88280	−	18.1054i	0.282709	−	0.870090i	0.987076	−	0.160253i	$-0.0512311\pi$
$434$	0.661278	−	8.04744i	0.0317424	−	0.386290i
$435$	−11.7708	−	14.5668i	−0.564365	−	0.698427i
$436$	−22.5782	+	10.0525i	−1.08130	+	0.481426i
$437$	3.35484	+	1.49367i	0.160484	+	0.0714520i
$438$	−3.59239	−	1.59944i	−0.171651	−	0.0764240i
$439$	19.1476	−	8.52507i	0.913866	−	0.406879i	0.104730	−	0.994501i	$-0.466602\pi$
$439$	19.1476	−	8.52507i	0.913866	−	0.406879i	0.809136	+	0.587621i	$0.199935\pi$
$440$	−6.07481	−	7.51784i	−0.289605	−	0.358399i
$441$	−6.77382	+	1.76506i	−0.322563	+	0.0840504i
$442$	−0.143454	+	0.441506i	−0.00682341	+	0.0210003i
$443$	−2.72267	+	4.71581i	−0.129358	+	0.224055i	−0.923428	−	0.383772i	$-0.874625\pi$
$443$	−2.72267	+	4.71581i	−0.129358	+	0.224055i	0.794070	+	0.607826i	$0.207958\pi$
$444$	−13.4418	+	2.85714i	−0.637919	+	0.135594i
$445$	−8.51845	−	0.455374i	−0.403813	−	0.0215868i
$446$	8.29671	+	1.76352i	0.392860	+	0.0835051i
$447$	2.71976	+	8.37057i	0.128640	+	0.395914i
$448$	12.6199	−	2.98378i	0.596234	−	0.140970i
$449$	12.5379			0.591698			0.295849	−	0.955235i	$-0.404397\pi$
$449$	12.5379			0.591698			0.295849	+	0.955235i	$0.404397\pi$
$450$	0.755723	−	1.68786i	0.0356251	−	0.0795666i
$451$	−4.94299	−	8.56151i	−0.232756	−	0.403146i
$452$	2.48173	−	23.6121i	0.116731	−	1.11062i
$453$	−4.80475	−	1.02128i	−0.225747	−	0.0479840i
$454$	1.09903	+	3.38246i	0.0515800	+	0.158747i
$455$	0.776633	−	1.25466i	0.0364091	−	0.0588191i
$456$	2.26760	−	6.97895i	0.106190	−	0.326819i
$457$	−11.3222	+	19.6107i	−0.529631	+	0.917348i	0.469772	+	0.882788i	$0.344336\pi$
$457$	−11.3222	+	19.6107i	−0.529631	+	0.917348i	−0.999403	+	0.0345599i	$0.988997\pi$
$458$	7.71005	−	1.63882i	0.360267	−	0.0765771i
$459$	4.59717	+	2.04679i	0.214578	+	0.0955361i
$460$	2.10878	−	2.10437i	0.0983224	−	0.0981168i
$461$	−23.6378	−	17.1738i	−1.10092	−	0.799866i	−0.119711	−	0.992809i	$-0.538197\pi$
$461$	−23.6378	−	17.1738i	−1.10092	−	0.799866i	−0.981210	+	0.192943i	$0.938197\pi$
$462$	2.67633	−	1.26523i	0.124514	−	0.0588639i
$463$	−7.30426	+	5.30686i	−0.339458	+	0.246631i	−0.744433	−	0.667697i	$-0.767280\pi$
$463$	−7.30426	+	5.30686i	−0.339458	+	0.246631i	0.404975	+	0.914328i	$0.367280\pi$
$464$	−24.4685	+	10.8941i	−1.13592	+	0.505745i
$465$	15.4845	−	10.0328i	0.718079	−	0.465258i
$466$	3.24359	+	1.44414i	0.150256	+	0.0668984i
$467$	10.9481	+	12.1591i	0.506619	+	0.562657i	0.941145	−	0.338002i	$-0.109751\pi$
$467$	10.9481	+	12.1591i	0.506619	+	0.562657i	−0.434527	+	0.900659i	$0.643084\pi$
$468$	−0.464715			−0.0214814
$469$	−17.5212	+	32.0063i	−0.809053	+	1.47791i
$470$	−0.465710	−	0.125309i	−0.0214816	−	0.00578008i
$471$	−0.331704	−	0.0705058i	−0.0152841	−	0.00324874i
$472$	6.39406	−	7.10132i	0.294310	−	0.326865i
$473$	−0.697026	+	6.63176i	−0.0320493	+	0.304929i
$474$	−2.87436	+	4.97854i	−0.132024	+	0.228672i
$475$	−5.39135	+	25.1058i	−0.247372	+	1.15193i
$476$	8.19996	+	23.4122i	0.375844	+	1.07310i
$477$	1.07267	+	0.779344i	0.0491144	+	0.0356837i
$478$	3.84145	+	0.816526i	0.175704	+	0.0373470i
$479$	−27.4525	+	30.4890i	−1.25433	+	1.39308i	−0.368138	+	0.929771i	$0.620004\pi$
$479$	−27.4525	+	30.4890i	−1.25433	+	1.39308i	−0.886197	+	0.463309i	$0.846662\pi$
$480$	−7.01546	−	5.69318i	−0.320211	−	0.259857i
$481$	1.23092	+	1.36708i	0.0561253	+	0.0623335i
$482$	4.73796			0.215808
$483$	0.982944	+	1.61650i	0.0447255	+	0.0735535i
$484$	−2.78626	+	2.02433i	−0.126648	+	0.0920152i
$485$	1.09794	−	6.88546i	0.0498549	−	0.312653i
$486$	0.0386614	−	0.367839i	0.00175372	−	0.0166855i
$487$	11.7206	+	5.21834i	0.531110	+	0.236466i	0.654728	−	0.755864i	$-0.272783\pi$
$487$	11.7206	+	5.21834i	0.531110	+	0.236466i	−0.123618	+	0.992330i	$0.539450\pi$
$488$	−0.330064	−	3.14035i	−0.0149413	−	0.142157i
$489$	5.15651	+	3.74643i	0.233186	+	0.169419i
$490$	0.559392	+	5.76221i	0.0252708	+	0.260310i
$491$	−0.189007	+	0.137322i	−0.00852978	+	0.00619725i	−0.592042	−	0.805907i	$-0.701678\pi$
$491$	−0.189007	+	0.137322i	−0.00852978	+	0.00619725i	0.583512	+	0.812104i	$0.301678\pi$
$492$	−4.07420	−	4.52486i	−0.183679	−	0.203996i
$493$	−21.0737	−	36.5007i	−0.949111	−	1.64391i
$494$	−0.463413	+	0.0985014i	−0.0208499	+	0.00443179i
$495$	6.02395	+	3.07730i	0.270757	+	0.138315i
$496$	−8.15411	−	25.0958i	−0.366130	−	1.12683i
$497$	−25.9064	−	10.8356i	−1.16206	−	0.486043i
$498$	4.28391	+	3.11244i	0.191967	+	0.139472i
$499$	−13.5027	+	23.3874i	−0.604465	+	1.04696i	0.387671	+	0.921798i	$0.373280\pi$
$499$	−13.5027	+	23.3874i	−0.604465	+	1.04696i	−0.992136	+	0.125166i	$0.960054\pi$
$500$	17.4348	+	11.4003i	0.779708	+	0.509837i
$501$	−10.1221	−	17.5321i	−0.452224	−	0.783275i
$502$	3.68316	−	1.63985i	0.164387	−	0.0731900i
$503$	0.353328	+	1.08743i	0.0157541	+	0.0484862i	0.958625	−	0.284673i	$-0.0918852\pi$
$503$	0.353328	+	1.08743i	0.0157541	+	0.0484862i	−0.942870	+	0.333160i	$0.891885\pi$
$504$	3.00712	−	2.29101i	0.133948	−	0.102050i
$505$	−0.998978	−	19.4512i	−0.0444539	−	0.865565i
$506$	−0.535365	−	0.594583i	−0.0237999	−	0.0264324i
$507$	−6.46890	−	11.2045i	−0.287294	−	0.497607i
$508$	17.3358	−	3.68485i	0.769153	−	0.163489i
