LMFDB - Embedded newform 627.2.be.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(10,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

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

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

chi := DirichletCharacter("627.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.be (of order $18$, degree $6$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	627.10
Dual form			627.2.be.a.439.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.485290 - 2.75222i) q^{2} +(0.642788 + 0.766044i) q^{3} +(-5.45980 + 1.98721i) q^{4} +(2.33741 + 0.850748i) q^{5} +(1.79638 - 2.14084i) q^{6} +(-2.71663 - 1.56845i) q^{7} +(5.32413 + 9.22167i) q^{8} +(-0.173648 + 0.984808i) q^{9} +(1.20712 - 6.84592i) q^{10} +(2.63517 - 2.01393i) q^{11} +(-5.03178 - 2.90510i) q^{12} +(0.434626 + 0.364694i) q^{13} +(-2.99835 + 8.23789i) q^{14} +(0.850748 + 2.33741i) q^{15} +(13.8945 - 11.6589i) q^{16} +(0.683491 - 0.120518i) q^{17} +2.79467 q^{18} +(4.17325 - 1.25855i) q^{19} -14.4524 q^{20} +(-0.544715 - 3.08923i) q^{21} +(-6.82158 - 6.27521i) q^{22} +(5.78855 - 2.10686i) q^{23} +(-3.64192 + 10.0061i) q^{24} +(0.909501 + 0.763162i) q^{25} +(0.792798 - 1.37317i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(17.9491 + 3.16491i) q^{28} +(1.36062 - 7.71648i) q^{29} +(6.02020 - 3.47577i) q^{30} +(2.78198 + 1.60618i) q^{31} +(-22.5166 - 18.8937i) q^{32} +(3.23661 + 0.724128i) q^{33} +(-0.663383 - 1.82263i) q^{34} +(-5.01552 - 5.97727i) q^{35} +(-1.00893 - 5.72193i) q^{36} -6.27298i q^{37} +(-5.48904 - 10.8749i) q^{38} +0.567364i q^{39} +(4.59937 + 26.0843i) q^{40} +(-6.64185 + 5.57318i) q^{41} +(-8.23789 + 2.99835i) q^{42} +(-1.86173 + 5.11506i) q^{43} +(-10.3854 + 16.2323i) q^{44} +(-1.24371 + 2.15417i) q^{45} +(-8.60766 - 14.9089i) q^{46} +(0.383009 - 2.17215i) q^{47} +(17.8625 + 3.14964i) q^{48} +(1.42004 + 2.45958i) q^{49} +(1.65901 - 2.87350i) q^{50} +(0.531662 + 0.446117i) q^{51} +(-3.09769 - 1.12747i) q^{52} +(0.598916 + 1.64551i) q^{53} +(1.79638 + 2.14084i) q^{54} +(7.87282 - 2.46551i) q^{55} -33.4024i q^{56} +(3.64662 + 2.38792i) q^{57} -21.8977 q^{58} +(12.3618 - 2.17973i) q^{59} +(-9.28984 - 11.0712i) q^{60} +(-0.813281 - 2.23447i) q^{61} +(3.07048 - 8.43608i) q^{62} +(2.01635 - 2.40300i) q^{63} +(-22.9344 + 39.7235i) q^{64} +(0.705637 + 1.22220i) q^{65} +(0.422264 - 9.25926i) q^{66} +(10.9237 + 1.92615i) q^{67} +(-3.49223 + 2.01624i) q^{68} +(5.33476 + 3.08002i) q^{69} +(-14.0168 + 16.7045i) q^{70} +(-4.33184 + 11.9016i) q^{71} +(-10.0061 + 3.64192i) q^{72} +(6.77532 + 8.07451i) q^{73} +(-17.2646 + 3.04421i) q^{74} +1.18727i q^{75} +(-20.2841 + 15.1645i) q^{76} +(-10.3175 + 1.33797i) q^{77} +(1.56151 - 0.275336i) q^{78} +(6.23838 - 5.23462i) q^{79} +(42.3960 - 15.4309i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(18.5618 + 15.5752i) q^{82} +(-7.28396 - 4.20539i) q^{83} +(9.11298 + 15.7841i) q^{84} +(1.70013 + 0.299779i) q^{85} +(14.9812 + 2.64159i) q^{86} +(6.78576 - 3.91776i) q^{87} +(32.6017 + 13.5782i) q^{88} +(-4.48539 + 5.34548i) q^{89} +(6.53230 + 2.37756i) q^{90} +(-0.608713 - 1.67243i) q^{91} +(-27.4176 + 23.0061i) q^{92} +(0.557820 + 3.16356i) q^{93} -6.16410 q^{94} +(10.8253 + 0.608641i) q^{95} -29.3933i q^{96} +(-6.06296 + 1.06906i) q^{97} +(6.08017 - 5.10187i) q^{98} +(1.52574 + 2.94485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) $ 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.485290	−	2.75222i	−0.343152	−	1.94611i	−0.323265	−	0.946309i	$-0.604780\pi$
$2$	−0.485290	−	2.75222i	−0.343152	−	1.94611i	−0.0198869	−	0.999802i	$-0.506331\pi$
$3$	0.642788	+	0.766044i	0.371114	+	0.442276i
$3$	0.642788	+	0.766044i	0.371114	+	0.442276i
$4$	−5.45980	+	1.98721i	−2.72990	+	0.993603i
$5$	2.33741	+	0.850748i	1.04532	+	0.380466i	0.806896	−	0.590694i	$-0.201146\pi$
$5$	2.33741	+	0.850748i	1.04532	+	0.380466i	0.238427	+	0.971160i	$0.423368\pi$
$6$	1.79638	−	2.14084i	0.733370	−	0.873996i
$7$	−2.71663	−	1.56845i	−1.02679	−	0.592817i	−0.110725	−	0.993851i	$-0.535317\pi$
$7$	−2.71663	−	1.56845i	−1.02679	−	0.592817i	−0.916063	+	0.401034i	$0.868651\pi$
$8$	5.32413	+	9.22167i	1.88237	+	3.26035i
$9$	−0.173648	+	0.984808i	−0.0578827	+	0.328269i
$10$	1.20712	−	6.84592i	0.381725	−	2.16487i
$11$	2.63517	−	2.01393i	0.794533	−	0.607221i
$11$	2.63517	−	2.01393i	0.794533	−	0.607221i
$12$	−5.03178	−	2.90510i	−1.45255	−	0.838630i
$13$	0.434626	+	0.364694i	0.120544	+	0.101148i	0.701067	−	0.713096i	$-0.252707\pi$
$13$	0.434626	+	0.364694i	0.120544	+	0.101148i	−0.580523	+	0.814244i	$0.697152\pi$
$14$	−2.99835	+	8.23789i	−0.801342	+	2.20167i
$15$	0.850748	+	2.33741i	0.219662	+	0.603517i
$16$	13.8945	−	11.6589i	3.47363	−	2.91472i
$17$	0.683491	−	0.120518i	0.165771	−	0.0292299i	−0.0901466	−	0.995929i	$-0.528734\pi$
$17$	0.683491	−	0.120518i	0.165771	−	0.0292299i	0.255918	+	0.966699i	$0.417622\pi$
$18$	2.79467			0.658711
$19$	4.17325	−	1.25855i	0.957410	−	0.288731i
$19$	4.17325	−	1.25855i	0.957410	−	0.288731i
$20$	−14.4524			−3.23166
$21$	−0.544715	−	3.08923i	−0.118867	−	0.674126i
$22$	−6.82158	−	6.27521i	−1.45437	−	1.33788i
$23$	5.78855	−	2.10686i	1.20700	−	0.439311i	0.341336	−	0.939942i	$-0.389121\pi$
$23$	5.78855	−	2.10686i	1.20700	−	0.439311i	0.865661	+	0.500631i	$0.166899\pi$
$24$	−3.64192	+	10.0061i	−0.743404	+	2.04249i
$25$	0.909501	+	0.763162i	0.181900	+	0.152632i
$26$	0.792798	−	1.37317i	0.155481	−	0.269300i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	17.9491	+	3.16491i	3.39206	+	0.598111i
$29$	1.36062	−	7.71648i	0.252662	−	1.43291i	−0.549343	−	0.835597i	$-0.685122\pi$
$29$	1.36062	−	7.71648i	0.252662	−	1.43291i	0.802005	−	0.597318i	$-0.203767\pi$
$30$	6.02020	−	3.47577i	1.09913	−	0.634585i
$31$	2.78198	+	1.60618i	0.499659	+	0.288478i	0.728573	−	0.684968i	$-0.240184\pi$
$31$	2.78198	+	1.60618i	0.499659	+	0.288478i	−0.228914	+	0.973447i	$0.573517\pi$
$32$	−22.5166	−	18.8937i	−3.98041	−	3.33996i
$33$	3.23661	+	0.724128i	0.563421	+	0.126055i
$34$	−0.663383	−	1.82263i	−0.113769	−	0.312578i
$35$	−5.01552	−	5.97727i	−0.847778	−	1.01034i
$36$	−1.00893	−	5.72193i	−0.168155	−	0.953655i
$37$		−	6.27298i		−	1.03127i	−0.856808	−	0.515636i	$-0.827556\pi$
$37$		−	6.27298i		−	1.03127i	0.856808	−	0.515636i	$-0.172444\pi$
$38$	−5.48904	−	10.8749i	−0.890440	−	1.76415i
$39$			0.567364i			0.0908509i
$40$	4.59937	+	26.0843i	0.727225	+	4.12430i
$41$	−6.64185	+	5.57318i	−1.03728	+	0.870384i	−0.991700	−	0.128577i	$-0.958959\pi$
$41$	−6.64185	+	5.57318i	−1.03728	+	0.870384i	−0.0455835	+	0.998961i	$0.514515\pi$
$42$	−8.23789	+	2.99835i	−1.27113	+	0.462655i
$43$	−1.86173	+	5.11506i	−0.283911	+	0.780039i	0.712975	+	0.701189i	$0.247347\pi$
$43$	−1.86173	+	5.11506i	−0.283911	+	0.780039i	−0.996886	+	0.0788501i	$0.974875\pi$
$44$	−10.3854	+	16.2323i	−1.56566	+	2.44710i
$45$	−1.24371	+	2.15417i	−0.185402	+	0.321125i
$46$	−8.60766	−	14.9089i	−1.26913	−	2.19820i
$47$	0.383009	−	2.17215i	0.0558676	−	0.316841i	−0.944048	−	0.329807i	$-0.893016\pi$
$47$	0.383009	−	2.17215i	0.0558676	−	0.316841i	0.999916	+	0.0129663i	$0.00412743\pi$
$48$	17.8625	+	3.14964i	2.57823	+	0.454611i
$49$	1.42004	+	2.45958i	0.202863	+	0.351369i
$50$	1.65901	−	2.87350i	0.234620	−	0.406374i
$51$	0.531662	+	0.446117i	0.0744475	+	0.0624689i
$52$	−3.09769	−	1.12747i	−0.429573	−	0.156352i
$53$	0.598916	+	1.64551i	0.0822675	+	0.226028i	0.974006	−	0.226524i	$-0.0727360\pi$
$53$	0.598916	+	1.64551i	0.0822675	+	0.226028i	−0.891738	+	0.452552i	$0.850514\pi$
$54$	1.79638	+	2.14084i	0.244457	+	0.291332i
$55$	7.87282	−	2.46551i	1.06157	−	0.332449i
$56$		−	33.4024i		−	4.46359i
$57$	3.64662	+	2.38792i	0.483007	+	0.316288i
$58$	−21.8977			−2.87531
$59$	12.3618	−	2.17973i	1.60937	−	0.283776i	0.704580	−	0.709625i	$-0.251136\pi$
$59$	12.3618	−	2.17973i	1.60937	−	0.283776i	0.904794	+	0.425849i	$0.140024\pi$
$60$	−9.28984	−	11.0712i	−1.19931	−	1.42929i
$61$	−0.813281	−	2.23447i	−0.104130	−	0.286095i	0.876676	−	0.481081i	$-0.159756\pi$
$61$	−0.813281	−	2.23447i	−0.104130	−	0.286095i	−0.980806	+	0.194987i	$0.937534\pi$
$62$	3.07048	−	8.43608i	0.389952	−	1.07138i
$63$	2.01635	−	2.40300i	0.254037	−	0.302749i
$64$	−22.9344	+	39.7235i	−2.86680	+	4.96543i
$65$	0.705637	+	1.22220i	0.0875235	+	0.151595i
$66$	0.422264	−	9.25926i	0.0519771	−	1.13974i
$67$	10.9237	+	1.92615i	1.33455	+	0.235316i	0.794984	−	0.606630i	$-0.207479\pi$
$67$	10.9237	+	1.92615i	1.33455	+	0.235316i	0.539561	+	0.841946i	$0.318590\pi$
$68$	−3.49223	+	2.01624i	−0.423495	+	0.244505i
$69$	5.33476	+	3.08002i	0.642229	+	0.370791i
$70$	−14.0168	+	16.7045i	−1.67532	+	1.99657i
$71$	−4.33184	+	11.9016i	−0.514095	+	1.41246i	0.362838	+	0.931852i	$0.381808\pi$
$71$	−4.33184	+	11.9016i	−0.514095	+	1.41246i	−0.876933	+	0.480612i	$0.840415\pi$
$72$	−10.0061	+	3.64192i	−1.17923	+	0.429205i
$73$	6.77532	+	8.07451i	0.792991	+	0.945050i	0.999442	−	0.0334068i	$-0.0106357\pi$
$73$	6.77532	+	8.07451i	0.792991	+	0.945050i	−0.206451	+	0.978457i	$0.566191\pi$
$74$	−17.2646	+	3.04421i	−2.00697	+	0.353883i
$75$			1.18727i			0.137094i
