LMFDB - Embedded newform 145.2.t.a.108.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(3,145)] 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("145.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.t (of order $28$, degree $12$, 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:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			108.5
Character	$\chi$	$=$	145.108
Dual form			145.2.t.a.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.419675 - 0.871464i) q^{2} +(1.77064 + 2.22031i) q^{3} +(0.663657 - 0.832199i) q^{4} +(0.626976 - 2.14637i) q^{5} +(1.19183 - 2.47485i) q^{6} +(-1.38886 - 0.156487i) q^{7} +(-2.88975 - 0.659568i) q^{8} +(-1.12705 + 4.93793i) q^{9} +(-2.13361 + 0.354390i) q^{10} +(4.68013 + 2.94072i) q^{11} +3.02283 q^{12} +(-3.87599 - 2.43545i) q^{13} +(0.446497 + 1.27601i) q^{14} +(5.87575 - 2.40836i) q^{15} +(0.164256 + 0.719651i) q^{16} +5.34543i q^{17} +(4.77622 - 1.09014i) q^{18} +(-3.75785 + 0.423408i) q^{19} +(-1.37011 - 1.94622i) q^{20} +(-2.11171 - 3.36077i) q^{21} +(0.598599 - 5.31271i) q^{22} +(-0.812207 - 2.32115i) q^{23} +(-3.65226 - 7.58400i) q^{24} +(-4.21380 - 2.69145i) q^{25} +(-0.495748 + 4.39988i) q^{26} +(-5.28338 + 2.54434i) q^{27} +(-1.05195 + 1.05195i) q^{28} +(3.20546 + 4.32724i) q^{29} +(-4.56470 - 4.10977i) q^{30} +(1.32279 - 3.78032i) q^{31} +(-4.07659 + 3.25097i) q^{32} +(1.75750 + 15.5983i) q^{33} +(4.65835 - 2.24334i) q^{34} +(-1.20666 + 2.88289i) q^{35} +(3.36136 + 4.21502i) q^{36} +(-0.826152 + 3.61961i) q^{37} +(1.94606 + 3.09714i) q^{38} +(-1.45553 - 12.9182i) q^{39} +(-3.22748 + 5.78895i) q^{40} +(-5.71038 - 5.71038i) q^{41} +(-2.04256 + 3.25072i) q^{42} +(0.669277 + 0.322307i) q^{43} +(5.55327 - 1.94317i) q^{44} +(9.89198 + 5.51503i) q^{45} +(-1.68194 + 1.68194i) q^{46} +(-0.00613776 - 0.0268913i) q^{47} +(-1.30701 + 1.63894i) q^{48} +(-4.92005 - 1.12297i) q^{49} +(-0.577072 + 4.80171i) q^{50} +(-11.8685 + 9.46480i) q^{51} +(-4.59910 + 1.60930i) q^{52} +(-1.64149 - 0.574381i) q^{53} +(4.43460 + 3.53648i) q^{54} +(9.24620 - 8.20152i) q^{55} +(3.91025 + 1.36826i) q^{56} +(-7.59388 - 7.59388i) q^{57} +(2.42578 - 4.60948i) q^{58} -4.00143i q^{59} +(1.89524 - 6.48811i) q^{60} +(3.92555 + 0.442303i) q^{61} +(-3.84955 + 0.433740i) q^{62} +(2.33803 - 6.68171i) q^{63} +(5.87407 + 2.82880i) q^{64} +(-7.65752 + 6.79234i) q^{65} +(12.8558 - 8.07781i) q^{66} +(6.04031 - 3.79538i) q^{67} +(4.44846 + 3.54753i) q^{68} +(3.71555 - 5.91327i) q^{69} +(3.01874 - 0.158316i) q^{70} +(3.42315 - 0.781312i) q^{71} +(6.51379 - 13.5260i) q^{72} +(1.39052 - 2.88745i) q^{73} +(3.50108 - 0.799098i) q^{74} +(-1.48527 - 14.1215i) q^{75} +(-2.14156 + 3.40828i) q^{76} +(-6.03986 - 4.81662i) q^{77} +(-10.6469 + 6.68988i) q^{78} +(-7.95966 + 5.00139i) q^{79} +(1.64762 + 0.0986510i) q^{80} +(-1.31416 - 0.632868i) q^{81} +(-2.57989 + 7.37289i) q^{82} +(14.7389 - 1.66068i) q^{83} +(-4.19829 - 0.473033i) q^{84} +(11.4733 + 3.35146i) q^{85} -0.718515i q^{86} +(-3.93209 + 14.7791i) q^{87} +(-11.5848 - 11.5848i) q^{88} +(12.9395 + 4.52773i) q^{89} +(0.654732 - 10.9350i) q^{90} +(5.00209 + 3.98903i) q^{91} +(-2.47069 - 0.864532i) q^{92} +(10.7356 - 3.75656i) q^{93} +(-0.0208589 + 0.0166344i) q^{94} +(-1.44729 + 8.33120i) q^{95} +(-14.4363 - 3.29499i) q^{96} +(5.48532 - 6.87837i) q^{97} +(1.08620 + 4.75893i) q^{98} +(-19.7958 + 19.7958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 14 q^{2} - 10 q^{3} + 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} - 14 q^{8} - 10 q^{9} - 6 q^{10} - 20 q^{11} - 20 q^{12} - 28 q^{13} - 4 q^{14} - 4 q^{15} - 34 q^{16} + 84 q^{18} + 6 q^{20} - 16 q^{21}+ \cdots - 76 q^{99}+O(q^{100}) $ 156 * q - 14 * q^2 - 10 * q^3 + 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 - 14 * q^8 - 10 * q^9 - 6 * q^10 - 20 * q^11 - 20 * q^12 - 28 * q^13 - 4 * q^14 - 4 * q^15 - 34 * q^16 + 84 * q^18 + 6 * q^20 - 16 * q^21 - 22 * q^22 - 10 * q^23 - 56 * q^24 - 108 * q^25 + 36 * q^26 + 32 * q^27 - 8 * q^28 - 44 * q^30 - 8 * q^31 - 14 * q^32 - 14 * q^33 + 24 * q^34 + 26 * q^35 + 78 * q^36 - 72 * q^37 - 120 * q^38 - 16 * q^39 - 46 * q^40 - 22 * q^41 - 18 * q^42 + 2 * q^43 + 112 * q^44 + 30 * q^45 + 4 * q^46 + 22 * q^47 + 38 * q^48 - 84 * q^49 - 24 * q^50 - 28 * q^51 + 86 * q^52 + 56 * q^53 - 60 * q^55 + 4 * q^56 - 12 * q^57 + 96 * q^58 + 14 * q^60 - 46 * q^61 - 112 * q^62 + 158 * q^63 + 30 * q^64 + 4 * q^65 - 48 * q^66 + 18 * q^67 + 140 * q^68 + 124 * q^69 + 94 * q^70 - 28 * q^71 - 98 * q^72 - 84 * q^73 - 112 * q^74 + 54 * q^75 - 48 * q^76 + 28 * q^77 + 70 * q^78 + 4 * q^79 + 170 * q^80 + 58 * q^81 + 16 * q^82 + 46 * q^83 - 120 * q^84 + 76 * q^85 + 68 * q^87 + 40 * q^88 - 46 * q^89 + 120 * q^90 - 28 * q^91 - 14 * q^92 - 22 * q^93 + 84 * q^94 + 190 * q^95 - 28 * q^96 - 76 * q^97 - 160 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.419675	−	0.871464i	−0.296755	−	0.616218i	0.698271	−	0.715834i	$-0.253953\pi$
$2$	−0.419675	−	0.871464i	−0.296755	−	0.616218i	−0.995026	+	0.0996153i	$0.968239\pi$
$3$	1.77064	+	2.22031i	1.02228	+	1.28189i	0.958851	+	0.283908i	$0.0916311\pi$
$3$	1.77064	+	2.22031i	1.02228	+	1.28189i	0.0634256	+	0.997987i	$0.479797\pi$
$4$	0.663657	−	0.832199i	0.331828	−	0.416100i
$5$	0.626976	−	2.14637i	0.280392	−	0.959885i
$5$	0.626976	−	2.14637i	0.280392	−	0.959885i
$6$	1.19183	−	2.47485i	0.486561	−	1.01035i
$7$	−1.38886	−	0.156487i	−0.524939	−	0.0591465i	−0.154481	−	0.987996i	$-0.549371\pi$
$7$	−1.38886	−	0.156487i	−0.524939	−	0.0591465i	−0.370458	+	0.928849i	$0.620799\pi$
$8$	−2.88975	−	0.659568i	−1.02168	−	0.233192i
$9$	−1.12705	+	4.93793i	−0.375683	+	1.64598i
$10$	−2.13361	+	0.354390i	−0.674707	+	0.112068i
$11$	4.68013	+	2.94072i	1.41111	+	0.886661i	0.999693	−	0.0247855i	$-0.00789028\pi$
$11$	4.68013	+	2.94072i	1.41111	+	0.886661i	0.411419	+	0.911446i	$0.365033\pi$
$12$	3.02283			0.872617
$13$	−3.87599	−	2.43545i	−1.07501	−	0.675471i	−0.126416	−	0.991977i	$-0.540347\pi$
$13$	−3.87599	−	2.43545i	−1.07501	−	0.675471i	−0.948590	+	0.316506i	$0.897490\pi$
$14$	0.446497	+	1.27601i	0.119331	+	0.341029i
$15$	5.87575	−	2.40836i	1.51711	−	0.621835i
$16$	0.164256	+	0.719651i	0.0410639	+	0.179913i
$17$			5.34543i			1.29646i	0.761446	+	0.648228i	$0.224490\pi$
$17$			5.34543i			1.29646i	−0.761446	+	0.648228i	$0.775510\pi$
$18$	4.77622	−	1.09014i	1.12577	−	0.256949i
$19$	−3.75785	+	0.423408i	−0.862110	+	0.0971365i	−0.531937	−	0.846784i	$-0.678536\pi$
$19$	−3.75785	+	0.423408i	−0.862110	+	0.0971365i	−0.330173	+	0.943920i	$0.607107\pi$
$20$	−1.37011	−	1.94622i	−0.306366	−	0.435188i
$21$	−2.11171	−	3.36077i	−0.460814	−	0.733381i
$22$	0.598599	−	5.31271i	0.127622	−	1.13267i
$23$	−0.812207	−	2.32115i	−0.169357	−	0.483994i	0.827655	−	0.561237i	$-0.189674\pi$
$23$	−0.812207	−	2.32115i	−0.169357	−	0.483994i	−0.997012	+	0.0772424i	$0.975388\pi$
$24$	−3.65226	−	7.58400i	−0.745515	−	1.54808i
$25$	−4.21380	−	2.69145i	−0.842760	−	0.538289i
$26$	−0.495748	+	4.39988i	−0.0972241	+	0.862888i
$27$	−5.28338	+	2.54434i	−1.01679	+	0.489659i
$28$	−1.05195	+	1.05195i	−0.198801	+	0.198801i
$29$	3.20546	+	4.32724i	0.595240	+	0.803548i
$29$	3.20546	+	4.32724i	0.595240	+	0.803548i
$30$	−4.56470	−	4.10977i	−0.833397	−	0.750339i
$31$	1.32279	−	3.78032i	0.237580	−	0.678965i	−0.761930	−	0.647660i	$-0.775748\pi$
$31$	1.32279	−	3.78032i	0.237580	−	0.678965i	0.999510	−	0.0313051i	$-0.00996635\pi$
$32$	−4.07659	+	3.25097i	−0.720646	+	0.574696i
$33$	1.75750	+	15.5983i	0.305942	+	2.71531i
$34$	4.65835	−	2.24334i	0.798900	−	0.384730i
$35$	−1.20666	+	2.88289i	−0.203963	+	0.487297i
$36$	3.36136	+	4.21502i	0.560227	+	0.702503i
$37$	−0.826152	+	3.61961i	−0.135819	+	0.595060i	0.860509	+	0.509436i	$0.170146\pi$
$37$	−0.826152	+	3.61961i	−0.135819	+	0.595060i	−0.996327	+	0.0856247i	$0.972711\pi$
$38$	1.94606	+	3.09714i	0.315693	+	0.502422i
$39$	−1.45553	−	12.9182i	−0.233071	−	2.06856i
$40$	−3.22748	+	5.78895i	−0.510310	+	0.915313i
$41$	−5.71038	−	5.71038i	−0.891811	−	0.891811i	0.102882	−	0.994694i	$-0.467193\pi$
$41$	−5.71038	−	5.71038i	−0.891811	−	0.891811i	−0.994694	+	0.102882i	$0.967193\pi$
$42$	−2.04256	+	3.25072i	−0.315174	+	0.501597i
$43$	0.669277	+	0.322307i	0.102064	+	0.0491513i	0.484219	−	0.874947i	$-0.339104\pi$
$43$	0.669277	+	0.322307i	0.102064	+	0.0491513i	−0.382155	+	0.924098i	$0.624818\pi$
$44$	5.55327	−	1.94317i	0.837186	−	0.292944i
$45$	9.89198	+	5.51503i	1.47461	+	0.822132i
$46$	−1.68194	+	1.68194i	−0.247989	+	0.247989i
$47$	−0.00613776	−	0.0268913i	−0.000895284	−	0.00392249i	0.974478	−	0.224482i	$-0.0720689\pi$
$47$	−0.00613776	−	0.0268913i	−0.000895284	−	0.00392249i	−0.975374	+	0.220559i	$0.929212\pi$
$48$	−1.30701	+	1.63894i	−0.188651	+	0.236560i
$49$	−4.92005	−	1.12297i	−0.702865	−	0.160424i
$50$	−0.577072	+	4.80171i	−0.0816103	+	0.679064i
$51$	−11.8685	+	9.46480i	−1.66192	+	1.32534i
$52$	−4.59910	+	1.60930i	−0.637781	+	0.223169i
$53$	−1.64149	−	0.574381i	−0.225476	−	0.0788973i	0.215177	−	0.976575i	$-0.430967\pi$
$53$	−1.64149	−	0.574381i	−0.225476	−	0.0788973i	−0.440653	+	0.897678i	$0.645253\pi$
$54$	4.43460	+	3.53648i	0.603473	+	0.481254i
$55$	9.24620	−	8.20152i	1.24676	−	1.10589i
$56$	3.91025	+	1.36826i	0.522529	+	0.182841i
$57$	−7.59388	−	7.59388i	−1.00583	−	1.00583i
$58$	2.42578	−	4.60948i	0.318521	−	0.605255i
$59$		−	4.00143i		−	0.520942i	−0.965482	−	0.260471i	$-0.916122\pi$
$59$		−	4.00143i		−	0.520942i	0.965482	−	0.260471i	$-0.0838778\pi$
$60$	1.89524	−	6.48811i	0.244675	−	0.837612i
$61$	3.92555	+	0.442303i	0.502615	+	0.0566311i	0.359632	−	0.933094i	$-0.382902\pi$
$61$	3.92555	+	0.442303i	0.502615	+	0.0566311i	0.142983	+	0.989725i	$0.454331\pi$
