LMFDB - Embedded newform 145.2.o.a.18.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(2,145)] 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("145.2"); 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([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.o (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			18.9
Character	$\chi$	$=$	145.18
Dual form			145.2.o.a.137.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.871464 + 0.419675i) q^{2} +(2.22031 + 1.77064i) q^{3} +(-0.663657 - 0.832199i) q^{4} +(-2.06901 + 0.848049i) q^{5} +(1.19183 + 2.47485i) q^{6} +(0.156487 + 1.38886i) q^{7} +(-0.659568 - 2.88975i) q^{8} +(1.12705 + 4.93793i) q^{9} +(-2.15898 - 0.129268i) q^{10} +(4.68013 - 2.94072i) q^{11} -3.02283i q^{12} +(-2.43545 - 3.87599i) q^{13} +(-0.446497 + 1.27601i) q^{14} +(-6.09543 - 1.78054i) q^{15} +(0.164256 - 0.719651i) q^{16} -5.34543 q^{17} +(-1.09014 + 4.77622i) q^{18} +(3.75785 + 0.423408i) q^{19} +(2.07886 + 1.15902i) q^{20} +(-2.11171 + 3.36077i) q^{21} +(5.31271 - 0.598599i) q^{22} +(-2.32115 - 0.812207i) q^{23} +(3.65226 - 7.58400i) q^{24} +(3.56162 - 3.50925i) q^{25} +(-0.495748 - 4.39988i) q^{26} +(-2.54434 + 5.28338i) 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} +(-3.25097 + 4.07659i) q^{32} +(15.5983 + 1.75750i) q^{33} +(-4.65835 - 2.24334i) q^{34} +(-1.50159 - 2.74086i) q^{35} +(3.36136 - 4.21502i) q^{36} +(-3.61961 + 0.826152i) q^{37} +(3.09714 + 1.94606i) q^{38} +(1.45553 - 12.9182i) q^{39} +(3.81531 + 5.41959i) q^{40} +(-5.71038 + 5.71038i) q^{41} +(-3.25072 + 2.04256i) q^{42} +(0.322307 + 0.669277i) q^{43} +(-5.55327 - 1.94317i) q^{44} +(-6.51948 - 9.26084i) q^{45} +(-1.68194 - 1.68194i) q^{46} +(0.0268913 + 0.00613776i) q^{47} +(1.63894 - 1.30701i) q^{48} +(4.92005 - 1.12297i) q^{49} +(4.57657 - 1.56346i) q^{50} +(-11.8685 - 9.46480i) q^{51} +(-1.60930 + 4.59910i) q^{52} +(-0.574381 - 1.64149i) q^{53} +(-4.43460 + 3.53648i) q^{54} +(-7.18937 + 10.0534i) q^{55} +(3.91025 - 1.36826i) q^{56} +(7.59388 + 7.59388i) q^{57} +(-4.60948 + 2.42578i) q^{58} -4.00143i q^{59} +(2.56351 + 6.25428i) q^{60} +(3.92555 - 0.442303i) q^{61} +(-0.433740 + 3.84955i) q^{62} +(-6.68171 + 2.33803i) q^{63} +(-5.87407 + 2.82880i) q^{64} +(8.32600 + 5.95409i) q^{65} +(12.8558 + 8.07781i) q^{66} +(3.79538 - 6.04031i) q^{67} +(3.54753 + 4.44846i) q^{68} +(-3.71555 - 5.91327i) q^{69} +(-0.158316 - 3.01874i) q^{70} +(3.42315 + 0.781312i) q^{71} +(13.5260 - 6.51379i) q^{72} +(-2.88745 + 1.39052i) q^{73} +(-3.50108 - 0.799098i) q^{74} +(14.1215 - 1.48527i) q^{75} +(-2.14156 - 3.40828i) q^{76} +(4.81662 + 6.03986i) q^{77} +(6.68988 - 10.6469i) q^{78} +(7.95966 + 5.00139i) q^{79} +(0.270453 + 1.62826i) q^{80} +(-1.31416 + 0.632868i) q^{81} +(-7.37289 + 2.57989i) q^{82} +(-1.66068 + 14.7389i) q^{83} +(4.19829 - 0.473033i) q^{84} +(11.0598 - 4.53318i) q^{85} +0.718515i q^{86} +(-14.7791 + 3.93209i) q^{87} +(-11.5848 - 11.5848i) q^{88} +(-12.9395 + 4.52773i) q^{89} +(-1.79496 - 10.8066i) q^{90} +(5.00209 - 3.98903i) q^{91} +(0.864532 + 2.47069i) q^{92} +(-3.75656 + 10.7356i) q^{93} +(0.0208589 + 0.0166344i) q^{94} +(-8.13411 + 2.31081i) q^{95} +(-14.4363 + 3.29499i) q^{96} +(6.87837 - 5.48532i) q^{97} +(4.75893 + 1.08620i) q^{98} +(19.7958 + 19.7958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 8 q^{2} - 14 q^{3} - 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} + 4 q^{8} + 10 q^{9} - 8 q^{10} - 20 q^{11} + 4 q^{14} - 24 q^{15} - 34 q^{16} - 48 q^{17} - 94 q^{18} + 6 q^{20} - 16 q^{21} - 6 q^{22}+ \cdots + 76 q^{99}+O(q^{100}) $ 156 * q - 8 * q^2 - 14 * q^3 - 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 + 4 * q^8 + 10 * q^9 - 8 * q^10 - 20 * q^11 + 4 * q^14 - 24 * q^15 - 34 * q^16 - 48 * q^17 - 94 * q^18 + 6 * q^20 - 16 * q^21 - 6 * q^22 - 10 * q^23 + 56 * q^24 + 60 * q^25 + 36 * q^26 - 56 * q^27 + 8 * q^28 - 44 * q^30 - 8 * q^31 + 28 * q^32 - 14 * q^33 - 24 * q^34 - 54 * q^35 + 78 * q^36 + 28 * q^37 + 92 * q^38 + 16 * q^39 + 8 * q^40 - 22 * q^41 - 10 * q^42 - 42 * q^43 - 112 * q^44 + 30 * q^45 + 4 * q^46 - 14 * q^47 + 154 * q^48 + 84 * q^49 + 34 * q^50 - 28 * q^51 - 166 * q^52 + 14 * q^53 - 20 * q^55 + 4 * q^56 + 12 * q^57 + 126 * q^58 - 138 * q^60 - 46 * q^61 + 84 * q^62 + 38 * q^63 - 30 * q^64 + 4 * q^65 - 48 * q^66 - 46 * q^67 - 44 * q^68 - 124 * q^69 - 86 * q^70 - 28 * q^71 + 60 * q^72 + 130 * q^73 + 112 * q^74 + 50 * q^75 - 48 * q^76 - 44 * q^77 - 210 * q^78 - 4 * q^79 + 194 * q^80 + 58 * q^81 + 72 * q^82 + 46 * q^83 + 120 * q^84 + 56 * q^85 - 144 * q^87 + 40 * q^88 + 46 * q^89 + 82 * q^90 - 28 * q^91 - 14 * q^92 - 6 * q^93 - 84 * q^94 - 74 * q^95 - 28 * q^96 + 154 * q^97 + 98 * q^98 + 76 * q^99

Character values

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

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.871464	+	0.419675i	0.616218	+	0.296755i	0.715834	−	0.698271i	$-0.246047\pi$
$2$	0.871464	+	0.419675i	0.616218	+	0.296755i	−0.0996153	+	0.995026i	$0.531761\pi$
$3$	2.22031	+	1.77064i	1.28189	+	1.02228i	0.997987	+	0.0634256i	$0.0202025\pi$
$3$	2.22031	+	1.77064i	1.28189	+	1.02228i	0.283908	+	0.958851i	$0.408369\pi$
$4$	−0.663657	−	0.832199i	−0.331828	−	0.416100i
$5$	−2.06901	+	0.848049i	−0.925290	+	0.379259i
$5$	−2.06901	+	0.848049i	−0.925290	+	0.379259i
$6$	1.19183	+	2.47485i	0.486561	+	1.01035i
$7$	0.156487	+	1.38886i	0.0591465	+	0.524939i	0.987996	+	0.154481i	$0.0493707\pi$
$7$	0.156487	+	1.38886i	0.0591465	+	0.524939i	−0.928849	+	0.370458i	$0.879201\pi$
$8$	−0.659568	−	2.88975i	−0.233192	−	1.02168i
$9$	1.12705	+	4.93793i	0.375683	+	1.64598i
$10$	−2.15898	−	0.129268i	−0.682728	−	0.0408782i
$11$	4.68013	−	2.94072i	1.41111	−	0.886661i	0.411419	−	0.911446i	$-0.365033\pi$
$11$	4.68013	−	2.94072i	1.41111	−	0.886661i	0.999693	+	0.0247855i	$0.00789028\pi$
$12$		−	3.02283i		−	0.872617i
$13$	−2.43545	−	3.87599i	−0.675471	−	1.07501i	−0.991977	−	0.126416i	$-0.959653\pi$
$13$	−2.43545	−	3.87599i	−0.675471	−	1.07501i	0.316506	−	0.948590i	$-0.397490\pi$
$14$	−0.446497	+	1.27601i	−0.119331	+	0.341029i
$15$	−6.09543	−	1.78054i	−1.57383	−	0.459733i
$16$	0.164256	−	0.719651i	0.0410639	−	0.179913i
$17$	−5.34543			−1.29646			−0.648228	−	0.761446i	$-0.724490\pi$
$17$	−5.34543			−1.29646			−0.648228	+	0.761446i	$0.724490\pi$
$18$	−1.09014	+	4.77622i	−0.256949	+	1.12577i
$19$	3.75785	+	0.423408i	0.862110	+	0.0971365i	0.531937	−	0.846784i	$-0.321464\pi$
$19$	3.75785	+	0.423408i	0.862110	+	0.0971365i	0.330173	+	0.943920i	$0.392893\pi$
$20$	2.07886	+	1.15902i	0.464847	+	0.259164i
$21$	−2.11171	+	3.36077i	−0.460814	+	0.733381i
$22$	5.31271	−	0.598599i	1.13267	−	0.127622i
$23$	−2.32115	−	0.812207i	−0.483994	−	0.169357i	0.0772424	−	0.997012i	$-0.475388\pi$
$23$	−2.32115	−	0.812207i	−0.483994	−	0.169357i	−0.561237	+	0.827655i	$0.689674\pi$
$24$	3.65226	−	7.58400i	0.745515	−	1.54808i
$25$	3.56162	−	3.50925i	0.712325	−	0.701850i
$26$	−0.495748	−	4.39988i	−0.0972241	−	0.862888i
$27$	−2.54434	+	5.28338i	−0.489659	+	1.01679i
$28$	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	0.999510	+	0.0313051i	$0.00996635\pi$
$31$	1.32279	+	3.78032i	0.237580	+	0.678965i	−0.761930	+	0.647660i	$0.775748\pi$
$32$	−3.25097	+	4.07659i	−0.574696	+	0.720646i
$33$	15.5983	+	1.75750i	2.71531	+	0.305942i
$34$	−4.65835	−	2.24334i	−0.798900	−	0.384730i
$35$	−1.50159	−	2.74086i	−0.253816	−	0.463290i
$36$	3.36136	−	4.21502i	0.560227	−	0.702503i
$37$	−3.61961	+	0.826152i	−0.595060	+	0.135819i	−0.509436	−	0.860509i	$-0.670146\pi$
$37$	−3.61961	+	0.826152i	−0.595060	+	0.135819i	−0.0856247	+	0.996327i	$0.527289\pi$
$38$	3.09714	+	1.94606i	0.502422	+	0.315693i
$39$	1.45553	−	12.9182i	0.233071	−	2.06856i
$40$	3.81531	+	5.41959i	0.603253	+	0.856913i
$41$	−5.71038	+	5.71038i	−0.891811	+	0.891811i	−0.994694	−	0.102882i	$-0.967193\pi$
$41$	−5.71038	+	5.71038i	−0.891811	+	0.891811i	0.102882	+	0.994694i	$0.467193\pi$
$42$	−3.25072	+	2.04256i	−0.501597	+	0.315174i
$43$	0.322307	+	0.669277i	0.0491513	+	0.102064i	0.924098	−	0.382155i	$-0.124818\pi$
$43$	0.322307	+	0.669277i	0.0491513	+	0.102064i	−0.874947	+	0.484219i	$0.839104\pi$
$44$	−5.55327	−	1.94317i	−0.837186	−	0.292944i
$45$	−6.51948	−	9.26084i	−0.971867	−	1.38052i
$46$	−1.68194	−	1.68194i	−0.247989	−	0.247989i
$47$	0.0268913	+	0.00613776i	0.00392249	+	0.000895284i	0.224482	−	0.974478i	$-0.427931\pi$
$47$	0.0268913	+	0.00613776i	0.00392249	+	0.000895284i	−0.220559	+	0.975374i	$0.570788\pi$
$48$	1.63894	−	1.30701i	0.236560	−	0.188651i
$49$	4.92005	−	1.12297i	0.702865	−	0.160424i
$50$	4.57657	−	1.56346i	0.647225	−	0.221107i
$51$	−11.8685	−	9.46480i	−1.66192	−	1.32534i
$52$	−1.60930	+	4.59910i	−0.223169	+	0.637781i
$53$	−0.574381	−	1.64149i	−0.0788973	−	0.225476i	0.897678	−	0.440653i	$-0.145253\pi$
$53$	−0.574381	−	1.64149i	−0.0788973	−	0.225476i	−0.976575	+	0.215177i	$0.930967\pi$
$54$	−4.43460	+	3.53648i	−0.603473	+	0.481254i
$55$	−7.18937	+	10.0534i	−0.969415	+	1.35560i
$56$	3.91025	−	1.36826i	0.522529	−	0.182841i
$57$	7.59388	+	7.59388i	1.00583	+	1.00583i
$58$	−4.60948	+	2.42578i	−0.605255	+	0.318521i
$59$		−	4.00143i		−	0.520942i	−0.965482	−	0.260471i	$-0.916122\pi$
$59$		−	4.00143i		−	0.520942i	0.965482	−	0.260471i	$-0.0838778\pi$
$60$	2.56351	+	6.25428i	0.330948	+	0.807424i
$61$	3.92555	−	0.442303i	0.502615	−	0.0566311i	0.142983	−	0.989725i	$-0.454331\pi$
