LMFDB - Embedded newform 633.2.k.a.23.7

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			23.7
Character	$\chi$	$=$	633.23
Dual form			633.2.k.a.578.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.718944 + 2.21268i) q^{2} +(1.57202 + 0.727145i) q^{3} +(-2.76105 - 2.00602i) q^{4} +(-2.27009 + 3.12451i) q^{5} +(-2.73914 + 2.95561i) q^{6} +(-0.855199 + 0.277871i) q^{7} +(2.65928 - 1.93208i) q^{8} +(1.94252 + 2.28618i) q^{9} +O(q^{10})$	\(q+(-0.718944 + 2.21268i) q^{2} +(1.57202 + 0.727145i) q^{3} +(-2.76105 - 2.00602i) q^{4} +(-2.27009 + 3.12451i) q^{5} +(-2.73914 + 2.95561i) q^{6} +(-0.855199 + 0.277871i) q^{7} +(2.65928 - 1.93208i) q^{8} +(1.94252 + 2.28618i) q^{9} +(-5.28148 - 7.26933i) q^{10} +(-0.412923 + 0.568340i) q^{11} +(-2.88177 - 5.16119i) q^{12} +(-1.88549 - 5.80295i) q^{13} -2.09206i q^{14} +(-5.84060 + 3.26112i) q^{15} +(0.253950 + 0.781577i) q^{16} +(-1.28704 - 3.96109i) q^{17} +(-6.45515 + 2.65455i) q^{18} +(1.90301 + 5.85685i) q^{19} +(12.5356 - 4.07307i) q^{20} +(-1.54645 - 0.185034i) q^{21} +(-0.960687 - 1.32227i) q^{22} +(-2.90469 + 8.93972i) q^{23} +(5.58535 - 1.10359i) q^{24} +(-3.06416 - 9.43053i) q^{25} +14.1956 q^{26} +(1.39131 + 5.00642i) q^{27} +(2.91866 + 0.948330i) q^{28} +(-0.675260 - 2.07824i) q^{29} +(-3.01675 - 15.2680i) q^{30} +4.55189i q^{31} +4.66213 q^{32} +(-1.06239 + 0.593190i) q^{33} +9.68994 q^{34} +(1.07317 - 3.30287i) q^{35} +(-0.777276 - 10.2090i) q^{36} +(3.01556 - 2.19094i) q^{37} -14.3275 q^{38} +(1.25554 - 10.4934i) q^{39} +12.6949i q^{40} +(3.40579 + 2.47445i) q^{41} +(1.52123 - 3.28876i) q^{42} +3.97307 q^{43} +(2.28020 - 0.740882i) q^{44} +(-11.5529 + 0.879596i) q^{45} +(-17.6924 - 12.8543i) q^{46} +(-3.01619 + 0.980019i) q^{47} +(-0.169104 + 1.41332i) q^{48} +(-5.00897 + 3.63923i) q^{49} +23.0697 q^{50} +(0.857034 - 7.16279i) q^{51} +(-6.43488 + 19.8045i) q^{52} +(-5.35436 - 7.36964i) q^{53} +(-12.0779 - 0.520816i) q^{54} +(-0.838411 - 2.58036i) q^{55} +(-1.73734 + 2.39125i) q^{56} +(-1.26721 + 10.5909i) q^{57} +5.08395 q^{58} +(-0.00381059 + 0.00524483i) q^{59} +(22.6680 + 2.71225i) q^{60} +(-4.69682 - 6.46461i) q^{61} +(-10.0719 - 3.27255i) q^{62} +(-2.29651 - 1.41537i) q^{63} +(-3.85971 + 11.8790i) q^{64} +(22.4116 + 7.28196i) q^{65} +(-0.548740 - 2.77720i) q^{66} +9.76938i q^{67} +(-4.39245 + 13.5186i) q^{68} +(-11.0667 + 11.9413i) q^{69} +(6.53665 + 4.74915i) q^{70} +(-7.77437 - 10.7005i) q^{71} +(9.58277 + 2.32648i) q^{72} +2.97716 q^{73} +(2.67982 + 8.24764i) q^{74} +(2.04042 - 17.0531i) q^{75} +(6.49466 - 19.9885i) q^{76} +(0.195206 - 0.600783i) q^{77} +(22.3159 + 10.3223i) q^{78} +(3.05461 + 2.21930i) q^{79} +(-3.01853 - 0.980780i) q^{80} +(-1.45322 + 8.88190i) q^{81} +(-7.92374 + 5.75693i) q^{82} +(-3.59515 + 4.94830i) q^{83} +(3.89863 + 3.61308i) q^{84} +(15.2981 + 4.97067i) q^{85} +(-2.85642 + 8.79115i) q^{86} +(0.449653 - 3.75805i) q^{87} +2.30917i q^{88} +(-1.38100 - 4.25027i) q^{89} +(6.35960 - 26.1952i) q^{90} +(3.22494 + 4.43875i) q^{91} +(25.9532 - 18.8561i) q^{92} +(-3.30988 + 7.15568i) q^{93} -7.37845i q^{94} +(-22.6198 - 7.34961i) q^{95} +(7.32899 + 3.39005i) q^{96} +(7.83971 + 10.7904i) q^{97} +(-4.45128 - 13.6996i) q^{98} +(-2.10144 + 0.159996i) 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 $

$2$	−0.718944	+	2.21268i	−0.508370	+	1.56460i	0.286660	+	0.958032i	$0.407455\pi$
$2$	−0.718944	+	2.21268i	−0.508370	+	1.56460i	−0.795030	+	0.606570i	$0.792545\pi$
$3$	1.57202	+	0.727145i	0.907609	+	0.419817i
$3$	1.57202	+	0.727145i	0.907609	+	0.419817i
$4$	−2.76105	−	2.00602i	−1.38052	−	1.00301i
$5$	−2.27009	+	3.12451i	−1.01521	+	1.39732i	−0.0997086	+	0.995017i	$0.531791\pi$
$5$	−2.27009	+	3.12451i	−1.01521	+	1.39732i	−0.915505	+	0.402306i	$0.868209\pi$
$6$	−2.73914	+	2.95561i	−1.11825	+	1.20662i
$7$	−0.855199	+	0.277871i	−0.323235	+	0.105025i	−0.466140	−	0.884711i	$-0.654356\pi$
$7$	−0.855199	+	0.277871i	−0.323235	+	0.105025i	0.142905	+	0.989736i	$0.454356\pi$
$8$	2.65928	−	1.93208i	0.940196	−	0.683092i
$9$	1.94252	+	2.28618i	0.647507	+	0.762060i
$10$	−5.28148	−	7.26933i	−1.67015	−	2.29876i
$11$	−0.412923	+	0.568340i	−0.124501	+	0.171361i	−0.866718	−	0.498799i	$-0.833775\pi$
$11$	−0.412923	+	0.568340i	−0.124501	+	0.171361i	0.742217	+	0.670160i	$0.233775\pi$
$12$	−2.88177	−	5.16119i	−0.831894	−	1.48991i
$13$	−1.88549	−	5.80295i	−0.522941	−	1.60945i	−0.768351	−	0.640028i	$-0.778923\pi$
$13$	−1.88549	−	5.80295i	−0.522941	−	1.60945i	0.245410	−	0.969419i	$-0.421077\pi$
$14$		−	2.09206i		−	0.559126i
$15$	−5.84060	+	3.26112i	−1.50804	+	0.842017i
$16$	0.253950	+	0.781577i	0.0634874	+	0.195394i
$17$	−1.28704	−	3.96109i	−0.312152	−	0.960706i	−0.976911	−	0.213647i	$-0.931466\pi$
$17$	−1.28704	−	3.96109i	−0.312152	−	0.960706i	0.664759	−	0.747058i	$-0.268534\pi$
$18$	−6.45515	+	2.65455i	−1.52149	+	0.625683i
$19$	1.90301	+	5.85685i	0.436580	+	1.34365i	0.891459	+	0.453101i	$0.149682\pi$
$19$	1.90301	+	5.85685i	0.436580	+	1.34365i	−0.454879	+	0.890553i	$0.650318\pi$
$20$	12.5356	−	4.07307i	2.80305	−	0.910767i
$21$	−1.54645	−	0.185034i	−0.337462	−	0.0403776i
$22$	−0.960687	−	1.32227i	−0.204819	−	0.281909i
$23$	−2.90469	+	8.93972i	−0.605670	+	1.86406i	−0.113552	+	0.993532i	$0.536223\pi$
$23$	−2.90469	+	8.93972i	−0.605670	+	1.86406i	−0.492118	+	0.870529i	$0.663777\pi$
$24$	5.58535	−	1.10359i	1.14010	−	0.225270i
$25$	−3.06416	−	9.43053i	−0.612833	−	1.88611i
$26$	14.1956			2.78399
$27$	1.39131	+	5.00642i	0.267757	+	0.963486i
$28$	2.91866	+	0.948330i	0.551575	+	0.179217i
$29$	−0.675260	−	2.07824i	−0.125393	−	0.385919i	0.868580	−	0.495549i	$-0.165033\pi$
$29$	−0.675260	−	2.07824i	−0.125393	−	0.385919i	−0.993972	+	0.109631i	$0.965033\pi$
$30$	−3.01675	−	15.2680i	−0.550781	−	2.78753i
$31$			4.55189i			0.817543i	0.912637	+	0.408772i	$0.134043\pi$
$31$			4.55189i			0.817543i	−0.912637	+	0.408772i	$0.865957\pi$
$32$	4.66213			0.824157
$33$	−1.06239	+	0.593190i	−0.184939	+	0.103261i
$34$	9.68994			1.66181
$35$	1.07317	−	3.30287i	0.181398	−	0.558287i
$36$	−0.777276	−	10.2090i	−0.129546	−	1.70150i
$37$	3.01556	−	2.19094i	0.495756	−	0.360188i	−0.311638	−	0.950201i	$-0.600878\pi$
$37$	3.01556	−	2.19094i	0.495756	−	0.360188i	0.807393	+	0.590013i	$0.200878\pi$
$38$	−14.3275			−2.32423
$39$	1.25554	−	10.4934i	0.201048	−	1.68029i
$40$			12.6949i			2.00724i
$41$	3.40579	+	2.47445i	0.531895	+	0.386444i	0.821066	−	0.570833i	$-0.193380\pi$
$41$	3.40579	+	2.47445i	0.531895	+	0.386444i	−0.289171	+	0.957277i	$0.593380\pi$
$42$	1.52123	−	3.28876i	0.234731	−	0.507467i
$43$	3.97307			0.605888			0.302944	−	0.953008i	$-0.402030\pi$
$43$	3.97307			0.605888			0.302944	+	0.953008i	$0.402030\pi$
$44$	2.28020	−	0.740882i	0.343753	−	0.111692i
$45$	−11.5529	+	0.879596i	−1.72220	+	0.131122i
$46$	−17.6924	−	12.8543i	−2.60861	−	1.89527i
$47$	−3.01619	+	0.980019i	−0.439956	+	0.142951i	−0.520616	−	0.853791i	$-0.674297\pi$
$47$	−3.01619	+	0.980019i	−0.439956	+	0.142951i	0.0806591	+	0.996742i	$0.474297\pi$
$48$	−0.169104	+	1.41332i	−0.0244081	+	0.203995i
$49$	−5.00897	+	3.63923i	−0.715567	+	0.519890i
$50$	23.0697			3.26255
$51$	0.857034	−	7.16279i	0.120009	−	1.00299i
$52$	−6.43488	+	19.8045i	−0.892358	+	2.74639i
$53$	−5.35436	−	7.36964i	−0.735477	−	1.01230i	−0.998866	−	0.0476081i	$-0.984840\pi$
$53$	−5.35436	−	7.36964i	−0.735477	−	1.01230i	0.263389	−	0.964690i	$-0.415160\pi$
$54$	−12.0779	−	0.520816i	−1.64359	−	0.0708741i
$55$	−0.838411	−	2.58036i	−0.113051	−	0.347936i
$56$	−1.73734	+	2.39125i	−0.232162	+	0.319544i
$57$	−1.26721	+	10.5909i	−0.167846	+	1.40280i
$58$	5.08395			0.667555
$59$	−0.00381059	+	0.00524483i	−0.000496097	+	0.000682818i	−0.809265	−	0.587444i	$-0.800134\pi$
$59$	−0.00381059	+	0.00524483i	−0.000496097	+	0.000682818i	0.808769	+	0.588127i	$0.200134\pi$
$60$	22.6680	+	2.71225i	2.92643	+	0.350150i
$61$	−4.69682	−	6.46461i	−0.601366	−	0.827709i	0.394467	−	0.918910i	$-0.370929\pi$
$61$	−4.69682	−	6.46461i	−0.601366	−	0.827709i	−0.995832	+	0.0912012i	$0.970929\pi$
$62$	−10.0719	−	3.27255i	−1.27913	−	0.415615i
$63$	−2.29651	−	1.41537i	−0.289332	−	0.178320i
$64$	−3.85971	+	11.8790i	−0.482464	+	1.48487i
$65$	22.4116	+	7.28196i	2.77981	+	0.903217i
$66$	−0.548740	−	2.77720i	−0.0675452	−	0.341850i
$67$			9.76938i			1.19352i	0.802420	+	0.596760i	$0.203546\pi$
$67$			9.76938i			1.19352i	−0.802420	+	0.596760i	$0.796454\pi$
$68$	−4.39245	+	13.5186i	−0.532663	+	1.63937i
$69$	−11.0667	+	11.9413i	−1.33228	+	1.43757i
$70$	6.53665	+	4.74915i	0.781279	+	0.567632i
$71$	−7.77437	−	10.7005i	−0.922649	−	1.26992i	−0.962659	−	0.270717i	$-0.912739\pi$
$71$	−7.77437	−	10.7005i	−0.922649	−	1.26992i	0.0400103	−	0.999199i	$-0.487261\pi$
$72$	9.58277	+	2.32648i	1.12934	+	0.274178i
$73$	2.97716			0.348450			0.174225	−	0.984706i	$-0.444258\pi$
$73$	2.97716			0.348450			0.174225	+	0.984706i	$0.444258\pi$
$74$	2.67982	+	8.24764i	0.311523	+	0.958769i
$75$	2.04042	−	17.0531i	0.235607	−	1.96912i
