LMFDB - Embedded newform 975.2.ce.a.44.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(44,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 18, 15]))

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

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

chi := DirichletCharacter("975.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.ce (of order $20$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$1088$
Relative dimension:	$136$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			44.4
Character	$\chi$	$=$	975.44
Dual form			975.2.ce.a.554.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38629 - 1.21588i) q^{2} +(0.387033 + 1.68826i) q^{3} +(3.04046 + 4.18483i) q^{4} +(2.19514 - 0.425880i) q^{5} +(1.12914 - 4.49925i) q^{6} +(1.27318 - 1.27318i) q^{7} +(-1.32926 - 8.39261i) q^{8} +(-2.70041 + 1.30682i) q^{9} +O(q^{10})$	\(q+(-2.38629 - 1.21588i) q^{2} +(0.387033 + 1.68826i) q^{3} +(3.04046 + 4.18483i) q^{4} +(2.19514 - 0.425880i) q^{5} +(1.12914 - 4.49925i) q^{6} +(1.27318 - 1.27318i) q^{7} +(-1.32926 - 8.39261i) q^{8} +(-2.70041 + 1.30682i) q^{9} +(-5.75605 - 1.65274i) q^{10} +(3.94089 + 2.00798i) q^{11} +(-5.88831 + 6.75274i) q^{12} +(-0.991763 + 3.46647i) q^{13} +(-4.58620 + 1.49015i) q^{14} +(1.56858 + 3.54112i) q^{15} +(-3.83544 + 11.8043i) q^{16} +(-4.57595 + 6.29826i) q^{17} +(8.03290 + 0.164913i) q^{18} +(-2.26113 + 0.358128i) q^{19} +(8.45646 + 7.89141i) q^{20} +(2.64221 + 1.65669i) q^{21} +(-6.96265 - 9.58326i) q^{22} +(-4.70327 + 1.52819i) q^{23} +(13.6544 - 5.49234i) q^{24} +(4.63725 - 1.86973i) q^{25} +(6.58143 - 7.06614i) q^{26} +(-3.25139 - 4.05320i) q^{27} +(9.19909 + 1.45699i) q^{28} +(1.81408 + 2.49686i) q^{29} +(0.562469 - 10.3574i) q^{30} +(0.491474 - 0.0778418i) q^{31} +(11.4881 - 11.4881i) q^{32} +(-1.86474 + 7.43038i) q^{33} +(18.5775 - 9.46568i) q^{34} +(2.25258 - 3.33702i) q^{35} +(-13.6793 - 7.32744i) q^{36} +(-1.17431 - 2.30471i) q^{37} +(5.83116 + 1.89466i) q^{38} +(-6.23613 - 0.332713i) q^{39} +(-6.49214 - 17.8568i) q^{40} +(-2.52019 + 1.28410i) q^{41} +(-4.29076 - 7.16594i) q^{42} +5.82558 q^{43} +(3.57904 + 22.5972i) q^{44} +(-5.37122 + 4.01870i) q^{45} +(13.0815 + 2.07190i) q^{46} +(-10.6475 - 1.68639i) q^{47} +(-21.4131 - 1.90656i) q^{48} +3.75804i q^{49} +(-13.3392 - 1.17661i) q^{50} +(-12.4041 - 5.28774i) q^{51} +(-17.5220 + 6.38929i) q^{52} +(7.37946 - 5.36149i) q^{53} +(2.83058 + 13.6254i) q^{54} +(9.50595 + 2.72945i) q^{55} +(-12.3777 - 8.99290i) q^{56} +(-1.47974 - 3.67876i) q^{57} +(-1.29304 - 8.16393i) q^{58} +(3.71545 + 7.29197i) q^{59} +(-10.0498 + 17.3309i) q^{60} +(-0.303174 - 0.933075i) q^{61} +(-1.26745 - 0.411818i) q^{62} +(-1.77429 + 5.10192i) q^{63} +(-17.7736 + 5.77501i) q^{64} +(-0.700758 + 8.03175i) q^{65} +(13.4842 - 15.4638i) q^{66} +(-0.599554 - 3.78543i) q^{67} -40.2702 q^{68} +(-4.40029 - 7.34886i) q^{69} +(-9.43271 + 5.22425i) q^{70} +(15.0834 + 2.38898i) q^{71} +(14.5572 + 20.9264i) q^{72} +(-6.61729 - 3.37168i) q^{73} +6.92753i q^{74} +(4.95135 + 7.10522i) q^{75} +(-8.37359 - 8.37359i) q^{76} +(7.57397 - 2.46093i) q^{77} +(14.4767 + 8.37631i) q^{78} +(-10.1273 + 7.35792i) q^{79} +(-3.39212 + 27.5455i) q^{80} +(5.58444 - 7.05790i) q^{81} +7.57522 q^{82} +(-4.97860 + 0.788533i) q^{83} +(1.10057 + 16.0943i) q^{84} +(-7.36254 + 15.7743i) q^{85} +(-13.9015 - 7.08318i) q^{86} +(-3.51323 + 4.02899i) q^{87} +(11.6138 - 35.7435i) q^{88} +(5.16117 + 2.62975i) q^{89} +(17.7035 - 3.05904i) q^{90} +(3.15074 + 5.67612i) q^{91} +(-20.6953 - 15.0360i) q^{92} +(0.321633 + 0.799606i) q^{93} +(23.3575 + 16.9702i) q^{94} +(-4.81098 + 1.74911i) q^{95} +(23.8412 + 14.9486i) q^{96} +(10.8639 + 1.72068i) q^{97} +(4.56930 - 8.96777i) q^{98} +(-13.2661 - 0.272348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9}+O(q^{10}) $ 1088 * q - 20 * q^3 + 2 * q^6 - 12 * q^9	$ 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9} - 20 q^{13} - 34 q^{15} + 248 q^{16} - 24 q^{19} + 12 q^{21} - 40 q^{22} - 28 q^{24} - 20 q^{27} - 100 q^{28} - 12 q^{31} + 40 q^{33} - 4 q^{34} - 140 q^{37} + 6 q^{39} + 32 q^{40} - 20 q^{42} + 30 q^{45} + 12 q^{46} - 20 q^{48} - 20 q^{52} - 100 q^{54} - 48 q^{55} - 140 q^{58} - 86 q^{60} + 72 q^{61} + 70 q^{63} - 36 q^{66} - 20 q^{67} - 192 q^{70} - 50 q^{72} + 60 q^{73} - 112 q^{76} + 60 q^{78} - 24 q^{79} + 20 q^{81} - 168 q^{84} - 196 q^{85} - 20 q^{87} - 44 q^{91} - 192 q^{94} - 20 q^{97} - 12 q^{99}+O(q^{100}) $ 1088 * q - 20 * q^3 + 2 * q^6 - 12 * q^9 - 20 * q^13 - 34 * q^15 + 248 * q^16 - 24 * q^19 + 12 * q^21 - 40 * q^22 - 28 * q^24 - 20 * q^27 - 100 * q^28 - 12 * q^31 + 40 * q^33 - 4 * q^34 - 140 * q^37 + 6 * q^39 + 32 * q^40 - 20 * q^42 + 30 * q^45 + 12 * q^46 - 20 * q^48 - 20 * q^52 - 100 * q^54 - 48 * q^55 - 140 * q^58 - 86 * q^60 + 72 * q^61 + 70 * q^63 - 36 * q^66 - 20 * q^67 - 192 * q^70 - 50 * q^72 + 60 * q^73 - 112 * q^76 + 60 * q^78 - 24 * q^79 + 20 * q^81 - 168 * q^84 - 196 * q^85 - 20 * q^87 - 44 * q^91 - 192 * q^94 - 20 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−2.38629	−	1.21588i	−1.68736	−	0.859754i	−0.989671	−	0.143356i	$-0.954211\pi$
$2$	−2.38629	−	1.21588i	−1.68736	−	0.859754i	−0.697691	−	0.716398i	$-0.745789\pi$
$3$	0.387033	+	1.68826i	0.223453	+	0.974715i
$3$	0.387033	+	1.68826i	0.223453	+	0.974715i
$4$	3.04046	+	4.18483i	1.52023	+	2.09242i
$5$	2.19514	−	0.425880i	0.981695	−	0.190459i
$5$	2.19514	−	0.425880i	0.981695	−	0.190459i
$6$	1.12914	−	4.49925i	0.460968	−	1.83681i
$7$	1.27318	−	1.27318i	0.481216	−	0.481216i	−0.424304	−	0.905520i	$-0.639481\pi$
$7$	1.27318	−	1.27318i	0.481216	−	0.481216i	0.905520	+	0.424304i	$0.139481\pi$
$8$	−1.32926	−	8.39261i	−0.469964	−	2.96723i
$9$	−2.70041	+	1.30682i	−0.900137	+	0.435607i
$10$	−5.75605	−	1.65274i	−1.82022	−	0.522643i
$11$	3.94089	+	2.00798i	1.18822	+	0.605430i	0.932447	−	0.361306i	$-0.117669\pi$
$11$	3.94089	+	2.00798i	1.18822	+	0.605430i	0.255776	+	0.966736i	$0.417669\pi$
$12$	−5.88831	+	6.75274i	−1.69981	+	1.94935i
$13$	−0.991763	+	3.46647i	−0.275066	+	0.961425i
$13$	−0.991763	+	3.46647i	−0.275066	+	0.961425i
$14$	−4.58620	+	1.49015i	−1.22571	+	0.398258i
$15$	1.56858	+	3.54112i	0.405006	+	0.914314i
$16$	−3.83544	+	11.8043i	−0.958861	+	2.95107i
$17$	−4.57595	+	6.29826i	−1.10983	+	1.52755i	−0.288167	+	0.957580i	$0.593046\pi$
$17$	−4.57595	+	6.29826i	−1.10983	+	1.52755i	−0.821664	+	0.569972i	$0.806954\pi$
$18$	8.03290	+	0.164913i	1.89337	+	0.0388703i
$19$	−2.26113	+	0.358128i	−0.518740	+	0.0821603i	−0.410314	−	0.911944i	$-0.634581\pi$
$19$	−2.26113	+	0.358128i	−0.518740	+	0.0821603i	−0.108426	+	0.994105i	$0.534581\pi$
$20$	8.45646	+	7.89141i	1.89092	+	1.76457i
$21$	2.64221	+	1.65669i	0.576578	+	0.361519i
$22$	−6.96265	−	9.58326i	−1.48444	−	2.04316i
$23$	−4.70327	+	1.52819i	−0.980700	+	0.318649i	−0.755128	−	0.655578i	$-0.772425\pi$
$23$	−4.70327	+	1.52819i	−0.980700	+	0.318649i	−0.225572	+	0.974226i	$0.572425\pi$
$24$	13.6544	−	5.49234i	2.78719	−	1.12112i
$25$	4.63725	−	1.86973i	0.927451	−	0.373946i
$26$	6.58143	−	7.06614i	1.29073	−	1.38578i
$27$	−3.25139	−	4.05320i	−0.625731	−	0.780039i
$28$	9.19909	+	1.45699i	1.73846	+	0.275346i
$29$	1.81408	+	2.49686i	0.336866	+	0.463656i	0.943523	−	0.331308i	$-0.107490\pi$
$29$	1.81408	+	2.49686i	0.336866	+	0.463656i	−0.606657	+	0.794964i	$0.707490\pi$
$30$	0.562469	−	10.3574i	0.102692	−	1.89098i
$31$	0.491474	−	0.0778418i	0.0882713	−	0.0139808i	−0.112143	−	0.993692i	$-0.535771\pi$
$31$	0.491474	−	0.0778418i	0.0882713	−	0.0139808i	0.200414	+	0.979711i	$0.435771\pi$
$32$	11.4881	−	11.4881i	2.03084	−	2.03084i
$33$	−1.86474	+	7.43038i	−0.324609	+	1.29346i
$34$	18.5775	−	9.46568i	3.18601	−	1.62335i
$35$	2.25258	−	3.33702i	0.380755	−	0.564059i
$36$	−13.6793	−	7.32744i	−2.27989	−	1.22124i
$37$	−1.17431	−	2.30471i	−0.193055	−	0.378892i	0.774106	−	0.633056i	$-0.218200\pi$
$37$	−1.17431	−	2.30471i	−0.193055	−	0.378892i	−0.967161	+	0.254164i	$0.918200\pi$
$38$	5.83116	+	1.89466i	0.945939	+	0.307354i
$39$	−6.23613	−	0.332713i	−0.998580	−	0.0532767i
$40$	−6.49214	−	17.8568i	−1.02650	−	2.82341i
$41$	−2.52019	+	1.28410i	−0.393588	+	0.200543i	−0.639573	−	0.768731i	$-0.720889\pi$
$41$	−2.52019	+	1.28410i	−0.393588	+	0.200543i	0.245985	+	0.969274i	$0.420889\pi$
$42$	−4.29076	−	7.16594i	−0.662078	−	1.10573i
$43$	5.82558			0.888392			0.444196	−	0.895930i	$-0.353489\pi$
$43$	5.82558			0.888392			0.444196	+	0.895930i	$0.353489\pi$
$44$	3.57904	+	22.5972i	0.539560	+	3.40665i
$45$	−5.37122	+	4.01870i	−0.800695	+	0.599072i
$46$	13.0815	+	2.07190i	1.92876	+	0.305485i
$47$	−10.6475	−	1.68639i	−1.55309	−	0.245986i	−0.679880	−	0.733324i	$-0.737968\pi$
$47$	−10.6475	−	1.68639i	−1.55309	−	0.245986i	−0.873213	+	0.487338i	$0.837968\pi$
$48$	−21.4131	−	1.90656i	−3.09071	−	0.275189i
$49$			3.75804i			0.536862i
$50$	−13.3392	−	1.17661i	−1.88645	−	0.166398i
$51$	−12.4041	−	5.28774i	−1.73692	−	0.740432i
$52$	−17.5220	+	6.38929i	−2.42987	+	0.886036i
$53$	7.37946	−	5.36149i	1.01365	−	0.736458i	0.0486763	−	0.998815i	$-0.484500\pi$
$53$	7.37946	−	5.36149i	1.01365	−	0.736458i	0.964971	+	0.262357i	$0.0844997\pi$
$54$	2.83058	+	13.6254i	0.385193	+	1.85418i
$55$	9.50595	+	2.72945i	1.28178	+	0.368040i
$56$	−12.3777	−	8.99290i	−1.65404	−	1.20173i
$57$	−1.47974	−	3.67876i	−0.195997	−	0.487264i
$58$	−1.29304	−	8.16393i	−0.169784	−	1.07198i
$59$	3.71545	+	7.29197i	0.483710	+	0.949334i	0.995900	+	0.0904620i	$0.0288344\pi$
$59$	3.71545	+	7.29197i	0.483710	+	0.949334i	−0.512190	+	0.858872i	$0.671166\pi$
$60$	−10.0498	+	17.3309i	−1.29742	+	2.23741i
