LMFDB - Embedded newform 930.2.bk.a.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.13
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-0.678564 + 1.59360i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.22925 - 1.86787i) q^{5} +(-1.46783 - 0.919503i) q^{6} +(-0.247778 + 0.126249i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.07910 - 2.16271i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.678564 + 1.59360i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.22925 - 1.86787i) q^{5} +(-1.46783 - 0.919503i) q^{6} +(-0.247778 + 0.126249i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.07910 - 2.16271i) q^{9} +(2.03717 - 0.921913i) q^{10} +(4.89005 + 1.58887i) q^{11} +(1.13780 - 1.30591i) q^{12} +(1.65549 - 0.262204i) q^{13} +(-0.0859340 - 0.264478i) q^{14} +(3.81076 - 0.691453i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.14265 - 1.60126i) q^{17} +(2.46133 - 1.71518i) q^{18} +(3.19412 + 4.39633i) q^{19} +(0.591879 + 2.15631i) q^{20} +(-0.0330572 - 0.480527i) q^{21} +(-2.33428 + 4.58129i) q^{22} +(1.57308 - 3.08735i) q^{23} +(1.11184 + 1.32808i) q^{24} +(-1.97790 + 4.59216i) q^{25} +1.67613i q^{26} +(4.85730 - 1.84571i) q^{27} +(0.274664 - 0.0435026i) q^{28} +(-3.84084 + 2.79053i) q^{29} +(0.0868056 + 3.87201i) q^{30} +(5.30488 - 1.69064i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.85023 + 6.71461i) q^{33} +(2.07316 - 2.85347i) q^{34} +(0.540399 + 0.307627i) q^{35} +(1.30903 + 2.69934i) q^{36} +(6.48500 + 6.48500i) q^{37} +(-4.84188 + 2.46706i) q^{38} +(-0.705509 + 2.81611i) q^{39} +(-2.22235 + 0.247270i) q^{40} +(0.922226 + 1.26933i) q^{41} +(0.479782 + 0.0425208i) q^{42} +(-1.50105 + 9.47723i) q^{43} +(-4.15972 - 3.02222i) q^{44} +(-1.48395 + 6.54201i) q^{45} +(2.80326 + 2.03669i) q^{46} +(-9.81204 + 1.55407i) q^{47} +(-1.48566 + 0.890397i) q^{48} +(-4.06904 + 5.60056i) q^{49} +(-4.22621 - 2.67192i) q^{50} +(4.68425 - 3.92156i) q^{51} +(-1.65549 - 0.262204i) q^{52} +(2.56771 - 5.03942i) q^{53} +(1.06314 + 5.08623i) q^{54} +(-3.04326 - 11.0871i) q^{55} +0.278088i q^{56} +(-9.17340 + 2.10695i) q^{57} +(-2.15534 - 4.23009i) q^{58} +(11.0873 + 8.05541i) q^{59} +(-3.83792 - 0.519979i) q^{60} +13.6678 q^{61} +(0.839960 + 5.50404i) q^{62} +(0.788198 + 0.273389i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-2.52477 - 2.76993i) q^{65} +(-5.71677 - 6.82860i) q^{66} +(-10.9958 - 10.9958i) q^{67} +(2.49402 + 2.49402i) q^{68} +(3.85256 + 4.60183i) q^{69} +(-0.388377 + 0.485622i) q^{70} +(3.34724 - 1.08758i) q^{71} +(-2.87089 + 0.870642i) q^{72} +(1.02998 + 2.02145i) q^{73} +(-7.41964 + 5.39068i) q^{74} +(-5.97591 - 6.26805i) q^{75} +(-1.67925 - 5.16820i) q^{76} +(-1.41224 + 0.223677i) q^{77} +(-2.67107 - 1.13736i) q^{78} +(11.2843 - 3.66648i) q^{79} +(0.103427 - 2.23367i) q^{80} +(-0.354669 + 8.99301i) q^{81} +(-1.39797 + 0.712304i) q^{82} +(-9.51036 - 1.50629i) q^{83} +(-0.117052 + 0.467224i) q^{84} +(0.872141 + 7.83841i) q^{85} +(-9.12573 - 2.96513i) q^{86} +(-1.84073 - 8.01431i) q^{87} +(3.63573 - 3.63573i) q^{88} +(0.335897 - 1.03379i) q^{89} +(-6.22933 - 2.48907i) q^{90} +(-0.377092 + 0.273973i) q^{91} +(-2.45014 + 2.45014i) q^{92} +(-0.905500 + 9.60105i) q^{93} -9.93435i q^{94} +(4.28543 - 11.3704i) q^{95} +(-0.647026 - 1.60666i) q^{96} +(2.95745 - 1.50690i) q^{97} +(-4.89506 - 4.89506i) q^{98} +(-6.73063 - 13.8792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−0.678564	+	1.59360i	−0.391769	+	0.920064i
$3$	−0.678564	+	1.59360i	−0.391769	+	0.920064i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−1.22925	−	1.86787i	−0.549736	−	0.835338i
$5$	−1.22925	−	1.86787i	−0.549736	−	0.835338i
$6$	−1.46783	−	0.919503i	−0.599238	−	0.375386i
$7$	−0.247778	+	0.126249i	−0.0936514	+	0.0477178i	−0.500189	−	0.865916i	$-0.666736\pi$
$7$	−0.247778	+	0.126249i	−0.0936514	+	0.0477178i	0.406537	+	0.913634i	$0.366736\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−2.07910	−	2.16271i	−0.693034	−	0.720905i
$10$	2.03717	−	0.921913i	0.644211	−	0.291535i
$11$	4.89005	+	1.58887i	1.47441	+	0.479063i	0.932436	−	0.361335i	$-0.117679\pi$
$11$	4.89005	+	1.58887i	1.47441	+	0.479063i	0.541969	+	0.840398i	$0.317679\pi$
$12$	1.13780	−	1.30591i	0.328455	−	0.376985i
$13$	1.65549	−	0.262204i	0.459151	−	0.0727223i	0.0774253	−	0.996998i	$-0.475330\pi$
$13$	1.65549	−	0.262204i	0.459151	−	0.0727223i	0.381725	+	0.924276i	$0.375330\pi$
$14$	−0.0859340	−	0.264478i	−0.0229668	−	0.0706846i
$15$	3.81076	−	0.691453i	0.983934	−	0.178532i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−3.14265	−	1.60126i	−0.762204	−	0.388363i	0.0292648	−	0.999572i	$-0.490683\pi$
$17$	−3.14265	−	1.60126i	−0.762204	−	0.388363i	−0.791469	+	0.611209i	$0.790683\pi$
$18$	2.46133	−	1.71518i	0.580141	−	0.404272i
$19$	3.19412	+	4.39633i	0.732782	+	1.00859i	0.999002	+	0.0446753i	$0.0142253\pi$
$19$	3.19412	+	4.39633i	0.732782	+	1.00859i	−0.266220	+	0.963912i	$0.585775\pi$
$20$	0.591879	+	2.15631i	0.132348	+	0.482166i
$21$	−0.0330572	−	0.480527i	−0.00721367	−	0.104860i
$22$	−2.33428	+	4.58129i	−0.497671	+	0.976734i
$23$	1.57308	−	3.08735i	0.328011	−	0.643757i	−0.666830	−	0.745210i	$-0.732349\pi$
$23$	1.57308	−	3.08735i	0.328011	−	0.643757i	0.994840	+	0.101453i	$0.0323491\pi$
$24$	1.11184	+	1.32808i	0.226954	+	0.271094i
$25$	−1.97790	+	4.59216i	−0.395581	+	0.918431i
$26$			1.67613i			0.328715i
$27$	4.85730	−	1.84571i	0.934788	−	0.355207i
$28$	0.274664	−	0.0435026i	0.0519067	−	0.00822121i
$29$	−3.84084	+	2.79053i	−0.713226	+	0.518189i	−0.884213	−	0.467084i	$-0.845305\pi$
$29$	−3.84084	+	2.79053i	−0.713226	+	0.518189i	0.170987	+	0.985273i	$0.445305\pi$
$30$	0.0868056	+	3.87201i	0.0158485	+	0.706929i
$31$	5.30488	−	1.69064i	0.952784	−	0.303648i
$31$	5.30488	−	1.69064i	0.952784	−	0.303648i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.85023	+	6.71461i	−1.01840	+	1.16886i
$34$	2.07316	−	2.85347i	0.355545	−	0.489365i
$35$	0.540399	+	0.307627i	0.0913441	+	0.0519985i
$36$	1.30903	+	2.69934i	0.218171	+	0.449890i
$37$	6.48500	+	6.48500i	1.06613	+	1.06613i	0.997653	+	0.0684753i	$0.0218134\pi$
$37$	6.48500	+	6.48500i	1.06613	+	1.06613i	0.0684753	+	0.997653i	$0.478187\pi$
$38$	−4.84188	+	2.46706i	−0.785456	+	0.400210i
$39$	−0.705509	+	2.81611i	−0.112972	+	0.450938i
$40$	−2.22235	+	0.247270i	−0.351385	+	0.0390969i
$41$	0.922226	+	1.26933i	0.144027	+	0.198237i	0.874936	−	0.484239i	$-0.160903\pi$
$41$	0.922226	+	1.26933i	0.144027	+	0.198237i	−0.730908	+	0.682476i	$0.760903\pi$
$42$	0.479782	+	0.0425208i	0.0740320	+	0.00656110i
$43$	−1.50105	+	9.47723i	−0.228907	+	1.44526i	0.558845	+	0.829272i	$0.311245\pi$
$43$	−1.50105	+	9.47723i	−0.228907	+	1.44526i	−0.787753	+	0.615992i	$0.788755\pi$
$44$	−4.15972	−	3.02222i	−0.627102	−	0.455616i
$45$	−1.48395	+	6.54201i	−0.221214	+	0.975225i
$46$	2.80326	+	2.03669i	0.413318	+	0.300293i
$47$	−9.81204	+	1.55407i	−1.43123	+	0.226685i	−0.823437	−	0.567408i	$-0.807946\pi$
$47$	−9.81204	+	1.55407i	−1.43123	+	0.226685i	−0.607797	+	0.794093i	$0.707946\pi$
$48$	−1.48566	+	0.890397i	−0.214437	+	0.128518i
$49$	−4.06904	+	5.60056i	−0.581292	+	0.800079i
$50$	−4.22621	−	2.67192i	−0.597676	−	0.377867i
$51$	4.68425	−	3.92156i	0.655926	−	0.549128i
$52$	−1.65549	−	0.262204i	−0.229575	−	0.0363611i
$53$	2.56771	−	5.03942i	0.352703	−	0.692218i	−0.644685	−	0.764448i	$-0.723012\pi$
$53$	2.56771	−	5.03942i	0.352703	−	0.692218i	0.997388	+	0.0722303i	$0.0230116\pi$
$54$	1.06314	+	5.08623i	0.144675	+	0.692148i
$55$	−3.04326	−	11.0871i	−0.410354	−	1.49499i
$56$			0.278088i			0.0371611i
$57$	−9.17340	+	2.10695i	−1.21505	+	0.279072i
$58$	−2.15534	−	4.23009i	−0.283010	−	0.555438i
$59$	11.0873	+	8.05541i	1.44345	+	1.04873i	0.987308	+	0.158817i	$0.0507679\pi$
$59$	11.0873	+	8.05541i	1.44345	+	1.04873i	0.456139	+	0.889909i	$0.349232\pi$
$60$	−3.83792	−	0.519979i	−0.495473	−	0.0671290i
$61$	13.6678			1.74999			0.874993	−	0.484135i	$-0.160866\pi$
$61$	13.6678			1.74999			0.874993	+	0.484135i	$0.160866\pi$
$62$	0.839960	+	5.50404i	0.106675	+	0.699014i
$63$	0.788198	+	0.273389i	0.0993036	+	0.0344437i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−2.52477	−	2.76993i	−0.313159	−	0.343568i
$66$	−5.71677	−	6.82860i	−0.703686	−	0.840543i
$67$	−10.9958	−	10.9958i	−1.34335	−	1.34335i	−0.892705	−	0.450642i	$-0.851195\pi$
$67$	−10.9958	−	10.9958i	−1.34335	−	1.34335i	−0.450642	−	0.892705i	$-0.648805\pi$
$68$	2.49402	+	2.49402i	0.302444	+	0.302444i
$69$	3.85256	+	4.60183i	0.463793	+	0.553995i
$70$	−0.388377	+	0.485622i	−0.0464199	+	0.0580429i
$71$	3.34724	−	1.08758i	0.397244	−	0.129072i	−0.103581	−	0.994621i	$-0.533030\pi$
$71$	3.34724	−	1.08758i	0.397244	−	0.129072i	0.500825	+	0.865549i	$0.333030\pi$
$72$	−2.87089	+	0.870642i	−0.338337	+	0.102606i
$73$	1.02998	+	2.02145i	0.120550	+	0.236593i	0.943394	−	0.331675i	$-0.107614\pi$
$73$	1.02998	+	2.02145i	0.120550	+	0.236593i	−0.822844	+	0.568268i	$0.807614\pi$
$74$	−7.41964	+	5.39068i	−0.862516	+	0.626654i
$75$	−5.97591	−	6.26805i	−0.690039	−	0.723772i
$76$	−1.67925	−	5.16820i	−0.192623	−	0.592833i
$77$	−1.41224	+	0.223677i	−0.160940	+	0.0254904i
$78$	−2.67107	−	1.13736i	−0.302439	−	0.128781i
$79$	11.2843	−	3.66648i	1.26958	−	0.412511i	0.404680	−	0.914458i	$-0.367383\pi$
$79$	11.2843	−	3.66648i	1.26958	−	0.412511i	0.864898	+	0.501947i	$0.167383\pi$
$80$	0.103427	−	2.23367i	0.0115635	−	0.249732i