$76$	6.49466	−	19.9885i	0.744989	−	2.29284i
$77$	0.195206	−	0.600783i	0.0222458	−	0.0684656i
$78$	22.3159	+	10.3223i	2.52678	+	1.16877i
$79$	3.05461	+	2.21930i	0.343670	+	0.249691i	0.746209	−	0.665712i	$-0.231872\pi$
$79$	3.05461	+	2.21930i	0.343670	+	0.249691i	−0.402538	+	0.915403i	$0.631872\pi$
$80$	−3.01853	−	0.980780i	−0.337482	−	0.109655i
$81$	−1.45322	+	8.88190i	−0.161469	+	0.986878i
$82$	−7.92374	+	5.75693i	−0.875031	+	0.635747i
$83$	−3.59515	+	4.94830i	−0.394619	+	0.543147i	−0.959383	−	0.282105i	$-0.908967\pi$
$83$	−3.59515	+	4.94830i	−0.394619	+	0.543147i	0.564764	+	0.825252i	$0.308967\pi$
$84$	3.89863	+	3.61308i	0.425375	+	0.394220i
$85$	15.2981	+	4.97067i	1.65932	+	0.539145i
$86$	−2.85642	+	8.79115i	−0.308015	+	0.947974i
$87$	0.449653	−	3.75805i	0.0482079	−	0.402905i
$88$			2.30917i			0.246159i
$89$	−1.38100	−	4.25027i	−0.146385	−	0.450528i	0.850801	−	0.525488i	$-0.176117\pi$
$89$	−1.38100	−	4.25027i	−0.146385	−	0.450528i	−0.997187	+	0.0749599i	$0.976117\pi$
$90$	6.35960	−	26.1952i	0.670361	−	2.76122i
$91$	3.22494	+	4.43875i	0.338066	+	0.465308i
$92$	25.9532	−	18.8561i	2.70581	−	1.96589i
$93$	−3.30988	+	7.15568i	−0.343219	+	0.742009i
$94$		−	7.37845i		−	0.761029i
$95$	−22.6198	−	7.34961i	−2.32074	−	0.754054i
$96$	7.32899	+	3.39005i	0.748012	+	0.345995i
$97$	7.83971	+	10.7904i	0.796002	+	1.09560i	0.993335	+	0.115266i	$0.0367721\pi$
$97$	7.83971	+	10.7904i	0.796002	+	1.09560i	−0.197333	+	0.980337i	$0.563228\pi$
$98$	−4.45128	−	13.6996i	−0.449648	−	1.38387i
$99$	−2.10144	+	0.159996i	−0.211203	+	0.0160802i
$100$	−10.4575	+	32.1849i	−1.04575	+	3.21849i
$101$			7.86471i			0.782568i	0.920270	+	0.391284i	$0.127969\pi$
$101$			7.86471i			0.782568i	−0.920270	+	0.391284i	$0.872031\pi$
$102$	15.2328	+	7.04599i	1.50827	+	0.697657i
$103$	1.66989	−	5.13939i	0.164539	−	0.506399i	−0.834463	−	0.551064i	$-0.814222\pi$
$103$	1.66989	−	5.13939i	0.164539	−	0.506399i	0.999002	+	0.0446648i	$0.0142220\pi$
$104$	−16.2258	−	11.7887i	−1.59107	−	1.15598i
$105$	4.08871	−	4.41184i	0.399017	−	0.430552i
$106$	20.1561	−	6.54913i	1.95774	−	0.636108i
$107$	−0.716512	+	0.986194i	−0.0692678	+	0.0953390i	−0.842245	−	0.539095i	$-0.818767\pi$
$107$	−0.716512	+	0.986194i	−0.0692678	+	0.0953390i	0.772977	+	0.634433i	$0.218767\pi$
$108$	6.20151	−	16.6139i	0.596740	−	1.59868i
$109$	−13.9064	+	10.1036i	−1.33199	+	0.967746i	−0.332289	+	0.943177i	$0.607821\pi$
$109$	−13.9064	+	10.1036i	−1.33199	+	0.967746i	−0.999698	+	0.0245681i	$0.992179\pi$
$110$	6.31229			0.601854
$111$	6.33367	−	1.25145i	0.601165	−	0.118783i
$112$	−0.434355	−	0.597839i	−0.0410427	−	0.0564904i
$113$	−15.3677	+	4.99326i	−1.44567	+	0.469727i	−0.923660	−	0.383212i	$-0.874818\pi$
$113$	−15.3677	+	4.99326i	−1.44567	+	0.469727i	−0.522010	+	0.852939i	$0.674818\pi$
$114$	−22.5232	−	10.4182i	−2.10949	−	0.975751i
$115$	−21.3383	−	29.3697i	−1.98981	−	2.73874i
$116$	−2.30455	+	7.09269i	−0.213972	+	0.658539i
$117$	9.60397	−	15.5829i	0.887887	−	1.44064i
$118$	−0.00886553	−	0.0122024i	−0.000816139	−	0.00112332i
$119$	2.20134	+	3.02989i	0.201797	+	0.277750i
$120$	−9.23104	+	19.9567i	−0.842675	+	1.82179i
$121$	3.24668	+	9.99226i	0.295153	+	0.908387i
$122$	17.6809	−	5.74487i	1.60075	−	0.520116i
$123$	3.55470	+	6.36640i	0.320516	+	0.574039i
$124$	9.13117	−	12.5680i	0.820003	−	1.12864i
$125$	18.0563	+	5.86684i	1.61500	+	0.524747i
$126$	4.78282	−	4.06386i	0.426087	−	0.362038i
$127$	7.47651	−	2.42926i	0.663433	−	0.215562i	0.0421051	−	0.999113i	$-0.486594\pi$
$127$	7.47651	−	2.42926i	0.663433	−	0.215562i	0.621328	+	0.783551i	$0.286594\pi$
$128$	−15.9660	−	11.6000i	−1.41121	−	1.02530i
$129$	6.24577	+	2.88900i	0.549909	+	0.254362i
$130$	−32.2253	+	44.3544i	−2.82635	+	3.89014i
$131$	−2.76530	+	8.51073i	−0.241606	+	0.743586i	0.754571	+	0.656219i	$0.227845\pi$
$131$	−2.76530	+	8.51073i	−0.241606	+	0.743586i	−0.996176	+	0.0873668i	$0.972155\pi$
$132$	4.12326	+	0.493351i	0.358884	+	0.0429407i
$133$	−3.25490	−	4.47999i	−0.282236	−	0.388464i
$134$	−21.6165	−	7.02364i	−1.86738	−	0.606750i
$135$	−18.8010	−	7.01787i	−1.61813	−	0.604002i
$136$	−11.0757	−	8.04698i	−0.949735	−	0.690023i
$137$	4.50905	−	1.46508i	0.385234	−	0.125170i	−0.109996	−	0.993932i	$-0.535084\pi$
$137$	4.50905	−	1.46508i	0.385234	−	0.125170i	0.495230	+	0.868762i	$0.335084\pi$
$138$	−18.4660	−	33.0723i	−1.57193	−	2.81530i
$139$	1.00135	+	3.08182i	0.0849330	+	0.261397i	0.984500	−	0.175387i	$-0.0561176\pi$
$139$	1.00135	+	3.08182i	0.0849330	+	0.261397i	−0.899567	+	0.436784i	$0.856118\pi$
$140$	−9.58867	+	6.96658i	−0.810391	+	0.588783i
$141$	−5.45414	−	0.652592i	−0.459321	−	0.0549582i
$142$	29.2662	−	9.50915i	2.45596	−	0.797990i
$143$	4.07661	+	1.32457i	0.340903	+	0.110766i
$144$	−1.29352	+	2.09880i	−0.107793	+	0.174900i
$145$	8.02636	+	2.60792i	0.666553	+	0.216576i
$146$	−2.14041	+	6.58750i	−0.177141	+	0.545185i
$147$	−10.5205	+	2.07871i	−0.867713	+	0.171449i
$148$	−12.7212			−1.04567
$149$	−4.15347	+	12.7831i	−0.340265	+	1.04723i	0.623805	+	0.781580i	$0.285586\pi$
$149$	−4.15347	+	12.7831i	−0.340265	+	1.04723i	−0.964070	+	0.265648i	$0.914414\pi$
$150$	36.2662	+	16.7750i	2.96112	+	1.36968i
$151$	15.2119	+	11.0521i	1.23793	+	0.899405i	0.997458	−	0.0712518i	$-0.0226994\pi$
$151$	15.2119	+	11.0521i	1.23793	+	0.899405i	0.240467	+	0.970657i	$0.422699\pi$
$152$	16.3765	+	11.8982i	1.32831	+	0.965074i
$153$	6.55567	−	10.6369i	0.529994	−	0.859942i
$154$	1.18900	+	0.863859i	0.0958124	+	0.0696118i
$155$	−14.2224	−	10.3332i	−1.14237	−	0.829982i
$156$	−24.5166	+	26.4541i	−1.96290	+	2.11802i
$157$			14.7803i			1.17960i	0.807551	+	0.589798i	$0.200793\pi$
$157$			14.7803i			1.17960i	−0.807551	+	0.589798i	$0.799207\pi$
$158$	−7.10671	+	5.16332i	−0.565379	+	0.410772i
$159$	−3.05838	−	15.4786i	−0.242546	−	1.22754i
$160$	−10.5835	+	14.5669i	−0.836695	+	1.15161i
$161$		−	8.45237i		−	0.666140i
$162$	−18.6080	−	9.60111i	−1.46198	−	0.754334i
$163$	−1.75213	−	1.27299i	−0.137237	−	0.0997086i	0.517049	−	0.855956i	$-0.327031\pi$
$163$	−1.75213	−	1.27299i	−0.137237	−	0.0997086i	−0.654286	+	0.756247i	$0.727031\pi$
$164$	−4.43975	−	13.6641i	−0.346686	−	1.06699i
$165$	0.558296	−	4.66604i	0.0434633	−	0.363251i
$166$	−8.36431	−	11.5125i	−0.649196	−	0.893542i
$167$	0.0451366	+	0.138916i	0.00349278	+	0.0107497i	0.952788	−	0.303637i	$-0.0982011\pi$
$167$	0.0451366	+	0.138916i	0.00349278	+	0.0107497i	−0.949295	+	0.314387i	$0.898201\pi$
$168$	−4.46993	+	2.49580i	−0.344862	+	0.192555i
$169$	−19.6019	+	14.2416i	−1.50784	+	1.09551i
$170$	−21.9970	+	30.2763i	−1.68709	+	2.32209i
$171$	−9.69318	+	15.7277i	−0.741256	+	1.20273i
$172$	−10.9698	−	7.97006i	−0.836443	−	0.607711i
$173$		−	11.3469i		−	0.862688i	−0.902188	−	0.431344i	$-0.858040\pi$
$173$		−	11.3469i		−	0.862688i	0.902188	−	0.431344i	$-0.141960\pi$
$174$	7.99209	+	3.69677i	0.605879	+	0.280251i
$175$	5.24094	+	7.21354i	0.396178	+	0.545292i
$176$	−0.549063	−	0.178401i	−0.0413872	−	0.0134475i
$177$	−0.00980409	+	0.00547415i	−0.000736921	+	0.000411462i
$178$	10.3974			0.779315
$179$			19.8436i			1.48318i	0.670854	+	0.741589i	$0.265928\pi$
$179$			19.8436i			1.48318i	−0.670854	+	0.741589i	$0.734072\pi$
$180$	33.6625	+	20.7467i	2.50905	+	1.54636i
$181$	−5.59767	−	1.81879i	−0.416071	−	0.135190i	0.0934977	−	0.995619i	$-0.470195\pi$
$181$	−5.59767	−	1.81879i	−0.416071	−	0.135190i	−0.509569	+	0.860430i	$0.670195\pi$
$182$	−12.1401	+	3.94456i	−0.899884	+	0.292390i
$183$	−2.68280	−	13.5778i	−0.198318	−	1.00370i
$184$	9.54785	+	29.3853i	0.703877	+	2.16631i
$185$			14.3958i			1.05840i
$186$	−13.4536	−	12.4682i	−0.986467	−	0.914216i
$187$	2.78269	+	0.904152i	0.203491	+	0.0661182i
$188$	10.2938	+	3.34465i	0.750751	+	0.243934i
$189$	−2.58098	−	3.89488i	−0.187739	−	0.283311i
$190$	32.5247	−	44.7664i	2.35959	−	3.24770i
$191$	−0.732614	−	2.25475i	−0.0530101	−	0.163148i	0.921047	−	0.389452i	$-0.127336\pi$
$191$	−0.732614	−	2.25475i	−0.0530101	−	0.163148i	−0.974057	+	0.226304i	$0.927336\pi$
$192$	−14.7053	+	15.8675i	−1.06126	+	1.14514i
$193$	−14.6216	−	10.6232i	−1.05249	−	0.764678i	−0.0798051	−	0.996810i	$-0.525430\pi$
$193$	−14.6216	−	10.6232i	−1.05249	−	0.764678i	−0.972684	+	0.232132i	$0.925430\pi$
$194$	−29.5121	+	9.58906i	−2.11885	+	0.688455i
$195$	29.9365	+	27.7439i	2.14380	+	1.98678i
$196$	21.1303			1.50931
$197$	20.3660			1.45102			0.725509	−	0.688213i	$-0.241605\pi$
$197$	20.3660			1.45102			0.725509	+	0.688213i	$0.241605\pi$
$198$	1.15680	−	4.76484i	0.0822099	−	0.338623i
$199$	−4.62617			−0.327941			−0.163970	−	0.986465i	$-0.552430\pi$
$199$	−4.62617			−0.327941			−0.163970	+	0.986465i	$0.552430\pi$
$200$	−26.3690	−	19.1582i	−1.86457	−	1.35469i
$201$	−7.10375	+	15.3577i	−0.501060	+	1.08325i
$202$	−17.4021	−	5.65428i	−1.22441	−	0.397834i
$203$	1.15496	+	1.58967i	0.0810625	+	0.111573i
$204$	−16.7350	+	18.0576i	−1.17168	+	1.26428i
$205$	−15.4629	+	5.02419i	−1.07997	+	0.350905i
$206$	10.1713	+	7.38987i	0.708667	+	0.514876i
$207$	−26.0802	+	10.7250i	−1.81270	+	0.745436i
