LMFDB - Embedded newform 1000.2.bd.a.109.145

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(29,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 25, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.bd (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$2960$
Relative dimension:	$148$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.145
Character	$\chi$	$=$	1000.109
Dual form			1000.2.bd.a.789.145

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40613 - 0.150998i) q^{2} +(0.961254 + 1.16196i) q^{3} +(1.95440 - 0.424645i) q^{4} +(0.926297 - 2.03518i) q^{5} +(1.52710 + 1.48871i) q^{6} +(-1.57483 + 0.511693i) q^{7} +(2.68402 - 0.892216i) q^{8} +(0.136010 - 0.712991i) q^{9} +(0.995186 - 3.00160i) q^{10} +(-0.244127 + 1.93246i) q^{11} +(2.37209 + 1.86274i) q^{12} +(0.678091 - 3.55468i) q^{13} +(-2.13715 + 0.957302i) q^{14} +(3.25520 - 0.880011i) q^{15} +(3.63935 - 1.65985i) q^{16} +(0.998724 + 3.88977i) q^{17} +(0.0835879 - 1.02309i) q^{18} +(3.62263 + 2.99690i) q^{19} +(0.946124 - 4.37091i) q^{20} +(-2.10838 - 1.33802i) q^{21} +(-0.0514761 + 2.75415i) q^{22} +(-0.187116 + 0.199259i) q^{23} +(3.61674 + 2.26107i) q^{24} +(-3.28395 - 3.77037i) q^{25} +(0.416735 - 5.10073i) q^{26} +(4.92369 - 2.70682i) q^{27} +(-2.86056 + 1.66880i) q^{28} +(-8.04286 + 0.506014i) q^{29} +(4.44436 - 1.72894i) q^{30} +(3.64202 - 0.935112i) q^{31} +(4.86677 - 2.88350i) q^{32} +(-2.48010 + 1.57392i) q^{33} +(1.99168 + 5.31872i) q^{34} +(-0.417371 + 3.67905i) q^{35} +(-0.0369496 - 1.45122i) q^{36} +(0.549591 + 0.302140i) q^{37} +(5.54640 + 3.66702i) q^{38} +(4.78220 - 2.62904i) q^{39} +(0.670375 - 6.28893i) q^{40} +(4.18703 - 3.93188i) q^{41} +(-3.16669 - 1.56306i) q^{42} +(-2.86923 + 2.08462i) q^{43} +(0.343489 + 3.88047i) q^{44} +(-1.32508 - 0.937247i) q^{45} +(-0.233022 + 0.308438i) q^{46} +(-1.07089 - 2.70475i) q^{47} +(5.42702 + 2.63323i) q^{48} +(-3.44486 + 2.50284i) q^{49} +(-5.18697 - 4.80576i) q^{50} +(-3.55972 + 4.89954i) q^{51} +(-0.184216 - 7.23521i) q^{52} +(-4.21407 + 6.64031i) q^{53} +(6.51462 - 4.54961i) q^{54} +(3.70678 + 2.28688i) q^{55} +(-3.77033 + 2.77848i) q^{56} +7.09011i q^{57} +(-11.2329 + 1.92598i) q^{58} +(-7.93757 + 3.73514i) q^{59} +(5.98827 - 3.10220i) q^{60} +(-2.62449 + 2.79480i) q^{61} +(4.97995 - 1.86483i) q^{62} +(0.150639 + 1.19243i) q^{63} +(6.40790 - 4.78945i) q^{64} +(-6.60631 - 4.67273i) q^{65} +(-3.24969 + 2.58763i) q^{66} +(-0.486377 + 7.73075i) q^{67} +(3.60368 + 7.17807i) q^{68} +(-0.411396 - 0.0258829i) q^{69} +(-0.0313493 + 5.23624i) q^{70} +(0.739900 - 0.292947i) q^{71} +(-0.271088 - 2.03503i) q^{72} +(-6.33312 - 2.98014i) q^{73} +(0.818418 + 0.341861i) q^{74} +(1.22430 - 7.44009i) q^{75} +(8.35267 + 4.31880i) q^{76} +(-0.604369 - 3.16821i) q^{77} +(6.32741 - 4.41887i) q^{78} +(-5.38851 - 6.51359i) q^{79} +(-0.00698044 - 8.94427i) q^{80} +(5.85350 + 2.31757i) q^{81} +(5.29379 - 6.16096i) q^{82} +(-10.7525 + 12.9976i) q^{83} +(-4.68879 - 1.71971i) q^{84} +(8.84152 + 1.57050i) q^{85} +(-3.71973 + 3.36449i) q^{86} +(-8.31920 - 8.85904i) q^{87} +(1.06893 + 5.40457i) q^{88} +(1.69389 - 3.59971i) q^{89} +(-2.00476 - 1.11781i) q^{90} +(0.751026 + 5.94499i) q^{91} +(-0.281086 + 0.468889i) q^{92} +(4.58747 + 3.33299i) q^{93} +(-1.91422 - 3.64153i) q^{94} +(9.45486 - 4.59669i) q^{95} +(8.02870 + 2.88319i) q^{96} +(-12.7689 + 0.803353i) q^{97} +(-4.46600 + 4.03948i) q^{98} +(1.34462 + 0.436894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) $ 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{27}{50}\right)$	$-1$	$1$

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 $

$2$	1.40613	−	0.150998i	0.994284	−	0.106772i
$2$	1.40613	−	0.150998i	0.994284	−	0.106772i
$3$	0.961254	+	1.16196i	0.554980	+	0.670856i	0.971161	−	0.238426i	$-0.0766315\pi$
$3$	0.961254	+	1.16196i	0.554980	+	0.670856i	−0.416180	+	0.909282i	$0.636631\pi$
$4$	1.95440	−	0.424645i	0.977200	−	0.212323i
$5$	0.926297	−	2.03518i	0.414253	−	0.910162i
$5$	0.926297	−	2.03518i	0.414253	−	0.910162i
$6$	1.52710	+	1.48871i	0.623436	+	0.607765i
$7$	−1.57483	+	0.511693i	−0.595229	+	0.193402i	−0.591112	−	0.806590i	$-0.701311\pi$
$7$	−1.57483	+	0.511693i	−0.595229	+	0.193402i	−0.00411778	+	0.999992i	$0.501311\pi$
$8$	2.68402	−	0.892216i	0.948944	−	0.315446i
$9$	0.136010	−	0.712991i	0.0453367	−	0.237664i
$10$	0.995186	−	3.00160i	0.314705	−	0.949189i
$11$	−0.244127	+	1.93246i	−0.0736070	+	0.582659i	0.911573	+	0.411137i	$0.134868\pi$
$11$	−0.244127	+	1.93246i	−0.0736070	+	0.582659i	−0.985180	+	0.171522i	$0.945132\pi$
$12$	2.37209	+	1.86274i	0.684764	+	0.537725i
$13$	0.678091	−	3.55468i	0.188069	−	0.985891i	−0.755609	−	0.655023i	$-0.772659\pi$
$13$	0.678091	−	3.55468i	0.188069	−	0.985891i	0.943677	−	0.330867i	$-0.107341\pi$
$14$	−2.13715	+	0.957302i	−0.571177	+	0.255850i
$15$	3.25520	−	0.880011i	0.840490	−	0.227218i
$16$	3.63935	−	1.65985i	0.909838	−	0.414963i
$17$	0.998724	+	3.88977i	0.242226	+	0.943409i	0.967073	+	0.254499i	$0.0819105\pi$
$17$	0.998724	+	3.88977i	0.242226	+	0.943409i	−0.724847	+	0.688910i	$0.758089\pi$
$18$	0.0835879	−	1.02309i	0.0197019	−	0.241146i
$19$	3.62263	+	2.99690i	0.831087	+	0.687535i	0.952324	−	0.305088i	$-0.0986860\pi$
$19$	3.62263	+	2.99690i	0.831087	+	0.687535i	−0.121237	+	0.992624i	$0.538686\pi$
$20$	0.946124	−	4.37091i	0.211560	−	0.977365i
$21$	−2.10838	−	1.33802i	−0.460085	−	0.291979i
$22$	−0.0514761	+	2.75415i	−0.0109747	+	0.587187i
$23$	−0.187116	+	0.199259i	−0.0390165	+	0.0415483i	−0.748181	−	0.663495i	$-0.769072\pi$
$23$	−0.187116	+	0.199259i	−0.0390165	+	0.0415483i	0.709164	+	0.705043i	$0.249072\pi$
$24$	3.61674	+	2.26107i	0.738264	+	0.461538i
$25$	−3.28395	−	3.77037i	−0.656789	−	0.754074i
$26$	0.416735	−	5.10073i	0.0817285	−	1.00034i
$27$	4.92369	−	2.70682i	0.947565	−	0.520928i
$28$	−2.86056	+	1.66880i	−0.540594	+	0.315373i
$29$	−8.04286	+	0.506014i	−1.49352	+	0.0939644i	−0.788418	−	0.615140i	$-0.789099\pi$
$29$	−8.04286	+	0.506014i	−1.49352	+	0.0939644i	−0.705103	+	0.709104i	$0.749099\pi$
$30$	4.44436	−	1.72894i	0.811425	−	0.315660i
$31$	3.64202	−	0.935112i	0.654126	−	0.167951i	0.0929803	−	0.995668i	$-0.470361\pi$
$31$	3.64202	−	0.935112i	0.654126	−	0.167951i	0.561146	+	0.827717i	$0.310361\pi$
$32$	4.86677	−	2.88350i	0.860331	−	0.509736i
$33$	−2.48010	+	1.57392i	−0.431731	+	0.273985i
$34$	1.99168	+	5.31872i	0.341571	+	0.912153i
$35$	−0.417371	+	3.67905i	−0.0705486	+	0.621872i
$36$	−0.0369496	−	1.45122i	−0.00615827	−	0.241871i
$37$	0.549591	+	0.302140i	0.0903522	+	0.0496715i	0.526289	−	0.850306i	$-0.323583\pi$
$37$	0.549591	+	0.302140i	0.0903522	+	0.0496715i	−0.435937	+	0.899977i	$0.643583\pi$
$38$	5.54640	+	3.66702i	0.899746	+	0.594868i
$39$	4.78220	−	2.62904i	0.765765	−	0.420983i
$40$	0.670375	−	6.28893i	0.105996	−	0.994367i
$41$	4.18703	−	3.93188i	0.653904	−	0.614056i	−0.284880	−	0.958563i	$-0.591954\pi$
$41$	4.18703	−	3.93188i	0.653904	−	0.614056i	0.938784	+	0.344507i	$0.111954\pi$
$42$	−3.16669	−	1.56306i	−0.488630	−	0.241186i
$43$	−2.86923	+	2.08462i	−0.437553	+	0.317901i	−0.784662	−	0.619924i	$-0.787163\pi$
$43$	−2.86923	+	2.08462i	−0.437553	+	0.317901i	0.347109	+	0.937825i	$0.387163\pi$
$44$	0.343489	+	3.88047i	0.0517830	+	0.585003i
$45$	−1.32508	−	0.937247i	−0.197531	−	0.139717i
$46$	−0.233022	+	0.308438i	−0.0343572	+	0.0454766i
$47$	−1.07089	−	2.70475i	−0.156205	−	0.394528i	0.830507	−	0.557008i	$-0.188051\pi$
$47$	−1.07089	−	2.70475i	−0.156205	−	0.394528i	−0.986712	+	0.162480i	$0.948051\pi$
$48$	5.42702	+	2.63323i	0.783323	+	0.380074i
$49$	−3.44486	+	2.50284i	−0.492123	+	0.357548i
$50$	−5.18697	−	4.80576i	−0.733548	−	0.679637i
$51$	−3.55972	+	4.89954i	−0.498461	+	0.686072i
$52$	−0.184216	−	7.23521i	−0.0255461	−	1.00334i
$53$	−4.21407	+	6.64031i	−0.578847	+	0.912117i	0.421140	+	0.906996i	$0.361630\pi$
$53$	−4.21407	+	6.64031i	−0.578847	+	0.912117i	−0.999987	+	0.00512144i	$0.998370\pi$
$54$	6.51462	−	4.54961i	0.886528	−	0.619124i
$55$	3.70678	+	2.28688i	0.499822	+	0.308362i
$56$	−3.77033	+	2.77848i	−0.503831	+	0.371290i
$57$			7.09011i			0.939108i
$58$	−11.2329	+	1.92598i	−1.47495	+	0.252893i
$59$	−7.93757	+	3.73514i	−1.03338	+	0.486273i	−0.866224	−	0.499656i	$-0.833460\pi$
$59$	−7.93757	+	3.73514i	−1.03338	+	0.486273i	−0.167160	+	0.985930i	$0.553460\pi$
$60$	5.98827	−	3.10220i	0.773083	−	0.400492i
$61$	−2.62449	+	2.79480i	−0.336032	+	0.357838i	−0.874687	−	0.484689i	$-0.838933\pi$
$61$	−2.62449	+	2.79480i	−0.336032	+	0.357838i	0.538655	+	0.842527i	$0.318933\pi$
$62$	4.97995	−	1.86483i	0.632455	−	0.236833i
$63$	0.150639	+	1.19243i	0.0189788	+	0.150233i
$64$	6.40790	−	4.78945i	0.800988	−	0.598681i
$65$	−6.60631	−	4.67273i	−0.819412	−	0.579581i
$66$	−3.24969	+	2.58763i	−0.400009	+	0.318515i
$67$	−0.486377	+	7.73075i	−0.0594204	+	0.944461i	0.849526	+	0.527547i	$0.176888\pi$
$67$	−0.486377	+	7.73075i	−0.0594204	+	0.944461i	−0.908946	+	0.416914i	$0.863112\pi$
$68$	3.60368	+	7.17807i	0.437010	+	0.870469i
$69$	−0.411396	−	0.0258829i	−0.0495263	−	0.00311593i
$70$	−0.0313493	+	5.23624i	−0.00374695	+	0.625850i
$71$	0.739900	−	0.292947i	0.0878100	−	0.0347664i	−0.323809	−	0.946123i	$-0.604963\pi$
$71$	0.739900	−	0.292947i	0.0878100	−	0.0347664i	0.411619	+	0.911356i	$0.364963\pi$
$72$	−0.271088	−	2.03503i	−0.0319480	−	0.239831i
$73$	−6.33312	−	2.98014i	−0.741236	−	0.348799i	0.0178056	−	0.999841i	$-0.494332\pi$
$73$	−6.33312	−	2.98014i	−0.741236	−	0.348799i	−0.759041	+	0.651042i	$0.774332\pi$