$509$	4.03710	+	38.4105i	0.178941	+	1.70251i	0.603704	+	0.797209i	$0.293691\pi$
$509$	4.03710	+	38.4105i	0.178941	+	1.70251i	−0.424763	+	0.905305i	$0.639642\pi$
$510$	2.27037	−	3.48806i	0.100534	−	0.154454i
$511$	19.2925	+	20.4709i	0.853449	+	0.905581i
$512$	−17.8469	+	12.9665i	−0.788729	+	0.573045i
$513$	0.536819	+	5.10750i	0.0237012	+	0.225501i
$514$	0.319815	−	3.04284i	0.0141064	−	0.134214i
$515$	16.4235	+	13.3279i	0.723704	+	0.587300i
$516$	0.429300	+	4.08452i	0.0188989	+	0.179811i
$517$	0.545124	−	1.67772i	0.0239745	−	0.0737861i
$518$	−7.09204	−	1.33975i	−0.311607	−	0.0588650i
$519$	3.69117	−	11.3603i	0.162024	−	0.498660i
$520$	−0.125486	+	0.786955i	−0.00550292	+	0.0345103i
$521$	−16.4789	+	18.3017i	−0.721954	+	0.801811i	−0.986708	−	0.162505i	$-0.948043\pi$
$521$	−16.4789	+	18.3017i	−0.721954	+	0.801811i	0.264754	+	0.964316i	$0.414709\pi$
$522$	−2.07283	+	2.30211i	−0.0907254	+	0.100761i
$523$	−24.8374	+	11.0583i	−1.08606	+	0.483546i	−0.870110	−	0.492858i	$-0.835952\pi$
$523$	−24.8374	+	11.0583i	−1.08606	+	0.483546i	−0.215953	+	0.976404i	$0.569286\pi$
$524$	−35.6835			−1.55884
$525$	−9.64612	+	9.05276i	−0.420991	+	0.395095i
$526$	−6.32562			−0.275810
$527$	37.9330	−	16.8889i	1.65239	−	0.735691i
$528$	6.47330	−	7.18932i	0.281714	−	0.312875i
$529$	−15.0479	+	16.7123i	−0.654255	+	0.726624i
$530$	0.776207	−	0.774584i	0.0337163	−	0.0336458i
$531$	−2.06661	+	6.36036i	−0.0896831	+	0.276016i
$532$	−16.5080	+	19.1939i	−0.715712	+	0.832163i
$533$	−0.251873	+	0.775184i	−0.0109098	+	0.0335770i
$534$	0.147494	+	1.40331i	0.00638267	+	0.0607270i
$535$	−14.9612	+	9.69367i	−0.646829	+	0.419094i
$536$	2.05982	−	19.5979i	0.0889706	−	0.846499i
$537$	1.23311	+	11.7322i	0.0532125	+	0.506283i
$538$	−3.91768	+	2.84636i	−0.168903	+	0.122715i
$539$	−21.1542	+	0.962398i	−0.911176	+	0.0414534i
$540$	4.02315	+	1.08251i	0.173129	+	0.0465840i
$541$	0.733012	+	6.97414i	0.0315147	+	0.299842i	0.998914	+	0.0465870i	$0.0148345\pi$
$541$	0.733012	+	6.97414i	0.0315147	+	0.299842i	−0.967400	+	0.253255i	$0.918499\pi$
$542$	−6.53344	+	1.38873i	−0.280635	+	0.0596509i
$543$	3.75861	+	6.51010i	0.161297	+	0.279375i
$544$	−13.6053	−	15.1102i	−0.583323	−	0.647846i
$545$	−18.6421	−	23.0704i	−0.798539	−	0.988227i
$546$	−0.225170	−	0.0941796i	−0.00963640	−	0.00403051i
$547$	8.96891	+	27.6035i	0.383483	+	1.18024i	0.937575	+	0.347783i	$0.113065\pi$
$547$	8.96891	+	27.6035i	0.383483	+	1.18024i	−0.554092	+	0.832455i	$0.686935\pi$
$548$	12.5664	−	5.59491i	0.536809	−	0.239003i
$549$	1.10495	+	1.91383i	0.0471582	+	0.0816803i
$550$	3.29783	−	4.51915i	0.140620	−	0.192697i
$551$	21.5067	−	37.2507i	0.916216	−	1.58693i
$552$	−0.826601	−	0.600561i	−0.0351825	−	0.0255616i
$553$	32.7107	−	24.9210i	1.39100	−	1.05975i
$554$	−1.02227	−	3.14622i	−0.0434320	−	0.133670i
$555$	−7.47192	−	14.7025i	−0.317165	−	0.624086i
$556$	1.43267	−	0.304523i	0.0607588	−	0.0129147i
$557$	21.7634	+	37.6953i	0.922146	+	1.59720i	0.796089	+	0.605180i	$0.206899\pi$
$557$	21.7634	+	37.6953i	0.922146	+	1.59720i	0.126057	+	0.992023i	$0.459768\pi$
$558$	−2.04212	−	2.26800i	−0.0864498	−	0.0960122i
$559$	0.444786	−	0.323156i	0.0188125	−	0.0136680i
$560$	8.95259	+	16.6669i	0.378316	+	0.704303i
$561$	12.3159	+	8.94802i	0.519977	+	0.377786i
$562$	1.04003	+	9.89522i	0.0438710	+	0.417405i
$563$	−14.0416	−	6.25174i	−0.591785	−	0.263479i	0.0889185	−	0.996039i	$-0.471659\pi$
$563$	−14.0416	−	6.25174i	−0.591785	−	0.263479i	−0.680703	+	0.732559i	$0.738326\pi$
$564$	0.113569	−	1.08054i	0.00478212	−	0.0454988i
$565$	28.1473	−	4.42790i	1.18417	−	0.186283i
$566$	0.563030	−	0.409065i	0.0236659	−	0.0171943i
$567$	−1.27045	+	2.32076i	−0.0533540	+	0.0974629i
$568$	15.1655			0.636330
$569$	13.5731	+	15.0745i	0.569014	+	0.631954i	0.957131	−	0.289656i	$-0.0935409\pi$
$569$	13.5731	+	15.0745i	0.569014	+	0.631954i	−0.388117	+	0.921610i	$0.626874\pi$
$570$	4.24133	+	0.226730i	0.177650	+	0.00949670i
$571$	−9.05818	+	10.0601i	−0.379073	+	0.421003i	−0.902245	−	0.431224i	$-0.858082\pi$
$571$	−9.05818	+	10.0601i	−0.379073	+	0.421003i	0.523172	+	0.852227i	$0.324749\pi$
$572$	−1.37511	−	0.292289i	−0.0574964	−	0.0122212i
$573$	13.5689	+	9.85838i	0.566849	+	0.411840i
$574$	−1.05708	−	3.01813i	−0.0441215	−	0.125974i
$575$	3.09259	+	1.79415i	0.128970	+	0.0748212i
$576$	2.45069	−	4.24472i	0.102112	−	0.176863i
$577$	−0.203551	+	1.93666i	−0.00847395	+	0.0806243i	−0.997942	−	0.0641304i	$-0.979573\pi$
$577$	−0.203551	+	1.93666i	−0.00847395	+	0.0806243i	0.989468	+	0.144755i	$0.0462393\pi$
$578$	2.05992	−	2.28778i	0.0856815	−	0.0951589i
$579$	−10.8732	−	2.31117i	−0.451875	−	0.0960491i
$580$	−21.9313	−	27.1409i	−0.910648	−	1.12697i
$581$	−19.6798	−	32.3645i	−0.816455	−	1.34271i
$582$	−1.15330			−0.0478060
$583$	2.68392	+	2.98079i	0.111156	+	0.123452i
$584$	−13.8781	−	6.17894i	−0.574281	−	0.255686i
$585$	−0.143783	−	0.538862i	−0.00594470	−	0.0222792i
$586$	−6.54482	+	2.91394i	−0.270364	+	0.120374i
$587$	−36.0597	+	26.1989i	−1.48834	+	1.08135i	−0.513598	+	0.858031i	$0.671688\pi$
$587$	−36.0597	+	26.1989i	−1.48834	+	1.08135i	−0.974746	+	0.223315i	$0.928312\pi$
$588$	−12.6210	+	3.28866i	−0.520480	+	0.135622i