$76$	−20.2841	+	15.1645i	−2.32675	+	1.73949i
$77$	−10.3175	+	1.33797i	−1.17579	+	0.152476i
$78$	1.56151	−	0.275336i	0.176806	−	0.0311757i
$79$	6.23838	−	5.23462i	0.701873	−	0.588941i	−0.220433	−	0.975402i	$-0.570747\pi$
$79$	6.23838	−	5.23462i	0.701873	−	0.588941i	0.922306	+	0.386461i	$0.126303\pi$
$80$	42.3960	−	15.4309i	4.74002	−	1.72523i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	18.5618	+	15.5752i	2.04981	+	1.71999i
$83$	−7.28396	−	4.20539i	−0.799518	−	0.461602i	0.0437844	−	0.999041i	$-0.486059\pi$
$83$	−7.28396	−	4.20539i	−0.799518	−	0.461602i	−0.843303	+	0.537439i	$0.819392\pi$
$84$	9.11298	+	15.7841i	0.994308	+	1.72219i
$85$	1.70013	+	0.299779i	0.184405	+	0.0325156i
$86$	14.9812	+	2.64159i	1.61547	+	0.284850i
$87$	6.78576	−	3.91776i	0.727510	−	0.420028i
$88$	32.6017	+	13.5782i	3.47536	+	1.44744i
$89$	−4.48539	+	5.34548i	−0.475450	+	0.566620i	−0.949455	−	0.313903i	$-0.898363\pi$
$89$	−4.48539	+	5.34548i	−0.475450	+	0.566620i	0.474005	+	0.880522i	$0.342808\pi$
$90$	6.53230	+	2.37756i	0.688565	+	0.250617i
$91$	−0.608713	−	1.67243i	−0.0638105	−	0.175318i
$92$	−27.4176	+	23.0061i	−2.85848	+	2.39855i
$93$	0.557820	+	3.16356i	0.0578433	+	0.328045i
$94$	−6.16410			−0.635778
$95$	10.8253	+	0.608641i	1.11065	+	0.0624453i
$96$		−	29.3933i		−	2.99994i
$97$	−6.06296	+	1.06906i	−0.615600	+	0.108547i	−0.472749	−	0.881197i	$-0.656738\pi$
$97$	−6.06296	+	1.06906i	−0.615600	+	0.108547i	−0.142851	+	0.989744i	$0.545627\pi$
$98$	6.08017	−	5.10187i	0.614190	−	0.515367i
$99$	1.52574	+	2.94485i	0.153342	+	0.295968i
$100$	−6.48225	−	2.35935i	−0.648225	−	0.235935i
$101$	−0.428950	+	0.511202i	−0.0426821	+	0.0508665i	−0.786963	−	0.617000i	$-0.788348\pi$
$101$	−0.428950	+	0.511202i	−0.0426821	+	0.0508665i	0.744281	+	0.667866i	$0.232792\pi$
$102$	0.969800	−	1.67974i	0.0960245	−	0.166319i
$103$	−7.39648	+	4.27036i	−0.728797	+	0.420771i	−0.817982	−	0.575244i	$-0.804907\pi$
$103$	−7.39648	+	4.27036i	−0.728797	+	0.420771i	0.0891852	+	0.996015i	$0.471574\pi$
$104$	−1.04909	+	5.94966i	−0.102871	+	0.583412i
$105$	1.35494	−	7.68423i	0.132228	−	0.749904i
$106$	4.23815	−	2.44690i	0.411645	−	0.237664i
$107$	−0.965599	+	1.67247i	−0.0933480	+	0.161684i	−0.908918	−	0.416975i	$-0.863090\pi$
$107$	−0.965599	+	1.67247i	−0.0933480	+	0.161684i	0.815570	+	0.578659i	$0.196424\pi$
$108$	3.73472	−	4.45087i	0.359374	−	0.428285i
$109$	−8.87919	−	3.23176i	−0.850472	−	0.309546i	−0.120239	−	0.992745i	$-0.538366\pi$
$109$	−8.87919	−	3.23176i	−0.850472	−	0.309546i	−0.730233	+	0.683198i	$0.760588\pi$
$110$	−10.6062	−	20.4712i	−1.01126	−	1.95185i
$111$	4.80538	−	4.03219i	0.456106	−	0.382719i
$112$	−56.0326	+	9.88006i	−5.29458	+	0.933578i
$113$		−	0.234237i		−	0.0220351i	−0.999939	−	0.0110176i	$-0.996493\pi$
$113$		−	0.234237i		−	0.0220351i	0.999939	−	0.0110176i	$-0.00350707\pi$
$114$	4.80240	−	11.1951i	0.449786	−	1.04852i
$115$	15.3226			1.42884
$116$	7.90550	+	44.8343i	0.734007	+	4.16276i
$117$	−0.434626	+	0.364694i	−0.0401812	+	0.0337160i
$118$	−11.9982	−	32.9647i	−1.10452	−	3.03464i
$119$	−2.04582	−	0.744616i	−0.187540	−	0.0682588i
$120$	−17.0253	+	20.2900i	−1.55419	+	1.85222i
$121$	2.88821	−	10.6141i	0.262564	−	0.964914i
$122$	−5.75507	+	3.32269i	−0.521040	+	0.300822i
$123$	−8.53860	−	1.50559i	−0.769900	−	0.135754i
$124$	−18.3809	−	3.24105i	−1.65065	−	0.291055i
$125$	−4.74194	−	8.21327i	−0.424132	−	0.734618i
$126$	−7.59208	−	4.38329i	−0.676357	−	0.390495i
$127$	9.55153	+	8.01469i	0.847561	+	0.711188i	0.959251	−	0.282555i	$-0.0911819\pi$
$127$	9.55153	+	8.01469i	0.847561	+	0.711188i	−0.111690	+	0.993743i	$0.535626\pi$
$128$	65.2160	+	23.7367i	5.76434	+	2.09805i
$129$	−5.11506	+	1.86173i	−0.450356	+	0.163916i
$130$	3.02132	−	2.53519i	0.264987	−	0.222350i
$131$	−12.7639	+	2.25062i	−1.11519	+	0.196637i	−0.700726	−	0.713430i	$-0.747141\pi$
$131$	−12.7639	+	2.25062i	−1.11519	+	0.196637i	−0.414460	+	0.910068i	$0.636029\pi$
$132$	−19.1102	+	2.47821i	−1.66333	+	0.215700i
$133$	−13.3111	−	3.12651i	−1.15422	−	0.271103i
$134$		−	30.9992i		−	2.67792i
$135$	−2.44963	+	0.431936i	−0.210831	+	0.0371752i
$136$	4.75037	+	5.66127i	0.407341	+	0.485450i
$137$	−13.8657	+	5.04670i	−1.18463	+	0.431168i	−0.857833	−	0.513928i	$-0.828190\pi$
$137$	−13.8657	+	5.04670i	−1.18463	+	0.431168i	−0.326792	+	0.945096i	$0.605968\pi$
$138$	5.88799	−	16.1771i	0.501219	−	1.37709i
$139$	1.91093	−	2.27736i	0.162083	−	0.193163i	−0.678890	−	0.734240i	$-0.737539\pi$
$139$	1.91093	−	2.27736i	0.162083	−	0.193163i	0.840973	+	0.541077i	$0.181983\pi$
$140$	39.2618	+	22.6678i	3.31823	+	1.91578i
$141$	1.91016	−	1.10283i	0.160864	−	0.0928750i
$142$	34.8581	+	6.14642i	2.92522	+	0.515796i
$143$	1.87978	+	0.0857264i	0.157195	+	0.00716880i
$144$	9.06901	+	15.7080i	0.755751	+	1.30900i
$145$	9.74513	−	16.8791i	0.809289	−	1.40173i
$146$	18.9348	−	22.5656i	1.56706	−	1.86754i
$147$	−0.971365	+	2.66880i	−0.0801168	+	0.220119i
$148$	12.4657	+	34.2492i	1.02467	+	2.81527i
$149$	1.97309	+	2.35144i	0.161642	+	0.192637i	0.840786	−	0.541368i	$-0.182093\pi$
$149$	1.97309	+	2.35144i	0.161642	+	0.192637i	−0.679144	+	0.734005i	$0.737649\pi$
$150$	3.26762	−	0.576170i	0.266800	−	0.0470441i
$151$	18.5671			1.51097			0.755483	−	0.655168i	$-0.227402\pi$
$151$	18.5671			1.51097			0.755483	+	0.655168i	$0.227402\pi$
$152$	33.8249	+	31.7837i	2.74356	+	2.57800i
$153$			0.694035i			0.0561094i
$154$	8.68936	+	27.7467i	0.700208	+	2.23589i
$155$	5.13619	+	6.12107i	0.412549	+	0.491656i
$156$	−1.12747	−	3.09769i	−0.0902697	−	0.248014i
$157$	11.5375	+	4.19931i	0.920794	+	0.335142i	0.758554	−	0.651610i	$-0.225906\pi$
$157$	11.5375	+	4.19931i	0.920794	+	0.335142i	0.162240	+	0.986751i	$0.448128\pi$
$158$	−17.4342	−	14.6291i	−1.38699	−	1.16383i
$159$	−0.875557	+	1.51651i	−0.0694362	+	0.120267i
$160$	−36.5568	−	63.3183i	−2.89007	−	5.00575i
$161$	−19.0298	−	3.35547i	−1.49976	−	0.264448i
$162$	−0.485290	+	2.75222i	−0.0381280	+	0.216235i
$163$	−5.63725	−	9.76400i	−0.441543	−	0.764775i	0.556261	−	0.831008i	$-0.312235\pi$
$163$	−5.63725	−	9.76400i	−0.441543	−	0.764775i	−0.997804	+	0.0662324i	$0.978902\pi$
$164$	25.1882	−	43.6272i	1.96686	−	3.40671i
$165$	6.94924	+	4.44613i	0.540997	+	0.346131i
$166$	−8.03932	+	22.0879i	−0.623973	+	1.71435i
$167$	−10.4870	+	3.81696i	−0.811509	+	0.295365i	−0.714247	−	0.699894i	$-0.753231\pi$
$167$	−10.4870	+	3.81696i	−0.811509	+	0.295365i	−0.0972617	+	0.995259i	$0.531008\pi$
$168$	25.5878	−	21.4707i	1.97414	−	1.65650i
$169$	−2.20153	−	12.4855i	−0.169348	−	0.960422i
$170$		−	4.82461i		−	0.370030i
$171$	0.514751	+	4.32840i	0.0393640	+	0.331001i
$172$		−	31.6268i		−	2.41152i
$173$	0.763749	+	4.33144i	0.0580668	+	0.329313i	0.999979	−	0.00654734i	$-0.00208410\pi$
$173$	0.763749	+	4.33144i	0.0580668	+	0.329313i	−0.941912	+	0.335860i	$0.890973\pi$
$174$	−14.0756	−	16.7746i	−1.06707	−	1.27168i
$175$	−1.27380	−	3.49973i	−0.0962900	−	0.264555i
$176$	13.1343	−	58.7057i	0.990032	−	4.42511i
$177$	9.61580	+	8.06862i	0.722768	+	0.606474i
$178$	16.8886	+	9.75065i	1.26586	+	0.730842i
$179$	8.23220	−	4.75286i	0.615303	−	0.355245i	−0.159735	−	0.987160i	$-0.551064\pi$
$179$	8.23220	−	4.75286i	0.615303	−	0.355245i	0.775038	+	0.631914i	$0.217731\pi$
$180$	2.50964	−	14.2329i	0.187057	−	1.06085i
$181$	−17.5318	−	3.09132i	−1.30313	−	0.229776i	−0.521354	−	0.853341i	$-0.674573\pi$
$181$	−17.5318	−	3.09132i	−1.30313	−	0.229776i	−0.781772	+	0.623565i	$0.785684\pi$
$182$	−4.30747	+	2.48692i	−0.319291	+	0.184343i
$183$	1.18894	−	2.05930i	0.0878888	−	0.152228i
$184$	50.2478	+	42.1629i	3.70432	+	3.10829i
$185$	5.33673	−	14.6625i	0.392364	−	1.07801i
$186$	8.43608	−	3.07048i	0.618564	−	0.225139i
$187$	1.55840	−	1.69408i	0.113961	−	0.123884i
$188$	2.22536	+	12.6206i	0.162301	+	0.920454i
$189$	3.13689			0.228175
$190$	−3.57831	−	30.0890i	−0.259598	−	2.18289i
$191$	24.3540			1.76220			0.881098	−	0.472934i	$-0.156805\pi$
$191$	24.3540			1.76220			0.881098	+	0.472934i	$0.156805\pi$
$192$	−45.1719	+	7.96502i	−3.26000	+	0.574826i
$193$	1.51244	−	1.26909i	0.108868	−	0.0913511i	−0.586729	−	0.809784i	$-0.699585\pi$
$193$	1.51244	−	1.26909i	0.108868	−	0.0913511i	0.695597	+	0.718432i	$0.255140\pi$
$194$	5.88459	+	16.1678i	0.422489	+	1.16078i
$195$	−0.482684	+	1.32616i	−0.0345657	+	0.0949685i
$196$	−12.6408	−	10.6069i	−0.902917	−	0.757637i
$197$	−7.27609	−	4.20085i	−0.518400	−	0.299298i	0.217880	−	0.975976i	$-0.430086\pi$
$197$	−7.27609	−	4.20085i	−0.518400	−	0.299298i	−0.736280	+	0.676677i	$0.763419\pi$
$198$	7.36443	−	5.62826i	0.523367	−	0.399983i
$199$	1.10838	−	6.28591i	0.0785707	−	0.445596i	−0.919989	−	0.391944i	$-0.871803\pi$
$199$	1.10838	−	6.28591i	0.0785707	−	0.445596i	0.998560	−	0.0536523i	$-0.0170863\pi$
$200$	−2.19532	+	12.4503i	−0.155233	+	0.880369i
$201$	5.54612	+	9.60616i	0.391193	+	0.677567i
$202$	1.61510	+	0.932481i	0.113638	+	0.0656091i
$203$	−15.7992	+	18.8287i	−1.10889	+	1.32152i
$204$	−3.78929	−	1.37919i	−0.265304	−	0.0965626i
$205$	−20.2661	+	7.37626i	−1.41545	+	0.515181i
$206$	15.3424	+	18.2843i	1.06895	+	1.27393i
$207$	1.06968	+	6.06646i	0.0743480	+	0.421648i
$208$	10.2909			0.713543
