LMFDB - Embedded newform 361.2.k.a.4.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(4,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(342)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.k (of order $171$, degree $108$, 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$3348$
Relative dimension:	$31$ over $\Q(\zeta_{171})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{171}]$

Embedding invariants

Embedding label			4.18
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.328494 + 0.00603573i) q^{2} +(0.508770 - 0.339105i) q^{3} +(-1.89078 - 0.0695056i) q^{4} +(0.597036 + 1.23561i) q^{5} +(0.169175 - 0.108323i) q^{6} +(-2.54147 + 1.03226i) q^{7} +(-1.27679 - 0.0704424i) q^{8} +(-1.01056 + 2.42394i) q^{9} +(0.188665 + 0.409493i) q^{10} +(-0.904649 + 2.89232i) q^{11} +(-0.985542 + 0.605810i) q^{12} +(-2.12545 + 0.517507i) q^{13} +(-0.841087 + 0.323750i) q^{14} +(0.722755 + 0.426182i) q^{15} +(3.35491 + 0.246989i) q^{16} +(0.0538641 + 0.0858493i) q^{17} +(-0.346592 + 0.790150i) q^{18} +(4.32444 + 0.546994i) q^{19} +(-1.04298 - 2.37776i) q^{20} +(-0.942981 + 1.38701i) q^{21} +(-0.314629 + 0.944649i) q^{22} +(-1.42317 + 0.703864i) q^{23} +(-0.673480 + 0.397127i) q^{24} +(1.93691 - 2.44192i) q^{25} +(-0.701319 + 0.157169i) q^{26} +(0.659479 + 3.37616i) q^{27} +(4.87710 - 1.77512i) q^{28} +(-6.68483 - 2.15846i) q^{29} +(0.234848 + 0.144361i) q^{30} +(-5.07802 + 4.42245i) q^{31} +(3.64725 + 0.335980i) q^{32} +(0.520543 + 1.77830i) q^{33} +(0.0171759 + 0.0285261i) q^{34} +(-2.79281 - 2.52396i) q^{35} +(2.07922 - 4.51290i) q^{36} +(5.54218 + 6.02041i) q^{37} +(1.41725 + 0.205785i) q^{38} +(-0.905875 + 0.984042i) q^{39} +(-0.675250 - 1.61967i) q^{40} +(-2.11411 - 5.97878i) q^{41} +(-0.318135 + 0.449931i) q^{42} +(-2.45885 - 3.47749i) q^{43} +(1.91152 - 5.40586i) q^{44} +(-3.59838 + 0.198528i) q^{45} +(-0.471752 + 0.222625i) q^{46} +(6.74687 + 3.49253i) q^{47} +(1.79063 - 1.01201i) q^{48} +(0.376032 - 0.365810i) q^{49} +(0.651000 - 0.790465i) q^{50} +(0.0565164 + 0.0254120i) q^{51} +(4.05472 - 0.830761i) q^{52} +(0.0771540 + 1.67865i) q^{53} +(0.196257 + 1.11303i) q^{54} +(-4.11388 + 0.609030i) q^{55} +(3.31763 - 1.13895i) q^{56} +(2.38564 - 1.18815i) q^{57} +(-2.18290 - 0.749390i) q^{58} +(2.08612 + 0.387631i) q^{59} +(-1.33695 - 0.856052i) q^{60} +(1.09242 - 9.10439i) q^{61} +(-1.69479 + 1.42210i) q^{62} +(0.0661730 - 7.20352i) q^{63} +(-5.49106 - 0.607751i) q^{64} +(-1.90840 - 2.31725i) q^{65} +(0.160262 + 0.587302i) q^{66} +(-1.38511 + 5.92501i) q^{67} +(-0.0958781 - 0.166066i) q^{68} +(-0.485385 + 0.840711i) q^{69} +(-0.902186 - 0.845962i) q^{70} +(1.68299 + 14.0263i) q^{71} +(1.46102 - 3.02368i) q^{72} +(6.97701 - 13.1802i) q^{73} +(1.78423 + 2.01112i) q^{74} +(0.157372 - 1.89919i) q^{75} +(-8.13854 - 1.33482i) q^{76} +(-0.686479 - 8.28457i) q^{77} +(-0.303514 + 0.317784i) q^{78} +(4.01264 - 0.369639i) q^{79} +(1.69782 + 4.29281i) q^{80} +(-4.06488 - 4.10240i) q^{81} +(-0.658384 - 1.97675i) q^{82} +(6.90798 + 1.95339i) q^{83} +(1.87937 - 2.55698i) q^{84} +(-0.0739172 + 0.117810i) q^{85} +(-0.786726 - 1.15717i) q^{86} +(-4.13299 + 1.16870i) q^{87} +(1.35879 - 3.62916i) q^{88} +(-3.89817 - 7.36400i) q^{89} +(-1.18324 + 0.0434964i) q^{90} +(4.86755 - 3.50923i) q^{91} +(2.73983 - 1.23193i) q^{92} +(-1.08387 + 3.97199i) q^{93} +(2.19522 + 1.18800i) q^{94} +(1.90598 + 5.66989i) q^{95} +(1.96955 - 1.06587i) q^{96} +(3.31917 + 14.1983i) q^{97} +(0.125732 - 0.117897i) q^{98} +(-6.09662 - 5.11567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) $ 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{171}\right)$

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 $

$2$	0.328494	+	0.00603573i	0.232280	+	0.00426790i	0.134387	−	0.990929i	$-0.457094\pi$
$2$	0.328494	+	0.00603573i	0.232280	+	0.00426790i	0.0978936	+	0.995197i	$0.468790\pi$
$3$	0.508770	−	0.339105i	0.293739	−	0.195782i	−0.399038	−	0.916934i	$-0.630656\pi$
$3$	0.508770	−	0.339105i	0.293739	−	0.195782i	0.692777	+	0.721152i	$0.256387\pi$
$4$	−1.89078	−	0.0695056i	−0.945389	−	0.0347528i
$5$	0.597036	+	1.23561i	0.267003	+	0.552580i	0.990462	−	0.137787i	$-0.0439988\pi$
$5$	0.597036	+	1.23561i	0.267003	+	0.552580i	−0.723459	+	0.690367i	$0.757449\pi$
$6$	0.169175	−	0.108323i	0.0690652	−	0.0442227i
$7$	−2.54147	+	1.03226i	−0.960585	+	0.390156i	−0.802089	−	0.597204i	$-0.796278\pi$
$7$	−2.54147	+	1.03226i	−0.960585	+	0.390156i	−0.158495	+	0.987360i	$0.550664\pi$
$8$	−1.27679	−	0.0704424i	−0.451413	−	0.0249052i
$9$	−1.01056	+	2.42394i	−0.336852	+	0.807980i
$10$	0.188665	+	0.409493i	0.0596610	+	0.129493i
$11$	−0.904649	+	2.89232i	−0.272762	+	0.872068i	0.712597	+	0.701574i	$0.247519\pi$
$11$	−0.904649	+	2.89232i	−0.272762	+	0.872068i	−0.985359	+	0.170494i	$0.945464\pi$
$12$	−0.985542	+	0.605810i	−0.284501	+	0.174882i
$13$	−2.12545	+	0.517507i	−0.589493	+	0.143531i	−0.520169	−	0.854063i	$-0.674131\pi$
$13$	−2.12545	+	0.517507i	−0.589493	+	0.143531i	−0.0693239	+	0.997594i	$0.522084\pi$
$14$	−0.841087	+	0.323750i	−0.224790	+	0.0865257i
$15$	0.722755	+	0.426182i	0.186615	+	0.110040i
$16$	3.35491	+	0.246989i	0.838726	+	0.0617471i
$17$	0.0538641	+	0.0858493i	0.0130640	+	0.0208215i	0.853541	−	0.521025i	$-0.174450\pi$
$17$	0.0538641	+	0.0858493i	0.0130640	+	0.0208215i	−0.840477	+	0.541847i	$0.817725\pi$
$18$	−0.346592	+	0.790150i	−0.0816925	+	0.186240i
$19$	4.32444	+	0.546994i	0.992095	+	0.125489i
$19$	4.32444	+	0.546994i	0.992095	+	0.125489i
$20$	−1.04298	−	2.37776i	−0.233218	−	0.531683i
$21$	−0.942981	+	1.38701i	−0.205775	+	0.302669i
$22$	−0.314629	+	0.944649i	−0.0670790	+	0.201400i
$23$	−1.42317	+	0.703864i	−0.296752	+	0.146766i	−0.585579	−	0.810616i	$-0.699133\pi$
$23$	−1.42317	+	0.703864i	−0.296752	+	0.146766i	0.288826	+	0.957381i	$0.406735\pi$
$24$	−0.673480	+	0.397127i	−0.137474	+	0.0810632i
$25$	1.93691	−	2.44192i	0.387381	−	0.488384i
$26$	−0.701319	+	0.157169i	−0.137540	+	0.0308234i
$27$	0.659479	+	3.37616i	0.126917	+	0.649743i
$28$	4.87710	−	1.77512i	0.921685	−	0.335466i
$29$	−6.68483	−	2.15846i	−1.24134	−	0.400817i	−0.387753	−	0.921763i	$-0.626749\pi$
$29$	−6.68483	−	2.15846i	−1.24134	−	0.400817i	−0.853589	+	0.520946i	$0.825579\pi$
$30$	0.234848	+	0.144361i	0.0428772	+	0.0263565i
$31$	−5.07802	+	4.42245i	−0.912039	+	0.794295i	−0.979084	−	0.203455i	$-0.934783\pi$
$31$	−5.07802	+	4.42245i	−0.912039	+	0.794295i	0.0670457	+	0.997750i	$0.478643\pi$
$32$	3.64725	+	0.335980i	0.644750	+	0.0593935i
$33$	0.520543	+	1.77830i	0.0906149	+	0.309562i
$34$	0.0171759	+	0.0285261i	0.00294564	+	0.00489218i
$35$	−2.79281	−	2.52396i	−0.472071	−	0.426628i
$36$	2.07922	−	4.51290i	0.346536	−	0.752149i
$37$	5.54218	+	6.02041i	0.911129	+	0.989749i	0.999980	−	0.00629545i	$-0.00200392\pi$
$37$	5.54218	+	6.02041i	0.911129	+	0.989749i	−0.0888517	+	0.996045i	$0.528320\pi$
$38$	1.41725	+	0.205785i	0.229908	+	0.0333828i
$39$	−0.905875	+	0.984042i	−0.145056	+	0.157573i
$40$	−0.675250	−	1.61967i	−0.106766	−	0.256092i
$41$	−2.11411	−	5.97878i	−0.330168	−	0.933728i	−0.984169	−	0.177234i	$-0.943285\pi$
$41$	−2.11411	−	5.97878i	−0.330168	−	0.933728i	0.654001	−	0.756494i	$-0.273089\pi$
$42$	−0.318135	+	0.449931i	−0.0490893	+	0.0694259i
$43$	−2.45885	−	3.47749i	−0.374970	−	0.530313i	0.584771	−	0.811199i	$-0.301185\pi$
$43$	−2.45885	−	3.47749i	−0.374970	−	0.530313i	−0.959741	+	0.280886i	$0.909372\pi$
$44$	1.91152	−	5.40586i	0.288173	−	0.814964i
$45$	−3.59838	+	0.198528i	−0.536415	+	0.0295948i
$46$	−0.471752	+	0.222625i	−0.0695560	+	0.0328243i
$47$	6.74687	+	3.49253i	0.984132	+	0.509438i	0.874756	−	0.484563i	$-0.161021\pi$
$47$	6.74687	+	3.49253i	0.984132	+	0.509438i	0.109376	+	0.994000i	$0.465115\pi$
$48$	1.79063	−	1.01201i	0.258455	−	0.146070i
$49$	0.376032	−	0.365810i	0.0537189	−	0.0522585i
$50$	0.651000	−	0.790465i	0.0920653	−	0.111789i
$51$	0.0565164	+	0.0254120i	0.00791388	+	0.00355839i
$52$	4.05472	−	0.830761i	0.562288	−	0.115206i
$53$	0.0771540	+	1.67865i	0.0105979	+	0.230580i	0.997569	+	0.0696831i	$0.0221988\pi$
$53$	0.0771540	+	1.67865i	0.0105979	+	0.230580i	−0.986971	+	0.160897i	$0.948561\pi$
$54$	0.196257	+	1.11303i	0.0267072	+	0.151464i
$55$	−4.11388	+	0.609030i	−0.554716	+	0.0821216i
$56$	3.31763	−	1.13895i	0.443338	−	0.152198i
$57$	2.38564	−	1.18815i	0.315985	−	0.157374i
$58$	−2.18290	−	0.749390i	−0.286629	−	0.0983997i
$59$	2.08612	+	0.387631i	0.271590	+	0.0504653i	0.316731	−	0.948515i	$-0.397415\pi$
$59$	2.08612	+	0.387631i	0.271590	+	0.0504653i	−0.0451410	+	0.998981i	$0.514374\pi$
$60$	−1.33695	−	0.856052i	−0.172599	−	0.110516i
$61$	1.09242	−	9.10439i	0.139870	−	1.16570i	−0.733865	−	0.679295i	$-0.762286\pi$
$61$	1.09242	−	9.10439i	0.139870	−	1.16570i	0.873735	−	0.486402i	$-0.161691\pi$
$62$	−1.69479	+	1.42210i	−0.215238	+	0.180606i
$63$	0.0661730	−	7.20352i	0.00833702	−	0.907559i
$64$	−5.49106	−	0.607751i	−0.686383	−	0.0759688i
$65$	−1.90840	−	2.31725i	−0.236708	−	0.287419i
$66$	0.160262	+	0.587302i	0.0197269	+	0.0722919i
$67$	−1.38511	+	5.92501i	−0.169218	+	0.723855i	0.819377	+	0.573255i	$0.194320\pi$
$67$	−1.38511	+	5.92501i	−0.169218	+	0.723855i	−0.988595	+	0.150600i	$0.951879\pi$
$68$	−0.0958781	−	0.166066i	−0.0116269	−	0.0201384i
$69$	−0.485385	+	0.840711i	−0.0584334	+	0.101210i
$70$	−0.902186	−	0.845962i	−0.107832	−	0.101112i
$71$	1.68299	+	14.0263i	0.199734	+	1.66462i	0.641226	+	0.767352i	$0.278426\pi$
$71$	1.68299	+	14.0263i	0.199734	+	1.66462i	−0.441492	+	0.897265i	$0.645551\pi$
$72$	1.46102	−	3.02368i	0.172183	−	0.356344i