$61$	−0.303174	−	0.933075i	−0.0388175	−	0.119468i	0.929770	−	0.368141i	$-0.120006\pi$
$61$	−0.303174	−	0.933075i	−0.0388175	−	0.119468i	−0.968588	+	0.248673i	$0.920006\pi$
$62$	−1.26745	−	0.411818i	−0.160966	−	0.0523009i
$63$	−1.77429	+	5.10192i	−0.223540	+	0.642781i
$64$	−17.7736	+	5.77501i	−2.22171	+	0.721876i
$65$	−0.700758	+	8.03175i	−0.0869183	+	0.996215i
$66$	13.4842	−	15.4638i	1.65979	−	1.90346i
$67$	−0.599554	−	3.78543i	−0.0732471	−	0.462464i	−0.996863	−	0.0791451i	$-0.974781\pi$
$67$	−0.599554	−	3.78543i	−0.0732471	−	0.462464i	0.923616	−	0.383319i	$-0.125219\pi$
$68$	−40.2702			−4.88347
$69$	−4.40029	−	7.34886i	−0.529732	−	0.884699i
$70$	−9.43271	+	5.22425i	−1.12743	+	0.624417i
$71$	15.0834	+	2.38898i	1.79007	+	0.283520i	0.961187	−	0.275897i	$-0.0889748\pi$
$71$	15.0834	+	2.38898i	1.79007	+	0.283520i	0.828887	+	0.559417i	$0.188975\pi$
$72$	14.5572	+	20.9264i	1.71558	+	2.46620i
$73$	−6.61729	−	3.37168i	−0.774496	−	0.394625i	0.0216228	−	0.999766i	$-0.493117\pi$
$73$	−6.61729	−	3.37168i	−0.774496	−	0.394625i	−0.796118	+	0.605141i	$0.793117\pi$
$74$			6.92753i			0.805309i
$75$	4.95135	+	7.10522i	0.571732	+	0.820440i
$76$	−8.37359	−	8.37359i	−0.960517	−	0.960517i
$77$	7.57397	−	2.46093i	0.863134	−	0.280449i
$78$	14.4767	+	8.37631i	1.63916	+	0.948430i
$79$	−10.1273	+	7.35792i	−1.13941	+	0.827831i	−0.987037	−	0.160492i	$-0.948692\pi$
$79$	−10.1273	+	7.35792i	−1.13941	+	0.827831i	−0.152375	+	0.988323i	$0.548692\pi$
$80$	−3.39212	+	27.5455i	−0.379251	+	3.07968i
$81$	5.58444	−	7.05790i	0.620494	−	0.784211i
$82$	7.57522			0.836543
$83$	−4.97860	+	0.788533i	−0.546473	+	0.0865528i	−0.423566	−	0.905865i	$-0.639222\pi$
$83$	−4.97860	+	0.788533i	−0.546473	+	0.0865528i	−0.122907	+	0.992418i	$0.539222\pi$
$84$	1.10057	+	16.0943i	0.120082	+	1.75603i
$85$	−7.36254	+	15.7743i	−0.798580	+	1.71097i
$86$	−13.9015	−	7.08318i	−1.49904	−	0.763799i
$87$	−3.51323	+	4.02899i	−0.376658	+	0.431953i
$88$	11.6138	−	35.7435i	1.23803	−	3.81027i
$89$	5.16117	+	2.62975i	0.547083	+	0.278753i	0.705608	−	0.708602i	$-0.250674\pi$
$89$	5.16117	+	2.62975i	0.547083	+	0.278753i	−0.158525	+	0.987355i	$0.550674\pi$
$90$	17.7035	−	3.05904i	1.86612	−	0.322451i
$91$	3.15074	+	5.67612i	0.330287	+	0.595019i
$92$	−20.6953	−	15.0360i	−2.15764	−	1.56761i
$93$	0.321633	+	0.799606i	0.0333518	+	0.0829153i
$94$	23.3575	+	16.9702i	2.40914	+	1.75035i
$95$	−4.81098	+	1.74911i	−0.493596	+	0.179455i
$96$	23.8412	+	14.9486i	2.43328	+	1.52569i
$97$	10.8639	+	1.72068i	1.10306	+	0.174708i	0.681305	−	0.732000i	$-0.261413\pi$
$97$	10.8639	+	1.72068i	1.10306	+	0.174708i	0.421759	+	0.906708i	$0.361413\pi$
$98$	4.56930	−	8.96777i	0.461569	−	0.905881i
$99$	−13.2661	−	0.272348i	−1.33329	−	0.0273720i
$100$	21.9239	+	13.7213i	2.19239	+	1.37213i
$101$	0.987361			0.0982461			0.0491231	−	0.998793i	$-0.484357\pi$
$101$	0.987361			0.0982461			0.0491231	+	0.998793i	$0.484357\pi$
$102$	23.1706	+	27.7000i	2.29423	+	2.74270i
$103$	7.38115	−	5.36272i	0.727287	−	0.528405i	−0.161417	−	0.986886i	$-0.551606\pi$
$103$	7.38115	−	5.36272i	0.727287	−	0.528405i	0.888704	+	0.458481i	$0.151606\pi$
$104$	30.4110	+	3.71565i	2.98205	+	0.364349i
$105$	6.50557	+	2.51139i	0.634878	+	0.245087i
$106$	−24.1285	+	3.82157i	−2.34356	+	0.371184i
$107$	7.63576			0.738177			0.369089	−	0.929394i	$-0.379670\pi$
$107$	7.63576			0.738177			0.369089	+	0.929394i	$0.379670\pi$
$108$	7.07624	−	25.9301i	0.680912	−	2.49513i
$109$	−6.82564	−	13.3961i	−0.653778	−	1.28311i	−0.945192	−	0.326514i	$-0.894126\pi$
$109$	−6.82564	−	13.3961i	−0.653778	−	1.28311i	0.291414	−	0.956597i	$-0.405874\pi$
$110$	−19.3653	−	18.0713i	−1.84641	−	1.72303i
$111$	3.43645	−	2.87453i	0.326173	−	0.272839i
$112$	10.1457	+	19.9122i	0.958683	+	1.88152i
$113$	−2.34601	+	7.22026i	−0.220694	+	0.679225i	0.778007	+	0.628256i	$0.216231\pi$
$113$	−2.34601	+	7.22026i	−0.220694	+	0.679225i	−0.998700	+	0.0509691i	$0.983769\pi$
$114$	−0.941818	+	10.5778i	−0.0882094	+	0.990700i
$115$	−9.67350	+	5.35760i	−0.902059	+	0.499599i
$116$	−4.93333	+	15.1832i	−0.458048	+	1.40973i
$117$	−1.85188	−	10.6569i	−0.171207	−	0.985235i
$118$		−	21.9183i		−	2.01774i
$119$	2.19280	+	13.8448i	0.201014	+	1.26915i
$120$	27.6342	−	17.8716i	2.52265	−	1.63144i
$121$	5.03297	+	6.92729i	0.457543	+	0.629754i
$122$	−0.411041	+	2.59521i	−0.0372139	+	0.234959i
$123$	−3.14329	−	3.75774i	−0.283421	−	0.338824i
$124$	1.82006	+	1.82006i	0.163446	+	0.163446i
$125$	9.38313	−	6.07922i	0.839252	−	0.543742i
$126$	10.4373	−	10.0173i	0.929826	−	0.892416i
$127$	−0.139910	−	0.430598i	−0.0124150	−	0.0382094i	0.944657	−	0.328059i	$-0.106395\pi$
$127$	−0.139910	−	0.430598i	−0.0124150	−	0.0382094i	−0.957072	+	0.289850i	$0.906395\pi$
$128$	17.3414	+	2.74662i	1.53278	+	0.242769i
$129$	2.25469	+	9.83506i	0.198514	+	0.865929i
$130$	11.4378	−	18.3140i	1.00316	−	1.60625i
$131$	−2.34721	+	3.23065i	−0.205076	+	0.282263i	−0.899150	−	0.437641i	$-0.855814\pi$
$131$	−2.34721	+	3.23065i	−0.205076	+	0.282263i	0.694074	+	0.719904i	$0.255814\pi$
$132$	−36.7646	+	14.7882i	−3.19994	+	1.28715i
$133$	−2.42286	+	3.33479i	−0.210089	+	0.289163i
$134$	−3.17191	+	9.76213i	−0.274011	+	0.843319i
$135$	−8.86343	−	7.51263i	−0.762843	−	0.646584i
$136$	58.9414	+	30.0322i	5.05419	+	2.57524i
$137$	4.33980	−	2.21124i	0.370774	−	0.188919i	−0.258668	−	0.965966i	$-0.583283\pi$
$137$	4.33980	−	2.21124i	0.370774	−	0.188919i	0.629442	+	0.777047i	$0.283283\pi$
$138$	1.56506	+	22.8867i	0.133227	+	1.94825i
$139$	0.148505	+	0.457050i	0.0125960	+	0.0387665i	0.957157	−	0.289570i	$-0.0935122\pi$
$139$	0.148505	+	0.457050i	0.0125960	+	0.0387665i	−0.944561	+	0.328336i	$0.893512\pi$
$140$	20.8138	−	0.719406i	1.75908	−	0.0608009i
$141$	−1.27386	−	18.6283i	−0.107278	−	1.56879i
$142$	−33.0888	−	24.0404i	−2.77675	−	2.01742i
$143$	−10.8690	+	11.6695i	−0.908915	+	0.975855i
$144$	−5.06880	−	36.8886i	−0.422400	−	3.07405i
$145$	5.04551	+	4.70838i	0.419007	+	0.391009i
$146$	11.6912	+	16.0916i	0.967574	+	1.33175i
$147$	−6.34452	+	1.45448i	−0.523287	+	0.119964i
$148$	6.07440	−	11.9217i	0.499312	−	0.979956i
$149$	−6.46889	−	6.46889i	−0.529952	−	0.529952i	0.390606	−	0.920558i	$-0.372266\pi$
$149$	−6.46889	−	6.46889i	−0.529952	−	0.529952i	−0.920558	+	0.390606i	$0.872266\pi$
$150$	−3.17629	−	22.9753i	−0.259343	−	1.87593i
$151$	7.38004	+	7.38004i	0.600579	+	0.600579i	0.940466	−	0.339887i	$-0.110389\pi$
$151$	7.38004	+	7.38004i	0.600579	+	0.600579i	−0.339887	+	0.940466i	$0.610389\pi$
$152$	6.01126	+	18.5008i	0.487578	+	1.50061i
$153$	4.12626	−	22.9878i	0.333589	−	1.85846i
$154$	−21.0659	−	3.33651i	−1.69754	−	0.268864i
$155$	1.04570	−	0.380182i	0.0839927	−	0.0305370i
$156$	−17.5684	−	27.1088i	−1.40659	−	2.17044i
$157$			8.17759i			0.652642i	0.945259	+	0.326321i	$0.105809\pi$
$157$			8.17759i			0.652642i	−0.945259	+	0.326321i	$0.894191\pi$
$158$	33.1130	−	5.24459i	2.63433	−	0.417237i
$159$	11.9077	+	10.3833i	0.944339	+	0.823453i
$160$	20.3255	−	30.1106i	1.60687	−	2.38045i
$161$	−4.04245	+	7.93375i	−0.318590	+	0.625267i
$162$	−21.9076	+	10.0522i	−1.72123	+	0.789777i
$163$	6.42734	+	12.6144i	0.503428	+	0.988034i	0.993226	+	0.116198i	$0.0370706\pi$
$163$	6.42734	+	12.6144i	0.503428	+	0.988034i	−0.489798	+	0.871836i	$0.662929\pi$
$164$	−13.0363	−	6.64232i	−1.01796	−	0.518678i
$165$	−0.928901	+	17.1049i	−0.0723149	+	1.33161i
$166$	12.8392	+	4.17169i	0.996511	+	0.323786i
$167$	3.37515	+	21.3099i	0.261177	+	1.64901i	0.674392	+	0.738374i	$0.264406\pi$
$167$	3.37515	+	21.3099i	0.261177	+	1.64901i	−0.413215	+	0.910634i	$0.635594\pi$
$168$	10.3917	−	24.3772i	0.801741	−	1.88074i
$169$	−11.0328	−	6.87583i	−0.848678	−	0.528910i
$170$	36.7488	−	28.6902i	2.81851	−	2.20044i
$171$	5.63798	−	3.92199i	0.431147	−	0.299922i
$172$	17.7124	+	24.3791i	1.35056	+	1.85889i
$173$	−5.15177	+	1.67391i	−0.391682	+	0.127265i	−0.498235	−	0.867042i	$-0.666018\pi$
$173$	−5.15177	+	1.67391i	−0.391682	+	0.127265i	0.106553	+	0.994307i	$0.466018\pi$
$174$	13.2824	−	5.34269i	1.00693	−	0.405028i
$175$	3.52355	−	8.28455i	0.266356	−	0.626253i
$176$	−38.8179	+	38.8179i	−2.92601	+	2.92601i
$177$	−10.8727	+	9.09485i	−0.817243	+	0.683611i
$178$	−9.11861	−	12.5507i	−0.683469	−	0.940714i
$179$	19.6713	−	14.2920i	1.47030	−	1.06824i	0.489774	−	0.871849i	$-0.337079\pi$
$179$	19.6713	−	14.2920i	1.47030	−	1.06824i	0.980527	−	0.196387i	$-0.0629207\pi$
$180$	−33.1486	−	10.2590i	−2.47075	−	0.764660i
$181$	−0.708593	+	0.975295i	−0.0526693	+	0.0724931i	−0.834539	−	0.550948i	$-0.814266\pi$
$181$	−0.708593	+	0.975295i	−0.0526693	+	0.0724931i	0.781870	+	0.623442i	$0.214266\pi$
$182$	−0.617122	−	17.3758i	−0.0457441	−	1.28798i
$183$	1.45793	−	0.872966i	0.107773	−	0.0645315i
$184$	19.0773	+	37.4414i	1.40640	+	2.76021i
$185$	−3.55930	−	4.55904i	−0.261685	−	0.335188i
$186$	0.204711	−	2.29916i	0.0150101	−	0.168582i
$187$	−30.6801	+	15.6323i	−2.24355	+	1.14315i
$188$	−25.3159	−	49.6853i	−1.84635	−	3.62367i
$189$	−9.30005	−	1.02084i	−0.676479	−	0.0742555i
$190$	13.6071	+	1.67566i	0.987163	+	0.121565i
$191$	−18.4314	−	5.98871i	−1.33365	−	0.433328i	−0.446486	−	0.894790i	$-0.647325\pi$
$191$	−18.4314	−	5.98871i	−1.33365	−	0.433328i	−0.887160	+	0.461462i	$0.847325\pi$
$192$	−16.6287	−	27.7713i	−1.20007	−	2.00422i
$193$	−17.5087	+	17.5087i	−1.26030	+	1.26030i	−0.309358	+	0.950946i	$0.600114\pi$
$193$	−17.5087	+	17.5087i	−1.26030	+	1.26030i	−0.950946	+	0.309358i	$0.899886\pi$
$194$	−23.8324	−	17.3152i	−1.71106	−	1.24316i
$195$	−13.8309	+	1.92549i	−0.990448	+	0.137887i
$196$	−15.7268	+	11.4262i	−1.12334	+	0.816154i
$197$	1.74761	−	11.0339i	0.124512	−	0.786136i	−0.843849	−	0.536581i	$-0.819716\pi$