$589$	34.2830	+	24.9080i	1.41261	+	1.02632i
$590$	4.92553	+	2.51618i	0.202781	+	0.103589i
$591$	−16.3119	−	7.26254i	−0.670983	−	0.298741i
$592$	−23.0709	+	4.90387i	−0.948208	+	0.201548i
$593$	−8.23952	+	14.2713i	−0.338356	+	0.586051i	−0.984124	−	0.177484i	$-0.943204\pi$
$593$	−8.23952	+	14.2713i	−0.338356	+	0.586051i	0.645767	+	0.763534i	$0.276538\pi$
$594$	0.345759	−	1.06414i	0.0141867	−	0.0436620i
$595$	−24.6107	+	16.7521i	−1.00894	+	0.686767i
$596$	5.06746	+	15.5960i	0.207571	+	0.638839i
$597$	13.9040	+	2.95539i	0.569054	+	0.120956i
$598$	−0.00689529	+	0.0656043i	−0.000281969	+	0.00268276i
$599$	−0.242946	−	0.420794i	−0.00992650	−	0.0171932i	0.861019	−	0.508572i	$-0.169826\pi$
$599$	−0.242946	−	0.420794i	−0.00992650	−	0.0171932i	−0.870946	+	0.491379i	$0.836493\pi$
$600$	2.91951	−	6.52055i	0.119188	−	0.266200i
$601$	22.1413			0.903164			0.451582	−	0.892230i	$-0.350860\pi$
$601$	22.1413			0.903164			0.451582	+	0.892230i	$0.350860\pi$
$602$	−0.619762	+	2.06609i	−0.0252596	+	0.0842076i
$603$	4.26174	+	13.1163i	0.173551	+	0.534136i
$604$	−8.95221	−	1.90285i	−0.364260	−	0.0774259i
$605$	−3.20939	−	2.60448i	−0.130480	−	0.105887i
$606$	−3.15123	+	0.669814i	−0.128010	+	0.0272093i
$607$	13.5254	−	23.4268i	0.548981	−	0.950863i	−0.449364	−	0.893349i	$-0.648349\pi$
$607$	13.5254	−	23.4268i	0.548981	−	0.950863i	0.998345	−	0.0575140i	$-0.0183174\pi$
$608$	6.41229	−	19.7350i	0.260053	−	0.800360i
$609$	20.0336	−	9.47087i	0.811802	−	0.383779i
$610$	1.70697	−	0.653197i	0.0691134	−	0.0264472i
$611$	−0.132869	+	0.0591570i	−0.00537529	+	0.00239323i
$612$	8.56545	+	3.81358i	0.346238	+	0.154155i
$613$	−25.4799	−	11.3444i	−1.02913	−	0.458196i	−0.178484	−	0.983943i	$-0.557119\pi$
$613$	−25.4799	−	11.3444i	−1.02913	−	0.458196i	−0.850641	+	0.525747i	$0.823786\pi$
$614$	−3.08409	+	1.37312i	−0.124464	+	0.0554147i
$615$	3.98625	−	6.12425i	0.160741	−	0.246953i
$616$	10.3392	−	4.88785i	0.416578	−	0.196937i
$617$	7.96583	−	24.5163i	0.320692	−	0.986989i	−0.652656	−	0.757655i	$-0.726345\pi$
$617$	7.96583	−	24.5163i	0.320692	−	0.986989i	0.973348	−	0.229334i	$-0.0736549\pi$
$618$	1.74928	−	3.02984i	0.0703663	−	0.121878i
$619$	−27.3278	+	5.80870i	−1.09840	+	0.233471i	−0.721245	−	0.692680i	$-0.756430\pi$
$619$	−27.3278	+	5.80870i	−1.09840	+	0.233471i	−0.377151	+	0.926152i	$0.623096\pi$
$620$	28.8508	−	18.6930i	1.15868	−	0.750730i
$621$	0.699443	+	0.148671i	0.0280677	+	0.00596597i
$622$	−0.519445	−	1.59869i	−0.0208278	−	0.0641015i
$623$	2.90008	−	9.66796i	0.116189	−	0.387339i
$624$	−0.797616			−0.0319302
$625$	−7.82490	+	23.7439i	−0.312996	+	0.949754i
$626$	−0.550647	−	0.953749i	−0.0220083	−	0.0381195i
$627$	−1.62396	+	15.4510i	−0.0648548	+	0.617052i
$628$	−0.618031	−	0.131366i	−0.0246621	−	0.00524209i
$629$	−11.4693	−	35.2988i	−0.457310	−	1.40746i
$630$	1.72997	+	1.33985i	0.0689237	+	0.0533809i
$631$	13.1013	−	40.3217i	0.521555	−	1.60518i	−0.249474	−	0.968382i	$-0.580258\pi$
$631$	13.1013	−	40.3217i	0.521555	−	1.60518i	0.771029	−	0.636800i	$-0.219742\pi$
$632$	−11.1042	+	19.2331i	−0.441703	+	0.765052i
$633$	25.6273	−	5.44725i	1.01859	−	0.216509i
$634$	10.6129	+	4.72517i	0.421492	+	0.187660i
$635$	9.63650	+	18.9617i	0.382413	+	0.752474i
$636$	1.99861	+	1.45207i	0.0792499	+	0.0575784i
$637$	1.22601	+	1.24304i	0.0485763	+	0.0492510i
$638$	−7.58156	+	5.50833i	−0.300157	+	0.218077i
$639$	−9.69608	+	4.31697i	−0.383571	+	0.170777i
$640$	−17.1785	−	13.9407i	−0.679041	−	0.551055i
$641$	−6.15898	−	2.74216i	−0.243265	−	0.108309i	0.281483	−	0.959566i	$-0.409174\pi$
$641$	−6.15898	−	2.74216i	−0.243265	−	0.108309i	−0.524748	+	0.851258i	$0.675840\pi$
$642$	1.97310	+	2.19135i	0.0778721	+	0.0864857i
$643$	−25.9778			−1.02446			−0.512232	−	0.858847i	$-0.671181\pi$
$643$	−25.9778			−1.02446			−0.512232	+	0.858847i	$0.671181\pi$
$644$	1.83142	+	3.01187i	0.0721681	+	0.118684i
$645$	−4.60339	+	1.76155i	−0.181258	+	0.0693610i
$646$	9.34978	+	1.98736i	0.367862	+	0.0781915i
$647$	2.05781	−	2.28543i	0.0809010	−	0.0898497i	−0.701335	−	0.712832i	$-0.747412\pi$
$647$	2.05781	−	2.28543i	0.0809010	−	0.0898497i	0.782236	+	0.622982i	$0.214079\pi$
$648$	0.149357	−	1.42103i	0.00586729	−	0.0558235i
$649$	−10.1156	+	17.5208i	−0.397074	+	0.687752i
$650$	−0.458827	+	0.0472537i	−0.0179967	+	0.00185344i
$651$	7.21637	+	20.6039i	0.282832	+	0.807532i
$652$	9.60761	+	6.98034i	0.376263	+	0.273371i
$653$	−11.1066	−	2.36078i	−0.434634	−	0.0923844i	−0.0146017	−	0.999893i	$-0.504648\pi$
$653$	−11.1066	−	2.36078i	−0.434634	−	0.0923844i	−0.420033	+	0.907509i	$0.637981\pi$
$654$	−3.28287	+	3.64600i	−0.128370	+	0.142570i
$655$	−11.0405	−	41.3769i	−0.431388	−	1.61673i
$656$	−6.99277	−	7.76626i	−0.273022	−	0.303222i
$657$	10.6319			0.414789
$658$	0.274011	−	0.500541i	0.0106821	−	0.0195131i
$659$	38.6857	−	28.1068i	1.50698	−	1.09488i	0.539485	−	0.841995i	$-0.318619\pi$
$659$	38.6857	−	28.1068i	1.50698	−	1.09488i	0.967495	−	0.252890i	$-0.0813810\pi$
$660$	11.2238	+	5.73363i	0.436887	+	0.223181i
$661$	−2.14204	+	20.3802i	−0.0833157	+	0.792696i	0.870473	+	0.492217i	$0.163813\pi$
$661$	−2.14204	+	20.3802i	−0.0833157	+	0.792696i	−0.953788	+	0.300479i	$0.902853\pi$
