LMFDB - Embedded newform 966.2.k.a.229.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.7
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.52184 - 2.63590i) q^{5} -1.00000i q^{6} +(1.49399 + 2.18358i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.52184 - 2.63590i) q^{5} -1.00000i q^{6} +(1.49399 + 2.18358i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.52184 + 2.63590i) q^{10} +(2.07367 - 1.19724i) q^{11} +(0.866025 + 0.500000i) q^{12} -4.32646i q^{13} +(-2.63803 + 0.202041i) q^{14} +3.04368i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.399743 - 0.692374i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.07775 + 1.86672i) q^{19} -3.04368 q^{20} +(-2.38562 - 1.14404i) q^{21} +2.39447i q^{22} +(-2.90512 - 3.81580i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.13198 - 3.69270i) q^{25} +(3.74682 + 2.16323i) q^{26} +1.00000i q^{27} +(1.14404 - 2.38562i) q^{28} -4.78811 q^{29} +(-2.63590 - 1.52184i) q^{30} +(3.53448 - 2.04063i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.19724 + 2.07367i) q^{33} +0.799485 q^{34} +(8.02929 - 0.614946i) q^{35} -1.00000 q^{36} +(-3.53978 - 2.04369i) q^{37} +(-1.07775 - 1.86672i) q^{38} +(2.16323 + 3.74682i) q^{39} +(1.52184 - 2.63590i) q^{40} -7.66774i q^{41} +(2.18358 - 1.49399i) q^{42} -3.15309i q^{43} +(-2.07367 - 1.19724i) q^{44} +(-1.52184 - 2.63590i) q^{45} +(4.75713 - 0.608007i) q^{46} +(7.12526 + 4.11377i) q^{47} -1.00000i q^{48} +(-2.53602 + 6.52446i) q^{49} +4.26396 q^{50} +(0.692374 + 0.399743i) q^{51} +(-3.74682 + 2.16323i) q^{52} +(9.49569 - 5.48234i) q^{53} +(-0.866025 - 0.500000i) q^{54} -7.28799i q^{55} +(1.49399 + 2.18358i) q^{56} -2.15551i q^{57} +(2.39406 - 4.14663i) q^{58} +(10.6576 - 6.15319i) q^{59} +(2.63590 - 1.52184i) q^{60} +(-2.01946 + 3.49780i) q^{61} +4.08126i q^{62} +(2.63803 - 0.202041i) q^{63} +1.00000 q^{64} +(-11.4041 - 6.58416i) q^{65} +(-1.19724 - 2.07367i) q^{66} +(-4.06092 + 2.34457i) q^{67} +(-0.399743 + 0.692374i) q^{68} +(4.42380 + 1.85202i) q^{69} +(-3.48209 + 7.26105i) q^{70} +6.20671 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.21583 - 1.27931i) q^{73} +(3.53978 - 2.04369i) q^{74} +(3.69270 + 2.13198i) q^{75} +2.15551 q^{76} +(5.71229 + 2.73937i) q^{77} -4.32646 q^{78} +(-7.62601 - 4.40288i) q^{79} +(1.52184 + 2.63590i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.64046 + 3.83387i) q^{82} -0.377697 q^{83} +(0.202041 + 2.63803i) q^{84} -2.43337 q^{85} +(2.73065 + 1.57654i) q^{86} +(4.14663 - 2.39406i) q^{87} +(2.07367 - 1.19724i) q^{88} +(0.328941 - 0.569742i) q^{89} +3.04368 q^{90} +(9.44715 - 6.46366i) q^{91} +(-1.85202 + 4.42380i) q^{92} +(-2.04063 + 3.53448i) q^{93} +(-7.12526 + 4.11377i) q^{94} +(3.28033 + 5.68170i) q^{95} +(0.866025 + 0.500000i) q^{96} -2.07359 q^{97} +(-4.38234 - 5.45849i) q^{98} -2.39447i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.52184	−	2.63590i	0.680587	−	1.17881i	−0.294216	−	0.955739i	$-0.595058\pi$
$5$	1.52184	−	2.63590i	0.680587	−	1.17881i	0.974802	−	0.223071i	$-0.0716083\pi$
$6$		−	1.00000i		−	0.408248i
$7$	1.49399	+	2.18358i	0.564673	+	0.825315i
$7$	1.49399	+	2.18358i	0.564673	+	0.825315i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.52184	+	2.63590i	0.481247	+	0.833545i
$11$	2.07367	−	1.19724i	0.625236	−	0.360980i	−0.153669	−	0.988122i	$-0.549109\pi$
$11$	2.07367	−	1.19724i	0.625236	−	0.360980i	0.778905	+	0.627142i	$0.215776\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	4.32646i		−	1.19994i	−0.800021	−	0.599971i	$-0.795179\pi$
$13$		−	4.32646i		−	1.19994i	0.800021	−	0.599971i	$-0.204821\pi$
$14$	−2.63803	+	0.202041i	−0.705042	+	0.0539976i
$15$			3.04368i			0.785874i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.399743	−	0.692374i	−0.0969518	−	0.167925i	0.813470	−	0.581607i	$-0.197576\pi$
$17$	−0.399743	−	0.692374i	−0.0969518	−	0.167925i	−0.910422	+	0.413682i	$0.864243\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.07775	+	1.86672i	−0.247254	+	0.428256i	−0.962763	−	0.270347i	$-0.912861\pi$
$19$	−1.07775	+	1.86672i	−0.247254	+	0.428256i	0.715509	+	0.698603i	$0.246195\pi$
$20$	−3.04368			−0.680587
$21$	−2.38562	−	1.14404i	−0.520584	−	0.249650i
$22$			2.39447i			0.510503i
$23$	−2.90512	−	3.81580i	−0.605759	−	0.795648i
$23$	−2.90512	−	3.81580i	−0.605759	−	0.795648i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−2.13198	−	3.69270i	−0.426396	−	0.738540i
$26$	3.74682	+	2.16323i	0.734812	+	0.424244i
$27$			1.00000i			0.192450i
$28$	1.14404	−	2.38562i	0.216203	−	0.450839i
$29$	−4.78811			−0.889130			−0.444565	−	0.895747i	$-0.646642\pi$
$29$	−4.78811			−0.889130			−0.444565	+	0.895747i	$0.646642\pi$
$30$	−2.63590	−	1.52184i	−0.481247	−	0.277848i
$31$	3.53448	−	2.04063i	0.634811	−	0.366508i	−0.147802	−	0.989017i	$-0.547220\pi$
$31$	3.53448	−	2.04063i	0.634811	−	0.366508i	0.782613	+	0.622509i	$0.213887\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.19724	+	2.07367i	−0.208412	+	0.360980i
$34$	0.799485			0.137111
$35$	8.02929	−	0.614946i	1.35720	−	0.103945i
$36$	−1.00000			−0.166667
$37$	−3.53978	−	2.04369i	−0.581937	−	0.335981i	0.179966	−	0.983673i	$-0.442401\pi$
$37$	−3.53978	−	2.04369i	−0.581937	−	0.335981i	−0.761903	+	0.647691i	$0.775735\pi$
$38$	−1.07775	−	1.86672i	−0.174835	−	0.302823i
$39$	2.16323	+	3.74682i	0.346394	+	0.599971i
$40$	1.52184	−	2.63590i	0.240624	−	0.416772i
$41$		−	7.66774i		−	1.19750i	−0.800936	−	0.598750i	$-0.795664\pi$
$41$		−	7.66774i		−	1.19750i	0.800936	−	0.598750i	$-0.204336\pi$
$42$	2.18358	−	1.49399i	0.336933	−	0.230527i
$43$		−	3.15309i		−	0.480841i	−0.970669	−	0.240421i	$-0.922715\pi$
$43$		−	3.15309i		−	0.480841i	0.970669	−	0.240421i	$-0.0772854\pi$
$44$	−2.07367	−	1.19724i	−0.312618	−	0.180490i
$45$	−1.52184	−	2.63590i	−0.226862	−	0.392937i
$46$	4.75713	−	0.608007i	0.701401	−	0.0896458i
$47$	7.12526	+	4.11377i	1.03933	+	0.600055i	0.919642	−	0.392757i	$-0.128479\pi$
$47$	7.12526	+	4.11377i	1.03933	+	0.600055i	0.119683	+	0.992812i	$0.461812\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−2.53602	+	6.52446i	−0.362288	+	0.932066i
$50$	4.26396			0.603015
$51$	0.692374	+	0.399743i	0.0969518	+	0.0559752i
$52$	−3.74682	+	2.16323i	−0.519590	+	0.299986i
$53$	9.49569	−	5.48234i	1.30433	−	0.753057i	0.323189	−	0.946334i	$-0.395245\pi$
$53$	9.49569	−	5.48234i	1.30433	−	0.753057i	0.981144	+	0.193277i	$0.0619117\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		−	7.28799i		−	0.982713i
$56$	1.49399	+	2.18358i	0.199642	+	0.291793i
$57$		−	2.15551i		−	0.285504i
$58$	2.39406	−	4.14663i	0.314355	−	0.544479i
$59$	10.6576	−	6.15319i	1.38751	−	0.801077i	0.394473	−	0.918908i	$-0.370927\pi$
$59$	10.6576	−	6.15319i	1.38751	−	0.801077i	0.993034	+	0.117831i	$0.0375940\pi$
$60$	2.63590	−	1.52184i	0.340293	−	0.196468i
$61$	−2.01946	+	3.49780i	−0.258565	+	0.447848i	−0.965858	−	0.259073i	$-0.916583\pi$
$61$	−2.01946	+	3.49780i	−0.258565	+	0.447848i	0.707293	+	0.706921i	$0.249916\pi$
$62$			4.08126i			0.518321i
$63$	2.63803	−	0.202041i	0.332360	−	0.0254547i
$64$	1.00000			0.125000
$65$	−11.4041	−	6.58416i	−1.41451	−	0.816665i
$66$	−1.19724	−	2.07367i	−0.147370	−	0.255251i
$67$	−4.06092	+	2.34457i	−0.496120	+	0.286435i	−0.727110	−	0.686521i	$-0.759137\pi$
$67$	−4.06092	+	2.34457i	−0.496120	+	0.286435i	0.230990	+	0.972956i	$0.425804\pi$
$68$	−0.399743	+	0.692374i	−0.0484759	+	0.0839627i
$69$	4.42380	+	1.85202i	0.532563	+	0.222957i
$70$	−3.48209	+	7.26105i	−0.416189	+	0.867861i
$71$	6.20671			0.736601			0.368300	−	0.929707i	$-0.379940\pi$
$71$	6.20671			0.736601			0.368300	+	0.929707i	$0.379940\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.21583	−	1.27931i	0.259344	−	0.149732i	−0.364691	−	0.931128i	$-0.618826\pi$
$73$	2.21583	−	1.27931i	0.259344	−	0.149732i	0.624035	+	0.781396i	$0.285492\pi$
$74$	3.53978	−	2.04369i	0.411491	−	0.237575i
$75$	3.69270	+	2.13198i	0.426396	+	0.246180i
$76$	2.15551			0.247254
$77$	5.71229	+	2.73937i	0.650976	+	0.312180i
$78$	−4.32646			−0.489875
$79$	−7.62601	−	4.40288i	−0.857993	−	0.495363i	0.00534663	−	0.999986i	$-0.498298\pi$
$79$	−7.62601	−	4.40288i	−0.857993	−	0.495363i	−0.863340	+	0.504623i	$0.831631\pi$
$80$	1.52184	+	2.63590i	0.170147	+	0.294703i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.64046	+	3.83387i	0.733316	+	0.423380i
$83$	−0.377697			−0.0414576			−0.0207288	−	0.999785i	$-0.506599\pi$
$83$	−0.377697			−0.0414576			−0.0207288	+	0.999785i	$0.506599\pi$
$84$	0.202041	+	2.63803i	0.0220444	+	0.287832i