$209$	8.46260	−	11.7211i	0.585370	−	0.810766i
$210$	−21.8062			−1.50477
$211$	1.68399	+	9.55038i	0.115931	+	0.657475i	0.986285	+	0.165050i	$0.0527785\pi$
$211$	1.68399	+	9.55038i	0.115931	+	0.657475i	−0.870355	+	0.492425i	$0.836110\pi$
$212$	−6.53993	−	7.79399i	−0.449164	−	0.535293i
$213$	−11.9016	+	4.33184i	−0.815487	+	0.296813i
$214$	5.07159	+	1.84591i	0.346687	+	0.126184i
$215$	−8.70326	+	10.3721i	−0.593557	+	0.707374i
$216$	−9.22167	−	5.32413i	−0.627455	−	0.362261i
$217$	−5.03841	−	8.72678i	−0.342029	−	0.592412i
$218$	−4.58552	+	26.0058i	−0.310571	+	1.76133i
$219$	−1.83034	+	10.3804i	−0.123683	+	0.701442i
$220$	−38.0845	+	29.1061i	−2.56766	+	1.96233i
$221$	0.341015	+	0.196885i	0.0229392	+	0.0132439i
$222$	−13.4295	−	11.2687i	−0.901327	−	0.756303i
$223$	−6.51568	+	17.9017i	−0.436322	+	1.19878i	0.505545	+	0.862800i	$0.331291\pi$
$223$	−6.51568	+	17.9017i	−0.436322	+	1.19878i	−0.941867	+	0.335985i	$0.890931\pi$
$224$	31.5355	+	86.6431i	2.10706	+	5.78909i
$225$	−0.909501	+	0.763162i	−0.0606334	+	0.0508775i
$226$	−0.644670	+	0.113673i	−0.0428828	+	0.00756139i
$227$	−25.1542			−1.66954			−0.834772	−	0.550596i	$-0.814401\pi$
$227$	−25.1542			−1.66954			−0.834772	+	0.550596i	$0.814401\pi$
$228$	−24.6551	−	5.79098i	−1.63282	−	0.383517i
$229$	6.86167			0.453432			0.226716	−	0.973961i	$-0.427201\pi$
$229$	6.86167			0.453432			0.226716	+	0.973961i	$0.427201\pi$
$230$	−7.43592	−	42.1712i	−0.490310	−	2.78069i
$231$	−7.65690	−	7.04363i	−0.503787	−	0.463437i
$232$	78.4030	−	28.5364i	5.14741	−	1.87350i
$233$	−10.0739	+	27.6777i	−0.659960	+	1.81323i	−0.0828460	+	0.996562i	$0.526401\pi$
$233$	−10.0739	+	27.6777i	−0.659960	+	1.81323i	−0.577114	+	0.816663i	$0.695821\pi$
$234$	1.21464	+	1.01920i	0.0794033	+	0.0666273i
$235$	2.74320	−	4.75137i	0.178947	−	0.309945i
$236$	−63.1616	+	36.4664i	−4.11147	+	2.37376i
$237$	8.01991	+	1.41413i	0.520949	+	0.0918573i
$238$	−1.05653	+	5.99188i	−0.0684847	+	0.388396i
$239$	−9.15367	+	5.28487i	−0.592102	+	0.341850i	−0.765928	−	0.642926i	$-0.777720\pi$
$239$	−9.15367	+	5.28487i	−0.592102	+	0.341850i	0.173826	+	0.984776i	$0.444387\pi$
$240$	39.0724	+	22.5585i	2.52211	+	1.45614i
$241$	−4.50311	−	3.77856i	−0.290071	−	0.243398i	0.486127	−	0.873888i	$-0.338409\pi$
$241$	−4.50311	−	3.77856i	−0.290071	−	0.243398i	−0.776197	+	0.630490i	$0.782854\pi$
$242$	−30.6138	−	2.79808i	−1.96793	−	0.179867i
$243$	−0.342020	−	0.939693i	−0.0219406	−	0.0602813i
$244$	8.88071	+	10.5836i	0.568529	+	0.677546i
$245$	1.22673	+	6.95716i	0.0783732	+	0.444476i
$246$			24.2307i			1.54489i
$247$	2.27279	+	0.974964i	0.144614	+	0.0620355i
$248$			34.2060i			2.17209i
$249$	−1.46052	−	8.28301i	−0.0925566	−	0.524914i
$250$	−20.3035	+	17.0367i	−1.28411	+	1.07749i
$251$	−17.3473	+	6.31391i	−1.09495	+	0.398531i	−0.825454	−	0.564470i	$-0.809081\pi$
$251$	−17.3473	+	6.31391i	−1.09495	+	0.398531i	−0.269500	+	0.963000i	$0.586858\pi$
$252$	−6.23365	+	17.1268i	−0.392683	+	1.07889i
$253$	11.0107	−	17.2096i	0.692239	−	1.08196i
$254$	17.4229	−	30.1773i	1.09321	−	1.89349i
$255$	0.863179	+	1.49507i	0.0540544	+	0.0936249i
$256$	17.7498	−	100.664i	1.10936	−	6.29150i
$257$	−4.90209	−	0.864371i	−0.305784	−	0.0539180i	0.0186507	−	0.999826i	$-0.494063\pi$
$257$	−4.90209	−	0.864371i	−0.305784	−	0.0539180i	−0.324435	+	0.945908i	$0.605174\pi$
$258$	7.60617	+	13.1743i	0.473539	+	0.820194i
$259$	−9.83882	+	17.0413i	−0.611355	+	1.05890i
$260$	−6.28140	−	5.27072i	−0.389556	−	0.326876i
$261$	7.36298	+	2.67991i	0.455757	+	0.165882i
$262$	12.3884	+	34.0368i	0.765356	+	2.10280i
$263$	−3.60343	−	4.29440i	−0.222197	−	0.264804i	0.643417	−	0.765516i	$-0.277516\pi$
$263$	−3.60343	−	4.29440i	−0.222197	−	0.264804i	−0.865614	+	0.500712i	$0.833072\pi$
$264$	10.5545	+	33.7023i	0.649582	+	2.07423i
$265$			4.35576i			0.267572i
$266$	−2.14507	+	38.1524i	−0.131523	+	2.33927i
$267$	−6.97803			−0.427048
$268$	−63.4690	+	11.1913i	−3.87699	+	0.683618i
$269$	12.8693	+	15.3370i	0.784655	+	0.935115i	0.999134	−	0.0416137i	$-0.0132499\pi$
$269$	12.8693	+	15.3370i	0.784655	+	0.935115i	−0.214479	+	0.976729i	$0.568805\pi$
$270$	2.37756	+	6.53230i	0.144694	+	0.397543i
$271$	1.95429	−	5.36936i	0.118715	−	0.326165i	−0.866076	−	0.499913i	$-0.833365\pi$
$271$	1.95429	−	5.36936i	0.118715	−	0.326165i	0.984790	+	0.173747i	$0.0555876\pi$
$272$	8.09168	−	9.64329i	0.490630	−	0.584710i
$273$	0.889879	−	1.54132i	0.0538579	−	0.0932847i
$274$	20.6185	+	35.7123i	1.24561	+	2.15746i
$275$	3.93364	+	0.179392i	0.237207	+	0.0108177i
$276$	−35.2474	−	6.21506i	−2.12164	−	0.374103i
$277$	−5.96025	+	3.44115i	−0.358117	+	0.206759i	−0.668254	−	0.743933i	$-0.732958\pi$
$277$	−5.96025	+	3.44115i	−0.358117	+	0.206759i	0.310138	+	0.950692i	$0.399625\pi$
$278$	−7.19515	−	4.15412i	−0.431536	−	0.249148i
$279$	−2.06486	+	2.46081i	−0.123620	+	0.147325i
$280$	28.4171	−	78.0753i	1.69825	−	4.66589i
$281$	21.8835	−	7.96493i	1.30546	−	0.475148i	0.406688	−	0.913567i	$-0.366684\pi$
$281$	21.8835	−	7.96493i	1.30546	−	0.475148i	0.898771	+	0.438419i	$0.144461\pi$
$282$	−3.96221	−	4.72197i	−0.235946	−	0.281189i
$283$	−14.5635	+	2.56794i	−0.865713	+	0.152648i	−0.588832	−	0.808256i	$-0.700412\pi$
$283$	−14.5635	+	2.56794i	−0.865713	+	0.152648i	−0.276881	+	0.960904i	$0.589301\pi$
$284$		−	73.5888i		−	4.36669i
$285$	6.49214	+	8.68391i	0.384561	+	0.514390i
$286$	−0.676300	−	5.21516i	−0.0399905	−	0.308379i
$287$	26.7847	−	4.72286i	1.58105	−	0.278781i
$288$	22.5166	−	18.8937i	1.32680	−	1.11332i
$289$	−15.5221	+	5.64960i	−0.913067	+	0.332329i
$290$	−51.1840	−	18.6295i	−3.00563	−	1.09396i
$291$	−4.71614	−	3.95731i	−0.276465	−	0.231982i
$292$	−53.0376	−	30.6213i	−3.10379	−	1.79198i
$293$	2.29612	+	3.97700i	0.134141	+	0.232339i	0.925269	−	0.379312i	$-0.123839\pi$
$293$	2.29612	+	3.97700i	0.134141	+	0.232339i	−0.791128	+	0.611650i	$0.790506\pi$
$294$	7.81652	+	1.37826i	0.455869	+	0.0803819i
$295$	30.7491	+	5.42190i	1.79028	+	0.315675i
$296$	57.8473	−	33.3982i	3.36231	−	1.94123i
$297$	−1.27516	+	3.06169i	−0.0739922	+	0.177658i
$298$	5.51415	−	6.57150i	0.319426	−	0.380677i
$299$	3.28421	+	1.19536i	0.189931	+	0.0691292i
$300$	−2.35935	−	6.48225i	−0.136217	−	0.374253i
$301$	13.0803	−	10.9757i	0.753937	−	0.632628i
$302$	−9.01041	−	51.1006i	−0.518491	−	2.94051i
$303$	−0.667327			−0.0383369
$304$	43.3121	−	66.1425i	2.48412	−	3.79353i
$305$		−	5.91478i		−	0.338679i
$306$	1.91013	−	0.336808i	0.109195	−	0.0192540i
$307$	−19.5602	+	16.4130i	−1.11636	+	0.936737i	−0.998415	−	0.0562833i	$-0.982075\pi$
$307$	−19.5602	+	16.4130i	−1.11636	+	0.936737i	−0.117945	+	0.993020i	$0.537631\pi$
$308$	53.6727	−	27.8080i	3.05828	−	1.58451i
$309$	−8.02565	−	2.92110i	−0.456563	−	0.166175i
$310$	14.3540	−	17.1064i	0.815251	−	0.971578i
$311$	−0.642577	+	1.11298i	−0.0364372	+	0.0631111i	−0.883669	−	0.468112i	$-0.844934\pi$
$311$	−0.642577	+	1.11298i	−0.0364372	+	0.0631111i	0.847232	+	0.531224i	$0.178268\pi$
$312$	−5.23204	+	3.02072i	−0.296206	+	0.171015i
$313$	0.434578	−	2.46461i	0.0245638	−	0.139308i	−0.970060	−	0.242867i	$-0.921912\pi$
$313$	0.434578	−	2.46461i	0.0245638	−	0.139308i	0.994623	+	0.103559i	$0.0330231\pi$
$314$	5.95838	−	33.7916i	0.336251	−	1.90697i
$315$	6.75740	−	3.90139i	0.380736	−	0.219818i
$316$	−23.6581	+	40.9769i	−1.33087	+	2.30513i
$317$	−21.0914	+	25.1358i	−1.18461	+	1.41177i	−0.294728	+	0.955581i	$0.595229\pi$
$317$	−21.0914	+	25.1358i	−1.18461	+	1.41177i	−0.889885	+	0.456186i	$0.849215\pi$
$318$	4.59866	+	1.67378i	0.257880	+	0.0938607i
$319$	−11.9550	−	23.0744i	−0.669349	−	1.29192i
$320$	−87.4017	+	73.3388i	−4.88591	+	4.09976i
$321$	−1.90186	+	0.335349i	−0.106151	+	0.0187174i
$322$			54.0026i			3.00945i
$323$	2.70070	−	1.36316i	0.150271	−	0.0758482i
$324$	5.81020			0.322789
$325$	0.116972	+	0.663380i	0.00648843	+	0.0367977i
$326$	−24.1369	+	20.2533i	−1.33682	+	1.12173i
$327$	−3.23176	−	8.87919i	−0.178717	−	0.491020i
$328$	−86.7561	−	31.5766i	−4.79030	−	1.74353i
$329$	−4.44739	+	5.30019i	−0.245193	+	0.292209i
$330$	8.86431	−	21.2835i	0.487964	−	1.17162i
$331$	4.21994	−	2.43638i	0.231949	−	0.133916i	−0.379522	−	0.925183i	$-0.623912\pi$
$331$	4.21994	−	2.43638i	0.231949	−	0.133916i	0.611471	+	0.791267i	$0.290578\pi$
$332$	48.1260	+	8.48590i	2.64125	+	0.465724i
$333$	6.17768	+	1.08929i	0.338535	+	0.0596928i
$334$	15.5943	+	27.0102i	0.853284	+	1.47793i
$335$	23.8946	+	13.7955i	1.30550	+	0.753731i
$336$	−43.5856	−	36.5727i	−2.37779	−	1.99520i
$337$	29.4012	+	10.7011i	1.60158	+	0.582929i	0.979751	−	0.200222i	$-0.0641662\pi$
$337$	29.4012	+	10.7011i	1.60158	+	0.582929i	0.621833	+	0.783150i	$0.286388\pi$
$338$	−33.2944	+	12.1182i	−1.81098	+	0.659141i
$339$	0.179436	−	0.150564i	0.00974561	−	0.00817753i
$340$	−9.87810	+	1.74178i	−0.535715	+	0.0944610i
$341$	10.5657	−	1.37016i	0.572166	−	0.0741983i
$342$	11.6629	−	3.51723i	0.630657	−	0.190190i
$343$			13.0492i			0.704591i
$344$	−57.0815	+	10.0650i	−3.07763	+	0.542669i
$345$	9.84920	+	11.7378i	0.530263	+	0.631943i
$346$	11.5504	−	4.20401i	0.620954	−	0.226009i
$347$	−1.86140	+	5.11415i	−0.0999251	+	0.274542i	−0.979575	−	0.201080i	$-0.935555\pi$
