LMFDB - Embedded newform 312.2.bt.d.115.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(19,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 0, 5]))

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

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

chi := DirichletCharacter("312.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.4
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.d.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18379 - 0.773723i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.802706 + 1.83185i) q^{4} +(2.96415 - 2.96415i) q^{5} +(0.0781697 - 1.41205i) q^{6} +(0.672672 - 0.180242i) q^{7} +(0.467108 - 2.78959i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.80236 + 1.21550i) q^{10} +(1.92093 + 0.514712i) q^{11} +(-1.18507 + 1.61109i) q^{12} +(-3.56375 - 0.547460i) q^{13} +(-0.935758 - 0.307093i) q^{14} +(4.04911 + 1.08496i) q^{15} +(-2.71133 + 2.94087i) q^{16} +(-2.22516 - 1.28470i) q^{17} +(1.26196 - 0.638329i) q^{18} +(3.02991 - 0.811863i) q^{19} +(7.80922 + 3.05053i) q^{20} +(0.492430 + 0.492430i) q^{21} +(-1.87573 - 2.09558i) q^{22} +(2.57061 + 4.45243i) q^{23} +(2.64941 - 0.990268i) q^{24} -12.5724i q^{25} +(3.79514 + 3.40543i) q^{26} -1.00000 q^{27} +(0.870133 + 1.08755i) q^{28} +(4.26557 - 2.46273i) q^{29} +(-3.95383 - 4.41724i) q^{30} +(0.871296 - 0.871296i) q^{31} +(5.48505 - 1.38355i) q^{32} +(0.514712 + 1.92093i) q^{33} +(1.64012 + 3.24247i) q^{34} +(1.45964 - 2.52817i) q^{35} +(-1.98778 - 0.220759i) q^{36} +(-2.61427 + 9.75657i) q^{37} +(-4.21493 - 1.38324i) q^{38} +(-1.30776 - 3.36002i) q^{39} +(-6.88419 - 9.65335i) q^{40} +(1.76270 - 6.57848i) q^{41} +(-0.201928 - 0.963937i) q^{42} +(1.33015 + 0.767960i) q^{43} +(0.599070 + 3.93201i) q^{44} +(1.08496 + 4.04911i) q^{45} +(0.401888 - 7.25967i) q^{46} +(-7.11089 - 7.11089i) q^{47} +(-3.90253 - 0.877641i) q^{48} +(-5.64218 + 3.25751i) q^{49} +(-9.72755 + 14.8831i) q^{50} -2.56939i q^{51} +(-1.85778 - 6.96769i) q^{52} +3.80757i q^{53} +(1.18379 + 0.773723i) q^{54} +(7.21961 - 4.16825i) q^{55} +(-0.188591 - 1.96067i) q^{56} +(2.21805 + 2.21805i) q^{57} +(-6.95500 - 0.385021i) q^{58} +(3.01758 + 11.2618i) q^{59} +(1.26277 + 8.28825i) q^{60} +(3.41145 + 1.96960i) q^{61} +(-1.70557 + 0.357288i) q^{62} +(-0.180242 + 0.672672i) q^{63} +(-7.56362 - 2.60608i) q^{64} +(-12.1862 + 8.94073i) q^{65} +(0.876958 - 2.67222i) q^{66} +(-3.44219 + 12.8464i) q^{67} +(0.567218 - 5.10739i) q^{68} +(-2.57061 + 4.45243i) q^{69} +(-3.68400 + 1.86346i) q^{70} +(-1.12141 - 4.18515i) q^{71} +(2.18230 + 1.79932i) q^{72} +(6.22477 - 6.22477i) q^{73} +(10.6436 - 9.52699i) q^{74} +(10.8880 - 6.28620i) q^{75} +(3.91934 + 4.89865i) q^{76} +1.38493 q^{77} +(-1.05162 + 4.98940i) q^{78} +16.9313i q^{79} +(0.680406 + 16.7540i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.17658 + 6.42369i) q^{82} +(-0.890596 - 0.890596i) q^{83} +(-0.506780 + 1.29733i) q^{84} +(-10.4038 + 2.78768i) q^{85} +(-0.980422 - 1.93827i) q^{86} +(4.26557 + 2.46273i) q^{87} +(2.33312 - 5.11818i) q^{88} +(-8.32774 - 2.23141i) q^{89} +(1.84853 - 5.63274i) q^{90} +(-2.49591 + 0.274075i) q^{91} +(-6.09272 + 8.28296i) q^{92} +(1.19021 + 0.318917i) q^{93} +(2.91592 + 13.9196i) q^{94} +(6.57464 - 11.3876i) q^{95} +(3.94072 + 4.05842i) q^{96} +(-9.59613 + 2.57127i) q^{97} +(9.19955 + 0.509278i) q^{98} +(-1.40622 + 1.40622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) $ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−1.18379	−	0.773723i	−0.837064	−	0.547105i