$197$	1.74761	−	11.0339i	0.124512	−	0.786136i	0.968361	−	0.249555i	$-0.0802844\pi$
$198$	31.3256	+	16.7798i	2.22621	+	1.19249i
$199$			2.38421i			0.169012i	0.996423	+	0.0845061i	$0.0269313\pi$
$199$			2.38421i			0.169012i	−0.996423	+	0.0845061i	$0.973069\pi$
$200$	−21.8560	−	36.4333i	−1.54545	−	2.57622i
$201$	6.15873	−	2.47729i	0.434403	−	0.174734i
$202$	−2.35613	−	1.20051i	−0.165777	−	0.0844675i
$203$	5.48859	+	0.869308i	0.385224	+	0.0610135i
$204$	−15.5859	−	67.9863i	−1.09123	−	4.75999i
$205$	−4.98529	+	3.89208i	−0.348188	+	0.271834i
$206$	−24.1340	+	3.82245i	−1.68149	+	0.266323i
$207$	10.7037	−	10.2731i	0.743959	−	0.714027i
$208$	−37.1153	−	25.0025i	−2.57348	−	1.73361i
$209$	−9.62999	−	3.12897i	−0.666120	−	0.216436i
$210$	−12.4706	−	13.9029i	−0.860555	−	0.959390i
$211$	−1.53010	−	4.70917i	−0.105337	−	0.324193i	0.884473	−	0.466592i	$-0.154518\pi$
$211$	−1.53010	−	4.70917i	−0.105337	−	0.324193i	−0.989809	+	0.142399i	$0.954518\pi$
$212$	44.8739	+	14.5804i	3.08195	+	1.00139i
$213$	1.80457	+	26.3893i	0.123647	+	1.80816i
$214$	−18.2212	−	9.28414i	−1.24557	−	0.634651i
$215$	12.7879	−	2.48099i	0.872130	−	0.169202i
$216$	−29.6950	+	32.6754i	−2.02049	+	2.22328i
$217$	0.526627	−	0.724840i	0.0357498	−	0.0492054i
$218$			40.2661i			2.72716i
$219$	3.13115	−	12.4766i	0.211583	−	0.843092i
$220$	17.4801	+	48.0796i	1.17851	+	3.24153i
$221$	−17.2945	−	22.1088i	−1.16335	−	1.48720i
$222$	−11.6954	+	2.68118i	−0.784946	+	0.179949i
$223$	2.83676	−	5.56745i	0.189963	−	0.372824i	−0.776307	−	0.630356i	$-0.782909\pi$
$223$	2.83676	−	5.56745i	0.189963	−	0.372824i	0.966270	+	0.257532i	$0.0829091\pi$
$224$		−	29.2529i		−	1.95454i
$225$	−10.0791	+	11.1091i	−0.671940	+	0.740606i
$226$	14.3772	−	14.3772i	0.956357	−	0.956357i
$227$	25.7413	+	13.1158i	1.70851	+	0.870529i	0.983298	+	0.182003i	$0.0582580\pi$
$227$	25.7413	+	13.1158i	1.70851	+	0.870529i	0.725211	+	0.688526i	$0.241742\pi$
$228$	10.8959	−	17.3776i	0.721599	−	1.15086i
$229$	10.3028	+	1.63181i	0.680831	+	0.107833i	0.487265	−	0.873254i	$-0.337995\pi$
$229$	10.3028	+	1.63181i	0.680831	+	0.107833i	0.193566	+	0.981087i	$0.437995\pi$
$230$	29.5980	−	1.02302i	1.95163	−	0.0674561i
$231$	7.08606	+	11.8343i	0.466228	+	0.778642i
$232$	18.5438	−	18.5438i	1.21746	−	1.21746i
$233$	−5.64578	+	7.77074i	−0.369867	+	0.509078i	−0.952865	−	0.303395i	$-0.901880\pi$
$233$	−5.64578	+	7.77074i	−0.369867	+	0.509078i	0.582998	+	0.812474i	$0.301880\pi$
$234$	−8.53840	+	27.6822i	−0.558173	+	1.80964i
$235$	−24.0909	+	0.832675i	−1.57151	+	0.0543177i
$236$	−19.2190	+	37.7195i	−1.25105	+	2.45533i
$237$	−16.3417	−	14.2497i	−1.06150	−	0.925620i
$238$	11.6009	−	35.7039i	0.751975	−	2.31434i
$239$	7.24882	−	14.2266i	0.468887	−	0.920243i	−0.528564	−	0.848893i	$-0.677269\pi$
$239$	7.24882	−	14.2266i	0.468887	−	0.920243i	0.997451	−	0.0713496i	$-0.0227306\pi$
$240$	−47.8166	+	4.93422i	−3.08655	+	0.318503i
$241$	−7.72627	+	3.93673i	−0.497693	+	0.253587i	−0.684772	−	0.728758i	$-0.740098\pi$
$241$	−7.72627	+	3.93673i	−0.497693	+	0.253587i	0.187079	+	0.982345i	$0.440098\pi$
$242$	−3.58741	−	22.6500i	−0.230607	−	1.45600i
$243$	14.0769	+	6.69633i	0.903034	+	0.429569i
$244$	2.98297	−	4.10571i	0.190965	−	0.262841i
$245$	1.60047	+	8.24940i	0.102250	+	0.527035i
$246$	2.93186	+	12.7889i	0.186928	+	0.815391i
$247$	1.00107	−	8.19333i	0.0636965	−	0.521329i
$248$	−1.30659	−	4.02127i	−0.0829686	−	0.255351i
$249$	−3.25813	−	8.09996i	−0.206475	−	0.513314i
$250$	−29.7825	+	3.09807i	−1.88361	+	0.195939i
$251$	7.53182			0.475404			0.237702	−	0.971338i	$-0.423606\pi$
$251$	7.53182			0.475404			0.237702	+	0.971338i	$0.423606\pi$
$252$	−26.7453	+	8.08707i	−1.68480	+	0.509438i
$253$	−21.6036	−	3.42168i	−1.35821	−	0.215119i
$254$	−0.189688	+	1.19764i	−0.0119021	+	0.0751469i
$255$	−29.4807	−	6.32466i	−1.84615	−	0.396066i
$256$	−7.80388	−	5.66985i	−0.487742	−	0.354366i
$257$			23.2606i			1.45095i	0.688246	+	0.725477i	$0.258381\pi$
$257$			23.2606i			1.45095i	−0.688246	+	0.725477i	$0.741619\pi$
$258$	6.57787	−	26.2107i	0.409520	−	1.63181i
$259$	−4.42941	−	1.43920i	−0.275230	−	0.0894278i
$260$	−35.7422	+	21.4876i	−2.21663	+	1.33261i
$261$	−8.16170	−	4.37188i	−0.505197	−	0.270613i
$262$	9.52919	−	4.85536i	0.588715	−	0.299965i
$263$	7.08585	−	21.8080i	0.436932	−	1.34474i	−0.454162	−	0.890919i	$-0.650061\pi$
$263$	7.08585	−	21.8080i	0.436932	−	1.34474i	0.891094	−	0.453819i	$-0.149939\pi$
$264$	64.8390	+	5.77309i	3.99056	+	0.355309i
$265$	13.9156	−	14.9120i	0.854827	−	0.916035i
$266$	9.83635	−	5.01187i	0.603105	−	0.307297i
$267$	−2.44214	+	9.73117i	−0.149457	+	0.595538i
$268$	14.0185	−	14.0185i	0.856315	−	0.856315i
$269$	3.36682	−	4.63403i	0.205279	−	0.282542i	−0.693948	−	0.720025i	$-0.744130\pi$
$269$	3.36682	−	4.63403i	0.205279	−	0.282542i	0.899226	+	0.437483i	$0.144130\pi$
$270$	12.0163	+	28.7042i	0.731288	+	1.74688i
$271$	26.6124	+	4.21499i	1.61659	+	0.256042i	0.898196	−	0.439596i	$-0.144878\pi$
$271$	26.6124	+	4.21499i	1.61659	+	0.256042i	0.718392	+	0.695638i	$0.244878\pi$
$272$	−56.7956	−	78.1724i	−3.44374	−	4.73990i
$273$	−8.36331	+	7.51610i	−0.506170	+	0.454895i
$274$	−13.0446			−0.788055
$275$	22.0293	+	1.94314i	1.32842	+	0.117175i
$276$	17.3749	−	40.7584i	1.04585	−	2.45337i
$277$	−3.82678	−	11.7776i	−0.229929	−	0.707649i	−0.997754	−	0.0669891i	$-0.978661\pi$
$277$	−3.82678	−	11.7776i	−0.229929	−	0.707649i	0.767825	−	0.640660i	$-0.221339\pi$
$278$	0.201341	−	1.27122i	0.0120756	−	0.0762426i
$279$	−1.22546	+	0.852473i	−0.0733661	+	0.0510362i
$280$	−31.0006	−	14.4693i	−1.85264	−	0.864703i
$281$	13.5045	−	2.13891i	0.805614	−	0.127597i	0.259973	−	0.965616i	$-0.416286\pi$
$281$	13.5045	−	2.13891i	0.805614	−	0.127597i	0.545641	+	0.838019i	$0.316286\pi$
$282$	−19.6100	+	46.0015i	−1.16776	+	2.73935i
$283$	0.171241	+	0.124414i	0.0101792	+	0.00739563i	0.592863	−	0.805303i	$-0.297997\pi$
$283$	0.171241	+	0.124414i	0.0101792	+	0.00739563i	−0.582684	+	0.812699i	$0.697997\pi$
$284$	35.8631	+	70.3853i	2.12808	+	4.17660i
$285$	−4.81495	−	7.44520i	−0.285213	−	0.441015i
$286$	40.1254	−	14.6315i	2.37266	−	0.865177i
$287$	−1.57376	+	4.84354i	−0.0928962	+	0.285905i
$288$	−16.0098	+	46.0356i	−0.943385	+	2.71268i
$289$	−13.4754	−	41.4731i	−0.792672	−	2.43959i
$290$	−6.31525	−	17.3703i	−0.370844	−	1.02002i
$291$	1.29975	+	19.0070i	0.0761928	+	1.11421i
$292$	−6.00970	−	37.9437i	−0.351691	−	2.22049i
$293$	−10.6315	−	10.6315i	−0.621098	−	0.621098i	0.324714	−	0.945812i	$-0.394732\pi$
$293$	−10.6315	−	10.6315i	−0.621098	−	0.621098i	−0.945812	+	0.324714i	$0.894732\pi$
$294$	16.9083	+	4.24333i	0.986115	+	0.247476i
$295$	11.2614	+	14.4245i	0.655665	+	0.839830i
$296$	−17.7816	+	12.9191i	−1.03353	+	0.750906i
$297$	−4.67462	−	22.5020i	−0.271249	−	1.30570i
$298$	7.57129	+	23.3020i	0.438593	+	1.34985i
$299$	−0.632875	−	17.8193i	−0.0366001	−	1.03052i
$300$	−14.6798	+	42.3237i	−0.847539	+	2.44356i
$301$	7.41700	−	7.41700i	0.427509	−	0.427509i
$302$	−8.63771	−	26.5841i	−0.497044	−	1.52975i
$303$	0.382141	+	1.66692i	0.0219534	+	0.0957619i
$304$	4.44500	−	28.0646i	0.254938	−	1.60962i
$305$	−1.06289	−	1.91911i	−0.0608607	−	0.109888i
$306$	−37.7968	+	49.8386i	−2.16070	+	2.84908i
$307$	7.98145	−	7.98145i	0.455526	−	0.455526i	−0.441658	−	0.897184i	$-0.645610\pi$
$307$	7.98145	−	7.98145i	0.455526	−	0.455526i	0.897184	+	0.441658i	$0.145610\pi$
$308$	33.3270	+	24.2135i	1.89898	+	1.37969i
$309$	11.9104	+	10.3857i	0.677559	+	0.590823i
$310$	−2.95760	−	0.364218i	−0.167980	−	0.0206862i
$311$	0.0637065	+	0.196069i	0.00361247	+	0.0111180i	0.952847	−	0.303453i	$-0.0981394\pi$
$311$	0.0637065	+	0.196069i	0.00361247	+	0.0111180i	−0.949234	+	0.314571i	$0.898139\pi$
$312$	5.49710	+	52.7796i	0.311212	+	2.98806i
$313$	6.73857	+	2.18949i	0.380886	+	0.123757i	0.493201	−	0.869915i	$-0.335827\pi$
$313$	6.73857	+	2.18949i	0.380886	+	0.123757i	−0.112315	+	0.993673i	$0.535827\pi$
$314$	9.94293	−	19.5141i	0.561112	−	1.10124i
$315$	−1.72201	+	11.9550i	−0.0970241	+	0.673591i
$316$	−61.5834	−	20.0097i	−3.46434	−	1.12563i
$317$	25.0630	−	3.96959i	1.40768	−	0.222954i	0.594091	−	0.804398i	$-0.297512\pi$
$317$	25.0630	−	3.96959i	1.40768	−	0.222954i	0.813587	+	0.581443i	$0.197512\pi$
$318$	−15.7903	−	39.2559i	−0.885476	−	2.20136i
$319$	2.13542	+	13.4825i	0.119560	+	0.754875i
$320$	−36.5561	+	20.2464i	−2.04355	+	1.13181i
$321$	2.95529	+	12.8911i	0.164948	+	0.719512i
$322$	19.2929	−	14.0171i	1.07515	−	0.781144i
$323$	8.09125	−	15.8800i	0.450209	−	0.883586i
$324$	46.5154	+	1.91070i	2.58419	+	0.106150i
$325$	1.88230	+	17.9292i	0.104411	+	0.994534i
$326$		−	37.9164i		−	2.10000i
$327$	19.9742	−	16.7081i	1.10458	−	0.923963i
$328$	14.1269	+	19.4441i	0.780030	+	1.07362i
$329$	−15.7032	+	11.4090i	−0.865746	+	0.629001i
$330$	23.0140	−	39.6877i	1.26688	−	2.18474i
$331$	12.2778	−	1.94462i	0.674850	−	0.106886i	0.190403	−	0.981706i	$-0.439021\pi$
$331$	12.2778	−	1.94462i	0.674850	−	0.106886i	0.484447	+	0.874820i	$0.339021\pi$
$332$	−18.4371	−	18.4371i	−1.01187	−	1.01187i
$333$	6.18296	+	4.68906i	0.338824	+	0.256959i
$334$	17.8561	−	54.9553i	0.977040	−	3.00702i
$335$	−2.92824	−	8.05420i	−0.159987	−	0.440048i
$336$	−29.6901	+	24.8353i	−1.61973	+	1.35488i
$337$	6.51986	−	20.0661i	0.355159	−	1.09307i	−0.600757	−	0.799431i	$-0.705134\pi$
$337$	6.51986	−	20.0661i	0.355159	−	1.09307i	0.955917	−	0.293637i	$-0.0948657\pi$
$338$	17.9673	+	29.8223i	0.977294	+	1.62212i
$339$	−13.0976	−	1.16618i	−0.711366	−	0.0633381i
$340$	−88.3985	+	17.1502i	−4.79408	+	0.930102i
$341$	2.09315	+	0.680105i	0.113350	+	0.0368298i
$342$	−18.2225	+	2.50392i	−0.985361	+	0.135396i
$343$	13.6969	+	13.6969i	0.739563	+	0.739563i
