LMFDB - Embedded newform 216.2.v.b.59.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(11,216)] 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("216.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.32
Character	$\chi$	$=$	216.59
Dual form			216.2.v.b.11.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41380 - 0.0343398i) q^{2} +(1.40807 + 1.00863i) q^{3} +(1.99764 - 0.0970990i) q^{4} +(-2.25586 + 0.821067i) q^{5} +(2.02536 + 1.37765i) q^{6} +(-1.95474 + 0.344674i) q^{7} +(2.82092 - 0.205877i) q^{8} +(0.965315 + 2.84045i) q^{9} +(-3.16114 + 1.23829i) q^{10} +(0.553700 - 1.52128i) q^{11} +(2.91075 + 1.87817i) q^{12} +(3.57715 - 4.26309i) q^{13} +(-2.75177 + 0.554424i) q^{14} +(-4.00457 - 1.11922i) q^{15} +(3.98114 - 0.387938i) q^{16} +(-6.40600 - 3.69851i) q^{17} +(1.46230 + 3.98267i) q^{18} +(-1.39557 - 2.41719i) q^{19} +(-4.42668 + 1.85924i) q^{20} +(-3.10006 - 1.48630i) q^{21} +(0.730579 - 2.16979i) q^{22} +(-0.465506 + 2.64002i) q^{23} +(4.17971 + 2.55539i) q^{24} +(0.584547 - 0.490493i) q^{25} +(4.91098 - 6.14998i) q^{26} +(-1.50575 + 4.97320i) q^{27} +(-3.87141 + 0.878338i) q^{28} +(-0.138481 + 0.116199i) q^{29} +(-5.70008 - 1.44484i) q^{30} +(1.76926 + 0.311969i) q^{31} +(5.61521 - 0.685177i) q^{32} +(2.31406 - 1.58358i) q^{33} +(-9.18379 - 5.00895i) q^{34} +(4.12663 - 2.38251i) q^{35} +(2.20416 + 5.58047i) q^{36} +(-3.55469 - 2.05230i) q^{37} +(-2.05606 - 3.36950i) q^{38} +(9.33677 - 2.39468i) q^{39} +(-6.19458 + 2.78060i) q^{40} +(-2.85334 + 3.40048i) q^{41} +(-4.43390 - 1.99486i) q^{42} +(11.1139 + 4.04511i) q^{43} +(0.958380 - 3.09273i) q^{44} +(-4.50982 - 5.61508i) q^{45} +(-0.567474 + 3.74843i) q^{46} +(2.08588 + 11.8296i) q^{47} +(5.99701 + 3.46927i) q^{48} +(-2.87563 + 1.04664i) q^{49} +(0.809587 - 0.713530i) q^{50} +(-5.28965 - 11.6691i) q^{51} +(6.73193 - 8.86346i) q^{52} -10.1087 q^{53} +(-1.95804 + 7.08280i) q^{54} +3.88642i q^{55} +(-5.44322 + 1.37474i) q^{56} +(0.473009 - 4.81119i) q^{57} +(-0.191794 + 0.169038i) q^{58} +(-1.96718 - 5.40478i) q^{59} +(-8.10836 - 1.84696i) q^{60} +(7.60780 - 1.34146i) q^{61} +(2.51209 + 0.380305i) q^{62} +(-2.86597 - 5.21963i) q^{63} +(7.91523 - 1.16153i) q^{64} +(-4.56929 + 12.5540i) q^{65} +(3.21723 - 2.31833i) q^{66} +(1.38817 + 1.16481i) q^{67} +(-13.1560 - 6.76627i) q^{68} +(-3.31828 + 3.24780i) q^{69} +(5.75240 - 3.51010i) q^{70} +(-1.25119 + 2.16713i) q^{71} +(3.30786 + 7.81396i) q^{72} +(-3.79038 - 6.56514i) q^{73} +(-5.09608 - 2.77947i) q^{74} +(1.31781 - 0.101054i) q^{75} +(-3.02255 - 4.69318i) q^{76} +(-0.557996 + 3.16455i) q^{77} +(13.1181 - 3.70621i) q^{78} +(6.77140 + 8.06984i) q^{79} +(-8.66239 + 4.14392i) q^{80} +(-7.13633 + 5.48386i) q^{81} +(-3.91727 + 4.90557i) q^{82} +(0.718131 + 0.855836i) q^{83} +(-6.33713 - 2.66807i) q^{84} +(17.4878 + 3.08357i) q^{85} +(15.8516 + 5.33732i) q^{86} +(-0.312194 + 0.0239400i) q^{87} +(1.24875 - 4.40541i) q^{88} +(9.87804 - 5.70309i) q^{89} +(-6.56879 - 7.78372i) q^{90} +(-5.52304 + 9.56619i) q^{91} +(-0.673572 + 5.31901i) q^{92} +(2.17658 + 2.22381i) q^{93} +(3.35523 + 16.6530i) q^{94} +(5.13289 + 4.30701i) q^{95} +(8.59769 + 4.69891i) q^{96} +(-5.25587 - 1.91298i) q^{97} +(-4.02961 + 1.57849i) q^{98} +(4.85561 + 0.104246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	1.41380	−	0.0343398i	0.999705	−	0.0242819i
$2$	1.41380	−	0.0343398i	0.999705	−	0.0242819i
$3$	1.40807	+	1.00863i	0.812949	+	0.582335i
$3$	1.40807	+	1.00863i	0.812949	+	0.582335i
$4$	1.99764	−	0.0970990i	0.998821	−	0.0485495i
$5$	−2.25586	+	0.821067i	−1.00885	+	0.367192i	−0.792992	−	0.609232i	$-0.791478\pi$
$5$	−2.25586	+	0.821067i	−1.00885	+	0.367192i	−0.215861	+	0.976424i	$0.569256\pi$
$6$	2.02536	+	1.37765i	0.826849	+	0.562423i
$7$	−1.95474	+	0.344674i	−0.738823	+	0.130274i	−0.530380	−	0.847760i	$-0.677951\pi$
$7$	−1.95474	+	0.344674i	−0.738823	+	0.130274i	−0.208443	+	0.978034i	$0.566840\pi$
$8$	2.82092	−	0.205877i	0.997347	−	0.0727884i
$9$	0.965315	+	2.84045i	0.321772	+	0.946817i
$10$	−3.16114	+	1.23829i	−0.999639	+	0.391581i
$11$	0.553700	−	1.52128i	0.166947	−	0.458683i	−0.827803	−	0.561019i	$-0.810410\pi$
$11$	0.553700	−	1.52128i	0.166947	−	0.458683i	0.994750	+	0.102336i	$0.0326317\pi$
$12$	2.91075	+	1.87817i	0.840262	+	0.542180i
$13$	3.57715	−	4.26309i	0.992124	−	1.18237i	0.00890108	−	0.999960i	$-0.497167\pi$
$13$	3.57715	−	4.26309i	0.992124	−	1.18237i	0.983223	−	0.182407i	$-0.0583889\pi$
$14$	−2.75177	+	0.554424i	−0.735442	+	0.148176i
$15$	−4.00457	−	1.11922i	−1.03397	−	0.288982i
$16$	3.98114	−	0.387938i	0.995286	−	0.0969845i
$17$	−6.40600	−	3.69851i	−1.55368	−	0.897020i	−0.997837	−	0.0657345i	$-0.979061\pi$
$17$	−6.40600	−	3.69851i	−1.55368	−	0.897020i	−0.555846	−	0.831285i	$-0.687606\pi$
$18$	1.46230	+	3.98267i	0.344667	+	0.938725i
$19$	−1.39557	−	2.41719i	−0.320165	−	0.554543i	0.660357	−	0.750952i	$-0.270405\pi$
$19$	−1.39557	−	2.41719i	−0.320165	−	0.554543i	−0.980522	+	0.196410i	$0.937072\pi$
$20$	−4.42668	+	1.85924i	−0.989836	+	0.415739i
$21$	−3.10006	−	1.48630i	−0.676489	−	0.324336i
$22$	0.730579	−	2.16979i	0.155760	−	0.462601i
$23$	−0.465506	+	2.64002i	−0.0970648	+	0.550482i	0.897030	+	0.441969i	$0.145720\pi$
$23$	−0.465506	+	2.64002i	−0.0970648	+	0.550482i	−0.994095	+	0.108513i	$0.965391\pi$
$24$	4.17971	+	2.55539i	0.853180	+	0.521617i
$25$	0.584547	−	0.490493i	0.116909	−	0.0980986i
$26$	4.91098	−	6.14998i	0.963122	−	1.20611i
$27$	−1.50575	+	4.97320i	−0.289781	+	0.957093i
$28$	−3.87141	+	0.878338i	−0.731627	+	0.165990i
$29$	−0.138481	+	0.116199i	−0.0257153	+	0.0215777i	−0.655555	−	0.755148i	$-0.727565\pi$
$29$	−0.138481	+	0.116199i	−0.0257153	+	0.0215777i	0.629839	+	0.776725i	$0.283121\pi$
$30$	−5.70008	−	1.44484i	−1.04069	−	0.263790i
$31$	1.76926	+	0.311969i	0.317769	+	0.0560313i	0.330258	−	0.943891i	$-0.392864\pi$
$31$	1.76926	+	0.311969i	0.317769	+	0.0560313i	−0.0124887	+	0.999922i	$0.503975\pi$
$32$	5.61521	−	0.685177i	0.992637	−	0.121123i
$33$	2.31406	−	1.58358i	0.402826	−	0.275667i
$34$	−9.18379	−	5.00895i	−1.57501	−	0.859029i
$35$	4.12663	−	2.38251i	0.697528	−	0.402718i
$36$	2.20416	+	5.58047i	0.367360	+	0.930079i
$37$	−3.55469	−	2.05230i	−0.584387	−	0.337396i	0.178488	−	0.983942i	$-0.442880\pi$
$37$	−3.55469	−	2.05230i	−0.584387	−	0.337396i	−0.762875	+	0.646546i	$0.776213\pi$
$38$	−2.05606	−	3.36950i	−0.333536	−	0.546605i
$39$	9.33677	−	2.39468i	1.49508	−	0.383456i
$40$	−6.19458	+	2.78060i	−0.979449	+	0.439651i
$41$	−2.85334	+	3.40048i	−0.445617	+	0.531066i	−0.941360	−	0.337404i	$-0.890451\pi$
$41$	−2.85334	+	3.40048i	−0.445617	+	0.531066i	0.495743	+	0.868469i	$0.334896\pi$
$42$	−4.43390	−	1.99486i	−0.684165	−	0.307814i
$43$	11.1139	+	4.04511i	1.69485	+	0.616874i	0.995222	−	0.0976364i	$-0.0311282\pi$
$43$	11.1139	+	4.04511i	1.69485	+	0.616874i	0.699625	+	0.714510i	$0.253350\pi$
$44$	0.958380	−	3.09273i	0.144481	−	0.466247i
$45$	−4.50982	−	5.61508i	−0.672284	−	0.837047i
$46$	−0.567474	+	3.74843i	−0.0836694	+	0.552676i
$47$	2.08588	+	11.8296i	0.304257	+	1.72552i	0.626983	+	0.779033i	$0.284289\pi$
$47$	2.08588	+	11.8296i	0.304257	+	1.72552i	−0.322727	+	0.946492i	$0.604599\pi$
$48$	5.99701	+	3.46927i	0.865594	+	0.500746i
$49$	−2.87563	+	1.04664i	−0.410804	+	0.149520i
$50$	0.809587	−	0.713530i	0.114493	−	0.100908i
$51$	−5.28965	−	11.6691i	−0.740699	−	1.63400i
$52$	6.73193	−	8.86346i	0.933551	−	1.22914i
$53$	−10.1087			−1.38854			−0.694271	−	0.719714i	$-0.744273\pi$
$53$	−10.1087			−1.38854			−0.694271	+	0.719714i	$0.744273\pi$
$54$	−1.95804	+	7.08280i	−0.266456	+	0.963847i
$55$			3.88642i			0.524045i
$56$	−5.44322	+	1.37474i	−0.727381	+	0.183707i
$57$	0.473009	−	4.81119i	0.0626516	−	0.637258i
$58$	−0.191794	+	0.169038i	−0.0251838	+	0.0221957i
$59$	−1.96718	−	5.40478i	−0.256105	−	0.703642i	−0.999399	−	0.0346769i	$-0.988960\pi$
$59$	−1.96718	−	5.40478i	−0.256105	−	0.703642i	0.743294	−	0.668965i	$-0.233262\pi$
$60$	−8.10836	−	1.84696i	−1.04679	−	0.238442i
$61$	7.60780	−	1.34146i	0.974079	−	0.171756i	0.336113	−	0.941822i	$-0.390887\pi$
$61$	7.60780	−	1.34146i	0.974079	−	0.171756i	0.637965	+	0.770065i	$0.279776\pi$
$62$	2.51209	+	0.380305i	0.319036	+	0.0482987i
$63$	−2.86597	−	5.21963i	−0.361079	−	0.657612i
$64$	7.91523	−	1.16153i	0.989404	−	0.145191i
$65$	−4.56929	+	12.5540i	−0.566751	+	1.55714i
$66$	3.21723	−	2.31833i	0.396014	−	0.285367i
$67$	1.38817	+	1.16481i	0.169592	+	0.142305i	0.723633	−	0.690184i	$-0.242471\pi$
$67$	1.38817	+	1.16481i	0.169592	+	0.142305i	−0.554041	+	0.832489i	$0.686915\pi$
$68$	−13.1560	−	6.76627i	−1.59540	−	0.820531i
$69$	−3.31828	+	3.24780i	−0.399474	+	0.390989i
$70$	5.75240	−	3.51010i	0.687544	−	0.419537i
$71$	−1.25119	+	2.16713i	−0.148489	+	0.257191i	−0.930669	−	0.365862i	$-0.880774\pi$
$71$	−1.25119	+	2.16713i	−0.148489	+	0.257191i	0.782180	+	0.623052i	$0.214108\pi$
$72$	3.30786	+	7.81396i	0.389835	+	0.920885i
$73$	−3.79038	−	6.56514i	−0.443631	−	0.768391i	0.554325	−	0.832300i	$-0.312976\pi$
$73$	−3.79038	−	6.56514i	−0.443631	−	0.768391i	−0.997956	+	0.0639093i	$0.979643\pi$
$74$	−5.09608	−	2.77947i	−0.592408	−	0.323107i
$75$	1.31781	−	0.101054i	0.152168	−	0.0116687i
$76$	−3.02255	−	4.69318i	−0.346710	−	0.538345i
$77$	−0.557996	+	3.16455i	−0.0635896	+	0.360634i
$78$	13.1181	−	3.70621i	1.48533	−	0.419646i