$2$	−1.18379	−	0.773723i	−0.837064	−	0.547105i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.802706	+	1.83185i	0.401353	+	0.915923i
$5$	2.96415	−	2.96415i	1.32561	−	1.32561i	0.416452	−	0.909158i	$-0.363274\pi$
$5$	2.96415	−	2.96415i	1.32561	−	1.32561i	0.909158	−	0.416452i	$-0.136726\pi$
$6$	0.0781697	−	1.41205i	0.0319126	−	0.576468i
$7$	0.672672	−	0.180242i	0.254246	−	0.0681250i	−0.129445	−	0.991587i	$-0.541319\pi$
$7$	0.672672	−	0.180242i	0.254246	−	0.0681250i	0.383691	+	0.923462i	$0.374653\pi$
$8$	0.467108	−	2.78959i	0.165147	−	0.986269i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−5.80236	+	1.21550i	−1.83487	+	0.384373i
$11$	1.92093	+	0.514712i	0.579182	+	0.155191i	0.536504	−	0.843897i	$-0.319744\pi$
$11$	1.92093	+	0.514712i	0.579182	+	0.155191i	0.0426777	+	0.999089i	$0.486411\pi$
$12$	−1.18507	+	1.61109i	−0.342101	+	0.465081i
$13$	−3.56375	−	0.547460i	−0.988405	−	0.151838i
$13$	−3.56375	−	0.547460i	−0.988405	−	0.151838i
$14$	−0.935758	−	0.307093i	−0.250092	−	0.0820742i
$15$	4.04911	+	1.08496i	1.04548	+	0.280134i
$16$	−2.71133	+	2.94087i	−0.677831	+	0.735217i
$17$	−2.22516	−	1.28470i	−0.539681	−	0.311585i	0.205269	−	0.978706i	$-0.434193\pi$
$17$	−2.22516	−	1.28470i	−0.539681	−	0.311585i	−0.744950	+	0.667121i	$0.767526\pi$
$18$	1.26196	−	0.638329i	0.297446	−	0.150456i
$19$	3.02991	−	0.811863i	0.695110	−	0.186254i	0.106071	−	0.994359i	$-0.466173\pi$
$19$	3.02991	−	0.811863i	0.695110	−	0.186254i	0.589039	+	0.808105i	$0.299506\pi$
$20$	7.80922	+	3.05053i	1.74619	+	0.682119i
$21$	0.492430	+	0.492430i	0.107457	+	0.107457i
$22$	−1.87573	−	2.09558i	−0.399907	−	0.446778i
$23$	2.57061	+	4.45243i	0.536009	+	0.928395i	0.999114	+	0.0420917i	$0.0134022\pi$
$23$	2.57061	+	4.45243i	0.536009	+	0.928395i	−0.463104	+	0.886304i	$0.653265\pi$
$24$	2.64941	−	0.990268i	0.540808	−	0.202138i
$25$		−	12.5724i		−	2.51448i
$26$	3.79514	+	3.40543i	0.744287	+	0.667859i
$27$	−1.00000			−0.192450
$28$	0.870133	+	1.08755i	0.164440	+	0.205528i
$29$	4.26557	−	2.46273i	0.792096	−	0.457317i	−0.0486038	−	0.998818i	$-0.515477\pi$
$29$	4.26557	−	2.46273i	0.792096	−	0.457317i	0.840700	+	0.541501i	$0.182144\pi$
$30$	−3.95383	−	4.41724i	−0.721867	−	0.806475i
$31$	0.871296	−	0.871296i	0.156489	−	0.156489i	−0.624520	−	0.781009i	$-0.714705\pi$
$31$	0.871296	−	0.871296i	0.156489	−	0.156489i	0.781009	+	0.624520i	$0.214705\pi$
$32$	5.48505	−	1.38355i	0.969629	−	0.244580i
$33$	0.514712	+	1.92093i	0.0895998	+	0.334391i
$34$	1.64012	+	3.24247i	0.281278	+	0.556078i
$35$	1.45964	−	2.52817i	0.246724	−	0.427338i
$36$	−1.98778	−	0.220759i	−0.331296	−	0.0367932i
$37$	−2.61427	+	9.75657i	−0.429783	+	1.60397i	0.323469	+	0.946239i	$0.395151\pi$
$37$	−2.61427	+	9.75657i	−0.429783	+	1.60397i	−0.753252	+	0.657732i	$0.771516\pi$
$38$	−4.21493	−	1.38324i	−0.683752	−	0.224391i
$39$	−1.30776	−	3.36002i	−0.209409	−	0.538035i
$40$	−6.88419	−	9.65335i	−1.08849	−	1.52633i