$73$	6.97701	−	13.1802i	0.816597	−	1.54263i	−0.0232031	−	0.999731i	$-0.507386\pi$
$73$	6.97701	−	13.1802i	0.816597	−	1.54263i	0.839800	−	0.542895i	$-0.182672\pi$
$74$	1.78423	+	2.01112i	0.207413	+	0.233788i
$75$	0.157372	−	1.89919i	0.0181717	−	0.219300i
$76$	−8.13854	−	1.33482i	−0.933555	−	0.153114i
$77$	−0.686479	−	8.28457i	−0.0782316	−	0.944115i
$78$	−0.303514	+	0.317784i	−0.0343661	+	0.0359820i
$79$	4.01264	−	0.369639i	0.451457	−	0.0415876i	0.136386	−	0.990656i	$-0.456451\pi$
$79$	4.01264	−	0.369639i	0.451457	−	0.0415876i	0.315071	+	0.949068i	$0.397972\pi$
$80$	1.69782	+	4.29281i	0.189822	+	0.479950i
$81$	−4.06488	−	4.10240i	−0.451654	−	0.455822i
$82$	−0.658384	−	1.97675i	−0.0727064	−	0.218296i
$83$	6.90798	+	1.95339i	0.758249	+	0.214412i	0.629219	−	0.777228i	$-0.283375\pi$
$83$	6.90798	+	1.95339i	0.758249	+	0.214412i	0.129030	+	0.991641i	$0.458814\pi$
$84$	1.87937	−	2.55698i	0.205056	−	0.278989i
$85$	−0.0739172	+	0.117810i	−0.00801744	+	0.0127783i
$86$	−0.786726	−	1.15717i	−0.0848349	−	0.124781i
$87$	−4.13299	+	1.16870i	−0.443103	+	0.125298i
$88$	1.35879	−	3.62916i	0.144847	−	0.386870i
$89$	−3.89817	−	7.36400i	−0.413205	−	0.780582i	0.586361	−	0.810050i	$-0.300560\pi$
$89$	−3.89817	−	7.36400i	−0.413205	−	0.780582i	−0.999566	+	0.0294680i	$0.990619\pi$
$90$	−1.18324	+	0.0434964i	−0.124725	+	0.00458492i
$91$	4.86755	−	3.50923i	0.510258	−	0.367867i
$92$	2.73983	−	1.23193i	0.285647	−	0.128438i
$93$	−1.08387	+	3.97199i	−0.112392	+	0.411876i
$94$	2.19522	+	1.18800i	0.226420	+	0.122532i
$95$	1.90598	+	5.66989i	0.195549	+	0.581718i
$96$	1.96955	−	1.06587i	0.201016	−	0.108784i
$97$	3.31917	+	14.1983i	0.337011	+	1.44162i	0.823194	+	0.567761i	$0.192190\pi$
$97$	3.31917	+	14.1983i	0.337011	+	1.44162i	−0.486183	+	0.873857i	$0.661611\pi$
$98$	0.125732	−	0.117897i	0.0127009	−	0.0119094i
$99$	−6.09662	−	5.11567i	−0.612733	−	0.514144i
$100$	−3.83199	+	4.48251i	−0.383199	+	0.448251i
$101$	9.29631	+	12.1730i	0.925018	+	1.21126i	0.977136	+	0.212615i	$0.0681980\pi$
$101$	9.29631	+	12.1730i	0.925018	+	1.21126i	−0.0521185	+	0.998641i	$0.516597\pi$
$102$	0.0184119	+	0.00868879i	0.00182305	+	0.000860318i
$103$	−9.26274	−	3.76220i	−0.912685	−	0.370701i	−0.128846	−	0.991665i	$-0.541127\pi$
$103$	−9.26274	−	3.76220i	−0.912685	−	0.370701i	−0.783839	+	0.620964i	$0.786741\pi$
$104$	2.75020	−	0.511026i	0.269680	−	0.0501103i
$105$	−2.27679	−	0.337062i	−0.222192	−	0.0328938i
$106$	0.0152127	+	0.551890i	0.00147759	+	0.0536043i
$107$	−2.89370	+	14.8141i	−0.279744	+	1.43213i	0.531317	+	0.847173i	$0.321697\pi$
$107$	−2.89370	+	14.8141i	−0.279744	+	1.43213i	−0.811061	+	0.584961i	$0.801110\pi$
$108$	−1.01227	−	6.42942i	−0.0974054	−	0.618671i
$109$	0.0301470	−	0.655911i	0.00288756	−	0.0628249i	−0.997008	−	0.0773033i	$-0.975369\pi$
$109$	0.0301470	−	0.655911i	0.00288756	−	0.0628249i	0.999895	+	0.0144784i	$0.00460879\pi$
$110$	−1.35506	+	0.175232i	−0.129200	+	0.0167077i
$111$	4.86125	+	1.18363i	0.461409	+	0.112345i
$112$	−8.78134	+	2.83541i	−0.829759	+	0.267921i
$113$	6.36347	−	4.95289i	0.598625	−	0.465929i	−0.269005	−	0.963139i	$-0.586695\pi$
$113$	6.36347	−	4.95289i	0.598625	−	0.465929i	0.867630	+	0.497210i	$0.165642\pi$
$114$	0.790838	−	0.375899i	0.0740687	−	0.0352062i
$115$	−1.71939	−	1.33825i	−0.160333	−	0.124793i
$116$	12.4895	+	4.54581i	1.15962	+	0.422068i
$117$	0.893477	−	5.67493i	0.0826020	−	0.524647i
$118$	0.682939	+	0.139926i	0.0628696	+	0.0128812i
$119$	−0.225512	−	0.162582i	−0.0206727	−	0.0149038i
$120$	−0.892785	−	0.595058i	−0.0814997	−	0.0543211i
$121$	1.49242	+	1.03482i	0.135674	+	0.0940744i
$122$	0.413804	−	2.98414i	0.0374641	−	0.270171i
$123$	−3.10303	−	2.32492i	−0.279791	−	0.209631i
$124$	9.90879	−	8.00892i	0.889836	−	0.719222i
$125$	10.8690	+	2.43581i	0.972156	+	0.217865i
$126$	0.0652159	−	2.36591i	0.00580990	−	0.210772i
$127$	1.54600	−	8.76781i	0.137185	−	0.778017i	−0.836128	−	0.548535i	$-0.815186\pi$
$127$	1.54600	−	8.76781i	0.137185	−	0.778017i	0.973313	−	0.229482i	$-0.0737032\pi$
$128$	−9.06501	−	1.17226i	−0.801241	−	0.103614i
$129$	−2.43022	−	0.935438i	−0.213969	−	0.0823607i
$130$	−0.612912	−	0.772719i	−0.0537560	−	0.0677720i
$131$	−4.30869	−	3.48256i	−0.376452	−	0.304272i	0.421693	−	0.906739i	$-0.361436\pi$
$131$	−4.30869	−	3.48256i	−0.376452	−	0.304272i	−0.798144	+	0.602466i	$0.794185\pi$
$132$	−0.860630	−	3.39855i	−0.0749082	−	0.295806i
$133$	−11.5551	+	3.07376i	−1.00195	+	0.266529i
$134$	−0.490760	+	1.93797i	−0.0423952	+	0.167415i
$135$	−3.77788	+	2.83055i	−0.325148	+	0.243615i
$136$	−0.0627257	−	0.113406i	−0.00537869	−	0.00972447i
$137$	6.40471	−	1.93883i	0.547191	−	0.165646i	−0.00404971	−	0.999992i	$-0.501289\pi$
$137$	6.40471	−	1.93883i	0.547191	−	0.165646i	0.551241	+	0.834346i	$0.314155\pi$
$138$	−0.164520	+	0.273238i	−0.0140049	+	0.0232596i
$139$	3.91558	+	1.02992i	0.332115	+	0.0873571i	0.416659	−	0.909063i	$-0.363201\pi$
$139$	3.91558	+	1.02992i	0.332115	+	0.0873571i	−0.0845443	+	0.996420i	$0.526943\pi$
$140$	5.10515	+	4.96637i	0.431464	+	0.419735i
$141$	4.61694	−	0.511003i	0.388817	−	0.0430342i
$142$	0.468193	+	4.61771i	0.0392899	+	0.387510i
$143$	0.425983	−	6.61564i	0.0356225	−	0.553227i
$144$	−3.98901	+	7.88250i	−0.332418	+	0.656875i
$145$	−1.32407	−	9.54851i	−0.109958	−	0.792961i
$146$	2.37146	−	4.28750i	0.196263	−	0.354836i
$147$	0.0672661	−	0.313628i	0.00554801	−	0.0258676i
$148$	−10.0606	−	11.7685i	−0.826974	−	0.967363i
$149$	0.115975	+	12.6249i	0.00950104	+	1.03427i	0.860604	+	0.509275i	$0.170086\pi$
$149$	0.115975	+	12.6249i	0.00950104	+	1.03427i	−0.851103	+	0.524999i	$0.824066\pi$
$150$	0.0631586	−	0.622923i	0.00515688	−	0.0508614i
$151$	10.4091	+	1.73698i	0.847083	+	0.141353i	0.572189	−	0.820121i	$-0.306094\pi$
$151$	10.4091	+	1.73698i	0.847083	+	0.141353i	0.274894	+	0.961475i	$0.411357\pi$
$152$	−5.48287	−	1.00302i	−0.444720	−	0.0813557i
$153$	−0.262526	+	0.0438079i	−0.0212240	+	0.00354166i
$154$	−0.175501	−	2.72557i	−0.0141422	−	0.219633i
$155$	−8.49617	−	3.63407i	−0.682429	−	0.291896i
$156$	1.78120	−	1.79764i	0.142611	−	0.143927i
$157$	−10.9230	−	5.40224i	−0.871752	−	0.431145i	−0.0485007	−	0.998823i	$-0.515444\pi$
$157$	−10.9230	−	5.40224i	−0.871752	−	0.431145i	−0.823251	+	0.567678i	$0.807842\pi$
$158$	1.32036	−	0.0972048i	0.105042	−	0.00773320i
$159$	0.608491	+	0.827882i	0.0482565	+	0.0656553i
$160$	1.76240	+	4.70717i	0.139330	+	0.372134i
$161$	2.89038	−	3.25793i	0.227794	−	0.256761i
$162$	−1.31053	−	1.37215i	−0.102965	−	0.107806i
$163$	0.246105	+	0.214333i	0.0192764	+	0.0167879i	0.666337	−	0.745651i	$-0.267861\pi$
$163$	0.246105	+	0.214333i	0.0192764	+	0.0167879i	−0.647060	+	0.762439i	$0.724002\pi$
$164$	3.58175	+	11.4515i	0.279688	+	0.894211i
$165$	−1.88650	+	1.70490i	−0.146864	+	0.132726i
$166$	2.25744	+	0.683371i	0.175211	+	0.0530399i
$167$	2.75511	+	12.8457i	0.213197	+	0.994030i	0.948619	+	0.316421i	$0.102481\pi$
$167$	2.75511	+	12.8457i	0.213197	+	0.994030i	−0.735422	+	0.677610i	$0.763016\pi$
$168$	1.30169	−	1.70449i	0.100428	−	0.131504i
$169$	−7.29519	+	3.77637i	−0.561168	+	0.290490i
$170$	−0.0249924	+	0.0382537i	−0.00191683	+	0.00293392i
$171$	−5.69598	+	9.92943i	−0.435582	+	0.759322i
$172$	4.40743	+	6.74607i	0.336063	+	0.514383i
$173$	7.22205	+	4.08166i	0.549083	+	0.310323i	0.741459	−	0.670998i	$-0.234134\pi$
$173$	7.22205	+	4.08166i	0.549083	+	0.310323i	−0.192377	+	0.981321i	$0.561619\pi$
$174$	−1.36472	+	0.358965i	−0.103459	+	0.0272130i
$175$	−2.40190	+	8.20545i	−0.181566	+	0.620274i
$176$	−3.74938	+	9.48003i	−0.282620	+	0.714584i
$177$	1.19281	−	0.510200i	0.0896568	−	0.0383490i
$178$	−1.23608	−	2.44255i	−0.0926479	−	0.183077i
$179$	0.767790	−	0.532374i	0.0573873	−	0.0397915i	−0.540767	−	0.841172i	$-0.681866\pi$
$179$	0.767790	−	0.532374i	0.0573873	−	0.0397915i	0.598154	+	0.801381i	$0.295901\pi$
$180$	6.81754	−	0.125265i	0.508149	−	0.00933671i
$181$	−22.2241	+	0.408344i	−1.65190	+	0.0303520i	−0.836303	−	0.548267i	$-0.815288\pi$
$181$	−22.2241	+	0.408344i	−1.65190	+	0.0303520i	−0.815598	+	0.578619i	$0.803592\pi$
$182$	1.62014	−	1.12338i	0.120093	−	0.0832705i
$183$	−2.53155	−	5.00249i	−0.187138	−	0.369794i
$184$	1.86667	−	0.798435i	0.137613	−	0.0588614i
$185$	−4.12998	+	10.4424i	−0.303642	+	0.767737i
$186$	−0.380018	+	1.29823i	−0.0278643	+	0.0951910i
$187$	−0.297032	+	0.0781290i	−0.0217211	+	0.00571336i
$188$	−12.5141	−	7.07254i	−0.912683	−	0.515818i
$189$	−5.16111	−	7.89966i	−0.375415	−	0.574616i
$190$	0.591879	+	1.87403i	0.0429394	+	0.135956i
$191$	−6.45193	+	9.87542i	−0.466845	+	0.714560i	−0.990522	−	0.137357i	$-0.956139\pi$
$191$	−6.45193	+	9.87542i	−0.466845	+	0.714560i	0.523676	+	0.851917i	$0.324560\pi$
$192$	−2.99978	+	1.55284i	−0.216491	+	0.112067i
$193$	−9.90230	+	12.9665i	−0.712783	+	0.933347i	−0.999697	−	0.0246090i	$-0.992166\pi$
$193$	−9.90230	+	12.9665i	−0.712783	+	0.933347i	0.286914	+	0.957956i	$0.407371\pi$
$194$	1.00463	+	4.68408i	0.0721282	+	0.336297i
$195$	−1.75673	−	0.531797i	−0.125802	−	0.0380828i
$196$	−0.736419	+	0.665529i	−0.0526014	+	0.0475378i
$197$	6.31273	+	20.1829i	0.449764	+	1.43797i	0.852533	+	0.522673i	$0.175065\pi$
$197$	6.31273	+	20.1829i	0.449764	+	1.43797i	−0.402770	+	0.915301i	$0.631953\pi$
$198$	−1.97182	−	1.71726i	−0.140131	−	0.122041i
$199$	3.66829	+	3.84076i	0.260038	+	0.272264i	0.840248	−	0.542203i	$-0.182410\pi$
$199$	3.66829	+	3.84076i	0.260038	+	0.272264i	−0.580210	+	0.814467i	$0.697029\pi$
$200$	−2.64504	+	2.98138i	−0.187032	+	0.210815i
$201$	1.30450	+	3.48417i	0.0920124	+	0.245754i
$202$	2.98031	+	4.05485i	0.209694	+	0.285298i
$203$	19.2174	−	1.41479i	1.34880	−	0.0992985i