$662$	−4.35636	−	1.93958i	−0.169315	−	0.0753837i
$663$	−0.131196	−	1.24825i	−0.00509524	−	0.0484780i
$664$	16.5496	+	12.0240i	0.642249	+	0.466621i
$665$	−27.3640	−	13.2033i	−1.06113	−	0.512001i
$666$	−2.20696	+	1.60345i	−0.0855179	+	0.0621324i
$667$	−4.00746	−	4.45073i	−0.155169	−	0.172333i
$668$	−18.8596	−	32.6657i	−0.729699	−	1.26388i
$669$	−22.4317	+	4.76801i	−0.867261	+	0.184342i
$670$	11.2674	−	1.77249i	0.435298	−	0.0684775i
$671$	2.06587	+	6.35810i	0.0797521	+	0.245452i
$672$	8.50350	−	6.47850i	0.328030	−	0.249914i
$673$	15.3327	+	11.1399i	0.591033	+	0.429411i	0.842685	−	0.538407i	$-0.180974\pi$
$673$	15.3327	+	11.1399i	0.591033	+	0.429411i	−0.251652	+	0.967818i	$0.580974\pi$
$674$	0.753366	−	1.30487i	0.0290186	−	0.0502616i
$675$	−0.0104670	+	4.99999i	−0.000402874	+	0.192450i
$676$	−12.0528	−	20.8761i	−0.463571	−	0.802929i
$677$	−1.34684	+	0.599652i	−0.0517633	+	0.0230465i	−0.432455	−	0.901656i	$-0.642353\pi$
$677$	−1.34684	+	0.599652i	−0.0517633	+	0.0230465i	0.380692	+	0.924702i	$0.375686\pi$
$678$	−1.45642	−	4.48239i	−0.0559333	−	0.172145i
$679$	7.61100	+	3.18337i	0.292083	+	0.122167i
$680$	8.77089	−	13.4751i	0.336348	−	0.516746i
$681$	−6.43420	−	7.14590i	−0.246559	−	0.273831i
$682$	−4.61624	−	7.99555i	−0.176765	−	0.306166i
$683$	36.9758	−	7.85945i	1.41484	−	0.300734i	0.563834	−	0.825888i	$-0.309326\pi$
$683$	36.9758	−	7.85945i	1.41484	−	0.300734i	0.851007	+	0.525155i	$0.175993\pi$
$684$	1.00020	+	9.51629i	0.0382437	+	0.363864i
$685$	10.3756	+	12.8403i	0.396433	+	0.490603i
$686$	−6.78178	−	0.964313i	−0.258929	−	0.0368176i
$687$	−17.2412	+	12.5265i	−0.657793	+	0.477915i
$688$	0.736831	+	7.01048i	0.0280914	+	0.267272i
$689$	0.0345678	−	0.328891i	0.00131693	−	0.0125297i
$690$	0.212514	−	0.551891i	0.00809027	−	0.0210101i
$691$	−3.17044	−	30.1647i	−0.120609	−	1.14752i	−0.872631	−	0.488381i	$-0.837588\pi$
$691$	−3.17044	−	30.1647i	−0.120609	−	1.14752i	0.752021	−	0.659139i	$-0.229079\pi$
$692$	6.87739	−	21.1664i	0.261439	−	0.804627i
$693$	−5.21901	+	6.06818i	−0.198254	+	0.230511i
$694$	−1.90895	+	5.87515i	−0.0724628	+	0.223018i
$695$	0.796381	+	1.56704i	0.0302085	+	0.0594411i
$696$	−8.00776	+	8.89352i	−0.303534	+	0.337108i
$697$	11.0038	−	12.2210i	0.416799	−	0.462902i
$698$	5.03705	−	2.24264i	0.190655	−	0.0848851i
$699$	−9.59958			−0.363090
$700$	−17.9726	+	16.8671i	−0.679302	+	0.637516i
$701$	−2.74962			−0.103852			−0.0519258	−	0.998651i	$-0.516536\pi$
$701$	−2.74962			−0.103852			−0.0519258	+	0.998651i	$0.516536\pi$
$702$	−0.0842753	+	0.0375218i	−0.00318076	+	0.00141617i
$703$	25.3453	−	28.1488i	0.955917	−	1.06165i
$704$	9.92150	−	11.0189i	0.373930	−	0.415292i
$705$	1.28808	−	0.202630i	0.0485118	−	0.00763148i
$706$	−0.215935	+	0.664578i	−0.00812681	+	0.0250117i
$707$	22.6447	+	4.27778i	0.851643	+	0.160882i
$708$	−3.85050	+	11.8506i	−0.144711	+	0.445374i
$709$	−3.13887	−	29.8644i	−0.117883	−	1.12158i	−0.880275	−	0.474464i	$-0.842642\pi$
$709$	−3.13887	−	29.8644i	−0.117883	−	1.12158i	0.762392	−	0.647116i	$-0.224025\pi$
$710$	2.26303	+	8.48124i	0.0849300	+	0.318295i
$711$	1.62466	−	15.4576i	0.0609296	−	0.579707i
$712$	0.569797	+	5.42126i	0.0213540	+	0.203170i
$713$	4.77345	−	3.46812i	0.178767	−	0.129882i
$714$	3.37739	+	3.58369i	0.126396	+	0.134116i
$715$	−0.0865362	−	1.68495i	−0.00323627	−	0.0630136i
$716$	2.29752	+	21.8595i	0.0858625	+	0.816927i
$717$	−10.3861	+	2.20763i	−0.387876	+	0.0824456i
$718$	−4.06250	−	7.03645i	−0.151611	−	0.262598i
$719$	15.3189	+	17.0133i	0.571298	+	0.634490i	0.957675	−	0.287850i	$-0.0929405\pi$
$719$	15.3189	+	17.0133i	0.571298	+	0.634490i	−0.386378	+	0.922341i	$0.626274\pi$
$720$	6.90516	+	1.85798i	0.257340	+	0.0692428i
$721$	−19.9070	+	15.1664i	−0.741377	+	0.564827i
$722$	0.842886	+	2.59414i	0.0313690	+	0.0965438i
$723$	−11.7025	+	5.21029i	−0.435220	+	0.193773i
$724$	7.00304	+	12.1296i	0.260266	+	0.450794i
$725$	24.6858	−	33.8280i	0.916808	−	1.25634i
$726$	−0.341835	+	0.592076i	−0.0126867	+	0.0219740i
$727$	29.5020	+	21.4345i	1.09417	+	0.794961i	0.980099	−	0.198512i	$-0.0636108\pi$
$727$	29.5020	+	21.4345i	1.09417	+	0.794961i	0.114071	+	0.993473i	$0.463611\pi$
$728$	−0.869878	−	0.363834i	−0.0322398	−	0.0134846i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.38462	−	8.68332i	0.0512472	−	0.321384i
$731$	−10.8500	+	2.30625i	−0.401303	+	0.0852997i
$732$	2.05875	+	3.56585i	0.0760934	+	0.131798i
$733$	−16.0694	−	17.8469i	−0.593537	−	0.659190i	0.369288	−	0.929315i	$-0.379602\pi$
$733$	−16.0694	−	17.8469i	−0.593537	−	0.659190i	−0.962825	+	0.270125i	$0.912935\pi$
$734$	10.2633	−	7.45669i	0.378824	−	0.275232i
$735$	−7.71831	−	13.6172i	−0.284694	−	0.502277i
$736$	−2.33745	−	1.69826i	−0.0861596	−	0.0625986i
$737$	4.36101	+	41.4922i	0.160640	+	1.52838i
$738$	−1.10419	−	0.491618i	−0.0406459	−	0.0180967i
$739$	−3.15903	+	30.0562i	−0.116207	+	1.10563i	0.768617	+	0.639709i	$0.220945\pi$
$739$	−3.15903	+	30.0562i	−0.116207	+	1.10563i	−0.884824	+	0.465926i	$0.845721\pi$
$740$	−13.9217	−	27.3937i	−0.511771	−	1.00701i
$741$	1.03628	−	0.752903i	0.0380688	−	0.0276586i
$742$	0.674115	+	1.10862i	0.0247475	+	0.0406987i