$61$	3.92555	−	0.442303i	0.502615	−	0.0566311i	0.359632	+	0.933094i	$0.382902\pi$
$62$	−0.433740	+	3.84955i	−0.0550851	+	0.488894i
$63$	−6.68171	+	2.33803i	−0.841817	+	0.294564i
$64$	−5.87407	+	2.82880i	−0.734258	+	0.353600i
$65$	8.32600	+	5.95409i	1.03271	+	0.738514i
$66$	12.8558	+	8.07781i	1.58243	+	0.994309i
$67$	3.79538	−	6.04031i	0.463679	−	0.737941i	−0.530264	−	0.847832i	$-0.677907\pi$
$67$	3.79538	−	6.04031i	0.463679	−	0.737941i	0.993944	+	0.109891i	$0.0350502\pi$
$68$	3.54753	+	4.44846i	0.430201	+	0.539455i
$69$	−3.71555	−	5.91327i	−0.447300	−	0.711874i
$70$	−0.158316	−	3.01874i	−0.0189224	−	0.360809i
$71$	3.42315	+	0.781312i	0.406253	+	0.0927247i	0.420764	−	0.907170i	$-0.361762\pi$
$71$	3.42315	+	0.781312i	0.406253	+	0.0927247i	−0.0145109	+	0.999895i	$0.504619\pi$
$72$	13.5260	−	6.51379i	1.59406	−	0.767658i
$73$	−2.88745	+	1.39052i	−0.337951	+	0.162748i	−0.595160	−	0.803607i	$-0.702911\pi$
$73$	−2.88745	+	1.39052i	−0.337951	+	0.162748i	0.257209	+	0.966356i	$0.417197\pi$
$74$	−3.50108	−	0.799098i	−0.406992	−	0.0928932i
$75$	14.1215	−	1.48527i	1.63061	−	0.171504i
$76$	−2.14156	−	3.40828i	−0.245654	−	0.390956i
$77$	4.81662	+	6.03986i	0.548905	+	0.688306i
$78$	6.68988	−	10.6469i	0.757479	−	1.20552i
$79$	7.95966	+	5.00139i	0.895532	+	0.562700i	0.899319	−	0.437293i	$-0.144063\pi$
$79$	7.95966	+	5.00139i	0.895532	+	0.562700i	−0.00378707	+	0.999993i	$0.501205\pi$
$80$	0.270453	+	1.62826i	0.0302375	+	0.182045i
$81$	−1.31416	+	0.632868i	−0.146018	+	0.0703186i
$82$	−7.37289	+	2.57989i	−0.814200	+	0.284901i
$83$	−1.66068	+	14.7389i	−0.182283	+	1.61780i	0.486042	+	0.873935i	$0.338440\pi$
$83$	−1.66068	+	14.7389i	−0.182283	+	1.61780i	−0.668325	+	0.743869i	$0.732989\pi$
$84$	4.19829	−	0.473033i	0.458071	−	0.0516122i
$85$	11.0598	−	4.53318i	1.19960	−	0.491693i
$86$			0.718515i			0.0774795i
$87$	−14.7791	+	3.93209i	−1.58448	+	0.421565i
$88$	−11.5848	−	11.5848i	−1.23495	−	1.23495i
$89$	−12.9395	+	4.52773i	−1.37159	+	0.479939i	−0.912727	−	0.408570i	$-0.866028\pi$
$89$	−12.9395	+	4.52773i	−1.37159	+	0.479939i	−0.458860	+	0.888509i	$0.651742\pi$
$90$	−1.79496	−	10.8066i	−0.189205	−	1.13911i
$91$	5.00209	−	3.98903i	0.524361	−	0.418164i
$92$	0.864532	+	2.47069i	0.0901337	+	0.257587i
$93$	−3.75656	+	10.7356i	−0.389537	+	1.11323i
$94$	0.0208589	+	0.0166344i	0.00215143	+	0.00171571i
$95$	−8.13411	+	2.31081i	−0.834542	+	0.237084i
$96$	−14.4363	+	3.29499i	−1.47340	+	0.336294i
$97$	6.87837	−	5.48532i	0.698393	−	0.556950i	−0.208649	−	0.977991i	$-0.566907\pi$
$97$	6.87837	−	5.48532i	0.698393	−	0.556950i	0.907042	+	0.421041i	$0.138335\pi$
$98$	4.75893	+	1.08620i	0.480725	+	0.109722i
$99$	19.7958	+	19.7958i	1.98955	+	1.98955i
$100$	−5.28409	−	0.635044i	−0.528409	−	0.0635044i
$101$	5.10791	+	1.78734i	0.508256	+	0.177847i	0.572211	−	0.820106i	$-0.306086\pi$
$101$	5.10791	+	1.78734i	0.508256	+	0.177847i	−0.0639551	+	0.997953i	$0.520371\pi$
$102$	−6.37082	−	13.2291i	−0.630805	−	1.30988i
$103$	−6.73869	+	4.23420i	−0.663983	+	0.417208i	−0.821422	−	0.570321i	$-0.806819\pi$
$103$	−6.73869	+	4.23420i	−0.663983	+	0.417208i	0.157439	+	0.987529i	$0.449676\pi$
$104$	−9.59432	+	9.59432i	−0.940800	+	0.940800i
$105$	1.51906	−	8.74432i	0.148245	−	0.853358i
$106$	0.188339	−	1.67155i	0.0182931	−	0.162355i
$107$	−9.64143	−	6.05811i	−0.932072	−	0.585660i	−0.0218417	−	0.999761i	$-0.506953\pi$
$107$	−9.64143	−	6.05811i	−0.932072	−	0.585660i	−0.910231	+	0.414102i	$0.864096\pi$
$108$	6.08539	−	1.38895i	0.585567	−	0.133652i
$109$	4.37246	−	5.48290i	0.418806	−	0.525166i	−0.527014	−	0.849856i	$-0.676689\pi$
$109$	4.37246	−	5.48290i	0.418806	−	0.525166i	0.945820	+	0.324690i	$0.105260\pi$
$110$	−10.4844	+	5.74395i	−0.999651	+	0.547664i
$111$	−9.49946	−	4.57470i	−0.901649	−	0.434211i
$112$	1.02520	+	0.115512i	0.0968721	+	0.0109149i
$113$	9.20127	−	11.5380i	0.865583	−	1.08541i	−0.130000	−	0.991514i	$-0.541498\pi$
$113$	9.20127	−	11.5380i	0.865583	−	1.08541i	0.995582	−	0.0938923i	$-0.0299309\pi$
$114$	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
$118$	1.67930	−	3.48710i	0.154592	−	0.321014i
$119$	−0.836489	−	7.42404i	−0.0766808	−	0.680561i
$120$	−1.12497	+	18.7887i	−0.102695	+	1.71516i
$121$	8.48306	−	17.6153i	0.771187	−	1.60139i
$122$	3.60660	+	1.26200i	0.326526	+	0.114256i
$123$	−22.7898	+	2.56779i	−2.05489	+	0.231530i
$124$	2.26810	−	3.60966i	0.203681	−	0.324157i
$125$	−4.39303	+	10.2811i	−0.392924	+	0.919571i
$126$	−6.80409	−	0.766637i	−0.606156	−	0.0682974i
$127$	−0.164908	+	0.722509i	−0.0146332	+	0.0641123i	−0.981717	−	0.190344i	$-0.939040\pi$
$127$	−0.164908	+	0.722509i	−0.0146332	+	0.0641123i	0.967084	+	0.254457i	$0.0818967\pi$
$128$	4.12209			0.364345
$129$	−0.469426	+	2.05669i	−0.0413306	+	0.181081i
$130$	4.75703	+	8.68299i	0.417219	+	0.761549i
$131$	−4.84709	+	13.8522i	−0.423493	+	1.21027i	0.512633	+	0.858608i	$0.328670\pi$
$131$	−4.84709	+	13.8522i	−0.423493	+	1.21027i	−0.936126	+	0.351665i	$0.885616\pi$
$132$	−8.88930	−	14.1472i	−0.773715	−	1.23136i
$133$			5.28538i			0.458301i
$134$	5.84251	−	3.67109i	0.504716	−	0.317134i
$135$	0.783707	−	13.0891i	0.0674508	−	1.12653i
$136$	3.52567	+	15.4470i	0.302324	+	1.32457i
$137$	−1.45940	−	6.39404i	−0.124685	−	0.546280i	−0.998226	−	0.0595303i	$-0.981040\pi$
$137$	−1.45940	−	6.39404i	−0.124685	−	0.546280i	0.873542	−	0.486749i	$-0.161817\pi$
$138$	−0.756320	−	6.71253i	−0.0643822	−	0.571408i
$139$	1.98467	+	4.12120i	0.168337	+	0.349556i	0.968022	−	0.250864i	$-0.0807146\pi$
$139$	1.98467	+	4.12120i	0.168337	+	0.349556i	−0.799685	+	0.600420i	$0.795000\pi$
$140$	−1.28440	+	3.06861i	−0.108551	+	0.259345i
$141$	0.0488391	+	0.0612423i	0.00411300	+	0.00515753i
$142$	2.65526	+	2.11750i	0.222824	+	0.177696i
$143$	−22.7964	−	10.9782i	−1.90633	−	0.918041i
$144$	3.73871			0.311559
$145$	2.96243	−	11.6715i	0.246016	−	0.969266i
$146$	−3.09988			−0.256548
$147$	12.9124	+	6.21829i	1.06500	+	0.512876i
$148$	3.08970	+	2.46396i	0.253972	+	0.202536i
$149$	−5.04369	−	6.32459i	−0.413195	−	0.518130i	0.531065	−	0.847331i	$-0.321792\pi$
$149$	−5.04369	−	6.32459i	−0.413195	−	0.518130i	−0.944260	+	0.329201i	$0.893221\pi$
$150$	12.9297	+	4.63208i	1.05571	+	0.378208i
$151$	−4.21845	−	8.75970i	−0.343292	−	0.712854i	0.655823	−	0.754915i	$-0.272322\pi$
$151$	−4.21845	−	8.75970i	−0.343292	−	0.712854i	−0.999115	+	0.0420610i	$0.986608\pi$
$152$	−1.25501	−	11.1385i	−0.101795	−	0.903454i
$153$	−6.02456	−	26.3953i	−0.487057	−	2.13393i
$154$	1.66274	+	7.28494i	0.133987	+	0.587037i
$155$	−5.94276	−	6.69973i	−0.477334	−	0.538135i
$156$	−11.7165	+	7.36194i	−0.938068	+	0.589427i
$157$			4.05125i			0.323325i	0.986846	+	0.161663i	$0.0516856\pi$
$157$			4.05125i			0.323325i	−0.986846	+	0.161663i	$0.948314\pi$
$158$	4.83760	+	7.69900i	0.384859	+	0.612500i
$159$	1.63117	−	4.66163i	0.129360	−	0.369691i
$160$	3.26915	−	11.1915i	0.258449	−	0.884766i
$161$	0.764811	−	3.35086i	0.0602755	−	0.264084i
$162$	−1.41084			−0.110846
$163$	1.31164	−	5.74667i	0.102736	−	0.450114i	−0.897228	−	0.441568i	$-0.854422\pi$
$163$	1.31164	−	5.74667i	0.102736	−	0.450114i	0.999963	−	0.00854627i	$-0.00272040\pi$
$164$	8.54190	+	0.962441i	0.667011	+	0.0751540i
$165$	−33.7635	+	9.59181i	−2.62848	+	0.746721i
$166$	−7.63277	+	12.1475i	−0.592418	+	0.942827i
$167$	13.9385	−	1.57049i	1.07859	−	0.121528i	0.445254	−	0.895404i	$-0.353113\pi$
$167$	13.9385	−	1.57049i	1.07859	−	0.121528i	0.633336	+	0.773877i	$0.281685\pi$
$168$	11.1046	+	3.88568i	0.856741	+	0.299787i
$169$	−3.45141	+	7.16693i	−0.265493	+	0.551302i
$170$	11.5406	+	0.690994i	0.885127	+	0.0529968i
$171$	2.14453	+	19.0332i	0.163996	+	1.45550i
$172$	0.343071	−	0.712394i	0.0261589	−	0.0543195i
$173$	9.47799	−	9.47799i	0.720598	−	0.720598i	−0.248129	−	0.968727i	$-0.579816\pi$
$173$	9.47799	−	9.47799i	0.720598	−	0.720598i	0.968727	+	0.248129i	$0.0798156\pi$
$174$	−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
$177$	7.08507	−	8.88440i	0.532547	−	0.667792i
$178$	−13.1765	−	1.48464i	−0.987621	−	0.111278i
$179$	3.08837	+	1.48728i	0.230836	+	0.111165i	0.545727	−	0.837963i	$-0.316254\pi$
$179$	3.08837	+	1.48728i	0.230836	+	0.111165i	−0.314891	+	0.949128i	$0.601968\pi$
$180$	−3.38016	+	11.5715i	−0.251942	+	0.862491i
$181$	11.0324	−	13.8343i	0.820036	−	1.02829i	−0.178977	−	0.983853i	$-0.557279\pi$
$181$	11.0324	−	13.8343i	0.820036	−	1.02829i	0.999012	−	0.0444387i	$-0.0141499\pi$
$182$	6.03324	−	1.37705i	0.447213	−	0.102074i
$183$	9.49908	+	5.96867i	0.702192	+	0.441217i
$184$	−0.816121	+	7.24327i	−0.0601652	+	0.533981i
$185$	6.78840	−	4.77893i	0.499093	−	0.351354i
$186$	−7.77919	+	7.77919i	−0.570398	+	0.570398i
$187$	−25.0173	+	15.7194i	−1.82945	+	1.14952i
$188$	−0.0127387	−	0.0264523i	−0.000929068	−	0.00192923i
$189$	−7.73602	−	2.70695i	−0.562713	−	0.196902i
$190$	−8.05838	−	1.39990i	−0.584616	−	0.101559i
$191$	−16.2424	−	16.2424i	−1.17526	−	1.17526i	−0.980938	−	0.194321i	$-0.937750\pi$
$191$	−16.2424	−	16.2424i	−1.17526	−	1.17526i	−0.194321	−	0.980938i	$-0.562250\pi$
$192$	−18.0510	−	4.12002i	−1.30272	−	0.297337i
$193$	−10.6262	+	8.47412i	−0.764891	+	0.609980i	−0.926248	−	0.376916i	$-0.876985\pi$
$193$	−10.6262	+	8.47412i	−0.764891	+	0.609980i	0.161356	+	0.986896i	$0.448413\pi$
$194$	8.29631	−	1.89358i	0.595640	−	0.135951i
$195$	7.94374	+	27.9622i	0.568863	+	2.00242i
$196$	−4.19976	−	3.34920i	−0.299983	−	0.239228i
$197$	−3.53390	+	10.0993i	−0.251780	+	0.719545i	0.746738	+	0.665118i	$0.231619\pi$