$74$	0.818418	+	0.341861i	0.0951392	+	0.0397405i
$75$	1.22430	−	7.44009i	0.141370	−	0.859107i
$76$	8.35267	+	4.31880i	0.958117	+	0.495401i
$77$	−0.604369	−	3.16821i	−0.0688743	−	0.361052i
$78$	6.32741	−	4.41887i	0.716439	−	0.500338i
$79$	−5.38851	−	6.51359i	−0.606254	−	0.732836i	0.374684	−	0.927152i	$-0.377751\pi$
$79$	−5.38851	−	6.51359i	−0.606254	−	0.732836i	−0.980939	+	0.194317i	$0.937751\pi$
$80$	−0.00698044	−	8.94427i	−0.000780437	−	1.00000i
$81$	5.85350	+	2.31757i	0.650389	+	0.257507i
$82$	5.29379	−	6.16096i	0.584602	−	0.680365i
$83$	−10.7525	+	12.9976i	−1.18025	+	1.42667i	−0.298846	+	0.954301i	$0.596602\pi$
$83$	−10.7525	+	12.9976i	−1.18025	+	1.42667i	−0.881400	+	0.472370i	$0.843398\pi$
$84$	−4.68879	−	1.71971i	−0.511589	−	0.187635i
$85$	8.84152	+	1.57050i	0.958998	+	0.170345i
$86$	−3.71973	+	3.36449i	−0.401109	+	0.362802i
$87$	−8.31920	−	8.85904i	−0.891911	−	0.949789i
$88$	1.06893	+	5.40457i	0.113949	+	0.576130i
$89$	1.69389	−	3.59971i	0.179552	−	0.381568i	−0.794709	−	0.606991i	$-0.792376\pi$
$89$	1.69389	−	3.59971i	0.179552	−	0.381568i	0.974261	+	0.225423i	$0.0723764\pi$
$90$	−2.00476	−	1.11781i	−0.211320	−	0.117827i
$91$	0.751026	+	5.94499i	0.0787290	+	0.623204i
$92$	−0.281086	+	0.468889i	−0.0293052	+	0.0488851i
$93$	4.58747	+	3.33299i	0.475698	+	0.345615i
$94$	−1.91422	−	3.64153i	−0.197436	−	0.375595i
$95$	9.45486	−	4.59669i	0.970049	−	0.471611i
$96$	8.02870	+	2.88319i	0.819426	+	0.294265i
$97$	−12.7689	+	0.803353i	−1.29649	+	0.0815682i	−0.695987	−	0.718055i	$-0.745033\pi$
$97$	−12.7689	+	0.803353i	−1.29649	+	0.0815682i	−0.600502	+	0.799623i	$0.705033\pi$
$98$	−4.46600	+	4.03948i	−0.451134	+	0.408049i
$99$	1.34462	+	0.436894i	0.135140	+	0.0439095i
$100$	−8.01921	−	5.97430i	−0.801921	−	0.597430i
$101$	10.8240	−	3.51694i	1.07703	−	0.349948i	0.283808	−	0.958881i	$-0.408402\pi$
$101$	10.8240	−	3.51694i	1.07703	−	0.349948i	0.793222	+	0.608933i	$0.208402\pi$
$102$	−4.26561	+	7.42689i	−0.422358	+	0.735372i
$103$	−0.0991875	+	0.386310i	−0.00977324	+	0.0380642i	−0.973283	−	0.229610i	$-0.926255\pi$
$103$	−0.0991875	+	0.386310i	−0.00977324	+	0.0380642i	0.963510	+	0.267674i	$0.0862550\pi$
$104$	−1.35153	−	10.1458i	−0.132529	−	0.994880i
$105$	−4.67609	+	3.05153i	−0.456340	+	0.297799i
$106$	−4.92286	+	9.97346i	−0.478150	+	0.968708i
$107$	−0.710079	+	2.18540i	−0.0686460	+	0.211271i	−0.979495	−	0.201470i	$-0.935428\pi$
$107$	−0.710079	+	2.18540i	−0.0686460	+	0.211271i	0.910849	+	0.412740i	$0.135428\pi$
$108$	8.47342	−	7.38104i	0.815356	−	0.710240i
$109$	−4.55687	+	8.28892i	−0.436469	+	0.793935i	−0.999471	−	0.0325211i	$-0.989646\pi$
$109$	−4.55687	+	8.28892i	−0.436469	+	0.793935i	0.563002	+	0.826456i	$0.309646\pi$
$110$	5.55753	+	2.65593i	0.529889	+	0.253233i
$111$	0.177223	+	0.929034i	0.0168212	+	0.0881800i
$112$	−4.88202	+	4.47621i	−0.461308	+	0.422963i
$113$	9.71084	−	4.56957i	0.913519	−	0.429869i	0.0892119	−	0.996013i	$-0.471565\pi$
$113$	9.71084	−	4.56957i	0.913519	−	0.429869i	0.824307	+	0.566143i	$0.191565\pi$
$114$	1.07059	+	9.96962i	0.100270	+	0.933740i
$115$	0.232203	+	0.565389i	0.0216530	+	0.0527228i
$116$	−15.5041	+	4.40431i	−1.43952	+	0.408930i
$117$	−2.44223	−	0.966945i	−0.225784	−	0.0893941i
$118$	−10.5973	+	6.45064i	−0.975556	+	0.593830i
$119$	−3.56319	−	5.61469i	−0.326637	−	0.514698i
$120$	7.95186	−	5.26631i	0.725902	−	0.480746i
$121$	6.97961	+	1.79206i	0.634510	+	0.162914i
$122$	−3.26837	+	4.32615i	−0.295904	+	0.391671i
$123$	8.59347	+	1.08561i	0.774847	+	0.0978859i
$124$	6.72087	−	3.37415i	0.603552	−	0.303008i
$125$	−10.7153	+	3.19095i	−0.958406	+	0.285407i
$126$	0.391873	+	1.65397i	0.0349109	+	0.147347i
$127$	0.343020	−	2.71528i	0.0304381	−	0.240942i	−0.969554	−	0.244877i	$-0.921252\pi$
$127$	0.343020	−	2.71528i	0.0304381	−	0.240942i	0.999992	+	0.00393455i	$0.00125241\pi$
$128$	8.28714	−	7.70216i	0.732487	−	0.680781i
$129$	−5.18029	−	1.33007i	−0.456099	−	0.117106i
$130$	−9.99490	−	5.57292i	−0.876611	−	0.488778i
$131$	7.72811	−	4.90441i	0.675208	−	0.428500i	−0.153525	−	0.988145i	$-0.549062\pi$
$131$	7.72811	−	4.90441i	0.675208	−	0.428500i	0.828733	+	0.559645i	$0.189062\pi$
$132$	−4.17876	+	4.12924i	−0.363714	+	0.359404i
$133$	−7.23851	−	2.86593i	−0.627658	−	0.248507i
$134$	0.483417	+	10.9439i	0.0417609	+	0.945406i
$135$	−0.948078	−	12.5279i	−0.0815976	−	1.07823i
$136$	6.15111	+	9.54915i	0.527454	+	0.818833i
$137$	−3.05418	+	1.43719i	−0.260937	+	0.122787i	−0.551798	−	0.833978i	$-0.686058\pi$
$137$	−3.05418	+	1.43719i	−0.260937	+	0.122787i	0.290862	+	0.956765i	$0.406058\pi$
$138$	−0.582385	+	0.0257253i	−0.0495759	+	0.00218988i
$139$	3.25520	−	0.620963i	0.276102	−	0.0526694i	−0.0474703	−	0.998873i	$-0.515116\pi$
$139$	3.25520	−	0.620963i	0.276102	−	0.0526694i	0.323573	+	0.946203i	$0.395116\pi$
$140$	0.746580	+	7.36756i	0.0630975	+	0.622672i
$141$	2.11341	−	3.84427i	0.177981	−	0.323746i
$142$	0.996161	−	0.523645i	0.0835960	−	0.0439433i
$143$	6.70374	+	2.17818i	0.560595	+	0.182148i
$144$	−0.688470	−	2.82058i	−0.0573725	−	0.235048i
$145$	−6.42025	+	16.8374i	−0.533173	+	1.39827i
$146$	−9.35518	−	3.23418i	−0.774240	−	0.267662i
$147$	−6.21958	−	1.59692i	−0.512982	−	0.131711i
$148$	1.20242	+	0.357121i	0.0988385	+	0.0293552i
$149$	0.284913	−	0.0925738i	0.0233410	−	0.00758394i	−0.297323	−	0.954777i	$-0.596094\pi$
$149$	0.284913	−	0.0925738i	0.0233410	−	0.00758394i	0.320664	+	0.947193i	$0.396094\pi$
$150$	0.598088	−	10.6466i	0.0488337	−	0.869291i
$151$	3.44430	−	10.6005i	0.280293	−	0.862655i	−0.707477	−	0.706737i	$-0.750166\pi$
$151$	3.44430	−	10.6005i	0.280293	−	0.862655i	0.987770	−	0.155918i	$-0.0498335\pi$
$152$	12.3971	+	4.81156i	1.00554	+	0.390269i
$153$	2.90921	−	0.183032i	0.235196	−	0.0147973i
$154$	−1.32821	−	4.36366i	−0.107031	−	0.351634i
$155$	1.47047	−	8.27837i	0.118111	−	0.664935i
$156$	8.22992	−	7.16893i	0.658921	−	0.573973i
$157$	−16.9631	−	12.3244i	−1.35380	−	0.983596i	−0.998812	−	0.0487259i	$-0.984484\pi$
$157$	−16.9631	−	12.3244i	−1.35380	−	0.983596i	−0.354991	−	0.934870i	$-0.615516\pi$
$158$	−8.56048	−	8.34529i	−0.681035	−	0.663916i
$159$	−11.7665	+	1.48646i	−0.933148	+	0.117884i
$160$	−1.36038	−	12.5757i	−0.107548	−	0.994200i
$161$	0.192717	−	0.409544i	0.0151882	−	0.0322766i
$162$	8.58073	+	2.37493i	0.674166	+	0.186592i
$163$	−12.8513	+	12.0682i	−1.00659	+	0.945255i	−0.998502	−	0.0547126i	$-0.982576\pi$
$163$	−12.8513	+	12.0682i	−1.00659	+	0.945255i	−0.00809183	+	0.999967i	$0.502576\pi$
$164$	6.51347	−	9.46246i	0.508616	−	0.738894i
$165$	0.905906	+	6.50539i	0.0705247	+	0.506444i
$166$	−13.1569	+	19.8999i	−1.02117	+	1.54453i
$167$	15.8752	+	13.1331i	1.22846	+	1.01627i	0.999078	+	0.0429309i	$0.0136695\pi$
$167$	15.8752	+	13.1331i	1.22846	+	1.01627i	0.229379	+	0.973337i	$0.426330\pi$
$168$	−6.85272	−	1.71013i	−0.528699	−	0.131940i
$169$	−0.0888396	−	0.0351741i	−0.00683382	−	0.00270570i
$170$	12.6695	+	0.873276i	0.971704	+	0.0669772i
$171$	2.62947	−	2.17529i	0.201081	−	0.166349i
$172$	−4.72239	+	5.29257i	−0.360079	+	0.403555i
$173$	2.55974	+	13.4186i	0.194614	+	1.02020i	0.936763	+	0.349966i	$0.113807\pi$
$173$	2.55974	+	13.4186i	0.194614	+	1.02020i	−0.742149	+	0.670235i	$0.766193\pi$
$174$	−13.0356	−	11.2008i	−0.988223	−	0.849129i
$175$	7.10093	+	4.25732i	0.536780	+	0.321823i
$176$	2.31914	+	7.43812i	0.174812	+	0.560670i
$177$	−11.9701	−	5.63270i	−0.899727	−	0.423379i
$178$	1.83829	−	5.31743i	0.137785	−	0.398558i
$179$	0.973764	+	2.45945i	0.0727825	+	0.183828i	0.961613	−	0.274408i	$-0.0884817\pi$
$179$	0.973764	+	2.45945i	0.0727825	+	0.183828i	−0.888831	+	0.458235i	$0.848482\pi$
$180$	−2.98773	−	1.26907i	−0.222693	−	0.0945906i
$181$	16.9156	+	1.06424i	1.25733	+	0.0791043i	0.677431	−	0.735587i	$-0.263093\pi$
$181$	16.9156	+	1.06424i	1.25733	+	0.0791043i	0.579896	+	0.814691i	$0.303093\pi$
$182$	1.95372	+	8.24602i	0.144819	+	0.611235i
$183$	−5.77025	−	0.363033i	−0.426549	−	0.0268362i
$184$	−0.324442	+	0.701762i	−0.0239182	+	0.0517346i
$185$	1.12400	−	0.838647i	0.0826378	−	0.0616585i
$186$	6.95385	+	3.99392i	0.509881	+	0.292848i
$187$	−7.76065	+	0.980399i	−0.567515	+	0.0716939i
$188$	−3.24150	−	4.83141i	−0.236411	−	0.352367i
$189$	−6.36891	+	6.78220i	−0.463270	+	0.493333i
$190$	12.6007	−	7.89121i	0.914149	−	0.572488i
$191$	−0.527243	−	1.12045i	−0.0381500	−	0.0810728i	0.884844	−	0.465888i	$-0.154265\pi$
$191$	−0.527243	−	1.12045i	−0.0381500	−	0.0810728i	−0.922994	+	0.384815i	$0.874265\pi$
$192$	11.7248	+	2.84183i	0.846161	+	0.205091i
$193$		−	11.4707i		−	0.825680i	−0.910804	−	0.412840i	$-0.864537\pi$
$193$		−	11.4707i		−	0.825680i	0.910804	−	0.412840i	$-0.135463\pi$
$194$	−17.8335	+	3.05770i	−1.28037	+	0.219530i
$195$	−0.920833	−	12.1679i	−0.0659422	−	0.871363i
$196$	−5.66982	+	6.35439i	−0.404987	+	0.453885i
$197$	4.69636	−	7.40028i	0.334602	−	0.527248i	−0.634816	−	0.772663i	$-0.718924\pi$
$197$	4.69636	−	7.40028i	0.334602	−	0.527248i	0.969418	+	0.245415i	$0.0789243\pi$
$198$	1.95668	+	0.411295i	0.139055	+	0.0292295i
$199$	−12.0197	−	8.73285i	−0.852057	−	0.619055i	0.0736557	−	0.997284i	$-0.476533\pi$
$199$	−12.0197	−	8.73285i	−0.852057	−	0.619055i	−0.925712	+	0.378228i	$0.876533\pi$
$200$	−12.1782	−	7.18975i	−0.861126	−	0.508392i
$201$	−9.45032	+	6.86606i	−0.666574	+	0.484295i
$202$	14.6889	−	6.57967i	1.03351	−	0.462944i
$203$	12.4072	−	4.91236i	0.870815	−	0.344780i
$204$	−4.87655	+	11.0873i	−0.341427	+	0.776264i
$205$	−4.12367	−	12.1635i	−0.288009	−	0.849533i
