LMFDB - Embedded newform 966.2.bd.a.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(59,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 11, 42]))

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

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

chi := DirichletCharacter("966.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bd (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			59.12
Character	$\chi$	$=$	966.59
Dual form			966.2.bd.a.131.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.945001 - 0.327068i) q^{2} +(-0.689077 - 1.58908i) q^{3} +(0.786053 + 0.618159i) q^{4} +(3.18017 - 0.303670i) q^{5} +(0.131442 + 1.72706i) q^{6} +(-2.23440 - 1.41685i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.05034 + 2.19000i) q^{9} +O(q^{10})$	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.689077 - 1.58908i) q^{3} +(0.786053 + 0.618159i) q^{4} +(3.18017 - 0.303670i) q^{5} +(0.131442 + 1.72706i) q^{6} +(-2.23440 - 1.41685i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.05034 + 2.19000i) q^{9} +(-3.10459 - 0.753165i) q^{10} +(-4.49631 + 1.55619i) q^{11} +(0.440652 - 1.67506i) q^{12} +(1.99627 + 6.79867i) q^{13} +(1.64810 + 2.06972i) q^{14} +(-2.67394 - 4.84430i) q^{15} +(0.235759 + 0.971812i) q^{16} +(4.50603 + 1.80394i) q^{17} +(2.65386 - 1.39895i) q^{18} +(1.66756 + 4.16536i) q^{19} +(2.68750 + 1.72715i) q^{20} +(-0.711811 + 4.52696i) q^{21} +4.75799 q^{22} +(-3.57120 + 3.20102i) q^{23} +(-0.964275 + 1.43881i) q^{24} +(5.11165 - 0.985189i) q^{25} +(0.337151 - 7.07767i) q^{26} +(4.89292 + 1.74908i) q^{27} +(-0.880519 - 2.49493i) q^{28} +(-7.51320 + 1.08024i) q^{29} +(0.942463 + 5.45242i) q^{30} +(6.02457 - 0.286986i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(5.57121 + 6.07266i) q^{33} +(-3.66819 - 3.17851i) q^{34} +(-7.53603 - 3.82731i) q^{35} +(-2.96545 + 0.454015i) q^{36} +(-6.11706 + 8.59021i) q^{37} +(-0.213488 - 4.48167i) q^{38} +(9.42804 - 7.85704i) q^{39} +(-1.97480 - 2.51116i) q^{40} +(1.04866 - 2.29625i) q^{41} +(2.15328 - 4.04517i) q^{42} +(-1.01471 - 0.652114i) q^{43} +(-4.49631 - 1.55619i) q^{44} +(-5.85542 + 7.58720i) q^{45} +(4.42174 - 1.85694i) q^{46} +(-1.51828 - 2.62974i) q^{47} +(1.38183 - 1.04429i) q^{48} +(2.98508 + 6.33161i) q^{49} +(-5.15273 - 0.740851i) q^{50} +(-0.238397 - 8.40350i) q^{51} +(-2.63349 + 6.57813i) q^{52} +(-3.30839 - 3.46974i) q^{53} +(-4.05175 - 3.25320i) q^{54} +(-13.8265 + 6.31434i) q^{55} +(0.0160784 + 2.64570i) q^{56} +(5.47000 - 5.52013i) q^{57} +(7.45329 + 1.43650i) q^{58} +(2.57686 - 10.6219i) q^{59} +(0.892685 - 5.46079i) q^{60} +(2.42326 - 4.70046i) q^{61} +(-5.78709 - 1.69924i) q^{62} +(7.68418 - 1.98830i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(8.41304 + 21.0148i) q^{65} +(-3.27863 - 7.56083i) q^{66} +(-4.69534 + 0.904952i) q^{67} +(2.42686 + 4.20344i) q^{68} +(7.54751 + 3.46916i) q^{69} +(5.86977 + 6.08160i) q^{70} +(3.09039 - 2.67784i) q^{71} +(2.95084 + 0.540858i) q^{72} +(-3.55761 + 4.52386i) q^{73} +(8.59021 - 6.11706i) q^{74} +(-5.08786 - 7.44394i) q^{75} +(-1.26406 + 4.30501i) q^{76} +(12.2514 + 2.89345i) q^{77} +(-11.4793 + 4.34130i) q^{78} +(3.55695 + 3.39154i) q^{79} +(1.04486 + 3.01894i) q^{80} +(-0.592174 - 8.98050i) q^{81} +(-1.74202 + 1.82698i) q^{82} +(3.60996 + 7.90471i) q^{83} +(-3.35790 + 3.11842i) q^{84} +(14.8778 + 4.36851i) q^{85} +(0.745615 + 0.948127i) q^{86} +(6.89376 + 11.1947i) q^{87} +(3.74004 + 2.94120i) q^{88} +(0.0276158 - 0.579727i) q^{89} +(8.01490 - 5.25479i) q^{90} +(5.17223 - 18.0194i) q^{91} +(-4.78589 + 0.308605i) q^{92} +(-4.60744 - 9.37577i) q^{93} +(0.574673 + 2.98168i) q^{94} +(6.56801 + 12.7402i) q^{95} +(-1.64738 + 0.534906i) q^{96} +(1.97891 + 0.903738i) q^{97} +(-0.750035 - 6.95970i) q^{98} +(5.81094 - 13.0376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 + 4 * q^9	$ 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$3$	−0.689077	−	1.58908i	−0.397839	−	0.917455i
$3$	−0.689077	−	1.58908i	−0.397839	−	0.917455i
$4$	0.786053	+	0.618159i	0.393027	+	0.309079i
$5$	3.18017	−	0.303670i	1.42222	−	0.135805i	0.644589	−	0.764530i	$-0.277029\pi$
$5$	3.18017	−	0.303670i	1.42222	−	0.135805i	0.777628	+	0.628724i	$0.216423\pi$
$6$	0.131442	+	1.72706i	0.0536609	+	0.705068i
$7$	−2.23440	−	1.41685i	−0.844524	−	0.535518i
$7$	−2.23440	−	1.41685i	−0.844524	−	0.535518i
$8$	−0.540641	−	0.841254i	−0.191145	−	0.297428i
$9$	−2.05034	+	2.19000i	−0.683448	+	0.729999i
$10$	−3.10459	−	0.753165i	−0.981757	−	0.238172i
$11$	−4.49631	+	1.55619i	−1.35569	+	0.469208i	−0.905735	−	0.423844i	$-0.860680\pi$
$11$	−4.49631	+	1.55619i	−1.35569	+	0.469208i	−0.449953	+	0.893052i	$0.648559\pi$
$12$	0.440652	−	1.67506i	0.127205	−	0.483548i
$13$	1.99627	+	6.79867i	0.553666	+	1.88561i	0.454998	+	0.890492i	$0.349640\pi$
$13$	1.99627	+	6.79867i	0.553666	+	1.88561i	0.0986676	+	0.995120i	$0.468542\pi$
$14$	1.64810	+	2.06972i	0.440474	+	0.553157i
$15$	−2.67394	−	4.84430i	−0.690409	−	1.25079i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	4.50603	+	1.80394i	1.09287	+	0.437520i	0.846898	−	0.531756i	$-0.178468\pi$
$17$	4.50603	+	1.80394i	1.09287	+	0.437520i	0.245975	+	0.969276i	$0.420892\pi$
$18$	2.65386	−	1.39895i	0.625520	−	0.329735i
$19$	1.66756	+	4.16536i	0.382564	+	0.955598i	0.987256	+	0.159139i	$0.0508718\pi$
$19$	1.66756	+	4.16536i	0.382564	+	0.955598i	−0.604692	+	0.796459i	$0.706704\pi$
$20$	2.68750	+	1.72715i	0.600944	+	0.386203i
$21$	−0.711811	+	4.52696i	−0.155330	+	0.987863i
$22$	4.75799			1.01441
$23$	−3.57120	+	3.20102i	−0.744646	+	0.667459i
$23$	−3.57120	+	3.20102i	−0.744646	+	0.667459i
$24$	−0.964275	+	1.43881i	−0.196832	+	0.293696i
$25$	5.11165	−	0.985189i	1.02233	−	0.197038i
$26$	0.337151	−	7.07767i	0.0661207	−	1.38804i
$27$	4.89292	+	1.74908i	0.941644	+	0.336611i
$28$	−0.880519	−	2.49493i	−0.166402	−	0.471498i
$29$	−7.51320	+	1.08024i	−1.39517	+	0.200595i	−0.798548	−	0.601930i	$-0.794398\pi$
$29$	−7.51320	+	1.08024i	−1.39517	+	0.200595i	−0.596618	+	0.802525i	$0.703489\pi$
$30$	0.942463	+	5.45242i	0.172069	+	0.995472i
$31$	6.02457	−	0.286986i	1.08204	−	0.0515442i	0.501025	−	0.865433i	$-0.332957\pi$
$31$	6.02457	−	0.286986i	1.08204	−	0.0515442i	0.581020	+	0.813889i	$0.302654\pi$
$32$	0.0950560	−	0.995472i	0.0168037	−	0.175976i
$33$	5.57121	+	6.07266i	0.969823	+	1.05711i
$34$	−3.66819	−	3.17851i	−0.629090	−	0.545109i
$35$	−7.53603	−	3.82731i	−1.27382	−	0.646933i
$36$	−2.96545	+	0.454015i	−0.494241	+	0.0756692i
$37$	−6.11706	+	8.59021i	−1.00564	+	1.41222i	−0.0966887	+	0.995315i	$0.530825\pi$
$37$	−6.11706	+	8.59021i	−1.00564	+	1.41222i	−0.908949	+	0.416906i	$0.863114\pi$
$38$	−0.213488	−	4.48167i	−0.0346324	−	0.727023i
$39$	9.42804	−	7.85704i	1.50970	−	1.25813i
$40$	−1.97480	−	2.51116i	−0.312243	−	0.397049i
$41$	1.04866	−	2.29625i	0.163774	−	0.358615i	−0.809897	−	0.586572i	$-0.800477\pi$
$41$	1.04866	−	2.29625i	0.163774	−	0.358615i	0.973671	+	0.227957i	$0.0732045\pi$
$42$	2.15328	−	4.04517i	0.332259	−	0.624183i
$43$	−1.01471	−	0.652114i	−0.154742	−	0.0994465i	0.460979	−	0.887411i	$-0.347498\pi$
$43$	−1.01471	−	0.652114i	−0.154742	−	0.0994465i	−0.615720	+	0.787965i	$0.711135\pi$
$44$	−4.49631	−	1.55619i	−0.677844	−	0.234604i
$45$	−5.85542	+	7.58720i	−0.872874	+	1.13103i
$46$	4.42174	−	1.85694i	0.651950	−	0.273791i
$47$	−1.51828	−	2.62974i	−0.221464	−	0.383587i	0.733789	−	0.679378i	$-0.237750\pi$
$47$	−1.51828	−	2.62974i	−0.221464	−	0.383587i	−0.955253	+	0.295791i	$0.904417\pi$
$48$	1.38183	−	1.04429i	0.199450	−	0.150731i
$49$	2.98508	+	6.33161i	0.426440	+	0.904516i
$50$	−5.15273	−	0.740851i	−0.728707	−	0.104772i
$51$	−0.238397	−	8.40350i	−0.0333822	−	1.17673i
$52$	−2.63349	+	6.57813i	−0.365199	+	0.912223i
$53$	−3.30839	−	3.46974i	−0.454442	−	0.476605i	0.456155	−	0.889900i	$-0.349226\pi$
$53$	−3.30839	−	3.46974i	−0.454442	−	0.476605i	−0.910597	+	0.413295i	$0.864378\pi$
$54$	−4.05175	−	3.25320i	−0.551373	−	0.442705i
$55$	−13.8265	+	6.31434i	−1.86436	+	0.851425i
$56$	0.0160784	+	2.64570i	0.00214857	+	0.353547i
$57$	5.47000	−	5.52013i	0.724520	−	0.731159i
$58$	7.45329	+	1.43650i	0.978665	+	0.188622i
$59$	2.57686	−	10.6219i	0.335478	−	1.38286i	−0.515153	−	0.857098i	$-0.672265\pi$
$59$	2.57686	−	10.6219i	0.335478	−	1.38286i	0.850632	−	0.525762i	$-0.176220\pi$
$60$	0.892685	−	5.46079i	0.115245	−	0.704986i
$61$	2.42326	−	4.70046i	0.310266	−	0.601832i	−0.681215	−	0.732083i	$-0.738548\pi$
$61$	2.42326	−	4.70046i	0.310266	−	0.601832i	0.991481	+	0.130251i	$0.0415784\pi$
$62$	−5.78709	−	1.69924i	−0.734961	−	0.215804i
$63$	7.68418	−	1.98830i	0.968116	−	0.250502i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	8.41304	+	21.0148i	1.04351	+	2.60656i
$66$	−3.27863	−	7.56083i	−0.403571	−	0.930674i
$67$	−4.69534	+	0.904952i	−0.573627	+	0.110557i	−0.467811	−	0.883828i	$-0.654957\pi$
$67$	−4.69534	+	0.904952i	−0.573627	+	0.110557i	−0.105815	+	0.994386i	$0.533745\pi$
$68$	2.42686	+	4.20344i	0.294300	+	0.509742i
$69$	7.54751	+	3.46916i	0.908613	+	0.417638i
$70$	5.86977	+	6.08160i	0.701571	+	0.726890i
$71$	3.09039	−	2.67784i	0.366762	−	0.317801i	−0.451909	−	0.892064i	$-0.649257\pi$
$71$	3.09039	−	2.67784i	0.366762	−	0.317801i	0.818671	+	0.574263i	$0.194711\pi$
$72$	2.95084	+	0.540858i	0.347760	+	0.0637407i
$73$	−3.55761	+	4.52386i	−0.416386	+	0.529478i	−0.948323	−	0.317306i	$-0.897222\pi$
$73$	−3.55761	+	4.52386i	−0.416386	+	0.529478i	0.531937	+	0.846784i	$0.321464\pi$
$74$	8.59021	−	6.11706i	0.998591	−	0.711094i