$85$	−2.43337			−0.263936
$86$	2.73065	+	1.57654i	0.294454	+	0.170003i
$87$	4.14663	−	2.39406i	0.444565	−	0.256670i
$88$	2.07367	−	1.19724i	0.221054	−	0.127626i
$89$	0.328941	−	0.569742i	0.0348676	−	0.0603925i	−0.848065	−	0.529892i	$-0.822232\pi$
$89$	0.328941	−	0.569742i	0.0348676	−	0.0603925i	0.882933	+	0.469500i	$0.155566\pi$
$90$	3.04368			0.320832
$91$	9.44715	−	6.46366i	0.990330	−	0.677576i
$92$	−1.85202	+	4.42380i	−0.193086	+	0.461213i
$93$	−2.04063	+	3.53448i	−0.211604	+	0.366508i
$94$	−7.12526	+	4.11377i	−0.734914	+	0.424303i
$95$	3.28033	+	5.68170i	0.336555	+	0.582930i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−2.07359			−0.210541			−0.105271	−	0.994444i	$-0.533571\pi$
$97$	−2.07359			−0.210541			−0.105271	+	0.994444i	$0.533571\pi$
$98$	−4.38234	−	5.45849i	−0.442683	−	0.551390i
$99$		−	2.39447i		−	0.240653i
$100$	−2.13198	+	3.69270i	−0.213198	+	0.369270i
$101$	15.0796	−	8.70623i	1.50048	−	0.866302i	0.500480	−	0.865748i	$-0.333157\pi$
$101$	15.0796	−	8.70623i	1.50048	−	0.866302i	1.00000		0.000554027i	$-0.000176352\pi$
$102$	−0.692374	+	0.399743i	−0.0685553	+	0.0395804i
$103$	−7.51800	+	13.0216i	−0.740771	+	1.28305i	0.211374	+	0.977405i	$0.432206\pi$
$103$	−7.51800	+	13.0216i	−0.740771	+	1.28305i	−0.952145	+	0.305647i	$0.901127\pi$
$104$		−	4.32646i		−	0.424244i
$105$	−6.64610	+	4.54721i	−0.648593	+	0.443762i
$106$			10.9647i			1.06498i
$107$	11.7687	+	6.79464i	1.13772	+	0.656863i	0.945865	−	0.324560i	$-0.105216\pi$
$107$	11.7687	+	6.79464i	1.13772	+	0.656863i	0.191855	+	0.981423i	$0.438550\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	3.63340	−	2.09774i	0.348017	−	0.200927i	−0.315795	−	0.948828i	$-0.602271\pi$
$109$	3.63340	−	2.09774i	0.348017	−	0.200927i	0.663811	+	0.747900i	$0.268938\pi$
$110$	6.31159	+	3.64400i	0.601786	+	0.347441i
$111$	4.08739			0.387958
$112$	−2.63803	+	0.202041i	−0.249270	+	0.0190910i
$113$			12.0077i			1.12959i	0.825231	+	0.564796i	$0.191045\pi$
$113$			12.0077i			1.12959i	−0.825231	+	0.564796i	$0.808955\pi$
$114$	1.86672	+	1.07775i	0.174835	+	0.100941i
$115$	−14.4792	+	1.85058i	−1.35019	+	0.172567i
$116$	2.39406	+	4.14663i	0.222283	+	0.385005i
$117$	−3.74682	−	2.16323i	−0.346394	−	0.199990i
$118$			12.3064i			1.13289i
$119$	0.914643	−	1.90727i	0.0838452	−	0.174839i
$120$			3.04368i			0.277848i
$121$	−2.63325	+	4.56093i	−0.239387	+	0.414630i
$122$	−2.01946	−	3.49780i	−0.182833	−	0.316676i
$123$	3.83387	+	6.64046i	0.345688	+	0.598750i
$124$	−3.53448	−	2.04063i	−0.317405	−	0.183254i
$125$	2.24027			0.200376
$126$	−1.14404	+	2.38562i	−0.101919	+	0.212528i
$127$	9.00515			0.799078			0.399539	−	0.916716i	$-0.369170\pi$
$127$	9.00515			0.799078			0.399539	+	0.916716i	$0.369170\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.57654	+	2.73065i	0.138807	+	0.240421i
$130$	11.4041	−	6.58416i	1.00021	−	0.577469i
$131$	5.63863	+	3.25546i	0.492649	+	0.284431i	0.725673	−	0.688040i	$-0.241529\pi$
$131$	5.63863	+	3.25546i	0.492649	+	0.284431i	−0.233024	+	0.972471i	$0.574862\pi$
$132$	2.39447			0.208412
$133$	−5.68628	+	0.435500i	−0.493063	+	0.0377626i
$134$		−	4.68915i		−	0.405080i
$135$	2.63590	+	1.52184i	0.226862	+	0.130979i
$136$	−0.399743	−	0.692374i	−0.0342776	−	0.0593706i
$137$	−7.83359	+	4.52273i	−0.669269	+	0.386403i	−0.795800	−	0.605560i	$-0.792949\pi$
$137$	−7.83359	+	4.52273i	−0.669269	+	0.386403i	0.126531	+	0.991963i	$0.459616\pi$
$138$	−3.81580	+	2.90512i	−0.324822	+	0.247300i
$139$		−	10.5668i		−	0.896264i	−0.893967	−	0.448132i	$-0.852090\pi$
$139$		−	10.5668i		−	0.896264i	0.893967	−	0.448132i	$-0.147910\pi$
$140$	−4.54721	−	6.64610i	−0.384309	−	0.561698i
$141$	−8.22754			−0.692884
$142$	−3.10335	+	5.37517i	−0.260428	+	0.451074i
$143$	−5.17979	−	8.97165i	−0.433156	−	0.750247i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−7.28673	+	12.6210i	−0.605130	+	1.04812i
$146$			2.55863i			0.211753i
$147$	−1.06598	−	6.91836i	−0.0879202	−	0.570617i
$148$			4.08739i			0.335981i
$149$	−3.19186	−	1.84282i	−0.261487	−	0.150970i	0.363526	−	0.931584i	$-0.381573\pi$
$149$	−3.19186	−	1.84282i	−0.261487	−	0.150970i	−0.625013	+	0.780614i	$0.714906\pi$
$150$	−3.69270	+	2.13198i	−0.301507	+	0.174075i
$151$	−12.2114	−	21.1507i	−0.993747	−	1.72122i	−0.593568	−	0.804783i	$-0.702281\pi$
$151$	−12.2114	−	21.1507i	−0.993747	−	1.72122i	−0.400179	−	0.916437i	$-0.631052\pi$
$152$	−1.07775	+	1.86672i	−0.0874174	+	0.151411i
$153$	−0.799485			−0.0646345
$154$	−5.22851	+	3.57730i	−0.421326	+	0.288267i
$155$		−	12.4220i		−	0.997762i
$156$	2.16323	−	3.74682i	0.173197	−	0.299986i
$157$	−4.68552	−	8.11555i	−0.373945	−	0.647692i	0.616223	−	0.787571i	$-0.288662\pi$
$157$	−4.68552	−	8.11555i	−0.373945	−	0.647692i	−0.990169	+	0.139880i	$0.955328\pi$
$158$	7.62601	−	4.40288i	0.606693	−	0.350274i
$159$	−5.48234	+	9.49569i	−0.434778	+	0.753057i
$160$	−3.04368			−0.240624
$161$	3.99188	−	12.0443i	0.314604	−	0.949223i
$162$	1.00000			0.0785674
$163$	−5.92061	+	10.2548i	−0.463738	+	0.803217i	−0.999144	−	0.0413775i	$-0.986825\pi$
$163$	−5.92061	+	10.2548i	−0.463738	+	0.803217i	0.535406	+	0.844595i	$0.320159\pi$
$164$	−6.64046	+	3.83387i	−0.518533	+	0.299375i
$165$	3.64400	+	6.31159i	0.283685	+	0.491356i
$166$	0.188848	−	0.327095i	0.0146575	−	0.0253875i
$167$		−	0.104509i		−	0.00808712i	−0.999992	−	0.00404356i	$-0.998713\pi$
$167$		−	0.104509i		−	0.00808712i	0.999992	−	0.00404356i	$-0.00128711\pi$
$168$	−2.38562	−	1.14404i	−0.184054	−	0.0882647i
$169$	−5.71822			−0.439863
$170$	1.21669	−	2.10736i	0.0933156	−	0.161627i
$171$	1.07775	+	1.86672i	0.0824179	+	0.142752i
$172$	−2.73065	+	1.57654i	−0.208210	+	0.120210i
$173$	−3.02723	−	1.74777i	−0.230156	−	0.132880i	0.380488	−	0.924786i	$-0.375756\pi$
$173$	−3.02723	−	1.74777i	−0.230156	−	0.132880i	−0.610644	+	0.791905i	$0.709089\pi$
$174$			4.78811i			0.362986i
$175$	4.87814	−	10.1722i	0.368753	−	0.768944i
$176$			2.39447i			0.180490i
$177$	−6.15319	+	10.6576i	−0.462502	+	0.801077i
$178$	0.328941	+	0.569742i	0.0246551	+	0.0427040i
$179$	−10.1370	−	17.5577i	−0.757672	−	1.31233i	−0.944035	−	0.329845i	$-0.893003\pi$
$179$	−10.1370	−	17.5577i	−0.757672	−	1.31233i	0.186363	−	0.982481i	$-0.440330\pi$
$180$	−1.52184	+	2.63590i	−0.113431	+	0.196468i
$181$	5.28828			0.393075			0.196537	−	0.980496i	$-0.437030\pi$
$181$	5.28828			0.393075			0.196537	+	0.980496i	$0.437030\pi$
$182$	0.874119	+	11.4133i	0.0647940	+	0.846010i
$183$		−	4.03891i		−	0.298565i
$184$	−2.90512	−	3.81580i	−0.214168	−	0.281304i
$185$	−10.7740	+	6.22034i	−0.792117	+	0.457329i
$186$	−2.04063	−	3.53448i	−0.149626	−	0.259160i
$187$	−1.65787	−	0.957172i	−0.121236	−	0.0699954i
$188$		−	8.22754i		−	0.600055i
$189$	−2.18358	+	1.49399i	−0.158832	+	0.108671i
$190$	−6.56067			−0.475961
$191$	−18.1430	−	10.4748i	−1.31278	−	0.757933i	−0.330223	−	0.943903i	$-0.607124\pi$
$191$	−18.1430	−	10.4748i	−1.31278	−	0.757933i	−0.982555	+	0.185970i	$0.940457\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−6.27262	−	10.8645i	−0.451513	−	0.782043i	0.546967	−	0.837154i	$-0.315782\pi$
$193$	−6.27262	−	10.8645i	−0.451513	−	0.782043i	−0.998480	+	0.0551106i	$0.982449\pi$
$194$	1.03680	−	1.79578i	0.0744377	−	0.128930i
$195$	13.1683			0.943003
$196$	6.91836	−	1.06598i	0.494169	−	0.0761412i
$197$	−20.6843			−1.47370			−0.736849	−	0.676057i	$-0.763687\pi$
$197$	−20.6843			−1.47370			−0.736849	+	0.676057i	$0.763687\pi$
$198$	2.07367	+	1.19724i	0.147370	+	0.0850838i
$199$	9.53909	+	16.5222i	0.676208	+	1.17123i	0.976114	+	0.217258i	$0.0697112\pi$
$199$	9.53909	+	16.5222i	0.676208	+	1.17123i	−0.299906	+	0.953969i	$0.596955\pi$
$200$	−2.13198	−	3.69270i	−0.150754	−	0.261113i
$201$	2.34457	−	4.06092i	0.165373	−	0.286435i
$202$			17.4125i			1.22514i
$203$	−7.15337	−	10.4552i	−0.502068	−	0.733812i
$204$		−	0.799485i		−	0.0559752i
$205$	−20.2114	−	11.6691i	−1.41162	−	0.815002i
$206$	−7.51800	−	13.0216i	−0.523804	−	0.907255i
$207$	−4.75713	+	0.608007i	−0.330644	+	0.0422594i
$208$	3.74682	+	2.16323i	0.259795	+	0.149993i
$209$			5.16130i			0.357015i
$210$	−0.614946	−	8.02929i	−0.0424353	−	0.554074i
$211$	20.7862			1.43098			0.715491	−	0.698622i	$-0.246203\pi$
$211$	20.7862			1.43098			0.715491	+	0.698622i	$0.246203\pi$
$212$	−9.49569	−	5.48234i	−0.652167	−	0.376529i
$213$	−5.37517	+	3.10335i	−0.368300	+	0.212638i
$214$	−11.7687	+	6.79464i	−0.804489	+	0.464472i
$215$	−8.31122	−	4.79849i	−0.566821	−	0.327254i
$216$			1.00000i			0.0680414i
$217$	9.73633	+	4.66913i	0.660945	+	0.316961i