$81$	−0.354669	+	8.99301i	−0.0394077	+	0.999223i
$82$	−1.39797	+	0.712304i	−0.154381	+	0.0786608i
$83$	−9.51036	−	1.50629i	−1.04390	−	0.165337i	−0.389142	−	0.921178i	$-0.627229\pi$
$83$	−9.51036	−	1.50629i	−1.04390	−	0.165337i	−0.654756	+	0.755840i	$0.727229\pi$
$84$	−0.117052	+	0.467224i	−0.0127714	+	0.0509783i
$85$	0.872141	+	7.83841i	0.0945970	+	0.850195i
$86$	−9.12573	−	2.96513i	−0.984053	−	0.319738i
$87$	−1.84073	−	8.01431i	−0.197347	−	0.859224i
$88$	3.63573	−	3.63573i	0.387570	−	0.387570i
$89$	0.335897	−	1.03379i	0.0356050	−	0.109581i	−0.931674	−	0.363294i	$-0.881652\pi$
$89$	0.335897	−	1.03379i	0.0356050	−	0.109581i	0.967279	+	0.253713i	$0.0816520\pi$
$90$	−6.22933	−	2.48907i	−0.656629	−	0.262371i
$91$	−0.377092	+	0.273973i	−0.0395300	+	0.0287202i
$92$	−2.45014	+	2.45014i	−0.255444	+	0.255444i
$93$	−0.905500	+	9.60105i	−0.0938960	+	0.995582i
$94$		−	9.93435i		−	1.02465i
$95$	4.28543	−	11.3704i	0.439676	−	1.16658i
$96$	−0.647026	−	1.60666i	−0.0660368	−	0.163979i
$97$	2.95745	−	1.50690i	0.300284	−	0.153002i	−0.297357	−	0.954767i	$-0.596105\pi$
$97$	2.95745	−	1.50690i	0.300284	−	0.153002i	0.597641	+	0.801764i	$0.296105\pi$
$98$	−4.89506	−	4.89506i	−0.494476	−	0.494476i
$99$	−6.73063	−	13.8792i	−0.676454	−	1.39491i
$100$	3.30015	−	3.75619i	0.330015	−	0.375619i
$101$	−9.38092	+	3.04805i	−0.933437	+	0.303292i	−0.735967	−	0.677017i	$-0.763272\pi$
$101$	−9.38092	+	3.04805i	−0.933437	+	0.303292i	−0.197469	+	0.980309i	$0.563272\pi$
$102$	3.14050	+	5.24005i	0.310956	+	0.518842i
$103$	−2.64153	+	16.6779i	−0.260277	+	1.64333i	0.417946	+	0.908472i	$0.362750\pi$
$103$	−2.64153	+	16.6779i	−0.260277	+	1.64333i	−0.678224	+	0.734855i	$0.737250\pi$
$104$	0.517952	−	1.59409i	0.0507893	−	0.156313i
$105$	−0.856929	+	0.652433i	−0.0836277	+	0.0636710i
$106$	4.57570	+	3.32444i	0.444431	+	0.322898i
$107$	9.73339	+	4.95941i	0.940962	+	0.479444i	0.856021	−	0.516942i	$-0.172930\pi$
$107$	9.73339	+	4.95941i	0.940962	+	0.479444i	0.0849418	+	0.996386i	$0.472930\pi$
$108$	−5.18992	+	0.254387i	−0.499400	+	0.0244784i
$109$	2.21460	−	3.04813i	0.212120	−	0.291958i	−0.689678	−	0.724117i	$-0.742248\pi$
$109$	2.21460	−	3.04813i	0.212120	−	0.291958i	0.901798	+	0.432158i	$0.142248\pi$
$110$	11.4267	−	1.27139i	1.08949	−	0.121222i
$111$	−14.7350	+	5.93399i	−1.39858	+	0.563230i
$112$	−0.274664	−	0.0435026i	−0.0259534	−	0.00411061i
$113$	15.0662	−	7.67659i	1.41730	−	0.722153i	0.433459	−	0.901173i	$-0.357293\pi$
$113$	15.0662	−	7.67659i	1.41730	−	0.722153i	0.983845	+	0.179021i	$0.0572929\pi$
$114$	−0.645975	−	9.39006i	−0.0605011	−	0.879459i
$115$	−7.70049	+	0.856796i	−0.718075	+	0.0798966i
$116$	4.51518	−	1.46707i	0.419224	−	0.136214i
$117$	−4.00901	−	3.03521i	−0.370633	−	0.280605i
$118$	−9.69068	+	9.69068i	−0.892099	+	0.892099i
$119$	0.980839			0.0899133
$120$	1.11396	−	3.70933i	0.101690	−	0.338614i
$121$	12.4889	+	9.07370i	1.13535	+	0.824882i
$122$	−2.13812	+	13.4996i	−0.193576	+	1.22219i
$123$	−2.64860	+	0.608331i	−0.238816	+	0.0548514i
$124$	−5.56768	−	0.0314035i	−0.499992	−	0.00282012i
$125$	11.0089	−	1.95042i	0.984666	−	0.174451i
$126$	−0.393324	+	0.735727i	−0.0350401	+	0.0655437i
$127$	1.70954	+	10.7936i	0.151697	+	0.957778i	0.939674	+	0.342072i	$0.111129\pi$
$127$	1.70954	+	10.7936i	0.151697	+	0.957778i	−0.787977	+	0.615705i	$0.788871\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	−14.0843	−	8.82297i	−1.24006	−	0.776819i
$130$	3.13079	−	2.06037i	0.274589	−	0.180707i
$131$	3.77838	+	1.22767i	0.330119	+	0.107262i	0.469387	−	0.882993i	$-0.344475\pi$
$131$	3.77838	+	1.22767i	0.330119	+	0.107262i	−0.139268	+	0.990255i	$0.544475\pi$
$132$	7.63883	−	4.57816i	0.664875	−	0.398477i
$133$	−1.34647	−	0.686060i	−0.116754	−	0.0594889i
$134$	12.5805	−	9.14027i	1.08679	−	0.789599i
$135$	−9.41837	−	6.80399i	−0.810605	−	0.585594i
$136$	−2.85347	+	2.07316i	−0.244683	+	0.177772i
$137$	0.838338	−	0.132780i	0.0716240	−	0.0113441i	−0.120520	−	0.992711i	$-0.538456\pi$
$137$	0.838338	−	0.132780i	0.0716240	−	0.0113441i	0.192144	+	0.981367i	$0.438456\pi$
$138$	−5.14784	+	3.08524i	−0.438214	+	0.262633i
$139$	−4.43878	+	6.10945i	−0.376492	+	0.518197i	−0.954651	−	0.297727i	$-0.903771\pi$
$139$	−4.43878	+	6.10945i	−0.376492	+	0.518197i	0.578159	+	0.815924i	$0.303771\pi$
$140$	−0.418888	−	0.459563i	−0.0354025	−	0.0388402i
$141$	4.18153	−	16.6910i	0.352148	−	1.40563i
$142$	0.550570	+	3.47616i	0.0462028	+	0.291713i
$143$	8.51204	+	1.34817i	0.711812	+	0.112740i
$144$	−0.410817	−	2.97174i	−0.0342348	−	0.247645i
$145$	9.93371	+	3.74395i	0.824950	+	0.310918i
$146$	−2.15769	+	0.701075i	−0.178571	+	0.0580214i
$147$	−6.16392	−	10.2847i	−0.508392	−	0.848272i
$148$	−4.16363	−	8.17158i	−0.342248	−	0.671700i
$149$	8.69375			0.712220			0.356110	−	0.934444i	$-0.384103\pi$
$149$	8.69375			0.712220			0.356110	+	0.934444i	$0.384103\pi$
$150$	7.12572	−	4.92180i	0.581813	−	0.401863i
$151$	−1.32926	+	4.09105i	−0.108174	+	0.332925i	−0.990462	−	0.137784i	$-0.956002\pi$
$151$	−1.32926	+	4.09105i	−0.108174	+	0.332925i	0.882288	+	0.470709i	$0.156002\pi$
$152$	5.36726	−	0.850091i	0.435342	−	0.0689515i
$153$	3.07082	+	10.1258i	0.248261	+	0.818625i
$154$		−	1.42985i		−	0.115220i
$155$	−9.67891	−	7.83063i	−0.777429	−	0.628971i
$156$	1.54120	−	2.46026i	0.123395	−	0.196979i
$157$	2.64496	+	0.418920i	0.211091	+	0.0334335i	0.261084	−	0.965316i	$-0.415920\pi$
$157$	2.64496	+	0.418920i	0.211091	+	0.0334335i	−0.0499934	+	0.998750i	$0.515920\pi$
$158$	1.85609	+	11.7189i	0.147663	+	0.932305i
$159$	6.28845	+	7.51147i	0.498706	+	0.595698i
$160$	2.18999	+	0.451577i	0.173134	+	0.0357003i
$161$			0.963580i			0.0759408i
$162$	−8.82681	−	1.75712i	−0.693500	−	0.138052i
$163$	16.1750	+	8.24158i	1.26693	+	0.645531i	0.952727	−	0.303827i	$-0.0982645\pi$
$163$	16.1750	+	8.24158i	1.26693	+	0.645531i	0.314198	+	0.949358i	$0.398264\pi$
$164$	−0.484843	−	1.49219i	−0.0378599	−	0.116521i
$165$	19.7334	+	2.67358i	1.53625	+	0.208138i
$166$	2.97550	−	9.15764i	0.230943	−	0.710771i
$167$	1.84946	−	11.6770i	0.143115	−	0.903593i	−0.806741	−	0.590905i	$-0.798771\pi$
$167$	1.84946	−	11.6770i	0.143115	−	0.903593i	0.949856	−	0.312688i	$-0.101229\pi$
$168$	−0.443160	−	0.188701i	−0.0341906	−	0.0145586i
$169$	−9.69184	+	3.14907i	−0.745526	+	0.242236i
$170$	−7.87834	−	0.364794i	−0.604241	−	0.0279784i
$171$	2.86711	−	16.0484i	0.219253	−	1.22725i
$172$	4.35620	−	8.54953i	0.332157	−	0.651896i
$173$	−0.276252	−	1.74419i	−0.0210031	−	0.132608i	0.974959	−	0.222386i	$-0.0713844\pi$
$173$	−0.276252	−	1.74419i	−0.0210031	−	0.132608i	−0.995962	+	0.0897775i	$0.971384\pi$
$174$	8.20359	−	0.564355i	0.621913	−	0.0427836i
$175$	−0.0896752	−	1.38755i	−0.00677881	−	0.104889i
$176$	3.02222	+	4.15972i	0.227808	+	0.313551i
$177$	−20.3605	+	12.2026i	−1.53039	+	0.917205i
$178$	0.968512	+	0.493481i	0.0725930	+	0.0369880i
$179$	4.28810	−	13.1974i	0.320507	−	0.986421i	−0.652920	−	0.757427i	$-0.726456\pi$
$179$	4.28810	−	13.1974i	0.320507	−	0.986421i	0.973428	−	0.228994i	$-0.0735436\pi$
$180$	3.43291	−	5.76326i	0.255874	−	0.429568i
$181$	−4.98012			−0.370169			−0.185085	−	0.982723i	$-0.559256\pi$
$181$	−4.98012			−0.370169			−0.185085	+	0.982723i	$0.559256\pi$
$182$	−0.211610	−	0.415308i	−0.0156856	−	0.0307847i
$183$	−9.27450	+	21.7810i	−0.685591	+	1.61010i
$184$	−2.03669	−	2.80326i	−0.150146	−	0.206659i
$185$	4.14150	−	20.0848i	0.304489	−	1.47667i
$186$	−9.34119	−	2.39629i	−0.684929	−	0.175704i
$187$	−12.8235	−	12.8235i	−0.937748	−	0.937748i
$188$	9.81204	+	1.55407i	0.715617	+	0.113343i
$189$	−0.970514	+	1.07056i	−0.0705945	+	0.0778717i
$190$	10.5600	+	6.01139i	0.766104	+	0.436112i
$191$			2.91888i			0.211202i	0.994409	+	0.105601i	$0.0336767\pi$
$191$			2.91888i			0.211202i	−0.994409	+	0.105601i	$0.966323\pi$
$192$	1.68810	−	0.387723i	0.121828	−	0.0279815i
$193$	4.93849	+	9.69233i	0.355480	+	0.697669i	0.997622	−	0.0689164i	$-0.0219542\pi$
$193$	4.93849	+	9.69233i	0.355480	+	0.697669i	−0.642142	+	0.766585i	$0.721954\pi$
$194$	1.02570	+	3.15677i	0.0736408	+	0.226643i
$195$	6.12738	−	2.14389i	0.438791	−	0.153527i
$196$	5.60056	−	4.06904i	0.400040	−	0.290646i
$197$	0.114511	+	0.224740i	0.00815854	+	0.0160120i	0.895050	−	0.445966i	$-0.147140\pi$
$197$	0.114511	+	0.224740i	0.00815854	+	0.0160120i	−0.886891	+	0.461978i	$0.847140\pi$
$198$	14.7612	−	4.47658i	1.04904	−	0.318137i
$199$	13.4378	−	18.4956i	0.952583	−	1.31112i	0.00221192	−	0.999998i	$-0.499296\pi$
$199$	13.4378	−	18.4956i	0.952583	−	1.31112i	0.950371	−	0.311120i	$-0.100704\pi$
$200$	3.19369	+	3.84712i	0.225828	+	0.272032i
$201$	24.9842	−	10.0615i	1.76225	−	0.709683i
$202$	−1.54302	−	9.74225i	−0.108567	−	0.685462i
$203$	0.599374	−	1.17634i	0.0420678	−	0.0825628i
$204$	−5.66682	+	2.28211i	−0.396756	+	0.159780i
$205$	1.23731	−	3.28293i	0.0864177	−	0.229290i
$206$	−16.0594	−	5.21801i	−1.11891	−	0.363556i
$207$	−9.94767	+	3.01679i	−0.691411	+	0.209681i
$208$	1.49344	+	0.760946i	0.103551	+	0.0527621i
$209$	8.63420	+	26.5733i	0.597240	+	1.83812i
$210$	−0.510348	−	0.948441i	−0.0352173	−	0.0654487i
$211$	4.88104			0.336024			0.168012	−	0.985785i	$-0.446265\pi$
$211$	4.88104			0.336024			0.168012	+	0.985785i	$0.446265\pi$
$212$	−3.99931	+	3.99931i	−0.274674	+	0.274674i
$213$	−0.538145	+	6.07214i	−0.0368731	+	0.416057i
$214$	−6.42099	+	8.83773i	−0.438930	+	0.604135i