$75$	−5.08786	−	7.44394i	−0.587496	−	0.859552i
$76$	−1.26406	+	4.30501i	−0.144998	+	0.493818i
$77$	12.2514	+	2.89345i	1.39618	+	0.329739i
$78$	−11.4793	+	4.34130i	−1.29977	+	0.491556i
$79$	3.55695	+	3.39154i	0.400188	+	0.381578i	0.863275	−	0.504735i	$-0.168410\pi$
$79$	3.55695	+	3.39154i	0.400188	+	0.381578i	−0.463087	+	0.886313i	$0.653258\pi$
$80$	1.04486	+	3.01894i	0.116819	+	0.337527i
$81$	−0.592174	−	8.98050i	−0.0657971	−	0.997833i
$82$	−1.74202	+	1.82698i	−0.192374	+	0.201756i
$83$	3.60996	+	7.90471i	0.396245	+	0.867655i	0.997637	+	0.0687011i	$0.0218855\pi$
$83$	3.60996	+	7.90471i	0.396245	+	0.867655i	−0.601393	+	0.798954i	$0.705387\pi$
$84$	−3.35790	+	3.11842i	−0.366377	+	0.340247i
$85$	14.8778	+	4.36851i	1.61372	+	0.473831i
$86$	0.745615	+	0.948127i	0.0804018	+	0.102239i
$87$	6.89376	+	11.1947i	0.739088	+	1.20020i
$88$	3.74004	+	2.94120i	0.398689	+	0.313533i
$89$	0.0276158	−	0.579727i	0.00292727	−	0.0614509i	−0.996931	−	0.0782849i	$-0.975056\pi$
$89$	0.0276158	−	0.579727i	0.00292727	−	0.0614509i	0.999858	+	0.0168339i	$0.00535866\pi$
$90$	8.01490	−	5.25479i	0.844845	−	0.553904i
$91$	5.17223	−	18.0194i	0.542197	−	1.88894i
$92$	−4.78589	+	0.308605i	−0.498964	+	0.0321743i
$93$	−4.60744	−	9.37577i	−0.477769	−	0.972222i
$94$	0.574673	+	2.98168i	0.0592730	+	0.307537i
$95$	6.56801	+	12.7402i	0.673864	+	1.30711i
$96$	−1.64738	+	0.534906i	−0.168135	+	0.0545936i
$97$	1.97891	+	0.903738i	0.200928	+	0.0917607i	0.513338	−	0.858187i	$-0.328409\pi$
$97$	1.97891	+	0.903738i	0.200928	+	0.0917607i	−0.312410	+	0.949947i	$0.601136\pi$
$98$	−0.750035	−	6.95970i	−0.0757650	−	0.703036i
$99$	5.81094	−	13.0376i	0.584021	−	1.31033i
$100$	4.62703	+	2.38540i	0.462703	+	0.238540i
$101$	0.245467	+	0.0234392i	0.0244249	+	0.00233229i	0.107261	−	0.994231i	$-0.465792\pi$
$101$	0.245467	+	0.0234392i	0.0244249	+	0.00233229i	−0.0828365	+	0.996563i	$0.526398\pi$
$102$	−2.52323	+	8.01928i	−0.249837	+	0.794027i
$103$	−2.67784	+	13.8939i	−0.263855	+	1.36901i	0.572087	+	0.820193i	$0.306134\pi$
$103$	−2.67784	+	13.8939i	−0.263855	+	1.36901i	−0.835942	+	0.548817i	$0.815078\pi$
$104$	4.64014	−	5.35501i	0.455003	−	0.525102i
$105$	−0.888982	+	14.6127i	−0.0867557	+	1.42605i
$106$	1.99159	+	4.36097i	0.193440	+	0.423575i
$107$	−1.80055	+	3.49258i	−0.174066	+	0.337640i	−0.959689	−	0.281065i	$-0.909312\pi$
$107$	−1.80055	+	3.49258i	−0.174066	+	0.337640i	0.785623	+	0.618705i	$0.212343\pi$
$108$	2.76489	+	4.39948i	0.266051	+	0.423340i
$109$	5.94259	+	2.37906i	0.569197	+	0.227872i	0.638366	−	0.769733i	$-0.279611\pi$
$109$	5.94259	+	2.37906i	0.569197	+	0.227872i	−0.0691691	+	0.997605i	$0.522035\pi$
$110$	15.1312	−	1.44486i	1.44271	−	0.137762i
$111$	17.8656	+	3.80117i	1.69573	+	0.360791i
$112$	0.850130	−	2.50545i	0.0803298	−	0.236743i
$113$	11.6150	−	10.0644i	1.09264	−	0.946782i	0.0938361	−	0.995588i	$-0.470087\pi$
$113$	11.6150	−	10.0644i	1.09264	−	0.946782i	0.998808	+	0.0488059i	$0.0155416\pi$
$114$	−6.97462	+	3.42747i	−0.653233	+	0.321012i
$115$	−10.3850	+	11.2643i	−0.968404	+	1.05040i
$116$	−6.57353	−	3.79523i	−0.610337	−	0.352378i
$117$	−18.9821	−	9.56780i	−1.75490	−	0.884543i
$118$	−5.90923	+	9.19494i	−0.543989	+	0.846463i
$119$	−7.51236	−	10.4151i	−0.688657	−	0.954750i
$120$	−2.62964	+	4.86849i	−0.240052	+	0.444430i
$121$	9.14849	−	7.19445i	0.831681	−	0.654041i
$122$	−3.82735	+	3.64937i	−0.346512	+	0.330398i
$123$	−4.37154	−	0.0841133i	−0.394169	−	0.00758424i
$124$	4.91304	+	3.49856i	0.441204	+	0.314180i
$125$	0.630583	−	0.185156i	0.0564011	−	0.0165609i
$126$	−7.91187	−	0.634305i	−0.704845	−	0.0565084i
$127$	4.46907	−	5.15759i	0.396566	−	0.457662i	−0.521990	−	0.852951i	$-0.674810\pi$
$127$	4.46907	−	5.15759i	0.396566	−	0.457662i	0.918557	+	0.395290i	$0.129356\pi$
$128$	0.690079	−	0.723734i	0.0609949	−	0.0639697i
$129$	−0.337048	+	2.06181i	−0.0296754	+	0.181532i
$130$	−1.07708	−	22.6106i	−0.0944658	−	1.98308i
$131$	3.71856	+	15.3281i	0.324892	+	1.33922i	0.866746	+	0.498750i	$0.166207\pi$
$131$	3.71856	+	15.3281i	0.324892	+	1.33922i	−0.541854	+	0.840473i	$0.682277\pi$
$132$	0.625400	+	8.21732i	0.0544341	+	0.715226i
$133$	2.17569	−	11.6697i	0.188656	−	1.01190i
$134$	4.73308	+	0.680514i	0.408876	+	0.0587874i
$135$	16.0915	+	4.07655i	1.38494	+	0.350854i
$136$	−0.918571	−	4.76600i	−0.0787668	−	0.408681i
$137$	−3.77912	−	2.18187i	−0.322872	−	0.186410i	0.329800	−	0.944051i	$-0.393019\pi$
$137$	−3.77912	−	2.18187i	−0.322872	−	0.186410i	−0.652672	+	0.757641i	$0.726352\pi$
$138$	−5.99775	−	5.74691i	−0.510562	−	0.489210i
$139$		−	7.23804i		−	0.613923i	−0.951722	−	0.306961i	$-0.900688\pi$
$139$		−	7.23804i		−	0.613923i	0.951722	−	0.306961i	$-0.0993122\pi$
$140$	−3.55784	−	7.66693i	−0.300692	−	0.647974i
$141$	−3.13265	+	4.22476i	−0.263817	+	0.355789i
$142$	−3.79626	+	1.51979i	−0.318575	+	0.127538i
$143$	−19.5559	−	27.4624i	−1.63534	−	2.29652i
$144$	−2.61165	−	1.47624i	−0.217638	−	0.123020i
$145$	−23.5653	+	5.71687i	−1.95699	+	0.474760i
$146$	4.84155	−	3.11148i	0.400690	−	0.257508i
$147$	8.00448	−	9.10650i	0.660198	−	0.751091i
$148$	−10.1184	+	2.97104i	−0.831731	+	0.244218i
$149$	0.554626	−	2.87767i	0.0454367	−	0.235748i	−0.952110	−	0.305757i	$-0.901091\pi$
$149$	0.554626	−	2.87767i	0.0454367	−	0.235748i	0.997546	+	0.0700086i	$0.0223027\pi$
$150$	2.37336	+	8.69861i	0.193784	+	0.710238i
$151$	−0.652577	+	2.68996i	−0.0531060	+	0.218906i	−0.992181	−	0.124806i	$-0.960169\pi$
$151$	−0.652577	+	2.68996i	−0.0531060	+	0.218906i	0.939075	+	0.343712i	$0.111684\pi$
$152$	2.60257	−	3.65480i	0.211096	−	0.296443i
$153$	−13.1895	+	6.16949i	−1.06631	+	0.498774i
$154$	−10.6313	−	6.74136i	−0.856691	−	0.543234i
$155$	19.0720	−	2.74214i	1.53190	−	0.220254i
$156$	12.2678	−	0.348024i	0.982214	−	0.0278642i
$157$	8.09300	−	10.2911i	0.645891	−	0.821318i	−0.347307	−	0.937751i	$-0.612904\pi$
$157$	8.09300	−	10.2911i	0.645891	−	0.821318i	0.993198	+	0.116434i	$0.0371463\pi$
$158$	−2.25205	−	4.36837i	−0.179164	−	0.347529i
$159$	−3.23395	+	7.64821i	−0.256469	+	0.606542i
$160$		−	3.19464i		−	0.252558i
$161$	12.5148	−	2.09251i	0.986308	−	0.164913i
$162$	−2.37763	+	8.68026i	−0.186804	+	0.681986i
$163$	−7.70750	+	22.2693i	−0.603698	+	1.74427i	0.0620292	+	0.998074i	$0.480243\pi$
$163$	−7.70750	+	22.2693i	−0.603698	+	1.74427i	−0.665727	+	0.746196i	$0.731878\pi$
$164$	2.24376	−	1.15674i	0.175208	−	0.0903260i
$165$	19.5615	+	17.6203i	1.52286	+	1.37174i
$166$	−0.826038	−	8.65066i	−0.0641130	−	0.671422i
$167$	0.656774	+	4.56796i	0.0508227	+	0.353479i	0.999326	+	0.0367120i	$0.0116884\pi$
$167$	0.656774	+	4.56796i	0.0508227	+	0.353479i	−0.948503	+	0.316768i	$0.897402\pi$
$168$	4.19315	−	1.84864i	0.323509	−	0.142626i
$169$	−31.3006	+	20.1157i	−2.40774	+	1.54736i
$170$	−12.6307	−	8.99428i	−0.968731	−	0.689830i
$171$	−12.5412	−	4.88847i	−0.959048	−	0.373831i
$172$	−0.394505	−	1.13985i	−0.0300807	−	0.0869126i
$173$	−13.0522	−	2.51560i	−0.992339	−	0.191258i	−0.332857	−	0.942977i	$-0.608013\pi$
$173$	−13.0522	−	2.51560i	−0.992339	−	0.191258i	−0.659483	+	0.751720i	$0.729225\pi$
$174$	−2.85318	−	12.8337i	−0.216299	−	0.972923i
$175$	−12.8173	−	5.04112i	−0.968899	−	0.381073i
$176$	−2.57237	−	4.00268i	−0.193899	−	0.301713i
$177$	−18.6548	+	3.22452i	−1.40218	+	0.242369i
$178$	−0.215707	+	0.538810i	−0.0161679	+	0.0403855i
$179$	−12.0198	+	8.55928i	−0.898404	+	0.639751i	−0.933088	−	0.359648i	$-0.882897\pi$
$179$	−12.0198	+	8.55928i	−0.898404	+	0.639751i	0.0346842	+	0.999398i	$0.488957\pi$
$180$	−9.29276	+	2.34436i	−0.692642	+	0.174739i
$181$	4.48007	−	6.97113i	0.333001	−	0.518160i	−0.633865	−	0.773444i	$-0.718532\pi$
$181$	4.48007	−	6.97113i	0.333001	−	0.518160i	0.966866	+	0.255284i	$0.0821689\pi$
$182$	−10.7813	+	15.3366i	−0.799164	+	1.13683i
$183$	−9.13921	−	0.611764i	−0.675590	−	0.0452229i
$184$	4.62361	+	1.27368i	0.340857	+	0.0938969i
$185$	−16.8447	+	29.1759i	−1.23845	+	2.14506i
$186$	1.28752	+	10.3671i	0.0944057	+	0.760149i
$187$	−23.0678	−	1.09885i	−1.68688	−	0.0803562i
$188$	0.432147	−	3.00565i	0.0315176	−	0.219210i
$189$	−8.45456	−	10.8407i	−0.614979	−	0.788544i
$190$	−2.03988	−	14.1877i	−0.147988	−	1.02928i
$191$	−3.40174	+	0.825253i	−0.246141	+	0.0597132i	−0.356931	−	0.934131i	$-0.616177\pi$
$191$	−3.40174	+	0.825253i	−0.246141	+	0.0597132i	0.110790	+	0.993844i	$0.464662\pi$
$192$	1.73173	+	0.0333204i	0.124977	+	0.00240469i
$193$	8.13431	+	0.776732i	0.585520	+	0.0559104i	0.383613	−	0.923494i	$-0.374680\pi$
$193$	8.13431	+	0.776732i	0.585520	+	0.0559104i	0.201908	+	0.979405i	$0.435286\pi$
$194$	−1.57449	−	1.50127i	−0.113042	−	0.107785i
$195$	27.5969	−	27.8498i	1.97625	−	1.99436i
$196$	−1.56751	+	6.82224i	−0.111965	+	0.487303i
$197$	−0.484171	−	1.64893i	−0.0344957	−	0.117482i	0.940445	−	0.339945i	$-0.110408\pi$
$197$	−0.484171	−	1.64893i	−0.0344957	−	0.117482i	−0.974941	+	0.222463i	$0.928590\pi$
$198$	−9.75553	+	10.4200i	−0.693295	+	0.740517i
$199$	1.04390	−	0.0497269i	0.0739998	−	0.00352505i	−0.0105493	−	0.999944i	$-0.503358\pi$
$199$	1.04390	−	0.0497269i	0.0739998	−	0.00352505i	0.0845492	+	0.996419i	$0.473055\pi$
$200$	−3.59236	−	3.76756i	−0.254018	−	0.266407i
$201$	4.67349	+	6.83768i	0.329643	+	0.482293i
$202$	−0.224300	−	0.102434i	−0.0157817	−	0.00720726i
$203$	18.3180	+	8.23139i	1.28567	+	0.577731i
$204$	5.00730	−	6.75296i	0.350581	−	0.472802i
$205$	2.63763	−	7.62094i	0.184220	−	0.532269i
$206$	7.07482	−	12.2539i	0.492926	−	0.853773i
$207$	0.311958	−	14.3841i	0.0216826	−	0.999765i
$208$	−6.13639	+	3.54285i	−0.425482	+	0.245652i
