LMFDB - Embedded newform 633.2.k.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(23,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("633.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.k (of order $10$, degree $4$, 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:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	633.23
Dual form			633.2.k.a.578.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.643573 + 1.98072i) q^{2} +(-1.36348 + 1.06814i) q^{3} +(-1.89101 - 1.37390i) q^{4} +(-1.09574 + 1.50816i) q^{5} +(-1.23818 - 3.38809i) q^{6} +(2.08360 - 0.677003i) q^{7} +(0.568519 - 0.413053i) q^{8} +(0.718149 - 2.91278i) q^{9} +O(q^{10})$	\(q+(-0.643573 + 1.98072i) q^{2} +(-1.36348 + 1.06814i) q^{3} +(-1.89101 - 1.37390i) q^{4} +(-1.09574 + 1.50816i) q^{5} +(-1.23818 - 3.38809i) q^{6} +(2.08360 - 0.677003i) q^{7} +(0.568519 - 0.413053i) q^{8} +(0.718149 - 2.91278i) q^{9} +(-2.28205 - 3.14097i) q^{10} +(3.67163 - 5.05357i) q^{11} +(4.04588 - 0.146583i) q^{12} +(0.209564 + 0.644972i) q^{13} +4.56272i q^{14} +(-0.116906 - 3.22676i) q^{15} +(-0.992348 - 3.05413i) q^{16} +(-2.45084 - 7.54290i) q^{17} +(5.30720 + 3.29703i) q^{18} +(-1.73277 - 5.33291i) q^{19} +(4.14413 - 1.34651i) q^{20} +(-2.11781 + 3.14866i) q^{21} +(7.64672 + 10.5248i) q^{22} +(-0.273775 + 0.842592i) q^{23} +(-0.333964 + 1.17045i) q^{24} +(0.471186 + 1.45016i) q^{25} -1.41238 q^{26} +(2.13207 + 4.73859i) q^{27} +(-4.87025 - 1.58244i) q^{28} +(-2.06048 - 6.34151i) q^{29} +(6.46653 + 1.84510i) q^{30} +1.82225i q^{31} +8.09348 q^{32} +(0.391731 + 10.8123i) q^{33} +16.5176 q^{34} +(-1.26206 + 3.88423i) q^{35} +(-5.35990 + 4.52143i) q^{36} +(-1.63371 + 1.18696i) q^{37} +11.6781 q^{38} +(-0.974657 - 0.655562i) q^{39} +1.31002i q^{40} +(-0.958737 - 0.696563i) q^{41} +(-4.87363 - 6.22117i) q^{42} -8.61616 q^{43} +(-13.8862 + 4.51190i) q^{44} +(3.60603 + 4.27474i) q^{45} +(-1.49274 - 1.08454i) q^{46} +(1.53596 - 0.499063i) q^{47} +(4.61529 + 3.10428i) q^{48} +(-1.78006 + 1.29329i) q^{49} -3.17560 q^{50} +(11.3985 + 7.66675i) q^{51} +(0.489839 - 1.50757i) q^{52} +(1.72440 + 2.37343i) q^{53} +(-10.7579 + 1.17340i) q^{54} +(3.59843 + 11.0748i) q^{55} +(0.904928 - 1.24553i) q^{56} +(8.05889 + 5.42047i) q^{57} +13.8868 q^{58} +(2.91576 - 4.01320i) q^{59} +(-4.21218 + 6.26246i) q^{60} +(-3.80326 - 5.23473i) q^{61} +(-3.60936 - 1.17275i) q^{62} +(-0.475621 - 6.55525i) q^{63} +(-3.22405 + 9.92260i) q^{64} +(-1.20235 - 0.390668i) q^{65} +(-21.6681 - 6.18257i) q^{66} -12.2469i q^{67} +(-5.72864 + 17.6309i) q^{68} +(-0.526721 - 1.44129i) q^{69} +(-6.88133 - 4.99958i) q^{70} +(-6.30991 - 8.68484i) q^{71} +(-0.794850 - 1.95260i) q^{72} -3.74134 q^{73} +(-1.29962 - 3.99981i) q^{74} +(-2.19143 - 1.47397i) q^{75} +(-4.05021 + 12.4653i) q^{76} +(4.22894 - 13.0153i) q^{77} +(1.92574 - 1.50862i) q^{78} +(11.3358 + 8.23592i) q^{79} +(5.69349 + 1.84993i) q^{80} +(-7.96852 - 4.18362i) q^{81} +(1.99671 - 1.45070i) q^{82} +(-6.57326 + 9.04731i) q^{83} +(8.33075 - 3.04449i) q^{84} +(14.0614 + 4.56883i) q^{85} +(5.54513 - 17.0662i) q^{86} +(9.58305 + 6.44563i) q^{87} -4.38963i q^{88} +(-2.02436 - 6.23032i) q^{89} +(-10.7878 + 4.39141i) q^{90} +(0.873296 + 1.20199i) q^{91} +(1.67535 - 1.21721i) q^{92} +(-1.94642 - 2.48460i) q^{93} +3.36348i q^{94} +(9.94157 + 3.23021i) q^{95} +(-11.0353 + 8.64497i) q^{96} +(1.49187 + 2.05339i) q^{97} +(-1.41604 - 4.35812i) q^{98} +(-12.0831 - 14.3239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.643573	+	1.98072i	−0.455075	+	1.40058i	0.415972	+	0.909378i	$0.363442\pi$
$2$	−0.643573	+	1.98072i	−0.455075	+	1.40058i	−0.871047	+	0.491200i	$0.836558\pi$
$3$	−1.36348	+	1.06814i	−0.787205	+	0.616692i
$3$	−1.36348	+	1.06814i	−0.787205	+	0.616692i
$4$	−1.89101	−	1.37390i	−0.945506	−	0.686951i
$5$	−1.09574	+	1.50816i	−0.490032	+	0.674471i	−0.980394	−	0.197048i	$-0.936865\pi$
$5$	−1.09574	+	1.50816i	−0.490032	+	0.674471i	0.490362	+	0.871519i	$0.336865\pi$
$6$	−1.23818	−	3.38809i	−0.505487	−	1.38318i
$7$	2.08360	−	0.677003i	0.787527	−	0.255883i	0.112476	−	0.993654i	$-0.464122\pi$
$7$	2.08360	−	0.677003i	0.787527	−	0.255883i	0.675051	+	0.737771i	$0.264122\pi$
$8$	0.568519	−	0.413053i	0.201002	−	0.146036i
$9$	0.718149	−	2.91278i	0.239383	−	0.970925i
$10$	−2.28205	−	3.14097i	−0.721647	−	0.993262i
$11$	3.67163	−	5.05357i	1.10704	−	1.52371i	0.281330	−	0.959611i	$-0.409224\pi$
$11$	3.67163	−	5.05357i	1.10704	−	1.52371i	0.825708	−	0.564097i	$-0.190776\pi$
$12$	4.04588	−	0.146583i	1.16794	−	0.0423149i
$13$	0.209564	+	0.644972i	0.0581226	+	0.178883i	0.975903	−	0.218206i	$-0.0700204\pi$
$13$	0.209564	+	0.644972i	0.0581226	+	0.178883i	−0.917780	+	0.397089i	$0.870020\pi$
$14$			4.56272i			1.21944i
$15$	−0.116906	−	3.22676i	−0.0301851	−	0.833145i
$16$	−0.992348	−	3.05413i	−0.248087	−	0.763533i
$17$	−2.45084	−	7.54290i	−0.594415	−	1.82942i	−0.557615	−	0.830100i	$-0.688284\pi$
$17$	−2.45084	−	7.54290i	−0.594415	−	1.82942i	−0.0368000	−	0.999323i	$-0.511716\pi$
$18$	5.30720	+	3.29703i	1.25092	+	0.777118i
$19$	−1.73277	−	5.33291i	−0.397524	−	1.22345i	−0.926978	−	0.375115i	$-0.877603\pi$
$19$	−1.73277	−	5.33291i	−0.397524	−	1.22345i	0.529454	−	0.848339i	$-0.322397\pi$
$20$	4.14413	−	1.34651i	0.926656	−	0.301089i
$21$	−2.11781	+	3.14866i	−0.462144	+	0.687094i
$22$	7.64672	+	10.5248i	1.63029	+	2.24390i
$23$	−0.273775	+	0.842592i	−0.0570860	+	0.175692i	−0.975534	−	0.219850i	$-0.929443\pi$
$23$	−0.273775	+	0.842592i	−0.0570860	+	0.175692i	0.918448	+	0.395542i	$0.129443\pi$
$24$	−0.333964	+	1.17045i	−0.0681702	+	0.238917i
$25$	0.471186	+	1.45016i	0.0942372	+	0.290032i
$26$	−1.41238			−0.276990
$27$	2.13207	+	4.73859i	0.410318	+	0.911943i
$28$	−4.87025	−	1.58244i	−0.920391	−	0.299053i
$29$	−2.06048	−	6.34151i	−0.382622	−	1.17759i	−0.938191	−	0.346119i	$-0.887499\pi$
$29$	−2.06048	−	6.34151i	−0.382622	−	1.17759i	0.555569	−	0.831470i	$-0.312501\pi$
$30$	6.46653	+	1.84510i	1.18062	+	0.336867i
$31$			1.82225i			0.327286i	0.986520	+	0.163643i	$0.0523245\pi$
$31$			1.82225i			0.327286i	−0.986520	+	0.163643i	$0.947676\pi$
$32$	8.09348			1.43074
$33$	0.391731	+	10.8123i	0.0681916	+	1.88217i
$34$	16.5176			2.83275
$35$	−1.26206	+	3.88423i	−0.213328	+	0.656555i
$36$	−5.35990	+	4.52143i	−0.893316	+	0.753572i
$37$	−1.63371	+	1.18696i	−0.268580	+	0.195135i	−0.713921	−	0.700226i	$-0.753083\pi$
$37$	−1.63371	+	1.18696i	−0.268580	+	0.195135i	0.445341	+	0.895361i	$0.353083\pi$
$38$	11.6781			1.89444
$39$	−0.974657	−	0.655562i	−0.156070	−	0.104974i
$40$			1.31002i			0.207132i
$41$	−0.958737	−	0.696563i	−0.149730	−	0.108785i	0.510398	−	0.859938i	$-0.329498\pi$
$41$	−0.958737	−	0.696563i	−0.149730	−	0.108785i	−0.660128	+	0.751153i	$0.729498\pi$
$42$	−4.87363	−	6.22117i	−0.752017	−	0.959948i
$43$	−8.61616			−1.31395			−0.656976	−	0.753911i	$-0.728165\pi$
$43$	−8.61616			−1.31395			−0.656976	+	0.753911i	$0.728165\pi$
$44$	−13.8862	+	4.51190i	−2.09342	+	0.680195i
$45$	3.60603	+	4.27474i	0.537555	+	0.637241i
$46$	−1.49274	−	1.08454i	−0.220093	−	0.159907i
$47$	1.53596	−	0.499063i	0.224042	−	0.0727958i	−0.194845	−	0.980834i	$-0.562420\pi$
$47$	1.53596	−	0.499063i	0.224042	−	0.0727958i	0.418887	+	0.908038i	$0.362420\pi$
$48$	4.61529	+	3.10428i	0.666160	+	0.448064i
$49$	−1.78006	+	1.29329i	−0.254294	+	0.184756i
$50$	−3.17560			−0.449098
$51$	11.3985	+	7.66675i	1.59612	+	1.07356i
$52$	0.489839	−	1.50757i	0.0679285	−	0.209062i
$53$	1.72440	+	2.37343i	0.236864	+	0.326015i	0.910857	−	0.412723i	$-0.135422\pi$
$53$	1.72440	+	2.37343i	0.236864	+	0.326015i	−0.673993	+	0.738738i	$0.735422\pi$
$54$	−10.7579	+	1.17340i	−1.46397	+	0.159679i
$55$	3.59843	+	11.0748i	0.485213	+	1.49333i
$56$	0.904928	−	1.24553i	0.120926	−	0.166440i
$57$	8.05889	+	5.42047i	1.06743	+	0.717959i
$58$	13.8868			1.82343
$59$	2.91576	−	4.01320i	0.379600	−	0.522474i	−0.575879	−	0.817535i	$-0.695340\pi$
$59$	2.91576	−	4.01320i	0.379600	−	0.522474i	0.955478	+	0.295061i	$0.0953400\pi$
$60$	−4.21218	+	6.26246i	−0.543789	+	0.808480i
$61$	−3.80326	−	5.23473i	−0.486957	−	0.670239i	0.492866	−	0.870105i	$-0.335949\pi$
$61$	−3.80326	−	5.23473i	−0.486957	−	0.670239i	−0.979823	+	0.199866i	$0.935949\pi$
$62$	−3.60936	−	1.17275i	−0.458389	−	0.148940i
$63$	−0.475621	−	6.55525i	−0.0599227	−	0.825884i
$64$	−3.22405	+	9.92260i	−0.403006	+	1.24033i
$65$	−1.20235	−	0.390668i	−0.149133	−	0.0484563i
$66$	−21.6681	−	6.18257i	−2.66716	−	0.761022i
$67$		−	12.2469i		−	1.49620i	−0.663586	−	0.748100i	$-0.730966\pi$
$67$		−	12.2469i		−	1.49620i	0.663586	−	0.748100i	$-0.269034\pi$
$68$	−5.72864	+	17.6309i	−0.694699	+	2.13806i
$69$	−0.526721	−	1.44129i	−0.0634097	−	0.173510i
$70$	−6.88133	−	4.99958i	−0.822476	−	0.597564i
$71$	−6.30991	−	8.68484i	−0.748848	−	1.03070i	−0.998060	−	0.0622523i	$-0.980172\pi$
$71$	−6.30991	−	8.68484i	−0.748848	−	1.03070i	0.249212	−	0.968449i	$-0.419828\pi$
$72$	−0.794850	−	1.95260i	−0.0936739	−	0.230116i
$73$	−3.74134			−0.437890			−0.218945	−	0.975737i	$-0.570262\pi$