$79$	6.77140	+	8.06984i	0.761842	+	0.907928i	0.997963	−	0.0637957i	$-0.0203206\pi$
$79$	6.77140	+	8.06984i	0.761842	+	0.907928i	−0.236121	+	0.971724i	$0.575876\pi$
$80$	−8.66239	+	4.14392i	−0.968485	+	0.463304i
$81$	−7.13633	+	5.48386i	−0.792926	+	0.609318i
$82$	−3.91727	+	4.90557i	−0.432590	+	0.541729i
$83$	0.718131	+	0.855836i	0.0788251	+	0.0939402i	0.804016	−	0.594608i	$-0.202693\pi$
$83$	0.718131	+	0.855836i	0.0788251	+	0.0939402i	−0.725191	+	0.688548i	$0.758248\pi$
$84$	−6.33713	−	2.66807i	−0.691438	−	0.291111i
$85$	17.4878	+	3.08357i	1.89682	+	0.334460i
$86$	15.8516	+	5.33732i	1.70933	+	0.575538i
$87$	−0.312194	+	0.0239400i	−0.0334707	+	0.00256664i
$88$	1.24875	−	4.40541i	0.133117	−	0.469618i
$89$	9.87804	−	5.70309i	1.04707	−	0.604526i	0.125243	−	0.992126i	$-0.460029\pi$
$89$	9.87804	−	5.70309i	1.04707	−	0.604526i	0.921828	+	0.387600i	$0.126696\pi$
$90$	−6.56879	−	7.78372i	−0.692411	−	0.820476i
$91$	−5.52304	+	9.56619i	−0.578972	+	1.00281i
$92$	−0.673572	+	5.31901i	−0.0702247	+	0.554545i
$93$	2.17658	+	2.22381i	0.225701	+	0.230599i
$94$	3.35523	+	16.6530i	0.346066	+	1.71763i
$95$	5.13289	+	4.30701i	0.526623	+	0.441890i
$96$	8.59769	+	4.69891i	0.877498	+	0.479581i
$97$	−5.25587	−	1.91298i	−0.533652	−	0.194234i	0.0611161	−	0.998131i	$-0.480534\pi$
$97$	−5.25587	−	1.91298i	−0.533652	−	0.194234i	−0.594768	+	0.803897i	$0.702756\pi$
$98$	−4.02961	+	1.57849i	−0.407052	+	0.159451i
$99$	4.85561	+	0.104246i	0.488007	+	0.0104771i
$100$	1.12009	−	1.03659i	0.112009	−	0.103659i
$101$	−1.90061	−	10.7789i	−0.189117	−	1.07254i	−0.920550	−	0.390624i	$-0.872259\pi$
$101$	−1.90061	−	10.7789i	−0.189117	−	1.07254i	0.731433	−	0.681913i	$-0.238852\pi$
$102$	−7.87920	−	16.3160i	−0.780157	−	1.61553i
$103$	−5.15163	−	14.1540i	−0.507605	−	1.39463i	−0.883701	−	0.468053i	$-0.844956\pi$
$103$	−5.15163	−	14.1540i	−0.507605	−	1.39463i	0.376095	−	0.926581i	$-0.377266\pi$
$104$	9.21321	−	12.7623i	0.903430	−	1.25145i
$105$	8.21367	+	0.807521i	0.801572	+	0.0788059i
$106$	−14.2917	+	0.347132i	−1.38813	+	0.0337164i
$107$			1.83241i			0.177146i	0.996070	+	0.0885728i	$0.0282306\pi$
$107$			1.83241i			0.177146i	−0.996070	+	0.0885728i	$0.971769\pi$
$108$	−2.52505	+	10.0809i	−0.242973	+	0.970033i
$109$		−	2.84696i		−	0.272689i	−0.990661	−	0.136345i	$-0.956465\pi$
$109$		−	2.84696i		−	0.272689i	0.990661	−	0.136345i	$-0.0435355\pi$
$110$	0.133459	+	5.49461i	0.0127248	+	0.523890i
$111$	−2.93523	−	6.47516i	−0.278599	−	0.614595i
$112$	−7.64840	+	2.13052i	−0.722706	+	0.201315i
$113$	4.14703	+	11.3939i	0.390120	+	1.07185i	0.966946	+	0.254980i	$0.0820688\pi$
$113$	4.14703	+	11.3939i	0.390120	+	1.07185i	−0.576826	+	0.816867i	$0.695709\pi$
$114$	0.503523	−	6.81829i	0.0471593	−	0.638592i
$115$	−1.11751	−	6.33773i	−0.104209	−	0.590997i
$116$	−0.265353	+	0.245571i	−0.0246374	+	0.0228007i
$117$	15.5622	+	6.04551i	1.43872	+	0.558908i
$118$	−2.96679	−	7.57370i	−0.273115	−	0.697216i
$119$	13.7969	+	5.02165i	1.26476	+	0.460334i
$120$	−11.5270	−	2.33279i	−1.05227	−	0.212954i
$121$	6.41878	+	5.38600i	0.583526	+	0.489636i
$122$	10.7098	−	2.15780i	0.969621	−	0.195358i
$123$	−7.44754	+	1.91013i	−0.671522	+	0.172231i
$124$	3.56465	+	0.451408i	0.320115	+	0.0405377i
$125$	5.08567	−	8.80864i	0.454876	−	0.787869i
$126$	−4.23114	−	7.28108i	−0.376940	−	0.648651i
$127$	0.655158	−	0.378256i	0.0581359	−	0.0335648i	−0.470650	−	0.882320i	$-0.655981\pi$
$127$	0.655158	−	0.378256i	0.0581359	−	0.0335648i	0.528786	+	0.848755i	$0.322647\pi$
$128$	11.1506	−	1.91397i	0.985586	−	0.169173i
$129$	11.5690	+	16.9056i	1.01860	+	1.48846i
$130$	−6.02895	+	17.9057i	−0.528774	+	1.57044i
$131$	3.17397	+	0.559656i	0.277311	+	0.0488974i	0.310574	−	0.950549i	$-0.399479\pi$
$131$	3.17397	+	0.559656i	0.277311	+	0.0488974i	−0.0332631	+	0.999447i	$0.510590\pi$
$132$	4.46890	−	3.38813i	0.388968	−	0.294899i
$133$	3.56112	+	4.24398i	0.308788	+	0.368000i
$134$	2.00259	+	1.59914i	0.172998	+	0.138145i
$135$	−0.686573	−	12.4552i	−0.0590908	−	1.07197i
$136$	−18.8323	−	9.11436i	−1.61485	−	0.781550i
$137$	−6.88493	−	8.20513i	−0.588219	−	0.701012i	0.387044	−	0.922061i	$-0.373496\pi$
$137$	−6.88493	−	8.20513i	−0.588219	−	0.701012i	−0.975263	+	0.221049i	$0.929052\pi$
$138$	−4.57984	+	4.70568i	−0.389862	+	0.400574i
$139$	−3.48804	+	19.7816i	−0.295851	+	1.67786i	0.367870	+	0.929877i	$0.380087\pi$
$139$	−3.48804	+	19.7816i	−0.295851	+	1.67786i	−0.663722	+	0.747980i	$0.731024\pi$
$140$	8.01219	−	5.16010i	0.677154	−	0.436108i
$141$	−8.99468	+	18.7608i	−0.757489	+	1.57994i
$142$	−1.69451	+	3.10684i	−0.142200	+	0.260720i
$143$	−4.50467	−	7.80232i	−0.376700	−	0.652463i
$144$	4.94498	+	10.9338i	0.412081	+	0.911147i
$145$	0.216987	−	0.375832i	0.0180198	−	0.0312112i
$146$	−5.58428	−	9.15161i	−0.462158	−	0.757392i
$147$	−5.10476	−	1.42671i	−0.421034	−	0.117673i
$148$	−7.30027	−	3.75460i	−0.600079	−	0.308627i
$149$	10.3687	+	8.70041i	0.849441	+	0.712765i	0.959666	−	0.281141i	$-0.0907130\pi$
$149$	10.3687	+	8.70041i	0.849441	+	0.712765i	−0.110226	+	0.993907i	$0.535157\pi$
$150$	1.85964	−	0.188123i	0.151839	−	0.0153602i
$151$	−3.05584	+	8.39584i	−0.248680	+	0.683244i	0.751055	+	0.660240i	$0.229545\pi$
$151$	−3.05584	+	8.39584i	−0.248680	+	0.683244i	−0.999735	+	0.0230040i	$0.992677\pi$
$152$	−4.43444	−	6.53141i	−0.359680	−	0.529767i
$153$	4.32162	−	21.7662i	0.349382	−	1.75969i
$154$	−0.680223	+	4.49320i	−0.0548139	+	0.362072i
$155$	−4.24737	+	0.748925i	−0.341157	+	0.0601551i
$156$	18.4190	−	5.69030i	1.47470	−	0.455589i
$157$	2.25685	+	6.20065i	0.180116	+	0.494866i	0.996590	−	0.0825175i	$-0.0262960\pi$
$157$	2.25685	+	6.20065i	0.180116	+	0.494866i	−0.816473	+	0.577383i	$0.804074\pi$
$158$	9.85050	+	11.1766i	0.783664	+	0.889161i
$159$	−14.2338	−	10.1960i	−1.12881	−	0.808597i
$160$	−12.1046	+	6.15613i	−0.956950	+	0.486685i
$161$		−	5.32100i		−	0.419354i
$162$	−9.90101	+	7.99812i	−0.777897	+	0.628392i
$163$	2.05597			0.161036			0.0805178	−	0.996753i	$-0.474343\pi$
$163$	2.05597			0.161036			0.0805178	+	0.996753i	$0.474343\pi$
$164$	−5.36977	+	7.07000i	−0.419309	+	0.552074i
$165$	−3.91998	+	5.47235i	−0.305170	+	0.426022i
$166$	1.04468	+	1.18532i	0.0810830	+	0.0919984i
$167$	−4.05523	+	1.47598i	−0.313803	+	0.114215i	−0.494120	−	0.869394i	$-0.664510\pi$
$167$	−4.05523	+	1.47598i	−0.313803	+	0.114215i	0.180317	+	0.983608i	$0.442288\pi$
$168$	−9.05103	−	3.55450i	−0.698302	−	0.274235i
$169$	−3.12045	−	17.6969i	−0.240034	−	1.36130i
$170$	24.8301	+	3.75901i	1.90438	+	0.288303i
$171$	5.51876	−	6.29740i	0.422030	−	0.481574i
$172$	22.5943	+	7.00154i	1.72280	+	0.533863i
$173$	3.48473	+	1.26834i	0.264939	+	0.0964298i	0.471074	−	0.882094i	$-0.343866\pi$
$173$	3.48473	+	1.26834i	0.264939	+	0.0964298i	−0.206135	+	0.978524i	$0.566089\pi$
$174$	−0.440556	+	0.0445670i	−0.0333985	+	0.00337862i
$175$	−0.973578	+	1.16027i	−0.0735956	+	0.0877078i
$176$	1.61420	−	6.27123i	0.121675	−	0.472712i
$177$	2.68152	−	9.59446i	0.201555	−	0.721164i
$178$	13.7697	−	8.40222i	1.03208	−	0.629773i
$179$	4.83050	+	2.78889i	0.361048	+	0.208451i	0.669541	−	0.742776i	$-0.266491\pi$
$179$	4.83050	+	2.78889i	0.361048	+	0.208451i	−0.308492	+	0.951227i	$0.599824\pi$
$180$	−9.55422	−	10.7790i	−0.712130	−	0.803421i
$181$	−21.9838	+	12.6923i	−1.63404	+	0.943415i	−0.651213	+	0.758895i	$0.725740\pi$
$181$	−21.9838	+	12.6923i	−1.63404	+	0.943415i	−0.982829	+	0.184520i	$0.940927\pi$
$182$	−7.47996	+	13.7143i	−0.554451	+	1.01657i
$183$	12.0653	+	5.78461i	0.891896	+	0.427611i
$184$	−0.769640	+	7.54313i	−0.0567386	+	0.556087i
$185$	9.70397	+	1.71107i	0.713450	+	0.125800i
$186$	3.15361	+	3.06928i	0.231234	+	0.225050i
$187$	−9.17346	+	7.69745i	−0.670830	+	0.562893i
$188$	5.31548	+	23.4288i	0.387671	+	1.70872i
$189$	1.22921	−	10.2403i	0.0894122	−	0.744874i
$190$	7.40476	+	5.91297i	0.537198	+	0.428972i
$191$	16.1419	−	13.5447i	1.16799	−	0.980060i	0.168006	−	0.985786i	$-0.446267\pi$
$191$	16.1419	−	13.5447i	1.16799	−	0.980060i	0.999984	+	0.00572593i	$0.00182263\pi$
$192$	12.3167	+	6.34806i	0.888884	+	0.458132i
$193$	2.14750	−	12.1791i	0.154580	−	0.876668i	−0.804589	−	0.593833i	$-0.797614\pi$
$193$	2.14750	−	12.1791i	0.154580	−	0.876668i	0.959169	−	0.282835i	$-0.0912748\pi$
$194$	−7.49642	−	2.52408i	−0.538211	−	0.181218i
$195$	−19.0963	+	13.0682i	−1.36751	+	0.935832i
$196$	−5.64285	+	2.37004i	−0.403061	+	0.169288i
$197$	−5.95187	−	10.3089i	−0.424054	−	0.734482i	0.572278	−	0.820060i	$-0.306060\pi$
$197$	−5.95187	−	10.3089i	−0.424054	−	0.734482i	−0.996332	+	0.0855775i	$0.972726\pi$
$198$	6.86843	−	0.0193588i	0.488118	−	0.00137577i
$199$	−18.0680	−	10.4316i	−1.28081	−	0.739475i	−0.303813	−	0.952732i	$-0.598260\pi$
$199$	−18.0680	−	10.4316i	−1.28081	−	0.739475i	−0.976996	+	0.213256i	$0.931593\pi$
$200$	1.54798	−	1.50399i	0.109459	−	0.106348i
$201$	0.779769	+	3.04029i	0.0550007	+	0.214446i
$202$	−3.05721	−	15.1739i	−0.215105	−	1.06763i
$203$	0.230644	−	0.274871i	0.0161880	−	0.0192921i
$204$	−11.6999	−	22.7970i	−0.819155	−	1.59611i
$205$	3.64473	−	10.0138i	0.254559	−	0.699394i
$206$	−7.76940	−	19.8340i	−0.541320	−	1.38190i
$207$	−7.94820	+	1.22620i	−0.552438	+	0.0852268i
$208$	12.5874	−	18.3597i	0.872776	−	1.27301i
$209$	−4.44995	+	0.784647i	−0.307810	+	0.0542751i
$210$	11.6402	+	0.859614i	0.803249	+	0.0593190i
$211$	−2.06728	+	0.752429i	−0.142317	+	0.0517993i	−0.412197	−	0.911095i	$-0.635238\pi$