$62$	−3.84955	+	0.433740i	−0.488894	+	0.0550851i
$63$	2.33803	−	6.68171i	0.294564	−	0.841817i
$64$	5.87407	+	2.82880i	0.734258	+	0.353600i
$65$	−7.65752	+	6.79234i	−0.949798	+	0.842486i
$66$	12.8558	−	8.07781i	1.58243	−	0.994309i
$67$	6.04031	−	3.79538i	0.737941	−	0.463679i	−0.109891	−	0.993944i	$-0.535050\pi$
$67$	6.04031	−	3.79538i	0.737941	−	0.463679i	0.847832	+	0.530264i	$0.177907\pi$
$68$	4.44846	+	3.54753i	0.539455	+	0.430201i
$69$	3.71555	−	5.91327i	0.447300	−	0.711874i
$70$	3.01874	−	0.158316i	0.360809	−	0.0189224i
$71$	3.42315	−	0.781312i	0.406253	−	0.0927247i	−0.0145109	−	0.999895i	$-0.504619\pi$
$71$	3.42315	−	0.781312i	0.406253	−	0.0927247i	0.420764	+	0.907170i	$0.361762\pi$
$72$	6.51379	−	13.5260i	0.767658	−	1.59406i
$73$	1.39052	−	2.88745i	0.162748	−	0.337951i	−0.803607	−	0.595160i	$-0.797089\pi$
$73$	1.39052	−	2.88745i	0.162748	−	0.337951i	0.966356	+	0.257209i	$0.0828030\pi$
$74$	3.50108	−	0.799098i	0.406992	−	0.0928932i
$75$	−1.48527	−	14.1215i	−0.171504	−	1.63061i
$76$	−2.14156	+	3.40828i	−0.245654	+	0.390956i
$77$	−6.03986	−	4.81662i	−0.688306	−	0.548905i
$78$	−10.6469	+	6.68988i	−1.20552	+	0.757479i
$79$	−7.95966	+	5.00139i	−0.895532	+	0.562700i	−0.899319	−	0.437293i	$-0.855937\pi$
$79$	−7.95966	+	5.00139i	−0.895532	+	0.562700i	0.00378707	+	0.999993i	$0.498795\pi$
$80$	1.64762	+	0.0986510i	0.184210	+	0.0110295i
$81$	−1.31416	−	0.632868i	−0.146018	−	0.0703186i
$82$	−2.57989	+	7.37289i	−0.284901	+	0.814200i
$83$	14.7389	−	1.66068i	1.61780	−	0.182283i	0.743869	−	0.668325i	$-0.232989\pi$
$83$	14.7389	−	1.66068i	1.61780	−	0.182283i	0.873935	+	0.486042i	$0.161560\pi$
$84$	−4.19829	−	0.473033i	−0.458071	−	0.0516122i
$85$	11.4733	+	3.35146i	1.24445	+	0.363516i
$86$		−	0.718515i		−	0.0774795i
$87$	−3.93209	+	14.7791i	−0.421565	+	1.58448i
$88$	−11.5848	−	11.5848i	−1.23495	−	1.23495i
$89$	12.9395	+	4.52773i	1.37159	+	0.479939i	0.912727	−	0.408570i	$-0.133972\pi$
$89$	12.9395	+	4.52773i	1.37159	+	0.479939i	0.458860	+	0.888509i	$0.348258\pi$
$90$	0.654732	−	10.9350i	0.0690149	−	1.15265i
$91$	5.00209	+	3.98903i	0.524361	+	0.418164i
$92$	−2.47069	−	0.864532i	−0.257587	−	0.0901337i
$93$	10.7356	−	3.75656i	1.11323	−	0.389537i
$94$	−0.0208589	+	0.0166344i	−0.00215143	+	0.00171571i
$95$	−1.44729	+	8.33120i	−0.148489	+	0.854763i
$96$	−14.4363	−	3.29499i	−1.47340	−	0.336294i
$97$	5.48532	−	6.87837i	0.556950	−	0.698393i	−0.421041	−	0.907042i	$-0.638335\pi$
$97$	5.48532	−	6.87837i	0.556950	−	0.698393i	0.977991	+	0.208649i	$0.0669065\pi$
$98$	1.08620	+	4.75893i	0.109722	+	0.480725i
$99$	−19.7958	+	19.7958i	−1.98955	+	1.98955i
$100$	−5.03634	+	1.72053i	−0.503634	+	0.172053i
$101$	5.10791	−	1.78734i	0.508256	−	0.177847i	−0.0639551	−	0.997953i	$-0.520371\pi$
$101$	5.10791	−	1.78734i	0.508256	−	0.177847i	0.572211	+	0.820106i	$0.306086\pi$
$102$	13.2291	+	6.37082i	1.30988	+	0.630805i
$103$	4.23420	−	6.73869i	0.417208	−	0.663983i	−0.570321	−	0.821422i	$-0.693181\pi$
$103$	4.23420	−	6.73869i	0.417208	−	0.663983i	0.987529	+	0.157439i	$0.0503239\pi$
$104$	9.59432	+	9.59432i	0.940800	+	0.940800i
$105$	−8.53746	+	2.42539i	−0.833171	+	0.236694i
$106$	0.188339	+	1.67155i	0.0182931	+	0.162355i
$107$	6.05811	+	9.64143i	0.585660	+	0.932072i	0.999761	+	0.0218417i	$0.00695297\pi$
$107$	6.05811	+	9.64143i	0.585660	+	0.932072i	−0.414102	+	0.910231i	$0.635904\pi$
$108$	−1.38895	+	6.08539i	−0.133652	+	0.585567i
$109$	−4.37246	−	5.48290i	−0.418806	−	0.525166i	0.527014	−	0.849856i	$-0.323311\pi$
$109$	−4.37246	−	5.48290i	−0.418806	−	0.525166i	−0.945820	+	0.324690i	$0.894740\pi$
$110$	−11.0277	−	4.61576i	−1.05145	−	0.440096i
$111$	−9.49946	+	4.57470i	−0.901649	+	0.434211i
$112$	−0.115512	−	1.02520i	−0.0109149	−	0.0968721i
$113$	−11.5380	+	9.20127i	−1.08541	+	0.865583i	−0.991514	−	0.130000i	$-0.958502\pi$
$113$	−11.5380	+	9.20127i	−1.08541	+	0.865583i	−0.0938923	+	0.995582i	$0.529931\pi$
$114$	−3.43083	+	9.80476i	−0.321327	+	0.918300i
$115$	−5.49129	+	0.287987i	−0.512065	+	0.0268549i
$116$	5.72845	+	0.204218i	0.531874	+	0.0189612i
$117$	16.3945	−	16.3945i	1.51567	−	1.51567i
$118$	−3.48710	+	1.67930i	−0.321014	+	0.154592i
$119$	0.836489	−	7.42404i	0.0766808	−	0.680561i
$120$	−18.5679	+	3.08411i	−1.69501	+	0.281540i
$121$	8.48306	+	17.6153i	0.771187	+	1.60139i
$122$	−1.26200	−	3.60660i	−0.114256	−	0.326526i
$123$	2.56779	−	22.7898i	0.231530	−	2.05489i
$124$	−2.26810	−	3.60966i	−0.203681	−	0.324157i
$125$	−8.41879	+	7.35690i	−0.753000	+	0.658021i
$126$	−6.80409	+	0.766637i	−0.606156	+	0.0682974i
$127$	−0.722509	+	0.164908i	−0.0641123	+	0.0146332i	−0.254457	−	0.967084i	$-0.581897\pi$
$127$	−0.722509	+	0.164908i	−0.0641123	+	0.0146332i	0.190344	+	0.981717i	$0.439040\pi$
$128$			4.12209i			0.364345i
$129$	0.469426	+	2.05669i	0.0413306	+	0.181081i
$130$	9.13295	+	3.82268i	0.801013	+	0.335271i
$131$	−4.84709	−	13.8522i	−0.423493	−	1.21027i	−0.936126	−	0.351665i	$-0.885616\pi$
$131$	−4.84709	−	13.8522i	−0.423493	−	1.21027i	0.512633	−	0.858608i	$-0.328670\pi$
$132$	14.1472	+	8.88930i	1.23136	+	0.773715i
$133$	5.28538			0.458301
$134$	−5.84251	−	3.67109i	−0.504716	−	0.317134i
$135$	2.14854	+	12.9353i	0.184917	+	1.11329i
$136$	3.52567	−	15.4470i	0.302324	−	1.32457i
$137$	6.39404	+	1.45940i	0.546280	+	0.124685i	0.486749	−	0.873542i	$-0.338183\pi$
$137$	6.39404	+	1.45940i	0.546280	+	0.124685i	0.0595303	+	0.998226i	$0.481040\pi$
$138$	−6.71253	−	0.756320i	−0.571408	−	0.0643822i
$139$	−1.98467	+	4.12120i	−0.168337	+	0.349556i	−0.968022	−	0.250864i	$-0.919285\pi$
$139$	−1.98467	+	4.12120i	−0.168337	+	0.349556i	0.799685	+	0.600420i	$0.205000\pi$
$140$	1.59833	+	2.91743i	0.135084	+	0.246568i
$141$	0.0488391	−	0.0612423i	0.00411300	−	0.00515753i
$142$	−2.11750	−	2.65526i	−0.177696	−	0.222824i
$143$	−10.9782	−	22.7964i	−0.918041	−	1.90633i
$144$	−3.73871			−0.311559
$145$	11.2976	−	4.16703i	0.938215	−	0.346053i
$146$	−3.09988			−0.256548
$147$	−6.21829	−	12.9124i	−0.512876	−	1.06500i
$148$	2.46396	+	3.08970i	0.202536	+	0.253972i
$149$	5.04369	−	6.32459i	0.413195	−	0.518130i	−0.531065	−	0.847331i	$-0.678208\pi$
$149$	5.04369	−	6.32459i	0.413195	−	0.518130i	0.944260	+	0.329201i	$0.106779\pi$
$150$	−11.6831	+	7.22080i	−0.953917	+	0.589576i
$151$	−4.21845	+	8.75970i	−0.343292	+	0.712854i	−0.999115	−	0.0420610i	$-0.986608\pi$
$151$	−4.21845	+	8.75970i	−0.343292	+	0.712854i	0.655823	+	0.754915i	$0.272322\pi$
$152$	11.1385	+	1.25501i	0.903454	+	0.101795i
$153$	−26.3953	−	6.02456i	−2.13393	−	0.487057i
$154$	−1.66274	+	7.28494i	−0.133987	+	0.587037i
$155$	−7.28459	−	5.20936i	−0.585113	−	0.418426i
$156$	−11.7165	−	7.36194i	−0.938068	−	0.589427i
$157$	−4.05125			−0.323325			−0.161663	−	0.986846i	$-0.551686\pi$
$157$	−4.05125			−0.323325			−0.161663	+	0.986846i	$0.551686\pi$
$158$	7.69900	+	4.83760i	0.612500	+	0.384859i
$159$	−1.63117	−	4.66163i	−0.129360	−	0.369691i
$160$	4.42186	+	10.7882i	0.349579	+	0.852878i
$161$	0.764811	+	3.35086i	0.0602755	+	0.264084i
$162$			1.41084i			0.110846i
$163$	−5.74667	+	1.31164i	−0.450114	+	0.102736i	−0.441568	−	0.897228i	$-0.645578\pi$
$163$	−5.74667	+	1.31164i	−0.450114	+	0.102736i	−0.00854627	+	0.999963i	$0.502720\pi$
$164$	−8.54190	+	0.962441i	−0.667011	+	0.0751540i
$165$	34.5816	+	6.00750i	2.69217	+	0.467683i
$166$	−7.63277	−	12.1475i	−0.592418	−	0.942827i
$167$	1.57049	−	13.9385i	0.121528	−	1.07859i	−0.773877	−	0.633336i	$-0.781685\pi$
$167$	1.57049	−	13.9385i	0.121528	−	1.07859i	0.895404	−	0.445254i	$-0.146887\pi$
$168$	3.88568	+	11.1046i	0.299787	+	0.856741i
$169$	3.45141	+	7.16693i	0.265493	+	0.551302i
$170$	−1.89437	−	11.4051i	−0.145291	−	0.874728i
$171$	2.14453	−	19.0332i	0.163996	−	1.45550i
$172$	0.712394	−	0.343071i	0.0543195	−	0.0261589i
$173$	−9.47799	+	9.47799i	−0.720598	+	0.720598i	−0.968727	−	0.248129i	$-0.920184\pi$
$173$	−9.47799	+	9.47799i	−0.720598	+	0.720598i	0.248129	+	0.968727i	$0.420184\pi$
$174$	14.5296	−	2.77573i	1.10149	−	0.210428i
$175$	5.43120	+	4.39744i	0.410560	+	0.332415i
$176$	−1.34756	+	3.85109i	−0.101576	+	0.290287i
$177$	8.88440	−	7.08507i	0.667792	−	0.532547i
$178$	−1.48464	−	13.1765i	−0.111278	−	0.987621i
$179$	−3.08837	+	1.48728i	−0.230836	+	0.111165i	−0.545727	−	0.837963i	$-0.683746\pi$
$179$	−3.08837	+	1.48728i	−0.230836	+	0.111165i	0.314891	+	0.949128i	$0.398032\pi$
$180$	11.1545	−	4.57201i	0.831406	−	0.340778i
$181$	11.0324	+	13.8343i	0.820036	+	1.02829i	0.999012	+	0.0444387i	$0.0141499\pi$
$181$	11.0324	+	13.8343i	0.820036	+	1.02829i	−0.178977	+	0.983853i	$0.557279\pi$
$182$	1.37705	−	6.03324i	0.102074	−	0.447213i
$183$	5.96867	+	9.49908i	0.441217	+	0.702192i
$184$	0.816121	+	7.24327i	0.0601652	+	0.533981i
$185$	7.25104	+	4.04264i	0.533107	+	0.297221i
$186$	−7.77919	−	7.77919i	−0.570398	−	0.570398i
$187$	−15.7194	+	25.0173i	−1.14952	+	1.82945i
$188$	−0.0264523	−	0.0127387i	−0.00192923	−	0.000929068i
$189$	7.73602	−	2.70695i	0.562713	−	0.196902i
$190$	7.86774	−	2.23513i	0.570786	−	0.162154i
$191$	−16.2424	+	16.2424i	−1.17526	+	1.17526i	−0.194321	+	0.980938i	$0.562250\pi$
$191$	−16.2424	+	16.2424i	−1.17526	+	1.17526i	−0.980938	+	0.194321i	$0.937750\pi$
$192$	4.12002	+	18.0510i	0.297337	+	1.30272i
$193$	8.47412	−	10.6262i	0.609980	−	0.764891i	−0.376916	−	0.926248i	$-0.623015\pi$
$193$	8.47412	−	10.6262i	0.609980	−	0.764891i	0.986896	+	0.161356i	$0.0515868\pi$
$194$	−8.29631	−	1.89358i	−0.595640	−	0.135951i
$195$	−28.6398	−	4.97529i	−2.05094	−	0.356288i
$196$	−4.19976	+	3.34920i	−0.299983	+	0.239228i
$197$	−10.0993	+	3.53390i	−0.719545	+	0.251780i	−0.665118	−	0.746738i	$-0.731619\pi$
$197$	−10.0993	+	3.53390i	−0.719545	+	0.251780i	−0.0544269	+	0.998518i	$0.517333\pi$