$215$	19.5474	−	8.84609i	1.33312	−	0.603298i
$216$	0.560627	−	5.16582i	0.0381459	−	0.351490i
$217$	−1.10099	+	1.08864i	−0.0747402	+	0.0739018i
$218$	2.66417	+	2.66417i	0.180440	+	0.180440i
$219$	−3.92028	+	0.269690i	−0.264908	+	0.0182240i
$220$	−0.531790	+	11.4849i	−0.0358533	+	0.774311i
$221$	−5.62248	−	1.82686i	−0.378209	−	0.122888i
$222$	−3.55588	−	15.4818i	−0.238655	−	1.03907i
$223$	−0.701954	+	0.701954i	−0.0470063	+	0.0470063i	−0.730219	−	0.683213i	$-0.760582\pi$
$223$	−0.701954	+	0.701954i	−0.0470063	+	0.0470063i	0.683213	+	0.730219i	$0.260582\pi$
$224$	0.0859340	−	0.264478i	0.00574171	−	0.0176712i
$225$	14.0438	−	5.26992i	0.936252	−	0.351328i
$226$	5.22521	+	16.0815i	0.347576	+	1.06973i
$227$	2.81886	−	17.7976i	0.187095	−	1.18127i	−0.698083	−	0.716017i	$-0.745964\pi$
$227$	2.81886	−	17.7976i	0.187095	−	1.18127i	0.885178	−	0.465253i	$-0.154036\pi$
$228$	9.37550	+	0.830906i	0.620908	+	0.0550281i
$229$	−15.0541	−	20.7202i	−0.994802	−	1.36923i	−0.928461	−	0.371430i	$-0.878867\pi$
$229$	−15.0541	−	20.7202i	−0.994802	−	1.36923i	−0.0663412	−	0.997797i	$-0.521133\pi$
$230$	0.358376	−	7.73972i	0.0236306	−	0.510342i
$231$	0.601845	−	2.40232i	0.0395985	−	0.158061i
$232$	0.742679	+	4.68909i	0.0487593	+	0.307854i
$233$	2.74496	+	17.3310i	0.179829	+	1.13539i	0.898152	+	0.439684i	$0.144910\pi$
$233$	2.74496	+	17.3310i	0.179829	+	1.13539i	−0.718324	+	0.695709i	$0.755090\pi$
$234$	3.62498	−	3.48484i	0.236973	−	0.227811i
$235$	14.9642	+	16.4173i	0.976159	+	1.07095i
$236$	−8.05541	−	11.0873i	−0.524363	−	0.721723i
$237$	−1.81420	+	20.4705i	−0.117845	+	1.32970i
$238$	−0.153437	+	0.968763i	−0.00994584	+	0.0627956i
$239$	−3.41258	−	10.5029i	−0.220742	−	0.679373i	−0.998696	−	0.0510522i	$-0.983742\pi$
$239$	−3.41258	−	10.5029i	−0.220742	−	0.679373i	0.777954	−	0.628321i	$-0.216258\pi$
$240$	3.48940	+	1.68051i	0.225240	+	0.108477i
$241$	−1.06540	+	3.27897i	−0.0686285	+	0.211217i	−0.979489	−	0.201497i	$-0.935419\pi$
$241$	−1.06540	+	3.27897i	−0.0686285	+	0.211217i	0.910861	+	0.412714i	$0.135419\pi$
$242$	−10.9157	+	10.9157i	−0.701686	+	0.701686i
$243$	−14.0906	−	6.66753i	−0.903910	−	0.427722i
$244$	−12.9989	−	4.22359i	−0.832168	−	0.270388i
$245$	15.4630	+	0.715989i	0.987894	+	0.0457429i
$246$	−0.186510	−	2.71115i	−0.0118914	−	0.172857i
$247$	6.44057	+	6.44057i	0.409804	+	0.409804i
$248$	0.901993	−	5.49422i	0.0572766	−	0.348883i
$249$	8.85381	−	14.1336i	0.561088	−	0.895679i
$250$	0.204237	+	11.1785i	0.0129171	+	0.706989i
$251$	−14.3164	+	19.7049i	−0.903644	+	1.24376i	0.0656464	+	0.997843i	$0.479089\pi$
$251$	−14.3164	+	19.7049i	−0.903644	+	1.24376i	−0.969291	+	0.245917i	$0.920911\pi$
$252$	−0.665139	−	0.503575i	−0.0418998	−	0.0317222i
$253$	12.5979	−	12.5979i	0.792021	−	0.792021i
$254$	−10.9281			−0.685693
$255$	−13.0831	−	3.92902i	−0.819294	−	0.246045i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−20.3104	−	10.3487i	−1.26693	−	0.645532i	−0.314200	−	0.949357i	$-0.601736\pi$
$257$	−20.3104	−	10.3487i	−1.26693	−	0.645532i	−0.952728	+	0.303825i	$0.901736\pi$
$258$	10.9176	−	12.5307i	0.679701	−	0.780128i
$259$	−2.42557	−	0.788116i	−0.150718	−	0.0489711i
$260$	1.54524	+	3.41456i	0.0958319	+	0.211762i
$261$	14.0206	+	2.50484i	0.867855	+	0.155046i
$262$	−1.80362	+	3.53981i	−0.111428	+	0.218690i
$263$	0.348371	+	2.19953i	0.0214815	+	0.135629i	0.996098	−	0.0882509i	$-0.0281277\pi$
$263$	0.348371	+	2.19953i	0.0214815	+	0.135629i	−0.974617	+	0.223880i	$0.928128\pi$
$264$	3.32681	+	8.26097i	0.204751	+	0.508427i
$265$	−12.5694	+	1.39853i	−0.772129	+	0.0859110i
$266$	0.888248	−	1.22257i	0.0544620	−	0.0749604i
$267$	1.41951	+	1.23677i	0.0868726	+	0.0756894i
$268$	7.05972	+	13.8555i	0.431241	+	0.846358i
$269$	−7.20938	+	5.23792i	−0.439564	+	0.319362i	−0.785461	−	0.618911i	$-0.787574\pi$
$269$	−7.20938	+	5.23792i	−0.439564	+	0.319362i	0.345898	+	0.938272i	$0.387574\pi$
$270$	8.19358	−	8.23804i	0.498645	−	0.501351i
$271$	−5.77260	−	17.7662i	−0.350660	−	1.07922i	−0.958483	−	0.285149i	$-0.907957\pi$
$271$	−5.77260	−	17.7662i	−0.350660	−	1.07922i	0.607823	−	0.794072i	$-0.292043\pi$
$272$	−1.60126	−	3.14265i	−0.0970906	−	0.190551i
$273$	−0.180722	−	0.786841i	−0.0109378	−	0.0476218i
$274$			0.848788i			0.0512772i
$275$	−16.9684	+	19.3132i	−1.02323	+	1.16463i
$276$	−2.24196	−	5.56710i	−0.134950	−	0.335100i
$277$	4.40294	+	0.697358i	0.264547	+	0.0419002i	0.287299	−	0.957841i	$-0.407243\pi$
$277$	4.40294	+	0.697358i	0.264547	+	0.0419002i	−0.0227516	+	0.999741i	$0.507243\pi$
$278$	−5.33986	−	5.33986i	−0.320263	−	0.320263i
$279$	−14.6858	−	7.95793i	−0.879213	−	0.476429i
$280$	0.519434	−	0.341839i	0.0310421	−	0.0204288i
$281$	−4.07395	−	5.60731i	−0.243031	−	0.334504i	0.670024	−	0.742339i	$-0.266284\pi$
$281$	−4.07395	−	5.60731i	−0.243031	−	0.334504i	−0.913056	+	0.407835i	$0.866284\pi$
$282$	15.8314	+	6.74109i	0.942743	+	0.401426i
$283$	−14.2290	−	27.9261i	−0.845828	−	1.66003i	−0.746899	−	0.664937i	$-0.768458\pi$
$283$	−14.2290	−	27.9261i	−0.845828	−	1.66003i	−0.0989291	−	0.995094i	$-0.531542\pi$
$284$	−3.51950			−0.208844
$285$	15.2119	+	14.5448i	0.901074	+	0.861558i
$286$	−2.66315	+	8.19634i	−0.157476	+	0.484660i
$287$	−0.388760	−	0.198083i	−0.0229478	−	0.0116925i
$288$	2.99942	+	0.0591230i	0.176742	+	0.00348385i
$289$	−2.68014	−	3.68890i	−0.157655	−	0.216994i
$290$	−5.25183	+	9.22573i	−0.308398	+	0.541753i
$291$	0.394567	+	5.73552i	0.0231299	+	0.336222i
$292$	−0.354907	−	2.24079i	−0.0207694	−	0.131133i
$293$	−6.21773	+	12.2030i	−0.363244	+	0.712906i	−0.998221	−	0.0596250i	$-0.981010\pi$
$293$	−6.21773	+	12.2030i	−0.363244	+	0.712906i	0.634977	+	0.772531i	$0.281010\pi$
$294$	11.1224	−	4.47915i	0.648670	−	0.261229i
$295$	1.41743	−	30.6118i	0.0825261	−	1.78229i
$296$	8.72231	−	2.83405i	0.506974	−	0.164726i
$297$	26.6850	−	1.30798i	1.54842	−	0.0758969i
$298$	−1.36000	+	8.58672i	−0.0787828	+	0.497415i
$299$	1.79471	−	5.52355i	0.103791	−	0.319435i
$300$	3.74650	+	7.80793i	0.216304	+	0.450791i
$301$	−0.824568	−	2.53776i	−0.0475273	−	0.146274i
$302$	−3.83274	−	1.95288i	−0.220549	−	0.112375i
$303$	1.50820	−	17.0177i	0.0866437	−	0.977642i
$304$			5.43416i			0.311671i
$305$	−16.8011	−	25.5298i	−0.962031	−	1.46183i
$306$	−10.4816	+	1.44898i	−0.599190	+	0.0828329i
$307$	−2.20041	−	13.8928i	−0.125584	−	0.792905i	−0.967421	−	0.253173i	$-0.918526\pi$
$307$	−2.20041	−	13.8928i	−0.125584	−	0.792905i	0.841837	−	0.539732i	$-0.181474\pi$
$308$	1.41224	+	0.223677i	0.0804700	+	0.0127452i
$309$	−24.7855	−	15.5266i	−1.41000	−	0.883276i
$310$	9.24834	−	8.33476i	0.525270	−	0.473383i
$311$		−	5.28439i		−	0.299650i	−0.988712	−	0.149825i	$-0.952129\pi$
$311$		−	5.28439i		−	0.299650i	0.988712	−	0.149825i	$-0.0478711\pi$
$312$	2.18888	+	1.90710i	0.123921	+	0.107968i
$313$	−22.7781	+	3.60770i	−1.28750	+	0.203919i	−0.762390	−	0.647118i	$-0.775974\pi$
$313$	−22.7781	+	3.60770i	−1.28750	+	0.203919i	−0.525106	+	0.851037i	$0.675974\pi$
$314$	−0.827525	+	2.54686i	−0.0466999	+	0.143728i
$315$	−0.458235	−	1.80832i	−0.0258186	−	0.101887i
$316$	−11.8650			−0.667457
$317$	0.580282	+	1.13887i	0.0325919	+	0.0639651i	0.906728	−	0.421715i	$-0.138572\pi$
$317$	0.580282	+	1.13887i	0.0325919	+	0.0639651i	−0.874136	+	0.485680i	$0.838572\pi$
$318$	−8.40272	+	5.03597i	−0.471201	+	0.282403i
$319$	−23.2157	+	7.54324i	−1.29983	+	0.422340i
$320$	−0.788608	+	2.09239i	−0.0440845	+	0.116968i
$321$	−14.5080	+	12.1458i	−0.809759	+	0.677914i
$322$	−0.951717	−	0.150737i	−0.0530371	−	0.00840025i
$323$	−2.99834	−	18.9307i	−0.166832	−	1.05333i
$324$	3.11630	−	8.44326i	0.173128	−	0.469070i
$325$	−2.07032	+	8.12089i	−0.114841	+	0.450466i
$326$	−10.6704	+	14.6866i	−0.590981	+	0.813416i
$327$	3.35475	+	5.59753i	0.185518	+	0.309544i
$328$	1.54967	−	0.245443i	0.0855661	−	0.0135523i
$329$	2.23501	−	1.62383i	0.123220	−	0.0895247i
$330$	−5.72765	+	19.0722i	−0.315297	+	1.04989i
$331$	18.3505	−	13.3324i	1.00863	−	0.732815i	0.0447110	−	0.999000i	$-0.485763\pi$
$331$	18.3505	−	13.3324i	1.00863	−	0.732815i	0.963922	+	0.266185i	$0.0857633\pi$
$332$	8.57942	+	4.37143i	0.470857	+	0.239914i
$333$	0.542227	−	27.5082i	0.0297139	−	1.50744i
$334$	11.2439	+	3.65337i	0.615240	+	0.199904i
$335$	−7.02219	+	34.0552i	−0.383663	+	1.86064i
$336$	0.255703	−	0.408185i	0.0139497	−	0.0222683i
$337$	3.56839	−	1.81818i	0.194382	−	0.0990427i	−0.354090	−	0.935211i	$-0.615209\pi$
$337$	3.56839	−	1.81818i	0.194382	−	0.0990427i	0.548473	+	0.836168i	$0.315209\pi$
$338$	−1.59416	−	10.0651i	−0.0867109	−	0.547471i
$339$	2.01004	+	29.2184i	0.109170	+	1.58693i
$340$	1.59275	−	7.72428i	0.0863789	−	0.418908i
$341$	28.6273	+	0.161467i	1.55026	+	0.00874395i
$342$	15.4023	+	5.34233i	0.832861	+	0.288880i
$343$	0.605672	−	3.82406i	0.0327032	−	0.206480i
$344$	7.76281	+	5.64001i	0.418543	+	0.304089i
$345$	3.85989	−	12.8529i	0.207809	−	0.691975i
$346$	1.76593			0.0949370
$347$	−23.3878	+	23.3878i	−1.25552	+	1.25552i	−0.302312	+	0.953209i	$0.597758\pi$
$347$	−23.3878	+	23.3878i	−1.25552	+	1.25552i	−0.953209	+	0.302312i	$0.902242\pi$
$348$	−0.725919	+	8.19088i	−0.0389133	+	0.439077i
$349$	16.6090	−	5.39658i	0.889058	−	0.288872i	0.171345	−	0.985211i	$-0.445189\pi$
$349$	16.6090	−	5.39658i	0.889058	−	0.288872i	0.717713	+	0.696339i	$0.245189\pi$
$350$	1.38449	+	0.128489i	0.0740042	+	0.00686802i
$351$	7.55726	−	4.32916i	0.403377	−	0.231073i
$352$	−4.58129	+	2.33428i	−0.244184	+	0.124418i