$218$			4.19549i			0.284154i
$219$	−1.27931	+	2.21583i	−0.0864479	+	0.149732i
$220$	−6.31159	+	3.64400i	−0.425527	+	0.245678i
$221$	−2.99553	+	1.72947i	−0.201501	+	0.116337i
$222$	−2.04369	+	3.53978i	−0.137164	+	0.237575i
$223$			15.2414i			1.02064i	0.859985	+	0.510319i	$0.170473\pi$
$223$			15.2414i			1.02064i	−0.859985	+	0.510319i	$0.829527\pi$
$224$	1.14404	−	2.38562i	0.0764394	−	0.159396i
$225$	−4.26396			−0.284264
$226$	−10.3990	−	6.00386i	−0.691731	−	0.399371i
$227$	4.63162	+	8.02220i	0.307412	+	0.532452i	0.977795	−	0.209562i	$-0.0672039\pi$
$227$	4.63162	+	8.02220i	0.307412	+	0.532452i	−0.670384	+	0.742015i	$0.733871\pi$
$228$	−1.86672	+	1.07775i	−0.123627	+	0.0713760i
$229$	−7.25789	+	12.5710i	−0.479615	+	0.830717i	−0.999727	−	0.0233811i	$-0.992557\pi$
$229$	−7.25789	+	12.5710i	−0.479615	+	0.830717i	0.520112	+	0.854098i	$0.325890\pi$
$230$	5.63694	−	13.4646i	0.371689	−	0.887831i
$231$	−6.31668	+	0.483780i	−0.415607	+	0.0318304i
$232$	−4.78811			−0.314355
$233$	−5.45759	+	9.45282i	−0.357539	+	0.619275i	−0.987549	−	0.157312i	$-0.949717\pi$
$233$	−5.45759	+	9.45282i	−0.357539	+	0.619275i	0.630010	+	0.776587i	$0.283051\pi$
$234$	3.74682	−	2.16323i	0.244937	−	0.141415i
$235$	21.6870	−	12.5210i	1.41470	−	0.816778i
$236$	−10.6576	−	6.15319i	−0.693753	−	0.400539i
$237$	8.80576			0.571995
$238$	1.19442	+	1.74574i	0.0774227	+	0.113159i
$239$	20.1227			1.30163			0.650816	−	0.759236i	$-0.274427\pi$
$239$	20.1227			1.30163			0.650816	+	0.759236i	$0.274427\pi$
$240$	−2.63590	−	1.52184i	−0.170147	−	0.0982342i
$241$	12.5697	+	21.7713i	0.809683	+	1.40241i	0.913084	+	0.407772i	$0.133694\pi$
$241$	12.5697	+	21.7713i	0.809683	+	1.40241i	−0.103401	+	0.994640i	$0.532973\pi$
$242$	−2.63325	−	4.56093i	−0.169272	−	0.293188i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.03891			0.258565
$245$	13.3384	+	16.6139i	0.852161	+	1.06142i
$246$	−7.66774			−0.488877
$247$	8.07630	+	4.66285i	0.513883	+	0.296690i
$248$	3.53448	−	2.04063i	0.224439	−	0.129580i
$249$	0.327095	−	0.188848i	0.0207288	−	0.0119678i
$250$	−1.12013	+	1.94013i	−0.0708435	+	0.122704i
$251$	−7.54744			−0.476390			−0.238195	−	0.971217i	$-0.576556\pi$
$251$	−7.54744			−0.476390			−0.238195	+	0.971217i	$0.576556\pi$
$252$	−1.49399	−	2.18358i	−0.0941122	−	0.137552i
$253$	−10.5927	−	4.43460i	−0.665955	−	0.278801i
$254$	−4.50257	+	7.79869i	−0.282517	+	0.489333i
$255$	2.10736	−	1.21669i	0.131968	−	0.0761919i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.1071	−	7.56741i	−0.817601	−	0.472042i	0.0319873	−	0.999488i	$-0.489816\pi$
$257$	−13.1071	−	7.56741i	−0.817601	−	0.472042i	−0.849589	+	0.527446i	$0.823150\pi$
$258$	−3.15309			−0.196303
$259$	−0.825818	−	10.7826i	−0.0513139	−	0.670001i
$260$			13.1683i			0.816665i
$261$	−2.39406	+	4.14663i	−0.148188	+	0.256670i
$262$	−5.63863	+	3.25546i	−0.348356	+	0.201123i
$263$	−11.4148	+	6.59033i	−0.703866	+	0.406377i	−0.808786	−	0.588104i	$-0.799875\pi$
$263$	−11.4148	+	6.59033i	−0.703866	+	0.406377i	0.104920	+	0.994481i	$0.466541\pi$
$264$	−1.19724	+	2.07367i	−0.0736848	+	0.127626i
$265$		−	33.3729i		−	2.05008i
$266$	2.46599	−	5.14222i	0.151199	−	0.315290i
$267$			0.657881i			0.0402617i
$268$	4.06092	+	2.34457i	0.248060	+	0.143218i
$269$	10.8165	−	6.24489i	0.659492	−	0.380758i	−0.132591	−	0.991171i	$-0.542330\pi$
$269$	10.8165	−	6.24489i	0.659492	−	0.380758i	0.792083	+	0.610413i	$0.208996\pi$
$270$	−2.63590	+	1.52184i	−0.160416	+	0.0926161i
$271$	2.91636	+	1.68376i	0.177156	+	0.102281i	0.585956	−	0.810343i	$-0.300719\pi$
$271$	2.91636	+	1.68376i	0.177156	+	0.102281i	−0.408800	+	0.912624i	$0.634053\pi$
$272$	0.799485			0.0484759
$273$	−4.94964	+	10.3213i	−0.299566	+	0.624672i
$274$		−	9.04546i		−	0.546456i
$275$	−8.84206	−	5.10496i	−0.533196	−	0.307841i
$276$	−0.608007	−	4.75713i	−0.0365977	−	0.286346i
$277$	−0.782895	−	1.35601i	−0.0470396	−	0.0814750i	0.841547	−	0.540184i	$-0.181645\pi$
$277$	−0.782895	−	1.35601i	−0.0470396	−	0.0814750i	−0.888587	+	0.458709i	$0.848312\pi$
$278$	9.15111	+	5.28340i	0.548847	+	0.316877i
$279$		−	4.08126i		−	0.244339i
$280$	8.02929	−	0.614946i	0.479842	−	0.0367500i
$281$			24.0099i			1.43231i	0.697940	+	0.716156i	$0.254100\pi$
$281$			24.0099i			1.43231i	−0.697940	+	0.716156i	$0.745900\pi$
$282$	4.11377	−	7.12526i	0.244971	−	0.424303i
$283$	13.8760	+	24.0340i	0.824845	+	1.42867i	0.902038	+	0.431657i	$0.142071\pi$
$283$	13.8760	+	24.0340i	0.824845	+	1.42867i	−0.0771934	+	0.997016i	$0.524596\pi$
$284$	−3.10335	−	5.37517i	−0.184150	−	0.318958i
$285$	−5.68170	−	3.28033i	−0.336555	−	0.194310i
$286$	10.3596			0.612574
$287$	16.7431	−	11.4555i	0.988314	−	0.676196i
$288$	−1.00000			−0.0589256
$289$	8.18041	−	14.1689i	0.481201	−	0.833464i
$290$	−7.28673	−	12.6210i	−0.427891	−	0.741130i
$291$	1.79578	−	1.03680i	0.105271	−	0.0607781i
$292$	−2.21583	−	1.27931i	−0.129672	−	0.0748661i
$293$	23.9833			1.40112			0.700560	−	0.713594i	$-0.252934\pi$
$293$	23.9833			1.40112			0.700560	+	0.713594i	$0.252934\pi$
$294$	6.52446	+	2.53602i	0.380514	+	0.147904i
$295$		−	37.4566i		−	2.18081i
$296$	−3.53978	−	2.04369i	−0.205746	−	0.118787i
$297$	1.19724	+	2.07367i	0.0694707	+	0.120327i
$298$	3.19186	−	1.84282i	0.184899	−	0.106752i
$299$	−16.5089	+	12.5689i	−0.954733	+	0.726876i
$300$		−	4.26396i		−	0.246180i
$301$	6.88501	−	4.71067i	0.396845	−	0.271518i
$302$	24.4227			1.40537
$303$	−8.70623	+	15.0796i	−0.500160	+	0.866302i
$304$	−1.07775	−	1.86672i	−0.0618134	−	0.107064i
$305$	6.14657	+	10.6462i	0.351952	+	0.609598i
$306$	0.399743	−	0.692374i	0.0228518	−	0.0395804i
$307$			32.7277i			1.86787i	0.357444	+	0.933935i	$0.383648\pi$
$307$			32.7277i			1.86787i	−0.357444	+	0.933935i	$0.616352\pi$
$308$	−0.483780	−	6.31668i	−0.0275659	−	0.359926i
$309$		−	15.0360i		−	0.855368i
$310$	10.7578	+	6.21102i	0.611002	+	0.352762i
$311$	−15.7420	+	9.08865i	−0.892647	+	0.515370i	−0.874807	−	0.484471i	$-0.839012\pi$
$311$	−15.7420	+	9.08865i	−0.892647	+	0.515370i	−0.0178397	+	0.999841i	$0.505679\pi$
$312$	2.16323	+	3.74682i	0.122469	+	0.212122i
$313$	−13.1187	+	22.7223i	−0.741514	+	1.28434i	0.210292	+	0.977639i	$0.432559\pi$
$313$	−13.1187	+	22.7223i	−0.741514	+	1.28434i	−0.951806	+	0.306701i	$0.900775\pi$
$314$	9.37104			0.528838
$315$	3.48209	−	7.26105i	0.196193	−	0.409114i
$316$			8.80576i			0.495363i
$317$	−11.2001	+	19.3992i	−0.629062	+	1.08957i	0.358678	+	0.933461i	$0.383228\pi$
$317$	−11.2001	+	19.3992i	−0.629062	+	1.08957i	−0.987740	+	0.156106i	$0.950106\pi$
$318$	−5.48234	−	9.49569i	−0.307434	−	0.532492i
$319$	−9.92898	+	5.73250i	−0.555916	+	0.320958i
$320$	1.52184	−	2.63590i	0.0850733	−	0.147351i
$321$	−13.5893			−0.758480
$322$	8.43472	+	9.47922i	0.470048	+	0.528256i
$323$	1.72330			0.0958868
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−15.9763	+	9.22392i	−0.886205	+	0.511651i
$326$	−5.92061	−	10.2548i	−0.327912	−	0.567961i
$327$	−2.09774	+	3.63340i	−0.116006	+	0.200927i
$328$		−	7.66774i		−	0.423380i
$329$	1.66230	+	21.7045i	0.0916454	+	1.19661i
$330$	−7.28799			−0.401191
$331$	0.644942	−	1.11707i	0.0354492	−	0.0613998i	−0.847756	−	0.530386i	$-0.822047\pi$
$331$	0.644942	−	1.11707i	0.0354492	−	0.0613998i	0.883206	+	0.468986i	$0.155380\pi$
$332$	0.188848	+	0.327095i	0.0103644	+	0.0179517i
$333$	−3.53978	+	2.04369i	−0.193979	+	0.111994i
$334$	0.0905071	+	0.0522543i	0.00495233	+	0.00285923i
$335$			14.2722i			0.779776i
$336$	2.18358	−	1.49399i	0.119124	−	0.0815036i
$337$		−	5.47567i		−	0.298279i	−0.988816	−	0.149139i	$-0.952350\pi$
$337$		−	5.47567i		−	0.298279i	0.988816	−	0.149139i	$-0.0476503\pi$
$338$	2.85911	−	4.95212i	0.155515	−	0.269360i
$339$	−6.00386	−	10.3990i	−0.326085	−	0.564796i
$340$	1.21669	+	2.10736i	0.0659841	+	0.114288i
$341$	4.88623	−	8.46320i	0.264604	−	0.458308i
$342$	−2.15551			−0.116557
$343$	−18.0354	+	4.20986i	−0.973822	+	0.227311i
$344$		−	3.15309i		−	0.170003i
$345$	11.6140	−	8.84223i	0.625279	−	0.476050i
$346$	3.02723	−	1.74777i	0.162745	−	0.0939607i
$347$	14.8210	+	25.6708i	0.795635	+	1.37808i	0.922435	+	0.386152i	$0.126196\pi$
$347$	14.8210	+	25.6708i	0.795635	+	1.37808i	−0.126801	+	0.991928i	$0.540471\pi$
$348$	−4.14663	−	2.39406i	−0.222283	−	0.128335i
$349$		−	3.81383i		−	0.204150i	−0.994777	−	0.102075i	$-0.967452\pi$
$349$		−	3.81383i		−	0.204150i	0.994777	−	0.102075i	$-0.0325481\pi$
$350$	6.37029	+	9.31068i	0.340506	+	0.497677i
$351$	4.32646			0.230929
$352$	−2.07367	−	1.19724i	−0.110527	−	0.0638129i
