LMFDB - Embedded newform 230.2.g.d.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	230.41
Dual form			230.2.g.d.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(2.00799 - 2.31734i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-2.57952 + 1.65776i) q^{6} +(0.414762 + 0.908202i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.911115 - 6.33694i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(2.00799 - 2.31734i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-2.57952 + 1.65776i) q^{6} +(0.414762 + 0.908202i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.911115 - 6.33694i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(4.67469 - 1.37261i) q^{11} +(2.94208 - 0.863872i) q^{12} +(-2.42639 + 5.31304i) q^{13} +(-0.142091 - 0.988265i) q^{14} +(-2.00799 - 2.31734i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.46855 + 2.22910i) q^{17} +(-0.911115 + 6.33694i) q^{18} +(-5.79427 - 3.72375i) q^{19} +(0.654861 - 0.755750i) q^{20} +(2.93745 + 0.862514i) q^{21} -4.87205 q^{22} +(4.02440 + 2.60849i) q^{23} -3.06629 q^{24} +(-0.959493 - 0.281733i) q^{25} +(3.82496 - 4.41424i) q^{26} +(-8.77581 - 5.63987i) q^{27} +(-0.142091 + 0.988265i) q^{28} +(3.04872 - 1.95929i) q^{29} +(1.27378 + 2.78919i) q^{30} +(1.09711 + 1.26614i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(6.20592 - 13.5891i) q^{33} +(3.95606 - 1.16160i) q^{34} +(0.957984 - 0.281290i) q^{35} +(2.65953 - 5.82356i) q^{36} +(-0.00888332 - 0.0617849i) q^{37} +(4.51046 + 5.20535i) q^{38} +(7.43999 + 16.2913i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-0.409905 + 2.85095i) q^{41} +(-2.57547 - 1.65515i) q^{42} +(-5.13385 + 5.92477i) q^{43} +(4.67469 + 1.37261i) q^{44} -6.40210 q^{45} +(-3.12649 - 3.63663i) q^{46} +5.30601 q^{47} +(2.94208 + 0.863872i) q^{48} +(3.93122 - 4.53687i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-1.79922 + 12.5138i) q^{51} +(-4.91365 + 3.15781i) q^{52} +(-1.43283 - 3.13746i) q^{53} +(6.83139 + 7.88385i) q^{54} +(-0.693364 - 4.82246i) q^{55} +(0.414762 - 0.908202i) q^{56} +(-20.2640 + 5.95006i) q^{57} +(-3.47722 + 1.02100i) q^{58} +(-4.84544 + 10.6100i) q^{59} +(-0.436378 - 3.03507i) q^{60} +(-0.283578 - 0.327266i) q^{61} +(-0.695961 - 1.52394i) q^{62} +(5.37732 - 3.45580i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.91365 + 3.15781i) q^{65} +(-9.78302 + 11.2902i) q^{66} +(4.86653 + 1.42894i) q^{67} -4.12307 q^{68} +(14.1257 - 4.08810i) q^{69} -0.998427 q^{70} +(7.68672 + 2.25702i) q^{71} +(-4.19249 + 4.83839i) q^{72} +(9.16147 + 5.88772i) q^{73} +(-0.00888332 + 0.0617849i) q^{74} +(-2.57952 + 1.65776i) q^{75} +(-2.86124 - 6.26524i) q^{76} +(3.18549 + 3.67626i) q^{77} +(-2.54883 - 17.7275i) q^{78} +(-6.44266 + 14.1075i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-12.2629 + 3.60072i) q^{81} +(1.19651 - 2.61999i) q^{82} +(-0.929434 - 6.46436i) q^{83} +(2.00483 + 2.31370i) q^{84} +(1.71279 + 3.75048i) q^{85} +(6.59509 - 4.23841i) q^{86} +(1.58144 - 10.9992i) q^{87} +(-4.09863 - 2.63403i) q^{88} +(4.28672 - 4.94714i) q^{89} +(6.14277 + 1.80368i) q^{90} -5.83169 q^{91} +(1.97529 + 4.37015i) q^{92} +5.13707 q^{93} +(-5.09108 - 1.49488i) q^{94} +(-4.51046 + 5.20535i) q^{95} +(-2.57952 - 1.65776i) q^{96} +(0.140212 - 0.975199i) q^{97} +(-5.05016 + 3.24554i) q^{98} +(-12.9574 - 28.3726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	2.00799	−	2.31734i	1.15931	−	1.33792i	0.228017	−	0.973657i	$-0.426776\pi$
$3$	2.00799	−	2.31734i	1.15931	−	1.33792i	0.931297	−	0.364262i	$-0.118679\pi$
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	−2.57952	+	1.65776i	−1.05309	+	0.676777i
$7$	0.414762	+	0.908202i	0.156765	+	0.343268i	0.971675	−	0.236319i	$-0.0759411\pi$
$7$	0.414762	+	0.908202i	0.156765	+	0.343268i	−0.814910	+	0.579587i	$0.803214\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.911115	−	6.33694i	−0.303705	−	2.11231i
$10$	−0.415415	+	0.909632i	−0.131366	+	0.287651i
$11$	4.67469	−	1.37261i	1.40947	−	0.413859i	0.513547	−	0.858061i	$-0.328331\pi$
$11$	4.67469	−	1.37261i	1.40947	−	0.413859i	0.895926	+	0.444203i	$0.146513\pi$
$12$	2.94208	−	0.863872i	0.849305	−	0.249378i
$13$	−2.42639	+	5.31304i	−0.672958	+	1.47357i	0.196977	+	0.980408i	$0.436888\pi$
$13$	−2.42639	+	5.31304i	−0.672958	+	1.47357i	−0.869936	+	0.493165i	$0.835840\pi$
$14$	−0.142091	−	0.988265i	−0.0379754	−	0.264125i
$15$	−2.00799	−	2.31734i	−0.518461	−	0.598336i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−3.46855	+	2.22910i	−0.841246	+	0.540636i	−0.888833	−	0.458231i	$-0.848483\pi$
$17$	−3.46855	+	2.22910i	−0.841246	+	0.540636i	0.0475868	+	0.998867i	$0.484847\pi$
$18$	−0.911115	+	6.33694i	−0.214752	+	1.49363i
$19$	−5.79427	−	3.72375i	−1.32930	−	0.854287i	−0.333226	−	0.942847i	$-0.608137\pi$
$19$	−5.79427	−	3.72375i	−1.32930	−	0.854287i	−0.996071	+	0.0885599i	$0.971774\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	2.93745	+	0.862514i	0.641005	+	0.188216i
$22$	−4.87205			−1.03872
$23$	4.02440	+	2.60849i	0.839145	+	0.543907i
$23$	4.02440	+	2.60849i	0.839145	+	0.543907i
$24$	−3.06629			−0.625903
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	3.82496	−	4.41424i	0.750136	−	0.865703i
$27$	−8.77581	−	5.63987i	−1.68891	−	1.08539i
$28$	−0.142091	+	0.988265i	−0.0268527	+	0.186765i
$29$	3.04872	−	1.95929i	0.566133	−	0.363832i	−0.226050	−	0.974116i	$-0.572581\pi$
$29$	3.04872	−	1.95929i	0.566133	−	0.363832i	0.792183	+	0.610284i	$0.208945\pi$
$30$	1.27378	+	2.78919i	0.232560	+	0.509234i
$31$	1.09711	+	1.26614i	0.197047	+	0.227405i	0.845671	−	0.533704i	$-0.179201\pi$
$31$	1.09711	+	1.26614i	0.197047	+	0.227405i	−0.648624	+	0.761109i	$0.724655\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	6.20592	−	13.5891i	1.08031	−	2.36555i
$34$	3.95606	−	1.16160i	0.678458	−	0.199213i
$35$	0.957984	−	0.281290i	0.161929	−	0.0475466i
$36$	2.65953	−	5.82356i	0.443255	−	0.970593i
$37$	−0.00888332	−	0.0617849i	−0.00146041	−	0.0101574i	0.989078	−	0.147392i	$-0.0470878\pi$
$37$	−0.00888332	−	0.0617849i	−0.00146041	−	0.0101574i	−0.990539	+	0.137234i	$0.956179\pi$
$38$	4.51046	+	5.20535i	0.731693	+	0.844419i
$39$	7.43999	+	16.2913i	1.19135	+	2.60870i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	−0.409905	+	2.85095i	−0.0640165	+	0.445244i	0.932453	+	0.361291i	$0.117664\pi$
$41$	−0.409905	+	2.85095i	−0.0640165	+	0.445244i	−0.996470	+	0.0839535i	$0.973245\pi$
$42$	−2.57547	−	1.65515i	−0.397403	−	0.255395i
$43$	−5.13385	+	5.92477i	−0.782904	+	0.903520i	−0.997316	−	0.0732239i	$-0.976671\pi$
$43$	−5.13385	+	5.92477i	−0.782904	+	0.903520i	0.214411	+	0.976743i	$0.431217\pi$
$44$	4.67469	+	1.37261i	0.704737	+	0.206929i
$45$	−6.40210			−0.954369
$46$	−3.12649	−	3.63663i	−0.460975	−	0.536192i
$47$	5.30601			0.773962			0.386981	−	0.922088i	$-0.373518\pi$
$47$	5.30601			0.773962			0.386981	+	0.922088i	$0.373518\pi$
$48$	2.94208	+	0.863872i	0.424653	+	0.124689i
$49$	3.93122	−	4.53687i	0.561603	−	0.648125i
$50$	0.841254	+	0.540641i	0.118971	+	0.0764582i
$51$	−1.79922	+	12.5138i	−0.251941	+	1.75229i
$52$	−4.91365	+	3.15781i	−0.681401	+	0.437910i
$53$	−1.43283	−	3.13746i	−0.196814	−	0.430963i	0.785334	−	0.619072i	$-0.212491\pi$
$53$	−1.43283	−	3.13746i	−0.196814	−	0.430963i	−0.982148	+	0.188110i	$0.939764\pi$
$54$	6.83139	+	7.88385i	0.929635	+	1.07286i
$55$	−0.693364	−	4.82246i	−0.0934932	−	0.650260i
$56$	0.414762	−	0.908202i	0.0554249	−	0.121364i
$57$	−20.2640	+	5.95006i	−2.68404	+	0.788105i
$58$	−3.47722	+	1.02100i	−0.456582	+	0.134064i
$59$	−4.84544	+	10.6100i	−0.630823	+	1.38131i	0.276557	+	0.960998i	$0.410807\pi$
$59$	−4.84544	+	10.6100i	−0.630823	+	1.38131i	−0.907380	+	0.420312i	$0.861921\pi$
$60$	−0.436378	−	3.03507i	−0.0563361	−	0.391826i
$61$	−0.283578	−	0.327266i	−0.0363084	−	0.0419021i	0.737305	−	0.675560i	$-0.236098\pi$
$61$	−0.283578	−	0.327266i	−0.0363084	−	0.0419021i	−0.773613	+	0.633658i	$0.781553\pi$
$62$	−0.695961	−	1.52394i	−0.0883871	−	0.193541i
$63$	5.37732	−	3.45580i	0.677479	−	0.435389i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	4.91365	+	3.15781i	0.609464	+	0.391679i
$66$	−9.78302	+	11.2902i	−1.20421	+	1.38973i
$67$	4.86653	+	1.42894i	0.594542	+	0.174573i	0.565141	−	0.824995i	$-0.308822\pi$
$67$	4.86653	+	1.42894i	0.594542	+	0.174573i	0.0294009	+	0.999568i	$0.490640\pi$
$68$	−4.12307			−0.499996
$69$	14.1257	−	4.08810i	1.70054	−	0.492150i
$70$	−0.998427			−0.119335
$71$	7.68672	+	2.25702i	0.912245	+	0.267859i	0.703986	−	0.710214i	$-0.251402\pi$
$71$	7.68672	+	2.25702i	0.912245	+	0.267859i	0.208260	+	0.978074i	$0.433220\pi$
$72$	−4.19249	+	4.83839i	−0.494089	+	0.570209i
$73$	9.16147	+	5.88772i	1.07227	+	0.689106i	0.952759	−	0.303727i	$-0.0982312\pi$
$73$	9.16147	+	5.88772i	1.07227	+	0.689106i	0.119510	+	0.992833i	$0.461868\pi$
$74$	−0.00888332	+	0.0617849i	−0.00103267	+	0.00718234i
$75$	−2.57952	+	1.65776i	−0.297858	+	0.191422i
$76$	−2.86124	−	6.26524i	−0.328207	−	0.718672i
$77$	3.18549	+	3.67626i	0.363021	+	0.418948i
$78$	−2.54883	−	17.7275i	−0.288598	−	2.00724i
$79$	−6.44266	+	14.1075i	−0.724856	+	1.58721i	0.0821146	+	0.996623i	$0.473833\pi$