$347$	−1.86140	+	5.11415i	−0.0999251	+	0.274542i	0.879650	+	0.475622i	$0.157777\pi$
$348$	−29.2635	+	34.8749i	−1.56869	+	1.86949i
$349$	4.70383	+	2.71576i	0.251790	+	0.145371i	0.620584	−	0.784140i	$-0.286896\pi$
$349$	4.70383	+	2.71576i	0.251790	+	0.145371i	−0.368793	+	0.929511i	$0.620229\pi$
$350$	−9.01385	+	5.20415i	−0.481810	+	0.278173i
$351$	−0.558744	−	0.0985217i	−0.0298236	−	0.00525870i
$352$	−97.3854	−	4.44122i	−5.19066	−	0.236718i
$353$	−16.5952	−	28.7437i	−0.883273	−	1.52987i	−0.847680	−	0.530508i	$-0.822001\pi$
$353$	−16.5952	−	28.7437i	−0.883273	−	1.52987i	−0.0355931	−	0.999366i	$-0.511332\pi$
$354$	17.5401	−	30.3804i	0.932247	−	1.61470i
$355$	−20.2506	+	24.1337i	−1.07479	+	1.28088i
$356$	13.8668	−	38.0986i	0.734937	−	2.01922i
$357$	−0.744616	−	2.04582i	−0.0394093	−	0.108276i
$358$	−17.0759	−	20.3503i	−0.902489	−	1.07555i
$359$	12.7951	−	2.25612i	0.675298	−	0.119073i	0.174526	−	0.984653i	$-0.444161\pi$
$359$	12.7951	−	2.25612i	0.675298	−	0.119073i	0.500772	+	0.865579i	$0.333050\pi$
$360$	−26.4867			−1.39597
$361$	15.8321	−	10.5045i	0.833269	−	0.552868i
$362$			49.7514i			2.61487i
$363$	9.98735	−	4.61009i	0.524200	−	0.241967i
$364$	6.64691	+	7.92147i	0.348393	+	0.415198i
$365$	8.96734	+	24.6376i	0.469372	+	1.28959i
$366$	−6.24462	−	2.27285i	−0.326411	−	0.118804i
$367$	−12.1307	−	10.1789i	−0.633219	−	0.531334i	0.268708	−	0.963222i	$-0.413403\pi$
$367$	−12.1307	−	10.1789i	−0.633219	−	0.531334i	−0.901927	+	0.431888i	$0.857848\pi$
$368$	55.8656	−	96.7620i	2.91219	−	5.04407i
$369$	−4.33516	−	7.50872i	−0.225679	−	0.390888i
$370$	−42.9443	−	7.57224i	−2.23257	−	0.393662i
$371$	0.953859	−	5.40960i	0.0495219	−	0.280853i
$372$	−9.33222	−	16.1639i	−0.483853	−	0.838058i
$373$	−5.91000	+	10.2364i	−0.306008	+	0.530022i	−0.977485	−	0.211004i	$-0.932327\pi$
$373$	−5.91000	+	10.2364i	−0.306008	+	0.530022i	0.671477	+	0.741025i	$0.265660\pi$
$374$	−5.41876	−	3.46693i	−0.280198	−	0.179271i
$375$	3.24368	−	8.91192i	0.167503	−	0.460210i
$376$	22.0700	−	8.03284i	1.13818	−	0.414262i
$377$	3.40552	−	2.85757i	0.175393	−	0.147172i
$378$	−1.52230	−	8.63340i	−0.0782987	−	0.444054i
$379$			6.14986i			0.315897i	0.987447	+	0.157948i	$0.0504880\pi$
$379$			6.14986i			0.315897i	−0.987447	+	0.157948i	$0.949512\pi$
$380$	−60.3136	+	18.1891i	−3.09402	+	0.933080i
$381$			12.4686i			0.638788i
$382$	−11.8188	−	67.0275i	−0.604701	−	3.42943i
$383$	14.6421	+	17.4498i	0.748175	+	0.891641i	0.997039	−	0.0768978i	$-0.0245015\pi$
$383$	14.6421	+	17.4498i	0.748175	+	0.891641i	−0.248864	+	0.968539i	$0.580057\pi$
$384$	23.7367	+	65.2160i	1.21131	+	3.32804i
$385$	−25.2545	−	5.65021i	−1.28709	−	0.287961i
$386$	−4.22678	−	3.54669i	−0.215138	−	0.180522i
$387$	−4.71406	−	2.72167i	−0.239629	−	0.138350i
$388$	30.9781	−	17.8852i	1.57267	−	0.907984i
$389$	3.26542	−	18.5191i	0.165564	−	0.938958i	−0.782918	−	0.622125i	$-0.786270\pi$
$389$	3.26542	−	18.5191i	0.165564	−	0.938958i	0.948481	−	0.316833i	$-0.102619\pi$
$390$	3.88413	+	0.684877i	0.196681	+	0.0346801i
$391$	3.70251	−	2.13764i	0.187244	−	0.108105i
$392$	−15.1210	+	26.1903i	−0.763724	+	1.32281i
$393$	−9.92854	−	8.33103i	−0.500829	−	0.420245i
$394$	−8.03064	+	22.0640i	−0.404578	+	1.11157i
$395$	19.0350	−	6.92818i	0.957755	−	0.348594i
$396$	−14.1822	−	13.0463i	−0.712685	−	0.655603i
$397$	−2.78781	−	15.8105i	−0.139916	−	0.793504i	−0.971309	−	0.237820i	$-0.923567\pi$
$397$	−2.78781	−	15.8105i	−0.139916	−	0.793504i	0.831393	−	0.555685i	$-0.187544\pi$
$398$	−17.8381			−0.894142
$399$	−6.16119	−	12.2066i	−0.308445	−	0.611095i
$400$	21.5347			1.07674
$401$	2.89594	−	0.510632i	0.144616	−	0.0254998i	−0.100871	−	0.994899i	$-0.532163\pi$
$401$	2.89594	−	0.510632i	0.144616	−	0.0254998i	0.245488	+	0.969400i	$0.421052\pi$
$402$	23.7468	−	19.9259i	1.18438	−	0.993814i
$403$	0.623358	+	1.71266i	0.0310517	+	0.0853137i
$404$	1.32612	−	3.64347i	0.0659767	−	0.181270i
$405$	−1.90548	−	1.59888i	−0.0946839	−	0.0794492i
$406$	59.4879	+	34.3454i	2.95234	+	1.70453i
$407$	−12.6333	−	16.5303i	−0.626210	−	0.819379i
$408$	−1.28331	+	7.27799i	−0.0635331	+	0.360314i
$409$	0.0195445	−	0.110843i	0.000966415	−	0.00548081i	−0.984321	−	0.176388i	$-0.943559\pi$
$409$	0.0195445	−	0.110843i	0.000966415	−	0.00548081i	0.985287	+	0.170907i	$0.0546698\pi$
$410$	30.1360	+	52.1971i	1.48831	+	2.57783i
$411$	−12.7787	−	7.37778i	−0.630326	−	0.363919i
$412$	31.8972	−	38.0136i	1.57146	−	1.87280i
$413$	−37.0013	−	13.4674i	−1.82071	−	0.662686i
$414$	16.1771	−	5.88799i	0.795062	−	0.289379i
$415$	−13.4479	−	16.0266i	−0.660130	−	0.786713i
$416$	−2.89588	−	16.4234i	−0.141982	−	0.805221i
$417$	2.97288			0.145583
$418$	−36.3658	−	17.6028i	−1.77871	−	0.860979i
$419$	−15.1259			−0.738948			−0.369474	−	0.929241i	$-0.620462\pi$
$419$	−15.1259			−0.738948			−0.369474	+	0.929241i	$0.620462\pi$
$420$	7.87245	+	44.6469i	0.384136	+	2.17855i
$421$	−14.0766	−	16.7758i	−0.686051	−	0.817604i	0.304821	−	0.952410i	$-0.401403\pi$
$421$	−14.0766	−	16.7758i	−0.686051	−	0.817604i	−0.990872	+	0.134806i	$0.956959\pi$
$422$	25.4675	−	9.26940i	1.23974	−	0.451228i
$423$	2.07264	+	0.754380i	0.100775	+	0.0366792i
$424$	−11.9856	+	14.2839i	−0.582074	+	0.693688i
$425$	0.713610	+	0.412003i	0.0346152	+	0.0199851i
$426$	17.6979	+	30.6537i	0.857466	+	1.48518i
$427$	−1.29526	+	7.34581i	−0.0626822	+	0.355489i
$428$	1.94845	−	11.0502i	0.0941817	−	0.534131i
$429$	1.14263	+	1.49510i	0.0551666	+	0.0721840i
$430$	32.7700	+	18.9197i	1.58031	+	0.912391i
$431$	10.4256	+	8.74808i	0.502181	+	0.421380i	0.858368	−	0.513035i	$-0.171479\pi$
$431$	10.4256	+	8.74808i	0.502181	+	0.421380i	−0.356187	+	0.934415i	$0.615923\pi$
$432$	−6.20357	+	17.0442i	−0.298469	+	0.820038i
$433$	−3.25747	−	8.94983i	−0.156544	−	0.430101i	0.836482	−	0.547994i	$-0.184608\pi$
$433$	−3.25747	−	8.94983i	−0.156544	−	0.430101i	−0.993026	+	0.117893i	$0.962386\pi$
$434$	−21.5729	+	18.1018i	−1.03553	+	0.868915i
$435$	19.1942	−	3.38445i	0.920289	−	0.162272i
$436$	54.9008			2.62927
$437$	21.5055	−	16.0776i	1.02875	−	0.769098i
$438$	29.4573			1.40753
$439$	0.320047	+	1.81508i	0.0152750	+	0.0866288i	0.991492	−	0.130166i	$-0.0415509\pi$
$439$	0.320047	+	1.81508i	0.0152750	+	0.0866288i	−0.976217	+	0.216795i	$0.930440\pi$
$440$	64.6520	+	59.4738i	3.08216	+	2.83530i
$441$	−2.66880	+	0.971365i	−0.127086	+	0.0462555i
$442$	0.376379	−	1.03409i	0.0179025	−	0.0491868i
$443$	16.1159	+	13.5229i	0.765690	+	0.642490i	0.939601	−	0.342271i	$-0.111196\pi$
$443$	16.1159	+	13.5229i	0.765690	+	0.642490i	−0.173911	+	0.984761i	$0.555641\pi$
$444$	−18.2236	+	31.5643i	−0.864855	+	1.49797i
$445$	−15.0319	+	8.67865i	−0.712578	+	0.411407i
$446$	52.4313	+	9.24505i	2.48269	+	0.437766i
$447$	−0.533028	+	3.02295i	−0.0252114	+	0.142981i
$448$	124.608	−	71.9426i	5.88718	−	3.39897i
$449$	−10.6173	−	6.12989i	−0.501061	−	0.289287i	0.228091	−	0.973640i	$-0.426752\pi$
$449$	−10.6173	−	6.12989i	−0.501061	−	0.289287i	−0.729151	+	0.684352i	$0.760085\pi$
$450$	2.54176	+	2.13279i	0.119820	+	0.100541i
$451$	−6.27843	+	28.0624i	−0.295640	+	1.32141i
$452$	0.465476	+	1.27889i	0.0218942	+	0.0601537i
$453$	11.9347	+	14.2232i	0.560740	+	0.668264i
$454$	12.2071	+	69.2299i	0.572907	+	3.24912i
$455$		−	4.42701i		−	0.207541i
$456$	−2.60550	+	46.3415i	−0.122014	+	2.17014i
$457$			17.6621i			0.826197i	0.910686	+	0.413099i	$0.135553\pi$
$457$			17.6621i			0.826197i	−0.910686	+	0.413099i	$0.864447\pi$
$458$	−3.32990	−	18.8848i	−0.155596	−	0.882428i
$459$	−0.531662	+	0.446117i	−0.0248158	+	0.0208230i
$460$	−83.6586	+	30.4492i	−3.90060	+	1.41970i
$461$	−1.36803	+	3.75862i	−0.0637153	+	0.175056i	−0.967465	−	0.253005i	$-0.918581\pi$
$461$	−1.36803	+	3.75862i	−0.0637153	+	0.175056i	0.903750	+	0.428061i	$0.140803\pi$
$462$	−15.6698	+	24.4917i	−0.729024	+	1.13945i
$463$	4.64637	−	8.04775i	0.215935	−	0.374011i	−0.737626	−	0.675209i	$-0.764053\pi$
$463$	4.64637	−	8.04775i	0.215935	−	0.374011i	0.953561	+	0.301199i	$0.0973867\pi$
$464$	−71.0605	−	123.080i	−3.29890	−	5.71386i
$465$	−1.38753	+	7.86910i	−0.0643454	+	0.364921i
$466$	81.0637	+	14.2937i	3.75520	+	0.662144i
$467$	−10.6985	−	18.5303i	−0.495066	−	0.857479i	0.504918	−	0.863167i	$-0.331523\pi$
$467$	−10.6985	−	18.5303i	−0.495066	−	0.857479i	−0.999984	+	0.00568801i	$0.998189\pi$
$468$	1.64825	−	2.85485i	0.0761903	−	0.131966i
$469$	−26.6546	−	22.3659i	−1.23080	−	1.03276i
$470$	−14.4080	−	5.24410i	−0.664593	−	0.241892i
$471$	4.19931	+	11.5375i	0.193494	+	0.531621i
$472$	85.9168	+	102.392i	3.95464	+	4.71296i
$473$	5.39538	+	17.2284i	0.248080	+	0.792163i
$474$		−	22.7588i		−	1.04535i
$475$	4.75606	+	2.04022i	0.218223	+	0.0936116i
$476$	12.6495			0.579787
$477$	−1.72451	+	0.304078i	−0.0789599	+	0.0139228i
$478$	18.9873	+	22.6282i	0.868459	+	1.03499i
$479$	−0.293354	−	0.805984i	−0.0134037	−	0.0368263i	0.932810	−	0.360368i	$-0.117349\pi$
$479$	−0.293354	−	0.805984i	−0.0134037	−	0.0368263i	−0.946214	+	0.323541i	$0.895127\pi$
$480$	25.0063	−	68.7043i	1.14138	−	3.13591i
$481$	2.28772	−	2.72640i	0.104311	−	0.124313i
$482$	−8.21409	+	14.2272i	−0.374141	+	0.648032i
$483$	−9.66170	−	16.7346i	−0.439622	−	0.761448i
$484$	5.32328	+	63.6901i	0.241967	+	2.89501i