$204$	−0.105094	−	0.0519766i	−0.00735803	−	0.00363909i
$205$	6.12522	−	6.18175i	0.427804	−	0.431752i
$206$	−3.02004	−	1.29177i	−0.210416	−	0.0900016i
$207$	−0.267927	−	4.16098i	−0.0186222	−	0.289208i
$208$	−7.25849	+	1.21123i	−0.503286	+	0.0839835i
$209$	−5.49418	+	12.0128i	−0.380041	+	0.830946i
$210$	−0.745876	−	0.124465i	−0.0514703	−	0.00858888i
$211$	−0.576954	+	5.69040i	−0.0397191	+	0.391743i	0.955568	+	0.294771i	$0.0952433\pi$
$211$	−0.576954	+	5.69040i	−0.0397191	+	0.391743i	−0.995287	+	0.0969724i	$0.969084\pi$
$212$	−0.0292058	−	3.17931i	−0.00200586	−	0.218356i
$213$	5.61265	+	6.56546i	0.384572	+	0.449858i
$214$	−1.03998	+	4.84888i	−0.0710912	+	0.331462i
$215$	2.82879	−	5.11435i	0.192922	−	0.348796i
$216$	−0.604191	−	4.35711i	−0.0411100	−	0.296464i
$217$	8.34052	−	16.4813i	0.566192	−	1.11882i
$218$	0.0138620	−	0.215281i	0.000938853	−	0.0145806i
$219$	−0.919780	−	9.07164i	−0.0621529	−	0.613004i
$220$	7.82077	−	0.865603i	0.527276	−	0.0583589i
$221$	−0.158913	−	0.154593i	−0.0106896	−	0.0103990i
$222$	1.58975	+	0.418155i	0.106697	+	0.0280647i
$223$	−9.40825	+	15.6254i	−0.630023	+	1.04636i	0.363376	+	0.931643i	$0.381624\pi$
$223$	−9.40825	+	15.6254i	−0.630023	+	1.04636i	−0.993399	+	0.114713i	$0.963405\pi$
$224$	−9.61620	+	2.91101i	−0.642509	+	0.194500i
$225$	3.96172	+	7.16265i	0.264115	+	0.477510i
$226$	2.12025	−	1.58858i	0.141037	−	0.105671i
$227$	−3.57421	+	14.1143i	−0.237229	+	0.936796i	0.730114	+	0.683325i	$0.239467\pi$
$227$	−3.57421	+	14.1143i	−0.237229	+	0.936796i	−0.967343	+	0.253471i	$0.918428\pi$
$228$	−4.59329	+	2.08071i	−0.304198	+	0.137798i
$229$	−6.98920	−	27.5997i	−0.461859	−	1.82384i	−0.559773	−	0.828646i	$-0.689112\pi$
$229$	−6.98920	−	27.5997i	−0.461859	−	1.82384i	0.0979135	−	0.995195i	$-0.468783\pi$
$230$	−0.556730	−	0.449985i	−0.0367097	−	0.0296711i
$231$	−3.15860	−	3.98216i	−0.207821	−	0.262007i
$232$	8.38308	+	3.22680i	0.550376	+	0.211850i
$233$	14.9092	+	1.92801i	0.976732	+	0.126308i	0.599987	−	0.800009i	$-0.295172\pi$
$233$	14.9092	+	1.92801i	0.976732	+	0.126308i	0.376744	+	0.926317i	$0.377044\pi$
$234$	0.327754	−	1.85879i	0.0214259	−	0.121513i
$235$	−0.287271	+	10.4216i	−0.0187395	+	0.679833i
$236$	−3.91746	−	0.877922i	−0.255005	−	0.0571479i
$237$	1.91616	−	1.54877i	0.124468	−	0.100603i
$238$	−0.0730981	−	0.0547682i	−0.00473824	−	0.00355009i
$239$	3.32358	−	23.9679i	0.214985	−	1.55036i	−0.509138	−	0.860685i	$-0.670036\pi$
$239$	3.32358	−	23.9679i	0.214985	−	1.55036i	0.724123	−	0.689671i	$-0.242245\pi$
$240$	2.31951	+	1.60831i	0.149724	+	0.103816i
$241$	1.39318	+	0.928580i	0.0897425	+	0.0598151i	0.598679	−	0.800989i	$-0.295692\pi$
$241$	1.39318	+	0.928580i	0.0897425	+	0.0598151i	−0.508937	+	0.860804i	$0.669961\pi$
$242$	0.484003	+	0.348939i	0.0311129	+	0.0224307i
$243$	−13.5691	−	2.78015i	−0.870460	−	0.178346i
$244$	−2.69833	+	17.1384i	−0.172743	+	1.09718i
$245$	0.676502	+	0.246227i	0.0432201	+	0.0157308i
$246$	−1.00529	−	0.782451i	−0.0640951	−	0.0498872i
$247$	−9.47444	+	1.07532i	−0.602844	+	0.0684213i
$248$	6.79509	−	5.28883i	0.431488	−	0.335841i
$249$	4.17698	−	1.34870i	0.264705	−	0.0854707i
$250$	3.55571	+	0.865750i	0.224883	+	0.0547548i
$251$	19.5736	−	2.53120i	1.23548	−	0.159768i	0.517407	−	0.855739i	$-0.326897\pi$
$251$	19.5736	−	2.53120i	1.23548	−	0.159768i	0.718070	+	0.695971i	$0.245026\pi$
$252$	−0.625804	+	13.6157i	−0.0394219	+	0.857706i
$253$	−0.748330	−	4.75303i	−0.0470471	−	0.298820i
$254$	0.560772	−	2.87084i	0.0351859	−	0.180132i
$255$	0.00234312	+	0.0850039i	0.000146732	+	0.00532315i
$256$	7.95934	+	1.17832i	0.497459	+	0.0736451i
$257$	11.4100	−	2.12013i	0.711734	−	0.132250i	0.185567	−	0.982632i	$-0.440588\pi$
$257$	11.4100	−	2.12013i	0.711734	−	0.132250i	0.526167	+	0.850381i	$0.323629\pi$
$258$	−0.792667	−	0.321953i	−0.0493493	−	0.0200439i
$259$	−20.2999	−	9.57974i	−1.26137	−	0.595256i
$260$	3.44731	+	4.51404i	0.213793	+	0.279949i
$261$	11.9874	−	14.0224i	0.742001	−	0.867965i
$262$	−1.39436	−	1.17000i	−0.0861436	−	0.0722831i
$263$	−4.33041	+	4.06054i	−0.267024	+	0.250383i	−0.805969	−	0.591958i	$-0.798355\pi$
$263$	−4.33041	+	4.06054i	−0.267024	+	0.250383i	0.538945	+	0.842341i	$0.318823\pi$
$264$	−0.539356	−	2.30718i	−0.0331951	−	0.141997i
$265$	−2.02808	+	1.09754i	−0.124584	+	0.0674216i
$266$	−3.81432	+	0.939967i	−0.233871	+	0.0576331i
$267$	−4.48044	−	2.42469i	−0.274199	−	0.148389i
$268$	3.03075	−	11.1066i	0.185133	−	0.678444i
$269$	4.65763	−	2.09425i	0.283980	−	0.127689i	−0.263100	−	0.964769i	$-0.584745\pi$
$269$	4.65763	−	2.09425i	0.283980	−	0.127689i	0.547081	+	0.837080i	$0.315739\pi$
$270$	−1.25809	+	0.907015i	−0.0765652	+	0.0551992i
$271$	−11.9345	+	0.438717i	−0.724971	+	0.0266502i	−0.396719	−	0.917940i	$-0.629851\pi$
$271$	−11.9345	+	0.438717i	−0.724971	+	0.0266502i	−0.328252	+	0.944590i	$0.606459\pi$
$272$	0.159505	+	0.301320i	0.00967143	+	0.0182702i
$273$	1.28647	−	3.43601i	0.0778606	−	0.207957i
$274$	2.11561	−	0.598237i	0.127809	−	0.0361408i
$275$	5.31061	+	7.81124i	0.320242	+	0.471035i
$276$	0.976189	−	1.55586i	0.0587597	−	0.0936518i
$277$	9.42484	−	12.8230i	0.566284	−	0.770457i	−0.424570	−	0.905395i	$-0.639575\pi$
$277$	9.42484	−	12.8230i	0.566284	−	0.770457i	0.990854	+	0.134938i	$0.0430836\pi$
$278$	1.28003	+	0.361957i	0.0767709	+	0.0217087i
$279$	−5.58813	−	16.7780i	−0.334553	−	1.00447i
$280$	3.38804	+	3.41930i	0.202474	+	0.204342i
$281$	−9.44942	−	23.8922i	−0.563705	−	1.42529i	−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−9.44942	−	23.8922i	−0.563705	−	1.42529i	0.315538	−	0.948913i	$-0.397815\pi$
$282$	1.51972	−	0.139995i	0.0904980	−	0.00833656i
$283$	2.98280	−	3.12304i	0.177309	−	0.185645i	−0.628521	−	0.777793i	$-0.716339\pi$
$283$	2.98280	−	3.12304i	0.177309	−	0.185645i	0.805830	+	0.592147i	$0.201720\pi$
$284$	−2.20726	−	26.6376i	−0.130977	−	1.58065i
$285$	2.89239	+	2.23834i	0.171331	+	0.132588i
$286$	0.179863	−	2.17062i	0.0106355	−	0.128352i
$287$	11.5446	+	13.0126i	0.681454	+	0.768108i
$288$	−4.50016	+	8.50120i	−0.265174	+	0.500938i
$289$	7.39165	−	15.2975i	0.434803	−	0.899855i
$290$	−0.377317	−	3.14462i	−0.0221568	−	0.184658i
$291$	6.50341	+	6.09812i	0.381237	+	0.357478i
$292$	−14.1081	+	24.4359i	−0.825613	+	1.43000i
$293$	−5.80618	−	10.0566i	−0.339201	−	0.587513i	0.645082	−	0.764113i	$-0.276823\pi$
$293$	−5.80618	−	10.0566i	−0.339201	−	0.587513i	−0.984283	+	0.176601i	$0.943490\pi$
$294$	0.0239895	−	0.102619i	0.00139909	−	0.00598484i
$295$	0.766531	+	2.80906i	0.0446291	+	0.163550i
$296$	−6.65210	−	8.07720i	−0.386646	−	0.469478i
$297$	−10.3616	−	1.14682i	−0.601238	−	0.0665450i
$298$	−0.0381035	+	4.14790i	−0.00220728	+	0.240282i
$299$	2.66062	−	2.23253i	0.153868	−	0.129110i
$300$	−0.429559	+	3.58001i	−0.0248006	+	0.206692i
$301$	9.83874	+	6.29978i	0.567095	+	0.363113i
$302$	3.40885	+	0.633413i	0.196157	+	0.0364488i
$303$	8.85761	+	3.04082i	0.508856	+	0.174691i
$304$	14.3730	+	2.90320i	0.824348	+	0.166510i
$305$	11.9017	−	4.08584i	0.681487	−	0.233955i
$306$	−0.0865027	+	0.0128061i	−0.00494503	+	0.000732075i
$307$	−3.17680	−	18.0166i	−0.181310	−	1.02826i	−0.930606	−	0.366024i	$-0.880719\pi$
$307$	−3.17680	−	18.0166i	−0.181310	−	1.02826i	0.749296	−	0.662235i	$-0.230392\pi$
$308$	0.722156	+	15.7120i	0.0411487	+	0.895275i
$309$	−5.98839	+	1.22695i	−0.340668	+	0.0697986i
$310$	−2.76900	−	1.24505i	−0.157269	−	0.0707141i
$311$	−17.1101	+	20.7756i	−0.970224	+	1.17808i	0.0137751	+	0.999905i	$0.495615\pi$
$311$	−17.1101	+	20.7756i	−0.970224	+	1.17808i	−0.983999	+	0.178173i	$0.942981\pi$
$312$	1.22593	−	1.19260i	0.0694046	−	0.0675178i
$313$	0.608040	−	0.343644i	0.0343684	−	0.0194239i	−0.474744	−	0.880124i	$-0.657459\pi$
$313$	0.608040	−	0.343644i	0.0343684	−	0.0194239i	0.509112	+	0.860700i	$0.329974\pi$
$314$	−3.55554	−	1.84053i	−0.200650	−	0.103867i
$315$	8.94023	−	4.21900i	0.503725	−	0.237714i
$316$	−7.61270	+	0.420004i	−0.428248	+	0.0236271i
$317$	3.98878	−	11.2804i	0.224032	−	0.633572i	−0.775964	−	0.630777i	$-0.782736\pi$
$317$	3.98878	−	11.2804i	0.224032	−	0.633572i	0.999996	−	0.00279493i	$-0.000889655\pi$
$318$	0.194889	+	0.275627i	0.0109288	+	0.0154564i
$319$	12.2904	−	17.3820i	0.688130	−	0.973208i
$320$	−2.52742	−	7.14765i	−0.141287	−	0.399566i
$321$	3.55132	+	8.51825i	0.198215	+	0.475442i
$322$	0.969136	−	1.05276i	0.0540079	−	0.0586682i
$323$	0.185973	+	0.400714i	0.0103478	+	0.0222963i
$324$	7.40065	+	8.03925i	0.411147	+	0.446625i
$325$	−2.85307	+	6.19254i	−0.158260	+	0.343500i
$326$	0.0795503	+	0.0718925i	0.00440588	+	0.00398175i
$327$	−0.207085	−	0.343931i	−0.0114518	−	0.0190194i
$328$	2.27811	+	7.78256i	0.125788	+	0.429720i
$329$	−20.7521	−	1.91166i	−1.14410	−	0.105393i
$330$	−0.629992	+	0.548661i	−0.0346799	+	0.0302028i
$331$	−2.16987	−	1.33381i	−0.119267	−	0.0733130i	0.462755	−	0.886486i	$-0.346861\pi$
$331$	−2.16987	−	1.33381i	−0.119267	−	0.0733130i	−0.582022	+	0.813173i	$0.697738\pi$
$332$	−12.9257	−	4.17357i	−0.709389	−	0.229055i
$333$	−20.1938	+	7.34995i	−1.10661	+	0.402775i
$334$	0.827504	+	4.23636i	0.0452790	+	0.231803i
$335$	−8.14794	+	1.82600i	−0.445170	+	0.0997649i
$336$	−3.50619	+	4.42037i	−0.191278	+	0.241151i
$337$	13.9500	−	8.22584i	0.759908	−	0.448090i	−0.0758980	−	0.997116i	$-0.524182\pi$
$337$	13.9500	−	8.22584i	0.759908	−	0.448090i	0.835806	+	0.549026i	$0.185001\pi$
$338$	−2.41922	+	1.19648i	−0.131588	+	0.0650800i
$339$	1.55800	−	4.67777i	0.0846187	−	0.254062i
$340$	0.147949	−	0.217615i	0.00802368	−	0.0118018i
$341$	−8.19733	−	18.6880i	−0.443910	−	1.01201i
$342$	−1.93102	+	3.22737i	−0.104418	+	0.174516i
$343$	7.13518	−	16.2666i	0.385263	−	0.878312i