$353$	−5.74580	+	3.31734i	−0.305818	+	0.176564i	−0.645054	−	0.764137i	$-0.723165\pi$
$353$	−5.74580	+	3.31734i	−0.305818	+	0.176564i	0.339235	+	0.940701i	$0.389832\pi$
$354$	−6.15319	−	10.6576i	−0.327038	−	0.566447i
$355$	9.44560	−	16.3603i	0.501321	−	0.868313i
$356$	−0.657881			−0.0348676
$357$	0.161528	+	2.10906i	0.00854899	+	0.111623i
$358$	20.2739			1.07151
$359$	−23.6674	−	13.6644i	−1.24912	−	0.721178i	−0.278184	−	0.960528i	$-0.589732\pi$
$359$	−23.6674	−	13.6644i	−1.24912	−	0.721178i	−0.970933	+	0.239350i	$0.923066\pi$
$360$	−1.52184	−	2.63590i	−0.0802079	−	0.138924i
$361$	7.17689	+	12.4307i	0.377731	+	0.654250i
$362$	−2.64414	+	4.57978i	−0.138973	+	0.240708i
$363$		−	5.26651i		−	0.276420i
$364$	−10.3213	−	4.94964i	−0.540981	−	0.259432i
$365$		−	7.78762i		−	0.407623i
$366$	3.49780	+	2.01946i	0.182833	+	0.105559i
$367$	−5.10915	−	8.84930i	−0.266695	−	0.461930i	0.701311	−	0.712855i	$-0.252598\pi$
$367$	−5.10915	−	8.84930i	−0.266695	−	0.461930i	−0.968006	+	0.250926i	$0.919265\pi$
$368$	4.75713	−	0.608007i	0.247983	−	0.0316946i
$369$	−6.64046	−	3.83387i	−0.345688	−	0.199583i
$370$		−	12.4407i		−	0.646761i
$371$	26.1575	+	12.5440i	1.35803	+	0.651254i
$372$	4.08126			0.211604
$373$	8.16295	+	4.71288i	0.422662	+	0.244024i	0.696215	−	0.717833i	$-0.254866\pi$
$373$	8.16295	+	4.71288i	0.422662	+	0.244024i	−0.273554	+	0.961857i	$0.588199\pi$
$374$	1.65787	−	0.957172i	0.0857265	−	0.0494942i
$375$	−1.94013	+	1.12013i	−0.100188	+	0.0578435i
$376$	7.12526	+	4.11377i	0.367457	+	0.212151i
$377$			20.7156i			1.06691i
$378$	−0.202041	−	2.63803i	−0.0103918	−	0.135685i
$379$		−	5.25144i		−	0.269748i	−0.990863	−	0.134874i	$-0.956937\pi$
$379$		−	5.25144i		−	0.269748i	0.990863	−	0.134874i	$-0.0430630\pi$
$380$	3.28033	−	5.68170i	0.168278	−	0.291465i
$381$	−7.79869	+	4.50257i	−0.399539	+	0.230674i
$382$	18.1430	−	10.4748i	0.928275	−	0.535940i
$383$	−1.43797	+	2.49064i	−0.0734768	+	0.127266i	−0.900423	−	0.435016i	$-0.856743\pi$
$383$	−1.43797	+	2.49064i	−0.0734768	+	0.127266i	0.826946	+	0.562281i	$0.190076\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	15.9139	−	10.8882i	0.811047	−	0.554912i
$386$	12.5452			0.638536
$387$	−2.73065	−	1.57654i	−0.138807	−	0.0801402i
$388$	1.03680	+	1.79578i	0.0526354	+	0.0911671i
$389$	5.89494	−	3.40344i	0.298885	−	0.172561i	−0.343057	−	0.939315i	$-0.611462\pi$
$389$	5.89494	−	3.40344i	0.298885	−	0.172561i	0.641942	+	0.766753i	$0.278129\pi$
$390$	−6.58416	+	11.4041i	−0.333402	+	0.577469i
$391$	−1.48066	+	3.53676i	−0.0748802	+	0.178862i
$392$	−2.53602	+	6.52446i	−0.128088	+	0.329535i
$393$	−6.51093			−0.328433
$394$	10.3422	−	17.9132i	0.521031	−	0.902453i
$395$	−23.2111	+	13.4009i	−1.16788	+	0.674274i
$396$	−2.07367	+	1.19724i	−0.104206	+	0.0601634i
$397$	30.7424	+	17.7492i	1.54292	+	0.890804i	0.998653	+	0.0518916i	$0.0165250\pi$
$397$	30.7424	+	17.7492i	1.54292	+	0.890804i	0.544266	+	0.838913i	$0.316808\pi$
$398$	−19.0782			−0.956302
$399$	4.70672	−	3.22030i	0.235631	−	0.161216i
$400$	4.26396			0.213198
$401$	−19.3925	−	11.1963i	−0.968417	−	0.559116i	−0.0696637	−	0.997571i	$-0.522193\pi$
$401$	−19.3925	−	11.1963i	−0.968417	−	0.559116i	−0.898753	+	0.438455i	$0.855526\pi$
$402$	2.34457	+	4.06092i	0.116937	+	0.202540i
$403$	−8.82870	−	15.2918i	−0.439789	−	0.761737i
$404$	−15.0796	−	8.70623i	−0.750240	−	0.433151i
$405$	−3.04368			−0.151241
$406$	12.6312	−	0.967393i	0.626874	−	0.0480109i
$407$	−9.78714			−0.485130
$408$	0.692374	+	0.399743i	0.0342776	+	0.0197902i
$409$	5.06658	−	2.92519i	0.250526	−	0.144641i	−0.369479	−	0.929239i	$-0.620464\pi$
$409$	5.06658	−	2.92519i	0.250526	−	0.144641i	0.620005	+	0.784598i	$0.287131\pi$
$410$	20.2114	−	11.6691i	0.998170	−	0.576293i
$411$	4.52273	−	7.83359i	0.223090	−	0.386403i
$412$	15.0360			0.740771
$413$	29.3583	+	14.0790i	1.44463	+	0.692782i
$414$	1.85202	−	4.42380i	0.0910217	−	0.217418i
$415$	−0.574793	+	0.995571i	−0.0282155	+	0.0488707i
$416$	−3.74682	+	2.16323i	−0.183703	+	0.106061i
$417$	5.28340	+	9.15111i	0.258729	+	0.448132i
$418$	−4.46982	−	2.58065i	−0.218626	−	0.126224i
$419$	−10.4963			−0.512776			−0.256388	−	0.966574i	$-0.582533\pi$
$419$	−10.4963			−0.512776			−0.256388	+	0.966574i	$0.582533\pi$
$420$	7.26105	+	3.48209i	0.354303	+	0.169909i
$421$		−	14.1358i		−	0.688937i	−0.938798	−	0.344469i	$-0.888059\pi$
$421$		−	14.1358i		−	0.688937i	0.938798	−	0.344469i	$-0.111941\pi$
$422$	−10.3931	+	18.0014i	−0.505929	+	0.876294i
$423$	7.12526	−	4.11377i	0.346442	−	0.200018i
$424$	9.49569	−	5.48234i	0.461151	−	0.266246i
$425$	−1.70449	+	2.95226i	−0.0826797	+	0.143205i
$426$		−	6.20671i		−	0.300716i
$427$	−10.6548	+	0.816024i	−0.515620	+	0.0394902i
$428$		−	13.5893i		−	0.656863i
$429$	8.97165	+	5.17979i	0.433156	+	0.250082i
$430$	8.31122	−	4.79849i	0.400803	−	0.231404i
$431$	5.07838	−	2.93200i	0.244617	−	0.141230i	−0.372680	−	0.927960i	$-0.621561\pi$
$431$	5.07838	−	2.93200i	0.244617	−	0.141230i	0.617297	+	0.786730i	$0.288228\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−15.8861			−0.763438			−0.381719	−	0.924278i	$-0.624668\pi$
$433$	−15.8861			−0.763438			−0.381719	+	0.924278i	$0.624668\pi$
$434$	−8.91175	+	6.09734i	−0.427778	+	0.292682i
$435$		−	14.5735i		−	0.698744i
$436$	−3.63340	−	2.09774i	−0.174008	−	0.100464i
$437$	10.2540	−	1.31056i	0.490517	−	0.0626928i
$438$	−1.27931	−	2.21583i	−0.0611279	−	0.105877i
$439$	17.8490	+	10.3051i	0.851888	+	0.491838i	0.861287	−	0.508118i	$-0.169659\pi$
$439$	17.8490	+	10.3051i	0.851888	+	0.491838i	−0.00939944	+	0.999956i	$0.502992\pi$
$440$		−	7.28799i		−	0.347441i
$441$	4.38234	+	5.45849i	0.208683	+	0.259928i
$442$		−	3.45894i		−	0.164525i
$443$	5.21749	−	9.03695i	0.247890	−	0.429358i	−0.715050	−	0.699073i	$-0.753596\pi$
$443$	5.21749	−	9.03695i	0.247890	−	0.429358i	0.962940	+	0.269715i	$0.0869294\pi$
$444$	−2.04369	−	3.53978i	−0.0969895	−	0.167991i
$445$	−1.00119	−	1.73411i	−0.0474609	−	0.0822047i
$446$	−13.1994	−	7.62069i	−0.625011	−	0.360850i
$447$	3.68564			0.174325
$448$	1.49399	+	2.18358i	0.0705842	+	0.103164i
$449$	−7.05546			−0.332968			−0.166484	−	0.986044i	$-0.553241\pi$
$449$	−7.05546			−0.332968			−0.166484	+	0.986044i	$0.553241\pi$
$450$	2.13198	−	3.69270i	0.100502	−	0.174075i
$451$	−9.18009	−	15.9004i	−0.432274	−	0.748720i
$452$	10.3990	−	6.00386i	0.489127	−	0.282398i
$453$	21.1507	+	12.2114i	0.993747	+	0.573740i
$454$	−9.26324			−0.434746
$455$	−2.66054	−	34.7384i	−0.124728	−	1.62856i
$456$		−	2.15551i		−	0.100941i
$457$	−17.6738	−	10.2040i	−0.826746	−	0.477322i	0.0259910	−	0.999662i	$-0.491726\pi$
$457$	−17.6738	−	10.2040i	−0.826746	−	0.477322i	−0.852737	+	0.522340i	$0.825059\pi$
$458$	−7.25789	−	12.5710i	−0.339139	−	0.587406i
$459$	0.692374	−	0.399743i	0.0323173	−	0.0186584i
$460$	8.84223	+	11.6140i	0.412271	+	0.541508i
$461$			19.2906i			0.898452i	0.893418	+	0.449226i	$0.148300\pi$
$461$			19.2906i			0.898452i	−0.893418	+	0.449226i	$0.851700\pi$
$462$	2.73937	−	5.71229i	0.127447	−	0.265760i
$463$	−16.9180			−0.786248			−0.393124	−	0.919486i	$-0.628606\pi$
$463$	−16.9180			−0.786248			−0.393124	+	0.919486i	$0.628606\pi$
$464$	2.39406	−	4.14663i	0.111141	−	0.192502i
$465$	6.21102	+	10.7578i	0.288029	+	0.498881i
$466$	−5.45759	−	9.45282i	−0.252818	−	0.437894i
$467$	13.4093	−	23.2256i	0.620508	−	1.07475i	−0.368883	−	0.929476i	$-0.620260\pi$
$467$	13.4093	−	23.2256i	0.620508	−	1.07475i	0.989391	−	0.145276i	$-0.0464070\pi$
$468$			4.32646i			0.199990i
$469$	−11.1865	−	5.36457i	−0.516545	−	0.247713i
$470$			25.0420i			1.15510i
$471$	8.11555	+	4.68552i	0.373945	+	0.215897i
$472$	10.6576	−	6.15319i	0.490558	−	0.283224i
$473$	−3.77499	−	6.53847i	−0.173574	−	0.300639i
$474$	−4.40288	+	7.62601i	−0.202231	+	0.350274i
$475$	9.19100			0.421712
$476$	−2.10906	+	0.161528i	−0.0966687	+	0.00740364i
$477$		−	10.9647i		−	0.502038i
$478$	−10.0614	+	17.4268i	−0.460196	+	0.797083i
$479$	−8.04405	−	13.9327i	−0.367542	−	0.636601i	0.621639	−	0.783304i	$-0.286467\pi$
$479$	−8.04405	−	13.9327i	−0.367542	−	0.636601i	−0.989181	+	0.146703i	$0.953134\pi$
$480$	2.63590	−	1.52184i	0.120312	−	0.0694621i
$481$	−8.84195	+	15.3147i	−0.403158	+	0.698291i
$482$	−25.1393			−1.14506
$483$	2.56507	+	12.4266i	0.116715	+	0.565430i
$484$	5.26651			0.239387
$485$	−3.15567	+	5.46578i	−0.143292	+	0.248188i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	13.3255	+	23.0804i	0.603834	+	1.04587i	0.992235	+	0.124381i	$0.0396944\pi$
$487$	13.3255	+	23.0804i	0.603834	+	1.04587i	−0.388401	+	0.921491i	$0.626972\pi$