$73$	−3.74134			−0.437890			−0.218945	+	0.975737i	$0.570262\pi$
$74$	−1.29962	−	3.99981i	−0.151078	−	0.464969i
$75$	−2.19143	−	1.47397i	−0.253044	−	0.170199i
$76$	−4.05021	+	12.4653i	−0.464591	+	1.42986i
$77$	4.22894	−	13.0153i	0.481932	−	1.48323i
$78$	1.92574	−	1.50862i	0.218048	−	0.170817i
$79$	11.3358	+	8.23592i	1.27537	+	0.926614i	0.999403	−	0.0345521i	$-0.0110005\pi$
$79$	11.3358	+	8.23592i	1.27537	+	0.926614i	0.275972	+	0.961166i	$0.411000\pi$
$80$	5.69349	+	1.84993i	0.636552	+	0.206828i
$81$	−7.96852	−	4.18362i	−0.885391	−	0.464846i
$82$	1.99671	−	1.45070i	0.220500	−	0.160203i
$83$	−6.57326	+	9.04731i	−0.721509	+	0.993072i	0.277963	+	0.960592i	$0.410341\pi$
$83$	−6.57326	+	9.04731i	−0.721509	+	0.993072i	−0.999472	+	0.0324802i	$0.989659\pi$
$84$	8.33075	−	3.04449i	0.908960	−	0.332181i
$85$	14.0614	+	4.56883i	1.52517	+	0.495559i
$86$	5.54513	−	17.0662i	0.597947	−	1.84029i
$87$	9.58305	+	6.44563i	1.02741	+	0.691044i
$88$		−	4.38963i		−	0.467936i
$89$	−2.02436	−	6.23032i	−0.214581	−	0.660413i	−0.999183	−	0.0404131i	$-0.987133\pi$
$89$	−2.02436	−	6.23032i	−0.214581	−	0.660413i	0.784602	−	0.620000i	$-0.212867\pi$
$90$	−10.7878	+	4.39141i	−1.13713	+	0.462895i
$91$	0.873296	+	1.20199i	0.0915463	+	0.126003i
$92$	1.67535	−	1.21721i	0.174667	−	0.126903i
$93$	−1.94642	−	2.48460i	−0.201834	−	0.257641i
$94$			3.36348i			0.346916i
$95$	9.94157	+	3.23021i	1.01998	+	0.331413i
$96$	−11.0353	+	8.64497i	−1.12628	+	0.882324i
$97$	1.49187	+	2.05339i	0.151477	+	0.208490i	0.878011	−	0.478640i	$-0.158870\pi$
$97$	1.49187	+	2.05339i	0.151477	+	0.208490i	−0.726534	+	0.687130i	$0.758870\pi$
$98$	−1.41604	−	4.35812i	−0.143041	−	0.440236i
$99$	−12.0831	−	14.3239i	−1.21440	−	1.43960i
$100$	1.10136	−	3.38964i	0.110136	−	0.338964i
$101$			19.2626i			1.91670i	0.285604	+	0.958348i	$0.407806\pi$
$101$			19.2626i			1.91670i	−0.285604	+	0.958348i	$0.592194\pi$
$102$	−22.5214	+	17.6432i	−2.22996	+	1.74693i
$103$	1.52007	−	4.67830i	0.149777	−	0.460967i	−0.847817	−	0.530289i	$-0.822084\pi$
$103$	1.52007	−	4.67830i	0.149777	−	0.460967i	0.997594	+	0.0693219i	$0.0220836\pi$
$104$	0.385549	+	0.280118i	0.0378062	+	0.0274678i
$105$	−2.42811	−	6.64413i	−0.236959	−	0.648401i
$106$	−5.81086	+	1.88806i	−0.564401	+	0.183385i
$107$	−6.74836	+	9.28832i	−0.652389	+	0.897936i	−0.999200	−	0.0399991i	$-0.987265\pi$
$107$	−6.74836	+	9.28832i	−0.652389	+	0.897936i	0.346811	+	0.937935i	$0.387265\pi$
$108$	2.47858	−	11.8900i	0.238501	−	1.14412i
$109$	7.80236	−	5.66875i	0.747331	−	0.542968i	−0.147667	−	0.989037i	$-0.547177\pi$
$109$	7.80236	−	5.66875i	0.747331	−	0.542968i	0.894998	+	0.446069i	$0.147177\pi$
$110$	−24.2520			−2.31233
$111$	0.959689	−	3.36343i	0.0910897	−	0.319243i
$112$	−4.13532	−	5.69177i	−0.390751	−	0.537822i
$113$	7.33096	−	2.38197i	0.689638	−	0.224077i	0.0568281	−	0.998384i	$-0.481901\pi$
$113$	7.33096	−	2.38197i	0.689638	−	0.224077i	0.632810	+	0.774307i	$0.281901\pi$
$114$	−15.9229	+	12.4739i	−1.49132	+	1.16829i
$115$	−0.970778	−	1.33616i	−0.0905255	−	0.124598i
$116$	−4.81621	+	14.8228i	−0.447174	+	1.37626i
$117$	2.02916	−	0.147227i	0.187596	−	0.0136111i
$118$	6.07250	+	8.35808i	0.559019	+	0.769424i
$119$	−10.2131	−	14.0572i	−0.936236	−	1.28862i
$120$	−1.39929	−	1.78618i	−0.127737	−	0.163056i
$121$	−8.65848	−	26.6481i	−0.787135	−	2.42255i
$122$	12.8162	−	4.16423i	1.16032	−	0.377012i
$123$	2.05125	−	0.0743172i	0.184955	−	0.00670096i
$124$	2.50359	−	3.44590i	0.224829	−	0.309451i
$125$	−11.5681	−	3.75872i	−1.03469	−	0.336190i
$126$	13.2902	+	3.27671i	1.18398	+	0.291913i
$127$	−0.502130	+	0.163152i	−0.0445568	+	0.0144774i	−0.331211	−	0.943557i	$-0.607457\pi$
$127$	−0.502130	+	0.163152i	−0.0445568	+	0.0144774i	0.286654	+	0.958034i	$0.407457\pi$
$128$	−4.48342	−	3.25740i	−0.396282	−	0.287916i
$129$	11.7480	−	9.20328i	1.03435	−	0.810303i
$130$	1.54760	−	2.13009i	0.135734	−	0.186821i
$131$	−2.85481	+	8.78619i	−0.249426	+	0.767653i	0.745451	+	0.666560i	$0.232234\pi$
$131$	−2.85481	+	8.78619i	−0.249426	+	0.767653i	−0.994877	+	0.101093i	$0.967766\pi$
$132$	14.1142	−	20.9843i	1.22848	−	1.82645i
$133$	−7.22079	−	9.93857i	−0.626122	−	0.861783i
$134$	24.2577	+	7.88180i	2.09554	+	0.680884i
$135$	−9.48278	−	1.97677i	−0.816147	−	0.170133i
$136$	−4.50897	−	3.27596i	−0.386641	−	0.280911i
$137$	17.5933	−	5.71641i	1.50310	−	0.488386i	0.562177	−	0.827017i	$-0.309964\pi$
$137$	17.5933	−	5.71641i	1.50310	−	0.488386i	0.940919	+	0.338631i	$0.109964\pi$
$138$	3.19376	−	0.115711i	0.271871	−	0.00984996i
$139$	−3.00117	−	9.23664i	−0.254556	−	0.783441i	−0.993917	−	0.110133i	$-0.964872\pi$
$139$	−3.00117	−	9.23664i	−0.254556	−	0.783441i	0.739361	−	0.673309i	$-0.235128\pi$
$140$	7.72313	−	5.61118i	0.652723	−	0.474231i
$141$	−1.56118	+	2.32108i	−0.131475	+	0.195470i
$142$	21.2631	−	6.90880i	1.78436	−	0.579773i
$143$	4.02885	+	1.30905i	0.336909	+	0.109469i
$144$	−9.60866	+	0.697164i	−0.800722	+	0.0580970i
$145$	11.8218	+	3.84113i	0.981746	+	0.318989i
$146$	2.40782	−	7.41052i	0.199273	−	0.613299i
$147$	1.04566	−	3.66473i	0.0862445	−	0.302262i
$148$	4.72013			0.387993
$149$	5.63997	−	17.3580i	0.462044	−	1.42203i	−0.400618	−	0.916245i	$-0.631205\pi$
$149$	5.63997	−	17.3580i	0.462044	−	1.42203i	0.862662	−	0.505781i	$-0.168795\pi$
$150$	4.32986	−	3.39199i	0.353532	−	0.276955i
$151$	4.71984	+	3.42917i	0.384095	+	0.279062i	0.763032	−	0.646361i	$-0.223710\pi$
$151$	4.71984	+	3.42917i	0.384095	+	0.279062i	−0.378936	+	0.925423i	$0.623710\pi$
$152$	−3.18789	−	2.31613i	−0.258572	−	0.187863i
$153$	−23.7308	+	1.72181i	−1.91853	+	0.139200i
$154$	23.0580	+	16.7526i	1.85807	+	1.34997i
$155$	−2.74825	−	1.99672i	−0.220745	−	0.160380i
$156$	0.942412	+	2.57876i	0.0754534	+	0.206466i
$157$		−	6.85335i		−	0.546957i	−0.961878	−	0.273479i	$-0.911826\pi$
$157$		−	6.85335i		−	0.546957i	0.961878	−	0.273479i	$-0.0881743\pi$
$158$	−23.6084	+	17.1525i	−1.87819	+	1.36458i
$159$	−4.88633	−	1.39422i	−0.387511	−	0.110569i
$160$	−8.86838	+	12.2063i	−0.701107	+	0.964991i
$161$			1.94097i			0.152970i
$162$	13.4149	−	13.0909i	1.05397	−	1.02852i
$163$	5.75423	+	4.18069i	0.450706	+	0.327457i	0.789875	−	0.613268i	$-0.210146\pi$
$163$	5.75423	+	4.18069i	0.450706	+	0.327457i	−0.339168	+	0.940726i	$0.610146\pi$
$164$	0.855975	+	2.63442i	0.0668404	+	0.205714i
$165$	−16.7359	−	11.2567i	−1.30289	−	0.876331i
$166$	−13.6898	−	18.8424i	−1.06253	−	1.46245i
$167$	4.99692	+	15.3789i	0.386673	+	1.19006i	0.935259	+	0.353963i	$0.115166\pi$
$167$	4.99692	+	15.3789i	0.386673	+	1.19006i	−0.548587	+	0.836094i	$0.684834\pi$
$168$	0.0965479	+	2.66484i	0.00744883	+	0.205597i
$169$	10.1451	−	7.37088i	0.780396	−	0.566991i
$170$	−18.0991	+	24.9113i	−1.38814	+	1.91061i
$171$	−16.7780	+	1.21734i	−1.28304	+	0.0930921i
$172$	16.2933	+	11.8378i	1.24235	+	0.902621i
$173$		−	11.4224i		−	0.868428i	−0.900810	−	0.434214i	$-0.857026\pi$
$173$		−	11.4224i		−	0.868428i	0.900810	−	0.434214i	$-0.142974\pi$
$174$	−18.9344	+	14.8331i	−1.43541	+	1.12449i
$175$	1.96353	+	2.70256i	0.148429	+	0.204295i
$176$	−19.0778	−	6.19876i	−1.43804	−	0.467249i
$177$	0.311086	+	8.58636i	0.0233827	+	0.645390i
$178$	13.6433			1.02261
$179$		−	13.7717i		−	1.02934i	−0.857387	−	0.514672i	$-0.827914\pi$
$179$		−	13.7717i		−	1.02934i	0.857387	−	0.514672i	$-0.172086\pi$
$180$	−0.945977	−	13.0379i	−0.0705090	−	0.971790i
$181$	9.04669	+	2.93945i	0.672435	+	0.218487i	0.625280	−	0.780400i	$-0.284985\pi$
$181$	9.04669	+	2.93945i	0.672435	+	0.218487i	0.0471546	+	0.998888i	$0.484985\pi$
$182$	−2.94283	+	0.956182i	−0.218137	+	0.0708770i
$183$	10.7771	+	3.07503i	0.796666	+	0.227313i
$184$	0.192389	+	0.592113i	0.0141831	+	0.0436511i
$185$		−	3.76451i		−	0.276772i
$186$	6.17395	−	2.25628i	0.452696	−	0.165439i
$187$	−47.1171	−	15.3093i	−3.44555	−	1.11953i
$188$	−3.59018	−	1.16652i	−0.261841	−	0.0850772i
$189$	7.65043	+	8.42992i	0.556487	+	0.613186i
$190$	−12.7963	+	17.6125i	−0.928338	+	1.27775i
$191$	6.71337	+	20.6616i	0.485762	+	1.49502i	0.830874	+	0.556461i	$0.187841\pi$
$191$	6.71337	+	20.6616i	0.485762	+	1.49502i	−0.345112	+	0.938562i	$0.612159\pi$
$192$	−6.20282	−	16.9730i	−0.447650	−	1.22492i
$193$	8.24415	+	5.98972i	0.593427	+	0.431150i	0.843540	−	0.537067i	$-0.180468\pi$
$193$	8.24415	+	5.98972i	0.593427	+	0.431150i	−0.250113	+	0.968217i	$0.580468\pi$
$194$	−5.02731	+	1.63347i	−0.360940	+	0.117276i
$195$	2.05667	−	0.751614i	0.147281	−	0.0538242i
$196$	5.14297			0.367355
$197$	5.86507			0.417869			0.208935	−	0.977930i	$-0.433000\pi$
$197$	5.86507			0.417869			0.208935	+	0.977930i	$0.433000\pi$
$198$	36.1479	−	14.7148i	2.56892	−	1.04573i
$199$	−1.45947			−0.103459			−0.0517295	−	0.998661i	$-0.516473\pi$
$199$	−1.45947			−0.103459			−0.0517295	+	0.998661i	$0.516473\pi$
$200$	0.866871	+	0.629819i	0.0612971	+	0.0445349i
$201$	13.0814	+	16.6984i	0.922694	+	1.17782i
$202$	−38.1536	−	12.3969i	−2.68448	−	0.872241i
$203$	−8.58644	−	11.8182i	−0.602650	−	0.829477i
$204$	−11.0214	−	30.1584i	−0.771656	−	2.11151i
$205$	2.10106	−	0.682676i	0.146745	−	0.0476802i