$79$	−6.44266	+	14.1075i	−0.724856	+	1.58721i	−0.806971	+	0.590591i	$0.798895\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−12.2629	+	3.60072i	−1.36255	+	0.400080i
$82$	1.19651	−	2.61999i	0.132132	−	0.289329i
$83$	−0.929434	−	6.46436i	−0.102019	−	0.709555i	−0.975065	−	0.221919i	$-0.928768\pi$
$83$	−0.929434	−	6.46436i	−0.102019	−	0.709555i	0.873047	−	0.487637i	$-0.162141\pi$
$84$	2.00483	+	2.31370i	0.218745	+	0.252445i
$85$	1.71279	+	3.75048i	0.185778	+	0.406796i
$86$	6.59509	−	4.23841i	0.711167	−	0.457039i
$87$	1.58144	−	10.9992i	0.169548	−	1.17924i
$88$	−4.09863	−	2.63403i	−0.436915	−	0.280788i
$89$	4.28672	−	4.94714i	0.454392	−	0.524396i	−0.481613	−	0.876384i	$-0.659949\pi$
$89$	4.28672	−	4.94714i	0.454392	−	0.524396i	0.936004	+	0.351988i	$0.114494\pi$
$90$	6.14277	+	1.80368i	0.647505	+	0.190125i
$91$	−5.83169			−0.611327
$92$	1.97529	+	4.37015i	0.205938	+	0.455620i
$93$	5.13707			0.532689
$94$	−5.09108	−	1.49488i	−0.525105	−	0.154185i
$95$	−4.51046	+	5.20535i	−0.462763	+	0.534057i
$96$	−2.57952	−	1.65776i	−0.263271	−	0.169194i
$97$	0.140212	−	0.975199i	0.0142364	−	0.0990165i	−0.981464	−	0.191645i	$-0.938618\pi$
$97$	0.140212	−	0.975199i	0.0142364	−	0.0990165i	0.995701	+	0.0926285i	$0.0295269\pi$
$98$	−5.05016	+	3.24554i	−0.510144	+	0.327849i
$99$	−12.9574	−	28.3726i	−1.30226	−	2.85156i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−2.47221	−	17.1946i	−0.245994	−	1.71093i	−0.620921	−	0.783874i	$-0.713241\pi$
$101$	−2.47221	−	17.1946i	−0.245994	−	1.71093i	0.374926	−	0.927055i	$-0.377668\pi$
$102$	5.25189	−	11.5000i	0.520015	−	1.13867i
$103$	−8.20525	+	2.40928i	−0.808487	+	0.237393i	−0.659752	−	0.751484i	$-0.729339\pi$
$103$	−8.20525	+	2.40928i	−0.808487	+	0.237393i	−0.148736	+	0.988877i	$0.547520\pi$
$104$	5.60428	−	1.64556i	0.549545	−	0.161361i
$105$	1.27178	−	2.78480i	0.124113	−	0.271769i
$106$	0.490865	+	3.41404i	0.0476770	+	0.331601i
$107$	−4.86662	−	5.61638i	−0.470474	−	0.542956i	0.470070	−	0.882629i	$-0.344229\pi$
$107$	−4.86662	−	5.61638i	−0.470474	−	0.542956i	−0.940543	+	0.339674i	$0.889683\pi$
$108$	−4.33354	−	9.48912i	−0.416995	−	0.913091i
$109$	−2.82426	+	1.81504i	−0.270515	+	0.173849i	−0.668865	−	0.743384i	$-0.733219\pi$
$109$	−2.82426	+	1.81504i	−0.270515	+	0.173849i	0.398350	+	0.917234i	$0.369583\pi$
$110$	−0.693364	+	4.82246i	−0.0661097	+	0.459803i
$111$	−0.161014	−	0.103478i	−0.0152828	−	0.00982166i
$112$	−0.653831	+	0.754561i	−0.0617812	+	0.0712993i
$113$	−9.49161	−	2.78699i	−0.892896	−	0.262178i	−0.197071	−	0.980389i	$-0.563143\pi$
$113$	−9.49161	−	2.78699i	−0.892896	−	0.262178i	−0.695825	+	0.718211i	$0.744961\pi$
$114$	21.1195			1.97803
$115$	3.15467	−	3.61221i	0.294174	−	0.336840i
$116$	3.62402			0.336482
$117$	35.8792	+	10.5351i	3.31703	+	0.973968i
$118$	7.63836	−	8.81514i	0.703168	−	0.811499i
$119$	−3.46309	−	2.22560i	−0.317461	−	0.204020i
$120$	−0.436378	+	3.03507i	−0.0398357	+	0.277063i
$121$	10.7149	−	6.88605i	0.974082	−	0.626005i
$122$	0.179889	+	0.393903i	0.0162864	+	0.0356623i
$123$	5.78355	+	6.67458i	0.521486	+	0.601826i
$124$	0.238426	+	1.65829i	0.0214112	+	0.148918i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−6.13311	+	1.80084i	−0.546381	+	0.160432i
$127$	−9.48208	+	2.78419i	−0.841399	+	0.247057i	−0.673907	−	0.738816i	$-0.735385\pi$
$127$	−9.48208	+	2.78419i	−0.841399	+	0.247057i	−0.167492	+	0.985873i	$0.553567\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	3.42103	+	23.7938i	0.301205	+	2.09492i
$130$	−3.82496	−	4.41424i	−0.335471	−	0.387154i
$131$	−8.27531	−	18.1204i	−0.723017	−	1.58319i	−0.809627	−	0.586945i	$-0.800330\pi$
$131$	−8.27531	−	18.1204i	−0.723017	−	1.58319i	0.0866094	−	0.996242i	$-0.472397\pi$
$132$	12.5676	−	8.07668i	1.09387	−	0.702985i
$133$	0.978675	−	6.80683i	0.0848619	−	0.590227i
$134$	−4.26682	−	2.74212i	−0.368597	−	0.236883i
$135$	−6.83139	+	7.88385i	−0.587953	+	0.678533i
$136$	3.95606	+	1.16160i	0.339229	+	0.0996067i
$137$	−0.287466			−0.0245598			−0.0122799	−	0.999925i	$-0.503909\pi$
$137$	−0.287466			−0.0245598			−0.0122799	+	0.999925i	$0.503909\pi$
$138$	−14.7053	−	0.0571696i	−1.25180	−	0.00486660i
$139$	−2.34636			−0.199015			−0.0995077	−	0.995037i	$-0.531727\pi$
$139$	−2.34636			−0.199015			−0.0995077	+	0.995037i	$0.531727\pi$
$140$	0.957984	+	0.281290i	0.0809644	+	0.0237733i
$141$	10.6544	−	12.2959i	0.897264	−	1.03550i
$142$	−6.73947	−	4.33120i	−0.565564	−	0.363466i
$143$	−4.04985	+	28.1673i	−0.338666	+	2.35547i
$144$	5.38579	−	3.46124i	0.448816	−	0.288437i
$145$	−1.50547	−	3.29652i	−0.125023	−	0.273761i
$146$	−7.13161	−	8.23031i	−0.590216	−	0.681146i
$147$	−2.61964	−	18.2200i	−0.216064	−	1.50276i
$148$	0.0259303	−	0.0567794i	0.00213146	−	0.00466724i
$149$	4.51190	−	1.32481i	0.369630	−	0.108533i	−0.0916420	−	0.995792i	$-0.529212\pi$
$149$	4.51190	−	1.32481i	0.369630	−	0.108533i	0.461272	+	0.887259i	$0.347393\pi$
$150$	2.94208	−	0.863872i	0.240220	−	0.0705349i
$151$	5.20666	−	11.4010i	0.423712	−	0.927799i	−0.570594	−	0.821232i	$-0.693287\pi$
$151$	5.20666	−	11.4010i	0.423712	−	0.927799i	0.994306	−	0.106567i	$-0.0339859\pi$
$152$	0.980217	+	6.81756i	0.0795061	+	0.552977i
$153$	17.2859	+	19.9490i	1.39748	+	1.61278i
$154$	−2.02074	−	4.42480i	−0.162836	−	0.356561i
$155$	1.40938	−	0.905756i	0.113204	−	0.0727521i
$156$	−2.54883	+	17.7275i	−0.204070	+	1.41933i
$157$	−12.1722	−	7.82257i	−0.971444	−	0.624309i	−0.0443019	−	0.999018i	$-0.514106\pi$
$157$	−12.1722	−	7.82257i	−0.971444	−	0.624309i	−0.927143	+	0.374709i	$0.877743\pi$
$158$	10.1562	−	11.7209i	0.807986	−	0.932465i
$159$	−10.1477	−	2.97962i	−0.804762	−	0.236300i
$160$	−1.00000			−0.0790569
$161$	−0.699865	+	4.73687i	−0.0551571	+	0.373317i
$162$	12.7806			1.00414
$163$	1.82656	+	0.536326i	0.143067	+	0.0420083i	0.352482	−	0.935819i	$-0.385338\pi$
$163$	1.82656	+	0.536326i	0.143067	+	0.0420083i	−0.209415	+	0.977827i	$0.567156\pi$
$164$	−1.88618	+	2.17676i	−0.147286	+	0.169977i
$165$	−12.5676	−	8.07668i	−0.978383	−	0.628769i
$166$	−0.929434	+	6.46436i	−0.0721381	+	0.501731i
$167$	−11.0211	+	7.08284i	−0.852839	+	0.548086i	−0.892459	−	0.451128i	$-0.851022\pi$
$167$	−11.0211	+	7.08284i	−0.852839	+	0.548086i	0.0396200	+	0.999215i	$0.487385\pi$
$168$	−1.27178	−	2.78480i	−0.0981198	−	0.214852i
$169$	−13.8279	−	15.9583i	−1.06368	−	1.22756i
$170$	−0.586774	−	4.08110i	−0.0450035	−	0.313006i
$171$	−18.3179	+	40.1107i	−1.40081	+	3.06734i
$172$	−7.52204	+	2.20867i	−0.573550	+	0.168410i
$173$	−2.63596	+	0.773988i	−0.200408	+	0.0588452i	−0.380396	−	0.924824i	$-0.624212\pi$
$173$	−2.63596	+	0.773988i	−0.200408	+	0.0588452i	0.179988	+	0.983669i	$0.442394\pi$
$174$	−4.61621	+	10.1081i	−0.349954	+	0.766292i
$175$	−0.142091	−	0.988265i	−0.0107411	−	0.0747058i
$176$	3.19051	+	3.68205i	0.240494	+	0.277545i
$177$	14.8575	+	32.5334i	1.11676	+	2.44536i
$178$	−5.50685	+	3.53904i	−0.412756	+	0.265262i
$179$	−0.666919	+	4.63852i	−0.0498479	+	0.346700i	0.949600	+	0.313465i	$0.101490\pi$
$179$	−0.666919	+	4.63852i	−0.0498479	+	0.346700i	−0.999448	+	0.0332345i	$0.989419\pi$
$180$	−5.38579	−	3.46124i	−0.401433	−	0.257986i
$181$	−13.9843	+	16.1387i	−1.03944	+	1.19958i	−0.0599310	+	0.998203i	$0.519088\pi$
$181$	−13.9843	+	16.1387i	−1.03944	+	1.19958i	−0.979513	+	0.201380i	$0.935457\pi$
$182$	5.59546	+	1.64298i	0.414763	+	0.121786i
$183$	−1.32781			−0.0981545
$184$	−0.664058	−	4.74963i	−0.0489550	−	0.350148i
$185$	−0.0624202			−0.00458923
$186$	−4.92898	−	1.44728i	−0.361410	−	0.106120i
$187$	−13.1547	+	15.1813i	−0.961967	+	1.11017i
$188$	4.46370	+	2.86865i	0.325549	+	0.209218i
$189$	1.48227	−	10.3094i	0.107819	−	0.749899i
$190$	5.79427	−	3.72375i	0.420361	−	0.270149i
$191$	3.83399	+	8.39527i	0.277418	+	0.607461i	0.996134	−	0.0878428i	$-0.0279973\pi$
$191$	3.83399	+	8.39527i	0.277418	+	0.607461i	−0.718716	+	0.695303i	$0.755270\pi$
$192$	2.00799	+	2.31734i	0.144914	+	0.167240i
$193$	−1.20552	−	8.38457i	−0.0867752	−	0.603535i	−0.986087	−	0.166228i	$-0.946841\pi$
$193$	−1.20552	−	8.38457i	−0.0867752	−	0.603535i	0.899312	−	0.437307i	$-0.144068\pi$
$194$	−0.409278	+	0.896194i	−0.0293845	+	0.0643430i
$195$	17.1843	−	5.04577i	1.23059	−	0.361335i
$196$	5.75997	−	1.69128i	0.411427	−	0.120806i
$197$	7.47240	−	16.3623i	0.532387	−	1.16576i	−0.432147	−	0.901803i	$-0.642244\pi$
$197$	7.47240	−	16.3623i	0.532387	−	1.16576i	0.964533	−	0.263961i	$-0.0850289\pi$
$198$	4.43899	+	30.8739i	0.315465	+	2.19411i
$199$	−0.539039	−	0.622084i	−0.0382115	−	0.0440984i	0.736322	−	0.676631i	$-0.236561\pi$
$199$	−0.539039	−	0.622084i	−0.0382115	−	0.0440984i	−0.774534	+	0.632533i	$0.782015\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	13.0833	−	8.40813i	0.922825	−	0.593064i
$202$	−2.47221	+	17.1946i	−0.173944	+	1.20981i
$203$	3.04393	+	1.95621i	0.213642	+	0.137299i
$204$	−8.27908	+	9.55457i	−0.579652	+	0.668954i
$205$	2.76360	+	0.811466i	0.193018	+	0.0566753i
$206$	8.55165			0.595822
$207$	12.8631	−	27.8790i	0.894050	−	1.93773i
$208$	−5.84087			−0.404992
$209$	−32.1977	−	9.45410i	−2.22716	−	0.653954i
$210$	−2.00483	+	2.31370i	−0.138347	+	0.159660i
$211$	18.9517	+	12.1795i	1.30469	+	0.838472i	0.993714	−	0.111946i	$-0.0357085\pi$