$198$	25.5591	+	8.94353i	1.81641	+	0.635589i
$199$	−8.87767	−	7.07970i	−0.629321	−	0.501867i	0.256104	−	0.966649i	$-0.417561\pi$
$199$	−8.87767	−	7.07970i	−0.629321	−	0.501867i	−0.885425	+	0.464782i	$0.846133\pi$
$200$	10.4017	+	10.5569i	0.735509	+	0.746486i
$201$	19.1221	+	6.69111i	1.34877	+	0.471955i
$202$	−3.70126	−	3.70126i	−0.260420	−	0.260420i
$203$	−3.77478	−	6.51154i	−0.264938	−	0.457020i
$204$			16.1583i			1.13131i
$205$	−15.8369	+	8.67631i	−1.10609	+	0.605980i
$206$	−7.64952	−	0.861893i	−0.532967	−	0.0600510i
$207$	12.3771	−	1.39456i	0.860267	−	0.0969288i
$208$	1.11602	−	3.18940i	0.0773819	−	0.221145i
$209$	−18.8324	−	9.06918i	−1.30266	−	0.627329i
$210$	5.69660	+	6.42221i	0.393103	+	0.443175i
$211$	1.27617	−	0.801873i	0.0878554	−	0.0552032i	−0.487388	−	0.873186i	$-0.662050\pi$
$211$	1.27617	−	0.801873i	0.0878554	−	0.0552032i	0.575243	+	0.817982i	$0.304907\pi$
$212$	−1.56738	+	0.984852i	−0.107648	+	0.0676399i
$213$	7.79591	+	6.21703i	0.534167	+	0.425984i
$214$	5.85972	−	9.32570i	0.400562	−	0.637492i
$215$	1.11141	−	1.23444i	0.0757976	−	0.0841879i
$216$	16.9458	−	3.86777i	1.15302	−	0.263169i
$217$	−2.42874	+	5.04333i	−0.164873	+	0.342363i
$218$	−2.94313	+	6.11148i	−0.199334	+	0.413922i
$219$	8.87314	−	2.02524i	0.599591	−	0.136853i
$220$	−0.688997	−	13.1377i	−0.0464522	−	0.885742i
$221$	13.0185	−	20.7188i	0.875719	−	1.39370i
$222$	7.97337	+	6.35855i	0.535138	+	0.426758i
$223$	7.42676	−	4.66654i	0.497333	−	0.312495i	−0.259905	−	0.965634i	$-0.583691\pi$
$223$	7.42676	−	4.66654i	0.497333	−	0.312495i	0.757238	+	0.653139i	$0.226548\pi$
$224$	6.17054	−	3.87721i	0.412287	−	0.259057i
$225$	18.0393	−	17.7740i	1.20262	−	1.18494i
$226$	12.8608	+	6.19344i	0.855488	+	0.411981i
$227$	6.85426	−	19.5884i	0.454934	−	1.30013i	−0.456883	−	0.889527i	$-0.651034\pi$
$227$	6.85426	−	19.5884i	0.454934	−	1.30013i	0.911816	−	0.410598i	$-0.134680\pi$
$228$	−11.3594	+	1.27989i	−0.752292	+	0.0847629i
$229$	−5.35144	−	0.602962i	−0.353633	−	0.0398449i	−0.0666386	−	0.997777i	$-0.521227\pi$
$229$	−5.35144	−	0.602962i	−0.353633	−	0.0398449i	−0.286994	+	0.957932i	$0.592656\pi$
$230$	2.55553	+	4.66460i	0.168506	+	0.307575i
$231$		−	21.9388i		−	1.44347i
$232$	−6.40890	−	14.6189i	−0.420765	−	0.959777i
$233$	13.8913	+	13.8913i	0.910051	+	0.910051i	0.996276	−	0.0862245i	$-0.0274802\pi$
$233$	13.8913	+	13.8913i	0.910051	+	0.910051i	−0.0862245	+	0.996276i	$0.527480\pi$
$234$	−21.1676	−	7.40685i	−1.38377	−	0.484201i
$235$	−0.0615668	−	0.00368630i	−0.00401618	−	0.000240468i
$236$	−3.32999	−	2.65558i	−0.216764	−	0.172863i
$237$	−25.1983	−	8.81726i	−1.63680	−	0.572743i
$238$	−6.82084	+	2.38672i	−0.442129	+	0.154708i
$239$	7.62904	−	6.08395i	0.493481	−	0.393538i	−0.344885	−	0.938645i	$-0.612082\pi$
$239$	7.62904	−	6.08395i	0.493481	−	0.393538i	0.838367	+	0.545107i	$0.183511\pi$
$240$	2.69830	+	3.83290i	0.174175	+	0.247413i
$241$	−19.6440	−	4.48362i	−1.26538	−	0.288815i	−0.463392	−	0.886153i	$-0.653368\pi$
$241$	−19.6440	−	4.48362i	−1.26538	−	0.288815i	−0.801990	+	0.597338i	$0.796225\pi$
$242$	11.7909	−	14.7854i	0.757950	−	0.950439i
$243$	2.99292	+	13.1128i	0.191996	+	0.841188i
$244$	2.97330	−	2.97330i	0.190346	−	0.190346i
$245$	−5.49507	+	9.85618i	−0.351067	+	0.629688i
$246$	−20.9381	+	7.32657i	−1.33497	+	0.467125i
$247$	15.5966	+	7.51092i	0.992386	+	0.477908i
$248$	−6.31591	+	10.0517i	−0.401061	+	0.638285i
$249$	29.7844	+	29.7844i	1.88751	+	1.88751i
$250$	9.94443	+	4.24917i	0.628941	+	0.268741i
$251$	−2.78070	−	24.6794i	−0.175516	−	1.55775i	−0.704863	−	0.709344i	$-0.748991\pi$
$251$	−2.78070	−	24.6794i	−0.175516	−	1.55775i	0.529347	−	0.848406i	$-0.322437\pi$
$252$	−4.00887	−	6.38007i	−0.252535	−	0.401907i
$253$	3.02463	−	13.2518i	0.190157	−	0.833132i
$254$	0.446930	+	0.560433i	0.0280429	+	0.0351647i
$255$	12.8737	+	31.4084i	0.806182	+	1.96687i
$256$	15.3404	−	7.38754i	0.958774	−	0.461721i
$257$	−0.115223	−	1.02264i	−0.00718744	−	0.0637903i	0.989606	−	0.143802i	$-0.0459328\pi$
$257$	−0.115223	−	1.02264i	−0.00718744	−	0.0637903i	−0.996794	+	0.0800116i	$0.974504\pi$
$258$	1.59532	−	1.27223i	0.0993206	−	0.0792055i
$259$	1.71383	−	4.89785i	0.106492	−	0.304337i
$260$	0.570613	+	10.8804i	0.0353879	+	0.674771i
$261$	−24.9803	+	10.9513i	−1.54624	+	0.677870i
$262$	−10.0375	+	10.0375i	−0.620118	+	0.620118i
$263$	−3.57239	+	1.72037i	−0.220283	+	0.106083i	−0.540771	−	0.841170i	$-0.681867\pi$
$263$	−3.57239	+	1.72037i	−0.220283	+	0.106083i	0.320488	+	0.947253i	$0.396153\pi$
$264$	5.20936	−	46.2344i	0.320614	−	2.84553i
$265$	−2.26201	+	3.16311i	−0.138954	+	0.194309i
$266$	−2.21814	−	4.60602i	−0.136003	−	0.282413i
$267$	12.8582	+	36.7467i	0.786910	+	2.24886i
$268$	0.850182	−	7.54557i	0.0519331	−	0.460919i
$269$	−3.84254	−	6.11537i	−0.234284	−	0.372861i	0.708803	−	0.705406i	$-0.249235\pi$
$269$	−3.84254	−	6.11537i	−0.234284	−	0.372861i	−0.943087	+	0.332546i	$0.892092\pi$
$270$	10.3710	−	7.30101i	0.631158	−	0.444325i
$271$	1.02753	−	0.115774i	0.0624178	−	0.00703279i	−0.0807004	−	0.996738i	$-0.525716\pi$
$271$	1.02753	−	0.115774i	0.0624178	−	0.00703279i	0.143118	+	0.989706i	$0.454287\pi$
$272$	−3.84684	+	0.878017i	−0.233249	+	0.0532376i
$273$			18.1693i			1.09966i
$274$	−1.41161	−	6.18465i	−0.0852782	−	0.373628i
$275$	−11.8063	−	24.9879i	−0.711949	−	1.50683i
$276$	−2.45517	−	7.01646i	−0.147784	−	0.422341i
$277$	−14.0865	−	8.85116i	−0.846378	−	0.531815i	0.0376270	−	0.999292i	$-0.488020\pi$
$277$	−14.0865	−	8.85116i	−0.846378	−	0.531815i	−0.884005	+	0.467477i	$0.845163\pi$
$278$	4.42440			0.265358
$279$	17.1761	+	10.7924i	1.02830	+	0.646126i
$280$	5.38841	−	7.53497i	0.322019	−	0.450301i
$281$	−3.44157	+	15.0785i	−0.205307	+	0.899507i	0.762336	+	0.647182i	$0.224052\pi$
$281$	−3.44157	+	15.0785i	−0.205307	+	0.899507i	−0.967642	+	0.252325i	$0.918805\pi$
$282$	−0.0738671	−	0.0168597i	−0.00439872	−	0.00100398i
$283$	3.77828	+	0.425710i	0.224596	+	0.0253059i	0.223545	−	0.974694i	$-0.428237\pi$
$283$	3.77828	+	0.425710i	0.224596	+	0.0253059i	0.00105059	+	0.999999i	$0.499666\pi$
$284$	1.62159	−	3.36727i	0.0962237	−	0.199811i
$285$	−21.0605	+	11.5381i	−1.24751	+	0.683457i
$286$	−15.2590	+	19.1342i	−0.902283	+	1.13143i
$287$	7.03731	+	8.82451i	0.415399	+	0.520894i
$288$	−11.4585	−	23.7939i	−0.675201	−	1.40207i
$289$	−11.5736			−0.680799
$290$	−8.37274	−	8.09666i	−0.491664	−	0.475452i
$291$	24.9846			1.46462
$292$	−1.48011	−	3.07347i	−0.0866166	−	0.179861i
$293$	−15.6752	−	19.6561i	−0.915755	−	1.14832i	−0.988538	−	0.150972i	$-0.951760\pi$
$293$	−15.6752	−	19.6561i	−0.915755	−	1.14832i	0.0727831	−	0.997348i	$-0.476812\pi$
$294$	−8.64304	+	10.8380i	−0.504072	+	0.632087i
$295$	−8.58854	−	2.50880i	−0.500044	−	0.146068i
$296$	4.77476	−	9.91488i	0.277527	−	0.576291i
$297$	−32.2091	−	3.62909i	−1.86896	−	0.210581i
$298$	−7.62836	−	1.74112i	−0.441899	−	0.100861i
$299$	−2.50494	+	10.9749i	−0.144864	+	0.634692i
$300$	−12.7376	−	8.13579i	−0.735406	−	0.469720i
$301$	−0.879095	−	0.552372i	−0.0506702	−	0.0318382i
$302$	9.40414			0.541147
$303$	13.0127	+	8.17641i	0.747559	+	0.469723i
$304$	−0.921955	−	2.63479i	−0.0528777	−	0.151116i
$305$	3.41057	−	8.14836i	0.195289	−	0.466574i
$306$	5.82727	+	25.5309i	0.333123	+	1.45951i
$307$			22.4912i			1.28364i	0.766855	+	0.641820i	$0.221820\pi$
$307$			22.4912i			1.28364i	−0.766855	+	0.641820i	$0.778180\pi$
$308$	−8.01678	+	1.82978i	−0.456799	+	0.104261i
$309$	22.4592	−	2.53054i	1.27766	−	0.143958i
$310$	−1.48261	+	8.53450i	−0.0842067	+	0.484727i
$311$	16.9687	+	27.0055i	0.962205	+	1.53134i	0.842615	+	0.538517i	$0.181015\pi$
$311$	16.9687	+	27.0055i	0.962205	+	1.53134i	0.119590	+	0.992823i	$0.461842\pi$
$312$	−4.31429	+	38.2904i	−0.244249	+	2.16777i
$313$	−8.44016	−	24.1206i	−0.477066	−	1.36338i	−0.891386	−	0.453245i	$-0.850266\pi$
$313$	−8.44016	−	24.1206i	−0.477066	−	1.36338i	0.414320	−	0.910131i	$-0.364019\pi$
$314$	1.70021	+	3.53052i	0.0959484	+	0.199239i
$315$	−12.8755	−	9.20756i	−0.725454	−	0.518787i
$316$	−1.12033	+	9.94323i	−0.0630237	+	0.559351i
$317$	−21.4059	+	10.3085i	−1.20228	+	0.578985i	−0.924323	−	0.381610i	$-0.875370\pi$
$317$	−21.4059	+	10.3085i	−1.20228	+	0.578985i	−0.277952	+	0.960595i	$0.589656\pi$
$318$	−3.37788	+	3.37788i	−0.189422	+	0.189422i
$319$	2.27678	+	29.6784i	0.127475	+	1.66167i
$320$	9.75455	−	10.8343i	0.545296	−	0.605657i
$321$	−10.6802	+	30.5223i	−0.596112	+	1.70359i
$322$	2.59918	−	2.07278i	0.144847	−	0.115511i
$323$	−2.26330	−	20.0873i	−0.125933	−	1.11769i
$324$	−1.39883	+	0.673639i	−0.0777125	+	0.0374244i
$325$	9.77778	+	20.6945i	0.542374	+	1.14792i
$326$	3.55478	+	4.45756i	0.196881	+	0.246881i
$327$	4.43167	−	19.4164i	0.245072	−	1.07373i
$328$	12.7352	+	20.2680i	0.703184	+	1.11911i
$329$	0.00431635	+	0.0383086i	0.000237968	+	0.00211202i
$330$	−9.27770	−	32.6578i	−0.510720	−	1.79775i
$331$	0.695071	+	0.695071i	0.0382046	+	0.0382046i	0.725951	−	0.687746i	$-0.241400\pi$
$331$	0.695071	+	0.695071i	0.0382046	+	0.0382046i	−0.687746	+	0.725951i	$0.741400\pi$
$332$	8.39956	−	13.3678i	0.460986	−	0.733654i
$333$	−16.9423	−	8.15896i	−0.928430	−	0.447108i
$334$	−12.8060	+	4.48100i	−0.700711	+	0.245189i
$335$	−4.35915	−	15.3444i	−0.238166	−	0.838351i
$336$	2.07172	−	2.07172i	0.113022	−	0.113022i
$337$	−6.13247	−	26.8681i	−0.334057	−	1.46360i	−0.811197	−	0.584772i	$-0.801184\pi$
$337$	−6.13247	−	26.8681i	−0.334057	−	1.46360i	0.477140	−	0.878827i	$-0.341673\pi$
$338$	4.79725	−	6.01556i	0.260936	−	0.327203i
$339$	−40.8593	−	9.32587i	−2.21917	−	0.506512i
$340$	10.4034	−	7.32382i	0.564203	−	0.397190i
$341$	17.3077	−	13.8024i	0.937263	−	0.747443i
$342$	−17.4868	+	6.11888i	−0.945575	+	0.330871i