$208$	4.05663	−	2.94731i	0.281277	−	0.204359i
$209$	−4.11448	−	1.33688i	−0.284605	−	0.0924736i
$210$	6.82245	+	12.2189i	0.470794	+	0.843182i
$211$	14.4730	+	1.23811i	0.996361	+	0.0852348i
$211$	14.4730	+	1.23811i	0.996361	+	0.0852348i
$212$			31.0888i			2.13519i
$213$	−4.44069	−	22.4746i	−0.304271	−	1.53993i
$214$	−1.66700	−	2.29443i	−0.113954	−	0.156844i
$215$	−9.01923	+	12.4139i	−0.615106	+	0.846621i
$216$	13.3727	+	10.6253i	0.909894	+	0.722963i
$217$	−1.26484	−	3.89277i	−0.0858628	−	0.264259i
$218$	−12.3581	−	38.0342i	−0.836994	−	2.57600i
$219$	4.68016	+	2.16482i	0.316256	+	0.146285i
$220$	−2.86136	+	8.80637i	−0.192913	+	0.593725i
$221$	−20.5593	+	14.9372i	−1.38297	+	1.00479i
$222$	−1.78449	+	14.9141i	−0.119767	+	1.00097i
$223$			4.18232i			0.280069i	0.990147	+	0.140034i	$0.0447213\pi$
$223$			4.18232i			0.280069i	−0.990147	+	0.140034i	$0.955279\pi$
$224$	−3.98705	+	1.29547i	−0.266396	+	0.0865574i
$225$	15.6077	−	25.3242i	1.04051	−	1.68828i
$226$		−	37.5937i		−	2.50069i
$227$	20.7383	−	6.73828i	1.37645	−	0.447235i	0.474949	−	0.880014i	$-0.342467\pi$
$227$	20.7383	−	6.73828i	1.37645	−	0.447235i	0.901500	+	0.432778i	$0.142467\pi$
$228$	24.7443	−	26.6999i	1.63873	−	1.76824i
$229$	12.5530	−	17.2777i	0.829526	−	1.14174i	−0.158486	−	0.987361i	$-0.550661\pi$
$229$	12.5530	−	17.2777i	0.829526	−	1.14174i	0.988011	−	0.154383i	$-0.0493389\pi$
$230$	80.3268	−	26.0998i	5.29659	−	1.72097i
$231$	0.743726	−	0.802503i	0.0489336	−	0.0528008i
$232$	−5.81101	−	4.22195i	−0.381512	−	0.277184i
$233$	11.8781	−	8.62998i	0.778163	−	0.565369i	−0.126264	−	0.991997i	$-0.540299\pi$
$233$	11.8781	−	8.62998i	0.778163	−	0.565369i	0.904427	+	0.426628i	$0.140299\pi$
$234$	27.5753	+	32.4538i	1.80266	+	2.12157i
$235$	3.78494	−	11.6488i	0.246902	−	0.759886i
$236$	0.0210424	−	0.00683710i	0.00136975	−	0.000445057i
$237$	3.18817	+	5.70994i	0.207094	+	0.370901i
$238$	−8.28683	+	2.69255i	−0.537155	+	0.174532i
$239$	5.35995	−	16.4962i	0.346707	−	1.06705i	−0.613957	−	0.789339i	$-0.710423\pi$
$239$	5.35995	−	16.4962i	0.346707	−	1.06705i	0.960664	−	0.277714i	$-0.0895767\pi$
$240$	−4.03204	−	3.73672i	−0.260267	−	0.241204i
$241$	5.03363	−	15.4919i	0.324244	−	0.997922i	−0.647536	−	0.762035i	$-0.724200\pi$
$241$	5.03363	−	15.4919i	0.324244	−	0.997922i	0.971780	−	0.235887i	$-0.0757995\pi$
$242$	−24.4439			−1.57131
$243$	−8.74293	+	12.9059i	−0.560859	+	0.827911i
$244$			27.2710i			1.74585i
$245$		−	23.9119i		−	1.52768i
$246$	−16.6424	+	3.28833i	−1.06108	+	0.209657i
$247$	30.3989	−	22.0861i	1.93424	−	1.40530i
$248$	8.79460	+	12.1047i	0.558458	+	0.768651i
$249$	−9.24980	+	5.16466i	−0.586182	+	0.327297i
$250$	−25.9629	+	35.7349i	−1.64204	+	2.26007i
$251$	23.4505			1.48018			0.740092	−	0.672505i	$-0.234782\pi$
$251$	23.4505			1.48018			0.740092	+	0.672505i	$0.234782\pi$
$252$	3.50150	+	8.51472i	0.220574	+	0.536377i
$253$	−3.88139	−	5.34227i	−0.244021	−	0.335866i
$254$			18.2896i			1.14759i
$255$	20.4347	+	18.9380i	1.27967	+	1.18594i
$256$	16.9359	−	12.3047i	1.05850	−	0.769043i
$257$	17.0710	−	23.4962i	1.06486	−	1.46565i	0.189684	−	0.981845i	$-0.439253\pi$
$257$	17.0710	−	23.4962i	1.06486	−	1.46565i	0.875174	−	0.483807i	$-0.160747\pi$
$258$	−10.8828	+	11.7429i	−0.677533	+	0.731079i
$259$	−1.97011	+	2.71162i	−0.122417	+	0.168492i
$260$	−47.2717	−	65.0639i	−2.93166	−	4.03509i
$261$	3.43951	−	5.58078i	0.212900	−	0.345442i
$262$	−16.8434	−	12.2375i	−1.04059	−	0.756033i
$263$	0.290596	+	0.0944204i	0.0179189	+	0.00582221i	0.317963	−	0.948103i	$-0.397001\pi$
$263$	0.290596	+	0.0944204i	0.0179189	+	0.00582221i	−0.300044	+	0.953925i	$0.597001\pi$
$264$	−1.67910	+	3.63008i	−0.103342	+	0.223416i
$265$	35.1814			2.16117
$266$	12.2529	−	3.98120i	0.751272	−	0.244103i
$267$	0.919602	−	7.68571i	0.0562787	−	0.470358i
$268$	19.5975	−	26.9737i	1.19711	−	1.64768i
$269$			2.05734i			0.125438i	0.998031	+	0.0627191i	$0.0199772\pi$
$269$			2.05734i			0.125438i	−0.998031	+	0.0627191i	$0.980023\pi$
$270$	29.0452	−	36.5552i	1.76763	−	2.22468i
$271$	−10.4390	+	14.3681i	−0.634125	+	0.872798i	−0.998285	−	0.0585385i	$-0.981356\pi$
$271$	−10.4390	+	14.3681i	−0.634125	+	0.872798i	0.364160	+	0.931336i	$0.381356\pi$
$272$	2.76905	−	2.01184i	0.167899	−	0.121985i
$273$	1.84207	+	9.32283i	0.111487	+	0.564243i
$274$			11.0304i			0.666371i
$275$	6.62501	+	2.15260i	0.399503	+	0.129807i
$276$	54.5102	−	10.7705i	3.28113	−	0.648310i
$277$	2.12986	−	6.55504i	0.127971	−	0.393854i	−0.866460	−	0.499247i	$-0.833610\pi$
$277$	2.12986	−	6.55504i	0.127971	−	0.393854i	0.994431	+	0.105393i	$0.0336100\pi$
$278$	−7.53901			−0.452159
$279$	−10.4064	+	8.84214i	−0.623017	+	0.529365i
$280$	−3.52755	−	10.8567i	−0.210811	−	0.648811i
$281$	−7.36082	+	10.1313i	−0.439110	+	0.604383i	−0.970014	−	0.243049i	$-0.921852\pi$
$281$	−7.36082	+	10.1313i	−0.439110	+	0.604383i	0.530904	+	0.847432i	$0.321852\pi$
$282$	5.36520	−	11.5991i	0.319493	−	0.690716i
$283$	−21.6834	+	7.04537i	−1.28894	+	0.418804i	−0.871722	−	0.490001i	$-0.836997\pi$
$283$	−21.6834	+	7.04537i	−1.28894	+	0.418804i	−0.417223	+	0.908804i	$0.636997\pi$
$284$			45.1401i			2.67857i
$285$	−30.2146	−	28.0016i	−1.78976	−	1.65867i
$286$	−5.86171	+	8.06795i	−0.346610	+	0.477068i
$287$	−3.60021	−	1.16978i	−0.212513	−	0.0690498i
$288$	9.05629	+	10.6585i	0.533647	+	0.628056i
$289$	−0.280489	+	0.203787i	−0.0164993	+	0.0119875i
$290$	−11.5410	+	15.8848i	−0.677711	+	0.932790i
$291$	4.47801	+	22.6634i	0.262505	+	1.32855i
$292$	−8.22007	−	5.97223i	−0.481043	−	0.349498i
$293$	17.9076	+	24.6478i	1.04618	+	1.43994i	0.892078	+	0.451881i	$0.149247\pi$
$293$	17.9076	+	24.6478i	1.04618	+	1.43994i	0.154097	+	0.988056i	$0.450753\pi$
$294$	2.96410	−	24.7729i	0.172870	−	1.44479i
$295$	−0.00773713	−	0.0238124i	−0.000450473	−	0.00138641i
$296$	3.78616	−	11.6526i	0.220066	−	0.677294i
$297$	−3.41985	−	1.27653i	−0.198440	−	0.0740719i
$298$	−25.2987	−	18.3806i	−1.46552	−	1.06476i
$299$	57.3535			3.31684
$300$	−39.8425	+	42.9913i	−2.30031	+	2.48210i
$301$	−3.39777	+	1.10400i	−0.195844	+	0.0636336i
$302$	−35.3912	+	25.7132i	−2.03654	+	1.47963i
$303$	−5.71878	+	12.3635i	−0.328535	+	0.710265i
$304$	−4.09431	+	2.97469i	−0.234825	+	0.170610i
$305$	30.8609			1.76709
$306$	18.8229	+	22.1529i	1.07603	+	1.26640i
$307$	11.4184	−	8.29596i	0.651683	−	0.473475i	−0.212161	−	0.977235i	$-0.568050\pi$
$307$	11.4184	−	8.29596i	0.651683	−	0.473475i	0.863844	+	0.503759i	$0.168050\pi$
$308$	−1.74416	+	1.26720i	−0.0993825	+	0.0722056i
$309$	6.36219	−	6.86500i	0.361932	−	0.390536i
$310$	33.0892	−	24.0407i	1.87934	−	1.36542i
$311$	−6.33306	−	2.05773i	−0.359115	−	0.116683i	0.123902	−	0.992294i	$-0.460459\pi$
$311$	−6.33306	−	2.05773i	−0.359115	−	0.116683i	−0.483017	+	0.875611i	$0.660459\pi$
$312$	−16.9352	−	30.3306i	−0.958768	−	1.71713i
$313$	−7.19616	−	9.90467i	−0.406751	−	0.559845i	0.555671	−	0.831402i	$-0.312461\pi$
$313$	−7.19616	−	9.90467i	−0.406751	−	0.559845i	−0.962422	+	0.271557i	$0.912461\pi$
$314$	−32.7041	−	10.6262i	−1.84560	−	0.599672i
$315$	9.63559	−	3.96244i	0.542904	−	0.223258i
$316$	−3.98196	−	12.2552i	−0.224003	−	0.689409i
$317$	−2.13190	−	6.56132i	−0.119739	−	0.368520i	0.873167	−	0.487422i	$-0.162063\pi$
$317$	−2.13190	−	6.56132i	−0.119739	−	0.368520i	−0.992906	+	0.118902i	$0.962063\pi$
$318$	36.4481	+	4.36105i	2.04391	+	0.244555i
$319$	1.45998	+	0.474375i	0.0817429	+	0.0265599i
$320$	−28.3541	−	39.0260i	−1.58504	−	2.18162i
$321$	−1.84348	+	1.02931i	−0.102893	+	0.0574506i
$322$	18.7024	+	6.07678i	1.04224	+	0.338646i
$323$	20.7503	−	15.0760i	1.15458	−	0.838849i
$324$	21.8297	−	21.6081i	1.21276	−	1.20045i
$325$	−48.9474	+	35.5624i	−2.71511	+	1.97265i
$326$	4.07641	−	2.96169i	0.225771	−	0.164033i
$327$	−29.2079	+	5.77111i	−1.61520	+	0.319143i
$328$	13.8378			0.764062
$329$	2.30712	−	1.67622i	0.127196	−	0.0924132i
$330$	9.92308	+	4.58995i	0.546248	+	0.252669i
$331$	−9.08203	+	6.59848i	−0.499194	+	0.362686i	−0.808709	−	0.588209i	$-0.799833\pi$
$331$	−9.08203	+	6.59848i	−0.499194	+	0.362686i	0.309515	+	0.950895i	$0.399833\pi$
$332$	19.8528	−	6.45056i	1.08956	−	0.354020i
$333$	10.8667	+	2.63818i	0.595490	+	0.144571i
$334$	−0.339828			−0.0185946
$335$	−30.5245	−	22.1774i	−1.66773	−	1.21168i
$336$	−0.248102	−	1.25566i	−0.0135351	−	0.0685017i
$337$	0.816251	−	2.51216i	0.0444640	−	0.136846i	−0.926360	−	0.376639i	$-0.877080\pi$
$337$	0.816251	−	2.51216i	0.0444640	−	0.136846i	0.970824	+	0.239793i	$0.0770796\pi$
$338$	−17.4195	−	53.6117i	−0.947495	−	2.91609i
$339$	−27.7892	−	3.32500i	−1.50930	−	0.180589i
$340$	−32.2676	−	44.4126i	−1.74996	−	2.40861i
$341$	−2.58702	−	1.87958i	−0.140095	−	0.101785i
$342$	−27.8315	−	32.7552i	−1.50495	−	1.77120i
$343$	6.97222	−	9.59644i	0.376465	−	0.518159i
$344$	10.5655	−	7.67629i	0.569654	−	0.413878i
$345$	−12.1884	−	61.6859i	−0.656199	−	3.32106i
$346$	25.1070	+	8.15777i	1.34976	+	0.438565i
$347$	8.38062	−	11.5349i	0.449895	−	0.619228i	−0.522480	−	0.852652i	$-0.674993\pi$