$211$	18.9517	+	12.1795i	1.30469	+	0.838472i	0.310974	+	0.950418i	$0.399345\pi$
$212$	0.490865	−	3.41404i	0.0337127	−	0.234477i
$213$	20.6651	−	13.2807i	1.41595	−	0.909977i
$214$	3.08717	+	6.75996i	0.211035	+	0.462101i
$215$	5.13385	+	5.92477i	0.350125	+	0.404066i
$216$	1.48460	+	10.3256i	0.101014	+	0.702571i
$217$	−0.694866	+	1.52154i	−0.0471706	+	0.103289i
$218$	3.22121	−	0.945834i	0.218168	−	0.0640599i
$219$	32.0400	−	9.40780i	2.16506	−	0.635720i
$220$	2.02392	−	4.43177i	0.136453	−	0.298790i
$221$	−3.42727	−	23.8372i	−0.230543	−	1.60346i
$222$	0.125339	+	0.144649i	0.00841221	+	0.00970821i
$223$	−2.12126	−	4.64491i	−0.142050	−	0.311046i	0.825213	−	0.564821i	$-0.191055\pi$
$223$	−2.12126	−	4.64491i	−0.142050	−	0.311046i	−0.967263	+	0.253775i	$0.918328\pi$
$224$	0.839931	−	0.539791i	0.0561202	−	0.0360663i
$225$	−0.911115	+	6.33694i	−0.0607410	+	0.422463i
$226$	8.32195	+	5.34819i	0.553568	+	0.355756i
$227$	10.3424	−	11.9357i	0.686446	−	0.792201i	−0.300409	−	0.953811i	$-0.597123\pi$
$227$	10.3424	−	11.9357i	0.686446	−	0.792201i	0.986855	+	0.161609i	$0.0516685\pi$
$228$	−20.2640	−	5.95006i	−1.34202	−	0.394052i
$229$	−15.2178			−1.00562			−0.502812	−	0.864396i	$-0.667701\pi$
$229$	−15.2178			−1.00562			−0.502812	+	0.864396i	$0.667701\pi$
$230$	−4.04456	+	2.57712i	−0.266690	+	0.169930i
$231$	14.9156			0.981374
$232$	−3.47722	−	1.02100i	−0.228291	−	0.0670322i
$233$	−14.4956	+	16.7288i	−0.949637	+	1.09594i	0.0456491	+	0.998958i	$0.485464\pi$
$233$	−14.4956	+	16.7288i	−0.949637	+	1.09594i	−0.995286	+	0.0969820i	$0.969081\pi$
$234$	−31.4577	−	20.2167i	−2.05646	−	1.32160i
$235$	0.755125	−	5.25201i	0.0492589	−	0.342603i
$236$	−9.81246	+	6.30609i	−0.638737	+	0.410491i
$237$	19.7550	+	43.2575i	1.28323	+	2.80988i
$238$	2.69579	+	3.11111i	0.174742	+	0.201663i
$239$	−1.44054	−	10.0192i	−0.0931807	−	0.648086i	−0.981867	−	0.189570i	$-0.939290\pi$
$239$	−1.44054	−	10.0192i	−0.0931807	−	0.648086i	0.888686	−	0.458515i	$-0.151619\pi$
$240$	1.27378	−	2.78919i	0.0822222	−	0.180042i
$241$	1.67628	−	0.492199i	0.107978	−	0.0317053i	−0.227297	−	0.973825i	$-0.572989\pi$
$241$	1.67628	−	0.492199i	0.107978	−	0.0317053i	0.335275	+	0.942120i	$0.391171\pi$
$242$	−12.2209	+	3.58838i	−0.785589	+	0.230670i
$243$	−3.27912	+	7.18026i	−0.210355	+	0.460614i
$244$	−0.0616273	−	0.428628i	−0.00394529	−	0.0274401i
$245$	−3.93122	−	4.53687i	−0.251157	−	0.289850i
$246$	−3.66883	−	8.03363i	−0.233916	−	0.512205i
$247$	33.8436	−	21.7500i	2.15342	−	1.38392i
$248$	0.238426	−	1.65829i	0.0151400	−	0.105301i
$249$	−16.8464	−	10.8265i	−1.06760	−	0.686104i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	−20.9149	−	6.14118i	−1.32014	−	0.387628i	−0.455596	−	0.890187i	$-0.650574\pi$
$251$	−20.9149	−	6.14118i	−1.32014	−	0.387628i	−0.864543	+	0.502559i	$0.832392\pi$
$252$	6.39204			0.402660
$253$	22.3933	+	6.66993i	1.40785	+	0.419335i
$254$	9.88239			0.620076
$255$	12.1304	+	3.56181i	0.759635	+	0.223049i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	3.11762	+	2.00358i	0.194472	+	0.124980i	0.634253	−	0.773125i	$-0.281308\pi$
$257$	3.11762	+	2.00358i	0.194472	+	0.124980i	−0.439781	+	0.898105i	$0.644944\pi$
$258$	3.42103	−	23.7938i	0.212984	−	1.48134i
$259$	0.0524286	−	0.0336938i	0.00325776	−	0.00209363i
$260$	2.42639	+	5.31304i	0.150478	+	0.329501i
$261$	−15.1937	−	17.5344i	−0.940464	−	1.08535i
$262$	2.83500	+	19.7178i	0.175147	+	1.21817i
$263$	−4.24138	+	9.28732i	−0.261535	+	0.572681i	−0.994156	−	0.107956i	$-0.965569\pi$
$263$	−4.24138	+	9.28732i	−0.261535	+	0.572681i	0.732621	+	0.680637i	$0.238297\pi$
$264$	−14.3339	+	4.20883i	−0.882193	+	0.259035i
$265$	−3.30943	+	0.971737i	−0.203297	+	0.0596933i
$266$	−2.85674	+	6.25539i	−0.175158	+	0.383542i
$267$	−2.85653	−	19.8676i	−0.174817	−	1.21588i
$268$	3.32144	+	3.83315i	0.202889	+	0.234147i
$269$	3.40247	+	7.45036i	0.207452	+	0.454257i	0.984546	−	0.175128i	$-0.0560341\pi$
$269$	3.40247	+	7.45036i	0.207452	+	0.454257i	−0.777093	+	0.629385i	$0.783307\pi$
$270$	8.77581	−	5.63987i	0.534079	−	0.343232i
$271$	−3.41525	+	23.7536i	−0.207462	+	1.44293i	0.573939	+	0.818898i	$0.305415\pi$
$271$	−3.41525	+	23.7536i	−0.207462	+	1.44293i	−0.781401	+	0.624029i	$0.785495\pi$
$272$	−3.46855	−	2.22910i	−0.210312	−	0.135159i
$273$	−11.7100	+	13.5140i	−0.708720	+	0.817906i
$274$	0.275821	+	0.0809884i	0.0166630	+	0.00489269i
$275$	−4.87205			−0.293795
$276$	14.0935	+	4.19781i	0.848329	+	0.252678i
$277$	22.0368			1.32406			0.662032	−	0.749476i	$-0.269694\pi$
$277$	22.0368			1.32406			0.662032	+	0.749476i	$0.269694\pi$
$278$	2.25131	+	0.661045i	0.135025	+	0.0396469i
$279$	7.02383	−	8.10594i	0.420506	−	0.485290i
$280$	−0.839931	−	0.539791i	−0.0501955	−	0.0322587i
$281$	2.71428	−	18.8782i	0.161920	−	1.12618i	−0.733089	−	0.680133i	$-0.761922\pi$
$281$	2.71428	−	18.8782i	0.161920	−	1.12618i	0.895009	−	0.446047i	$-0.147169\pi$
$282$	−13.6870	+	8.79609i	−0.815048	+	0.523800i
$283$	−8.64786	−	18.9362i	−0.514062	−	1.12564i	−0.971639	−	0.236469i	$-0.924010\pi$
$283$	−8.64786	−	18.9362i	−0.514062	−	1.12564i	0.457577	−	0.889170i	$-0.348717\pi$
$284$	5.24624	+	6.05448i	0.311307	+	0.359267i
$285$	3.00562	+	20.9046i	0.178038	+	1.23828i
$286$	11.8215	−	25.8854i	0.699018	−	1.53064i
$287$	−2.75925	+	0.810190i	−0.162874	+	0.0478240i
$288$	−6.14277	+	1.80368i	−0.361966	+	0.106283i
$289$	−0.000118735	0	0.000259993i	−6.98440e−6	0	1.52937e-5i
$290$	0.515752	+	3.58713i	0.0302860	+	0.210644i
$291$	−1.97833	−	2.28311i	−0.115972	−	0.133838i
$292$	4.52398	+	9.90613i	0.264746	+	0.579713i
$293$	−8.61054	+	5.53366i	−0.503033	+	0.323280i	−0.767428	−	0.641135i	$-0.778464\pi$
$293$	−8.61054	+	5.53366i	−0.503033	+	0.323280i	0.264395	+	0.964414i	$0.414828\pi$
$294$	−2.61964	+	18.2200i	−0.152780	+	1.06261i
$295$	9.81246	+	6.30609i	0.571304	+	0.367155i
$296$	−0.0408765	+	0.0471740i	−0.00237590	+	0.00274194i
$297$	−48.7656	−	14.3189i	−2.82967	−	0.830865i
$298$	−4.70238			−0.272402
$299$	−23.6238	+	15.0526i	−1.36620	+	0.870515i
$300$	−3.06629			−0.177032
$301$	−7.51021	−	2.20520i	−0.432881	−	0.127105i
$302$	−8.20778	+	9.47229i	−0.472305	+	0.545069i
$303$	−44.8100	−	28.7976i	−2.57427	−	1.65438i
$304$	0.980217	−	6.81756i	0.0562193	−	0.391014i
$305$	−0.364292	+	0.234117i	−0.0208593	+	0.0134055i
$306$	−10.9654	−	24.0109i	−0.626852	−	1.37261i
$307$	14.6204	+	16.8728i	0.834428	+	0.962981i	0.999729	−	0.0232619i	$-0.00740515\pi$
$307$	14.6204	+	16.8728i	0.834428	+	0.962981i	−0.165301	+	0.986243i	$0.552860\pi$
$308$	0.692274	+	4.81487i	0.0394460	+	0.274353i
$309$	−10.8929	+	23.8522i	−0.619677	+	1.35690i
$310$	−1.60748	+	0.471997i	−0.0912985	+	0.0268077i
$311$	21.3436	−	6.26704i	1.21028	−	0.355371i	0.386507	−	0.922286i	$-0.373681\pi$
$311$	21.3436	−	6.26704i	1.21028	−	0.355371i	0.823776	+	0.566915i	$0.191863\pi$
$312$	7.43999	−	16.2913i	0.421207	−	0.922314i
$313$	−2.79875	−	19.4657i	−0.158195	−	1.10027i	−0.901958	−	0.431824i	$-0.857870\pi$
$313$	−2.79875	−	19.4657i	−0.158195	−	1.10027i	0.743763	−	0.668443i	$-0.233039\pi$
$314$	9.47523	+	10.9350i	0.534718	+	0.617098i
$315$	−2.65535	−	5.81440i	−0.149612	−	0.327604i
$316$	−13.0470	+	8.38479i	−0.733950	+	0.471681i
$317$	−1.23214	+	8.56970i	−0.0692037	+	0.481322i	0.925517	+	0.378705i	$0.123631\pi$
$317$	−1.23214	+	8.56970i	−0.0692037	+	0.481322i	−0.994721	+	0.102617i	$0.967278\pi$
$318$	8.89716	+	5.71786i	0.498928	+	0.320641i
$319$	11.5625	−	13.3438i	0.647374	−	0.747110i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	−22.7872			−1.27186
$322$	2.00605	−	4.34782i	0.111793	−	0.242294i
$323$	28.3983			1.58012
$324$	−12.2629	−	3.60072i	−0.681274	−	0.200040i
$325$	3.82496	−	4.41424i	0.212171	−	0.244858i
$326$	−1.60147	−	1.02920i	−0.0886973	−	0.0570023i
$327$	−1.46501	+	10.1894i	−0.0810152	+	0.563473i
$328$	2.42304	−	1.55719i	0.133790	−	0.0859815i
$329$	2.20073	+	4.81893i	0.121330	+	0.265676i
$330$	9.78302	+	11.2902i	0.538537	+	0.621505i
$331$	2.74871	+	19.1177i	0.151083	+	1.05081i	0.914409	+	0.404792i	$0.132656\pi$
$331$	2.74871	+	19.1177i	0.151083	+	1.05081i	−0.763326	+	0.646014i	$0.776435\pi$
$332$	2.71301	−	5.94065i	0.148896	−	0.326036i
$333$	−0.383433	+	0.112586i	−0.0210120	+	0.00616968i
$334$	12.5701	−	3.69093i	0.687808	−	0.201959i
$335$	2.10698	−	4.61364i	0.115117	−	0.252070i
$336$	0.435692	+	3.03030i	0.0237689	+	0.165317i
$337$	−5.38066	−	6.20962i	−0.293103	−	0.338259i	0.590030	−	0.807381i	$-0.299116\pi$
$337$	−5.38066	−	6.20962i	−0.293103	−	0.338259i	−0.883133	+	0.469122i	$0.844570\pi$
$338$	8.77182	+	19.2076i	0.477124	+	1.04476i
$339$	−25.5175	+	16.3991i	−1.38592	+	0.890676i
$340$	−0.586774	+	4.08110i	−0.0318223	+	0.221329i
$341$	6.86659	+	4.41289i	0.371846	+	0.238971i
$342$	28.8764	−	33.3252i	1.56146	−	1.80202i
$343$	12.4568	+	3.65765i	0.672604	+	0.197494i
$344$	7.83960			0.422683
$345$	−2.03619	−	14.5637i	−0.109625	−	0.784085i
$346$	2.74724			0.147693
$347$	−18.5619	−	5.45028i	−0.996457	−	0.292586i	−0.257456	−	0.966290i	$-0.582884\pi$
$347$	−18.5619	−	5.45028i	−0.996457	−	0.292586i	−0.739002	+	0.673704i	$0.764702\pi$
$348$	7.27700	−	8.39810i	0.390088	−	0.450185i
$349$	22.7619	+	14.6282i	1.21842	+	0.783028i	0.982047	−	0.188636i	$-0.0604065\pi$