$343$	15.8920	+	5.56087i	0.858090	+	0.300259i
$344$	−1.72146	−	1.37282i	−0.0928151	−	0.0740176i
$345$	−10.3625	−	11.6824i	−0.557898	−	0.628961i
$346$	12.2374	+	4.28205i	0.657887	+	0.230205i
$347$	−0.132362	−	0.132362i	−0.00710559	−	0.00710559i	0.703545	−	0.710651i	$-0.251599\pi$
$347$	−0.132362	−	0.132362i	−0.00710559	−	0.00710559i	−0.710651	+	0.703545i	$0.751599\pi$
$348$	9.68958	+	13.0805i	0.519416	+	0.701189i
$349$			32.4359i			1.73625i	0.496342	+	0.868127i	$0.334676\pi$
$349$			32.4359i			1.73625i	−0.496342	+	0.868127i	$0.665324\pi$
$350$	1.55288	−	6.57859i	0.0830047	−	0.351641i
$351$	26.6749	+	3.00554i	1.42380	+	0.160424i
$352$	−28.6392	+	3.22686i	−1.52647	+	0.171992i
$353$	−6.46469	+	18.4750i	−0.344081	+	0.983326i	0.633679	+	0.773596i	$0.281544\pi$
$353$	−6.46469	+	18.4750i	−0.344081	+	0.983326i	−0.977759	+	0.209730i	$0.932742\pi$
$354$	−9.90295	−	4.76901i	−0.526336	−	0.253470i
$355$	0.469251	−	7.83721i	0.0249053	−	0.415956i
$356$	12.3554	−	7.76340i	0.654834	−	0.411459i
$357$	17.9648	−	11.2880i	0.950796	−	0.597425i
$358$	2.59223	+	2.06723i	0.137003	+	0.109257i
$359$	8.60134	−	13.6890i	0.453962	−	0.722476i	−0.538819	−	0.842422i	$-0.681129\pi$
$359$	8.60134	−	13.6890i	0.453962	−	0.722476i	0.992780	+	0.119946i	$0.0382721\pi$
$360$	−24.9479	−	22.4615i	−1.31487	−	1.18383i
$361$	−4.58146	+	1.04569i	−0.241130	+	0.0550362i
$362$	7.42601	−	15.4203i	0.390303	−	0.810472i
$363$	−24.0909	+	50.0252i	−1.26444	+	2.62564i
$364$	6.63934	−	1.51539i	0.347996	−	0.0794278i
$365$	−5.32571	−	4.79494i	−0.278761	−	0.250979i
$366$	5.77321	−	9.18801i	0.301771	−	0.480265i
$367$	10.9440	+	8.72758i	0.571274	+	0.455576i	0.866027	−	0.499997i	$-0.166666\pi$
$367$	10.9440	+	8.72758i	0.571274	+	0.455576i	−0.294752	+	0.955574i	$0.595237\pi$
$368$	1.53701	−	0.965769i	0.0801223	−	0.0503442i
$369$	34.6333	−	21.7615i	1.80294	−	1.13286i
$370$	0.479934	−	8.01562i	0.0249506	−	0.416712i
$371$	2.18991	+	1.05461i	0.113695	+	0.0547524i
$372$	3.99857	−	11.4273i	0.207316	−	0.592476i
$373$	19.8878	−	2.24082i	1.02975	−	0.116025i	0.419112	−	0.907934i	$-0.362341\pi$
$373$	19.8878	−	2.24082i	1.02975	−	0.116025i	0.610639	+	0.791909i	$0.290913\pi$
$374$	28.3987	+	3.19977i	1.46846	+	0.165456i
$375$	−31.2412	−	5.66591i	−1.61329	−	0.292586i
$376$			0.0817574i			0.00421632i
$377$	−1.88558	−	24.5791i	−0.0971125	−	1.26589i
$378$	−5.60563	−	5.60563i	−0.288322	−	0.288322i
$379$	−28.3344	−	9.91464i	−1.45544	−	0.509281i	−0.517382	−	0.855755i	$-0.673093\pi$
$379$	−28.3344	−	9.91464i	−1.45544	−	0.509281i	−0.938060	+	0.346474i	$0.887379\pi$
$380$	5.97271	+	6.73350i	0.306394	+	0.345421i
$381$	−1.64545	−	1.31220i	−0.0842988	−	0.0672260i
$382$	20.9712	+	7.33814i	1.07298	+	0.375452i
$383$	4.50789	−	1.57738i	0.230342	−	0.0806003i	−0.212640	−	0.977131i	$-0.568206\pi$
$383$	4.50789	−	1.57738i	0.230342	−	0.0806003i	0.442982	+	0.896530i	$0.353920\pi$
$384$	−9.15232	+	7.29873i	−0.467052	+	0.372462i
$385$	−14.1251	+	9.94385i	−0.719882	+	0.506786i
$386$	−12.8167	−	2.92534i	−0.652355	−	0.148896i
$387$	−2.34584	+	2.94159i	−0.119246	+	0.149529i
$388$	−2.08381	−	9.12976i	−0.105789	−	0.463493i
$389$	−11.4859	+	11.4859i	−0.582361	+	0.582361i	−0.935551	−	0.353191i	$-0.885097\pi$
$389$	−11.4859	+	11.4859i	−0.582361	+	0.582361i	0.353191	+	0.935551i	$0.385097\pi$
$390$	7.68360	+	27.0465i	0.389074	+	1.36955i
$391$	12.4076	−	4.34159i	0.627477	−	0.219564i
$392$	13.4771	+	6.49022i	0.680695	+	0.327806i
$393$	22.1737	−	35.2892i	1.11852	−	1.78011i
$394$	7.31809	+	7.31809i	0.368680	+	0.368680i
$395$	5.74430	+	20.2201i	0.289027	+	1.01739i
$396$	3.33643	+	29.6117i	0.167662	+	1.48804i
$397$	0.0321198	+	0.0511183i	0.00161204	+	0.00256555i	0.847529	−	0.530749i	$-0.178089\pi$
$397$	0.0321198	+	0.0511183i	0.00161204	+	0.00256555i	−0.845917	+	0.533314i	$0.820946\pi$
$398$	−2.44397	+	10.7077i	−0.122505	+	0.536731i
$399$	9.35849	+	11.7352i	0.468510	+	0.587493i
$400$	1.24476	−	3.47455i	0.0622381	−	0.173728i
$401$	−31.3147	+	15.0804i	−1.56378	+	0.753078i	−0.997468	−	0.0711105i	$-0.977346\pi$
$401$	−31.3147	+	15.0804i	−1.56378	+	0.753078i	−0.566315	+	0.824189i	$0.691631\pi$
$402$	−2.19400	−	19.4723i	−0.109427	−	0.971191i
$403$	−14.3339	+	11.4309i	−0.714021	+	0.569413i
$404$	1.90248	−	5.43698i	0.0946520	−	0.270500i
$405$	−2.18232	+	2.42389i	−0.108440	+	0.120444i
$406$	−4.09039	+	6.02232i	−0.203003	+	0.298883i
$407$	−14.5108	+	14.5108i	−0.719272	+	0.719272i
$408$	40.5397	−	19.5229i	2.00701	−	0.966527i
$409$	−3.06651	+	27.2160i	−0.151629	+	1.34575i	0.655421	+	0.755264i	$0.272491\pi$
$409$	−3.06651	+	27.2160i	−0.151629	+	1.34575i	−0.807050	+	0.590483i	$0.798937\pi$
$410$	14.2074	+	10.1600i	0.701655	+	0.501768i
$411$	8.08120	+	16.7808i	0.398616	+	0.827735i
$412$	−2.79788	−	7.99588i	−0.137842	−	0.393928i
$413$	−0.626171	+	5.55742i	−0.0308119	+	0.273463i
$414$	−6.40967	−	10.2009i	−0.315018	−	0.501348i
$415$	5.67652	−	32.6763i	0.278649	−	1.60402i
$416$	23.7184	−	2.67242i	1.16289	−	0.131026i
$417$	−12.6645	+	2.89058i	−0.620181	+	0.141552i
$418$			20.2178i			0.988887i
$419$	1.69231	+	7.41451i	0.0826749	+	0.362222i	0.999295	−	0.0375364i	$-0.0119510\pi$
$419$	1.69231	+	7.41451i	0.0826749	+	0.362222i	−0.916620	+	0.399759i	$0.869094\pi$
$420$	−3.64753	+	8.71449i	−0.177981	+	0.425224i
$421$	−7.52865	−	21.5156i	−0.366924	−	1.04861i	−0.968332	−	0.249666i	$-0.919679\pi$
$421$	−7.52865	−	21.5156i	−0.366924	−	1.04861i	0.601408	−	0.798942i	$-0.294607\pi$
$422$	−1.23438	−	0.775613i	−0.0600888	−	0.0377563i
$423$	0.139705			0.00679267
$424$	4.36465	+	2.74249i	0.211966	+	0.133187i
$425$	14.3869	−	22.5246i	0.697868	−	1.09260i
$426$	2.14617	−	9.40298i	0.103982	−	0.455576i
$427$	−5.38282	−	1.22859i	−0.260493	−	0.0594558i
$428$	12.0441	+	1.35704i	0.582174	+	0.0655952i
$429$	31.1767	−	64.7390i	1.50522	−	3.12563i
$430$	−1.54220	−	0.450492i	−0.0743714	−	0.0217247i
$431$	−20.2333	+	25.3717i	−0.974602	+	1.22211i	0.000418849		1.00000i	$0.499867\pi$
$431$	−20.2333	+	25.3717i	−0.974602	+	1.22211i	−0.975021	+	0.222113i	$0.928705\pi$
$432$	−2.69886	−	3.38427i	−0.129849	−	0.162826i
$433$	14.0582	+	29.1921i	0.675592	+	1.40288i	0.903239	+	0.429138i	$0.141183\pi$
$433$	14.0582	+	29.1921i	0.675592	+	1.40288i	−0.227646	+	0.973744i	$0.573103\pi$
$434$	5.41436			0.259898
$435$	29.2560	+	17.7059i	1.40272	+	0.848931i
$436$	−7.46468			−0.357493
$437$	4.03495	+	8.37866i	0.193018	+	0.400806i
$438$	−5.48876	−	6.88268i	−0.262263	−	0.328867i
$439$	10.5436	−	13.2212i	0.503218	−	0.631015i	−0.463734	−	0.885975i	$-0.653491\pi$
$439$	10.5436	−	13.2212i	0.503218	−	0.631015i	0.966952	+	0.254959i	$0.0820620\pi$
$440$	−32.1287	+	17.6019i	−1.53168	+	0.839138i
$441$	11.0903	−	23.0292i	0.528109	−	1.09663i
$442$	−23.5192	−	2.64998i	−1.11870	−	0.126047i
$443$	31.8950	+	7.27982i	1.51538	+	0.345875i	0.897718	−	0.440571i	$-0.145224\pi$
$443$	31.8950	+	7.27982i	1.51538	+	0.345875i	0.617659	+	0.786446i	$0.288081\pi$
$444$	−2.49732	+	10.9415i	−0.118518	+	0.519259i
$445$	17.8310	−	24.9342i	0.845269	−	1.18199i
$446$	−7.18355	−	4.51373i	−0.340151	−	0.213731i
$447$	22.9731			1.08659
$448$	−7.71558	−	4.84802i	−0.364527	−	0.229047i
$449$	1.53366	+	4.38294i	0.0723777	+	0.206844i	0.974389	−	0.224869i	$-0.0721953\pi$
$449$	1.53366	+	4.38294i	0.0723777	+	0.206844i	−0.902011	+	0.431712i	$0.857910\pi$
$450$	−23.0601	−	8.26130i	−1.08706	−	0.389441i
$451$	−9.93268	−	43.5179i	−0.467712	−	2.04918i
$452$			15.7084i			0.738862i
$453$	−26.9185	+	6.14398i	−1.26474	+	0.288670i
$454$	−19.9471	+	2.24750i	−0.936165	+	0.105480i
$455$	11.6981	−	8.23530i	0.548417	−	0.386077i
$456$	16.9358	+	26.9531i	0.793090	+	1.26220i
$457$	−0.572244	+	5.07881i	−0.0267684	+	0.237577i	0.973202	+	0.229950i	$0.0738562\pi$
$457$	−0.572244	+	5.07881i	−0.0267684	+	0.237577i	−0.999971	+	0.00762663i	$0.997572\pi$
$458$	1.72040	+	4.91663i	0.0803892	+	0.229739i
$459$	−13.6006	−	28.2419i	−0.634821	−	1.31822i
$460$	−3.40467	+	4.76097i	−0.158743	+	0.221981i
$461$	1.19509	−	10.6068i	0.0556611	−	0.494006i	−0.934694	−	0.355453i	$-0.884326\pi$
$461$	1.19509	−	10.6068i	0.0556611	−	0.494006i	0.990355	−	0.138553i	$-0.0442450\pi$
$462$	−19.1189	+	9.20718i	−0.889492	+	0.428357i
$463$	3.63850	−	3.63850i	0.169096	−	0.169096i	−0.617486	−	0.786582i	$-0.711849\pi$
$463$	3.63850	−	3.63850i	0.169096	−	0.169096i	0.786582	+	0.617486i	$0.211849\pi$
$464$	−2.58759	+	3.01759i	−0.120126	+	0.140088i
$465$	−1.33198	−	25.3979i	−0.0617690	−	1.17780i
$466$	6.27595	−	17.9356i	0.290728	−	0.830853i
$467$	3.58602	−	2.85976i	0.165941	−	0.132334i	−0.536998	−	0.843583i	$-0.680442\pi$
$467$	3.58602	−	2.85976i	0.165941	−	0.132334i	0.702940	+	0.711250i	$0.251870\pi$
$468$	−2.76317	−	24.5238i	−0.127727	−	1.13361i
$469$	−8.98307	+	4.32602i	−0.414799	+	0.199757i
$470$	0.0226256	+	0.0552003i	0.00104364	+	0.00254620i
$471$	−7.17330	−	8.99503i	−0.330528	−	0.414469i
$472$	−2.63921	+	11.5631i	−0.121480	+	0.532237i
$473$	2.18449	+	3.47660i	0.100443	+	0.159854i
$474$	2.89116	+	25.6598i	0.132796	+	1.17859i
$475$	16.9744	+	8.32989i	0.778840	+	0.382202i
$476$	−5.62314	−	5.62314i	−0.257736	−	0.257736i
$477$	4.68629	−	7.45819i	0.214570	−	0.341487i
$478$	−8.50367	−	4.09515i	−0.388949	−	0.187308i
$479$	29.4941	−	10.3204i	1.34762	−	0.471553i	0.442523	−	0.896757i	$-0.354084\pi$
$479$	29.4941	−	10.3204i	1.34762	−	0.471553i	0.905097	+	0.425205i	$0.139798\pi$
$480$	−16.1235	+	28.9198i	−0.735934	+	1.32000i
$481$	12.0175	−	12.0175i	0.547952	−	0.547952i
$482$	4.33679	+	19.0007i	0.197535	+	0.865459i
$483$	−6.08573	+	7.63126i	−0.276910	+	0.347234i
$484$	20.2892	+	4.63089i	0.922238	+	0.210495i
$485$	−11.3244	−	16.0861i	−0.514213	−	0.730432i
$486$	10.1713	−	8.11134i	0.461380	−	0.367938i