$197$	−3.53390	+	10.0993i	−0.251780	+	0.719545i	−0.998518	+	0.0544269i	$0.982667\pi$
$198$	8.94353	+	25.5591i	0.635589	+	1.81641i
$199$	8.87767	−	7.07970i	0.629321	−	0.501867i	−0.256104	−	0.966649i	$-0.582439\pi$
$199$	8.87767	−	7.07970i	0.629321	−	0.501867i	0.885425	+	0.464782i	$0.153867\pi$
$200$	−12.4900	−	7.97763i	−0.883177	−	0.564104i
$201$	19.1221	−	6.69111i	1.34877	−	0.471955i
$202$	3.70126	+	3.70126i	0.260420	+	0.260420i
$203$	−6.51154	−	3.77478i	−0.457020	−	0.264938i
$204$			16.1583i			1.13131i
$205$	6.97216	−	16.6575i	0.486957	−	1.16341i
$206$	−7.64952	+	0.861893i	−0.532967	+	0.0600510i
$207$	1.39456	−	12.3771i	0.0969288	−	0.860267i
$208$	−3.18940	+	1.11602i	−0.221145	+	0.0773819i
$209$	18.8324	−	9.06918i	1.30266	−	0.627329i
$210$	4.99358	−	6.98285i	0.344590	−	0.481863i
$211$	1.27617	+	0.801873i	0.0878554	+	0.0552032i	0.575243	−	0.817982i	$-0.304907\pi$
$211$	1.27617	+	0.801873i	0.0878554	+	0.0552032i	−0.487388	+	0.873186i	$0.662050\pi$
$212$	−0.984852	+	1.56738i	−0.0676399	+	0.107648i
$213$	6.21703	+	7.79591i	0.425984	+	0.534167i
$214$	−5.85972	−	9.32570i	−0.400562	−	0.637492i
$215$	−1.23444	−	1.11141i	−0.0841879	−	0.0757976i
$216$	16.9458	+	3.86777i	1.15302	+	0.263169i
$217$	−5.04333	+	2.42874i	−0.342363	+	0.164873i
$218$	6.11148	−	2.94313i	0.413922	−	0.199334i
$219$	−8.87314	−	2.02524i	−0.599591	−	0.136853i
$220$	13.1377	−	0.688997i	0.885742	−	0.0464522i
$221$	13.0185	+	20.7188i	0.875719	+	1.39370i
$222$	−6.35855	−	7.97337i	−0.426758	−	0.535138i
$223$	−4.66654	+	7.42676i	−0.312495	+	0.497333i	−0.965634	−	0.259905i	$-0.916309\pi$
$223$	−4.66654	+	7.42676i	−0.312495	+	0.497333i	0.653139	+	0.757238i	$0.273452\pi$
$224$	−6.17054	−	3.87721i	−0.412287	−	0.259057i
$225$	21.3425	+	13.6319i	1.42284	+	0.908796i
$226$	12.8608	−	6.19344i	0.855488	−	0.411981i
$227$	19.5884	−	6.85426i	1.30013	−	0.454934i	0.410598	−	0.911816i	$-0.365320\pi$
$227$	19.5884	−	6.85426i	1.30013	−	0.454934i	0.889527	+	0.456883i	$0.151034\pi$
$228$	1.27989	−	11.3594i	0.0847629	−	0.752292i
$229$	5.35144	−	0.602962i	0.353633	−	0.0398449i	0.0666386	−	0.997777i	$-0.478773\pi$
$229$	5.35144	−	0.602962i	0.353633	−	0.0398449i	0.286994	+	0.957932i	$0.407344\pi$
$230$	4.90632	+	2.05359i	0.323513	+	0.135409i
$231$			21.9388i			1.44347i
$232$	14.6189	+	6.40890i	0.959777	+	0.420765i
$233$	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
$235$	−0.0608435	+	0.0101060i	−0.00396899	+	0.000659244i
$236$	−3.32999	+	2.65558i	−0.216764	+	0.172863i
$237$	8.81726	+	25.1983i	0.572743	+	1.63680i
$238$	2.38672	−	6.82084i	0.154708	−	0.442129i
$239$	−7.62904	−	6.08395i	−0.493481	−	0.393538i	0.344885	−	0.938645i	$-0.387918\pi$
$239$	−7.62904	−	6.08395i	−0.493481	−	0.393538i	−0.838367	+	0.545107i	$0.816489\pi$
$240$	−2.28257	+	4.09412i	−0.147340	+	0.264274i
$241$	−19.6440	+	4.48362i	−1.26538	+	0.288815i	−0.801990	−	0.597338i	$-0.796225\pi$
$241$	−19.6440	+	4.48362i	−1.26538	+	0.288815i	−0.463392	+	0.886153i	$0.653368\pi$
$242$	14.7854	−	11.7909i	0.950439	−	0.757950i
$243$	13.1128	+	2.99292i	0.841188	+	0.191996i
$244$	−2.97330	−	2.97330i	−0.190346	−	0.190346i
$245$	−9.22732	+	6.49589i	−0.589512	+	0.415007i
$246$	−20.9381	−	7.32657i	−1.33497	−	0.467125i
$247$	−7.51092	−	15.5966i	−0.477908	−	0.992386i
$248$	10.0517	−	6.31591i	0.638285	−	0.401061i
$249$	−29.7844	+	29.7844i	−1.88751	+	1.88751i
$250$	−8.14310	+	7.11598i	−0.515015	+	0.450054i
$251$	−2.78070	+	24.6794i	−0.175516	+	1.55775i	0.529347	+	0.848406i	$0.322437\pi$
$251$	−2.78070	+	24.6794i	−0.175516	+	1.55775i	−0.704863	+	0.709344i	$0.748991\pi$
$252$	6.38007	+	4.00887i	0.401907	+	0.252535i
$253$	−13.2518	+	3.02463i	−0.833132	+	0.190157i
$254$	−0.446930	+	0.560433i	−0.0280429	+	0.0351647i
$255$	32.5827	+	9.51773i	2.04041	+	0.596023i
$256$	15.3404	+	7.38754i	0.958774	+	0.461721i
$257$	1.02264	+	0.115223i	0.0637903	+	0.00718744i	0.143802	−	0.989606i	$-0.454067\pi$
$257$	1.02264	+	0.115223i	0.0637903	+	0.00718744i	−0.0800116	+	0.996794i	$0.525496\pi$
$258$	−1.27223	+	1.59532i	−0.0792055	+	0.0993206i
$259$	−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
$263$	1.72037	−	3.57239i	0.106083	−	0.220283i	−0.841170	−	0.540771i	$-0.818133\pi$
$263$	1.72037	−	3.57239i	0.106083	−	0.220283i	0.947253	+	0.320488i	$0.103847\pi$
$264$	−5.20936	−	46.2344i	−0.320614	−	2.84553i
$265$	2.58046	+	2.90915i	0.158517	+	0.178708i
$266$	−2.21814	+	4.60602i	−0.136003	+	0.282413i
$267$	−36.7467	−	12.8582i	−2.24886	−	0.786910i
$268$	−7.54557	+	0.850182i	−0.460919	+	0.0519331i
$269$	3.84254	−	6.11537i	0.234284	−	0.372861i	−0.708803	−	0.705406i	$-0.750765\pi$
$269$	3.84254	−	6.11537i	0.234284	−	0.372861i	0.943087	+	0.332546i	$0.107908\pi$
$270$	6.17614	−	11.0778i	0.375868	−	0.674172i
$271$	1.02753	+	0.115774i	0.0624178	+	0.00703279i	0.143118	−	0.989706i	$-0.454287\pi$
$271$	1.02753	+	0.115774i	0.0624178	+	0.00703279i	−0.0807004	+	0.996738i	$0.525716\pi$
$272$	−0.878017	+	3.84684i	−0.0532376	+	0.233249i
$273$	18.1693			1.09966
$274$	1.41161	−	6.18465i	0.0852782	−	0.373628i
$275$	6.34914	−	26.8975i	0.382868	−	1.62198i
$276$	−2.45517	+	7.01646i	−0.147784	+	0.422341i
$277$	8.85116	+	14.0865i	0.531815	+	0.846378i	0.999292	−	0.0376270i	$-0.0119799\pi$
$277$	8.85116	+	14.0865i	0.531815	+	0.846378i	−0.467477	+	0.884005i	$0.654837\pi$
$278$			4.42440i			0.265358i
$279$	−17.1761	+	10.7924i	−1.02830	+	0.646126i
$280$	−6.93000	+	6.14702i	−0.414147	+	0.367355i
$281$	−3.44157	−	15.0785i	−0.205307	−	0.899507i	−0.967642	−	0.252325i	$-0.918805\pi$
$281$	−3.44157	−	15.0785i	−0.205307	−	0.899507i	0.762336	−	0.647182i	$-0.224052\pi$
$282$	0.0168597	+	0.0738671i	0.00100398	+	0.00439872i
$283$	0.425710	+	3.77828i	0.0253059	+	0.224596i	0.999999	+	0.00105059i	$0.000334412\pi$
$283$	0.425710	+	3.77828i	0.0253059	+	0.224596i	−0.974694	+	0.223545i	$0.928237\pi$
$284$	−1.62159	−	3.36727i	−0.0962237	−	0.199811i
$285$	−22.1518	−	9.27185i	−1.31216	−	0.549217i
$286$	−15.2590	−	19.1342i	−0.902283	−	1.13143i
$287$	−8.82451	−	7.03731i	−0.520894	−	0.415399i
$288$	−23.7939	−	11.4585i	−1.40207	−	0.675201i
$289$	11.5736			0.680799
$290$	7.47989	−	8.92804i	0.439234	−	0.524273i
$291$	24.9846			1.46462
$292$	3.07347	+	1.48011i	0.179861	+	0.0866166i
$293$	−19.6561	−	15.6752i	−1.14832	−	0.915755i	−0.150972	−	0.988538i	$-0.548240\pi$
$293$	−19.6561	−	15.6752i	−1.14832	−	0.915755i	−0.997348	+	0.0727831i	$0.976812\pi$
$294$	8.64304	+	10.8380i	0.504072	+	0.632087i
$295$	3.39341	+	8.27901i	0.197572	+	0.482022i
$296$	4.77476	+	9.91488i	0.277527	+	0.576291i
$297$	3.62909	+	32.2091i	0.210581	+	1.86896i
$298$	−1.74112	−	7.62836i	−0.100861	−	0.441899i
$299$	2.50494	+	10.9749i	0.144864	+	0.634692i
$300$	−10.6079	−	10.7662i	−0.612446	−	0.621586i
$301$	−0.879095	+	0.552372i	−0.0506702	+	0.0318382i
$302$		−	9.40414i		−	0.541147i
$303$	8.17641	+	13.0127i	0.469723	+	0.747559i
$304$	0.921955	−	2.63479i	0.0528777	−	0.151116i
$305$	−7.74692	+	4.24419i	−0.443587	+	0.243022i
$306$	5.82727	−	25.5309i	0.333123	−	1.45951i
$307$	−22.4912			−1.28364			−0.641820	−	0.766855i	$-0.721820\pi$
$307$	−22.4912			−1.28364			−0.641820	+	0.766855i	$0.721820\pi$
$308$	1.82978	−	8.01678i	0.104261	−	0.456799i
$309$	−22.4592	−	2.53054i	−1.27766	−	0.143958i
$310$	−2.36720	−	8.33260i	−0.134448	−	0.473260i
$311$	16.9687	−	27.0055i	0.962205	−	1.53134i	0.119590	−	0.992823i	$-0.461842\pi$
$311$	16.9687	−	27.0055i	0.962205	−	1.53134i	0.842615	−	0.538517i	$-0.181015\pi$
$312$	−38.2904	+	4.31429i	−2.16777	+	0.244249i
$313$	−24.1206	−	8.44016i	−1.36338	−	0.477066i	−0.453245	−	0.891386i	$-0.649734\pi$
$313$	−24.1206	−	8.44016i	−1.36338	−	0.477066i	−0.910131	+	0.414320i	$0.864019\pi$
$314$	−1.70021	+	3.53052i	−0.0959484	+	0.199239i
$315$	11.8418	−	10.5038i	0.667209	−	0.591824i
$316$	−1.12033	−	9.94323i	−0.0630237	−	0.559351i
$317$	−10.3085	+	21.4059i	−0.578985	+	1.20228i	0.381610	+	0.924323i	$0.375370\pi$
$317$	−10.3085	+	21.4059i	−0.578985	+	1.20228i	−0.960595	+	0.277952i	$0.910344\pi$
$318$	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
$322$	2.07278	−	2.59918i	0.115511	−	0.144847i
$323$	−20.0873	−	2.26330i	−1.11769	−	0.125933i
$324$	1.39883	+	0.673639i	0.0777125	+	0.0374244i
$325$	−22.2760	−	5.25823i	−1.23565	−	0.291674i
$326$	3.55478	−	4.45756i	0.196881	−	0.246881i
$327$	19.4164	−	4.43167i	1.07373	−	0.245072i
$328$	20.2680	+	12.7352i	1.11911	+	0.703184i
$329$	−0.00431635	+	0.0383086i	−0.000237968	+	0.00211202i
$330$	−33.4491	−	5.81077i	−1.84131	−	0.319872i
$331$	0.695071	−	0.695071i	0.0382046	−	0.0382046i	−0.687746	−	0.725951i	$-0.741400\pi$
$331$	0.695071	−	0.695071i	0.0382046	−	0.0382046i	0.725951	+	0.687746i	$0.241400\pi$
$332$	13.3678	−	8.39956i	0.733654	−	0.460986i
$333$	−8.15896	−	16.9423i	−0.447108	−	0.928430i
$334$	12.8060	+	4.48100i	0.700711	+	0.245189i
$335$	−2.73020	+	15.7161i	−0.149167	+	0.858665i
$336$	2.07172	+	2.07172i	0.113022	+	0.113022i
$337$	26.8681	+	6.13247i	1.46360	+	0.334057i	0.878827	−	0.477140i	$-0.158327\pi$
$337$	26.8681	+	6.13247i	1.46360	+	0.334057i	0.584772	+	0.811197i	$0.301184\pi$
$338$	−6.01556	+	4.79725i	−0.327203	+	0.260936i
$339$	40.8593	−	9.32587i	2.21917	−	0.506512i
$340$	−11.1124	−	6.19544i	−0.602654	−	0.335995i
$341$	17.3077	+	13.8024i	0.937263	+	0.747443i
$342$	−6.11888	+	17.4868i	−0.330871	+	0.945575i
$343$	5.56087	+	15.8920i	0.300259	+	0.858090i