$743$	40.9573			1.50258			0.751288	−	0.659974i	$-0.229433\pi$
$743$	40.9573			1.50258			0.751288	+	0.659974i	$0.229433\pi$
$744$	−7.88912	−	8.76175i	−0.289229	−	0.321221i
$745$	−16.5166	+	10.7014i	−0.605120	+	0.392070i
$746$	8.21527	−	9.12398i	0.300782	−	0.334053i
$747$	−14.0037	−	2.97659i	−0.512370	−	0.108908i
$748$	22.9470	+	16.6719i	0.839024	+	0.609587i
$749$	−6.97248	−	19.9076i	−0.254769	−	0.727407i
$750$	4.08225	+	0.659712i	0.149063	+	0.0240893i
$751$	11.8421	−	20.5112i	0.432125	−	0.748463i	−0.564931	−	0.825138i	$-0.691097\pi$
$751$	11.8421	−	20.5112i	0.432125	−	0.748463i	0.997056	+	0.0766753i	$0.0244305\pi$
$752$	0.194925	−	1.85459i	0.00710817	−	0.0676298i
$753$	−7.29387	+	8.10066i	−0.265803	+	0.295205i
$754$	0.755761	+	0.160642i	0.0275232	+	0.00585024i
$755$	−0.563365	−	10.9693i	−0.0205030	−	0.399214i
$756$	−2.36711	+	4.32405i	−0.0860909	+	0.157264i
$757$	31.0914			1.13004			0.565019	−	0.825078i	$-0.308869\pi$
$757$	31.0914			1.13004			0.565019	+	0.825078i	$0.308869\pi$
$758$	−4.90265	−	5.44495i	−0.178072	−	0.197769i
$759$	1.97618	+	0.879851i	0.0717307	+	0.0319366i
$760$	16.3851	+	0.875905i	0.594350	+	0.0317724i
$761$	23.1093	−	10.2889i	0.837710	−	0.372973i	0.0573894	−	0.998352i	$-0.481722\pi$
$761$	23.1093	−	10.2889i	0.837710	−	0.372973i	0.780321	+	0.625379i	$0.215056\pi$
$762$	2.84631	−	2.06796i	0.103111	−	0.0749144i
$763$	31.7284	−	14.9996i	1.14864	−	0.543021i
$764$	25.2816	+	18.3681i	0.914655	+	0.664536i
$765$	−1.77190	+	11.1120i	−0.0640630	+	0.401756i
$766$	−7.60734	−	3.38701i	−0.274864	−	0.122377i
$767$	1.63157	−	0.346802i	0.0589127	−	0.0125223i
$768$	3.07168	−	5.32031i	0.110840	−	0.191980i
$769$	0.0833043	−	0.256384i	0.00300403	−	0.00924546i	−0.949543	−	0.313636i	$-0.898453\pi$
$769$	0.0833043	−	0.256384i	0.00300403	−	0.00924546i	0.952547	+	0.304391i	$0.0984528\pi$
$770$	4.27635	+	5.05278i	0.154109	+	0.182089i
$771$	2.55625	+	7.86733i	0.0920611	+	0.283335i
$772$	−20.2590	−	4.30618i	−0.729136	−	0.154983i
$773$	1.03534	−	9.85060i	0.0372386	−	0.354301i	−0.959998	−	0.280008i	$-0.909663\pi$
$773$	1.03534	−	9.85060i	0.0372386	−	0.354301i	0.997236	−	0.0742939i	$-0.0236703\pi$
$774$	0.407643	+	0.706058i	0.0146524	+	0.0253787i
$775$	30.6020	+	27.6704i	1.09926	+	0.993951i
$776$	−4.45544			−0.159941
$777$	18.9903	−	4.48995i	0.681272	−	0.161076i
$778$	3.14294	+	9.67299i	0.112680	+	0.346793i
$779$	16.4161	+	3.48935i	0.588168	+	0.125019i
$780$	−0.267897	−	1.00401i	−0.00959224	−	0.0359492i
$781$	−31.4064	+	6.67564i	−1.12381	+	0.238873i
$782$	0.665459	−	1.15261i	0.0237968	−	0.0412172i
$783$	2.58817	−	7.96556i	0.0924936	−	0.284666i
$784$	−21.6621	+	5.64450i	−0.773646	+	0.201589i
$785$	−0.0388928	−	0.757285i	−0.00138814	−	0.0270286i
$786$	−6.47115	+	2.88114i	−0.230818	+	0.102767i
$787$	31.7254	+	14.1251i	1.13089	+	0.503504i	0.884906	−	0.465770i	$-0.154223\pi$
$787$	31.7254	+	14.1251i	1.13089	+	0.503504i	0.245983	+	0.969274i	$0.420889\pi$
$788$	−30.3924	−	13.5316i	−1.08268	−	0.482042i
$789$	15.6239	−	6.95622i	0.556227	−	0.247648i
$790$	−12.4130	−	3.34000i	−0.441636	−	0.118832i
$791$	−2.76105	+	33.6007i	−0.0981716	+	1.19470i
$792$	1.33573	−	4.11097i	0.0474633	−	0.146077i
$793$	0.275594	−	0.477343i	0.00978664	−	0.0169510i
$794$	−2.70573	+	0.575120i	−0.0960226	+	0.0204102i
$795$	−1.06539	+	2.76677i	−0.0377853	+	0.0981271i
$796$	25.9060	+	5.50648i	0.918213	+	0.195172i
$797$	−1.72542	−	5.31031i	−0.0611176	−	0.188101i	0.915836	−	0.401553i	$-0.131529\pi$
$797$	−1.72542	−	5.31031i	−0.0611176	−	0.188101i	−0.976954	+	0.213452i	$0.931529\pi$
$798$	−1.44395	+	4.81367i	−0.0511152	+	0.170402i
$799$	2.93445			0.103813
$800$	8.25575	−	18.4387i	0.291885	−	0.651908i
$801$	−1.90750	−	3.30389i	−0.0673983	−	0.116737i
$802$	−0.362174	+	3.44586i	−0.0127888	+	0.121678i
$803$	31.4603	+	6.68709i	1.11021	+	0.235982i
$804$	7.94047	+	24.4383i	0.280039	+	0.861871i
$805$	−2.92578	+	3.05551i	−0.103120	+	0.107692i
$806$	−0.235223	+	0.723941i	−0.00828537	+	0.0254997i
$807$	6.54634	−	11.3386i	0.230442	−	0.399137i
$808$	−12.1738	+	2.58763i	−0.428274	+	0.0910324i
$809$	−17.5166	−	7.79891i	−0.615852	−	0.274195i	0.0750086	−	0.997183i	$-0.476102\pi$
$809$	−17.5166	−	7.79891i	−0.615852	−	0.274195i	−0.690861	+	0.722988i	$0.742768\pi$
$810$	0.816996	−	0.128523i	0.0287063	−	0.00451584i
$811$	−22.5661	−	16.3952i	−0.792402	−	0.575714i	0.116273	−	0.993217i	$-0.462905\pi$
$811$	−22.5661	−	16.3952i	−0.792402	−	0.575714i	−0.908675	+	0.417503i	$0.862905\pi$
$812$	37.3266	−	17.6461i	1.30991	−	0.619257i
$813$	14.6101	−	10.6148i	0.512397	−	0.372278i
$814$	−7.53901	+	3.35658i	−0.264242	+	0.117648i
$815$	−5.12147	+	13.3003i	−0.179397	+	0.465888i
$816$	14.7014	+	6.54546i	0.514650	+	0.229137i
$817$	−7.57480	−	8.41267i	−0.265009	−	0.294322i
$818$	11.6484			0.407276
$819$	0.659726	−	0.0149992i	0.0230527	−	0.000524113i
$820$	7.42718	−	11.4107i	0.259369	−	0.398479i
$821$	−22.3280	−	4.74597i	−0.779254	−	0.165635i	−0.198922	−	0.980015i	$-0.563744\pi$
$821$	−22.3280	−	4.74597i	−0.779254	−	0.165635i	−0.580332	+	0.814380i	$0.697077\pi$
$822$	1.82715	−	2.02926i	0.0637292	−	0.0707784i