$485$	−15.0811	−	2.65921i	−0.684799	−	0.120749i
$486$	−2.42026	+	1.39734i	−0.109785	+	0.0633845i
$487$	−0.335512	−	0.193708i	−0.0152035	−	0.00877774i	0.492379	−	0.870381i	$-0.336127\pi$
$487$	−0.335512	−	0.193708i	−0.0152035	−	0.00877774i	−0.507582	+	0.861603i	$0.669461\pi$
$488$	16.2755	−	19.3964i	0.736759	−	0.878035i
$489$	3.85610	−	10.5946i	0.174379	−	0.479102i
$490$	18.5523	−	6.75248i	0.838106	−	0.305046i
$491$	−2.72812	−	3.25125i	−0.123118	−	0.146727i	0.700964	−	0.713196i	$-0.252753\pi$
$491$	−2.72812	−	3.25125i	−0.123118	−	0.146727i	−0.824083	+	0.566470i	$0.808309\pi$
$492$	49.6110	−	8.74776i	2.23664	−	0.394379i
$493$		−	5.43813i		−	0.244921i
$494$	1.58035	−	6.72835i	0.0711033	−	0.302723i
$495$	1.06095	+	8.18134i	0.0476863	+	0.367724i
$496$	57.3807	−	10.1178i	2.57647	−	0.454301i
$497$	30.4351	−	25.5380i	1.36520	−	1.14554i
$498$	−22.0879	+	8.03932i	−0.989781	+	0.360251i
$499$	12.8347	+	4.67144i	0.574559	+	0.209122i	0.612924	−	0.790141i	$-0.289993\pi$
$499$	12.8347	+	4.67144i	0.574559	+	0.209122i	−0.0383657	+	0.999264i	$0.512215\pi$
$500$	42.2115	+	35.4197i	1.88776	+	1.58401i
$501$	−9.66487	−	5.58002i	−0.431795	−	0.249297i
$502$	25.7957	+	44.6795i	1.15132	+	1.99414i
$503$	−18.0528	−	3.18320i	−0.804936	−	0.141932i	−0.243983	−	0.969779i	$-0.578454\pi$
$503$	−18.0528	−	3.18320i	−0.804936	−	0.141932i	−0.560953	+	0.827847i	$0.689565\pi$
$504$	32.8950	+	5.80027i	1.46526	+	0.258365i
$505$	−1.43754	+	0.829962i	−0.0639695	+	0.0369328i
$506$	−52.7081	−	21.9523i	−2.34316	−	0.975897i
$507$	8.14932	−	9.71199i	0.361924	−	0.431324i
$508$	−68.0763	−	24.7777i	−3.02040	−	1.09933i
$509$	0.123484	+	0.339269i	0.00547333	+	0.0150379i	0.942399	−	0.334490i	$-0.108564\pi$
$509$	0.123484	+	0.339269i	0.00547333	+	0.0150379i	−0.936926	+	0.349528i	$0.886342\pi$
$510$	3.69586	−	3.10120i	0.163656	−	0.137323i
$511$	−5.74159	−	32.5622i	−0.253993	−	1.44046i
$512$	−146.860			−6.49036
$513$	−2.98487	+	3.17656i	−0.131785	+	0.140249i
$514$			13.9111i			0.613592i
$515$	−20.9216	+	3.68905i	−0.921917	+	0.162559i
$516$	24.2276	−	20.3293i	1.06656	−	0.894950i
$517$	−3.36526	−	6.49533i	−0.148004	−	0.285664i
$518$	51.6761	+	18.8086i	2.27052	+	0.826401i
$519$	−2.82714	+	3.36926i	−0.124098	+	0.147894i
$520$	−7.51381	+	13.0143i	−0.329502	+	0.570715i
$521$	−29.5859	+	17.0815i	−1.29618	+	0.748352i	−0.979743	−	0.200260i	$-0.935821\pi$
$521$	−29.5859	+	17.0815i	−1.29618	+	0.748352i	−0.316441	+	0.948612i	$0.602488\pi$
$522$	3.80250	−	21.5651i	0.166431	−	0.943877i
$523$	−3.47642	+	19.7157i	−0.152013	+	0.862109i	0.809453	+	0.587185i	$0.199764\pi$
$523$	−3.47642	+	19.7157i	−0.152013	+	0.862109i	−0.961466	+	0.274924i	$0.911347\pi$
$524$	65.2158	−	37.6524i	2.84897	−	1.64485i
$525$	1.86217	−	3.22537i	0.0812716	−	0.140767i
$526$	−10.0704	+	12.0015i	−0.439091	+	0.523288i
$527$	2.09503	+	0.762530i	0.0912611	+	0.0332163i
$528$	53.4137	−	27.6739i	2.32453	−	1.20435i
$529$	11.4494	−	9.60723i	0.497802	−	0.417706i
$530$	11.9880	−	2.11381i	0.520725	−	0.0918179i
$531$			12.5525i			0.544734i
$532$	78.8892	−	9.38183i	3.42028	−	0.406754i
$533$	−4.91923			−0.213075
$534$	3.38637	+	19.2050i	0.146542	+	0.831083i
$535$	−3.67985	+	3.08776i	−0.159094	+	0.133496i
$536$	40.3971	+	110.990i	1.74489	+	4.79404i
$537$	8.93246	+	3.25115i	0.385464	+	0.140297i
$538$	35.9655	−	42.8620i	1.55058	−	1.84791i
$539$	8.69546	+	3.62155i	0.374540	+	0.155991i
$540$	12.5162	−	7.22621i	0.538610	−	0.310967i
$541$	4.29764	+	0.757789i	0.184770	+	0.0325799i	0.265267	−	0.964175i	$-0.414540\pi$
$541$	4.29764	+	0.757789i	0.184770	+	0.0325799i	−0.0804975	+	0.996755i	$0.525651\pi$
$542$	−15.7260	−	2.77293i	−0.675491	−	0.119107i
$543$	−8.90111	−	15.4172i	−0.381983	−	0.661614i
$544$	−17.6669	−	10.2000i	−0.757463	−	0.437321i
$545$	−18.0049	−	15.1079i	−0.771246	−	0.647152i
$546$	−4.67388	−	1.70115i	−0.200024	−	0.0728027i
$547$	27.9586	−	10.1761i	1.19542	−	0.435099i	0.333799	−	0.942644i	$-0.391669\pi$
$547$	27.9586	−	10.1761i	1.19542	−	0.435099i	0.861625	+	0.507546i	$0.169447\pi$
$548$	65.6751	−	55.1079i	2.80550	−	2.35409i
$549$	2.34175	−	0.412914i	0.0999434	−	0.0176227i
$550$	−1.41523	−	10.9133i	−0.0603456	−	0.465344i
$551$	−4.03334	−	33.9153i	−0.171826	−	1.44484i
$552$			65.5938i			2.79186i
$553$	−25.1576	+	4.43596i	−1.06981	+	0.188636i
$554$	12.3632	+	14.7339i	0.525264	+	0.625985i
$555$	14.6625	−	5.33673i	0.622390	−	0.226531i
$556$	−5.90773	+	16.2314i	−0.250544	+	0.688363i
$557$	−4.65330	+	5.54558i	−0.197166	+	0.234974i	−0.855565	−	0.517696i	$-0.826790\pi$
$557$	−4.65330	+	5.54558i	−0.197166	+	0.234974i	0.658398	+	0.752670i	$0.271234\pi$
$558$	7.77474	+	4.48875i	0.329131	+	0.190024i
$559$	−2.67459	+	1.54417i	−0.113123	+	0.0653116i
$560$	−139.377	−	24.5759i	−5.88974	−	1.03852i
$561$	2.29946	+	0.104866i	0.0970834	+	0.00442744i
$562$	−32.5411	−	56.3628i	−1.37266	−	2.37752i
$563$	−8.52143	+	14.7595i	−0.359135	+	0.622041i	−0.987817	−	0.155622i	$-0.950262\pi$
$563$	−8.52143	+	14.7595i	−0.359135	+	0.622041i	0.628681	+	0.777663i	$0.283595\pi$
$564$	−8.23753	+	9.81711i	−0.346863	+	0.413375i
$565$	0.199276	−	0.547507i	0.00838362	−	0.0230338i
$566$	14.1351	+	38.8358i	0.594142	+	1.63239i
$567$	2.01635	+	2.40300i	0.0846789	+	0.100916i
$568$	−132.816	+	23.4191i	−5.57285	+	0.982643i
$569$	−1.74134			−0.0730009			−0.0365005	−	0.999334i	$-0.511621\pi$
$569$	−1.74134			−0.0730009			−0.0365005	+	0.999334i	$0.511621\pi$
$570$	20.7494	−	22.0820i	0.869098	−	0.924912i
$571$		−	42.3168i		−	1.77090i	−0.464733	−	0.885451i	$-0.653850\pi$
$571$		−	42.3168i		−	1.77090i	0.464733	−	0.885451i	$-0.346150\pi$
$572$	−10.4336	+	3.26746i	−0.436250	+	0.136619i
$573$	15.6545	+	18.6563i	0.653975	+	0.779377i
$574$	−25.9966	−	71.4252i	−1.08508	−	2.98123i
$575$	6.87257	+	2.50141i	0.286606	+	0.104316i
$576$	−35.1375	−	29.4838i	−1.46406	−	1.22849i
$577$	−18.6258	+	32.2609i	−0.775403	+	1.34304i	0.159164	+	0.987252i	$0.449120\pi$
$577$	−18.6258	+	32.2609i	−0.775403	+	1.34304i	−0.934568	+	0.355786i	$0.884213\pi$
$578$	23.0817	+	39.9786i	0.960070	+	1.66289i
$579$	1.94436	+	0.342843i	0.0808048	+	0.0142481i
$580$	−19.6643	+	111.522i	−0.816516	+	4.63069i
$581$	13.1919	+	22.8490i	0.547291	+	0.947935i
$582$	−8.60269	+	14.9003i	−0.356593	+	0.617637i
$583$	4.89218	+	3.13002i	0.202613	+	0.129632i
$584$	−38.3878	+	105.470i	−1.58850	+	4.36436i
$585$	−1.32616	+	0.482684i	−0.0548301	+	0.0199565i
$586$	9.83127	−	8.24941i	0.406126	−	0.340780i
$587$	−5.21910	−	29.5990i	−0.215415	−	1.22168i	−0.880184	−	0.474633i	$-0.842581\pi$
$587$	−5.21910	−	29.5990i	−0.215415	−	1.22168i	0.664769	−	0.747049i	$-0.268530\pi$
$588$		−	16.5014i		−	0.680508i
$589$	13.6314	+	3.20173i	0.561671	+	0.131925i
$590$		−	87.2594i		−	3.59241i
$591$	−1.45894	−	8.27407i	−0.0600128	−	0.340350i
$592$	−73.1360	−	87.1601i	−3.00587	−	3.58226i
$593$	−1.18604	−	3.25862i	−0.0487048	−	0.133815i	0.912955	−	0.408060i	$-0.133795\pi$
$593$	−1.18604	−	3.25862i	−0.0487048	−	0.133815i	−0.961660	+	0.274244i	$0.911572\pi$
$594$	9.04527	+	2.02370i	0.371132	+	0.0830335i
$595$	−4.14843	−	3.48095i	−0.170069	−	0.142705i
$596$	−15.4455	−	8.91745i	−0.632672	−	0.365273i
$597$	5.52774	−	3.19144i	0.226235	−	0.130617i
$598$	1.69608	−	9.61896i	0.0693580	−	0.393349i
$599$	−9.25636	−	1.63215i	−0.378205	−	0.0666877i	−0.0186855	−	0.999825i	$-0.505948\pi$
$599$	−9.25636	−	1.63215i	−0.378205	−	0.0666877i	−0.359519	+	0.933138i	$0.617059\pi$
$600$	−10.9486	+	6.32118i	−0.446975	+	0.258061i
$601$	−11.2091	+	19.4147i	−0.457228	+	0.791943i	−0.998813	−	0.0487034i	$-0.984491\pi$
$601$	−11.2091	+	19.4147i	−0.457228	+	0.791943i	0.541585	+	0.840646i	$0.317824\pi$
$602$	−36.5552	−	30.6735i	−1.48988	−	1.25016i
$603$	−3.79377	+	10.4233i	−0.154494	+	0.424470i
$604$	−101.373	+	36.8966i	−4.12479	+	1.50130i
$605$	15.7808	−	22.3523i	0.641582	−	0.908750i
$606$	0.323847	+	1.83663i	0.0131554	+	0.0746079i
$607$	15.5950			0.632982			0.316491	−	0.948595i	$-0.397495\pi$
$607$	15.5950			0.632982			0.316491	+	0.948595i	$0.397495\pi$
$608$	−117.746	−	50.5098i	−4.77524	−	2.04844i
$609$	−24.5792			−0.995998
$610$	−16.2787	+	2.87038i	−0.659107	+	0.116218i
$611$	0.958637	−	0.804392i	0.0387823	−	0.0325422i
$612$	−1.37919	−	3.78929i	−0.0557504	−	0.153173i
$613$	8.10276	−	22.2621i	0.327267	−	0.899159i	−0.661533	−	0.749916i	$-0.730094\pi$
$613$	8.10276	−	22.2621i	0.327267	−	0.899159i	0.988800	−	0.149243i	$-0.0476838\pi$
$614$	54.6644	+	45.8689i	2.20607	+	1.85112i
$615$	−18.6774	−	10.7834i	−0.753144	−	0.434828i
$616$	−67.2700	−	88.0210i	−2.71039	−	3.54647i
$617$	1.56406	−	8.87024i	0.0629668	−	0.357102i	−0.937003	−	0.349321i	$-0.886412\pi$
$617$	1.56406	−	8.87024i	0.0629668	−	0.357102i	0.999970	−	0.00778093i	$-0.00247677\pi$
$618$	−4.14472	+	23.5059i	−0.166725	+	0.945546i
$619$	22.2659	+	38.5657i	0.894943	+	1.55009i	0.833876	+	0.551952i	$0.186117\pi$
$619$	22.2659	+	38.5657i	0.894943	+	1.55009i	0.0610669	+	0.998134i	$0.480550\pi$
$620$	−40.2064	−	23.2132i	−1.61473	−	0.932264i
$621$	−3.95960	+	4.71887i	−0.158893	+	0.189362i
$622$	3.37499	+	1.22839i	0.135325	+	0.0492541i
$623$	20.5692	−	7.48658i	0.824088	−	0.299944i