$344$	1.72146	−	1.37282i	0.0928151	−	0.0740176i
$345$	12.7023	+	9.08365i	0.683867	+	0.489047i
$346$	12.2374	−	4.28205i	0.657887	−	0.230205i
$347$	0.132362	+	0.132362i	0.00710559	+	0.00710559i	0.710651	−	0.703545i	$-0.248401\pi$
$347$	0.132362	+	0.132362i	0.00710559	+	0.00710559i	−0.703545	+	0.710651i	$0.748401\pi$
$348$	13.0805	+	9.68958i	0.701189	+	0.519416i
$349$			32.4359i			1.73625i	0.496342	+	0.868127i	$0.334676\pi$
$349$			32.4359i			1.73625i	−0.496342	+	0.868127i	$0.665324\pi$
$350$	2.88760	+	6.11155i	0.154349	+	0.326676i
$351$	26.6749	−	3.00554i	1.42380	−	0.160424i
$352$	−3.22686	+	28.6392i	−0.171992	+	1.52647i
$353$	18.4750	−	6.46469i	0.983326	−	0.344081i	0.209730	−	0.977759i	$-0.432742\pi$
$353$	18.4750	−	6.46469i	0.983326	−	0.344081i	0.773596	+	0.633679i	$0.218456\pi$
$354$	9.90295	−	4.76901i	0.526336	−	0.253470i
$355$	−7.74513	+	1.28646i	−0.411069	+	0.0682780i
$356$	12.3554	+	7.76340i	0.654834	+	0.411459i
$357$	11.2880	−	17.9648i	0.597425	−	0.950796i
$358$	2.06723	+	2.59223i	0.109257	+	0.137003i
$359$	−8.60134	−	13.6890i	−0.453962	−	0.722476i	0.538819	−	0.842422i	$-0.318871\pi$
$359$	−8.60134	−	13.6890i	−0.453962	−	0.722476i	−0.992780	+	0.119946i	$0.961728\pi$
$360$	−22.4615	+	24.9479i	−1.18383	+	1.31487i
$361$	−4.58146	−	1.04569i	−0.241130	−	0.0550362i
$362$	15.4203	−	7.42601i	0.810472	−	0.390303i
$363$	50.0252	−	24.0909i	2.62564	−	1.26444i
$364$	−6.63934	−	1.51539i	−0.347996	−	0.0794278i
$365$	4.79494	−	5.32571i	0.250979	−	0.278761i
$366$	5.77321	+	9.18801i	0.301771	+	0.480265i
$367$	−8.72758	−	10.9440i	−0.455576	−	0.571274i	0.499997	−	0.866027i	$-0.333334\pi$
$367$	−8.72758	−	10.9440i	−0.455576	−	0.571274i	−0.955574	+	0.294752i	$0.904763\pi$
$368$	−0.965769	+	1.53701i	−0.0503442	+	0.0801223i
$369$	−34.6333	−	21.7615i	−1.80294	−	1.13286i
$370$	7.92145	−	1.31574i	0.411816	−	0.0684022i
$371$	2.18991	−	1.05461i	0.113695	−	0.0547524i
$372$	11.4273	−	3.99857i	0.592476	−	0.207316i
$373$	−2.24082	+	19.8878i	−0.116025	+	1.02975i	0.791909	+	0.610639i	$0.209087\pi$
$373$	−2.24082	+	19.8878i	−0.116025	+	1.02975i	−0.907934	+	0.419112i	$0.862341\pi$
$374$	−28.3987	+	3.19977i	−1.46846	+	0.165456i
$375$	−27.9580	+	15.0488i	−1.44374	+	0.777115i
$376$		−	0.0817574i		−	0.00421632i
$377$	24.5791	+	1.88558i	1.26589	+	0.0971125i
$378$	−5.60563	−	5.60563i	−0.288322	−	0.288322i
$379$	28.3344	−	9.91464i	1.45544	−	0.509281i	0.517382	−	0.855755i	$-0.326907\pi$
$379$	28.3344	−	9.91464i	1.45544	−	0.509281i	0.938060	+	0.346474i	$0.112621\pi$
$380$	7.32131	+	5.23562i	0.375575	+	0.268582i
$381$	−1.64545	+	1.31220i	−0.0842988	+	0.0672260i
$382$	−7.33814	−	20.9712i	−0.375452	−	1.07298i
$383$	−1.57738	+	4.50789i	−0.0806003	+	0.230342i	−0.977131	−	0.212640i	$-0.931794\pi$
$383$	−1.57738	+	4.50789i	−0.0806003	+	0.230342i	0.896530	+	0.442982i	$0.146080\pi$
$384$	9.15232	+	7.29873i	0.467052	+	0.372462i
$385$	−15.0878	−	8.41180i	−0.768943	−	0.428705i
$386$	−12.8167	+	2.92534i	−0.652355	+	0.148896i
$387$	−2.94159	+	2.34584i	−0.149529	+	0.119246i
$388$	−9.12976	−	2.08381i	−0.463493	−	0.105789i
$389$	11.4859	+	11.4859i	0.582361	+	0.582361i	0.935551	−	0.353191i	$-0.114903\pi$
$389$	11.4859	+	11.4859i	0.582361	+	0.582361i	−0.353191	+	0.935551i	$0.614903\pi$
$390$	−4.81236	+	27.7019i	−0.243683	+	1.40274i
$391$	12.4076	+	4.34159i	0.627477	+	0.219564i
$392$	−6.49022	−	13.4771i	−0.327806	−	0.680695i
$393$	−35.2892	+	22.1737i	−1.78011	+	1.11852i
$394$	−7.31809	+	7.31809i	−0.368680	+	0.368680i
$395$	−20.7101	−	3.59775i	−1.04204	−	0.181022i
$396$	3.33643	−	29.6117i	0.167662	−	1.48804i
$397$	−0.0511183	−	0.0321198i	−0.00256555	−	0.00161204i	0.530749	−	0.847529i	$-0.321911\pi$
$397$	−0.0511183	−	0.0321198i	−0.00256555	−	0.00161204i	−0.533314	+	0.845917i	$0.679054\pi$
$398$	10.7077	−	2.44397i	0.536731	−	0.122505i
$399$	−9.35849	+	11.7352i	−0.468510	+	0.587493i
$400$	−1.94042	−	3.13954i	−0.0970209	−	0.156977i
$401$	−31.3147	−	15.0804i	−1.56378	−	0.753078i	−0.566315	−	0.824189i	$-0.691631\pi$
$401$	−31.3147	−	15.0804i	−1.56378	−	0.753078i	−0.997468	+	0.0711105i	$0.977346\pi$
$402$	19.4723	+	2.19400i	0.971191	+	0.109427i
$403$	11.4309	−	14.3339i	0.569413	−	0.714021i
$404$	−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
$408$	−19.5229	+	40.5397i	−0.966527	+	2.00701i
$409$	3.06651	+	27.2160i	0.151629	+	1.34575i	0.807050	+	0.590483i	$0.201063\pi$
$409$	3.06651	+	27.2160i	0.151629	+	1.34575i	−0.655421	+	0.755264i	$0.727509\pi$
$410$	13.0667	−	11.5904i	0.645320	−	0.572409i
$411$	8.08120	−	16.7808i	0.398616	−	0.827735i
$412$	7.99588	+	2.79788i	0.393928	+	0.137842i
$413$	5.55742	−	0.626171i	0.273463	−	0.0308119i
$414$	6.40967	−	10.2009i	0.315018	−	0.501348i
$415$	−9.06336	−	31.9033i	−0.444903	−	1.56607i
$416$	23.7184	+	2.67242i	1.16289	+	0.131026i
$417$	−2.89058	+	12.6645i	−0.141552	+	0.620181i
$418$	20.2178			0.988887
$419$	−1.69231	+	7.41451i	−0.0826749	+	0.362222i	−0.999295	−	0.0375364i	$-0.988049\pi$
$419$	−1.69231	+	7.41451i	−0.0826749	+	0.362222i	0.916620	+	0.399759i	$0.130906\pi$
$420$	−8.28515	+	4.53907i	−0.404274	+	0.221484i
$421$	−7.52865	+	21.5156i	−0.366924	+	1.04861i	0.601408	+	0.798942i	$0.294607\pi$
$421$	−7.52865	+	21.5156i	−0.366924	+	1.04861i	−0.968332	+	0.249666i	$0.919679\pi$
$422$	0.775613	+	1.23438i	0.0377563	+	0.0600888i
$423$			0.139705i			0.00679267i
$424$	−4.36465	+	2.74249i	−0.211966	+	0.133187i
$425$	−19.0384	+	18.7584i	−0.923498	+	0.909918i
$426$	2.14617	+	9.40298i	0.103982	+	0.455576i
$427$	1.22859	+	5.38282i	0.0594558	+	0.260493i
$428$	1.35704	+	12.0441i	0.0655952	+	0.582174i
$429$	−31.1767	−	64.7390i	−1.50522	−	3.12563i
$430$	−0.609336	−	1.48662i	−0.0293848	−	0.0716910i
$431$	−20.2333	−	25.3717i	−0.974602	−	1.22211i	−0.975021	−	0.222113i	$-0.928705\pi$
$431$	−20.2333	−	25.3717i	−0.974602	−	1.22211i	0.000418849	−	1.00000i	$-0.499867\pi$
$432$	3.38427	+	2.69886i	0.162826	+	0.129849i
$433$	29.1921	+	14.0582i	1.40288	+	0.675592i	0.973744	−	0.227646i	$-0.0731030\pi$
$433$	29.1921	+	14.0582i	1.40288	+	0.675592i	0.429138	+	0.903239i	$0.358817\pi$
$434$	−5.41436			−0.259898
$435$	27.2435	−	20.6689i	1.30623	−	0.991000i
$436$	−7.46468			−0.357493
$437$	−8.37866	−	4.03495i	−0.400806	−	0.193018i
$438$	−6.88268	−	5.48876i	−0.328867	−	0.262263i
$439$	−10.5436	−	13.2212i	−0.503218	−	0.631015i	0.463734	−	0.885975i	$-0.346509\pi$
$439$	−10.5436	−	13.2212i	−0.503218	−	0.631015i	−0.966952	+	0.254959i	$0.917938\pi$
$440$	33.7936	+	14.1446i	1.61105	+	0.674319i
$441$	11.0903	+	23.0292i	0.528109	+	1.09663i
$442$	2.64998	+	23.5192i	0.126047	+	1.11870i
$443$	7.27982	+	31.8950i	0.345875	+	1.51538i	0.786446	+	0.617659i	$0.211919\pi$
$443$	7.27982	+	31.8950i	0.345875	+	1.51538i	−0.440571	+	0.897718i	$0.645224\pi$
$444$	2.49732	+	10.9415i	0.118518	+	0.519259i
$445$	22.9323	−	20.3413i	1.08709	−	0.964270i
$446$	−7.18355	+	4.51373i	−0.340151	+	0.213731i
$447$		−	22.9731i		−	1.08659i
$448$	−4.84802	−	7.71558i	−0.229047	−	0.364527i
$449$	−1.53366	+	4.38294i	−0.0723777	+	0.206844i	−0.974389	−	0.224869i	$-0.927805\pi$
$449$	−1.53366	+	4.38294i	−0.0723777	+	0.206844i	0.902011	+	0.431712i	$0.142090\pi$
$450$	12.8783	+	20.8367i	0.607088	+	0.982251i
$451$	−9.93268	+	43.5179i	−0.467712	+	2.04918i
$452$	−15.7084			−0.738862
$453$	6.14398	−	26.9185i	0.288670	−	1.26474i
$454$	19.9471	+	2.24750i	0.936165	+	0.105480i
$455$	−6.96649	+	12.4954i	−0.326594	+	0.585792i
$456$	16.9358	−	26.9531i	0.793090	−	1.26220i
$457$	−5.07881	+	0.572244i	−0.237577	+	0.0267684i	−0.229950	−	0.973202i	$-0.573856\pi$
$457$	−5.07881	+	0.572244i	−0.237577	+	0.0267684i	−0.00762663	+	0.999971i	$0.502428\pi$
$458$	4.91663	+	1.72040i	0.229739	+	0.0803892i
$459$	13.6006	−	28.2419i	0.634821	−	1.31822i
$460$	−3.88399	−	4.37872i	−0.181092	−	0.204159i
$461$	1.19509	+	10.6068i	0.0556611	+	0.494006i	0.990355	+	0.138553i	$0.0442450\pi$
$461$	1.19509	+	10.6068i	0.0556611	+	0.494006i	−0.934694	+	0.355453i	$0.884326\pi$
$462$	−9.20718	+	19.1189i	−0.428357	+	0.889492i
$463$	−3.63850	+	3.63850i	−0.169096	+	0.169096i	−0.786582	−	0.617486i	$-0.788151\pi$
$463$	−3.63850	+	3.63850i	−0.169096	+	0.169096i	0.617486	+	0.786582i	$0.288151\pi$
$464$	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
$467$	2.85976	−	3.58602i	0.132334	−	0.165941i	−0.711250	−	0.702940i	$-0.751870\pi$
$467$	2.85976	−	3.58602i	0.132334	−	0.165941i	0.843583	+	0.536998i	$0.180442\pi$
$468$	−24.5238	−	2.76317i	−1.13361	−	0.127727i
$469$	8.98307	+	4.32602i	0.414799	+	0.199757i
$470$	−0.0572642	−	0.0167275i	−0.00264140	−	0.000771580i
$471$	−7.17330	+	8.99503i	−0.330528	+	0.414469i
$472$	−11.5631	+	2.63921i	−0.532237	+	0.121480i
$473$	3.47660	+	2.18449i	0.159854	+	0.100443i
$474$	−2.89116	+	25.6598i	−0.132796	+	1.17859i
$475$	14.8699	−	11.6792i	0.682278	−	0.535879i
$476$	−5.62314	+	5.62314i	−0.257736	+	0.257736i
$477$	7.45819	−	4.68629i	0.341487	−	0.214570i
$478$	−4.09515	−	8.50367i	−0.187308	−	0.388949i
$479$	−29.4941	−	10.3204i	−1.34762	−	0.471553i	−0.442523	−	0.896757i	$-0.645916\pi$
$479$	−29.4941	−	10.3204i	−1.34762	−	0.471553i	−0.905097	+	0.425205i	$0.860202\pi$
$480$	27.0746	−	19.0601i	1.23578	−	0.869970i
$481$	12.0175	+	12.0175i	0.547952	+	0.547952i
$482$	−19.0007	−	4.33679i	−0.865459	−	0.197535i
$483$	7.63126	−	6.08573i	0.347234	−	0.276910i
$484$	−20.2892	+	4.63089i	−0.922238	+	0.210495i
$485$	−9.57962	+	17.1824i	−0.434988	+	0.780212i