$209$	−13.9799	−	16.1337i	−0.967012	−	1.11599i
$210$	5.61942	−	13.5182i	0.387777	−	0.932846i
$211$	−0.0320494	+	0.222909i	−0.00220637	+	0.0153457i	−0.990895	−	0.134638i	$-0.957013\pi$
$211$	−0.0320494	+	0.222909i	−0.00220637	+	0.0153457i	0.988689	+	0.149983i	$0.0479220\pi$
$212$	−0.455719	−	4.77251i	−0.0312989	−	0.327777i
$213$	−6.38482	−	3.06564i	−0.437481	−	0.210054i
$214$	2.84383	−	2.71159i	0.194400	−	0.185360i
$215$	−3.42498	−	1.76570i	−0.233582	−	0.120420i
$216$	−1.17389	−	5.06182i	−0.0798733	−	0.344413i
$217$	−13.8679	−	7.89467i	−0.941415	−	0.535925i
$218$	−4.83764	−	4.19184i	−0.327646	−	0.283907i
$219$	9.64024	+	2.53602i	0.651427	+	0.171369i
$220$	−14.7716	−	3.58355i	−0.995902	−	0.241603i
$221$	−3.26916	+	34.2362i	−0.219908	+	2.30298i
$222$	−15.6398	−	9.43539i	−1.04968	−	0.633262i
$223$	2.62462	−	8.93864i	0.175758	−	0.598575i	−0.823743	−	0.566964i	$-0.808118\pi$
$223$	2.62462	−	8.93864i	0.175758	−	0.598575i	0.999500	−	0.0316114i	$-0.0100639\pi$
$224$	−1.62283	+	2.08960i	−0.108430	+	0.139617i
$225$	−8.32308	+	13.2145i	−0.554872	+	0.880965i
$226$	−14.2679	+	5.71201i	−0.949087	+	0.379957i
$227$	−0.202888	+	0.104596i	−0.0134661	+	0.00694228i	−0.464946	−	0.885339i	$-0.653926\pi$
$227$	−0.202888	+	0.104596i	−0.0134661	+	0.00694228i	0.451480	+	0.892281i	$0.350896\pi$
$228$	7.71203	−	0.957785i	0.510742	−	0.0634309i
$229$	8.79648	−	5.07865i	0.581288	−	0.335607i	−0.180357	−	0.983601i	$-0.557725\pi$
$229$	8.79648	−	5.07865i	0.581288	−	0.335607i	0.761645	+	0.647995i	$0.224392\pi$
$230$	13.4980	−	7.24815i	0.890031	−	0.477929i
$231$	−3.84427	−	21.4623i	−0.252935	−	1.41212i
$232$	4.97070	+	5.73649i	0.326342	+	0.376619i
$233$	13.1411	+	0.625989i	0.860904	+	0.0410099i	0.473389	−	0.880854i	$-0.343031\pi$
$233$	13.1411	+	0.625989i	0.860904	+	0.0410099i	0.387515	+	0.921863i	$0.373334\pi$
$234$	14.8088	+	15.2500i	0.968081	+	0.996925i
$235$	−5.62696	−	7.90197i	−0.367063	−	0.515467i
$236$	8.59160	−	6.75651i	0.559266	−	0.439811i
$237$	2.93842	−	7.98931i	0.190871	−	0.518961i
$238$	3.69274	+	12.2993i	0.239365	+	0.797247i
$239$	10.2452	−	4.67884i	0.662708	−	0.302649i	−0.0555186	−	0.998458i	$-0.517681\pi$
$239$	10.2452	−	4.67884i	0.662708	−	0.302649i	0.718227	+	0.695809i	$0.244954\pi$
$240$	4.07734	−	3.74065i	0.263191	−	0.241458i
$241$	10.3454	−	3.58059i	0.666408	−	0.230646i	0.0271418	−	0.999632i	$-0.491359\pi$
$241$	10.3454	−	3.58059i	0.666408	−	0.230646i	0.639266	+	0.768986i	$0.279238\pi$
$242$	−10.9984	+	3.80658i	−0.707004	+	0.244697i
$243$	−13.8627	+	7.12927i	−0.889290	+	0.457343i
$244$	4.81044	−	2.19685i	0.307957	−	0.140639i
$245$	11.4158	+	19.2291i	0.729328	+	1.22851i
$246$	4.10360	+	1.50928i	0.261636	+	0.0962280i
$247$	−24.9900	+	19.6524i	−1.59008	+	1.25045i
$248$	−3.49856	−	4.91304i	−0.222159	−	0.311978i
$249$	10.0737	−	11.1835i	0.638393	−	0.708724i
$250$	−0.656461	−	0.0312711i	−0.0415182	−	0.00197776i
$251$	2.05123	+	2.36724i	0.129472	+	0.149419i	0.816784	−	0.576944i	$-0.195755\pi$
$251$	2.05123	+	2.36724i	0.129472	+	0.149419i	−0.687312	+	0.726363i	$0.741209\pi$
$252$	7.26926	+	3.18714i	0.457920	+	0.200771i
$253$	11.0758	−	19.9502i	0.696331	−	1.25426i
$254$	−5.91016	+	3.41223i	−0.370836	+	0.214102i
$255$	−3.31003	−	26.6522i	−0.207282	−	1.66902i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−12.6400	+	5.06028i	−0.788460	+	0.315652i	−0.730718	−	0.682680i	$-0.760814\pi$
$257$	−12.6400	+	5.06028i	−0.788460	+	0.315652i	−0.0577421	+	0.998332i	$0.518390\pi$
$258$	0.992862	−	1.83817i	0.0618129	−	0.114440i
$259$	25.8390	−	10.5270i	1.60556	−	0.654116i
$260$	−6.37737	+	21.7193i	−0.395507	+	1.34697i
$261$	13.0389	−	18.6687i	0.807090	−	1.15557i
$262$	1.49929	−	15.7013i	0.0926266	−	0.970029i
$263$	−17.0423	−	4.13441i	−1.05087	−	0.254939i	−0.327108	−	0.944987i	$-0.606074\pi$
$263$	−17.0423	−	4.13441i	−1.05087	−	0.254939i	−0.723763	+	0.690049i	$0.757589\pi$
$264$	2.09662	−	7.96993i	0.129038	−	0.490515i
$265$	−11.5749	−	10.0297i	−0.711041	−	0.616120i
$266$	−5.87283	+	10.3163i	−0.360086	+	0.632534i
$267$	−0.940261	+	0.355593i	−0.0575431	+	0.0217619i
$268$	−4.25019	−	2.19112i	−0.259621	−	0.133844i
$269$	11.3734	−	10.8445i	0.693446	−	0.661199i	−0.259010	−	0.965875i	$-0.583396\pi$
$269$	11.3734	−	10.8445i	0.693446	−	0.661199i	0.952456	+	0.304675i	$0.0985479\pi$
$270$	−13.8732	−	9.11536i	−0.844294	−	0.554743i
$271$	1.44788	+	15.1629i	0.0879527	+	0.921083i	0.926510	+	0.376270i	$0.122793\pi$
$271$	1.44788	+	15.1629i	0.0879527	+	0.921083i	−0.838558	+	0.544813i	$0.816601\pi$
$272$	−0.690755	+	4.80431i	−0.0418832	+	0.291304i
$273$	−32.1983	+	4.19766i	−1.94873	+	0.254054i
$274$	2.85765	+	3.29790i	0.172637	+	0.199233i
$275$	−21.4504	+	12.3844i	−1.29351	+	0.746807i
$276$	3.78825	+	7.39251i	0.228026	+	0.444977i
$277$	0.375694	−	0.650721i	0.0225733	−	0.0390980i	−0.854518	−	0.519422i	$-0.826147\pi$
$277$	0.375694	−	0.650721i	0.0225733	−	0.0390980i	0.877091	+	0.480324i	$0.159481\pi$
$278$	−2.36733	+	6.83995i	−0.141983	+	0.410233i
$279$	−11.7239	+	13.7822i	−0.701895	+	0.825120i
$280$	0.854552	+	8.40891i	0.0510692	+	0.502529i
$281$	10.0081	+	4.57056i	0.597035	+	0.272657i	0.690926	−	0.722926i	$-0.257203\pi$
$281$	10.0081	+	4.57056i	0.597035	+	0.272657i	−0.0938909	+	0.995582i	$0.529930\pi$
$282$	4.34214	−	2.96781i	0.258571	−	0.176731i
$283$	7.89449	+	8.27951i	0.469279	+	0.492166i	0.915253	−	0.402881i	$-0.131991\pi$
$283$	7.89449	+	8.27951i	0.469279	+	0.492166i	−0.445974	+	0.895046i	$0.647143\pi$
$284$	4.08455	−	0.194571i	0.242373	−	0.0115457i
$285$	15.7193	−	19.2161i	0.931129	−	1.13826i
$286$	9.49825	+	32.3481i	0.561643	+	1.91278i
$287$	−5.59658	+	3.64495i	−0.330356	+	0.215155i
$288$	1.98518	+	2.24923i	0.116978	+	0.132537i
$289$	4.74663	+	4.52591i	0.279214	+	0.266230i
$290$	24.1390	+	2.30499i	1.41749	+	0.135354i
$291$	0.0724888	−	3.76739i	0.00424937	−	0.220848i
$292$	−5.59293	+	1.35683i	−0.327302	+	0.0794025i
$293$	3.65343	+	25.4101i	0.213435	+	1.48448i	0.761568	+	0.648085i	$0.224430\pi$
$293$	3.65343	+	25.4101i	0.213435	+	1.48448i	−0.548133	+	0.836391i	$0.684661\pi$
$294$	−10.5427	+	5.98764i	−0.614862	+	0.349206i
$295$	4.96929	−	34.5622i	0.289323	−	2.01229i
$296$	10.5337	+	0.501781i	0.612257	+	0.0291654i
$297$	−24.7220	−	0.250104i	−1.43452	−	0.0145125i
$298$	−1.46532	+	2.53800i	−0.0848835	+	0.147023i
$299$	−28.8918	−	17.8893i	−1.67085	−	1.03457i
$300$	0.602207	−	8.99644i	0.0347684	−	0.519410i
$301$	1.34332	+	2.89477i	0.0774276	+	0.166852i
$302$	1.49649	−	2.32858i	0.0861131	−	0.133995i
$303$	−0.131899	−	0.406218i	−0.00757739	−	0.0233366i
$304$	−3.65480	+	2.60257i	−0.209617	+	0.149268i
$305$	6.27899	−	15.6841i	0.359534	−	0.898072i
$306$	14.4820	−	1.51630i	0.827880	−	0.0866809i
$307$	−11.4259	−	17.7791i	−0.652111	−	1.01471i	−0.997100	−	0.0760984i	$-0.975754\pi$
$307$	−11.4259	−	17.7791i	−0.652111	−	1.01471i	0.344989	−	0.938607i	$-0.387883\pi$
$308$	7.84167	+	9.84773i	0.446820	+	0.561127i
$309$	23.9238	−	5.31870i	1.36098	−	0.302570i
$310$	−18.9200	−	3.64652i	−1.07458	−	0.207109i
$311$	3.26263	+	9.42676i	0.185007	+	0.534543i	0.998921	−	0.0464429i	$-0.0147885\pi$
$311$	3.26263	+	9.42676i	0.185007	+	0.534543i	−0.813914	+	0.580985i	$0.802667\pi$
$312$	−11.7070	−	3.68354i	−0.662776	−	0.208539i
$313$	9.65287	+	6.87377i	0.545612	+	0.388529i	0.819366	−	0.573271i	$-0.194326\pi$
$313$	9.65287	+	6.87377i	0.545612	+	0.388529i	−0.273753	+	0.961800i	$0.588265\pi$
$314$	−11.0138	+	7.07812i	−0.621543	+	0.399441i
$315$	23.8333	−	8.65659i	1.34285	−	0.487744i
$316$	0.699437	+	4.86469i	0.0393464	+	0.273660i
$317$	−0.658611	−	6.89729i	−0.0369913	−	0.387390i	−0.994942	−	0.100456i	$-0.967970\pi$
$317$	−0.658611	−	6.89729i	−0.0369913	−	0.387390i	0.957950	−	0.286934i	$-0.0926362\pi$
$318$	5.55757	−	6.16984i	0.311653	−	0.345988i
$319$	32.1006	−	16.5490i	1.79729	−	0.926568i
$320$	−1.04486	+	3.01894i	−0.0584097	+	0.168764i
$321$	6.79070	+	0.454558i	0.379020	+	0.0253710i
$322$	−12.5109	−	2.11578i	−0.697207	−	0.117908i
$323$			21.7774i			1.21173i
$324$	5.08589	−	7.42521i	0.282550	−	0.412511i
$325$	16.9022	+	32.7857i	0.937566	+	1.81862i
$326$	14.5672	−	18.5237i	0.806801	−	1.02593i
$327$	−0.314400	−	11.0826i	−0.0173863	−	0.612869i
$328$	−2.49868	+	0.359256i	−0.137967	+	0.0198366i
$329$	−0.333497	+	8.02706i	−0.0183863	+	0.442546i
$330$	−12.7226	−	23.0491i	−0.700356	−	1.26881i
$331$	−9.78116	+	13.7357i	−0.537621	+	0.754983i	−0.990637	−	0.136519i	$-0.956409\pi$
$331$	−9.78116	+	13.7357i	−0.537621	+	0.754983i	0.453016	+	0.891502i	$0.350348\pi$
$332$	−2.04875	+	8.44505i	−0.112440	+	0.463482i
$333$	−6.27045	−	31.0092i	−0.343618	−	1.69929i
$334$	0.873382	−	4.53154i	0.0477893	−	0.247955i
$335$	−14.6572	+	4.30374i	−0.800807	+	0.235138i
$336$	−4.56716	+	0.375524i	−0.249159	+	0.0204865i
$337$	−5.18483	+	3.33209i	−0.282436	+	0.181510i	−0.674187	−	0.738561i	$-0.735506\pi$
$337$	−5.18483	+	3.33209i	−0.282436	+	0.181510i	0.391751	+	0.920071i	$0.371869\pi$
$338$	36.1583	−	8.77190i	1.96675	−	0.477128i
$339$	−23.9968	−	11.5219i	−1.30333	−	0.625786i
$340$	8.99428	+	12.6307i	0.487784	+	0.684996i
$341$	−26.6417	+	10.6657i	−1.44273	+	0.577582i
$342$	10.2526	+	8.72143i	0.554395	+	0.471601i
$343$	2.30108	−	18.3768i	0.124246	−	0.992251i
$344$			1.20619i			0.0650333i
$345$	25.0559	+	8.74060i	1.34896	+	0.470578i
$346$	11.5116	+	6.64620i	0.618865	+	0.357302i
$347$	0.660067	+	3.42475i	0.0354342	+	0.183850i	0.995333	−	0.0964949i	$-0.0307632\pi$
$347$	0.660067	+	3.42475i	0.0354342	+	0.183850i	−0.959899	+	0.280345i	$0.909551\pi$