$344$	−7.74370	−	48.8918i	−0.417512	−	2.63607i
$345$	−12.7890	−	14.2578i	−0.688535	−	0.767613i
$346$	14.3289	+	2.26948i	0.770327	+	0.122008i
$347$	−19.0430	+	13.8356i	−1.02228	+	0.742732i	−0.966749	−	0.255725i	$-0.917686\pi$
$347$	−19.0430	+	13.8356i	−1.02228	+	0.742732i	−0.0555328	+	0.998457i	$0.517686\pi$
$348$	−27.5425	−	2.45231i	−1.47643	−	0.131458i
$349$	−13.5832	−	13.5832i	−0.727091	−	0.727091i	0.242948	−	0.970039i	$-0.421885\pi$
$349$	−13.5832	−	13.5832i	−0.727091	−	0.727091i	−0.970039	+	0.242948i	$0.921885\pi$
$350$	−18.4812	+	15.4851i	−0.987862	+	0.827715i
$351$	17.2749	−	7.25104i	0.922066	−	0.387032i
$352$	68.3415	−	22.2055i	3.64261	−	1.18356i
$353$	3.83988	−	24.2441i	0.204376	−	1.29038i	−0.645647	−	0.763636i	$-0.723412\pi$
$353$	3.83988	−	24.2441i	0.204376	−	1.29038i	0.850023	−	0.526746i	$-0.176588\pi$
$354$	37.0037	−	8.48310i	1.96672	−	0.450872i
$355$	34.1276	−	1.17959i	1.81131	−	0.0626059i
$356$	4.68728	+	29.5943i	0.248425	+	1.56849i
$357$	−22.5249	+	9.06040i	−1.19214	+	0.479527i
$358$	−64.3187	+	10.1871i	−3.39935	+	0.538404i
$359$	1.32389	+	2.59828i	0.0698721	+	0.137132i	0.923300	−	0.384078i	$-0.125481\pi$
$359$	1.32389	+	2.59828i	0.0698721	+	0.137132i	−0.853428	+	0.521210i	$0.825481\pi$
$360$	40.8671	+	39.7367i	2.15389	+	2.09431i
$361$	−13.0856	+	4.25177i	−0.688716	+	0.223777i
$362$	2.87675	−	1.46578i	0.151198	−	0.0770394i
$363$	−9.74711	+	11.1780i	−0.511591	+	0.586694i
$364$	−14.1739	+	30.4434i	−0.742916	+	1.59567i
$365$	−15.9618	−	4.58313i	−0.835478	−	0.239892i
$366$	−4.54046	+	0.310489i	−0.237334	+	0.0162295i
$367$	−1.23871	+	1.70493i	−0.0646599	+	0.0889968i	−0.840122	−	0.542397i	$-0.817517\pi$
$367$	−1.23871	+	1.70493i	−0.0646599	+	0.0889968i	0.775462	+	0.631394i	$0.217517\pi$
$368$		−	61.3800i		−	3.19965i
$369$	5.12746	−	6.76104i	0.266925	−	0.351966i
$370$	2.95029	+	15.2069i	0.153378	+	0.790568i
$371$	2.56923	−	16.2215i	0.133388	−	0.842179i
$372$	−2.36830	+	3.77715i	−0.122791	+	0.195836i
$373$	3.56740	−	1.15912i	0.184713	−	0.0600169i	−0.215200	−	0.976570i	$-0.569040\pi$
$373$	3.56740	−	1.15912i	0.184713	−	0.0600169i	0.399913	+	0.916553i	$0.369040\pi$
$374$	92.2186			4.76851
$375$	13.8949	+	13.4883i	0.717527	+	0.696531i
$376$			91.6017i			4.72400i
$377$	−10.4544	+	3.81214i	−0.538431	+	0.196335i
$378$	20.9514	+	13.7437i	1.07762	+	0.706902i
$379$	−0.190217	+	1.20098i	−0.00977079	+	0.0616904i	−0.992092	−	0.125513i	$-0.959942\pi$
$379$	−0.190217	+	1.20098i	−0.00977079	+	0.0616904i	0.982321	+	0.187203i	$0.0599423\pi$
$380$	−21.9473	−	14.8150i	−1.12587	−	0.759996i
$381$	0.672809	−	0.402859i	0.0344691	−	0.0206391i
$382$	36.7011	+	36.7011i	1.87779	+	1.87779i
$383$	22.0879	−	3.49838i	1.12864	−	0.178759i	0.435933	−	0.899979i	$-0.356419\pi$
$383$	22.0879	−	3.49838i	1.12864	−	0.178759i	0.692706	+	0.721220i	$0.256419\pi$
$384$	2.07472	+	30.3398i	0.105875	+	1.54827i
$385$	15.5778	−	8.62769i	0.793921	−	0.439708i
$386$	63.0693	−	20.4924i	3.21014	−	1.04304i
$387$	−15.7315	+	7.61298i	−0.799675	+	0.386990i
$388$	25.8306	+	50.6954i	1.31135	+	2.57367i
$389$	−8.89141	−	27.3649i	−0.450812	−	1.38746i	−0.875982	−	0.482344i	$-0.839785\pi$
$389$	−8.89141	−	27.3649i	−0.450812	−	1.38746i	0.425169	−	0.905114i	$-0.360215\pi$
$390$	35.3456	+	12.2218i	1.78979	+	0.618876i
$391$	11.8970	−	36.6153i	0.601659	−	1.85172i
$392$	31.5397	−	4.99540i	1.59300	−	0.252306i
$393$	−6.36261	−	2.71231i	−0.320951	−	0.136818i
$394$	−17.5862	+	24.2053i	−0.885980	+	1.21945i
$395$	−19.0972	+	20.4647i	−0.960887	+	1.02969i
$396$	−39.1953	−	56.3445i	−1.96964	−	2.83142i
$397$	−2.97796	+	18.8021i	−0.149460	+	0.943651i	0.792973	+	0.609256i	$0.208532\pi$
$397$	−2.97796	+	18.8021i	−0.149460	+	0.943651i	−0.942433	+	0.334395i	$0.891468\pi$
$398$	2.89891	−	5.68942i	0.145309	−	0.285185i
$399$	−6.56770	−	2.79974i	−0.328796	−	0.140162i
$400$	4.28487	+	61.9107i	0.214244	+	3.09553i
$401$	−10.3459	+	10.3459i	−0.516649	+	0.516649i	−0.916556	−	0.399907i	$-0.869043\pi$
$401$	−10.3459	+	10.3459i	−0.516649	+	0.516649i	0.399907	+	0.916556i	$0.369043\pi$
$402$	−17.7086	−	1.57673i	−0.883224	−	0.0786400i
$403$	−0.217590	+	1.78088i	−0.0108389	+	0.0887119i
$404$	3.00203	+	4.13194i	0.149357	+	0.205572i
$405$	9.25280	−	17.8714i	0.459775	−	0.888035i
$406$	−12.0404	−	8.74787i	−0.597556	−	0.434150i
$407$		−	11.4406i		−	0.567090i
$408$	−27.8897	+	111.132i	−1.38074	+	5.50183i
$409$	−2.51251	−	4.93109i	−0.124236	−	0.243827i	0.820509	−	0.571634i	$-0.193690\pi$
$409$	−2.51251	−	4.93109i	−0.124236	−	0.243827i	−0.944745	+	0.327807i	$0.893690\pi$
$410$	16.6286	−	3.22613i	0.821230	−	0.159327i
$411$	5.41278	+	6.47087i	0.266993	+	0.319185i
$412$	44.8842	+	14.5838i	2.21129	+	0.718491i
$413$	14.0144	+	4.55356i	0.689604	+	0.224066i
$414$	−38.0329	+	11.5001i	−1.86922	+	0.565201i
$415$	−10.5929	+	3.85122i	−0.519985	+	0.189049i
$416$	28.4298	+	51.2168i	1.39388	+	2.51111i
$417$	−0.714141	+	0.427607i	−0.0349716	+	0.0209400i
$418$	19.1755	+	19.1755i	0.937905	+	0.937905i
$419$	−12.2683	+	16.8858i	−0.599343	+	0.824925i	−0.995648	−	0.0931937i	$-0.970292\pi$
$419$	−12.2683	+	16.8858i	−0.599343	+	0.824925i	0.396305	+	0.918119i	$0.370292\pi$
$420$	9.27015	+	34.8605i	0.452337	+	1.70102i
$421$	1.64952	−	10.4147i	0.0803926	−	0.507579i	−0.914329	−	0.404972i	$-0.867281\pi$
$421$	1.64952	−	10.4147i	0.0803926	−	0.507579i	0.994722	−	0.102608i	$-0.0327186\pi$
$422$	−2.07450	+	13.0979i	−0.100985	+	0.637594i
$423$	30.9564	−	9.36037i	1.50515	−	0.455117i
$424$	−54.8061	−	54.8061i	−2.66162	−	2.66162i
$425$	−9.44382	+	37.7624i	−0.458092	+	1.83175i
$426$	27.7799	−	65.1667i	1.34594	−	3.15734i
$427$	−1.57396	−	0.801975i	−0.0761695	−	0.0388103i
$428$	23.2162	+	31.9544i	1.12220	+	1.54457i
$429$	−23.9078	−	13.8332i	−1.15428	−	0.667874i
$430$	−33.5323	−	9.62818i	−1.61707	−	0.464312i
$431$	0.651474	+	4.11324i	0.0313804	+	0.198128i	0.998398	−	0.0565816i	$-0.0180201\pi$
$431$	0.651474	+	4.11324i	0.0313804	+	0.198128i	−0.967018	+	0.254710i	$0.918020\pi$
$432$	60.3157	−	22.8345i	2.90194	−	1.09863i
$433$	1.90152	+	1.38154i	0.0913813	+	0.0663924i	0.632538	−	0.774530i	$-0.282013\pi$
$433$	1.90152	+	1.38154i	0.0913813	+	0.0663924i	−0.541156	+	0.840922i	$0.682013\pi$
$434$	−2.13800	+	1.08937i	−0.102627	+	0.0522913i
$435$	−5.99617	+	10.3404i	−0.287494	+	0.495785i
$436$	35.3073	−	69.2944i	1.69091	−	3.31860i
$437$	10.0874	−	5.13981i	0.482548	−	0.245870i
$438$	−22.6419	+	25.9658i	−1.08187	+	1.24069i
$439$	19.7270	−	6.40969i	0.941519	−	0.305918i	0.202254	−	0.979333i	$-0.435173\pi$
$439$	19.7270	−	6.40969i	0.941519	−	0.305918i	0.739265	+	0.673415i	$0.235173\pi$
$440$	10.2714	−	83.4079i	0.489668	−	3.97631i
$441$	−4.91108	−	10.1482i	−0.233861	−	0.483250i
$442$	14.3881	+	73.7859i	0.684370	+	3.50964i
$443$	9.03392			0.429215			0.214607	−	0.976700i	$-0.431153\pi$
$443$	9.03392			0.429215			0.214607	+	0.976700i	$0.431153\pi$
$444$	22.4778	+	5.64105i	1.06675	+	0.267713i
$445$	12.4494	+	3.57462i	0.590160	+	0.169453i
$446$	−13.5387	+	9.83641i	−0.641074	+	0.465768i
$447$	8.41746	−	13.4248i	0.398132	−	0.634972i
$448$	−15.2764	+	29.9816i	−0.721742	+	1.41650i
$449$	−4.00234	+	4.00234i	−0.188882	+	0.188882i	−0.795213	−	0.606331i	$-0.792641\pi$
$449$	−4.00234	+	4.00234i	−0.188882	+	0.188882i	0.606331	+	0.795213i	$0.292641\pi$
$450$	37.5589	−	14.2546i	1.77054	−	0.671968i
$451$	−12.5102			−0.589085
$452$	−37.3485	+	12.1353i	−1.75673	+	0.570795i
$453$	−9.60308	+	15.3157i	−0.451192	+	0.719595i
$454$	−45.4790	−	62.5964i	−2.13443	−	2.93780i
$455$	9.33365	+	11.1180i	0.437568	+	0.521221i
$456$	−28.9074	+	17.3089i	−1.35372	+	0.810566i
$457$	2.87098	+	2.87098i	0.134299	+	0.134299i	0.771061	−	0.636762i	$-0.219727\pi$
$457$	2.87098	+	2.87098i	0.134299	+	0.134299i	−0.636762	+	0.771061i	$0.719727\pi$
$458$	−22.6015	−	16.4210i	−1.05610	−	0.767301i
$459$	40.4063	−	1.93086i	1.88601	−	0.0901247i
$460$	−51.8326	−	24.1924i	−2.41671	−	1.12798i
$461$	16.5829	−	32.5458i	0.772343	−	1.51581i	−0.0823084	−	0.996607i	$-0.526229\pi$
$461$	16.5829	−	32.5458i	0.772343	−	1.51581i	0.854652	−	0.519202i	$-0.173771\pi$
$462$	−2.52031	−	36.8559i	−0.117255	−	1.71469i
$463$	−7.73789	−	15.1865i	−0.359610	−	0.705775i	0.638341	−	0.769754i	$-0.279621\pi$
$463$	−7.73789	−	15.1865i	−0.359610	−	0.705775i	−0.997951	+	0.0639787i	$0.979621\pi$
$464$	−36.4315	+	11.8373i	−1.69129	+	0.549533i
$465$	1.04656	+	1.61827i	0.0485333	+	0.0750454i
$466$	22.9207	−	11.6787i	1.06178	−	0.541005i
$467$	4.17093	−	5.74080i	0.193008	−	0.265652i	−0.701535	−	0.712635i	$-0.747501\pi$
$467$	4.17093	−	5.74080i	0.193008	−	0.265652i	0.894543	+	0.446983i	$0.147501\pi$
$468$	38.9670	−	40.1518i	1.80125	−	1.85602i
$469$	−5.58287	−	4.05619i	−0.257793	−	0.187297i
$470$	58.5002	+	27.3045i	2.69841	+	1.25946i
$471$	−13.8059	+	3.16499i	−0.636140	+	0.145835i
$472$	56.2599	−	40.8752i	2.58957	−	1.88143i
$473$	22.9580	+	11.6977i	1.05561	+	0.537859i
$474$	21.6700	+	53.8734i	0.995338	+	2.47449i
$475$	−9.81585	+	5.88844i	−0.450382	+	0.270180i
$476$	−51.2711	+	51.2711i	−2.35001	+	2.35001i
$477$	−12.9211	+	24.1219i	−0.591616	+	1.10446i
$478$	−34.5956	+	25.1352i	−1.58237	+	1.14966i
$479$	2.44492	−	15.4366i	0.111711	−	0.705316i	−0.866728	−	0.498781i	$-0.833781\pi$
$479$	2.44492	−	15.4366i	0.111711	−	0.705316i	0.978439	−	0.206535i	$-0.0662188\pi$
$480$	58.7010	+	22.6608i	2.67932	+	1.03432i
$481$	9.15385	−	1.78498i	0.417380	−	0.0813880i
$482$	23.2237			1.05781
$483$	−14.9588	−	3.75406i	−0.680647	−	0.170816i
$484$	−13.6870	+	42.1243i	−0.622137	+	1.91474i
$485$	24.5806	−	0.849602i	1.11615	−	0.0385785i
$486$	−25.4497	−	33.0952i	−1.15442	−	1.50123i