$353$	1.05343	+	0.166847i	0.0560685	+	0.00888039i	0.184406	−	0.982850i	$-0.440964\pi$
$353$	1.05343	+	0.166847i	0.0560685	+	0.00888039i	−0.128337	+	0.991731i	$0.540964\pi$
$354$	−8.86729	−	22.0188i	−0.471291	−	1.17028i
$355$	−6.14605	−	4.91531i	−0.326199	−	0.260878i
$356$	−0.638915	+	0.879390i	−0.0338624	+	0.0466076i
$357$	−0.665562	+	1.56306i	−0.0352253	+	0.0827260i
$358$	12.3641	+	6.29983i	0.653464	+	0.332957i
$359$	22.1268	+	16.0760i	1.16781	+	0.848461i	0.990745	−	0.135739i	$-0.0433409\pi$
$359$	22.1268	+	16.0760i	1.16781	+	0.848461i	0.177061	+	0.984200i	$0.443341\pi$
$360$	5.15528	+	4.29222i	0.271707	+	0.226220i
$361$	−3.25399	+	10.0148i	−0.171263	+	0.527093i
$362$	0.779062	−	4.91880i	0.0409466	−	0.258527i
$363$	−22.9343	+	13.7451i	−1.20374	+	0.721433i
$364$	0.443298	−	0.144036i	0.0232351	−	0.00754955i
$365$	2.50971	−	4.40873i	0.131364	−	0.230764i
$366$	−20.0620	−	12.5676i	−1.04866	−	0.656920i
$367$	−3.19521	−	3.19521i	−0.166789	−	0.166789i	0.618778	−	0.785566i	$-0.287628\pi$
$367$	−3.19521	−	3.19521i	−0.166789	−	0.166789i	−0.785566	+	0.618778i	$0.787628\pi$
$368$	3.08735	−	1.57308i	0.160939	−	0.0820027i
$369$	0.827807	−	4.63359i	0.0430939	−	0.241215i
$370$	19.1897	+	7.23247i	0.997624	+	0.375998i
$371$			1.57283i			0.0816574i
$372$	3.82807	−	8.85132i	0.198476	−	0.458920i
$373$	−12.0359	+	12.0359i	−0.623195	+	0.623195i	−0.946347	−	0.323152i	$-0.895257\pi$
$373$	−12.0359	+	12.0359i	−0.623195	+	0.623195i	0.323152	+	0.946347i	$0.395257\pi$
$374$	14.6717	−	10.6596i	0.758654	−	0.551194i
$375$	−4.36206	+	18.8672i	−0.225256	+	0.974300i
$376$	−3.06988	+	9.44813i	−0.158317	+	0.487250i
$377$	−5.62679	+	5.62679i	−0.289794	+	0.289794i
$378$	−0.905556	−	1.12604i	−0.0465768	−	0.0579171i
$379$	−25.2934	−	8.21832i	−1.29923	−	0.422147i	−0.423919	−	0.905700i	$-0.639346\pi$
$379$	−25.2934	−	8.21832i	−1.29923	−	0.422147i	−0.875315	+	0.483553i	$0.839346\pi$
$380$	−7.58933	+	9.48962i	−0.389324	+	0.486807i
$381$	−18.3607	−	4.59983i	−0.940647	−	0.235657i
$382$	−2.88294	−	0.456613i	−0.147504	−	0.0233623i
$383$	2.49731	−	1.27244i	0.127607	−	0.0650189i	−0.389022	−	0.921229i	$-0.627187\pi$
$383$	2.49731	−	1.27244i	0.127607	−	0.0650189i	0.516628	+	0.856210i	$0.327187\pi$
$384$	0.118873	+	1.72797i	0.00606621	+	0.0881799i
$385$	2.15380	+	2.36294i	0.109768	+	0.120426i
$386$	−10.3455	+	3.36147i	−0.526575	+	0.171094i
$387$	23.6174	−	16.4578i	1.20054	−	0.836596i
$388$	−3.27836	+	0.519242i	−0.166434	+	0.0263605i
$389$	2.76240	+	8.50181i	0.140059	+	0.431059i	0.996343	−	0.0854479i	$-0.0272321\pi$
$389$	2.76240	+	8.50181i	0.140059	+	0.431059i	−0.856283	+	0.516507i	$0.827232\pi$
$390$	1.15896	+	6.38732i	0.0586863	+	0.323434i
$391$	−9.88731	+	7.18355i	−0.500023	+	0.363288i
$392$	3.14283	+	6.16814i	0.158737	+	0.311538i
$393$	−4.52028	+	5.18816i	−0.228018	+	0.261708i
$394$	−0.239886	+	0.0779437i	−0.0120853	+	0.00392675i
$395$	−20.7197	−	16.5706i	−1.04252	−	0.833755i
$396$	2.11230	+	15.2798i	0.106147	+	0.767838i
$397$	1.69411	+	1.69411i	0.0850250	+	0.0850250i	0.748340	−	0.663315i	$-0.230851\pi$
$397$	1.69411	+	1.69411i	0.0850250	+	0.0850250i	−0.663315	+	0.748340i	$0.730851\pi$
$398$	16.1657	+	16.1657i	0.810315	+	0.810315i
$399$	2.00697	−	1.68019i	0.100474	−	0.0841148i
$400$	−4.29936	+	2.55255i	−0.214968	+	0.127627i
$401$	−1.16316	−	1.60095i	−0.0580852	−	0.0799474i	0.778986	−	0.627041i	$-0.215734\pi$
$401$	−1.16316	−	1.60095i	−0.0580852	−	0.0799474i	−0.837071	+	0.547094i	$0.815734\pi$
$402$	6.02923	+	26.2505i	0.300711	+	1.30926i
$403$	8.33888	−	4.18980i	0.415389	−	0.208709i
$404$	9.86369			0.490737
$405$	17.2338	−	10.3922i	0.856353	−	0.516390i
$406$	1.06809	+	0.776015i	0.0530086	+	0.0385130i
$407$	21.4081	+	42.0158i	1.06116	+	2.08265i
$408$	−1.36753	−	5.95405i	−0.0677028	−	0.294769i
$409$		−	8.28461i		−	0.409647i	−0.978799	−	0.204824i	$-0.934338\pi$
$409$		−	8.28461i		−	0.409647i	0.978799	−	0.204824i	$-0.0656621\pi$
$410$	3.04895	+	1.73564i	0.150577	+	0.0857173i
$411$	−0.357269	+	1.42607i	−0.0176228	+	0.0703430i
$412$	7.66601	−	15.0454i	0.377677	−	0.741233i
$413$	−3.76419	−	0.596189i	−0.185224	−	0.0293366i
$414$	−1.42349	−	10.2971i	−0.0699606	−	0.506076i
$415$	8.87702	+	19.6158i	0.435756	+	0.962900i
$416$	−0.985202	+	1.35601i	−0.0483035	+	0.0664841i
$417$	−6.72401	−	11.2193i	−0.329276	−	0.549410i
$418$	−27.5969	+	4.37091i	−1.34981	+	0.213788i
$419$	−20.3613	−	14.7934i	−0.994717	−	0.722704i	−0.0337680	−	0.999430i	$-0.510751\pi$
$419$	−20.3613	−	14.7934i	−0.994717	−	0.722704i	−0.960949	+	0.276726i	$0.910751\pi$
$420$	1.01660	−	0.355695i	0.0496050	−	0.0173562i
$421$	−11.9165	−	8.65783i	−0.580774	−	0.421957i	0.258229	−	0.966084i	$-0.416861\pi$
$421$	−11.9165	−	8.65783i	−0.580774	−	0.421957i	−0.839003	+	0.544127i	$0.816861\pi$
$422$	−0.763562	+	4.82094i	−0.0371696	+	0.234680i
$423$	23.7613	+	17.9896i	1.15531	+	0.874683i
$424$	−3.32444	−	4.57570i	−0.161449	−	0.222216i
$425$	13.5691	−	11.2644i	0.658198	−	0.546404i
$426$	−5.91320	−	1.48141i	−0.286496	−	0.0717747i
$427$	−3.38659	+	1.72556i	−0.163889	+	0.0835055i
$428$	−7.72446	−	7.72446i	−0.373376	−	0.373376i
$429$	−7.92441	+	12.6499i	−0.382594	+	0.610745i
$430$	5.67929	+	20.6906i	0.273880	+	0.997789i
$431$	4.18735	−	5.76339i	0.201697	−	0.277613i	−0.696172	−	0.717875i	$-0.745115\pi$
$431$	4.18735	−	5.76339i	0.201697	−	0.277613i	0.897869	+	0.440263i	$0.145115\pi$
$432$	5.01452	+	1.36184i	0.241261	+	0.0655214i
$433$	0.626603	−	0.626603i	0.0301126	−	0.0301126i	−0.691890	−	0.722003i	$-0.743222\pi$
$433$	0.626603	−	0.626603i	0.0301126	−	0.0301126i	0.722003	+	0.691890i	$0.243222\pi$
$434$	−0.903006	−	1.25774i	−0.0433457	−	0.0603734i
$435$	−12.7070	+	13.2898i	−0.609254	+	0.637198i
$436$	−3.04813	+	2.21460i	−0.145979	+	0.106060i
$437$	18.5976	−	2.94558i	0.889646	−	0.140906i
$438$	0.346897	−	3.91421i	0.0165754	−	0.187028i
$439$			36.6646i			1.74990i	0.484210	+	0.874952i	$0.339107\pi$
$439$			36.6646i			1.74990i	−0.484210	+	0.874952i	$0.660893\pi$
$440$	−11.2603	−	2.32187i	−0.536814	−	0.110691i
$441$	20.5724	−	2.84395i	0.979636	−	0.135426i
$442$	2.68391	−	5.26748i	0.127661	−	0.250548i
$443$	3.50967	−	6.88812i	0.166749	−	0.327264i	−0.792477	−	0.609901i	$-0.791209\pi$
$443$	3.50967	−	6.88812i	0.166749	−	0.327264i	0.959227	+	0.282637i	$0.0912091\pi$
$444$	15.8475	−	1.09021i	0.752089	−	0.0517389i
$445$	−2.34388	+	0.643364i	−0.111111	+	0.0304984i
$446$	−0.583502	−	0.803122i	−0.0276296	−	0.0380289i
$447$	−5.89927	+	13.8543i	−0.279026	+	0.655288i
$448$	0.247778	+	0.126249i	0.0117064	+	0.00596472i
$449$	2.94452	+	2.13932i	0.138960	+	0.100961i	0.655094	−	0.755548i	$-0.272629\pi$
$449$	2.94452	+	2.13932i	0.138960	+	0.100961i	−0.516133	+	0.856508i	$0.672629\pi$
$450$	3.00811	+	14.6953i	0.141804	+	0.692742i
$451$	2.49292	+	7.67241i	0.117387	+	0.361280i
$452$	−16.7010	+	2.64517i	−0.785547	+	0.124418i
$453$	−5.61749	−	4.89434i	−0.263933	−	0.229956i
$454$	17.1375	+	5.56832i	0.804304	+	0.261334i
$455$	0.975286	+	0.367579i	0.0457221	+	0.0172324i
$456$	−2.28733	+	9.13009i	−0.107114	+	0.427556i
$457$	4.51963	−	8.87027i	0.211419	−	0.414934i	−0.760806	−	0.648979i	$-0.775196\pi$
$457$	4.51963	−	8.87027i	0.211419	−	0.414934i	0.972226	+	0.234045i	$0.0751964\pi$
$458$	22.8200	−	11.6274i	1.06631	−	0.543313i
$459$	−18.2202	−	1.97738i	−0.850448	−	0.0922960i
$460$	7.58837	+	1.56472i	0.353810	+	0.0729556i
$461$	2.39102	+	0.776890i	0.111361	+	0.0361834i	0.364167	−	0.931333i	$-0.381354\pi$
$461$	2.39102	+	0.776890i	0.111361	+	0.0361834i	−0.252806	+	0.967517i	$0.581354\pi$
$462$	2.27860	+	0.970242i	0.106010	+	0.0451398i
$463$	0.378276	−	2.38834i	0.0175800	−	0.110996i	−0.977338	−	0.211685i	$-0.932105\pi$
$463$	0.378276	−	2.38834i	0.0175800	−	0.110996i	0.994918	+	0.100690i	$0.0321049\pi$
$464$	−4.74754			−0.220399
$465$	19.0466	−	10.1107i	0.883266	−	0.468872i
$466$	−17.5471			−0.812852
$467$	6.47353	−	40.8723i	0.299559	−	1.89134i	−0.135237	−	0.990813i	$-0.543179\pi$
$467$	6.47353	−	40.8723i	0.299559	−	1.89134i	0.434796	−	0.900529i	$-0.356821\pi$
$468$	2.87486	+	4.12550i	0.132891	+	0.190701i
$469$	4.11272	+	1.33630i	0.189908	+	0.0617048i
$470$	−18.5561	+	12.2118i	−0.855930	+	0.563287i
$471$	−2.46236	+	3.93073i	−0.113460	+	0.181119i
$472$	12.2110	−	6.22180i	0.562055	−	0.286381i
$473$	−22.3983	+	43.9591i	−1.02987	+	2.02124i
$474$	−19.9347	−	4.99416i	−0.915630	−	0.229389i
$475$	−26.5063	+	5.97239i	−1.21619	+	0.274032i
$476$	−0.932833	−	0.303096i	−0.0427563	−	0.0138924i
$477$	−16.2374	+	4.92424i	−0.743458	+	0.225465i
$478$	10.9074	−	1.72756i	0.498893	−	0.0790168i
$479$	−5.07755	−	15.6271i	−0.231999	−	0.714020i	−0.997505	−	0.0705912i	$-0.977511\pi$
$479$	−5.07755	−	15.6271i	−0.231999	−	0.714020i	0.765506	−	0.643428i	$-0.222489\pi$
$480$	−2.20568	+	3.18355i	−0.100675	+	0.145308i
$481$	12.4363	+	9.03547i	0.567045	+	0.411982i
$482$	−3.07193	−	1.56523i	−0.139923	−	0.0712942i
$483$	−1.53556	−	0.653851i	−0.0698703	−	0.0297512i
$484$	−9.07370	−	12.4889i	−0.412441	−	0.567676i
$485$	−6.45014	−	3.67180i	−0.292886	−	0.166728i
$486$	8.78969	−	12.8741i	0.398709	−	0.583979i
$487$	15.1225	−	29.6795i	0.685265	−	1.34491i	−0.241917	−	0.970297i	$-0.577776\pi$
$487$	15.1225	−	29.6795i	0.685265	−	1.34491i	0.927182	−	0.374611i	$-0.122224\pi$
$488$	6.20507	−	12.1781i	0.280890	−	0.551278i
$489$	−24.1095	+	20.1840i	−1.09027	+	0.912753i