$206$	−0.0811385	+	0.558179i	−0.00565319	+	0.0388902i
$207$	0.116620	+	0.160513i	0.00810564	+	0.0111565i
$208$	−3.43243	−	14.0623i	−0.237996	−	0.975042i
$209$	−6.67577	+	6.26896i	−0.461772	+	0.433633i
$210$	−6.11441	+	4.99693i	−0.421935	+	0.344821i
$211$	−7.44727	−	13.5465i	−0.512691	−	0.932582i	−0.998293	−	0.0584017i	$-0.981400\pi$
$211$	−7.44727	−	13.5465i	−0.512691	−	0.932582i	0.485602	−	0.874180i	$-0.338600\pi$
$212$	−5.41620	+	14.7673i	−0.371986	+	1.01422i
$213$	1.05162	+	0.578135i	0.0720561	+	0.0396132i
$214$	−0.668473	+	3.18017i	−0.0456958	+	0.217392i
$215$	1.58482	+	7.77038i	0.108084	+	0.529935i
$216$	10.8002	−	11.6582i	0.734861	−	0.793237i
$217$	−5.25707	+	3.33624i	−0.356873	+	0.226479i
$218$	−5.15594	+	12.3434i	−0.349204	+	0.835999i
$219$	−2.62494	−	10.2235i	−0.177377	−	0.690839i
$220$	8.21564	+	2.89540i	0.553898	+	0.195208i
$221$	14.5041	−	0.912522i	0.975653	−	0.0613829i
$222$	0.389480	+	1.27958i	0.0261402	+	0.0858799i
$223$	−4.60190	−	8.37082i	−0.308166	−	0.560552i	0.676193	−	0.736724i	$-0.263628\pi$
$223$	−4.60190	−	8.37082i	−0.308166	−	0.560552i	−0.984359	+	0.176172i	$0.943628\pi$
$224$	−6.18886	+	7.03131i	−0.413510	+	0.469799i
$225$	−3.13489	+	1.82861i	−0.208993	+	0.121908i
$226$	12.9647	−	7.89173i	0.862399	−	0.524950i
$227$	−14.6382	−	13.7462i	−0.971574	−	0.912368i	0.0246059	−	0.999697i	$-0.492167\pi$
$227$	−14.6382	−	13.7462i	−0.971574	−	0.912368i	−0.996180	+	0.0873289i	$0.972167\pi$
$228$	3.01078	+	13.8569i	0.199394	+	0.917696i
$229$	−17.0635	−	10.8288i	−1.12759	−	0.715588i	−0.164928	−	0.986306i	$-0.552739\pi$
$229$	−17.0635	−	10.8288i	−1.12759	−	0.715588i	−0.962659	+	0.270717i	$0.912739\pi$
$230$	0.411879	+	0.759948i	0.0271585	+	0.0501095i
$231$	3.10038	−	3.74771i	0.203990	−	0.246581i
$232$	−21.1357	+	8.53412i	−1.38763	+	0.560292i
$233$	−4.49502	−	17.5070i	−0.294479	−	1.14692i	−0.927815	−	0.373042i	$-0.878315\pi$
$233$	−4.49502	−	17.5070i	−0.294479	−	1.14692i	0.633336	−	0.773877i	$-0.281685\pi$
$234$	−3.58009	−	0.990879i	−0.234038	−	0.0647758i
$235$	−6.49662	−	0.325953i	−0.423793	−	0.0212628i
$236$	−13.9271	+	10.6706i	−0.906575	+	0.694597i
$237$	2.38878	−	12.5224i	0.155168	−	0.813419i
$238$	−5.85811	−	7.35695i	−0.379725	−	0.476880i
$239$	17.5063	+	2.21156i	1.13239	+	0.143054i	0.669114	−	0.743160i	$-0.266674\pi$
$239$	17.5063	+	2.21156i	1.13239	+	0.143054i	0.463276	+	0.886214i	$0.346674\pi$
$240$	10.3861	−	8.60583i	0.670423	−	0.555504i
$241$	−3.74609	+	19.6377i	−0.241307	+	1.26498i	0.630909	+	0.775857i	$0.282682\pi$
$241$	−3.74609	+	19.6377i	−0.241307	+	1.26498i	−0.872217	+	0.489120i	$0.837318\pi$
$242$	10.0848	+	1.46596i	0.648277	+	0.0942355i
$243$	−2.27502	−	7.00178i	−0.145942	−	0.449164i
$244$	−3.94251	+	6.57664i	−0.252393	+	0.421026i
$245$	1.90277	+	9.32930i	0.121564	+	0.596027i
$246$	12.2475	+	0.228909i	0.780869	+	0.0145947i
$247$	13.1095	−	10.8451i	0.834136	−	0.690057i
$248$	8.94093	−	5.75933i	0.567749	−	0.365718i
$249$	−25.4386			−1.61210
$250$	−14.5853	+	6.10488i	−0.922454	+	0.386106i
$251$			7.10516i			0.448474i	0.974535	+	0.224237i	$0.0719890\pi$
$251$			7.10516i			0.448474i	−0.974535	+	0.224237i	$0.928011\pi$
$252$	0.800771	+	2.26652i	0.0504438	+	0.142778i
$253$	−0.339380	−	0.410239i	−0.0213366	−	0.0257915i
$254$	0.0723286	−	3.86984i	0.00453830	−	0.242815i
$255$	6.67410	+	11.7831i	0.417948	+	0.737887i
$256$	10.4898	−	12.0816i	0.655611	−	0.755098i
$257$	−23.2497	+	7.55430i	−1.45028	+	0.471224i	−0.925085	−	0.379759i	$-0.876007\pi$
$257$	−23.2497	+	7.55430i	−1.45028	+	0.471224i	−0.525193	+	0.850983i	$0.676007\pi$
$258$	−7.48499	−	1.08804i	−0.465995	−	0.0677385i
$259$	−1.02011	−	0.194597i	−0.0633868	−	0.0120917i
$260$	−14.8956	−	6.32704i	−0.923787	−	0.392387i
$261$	−0.733128	+	5.80330i	−0.0453795	+	0.359216i
$262$	10.1262	−	8.06316i	0.625597	−	0.498144i
$263$	14.4871	+	2.76357i	0.893316	+	0.170409i	0.613547	−	0.789658i	$-0.289742\pi$
$263$	14.4871	+	2.76357i	0.893316	+	0.170409i	0.279769	+	0.960067i	$0.409742\pi$
$264$	−5.25236	+	6.43722i	−0.323261	+	0.396184i
$265$	9.61078	+	14.7273i	0.590385	+	0.904692i
$266$	−10.6110	−	2.93687i	−0.650604	−	0.180071i
$267$	5.81097	−	1.49200i	0.355625	−	0.0913091i
$268$	2.33225	+	15.3155i	0.142465	+	0.935543i
$269$	−8.85248	−	7.32341i	−0.539745	−	0.446516i	0.327175	−	0.944964i	$-0.393903\pi$
$269$	−8.85248	−	7.32341i	−0.539745	−	0.446516i	−0.866920	+	0.498448i	$0.833903\pi$
$270$	−3.22481	−	17.4728i	−0.196256	−	1.06336i
$271$	−1.30582	+	2.05764i	−0.0793227	+	0.124993i	−0.881673	−	0.471861i	$-0.843583\pi$
$271$	−1.30582	+	2.05764i	−0.0793227	+	0.124993i	0.802350	+	0.596853i	$0.203583\pi$
$272$	10.0912	+	12.4985i	0.611867	+	0.757835i
$273$	−6.18589	+	6.58730i	−0.374387	+	0.398682i
$274$	−4.07756	+	2.48205i	−0.246335	+	0.149946i
$275$	8.08780	−	5.42565i	0.487712	−	0.327179i
$276$	−0.815024	+	0.124112i	−0.0490587	+	0.00747066i
$277$	20.1597	−	11.0829i	1.21128	−	0.665905i	0.257458	−	0.966289i	$-0.417115\pi$
$277$	20.1597	−	11.0829i	1.21128	−	0.665905i	0.953818	+	0.300385i	$0.0971151\pi$
$278$	4.48347	−	1.36468i	0.268901	−	0.0818482i
$279$	−0.171374	−	2.72391i	−0.0102599	−	0.163076i
$280$	2.16227	+	10.2470i	0.129221	+	0.612376i
$281$	15.1429	−	3.88805i	0.903353	−	0.231942i	0.231682	−	0.972792i	$-0.425577\pi$
$281$	15.1429	−	3.88805i	0.903353	−	0.231942i	0.671670	+	0.740850i	$0.265577\pi$
$282$	2.39125	−	5.72467i	0.142397	−	0.340899i
$283$	5.05884	+	7.97146i	0.300717	+	0.473854i	0.960763	−	0.277371i	$-0.0894632\pi$
$283$	5.05884	+	7.97146i	0.300717	+	0.473854i	−0.660046	+	0.751225i	$0.729463\pi$
$284$	1.32166	−	0.886731i	0.0784262	−	0.0526178i
$285$	14.4297	+	6.56755i	0.854741	+	0.389028i
$286$	9.75522	+	2.05055i	0.576839	+	0.121251i
$287$	−4.58194	+	8.33451i	−0.270463	+	0.491971i
$288$	−1.39398	−	3.86214i	−0.0821410	−	0.227579i
$289$	0.764315	−	0.420186i	0.0449597	−	0.0247168i
$290$	−6.48529	+	24.6450i	−0.380829	+	1.44721i
$291$	−13.2077	−	14.0647i	−0.774246	−	0.824489i
$292$	−13.6429	−	3.13506i	−0.798393	−	0.183465i
$293$	−21.5590	+	15.6635i	−1.25949	+	0.915072i	−0.998732	−	0.0503334i	$-0.983972\pi$
$293$	−21.5590	+	15.6635i	−1.25949	+	0.915072i	−0.260755	+	0.965405i	$0.583972\pi$
$294$	−8.98666	−	1.30633i	−0.524113	−	0.0761866i
$295$	0.249139	+	19.6143i	0.0145054	+	1.14199i
$296$	1.74469	+	0.320596i	0.101408	+	0.0186342i
$297$	4.02883	+	10.1757i	0.233776	+	0.590451i
$298$	0.386646	−	0.173192i	0.0223978	−	0.0100327i
$299$	0.581419	+	0.800254i	0.0336243	+	0.0462799i
$300$	−0.766623	−	15.0608i	−0.0442610	−	0.869535i
$301$	3.45186	−	4.75108i	0.198962	−	0.273847i
$302$	3.24249	−	15.4257i	0.186584	−	0.887651i
$303$	14.4912	+	9.19637i	0.832495	+	0.528317i
$304$	18.1584	+	4.89374i	1.04146	+	0.280675i
$305$	3.25687	+	7.93015i	0.186488	+	0.454079i
$306$	4.06309	−	0.696651i	0.232271	−	0.0398249i
$307$	29.8216			1.70201			0.851005	−	0.525157i	$-0.175993\pi$
$307$	29.8216			1.70201			0.851005	+	0.525157i	$0.175993\pi$
$308$	−2.52655	−	5.93531i	−0.143963	−	0.338196i
$309$	−0.544220	+	0.256090i	−0.0309596	+	0.0145685i
$310$	0.817654	−	11.8625i	0.0464396	−	0.673745i
$311$	10.7046	+	10.0523i	0.607004	+	0.570015i	0.925897	−	0.377776i	$-0.123311\pi$
$311$	10.7046	+	10.0523i	0.607004	+	0.570015i	−0.318893	+	0.947791i	$0.603311\pi$
$312$	10.4898	−	11.3231i	0.593870	−	0.641046i
$313$	−0.526835	−	4.17033i	−0.0297785	−	0.235721i	0.970200	−	0.242306i	$-0.0779038\pi$
$313$	−0.526835	−	4.17033i	−0.0297785	−	0.235721i	−0.999978	+	0.00658526i	$0.997904\pi$
$314$	−25.7133	−	14.7683i	−1.45108	−	0.833425i
$315$	2.56636	+	0.797969i	0.144598	+	0.0449605i
$316$	−13.2973	−	10.4419i	−0.748029	−	0.587405i
$317$	−0.758726	+	12.0596i	−0.0426143	+	0.677334i	0.917502	+	0.397732i	$0.130203\pi$
$317$	−0.758726	+	12.0596i	−0.0426143	+	0.677334i	−0.960116	+	0.279602i	$0.909797\pi$
$318$	−16.3208	+	3.86688i	−0.915227	+	0.216844i
$319$	0.985624	−	15.6660i	0.0551843	−	0.877130i
$320$	−3.81178	−	17.4777i	−0.213085	−	0.977034i
$321$	−3.22191	+	1.27564i	−0.179829	+	0.0711994i
$322$	0.209145	−	0.604972i	0.0116552	−	0.0337138i
$323$	−8.03925	+	17.0843i	−0.447316	+	0.950594i
$324$	12.4242	+	2.04379i	0.690235	+	0.113544i
$325$	−15.6293	+	9.11672i	−0.866956	+	0.505705i
$326$	−16.2484	+	18.9100i	−0.899913	+	1.04733i
$327$	−14.0117	+	2.67287i	−0.774848	+	0.147810i
$328$	7.72997	−	14.2890i	0.426816	−	0.788976i
$329$	3.07046	+	3.71155i	0.169280	+	0.204625i
$330$	2.25612	+	9.01063i	0.124195	+	0.496019i
$331$	5.91672	−	14.9439i	0.325212	−	0.821392i	−0.671548	−	0.740961i	$-0.734370\pi$
$331$	5.91672	−	14.9439i	0.325212	−	0.821392i	0.996760	−	0.0804311i	$-0.0256297\pi$
$332$	−15.4954	+	29.9685i	−0.850421	+	1.64474i
$333$	0.290173	−	0.350759i	0.0159014	−	0.0192215i
$334$	24.3056	+	16.0697i	1.32994	+	0.879294i
$335$	15.2830	+	8.15084i	0.834997	+	0.445328i
$336$	−9.89403	−	1.36992i	−0.539764	−	0.0747353i
$337$	19.1333	+	20.3749i	1.04226	+	1.10989i	0.993813	+	0.111066i	$0.0354266\pi$
$337$	19.1333	+	20.3749i	1.04226	+	1.10989i	0.0484452	+	0.998826i	$0.484573\pi$
$338$	−0.130231	−	0.0360447i	−0.00708364	−	0.00196058i
$339$	14.6442	+	6.89105i	0.795365	+	0.374270i
$340$	17.9468	−	0.685123i	0.973300	−	0.0371560i
$341$	0.917954	+	7.26635i	0.0497100	+	0.393495i
$342$	3.36891	−	3.45578i	0.182170	−	0.186867i
$343$	10.9575	−	15.0817i	0.591648	−	0.814333i
$344$	−5.84113	+	8.15512i	−0.314933	+	0.439694i
$345$	−0.433752	+	0.813292i	−0.0233524	+	0.0437862i
$346$	5.62552	+	18.4818i	0.302430	+	0.993590i