$348$	−1.50125	+	13.0611i	−0.0804754	+	0.700147i
$349$	30.1036	+	4.32825i	1.61141	+	0.231686i	0.888373	−	0.459122i	$-0.151836\pi$
$349$	30.1036	+	4.32825i	1.61141	+	0.231686i	0.723038	+	0.690808i	$0.242745\pi$
$350$	10.4636	+	8.95600i	0.559302	+	0.478718i
$351$	−2.12384	+	36.7570i	−0.113362	+	1.96195i
$352$	1.12174	+	4.62387i	0.0597889	+	0.246453i
$353$	−1.05862	−	22.2232i	−0.0563448	−	1.18282i	−0.833137	−	0.553067i	$-0.813458\pi$
$353$	−1.05862	−	22.2232i	−0.0563448	−	1.18282i	0.776792	−	0.629757i	$-0.216845\pi$
$354$	18.6834	+	3.05421i	0.993012	+	0.162329i
$355$	9.01481	−	9.45446i	0.478456	−	0.501791i
$356$	0.380071	−	0.438625i	0.0201437	−	0.0232471i
$357$	−11.3738	+	19.1145i	−0.601966	+	1.01165i
$358$	14.1582	−	4.15723i	0.748285	−	0.219716i
$359$	−29.0213	−	20.6660i	−1.53169	−	1.09071i	−0.963465	−	0.267833i	$-0.913692\pi$
$359$	−29.0213	−	20.6660i	−1.53169	−	1.09071i	−0.568221	−	0.822876i	$-0.692368\pi$
$360$	9.54844	+	0.823940i	0.503247	+	0.0434255i
$361$	−0.818499	+	0.780437i	−0.0430789	+	0.0410756i
$362$	−6.51371	+	5.12244i	−0.342353	+	0.269229i
$363$	−17.7366	−	9.58014i	−0.930928	−	0.502827i
$364$	15.2045	−	10.9669i	0.796931	−	0.574823i
$365$	−9.94005	+	15.4670i	−0.520286	+	0.809580i
$366$	8.43648	+	3.56726i	0.440982	+	0.186464i
$367$	7.52707	+	4.34576i	0.392910	+	0.226847i	0.683420	−	0.730025i	$-0.260492\pi$
$367$	7.52707	+	4.34576i	0.392910	+	0.226847i	−0.290510	+	0.956872i	$0.593825\pi$
$368$	−3.95273	−	2.71586i	−0.206050	−	0.141574i
$369$	2.87867	+	7.00468i	0.149857	+	0.364649i
$370$	25.4608	−	22.0619i	1.32364	−	1.14694i
$371$	2.47617	+	12.4403i	0.128556	+	0.645866i
$372$	2.17402	−	10.2180i	0.112718	−	0.529778i
$373$	−29.4328	+	2.81049i	−1.52397	+	0.145522i	−0.823154	−	0.567818i	$-0.807788\pi$
$373$	−29.4328	+	2.81049i	−1.52397	+	0.145522i	−0.700819	+	0.713339i	$0.747182\pi$
$374$	21.4397	+	8.58315i	1.10862	+	0.443824i
$375$	−0.728748	−	0.874460i	−0.0376324	−	0.0451569i
$376$	−1.39143	+	2.69900i	−0.0717576	+	0.139190i
$377$	−22.3426	−	48.9234i	−1.15070	−	2.51968i
$378$	4.44393	+	13.0097i	0.228571	+	0.669145i
$379$	−2.21462	+	2.55580i	−0.113757	+	0.131283i	−0.809772	−	0.586744i	$-0.800409\pi$
$379$	−2.21462	+	2.55580i	−0.113757	+	0.131283i	0.696015	+	0.718027i	$0.254955\pi$
$380$	−2.71264	+	14.0745i	−0.139156	+	0.722008i
$381$	−11.2753	−	3.54773i	−0.577654	−	0.181756i
$382$	3.48456	+	0.332735i	0.178286	+	0.0170242i
$383$	25.8500	+	13.3266i	1.32087	+	0.680957i	0.967105	−	0.254377i	$-0.0818705\pi$
$383$	25.8500	+	13.3266i	1.32087	+	0.680957i	0.353766	+	0.935334i	$0.384901\pi$
$384$	−1.62559	−	0.597881i	−0.0829555	−	0.0305105i
$385$	39.8403	+	5.48127i	2.03045	+	0.279351i
$386$	−7.43288	−	3.39448i	−0.378324	−	0.172775i
$387$	3.50863	−	0.885152i	0.178354	−	0.0449948i
$388$	0.996875	+	1.93367i	0.0506086	+	0.0981671i
$389$	4.62822	+	24.0135i	0.234660	+	1.21753i	0.887777	+	0.460274i	$0.152249\pi$
$389$	4.62822	+	24.0135i	0.234660	+	1.21753i	−0.653117	+	0.757257i	$0.726539\pi$
$390$	−35.1878	+	17.2920i	−1.78181	+	0.875615i
$391$	−21.8664	+	7.98167i	−1.10583	+	0.403650i
$392$	3.71263	−	5.93434i	0.187516	−	0.299729i
$393$	21.7952	−	16.4713i	1.09942	−	0.830869i
$394$	−0.0817718	+	1.71660i	−0.00411960	+	0.0864811i
$395$	12.3416	+	9.70556i	0.620974	+	0.488340i
$396$	12.6270	−	6.65618i	0.634532	−	0.334486i
$397$	−16.9334	−	21.5325i	−0.849861	−	1.08069i	−0.995815	−	0.0913950i	$-0.970867\pi$
$397$	−16.9334	−	21.5325i	−0.849861	−	1.08069i	0.145953	−	0.989291i	$-0.453375\pi$
$398$	−1.00275	−	0.294433i	−0.0502632	−	0.0147586i
$399$	−20.0434	+	4.58401i	−1.00342	+	0.229488i
$400$	2.16253	+	4.73529i	0.108127	+	0.236765i
$401$	7.59207	−	7.96233i	0.379130	−	0.397620i	−0.506327	−	0.862342i	$-0.668997\pi$
$401$	7.59207	−	7.96233i	0.379130	−	0.397620i	0.885457	+	0.464722i	$0.153846\pi$
$402$	−2.18007	−	7.99016i	−0.108732	−	0.398513i
$403$	13.9778	+	40.3862i	0.696284	+	2.01178i
$404$	0.178461	+	0.170162i	0.00887876	+	0.00846588i
$405$	−4.61032	−	28.3797i	−0.229089	−	1.41020i
$406$	−14.6183	−	13.7699i	−0.725495	−	0.683389i
$407$	14.1362	−	48.1435i	0.700706	−	2.38639i
$408$	−6.94058	+	4.74383i	−0.343610	+	0.234854i
$409$	16.3165	−	11.6190i	0.806801	−	0.574521i	−0.100531	−	0.994934i	$-0.532054\pi$
$409$	16.3165	−	11.6190i	0.806801	−	0.574521i	0.907333	+	0.420413i	$0.138115\pi$
$410$	−4.98513	+	6.33911i	−0.246198	+	0.313066i
$411$	−0.863066	+	7.50880i	−0.0425719	+	0.370382i
$412$	−10.6936	+	9.26604i	−0.526835	+	0.456505i
$413$	−20.8074	+	20.0827i	−1.02387	+	0.988203i
$414$	−4.99938	+	13.4910i	−0.245706	+	0.663045i
$415$	13.8807	+	24.0421i	0.681378	+	1.18018i
$416$	6.95765	−	1.34098i	0.341127	−	0.0657468i
$417$	−11.5018	+	4.98757i	−0.563246	+	0.244242i
$418$	7.93423	+	19.8187i	0.388076	+	0.969366i
$419$	11.1998	−	24.5241i	0.547146	−	1.19808i	−0.410956	−	0.911655i	$-0.634805\pi$
$419$	11.1998	−	24.5241i	0.547146	−	1.19808i	0.958102	−	0.286427i	$-0.0924677\pi$
$420$	−9.73173	+	10.9368i	−0.474860	+	0.533661i
$421$	−27.4032	−	8.04630i	−1.33555	−	0.392153i	−0.465470	−	0.885064i	$-0.654115\pi$
$421$	−27.4032	−	8.04630i	−1.33555	−	0.392153i	−0.870080	+	0.492911i	$0.835933\pi$
$422$	0.103193	−	0.200167i	0.00502336	−	0.00974395i
$423$	8.87211	+	2.06684i	0.431377	+	0.100493i
$424$	−1.13028	+	4.65908i	−0.0548912	+	0.226265i
$425$	24.8105	+	4.78183i	1.20348	+	0.231953i
$426$	5.03099	+	4.98530i	0.243752	+	0.241539i
$427$	−12.0744	+	7.06932i	−0.584319	+	0.342108i
$428$	−3.57429	+	1.63233i	−0.172770	+	0.0789014i
$429$	−30.1644	+	49.9995i	−1.45635	+	2.41400i
$430$	2.65910	+	2.78879i	0.128233	+	0.134487i
$431$	6.11970	−	15.2863i	0.294776	−	0.736314i	−0.704861	−	0.709346i	$-0.748991\pi$
$431$	6.11970	−	15.2863i	0.294776	−	0.736314i	0.999636	−	0.0269680i	$-0.00858523\pi$
$432$	−0.546227	+	5.16736i	−0.0262804	+	0.248615i
$433$	−24.3552	−	3.50176i	−1.17044	−	0.168284i	−0.470443	−	0.882431i	$-0.655906\pi$
$433$	−24.3552	−	3.50176i	−1.17044	−	0.168284i	−0.699996	+	0.714147i	$0.746815\pi$
$434$	10.5231	+	11.9962i	0.505125	+	0.575837i
$435$	25.3228	+	33.5077i	1.21414	+	1.60657i
$436$	3.20056	+	5.54353i	0.153279	+	0.265487i
$437$	−19.2886	−	9.53743i	−0.922698	−	0.456237i
$438$	−8.28059	−	5.54956i	−0.395662	−	0.265168i
$439$	7.19043	+	2.48863i	0.343181	+	0.118776i	0.493221	−	0.869904i	$-0.335819\pi$
$439$	7.19043	+	2.48863i	0.343181	+	0.118776i	−0.150041	+	0.988680i	$0.547940\pi$
$440$	12.7871	+	8.21778i	0.609602	+	0.391767i
$441$	−19.9867	−	6.44467i	−0.951745	−	0.306889i
$442$	14.2869	−	31.2840i	0.679560	−	1.48803i
$443$	−20.9420	−	26.6299i	−0.994984	−	1.26523i	−0.964055	−	0.265704i	$-0.914396\pi$
$443$	−20.9420	−	26.6299i	−0.994984	−	1.26523i	−0.0309295	−	0.999522i	$-0.509847\pi$
$444$	11.6936	+	14.0317i	0.554954	+	0.665916i
$445$	−0.0882225	−	1.85202i	−0.00418215	−	0.0877941i
$446$	−5.40381	+	7.58859i	−0.255878	+	0.359330i
$447$	−4.95503	+	1.10160i	−0.234365	+	0.0521037i
$448$	2.21701	−	1.44390i	0.104744	−	0.0682179i
$449$	14.3308	+	12.4178i	0.676315	+	0.586030i	0.923806	−	0.382860i	$-0.125061\pi$
$449$	14.3308	+	12.4178i	0.676315	+	0.586030i	−0.247492	+	0.968890i	$0.579606\pi$
$450$	12.1873	−	9.76547i	0.574517	−	0.460349i
$451$	−1.14172	+	11.9566i	−0.0537613	+	0.563014i
$452$	15.3514	−	0.731277i	0.722069	−	0.0343964i
$453$	4.72424	−	0.816594i	0.221964	−	0.0383669i
$454$	0.225939	−	0.0324852i	0.0106039	−	0.00152460i
$455$	10.9766	−	58.8754i	0.514593	−	2.76012i
$456$	−7.60114	−	1.61725i	−0.355956	−	0.0757347i
$457$	−0.664257	+	13.9445i	−0.0310726	+	0.652295i	0.928584	+	0.371121i	$0.121027\pi$
$457$	−0.664257	+	13.9445i	−0.0310726	+	0.652295i	−0.959657	+	0.281173i	$0.909276\pi$
$458$	−9.97375	+	1.92228i	−0.466043	+	0.0898223i
$459$	18.8924	+	16.7080i	0.881823	+	0.779862i
$460$	−15.1263	+	2.43475i	−0.705265	+	0.113521i
$461$	−14.2393			−0.663192			−0.331596	−	0.943422i	$-0.607587\pi$
$461$	−14.2393			−0.663192			−0.331596	+	0.943422i	$0.607587\pi$
$462$	−3.38679	+	21.5392i	−0.157568	+	1.00210i
$463$	13.5694	+	8.72055i	0.630626	+	0.405278i	0.816541	−	0.577287i	$-0.195889\pi$
$463$	13.5694	+	8.72055i	0.630626	+	0.405278i	−0.185916	+	0.982566i	$0.559525\pi$
$464$	−2.82109	−	7.04674i	−0.130966	−	0.327137i
$465$	−17.4996	−	28.4174i	−0.811524	−	1.31783i
$466$	−12.2136	−	4.88960i	−0.565786	−	0.226506i
$467$	−2.47521	−	10.2030i	−0.114539	−	0.472137i	−0.999973	−	0.00737118i	$-0.997654\pi$
$467$	−2.47521	−	10.2030i	−0.114539	−	0.472137i	0.885434	−	0.464766i	$-0.153861\pi$
$468$	−9.00653	−	19.2548i	−0.416327	−	0.890052i
$469$	11.7734	+	4.63056i	0.543647	+	0.213819i
$470$	2.73301	+	9.30776i	0.126064	+	0.429335i
$471$	−21.9300	−	5.76906i	−1.01048	−	0.265824i
$472$	−10.3289	+	3.57487i	−0.475426	+	0.164547i
$473$	5.57726	+	1.35303i	0.256443	+	0.0622123i
$474$	−5.38985	+	6.58884i	−0.247564	+	0.302635i
$475$	12.6276	+	19.6490i	0.579395	+	0.901557i
$476$	0.533071	−	12.8306i	0.0244333	−	0.588092i
$477$	14.3821	−	0.131203i	0.658509	−	0.00600736i
$478$	−11.2120	+	1.07062i	−0.512827	+	0.0489690i
$479$	−3.35950	−	2.64194i	−0.153500	−	0.120713i	0.538456	−	0.842654i	$-0.319008\pi$
$479$	−3.35950	−	2.64194i	−0.153500	−	0.120713i	−0.691955	+	0.721941i	$0.743250\pi$
$480$	−5.07653	+	2.20135i	−0.231711	+	0.100478i
$481$	−70.6133	−	24.4395i	−3.21969	−	1.11435i
$482$	−10.9475			−0.498647
$483$	−11.9489	−	18.4452i	−0.543692	−	0.839285i
$484$	11.6385			0.529023
$485$	6.56772	+	2.27311i	0.298225	+	0.103217i
$486$	15.4320	−	2.20313i	0.700009	−	0.0999361i
$487$	−18.3777	−	14.4524i	−0.832774	−	0.654901i	0.107919	−	0.994160i	$-0.465581\pi$