$487$	4.92544	−	1.72349i	0.223193	−	0.0780986i	−0.216366	−	0.976312i	$-0.569420\pi$
$487$	4.92544	−	1.72349i	0.223193	−	0.0780986i	0.439559	+	0.898214i	$0.355135\pi$
$488$	−11.0521	−	3.86731i	−0.500307	−	0.175065i
$489$	−13.0875	−	10.4369i	−0.591838	−	0.471975i
$490$	10.8954	+	0.652363i	0.492206	+	0.0294707i
$491$	2.20709	+	0.772293i	0.0996044	+	0.0348531i	0.379621	−	0.925142i	$-0.376054\pi$
$491$	2.20709	+	0.772293i	0.0996044	+	0.0348531i	−0.280017	+	0.959995i	$0.590340\pi$
$492$	−17.2615	−	17.2615i	−0.778209	−	0.778209i
$493$	−23.1309	+	17.1346i	−1.04177	+	0.771702i
$494$		−	16.7440i		−	0.753348i
$495$	30.0776	+	54.9006i	1.35189	+	2.46760i
$496$	2.93778	+	0.331009i	0.131910	+	0.0148627i
$497$	−4.87654	+	0.549454i	−0.218743	+	0.0246464i
$498$	13.4563	−	38.4558i	0.602990	−	1.72325i
$499$	20.3394	+	9.79495i	0.910517	+	0.438482i	0.829676	−	0.558245i	$-0.188525\pi$
$499$	20.3394	+	9.79495i	0.910517	+	0.438482i	0.0808412	+	0.996727i	$0.474239\pi$
$500$	0.535219	+	11.8886i	0.0239357	+	0.531673i
$501$	33.7284	−	21.1930i	1.50687	−	0.946832i
$502$	−20.3402	+	12.7806i	−0.907828	+	0.570426i
$503$	8.82703	+	7.03932i	0.393578	+	0.313868i	0.800205	−	0.599726i	$-0.204724\pi$
$503$	8.82703	+	7.03932i	0.393578	+	0.313868i	−0.406627	+	0.913594i	$0.633295\pi$
$504$	−11.1634	+	17.7664i	−0.497257	+	0.791379i
$505$	−0.633742	−	12.0841i	−0.0282011	−	0.537735i
$506$	−12.8178	+	2.92558i	−0.569821	+	0.130058i
$507$	−9.80159	+	20.3532i	−0.435304	+	0.903918i
$508$	−0.342262	+	0.710714i	−0.0151854	+	0.0315328i
$509$	−33.9185	+	7.74166i	−1.50341	+	0.343143i	−0.893404	−	0.449254i	$-0.851690\pi$
$509$	−33.9185	+	7.74166i	−1.50341	+	0.343143i	−0.610005	+	0.792398i	$0.708833\pi$
$510$	21.9685	−	24.4003i	0.972781	−	1.08046i
$511$	−2.38309	+	3.79266i	−0.105422	+	0.167778i
$512$	−6.43039	−	5.12807i	−0.284186	−	0.226631i
$513$	18.7768	−	11.7983i	0.829018	−	0.520907i
$514$	−0.842835	+	0.529588i	−0.0371758	+	0.0233591i
$515$	−11.8090	−	13.3132i	−0.520366	−	0.586648i
$516$	2.02311	+	0.974280i	0.0890626	+	0.0428903i
$517$	0.0503542	−	0.143904i	0.00221458	−	0.00632889i
$518$	−4.98755	+	0.561962i	−0.219140	+	0.0246912i
$519$	−37.8261	−	4.26198i	−1.66038	−	0.187080i
$520$	26.6084	−	14.5775i	1.16685	−	0.639267i
$521$			7.44577i			0.326205i	0.986609	+	0.163102i	$0.0521501\pi$
$521$			7.44577i			0.326205i	−0.986609	+	0.163102i	$0.947850\pi$
$522$	20.0273	+	17.1734i	0.876571	+	0.751661i
$523$	−27.9535	−	27.9535i	−1.22232	−	1.22232i	−0.966805	−	0.255514i	$-0.917755\pi$
$523$	−27.9535	−	27.9535i	−1.22232	−	1.22232i	−0.255514	−	0.966805i	$-0.582245\pi$
$524$	−14.7446	−	5.15936i	−0.644121	−	0.225388i
$525$	−0.146998	+	19.8452i	−0.00641550	+	0.866116i
$526$	2.99848	+	2.39121i	0.130740	+	0.104262i
$527$	20.2074	+	7.07087i	0.880248	+	0.308012i
$528$	−10.9366	+	3.82689i	−0.475956	+	0.166544i
$529$	13.2540	−	10.5697i	0.576263	−	0.459554i
$530$	3.70585	+	0.643779i	0.160972	+	0.0279640i
$531$	19.7588	+	4.50981i	0.857457	+	0.195709i
$532$	3.50768	−	4.39849i	0.152077	−	0.190699i
$533$	8.22605	+	36.0407i	0.356310	+	1.56110i
$534$	26.6271	−	26.6271i	1.15227	−	1.15227i
$535$	24.4924	−	6.95800i	1.05890	−	0.300820i
$536$	−19.9583	+	6.98372i	−0.862068	+	0.301651i
$537$	−8.77060	−	4.22370i	−0.378480	−	0.182266i
$538$	−3.71671	+	5.91511i	−0.160239	+	0.255018i
$539$	−19.7242	−	19.7242i	−0.849579	−	0.849579i
$540$	12.1907	+	6.79660i	0.524602	+	0.292479i
$541$	1.67468	+	14.8632i	0.0720000	+	0.639018i	0.976945	+	0.213490i	$0.0684830\pi$
$541$	1.67468	+	14.8632i	0.0720000	+	0.639018i	−0.904945	+	0.425528i	$0.860088\pi$
$542$	−0.532120	−	0.846865i	−0.0228565	−	0.0363760i
$543$	−11.1818	+	48.9908i	−0.479859	+	2.10240i
$544$	−17.3778	−	21.7911i	−0.745068	−	0.934286i
$545$	−14.5098	+	5.94728i	−0.621530	+	0.254753i
$546$	15.8339	−	7.62520i	0.677628	−	0.326328i
$547$	−2.28505	−	20.2804i	−0.0977017	−	0.867127i	−0.942991	−	0.332818i	$-0.892001\pi$
$547$	−2.28505	−	20.2804i	−0.0977017	−	0.867127i	0.845289	−	0.534309i	$-0.179428\pi$
$548$	5.45796	−	4.35257i	0.233152	−	0.185933i
$549$	−6.60835	+	18.8856i	−0.282037	+	0.806017i
$550$	−16.8213	+	20.7756i	−0.717261	+	0.885875i
$551$	−13.8778	−	14.9039i	−0.591216	−	0.634928i
$552$	−14.6372	+	14.6372i	−0.623002	+	0.623002i
$553$	11.8375	−	5.70064i	0.503382	−	0.242416i
$554$	−1.80170	+	15.9905i	−0.0765469	+	0.679372i
$555$	3.86305	+	23.2576i	0.163978	+	0.987229i
$556$	2.11253	+	4.38670i	0.0895910	+	0.186038i
$557$	10.1752	+	29.0790i	0.431137	+	1.23212i	0.930682	+	0.365830i	$0.119215\pi$
$557$	10.1752	+	29.0790i	0.431137	+	1.23212i	−0.499545	+	0.866288i	$0.666499\pi$
$558$	2.19686	−	19.4976i	0.0930004	−	0.825401i
$559$	−1.80915	−	2.87925i	−0.0765189	−	0.121779i
$560$	−2.27288	−	0.394843i	−0.0960466	−	0.0166852i
$561$	−83.3794	+	9.39460i	−3.52028	+	0.396640i
$562$	14.5847	−	3.32886i	0.615219	−	0.140420i
$563$			12.4601i			0.525130i	0.964914	+	0.262565i	$0.0845685\pi$
$563$			12.4601i			0.525130i	−0.964914	+	0.262565i	$0.915432\pi$
$564$	−0.0185534	−	0.0812878i	−0.000781239	−	0.00342283i
$565$	12.5153	+	30.5338i	0.526521	+	1.28457i
$566$	−1.21466	−	3.47130i	−0.0510560	−	0.145910i
$567$	1.72615	+	1.08461i	0.0724915	+	0.0455495i
$568$	−10.4074			−0.436685
$569$	−3.79658	−	2.38555i	−0.159161	−	0.100007i	0.450097	−	0.892980i	$-0.351390\pi$
$569$	−3.79658	−	2.38555i	−0.159161	−	0.100007i	−0.609258	+	0.792972i	$0.708532\pi$
$570$	18.8936	+	13.5112i	0.791365	+	0.565921i
$571$	−1.25968	+	5.51903i	−0.0527160	+	0.230964i	−0.994422	−	0.105472i	$-0.966365\pi$
$571$	−1.25968	+	5.51903i	−0.0527160	+	0.230964i	0.941706	+	0.336436i	$0.109222\pi$
$572$	−26.2569	−	5.99296i	−1.09786	−	0.250578i
$573$	−64.8225	−	7.30374i	−2.70800	−	0.305118i
$574$	4.73686	−	9.83619i	0.197713	−	0.410555i
$575$	−2.82478	+	11.9669i	−0.117802	+	0.499054i
$576$	−20.5888	+	25.8175i	−0.857865	+	1.07573i
$577$	29.4491	+	36.9281i	1.22598	+	1.53734i	0.755857	+	0.654736i	$0.227220\pi$
$577$	29.4491	+	36.9281i	1.22598	+	1.53734i	0.470127	+	0.882599i	$0.344208\pi$
$578$	4.85714	+	10.0860i	0.202030	+	0.419521i
$579$	38.5980			1.60408
$580$	4.02993	−	12.1673i	0.167334	−	0.505221i
$581$	−20.7301			−0.860031
$582$	−10.4854	−	21.7732i	−0.434634	−	0.902528i
$583$	−5.99328	−	7.51533i	−0.248216	−	0.311253i
$584$	−5.92274	+	7.42688i	−0.245085	+	0.307327i
$585$	−24.9097	−	45.4676i	−1.02989	−	1.87985i
$586$	−10.5511	+	21.9095i	−0.435861	+	0.905075i
$587$	13.8431	+	1.55975i	0.571367	+	0.0643776i	0.392921	−	0.919572i	$-0.371464\pi$
$587$	13.8431	+	1.55975i	0.571367	+	0.0643776i	0.178446	+	0.983950i	$0.442893\pi$
$588$	−14.8725	−	3.39455i	−0.613332	−	0.139989i
$589$	−3.37023	+	14.7659i	−0.138868	+	0.608420i
$590$	1.41807	+	8.53749i	0.0583809	+	0.351483i
$591$	−25.7285	−	16.1663i	−1.05833	−	0.664993i
$592$	−2.74056			−0.112636
$593$	−18.0409	−	11.3359i	−0.740852	−	0.465508i	0.107992	−	0.994152i	$-0.465558\pi$
$593$	−18.0409	−	11.3359i	−0.740852	−	0.465508i	−0.848844	+	0.528643i	$0.822701\pi$
$594$	10.3547	+	29.5921i	0.424860	+	1.21418i
$595$	−15.4103	−	6.45011i	−0.631760	−	0.264429i
$596$	−1.91604	−	8.39471i	−0.0784840	−	0.343861i
$597$		−	32.2467i		−	1.31977i
$598$	10.6155	−	2.42291i	0.434098	−	0.0990801i
$599$	−9.52133	+	1.07280i	−0.389031	+	0.0438332i	−0.304314	−	0.952572i	$-0.598427\pi$
$599$	−9.52133	+	1.07280i	−0.389031	+	0.0438332i	−0.0847169	+	0.996405i	$0.526999\pi$
$600$	−5.02202	+	41.7873i	−0.205023	+	1.70596i
$601$	−18.7867	−	29.8988i	−0.766324	−	1.21960i	−0.970603	−	0.240685i	$-0.922628\pi$
$601$	−18.7867	−	29.8988i	−0.766324	−	1.21960i	0.204279	−	0.978913i	$-0.434515\pi$
$602$	−0.112438	+	0.997916i	−0.00458264	+	0.0406720i
$603$	11.9336	+	34.1042i	0.485973	+	1.38883i
$604$	4.49021	+	9.32402i	0.182704	+	0.379389i
$605$	43.1275	−	7.16343i	1.75338	−	0.291235i
$606$	1.66435	−	14.7715i	0.0676096	−	0.600052i
$607$	27.6914	−	13.3355i	1.12396	−	0.541270i	0.222846	−	0.974854i	$-0.428465\pi$
$607$	27.6914	−	13.3355i	1.12396	−	0.541270i	0.901113	+	0.433583i	$0.142751\pi$
$608$	13.9427	−	13.9427i	0.565452	−	0.565452i
$609$	7.77385	−	19.9107i	0.315012	−	0.806824i
$610$	−8.53234	+	0.447473i	−0.345464	+	0.0181177i
$611$	−0.0417023	+	0.119178i	−0.00168710	+	0.00482144i
$612$	−22.5311	+	17.9679i	−0.910764	+	0.726310i
$613$	−0.611887	−	5.43065i	−0.0247139	−	0.219342i	0.975285	−	0.220951i	$-0.0709162\pi$
$613$	−0.611887	−	5.43065i	−0.0247139	−	0.219342i	−0.999999	+	0.00160954i	$0.999488\pi$
$614$	19.6003	−	9.43899i	0.791003	−	0.380927i
$615$	−47.3054	−	19.8001i	−1.90754	−	0.798417i
$616$	14.2768	+	17.9026i	0.575229	+	0.721315i
$617$	−1.94013	+	8.50028i	−0.0781068	+	0.342208i	−0.998849	−	0.0479630i	$-0.984727\pi$
$617$	−1.94013	+	8.50028i	−0.0781068	+	0.342208i	0.920742	+	0.390171i	$0.127584\pi$
$618$	−11.6308	−	18.5104i	−0.467861	−	0.744596i
$619$	−0.314355	−	2.78998i	−0.0126350	−	0.112139i	0.985812	−	0.167855i	$-0.0536842\pi$
$619$	−0.314355	−	2.78998i	−0.0126350	−	0.112139i	−0.998447	+	0.0557167i	$0.982256\pi$
$620$	−9.16970	+	2.60500i	−0.368264	+	0.104620i
$621$	10.1970	+	10.1970i	0.409192	+	0.409192i
$622$	16.4130	−	26.1211i	0.658101	−	1.04736i
$623$	−17.2626	−	8.31325i	−0.691613	−	0.333063i
$624$	9.05750	−	3.16936i	0.362590	−	0.126876i
$625$	10.5122	+	22.6824i	0.420490	+	0.907297i
$626$	−17.4781	+	17.4781i	−0.698566	+	0.698566i
$627$	−13.2089	−	57.8718i	−0.527511	−	2.31118i
$628$	−2.68864	+	3.37145i	−0.107289	+	0.134536i
$629$	−19.3484	−	4.41614i	−0.771470	−	0.176083i
$630$	−2.62052	+	15.0848i	−0.104404	+	0.600991i
$631$	34.6785	−	27.6552i	1.38053	−	1.10093i	0.397476	−	0.917613i	$-0.369886\pi$
$631$	34.6785	−	27.6552i	1.38053	−	1.10093i	0.983053	−	0.183322i	$-0.0586851\pi$
$632$	26.3002	−	9.20285i	1.04617	−	0.366070i