$211$	−2.06728	+	0.752429i	−0.142317	+	0.0517993i	0.269879	+	0.962894i	$0.413016\pi$
$212$	−20.1936	+	0.981548i	−1.38690	+	0.0674130i
$213$	−3.94760	+	1.78947i	−0.270485	+	0.122612i
$214$	0.0629246	+	2.59065i	0.00430143	+	0.177093i
$215$	−28.3927			−1.93636
$216$	−3.22373	+	14.3390i	−0.219347	+	0.975647i
$217$	−3.56598			−0.242075
$218$	−0.0977640	−	4.02502i	−0.00662141	−	0.272609i
$219$	1.28470	−	13.0673i	0.0868119	−	0.883004i
$220$	0.377368	+	7.76368i	0.0254421	+	0.523427i
$221$	−38.6823	+	14.0792i	−2.60205	+	0.947070i
$222$	−4.37217	−	9.05376i	−0.293441	−	0.607649i
$223$	−18.9371	+	3.33912i	−1.26812	+	0.223604i	−0.766929	−	0.641732i	$-0.778216\pi$
$223$	−18.9371	+	3.33912i	−1.26812	+	0.223604i	−0.501193	+	0.865336i	$0.667105\pi$
$224$	−10.7401	+	3.27476i	−0.717604	+	0.218804i
$225$	1.95749	+	1.18690i	0.130500	+	0.0791264i
$226$	6.25433	+	15.9662i	0.416032	+	1.06206i
$227$	5.41355	−	14.8736i	0.359310	−	0.987195i	−0.619960	−	0.784634i	$-0.712851\pi$
$227$	5.41355	−	14.8736i	0.359310	−	0.987195i	0.979269	−	0.202562i	$-0.0649267\pi$
$228$	0.477741	−	9.65697i	0.0316391	−	0.639548i
$229$	11.5655	−	13.7832i	0.764268	−	0.910819i	−0.233842	−	0.972275i	$-0.575130\pi$
$229$	11.5655	−	13.7832i	0.764268	−	0.910819i	0.998110	+	0.0614553i	$0.0195742\pi$
$230$	−1.79757	−	8.92189i	−0.118528	−	0.588292i
$231$	−3.97757	+	3.89310i	−0.261705	+	0.256147i
$232$	−0.366722	+	0.356300i	−0.0240765	+	0.0233922i
$233$	4.58811	+	2.64895i	0.300577	+	0.173538i	0.642702	−	0.766116i	$-0.277813\pi$
$233$	4.58811	+	2.64895i	0.300577	+	0.173538i	−0.342125	+	0.939654i	$0.611147\pi$
$234$	22.2093	+	8.01273i	1.45187	+	0.523808i
$235$	−14.4184	−	24.9733i	−0.940550	−	1.62908i
$236$	−4.45451	−	10.6058i	−0.289964	−	0.690379i
$237$	1.39508	+	18.1928i	0.0906203	+	1.18175i
$238$	19.6784	+	6.62581i	1.27556	+	0.429487i
$239$	4.48956	−	25.4615i	0.290405	−	1.64697i	−0.394907	−	0.918721i	$-0.629223\pi$
$239$	4.48956	−	25.4615i	0.290405	−	1.64697i	0.685312	−	0.728249i	$-0.259666\pi$
$240$	−16.3769	−	2.90226i	−1.05713	−	0.187340i
$241$	−18.4759	+	15.5031i	−1.19014	+	0.998644i	−0.190281	+	0.981730i	$0.560940\pi$
$241$	−18.4759	+	15.5031i	−1.19014	+	0.998644i	−0.999857	+	0.0169143i	$0.994616\pi$
$242$	9.25981	+	7.39429i	0.595243	+	0.475323i
$243$	−15.5797	+	0.523705i	−0.999436	+	0.0335957i
$244$	15.0674	−	3.41847i	0.964591	−	0.218845i
$245$	5.62766	−	4.72217i	0.359538	−	0.301688i
$246$	−10.4637	+	2.95628i	−0.667142	+	0.188486i
$247$	−15.2969	−	2.69725i	−0.973317	−	0.171622i
$248$	5.05519	+	0.515791i	0.321005	+	0.0327527i
$249$	0.147953	+	1.92941i	0.00937616	+	0.122271i
$250$	6.88762	−	12.6283i	0.435611	−	0.798682i
$251$	2.91308	−	1.68187i	0.183872	−	0.106159i	−0.405239	−	0.914211i	$-0.632812\pi$
$251$	2.91308	−	1.68187i	0.183872	−	0.106159i	0.589111	+	0.808052i	$0.299478\pi$
$252$	−6.23201	−	10.1487i	−0.392579	−	0.639306i
$253$	3.75845	+	2.16994i	0.236292	+	0.136423i
$254$	0.913271	−	0.557275i	0.0573037	−	0.0349665i
$255$	21.5138	+	21.9807i	1.34725	+	1.37648i
$256$	15.6990	−	3.08887i	0.981188	−	0.193055i
$257$	1.68413	−	2.00707i	0.105053	−	0.125198i	−0.710956	−	0.703237i	$-0.751737\pi$
$257$	1.68413	−	2.00707i	0.105053	−	0.125198i	0.816009	+	0.578039i	$0.196182\pi$
$258$	16.9368	+	23.5038i	1.05444	+	1.46328i
$259$	7.65588	+	2.78651i	0.475713	+	0.173145i
$260$	−7.90882	+	25.5221i	−0.490484	+	1.58281i
$261$	−0.463737	−	0.281180i	−0.0287046	−	0.0174046i
$262$	4.50656	+	0.682246i	0.278416	+	0.0421493i
$263$	0.304745	+	1.72830i	0.0187914	+	0.106571i	0.992761	−	0.120108i	$-0.0383241\pi$
$263$	0.304745	+	1.72830i	0.0187914	+	0.106571i	−0.973969	+	0.226679i	$0.927213\pi$
$264$	6.20177	−	4.94358i	0.381692	−	0.304256i
$265$	22.8039	−	8.29996i	1.40083	−	0.509862i
$266$	5.18044	+	5.87783i	0.317633	+	0.360393i
$267$	19.6613	+	1.93299i	1.20325	+	0.118297i
$268$	2.88617	+	2.19209i	0.176301	+	0.133903i
$269$	28.6840			1.74889			0.874447	−	0.485121i	$-0.161224\pi$
$269$	28.6840			1.74889			0.874447	+	0.485121i	$0.161224\pi$
$270$	−1.39838	−	17.5855i	−0.0851029	−	1.07022i
$271$		−	0.381213i		−	0.0231571i	−0.999933	−	0.0115785i	$-0.996314\pi$
$271$		−	0.381213i		−	0.0231571i	0.999933	−	0.0115785i	$-0.00368564\pi$
$272$	−26.9380	−	12.2392i	−1.63336	−	0.742108i
$273$	−17.4256	+	7.89912i	−1.05465	+	0.478077i
$274$	−10.0156	−	11.3640i	−0.605067	−	0.686522i
$275$	−0.422513	−	1.16084i	−0.0254785	−	0.0700015i
$276$	−6.31337	+	6.81014i	−0.380020	+	0.409922i
$277$	−15.5188	+	2.73638i	−0.932435	+	0.164413i	−0.619174	−	0.785254i	$-0.712532\pi$
$277$	−15.5188	+	2.73638i	−0.932435	+	0.164413i	−0.313261	+	0.949667i	$0.601421\pi$
$278$	−4.25208	+	28.0870i	−0.255023	+	1.68455i
$279$	0.821764	+	5.32666i	0.0491977	+	0.318899i
$280$	11.1504	−	7.57047i	0.666365	−	0.452422i
$281$	−2.04517	+	5.61906i	−0.122005	+	0.335205i	−0.985627	−	0.168933i	$-0.945968\pi$
$281$	−2.04517	+	5.61906i	−0.122005	+	0.335205i	0.863623	+	0.504139i	$0.168190\pi$
$282$	−12.0724	+	26.8328i	−0.718901	+	1.59787i
$283$	2.23671	+	1.87682i	0.132959	+	0.111566i	0.706842	−	0.707372i	$-0.250119\pi$
$283$	2.23671	+	1.87682i	0.132959	+	0.111566i	−0.573883	+	0.818937i	$0.694564\pi$
$284$	−2.28901	+	4.45063i	−0.135828	+	0.264096i
$285$	2.88327	+	11.2418i	0.170790	+	0.665905i
$286$	−6.63662	−	10.8762i	−0.392432	−	0.643123i
$287$	4.40549	−	7.63053i	0.260048	−	0.450416i
$288$	7.36665	+	15.2883i	0.434084	+	0.900872i
$289$	18.8579	+	32.6628i	1.10929	+	1.92134i
$290$	0.293869	−	0.538802i	0.0172566	−	0.0316395i
$291$	−5.47113	−	7.99485i	−0.320723	−	0.468666i
$292$	−8.20929	−	12.7467i	−0.480413	−	0.745947i
$293$	0.0144950	−	0.0822052i	0.000846807	−	0.00480248i	−0.984381	−	0.176049i	$-0.943668\pi$
$293$	0.0144950	−	0.0822052i	0.000846807	−	0.00480248i	0.985228	+	0.171246i	$0.0547794\pi$
$294$	−7.26609	−	1.84178i	−0.423767	−	0.107415i
$295$	8.87537	+	10.5773i	0.516744	+	0.615832i
$296$	−10.4500	−	5.05756i	−0.607396	−	0.293965i
$297$	6.73189	+	5.04432i	0.390624	+	0.292701i
$298$	14.9581	+	11.9445i	0.866497	+	0.691929i
$299$	9.58944	+	11.4282i	0.554571	+	0.660913i
$300$	2.62270	−	0.329828i	0.151422	−	0.0190426i
$301$	−23.1190	−	4.07650i	−1.33256	−	0.234965i
$302$	−4.03202	+	11.9749i	−0.232017	+	0.689081i
$303$	8.19575	−	17.0944i	0.470833	−	0.982048i
$304$	−6.49368	−	9.08181i	−0.372438	−	0.520877i
$305$	−16.0607	+	9.27266i	−0.919634	+	0.530951i
$306$	5.36245	−	30.9213i	0.306551	−	1.76765i
$307$	15.0297	−	26.0322i	0.857789	−	1.48573i	−0.0162438	−	0.999868i	$-0.505171\pi$
$307$	15.0297	−	26.0322i	0.857789	−	1.48573i	0.874033	−	0.485866i	$-0.161496\pi$
$308$	−0.807402	+	6.37583i	−0.0460060	+	0.363296i
$309$	7.02234	−	25.1259i	0.399487	−	1.42936i
$310$	−5.97919	+	1.20468i	−0.339595	+	0.0684213i
$311$	21.1476	+	17.7450i	1.19917	+	1.00622i	0.999653	+	0.0263305i	$0.00838223\pi$
$311$	21.1476	+	17.7450i	1.19917	+	1.00622i	0.199518	+	0.979894i	$0.436062\pi$
$312$	25.8453	−	8.67743i	1.46320	−	0.491263i
$313$	7.89699	+	2.87427i	0.446365	+	0.162463i	0.555416	−	0.831573i	$-0.312559\pi$
$313$	7.89699	+	2.87427i	0.446365	+	0.162463i	−0.109051	+	0.994036i	$0.534781\pi$
$314$	3.40366	+	8.68896i	0.192080	+	0.490346i
$315$	10.7509	+	9.42163i	0.605745	+	0.530849i
$316$	14.3104	+	15.4632i	0.805023	+	0.869870i
$317$	−4.49026	−	25.4655i	−0.252198	−	1.43029i	−0.803163	−	0.595759i	$-0.796851\pi$
$317$	−4.49026	−	25.4655i	−0.252198	−	1.43029i	0.550965	−	0.834528i	$-0.314260\pi$
$318$	−20.4738	−	13.9263i	−1.14812	−	0.780949i
$319$	0.100095	+	0.275008i	0.00560423	+	0.0153975i
$320$	−16.9020	+	9.11918i	−0.944850	+	0.509778i
$321$	−1.84823	+	2.58016i	−0.103158	+	0.144010i
$322$	−0.182722	−	7.52282i	−0.0101827	−	0.419230i
$323$			20.6461i			1.14878i
$324$	−13.7234	+	11.6477i	−0.762409	+	0.647096i
$325$		−	4.24654i		−	0.235556i
$326$	2.90672	−	0.0706014i	0.160988	−	0.00391025i
$327$	2.87154	−	4.00871i	0.158797	−	0.221682i
$328$	−7.34898	+	10.1799i	−0.405780	+	0.562093i
$329$	−8.15471	−	22.4049i	−0.449584	−	1.23522i
$330$	−5.35413	+	7.87140i	−0.294735	+	0.433306i
$331$	1.02889	+	5.83510i	0.0565527	+	0.320726i	0.999940	−	0.0109673i	$-0.00349108\pi$
$331$	1.02889	+	5.83510i	0.0565527	+	0.320726i	−0.943387	+	0.331694i	$0.892380\pi$
$332$	1.51767	+	1.63992i	0.0832929	+	0.0900025i
$333$	2.39807	−	12.0780i	0.131413	−	0.661873i
$334$	−5.68258	+	2.22599i	−0.310937	+	0.121801i
$335$	−4.08791	−	1.48788i	−0.223347	−	0.0812915i
$336$	−12.9184	−	4.71452i	−0.704756	−	0.257198i
$337$	−7.82014	−	6.56188i	−0.425990	−	0.357448i	0.404446	−	0.914562i	$-0.367464\pi$
$337$	−7.82014	−	6.56188i	−0.425990	−	0.357448i	−0.830436	+	0.557114i	$0.811909\pi$
$338$	−5.01939	−	24.9127i	−0.273019	−	1.35507i
$339$	−5.65295	+	20.2262i	−0.307026	+	1.09854i
$340$	35.2337	+	4.46182i	1.91082	+	0.241976i
$341$	1.45423	−	2.51881i	0.0787511	−	0.136401i
$342$	7.58616	−	9.09275i	0.410212	−	0.491680i
$343$	17.2932	−	9.98422i	0.933743	−	0.539097i
$344$	32.1841	+	9.12287i	1.73525	+	0.491872i
$345$	4.81892	−	10.0511i	0.259442	−	0.541134i
$346$	4.97025	+	1.67350i	0.267202	+	0.0899682i
$347$	−25.6701	−	4.52634i	−1.37805	−	0.242987i	−0.564954	−	0.825123i	$-0.691106\pi$
$347$	−25.6701	−	4.52634i	−1.37805	−	0.242987i	−0.813091	+	0.582136i	$0.802217\pi$
$348$	−0.621326	+	0.0781373i	−0.0333066	+	0.00418860i
$349$	3.94641	+	4.70314i	0.211246	+	0.251753i	0.861255	−	0.508173i	$-0.169679\pi$
$349$	3.94641	+	4.70314i	0.211246	+	0.251753i	−0.650008	+	0.759927i	$0.725235\pi$