$487$	−18.3777	−	14.4524i	−0.832774	−	0.654901i	−0.940693	+	0.339259i	$0.889824\pi$
$488$	−5.26439	+	0.502688i	−0.238308	+	0.0227556i
$489$	40.6988	−	3.09748i	1.84046	−	0.140073i
$490$	−4.49869	−	21.9053i	−0.203230	−	0.989581i
$491$	11.5208	+	17.9267i	0.519926	+	0.809021i	0.997580	−	0.0695274i	$-0.0221491\pi$
$491$	11.5208	+	17.9267i	0.519926	+	0.809021i	−0.477654	+	0.878548i	$0.658513\pi$
$492$	−3.38427	−	2.76842i	−0.152575	−	0.124810i
$493$	−35.8034	−	8.68581i	−1.61250	−	0.391189i
$494$	30.0432	−	10.3981i	1.35171	−	0.467831i
$495$	14.5207	−	43.2265i	0.652655	−	1.94289i
$496$	1.69924	+	5.78709i	0.0762982	+	0.259848i
$497$	−10.6993	+	1.60475i	−0.479928	+	0.0719827i
$498$	−13.1774	+	7.27361i	−0.590493	+	0.325938i
$499$	−8.47888	−	34.9504i	−0.379567	−	1.56460i	−0.766349	−	0.642424i	$-0.777929\pi$
$499$	−8.47888	−	34.9504i	−0.379567	−	1.56460i	0.386783	−	0.922171i	$-0.373586\pi$
$500$	0.610128	+	0.244258i	0.0272858	+	0.0109236i
$501$	6.80628	−	4.19134i	0.304082	−	0.187255i
$502$	−1.16416	−	2.90794i	−0.0519591	−	0.129788i
$503$	25.5604	+	16.4267i	1.13968	+	0.732430i	0.967559	−	0.252646i	$-0.0813007\pi$
$503$	25.5604	+	16.4267i	1.13968	+	0.732430i	0.172124	+	0.985075i	$0.444937\pi$
$504$	−5.82705	−	5.38939i	−0.259557	−	0.240063i
$505$	0.787745			0.0350542
$506$	−16.9917	+	15.2304i	−0.755375	+	0.677076i
$507$	53.5339	+	35.8778i	2.37752	+	1.59339i
$508$	6.70114	−	1.29154i	0.297315	−	0.0573027i
$509$	0.0476629	−	1.00057i	0.00211262	−	0.0443493i	−0.997565	−	0.0697449i	$-0.977781\pi$
$509$	0.0476629	−	1.00057i	0.00211262	−	0.0443493i	0.999677	+	0.0253955i	$0.00808452\pi$
$510$	−5.58909	+	26.2689i	−0.247489	+	1.16321i
$511$	14.3587	−	5.06753i	0.635193	−	0.224174i
$512$	0.989821	−	0.142315i	0.0437443	−	0.00628949i
$513$	0.873681	+	23.2975i	0.0385740	+	1.02861i
$514$	13.5998	−	0.647840i	0.599863	−	0.0285750i
$515$	−4.29682	+	44.9983i	−0.189340	+	1.98286i
$516$	−1.53946	+	1.41234i	−0.0677711	+	0.0621750i
$517$	10.9190	+	9.46138i	0.480218	+	0.416111i
$518$	−27.8609	+	1.49693i	−1.22414	+	0.0657712i
$519$	4.99648	+	22.4744i	0.219321	+	0.986517i
$520$	13.1303	−	18.4389i	0.575802	−	0.808601i
$521$	0.686318	+	14.4076i	0.0300681	+	0.631208i	0.962731	+	0.270460i	$0.0871756\pi$
$521$	0.686318	+	14.4076i	0.0300681	+	0.631208i	−0.932663	+	0.360748i	$0.882521\pi$
$522$	−18.4278	+	13.3774i	−0.806561	+	0.585511i
$523$	25.1647	+	31.9996i	1.10038	+	1.39924i	0.908530	+	0.417819i	$0.137205\pi$
$523$	25.1647	+	31.9996i	1.10038	+	1.39924i	0.191847	+	0.981425i	$0.438552\pi$
$524$	−6.55222	+	14.3474i	−0.286235	+	0.626768i
$525$	0.821383	+	23.8415i	0.0358481	+	1.04053i
$526$	14.7527	+	9.48100i	0.643249	+	0.413391i
$527$	27.6646	+	9.57482i	1.20509	+	0.417086i
$528$	−4.58802	+	6.84585i	−0.199668	+	0.297927i
$529$	2.50692	−	22.8630i	0.108996	−	0.994042i
$530$	7.65790	+	13.2639i	0.332638	+	0.576146i
$531$	17.9786	+	27.4220i	0.780204	+	1.19001i
$532$	8.92397	−	7.82812i	0.386903	−	0.339392i
$533$	17.7049	+	2.54558i	0.766884	+	0.110261i
$534$	1.00485	−	0.0285064i	0.0434841	−	0.00123359i
$535$	−4.66547	+	11.6538i	−0.201706	+	0.503837i
$536$	3.29978	+	3.46071i	0.142529	+	0.149480i
$537$	21.8840	+	13.2024i	0.944363	+	0.569728i
$538$	−14.2947	+	6.52818i	−0.616289	+	0.281450i
$539$	−23.2750	−	23.8235i	−1.00253	−	1.02615i
$540$	10.1288	+	13.1515i	0.435875	+	0.565950i
$541$	45.0603	+	8.68465i	1.93729	+	0.373382i	0.999669	+	0.0257275i	$0.00819023\pi$
$541$	45.0603	+	8.68465i	1.93729	+	0.373382i	0.937623	+	0.347655i	$0.113022\pi$
$542$	3.59106	−	14.8025i	0.154249	−	0.635824i
$543$	−14.1648	−	2.31554i	−0.607870	−	0.0993694i
$544$	2.22410	−	4.31415i	0.0953575	−	0.184968i
$545$	19.6209	+	5.76122i	0.840468	+	0.246784i
$546$	31.8003	+	6.56423i	1.36093	+	0.280923i
$547$	4.43973	−	9.72166i	0.189829	−	0.415668i	−0.790656	−	0.612261i	$-0.790260\pi$
$547$	4.43973	−	9.72166i	0.189829	−	0.415668i	0.980485	+	0.196593i	$0.0629876\pi$
$548$	−1.62184	−	4.05116i	−0.0692816	−	0.173057i
$549$	5.32548	+	14.9445i	0.227286	+	0.637815i
$550$	24.3212	−	4.68752i	1.03706	−	0.199877i
$551$	−17.0283	−	29.4938i	−0.725428	−	1.25648i
$552$	−1.16204	−	8.22494i	−0.0494599	−	0.350077i
$553$	−3.14234	−	12.6177i	−0.133626	−	0.536560i
$554$	−0.567861	+	0.492054i	−0.0241261	+	0.0209054i
$555$	57.9702	+	6.66313i	2.46070	+	0.282834i
$556$	4.47426	−	5.68948i	0.189751	−	0.241288i
$557$	−2.71705	+	1.93481i	−0.115125	+	0.0819803i	−0.636169	−	0.771549i	$-0.719482\pi$
$557$	−2.71705	+	1.93481i	−0.115125	+	0.0819803i	0.521044	+	0.853530i	$0.325543\pi$
$558$	15.5869	−	9.18967i	0.659845	−	0.389030i
$559$	2.40788	−	8.20047i	0.101842	−	0.346843i
$560$	1.94273	−	8.22592i	0.0820955	−	0.347609i
$561$	14.1493	+	37.4137i	0.597385	+	1.57961i
$562$	−7.96280	−	7.59252i	−0.335891	−	0.320271i
$563$	4.32854	+	12.5065i	0.182426	+	0.527086i	0.998722	−	0.0505490i	$-0.0160971\pi$
$563$	4.32854	+	12.5065i	0.182426	+	0.527086i	−0.816296	+	0.577635i	$0.803976\pi$
$564$	−5.07400	+	1.38441i	−0.213654	+	0.0582942i
$565$	33.8814	−	35.5337i	1.42540	−	1.49492i
$566$	−4.75234	−	10.4062i	−0.199756	−	0.437404i
$567$	−11.4009	+	20.9050i	−0.478791	+	0.877929i
$568$	−3.92354	−	1.15205i	−0.164628	−	0.0483391i
$569$	19.0870	+	24.2711i	0.800167	+	1.01750i	0.999296	+	0.0375222i	$0.0119465\pi$
$569$	19.0870	+	24.2711i	0.800167	+	1.01750i	−0.199128	+	0.979973i	$0.563811\pi$
$570$	−21.1397	+	13.0179i	−0.885444	+	0.545261i
$571$	−5.10971	−	4.01832i	−0.213835	−	0.168161i	0.505497	−	0.862829i	$-0.331309\pi$
$571$	−5.10971	−	4.01832i	−0.213835	−	0.168161i	−0.719331	+	0.694667i	$0.755552\pi$
$572$	1.60416	−	33.6755i	0.0670734	−	1.40804i
$573$	3.65546	+	4.83697i	0.152709	+	0.202067i
$574$	6.48092	−	1.61402i	0.270508	−	0.0673679i
$575$	−15.1011	+	19.8808i	−0.629759	+	0.829087i
$576$	−1.14035	−	2.77482i	−0.0475145	−	0.115617i
$577$	5.15104	+	26.7261i	0.214441	+	1.11262i	0.916356	+	0.400364i	$0.131116\pi$
$577$	5.15104	+	26.7261i	0.214441	+	1.11262i	−0.701916	+	0.712260i	$0.747672\pi$
$578$	−3.00529	−	5.82946i	−0.125004	−	0.242473i
$579$	−4.37088	−	13.4613i	−0.181648	−	0.559432i
$580$	−22.0575	−	10.0733i	−0.915887	−	0.418272i
$581$	3.13369	−	22.7770i	0.130007	−	0.944951i
$582$	−1.30069	+	3.53648i	−0.0539155	+	0.146592i
$583$	20.2751	+	10.4525i	0.839709	+	0.432900i
$584$	5.72910	+	0.547063i	0.237072	+	0.0226376i
$585$	−63.2719	−	24.6630i	−2.61597	−	1.01969i
$586$	4.85835	−	25.2075i	0.200697	−	1.04131i
$587$	−8.58249	+	9.90472i	−0.354237	+	0.408812i	−0.904701	−	0.426048i	$-0.859906\pi$
$587$	−8.58249	+	9.90472i	−0.354237	+	0.408812i	0.550463	+	0.834859i	$0.314451\pi$
$588$	11.9212	−	2.21015i	0.491622	−	0.0911450i
$589$	11.2417	+	24.6159i	0.463207	+	1.01428i
$590$	−16.0002	+	31.0360i	−0.658716	+	1.27773i
$591$	−2.28666	+	1.90563i	−0.0940604	+	0.0783871i
$592$	−9.79021	−	3.91941i	−0.402375	−	0.161087i
$593$	47.6248	−	4.54762i	1.95572	−	0.186748i	0.960056	−	0.279806i	$-0.0902703\pi$
$593$	47.6248	−	4.54762i	1.95572	−	0.186748i	0.995661	+	0.0930581i	$0.0296642\pi$
$594$	23.2805	+	8.32212i	0.955211	+	0.341461i
$595$	−27.0534	−	30.8405i	−1.10908	−	1.26434i
$596$	2.21483	−	1.91916i	0.0907228	−	0.0786117i
$597$	−0.798345	−	1.62457i	−0.0326741	−	0.0664891i
$598$	21.4517	+	26.3550i	0.877227	+	1.07774i
$599$	−40.0343	−	23.1138i	−1.63576	−	0.944404i	−0.982272	−	0.187464i	$-0.939973\pi$
$599$	−40.0343	−	23.1138i	−1.63576	−	0.944404i	−0.653484	−	0.756940i	$-0.726693\pi$
$600$	−3.51153	+	8.30468i	−0.143358	+	0.339037i
$601$	12.6140	−	19.6277i	0.514535	−	0.800632i	−0.482635	−	0.875822i	$-0.660320\pi$
$601$	12.6140	−	19.6277i	0.514535	−	0.800632i	0.997169	+	0.0751902i	$0.0239564\pi$
$602$	−0.322650	−	3.17492i	−0.0131502	−	0.129400i
$603$	7.64521	−	12.1382i	0.311337	−	0.494307i
$604$	−2.17578	+	1.71105i	−0.0885314	+	0.0696218i
$605$	26.9090	−	25.6577i	1.09401	−	1.04313i
$606$	−0.00821626	+	0.427016i	−0.000333763	+	0.0173463i
$607$	3.91856	+	2.79039i	0.159049	+	0.113259i	0.656811	−	0.754056i	$-0.271905\pi$
$607$	3.91856	+	2.79039i	0.159049	+	0.113259i	−0.497761	+	0.867314i	$0.665844\pi$
$608$	4.30501	−	1.26406i	0.174591	−	0.0512646i
$609$	0.457799	−	34.7809i	0.0185510	−	1.40939i
$610$	−11.0634	+	12.7679i	−0.447945	+	0.516956i
$611$	14.8478	−	15.5720i	0.600679	−	0.629974i
$612$	−14.1814	−	3.30369i	−0.573250	−	0.133544i
$613$	0.863203	+	18.1209i	0.0348644	+	0.731895i	0.946851	+	0.321674i	$0.104245\pi$
$613$	0.863203	+	18.1209i	0.0348644	+	0.731895i	−0.911986	+	0.410221i	$0.865452\pi$
$614$	4.98253	+	20.5383i	0.201079	+	0.828858i
$615$	−13.9278	+	1.06001i	−0.561623	+	0.0427437i
$616$	−4.18950	−	11.8709i	−0.168800	−	0.478291i
$617$	−38.5306	−	5.53986i	−1.55118	−	0.223026i	−0.687169	−	0.726497i	$-0.741147\pi$
$617$	−38.5306	−	5.53986i	−1.55118	−	0.223026i	−0.864012	+	0.503471i	$0.832056\pi$
$618$	−24.3476	−	2.79853i	−0.979403	−	0.112573i
$619$	3.04437	+	15.7957i	0.122363	+	0.634882i	0.990383	+	0.138352i	$0.0441806\pi$
$619$	3.04437	+	15.7957i	0.122363	+	0.634882i	−0.868020	+	0.496530i	$0.834607\pi$
$620$	16.6867	+	9.63408i	0.670155	+	0.386914i
$621$	−23.0725	+	9.41604i	−0.925866	+	0.377853i
$622$		−	9.97540i		−	0.399977i
$623$	−0.883090	+	1.25621i	−0.0353803	+	0.0503291i
$624$	9.85831	+	7.30991i	0.394648	+	0.292631i
$625$	−22.2150	+	8.89354i	−0.888599	+	0.355742i
$626$	−6.87377	−	9.65287i	−0.274731	−	0.385806i
$627$	−16.0045	+	33.3326i	−0.639157	+	1.33117i
$628$	12.7230	−	3.08658i	0.507705	−	0.123168i
$629$	−43.0599	+	27.6729i	−1.71691	+	1.10339i
$630$	−25.3537	+	0.385394i	−1.01012	+	0.0153545i