$486$	10.1713	+	8.11134i	0.461380	+	0.367938i
$487$	1.72349	−	4.92544i	0.0780986	−	0.223193i	−0.898214	−	0.439559i	$-0.855135\pi$
$487$	1.72349	−	4.92544i	0.0780986	−	0.223193i	0.976312	+	0.216366i	$0.0694205\pi$
$488$	−3.86731	−	11.0521i	−0.175065	−	0.500307i
$489$	13.0875	−	10.4369i	0.591838	−	0.471975i
$490$	−10.7674	+	1.78846i	−0.486423	+	0.0807943i
$491$	2.20709	−	0.772293i	0.0996044	−	0.0348531i	−0.280017	−	0.959995i	$-0.590340\pi$
$491$	2.20709	−	0.772293i	0.0996044	−	0.0348531i	0.379621	+	0.925142i	$0.376054\pi$
$492$	17.2615	+	17.2615i	0.778209	+	0.778209i
$493$	17.1346	−	23.1309i	0.771702	−	1.04177i
$494$		−	16.7440i		−	0.753348i
$495$	−57.7456	−	24.1699i	−2.59547	−	1.08636i
$496$	2.93778	−	0.331009i	0.131910	−	0.0148627i
$497$	−0.549454	+	4.87654i	−0.0246464	+	0.218743i
$498$	−38.4558	+	13.4563i	−1.72325	+	0.602990i
$499$	−20.3394	+	9.79495i	−0.910517	+	0.438482i	−0.829676	−	0.558245i	$-0.811475\pi$
$499$	−20.3394	+	9.79495i	−0.910517	+	0.438482i	−0.0808412	+	0.996727i	$0.525761\pi$
$500$	11.4714	−	3.16726i	0.513017	−	0.141644i
$501$	33.7284	+	21.1930i	1.50687	+	0.946832i
$502$	−12.7806	+	20.3402i	−0.570426	+	0.907828i
$503$	7.03932	+	8.82703i	0.313868	+	0.393578i	0.913594	−	0.406627i	$-0.133295\pi$
$503$	7.03932	+	8.82703i	0.313868	+	0.393578i	−0.599726	+	0.800205i	$0.704724\pi$
$504$	11.1634	+	17.7664i	0.497257	+	0.791379i
$505$	−12.0841	+	0.633742i	−0.537735	+	0.0282011i
$506$	−12.8178	−	2.92558i	−0.569821	−	0.130058i
$507$	−20.3532	+	9.80159i	−0.903918	+	0.435304i
$508$	0.710714	−	0.342262i	0.0315328	−	0.0151854i
$509$	33.9185	+	7.74166i	1.50341	+	0.343143i	0.893404	−	0.449254i	$-0.148310\pi$
$509$	33.9185	+	7.74166i	1.50341	+	0.343143i	0.610005	+	0.792398i	$0.291167\pi$
$510$	24.4003	+	21.9685i	1.08046	+	0.972781i
$511$	−2.38309	−	3.79266i	−0.105422	−	0.167778i
$512$	5.12807	+	6.43039i	0.226631	+	0.284186i
$513$	−11.7983	+	18.7768i	−0.520907	+	0.829018i
$514$	0.842835	+	0.529588i	0.0371758	+	0.0233591i
$515$	10.3516	−	14.4754i	0.456147	−	0.637860i
$516$	2.02311	−	0.974280i	0.0890626	−	0.0428903i
$517$	0.143904	−	0.0503542i	0.00632889	−	0.00221458i
$518$	0.561962	−	4.98755i	0.0246912	−	0.219140i
$519$	37.8261	−	4.26198i	1.66038	−	0.187080i
$520$	11.7143	−	27.9872i	0.513706	−	1.22732i
$521$		−	7.44577i		−	0.326205i	−0.986609	−	0.163102i	$-0.947850\pi$
$521$		−	7.44577i		−	0.326205i	0.986609	−	0.163102i	$-0.0521501\pi$
$522$	−17.1734	−	20.0273i	−0.751661	−	0.876571i
$523$	−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
$525$	4.27266	+	19.3803i	0.186474	+	0.845828i
$526$	2.99848	−	2.39121i	0.130740	−	0.104262i
$527$	−7.07087	−	20.2074i	−0.308012	−	0.880248i
$528$	3.82689	−	10.9366i	0.166544	−	0.475956i
$529$	−13.2540	−	10.5697i	−0.576263	−	0.459554i
$530$	1.02788	+	3.61818i	0.0446484	+	0.157164i
$531$	19.7588	−	4.50981i	0.857457	−	0.195709i
$532$	4.39849	−	3.50768i	0.190699	−	0.152077i
$533$	36.0407	+	8.22605i	1.56110	+	0.356310i
$534$	−26.6271	−	26.6271i	−1.15227	−	1.15227i
$535$	25.0858	+	4.35790i	1.08455	+	0.188408i
$536$	−19.9583	−	6.98372i	−0.862068	−	0.301651i
$537$	4.22370	+	8.77060i	0.182266	+	0.378480i
$538$	5.91511	−	3.71671i	0.255018	−	0.160239i
$539$	19.7242	−	19.7242i	0.849579	−	0.849579i
$540$	−11.4129	+	8.03447i	−0.491131	+	0.345748i
$541$	1.67468	−	14.8632i	0.0720000	−	0.639018i	−0.904945	−	0.425528i	$-0.860088\pi$
$541$	1.67468	−	14.8632i	0.0720000	−	0.639018i	0.976945	−	0.213490i	$-0.0684830\pi$
$542$	0.846865	+	0.532120i	0.0363760	+	0.0228565i
$543$	48.9908	−	11.1818i	2.10240	−	0.479859i
$544$	17.3778	−	21.7911i	0.745068	−	0.934286i
$545$	−4.39692	+	15.0522i	−0.188343	+	0.644767i
$546$	15.8339	+	7.62520i	0.677628	+	0.326328i
$547$	20.2804	+	2.28505i	0.867127	+	0.0977017i	0.534309	−	0.845289i	$-0.320572\pi$
$547$	20.2804	+	2.28505i	0.867127	+	0.0977017i	0.332818	+	0.942991i	$0.392001\pi$
$548$	−4.35257	+	5.45796i	−0.185933	+	0.233152i
$549$	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
$553$	−5.70064	+	11.8375i	−0.242416	+	0.503382i
$554$	1.80170	+	15.9905i	0.0765469	+	0.679372i
$555$	23.5341	+	1.40910i	0.998966	+	0.0598129i
$556$	2.11253	−	4.38670i	0.0895910	−	0.186038i
$557$	−29.0790	−	10.1752i	−1.23212	−	0.431137i	−0.365830	−	0.930682i	$-0.619215\pi$
$557$	−29.0790	−	10.1752i	−1.23212	−	0.431137i	−0.866288	+	0.499545i	$0.833501\pi$
$558$	−19.4976	+	2.19686i	−0.825401	+	0.0930004i
$559$	1.80915	−	2.87925i	0.0765189	−	0.121779i
$560$	−2.21911	+	0.630422i	−0.0937744	+	0.0266402i
$561$	−83.3794	−	9.39460i	−3.52028	−	0.396640i
$562$	3.32886	−	14.5847i	0.140420	−	0.615219i
$563$	12.4601			0.525130			0.262565	−	0.964914i	$-0.415432\pi$
$563$	12.4601			0.525130			0.262565	+	0.964914i	$0.415432\pi$
$564$	0.0185534	−	0.0812878i	0.000781239	−	0.00342283i
$565$	−9.25273	+	31.6755i	−0.389265	+	1.33260i
$566$	−1.21466	+	3.47130i	−0.0510560	+	0.145910i
$567$	−1.08461	−	1.72615i	−0.0455495	−	0.0724915i
$568$		−	10.4074i		−	0.436685i
$569$	3.79658	−	2.38555i	0.159161	−	0.100007i	−0.450097	−	0.892980i	$-0.648610\pi$
$569$	3.79658	−	2.38555i	0.159161	−	0.100007i	0.609258	+	0.792972i	$0.291468\pi$
$570$	−15.4134	−	17.3767i	−0.645594	−	0.727828i
$571$	−1.25968	−	5.51903i	−0.0527160	−	0.230964i	0.941706	−	0.336436i	$-0.109222\pi$
$571$	−1.25968	−	5.51903i	−0.0527160	−	0.230964i	−0.994422	+	0.105472i	$0.966365\pi$
$572$	5.99296	+	26.2569i	0.250578	+	1.09786i
$573$	−7.30374	−	64.8225i	−0.305118	−	2.70800i
$574$	−4.73686	−	9.83619i	−0.197713	−	0.410555i
$575$	−11.1173	+	5.25273i	−0.463624	+	0.219054i
$576$	−20.5888	−	25.8175i	−0.857865	−	1.07573i
$577$	−36.9281	−	29.4491i	−1.53734	−	1.22598i	−0.882599	−	0.470127i	$-0.844208\pi$
$577$	−36.9281	−	29.4491i	−1.53734	−	1.22598i	−0.654736	−	0.755857i	$-0.727220\pi$
$578$	10.0860	+	4.85714i	0.419521	+	0.202030i
$579$	−38.5980			−1.60408
$580$	−11.6791	+	5.28054i	−0.484946	+	0.219263i
$581$	−20.7301			−0.860031
$582$	21.7732	+	10.4854i	0.902528	+	0.434634i
$583$	−7.51533	−	5.99328i	−0.311253	−	0.248216i
$584$	5.92274	+	7.42688i	0.245085	+	0.307327i
$585$	−20.0171	+	47.8237i	−0.827603	+	1.97727i
$586$	−10.5511	−	21.9095i	−0.435861	−	0.905075i
$587$	−1.55975	−	13.8431i	−0.0643776	−	0.571367i	−0.983950	−	0.178446i	$-0.942893\pi$
$587$	−1.55975	−	13.8431i	−0.0643776	−	0.571367i	0.919572	−	0.392921i	$-0.128536\pi$
$588$	−3.39455	−	14.8725i	−0.139989	−	0.613332i
$589$	3.37023	+	14.7659i	0.138868	+	0.608420i
$590$	−0.517258	+	8.63899i	−0.0212952	+	0.355661i
$591$	−25.7285	+	16.1663i	−1.05833	+	0.664993i
$592$			2.74056i			0.112636i
$593$	−11.3359	−	18.0409i	−0.465508	−	0.740852i	0.528643	−	0.848844i	$-0.322701\pi$
$593$	−11.3359	−	18.0409i	−0.465508	−	0.740852i	−0.994152	+	0.107992i	$0.965558\pi$
$594$	−10.3547	+	29.5921i	−0.424860	+	1.21418i
$595$	8.02666	+	14.6511i	0.329061	+	0.600635i
$596$	−1.91604	+	8.39471i	−0.0784840	+	0.343861i
$597$	32.2467			1.31977
$598$	−2.42291	+	10.6155i	−0.0990801	+	0.434098i
$599$	9.52133	+	1.07280i	0.389031	+	0.0438332i	0.304314	−	0.952572i	$-0.401573\pi$
$599$	9.52133	+	1.07280i	0.389031	+	0.0438332i	0.0847169	+	0.996405i	$0.473001\pi$
$600$	−13.6062	−	39.8280i	−0.555469	−	1.62597i
$601$	−18.7867	+	29.8988i	−0.766324	+	1.21960i	0.204279	+	0.978913i	$0.434515\pi$
$601$	−18.7867	+	29.8988i	−0.766324	+	1.21960i	−0.970603	+	0.240685i	$0.922628\pi$
$602$	−0.997916	+	0.112438i	−0.0406720	+	0.00458264i
$603$	34.1042	+	11.9336i	1.38883	+	0.485973i
$604$	−4.49021	+	9.32402i	−0.182704	+	0.379389i
$605$	−2.61295	+	43.6402i	−0.106232	+	1.77423i
$606$	1.66435	+	14.7715i	0.0676096	+	0.600052i
$607$	13.3355	−	27.6914i	0.541270	−	1.12396i	−0.433583	−	0.901113i	$-0.642751\pi$
$607$	13.3355	−	27.6914i	0.541270	−	1.12396i	0.974854	−	0.222846i	$-0.0715347\pi$
$608$	−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
$612$	−17.9679	+	22.5311i	−0.726310	+	0.910764i
$613$	−5.43065	−	0.611887i	−0.219342	−	0.0247139i	0.00160954	−	0.999999i	$-0.499488\pi$
$613$	−5.43065	−	0.611887i	−0.219342	−	0.0247139i	−0.220951	+	0.975285i	$0.570916\pi$
$614$	−19.6003	−	9.43899i	−0.791003	−	0.380927i
$615$	44.9747	−	24.6397i	1.81356	−	0.993567i
$616$	14.2768	−	17.9026i	0.575229	−	0.721315i
$617$	−8.50028	+	1.94013i	−0.342208	+	0.0781068i	−0.390171	−	0.920742i	$-0.627584\pi$
$617$	−8.50028	+	1.94013i	−0.342208	+	0.0781068i	0.0479630	+	0.998849i	$0.484727\pi$
$618$	−18.5104	−	11.6308i	−0.744596	−	0.467861i
$619$	0.314355	−	2.78998i	0.0126350	−	0.112139i	−0.985812	−	0.167855i	$-0.946316\pi$
$619$	0.314355	−	2.78998i	0.0126350	−	0.112139i	0.998447	+	0.0557167i	$0.0177444\pi$
$620$	−1.63155	+	9.39188i	−0.0655248	+	0.377187i
$621$	10.1970	−	10.1970i	0.409192	−	0.409192i
$622$	26.1211	−	16.4130i	1.04736	−	0.658101i
$623$	−8.31325	−	17.2626i	−0.333063	−	0.691613i
$624$	−9.05750	−	3.16936i	−0.362590	−	0.126876i
$625$	0.370340	−	24.9973i	0.0148136	−	0.999890i
$626$	−17.4781	−	17.4781i	−0.698566	−	0.698566i
$627$	57.8718	+	13.2089i	2.31118	+	0.527511i
$628$	3.37145	−	2.68864i	0.134536	−	0.107289i
$629$	19.3484	−	4.41614i	0.771470	−	0.176083i
$630$	14.7279	−	4.18402i	0.586773	−	0.166695i
$631$	34.6785	+	27.6552i	1.38053	+	1.10093i	0.983053	+	0.183322i	$0.0586851\pi$
$631$	34.6785	+	27.6552i	1.38053	+	1.10093i	0.397476	+	0.917613i	$0.369886\pi$
$632$	9.20285	−	26.3002i	0.366070	−	1.04617i
$633$	1.41367	+	4.04004i	0.0561884	+	0.160577i
$634$	−17.9670	+	14.3282i	−0.713563	+	0.569047i