$487$	−14.4899	+	7.38296i	−0.656599	+	0.334554i	−0.750349	−	0.661042i	$-0.770115\pi$
$487$	−14.4899	+	7.38296i	−0.656599	+	0.334554i	0.0937500	+	0.995596i	$0.470115\pi$
$488$	−7.42793	+	3.78472i	−0.336247	+	0.171326i
$489$	−18.8087	+	15.7332i	−0.850558	+	0.711478i
$490$	6.21106	−	21.6314i	0.280587	−	0.977209i
$491$	−10.7816	+	33.1823i	−0.486565	+	1.49749i	0.343136	+	0.939286i	$0.388511\pi$
$491$	−10.7816	+	33.1823i	−0.486565	+	1.49749i	−0.829701	+	0.558208i	$0.811489\pi$
$492$	6.16846	−	24.5794i	0.278096	−	1.10812i
$493$	−24.0270			−1.08212
$494$	−12.3509	+	18.3345i	−0.555694	+	0.824908i
$495$	−29.2369	+	5.05192i	−1.31410	+	0.227067i
$496$	−0.966153	+	6.10005i	−0.0433816	+	0.273900i
$497$	22.2455	−	16.1623i	0.997847	−	0.724978i
$498$	−2.07371	+	23.2903i	−0.0929252	+	1.04367i
$499$	−6.58962	+	6.58962i	−0.294992	+	0.294992i	−0.839049	−	0.544057i	$-0.816888\pi$
$499$	−6.58962	+	6.58962i	−0.294992	+	0.294992i	0.544057	+	0.839049i	$0.316888\pi$
$500$	53.9696	+	20.7832i	2.41359	+	0.929453i
$501$	−34.6702	+	13.9457i	−1.54895	+	0.623049i
$502$	−17.9731	−	9.15775i	−0.802179	−	0.408731i
$503$	7.96657	−	5.78805i	0.355212	−	0.258076i	−0.395840	−	0.918319i	$-0.629547\pi$
$503$	7.96657	−	5.78805i	0.355212	−	0.258076i	0.751052	+	0.660243i	$0.229547\pi$
$504$	45.1769	+	8.10915i	2.01234	+	0.361210i
$505$	2.16739	−	0.420497i	0.0964477	−	0.0187119i
$506$	47.3922	+	34.4325i	2.10684	+	1.53071i
$507$	7.33810	−	21.2874i	0.325897	−	0.945405i
$508$	1.37659	−	1.89471i	0.0610763	−	0.0840643i
$509$	−25.3636	+	12.9234i	−1.12422	+	0.572819i	−0.914356	−	0.404911i	$-0.867302\pi$
$509$	−25.3636	+	12.9234i	−1.12422	+	0.572819i	−0.209865	+	0.977730i	$0.567302\pi$
$510$	62.6594	+	50.9373i	2.77461	+	2.25554i
$511$	−12.7177	+	4.13224i	−0.562600	+	0.182800i
$512$	−4.21349	−	8.26944i	−0.186212	−	0.365461i
$513$	8.80340	+	8.00041i	0.388680	+	0.353227i
$514$	28.2820	−	55.5065i	1.24746	−	2.44829i
$515$	13.9188	−	14.9154i	0.613334	−	0.657251i
$516$	−34.3028	+	39.3386i	−1.51010	+	1.73179i
$517$	−38.5742	−	28.0258i	−1.69649	−	1.23257i
$518$	8.81998	+	8.81998i	0.387528	+	0.387528i
$519$	−4.81990	−	8.04965i	−0.211570	−	0.353340i
$520$	68.3388	−	4.79508i	2.99685	−	0.210278i
$521$	−5.92074	−	8.14920i	−0.259392	−	0.357023i	0.659381	−	0.751809i	$-0.270819\pi$
$521$	−5.92074	−	8.14920i	−0.259392	−	0.357023i	−0.918773	+	0.394786i	$0.870819\pi$
$522$	14.1605	+	20.3562i	0.619790	+	0.890967i
$523$	8.49412	−	2.75991i	0.371422	−	0.120682i	−0.117357	−	0.993090i	$-0.537442\pi$
$523$	8.49412	−	2.75991i	0.371422	−	0.120682i	0.488779	+	0.872407i	$0.337442\pi$
$524$	−20.6563			−0.902376
$525$	15.3502	+	2.74227i	0.669936	+	0.119682i
$526$	−43.4247	+	43.4247i	−1.89341	+	1.89341i
$527$	−1.75869	+	3.45163i	−0.0766099	+	0.150355i
$528$	−80.5582	−	50.5107i	−3.50585	−	2.19819i
$529$	1.17802	−	0.855881i	0.0512182	−	0.0372122i
$530$	−51.3377	+	18.6647i	−2.22997	+	0.810743i
$531$	−19.5625	−	14.8359i	−0.848942	−	0.643824i
$532$	−21.3222			−0.924433
$533$	−1.95186	−	10.0097i	−0.0845446	−	0.433568i
$534$	17.6596	−	20.2521i	0.764204	−	0.876393i
$535$	16.7615	−	3.25192i	0.724665	−	0.140593i
$536$	−30.9727	+	10.0636i	−1.33782	+	0.434683i
$537$	31.7420	+	27.6787i	1.36977	+	1.19442i
$538$	−13.6686	+	6.96451i	−0.589296	+	0.300261i
$539$	−7.54607	+	14.8100i	−0.325032	+	0.637912i
$540$	4.49021	−	59.9338i	0.193228	−	2.57914i
$541$	−23.8611	+	12.1578i	−1.02587	+	0.522706i	−0.884151	−	0.467201i	$-0.845263\pi$
$541$	−23.8611	+	12.1578i	−1.02587	+	0.522706i	−0.141718	+	0.989907i	$0.545263\pi$
$542$	−58.3800	−	42.4156i	−2.50764	−	1.82190i
$543$	−1.92079	−	0.818815i	−0.0824292	−	0.0351387i
$544$	19.7861	+	124.924i	0.848322	+	5.35609i
$545$	−20.6883	−	26.4993i	−0.886191	−	1.13511i
$546$	29.0959	−	7.76686i	1.24519	−	0.332391i
$547$	18.8555	+	25.9523i	0.806201	+	1.10964i	0.991898	+	0.127034i	$0.0405456\pi$
$547$	18.8555	+	25.9523i	0.806201	+	1.10964i	−0.185697	+	0.982607i	$0.559454\pi$
$548$	22.4487	+	11.4382i	0.958960	+	0.488614i
$549$	2.03806	+	2.12349i	0.0869821	+	0.0906284i
$550$	−50.2057	−	31.4218i	−2.14078	−	1.33983i
$551$	−4.99607	−	4.99607i	−0.212840	−	0.212840i
$552$	−55.8270	+	46.6984i	−2.37616	+	1.98762i
$553$	−3.52593	+	22.2618i	−0.149938	+	0.946669i
$554$	−5.18832	+	32.7578i	−0.220431	+	1.39174i
$555$	6.31926	−	7.77351i	0.268238	−	0.329967i
$556$	−1.46116	+	2.01111i	−0.0619669	+	0.0852901i
$557$	6.49043	+	6.49043i	0.275008	+	0.275008i	0.831113	−	0.556104i	$-0.187704\pi$
$557$	6.49043	+	6.49043i	0.275008	+	0.275008i	−0.556104	+	0.831113i	$0.687704\pi$
$558$	3.96080	−	0.544245i	0.167674	−	0.0230397i
$559$	−5.77759	+	20.1942i	−0.244366	+	0.854123i
$560$	30.7515	+	39.3890i	1.29949	+	1.66449i
$561$	−38.2655	−	45.7456i	−1.61557	−	1.93138i
$562$	−34.8264	−	11.3158i	−1.46906	−	0.477328i
$563$	−11.7752	−	3.82598i	−0.496264	−	0.161246i	0.0501823	−	0.998740i	$-0.484020\pi$
$563$	−11.7752	−	3.82598i	−0.496264	−	0.161246i	−0.546446	+	0.837494i	$0.684020\pi$
$564$	74.0834	−	61.9696i	3.11947	−	2.60939i
$565$	−2.07484	+	16.8486i	−0.0872892	+	0.708825i
$566$	−0.257359	−	0.505095i	−0.0108176	−	0.0212307i
$567$	−1.87598	−	16.0960i	−0.0787836	−	0.675967i
$568$		−	129.765i		−	5.44481i
$569$	21.4096	+	15.5550i	0.897537	+	0.652099i	0.937832	−	0.347089i	$-0.112830\pi$
$569$	21.4096	+	15.5550i	0.897537	+	0.652099i	−0.0402951	+	0.999188i	$0.512830\pi$
$570$	2.43744	+	23.6208i	0.102093	+	0.989366i
$571$	−7.43165	−	10.2288i	−0.311005	−	0.428062i	0.624689	−	0.780873i	$-0.285226\pi$
$571$	−7.43165	−	10.2288i	−0.311005	−	0.428062i	−0.935694	+	0.352812i	$0.885226\pi$
$572$	−81.8819	−	10.0044i	−3.42365	−	0.418305i
$573$	2.97693	−	33.4347i	0.124363	−	1.39675i
$574$	9.64460	−	9.64460i	0.402558	−	0.402558i
$575$	−18.9530	+	15.8804i	−0.790393	+	0.662259i
$576$	40.4492	−	38.8218i	1.68539	−	1.61758i
$577$	4.76697	−	9.35570i	0.198451	−	0.389483i	−0.770239	−	0.637756i	$-0.779863\pi$
$577$	4.76697	−	9.35570i	0.198451	−	0.389483i	0.968690	+	0.248273i	$0.0798629\pi$
$578$	−18.2698	+	115.351i	−0.759925	+	4.79798i
$579$	−36.3356	−	22.7827i	−1.51006	−	0.946817i
$580$	−4.36311	+	35.4303i	−0.181168	+	1.47116i
$581$	−5.33470	+	7.34259i	−0.221321	+	0.304622i
$582$	20.0086	−	46.9366i	0.829383	−	1.94559i
$583$	39.8474	−	6.31121i	1.65031	−	0.261384i
$584$	−19.5011	+	60.0182i	−0.806961	+	2.48357i
$585$	−8.60371	−	22.6048i	−0.355720	−	0.934593i
$586$	12.4433	+	38.2964i	0.514026	+	1.58201i
$587$	−1.50008	−	2.94408i	−0.0619151	−	0.121515i	0.857975	−	0.513691i	$-0.171722\pi$
$587$	−1.50008	−	2.94408i	−0.0619151	−	0.121515i	−0.919890	+	0.392176i	$0.871722\pi$
$588$	−25.3770	−	22.1285i	−1.04653	−	0.912563i
$589$	−1.08341	+	0.352021i	−0.0446412	+	0.0145048i
$590$	−9.33455	−	48.1137i	−0.384297	−	1.98081i
$591$	19.3045	−	1.32009i	0.794081	−	0.0543014i
$592$	31.7095	−	5.02229i	1.30325	−	0.206415i
$593$	2.14974	+	2.14974i	0.0882791	+	0.0882791i	0.749867	−	0.661588i	$-0.230117\pi$
$593$	2.14974	+	2.14974i	0.0882791	+	0.0882791i	−0.661588	+	0.749867i	$0.730117\pi$
$594$	−16.2046	+	59.3800i	−0.664882	+	2.43639i
$595$	10.7097	+	29.4574i	0.439056	+	1.20763i
$596$	7.40283	−	46.7396i	0.303232	−	1.91453i
$597$	−4.02516	+	0.922768i	−0.164739	+	0.0377664i
$598$	−20.1559	+	43.2916i	−0.824235	+	1.77033i
$599$		−	22.1664i		−	0.905693i	−0.891588	−	0.452847i	$-0.850409\pi$
$599$		−	22.1664i		−	0.905693i	0.891588	−	0.452847i	$-0.149591\pi$
$600$	53.0497	−	50.9994i	2.16575	−	2.08204i
$601$	31.4755			1.28391			0.641956	−	0.766741i	$-0.278123\pi$
$601$	31.4755			1.28391			0.641956	+	0.766741i	$0.278123\pi$
$602$	−26.7173	+	8.68097i	−1.08891	+	0.353810i
$603$	6.56592	+	9.43871i	0.267385	+	0.384374i
$604$	−8.44553	+	53.3230i	−0.343644	+	2.16968i
$605$	13.9983	+	13.0629i	0.569110	+	0.531083i
$606$	1.11487	−	4.44239i	0.0452883	−	0.180460i
$607$			35.7097i			1.44941i	0.689057	+	0.724707i	$0.258025\pi$
$607$			35.7097i			1.44941i	−0.689057	+	0.724707i	$0.741975\pi$
$608$	−21.8620	+	30.0904i	−0.886621	+	1.22033i
$609$	0.656652	+	9.60260i	0.0266089	+	0.389117i
$610$	0.202956	+	5.87190i	0.00821744	+	0.237746i
$611$	16.4056	−	35.2366i	0.663699	−	1.42552i
$612$	108.746	−	52.6259i	4.39580	−	2.12727i
$613$	39.3240	−	20.0366i	1.58828	−	0.809269i	0.588280	−	0.808657i	$-0.299805\pi$
$613$	39.3240	−	20.0366i	1.58828	−	0.809269i	1.00000		0.000611660i	$-0.000194697\pi$
$614$	−28.7505	+	9.34161i	−1.16028	+	0.376997i
$615$	−8.50029	−	6.91008i	−0.342765	−	0.278642i
$616$	−30.7214	−	60.2942i	−1.23780	−	2.42932i
$617$	29.9534	−	4.74416i	1.20588	−	0.190993i	0.479036	−	0.877795i	$-0.340986\pi$
$617$	29.9534	−	4.74416i	1.20588	−	0.190993i	0.726844	+	0.686803i	$0.240986\pi$
$618$	−15.7939	−	39.2649i	−0.635324	−	1.57947i
$619$	−6.62092	−	41.8029i	−0.266117	−	1.68020i	−0.652444	−	0.757837i	$-0.726256\pi$
$619$	−6.62092	−	41.8029i	−0.266117	−	1.68020i	0.386327	−	0.922362i	$-0.373744\pi$
$620$	4.77041	+	3.22016i	0.191584	+	0.129325i
$621$	21.4862	+	14.0946i	0.862213	+	0.565596i
$622$	0.0863727	−	0.545336i	0.00346323	−	0.0218660i
$623$	9.91923	−	3.22295i	0.397406	−	0.129125i
$624$	27.8458	−	72.3369i	1.11472	−	2.89579i
$625$	18.0082	−	17.3408i	0.720329	−	0.693632i
$626$	−13.4180	−	13.4180i	−0.536292	−	0.536292i
$627$	1.55538	−	17.4689i	0.0621161	−	0.697641i
$628$	−34.2218	+	24.8636i	−1.36560	+	0.992166i
$629$	19.8893	+	3.15015i	0.793036	+	0.125605i
$630$	18.6451	−	26.4345i	0.742837	−	1.05317i
$631$	−1.76520	−	11.1450i	−0.0702715	−	0.443677i	−0.997589	−	0.0694008i	$-0.977891\pi$
$631$	−1.76520	−	11.1450i	−0.0702715	−	0.443677i	0.927317	−	0.374276i	$-0.122109\pi$
$632$	75.2140	+	75.2140i	2.99185	+	2.99185i
$633$	7.35808	−	4.40581i	0.292458	−	0.175115i