$349$	22.7619	+	14.6282i	1.21842	+	0.783028i	0.236368	+	0.971664i	$0.424043\pi$
$350$	−0.142091	+	0.988265i	−0.00759509	+	0.0528250i
$351$	51.2584	−	32.9418i	2.73597	−	1.75830i
$352$	−2.02392	−	4.43177i	−0.107875	−	0.236214i
$353$	−21.6452	−	24.9799i	−1.15206	−	1.32955i	−0.935521	−	0.353272i	$-0.885069\pi$
$353$	−21.6452	−	24.9799i	−1.15206	−	1.32955i	−0.216538	−	0.976274i	$-0.569477\pi$
$354$	−5.08995	−	35.4014i	−0.270528	−	1.88156i
$355$	3.32798	−	7.28727i	0.176631	−	0.386768i
$356$	6.28085	−	1.84422i	0.332884	−	0.0977436i
$357$	−12.1113	+	3.55621i	−0.640999	+	0.188214i
$358$	1.94673	−	4.26274i	0.102888	−	0.225293i
$359$	2.18894	+	15.2244i	0.115528	+	0.803514i	0.962384	+	0.271692i	$0.0875833\pi$
$359$	2.18894	+	15.2244i	0.115528	+	0.803514i	−0.846856	+	0.531822i	$0.821508\pi$
$360$	4.19249	+	4.83839i	0.220963	+	0.255005i
$361$	11.8144	+	25.8698i	0.621808	+	1.36157i
$362$	17.9646	−	11.5452i	0.944200	−	0.606801i
$363$	5.55807	−	38.6572i	0.291723	−	2.02898i
$364$	−4.90593	−	3.15285i	−0.257140	−	0.165254i
$365$	7.13161	−	8.23031i	0.373285	−	0.430794i
$366$	1.27402	+	0.374087i	0.0665943	+	0.0195538i
$367$	−27.1360			−1.41649			−0.708244	−	0.705968i	$-0.750512\pi$
$367$	−27.1360			−1.41649			−0.708244	+	0.705968i	$0.750512\pi$
$368$	−0.700968	+	4.74433i	−0.0365405	+	0.247315i
$369$	18.4398			0.959937
$370$	0.0598918	+	0.0175858i	0.00311362	+	0.000914242i
$371$	2.25516	−	2.60259i	0.117082	−	0.135120i
$372$	4.32157	+	2.77731i	0.224063	+	0.143997i
$373$	2.18747	−	15.2142i	0.113263	−	0.787762i	−0.851446	−	0.524443i	$-0.824274\pi$
$373$	2.18747	−	15.2142i	0.113263	−	0.787762i	0.964709	−	0.263319i	$-0.0848172\pi$
$374$	16.8989	−	10.8603i	0.873823	−	0.561572i
$375$	1.27378	+	2.78919i	0.0657778	+	0.144033i
$376$	−3.47470	−	4.01002i	−0.179194	−	0.206801i
$377$	3.01244	+	20.9520i	0.155149	+	1.07908i
$378$	−4.32672	+	9.47420i	−0.222543	+	0.487300i
$379$	23.9783	−	7.04066i	1.23168	−	0.361654i	0.399797	−	0.916604i	$-0.369081\pi$
$379$	23.9783	−	7.04066i	1.23168	−	0.361654i	0.831884	+	0.554949i	$0.187262\pi$
$380$	−6.60866	+	1.94048i	−0.339017	+	0.0995445i
$381$	−12.5880	+	27.5639i	−0.644903	+	1.41214i
$382$	−1.31347	−	9.13536i	−0.0672028	−	0.467406i
$383$	11.0561	+	12.7594i	0.564942	+	0.651977i	0.964298	−	0.264818i	$-0.0853120\pi$
$383$	11.0561	+	12.7594i	0.564942	+	0.651977i	−0.399357	+	0.916796i	$0.630767\pi$
$384$	−1.27378	−	2.78919i	−0.0650024	−	0.142335i
$385$	4.09218	−	2.62988i	0.208557	−	0.134031i
$386$	−1.20552	+	8.38457i	−0.0613593	+	0.426764i
$387$	42.2225	+	27.1347i	2.14629	+	1.37934i
$388$	0.645187	−	0.744585i	0.0327544	−	0.0378006i
$389$	−9.88387	−	2.90217i	−0.501132	−	0.147146i	0.0213904	−	0.999771i	$-0.493191\pi$
$389$	−9.88387	−	2.90217i	−0.501132	−	0.147146i	−0.522522	+	0.852626i	$0.675009\pi$
$390$	−17.9098			−0.906897
$391$	−19.7734	−	0.0768729i	−0.999984	−	0.00388763i
$392$	−6.00314			−0.303204
$393$	−58.6080	−	17.2088i	−2.95638	−	0.868072i
$394$	−11.7795	+	13.5943i	−0.593443	+	0.684869i
$395$	13.0470	+	8.38479i	0.656465	+	0.421885i
$396$	4.43899	−	30.8739i	0.223068	−	1.55147i
$397$	−5.45002	+	3.50252i	−0.273529	+	0.175786i	−0.670213	−	0.742169i	$-0.733797\pi$
$397$	−5.45002	+	3.50252i	−0.273529	+	0.175786i	0.396684	+	0.917955i	$0.370161\pi$
$398$	0.341943	+	0.748750i	0.0171400	+	0.0375315i
$399$	−13.8086	−	15.9360i	−0.691295	−	0.797797i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	2.31407	−	5.06711i	0.115559	−	0.253039i	−0.843011	−	0.537897i	$-0.819219\pi$
$401$	2.31407	−	5.06711i	0.115559	−	0.253039i	0.958570	+	0.284858i	$0.0919463\pi$
$402$	−14.9222	+	4.38155i	−0.744251	+	0.218532i
$403$	−9.38906	+	2.75688i	−0.467702	+	0.137330i
$404$	7.21635	−	15.8016i	0.359027	−	0.786159i
$405$	1.81887	+	12.6505i	0.0903806	+	0.628611i
$406$	−2.36950	−	2.73454i	−0.117596	−	0.135713i
$407$	−0.126334	−	0.276632i	−0.00626212	−	0.0137121i
$408$	10.6356	−	6.83506i	0.526539	−	0.338386i
$409$	2.73141	−	18.9974i	0.135060	−	0.939360i	−0.803761	−	0.594953i	$-0.797171\pi$
$409$	2.73141	−	18.9974i	0.135060	−	0.939360i	0.938820	−	0.344407i	$-0.111920\pi$
$410$	−2.42304	−	1.55719i	−0.119665	−	0.0769042i
$411$	−0.577228	+	0.666157i	−0.0284726	+	0.0328591i
$412$	−8.20525	−	2.40928i	−0.404244	−	0.118697i
$413$	−11.6458			−0.573050
$414$	−20.1965	+	23.1258i	−0.992605	+	1.13657i
$415$	−6.53083			−0.320586
$416$	5.60428	+	1.64556i	0.274772	+	0.0806804i
$417$	−4.71146	+	5.43732i	−0.230721	+	0.266267i
$418$	28.2300	+	18.1423i	1.38077	+	0.887368i
$419$	−4.81801	+	33.5100i	−0.235375	+	1.63707i	0.438862	+	0.898554i	$0.355382\pi$
$419$	−4.81801	+	33.5100i	−0.235375	+	1.63707i	−0.674237	+	0.738515i	$0.735527\pi$
$420$	2.57547	−	1.65515i	0.125670	−	0.0807631i
$421$	−3.18322	−	6.97029i	−0.155141	−	0.339711i	0.816062	−	0.577964i	$-0.196153\pi$
$421$	−3.18322	−	6.97029i	−0.155141	−	0.339711i	−0.971203	+	0.238253i	$0.923425\pi$
$422$	−14.7526	−	17.0255i	−0.718148	−	0.828787i
$423$	−4.83439	−	33.6239i	−0.235056	−	1.63485i
$424$	−1.43283	+	3.13746i	−0.0695843	+	0.152368i
$425$	3.95606	−	1.16160i	0.191897	−	0.0563460i
$426$	−23.5697	+	6.92068i	−1.14195	+	0.335308i
$427$	0.179606	−	0.393283i	0.00869176	−	0.0190323i
$428$	−1.05762	−	7.35589i	−0.0511218	−	0.355560i
$429$	57.1414	+	65.9447i	2.75881	+	3.18384i
$430$	−3.25669	−	7.13115i	−0.157051	−	0.343895i
$431$	15.7903	−	10.1478i	0.760592	−	0.488803i	−0.101949	−	0.994790i	$-0.532508\pi$
$431$	15.7903	−	10.1478i	0.760592	−	0.488803i	0.862541	+	0.505987i	$0.168872\pi$
$432$	1.48460	−	10.3256i	0.0714280	−	0.496793i
$433$	24.9444	+	16.0308i	1.19875	+	0.770391i	0.978740	−	0.205106i	$-0.0657539\pi$
$433$	24.9444	+	16.0308i	1.19875	+	0.770391i	0.220012	+	0.975497i	$0.429390\pi$
$434$	1.09539	−	1.26415i	0.0525803	−	0.0606809i
$435$	−10.6622	−	3.13069i	−0.511211	−	0.150105i
$436$	−3.35720			−0.160781
$437$	−13.6051	−	30.1001i	−0.650820	−	1.43989i
$438$	−33.3927			−1.59556
$439$	18.1651	+	5.33374i	0.866971	+	0.254566i	0.684826	−	0.728706i	$-0.259878\pi$
$439$	18.1651	+	5.33374i	0.866971	+	0.254566i	0.182144	+	0.983272i	$0.441696\pi$
$440$	−3.19051	+	3.68205i	−0.152102	+	0.175535i
$441$	−32.3317	−	20.7783i	−1.53960	−	0.989443i
$442$	−3.42727	+	23.8372i	−0.163019	+	1.13382i
$443$	16.4781	−	10.5898i	0.782896	−	0.503137i	−0.0870975	−	0.996200i	$-0.527759\pi$
$443$	16.4781	−	10.5898i	0.782896	−	0.503137i	0.869994	+	0.493063i	$0.164123\pi$
$444$	−0.0795097	−	0.174102i	−0.00377336	−	0.00826251i
$445$	−4.28672	−	4.94714i	−0.203210	−	0.234517i
$446$	0.726711	+	5.05439i	0.0344108	+	0.239332i
$447$	5.98981	−	13.1158i	0.283308	−	0.620358i
$448$	−0.957984	+	0.281290i	−0.0452605	+	0.0132897i
$449$	−15.5044	+	4.55250i	−0.731698	+	0.214846i	−0.626298	−	0.779584i	$-0.715430\pi$
$449$	−15.5044	+	4.55250i	−0.731698	+	0.214846i	−0.105400	+	0.994430i	$0.533612\pi$
$450$	2.65953	−	5.82356i	0.125371	−	0.274525i
$451$	1.99708	+	13.8900i	0.0940387	+	0.654054i
$452$	−6.47809	−	7.47612i	−0.304704	−	0.351647i
$453$	−15.9651	−	34.9587i	−0.750106	−	1.64250i
$454$	−13.2861	+	8.53846i	−0.623547	+	0.400730i
$455$	−0.829936	+	5.77233i	−0.0389080	+	0.270611i
$456$	17.7669	+	11.4181i	0.832011	+	0.534701i
$457$	23.4060	−	27.0119i	1.09488	−	1.26356i	0.132703	−	0.991156i	$-0.457634\pi$
$457$	23.4060	−	27.0119i	1.09488	−	1.26356i	0.962182	−	0.272409i	$-0.0878202\pi$
$458$	14.6014	+	4.28736i	0.682280	+	0.200335i
$459$	43.0111			2.00759
$460$	4.60678	−	1.33324i	0.214792	−	0.0621627i
$461$	−0.555235			−0.0258599			−0.0129299	−	0.999916i	$-0.504116\pi$
$461$	−0.555235			−0.0258599			−0.0129299	+	0.999916i	$0.504116\pi$
$462$	−14.3114	−	4.20221i	−0.665827	−	0.195504i
$463$	−16.6621	+	19.2291i	−0.774355	+	0.893654i	−0.996688	−	0.0813170i	$-0.974087\pi$
$463$	−16.6621	+	19.2291i	−0.774355	+	0.893654i	0.222333	+	0.974971i	$0.428633\pi$
$464$	3.04872	+	1.95929i	0.141533	+	0.0909579i
$465$	0.731081	−	5.08478i	0.0339031	−	0.235801i
$466$	18.6215	−	11.9673i	0.862622	−	0.554374i
$467$	10.2380	+	22.4181i	0.473759	+	1.03739i	0.984133	+	0.177434i	$0.0567797\pi$
$467$	10.2380	+	22.4181i	0.473759	+	1.03739i	−0.510374	+	0.859953i	$0.670493\pi$
$468$	24.4878	+	28.2604i	1.13195	+	1.30634i
$469$	0.720683	+	5.01246i	0.0332781	+	0.231454i
$470$	−2.20420	+	4.82652i	−0.101672	+	0.222631i
$471$	−42.5692	+	12.4994i	−1.96148	+	0.575944i
$472$	11.1916	−	3.28616i	0.515136	−	0.151258i
$473$	−15.8667	+	34.7433i	−0.729553	+	1.59750i
$474$	−6.76778	−	47.0709i	−0.310854	−	2.16204i
$475$	4.51046	+	5.20535i	0.206954	+	0.238838i
$476$	−1.71009	−	3.74458i	−0.0783819	−	0.171633i
$477$	−18.5764	+	11.9383i	−0.850555	+	0.546618i
$478$	−1.44054	+	10.0192i	−0.0658887	+	0.458266i
$479$	8.68880	+	5.58396i	0.397002	+	0.255137i	0.723876	−	0.689930i	$-0.242359\pi$
$479$	8.68880	+	5.58396i	0.397002	+	0.255137i	−0.326874	+	0.945068i	$0.605995\pi$
$480$	−2.00799	+	2.31734i	−0.0916518	+	0.105772i
$481$	0.349820	+	0.102716i	0.0159504	+	0.00468347i
$482$	−1.74704			−0.0795757
$483$	9.57163	+	11.1334i	0.435524	+	0.506588i
$484$	12.7368			0.578947
$485$	−0.945319	−	0.277571i	−0.0429247	−	0.0126038i
$486$	5.16920	−	5.96558i	0.234480	−	0.270604i
$487$	−4.75108	−	3.05333i	−0.215292	−	0.138360i	0.428551	−	0.903518i	$-0.359024\pi$