$344$	2.89447	+	4.61323i	0.156059	+	0.248729i
$345$	−1.32858	−	0.0978102i	−0.0715284	−	0.00526593i
$346$	2.34776	+	1.38439i	0.126217	+	0.0744253i
$347$	3.02791	−	1.16550i	0.162547	−	0.0625673i	−0.276587	−	0.960989i	$-0.589203\pi$
$347$	3.02791	−	1.16550i	0.162547	−	0.0625673i	0.439134	+	0.898422i	$0.355285\pi$
$348$	7.89580	−	1.92248i	0.423260	−	0.103056i
$349$	18.2300	−	11.2059i	0.975829	−	0.599840i	0.0586344	−	0.998280i	$-0.481325\pi$
$349$	18.2300	−	11.2059i	0.975829	−	0.599840i	0.917195	+	0.398440i	$0.130448\pi$
$350$	−0.838533	+	2.68094i	−0.0448215	+	0.143302i
$351$	−3.14888	−	6.83457i	−0.168075	−	0.364802i
$352$	−4.27125	+	10.2451i	−0.227658	+	0.546065i
$353$	36.9444	+	2.03828i	1.96635	+	0.108487i	0.992784	−	0.119920i	$-0.0382638\pi$
$353$	36.9444	+	2.03828i	1.96635	+	0.108487i	0.973566	+	0.228407i	$0.0733516\pi$
$354$	0.394909	−	0.160398i	0.0209892	−	0.00852506i
$355$	−16.3262	+	10.4537i	−0.866505	+	0.554826i
$356$	6.85874	+	14.1946i	0.363512	+	0.752314i
$357$	−0.169866	−	0.00624434i	−0.00899028	−	0.000330485i
$358$	0.255427	−	0.170247i	0.0134998	−	0.00899784i
$359$	−33.7612	−	0.620326i	−1.78185	−	0.0327396i	−0.882585	−	0.470153i	$-0.844199\pi$
$359$	−33.7612	−	0.620326i	−1.78185	−	0.0327396i	−0.899261	+	0.437413i	$0.855895\pi$
$360$	4.60836			0.242882
$361$	18.4016	+	4.73089i	0.968505	+	0.248994i
$362$	−7.30293			−0.383833
$363$	1.11021	+	0.0203989i	0.0582709	+	0.00107067i
$364$	−9.44738	+	6.29686i	−0.495177	+	0.330045i
$365$	20.4511	+	0.751788i	1.07046	+	0.0393504i
$366$	−0.801406	−	1.65856i	−0.0418901	−	0.0866946i
$367$	19.6813	−	12.6020i	1.02736	−	0.657821i	0.0863703	−	0.996263i	$-0.472473\pi$
$367$	19.6813	−	12.6020i	1.02736	−	0.657821i	0.940987	+	0.338443i	$0.109900\pi$
$368$	−4.94846	+	2.00989i	−0.257956	+	0.104773i
$369$	16.6286	+	0.917427i	0.865652	+	0.0477593i
$370$	−1.41970	+	3.40532i	−0.0738067	+	0.177034i
$371$	−1.92887	−	4.18658i	−0.100142	−	0.217356i
$372$	2.32543	−	7.43482i	0.120568	−	0.385478i
$373$	−15.5811	+	9.57764i	−0.806757	+	0.495912i	−0.864628	−	0.502412i	$-0.832446\pi$
$373$	−15.5811	+	9.57764i	−0.806757	+	0.495912i	0.0578713	+	0.998324i	$0.481569\pi$
$374$	−0.0980447	+	0.0238721i	−0.00506977	+	0.00123440i
$375$	6.35584	−	2.44648i	0.328214	−	0.126336i
$376$	−8.36831	−	4.93449i	−0.431563	−	0.254477i
$377$	15.3253	+	1.12825i	0.789292	+	0.0581078i
$378$	−1.64771	−	2.62614i	−0.0847491	−	0.135074i
$379$	1.23191	−	2.80847i	0.0632789	−	0.144261i	−0.881289	−	0.472578i	$-0.843323\pi$
$379$	1.23191	−	2.80847i	0.0632789	−	0.144261i	0.944568	+	0.328317i	$0.106481\pi$
$380$	−3.20969	−	10.8530i	−0.164654	−	0.556746i
$381$	−2.18665	−	4.98506i	−0.112025	−	0.255392i
$382$	−2.17902	+	3.20507i	−0.111489	+	0.163986i
$383$	−0.129064	+	0.387505i	−0.00659486	+	0.0198006i	−0.952006	−	0.306080i	$-0.900982\pi$
$383$	−0.129064	+	0.387505i	−0.00659486	+	0.0198006i	0.945411	+	0.325881i	$0.105661\pi$
$384$	−5.00953	+	2.47758i	−0.255641	+	0.126434i
$385$	9.82663	−	5.79441i	0.500811	−	0.295310i
$386$	−3.33110	+	4.19964i	−0.169549	+	0.213756i
$387$	10.9140	−	2.44589i	0.554792	−	0.124332i
$388$	−5.28896	−	27.0765i	−0.268506	−	1.37460i
$389$	−12.5511	+	4.56824i	−0.636368	+	0.231619i	−0.640001	−	0.768374i	$-0.721066\pi$
$389$	−12.5511	+	4.56824i	−0.636368	+	0.231619i	0.00363276	+	0.999993i	$0.498844\pi$
$390$	−0.573865	−	0.185295i	−0.0290588	−	0.00938278i
$391$	−0.137084	−	0.0842654i	−0.00693265	−	0.00426148i
$392$	−0.505883	+	0.440573i	−0.0255509	+	0.0222523i
$393$	−3.37309	−	0.310724i	−0.170150	−	0.0156740i
$394$	1.95187	+	6.66807i	0.0983340	+	0.335932i
$395$	2.85242	+	4.73736i	0.143521	+	0.238362i
$396$	11.1718	+	10.0964i	0.561404	+	0.507361i
$397$	2.85554	−	6.19790i	0.143316	−	0.311064i	−0.823165	−	0.567802i	$-0.807794\pi$
$397$	2.85554	−	6.19790i	0.143316	−	0.311064i	0.966481	+	0.256738i	$0.0826478\pi$
$398$	1.18183	+	1.28381i	0.0592396	+	0.0643514i
$399$	−4.83655	+	5.48222i	−0.242130	+	0.274454i
$400$	7.10126	−	7.71403i	0.355063	−	0.385701i
$401$	−11.9825	−	28.7414i	−0.598377	−	1.43528i	−0.879637	−	0.475647i	$-0.842214\pi$
$401$	−11.9825	−	28.7414i	−0.598377	−	1.43528i	0.281259	−	0.959632i	$-0.409248\pi$
$402$	0.407491	+	1.15240i	0.0203238	+	0.0574765i
$403$	8.50440	−	12.0276i	0.423634	−	0.599137i
$404$	−16.7312	−	23.6625i	−0.832407	−	1.17726i
$405$	2.64207	−	7.47188i	0.131285	−	0.371281i
$406$	6.32133	−	0.348757i	0.313722	−	0.0173085i
$407$	−22.4267	+	10.5834i	−1.11165	+	0.524600i
$408$	−0.0703695	−	0.0364269i	−0.00348381	−	0.00180340i
$409$	−9.84394	+	5.56346i	−0.486751	+	0.275096i	−0.715782	−	0.698324i	$-0.753930\pi$
$409$	−9.84394	+	5.56346i	−0.486751	+	0.275096i	0.229031	+	0.973419i	$0.426444\pi$
$410$	2.04941	−	1.99370i	0.101213	−	0.0984616i
$411$	2.60106	−	3.15829i	0.128301	−	0.155787i
$412$	17.2523	+	7.75730i	0.849960	+	0.382175i
$413$	−5.70195	+	1.16826i	−0.280575	+	0.0574863i
$414$	−0.0628979	−	1.36847i	−0.00309126	−	0.0672568i
$415$	1.71069	+	9.70179i	0.0839744	+	0.476242i
$416$	−7.92592	+	1.17337i	−0.388600	+	0.0575294i
$417$	2.34138	−	0.803798i	0.114658	−	0.0393622i
$418$	−1.87731	+	3.91298i	−0.0918223	+	0.191390i
$419$	11.5037	+	3.94922i	0.561992	+	0.192932i	0.591035	−	0.806646i	$-0.298720\pi$
$419$	11.5037	+	3.94922i	0.561992	+	0.192932i	−0.0290426	+	0.999578i	$0.509246\pi$
$420$	4.28147	+	0.795558i	0.208915	+	0.0388193i
$421$	−7.23574	−	4.63307i	−0.352648	−	0.225802i	0.350959	−	0.936391i	$-0.385856\pi$
$421$	−7.23574	−	4.63307i	−0.352648	−	0.225802i	−0.703607	+	0.710589i	$0.748429\pi$
$422$	−0.223871	+	1.86578i	−0.0108979	+	0.0908247i
$423$	−15.2838	+	12.8246i	−0.743123	+	0.623554i
$424$	0.0197385	−	2.14871i	0.000958586	−	0.104351i
$425$	0.313967	+	0.0347499i	0.0152296	+	0.00168562i
$426$	1.80409	+	2.19059i	0.0874086	+	0.106134i
$427$	6.62170	+	24.2662i	0.320447	+	1.17432i
$428$	6.50100	−	27.8091i	0.314238	−	1.34420i
$429$	−2.02667	−	3.51029i	−0.0978485	−	0.169479i
$430$	0.960110	−	1.66296i	0.0463006	−	0.0801950i
$431$	16.6852	+	15.6454i	0.803699	+	0.753613i	0.972716	−	0.232000i	$-0.0745270\pi$
$431$	16.6852	+	15.6454i	0.803699	+	0.753613i	−0.169017	+	0.985613i	$0.554059\pi$
$432$	1.37862	+	11.4896i	0.0663287	+	0.552794i
$433$	2.03779	−	4.21734i	0.0979298	−	0.202672i	−0.845713	−	0.533638i	$-0.820825\pi$
$433$	2.03779	−	4.21734i	0.0979298	−	0.202672i	0.943643	+	0.330965i	$0.107374\pi$
$434$	2.83929	−	5.36367i	0.136290	−	0.257464i
$435$	−3.91160	−	4.40900i	−0.187547	−	0.211395i
$436$	−0.102591	+	1.23809i	−0.00491321	+	0.0592936i
$437$	−6.53944	+	2.26535i	−0.312824	+	0.108366i
$438$	−0.247388	−	2.98553i	−0.0118206	−	0.142654i
$439$	−7.75038	+	8.11479i	−0.369906	+	0.387298i	−0.881700	−	0.471810i	$-0.843601\pi$
$439$	−7.75038	+	8.11479i	−0.369906	+	0.387298i	0.511795	+	0.859108i	$0.328981\pi$
$440$	5.29546	−	0.487811i	0.252451	−	0.0232555i
$441$	0.506699	+	1.28115i	0.0241285	+	0.0610072i
$442$	−0.0512688	−	0.0517420i	−0.00243861	−	0.00246111i
$443$	1.93565	+	5.81166i	0.0919657	+	0.276120i	0.984644	−	0.174574i	$-0.0558548\pi$
$443$	1.93565	+	5.81166i	0.0919657	+	0.276120i	−0.892678	+	0.450694i	$0.851176\pi$
$444$	−9.10928	−	2.57586i	−0.432307	−	0.122245i
$445$	6.77166	−	9.21318i	0.321008	−	0.436746i
$446$	−3.18486	+	5.07607i	−0.150808	+	0.240359i
$447$	4.34018	+	6.38386i	0.205283	+	0.301946i
$448$	14.5827	−	4.12360i	0.688969	−	0.194822i
$449$	4.87850	−	13.0299i	0.230231	−	0.614919i	−0.769487	−	0.638662i	$-0.779488\pi$
$449$	4.87850	−	13.0299i	0.230231	−	0.614919i	0.999718	+	0.0237431i	$0.00755838\pi$
$450$	1.25817	+	2.37680i	0.0593107	+	0.112043i
$451$	19.2051	−	0.705985i	0.904332	−	0.0332435i
$452$	−12.3762	+	8.92252i	−0.582126	+	0.419680i
$453$	5.88488	−	2.64607i	0.276496	−	0.124323i
$454$	−1.25930	+	4.61487i	−0.0591017	+	0.216587i
$455$	7.24214	+	3.91925i	0.339517	+	0.183737i
$456$	−3.12965	+	1.34896i	−0.146559	+	0.0631710i
$457$	4.81663	−	2.60663i	0.225312	−	0.121933i	−0.359370	−	0.933195i	$-0.617009\pi$
$457$	4.81663	−	2.60663i	0.225312	−	0.121933i	0.584683	+	0.811262i	$0.301219\pi$
$458$	−2.12932	−	9.10852i	−0.0994967	−	0.425613i
$459$	−0.254319	+	0.238470i	−0.0118706	+	0.0111308i
$460$	3.15796	+	2.64984i	0.147241	+	0.123550i
$461$	2.54346	−	2.97524i	0.118461	−	0.138571i	−0.697713	−	0.716378i	$-0.745799\pi$
$461$	2.54346	−	2.97524i	0.118461	−	0.138571i	0.816174	+	0.577807i	$0.196091\pi$
$462$	−1.01355	−	1.32718i	−0.0471544	−	0.0617459i
$463$	−30.8823	−	14.5737i	−1.43522	−	0.677298i	−0.457890	−	0.889009i	$-0.651395\pi$
$463$	−30.8823	−	14.5737i	−1.43522	−	0.677298i	−0.977332	+	0.211711i	$0.932096\pi$
$464$	−21.8939	−	8.89252i	−1.01640	−	0.412825i
$465$	−5.55493	+	1.03218i	−0.257604	+	0.0478664i
$466$	4.88593	+	0.723326i	0.226336	+	0.0335074i
$467$	−0.107975	−	3.91713i	−0.00499648	−	0.181263i	−0.998001	−	0.0631907i	$-0.979872\pi$
$467$	−0.107975	−	3.91713i	−0.00499648	−	0.181263i	0.993005	−	0.118072i	$-0.0376715\pi$
$468$	−2.08381	+	10.6679i	−0.0963240	+	0.493125i
$469$	−2.59592	−	16.4880i	−0.119868	−	0.761346i
$470$	−0.157269	+	3.42171i	−0.00725427	+	0.157832i
$471$	−7.38923	+	0.955553i	−0.340478	+	0.0440296i
$472$	−2.63624	−	0.641875i	−0.121343	−	0.0295447i
$473$	12.2824	−	3.96587i	0.564746	−	0.182351i
$474$	0.638796	−	0.497195i	0.0293409	−	0.0228369i
$475$	9.71175	−	9.50048i	0.445606	−	0.435912i
$476$	0.415094	+	0.323080i	0.0190258	+	0.0148084i
$477$	−4.14691	−	1.50935i	−0.189874	−	0.0691084i
$478$	1.23644	−	7.85325i	0.0565534	−	0.359199i
$479$	13.0189	+	2.66741i	0.594849	+	0.121877i	0.488668	−	0.872470i	$-0.337483\pi$
$479$	13.0189	+	2.66741i	0.594849	+	0.121877i	0.106181	+	0.994347i	$0.466138\pi$