$206$	8.28811	+	6.02166i	0.577460	+	0.419549i
$207$	2.25767	+	1.40255i	0.156919	+	0.0974840i
$208$	1.76187	−	1.28007i	0.122164	−	0.0887571i
$209$	−33.3123	−	10.8238i	−2.30426	−	0.748700i
$210$	14.7228	−	0.533411i	1.01597	−	0.0368088i
$211$	−8.70627	+	11.6276i	−0.599365	+	0.800476i
$211$	−8.70627	+	11.6276i	−0.599365	+	0.800476i
$212$		−	6.85733i		−	0.470963i
$213$	17.8801	+	5.10173i	1.22512	+	0.349565i
$214$	−14.0545	−	19.3443i	−0.960743	−	1.32235i
$215$	9.44111	−	12.9946i	0.643879	−	0.886223i
$216$	3.16941	+	1.81332i	0.215651	+	0.123381i
$217$	1.23367	+	3.79684i	0.0837469	+	0.257746i
$218$	6.20679	+	19.1025i	0.420377	+	1.29379i
$219$	5.10123	−	3.99627i	0.344709	−	0.270043i
$220$	8.41105	−	25.8866i	0.567073	−	1.74527i
$221$	4.35135	−	3.16144i	0.292704	−	0.212662i
$222$	6.04437	+	4.06548i	0.405671	+	0.272857i
$223$			9.55853i			0.640086i	0.947403	+	0.320043i	$0.103697\pi$
$223$			9.55853i			0.640086i	−0.947403	+	0.320043i	$0.896303\pi$
$224$	16.8636	−	5.47931i	1.12674	−	0.366102i
$225$	4.56238	−	0.331027i	0.304158	−	0.0220684i
$226$			16.0535i			1.06786i
$227$	−23.5373	+	7.64774i	−1.56223	+	0.507598i	−0.957402	−	0.288760i	$-0.906757\pi$
$227$	−23.5373	+	7.64774i	−1.56223	+	0.507598i	−0.604825	+	0.796358i	$0.706757\pi$
$228$	−7.79228	−	21.3223i	−0.516056	−	1.41210i
$229$	−6.41414	+	8.82830i	−0.423858	+	0.583391i	−0.966530	−	0.256554i	$-0.917413\pi$
$229$	−6.41414	+	8.82830i	−0.423858	+	0.583391i	0.542672	+	0.839945i	$0.317413\pi$
$230$	3.27132	−	1.06292i	0.215705	−	0.0700867i
$231$	8.13614	+	22.2632i	0.535319	+	1.46481i
$232$	−3.79080	−	2.75418i	−0.248878	−	0.180821i
$233$	3.50131	−	2.54385i	0.229378	−	0.166653i	−0.467160	−	0.884173i	$-0.654723\pi$
$233$	3.50131	−	2.54385i	0.229378	−	0.166653i	0.696538	+	0.717520i	$0.254723\pi$
$234$	−1.01430	+	4.11393i	−0.0663066	+	0.268936i
$235$	−0.930349	+	2.86332i	−0.0606893	+	0.186782i
$236$	−11.0275	+	3.58305i	−0.717828	+	0.233236i
$237$	−24.2532	+	0.878701i	−1.57542	+	0.0570777i
$238$	34.4162	−	11.1825i	2.23087	−	0.724853i
$239$	−7.72320	+	23.7696i	−0.499572	+	1.53753i	0.310135	+	0.950692i	$0.399626\pi$
$239$	−7.72320	+	23.7696i	−0.499572	+	1.53753i	−0.809708	+	0.586833i	$0.800374\pi$
$240$	−9.73894	+	3.55911i	−0.628646	+	0.229740i
$241$	2.06762	−	6.36347i	0.133187	−	0.409907i	−0.862117	−	0.506710i	$-0.830862\pi$
$241$	2.06762	−	6.36347i	0.133187	−	0.409907i	0.995304	+	0.0968028i	$0.0308616\pi$
$242$	58.3546			3.75118
$243$	15.3336	−	2.80724i	0.983651	−	0.180084i
$244$			15.1242i			0.968231i
$245$		−	4.10173i		−	0.262050i
$246$	−1.17293	+	4.11076i	−0.0747831	+	0.262093i
$247$	3.07645	−	2.23517i	0.195750	−	0.142221i
$248$	0.752686	+	1.03598i	0.0477956	+	0.0657850i
$249$	−0.701309	−	19.3570i	−0.0444437	−	1.22670i
$250$	14.8899	−	20.4942i	0.941719	−	1.29617i
$251$	−12.5567			−0.792573			−0.396287	−	0.918127i	$-0.629701\pi$
$251$	−12.5567			−0.792573			−0.396287	+	0.918127i	$0.629701\pi$
$252$	−8.10686	+	13.0495i	−0.510684	+	0.822043i
$253$	3.25289	+	4.47722i	0.204508	+	0.281481i
$254$		−	1.09958i		−	0.0689935i
$255$	−24.0526	+	8.79007i	−1.50623	+	0.550456i
$256$	−7.54395	+	5.48100i	−0.471497	+	0.342563i
$257$	16.7306	−	23.0276i	1.04362	−	1.43642i	0.149414	−	0.988775i	$-0.452261\pi$
$257$	16.7306	−	23.0276i	1.04362	−	1.43642i	0.894209	−	0.447649i	$-0.147739\pi$
$258$	10.6684	+	29.1923i	0.664186	+	1.81744i
$259$	−2.60043	+	3.57918i	−0.161583	+	0.222399i
$260$	1.73692	+	2.39067i	0.107719	+	0.148263i
$261$	−19.9511	+	1.44757i	−1.23494	+	0.0896023i
$262$	−15.5657	−	11.3091i	−0.961650	−	0.698680i
$263$	15.8946	+	5.16447i	0.980103	+	0.318455i	0.754888	−	0.655854i	$-0.227691\pi$
$263$	15.8946	+	5.16447i	0.980103	+	0.318455i	0.225215	+	0.974309i	$0.427691\pi$
$264$	4.68874	+	5.98516i	0.288572	+	0.368361i
$265$	−5.46901			−0.335959
$266$	24.3326	−	7.90614i	1.49193	−	0.484756i
$267$	9.41503	+	6.33262i	0.576191	+	0.387550i
$268$	−16.8261	+	23.1591i	−1.02782	+	1.41467i
$269$			10.2138i			0.622748i	0.950288	+	0.311374i	$0.100789\pi$
$269$			10.2138i			0.622748i	−0.950288	+	0.311374i	$0.899211\pi$
$270$	10.0183	−	17.5105i	0.609693	−	1.06565i
$271$	−12.7557	+	17.5567i	−0.774854	+	1.06650i	0.220977	+	0.975279i	$0.429075\pi$
$271$	−12.7557	+	17.5567i	−0.774854	+	1.06650i	−0.995831	+	0.0912162i	$0.970925\pi$
$272$	−20.6049	+	14.9704i	−1.24936	+	0.907712i
$273$	−2.47461	−	0.706083i	−0.149770	−	0.0427341i
$274$			38.5262i			2.32746i
$275$	9.05851	+	2.94329i	0.546249	+	0.177487i
$276$	−0.984148	+	3.44915i	−0.0592388	+	0.207615i
$277$	−1.02120	+	3.14292i	−0.0613577	+	0.188840i	−0.977037	−	0.213071i	$-0.931654\pi$
$277$	−1.02120	+	3.14292i	−0.0613577	+	0.188840i	0.915679	+	0.401910i	$0.131654\pi$
$278$	20.2266			1.21311
$279$	5.30780	+	1.30865i	0.317770	+	0.0783466i
$280$	0.886887	+	2.72956i	0.0530016	+	0.163122i
$281$	11.7727	−	16.2037i	0.702299	−	0.966631i	−0.297630	−	0.954681i	$-0.596196\pi$
$281$	11.7727	−	16.2037i	0.702299	−	0.966631i	0.999929	−	0.0119500i	$-0.00380388\pi$
$282$	−3.59267	−	4.58603i	−0.213940	−	0.273094i
$283$	12.4371	−	4.04105i	0.739308	−	0.240216i	0.0849335	−	0.996387i	$-0.472932\pi$
$283$	12.4371	−	4.04105i	0.739308	−	0.240216i	0.654374	+	0.756171i	$0.272932\pi$
$284$			25.0923i			1.48896i
$285$	−17.0054	+	6.21467i	−1.00732	+	0.368125i
$286$	−5.18572	+	7.13754i	−0.306638	+	0.422051i
$287$	−2.46920	−	0.802292i	−0.145752	−	0.0473578i
$288$	5.81232	−	23.5745i	0.342494	−	1.38914i
$289$	−37.1355	+	26.9805i	−2.18444	+	1.58709i
$290$	−15.2164	+	20.9436i	−0.893537	+	1.22985i
$291$	−4.22745	−	1.20622i	−0.247817	−	0.0707099i
$292$	7.07491	+	5.14023i	0.414028	+	0.300809i
$293$	13.0507	+	17.9627i	0.762427	+	1.04939i	0.997008	+	0.0772946i	$0.0246282\pi$
$293$	13.0507	+	17.9627i	0.762427	+	1.04939i	−0.234581	+	0.972097i	$0.575372\pi$
$294$	6.58582	+	4.42967i	0.384093	+	0.258344i
$295$	2.85763	+	8.79488i	0.166378	+	0.512058i
$296$	−0.438518	+	1.34962i	−0.0254883	+	0.0784450i
$297$	31.7750	+	6.62379i	1.84377	+	0.384351i
$298$	30.7516	+	22.3423i	1.78139	+	1.29426i
$299$	−0.600821			−0.0347464
$300$	2.11893	+	5.79810i	0.122336	+	0.334754i
$301$	−17.9526	+	5.83317i	−1.03477	+	0.336218i
$302$	−9.82977	+	7.14174i	−0.565640	+	0.410961i
$303$	−20.5751	−	26.2641i	−1.18201	−	1.50883i
$304$	−14.5679	+	10.5842i	−0.835527	+	0.607046i
$305$	12.0622			0.690681
$306$	11.8621	−	48.1122i	0.678113	−	2.75039i
$307$	−12.3745	+	8.99061i	−0.706251	+	0.513121i	−0.881962	−	0.471321i	$-0.843777\pi$
$307$	−12.3745	+	8.99061i	−0.706251	+	0.513121i	0.175711	+	0.984442i	$0.443777\pi$
$308$	−25.8787	+	18.8020i	−1.47458	+	1.07134i
$309$	2.92450	+	8.00242i	0.166369	+	0.455242i
$310$	5.72363	−	4.15846i	0.325080	−	0.236185i
$311$	15.7559	+	5.11940i	0.893434	+	0.290294i	0.719524	−	0.694467i	$-0.244360\pi$
$311$	15.7559	+	5.11940i	0.893434	+	0.290294i	0.173910	+	0.984762i	$0.444360\pi$
$312$	−0.824893	+	0.0298861i	−0.0467003	+	0.00169197i
$313$	−10.7359	−	14.7767i	−0.606827	−	0.835226i	0.389485	−	0.921033i	$-0.372653\pi$
$313$	−10.7359	−	14.7767i	−0.606827	−	0.835226i	−0.996312	+	0.0858071i	$0.972653\pi$
$314$	13.5745	+	4.41064i	0.766056	+	0.248907i
$315$	10.4075	+	6.46556i	0.586399	+	0.364293i
$316$	−10.1208	−	31.1485i	−0.569337	−	1.75224i
$317$	−7.76202	−	23.8890i	−0.435958	−	1.34174i	−0.892101	−	0.451835i	$-0.850769\pi$
$317$	−7.76202	−	23.8890i	−0.435958	−	1.34174i	0.456143	−	0.889906i	$-0.349231\pi$
$318$	5.90627	−	8.78115i	0.331207	−	0.492423i
$319$	−39.6126	−	12.8709i	−2.21788	−	0.720633i
$320$	−11.4322	−	15.7350i	−0.639078	−	0.879615i
$321$	−0.719991	−	19.8726i	−0.0401860	−	1.10918i
$322$	−3.84451	−	1.24916i	−0.214246	−	0.0696128i
$323$	−35.9789	+	26.1402i	−2.00192	+	1.45448i
$324$	9.32071	+	18.8592i	0.517817	+	1.04774i
$325$	−0.836569	+	0.607803i	−0.0464045	+	0.0337149i
$326$	−11.9840	+	8.70691i	−0.663734	+	0.482231i
$327$	−4.58333	+	16.0632i	−0.253459	+	0.888300i
$328$	−0.832778			−0.0459825
$329$	2.86246	−	2.07970i	0.157812	−	0.114657i
$330$	33.0670	−	25.9045i	1.82028	−	1.42600i
$331$	12.0465	−	8.75226i	0.662133	−	0.481068i	−0.205250	−	0.978710i	$-0.565801\pi$
$331$	12.0465	−	8.75226i	0.662133	−	0.481068i	0.867383	+	0.497642i	$0.165801\pi$
$332$	24.8602	−	8.07758i	1.36438	−	0.443315i
$333$	2.28410	+	5.61105i	0.125168	+	0.307484i
$334$	−33.6772			−1.84273
$335$	18.4704	+	13.4195i	1.00914	+	0.733186i
$336$	11.7180	+	3.34351i	0.639271	+	0.182404i
$337$	1.57606	−	4.85063i	0.0858537	−	0.264231i	−0.898909	−	0.438136i	$-0.855639\pi$
$337$	1.57606	−	4.85063i	0.0858537	−	0.264231i	0.984762	+	0.173906i	$0.0556388\pi$
$338$	8.07047	+	24.8384i	0.438976	+	1.35103i
$339$	−7.45132	+	11.0783i	−0.404700	+	0.601689i
$340$	−20.3132	−	27.9587i	−1.10164	−	1.51627i
$341$	9.20886	+	6.69063i	0.498688	+	0.362318i
$342$	8.38665	−	34.0158i	0.453498	−	1.83936i
$343$	−11.8475	+	16.3067i	−0.639706	+	0.880480i
$344$	−4.89845	+	3.55893i	−0.264107	+	0.191885i
$345$	2.75084	+	0.784900i	0.148101	+	0.0422576i
$346$	22.6245	+	7.35115i	1.21630	+	0.395200i