$487$	−4.75108	−	3.05333i	−0.215292	−	0.138360i	−0.643842	+	0.765158i	$0.722661\pi$
$488$	−0.0616273	+	0.428628i	−0.00278974	+	0.0194031i
$489$	4.91057	−	3.15583i	0.222063	−	0.142712i
$490$	2.49380	+	5.46065i	0.112658	+	0.246687i
$491$	−5.85756	−	6.75998i	−0.264348	−	0.305074i	0.608022	−	0.793920i	$-0.291963\pi$
$491$	−5.85756	−	6.75998i	−0.264348	−	0.305074i	−0.872370	+	0.488847i	$0.837418\pi$
$492$	1.25689	+	8.74184i	0.0566648	+	0.394112i
$493$	−6.20717	+	13.5918i	−0.279557	+	0.612144i
$494$	−38.6004	+	11.3341i	−1.73671	+	0.509945i
$495$	−29.9279	+	8.78762i	−1.34516	+	0.394974i
$496$	−0.695961	+	1.52394i	−0.0312496	+	0.0684270i
$497$	1.13832	+	7.91721i	0.0510608	+	0.355136i
$498$	13.1138	+	15.1342i	0.587645	+	0.678179i
$499$	−9.61791	−	21.0603i	−0.430557	−	0.942788i	−0.993236	−	0.116112i	$-0.962957\pi$
$499$	−9.61791	−	21.0603i	−0.430557	−	0.942788i	0.562679	−	0.826675i	$-0.309771\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−5.71691	+	39.7620i	−0.255413	+	1.77643i
$502$	18.3376	+	11.7848i	0.818446	+	0.525983i
$503$	−7.30339	+	8.42856i	−0.325642	+	0.375811i	−0.894838	−	0.446391i	$-0.852709\pi$
$503$	−7.30339	+	8.42856i	−0.325642	+	0.375811i	0.569196	+	0.822202i	$0.307255\pi$
$504$	−6.13311	−	1.80084i	−0.273191	−	0.0802160i
$505$	−17.3714			−0.773019
$506$	−19.6071	−	12.7087i	−0.871640	−	0.564969i
$507$	−64.7470			−2.87552
$508$	−9.48208	−	2.78419i	−0.420699	−	0.123528i
$509$	18.6318	−	21.5022i	0.825839	−	0.953069i	−0.173657	−	0.984806i	$-0.555559\pi$
$509$	18.6318	−	21.5022i	0.825839	−	0.953069i	0.999496	+	0.0317372i	$0.0101040\pi$
$510$	−10.6356	−	6.83506i	−0.470950	−	0.302661i
$511$	−1.54741	+	10.7625i	−0.0684533	+	0.476103i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	29.8479	+	65.3579i	1.31782	+	2.88562i
$514$	−2.42687	−	2.80075i	−0.107044	−	0.123536i
$515$	1.21703	+	8.46461i	0.0536286	+	0.372995i
$516$	−9.98593	+	21.8661i	−0.439606	+	0.962603i
$517$	24.8040	−	7.28311i	1.09088	−	0.320311i
$518$	−0.0597976	+	0.0175582i	−0.00262735	+	0.000771461i
$519$	−3.49939	+	7.66259i	−0.153606	+	0.336350i
$520$	−0.831243	−	5.78142i	−0.0364524	−	0.253532i
$521$	−18.2828	−	21.0995i	−0.800984	−	0.924385i	0.197451	−	0.980313i	$-0.436734\pi$
$521$	−18.2828	−	21.0995i	−0.800984	−	0.924385i	−0.998435	+	0.0559282i	$0.982188\pi$
$522$	9.63819	+	21.1047i	0.421852	+	0.923727i
$523$	29.4445	−	18.9228i	1.28752	−	0.827438i	0.295723	−	0.955274i	$-0.404439\pi$
$523$	29.4445	−	18.9228i	1.28752	−	0.827438i	0.991795	+	0.127835i	$0.0408029\pi$
$524$	2.83500	−	19.7178i	0.123847	−	0.861377i
$525$	−2.57547	−	1.65515i	−0.112403	−	0.0722368i
$526$	6.68611	−	7.71618i	0.291528	−	0.336442i
$527$	−6.62774	−	1.94608i	−0.288709	−	0.0847725i
$528$	14.9391			0.650140
$529$	9.39159	+	20.9952i	0.408330	+	0.912834i
$530$	3.44915			0.149821
$531$	71.6499	+	21.0383i	3.10934	+	0.912985i
$532$	4.50337	−	5.19716i	0.195246	−	0.225326i
$533$	−14.1527	−	9.09536i	−0.613020	−	0.393964i
$534$	−2.85653	+	19.8676i	−0.123614	+	0.859756i
$535$	−6.25180	+	4.01779i	−0.270289	+	0.173704i
$536$	−2.10698	−	4.61364i	−0.0910076	−	0.199279i
$537$	9.40989	+	10.8596i	0.406067	+	0.468626i
$538$	−1.16563	−	8.10716i	−0.0502540	−	0.349524i
$539$	12.1499	−	26.6045i	0.523333	−	1.14594i
$540$	−10.0093	+	2.93898i	−0.430730	+	0.126474i
$541$	39.5942	−	11.6259i	1.70229	−	0.499836i	0.721089	−	0.692842i	$-0.243642\pi$
$541$	39.5942	−	11.6259i	1.70229	−	0.499836i	0.981198	+	0.193006i	$0.0618236\pi$
$542$	9.96907	−	21.8292i	0.428208	−	0.937645i
$543$	9.31868	+	64.8128i	0.399903	+	2.78138i
$544$	2.70004	+	3.11601i	0.115763	+	0.133598i
$545$	1.39463	+	3.05382i	0.0597395	+	0.130811i
$546$	15.0430	−	9.66753i	0.643780	−	0.413732i
$547$	2.02857	−	14.1090i	0.0867354	−	0.603258i	−0.899376	−	0.437175i	$-0.855979\pi$
$547$	2.02857	−	14.1090i	0.0867354	−	0.603258i	0.986112	−	0.166083i	$-0.0531119\pi$
$548$	−0.241831	−	0.155416i	−0.0103305	−	0.00663903i
$549$	−1.81549	+	2.09519i	−0.0774834	+	0.0894206i
$550$	4.67469	+	1.37261i	0.199330	+	0.0585285i
$551$	−24.9610			−1.06338
$552$	−12.3400	−	7.99837i	−0.525223	−	0.340433i
$553$	−15.4846			−0.658472
$554$	−21.1442	−	6.20849i	−0.898329	−	0.263773i
$555$	−0.125339	+	0.144649i	−0.00532035	+	0.00614001i
$556$	−1.97388	−	1.26854i	−0.0837112	−	0.0537979i
$557$	−1.33279	+	9.26977i	−0.0564722	+	0.392773i	0.941908	+	0.335872i	$0.109031\pi$
$557$	−1.33279	+	9.26977i	−0.0564722	+	0.392773i	−0.998380	+	0.0569007i	$0.981878\pi$
$558$	−9.02303	+	5.79875i	−0.381975	+	0.245481i
$559$	−19.0219	−	41.6521i	−0.804540	−	1.76170i
$560$	0.653831	+	0.754561i	0.0276294	+	0.0318860i
$561$	8.76587	+	60.9680i	0.370095	+	2.57407i
$562$	−7.92294	+	17.3488i	−0.334209	+	0.731816i
$563$	29.7942	−	8.74838i	1.25568	−	0.368700i	0.414794	−	0.909915i	$-0.363854\pi$
$563$	29.7942	−	8.74838i	1.25568	−	0.368700i	0.840884	+	0.541215i	$0.182036\pi$
$564$	15.6107	−	4.58372i	0.657330	−	0.193009i
$565$	−4.10942	+	8.99837i	−0.172885	+	0.378564i
$566$	2.96262	+	20.6055i	0.124528	+	0.866114i
$567$	−8.35637	−	9.64377i	−0.350935	−	0.405000i
$568$	−3.32798	−	7.28727i	−0.139639	−	0.305767i
$569$	26.0705	−	16.7545i	1.09293	−	0.702386i	0.135424	−	0.990788i	$-0.456760\pi$
$569$	26.0705	−	16.7545i	1.09293	−	0.702386i	0.957509	+	0.288402i	$0.0931240\pi$
$570$	3.00562	−	20.9046i	0.125892	−	0.875596i
$571$	−24.9867	−	16.0580i	−1.04566	−	0.672005i	−0.0992795	−	0.995060i	$-0.531654\pi$
$571$	−24.9867	−	16.0580i	−1.04566	−	0.672005i	−0.946380	+	0.323055i	$0.895290\pi$
$572$	−18.6354	+	21.5064i	−0.779184	+	0.899226i
$573$	27.1533	+	7.97294i	1.13435	+	0.333074i
$574$	2.87574			0.120031
$575$	−3.12649	−	3.63663i	−0.130384	−	0.151658i
$576$	6.40210			0.266754
$577$	14.9900	+	4.40146i	0.624042	+	0.183235i	0.578441	−	0.815725i	$-0.303661\pi$
$577$	14.9900	+	4.40146i	0.624042	+	0.183235i	0.0456012	+	0.998960i	$0.485480\pi$
$578$	0.000187174	0	0.000216010i	7.78540e−6	0	8.98482e-6i
$579$	−21.8506	−	14.0425i	−0.908080	−	0.583588i
$580$	0.515752	−	3.58713i	0.0214154	−	0.148948i
$581$	5.48545	−	3.52528i	0.227575	−	0.146253i
$582$	1.25496	+	2.74799i	0.0520199	+	0.113908i
$583$	−11.0045	−	12.6999i	−0.455762	−	0.525977i
$584$	−1.54985	−	10.7794i	−0.0641331	−	0.446055i
$585$	15.5340	−	34.0147i	0.642251	−	1.40633i
$586$	9.82076	−	2.88364i	0.405692	−	0.119122i
$587$	26.5069	−	7.78313i	1.09406	−	0.321244i	0.315568	−	0.948903i	$-0.397805\pi$
$587$	26.5069	−	7.78313i	1.09406	−	0.321244i	0.778488	+	0.627659i	$0.215987\pi$
$588$	7.64669	−	16.7439i	0.315344	−	0.690507i
$589$	−1.64219	−	11.4217i	−0.0676654	−	0.470623i
$590$	−7.63836	−	8.81514i	−0.314466	−	0.362913i
$591$	−22.9125	−	50.1714i	−0.942495	−	2.06378i
$592$	0.0525112	−	0.0337469i	0.00215820	−	0.00138699i
$593$	−1.29617	+	9.01505i	−0.0532273	+	0.370204i	0.945746	+	0.324906i	$0.105333\pi$
$593$	−1.29617	+	9.01505i	−0.0532273	+	0.370204i	−0.998974	+	0.0452976i	$0.985576\pi$
$594$	42.7561	+	27.4777i	1.75431	+	1.12742i
$595$	−2.69579	+	3.11111i	−0.110517	+	0.127543i
$596$	4.51190	+	1.32481i	0.184815	+	0.0542665i
$597$	−2.52397			−0.103299
$598$	26.9076	−	7.78730i	1.10034	−	0.318446i
$599$	−15.9248			−0.650671			−0.325336	−	0.945599i	$-0.605477\pi$
$599$	−15.9248			−0.650671			−0.325336	+	0.945599i	$0.605477\pi$
$600$	2.94208	+	0.863872i	0.120110	+	0.0352674i
$601$	−20.6446	+	23.8251i	−0.842109	+	0.971846i	−0.999878	−	0.0156300i	$-0.995025\pi$
$601$	−20.6446	+	23.8251i	−0.842109	+	0.971846i	0.157768	+	0.987476i	$0.449570\pi$
$602$	6.58472	+	4.23174i	0.268373	+	0.172473i
$603$	4.62116	−	32.1409i	0.188188	−	1.30888i
$604$	10.5440	−	6.77619i	0.429028	−	0.275719i
$605$	−5.29107	−	11.5858i	−0.215113	−	0.471031i
$606$	34.8817	+	40.2556i	1.41697	+	1.63527i
$607$	−3.87004	−	26.9167i	−0.157080	−	1.09252i	−0.903978	−	0.427578i	$-0.859367\pi$
$607$	−3.87004	−	26.9167i	−0.157080	−	1.09252i	0.746898	−	0.664938i	$-0.231542\pi$
$608$	−2.86124	+	6.26524i	−0.116039	+	0.254089i
$609$	10.6454	−	3.12577i	0.431373	−	0.126662i
$610$	0.415494	−	0.122000i	0.0168229	−	0.00493964i
$611$	−12.8744	+	28.1911i	−0.520844	+	1.14049i
$612$	3.75659	+	26.1277i	0.151851	+	1.05615i
$613$	−9.47056	−	10.9296i	−0.382512	−	0.441443i	0.531544	−	0.847031i	$-0.321612\pi$
$613$	−9.47056	−	10.9296i	−0.382512	−	0.441443i	−0.914056	+	0.405588i	$0.867067\pi$
$614$	−9.27452	−	20.3084i	−0.374289	−	0.819579i
$615$	7.42973	−	4.77480i	0.299595	−	0.192538i
$616$	0.692274	−	4.81487i	0.0278925	−	0.193997i
$617$	−12.3616	−	7.94433i	−0.497660	−	0.319827i	0.267620	−	0.963525i	$-0.413763\pi$
$617$	−12.3616	−	7.94433i	−0.497660	−	0.319827i	−0.765280	+	0.643698i	$0.777399\pi$
$618$	17.1716	−	19.8171i	0.690744	−	0.797161i
$619$	−23.3230	−	6.84824i	−0.937430	−	0.275254i	−0.222885	−	0.974845i	$-0.571548\pi$
$619$	−23.3230	−	6.84824i	−0.937430	−	0.275254i	−0.714544	+	0.699590i	$0.753366\pi$
$620$	1.67534			0.0672832
$621$	−20.6058	−	45.5887i	−0.826884	−	1.82941i
$622$	−22.2447			−0.891929
$623$	6.27097	+	1.84132i	0.251241	+	0.0737711i
$624$	−11.7284	+	13.5353i	−0.469512	+	0.541846i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−2.79875	+	19.4657i	−0.111861	+	0.778007i
$627$	−86.5611	+	55.6294i	−3.45692	+	2.22163i