$634$	−64.6341	−	21.0009i	−2.56695	−	0.834052i
$635$	−0.490504	−	0.885636i	−0.0194650	−	0.0351454i
$636$	−7.24780	+	81.4017i	−0.287394	+	3.22779i
$637$	−13.0271	−	3.72708i	−0.516153	−	0.147672i
$638$	11.2973	−	34.7696i	0.447265	−	1.37654i
$639$	−43.8534	+	13.2601i	−1.73482	+	0.524561i
$640$	39.2366	−	1.35617i	1.55096	−	0.0536074i
$641$	−3.37055	+	10.3735i	−0.133129	+	0.409728i	−0.995294	−	0.0968986i	$-0.969108\pi$
$641$	−3.37055	+	10.3735i	−0.133129	+	0.409728i	0.862166	+	0.506627i	$0.169108\pi$
$642$	8.62182	−	34.3552i	0.340276	−	1.35589i
$643$	23.3418	+	23.3418i	0.920513	+	0.920513i	0.997066	−	0.0765530i	$-0.0243914\pi$
$643$	23.3418	+	23.3418i	0.920513	+	0.920513i	−0.0765530	+	0.997066i	$0.524391\pi$
$644$	−45.4924	+	7.20528i	−1.79265	+	0.283928i
$645$	9.13790	+	20.6291i	0.359805	+	0.812269i
$646$	−38.6162	+	28.0563i	−1.51933	+	1.10386i
$647$	−8.49267	−	11.6892i	−0.333881	−	0.459548i	0.608761	−	0.793354i	$-0.291667\pi$
$647$	−8.49267	−	11.6892i	−0.333881	−	0.459548i	−0.942642	+	0.333806i	$0.891667\pi$
$648$	−66.6574	−	37.4863i	−2.61855	−	1.47260i
$649$			36.1974i			1.42087i
$650$	17.3080	−	45.0730i	0.678876	−	1.76791i
$651$	1.42754	+	0.608544i	0.0559496	+	0.0238507i
$652$	−33.2470	+	65.2509i	−1.30205	+	2.55542i
$653$	38.3679	−	27.8759i	1.50145	−	1.09087i	0.531656	−	0.846960i	$-0.321570\pi$
$653$	38.3679	−	27.8759i	1.50145	−	1.09087i	0.969798	−	0.243910i	$-0.0784300\pi$
$654$	−67.9794	+	15.5843i	−2.65820	+	0.609394i
$655$	−3.77657	+	8.09135i	−0.147563	+	0.316155i
$656$	−5.49185	−	34.6741i	−0.214421	−	1.35380i
$657$	22.2756	+	0.457310i	0.869054	+	0.0178414i
$658$	51.3444	−	8.13215i	2.00161	−	0.317024i
$659$	−38.2016	−	12.4125i	−1.48812	−	0.483521i	−0.551595	−	0.834112i	$-0.685981\pi$
$659$	−38.2016	−	12.4125i	−1.48812	−	0.483521i	−0.936529	+	0.350591i	$0.885981\pi$
$660$	−74.4053	+	48.1193i	−2.89622	+	1.87304i
$661$	8.37654	−	16.4399i	0.325810	−	0.639437i	−0.668764	−	0.743475i	$-0.733176\pi$
$661$	8.37654	−	16.4399i	0.325810	−	0.639437i	0.994573	+	0.104038i	$0.0331763\pi$
$662$	−31.6629	−	10.2879i	−1.23061	−	0.399850i
$663$	30.6317	−	37.7543i	1.18964	−	1.46625i
$664$	13.2357	+	40.7353i	0.513645	+	1.58084i
$665$	−3.89830	+	8.35216i	−0.151170	+	0.323883i
$666$	−9.05303	−	18.7072i	−0.350798	−	0.724888i
$667$	−12.3478	−	8.97118i	−0.478107	−	0.347365i
$668$	−78.9163	+	78.9163i	−3.05336	+	3.05336i
$669$	10.4972	+	2.63439i	0.405845	+	0.101851i
$670$	−2.80528	+	22.7801i	−0.108377	+	0.880070i
$671$	0.678822	−	4.28591i	0.0262056	−	0.165456i
$672$	49.3864	−	11.3218i	1.90512	−	0.436749i
$673$	−7.97790	−	24.5534i	−0.307525	−	0.946466i	−0.978723	−	0.205187i	$-0.934220\pi$
$673$	−7.97790	−	24.5534i	−0.307525	−	0.946466i	0.671197	−	0.741279i	$-0.265780\pi$
$674$	−39.9561	+	39.9561i	−1.53905	+	1.53905i
$675$	−22.6559	−	12.7165i	−0.872027	−	0.489458i
$676$	−4.77060	−	67.0762i	−0.183485	−	2.57985i
$677$	−4.19835	−	12.9212i	−0.161356	−	0.496602i	0.837394	−	0.546600i	$-0.184078\pi$
$677$	−4.19835	−	12.9212i	−0.161356	−	0.496602i	−0.998749	+	0.0499988i	$0.984078\pi$
$678$	29.8368	+	18.7079i	1.14588	+	0.718474i
$679$	16.0224	−	11.6410i	0.614885	−	0.446740i
$680$	142.175	+	40.8227i	5.45215	+	1.56548i
$681$	−12.1802	+	48.5341i	−0.466745	+	1.85983i
$682$	−4.16794	−	4.16794i	−0.159599	−	0.159599i
$683$	−2.41186	−	15.2279i	−0.0922873	−	0.582679i	−0.989886	−	0.141865i	$-0.954690\pi$
$683$	−2.41186	−	15.2279i	−0.0922873	−	0.582679i	0.897599	−	0.440814i	$-0.145310\pi$
$684$	33.5549	+	11.6694i	1.28300	+	0.446189i
$685$	8.58474	−	6.70221i	0.328006	−	0.256078i
$686$	−16.0311	−	49.3385i	−0.612068	−	1.88375i
$687$	1.23263	+	18.0254i	0.0470276	+	0.687711i
$688$	−22.3437	+	68.7668i	−0.851845	+	2.62171i
$689$	11.2668	+	30.8980i	0.429230	+	1.17712i
$690$	13.1825	+	49.5730i	0.501849	+	1.88721i
$691$	4.34015	+	8.51803i	0.165107	+	0.324041i	0.958705	−	0.284401i	$-0.0917947\pi$
$691$	4.34015	+	8.51803i	0.165107	+	0.324041i	−0.793598	+	0.608442i	$0.791795\pi$
$692$	−22.6688	−	16.4699i	−0.861739	−	0.626090i
$693$	−17.2368	+	16.5434i	−0.654774	+	0.628430i
$694$	62.2645	−	9.86173i	2.36353	−	0.374346i
$695$	0.520636	+	0.940043i	0.0197489	+	0.0356579i
$696$	38.4837	+	24.1296i	1.45872	+	0.914631i
$697$	3.44467	−	21.7488i	0.130476	−	0.823795i
$698$	15.8980	+	48.9289i	0.601747	+	1.85199i
$699$	−15.3041	−	6.52398i	−0.578854	−	0.246760i
$700$	45.3827	−	10.4433i	1.71530	−	0.394721i
$701$	39.6685			1.49826			0.749130	−	0.662423i	$-0.230472\pi$
$701$	39.6685			1.49826			0.749130	+	0.662423i	$0.230472\pi$
$702$	−50.0393	−	3.70106i	−1.88861	−	0.139688i
$703$	3.48065	+	4.79071i	0.131275	+	0.180685i
$704$	−81.6401	−	12.9305i	−3.07693	−	0.487337i
$705$	−10.7297	−	40.3492i	−0.404104	−	1.51964i
$706$	−38.6409	+	53.1846i	−1.45427	+	2.00163i
$707$	1.25709	−	1.25709i	0.0472776	−	0.0472776i
$708$	−71.1185	−	17.8480i	−2.67280	−	0.670768i
$709$	35.9273	−	18.3059i	1.34928	−	0.687492i	0.378082	−	0.925772i	$-0.376584\pi$
$709$	35.9273	−	18.3059i	1.34928	−	0.687492i	0.971196	+	0.238280i	$0.0765837\pi$
$710$	−82.8727	−	38.6801i	−3.11016	−	1.45164i
$711$	17.7324	−	33.1040i	0.665018	−	1.24150i
$712$	15.2099	−	46.8113i	0.570016	−	1.75433i
$713$	−2.19258	+	1.11717i	−0.0821127	+	0.0418385i
$714$	64.7672	+	5.76670i	2.42385	+	0.215813i
$715$	−18.8892	+	30.2451i	−0.706417	+	1.13110i
$716$	119.619	+	38.8667i	4.47039	+	1.45252i
$717$	26.8237	+	6.73169i	1.00175	+	0.251400i
$718$		−	7.80993i		−	0.291464i
$719$	−28.3260	−	20.5801i	−1.05638	−	0.767507i	−0.0829674	−	0.996552i	$-0.526440\pi$
$719$	−28.3260	−	20.5801i	−1.05638	−	0.767507i	−0.973416	+	0.229045i	$0.926440\pi$
$720$	−26.8368	−	78.8169i	−1.00015	−	2.93733i
$721$	2.56982	−	16.2252i	0.0957052	−	0.604259i
$722$	36.3957	+	5.76451i	1.35451	+	0.214533i
$723$	−9.63653	−	11.5203i	−0.358386	−	0.428444i
$724$	−6.23589			−0.231755
$725$	13.0808	+	8.18675i	0.485808	+	0.304048i
$726$	36.8505	−	14.8227i	1.36765	−	0.550124i
$727$	15.7456	+	48.4599i	0.583971	+	1.79728i	0.603363	+	0.797467i	$0.293827\pi$
$727$	15.7456	+	48.4599i	0.583971	+	1.79728i	−0.0193919	+	0.999812i	$0.506173\pi$
$728$	43.4493	−	33.9880i	1.61034	−	1.25968i
$729$	−5.85688	+	26.3571i	−0.216922	+	0.976189i
$730$	32.5170	+	30.3442i	1.20351	+	1.12309i
$731$	−26.6576	+	36.6910i	−0.985966	+	1.35707i
$732$	8.08599	+	3.44698i	0.298867	+	0.127404i
$733$	0.397595	+	2.51031i	0.0146855	+	0.0927205i	0.993942	−	0.109902i	$-0.0350536\pi$
$733$	0.397595	+	2.51031i	0.0146855	+	0.0927205i	−0.979257	+	0.202622i	$0.935054\pi$
$734$	5.02890	−	2.56235i	0.185620	−	0.0945782i
$735$	−13.3077	+	5.89479i	−0.490860	+	0.217433i
$736$	−36.4758	+	71.5879i	−1.34452	+	2.63876i
$737$	5.23831	−	16.1219i	0.192956	−	0.593856i
$738$	−20.4562	+	9.89945i	−0.753003	+	0.364404i
$739$	−7.28578	+	14.2991i	−0.268012	+	0.526003i	−0.985312	−	0.170761i	$-0.945377\pi$
$739$	−7.28578	+	14.2991i	−0.268012	+	0.526003i	0.717301	+	0.696764i	$0.245377\pi$
$740$	8.25693	−	28.7567i	0.303531	−	1.05712i
$741$	14.2199	−	1.48103i	0.522380	−	0.0544069i
$742$	−25.8543	+	35.5854i	−0.949141	+	1.30638i
$743$	7.35164	−	7.35164i	0.269705	−	0.269705i	−0.559276	−	0.828982i	$-0.688921\pi$
$743$	7.35164	−	7.35164i	0.269705	−	0.269705i	0.828982	+	0.559276i	$0.188921\pi$
$744$	6.28324	−	3.76222i	0.230355	−	0.137930i
$745$	−16.9551	−	11.4451i	−0.621186	−	0.419317i
$746$	−9.92220	−	1.57152i	−0.363278	−	0.0575375i
$747$	12.4138	−	8.63550i	0.454197	−	0.315956i
$748$	−158.700	−	80.8618i	−5.80265	−	2.95660i
$749$	9.72169	−	9.72169i	0.355223	−	0.355223i
$750$	−16.7571	−	49.0813i	−0.611883	−	1.79220i
$751$			33.6919i			1.22944i	0.788747	+	0.614718i	$0.210730\pi$
$751$			33.6919i			1.22944i	−0.788747	+	0.614718i	$0.789270\pi$
$752$	60.7444	−	119.218i	2.21512	−	4.34742i
$753$	2.91506	+	12.7156i	0.106231	+	0.463383i
$754$	29.5824	+	3.61441i	1.07733	+	0.131629i
$755$	19.3432	+	13.0572i	0.703972	+	0.475200i
$756$	−24.0044	−	42.0230i	−0.873030	−	1.52836i
$757$			11.1354i			0.404722i	0.979311	+	0.202361i	$0.0648614\pi$
$757$			11.1354i			0.404722i	−0.979311	+	0.202361i	$0.935139\pi$
$758$	1.91416	−	2.63462i	0.0695254	−	0.0956935i
$759$	−2.58465	−	37.7968i	−0.0938167	−	1.37194i
$760$	21.0746	+	38.0516i	0.764457	+	1.38028i
$761$	−30.9100	−	15.7494i	−1.12049	−	0.570916i	−0.207225	−	0.978293i	$-0.566443\pi$
$761$	−30.9100	−	15.7494i	−1.12049	−	0.570916i	−0.913260	+	0.407378i	$0.866443\pi$
$762$	−2.09534	+	0.143285i	−0.0759063	+	0.00519068i
$763$	−25.7458	−	8.36533i	−0.932062	−	0.302845i
$764$	−30.9780	−	95.3406i	−1.12075	−	3.44930i
$765$	−0.732334	−	52.2187i	−0.0264776	−	1.88797i
$766$	−56.9617	−	18.5080i	−2.05811	−	0.668721i
$767$	−28.9622	+	5.64757i	−1.04577	+	0.203922i
$768$	6.55180	−	15.3694i	0.236418	−	0.554594i
$769$	−31.1058	+	4.92667i	−1.12170	+	0.177660i	−0.689619	−	0.724173i	$-0.742222\pi$
$769$	−31.1058	+	4.92667i	−1.12170	+	0.177660i	−0.432085	+	0.901833i	$0.642222\pi$
$770$	−47.6635	+	1.64744i	−1.71767	+	0.0593695i
$771$	−39.2698	+	9.00260i	−1.41427	+	0.324221i
$772$	−126.506	−	20.0365i	−4.55303	−	0.721130i
$773$	−39.4776	−	20.1149i	−1.41991	−	0.723481i	−0.435636	−	0.900123i	$-0.643477\pi$
$773$	−39.4776	−	20.1149i	−1.41991	−	0.723481i	−0.984275	+	0.176642i	$0.943477\pi$
$774$	46.7963	+	0.960711i	1.68206	+	0.0345320i
$775$	2.13355	−	1.27989i	0.0766392	−	0.0459752i
$776$		−	93.4638i		−	3.35516i
$777$	0.715415	−	8.03500i	0.0256654	−	0.288254i
$778$	−12.0549	+	76.1116i	−0.432189	+	2.72873i
$779$	5.23862	−	3.80608i	0.187693	−	0.136367i
$780$	−50.1100	−	52.0255i	−1.79423	−	1.86281i
$781$	54.6451	+	39.7020i	1.95536	+	1.42065i
$782$	−72.9095	+	72.9095i	−2.60724	+	2.60724i
$783$	4.22201	−	15.4711i	0.150882	−	0.552892i