$347$	1.84537	+	29.3312i	0.0990644	+	1.57458i	0.662907	+	0.748702i	$0.269322\pi$
$347$	1.84537	+	29.3312i	0.0990644	+	1.57458i	−0.563843	+	0.825882i	$0.690678\pi$
$348$	−20.0210	−	13.7814i	−1.07324	−	0.738761i
$349$	24.5427	+	7.97439i	1.31374	+	0.426859i	0.880340	−	0.474343i	$-0.157314\pi$
$349$	24.5427	+	7.97439i	1.31374	+	0.426859i	0.433398	+	0.901203i	$0.357314\pi$
$350$	10.6277	+	4.91411i	0.568073	+	0.262670i
$351$	−6.28317	−	19.3376i	−0.335371	−	1.03217i
$352$	4.38415	+	10.1088i	0.233676	+	0.538800i
$353$	−3.42048	+	13.3219i	−0.182054	+	0.709052i	0.810341	+	0.585958i	$0.199282\pi$
$353$	−3.42048	+	13.3219i	−0.182054	+	0.709052i	−0.992395	+	0.123094i	$0.960718\pi$
$354$	−17.6820	−	6.11284i	−0.939789	−	0.324894i
$355$	0.0891663	−	1.77719i	0.00473245	−	0.0943234i
$356$	1.78195	−	7.75457i	0.0944430	−	0.410991i
$357$	3.09889	−	9.53742i	0.164011	−	0.504774i
$358$	1.74061	+	3.31126i	0.0919941	+	0.175006i
$359$	4.01395	+	2.20669i	0.211848	+	0.116464i	0.584145	−	0.811649i	$-0.301430\pi$
$359$	4.01395	+	2.20669i	0.211848	+	0.116464i	−0.372297	+	0.928114i	$0.621430\pi$
$360$	−4.39277	−	1.33333i	−0.231519	−	0.0702726i
$361$	0.581782	+	3.04981i	0.0306201	+	0.160516i
$362$	23.9462	−	1.05776i	1.25858	−	0.0555947i
$363$	4.62688	+	9.83262i	0.242848	+	0.516079i
$364$	3.99231	+	11.3000i	0.209254	+	0.592279i
$365$	−11.9315	+	10.1286i	−0.624523	+	0.530154i
$366$	−8.16853	+	0.360823i	−0.426976	+	0.0188605i
$367$	−7.48517	+	18.9054i	−0.390723	+	0.986852i	0.592684	+	0.805435i	$0.298068\pi$
$367$	−7.48517	+	18.9054i	−0.390723	+	0.986852i	−0.983406	+	0.181417i	$0.941932\pi$
$368$	−0.350243	+	1.03576i	−0.0182577	+	0.0539926i
$369$	−2.23391	−	3.52009i	−0.116293	−	0.183248i
$370$	1.45385	−	1.34897i	0.0755820	−	0.0701294i
$371$	3.23864	−	12.6137i	0.168142	−	0.654869i
$372$	10.3811	+	4.56595i	0.538234	+	0.236733i
$373$	−18.1283	−	2.29014i	−0.938650	−	0.118579i	−0.358902	−	0.933375i	$-0.616849\pi$
$373$	−18.1283	−	2.29014i	−0.938650	−	0.118579i	−0.579748	+	0.814796i	$0.696849\pi$
$374$	−10.7644	+	2.55041i	−0.556616	+	0.131879i
$375$	−14.0079	−	9.38341i	−0.723364	−	0.484557i
$376$	−5.28750	−	6.30413i	−0.272682	−	0.325111i
$377$	−3.65508	+	28.9329i	−0.188246	+	1.49012i
$378$	−7.93142	+	10.4983i	−0.407948	+	0.539977i
$379$	7.66480	−	29.8524i	0.393715	−	1.53342i	−0.395014	−	0.918675i	$-0.629260\pi$
$379$	7.66480	−	29.8524i	0.393715	−	1.53342i	0.788728	−	0.614742i	$-0.210740\pi$
$380$	16.5266	−	12.9987i	0.847798	−	0.666821i
$381$	3.48477	−	2.21150i	0.178530	−	0.113299i
$382$	−0.910557	−	1.49588i	−0.0465881	−	0.0765360i
$383$	0.335945	−	0.848500i	0.0171660	−	0.0433563i	−0.920941	−	0.389703i	$-0.872578\pi$
$383$	0.335945	−	0.848500i	0.0171660	−	0.0433563i	0.938107	+	0.346346i	$0.112578\pi$
$384$	16.9156	+	2.22556i	0.863222	+	0.113573i
$385$	−7.00772	−	1.70471i	−0.357147	−	0.0868799i
$386$	−1.73205	−	16.1293i	−0.0881591	−	0.820960i
$387$	1.09607	+	2.32926i	0.0557162	+	0.118403i
$388$	−24.6145	+	6.99234i	−1.24961	+	0.354982i
$389$	−12.3919	+	2.36389i	−0.628296	+	0.119854i	−0.491688	−	0.870771i	$-0.663620\pi$
$389$	−12.3919	+	2.36389i	−0.628296	+	0.119854i	−0.136608	+	0.990625i	$0.543620\pi$
$390$	−3.13214	−	16.9706i	−0.158602	−	0.859342i
$391$	−0.961949	−	0.528836i	−0.0486479	−	0.0267444i
$392$	−7.01300	+	9.79123i	−0.354210	+	0.494532i
$393$	13.1274	+	4.26535i	0.662189	+	0.215158i
$394$	5.48626	−	11.1149i	0.276394	−	0.559960i
$395$	−18.2477	+	4.93308i	−0.918142	+	0.248210i
$396$	2.81346	+	0.282879i	0.141381	+	0.0142152i
$397$	−4.96187	−	1.27399i	−0.249029	−	0.0639398i	0.122112	−	0.992516i	$-0.461033\pi$
$397$	−4.96187	−	1.27399i	−0.249029	−	0.0639398i	−0.371141	+	0.928577i	$0.621033\pi$
$398$	−18.2199	−	10.4646i	−0.913283	−	0.524541i
$399$	−3.62796	−	11.1657i	−0.181625	−	0.558985i
$400$	−18.2097	−	8.27085i	−0.910485	−	0.413542i
$401$	9.42879	−	29.0188i	0.470851	−	1.44913i	−0.380620	−	0.924731i	$-0.624289\pi$
$401$	9.42879	−	29.0188i	0.470851	−	1.44913i	0.851472	−	0.524400i	$-0.175711\pi$
$402$	−12.2516	+	11.0816i	−0.611055	+	0.552698i
$403$	−0.854401	−	13.5803i	−0.0425607	−	0.676483i
$404$	19.6610	−	11.4699i	0.978171	−	0.570647i
$405$	10.1388	−	9.76620i	0.503799	−	0.485286i
$406$	16.7044	−	8.78087i	0.829024	−	0.435787i
$407$	−0.718044	+	0.988303i	−0.0355921	+	0.0489883i
$408$	−5.18291	+	16.3265i	−0.256592	+	0.808281i
$409$	32.7923	−	4.14263i	1.62148	−	0.204840i	0.738498	−	0.674256i	$-0.235535\pi$
$409$	32.7923	−	4.14263i	1.62148	−	0.204840i	0.882977	+	0.469416i	$0.155535\pi$
$410$	−7.63506	−	16.4807i	−0.377069	−	0.813925i
$411$	−4.60580	−	2.16732i	−0.227187	−	0.106906i
$412$	−0.0298074	+	0.797123i	−0.00146851	+	0.0392714i
$413$	10.5891	−	9.94380i	0.521054	−	0.489302i
$414$	0.188220	+	0.208093i	0.00925049	+	0.0102272i
$415$	16.4924	+	33.9231i	0.809582	+	1.66522i
$416$	−6.94981	−	19.2551i	−0.340742	−	0.944058i
$417$	3.85061	+	3.18550i	0.188565	+	0.155995i
$418$	−8.44039	+	9.82300i	−0.412833	+	0.480458i
$419$	6.75736	−	17.0671i	0.330119	−	0.833784i	−0.666015	−	0.745938i	$-0.732002\pi$
$419$	6.75736	−	17.0671i	0.330119	−	0.833784i	0.996134	−	0.0878465i	$-0.0279985\pi$
$420$	−7.84313	+	7.94959i	−0.382706	+	0.387900i
$421$	27.3547	−	22.6298i	1.33319	−	1.10291i	0.346893	−	0.937905i	$-0.387237\pi$
$421$	27.3547	−	22.6298i	1.33319	−	1.10291i	0.986293	−	0.165003i	$-0.0527632\pi$
$422$	−12.5173	−	17.9237i	−0.609334	−	0.872510i
$423$	−2.07411	+	0.395658i	−0.100847	+	0.0192376i
$424$	−5.38605	+	21.5826i	−0.261570	+	1.04814i
$425$	11.3861	−	16.5394i	0.552309	−	0.802277i
$426$	1.56602	+	0.654140i	0.0758738	+	0.0316932i
$427$	2.70305	−	5.74427i	0.130810	−	0.277985i
$428$	−0.459759	+	4.57267i	−0.0222233	+	0.221029i
$429$	3.91305	+	9.88324i	0.188924	+	0.477167i
$430$	3.40177	+	10.6869i	0.164048	+	0.515366i
$431$	−1.33032	+	21.1448i	−0.0640792	+	1.01851i	0.826283	+	0.563256i	$0.190451\pi$
$431$	−1.33032	+	21.1448i	−0.0640792	+	1.01851i	−0.890362	+	0.455254i	$0.849549\pi$
$432$	13.4261	−	18.0237i	0.645965	−	0.867165i
$433$	22.1834	+	1.39566i	1.06607	+	0.0670713i	0.586119	−	0.810225i	$-0.300655\pi$
$433$	22.1834	+	1.39566i	1.06607	+	0.0670713i	0.479949	+	0.877296i	$0.340655\pi$
$434$	−6.88836	+	5.48499i	−0.330652	+	0.263288i
$435$	−25.7358	+	8.72498i	−1.23394	+	0.418331i
$436$	−5.38610	+	18.1349i	−0.257947	+	0.868505i
$437$	−1.27501	+	0.161071i	−0.0609920	+	0.00770508i
$438$	−5.23474	−	13.9792i	−0.250125	−	0.667951i
$439$	−27.1522	−	25.4976i	−1.29590	−	1.21693i	−0.961596	−	0.274469i	$-0.911498\pi$
$439$	−27.1522	−	25.4976i	−1.29590	−	1.21693i	−0.334307	−	0.942464i	$-0.608502\pi$
$440$	11.9895	+	2.83077i	0.571575	+	0.134952i
$441$	1.31596	+	2.79657i	0.0626650	+	0.133170i
$442$	20.2569	−	3.47322i	0.963522	−	0.165204i
$443$	37.5978			1.78632			0.893162	−	0.449736i	$-0.148482\pi$
$443$	37.5978			1.78632			0.893162	+	0.449736i	$0.148482\pi$
$444$	0.740874	+	1.74045i	0.0351603	+	0.0825979i
$445$	−5.75702	−	6.78179i	−0.272909	−	0.321487i
$446$	−7.73484	−	11.0756i	−0.366255	−	0.524444i
$447$	0.381440	+	0.242069i	0.0180415	+	0.0114495i
$448$	−7.64062	+	10.8214i	−0.360985	+	0.511265i
$449$	−27.8650	−	20.2451i	−1.31503	−	0.955427i	−0.999980	−	0.00635305i	$-0.997978\pi$
$449$	−27.8650	−	20.2451i	−1.31503	−	0.955427i	−0.315053	−	0.949074i	$-0.602022\pi$
$450$	−4.13194	+	3.04463i	−0.194782	+	0.143525i
$451$	6.57604	+	9.05114i	0.309654	+	0.426202i
$452$	17.0384	−	13.0544i	0.801419	−	0.614029i
$453$	15.6281	−	6.18762i	0.734274	−	0.290720i
$454$	−22.6589	−	17.1186i	−1.06343	−	0.803416i
$455$	12.7948	+	3.97835i	0.599830	+	0.186508i
$456$	6.32591	+	19.0300i	0.296238	+	0.891161i
$457$	−21.5571	−	29.6708i	−1.00840	−	1.38794i	−0.920029	−	0.391851i	$-0.871835\pi$
$457$	−21.5571	−	29.6708i	−1.00840	−	1.38794i	−0.0883682	−	0.996088i	$-0.528165\pi$
$458$	−25.6286	−	12.6502i	−1.19755	−	0.591104i
$459$	15.4463	+	16.4487i	0.720974	+	0.767759i
$460$	0.693906	+	1.00639i	0.0323535	+	0.0469233i
$461$	−4.35820	−	7.92754i	−0.202982	−	0.369222i	0.755149	−	0.655553i	$-0.227564\pi$
$461$	−4.35820	−	7.92754i	−0.202982	−	0.369222i	−0.958131	+	0.286331i	$0.907564\pi$
$462$	3.79363	−	5.73791i	0.176496	−	0.266952i
$463$	1.12448	−	2.04543i	0.0522591	−	0.0950590i	−0.848887	−	0.528574i	$-0.822727\pi$
$463$	1.12448	−	2.04543i	0.0522591	−	0.0950590i	0.901146	+	0.433515i	$0.142727\pi$
$464$	−28.4309	+	15.1915i	−1.31987	+	0.705248i
$465$	11.0326	−	6.24900i	0.511625	−	0.289790i
$466$	−8.96409	−	23.9383i	−0.415254	−	1.10892i
$467$	10.4105	+	16.4044i	0.481742	+	0.759103i	0.995079	−	0.0990836i	$-0.0315911\pi$
$467$	10.4105	+	16.4044i	0.481742	+	0.759103i	−0.513338	+	0.858187i	$0.671591\pi$
$468$	−5.18369	−	0.852718i	−0.239616	−	0.0394169i
$469$	−3.18981	−	12.4235i	−0.147292	−	0.573663i
$470$	−9.18431	+	0.522645i	−0.423641	+	0.0241078i
$471$	−1.98542	−	31.5573i	−0.0914832	−	1.45408i
$472$	−17.9720	+	17.1072i	−0.827230	+	0.787423i
$473$	−3.32798	−	6.05358i	−0.153021	−	0.278344i
$474$	1.46807	−	17.9688i	0.0674309	−	0.825337i
$475$	−0.597095	−	23.5003i	−0.0273966	−	1.07827i
$476$	−9.34815	−	9.46025i	−0.428472	−	0.433610i
$477$	4.16132	+	3.90774i	0.190534	+	0.178923i
$478$	24.9501	+	0.466326i	1.14119	+	0.0213293i
$479$	12.9337	−	20.3803i	0.590958	−	0.931200i	−0.408869	−	0.912593i	$-0.634077\pi$
$479$	12.9337	−	20.3803i	0.590958	−	0.931200i	0.999827	−	0.0186073i	$-0.00592324\pi$
$480$	13.3048	−	13.6692i	0.607278	−	0.623910i
$481$	1.44668	−	1.74874i	0.0659631	−	0.0797357i
$482$	−2.30224	+	28.1788i	−0.104864	+	1.28351i