$347$	8.38062	−	11.5349i	0.449895	−	0.619228i	0.972375	+	0.233424i	$0.0749930\pi$
$348$	−8.78022	+	9.47413i	−0.470669	+	0.507867i
$349$			4.44928i			0.238165i	0.992884	+	0.119082i	$0.0379952\pi$
$349$			4.44928i			0.238165i	−0.992884	+	0.119082i	$0.962005\pi$
$350$	−19.7292	+	6.41041i	−1.05457	+	0.342651i
$351$	26.4287	−	17.5133i	1.41066	−	0.934788i
$352$	−1.92510	+	2.64968i	−0.102608	+	0.141228i
$353$	−0.828787	−	2.55074i	−0.0441119	−	0.135762i	0.926575	−	0.376110i	$-0.122739\pi$
$353$	−0.828787	−	2.55074i	−0.0441119	−	0.135762i	−0.970687	+	0.240348i	$0.922739\pi$
$354$	−0.00506395	−	0.0256289i	−0.000269146	−	0.00136216i
$355$	51.0823			2.71117
$356$	−4.71312	+	14.5055i	−0.249795	+	0.768790i
$357$	1.25740	+	6.36376i	0.0665486	+	0.336806i
$358$	−43.9075	−	14.2664i	−2.32058	−	0.754003i
$359$			13.2262i			0.698054i	0.937113	+	0.349027i	$0.113488\pi$
$359$			13.2262i			0.698054i	−0.937113	+	0.349027i	$0.886512\pi$
$360$	−29.0228	+	24.6601i	−1.52964	+	1.29970i
$361$	−15.3100	+	11.1233i	−0.805788	+	0.585439i
$362$	8.04882	−	11.0782i	0.423037	−	0.582260i
$363$	−2.16196	+	18.0689i	−0.113473	+	0.948370i
$364$		−	18.7249i		−	0.981451i
$365$	−6.75841	+	9.30215i	−0.353751	+	0.486897i
$366$	31.9721	+	3.82549i	1.67121	+	0.199962i
$367$	−12.1451	+	3.94620i	−0.633971	+	0.205990i	−0.608333	−	0.793682i	$-0.708162\pi$
$367$	−12.1451	+	3.94620i	−0.633971	+	0.205990i	−0.0256378	+	0.999671i	$0.508162\pi$
$368$	−7.72473			−0.402679
$369$	0.958781	+	12.5929i	0.0499121	+	0.655561i
$370$	−31.8533	−	10.3498i	−1.65597	−	0.538058i
$371$	6.62685	+	4.81469i	0.344049	+	0.249966i
$372$	23.4932	−	13.1175i	1.21806	−	0.680110i
$373$	7.84376	+	10.7960i	0.406134	+	0.558996i	0.962270	−	0.272095i	$-0.0877166\pi$
$373$	7.84376	+	10.7960i	0.406134	+	0.558996i	−0.556136	+	0.831091i	$0.687717\pi$
$374$	−4.00120	+	5.50718i	−0.206897	+	0.284770i
$375$	24.1189	+	22.3524i	1.24549	+	1.15427i
$376$	−6.12741	+	8.43365i	−0.315997	+	0.434932i
$377$	−10.7867	+	7.83699i	−0.555543	+	0.403626i
$378$	10.4737	−	2.91069i	0.538710	−	0.149710i
$379$		−	2.60283i		−	0.133698i	−0.997763	−	0.0668492i	$-0.978705\pi$
$379$		−	2.60283i		−	0.133698i	0.997763	−	0.0668492i	$-0.0212947\pi$
$380$	47.7108	+	65.6683i	2.44751	+	3.36871i
$381$	13.5197	+	1.61764i	0.692634	+	0.0828742i
$382$	5.51576			0.282211
$383$	−7.04729	+	9.69977i	−0.360100	+	0.495635i	−0.950177	−	0.311712i	$-0.899098\pi$
$383$	−7.04729	+	9.69977i	−0.360100	+	0.495635i	0.590077	+	0.807347i	$0.299098\pi$
$384$	−16.6641	−	29.8450i	−0.850384	−	1.52302i
$385$	1.43402	+	1.97375i	0.0730843	+	0.100592i
$386$	34.0180	−	24.7155i	1.73147	−	1.25799i
$387$	7.71778	+	9.08316i	0.392317	+	0.461723i
$388$		−	45.5195i		−	2.31090i
$389$			22.5924i			1.14548i	0.819737	+	0.572740i	$0.194119\pi$
$389$			22.5924i			1.14548i	−0.819737	+	0.572740i	$0.805881\pi$
$390$	−82.9111	+	46.2937i	−4.19837	+	2.34417i
$391$	39.1495			1.97987
$392$	−6.28895	+	19.3554i	−0.317640	+	0.977596i
$393$	−10.5357	+	11.3683i	−0.531454	+	0.573455i
$394$	−14.6420	+	45.0635i	−0.737654	+	2.27026i
$395$	−13.8685	+	4.50614i	−0.697798	+	0.226728i
$396$	6.12313	+	3.77377i	0.307699	+	0.189639i
$397$	28.3068	−	9.19744i	1.42068	−	0.461606i	0.504860	−	0.863201i	$-0.331544\pi$
$397$	28.3068	−	9.19744i	1.42068	−	0.461606i	0.915817	+	0.401595i	$0.131544\pi$
$398$	3.32596	−	10.2362i	0.166715	−	0.513097i
$399$	−1.85918	−	9.40943i	−0.0930756	−	0.471061i
$400$	6.59254	−	4.78976i	0.329627	−	0.239488i
$401$	22.3997	+	16.2743i	1.11859	+	0.812702i	0.983994	−	0.178199i	$-0.0570272\pi$
$401$	22.3997	+	16.2743i	1.11859	+	0.812702i	0.134593	+	0.990901i	$0.457027\pi$
$402$	−28.8745	−	26.7597i	−1.44013	−	1.33465i
$403$	26.4144	−	8.58255i	1.31579	−	0.427527i
$404$	15.7767	−	21.7148i	0.784922	−	1.08035i
$405$	−24.4526	−	24.7033i	−1.21506	−	1.22752i
$406$	−4.34779	+	1.41268i	−0.215777	+	0.0701102i
$407$			2.61855i			0.129797i
$408$	−11.5600	−	20.7037i	−0.572304	−	1.02499i
$409$	−16.7990	+	5.45833i	−0.830658	+	0.269897i	−0.693323	−	0.720627i	$-0.743854\pi$
$409$	−16.7990	+	5.45833i	−0.830658	+	0.269897i	−0.137336	+	0.990525i	$0.543854\pi$
$410$		−	37.8265i		−	1.86812i
$411$	8.15366	+	0.975592i	0.402190	+	0.0481224i
$412$	−14.9203	+	10.8403i	−0.735073	+	0.534062i
$413$	0.00180143	−	0.00554423i	8.86425e−5	−	0.000272813i
$414$	−4.98069	−	65.4179i	−0.244788	−	3.21511i
$415$	−7.29970	−	22.4662i	−0.358328	−	1.10282i
$416$	−8.79042	−	27.0541i	−0.430986	−	1.32644i
$417$	−0.666793	+	5.57282i	−0.0326530	+	0.272902i
$418$	5.91616	−	8.14290i	0.289369	−	0.398282i
$419$	10.8944	+	14.9948i	0.532226	+	0.732546i	0.987468	−	0.157822i	$-0.0504473\pi$
$419$	10.8944	+	14.9948i	0.532226	+	0.732546i	−0.455242	+	0.890368i	$0.650447\pi$
$420$	−20.1393	+	3.97928i	−0.982699	+	0.194169i
$421$			14.3567i			0.699702i	0.936805	+	0.349851i	$0.113768\pi$
$421$			14.3567i			0.699702i	−0.936805	+	0.349851i	$0.886232\pi$
$422$	−13.1448	+	31.1340i	−0.639879	+	1.51558i
$423$	−8.09951	−	4.99184i	−0.393812	−	0.242712i
$424$	−28.4774	−	9.25287i	−1.38299	−	0.449359i
$425$	−33.4115	+	24.2749i	−1.62070	+	1.17750i
$426$	52.9216	+	6.33212i	2.56406	+	0.306792i
$427$	5.81304	+	4.22342i	0.281313	+	0.204386i
$428$	3.95664	−	1.28559i	0.191252	−	0.0621414i
$429$	5.44538	+	5.04654i	0.262905	+	0.243649i
$430$	−20.9837	−	28.8816i	−1.01192	−	1.39279i
$431$	−20.6541	−	6.71093i	−0.994873	−	0.323254i	−0.234058	−	0.972223i	$-0.575201\pi$
$431$	−20.6541	−	6.71093i	−0.994873	−	0.323254i	−0.760815	+	0.648969i	$0.775201\pi$
$432$	−3.55958	+	2.35879i	−0.171260	+	0.113488i
$433$	24.4418	+	17.7580i	1.17460	+	0.853395i	0.991552	−	0.129709i	$-0.0414043\pi$
$433$	24.4418	+	17.7580i	1.17460	+	0.853395i	0.183046	+	0.983104i	$0.441404\pi$
$434$	9.52281			0.457110
$435$	10.7213	+	9.93605i	0.514047	+	0.476397i
$436$	58.6640			2.80950
$437$	−57.8863			−2.76908
$438$	−8.15484	+	8.79932i	−0.389653	+	0.420448i
$439$	−3.97438	+	1.29135i	−0.189687	+	0.0616330i	−0.402320	−	0.915499i	$-0.631796\pi$
$439$	−3.97438	+	1.29135i	−0.189687	+	0.0616330i	0.212633	+	0.977132i	$0.431796\pi$
$440$	−7.21503	−	5.24202i	−0.343963	−	0.249904i
$441$	−18.0499	−	4.38212i	−0.859521	−	0.208672i
$442$	−18.2703	−	56.2302i	−0.869030	−	2.67460i
$443$	11.0030	−	15.1443i	0.522766	−	0.719526i	−0.463240	−	0.886233i	$-0.653313\pi$
$443$	11.0030	−	15.1443i	0.522766	−	0.719526i	0.986007	+	0.166707i	$0.0533133\pi$
$444$	−19.9980	−	9.25013i	−0.949062	−	0.438992i
$445$	16.4150	+	5.33355i	0.778145	+	0.252835i
$446$	−9.25413	−	3.00685i	−0.438196	−	0.142378i
$447$	−15.8245	+	17.0751i	−0.748472	+	0.807624i
$448$		−	11.2314i		−	0.530633i
$449$	3.39303	+	10.4427i	0.160127	+	0.492821i	0.998644	−	0.0520546i	$-0.0165770\pi$
$449$	3.39303	+	10.4427i	0.160127	+	0.492821i	−0.838517	+	0.544875i	$0.816577\pi$
$450$	44.8134	+	52.7415i	2.11252	+	2.48626i
$451$	−2.81266	+	0.913888i	−0.132443	+	0.0430333i
$452$	52.4475	+	17.0412i	2.46692	+	0.801551i
$453$	15.8770	+	28.4354i	0.745966	+	1.33601i
$454$			50.7317i			2.38096i
$455$	−21.1898			−0.993394
$456$	17.0925	+	30.6124i	0.800431	+	1.43356i
$457$	−7.03562	−	2.28601i	−0.329112	−	0.106935i	0.139800	−	0.990180i	$-0.455354\pi$
$457$	−7.03562	−	2.28601i	−0.329112	−	0.106935i	−0.468912	+	0.883245i	$0.655354\pi$
$458$	29.2052	+	40.1975i	1.36467	+	1.87831i
$459$	18.0402	−	11.9545i	0.842046	−	0.557990i
$460$			123.896i			5.77668i
$461$	18.6426	+	13.5446i	0.868273	+	0.630837i	0.930123	−	0.367248i	$-0.119700\pi$
$461$	18.6426	+	13.5446i	0.868273	+	0.630837i	−0.0618501	+	0.998085i	$0.519700\pi$
$462$	1.24099	+	2.22258i	0.0577359	+	0.103404i
$463$	8.91734	−	12.2737i	0.414424	−	0.570406i	−0.549866	−	0.835253i	$-0.685321\pi$
$463$	8.91734	−	12.2737i	0.414424	−	0.570406i	0.964291	+	0.264847i	$0.0853214\pi$
$464$	1.45282	−	1.05553i	0.0674454	−	0.0490020i
$465$	−14.8443	−	26.5858i	−0.688386	−	1.23289i
$466$	10.5557	+	32.4870i	0.488982	+	1.50493i
$467$	4.84979	+	6.67516i	0.224421	+	0.308889i	0.906349	−	0.422530i	$-0.138858\pi$
$467$	4.84979	+	6.67516i	0.224421	+	0.308889i	−0.681927	+	0.731420i	$0.738858\pi$
$468$	−57.7766	+	23.7594i	−2.67072	+	1.09828i
$469$	−2.71463	−	8.35477i	−0.125350	−	0.385787i
$470$	23.0540	+	16.7497i	1.06340	+	0.772607i
$471$	−10.7474	+	23.2350i	−0.495215	+	1.07061i
$472$			0.0213098i			0.000980863i
$473$	−1.64058	+	2.25806i	−0.0754337	+	0.103826i
$474$	−14.9264	+	2.94927i	−0.685592	+	0.135464i
$475$	49.4021	−	35.8927i	2.26672	−	1.64687i
$476$		−	12.7816i		−	0.585844i
$477$	6.44736	−	26.5567i	0.295204	−	1.21595i
$478$	32.6474	+	23.7197i	1.49326	+	1.08492i
$479$	−1.03564	−	0.752436i	−0.0473196	−	0.0343797i	0.563874	−	0.825861i	$-0.309310\pi$
$479$	−1.03564	−	0.752436i	−0.0473196	−	0.0343797i	−0.611194	+	0.791481i	$0.709310\pi$
$480$	−27.2297	+	15.2038i	−1.24286	+	0.693954i
$481$	−18.3997	−	13.3682i	−0.838954	−	0.609536i
$482$	30.6598	+	22.2756i	1.39651	+	1.01463i
$483$	6.14610	−	13.2873i	0.279657	−	0.604595i
$484$	11.0804	−	34.1020i	0.503655	−	1.55009i
$485$	−51.5116			−2.33902
$486$	−22.2709	−	28.6239i	−1.01023	−	1.29841i