$635$	−0.271527	−	1.63473i	−0.0107752	−	0.0648723i
$636$	−4.96194	+	1.73626i	−0.196754	+	0.0688471i
$637$	−16.3351	−	16.3351i	−0.647222	−	0.647222i
$638$	−14.4394	+	24.9082i	−0.571662	+	0.986124i
$639$			17.7838i			0.703518i
$640$	−8.52867	+	3.49574i	−0.337125	+	0.138181i
$641$	19.6936	−	2.21894i	0.777852	−	0.0876428i	0.285893	−	0.958261i	$-0.407710\pi$
$641$	19.6936	−	2.21894i	0.777852	−	0.0876428i	0.491959	+	0.870619i	$0.336281\pi$
$642$	3.50203	−	31.0813i	0.138214	−	1.22668i
$643$	−28.6585	+	10.0280i	−1.13018	+	0.395467i	−0.829638	−	0.558302i	$-0.811453\pi$
$643$	−28.6585	+	10.0280i	−1.13018	+	0.395467i	−0.300542	+	0.953769i	$0.597167\pi$
$644$	−3.29615	+	1.58734i	−0.129887	+	0.0625501i
$645$	−0.772926	−	4.65341i	−0.0304339	−	0.183228i
$646$	−16.5555	−	10.4025i	−0.651368	−	0.409282i
$647$	−2.55620	+	4.06817i	−0.100495	+	0.159936i	−0.893187	−	0.449686i	$-0.851536\pi$
$647$	−2.55620	+	4.06817i	−0.100495	+	0.159936i	0.792692	+	0.609622i	$0.208679\pi$
$648$	2.69561	+	3.38019i	0.105894	+	0.132786i
$649$	−11.7671	−	18.7272i	−0.461898	−	0.735107i
$650$	−17.2060	−	13.9310i	−0.674873	−	0.546420i
$651$	−15.4981	−	3.53735i	−0.607420	−	0.138640i
$652$	−5.65286	+	2.72227i	−0.221383	+	0.106612i
$653$	28.0887	−	13.5268i	1.09920	−	0.529345i	0.205791	−	0.978596i	$-0.434023\pi$
$653$	28.0887	−	13.5268i	1.09920	−	0.529345i	0.893406	+	0.449251i	$0.148309\pi$
$654$	18.7806	+	4.28655i	0.734379	+	0.167617i
$655$	−1.71865	−	32.7710i	−0.0671532	−	1.28047i
$656$	3.17152	+	5.04744i	0.123827	+	0.197070i
$657$	−10.1206	−	12.6908i	−0.394842	−	0.495117i
$658$	−0.0198387	+	0.0315732i	−0.000773394	+	0.00123085i
$659$	−11.5058	−	7.22958i	−0.448203	−	0.281624i	0.288958	−	0.957342i	$-0.406691\pi$
$659$	−11.5058	−	7.22958i	−0.448203	−	0.281624i	−0.737161	+	0.675717i	$0.763834\pi$
$660$	30.3896	+	21.7323i	1.18292	+	0.845927i
$661$	−20.4402	+	9.84350i	−0.795033	+	0.382868i	−0.786886	−	0.617099i	$-0.788308\pi$
$661$	−20.4402	+	9.84350i	−0.795033	+	0.382868i	−0.00814767	+	0.999967i	$0.502594\pi$
$662$	0.897434	−	0.314026i	0.0348797	−	0.0122050i
$663$	−7.78042	+	69.0531i	−0.302166	+	2.68180i
$664$	43.6871	−	4.92236i	1.69539	−	0.191025i
$665$	−4.48227	−	10.9355i	−0.173815	−	0.424061i
$666$		−	18.1887i		−	0.704797i
$667$	10.9550	−	7.44069i	0.424179	−	0.288105i
$668$	−10.5573	−	10.5573i	−0.408475	−	0.408475i
$669$	−23.5113	+	8.22694i	−0.908997	+	0.318072i
$670$	−8.97495	+	12.5503i	−0.346733	+	0.484859i
$671$	17.0714	−	13.6140i	0.659034	−	0.525562i
$672$	−6.83538	−	19.5344i	−0.263680	−	0.753555i
$673$	3.92195	−	11.2083i	0.151180	−	0.432048i	−0.843240	−	0.537537i	$-0.819355\pi$
$673$	3.92195	−	11.2083i	0.151180	−	0.432048i	0.994421	+	0.105489i	$0.0336407\pi$
$674$	20.8410	+	16.6201i	0.802764	+	0.640183i
$675$	9.47870	+	27.7461i	0.364835	+	1.06795i
$676$	8.25486	−	1.88412i	0.317495	−	0.0724661i
$677$	−0.860917	+	0.686559i	−0.0330877	+	0.0263866i	−0.639894	−	0.768463i	$-0.721022\pi$
$677$	−0.860917	+	0.686559i	−0.0330877	+	0.0263866i	0.606806	+	0.794850i	$0.292450\pi$
$678$	39.5212	+	9.02047i	1.51780	+	0.346429i
$679$	8.69471	+	8.69471i	0.333672	+	0.333672i
$680$	−20.3944	−	28.9700i	−0.782091	−	1.11095i
$681$	55.6286	+	19.4653i	2.13169	+	0.745911i
$682$	9.29049	+	19.2919i	0.355751	+	0.738725i
$683$	−0.322462	+	0.202616i	−0.0123387	+	0.00775289i	−0.538187	−	0.842825i	$-0.680891\pi$
$683$	−0.322462	+	0.202616i	−0.0123387	+	0.00775289i	0.525849	+	0.850578i	$0.323748\pi$
$684$	14.4162	−	14.4162i	0.551216	−	0.551216i
$685$	8.44197	+	11.9917i	0.322551	+	0.458179i
$686$	−1.82340	+	16.1831i	−0.0696177	+	0.617874i
$687$	12.9495	+	8.13668i	0.494053	+	0.310434i
$688$	0.534587	−	0.122016i	0.0203809	−	0.00465182i
$689$	−4.96351	+	6.22405i	−0.189095	+	0.237117i
$690$	7.25739	+	13.2469i	0.276284	+	0.504301i
$691$	−9.56118	−	4.60442i	−0.363724	−	0.175160i	0.243091	−	0.970004i	$-0.421839\pi$
$691$	−9.56118	−	4.60442i	−0.363724	−	0.175160i	−0.606815	+	0.794843i	$0.707553\pi$
$692$	−14.1777	−	1.59744i	−0.538956	−	0.0607257i
$693$	−24.3958	+	30.5914i	−0.926719	+	1.16207i
$694$	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
$698$	−13.6125	+	28.2667i	−0.515242	+	1.06991i
$699$	6.24653	+	55.4395i	0.236266	+	2.09691i
$700$	0.0550965	−	7.43823i	0.00208245	−	0.281139i
$701$	−7.04923	+	14.6379i	−0.266246	+	0.552865i	−0.990637	−	0.136524i	$-0.956407\pi$
$701$	−7.04923	+	14.6379i	−0.266246	+	0.552865i	0.724391	+	0.689389i	$0.242121\pi$
$702$	24.5076	+	8.57558i	0.924979	+	0.323664i
$703$	−13.9518	+	1.57199i	−0.526200	+	0.0592885i
$704$	−19.1727	+	30.5131i	−0.722597	+	1.15001i
$705$	−0.152985	−	0.0852932i	−0.00576176	−	0.00321233i
$706$	18.8134	+	2.11976i	0.708052	+	0.0797782i
$707$	−1.68304	+	7.37386i	−0.0632971	+	0.277323i
$708$	−12.0956			−0.454582
$709$	5.20526	−	22.8057i	0.195488	−	0.856488i	−0.778094	−	0.628148i	$-0.783813\pi$
$709$	5.20526	−	22.8057i	0.195488	−	0.856488i	0.973582	−	0.228340i	$-0.0733296\pi$
$710$	−7.28950	−	2.12934i	−0.273570	−	0.0799126i
$711$	−15.7256	+	44.9410i	−0.589754	+	1.68542i
$712$	21.6185	+	34.4057i	0.810189	+	1.28941i
$713$		−	9.84907i		−	0.368851i
$714$	17.3765	−	10.9184i	0.650298	−	0.408609i
$715$	56.4761	+	3.38149i	2.11209	+	0.126461i
$716$	−0.811905	−	3.55719i	−0.0303423	−	0.132938i
$717$	−6.16634	−	27.0165i	−0.230286	−	1.00895i
$718$	−1.75085	−	15.5392i	−0.0653411	−	0.579918i
$719$	14.4691	+	30.0454i	0.539606	+	1.12050i	0.975397	+	0.220456i	$0.0707546\pi$
$719$	14.4691	+	30.0454i	0.539606	+	1.12050i	−0.435790	+	0.900048i	$0.643531\pi$
$720$	−7.73543	+	3.17061i	−0.288283	+	0.118162i
$721$	−6.93522	−	8.69649i	−0.258281	−	0.323874i
$722$	−3.55373	−	2.83401i	−0.132256	−	0.105471i
$723$	−51.5546	−	24.8274i	−1.91734	−	0.923340i
$724$	−18.8346			−0.699983
$725$	3.76871	+	26.6608i	0.139966	+	0.990156i
$726$	53.7055			1.99320
$727$	−13.9547	−	6.72024i	−0.517552	−	0.249240i	0.156826	−	0.987626i	$-0.449874\pi$
$727$	−13.9547	−	6.72024i	−0.517552	−	0.249240i	−0.674378	+	0.738386i	$0.735588\pi$
$728$	−14.8265	−	11.8238i	−0.549508	−	0.438218i
$729$	26.5434	+	33.2844i	0.983089	+	1.23275i
$730$	6.41369	−	2.62885i	0.237381	−	0.0972981i
$731$	−1.72287	−	3.57757i	−0.0637226	−	0.132321i
$732$	−1.33701	−	11.8663i	−0.0494173	−	0.438590i
$733$	−6.90248	−	30.2417i	−0.254949	−	1.11700i	−0.926574	−	0.376113i	$-0.877261\pi$
$733$	−6.90248	−	30.2417i	−0.254949	−	1.11700i	0.671625	−	0.740891i	$-0.265597\pi$
$734$	−3.01284	−	13.2001i	−0.111206	−	0.487224i
$735$	−31.9893	−	1.91535i	−1.17994	−	0.0706489i
$736$	10.8570	−	6.82193i	0.400196	−	0.251460i
$737$		−	39.4306i		−	1.45244i
$738$	−21.0489	−	33.4991i	−0.774821	−	1.23312i
$739$	−3.03598	+	8.67634i	−0.111680	+	0.319164i	−0.986135	−	0.165942i	$-0.946933\pi$
$739$	−3.03598	+	8.67634i	−0.111680	+	0.319164i	0.874455	+	0.485107i	$0.161219\pi$
$740$	−8.48219	−	2.47773i	−0.311811	−	0.0910833i
$741$	10.9393	−	47.9283i	0.401866	−	1.76069i
$742$	2.35102			0.0863087
$743$	−4.77394	+	20.9160i	−0.175139	+	0.767334i	0.808692	+	0.588233i	$0.200176\pi$
$743$	−4.77394	+	20.9160i	−0.175139	+	0.767334i	−0.983831	+	0.179101i	$0.942681\pi$
$744$	33.5011	+	3.77466i	1.22821	+	0.138386i
$745$	15.7990	+	8.80835i	0.578831	+	0.322713i
$746$	−10.2992	+	16.3911i	−0.377081	+	0.600120i
$747$	−74.6513	+	8.41118i	−2.73135	+	0.307749i
$748$	29.6846	+	10.3871i	1.08538	+	0.379789i
$749$	6.90511	−	14.3386i	0.252307	−	0.523921i
$750$	−30.6800	+	1.38120i	−1.12027	+	0.0504343i
$751$	−4.39473	−	39.0043i	−0.160366	−	1.42329i	−0.773744	−	0.633499i	$-0.781618\pi$
$751$	−4.39473	−	39.0043i	−0.160366	−	1.42329i	0.613378	−	0.789790i	$-0.289810\pi$
$752$	0.00883409	−	0.0183442i	0.000322146	−	0.000668943i
$753$	−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
$757$	26.9647	−	33.8127i	0.980049	−	1.22894i	0.00661456	−	0.999978i	$-0.497895\pi$
$757$	26.9647	−	33.8127i	0.980049	−	1.22894i	0.973435	−	0.228965i	$-0.0735341\pi$
$758$	28.8534	+	3.25099i	1.04800	+	0.118081i
$759$	−34.7785	−	16.7485i	−1.26238	−	0.607931i
$760$	12.0427	+	21.9815i	0.436833	+	0.797351i
$761$	−10.1735	+	12.7572i	−0.368791	+	0.462449i	−0.931253	−	0.364374i	$-0.881283\pi$
$761$	−10.1735	+	12.7572i	−0.368791	+	0.462449i	0.562462	+	0.826823i	$0.309854\pi$
$762$	−1.98464	+	0.452982i	−0.0718961	+	0.0164098i
$763$	8.29920	+	5.21473i	0.300451	+	0.188786i
$764$	−2.73753	+	24.2963i	−0.0990405	+	0.879009i
$765$	34.8494	+	49.5031i	1.25998	+	1.78979i
$766$	−3.26648	+	3.26648i	−0.118023	+	0.118023i
$767$	−15.5095	+	9.74526i	−0.560015	+	0.351881i
$768$	20.9797	+	43.5649i	0.757041	+	1.57201i
$769$	−35.8462	−	12.5431i	−1.29265	−	0.452317i	−0.405624	−	0.914040i	$-0.632946\pi$
$769$	−35.8462	−	12.5431i	−1.29265	−	0.452317i	−0.887024	+	0.461723i	$0.847232\pi$
$770$	−9.61821	−	13.6625i	−0.346616	−	0.492364i
$771$	2.06655	+	2.06655i	0.0744249	+	0.0744249i
$772$	14.1043	+	3.21922i	0.507625	+	0.115862i
$773$	41.9634	−	33.4647i	1.50932	−	1.20364i	0.591716	−	0.806147i	$-0.298451\pi$
$773$	41.9634	−	33.4647i	1.50932	−	1.20364i	0.917604	−	0.397496i	$-0.130121\pi$
$774$	−3.54798	+	0.809802i	−0.127529	+	0.0291077i
$775$	17.9773	+	8.82207i	0.645765	+	0.316898i
$776$	−20.3880	−	16.2589i	−0.731886	−	0.583659i
$777$	4.86707	−	13.9093i	0.174605	−	0.498993i
$778$	5.18923	+	14.8300i	0.186043	+	0.531680i
$779$	−23.8766	+	19.0409i	−0.855467	+	0.682212i
$780$	17.9982	−	25.1681i	0.644440	−	0.901162i
$781$	18.3184	−	6.40989i	0.655484	−	0.229364i
$782$	8.99069	+	8.99069i	0.321506	+	0.321506i