$490$	−3.12612	+	15.1606i	−0.141224	+	0.684886i
$491$			9.94568i			0.448842i	0.974492	+	0.224421i	$0.0720491\pi$
$491$			9.94568i			0.448842i	−0.974492	+	0.224421i	$0.927951\pi$
$492$	2.70695	+	0.239904i	0.122039	+	0.0108157i
$493$	16.5388	−	2.61949i	0.744870	−	0.117976i
$494$	−7.36881	+	5.35375i	−0.331538	+	0.240877i
$495$	−17.6510	+	29.6329i	−0.793353	+	1.33190i
$496$	5.28547	+	1.75037i	0.237325	+	0.0785941i
$497$	−0.692067	+	0.692067i	−0.0310434	+	0.0310434i
$498$	12.5745	+	10.9558i	0.563478	+	0.490941i
$499$	−10.3016	+	14.1790i	−0.461164	+	0.634737i	−0.974750	−	0.223301i	$-0.928317\pi$
$499$	−10.3016	+	14.1790i	−0.461164	+	0.634737i	0.513586	+	0.858038i	$0.328317\pi$
$500$	−11.0728	−	1.54698i	−0.495191	−	0.0691829i
$501$	17.3535	+	10.8709i	0.775295	+	0.485675i
$502$	−17.2227	−	17.2227i	−0.768686	−	0.768686i
$503$	−17.7955	+	9.06727i	−0.793463	+	0.404290i	−0.803235	−	0.595662i	$-0.796890\pi$
$503$	−17.7955	+	9.06727i	−0.793463	+	0.404290i	0.00977146	+	0.999952i	$0.496890\pi$
$504$	0.601425	−	0.578174i	0.0267896	−	0.0257539i
$505$	17.2248	+	13.7756i	0.766495	+	0.613005i
$506$	10.4720	+	14.4135i	0.465538	+	0.640759i
$507$	1.55818	−	17.5817i	0.0692014	−	0.780832i
$508$	1.70954	−	10.7936i	0.0758485	−	0.478889i
$509$	11.0189	+	8.00567i	0.488402	+	0.354845i	0.804570	−	0.593858i	$-0.202396\pi$
$509$	11.0189	+	8.00567i	0.488402	+	0.354845i	−0.316167	+	0.948703i	$0.602396\pi$
$510$	5.92729	−	12.3074i	0.262465	−	0.544979i
$511$	−0.510413	−	0.370837i	−0.0225794	−	0.0164049i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	23.6292	+	15.4589i	1.04325	+	0.682526i
$514$	13.3985	−	18.4415i	0.590982	−	0.813418i
$515$	34.3994	−	15.5673i	1.51582	−	0.685976i
$516$	10.6685	+	12.7434i	0.469656	+	0.560998i
$517$	−50.4506	−	7.99059i	−2.21881	−	0.351426i
$518$	1.15786	−	2.27242i	0.0508733	−	0.0998444i
$519$	2.96699	+	0.743308i	0.130236	+	0.0326276i
$520$	−3.61425	+	0.992064i	−0.158495	+	0.0435049i
$521$			12.8760i			0.564106i	0.959399	+	0.282053i	$0.0910154\pi$
$521$			12.8760i			0.564106i	−0.959399	+	0.282053i	$0.908985\pi$
$522$	−4.66731	+	13.4562i	−0.204283	+	0.588961i
$523$	−3.72517	−	7.31106i	−0.162890	−	0.319690i	0.795106	−	0.606470i	$-0.207415\pi$
$523$	−3.72517	−	7.31106i	−0.162890	−	0.319690i	−0.957996	+	0.286780i	$0.907415\pi$
$524$	−3.21408	−	2.33517i	−0.140408	−	0.102012i
$525$	2.27204	+	0.798633i	0.0991599	+	0.0348552i
$526$	−2.22695			−0.0970995
$527$	−19.3785	−	3.18140i	−0.844142	−	0.138584i
$528$	−8.67969	+	1.99356i	−0.377735	+	0.0867584i
$529$	6.46191	+	8.89406i	0.280953	+	0.386698i
$530$	0.584969	−	12.6334i	0.0254094	−	0.548759i
$531$	−5.63012	−	40.7267i	−0.244326	−	1.76739i
$532$	1.06856	+	1.06856i	0.0463281	+	0.0463281i
$533$	1.85956	+	1.85956i	0.0805465	+	0.0805465i
$534$	−1.44361	+	1.20856i	−0.0624710	+	0.0522995i
$535$	−2.70119	−	24.2771i	−0.116783	−	1.04959i
$536$	−14.7893	+	4.80533i	−0.638799	+	0.207558i
$537$	18.1216	+	15.7888i	0.782005	+	0.681336i
$538$	−4.04564	−	7.94001i	−0.174420	−	0.342318i
$539$	−28.7964	+	20.9218i	−1.24035	+	0.901166i
$540$	6.85486	+	9.38141i	0.294986	+	0.403712i
$541$	−5.18368	−	15.9537i	−0.222864	−	0.685904i	−0.998501	−	0.0547254i	$-0.982572\pi$
$541$	−5.18368	−	15.9537i	−0.222864	−	0.685904i	0.775638	−	0.631178i	$-0.217428\pi$
$542$	18.4505	−	2.92228i	0.792518	−	0.125522i
$543$	3.37933	−	7.93630i	0.145021	−	0.340579i
$544$	3.35445	−	1.08993i	0.143821	−	0.0467302i
$545$	−8.41582	−	0.389681i	−0.360494	−	0.0166921i
$546$	0.805424	−	0.0554080i	0.0344690	−	0.00237124i
$547$	20.2906	−	10.3386i	0.867566	−	0.442047i	0.0372275	−	0.999307i	$-0.488147\pi$
$547$	20.2906	−	10.3386i	0.867566	−	0.442047i	0.830338	+	0.557260i	$0.188147\pi$
$548$	−0.838338	−	0.132780i	−0.0358120	−	0.00567207i
$549$	−28.4168	−	29.5596i	−1.21280	−	1.26157i
$550$	−16.4210	−	19.7807i	−0.700194	−	0.843454i
$551$	−24.5362	−	7.97231i	−1.04528	−	0.339632i
$552$	5.84928	−	1.34347i	0.248962	−	0.0571817i
$553$	−2.33310	+	2.33310i	−0.0992137	+	0.0992137i
$554$	−1.37754	+	4.23965i	−0.0585263	+	0.180125i
$555$	29.1969	+	20.2287i	1.23934	+	0.858661i
$556$	6.10945	−	4.43878i	0.259098	−	0.188246i
$557$	−11.5147	+	11.5147i	−0.487894	+	0.487894i	−0.907641	−	0.419747i	$-0.862119\pi$
$557$	−11.5147	+	11.5147i	−0.487894	+	0.487894i	0.419747	+	0.907641i	$0.362119\pi$
$558$	10.1573	−	13.2601i	0.429993	−	0.561343i
$559$			16.0830i			0.680240i
$560$	0.256373	+	0.566514i	0.0108337	+	0.0239396i
$561$	29.1371	−	11.7339i	1.23017	−	0.495407i
$562$	6.17558	−	3.14662i	0.260501	−	0.132732i
$563$	−26.8411	−	26.8411i	−1.13122	−	1.13122i	−0.989975	−	0.141242i	$-0.954890\pi$
$563$	−26.8411	−	26.8411i	−1.13122	−	1.13122i	−0.141242	−	0.989975i	$-0.545110\pi$
$564$	−9.13467	+	14.5819i	−0.384639	+	0.614009i
$565$	−32.8589	−	18.7052i	−1.38238	−	0.786935i
$566$	29.8082	−	9.68526i	1.25293	−	0.407102i
$567$	−1.04748	−	2.27305i	−0.0439901	−	0.0954591i
$568$	0.550570	−	3.47616i	0.0231014	−	0.145857i
$569$	−11.6647	+	35.9004i	−0.489011	+	1.50502i	0.337075	+	0.941478i	$0.390562\pi$
$569$	−11.6647	+	35.9004i	−0.489011	+	1.50502i	−0.826086	+	0.563544i	$0.809438\pi$
$570$	−16.7454	+	12.7493i	−0.701387	+	0.534009i
$571$	−19.3759	−	14.0774i	−0.810855	−	0.589121i	0.103223	−	0.994658i	$-0.467084\pi$
$571$	−19.3759	−	14.0774i	−0.810855	−	0.589121i	−0.914078	+	0.405537i	$0.867084\pi$
$572$	−7.67882	−	3.91255i	−0.321068	−	0.163592i
$573$	−4.65151	−	1.98064i	−0.194320	−	0.0827426i
$574$	0.256460	−	0.352987i	0.0107044	−	0.0147334i
$575$	11.0662	+	13.3303i	0.461492	+	0.555913i
$576$	−0.527607	+	2.95324i	−0.0219836	+	0.123052i
$577$	4.45608	+	0.705773i	0.185509	+	0.0293817i	0.248498	−	0.968633i	$-0.420063\pi$
$577$	4.45608	+	0.705773i	0.185509	+	0.0293817i	−0.0629886	+	0.998014i	$0.520063\pi$
$578$	4.06274	−	2.07007i	0.168988	−	0.0861036i
$579$	−18.7967	+	1.29309i	−0.781166	+	0.0537392i
$580$	−8.29058	−	6.63039i	−0.344247	−	0.275312i
$581$	2.54663	−	0.827451i	0.105652	−	0.0343284i
$582$	−5.72663	−	0.507524i	−0.237376	−	0.0210375i
$583$	20.5632	−	20.5632i	0.851643	−	0.851643i
$584$	2.26873			0.0938805
$585$	−0.741320	+	11.2193i	−0.0306498	+	0.463862i
$586$	−11.0801	−	8.05015i	−0.457714	−	0.332549i
$587$	−6.95910	+	43.9380i	−0.287233	+	1.81352i	0.247941	+	0.968775i	$0.420246\pi$
$587$	−6.95910	+	43.9380i	−0.287233	+	1.81352i	−0.535174	+	0.844742i	$0.679754\pi$
$588$	2.68408	+	11.6861i	0.110689	+	0.481928i
$589$	24.3770	+	17.9219i	1.00444	+	0.738459i
$590$	30.0132	+	6.18872i	1.23562	+	0.254786i
$591$	−0.435847	+	0.0299835i	−0.0179284	+	0.00123336i
$592$	1.43469	+	9.05827i	0.0589653	+	0.372293i
$593$	−24.3364	+	12.4000i	−0.999375	+	0.509207i	−0.875566	−	0.483099i	$-0.839511\pi$
$593$	−24.3364	+	12.4000i	−0.999375	+	0.509207i	−0.123809	+	0.992306i	$0.539511\pi$
$594$	−2.88258	+	26.5611i	−0.118274	+	1.08982i
$595$	−1.20569	−	1.83208i	−0.0494286	−	0.0751081i
$596$	−8.26825	−	2.68652i	−0.338681	−	0.110044i
$597$	20.3561	+	33.9649i	0.833119	+	1.39009i
$598$	5.17479	+	2.63669i	0.211613	+	0.107822i
$599$	22.6168	−	16.4321i	0.924099	−	0.671397i	−0.0204418	−	0.999791i	$-0.506507\pi$
$599$	22.6168	−	16.4321i	0.924099	−	0.671397i	0.944541	+	0.328394i	$0.106507\pi$
$600$	−8.29788	+	2.47894i	−0.338760	+	0.101202i
$601$	−38.9709	+	28.3140i	−1.58966	+	1.15495i	−0.685224	+	0.728332i	$0.740296\pi$
$601$	−38.9709	+	28.3140i	−1.58966	+	1.15495i	−0.904431	+	0.426620i	$0.859704\pi$
$602$	2.63550	−	0.417423i	0.107415	−	0.0170129i
$603$	−0.919384	+	46.6420i	−0.0374402	+	1.89941i
$604$	2.52841	−	3.48005i	0.102879	−	0.141601i
$605$	1.59661	−	34.4815i	0.0649114	−	1.40187i
$606$	16.5723	+	4.15179i	0.673202	+	0.168655i
$607$	4.66910	+	29.4795i	0.189513	+	1.19654i	0.880634	+	0.473798i	$0.157117\pi$
$607$	4.66910	+	29.4795i	0.189513	+	1.19654i	−0.691121	+	0.722739i	$0.742883\pi$
$608$	−5.36726	−	0.850091i	−0.217671	−	0.0344757i
$609$	1.46790	+	1.75338i	0.0594821	+	0.0710506i
$610$	27.8438	−	12.6006i	1.12736	−	0.510182i
$611$	−15.8363	+	5.14551i	−0.640667	+	0.208165i
$612$	0.208531	−	10.5792i	0.00842938	−	0.427638i
$613$	−6.72653	−	13.2016i	−0.271682	−	0.533206i	0.714345	−	0.699794i	$-0.246725\pi$
$613$	−6.72653	−	13.2016i	−0.271682	−	0.533206i	−0.986027	+	0.166588i	$0.946725\pi$
$614$	14.0660			0.567657
$615$	4.39207	+	4.19945i	0.177105	+	0.169338i
$616$	−0.441847	+	1.35986i	−0.0178025	+	0.0547905i
$617$	−1.70538	+	0.270106i	−0.0686560	+	0.0108740i	−0.190668	−	0.981655i	$-0.561065\pi$
$617$	−1.70538	+	0.270106i	−0.0686560	+	0.0108740i	0.122012	+	0.992529i	$0.461065\pi$
$618$	19.2127	−	22.0514i	0.772849	−	0.887039i
$619$			6.55143i			0.263324i	0.991295	+	0.131662i	$0.0420314\pi$
$619$			6.55143i			0.263324i	−0.991295	+	0.131662i	$0.957969\pi$
$620$	6.78539	+	10.4383i	0.272508	+	0.419213i
$621$	1.94258	−	17.8997i	0.0779532	−	0.718288i
$622$	5.21933	+	0.826661i	0.209276	+	0.0331461i
$623$	0.0472867	+	0.298557i	0.00189450	+	0.0119614i
$624$	−2.22603	+	1.86359i	−0.0891127	+	0.0746033i
$625$	−17.1758	−	18.1657i	−0.687032	−	0.726627i
$626$		−	23.0621i		−	0.921745i
$627$	−48.2060	−	4.27227i	−1.92516	−	0.170618i
$628$	−2.38605	−	1.21575i	−0.0952138	−	0.0485138i
$629$	−9.99592	−	30.7643i	−0.398563	−	1.22665i
$630$	1.85774	−	0.169710i	0.0740140	−	0.00676141i
$631$	−12.2555	+	37.7185i	−0.487883	+	1.50155i	0.339878	+	0.940470i	$0.389614\pi$
$631$	−12.2555	+	37.7185i	−0.487883	+	1.50155i	−0.827761	+	0.561081i	$0.810386\pi$