$488$	−2.01946	+	3.49780i	−0.0914165	+	0.158338i
$489$		−	11.8412i		−	0.535478i
$490$	−21.0572	+	3.24449i	−0.951269	+	0.146571i
$491$	22.4635			1.01376			0.506882	−	0.862015i	$-0.330798\pi$
$491$	22.4635			1.01376			0.506882	+	0.862015i	$0.330798\pi$
$492$	3.83387	−	6.64046i	0.172844	−	0.299375i
$493$	1.91401	+	3.31517i	0.0862028	+	0.149308i
$494$	−8.07630	+	4.66285i	−0.363370	+	0.209792i
$495$	−6.31159	−	3.64400i	−0.283685	−	0.163785i
$496$			4.08126i			0.183254i
$497$	9.27273	+	13.5528i	0.415939	+	0.607927i
$498$			0.377697i			0.0169250i
$499$	−2.37249	+	4.10928i	−0.106207	+	0.183956i	−0.914231	−	0.405194i	$-0.867204\pi$
$499$	−2.37249	+	4.10928i	−0.106207	+	0.183956i	0.808024	+	0.589150i	$0.200537\pi$
$500$	−1.12013	−	1.94013i	−0.0500939	−	0.0867652i
$501$	0.0522543	+	0.0905071i	0.00233455	+	0.00404356i
$502$	3.77372	−	6.53628i	0.168429	−	0.291728i
$503$	40.9737			1.82693			0.913463	−	0.406922i	$-0.133398\pi$
$503$	40.9737			1.82693			0.913463	+	0.406922i	$0.133398\pi$
$504$	2.63803	−	0.202041i	0.117507	−	0.00899960i
$505$		−	52.9979i		−	2.35837i
$506$	9.13681	−	6.95622i	0.406181	−	0.309242i
$507$	4.95212	−	2.85911i	0.219931	−	0.126977i
$508$	−4.50257	−	7.79869i	−0.199769	−	0.346011i
$509$	−16.3212	−	9.42303i	−0.723423	−	0.417668i	0.0925884	−	0.995704i	$-0.470486\pi$
$509$	−16.3212	−	9.42303i	−0.723423	−	0.417668i	−0.816011	+	0.578036i	$0.803819\pi$
$510$			2.43337i			0.107752i
$511$	6.10390	+	2.92717i	0.270021	+	0.129490i
$512$	1.00000			0.0441942
$513$	−1.86672	−	1.07775i	−0.0824179	−	0.0475840i
$514$	13.1071	−	7.56741i	0.578131	−	0.333784i
$515$	22.8824	+	39.6334i	1.00832	+	1.74646i
$516$	1.57654	−	2.73065i	0.0694035	−	0.120210i
$517$	19.7006			0.866431
$518$	9.75095	+	4.67614i	0.428432	+	0.205458i
$519$	3.49554			0.153437
$520$	−11.4041	−	6.58416i	−0.500103	−	0.288735i
$521$	−1.23201	−	2.13390i	−0.0539751	−	0.0934877i	0.837775	−	0.546015i	$-0.183856\pi$
$521$	−1.23201	−	2.13390i	−0.0539751	−	0.0934877i	−0.891751	+	0.452527i	$0.850523\pi$
$522$	−2.39406	−	4.14663i	−0.104785	−	0.181493i
$523$	−10.2857	+	17.8154i	−0.449764	+	0.779014i	−0.998370	−	0.0570665i	$-0.981825\pi$
$523$	−10.2857	+	17.8154i	−0.449764	+	0.779014i	0.548606	+	0.836081i	$0.315159\pi$
$524$		−	6.51093i		−	0.284431i
$525$	0.861493	+	11.2484i	0.0375986	+	0.490922i
$526$		−	13.1807i		−	0.574704i
$527$	−2.82576	−	1.63145i	−0.123092	−	0.0710673i
$528$	−1.19724	−	2.07367i	−0.0521030	−	0.0902450i
$529$	−6.12059	+	22.1707i	−0.266113	+	0.963942i
$530$	28.9018	+	16.6865i	1.25541	+	0.724813i
$531$		−	12.3064i		−	0.534051i
$532$	3.22030	+	4.70672i	0.139618	+	0.204062i
$533$	−33.1741			−1.43693
$534$	−0.569742	−	0.328941i	−0.0246551	−	0.0142347i
$535$	35.8200	−	20.6807i	1.54863	−	0.894104i
$536$	−4.06092	+	2.34457i	−0.175405	+	0.101270i
$537$	17.5577	+	10.1370i	0.757672	+	0.437442i
$538$			12.4898i			0.538473i
$539$	2.55245	+	16.5658i	0.109942	+	0.713540i
$540$		−	3.04368i		−	0.130979i
$541$	−8.91227	+	15.4365i	−0.383168	+	0.663667i	−0.991513	−	0.130006i	$-0.958500\pi$
$541$	−8.91227	+	15.4365i	−0.383168	+	0.663667i	0.608345	+	0.793673i	$0.291834\pi$
$542$	−2.91636	+	1.68376i	−0.125268	+	0.0723236i
$543$	−4.57978	+	2.64414i	−0.196537	+	0.113471i
$544$	−0.399743	+	0.692374i	−0.0171388	+	0.0296853i
$545$		−	12.7697i		−	0.546994i
$546$	−6.46366	−	9.44715i	−0.276619	−	0.404301i
$547$	−1.99506			−0.0853026			−0.0426513	−	0.999090i	$-0.513580\pi$
$547$	−1.99506			−0.0853026			−0.0426513	+	0.999090i	$0.513580\pi$
$548$	7.83359	+	4.52273i	0.334635	+	0.193201i
$549$	2.01946	+	3.49780i	0.0861883	+	0.149283i
$550$	8.84206	−	5.10496i	0.377027	−	0.217676i
$551$	5.16041	−	8.93809i	0.219841	−	0.380775i
$552$	4.42380	+	1.85202i	0.188290	+	0.0788271i
$553$	−1.77912	−	23.2298i	−0.0756559	−	0.987832i
$554$	1.56579			0.0665241
$555$	6.22034	−	10.7740i	0.264039	−	0.457329i
$556$	−9.15111	+	5.28340i	−0.388094	+	0.224066i
$557$	−0.0975129	+	0.0562991i	−0.00413175	+	0.00238547i	−0.502064	−	0.864830i	$-0.667426\pi$
$557$	−0.0975129	+	0.0562991i	−0.00413175	+	0.00238547i	0.497933	+	0.867216i	$0.334093\pi$
$558$	3.53448	+	2.04063i	0.149626	+	0.0863868i
$559$	−13.6417			−0.576982
$560$	−3.48209	+	7.26105i	−0.147145	+	0.306835i
$561$	1.91434			0.0808237
$562$	−20.7932	−	12.0050i	−0.877108	−	0.506399i
$563$	14.9248	+	25.8506i	0.629007	+	1.08947i	0.987751	+	0.156036i	$0.0498715\pi$
$563$	14.9248	+	25.8506i	0.629007	+	1.08947i	−0.358745	+	0.933436i	$0.616795\pi$
$564$	4.11377	+	7.12526i	0.173221	+	0.300027i
$565$	31.6512	+	18.2738i	1.33157	+	0.768785i
$566$	−27.7521			−1.16651
$567$	1.14404	−	2.38562i	0.0480452	−	0.100187i
$568$	6.20671			0.260428
$569$	30.8972	+	17.8385i	1.29528	+	0.747829i	0.979585	−	0.201032i	$-0.0644297\pi$
$569$	30.8972	+	17.8385i	1.29528	+	0.747829i	0.315693	+	0.948861i	$0.397763\pi$
$570$	5.68170	−	3.28033i	0.237980	−	0.137398i
$571$	−29.9445	+	17.2885i	−1.25314	+	0.723499i	−0.971731	−	0.236089i	$-0.924134\pi$
$571$	−29.9445	+	17.2885i	−1.25314	+	0.723499i	−0.281406	+	0.959589i	$0.590801\pi$
$572$	−5.17979	+	8.97165i	−0.216578	+	0.375124i
$573$	20.9497			0.875186
$574$	1.54919	+	20.2277i	0.0646621	+	0.844288i
$575$	−7.89693	+	18.8629i	−0.329325	+	0.786638i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	16.5610	−	9.56149i	0.689443	−	0.398050i	−0.113961	−	0.993485i	$-0.536354\pi$
$577$	16.5610	−	9.56149i	0.689443	−	0.398050i	0.803403	+	0.595435i	$0.203020\pi$
$578$	8.18041	+	14.1689i	0.340260	+	0.589348i
$579$	10.8645	+	6.27262i	0.451513	+	0.260681i
$580$	14.5735			0.605130
$581$	−0.564273	−	0.824730i	−0.0234100	−	0.0342156i
$582$			2.07359i			0.0859532i
$583$	13.1273	−	22.7372i	0.543677	−	0.941677i
$584$	2.21583	−	1.27931i	0.0916919	−	0.0529383i
$585$	−11.4041	+	6.58416i	−0.471502	+	0.272222i
$586$	−11.9916	+	20.7701i	−0.495370	+	0.858007i
$587$			38.6271i			1.59431i	0.603774	+	0.797155i	$0.293663\pi$
$587$			38.6271i			1.59431i	−0.603774	+	0.797155i	$0.706337\pi$
$588$	−5.45849	+	4.38234i	−0.225104	+	0.180725i
$589$			8.79719i			0.362482i
$590$	32.4384	+	18.7283i	1.33547	+	0.771032i
$591$	17.9132	−	10.3422i	0.736849	−	0.425420i
$592$	3.53978	−	2.04369i	0.145484	−	0.0839953i
$593$	−0.782667	−	0.451873i	−0.0321403	−	0.0185562i	0.483844	−	0.875154i	$-0.339240\pi$
$593$	−0.782667	−	0.451873i	−0.0321403	−	0.0185562i	−0.515984	+	0.856598i	$0.672574\pi$
$594$	−2.39447			−0.0982463
$595$	−3.63542	−	5.31346i	−0.149038	−	0.217831i
$596$			3.68564i			0.150970i
$597$	−16.5222	−	9.53909i	−0.676208	−	0.390409i
$598$	−2.63052	−	20.5815i	−0.107570	−	0.841641i
$599$	−13.8142	−	23.9269i	−0.564434	−	0.977628i	−0.997102	−	0.0760748i	$-0.975761\pi$
$599$	−13.8142	−	23.9269i	−0.564434	−	0.977628i	0.432668	−	0.901553i	$-0.357572\pi$
$600$	3.69270	+	2.13198i	0.150754	+	0.0870377i
$601$		−	43.6360i		−	1.77995i	−0.456009	−	0.889975i	$-0.650721\pi$
$601$		−	43.6360i		−	1.77995i	0.456009	−	0.889975i	$-0.349279\pi$
$602$	0.637052	+	8.31793i	0.0259643	+	0.339013i
$603$			4.68915i			0.190957i
$604$	−12.2114	+	21.1507i	−0.496874	+	0.860610i
$605$	8.01477	+	13.8820i	0.325847	+	0.564383i
$606$	−8.70623	−	15.0796i	−0.353666	−	0.612568i
$607$	4.23392	+	2.44445i	0.171849	+	0.0992173i	0.583458	−	0.812144i	$-0.301699\pi$
$607$	4.23392	+	2.44445i	0.171849	+	0.0992173i	−0.411608	+	0.911361i	$0.635033\pi$
$608$	2.15551			0.0874174
$609$	11.4226	+	5.47779i	0.462867	+	0.221971i
$610$	−12.2931			−0.497735
$611$	17.7980	−	30.8271i	0.720032	−	1.24713i
$612$	0.399743	+	0.692374i	0.0161586	+	0.0279876i
$613$	6.30762	−	3.64171i	0.254762	−	0.147087i	−0.367181	−	0.930150i	$-0.619677\pi$
$613$	6.30762	−	3.64171i	0.254762	−	0.147087i	0.621943	+	0.783063i	$0.286344\pi$
$614$	−28.3430	−	16.3639i	−1.14383	−	0.660392i
$615$	23.3381			0.941083
$616$	5.71229	+	2.73937i	0.230155	+	0.110372i
$617$		−	33.9874i		−	1.36828i	−0.729350	−	0.684141i	$-0.760177\pi$
$617$		−	33.9874i		−	1.36828i	0.729350	−	0.684141i	$-0.239823\pi$
$618$	13.0216	+	7.51800i	0.523804	+	0.302418i
$619$	8.69677	+	15.0632i	0.349553	+	0.605443i	0.986170	−	0.165737i	$-0.0530002\pi$
$619$	8.69677	+	15.0632i	0.349553	+	0.605443i	−0.636617	+	0.771180i	$0.719667\pi$
$620$	−10.7578	+	6.21102i	−0.432044	+	0.249440i
$621$	3.81580	−	2.90512i	0.153123	−	0.116578i
$622$		−	18.1773i		−	0.728843i
$623$	1.73551	−	0.132919i	0.0695316	−	0.00532527i
$624$	−4.32646			−0.173197
$625$	14.0692	−	24.3686i	0.562769	−	0.974744i
$626$	−13.1187	−	22.7223i	−0.524330	−	0.908166i
$627$	−2.58065	−	4.46982i	−0.103061	−	0.178507i