$483$	0.661123	−	0.169748i	0.0300821	−	0.00772378i
$484$	14.4019	+	0.538542i	0.654633	+	0.0244792i
$485$	−10.1929	+	26.7313i	−0.462834	+	1.21380i
$486$	−4.25622	−	9.50188i	−0.193066	−	0.431014i
$487$	10.8633	+	2.07228i	0.492261	+	0.0939038i	0.427534	−	0.903999i	$-0.359382\pi$
$487$	10.8633	+	2.07228i	0.492261	+	0.0939038i	0.0647269	+	0.997903i	$0.479382\pi$
$488$	−4.55062	+	9.84292i	−0.205997	+	0.445568i
$489$	−26.3761	−	3.33208i	−1.19277	−	0.150682i
$490$	4.08425	+	12.8309i	0.184507	+	0.579641i
$491$	24.4680	+	4.66753i	1.10423	+	0.210642i	0.707094	−	0.707119i	$-0.250006\pi$
$491$	24.4680	+	4.66753i	1.10423	+	0.210642i	0.397132	+	0.917762i	$0.370006\pi$
$492$	17.2561	−	1.52746i	0.777964	−	0.0688634i
$493$	−10.0009	−	30.7795i	−0.450417	−	1.38624i
$494$	16.7960	−	17.2291i	0.755689	−	0.775175i
$495$	2.13468	−	2.33186i	0.0959468	−	0.104809i
$496$	11.7025	−	9.44842i	0.525456	−	0.424247i
$497$	−1.01532	+	0.839944i	−0.0455432	+	0.0376766i
$498$	−35.7699	+	3.84117i	−1.60289	+	0.172127i
$499$		−	3.21970i		−	0.144134i	−0.997400	−	0.0720668i	$-0.977041\pi$
$499$		−	3.21970i		−	0.144134i	0.997400	−	0.0720668i	$-0.0229595\pi$
$500$	−19.5870	+	10.7866i	−0.875956	+	0.482391i
$501$			31.0705i			1.38813i
$502$	1.07286	+	9.99078i	0.0478843	+	0.445910i
$503$	−28.8128	+	23.8360i	−1.28470	+	1.06280i	−0.290320	+	0.956930i	$0.593762\pi$
$503$	−28.8128	+	23.8360i	−1.28470	+	1.06280i	−0.994380	+	0.105867i	$0.966238\pi$
$504$	1.46823	+	3.06611i	0.0654000	+	0.136575i
$505$	2.86865	−	25.2866i	0.127653	−	1.12524i
$506$	−0.539157	−	0.525604i	−0.0239684	−	0.0233660i
$507$	−0.0445267	−	0.137039i	−0.00197750	−	0.00608612i
$508$	−0.482634	−	5.45241i	−0.0214134	−	0.241912i
$509$	−25.6406	−	4.89121i	−1.13650	−	0.216799i	−0.415406	−	0.909636i	$-0.636360\pi$
$509$	−25.6406	−	4.89121i	−1.13650	−	0.216799i	−0.721094	+	0.692837i	$0.756360\pi$
$510$	11.1639	+	15.5608i	0.494344	+	0.689044i
$511$	11.4985	+	1.45260i	0.508664	+	0.0642592i
$512$	12.9257	−	18.5722i	0.571241	−	0.820783i
$513$	25.9488	+	4.94999i	1.14567	+	0.218547i
$514$	−31.5514	+	14.1330i	−1.39167	+	0.623379i
$515$	0.694335	+	0.559703i	0.0305960	+	0.0246635i
$516$	−10.6892	−	0.399708i	−0.470564	−	0.0175962i
$517$	5.48826	−	1.40914i	0.241373	−	0.0619741i
$518$	−1.46380	−	0.119594i	−0.0643155	−	0.00525465i
$519$	−13.1313	+	15.8730i	−0.576401	+	0.696749i
$520$	−21.9005	−	6.64743i	−0.960402	−	0.291509i
$521$	12.6573	−	19.9448i	0.554528	−	0.873797i	−0.445238	−	0.895412i	$-0.646881\pi$
$521$	12.6573	−	19.9448i	0.554528	−	0.873797i	0.999766	+	0.0216155i	$0.00688096\pi$
$522$	−0.154586	+	8.27090i	−0.00676604	+	0.362007i
$523$	11.2353	+	10.5507i	0.491287	+	0.461349i	0.890154	−	0.455660i	$-0.150597\pi$
$523$	11.2353	+	10.5507i	0.491287	+	0.461349i	−0.398867	+	0.917009i	$0.630597\pi$
$524$	13.0212	−	12.8669i	0.568833	−	0.562092i
$525$	1.87898	+	12.3433i	0.0820052	+	0.538707i
$526$	20.7881	+	1.69841i	0.906404	+	0.0740542i
$527$	7.27475	+	13.2327i	0.316893	+	0.576426i
$528$	−6.41350	+	9.84466i	−0.279112	+	0.428434i
$529$	1.43949	+	22.8800i	0.0625865	+	0.994785i
$530$	15.7378	+	19.2573i	0.683606	+	0.836484i
$531$	1.58353	+	6.16743i	0.0687192	+	0.267644i
$532$	−15.3639	−	2.52737i	−0.666111	−	0.109575i
$533$	−11.1374	−	17.5497i	−0.482414	−	0.760162i
$534$	7.94568	−	2.97539i	0.343843	−	0.128758i
$535$	3.78994	+	3.46947i	0.163854	+	0.149998i
$536$	5.59205	+	21.1834i	0.241540	+	0.914984i
$537$	−1.92174	+	3.49562i	−0.0829290	+	0.150847i
$538$	−13.5535	−	8.96095i	−0.584335	−	0.386334i
$539$	−3.99566	−	7.26807i	−0.172105	−	0.313058i
$540$	−7.17285	−	24.0820i	−0.308670	−	1.03632i
$541$	7.80706	+	8.31368i	0.335652	+	0.357433i	0.874548	−	0.484939i	$-0.161158\pi$
$541$	7.80706	+	8.31368i	0.335652	+	0.357433i	−0.538896	+	0.842372i	$0.681158\pi$
$542$	−1.52545	+	3.09048i	−0.0655236	+	0.132747i
$543$	15.0236	+	20.6782i	0.644724	+	0.887386i
$544$	16.0767	+	16.0508i	0.689284	+	0.688173i
$545$	12.6485	+	16.9521i	0.541800	+	0.726147i
$546$	−7.70349	+	10.1967i	−0.329679	+	0.436377i
$547$	−42.1219	+	16.6773i	−1.80100	+	0.713068i	−0.808854	+	0.588009i	$0.799912\pi$
$547$	−42.1219	+	16.6773i	−1.80100	+	0.713068i	−0.992149	+	0.125058i	$0.960088\pi$
$548$	−5.35880	+	4.10579i	−0.228917	+	0.175391i
$549$	1.63571	+	2.25136i	0.0698104	+	0.0960858i
$550$	10.5532	−	8.85041i	0.449991	−	0.377383i
$551$	−30.6527	−	22.2705i	−1.30585	−	0.948756i
$552$	−1.12729	+	0.297584i	−0.0479806	+	0.0126660i
$553$	11.8189	+	7.50052i	0.502592	+	0.318955i
$554$	26.6736	−	18.6280i	1.13325	−	0.791428i
$555$	2.05492	+	0.499881i	0.0872263	+	0.0212188i
$556$	6.09827	−	2.59591i	0.258624	−	0.110091i
$557$	26.0396			1.10333			0.551666	−	0.834065i	$-0.313992\pi$
$557$	26.0396			1.10333			0.551666	+	0.834065i	$0.313992\pi$
$558$	−0.652279	−	3.80429i	−0.0276132	−	0.161049i
$559$	5.46454	+	11.6127i	0.231125	+	0.491167i
$560$	4.58771	+	14.0821i	0.193866	+	0.595078i
$561$	−8.59914	−	8.07513i	−0.363056	−	0.340932i
$562$	20.7059	−	7.75365i	0.873424	−	0.327068i
$563$	41.9948	−	5.30518i	1.76987	−	0.223587i	0.828273	−	0.560324i	$-0.189324\pi$
$563$	41.9948	−	5.30518i	1.76987	−	0.223587i	0.941599	+	0.336738i	$0.109324\pi$
$564$	2.49799	−	8.41070i	0.105184	−	0.354154i
$565$	−0.304797	−	23.9961i	−0.0128229	−	1.00952i
$566$	8.31706	+	10.4450i	0.349592	+	0.439037i
$567$	−10.4042	−	0.654574i	−0.436933	−	0.0274895i
$568$	1.72453	−	1.44643i	0.0723598	−	0.0606907i
$569$	0.971821	−	15.4467i	0.0407409	−	0.647558i	−0.923677	−	0.383173i	$-0.874831\pi$
$569$	0.971821	−	15.4467i	0.0407409	−	0.647558i	0.964417	−	0.264384i	$-0.0851688\pi$
$570$	21.2817	+	7.05598i	0.891392	+	0.295542i
$571$	1.47409	+	3.72312i	0.0616886	+	0.155808i	0.957351	−	0.288926i	$-0.0932983\pi$
$571$	1.47409	+	3.72312i	0.0616886	+	0.155808i	−0.895663	+	0.444734i	$0.853298\pi$
$572$	14.0267	+	1.41032i	0.586487	+	0.0589683i
$573$	0.795098	−	1.68967i	0.0332157	−	0.0705869i
$574$	−5.18430	+	12.4113i	−0.216389	+	0.518036i
$575$	1.36576	+	0.0511433i	0.0569561	+	0.00213282i
$576$	−2.54329	−	5.22019i	−0.105970	−	0.217508i
$577$	22.1375	−	4.22294i	0.921594	−	0.175803i	0.295313	−	0.955401i	$-0.404576\pi$
$577$	22.1375	−	4.22294i	0.921594	−	0.175803i	0.626281	+	0.779597i	$0.284576\pi$
$578$	1.01128	−	0.706246i	0.0420637	−	0.0293759i
$579$	13.3285	−	11.0263i	0.553912	−	0.458236i
$580$	−5.39780	+	35.6334i	−0.224132	+	1.47959i
$581$	10.2826	−	25.9710i	0.426596	−	1.07746i
$582$	−20.6954	−	17.7825i	−0.857852	−	0.737108i
$583$	−11.8034	−	9.76461i	−0.488846	−	0.404409i
$584$	−19.6571	−	2.34824i	−0.813418	−	0.0971708i
$585$	−4.23014	+	4.07470i	−0.174895	+	0.168468i
$586$	−27.9495	+	25.2803i	−1.15458	+	1.04432i
$587$	−7.17724	+	6.73988i	−0.296237	+	0.278185i	−0.818385	−	0.574670i	$-0.805131\pi$
$587$	−7.17724	+	6.73988i	−0.296237	+	0.278185i	0.522149	+	0.852854i	$0.325131\pi$
$588$	−12.8337	−	0.479899i	−0.529251	−	0.0197907i
$589$	15.9961	+	7.52720i	0.659108	+	0.310153i
$590$	3.31203	+	27.5426i	0.136354	+	1.13391i
$591$	13.1132	−	1.65658i	0.539405	−	0.0681427i
$592$	2.50166	+	0.187355i	0.102818	+	0.00770025i
$593$	2.50560	−	3.44866i	0.102893	−	0.141620i	−0.754466	−	0.656339i	$-0.772104\pi$
$593$	2.50560	−	3.44866i	0.102893	−	0.141620i	0.857358	+	0.514720i	$0.172104\pi$
$594$	7.20155	+	13.6999i	0.295483	+	0.562115i
$595$	−14.7275	+	2.05087i	−0.603769	+	0.0840777i
$596$	0.517523	−	0.301913i	0.0211985	−	0.0123668i
$597$	−1.40683	−	22.3609i	−0.0575777	−	0.915171i
$598$	0.938386	+	1.03747i	0.0383735	+	0.0424252i
$599$	−9.10450	+	28.0208i	−0.372000	+	1.14490i	0.573480	+	0.819219i	$0.305593\pi$
$599$	−9.10450	+	28.0208i	−0.372000	+	1.14490i	−0.945480	+	0.325679i	$0.894407\pi$
$600$	−3.35212	−	21.0617i	−0.136850	−	0.859839i
$601$	−6.47125	−	19.9165i	−0.263968	−	0.812410i	−0.991929	−	0.126792i	$-0.959532\pi$
$601$	−6.47125	−	19.9165i	−0.263968	−	0.812410i	0.727961	−	0.685618i	$-0.240468\pi$
$602$	4.13636	−	7.20185i	0.168585	−	0.293526i
$603$	5.44580	+	1.39824i	0.221770	+	0.0569409i
$604$	2.23010	−	22.1802i	0.0907417	−	0.902498i
$605$	10.1124	−	12.5448i	0.411126	−	0.510019i
$606$	21.7651	+	10.7431i	0.884145	+	0.436410i
$607$	−42.8607	−	13.9263i	−1.73966	−	0.565250i	−0.744873	−	0.667206i	$-0.767490\pi$
$607$	−42.8607	−	13.9263i	−1.73966	−	0.565250i	−0.994789	+	0.101956i	$0.967490\pi$
$608$	26.2720	+	4.13935i	1.06547	+	0.167873i
$609$	17.6344	+	9.69461i	0.714583	+	0.392845i
$610$	5.77702	+	10.6590i	0.233905	+	0.431572i
$611$	−10.3407	+	1.97259i	−0.418339	+	0.0798024i
$612$	5.60803	−	1.59310i	0.226691	−	0.0643972i
$613$	10.7934	+	22.9372i	0.435943	+	0.926426i	0.995240	+	0.0974584i	$0.0310713\pi$
$613$	10.7934	+	22.9372i	0.435943	+	0.926426i	−0.559297	+	0.828968i	$0.688929\pi$
$614$	41.9331	−	4.50300i	1.69228	−	0.181726i
$615$	10.1695	−	16.4837i	0.410075	−	0.664687i
$616$	−4.44887	−	7.96431i	−0.179250	−	0.320891i
$617$	1.63225	−	4.12260i	0.0657120	−	0.165970i	−0.893210	−	0.449640i	$-0.851552\pi$
$617$	1.63225	−	4.12260i	0.0657120	−	0.165970i	0.958922	+	0.283671i	$0.0915522\pi$
$618$	−0.726574	+	0.442272i	−0.0292271	+	0.0177908i
$619$	34.4340	−	21.8525i	1.38402	−	0.878325i	0.385013	−	0.922911i	$-0.374197\pi$
$619$	34.4340	−	21.8525i	1.38402	−	0.878325i	0.999006	+	0.0445859i	$0.0141968\pi$
$620$	−0.641485	−	16.8037i	−0.0257627	−	0.674852i
$621$	−0.381945	+	1.48758i	−0.0153269	+	0.0596945i
$622$	16.5700	+	12.5185i	0.664395	+	0.501945i
$623$	−0.825648	+	6.53568i	−0.0330789	+	0.261846i
$624$	13.0403	−	17.5057i	0.522030	−	0.700790i