$633$	4.04004	+	1.41367i	0.160577	+	0.0561884i
$634$	17.9670	+	14.3282i	0.713563	+	0.569047i
$635$	−0.0990427	+	1.65416i	−0.00393039	+	0.0656435i
$636$	−4.96194	−	1.73626i	−0.196754	−	0.0688471i
$637$	16.3351	+	16.3351i	0.647222	+	0.647222i
$638$	24.9082	−	14.4394i	0.986124	−	0.571662i
$639$			17.7838i			0.703518i
$640$	8.84754	+	2.58446i	0.349730	+	0.102160i
$641$	19.6936	+	2.21894i	0.777852	+	0.0876428i	0.491959	−	0.870619i	$-0.336281\pi$
$641$	19.6936	+	2.21894i	0.777852	+	0.0876428i	0.285893	+	0.958261i	$0.407710\pi$
$642$	31.0813	−	3.50203i	1.22668	−	0.138214i
$643$	10.0280	−	28.6585i	0.395467	−	1.13018i	−0.558302	−	0.829638i	$-0.688547\pi$
$643$	10.0280	−	28.6585i	0.395467	−	1.13018i	0.953769	−	0.300542i	$-0.0971675\pi$
$644$	3.29615	+	1.58734i	0.129887	+	0.0625501i
$645$	4.70873	+	0.281934i	0.185406	+	0.0111012i
$646$	−16.5555	+	10.4025i	−0.651368	+	0.409282i
$647$	−4.06817	+	2.55620i	−0.159936	+	0.100495i	−0.609622	−	0.792692i	$-0.708679\pi$
$647$	−4.06817	+	2.55620i	−0.159936	+	0.100495i	0.449686	+	0.893187i	$0.351536\pi$
$648$	3.38019	+	2.69561i	0.132786	+	0.105894i
$649$	11.7671	−	18.7272i	0.461898	−	0.735107i
$650$	13.9310	−	17.2060i	0.546420	−	0.674873i
$651$	−15.4981	+	3.53735i	−0.607420	+	0.138640i
$652$	−2.72227	+	5.65286i	−0.106612	+	0.221383i
$653$	−13.5268	+	28.0887i	−0.529345	+	1.09920i	0.449251	+	0.893406i	$0.351691\pi$
$653$	−13.5268	+	28.0887i	−0.529345	+	1.09920i	−0.978596	+	0.205791i	$0.934023\pi$
$654$	−18.7806	+	4.28655i	−0.734379	+	0.167617i
$655$	−32.7710	+	1.71865i	−1.28047	+	0.0671532i
$656$	3.17152	−	5.04744i	0.123827	−	0.197070i
$657$	12.6908	+	10.1206i	0.495117	+	0.394842i
$658$	0.0315732	−	0.0198387i	0.00123085	−	0.000773394i
$659$	11.5058	−	7.22958i	0.448203	−	0.281624i	−0.288958	−	0.957342i	$-0.593309\pi$
$659$	11.5058	−	7.22958i	0.448203	−	0.281624i	0.737161	+	0.675717i	$0.236166\pi$
$660$	27.9497	−	24.7918i	1.08794	−	0.965021i
$661$	−20.4402	−	9.84350i	−0.795033	−	0.382868i	−0.00814767	−	0.999967i	$-0.502594\pi$
$661$	−20.4402	−	9.84350i	−0.795033	−	0.382868i	−0.786886	+	0.617099i	$0.788308\pi$
$662$	0.314026	−	0.897434i	0.0122050	−	0.0348797i
$663$	69.0531	−	7.78042i	2.68180	−	0.302166i
$664$	−43.6871	−	4.92236i	−1.69539	−	0.191025i
$665$	3.31381	−	11.3444i	0.128504	−	0.439916i
$666$			18.1887i			0.704797i
$667$	7.44069	−	10.9550i	0.288105	−	0.424179i
$668$	−10.5573	−	10.5573i	−0.408475	−	0.408475i
$669$	23.5113	+	8.22694i	0.908997	+	0.318072i
$670$	−11.5426	+	10.2385i	−0.445931	+	0.395547i
$671$	17.0714	+	13.6140i	0.659034	+	0.525562i
$672$	19.5344	+	6.83538i	0.753555	+	0.263680i
$673$	−11.2083	+	3.92195i	−0.432048	+	0.151180i	−0.537537	−	0.843240i	$-0.680645\pi$
$673$	−11.2083	+	3.92195i	−0.432048	+	0.151180i	0.105489	+	0.994421i	$0.466359\pi$
$674$	−20.8410	+	16.6201i	−0.802764	+	0.640183i
$675$	29.1111	+	3.49858i	1.12048	+	0.134660i
$676$	8.25486	+	1.88412i	0.317495	+	0.0724661i
$677$	−0.686559	+	0.860917i	−0.0263866	+	0.0330877i	−0.794850	−	0.606806i	$-0.792450\pi$
$677$	−0.686559	+	0.860917i	−0.0263866	+	0.0330877i	0.768463	+	0.639894i	$0.221022\pi$
$678$	9.02047	+	39.5212i	0.346429	+	1.51780i
$679$	−8.69471	+	8.69471i	−0.333672	+	0.333672i
$680$	−30.9444	−	17.2523i	−1.18666	−	0.661595i
$681$	55.6286	−	19.4653i	2.13169	−	0.745911i
$682$	−19.2919	−	9.29049i	−0.738725	−	0.355751i
$683$	0.202616	−	0.322462i	0.00775289	−	0.0123387i	−0.842825	−	0.538187i	$-0.819109\pi$
$683$	0.202616	−	0.322462i	0.00775289	−	0.0123387i	0.850578	+	0.525849i	$0.176252\pi$
$684$	−14.4162	−	14.4162i	−0.551216	−	0.551216i
$685$	7.14132	−	12.8090i	0.272856	−	0.489405i
$686$	−1.82340	−	16.1831i	−0.0696177	−	0.617874i
$687$	−8.13668	−	12.9495i	−0.310434	−	0.494053i
$688$	−0.122016	+	0.534587i	−0.00465182	+	0.0203809i
$689$	4.96351	+	6.22405i	0.189095	+	0.237117i
$690$	−5.83194	+	13.9334i	−0.222018	+	0.530434i
$691$	−9.56118	+	4.60442i	−0.363724	+	0.175160i	−0.606815	−	0.794843i	$-0.707553\pi$
$691$	−9.56118	+	4.60442i	−0.363724	+	0.175160i	0.243091	+	0.970004i	$0.421839\pi$
$692$	1.59744	+	14.1777i	0.0607257	+	0.538956i
$693$	30.5914	−	24.3958i	1.16207	−	0.926719i
$694$	−0.0597999	+	0.170898i	−0.00226997	+	0.00648722i
$695$	7.60129	+	6.84373i	0.288333	+	0.259597i
$696$	21.1106	−	40.1144i	0.800195	−	1.52053i
$697$	30.5244	−	30.5244i	1.15619	−	1.15619i
$698$	28.2667	−	13.6125i	1.06991	−	0.515242i
$699$	−6.24653	+	55.4395i	−0.236266	+	2.09691i
$700$	7.26400	−	1.60145i	0.274553	−	0.0605290i
$701$	−7.04923	−	14.6379i	−0.266246	−	0.552865i	0.724391	−	0.689389i	$-0.242121\pi$
$701$	−7.04923	−	14.6379i	−0.266246	−	0.552865i	−0.990637	+	0.136524i	$0.956407\pi$
$702$	−8.57558	−	24.5076i	−0.323664	−	0.924979i
$703$	1.57199	−	13.9518i	0.0592885	−	0.526200i
$704$	19.1727	+	30.5131i	0.722597	+	1.15001i
$705$	−0.100828	−	0.143224i	−0.00379739	−	0.00539414i
$706$	18.8134	−	2.11976i	0.708052	−	0.0797782i
$707$	−7.37386	+	1.68304i	−0.277323	+	0.0632971i
$708$		−	12.0956i		−	0.454582i
$709$	−5.20526	−	22.8057i	−0.195488	−	0.856488i	−0.973582	−	0.228340i	$-0.926670\pi$
$709$	−5.20526	−	22.8057i	−0.195488	−	0.856488i	0.778094	−	0.628148i	$-0.216187\pi$
$710$	−7.02678	+	2.88015i	−0.263710	+	0.108090i
$711$	−15.7256	−	44.9410i	−0.589754	−	1.68542i
$712$	−34.4057	−	21.6185i	−1.28941	−	0.810189i
$713$	−9.84907			−0.368851
$714$	−17.3765	−	10.9184i	−0.650298	−	0.408609i
$715$	−55.8126	+	9.27040i	−2.08727	+	0.346693i
$716$	−0.811905	+	3.55719i	−0.0303423	+	0.132938i
$717$	27.0165	+	6.16634i	1.00895	+	0.230286i
$718$	−15.5392	−	1.75085i	−0.579918	−	0.0653411i
$719$	−14.4691	+	30.0454i	−0.539606	+	1.12050i	0.435790	+	0.900048i	$0.356469\pi$
$719$	−14.4691	+	30.0454i	−0.539606	+	1.12050i	−0.975397	+	0.220456i	$0.929245\pi$
$720$	−2.34408	+	8.02465i	−0.0873588	+	0.299061i
$721$	−6.93522	+	8.69649i	−0.258281	+	0.323874i
$722$	2.83401	+	3.55373i	0.105471	+	0.132256i
$723$	−24.8274	−	51.5546i	−0.923340	−	1.91734i
$724$	18.8346			0.699983
$725$	−1.86065	−	26.8615i	−0.0691029	−	0.997610i
$726$	53.7055			1.99320
$727$	6.72024	+	13.9547i	0.249240	+	0.517552i	0.987626	−	0.156826i	$-0.0501262\pi$
$727$	6.72024	+	13.9547i	0.249240	+	0.517552i	−0.738386	+	0.674378i	$0.764412\pi$
$728$	−11.8238	−	14.8265i	−0.438218	−	0.549508i
$729$	−26.5434	+	33.2844i	−0.983089	+	1.23275i
$730$	−1.94355	+	6.65349i	−0.0719341	+	0.246257i
$731$	−1.72287	+	3.57757i	−0.0637226	+	0.132321i
$732$	11.8663	+	1.33701i	0.438590	+	0.0494173i
$733$	−30.2417	−	6.90248i	−1.11700	−	0.254949i	−0.376113	−	0.926574i	$-0.622739\pi$
$733$	−30.2417	−	6.90248i	−1.11700	−	0.254949i	−0.740891	+	0.671625i	$0.765597\pi$
$734$	3.01284	−	13.2001i	0.111206	−	0.487224i
$735$	−31.6135	+	5.25096i	−1.16608	+	0.193685i
$736$	10.8570	+	6.82193i	0.400196	+	0.251460i
$737$	39.4306			1.45244
$738$	−33.4991	−	21.0489i	−1.23312	−	0.774821i
$739$	3.03598	+	8.67634i	0.111680	+	0.319164i	0.986135	−	0.165942i	$-0.0530665\pi$
$739$	3.03598	+	8.67634i	0.111680	+	0.319164i	−0.874455	+	0.485107i	$0.838781\pi$
$740$	8.17648	−	3.35139i	0.300574	−	0.123199i
$741$	10.9393	+	47.9283i	0.401866	+	1.76069i
$742$		−	2.35102i		−	0.0863087i
$743$	20.9160	−	4.77394i	0.767334	−	0.175139i	0.179101	−	0.983831i	$-0.442681\pi$
$743$	20.9160	−	4.77394i	0.767334	−	0.175139i	0.588233	+	0.808692i	$0.299824\pi$
$744$	−33.5011	+	3.77466i	−1.22821	+	0.138386i
$745$	−10.4126	−	14.7910i	−0.381489	−	0.541900i
$746$	−10.2992	−	16.3911i	−0.377081	−	0.600120i
$747$	−8.41118	+	74.6513i	−0.307749	+	2.73135i
$748$	10.3871	+	29.6846i	0.379789	+	1.08538i
$749$	−6.90511	−	14.3386i	−0.252307	−	0.523921i
$750$	8.17351	+	29.6034i	0.298454	+	1.08096i
$751$	−4.39473	+	39.0043i	−0.160366	+	1.42329i	0.613378	+	0.789790i	$0.289810\pi$
$751$	−4.39473	+	39.0043i	−0.160366	+	1.42329i	−0.773744	+	0.633499i	$0.781618\pi$
$752$	0.0183442	−	0.00883409i	0.000668943	−	0.000322146i
$753$	49.8722	−	49.8722i	1.81744	−	1.81744i
$754$	−20.6284	+	11.9584i	−0.751244	+	0.435501i
$755$	16.1567	+	14.5465i	0.588002	+	0.529400i
$756$	2.88134	−	8.23440i	0.104793	−	0.299482i
$757$	33.8127	−	26.9647i	1.22894	−	0.980049i	0.228965	−	0.973435i	$-0.426466\pi$
$757$	33.8127	−	26.9647i	1.22894	−	0.980049i	0.999978	−	0.00661456i	$-0.00210549\pi$
$758$	3.25099	+	28.8534i	0.118081	+	1.04800i
$759$	34.7785	−	16.7485i	1.26238	−	0.607931i
$760$	9.67732	−	23.1205i	0.351033	−	0.838670i
$761$	−10.1735	−	12.7572i	−0.368791	−	0.462449i	0.562462	−	0.826823i	$-0.309854\pi$
$761$	−10.1735	−	12.7572i	−0.368791	−	0.462449i	−0.931253	+	0.364374i	$0.881283\pi$
$762$	−0.452982	+	1.98464i	−0.0164098	+	0.0718961i
$763$	5.21473	+	8.29920i	0.188786	+	0.300451i
$764$	2.73753	+	24.2963i	0.0990405	+	0.879009i
$765$	−29.4802	+	52.8768i	−1.06586	+	1.91177i
$766$	−3.26648	−	3.26648i	−0.118023	−	0.118023i
$767$	−9.74526	+	15.5095i	−0.351881	+	0.560015i
$768$	43.5649	+	20.9797i	1.57201	+	0.757041i
$769$	35.8462	−	12.5431i	1.29265	−	0.452317i	0.405624	−	0.914040i	$-0.367054\pi$
$769$	35.8462	−	12.5431i	1.29265	−	0.452317i	0.887024	+	0.461723i	$0.152768\pi$
$770$	14.5937	+	8.13634i	0.525919	+	0.293213i
$771$	2.06655	−	2.06655i	0.0744249	−	0.0744249i
$772$	−3.21922	−	14.1043i	−0.115862	−	0.507625i
$773$	−33.4647	+	41.9634i	−1.20364	+	1.50932i	−0.397496	+	0.917604i	$0.630121\pi$
$773$	−33.4647	+	41.9634i	−1.20364	+	1.50932i	−0.806147	+	0.591716i	$0.798451\pi$
$774$	3.54798	+	0.809802i	0.127529	+	0.0291077i
$775$	−15.7485	+	12.3693i	−0.565702	+	0.444318i
$776$	−20.3880	+	16.2589i	−0.731886	+	0.583659i
$777$	13.9093	−	4.86707i	0.498993	−	0.174605i
$778$	14.8300	+	5.18923i	0.531680	+	0.186043i
$779$	23.8766	+	19.0409i	0.855467	+	0.682212i
$780$	−23.1474	+	20.5321i	−0.828810	+	0.735167i
