LMFDB - Embedded newform 190.2.i.a.159.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(49,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("190.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.i (of order $6$, degree $2$, 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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 270 x^{16} - 1928 x^{14} + 9835 x^{12} - 29980 x^{10} + 66046 x^{8} - 89920 x^{6} + \cdots + 10000 $ x^20 - 20x^18 + 270x^16 - 1928x^14 + 9835x^12 - 29980x^10 + 66046x^8 - 89920x^6 + 85425x^4 - 34500*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.7
Root			$1.15118 - 0.664633i$ of defining polynomial
Character	$\chi$	$=$	190.159
Dual form			190.2.i.a.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.15118 + 0.664633i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.21845 + 0.280148i) q^{5} +(-0.664633 + 1.15118i) q^{6} -2.32927i q^{7} -1.00000i q^{8} +(-0.616527 + 1.06786i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.15118 + 0.664633i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.21845 + 0.280148i) q^{5} +(-0.664633 + 1.15118i) q^{6} -2.32927i q^{7} -1.00000i q^{8} +(-0.616527 + 1.06786i) q^{9} +(2.06131 - 0.866610i) q^{10} +6.39380 q^{11} +1.32927i q^{12} +(0.743604 + 0.429320i) q^{13} +(-1.16463 - 2.01720i) q^{14} +(-2.74002 + 1.15195i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.06176 + 2.34506i) q^{17} +1.23305i q^{18} +(-3.75178 - 2.21903i) q^{19} +(1.35184 - 1.78116i) q^{20} +(1.54811 + 2.68140i) q^{21} +(5.53719 - 3.19690i) q^{22} +(-3.00565 - 1.73531i) q^{23} +(0.664633 + 1.15118i) q^{24} +(4.84303 + 1.24299i) q^{25} +0.858640 q^{26} -5.62685i q^{27} +(-2.01720 - 1.16463i) q^{28} +(-2.21048 + 3.82866i) q^{29} +(-1.79695 + 2.36763i) q^{30} -8.25244 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-7.36040 + 4.24953i) q^{33} +(-2.34506 + 4.06176i) q^{34} +(0.652538 - 5.16736i) q^{35} +(0.616527 + 1.06786i) q^{36} +9.76821i q^{37} +(-4.35866 - 0.0458469i) q^{38} -1.14136 q^{39} +(0.280148 - 2.21845i) q^{40} +(-1.84506 - 3.19574i) q^{41} +(2.68140 + 1.54811i) q^{42} +(-6.17012 + 3.56232i) q^{43} +(3.19690 - 5.53719i) q^{44} +(-1.66689 + 2.19627i) q^{45} -3.47063 q^{46} +(6.22992 + 3.59684i) q^{47} +(1.15118 + 0.664633i) q^{48} +1.57452 q^{49} +(4.81568 - 1.34506i) q^{50} +(3.11721 - 5.39916i) q^{51} +(0.743604 - 0.429320i) q^{52} +(-5.37446 - 3.10295i) q^{53} +(-2.81343 - 4.87300i) q^{54} +(14.1843 + 1.79121i) q^{55} -2.32927 q^{56} +(5.79381 + 0.0609427i) q^{57} +4.42096i q^{58} +(-3.09395 - 5.35888i) q^{59} +(-0.372391 + 2.94891i) q^{60} +(4.01037 - 6.94616i) q^{61} +(-7.14682 + 4.12622i) q^{62} +(2.48732 + 1.43605i) q^{63} -1.00000 q^{64} +(1.52937 + 1.16074i) q^{65} +(-4.24953 + 7.36040i) q^{66} +(4.24798 + 2.45257i) q^{67} +4.69012i q^{68} +4.61338 q^{69} +(-2.01856 - 4.80133i) q^{70} +(-1.10005 - 1.90535i) q^{71} +(1.06786 + 0.616527i) q^{72} +(4.03323 - 2.32859i) q^{73} +(4.88411 + 8.45952i) q^{74} +(-6.40132 + 1.78794i) q^{75} +(-3.79763 + 2.13962i) q^{76} -14.8928i q^{77} +(-0.988447 + 0.570680i) q^{78} +(5.79153 + 10.0312i) q^{79} +(-0.866610 - 2.06131i) q^{80} +(1.89021 + 3.27394i) q^{81} +(-3.19574 - 1.84506i) q^{82} -6.07809i q^{83} +3.09621 q^{84} +(-9.66777 + 4.06450i) q^{85} +(-3.56232 + 6.17012i) q^{86} -5.87663i q^{87} -6.39380i q^{88} +(5.64947 - 9.78517i) q^{89} +(-0.345437 + 2.73547i) q^{90} +(1.00000 - 1.73205i) q^{91} +(-3.00565 + 1.73531i) q^{92} +(9.50002 - 5.48484i) q^{93} +7.19369 q^{94} +(-7.70149 - 5.97387i) q^{95} +1.32927 q^{96} +(-9.82939 + 5.67500i) q^{97} +(1.36358 - 0.787262i) q^{98} +(-3.94195 + 6.82766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.15118	+	0.664633i	−0.664633	+	0.383726i	−0.794040	−	0.607866i	$-0.792026\pi$
$3$	−1.15118	+	0.664633i	−0.664633	+	0.383726i	0.129407	+	0.991592i	$0.458693\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.21845	+	0.280148i	0.992121	+	0.125286i
$5$	2.21845	+	0.280148i	0.992121	+	0.125286i
$6$	−0.664633	+	1.15118i	−0.271335	+	0.469966i
$7$		−	2.32927i		−	0.880379i	−0.897905	−	0.440190i	$-0.854911\pi$
$7$		−	2.32927i		−	0.880379i	0.897905	−	0.440190i	$-0.145089\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.616527	+	1.06786i	−0.205509	+	0.355952i
$10$	2.06131	−	0.866610i	0.651843	−	0.274046i
$11$	6.39380			1.92780			0.963901	−	0.266260i	$-0.0857880\pi$
$11$	6.39380			1.92780			0.963901	+	0.266260i	$0.0857880\pi$
$12$			1.32927i			0.383726i
$13$	0.743604	+	0.429320i	0.206239	+	0.119072i	0.599562	−	0.800328i	$-0.295341\pi$
$13$	0.743604	+	0.429320i	0.206239	+	0.119072i	−0.393324	+	0.919400i	$0.628675\pi$
$14$	−1.16463	−	2.01720i	−0.311261	−	0.539120i
$15$	−2.74002	+	1.15195i	−0.707471	+	0.297433i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.06176	+	2.34506i	−0.985122	+	0.568760i	−0.903813	−	0.427929i	$-0.859243\pi$
$17$	−4.06176	+	2.34506i	−0.985122	+	0.568760i	−0.0813093	+	0.996689i	$0.525910\pi$
$18$			1.23305i			0.290634i
$19$	−3.75178	−	2.21903i	−0.860718	−	0.509081i
$19$	−3.75178	−	2.21903i	−0.860718	−	0.509081i
$20$	1.35184	−	1.78116i	0.302281	−	0.398279i
$21$	1.54811	+	2.68140i	0.337824	+	0.585129i
$22$	5.53719	−	3.19690i	1.18053	−	0.681581i
$23$	−3.00565	−	1.73531i	−0.626721	−	0.361838i	0.152760	−	0.988263i	$-0.451184\pi$
$23$	−3.00565	−	1.73531i	−0.626721	−	0.361838i	−0.779481	+	0.626426i	$0.784517\pi$
$24$	0.664633	+	1.15118i	0.135668	+	0.234983i
$25$	4.84303	+	1.24299i	0.968607	+	0.248597i
$26$	0.858640			0.168393
$27$		−	5.62685i		−	1.08289i
$28$	−2.01720	−	1.16463i	−0.381216	−	0.220095i
$29$	−2.21048	+	3.82866i	−0.410476	+	0.710965i	−0.994942	−	0.100453i	$-0.967971\pi$
$29$	−2.21048	+	3.82866i	−0.410476	+	0.710965i	0.584466	+	0.811418i	$0.301304\pi$
$30$	−1.79695	+	2.36763i	−0.328077	+	0.432269i
$31$	−8.25244			−1.48218			−0.741091	−	0.671405i	$-0.765691\pi$
$31$	−8.25244			−1.48218			−0.741091	+	0.671405i	$0.765691\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−7.36040	+	4.24953i	−1.28128	+	0.739748i
$34$	−2.34506	+	4.06176i	−0.402174	+	0.696586i
$35$	0.652538	−	5.16736i	0.110299	−	0.873443i
$36$	0.616527	+	1.06786i	0.102754	+	0.177976i
$37$			9.76821i			1.60588i	0.596057	+	0.802942i	$0.296733\pi$
$37$			9.76821i			1.60588i	−0.596057	+	0.802942i	$0.703267\pi$
$38$	−4.35866	−	0.0458469i	−0.707068	−	0.00743735i
$39$	−1.14136			−0.182764
$40$	0.280148	−	2.21845i	0.0442952	−	0.350768i
$41$	−1.84506	−	3.19574i	−0.288150	−	0.499090i	0.685218	−	0.728338i	$-0.259707\pi$
$41$	−1.84506	−	3.19574i	−0.288150	−	0.499090i	−0.973368	+	0.229248i	$0.926373\pi$
$42$	2.68140	+	1.54811i	0.413749	+	0.238878i
$43$	−6.17012	+	3.56232i	−0.940934	+	0.543249i	−0.890253	−	0.455466i	$-0.849473\pi$
$43$	−6.17012	+	3.56232i	−0.940934	+	0.543249i	−0.0506811	+	0.998715i	$0.516139\pi$
$44$	3.19690	−	5.53719i	0.481951	−	0.834763i
$45$	−1.66689	+	2.19627i	−0.248485	+	0.327400i
$46$	−3.47063			−0.511716
$47$	6.22992	+	3.59684i	0.908727	+	0.524654i	0.880021	−	0.474934i	$-0.157528\pi$
$47$	6.22992	+	3.59684i	0.908727	+	0.524654i	0.0287055	+	0.999588i	$0.490862\pi$
$48$	1.15118	+	0.664633i	0.166158	+	0.0959315i
$49$	1.57452			0.224932
$50$	4.81568	−	1.34506i	0.681041	−	0.190220i
$51$	3.11721	−	5.39916i	0.436496	−	0.756033i
$52$	0.743604	−	0.429320i	0.103119	−	0.0595360i
$53$	−5.37446	−	3.10295i	−0.738239	−	0.426222i	0.0831897	−	0.996534i	$-0.473489\pi$
$53$	−5.37446	−	3.10295i	−0.738239	−	0.426222i	−0.821429	+	0.570311i	$0.806823\pi$
$54$	−2.81343	−	4.87300i	−0.382859	−	0.663131i
$55$	14.1843	+	1.79121i	1.91261	+	0.241526i
$56$	−2.32927			−0.311261
$57$	5.79381	+	0.0609427i	0.767409	+	0.00807206i
$58$			4.42096i			0.580500i
$59$	−3.09395	−	5.35888i	−0.402798	−	0.697667i	0.591264	−	0.806478i	$-0.298629\pi$
$59$	−3.09395	−	5.35888i	−0.402798	−	0.697667i	−0.994062	+	0.108811i	$0.965296\pi$
$60$	−0.372391	+	2.94891i	−0.0480754	+	0.380702i
$61$	4.01037	−	6.94616i	0.513475	−	0.889365i	−0.486403	−	0.873735i	$-0.661691\pi$
$61$	4.01037	−	6.94616i	0.513475	−	0.889365i	0.999878	−	0.0156304i	$-0.00497553\pi$
$62$	−7.14682	+	4.12622i	−0.907647	+	0.524030i
$63$	2.48732	+	1.43605i	0.313373	+	0.180926i
$64$	−1.00000			−0.125000
$65$	1.52937	+	1.16074i	0.189696	+	0.143973i
$66$	−4.24953	+	7.36040i	−0.523081	+	0.906002i
$67$	4.24798	+	2.45257i	0.518973	+	0.299629i	0.736515	−	0.676422i	$-0.236470\pi$
$67$	4.24798	+	2.45257i	0.518973	+	0.299629i	−0.217541	+	0.976051i	$0.569804\pi$
$68$			4.69012i			0.568760i
$69$	4.61338			0.555386
$70$	−2.01856	−	4.80133i	−0.241265	−	0.573869i
$71$	−1.10005	−	1.90535i	−0.130552	−	0.226124i	0.793337	−	0.608782i	$-0.208342\pi$
$71$	−1.10005	−	1.90535i	−0.130552	−	0.226124i	−0.923890	+	0.382659i	$0.875008\pi$