$480$	2.49288	+	1.79723i	0.113784	+	0.0820318i
$481$	−14.8952	−	9.92794i	−0.679163	−	0.452675i
$482$	0.452046	+	0.313441i	0.0205901	+	0.0142769i
$483$	0.365761	−	2.63768i	0.0166427	−	0.120019i
$484$	−2.74990	−	2.06034i	−0.124996	−	0.0936520i
$485$	−15.5618	+	12.5781i	−0.706627	+	0.571141i
$486$	−4.44059	−	0.995160i	−0.201429	−	0.0451414i
$487$	−0.849157	+	30.8058i	−0.0384790	+	1.39595i	0.696354	+	0.717698i	$0.254804\pi$
$487$	−0.849157	+	30.8058i	−0.0384790	+	1.39595i	−0.734833	+	0.678248i	$0.762740\pi$
$488$	−2.03612	+	11.5474i	−0.0921710	+	0.522728i
$489$	0.197892	+	0.0255908i	0.00894900	+	0.00115726i
$490$	0.220740	+	0.0849670i	0.00997204	+	0.00383842i
$491$	−1.18339	−	1.49194i	−0.0534055	−	0.0673301i	0.756039	−	0.654527i	$-0.227132\pi$
$491$	−1.18339	−	1.49194i	−0.0534055	−	0.0673301i	−0.809444	+	0.587197i	$0.800232\pi$
$492$	5.70554	+	4.61159i	0.257226	+	0.207906i
$493$	−0.174770	−	0.690152i	−0.00787126	−	0.0310829i
$494$	−3.11878	+	0.296052i	−0.140321	+	0.0133200i
$495$	2.68106	−	10.5873i	0.120505	−	0.475862i
$496$	−18.1286	+	13.5827i	−0.813996	+	0.609881i
$497$	−18.7560	−	33.9101i	−0.841322	−	1.52108i
$498$	1.38025	−	0.417830i	0.0618506	−	0.0187234i
$499$	1.56991	−	2.60734i	0.0702788	−	0.116720i	−0.819564	−	0.572987i	$-0.805784\pi$
$499$	1.56991	−	2.60734i	0.0702788	−	0.116720i	0.889843	+	0.456267i	$0.150814\pi$
$500$	−20.3816	−	5.36103i	−0.911494	−	0.239753i
$501$	5.75777	+	5.60124i	0.257238	+	0.250245i
$502$	6.44509	−	0.713343i	0.287659	−	0.0318380i
$503$	3.85180	+	37.9897i	0.171743	+	1.69387i	0.607908	+	0.794008i	$0.292009\pi$
$503$	3.85180	+	37.9897i	0.171743	+	1.69387i	−0.436164	+	0.899867i	$0.643663\pi$
$504$	−0.591923	+	9.19272i	−0.0263663	+	0.409476i
$505$	−9.49078	+	18.7543i	−0.422334	+	0.834555i
$506$	−0.217134	−	1.56586i	−0.00965277	−	0.0696108i
$507$	−2.43099	+	4.39514i	−0.107964	+	0.195195i
$508$	−3.53256	+	16.4705i	−0.156732	+	0.730761i
$509$	7.62225	+	8.91621i	0.337850	+	0.395204i	0.902899	−	0.429854i	$-0.141435\pi$
$509$	7.62225	+	8.91621i	0.337850	+	0.395204i	−0.565048	+	0.825058i	$0.691142\pi$
$510$	0.000256639		0.0279374i	1.13641e−5		0.00123709i
$511$	−4.12651	+	40.6991i	−0.182546	+	1.80042i
$512$	20.6391	+	3.44406i	0.912130	+	0.152208i
$513$	1.00514	+	14.9608i	0.0443779	+	0.660534i
$514$	3.76090	−	0.627583i	0.165886	−	0.0276815i
$515$	−0.881586	−	13.6913i	−0.0388473	−	0.603310i
$516$	4.53000	+	1.93762i	0.199422	+	0.0852989i
$517$	−16.2051	+	16.3546i	−0.712698	+	0.719275i
$518$	−6.61056	−	3.26941i	−0.290451	−	0.143650i
$519$	5.05848	−	0.372406i	0.222043	−	0.0163468i
$520$	2.27340	+	3.09307i	0.0996951	+	0.135640i
$521$	−1.22572	−	3.27375i	−0.0536998	−	0.143426i	0.906912	−	0.421321i	$-0.138433\pi$
$521$	−1.22572	−	3.27375i	−0.0536998	−	0.143426i	−0.960611	+	0.277895i	$0.910363\pi$
$522$	4.02242	−	4.53392i	0.176057	−	0.198444i
$523$	2.75704	+	2.88667i	0.120557	+	0.126225i	0.780677	−	0.624935i	$-0.214875\pi$
$523$	2.75704	+	2.88667i	0.120557	+	0.126225i	−0.660120	+	0.751160i	$0.729495\pi$
$524$	7.90471	+	6.88422i	0.345319	+	0.300739i
$525$	1.56050	+	4.98918i	0.0681056	+	0.217746i
$526$	−1.44702	+	1.30772i	−0.0630930	+	0.0570195i
$527$	−0.653187	−	0.197733i	−0.0284533	−	0.00861337i
$528$	1.30715	+	6.09459i	0.0568865	+	0.265233i
$529$	−12.4296	+	16.2758i	−0.540416	+	0.707643i
$530$	−0.672837	+	0.348295i	−0.0292262	+	0.0151290i
$531$	−3.04774	+	4.66492i	−0.132261	+	0.202440i
$532$	22.0617	−	5.00866i	0.956497	−	0.217153i
$533$	7.58748	+	11.6135i	0.328650	+	0.503037i
$534$	−1.45716	−	0.823540i	−0.0630576	−	0.0356380i
$535$	−20.0321	+	5.26908i	−0.866062	+	0.227802i
$536$	2.18586	−	7.46742i	0.0944148	−	0.322544i
$537$	0.210098	−	0.531217i	0.00906640	−	0.0229237i
$538$	1.54264	−	0.659835i	0.0665080	−	0.0284475i
$539$	0.717863	+	1.41854i	0.0309205	+	0.0611007i
$540$	7.33987	−	5.08936i	0.315858	−	0.219011i
$541$	27.6364	−	0.507789i	1.18818	−	0.0218316i	0.579314	−	0.815105i	$-0.303321\pi$
$541$	27.6364	−	0.507789i	1.18818	−	0.0218316i	0.608866	+	0.793273i	$0.291625\pi$
$542$	−3.92306	+	0.0720822i	−0.168510	+	0.00309620i
$543$	−11.1685	+	7.74405i	−0.479285	+	0.332329i
$544$	0.167613	+	0.331211i	0.00718633	+	0.0142006i
$545$	0.828447	−	0.354353i	0.0354868	−	0.0151788i
$546$	0.443336	−	1.12094i	0.0189730	−	0.0479719i
$547$	8.44252	−	28.8417i	0.360976	−	1.23318i	−0.554967	−	0.831872i	$-0.687269\pi$
$547$	8.44252	−	28.8417i	0.360976	−	1.23318i	0.915943	−	0.401308i	$-0.131444\pi$
$548$	−12.2446	+	3.22074i	−0.523065	+	0.137583i
$549$	20.9645	+	11.8485i	0.894745	+	0.505680i
$550$	1.69735	+	2.59799i	0.0723754	+	0.110779i
$551$	−27.7275	−	12.9907i	−1.18123	−	0.553423i
$552$	0.678956	−	1.03922i	0.0288983	−	0.0442321i
$553$	−9.81643	+	5.08149i	−0.417437	+	0.216087i
$554$	3.17340	−	4.15537i	0.134825	−	0.176545i
$555$	1.43984	+	6.71326i	0.0611180	+	0.284962i
$556$	−7.33191	−	2.21951i	−0.310942	−	0.0941284i
$557$	−15.4292	+	13.9439i	−0.653756	+	0.590823i	−0.928788	−	0.370612i	$-0.879148\pi$
$557$	−15.4292	+	13.9439i	−0.653756	+	0.590823i	0.275032	+	0.961435i	$0.411312\pi$
$558$	−1.73440	−	5.54518i	−0.0734229	−	0.234746i
$559$	7.02577	+	6.11875i	0.297159	+	0.258796i
$560$	−8.74622	−	9.15745i	−0.369595	−	0.386973i
$561$	−0.124627	+	0.140475i	−0.00526176	+	0.00593085i
$562$	−2.95987	−	7.90545i	−0.124854	−	0.333471i
$563$	23.5740	+	32.0736i	0.993527	+	1.35174i	0.935461	+	0.353430i	$0.114985\pi$
$563$	23.5740	+	32.0736i	0.993527	+	1.35174i	0.0580660	+	0.998313i	$0.481507\pi$
$564$	−8.76513	+	0.645290i	−0.369079	+	0.0271716i
$565$	9.91905	+	4.90570i	0.417297	+	0.206384i
$566$	0.998679	−	1.00790i	0.0419776	−	0.0423650i
$567$	14.5655	+	6.23011i	0.611693	+	0.261640i
$568$	−1.16078	−	18.0272i	−0.0487052	−	0.756405i
$569$	20.9004	−	3.48767i	0.876192	−	0.146211i	0.290628	−	0.956836i	$-0.406136\pi$
$569$	20.9004	−	3.48767i	0.876192	−	0.146211i	0.585565	+	0.810626i	$0.300873\pi$
$570$	0.936623	+	0.752739i	0.0392308	+	0.0315288i
$571$	−40.2880	−	6.72288i	−1.68600	−	0.281344i	−0.757545	−	0.652783i	$-0.773601\pi$
$571$	−40.2880	−	6.72288i	−1.68600	−	0.281344i	−0.928457	+	0.371439i	$0.878864\pi$
$572$	−1.26526	+	12.4791i	−0.0529034	+	0.521777i
$573$	0.0662528	+	7.21220i	0.00276775	+	0.301294i
$574$	3.71377	+	4.34423i	0.155010	+	0.181325i
$575$	−1.03777	+	4.83860i	−0.0432780	+	0.201783i
$576$	7.02219	−	12.6958i	0.292591	−	0.528994i
$577$	4.49320	+	32.4026i	0.187055	+	1.34894i	0.818941	+	0.573878i	$0.194562\pi$
$577$	4.49320	+	32.4026i	0.187055	+	1.34894i	−0.631886	+	0.775061i	$0.717719\pi$
$578$	2.52044	−	4.98053i	0.104837	−	0.207163i
$579$	−0.640998	+	9.95488i	−0.0266390	+	0.413711i
$580$	1.83985	+	18.1461i	0.0763956	+	0.753478i
$581$	−19.5728	+	2.16632i	−0.812017	+	0.0898740i
$582$	2.09952	+	2.04245i	0.0870280	+	0.0846621i
$583$	−4.92498	−	1.29543i	−0.203972	−	0.0536512i
$584$	−9.83662	+	16.3369i	−0.407042	+	0.676025i
$585$	7.54542	−	2.28415i	0.311965	−	0.0944379i
$586$	−1.84659	−	3.33857i	−0.0762821	−	0.137915i
$587$	−2.92104	+	2.18857i	−0.120564	+	0.0903319i	−0.658191	−	0.752851i	$-0.728678\pi$
$587$	−2.92104	+	2.18857i	−0.120564	+	0.0903319i	0.537626	+	0.843183i	$0.319321\pi$
$588$	−0.148984	+	0.588325i	−0.00614400	+	0.0242621i
$589$	−24.3786	+	16.3470i	−1.00450	+	0.673565i
$590$	0.234846	+	0.927385i	0.00966845	+	0.0381798i
$591$	10.0559	+	8.12780i	0.413643	+	0.334333i
$592$	17.1065	+	21.5668i	0.703073	+	0.886389i
$593$	7.24213	+	2.78763i	0.297399	+	0.114474i	0.503335	−	0.864091i	$-0.332106\pi$
$593$	7.24213	+	2.78763i	0.297399	+	0.114474i	−0.205937	+	0.978565i	$0.566024\pi$
$594$	−3.39678	−	0.439261i	−0.139372	−	0.0180231i
$595$	0.0662481	−	0.375712i	0.00271591	−	0.0154027i
$596$	0.658219	−	23.8790i	0.0269617	−	0.978121i
$597$	3.16874	+	0.710130i	0.129688	+	0.0290637i
$598$	0.887473	−	0.717313i	0.0362915	−	0.0293331i
$599$	−7.48246	−	5.60618i	−0.305725	−	0.229062i	0.435709	−	0.900087i	$-0.356498\pi$
$599$	−7.48246	−	5.60618i	−0.305725	−	0.229062i	−0.741435	+	0.671025i	$0.765854\pi$
$600$	−0.334714	+	2.41378i	−0.0136646	+	0.0985423i
$601$	−6.19941	−	4.29858i	−0.252879	−	0.175343i	0.436583	−	0.899664i	$-0.356188\pi$
$601$	−6.19941	−	4.29858i	−0.252879	−	0.175343i	−0.689463	+	0.724321i	$0.742153\pi$
$602$	3.19394	+	2.12882i	0.130175	+	0.0867643i
$603$	−12.9622	−	9.34498i	−0.527860	−	0.380557i
$604$	−19.5606	−	4.00773i	−0.795911	−	0.163072i
$605$	−0.387603	+	2.46186i	−0.0157583	+	0.100089i
$606$	2.89131	+	1.05235i	0.117452	+	0.0427489i
$607$	−17.4258	−	13.5631i	−0.707293	−	0.550509i	0.195436	−	0.980716i	$-0.437388\pi$
$607$	−17.4258	−	13.5631i	−0.707293	−	0.550509i	−0.902730	+	0.430208i	$0.858440\pi$
$608$	15.5886	+	3.44795i	0.632200	+	0.139833i
$609$	9.29747	−	7.23651i	0.376753	−	0.293238i
$610$	3.93428	−	1.27034i	0.159294	−	0.0514345i
$611$	−16.1475	−	3.93163i	−0.653259	−	0.159057i
$612$	0.499424	−	0.0645840i	0.0201880	−	0.00261065i
$613$	0.841477	−	18.3081i	0.0339869	−	0.739457i	−0.911011	−	0.412381i	$-0.864697\pi$
$613$	0.841477	−	18.3081i	0.0339869	−	0.739457i	0.944998	−	0.327075i	$-0.106063\pi$
$614$	−0.934817	−	5.93750i	−0.0377261	−	0.239618i
$615$	1.02007	−	5.22219i	0.0411332	−	0.210579i
$616$	0.292904	+	10.6260i	0.0118014	+	0.428134i
$617$	−37.7121	−	5.58299i	−1.51823	−	0.224763i	−0.665217	−	0.746650i	$-0.731661\pi$
$617$	−37.7121	−	5.58299i	−1.51823	−	0.224763i	−0.853014	+	0.521887i	$0.825228\pi$
$618$	−1.97455	+	0.366900i	−0.0794282	+	0.0147589i
$619$	−26.8122	−	10.8902i	−1.07767	−	0.437712i	−0.232714	−	0.972545i	$-0.574761\pi$
$619$	−26.8122	−	10.8902i	−1.07767	−	0.437712i	−0.844958	+	0.534833i	$0.820375\pi$