$347$	−0.0935366	+	0.128742i	−0.00502131	+	0.00691123i	−0.811520	−	0.584324i	$-0.801360\pi$
$347$	−0.0935366	+	0.128742i	−0.00502131	+	0.00691123i	0.806499	+	0.591236i	$0.201360\pi$
$348$	−9.26601	−	25.3549i	−0.496710	−	1.35917i
$349$			18.4878i			0.989630i	0.868998	+	0.494815i	$0.164764\pi$
$349$			18.4878i			0.989630i	−0.868998	+	0.494815i	$0.835236\pi$
$350$	−6.61668	+	2.14989i	−0.353676	+	0.114916i
$351$	−2.60945	+	2.36817i	−0.139282	+	0.126403i
$352$	29.7163	−	40.9009i	1.58388	−	2.18003i
$353$	4.93846	+	15.1990i	0.262848	+	0.808961i	0.992181	+	0.124804i	$0.0398301\pi$
$353$	4.93846	+	15.1990i	0.262848	+	0.808961i	−0.729334	+	0.684158i	$0.760170\pi$
$354$	−17.2073	−	4.90978i	−0.914560	−	0.260952i
$355$	20.0122			1.06214
$356$	−4.73177	+	14.5629i	−0.250783	+	0.771832i
$357$	28.9404	+	8.25759i	1.53169	+	0.437038i
$358$	27.2778	+	8.86310i	1.44168	+	0.468429i
$359$		−	18.2010i		−	0.960612i	−0.877101	−	0.480306i	$-0.840526\pi$
$359$		−	18.2010i		−	0.960612i	0.877101	−	0.480306i	$-0.159474\pi$
$360$	3.81579	+	0.940789i	0.201110	+	0.0495840i
$361$	−10.0661	+	7.31347i	−0.529796	+	0.384919i
$362$	−11.6444	+	16.0272i	−0.612017	+	0.842369i
$363$	40.2695	+	27.0856i	2.11360	+	1.42162i
$364$		−	3.47280i		−	0.182024i
$365$	4.09955	−	5.64254i	0.214580	−	0.295344i
$366$	−13.0266	+	19.3673i	−0.680912	+	1.01235i
$367$	−5.97527	+	1.94148i	−0.311907	+	0.101345i	−0.460787	−	0.887511i	$-0.652433\pi$
$367$	−5.97527	+	1.94148i	−0.311907	+	0.101345i	0.148881	+	0.988855i	$0.452433\pi$
$368$	2.84507			0.148309
$369$	−2.71745	+	2.29235i	−0.141465	+	0.119335i
$370$	7.45642	+	2.42274i	0.387641	+	0.125952i
$371$	5.19977	+	3.77785i	0.269959	+	0.196136i
$372$	0.267111	+	7.37260i	0.0138491	+	0.382251i
$373$	−11.0646	−	15.2290i	−0.572901	−	0.788530i	0.419994	−	0.907527i	$-0.362032\pi$
$373$	−11.0646	−	15.2290i	−0.572901	−	0.788530i	−0.992895	+	0.118997i	$0.962032\pi$
$374$	60.6467	−	83.4730i	3.13596	−	4.31629i
$375$	19.7877	−	7.23147i	1.02183	−	0.373432i
$376$	0.667081	−	0.918159i	0.0344021	−	0.0473504i
$377$	3.65829	−	2.65791i	0.188412	−	0.136889i
$378$	−21.6209	+	9.72806i	−1.11206	+	0.500357i
$379$		−	4.60076i		−	0.236325i	−0.992994	−	0.118163i	$-0.962300\pi$
$379$		−	4.60076i		−	0.236325i	0.992994	−	0.118163i	$-0.0377004\pi$
$380$	−14.3616	−	19.7671i	−0.736737	−	1.01403i
$381$	0.510374	−	0.758799i	0.0261472	−	0.0388745i
$382$	−45.2453			−2.31495
$383$	19.1728	−	26.3890i	0.979682	−	1.34842i	0.0426815	−	0.999089i	$-0.486410\pi$
$383$	19.1728	−	26.3890i	0.979682	−	1.34842i	0.937001	−	0.349328i	$-0.113590\pi$
$384$	9.59241	−	0.347536i	0.489511	−	0.0177351i
$385$	14.9954	+	20.6394i	0.764236	+	1.05188i
$386$	−17.1697	+	12.4745i	−0.873912	+	0.634934i
$387$	−6.18769	+	25.0969i	−0.314538	+	1.27575i
$388$		−	5.93267i		−	0.301186i
$389$		−	32.2882i		−	1.63708i	−0.574451	−	0.818539i	$-0.694784\pi$
$389$		−	32.2882i		−	1.63708i	0.574451	−	0.818539i	$-0.305216\pi$
$390$	0.165116	+	4.55739i	0.00836095	+	0.230773i
$391$	7.02656			0.355349
$392$	−0.477800	+	1.47052i	−0.0241326	+	0.0742724i
$393$	−5.49243	−	15.0291i	−0.277056	−	0.758119i
$394$	−3.77461	+	11.6170i	−0.190162	+	0.585258i
$395$	−24.8422	+	8.07173i	−1.24995	+	0.406133i
$396$	3.16979	+	43.6876i	0.159288	+	2.19539i
$397$	6.97543	−	2.26645i	0.350087	−	0.113750i	−0.128695	−	0.991684i	$-0.541079\pi$
$397$	6.97543	−	2.26645i	0.350087	−	0.113750i	0.478781	+	0.877934i	$0.341079\pi$
$398$	0.939275	−	2.89079i	0.0470816	−	0.144902i
$399$	20.4612	+	5.83820i	1.02434	+	0.292276i
$400$	3.96141	−	2.87813i	0.198070	−	0.143906i
$401$	−10.9866	−	7.98222i	−0.548644	−	0.398613i	0.278641	−	0.960395i	$-0.410116\pi$
$401$	−10.9866	−	7.98222i	−0.548644	−	0.398613i	−0.827285	+	0.561782i	$0.810116\pi$
$402$	−41.4937	+	15.1640i	−2.06952	+	0.756310i
$403$	−1.17530	+	0.381878i	−0.0585458	+	0.0190227i
$404$	26.4648	−	36.4257i	1.31668	−	1.81225i
$405$	15.0410	−	7.43366i	0.747395	−	0.369381i
$406$	28.9345	−	9.40140i	1.43600	−	0.466584i
$407$			12.6142i			0.625260i
$408$	9.64706	−	0.349516i	0.477601	−	0.0173036i
$409$	2.56903	−	0.834730i	0.127031	−	0.0412747i	−0.244812	−	0.969571i	$-0.578726\pi$
$409$	2.56903	−	0.834730i	0.127031	−	0.0412747i	0.371842	+	0.928296i	$0.378726\pi$
$410$			4.60096i			0.227225i
$411$	−17.8822	+	26.5863i	−0.882062	+	1.31141i
$412$	−9.30200	+	6.75830i	−0.458277	+	0.332957i
$413$	3.35833	−	10.3359i	0.165253	−	0.508596i
$414$	−4.23103	+	3.56916i	−0.207944	+	0.175414i
$415$	−6.44221	−	19.8271i	−0.316236	−	0.973273i
$416$	1.69610	+	5.22006i	0.0831582	+	0.255935i
$417$	13.9581	+	9.38829i	0.683529	+	0.459747i
$418$	42.8778	−	59.0163i	2.09722	−	2.88658i
$419$	12.4894	+	17.1902i	0.610149	+	0.839799i	0.996590	−	0.0825158i	$-0.0262955\pi$
$419$	12.4894	+	17.1902i	0.610149	+	0.839799i	−0.386440	+	0.922314i	$0.626295\pi$
$420$	−4.53679	+	15.9001i	−0.221373	+	0.775846i
$421$		−	18.2892i		−	0.891363i	−0.895192	−	0.445681i	$-0.852961\pi$
$421$		−	18.2892i		−	0.891363i	0.895192	−	0.445681i	$-0.147039\pi$
$422$	−17.4278	−	24.7279i	−0.848373	−	1.20373i
$423$	−0.350611	−	4.83230i	−0.0170473	−	0.234955i
$424$	1.96070	+	0.637071i	0.0952202	+	0.0309389i
$425$	9.78362	−	7.10822i	0.474575	−	0.344799i
$426$	−21.6122	+	32.1320i	−1.04711	+	1.55680i
$427$	−11.4684	−	8.33228i	−0.554995	−	0.403227i
$428$	25.5225	−	8.29275i	1.23368	−	0.400845i
$429$	−6.89151	+	2.51852i	−0.332725	+	0.121595i
$430$	19.6625	+	27.0631i	0.948210	+	1.30510i
$431$	11.3436	+	3.68575i	0.546400	+	0.177536i	0.569193	−	0.822204i	$-0.307256\pi$
$431$	11.3436	+	3.68575i	0.546400	+	0.177536i	−0.0227926	+	0.999740i	$0.507256\pi$
$432$	12.3565	−	11.2140i	0.594504	−	0.539533i
$433$	27.4427	+	19.9383i	1.31881	+	0.958175i	0.999946	+	0.0103756i	$0.00330273\pi$
$433$	27.4427	+	19.9383i	1.31881	+	0.958175i	0.318868	+	0.947799i	$0.396697\pi$
$434$	−8.31442			−0.399105
$435$	−20.2216	+	7.39004i	−0.969553	+	0.354325i
$436$	−22.5427			−1.07960
$437$	4.96785			0.237645
$438$	4.63246	+	12.6760i	0.221348	+	0.605682i
$439$	16.2737	−	5.28764i	0.776700	−	0.252365i	0.106269	−	0.994337i	$-0.466109\pi$
$439$	16.2737	−	5.28764i	0.776700	−	0.252365i	0.670431	+	0.741972i	$0.266109\pi$
$440$	6.62027	+	4.80991i	0.315609	+	0.229303i
$441$	2.48871	+	6.11369i	0.118510	+	0.291128i
$442$	3.46150	+	10.6534i	0.164647	+	0.506731i
$443$	−16.5704	+	22.8072i	−0.787285	+	1.08360i	0.207156	+	0.978308i	$0.433579\pi$
$443$	−16.5704	+	22.8072i	−0.787285	+	1.08360i	−0.994441	+	0.105297i	$0.966421\pi$
$444$	−6.43580	+	5.04177i	−0.305430	+	0.239272i
$445$	11.6145	+	3.77379i	0.550581	+	0.178895i
$446$	−18.9327	−	6.15161i	−0.896490	−	0.291287i
$447$	10.8509	+	29.6916i	0.513228	+	1.40436i
$448$			22.8574i			1.07991i
$449$	−4.11518	−	12.6652i	−0.194207	−	0.597709i	−0.999985	−	0.00549042i	$-0.998252\pi$
$449$	−4.11518	−	12.6652i	−0.194207	−	0.597709i	0.805778	−	0.592218i	$-0.201748\pi$
$450$	−2.28055	+	9.24981i	−0.107506	+	0.436040i
$451$	−7.04026	+	2.28752i	−0.331513	+	0.107715i
$452$	−17.1355	−	5.56767i	−0.805987	−	0.261881i
$453$	−10.0982	+	0.365862i	−0.474457	+	0.0171897i
$454$		−	51.5426i		−	2.41902i
$455$	−2.76970			−0.129846
$456$	6.82057	−	0.247111i	0.319403	−	0.0115720i
$457$	1.20476	+	0.391449i	0.0563561	+	0.0183112i	0.337059	−	0.941483i	$-0.390568\pi$
$457$	1.20476	+	0.391449i	0.0563561	+	0.0183112i	−0.280703	+	0.959795i	$0.590568\pi$
$458$	−13.3584	−	18.3862i	−0.624196	−	0.859133i
$459$	30.5174	−	27.6955i	1.42443	−	1.29272i
$460$			3.86045i			0.179995i
$461$	−11.6467	−	8.46183i	−0.542441	−	0.394107i	0.282550	−	0.959253i	$-0.408820\pi$
$461$	−11.6467	−	8.46183i	−0.542441	−	0.394107i	−0.824991	+	0.565146i	$0.808820\pi$
$462$	−49.3333	+	1.78736i	−2.29519	+	0.0831555i
$463$	21.9331	−	30.1883i	1.01932	−	1.40297i	0.106638	−	0.994298i	$-0.465991\pi$
$463$	21.9331	−	30.1883i	1.01932	−	1.40297i	0.912681	−	0.408674i	$-0.134009\pi$
$464$	−17.3231	+	12.5860i	−0.804205	+	0.584289i
$465$	5.87996	−	0.213032i	0.272676	−	0.00987914i
$466$	2.78529	+	8.57225i	0.129026	+	0.397102i
$467$	−10.4566	−	14.3923i	−0.483873	−	0.665994i	0.495370	−	0.868682i	$-0.335032\pi$
$467$	−10.4566	−	14.3923i	−0.483873	−	0.665994i	−0.979243	+	0.202688i	$0.935032\pi$
$468$	−4.03944	−	2.50945i	−0.186723	−	0.115999i
$469$	−8.29121	−	25.5177i	−0.382852	−	1.17830i
$470$	−5.07267	−	3.68551i	−0.233985	−	0.170000i
$471$	7.32035	+	9.34440i	0.337304	+	0.430567i
$472$		−	3.48594i		−	0.160454i
$473$	−31.6354	+	43.5424i	−1.45460	+	2.00208i
$474$	13.8683	−	48.6042i	0.636991	−	2.23247i
$475$	6.91712	−	5.02558i	0.317379	−	0.230590i
$476$			40.6141i			1.86155i
$477$	8.15163	−	3.31830i	0.373238	−	0.151935i
$478$	−42.1103	−	30.5949i	−1.92608	−	1.39938i
$479$	−24.2187	−	17.5959i	−1.10658	−	0.803977i	−0.124458	−	0.992225i	$-0.539719\pi$
$479$	−24.2187	−	17.5959i	−1.10658	−	0.803977i	−0.982121	+	0.188248i	$0.939719\pi$
$480$	−0.946178	−	26.1157i	−0.0431869	−	1.19201i
$481$	−1.10792	−	0.804953i	−0.0505169	−	0.0367027i
$482$	11.2736	+	8.19072i	0.513496	+	0.373077i
$483$	−2.07323	−	2.64647i	−0.0943353	−	0.120419i
$484$	−20.2385	+	62.2877i	−0.919932	+	2.83126i