$72$	1.06786	+	0.616527i	0.125848	+	0.0726584i
$73$	4.03323	−	2.32859i	0.472054	−	0.272540i	−0.245045	−	0.969512i	$-0.578803\pi$
$73$	4.03323	−	2.32859i	0.472054	−	0.272540i	0.717099	+	0.696971i	$0.245469\pi$
$74$	4.88411	+	8.45952i	0.567766	+	0.983399i
$75$	−6.40132	+	1.78794i	−0.739161	+	0.206454i
$76$	−3.79763	+	2.13962i	−0.435618	+	0.245432i
$77$		−	14.8928i		−	1.69720i
$78$	−0.988447	+	0.570680i	−0.111920	+	0.0646168i
$79$	5.79153	+	10.0312i	0.651598	+	1.12860i	0.982735	+	0.185018i	$0.0592344\pi$
$79$	5.79153	+	10.0312i	0.651598	+	1.12860i	−0.331137	+	0.943583i	$0.607432\pi$
$80$	−0.866610	−	2.06131i	−0.0968899	−	0.230461i
$81$	1.89021	+	3.27394i	0.210023	+	0.363771i
$82$	−3.19574	−	1.84506i	−0.352910	−	0.203753i
$83$		−	6.07809i		−	0.667157i	−0.942722	−	0.333579i	$-0.891744\pi$
$83$		−	6.07809i		−	0.667157i	0.942722	−	0.333579i	$-0.108256\pi$
$84$	3.09621			0.337824
$85$	−9.66777	+	4.06450i	−1.04862	+	0.440857i
$86$	−3.56232	+	6.17012i	−0.384135	+	0.665341i
$87$		−	5.87663i		−	0.630041i
$88$		−	6.39380i		−	0.681581i
$89$	5.64947	−	9.78517i	0.598843	−	1.03723i	−0.394149	−	0.919046i	$-0.628961\pi$
$89$	5.64947	−	9.78517i	0.598843	−	1.03723i	0.992992	−	0.118180i	$-0.0377059\pi$
$90$	−0.345437	+	2.73547i	−0.0364123	+	0.288344i
$91$	1.00000	−	1.73205i	0.104828	−	0.181568i
$92$	−3.00565	+	1.73531i	−0.313361	+	0.180919i
$93$	9.50002	−	5.48484i	0.985106	−	0.568751i
$94$	7.19369			0.741972
$95$	−7.70149	−	5.97387i	−0.790156	−	0.612906i
$96$	1.32927			0.135668
$97$	−9.82939	+	5.67500i	−0.998024	+	0.576209i	−0.907663	−	0.419700i	$-0.862135\pi$
$97$	−9.82939	+	5.67500i	−0.998024	+	0.576209i	−0.0903607	+	0.995909i	$0.528802\pi$
$98$	1.36358	−	0.787262i	0.137742	−	0.0795254i
$99$	−3.94195	+	6.82766i	−0.396181	+	0.686205i
$100$	3.49798	−	3.57270i	0.349798	−	0.357270i
$101$	−1.11042	+	1.92331i	−0.110491	+	0.191377i	−0.915968	−	0.401250i	$-0.868576\pi$
$101$	−1.11042	+	1.92331i	−0.110491	+	0.191377i	0.805477	+	0.592627i	$0.201909\pi$
$102$		−	6.23441i		−	0.617299i
$103$			3.26464i			0.321675i	0.986981	+	0.160837i	$0.0514195\pi$
$103$			3.26464i			0.321675i	−0.986981	+	0.160837i	$0.948581\pi$
$104$	0.429320	−	0.743604i	0.0420983	−	0.0729164i
$105$	2.68321	+	6.38224i	0.261854	+	0.622843i
$106$	−6.20589			−0.602770
$107$		−	10.0000i		−	0.966736i	−0.875417	−	0.483368i	$-0.839413\pi$
$107$		−	10.0000i		−	0.966736i	0.875417	−	0.483368i	$-0.160587\pi$
$108$	−4.87300	−	2.81343i	−0.468904	−	0.270722i
$109$	−1.51717	−	2.62782i	−0.145319	−	0.251699i	0.784173	−	0.620542i	$-0.213087\pi$
$109$	−1.51717	−	2.62782i	−0.145319	−	0.251699i	−0.929492	+	0.368843i	$0.879754\pi$
$110$	13.1796	−	5.54093i	1.25662	−	0.528307i
$111$	−6.49227	−	11.2449i	−0.616219	−	1.06732i
$112$	−2.01720	+	1.16463i	−0.190608	+	0.110047i
$113$			4.97420i			0.467933i	0.972245	+	0.233966i	$0.0751706\pi$
$113$			4.97420i			0.467933i	−0.972245	+	0.233966i	$0.924829\pi$
$114$	5.04806	−	2.84413i	0.472794	−	0.266377i
$115$	−6.18174	−	4.69173i	−0.576450	−	0.437506i
$116$	2.21048	+	3.82866i	0.205238	+	0.355482i
$117$	−0.916904	+	0.529375i	−0.0847678	+	0.0489407i
$118$	−5.35888	−	3.09395i	−0.493325	−	0.284821i
$119$	5.46226	+	9.46092i	0.500725	+	0.867281i
$120$	1.15195	+	2.74002i	0.105159	+	0.250129i
$121$	29.8806			2.71642
$122$		−	8.02074i		−	0.726164i
$123$	4.24798	+	2.45257i	0.383028	+	0.221141i
$124$	−4.12622	+	7.14682i	−0.370545	+	0.641803i
$125$	10.3958	+	4.11427i	0.929829	+	0.367991i
$126$	2.87211			0.255868
$127$	12.3833	+	7.14949i	1.09884	+	0.634415i	0.935916	−	0.352224i	$-0.114574\pi$
$127$	12.3833	+	7.14949i	1.09884	+	0.634415i	0.162923	+	0.986639i	$0.447908\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.73527	−	8.20172i	0.416917	−	0.722121i
$130$	1.90485	+	0.240546i	0.167066	+	0.0210973i
$131$	−1.18947	−	2.06022i	−0.103924	−	0.180002i	0.809374	−	0.587294i	$-0.199807\pi$
$131$	−1.18947	−	2.06022i	−0.103924	−	0.180002i	−0.913298	+	0.407292i	$0.866473\pi$
$132$			8.49905i			0.739748i
$133$	−5.16872	+	8.73890i	−0.448185	+	0.757759i
$134$	4.90515			0.423740
$135$	1.57635	−	12.4829i	0.135671	−	1.07436i
$136$	2.34506	+	4.06176i	0.201087	+	0.348293i
$137$	7.87364	+	4.54585i	0.672690	+	0.388378i	0.797095	−	0.603854i	$-0.206369\pi$
$137$	7.87364	+	4.54585i	0.672690	+	0.388378i	−0.124405	+	0.992232i	$0.539702\pi$
$138$	3.99531	−	2.30669i	0.340103	−	0.196359i
$139$	−10.5329	+	18.2435i	−0.893389	+	1.54739i	−0.0576028	+	0.998340i	$0.518346\pi$
$139$	−10.5329	+	18.2435i	−0.893389	+	1.54739i	−0.835786	+	0.549055i	$0.814988\pi$
$140$	−4.14879	−	3.14879i	−0.350637	−	0.266122i
$141$	−9.56232			−0.805293
$142$	−1.90535	−	1.10005i	−0.159893	−	0.0923145i
$143$	4.75445	+	2.74498i	0.397587	+	0.229547i
$144$	1.23305			0.102754
$145$	−5.97643	+	7.87443i	−0.496315	+	0.653936i
$146$	2.32859	−	4.03323i	0.192715	−	0.333793i
$147$	−1.81256	+	1.04648i	−0.149497	+	0.0863122i
$148$	8.45952	+	4.88411i	0.695368	+	0.401471i
$149$	−3.17889	−	5.50600i	−0.260425	−	0.451069i	0.705930	−	0.708282i	$-0.250529\pi$
$149$	−3.17889	−	5.50600i	−0.260425	−	0.451069i	−0.966355	+	0.257212i	$0.917196\pi$
$150$	−4.64974	+	4.74906i	−0.379649	+	0.387759i
$151$	−3.05559			−0.248660			−0.124330	−	0.992241i	$-0.539678\pi$
$151$	−3.05559			−0.248660			−0.124330	+	0.992241i	$0.539678\pi$
$152$	−2.21903	+	3.75178i	−0.179987	+	0.304310i
$153$		−	5.78317i		−	0.467541i
$154$	−7.44642	−	12.8976i	−0.600050	−	1.03932i
$155$	−18.3076	−	2.31190i	−1.47050	−	0.185696i
$156$	−0.570680	+	0.988447i	−0.0456910	+	0.0791391i
$157$	−7.05180	+	4.07136i	−0.562795	+	0.324930i	−0.754267	−	0.656568i	$-0.772007\pi$
$157$	−7.05180	+	4.07136i	−0.562795	+	0.324930i	0.191472	+	0.981498i	$0.438674\pi$
$158$	10.0312	+	5.79153i	0.798041	+	0.460749i
$159$	8.24928			0.654210
$160$	−1.78116	−	1.35184i	−0.140813	−	0.106872i
$161$	−4.04200	+	7.00096i	−0.318554	+	0.551753i
$162$	3.27394	+	1.89021i	0.257225	+	0.148509i
$163$		−	13.4100i		−	1.05035i	−0.850993	−	0.525177i	$-0.823999\pi$
$163$		−	13.4100i		−	1.05035i	0.850993	−	0.525177i	$-0.176001\pi$
$164$	−3.69012			−0.288150
$165$	−17.5192	+	7.36536i	−1.36386	+	0.573393i
$166$	−3.03905	−	5.26378i	−0.235876	−	0.408549i
$167$	−11.2450	−	6.49232i	−0.870166	−	0.502391i	−0.00276265	−	0.999996i	$-0.500879\pi$
$167$	−11.2450	−	6.49232i	−0.870166	−	0.502391i	−0.867403	+	0.497606i	$0.834213\pi$
$168$	2.68140	−	1.54811i	0.206874	−	0.119439i
$169$	−6.13137	−	10.6198i	−0.471644	−	0.816911i
$170$	−6.34029	+	8.35385i	−0.486278	+	0.640711i
$171$	4.68269	−	2.63827i	0.358094	−	0.201754i
$172$			7.12464i			0.543249i
$173$	1.83216	−	1.05780i	0.139296	−	0.0804228i	−0.428732	−	0.903432i	$-0.641040\pi$
$173$	1.83216	−	1.05780i	0.139296	−	0.0804228i	0.568029	+	0.823009i	$0.307706\pi$
$174$	−2.93831	−	5.08931i	−0.222753	−	0.385819i
$175$	2.89525	−	11.2807i	0.218860	−	0.852742i
$176$	−3.19690	−	5.53719i	−0.240975	−	0.417381i
$177$	7.12338	+	4.11268i	0.535426	+	0.309128i
$178$		−	11.2989i		−	0.846892i
$179$	9.87938			0.738420			0.369210	−	0.929346i	$-0.379628\pi$
$179$	9.87938			0.738420			0.369210	+	0.929346i	$0.379628\pi$
$180$	1.06858	+	2.54170i	0.0796470	+	0.189447i
$181$	−7.53974	+	13.0592i	−0.560425	+	0.970684i	0.437034	+	0.899445i	$0.356029\pi$
$181$	−7.53974	+	13.0592i	−0.560425	+	0.970684i	−0.997459	+	0.0712395i	$0.977305\pi$
$182$		−	2.00000i		−	0.148250i
$183$			10.6617i			0.788135i
$184$	−1.73531	+	3.00565i	−0.127929	+	0.221579i
$185$	−2.73654	+	21.6703i	−0.201195	+	1.59323i
$186$	5.48484	−	9.50002i	0.402168	−	0.696575i
$187$	−25.9701	+	14.9938i	−1.89912	+	1.09646i
$188$	6.22992	−	3.59684i	0.454363	−	0.262327i
$189$	−13.1064			−0.953352
$190$	−9.65662	−	1.32278i	−0.700565	−	0.0959643i
$191$	8.84192			0.639779			0.319889	−	0.947455i	$-0.396354\pi$
$191$	8.84192			0.639779			0.319889	+	0.947455i	$0.396354\pi$
$192$	1.15118	−	0.664633i	0.0830791	−	0.0479657i
$193$	16.1885	−	9.34642i	1.16527	−	0.672770i	0.212710	−	0.977115i	$-0.431771\pi$
$193$	16.1885	−	9.34642i	1.16527	−	0.672770i	0.952562	+	0.304346i	$0.0984378\pi$
$194$	−5.67500	+	9.82939i	−0.407441	+	0.705709i
$195$	−2.53205	−	0.319749i	−0.181324	−	0.0228977i
$196$	0.787262	−	1.36358i	0.0562330	−	0.0973984i
$197$		−	16.3169i		−	1.16253i	−0.813713	−	0.581267i	$-0.802557\pi$
$197$		−	16.3169i		−	1.16253i	0.813713	−	0.581267i	$-0.197443\pi$
$198$			7.88390i			0.560284i
$199$	−1.57452	+	2.72715i	−0.111615	+	0.193323i	−0.916422	−	0.400214i	$-0.868936\pi$
$199$	−1.57452	+	2.72715i	−0.111615	+	0.193323i	0.804807	+	0.593537i	$0.202269\pi$
$200$	1.24299	−	4.84303i	0.0878924	−	0.342454i
$201$	−6.52024			−0.459902
$202$			2.22085i			0.156258i
$203$	8.91797	+	5.14879i	0.625919	+	0.361374i
$204$	−3.11721	−	5.39916i	−0.218248	−	0.378017i
$205$	−3.19789	−	7.60647i	−0.223350	−	0.531259i