$784$	−44.3609	−	14.4137i	−1.58432	−	0.514776i
$785$	3.48267	+	17.9509i	0.124302	+	0.640696i
$786$	11.8852	+	14.2085i	0.423931	+	0.506801i
$787$	−14.9218	−	29.2857i	−0.531904	−	1.04392i	−0.988067	−	0.154025i	$-0.950776\pi$
$787$	−14.9218	−	29.2857i	−0.531904	−	1.04392i	0.456163	−	0.889896i	$-0.349224\pi$
$788$	51.4888	−	26.2348i	1.83421	−	0.934577i
$789$	39.5599	+	3.52231i	1.40837	+	0.125398i
$790$	70.4541	−	25.6148i	2.50664	−	0.911332i
$791$	6.20580	+	12.1796i	0.220653	+	0.433055i
$792$	15.3484	+	111.699i	0.545380	+	3.96906i
$793$	3.53515	−	0.125555i	0.125537	−	0.00445859i
$794$	29.9673	−	41.2465i	1.06350	−	1.46378i
$795$	30.5610	+	17.7216i	1.08389	+	0.628522i
$796$	−9.97753	+	7.24910i	−0.353644	+	0.256937i
$797$	1.26109	+	1.73574i	0.0446700	+	0.0614829i	0.830768	−	0.556619i	$-0.187902\pi$
$797$	1.26109	+	1.73574i	0.0446700	+	0.0614829i	−0.786098	+	0.618102i	$0.787902\pi$
$798$	12.2683	+	14.6665i	0.434293	+	0.519189i
$799$	59.3436	−	59.3436i	2.09943	−	2.09943i
$800$	31.7937	−	74.7531i	1.12408	−	2.64292i
$801$	−17.3739	−	0.356680i	−0.613876	−	0.0126027i
$802$	37.2676	−	12.1090i	1.31597	−	0.427583i
$803$	−19.3077	−	26.5748i	−0.681355	−	0.937805i
$804$	29.0924	+	18.2412i	1.02601	+	0.643316i
$805$	−5.49491	+	19.1373i	−0.193670	+	0.674500i
$806$	2.68456	−	3.98513i	0.0945596	−	0.140370i
$807$	9.12650	+	3.89053i	0.321268	+	0.136953i
$808$	−1.31246	−	8.28653i	−0.0461721	−	0.291519i
$809$	−23.4681	−	7.62525i	−0.825095	−	0.268090i	−0.134117	−	0.990966i	$-0.542820\pi$
$809$	−23.4681	−	7.62525i	−0.825095	−	0.268090i	−0.690978	+	0.722876i	$0.742820\pi$
$810$	−43.8092	+	31.3960i	−1.53930	+	1.10314i
$811$	41.9071	+	21.3527i	1.47156	+	0.749796i	0.991823	−	0.127617i	$-0.0407329\pi$
$811$	41.9071	+	21.3527i	1.47156	+	0.749796i	0.479735	+	0.877414i	$0.340733\pi$
$812$	13.0499	+	25.6120i	0.457963	+	0.898803i
$813$	3.18389	+	46.5598i	0.111664	+	1.63293i
$814$	−13.9104	+	27.3006i	−0.487558	+	0.956886i
$815$	19.4811	+	24.9530i	0.682393	+	0.874065i
$816$	109.993	−	126.141i	3.85053	−	4.41581i
$817$	−13.1724	+	2.08630i	−0.460844	+	0.0729906i
$818$			14.8219i			0.518236i
$819$	−15.9260	−	11.2104i	−0.556498	−	0.391724i
$820$	−31.4453	−	9.02892i	−1.09812	−	0.315304i
$821$	−35.1955	−	5.57443i	−1.22833	−	0.194549i	−0.491653	−	0.870791i	$-0.663607\pi$
$821$	−35.1955	−	5.57443i	−1.22833	−	0.194549i	−0.736679	+	0.676242i	$0.763607\pi$
$822$	−5.04870	−	22.0227i	−0.176094	−	0.768128i
$823$	9.66616	+	29.7494i	0.336941	+	1.03700i	0.965758	+	0.259445i	$0.0835395\pi$
$823$	9.66616	+	29.7494i	0.336941	+	1.03700i	−0.628817	+	0.777553i	$0.716461\pi$
$824$	−54.8187	−	54.8187i	−1.90970	−	1.90970i
$825$	5.24554	+	37.9431i	0.182626	+	1.32101i
$826$	−27.9059	−	27.9059i	−0.970970	−	0.970970i
$827$	−6.10450	+	11.9808i	−0.212274	+	0.416612i	−0.972452	−	0.233103i	$-0.925112\pi$
$827$	−6.10450	+	11.9808i	−0.212274	+	0.416612i	0.760178	+	0.649715i	$0.225112\pi$
$828$	75.5352	+	13.5584i	2.62503	+	0.471187i
$829$	7.69309	+	10.5886i	0.267192	+	0.367758i	0.921439	−	0.388523i	$-0.127014\pi$
$829$	7.69309	+	10.5886i	0.267192	+	0.367758i	−0.654247	+	0.756281i	$0.727014\pi$
$830$	29.9603	+	3.68951i	1.03994	+	0.128065i
$831$	18.4026	−	11.0189i	0.638378	−	0.382242i
$832$	−2.39163	−	67.3392i	−0.0829149	−	2.33457i
$833$	−23.6691	−	17.1966i	−0.820085	−	0.595826i
$834$	2.22407	−	0.152088i	0.0770131	−	0.00526637i
$835$	16.4844	+	45.3407i	0.570465	+	1.56908i
$836$	−16.1854	−	49.8134i	−0.559783	−	1.72283i
$837$	−1.91348	−	1.73895i	−0.0661397	−	0.0601068i
$838$	49.8067	−	25.3778i	1.72054	−	0.876660i
$839$	8.75518	+	4.46099i	0.302262	+	0.154010i	0.598543	−	0.801090i	$-0.295746\pi$
$839$	8.75518	+	4.46099i	0.302262	+	0.154010i	−0.296281	+	0.955101i	$0.595746\pi$
$840$	12.4296	−	57.9369i	0.428861	−	1.99901i
$841$	6.01804	−	18.5216i	0.207519	−	0.638677i
$842$	−16.5992	+	22.8468i	−0.572045	+	0.787352i
$843$	8.83773	+	21.9713i	0.304388	+	0.756732i
$844$	15.0549	−	20.7213i	0.518210	−	0.713255i
$845$	−27.1468	−	10.3947i	−0.933879	−	0.357590i
$846$	−85.2519	−	15.3025i	−2.93102	−	0.526112i
$847$	15.2275	+	2.41181i	0.523225	+	0.0828706i
$848$	34.9851	+	107.673i	1.20139	+	3.69751i
$849$	−0.143766	+	0.337251i	−0.00493405	+	0.0115744i
$850$	68.4501	−	78.6296i	2.34782	−	2.69697i
$851$	9.04512	+	9.04512i	0.310063	+	0.310063i
$852$	−104.948	+	87.7874i	−3.59546	+	3.00755i
$853$	−1.42929	+	9.02418i	−0.0489380	+	0.308982i	−1.00000		1.78425e-5i	$-0.999994\pi$
$853$	−1.42929	+	9.02418i	−0.0489380	+	0.308982i	0.951062	+	0.309000i	$0.0999943\pi$
$854$	2.78084	+	3.82749i	0.0951583	+	0.130974i
$855$	10.7058	−	11.0104i	0.366132	−	0.376548i
$856$	−10.1499	−	64.0840i	−0.346916	−	2.19034i
$857$			15.2603i			0.521282i	0.965436	+	0.260641i	$0.0839339\pi$
$857$			15.2603i			0.521282i	−0.965436	+	0.260641i	$0.916066\pi$
$858$	40.2315	+	62.0790i	1.37348	+	2.11934i
$859$	6.81706	−	20.9807i	0.232595	−	0.715854i	−0.764836	−	0.644225i	$-0.777180\pi$
$859$	6.81706	−	20.9807i	0.232595	−	0.715854i	0.997431	−	0.0716292i	$-0.0228198\pi$
$860$	49.2638	+	45.9721i	1.67988	+	1.56763i
$861$	−8.78623	−	0.782303i	−0.299434	−	0.0266608i
$862$	3.44659	−	10.6075i	0.117391	−	0.361293i
$863$	−14.6123	−	28.6783i	−0.497410	−	0.976222i	−0.994118	−	0.108304i	$-0.965458\pi$
$863$	−14.6123	−	28.6783i	−0.497410	−	0.976222i	0.496708	−	0.867918i	$-0.334542\pi$
$864$	−83.9162	−	9.21129i	−2.85489	−	0.313374i
$865$	−10.5960	+	5.86850i	−0.360274	+	0.199535i
$866$	−2.85781	−	5.60876i	−0.0971122	−	0.190593i
$867$	64.8017	−	38.8014i	2.20078	−	1.31776i
$868$	4.63452			0.157306
$869$	−54.6852	+	8.66128i	−1.85507	+	0.293814i
$870$	26.8812	−	17.3846i	0.911360	−	0.589394i
$871$	13.7167	+	1.67592i	0.464773	+	0.0567863i
$872$	−103.355	+	75.0918i	−3.50004	+	2.54293i
$873$	−31.5857	+	9.55066i	−1.06901	+	0.323241i
$874$	−30.3209			−1.02562
$875$	4.20646	−	19.6863i	0.142204	−	0.665519i
$876$	61.7328	−	24.8314i	2.08576	−	0.838974i
$877$	6.89406	−	13.5304i	0.232796	−	0.456887i	−0.744826	−	0.667259i	$-0.767467\pi$
$877$	6.89406	−	13.5304i	0.232796	−	0.456887i	0.977621	+	0.210372i	$0.0674674\pi$
$878$	−54.8678	−	8.69020i	−1.85170	−	0.293280i
$879$	13.8339	−	22.0634i	0.466607	−	0.744180i
$880$	−68.6788	+	101.742i	−2.31516	+	3.42973i
$881$	6.51227	+	4.73144i	0.219404	+	0.159406i	0.692058	−	0.721842i	$-0.256704\pi$
$881$	6.51227	+	4.73144i	0.219404	+	0.159406i	−0.472654	+	0.881248i	$0.656704\pi$
$882$	−0.619747	+	30.1879i	−0.0208680	+	1.01648i
$883$	13.0859	+	9.50748i	0.440376	+	0.319952i	0.785784	−	0.618500i	$-0.212259\pi$
$883$	13.0859	+	9.50748i	0.440376	+	0.319952i	−0.345408	+	0.938453i	$0.612259\pi$
$884$	39.9385	−	139.595i	1.34328	−	4.69510i
$885$	−19.9938	+	24.5949i	−0.672084	+	0.826749i
$886$	−21.5576	−	10.9841i	−0.724241	−	0.369019i
$887$	−2.02685	+	6.23802i	−0.0680551	+	0.209452i	−0.979301	−	0.202412i	$-0.935122\pi$
$887$	−2.02685	+	6.23802i	−0.0680551	+	0.209452i	0.911245	+	0.411864i	$0.135122\pi$
$888$	−28.6927	−	25.0197i	−0.962866	−	0.839608i
$889$	−0.726358	−	0.370098i	−0.0243612	−	0.0124127i
$890$	−25.3617	−	23.6671i	−0.850126	−	0.793322i
$891$	36.1798	−	16.6009i	1.21207	−	0.556153i
$892$	31.9239	−	5.05625i	1.06889	−	0.169296i
$893$	24.6793			0.825861
$894$	−36.4094	+	21.8009i	−1.21771	+	0.729131i
$895$	37.0945	−	39.7505i	1.23993	−	1.32871i
$896$	25.5757	−	18.5818i	0.854424	−	0.620775i
$897$	29.8387	−	7.96512i	0.996284	−	0.265948i
$898$	14.4171	−	4.68440i	0.481105	−	0.156320i
$899$	1.08593	+	1.08593i	0.0362178	+	0.0362178i
$900$	−77.1348	−	8.40259i	−2.57116	−	0.280086i
$901$			71.0117i			2.36574i
$902$	29.8531	+	15.2109i	0.993999	+	0.506468i
$903$	15.3924	+	9.65116i	0.512227	+	0.321171i
$904$	63.7153	+	10.0915i	2.11914	+	0.335639i
$905$	−1.14010	+	2.44268i	−0.0378982	+	0.0811974i
$906$	41.5377	−	24.8716i	1.38000	−	0.826303i
$907$	0.0281624			0.000935118			0.000467559	−	1.00000i	$-0.499851\pi$
$907$	0.0281624			0.000935118			0.000467559		1.00000i	$0.499851\pi$
$908$	23.3777	+	147.601i	0.775818	+	4.89832i
$909$	−2.66628	+	1.29030i	−0.0884350	+	0.0427967i
$910$	−8.75466	−	37.8794i	−0.290214	−	1.25569i
$911$	18.9671	−	6.16279i	0.628409	−	0.204182i	0.0225386	−	0.999746i	$-0.492825\pi$
$911$	18.9671	−	6.16279i	0.628409	−	0.204182i	0.605870	+	0.795564i	$0.292825\pi$
$912$	49.1006	−	3.35764i	1.62588	−	0.111182i
$913$	−21.2035	−	6.88943i	−0.701733	−	0.228007i
$914$	−3.36024	−	10.3418i	−0.111147	−	0.342075i
$915$	2.82858	−	2.53718i	0.0935099	−	0.0838767i
$916$	24.4965	+	48.0771i	0.809388	+	1.58851i
$917$	1.12478	+	7.10160i	0.0371436	+	0.234516i
$918$	−98.7689	−	44.5215i	−3.25986	−	1.46943i
$919$	−12.2542	−	8.90320i	−0.404229	−	0.293690i	0.367032	−	0.930208i	$-0.380374\pi$
$919$	−12.2542	−	8.90320i	−0.404229	−	0.293690i	−0.771261	+	0.636519i	$0.780374\pi$
$920$	57.8228	+	74.0643i	1.90636	+	2.44183i
$921$	16.5638	+	10.3856i	0.545796	+	0.342219i
$922$	−79.1433	+	57.5010i	−2.60645	+	1.89369i
$923$	−23.2405	+	49.9169i	−0.764971	+	1.64304i
$924$	−27.9799	+	65.6358i	−0.920470	+	2.15926i
$925$	−9.75475	−	8.49189i	−0.320734	−	0.279212i
$926$			45.6477i			1.50007i
$927$	−12.9240	+	24.1274i	−0.424481	+	0.792448i
$928$	49.5247	+	7.84394i	1.62573	+	0.257490i
$929$	−27.2283	−	4.31254i	−0.893333	−	0.141490i	−0.307143	−	0.951664i	$-0.599373\pi$
$929$	−27.2283	−	4.31254i	−0.893333	−	0.141490i	−0.586190	+	0.810173i	$0.699373\pi$
$930$	−0.529796	−	5.13415i	−0.0173727	−	0.168355i
$931$	−1.34586	−	8.49742i	−0.0441087	−	0.278492i
$932$	−49.6850			−1.62749
$933$	−0.306357	+	0.183438i	−0.0100297	+	0.00600549i
$934$	−16.9332	+	8.62788i	−0.554070	+	0.282313i
$935$	−60.6896	+	47.3811i	−1.98476	+	1.54953i