$485$	−4.73156			−0.214849
$486$	−4.30796	+	32.1782i	−0.195413	+	1.45963i
$487$	7.82973	−	24.0974i	0.354799	−	1.09196i	−0.601327	−	0.799003i	$-0.705361\pi$
$487$	7.82973	−	24.0974i	0.354799	−	1.09196i	0.956126	−	0.292956i	$-0.0946389\pi$
$488$	−4.32445	−	1.40510i	−0.195758	−	0.0636058i
$489$	−12.3113	+	0.446043i	−0.556738	+	0.0201708i
$490$	8.12437	+	2.63977i	0.367022	+	0.119253i
$491$	9.45374	−	3.07171i	0.426641	−	0.138624i	−0.0878227	−	0.996136i	$-0.527991\pi$
$491$	9.45374	−	3.07171i	0.426641	−	0.138624i	0.514464	+	0.857512i	$0.327991\pi$
$492$	−3.98104	−	2.67767i	−0.179479	−	0.120719i
$493$	−42.7835	+	31.0840i	−1.92687	+	1.39995i
$494$	2.44732	+	7.53207i	0.110110	+	0.338884i
$495$	34.8427	−	2.52804i	1.56606	−	0.113627i
$496$	5.56539	−	1.80831i	0.249894	−	0.0811953i
$497$	−19.0270	−	13.8239i	−0.853477	−	0.620088i
$498$	38.7920	+	11.0686i	1.73831	+	0.495994i
$499$	0.958691	+	0.311498i	0.0429169	+	0.0139446i	0.330397	−	0.943842i	$-0.392817\pi$
$499$	0.958691	+	0.311498i	0.0429169	+	0.0139446i	−0.287480	+	0.957787i	$0.592817\pi$
$500$	16.7114	+	23.0013i	0.747356	+	1.02865i
$501$	−23.2400	−	15.6314i	−1.03829	−	0.698361i
$502$	8.08117	−	24.8713i	0.360680	−	1.11006i
$503$	2.42286	−	3.33479i	0.108030	−	0.148691i	−0.751579	−	0.659643i	$-0.770707\pi$
$503$	2.42286	−	3.33479i	0.108030	−	0.148691i	0.859609	+	0.510953i	$0.170707\pi$
$504$	−2.97807	−	3.53033i	−0.132654	−	0.157253i
$505$	−29.0511	−	21.1068i	−1.29276	−	0.939242i
$506$	−10.9616	+	3.56163i	−0.487302	+	0.158334i
$507$	−5.95955	+	20.8865i	−0.264673	+	0.927602i
$508$	1.17369	+	0.381354i	0.0520740	+	0.0169199i
$509$	14.0359	−	19.3187i	0.622129	−	0.856287i	−0.375377	−	0.926872i	$-0.622487\pi$
$509$	14.0359	−	19.3187i	0.622129	−	0.856287i	0.997506	+	0.0705851i	$0.0224866\pi$
$510$	−1.93102	−	53.2984i	−0.0855068	−	2.36009i
$511$	−7.79545	+	2.53290i	−0.344850	+	0.112049i
$512$	−9.42625	−	29.0110i	−0.416585	−	1.28212i
$513$	21.5761	−	19.5810i	0.952608	−	0.864524i
$514$	34.8438	+	47.9584i	1.53690	+	2.11536i
$515$	5.39003	+	7.41874i	0.237513	+	0.326909i
$516$	−34.8599	+	1.26298i	−1.53462	+	0.0555998i
$517$	3.11742	−	9.59444i	0.137104	−	0.421963i
$518$	−5.41577	−	7.45417i	−0.237955	−	0.327517i
$519$	12.2007	+	15.5742i	0.535552	+	0.683631i
$520$	−0.844926	+	0.274533i	−0.0370524	+	0.0120391i
$521$	14.8315	+	20.4138i	0.649780	+	0.894345i	0.999090	−	0.0426623i	$-0.0135839\pi$
$521$	14.8315	+	20.4138i	0.649780	+	0.894345i	−0.349310	+	0.937007i	$0.613584\pi$
$522$	9.97279	−	40.4491i	0.436497	−	1.77041i
$523$	−28.9566			−1.26618			−0.633091	−	0.774078i	$-0.718214\pi$
$523$	−28.9566			−1.26618			−0.633091	+	0.774078i	$0.718214\pi$
$524$	17.4698	−	12.6926i	0.763174	−	0.554478i
$525$	−5.56394	−	1.58756i	−0.242830	−	0.0692869i
$526$	−20.4587	+	28.1590i	−0.892041	+	1.22779i
$527$	13.7450	−	4.46604i	0.598744	−	0.194544i
$528$	32.6333	−	11.9259i	1.42018	−	0.519009i
$529$	17.9724	+	13.0577i	0.781408	+	0.567726i
$530$	3.51971	−	10.8326i	0.152886	−	0.470536i
$531$	−9.59560	−	11.3750i	−0.416414	−	0.493634i
$532$			28.7146i			1.24494i
$533$	0.248347	−	0.764333i	0.0107571	−	0.0331069i
$534$	−18.6024	+	14.5730i	−0.805004	+	0.630635i
$535$	−6.61382	−	20.3553i	−0.285940	−	0.880034i
$536$	−5.05863	−	6.96261i	−0.218500	−	0.300739i
$537$	14.7101	+	18.7774i	0.634788	+	0.810305i
$538$	−20.2307	−	6.57334i	−0.872206	−	0.283397i
$539$			13.7441i			0.592002i
$540$	15.2162	+	16.7665i	0.654799	+	0.721515i
$541$	4.64693	−	3.37619i	0.199787	−	0.145154i	−0.483394	−	0.875403i	$-0.660596\pi$
$541$	4.64693	−	3.37619i	0.199787	−	0.145154i	0.683181	+	0.730249i	$0.260596\pi$
$542$	−26.5656	−	36.5645i	−1.14109	−	1.57058i
$543$	−15.4747	+	5.65526i	−0.664083	+	0.242691i
$544$	−19.8358	−	61.0483i	−0.850452	−	2.61742i
$545$			17.9787i			0.770124i
$546$	2.99114	−	4.44709i	0.128009	−	0.190318i
$547$	−0.145563	+	0.447995i	−0.00622380	+	0.0191549i	−0.954120	−	0.299424i	$-0.903206\pi$
$547$	−0.145563	+	0.447995i	−0.00622380	+	0.0191549i	0.947896	+	0.318579i	$0.103206\pi$
$548$	−41.1229	−	13.3616i	−1.75668	−	0.570781i
$549$	−17.9789	+	7.31871i	−0.767321	+	0.312355i
$550$	−11.6596	+	16.0481i	−0.497168	+	0.684294i
$551$	−30.2484	+	21.9767i	−1.28862	+	0.936240i
$552$	−0.894778	−	0.601834i	−0.0380843	−	0.0256158i
$553$	29.1950	+	9.48602i	1.24150	+	0.403387i
$554$	−5.56801	−	4.04540i	−0.236562	−	0.171872i
$555$	4.02102	+	5.13283i	0.170683	+	0.217876i
$556$	−7.01499	+	21.5899i	−0.297502	+	0.915616i
$557$	−3.48652	+	10.7304i	−0.147729	+	0.454662i	−0.997352	−	0.0727281i	$-0.976829\pi$
$557$	−3.48652	+	10.7304i	−0.147729	+	0.454662i	0.849623	+	0.527390i	$0.176829\pi$
$558$	−6.00802	+	9.67104i	−0.254340	+	0.409408i
$559$	−1.80564	−	5.55718i	−0.0763704	−	0.235044i
$560$	13.1154			0.554225
$561$	80.5957	−	29.4539i	3.40275	−	1.24354i
$562$	24.5183	+	33.7466i	1.03424	+	1.42351i
$563$	11.4685	+	8.33234i	0.483339	+	0.351166i	0.802617	−	0.596495i	$-0.203440\pi$
$563$	11.4685	+	8.33234i	0.483339	+	0.351166i	−0.319278	+	0.947661i	$0.603440\pi$
$564$	6.14114	−	2.24429i	0.258589	−	0.0945018i
$565$	−4.44045	+	13.6663i	−0.186811	+	0.574946i
$566$			27.2350i			1.14477i
$567$	−19.4355	−	3.32227i	−0.816216	−	0.139522i
$568$	−7.17460	−	2.33117i	−0.301040	−	0.0978137i
$569$	−10.0290	+	30.8660i	−0.420436	+	1.29397i	0.486861	+	0.873480i	$0.338142\pi$
$569$	−10.0290	+	30.8660i	−0.420436	+	1.29397i	−0.907297	+	0.420490i	$0.861858\pi$
$570$	−1.36525	−	37.6825i	−0.0571840	−	1.57835i
$571$	5.81844	+	1.89053i	0.243494	+	0.0791161i	0.428222	−	0.903674i	$-0.359140\pi$
$571$	5.81844	+	1.89053i	0.243494	+	0.0791161i	−0.184727	+	0.982790i	$0.559140\pi$
$572$	−5.82010	−	8.01068i	−0.243351	−	0.334943i
$573$	−31.2231	−	21.0009i	−1.30436	−	0.877324i
$574$	3.17823	−	4.37445i	0.132657	−	0.182586i
$575$	−1.35089			−0.0563361
$576$	26.5870	+	16.5168i	1.10779	+	0.688202i
$577$	7.55367	−	10.3967i	0.314463	−	0.432822i	−0.622303	−	0.782776i	$-0.713803\pi$
$577$	7.55367	−	10.3967i	0.314463	−	0.432822i	0.936767	+	0.349954i	$0.113803\pi$
$578$	−29.5413	−	90.9187i	−1.22876	−	3.78172i
$579$	−17.6386	+	0.639051i	−0.733035	+	0.0265580i
$580$	−17.0778	−	23.5056i	−0.709118	−	0.976017i
$581$	−7.57099	+	23.3011i	−0.314098	+	0.966693i
$582$	5.10985	−	7.59708i	0.211810	−	0.314909i
$583$	18.3256			0.758970
$584$	−2.12702	+	1.54537i	−0.0880167	+	0.0639479i
$585$	−2.00139	+	3.22162i	−0.0827475	+	0.133198i
$586$	−43.9780	+	14.2893i	−1.81672	+	0.590287i
$587$	−21.2894	−	15.4676i	−0.878706	−	0.638417i	0.0542030	−	0.998530i	$-0.482738\pi$
$587$	−21.2894	−	15.4676i	−0.878706	−	0.638417i	−0.932909	+	0.360113i	$0.882738\pi$
$588$	−7.01233	+	5.49341i	−0.289183	+	0.226545i
$589$	9.71789	−	3.15753i	0.400419	−	0.130104i
$590$	−19.2593			−0.792891
$591$	−7.99690	+	6.26473i	−0.328949	+	0.257696i
$592$	5.24635	+	3.81169i	0.215624	+	0.156660i
$593$			1.56950i			0.0644517i	0.999481	+	0.0322259i	$0.0102596\pi$
$593$			1.56950i			0.0644517i	−0.999481	+	0.0322259i	$0.989740\pi$
$594$	−33.5694	+	58.6743i	−1.37737	+	2.40744i
$595$	32.3915			1.32792
$596$	−34.5135	+	25.0755i	−1.41373	+	1.02713i
$597$	1.98995	−	1.55892i	0.0814434	−	0.0638023i
$598$	0.386673	−	1.19006i	0.0158122	−	0.0486650i
$599$	17.2747			0.705827			0.352913	−	0.935656i	$-0.385191\pi$
$599$	17.2747			0.705827			0.352913	+	0.935656i	$0.385191\pi$
$600$	−1.85470	+	0.0671962i	−0.0757177	+	0.00274327i
$601$	22.5603			0.920255			0.460128	−	0.887853i	$-0.347804\pi$
$601$	22.5603			0.920255			0.460128	+	0.887853i	$0.347804\pi$
$602$		−	39.3132i		−	1.60228i
$603$	−35.6726	−	8.79512i	−1.45270	−	0.358165i
$604$	−4.21395	−	12.9692i	−0.171463	−	0.527709i
$605$	49.6771	+	16.1411i	2.01966	+	0.656228i
$606$	65.2633	−	23.8506i	2.65114	−	0.968864i
$607$	−9.51872			−0.386353			−0.193176	−	0.981164i	$-0.561879\pi$
$607$	−9.51872			−0.386353			−0.193176	+	0.981164i	$0.561879\pi$
$608$	−14.0241	−	43.1618i	−0.568753	−	1.75044i
$609$	24.3310	+	6.94237i	0.985940	+	0.281319i
$610$	−7.76293	+	23.8918i	−0.314312	+	0.967352i
$611$	0.643763	+	0.886064i	0.0260439	+	0.0358463i
$612$	47.2409	+	29.3479i	1.90960	+	1.18632i
$613$	−33.3310	+	10.8299i	−1.34622	+	0.437415i	−0.891421	−	0.453177i	$-0.850291\pi$
$613$	−33.3310	+	10.8299i	−1.34622	+	0.437415i	−0.454804	+	0.890592i	$0.650291\pi$
$614$	−9.84393	−	30.2965i	−0.397269	−	1.22267i
$615$	−2.13556	+	3.17505i	−0.0861141	+	0.128030i
$616$	−2.97179	−	9.14623i	−0.119737	−	0.368512i
$617$	−0.858925	−	2.64350i	−0.0345790	−	0.106423i	0.932277	−	0.361745i	$-0.117819\pi$
$617$	−0.858925	−	2.64350i	−0.0345790	−	0.106423i	−0.966856	+	0.255321i	$0.917819\pi$
$618$	−17.7326	+	0.642458i	−0.713311	+	0.0258435i
$619$		−	15.3577i		−	0.617277i	−0.951179	−	0.308639i	$-0.900127\pi$
$619$		−	15.3577i		−	0.617277i	0.951179	−	0.308639i	$-0.0998734\pi$
$620$	2.45368	+	7.55164i	0.0985421	+	0.303281i
$621$	−4.57641	+	0.499161i	−0.183645	+	0.0200307i
$622$	−20.2801	+	27.9132i	−0.813159	+	1.11922i
$623$	−8.43590	−	11.6110i	−0.337977	−	0.465186i
$624$	−1.03497	+	3.62728i	−0.0414321	+	0.145207i