$487$	−0.795882	+	2.44947i	−0.0360648	+	0.110996i	−0.967468	−	0.252992i	$-0.918585\pi$
$487$	−0.795882	+	2.44947i	−0.0360648	+	0.110996i	0.931403	+	0.363988i	$0.118585\pi$
$488$	−24.9803	−	8.11658i	−1.13080	−	0.367420i
$489$	−1.82873	−	3.27523i	−0.0826982	−	0.148111i
$490$	52.9095	+	17.1913i	2.39021	+	0.776625i
$491$	−18.4479	+	5.99410i	−0.832544	+	0.270510i	−0.694116	−	0.719863i	$-0.744205\pi$
$491$	−18.4479	+	5.99410i	−0.832544	+	0.270510i	−0.138427	+	0.990373i	$0.544205\pi$
$492$	2.95642	−	24.7087i	0.133286	−	1.11395i
$493$	−7.36300	+	5.34953i	−0.331613	+	0.240931i
$494$	27.0144	+	83.1418i	1.21544	+	3.74072i
$495$	4.27054	−	6.92917i	0.191947	−	0.311443i
$496$	−3.55765	+	1.15595i	−0.159743	+	0.0519037i
$497$	9.62200	+	6.99079i	0.431606	+	0.313580i
$498$	−4.77765	−	24.1800i	−0.214092	−	1.08353i
$499$	5.09436	+	1.65526i	0.228055	+	0.0740995i	0.420815	−	0.907146i	$-0.361744\pi$
$499$	5.09436	+	1.65526i	0.228055	+	0.0740995i	−0.192761	+	0.981246i	$0.561744\pi$
$500$	−38.0853	−	52.4199i	−1.70322	−	2.34429i
$501$	−0.0300563	+	0.251200i	−0.00134282	+	0.0112228i
$502$	−16.8596	+	51.8886i	−0.752482	+	2.31590i
$503$	7.31437	−	10.0674i	0.326132	−	0.448882i	−0.614195	−	0.789154i	$-0.710519\pi$
$503$	7.31437	−	10.0674i	0.326132	−	0.448882i	0.940327	+	0.340272i	$0.110519\pi$
$504$	−8.84164	+	0.673172i	−0.393838	+	0.0299855i
$505$	−24.5733	−	17.8536i	−1.09350	−	0.794474i
$506$	14.6112	−	4.74748i	0.649549	−	0.211051i
$507$	−41.1704	+	8.13474i	−1.82844	+	0.361277i
$508$	−25.5161	−	8.29069i	−1.13210	−	0.367840i
$509$	1.73780	−	2.39188i	0.0770266	−	0.106018i	−0.768765	−	0.639531i	$-0.779129\pi$
$509$	1.73780	−	2.39188i	0.0770266	−	0.106018i	0.845792	+	0.533513i	$0.179129\pi$
$510$	−56.5951	+	31.6001i	−2.50607	+	1.39927i
$511$	−2.54606	+	0.827266i	−0.112631	+	0.0365961i
$512$	2.85344	+	8.78197i	0.126105	+	0.388112i
$513$	−26.6742	+	17.6759i	−1.17770	+	0.780412i
$514$	39.7165	+	54.6651i	1.75182	+	2.41117i
$515$	12.2673	+	16.8844i	0.540561	+	0.744018i
$516$	−11.4495	−	20.5058i	−0.504035	−	0.902717i
$517$	0.688471	−	2.11889i	0.0302789	−	0.0931889i
$518$	−4.58356	−	6.30873i	−0.201390	−	0.277190i
$519$	8.25083	−	17.8376i	0.362171	−	0.782983i
$520$	73.6679	−	23.9361i	3.23055	−	1.04967i
$521$	8.64577	+	11.8999i	0.378778	+	0.521343i	0.955260	−	0.295766i	$-0.0955750\pi$
$521$	8.64577	+	11.8999i	0.378778	+	0.521343i	−0.576482	+	0.817110i	$0.695575\pi$
$522$	9.87568	+	11.6228i	0.432247	+	0.508717i
$523$	1.97356			0.0862977			0.0431488	−	0.999069i	$-0.486261\pi$
$523$	1.97356			0.0862977			0.0431488	+	0.999069i	$0.486261\pi$
$524$	24.7078	−	17.9513i	1.07937	−	0.784205i
$525$	2.99360	+	15.1508i	0.130652	+	0.661234i
$526$	−0.417845	+	0.575114i	−0.0182189	+	0.0250761i
$527$	18.0304	−	5.85845i	0.785419	−	0.255198i
$528$	−0.733417	−	0.679700i	−0.0319179	−	0.0295801i
$529$	−52.8740	−	38.4152i	−2.29887	−	1.67023i
$530$	−25.2934	+	77.8451i	−1.09868	+	3.38138i
$531$	−0.0193928	+	0.00147650i	−0.000841574	+	6.40746e-5i
$532$			18.8988i			0.819368i
$533$	7.93752	−	24.4292i	0.343812	−	1.05814i
$534$	16.3449	+	7.56038i	0.707313	+	0.327170i
$535$	−1.45483	−	4.47749i	−0.0628976	−	0.193579i
$536$	18.8752	+	25.9795i	0.815284	+	1.12214i
$537$	−14.4292	+	31.1946i	−0.622664	+	1.34615i
$538$	−4.55223	−	1.47911i	−0.196261	−	0.0637690i
$539$		−	4.34952i		−	0.187347i
$540$	37.8324	+	57.0918i	1.62805	+	2.45684i
$541$	−20.8760	+	15.1673i	−0.897529	+	0.652093i	−0.937830	−	0.347094i	$-0.887168\pi$
$541$	−20.8760	+	15.1673i	−0.897529	+	0.652093i	0.0403009	+	0.999188i	$0.487168\pi$
$542$	−24.2869	−	33.4280i	−1.04321	−	1.43586i
$543$	−7.47715	−	6.92950i	−0.320875	−	0.297373i
$544$	−6.00034	−	18.4671i	−0.257262	−	0.791772i
$545$		−	66.3865i		−	2.84368i
$546$	−21.9528	−	2.62667i	−0.939493	−	0.112411i
$547$	3.16057	−	9.72724i	0.135136	−	0.415907i	−0.860475	−	0.509493i	$-0.829833\pi$
$547$	3.16057	−	9.72724i	0.135136	−	0.415907i	0.995611	+	0.0935860i	$0.0298330\pi$
$548$	−15.3887	−	5.00008i	−0.657371	−	0.213593i
$549$	5.65560	−	23.2954i	0.241375	−	0.994224i
$550$	−9.52603	+	13.1115i	−0.406191	+	0.559074i
$551$	10.8869	−	7.90979i	0.463797	−	0.336969i
$552$	−6.35789	+	53.1370i	−0.270610	+	2.26166i
$553$	−3.22898	−	1.04916i	−0.137310	−	0.0446148i
$554$	12.9730	+	9.42542i	0.551169	+	0.400448i
$555$	−10.4678	+	22.6305i	−0.444334	+	0.960611i
$556$	3.41743	−	10.5178i	0.144931	−	0.446053i
$557$	−4.63002	+	14.2497i	−0.196180	+	0.603781i	0.803781	+	0.594926i	$0.202819\pi$
$557$	−4.63002	+	14.2497i	−0.196180	+	0.603781i	−0.999961	+	0.00885479i	$0.997181\pi$
$558$	−12.0832	−	29.3831i	−0.511523	−	1.24389i
$559$	−7.49120	−	23.0555i	−0.316844	−	0.975146i
$560$	2.85398			0.120602
$561$	3.71701	+	3.44477i	0.156932	+	0.145438i
$562$	−17.1253	−	23.5710i	−0.722389	−	0.994282i
$563$	8.52318	+	6.19245i	0.359209	+	0.260981i	0.752722	−	0.658338i	$-0.228740\pi$
$563$	8.52318	+	6.19245i	0.359209	+	0.260981i	−0.393513	+	0.919319i	$0.628740\pi$
$564$	13.7500	+	12.7429i	0.578980	+	0.536574i
$565$	19.2845	−	59.3516i	0.811305	−	2.49694i
$566$		−	53.0437i		−	2.22959i
$567$	−1.22523	−	7.99960i	−0.0514547	−	0.335952i
$568$	−41.3484	−	13.4349i	−1.73494	−	0.563716i
$569$	1.67328	−	5.14984i	0.0701477	−	0.215892i	−0.909837	−	0.414966i	$-0.863793\pi$
$569$	1.67328	−	5.14984i	0.0701477	−	0.215892i	0.979984	+	0.199074i	$0.0637934\pi$
$570$	83.6813	−	46.7237i	3.50502	−	1.95704i
$571$	−21.5482	−	7.00144i	−0.901764	−	0.293001i	−0.178799	−	0.983886i	$-0.557221\pi$
$571$	−21.5482	−	7.00144i	−0.901764	−	0.293001i	−0.722965	+	0.690885i	$0.757221\pi$
$572$	−8.59860	−	11.8350i	−0.359525	−	0.494844i
$573$	0.487845	−	4.07724i	0.0203800	−	0.170329i
$574$	5.17669	−	7.12510i	0.216071	−	0.297396i
$575$	93.2068			3.88699
$576$	−34.6550	+	14.2512i	−1.44396	+	0.593798i
$577$	23.5291	−	32.3850i	0.979530	−	1.34821i	0.0424474	−	0.999099i	$-0.486485\pi$
$577$	23.5291	−	32.3850i	0.979530	−	1.34821i	0.937082	−	0.349108i	$-0.113515\pi$
$578$	−0.249260	−	0.767144i	−0.0103679	−	0.0319090i
$579$	−15.2609	−	27.3321i	−0.634223	−	1.13588i
$580$	−16.9296	−	23.3016i	−0.702964	−	0.967547i
$581$	1.69958	−	5.23077i	0.0705105	−	0.217009i
$582$	−53.3664	−	6.38533i	−2.21211	−	0.264680i
$583$	6.39940			0.265036
$584$	7.91708	−	5.75210i	0.327611	−	0.238023i
$585$	26.8871	+	65.3822i	1.11164	+	2.70322i
$586$	−67.4122	+	21.9036i	−2.78477	+	0.904828i
$587$	−28.3476	−	20.5958i	−1.17003	−	0.850078i	−0.179019	−	0.983846i	$-0.557292\pi$
$587$	−28.3476	−	20.5958i	−1.17003	−	0.850078i	−0.991013	+	0.133768i	$0.957292\pi$
$588$	33.2174	+	15.3648i	1.36986	+	0.633634i
$589$	−26.6597	+	8.66228i	−1.09850	+	0.356923i
$590$	0.0582519			0.00239819
$591$	32.0158	+	14.8090i	1.31696	+	0.609162i
$592$	2.47819	+	1.80051i	0.101853	+	0.0740004i
$593$		−	24.8126i		−	1.01893i	−0.860491	−	0.509466i	$-0.829843\pi$
$593$		−	24.8126i		−	1.01893i	0.860491	−	0.509466i	$-0.170157\pi$
$594$	5.28324	−	6.64929i	0.216774	−	0.272824i
$595$	−14.4642			−0.592973
$596$	37.1109	−	26.9627i	1.52012	−	1.10443i
$597$	−7.27245	−	3.36390i	−0.297642	−	0.137675i
$598$	−41.2339	+	126.905i	−1.68618	+	5.18953i
$599$	21.2067			0.866483			0.433241	−	0.901278i	$-0.357370\pi$
$599$	21.2067			0.866483			0.433241	+	0.901278i	$0.357370\pi$
$600$	−27.5219	−	49.2912i	−1.12358	−	2.01230i
$601$	17.8623			0.728620			0.364310	−	0.931278i	$-0.381305\pi$
$601$	17.8623			0.728620			0.364310	+	0.931278i	$0.381305\pi$
$602$		−	8.31190i		−	0.338768i
$603$	−22.3346	+	18.9772i	−0.909533	+	0.772813i
$604$	−19.8300	−	61.0306i	−0.806873	−	2.48330i
$605$	−38.5911	−	12.5390i	−1.56895	−	0.509784i
$606$	−23.2450	−	21.5425i	−0.944265	−	0.875105i
$607$	−46.6436			−1.89320			−0.946602	−	0.322404i	$-0.895509\pi$
$607$	−46.6436			−1.89320			−0.946602	+	0.322404i	$0.895509\pi$
$608$	8.87207	+	27.3054i	0.359810	+	1.10738i
$609$	0.659710	+	3.33883i	0.0267328	+	0.135296i
$610$	−22.1873	+	68.2854i	−0.898336	+	2.76479i
$611$	11.3740	+	15.6550i	0.460143	+	0.633332i
$612$	−39.4383	+	16.2182i	−1.59420	+	0.655581i
$613$	16.6610	−	5.41350i	0.672933	−	0.218649i	0.0474342	−	0.998874i	$-0.484896\pi$
$613$	16.6610	−	5.41350i	0.672933	−	0.218649i	0.625499	+	0.780225i	$0.284896\pi$
$614$	10.1471	+	31.2296i	0.409505	+	1.26033i
$615$	−27.9613	−	3.34560i	−1.12751	−	0.134907i
$616$	−0.641652	−	1.97480i	−0.0258529	−	0.0795671i
$617$	−5.84456	−	17.9877i	−0.235293	−	0.724157i	−0.997082	−	0.0763327i	$-0.975679\pi$
$617$	−5.84456	−	17.9877i	−0.235293	−	0.724157i	0.761789	−	0.647825i	$-0.224321\pi$
$618$	10.6160	+	19.0130i	0.427038	+	0.764817i
$619$			15.7732i			0.633980i	0.948429	+	0.316990i	$0.102672\pi$
$619$			15.7732i			0.633980i	−0.948429	+	0.316990i	$0.897328\pi$
$620$	18.5402	+	57.0608i	0.744591	+	2.29162i
$621$	−48.7973	−	2.10421i	−1.95817	−	0.0844391i
$622$	9.10622	−	12.5336i	0.365126	−	0.502553i
$623$	2.36205	+	3.25109i	0.0946337	+	0.130252i
$624$	8.52024	−	1.68349i	0.341083	−	0.0673936i
$625$	−19.2099	+	13.9568i	−0.768397	+	0.558273i