$628$	−6.01067	−	13.1615i	−0.239852	−	0.525203i
$629$	0.168537	+	0.194502i	0.00672001	+	0.00775530i
$630$	0.909682	+	6.32698i	0.0362426	+	0.252073i
$631$	−1.56387	+	3.42440i	−0.0622566	+	0.136323i	−0.938203	−	0.346086i	$-0.887511\pi$
$631$	−1.56387	+	3.42440i	−0.0622566	+	0.136323i	0.875946	+	0.482409i	$0.160238\pi$
$632$	14.8808	−	4.36939i	0.591925	−	0.173805i
$633$	66.2789	−	19.4612i	2.63435	−	0.773515i
$634$	3.59659	−	7.87543i	0.142839	−	0.312773i
$635$	1.40641	+	9.78180i	0.0558117	+	0.388179i
$636$	−6.92585	−	7.99286i	−0.274628	−	0.316938i
$637$	14.5659	+	31.8950i	0.577124	+	1.26372i
$638$	−14.8535	+	9.54577i	−0.588056	+	0.377921i
$639$	7.29914	−	50.7667i	0.288750	−	2.00830i
$640$	−0.841254	−	0.540641i	−0.0332535	−	0.0213707i
$641$	−4.67238	+	5.39222i	−0.184548	+	0.212980i	−0.840483	−	0.541837i	$-0.817729\pi$
$641$	−4.67238	+	5.39222i	−0.184548	+	0.212980i	0.655935	+	0.754817i	$0.272274\pi$
$642$	21.8642	+	6.41989i	0.862909	+	0.253373i
$643$	8.12944			0.320594			0.160297	−	0.987069i	$-0.448755\pi$
$643$	8.12944			0.320594			0.160297	+	0.987069i	$0.448755\pi$
$644$	−3.14971	+	3.60653i	−0.124116	+	0.142117i
$645$	24.0384			0.946513
$646$	−27.2480	−	8.00073i	−1.07206	−	0.314785i
$647$	3.33009	−	3.84313i	0.130919	−	0.151089i	−0.686505	−	0.727125i	$-0.740856\pi$
$647$	3.33009	−	3.84313i	0.130919	−	0.151089i	0.817424	+	0.576036i	$0.195401\pi$
$648$	10.7518	+	6.90973i	0.422369	+	0.271440i
$649$	−8.08747	+	56.2496i	−0.317461	+	2.20799i
$650$	−4.91365	+	3.15781i	−0.192729	+	0.123860i
$651$	2.13066	+	4.66549i	0.0835071	+	0.182855i
$652$	1.24664	+	1.43870i	0.0488222	+	0.0563438i
$653$	2.80793	+	19.5296i	0.109883	+	0.764251i	0.968028	+	0.250843i	$0.0807079\pi$
$653$	2.80793	+	19.5296i	0.109883	+	0.764251i	−0.858145	+	0.513407i	$0.828383\pi$
$654$	4.27634	−	9.36388i	0.167218	−	0.366157i
$655$	−19.1137	+	5.61228i	−0.746833	+	0.219290i
$656$	−2.76360	+	0.811466i	−0.107900	+	0.0316824i
$657$	28.9630	−	63.4201i	1.12995	−	2.47425i
$658$	−0.753937	−	5.24375i	−0.0293915	−	0.204423i
$659$	8.20440	+	9.46839i	0.319598	+	0.368836i	0.892703	−	0.450646i	$-0.148806\pi$
$659$	8.20440	+	9.46839i	0.319598	+	0.368836i	−0.573104	+	0.819482i	$0.694261\pi$
$660$	−6.20592	−	13.5891i	−0.241565	−	0.528954i
$661$	−30.1067	+	19.3484i	−1.17102	+	0.752566i	−0.973713	−	0.227777i	$-0.926854\pi$
$661$	−30.1067	+	19.3484i	−1.17102	+	0.752566i	−0.197302	+	0.980343i	$0.563218\pi$
$662$	2.74871	−	19.1177i	0.106832	−	0.743032i
$663$	−62.1209	−	39.9227i	−2.41258	−	1.55047i
$664$	−4.27679	+	4.93567i	−0.165971	+	0.191541i
$665$	−6.59827	−	1.93743i	−0.255870	−	0.0751302i
$666$	0.399621			0.0154850
$667$	17.3801	+	0.0675683i	0.672959	+	0.00261626i
$668$	−13.1008			−0.506886
$669$	−15.0233	−	4.41125i	−0.580835	−	0.170549i
$670$	−3.32144	+	3.83315i	−0.128319	+	0.148087i
$671$	−1.77485	−	1.14063i	−0.0685173	−	0.0440334i
$672$	0.435692	−	3.03030i	0.0168072	−	0.116896i
$673$	−9.10217	+	5.84961i	−0.350863	+	0.225486i	−0.704186	−	0.710015i	$-0.748688\pi$
$673$	−9.10217	+	5.84961i	−0.350863	+	0.225486i	0.353323	+	0.935501i	$0.385052\pi$
$674$	3.41326	+	7.47399i	0.131474	+	0.287887i
$675$	6.83139	+	7.88385i	0.262940	+	0.303449i
$676$	−3.00509	−	20.9009i	−0.115580	−	0.803879i
$677$	11.7155	−	25.6533i	0.450262	−	0.985936i	−0.539338	−	0.842089i	$-0.681325\pi$
$677$	11.7155	−	25.6533i	0.450262	−	0.985936i	0.989600	−	0.143847i	$-0.0459472\pi$
$678$	29.1040	−	8.54570i	1.11773	−	0.328196i
$679$	0.943832	−	0.277134i	0.0362210	−	0.0106354i
$680$	1.71279	−	3.75048i	0.0656823	−	0.143824i
$681$	−6.89181	−	47.9336i	−0.264095	−	1.83682i
$682$	−5.34519	−	6.16867i	−0.204678	−	0.236211i
$683$	−2.00474	−	4.38977i	−0.0767092	−	0.167970i	0.867392	−	0.497626i	$-0.165795\pi$
$683$	−2.00474	−	4.38977i	−0.0767092	−	0.167970i	−0.944101	+	0.329656i	$0.893067\pi$
$684$	−37.0955	+	23.8398i	−1.41838	+	0.911539i
$685$	−0.0409106	+	0.284540i	−0.00156311	+	0.0108717i
$686$	−10.9217	−	7.01897i	−0.416994	−	0.267986i
$687$	−30.5573	+	35.2650i	−1.16583	+	1.34544i
$688$	−7.52204	−	2.20867i	−0.286775	−	0.0842048i
$689$	20.1460			0.767503
$690$	−2.14937	+	14.5475i	−0.0818250	+	0.553812i
$691$	−19.3152			−0.734786			−0.367393	−	0.930066i	$-0.619750\pi$
$691$	−19.3152			−0.734786			−0.367393	+	0.930066i	$0.619750\pi$
$692$	−2.63596	−	0.773988i	−0.100204	−	0.0294226i
$693$	20.3939	−	23.5358i	0.774699	−	0.894050i
$694$	16.2745	+	10.4590i	0.617773	+	0.397019i
$695$	−0.333922	+	2.32248i	−0.0126664	+	0.0880965i
$696$	−9.34824	+	6.00775i	−0.354344	+	0.227723i
$697$	−4.93329	−	10.8024i	−0.186862	−	0.409170i
$698$	−17.7186	−	20.4484i	−0.670660	−	0.773983i
$699$	9.65938	+	67.1825i	0.365351	+	2.54107i
$700$	0.414762	−	0.908202i	0.0156765	−	0.0343268i
$701$	17.4831	−	5.13350i	0.660328	−	0.193890i	0.0656361	−	0.997844i	$-0.479092\pi$
$701$	17.4831	−	5.13350i	0.660328	−	0.193890i	0.594692	+	0.803954i	$0.297274\pi$
$702$	−58.4628	+	17.1662i	−2.20654	+	0.647898i
$703$	−0.178599	+	0.391077i	−0.00673599	+	0.0147498i
$704$	0.693364	+	4.82246i	0.0261322	+	0.181753i
$705$	−10.6544	−	12.2959i	−0.401269	−	0.463089i
$706$	13.7308	+	30.0662i	0.516765	+	1.13156i
$707$	14.5908	−	9.37694i	0.548743	−	0.352656i
$708$	−5.08995	+	35.4014i	−0.191292	+	1.33047i
$709$	5.23725	+	3.36578i	0.196689	+	0.126404i	0.635278	−	0.772283i	$-0.280885\pi$
$709$	5.23725	+	3.36578i	0.196689	+	0.126404i	−0.438589	+	0.898688i	$0.644522\pi$
$710$	−5.24624	+	6.05448i	−0.196888	+	0.227221i
$711$	95.2682	+	27.9733i	3.57284	+	1.04908i
$712$	−6.54601			−0.245322
$713$	1.11252	+	7.95725i	0.0416643	+	0.298001i
$714$	12.6226			0.472390
$715$	27.3043	+	8.01726i	1.02112	+	0.299829i
$716$	−3.06882	+	3.54161i	−0.114687	+	0.132356i
$717$	−26.1104	−	16.7802i	−0.975112	−	0.626666i
$718$	2.18894	−	15.2244i	0.0816905	−	0.568170i
$719$	18.6343	−	11.9756i	0.694943	−	0.446613i	−0.144897	−	0.989447i	$-0.546285\pi$
$719$	18.6343	−	11.9756i	0.694943	−	0.446613i	0.839840	+	0.542834i	$0.182649\pi$
$720$	−2.65953	−	5.82356i	−0.0991148	−	0.217031i
$721$	−5.59134	−	6.45274i	−0.208232	−	0.240313i
$722$	−4.04742	−	28.1504i	−0.150629	−	1.04765i
$723$	2.22535	−	4.87284i	0.0827617	−	0.181223i
$724$	−20.4896	+	6.01629i	−0.761490	+	0.223594i
$725$	−3.47722	+	1.02100i	−0.129141	+	0.0379192i
$726$	−16.2239	+	35.5255i	−0.602127	+	1.31847i
$727$	−0.248356	−	1.72735i	−0.00921101	−	0.0640640i	0.984698	−	0.174272i	$-0.0557573\pi$
$727$	−0.248356	−	1.72735i	−0.00921101	−	0.0640640i	−0.993909	+	0.110208i	$0.964848\pi$
$728$	3.81894	+	4.40730i	0.141539	+	0.163345i
$729$	−5.87309	−	12.8603i	−0.217522	−	0.476307i
$730$	−9.16147	+	5.88772i	−0.339081	+	0.217914i
$731$	4.60007	−	31.9942i	0.170140	−	1.18335i
$732$	−1.11702	−	0.717868i	−0.0412864	−	0.0265332i
$733$	18.1912	−	20.9937i	0.671906	−	0.775421i	−0.312767	−	0.949830i	$-0.601256\pi$
$733$	18.1912	−	20.9937i	0.671906	−	0.775421i	0.984673	+	0.174409i	$0.0558014\pi$
$734$	26.0368	+	7.64510i	0.961036	+	0.282186i
$735$	−18.4073			−0.678965
$736$	2.00921	−	4.35466i	0.0740603	−	0.160515i
$737$	24.7109			0.910239
$738$	−17.6929	−	5.19509i	−0.651283	−	0.191234i
$739$	31.4094	−	36.2484i	1.15541	−	1.33342i	0.221817	−	0.975088i	$-0.428801\pi$
$739$	31.4094	−	36.2484i	1.15541	−	1.33342i	0.933595	−	0.358329i	$-0.116653\pi$
$740$	−0.0525112	−	0.0337469i	−0.00193035	−	0.00124056i
$741$	17.5555	−	122.101i	0.644916	−	4.48549i
$742$	−2.89705	+	1.86182i	−0.106354	+	0.0683495i
$743$	11.9335	+	26.1306i	0.437796	+	0.958640i	0.991997	+	0.126258i	$0.0402966\pi$
$743$	11.9335	+	26.1306i	0.437796	+	0.958640i	−0.554201	+	0.832383i	$0.686976\pi$
$744$	−3.36406	−	3.88234i	−0.123333	−	0.142333i
$745$	−0.669219	−	4.65452i	−0.0245183	−	0.170528i
$746$	−6.38520	+	13.9816i	−0.233779	+	0.511904i
$747$	−40.1174	+	11.7795i	−1.46782	+	0.430991i
$748$	−19.2741	+	5.65938i	−0.704731	+	0.206928i
$749$	3.08231	−	6.74933i	0.112625	−	0.246615i
$750$	−0.436378	−	3.03507i	−0.0159343	−	0.110825i
$751$	21.4218	+	24.7221i	0.781694	+	0.902123i	0.997231	−	0.0743727i	$-0.0236955\pi$
$751$	21.4218	+	24.7221i	0.781694	+	0.902123i	−0.215536	+	0.976496i	$0.569150\pi$
$752$	2.20420	+	4.82652i	0.0803788	+	0.176005i
$753$	−56.2282	+	36.1357i	−2.04907	+	1.31686i
$754$	3.01244	−	20.9520i	0.109707	−	0.763026i
$755$	−10.5440	−	6.77619i	−0.383734	−	0.246611i
$756$	6.82065	−	7.87145i	0.248065	−	0.286282i
$757$	−43.4869	−	12.7689i	−1.58056	−	0.464094i	−0.630507	−	0.776184i	$-0.717153\pi$
$757$	−43.4869	−	12.7689i	−1.58056	−	0.464094i	−0.950053	+	0.312089i	$0.898971\pi$
$758$	−24.9906			−0.907698
$759$	60.4220	−	38.4998i	2.19318	−	1.39745i
$760$	6.88766			0.249842
$761$	−22.7009	−	6.66558i	−0.822906	−	0.241627i	−0.156939	−	0.987608i	$-0.550163\pi$
$761$	−22.7009	−	6.66558i	−0.822906	−	0.241627i	−0.665967	+	0.745981i	$0.731981\pi$
$762$	19.8437	−	22.9009i	0.718863	−	0.829612i
$763$	−2.81982	−	1.81219i	−0.102084	−	0.0656056i
$764$	−1.31347	+	9.13536i	−0.0475196	+	0.330506i
$765$	22.2060	−	14.2709i	0.802860	−	0.515967i
$766$	−7.01352	−	15.3575i	−0.253409	−	0.554888i
$767$	−44.6147	−	51.4881i	−1.61094	−	1.85913i
$768$	0.436378	+	3.03507i	0.0157464	+	0.109519i
$769$	−9.18035	+	20.1022i	−0.331052	+	0.724902i	−0.999828	−	0.0185617i	$-0.994091\pi$