$823$	−3.71482	+	35.3441i	−0.129490	+	1.23202i	0.716027	+	0.698072i	$0.245959\pi$
$823$	−3.71482	+	35.3441i	−0.129490	+	1.23202i	−0.845518	+	0.533947i	$0.820708\pi$
$824$	6.75781	−	11.7049i	0.235419	−	0.407758i
$825$	−3.17579	+	14.7886i	−0.110567	+	0.514874i
$826$	−4.26736	+	4.96169i	−0.148480	+	0.172639i
$827$	0.542957	+	0.394481i	0.0188805	+	0.0137175i	0.597185	−	0.802103i	$-0.296286\pi$
$827$	0.542957	+	0.394481i	0.0188805	+	0.0137175i	−0.578305	+	0.815821i	$0.696286\pi$
$828$	1.30320	+	0.277004i	0.0452894	+	0.00962656i
$829$	31.2012	−	34.6524i	1.08366	−	1.20353i	0.105775	−	0.994390i	$-0.466268\pi$
$829$	31.2012	−	34.6524i	1.08366	−	1.20353i	0.977886	−	0.209138i	$-0.0670658\pi$
$830$	−4.25480	+	11.0496i	−0.147686	+	0.383536i
$831$	5.98481	+	6.64680i	0.207611	+	0.230575i
$832$	−1.22249			−0.0423822
$833$	−12.3966	−	32.9722i	−0.429517	−	1.14242i
$834$	0.235225	−	0.170901i	0.00814517	−	0.00591781i
$835$	32.0425	−	31.9755i	1.10888	−	1.10656i
$836$	−3.02577	+	28.7882i	−0.104648	+	0.995662i
$837$	7.53802	+	3.35614i	0.260552	+	0.116005i
$838$	0.778241	+	7.40446i	0.0268839	+	0.255783i
$839$	0.497188	+	0.361228i	0.0171648	+	0.0124710i	0.596335	−	0.802736i	$-0.296623\pi$
$839$	0.497188	+	0.361228i	0.0171648	+	0.0124710i	−0.579170	+	0.815207i	$0.696623\pi$
$840$	6.68322	+	5.17611i	0.230593	+	0.178593i
$841$	−33.2901	+	24.1867i	−1.14793	+	0.834023i
$842$	−6.38852	−	7.09517i	−0.220163	−	0.244516i
$843$	−13.4505	−	23.2969i	−0.463260	−	0.802389i
$844$	47.7488	−	10.1493i	1.64358	−	0.349354i
$845$	20.4778	−	20.4350i	0.704459	−	0.702986i
$846$	−0.0666486	−	0.205123i	−0.00229143	−	0.00705228i
$847$	3.89014	−	2.96375i	0.133667	−	0.101836i
$848$	3.43032	+	2.49227i	0.117798	+	0.0855851i
$849$	−0.940808	+	1.62953i	−0.0322885	+	0.0559252i
$850$	8.84470	+	2.89430i	0.303371	+	0.0992738i
$851$	−2.63701	−	4.56743i	−0.0903955	−	0.156570i
$852$	−18.0657	+	8.04338i	−0.618922	+	0.275562i
$853$	12.1938	+	37.5288i	0.417509	+	1.28496i	0.909987	+	0.414636i	$0.136091\pi$
$853$	12.1938	+	37.5288i	0.417509	+	1.28496i	−0.492478	+	0.870325i	$0.663909\pi$
$854$	0.274874	+	2.14500i	0.00940598	+	0.0734006i
$855$	−10.7252	+	4.10414i	−0.366793	+	0.140358i
$856$	7.62248	+	8.46562i	0.260531	+	0.289349i
$857$	−16.3132	−	28.2553i	−0.557248	−	0.965182i	−0.997725	−	0.0674178i	$-0.978524\pi$
$857$	−16.3132	−	28.2553i	−0.557248	−	0.965182i	0.440477	−	0.897764i	$-0.354809\pi$
$858$	−0.272974	+	0.0580225i	−0.00931919	+	0.00198086i
$859$	2.45914	+	23.3972i	0.0839049	+	0.798302i	0.952860	+	0.303411i	$0.0981254\pi$
$859$	2.45914	+	23.3972i	0.0839049	+	0.798302i	−0.868955	+	0.494891i	$0.835208\pi$
$860$	−8.57704	+	3.28212i	−0.292475	+	0.111919i
$861$	5.92993	+	6.29215i	0.202091	+	0.214436i
$862$	−3.83881	+	2.78906i	−0.130751	+	0.0949958i
$863$	0.0342173	+	0.325556i	0.00116477	+	0.0110821i	0.995089	−	0.0989858i	$-0.0315598\pi$
$863$	0.0342173	+	0.325556i	0.00116477	+	0.0110821i	−0.993924	+	0.110068i	$0.964893\pi$
$864$	0.422349	−	4.01839i	0.0143686	−	0.136708i
$865$	26.6715	+	1.42579i	0.906858	+	0.0484783i
$866$	−0.736002	−	7.00259i	−0.0250104	−	0.237958i
$867$	−2.57205	+	7.91595i	−0.0873514	+	0.268840i
$868$	13.4455	+	38.3893i	0.456372	+	1.30302i
$869$	14.5298	−	44.7180i	0.492889	−	1.51696i
$870$	−6.16861	−	3.15120i	−0.209135	−	0.106836i
$871$	2.30167	−	2.55626i	0.0779890	−	0.0866155i
$872$	−12.6824	+	14.0852i	−0.429480	+	0.476985i
$873$	2.84859	−	1.26828i	0.0964103	−	0.0429246i
$874$	1.35827			0.0459440
$875$	−25.1191	−	15.6216i	−0.849179	−	0.528105i
$876$	19.8093			0.669295
$877$	−40.0843	+	17.8467i	−1.35355	+	0.602639i	−0.949980	−	0.312310i	$-0.898897\pi$
$877$	−40.0843	+	17.8467i	−1.35355	+	0.602639i	−0.403569	+	0.914949i	$0.632231\pi$
$878$	5.18727	−	5.76104i	0.175062	−	0.194426i
$879$	12.9609	−	14.3945i	0.437160	−	0.485516i
$880$	19.2641	+	9.84096i	0.649392	+	0.331739i
$881$	4.99635	−	15.3772i	0.168331	−	0.518071i	−0.830935	−	0.556370i	$-0.812194\pi$
$881$	4.99635	−	15.3772i	0.168331	−	0.518071i	0.999266	+	0.0382988i	$0.0121939\pi$
$882$	−2.02326	+	1.61543i	−0.0681268	+	0.0543943i
$883$	13.9991	−	43.0847i	0.471106	−	1.44991i	−0.380032	−	0.924973i	$-0.624087\pi$
$883$	13.9991	−	43.0847i	0.471106	−	1.44991i	0.851138	−	0.524942i	$-0.175913\pi$
$884$	−0.244445	−	2.32574i	−0.00822158	−	0.0782231i
$885$	−14.9328	−	0.798268i	−0.501960	−	0.0268335i
$886$	−0.210525	+	2.00301i	−0.00707271	+	0.0672924i
$887$	−5.23955	−	49.8510i	−0.175927	−	1.67383i	−0.625221	−	0.780448i	$-0.714991\pi$
$887$	−5.23955	−	49.8510i	−0.175927	−	1.67383i	0.449294	−	0.893384i	$-0.351676\pi$
$888$	−8.52592	+	6.19444i	−0.286111	+	0.207872i
$889$	−24.4917	+	5.79068i	−0.821424	+	0.194213i
$890$	−2.94679	+	1.12763i	−0.0987767	+	0.0377982i
$891$	0.316215	+	3.00858i	0.0105936	+	0.100791i
$892$	−41.7948	+	8.88376i	−1.39939	+	0.297450i
$893$	1.49737	+	2.59352i	0.0501076	+	0.0867889i
$894$	2.17822	+	2.41916i	0.0728507	+	0.0809089i
$895$	−24.6364	+	9.42744i	−0.823503	+	0.315125i
$896$	20.8223	−	15.8637i	0.695623	−	0.529969i
$897$	−0.0551134	−	0.169622i	−0.00184018	−	0.00566350i
$898$	4.23640	−	1.88617i	0.141370	−	0.0629422i
$899$	−34.5547	−	59.8505i	−1.15246	−	1.99613i