$781$	18.3184	+	6.40989i	0.655484	+	0.229364i
$782$	−8.99069	−	8.99069i	−0.321506	−	0.321506i
$783$	−27.9456	−	14.7067i	−0.998696	−	0.525573i
$784$		−	3.72518i		−	0.133042i
$785$	−2.54004	+	8.69549i	−0.0906579	+	0.310355i
$786$	−40.0591	−	4.51357i	−1.42886	−	0.160994i
$787$	−42.8076	+	4.82326i	−1.52593	+	0.171931i	−0.834699	−	0.550707i	$-0.814358\pi$
$787$	−42.8076	+	4.82326i	−1.52593	+	0.171931i	−0.691227	+	0.722637i	$0.742930\pi$
$788$	−3.76156	+	10.7499i	−0.134000	+	0.382950i
$789$	−10.1452	−	4.88565i	−0.361177	−	0.173934i
$790$	15.2104	−	13.4918i	0.541161	−	0.480018i
$791$	17.4646	−	10.9737i	0.620969	−	0.390180i
$792$	70.2617	−	44.1483i	2.49664	−	1.56874i
$793$	−14.1382	−	11.2748i	−0.502062	−	0.400381i
$794$	0.0310679	−	0.0494443i	0.00110256	−	0.00175471i
$795$	−11.0283	+	0.578371i	−0.391133	+	0.0205127i
$796$	−11.7834	+	2.68949i	−0.417653	+	0.0953266i
$797$	−12.9305	+	26.8505i	−0.458023	+	0.951095i	0.536233	+	0.844070i	$0.319847\pi$
$797$	−12.9305	+	26.8505i	−0.458023	+	0.951095i	−0.994256	+	0.107025i	$0.965868\pi$
$798$	6.29926	−	13.0805i	0.222991	−	0.463046i
$799$	0.143745	−	0.0328089i	0.00508534	−	0.00116070i
$800$	25.9278	−	2.72703i	0.916685	−	0.0964150i
$801$	−36.9411	+	58.7914i	−1.30525	+	2.07729i
$802$	26.2840	+	20.9608i	0.928121	+	0.740152i
$803$	14.9990	−	9.42451i	0.529304	−	0.332584i
$804$	18.2588	−	11.4728i	0.643940	−	0.404614i
$805$	7.67169	+	0.459341i	0.270392	+	0.0161896i
$806$	15.9772	+	7.69420i	0.562772	+	0.271017i
$807$	6.77426	−	19.3597i	0.238465	−	0.681494i
$808$	−15.9395	+	1.79595i	−0.560749	+	0.0631812i
$809$	22.8571	+	2.57537i	0.803612	+	0.0905453i	0.504209	−	0.863582i	$-0.331784\pi$
$809$	22.8571	+	2.57537i	0.803612	+	0.0905453i	0.299403	+	0.954127i	$0.403213\pi$
$810$	3.02819	+	0.884566i	0.106400	+	0.0310805i
$811$			19.6076i			0.688516i	0.938875	+	0.344258i	$0.111869\pi$
$811$			19.6076i			0.688516i	−0.938875	+	0.344258i	$0.888131\pi$
$812$	−7.92406	−	1.18006i	−0.278080	−	0.0414119i
$813$	2.07643	+	2.07643i	0.0728236	+	0.0728236i
$814$	18.7354	+	6.55581i	0.656676	+	0.229781i
$815$	−0.787764	+	13.1568i	−0.0275942	+	0.460864i
$816$	−8.76082	−	6.98652i	−0.306690	−	0.244577i
$817$	−2.65151	−	0.927804i	−0.0927646	−	0.0324598i
$818$	25.0047	−	8.74954i	0.874270	−	0.305920i
$819$	−25.3351	+	20.2041i	−0.885282	+	0.705988i
$820$	−3.28982	+	18.9375i	−0.114885	+	0.661326i
$821$	−3.20785	−	0.732172i	−0.111955	−	0.0255530i	0.166176	−	0.986096i	$-0.446858\pi$
$821$	−3.20785	−	0.732172i	−0.111955	−	0.0255530i	−0.278131	+	0.960543i	$0.589715\pi$
$822$	11.2324	−	14.0850i	0.391774	−	0.491269i
$823$	3.76096	+	16.4779i	0.131099	+	0.574382i	0.997218	+	0.0745439i	$0.0237501\pi$
$823$	3.76096	+	16.4779i	0.131099	+	0.574382i	−0.866119	+	0.499838i	$0.833393\pi$
$824$	−16.6804	+	16.6804i	−0.581090	+	0.581090i
$825$	34.5761	−	70.4582i	1.20379	−	2.45304i
$826$	5.10588	−	1.78663i	0.177656	−	0.0621646i
$827$	−0.120242	−	0.0579057i	−0.00418124	−	0.00201358i	0.431792	−	0.901973i	$-0.357881\pi$
$827$	−0.120242	−	0.0579057i	−0.00418124	−	0.00201358i	−0.435973	+	0.899960i	$0.643596\pi$
$828$	7.05358	−	11.2257i	0.245129	−	0.390120i
$829$	−28.0352	−	28.0352i	−0.973704	−	0.973704i	0.0259593	−	0.999663i	$-0.491736\pi$
$829$	−28.0352	−	28.0352i	−0.973704	−	0.973704i	−0.999663	+	0.0259593i	$0.991736\pi$
$830$	−30.8585	+	8.76655i	−1.07112	+	0.304291i
$831$	−5.28984	−	46.9486i	−0.183502	−	1.62863i
$832$	−15.8784	−	25.2704i	−0.550485	−	0.876092i
$833$	6.00275	−	26.2998i	0.207983	−	0.911234i
$834$	7.83400	+	9.82352i	0.271269	+	0.340161i
$835$	−28.9324	−	12.1099i	−1.00125	−	0.419081i
$836$	−20.0456	+	9.65345i	−0.693291	+	0.333871i
$837$	2.62961	+	23.3385i	0.0908927	+	0.806695i
$838$	5.75126	−	4.58647i	0.198674	−	0.158437i
$839$	0.960023	−	2.74359i	0.0331437	−	0.0947192i	−0.926123	−	0.377223i	$-0.876879\pi$
$839$	0.960023	−	2.74359i	0.0331437	−	0.0947192i	0.959266	+	0.282503i	$0.0911649\pi$
$840$	26.2709	−	1.37776i	0.906431	−	0.0475372i
$841$	−8.45001	+	27.7416i	−0.291380	+	0.956607i
$842$	−15.5905	+	15.5905i	−0.537285	+	0.537285i
$843$	−39.5726	+	19.0572i	−1.36295	+	0.656364i
$844$	0.179623	−	1.59420i	0.00618288	−	0.0548746i
$845$	17.5468	−	2.91451i	0.603629	−	0.100262i
$846$	−0.0586305	−	0.121748i	−0.00201576	−	0.00418577i
$847$	−9.02522	−	25.7926i	−0.310110	−	0.886244i
$848$	0.143731	−	1.27564i	0.00493573	−	0.0438058i
$849$	5.74476	+	9.14273i	0.197160	+	0.313778i
$850$	−25.6672	−	3.08469i	−0.880377	−	0.105804i
$851$	9.07268	−	1.02225i	0.311007	−	0.0350421i
$852$	10.3476	−	2.36177i	0.354503	−	0.0809131i
$853$		−	19.9191i		−	0.682018i	−0.940060	−	0.341009i	$-0.889231\pi$
$853$		−	19.9191i		−	0.682018i	0.940060	−	0.341009i	$-0.110769\pi$
$854$	1.18836	+	5.20655i	0.0406648	+	0.178164i
$855$	−39.5077	−	16.5363i	−1.35113	−	0.565530i
$856$	−11.1473	−	31.8571i	−0.381006	−	1.08885i
$857$	−28.1515	−	17.6888i	−0.961638	−	0.604237i	−0.0428889	−	0.999080i	$-0.513656\pi$
$857$	−28.1515	−	17.6888i	−0.961638	−	0.604237i	−0.918749	+	0.394843i	$0.870799\pi$
$858$	−69.5018			−2.37275
$859$	−14.3941	−	9.04440i	−0.491120	−	0.308591i	0.263607	−	0.964630i	$-0.415088\pi$
$859$	−14.3941	−	9.04440i	−0.491120	−	0.308591i	−0.754727	+	0.656039i	$0.772231\pi$
$860$	−0.289702	−	1.74416i	−0.00987877	−	0.0594753i
$861$	−7.13260	+	31.2500i	−0.243078	+	1.06500i
$862$	30.6019	+	6.98469i	1.04231	+	0.237900i
$863$	9.57890	+	1.07928i	0.326070	+	0.0367392i	0.273482	−	0.961877i	$-0.411825\pi$
$863$	9.57890	+	1.07928i	0.326070	+	0.0367392i	0.0525876	+	0.998616i	$0.483253\pi$
$864$	13.2666	−	27.5483i	0.451338	−	0.937214i
$865$	14.4008	+	26.2858i	0.489642	+	0.893742i
$866$	19.5400	−	24.5024i	0.663996	−	0.832625i
$867$	−20.4926	−	25.6969i	−0.695965	−	0.872712i
$868$	2.58520	+	5.36823i	0.0877475	+	0.182210i
$869$	−51.9599			−1.76262
$870$	3.15200	−	32.9263i	0.106863	−	1.11631i
$871$	−32.6556			−1.10649
$872$	9.01901	+	18.7282i	0.305422	+	0.634216i
$873$	27.7827	+	34.8384i	0.940301	+	1.17910i
$874$	5.60833	−	7.03263i	0.189705	−	0.237882i
$875$	12.8438	−	8.90027i	0.434199	−	0.300884i
$876$	4.20332	−	8.72828i	0.142017	−	0.294901i
$877$	−26.5240	−	2.98854i	−0.895652	−	0.100916i	−0.347876	−	0.937541i	$-0.613097\pi$
$877$	−26.5240	−	2.98854i	−0.895652	−	0.100916i	−0.547776	+	0.836625i	$0.684525\pi$
$878$	−15.9467	−	3.63974i	−0.538176	−	0.122835i
$879$	15.8875	−	69.6075i	0.535871	−	2.34780i
$880$	7.42098	+	5.30689i	0.250161	+	0.178895i
$881$	19.0940	+	11.9976i	0.643294	+	0.404209i	0.813798	−	0.581148i	$-0.197396\pi$
$881$	19.0940	+	11.9976i	0.643294	+	0.404209i	−0.170503	+	0.985357i	$0.554539\pi$
$882$	−24.7235			−0.832482
$883$	2.02364	+	1.27154i	0.0681010	+	0.0427907i	0.565652	−	0.824644i	$-0.308624\pi$
$883$	2.02364	+	1.27154i	0.0681010	+	0.0427907i	−0.497551	+	0.867435i	$0.665767\pi$
$884$	−8.60237	−	24.5842i	−0.289329	−	0.826855i
$885$	−9.63687	−	23.5114i	−0.323940	−	0.790326i
$886$	−7.04143	−	30.8505i	−0.236561	−	1.03644i
$887$		−	24.2760i		−	0.815109i	−0.913181	−	0.407554i	$-0.866382\pi$
$887$		−	24.2760i		−	0.815109i	0.913181	−	0.407554i	$-0.133618\pi$
$888$	30.4684	−	6.95422i	1.02245	−	0.233368i
$889$	1.02927	−	0.115971i	0.0345206	−	0.00388953i
$890$	−29.2125	−	5.07478i	−0.979205	−	0.170107i
$891$	−4.28937	−	6.82649i	−0.143699	−	0.228696i
$892$	1.04533	−	9.27753i	0.0350001	−	0.310635i
$893$	0.0344507	+	0.0984546i	0.00115285	+	0.00329466i
$894$	−9.64122	−	20.0202i	−0.322451	−	0.669576i
$895$	1.25592	+	7.56128i	0.0419807	+	0.252746i
$896$	0.645054	−	5.72501i	0.0215497	−	0.191259i
$897$	−28.8029	+	13.8707i	−0.961700	+	0.463130i
$898$	3.17594	−	3.17594i	0.105982	−	0.105982i
$899$	20.5985	−	6.39363i	0.686998	−	0.213240i
$900$	−2.81963	−	26.8082i	−0.0939876	−	0.893606i
$901$	3.07031	−	8.77445i	0.102287	−	0.292319i
$902$	−33.7558	+	26.9194i	−1.12395	+	0.896317i
$903$	−0.330122	−	2.92991i	−0.0109858	−	0.0975013i
$904$	39.4109	−	18.9793i	1.31079	−	0.631242i
$905$	36.6105	−	15.0060i	1.21697	−	0.498815i
$906$	16.6513	+	20.8801i	0.553203	+	0.693694i
$907$	−8.63900	+	37.8499i	−0.286853	+	1.25679i	0.601964	+	0.798523i	$0.294385\pi$
$907$	−8.63900	+	37.8499i	−0.286853	+	1.25679i	−0.888817	+	0.458262i	$0.848472\pi$
$908$	−11.7525	−	18.7041i	−0.390022	−	0.620716i
$909$	3.06886	+	27.2369i	0.101788	+	0.903391i
$910$	−12.0862	−	6.73835i	−0.400653	−	0.223374i
$911$	42.3681	+	42.3681i	1.40372	+	1.40372i	0.787850	+	0.615867i	$0.211194\pi$
$911$	42.3681	+	42.3681i	1.40372	+	1.40372i	0.615867	+	0.787850i	$0.288806\pi$
$912$	4.21761	−	6.71228i	0.139659	−	0.222266i
$913$	73.8635	+	35.5708i	2.44453	+	1.17722i
$914$	4.66615	−	1.63276i	0.154343	−	0.0540068i
$915$	24.1308	−	6.85527i	0.797738	−	0.226628i
$916$	−4.05330	+	4.05330i	−0.133925	+	0.133925i
$917$	4.56424	+	19.9973i	0.150725	+	0.660368i
$918$	−18.9040	+	23.7048i	−0.623924	+	0.782376i
$919$	35.7935	+	8.16963i	1.18072	+	0.269491i	0.767444	−	0.641115i	$-0.221528\pi$
$919$	35.7935	+	8.16963i	1.18072	+	0.269491i	0.413274	+	0.910607i	$0.364385\pi$
$920$	16.0584	+	2.78966i	0.529431	+	0.0919725i
$921$	−49.9374	+	39.8237i	−1.64549	+	1.31224i
$922$	−9.74496	+	3.40991i	−0.320933	+	0.112299i
$923$	−15.1709	−	5.30854i	−0.499358	−	0.174733i
$924$	−18.2575	−	14.5598i	−0.600627	−	0.478984i
$925$	13.2232	−	13.0288i	0.434777	−	0.428383i
$926$	−4.69781	−	1.64384i	−0.154380	−	0.0540198i
$927$	28.5030	+	28.5030i	0.936161	+	0.936161i
$928$	−27.1351	−	7.21951i	−0.890753	−	0.236992i
$929$			28.6797i			0.940951i	0.882413	+	0.470476i	$0.155918\pi$
$929$			28.6797i			0.940951i	−0.882413	+	0.470476i	$0.844082\pi$
$930$	−21.5744	+	11.8196i	−0.707452	+	0.387581i
$931$	18.9643	+	2.13676i	0.621530	+	0.0700296i
$932$	20.7794	−	2.34128i	0.680653	−	0.0766912i