$625$	−3.43140	+	24.7634i	−0.137256	+	0.990536i
$626$	−1.37051	−	5.78447i	−0.0547765	−	0.231194i
$627$	−13.7014	−	1.73089i	−0.547180	−	0.0691249i
$628$	−38.3862	−	16.8835i	−1.53178	−	0.673726i
$629$	−0.626367	+	2.43954i	−0.0249749	+	0.0972708i
$630$	3.72912	+	0.734533i	0.148572	+	0.0292645i
$631$	−9.21858	−	14.5262i	−0.366986	−	0.578277i	0.609784	−	0.792568i	$-0.291256\pi$
$631$	−9.21858	−	14.5262i	−0.366986	−	0.578277i	−0.976770	+	0.214290i	$0.931256\pi$
$632$	−20.2744	−	12.6749i	−0.806471	−	0.504179i
$633$	8.58176	−	21.6751i	0.341095	−	0.861506i
$634$	0.754107	+	17.0719i	0.0299494	+	0.678013i
$635$	−5.20836	−	3.21327i	−0.206688	−	0.127515i
$636$	−22.3653	+	7.90175i	−0.886843	+	0.313325i
$637$	6.56086	+	13.9425i	0.259951	+	0.552423i
$638$	−0.979625	−	22.1773i	−0.0387837	−	0.878008i
$639$	−0.108235	−	0.567386i	−0.00428170	−	0.0224454i
$640$	−7.99896	−	24.0003i	−0.316186	−	0.948697i
$641$	−1.27062	−	0.698530i	−0.0501865	−	0.0275903i	0.456463	−	0.889742i	$-0.349116\pi$
$641$	−1.27062	−	0.698530i	−0.0501865	−	0.0275903i	−0.506649	+	0.862152i	$0.669116\pi$
$642$	−4.33780	+	2.28022i	−0.171199	+	0.0899931i
$643$	−14.2511	+	43.8604i	−0.562008	+	1.72968i	0.114669	+	0.993404i	$0.463419\pi$
$643$	−14.2511	+	43.8604i	−0.562008	+	1.72968i	−0.676677	+	0.736280i	$0.736581\pi$
$644$	0.202735	−	0.882250i	0.00798887	−	0.0347655i
$645$	−7.50543	+	9.31080i	−0.295526	+	0.366612i
$646$	−8.72453	+	25.2366i	−0.343262	+	0.992921i
$647$	0.384682	−	1.49824i	0.0151234	−	0.0589018i	−0.960574	−	0.278026i	$-0.910320\pi$
$647$	0.384682	−	1.49824i	0.0151234	−	0.0589018i	0.975697	+	0.219124i	$0.0703199\pi$
$648$	17.7787	+	0.997798i	0.698412	+	0.0391972i
$649$	−5.28024	−	16.2509i	−0.207267	−	0.637903i
$650$	−20.6002	+	15.1793i	−0.808005	+	0.595380i
$651$	−8.92994	−	2.90151i	−0.349992	−	0.113719i
$652$	−19.9919	+	29.0433i	−0.782944	+	1.13743i
$653$	−2.04429	−	32.4930i	−0.0799991	−	1.27155i	−0.809316	−	0.587373i	$-0.800162\pi$
$653$	−2.04429	−	32.4930i	−0.0799991	−	1.27155i	0.729317	−	0.684176i	$-0.239838\pi$
$654$	−19.2986	+	5.87414i	−0.754636	+	0.229697i
$655$	−2.82284	−	20.2711i	−0.110298	−	0.792056i
$656$	8.71173	−	21.2593i	0.340136	−	0.830038i
$657$	−2.98618	+	4.11013i	−0.116502	+	0.160351i
$658$	4.87791	+	4.75529i	0.190161	+	0.185381i
$659$	2.32795	+	18.4277i	0.0906842	+	0.717839i	0.970257	+	0.242076i	$0.0778283\pi$
$659$	2.32795	+	18.4277i	0.0906842	+	0.717839i	−0.879573	+	0.475764i	$0.842172\pi$
$660$	4.53298	+	12.3294i	0.176446	+	0.479923i
$661$	−3.41884	−	1.60879i	−0.132978	−	0.0625745i	0.358139	−	0.933668i	$-0.383411\pi$
$661$	−3.41884	−	1.60879i	−0.132978	−	0.0625745i	−0.491117	+	0.871094i	$0.663411\pi$
$662$	6.06317	−	21.9065i	0.235652	−	0.851420i
$663$	15.0025	+	15.9760i	0.582647	+	0.620456i
$664$	−17.2634	+	44.4794i	−0.669949	+	1.72613i
$665$	−12.5377	+	12.0770i	−0.486191	+	0.468326i
$666$	0.355057	−	0.537028i	0.0137582	−	0.0208094i
$667$	1.40412	−	1.69729i	0.0543678	−	0.0657194i
$668$	36.6033	+	18.9260i	1.41622	+	0.732268i
$669$	5.30294	−	13.3937i	0.205023	−	0.517830i
$670$	22.7206	+	9.15344i	0.877772	+	0.353628i
$671$	−4.76014	−	5.75402i	−0.183763	−	0.222131i
$672$	−14.1191	−	0.432308i	−0.544658	−	0.0166766i
$673$	11.2010	−	2.13671i	0.431769	−	0.0823643i	0.0330845	−	0.999453i	$-0.489467\pi$
$673$	11.2010	−	2.13671i	0.431769	−	0.0823643i	0.398684	+	0.917088i	$0.369467\pi$
$674$	29.9805	+	25.7607i	1.15481	+	0.992264i
$675$	−26.3749	−	9.67509i	−1.01517	−	0.372394i
$676$	−0.188565	−	0.0310189i	−0.00725248	−	0.00119304i
$677$	0.613083	−	1.30287i	0.0235627	−	0.0500733i	−0.892699	−	0.450653i	$-0.851191\pi$
$677$	0.613083	−	1.30287i	0.0235627	−	0.0500733i	0.916262	+	0.400580i	$0.131191\pi$
$678$	21.6322	+	7.47846i	0.830780	+	0.287209i
$679$	19.6978	−	7.79892i	0.755933	−	0.299295i
$680$	25.1320	−	3.67330i	0.963769	−	0.140864i
$681$	1.90144	−	30.2226i	0.0728635	−	1.15813i
$682$	2.38797	+	10.0788i	0.0914399	+	0.385938i
$683$	−0.449736	+	7.14835i	−0.0172087	+	0.273524i	0.980008	+	0.198960i	$0.0637565\pi$
$683$	−0.449736	+	7.14835i	−0.0172087	+	0.273524i	−0.997216	+	0.0745639i	$0.976244\pi$
$684$	4.21531	−	5.36798i	0.161177	−	0.205250i
$685$	0.0958627	+	7.54709i	0.00366272	+	0.288359i
$686$	13.1303	−	22.8613i	0.501318	−	0.872849i
$687$	−3.81973	−	30.2363i	−0.145732	−	1.15359i
$688$	−6.98198	+	12.3491i	−0.266185	+	0.470807i
$689$	20.7467	+	19.4824i	0.790385	+	0.742221i
$690$	−0.487106	+	1.20909i	−0.0185438	+	0.0460292i
$691$	−29.7575	+	14.0028i	−1.13203	+	0.532692i	−0.898201	−	0.439586i	$-0.855125\pi$
$691$	−29.7575	+	14.0028i	−1.13203	+	0.532692i	−0.233828	+	0.972278i	$0.575125\pi$
$692$	10.7009	+	25.1384i	0.406788	+	0.955619i
$693$	−2.34111			−0.0889313
$694$	7.02378	+	40.9649i	0.266619	+	1.55501i
$695$	1.75151	−	7.20013i	0.0664386	−	0.273116i
$696$	−30.2331	−	16.3553i	−1.14598	−	0.619946i
$697$	19.4758	+	12.3597i	0.737699	+	0.468158i
$698$	35.7143	+	7.50714i	1.35180	+	0.284149i
$699$	16.0215	−	22.0516i	0.605987	−	0.834070i
$700$	15.6859	+	5.30513i	0.592871	+	0.200515i
$701$	20.4765	+	28.1835i	0.773388	+	1.06448i	0.995981	+	0.0895658i	$0.0285479\pi$
$701$	20.4765	+	28.1835i	0.773388	+	1.06448i	−0.222593	+	0.974911i	$0.571452\pi$
$702$	−11.7549	−	26.2425i	−0.443660	−	0.990457i
$703$	1.08548	+	2.74161i	0.0409396	+	0.103402i
$704$	7.69108	+	13.5523i	0.289869	+	0.510770i
$705$	−5.86616	−	7.86212i	−0.220932	−	0.296104i
$706$	−2.79806	+	19.2488i	−0.105306	+	0.724437i
$707$	−15.2464	+	11.0771i	−0.573399	+	0.416599i
$708$	−25.7862	−	5.92550i	−0.969106	−	0.222694i
$709$	0.448683	+	0.477799i	0.0168506	+	0.0179441i	0.737339	−	0.675523i	$-0.236082\pi$
$709$	0.448683	+	0.477799i	0.0168506	+	0.0179441i	−0.720488	+	0.693467i	$0.756082\pi$
$710$	−0.142973	−	2.51242i	−0.00536566	−	0.0942895i
$711$	−5.37702	+	2.95604i	−0.201654	+	0.110860i
$712$	1.33472	−	11.1730i	0.0500209	−	0.418726i
$713$	−0.495152	+	0.900679i	−0.0185436	+	0.0337307i
$714$	2.91732	−	13.8788i	0.109178	−	0.519400i
$715$	10.6426	−	11.6257i	0.398012	−	0.434777i
$716$	2.94752	+	4.39324i	0.110154	+	0.164183i
$717$	14.2583	+	22.4675i	0.532486	+	0.839063i
$718$	5.97734	+	2.49679i	0.223072	+	0.0931794i
$719$	−11.6390	+	2.98839i	−0.434062	+	0.111448i	−0.459398	−	0.888231i	$-0.651935\pi$
$719$	−11.6390	+	2.98839i	−0.434062	+	0.111448i	0.0253353	+	0.999679i	$0.491935\pi$
$720$	−6.37813	−	1.21154i	−0.237699	−	0.0451512i
$721$	−0.0414687	−	0.659126i	−0.00154437	−	0.0245471i
$722$	1.27858	+	4.20058i	0.0475837	+	0.156329i
$723$	−26.4191	+	14.5240i	−0.982538	+	0.540155i
$724$	33.5118	−	5.10318i	1.24545	−	0.189658i
$725$	28.3202	+	28.6628i	1.05178	+	1.06451i
$726$	7.99070	+	13.1273i	0.296563	+	0.487199i
$727$	12.7826	−	13.6121i	0.474081	−	0.504845i	−0.446830	−	0.894619i	$-0.647447\pi$
$727$	12.7826	−	13.6121i	0.474081	−	0.504845i	0.920910	+	0.389774i	$0.127447\pi$
$728$	7.31998	+	15.2864i	0.271296	+	0.566551i
$729$	16.0690	−	25.3206i	0.595146	−	0.937801i
$730$	−15.2478	+	16.0437i	−0.564347	+	0.593804i
$731$	−10.9743	−	9.07869i	−0.405897	−	0.335788i
$732$	−11.4315	+	1.74079i	−0.422521	+	0.0643416i
$733$	−0.714688	+	0.183501i	−0.0263976	+	0.00677775i	−0.261866	−	0.965104i	$-0.584338\pi$
$733$	−0.714688	+	0.183501i	−0.0263976	+	0.00677775i	0.235468	+	0.971882i	$0.424338\pi$
$734$	−7.67044	+	27.7136i	−0.283121	+	1.02293i
$735$	−9.01120	+	11.1788i	−0.332383	+	0.412335i
$736$	−0.336089	+	1.50930i	−0.0123884	+	0.0556334i
$737$	−14.8206	−	2.82719i	−0.545925	−	0.104141i
$738$	−3.67270	−	4.61238i	−0.135194	−	0.169784i
$739$	3.77282	−	29.8649i	0.138785	−	1.09860i	−0.756780	−	0.653669i	$-0.773229\pi$
$739$	3.77282	−	29.8649i	0.138785	−	1.09860i	0.895566	−	0.444929i	$-0.146771\pi$
$740$	1.84061	−	2.11635i	0.0676621	−	0.0777986i
$741$	25.2031	+	4.80774i	0.925858	+	0.176617i
$742$	2.64931	−	18.2255i	0.0972592	−	0.669078i
$743$	−16.1811	+	5.25754i	−0.593625	+	0.192881i	−0.590395	−	0.807114i	$-0.701028\pi$
$743$	−16.1811	+	5.25754i	−0.593625	+	0.192881i	−0.00323005	+	0.999995i	$0.501028\pi$
$744$	15.2866	+	4.85279i	0.560434	+	0.177912i
$745$	0.0755094	−	0.665601i	0.00276645	−	0.0243857i
$746$	−25.8366	−	0.482895i	−0.945945	−	0.0176800i
$747$	7.80471	+	9.43427i	0.285559	+	0.345182i
$748$	−14.7511	+	5.21161i	−0.539354	+	0.190555i
$749$		−	3.80497i		−	0.139031i
$750$	−21.1138	−	11.0791i	−0.770966	−	0.404553i
$751$	−39.7689			−1.45119			−0.725595	−	0.688123i	$-0.758435\pi$
$751$	−39.7689			−1.45119			−0.725595	+	0.688123i	$0.758435\pi$
$752$	−8.38682	−	8.06603i	−0.305836	−	0.294138i
$753$	−8.25589	+	6.82987i	−0.300861	+	0.248894i
$754$	−0.770702	+	41.2353i	−0.0280673	+	1.50170i
$755$	−18.3835	−	16.8290i	−0.669043	−	0.612470i
$756$	−9.56737	+	15.9597i	−0.347962	+	0.580447i
$757$	−11.3269	−	34.8607i	−0.411685	−	1.26704i	−0.915183	−	0.403039i	$-0.867954\pi$
$757$	−11.3269	−	34.8607i	−0.411685	−	1.26704i	0.503498	−	0.863996i	$-0.332046\pi$
$758$	6.27005	−	43.1338i	0.227738	−	1.56669i
$759$	0.150450	−	0.788689i	0.00546100	−	0.0286276i
$760$	21.2758	−	20.7734i	0.771754	−	0.753530i
$761$	−7.78714	−	0.983744i	−0.282284	−	0.0356607i	−0.0170833	−	0.999854i	$-0.505438\pi$
$761$	−7.78714	−	0.983744i	−0.282284	−	0.0356607i	−0.265200	+	0.964193i	$0.585438\pi$
$762$	4.56611	−	3.63585i	0.165413	−	0.131713i
$763$	2.93491	−	15.3854i	0.106251	−	0.556987i
$764$	−1.50624	−	1.96591i	−0.0544937	−	0.0711242i
$765$	2.32229	−	6.09032i	0.0839626	−	0.220196i
$766$	0.344260	−	1.24383i	0.0124386	−	0.0449413i
$767$	7.89482	+	30.7483i	0.285065	+	1.11026i