$350$	−1.33660	+	1.67381i	−0.0714442	+	0.0894690i
$351$	15.8149	+	24.2090i	0.844137	+	1.29218i
$352$	2.06679	−	8.92167i	0.110161	−	0.475527i
$353$	4.80018	+	5.72064i	0.255488	+	0.304479i	0.878508	−	0.477727i	$-0.158539\pi$
$353$	4.80018	+	5.72064i	0.255488	+	0.304479i	−0.623020	+	0.782206i	$0.714095\pi$
$354$	3.46165	−	13.6567i	0.183985	−	0.725845i
$355$	1.04316	−	5.91605i	0.0553652	−	0.313992i
$356$	19.1790	−	12.3519i	1.01649	−	0.654648i
$357$	14.3619	+	20.9868i	0.760114	+	1.11074i
$358$	6.92511	+	3.77704i	0.366004	+	0.199623i
$359$	−1.79899	−	3.11595i	−0.0949473	−	0.164454i	0.814639	−	0.579968i	$-0.196935\pi$
$359$	−1.79899	−	3.11595i	−0.0949473	−	0.164454i	−0.909587	+	0.415514i	$0.863602\pi$
$360$	−13.8779	−	14.9113i	−0.731428	−	0.785892i
$361$	5.60478	−	9.70776i	0.294988	−	0.510935i
$362$	−30.6448	+	18.6993i	−1.61065	+	0.982814i
$363$	3.60559	+	14.0581i	0.189244	+	0.737857i
$364$	−10.1042	+	19.6461i	−0.529604	+	1.02974i
$365$	13.9410	+	11.6979i	0.729705	+	0.612296i
$366$	17.2566	+	7.76395i	0.902016	+	0.405828i
$367$	−6.74224	+	18.5242i	−0.351942	+	0.966954i	0.629803	+	0.776755i	$0.283135\pi$
$367$	−6.74224	+	18.5242i	−0.351942	+	0.966954i	−0.981746	+	0.190199i	$0.939087\pi$
$368$	−0.829085	+	10.6909i	−0.0432190	+	0.557301i
$369$	−12.4133	−	4.82224i	−0.646209	−	0.251036i
$370$	13.7782	+	2.08588i	0.716294	+	0.108439i
$371$	19.7600	−	3.48422i	1.02589	−	0.180892i
$372$	4.56396	+	4.23104i	0.236630	+	0.219369i
$373$	3.75330	+	10.3121i	0.194339	+	0.533941i	0.998140	−	0.0609560i	$-0.0194149\pi$
$373$	3.75330	+	10.3121i	0.194339	+	0.533941i	−0.803802	+	0.594897i	$0.797193\pi$
$374$	−12.7051	+	11.1976i	−0.656964	+	0.579016i
$375$	16.0457	−	7.27359i	0.828595	−	0.375607i
$376$	8.31955	+	32.9410i	0.429048	+	1.69880i
$377$			1.00602i			0.0518127i
$378$	1.38621	−	14.5199i	0.0712989	−	0.746825i
$379$	28.6955			1.47399			0.736993	−	0.675900i	$-0.236245\pi$
$379$	28.6955			1.47399			0.736993	+	0.675900i	$0.236245\pi$
$380$	10.6719	+	8.10546i	0.547456	+	0.415801i
$381$	1.30403	+	0.128205i	0.0668075	+	0.00656813i
$382$	22.3563	−	19.7038i	1.14385	−	1.00813i
$383$	−13.4068	+	4.87966i	−0.685054	+	0.249339i	−0.661016	−	0.750372i	$-0.729874\pi$
$383$	−13.4068	+	4.87966i	−0.685054	+	0.249339i	−0.0240379	+	0.999711i	$0.507652\pi$
$384$	17.6314	+	8.55191i	0.899746	+	0.436413i
$385$	−1.33955	−	7.59695i	−0.0682697	−	0.387177i
$386$	2.61790	−	17.2925i	0.133247	−	0.880163i
$387$	−0.761577	+	35.4732i	−0.0387131	+	1.80320i
$388$	−10.6851	−	3.31111i	−0.542453	−	0.168096i
$389$	−1.60139	−	0.582859i	−0.0811938	−	0.0295521i	0.301104	−	0.953591i	$-0.402645\pi$
$389$	−1.60139	−	0.582859i	−0.0811938	−	0.0295521i	−0.382298	+	0.924039i	$0.624867\pi$
$390$	−26.5495	+	19.1315i	−1.34439	+	0.968762i
$391$	12.7462	−	15.1903i	0.644601	−	0.768205i
$392$	−7.89645	+	3.54453i	−0.398831	+	0.179026i
$393$	3.90468	+	3.98940i	0.196965	+	0.201239i
$394$	−8.76875	−	14.3704i	−0.441763	−	0.723969i
$395$	−21.9012	−	12.6447i	−1.10197	−	0.636223i
$396$	9.70990	−	0.263230i	0.487941	−	0.0132278i
$397$	−18.7381	+	10.8185i	−0.940440	+	0.542963i	−0.890098	−	0.455769i	$-0.849364\pi$
$397$	−18.7381	+	10.8185i	−0.940440	+	0.542963i	−0.0503416	+	0.998732i	$0.516031\pi$
$398$	−25.9027	−	14.1277i	−1.29839	−	0.708157i
$399$	0.733682	+	9.56768i	0.0367300	+	0.478983i
$400$	2.13688	−	2.17949i	0.106844	−	0.108975i
$401$	2.47080	+	0.435668i	0.123386	+	0.0217562i	0.235000	−	0.971995i	$-0.424491\pi$
$401$	2.47080	+	0.435668i	0.123386	+	0.0217562i	−0.111614	+	0.993752i	$0.535602\pi$
$402$	1.20684	+	4.27158i	0.0601916	+	0.213047i
$403$	7.65888	−	6.42656i	0.381516	−	0.320130i
$404$	−4.84334	−	21.3478i	−0.240965	−	1.06209i
$405$	11.5960	−	18.2303i	0.576209	−	0.905869i
$406$	0.316645	−	0.396532i	0.0157148	−	0.0196795i
$407$	−5.09035	+	4.27131i	−0.252319	+	0.211721i
$408$	−17.3241	−	31.8285i	−0.857670	−	1.57575i
$409$	3.62286	−	20.5463i	0.179139	−	1.01595i	−0.754118	−	0.656739i	$-0.771935\pi$
$409$	3.62286	−	20.5463i	0.179139	−	1.01595i	0.933257	−	0.359209i	$-0.116953\pi$
$410$	4.80903	−	14.2826i	0.237501	−	0.705369i
$411$	−1.41847	−	18.4978i	−0.0699680	−	0.912427i
$412$	−11.6654	−	27.7744i	−0.574715	−	1.36835i
$413$	5.70821	+	9.88691i	0.280883	+	0.486503i
$414$	−11.1950	+	2.00654i	−0.550206	+	0.0986159i
$415$	−2.32270	−	1.34101i	−0.114017	−	0.0658278i
$416$	17.1655	−	26.3891i	0.841607	−	1.29383i
$417$	−24.8638	+	24.3358i	−1.21759	+	1.19173i
$418$	−6.26438	+	1.26214i	−0.306401	+	0.0617334i
$419$	−12.9085	+	15.3838i	−0.630621	+	0.751545i	−0.982858	−	0.184366i	$-0.940977\pi$
$419$	−12.9085	+	15.3838i	−0.630621	+	0.751545i	0.352236	+	0.935911i	$0.385421\pi$
$420$	16.4864	+	0.815598i	0.804452	+	0.0397971i
$421$	8.54145	−	23.4674i	0.416285	−	1.14373i	−0.537506	−	0.843260i	$-0.680633\pi$
$421$	8.54145	−	23.4674i	0.416285	−	1.14373i	0.953790	−	0.300473i	$-0.0971444\pi$
$422$	−2.89688	+	1.13477i	−0.141018	+	0.0552398i
$423$	−31.5879	+	17.3441i	−1.53586	+	0.843300i
$424$	−28.5160	+	2.08116i	−1.38486	+	0.101070i
$425$	−5.55870	+	0.980148i	−0.269636	+	0.0475442i
$426$	−5.51966	+	2.66551i	−0.267428	+	0.129144i
$427$	−14.4089	+	5.24442i	−0.697297	+	0.253795i
$428$	0.177925	+	3.66050i	0.00860033	+	0.176937i
$429$	1.52680	−	15.5298i	0.0737145	−	0.749784i
$430$	−40.1414	+	0.974998i	−1.93579	+	0.0470186i
$431$	−3.07869			−0.148295			−0.0741477	−	0.997247i	$-0.523624\pi$
$431$	−3.07869			−0.148295			−0.0741477	+	0.997247i	$0.523624\pi$
$432$	−4.06530	+	20.3832i	−0.195592	+	0.980685i
$433$	−13.9338			−0.669615			−0.334808	−	0.942287i	$-0.608671\pi$
$433$	−13.9338			−0.669615			−0.334808	+	0.942287i	$0.608671\pi$
$434$	−5.04158	+	0.122455i	−0.242003	+	0.00587804i
$435$	0.684610	−	0.310337i	0.0328245	−	0.0148795i
$436$	−0.276437	−	5.68720i	−0.0132389	−	0.272368i
$437$	7.03108	−	2.55911i	0.336342	−	0.122419i
$438$	1.36758	−	18.5186i	0.0653453	−	0.884852i
$439$	27.1825	−	4.79300i	1.29735	−	0.228757i	0.518017	−	0.855370i	$-0.326670\pi$
$439$	27.1825	−	4.79300i	1.29735	−	0.228757i	0.779331	+	0.626613i	$0.215559\pi$
$440$	0.800124	+	10.9633i	0.0381444	+	0.522655i
$441$	−5.74883	−	7.15774i	−0.273754	−	0.340845i
$442$	−54.2054	+	21.2335i	−2.57829	+	1.00997i
$443$	7.98934	−	21.9505i	0.379585	−	1.04290i	−0.591944	−	0.805979i	$-0.701639\pi$
$443$	7.98934	−	21.9505i	0.379585	−	1.04290i	0.971529	−	0.236922i	$-0.0761385\pi$
$444$	−6.49226	−	12.6500i	−0.308109	−	0.600344i
$445$	−17.6009	+	20.9759i	−0.834363	+	0.994355i
$446$	−26.6585	+	5.37114i	−1.26232	+	0.254331i
$447$	5.82437	+	22.7090i	0.275483	+	1.07410i
$448$	−15.0719	+	4.99866i	−0.712080	+	0.236164i
$449$	2.35310	+	1.35856i	0.111050	+	0.0641146i	0.554496	−	0.832186i	$-0.312911\pi$
$449$	2.35310	+	1.35856i	0.111050	+	0.0641146i	−0.443446	+	0.896301i	$0.646244\pi$
$450$	2.80825	+	1.61081i	0.132382	+	0.0759343i
$451$	3.59318	+	6.22357i	0.169196	+	0.293057i
$452$	9.39062	+	22.3582i	0.441698	+	1.05164i
$453$	−12.7712	+	8.73970i	−0.600041	+	0.410627i
$454$	7.14290	−	21.2141i	0.335233	−	0.995629i
$455$	4.60475	−	26.1148i	0.215874	−	1.22428i
$456$	0.343810	−	13.6694i	0.0161004	−	0.640128i
$457$	−20.8383	+	17.4854i	−0.974775	+	0.817933i	−0.983293	−	0.182030i	$-0.941733\pi$
$457$	−20.8383	+	17.4854i	−0.974775	+	0.817933i	0.00851782	+	0.999964i	$0.497289\pi$
$458$	15.8779	−	19.8838i	0.741926	−	0.929109i
$459$	28.0392	−	26.2893i	1.30876	−	1.22708i
$460$	−2.84778	−	12.5520i	−0.132778	−	0.585240i
$461$	−2.70287	+	2.26798i	−0.125885	+	0.105630i	−0.703557	−	0.710639i	$-0.748406\pi$
$461$	−2.70287	+	2.26798i	−0.125885	+	0.105630i	0.577672	+	0.816269i	$0.303961\pi$
$462$	−5.48979	+	5.64063i	−0.255408	+	0.262426i
$463$	−4.87079	−	0.858852i	−0.226365	−	0.0399142i	0.0593151	−	0.998239i	$-0.481108\pi$
$463$	−4.87079	−	0.858852i	−0.226365	−	0.0399142i	−0.285680	+	0.958325i	$0.592219\pi$
$464$	−0.506235	+	0.516329i	−0.0235014	+	0.0239700i
$465$	−6.73597	−	3.22950i	−0.312373	−	0.149764i
$466$	6.57762	+	3.58751i	0.304702	+	0.166188i
$467$	−20.1954	+	11.6598i	−0.934532	+	0.539552i	−0.888242	−	0.459376i	$-0.848073\pi$
$467$	−20.1954	+	11.6598i	−0.934532	+	0.539552i	−0.0462901	+	0.998928i	$0.514740\pi$
$468$	31.6747	+	10.5657i	1.46416	+	0.488400i
$469$	−3.11500	−	1.79845i	−0.143837	−	0.0830445i
$470$	−21.2422	−	34.8121i	−0.979830	−	1.60576i
$471$	−3.07638	+	11.0073i	−0.141752	+	0.507189i
$472$	−6.66198	−	14.8415i	−0.306642	−	0.683134i
$473$	12.3075	−	14.6675i	0.565899	−	0.674412i
$474$	2.59710	+	25.6729i	0.119289	+	1.17920i
$475$	−2.00139	−	0.728447i	−0.0918301	−	0.0334234i
$476$	28.0488	+	8.69179i	1.28561	+	0.398388i
$477$	−9.75812	−	28.7134i	−0.446794	−	1.31470i
$478$	5.47298	−	36.1516i	0.250328	−	1.65354i
$479$	3.57935	+	20.2995i	0.163545	+	0.927509i	0.950552	+	0.310565i	$0.100518\pi$
$479$	3.57935	+	20.2995i	0.163545	+	0.927509i	−0.787007	+	0.616944i	$0.788371\pi$
$480$	−23.2533	−	3.54082i	−1.06136	−	0.161616i
$481$	−21.4648	+	7.81255i	−0.978711	+	0.356222i
$482$	−25.5888	+	22.5527i	−1.16554	+	1.02725i
$483$	5.36695	−	7.49234i	0.244204	−	0.340913i
$484$	13.3454	+	10.1360i	0.606609	+	0.460729i
$485$	13.4272			0.609698
$486$	−22.0085	+	1.27541i	−0.998325	+	0.0578540i
$487$			8.50350i			0.385330i	0.981265	+	0.192665i	$0.0617131\pi$
$487$			8.50350i			0.385330i	−0.981265	+	0.192665i	$0.938287\pi$
$488$	21.1848	−	5.35043i	0.958993	−	0.242202i