$620$	15.8118	+	7.46176i	0.635016	+	0.299671i
$621$	−3.31491	−	4.34068i	−0.133023	−	0.174186i
$622$	−5.74595	+	6.72139i	−0.230392	+	0.269503i
$623$	17.5086	+	14.6915i	0.701467	+	0.588601i
$624$	−3.28217	+	3.07763i	−0.131392	+	0.123204i
$625$	−0.0679949	−	0.290859i	−0.00271980	−	0.0116344i
$626$	0.201811	−	0.109215i	0.00806601	−	0.00436510i
$627$	1.27834	+	7.97488i	0.0510520	+	0.318486i
$628$	20.2775	+	10.9736i	0.809161	+	0.437896i
$629$	−0.218323	+	0.800076i	−0.00870512	+	0.0319011i
$630$	2.96227	−	1.33195i	0.118020	−	0.0530663i
$631$	8.01600	−	5.77908i	0.319112	−	0.230062i	−0.413828	−	0.910355i	$-0.635809\pi$
$631$	8.01600	−	5.77908i	0.319112	−	0.230062i	0.732940	+	0.680294i	$0.238148\pi$
$632$	−5.14933	+	0.189291i	−0.204829	+	0.00752959i
$633$	1.63611	+	3.09076i	0.0650294	+	0.122846i
$634$	1.37838	−	3.68148i	0.0547423	−	0.146210i
$635$	11.7566	−	3.32444i	0.466546	−	0.131927i
$636$	−1.09298	−	1.60763i	−0.0433394	−	0.0637469i
$637$	−0.609927	+	0.972108i	−0.0241662	+	0.0385163i
$638$	4.14223	−	5.63571i	0.163993	−	0.223120i
$639$	−35.6997	−	10.0949i	−1.41226	−	0.399349i
$640$	−3.96368	−	11.9007i	−0.156678	−	0.470415i
$641$	−26.4550	−	26.6991i	−1.04491	−	1.05455i	−0.998451	−	0.0556318i	$-0.982283\pi$
$641$	−26.4550	−	26.6991i	−1.04491	−	1.05455i	−0.0464579	−	0.998920i	$-0.514793\pi$
$642$	1.11517	+	2.81963i	0.0440123	+	0.111282i
$643$	20.5814	−	1.89593i	0.811649	−	0.0747681i	0.322058	−	0.946720i	$-0.395625\pi$
$643$	20.5814	−	1.89593i	0.811649	−	0.0747681i	0.489591	+	0.871952i	$0.337146\pi$
$644$	−5.69152	+	5.95912i	−0.224277	+	0.234822i
$645$	−0.295097	−	3.56129i	−0.0116194	−	0.140226i
$646$	0.0586725	+	0.132754i	0.00230844	+	0.00522315i
$647$	−1.92840	+	23.2723i	−0.0758131	+	0.914928i	0.847479	+	0.530829i	$0.178119\pi$
$647$	−1.92840	+	23.2723i	−0.0758131	+	0.914928i	−0.923292	+	0.384099i	$0.874512\pi$
$648$	4.90102	+	5.52424i	0.192530	+	0.217012i
$649$	−3.00836	+	5.68307i	−0.118089	+	0.223080i
$650$	−0.974593	+	2.01699i	−0.0382267	+	0.0791128i
$651$	−1.34549	−	11.2135i	−0.0527339	−	0.439493i
$652$	−0.450433	−	0.422362i	−0.0176403	−	0.0165410i
$653$	−2.68291	+	4.64694i	−0.104991	+	0.181849i	−0.913734	−	0.406312i	$-0.866815\pi$
$653$	−2.68291	+	4.64694i	−0.104991	+	0.181849i	0.808744	+	0.588161i	$0.200148\pi$
$654$	−0.0659502	−	0.114229i	−0.00257886	−	0.00446671i
$655$	1.73063	−	7.40305i	0.0676214	−	0.289261i
$656$	−5.61594	−	20.5804i	−0.219266	−	0.803529i
$657$	24.8974	+	30.2312i	0.971339	+	1.17943i
$658$	−6.80541	−	0.753222i	−0.265302	−	0.0293637i
$659$	0.399115	−	43.4473i	0.0155473	−	1.69246i	−0.524961	−	0.851126i	$-0.675920\pi$
$659$	0.399115	−	43.4473i	0.0155473	−	1.69246i	0.540509	−	0.841339i	$-0.318232\pi$
$660$	3.68545	−	3.09246i	0.143456	−	0.120374i
$661$	0.618956	−	5.15848i	0.0240746	−	0.200641i	−0.975760	−	0.218845i	$-0.929771\pi$
$661$	0.618956	−	5.15848i	0.0240746	−	0.200641i	0.999834	+	0.0182032i	$0.00579459\pi$
$662$	−0.704737	−	0.451246i	−0.0273904	−	0.0175382i
$663$	−0.133273	−	0.0247641i	−0.00517591	−	0.000961758i
$664$	−8.68244	−	2.98068i	−0.336944	−	0.115673i
$665$	−10.6967	−	12.4424i	−0.414802	−	0.482495i
$666$	−6.67790	+	2.29253i	−0.258763	+	0.0888336i
$667$	11.0329	−	1.63335i	0.427197	−	0.0632434i
$668$	−4.31646	−	24.4799i	−0.167009	−	0.947155i
$669$	0.512023	+	11.1401i	0.0197960	+	0.430703i
$670$	−2.68757	+	0.550650i	−0.103830	+	0.0212735i
$671$	25.3446	+	11.3959i	0.978416	+	0.439934i
$672$	−3.90530	+	4.74194i	−0.150650	+	0.182924i
$673$	−31.8685	+	31.0022i	−1.22844	+	1.19505i	−0.254793	+	0.966996i	$0.582007\pi$
$673$	−31.8685	+	31.0022i	−1.22844	+	1.19505i	−0.973649	+	0.228051i	$0.926765\pi$
$674$	4.63215	−	2.61794i	0.178424	−	0.100839i
$675$	9.52168	+	4.92891i	0.366490	+	0.189714i
$676$	14.0561	−	6.63322i	0.540618	−	0.255124i
$677$	13.7489	−	0.758546i	0.528412	−	0.0291533i	0.211082	−	0.977468i	$-0.432301\pi$
$677$	13.7489	−	0.758546i	0.528412	−	0.0291533i	0.317330	+	0.948315i	$0.397214\pi$
$678$	0.540026	−	1.52721i	0.0207396	−	0.0586523i
$679$	−23.0918	−	32.6583i	−0.886183	−	1.25331i
$680$	0.102675	−	0.145212i	0.00393743	−	0.00556861i
$681$	2.96776	+	8.39295i	0.113725	+	0.321619i
$682$	−2.57997	−	6.18837i	−0.0987923	−	0.236965i
$683$	11.5173	−	12.5112i	0.440698	−	0.478726i	−0.475348	−	0.879798i	$-0.657678\pi$
$683$	11.5173	−	12.5112i	0.440698	−	0.478726i	0.916047	+	0.401072i	$0.131362\pi$
$684$	11.4600	−	18.3784i	0.438183	−	0.702717i
$685$	6.21947	+	6.75615i	0.237634	+	0.258139i
$686$	2.44204	−	5.30040i	0.0932376	−	0.202370i
$687$	−12.9151	−	11.6718i	−0.492742	−	0.445309i
$688$	−7.39029	−	12.2740i	−0.281752	−	0.467940i
$689$	−1.03270	−	3.52794i	−0.0393427	−	0.134404i
$690$	−0.435840	−	0.0401490i	−0.0165921	−	0.00152845i
$691$	30.8965	−	26.9078i	1.17536	−	1.02362i	0.176131	−	0.984367i	$-0.443642\pi$
$691$	30.8965	−	26.9078i	1.17536	−	1.02362i	0.999229	−	0.0392552i	$-0.0124985\pi$
$692$	−13.3716	−	8.21950i	−0.508312	−	0.312458i
$693$	20.7750	+	6.70805i	0.789179	+	0.254818i
$694$	1.00169	−	0.364584i	0.0380235	−	0.0138394i
$695$	1.06516	+	5.45302i	0.0404038	+	0.206845i
$696$	5.35929	−	1.20104i	0.203143	−	0.0455255i
$697$	0.399399	−	0.503536i	0.0151283	−	0.0190728i
$698$	6.05607	−	3.57105i	0.229226	−	0.135166i
$699$	8.23914	−	4.07486i	0.311633	−	0.154125i
$700$	5.11178	−	15.3477i	0.193207	−	0.580090i
$701$	24.6765	−	36.2961i	0.932020	−	1.37088i	0.00334330	−	0.999994i	$-0.498936\pi$
$701$	24.6765	−	36.2961i	0.932020	−	1.37088i	0.928677	−	0.370890i	$-0.120947\pi$
$702$	−0.993135	−	2.26412i	−0.0374835	−	0.0854537i
$703$	20.6737	+	29.0665i	0.779723	+	1.09626i
$704$	6.72529	−	15.3321i	0.253469	−	0.577851i
$705$	3.38788	+	5.39964i	0.127595	+	0.203362i
$706$	12.1237	+	0.892547i	0.456281	+	0.0335914i
$707$	−36.1919	−	21.3410i	−1.36114	−	0.802613i
$708$	−2.29079	+	0.881769i	−0.0860933	+	0.0331389i
$709$	34.5678	−	8.41662i	1.29822	−	0.316093i	0.473079	−	0.881020i	$-0.343143\pi$
$709$	34.5678	−	8.41662i	1.29822	−	0.316093i	0.825141	+	0.564927i	$0.191096\pi$
$710$	−5.42615	+	3.33544i	−0.203640	+	0.125177i
$711$	−3.15902	+	10.0999i	−0.118472	+	0.378777i
$712$	4.45840	+	9.67687i	0.167086	+	0.362656i
$713$	4.11409	−	9.86814i	0.154074	−	0.369565i
$714$	−0.0557623	−	0.00307649i	−0.00208685	−	0.000115135i
$715$	8.42866	−	3.42342i	0.315214	−	0.128029i
$716$	−1.48872	+	0.953235i	−0.0556362	+	0.0356241i
$717$	−6.43671	−	13.3212i	−0.240383	−	0.497490i
$718$	−11.0866	−	0.407546i	−0.413748	−	0.0152095i
$719$	17.7372	−	11.8222i	0.661487	−	0.440894i	−0.178178	−	0.983998i	$-0.557020\pi$
$719$	17.7372	−	11.8222i	0.661487	−	0.440894i	0.839665	+	0.543105i	$0.182751\pi$
$720$	−12.1213	−	0.222715i	−0.451732	−	0.00830011i
$721$	27.4245			1.02134
$722$	6.01625	+	1.66513i	0.223902	+	0.0619699i
$723$	1.02369			0.0380716
$724$	42.0492	+	0.772609i	1.56274	+	0.0287138i
$725$	−18.2187	+	12.1431i	−0.676625	+	0.450984i
$726$	0.364574	+	0.0134018i	0.0135306	+	0.000497389i
$727$	14.0842	+	29.1483i	0.522354	+	1.08105i	0.981282	+	0.192575i	$0.0616840\pi$
$727$	14.0842	+	29.1483i	0.522354	+	1.08105i	−0.458928	+	0.888474i	$0.651766\pi$
$728$	−6.46204	+	4.13767i	−0.239499	+	0.153352i
$729$	8.20573	−	3.33288i	0.303916	−	0.123440i
$730$	6.71351	+	0.370395i	0.248478	+	0.0137089i
$731$	0.166097	−	0.398402i	0.00614330	−	0.0147354i
$732$	4.43891	+	9.63455i	0.164067	+	0.356103i
$733$	−4.61934	+	14.7688i	−0.170619	+	0.545500i	−0.999911	−	0.0133154i	$-0.995761\pi$
$733$	−4.61934	+	14.7688i	−0.170619	+	0.545500i	0.829292	+	0.558815i	$0.188744\pi$
$734$	6.54126	−	4.02090i	0.241442	−	0.148414i
$735$	0.427681	−	0.104132i	0.0157752	−	0.00384099i
$736$	−5.42716	+	2.08901i	−0.200048	+	0.0770021i
$737$	−15.8840	−	9.36623i	−0.585095	−	0.345009i
$738$	5.45686	+	0.401735i	0.200870	+	0.0147881i
$739$	10.2616	+	16.3550i	0.377477	+	0.601628i	0.980600	−	0.196021i	$-0.0628021\pi$
$739$	10.2616	+	16.3550i	0.377477	+	0.601628i	−0.603122	+	0.797649i	$0.706077\pi$
$740$	8.53469	−	19.4571i	0.313741	−	0.715258i
$741$	−4.45567	+	3.75993i	−0.163683	+	0.138124i
$742$	−0.608354	−	1.38691i	−0.0223334	−	0.0509150i
$743$	6.09971	−	8.97190i	0.223777	−	0.329147i	−0.698548	−	0.715563i	$-0.746170\pi$
$743$	6.09971	−	8.97190i	0.223777	−	0.329147i	0.922325	+	0.386416i	$0.126287\pi$
$744$	1.66367	−	4.99505i	0.0609931	−	0.183127i
$745$	−15.5302	+	7.68083i	−0.568982	+	0.281404i
$746$	−5.17609	+	3.05215i	−0.189510	+	0.111747i
$747$	−11.7158	+	14.7705i	−0.428659	+	0.540425i
$748$	0.567052	−	0.127079i	0.0207335	−	0.00464648i
$749$	−7.93771	−	40.6366i	−0.290038	−	1.48483i
$750$	2.10262	−	0.765290i	0.0767768	−	0.0279445i
$751$	−40.0386	−	12.9281i	−1.46103	−	0.471751i	−0.533596	−	0.845740i	$-0.679160\pi$
$751$	−40.0386	−	12.9281i	−1.46103	−	0.471751i	−0.927433	+	0.373989i	$0.877990\pi$
$752$	21.7725	+	13.3835i	0.793961	+	0.488046i
$753$	9.10015	−	7.92532i	0.331628	−	0.288815i
$754$	5.02745	+	0.463122i	0.183089	+	0.0168659i
$755$	4.06840	+	13.8986i	0.148064	+	0.505823i
$756$	9.20944	+	15.2952i	0.334944	+	0.556283i
$757$	14.7377	+	13.3190i	0.535650	+	0.484086i	0.893108	−	0.449843i	$-0.148520\pi$
$757$	14.7377	+	13.3190i	0.535650	+	0.484086i	−0.357458	+	0.933929i	$0.616356\pi$
$758$	0.421625	−	0.915128i	0.0153141	−	0.0332390i
$759$	−1.99250	−	2.16444i	−0.0723233	−	0.0785641i
$760$	−2.03413	−	7.37351i	−0.0737857	−	0.267465i
$761$	−26.1668	+	28.4247i	−0.948546	+	1.03040i	0.0509518	+	0.998701i	$0.483775\pi$
$761$	−26.1668	+	28.4247i	−0.948546	+	1.03040i	−0.999498	+	0.0316943i	$0.989910\pi$
$762$	−0.688212	−	1.65076i	−0.0249313	−	0.0598006i
$763$	0.600450	+	1.69810i	0.0217377	+	0.0614752i
$764$	12.8856	−	18.2238i	0.466184	−	0.659313i