$900$	−0.0195021	+	9.31598i	−0.000650069	+	0.310533i
$901$	−3.33611	+	5.77832i	−0.111142	+	0.192504i
$902$	−2.95815	−	2.14922i	−0.0984956	−	0.0715613i
$903$	−0.741282	−	5.78467i	−0.0246683	−	0.192502i
$904$	−5.62643	−	17.3164i	−0.187132	−	0.575934i
$905$	−11.8982	+	11.8733i	−0.395509	+	0.394682i
$906$	−1.77711	+	0.377736i	−0.0590405	+	0.0125494i
$907$	−20.9598	−	36.3034i	−0.695958	−	1.20544i	−0.969857	−	0.243677i	$-0.921646\pi$
$907$	−20.9598	−	36.3034i	−0.695958	−	1.20544i	0.273898	−	0.961759i	$-0.411687\pi$
$908$	−11.9882	−	13.3142i	−0.397842	−	0.441849i
$909$	7.04677	−	5.11978i	0.233727	−	0.169812i
$910$	0.0736679	−	0.540768i	0.00244207	−	0.0179263i
$911$	12.5494	+	9.11764i	0.415779	+	0.302081i	0.775937	−	0.630810i	$-0.217277\pi$
$911$	12.5494	+	9.11764i	0.415779	+	0.302081i	−0.360158	+	0.932891i	$0.617277\pi$
$912$	1.71670	+	16.3333i	0.0568457	+	0.540851i
$913$	−39.5656	−	17.6157i	−1.30943	−	0.582996i
$914$	−0.875466	+	8.32950i	−0.0289578	+	0.275515i
$915$	−3.49782	+	3.49050i	−0.115634	+	0.115392i
$916$	−32.1238	+	23.3393i	−1.06140	+	0.771153i
$917$	50.6576	−	1.15172i	1.67286	−	0.0380333i
$918$	1.86124			0.0614302
$919$	−21.2300	−	23.5783i	−0.700312	−	0.777775i	0.283114	−	0.959086i	$-0.408632\pi$
$919$	−21.2300	−	23.5783i	−0.700312	−	0.777775i	−0.983426	+	0.181311i	$0.941966\pi$
$920$	0.820984	−	2.13206i	0.0270670	−	0.0702921i
$921$	6.10751	−	6.78308i	0.201249	−	0.223510i
$922$	−10.5705	−	2.24683i	−0.348122	−	0.0739955i
$923$	2.14166	+	1.55601i	0.0704936	+	0.0512166i
$924$	−9.72407	+	11.3062i	−0.319898	+	0.371948i
$925$	27.4570	−	24.6186i	0.902782	−	0.809453i
$926$	−1.66967	+	2.89196i	−0.0548689	+	0.0950357i
$927$	−0.988736	+	9.40719i	−0.0324743	+	0.308973i
$928$	−22.6443	+	25.1490i	−0.743335	+	0.825557i
$929$	−28.0681	−	5.96607i	−0.920886	−	0.195740i	−0.277007	−	0.960868i	$-0.589343\pi$
$929$	−28.0681	−	5.96607i	−0.920886	−	0.195740i	−0.643879	+	0.765127i	$0.722676\pi$
$930$	3.72274	−	5.71941i	0.122074	−	0.187547i
$931$	22.8158	−	27.7812i	0.747759	−	0.910493i
$932$	−17.8859			−0.585874
$933$	3.04106	+	3.37744i	0.0995598	+	0.110572i
$934$	5.52843	+	2.46142i	0.180896	+	0.0805400i
$935$	−12.2322	+	31.7665i	−0.400036	+	1.03888i
$936$	−0.325572	+	0.144954i	−0.0106417	+	0.00473797i
$937$	−12.8621	+	9.34483i	−0.420185	+	0.305282i	−0.777712	−	0.628620i	$-0.783620\pi$
$937$	−12.8621	+	9.34483i	−0.420185	+	0.305282i	0.357527	+	0.933903i	$0.383620\pi$
$938$	−1.10525	+	13.4504i	−0.0360878	+	0.439171i
$939$	2.40890	+	1.75017i	0.0786114	+	0.0571145i
$940$	2.39995	−	0.377540i	0.0782777	−	0.0123140i
$941$	3.10656	+	1.38313i	0.101271	+	0.0450888i	0.456747	−	0.889597i	$-0.349014\pi$
$941$	3.10656	+	1.38313i	0.101271	+	0.0450888i	−0.355476	+	0.934685i	$0.615681\pi$
$942$	−0.122686	+	0.0260776i	−0.00399731	+	0.000849655i
$943$	1.16840	−	2.02372i	0.0380482	−	0.0659014i
$944$	−6.60883	+	20.3399i	−0.215099	+	0.662007i
$945$	−5.74635	−	1.40693i	−0.186929	−	0.0457673i
$946$	0.762149	+	2.34565i	0.0247796	+	0.0762638i
$947$	0.191602	+	0.0407262i	0.00622622	+	0.00132342i	0.211024	−	0.977481i	$-0.432320\pi$
$947$	0.191602	+	0.0407262i	0.00622622	+	0.00132342i	−0.204798	+	0.978804i	$0.565654\pi$
$948$	3.02707	−	28.8007i	0.0983147	−	0.935402i
$949$	−1.32589	−	2.29651i	−0.0430402	−	0.0745478i
$950$	1.95518	+	9.29401i	0.0634343	+	0.301538i
$951$	−31.4095			−1.01852
$952$	13.0475	+	13.8445i	0.422873	+	0.448704i
$953$	−0.687248	−	2.11513i	−0.0222622	−	0.0685159i	0.939308	−	0.343074i	$-0.111468\pi$
$953$	−0.687248	−	2.11513i	−0.0222622	−	0.0685159i	−0.961570	+	0.274559i	$0.911468\pi$
$954$	0.479687	+	0.101961i	0.0155304	+	0.00330110i
$955$	−13.4767	+	34.9985i	−0.436096	+	1.13252i
$956$	−19.3514	+	4.11326i	−0.625868	+	0.133032i
$957$	12.6686	−	21.9426i	0.409517	−	0.709304i
$958$	−4.68917	+	14.4318i	−0.151500	+	0.466269i
$959$	−17.6591	+	8.34834i	−0.570242	+	0.269582i
$960$	10.5834	+	2.84769i	0.341578	+	0.0919088i
$961$	33.8793	−	15.0840i	1.09288	−	0.486581i
$962$	0.621575	+	0.276743i	0.0200404	+	0.00892255i
$963$	−7.28325	−	3.24271i	−0.234700	−	0.104495i
$964$	−21.8041	+	9.70780i	−0.702262	+	0.312667i
$965$	−1.27490	−	24.8237i	−0.0410406	−	0.799103i
$966$	0.575308	+	0.398326i	0.0185102	+	0.0128159i
$967$	−8.57944	+	26.4048i	−0.275896	+	0.849121i	0.713085	+	0.701078i	$0.247298\pi$
$967$	−8.57944	+	26.4048i	−0.275896	+	0.849121i	−0.988981	+	0.148043i	$0.952702\pi$
$968$	−1.32058	+	2.28731i	−0.0424450	+	0.0735169i
$969$	−25.2789	+	5.37320i	−0.812076	+	0.172612i
$970$	−0.664852	−	2.49169i	−0.0213471	−	0.0800033i
$971$	−16.5115	−	3.50962i	−0.529878	−	0.112629i	−0.0647993	−	0.997898i	$-0.520641\pi$
$971$	−16.5115	−	3.50962i	−0.529878	−	0.112629i	−0.465079	+	0.885269i	$0.653974\pi$
$972$	0.575760	+	1.77201i	0.0184675	+	0.0568372i
$973$	−2.02404	+	0.478554i	−0.0648878	+	0.0153417i
$974$	4.74528			0.152049
$975$	1.08131	−	0.621281i	0.0346297	−	0.0198969i
$976$	3.53354	+	6.12027i	0.113106	+	0.195905i
$977$	2.61851	−	24.9135i	0.0837736	−	0.797052i	−0.869294	−	0.494295i	$-0.835426\pi$
$977$	2.61851	−	24.9135i	0.0837736	−	0.797052i	0.953068	−	0.302757i	$-0.0979071\pi$