$206$	1.63232	+	2.82726i	0.113729	+	0.196985i
$207$	3.70613	−	2.13973i	0.257594	−	0.148722i
$208$		−	0.858640i		−	0.0595360i
$209$	−23.9882	−	14.1881i	−1.65930	−	0.981408i
$210$	5.51485	+	4.18558i	0.380561	+	0.288833i
$211$	3.95415	+	6.84879i	0.272215	+	0.471490i	0.969429	−	0.245373i	$-0.0789104\pi$
$211$	3.95415	+	6.84879i	0.272215	+	0.471490i	−0.697214	+	0.716863i	$0.745577\pi$
$212$	−5.37446	+	3.10295i	−0.369119	+	0.213111i
$213$	2.53272	+	1.46226i	0.173539	+	0.100193i
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$	−14.6861	+	6.17428i	−1.00158	+	0.421082i
$216$	−5.62685			−0.382859
$217$			19.2221i			1.30488i
$218$	−2.62782	−	1.51717i	−0.177978	−	0.102756i
$219$	−3.09531	+	5.36123i	−0.209162	+	0.362279i
$220$	8.64339	−	11.3884i	0.582737	−	0.767804i
$221$	−4.02712			−0.270894
$222$	−11.2449	−	6.49227i	−0.754711	−	0.435733i
$223$	−7.21336	+	4.16463i	−0.483042	+	0.278884i	−0.721683	−	0.692223i	$-0.756631\pi$
$223$	−7.21336	+	4.16463i	−0.483042	+	0.278884i	0.238641	+	0.971108i	$0.423298\pi$
$224$	−1.16463	+	2.01720i	−0.0778153	+	0.134780i
$225$	−4.31319	+	4.40533i	−0.287546	+	0.293689i
$226$	2.48710	+	4.30778i	0.165439	+	0.286549i
$227$		−	11.3680i		−	0.754523i	−0.926107	−	0.377261i	$-0.876866\pi$
$227$		−	11.3680i		−	0.754523i	0.926107	−	0.377261i	$-0.123134\pi$
$228$	2.94968	−	4.98712i	0.195348	−	0.330280i
$229$	2.25560			0.149054			0.0745270	−	0.997219i	$-0.476255\pi$
$229$	2.25560			0.149054			0.0745270	+	0.997219i	$0.476255\pi$
$230$	−7.69941	−	0.972288i	−0.507684	−	0.0641108i
$231$	9.89827	+	17.1443i	0.651259	+	1.12801i
$232$	3.82866	+	2.21048i	0.251364	+	0.145125i
$233$	13.8027	−	7.96900i	0.904246	−	0.522067i	0.0256705	−	0.999670i	$-0.491828\pi$
$233$	13.8027	−	7.96900i	0.904246	−	0.522067i	0.878575	+	0.477604i	$0.158495\pi$
$234$	−0.529375	+	0.916904i	−0.0346063	+	0.0599399i
$235$	12.8131	+	9.72471i	0.835835	+	0.634370i
$236$	−6.18791			−0.402798
$237$	−13.3342	−	7.69848i	−0.866147	−	0.500070i
$238$	9.46092	+	5.46226i	0.613260	+	0.354066i
$239$	−6.63412			−0.429126			−0.214563	−	0.976710i	$-0.568833\pi$
$239$	−6.63412			−0.429126			−0.214563	+	0.976710i	$0.568833\pi$
$240$	2.36763	+	1.79695i	0.152830	+	0.115993i
$241$	11.0397	−	19.1213i	0.711130	−	1.23171i	−0.253304	−	0.967387i	$-0.581517\pi$
$241$	11.0397	−	19.1213i	0.711130	−	1.23171i	0.964433	−	0.264326i	$-0.0851494\pi$
$242$	25.8774	−	14.9403i	1.66346	−	0.960400i
$243$	10.2671	+	5.92769i	0.658632	+	0.380261i
$244$	−4.01037	−	6.94616i	−0.256738	−	0.444683i
$245$	3.49300	+	0.441099i	0.223160	+	0.0281808i
$246$	4.90515			0.312741
$247$	−1.83717	−	3.26080i	−0.116896	−	0.207480i
$248$			8.25244i			0.524030i
$249$	4.03970	+	6.99696i	0.256006	+	0.443415i
$250$	11.0602	−	1.63484i	0.699506	−	0.103397i
$251$	−4.72558	+	8.18494i	−0.298276	+	0.516629i	−0.975742	−	0.218926i	$-0.929745\pi$
$251$	−4.72558	+	8.18494i	−0.298276	+	0.516629i	0.677466	+	0.735554i	$0.263078\pi$
$252$	2.48732	−	1.43605i	0.156686	−	0.0904630i
$253$	−19.2175	−	11.0952i	−1.20819	−	0.697552i
$254$	14.2990			0.897198
$255$	8.42792	−	11.1045i	0.527777	−	0.695390i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.1999	+	13.3945i	1.44717	+	0.835524i	0.998312	−	0.0580783i	$-0.0184973\pi$
$257$	23.1999	+	13.3945i	1.44717	+	0.835524i	0.448859	+	0.893603i	$0.351831\pi$
$258$		−	9.47053i		−	0.589610i
$259$	22.7528			1.41379
$260$	1.76992	−	0.744106i	0.109766	−	0.0461475i
$261$	−2.72564	−	4.72095i	−0.168713	−	0.292219i
$262$	−2.06022	−	1.18947i	−0.127281	−	0.0734854i
$263$	−12.4598	+	7.19364i	−0.768301	+	0.443579i	−0.832268	−	0.554373i	$-0.812958\pi$
$263$	−12.4598	+	7.19364i	−0.768301	+	0.443579i	0.0639670	+	0.997952i	$0.479625\pi$
$264$	4.24953	+	7.36040i	0.261540	+	0.453001i
$265$	−11.0537	−	8.38937i	−0.679022	−	0.515355i
$266$	−0.106790	+	10.1525i	−0.00654769	+	0.622488i
$267$			15.0193i			0.919166i
$268$	4.24798	−	2.45257i	0.259487	−	0.149815i
$269$	6.44486	+	11.1628i	0.392950	+	0.680609i	0.992837	−	0.119475i	$-0.0381212\pi$
$269$	6.44486	+	11.1628i	0.392950	+	0.680609i	−0.599887	+	0.800085i	$0.704788\pi$
$270$	−4.87628	−	11.5987i	−0.296761	−	0.705873i
$271$	−10.0907	−	17.4776i	−0.612966	−	1.06169i	−0.990738	−	0.135790i	$-0.956643\pi$
$271$	−10.0907	−	17.4776i	−0.612966	−	1.06169i	0.377772	−	0.925899i	$-0.376690\pi$
$272$	4.06176	+	2.34506i	0.246280	+	0.142190i
$273$			2.65853i			0.160902i
$274$	9.09169			0.549249
$275$	30.9654	+	7.94741i	1.86728	+	0.479247i
$276$	2.30669	−	3.99531i	0.138846	−	0.240489i
$277$			7.40098i			0.444682i	0.974969	+	0.222341i	$0.0713698\pi$
$277$			7.40098i			0.444682i	−0.974969	+	0.222341i	$0.928630\pi$
$278$			21.0658i			1.26344i
$279$	5.08785	−	8.81242i	0.304602	−	0.527586i
$280$	−5.16736	−	0.652538i	−0.308809	−	0.0389966i
$281$	−1.36083	+	2.35703i	−0.0811805	+	0.140609i	−0.903757	−	0.428045i	$-0.859202\pi$
$281$	−1.36083	+	2.35703i	−0.0811805	+	0.140609i	0.822577	+	0.568654i	$0.192536\pi$
$282$	−8.28121	+	4.78116i	−0.493139	+	0.284714i
$283$	17.7918	−	10.2721i	1.05761	−	0.610613i	0.132842	−	0.991137i	$-0.457590\pi$
$283$	17.7918	−	10.2721i	1.05761	−	0.610613i	0.924771	+	0.380524i	$0.124256\pi$
$284$	−2.20011			−0.130552
$285$	12.8362	+	1.75832i	0.760351	+	0.104154i
$286$	5.48997			0.324629
$287$	−7.44372	+	4.29763i	−0.439389	+	0.253681i
$288$	1.06786	−	0.616527i	0.0629240	−	0.0363292i
$289$	2.49860	−	4.32771i	0.146977	−	0.254571i
$290$	−1.23852	+	9.80767i	−0.0727285	+	0.575926i
$291$	7.54358	−	13.0659i	0.442213	−	0.765935i
$292$		−	4.65717i		−	0.272540i
$293$		−	26.7315i		−	1.56167i	−0.624736	−	0.780836i	$-0.714794\pi$
$293$		−	26.7315i		−	1.56167i	0.624736	−	0.780836i	$-0.285206\pi$
$294$	−1.04648	+	1.81256i	−0.0610319	+	0.105710i
$295$	−5.36250	−	12.7552i	−0.312217	−	0.742635i
$296$	9.76821			0.567766
$297$		−	35.9769i		−	2.08759i
$298$	−5.50600	−	3.17889i	−0.318954	−	0.184148i
$299$	−1.49001	−	2.58077i	−0.0861694	−	0.149250i
$300$	−1.65226	+	6.43768i	−0.0953932	+	0.371679i
$301$	8.29759	+	14.3718i	0.478265	+	0.828379i
$302$	−2.64622	+	1.52779i	−0.152273	+	0.0879147i
$303$		−	2.95210i		−	0.169594i
$304$	−0.0458469	+	4.35866i	−0.00262950	+	0.249986i
$305$	10.8428	−	14.2862i	0.620854	−	0.818026i
$306$	−2.89158	−	5.00837i	−0.165301	−	0.286310i
$307$	−11.0509	+	6.38026i	−0.630710	+	0.364141i	−0.781027	−	0.624497i	$-0.785304\pi$
$307$	−11.0509	+	6.38026i	−0.630710	+	0.364141i	0.150317	+	0.988638i	$0.451971\pi$
$308$	−12.8976	−	7.44642i	−0.734908	−	0.424299i
$309$	−2.16979	−	3.75818i	−0.123435	−	0.213795i
$310$	−17.0108	+	7.15164i	−0.966149	+	0.406186i
$311$	−6.96646			−0.395031			−0.197516	−	0.980300i	$-0.563287\pi$
$311$	−6.96646			−0.395031			−0.197516	+	0.980300i	$0.563287\pi$
$312$			1.14136i			0.0646168i
$313$	22.6632	+	13.0846i	1.28100	+	0.739585i	0.977031	−	0.213097i	$-0.0683551\pi$
$313$	22.6632	+	13.0846i	1.28100	+	0.739585i	0.303968	+	0.952682i	$0.401688\pi$
$314$	−4.07136	+	7.05180i	−0.229760	+	0.397956i
$315$	5.11569	+	3.88263i	0.288236	+	0.218762i
$316$	11.5831			0.651598
$317$	−7.58413	−	4.37870i	−0.425967	−	0.245932i	0.271660	−	0.962393i	$-0.412427\pi$
$317$	−7.58413	−	4.37870i	−0.425967	−	0.245932i	−0.697627	+	0.716461i	$0.745761\pi$
$318$	7.14408	−	4.12464i	0.400620	−	0.231298i
$319$	−14.1334	+	24.4797i	−0.791316	+	1.37060i
$320$	−2.21845	−	0.280148i	−0.124015	−	0.0156607i
$321$	6.64633	+	11.5118i	0.370962	+	0.642525i
$322$			8.08401i			0.450504i
$323$	20.4426	+	0.215028i	1.13746	+	0.0119645i
$324$	3.78042			0.210023
$325$	3.06766	+	3.00350i	0.170163	+	0.166604i
$326$	−6.70501	−	11.6134i	−0.371356	−	0.643208i
$327$	3.49306	+	2.01672i	0.193167	+	0.111525i
$328$	−3.19574	+	1.84506i	−0.176455	+	0.101876i
$329$	8.37800	−	14.5111i	0.461894	−	0.800024i
$330$	−11.4894	+	15.1382i	−0.632468	+	0.833329i
$331$	−9.34738			−0.513779			−0.256889	−	0.966441i	$-0.582698\pi$
$331$	−9.34738			−0.513779			−0.256889	+	0.966441i	$0.582698\pi$
$332$	−5.26378	−	3.03905i	−0.288888	−	0.166789i
$333$	−10.4310	−	6.02237i	−0.571618	−	0.330024i
$334$	−12.9846			−0.710488
$335$	8.73685	+	6.63097i	0.477345	+	0.362289i
$336$	1.54811	−	2.68140i	0.0844561	−	0.146282i
$337$	8.44159	−	4.87376i	0.459843	−	0.265490i	−0.252135	−	0.967692i	$-0.581133\pi$
$337$	8.44159	−	4.87376i	0.459843	−	0.265490i	0.711978	+	0.702202i	$0.247799\pi$
$338$	−10.6198	−	6.13137i	−0.577643	−	0.333502i
$339$	−3.30601	−	5.72618i	−0.179558	−	0.311003i
$340$	−1.31393	+	10.4048i	−0.0712576	+	0.564279i
$341$	−52.7644			−2.85735
$342$	2.73619	−	4.62615i	0.147956	−	0.250154i
$343$		−	19.9723i		−	1.07840i
$344$	3.56232	+	6.17012i	0.192067	+	0.332670i
$345$	10.2346	+	1.29243i	0.551010	+	0.0695820i
$346$	1.05780	−	1.83216i	0.0568675	−	0.0984975i