$765$	−0.210867	−	0.298225i	−0.00762391	−	0.0107823i
$766$	−0.0447356	+	0.126514i	−0.00161636	+	0.00457113i
$767$	−4.63455	+	0.255695i	−0.167344	+	0.00923261i
$768$	4.44905	−	2.09956i	0.160541	−	0.0757613i
$769$	24.1894	+	12.5217i	0.872293	+	0.451544i	0.836597	−	0.547819i	$-0.184542\pi$
$769$	24.1894	+	12.5217i	0.872293	+	0.451544i	0.0356962	+	0.999363i	$0.488635\pi$
$770$	3.26296	−	1.84411i	0.117589	−	0.0664573i
$771$	5.08611	−	4.94784i	0.183172	−	0.178192i
$772$	19.6243	−	23.8285i	0.706294	−	0.857605i
$773$	−17.5477	−	7.89012i	−0.631146	−	0.283788i	0.0691871	−	0.997604i	$-0.477959\pi$
$773$	−17.5477	−	7.89012i	−0.631146	−	0.283788i	−0.700333	+	0.713816i	$0.746965\pi$
$774$	3.59996	−	0.737586i	0.129398	−	0.0265120i
$775$	0.963639	+	20.9660i	0.0346150	+	0.753120i
$776$	−3.23772	−	18.3620i	−0.116227	−	0.659159i
$777$	−13.5765	+	2.00990i	−0.487055	+	0.0721049i
$778$	−4.15054	+	1.42488i	−0.148804	+	0.0510845i
$779$	−5.87197	−	27.0113i	−0.210385	−	0.967779i
$780$	3.28462	+	1.12761i	0.117608	+	0.0403750i
$781$	−42.0911	−	7.82113i	−1.50614	−	0.279862i
$782$	−0.0445227	−	0.0285080i	−0.00159213	−	0.00101945i
$783$	2.87882	−	23.9926i	0.102881	−	0.857424i
$784$	1.35190	−	1.13438i	0.0482823	−	0.0405136i
$785$	0.153611	−	16.7219i	0.00548260	−	0.596830i
$786$	−1.10616	−	0.122430i	−0.0394555	−	0.00436693i
$787$	25.1597	+	30.5497i	0.896846	+	1.08898i	0.995585	+	0.0938668i	$0.0299228\pi$
$787$	25.1597	+	30.5497i	0.896846	+	1.08898i	−0.0987384	+	0.995113i	$0.531481\pi$
$788$	−10.5331	−	38.6002i	−0.375228	−	1.37508i
$789$	−0.826233	+	3.53434i	−0.0294147	+	0.125826i
$790$	0.908407	+	1.57341i	0.0323197	+	0.0559793i
$791$	−11.0599	+	19.1563i	−0.393245	+	0.681121i
$792$	7.42374	+	6.96110i	0.263791	+	0.247352i
$793$	2.38971	+	19.9162i	0.0848611	+	0.707246i
$794$	0.975437	−	2.01874i	0.0346170	−	0.0716422i
$795$	−0.659646	+	1.24613i	−0.0233952	+	0.0441957i
$796$	−6.66896	−	7.51699i	−0.236375	−	0.266433i
$797$	−2.90106	+	35.0105i	−0.102761	+	1.24014i	0.728809	+	0.684717i	$0.240074\pi$
$797$	−2.90106	+	35.0105i	−0.102761	+	1.24014i	−0.831570	+	0.555420i	$0.812557\pi$
$798$	−1.62187	+	1.77168i	−0.0574134	+	0.0627169i
$799$	0.0635833	+	0.767336i	0.00224941	+	0.0271464i
$800$	7.88482	−	8.25555i	0.278771	−	0.291878i
$801$	21.7892	−	2.00719i	0.769884	−	0.0709207i
$802$	−3.76270	−	9.51370i	−0.132865	−	0.335940i
$803$	31.8097	+	32.1032i	1.12254	+	1.13290i
$804$	−2.22435	−	6.67846i	−0.0784469	−	0.235531i
$805$	5.75118	+	1.62628i	0.202702	+	0.0573188i
$806$	2.86624	−	3.89966i	0.100959	−	0.137360i
$807$	1.65949	−	2.64492i	0.0584169	−	0.0931055i
$808$	−11.0119	−	16.1972i	−0.387399	−	0.569815i
$809$	−27.4264	+	7.75544i	−0.964260	+	0.272667i	−0.717616	−	0.696439i	$-0.754767\pi$
$809$	−27.4264	+	7.75544i	−0.964260	+	0.272667i	−0.246644	+	0.969106i	$0.579328\pi$
$810$	0.913001	−	2.43852i	0.0320796	−	0.0856808i
$811$	−4.75562	−	8.98381i	−0.166993	−	0.315464i	0.786123	−	0.618070i	$-0.212085\pi$
$811$	−4.75562	−	8.98381i	−0.166993	−	0.315464i	−0.953116	+	0.302606i	$0.902144\pi$
$812$	−36.4341	+	1.33933i	−1.27859	+	0.0470013i
$813$	−5.92316	+	4.27027i	−0.207734	+	0.149765i
$814$	−7.43090	+	3.34122i	−0.260453	+	0.117110i
$815$	−0.117898	+	0.432054i	−0.00412978	+	0.0151342i
$816$	0.183331	+	0.0992137i	0.00641786	+	0.00347317i
$817$	−8.73097	−	16.3832i	−0.305458	−	0.573175i
$818$	−3.26725	+	1.76815i	−0.114237	+	0.0618218i
$819$	3.58723	+	15.3449i	0.125348	+	0.536196i
$820$	−12.0111	+	11.2626i	−0.419446	+	0.393306i
$821$	−25.1346	−	21.0904i	−0.877202	−	0.736060i	0.0883999	−	0.996085i	$-0.471825\pi$
$821$	−25.1346	−	21.0904i	−0.877202	−	0.736060i	−0.965602	+	0.260025i	$0.916269\pi$
$822$	0.873494	−	1.02178i	0.0304666	−	0.0356386i
$823$	−13.1026	−	17.1571i	−0.456728	−	0.598058i	0.507984	−	0.861367i	$-0.330391\pi$
$823$	−13.1026	−	17.1571i	−0.456728	−	0.598058i	−0.964712	+	0.263309i	$0.915186\pi$
$824$	11.5616	+	5.45603i	0.402766	+	0.190070i
$825$	5.35071	+	2.17327i	0.186288	+	0.0756636i
$826$	−1.88011	+	0.349350i	−0.0654173	+	0.0121555i
$827$	47.6975	+	7.06126i	1.65860	+	0.245544i	0.909137	−	0.416497i	$-0.136742\pi$
$827$	47.6975	+	7.06126i	1.65860	+	0.245544i	0.749467	+	0.662041i	$0.230310\pi$
$828$	0.217379	+	7.88612i	0.00755446	+	0.274062i
$829$	6.98578	−	35.7633i	0.242626	−	1.24211i	−0.638646	−	0.769501i	$-0.720505\pi$
$829$	6.98578	−	35.7633i	0.242626	−	1.24211i	0.881272	−	0.472610i	$-0.156688\pi$
$830$	0.503393	+	3.19730i	0.0174730	+	0.110980i
$831$	0.446749	−	9.71995i	0.0154975	−	0.337181i
$832$	11.9855	−	1.54992i	0.415522	−	0.0537340i
$833$	0.0516592	+	0.0125781i	0.00178988	+	0.000435804i
$834$	0.773981	−	0.249911i	0.0268008	−	0.00865370i
$835$	−14.2273	+	11.0736i	−0.492357	+	0.383217i
$836$	11.2232	−	22.3317i	0.388164	−	0.772360i
$837$	−18.2798	−	14.2277i	−0.631841	−	0.491782i
$838$	3.75505	+	1.36673i	0.129716	+	0.0472128i
$839$	−6.01773	+	38.2217i	−0.207755	+	1.31956i	0.631311	+	0.775529i	$0.282517\pi$
$839$	−6.01773	+	38.2217i	−0.207755	+	1.31956i	−0.839067	+	0.544029i	$0.816898\pi$
$840$	2.88324	+	0.590739i	0.0994811	+	0.0203824i
$841$	16.5041	+	11.8985i	0.569106	+	0.410293i
$842$	−2.34893	−	1.56561i	−0.0809494	−	0.0539543i
$843$	−12.9095	−	8.95127i	−0.444628	−	0.308298i
$844$	1.48641	−	10.7192i	0.0511642	−	0.368970i
$845$	−9.02159	−	6.75936i	−0.310352	−	0.232529i
$846$	−5.09803	+	4.12056i	−0.175274	+	0.141668i
$847$	−4.86112	−	1.08940i	−0.167030	−	0.0374323i
$848$	−0.155762	+	5.65075i	−0.00534889	+	0.194048i
$849$	0.458519	−	2.60039i	0.0157363	−	0.0892452i
$850$	0.102926	+	0.0133101i	0.00353035	+	0.000456534i
$851$	−12.1250	−	4.66715i	−0.415641	−	0.159988i
$852$	−10.1559	−	12.8039i	−0.347937	−	0.438656i
$853$	−17.7814	−	14.3721i	−0.608825	−	0.492091i	0.274040	−	0.961718i	$-0.411640\pi$
$853$	−17.7814	−	14.3721i	−0.608825	−	0.492091i	−0.882865	+	0.469627i	$0.844388\pi$
$854$	2.02872	+	8.01125i	0.0694215	+	0.274139i
$855$	−15.6696	−	1.10977i	−0.535888	−	0.0379533i
$856$	4.73819	−	18.7107i	0.161948	−	0.639518i
$857$	−35.7156	+	26.7597i	−1.22002	+	0.914092i	−0.998139	−	0.0609809i	$-0.980577\pi$
$857$	−35.7156	+	26.7597i	−1.22002	+	0.914092i	−0.221883	+	0.975073i	$0.571220\pi$
$858$	−0.644561	−	1.16534i	−0.0220049	−	0.0397841i
$859$	−9.12373	+	2.76193i	−0.311297	+	0.0942359i	−0.441527	−	0.897248i	$-0.645563\pi$
$859$	−9.12373	+	2.76193i	−0.311297	+	0.0942359i	0.130230	+	0.991484i	$0.458429\pi$
$860$	−5.70410	+	9.47349i	−0.194508	+	0.323043i
$861$	10.2862	+	2.70559i	0.350551	+	0.0922064i
$862$	5.38656	+	5.24013i	0.183467	+	0.178479i
$863$	18.7990	−	2.08068i	0.639927	−	0.0708271i	0.215811	−	0.976435i	$-0.430760\pi$
$863$	18.7990	−	2.08068i	0.639927	−	0.0708271i	0.424116	+	0.905608i	$0.360585\pi$
$864$	1.27096	+	12.5353i	0.0432390	+	0.426460i
$865$	−0.731508	+	11.3605i	−0.0248720	+	0.386269i
$866$	0.694855	−	1.37307i	0.0236121	−	0.0466588i
$867$	−1.42682	−	10.2895i	−0.0484573	−	0.349449i
$868$	−16.9156	+	30.5828i	−0.574154	+	1.03805i
$869$	−2.56091	+	11.9402i	−0.0868730	+	0.405045i
$870$	−1.25832	−	1.47194i	−0.0426612	−	0.0499034i
$871$	−0.122269	−	13.3101i	−0.00414293	−	0.450995i
$872$	−0.0846954	+	0.835337i	−0.00286815	+	0.0282881i
$873$	−37.7700	−	6.30270i	−1.27832	−	0.213314i
$874$	−2.16184	+	0.704684i	−0.0731252	+	0.0238363i
$875$	−30.1377	+	5.02909i	−1.01884	+	0.170014i
$876$	1.10857	+	17.2164i	0.0374551	+	0.581688i
$877$	47.1389	+	20.1628i	1.59177	+	0.680849i	0.992784	−	0.119912i	$-0.0382614\pi$
$877$	47.1389	+	20.1628i	1.59177	+	0.680849i	0.598984	+	0.800761i	$0.295571\pi$
$878$	−2.59493	+	2.61888i	−0.0875747	+	0.0883828i
$879$	−6.36425	−	3.14759i	−0.214661	−	0.106166i
$880$	−13.9521	+	1.02716i	−0.470326	+	0.0346254i
$881$	23.4079	+	31.8476i	0.788632	+	1.07297i	0.995515	+	0.0946062i	$0.0301592\pi$
$881$	23.4079	+	31.8476i	0.788632	+	1.07297i	−0.206883	+	0.978366i	$0.566332\pi$
$882$	0.158715	+	0.423909i	0.00534421	+	0.0142737i
$883$	25.8161	−	29.0989i	0.868780	−	0.979255i	−0.131146	−	0.991363i	$-0.541866\pi$
$883$	25.8161	−	29.0989i	0.868780	−	0.979255i	0.999927	+	0.0121077i	$0.00385409\pi$
$884$	0.289724	+	0.303346i	0.00974448	+	0.0102026i
$885$	1.34255	+	1.16923i	0.0451295	+	0.0393033i
$886$	0.600772	+	1.92078i	0.0201833	+	0.0645297i
$887$	24.7020	−	22.3241i	0.829413	−	0.749571i	−0.141260	−	0.989973i	$-0.545115\pi$
$887$	24.7020	−	22.3241i	0.829413	−	0.749571i	0.970674	+	0.240402i	$0.0772791\pi$
$888$	−6.12341	−	1.85368i	−0.205488	−	0.0622054i
$889$	5.12150	+	23.8790i	0.171770	+	0.800875i
$890$	2.28006	−	2.98560i	0.0764277	−	0.100077i
$891$	15.5427	−	8.04573i	0.520701	−	0.269542i
$892$	18.8750	−	28.8903i	0.631981	−	0.967318i
$893$	27.2661	+	18.7937i	0.912424	+	0.628908i
$894$	1.38719	+	2.12325i	0.0463946	+	0.0710122i
$895$	1.11620	+	0.630840i	0.0373105	+	0.0210867i
$896$	24.2485	−	6.37815i	0.810086	−	0.213079i
$897$	0.596585	−	2.03808i	0.0199194	−	0.0680494i
$898$	1.68120	−	4.25079i	0.0561024	−	0.141851i
$899$	43.4914	−	18.6026i	1.45052	−	0.620432i
$900$	−6.99290	−	13.8183i	−0.233097	−	0.460611i
$901$	−0.139955	+	0.0970424i	−0.00466257	+	0.00323295i
$902$	6.31301	−	0.115995i	0.210200	−	0.00386221i
$903$	7.14195	−	0.131226i	0.237669	−	0.00436692i
$904$	−8.47371	+	5.87554i	−0.281831	+	0.195418i
$905$	−13.7731	−	27.2164i	−0.457834	−	0.904704i
$906$	1.94912	−	0.833697i	0.0647550	−	0.0276977i
$907$	16.2623	−	41.1179i	0.539979	−	1.36530i	−0.361458	−	0.932388i	$-0.617721\pi$
$907$	16.2623	−	41.1179i	0.539979	−	1.36530i	0.901437	−	0.432909i	$-0.142513\pi$
$908$	7.73907	−	26.4385i	0.256830	−	0.877392i
$909$	−38.9010	+	10.2322i	−1.29027	+	0.339382i