$769$	−9.18035	+	20.1022i	−0.331052	+	0.724902i	0.668776	+	0.743464i	$0.266819\pi$
$770$	−4.66734	+	1.37046i	−0.168199	+	0.0493878i
$771$	10.9031	−	3.20145i	0.392667	−	0.115297i
$772$	3.51890	−	7.70531i	0.126648	−	0.277320i
$773$	1.72178	+	11.9752i	0.0619280	+	0.430719i	0.997073	+	0.0764538i	$0.0243598\pi$
$773$	1.72178	+	11.9752i	0.0619280	+	0.430719i	−0.935145	+	0.354265i	$0.884731\pi$
$774$	−32.8674	−	37.9310i	−1.18139	−	1.36340i
$775$	−0.695961	−	1.52394i	−0.0249996	−	0.0547416i
$776$	−0.828826	+	0.532654i	−0.0297531	+	0.0191212i
$777$	0.0271960	−	0.189152i	0.000975650	−	0.00678579i
$778$	8.66587	+	5.56921i	0.310686	+	0.199666i
$779$	12.9913	−	14.9928i	0.465463	−	0.537173i
$780$	17.1843	+	5.04577i	0.615297	+	0.180667i
$781$	39.0311			1.39664
$782$	18.9508	+	5.64457i	0.677679	+	0.201849i
$783$	−37.8051			−1.35105
$784$	5.75997	+	1.69128i	0.205713	+	0.0604029i
$785$	−9.47523	+	10.9350i	−0.338186	+	0.390287i
$786$	51.3856	+	33.0235i	1.83286	+	1.17791i
$787$	−1.78710	+	12.4296i	−0.0637034	+	0.443067i	0.932860	+	0.360238i	$0.117305\pi$
$787$	−1.78710	+	12.4296i	−0.0637034	+	0.443067i	−0.996564	+	0.0828288i	$0.973605\pi$
$788$	15.1323	−	9.72494i	0.539066	−	0.346437i
$789$	13.0053	+	28.4776i	0.463000	+	1.01383i
$790$	−10.1562	−	11.7209i	−0.361342	−	0.417011i
$791$	−1.40561	−	9.77623i	−0.0499777	−	0.347603i
$792$	−12.9574	+	28.3726i	−0.460420	+	1.00818i
$793$	2.42685	−	0.712587i	0.0861799	−	0.0253047i
$794$	6.21603	−	1.82519i	0.220599	−	0.0647736i
$795$	−4.39346	+	9.62033i	−0.155820	+	0.341198i
$796$	−0.117144	−	0.814757i	−0.00415207	−	0.0288783i
$797$	−30.4582	−	35.1507i	−1.07889	−	1.24510i	−0.967915	−	0.251277i	$-0.919150\pi$
$797$	−30.4582	−	35.1507i	−1.07889	−	1.24510i	−0.110970	−	0.993824i	$-0.535396\pi$
$798$	8.75958	+	19.1808i	0.310086	+	0.678993i
$799$	−18.4042	+	11.8276i	−0.651093	+	0.418432i
$800$	−0.142315	+	0.989821i	−0.00503159	+	0.0349955i
$801$	−35.2554	−	22.6573i	−1.24569	−	0.800556i
$802$	−3.64790	+	4.20990i	−0.128812	+	0.148657i
$803$	50.9087	+	14.9481i	1.79653	+	0.527508i
$804$	15.5521			0.548482
$805$	4.58905	+	1.36687i	0.161743	+	0.0481758i
$806$	9.78544			0.344677
$807$	24.0972	+	7.07557i	0.848261	+	0.249072i
$808$	−11.3759	+	13.1285i	−0.400202	+	0.461857i
$809$	45.4478	+	29.2075i	1.59786	+	1.02688i	0.968254	+	0.249968i	$0.0804202\pi$
$809$	45.4478	+	29.2075i	1.59786	+	1.02688i	0.629606	+	0.776914i	$0.283216\pi$
$810$	1.81887	−	12.6505i	0.0639087	−	0.444495i
$811$	−20.0396	+	12.8787i	−0.703687	+	0.452232i	−0.842928	−	0.538026i	$-0.819170\pi$
$811$	−20.0396	+	12.8787i	−0.703687	+	0.452232i	0.139241	+	0.990259i	$0.455534\pi$
$812$	1.50310	+	3.29134i	0.0527486	+	0.115503i
$813$	48.1874	+	55.6113i	1.69001	+	1.95037i
$814$	0.0432800	+	0.301019i	0.00151696	+	0.0105507i
$815$	0.790814	−	1.73164i	0.0277010	−	0.0606567i
$816$	−12.1304	+	3.56181i	−0.424649	+	0.124688i
$817$	51.8093	−	15.2126i	1.81258	−	0.532221i
$818$	−7.97295	+	17.4583i	−0.278768	+	0.610416i
$819$	5.31334	+	36.9551i	0.185663	+	1.29131i
$820$	1.88618	+	2.17676i	0.0658681	+	0.0760159i
$821$	−2.91277	−	6.37808i	−0.101656	−	0.222597i	0.851969	−	0.523592i	$-0.175408\pi$
$821$	−2.91277	−	6.37808i	−0.101656	−	0.222597i	−0.953626	+	0.300995i	$0.902681\pi$
$822$	0.741524	−	0.476549i	0.0258636	−	0.0166215i
$823$	−1.05854	+	7.36228i	−0.0368982	+	0.256633i	−0.999918	−	0.0127975i	$-0.995926\pi$
$823$	−1.05854	+	7.36228i	−0.0368982	+	0.256633i	0.963020	+	0.269430i	$0.0868354\pi$
$824$	7.19411	+	4.62337i	0.250619	+	0.161063i
$825$	−9.78302	+	11.2902i	−0.340601	+	0.393074i
$826$	11.1740	+	3.28099i	0.388794	+	0.114160i
$827$	46.8003			1.62741			0.813703	−	0.581280i	$-0.197448\pi$
$827$	46.8003			1.62741			0.813703	+	0.581280i	$0.197448\pi$
$828$	25.8937	−	16.4990i	0.899868	−	0.573379i
$829$	−9.21991			−0.320221			−0.160110	−	0.987099i	$-0.551185\pi$
$829$	−9.21991			−0.320221			−0.160110	+	0.987099i	$0.551185\pi$
$830$	6.26629	+	1.83995i	0.217506	+	0.0638655i
$831$	44.2497	−	51.0669i	1.53500	−	1.77149i
$832$	−4.91365	−	3.15781i	−0.170350	−	0.109478i
$833$	−3.52249	+	24.4994i	−0.122047	+	0.848856i
$834$	6.05248	−	3.88970i	0.209580	−	0.134689i
$835$	5.44228	+	11.9169i	0.188338	+	0.412402i
$836$	−21.9752	−	25.3607i	−0.760027	−	0.877118i
$837$	−2.48721	−	17.2989i	−0.0859707	−	0.597939i
$838$	14.0637	−	30.7952i	0.485822	−	1.06380i
$839$	−12.4215	+	3.64728i	−0.428838	+	0.125918i	−0.489026	−	0.872269i	$-0.662648\pi$
$839$	−12.4215	+	3.64728i	−0.428838	+	0.125918i	0.0601890	+	0.998187i	$0.480830\pi$
$840$	−2.93745	+	0.862514i	−0.101352	+	0.0297596i
$841$	−6.59117	+	14.4327i	−0.227282	+	0.497678i
$842$	1.09052	+	7.58476i	0.0375819	+	0.261388i
$843$	−38.2971	−	44.1972i	−1.31902	−	1.52223i
$844$	9.35844	+	20.4921i	0.322131	+	0.705368i
$845$	−17.7637	+	11.4161i	−0.611091	+	0.392724i
$846$	−4.83439	+	33.6239i	−0.166210	+	1.15601i
$847$	10.6981	+	6.87522i	0.367590	+	0.236235i
$848$	2.25871	−	2.60669i	0.0775645	−	0.0895142i
$849$	−61.2464	−	17.9836i	−2.10197	−	0.617195i
$850$	−4.12307			−0.141420
$851$	0.125415	−	0.271819i	0.00429917	−	0.00931784i
$852$	24.5647			0.841573
$853$	−37.0638	−	10.8829i	−1.26904	−	0.372624i	−0.423190	−	0.906041i	$-0.639090\pi$
$853$	−37.0638	−	10.8829i	−1.26904	−	0.372624i	−0.845853	+	0.533417i	$0.820908\pi$
$854$	−0.283132	+	0.326752i	−0.00968857	+	0.0111812i
$855$	37.0955	+	23.8398i	1.26864	+	0.815306i
$856$	−1.05762	+	7.35589i	−0.0361486	+	0.251419i
$857$	−4.87988	+	3.13611i	−0.166693	+	0.107127i	−0.621328	−	0.783551i	$-0.713406\pi$
$857$	−4.87988	+	3.13611i	−0.166693	+	0.107127i	0.454634	+	0.890678i	$0.349770\pi$
$858$	−36.2480	−	79.3720i	−1.23749	−	2.70972i
$859$	26.2766	+	30.3248i	0.896547	+	1.03467i	0.999202	+	0.0399528i	$0.0127208\pi$
$859$	26.2766	+	30.3248i	0.896547	+	1.03467i	−0.102655	+	0.994717i	$0.532734\pi$
$860$	1.11569	+	7.75980i	0.0380448	+	0.264607i
$861$	−3.66306	+	8.02099i	−0.124837	+	0.273355i
$862$	−18.0096	+	5.28811i	−0.613411	+	0.180114i
$863$	22.5940	−	6.63418i	0.769107	−	0.225830i	0.126438	−	0.991974i	$-0.459645\pi$
$863$	22.5940	−	6.63418i	0.769107	−	0.225830i	0.642669	+	0.766144i	$0.277827\pi$
$864$	−4.33354	+	9.48912i	−0.147430	+	0.322826i
$865$	0.390974	+	2.71928i	0.0132935	+	0.0924584i
$866$	−19.4176	−	22.4091i	−0.659837	−	0.761492i
$867$	0.000364075	0	0.000797212i	1.23646e−5	0	2.70747e-5i
$868$	−1.40717	+	0.904332i	−0.0477624	+	0.0306950i
$869$	−10.7534	+	74.7914i	−0.364783	+	2.53712i
$870$	9.34824	+	6.00775i	0.316935	+	0.203682i
$871$	−19.4001	+	22.3889i	−0.657348	+	0.758620i
$872$	3.22121	+	0.945834i	0.109084	+	0.0320300i
$873$	−6.30753			−0.213478
$874$	4.57381	+	32.7139i	0.154711	+	1.10656i
$875$	−0.998427			−0.0337530
$876$	32.0400	+	9.40780i	1.08253	+	0.317860i
$877$	−11.1407	+	12.8571i	−0.376195	+	0.434152i	−0.912000	−	0.410190i	$-0.865463\pi$
$877$	−11.1407	+	12.8571i	−0.376195	+	0.434152i	0.535806	+	0.844341i	$0.320008\pi$
$878$	−15.9266	−	10.2354i	−0.537495	−	0.345427i
$879$	−4.46649	+	31.0651i	−0.150651	+	1.04780i
$880$	4.09863	−	2.63403i	0.138165	−	0.0887930i
$881$	5.21083	+	11.4101i	0.175557	+	0.384417i	0.976872	−	0.213827i	$-0.0685928\pi$
$881$	5.21083	+	11.4101i	0.175557	+	0.384417i	−0.801314	+	0.598244i	$0.795866\pi$
$882$	25.1681	+	29.0455i	0.847454	+	0.978014i
$883$	−2.98299	−	20.7471i	−0.100385	−	0.698196i	−0.976409	−	0.215928i	$-0.930722\pi$
$883$	−2.98299	−	20.7471i	−0.100385	−	0.698196i	0.876024	−	0.482268i	$-0.160187\pi$
$884$	10.0042	−	21.9061i	0.336476	−	0.736781i
$885$	34.3167	−	10.0763i	1.15354	−	0.338711i
$886$	−18.7941	+	5.51844i	−0.631399	+	0.185396i
$887$	−22.2864	+	48.8004i	−0.748303	+	1.63856i	0.0210873	+	0.999778i	$0.493287\pi$
$887$	−22.2864	+	48.8004i	−0.748303	+	1.63856i	−0.769391	+	0.638778i	$0.779440\pi$
$888$	0.0272388	+	0.189450i	0.000914074	+	0.00635753i
$889$	−6.46141	−	7.45687i	−0.216709	−	0.250095i
$890$	2.71931	+	5.95446i	0.0911515	+	0.199594i
$891$	−52.3830	+	33.6645i	−1.75490	+	1.12780i
$892$	0.726711	−	5.05439i	0.0243321	−	0.169233i
$893$	−30.7445	−	19.7583i	−1.02882	−	0.661186i
$894$	−9.44234	+	10.8970i	−0.315799	+	0.364452i
$895$	4.49640	+	1.32026i	0.150298	+	0.0441315i
$896$	0.998427			0.0333551
$897$	−12.5542	+	84.9699i	−0.419172	+	2.83706i
$898$	16.1589			0.539231
$899$	5.82552	+	1.71053i	0.194292	+	0.0570493i
$900$	−4.19249	+	4.83839i	−0.139750	+	0.161280i
$901$	11.9635	+	7.68850i	0.398563	+	0.256141i
$902$	1.99708	−	13.8900i	0.0664954	−	0.462486i
$903$	−20.1906	+	12.9757i	−0.671902	+	0.431805i
$904$	4.10942	+	8.99837i	0.136677	+	0.299281i
$905$	13.9843	+	16.1387i	0.464854	+	0.536470i
$906$	5.46940	+	38.0405i	0.181709	+	1.26381i
$907$	−1.42514	+	3.12063i	−0.0473211	+	0.103619i	−0.931816	−	0.362931i	$-0.881776\pi$
$907$	−1.42514	+	3.12063i	−0.0473211	+	0.103619i	0.884495	+	0.466550i	$0.154503\pi$
$908$	15.1535	−	4.44946i	0.502886	−	0.147661i
$909$	−106.709	+	31.3325i	−3.53931	+	1.03923i
$910$	2.42257	−	5.30469i	0.0803074	−	0.175849i
$911$	3.86889	+	26.9087i	0.128182	+	0.891525i	0.947857	+	0.318696i	$0.103245\pi$
$911$	3.86889	+	26.9087i	0.128182	+	0.891525i	−0.819675	+	0.572829i	$0.805846\pi$