$489$	2.89494	+	2.07372i	0.130914	+	0.0937767i
$490$	7.79421	−	6.86944i	0.352107	−	0.310330i
$491$	−10.7502	−	29.5360i	−0.485151	−	1.33294i	−0.905025	−	0.425359i	$-0.860148\pi$
$491$	−10.7502	−	29.5360i	−0.485151	−	1.33294i	0.419874	−	0.907583i	$-0.362074\pi$
$492$	−14.6920	+	4.53891i	−0.662368	+	0.204630i
$493$	1.31687	−	0.232200i	0.0593090	−	0.0104578i
$494$	−21.7193	−	3.28807i	−0.977197	−	0.147937i
$495$	−11.0392	+	3.75162i	−0.496175	+	0.168623i
$496$	7.16472	+	0.555629i	0.321705	+	0.0249485i
$497$	1.69881	−	4.66743i	0.0762018	−	0.209363i
$498$	0.275431	+	2.72271i	0.0123424	+	0.122007i
$499$	−17.3039	−	14.5197i	−0.774628	−	0.649990i	0.167262	−	0.985913i	$-0.446507\pi$
$499$	−17.3039	−	14.5197i	−0.774628	−	0.649990i	−0.941890	+	0.335923i	$0.890952\pi$
$500$	9.30404	−	18.0903i	0.416089	−	0.809023i
$501$	−7.19876	−	2.01195i	−0.321617	−	0.0898875i
$502$	4.06075	−	2.47785i	0.181240	−	0.110592i
$503$	−9.33255	+	16.1645i	−0.416118	+	0.720738i	−0.995545	−	0.0942866i	$-0.969943\pi$
$503$	−9.33255	+	16.1645i	−0.416118	+	0.720738i	0.579427	+	0.815024i	$0.303276\pi$
$504$	−9.15929	−	14.1342i	−0.407987	−	0.629585i
$505$	13.1377	+	22.7551i	0.584619	+	1.01259i
$506$	5.38820	+	2.93879i	0.239535	+	0.130645i
$507$	13.4559	−	28.0659i	0.597599	−	1.24645i
$508$	1.27204	−	0.819235i	0.0564378	−	0.0363477i
$509$	1.23732	−	7.01719i	0.0548432	−	0.311031i	−0.945029	−	0.326985i	$-0.893967\pi$
$509$	1.23732	−	7.01719i	0.0548432	−	0.311031i	0.999873	+	0.0159536i	$0.00507841\pi$
$510$	31.1710	+	30.3374i	1.38027	+	1.34336i
$511$	9.67205	+	11.5267i	0.427867	+	0.509911i
$512$	22.0891	−	4.90614i	0.976211	−	0.216823i
$513$	14.1226	−	3.30076i	0.623527	−	0.145732i
$514$	2.31210	−	2.89543i	0.101982	−	0.127712i
$515$	23.2427	+	27.6996i	1.02420	+	1.22059i
$516$	24.7523	+	32.6480i	1.08966	+	1.43725i
$517$	19.1511	+	3.37685i	0.842263	+	0.148514i
$518$	10.9195	+	3.67666i	0.479777	+	0.161543i
$519$	3.62745	+	5.30072i	0.159227	+	0.232676i
$520$	−10.3050	+	36.3547i	−0.451906	+	1.59426i
$521$	20.6589	−	11.9274i	0.905083	−	0.522550i	0.0262370	−	0.999656i	$-0.491648\pi$
$521$	20.6589	−	11.9274i	0.905083	−	0.522550i	0.878846	+	0.477106i	$0.158314\pi$
$522$	−0.665285	−	0.381606i	−0.0291187	−	0.0167025i
$523$	−17.6879	+	30.6364i	−0.773440	+	1.33964i	0.162227	+	0.986753i	$0.448132\pi$
$523$	−17.6879	+	30.6364i	−0.773440	+	1.33964i	−0.935667	+	0.352884i	$0.885201\pi$
$524$	6.39479	+	0.809803i	0.279358	+	0.0353764i
$525$	−2.54115	+	0.651749i	−0.110905	+	0.0284447i
$526$	0.490198	+	2.43300i	0.0213736	+	0.106084i
$527$	−10.1801	−	8.54211i	−0.443452	−	0.372100i
$528$	8.59828	−	7.20219i	0.374192	−	0.313435i
$529$	14.8599	+	5.40857i	0.646084	+	0.235155i
$530$	31.9551	−	12.5175i	1.38804	−	0.543727i
$531$	13.4531	−	10.8050i	0.583813	−	0.468896i
$532$	7.52593	+	8.13217i	0.326290	+	0.352574i
$533$	4.28970	+	24.3281i	0.185807	+	1.05377i
$534$	27.8635	+	2.05768i	1.20577	+	0.0890447i
$535$	−1.50453	−	4.13366i	−0.0650465	−	0.178714i
$536$	4.15573	+	3.00006i	0.179500	+	0.129583i
$537$	3.98870	+	8.79915i	0.172125	+	0.379711i
$538$	40.5533	−	0.985003i	1.74838	−	0.0424665i
$539$			4.95416i			0.213391i
$540$	−2.58091	−	24.8143i	−0.111065	−	1.06784i
$541$		−	25.7473i		−	1.10696i	−0.832862	−	0.553480i	$-0.813299\pi$
$541$		−	25.7473i		−	1.10696i	0.832862	−	0.553480i	$-0.186701\pi$
$542$	−0.0130908	−	0.538958i	−0.000562298	−	0.0231502i
$543$	−43.7566	−	4.30190i	−1.87778	−	0.184612i
$544$	−38.5051	−	16.3786i	−1.65089	−	0.702228i
$545$	2.33755	+	6.42235i	0.100129	+	0.275103i
$546$	−24.3650	+	11.7661i	−1.04273	+	0.503545i
$547$	−1.96276	−	11.1313i	−0.0839214	−	0.475942i	−0.997584	−	0.0694689i	$-0.977870\pi$
$547$	−1.96276	−	11.1313i	−0.0839214	−	0.475942i	0.913663	−	0.406473i	$-0.133242\pi$
$548$	−14.5503	−	15.7224i	−0.621559	−	0.671628i
$549$	11.1543	+	20.3146i	0.476053	+	0.867008i
$550$	−0.637210	−	1.62669i	−0.0271707	−	0.0693622i
$551$	0.474136	+	0.172572i	0.0201989	+	0.00735179i
$552$	−8.69196	+	9.84496i	−0.369954	+	0.419029i
$553$	−16.0178	−	13.4405i	−0.681147	−	0.571550i
$554$	−21.8465	+	4.40160i	−0.928167	+	0.187006i
$555$	11.9380	+	12.1971i	0.506740	+	0.517736i
$556$	−5.04707	+	39.8553i	−0.214043	+	1.69024i
$557$	3.17566	−	5.50041i	0.134557	−	0.233060i	−0.790871	−	0.611983i	$-0.790372\pi$
$557$	3.17566	−	5.50041i	0.134557	−	0.233060i	0.925428	+	0.378923i	$0.123705\pi$
$558$	1.34472	+	7.50259i	0.0569267	+	0.317610i
$559$	57.0006	−	32.9093i	2.41087	−	1.39192i
$560$	15.5045	−	11.0860i	0.655183	−	0.468469i
$561$	−20.6808	+	1.58587i	−0.873143	+	0.0669555i
$562$	−2.69850	+	8.01444i	−0.113829	+	0.338069i
$563$	−2.69663	−	0.475489i	−0.113649	−	0.0200395i	0.116534	−	0.993187i	$-0.462822\pi$
$563$	−2.69663	−	0.475489i	−0.113649	−	0.0200395i	−0.230184	+	0.973147i	$0.573933\pi$
$564$	−16.1465	+	38.3507i	−0.679890	+	1.61486i
$565$	−18.7103	−	22.2981i	−0.787148	−	0.938086i
$566$	3.22670	+	2.57664i	0.135628	+	0.108304i
$567$	12.0596	−	13.1792i	0.506454	−	0.553476i
$568$	−3.08336	+	6.37089i	−0.129375	+	0.267317i
$569$	2.40329	+	2.86413i	0.100751	+	0.120071i	0.814064	−	0.580775i	$-0.197251\pi$
$569$	2.40329	+	2.86413i	0.100751	+	0.120071i	−0.713313	+	0.700846i	$0.752806\pi$
$570$	4.46240	+	15.7946i	0.186909	+	0.661561i
$571$	2.53820	−	14.3948i	0.106220	−	0.602405i	−0.884506	−	0.466529i	$-0.845504\pi$
$571$	2.53820	−	14.3948i	0.106220	−	0.602405i	0.990726	−	0.135876i	$-0.0433847\pi$
$572$	−9.75632	−	15.1488i	−0.407932	−	0.633405i
$573$	36.3906	−	2.79055i	1.52024	−	0.116577i
$574$	5.96644	−	10.9393i	0.249034	−	0.456598i
$575$	1.02280	+	1.77154i	0.0426537	+	0.0738784i
$576$	10.9399	+	21.3616i	0.455831	+	0.890066i
$577$	−4.35731	+	7.54709i	−0.181397	+	0.314189i	−0.942357	−	0.334610i	$-0.891395\pi$
$577$	−4.35731	+	7.54709i	−0.181397	+	0.314189i	0.760959	+	0.648800i	$0.224729\pi$
$578$	27.7829	+	45.5310i	1.15561	+	1.89384i
$579$	15.3080	−	14.9829i	0.636180	−	0.622668i
$580$	0.396969	−	0.771847i	0.0164832	−	0.0320492i
$581$	−1.69875	−	1.42542i	−0.0704759	−	0.0591363i
$582$	−8.00960	−	11.1152i	−0.332009	−	0.460740i
$583$	−5.59721	+	15.3782i	−0.231813	+	0.636900i
$584$	−12.0440	−	17.7394i	−0.498384	−	0.734062i
$585$	−40.0699	−	0.860264i	−1.65669	−	0.0355675i
$586$	0.0176701	−	0.116719i	0.000729944	−	0.00482163i
$587$	2.90950	−	0.513023i	0.120088	−	0.0211747i	−0.113281	−	0.993563i	$-0.536136\pi$
$587$	2.90950	−	0.513023i	0.120088	−	0.0211747i	0.233369	+	0.972388i	$0.425025\pi$
$588$	−10.3360	−	2.35439i	−0.426250	−	0.0970934i
$589$	−1.71504	−	4.71203i	−0.0706669	−	0.194156i
$590$	12.9112	+	14.6493i	0.531545	+	0.603102i
$591$	2.01731	−	20.5190i	0.0829810	−	0.844038i
$592$	−14.9479	−	6.79151i	−0.614355	−	0.279129i
$593$		−	28.7111i		−	1.17902i	−0.807760	−	0.589511i	$-0.799320\pi$
$593$		−	28.7111i		−	1.17902i	0.807760	−	0.589511i	$-0.200680\pi$
$594$	9.69075	+	6.90047i	0.397616	+	0.283130i
$595$	−35.2470			−1.44498
$596$	21.5578	+	16.3735i	0.883043	+	0.670685i
$597$	−14.9194	−	32.9124i	−0.610610	−	1.34702i
$598$	13.9500	+	15.8279i	0.570456	+	0.647252i
$599$	−10.3057	+	3.75098i	−0.421080	+	0.153261i	−0.543865	−	0.839173i	$-0.683040\pi$
$599$	−10.3057	+	3.75098i	−0.421080	+	0.153261i	0.122785	+	0.992433i	$0.460818\pi$
$600$	3.69664	−	0.556372i	0.150915	−	0.0227138i
$601$	5.74041	+	32.5555i	0.234156	+	1.32797i	0.844384	+	0.535739i	$0.179967\pi$
$601$	5.74041	+	32.5555i	0.234156	+	1.32797i	−0.610227	+	0.792226i	$0.708922\pi$
$602$	−32.8255	−	4.96944i	−1.33787	−	0.202539i
$603$	−1.96858	+	5.06745i	−0.0801666	+	0.206362i
$604$	−5.28924	+	17.0686i	−0.215216	+	0.694511i
$605$	−18.9022	−	6.87983i	−0.768482	−	0.279705i
$606$	11.0001	−	24.4494i	0.446849	−	0.993191i
$607$	−4.64372	+	5.53417i	−0.188483	+	0.224625i	−0.852008	−	0.523529i	$-0.824615\pi$
$607$	−4.64372	+	5.53417i	−0.188483	+	0.224625i	0.663525	+	0.748154i	$0.269060\pi$
$608$	−9.49261	−	12.6168i	−0.384976	−	0.511680i
$609$	0.602007	−	0.154402i	0.0243945	−	0.00625667i
$610$	−22.3882	+	13.6612i	−0.906471	+	0.553125i
$611$	57.8921	+	33.4240i	2.34206	+	1.35219i
$612$	6.51958	−	43.9006i	0.263538	−	1.77458i
$613$	−24.6364	+	14.2239i	−0.995057	+	0.574496i	−0.906782	−	0.421600i	$-0.861469\pi$
$613$	−24.6364	+	14.2239i	−0.995057	+	0.574496i	−0.0882748	+	0.996096i	$0.528135\pi$
$614$	20.3550	−	37.3203i	0.821460	−	1.50613i
$615$	15.2323	−	10.4239i	0.614225	−	0.420333i
$616$	−0.922557	+	9.04185i	−0.0371709	+	0.364306i
$617$	21.5217	+	3.79486i	0.866432	+	0.152775i	0.589160	−	0.808016i	$-0.299459\pi$
$617$	21.5217	+	3.79486i	0.866432	+	0.152775i	0.277272	+	0.960792i	$0.410570\pi$
$618$	9.06535	−	35.7640i	0.364662	−	1.43864i
$619$	4.96839	−	4.16897i	0.199696	−	0.167565i	−0.537456	−	0.843292i	$-0.680615\pi$
$619$	4.96839	−	4.16897i	0.199696	−	0.167565i	0.737152	+	0.675727i	$0.236170\pi$
$620$	−8.41199	+	1.90850i	−0.337834	+	0.0766472i
$621$	−12.4284	−	6.29025i	−0.498735	−	0.252419i
$622$	30.5078	+	24.3616i	1.22325	+	0.976810i
$623$	−17.3433	+	14.5528i	−0.694846	+	0.583045i
$624$	36.2420	−	13.1557i	1.45084	−	0.526648i
$625$	−4.90262	+	27.8042i	−0.196105	+	1.11217i
$626$	11.2634	+	3.79245i	0.450178	+	0.151577i
$627$	−7.05726	−	3.38354i	−0.281840	−	0.135125i
$628$	5.11046	+	12.1675i	0.203930	+	0.485538i
$629$	15.1809	+	26.2941i	0.605302	+	1.04841i
$630$	15.5231	+	12.9511i	0.618457	+	0.515983i
$631$	31.9060	+	18.4209i	1.27016	+	0.733325i	0.975017	−	0.222129i	$-0.0713006\pi$