$624$	6.61484	+	7.88326i	0.264805	+	0.315583i
$625$	−5.12726	−	29.0782i	−0.205091	−	1.16313i
$626$	−6.99404			−0.279538
$627$	14.4185	−	1.05146i	0.575821	−	0.0419913i
$628$	−71.3375			−2.84668
$629$	−0.756006	−	4.28752i	−0.0301439	−	0.170955i
$630$	−14.0168	−	16.7045i	−0.558441	−	0.665524i
$631$	12.7502	−	4.64071i	0.507579	−	0.184744i	−0.0755207	−	0.997144i	$-0.524062\pi$
$631$	12.7502	−	4.64071i	0.507579	−	0.184744i	0.583100	+	0.812401i	$0.301840\pi$
$632$	81.4859	+	29.6584i	3.24134	+	1.17975i
$633$	−6.23357	+	7.42887i	−0.247762	+	0.295271i
$634$	79.4146	+	45.8500i	3.15396	+	1.82094i
$635$	15.5074	+	26.8596i	0.615392	+	1.06589i
$636$	1.76675	−	10.0198i	0.0700563	−	0.397309i
$637$	−0.279810	+	1.58688i	−0.0110865	+	0.0628744i
$638$	−57.7042	+	44.1004i	−2.28453	+	1.74595i
$639$	−10.9686	−	6.33273i	−0.433911	−	0.250519i
$640$	132.243	+	110.965i	5.22735	+	4.38627i
$641$	−14.7832	+	40.6165i	−0.583901	+	1.60425i	0.197554	+	0.980292i	$0.436700\pi$
$641$	−14.7832	+	40.6165i	−0.583901	+	1.60425i	−0.781455	+	0.623962i	$0.785522\pi$
$642$	1.84591	+	5.07159i	0.0728521	+	0.200160i
$643$	36.3568	−	30.5070i	1.43377	−	1.20308i	0.490333	−	0.871535i	$-0.336875\pi$
$643$	36.3568	−	30.5070i	1.43377	−	1.20308i	0.943440	−	0.331543i	$-0.107569\pi$
$644$	110.567	−	19.4960i	4.35696	−	0.768249i
$645$	−13.5399			−0.533132
$646$	−5.06233	−	6.77139i	−0.199175	−	0.266417i
$647$	−20.5385			−0.807450			−0.403725	−	0.914880i	$-0.632285\pi$
$647$	−20.5385			−0.807450			−0.403725	+	0.914880i	$0.632285\pi$
$648$	−1.84905	−	10.4865i	−0.0726376	−	0.411948i
$649$	28.1857	−	30.6398i	1.10639	−	1.20272i
$650$	1.76900	−	0.643863i	0.0693859	−	0.0252544i
$651$	3.44647	−	9.46911i	0.135078	−	0.371124i
$652$	50.1813	+	42.1071i	1.96525	+	1.64904i
$653$	−3.83891	+	6.64918i	−0.150228	+	0.260202i	−0.931311	−	0.364224i	$-0.881334\pi$
$653$	−3.83891	+	6.64918i	−0.150228	+	0.260202i	0.781083	+	0.624427i	$0.214667\pi$
$654$	−22.8691	+	13.2035i	−0.894253	+	0.516297i
$655$	−31.7492	−	5.59824i	−1.24054	−	0.218741i
$656$	−27.3084	+	154.873i	−1.06621	+	6.04679i
$657$	−9.12836	+	5.27026i	−0.356131	+	0.205613i
$658$	16.7456	+	9.66805i	0.652810	+	0.376900i
$659$	27.9599	+	23.4612i	1.08916	+	0.913918i	0.996649	−	0.0817934i	$-0.0260648\pi$
$659$	27.9599	+	23.4612i	1.08916	+	0.913918i	0.0925155	+	0.995711i	$0.470509\pi$
$660$	−46.7768	−	10.4654i	−1.82079	−	0.407366i
$661$	−10.0531	−	27.6207i	−0.391020	−	1.07432i	−0.966536	−	0.256529i	$-0.917421\pi$
$661$	−10.0531	−	27.6207i	−0.391020	−	1.07432i	0.575516	−	0.817790i	$-0.304801\pi$
$662$	−8.75335	−	10.4318i	−0.340209	−	0.405445i
$663$	0.0683775	+	0.387788i	0.00265556	+	0.0150604i
$664$		−	89.5603i		−	3.47561i
$665$	−28.4537	−	18.6324i	−1.10339	−	0.722533i
$666$		−	17.5309i		−	0.679310i
$667$	−8.38151	−	47.5339i	−0.324533	−	1.84052i
$668$	49.6719	−	41.6797i	1.92186	−	1.61263i
$669$	−17.9017	+	6.51568i	−0.692119	+	0.251911i
$670$	26.3725	−	72.4579i	1.01886	−	2.79929i
$671$	−6.64319	−	4.25032i	−0.256457	−	0.164082i
$672$	−46.1018	+	79.8507i	−1.77842	+	3.08031i
$673$	8.23478	+	14.2631i	0.317427	+	0.549800i	0.979950	−	0.199241i	$-0.0638477\pi$
$673$	8.23478	+	14.2631i	0.317427	+	0.549800i	−0.662523	+	0.749041i	$0.730514\pi$
$674$	15.1838	−	86.1115i	0.584857	−	3.31689i
$675$	−1.16923	−	0.206167i	−0.0450038	−	0.00793538i
$676$	36.8311	+	63.7934i	1.41658	+	2.45359i
$677$	23.2375	−	40.2486i	0.893091	−	1.54688i	0.0569406	−	0.998378i	$-0.481865\pi$
$677$	23.2375	−	40.2486i	0.893091	−	1.54688i	0.836150	−	0.548501i	$-0.184801\pi$
$678$	−0.501464	−	0.420778i	−0.0192586	−	0.0161599i
$679$	18.1476	+	6.60517i	0.696439	+	0.253483i
$680$	6.28726	+	17.2741i	0.241105	+	0.662432i
$681$	−16.1688	−	19.2693i	−0.619591	−	0.738399i
$682$	−8.89841	−	28.4142i	−0.340738	−	1.08804i
$683$		−	26.0842i		−	0.998086i	−0.866577	−	0.499043i	$-0.833685\pi$
$683$		−	26.0842i		−	0.998086i	0.866577	−	0.499043i	$-0.166315\pi$
$684$	−11.4119	−	22.6093i	−0.436343	−	0.864488i
$685$	−36.7033			−1.40236
$686$	35.9142	−	6.33265i	1.37121	−	0.241782i
$687$	4.41060	+	5.25634i	0.168275	+	0.200542i
$688$	33.7681	+	92.7771i	1.28740	+	3.53709i
$689$	−0.339803	+	0.933602i	−0.0129455	+	0.0355674i
$690$	27.5253	−	32.8034i	1.04787	−	1.24880i
$691$	6.93647	−	12.0143i	0.263876	−	0.457046i	−0.703393	−	0.710801i	$-0.748332\pi$
$691$	6.93647	−	12.0143i	0.263876	−	0.457046i	0.967268	+	0.253755i	$0.0816658\pi$
$692$	−12.7774	−	22.1311i	−0.485723	−	0.841297i
$693$	0.473972	−	10.3931i	0.0180047	−	0.394801i
$694$	14.9786	+	2.64113i	0.568579	+	0.100256i
$695$	6.40410	−	3.69741i	0.242921	−	0.140251i
$696$	72.2566	+	41.7174i	2.73888	+	1.58129i
$697$	−3.86798	+	4.60968i	−0.146510	+	0.174604i
$698$	5.19163	−	14.2639i	0.196506	−	0.539896i
$699$	−27.6777	+	10.0739i	−1.04687	+	0.381028i
$700$	13.9094	+	16.5765i	0.525724	+	0.626534i
$701$	17.4105	−	3.06994i	0.657586	−	0.115950i	0.165108	−	0.986275i	$-0.447203\pi$
$701$	17.4105	−	3.06994i	0.657586	−	0.115950i	0.492477	+	0.870325i	$0.336091\pi$
$702$			1.58560i			0.0598445i
$703$	−7.89485	−	26.1787i	−0.297760	−	0.987350i
$704$	19.5643	+	150.866i	0.737356	+	5.68598i
$705$	5.40305	−	0.952704i	0.203491	−	0.0358809i
$706$	−71.0555	+	59.6226i	−2.67421	+	2.24393i
$707$	1.96709	−	0.715962i	0.0739800	−	0.0269265i
$708$	−68.5344	−	24.9445i	−2.57568	−	0.937471i
$709$	12.1400	+	10.1867i	0.455927	+	0.382568i	0.841630	−	0.540055i	$-0.181597\pi$
$709$	12.1400	+	10.1867i	0.455927	+	0.382568i	−0.385703	+	0.922623i	$0.626041\pi$
$710$	76.2486	+	44.0222i	2.86156	+	1.65212i
$711$	4.07181	+	7.05259i	0.152705	+	0.264493i
$712$	−73.1750	−	12.9027i	−2.74235	−	0.483550i
$713$	19.4877	+	3.43620i	0.729818	+	0.128687i
$714$	−5.26917	+	3.04216i	−0.197194	+	0.113850i
$715$	4.32089	+	1.79960i	0.161592	+	0.0673011i
$716$	−35.5013	+	42.3087i	−1.32674	+	1.58115i
$717$	−9.93231	−	3.61507i	−0.370929	−	0.135007i
$718$	−12.4186	−	34.1199i	−0.463459	−	1.27334i
$719$	6.56506	−	5.50874i	0.244835	−	0.205441i	−0.512109	−	0.858920i	$-0.671136\pi$
$719$	6.56506	−	5.50874i	0.244835	−	0.205441i	0.756945	+	0.653479i	$0.226691\pi$
$720$	7.83447	+	44.4315i	0.291974	+	1.65586i
$721$	26.7913			0.997760
$722$	−36.5938	−	38.4757i	−1.36188	−	1.43192i
$723$		−	5.87839i		−	0.218620i
$724$	101.863	−	17.9612i	3.78571	−	0.667523i
$725$	7.12641	−	5.97977i	0.264668	−	0.222083i
$726$	−17.5347	−	25.2501i	−0.650775	−	0.937119i
$727$	−25.3019	−	9.20914i	−0.938396	−	0.341548i	−0.172864	−	0.984946i	$-0.555302\pi$
$727$	−25.3019	−	9.20914i	−0.938396	−	0.341548i	−0.765532	+	0.643398i	$0.777524\pi$
$728$	12.1817	−	14.5176i	0.451483	−	0.538057i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	63.4561	−	36.6364i	2.34862	−	1.35597i
$731$	−0.656019	+	3.72047i	−0.0242637	+	0.137606i
$732$	−2.39911	+	13.6060i	−0.0886737	+	0.502893i
$733$	−15.3416	+	8.85747i	−0.566655	+	0.327158i	−0.755812	−	0.654789i	$-0.772758\pi$
$733$	−15.3416	+	8.85747i	−0.566655	+	0.327158i	0.189157	+	0.981947i	$0.439424\pi$
$734$	−22.1276	+	38.3261i	−0.816745	+	1.41464i
$735$	−4.54096	+	5.41171i	−0.167496	+	0.199614i
$736$	−170.145	−	61.9277i	−6.27162	−	2.28268i
$737$	32.6650	−	16.9239i	1.20323	−	0.623398i
$738$	−18.5618	+	15.5752i	−0.683270	+	0.573331i
$739$	43.2576	−	7.62748i	1.59126	−	0.280581i	0.693294	−	0.720655i	$-0.256159\pi$
$739$	43.2576	−	7.62748i	1.59126	−	0.280581i	0.897962	+	0.440073i	$0.145048\pi$
$740$			90.6597i			3.33272i
$741$	0.714055	+	2.36775i	0.0262315	+	0.0869816i
$742$	−15.3513			−0.563564
$743$	−3.49309	−	19.8103i	−0.128149	−	0.726769i	−0.979388	−	0.201990i	$-0.935259\pi$
$743$	−3.49309	−	19.8103i	−0.128149	−	0.726769i	0.851239	−	0.524779i	$-0.175852\pi$
$744$	−26.2034	+	21.9872i	−0.960662	+	0.806091i
$745$	2.61144	+	7.17489i	0.0956759	+	0.262867i
$746$	31.0409	+	11.2980i	1.13649	+	0.413648i
$747$	5.40635	−	6.44304i	0.197808	−	0.235738i
$748$	−5.14205	+	12.3462i	−0.188012	+	0.451423i
$749$	5.24635	−	3.02898i	0.191697	−	0.110677i
$750$	−26.1017	−	4.60243i	−0.953098	−	0.168057i
$751$	30.5086	+	5.37950i	1.11328	+	0.196301i	0.699887	−	0.714254i	$-0.253234\pi$
$751$	30.5086	+	5.37950i	1.11328	+	0.196301i	0.413389	+	0.910554i	$0.364345\pi$
$752$	−20.0032	−	34.6465i	−0.729440	−	1.26343i
$753$	−15.9874	−	9.23032i	−0.582613	−	0.336372i
$754$	−9.51732	−	7.98598i	−0.346600	−	0.290832i
$755$	43.3989	+	15.7959i	1.57945	+	0.574872i
$756$	−17.1268	+	6.23365i	−0.622896	+	0.226716i
$757$	7.29886	−	6.12447i	0.265282	−	0.222598i	−0.500438	−	0.865772i	$-0.666828\pi$
$757$	7.29886	−	6.12447i	0.265282	−	0.222598i	0.765719	+	0.643175i	$0.222383\pi$
$758$	16.9257	−	2.98446i	0.614770	−	0.108401i
$759$	20.2609	−	2.62743i	0.735425	−	0.0953696i
$760$	52.0228	+	103.068i	1.88706	+	3.73867i
$761$		−	16.6917i		−	0.605075i	−0.953138	−	0.302537i	$-0.902166\pi$
$761$		−	16.6917i		−	0.605075i	0.953138	−	0.302537i	$-0.0978337\pi$
$762$	34.3164	−	6.05090i	1.24315	−	0.219201i
$763$	19.0526	+	22.7060i	0.689751	+	0.822013i
$764$	−132.968	+	48.3965i	−4.81062	+	1.75092i
$765$	−0.590449	+	1.62225i	−0.0213477	+	0.0586524i
$766$	40.9198	−	48.7664i	1.47849	−	1.76200i
$767$	6.16771	+	3.56093i	0.222703	+	0.128578i