$631$	11.2869	−	3.31412i	0.449323	−	0.131933i	−0.0492394	−	0.998787i	$-0.515680\pi$
$631$	11.2869	−	3.31412i	0.449323	−	0.131933i	0.498562	+	0.866854i	$0.333862\pi$
$632$	0.930116	−	4.82590i	0.0369980	−	0.191964i
$633$	0.376304	−	0.102672i	0.0149567	−	0.00408086i
$634$	−1.63349	+	6.73335i	−0.0648743	+	0.267416i
$635$	12.6462	−	17.7591i	0.501850	−	0.704750i
$636$	−7.26987	+	4.01280i	−0.288269	+	0.159118i
$637$	−37.0875	+	32.9342i	−1.46946	+	1.30490i
$638$	−35.7478	+	5.13975i	−1.41527	+	0.203485i
$639$	−0.471907	+	12.2585i	−0.0186684	+	0.484937i
$640$	1.97480	−	2.51116i	0.0780606	−	0.0992622i
$641$	20.5312	+	39.8249i	0.810933	+	1.57299i	0.819537	+	0.573027i	$0.194231\pi$
$641$	20.5312	+	39.8249i	0.810933	+	1.57299i	−0.00860404	+	0.999963i	$0.502739\pi$
$642$	−6.26854	−	2.65058i	−0.247400	−	0.104610i
$643$		−	16.6358i		−	0.656050i	−0.944669	−	0.328025i	$-0.893617\pi$
$643$		−	16.6358i		−	0.656050i	0.944669	−	0.328025i	$-0.106383\pi$
$644$	11.1308	+	6.09134i	0.438617	+	0.240032i
$645$	−0.445760	+	6.65927i	−0.0175518	+	0.262208i
$646$	7.12269	−	20.5797i	0.280239	−	0.809696i
$647$	−8.25176	+	4.25408i	−0.324410	+	0.167245i	−0.612737	−	0.790287i	$-0.709931\pi$
$647$	−8.25176	+	4.25408i	−0.324410	+	0.167245i	0.288327	+	0.957532i	$0.406901\pi$
$648$	−7.23472	+	5.35339i	−0.284207	+	0.210301i
$649$	4.94340	+	51.7696i	0.194045	+	2.03214i
$650$	−5.24945	−	36.5107i	−0.205900	−	1.43207i
$651$	−2.98918	+	27.4772i	−0.117155	+	1.07692i
$652$	−19.8245	+	12.7404i	−0.776387	+	0.498954i
$653$	−12.6685	−	9.02120i	−0.495757	−	0.353027i	0.304669	−	0.952458i	$-0.401454\pi$
$653$	−12.6685	−	9.02120i	−0.495757	−	0.353027i	−0.800426	+	0.599431i	$0.795393\pi$
$654$	−3.32766	+	10.5759i	−0.130122	+	0.413550i
$655$	16.4803	+	47.6168i	0.643940	+	1.86054i
$656$	2.47876	+	0.477742i	0.0967793	+	0.0186527i
$657$	−2.61293	−	17.0666i	−0.101940	−	0.665833i
$658$	2.94055	−	7.47650i	0.114634	−	0.291464i
$659$	−14.3250	−	22.2901i	−0.558023	−	0.868300i	0.441559	−	0.897232i	$-0.354426\pi$
$659$	−14.3250	−	22.2901i	−0.558023	−	0.868300i	−0.999581	+	0.0289320i	$0.990789\pi$
$660$	4.48423	+	25.9426i	0.174549	+	1.00981i
$661$	3.38488	−	8.45502i	0.131657	−	0.328862i	−0.847862	−	0.530217i	$-0.822110\pi$
$661$	3.38488	−	8.45502i	0.131657	−	0.328862i	0.979518	+	0.201355i	$0.0645345\pi$
$662$	13.7357	−	9.78116i	0.533854	−	0.380156i
$663$	56.6567	−	18.3964i	2.20037	−	0.714458i
$664$	4.69817	−	7.31050i	0.182325	−	0.283702i
$665$	3.37533	−	37.7725i	0.130890	−	1.46476i
$666$	−4.21654	+	31.3546i	−0.163388	+	1.21497i
$667$	23.3733	−	27.9077i	0.905017	−	1.08059i
$668$	−2.30747	+	3.99665i	−0.0892786	+	0.154635i
$669$	−16.0128	+	1.98868i	−0.619089	+	0.0768869i
$670$	15.2587	+	0.726859i	0.589493	+	0.0280810i
$671$	−3.58091	+	24.9058i	−0.138239	+	0.961476i
$672$	4.43880	+	1.13890i	0.171230	+	0.0439341i
$673$	0.689946	+	4.79868i	0.0265955	+	0.184976i	0.998789	−	0.0492044i	$-0.0156686\pi$
$673$	0.689946	+	4.79868i	0.0265955	+	0.184976i	−0.972193	+	0.234180i	$0.924759\pi$
$674$	5.98948	−	1.45303i	0.230706	−	0.0559687i
$675$	26.7341	+	4.12023i	1.02900	+	0.158588i
$676$	−37.0386	−	3.53676i	−1.42456	−	0.136029i
$677$	12.9701	+	12.3669i	0.498480	+	0.475300i	0.897107	−	0.441814i	$-0.145665\pi$
$677$	12.9701	+	12.3669i	0.498480	+	0.475300i	−0.398627	+	0.917113i	$0.630513\pi$
$678$	18.9085	+	18.7368i	0.726178	+	0.719583i
$679$	−3.14122	−	4.82313i	−0.120549	−	0.185095i
$680$	−4.36851	−	14.8778i	−0.167525	−	0.570536i
$681$	0.306017	+	0.250330i	0.0117266	+	0.00959267i
$682$	28.6649	−	1.36548i	1.09763	−	0.0522868i
$683$	19.0380	+	19.9665i	0.728469	+	0.763996i	0.978944	−	0.204127i	$-0.0654355\pi$
$683$	19.0380	+	19.9665i	0.728469	+	0.763996i	−0.250476	+	0.968123i	$0.580587\pi$
$684$	−6.83618	−	11.5950i	−0.261388	−	0.443348i
$685$	−12.6808	−	5.79114i	−0.484509	−	0.221268i
$686$	−8.18497	+	16.6134i	−0.312503	+	0.634304i
$687$	−14.1318	−	10.4787i	−0.539163	−	0.399788i
$688$	0.394505	−	1.13985i	0.0150404	−	0.0434563i
$689$	16.9852	−	29.4192i	0.647084	−	1.12078i
$690$	−20.8191	−	16.4548i	−0.792568	−	0.626425i
$691$	3.75536	−	2.16816i	0.142861	−	0.0824806i	−0.426866	−	0.904315i	$-0.640382\pi$
$691$	3.75536	−	2.16816i	0.142861	−	0.0824806i	0.569727	+	0.821834i	$0.307049\pi$
$692$	−8.70467	−	10.0457i	−0.330902	−	0.381881i
$693$	−31.4563	+	20.8980i	−1.19493	+	0.793851i
$694$	0.496363	−	3.45228i	0.0188417	−	0.131047i
$695$	−2.19797	−	23.0182i	−0.0833739	−	0.873131i
$696$	5.69054	−	11.8517i	0.215699	−	0.449238i
$697$	8.86763	−	8.45526i	0.335885	−	0.320266i
$698$	−27.0323	−	13.9361i	−1.02319	−	0.527491i
$699$	−8.06051	−	21.3136i	−0.304876	−	0.806156i
$700$	−6.95888	−	11.8857i	−0.263021	−	0.449239i
$701$	−23.1405	−	20.0514i	−0.874006	−	0.757330i	0.0972772	−	0.995257i	$-0.468987\pi$
$701$	−23.1405	−	20.0514i	−0.874006	−	0.757330i	−0.971283	+	0.237927i	$0.923532\pi$
$702$	14.0291	−	34.0408i	0.529493	−	1.28479i
$703$	−45.9818	−	11.1551i	−1.73424	−	0.420721i
$704$	0.452276	−	4.73645i	0.0170458	−	0.178512i
$705$	−8.67943	+	14.3868i	−0.326886	+	0.541837i
$706$	−6.26811	+	21.3472i	−0.235903	+	0.803413i
$707$	−0.515261	−	0.400162i	−0.0193784	−	0.0150496i
$708$	−16.6569	−	8.99697i	−0.626005	−	0.338127i
$709$	−0.886430	+	0.354873i	−0.0332906	+	0.0133275i	−0.388248	−	0.921555i	$-0.626920\pi$
$709$	−0.886430	+	0.354873i	−0.0332906	+	0.0133275i	0.354957	+	0.934882i	$0.384495\pi$
$710$	−11.6113	+	5.98602i	−0.435763	+	0.224651i
$711$	−14.7204	+	0.835874i	−0.552059	+	0.0313477i
$712$	−0.502627	+	0.290192i	−0.0188368	+	0.0108754i
$713$	−20.5963	+	20.3097i	−0.771337	+	0.760603i
$714$	17.0000	−	14.3432i	0.636210	−	0.536783i
$715$	−70.5305	−	81.3966i	−2.63769	−	3.04406i
$716$	−14.7392	−	0.702115i	−0.550830	−	0.0262393i
$717$	−14.4948	−	13.0564i	−0.541318	−	0.487600i
$718$	20.6660	+	29.0213i	0.771248	+	1.08307i
$719$	21.7744	−	17.1236i	0.812047	−	0.638601i	−0.123285	−	0.992371i	$-0.539343\pi$
$719$	21.7744	−	17.1236i	0.812047	−	0.638601i	0.935332	+	0.353770i	$0.115101\pi$
$720$	−8.75379	−	3.90161i	−0.326235	−	0.145404i
$721$	25.6690	−	27.2505i	0.955962	−	1.01486i
$722$	1.02874	−	0.469809i	0.0382857	−	0.0174845i
$723$	−12.8186	−	13.9724i	−0.476731	−	0.519639i
$724$	7.83084	−	2.71028i	0.291031	−	0.100727i
$725$	−37.3406	+	12.9237i	−1.38680	+	0.479974i
$726$	13.6277	+	14.8543i	0.505772	+	0.551295i
$727$	8.36087	−	3.81828i	0.310088	−	0.141612i	−0.254292	−	0.967127i	$-0.581843\pi$
$727$	8.36087	−	3.81828i	0.310088	−	0.141612i	0.564380	+	0.825515i	$0.309115\pi$
$728$	−17.9552	+	5.39085i	−0.665463	+	0.199798i
$729$	20.8814	+	17.1163i	0.773386	+	0.633935i
$730$	14.4521	−	11.3653i	0.534897	−	0.420647i
$731$	−3.39594	−	4.76892i	−0.125603	−	0.176385i
$732$	−6.80574	−	6.13037i	−0.251547	−	0.226585i
$733$	33.8757	+	1.61370i	1.25123	+	0.0596033i	0.662706	−	0.748879i	$-0.269408\pi$
$733$	33.8757	+	1.61370i	1.25123	+	0.0596033i	0.588520	+	0.808483i	$0.299711\pi$
$734$	−5.69173	−	6.56861i	−0.210086	−	0.242452i
$735$	22.6903	−	31.3910i	0.836943	−	1.15787i
$736$	2.84706	+	3.85930i	0.104944	+	0.142256i
$737$	19.7034	−	11.3758i	0.725784	−	0.419032i
$738$	−0.429335	−	7.56095i	−0.0158040	−	0.278322i
$739$	43.4126	−	22.3808i	1.59696	−	0.823290i	0.597184	−	0.802104i	$-0.296286\pi$
$739$	43.4126	−	22.3808i	1.59696	−	0.823290i	0.999776	−	0.0211854i	$-0.00674402\pi$
$740$	−31.2762	+	12.5211i	−1.14974	+	0.460285i
$741$	48.4492	+	26.1691i	1.77983	+	0.961346i
$742$	1.72883	−	12.5659i	0.0634675	−	0.461310i
$743$	−0.983544	+	3.34964i	−0.0360827	+	0.122886i	−0.975565	−	0.219711i	$-0.929489\pi$
$743$	−0.983544	+	3.34964i	−0.0360827	+	0.122886i	0.939482	+	0.342598i	$0.111307\pi$
$744$	−5.39643	+	8.94495i	−0.197843	+	0.327938i
$745$	0.889945	−	9.31992i	0.0326051	−	0.341456i
$746$	28.7333	+	6.97061i	1.05200	+	0.255212i
$747$	−24.7130	−	8.30158i	−0.904200	−	0.303739i
$748$	−17.4532	−	15.1233i	−0.638154	−	0.552963i
$749$	8.97160	−	5.25271i	0.327815	−	0.191930i
$750$	0.402660	+	1.06472i	0.0147031	+	0.0388779i
$751$	−12.6676	−	6.53060i	−0.462247	−	0.238305i	0.211340	−	0.977413i	$-0.432217\pi$
$751$	−12.6676	−	6.53060i	−0.462247	−	0.238305i	−0.673587	+	0.739108i	$0.735247\pi$
$752$	2.19766	−	2.09547i	0.0801405	−	0.0764138i
$753$	2.34828	−	4.89078i	0.0855762	−	0.178230i
$754$	5.11247	+	53.5402i	0.186185	+	1.94982i
$755$	−1.25845	+	8.75271i	−0.0457997	+	0.318544i
$756$	0.0555300	−	13.7476i	0.00201961	−	0.499996i
$757$	4.38931	+	5.06553i	0.159532	+	0.184110i	0.829888	−	0.557930i	$-0.188404\pi$
$757$	4.38931	+	5.06553i	0.159532	+	0.184110i	−0.670356	+	0.742039i	$0.733859\pi$
$758$	2.92874	−	1.69091i	0.106377	−	0.0614165i
$759$	−39.3346	−	3.85309i	−1.42776	−	0.139858i
$760$	7.16678	−	12.4132i	0.259966	−	0.450275i
$761$	13.6904	−	39.5557i	0.496275	−	1.43389i	−0.367504	−	0.930022i	$-0.619788\pi$
$761$	13.6904	−	39.5557i	0.496275	−	1.43389i	0.863779	−	0.503871i	$-0.168091\pi$
$762$	9.49486	+	7.04042i	0.343963	+	0.255047i
$763$	−9.90736	−	13.7355i	−0.358671	−	0.497259i
$764$	−3.18409	−	1.45412i	−0.115196	−	0.0526083i
$765$	−40.0716	+	23.6253i	−1.44879	+	0.854175i
$766$	−20.0695	−	21.0483i	−0.725142	−	0.760507i
$767$	77.3593	−	3.68508i	2.79328	−	0.133060i
$768$	1.34063	+	1.09668i	0.0483760	+	0.0395729i
$769$	−14.1599	−	48.2241i	−0.510618	−	1.73901i	−0.661008	−	0.750379i	$-0.729871\pi$
$769$	−14.1599	−	48.2241i	−0.510618	−	1.73901i	0.150390	−	0.988627i	$-0.451947\pi$
$770$	−35.8564	−	18.2103i	−1.29217	−	0.656254i
$771$	16.7511	+	16.5990i	0.603276	+	0.597798i