$632$	1.85609	−	11.7189i	0.0738313	−	0.466152i
$633$	−3.31210	+	7.77841i	−0.131644	+	0.309164i
$634$	−1.21562	+	0.394979i	−0.0482785	+	0.0156866i
$635$	18.0596	−	16.4612i	0.716675	−	0.653243i
$636$	−3.65950	−	9.08707i	−0.145109	−	0.360326i
$637$	−5.26777	+	10.3386i	−0.208717	+	0.409630i
$638$	−3.81863	−	24.1099i	−0.151181	−	0.954520i
$639$	−9.31139	−	4.97792i	−0.368353	−	0.196924i
$640$	−1.94326	−	1.10622i	−0.0768143	−	0.0437272i
$641$	−3.47640	−	4.78485i	−0.137309	−	0.188990i	0.734825	−	0.678257i	$-0.237264\pi$
$641$	−3.47640	−	4.78485i	−0.137309	−	0.188990i	−0.872134	+	0.489267i	$0.837264\pi$
$642$	−9.72673	−	16.2294i	−0.383884	−	0.640525i
$643$	18.4514	+	9.40147i	0.727653	+	0.370758i	0.778244	−	0.627962i	$-0.216111\pi$
$643$	18.4514	+	9.40147i	0.727653	+	0.370758i	−0.0505912	+	0.998719i	$0.516111\pi$
$644$	0.297763	−	0.916419i	0.0117335	−	0.0361120i
$645$	0.832931	+	37.1533i	0.0327966	+	1.46291i
$646$	19.1667			0.754104
$647$	−1.90293	−	3.73470i	−0.0748117	−	0.146826i	0.850571	−	0.525860i	$-0.176256\pi$
$647$	−1.90293	−	3.73470i	−0.0748117	−	0.146826i	−0.925383	+	0.379034i	$0.876256\pi$
$648$	7.85181	+	4.39875i	0.308448	+	0.172799i
$649$	41.4185	+	57.0077i	1.62582	+	2.23775i
$650$	−7.69704	−	3.31522i	−0.301903	−	0.130033i
$651$	−0.987763	−	2.49325i	−0.0387135	−	0.0977182i
$652$	−12.8366	−	12.8366i	−0.502719	−	0.502719i
$653$	4.67056	+	0.739744i	0.182773	+	0.0289484i	0.247150	−	0.968977i	$-0.420506\pi$
$653$	4.67056	+	0.739744i	0.182773	+	0.0289484i	−0.0643769	+	0.997926i	$0.520506\pi$
$654$	−6.05342	+	2.43780i	−0.236707	+	0.0953256i
$655$	−2.35143	−	8.56664i	−0.0918780	−	0.334727i
$656$			1.56898i			0.0612585i
$657$	2.23038	−	6.43035i	0.0870156	−	0.250872i
$658$	1.25421	+	2.46152i	0.0488940	+	0.0959599i
$659$	4.69017	+	14.4349i	0.182703	+	0.562302i	0.999901	−	0.0140547i	$-0.00447391\pi$
$659$	4.69017	+	14.4349i	0.182703	+	0.562302i	−0.817198	+	0.576357i	$0.804474\pi$
$660$	−17.9414	−	8.64069i	−0.698369	−	0.336338i
$661$	25.0598	−	18.2070i	0.974712	−	0.708170i	0.0181913	−	0.999835i	$-0.494209\pi$
$661$	25.0598	−	18.2070i	0.974712	−	0.708170i	0.956521	+	0.291665i	$0.0942092\pi$
$662$	10.2976	+	20.2102i	0.400228	+	0.785491i
$663$	6.72648	−	7.72033i	0.261235	−	0.299833i
$664$	−5.65973	+	7.78995i	−0.219640	+	0.302309i
$665$	0.373669	+	3.35837i	0.0144903	+	0.130232i
$666$	27.0847	+	4.83878i	1.04951	+	0.187499i
$667$	2.57340	+	16.2478i	0.0996423	+	0.629117i
$668$	−5.36733	+	10.5340i	−0.207668	+	0.407572i
$669$	−0.642311	−	1.59495i	−0.0248332	−	0.0616645i
$670$	−32.5374	−	12.2631i	−1.25703	−	0.473767i
$671$	66.8364	+	21.7165i	2.58019	+	0.838355i
$672$	0.363159	+	0.316409i	0.0140092	+	0.0122057i
$673$	12.5051	+	6.37166i	0.482035	+	0.245609i	0.678083	−	0.734985i	$-0.262811\pi$
$673$	12.5051	+	6.37166i	0.482035	+	0.245609i	−0.196048	+	0.980594i	$0.562811\pi$
$674$	1.23758	+	3.80888i	0.0476698	+	0.146713i
$675$	−1.13148	+	25.9561i	−0.0435506	+	0.999051i
$676$	10.1906			0.391946
$677$	0.920959	−	0.920959i	0.0353953	−	0.0353953i	−0.689188	−	0.724583i	$-0.742032\pi$
$677$	0.920959	−	0.920959i	0.0353953	−	0.0353953i	0.724583	+	0.689188i	$0.242032\pi$
$678$	−29.1731	−	2.58548i	−1.12039	−	0.0992946i
$679$	−0.542548	+	0.746754i	−0.0208211	+	0.0286578i
$680$	7.38002	+	2.78148i	0.283011	+	0.106665i
$681$	26.4494	+	16.5690i	1.01354	+	0.634924i
$682$	−4.63778	+	28.2496i	−0.177590	+	1.08173i
$683$	−1.04960	−	1.04960i	−0.0401616	−	0.0401616i	0.686741	−	0.726902i	$-0.259041\pi$
$683$	−1.04960	−	1.04960i	−0.0401616	−	0.0401616i	−0.726902	+	0.686741i	$0.759041\pi$
$684$	−7.68601	+	14.3769i	−0.293882	+	0.549716i
$685$	−1.27854	−	1.40269i	−0.0488505	−	0.0535940i
$686$	3.68223	+	1.19643i	0.140588	+	0.0456799i
$687$	43.2348	−	9.93018i	1.64951	−	0.378860i
$688$	−6.78495	+	6.78495i	−0.258674	+	0.258674i
$689$	2.92947	−	9.01598i	0.111604	−	0.343481i
$690$	12.0908	+	5.82300i	0.460289	+	0.221678i
$691$	−7.49045	−	23.0532i	−0.284950	−	0.876986i	−0.986414	−	0.164281i	$-0.947470\pi$
$691$	−7.49045	−	23.0532i	−0.284950	−	0.876986i	0.701463	−	0.712705i	$-0.252530\pi$
$692$	−0.276252	+	1.74419i	−0.0105015	+	0.0663041i
$693$	3.41995	+	2.58923i	0.129913	+	0.0983567i
$694$	−19.4412	−	26.7585i	−0.737977	−	1.01574i
$695$	16.8680	+	0.781048i	0.639841	+	0.0296268i
$696$	−7.97648	−	1.99832i	−0.302348	−	0.0757460i
$697$	−0.865697	−	5.46580i	−0.0327906	−	0.207032i
$698$	2.73193	+	17.2487i	0.103405	+	0.652873i
$699$	−29.4813	−	7.38584i	−1.11509	−	0.279358i
$700$	−0.343489	+	1.34735i	−0.0129827	+	0.0509249i
$701$	8.24162	+	11.3436i	0.311282	+	0.428442i	0.935780	−	0.352583i	$-0.114697\pi$
$701$	8.24162	+	11.3436i	0.311282	+	0.428442i	−0.624499	+	0.781026i	$0.714697\pi$
$702$	3.09364	+	8.14145i	0.116762	+	0.307279i
$703$	−7.79634	+	49.2241i	−0.294044	+	1.85652i
$704$	−1.58887	−	4.89005i	−0.0598829	−	0.184301i
$705$	−36.3168	+	12.7068i	−1.36777	+	0.478565i
$706$	−0.329586	+	1.01436i	−0.0124041	+	0.0381760i
$707$	1.93958	−	1.93958i	0.0729453	−	0.0729453i
$708$	23.1348	−	5.31362i	0.869461	−	0.199698i
$709$	8.48101	+	2.75565i	0.318511	+	0.103491i	0.463909	−	0.885883i	$-0.346446\pi$
$709$	8.48101	+	2.75565i	0.318511	+	0.103491i	−0.145398	+	0.989373i	$0.546446\pi$
$710$	5.81625	−	5.30146i	0.218280	−	0.198960i
$711$	−31.3907	−	16.7816i	−1.17724	−	0.629361i
$712$	−0.768615	−	0.768615i	−0.0288051	−	0.0288051i
$713$	3.12542	−	19.0375i	0.117048	−	0.712962i
$714$	−1.43970	−	0.901884i	−0.0538794	−	0.0337522i
$715$	−7.94518	−	17.5567i	−0.297133	−	0.656582i
$716$	−8.15645	+	11.2264i	−0.304821	+	0.419550i
$717$	19.0530	+	1.68857i	0.711546	+	0.0630610i
$718$	−19.3395	+	19.3395i	−0.721744	+	0.721744i
$719$	−3.57501			−0.133325			−0.0666627	−	0.997776i	$-0.521235\pi$
$719$	−3.57501			−0.133325			−0.0666627	+	0.997776i	$0.521235\pi$
$720$	−5.04584	+	4.42036i	−0.188047	+	0.164737i
$721$	−1.45107	−	4.46593i	−0.0540406	−	0.166320i
$722$	−9.38243	−	4.78059i	−0.349178	−	0.177915i
$723$	−4.50241	−	3.92281i	−0.167446	−	0.145891i
$724$	4.73637	+	1.53894i	0.176026	+	0.0571943i
$725$	−5.21776	−	23.1572i	−0.193783	−	0.860035i
$726$	−9.98820	−	24.8022i	−0.370697	−	0.920495i
$727$	17.6554	−	34.6507i	0.654804	−	1.28513i	−0.289855	−	0.957071i	$-0.593607\pi$
$727$	17.6554	−	34.6507i	0.654804	−	1.28513i	0.944659	−	0.328054i	$-0.106393\pi$
$728$	0.0729158	+	0.460372i	0.00270244	+	0.0170625i
$729$	20.1867	−	17.9303i	0.747656	−	0.664087i
$730$	3.96185	+	3.16849i	0.146635	+	0.117271i
$731$	19.8928	−	27.3800i	0.735760	−	1.01269i
$732$	15.5513	−	17.8490i	0.574792	−	0.659718i
$733$	−16.6887	−	32.7535i	−0.616413	−	1.20978i	−0.962425	−	0.271548i	$-0.912464\pi$
$733$	−16.6887	−	32.7535i	−0.616413	−	1.20978i	0.346012	−	0.938230i	$-0.387536\pi$
$734$	3.65571	−	2.65603i	0.134935	−	0.0980359i
$735$	−11.6336	+	24.1559i	−0.429113	+	0.891005i
$736$	1.07075	+	3.29543i	0.0394683	+	0.121471i
$737$	−36.2990	−	71.2407i	−1.33709	−	2.62419i
$738$	4.44704	+	1.54247i	0.163698	+	0.0567790i
$739$		−	49.7837i		−	1.83132i	−0.401949	−	0.915662i	$-0.631667\pi$
$739$		−	49.7837i		−	1.83132i	0.401949	−	0.915662i	$-0.368333\pi$
$740$	−10.1454	+	17.8220i	−0.372951	+	0.655151i
$741$	−14.6340	+	5.89334i	−0.537594	+	0.216497i
$742$	−1.55347	−	0.246045i	−0.0570296	−	0.00903260i
$743$	−16.5605	−	16.5605i	−0.607545	−	0.607545i	0.334759	−	0.942304i	$-0.391345\pi$
$743$	−16.5605	−	16.5605i	−0.607545	−	0.607545i	−0.942304	+	0.334759i	$0.891345\pi$
$744$	8.14351	+	5.16559i	0.298555	+	0.189380i
$745$	−10.6868	−	16.2388i	−0.391533	−	0.594945i
$746$	−10.0049	−	13.7705i	−0.366305	−	0.504175i
$747$	16.5153	+	23.6999i	0.604265	+	0.867136i
$748$	8.23320	+	16.1586i	0.301036	+	0.590816i
$749$	−3.03785			−0.111001
$750$	−17.9526	−	7.25984i	−0.655535	−	0.265092i
$751$	10.6567	−	32.7980i	0.388869	−	1.19681i	−0.544766	−	0.838588i	$-0.683382\pi$
$751$	10.6567	−	32.7980i	0.388869	−	1.19681i	0.933635	−	0.358227i	$-0.116618\pi$
$752$	−8.85157	−	4.51010i	−0.322784	−	0.164466i
$753$	−21.6870	−	36.1856i	−0.790318	−	1.31868i
$754$	−4.67729	−	6.43774i	−0.170337	−	0.234449i
$755$	9.27555	−	2.54601i	0.337572	−	0.0926590i
$756$	1.25383	−	0.718256i	0.0456015	−	0.0261227i
$757$	−2.69246	−	16.9995i	−0.0978592	−	0.617859i	−0.987061	−	0.160344i	$-0.948740\pi$
$757$	−2.69246	−	16.9995i	−0.0978592	−	0.617859i	0.889202	−	0.457515i	$-0.151260\pi$
$758$	12.0739	−	23.6964i	0.438544	−	0.860691i
$759$	11.5275	+	28.6244i	0.418421	+	1.03900i
$760$	−8.18555	−	8.98039i	−0.296921	−	0.325753i
$761$	16.1488	−	5.24706i	0.585394	−	0.190206i	−0.00132174	−	0.999999i	$-0.500421\pi$
$761$	16.1488	−	5.24706i	0.585394	−	0.190206i	0.586715	+	0.809793i	$0.300421\pi$
$762$	7.41545	−	17.4151i	0.268633	−	0.630881i
$763$	−0.163905	+	1.03485i	−0.00593375	+	0.0374642i
$764$	0.901982	−	2.77602i	0.0326326	−	0.100433i
$765$	15.1390	−	18.1831i	0.547351	−	0.657410i
$766$	0.866113	+	2.66562i	0.0312939	+	0.0963128i
$767$	20.4671	+	10.4285i	0.739025	+	0.376552i
$768$	−1.72529	−	0.152904i	−0.0622560	−	0.00551745i
$769$		−	24.7513i		−	0.892556i	−0.894894	−	0.446278i	$-0.852749\pi$
$769$		−	24.7513i		−	0.892556i	0.894894	−	0.446278i	$-0.147251\pi$
$770$	−2.67077	+	1.75763i	−0.0962480	+	0.0633408i
$771$	30.2735	−	25.3444i	1.09027	−	0.912755i
$772$	−1.70169	−	10.7440i	−0.0612450	−	0.386686i
$773$	18.4991	+	2.92998i	0.665368	+	0.105384i	0.479977	−	0.877281i	$-0.340645\pi$