$933$	−29.9151	+	85.4925i	−0.979377	+	2.79890i
$934$	−3.99714	−	1.92492i	−0.130790	−	0.0629854i
$935$	43.8406	+	49.4249i	1.43374	+	1.61637i
$936$	−58.1893	+	36.5628i	−1.90198	+	1.19509i
$937$	−17.6540	+	11.0928i	−0.576732	+	0.362385i	−0.788594	−	0.614915i	$-0.789190\pi$
$937$	−17.6540	+	11.0928i	−0.576732	+	0.362385i	0.211861	+	0.977300i	$0.432048\pi$
$938$	7.53994	+	6.01290i	0.246188	+	0.196328i
$939$	38.6107	−	61.4485i	1.26001	−	2.00530i
$940$	−0.0439270	+	0.0487894i	−0.00143274	+	0.00159134i
$941$	25.0472	−	5.71686i	0.816515	−	0.186364i	0.206187	−	0.978513i	$-0.433895\pi$
$941$	25.0472	−	5.71686i	0.816515	−	0.186364i	0.610328	+	0.792148i	$0.291037\pi$
$942$	−4.82839	+	10.0263i	−0.157318	+	0.326673i
$943$	−8.61666	+	17.8927i	−0.280597	+	0.582666i
$944$	2.87963	−	0.657257i	0.0937241	−	0.0213919i
$945$	−0.959813	−	18.3016i	−0.0312227	−	0.595349i
$946$	2.11295	−	3.36275i	0.0686980	−	0.109332i
$947$	−44.0039	−	35.0919i	−1.42993	−	1.14033i	−0.967254	−	0.253809i	$-0.918317\pi$
$947$	−44.0039	−	35.0919i	−1.42993	−	1.14033i	−0.462680	−	0.886526i	$-0.653112\pi$
$948$	−24.0607	+	15.1184i	−0.781456	+	0.491021i
$949$	−12.4219	+	7.80519i	−0.403232	+	0.253367i
$950$	0.135466	−	18.2884i	0.00439511	−	0.593356i
$951$	−60.7902	−	29.2750i	−1.97126	−	0.949307i
$952$	−7.31391	+	20.9019i	−0.237045	+	0.677436i
$953$	9.89638	−	1.11505i	0.320575	−	0.0361202i	0.0497894	−	0.998760i	$-0.484145\pi$
$953$	9.89638	−	1.11505i	0.320575	−	0.0361202i	0.270786	+	0.962640i	$0.412716\pi$
$954$	−8.46626	−	0.953919i	−0.274105	−	0.0308843i
$955$	24.6786	+	45.0458i	0.798580	+	1.45765i
$956$		−	10.3865i		−	0.335925i
$957$	−61.8638	+	57.6048i	−1.99977	+	1.86210i
$958$	−21.3718	−	21.3718i	−0.690493	−	0.690493i
$959$	−8.65204	−	3.02748i	−0.279389	−	0.0977624i
$960$	41.3273	+	2.47446i	1.33383	+	0.0798629i
$961$	11.6958	+	9.32706i	0.377283	+	0.300873i
$962$	−15.5163	−	5.42939i	−0.500265	−	0.175050i
$963$	−54.4365	+	19.0481i	−1.75419	+	0.613818i
$964$	−16.7681	+	13.3721i	−0.540065	+	0.430688i
$965$	−17.4947	−	24.8510i	−0.563174	−	0.799981i
$966$	9.20440	+	2.10084i	0.296147	+	0.0675935i
$967$	−22.1233	+	27.7417i	−0.711437	+	0.892114i	−0.997820	−	0.0660016i	$-0.978976\pi$
$967$	−22.1233	+	27.7417i	−0.711437	+	0.892114i	0.286383	+	0.958115i	$0.407547\pi$
$968$	−12.8955	−	56.4989i	−0.414477	−	1.81594i
$969$	40.5925	−	40.5925i	1.30402	−	1.30402i
$970$	−9.26591	+	16.6197i	−0.297510	+	0.533627i
$971$	−21.6352	+	7.57047i	−0.694306	+	0.242948i	−0.654282	−	0.756251i	$-0.727029\pi$
$971$	−21.6352	+	7.57047i	−0.694306	+	0.242948i	−0.0400236	+	0.999199i	$0.512743\pi$
$972$	12.8987	+	6.21171i	0.413727	+	0.199241i
$973$	3.40134	−	5.41320i	0.109042	−	0.173539i
$974$	−3.56904	−	3.56904i	−0.114359	−	0.114359i
$975$	−28.6353	+	58.3521i	−0.917062	+	1.86876i
$976$	0.326490	+	2.89768i	0.0104507	+	0.0927524i
$977$	0.555488	+	0.884054i	0.0177716	+	0.0282834i	0.855492	−	0.517816i	$-0.173255\pi$
$977$	0.555488	+	0.884054i	0.0177716	+	0.0282834i	−0.837720	+	0.546100i	$0.816112\pi$
$978$	−3.60292	+	15.7854i	−0.115209	+	0.504762i
$979$	47.2438	+	59.2419i	1.50992	+	1.89338i
$980$	4.55546	+	11.1141i	0.145519	+	0.355027i
$981$	32.0021	−	15.4114i	1.02175	−	0.492048i
$982$	−0.253233	−	2.24751i	−0.00808100	−	0.0717209i
$983$	20.1477	−	16.0672i	0.642611	−	0.512465i	−0.247100	−	0.968990i	$-0.579478\pi$
$983$	20.1477	−	16.0672i	0.642611	−	0.512465i	0.889710	+	0.456525i	$0.150906\pi$
$984$	−22.4517	+	64.1633i	−0.715734	+	2.04545i
$985$	1.25303	+	23.8925i	0.0399247	+	0.761278i
$986$	24.6396	+	12.9668i	0.784686	+	0.412948i
$987$	−0.0774143	+	0.0774143i	−0.00246412	+	0.00246412i
$988$	16.6014	−	7.99479i	0.528159	−	0.254348i
$989$	0.204532	−	1.81528i	0.00650375	−	0.0577224i
$990$	35.2211	−	49.2520i	1.11940	−	1.56533i
$991$	−10.0068	−	20.7794i	−0.317877	−	0.660078i	0.679405	−	0.733764i	$-0.262238\pi$
$991$	−10.0068	−	20.7794i	−0.317877	−	0.660078i	−0.997282	+	0.0736856i	$0.976524\pi$
$992$	6.89723	+	19.7111i	0.218987	+	0.625830i
$993$	−0.312553	+	2.77399i	−0.00991858	+	0.0880299i
$994$	2.52539	+	4.01914i	0.0801005	+	0.127479i
$995$	−20.7617	+	14.6159i	−0.658191	+	0.463356i
$996$	44.5532	−	5.01994i	1.41172	−	0.159063i
$997$	−6.12892	+	1.39888i	−0.194105	+	0.0443031i	−0.318468	−	0.947934i	$-0.603168\pi$
$997$	−6.12892	+	1.39888i	−0.194105	+	0.0443031i	0.124363	+	0.992237i	$0.460311\pi$
$998$		−	21.8358i		−	0.691199i
$999$	−4.84465	−	21.2258i	−0.153278	−	0.671554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.t.a.108.5	yes	156
5.2	odd	4		145.2.o.a.137.9	yes	156
5.3	odd	4		725.2.y.b.282.5		156
5.4	even	2		725.2.bd.b.543.9		156
29.18	odd	28		145.2.o.a.18.9	✓	156
145.18	even	28		725.2.bd.b.482.9		156
145.47	even	28	inner	145.2.t.a.47.5	yes	156
145.134	odd	28		725.2.y.b.18.5		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.9	✓	156	29.18	odd	28
145.2.o.a.137.9	yes	156	5.2	odd	4
145.2.t.a.47.5	yes	156	145.47	even	28	inner
145.2.t.a.108.5	yes	156	1.1	even	1	trivial
725.2.y.b.18.5		156	145.134	odd	28
725.2.y.b.282.5		156	5.3	odd	4
725.2.bd.b.482.9		156	145.18	even	28
725.2.bd.b.543.9		156	5.4	even	2

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.t (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.419675 - 0.871464i) q^{2} +(1.77064 + 2.22031i) q^{3} +(0.663657 - 0.832199i) q^{4} +(0.626976 - 2.14637i) q^{5} +(1.19183 - 2.47485i) q^{6} +(-1.38886 - 0.156487i) q^{7} +(-2.88975 - 0.659568i) q^{8} +(-1.12705 + 4.93793i) q^{9} +(-2.13361 + 0.354390i) q^{10} +(4.68013 + 2.94072i) q^{11} +3.02283 q^{12} +(-3.87599 - 2.43545i) q^{13} +(0.446497 + 1.27601i) q^{14} +(5.87575 - 2.40836i) q^{15} +(0.164256 + 0.719651i) q^{16} +5.34543i q^{17} +(4.77622 - 1.09014i) q^{18} +(-3.75785 + 0.423408i) q^{19} +(-1.37011 - 1.94622i) q^{20} +(-2.11171 - 3.36077i) q^{21} +(0.598599 - 5.31271i) q^{22} +(-0.812207 - 2.32115i) q^{23} +(-3.65226 - 7.58400i) q^{24} +(-4.21380 - 2.69145i) q^{25} +(-0.495748 + 4.39988i) q^{26} +(-5.28338 + 2.54434i) q^{27} +(-1.05195 + 1.05195i) q^{28} +(3.20546 + 4.32724i) q^{29} +(-4.56470 - 4.10977i) q^{30} +(1.32279 - 3.78032i) q^{31} +(-4.07659 + 3.25097i) q^{32} +(1.75750 + 15.5983i) q^{33} +(4.65835 - 2.24334i) q^{34} +(-1.20666 + 2.88289i) q^{35} +(3.36136 + 4.21502i) q^{36} +(-0.826152 + 3.61961i) q^{37} +(1.94606 + 3.09714i) q^{38} +(-1.45553 - 12.9182i) q^{39} +(-3.22748 + 5.78895i) q^{40} +(-5.71038 - 5.71038i) q^{41} +(-2.04256 + 3.25072i) q^{42} +(0.669277 + 0.322307i) q^{43} +(5.55327 - 1.94317i) q^{44} +(9.89198 + 5.51503i) q^{45} +(-1.68194 + 1.68194i) q^{46} +(-0.00613776 - 0.0268913i) q^{47} +(-1.30701 + 1.63894i) q^{48} +(-4.92005 - 1.12297i) q^{49} +(-0.577072 + 4.80171i) q^{50} +(-11.8685 + 9.46480i) q^{51} +(-4.59910 + 1.60930i) q^{52} +(-1.64149 - 0.574381i) q^{53} +(4.43460 + 3.53648i) q^{54} +(9.24620 - 8.20152i) q^{55} +(3.91025 + 1.36826i) q^{56} +(-7.59388 - 7.59388i) q^{57} +(2.42578 - 4.60948i) q^{58} -4.00143i q^{59} +(1.89524 - 6.48811i) q^{60} +(3.92555 + 0.442303i) q^{61} +(-3.84955 + 0.433740i) q^{62} +(2.33803 - 6.68171i) q^{63} +(5.87407 + 2.82880i) q^{64} +(-7.65752 + 6.79234i) q^{65} +(12.8558 - 8.07781i) q^{66} +(6.04031 - 3.79538i) q^{67} +(4.44846 + 3.54753i) q^{68} +(3.71555 - 5.91327i) q^{69} +(3.01874 - 0.158316i) q^{70} +(3.42315 - 0.781312i) q^{71} +(6.51379 - 13.5260i) q^{72} +(1.39052 - 2.88745i) q^{73} +(3.50108 - 0.799098i) q^{74} +(-1.48527 - 14.1215i) q^{75} +(-2.14156 + 3.40828i) q^{76} +(-6.03986 - 4.81662i) q^{77} +(-10.6469 + 6.68988i) q^{78} +(-7.95966 + 5.00139i) q^{79} +(1.64762 + 0.0986510i) q^{80} +(-1.31416 - 0.632868i) q^{81} +(-2.57989 + 7.37289i) q^{82} +(14.7389 - 1.66068i) q^{83} +(-4.19829 - 0.473033i) q^{84} +(11.4733 + 3.35146i) q^{85} -0.718515i q^{86} +(-3.93209 + 14.7791i) q^{87} +(-11.5848 - 11.5848i) q^{88} +(12.9395 + 4.52773i) q^{89} +(0.654732 - 10.9350i) q^{90} +(5.00209 + 3.98903i) q^{91} +(-2.47069 - 0.864532i) q^{92} +(10.7356 - 3.75656i) q^{93} +(-0.0208589 + 0.0166344i) q^{94} +(-1.44729 + 8.33120i) q^{95} +(-14.4363 - 3.29499i) q^{96} +(5.48532 - 6.87837i) q^{97} +(1.08620 + 4.75893i) q^{98} +(-19.7958 + 19.7958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 14 q^{2} - 10 q^{3} + 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} - 14 q^{8} - 10 q^{9} - 6 q^{10} - 20 q^{11} - 20 q^{12} - 28 q^{13} - 4 q^{14} - 4 q^{15} - 34 q^{16} + 84 q^{18} + 6 q^{20} - 16 q^{21}+ \cdots - 76 q^{99}+O(q^{100}) \) 156 * q - 14 * q^2 - 10 * q^3 + 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 - 14 * q^8 - 10 * q^9 - 6 * q^10 - 20 * q^11 - 20 * q^12 - 28 * q^13 - 4 * q^14 - 4 * q^15 - 34 * q^16 + 84 * q^18 + 6 * q^20 - 16 * q^21 - 22 * q^22 - 10 * q^23 - 56 * q^24 - 108 * q^25 + 36 * q^26 + 32 * q^27 - 8 * q^28 - 44 * q^30 - 8 * q^31 - 14 * q^32 - 14 * q^33 + 24 * q^34 + 26 * q^35 + 78 * q^36 - 72 * q^37 - 120 * q^38 - 16 * q^39 - 46 * q^40 - 22 * q^41 - 18 * q^42 + 2 * q^43 + 112 * q^44 + 30 * q^45 + 4 * q^46 + 22 * q^47 + 38 * q^48 - 84 * q^49 - 24 * q^50 - 28 * q^51 + 86 * q^52 + 56 * q^53 - 60 * q^55 + 4 * q^56 - 12 * q^57 + 96 * q^58 + 14 * q^60 - 46 * q^61 - 112 * q^62 + 158 * q^63 + 30 * q^64 + 4 * q^65 - 48 * q^66 + 18 * q^67 + 140 * q^68 + 124 * q^69 + 94 * q^70 - 28 * q^71 - 98 * q^72 - 84 * q^73 - 112 * q^74 + 54 * q^75 - 48 * q^76 + 28 * q^77 + 70 * q^78 + 4 * q^79 + 170 * q^80 + 58 * q^81 + 16 * q^82 + 46 * q^83 - 120 * q^84 + 76 * q^85 + 68 * q^87 + 40 * q^88 - 46 * q^89 + 120 * q^90 - 28 * q^91 - 14 * q^92 - 22 * q^93 + 84 * q^94 + 190 * q^95 - 28 * q^96 - 76 * q^97 - 160 * q^98 - 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more