$347$	12.7853	−	7.38162i	0.686353	−	0.396266i	−0.115891	−	0.993262i	$-0.536972\pi$
$347$	12.7853	−	7.38162i	0.686353	−	0.396266i	0.802244	+	0.596996i	$0.203639\pi$
$348$	−5.08931	−	2.93831i	−0.272816	−	0.157510i
$349$	−14.8315			−0.793913			−0.396956	−	0.917837i	$-0.629934\pi$
$349$	−14.8315			−0.793913			−0.396956	+	0.917837i	$0.629934\pi$
$350$	−3.13300	−	11.2170i	−0.167466	−	0.599574i
$351$	2.41572	−	4.18415i	0.128942	−	0.223333i
$352$	−5.53719	−	3.19690i	−0.295133	−	0.170395i
$353$			26.8115i			1.42703i	0.700639	+	0.713516i	$0.252898\pi$
$353$			26.8115i			1.42703i	−0.700639	+	0.713516i	$0.747102\pi$
$354$	8.22537			0.437173
$355$	−1.90664	−	4.53510i	−0.101194	−	0.240698i
$356$	−5.64947	−	9.78517i	−0.299421	−	0.518613i
$357$	−12.5761	−	7.26080i	−0.665596	−	0.384282i
$358$	8.55579	−	4.93969i	0.452188	−	0.261071i
$359$	0.197846	+	0.342680i	0.0104419	+	0.0180859i	0.871199	−	0.490930i	$-0.163343\pi$
$359$	0.197846	+	0.342680i	0.0104419	+	0.0180859i	−0.860757	+	0.509016i	$0.830010\pi$
$360$	2.19627	+	1.66689i	0.115753	+	0.0878529i
$361$	9.15178	+	16.6507i	0.481673	+	0.876351i
$362$			15.0795i			0.792560i
$363$	−34.3979	+	19.8597i	−1.80542	+	1.04236i
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	9.59987	−	4.03595i	0.502480	−	0.211251i
$366$	5.33085	+	9.23330i	0.278648	+	0.482632i
$367$	6.04879	+	3.49227i	0.315744	+	0.182295i	0.649494	−	0.760367i	$-0.274981\pi$
$367$	6.04879	+	3.49227i	0.315744	+	0.182295i	−0.333750	+	0.942662i	$0.608314\pi$
$368$			3.47063i			0.180919i
$369$	4.55011			0.236870
$370$	8.46523	+	20.1353i	0.440086	+	1.04678i
$371$	−7.22758	+	12.5185i	−0.375237	+	0.649930i
$372$		−	10.9697i		−	0.568751i
$373$			2.52621i			0.130802i	0.997859	+	0.0654012i	$0.0208327\pi$
$373$			2.52621i			0.130802i	−0.997859	+	0.0654012i	$0.979167\pi$
$374$	−14.9938	+	25.9701i	−0.775313	+	1.34288i
$375$	−14.7019	+	2.17314i	−0.759203	+	0.112220i
$376$	3.59684	−	6.22992i	0.185493	−	0.321283i
$377$	−3.28744	+	1.89801i	−0.169312	+	0.0977523i
$378$	−11.3505	+	6.55321i	−0.583807	+	0.337061i
$379$	29.3075			1.50543			0.752713	−	0.658349i	$-0.228745\pi$
$379$	29.3075			1.50543			0.752713	+	0.658349i	$0.228745\pi$
$380$	−9.02426	+	3.68275i	−0.462935	+	0.188921i
$381$	−19.0071			−0.973765
$382$	7.65733	−	4.42096i	0.391783	−	0.226196i
$383$	5.39911	−	3.11717i	0.275881	−	0.159280i	−0.355676	−	0.934609i	$-0.615749\pi$
$383$	5.39911	−	3.11717i	0.275881	−	0.159280i	0.631557	+	0.775329i	$0.282416\pi$
$384$	0.664633	−	1.15118i	0.0339169	−	0.0587458i
$385$	4.17220	−	33.0390i	0.212635	−	1.68383i
$386$	9.34642	−	16.1885i	0.475720	−	0.823971i
$387$		−	8.78506i		−	0.446570i
$388$			11.3500i			0.576209i
$389$	13.2183	−	22.8947i	0.670193	−	1.16081i	−0.307656	−	0.951498i	$-0.599545\pi$
$389$	13.2183	−	22.8947i	0.670193	−	1.16081i	0.977849	−	0.209311i	$-0.0671220\pi$
$390$	−2.35269	+	0.989114i	−0.119133	+	0.0500857i
$391$	16.2776			0.823196
$392$		−	1.57452i		−	0.0795254i
$393$	2.73857	+	1.58112i	0.138143	+	0.0797567i
$394$	−8.15847	−	14.1309i	−0.411018	−	0.711903i
$395$	10.0380	+	23.8762i	0.505066	+	1.20134i
$396$	3.94195	+	6.82766i	0.198090	+	0.343103i
$397$	7.56171	−	4.36575i	0.379511	−	0.219111i	−0.298094	−	0.954536i	$-0.596351\pi$
$397$	7.56171	−	4.36575i	0.379511	−	0.219111i	0.677606	+	0.735426i	$0.263018\pi$
$398$			3.14905i			0.157847i
$399$	0.141952	−	13.4953i	0.00710648	−	0.675611i
$400$	−1.34506	−	4.81568i	−0.0672530	−	0.240784i
$401$	1.58356	+	2.74281i	0.0790794	+	0.136969i	0.902853	−	0.429949i	$-0.141469\pi$
$401$	1.58356	+	2.74281i	0.0790794	+	0.136969i	−0.823774	+	0.566919i	$0.808135\pi$
$402$	−5.64669	+	3.26012i	−0.281631	+	0.162600i
$403$	−6.13654	−	3.54294i	−0.305683	−	0.176486i
$404$	1.11042	+	1.92331i	0.0552457	+	0.0956884i
$405$	3.27614	+	7.79260i	0.162793	+	0.387217i
$406$	10.2976			0.511061
$407$			62.4560i			3.09583i
$408$	−5.39916	−	3.11721i	−0.267298	−	0.154325i
$409$	8.54431	−	14.7992i	0.422489	−	0.731773i	−0.573693	−	0.819070i	$-0.694490\pi$
$409$	8.54431	−	14.7992i	0.422489	−	0.731773i	0.996182	+	0.0872978i	$0.0278232\pi$
$410$	−6.57269	−	4.98845i	−0.324602	−	0.246362i
$411$	−12.0853			−0.596123
$412$	2.82726	+	1.63232i	0.139289	+	0.0804187i
$413$	−12.4823	+	7.20664i	−0.614212	+	0.354615i
$414$	2.13973	−	3.70613i	0.105162	−	0.182146i
$415$	1.70276	−	13.4839i	0.0835854	−	0.661901i
$416$	−0.429320	−	0.743604i	−0.0210491	−	0.0364582i
$417$		−	28.0020i		−	1.37127i
$418$	−27.8684	−	0.293136i	−1.36309	−	0.0143378i
$419$	−7.80296			−0.381200			−0.190600	−	0.981668i	$-0.561043\pi$
$419$	−7.80296			−0.381200			−0.190600	+	0.981668i	$0.561043\pi$
$420$	6.86879	+	0.867396i	0.335163	+	0.0423246i
$421$	−16.9845	−	29.4180i	−0.827773	−	1.43374i	−0.899782	−	0.436340i	$-0.856274\pi$
$421$	−16.9845	−	29.4180i	−0.827773	−	1.43374i	0.0720091	−	0.997404i	$-0.477059\pi$
$422$	6.84879	+	3.95415i	0.333394	+	0.192485i
$423$	−7.68182	+	4.43510i	−0.373503	+	0.215642i
$424$	−3.10295	+	5.37446i	−0.150692	+	0.261007i
$425$	−22.5861	+	6.30849i	−1.09559	+	0.306007i
$426$	2.92453			0.141694
$427$	−16.1795	−	9.34122i	−0.782979	−	0.452053i
$428$	−8.66025	−	5.00000i	−0.418609	−	0.241684i
$429$	−7.29763			−0.352333
$430$	−9.63137	+	12.6901i	−0.464466	+	0.611972i
$431$	−9.07565	+	15.7195i	−0.437158	+	0.757181i	−0.997469	−	0.0711019i	$-0.977348\pi$
$431$	−9.07565	+	15.7195i	−0.437158	+	0.757181i	0.560311	+	0.828283i	$0.310682\pi$
$432$	−4.87300	+	2.81343i	−0.234452	+	0.135361i
$433$	0.272199	+	0.157154i	0.0130810	+	0.00755234i	0.506526	−	0.862225i	$-0.330929\pi$
$433$	0.272199	+	0.157154i	0.0130810	+	0.00755234i	−0.493445	+	0.869777i	$0.664263\pi$
$434$	9.61106	+	16.6468i	0.461346	+	0.799074i
$435$	1.64632	−	13.0370i	0.0789352	−	0.625076i
$436$	−3.03434			−0.145319
$437$	7.42583	+	13.1802i	0.355226	+	0.630492i
$438$			6.19062i			0.295799i
$439$	4.33220	+	7.50359i	0.206765	+	0.358127i	0.950694	−	0.310132i	$-0.100373\pi$
$439$	4.33220	+	7.50359i	0.206765	+	0.358127i	−0.743929	+	0.668259i	$0.767040\pi$
$440$	1.79121	−	14.1843i	0.0853925	−	0.676211i
$441$	−0.970736	+	1.68136i	−0.0462255	+	0.0800650i
$442$	−3.48759	+	2.01356i	−0.165888	+	0.0957753i
$443$	−3.36744	−	1.94419i	−0.159992	−	0.0923714i	0.417866	−	0.908509i	$-0.362778\pi$
$443$	−3.36744	−	1.94419i	−0.159992	−	0.0923714i	−0.577858	+	0.816137i	$0.696111\pi$
$444$	−12.9845			−0.616219
$445$	15.2744	−	20.1252i	0.724074	−	0.954027i
$446$	−4.16463	+	7.21336i	−0.197201	+	0.341562i
$447$	7.31894	+	4.22559i	0.346174	+	0.199864i
$448$			2.32927i			0.110047i
$449$	−32.9375			−1.55442			−0.777208	−	0.629243i	$-0.783365\pi$
$449$	−32.9375			−1.55442			−0.777208	+	0.629243i	$0.783365\pi$
$450$	−1.53267	+	5.97172i	−0.0722508	+	0.281510i
$451$	−11.7969	−	20.4329i	−0.555496	−	0.962147i
$452$	4.30778	+	2.48710i	0.202621	+	0.116983i
$453$	3.51752	−	2.03084i	0.165268	−	0.0954174i
$454$	−5.68402	−	9.84500i	−0.266764	−	0.462049i
$455$	2.70368	−	3.56232i	0.126750	−	0.167004i
$456$	0.0609427	−	5.79381i	0.00285390	−	0.271320i
$457$			1.22533i			0.0573184i	0.999589	+	0.0286592i	$0.00912376\pi$
$457$			1.22533i			0.0573184i	−0.999589	+	0.0286592i	$0.990876\pi$
$458$	1.95341	−	1.12780i	0.0912766	−	0.0526986i
$459$	13.1953	+	22.8549i	0.615904	+	1.06678i
$460$	−7.15403	+	3.00768i	−0.333558	+	0.140234i
$461$	19.5927	+	33.9356i	0.912524	+	1.58054i	0.810486	+	0.585758i	$0.199203\pi$
$461$	19.5927	+	33.9356i	0.912524	+	1.58054i	0.102038	+	0.994781i	$0.467464\pi$
$462$	17.1443	+	9.89827i	0.797626	+	0.460509i
$463$			32.5754i			1.51391i	0.653469	+	0.756953i	$0.273313\pi$
$463$			32.5754i			1.51391i	−0.653469	+	0.756953i	$0.726687\pi$
$464$	4.42096			0.205238
$465$	22.6119	−	9.50643i	1.04860	−	0.440850i
$466$	7.96900	−	13.8027i	0.369157	−	0.639398i
$467$		−	16.9079i		−	0.782406i	−0.920304	−	0.391203i	$-0.872059\pi$
$467$		−	16.9079i		−	0.782406i	0.920304	−	0.391203i	$-0.127941\pi$
$468$			1.05875i			0.0489407i
$469$	5.71269	−	9.89467i	0.263788	−	0.456894i
$470$	15.9588	+	2.01530i	0.736126	+	0.0929586i
$471$	5.41192	−	9.37371i	0.249368	−	0.431918i
$472$	−5.35888	+	3.09395i	−0.246663	+	0.142411i
$473$	−39.4505	+	22.7767i	−1.81394	+	1.04728i
$474$	−15.3970			−0.707206
$475$	−15.4118	−	15.4103i	−0.707142	−	0.707072i
$476$	10.9245			0.500725
$477$	6.62700	−	3.82610i	0.303429	−	0.175185i
$478$	−5.74532	+	3.31706i	−0.262785	+	0.151719i
$479$	1.82570	−	3.16220i	0.0834181	−	0.144484i	−0.821298	−	0.570500i	$-0.806750\pi$
$479$	1.82570	−	3.16220i	0.0834181	−	0.144484i	0.904716	+	0.426015i	$0.140083\pi$
$480$	2.94891	+	0.372391i	0.134599	+	0.0169972i
$481$	−4.19369	+	7.26368i	−0.191216	+	0.331195i
$482$		−	22.0794i		−	1.00569i
$483$		−	10.7458i		−	0.488950i
$484$	14.9403	−	25.8774i	0.679106	−	1.17625i
$485$	−23.3958	+	9.83602i	−1.06235	+	0.446631i
$486$	11.8554			0.537771