$626$	27.0895	−	8.80192i	1.08271	−	0.351795i
$627$	−5.49596	−	5.09343i	−0.219488	−	0.203412i
$628$	29.6495	−	40.8091i	1.18315	−	1.62846i
$629$	−12.5596	−	9.12511i	−0.500786	−	0.363842i
$630$	1.84017	+	24.1693i	0.0733139	+	0.962927i
$631$	13.3135	−	40.9747i	0.530001	−	1.63118i	−0.224208	−	0.974541i	$-0.571979\pi$
$631$	13.3135	−	40.9747i	0.530001	−	1.63118i	0.754209	−	0.656635i	$-0.228021\pi$
$632$	12.4109			0.493680
$633$	21.8516	+	12.4703i	0.868523	+	0.495649i
$634$	16.0508			0.637460
$635$	−9.38207	+	28.8750i	−0.372316	+	1.14587i
$636$	−22.6061	+	48.8724i	−0.896390	+	1.93792i
$637$	30.5626	+	22.2050i	1.21093	+	0.879795i
$638$	−2.09928	+	2.88941i	−0.0831113	+	0.114393i
$639$	9.36139	−	38.5596i	0.370331	−	1.52539i
$640$	72.4883	−	23.5529i	2.86535	−	0.931010i
$641$	33.3442	−	24.2260i	1.31702	−	0.956869i	0.317053	−	0.948408i	$-0.397307\pi$
$641$	33.3442	−	24.2260i	1.31702	−	0.956869i	0.999964	−	0.00846171i	$-0.00269348\pi$
$642$	−0.952183	−	4.81905i	−0.0375797	−	0.190193i
$643$	22.5937	+	31.0975i	0.891007	+	1.22637i	0.973249	+	0.229754i	$0.0737921\pi$
$643$	22.5937	+	31.0975i	0.891007	+	1.22637i	−0.0822416	+	0.996612i	$0.526208\pi$
$644$	−16.9556	+	23.3374i	−0.668144	+	0.919622i
$645$	−23.2052	+	12.9567i	−0.913702	+	0.510168i
$646$	18.4400	+	56.7526i	0.725513	+	2.23290i
$647$			11.5589i			0.454427i	0.973845	+	0.227213i	$0.0729615\pi$
$647$			11.5589i			0.454427i	−0.973845	+	0.227213i	$0.927038\pi$
$648$	13.2960	+	26.4272i	0.522316	+	1.03816i
$649$	−0.00140736	−	0.00433142i	−5.52439e−5	−	0.000170023i
$650$	−43.4978	−	133.872i	−1.70612	−	5.25091i
$651$	0.842252	−	7.03925i	0.0330105	−	0.275890i
$652$	2.28405	+	7.02959i	0.0894504	+	0.275300i
$653$	−43.7200	+	14.2055i	−1.71090	+	0.555904i	−0.990482	−	0.137641i	$-0.956048\pi$
$653$	−43.7200	+	14.2055i	−1.71090	+	0.555904i	−0.720413	+	0.693545i	$0.756048\pi$
$654$	8.22920	−	68.7769i	0.321787	−	2.68939i
$655$	−20.3144	−	27.9603i	−0.793747	−	1.09250i
$656$	−1.06907	+	3.29027i	−0.0417403	+	0.128464i
$657$	5.78319	+	6.80631i	0.225624	+	0.265540i
$658$	2.05026	+	6.31004i	0.0799273	+	0.245991i
$659$	−20.8966			−0.814014			−0.407007	−	0.913425i	$-0.633428\pi$
$659$	−20.8966			−0.814014			−0.407007	+	0.913425i	$0.633428\pi$
$660$	−10.9016	+	11.7632i	−0.424346	+	0.457882i
$661$	1.43708	+	0.466937i	0.0558960	+	0.0181617i	0.336832	−	0.941565i	$-0.390645\pi$
$661$	1.43708	+	0.466937i	0.0558960	+	0.0181617i	−0.280936	+	0.959727i	$0.590645\pi$
$662$	−8.07087	−	24.8396i	−0.313683	−	0.965418i
$663$	−43.1812	+	8.53206i	−1.67702	+	0.331358i
$664$			20.1050i			0.780226i
$665$	21.3867			0.829339
$666$	−13.6500	+	22.1478i	−0.528926	+	0.858209i
$667$	20.5403			0.795322
$668$	0.154044	−	0.474099i	0.00596014	−	0.0183434i
$669$	−3.04115	+	6.57470i	−0.117578	+	0.254193i
$670$	71.0168	−	51.5967i	2.74362	−	1.99336i
$671$	5.61353			0.216708
$672$	−7.20974	−	0.862651i	−0.278122	−	0.0332775i
$673$			22.2638i			0.858205i	0.903256	+	0.429103i	$0.141170\pi$
$673$			22.2638i			0.858205i	−0.903256	+	0.429103i	$0.858830\pi$
$674$	4.97178	+	3.61221i	0.191506	+	0.139137i
$675$	42.9500	−	28.4613i	1.65315	−	1.09547i
$676$	82.6906			3.18041
$677$	21.0653	−	6.84453i	0.809605	−	0.263057i	0.125175	−	0.992135i	$-0.460051\pi$
$677$	21.0653	−	6.84453i	0.809605	−	0.263057i	0.684431	+	0.729078i	$0.260051\pi$
$678$	27.3360	−	59.0982i	1.04983	−	2.26965i
$679$	−9.70286	−	7.04954i	−0.372362	−	0.270537i
$680$	50.2857	−	16.3388i	1.92837	−	0.626565i
$681$	37.5008	+	4.48700i	1.43703	+	0.171942i
$682$	6.01884	−	4.37294i	0.230473	−	0.167449i
$683$	−20.1971			−0.772819			−0.386410	−	0.922327i	$-0.626285\pi$
$683$	−20.1971			−0.772819			−0.386410	+	0.922327i	$0.626285\pi$
$684$	58.3133	−	23.9801i	2.22966	−	0.916904i
$685$	−5.65829	+	17.4144i	−0.216192	+	0.665370i
$686$	16.2212	+	22.3266i	0.619330	+	0.852434i
$687$	32.2970	−	18.0332i	1.23221	−	0.688008i
$688$	1.00896	+	3.10526i	0.0384663	+	0.118387i
$689$	−32.6700	+	44.9664i	−1.24463	+	1.71309i
$690$	145.254	+	17.3798i	5.52973	+	0.661636i
$691$	−45.1494			−1.71757			−0.858783	−	0.512340i	$-0.828779\pi$
$691$	−45.1494			−1.71757			−0.858783	+	0.512340i	$0.828779\pi$
$692$	−22.7620	+	31.3293i	−0.865283	+	1.19096i
$693$	1.75269	−	0.720758i	0.0665792	−	0.0273793i
$694$	19.4979	+	26.8366i	0.740132	+	1.01870i
$695$	−11.9023	−	3.86730i	−0.451481	−	0.146695i
$696$	−6.06509	−	10.8625i	−0.229896	−	0.411740i
$697$	5.41815	−	16.6753i	0.205227	−	0.631624i
$698$	−9.84485	−	3.19878i	−0.372633	−	0.121076i
$699$	24.9480	−	4.92941i	0.943619	−	0.186447i
$700$		−	30.4303i		−	1.15016i
$701$	−12.3900	+	38.1326i	−0.467965	+	1.44025i	0.387251	+	0.921974i	$0.373425\pi$
$701$	−12.3900	+	38.1326i	−0.467965	+	1.44025i	−0.855215	+	0.518273i	$0.826575\pi$
$702$	19.7505	+	71.0694i	0.745434	+	2.68234i
$703$	18.5706	+	13.4924i	0.700405	+	0.508874i
$704$	−5.15753	−	7.09873i	−0.194382	−	0.267544i
$705$	14.4204	−	15.5601i	0.543104	−	0.586026i
$706$	6.23983			0.234839
$707$	−2.18538	−	6.72589i	−0.0821895	−	0.252953i
$708$	0.0380508	+	0.00455281i	0.00143004	+	0.000171105i
$709$	4.98932	−	15.3555i	0.187378	−	0.576690i	−0.812603	−	0.582817i	$-0.801950\pi$
$709$	4.98932	−	15.3555i	0.187378	−	0.576690i	0.999981	+	0.00612738i	$0.00195042\pi$
$710$	−36.7253	+	113.029i	−1.37828	+	4.24190i
$711$	0.859919	+	11.2944i	0.0322495	+	0.423574i
$712$	−11.8843	−	8.63445i	−0.445383	−	0.323590i
$713$	−40.6926	−	13.2218i	−1.52395	−	0.495161i
$714$	−14.9850	−	1.79296i	−0.560798	−	0.0671000i
$715$	−13.3929	+	9.73051i	−0.500866	+	0.363900i
$716$	39.8066	−	54.7890i	1.48764	−	2.04756i
$717$	20.4211	−	22.0350i	0.762641	−	0.822913i
$718$	−29.2654	−	9.50892i	−1.09218	−	0.354870i
$719$	15.4938	−	47.6852i	0.577823	−	1.77836i	−0.0485361	−	0.998821i	$-0.515456\pi$
$719$	15.4938	−	47.6852i	0.577823	−	1.77836i	0.626359	−	0.779535i	$-0.284544\pi$
$720$	−3.62132	−	8.80609i	−0.134959	−	0.328184i
$721$			4.85922i			0.180967i
$722$	−13.6054	−	41.8732i	−0.506341	−	1.55836i
$723$	19.1778	−	20.6935i	0.713232	−	0.769599i
$724$	11.8069	+	16.2508i	0.438800	+	0.603956i
$725$	−17.5298	+	12.7361i	−0.651039	+	0.473007i
$726$	−38.4264	−	17.7742i	−1.42614	−	0.659664i
$727$			21.8916i			0.811914i	0.913892	+	0.405957i	$0.133062\pi$
$727$			21.8916i			0.811914i	−0.913892	+	0.405957i	$0.866938\pi$
$728$	17.1520	+	5.57303i	0.635696	+	0.206550i
$729$	−23.1285	+	13.9309i	−0.856612	+	0.515961i
$730$	−15.7238	−	21.6419i	−0.581963	−	0.801004i
$731$	−5.11349	−	15.7377i	−0.189129	−	0.582080i
$732$	−19.8300	+	42.8707i	−0.732936	+	1.58455i
$733$	−8.73503	+	26.8837i	−0.322636	+	0.992971i	0.649861	+	0.760053i	$0.274827\pi$
$733$	−8.73503	+	26.8837i	−0.322636	+	0.992971i	−0.972496	+	0.232918i	$0.925173\pi$
$734$		−	29.7104i		−	1.09663i
$735$	17.3874	−	37.5901i	0.641345	−	1.38653i
$736$	−13.5421	+	41.6782i	−0.499167	+	1.53628i
$737$	−5.55233	−	4.03401i	−0.204523	−	0.148594i
$738$	−28.5534	−	6.93212i	−1.05107	−	0.255175i
$739$	−16.6485	+	5.40941i	−0.612423	+	0.198988i	−0.598773	−	0.800918i	$-0.704345\pi$
$739$	−16.6485	+	5.40941i	−0.612423	+	0.198988i	−0.0136498	+	0.999907i	$0.504345\pi$
$740$	28.8782	−	39.7474i	1.06158	−	1.46114i
$741$	63.8476	−	12.6155i	2.34550	−	0.463441i
$742$	−15.4177	+	11.2016i	−0.566002	+	0.411224i
$743$	−3.92910			−0.144145			−0.0720723	−	0.997399i	$-0.522961\pi$
$743$	−3.92910			−0.144145			−0.0720723	+	0.997399i	$0.522961\pi$
$744$	5.02343	+	25.4239i	0.184168	+	0.932084i
$745$	−30.5120	−	41.9962i	−1.11787	−	1.53862i
$746$	−29.5274	+	9.59402i	−1.08107	+	0.351262i
$747$	−18.2964	+	1.39302i	−0.669429	+	0.0509680i
$748$	−5.86940	−	8.07854i	−0.214607	−	0.295381i
$749$	0.338726	−	1.04249i	0.0123768	−	0.0380918i
$750$	−66.7988	+	37.2973i	−2.43915	+	1.36191i
$751$	−2.83502	−	3.90207i	−0.103451	−	0.142389i	0.754153	−	0.656699i	$-0.228048\pi$
$751$	−2.83502	−	3.90207i	−0.103451	−	0.142389i	−0.857604	+	0.514311i	$0.828048\pi$
$752$	−1.53192	−	2.10851i	−0.0558634	−	0.0768894i
$753$	36.8648	+	17.0519i	1.34343	+	0.621407i
$754$	−9.58574	−	29.5019i	−0.349092	−	1.07440i
$755$	−69.0646	+	22.4405i	−2.51352	+	0.816692i
$756$	−0.686987	+	15.9315i	−0.0249855	+	0.579421i
$757$	−14.4282	+	19.8588i	−0.524403	+	0.721779i	−0.986265	−	0.165173i	$-0.947182\pi$
$757$	−14.4282	+	19.8588i	−0.524403	+	0.721779i	0.461861	+	0.886952i	$0.347182\pi$
$758$	5.75924	+	1.87129i	0.209185	+	0.0679683i
$759$	−2.21703	−	11.2205i	−0.0804731	−	0.407279i
$760$	−74.3522	+	24.1585i	−2.69704	+	0.876321i
$761$	9.97849	+	7.24980i	0.361720	+	0.262805i	0.753769	−	0.657139i	$-0.228234\pi$
$761$	9.97849	+	7.24980i	0.361720	+	0.262805i	−0.392049	+	0.919944i	$0.628234\pi$
$762$	−13.2992	+	28.7518i	−0.481780	+	1.04157i
$763$	9.08522	−	12.5047i	0.328907	−	0.452702i
$764$	−2.50029	+	7.69511i	−0.0904575	+	0.278399i
$765$	18.3531	+	44.6299i	0.663559	+	1.61360i
$766$	−16.3959	−	22.5670i	−0.592408	−	0.815379i
$767$	0.0376203	+	0.0122236i	0.00135839	+	0.000441368i
$768$	35.5710	−	7.02838i	1.28356	−	0.253615i