$772$	5.91385	+	5.63885i	0.212844	+	0.202947i
$773$	24.8079	+	2.36886i	0.892277	+	0.0852021i	0.531114	−	0.847301i	$-0.321774\pi$
$773$	24.8079	+	2.36886i	0.892277	+	0.0852021i	0.361163	+	0.932503i	$0.382380\pi$
$774$	−3.60516	−	0.311092i	−0.129585	−	0.0111820i
$775$	30.5127	−	7.40231i	1.09605	−	0.265899i
$776$	−0.309607	−	2.15336i	−0.0111142	−	0.0773012i
$777$	−34.5333	−	33.8062i	−1.23887	−	1.21279i
$778$	3.48037	−	24.2065i	0.124777	−	0.867844i
$779$	11.3134	+	0.538925i	0.405345	+	0.0193090i
$780$	38.9082	−	4.83215i	1.39314	−	0.173019i
$781$	−9.72814	+	16.8496i	−0.348100	+	0.602927i
$782$	23.2743	−	0.390886i	0.832288	−	0.0139781i
$783$	−38.6510	−	7.85570i	−1.38127	−	0.280740i
$784$	−5.44937	+	4.39367i	−0.194620	+	0.156917i
$785$	22.6120	−	35.1850i	0.807058	−	1.25581i
$786$	−25.9837	+	8.43691i	−0.926809	+	0.300935i
$787$	28.2873	−	20.1433i	1.00833	−	0.718032i	0.0485649	−	0.998820i	$-0.484535\pi$
$787$	28.2873	−	20.1433i	1.00833	−	0.718032i	0.959770	+	0.280788i	$0.0905958\pi$
$788$	0.638720	−	1.59544i	0.0227534	−	0.0568354i
$789$	5.17354	+	29.9304i	0.184183	+	1.06555i
$790$	−8.48846	−	13.2083i	−0.302006	−	0.469930i
$791$	−40.2122	+	6.03130i	−1.42978	+	0.214448i
$792$	−14.1096	+	2.16020i	−0.501362	+	0.0767594i
$793$	36.7944	+	7.09153i	1.30661	+	0.251828i
$794$	8.95944	+	25.8866i	0.317959	+	0.918682i
$795$	−7.96200	+	25.3047i	−0.282383	+	0.897465i
$796$	0.851297	+	0.606206i	0.0301734	+	0.0214864i
$797$	−38.1634	+	24.5261i	−1.35182	+	0.868760i	−0.997788	−	0.0664738i	$-0.978825\pi$
$797$	−38.1634	+	24.5261i	−1.35182	+	0.868760i	−0.354029	+	0.935234i	$0.615189\pi$
$798$	20.4403	+	2.22365i	0.723578	+	0.0787163i
$799$	−2.09752	−	14.5886i	−0.0742049	−	0.516107i
$800$	−0.494835	−	5.18215i	−0.0174951	−	0.183217i
$801$	1.21298	+	1.24912i	0.0428585	+	0.0441354i
$802$	−9.77874	+	5.04129i	−0.345299	+	0.178014i
$803$	8.95611	−	25.8770i	0.316054	−	0.913179i
$804$	−0.553161	+	8.26374i	−0.0195085	+	0.291440i
$805$	39.1640	−	10.4549i	1.38035	−	0.368488i
$806$		−	42.7367i		−	1.50534i
$807$	−25.0699	−	10.6005i	−0.882501	−	0.373155i
$808$	−0.112991	−	0.219172i	−0.00397501	−	0.00771045i
$809$	24.8818	−	31.6397i	0.874796	−	1.11239i	−0.118052	−	0.993007i	$-0.537665\pi$
$809$	24.8818	−	31.6397i	0.874796	−	1.11239i	0.992848	−	0.119386i	$-0.0380926\pi$
$810$	−4.92534	+	28.3267i	−0.173059	+	0.995300i
$811$	−8.16688	+	1.17422i	−0.286778	+	0.0412324i	−0.284203	−	0.958764i	$-0.591729\pi$
$811$	−8.16688	+	1.17422i	−0.286778	+	0.0412324i	−0.00257523	+	0.999997i	$0.500820\pi$
$812$	9.31063	+	17.7938i	0.326739	+	0.624439i
$813$	23.0974	−	12.7492i	0.810061	−	0.447135i
$814$	−29.1049	+	40.8722i	−1.02013	+	1.43257i
$815$	−17.7486	+	73.1609i	−0.621708	+	2.56272i
$816$	8.11041	−	2.21288i	0.283921	−	0.0774662i
$817$	1.02420	−	5.31406i	0.0358323	−	0.185916i
$818$	−19.2193	+	5.64331i	−0.671988	+	0.197314i
$819$	28.8575	+	48.2731i	1.00836	+	1.68680i
$820$	6.78427	−	4.35998i	0.236917	−	0.152257i
$821$	3.64824	−	0.885054i	0.127325	−	0.0308886i	−0.171590	−	0.985168i	$-0.554891\pi$
$821$	3.64824	−	0.885054i	0.127325	−	0.0308886i	0.298915	+	0.954280i	$0.403375\pi$
$822$	3.27148	−	6.81354i	0.114106	−	0.237649i
$823$	−2.08178	−	2.92345i	−0.0725664	−	0.101905i	0.776698	−	0.629874i	$-0.216893\pi$
$823$	−2.08178	−	2.92345i	−0.0725664	−	0.101905i	−0.849264	+	0.527968i	$0.822954\pi$
$824$	13.1361	−	5.25889i	0.457617	−	0.183202i
$825$	34.4608	+	25.5526i	1.19977	+	0.889627i
$826$	26.2314	−	12.1727i	0.912708	−	0.423542i
$827$			37.3581i			1.29907i	0.760332	+	0.649534i	$0.225036\pi$
$827$			37.3581i			1.29907i	−0.760332	+	0.649534i	$0.774964\pi$
$828$	9.13688	−	11.1138i	0.317529	−	0.386233i
$829$	−23.5725	−	13.6096i	−0.818707	−	0.472681i	0.0312632	−	0.999511i	$-0.490047\pi$
$829$	−23.5725	−	13.6096i	−0.818707	−	0.472681i	−0.849970	+	0.526830i	$0.823380\pi$
$830$	−5.25389	−	27.2598i	−0.182365	−	0.946200i
$831$	−1.29293	−	0.148610i	−0.0448512	−	0.00515523i
$832$	−7.01357	−	1.00840i	−0.243152	−	0.0349600i
$833$	2.02900	+	33.9154i	0.0703006	+	1.17510i
$834$	12.5005	−	0.951382i	0.432857	−	0.0329437i
$835$	3.47581	+	14.3275i	0.120285	+	0.495823i
$836$	−1.01578	−	21.3238i	−0.0351313	−	0.737498i
$837$	29.9797	+	9.13327i	1.03625	+	0.315692i
$838$	−18.6049	+	19.5122i	−0.642695	+	0.674039i
$839$	−5.84129	+	6.74121i	−0.201664	+	0.232732i	−0.847569	−	0.530685i	$-0.821935\pi$
$839$	−5.84129	+	6.74121i	−0.201664	+	0.232732i	0.645905	+	0.763418i	$0.276480\pi$
$840$	12.7736	−	7.15234i	0.440730	−	0.246779i
$841$	27.4560	−	8.06181i	0.946759	−	0.277994i
$842$	23.2644	+	16.5665i	0.801742	+	0.570918i
$843$	0.366604	−	19.0532i	0.0126265	−	0.656226i
$844$	−0.162986	+	0.155406i	−0.00561019	+	0.00534931i
$845$	−93.4327	+	73.4763i	−3.21418	+	2.52766i
$846$	−7.70816	−	4.85495i	−0.265012	−	0.166917i
$847$	−30.6348	+	3.11325i	−1.05263	+	0.106973i
$848$	2.59195	−	4.03315i	0.0890079	−	0.138499i
$849$	7.71687	−	18.2502i	0.264842	−	0.626345i
$850$	−21.8819	−	12.6335i	−0.750544	−	0.433327i
$851$	−5.65221	−	50.2582i	−0.193755	−	1.72283i
$852$	−3.12376	−	6.35659i	−0.107018	−	0.217773i
$853$	−17.3893	+	15.0680i	−0.595400	+	0.515917i	−0.899614	−	0.436687i	$-0.856152\pi$
$853$	−17.3893	+	15.0680i	−0.595400	+	0.515917i	0.304214	+	0.952604i	$0.401606\pi$
$854$	13.7224	−	2.73137i	0.469572	−	0.0934657i
$855$	−41.3676	−	11.7378i	−1.41474	−	0.401425i
$856$	3.91159	−	0.373512i	0.133695	−	0.0127664i
$857$	−25.2148	−	10.0945i	−0.861321	−	0.344821i	−0.101407	−	0.994845i	$-0.532335\pi$
$857$	−25.2148	−	10.0945i	−0.861321	−	0.344821i	−0.759914	+	0.650024i	$0.774759\pi$
$858$	44.8586	−	37.3838i	1.53145	−	1.27626i
$859$	10.6054	−	20.5717i	0.361853	−	0.701896i	−0.635691	−	0.771944i	$-0.719285\pi$
$859$	10.6054	−	20.5717i	0.361853	−	0.701896i	0.997544	+	0.0700473i	$0.0223150\pi$
$860$	−1.60073	−	3.50512i	−0.0545845	−	0.119523i
$861$	9.64859	+	6.38175i	0.328823	+	0.217490i
$862$	−10.7828	+	12.4440i	−0.367263	+	0.423844i
$863$	−4.75290	+	24.6604i	−0.161791	+	0.839449i	0.806807	+	0.590815i	$0.201194\pi$
$863$	−4.75290	+	24.6604i	−0.161791	+	0.839449i	−0.968597	+	0.248634i	$0.920018\pi$
$864$	2.20626	−	4.70451i	0.0750586	−	0.160051i
$865$	−42.2721	−	4.03650i	−1.43730	−	0.137245i
$866$	21.8704	+	11.2750i	0.743187	+	0.383139i
$867$	3.92122	−	10.6615i	0.133172	−	0.362083i
$868$	−6.02076	−	14.7782i	−0.204358	−	0.501605i
$869$	−21.2710	−	9.71414i	−0.721570	−	0.329530i
$870$	−12.9708	−	39.9471i	−0.439752	−	1.35433i
$871$	−15.5256	−	30.1155i	−0.526066	−	1.02043i
$872$	−1.21142	−	6.28544i	−0.0410238	−	0.212852i
$873$	−6.03663	+	2.48083i	−0.204309	+	0.0839635i
$874$	15.1083	+	15.3216i	0.511047	+	0.518259i
$875$	−1.67131	−	0.479729i	−0.0565007	−	0.0162178i
$876$	6.01008	+	7.95265i	0.203062	+	0.268695i
$877$	0.681501	−	14.3065i	0.0230127	−	0.483095i	−0.957715	−	0.287717i	$-0.907104\pi$
$877$	0.681501	−	14.3065i	0.0230127	−	0.483095i	0.980728	−	0.195378i	$-0.0625933\pi$
$878$	−5.98101	−	4.70352i	−0.201849	−	0.158736i
$879$	37.8612	−	23.3151i	1.27703	−	0.786400i
$880$	−9.39606	−	11.9481i	−0.316741	−	0.402769i
$881$	1.10625	+	0.324823i	0.0372704	+	0.0109436i	0.300315	−	0.953840i	$-0.402908\pi$
$881$	1.10625	+	0.324823i	0.0372704	+	0.0109436i	−0.263044	+	0.964784i	$0.584727\pi$
$882$	16.7796	+	12.6272i	0.564997	+	0.425180i
$883$	−11.0313	−	24.1552i	−0.371233	−	0.812888i	−0.999394	−	0.0348041i	$-0.988919\pi$
$883$	−11.0313	−	24.1552i	−0.371233	−	0.812888i	0.628161	−	0.778084i	$-0.283808\pi$
$884$	−23.7331	+	24.8906i	−0.798232	+	0.837162i
$885$	−58.3462	+	15.9194i	−1.96129	+	0.535125i
$886$	11.0804	+	32.0147i	0.372254	+	1.07556i
$887$	−8.02621	−	7.65298i	−0.269494	−	0.256962i	0.543266	−	0.839561i	$-0.317187\pi$
$887$	−8.02621	−	7.65298i	−0.269494	−	0.256962i	−0.812760	+	0.582599i	$0.802036\pi$
$888$	−6.46115	−	17.0846i	−0.216822	−	0.573322i
$889$	−17.2932	+	5.19210i	−0.579996	+	0.174138i
$890$	−0.522365	+	1.77901i	−0.0175097	+	0.0596327i
$891$	16.6379	+	39.4576i	0.557392	+	1.32188i
$892$	7.58859	−	5.40381i	0.254085	−	0.180933i
$893$	8.42197	−	10.7094i	0.281831	−	0.358377i
$894$	5.04280	+	0.579624i	0.168657	+	0.0193855i
$895$	−35.6259	+	30.8701i	−1.19084	+	1.03187i
$896$	−2.56733	+	0.639373i	−0.0857686	+	0.0213600i
$897$	−8.51885	+	58.2384i	−0.284436	+	1.94453i
$898$	−9.48122	−	16.4219i	−0.316392	−	0.548007i
$899$	−44.9538	+	8.66414i	−1.49929	+	0.288965i
$900$	−14.7110	+	5.24229i	−0.490367	+	0.174743i
$901$	−8.64849	−	21.6029i	−0.288123	−	0.719697i
$902$	4.98954	−	10.9256i	0.166133	−	0.363782i
$903$	3.67437	−	4.12936i	0.122275	−	0.137417i
$904$	−14.7463	−	4.32989i	−0.490453	−	0.144010i
$905$	12.1305	−	23.5299i	0.403231	−	0.782159i
$906$	−4.73149	−	0.773464i	−0.157193	−	0.0256966i
$907$	2.66327	−	10.9782i	0.0884326	−	0.364524i	−0.910351	−	0.413837i	$-0.864188\pi$
$907$	2.66327	−	10.9782i	0.0884326	−	0.364524i	0.998783	+	0.0493135i	$0.0157033\pi$
$908$	−0.224138	−	0.0431990i	−0.00743827	−	0.00143361i
$909$	−0.554624	+	0.489513i	−0.0183957	+	0.0162361i
$910$	−29.6292	+	52.0472i	−0.982198	+	1.72535i
$911$	−7.29638	+	3.33215i	−0.241740	+	0.110399i	−0.532601	−	0.846366i	$-0.678785\pi$
$911$	−7.29638	+	3.33215i	−0.241740	+	0.110399i	0.290861	+	0.956765i	$0.406058\pi$
$912$	6.65413	+	4.01439i	0.220340	+	0.132930i
$913$	−28.5327	−	29.9242i	−0.944295	−	0.990348i
$914$	5.18851	−	12.9603i	0.171621	−	0.428688i
$915$	−29.2501	+	0.829788i	−0.966977	+	0.0274319i
$916$	10.0539	+	1.44553i	0.332191	+	0.0477618i
$917$	13.4089	−	39.5177i	0.442800	−	1.30499i
$918$	−12.3887	−	21.9682i	−0.408889	−	0.725057i