$631$	31.9060	+	18.4209i	1.27016	+	0.733325i	0.295139	+	0.955454i	$0.404634\pi$
$632$	20.7630	+	21.3703i	0.825908	+	0.850066i
$633$	−3.66980	−	1.02566i	−0.145861	−	0.0407663i
$634$	−7.22280	−	35.8489i	−0.286854	−	1.42374i
$635$	−1.16737	+	1.39122i	−0.0463258	+	0.0552090i
$636$	−29.4241	−	18.9859i	−1.16674	−	0.752840i
$637$	−5.82464	+	16.0031i	−0.230781	+	0.634064i
$638$	0.150957	+	0.385368i	0.00597645	+	0.0152569i
$639$	−7.36341	−	1.46199i	−0.291292	−	0.0578354i
$640$	−23.5828	+	13.4731i	−0.932193	+	0.532570i
$641$	21.8735	−	3.85688i	0.863950	−	0.152338i	0.275923	−	0.961180i	$-0.411016\pi$
$641$	21.8735	−	3.85688i	0.863950	−	0.152338i	0.588026	+	0.808842i	$0.299905\pi$
$642$	−2.52442	+	3.71129i	−0.0996309	+	0.146473i
$643$	14.8220	−	5.39476i	0.584522	−	0.212749i	−0.0327965	−	0.999462i	$-0.510441\pi$
$643$	14.8220	−	5.39476i	0.584522	−	0.212749i	0.617318	+	0.786714i	$0.288219\pi$
$644$	−0.516664	−	10.6295i	−0.0203594	−	0.418859i
$645$	−39.9788	−	28.6378i	−1.57416	−	1.12761i
$646$	0.708982	+	29.1893i	0.0278945	+	1.14844i
$647$	23.4148			0.920530			0.460265	−	0.887782i	$-0.347754\pi$
$647$	23.4148			0.920530			0.460265	+	0.887782i	$0.347754\pi$
$648$	−19.0021	+	16.9388i	−0.746471	+	0.665418i
$649$	−9.31140			−0.365504
$650$	−0.145825	−	6.00375i	−0.00571974	−	0.235486i
$651$	−5.02115	−	3.59677i	−0.196794	−	0.140969i
$652$	4.10708	−	0.199632i	0.160846	−	0.00781820i
$653$	−20.9780	+	7.63537i	−0.820933	+	0.298795i	−0.718132	−	0.695907i	$-0.755003\pi$
$653$	−20.9780	+	7.63537i	−0.820933	+	0.298795i	−0.102801	+	0.994702i	$0.532780\pi$
$654$	3.92212	−	5.76612i	0.153367	−	0.225473i
$655$	−7.61955	+	1.34353i	−0.297720	+	0.0524962i
$656$	−10.0404	+	14.6447i	−0.392011	+	0.571780i
$657$	14.9890	−	17.1038i	0.584778	−	0.667284i
$658$	−12.2985	−	31.3959i	−0.479445	−	1.22394i
$659$	−12.5163	+	34.3882i	−0.487565	+	1.33957i	0.415313	+	0.909679i	$0.363672\pi$
$659$	−12.5163	+	34.3882i	−0.487565	+	1.33957i	−0.902878	+	0.429896i	$0.858550\pi$
$660$	−7.29935	+	11.3124i	−0.284127	+	0.440335i
$661$	−12.4241	+	14.8064i	−0.483240	+	0.575902i	−0.951485	−	0.307696i	$-0.900442\pi$
$661$	−12.4241	+	14.8064i	−0.483240	+	0.575902i	0.468245	+	0.883599i	$0.344886\pi$
$662$	1.65501	+	8.21432i	0.0643239	+	0.319259i
$663$	−68.6681	−	19.1918i	−2.66685	−	0.745348i
$664$	2.20199	+	2.26640i	0.0854538	+	0.0879534i
$665$	−11.5180	−	6.64992i	−0.446649	−	0.257873i
$666$	2.97562	−	17.1582i	0.115303	−	0.664868i
$667$	−0.242305	−	0.419684i	−0.00938207	−	0.0162502i
$668$	−7.95757	+	3.34224i	−0.307888	+	0.129315i
$669$	−30.0327	−	14.3989i	−1.16113	−	0.556693i
$670$	−5.83057	−	1.96318i	−0.225255	−	0.0758443i
$671$	2.17170	−	12.3163i	0.0838377	−	0.475467i
$672$	−18.4259	−	6.22176i	−0.710793	−	0.240010i
$673$	22.1943	−	18.6232i	0.855526	−	0.717872i	−0.105473	−	0.994422i	$-0.533636\pi$
$673$	22.1943	−	18.6232i	0.855526	−	0.717872i	0.960999	+	0.276550i	$0.0891912\pi$
$674$	−11.2814	−	9.00862i	−0.434544	−	0.346999i
$675$	1.55914	+	3.64563i	0.0600113	+	0.140320i
$676$	−7.95189	−	35.0491i	−0.305842	−	1.34804i
$677$	−21.1510	+	17.7478i	−0.812897	+	0.682102i	−0.951297	−	0.308275i	$-0.900248\pi$
$677$	−21.1510	+	17.7478i	−0.812897	+	0.682102i	0.138400	+	0.990376i	$0.455804\pi$
$678$	−7.29756	+	28.7899i	−0.280261	+	1.10567i
$679$	10.9332	+	1.92782i	0.419578	+	0.0739830i
$680$	49.9666	+	5.09818i	1.91613	+	0.195506i
$681$	22.6247	−	15.4828i	0.866979	−	0.593301i
$682$	1.96949	−	3.61102i	0.0754159	−	0.138273i
$683$	−26.7048	+	15.4180i	−1.02183	+	0.589954i	−0.914633	−	0.404284i	$-0.867521\pi$
$683$	−26.7048	+	15.4180i	−1.02183	+	0.589954i	−0.107196	+	0.994238i	$0.534187\pi$
$684$	10.4130	−	13.1158i	0.398153	−	0.501496i
$685$	22.2684	+	12.8567i	0.850833	+	0.491228i
$686$	24.1062	−	14.7095i	0.920378	−	0.561611i
$687$	30.1872	−	7.74236i	1.15171	−	0.295389i
$688$	45.8151	+	11.7927i	1.74668	+	0.449592i
$689$	−36.1605	+	43.0944i	−1.37761	+	1.64177i
$690$	6.46781	−	14.3757i	0.246225	−	0.547274i
$691$	−5.99355	−	2.18147i	−0.228006	−	0.0829872i	0.225491	−	0.974245i	$-0.427601\pi$
$691$	−5.99355	−	2.18147i	−0.228006	−	0.0829872i	−0.453497	+	0.891258i	$0.649824\pi$
$692$	7.08439	+	2.19532i	0.269308	+	0.0834535i
$693$	−9.52741	+	1.46983i	−0.361916	+	0.0558342i
$694$	−36.4478	−	5.51781i	−1.38354	−	0.209453i
$695$	−8.37352	−	47.4886i	−0.317626	−	1.80135i
$696$	−0.875746	+	0.131806i	−0.0331951	+	0.00499611i
$697$	30.8552	−	11.2304i	1.16872	−	0.425381i
$698$	5.74092	+	6.51377i	0.217297	+	0.246550i
$699$	3.78855	+	8.35762i	0.143296	+	0.316114i
$700$	−1.83220	+	2.41233i	−0.0692506	+	0.0911774i
$701$	4.03941			0.152566			0.0762832	−	0.997086i	$-0.475695\pi$
$701$	4.03941			0.152566			0.0762832	+	0.997086i	$0.475695\pi$
$702$	23.1904	+	33.6836i	0.875265	+	1.27130i
$703$			11.4565i			0.432090i
$704$	2.61566	−	12.6844i	0.0985814	−	0.478062i
$705$	4.88691	−	49.7070i	0.184052	−	1.87207i
$706$	6.98293	+	7.92298i	0.262806	+	0.298185i
$707$	7.43039	+	20.4148i	0.279449	+	0.767779i
$708$	4.42510	−	19.4267i	0.166306	−	0.730099i
$709$	9.31231	−	1.64201i	0.349731	−	0.0616670i	0.00397676	−	0.999992i	$-0.498734\pi$
$709$	9.31231	−	1.64201i	0.349731	−	0.0616670i	0.345754	+	0.938325i	$0.387623\pi$
$710$	1.27166	−	8.39992i	0.0477246	−	0.315243i
$711$	−16.3855	+	27.0238i	−0.614503	+	1.01347i
$712$	26.6911	−	18.1217i	1.00029	−	0.679138i
$713$	−1.64721	+	4.52566i	−0.0616884	+	0.169487i
$714$	21.0255	+	29.1779i	0.786861	+	1.09196i
$715$	16.5682	+	13.9023i	0.619614	+	0.519918i
$716$	9.92040	+	5.10216i	0.370743	+	0.190677i
$717$	32.0030	−	31.3233i	1.19517	−	1.16979i
$718$	−2.65041	−	4.34354i	−0.0989125	−	0.162100i
$719$	−16.9409	+	29.3425i	−0.631789	+	1.09429i	0.355397	+	0.934716i	$0.384346\pi$
$719$	−16.9409	+	29.3425i	−0.631789	+	1.09429i	−0.987186	+	0.159575i	$0.948988\pi$
$720$	−20.1325	−	20.6049i	−0.750296	−	0.767900i
$721$	14.9486	+	25.8918i	0.556716	+	0.964260i
$722$	7.59066	−	13.9173i	0.282495	−	0.517947i
$723$	−41.6523	+	3.19404i	−1.54907	+	0.118788i
$724$	−42.6833	+	27.4894i	−1.58631	+	1.02163i
$725$	−0.0239537	+	0.135848i	−0.000889617	+	0.00504527i
$726$	5.58032	+	19.7514i	0.207105	+	0.733044i
$727$	−23.2473	−	27.7051i	−0.862196	−	1.02753i	−0.999316	−	0.0369707i	$-0.988229\pi$
$727$	−23.2473	−	27.7051i	−0.862196	−	1.02753i	0.137120	−	0.990554i	$-0.456215\pi$
$728$	−13.6106	+	28.1226i	−0.504443	+	1.04229i
$729$	−22.4655	−	14.9768i	−0.832054	−	0.554695i
$730$	20.1114	+	16.0597i	0.744358	+	0.594396i
$731$	−56.2345	−	67.0177i	−2.07991	−	2.47874i
$732$	24.6639	+	10.3841i	0.911604	+	0.383806i
$733$	36.2493	+	6.39173i	1.33890	+	0.236084i	0.796806	−	0.604235i	$-0.206521\pi$
$733$	36.2493	+	6.39173i	1.33890	+	0.236084i	0.542092	+	0.840319i	$0.317632\pi$
$734$	−8.89605	+	26.4209i	−0.328359	+	0.975214i
$735$	12.6871	−	0.972887i	0.467970	−	0.0358855i
$736$	−0.805035	+	15.1432i	−0.0296740	+	0.558186i
$737$	2.54064	−	1.46684i	0.0935855	−	0.0540316i
$738$	−17.7154	−	6.39140i	−0.652114	−	0.235271i
$739$	5.13319	−	8.89094i	0.188827	−	0.327058i	−0.756032	−	0.654534i	$-0.772865\pi$
$739$	5.13319	−	8.89094i	0.188827	−	0.327058i	0.944860	+	0.327476i	$0.106198\pi$
$740$	19.5512	+	2.47586i	0.718716	+	0.0910145i
$741$	−18.8185	−	19.2269i	−0.691315	−	0.706316i
$742$	27.8170	−	5.60453i	1.02119	−	0.205749i
$743$	−6.80751	−	5.71218i	−0.249743	−	0.209559i	0.509319	−	0.860578i	$-0.329898\pi$
$743$	−6.80751	−	5.71218i	−0.249743	−	0.209559i	−0.759062	+	0.651019i	$0.774342\pi$
$744$	6.59781	+	5.82510i	0.241887	+	0.213559i
$745$	−30.5341	−	11.1135i	−1.11868	−	0.407167i
$746$	5.66053	+	14.4504i	0.207247	+	0.529065i
$747$	−1.73774	+	2.86597i	−0.0635805	+	0.104860i
$748$	−17.5779	+	16.2675i	−0.642711	+	0.594798i
$749$	−0.631584	−	3.58189i	−0.0230776	−	0.130879i
$750$	22.4355	−	10.8344i	0.819230	−	0.395616i
$751$	−2.65250	−	7.28768i	−0.0967911	−	0.265931i	0.881842	−	0.471545i	$-0.156303\pi$
$751$	−2.65250	−	7.28768i	−0.0967911	−	0.265931i	−0.978633	+	0.205613i	$0.934081\pi$
$752$	12.8933	+	46.2862i	0.470171	+	1.68788i
$753$	5.79821	+	0.570047i	0.211298	+	0.0207737i
$754$	0.0345465	+	1.42231i	0.00125811	+	0.0517974i
$755$		−	21.4489i		−	0.780606i
$756$	1.46121	−	20.5758i	0.0531435	−	0.748336i
$757$			5.79367i			0.210575i	0.994442	+	0.105287i	$0.0335762\pi$
$757$			5.79367i			0.210575i	−0.994442	+	0.105287i	$0.966424\pi$
$758$	40.5695	−	0.985396i	1.47355	−	0.0357912i
$759$	3.10348	+	6.84633i	0.112649	+	0.248506i
$760$	15.3662	+	11.0930i	0.557391	+	0.402385i
$761$	4.04229	+	11.1061i	0.146533	+	0.402596i	0.991145	−	0.132782i	$-0.0423912\pi$
$761$	4.04229	+	11.1061i	0.146533	+	0.402596i	−0.844612	+	0.535379i	$0.820169\pi$
$762$	1.84803	+	0.136475i	0.0669472	+	0.00494398i
$763$	0.981273	+	5.56507i	0.0355245	+	0.201469i
$764$	30.9306	−	28.6248i	1.11903	−	1.03561i
$765$	8.12249	+	52.6498i	0.293669	+	1.90356i
$766$	−18.7869	+	7.35924i	−0.678797	+	0.265900i
$767$	−30.0779	−	10.9475i	−1.08605	−	0.395290i
$768$	25.2208	+	11.4852i	0.910078	+	0.414437i
$769$	24.2973	+	20.3879i	0.876183	+	0.735205i	0.965391	−	0.260808i	$-0.0839890\pi$
$769$	24.2973	+	20.3879i	0.876183	+	0.735205i	−0.0892076	+	0.996013i	$0.528433\pi$
$770$	−2.15473	−	10.6945i	−0.0776509	−	0.385405i
$771$	4.39578	−	1.12742i	0.158310	−	0.0406031i
$772$	3.10735	−	24.5379i	0.111836	−	0.883139i