$628$	−4.68552	+	8.11555i	−0.186973	+	0.323846i
$629$			3.26781i			0.130296i
$630$	4.54721	+	6.64610i	0.181165	+	0.264787i
$631$			28.9833i			1.15381i	0.816812	+	0.576903i	$0.195739\pi$
$631$			28.9833i			1.15381i	−0.816812	+	0.576903i	$0.804261\pi$
$632$	−7.62601	−	4.40288i	−0.303346	−	0.175137i
$633$	−18.0014	+	10.3931i	−0.715491	+	0.413089i
$634$	−11.2001	−	19.3992i	−0.444814	−	0.770441i
$635$	13.7044	−	23.7367i	0.543841	−	0.941961i
$636$	10.9647			0.434778
$637$	28.2278	+	10.9720i	1.11843	+	0.434725i
$638$		−	11.4650i		−	0.453904i
$639$	3.10335	−	5.37517i	0.122767	−	0.212638i
$640$	1.52184	+	2.63590i	0.0601559	+	0.104193i
$641$	16.3277	−	9.42678i	0.644904	−	0.372335i	−0.141597	−	0.989924i	$-0.545224\pi$
$641$	16.3277	−	9.42678i	0.644904	−	0.372335i	0.786501	+	0.617589i	$0.211890\pi$
$642$	6.79464	−	11.7687i	0.268163	−	0.464472i
$643$	−48.6652			−1.91917			−0.959584	−	0.281422i	$-0.909194\pi$
$643$	−48.6652			−1.91917			−0.959584	+	0.281422i	$0.909194\pi$
$644$	−12.4266	+	2.56507i	−0.489677	+	0.101078i
$645$	9.59698			0.377881
$646$	−0.861648	+	1.49242i	−0.0339011	+	0.0587184i
$647$	11.4722	−	6.62349i	0.451020	−	0.260396i	−0.257241	−	0.966347i	$-0.582813\pi$
$647$	11.4722	−	6.62349i	0.451020	−	0.260396i	0.708261	+	0.705951i	$0.249480\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	14.7336	−	25.5194i	0.578346	−	1.00172i
$650$		−	18.4478i		−	0.723584i
$651$	−10.7665	+	0.824580i	−0.421971	+	0.0323178i
$652$	11.8412			0.463738
$653$	−14.8034	+	25.6402i	−0.579300	+	1.00338i	0.416259	+	0.909246i	$0.363341\pi$
$653$	−14.8034	+	25.6402i	−0.579300	+	1.00338i	−0.995560	+	0.0941318i	$0.969992\pi$
$654$	−2.09774	−	3.63340i	−0.0820283	−	0.142077i
$655$	17.1622	−	9.90857i	0.670581	−	0.387160i
$656$	6.64046	+	3.83387i	0.259266	+	0.149687i
$657$		−	2.55863i		−	0.0998215i
$658$	−19.6278	−	9.41264i	−0.765170	−	0.366943i
$659$			39.8104i			1.55079i	0.631474	+	0.775397i	$0.282450\pi$
$659$			39.8104i			1.55079i	−0.631474	+	0.775397i	$0.717550\pi$
$660$	3.64400	−	6.31159i	0.141842	−	0.245678i
$661$	−14.0002	−	24.2490i	−0.544544	−	0.943178i	−0.998635	−	0.0522226i	$-0.983369\pi$
$661$	−14.0002	−	24.2490i	−0.544544	−	0.943178i	0.454092	−	0.890955i	$-0.349964\pi$
$662$	0.644942	+	1.11707i	0.0250664	+	0.0434162i
$663$	1.72947	−	2.99553i	0.0671670	−	0.116337i
$664$	−0.377697			−0.0146575
$665$	−7.50567	+	15.6512i	−0.291057	+	0.606929i
$666$		−	4.08739i		−	0.158383i
$667$	13.9100	+	18.2705i	0.538598	+	0.707435i
$668$	−0.0905071	+	0.0522543i	−0.00350183	+	0.00202178i
$669$	−7.62069	−	13.1994i	−0.294633	−	0.510319i
$670$	−12.3601	−	7.13612i	−0.477513	−	0.275692i
$671$			9.67106i			0.373347i
$672$	0.202041	+	2.63803i	0.00779388	+	0.101764i
$673$	−25.5988			−0.986760			−0.493380	−	0.869814i	$-0.664239\pi$
$673$	−25.5988			−0.986760			−0.493380	+	0.869814i	$0.664239\pi$
$674$	4.74207	+	2.73784i	0.182658	+	0.105458i
$675$	3.69270	−	2.13198i	0.142132	−	0.0820599i
$676$	2.85911	+	4.95212i	0.109966	+	0.190466i
$677$	23.6160	−	40.9042i	0.907638	−	1.57208i	0.0903020	−	0.995914i	$-0.471217\pi$
$677$	23.6160	−	40.9042i	0.907638	−	1.57208i	0.817336	−	0.576161i	$-0.195450\pi$
$678$	12.0077			0.461154
$679$	−3.09792	−	4.52785i	−0.118887	−	0.173763i
$680$	−2.43337			−0.0933156
$681$	−8.02220	−	4.63162i	−0.307412	−	0.177484i
$682$	4.88623	+	8.46320i	0.187103	+	0.324073i
$683$	−22.2497	−	38.5377i	−0.851362	−	1.47460i	−0.879979	−	0.475013i	$-0.842443\pi$
$683$	−22.2497	−	38.5377i	−0.851362	−	1.47460i	0.0286165	−	0.999590i	$-0.490890\pi$
$684$	1.07775	−	1.86672i	0.0412089	−	0.0713760i
$685$			27.5314i			1.05192i
$686$	5.37187	−	17.7241i	0.205099	−	0.676708i
$687$		−	14.5158i		−	0.553811i
$688$	2.73065	+	1.57654i	0.104105	+	0.0601052i
$689$	−23.7191	−	41.0827i	−0.903625	−	1.56513i
$690$	1.85058	+	14.4792i	0.0704502	+	0.551213i
$691$	−29.3090	−	16.9215i	−1.11497	−	0.643726i	−0.174855	−	0.984594i	$-0.555946\pi$
$691$	−29.3090	−	16.9215i	−1.11497	−	0.643726i	−0.940111	+	0.340869i	$0.889279\pi$
$692$			3.49554i			0.132880i
$693$	5.22851	−	3.57730i	0.198615	−	0.135891i
$694$	−29.6421			−1.12520
$695$	−27.8530	−	16.0809i	−1.05653	−	0.609985i
$696$	4.14663	−	2.39406i	0.157177	−	0.0907465i
$697$	−5.30895	+	3.06512i	−0.201091	+	0.116100i
$698$	3.30287	+	1.90691i	0.125016	+	0.0721778i
$699$		−	10.9152i		−	0.412850i
$700$	−11.2484	+	0.861493i	−0.425151	+	0.0325614i
$701$			26.6557i			1.00677i	0.864062	+	0.503386i	$0.167913\pi$
$701$			26.6557i			1.00677i	−0.864062	+	0.503386i	$0.832087\pi$
$702$	−2.16323	+	3.74682i	−0.0816458	+	0.141415i
$703$	7.63003	−	4.40520i	0.287772	−	0.166145i
$704$	2.07367	−	1.19724i	0.0781545	−	0.0451225i
$705$	−12.5210	+	21.6870i	−0.471567	+	0.816778i
$706$		−	6.63468i		−	0.249700i
$707$	41.5395	+	19.9206i	1.56225	+	0.749190i
$708$	12.3064			0.462502
$709$	−27.0586	−	15.6223i	−1.01621	−	0.586708i	−0.103205	−	0.994660i	$-0.532910\pi$
$709$	−27.0586	−	15.6223i	−1.01621	−	0.586708i	−0.913003	+	0.407952i	$0.866243\pi$
$710$	9.44560	+	16.3603i	0.354487	+	0.613990i
$711$	−7.62601	+	4.40288i	−0.285998	+	0.165121i
$712$	0.328941	−	0.569742i	0.0123276	−	0.0213520i
$713$	−18.0547	−	7.55857i	−0.676154	−	0.283071i
$714$	−1.90727	−	0.914643i	−0.0713776	−	0.0342297i
$715$	−31.5312			−1.17920
$716$	−10.1370	+	17.5577i	−0.378836	+	0.656163i
$717$	−17.4268	+	10.0614i	−0.650816	+	0.375749i
$718$	23.6674	−	13.6644i	0.883259	−	0.509950i
$719$	2.92333	+	1.68779i	0.109022	+	0.0629438i	0.553519	−	0.832836i	$-0.313284\pi$
$719$	2.92333	+	1.68779i	0.109022	+	0.0629438i	−0.444498	+	0.895780i	$0.646618\pi$
$720$	3.04368			0.113431
$721$	−39.6654	+	3.03788i	−1.47722	+	0.113137i
$722$	−14.3538			−0.534193
$723$	−21.7713	−	12.5697i	−0.809683	−	0.467471i
$724$	−2.64414	−	4.57978i	−0.0982687	−	0.170206i
$725$	10.2082	+	17.6810i	0.379122	+	0.656658i
$726$	4.56093	+	2.63325i	0.169272	+	0.0977292i
$727$	23.0380			0.854433			0.427216	−	0.904149i	$-0.359494\pi$
$727$	23.0380			0.854433			0.427216	+	0.904149i	$0.359494\pi$
$728$	9.44715	−	6.46366i	0.350135	−	0.239559i
$729$	−1.00000			−0.0370370
$730$	6.74428	+	3.89381i	0.249617	+	0.144116i
$731$	−2.18312	+	1.26042i	−0.0807455	+	0.0466184i
$732$	−3.49780	+	2.01946i	−0.129282	+	0.0746413i
$733$	8.86114	−	15.3479i	0.327294	−	0.566889i	−0.654680	−	0.755906i	$-0.727197\pi$
$733$	8.86114	−	15.3479i	0.327294	−	0.566889i	0.981974	+	0.189017i	$0.0605300\pi$
$734$	10.2183			0.377164
$735$	−19.8583	−	7.71881i	−0.732486	−	0.284713i
$736$	−1.85202	+	4.42380i	−0.0682663	+	0.163064i
$737$	−5.61401	+	9.72375i	−0.206795	+	0.358179i
$738$	6.64046	−	3.83387i	0.244439	−	0.141127i
$739$	18.7794	+	32.5269i	0.690812	+	1.19652i	0.971572	+	0.236744i	$0.0760801\pi$
$739$	18.7794	+	32.5269i	0.690812	+	1.19652i	−0.280760	+	0.959778i	$0.590587\pi$
$740$	10.7740	+	6.22034i	0.396058	+	0.228664i
$741$	−9.32571			−0.342588
$742$	−23.9422	+	16.3811i	−0.878946	+	0.601368i
$743$		−	40.0707i		−	1.47005i	−0.678040	−	0.735025i	$-0.737170\pi$
$743$		−	40.0707i		−	1.47005i	0.678040	−	0.735025i	$-0.262830\pi$
$744$	−2.04063	+	3.53448i	−0.0748132	+	0.129580i
$745$	−9.71498	+	5.60895i	−0.355929	+	0.205496i
$746$	−8.16295	+	4.71288i	−0.298867	+	0.172551i
$747$	−0.188848	+	0.327095i	−0.00690960	+	0.0119678i
$748$			1.91434i			0.0699954i
$749$	2.74559	+	35.8489i	0.100322	+	1.30989i
$750$		−	2.24027i		−	0.0818030i
$751$	36.9816	+	21.3513i	1.34948	+	0.779122i	0.988176	−	0.153327i	$-0.0489987\pi$
$751$	36.9816	+	21.3513i	1.34948	+	0.779122i	0.361303	+	0.932449i	$0.382332\pi$
$752$	−7.12526	+	4.11377i	−0.259831	+	0.150014i
$753$	6.53628	−	3.77372i	0.238195	−	0.137522i
$754$	−17.9402	−	10.3578i	−0.653343	−	0.377208i
$755$	−74.3349			−2.70532
$756$	2.38562	+	1.14404i	0.0867641	+	0.0416084i
$757$			16.6847i			0.606417i	0.952924	+	0.303208i	$0.0980578\pi$
$757$			16.6847i			0.606417i	−0.952924	+	0.303208i	$0.901942\pi$
$758$	4.54788	+	2.62572i	0.165187	+	0.0953705i
$759$	11.3908	−	1.45586i	0.413461	−	0.0528442i
$760$	3.28033	+	5.68170i	0.118990	+	0.206097i
$761$	22.1967	+	12.8153i	0.804631	+	0.464554i	0.845088	−	0.534627i	$-0.179548\pi$
$761$	22.1967	+	12.8153i	0.804631	+	0.464554i	−0.0404567	+	0.999181i	$0.512881\pi$
$762$		−	9.00515i		−	0.326222i
$763$	10.0088	+	4.79981i	0.362344	+	0.173765i
$764$			20.9497i			0.757933i
$765$	−1.21669	+	2.10736i	−0.0439894	+	0.0761919i
$766$	−1.43797	−	2.49064i	−0.0519560	−	0.0899904i
$767$	−26.6215	−	46.1098i	−0.961247	−	1.66493i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	4.61225			0.166322			0.0831610	−	0.996536i	$-0.473498\pi$