$912$	−13.8304	−	15.9611i	−0.457969	−	0.528524i
$913$	−13.2179	−	28.9431i	−0.437448	−	0.957878i
$914$	−30.0680	+	19.3235i	−0.994561	+	0.639165i
$915$	−0.188967	+	1.31429i	−0.00624706	+	0.0434492i
$916$	−12.8021	−	8.22739i	−0.422992	−	0.271841i
$917$	13.0247	−	15.0313i	0.430113	−	0.496377i
$918$	−41.2689	−	12.1176i	−1.36208	−	0.399942i
$919$	−19.0098			−0.627075			−0.313537	−	0.949576i	$-0.601514\pi$
$919$	−19.0098			−0.627075			−0.313537	+	0.949576i	$0.601514\pi$
$920$	−4.79580	−	0.0186446i	−0.158113	−	0.000614693i
$921$	68.4576			2.25575
$922$	0.532744	+	0.156428i	0.0175450	+	0.00515168i
$923$	−30.6426	+	35.3635i	−1.00861	+	1.16400i
$924$	12.5478	+	8.06398i	0.412792	+	0.265285i
$925$	−0.00888332	+	0.0617849i	−0.000292082	+	0.00203147i
$926$	21.4047	−	13.7560i	0.703402	−	0.452049i
$927$	22.7434	+	49.8011i	0.746991	+	1.63568i
$928$	−2.37323	−	2.73885i	−0.0779050	−	0.0899072i
$929$	−5.02141	−	34.9246i	−0.164747	−	1.14584i	−0.889534	−	0.456868i	$-0.848971\pi$
$929$	−5.02141	−	34.9246i	−0.164747	−	1.14584i	0.724788	−	0.688972i	$-0.241938\pi$
$930$	−2.13401	+	4.67284i	−0.0699771	+	0.153228i
$931$	−39.6727	+	11.6490i	−1.30022	+	0.381780i
$932$	−21.2387	+	6.23625i	−0.695698	+	0.204275i
$933$	28.3348	−	62.0446i	0.927640	−	2.03125i
$934$	−3.50739	−	24.3944i	−0.114765	−	0.798209i
$935$	13.1547	+	15.1813i	0.430205	+	0.496483i
$936$	−15.5340	−	34.0147i	−0.507744	−	1.11180i
$937$	−10.7450	+	6.90539i	−0.351024	+	0.225589i	−0.704256	−	0.709946i	$-0.748719\pi$
$937$	−10.7450	+	6.90539i	−0.351024	+	0.225589i	0.353232	+	0.935536i	$0.385083\pi$
$938$	0.720683	−	5.01246i	0.0235311	−	0.163663i
$939$	−50.7286	−	32.6013i	−1.65547	−	1.06390i
$940$	3.47470	−	4.01002i	0.113332	−	0.130792i
$941$	44.9982	+	13.2126i	1.46690	+	0.430720i	0.915089	−	0.403251i	$-0.132120\pi$
$941$	44.9982	+	13.2126i	1.46690	+	0.430720i	0.551808	+	0.833971i	$0.313938\pi$
$942$	44.3663			1.44553
$943$	−9.08630	+	10.4041i	−0.295891	+	0.338806i
$944$	−11.6641			−0.379634
$945$	−9.99352	−	2.93436i	−0.325089	−	0.0954548i
$946$	25.0123	−	28.8658i	0.813221	−	0.938507i
$947$	31.8527	+	20.4705i	1.03507	+	0.665201i	0.943763	−	0.330622i	$-0.107258\pi$
$947$	31.8527	+	20.4705i	1.03507	+	0.665201i	0.0913095	+	0.995823i	$0.470895\pi$
$948$	−6.76778	+	47.0709i	−0.219807	+	1.52879i
$949$	−53.5110	+	34.3894i	−1.73704	+	1.11633i
$950$	−2.86124	−	6.26524i	−0.0928308	−	0.203271i
$951$	17.3848	+	20.0632i	0.563741	+	0.650592i
$952$	0.585851	+	4.07469i	0.0189876	+	0.132061i
$953$	6.46417	−	14.1546i	0.209395	−	0.458511i	−0.775571	−	0.631261i	$-0.782538\pi$
$953$	6.46417	−	14.1546i	0.209395	−	0.458511i	0.984966	+	0.172749i	$0.0552651\pi$
$954$	21.1873	−	6.22116i	0.685965	−	0.201418i
$955$	8.85545	−	2.60020i	0.286556	−	0.0841404i
$956$	4.20491	−	9.20747i	0.135997	−	0.297791i
$957$	−7.70486	−	53.5885i	−0.249063	−	1.73227i
$958$	−6.76366	−	7.80568i	−0.218524	−	0.252190i
$959$	−0.119230	−	0.261077i	−0.00385013	−	0.00843061i
$960$	2.57952	−	1.65776i	0.0832538	−	0.0535039i
$961$	4.01232	−	27.9063i	0.129430	−	0.900202i
$962$	−0.306711	−	0.197111i	−0.00988877	−	0.00635513i
$963$	−31.1566	+	35.9566i	−1.00401	+	1.15869i
$964$	1.67628	+	0.492199i	0.0539892	+	0.0158527i
$965$	−8.47079			−0.272685
$966$	−6.04726	−	13.3791i	−0.194568	−	0.430464i
$967$	1.27815			0.0411027			0.0205513	−	0.999789i	$-0.493458\pi$
$967$	1.27815			0.0411027			0.0205513	+	0.999789i	$0.493458\pi$
$968$	−12.2209	−	3.58838i	−0.392795	−	0.115335i
$969$	57.0235	−	65.8087i	1.83186	−	2.11408i
$970$	0.828826	+	0.532654i	0.0266120	+	0.0171025i
$971$	−4.12888	+	28.7170i	−0.132502	+	0.921572i	0.809776	+	0.586740i	$0.199589\pi$
$971$	−4.12888	+	28.7170i	−0.132502	+	0.921572i	−0.942278	+	0.334832i	$0.891320\pi$
$972$	−6.64051	+	4.26760i	−0.212995	+	0.136883i
$973$	−0.973179	−	2.13097i	−0.0311987	−	0.0683156i
$974$	3.69840	+	4.26818i	0.118504	+	0.136761i
$975$	−2.54883	−	17.7275i	−0.0816278	−	0.567734i
$976$	0.179889	−	0.393903i	0.00575812	−	0.0126085i
$977$	31.6858	−	9.30380i	1.01372	−	0.297655i	0.267645	−	0.963518i	$-0.413755\pi$
$977$	31.6858	−	9.30380i	1.01372	−	0.297655i	0.746074	+	0.665863i	$0.231936\pi$
$978$	−5.60075	+	1.64453i	−0.179092	+	0.0525863i
$979$	13.2486	−	29.0104i	0.423427	−	0.927176i
$980$	−0.854336	−	5.94204i	−0.0272908	−	0.189811i
$981$	14.0750	+	16.2435i	0.449381	+	0.518614i
$982$	3.71578	+	8.13642i	0.118575	+	0.259644i
$983$	−41.5696	+	26.7152i	−1.32586	+	0.852082i	−0.995771	−	0.0918667i	$-0.970717\pi$
$983$	−41.5696	+	26.7152i	−1.32586	+	0.852082i	−0.330093	+	0.943948i	$0.607080\pi$
$984$	1.25689	−	8.74184i	0.0400681	−	0.278680i
$985$	−15.1323	−	9.72494i	−0.482155	−	0.309862i
$986$	9.78499	−	11.2925i	0.311618	−	0.359626i
$987$	15.5862	+	4.57651i	0.496113	+	0.145672i
$988$	40.2300			1.27989
$989$	−36.1153	+	10.4521i	−1.14840	+	0.332357i
$990$	31.1913			0.991326
$991$	−15.6548	−	4.59666i	−0.497291	−	0.146018i	0.0234629	−	0.999725i	$-0.492531\pi$
$991$	−15.6548	−	4.59666i	−0.497291	−	0.146018i	−0.520754	+	0.853707i	$0.674349\pi$
$992$	1.09711	−	1.26614i	0.0348334	−	0.0401999i
$993$	49.8217	+	32.0185i	1.58105	+	1.01608i
$994$	1.13832	−	7.91721i	0.0361054	−	0.251119i
$995$	−0.692466	+	0.445021i	−0.0219526	+	0.0141081i
$996$	−8.31885	−	18.2157i	−0.263593	−	0.577188i
$997$	29.3415	+	33.8619i	0.929254	+	1.07242i	0.997204	+	0.0747274i	$0.0238087\pi$
$997$	29.3415	+	33.8619i	0.929254	+	1.07242i	−0.0679502	+	0.997689i	$0.521646\pi$
$998$	3.29495	+	22.9169i	0.104300	+	0.725421i
$999$	−0.270500	+	0.592313i	−0.00855825	+	0.0187400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.41.3	✓	30
23.3	even	11		5290.2.a.bk.1.2		15
23.9	even	11	inner	230.2.g.d.101.3	yes	30
23.20	odd	22		5290.2.a.bl.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.41.3	✓	30	1.1	even	1	trivial
230.2.g.d.101.3	yes	30	23.9	even	11	inner
5290.2.a.bk.1.2		15	23.3	even	11
5290.2.a.bl.1.2		15	23.20	odd	22

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(2.00799 - 2.31734i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-2.57952 + 1.65776i) q^{6} +(0.414762 + 0.908202i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.911115 - 6.33694i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(2.00799 - 2.31734i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-2.57952 + 1.65776i) q^{6} +(0.414762 + 0.908202i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.911115 - 6.33694i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(4.67469 - 1.37261i) q^{11} +(2.94208 - 0.863872i) q^{12} +(-2.42639 + 5.31304i) q^{13} +(-0.142091 - 0.988265i) q^{14} +(-2.00799 - 2.31734i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.46855 + 2.22910i) q^{17} +(-0.911115 + 6.33694i) q^{18} +(-5.79427 - 3.72375i) q^{19} +(0.654861 - 0.755750i) q^{20} +(2.93745 + 0.862514i) q^{21} -4.87205 q^{22} +(4.02440 + 2.60849i) q^{23} -3.06629 q^{24} +(-0.959493 - 0.281733i) q^{25} +(3.82496 - 4.41424i) q^{26} +(-8.77581 - 5.63987i) q^{27} +(-0.142091 + 0.988265i) q^{28} +(3.04872 - 1.95929i) q^{29} +(1.27378 + 2.78919i) q^{30} +(1.09711 + 1.26614i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(6.20592 - 13.5891i) q^{33} +(3.95606 - 1.16160i) q^{34} +(0.957984 - 0.281290i) q^{35} +(2.65953 - 5.82356i) q^{36} +(-0.00888332 - 0.0617849i) q^{37} +(4.51046 + 5.20535i) q^{38} +(7.43999 + 16.2913i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-0.409905 + 2.85095i) q^{41} +(-2.57547 - 1.65515i) q^{42} +(-5.13385 + 5.92477i) q^{43} +(4.67469 + 1.37261i) q^{44} -6.40210 q^{45} +(-3.12649 - 3.63663i) q^{46} +5.30601 q^{47} +(2.94208 + 0.863872i) q^{48} +(3.93122 - 4.53687i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-1.79922 + 12.5138i) q^{51} +(-4.91365 + 3.15781i) q^{52} +(-1.43283 - 3.13746i) q^{53} +(6.83139 + 7.88385i) q^{54} +(-0.693364 - 4.82246i) q^{55} +(0.414762 - 0.908202i) q^{56} +(-20.2640 + 5.95006i) q^{57} +(-3.47722 + 1.02100i) q^{58} +(-4.84544 + 10.6100i) q^{59} +(-0.436378 - 3.03507i) q^{60} +(-0.283578 - 0.327266i) q^{61} +(-0.695961 - 1.52394i) q^{62} +(5.37732 - 3.45580i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(4.91365 + 3.15781i) q^{65} +(-9.78302 + 11.2902i) q^{66} +(4.86653 + 1.42894i) q^{67} -4.12307 q^{68} +(14.1257 - 4.08810i) q^{69} -0.998427 q^{70} +(7.68672 + 2.25702i) q^{71} +(-4.19249 + 4.83839i) q^{72} +(9.16147 + 5.88772i) q^{73} +(-0.00888332 + 0.0617849i) q^{74} +(-2.57952 + 1.65776i) q^{75} +(-2.86124 - 6.26524i) q^{76} +(3.18549 + 3.67626i) q^{77} +(-2.54883 - 17.7275i) q^{78} +(-6.44266 + 14.1075i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-12.2629 + 3.60072i) q^{81} +(1.19651 - 2.61999i) q^{82} +(-0.929434 - 6.46436i) q^{83} +(2.00483 + 2.31370i) q^{84} +(1.71279 + 3.75048i) q^{85} +(6.59509 - 4.23841i) q^{86} +(1.58144 - 10.9992i) q^{87} +(-4.09863 - 2.63403i) q^{88} +(4.28672 - 4.94714i) q^{89} +(6.14277 + 1.80368i) q^{90} -5.83169 q^{91} +(1.97529 + 4.37015i) q^{92} +5.13707 q^{93} +(-5.09108 - 1.49488i) q^{94} +(-4.51046 + 5.20535i) q^{95} +(-2.57952 - 1.65776i) q^{96} +(0.140212 - 0.975199i) q^{97} +(-5.05016 + 3.24554i) q^{98} +(-12.9574 - 28.3726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more