$768$	88.5224	−	51.1085i	3.19428	−	1.84422i
$769$	0.116637	+	0.0205662i	0.00420602	+	0.000741636i	0.175751	−	0.984435i	$-0.443765\pi$
$769$	0.116637	+	0.0205662i	0.00420602	+	0.000741636i	−0.171545	+	0.985176i	$0.554876\pi$
$770$	−3.29483	+	72.2479i	−0.118737	+	2.60363i
$771$	−2.48886	−	4.31083i	−0.0896340	−	0.155251i
$772$	−5.73570	+	9.93452i	−0.206432	+	0.357551i
$773$	2.79598	−	3.33212i	0.100564	−	0.119848i	−0.713415	−	0.700742i	$-0.752852\pi$
$773$	2.79598	−	3.33212i	0.100564	−	0.119848i	0.813979	+	0.580894i	$0.197297\pi$
$774$	−5.20292	+	14.2949i	−0.187015	+	0.513820i
$775$	1.30444	+	3.58393i	0.0468569	+	0.128738i
$776$	−42.1385	−	50.2188i	−1.51269	−	1.80275i
$777$	−19.3787	+	3.41699i	−0.695207	+	0.122584i
$778$	−52.5534			−1.88413
$779$	−20.7040	+	31.6174i	−0.741799	+	1.13281i
$780$		−	8.19978i		−	0.293599i
$781$	12.5539	+	40.0868i	0.449213	+	1.43442i
$782$	−7.68005	−	9.15273i	−0.274638	−	0.327301i
$783$	2.67991	+	7.36298i	0.0957720	+	0.263132i
$784$	48.4068	+	17.6186i	1.72882	+	0.629237i
$785$	23.3954	+	19.6311i	0.835017	+	0.700662i
$786$	−18.1106	+	31.3685i	−0.645983	+	1.11888i
$787$	−15.8905	−	27.5232i	−0.566437	−	0.981097i	−0.996914	−	0.0784958i	$-0.974988\pi$
$787$	−15.8905	−	27.5232i	−0.566437	−	0.981097i	0.430478	−	0.902601i	$-0.358345\pi$
$788$	48.0740	+	8.47674i	1.71256	+	0.301971i
$789$	0.973462	−	5.52078i	0.0346562	−	0.196545i
$790$	−28.3053	−	49.0263i	−1.00706	−	1.74428i
$791$	−0.367387	+	0.636333i	−0.0130628	+	0.0226254i
$792$	−19.0332	+	29.7486i	−0.676314	+	1.05707i
$793$	0.461426	−	1.26776i	0.0163857	−	0.0450194i
$794$	−42.1609	+	15.3453i	−1.49623	+	0.544585i
$795$	−3.33671	+	2.79983i	−0.118341	+	0.0992997i
$796$	6.43989	+	36.5224i	0.228256	+	1.29450i
$797$			51.0839i			1.80948i	0.425960	+	0.904742i	$0.359936\pi$
$797$			51.0839i			1.80948i	−0.425960	+	0.904742i	$0.640064\pi$
$798$	−30.6053	+	22.8807i	−1.08341	+	0.809967i
$799$		−	1.53080i		−	0.0541560i
$800$	−6.05994	−	34.3676i	−0.214251	−	1.21508i
$801$	−4.48539	−	5.34548i	−0.158483	−	0.188873i
$802$	−2.81074	−	7.72245i	−0.0992507	−	0.272689i
$803$	34.1156	+	7.63270i	1.20391	+	0.269352i
$804$	−49.3702	−	41.4265i	−1.74115	−	1.46100i
$805$	−41.6259	−	24.0327i	−1.46712	−	0.847042i
$806$	4.41110	−	2.54675i	0.155375	−	0.0897055i
$807$	−3.47662	+	19.7169i	−0.122383	+	0.694068i
$808$	−6.99792	−	1.23392i	−0.246186	−	0.0434092i
$809$	−20.5977	+	11.8921i	−0.724176	+	0.418103i	−0.816288	−	0.577645i	$-0.803972\pi$
$809$	−20.5977	+	11.8921i	−0.724176	+	0.418103i	0.0921118	+	0.995749i	$0.470638\pi$
$810$	−3.47577	+	6.02020i	−0.122126	+	0.211528i
$811$	9.63661	+	8.08607i	0.338387	+	0.283940i	0.796107	−	0.605156i	$-0.206889\pi$
$811$	9.63661	+	8.08607i	0.338387	+	0.283940i	−0.457720	+	0.889096i	$0.651334\pi$
$812$	48.8439	−	134.197i	1.71408	−	4.70941i
$813$	5.36936	−	1.95429i	0.188312	−	0.0685399i
$814$	−39.3643	+	42.7916i	−1.37972	+	1.49985i
$815$	−4.86986	−	27.6184i	−0.170584	−	0.967429i
$816$	12.5884			0.440683
$817$	−1.33192	+	23.6895i	−0.0465978	+	0.828791i
$818$	−0.314547			−0.0109979
$819$	1.75272	−	0.309052i	0.0612450	−	0.0107991i
$820$	95.9909	−	80.5459i	3.35215	−	2.81278i
$821$	−3.63028	−	9.97411i	−0.126698	−	0.348099i	0.860084	−	0.510152i	$-0.170411\pi$
$821$	−3.63028	−	9.97411i	−0.126698	−	0.348099i	−0.986782	+	0.162053i	$0.948189\pi$
$822$	−14.1039	+	38.7501i	−0.491929	+	1.35156i
$823$	5.68208	+	4.76783i	0.198065	+	0.166196i	0.736426	−	0.676518i	$-0.236512\pi$
$823$	5.68208	+	4.76783i	0.198065	+	0.166196i	−0.538361	+	0.842714i	$0.680956\pi$
$824$	−78.7597	−	45.4719i	−2.74372	−	1.58409i
$825$	2.39107	+	3.12865i	0.0832464	+	0.108926i
$826$	−19.1087	+	108.371i	−0.664878	+	3.77071i
$827$	9.46052	−	53.6533i	0.328975	−	1.86571i	−0.151156	−	0.988510i	$-0.548300\pi$
$827$	9.46052	−	53.6533i	0.328975	−	1.86571i	0.480130	−	0.877197i	$-0.340589\pi$
$828$	−17.8956	−	30.9960i	−0.621914	−	1.07719i
$829$	−19.3749	−	11.1861i	−0.672919	−	0.388510i	0.124263	−	0.992249i	$-0.460343\pi$
$829$	−19.3749	−	11.1861i	−0.672919	−	0.388510i	−0.797182	+	0.603739i	$0.793677\pi$
$830$	−37.5824	+	44.7890i	−1.30451	+	1.55465i
$831$	−6.46725	−	2.35389i	−0.224346	−	0.0816554i
$832$	−24.4548	+	8.90082i	−0.847818	+	0.308580i
$833$	1.26701	+	1.50996i	0.0438992	+	0.0523171i
$834$	−1.44271	−	8.18202i	−0.0499570	−	0.283320i
$835$	−27.7597			−0.960665
$836$	−22.9118	+	80.8119i	−0.792423	+	2.79494i
$837$	−3.21236			−0.111035
$838$	7.34045	+	41.6297i	0.253571	+	1.43808i
$839$	32.0886	+	38.2417i	1.10782	+	1.32025i	0.942573	+	0.333999i	$0.108398\pi$
$839$	32.0886	+	38.2417i	1.10782	+	1.32025i	0.165248	+	0.986252i	$0.447157\pi$
$840$	78.0753	−	28.4171i	2.69385	−	0.980482i
$841$	−30.4417	−	11.0799i	−1.04971	−	0.382065i
$842$	−39.3395	+	46.8830i	−1.35573	+	1.61569i
$843$	20.1679	+	11.6440i	0.694620	+	0.401039i
$844$	−28.1728	−	48.7967i	−0.969748	−	1.67965i
$845$	5.47613	−	31.0567i	0.188385	−	1.06838i
$846$	1.07038	−	6.07045i	0.0368006	−	0.208706i
$847$	−24.4938	+	24.3044i	−0.841615	+	0.835111i
$848$	27.5065	+	15.8809i	0.944577	+	0.545352i
$849$	−11.3284	−	9.50568i	−0.388790	−	0.326234i
$850$	0.787614	−	2.16395i	0.0270149	−	0.0742229i
$851$	−13.2163	−	36.3115i	−0.453049	−	1.24474i
$852$	56.3723	−	47.3020i	1.93128	−	1.62054i
$853$	23.8376	−	4.20322i	0.816185	−	0.143915i	0.250055	−	0.968232i	$-0.419551\pi$
$853$	23.8376	−	4.20322i	0.816185	−	0.143915i	0.566130	+	0.824316i	$0.308440\pi$
$854$	20.8458			0.713330
$855$	−2.47919	+	10.5552i	−0.0847866	+	0.360979i
$856$	−20.5639			−0.702860
$857$	6.90803	+	39.1774i	0.235974	+	1.33827i	0.840553	+	0.541729i	$0.182230\pi$
$857$	6.90803	+	39.1774i	0.235974	+	1.33827i	−0.604579	+	0.796545i	$0.706659\pi$
$858$	3.56033	−	3.87032i	0.121548	−	0.132130i
$859$	20.4365	−	7.43827i	0.697283	−	0.253790i	0.0310328	−	0.999518i	$-0.490120\pi$
$859$	20.4365	−	7.43827i	0.697283	−	0.253790i	0.666251	+	0.745728i	$0.267898\pi$
$860$	26.9065	−	73.9250i	0.917504	−	2.52082i
$861$	20.8348	+	17.4824i	0.710047	+	0.595800i
$862$	19.0172	−	32.9387i	0.647728	−	1.12190i
$863$	24.0823	−	13.9039i	0.819771	−	0.473295i	−0.0305666	−	0.999533i	$-0.509731\pi$
$863$	24.0823	−	13.9039i	0.819771	−	0.473295i	0.850337	+	0.526238i	$0.176398\pi$
$864$	28.9468	+	5.10410i	0.984790	+	0.173645i
$865$	−1.89977	+	10.7741i	−0.0645940	+	0.366331i
$866$	−23.0510	+	13.3085i	−0.783306	+	0.452242i
$867$	−14.3053	−	8.25916i	−0.485833	−	0.280496i
$868$	44.8506	+	37.6341i	1.52233	+	1.27739i
$869$	5.89703	−	26.3577i	0.200043	−	0.894125i
$870$	−18.6295	−	51.1840i	−0.631598	−	1.73530i
$871$	4.04528	+	4.82098i	0.137069	+	0.163353i
$872$	−17.4718	−	99.0873i	−0.591668	−	3.35552i
$873$		−	6.15649i		−	0.208366i
$874$	−54.6856	−	51.3855i	−1.84977	−	1.73814i
$875$			29.7499i			1.00573i
$876$	−10.6347	−	60.3122i	−0.359312	−	2.03776i
$877$	−9.79723	+	8.22085i	−0.330829	+	0.277598i	−0.793037	−	0.609173i	$-0.791502\pi$
$877$	−9.79723	+	8.22085i	−0.330829	+	0.277598i	0.462209	+	0.886771i	$0.347057\pi$
$878$	4.84017	−	1.76168i	0.163348	−	0.0594537i
$879$	−1.57064	+	4.31529i	−0.0529763	+	0.145551i
$880$	80.6440	−	126.045i	2.71851	−	4.24899i
$881$	−15.7154	+	27.2198i	−0.529464	+	0.917059i	0.469945	+	0.882696i	$0.344274\pi$
$881$	−15.7154	+	27.2198i	−0.529464	+	0.917059i	−0.999409	+	0.0343634i	$0.989060\pi$
$882$	3.96855	+	6.87373i	0.133628	+	0.231451i
$883$	−7.18730	+	40.7612i	−0.241872	+	1.37172i	0.585774	+	0.810474i	$0.300790\pi$
$883$	−7.18730	+	40.7612i	−0.241872	+	1.37172i	−0.827646	+	0.561250i	$0.810321\pi$
$884$	−2.25313	−	0.397287i	−0.0757808	−	0.0133622i
$885$	15.6117	+	27.0403i	0.524783	+	0.908950i
$886$	29.3969	−	50.9170i	0.987609	−	1.71059i
$887$	13.9230	+	11.6828i	0.467489	+	0.392269i	0.845878	−	0.533377i	$-0.179077\pi$
$887$	13.9230	+	11.6828i	0.467489	+	0.392269i	−0.378389	+	0.925647i	$0.623522\pi$
$888$	62.7680	+	22.8457i	2.10636	+	0.766651i
$889$	−13.3773	−	36.7540i	−0.448662	−	1.23269i
$890$	31.1803	+	37.1593i	1.04517	+	1.24558i
$891$	−3.16505	+	0.991191i	−0.106033	+	0.0332061i
$892$		−	110.688i		−	3.70610i
$893$	−1.13537	−	9.54697i	−0.0379936	−	0.319477i
$894$	8.57849			0.286908
$895$	23.2855	−	4.10587i	0.778349	−	0.137244i
$896$	−139.938	−	166.771i	−4.67500	−	5.57144i
$897$	1.19536	+	3.28421i	0.0399118	+	0.109657i
$898$	−11.7183	+	32.1958i	−0.391046	+	1.07439i
$899$	16.1793	−	19.2817i	0.539610	−	0.643082i
$900$	3.44914	−	5.97408i	0.114971	−	0.199136i
$901$	0.607667	+	1.05251i	0.0202443	+	0.0350642i
$902$	80.2808	+	3.66117i	2.67306	+	0.121903i
$903$	16.8157	+	2.96507i	0.559592	+	0.0986712i
$904$	2.16005	−	1.24711i	0.0718423	−	0.0414782i
$905$	−38.3490	−	22.1408i	−1.27476	−	0.735986i
$906$	33.3535	−	39.7492i	1.10810	−	1.32058i
$907$	−12.6048	+	34.6315i	−0.418537	+	1.14992i	0.533996	+	0.845487i	$0.320690\pi$
$907$	−12.6048	+	34.6315i	−0.418537	+	1.14992i	−0.952533	+	0.304434i	$0.901533\pi$
$908$	137.337	−	49.9866i	4.55769	−	1.65886i
$909$	−0.428950	−	0.511202i	−0.0142274	−	0.0169555i
$910$	−12.1841	+	2.14838i	−0.403899	+	0.0712182i
$911$		−	19.1853i		−	0.635636i	−0.948152	−	0.317818i	$-0.897050\pi$
$911$		−	19.1853i		−	0.635636i	0.948152	−	0.317818i	$-0.102950\pi$