$487$		−	13.7416i		−	0.622691i	−0.950297	−	0.311346i	$-0.899220\pi$
$487$		−	13.7416i		−	0.622691i	0.950297	−	0.311346i	$-0.100780\pi$
$488$	−6.94616	−	4.01037i	−0.314438	−	0.181541i
$489$	8.91274	+	15.4373i	0.403048	+	0.698099i
$490$	3.24558	−	1.36450i	0.146620	−	0.0616417i
$491$	17.3839	+	30.1098i	0.784525	+	1.35884i	0.929283	+	0.369369i	$0.120426\pi$
$491$	17.3839	+	30.1098i	0.784525	+	1.35884i	−0.144758	+	0.989467i	$0.546240\pi$
$492$	4.24798	−	2.45257i	0.191514	−	0.110571i
$493$		−	20.7348i		−	0.933849i
$494$	−3.22143	−	1.90535i	−0.144939	−	0.0857258i
$495$	−10.6578	+	14.0425i	−0.479031	+	0.631163i
$496$	4.12622	+	7.14682i	0.185273	+	0.320902i
$497$	−4.43807	+	2.56232i	−0.199075	+	0.114936i
$498$	6.99696	+	4.03970i	0.313541	+	0.181023i
$499$	8.31410	+	14.4005i	0.372190	+	0.644653i	0.989902	−	0.141752i	$-0.0452735\pi$
$499$	8.31410	+	14.4005i	0.372190	+	0.644653i	−0.617712	+	0.786405i	$0.711940\pi$
$500$	8.76096	−	6.94590i	0.391802	−	0.310630i
$501$	17.2600			0.771121
$502$			9.45115i			0.421825i
$503$	4.12176	+	2.37970i	0.183780	+	0.106106i	0.589068	−	0.808084i	$-0.299495\pi$
$503$	4.12176	+	2.37970i	0.183780	+	0.106106i	−0.405287	+	0.914189i	$0.632829\pi$
$504$	1.43605	−	2.48732i	0.0639670	−	0.110794i
$505$	−3.00223	+	3.95569i	−0.133598	+	0.176026i
$506$	−22.1905			−0.986487
$507$	14.1166	+	8.15022i	0.626940	+	0.361964i
$508$	12.3833	−	7.14949i	0.549419	−	0.317207i
$509$	−1.41576	+	2.45217i	−0.0627524	+	0.108690i	−0.895695	−	0.444669i	$-0.853321\pi$
$509$	−1.41576	+	2.45217i	−0.0627524	+	0.108690i	0.832942	+	0.553360i	$0.186655\pi$
$510$	1.74656	−	13.8307i	0.0773388	−	0.612435i
$511$	−5.42390	−	9.39446i	−0.239939	−	0.415587i
$512$			1.00000i			0.0441942i
$513$	−12.4862	+	21.1107i	−0.551278	+	0.932062i
$514$	26.7890			1.18161
$515$	−0.914582	+	7.24244i	−0.0403013	+	0.319140i
$516$	−4.73527	−	8.20172i	−0.208459	−	0.361061i
$517$	39.8328	+	22.9975i	1.75185	+	1.01143i
$518$	19.7045	−	11.3764i	0.865764	−	0.499849i
$519$	−1.40609	+	2.43542i	−0.0617206	+	0.106903i
$520$	1.16074	−	1.52937i	0.0509020	−	0.0670675i
$521$	4.92317			0.215688			0.107844	−	0.994168i	$-0.465605\pi$
$521$	4.92317			0.215688			0.107844	+	0.994168i	$0.465605\pi$
$522$	−4.72095	−	2.72564i	−0.206630	−	0.119298i
$523$	−25.0190	−	14.4447i	−1.09400	−	0.631624i	−0.159365	−	0.987220i	$-0.550945\pi$
$523$	−25.0190	−	14.4447i	−1.09400	−	0.631624i	−0.934640	+	0.355596i	$0.884278\pi$
$524$	−2.37893			−0.103924
$525$	4.16459	+	14.9104i	0.181757	+	0.650742i
$526$	−7.19364	+	12.4598i	−0.313658	+	0.543271i
$527$	33.5194	−	19.3525i	1.46013	−	0.843006i
$528$	7.36040	+	4.24953i	0.320320	+	0.184937i
$529$	−5.47738	−	9.48710i	−0.238147	−	0.412483i
$530$	−13.7675	−	1.73857i	−0.598020	−	0.0755185i
$531$	7.63002			0.331115
$532$	4.98375	+	8.84569i	0.216073	+	0.383509i
$533$		−	3.16848i		−	0.137242i
$534$	7.50965	+	13.0071i	0.324974	+	0.562872i
$535$	2.80148	−	22.1845i	0.121118	−	0.959119i
$536$	2.45257	−	4.24798i	0.105935	−	0.183485i
$537$	−11.3729	+	6.56616i	−0.490778	+	0.283351i
$538$	11.1628	+	6.44486i	0.481264	+	0.277858i
$539$	10.0672			0.433624
$540$	−10.0223	−	7.60660i	−0.431292	−	0.327336i
$541$	−2.30730	+	3.99637i	−0.0991987	+	0.171817i	−0.911353	−	0.411625i	$-0.864961\pi$
$541$	−2.30730	+	3.99637i	−0.0991987	+	0.171817i	0.812154	+	0.583442i	$0.198295\pi$
$542$	−17.4776	−	10.0907i	−0.750727	−	0.433433i
$543$		−	20.0446i		−	0.860198i
$544$	4.69012			0.201087
$545$	−2.62959	−	6.25471i	−0.112639	−	0.267922i
$546$	1.32927	+	2.30235i	0.0568873	+	0.0985317i
$547$	−21.0552	−	12.1562i	−0.900255	−	0.519763i	−0.0229724	−	0.999736i	$-0.507313\pi$
$547$	−21.0552	−	12.1562i	−0.900255	−	0.519763i	−0.877283	+	0.479973i	$0.840646\pi$
$548$	7.87364	−	4.54585i	0.336345	−	0.194189i
$549$	4.94500	+	8.56500i	0.211048	+	0.365545i
$550$	30.7905	−	8.60004i	1.31291	−	0.366707i
$551$	16.7892	−	9.45919i	0.715243	−	0.402975i
$552$		−	4.61338i		−	0.196359i
$553$	23.3654	−	13.4900i	0.993597	−	0.573654i
$554$	3.70049	+	6.40943i	0.157219	+	0.272311i
$555$	−11.2525	−	26.7651i	−0.477643	−	1.13612i
$556$	10.5329	+	18.2435i	0.446694	+	0.773697i
$557$	−21.1577	−	12.2154i	−0.896479	−	0.517582i	−0.0204227	−	0.999791i	$-0.506501\pi$
$557$	−21.1577	−	12.2154i	−0.896479	−	0.517582i	−0.876056	+	0.482209i	$0.839835\pi$
$558$		−	10.1757i		−	0.430772i
$559$	−6.11750			−0.258743
$560$	−4.80133	+	2.01856i	−0.202893	+	0.0852999i
$561$	19.9308	−	34.5211i	0.841478	−	1.45748i
$562$			2.72167i			0.114807i
$563$			19.7981i			0.834390i	0.908817	+	0.417195i	$0.136987\pi$
$563$			19.7981i			0.834390i	−0.908817	+	0.417195i	$0.863013\pi$
$564$	−4.78116	+	8.28121i	−0.201323	+	0.348702i
$565$	−1.39351	+	11.0350i	−0.0586254	+	0.464246i
$566$	10.2721	−	17.7918i	0.431769	−	0.747845i
$567$	7.62587	−	4.40280i	0.320256	−	0.184900i
$568$	−1.90535	+	1.10005i	−0.0799467	+	0.0461573i
$569$	39.9935			1.67662			0.838308	−	0.545197i	$-0.183545\pi$
$569$	39.9935			1.67662			0.838308	+	0.545197i	$0.183545\pi$
$570$	11.9956	−	4.89535i	0.502442	−	0.205044i
$571$	−30.3255			−1.26908			−0.634542	−	0.772889i	$-0.718811\pi$
$571$	−30.3255			−1.26908			−0.634542	+	0.772889i	$0.718811\pi$
$572$	4.75445	−	2.74498i	0.198794	−	0.114774i
$573$	−10.1786	+	5.87663i	−0.425218	+	0.245500i
$574$	−4.29763	+	7.44372i	−0.179380	+	0.310695i
$575$	−12.3995	−	12.1402i	−0.517095	−	0.506280i
$576$	0.616527	−	1.06786i	0.0256886	−	0.0444940i
$577$			31.8330i			1.32523i	0.748962	+	0.662613i	$0.230552\pi$
$577$			31.8330i			1.32523i	−0.748962	+	0.662613i	$0.769448\pi$
$578$		−	4.99721i		−	0.207856i
$579$	−12.4239	+	21.5188i	−0.516318	+	0.894289i
$580$	3.83125	+	9.11296i	0.159084	+	0.378395i
$581$	−14.1575			−0.587352
$582$		−	15.0872i		−	0.625383i
$583$	−34.3632	−	19.8396i	−1.42318	−	0.821673i
$584$	−2.32859	−	4.03323i	−0.0963576	−	0.166896i
$585$	−2.18241	+	0.917522i	−0.0902315	+	0.0379349i
$586$	−13.3658	−	23.1502i	−0.552134	−	0.956324i
$587$	0.919322	−	0.530771i	0.0379445	−	0.0219073i	−0.480908	−	0.876771i	$-0.659693\pi$
$587$	0.919322	−	0.530771i	0.0379445	−	0.0219073i	0.518852	+	0.854864i	$0.326359\pi$
$588$			2.09296i			0.0863122i
$589$	30.9614	+	18.3124i	1.27574	+	0.754551i
$590$	−11.0216	−	8.36506i	−0.453754	−	0.344384i
$591$	10.8448	+	18.7837i	0.446094	+	0.772657i
$592$	8.45952	−	4.88411i	0.347684	−	0.200736i
$593$	−32.5188	−	18.7747i	−1.33539	−	0.770985i	−0.349266	−	0.937024i	$-0.613569\pi$
$593$	−32.5188	−	18.7747i	−1.33539	−	0.770985i	−0.986119	+	0.166039i	$0.946902\pi$
$594$	−17.9885	−	31.1570i	−0.738076	−	1.27839i
$595$	9.46730	+	22.5188i	0.388122	+	0.923181i
$596$	−6.35778			−0.260425
$597$		−	4.18592i		−	0.171318i
$598$	−2.58077	−	1.49001i	−0.105536	−	0.0609310i
$599$	−5.02165	+	8.69775i	−0.205179	+	0.355380i	−0.950190	−	0.311672i	$-0.899111\pi$
$599$	−5.02165	+	8.69775i	−0.205179	+	0.355380i	0.745011	+	0.667052i	$0.232444\pi$
$600$	1.78794	+	6.40132i	0.0729924	+	0.261333i
$601$	7.56630			0.308636			0.154318	−	0.988021i	$-0.450682\pi$
$601$	7.56630			0.308636			0.154318	+	0.988021i	$0.450682\pi$
$602$	14.3718	+	8.29759i	0.585753	+	0.338184i
$603$	−5.23799	+	3.02415i	−0.213307	+	0.123153i
$604$	−1.52779	+	2.64622i	−0.0621651	+	0.107673i
$605$	66.2887	+	8.37099i	2.69502	+	0.340329i
$606$	−1.47605	−	2.55659i	−0.0599604	−	0.103854i
$607$			30.8174i			1.25084i	0.780288	+	0.625420i	$0.215072\pi$
$607$			30.8174i			1.25084i	−0.780288	+	0.625420i	$0.784928\pi$
$608$	2.13962	+	3.79763i	0.0867732	+	0.154014i
$609$	−13.6882			−0.554675
$610$	2.24699	−	17.7936i	0.0909780	−	0.720442i
$611$	3.08839	+	5.34925i	0.124943	+	0.216408i
$612$	−5.00837	−	2.89158i	−0.202451	−	0.116885i
$613$	−16.2208	+	9.36510i	−0.655153	+	0.378253i	−0.790428	−	0.612555i	$-0.790142\pi$
$613$	−16.2208	+	9.36510i	−0.655153	+	0.378253i	0.135275	+	0.990808i	$0.456808\pi$
$614$	−6.38026	+	11.0509i	−0.257486	+	0.445980i
$615$	8.73685	+	6.63097i	0.352304	+	0.267387i
$616$	−14.8928			−0.600050
$617$	−40.1386	−	23.1741i	−1.61592	−	0.932952i	−0.987960	−	0.154707i	$-0.950557\pi$
$617$	−40.1386	−	23.1741i	−1.61592	−	0.932952i	−0.627960	−	0.778245i	$-0.716110\pi$
$618$	−3.75818	−	2.16979i	−0.151176	−	0.0872816i
$619$	−11.5591			−0.464600			−0.232300	−	0.972644i	$-0.574625\pi$
$619$	−11.5591			−0.464600			−0.232300	+	0.972644i	$0.574625\pi$
$620$	−11.1560	+	14.6989i	−0.448035	+	0.590322i
$621$	−9.76435	+	16.9123i	−0.391830	+	0.678669i
$622$	−6.03313	+	3.48323i	−0.241906	+	0.139665i
$623$	−22.7923	−	13.1591i	−0.913153	−	0.527209i
$624$	0.570680	+	0.988447i	0.0228455	+	0.0395695i
$625$	21.9100	+	12.0397i	0.876399	+	0.481586i
$626$	26.1692			1.04593
$627$	37.0445	+	0.389655i	1.47941	+	0.0155613i
$628$			8.14272i			0.324930i
$629$	−22.9070	−	39.6761i	−0.913363	−	1.58199i