$773$	18.4991	+	2.92998i	0.665368	+	0.105384i	0.185391	+	0.982665i	$0.440645\pi$
$774$	12.5606	+	25.9012i	0.451481	+	0.930998i
$775$	−2.72885	+	27.7048i	−0.0980234	+	0.995184i
$776$		−	3.31923i		−	0.119153i
$777$	2.90184	−	3.33060i	0.104103	−	0.119484i
$778$	−8.82927	+	1.39842i	−0.316545	+	0.0501358i
$779$	−2.63472	+	8.10882i	−0.0943985	+	0.290529i
$780$	−6.48998	+	0.145497i	−0.232379	+	0.00520963i
$781$	18.0962			0.647533
$782$	−5.54839	−	10.8893i	−0.198410	−	0.389402i
$783$	−13.5056	+	20.6435i	−0.482651	+	0.737740i
$784$	−6.58385	+	2.13922i	−0.235137	+	0.0764008i
$785$	−2.46882	−	5.45540i	−0.0881158	−	0.194712i
$786$	−4.41716	−	5.27624i	−0.157555	−	0.188197i
$787$	−0.527979	−	0.0836237i	−0.0188204	−	0.00298086i	0.147017	−	0.989134i	$-0.453033\pi$
$787$	−0.527979	−	0.0836237i	−0.0188204	−	0.00298086i	−0.165838	+	0.986153i	$0.553033\pi$
$788$	−0.0394576	−	0.249126i	−0.00140562	−	0.00887474i
$789$	−3.74156	−	0.937358i	−0.133203	−	0.0333708i
$790$	19.6078	−	17.8724i	0.697615	−	0.635870i
$791$	−2.76390	+	3.80418i	−0.0982730	+	0.135261i
$792$	−15.4221	−	0.303993i	−0.548001	−	0.0108019i
$793$	22.6270	−	3.58376i	0.803507	−	0.127263i
$794$	−1.93827	+	1.40824i	−0.0687867	+	0.0499764i
$795$	6.30042	−	20.9795i	0.223453	−	0.744065i
$796$	−18.4956	+	13.4378i	−0.655559	+	0.476291i
$797$	5.58026	+	2.84329i	0.197663	+	0.100714i	0.550021	−	0.835151i	$-0.314620\pi$
$797$	5.58026	+	2.84329i	0.197663	+	0.100714i	−0.352357	+	0.935865i	$0.614620\pi$
$798$	1.34555	+	2.24510i	0.0476319	+	0.0794756i
$799$	33.3243	+	10.8277i	1.17893	+	0.383057i
$800$	−1.84856	−	4.64573i	−0.0653563	−	0.164251i
$801$	−2.93415	+	1.42290i	−0.103673	+	0.0502755i
$802$	1.76319	−	0.898392i	0.0622605	−	0.0317233i
$803$	1.82483	+	11.5215i	0.0643967	+	0.406585i
$804$	−26.8705	+	1.84852i	−0.947650	+	0.0651922i
$805$	1.79985	−	1.18448i	0.0634362	−	0.0417474i
$806$	2.83373	+	8.89165i	0.0998138	+	0.313195i
$807$	−3.45511	−	15.0431i	−0.121626	−	0.529542i
$808$	−1.54302	+	9.74225i	−0.0542833	+	0.342731i
$809$	23.6876	+	17.2100i	0.832811	+	0.605073i	0.920353	−	0.391088i	$-0.127901\pi$
$809$	23.6876	+	17.2100i	0.832811	+	0.605073i	−0.0875422	+	0.996161i	$0.527901\pi$
$810$	7.56825	+	18.6473i	0.265921	+	0.655199i
$811$	−2.02048			−0.0709486			−0.0354743	−	0.999371i	$-0.511294\pi$
$811$	−2.02048			−0.0709486			−0.0354743	+	0.999371i	$0.511294\pi$
$812$	−0.933547	+	0.933547i	−0.0327611	+	0.0327611i
$813$	32.2293	+	2.85633i	1.13033	+	0.100176i
$814$	−44.8475	+	14.5718i	−1.57190	+	0.510743i
$815$	−4.48886	−	40.3438i	−0.157238	−	1.41318i
$816$	6.09467	−	0.419274i	0.213356	−	0.0146775i
$817$	−46.4596	+	23.6723i	−1.62541	+	0.828190i
$818$	8.18261	+	1.29600i	0.286098	+	0.0453135i
$819$	1.37654	+	0.245924i	0.0481001	+	0.00859327i
$820$	−2.19124	+	2.73990i	−0.0765213	+	0.0956814i
$821$	−29.8352	+	41.0647i	−1.04126	+	1.43317i	−0.145107	+	0.989416i	$0.546353\pi$
$821$	−29.8352	+	41.0647i	−1.04126	+	1.43317i	−0.896150	+	0.443752i	$0.853647\pi$
$822$	−1.35263	−	0.575957i	−0.0471782	−	0.0200888i
$823$	−5.07617	−	2.58644i	−0.176944	−	0.0901576i	0.363275	−	0.931682i	$-0.381659\pi$
$823$	−5.07617	−	2.58644i	−0.176944	−	0.0901576i	−0.540219	+	0.841524i	$0.681659\pi$
$824$	13.6609	+	9.92525i	0.475901	+	0.345762i
$825$	−19.2634	−	40.1460i	−0.670664	−	1.39771i
$826$	1.17770	−	3.62458i	0.0409774	−	0.126115i
$827$	−0.810808	+	5.11924i	−0.0281945	+	0.178013i	−0.997767	−	0.0667913i	$-0.978724\pi$
$827$	−0.810808	+	5.11924i	−0.0281945	+	0.178013i	0.969572	+	0.244805i	$0.0787238\pi$
$828$	10.3930	+	0.204862i	0.361183	+	0.00711945i
$829$	18.6303	−	6.05335i	0.647057	−	0.210242i	0.0329410	−	0.999457i	$-0.489513\pi$
$829$	18.6303	−	6.05335i	0.647057	−	0.210242i	0.614116	+	0.789216i	$0.289513\pi$
$830$	−20.7629	+	5.69915i	−0.720692	+	0.197820i
$831$	−4.09899	+	6.54332i	−0.142192	+	0.226985i
$832$	−1.18520	−	1.18520i	−0.0410894	−	0.0410894i
$833$	21.7555	−	11.0850i	0.753784	−	0.384072i
$834$	12.1330	−	4.88615i	0.420132	−	0.169193i
$835$	−24.0846	+	10.8994i	−0.833482	+	0.377188i
$836$		−	27.9409i		−	0.966355i
$837$	22.6469	−	18.0032i	0.782793	−	0.622282i
$838$	17.7965	−	17.7965i	0.614769	−	0.614769i
$839$	37.1471	−	26.9889i	1.28246	−	0.931762i	0.282835	−	0.959168i	$-0.408725\pi$
$839$	37.1471	−	26.9889i	1.28246	−	0.931762i	0.999624	+	0.0274070i	$0.00872500\pi$
$840$	0.192285	+	1.05973i	0.00663446	+	0.0365641i
$841$	−1.99651	+	6.14463i	−0.0688452	+	0.211884i
$842$	10.4154	−	10.4154i	0.358938	−	0.358938i
$843$	11.7002	−	2.68731i	0.402977	−	0.0925560i
$844$	−4.64214	−	1.50832i	−0.159789	−	0.0519186i
$845$	17.7957	+	14.2321i	0.612191	+	0.489601i
$846$	−21.4852	+	20.6545i	−0.738675	+	0.710117i
$847$	−4.24002	−	0.671553i	−0.145689	−	0.0230748i
$848$	5.03942	−	2.56771i	0.173054	−	0.0881756i
$849$	54.1582	−	3.72573i	1.85870	−	0.127867i
$850$	9.00304	+	15.1642i	0.308802	+	0.520127i
$851$	30.2230	−	9.82003i	1.03603	−	0.336626i
$852$	2.38820	−	5.60866i	0.0818185	−	0.192149i
$853$	27.3593	−	4.33328i	0.936764	−	0.148369i	0.330656	−	0.943751i	$-0.392730\pi$
$853$	27.3593	−	4.33328i	0.936764	−	0.148369i	0.606108	+	0.795382i	$0.292730\pi$
$854$	−1.17453	−	3.61484i	−0.0401916	−	0.123697i
$855$	−33.5008	+	14.3721i	−1.14570	+	0.491514i
$856$	8.83773	−	6.42099i	0.302068	−	0.219465i
$857$	5.63495	+	11.0592i	0.192486	+	0.377776i	0.966998	−	0.254784i	$-0.0820044\pi$
$857$	5.63495	+	11.0592i	0.192486	+	0.377776i	−0.774512	+	0.632560i	$0.782004\pi$
$858$	−11.2545	−	9.80573i	−0.384224	−	0.334762i
$859$	−9.33082	+	3.03177i	−0.318363	+	0.103443i	−0.463840	−	0.885919i	$-0.653529\pi$
$859$	−9.33082	+	3.03177i	−0.318363	+	0.103443i	0.145476	+	0.989362i	$0.453529\pi$
$860$	−21.3243	+	2.37265i	−0.727152	+	0.0809066i
$861$	0.579464	−	0.485115i	0.0197481	−	0.0165327i
$862$	5.03739	+	5.03739i	0.171574	+	0.171574i
$863$	6.62387	+	6.62387i	0.225479	+	0.225479i	0.810801	−	0.585322i	$-0.199032\pi$
$863$	6.62387	+	6.62387i	0.225479	+	0.225479i	−0.585322	+	0.810801i	$0.699032\pi$
$864$	−2.12951	+	4.73974i	−0.0724476	+	0.161249i
$865$	−2.91834	+	2.66004i	−0.0992266	+	0.0904442i
$866$	0.520866	+	0.716910i	0.0176997	+	0.0243616i
$867$	7.69726	−	1.76791i	0.261413	−	0.0600414i
$868$	1.38351	−	0.695135i	0.0469595	−	0.0235944i
$869$	61.0061			2.06949
$870$	−11.1384	−	14.6295i	−0.377627	−	0.495988i
$871$	−21.0865	−	15.3203i	−0.714490	−	0.519107i
$872$	−1.71050	−	3.35705i	−0.0579249	−	0.113684i
$873$	−9.40784	−	3.26314i	−0.318407	−	0.110440i
$874$			18.8295i			0.636916i
$875$	−2.48153	+	1.87314i	−0.0838910	+	0.0633237i
$876$	3.81175	+	0.954943i	0.128787	+	0.0322645i
$877$	−18.6119	+	36.5278i	−0.628478	+	1.23346i	0.328831	+	0.944389i	$0.393345\pi$
$877$	−18.6119	+	36.5278i	−0.628478	+	1.23346i	−0.957309	+	0.289068i	$0.906655\pi$
$878$	−36.2132	−	5.73560i	−1.22213	−	0.193567i
$879$	−15.2275	−	18.1891i	−0.513611	−	0.613502i
$880$	4.05479	−	10.7584i	0.136687	−	0.362667i
$881$	−25.9980	+	35.7832i	−0.875896	+	1.20557i	0.101644	+	0.994821i	$0.467590\pi$
$881$	−25.9980	+	35.7832i	−0.875896	+	1.20557i	−0.977541	+	0.210747i	$0.932410\pi$
$882$	−0.409289	+	20.7640i	−0.0137815	+	0.699159i
$883$	29.7672	−	4.71466i	1.00174	−	0.158661i	0.366045	−	0.930597i	$-0.380712\pi$
$883$	29.7672	−	4.71466i	1.00174	−	0.158661i	0.635700	+	0.771936i	$0.280712\pi$
$884$	4.78277	+	3.47489i	0.160862	+	0.116873i
$885$	47.8211	+	23.0309i	1.60749	+	0.774175i
$886$	6.25428	+	4.54400i	0.210117	+	0.152659i
$887$	5.92287	−	37.3956i	0.198871	−	1.25562i	−0.663049	−	0.748576i	$-0.730738\pi$
$887$	5.92287	−	37.3956i	0.198871	−	1.25562i	0.861920	−	0.507044i	$-0.169262\pi$
$888$	−1.40231	+	15.8229i	−0.0470585	+	0.530983i
$889$	−1.78627	−	2.45859i	−0.0599097	−	0.0824586i
$890$	−0.268779	−	2.41567i	−0.00900951	−	0.0809734i
$891$	−16.0231	+	43.4127i	−0.536794	+	1.45438i
$892$	0.884514	−	0.450683i	0.0296157	−	0.0150900i
$893$	−38.1731	−	38.1731i	−1.27741	−	1.27741i
$894$	−12.7609	−	7.99393i	−0.426789	−	0.267357i
$895$	−29.9222	+	8.21325i	−1.00019	+	0.274539i
$896$	−0.163456	+	0.224978i	−0.00546069	+	0.00751599i
$897$	7.58449	+	6.60813i	0.253239	+	0.220639i
$898$	−2.57360	+	2.57360i	−0.0858822	+	0.0858822i
$899$	−15.6574	+	21.2969i	−0.522204	+	0.710292i
$900$	−14.9849	+	0.672224i	−0.499498	+	0.0224075i
$901$	−16.1388	+	11.7256i	−0.537663	+	0.390635i
$902$	−7.96793	+	1.26200i	−0.265303	+	0.0420199i
$903$	4.60369	+	0.408003i	0.153201	+	0.0135775i
$904$		−	16.9091i		−	0.562390i
$905$	6.12179	+	9.30223i	0.203495	+	0.309217i
$906$	5.71286	−	4.78269i	0.189797	−	0.158894i
$907$	23.4101	−	45.9449i	0.777319	−	1.52557i	−0.0718280	−	0.997417i	$-0.522883\pi$
$907$	23.4101	−	45.9449i	0.777319	−	1.52557i	0.849147	−	0.528157i	$-0.177117\pi$
$908$	−8.18066	+	16.0555i	−0.271485	+	0.532819i
$909$	26.0960	+	13.9511i	0.865548	+	0.462727i
$910$	−0.515622	+	0.905777i	−0.0170927	+	0.0300262i
$911$	16.1666	+	22.2514i	0.535622	+	0.737220i	0.987974	−	0.154619i	$-0.0494150\pi$
$911$	16.1666	+	22.2514i	0.535622	+	0.737220i	−0.452352	+	0.891839i	$0.649415\pi$
$912$	−8.65987	−	3.68743i	−0.286757	−	0.122103i
$913$	−44.1128	−	22.4766i	−1.45992	−	0.743867i
$914$	8.05404	+	5.85160i	0.266404	+	0.193554i
$915$	52.0848	−	9.45066i	1.72187	−	0.312429i
$916$	7.91440	+	24.3580i	0.261499	+	0.804812i
$917$	−1.09119	+	0.172828i	−0.0360344	+	0.00570729i
$918$	4.80331	−	17.6866i	0.158533	−	0.583745i
$919$	−13.1442	−	4.27080i	−0.433586	−	0.140881i	0.0840886	−	0.996458i	$-0.473202\pi$