$783$	−14.7067	−	27.9456i	−0.525573	−	0.998696i
$784$		−	3.72518i		−	0.133042i
$785$	−3.43566	−	8.38209i	−0.122624	−	0.299170i
$786$	−40.0591	+	4.51357i	−1.42886	+	0.160994i
$787$	−4.82326	+	42.8076i	−0.171931	+	1.52593i	0.550707	+	0.834699i	$0.314358\pi$
$787$	−4.82326	+	42.8076i	−0.171931	+	1.52593i	−0.722637	+	0.691227i	$0.757070\pi$
$788$	10.7499	−	3.76156i	0.382950	−	0.134000i
$789$	10.1452	−	4.88565i	0.361177	−	0.173934i
$790$	−16.5382	−	11.8268i	−0.588403	−	0.420779i
$791$	17.4646	+	10.9737i	0.620969	+	0.390180i
$792$	44.1483	−	70.2617i	1.56874	−	2.49664i
$793$	−11.2748	−	14.1382i	−0.400381	−	0.502062i
$794$	−0.0310679	−	0.0494443i	−0.00110256	−	0.00175471i
$795$	0.578371	+	11.0283i	0.0205127	+	0.391133i
$796$	−11.7834	−	2.68949i	−0.417653	−	0.0953266i
$797$	−26.8505	+	12.9305i	−0.951095	+	0.458023i	−0.844070	−	0.536233i	$-0.819847\pi$
$797$	−26.8505	+	12.9305i	−0.951095	+	0.458023i	−0.107025	+	0.994256i	$0.534132\pi$
$798$	−13.0805	+	6.29926i	−0.463046	+	0.222991i
$799$	−0.143745	−	0.0328089i	−0.00508534	−	0.00116070i
$800$	2.72703	+	25.9278i	0.0964150	+	0.916685i
$801$	−36.9411	−	58.7914i	−1.30525	−	2.07729i
$802$	−20.9608	−	26.2840i	−0.740152	−	0.928121i
$803$	−9.42451	+	14.9990i	−0.332584	+	0.529304i
$804$	−18.2588	−	11.4728i	−0.643940	−	0.404614i
$805$	1.25929	+	7.58156i	0.0443841	+	0.267215i
$806$	15.9772	−	7.69420i	0.562772	−	0.271017i
$807$	19.3597	−	6.77426i	0.681494	−	0.238465i
$808$	1.79595	−	15.9395i	0.0631812	−	0.560749i
$809$	−22.8571	+	2.57537i	−0.803612	+	0.0905453i	−0.504209	−	0.863582i	$-0.668216\pi$
$809$	−22.8571	+	2.57537i	−0.803612	+	0.0905453i	−0.299403	+	0.954127i	$0.596787\pi$
$810$	2.91906	−	1.19647i	0.102565	−	0.0420395i
$811$		−	19.6076i		−	0.688516i	−0.938875	−	0.344258i	$-0.888131\pi$
$811$		−	19.6076i		−	0.688516i	0.938875	−	0.344258i	$-0.111869\pi$
$812$	1.18006	+	7.92406i	0.0414119	+	0.278080i
$813$	2.07643	+	2.07643i	0.0728236	+	0.0728236i
$814$	−18.7354	+	6.55581i	−0.656676	+	0.229781i
$815$	2.15966	+	13.0023i	0.0756496	+	0.455450i
$816$	−8.76082	+	6.98652i	−0.306690	+	0.244577i
$817$	0.927804	+	2.65151i	0.0324598	+	0.0927646i
$818$	−8.74954	+	25.0047i	−0.305920	+	0.874270i
$819$	25.3351	+	20.2041i	0.885282	+	0.705988i
$820$	−18.4895	+	5.25265i	−0.645681	+	0.183431i
$821$	−3.20785	+	0.732172i	−0.111955	+	0.0255530i	−0.278131	−	0.960543i	$-0.589715\pi$
$821$	−3.20785	+	0.732172i	−0.111955	+	0.0255530i	0.166176	+	0.986096i	$0.446858\pi$
$822$	14.0850	−	11.2324i	0.491269	−	0.391774i
$823$	16.4779	+	3.76096i	0.574382	+	0.131099i	0.499838	−	0.866119i	$-0.333393\pi$
$823$	16.4779	+	3.76096i	0.574382	+	0.131099i	0.0745439	+	0.997218i	$0.476250\pi$
$824$	16.6804	+	16.6804i	0.581090	+	0.581090i
$825$	61.7227	−	48.4787i	2.14891	−	1.68781i
$826$	5.10588	+	1.78663i	0.177656	+	0.0621646i
$827$	0.0579057	+	0.120242i	0.00201358	+	0.00418124i	0.901973	−	0.431792i	$-0.142119\pi$
$827$	0.0579057	+	0.120242i	0.00201358	+	0.00418124i	−0.899960	+	0.435973i	$0.856404\pi$
$828$	−11.2257	+	7.05358i	−0.390120	+	0.245129i
$829$	28.0352	−	28.0352i	0.973704	−	0.973704i	−0.0259593	−	0.999663i	$-0.508264\pi$
$829$	28.0352	−	28.0352i	0.973704	−	0.973704i	0.999663	+	0.0259593i	$0.00826403\pi$
$830$	5.49063	−	31.6063i	0.190582	−	1.09707i
$831$	−5.28984	+	46.9486i	−0.183502	+	1.62863i
$832$	25.2704	+	15.8784i	0.876092	+	0.550485i
$833$	−26.2998	+	6.00275i	−0.911234	+	0.207983i
$834$	−7.83400	+	9.82352i	−0.271269	+	0.340161i
$835$	−27.5070	+	15.0699i	−0.951919	+	0.521514i
$836$	−20.0456	−	9.65345i	−0.693291	−	0.333871i
$837$	−23.3385	−	2.62961i	−0.806695	−	0.0908927i
$838$	−4.58647	+	5.75126i	−0.158437	+	0.198674i
$839$	−0.960023	−	2.74359i	−0.0331437	−	0.0947192i	0.926123	−	0.377223i	$-0.123121\pi$
$839$	−0.960023	−	2.74359i	−0.0331437	−	0.0947192i	−0.959266	+	0.282503i	$0.908835\pi$
$840$	−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
$843$	19.0572	−	39.5726i	0.656364	−	1.36295i
$844$	−0.179623	−	1.59420i	−0.00618288	−	0.0548746i
$845$	1.06310	−	17.7554i	0.0365718	−	0.610805i
$846$	−0.0586305	+	0.121748i	−0.00201576	+	0.00418577i
$847$	25.7926	+	9.02522i	0.886244	+	0.310110i
$848$	−1.27564	+	0.143731i	−0.0438058	+	0.00493573i
$849$	−5.74476	+	9.14273i	−0.197160	+	0.313778i
$850$	−24.4637	+	8.35736i	−0.839099	+	0.286655i
$851$	9.07268	+	1.02225i	0.311007	+	0.0350421i
$852$	2.36177	−	10.3476i	0.0809131	−	0.354503i
$853$	−19.9191			−0.682018			−0.341009	−	0.940060i	$-0.610769\pi$
$853$	−19.9191			−0.682018			−0.341009	+	0.940060i	$0.610769\pi$
$854$	−1.18836	+	5.20655i	−0.0406648	+	0.178164i
$855$	−20.5781	−	37.5612i	−0.703757	−	1.28457i
$856$	−11.1473	+	31.8571i	−0.381006	+	1.08885i
$857$	17.6888	+	28.1515i	0.604237	+	0.961638i	0.999080	+	0.0428889i	$0.0136561\pi$
$857$	17.6888	+	28.1515i	0.604237	+	0.961638i	−0.394843	+	0.918749i	$0.629201\pi$
$858$		−	69.5018i		−	2.37275i
$859$	14.3941	−	9.04440i	0.491120	−	0.308591i	−0.263607	−	0.964630i	$-0.584912\pi$
$859$	14.3941	−	9.04440i	0.491120	−	0.308591i	0.754727	+	0.656039i	$0.227769\pi$
$860$	−0.105673	+	1.76489i	−0.00360341	+	0.0601823i
$861$	−7.13260	−	31.2500i	−0.243078	−	1.06500i
$862$	−6.98469	−	30.6019i	−0.237900	−	1.04231i
$863$	1.07928	+	9.57890i	0.0367392	+	0.326070i	0.998616	+	0.0525876i	$0.0167469\pi$
$863$	1.07928	+	9.57890i	0.0367392	+	0.326070i	−0.961877	+	0.273482i	$0.911825\pi$
$864$	−13.2666	−	27.5483i	−0.451338	−	0.937214i
$865$	−11.5723	+	27.6479i	−0.393469	+	0.940056i
$866$	19.5400	+	24.5024i	0.663996	+	0.832625i
$867$	25.6969	+	20.4926i	0.872712	+	0.695965i
$868$	5.36823	+	2.58520i	0.182210	+	0.0877475i
$869$	51.9599			1.76262
$870$	32.4160	−	6.57883i	1.09900	−	0.223043i
$871$	−32.6556			−1.10649
$872$	−18.7282	−	9.01901i	−0.634216	−	0.305422i
$873$	34.8384	+	27.7827i	1.17910	+	0.940301i
$874$	−5.60833	−	7.03263i	−0.189705	−	0.237882i
$875$	−14.9665	−	4.49244i	−0.505959	−	0.151872i
$876$	4.20332	+	8.72828i	0.142017	+	0.294901i
$877$	2.98854	+	26.5240i	0.100916	+	0.895652i	0.937541	+	0.347876i	$0.113097\pi$
$877$	2.98854	+	26.5240i	0.100916	+	0.895652i	−0.836625	+	0.547776i	$0.815475\pi$
$878$	−3.63974	−	15.9467i	−0.122835	−	0.538176i
$879$	−15.8875	−	69.6075i	−0.535871	−	2.34780i
$880$	6.05402	+	6.82516i	0.204081	+	0.230076i
$881$	19.0940	−	11.9976i	0.643294	−	0.404209i	−0.170503	−	0.985357i	$-0.554539\pi$
$881$	19.0940	−	11.9976i	0.643294	−	0.404209i	0.813798	+	0.581148i	$0.197396\pi$
$882$			24.7235i			0.832482i
$883$	1.27154	+	2.02364i	0.0427907	+	0.0681010i	0.867435	−	0.497551i	$-0.165767\pi$
$883$	1.27154	+	2.02364i	0.0427907	+	0.0681010i	−0.824644	+	0.565652i	$0.808624\pi$
$884$	8.60237	−	24.5842i	0.289329	−	0.826855i
$885$	−7.12469	+	24.3904i	−0.239494	+	0.819875i
$886$	−7.04143	+	30.8505i	−0.236561	+	1.03644i
$887$	24.2760			0.815109			0.407554	−	0.913181i	$-0.366382\pi$
$887$	24.2760			0.815109			0.407554	+	0.913181i	$0.366382\pi$
$888$	−6.95422	+	30.4684i	−0.233368	+	1.02245i
$889$	−1.02927	−	0.115971i	−0.0345206	−	0.00388953i
$890$	28.5214	−	8.10260i	0.956040	−	0.271600i
$891$	−4.28937	+	6.82649i	−0.143699	+	0.228696i
$892$	9.27753	−	1.04533i	0.310635	−	0.0350001i
$893$	0.0984546	+	0.0344507i	0.00329466	+	0.00115285i
$894$	9.64122	−	20.0202i	0.322451	−	0.669576i
$895$	−7.65117	−	0.458112i	−0.255750	−	0.0153130i
$896$	0.645054	+	5.72501i	0.0215497	+	0.191259i
$897$	−13.8707	+	28.8029i	−0.463130	+	0.961700i
$898$	−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
$902$	−26.9194	+	33.7558i	−0.896317	+	1.12395i
$903$	−2.92991	−	0.330122i	−0.0975013	−	0.0109858i
$904$	−39.4109	−	18.9793i	−1.31079	−	0.631242i
$905$	−11.0941	+	37.9793i	−0.368782	+	1.26247i
$906$	16.6513	−	20.8801i	0.553203	−	0.693694i
$907$	−37.8499	+	8.63900i	−1.25679	+	0.286853i	−0.798523	−	0.601964i	$-0.794385\pi$
$907$	−37.8499	+	8.63900i	−1.25679	+	0.286853i	−0.458262	+	0.888817i	$0.651528\pi$
$908$	−18.7041	−	11.7525i	−0.620716	−	0.390022i
$909$	−3.06886	+	27.2369i	−0.101788	+	0.903391i
$910$	−11.3150	+	7.96561i	−0.375090	+	0.264057i
$911$	42.3681	−	42.3681i	1.40372	−	1.40372i	0.615867	−	0.787850i	$-0.288806\pi$
$911$	42.3681	−	42.3681i	1.40372	−	1.40372i	0.787850	−	0.615867i	$-0.211194\pi$
$912$	6.71228	−	4.21761i	0.222266	−	0.139659i
$913$	35.5708	+	73.8635i	1.17722	+	2.44453i
$914$	−4.66615	−	1.63276i	−0.154343	−	0.0540068i
$915$	−24.7154	−	4.29356i	−0.817067	−	0.141941i
$916$	−4.05330	−	4.05330i	−0.133925	−	0.133925i
$917$	−19.9973	−	4.56424i	−0.660368	−	0.150725i
$918$	23.7048	−	18.9040i	0.782376	−	0.623924i
$919$	−35.7935	+	8.16963i	−1.18072	+	0.269491i	−0.767444	−	0.641115i	$-0.778472\pi$
$919$	−35.7935	+	8.16963i	−1.18072	+	0.269491i	−0.413274	+	0.910607i	$0.635615\pi$
$920$	−4.45409	−	15.6785i	−0.146847	−	0.516906i
$921$	−49.9374	−	39.8237i	−1.64549	−	1.31224i
$922$	−3.40991	+	9.74496i	−0.112299	+	0.320933i
$923$	−5.30854	−	15.1709i	−0.174733	−	0.499358i
$924$	18.2575	−	14.5598i	0.600627	−	0.478984i
$925$	−9.99252	+	15.6446i	−0.328552	+	0.514390i
$926$	−4.69781	+	1.64384i	−0.154380	+	0.0540198i
$927$	−28.5030	−	28.5030i	−0.936161	−	0.936161i
$928$	−7.21951	−	27.1351i	−0.236992	−	0.890753i
$929$			28.6797i			0.940951i	0.882413	+	0.470476i	$0.155918\pi$
$929$			28.6797i			0.940951i	−0.882413	+	0.470476i	$0.844082\pi$
$930$	9.49810	−	22.6924i	0.311455	−	0.744112i
$931$	18.9643	−	2.13676i	0.621530	−	0.0700296i
$932$	2.34128	−	20.7794i	0.0766912	−	0.680653i