$769$	−4.00280	−	2.90821i	−0.144345	−	0.104873i	0.513269	−	0.858228i	$-0.328434\pi$
$769$	−4.00280	−	2.90821i	−0.144345	−	0.104873i	−0.657614	+	0.753355i	$0.728434\pi$
$770$	−5.39827	+	1.75400i	−0.194540	+	0.0632099i
$771$	43.9211	−	24.5235i	1.58178	−	0.883193i
$772$	19.0606	+	58.6626i	0.686007	+	2.11131i
$773$	27.5277	−	20.0000i	0.990101	−	0.719351i	0.0301581	−	0.999545i	$-0.490399\pi$
$773$	27.5277	−	20.0000i	0.990101	−	0.719351i	0.959943	+	0.280194i	$0.0903989\pi$
$774$	−25.6468	+	10.5467i	−0.921855	+	0.379094i
$775$	42.9267	−	13.9477i	1.54197	−	0.501018i
$776$	41.6959	+	13.5478i	1.49680	+	0.486338i
$777$	−5.06881	+	2.83018i	−0.181842	+	0.101532i
$778$	−49.9898	−	16.2427i	−1.79222	−	0.582328i
$779$	−8.01125	+	24.6561i	−0.287033	+	0.883396i
$780$	−27.0014	−	136.655i	−0.966804	−	4.89305i
$781$	9.29175			0.332485
$782$	−28.1463	+	86.6254i	−1.00651	+	3.09772i
$783$	9.46503	−	6.27210i	0.338253	−	0.224147i
$784$	−4.11636	−	2.99071i	−0.147013	−	0.106811i
$785$	−46.1812	−	33.5526i	−1.64828	−	1.19754i
$786$	−17.5799	−	31.4852i	−0.627053	−	1.12304i
$787$	32.2098	+	23.4018i	1.14815	+	0.834183i	0.988234	−	0.152947i	$-0.0488764\pi$
$787$	32.2098	+	23.4018i	1.14815	+	0.834183i	0.159920	+	0.987130i	$0.448876\pi$
$788$	−56.2315	−	40.8545i	−2.00316	−	1.45538i
$789$	0.388167	+	0.359737i	0.0138191	+	0.0128070i
$790$		−	33.9262i		−	1.20704i
$791$	11.7550	−	8.54047i	0.417958	−	0.303664i
$792$	−5.27918	+	4.48562i	−0.187588	+	0.159389i
$793$	−28.6580	+	39.4444i	−1.01768	+	1.40071i
$794$			69.2464i			2.45746i
$795$	55.3059	+	25.5819i	1.96150	+	0.907298i
$796$	12.7731	+	9.28018i	0.452729	+	0.328927i
$797$	13.0787	+	40.2520i	0.463270	+	1.42580i	0.861145	+	0.508359i	$0.169748\pi$
$797$	13.0787	+	40.2520i	0.463270	+	1.42580i	−0.397875	+	0.917440i	$0.630252\pi$
$798$	22.1567	+	2.65107i	0.784339	+	0.0938468i
$799$	7.76389	+	10.6861i	0.274667	+	0.378046i
$800$	−14.2855	−	43.9664i	−0.505070	−	1.55445i
$801$	7.03426	−	11.4134i	0.248543	−	0.403274i
$802$	−52.1141	+	37.8631i	−1.84021	+	1.33699i
$803$	−1.22934	+	1.69204i	−0.0433824	+	0.0597107i
$804$	50.4216	−	28.1531i	1.77823	−	0.992882i
$805$	26.4095	+	19.1876i	0.930813	+	0.676275i
$806$			64.6170i			2.27604i
$807$	−1.49598	+	3.23419i	−0.0526611	+	0.113849i
$808$	15.1952	+	20.9144i	0.534566	+	0.735767i
$809$	−29.9477	−	9.73059i	−1.05290	−	0.342109i	−0.269097	−	0.963113i	$-0.586725\pi$
$809$	−29.9477	−	9.73059i	−1.05290	−	0.342109i	−0.783808	+	0.621004i	$0.786725\pi$
$810$	72.2406	−	36.3456i	2.53828	−	1.27705i
$811$	38.3666			1.34724			0.673618	−	0.739080i	$-0.264740\pi$
$811$	38.3666			1.34724			0.673618	+	0.739080i	$0.264740\pi$
$812$		−	6.70603i		−	0.235335i
$813$	−26.8580	+	14.9963i	−0.941953	+	0.525942i
$814$	−5.79403	−	1.88259i	−0.203081	−	0.0659849i
$815$	7.95496	−	2.58472i	0.278650	−	0.0905389i
$816$	5.81592	−	1.14915i	0.203598	−	0.0402283i
$817$	7.56079	+	23.2697i	0.264519	+	0.814104i
$818$		−	41.0951i		−	1.43686i
$819$	−3.88326	+	15.9952i	−0.135692	+	0.558916i
$820$	52.7723	+	17.1468i	1.84289	+	0.598791i
$821$	−6.02142	−	1.95648i	−0.210149	−	0.0682816i	0.202051	−	0.979375i	$-0.435239\pi$
$821$	−6.02142	−	1.95648i	−0.210149	−	0.0682816i	−0.412200	+	0.911094i	$0.635239\pi$
$822$	−8.02070	+	17.3401i	−0.279754	+	0.604804i
$823$	27.2731	−	37.5382i	0.950681	−	1.30850i	−0.000542954	−	1.00000i	$-0.500173\pi$
$823$	27.2731	−	37.5382i	0.950681	−	1.30850i	0.951224	−	0.308501i	$-0.0998272\pi$
$824$	−5.48900	−	16.8934i	−0.191218	−	0.588510i
$825$	8.84943	+	8.20128i	0.308098	+	0.285532i
$826$	0.0109725	+	0.00797197i	0.000381781	+	0.000277380i
$827$	40.4927	−	13.1569i	1.40807	−	0.457509i	0.496278	−	0.868164i	$-0.334700\pi$
$827$	40.4927	−	13.1569i	1.40807	−	0.457509i	0.911791	+	0.410654i	$0.134700\pi$
$828$	93.5231	+	22.7053i	3.25015	+	0.789063i
$829$	29.7178			1.03214			0.516071	−	0.856546i	$-0.327394\pi$
$829$	29.7178			1.03214			0.516071	+	0.856546i	$0.327394\pi$
$830$	54.9586			1.90764
$831$	8.11466	−	8.75597i	0.281495	−	0.303741i
$832$	76.2105			2.64212
$833$	20.8620	+	15.1572i	0.722826	+	0.525164i
$834$	−11.8515	−	5.48195i	−0.410384	−	0.189824i
$835$	−0.536509	−	0.174322i	−0.0185667	−	0.00603267i
$836$	8.67847	+	11.9449i	0.300151	+	0.413123i
$837$	−22.7887	+	6.33308i	−0.787692	+	0.218903i
$838$	−41.0112	+	13.3254i	−1.41671	+	0.460317i
$839$	−7.40328	−	5.37879i	−0.255589	−	0.185697i	0.452611	−	0.891708i	$-0.350493\pi$
$839$	−7.40328	−	5.37879i	−0.255589	−	0.185697i	−0.708200	+	0.706012i	$0.750493\pi$
$840$	2.34898	−	19.6320i	0.0810477	−	0.677368i
$841$	19.5984	−	14.2391i	0.675807	−	0.491003i
$842$	−31.7668	−	10.3216i	−1.09475	−	0.355707i
$843$	−18.9383	+	10.5743i	−0.652270	+	0.364197i
$844$	−37.4769	−	32.4515i	−1.29001	−	1.11703i
$845$		−	93.5760i		−	3.21911i
$846$	16.8684	−	14.3328i	0.579949	−	0.492771i
$847$	−5.55312	−	7.64321i	−0.190807	−	0.262624i
$848$	4.40020	−	6.05636i	0.151104	−	0.207976i
$849$	−39.2098	−	4.69149i	−1.34568	−	0.161011i
$850$	−29.6916	−	91.3813i	−1.01841	−	3.13435i
$851$	10.8271	+	33.3223i	0.371147	+	1.14227i
$852$	−32.8234	+	70.9614i	−1.12451	+	2.43110i
$853$	−10.0649	+	30.9765i	−0.344615	+	1.06062i	0.617174	+	0.786826i	$0.288277\pi$
$853$	−10.0649	+	30.9765i	−0.344615	+	1.06062i	−0.961790	+	0.273790i	$0.911723\pi$
$854$	−13.5243	+	9.82601i	−0.462793	+	0.336239i
$855$	−27.1369	−	65.9896i	−0.928061	−	2.25680i
$856$			4.00692i			0.136954i
$857$	0.412298	−	0.133964i	0.0140838	−	0.00457612i	−0.301967	−	0.953319i	$-0.597643\pi$
$857$	0.412298	−	0.133964i	0.0140838	−	0.00457612i	0.316050	+	0.948742i	$0.397643\pi$
$858$	−15.0813	+	8.42070i	−0.514868	+	0.287478i
$859$			52.8645i			1.80371i	0.432037	+	0.901856i	$0.357795\pi$
$859$			52.8645i			1.80371i	−0.432037	+	0.901856i	$0.642205\pi$
$860$	49.8050	−	16.1826i	1.69834	−	0.551823i
$861$	−4.80901	−	4.45679i	−0.163891	−	0.151887i
$862$	29.6983	−	40.8762i	1.01153	−	1.39225i
$863$	2.32775	−	0.756332i	0.0792375	−	0.0257458i	−0.269130	−	0.963104i	$-0.586736\pi$
$863$	2.32775	−	0.756332i	0.0792375	−	0.0257458i	0.348368	+	0.937358i	$0.386736\pi$
$864$	6.48646	+	23.3406i	0.220674	+	0.794064i
$865$	35.4534	+	25.7584i	1.20545	+	0.875813i
$866$	−56.8651	+	41.3149i	−1.93235	+	1.40394i
$867$	−0.589118	+	0.116402i	−0.0200075	+	0.00395323i
$868$	−4.31669	+	13.2854i	−0.146518	+	0.450936i
$869$	−2.52264	+	0.819655i	−0.0855747	+	0.0278049i
$870$	−29.6933	+	16.5794i	−1.00670	+	0.562093i
$871$	56.6912	−	18.4201i	1.92091	−	0.624141i
$872$	−17.4600	+	53.7363i	−0.591270	+	1.81974i
$873$	−9.44006	+	38.8836i	−0.319498	+	1.31601i
$874$	41.6170	−	128.084i	1.40772	−	4.33250i
$875$	−17.0720			−0.577137
$876$	−8.57947	−	15.3657i	−0.289873	−	0.519158i
$877$		−	1.70633i		−	0.0576188i	−0.999585	−	0.0288094i	$-0.990828\pi$
$877$		−	1.70633i		−	0.0576188i	0.999585	−	0.0288094i	$-0.00917159\pi$
$878$		−	9.72245i		−	0.328117i
$879$	10.2288	+	51.7683i	0.345008	+	1.74610i
$880$	1.80384	−	1.31057i	0.0608074	−	0.0441792i
$881$	−8.84322	−	12.1717i	−0.297936	−	0.410073i	0.633636	−	0.773632i	$-0.281562\pi$
$881$	−8.84322	−	12.1717i	−0.297936	−	0.410073i	−0.931572	+	0.363558i	$0.881562\pi$
$882$	22.6731	−	36.7883i	0.763444	−	1.23873i
$883$	2.31347	−	3.18423i	0.0778546	−	0.107158i	−0.768314	−	0.640074i	$-0.778904\pi$
$883$	2.31347	−	3.18423i	0.0778546	−	0.107158i	0.846168	+	0.532916i	$0.178904\pi$
$884$	86.7295			2.91703
$885$	0.00515213	−	0.0430597i	0.000173187	−	0.00144744i
$886$	25.5989	+	35.2339i	0.860013	+	1.18371i
$887$		−	33.7780i		−	1.13415i	−0.823665	−	0.567076i	$-0.808074\pi$
$887$		−	33.7780i		−	1.13415i	0.823665	−	0.567076i	$-0.191926\pi$
$888$	14.4251	−	15.5651i	0.484074	−	0.522330i
$889$	−5.71888	+	4.15501i	−0.191805	+	0.139355i
$890$	−23.6029	+	32.4866i	−0.791171	+	1.08895i
$891$	−4.44787	−	4.49347i	−0.149009	−	0.150537i
$892$	8.38980	−	11.5476i	0.280911	−	0.386641i
$893$	−11.4797	−	15.8004i	−0.384152	−	0.528740i
$894$	−26.4048	−	47.2906i	−0.883110	−	1.58163i
$895$	−62.0014	−	45.0467i	−2.07248	−	1.50574i
$896$	16.8774	+	5.48379i	0.563834	+	0.183201i
$897$	90.1611	+	41.7043i	3.01039	+	1.39247i
$898$	−25.5457			−0.852472
$899$	9.45990	−	3.07371i	0.315505	−	0.102514i
$900$	−93.8943	+	38.6121i	−3.12981	+	1.28707i
$901$	−22.3006	+	30.6941i	−0.742939	+	1.02257i
$902$		−	6.88055i		−	0.229097i
$903$	−6.14415	−	0.735152i	−0.204464	−	0.0244643i
$904$	−31.2195	+	42.9700i	−1.03835	+	1.42916i
$905$	18.3900	−	13.3611i	0.611305	−	0.444139i
$906$	−74.3331	+	14.6873i	−2.46955	+	0.487952i
$907$		−	43.4138i		−	1.44153i	−0.693179	−	0.720765i	$-0.743791\pi$
$907$		−	43.4138i		−	1.44153i	0.693179	−	0.720765i	$-0.256209\pi$
$908$	−70.7765	−	22.9967i	−2.34880	−	0.763172i
$909$	−17.9801	+	15.2774i	−0.596363	+	0.506718i
$910$	15.2343	−	46.8863i	0.505012	−	1.55427i
$911$	−24.8083			−0.821936			−0.410968	−	0.911650i	$-0.634809\pi$
$911$	−24.8083			−0.821936			−0.410968	+	0.911650i	$0.634809\pi$
$912$	−8.59939	+	1.69913i	−0.284754	+	0.0562638i
$913$	−1.32780	−	4.08654i	−0.0439437	−	0.135245i
$914$	10.1164	−	13.9241i	0.334622	−	0.460567i