$625$	12.1766	−	8.84680i	0.487063	−	0.353872i
$626$	36.1777	−	11.7548i	1.44595	−	0.469818i
$627$	56.9820	−	20.8242i	2.27564	−	0.831638i
$628$	−9.41583	+	12.9598i	−0.375733	+	0.517151i
$629$	12.9571	+	9.41387i	0.516633	+	0.375356i
$630$	−19.5045	+	16.4533i	−0.777076	+	0.655516i
$631$	2.87217	−	8.83962i	0.114339	−	0.351900i	−0.877469	−	0.479632i	$-0.840770\pi$
$631$	2.87217	−	8.83962i	0.114339	−	0.351900i	0.991809	+	0.127733i	$0.0407700\pi$
$632$	9.84647			0.391672
$633$	−0.549086	−	25.1535i	−0.0218242	−	0.999762i
$634$	52.3128			2.07761
$635$	0.304146	−	0.936066i	0.0120697	−	0.0371466i
$636$	7.32460	+	9.34983i	0.290439	+	0.370745i
$637$	−1.20717	−	0.877061i	−0.0478299	−	0.0347504i
$638$	50.9872	−	70.1779i	2.01860	−	2.77837i
$639$	−29.8285	+	12.1423i	−1.18000	+	0.480343i
$640$	9.82537	−	3.19246i	0.388382	−	0.126193i
$641$	0.824405	−	0.598966i	0.0325621	−	0.0236577i	−0.571385	−	0.820682i	$-0.693594\pi$
$641$	0.824405	−	0.598966i	0.0325621	−	0.0236577i	0.603947	+	0.797024i	$0.293594\pi$
$642$	39.8254	+	11.3634i	1.57178	+	0.448478i
$643$	8.91286	+	12.2675i	0.351489	+	0.483783i	0.947753	−	0.319005i	$-0.103349\pi$
$643$	8.91286	+	12.2675i	0.351489	+	0.483783i	−0.596264	+	0.802788i	$0.703349\pi$
$644$	2.66670	−	3.67040i	0.105083	−	0.144634i
$645$	1.00728	+	27.8023i	0.0396618	+	1.09471i
$646$	−28.6212	−	88.0871i	−1.12609	−	3.46574i
$647$		−	43.4836i		−	1.70952i	−0.519025	−	0.854759i	$-0.673705\pi$
$647$		−	43.4836i		−	1.70952i	0.519025	−	0.854759i	$-0.326295\pi$
$648$	−6.25831	+	0.912959i	−0.245850	+	0.0358644i
$649$	−9.57538	−	29.4700i	−0.375867	−	1.15680i
$650$	−0.665491	−	2.04817i	−0.0261027	−	0.0803359i
$651$	−5.73764	−	3.85918i	−0.224876	−	0.151253i
$652$	−5.13747	−	15.8115i	−0.201199	−	0.619226i
$653$	−17.7393	+	5.76386i	−0.694194	+	0.225557i	−0.634799	−	0.772677i	$-0.718917\pi$
$653$	−17.7393	+	5.76386i	−0.694194	+	0.225557i	−0.0593950	+	0.998235i	$0.518917\pi$
$654$	−28.8670	−	19.4162i	−1.12879	−	0.759232i
$655$	−10.1229	−	13.9329i	−0.395533	−	0.544405i
$656$	−1.17600	+	3.61935i	−0.0459150	+	0.141312i
$657$	−2.68684	+	10.8977i	−0.104824	+	0.425159i
$658$	2.27709	+	7.00815i	0.0887700	+	0.273206i
$659$	25.5181			0.994044			0.497022	−	0.867738i	$-0.334427\pi$
$659$	25.5181			0.994044			0.497022	+	0.867738i	$0.334427\pi$
$660$	16.1822	+	44.2800i	0.629891	+	1.72359i
$661$	−20.1520	−	6.54778i	−0.783821	−	0.254679i	−0.110350	−	0.993893i	$-0.535197\pi$
$661$	−20.1520	−	6.54778i	−0.783821	−	0.254679i	−0.673471	+	0.739214i	$0.735197\pi$
$662$	9.58296	+	29.4933i	0.372452	+	1.14629i
$663$	−2.55611	+	8.95842i	−0.0992711	+	0.347916i
$664$			7.85867i			0.304976i
$665$	22.9011			0.888067
$666$	−12.5839	+	0.913033i	−0.487615	+	0.0353793i
$667$	5.90741			0.228736
$668$	11.6799	−	35.9470i	0.451909	−	1.39083i
$669$	−10.2099	−	13.0328i	−0.394736	−	0.503879i
$670$	−38.4673	+	27.9481i	−1.48612	+	1.07973i
$671$	−40.4182			−1.56033
$672$	−17.1405	+	25.4836i	−0.661207	+	0.983051i
$673$		−	3.50620i		−	0.135154i	−0.997714	−	0.0675770i	$-0.978473\pi$
$673$		−	3.50620i		−	0.135154i	0.997714	−	0.0675770i	$-0.0215268\pi$
$674$	8.59340	+	6.24347i	0.331005	+	0.240489i
$675$	−5.86712	+	5.32461i	−0.225826	+	0.204944i
$676$	−29.3115			−1.12736
$677$	5.03861	−	1.63714i	0.193650	−	0.0629206i	−0.210587	−	0.977575i	$-0.567537\pi$
$677$	5.03861	−	1.63714i	0.193650	−	0.0629206i	0.404236	+	0.914655i	$0.367537\pi$
$678$	−17.1474	−	21.8886i	−0.658543	−	0.840628i
$679$	4.49862	+	3.26844i	0.172641	+	0.125431i
$680$	9.88135	−	3.21064i	0.378932	−	0.123123i
$681$	23.9238	−	35.5687i	0.916761	−	1.36300i
$682$	−19.1788	+	13.9342i	−0.734395	+	0.533569i
$683$	−32.7798			−1.25429			−0.627143	−	0.778904i	$-0.715776\pi$
$683$	−32.7798			−1.25429			−0.627143	+	0.778904i	$0.715776\pi$
$684$	33.3998	+	20.7493i	1.27707	+	0.793368i
$685$	−10.6565	+	32.7973i	−0.407163	+	1.25312i
$686$	−24.6742	−	33.9612i	−0.942066	−	1.29664i
$687$	−0.684332	−	18.8884i	−0.0261089	−	0.720638i
$688$	8.55023	+	26.3149i	0.325975	+	1.00325i
$689$	−1.16942	+	1.60957i	−0.0445514	+	0.0613198i
$690$	−3.32503	+	4.94350i	−0.126582	+	0.188196i
$691$	16.2518			0.618246			0.309123	−	0.951022i	$-0.399965\pi$
$691$	16.2518			0.618246			0.309123	+	0.951022i	$0.399965\pi$
$692$	−15.6932	+	21.5999i	−0.596567	+	0.821105i
$693$	−34.8737	−	21.6649i	−1.32474	−	0.822981i
$694$	−0.194804	−	0.268124i	−0.00739465	−	0.0101779i
$695$	17.2189	+	5.59475i	0.653149	+	0.212221i
$696$	8.11053	−	0.293847i	0.307429	−	0.0111382i
$697$	−2.90440	+	8.93882i	−0.110012	+	0.338582i
$698$	−36.6191	−	11.8983i	−1.38605	−	0.450356i
$699$	−2.05677	+	7.20838i	−0.0777942	+	0.272646i
$700$		−	7.80827i		−	0.295125i
$701$	−0.244773	+	0.753332i	−0.00924493	+	0.0284530i	−0.955573	−	0.294756i	$-0.904762\pi$
$701$	−0.244773	+	0.753332i	−0.00924493	+	0.0284530i	0.946328	+	0.323209i	$0.104762\pi$
$702$	−3.01129	−	6.69267i	−0.113654	−	0.252599i
$703$	9.16080	+	6.65571i	0.345506	+	0.251025i
$704$	38.3070	+	52.7251i	1.44375	+	1.98715i
$705$	−1.78992	−	4.89782i	−0.0674122	−	0.184463i
$706$	−33.2832			−1.25263
$707$	13.0408	+	40.1355i	0.490450	+	1.50945i
$708$	11.2085	−	16.6643i	0.421243	−	0.626283i
$709$	−11.0935	+	34.1423i	−0.416626	+	1.28224i	0.494163	+	0.869370i	$0.335475\pi$
$709$	−11.0935	+	34.1423i	−0.416626	+	1.28224i	−0.910789	+	0.412873i	$0.864525\pi$
$710$	−12.8793	+	39.6385i	−0.483352	+	1.48761i
$711$	32.1302	−	27.1039i	1.20498	−	1.01648i
$712$	−3.72434	−	2.70589i	−0.139576	−	0.101408i
$713$	−1.53541	−	0.498886i	−0.0575016	−	0.0186834i
$714$	−34.9812	+	52.0084i	−1.30914	+	1.94637i
$715$	−6.38886	+	4.64178i	−0.238930	+	0.173593i
$716$	−18.9209	+	26.0425i	−0.707109	+	0.973252i
$717$	−14.8588	−	40.6588i	−0.554913	−	1.51843i
$718$	36.0510	+	11.7137i	1.34541	+	0.437151i
$719$	−5.67924	+	17.4789i	−0.211800	+	0.651853i	0.787565	+	0.616231i	$0.211341\pi$
$719$	−5.67924	+	17.4789i	−0.211800	+	0.651853i	−0.999365	+	0.0356221i	$0.988659\pi$
$720$	9.47720	−	15.2553i	0.353194	−	0.568533i
$721$		−	10.7768i		−	0.401349i
$722$	−8.00761	−	24.6449i	−0.298012	−	0.917188i
$723$	3.97793	+	10.8850i	0.147941	+	0.404816i
$724$	−13.0689	−	17.9878i	−0.485702	−	0.668511i
$725$	8.22534	−	5.97606i	0.305482	−	0.221945i
$726$	−79.5653	+	62.3309i	−2.95294	+	2.31332i
$727$			22.0733i			0.818652i	0.912388	+	0.409326i	$0.134236\pi$
$727$			22.0733i			0.818652i	−0.912388	+	0.409326i	$0.865764\pi$
$728$	0.992970	+	0.322636i	0.0368019	+	0.0119577i
$729$	−17.9085	+	20.2061i	−0.663279	+	0.748373i
$730$	8.53791	+	11.7514i	0.316002	+	0.434940i
$731$	21.1168	+	64.9909i	0.781034	+	2.40377i
$732$	−16.1548	−	20.6216i	−0.597100	−	0.762196i
$733$	6.20935	−	19.1104i	0.229348	−	0.705859i	−0.768474	−	0.639882i	$-0.778983\pi$
$733$	6.20935	−	19.1104i	0.229348	−	0.705859i	0.997821	−	0.0659776i	$-0.0210166\pi$
$734$		−	13.0848i		−	0.482969i
$735$	4.38123	+	5.59263i	0.161604	+	0.206287i
$736$	−2.21579	+	6.81949i	−0.0816750	+	0.251370i
$737$	−61.8907	−	44.9662i	−2.27977	−	1.65635i
$738$	−2.79162	−	6.85779i	−0.102761	−	0.252439i
$739$	7.16552	−	2.32822i	0.263588	−	0.0856449i	−0.174242	−	0.984703i	$-0.555747\pi$
$739$	7.16552	−	2.32822i	0.263588	−	0.0856449i	0.437829	+	0.899058i	$0.355747\pi$
$740$	−5.17206	+	7.11873i	−0.190129	+	0.261690i
$741$	−1.80720	+	6.33369i	−0.0663890	+	0.232674i
$742$	−10.8293	+	7.86794i	−0.397556	+	0.288841i
$743$	41.1142			1.50833			0.754167	−	0.656682i	$-0.228041\pi$
$743$	41.1142			1.50833			0.754167	+	0.656682i	$0.228041\pi$
$744$	−2.13285	−	0.608566i	−0.0781940	−	0.0223111i
$745$	19.9988	+	27.5260i	0.732699	+	1.00847i
$746$	37.2853	−	12.1147i	1.36511	−	0.443551i
$747$	21.6322	+	25.6438i	0.791481	+	0.938256i
$748$	68.0657	+	93.6843i	2.48873	+	3.42544i
$749$	−7.77267	+	23.9218i	−0.284007	+	0.874084i
$750$	1.58862	+	43.8479i	0.0580082	+	1.60110i
$751$	−20.0230	−	27.5592i	−0.730648	−	1.00565i	−0.999102	−	0.0423586i	$-0.986513\pi$
$751$	−20.0230	−	27.5592i	−0.730648	−	1.00565i	0.268454	−	0.963292i	$-0.413487\pi$
$752$	−3.04841	−	4.19578i	−0.111164	−	0.153004i
$753$	17.1208	−	13.4124i	0.623918	−	0.488773i
$754$	2.91017	+	8.95660i	0.105982	+	0.326180i
$755$	−10.3435	+	3.36080i	−0.376438	+	0.122312i
$756$	−2.88519	−	26.4520i	−0.104934	−	0.962051i
$757$	10.3245	−	14.2104i	0.375249	−	0.516487i	−0.579069	−	0.815279i	$-0.696584\pi$
$757$	10.3245	−	14.2104i	0.375249	−	0.516487i	0.954318	+	0.298792i	$0.0965837\pi$
$758$	9.11279	+	2.96093i	0.330992	+	0.107546i
$759$	−9.21756	−	2.63005i	−0.334576	−	0.0954648i
$760$	6.98622	−	2.26996i	0.253417	−	0.0823401i
$761$	−24.0755	−	17.4919i	−0.872737	−	0.634081i	0.0585830	−	0.998283i	$-0.481342\pi$
$761$	−24.0755	−	17.4919i	−0.872737	−	0.634081i	−0.931320	+	0.364202i	$0.881342\pi$
$762$	1.17450	+	1.49925i	0.0425477	+	0.0543120i
$763$	12.4193	−	17.0936i	0.449607	−	0.618831i
$764$	15.6920	−	48.2949i	0.567715	−	1.74725i
$765$	23.4062	−	37.6766i	0.846252	−	1.36220i
$766$	39.9301	+	54.9591i	1.44273	+	1.98575i
$767$	3.19944	+	1.03956i	0.115525	+	0.0375364i
$768$	4.43154	−	15.5312i	0.159909	−	0.560435i