$933$	85.4925	−	29.9151i	2.79890	−	0.979377i
$934$	3.99714	−	1.92492i	0.130790	−	0.0629854i
$935$	38.4302	−	53.7395i	1.25680	−	1.75747i
$936$	−58.1893	−	36.5628i	−1.90198	−	1.19509i
$937$	−11.0928	+	17.6540i	−0.362385	+	0.576732i	−0.977300	−	0.211861i	$-0.932048\pi$
$937$	−11.0928	+	17.6540i	−0.362385	+	0.576732i	0.614915	+	0.788594i	$0.289190\pi$
$938$	6.01290	+	7.53994i	0.196328	+	0.246188i
$939$	−38.6107	−	61.4485i	−1.26001	−	2.00530i
$940$	0.0487894	+	0.0439270i	0.00159134	+	0.00143274i
$941$	25.0472	+	5.71686i	0.816515	+	0.186364i	0.610328	−	0.792148i	$-0.291037\pi$
$941$	25.0472	+	5.71686i	0.816515	+	0.186364i	0.206187	+	0.978513i	$0.433895\pi$
$942$	−10.0263	+	4.82839i	−0.326673	+	0.157318i
$943$	17.8927	−	8.61666i	0.582666	−	0.280597i
$944$	−2.87963	−	0.657257i	−0.0937241	−	0.0213919i
$945$	18.3016	−	0.959813i	0.595349	−	0.0312227i
$946$	2.11295	+	3.36275i	0.0686980	+	0.109332i
$947$	35.0919	+	44.0039i	1.14033	+	1.42993i	0.886526	+	0.462680i	$0.153112\pi$
$947$	35.0919	+	44.0039i	1.14033	+	1.42993i	0.253809	+	0.967254i	$0.418317\pi$
$948$	15.1184	−	24.0607i	0.491021	−	0.781456i
$949$	12.4219	+	7.80519i	0.403232	+	0.253367i
$950$	17.8601	−	3.93749i	0.579457	−	0.127749i
$951$	−60.7902	+	29.2750i	−1.97126	+	0.949307i
$952$	−20.9019	+	7.31391i	−0.677436	+	0.237045i
$953$	−1.11505	+	9.89638i	−0.0361202	+	0.320575i	0.962640	+	0.270786i	$0.0872836\pi$
$953$	−1.11505	+	9.89638i	−0.0361202	+	0.320575i	−0.998760	+	0.0497894i	$0.984145\pi$
$954$	8.46626	−	0.953919i	0.274105	−	0.0308843i
$955$	47.3801	+	19.8314i	1.53318	+	0.641728i
$956$			10.3865i			0.335925i
$957$	−57.6048	+	61.8638i	−1.86210	+	1.99977i
$958$	−21.3718	−	21.3718i	−0.690493	−	0.690493i
$959$	8.65204	−	3.02748i	0.279389	−	0.0977624i
$960$	40.8417	−	6.78376i	1.31816	−	0.218945i
$961$	11.6958	−	9.32706i	0.377283	−	0.300873i
$962$	5.42939	+	15.5163i	0.175050	+	0.500265i
$963$	19.0481	−	54.4365i	0.613818	−	1.75419i
$964$	16.7681	+	13.3721i	0.540065	+	0.430688i
$965$	14.7993	−	26.5446i	0.476406	−	0.854501i
$966$	9.20440	−	2.10084i	0.296147	−	0.0675935i
$967$	−27.7417	+	22.1233i	−0.892114	+	0.711437i	−0.958115	−	0.286383i	$-0.907547\pi$
$967$	−27.7417	+	22.1233i	−0.892114	+	0.711437i	0.0660016	+	0.997820i	$0.478976\pi$
$968$	−56.4989	−	12.8955i	−1.81594	−	0.414477i
$969$	−40.5925	−	40.5925i	−1.30402	−	1.30402i
$970$	−15.5593	+	10.9535i	−0.499580	+	0.351696i
$971$	−21.6352	−	7.57047i	−0.694306	−	0.242948i	−0.0400236	−	0.999199i	$-0.512743\pi$
$971$	−21.6352	−	7.57047i	−0.694306	−	0.242948i	−0.654282	+	0.756251i	$0.727029\pi$
$972$	−6.21171	−	12.8987i	−0.199241	−	0.413727i
$973$	−5.41320	+	3.40134i	−0.173539	+	0.109042i
$974$	3.56904	−	3.56904i	0.114359	−	0.114359i
$975$	−40.1490	−	51.1175i	−1.28580	−	1.63707i
$976$	0.326490	−	2.89768i	0.0104507	−	0.0927524i
$977$	−0.884054	−	0.555488i	−0.0282834	−	0.0177716i	0.517816	−	0.855492i	$-0.326745\pi$
$977$	−0.884054	−	0.555488i	−0.0282834	−	0.0177716i	−0.546100	+	0.837720i	$0.683888\pi$
$978$	15.7854	−	3.60292i	0.504762	−	0.115209i
$979$	−47.2438	+	59.2419i	−1.50992	+	1.89338i
$980$	11.5296	+	3.36793i	0.368301	+	0.107585i
$981$	32.0021	+	15.4114i	1.02175	+	0.492048i
$982$	2.24751	+	0.253233i	0.0717209	+	0.00808100i
$983$	−16.0672	+	20.1477i	−0.512465	+	0.642611i	−0.968990	−	0.247100i	$-0.920522\pi$
$983$	−16.0672	+	20.1477i	−0.512465	+	0.642611i	0.456525	+	0.889710i	$0.349094\pi$
$984$	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
$988$	−7.99479	+	16.6014i	−0.254348	+	0.528159i
$989$	−0.204532	−	1.81528i	−0.00650375	−	0.0577224i
$990$	−40.1797	−	45.2976i	−1.27699	−	1.43965i
$991$	−10.0068	+	20.7794i	−0.317877	+	0.660078i	−0.997282	−	0.0736856i	$-0.976524\pi$
$991$	−10.0068	+	20.7794i	−0.317877	+	0.660078i	0.679405	+	0.733764i	$0.262238\pi$
$992$	−19.7111	−	6.89723i	−0.625830	−	0.218987i
$993$	2.77399	−	0.312553i	0.0880299	−	0.00991858i
$994$	−2.52539	+	4.01914i	−0.0801005	+	0.127479i
$995$	−12.3641	+	22.1767i	−0.391967	+	0.703048i
$996$	44.5532	+	5.01994i	1.41172	+	0.159063i
$997$	−1.39888	+	6.12892i	−0.0443031	+	0.194105i	−0.992237	−	0.124363i	$-0.960311\pi$
$997$	−1.39888	+	6.12892i	−0.0443031	+	0.194105i	0.947934	+	0.318468i	$0.103168\pi$
$998$	−21.8358			−0.691199
$999$	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.o.a.18.9	✓	156
5.2	odd	4		145.2.t.a.47.5	yes	156
5.3	odd	4		725.2.bd.b.482.9		156
5.4	even	2		725.2.y.b.18.5		156
29.21	odd	28		145.2.t.a.108.5	yes	156
145.79	odd	28		725.2.bd.b.543.9		156
145.108	even	28		725.2.y.b.282.5		156
145.137	even	28	inner	145.2.o.a.137.9	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.9	✓	156	1.1	even	1	trivial
145.2.o.a.137.9	yes	156	145.137	even	28	inner
145.2.t.a.47.5	yes	156	5.2	odd	4
145.2.t.a.108.5	yes	156	29.21	odd	28
725.2.y.b.18.5		156	5.4	even	2
725.2.y.b.282.5		156	145.108	even	28
725.2.bd.b.482.9		156	5.3	odd	4
725.2.bd.b.543.9		156	145.79	odd	28

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.o (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.871464 + 0.419675i) q^{2} +(2.22031 + 1.77064i) q^{3} +(-0.663657 - 0.832199i) q^{4} +(-2.06901 + 0.848049i) q^{5} +(1.19183 + 2.47485i) q^{6} +(0.156487 + 1.38886i) q^{7} +(-0.659568 - 2.88975i) q^{8} +(1.12705 + 4.93793i) q^{9} +(-2.15898 - 0.129268i) q^{10} +(4.68013 - 2.94072i) q^{11} -3.02283i q^{12} +(-2.43545 - 3.87599i) q^{13} +(-0.446497 + 1.27601i) q^{14} +(-6.09543 - 1.78054i) q^{15} +(0.164256 - 0.719651i) q^{16} -5.34543 q^{17} +(-1.09014 + 4.77622i) q^{18} +(3.75785 + 0.423408i) q^{19} +(2.07886 + 1.15902i) q^{20} +(-2.11171 + 3.36077i) q^{21} +(5.31271 - 0.598599i) q^{22} +(-2.32115 - 0.812207i) q^{23} +(3.65226 - 7.58400i) q^{24} +(3.56162 - 3.50925i) q^{25} +(-0.495748 - 4.39988i) q^{26} +(-2.54434 + 5.28338i) 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} +(-3.25097 + 4.07659i) q^{32} +(15.5983 + 1.75750i) q^{33} +(-4.65835 - 2.24334i) q^{34} +(-1.50159 - 2.74086i) q^{35} +(3.36136 - 4.21502i) q^{36} +(-3.61961 + 0.826152i) q^{37} +(3.09714 + 1.94606i) q^{38} +(1.45553 - 12.9182i) q^{39} +(3.81531 + 5.41959i) q^{40} +(-5.71038 + 5.71038i) q^{41} +(-3.25072 + 2.04256i) q^{42} +(0.322307 + 0.669277i) q^{43} +(-5.55327 - 1.94317i) q^{44} +(-6.51948 - 9.26084i) q^{45} +(-1.68194 - 1.68194i) q^{46} +(0.0268913 + 0.00613776i) q^{47} +(1.63894 - 1.30701i) q^{48} +(4.92005 - 1.12297i) q^{49} +(4.57657 - 1.56346i) q^{50} +(-11.8685 - 9.46480i) q^{51} +(-1.60930 + 4.59910i) q^{52} +(-0.574381 - 1.64149i) q^{53} +(-4.43460 + 3.53648i) q^{54} +(-7.18937 + 10.0534i) q^{55} +(3.91025 - 1.36826i) q^{56} +(7.59388 + 7.59388i) q^{57} +(-4.60948 + 2.42578i) q^{58} -4.00143i q^{59} +(2.56351 + 6.25428i) q^{60} +(3.92555 - 0.442303i) q^{61} +(-0.433740 + 3.84955i) q^{62} +(-6.68171 + 2.33803i) q^{63} +(-5.87407 + 2.82880i) q^{64} +(8.32600 + 5.95409i) q^{65} +(12.8558 + 8.07781i) q^{66} +(3.79538 - 6.04031i) q^{67} +(3.54753 + 4.44846i) q^{68} +(-3.71555 - 5.91327i) q^{69} +(-0.158316 - 3.01874i) q^{70} +(3.42315 + 0.781312i) q^{71} +(13.5260 - 6.51379i) q^{72} +(-2.88745 + 1.39052i) q^{73} +(-3.50108 - 0.799098i) q^{74} +(14.1215 - 1.48527i) q^{75} +(-2.14156 - 3.40828i) q^{76} +(4.81662 + 6.03986i) q^{77} +(6.68988 - 10.6469i) q^{78} +(7.95966 + 5.00139i) q^{79} +(0.270453 + 1.62826i) q^{80} +(-1.31416 + 0.632868i) q^{81} +(-7.37289 + 2.57989i) q^{82} +(-1.66068 + 14.7389i) q^{83} +(4.19829 - 0.473033i) q^{84} +(11.0598 - 4.53318i) q^{85} +0.718515i q^{86} +(-14.7791 + 3.93209i) q^{87} +(-11.5848 - 11.5848i) q^{88} +(-12.9395 + 4.52773i) q^{89} +(-1.79496 - 10.8066i) q^{90} +(5.00209 - 3.98903i) q^{91} +(0.864532 + 2.47069i) q^{92} +(-3.75656 + 10.7356i) q^{93} +(0.0208589 + 0.0166344i) q^{94} +(-8.13411 + 2.31081i) q^{95} +(-14.4363 + 3.29499i) q^{96} +(6.87837 - 5.48532i) q^{97} +(4.75893 + 1.08620i) q^{98} +(19.7958 + 19.7958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 8 q^{2} - 14 q^{3} - 22 q^{4} - 14 q^{5} - 28 q^{6} - 10 q^{7} + 4 q^{8} + 10 q^{9} - 8 q^{10} - 20 q^{11} + 4 q^{14} - 24 q^{15} - 34 q^{16} - 48 q^{17} - 94 q^{18} + 6 q^{20} - 16 q^{21} - 6 q^{22}+ \cdots + 76 q^{99}+O(q^{100}) \) 156 * q - 8 * q^2 - 14 * q^3 - 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 + 4 * q^8 + 10 * q^9 - 8 * q^10 - 20 * q^11 + 4 * q^14 - 24 * q^15 - 34 * q^16 - 48 * q^17 - 94 * q^18 + 6 * q^20 - 16 * q^21 - 6 * q^22 - 10 * q^23 + 56 * q^24 + 60 * q^25 + 36 * q^26 - 56 * q^27 + 8 * q^28 - 44 * q^30 - 8 * q^31 + 28 * q^32 - 14 * q^33 - 24 * q^34 - 54 * q^35 + 78 * q^36 + 28 * q^37 + 92 * q^38 + 16 * q^39 + 8 * q^40 - 22 * q^41 - 10 * q^42 - 42 * q^43 - 112 * q^44 + 30 * q^45 + 4 * q^46 - 14 * q^47 + 154 * q^48 + 84 * q^49 + 34 * q^50 - 28 * q^51 - 166 * q^52 + 14 * q^53 - 20 * q^55 + 4 * q^56 + 12 * q^57 + 126 * q^58 - 138 * q^60 - 46 * q^61 + 84 * q^62 + 38 * q^63 - 30 * q^64 + 4 * q^65 - 48 * q^66 - 46 * q^67 - 44 * q^68 - 124 * q^69 - 86 * q^70 - 28 * q^71 + 60 * q^72 + 130 * q^73 + 112 * q^74 + 50 * q^75 - 48 * q^76 - 44 * q^77 - 210 * q^78 - 4 * q^79 + 194 * q^80 + 58 * q^81 + 72 * q^82 + 46 * q^83 + 120 * q^84 + 56 * q^85 - 144 * q^87 + 40 * q^88 + 46 * q^89 + 82 * q^90 - 28 * q^91 - 14 * q^92 - 6 * q^93 - 84 * q^94 - 74 * q^95 - 28 * q^96 + 154 * q^97 + 98 * q^98 + 76 * q^99

Introduction

L-functions

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