$915$	48.5141	+	22.4404i	1.60383	+	0.741855i
$916$	−69.3188	+	22.5230i	−2.29036	+	0.744182i
$917$		−	8.04677i		−	0.265728i
$918$	13.4817	+	48.5119i	0.444962	+	1.60113i
$919$	−2.38745	+	3.28604i	−0.0787546	+	0.108396i	−0.846577	−	0.532267i	$-0.821340\pi$
$919$	−2.38745	+	3.28604i	−0.0787546	+	0.108396i	0.767822	+	0.640663i	$0.221340\pi$
$920$	−113.489	−	36.8748i	−3.74162	−	1.21573i
$921$	23.9824	−	4.73861i	0.790246	−	0.156143i
$922$	−43.3730	+	31.5123i	−1.42841	+	1.03780i
$923$	−47.4360	+	65.2900i	−1.56137	+	2.14905i
$924$	−3.66330	+	0.723821i	−0.120514	+	0.0238120i
$925$	−29.9019	−	21.7250i	−0.983168	−	0.714313i
$926$	20.7467	+	28.5553i	0.681778	+	0.938386i
$927$	14.9934	−	6.16571i	0.492447	−	0.202508i
$928$	−3.14815	−	9.68901i	−0.103343	−	0.318057i
$929$	8.51935	−	26.2199i	0.279511	−	0.860246i	−0.708479	−	0.705731i	$-0.750619\pi$
$929$	8.51935	−	26.2199i	0.279511	−	0.860246i	0.987990	−	0.154515i	$-0.0493815\pi$
$930$	69.4980	−	13.7319i	2.27893	−	0.450288i
$931$	−30.8465	−	22.4113i	−1.01095	−	0.734501i
$932$	−50.1080			−1.64134
$933$	−8.45945	−	7.83986i	−0.276950	−	0.256665i
$934$	−18.2567	+	5.93197i	−0.597378	+	0.194100i
$935$	−9.14199	+	6.64205i	−0.298975	+	0.217218i
$936$	−4.56780	−	59.9949i	−0.149303	−	1.96099i
$937$	−33.5203	+	24.3539i	−1.09506	+	0.795609i	−0.980247	−	0.197778i	$-0.936627\pi$
$937$	−33.5203	+	24.3539i	−1.09506	+	0.795609i	−0.114815	+	0.993387i	$0.536627\pi$
$938$	20.4381			0.667328
$939$	−4.11042	−	20.8030i	−0.134138	−	0.678881i
$940$	−33.8181	+	24.5703i	−1.10303	+	0.801396i
$941$	21.4931	−	15.6157i	0.700656	−	0.509057i	−0.179490	−	0.983760i	$-0.557445\pi$
$941$	21.4931	−	15.6157i	0.700656	−	0.509057i	0.880146	+	0.474703i	$0.157445\pi$
$942$	−43.6849	−	40.4853i	−1.42333	−	1.31908i
$943$	−32.0137	+	23.2593i	−1.04251	+	0.757426i
$944$	−0.00506694	−	0.00164635i	−0.000164915	−	5.35840e-5i
$945$	18.0287	+	0.777421i	0.586472	+	0.0252895i
$946$	−3.81688	−	5.25349i	−0.124098	−	0.170806i
$947$	−31.4100	−	10.2057i	−1.02069	−	0.331642i	−0.249586	−	0.968353i	$-0.580294\pi$
$947$	−31.4100	−	10.2057i	−1.02069	−	0.331642i	−0.771102	+	0.636711i	$0.780294\pi$
$948$	2.65157	−	22.1609i	0.0861191	−	0.719754i
$949$	−5.61340	−	17.2763i	−0.182219	−	0.560812i
$950$	43.9018	+	135.116i	1.42436	+	4.38374i
$951$	1.41963	−	11.8647i	0.0460346	−	0.384741i
$952$	11.7080	+	3.80415i	0.379457	+	0.123293i
$953$	5.50096	+	7.57143i	0.178194	+	0.245263i	0.888766	−	0.458362i	$-0.151564\pi$
$953$	5.50096	+	7.57143i	0.178194	+	0.245263i	−0.710572	+	0.703625i	$0.751564\pi$
$954$	54.1262	+	33.3587i	1.75240	+	1.08003i
$955$	8.70809	+	2.82943i	0.281787	+	0.0915582i
$956$	−47.8908	+	34.7947i	−1.54890	+	1.12534i
$957$	1.95018	+	1.80734i	0.0630403	+	0.0584231i
$958$	2.40947	−	1.75058i	0.0778464	−	0.0565587i
$959$	−3.44903	+	2.50587i	−0.111375	+	0.0809187i
$960$	−16.1957	−	81.9673i	−0.522714	−	2.64548i
$961$	10.2803			0.331623
$962$	42.8079	−	31.1017i	1.38018	−	1.00276i
$963$	−3.64645	+	0.277628i	−0.117505	+	0.00894645i
$964$	−44.9751	+	32.6763i	−1.44855	+	1.05243i
$965$	66.3848	−	21.5697i	2.13700	−	0.694355i
$966$	24.9819	+	23.1522i	0.803781	+	0.744910i
$967$	−19.2127			−0.617837			−0.308919	−	0.951088i	$-0.599967\pi$
$967$	−19.2127			−0.617837			−0.308919	+	0.951088i	$0.599967\pi$
$968$	27.9396	+	20.2993i	0.898014	+	0.652445i
$969$	43.5824	−	8.61132i	1.40007	−	0.276636i
$970$	37.0340	−	113.979i	1.18909	−	3.65964i
$971$	−4.09728	−	12.6101i	−0.131488	−	0.404679i	0.863539	−	0.504282i	$-0.168243\pi$
$971$	−4.09728	−	12.6101i	−0.131488	−	0.404679i	−0.995027	+	0.0996032i	$0.968243\pi$
$972$	50.0290	−	18.0952i	1.60468	−	0.580404i
$973$	−1.71270	−	2.35733i	−0.0549066	−	0.0755725i
$974$	−4.84771	−	3.52206i	−0.155331	−	0.112854i
$975$	−102.806	+	20.3131i	−3.29241	+	0.650539i
$976$	3.85984	−	5.31261i	0.123550	−	0.170053i
$977$	8.14905	−	5.92063i	0.260711	−	0.189418i	−0.449749	−	0.893155i	$-0.648487\pi$
$977$	8.14905	−	5.92063i	0.260711	−	0.189418i	0.710461	+	0.703737i	$0.248487\pi$
$978$	8.56179	−	1.69170i	0.273776	−	0.0540946i
$979$	2.98585	+	0.970160i	0.0954280	+	0.0310065i
$980$	−47.9677	+	66.0219i	−1.53227	+	2.10899i
$981$	−50.1119	−	12.1660i	−1.59995	−	0.388432i
$982$		−	45.1288i		−	1.44012i
$983$	−28.4954	+	9.25872i	−0.908863	+	0.295307i	−0.725890	−	0.687811i	$-0.758572\pi$
$983$	−28.4954	+	9.25872i	−0.908863	+	0.295307i	−0.182973	+	0.983118i	$0.558572\pi$
$984$	21.7533	+	10.0621i	0.693470	+	0.320767i
$985$	−46.2326	+	63.6337i	−1.47309	+	2.02754i
$986$	−6.54323	−	20.1380i	−0.208379	−	0.641324i
$987$	4.84571	−	0.957451i	0.154241	−	0.0304760i
$988$	−128.238			−4.07979
$989$	−11.5406	+	35.5182i	−0.366968	+	1.12941i
$990$	12.2618	+	14.4310i	0.389704	+	0.458648i
$991$	30.7337	+	9.98599i	0.976289	+	0.317215i	0.753352	−	0.657618i	$-0.228436\pi$
$991$	30.7337	+	9.98599i	0.976289	+	0.317215i	0.222937	+	0.974833i	$0.428436\pi$
$992$			21.2215i			0.673784i
$993$	−19.0752	+	3.76902i	−0.605334	+	0.119606i
$994$	−22.3861	+	16.2644i	−0.710043	+	0.515877i
$995$	10.5018	−	14.4545i	0.332930	−	0.458239i
$996$	35.8995	+	4.29541i	1.13752	+	0.136105i
$997$		−	18.2615i		−	0.578347i	−0.957277	−	0.289174i	$-0.906620\pi$
$997$		−	18.2615i		−	0.578347i	0.957277	−	0.289174i	$-0.0933805\pi$
$998$	−7.32511	+	10.0822i	−0.231872	+	0.319145i
$999$	15.1643	+	12.0489i	0.479778	+	0.381211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.k.a.23.7	✓	272
3.2	odd	2	inner	633.2.k.a.23.62	yes	272
211.156	odd	10	inner	633.2.k.a.578.62	yes	272
633.578	even	10	inner	633.2.k.a.578.7	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.k.a.23.7	✓	272	1.1	even	1	trivial
633.2.k.a.23.62	yes	272	3.2	odd	2	inner
633.2.k.a.578.7	yes	272	633.578	even	10	inner
633.2.k.a.578.62	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)

\(f(q)\)	\(=\)	\(q+(-0.718944 + 2.21268i) q^{2} +(1.57202 + 0.727145i) q^{3} +(-2.76105 - 2.00602i) q^{4} +(-2.27009 + 3.12451i) q^{5} +(-2.73914 + 2.95561i) q^{6} +(-0.855199 + 0.277871i) q^{7} +(2.65928 - 1.93208i) q^{8} +(1.94252 + 2.28618i) q^{9} +O(q^{10})\)	\(q+(-0.718944 + 2.21268i) q^{2} +(1.57202 + 0.727145i) q^{3} +(-2.76105 - 2.00602i) q^{4} +(-2.27009 + 3.12451i) q^{5} +(-2.73914 + 2.95561i) q^{6} +(-0.855199 + 0.277871i) q^{7} +(2.65928 - 1.93208i) q^{8} +(1.94252 + 2.28618i) q^{9} +(-5.28148 - 7.26933i) q^{10} +(-0.412923 + 0.568340i) q^{11} +(-2.88177 - 5.16119i) q^{12} +(-1.88549 - 5.80295i) q^{13} -2.09206i q^{14} +(-5.84060 + 3.26112i) q^{15} +(0.253950 + 0.781577i) q^{16} +(-1.28704 - 3.96109i) q^{17} +(-6.45515 + 2.65455i) q^{18} +(1.90301 + 5.85685i) q^{19} +(12.5356 - 4.07307i) q^{20} +(-1.54645 - 0.185034i) q^{21} +(-0.960687 - 1.32227i) q^{22} +(-2.90469 + 8.93972i) q^{23} +(5.58535 - 1.10359i) q^{24} +(-3.06416 - 9.43053i) q^{25} +14.1956 q^{26} +(1.39131 + 5.00642i) q^{27} +(2.91866 + 0.948330i) q^{28} +(-0.675260 - 2.07824i) q^{29} +(-3.01675 - 15.2680i) q^{30} +4.55189i q^{31} +4.66213 q^{32} +(-1.06239 + 0.593190i) q^{33} +9.68994 q^{34} +(1.07317 - 3.30287i) q^{35} +(-0.777276 - 10.2090i) q^{36} +(3.01556 - 2.19094i) q^{37} -14.3275 q^{38} +(1.25554 - 10.4934i) q^{39} +12.6949i q^{40} +(3.40579 + 2.47445i) q^{41} +(1.52123 - 3.28876i) q^{42} +3.97307 q^{43} +(2.28020 - 0.740882i) q^{44} +(-11.5529 + 0.879596i) q^{45} +(-17.6924 - 12.8543i) q^{46} +(-3.01619 + 0.980019i) q^{47} +(-0.169104 + 1.41332i) q^{48} +(-5.00897 + 3.63923i) q^{49} +23.0697 q^{50} +(0.857034 - 7.16279i) q^{51} +(-6.43488 + 19.8045i) q^{52} +(-5.35436 - 7.36964i) q^{53} +(-12.0779 - 0.520816i) q^{54} +(-0.838411 - 2.58036i) q^{55} +(-1.73734 + 2.39125i) q^{56} +(-1.26721 + 10.5909i) q^{57} +5.08395 q^{58} +(-0.00381059 + 0.00524483i) q^{59} +(22.6680 + 2.71225i) q^{60} +(-4.69682 - 6.46461i) q^{61} +(-10.0719 - 3.27255i) q^{62} +(-2.29651 - 1.41537i) q^{63} +(-3.85971 + 11.8790i) q^{64} +(22.4116 + 7.28196i) q^{65} +(-0.548740 - 2.77720i) q^{66} +9.76938i q^{67} +(-4.39245 + 13.5186i) q^{68} +(-11.0667 + 11.9413i) q^{69} +(6.53665 + 4.74915i) q^{70} +(-7.77437 - 10.7005i) q^{71} +(9.58277 + 2.32648i) q^{72} +2.97716 q^{73} +(2.67982 + 8.24764i) q^{74} +(2.04042 - 17.0531i) q^{75} +(6.49466 - 19.9885i) q^{76} +(0.195206 - 0.600783i) q^{77} +(22.3159 + 10.3223i) q^{78} +(3.05461 + 2.21930i) q^{79} +(-3.01853 - 0.980780i) q^{80} +(-1.45322 + 8.88190i) q^{81} +(-7.92374 + 5.75693i) q^{82} +(-3.59515 + 4.94830i) q^{83} +(3.89863 + 3.61308i) q^{84} +(15.2981 + 4.97067i) q^{85} +(-2.85642 + 8.79115i) q^{86} +(0.449653 - 3.75805i) q^{87} +2.30917i q^{88} +(-1.38100 - 4.25027i) q^{89} +(6.35960 - 26.1952i) q^{90} +(3.22494 + 4.43875i) q^{91} +(25.9532 - 18.8561i) q^{92} +(-3.30988 + 7.15568i) q^{93} -7.37845i q^{94} +(-22.6198 - 7.34961i) q^{95} +(7.32899 + 3.39005i) q^{96} +(7.83971 + 10.7904i) q^{97} +(-4.45128 - 13.6996i) q^{98} +(-2.10144 + 0.159996i) 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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