$630$	6.37163	+	0.804615i	0.253852	+	0.0320566i
$631$	−22.4567	+	38.8962i	−0.893989	+	1.54843i	−0.0589383	+	0.998262i	$0.518772\pi$
$631$	−22.4567	+	38.8962i	−0.893989	+	1.54843i	−0.835051	+	0.550173i	$0.814562\pi$
$632$	10.0312	−	5.79153i	0.399021	−	0.230375i
$633$	−9.10386	−	5.25612i	−0.361846	−	0.208912i
$634$	−8.75740			−0.347801
$635$	25.4688	+	19.3299i	1.01070	+	0.767085i
$636$	4.12464	−	7.14408i	0.163553	−	0.283281i
$637$	1.17082	+	0.675974i	0.0463897	+	0.0267831i
$638$			28.2667i			1.11909i
$639$	2.71285			0.107319
$640$	−2.06131	+	0.866610i	−0.0814803	+	0.0342558i
$641$	17.3522	+	30.0549i	0.685371	+	1.18710i	0.973320	+	0.229451i	$0.0736932\pi$
$641$	17.3522	+	30.0549i	0.685371	+	1.18710i	−0.287949	+	0.957646i	$0.592973\pi$
$642$	11.5118	+	6.64633i	0.454333	+	0.262310i
$643$	32.4734	−	18.7485i	1.28062	−	0.739369i	0.303662	−	0.952780i	$-0.401791\pi$
$643$	32.4734	−	18.7485i	1.28062	−	0.739369i	0.976963	+	0.213411i	$0.0684573\pi$
$644$	4.04200	+	7.00096i	0.159277	+	0.275876i
$645$	12.8026	−	16.8685i	0.504104	−	0.664198i
$646$	17.8113	−	10.0351i	0.700778	−	0.394825i
$647$		−	22.6592i		−	0.890823i	−0.895326	−	0.445412i	$-0.853057\pi$
$647$		−	22.6592i		−	0.890823i	0.895326	−	0.445412i	$-0.146943\pi$
$648$	3.27394	−	1.89021i	0.128612	−	0.0742544i
$649$	−19.7821	−	34.2636i	−0.776516	−	1.34496i
$650$	4.15842	+	1.06728i	0.163107	+	0.0418621i
$651$	−12.7756	−	22.1281i	−0.500717	−	0.867267i
$652$	−11.6134	−	6.70501i	−0.454817	−	0.262588i
$653$			17.7667i			0.695266i	0.937631	+	0.347633i	$0.113014\pi$
$653$			17.7667i			0.695266i	−0.937631	+	0.347633i	$0.886986\pi$
$654$	4.03344			0.157720
$655$	−2.06160	−	4.90371i	−0.0805536	−	0.191604i
$656$	−1.84506	+	3.19574i	−0.0720375	+	0.124773i
$657$			5.74255i			0.224038i
$658$		−	16.7560i		−	0.653217i
$659$	0.991869	−	1.71797i	0.0386377	−	0.0669225i	−0.846060	−	0.533088i	$-0.821031\pi$
$659$	0.991869	−	1.71797i	0.0386377	−	0.0669225i	0.884698	+	0.466165i	$0.154365\pi$
$660$	−2.38099	+	18.8547i	−0.0926799	+	0.733919i
$661$	−13.1253	+	22.7337i	−0.510515	+	0.884237i	0.489411	+	0.872053i	$0.337212\pi$
$661$	−13.1253	+	22.7337i	−0.510515	+	0.884237i	−0.999926	+	0.0121841i	$0.996122\pi$
$662$	−8.09507	+	4.67369i	−0.314624	+	0.181648i
$663$	4.63593	−	2.67656i	0.180045	−	0.103949i
$664$	−6.07809			−0.235876
$665$	−13.9147	+	17.9388i	−0.539590	+	0.695637i
$666$	−12.0447			−0.466724
$667$	13.2879	−	7.67175i	0.514508	−	0.297051i
$668$	−11.2450	+	6.49232i	−0.435083	+	0.251195i
$669$	5.53590	−	9.58846i	0.214030	−	0.370711i
$670$	10.8818	+	1.37417i	0.420401	+	0.0530886i
$671$	25.6415	−	44.4124i	0.989879	−	1.71452i
$672$		−	3.09621i		−	0.119439i
$673$			16.0432i			0.618418i	0.950994	+	0.309209i	$0.100064\pi$
$673$			16.0432i			0.618418i	−0.950994	+	0.309209i	$0.899936\pi$
$674$	4.87376	−	8.44159i	0.187730	−	0.325158i
$675$	6.99410	−	27.2510i	0.269203	−	1.04889i
$676$	−12.2627			−0.471644
$677$		−	48.5483i		−	1.86586i	−0.360056	−	0.932931i	$-0.617243\pi$
$677$		−	48.5483i		−	1.86586i	0.360056	−	0.932931i	$-0.382757\pi$
$678$	−5.72618	−	3.30601i	−0.219913	−	0.126967i
$679$	13.2186	+	22.8953i	0.507283	+	0.878640i
$680$	4.06450	+	9.66777i	0.155867	+	0.370742i
$681$	7.55556	+	13.0866i	0.289530	+	0.501480i
$682$	−45.6953	+	26.3822i	−1.74976	+	1.01023i
$683$			13.3802i			0.511981i	0.966679	+	0.255990i	$0.0824015\pi$
$683$			13.3802i			0.511981i	−0.966679	+	0.255990i	$0.917598\pi$
$684$	0.0565317	−	5.37446i	0.00216155	−	0.205498i
$685$	16.1938	+	12.2905i	0.618732	+	0.469596i
$686$	−9.98617	−	17.2966i	−0.381274	−	0.660385i
$687$	−2.59659	+	1.49914i	−0.0990662	+	0.0571959i
$688$	6.17012	+	3.56232i	0.235234	+	0.135812i
$689$	−2.66431	−	4.61473i	−0.101502	−	0.175807i
$690$	9.50960	−	3.99800i	0.362024	−	0.152201i
$691$	−25.8354			−0.982825			−0.491413	−	0.870927i	$-0.663519\pi$
$691$	−25.8354			−0.982825			−0.491413	+	0.870927i	$0.663519\pi$
$692$		−	2.11559i		−	0.0804228i
$693$	15.9034	+	9.18184i	0.604121	+	0.348789i
$694$	7.38162	−	12.7853i	0.280202	−	0.485325i
$695$	−28.4776	+	37.5215i	−1.08022	+	1.42327i
$696$	−5.87663			−0.222753
$697$	14.9884	+	8.65354i	0.567725	+	0.327776i
$698$	−12.8445	+	7.41576i	−0.486170	+	0.280691i
$699$	−10.5929	+	18.3475i	−0.400661	+	0.693965i
$700$	−8.32176	−	8.14771i	−0.314533	−	0.307955i
$701$	−24.6167	−	42.6373i	−0.929758	−	1.61039i	−0.783724	−	0.621109i	$-0.786682\pi$
$701$	−24.6167	−	42.6373i	−0.929758	−	1.61039i	−0.146034	−	0.989280i	$-0.546651\pi$
$702$		−	4.83144i		−	0.182351i
$703$	21.6760	−	36.6482i	0.817525	−	1.38221i
$704$	−6.39380			−0.240975
$705$	−21.2135	−	2.67886i	−0.798947	−	0.100892i
$706$	13.4058	+	23.2194i	0.504532	+	0.873875i
$707$	4.47990	+	2.58647i	0.168484	+	0.0972744i
$708$	7.12338	−	4.11268i	0.267713	−	0.154564i
$709$	5.44796	−	9.43614i	0.204602	−	0.354382i	−0.745404	−	0.666613i	$-0.767743\pi$
$709$	5.44796	−	9.43614i	0.204602	−	0.354382i	0.950006	+	0.312232i	$0.101077\pi$
$710$	−3.91875	−	2.97420i	−0.147068	−	0.111620i
$711$	−14.2825			−0.535637
$712$	−9.78517	−	5.64947i	−0.366715	−	0.211723i
$713$	24.8039	+	14.3206i	0.928915	+	0.536309i
$714$	−14.5216			−0.543457
$715$	9.77851	+	7.42156i	0.365696	+	0.277551i
$716$	4.93969	−	8.55579i	0.184605	−	0.319745i
$717$	7.63705	−	4.40925i	0.285211	−	0.164667i
$718$	0.342680	+	0.197846i	0.0127887	+	0.00738355i
$719$	−16.9141	−	29.2961i	−0.630789	−	1.09256i	−0.987391	−	0.158302i	$-0.949398\pi$
$719$	−16.9141	−	29.2961i	−0.630789	−	1.09256i	0.356602	−	0.934257i	$-0.383935\pi$
$720$	2.73547	+	0.345437i	0.101945	+	0.0128737i
$721$	7.60422			0.283196
$722$	16.2510	+	9.84402i	0.604800	+	0.366356i
$723$			29.3494i			1.09152i
$724$	7.53974	+	13.0592i	0.280212	+	0.485342i
$725$	−15.4644	+	15.7947i	−0.574334	+	0.586602i
$726$	−19.8597	+	34.3979i	−0.737061	+	1.27663i
$727$	−44.1108	+	25.4674i	−1.63598	+	0.944533i	−0.653780	+	0.756684i	$0.726818\pi$
$727$	−44.1108	+	25.4674i	−1.63598	+	0.944533i	−0.982198	+	0.187848i	$0.939849\pi$
$728$	−1.73205	−	1.00000i	−0.0641941	−	0.0370625i
$729$	−27.1002			−1.00371
$730$	6.29575	−	8.29517i	0.233016	−	0.307018i
$731$	16.7077	−	28.9386i	0.617957	−	1.07033i
$732$	9.23330	+	5.33085i	0.341272	+	0.197034i
$733$			30.8270i			1.13862i	0.822123	+	0.569310i	$0.192790\pi$
$733$			30.8270i			1.13862i	−0.822123	+	0.569310i	$0.807210\pi$
$734$	6.98454			0.257804
$735$	−4.31423	+	1.81378i	−0.159133	+	0.0669022i
$736$	1.73531	+	3.00565i	0.0639645	+	0.110790i
$737$	27.1607	+	15.6813i	1.00048	+	0.577626i
$738$	3.94052	−	2.27506i	0.145052	−	0.0837460i
$739$	−18.8645	−	32.6742i	−0.693941	−	1.20194i	−0.970536	−	0.240954i	$-0.922540\pi$
$739$	−18.8645	−	32.6742i	−0.693941	−	1.20194i	0.276596	−	0.960986i	$-0.410794\pi$
$740$	17.3987	+	13.2051i	0.639591	+	0.485428i
$741$	4.28214	+	2.53272i	0.157308	+	0.0930417i
$742$			14.4552i			0.530666i
$743$	28.4038	−	16.3990i	1.04204	−	0.601619i	0.121626	−	0.992576i	$-0.461189\pi$
$743$	28.4038	−	16.3990i	1.04204	−	0.601619i	0.920409	+	0.390957i	$0.127856\pi$
$744$	−5.48484	−	9.50002i	−0.201084	−	0.348288i
$745$	−5.50972	−	13.1053i	−0.201860	−	0.480143i
$746$	1.26311	+	2.18777i	0.0462456	+	0.0800998i
$747$	6.49053	+	3.74731i	0.237476	+	0.137107i
$748$			29.9877i			1.09646i
$749$	−23.2927			−0.851095
$750$	−11.6456	+	9.23294i	−0.425239	+	0.337139i
$751$	−2.19685	+	3.80505i	−0.0801641	+	0.138848i	−0.903320	−	0.428967i	$-0.858878\pi$
$751$	−2.19685	+	3.80505i	−0.0801641	+	0.138848i	0.823156	+	0.567815i	$0.192211\pi$
$752$		−	7.19369i		−	0.262327i
$753$		−	12.5631i		−	0.457824i
$754$	−1.89801	+	3.28744i	−0.0691213	+	0.119722i
$755$	−6.77867	−	0.856016i	−0.246701	−	0.0311536i
$756$	−6.55321	+	11.3505i	−0.238338	+	0.412814i
$757$	−44.1472	+	25.4884i	−1.60456	+	0.926391i	−0.613997	+	0.789309i	$0.710439\pi$
$757$	−44.1472	+	25.4884i	−1.60456	+	0.926391i	−0.990560	+	0.137082i	$0.956227\pi$
$758$	25.3811	−	14.6538i	0.921881	−	0.532248i
$759$	29.4970			1.07067
$760$	−5.97387	+	7.70149i	−0.216695	+	0.279362i
$761$	10.5364			0.381945			0.190973	−	0.981595i	$-0.438836\pi$
$761$	10.5364			0.381945			0.190973	+	0.981595i	$0.438836\pi$
$762$	−16.4607	+	9.50357i	−0.596307	+	0.344278i
$763$	−6.12088	+	3.53389i	−0.221591	+	0.127935i
$764$	4.42096	−	7.65733i	0.159945	−	0.277032i
$765$	1.62014	−	12.8297i	0.0585763	−	0.463858i
$766$	3.11717	−	5.39911i	0.112628	−	0.195078i
$767$		−	5.31318i		−	0.191848i
$768$		−	1.32927i		−	0.0479657i
$769$	−22.2243	+	38.4936i	−0.801429	+	1.38812i	0.117246	+	0.993103i	$0.462593\pi$
$769$	−22.2243	+	38.4936i	−0.801429	+	1.38812i	−0.918676	+	0.395013i	$0.870740\pi$
$770$	−12.9063	−	30.6987i	−0.465110	−	1.10631i
$771$	−35.6096			−1.28245
$772$		−	18.6928i		−	0.672770i
$773$	40.1667	+	23.1902i	1.44469	+	0.834095i	0.998158	−	0.0606710i	$-0.0193241\pi$