$912$	78.5086	−	9.33657i	2.59968	−	0.309165i
$913$	−27.6638	+	3.58743i	−0.915538	+	0.118727i
$914$	48.6099	−	8.57123i	1.60787	−	0.283511i
$915$	4.53098	−	3.80195i	0.149790	−	0.125688i
$916$	−37.4634	+	13.6355i	−1.23782	+	0.450531i
$917$	38.2047	+	13.9054i	1.26163	+	0.459196i
$918$	1.48582	+	1.24675i	0.0490394	+	0.0411489i
$919$	−26.0870	−	15.0613i	−0.860530	−	0.496827i	0.00366007	−	0.999993i	$-0.498835\pi$
$919$	−26.0870	−	15.0613i	−0.860530	−	0.496827i	−0.864190	+	0.503166i	$0.832168\pi$
$920$	81.5798	+	141.300i	2.68961	+	4.65853i
$921$	−25.1461	−	4.43394i	−0.828592	−	0.146103i
$922$	11.0084	+	1.94108i	0.362543	+	0.0639262i
$923$	−6.22319	+	3.59296i	−0.204839	+	0.118264i
$924$	55.8023	+	23.2410i	1.83576	+	0.764572i
$925$	4.78730	−	5.70528i	0.157405	−	0.187588i
$926$	−24.4040	−	8.88232i	−0.801965	−	0.291891i
$927$	−2.92110	−	8.02565i	−0.0959414	−	0.263597i
$928$	−176.429	+	148.042i	−5.79158	+	4.85971i
$929$	5.97749	+	33.9001i	0.196115	+	1.11222i	0.910822	+	0.412800i	$0.135449\pi$
$929$	5.97749	+	33.9001i	0.196115	+	1.11222i	−0.714706	+	0.699425i	$0.753440\pi$
$930$	22.3308			0.732256
$931$	9.02170	+	8.47727i	0.295674	+	0.277831i
$932$		−	171.134i		−	5.60567i
$933$	−1.26563	+	0.223165i	−0.0414348	+	0.00730608i
$934$	−45.8075	+	38.4371i	−1.49887	+	1.25770i
$935$	5.08386	−	2.63397i	0.166260	−	0.0861400i
$936$	−5.67710	−	2.06629i	−0.185562	−	0.0675389i
$937$	−14.6504	+	17.4597i	−0.478608	+	0.570383i	−0.950282	−	0.311390i	$-0.899205\pi$
$937$	−14.6504	+	17.4597i	−0.478608	+	0.570383i	0.471674	+	0.881773i	$0.343650\pi$
$938$	−48.6205	+	84.2133i	−1.58752	+	2.74966i
$939$	2.16734	−	1.25132i	0.0707286	−	0.0408352i
$940$	−5.53540	+	31.3928i	−0.180545	+	1.02392i
$941$	−1.14023	+	6.46656i	−0.0371704	+	0.210804i	−0.997736	−	0.0672488i	$-0.978578\pi$
$941$	−1.14023	+	6.46656i	−0.0371704	+	0.210804i	0.960566	+	0.278053i	$0.0896890\pi$
$942$	29.7159	−	17.1565i	0.968195	−	0.558988i
$943$	−26.7048	+	46.2541i	−0.869628	+	1.50624i
$944$	146.349	−	174.412i	4.76325	−	5.67662i
$945$	7.33221	+	2.66870i	0.238517	+	0.0868130i
$946$	44.7980	−	23.2100i	1.45651	−	0.754623i
$947$	−3.56833	+	2.99419i	−0.115955	+	0.0972980i	−0.698922	−	0.715198i	$-0.746336\pi$
$947$	−3.56833	+	2.99419i	−0.115955	+	0.0972980i	0.582966	+	0.812496i	$0.301892\pi$
$948$	−46.5973	+	8.21635i	−1.51341	+	0.266855i
$949$			5.98031i			0.194129i
$950$	3.30705	−	14.0798i	0.107295	−	0.456809i
$951$	−32.8124			−1.06402
$952$	−4.02559	−	22.8303i	−0.130470	−	0.739933i
$953$	−39.4945	+	33.1398i	−1.27935	+	1.07350i	−0.286018	+	0.958224i	$0.592332\pi$
$953$	−39.4945	+	33.1398i	−1.27935	+	1.07350i	−0.993333	+	0.115279i	$0.963224\pi$
$954$	1.67378	+	4.59866i	0.0541905	+	0.148887i
$955$	56.9254	+	20.7192i	1.84206	+	0.670456i
$956$	39.4751	−	47.0446i	1.27672	−	1.52153i
$957$	9.99153	−	23.9900i	0.322980	−	0.775486i
$958$	−2.07588	+	1.19851i	−0.0670686	+	0.0387221i
$959$	45.5834	+	8.03758i	1.47196	+	0.259547i
$960$	−112.362	−	19.8124i	−3.62645	−	0.639441i
$961$	−10.3404	−	17.9101i	−0.333561	−	0.577744i
$962$	−8.61385	−	4.97321i	−0.277722	−	0.160343i
$963$	−1.47938	−	1.24135i	−0.0476725	−	0.0400020i
$964$	32.0948	+	11.6816i	1.03371	+	0.376238i
$965$	4.61488	−	1.67968i	0.148558	−	0.0540708i
$966$	−41.3684	+	34.7122i	−1.33101	+	1.11685i
$967$	21.9787	−	3.87544i	0.706788	−	0.124626i	0.191311	−	0.981529i	$-0.438726\pi$
$967$	21.9787	−	3.87544i	0.706788	−	0.124626i	0.515477	+	0.856904i	$0.327615\pi$
$968$	113.257	−	29.8766i	3.64020	−	0.960269i
$969$	2.78022	+	1.19264i	0.0893135	+	0.0383130i
$970$			42.7970i			1.37413i
$971$	−37.8262	+	6.66977i	−1.21390	+	0.214043i	−0.743698	−	0.668516i	$-0.766930\pi$
$971$	−37.8262	+	6.66977i	−1.21390	+	0.214043i	−0.470201	+	0.882559i	$0.655819\pi$
$972$	3.73472	+	4.45087i	0.119791	+	0.142762i
$973$	−8.76321	+	3.18955i	−0.280935	+	0.102252i
$974$	−0.370305	+	1.01741i	−0.0118653	+	0.0325998i
$975$	−0.432990	+	0.516018i	−0.0138668	+	0.0165258i
$976$	−37.3516	−	21.5650i	−1.19560	−	0.690278i
$977$	−24.7553	+	14.2925i	−0.791992	+	0.457257i	−0.840663	−	0.541558i	$-0.817835\pi$
$977$	−24.7553	+	14.2925i	−0.791992	+	0.457257i	0.0486713	+	0.998815i	$0.484501\pi$
$978$	−31.0298	−	5.47140i	−0.992225	−	0.174956i
$979$	−1.05435	+	23.1195i	−0.0336972	+	0.738901i
$980$	−20.5230	−	35.5469i	−0.655584	−	1.13550i
$981$	4.72452	−	8.18310i	0.150842	−	0.261266i
$982$	−7.62420	+	9.08617i	−0.243298	+	0.289951i
$983$	2.80838	−	7.71596i	0.0895734	−	0.246101i	−0.886814	−	0.462126i	$-0.847087\pi$
$983$	2.80838	−	7.71596i	0.0895734	−	0.246101i	0.976388	+	0.216025i	$0.0693091\pi$
$984$	−31.5766	−	86.7561i	−1.00663	−	2.76568i
$985$	−13.4334	−	16.0093i	−0.428022	−	0.510097i
$986$	−14.9669	+	2.63907i	−0.476643	+	0.0840450i
$987$	−6.91891			−0.220231
$988$	−14.3464	−	0.806612i	−0.456421	−	0.0256617i
$989$			33.5312i			1.06623i
$990$	22.0019	−	6.89030i	0.699268	−	0.218988i
$991$	19.0661	+	22.7220i	0.605653	+	0.721789i	0.978533	−	0.206090i	$-0.0660741\pi$
$991$	19.0661	+	22.7220i	0.605653	+	0.721789i	−0.372880	+	0.927880i	$0.621630\pi$
$992$	−32.2942	−	88.7276i	−1.02534	−	2.81710i
$993$	4.57890	+	1.66658i	0.145307	+	0.0528875i
$994$	−85.0560	−	71.3705i	−2.69781	−	2.26373i
$995$	7.93846	−	13.7498i	0.251666	−	0.435899i
$996$	24.4342	+	42.3213i	0.774227	+	1.34100i
$997$	9.29844	+	1.63957i	0.294485	+	0.0519256i	0.318939	−	0.947775i	$-0.396674\pi$
$997$	9.29844	+	1.63957i	0.294485	+	0.0519256i	−0.0244540	+	0.999701i	$0.507785\pi$
$998$	6.62827	−	37.5908i	0.209814	−	1.18992i
$999$	3.13649	+	5.43256i	0.0992341	+	0.171879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.be.a.10.1	✓	240
11.10	odd	2	inner	627.2.be.a.10.40	yes	240
19.2	odd	18	inner	627.2.be.a.439.40	yes	240
209.21	even	18	inner	627.2.be.a.439.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.be.a.10.1	✓	240	1.1	even	1	trivial
627.2.be.a.10.40	yes	240	11.10	odd	2	inner
627.2.be.a.439.1	yes	240	209.21	even	18	inner
627.2.be.a.439.40	yes	240	19.2	odd	18	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.485290 - 2.75222i) q^{2} +(0.642788 + 0.766044i) q^{3} +(-5.45980 + 1.98721i) q^{4} +(2.33741 + 0.850748i) q^{5} +(1.79638 - 2.14084i) q^{6} +(-2.71663 - 1.56845i) q^{7} +(5.32413 + 9.22167i) q^{8} +(-0.173648 + 0.984808i) q^{9} +(1.20712 - 6.84592i) q^{10} +(2.63517 - 2.01393i) q^{11} +(-5.03178 - 2.90510i) q^{12} +(0.434626 + 0.364694i) q^{13} +(-2.99835 + 8.23789i) q^{14} +(0.850748 + 2.33741i) q^{15} +(13.8945 - 11.6589i) q^{16} +(0.683491 - 0.120518i) q^{17} +2.79467 q^{18} +(4.17325 - 1.25855i) q^{19} -14.4524 q^{20} +(-0.544715 - 3.08923i) q^{21} +(-6.82158 - 6.27521i) q^{22} +(5.78855 - 2.10686i) q^{23} +(-3.64192 + 10.0061i) q^{24} +(0.909501 + 0.763162i) q^{25} +(0.792798 - 1.37317i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(17.9491 + 3.16491i) q^{28} +(1.36062 - 7.71648i) q^{29} +(6.02020 - 3.47577i) q^{30} +(2.78198 + 1.60618i) q^{31} +(-22.5166 - 18.8937i) q^{32} +(3.23661 + 0.724128i) q^{33} +(-0.663383 - 1.82263i) q^{34} +(-5.01552 - 5.97727i) q^{35} +(-1.00893 - 5.72193i) q^{36} -6.27298i q^{37} +(-5.48904 - 10.8749i) q^{38} +0.567364i q^{39} +(4.59937 + 26.0843i) q^{40} +(-6.64185 + 5.57318i) q^{41} +(-8.23789 + 2.99835i) q^{42} +(-1.86173 + 5.11506i) q^{43} +(-10.3854 + 16.2323i) q^{44} +(-1.24371 + 2.15417i) q^{45} +(-8.60766 - 14.9089i) q^{46} +(0.383009 - 2.17215i) q^{47} +(17.8625 + 3.14964i) q^{48} +(1.42004 + 2.45958i) q^{49} +(1.65901 - 2.87350i) q^{50} +(0.531662 + 0.446117i) q^{51} +(-3.09769 - 1.12747i) q^{52} +(0.598916 + 1.64551i) q^{53} +(1.79638 + 2.14084i) q^{54} +(7.87282 - 2.46551i) q^{55} -33.4024i q^{56} +(3.64662 + 2.38792i) q^{57} -21.8977 q^{58} +(12.3618 - 2.17973i) q^{59} +(-9.28984 - 11.0712i) q^{60} +(-0.813281 - 2.23447i) q^{61} +(3.07048 - 8.43608i) q^{62} +(2.01635 - 2.40300i) q^{63} +(-22.9344 + 39.7235i) q^{64} +(0.705637 + 1.22220i) q^{65} +(0.422264 - 9.25926i) q^{66} +(10.9237 + 1.92615i) q^{67} +(-3.49223 + 2.01624i) q^{68} +(5.33476 + 3.08002i) q^{69} +(-14.0168 + 16.7045i) q^{70} +(-4.33184 + 11.9016i) q^{71} +(-10.0061 + 3.64192i) q^{72} +(6.77532 + 8.07451i) q^{73} +(-17.2646 + 3.04421i) q^{74} +1.18727i q^{75} +(-20.2841 + 15.1645i) q^{76} +(-10.3175 + 1.33797i) q^{77} +(1.56151 - 0.275336i) q^{78} +(6.23838 - 5.23462i) q^{79} +(42.3960 - 15.4309i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(18.5618 + 15.5752i) q^{82} +(-7.28396 - 4.20539i) q^{83} +(9.11298 + 15.7841i) q^{84} +(1.70013 + 0.299779i) q^{85} +(14.9812 + 2.64159i) q^{86} +(6.78576 - 3.91776i) q^{87} +(32.6017 + 13.5782i) q^{88} +(-4.48539 + 5.34548i) q^{89} +(6.53230 + 2.37756i) q^{90} +(-0.608713 - 1.67243i) q^{91} +(-27.4176 + 23.0061i) q^{92} +(0.557820 + 3.16356i) q^{93} -6.16410 q^{94} +(10.8253 + 0.608641i) q^{95} -29.3933i q^{96} +(-6.06296 + 1.06906i) q^{97} +(6.08017 - 5.10187i) q^{98} +(1.52574 + 2.94485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) \) 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Introduction

L-functions

Modular forms

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