$919$	8.63724	+	14.9601i	0.284916	+	0.493489i	0.972589	−	0.232532i	$-0.0747009\pi$
$919$	8.63724	+	14.9601i	0.284916	+	0.493489i	−0.687673	+	0.726021i	$0.741368\pi$
$920$	15.0907	+	2.64647i	0.497524	+	0.0872517i
$921$	−20.3790	+	30.4078i	−0.671511	+	1.00197i
$922$	13.4562	+	4.65723i	0.443156	+	0.153378i
$923$	24.3750	+	15.6649i	0.802314	+	0.515616i
$924$	10.2453	−	19.2469i	0.337046	−	0.633176i
$925$	−22.8053	+	49.9366i	−0.749832	+	1.64190i
$926$	−9.97092	−	12.6791i	−0.327665	−	0.416660i
$927$	−24.9372	−	34.3518i	−0.819045	−	1.12826i
$928$	0.361169	+	7.58187i	0.0118559	+	0.248887i
$929$	−12.5790	+	17.6648i	−0.412704	+	0.579562i	−0.967641	−	0.252331i	$-0.918803\pi$
$929$	−12.5790	+	17.6648i	−0.412704	+	0.579562i	0.554937	+	0.831892i	$0.312742\pi$
$930$	7.24270	+	32.5780i	0.237498	+	1.06828i
$931$	−21.3956	+	22.9922i	−0.701213	+	0.753540i
$932$	9.94266	+	8.61537i	0.325683	+	0.282206i
$933$	12.7317	−	11.6803i	0.416816	−	0.382397i
$934$	−0.997985	+	10.4514i	−0.0326551	+	0.341979i
$935$	−73.6933	+	3.51044i	−2.41003	+	0.114804i
$936$	2.21357	+	21.1415i	0.0723526	+	0.691032i
$937$	−3.79283	+	0.545327i	−0.123906	+	0.0178151i	−0.203989	−	0.978973i	$-0.565391\pi$
$937$	−3.79283	+	0.545327i	−0.123906	+	0.0178151i	0.0800826	+	0.996788i	$0.474482\pi$
$938$	−9.61140	−	8.22659i	−0.313823	−	0.268608i
$939$	4.27140	−	20.0757i	0.139392	−	0.655147i
$940$	0.461578	−	9.68972i	0.0150550	−	0.316044i
$941$	31.5768	−	6.08593i	1.02937	−	0.198396i	0.353517	−	0.935428i	$-0.384986\pi$
$941$	31.5768	−	6.08593i	1.02937	−	0.198396i	0.675857	+	0.737033i	$0.263774\pi$
$942$	18.8370	+	12.6244i	0.613744	+	0.411324i
$943$	3.60537	+	11.5572i	0.117407	+	0.376353i
$944$	10.9301			0.355743
$945$	−30.1790	−	31.9079i	−0.981722	−	1.03796i
$946$	−4.82798	−	3.10275i	−0.156971	−	0.100879i
$947$	19.5930	+	48.9409i	0.636686	+	1.59037i	0.797458	+	0.603374i	$0.206177\pi$
$947$	19.5930	+	48.9409i	0.636686	+	1.59037i	−0.160772	+	0.986992i	$0.551398\pi$
$948$	7.24841	−	4.46361i	0.235417	−	0.144971i
$949$	−37.8582	−	15.1561i	−1.22893	−	0.491989i
$950$	−5.50657	−	22.6984i	−0.178657	−	0.736433i
$951$	−10.5065	+	5.79935i	−0.340697	+	0.188057i
$952$	−4.70025	+	11.9506i	−0.152336	+	0.387322i
$953$	3.84470	+	13.0938i	0.124542	+	0.424151i	0.998033	−	0.0626889i	$-0.0199676\pi$
$953$	3.84470	+	13.0938i	0.124542	+	0.424151i	−0.873491	+	0.486840i	$0.838149\pi$
$954$	−13.6340	−	4.57992i	−0.441416	−	0.148280i
$955$	−10.5675	+	3.65745i	−0.341957	+	0.118352i
$956$	10.9456	+	2.65536i	0.354005	+	0.0858806i
$957$	−48.4175	−	39.6069i	−1.56512	−	1.28031i
$958$	2.31064	+	3.59542i	0.0746533	+	0.116163i
$959$	5.35267	+	10.2296i	0.172847	+	0.330331i
$960$	5.51732	−	0.419909i	0.178071	−	0.0135525i
$961$	5.35347	−	0.511195i	0.172693	−	0.0164901i
$962$	58.7363	+	46.1907i	1.89373	+	1.48925i
$963$	−3.95699	−	11.1042i	−0.127512	−	0.357827i
$964$	10.3454	+	3.58059i	0.333204	+	0.115323i
$965$	26.1044			0.840330
$966$	5.25886	+	21.3388i	0.169201	+	0.686565i
$967$	−59.2256			−1.90457			−0.952284	−	0.305214i	$-0.901272\pi$
$967$	−59.2256			−1.90457			−0.952284	+	0.305214i	$0.901272\pi$
$968$	−10.9984	−	3.80658i	−0.353502	−	0.122348i
$969$	34.6060	−	15.0063i	1.11171	−	0.482072i
$970$	−5.46304	−	4.29618i	−0.175408	−	0.137942i
$971$	15.8424	−	1.51277i	0.508408	−	0.0485471i	0.162300	−	0.986742i	$-0.448109\pi$
$971$	15.8424	−	1.51277i	0.508408	−	0.0485471i	0.346109	+	0.938194i	$0.387503\pi$
$972$	−15.3038	−	2.96535i	−0.490870	−	0.0951136i
$973$	−10.2552	+	16.1727i	−0.328767	+	0.518472i
$974$	12.6400	+	19.6683i	0.405013	+	0.630213i
$975$	40.4522	−	49.4508i	1.29551	−	1.58369i
$976$	5.13927	+	1.24677i	0.164504	+	0.0399082i
$977$	36.2606	−	12.5499i	1.16008	−	0.401507i	0.321831	−	0.946797i	$-0.395702\pi$
$977$	36.2606	−	12.5499i	1.16008	−	0.401507i	0.838247	+	0.545290i	$0.183580\pi$
$978$	−39.4735	−	10.3842i	−1.26222	−	0.332049i
$979$	0.777995	+	2.64961i	0.0248648	+	0.0846818i
$980$	−2.91325	+	22.1719i	−0.0930604	+	0.708255i
$981$	−17.3945	+	8.13638i	−0.555363	+	0.259775i
$982$	−5.02391	−	20.7088i	−0.160319	−	0.660845i
$983$	39.1431	+	15.6705i	1.24847	+	0.499813i	0.899335	−	0.437259i	$-0.144051\pi$
$983$	39.1431	+	15.6705i	1.24847	+	0.499813i	0.349136	+	0.937072i	$0.386475\pi$
$984$	2.29267	+	3.72305i	0.0730877	+	0.118686i
$985$	−2.04048	−	5.09687i	−0.0650151	−	0.162400i
$986$	30.9934	+	19.9183i	0.987031	+	0.634326i
$987$	12.9854	−	5.00131i	0.413331	−	0.159193i
$988$	−31.7917			−1.01143
$989$	5.71116	−	0.919278i	0.181604	−	0.0292313i
$990$	−27.8600	+	36.0999i	−0.885450	+	1.14733i
$991$	44.0024	−	8.48076i	1.39778	−	0.269400i	0.565955	−	0.824436i	$-0.308508\pi$
$991$	44.0024	−	8.48076i	1.39778	−	0.269400i	0.831826	+	0.555036i	$0.187296\pi$
$992$	0.286986	−	6.02457i	0.00911181	−	0.191280i
$993$	28.5671	+	6.07806i	0.906550	+	0.192882i
$994$	10.6357	+	1.98290i	0.337343	+	0.0628938i
$995$	3.30467	−	0.475140i	0.104765	−	0.0150629i
$996$	14.8316	−	2.56367i	0.469957	−	0.0812331i
$997$	−37.9112	+	1.80593i	−1.20066	+	0.0571945i	−0.638360	−	0.769738i	$-0.720387\pi$
$997$	−37.9112	+	1.80593i	−1.20066	+	0.0571945i	−0.562301	+	0.826933i	$0.690084\pi$
$998$	−3.41861	+	35.8013i	−0.108214	+	1.13327i
$999$	−44.9553	+	31.3320i	−1.42232	+	0.991300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bd.a.59.12	✓	1280
3.2	odd	2	inner	966.2.bd.a.59.42	yes	1280
7.5	odd	6	inner	966.2.bd.a.887.35	yes	1280
21.5	even	6	inner	966.2.bd.a.887.1	yes	1280
23.16	even	11	inner	966.2.bd.a.269.1	yes	1280
69.62	odd	22	inner	966.2.bd.a.269.35	yes	1280
161.131	odd	66	inner	966.2.bd.a.131.42	yes	1280
483.131	even	66	inner	966.2.bd.a.131.12	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bd.a.59.12	✓	1280	1.1	even	1	trivial
966.2.bd.a.59.42	yes	1280	3.2	odd	2	inner
966.2.bd.a.131.12	yes	1280	483.131	even	66	inner
966.2.bd.a.131.42	yes	1280	161.131	odd	66	inner
966.2.bd.a.269.1	yes	1280	23.16	even	11	inner
966.2.bd.a.269.35	yes	1280	69.62	odd	22	inner
966.2.bd.a.887.1	yes	1280	21.5	even	6	inner
966.2.bd.a.887.35	yes	1280	7.5	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.689077 - 1.58908i) q^{3} +(0.786053 + 0.618159i) q^{4} +(3.18017 - 0.303670i) q^{5} +(0.131442 + 1.72706i) q^{6} +(-2.23440 - 1.41685i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.05034 + 2.19000i) q^{9} +O(q^{10})\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.689077 - 1.58908i) q^{3} +(0.786053 + 0.618159i) q^{4} +(3.18017 - 0.303670i) q^{5} +(0.131442 + 1.72706i) q^{6} +(-2.23440 - 1.41685i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.05034 + 2.19000i) q^{9} +(-3.10459 - 0.753165i) q^{10} +(-4.49631 + 1.55619i) q^{11} +(0.440652 - 1.67506i) q^{12} +(1.99627 + 6.79867i) q^{13} +(1.64810 + 2.06972i) q^{14} +(-2.67394 - 4.84430i) q^{15} +(0.235759 + 0.971812i) q^{16} +(4.50603 + 1.80394i) q^{17} +(2.65386 - 1.39895i) q^{18} +(1.66756 + 4.16536i) q^{19} +(2.68750 + 1.72715i) q^{20} +(-0.711811 + 4.52696i) q^{21} +4.75799 q^{22} +(-3.57120 + 3.20102i) q^{23} +(-0.964275 + 1.43881i) q^{24} +(5.11165 - 0.985189i) q^{25} +(0.337151 - 7.07767i) q^{26} +(4.89292 + 1.74908i) q^{27} +(-0.880519 - 2.49493i) q^{28} +(-7.51320 + 1.08024i) q^{29} +(0.942463 + 5.45242i) q^{30} +(6.02457 - 0.286986i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(5.57121 + 6.07266i) q^{33} +(-3.66819 - 3.17851i) q^{34} +(-7.53603 - 3.82731i) q^{35} +(-2.96545 + 0.454015i) q^{36} +(-6.11706 + 8.59021i) q^{37} +(-0.213488 - 4.48167i) q^{38} +(9.42804 - 7.85704i) q^{39} +(-1.97480 - 2.51116i) q^{40} +(1.04866 - 2.29625i) q^{41} +(2.15328 - 4.04517i) q^{42} +(-1.01471 - 0.652114i) q^{43} +(-4.49631 - 1.55619i) q^{44} +(-5.85542 + 7.58720i) q^{45} +(4.42174 - 1.85694i) q^{46} +(-1.51828 - 2.62974i) q^{47} +(1.38183 - 1.04429i) q^{48} +(2.98508 + 6.33161i) q^{49} +(-5.15273 - 0.740851i) q^{50} +(-0.238397 - 8.40350i) q^{51} +(-2.63349 + 6.57813i) q^{52} +(-3.30839 - 3.46974i) q^{53} +(-4.05175 - 3.25320i) q^{54} +(-13.8265 + 6.31434i) q^{55} +(0.0160784 + 2.64570i) q^{56} +(5.47000 - 5.52013i) q^{57} +(7.45329 + 1.43650i) q^{58} +(2.57686 - 10.6219i) q^{59} +(0.892685 - 5.46079i) q^{60} +(2.42326 - 4.70046i) q^{61} +(-5.78709 - 1.69924i) q^{62} +(7.68418 - 1.98830i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(8.41304 + 21.0148i) q^{65} +(-3.27863 - 7.56083i) q^{66} +(-4.69534 + 0.904952i) q^{67} +(2.42686 + 4.20344i) q^{68} +(7.54751 + 3.46916i) q^{69} +(5.86977 + 6.08160i) q^{70} +(3.09039 - 2.67784i) q^{71} +(2.95084 + 0.540858i) q^{72} +(-3.55761 + 4.52386i) q^{73} +(8.59021 - 6.11706i) q^{74} +(-5.08786 - 7.44394i) q^{75} +(-1.26406 + 4.30501i) q^{76} +(12.2514 + 2.89345i) q^{77} +(-11.4793 + 4.34130i) q^{78} +(3.55695 + 3.39154i) q^{79} +(1.04486 + 3.01894i) q^{80} +(-0.592174 - 8.98050i) q^{81} +(-1.74202 + 1.82698i) q^{82} +(3.60996 + 7.90471i) q^{83} +(-3.35790 + 3.11842i) q^{84} +(14.8778 + 4.36851i) q^{85} +(0.745615 + 0.948127i) q^{86} +(6.89376 + 11.1947i) q^{87} +(3.74004 + 2.94120i) q^{88} +(0.0276158 - 0.579727i) q^{89} +(8.01490 - 5.25479i) q^{90} +(5.17223 - 18.0194i) q^{91} +(-4.78589 + 0.308605i) q^{92} +(-4.60744 - 9.37577i) q^{93} +(0.574673 + 2.98168i) q^{94} +(6.56801 + 12.7402i) q^{95} +(-1.64738 + 0.534906i) q^{96} +(1.97891 + 0.903738i) q^{97} +(-0.750035 - 6.95970i) q^{98} +(5.81094 - 13.0376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 + 4 * q^9	\( 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

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