$773$	−13.7342	+	23.7883i	−0.493984	+	0.855605i	−0.999976	−	0.00693313i	$-0.997793\pi$
$773$	−13.7342	+	23.7883i	−0.493984	+	0.855605i	0.505992	+	0.862538i	$0.331126\pi$
$774$	0.141427	+	50.1780i	0.00508350	+	1.80361i
$775$	1.18724	−	0.685451i	0.0426468	−	0.0246221i
$776$	−15.2202	−	4.31431i	−0.546375	−	0.154875i
$777$	7.96943	+	11.6456i	0.285902	+	0.417783i
$778$	−2.28406	−	0.769052i	−0.0818874	−	0.0275719i
$779$	12.2017	+	2.15148i	0.437170	+	0.0770848i
$780$	−36.8786	+	27.9598i	−1.32047	+	1.00112i
$781$	2.60402	+	3.10335i	0.0931791	+	0.111047i
$782$	17.4988	−	21.9137i	0.625757	−	0.783631i
$783$	−0.369366	−	0.863661i	−0.0132001	−	0.0308647i
$784$	−11.0423	+	5.28240i	−0.394366	+	0.188657i
$785$	−10.1823	−	12.1348i	−0.363422	−	0.433109i
$786$	5.65741	+	5.50612i	0.201793	+	0.196397i
$787$	3.52810	−	20.0088i	0.125763	−	0.713238i	−0.855089	−	0.518482i	$-0.826497\pi$
$787$	3.52810	−	20.0088i	0.125763	−	0.713238i	0.980852	−	0.194756i	$-0.0623915\pi$
$788$	−12.8907	−	20.0157i	−0.459212	−	0.713029i
$789$	−1.31412	+	2.74094i	−0.0467838	+	0.0975800i
$790$	−31.3981	−	17.1249i	−1.11709	−	0.609278i
$791$	−12.0336	−	20.8427i	−0.427864	−	0.741083i
$792$	13.7188	−	0.705589i	0.487476	−	0.0250720i
$793$	21.4955	−	37.2313i	0.763328	−	1.32212i
$794$	−26.1204	+	15.9386i	−0.926978	+	0.565639i
$795$	40.4811	+	11.3139i	1.43572	+	0.401263i
$796$	−37.1063	−	19.0842i	−1.31520	−	0.676421i
$797$	32.7465	+	27.4776i	1.15994	+	0.973305i	0.999905	−	0.0138066i	$-0.00439492\pi$
$797$	32.7465	+	27.4776i	1.15994	+	0.973305i	0.160035	+	0.987111i	$0.448839\pi$
$798$	1.36583	+	13.5016i	0.0483498	+	0.477950i
$799$	30.3897	−	83.4951i	1.07511	−	2.95384i
$800$	2.94628	−	3.15474i	0.104167	−	0.111537i
$801$	25.7348	+	22.5528i	0.909294	+	0.796865i
$802$	3.50816	+	0.531099i	0.123878	+	0.0187538i
$803$	−12.0861	+	2.13111i	−0.426510	+	0.0752053i
$804$	1.85291	+	5.99770i	0.0653471	+	0.211523i
$805$	4.36890	+	12.0035i	0.153984	+	0.423066i
$806$	10.6074	−	9.34886i	0.373630	−	0.329300i
$807$	40.3890	+	28.9317i	1.42176	+	1.01844i
$808$	−7.58058	−	30.0151i	−0.266684	−	1.05593i
$809$		−	8.70983i		−	0.306221i	−0.988209	−	0.153111i	$-0.951071\pi$
$809$		−	8.70983i		−	0.306221i	0.988209	−	0.153111i	$-0.0489291\pi$
$810$	15.7683	−	26.1721i	0.554043	−	0.919593i
$811$	8.59239			0.301719			0.150860	−	0.988555i	$-0.451796\pi$
$811$	8.59239			0.301719			0.150860	+	0.988555i	$0.451796\pi$
$812$	0.434054	−	0.571489i	0.0152323	−	0.0200553i
$813$	0.384505	−	0.536775i	0.0134852	−	0.0188255i
$814$	−7.05005	+	6.21357i	−0.247104	+	0.217785i
$815$	−4.63798	+	1.68809i	−0.162461	+	0.0591311i
$816$	−25.5857	−	44.4042i	−0.895680	−	1.55446i
$817$	−5.73232	−	32.5096i	−0.200548	−	1.13737i
$818$	4.41643	−	29.1727i	0.154417	−	1.02000i
$819$	−32.5038	−	6.45355i	−1.13577	−	0.225505i
$820$	6.30853	−	20.3579i	0.220303	−	0.710928i
$821$	9.68233	+	3.52408i	0.337916	+	0.122991i	0.505404	−	0.862883i	$-0.331343\pi$
$821$	9.68233	+	3.52408i	0.337916	+	0.122991i	−0.167488	+	0.985874i	$0.553566\pi$
$822$	−2.64064	−	26.1034i	−0.0921028	−	0.910459i
$823$	−25.2011	+	30.0335i	−0.878455	+	1.04690i	0.120079	+	0.992764i	$0.461685\pi$
$823$	−25.2011	+	30.0335i	−0.878455	+	1.04690i	−0.998533	+	0.0541373i	$0.982759\pi$
$824$	−17.4463	−	38.8667i	−0.607772	−	1.35399i
$825$	0.575940	−	2.06071i	0.0200517	−	0.0717447i
$826$	8.40977	+	13.7821i	0.292613	+	0.479539i
$827$	−6.85389	−	3.95709i	−0.238333	−	0.137602i	0.376077	−	0.926588i	$-0.377273\pi$
$827$	−6.85389	−	3.95709i	−0.238333	−	0.137602i	−0.614410	+	0.788987i	$0.710606\pi$
$828$	−15.7586	+	3.22127i	−0.547649	+	0.111947i
$829$	12.0986	−	6.98514i	0.420202	−	0.242604i	−0.274962	−	0.961455i	$-0.588665\pi$
$829$	12.0986	−	6.98514i	0.420202	−	0.242604i	0.695164	+	0.718851i	$0.255332\pi$
$830$	−3.32988	−	1.81616i	−0.115582	−	0.0630398i
$831$	−24.6116	−	11.7998i	−0.853765	−	0.409330i
$832$	23.3623	−	37.8983i	0.809943	−	1.31389i
$833$	22.2923	+	3.93073i	0.772382	+	0.136192i
$834$	−34.3167	+	35.2596i	−1.18829	+	1.22094i
$835$	7.93615	−	6.65922i	0.274642	−	0.230452i
$836$	−8.81322	+	1.99953i	−0.304812	+	0.0691551i
$837$	−4.21555	+	8.32916i	−0.145711	+	0.287898i
$838$	−17.7217	+	22.1928i	−0.612187	+	0.766636i
$839$	−28.1095	+	23.5867i	−0.970449	+	0.814303i	−0.982621	−	0.185623i	$-0.940570\pi$
$839$	−28.1095	+	23.5867i	−0.970449	+	0.814303i	0.0121723	+	0.999926i	$0.496125\pi$
$840$	23.3364	+	0.586952i	0.805182	+	0.0202518i
$841$	−5.03012	+	28.5272i	−0.173452	+	0.983698i
$842$	11.2700	−	33.4715i	0.388390	−	1.15350i
$843$	−8.54732	+	5.84920i	−0.294385	+	0.201457i
$844$	−4.05663	+	1.70381i	−0.139635	+	0.0586477i
$845$	21.5697	+	37.3598i	0.742020	+	1.28522i
$846$	−44.0633	+	25.6058i	−1.51493	+	0.880345i
$847$	−14.4035	−	8.31586i	−0.494910	−	0.285736i
$848$	−40.2443	+	3.92156i	−1.38200	+	0.134667i
$849$	1.25641	+	4.89872i	0.0431200	+	0.168124i
$850$	−7.82521	+	1.57661i	−0.268402	+	0.0540774i
$851$	7.07284	−	8.42908i	0.242454	−	0.288945i
$852$	−7.71214	+	3.95803i	−0.264213	+	0.135600i
$853$	6.77335	−	18.6096i	0.231915	−	0.637181i	−0.768080	−	0.640354i	$-0.778788\pi$
$853$	6.77335	−	18.6096i	0.231915	−	0.637181i	0.999995	+	0.00317269i	$0.00100990\pi$
$854$	−20.1912	+	7.90934i	−0.690928	+	0.270652i
$855$	−7.27899	+	18.7373i	−0.248936	+	0.640804i
$856$	0.377251	+	5.16909i	0.0128942	+	0.176676i
$857$	−36.8632	+	6.49998i	−1.25922	+	0.222035i	−0.763136	−	0.646238i	$-0.776342\pi$
$857$	−36.8632	+	6.49998i	−1.25922	+	0.222035i	−0.496087	+	0.868273i	$0.665230\pi$
$858$	1.62529	−	22.0084i	0.0554866	−	0.751353i
$859$	−42.5547	+	15.4886i	−1.45195	+	0.528466i	−0.943135	−	0.332411i	$-0.892138\pi$
$859$	−42.5547	+	15.4886i	−1.45195	+	0.528466i	−0.508813	+	0.860877i	$0.669916\pi$
$860$	−56.7183	+	2.75690i	−1.93408	+	0.0940094i
$861$	13.8997	−	6.30079i	0.473699	−	0.214730i
$862$	−4.35264	+	0.105722i	−0.148252	+	0.00360089i
$863$	13.2305			0.450371			0.225186	−	0.974316i	$-0.427701\pi$
$863$	13.2305			0.450371			0.225186	+	0.974316i	$0.427701\pi$
$864$	−5.04755	+	28.9572i	−0.171721	+	0.985146i
$865$	−8.90245			−0.302693
$866$	−19.6995	+	0.478483i	−0.669418	+	0.0162595i
$867$	−6.39163	+	65.0122i	−0.217071	+	2.20793i
$868$	−7.12356	+	0.346253i	−0.241789	+	0.0117526i
$869$	16.0258	−	5.83291i	0.543638	−	0.197868i
$870$	0.957242	−	0.462263i	0.0324535	−	0.0156722i
$871$	9.93140	−	1.75117i	0.336513	−	0.0593363i
$872$	−0.586123	−	8.03106i	−0.0198486	−	0.271966i
$873$	0.360158	−	16.7757i	0.0121895	−	0.567770i
$874$	9.85264	−	3.85950i	0.333271	−	0.130550i
$875$	−6.90507	+	18.9715i	−0.233434	+	0.641354i
$876$	1.29755	−	26.2285i	0.0438402	−	0.886178i
$877$	−10.6749	+	12.7219i	−0.360467	+	0.429588i	−0.915548	−	0.402208i	$-0.868243\pi$
$877$	−10.6749	+	12.7219i	−0.360467	+	0.429588i	0.555081	+	0.831796i	$0.312687\pi$
$878$	38.2659	−	7.70977i	1.29141	−	0.260192i
$879$	0.103325	−	0.101130i	0.00348506	−	0.00341105i
$880$	1.50769	+	15.4724i	0.0508242	+	0.521575i
$881$	−2.10484	−	1.21523i	−0.0709140	−	0.0409422i	0.464124	−	0.885770i	$-0.346369\pi$
$881$	−2.10484	−	1.21523i	−0.0709140	−	0.0409422i	−0.535038	+	0.844828i	$0.679703\pi$
$882$	−8.37347	−	9.92218i	−0.281949	−	0.334097i
$883$	−26.9993	−	46.7641i	−0.908598	−	1.57374i	−0.816013	−	0.578033i	$-0.803820\pi$
$883$	−26.9993	−	46.7641i	−0.908598	−	1.57374i	−0.0925850	−	0.995705i	$-0.529513\pi$
$884$	−75.9063	+	31.8812i	−2.55301	+	1.07228i
$885$	1.82855	+	23.8455i	0.0614661	+	0.801558i
$886$	10.5415	−	31.3079i	0.354149	−	1.05181i
$887$	6.75263	−	38.2961i	0.226731	−	1.28586i	−0.632617	−	0.774465i	$-0.718019\pi$
$887$	6.75263	−	38.2961i	0.226731	−	1.28586i	0.859348	−	0.511391i	$-0.170870\pi$
$888$	−9.61314	−	17.6616i	−0.322596	−	0.592686i
$889$	−1.15029	+	0.965209i	−0.0385795	+	0.0323721i
$890$	−24.1638	+	30.2601i	−0.809972	+	1.01432i
$891$	4.39109	+	13.8928i	0.147107	+	0.465425i
$892$	−37.5053	+	8.50914i	−1.25577	+	0.284907i
$893$	25.6835	−	21.5510i	0.859465	−	0.721176i
$894$	9.01431	+	31.9060i	0.301483	+	1.06709i
$895$	−13.1868	−	2.32519i	−0.440786	−	0.0777225i
$896$	−21.1369	+	7.58465i	−0.706135	+	0.253385i
$897$	1.97567	+	25.7640i	0.0659657	+	0.860234i
$898$	3.37346	+	1.83993i	0.112574	+	0.0613992i
$899$	−0.281260	+	0.162386i	−0.00938055	+	0.00541586i
$900$	4.02562	+	2.18092i	0.134187	+	0.0726974i
$901$	64.7566	+	37.3872i	2.15736	+	1.24555i
$902$	5.29374	+	8.67548i	0.176262	+	0.288862i
$903$	−28.4414	−	29.0586i	−0.946471	−	0.967009i
$904$	14.0442	+	31.2875i	0.467103	+	1.04061i
$905$	39.1712	−	46.6824i	1.30209	−	1.55177i
$906$	−17.7557	+	12.7947i	−0.589893	+	0.425076i
$907$	20.5550	+	7.48139i	0.682516	+	0.248416i	0.659928	−	0.751329i	$-0.270587\pi$
$907$	20.5550	+	7.48139i	0.682516	+	0.248416i	0.0225887	+	0.999745i	$0.492809\pi$
$908$	9.37011	−	30.2378i	0.310958	−	1.00348i
$909$	28.7822	−	15.8036i	0.954644	−	0.524172i
$910$	5.61340	−	37.0792i	0.186082	−	1.22916i
$911$	8.10127	+	45.9446i	0.268407	+	1.52221i	0.759155	+	0.650910i	$0.225612\pi$
$911$	8.10127	+	45.9446i	0.268407	+	1.52221i	−0.490748	+	0.871302i	$0.663276\pi$
$912$	0.0166728	−	19.3376i	0.000552092	−	0.640330i
$913$	1.69959	−	0.618601i	0.0562483	−	0.0204727i
$914$	−28.8607	+	25.4364i	−0.954627	+	0.841362i
$915$	−31.9673	−	3.14284i	−1.05681	−	0.103899i
$916$	21.7653	−	28.6569i	0.719147	−	0.946850i
$917$	−6.39719			−0.211254
$918$	38.7390	−	38.1306i	1.27858	−	1.25850i
$919$			35.1223i			1.15858i	0.815122	+	0.579289i	$0.196670\pi$