$768$	24.1216	+	0.575208i	0.870414	+	0.0207560i
$769$	28.2543	−	34.1536i	1.01888	−	1.23161i	0.0463231	−	0.998927i	$-0.485250\pi$
$769$	28.2543	−	34.1536i	1.01888	−	1.23161i	0.972553	−	0.232683i	$-0.0747504\pi$
$770$	−10.1112	−	1.33889i	−0.364381	−	0.0482501i
$771$	−31.1267	−	19.7536i	−1.12100	−	0.711408i
$772$	−4.87098	−	22.4183i	−0.175310	−	0.806854i
$773$	−2.89035	−	2.71422i	−0.103959	−	0.0976236i	0.630825	−	0.775925i	$-0.282716\pi$
$773$	−2.89035	−	2.71422i	−0.103959	−	0.0976236i	−0.734784	+	0.678301i	$0.762716\pi$
$774$	1.89293	+	3.10974i	0.0680398	+	0.111777i
$775$	−15.4859	−	10.6609i	−0.556271	−	0.382951i
$776$	−33.5553	+	13.5489i	−1.20456	+	0.486376i
$777$	−0.754476	−	1.37239i	−0.0270667	−	0.0492341i
$778$	−17.0677	+	5.19509i	−0.611908	+	0.186253i
$779$	26.9515	−	1.69564i	0.965636	−	0.0607527i
$780$	−6.96673	−	23.3900i	−0.249449	−	0.837495i
$781$	0.385480	+	1.50134i	0.0137936	+	0.0537223i
$782$	−1.43248	−	0.598359i	−0.0512253	−	0.0213973i
$783$	−38.2309	+	24.2621i	−1.36626	+	0.867055i
$784$	−8.38273	+	14.8267i	−0.299383	+	0.529524i
$785$	−40.7953	+	23.1070i	−1.45605	+	0.824723i
$786$	19.1029	+	4.01542i	0.681376	+	0.143225i
$787$	−18.3884	−	10.1091i	−0.655476	−	0.360351i	0.119054	−	0.992888i	$-0.462014\pi$
$787$	−18.3884	−	10.1091i	−0.655476	−	0.360351i	−0.774530	+	0.632537i	$0.782014\pi$
$788$	6.03607	−	16.4574i	0.215026	−	0.586270i
$789$	10.7147	+	19.4899i	0.381453	+	0.693860i
$790$	−24.9138	+	9.69192i	−0.886391	+	0.344823i
$791$	−12.9547	+	12.1653i	−0.460616	+	0.432547i
$792$	3.99880	−	0.0270617i	0.142091	−	0.000961594i
$793$	8.15498	+	11.2244i	0.289592	+	0.398589i
$794$	−7.16940	−	1.04217i	−0.254433	−	0.0369851i
$795$	−7.87410	+	25.3240i	−0.279266	+	0.898150i
$796$	−27.1997	−	11.9634i	−0.964069	−	0.424030i
$797$	−2.72764	+	1.07995i	−0.0966181	+	0.0382538i	−0.415936	−	0.909394i	$-0.636546\pi$
$797$	−2.72764	+	1.07995i	−0.0966181	+	0.0382538i	0.319318	+	0.947648i	$0.396546\pi$
$798$	−6.78738	−	15.1526i	−0.240271	−	0.536397i
$799$	9.45135	−	6.86681i	0.334365	−	0.242930i
$800$	−26.8541	−	8.88026i	−0.949435	−	0.313964i
$801$	−2.33617	−	1.69733i	−0.0825445	−	0.0599721i
$802$	8.87632	−	42.2280i	0.313434	−	1.49112i
$803$	7.30509	−	11.5110i	0.257791	−	0.406214i
$804$	−15.5541	+	17.4321i	−0.548550	+	0.614781i
$805$	−0.654985	−	0.771574i	−0.0230852	−	0.0271944i
$806$	−3.25200	−	18.9667i	−0.114547	−	0.668072i
$807$		−	17.3258i		−	0.609899i
$808$	25.9140	−	19.0969i	0.911651	−	0.671826i
$809$	−2.49736	−	5.30715i	−0.0878024	−	0.186590i	0.856103	−	0.516805i	$-0.172879\pi$
$809$	−2.49736	−	5.30715i	−0.0878024	−	0.186590i	−0.943906	+	0.330215i	$0.892879\pi$
$810$	12.7817	−	15.2635i	0.449104	−	0.536304i
$811$	−15.6128	+	16.6259i	−0.548239	+	0.583816i	−0.942091	−	0.335359i	$-0.891143\pi$
$811$	−15.6128	+	16.6259i	−0.548239	+	0.583816i	0.393851	+	0.919174i	$0.371143\pi$
$812$	22.1626	−	14.8694i	0.777755	−	0.521813i
$813$	−3.64611	+	0.460610i	−0.127875	+	0.0161543i
$814$	−0.860431	+	1.49810i	−0.0301581	+	0.0525085i
$815$	12.6569	+	37.3336i	0.443350	+	1.30774i
$816$	−4.82258	+	23.7398i	−0.168824	+	0.831058i
$817$	−16.6415	−	1.04700i	−0.582213	−	0.0366297i
$818$	45.4847	−	10.7766i	1.59034	−	0.376797i
$819$	4.34087	+	0.273104i	0.151682	+	0.00954303i
$820$	−13.2244	−	22.0212i	−0.461818	−	0.769012i
$821$	16.2790	+	41.1161i	0.568141	+	1.43496i	0.875431	+	0.483344i	$0.160578\pi$
$821$	16.2790	+	41.1161i	0.568141	+	1.43496i	−0.307290	+	0.951616i	$0.599422\pi$
$822$	−6.80361	−	2.35207i	−0.237303	−	0.0820379i
$823$	29.5237	+	13.8928i	1.02913	+	0.484273i	0.864792	−	0.502131i	$-0.167450\pi$
$823$	29.5237	+	13.8928i	1.02913	+	0.484273i	0.164340	+	0.986404i	$0.447450\pi$
$824$	0.0784508	+	1.12536i	0.00273296	+	0.0392038i
$825$	14.0788	+	4.18224i	0.490161	+	0.145607i
$826$	13.3881	−	15.5812i	0.465832	−	0.542139i
$827$	3.15265	+	16.5267i	0.109628	+	0.574691i	0.994133	+	0.108161i	$0.0344962\pi$
$827$	3.15265	+	16.5267i	0.109628	+	0.574691i	−0.884505	+	0.466530i	$0.845504\pi$
$828$	0.296083	+	0.264185i	0.0102896	+	0.00918107i
$829$	−4.68024	+	3.87183i	−0.162551	+	0.134474i	−0.715144	−	0.698978i	$-0.753639\pi$
$829$	−4.68024	+	3.87183i	−0.162551	+	0.134474i	0.552592	+	0.833452i	$0.313639\pi$
$830$	28.3128	+	45.2099i	0.982752	+	1.56926i
$831$	32.2564	+	12.7712i	1.11896	+	0.443028i
$832$	−12.6798	−	26.0257i	−0.439593	−	0.902279i
$833$	−13.1759	−	10.9001i	−0.456520	−	0.377666i
$834$	5.89545	+	3.89779i	0.204143	+	0.134969i
$835$	41.4333	−	20.1437i	1.43386	−	0.697103i
$836$	−10.3850	+	15.0869i	−0.359174	+	0.521791i
$837$	15.4010	−	14.4625i	0.532337	−	0.499898i
$838$	6.92462	−	25.0190i	0.239207	−	0.864265i
$839$	−18.9600	+	40.2920i	−0.654571	+	1.39103i	0.251479	+	0.967863i	$0.419083\pi$
$839$	−18.9600	+	40.2920i	−0.654571	+	1.39103i	−0.906050	+	0.423171i	$0.860917\pi$
$840$	−9.82809	+	12.3624i	−0.339101	+	0.426545i
$841$	35.6602	−	4.50493i	1.22966	−	0.155342i
$842$	35.0472	−	35.9509i	1.20781	−	1.23895i
$843$	19.0740	+	13.8580i	0.656942	+	0.477296i
$844$	−20.3074	−	23.3129i	−0.699010	−	0.802463i
$845$	−0.153878	+	0.148223i	−0.00529355	+	0.00509904i
$846$	−2.85673	+	0.869533i	−0.0982163	+	0.0298952i
$847$	−11.9087	+	0.749230i	−0.409187	+	0.0257438i
$848$	−4.31455	+	31.1612i	−0.148162	+	1.07008i
$849$	−4.39966	+	13.5408i	−0.150996	+	0.464718i
$850$	13.5130	−	24.9758i	0.463491	−	0.856662i
$851$	−0.163041	+	0.0529754i	−0.00558899	+	0.00181597i
$852$	2.30080	+	0.683340i	0.0788240	+	0.0234108i
$853$	−51.5909	−	13.2463i	−1.76644	−	0.453544i	−0.781135	−	0.624362i	$-0.785359\pi$
$853$	−51.5909	−	13.2463i	−1.76644	−	0.453544i	−0.985303	+	0.170818i	$0.945359\pi$
$854$	2.93346	−	8.48534i	0.100381	−	0.290362i
$855$	−1.99144	−	7.36643i	−0.0681058	−	0.251926i
$856$	0.0439830	+	6.49919i	0.00150331	+	0.222138i
$857$	27.4524	+	8.91983i	0.937757	+	0.304696i	0.737731	−	0.675095i	$-0.235897\pi$
$857$	27.4524	+	8.91983i	0.937757	+	0.304696i	0.200026	+	0.979791i	$0.435897\pi$
$858$	6.99460	+	13.3062i	0.238792	+	0.454268i
$859$	3.68888	−	6.71005i	0.125863	−	0.228944i	−0.805866	−	0.592098i	$-0.798300\pi$
$859$	3.68888	−	6.71005i	0.125863	−	0.228944i	0.931729	+	0.363154i	$0.118300\pi$
$860$	6.39702	+	14.5134i	0.218137	+	0.494904i
$861$	−14.0887	+	2.68757i	−0.480143	+	0.0915922i
$862$	1.32222	+	29.9332i	0.0450350	+	1.01953i
$863$	9.79317	−	4.60832i	0.333363	−	0.156869i	−0.251811	−	0.967776i	$-0.581026\pi$
$863$	9.79317	−	4.60832i	0.333363	−	0.156869i	0.585174	+	0.810908i	$0.301026\pi$
$864$	16.1573	−	27.3710i	0.549684	−	0.931179i
$865$	29.6805	+	7.22011i	1.00917	+	0.245491i
$866$	31.4035	−	1.38717i	1.06714	−	0.0471379i
$867$	1.22294	+	0.484196i	0.0415332	+	0.0164442i
$868$	−8.85770	+	8.75273i	−0.300650	+	0.297087i
$869$	13.9027	−	8.82294i	0.471618	−	0.299298i
$870$	−34.8705	+	16.1545i	−1.18222	+	0.547689i
$871$	27.1505	+	6.97107i	0.919960	+	0.236206i
$872$	−4.83522	+	26.3133i	−0.163741	+	0.891082i
$873$	−1.16392	+	9.21339i	−0.0393928	+	0.311826i
$874$	−1.76851	+	0.419011i	−0.0598207	+	0.0141733i
$875$	15.2420	−	10.5081i	0.515273	−	0.355240i
$876$	−9.47154	−	18.8661i	−0.320014	−	0.637427i
$877$	−12.4870	−	1.57748i	−0.421656	−	0.0532676i	−0.0883575	−	0.996089i	$-0.528162\pi$
$877$	−12.4870	−	1.57748i	−0.421656	−	0.0532676i	−0.333299	+	0.942821i	$0.608162\pi$
$878$	−42.0295	−	31.7530i	−1.41843	−	1.07161i
$879$	−38.9239	−	9.99397i	−1.31287	−	0.337088i
$880$	17.2862	+	2.17004i	0.582716	+	0.0731522i
$881$	3.90879	+	6.15926i	0.131690	+	0.207511i	0.903774	−	0.428010i	$-0.140785\pi$
$881$	3.90879	+	6.15926i	0.131690	+	0.207511i	−0.772084	+	0.635521i	$0.780785\pi$
$882$	2.27269	+	3.73363i	0.0765255	+	0.125718i
$883$	−16.0437	−	6.35214i	−0.539913	−	0.213767i	0.0823100	−	0.996607i	$-0.473770\pi$
$883$	−16.0437	−	6.35214i	−0.539913	−	0.213767i	−0.622223	+	0.782840i	$0.713770\pi$
$884$	27.9594	−	7.94254i	0.940375	−	0.267136i
$885$	−22.5514	+	19.1438i	−0.758058	+	0.643511i
$886$	52.8673	−	5.67718i	1.77611	−	0.190729i
$887$	−45.7785	+	21.5417i	−1.53709	+	0.723301i	−0.993262	−	0.115894i	$-0.963027\pi$
$887$	−45.7785	+	21.5417i	−1.53709	+	0.723301i	−0.543831	+	0.839195i	$0.683027\pi$
$888$	1.30457	+	2.33542i	0.0437784	+	0.0783717i
$889$	0.849194	+	4.45163i	0.0284810	+	0.149303i
$890$	−9.11915	−	8.66677i	−0.305674	−	0.290511i
$891$	−5.90760	+	10.7459i	−0.197912	+	0.360001i
$892$	−12.5486	−	14.4058i	−0.420157	−	0.482340i
$893$	4.22644	−	13.0076i	0.141432	−	0.435284i
$894$	0.572907	+	0.282784i	0.0191609	+	0.00945772i
$895$	5.90742	+	0.296391i	0.197463	+	0.00990725i
$896$	−9.10969	+	16.3701i	−0.304333	+	0.546885i
$897$	−0.370969	+	1.44483i	−0.0123863	+	0.0482415i
$898$	−42.2388	−	24.2597i	−1.40953	−	0.809557i
$899$	−28.8191	+	9.36389i	−0.961170	+	0.312303i
$900$	−5.35031	+	4.90506i	−0.178344	+	0.163502i
$901$	−30.0380	−	9.75994i	−1.00071	−	0.325151i
$902$	10.6135	+	11.7341i	0.353390	+	0.390703i
$903$	8.83866	−	0.556081i	0.294132	−	0.0185052i
$904$	21.9870	−	20.9290i	0.731277	−	0.696087i
$905$	17.8348	−	33.4405i	0.592849	−	1.11160i
$906$	21.0409	−	11.0604i	0.699036	−	0.367458i
$907$	3.38417	+	2.45874i	0.112369	+	0.0816412i	0.642551	−	0.766243i	$-0.277876\pi$
$907$	3.38417	+	2.45874i	0.112369	+	0.0816412i	−0.530181	+	0.847884i	$0.677876\pi$
$908$	−34.4462	−	20.6495i	−1.14314	−	0.685279i
$909$	−1.03537	−	8.19576i	−0.0343409	−	0.271836i
$910$	18.5919	+	3.66208i	0.616315	+	0.121397i
$911$	2.76330	−	5.87230i	0.0915521	−	0.194558i	−0.853807	−	0.520590i	$-0.825712\pi$