$919$	−13.1442	−	4.27080i	−0.433586	−	0.140881i	−0.517674	+	0.855578i	$0.673202\pi$
$920$	−2.73254	+	7.25017i	−0.0900892	+	0.239031i
$921$	23.6327	+	5.92060i	0.778723	+	0.195090i
$922$	−1.14136	+	2.24005i	−0.0375888	+	0.0737722i
$923$	5.25615	−	2.67814i	0.173008	−	0.0881522i
$924$	−1.31475	+	2.09877i	−0.0432520	+	0.0690443i
$925$	−42.6069	+	16.9534i	−1.40091	+	0.557426i
$926$	2.29976	+	0.747238i	0.0755748	+	0.0245558i
$927$	41.5616	−	28.9623i	1.36506	−	0.951246i
$928$	0.742679	−	4.68909i	0.0243796	−	0.153927i
$929$	−55.1696			−1.81006			−0.905028	−	0.425352i	$-0.860150\pi$
$929$	−55.1696			−1.81006			−0.905028	+	0.425352i	$0.860150\pi$
$930$	7.00667	+	20.3938i	0.229758	+	0.668739i
$931$	−37.6189			−1.23291
$932$	2.74496	−	17.3310i	0.0899143	−	0.567697i
$933$	8.42119	+	3.58580i	0.275697	+	0.117394i
$934$	39.3564	+	12.7877i	1.28778	+	0.418425i
$935$	−8.18943	+	39.7160i	−0.267823	+	1.29885i
$936$	−4.52444	+	2.19410i	−0.147886	+	0.0717163i
$937$	−17.2459	+	8.78722i	−0.563399	+	0.287066i	−0.712403	−	0.701771i	$-0.752393\pi$
$937$	−17.2459	+	8.78722i	−0.563399	+	0.287066i	0.149004	+	0.988837i	$0.452393\pi$
$938$	−1.96322	+	3.85304i	−0.0641015	+	0.125806i
$939$	9.70719	−	38.7472i	0.316782	−	1.26447i
$940$	−9.15861	−	20.2380i	−0.298721	−	0.660091i
$941$	−29.0542	−	9.44028i	−0.947139	−	0.307744i	−0.205587	−	0.978639i	$-0.565910\pi$
$941$	−29.0542	−	9.44028i	−0.947139	−	0.307744i	−0.741553	+	0.670895i	$0.765910\pi$
$942$	−3.49714	−	3.04695i	−0.113943	−	0.0992749i
$943$	5.36962	−	0.850465i	0.174859	−	0.0276949i
$944$	4.23498	+	13.0339i	0.137837	+	0.424218i
$945$	3.19267	+	0.496817i	0.103858	+	0.0161614i
$946$	−39.9141	−	28.9993i	−1.29772	−	0.942847i
$947$	10.1330	+	5.16303i	0.329279	+	0.167776i	0.610812	−	0.791775i	$-0.290843\pi$
$947$	10.1330	+	5.16303i	0.329279	+	0.167776i	−0.281533	+	0.959551i	$0.590843\pi$
$948$	8.05114	−	18.9080i	0.261489	−	0.614103i
$949$	2.23515	+	3.07643i	0.0725562	+	0.0998650i
$950$	−1.75236	−	27.1143i	−0.0568540	−	0.879703i
$951$	−2.20865	+	0.151941i	−0.0716205	+	0.00492703i
$952$	0.445291	−	0.873934i	0.0144320	−	0.0283243i
$953$	10.4944	−	20.5965i	0.339948	−	0.667185i	−0.656228	−	0.754563i	$-0.727849\pi$
$953$	10.4944	−	20.5965i	0.339948	−	0.667185i	0.996175	+	0.0873783i	$0.0278489\pi$
$954$	−2.32353	−	16.8078i	−0.0752271	−	0.544172i
$955$	5.45209	−	3.58802i	0.176425	−	0.116106i
$956$			11.0434i			0.357168i
$957$	3.73246	−	42.1151i	0.120653	−	1.36139i
$958$	16.2290	−	2.57042i	0.524335	−	0.0830465i
$959$	−0.190959	+	0.138740i	−0.00616638	+	0.00448013i
$960$	−2.79931	−	2.67654i	−0.0903472	−	0.0863851i
$961$	25.2835	−	17.9373i	0.815596	−	0.578622i
$962$	−10.8697	+	10.8697i	−0.350453	+	0.350453i
$963$	−9.51092	−	31.3617i	−0.306485	−	1.01062i
$964$	2.02651	−	2.78926i	0.0652696	−	0.0898359i
$965$	12.0334	−	21.1387i	0.387370	−	0.680480i
$966$	0.886015	−	1.41437i	0.0285071	−	0.0455066i
$967$	39.0488	+	39.0488i	1.25572	+	1.25572i	0.953115	+	0.302609i	$0.0978578\pi$
$967$	39.0488	+	39.0488i	1.25572	+	1.25572i	0.302609	+	0.953115i	$0.402142\pi$
$968$	13.7546	−	7.00829i	0.442088	−	0.225255i
$969$	32.2025	+	8.06758i	1.03449	+	0.259168i
$970$	4.63562	−	5.79633i	0.148841	−	0.186109i
$971$	4.43991	+	6.11101i	0.142483	+	0.196112i	0.874294	−	0.485396i	$-0.161325\pi$
$971$	4.43991	+	6.11101i	0.142483	+	0.196112i	−0.731811	+	0.681508i	$0.761325\pi$
$972$	11.3405	+	10.6954i	0.363748	+	0.343056i
$973$	0.328518	−	2.07418i	0.0105318	−	0.0664953i
$974$	26.9485	+	19.5792i	0.863484	+	0.627358i
$975$	−11.5366	−	8.80979i	−0.369466	−	0.282139i
$976$	11.0575	+	8.03375i	0.353942	+	0.257154i
$977$	−35.2082	+	5.57643i	−1.12641	+	0.178406i	−0.691714	−	0.722171i	$-0.743144\pi$
$977$	−35.2082	+	5.57643i	−1.12641	+	0.178406i	−0.434696	+	0.900577i	$0.643144\pi$
$978$	−16.1640	−	26.9702i	−0.516866	−	0.862412i
$979$	3.28511	−	4.52156i	0.104993	−	0.144510i
$980$	−14.4849	−	5.45927i	−0.462704	−	0.174390i
$981$	−11.1966	+	1.54784i	−0.357481	+	0.0494186i
$982$	−9.82323	−	1.55585i	−0.313472	−	0.0496491i
$983$	18.0391	−	35.4036i	0.575357	−	1.12920i	−0.401610	−	0.915811i	$-0.631549\pi$
$983$	18.0391	−	35.4036i	0.575357	−	1.12920i	0.976967	−	0.213390i	$-0.0684506\pi$
$984$	−0.660411	+	2.63609i	−0.0210531	+	0.0840356i
$985$	0.279023	−	0.490152i	0.00889043	−	0.0156175i
$986$			16.7449i			0.533268i
$987$	1.07113	+	4.66358i	0.0340946	+	0.148443i
$988$	−4.13510	−	8.11560i	−0.131555	−	0.258192i
$989$	26.8983	+	19.5427i	0.855315	+	0.621423i
$990$	−26.5069	−	22.0693i	−0.842444	−	0.701408i
$991$	−4.90351			−0.155765			−0.0778825	−	0.996963i	$-0.524816\pi$
$991$	−4.90351			−0.155765			−0.0778825	+	0.996963i	$0.524816\pi$
$992$	−2.55565	+	4.94658i	−0.0811421	+	0.157054i
$993$	8.79450	+	38.2901i	0.279085	+	1.21510i
$994$	−0.575283	−	0.791809i	−0.0182469	−	0.0251147i
$995$	−51.0658	−	2.36452i	−1.61890	−	0.0749604i
$996$	−12.7880	+	10.7058i	−0.405203	+	0.339228i
$997$	23.1249	+	23.1249i	0.732373	+	0.732373i	0.971089	−	0.238716i	$-0.0767265\pi$
$997$	23.1249	+	23.1249i	0.732373	+	0.732373i	−0.238716	+	0.971089i	$0.576727\pi$
$998$	−12.3929	−	12.3929i	−0.392289	−	0.392289i
$999$	43.4690	+	19.5302i	1.37530	+	0.617907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.13	✓	512
3.2	odd	2	inner	930.2.bk.a.47.40	yes	512
5.3	odd	4	inner	930.2.bk.a.233.36	yes	512
15.8	even	4	inner	930.2.bk.a.233.25	yes	512
31.2	even	5	inner	930.2.bk.a.467.25	yes	512
93.2	odd	10	inner	930.2.bk.a.467.36	yes	512
155.33	odd	20	inner	930.2.bk.a.653.40	yes	512
465.188	even	20	inner	930.2.bk.a.653.13	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.13	✓	512	1.1	even	1	trivial
930.2.bk.a.47.40	yes	512	3.2	odd	2	inner
930.2.bk.a.233.25	yes	512	15.8	even	4	inner
930.2.bk.a.233.36	yes	512	5.3	odd	4	inner
930.2.bk.a.467.25	yes	512	31.2	even	5	inner
930.2.bk.a.467.36	yes	512	93.2	odd	10	inner
930.2.bk.a.653.13	yes	512	465.188	even	20	inner
930.2.bk.a.653.40	yes	512	155.33	odd	20	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.678564 + 1.59360i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.22925 - 1.86787i) q^{5} +(-1.46783 - 0.919503i) q^{6} +(-0.247778 + 0.126249i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.07910 - 2.16271i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.678564 + 1.59360i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.22925 - 1.86787i) q^{5} +(-1.46783 - 0.919503i) q^{6} +(-0.247778 + 0.126249i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.07910 - 2.16271i) q^{9} +(2.03717 - 0.921913i) q^{10} +(4.89005 + 1.58887i) q^{11} +(1.13780 - 1.30591i) q^{12} +(1.65549 - 0.262204i) q^{13} +(-0.0859340 - 0.264478i) q^{14} +(3.81076 - 0.691453i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.14265 - 1.60126i) q^{17} +(2.46133 - 1.71518i) q^{18} +(3.19412 + 4.39633i) q^{19} +(0.591879 + 2.15631i) q^{20} +(-0.0330572 - 0.480527i) q^{21} +(-2.33428 + 4.58129i) q^{22} +(1.57308 - 3.08735i) q^{23} +(1.11184 + 1.32808i) q^{24} +(-1.97790 + 4.59216i) q^{25} +1.67613i q^{26} +(4.85730 - 1.84571i) q^{27} +(0.274664 - 0.0435026i) q^{28} +(-3.84084 + 2.79053i) q^{29} +(0.0868056 + 3.87201i) q^{30} +(5.30488 - 1.69064i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.85023 + 6.71461i) q^{33} +(2.07316 - 2.85347i) q^{34} +(0.540399 + 0.307627i) q^{35} +(1.30903 + 2.69934i) q^{36} +(6.48500 + 6.48500i) q^{37} +(-4.84188 + 2.46706i) q^{38} +(-0.705509 + 2.81611i) q^{39} +(-2.22235 + 0.247270i) q^{40} +(0.922226 + 1.26933i) q^{41} +(0.479782 + 0.0425208i) q^{42} +(-1.50105 + 9.47723i) q^{43} +(-4.15972 - 3.02222i) q^{44} +(-1.48395 + 6.54201i) q^{45} +(2.80326 + 2.03669i) q^{46} +(-9.81204 + 1.55407i) q^{47} +(-1.48566 + 0.890397i) q^{48} +(-4.06904 + 5.60056i) q^{49} +(-4.22621 - 2.67192i) q^{50} +(4.68425 - 3.92156i) q^{51} +(-1.65549 - 0.262204i) q^{52} +(2.56771 - 5.03942i) q^{53} +(1.06314 + 5.08623i) q^{54} +(-3.04326 - 11.0871i) q^{55} +0.278088i q^{56} +(-9.17340 + 2.10695i) q^{57} +(-2.15534 - 4.23009i) q^{58} +(11.0873 + 8.05541i) q^{59} +(-3.83792 - 0.519979i) q^{60} +13.6678 q^{61} +(0.839960 + 5.50404i) q^{62} +(0.788198 + 0.273389i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-2.52477 - 2.76993i) q^{65} +(-5.71677 - 6.82860i) q^{66} +(-10.9958 - 10.9958i) q^{67} +(2.49402 + 2.49402i) q^{68} +(3.85256 + 4.60183i) q^{69} +(-0.388377 + 0.485622i) q^{70} +(3.34724 - 1.08758i) q^{71} +(-2.87089 + 0.870642i) q^{72} +(1.02998 + 2.02145i) q^{73} +(-7.41964 + 5.39068i) q^{74} +(-5.97591 - 6.26805i) q^{75} +(-1.67925 - 5.16820i) q^{76} +(-1.41224 + 0.223677i) q^{77} +(-2.67107 - 1.13736i) q^{78} +(11.2843 - 3.66648i) q^{79} +(0.103427 - 2.23367i) q^{80} +(-0.354669 + 8.99301i) q^{81} +(-1.39797 + 0.712304i) q^{82} +(-9.51036 - 1.50629i) q^{83} +(-0.117052 + 0.467224i) q^{84} +(0.872141 + 7.83841i) q^{85} +(-9.12573 - 2.96513i) q^{86} +(-1.84073 - 8.01431i) q^{87} +(3.63573 - 3.63573i) q^{88} +(0.335897 - 1.03379i) q^{89} +(-6.22933 - 2.48907i) q^{90} +(-0.377092 + 0.273973i) q^{91} +(-2.45014 + 2.45014i) q^{92} +(-0.905500 + 9.60105i) q^{93} -9.93435i q^{94} +(4.28543 - 11.3704i) q^{95} +(-0.647026 - 1.60666i) q^{96} +(2.95745 - 1.50690i) q^{97} +(-4.89506 - 4.89506i) q^{98} +(-6.73063 - 13.8792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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