$910$	2.35534	+	1.33116i	0.0780788	+	0.0441275i
$911$	32.1171	+	49.1589i	1.06409	+	1.62871i	0.726149	+	0.687538i	$0.241308\pi$
$911$	32.1171	+	49.1589i	1.06409	+	1.62871i	0.337938	+	0.941168i	$0.390271\pi$
$912$	8.29704	−	3.39689i	0.274743	−	0.112482i
$913$	−11.8991	+	18.2130i	−0.393804	+	0.602761i
$914$	1.59796	−	0.827189i	0.0528560	−	0.0273610i
$915$	4.66968	−	6.11467i	0.154375	−	0.202145i
$916$	11.2967	+	52.6707i	0.373253	+	1.74029i
$917$	14.5453	+	4.40314i	0.480327	+	0.145405i
$918$	−0.0849815	+	0.0768009i	−0.00280481	+	0.00253481i
$919$	−17.9036	−	57.2411i	−0.590586	−	1.88821i	−0.435132	−	0.900367i	$-0.643298\pi$
$919$	−17.9036	−	57.2411i	−0.590586	−	1.88821i	−0.155454	−	0.987843i	$-0.549684\pi$
$920$	2.10102	+	1.82978i	0.0692687	+	0.0603262i
$921$	−7.72577	−	8.08902i	−0.254573	−	0.266542i
$922$	0.853469	−	0.961997i	0.0281075	−	0.0316817i
$923$	−10.8358	−	28.9412i	−0.356666	−	0.952611i
$924$	5.69543	+	7.74892i	0.187366	+	0.254921i
$925$	25.4360	−	1.87261i	0.836332	−	0.0615709i
$926$	−10.0567	−	4.97377i	−0.330483	−	0.163448i
$927$	18.4799	−	18.6504i	0.606959	−	0.612560i
$928$	−23.6561	−	10.1184i	−0.776549	−	0.332154i
$929$	2.30091	+	35.7337i	0.0754903	+	1.17239i	0.845365	+	0.534190i	$0.179383\pi$
$929$	2.30091	+	35.7337i	0.0754903	+	1.17239i	−0.769874	+	0.638196i	$0.779681\pi$
$930$	−1.83099	+	0.305538i	−0.0600405	+	0.0100190i
$931$	1.82623	−	1.37624i	0.0598521	−	0.0451043i
$932$	−28.0559	−	4.68170i	−0.919002	−	0.153354i
$933$	−1.65998	+	16.3721i	−0.0543454	+	0.536000i
$934$	−0.0118263	−	1.28740i	−0.000386970	−	0.0421251i
$935$	−0.273876	−	0.320369i	−0.00895669	−	0.0104772i
$936$	−1.54054	+	7.18275i	−0.0503541	+	0.234776i
$937$	3.12329	−	5.64678i	0.102033	−	0.184472i	−0.819173	−	0.573546i	$-0.805567\pi$
$937$	3.12329	−	5.64678i	0.102033	−	0.184472i	0.921207	+	0.389074i	$0.127205\pi$
$938$	−0.753226	−	5.43187i	−0.0245937	−	0.177357i
$939$	0.192821	−	0.381025i	0.00629249	−	0.0124343i
$940$	1.26753	−	19.6851i	0.0413422	−	0.642056i
$941$	−0.839922	−	8.28401i	−0.0273807	−	0.270051i	−0.999384	−	0.0350854i	$-0.988830\pi$
$941$	−0.839922	−	8.28401i	−0.0273807	−	0.270051i	0.972004	−	0.234966i	$-0.0754978\pi$
$942$	−2.43308	+	0.269294i	−0.0792742	+	0.00877406i
$943$	7.21699	+	7.02079i	0.235017	+	0.228628i
$944$	6.90301	+	1.81572i	0.224674	+	0.0590965i
$945$	6.67952	−	11.0935i	0.217285	−	0.360871i
$946$	4.05863	−	1.22863i	0.131958	−	0.0399462i
$947$	−12.1263	−	21.9239i	−0.394051	−	0.712430i	0.602255	−	0.798304i	$-0.294269\pi$
$947$	−12.1263	−	21.9239i	−0.394051	−	0.712430i	−0.996306	+	0.0858740i	$0.972632\pi$
$948$	−3.73069	+	2.79519i	−0.121167	+	0.0907836i
$949$	−8.00840	+	31.6245i	−0.259964	+	1.02657i
$950$	3.24759	−	3.06223i	0.105366	−	0.0993518i
$951$	−1.79588	−	7.09177i	−0.0582354	−	0.229966i
$952$	0.276479	+	0.223468i	0.00896074	+	0.00724265i
$953$	−10.7053	−	13.4966i	−0.346779	−	0.437197i	0.578962	−	0.815355i	$-0.303458\pi$
$953$	−10.7053	−	13.4966i	−0.346779	−	0.437197i	−0.925741	+	0.378158i	$0.876558\pi$
$954$	−1.35312	−	0.520842i	−0.0438090	−	0.0168629i
$955$	−16.0542	−	2.07608i	−0.519501	−	0.0671802i
$956$	−7.95006	+	45.0870i	−0.257123	+	1.45822i
$957$	0.358651	−	13.0112i	0.0115936	−	0.420593i
$958$	4.26053	+	0.954807i	0.137651	+	0.0308484i
$959$	−14.2760	+	11.5388i	−0.460996	+	0.372606i
$960$	−3.70968	−	2.77945i	−0.119729	−	0.0897064i
$961$	1.97024	−	14.2083i	0.0635562	−	0.458334i
$962$	−4.83306	−	3.35117i	−0.155824	−	0.108046i
$963$	−32.9843	−	21.9847i	−1.06290	−	0.708446i
$964$	−2.56965	−	1.85257i	−0.0827628	−	0.0596673i
$965$	−21.9335	−	4.49390i	−0.706064	−	0.144664i
$966$	0.136071	−	0.864254i	0.00437800	−	0.0278069i
$967$	16.7896	+	6.11093i	0.539918	+	0.196514i	0.597562	−	0.801823i	$-0.296136\pi$
$967$	16.7896	+	6.11093i	0.539918	+	0.196514i	−0.0576431	+	0.998337i	$0.518359\pi$
$968$	−1.83261	−	1.42637i	−0.0589022	−	0.0458454i
$969$	0.230502	+	0.140807i	0.00740478	+	0.00452336i
$970$	−5.18788	+	4.03789i	−0.166573	+	0.129649i
$971$	−16.2730	+	5.25437i	−0.522224	+	0.168621i	−0.556588	−	0.830788i	$-0.687890\pi$
$971$	−16.2730	+	5.25437i	−0.522224	+	0.168621i	0.0343639	+	0.999409i	$0.489059\pi$
$972$	25.4630	+	6.19977i	0.816725	+	0.198858i
$973$	−11.0145	+	1.42436i	−0.353108	+	0.0456628i
$974$	−0.464878	+	10.1144i	−0.0148957	+	0.324086i
$975$	0.648361	+	4.11807i	0.0207642	+	0.131884i
$976$	5.91364	−	30.2745i	0.189291	−	0.969064i
$977$	1.47659	+	53.5681i	0.0472404	+	1.71379i	0.538371	+	0.842708i	$0.319040\pi$
$977$	1.47659	+	53.5681i	0.0472404	+	1.71379i	−0.491130	+	0.871086i	$0.663416\pi$
$978$	0.0648519	+	0.00960085i	0.00207374	+	0.000307001i
$979$	24.8255	−	4.61293i	0.793427	−	0.147430i
$980$	−1.26200	−	0.512581i	−0.0403131	−	0.0163738i
$981$	1.55942	+	0.735910i	0.0497886	+	0.0234958i
$982$	−0.379730	−	0.497234i	−0.0121177	−	0.0158674i
$983$	−15.5695	+	18.2126i	−0.496591	+	0.580893i	−0.950723	−	0.310041i	$-0.899657\pi$
$983$	−15.5695	+	18.2126i	−0.496591	+	0.580893i	0.454132	+	0.890934i	$0.349949\pi$
$984$	3.79814	+	3.18702i	0.121080	+	0.101598i
$985$	−21.1692	+	19.8500i	−0.674508	+	0.632473i
$986$	−0.0532453	−	0.227765i	−0.00169568	−	0.00725353i
$987$	−11.2063	+	6.06456i	−0.356701	+	0.193037i
$988$	17.9888	−	1.37467i	0.572300	−	0.0437342i
$989$	5.94705	+	3.21838i	0.189105	+	0.102339i
$990$	0.944613	−	3.46167i	0.0300218	−	0.110019i
$991$	30.7916	−	13.8451i	0.978126	−	0.439803i	0.142916	−	0.989735i	$-0.454352\pi$
$991$	30.7916	−	13.8451i	0.978126	−	0.439803i	0.835210	+	0.549931i	$0.185346\pi$
$992$	−20.0067	+	14.4237i	−0.635213	+	0.457952i
$993$	−1.55627	+	0.0572089i	−0.0493866	+	0.00181547i
$994$	−5.95655	−	11.2525i	−0.188930	−	0.356907i
$995$	−2.55557	+	6.82563i	−0.0810171	+	0.216387i
$996$	−7.99149	+	2.25978i	−0.253220	+	0.0716038i
$997$	17.4324	+	25.6409i	0.552091	+	0.812056i	0.996485	−	0.0837758i	$-0.0266979\pi$
$997$	17.4324	+	25.6409i	0.552091	+	0.812056i	−0.444394	+	0.895831i	$0.646581\pi$
$998$	0.531442	−	0.847019i	0.0168225	−	0.0268119i
$999$	−16.6709	+	22.6816i	−0.527445	+	0.717615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.18	✓	3348
361.271	even	171	inner	361.2.k.a.271.18	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.18	✓	3348	1.1	even	1	trivial
361.2.k.a.271.18	yes	3348	361.271	even	171	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.k (of order \(171\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(0.328494 + 0.00603573i) q^{2} +(0.508770 - 0.339105i) q^{3} +(-1.89078 - 0.0695056i) q^{4} +(0.597036 + 1.23561i) q^{5} +(0.169175 - 0.108323i) q^{6} +(-2.54147 + 1.03226i) q^{7} +(-1.27679 - 0.0704424i) q^{8} +(-1.01056 + 2.42394i) q^{9} +(0.188665 + 0.409493i) q^{10} +(-0.904649 + 2.89232i) q^{11} +(-0.985542 + 0.605810i) q^{12} +(-2.12545 + 0.517507i) q^{13} +(-0.841087 + 0.323750i) q^{14} +(0.722755 + 0.426182i) q^{15} +(3.35491 + 0.246989i) q^{16} +(0.0538641 + 0.0858493i) q^{17} +(-0.346592 + 0.790150i) q^{18} +(4.32444 + 0.546994i) q^{19} +(-1.04298 - 2.37776i) q^{20} +(-0.942981 + 1.38701i) q^{21} +(-0.314629 + 0.944649i) q^{22} +(-1.42317 + 0.703864i) q^{23} +(-0.673480 + 0.397127i) q^{24} +(1.93691 - 2.44192i) q^{25} +(-0.701319 + 0.157169i) q^{26} +(0.659479 + 3.37616i) q^{27} +(4.87710 - 1.77512i) q^{28} +(-6.68483 - 2.15846i) q^{29} +(0.234848 + 0.144361i) q^{30} +(-5.07802 + 4.42245i) q^{31} +(3.64725 + 0.335980i) q^{32} +(0.520543 + 1.77830i) q^{33} +(0.0171759 + 0.0285261i) q^{34} +(-2.79281 - 2.52396i) q^{35} +(2.07922 - 4.51290i) q^{36} +(5.54218 + 6.02041i) q^{37} +(1.41725 + 0.205785i) q^{38} +(-0.905875 + 0.984042i) q^{39} +(-0.675250 - 1.61967i) q^{40} +(-2.11411 - 5.97878i) q^{41} +(-0.318135 + 0.449931i) q^{42} +(-2.45885 - 3.47749i) q^{43} +(1.91152 - 5.40586i) q^{44} +(-3.59838 + 0.198528i) q^{45} +(-0.471752 + 0.222625i) q^{46} +(6.74687 + 3.49253i) q^{47} +(1.79063 - 1.01201i) q^{48} +(0.376032 - 0.365810i) q^{49} +(0.651000 - 0.790465i) q^{50} +(0.0565164 + 0.0254120i) q^{51} +(4.05472 - 0.830761i) q^{52} +(0.0771540 + 1.67865i) q^{53} +(0.196257 + 1.11303i) q^{54} +(-4.11388 + 0.609030i) q^{55} +(3.31763 - 1.13895i) q^{56} +(2.38564 - 1.18815i) q^{57} +(-2.18290 - 0.749390i) q^{58} +(2.08612 + 0.387631i) q^{59} +(-1.33695 - 0.856052i) q^{60} +(1.09242 - 9.10439i) q^{61} +(-1.69479 + 1.42210i) q^{62} +(0.0661730 - 7.20352i) q^{63} +(-5.49106 - 0.607751i) q^{64} +(-1.90840 - 2.31725i) q^{65} +(0.160262 + 0.587302i) q^{66} +(-1.38511 + 5.92501i) q^{67} +(-0.0958781 - 0.166066i) q^{68} +(-0.485385 + 0.840711i) q^{69} +(-0.902186 - 0.845962i) q^{70} +(1.68299 + 14.0263i) q^{71} +(1.46102 - 3.02368i) q^{72} +(6.97701 - 13.1802i) q^{73} +(1.78423 + 2.01112i) q^{74} +(0.157372 - 1.89919i) q^{75} +(-8.13854 - 1.33482i) q^{76} +(-0.686479 - 8.28457i) q^{77} +(-0.303514 + 0.317784i) q^{78} +(4.01264 - 0.369639i) q^{79} +(1.69782 + 4.29281i) q^{80} +(-4.06488 - 4.10240i) q^{81} +(-0.658384 - 1.97675i) q^{82} +(6.90798 + 1.95339i) q^{83} +(1.87937 - 2.55698i) q^{84} +(-0.0739172 + 0.117810i) q^{85} +(-0.786726 - 1.15717i) q^{86} +(-4.13299 + 1.16870i) q^{87} +(1.35879 - 3.62916i) q^{88} +(-3.89817 - 7.36400i) q^{89} +(-1.18324 + 0.0434964i) q^{90} +(4.86755 - 3.50923i) q^{91} +(2.73983 - 1.23193i) q^{92} +(-1.08387 + 3.97199i) q^{93} +(2.19522 + 1.18800i) q^{94} +(1.90598 + 5.66989i) q^{95} +(1.96955 - 1.06587i) q^{96} +(3.31917 + 14.1983i) q^{97} +(0.125732 - 0.117897i) q^{98} +(-6.09662 - 5.11567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) \) 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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