$911$	2.76330	−	5.87230i	0.0915521	−	0.194558i	0.945359	+	0.326032i	$0.105712\pi$
$912$	11.7685	+	25.8034i	0.389695	+	0.854437i
$913$	−22.4924	−	23.9519i	−0.744389	−	0.792694i
$914$	−34.7922	−	38.4658i	−1.15082	−	1.27234i
$915$	−6.08380	+	11.4072i	−0.201124	+	0.377112i
$916$	−37.9473	−	13.9179i	−1.25381	−	0.459861i
$917$	−9.66090	+	11.6780i	−0.319031	+	0.385642i
$918$	24.2033	+	20.7966i	0.798827	+	0.686391i
$919$	44.3256	+	17.5497i	1.46217	+	0.578912i	0.958527	−	0.285002i	$-0.0919943\pi$
$919$	44.3256	+	17.5497i	1.46217	+	0.578912i	0.503639	+	0.863914i	$0.331994\pi$
$920$	1.12768	+	1.31034i	0.0371787	+	0.0432006i
$921$	28.6662	+	34.6514i	0.944582	+	1.14180i
$922$	−7.32523	−	10.4891i	−0.241244	−	0.345439i
$923$	−0.539613	−	2.82875i	−0.0177616	−	0.0931095i
$924$	4.46792	−	8.64108i	0.146984	−	0.284271i
$925$	−0.665646	−	3.06437i	−0.0218863	−	0.100756i
$926$	1.27231	−	3.04593i	0.0418108	−	0.100095i
$927$	0.261945	+	0.123262i	0.00860340	+	0.00404845i
$928$	−37.6836	+	25.6542i	−1.23703	+	0.842142i
$929$	16.3115	−	6.45819i	0.535163	−	0.211886i	−0.0849686	−	0.996384i	$-0.527079\pi$
$929$	16.3115	−	6.45819i	0.535163	−	0.211886i	0.620132	+	0.784497i	$0.287079\pi$
$930$	14.5697	−	10.4528i	0.477759	−	0.342761i
$931$	−19.9802	−	1.25705i	−0.654824	−	0.0411981i
$932$	−16.2193	−	32.3068i	−0.531281	−	1.05824i
$933$	−1.39049	+	22.1011i	−0.0455225	+	0.723559i
$934$	17.1156	+	21.4947i	0.560038	+	0.703327i
$935$	−5.19338	+	16.7025i	−0.169842	+	0.546230i
$936$	−7.41770	−	0.416306i	−0.242455	−	0.0136074i
$937$	−4.92445	−	38.9811i	−0.160875	−	1.27346i	−0.841272	−	0.540612i	$-0.818193\pi$
$937$	−4.92445	−	38.9811i	−0.160875	−	1.27346i	0.680397	−	0.732844i	$-0.261807\pi$
$938$	−6.36120	−	16.9874i	−0.207701	−	0.554657i
$939$	4.33932	−	4.62090i	0.141608	−	0.150798i
$940$	−12.8354	+	2.12172i	−0.418645	+	0.0692028i
$941$	−31.7911	+	14.9597i	−1.03636	+	0.487674i	−0.867223	−	0.497919i	$-0.834098\pi$
$941$	−31.7911	+	14.9597i	−1.03636	+	0.487674i	−0.169136	+	0.985593i	$0.554098\pi$
$942$	−7.55684	−	44.0738i	−0.246215	−	1.43600i
$943$			1.57002i			0.0511269i
$944$	−22.6878	+	26.7687i	−0.738427	+	0.871246i
$945$	7.90352	+	19.2442i	0.257102	+	0.626015i
$946$	−5.59365	−	8.00960i	−0.181865	−	0.260415i
$947$	−18.7970	+	29.6193i	−0.610820	+	0.962498i	0.388340	+	0.921516i	$0.373049\pi$
$947$	−18.7970	+	29.6193i	−0.610820	+	0.962498i	−0.999160	+	0.0409817i	$0.986951\pi$
$948$	−0.648955	−	25.4882i	−0.0210771	−	0.827818i
$949$	−14.8879	+	20.4914i	−0.483281	+	0.665179i
$950$	−4.38809	−	32.9543i	−0.142368	−	1.06918i
$951$	−14.7421	+	10.7107i	−0.478044	+	0.347319i
$952$	−14.5732	−	11.8908i	−0.472320	−	0.385383i
$953$	13.6147	+	34.3869i	0.441025	+	1.11390i	0.965019	+	0.262180i	$0.0844414\pi$
$953$	13.6147	+	34.3869i	0.441025	+	1.11390i	−0.523994	+	0.851722i	$0.675559\pi$
$954$	6.44142	+	4.86644i	0.208549	+	0.157557i
$955$	−2.76870	+	0.0351679i	−0.0895931	+	0.00113801i
$956$	35.1535	−	3.11170i	1.13694	−	0.100639i
$957$	19.1507	−	13.9138i	0.619054	−	0.449769i
$958$	15.1091	−	30.6103i	0.488154	−	0.988975i
$959$	4.07442	−	3.82613i	0.131570	−	0.123552i
$960$	16.6442	−	21.2296i	0.537191	−	0.685184i
$961$	−14.7756	+	8.12297i	−0.476633	+	0.262031i
$962$	1.77017	−	2.67740i	0.0570725	−	0.0863229i
$963$	1.46159	+	0.803516i	0.0470991	+	0.0258930i
$964$	1.01769	+	39.9707i	0.0327777	+	1.28737i
$965$	−23.3450	−	10.6253i	−0.751502	−	0.342040i
$966$	0.903993	−	0.338515i	0.0290855	−	0.0108915i
$967$	17.0521	−	10.8216i	0.548358	−	0.347999i	−0.232609	−	0.972570i	$-0.574726\pi$
$967$	17.0521	−	10.8216i	0.548358	−	0.347999i	0.780968	+	0.624572i	$0.214726\pi$
$968$	20.3323	−	1.41740i	0.653504	−	0.0455570i
$969$	−27.5789	+	7.08107i	−0.885963	+	0.227477i
$970$	−10.2961	+	39.1267i	−0.330588	+	1.25628i
$971$	−30.9138	+	1.94493i	−0.992070	+	0.0624158i	−0.550521	−	0.834821i	$-0.685571\pi$
$971$	−30.9138	+	1.94493i	−0.992070	+	0.0624158i	−0.441549	+	0.897237i	$0.645571\pi$
$972$	−7.41956	−	12.7182i	−0.237983	−	0.407936i
$973$	−4.80864	+	2.64357i	−0.154158	+	0.0847490i
$974$	15.5881	+	1.27356i	0.499473	+	0.0408075i
$975$	−25.6169	−	9.39706i	−0.820398	−	0.300947i
$976$	−4.91250	+	14.5275i	−0.157245	+	0.465015i
$977$	2.91316	−	3.10220i	0.0932002	−	0.0992481i	−0.680678	−	0.732583i	$-0.738314\pi$
$977$	2.91316	−	3.10220i	0.0932002	−	0.0992481i	0.773878	+	0.633335i	$0.218314\pi$
$978$	−37.5914	−	0.702596i	−1.20204	−	0.0224665i
$979$	6.54277	+	4.15217i	0.209108	+	0.132704i
$980$	7.68041	+	17.4252i	0.245342	+	0.556627i
$981$	5.29014	+	4.37638i	0.168901	+	0.139727i
$982$	35.1100	+	2.86852i	1.12040	+	0.0915383i
$983$	4.26859	+	16.6251i	0.136147	+	0.530257i	0.999664	+	0.0259367i	$0.00825684\pi$
$983$	4.26859	+	16.6251i	0.136147	+	0.530257i	−0.863517	+	0.504320i	$0.831743\pi$
$984$	24.0336	−	4.75344i	0.766164	−	0.151534i
$985$	−10.7107	−	16.4128i	−0.341271	−	0.522956i
$986$	−18.7102	−	41.7699i	−0.595853	−	1.33022i
$987$	−1.36117	+	7.13549i	−0.0433264	+	0.227125i
$988$	21.0158	−	26.7625i	0.668603	−	0.851430i
$989$	0.121502	−	0.961784i	0.00386353	−	0.0305830i
$990$	2.64953	−	3.60123i	0.0842077	−	0.114455i
$991$	3.54843	−	18.6015i	0.112720	−	0.590897i	−0.880442	−	0.474153i	$-0.842754\pi$
$991$	3.54843	−	18.6015i	0.112720	−	0.590897i	0.993162	−	0.116744i	$-0.0372457\pi$
$992$	15.0285	−	15.0527i	0.477154	−	0.477925i
$993$	23.0517	−	7.48994i	0.731522	−	0.237686i
$994$	−1.30084	+	1.33438i	−0.0412601	+	0.0423240i
$995$	−28.9068	+	16.3732i	−0.916407	+	0.519064i
$996$	−49.7171	+	10.8024i	−1.57535	+	0.342286i
$997$	−37.1430	−	44.8982i	−1.17633	−	1.42194i	−0.885171	−	0.465267i	$-0.845958\pi$
$997$	−37.1430	−	44.8982i	−1.17633	−	1.42194i	−0.291161	−	0.956674i	$-0.594042\pi$
$998$	−0.486168	−	4.52732i	−0.0153894	−	0.143310i
$999$	3.52386			0.111490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.bd.a.109.145	yes	2960
8.5	even	2	inner	1000.2.bd.a.109.17	✓	2960
125.39	even	50	inner	1000.2.bd.a.789.17	yes	2960
1000.789	even	50	inner	1000.2.bd.a.789.145	yes	2960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.bd.a.109.17	✓	2960	8.5	even	2	inner
1000.2.bd.a.109.145	yes	2960	1.1	even	1	trivial
1000.2.bd.a.789.17	yes	2960	125.39	even	50	inner
1000.2.bd.a.789.145	yes	2960	1000.789	even	50	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.bd (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40613 - 0.150998i) q^{2} +(0.961254 + 1.16196i) q^{3} +(1.95440 - 0.424645i) q^{4} +(0.926297 - 2.03518i) q^{5} +(1.52710 + 1.48871i) q^{6} +(-1.57483 + 0.511693i) q^{7} +(2.68402 - 0.892216i) q^{8} +(0.136010 - 0.712991i) q^{9} +(0.995186 - 3.00160i) q^{10} +(-0.244127 + 1.93246i) q^{11} +(2.37209 + 1.86274i) q^{12} +(0.678091 - 3.55468i) q^{13} +(-2.13715 + 0.957302i) q^{14} +(3.25520 - 0.880011i) q^{15} +(3.63935 - 1.65985i) q^{16} +(0.998724 + 3.88977i) q^{17} +(0.0835879 - 1.02309i) q^{18} +(3.62263 + 2.99690i) q^{19} +(0.946124 - 4.37091i) q^{20} +(-2.10838 - 1.33802i) q^{21} +(-0.0514761 + 2.75415i) q^{22} +(-0.187116 + 0.199259i) q^{23} +(3.61674 + 2.26107i) q^{24} +(-3.28395 - 3.77037i) q^{25} +(0.416735 - 5.10073i) q^{26} +(4.92369 - 2.70682i) q^{27} +(-2.86056 + 1.66880i) q^{28} +(-8.04286 + 0.506014i) q^{29} +(4.44436 - 1.72894i) q^{30} +(3.64202 - 0.935112i) q^{31} +(4.86677 - 2.88350i) q^{32} +(-2.48010 + 1.57392i) q^{33} +(1.99168 + 5.31872i) q^{34} +(-0.417371 + 3.67905i) q^{35} +(-0.0369496 - 1.45122i) q^{36} +(0.549591 + 0.302140i) q^{37} +(5.54640 + 3.66702i) q^{38} +(4.78220 - 2.62904i) q^{39} +(0.670375 - 6.28893i) q^{40} +(4.18703 - 3.93188i) q^{41} +(-3.16669 - 1.56306i) q^{42} +(-2.86923 + 2.08462i) q^{43} +(0.343489 + 3.88047i) q^{44} +(-1.32508 - 0.937247i) q^{45} +(-0.233022 + 0.308438i) q^{46} +(-1.07089 - 2.70475i) q^{47} +(5.42702 + 2.63323i) q^{48} +(-3.44486 + 2.50284i) q^{49} +(-5.18697 - 4.80576i) q^{50} +(-3.55972 + 4.89954i) q^{51} +(-0.184216 - 7.23521i) q^{52} +(-4.21407 + 6.64031i) q^{53} +(6.51462 - 4.54961i) q^{54} +(3.70678 + 2.28688i) q^{55} +(-3.77033 + 2.77848i) q^{56} +7.09011i q^{57} +(-11.2329 + 1.92598i) q^{58} +(-7.93757 + 3.73514i) q^{59} +(5.98827 - 3.10220i) q^{60} +(-2.62449 + 2.79480i) q^{61} +(4.97995 - 1.86483i) q^{62} +(0.150639 + 1.19243i) q^{63} +(6.40790 - 4.78945i) q^{64} +(-6.60631 - 4.67273i) q^{65} +(-3.24969 + 2.58763i) q^{66} +(-0.486377 + 7.73075i) q^{67} +(3.60368 + 7.17807i) q^{68} +(-0.411396 - 0.0258829i) q^{69} +(-0.0313493 + 5.23624i) q^{70} +(0.739900 - 0.292947i) q^{71} +(-0.271088 - 2.03503i) q^{72} +(-6.33312 - 2.98014i) q^{73} +(0.818418 + 0.341861i) q^{74} +(1.22430 - 7.44009i) q^{75} +(8.35267 + 4.31880i) q^{76} +(-0.604369 - 3.16821i) q^{77} +(6.32741 - 4.41887i) q^{78} +(-5.38851 - 6.51359i) q^{79} +(-0.00698044 - 8.94427i) q^{80} +(5.85350 + 2.31757i) q^{81} +(5.29379 - 6.16096i) q^{82} +(-10.7525 + 12.9976i) q^{83} +(-4.68879 - 1.71971i) q^{84} +(8.84152 + 1.57050i) q^{85} +(-3.71973 + 3.36449i) q^{86} +(-8.31920 - 8.85904i) q^{87} +(1.06893 + 5.40457i) q^{88} +(1.69389 - 3.59971i) q^{89} +(-2.00476 - 1.11781i) q^{90} +(0.751026 + 5.94499i) q^{91} +(-0.281086 + 0.468889i) q^{92} +(4.58747 + 3.33299i) q^{93} +(-1.91422 - 3.64153i) q^{94} +(9.45486 - 4.59669i) q^{95} +(8.02870 + 2.88319i) q^{96} +(-12.7689 + 0.803353i) q^{97} +(-4.46600 + 4.03948i) q^{98} +(1.34462 + 0.436894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) \) 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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