$769$	4.61225			0.166322			0.0831610	+	0.996536i	$0.473498\pi$
$770$	1.47247	+	19.2259i	0.0530641	+	0.692854i
$771$	15.1348			0.545067
$772$	−6.27262	+	10.8645i	−0.225756	+	0.391022i
$773$	−22.1352	−	38.3393i	−0.796147	−	1.37897i	−0.922108	−	0.386933i	$-0.873535\pi$
$773$	−22.1352	−	38.3393i	−0.796147	−	1.37897i	0.125961	−	0.992035i	$-0.459799\pi$
$774$	2.73065	−	1.57654i	0.0981513	−	0.0566677i
$775$	−15.0709	−	8.70117i	−0.541361	−	0.312555i
$776$	−2.07359			−0.0744377
$777$	6.10650	+	8.92513i	0.219069	+	0.320187i
$778$			6.80689i			0.244039i
$779$	14.3136	+	8.26393i	0.512836	+	0.296086i
$780$	−6.58416	−	11.4041i	−0.235751	−	0.408332i
$781$	12.8707	−	7.43089i	0.460549	−	0.265898i
$782$	−2.32260	−	3.05067i	−0.0830559	−	0.109092i
$783$		−	4.78811i		−	0.171113i
$784$	−4.38234	−	5.45849i	−0.156512	−	0.194946i
$785$	−28.5224			−1.01801
$786$	3.25546	−	5.63863i	0.116119	−	0.201123i
$787$	24.1723	+	41.8676i	0.861649	+	1.49242i	0.870336	+	0.492458i	$0.163901\pi$
$787$	24.1723	+	41.8676i	0.861649	+	1.49242i	−0.00868697	+	0.999962i	$0.502765\pi$
$788$	10.3422	+	17.9132i	0.368425	+	0.638130i
$789$	6.59033	−	11.4148i	0.234622	−	0.406377i
$790$		−	26.8019i		−	0.953568i
$791$	−26.2198	+	17.9394i	−0.932268	+	0.637850i
$792$		−	2.39447i		−	0.0850838i
$793$	15.1331	+	8.73709i	0.537392	+	0.310263i
$794$	−30.7424	+	17.7492i	−1.09101	+	0.629894i
$795$	16.6865	+	28.9018i	0.591808	+	1.02504i
$796$	9.53909	−	16.5222i	0.338104	−	0.585613i
$797$	−54.2267			−1.92081			−0.960404	−	0.278612i	$-0.910126\pi$
$797$	−54.2267			−1.92081			−0.960404	+	0.278612i	$0.910126\pi$
$798$	0.435500	+	5.68628i	0.0154165	+	0.201292i
$799$		−	6.57779i		−	0.232706i
$800$	−2.13198	+	3.69270i	−0.0753769	+	0.130557i
$801$	−0.328941	−	0.569742i	−0.0116225	−	0.0201308i
$802$	19.3925	−	11.1963i	0.684774	−	0.395355i
$803$	3.06328	−	5.30575i	0.108101	−	0.187236i
$804$	−4.68915			−0.165373
$805$	−25.6725	−	28.8517i	−0.904838	−	1.01689i
$806$	17.6574			0.621955
$807$	−6.24489	+	10.8165i	−0.219831	+	0.380758i
$808$	15.0796	−	8.70623i	0.530500	−	0.306284i
$809$	−22.9145	−	39.6890i	−0.805629	−	1.39539i	−0.915865	−	0.401485i	$-0.868494\pi$
$809$	−22.9145	−	39.6890i	−0.805629	−	1.39539i	0.110236	−	0.993905i	$-0.464839\pi$
$810$	1.52184	−	2.63590i	0.0534719	−	0.0926161i
$811$			14.0502i			0.493368i	0.969096	+	0.246684i	$0.0793409\pi$
$811$			14.0502i			0.493368i	−0.969096	+	0.246684i	$0.920659\pi$
$812$	−5.47779	+	11.4226i	−0.192233	+	0.400855i
$813$	−3.36752			−0.118104
$814$	4.89357	−	8.47591i	0.171519	−	0.297080i
$815$	18.0204	+	31.2123i	0.631227	+	1.09332i
$816$	−0.692374	+	0.399743i	−0.0242380	+	0.0139938i
$817$	5.88595	+	3.39825i	0.205923	+	0.118890i
$818$			5.85038i			0.204554i
$819$	−0.874119	−	11.4133i	−0.0305442	−	0.398813i
$820$			23.3381i			0.815002i
$821$	4.84622	−	8.39390i	0.169134	−	0.292949i	−0.768981	−	0.639271i	$-0.779236\pi$
$821$	4.84622	−	8.39390i	0.169134	−	0.292949i	0.938116	+	0.346322i	$0.112570\pi$
$822$	4.52273	+	7.83359i	0.157748	+	0.273228i
$823$	−2.12993	−	3.68915i	−0.0742448	−	0.128596i	0.826513	−	0.562918i	$-0.190321\pi$
$823$	−2.12993	−	3.68915i	−0.0742448	−	0.128596i	−0.900758	+	0.434322i	$0.856988\pi$
$824$	−7.51800	+	13.0216i	−0.261902	+	0.453627i
$825$	10.2099			0.355464
$826$	−26.8719	+	18.3855i	−0.934994	+	0.639715i
$827$			40.2206i			1.39861i	0.714825	+	0.699304i	$0.246506\pi$
$827$			40.2206i			1.39861i	−0.714825	+	0.699304i	$0.753494\pi$
$828$	2.90512	+	3.81580i	0.100960	+	0.132608i
$829$	22.7148	−	13.1144i	0.788917	−	0.455481i	−0.0506642	−	0.998716i	$-0.516134\pi$
$829$	22.7148	−	13.1144i	0.788917	−	0.455481i	0.839581	+	0.543234i	$0.182800\pi$
$830$	−0.574793	−	0.995571i	−0.0199514	−	0.0345568i
$831$	1.35601	+	0.782895i	0.0470396	+	0.0271583i
$832$		−	4.32646i		−	0.149993i
$833$	5.53113	−	0.852232i	0.191642	−	0.0295281i
$834$	−10.5668			−0.365898
$835$	−0.275474	−	0.159045i	−0.00953318	−	0.00550398i
$836$	4.46982	−	2.58065i	0.154592	−	0.0892537i
$837$	2.04063	+	3.53448i	0.0705345	+	0.122169i
$838$	5.24814	−	9.09004i	0.181294	−	0.314010i
$839$	24.1849			0.834954			0.417477	−	0.908687i	$-0.362914\pi$
$839$	24.1849			0.834954			0.417477	+	0.908687i	$0.362914\pi$
$840$	−6.64610	+	4.54721i	−0.229312	+	0.156893i
$841$	−6.07398			−0.209448
$842$	12.2420	+	7.06791i	0.421886	+	0.243576i
$843$	−12.0050	−	20.7932i	−0.413473	−	0.716156i
$844$	−10.3931	−	18.0014i	−0.357746	−	0.619634i
$845$	−8.70220	+	15.0726i	−0.299365	+	0.518515i
$846$			8.22754i			0.282869i
$847$	−13.8932	+	1.06405i	−0.477375	+	0.0365611i
$848$			10.9647i			0.376529i
$849$	−24.0340	−	13.8760i	−0.824845	−	0.476224i
$850$	−1.70449	−	2.95226i	−0.0584634	−	0.101262i
$851$	2.48516	+	19.4443i	0.0851903	+	0.666541i
$852$	5.37517	+	3.10335i	0.184150	+	0.106319i
$853$		−	39.8471i		−	1.36434i	−0.731193	−	0.682170i	$-0.761036\pi$
$853$		−	39.8471i		−	1.36434i	0.731193	−	0.682170i	$-0.238964\pi$
$854$	4.62068	−	9.63530i	0.158116	−	0.329713i
$855$	6.56067			0.224370
$856$	11.7687	+	6.79464i	0.402245	+	0.232236i
$857$	−20.6008	+	11.8939i	−0.703709	+	0.406287i	−0.808728	−	0.588183i	$-0.799843\pi$
$857$	−20.6008	+	11.8939i	−0.703709	+	0.406287i	0.105018	+	0.994470i	$0.466510\pi$
$858$	−8.97165	+	5.17979i	−0.306287	+	0.176835i
$859$	−24.2200	−	13.9834i	−0.826377	−	0.477109i	0.0262339	−	0.999656i	$-0.491649\pi$
$859$	−24.2200	−	13.9834i	−0.826377	−	0.477109i	−0.852610	+	0.522547i	$0.824982\pi$
$860$			9.59698i			0.327254i
$861$	−8.77220	+	18.2923i	−0.298956	+	0.623400i
$862$			5.86400i			0.199729i
$863$	−7.98752	+	13.8348i	−0.271898	+	0.470942i	−0.969348	−	0.245692i	$-0.920985\pi$
$863$	−7.98752	+	13.8348i	−0.271898	+	0.470942i	0.697450	+	0.716634i	$0.254318\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−9.21389	+	5.31964i	−0.313282	+	0.180873i
$866$	7.94306	−	13.7578i	0.269916	−	0.467508i
$867$			16.3608i			0.555643i
$868$	−0.824580	−	10.7665i	−0.0279881	−	0.365438i
$869$	−21.0851			−0.715264
$870$	12.6210	+	7.28673i	0.427891	+	0.247043i
$871$	10.1437	+	17.5694i	0.343706	+	0.595316i
$872$	3.63340	−	2.09774i	0.123042	−	0.0710386i
$873$	−1.03680	+	1.79578i	−0.0350902	+	0.0607781i
$874$	−3.99204	+	9.53554i	−0.135033	+	0.322544i
$875$	3.34693	+	4.89180i	0.113147	+	0.165373i
$876$	2.55863			0.0864479
$877$	14.0832	−	24.3928i	0.475555	−	0.823686i	−0.524053	−	0.851686i	$-0.675581\pi$
$877$	14.0832	−	24.3928i	0.475555	−	0.823686i	0.999608	+	0.0280001i	$0.00891386\pi$
$878$	−17.8490	+	10.3051i	−0.602376	+	0.347782i
$879$	−20.7701	+	11.9916i	−0.700560	+	0.404468i
$880$	6.31159	+	3.64400i	0.212764	+	0.122839i
$881$	−35.4459			−1.19420			−0.597102	−	0.802166i	$-0.703681\pi$
$881$	−35.4459			−1.19420			−0.597102	+	0.802166i	$0.703681\pi$
$882$	−6.91836	+	1.06598i	−0.232953	+	0.0358933i
$883$	−23.4131			−0.787913			−0.393957	−	0.919129i	$-0.628894\pi$
$883$	−23.4131			−0.787913			−0.393957	+	0.919129i	$0.628894\pi$
$884$	2.99553	+	1.72947i	0.100750	+	0.0581683i
$885$	18.7283	+	32.4384i	0.629545	+	1.09040i
$886$	5.21749	+	9.03695i	0.175285	+	0.303602i
$887$	−2.04900	−	1.18299i	−0.0687987	−	0.0397209i	0.465206	−	0.885202i	$-0.345980\pi$
$887$	−2.04900	−	1.18299i	−0.0687987	−	0.0397209i	−0.534005	+	0.845481i	$0.679314\pi$
$888$	4.08739			0.137164
$889$	13.4536	+	19.6634i	0.451218	+	0.659490i
$890$	2.00238			0.0671198
$891$	−2.07367	−	1.19724i	−0.0694707	−	0.0401089i
$892$	13.1994	−	7.62069i	0.441950	−	0.255160i
$893$	−15.3585	+	8.86726i	−0.513954	+	0.296732i
$894$	−1.84282	+	3.19186i	−0.0616331	+	0.106752i
$895$	−61.7072			−2.06265
$896$	−2.63803	+	0.202041i	−0.0881303	+	0.00674970i
$897$	8.01267	−	19.1394i	0.267535	−	0.639045i
$898$	3.52773	−	6.11021i	0.117722	−	0.203900i
$899$	−16.9235	+	9.77077i	−0.564429	+	0.325873i
$900$	2.13198	+	3.69270i	0.0710660	+	0.123090i
$901$	−7.59166	−	4.38305i	−0.252915	−	0.146020i
$902$	18.3602			0.611327
$903$	−3.60726	+	7.52206i	−0.120042	+	0.250319i
$904$			12.0077i			0.399371i
$905$	8.04790	−	13.9394i	0.267521	−	0.463361i
$906$	−21.1507	+	12.2114i	−0.702685	+	0.405696i
$907$	33.1958	−	19.1656i	1.10225	−	0.636383i	0.165437	−	0.986220i	$-0.447097\pi$
$907$	33.1958	−	19.1656i	1.10225	−	0.636383i	0.936810	+	0.349838i	$0.113763\pi$
$908$	4.63162	−	8.02220i	0.153706	−	0.266226i
$909$		−	17.4125i		−	0.577535i
$910$	31.4146	+	15.0651i	1.04138	+	0.499403i
$911$		−	27.5063i		−	0.911324i	−0.890153	−	0.455662i	$-0.849403\pi$