$978$	2.30593	+	0.490140i	0.0737355	+	0.0156730i
$979$	−3.56636	−	10.9761i	−0.113981	−	0.350799i
$980$	−14.3808	−	25.3715i	−0.459377	−	0.810464i
$981$	4.09904	−	12.6155i	0.130872	−	0.402783i
$982$	−0.0432050	+	0.0748332i	−0.00137873	+	0.00238802i
$983$	52.4541	−	11.1495i	1.67302	−	0.355612i	0.728752	−	0.684777i	$-0.240101\pi$
$983$	52.4541	−	11.1495i	1.67302	−	0.355612i	0.944272	+	0.329165i	$0.106767\pi$
$984$	−4.26572	−	1.89922i	−0.135986	−	0.0605449i
$985$	6.28714	−	39.4283i	0.200325	−	1.25629i
$986$	−12.6116	−	9.16289i	−0.401636	−	0.291806i
$987$	−0.126351	+	1.53764i	−0.00402180	+	0.0489435i
$988$	1.93080	−	1.40281i	0.0614270	−	0.0446293i
$989$	−1.43994	+	0.641103i	−0.0457875	+	0.0203859i
$990$	2.49837	+	0.133556i	0.0794033	+	0.00424469i
$991$	12.4028	+	5.52209i	0.393988	+	0.175415i	0.594162	−	0.804346i	$-0.297484\pi$
$991$	12.4028	+	5.52209i	0.393988	+	0.175415i	−0.200173	+	0.979760i	$0.564151\pi$
$992$	−22.3088	−	24.7764i	−0.708304	−	0.786651i
$993$	12.8929			0.409144
$994$	−10.3836	+	0.236075i	−0.329346	+	0.00748783i
$995$	1.63027	+	31.7431i	0.0516830	+	1.00632i
$996$	−26.0918	−	5.54598i	−0.826750	−	0.175731i
$997$	24.2864	−	26.9728i	0.769158	−	0.854237i	−0.223561	−	0.974690i	$-0.571768\pi$
$997$	24.2864	−	26.9728i	0.769158	−	0.854237i	0.992719	+	0.120453i	$0.0384348\pi$
$998$	−1.04407	+	9.93365i	−0.0330494	+	0.314444i
$999$	3.68777	−	6.38740i	0.116676	−	0.202088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.13	✓	160
7.4	even	3	inner	525.2.bg.a.466.8	yes	160
25.11	even	5	inner	525.2.bg.a.436.8	yes	160
175.11	even	15	inner	525.2.bg.a.361.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.13	✓	160	1.1	even	1	trivial
525.2.bg.a.361.13	yes	160	175.11	even	15	inner
525.2.bg.a.436.8	yes	160	25.11	even	5	inner
525.2.bg.a.466.8	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.337888 - 0.150438i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.24672 + 1.38463i) q^{4} +(-1.99129 - 1.01724i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 - 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.337888 - 0.150438i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.24672 + 1.38463i) q^{4} +(-1.99129 - 1.01724i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 - 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.825864 - 0.0441485i) q^{10} +(0.316215 - 3.00858i) q^{11} +(-0.194757 - 1.85299i) q^{12} +(-0.201783 + 0.146604i) q^{13} +(0.281163 - 0.937309i) q^{14} +(2.08839 - 0.799150i) q^{15} +(-0.334273 - 3.18040i) q^{16} +(4.92226 - 1.04626i) q^{17} +(-0.184932 - 0.320312i) q^{18} +(3.43641 + 3.81652i) q^{19} +(3.89108 - 1.48898i) q^{20} +(0.336292 + 2.62429i) q^{21} +(-0.345759 - 1.06414i) q^{22} +(0.653248 - 0.290845i) q^{23} +(-0.714431 - 1.23743i) q^{24} +(2.93045 + 4.05123i) q^{25} +(-0.0461254 + 0.0798915i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.626580 + 4.88958i) q^{28} +(-2.58817 - 7.96556i) q^{29} +(0.585419 - 0.584195i) q^{30} +(8.07108 - 1.71556i) q^{31} +(-2.02026 - 3.49919i) q^{32} +(2.02422 + 2.24813i) q^{33} +(1.50578 - 1.09401i) q^{34} +(-5.47587 + 2.23939i) q^{35} +(1.50736 + 1.09516i) q^{36} +(-0.770953 - 7.33513i) q^{37} +(1.73527 + 0.772592i) q^{38} +(0.0260712 - 0.248051i) q^{39} +(2.26159 - 2.25686i) q^{40} +(2.64381 - 1.92084i) q^{41} +(0.508421 + 0.836127i) q^{42} -2.20428 q^{43} +(3.77153 + 4.18871i) q^{44} +(-0.803520 + 2.08671i) q^{45} +(0.176971 - 0.196546i) q^{46} +(0.570388 + 0.121240i) q^{47} +(2.58717 + 1.87969i) q^{48} +(-1.04733 - 6.92121i) q^{49} +(1.59962 + 0.928013i) q^{50} +(-2.51611 + 4.35804i) q^{51} +(0.0485759 - 0.462169i) q^{52} +(-0.887199 + 0.985335i) q^{53} +(0.361782 + 0.0768992i) q^{54} +(-3.69012 + 5.66929i) q^{55} +(1.96413 + 3.23012i) q^{56} -5.13563 q^{57} +(-2.07283 - 2.30211i) q^{58} +(-6.10950 - 2.72013i) q^{59} +(-1.49712 + 3.88796i) q^{60} +(-2.01885 + 0.898848i) q^{61} +(2.46904 - 1.79386i) q^{62} +(-2.17525 - 1.50608i) q^{63} +(3.96530 + 2.88096i) q^{64} +(0.550939 - 0.0866691i) q^{65} +(1.02216 + 0.455097i) q^{66} +(-13.4899 + 2.86737i) q^{67} +(-4.68802 + 8.11990i) q^{68} +(-0.220968 + 0.680071i) q^{69} +(-1.51334 + 1.58044i) q^{70} +(-3.27981 - 10.0942i) q^{71} +(1.39764 + 0.297077i) q^{72} +(-1.11133 + 10.5736i) q^{73} +(-1.36398 - 2.36247i) q^{74} +(-4.97150 - 0.533051i) q^{75} -9.56870 q^{76} +(-5.48941 - 5.82472i) q^{77} +(-0.0285071 - 0.0877357i) q^{78} +(15.2031 + 3.23153i) q^{79} +(-2.56959 + 6.67312i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.604345 - 1.04676i) q^{82} +(4.42407 - 13.6159i) q^{83} +(-4.05293 - 2.80613i) q^{84} +(-10.8659 - 2.92371i) q^{85} +(-0.744801 + 0.331607i) q^{86} +(7.65139 + 3.40662i) q^{87} +(3.94883 + 1.75813i) q^{88} +(3.48518 - 1.55170i) q^{89} +(0.0424196 + 0.825954i) q^{90} +(-0.0540432 + 0.657680i) q^{91} +(-0.411708 + 1.26711i) q^{92} +(-4.12570 + 7.14591i) q^{93} +(0.210966 - 0.0448423i) q^{94} +(-2.96057 - 11.0954i) q^{95} +(3.95222 + 0.840071i) q^{96} +(0.963569 + 2.96556i) q^{97} +(-1.39509 - 2.18104i) q^{98} -3.02516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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