$769$	19.9732	+	14.5114i	0.720252	+	0.523294i	0.886465	−	0.462796i	$-0.153154\pi$
$769$	19.9732	+	14.5114i	0.720252	+	0.523294i	−0.166212	+	0.986090i	$0.553154\pi$
$770$	−50.5314	+	16.4186i	−1.82103	+	0.591687i
$771$	1.78500	+	49.2683i	0.0642853	+	1.77435i
$772$	−7.36050	−	22.6533i	−0.264910	−	0.815310i
$773$	−42.3441	+	30.7648i	−1.52301	+	1.10653i	−0.563042	+	0.826429i	$0.690369\pi$
$773$	−42.3441	+	30.7648i	−1.52301	+	1.10653i	−0.959970	+	0.280104i	$0.909631\pi$
$774$	−45.7277	−	28.4078i	−1.64365	−	1.02110i
$775$	−2.64255	+	0.858618i	−0.0949234	+	0.0308425i
$776$	1.69632	+	0.551167i	0.0608943	+	0.0197857i
$777$	−0.277443	−	7.65776i	−0.00995320	−	0.274720i
$778$	63.9538	+	20.7798i	2.29285	+	0.744994i
$779$	−2.05344	+	6.31984i	−0.0735722	+	0.226432i
$780$	−4.92183	−	1.40435i	−0.176230	−	0.0502837i
$781$	−67.0571			−2.39949
$782$	−4.52211	+	13.9176i	−0.161710	+	0.497693i
$783$	25.6567	−	23.2844i	0.916897	−	0.832115i
$784$	5.71632	+	4.15315i	0.204154	+	0.148327i
$785$	10.3360	+	7.50952i	0.368907	+	0.268026i
$786$	33.3032	−	1.20658i	1.18789	−	0.0430374i
$787$	22.4503	+	16.3111i	0.800268	+	0.581429i	0.910993	−	0.412423i	$-0.135317\pi$
$787$	22.4503	+	16.3111i	0.800268	+	0.581429i	−0.110725	+	0.993851i	$0.535317\pi$
$788$	−11.0909	−	8.05803i	−0.395098	−	0.287055i
$789$	−27.1883	+	9.93603i	−0.967930	+	0.353732i
$790$		−	54.4001i		−	1.93547i
$791$	13.6622	−	9.92616i	0.485771	−	0.352934i
$792$	−12.7860	−	3.15241i	−0.454331	−	0.112016i
$793$	2.57923	−	3.55001i	0.0915911	−	0.126064i
$794$			15.2750i			0.542088i
$795$	7.45688	−	5.84168i	0.264468	−	0.207183i
$796$	2.75987	+	2.00517i	0.0978212	+	0.0710712i
$797$	1.35069	+	4.15700i	0.0478440	+	0.147249i	0.972124	−	0.234465i	$-0.0753339\pi$
$797$	1.35069	+	4.15700i	0.0478440	+	0.147249i	−0.924280	+	0.381714i	$0.875334\pi$
$798$	−24.7321	+	36.7705i	−0.875507	+	1.30166i
$799$	−7.52876	−	10.3625i	−0.266349	−	0.366597i
$800$	3.81353	+	11.7368i	0.134829	+	0.414960i
$801$	−19.6013	+	1.42219i	−0.692579	+	0.0502506i
$802$	22.8812	−	16.6241i	0.807962	−	0.587019i
$803$	−13.7368	+	18.9071i	−0.484761	+	0.667217i
$804$	−1.79519	−	49.5496i	−0.0633116	−	1.74748i
$805$	−2.92730	−	2.12681i	−0.103174	−	0.0749601i
$806$		−	2.57370i		−	0.0906547i
$807$	−10.9098	−	13.9263i	−0.384043	−	0.490230i
$808$	7.95646	+	10.9511i	0.279907	+	0.385259i
$809$	−12.6567	−	4.11241i	−0.444986	−	0.144585i	0.0779490	−	0.996957i	$-0.475163\pi$
$809$	−12.6567	−	4.11241i	−0.444986	−	0.144585i	−0.522935	+	0.852373i	$0.675163\pi$
$810$	5.04395	+	34.5761i	0.177226	+	1.21488i
$811$	−20.0438			−0.703831			−0.351916	−	0.936032i	$-0.614470\pi$
$811$	−20.0438			−0.703831			−0.351916	+	0.936032i	$0.614470\pi$
$812$			34.1453i			1.19827i
$813$	−1.36092	−	37.5631i	−0.0477296	−	1.31740i
$814$	−24.9850	−	8.11813i	−0.875725	−	0.284540i
$815$	−12.6103	+	4.09735i	−0.441721	+	0.143524i
$816$	12.1039	−	42.4208i	0.423723	−	1.48502i
$817$	14.9298	+	45.9492i	0.522328	+	1.60756i
$818$			5.62574i			0.196699i
$819$	4.12828	−	1.68051i	0.144254	−	0.0587217i
$820$	−4.91107	−	1.59570i	−0.171502	−	0.0557243i
$821$	47.5760	+	15.4584i	1.66041	+	0.539501i	0.980959	−	0.194215i	$-0.0622160\pi$
$821$	47.5760	+	15.4584i	1.66041	+	0.539501i	0.679456	+	0.733717i	$0.262216\pi$
$822$	−41.1515	−	52.5297i	−1.43532	−	1.83218i
$823$	−1.40984	+	1.94048i	−0.0491439	+	0.0676407i	−0.832882	−	0.553451i	$-0.813311\pi$
$823$	−1.40984	+	1.94048i	−0.0491439	+	0.0676407i	0.783738	+	0.621092i	$0.213311\pi$
$824$	−1.06820	−	3.28757i	−0.0372124	−	0.114528i
$825$	−15.4949	+	5.66265i	−0.539464	+	0.197148i
$826$	18.3111	+	13.3038i	0.637125	+	0.462898i
$827$	22.7379	−	7.38800i	0.790676	−	0.256906i	0.114284	−	0.993448i	$-0.463543\pi$
$827$	22.7379	−	7.38800i	0.790676	−	0.256906i	0.676392	+	0.736542i	$0.263543\pi$
$828$	−2.34232	−	5.75406i	−0.0814011	−	0.199967i
$829$	46.4965			1.61489			0.807444	−	0.589944i	$-0.200850\pi$
$829$	46.4965			1.61489			0.807444	+	0.589944i	$0.200850\pi$
$830$	43.4179			1.50706
$831$	−1.96470	−	5.37608i	−0.0681547	−	0.186494i
$832$	−7.07544			−0.245297
$833$	14.1178	+	10.2572i	0.489152	+	0.355390i
$834$	−27.5786	+	21.6049i	−0.954968	+	0.748116i
$835$	−28.6693	−	9.31521i	−0.992141	−	0.322366i
$836$	48.1231	+	66.2358i	1.66437	+	2.29081i
$837$	−8.63490	+	3.88517i	−0.298466	+	0.134291i
$838$	−42.0869	+	13.6749i	−1.45387	+	0.472390i
$839$	32.3288	+	23.4883i	1.11612	+	0.810905i	0.983616	−	0.180278i	$-0.0576997\pi$
$839$	32.3288	+	23.4883i	1.11612	+	0.810905i	0.132500	+	0.991183i	$0.457700\pi$
$840$	−4.12480	−	2.77437i	−0.142319	−	0.0957250i
$841$	−12.5077	+	9.08736i	−0.431299	+	0.313357i
$842$	36.2258	+	11.7705i	1.24842	+	0.405637i
$843$	1.25604	+	34.6683i	0.0432603	+	1.19404i
$844$	32.4388	−	10.0264i	1.11659	−	0.345122i
$845$			23.3771i			0.804198i
$846$	9.79706	+	2.41548i	0.336830	+	0.0830459i
$847$	−36.0816	−	49.6621i	−1.23978	−	1.70641i
$848$	5.53756	−	7.62180i	0.190161	−	0.261734i
$849$	−12.6413	+	18.7944i	−0.433848	+	0.645024i
$850$	7.78288	+	23.9532i	0.266950	+	0.821589i
$851$	−0.552854	−	1.70151i	−0.0189516	−	0.0583270i
$852$	−26.8022	−	34.2129i	−0.918227	−	1.17211i
$853$	−0.564845	+	1.73841i	−0.0193399	+	0.0595221i	−0.960261	−	0.279105i	$-0.909962\pi$
$853$	−0.564845	+	1.73841i	−0.0193399	+	0.0595221i	0.940921	+	0.338627i	$0.109962\pi$
$854$	23.8846	−	17.3532i	0.817315	−	0.593814i
$855$	16.5484	−	26.6378i	0.565944	−	0.910993i
$856$			8.06802i			0.275759i
$857$	−12.4604	+	4.04862i	−0.425639	+	0.138298i	−0.514000	−	0.857790i	$-0.671837\pi$
$857$	−12.4604	+	4.04862i	−0.425639	+	0.138298i	0.0883615	+	0.996088i	$0.471837\pi$
$858$	−0.553271	−	15.2710i	−0.0188884	−	0.521342i
$859$		−	8.47386i		−	0.289124i	−0.989496	−	0.144562i	$-0.953823\pi$
$859$		−	8.47386i		−	0.289124i	0.989496	−	0.144562i	$-0.0461774\pi$
$860$	−35.7065	+	11.6018i	−1.21758	+	0.395617i
$861$	4.22367	−	1.54355i	0.143942	−	0.0526039i
$862$	−14.6008	+	20.0963i	−0.497307	+	0.684484i
$863$	−24.4096	+	7.93117i	−0.830913	+	0.269980i	−0.693430	−	0.720524i	$-0.743901\pi$
$863$	−24.4096	+	7.93117i	−0.830913	+	0.269980i	−0.137483	+	0.990504i	$0.543901\pi$
$864$	17.2559	+	38.3517i	0.587057	+	1.30475i
$865$	17.2268	+	12.5160i	0.585730	+	0.425558i
$866$	−57.1536	+	41.5245i	−1.94216	+	1.41106i
$867$	21.8144	−	76.4532i	0.740857	−	2.59649i
$868$	2.88360	−	8.87481i	0.0978758	−	0.301231i
$869$	83.2416	−	27.0468i	2.82378	−	0.917501i
$870$	−1.62345	−	44.8093i	−0.0550403	−	1.51918i
$871$	7.89892	−	2.56652i	0.267645	−	0.0869631i
$872$	2.09430	−	6.44558i	0.0709218	−	0.218275i
$873$	7.05245	−	2.87086i	0.238689	−	0.0971638i
$874$	−3.19718	+	9.83990i	−0.108146	+	0.332840i
$875$	−26.6480			−0.900868
$876$	−15.1370	+	0.548417i	−0.511431	+	0.0185293i
$877$		−	27.9615i		−	0.944193i	−0.881547	−	0.472097i	$-0.843497\pi$
$877$		−	27.9615i		−	0.944193i	0.881547	−	0.472097i	$-0.156503\pi$
$878$			35.6365i			1.20267i
$879$	−36.9810	−	10.5518i	−1.24734	−	0.355903i
$880$	30.2531	−	21.9802i	1.01983	−	0.740952i
$881$	−14.2942	−	19.6742i	−0.481583	−	0.662842i	0.497225	−	0.867621i	$-0.334352\pi$
$881$	−14.2942	−	19.6742i	−0.481583	−	0.662842i	−0.978808	+	0.204780i	$0.934352\pi$
$882$	−13.7111	+	0.994823i	−0.461678	+	0.0334974i
$883$	22.3620	−	30.7787i	0.752542	−	1.03578i	−0.245256	−	0.969458i	$-0.578872\pi$
$883$	22.3620	−	30.7787i	0.752542	−	1.03578i	0.997798	−	0.0663264i	$-0.0211279\pi$
$884$	−12.5720			−0.422841
$885$	−13.2905	−	8.93928i	−0.446755	−	0.300491i
$886$	−34.5104	−	47.4994i	−1.15940	−	1.59577i
$887$			0.0426642i			0.00143252i	1.00000		0.000716262i	$0.000227993\pi$
$887$			0.0426642i			0.00143252i	−1.00000		0.000716262i	$0.999772\pi$
$888$	−0.843674	−	2.30858i	−0.0283118	−	0.0774707i
$889$	−0.935783	+	0.679886i	−0.0313852	+	0.0228027i
$890$	−14.9496	+	20.5763i	−0.501112	+	0.689721i
$891$	−50.3997	+	24.9088i	−1.68845	+	0.834476i
$892$	13.1325	−	18.0753i	0.439708	−	0.605206i
$893$	−5.32292	−	7.32637i	−0.178125	−	0.245167i
$894$	−65.7939	+	2.38373i	−2.20048	+	0.0797239i
$895$	20.7700	+	15.0903i	0.694263	+	0.504412i
$896$	−11.5469	−	3.75183i	−0.385756	−	0.125340i
$897$	0.819207	−	0.641762i	0.0273525	−	0.0214278i
$898$	27.7346			0.925516
$899$	11.5558	−	3.75471i	0.385408	−	0.125227i
$900$	−9.08231	−	5.64228i	−0.302744	−	0.188076i
$901$	13.6763	−	18.8238i	0.455624	−	0.627113i
$902$		−	15.4169i		−	0.513328i
$903$	18.2474	−	27.1294i	0.607236	−	0.902809i
$904$	3.18391	−	4.38227i	0.105895	−	0.145752i
$905$	−14.3460	+	10.4230i	−0.476878	+	0.346472i
$906$	5.77429	−	20.2372i	0.191838	−	0.672336i
$907$		−	21.7404i		−	0.721880i	−0.932589	−	0.360940i	$-0.882456\pi$
$907$		−	21.7404i		−	0.721880i	0.932589	−	0.360940i	$-0.117544\pi$
$908$	55.0166	+	17.8760i	1.82579	+	0.593235i
$909$	56.1075	+	13.8334i	1.86097	+	0.458824i
$910$	1.78251	−	5.48599i	0.0590895	−	0.181859i
$911$	13.3486			0.442259			0.221130	−	0.975244i	$-0.429026\pi$
$911$	13.3486			0.442259			0.221130	+	0.975244i	$0.429026\pi$
$912$	8.55761	−	29.9919i	0.283371	−	0.993132i