$936$	−86.9779	+	29.7080i	−2.84296	+	0.971035i
$937$	−29.0111	−	9.42627i	−0.947750	−	0.307943i	−0.205949	−	0.978563i	$-0.566028\pi$
$937$	−29.0111	−	9.42627i	−0.947750	−	0.307943i	−0.741801	+	0.670620i	$0.766028\pi$
$938$	8.39052	+	16.4673i	0.273960	+	0.537677i
$939$	−1.08838	+	12.2238i	−0.0355178	+	0.398909i
$940$	−76.7319	−	98.2845i	−2.50272	−	3.20569i
$941$	−3.21479	+	1.63802i	−0.104799	+	0.0533979i	−0.505604	−	0.862765i	$-0.668730\pi$
$941$	−3.21479	+	1.63802i	−0.104799	+	0.0533979i	0.400805	+	0.916163i	$0.368730\pi$
$942$	36.7930	+	9.23361i	1.19878	+	0.300847i
$943$	9.89080	−	9.89080i	0.322089	−	0.322089i
$944$	−100.327	+	15.8902i	−3.26536	+	0.517183i
$945$	−20.8496	+	1.71981i	−0.678239	+	0.0559453i
$946$	−40.5615	−	55.8281i	−1.31877	−	1.81513i
$947$	−19.4725	−	3.08414i	−0.632770	−	0.100221i	−0.168194	−	0.985754i	$-0.553793\pi$
$947$	−19.4725	−	3.08414i	−0.632770	−	0.100221i	−0.464577	+	0.885533i	$0.653793\pi$
$948$	9.94662	−	111.713i	0.323051	−	3.62826i
$949$	18.2506	−	19.5947i	0.592440	−	0.636072i
$950$	30.5831	−	2.11667i	0.992246	−	0.0686739i
$951$	16.4019	+	40.7764i	0.531867	+	1.32226i
$952$	113.279	−	36.8066i	3.67140	−	1.19291i
$953$	−22.7857	−	31.3619i	−0.738102	−	1.01591i	−0.998726	−	0.0504700i	$-0.983928\pi$
$953$	−22.7857	−	31.3619i	−0.738102	−	1.01591i	0.260623	−	0.965441i	$-0.416072\pi$
$954$	60.1627	−	41.8514i	1.94784	−	1.35499i
$955$	−43.0098	−	5.29650i	−1.39177	−	0.171391i
$956$	81.5758	−	12.9203i	2.63835	−	0.417873i
$957$	−21.9354	+	8.82330i	−0.709071	+	0.285217i
$958$	−24.6033	+	33.8635i	−0.794896	+	1.09408i
$959$	2.71004	−	8.34064i	0.0875117	−	0.269333i
$960$	−48.3294	−	53.8801i	−1.55983	−	1.73897i
$961$	−29.2473	+	9.50301i	−0.943460	+	0.306549i
$962$	−24.0141	−	6.87047i	−0.774244	−	0.221513i
$963$	−20.6197	+	9.97857i	−0.664461	+	0.321555i
$964$	−39.9660	−	20.3637i	−1.28722	−	0.655870i
$965$	−30.9774	+	45.8906i	−0.997198	+	1.47727i
$966$	31.1315	+	27.1463i	1.00164	+	0.873418i
$967$	4.60553	+	29.0782i	0.148104	+	0.935090i	0.944069	+	0.329748i	$0.106964\pi$
$967$	4.60553	+	29.0782i	0.148104	+	0.935090i	−0.795965	+	0.605342i	$0.793036\pi$
$968$	51.4479	−	51.4479i	1.65360	−	1.65360i
$969$	29.9410	+	7.51403i	0.961845	+	0.241385i
$970$	−59.6895	−	27.8596i	−1.91651	−	0.894517i
$971$	13.2871	+	18.2881i	0.426402	+	0.586892i	0.967123	−	0.254310i	$-0.0818484\pi$
$971$	13.2871	+	18.2881i	0.426402	+	0.586892i	−0.540721	+	0.841202i	$0.681848\pi$
$972$	14.7773	+	79.2694i	0.473981	+	2.54257i
$973$	0.770979	+	0.392833i	0.0247165	+	0.0125937i
$974$	43.5538			1.39555
$975$	−29.5406	+	10.1170i	−0.946056	+	0.324003i
$976$	12.1771			0.389779
$977$	39.3927	+	20.0716i	1.26029	+	0.642147i	0.951108	−	0.308857i	$-0.0999465\pi$
$977$	39.3927	+	20.0716i	1.26029	+	0.642147i	0.309177	+	0.951005i	$0.399947\pi$
$978$	64.0126	−	14.6749i	2.04690	−	0.469251i
$979$	15.0591	+	20.7271i	0.481291	+	0.662441i
$980$	−29.6562	+	31.7797i	−0.947333	+	1.01516i
$981$	35.9383	+	27.2550i	1.14742	+	0.870186i
$982$	66.0735	−	66.0735i	2.10849	−	2.10849i
$983$	3.24366	+	20.4797i	0.103457	+	0.653200i	0.983855	+	0.178965i	$0.0572750\pi$
$983$	3.24366	+	20.4797i	0.103457	+	0.653200i	−0.880399	+	0.474234i	$0.842725\pi$
$984$	−27.3590	+	31.3754i	−0.872172	+	1.00021i
$985$	−0.862899	−	24.9653i	−0.0274943	−	0.795460i
$986$	57.3354	+	29.2139i	1.82593	+	0.930359i
$987$	−25.3390	−	22.0953i	−0.806550	−	0.703302i
$988$	37.3314	−	20.7222i	1.18767	−	0.659260i
$989$	−27.3993	+	8.90256i	−0.871246	+	0.283085i
$990$	75.9102	+	23.4931i	2.41258	+	0.746659i
$991$	−9.49530	+	29.2235i	−0.301628	+	0.928316i	0.679286	+	0.733874i	$0.262290\pi$
$991$	−9.49530	+	29.2235i	−0.301628	+	0.928316i	−0.980914	+	0.194442i	$0.937710\pi$
$992$	4.75186	−	6.54038i	0.150872	−	0.207657i
$993$	8.03493	+	19.9755i	0.254981	+	0.633902i
$994$	−72.7356	+	11.5202i	−2.30703	+	0.365398i
$995$	1.01539	+	5.23367i	0.0321899	+	0.165918i
$996$	23.9908	−	38.2623i	0.760177	−	1.21239i
$997$	−16.6812	−	22.9597i	−0.528300	−	0.727142i	0.458570	−	0.888658i	$-0.348362\pi$
$997$	−16.6812	−	22.9597i	−0.528300	−	0.727142i	−0.986870	+	0.161516i	$0.948362\pi$
$998$	23.7369	−	7.71259i	0.751379	−	0.244138i
$999$	−5.52332	+	12.2532i	−0.174750	+	0.387675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.ce.a.44.4	✓	1088
3.2	odd	2	inner	975.2.ce.a.44.133	yes	1088
13.8	odd	4	inner	975.2.ce.a.944.133	yes	1088
25.4	even	10	inner	975.2.ce.a.629.4	yes	1088
39.8	even	4	inner	975.2.ce.a.944.4	yes	1088
75.29	odd	10	inner	975.2.ce.a.629.133	yes	1088
325.229	odd	20	inner	975.2.ce.a.554.133	yes	1088
975.554	even	20	inner	975.2.ce.a.554.4	yes	1088

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.ce.a.44.4	✓	1088	1.1	even	1	trivial
975.2.ce.a.44.133	yes	1088	3.2	odd	2	inner
975.2.ce.a.554.4	yes	1088	975.554	even	20	inner
975.2.ce.a.554.133	yes	1088	325.229	odd	20	inner
975.2.ce.a.629.4	yes	1088	25.4	even	10	inner
975.2.ce.a.629.133	yes	1088	75.29	odd	10	inner
975.2.ce.a.944.4	yes	1088	39.8	even	4	inner
975.2.ce.a.944.133	yes	1088	13.8	odd	4	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.ce (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38629 - 1.21588i) q^{2} +(0.387033 + 1.68826i) q^{3} +(3.04046 + 4.18483i) q^{4} +(2.19514 - 0.425880i) q^{5} +(1.12914 - 4.49925i) q^{6} +(1.27318 - 1.27318i) q^{7} +(-1.32926 - 8.39261i) q^{8} +(-2.70041 + 1.30682i) q^{9} +O(q^{10})\)	\(q+(-2.38629 - 1.21588i) q^{2} +(0.387033 + 1.68826i) q^{3} +(3.04046 + 4.18483i) q^{4} +(2.19514 - 0.425880i) q^{5} +(1.12914 - 4.49925i) q^{6} +(1.27318 - 1.27318i) q^{7} +(-1.32926 - 8.39261i) q^{8} +(-2.70041 + 1.30682i) q^{9} +(-5.75605 - 1.65274i) q^{10} +(3.94089 + 2.00798i) q^{11} +(-5.88831 + 6.75274i) q^{12} +(-0.991763 + 3.46647i) q^{13} +(-4.58620 + 1.49015i) q^{14} +(1.56858 + 3.54112i) q^{15} +(-3.83544 + 11.8043i) q^{16} +(-4.57595 + 6.29826i) q^{17} +(8.03290 + 0.164913i) q^{18} +(-2.26113 + 0.358128i) q^{19} +(8.45646 + 7.89141i) q^{20} +(2.64221 + 1.65669i) q^{21} +(-6.96265 - 9.58326i) q^{22} +(-4.70327 + 1.52819i) q^{23} +(13.6544 - 5.49234i) q^{24} +(4.63725 - 1.86973i) q^{25} +(6.58143 - 7.06614i) q^{26} +(-3.25139 - 4.05320i) q^{27} +(9.19909 + 1.45699i) q^{28} +(1.81408 + 2.49686i) q^{29} +(0.562469 - 10.3574i) q^{30} +(0.491474 - 0.0778418i) q^{31} +(11.4881 - 11.4881i) q^{32} +(-1.86474 + 7.43038i) q^{33} +(18.5775 - 9.46568i) q^{34} +(2.25258 - 3.33702i) q^{35} +(-13.6793 - 7.32744i) q^{36} +(-1.17431 - 2.30471i) q^{37} +(5.83116 + 1.89466i) q^{38} +(-6.23613 - 0.332713i) q^{39} +(-6.49214 - 17.8568i) q^{40} +(-2.52019 + 1.28410i) q^{41} +(-4.29076 - 7.16594i) q^{42} +5.82558 q^{43} +(3.57904 + 22.5972i) q^{44} +(-5.37122 + 4.01870i) q^{45} +(13.0815 + 2.07190i) q^{46} +(-10.6475 - 1.68639i) q^{47} +(-21.4131 - 1.90656i) q^{48} +3.75804i q^{49} +(-13.3392 - 1.17661i) q^{50} +(-12.4041 - 5.28774i) q^{51} +(-17.5220 + 6.38929i) q^{52} +(7.37946 - 5.36149i) q^{53} +(2.83058 + 13.6254i) q^{54} +(9.50595 + 2.72945i) q^{55} +(-12.3777 - 8.99290i) q^{56} +(-1.47974 - 3.67876i) q^{57} +(-1.29304 - 8.16393i) q^{58} +(3.71545 + 7.29197i) q^{59} +(-10.0498 + 17.3309i) q^{60} +(-0.303174 - 0.933075i) q^{61} +(-1.26745 - 0.411818i) q^{62} +(-1.77429 + 5.10192i) q^{63} +(-17.7736 + 5.77501i) q^{64} +(-0.700758 + 8.03175i) q^{65} +(13.4842 - 15.4638i) q^{66} +(-0.599554 - 3.78543i) q^{67} -40.2702 q^{68} +(-4.40029 - 7.34886i) q^{69} +(-9.43271 + 5.22425i) q^{70} +(15.0834 + 2.38898i) q^{71} +(14.5572 + 20.9264i) q^{72} +(-6.61729 - 3.37168i) q^{73} +6.92753i q^{74} +(4.95135 + 7.10522i) q^{75} +(-8.37359 - 8.37359i) q^{76} +(7.57397 - 2.46093i) q^{77} +(14.4767 + 8.37631i) q^{78} +(-10.1273 + 7.35792i) q^{79} +(-3.39212 + 27.5455i) q^{80} +(5.58444 - 7.05790i) q^{81} +7.57522 q^{82} +(-4.97860 + 0.788533i) q^{83} +(1.10057 + 16.0943i) q^{84} +(-7.36254 + 15.7743i) q^{85} +(-13.9015 - 7.08318i) q^{86} +(-3.51323 + 4.02899i) q^{87} +(11.6138 - 35.7435i) q^{88} +(5.16117 + 2.62975i) q^{89} +(17.7035 - 3.05904i) q^{90} +(3.15074 + 5.67612i) q^{91} +(-20.6953 - 15.0360i) q^{92} +(0.321633 + 0.799606i) q^{93} +(23.3575 + 16.9702i) q^{94} +(-4.81098 + 1.74911i) q^{95} +(23.8412 + 14.9486i) q^{96} +(10.8639 + 1.72068i) q^{97} +(4.56930 - 8.96777i) q^{98} +(-13.2661 - 0.272348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 1088 * q - 20 * q^3 + 2 * q^6 - 12 * q^9	\( 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9} - 20 q^{13} - 34 q^{15} + 248 q^{16} - 24 q^{19} + 12 q^{21} - 40 q^{22} - 28 q^{24} - 20 q^{27} - 100 q^{28} - 12 q^{31} + 40 q^{33} - 4 q^{34} - 140 q^{37} + 6 q^{39} + 32 q^{40} - 20 q^{42} + 30 q^{45} + 12 q^{46} - 20 q^{48} - 20 q^{52} - 100 q^{54} - 48 q^{55} - 140 q^{58} - 86 q^{60} + 72 q^{61} + 70 q^{63} - 36 q^{66} - 20 q^{67} - 192 q^{70} - 50 q^{72} + 60 q^{73} - 112 q^{76} + 60 q^{78} - 24 q^{79} + 20 q^{81} - 168 q^{84} - 196 q^{85} - 20 q^{87} - 44 q^{91} - 192 q^{94} - 20 q^{97} - 12 q^{99}+O(q^{100}) \) 1088 * q - 20 * q^3 + 2 * q^6 - 12 * q^9 - 20 * q^13 - 34 * q^15 + 248 * q^16 - 24 * q^19 + 12 * q^21 - 40 * q^22 - 28 * q^24 - 20 * q^27 - 100 * q^28 - 12 * q^31 + 40 * q^33 - 4 * q^34 - 140 * q^37 + 6 * q^39 + 32 * q^40 - 20 * q^42 + 30 * q^45 + 12 * q^46 - 20 * q^48 - 20 * q^52 - 100 * q^54 - 48 * q^55 - 140 * q^58 - 86 * q^60 + 72 * q^61 + 70 * q^63 - 36 * q^66 - 20 * q^67 - 192 * q^70 - 50 * q^72 + 60 * q^73 - 112 * q^76 + 60 * q^78 - 24 * q^79 + 20 * q^81 - 168 * q^84 - 196 * q^85 - 20 * q^87 - 44 * q^91 - 192 * q^94 - 20 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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