$911$		−	27.5063i		−	0.911324i	0.890153	−	0.455662i	$-0.150597\pi$
$912$	1.86672	+	1.07775i	0.0618134	+	0.0356880i
$913$	−0.783219	+	0.452192i	−0.0259208	+	0.0149654i
$914$	17.6738	−	10.2040i	0.584598	−	0.337518i
$915$	−10.6462	−	6.14657i	−0.351952	−	0.203199i
$916$	14.5158			0.479615
$917$	1.31547	+	17.1760i	0.0434407	+	0.567201i
$918$			0.799485i			0.0263869i
$919$	41.4042	+	23.9047i	1.36580	+	0.788544i	0.990388	−	0.138315i	$-0.0441687\pi$
$919$	41.4042	+	23.9047i	1.36580	+	0.788544i	0.375410	+	0.926859i	$0.377502\pi$
$920$	−14.4792	+	1.85058i	−0.477364	+	0.0610117i
$921$	−16.3639	−	28.3430i	−0.539207	−	0.933935i
$922$	−16.7061	−	9.64529i	−0.550187	−	0.317651i
$923$		−	26.8531i		−	0.883879i
$924$	3.57730	+	5.22851i	0.117685	+	0.172005i
$925$			17.4285i			0.573044i
$926$	8.45902	−	14.6514i	0.277981	−	0.481476i
$927$	7.51800	+	13.0216i	0.246924	+	0.427684i
$928$	2.39406	+	4.14663i	0.0785887	+	0.136120i
$929$	−18.2769	−	10.5522i	−0.599647	−	0.346206i	0.169256	−	0.985572i	$-0.445864\pi$
$929$	−18.2769	−	10.5522i	−0.599647	−	0.346206i	−0.768903	+	0.639366i	$0.779197\pi$
$930$	−12.4220			−0.407335
$931$	−9.44617	−	11.7658i	−0.309586	−	0.385609i
$932$	10.9152			0.357539
$933$	9.08865	−	15.7420i	0.297549	−	0.515370i
$934$	13.4093	+	23.2256i	0.438766	+	0.759964i
$935$	−5.04602	+	2.91332i	−0.165023	+	0.0952758i
$936$	−3.74682	−	2.16323i	−0.122469	−	0.0707073i
$937$	53.7539			1.75606			0.878032	−	0.478603i	$-0.158857\pi$
$937$	53.7539			1.75606			0.878032	+	0.478603i	$0.158857\pi$
$938$	10.2391	−	7.00551i	0.334319	−	0.228738i
$939$		−	26.2374i		−	0.856227i
$940$	−21.6870	−	12.5210i	−0.707351	−	0.408389i
$941$	19.2827	+	33.3986i	0.628597	+	1.08876i	0.987833	+	0.155516i	$0.0497040\pi$
$941$	19.2827	+	33.3986i	0.628597	+	1.08876i	−0.359236	+	0.933247i	$0.616963\pi$
$942$	−8.11555	+	4.68552i	−0.264419	+	0.152662i
$943$	−29.2585	+	22.2757i	−0.952789	+	0.725396i
$944$			12.3064i			0.400539i
$945$	0.614946	+	8.02929i	0.0200042	+	0.261193i
$946$	7.54998			0.245471
$947$	20.6952	−	35.8451i	0.672503	−	1.16481i	−0.304689	−	0.952452i	$-0.598552\pi$
$947$	20.6952	−	35.8451i	0.672503	−	1.16481i	0.977192	−	0.212358i	$-0.0681142\pi$
$948$	−4.40288	−	7.62601i	−0.142999	−	0.247681i
$949$	−5.53489	−	9.58671i	−0.179670	−	0.311198i
$950$	−4.59550	+	7.95964i	−0.149098	+	0.258245i
$951$		−	22.4003i		−	0.726378i
$952$	0.914643	−	1.90727i	0.0296438	−	0.0618148i
$953$			26.9984i			0.874564i	0.899324	+	0.437282i	$0.144059\pi$
$953$			26.9984i			0.874564i	−0.899324	+	0.437282i	$0.855941\pi$
$954$	9.49569	+	5.48234i	0.307434	+	0.177497i
$955$	−55.2213	+	31.8820i	−1.78692	+	1.03168i
$956$	−10.0614	−	17.4268i	−0.325408	−	0.563623i
$957$	5.73250	−	9.92898i	0.185305	−	0.320958i
$958$	16.0881			0.519783
$959$	−21.5790	−	10.3484i	−0.696822	−	0.334166i
$960$			3.04368i			0.0982342i
$961$	−7.17165	+	12.4217i	−0.231344	+	0.400699i
$962$	−8.84195	−	15.3147i	−0.285076	−	0.493766i
$963$	11.7687	−	6.79464i	0.379240	−	0.218954i
$964$	12.5697	−	21.7713i	0.404841	−	0.701206i
$965$	−38.1836			−1.22917
$966$	−12.0443	−	3.99188i	−0.387519	−	0.128437i
$967$	7.63681			0.245583			0.122792	−	0.992432i	$-0.460815\pi$
$967$	7.63681			0.245583			0.122792	+	0.992432i	$0.460815\pi$
$968$	−2.63325	+	4.56093i	−0.0846360	+	0.146594i
$969$	−1.49242	+	0.861648i	−0.0479434	+	0.0276801i
$970$	−3.15567	−	5.46578i	−0.101323	−	0.175496i
$971$	14.3330	−	24.8254i	0.459967	−	0.796686i	−0.538992	−	0.842311i	$-0.681195\pi$
$971$	14.3330	−	24.8254i	0.459967	−	0.796686i	0.998959	+	0.0456248i	$0.0145279\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	23.0734	−	15.7866i	0.739699	−	0.506096i
$974$	−26.6509			−0.853950
$975$	9.22392	−	15.9763i	0.295402	−	0.511651i
$976$	−2.01946	−	3.49780i	−0.0646412	−	0.111962i
$977$	−6.00035	+	3.46430i	−0.191968	+	0.110833i	−0.592904	−	0.805273i	$-0.702018\pi$
$977$	−6.00035	+	3.46430i	−0.191968	+	0.110833i	0.400936	+	0.916106i	$0.368685\pi$
$978$	10.2548	+	5.92061i	0.327912	+	0.189320i
$979$		−	1.57528i		−	0.0503461i
$980$	7.71881	−	19.8583i	0.246568	−	0.634352i
$981$		−	4.19549i		−	0.133952i
$982$	−11.2318	+	19.4540i	−0.358420	+	0.620801i
$983$	13.2988	+	23.0343i	0.424167	+	0.734679i	0.996342	−	0.0854527i	$-0.0272337\pi$
$983$	13.2988	+	23.0343i	0.424167	+	0.734679i	−0.572175	+	0.820131i	$0.693900\pi$
$984$	3.83387	+	6.64046i	0.122219	+	0.211690i
$985$	−31.4782	+	54.5219i	−1.00298	+	1.73721i
$986$	−3.82802			−0.121909
$987$	−12.2918	−	17.9655i	−0.391253	−	0.571847i
$988$		−	9.32571i		−	0.296690i
$989$	−12.0315	+	9.16009i	−0.382581	+	0.291274i
$990$	6.31159	−	3.64400i	0.200595	−	0.115814i
$991$	8.16021	+	14.1339i	0.259217	+	0.448978i	0.966033	−	0.258421i	$-0.0832020\pi$
$991$	8.16021	+	14.1339i	0.259217	+	0.448978i	−0.706815	+	0.707398i	$0.749869\pi$
$992$	−3.53448	−	2.04063i	−0.112220	−	0.0647901i
$993$			1.28988i			0.0409332i
$994$	−16.3735	+	1.25401i	−0.519335	+	0.0397747i
$995$	58.0678			1.84087
$996$	−0.327095	−	0.188848i	−0.0103644	−	0.00598389i
$997$	20.7618	−	11.9868i	0.657533	−	0.379627i	−0.133803	−	0.991008i	$-0.542719\pi$
$997$	20.7618	−	11.9868i	0.657533	−	0.379627i	0.791336	+	0.611381i	$0.209386\pi$
$998$	−2.37249	−	4.10928i	−0.0750999	−	0.130077i
$999$	2.04369	−	3.53978i	0.0646596	−	0.111994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.7	yes	32
7.3	odd	6	inner	966.2.k.a.367.2	yes	32
23.22	odd	2	inner	966.2.k.a.229.2	✓	32
161.45	even	6	inner	966.2.k.a.367.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.2	✓	32	23.22	odd	2	inner
966.2.k.a.229.7	yes	32	1.1	even	1	trivial
966.2.k.a.367.2	yes	32	7.3	odd	6	inner
966.2.k.a.367.7	yes	32	161.45	even	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.52184 - 2.63590i) q^{5} -1.00000i q^{6} +(1.49399 + 2.18358i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.52184 - 2.63590i) q^{5} -1.00000i q^{6} +(1.49399 + 2.18358i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.52184 + 2.63590i) q^{10} +(2.07367 - 1.19724i) q^{11} +(0.866025 + 0.500000i) q^{12} -4.32646i q^{13} +(-2.63803 + 0.202041i) q^{14} +3.04368i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.399743 - 0.692374i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.07775 + 1.86672i) q^{19} -3.04368 q^{20} +(-2.38562 - 1.14404i) q^{21} +2.39447i q^{22} +(-2.90512 - 3.81580i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.13198 - 3.69270i) q^{25} +(3.74682 + 2.16323i) q^{26} +1.00000i q^{27} +(1.14404 - 2.38562i) q^{28} -4.78811 q^{29} +(-2.63590 - 1.52184i) q^{30} +(3.53448 - 2.04063i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.19724 + 2.07367i) q^{33} +0.799485 q^{34} +(8.02929 - 0.614946i) q^{35} -1.00000 q^{36} +(-3.53978 - 2.04369i) q^{37} +(-1.07775 - 1.86672i) q^{38} +(2.16323 + 3.74682i) q^{39} +(1.52184 - 2.63590i) q^{40} -7.66774i q^{41} +(2.18358 - 1.49399i) q^{42} -3.15309i q^{43} +(-2.07367 - 1.19724i) q^{44} +(-1.52184 - 2.63590i) q^{45} +(4.75713 - 0.608007i) q^{46} +(7.12526 + 4.11377i) q^{47} -1.00000i q^{48} +(-2.53602 + 6.52446i) q^{49} +4.26396 q^{50} +(0.692374 + 0.399743i) q^{51} +(-3.74682 + 2.16323i) q^{52} +(9.49569 - 5.48234i) q^{53} +(-0.866025 - 0.500000i) q^{54} -7.28799i q^{55} +(1.49399 + 2.18358i) q^{56} -2.15551i q^{57} +(2.39406 - 4.14663i) q^{58} +(10.6576 - 6.15319i) q^{59} +(2.63590 - 1.52184i) q^{60} +(-2.01946 + 3.49780i) q^{61} +4.08126i q^{62} +(2.63803 - 0.202041i) q^{63} +1.00000 q^{64} +(-11.4041 - 6.58416i) q^{65} +(-1.19724 - 2.07367i) q^{66} +(-4.06092 + 2.34457i) q^{67} +(-0.399743 + 0.692374i) q^{68} +(4.42380 + 1.85202i) q^{69} +(-3.48209 + 7.26105i) q^{70} +6.20671 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.21583 - 1.27931i) q^{73} +(3.53978 - 2.04369i) q^{74} +(3.69270 + 2.13198i) q^{75} +2.15551 q^{76} +(5.71229 + 2.73937i) q^{77} -4.32646 q^{78} +(-7.62601 - 4.40288i) q^{79} +(1.52184 + 2.63590i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.64046 + 3.83387i) q^{82} -0.377697 q^{83} +(0.202041 + 2.63803i) q^{84} -2.43337 q^{85} +(2.73065 + 1.57654i) q^{86} +(4.14663 - 2.39406i) q^{87} +(2.07367 - 1.19724i) q^{88} +(0.328941 - 0.569742i) q^{89} +3.04368 q^{90} +(9.44715 - 6.46366i) q^{91} +(-1.85202 + 4.42380i) q^{92} +(-2.04063 + 3.53448i) q^{93} +(-7.12526 + 4.11377i) q^{94} +(3.28033 + 5.68170i) q^{95} +(0.866025 + 0.500000i) q^{96} -2.07359 q^{97} +(-4.38234 - 5.45849i) q^{98} -2.39447i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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