$913$	21.5866	+	66.4368i	0.714413	+	2.19874i
$914$	−1.55070	+	2.13435i	−0.0512925	+	0.0705981i
$915$	−16.4466	+	12.8842i	−0.543708	+	0.425937i
$916$	24.2584	−	7.88204i	0.801521	−	0.260430i
$917$			20.2396i			0.668372i
$918$	35.2168	+	78.2703i	1.16233	+	2.58331i
$919$	−12.8835	+	17.7326i	−0.424987	+	0.584944i	−0.966793	−	0.255559i	$-0.917740\pi$
$919$	−12.8835	+	17.7326i	−0.424987	+	0.584944i	0.541807	+	0.840503i	$0.317740\pi$
$920$	−1.10381	−	0.358650i	−0.0363916	−	0.0118243i
$921$	7.26914	−	25.4762i	0.239526	−	0.839470i
$922$	24.2560	−	17.6230i	0.798828	−	0.580383i
$923$	4.27915	−	5.88974i	0.140850	−	0.193863i
$924$	15.2019	−	53.2783i	0.500107	−	1.75273i
$925$	−2.49107	−	1.80986i	−0.0819057	−	0.0595080i
$926$	45.6790	+	62.8717i	1.50110	+	2.06609i
$927$	−12.5352	−	7.78735i	−0.411710	−	0.255770i
$928$	−16.6765	−	51.3249i	−0.547432	−	1.68482i
$929$	−0.893573	+	2.75013i	−0.0293172	+	0.0902290i	−0.964644	−	0.263555i	$-0.915105\pi$
$929$	−0.893573	+	2.75013i	−0.0293172	+	0.0902290i	0.935327	+	0.353784i	$0.115105\pi$
$930$	−3.36223	+	11.7836i	−0.110252	+	0.386400i
$931$	9.98142	+	7.25193i	0.327128	+	0.237672i
$932$	−10.1160			−0.331361
$933$	−26.9510	+	9.84932i	−0.882338	+	0.322452i
$934$	35.2366	−	11.4491i	1.15298	−	0.374624i
$935$	74.7172	−	54.2852i	2.44351	−	1.77532i
$936$	1.09280	−	0.921851i	0.0357193	−	0.0301316i
$937$	43.4202	−	31.5466i	1.41848	−	1.03058i	0.426455	−	0.904509i	$-0.359762\pi$
$937$	43.4202	−	31.5466i	1.41848	−	1.03058i	0.992021	−	0.126074i	$-0.0402376\pi$
$938$	55.8793			1.82452
$939$	30.4217	+	8.68023i	0.992774	+	0.283269i
$940$	5.69322	−	4.13637i	0.185692	−	0.134913i
$941$	−8.25926	+	6.00070i	−0.269244	+	0.195617i	−0.714212	−	0.699929i	$-0.753215\pi$
$941$	−8.25926	+	6.00070i	−0.269244	+	0.195617i	0.444968	+	0.895546i	$0.353215\pi$
$942$	−23.2198	+	8.48572i	−0.756541	+	0.276480i
$943$	0.849396	−	0.617123i	0.0276602	−	0.0200963i
$944$	−15.1503	−	4.92263i	−0.493100	−	0.160218i
$945$	−21.0966	+	2.30106i	−0.686273	+	0.0748536i
$946$	−65.8853	−	90.6834i	−2.14212	−	2.94837i
$947$	41.7301	+	13.5589i	1.35605	+	0.440606i	0.894721	−	0.446626i	$-0.147374\pi$
$947$	41.7301	+	13.5589i	1.35605	+	0.440606i	0.461324	+	0.887232i	$0.347374\pi$
$948$	47.0704	+	31.6599i	1.52878	+	1.02827i
$949$	−0.784049	−	2.41306i	−0.0254513	−	0.0783311i
$950$	5.50258	+	16.9352i	0.178527	+	0.549450i
$951$	36.1002	+	24.2813i	1.17063	+	0.787374i
$952$	−11.6127	−	3.77320i	−0.376370	−	0.122290i
$953$	30.9487	+	42.5972i	1.00253	+	1.37986i	0.923762	+	0.382967i	$0.125098\pi$
$953$	30.9487	+	42.5972i	1.00253	+	1.37986i	0.0787650	+	0.996893i	$0.474902\pi$
$954$	1.32644	+	18.2816i	0.0429450	+	0.591890i
$955$	−38.5172	−	12.5150i	−1.24639	−	0.404976i
$956$	47.2617	−	34.3376i	1.52855	−	1.11056i
$957$	67.7589	−	24.7626i	2.19033	−	0.800462i
$958$	50.4389	−	36.6460i	1.62961	−	1.18398i
$959$	32.7874	−	23.8214i	1.05876	−	0.769234i
$960$	32.3947	+	9.24321i	1.04554	+	0.298323i
$961$	27.6794			0.892884
$962$	2.30741	−	1.67643i	0.0743940	−	0.0540504i
$963$	22.2085	+	26.3269i	0.715658	+	0.848371i
$964$	−12.6527	+	9.19270i	−0.407515	+	0.296077i
$965$	−18.0670	+	5.87031i	−0.581596	+	0.188972i
$966$	6.57619	−	2.40328i	0.211585	−	0.0773243i
$967$	13.3031			0.427800			0.213900	−	0.976856i	$-0.431383\pi$
$967$	13.3031			0.427800			0.213900	+	0.976856i	$0.431383\pi$
$968$	−15.9296	−	11.5735i	−0.511996	−	0.371987i
$969$	21.1350	−	74.0721i	0.678955	−	2.37954i
$970$	3.04511	−	9.37187i	0.0977724	−	0.300913i
$971$	−0.641520	−	1.97439i	−0.0205873	−	0.0633613i	0.940235	−	0.340526i	$-0.110605\pi$
$971$	−0.641520	−	1.97439i	−0.0205873	−	0.0633613i	−0.960822	+	0.277165i	$0.910605\pi$
$972$	−32.8529	−	15.7583i	−1.05376	−	0.505449i
$973$	−12.5065	−	17.2137i	−0.400939	−	0.551845i
$974$	42.6911	+	31.0169i	1.36791	+	0.993847i
$975$	0.491425	−	1.72230i	0.0157382	−	0.0551578i
$976$	−12.2134	+	16.8103i	−0.390942	+	0.538086i
$977$	−17.3966	+	12.6394i	−0.556567	+	0.404370i	−0.830201	−	0.557464i	$-0.811774\pi$
$977$	−17.3966	+	12.6394i	−0.556567	+	0.404370i	0.273634	+	0.961834i	$0.411774\pi$
$978$	7.03977	−	24.6723i	0.225107	−	0.788934i
$979$	−38.9181	−	12.6452i	−1.24383	−	0.404144i
$980$	−5.63538	+	7.75643i	−0.180016	+	0.247770i
$981$	−10.9085	−	26.7975i	−0.348283	−	0.855580i
$982$			20.7020i			0.660629i
$983$	−3.16528	+	1.02846i	−0.100957	+	0.0328029i	−0.359060	−	0.933315i	$-0.616903\pi$
$983$	−3.16528	+	1.02846i	−0.100957	+	0.0328029i	0.258103	+	0.966117i	$0.416903\pi$
$984$	1.13548	−	0.889524i	0.0361976	−	0.0283570i
$985$	−6.42662	+	8.84548i	−0.204769	+	0.281841i
$986$	−34.0343	−	104.747i	−1.08387	−	3.33582i
$987$	−1.68149	+	5.89313i	−0.0535224	+	0.187580i
$988$	−8.88852			−0.282781
$989$	2.35889	−	7.25991i	0.0750082	−	0.230852i
$990$	−17.4165	+	70.6405i	−0.553533	+	2.24510i
$991$	2.39726	+	0.778917i	0.0761515	+	0.0247431i	0.346845	−	0.937922i	$-0.387253\pi$
$991$	2.39726	+	0.778917i	0.0761515	+	0.0247431i	−0.270694	+	0.962666i	$0.587253\pi$
$992$			14.7483i			0.468260i
$993$	−7.07643	+	24.8008i	−0.224564	+	0.787031i
$994$	39.6265	−	28.7903i	1.25688	−	0.913174i
$995$	1.59920	−	2.20112i	0.0506982	−	0.0697801i
$996$	−25.2684	+	37.5678i	−0.800660	+	1.19038i
$997$			55.9412i			1.77168i	0.463994	+	0.885838i	$0.346416\pi$
$997$			55.9412i			1.77168i	−0.463994	+	0.885838i	$0.653584\pi$
$998$	−1.23398	+	1.69842i	−0.0390609	+	0.0537627i
$999$	−9.10771	−	5.21080i	−0.288155	−	0.164863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.k.a.23.11	✓	272
3.2	odd	2	inner	633.2.k.a.23.58	yes	272
211.156	odd	10	inner	633.2.k.a.578.58	yes	272
633.578	even	10	inner	633.2.k.a.578.11	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.k.a.23.11	✓	272	1.1	even	1	trivial
633.2.k.a.23.58	yes	272	3.2	odd	2	inner
633.2.k.a.578.11	yes	272	633.578	even	10	inner
633.2.k.a.578.58	yes	272	211.156	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.643573 + 1.98072i) q^{2} +(-1.36348 + 1.06814i) q^{3} +(-1.89101 - 1.37390i) q^{4} +(-1.09574 + 1.50816i) q^{5} +(-1.23818 - 3.38809i) q^{6} +(2.08360 - 0.677003i) q^{7} +(0.568519 - 0.413053i) q^{8} +(0.718149 - 2.91278i) q^{9} +O(q^{10})\)	\(q+(-0.643573 + 1.98072i) q^{2} +(-1.36348 + 1.06814i) q^{3} +(-1.89101 - 1.37390i) q^{4} +(-1.09574 + 1.50816i) q^{5} +(-1.23818 - 3.38809i) q^{6} +(2.08360 - 0.677003i) q^{7} +(0.568519 - 0.413053i) q^{8} +(0.718149 - 2.91278i) q^{9} +(-2.28205 - 3.14097i) q^{10} +(3.67163 - 5.05357i) q^{11} +(4.04588 - 0.146583i) q^{12} +(0.209564 + 0.644972i) q^{13} +4.56272i q^{14} +(-0.116906 - 3.22676i) q^{15} +(-0.992348 - 3.05413i) q^{16} +(-2.45084 - 7.54290i) q^{17} +(5.30720 + 3.29703i) q^{18} +(-1.73277 - 5.33291i) q^{19} +(4.14413 - 1.34651i) q^{20} +(-2.11781 + 3.14866i) q^{21} +(7.64672 + 10.5248i) q^{22} +(-0.273775 + 0.842592i) q^{23} +(-0.333964 + 1.17045i) q^{24} +(0.471186 + 1.45016i) q^{25} -1.41238 q^{26} +(2.13207 + 4.73859i) q^{27} +(-4.87025 - 1.58244i) q^{28} +(-2.06048 - 6.34151i) q^{29} +(6.46653 + 1.84510i) q^{30} +1.82225i q^{31} +8.09348 q^{32} +(0.391731 + 10.8123i) q^{33} +16.5176 q^{34} +(-1.26206 + 3.88423i) q^{35} +(-5.35990 + 4.52143i) q^{36} +(-1.63371 + 1.18696i) q^{37} +11.6781 q^{38} +(-0.974657 - 0.655562i) q^{39} +1.31002i q^{40} +(-0.958737 - 0.696563i) q^{41} +(-4.87363 - 6.22117i) q^{42} -8.61616 q^{43} +(-13.8862 + 4.51190i) q^{44} +(3.60603 + 4.27474i) q^{45} +(-1.49274 - 1.08454i) q^{46} +(1.53596 - 0.499063i) q^{47} +(4.61529 + 3.10428i) q^{48} +(-1.78006 + 1.29329i) q^{49} -3.17560 q^{50} +(11.3985 + 7.66675i) q^{51} +(0.489839 - 1.50757i) q^{52} +(1.72440 + 2.37343i) q^{53} +(-10.7579 + 1.17340i) q^{54} +(3.59843 + 11.0748i) q^{55} +(0.904928 - 1.24553i) q^{56} +(8.05889 + 5.42047i) q^{57} +13.8868 q^{58} +(2.91576 - 4.01320i) q^{59} +(-4.21218 + 6.26246i) q^{60} +(-3.80326 - 5.23473i) q^{61} +(-3.60936 - 1.17275i) q^{62} +(-0.475621 - 6.55525i) q^{63} +(-3.22405 + 9.92260i) q^{64} +(-1.20235 - 0.390668i) q^{65} +(-21.6681 - 6.18257i) q^{66} -12.2469i q^{67} +(-5.72864 + 17.6309i) q^{68} +(-0.526721 - 1.44129i) q^{69} +(-6.88133 - 4.99958i) q^{70} +(-6.30991 - 8.68484i) q^{71} +(-0.794850 - 1.95260i) q^{72} -3.74134 q^{73} +(-1.29962 - 3.99981i) q^{74} +(-2.19143 - 1.47397i) q^{75} +(-4.05021 + 12.4653i) q^{76} +(4.22894 - 13.0153i) q^{77} +(1.92574 - 1.50862i) q^{78} +(11.3358 + 8.23592i) q^{79} +(5.69349 + 1.84993i) q^{80} +(-7.96852 - 4.18362i) q^{81} +(1.99671 - 1.45070i) q^{82} +(-6.57326 + 9.04731i) q^{83} +(8.33075 - 3.04449i) q^{84} +(14.0614 + 4.56883i) q^{85} +(5.54513 - 17.0662i) q^{86} +(9.58305 + 6.44563i) q^{87} -4.38963i q^{88} +(-2.02436 - 6.23032i) q^{89} +(-10.7878 + 4.39141i) q^{90} +(0.873296 + 1.20199i) q^{91} +(1.67535 - 1.21721i) q^{92} +(-1.94642 - 2.48460i) q^{93} +3.36348i q^{94} +(9.94157 + 3.23021i) q^{95} +(-11.0353 + 8.64497i) q^{96} +(1.49187 + 2.05339i) q^{97} +(-1.41604 - 4.35812i) q^{98} +(-12.0831 - 14.3239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

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