$919$			35.1223i			1.15858i	−0.815122	+	0.579289i	$0.803330\pi$
$920$	−4.45721	−	17.6482i	−0.146950	−	0.581844i
$921$	47.4198	−	21.4956i	1.56253	−	0.708305i
$922$	−3.74343	+	3.29927i	−0.123283	+	0.108656i
$923$	4.76295	+	13.0861i	0.156774	+	0.430734i
$924$	−7.56775	+	8.16323i	−0.248961	+	0.268550i
$925$	−3.08452	+	0.543884i	−0.101418	+	0.0178828i
$926$	−6.91580	−	1.04698i	−0.227267	−	0.0344059i
$927$	35.2308	−	28.2960i	1.15713	−	0.929363i
$928$	−0.697982	+	0.747368i	−0.0229124	+	0.0245335i
$929$	20.6174	−	56.6459i	0.676436	−	1.85849i	0.198488	−	0.980103i	$-0.436397\pi$
$929$	20.6174	−	56.6459i	0.676436	−	1.85849i	0.477948	−	0.878388i	$-0.341381\pi$
$930$	−9.63420	−	4.33454i	−0.315918	−	0.142135i
$931$	6.54308	+	5.49029i	0.214441	+	0.179937i
$932$	9.42260	+	4.84614i	0.308648	+	0.158741i
$933$	11.8791	+	46.3163i	0.388905	+	1.51633i
$934$	−28.1518	+	17.1781i	−0.921155	+	0.562086i
$935$	14.3740	−	24.8964i	0.470079	−	0.814200i
$936$	45.1443	+	13.8500i	1.47559	+	0.452703i
$937$	−7.33770	−	12.7093i	−0.239712	−	0.415194i	0.720919	−	0.693019i	$-0.243720\pi$
$937$	−7.33770	−	12.7093i	−0.239712	−	0.415194i	−0.960632	+	0.277825i	$0.910386\pi$
$938$	−4.46573	−	2.43567i	−0.145811	−	0.0795274i
$939$	8.22042	+	12.0123i	0.268263	+	0.392008i
$940$	−31.2276	−	48.4877i	−1.01853	−	1.58150i
$941$	7.44311	−	42.2120i	0.242638	−	1.37607i	−0.583276	−	0.812274i	$-0.698229\pi$
$941$	7.44311	−	42.2120i	0.242638	−	1.37607i	0.825914	−	0.563796i	$-0.190660\pi$
$942$	−3.97139	+	15.6677i	−0.129395	+	0.510481i
$943$	−7.64908	−	9.11582i	−0.249088	−	0.296852i
$944$	−9.92834	−	20.7540i	−0.323140	−	0.675487i
$945$	5.63505	+	24.1100i	0.183308	+	0.784299i
$946$	16.8966	−	21.1595i	0.549356	−	0.687954i
$947$	−14.9721	−	17.8430i	−0.486527	−	0.579820i	0.465804	−	0.884888i	$-0.345765\pi$
$947$	−14.9721	−	17.8430i	−0.486527	−	0.579820i	−0.952331	+	0.305068i	$0.901321\pi$
$948$	4.55337	+	36.2071i	0.147887	+	1.17595i
$949$	−41.5465	−	7.32577i	−1.34866	−	0.237805i
$950$	−2.85458	−	0.961148i	−0.0926147	−	0.0311838i
$951$	19.3628	−	40.3863i	0.627882	−	1.30961i
$952$	39.9538	+	11.3252i	1.29491	+	0.367053i
$953$	−40.0401	+	23.1172i	−1.29703	+	0.748838i	−0.979889	−	0.199542i	$-0.936055\pi$
$953$	−40.0401	+	23.1172i	−1.29703	+	0.748838i	−0.317136	+	0.948380i	$0.602721\pi$
$954$	−14.7820	−	40.2598i	−0.478585	−	1.30346i
$955$	−25.2929	+	43.8086i	−0.818459	+	1.41761i
$956$	6.49624	−	51.2990i	0.210103	−	1.65913i
$957$	−0.136442	+	0.488189i	−0.00441055	+	0.0157809i
$958$	5.75756	+	28.5765i	0.186018	+	0.923264i
$959$	16.2864	+	13.6659i	0.525914	+	0.441294i
$960$	−32.9971	−	4.20749i	−1.06498	−	0.135796i
$961$	−26.0975	−	9.49871i	−0.841855	−	0.306410i
$962$	−30.0786	+	11.7825i	−0.969773	+	0.379882i
$963$	−5.20487	+	1.76885i	−0.167725	+	0.0570005i
$964$	−35.4029	+	32.7637i	−1.14025	+	1.05525i
$965$	5.15536	+	29.2375i	0.165957	+	0.941189i
$966$	7.33048	−	10.7769i	0.235854	−	0.346742i
$967$	12.2837	+	33.7493i	0.395018	+	1.08530i	0.964680	+	0.263425i	$0.0848520\pi$
$967$	12.2837	+	33.7493i	0.395018	+	1.08530i	−0.569662	+	0.821879i	$0.692926\pi$
$968$	19.2158	+	13.8720i	0.617618	+	0.445864i
$969$	−20.8243	+	29.0711i	−0.668974	+	0.933898i
$970$	18.9833	−	0.461087i	0.609518	−	0.0148046i
$971$		−	8.00721i		−	0.256963i	−0.991712	−	0.128482i	$-0.958990\pi$
$971$		−	8.00721i		−	0.256963i	0.991712	−	0.128482i	$-0.0410104\pi$
$972$	−31.0717	+	2.55894i	−0.996626	+	0.0820781i
$973$		−	39.8703i		−	1.27818i
$974$	0.292008	+	12.0222i	0.00935656	+	0.385217i
$975$	4.28321	−	5.97942i	0.137172	−	0.191495i
$976$	29.7673	−	8.29190i	0.952829	−	0.265417i
$977$	1.76473	+	4.84855i	0.0564587	+	0.155119i	0.964716	−	0.263294i	$-0.0848088\pi$
$977$	1.76473	+	4.84855i	0.0564587	+	0.155119i	−0.908257	+	0.418413i	$0.862587\pi$
$978$	4.16407	+	2.83240i	0.133152	+	0.0905702i
$979$	−3.20652	−	18.1851i	−0.102481	−	0.581197i
$980$	10.7835	−	9.97964i	0.344467	−	0.318788i
$981$	8.08665	−	2.74821i	0.258187	−	0.0877437i
$982$	−16.2129	−	41.3888i	−0.517374	−	1.32077i
$983$	38.8483	+	14.1396i	1.23907	+	0.450984i	0.876693	−	0.481049i	$-0.159744\pi$
$983$	38.8483	+	14.1396i	1.23907	+	0.450984i	0.362374	+	0.932033i	$0.381966\pi$
$984$	−20.6157	+	6.92161i	−0.657204	+	0.220653i
$985$	21.8910	+	18.3687i	0.697504	+	0.585275i
$986$	1.85382	−	0.373505i	0.0590376	−	0.0118948i
$987$	11.1159	−	39.7727i	0.353824	−	1.26598i
$988$	−30.8196	−	3.90283i	−0.980501	−	0.124166i
$989$	−15.8527	+	27.4578i	−0.504088	+	0.873106i
$990$	−15.4783	+	5.68311i	−0.491934	+	0.180621i
$991$	7.71200	−	4.45253i	0.244980	−	0.141439i	−0.372484	−	0.928039i	$-0.621494\pi$
$991$	7.71200	−	4.45253i	0.244980	−	0.141439i	0.617463	+	0.786600i	$0.288160\pi$
$992$	10.1485	+	0.539511i	0.322216	+	0.0171295i
$993$	−4.43674	+	9.25400i	−0.140796	+	0.293667i
$994$	2.24149	−	6.65713i	0.0710956	−	0.211151i
$995$	49.3240	+	8.69716i	1.56368	+	0.275719i
$996$	0.482901	+	3.83990i	0.0153013	+	0.121672i
$997$	−25.0177	−	29.8149i	−0.792317	−	0.944247i	0.207102	−	0.978319i	$-0.433597\pi$
$997$	−25.0177	−	29.8149i	−0.792317	−	0.944247i	−0.999419	+	0.0340726i	$0.989152\pi$
$998$	−24.9628	−	19.9337i	−0.790182	−	0.630989i
$999$	15.5590	−	14.5879i	0.492264	−	0.461542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.59.32	yes	192
3.2	odd	2		648.2.v.b.611.1		192
4.3	odd	2		864.2.bh.b.815.5		192
8.3	odd	2	inner	216.2.v.b.59.16	yes	192
8.5	even	2		864.2.bh.b.815.6		192
24.11	even	2		648.2.v.b.611.17		192
27.11	odd	18	inner	216.2.v.b.11.16	✓	192
27.16	even	9		648.2.v.b.35.17		192
108.11	even	18		864.2.bh.b.335.6		192
216.11	even	18	inner	216.2.v.b.11.32	yes	192
216.43	odd	18		648.2.v.b.35.1		192
216.173	odd	18		864.2.bh.b.335.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.16	✓	192	27.11	odd	18	inner
216.2.v.b.11.32	yes	192	216.11	even	18	inner
216.2.v.b.59.16	yes	192	8.3	odd	2	inner
216.2.v.b.59.32	yes	192	1.1	even	1	trivial
648.2.v.b.35.1		192	216.43	odd	18
648.2.v.b.35.17		192	27.16	even	9
648.2.v.b.611.1		192	3.2	odd	2
648.2.v.b.611.17		192	24.11	even	2
864.2.bh.b.335.5		192	216.173	odd	18
864.2.bh.b.335.6		192	108.11	even	18
864.2.bh.b.815.5		192	4.3	odd	2
864.2.bh.b.815.6		192	8.5	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41380 - 0.0343398i) q^{2} +(1.40807 + 1.00863i) q^{3} +(1.99764 - 0.0970990i) q^{4} +(-2.25586 + 0.821067i) q^{5} +(2.02536 + 1.37765i) q^{6} +(-1.95474 + 0.344674i) q^{7} +(2.82092 - 0.205877i) q^{8} +(0.965315 + 2.84045i) q^{9} +(-3.16114 + 1.23829i) q^{10} +(0.553700 - 1.52128i) q^{11} +(2.91075 + 1.87817i) q^{12} +(3.57715 - 4.26309i) q^{13} +(-2.75177 + 0.554424i) q^{14} +(-4.00457 - 1.11922i) q^{15} +(3.98114 - 0.387938i) q^{16} +(-6.40600 - 3.69851i) q^{17} +(1.46230 + 3.98267i) q^{18} +(-1.39557 - 2.41719i) q^{19} +(-4.42668 + 1.85924i) q^{20} +(-3.10006 - 1.48630i) q^{21} +(0.730579 - 2.16979i) q^{22} +(-0.465506 + 2.64002i) q^{23} +(4.17971 + 2.55539i) q^{24} +(0.584547 - 0.490493i) q^{25} +(4.91098 - 6.14998i) q^{26} +(-1.50575 + 4.97320i) q^{27} +(-3.87141 + 0.878338i) q^{28} +(-0.138481 + 0.116199i) q^{29} +(-5.70008 - 1.44484i) q^{30} +(1.76926 + 0.311969i) q^{31} +(5.61521 - 0.685177i) q^{32} +(2.31406 - 1.58358i) q^{33} +(-9.18379 - 5.00895i) q^{34} +(4.12663 - 2.38251i) q^{35} +(2.20416 + 5.58047i) q^{36} +(-3.55469 - 2.05230i) q^{37} +(-2.05606 - 3.36950i) q^{38} +(9.33677 - 2.39468i) q^{39} +(-6.19458 + 2.78060i) q^{40} +(-2.85334 + 3.40048i) q^{41} +(-4.43390 - 1.99486i) q^{42} +(11.1139 + 4.04511i) q^{43} +(0.958380 - 3.09273i) q^{44} +(-4.50982 - 5.61508i) q^{45} +(-0.567474 + 3.74843i) q^{46} +(2.08588 + 11.8296i) q^{47} +(5.99701 + 3.46927i) q^{48} +(-2.87563 + 1.04664i) q^{49} +(0.809587 - 0.713530i) q^{50} +(-5.28965 - 11.6691i) q^{51} +(6.73193 - 8.86346i) q^{52} -10.1087 q^{53} +(-1.95804 + 7.08280i) q^{54} +3.88642i q^{55} +(-5.44322 + 1.37474i) q^{56} +(0.473009 - 4.81119i) q^{57} +(-0.191794 + 0.169038i) q^{58} +(-1.96718 - 5.40478i) q^{59} +(-8.10836 - 1.84696i) q^{60} +(7.60780 - 1.34146i) q^{61} +(2.51209 + 0.380305i) q^{62} +(-2.86597 - 5.21963i) q^{63} +(7.91523 - 1.16153i) q^{64} +(-4.56929 + 12.5540i) q^{65} +(3.21723 - 2.31833i) q^{66} +(1.38817 + 1.16481i) q^{67} +(-13.1560 - 6.76627i) q^{68} +(-3.31828 + 3.24780i) q^{69} +(5.75240 - 3.51010i) q^{70} +(-1.25119 + 2.16713i) q^{71} +(3.30786 + 7.81396i) q^{72} +(-3.79038 - 6.56514i) q^{73} +(-5.09608 - 2.77947i) q^{74} +(1.31781 - 0.101054i) q^{75} +(-3.02255 - 4.69318i) q^{76} +(-0.557996 + 3.16455i) q^{77} +(13.1181 - 3.70621i) q^{78} +(6.77140 + 8.06984i) q^{79} +(-8.66239 + 4.14392i) q^{80} +(-7.13633 + 5.48386i) q^{81} +(-3.91727 + 4.90557i) q^{82} +(0.718131 + 0.855836i) q^{83} +(-6.33713 - 2.66807i) q^{84} +(17.4878 + 3.08357i) q^{85} +(15.8516 + 5.33732i) q^{86} +(-0.312194 + 0.0239400i) q^{87} +(1.24875 - 4.40541i) q^{88} +(9.87804 - 5.70309i) q^{89} +(-6.56879 - 7.78372i) q^{90} +(-5.52304 + 9.56619i) q^{91} +(-0.673572 + 5.31901i) q^{92} +(2.17658 + 2.22381i) q^{93} +(3.35523 + 16.6530i) q^{94} +(5.13289 + 4.30701i) q^{95} +(8.59769 + 4.69891i) q^{96} +(-5.25587 - 1.91298i) q^{97} +(-4.02961 + 1.57849i) q^{98} +(4.85561 + 0.104246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

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Groups

Database

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