$773$	40.1667	+	23.1902i	1.44469	+	0.834095i	0.446536	+	0.894766i	$0.352657\pi$
$774$	−4.39253	−	7.60809i	−0.157886	−	0.273467i
$775$	−39.9668	−	10.2577i	−1.43565	−	0.368466i
$776$	5.67500	+	9.82939i	0.203721	+	0.352855i
$777$	−26.1925	+	15.1222i	−0.939649	+	0.542507i
$778$		−	26.4365i		−	0.947796i
$779$	−0.169181	+	16.0840i	−0.00606152	+	0.576268i
$780$	−1.54294	+	2.03294i	−0.0552460	+	0.0727911i
$781$	−7.03353	−	12.1824i	−0.251679	−	0.435921i
$782$	14.0969	−	8.13882i	0.504102	−	0.291044i
$783$	21.5433	+	12.4380i	0.769895	+	0.444499i
$784$	−0.787262	−	1.36358i	−0.0281165	−	0.0486992i
$785$	−16.7846	+	7.05656i	−0.599070	+	0.251859i
$786$	3.16223			0.112793
$787$		−	13.6958i		−	0.488204i	−0.969750	−	0.244102i	$-0.921507\pi$
$787$		−	13.6958i		−	0.488204i	0.969750	−	0.244102i	$-0.0784932\pi$
$788$	−14.1309	−	8.15847i	−0.503392	−	0.290633i
$789$	9.56226	−	16.5623i	0.340425	−	0.589634i
$790$	20.6313	+	15.6584i	0.734028	+	0.557102i
$791$	11.5862			0.411959
$792$	6.82766	+	3.94195i	0.242610	+	0.140071i
$793$	5.96425	−	3.44346i	0.211797	−	0.122281i
$794$	4.36575	−	7.56171i	0.154935	−	0.268355i
$795$	18.3006	+	2.31102i	0.649055	+	0.0819633i
$796$	1.57452	+	2.72715i	0.0558075	+	0.0966614i
$797$			30.5751i			1.08303i	0.840692	+	0.541513i	$0.182148\pi$
$797$			30.5751i			1.08303i	−0.840692	+	0.541513i	$0.817852\pi$
$798$	−6.62473	−	11.7583i	−0.234513	−	0.416238i
$799$	−33.7392			−1.19361
$800$	−3.57270	−	3.49798i	−0.126314	−	0.123672i
$801$	6.96610	+	12.0656i	0.246135	+	0.426319i
$802$	2.74281	+	1.58356i	0.0968520	+	0.0559175i
$803$	25.7877	−	14.8885i	0.910027	−	0.525404i
$804$	−3.26012	+	5.64669i	−0.114976	+	0.199144i
$805$	−10.9283	+	14.3989i	−0.385171	+	0.507495i
$806$	−7.08587			−0.249589
$807$	−14.8384	−	8.56693i	−0.522335	−	0.301570i
$808$	1.92331	+	1.11042i	0.0676619	+	0.0390646i
$809$	27.5436			0.968381			0.484191	−	0.874963i	$-0.339114\pi$
$809$	27.5436			0.968381			0.484191	+	0.874963i	$0.339114\pi$
$810$	6.73352	+	5.11052i	0.236592	+	0.179565i
$811$	9.07845	−	15.7243i	0.318787	−	0.552156i	−0.661448	−	0.749991i	$-0.730058\pi$
$811$	9.07845	−	15.7243i	0.318787	−	0.552156i	0.980235	+	0.197835i	$0.0633911\pi$
$812$	8.91797	−	5.14879i	0.312959	−	0.180687i
$813$	23.2324	+	13.4132i	0.814795	+	0.470422i
$814$	31.2280	+	54.0885i	1.09454	+	1.89580i
$815$	3.75679	−	29.7494i	0.131594	−	1.04208i
$816$	−6.23441			−0.218248
$817$	31.0539	+	0.326643i	1.08644	+	0.0114278i
$818$		−	17.0886i		−	0.597490i
$819$	1.23305	+	2.13571i	0.0430864	+	0.0746278i
$820$	−8.18634	−	1.03378i	−0.285879	−	0.0361011i
$821$	12.2072	−	21.1436i	0.426036	−	0.737916i	−0.570481	−	0.821311i	$-0.693243\pi$
$821$	12.2072	−	21.1436i	0.426036	−	0.737916i	0.996517	+	0.0833952i	$0.0265764\pi$
$822$	−10.4662	+	6.04264i	−0.365049	+	0.210761i
$823$	9.74999	+	5.62916i	0.339863	+	0.196220i	0.660212	−	0.751080i	$-0.270467\pi$
$823$	9.74999	+	5.62916i	0.339863	+	0.196220i	−0.320348	+	0.947300i	$0.603800\pi$
$824$	3.26464			0.113729
$825$	−40.9288	+	11.4317i	−1.42496	+	0.398002i
$826$	−7.20664	+	12.4823i	−0.250751	+	0.434313i
$827$	−46.9696	−	27.1179i	−1.63329	−	0.942983i	−0.983068	−	0.183243i	$-0.941340\pi$
$827$	−46.9696	−	27.1179i	−1.63329	−	0.942983i	−0.650227	−	0.759740i	$-0.725326\pi$
$828$		−	4.27947i		−	0.148722i
$829$	−1.30919			−0.0454701			−0.0227350	−	0.999742i	$-0.507237\pi$
$829$	−1.30919			−0.0454701			−0.0227350	+	0.999742i	$0.507237\pi$
$830$	−5.26733	−	12.5288i	−0.182832	−	0.434882i
$831$	−4.91893	−	8.51984i	−0.170636	−	0.295550i
$832$	−0.743604	−	0.429320i	−0.0257798	−	0.0148840i
$833$	−6.39534	+	3.69235i	−0.221585	+	0.127932i
$834$	−14.0010	−	24.2505i	−0.484816	−	0.839725i
$835$	−23.1277	−	17.5531i	−0.800367	−	0.607452i
$836$	−24.2813	+	13.6803i	−0.839786	+	0.473144i
$837$			46.4352i			1.60504i
$838$	−6.75756	+	3.90148i	−0.233436	+	0.134774i
$839$	−14.7642	−	25.5723i	−0.509716	−	0.882854i	−0.999937	−	0.0112559i	$-0.996417\pi$
$839$	−14.7642	−	25.5723i	−0.509716	−	0.882854i	0.490220	−	0.871598i	$-0.336916\pi$
$840$	6.38224	−	2.68321i	0.220208	−	0.0925794i
$841$	4.72756	+	8.18837i	0.163019	+	0.282358i
$842$	−29.4180	−	16.9845i	−1.01381	−	0.585324i
$843$		−	3.61782i		−	0.124604i
$844$	7.90831			0.272215
$845$	−10.6270	−	25.2773i	−0.365580	−	0.869565i
$846$	−4.43510	+	7.68182i	−0.152482	+	0.264107i
$847$		−	69.5999i		−	2.39148i
$848$			6.20589i			0.213111i
$849$	−13.6543	+	23.6500i	−0.468616	+	0.811667i
$850$	−16.4059	+	16.7564i	−0.562718	+	0.574739i
$851$	16.9509	−	29.3598i	0.581069	−	1.00644i
$852$	2.53272	−	1.46226i	0.0867694	−	0.0500964i
$853$	7.28928	−	4.20847i	0.249580	−	0.144095i	−0.369992	−	0.929035i	$-0.620639\pi$
$853$	7.28928	−	4.20847i	0.249580	−	0.144095i	0.619572	+	0.784940i	$0.287306\pi$
$854$	−18.6824			−0.639300
$855$	11.1274	−	4.54103i	0.380549	−	0.155300i
$856$	−10.0000			−0.341793
$857$	−11.8141	+	6.82088i	−0.403562	+	0.232997i	−0.688020	−	0.725692i	$-0.741520\pi$
$857$	−11.8141	+	6.82088i	−0.403562	+	0.232997i	0.284458	+	0.958689i	$0.408187\pi$
$858$	−6.31993	+	3.64881i	−0.215759	+	0.124568i
$859$	−7.70524	+	13.3459i	−0.262899	+	0.455355i	−0.967011	−	0.254734i	$-0.918012\pi$
$859$	−7.70524	+	13.3459i	−0.262899	+	0.455355i	0.704112	+	0.710089i	$0.251345\pi$
$860$	−1.99595	+	15.8056i	−0.0680614	+	0.538968i
$861$	5.71269	−	9.89467i	0.194688	−	0.337210i
$862$			18.1513i			0.618235i
$863$		−	45.4425i		−	1.54688i	−0.633869	−	0.773440i	$-0.718534\pi$
$863$		−	45.4425i		−	1.54688i	0.633869	−	0.773440i	$-0.281466\pi$
$864$	−2.81343	+	4.87300i	−0.0957147	+	0.165783i
$865$	4.36089	−	1.83339i	0.148275	−	0.0623373i
$866$	0.314308			0.0106806
$867$			6.64261i			0.225595i
$868$	16.6468	+	9.61106i	0.565031	+	0.326221i
$869$	37.0299	+	64.1376i	1.25615	+	2.17572i
$870$	−5.09274	−	12.1135i	−0.172660	−	0.410687i
$871$	2.10588	+	3.64749i	0.0713549	+	0.123590i
$872$	−2.62782	+	1.51717i	−0.0889891	+	0.0513779i
$873$		−	13.9952i		−	0.473665i
$874$	13.0210	+	7.70143i	0.440443	+	0.260505i
$875$	9.58322	−	24.2146i	0.323972	−	0.818603i
$876$	3.09531	+	5.36123i	0.104581	+	0.181139i
$877$	32.3964	−	18.7041i	1.09395	−	0.631591i	0.159323	−	0.987226i	$-0.449069\pi$
$877$	32.3964	−	18.7041i	1.09395	−	0.631591i	0.934625	+	0.355635i	$0.115735\pi$
$878$	7.50359	+	4.33220i	0.253234	+	0.146205i
$879$	17.7666	+	30.7727i	0.599254	+	1.03794i
$880$	−5.54093	−	13.1796i	−0.186785	−	0.444284i
$881$	3.04062			0.102441			0.0512206	−	0.998687i	$-0.483689\pi$
$881$	3.04062			0.102441			0.0512206	+	0.998687i	$0.483689\pi$
$882$			1.94147i			0.0653728i
$883$	7.05837	+	4.07515i	0.237533	+	0.137140i	0.614042	−	0.789273i	$-0.289542\pi$
$883$	7.05837	+	4.07515i	0.237533	+	0.137140i	−0.376509	+	0.926413i	$0.622876\pi$
$884$	−2.01356	+	3.48759i	−0.0677234	+	0.117300i
$885$	14.6507	+	11.1194i	0.492478	+	0.373774i
$886$	−3.88838			−0.130633
$887$	39.9704	+	23.0769i	1.34207	+	0.774847i	0.987112	−	0.160034i	$-0.0511603\pi$
$887$	39.9704	+	23.0769i	1.34207	+	0.774847i	0.354963	+	0.934881i	$0.384494\pi$
$888$	−11.2449	+	6.49227i	−0.377356	+	0.217866i
$889$	16.6531	−	28.8439i	0.558526	−	0.967395i
$890$	3.16537	−	25.0661i	0.106104	−	0.840219i
$891$	12.0856	+	20.9329i	0.404883	+	0.701278i
$892$			8.32927i			0.278884i
$893$	−15.3918	−	27.3190i	−0.515067	−	0.914195i
$894$	8.45118			0.282650
$895$	21.9169	+	2.76769i	0.732601	+	0.0925135i
$896$	1.16463	+	2.01720i	0.0389076	+	0.0673900i
$897$	3.43053	+	1.98062i	0.114542	+	0.0661309i
$898$	−28.5247	+	16.4687i	−0.951882	+	0.549569i
$899$	18.2418	−	31.5958i	0.608400	−	1.05378i
$900$	1.65853	+	5.93800i	0.0552843	+	0.197933i
$901$	29.1064			0.969674
$902$	−20.4329	−	11.7969i	−0.680341	−	0.392795i
$903$	−19.1040	−	11.0297i	−0.635741	−	0.367045i
$904$	4.97420			0.165439
$905$	−20.3851	+	26.8590i	−0.677622	+	0.892823i
$906$	2.03084	−	3.51752i	0.0674703	−	0.116862i
$907$	27.0823	−	15.6360i	0.899252	−	0.519184i	0.0222948	−	0.999751i	$-0.492903\pi$
$907$	27.0823	−	15.6360i	0.899252	−	0.519184i	0.876958	+	0.480568i	$0.159569\pi$
$908$	−9.84500	−	5.68402i	−0.326718	−	0.188631i
$909$	−1.36921	−	2.37155i	−0.0454140	−	0.0786593i
$910$	0.560295	−	4.43690i	0.0185736	−	0.147082i
$911$	40.3430			1.33662			0.668312	−	0.743881i	$-0.267017\pi$
$911$	40.3430			1.33662			0.668312	+	0.743881i	$0.267017\pi$
$912$	−2.84413	−	5.04806i	−0.0941785	−	0.167158i
$913$		−	38.8621i		−	1.28615i
$914$	0.612664	+	1.06116i	0.0202651	+	0.0351002i
$915$	−2.98685	+	23.6524i	−0.0987422	+	0.781925i
$916$	1.12780	−	1.95341i	0.0372635	−	0.0645423i
$917$	−4.79879	+	2.77058i	−0.158470	+	0.0914927i
$918$	22.8549	+	13.1953i	0.754325	+	0.435510i
$919$	−33.5859			−1.10790			−0.553948	−	0.832552i	$-0.686879\pi$
$919$	−33.5859			−1.10790			−0.553948	+	0.832552i	$0.686879\pi$
$920$	−4.69173	+	6.18174i	−0.154682	+	0.203806i
$921$	8.48106	−	14.6896i	0.279460	−	0.484040i
$922$	33.9356	+	19.5927i	1.11761	+	0.645252i
$923$		−	1.88910i		−	0.0621805i
$924$	19.7965			0.651259
$925$	−12.1418	+	47.3078i	−0.399219	+	1.55547i
$926$	16.2877	+	28.2111i	0.535247	+	0.927075i
$927$	−3.48617	−	2.01274i	−0.114501	−	0.0661070i
$928$	3.82866	−	2.21048i	0.125682	−	0.0725625i
$929$	4.06819	+	7.04632i	0.133473	+	0.231182i	0.925013	−	0.379935i	$-0.124054\pi$
$929$	4.06819	+	7.04632i	0.133473	+	0.231182i	−0.791540	+	0.611117i	$0.790720\pi$
$930$	14.8292	−	19.5387i	0.486270	−	0.640701i
$931$	−5.90727	−	3.49392i	−0.193603	−	0.114509i
$932$		−	15.9380i		−	0.522067i
$933$	8.01963	−	4.63013i	0.262551	−	0.151584i
$934$	−8.45397	−	14.6427i	−0.276622	−	0.479124i
$935$	−61.8138	+	25.9876i	−2.02153	+	0.849885i
$936$	0.529375	+	0.916904i	0.0173032	+	0.0299699i
$937$	−12.6488	−	7.30278i	−0.413218	−	0.238571i	0.278953	−	0.960305i	$-0.410012\pi$
$937$	−12.6488	−	7.30278i	−0.413218	−	0.238571i	−0.692171	+	0.721733i	$0.743346\pi$
$938$		−	11.4254i		−	0.373052i
$939$	−34.7858			−1.13519
$940$	14.8284	−	6.23412i	0.483649	−	0.203335i
$941$	9.92629	−	17.1928i	0.323588	−	0.560471i	−0.657638	−	0.753334i	$-0.728444\pi$
$941$	9.92629	−	17.1928i	0.323588	−	0.560471i	0.981226	+	0.192864i	$0.0617775\pi$
$942$		−	10.8238i		−	0.352659i
$943$			12.8070i			0.417054i
$944$	−3.09395	+	5.35888i	−0.100700	+	0.174417i
$945$	−29.0759	−	3.67174i	−0.945841	−	0.119442i
$946$	−22.7767	+	39.4505i	−0.740536	+	1.28265i
$947$	−18.9171	+	10.9218i	−0.614724	+	0.354911i	−0.774812	−	0.632191i	$-0.782156\pi$
$947$	−18.9171	+	10.9218i	−0.614724	+	0.354911i	0.160088	+	0.987103i	$0.448822\pi$
$948$	−13.3342	+	7.69848i	−0.433073	+	0.250035i
$949$	3.99883			0.129808
$950$	−21.0521	−	5.63979i	−0.683022	−	0.182979i
$951$	11.6409			0.377482
$952$	9.46092	−	5.46226i	0.306630	−	0.177033i
$953$	−4.76776	+	2.75267i	−0.154443	+	0.0891676i	−0.575230	−	0.817992i	$-0.695087\pi$
$953$	−4.76776	+	2.75267i	−0.154443	+	0.0891676i	0.420787	+	0.907160i	$0.361754\pi$
$954$	3.82610	−	6.62700i	0.123875	−	0.214557i
$955$	19.6153	+	2.47704i	0.634738	+	0.0801552i
$956$	−3.31706	+	5.74532i	−0.107281	+	0.185817i
$957$		−	37.5740i		−	1.21459i
$958$		−	3.65139i		−	0.117971i
$959$	10.5885	−	18.3398i	0.341920	−	0.592223i
$960$	2.74002	−	1.15195i	0.0884339	−	0.0371792i
$961$	37.1027			1.19686
$962$			8.38738i			0.270420i
$963$	10.6786	+	6.16527i	0.344112	+	0.198673i
$964$	−11.0397	−	19.1213i	−0.355565	−	0.615856i
$965$	38.5317	−	16.1994i	1.24038	−	0.521477i
$966$	−5.37289	−	9.30613i	−0.172870	−	0.299420i
$967$	−49.1371	+	28.3693i	−1.58014	+	0.912295i	−0.585304	+	0.810814i	$0.699025\pi$
$967$	−49.1371	+	28.3693i	−1.58014	+	0.912295i	−0.994837	+	0.101481i	$0.967642\pi$
$968$		−	29.8806i		−	0.960400i
$969$	−23.6760	+	13.3393i	−0.760583	+	0.428520i
$970$	−15.3434	+	20.2162i	−0.492646	+	0.649102i
$971$	7.20815	+	12.4849i	0.231321	+	0.400659i	0.958197	−	0.286109i	$-0.0923620\pi$
$971$	7.20815	+	12.4849i	0.231321	+	0.400659i	−0.726876	+	0.686768i	$0.759029\pi$
$972$	10.2671	−	5.92769i	0.329316	−	0.190131i
$973$	42.4940	+	24.5339i	1.36229	+	0.786521i
$974$	−6.87080	−	11.9006i	−0.220155	−	0.381319i
$975$	−5.52765	−	1.41870i	−0.177026	−	0.0454346i
$976$	−8.02074			−0.256738
$977$		−	31.9776i		−	1.02305i	−0.859267	−	0.511527i	$-0.829080\pi$
$977$		−	31.9776i		−	1.02305i	0.859267	−	0.511527i	$-0.170920\pi$
$978$	15.4373	+	8.91274i	0.493631	+	0.284998i
$979$	36.1216	−	62.5644i	1.15445	−	1.99957i
$980$	2.12850	−	2.80448i	0.0679925	−	0.0895858i
$981$	3.74151			0.119457
$982$	30.1098	+	17.3839i	0.960842	+	0.554743i
$983$	13.1917	−	7.61623i	0.420750	−	0.242920i	−0.274648	−	0.961545i	$-0.588561\pi$
$983$	13.1917	−	7.61623i	0.420750	−	0.242920i	0.695398	+	0.718625i	$0.255228\pi$
$984$	2.45257	−	4.24798i	0.0781852	−	0.135421i
$985$	4.57115	−	36.1983i	0.145649	−	1.15337i
$986$	−10.3674	−	17.9569i	−0.330166	−	0.571864i
$987$			22.2732i			0.708963i
$988$	−3.74252	−	0.0393660i	−0.119065	−	0.00125240i
$989$	24.7270			0.786271
$990$	−2.20866	+	17.4900i	−0.0701957	+	0.555870i
$991$	8.16214	+	14.1372i	0.259279	+	0.449084i	0.966049	−	0.258359i	$-0.0831818\pi$
$991$	8.16214	+	14.1372i	0.259279	+	0.449084i	−0.706770	+	0.707443i	$0.749848\pi$
$992$	7.14682	+	4.12622i	0.226912	+	0.131008i
$993$	10.7605	−	6.21258i	0.341474	−	0.197150i
$994$	−2.56232	+	4.43807i	−0.0812718	+	0.140767i
$995$	−4.25701	+	5.60896i	−0.134956	+	0.177816i
$996$	8.07940			0.256006
$997$	−19.2635	−	11.1218i	−0.610081	−	0.352230i	0.162916	−	0.986640i	$-0.447910\pi$
$997$	−19.2635	−	11.1218i	−0.610081	−	0.352230i	−0.772997	+	0.634410i	$0.781243\pi$
$998$	14.4005	+	8.31410i	0.455838	+	0.263178i
$999$	54.9643			1.73899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.i.a.159.7	yes	20
3.2	odd	2		1710.2.t.d.919.1		20
5.2	odd	4		950.2.e.o.501.4		10
5.3	odd	4		950.2.e.n.501.2		10
5.4	even	2	inner	190.2.i.a.159.4	yes	20
15.14	odd	2		1710.2.t.d.919.9		20
19.11	even	3	inner	190.2.i.a.49.4	✓	20
57.11	odd	6		1710.2.t.d.1189.9		20
95.49	even	6	inner	190.2.i.a.49.7	yes	20
95.68	odd	12		950.2.e.n.201.2		10
95.87	odd	12		950.2.e.o.201.4		10
285.239	odd	6		1710.2.t.d.1189.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.4	✓	20	19.11	even	3	inner
190.2.i.a.49.7	yes	20	95.49	even	6	inner
190.2.i.a.159.4	yes	20	5.4	even	2	inner
190.2.i.a.159.7	yes	20	1.1	even	1	trivial
950.2.e.n.201.2		10	95.68	odd	12
950.2.e.n.501.2		10	5.3	odd	4
950.2.e.o.201.4		10	95.87	odd	12
950.2.e.o.501.4		10	5.2	odd	4
1710.2.t.d.919.1		20	3.2	odd	2
1710.2.t.d.919.9		20	15.14	odd	2
1710.2.t.d.1189.1		20	285.239	odd	6
1710.2.t.d.1189.9		20	57.11	odd	6

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.15118 + 0.664633i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.21845 + 0.280148i) q^{5} +(-0.664633 + 1.15118i) q^{6} -2.32927i q^{7} -1.00000i q^{8} +(-0.616527 + 1.06786i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.15118 + 0.664633i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.21845 + 0.280148i) q^{5} +(-0.664633 + 1.15118i) q^{6} -2.32927i q^{7} -1.00000i q^{8} +(-0.616527 + 1.06786i) q^{9} +(2.06131 - 0.866610i) q^{10} +6.39380 q^{11} +1.32927i q^{12} +(0.743604 + 0.429320i) q^{13} +(-1.16463 - 2.01720i) q^{14} +(-2.74002 + 1.15195i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.06176 + 2.34506i) q^{17} +1.23305i q^{18} +(-3.75178 - 2.21903i) q^{19} +(1.35184 - 1.78116i) q^{20} +(1.54811 + 2.68140i) q^{21} +(5.53719 - 3.19690i) q^{22} +(-3.00565 - 1.73531i) q^{23} +(0.664633 + 1.15118i) q^{24} +(4.84303 + 1.24299i) q^{25} +0.858640 q^{26} -5.62685i q^{27} +(-2.01720 - 1.16463i) q^{28} +(-2.21048 + 3.82866i) q^{29} +(-1.79695 + 2.36763i) q^{30} -8.25244 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-7.36040 + 4.24953i) q^{33} +(-2.34506 + 4.06176i) q^{34} +(0.652538 - 5.16736i) q^{35} +(0.616527 + 1.06786i) q^{36} +9.76821i q^{37} +(-4.35866 - 0.0458469i) q^{38} -1.14136 q^{39} +(0.280148 - 2.21845i) q^{40} +(-1.84506 - 3.19574i) q^{41} +(2.68140 + 1.54811i) q^{42} +(-6.17012 + 3.56232i) q^{43} +(3.19690 - 5.53719i) q^{44} +(-1.66689 + 2.19627i) q^{45} -3.47063 q^{46} +(6.22992 + 3.59684i) q^{47} +(1.15118 + 0.664633i) q^{48} +1.57452 q^{49} +(4.81568 - 1.34506i) q^{50} +(3.11721 - 5.39916i) q^{51} +(0.743604 - 0.429320i) q^{52} +(-5.37446 - 3.10295i) q^{53} +(-2.81343 - 4.87300i) q^{54} +(14.1843 + 1.79121i) q^{55} -2.32927 q^{56} +(5.79381 + 0.0609427i) q^{57} +4.42096i q^{58} +(-3.09395 - 5.35888i) q^{59} +(-0.372391 + 2.94891i) q^{60} +(4.01037 - 6.94616i) q^{61} +(-7.14682 + 4.12622i) q^{62} +(2.48732 + 1.43605i) q^{63} -1.00000 q^{64} +(1.52937 + 1.16074i) q^{65} +(-4.24953 + 7.36040i) q^{66} +(4.24798 + 2.45257i) q^{67} +4.69012i q^{68} +4.61338 q^{69} +(-2.01856 - 4.80133i) q^{70} +(-1.10005 - 1.90535i) q^{71} +(1.06786 + 0.616527i) q^{72} +(4.03323 - 2.32859i) q^{73} +(4.88411 + 8.45952i) q^{74} +(-6.40132 + 1.78794i) q^{75} +(-3.79763 + 2.13962i) q^{76} -14.8928i q^{77} +(-0.988447 + 0.570680i) q^{78} +(5.79153 + 10.0312i) q^{79} +(-0.866610 - 2.06131i) q^{80} +(1.89021 + 3.27394i) q^{81} +(-3.19574 - 1.84506i) q^{82} -6.07809i q^{83} +3.09621 q^{84} +(-9.66777 + 4.06450i) q^{85} +(-3.56232 + 6.17012i) q^{86} -5.87663i q^{87} -6.39380i q^{88} +(5.64947 - 9.78517i) q^{89} +(-0.345437 + 2.73547i) q^{90} +(1.00000 - 1.73205i) q^{91} +(-3.00565 + 1.73531i) q^{92} +(9.50002 - 5.48484i) q^{93} +7.19369 q^{94} +(-7.70149 - 5.97387i) q^{95} +1.32927 q^{96} +(-9.82939 + 5.67500i) q^{97} +(1.36358 - 0.787262i) q^{98} +(-3.94195 + 6.82766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

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