$41$	1.76270	−	6.57848i	0.275287	−	1.02739i	−0.680361	−	0.732877i	$-0.738177\pi$
$41$	1.76270	−	6.57848i	0.275287	−	1.02739i	0.955649	−	0.294510i	$-0.0951563\pi$
$42$	−0.201928	−	0.963937i	−0.0311582	−	0.148739i
$43$	1.33015	+	0.767960i	0.202845	+	0.117113i	0.597982	−	0.801510i	$-0.295969\pi$
$43$	1.33015	+	0.767960i	0.202845	+	0.117113i	−0.395137	+	0.918622i	$0.629303\pi$
$44$	0.599070	+	3.93201i	0.0903132	+	0.592773i
$45$	1.08496	+	4.04911i	0.161736	+	0.603605i
$46$	0.401888	−	7.25967i	0.0592551	−	1.07038i
$47$	−7.11089	−	7.11089i	−1.03723	−	1.03723i	−0.999280	−	0.0379496i	$-0.987917\pi$
$47$	−7.11089	−	7.11089i	−1.03723	−	1.03723i	−0.0379496	−	0.999280i	$-0.512083\pi$
$48$	−3.90253	−	0.877641i	−0.563282	−	0.126677i
$49$	−5.64218	+	3.25751i	−0.806025	+	0.465359i
$50$	−9.72755	+	14.8831i	−1.37568	+	2.10478i
$51$		−	2.56939i		−	0.359787i
$52$	−1.85778	−	6.96769i	−0.257627	−	0.966244i
$53$			3.80757i			0.523010i	0.965202	+	0.261505i	$0.0842188\pi$
$53$			3.80757i			0.523010i	−0.965202	+	0.261505i	$0.915781\pi$
$54$	1.18379	+	0.773723i	0.161093	+	0.105290i
$55$	7.21961	−	4.16825i	0.973493	−	0.562046i
$56$	−0.188591	−	1.96067i	−0.0252015	−	0.262006i
$57$	2.21805	+	2.21805i	0.293788	+	0.293788i
$58$	−6.95500	−	0.385021i	−0.913236	−	0.0505558i
$59$	3.01758	+	11.2618i	0.392855	+	1.46616i	0.825402	+	0.564545i	$0.190948\pi$
$59$	3.01758	+	11.2618i	0.392855	+	1.46616i	−0.432547	+	0.901611i	$0.642385\pi$
$60$	1.26277	+	8.28825i	0.163023	+	1.07001i
$61$	3.41145	+	1.96960i	0.436791	+	0.252181i	0.702235	−	0.711945i	$-0.252185\pi$
$61$	3.41145	+	1.96960i	0.436791	+	0.252181i	−0.265444	+	0.964126i	$0.585519\pi$
$62$	−1.70557	+	0.357288i	−0.216608	+	0.0453756i
$63$	−0.180242	+	0.672672i	−0.0227083	+	0.0847487i
$64$	−7.56362	−	2.60608i	−0.945453	−	0.325760i
$65$	−12.1862	+	8.94073i	−1.51152	+	1.10896i
$66$	0.876958	−	2.67222i	0.107946	−	0.328927i
$67$	−3.44219	+	12.8464i	−0.420530	+	1.56944i	0.352965	+	0.935636i	$0.385173\pi$
$67$	−3.44219	+	12.8464i	−0.420530	+	1.56944i	−0.773495	+	0.633802i	$0.781493\pi$
$68$	0.567218	−	5.10739i	0.0687853	−	0.619362i
$69$	−2.57061	+	4.45243i	−0.309465	+	0.536009i
$70$	−3.68400	+	1.86346i	−0.440322	+	0.222726i
$71$	−1.12141	−	4.18515i	−0.133087	−	0.496686i	0.866912	−	0.498462i	$-0.166101\pi$
$71$	−1.12141	−	4.18515i	−0.133087	−	0.496686i	−0.999998	+	0.00177558i	$0.999435\pi$
$72$	2.18230	+	1.79932i	0.257187	+	0.212052i
$73$	6.22477	−	6.22477i	0.728554	−	0.728554i	−0.241778	−	0.970332i	$-0.577730\pi$
$73$	6.22477	−	6.22477i	0.728554	−	0.728554i	0.970332	+	0.241778i	$0.0777304\pi$
$74$	10.6436	−	9.52699i	1.23730	−	1.10749i
$75$	10.8880	−	6.28620i	1.25724	−	0.725868i
$76$	3.91934	+	4.89865i	0.449579	+	0.561914i
$77$	1.38493			0.157827
$78$	−1.05162	+	4.98940i	−0.119072	+	0.564938i
$79$			16.9313i			1.90493i	0.304656	+	0.952463i	$0.401459\pi$
$79$			16.9313i			1.90493i	−0.304656	+	0.952463i	$0.598541\pi$
$80$	0.680406	+	16.7540i	0.0760717	+	1.87315i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.17658	+	6.42369i	−0.792521	+	0.709378i
$83$	−0.890596	−	0.890596i	−0.0977556	−	0.0977556i	0.656538	−	0.754293i	$-0.272020\pi$
$83$	−0.890596	−	0.890596i	−0.0977556	−	0.0977556i	−0.754293	+	0.656538i	$0.772020\pi$
$84$	−0.506780	+	1.29733i	−0.0552942	+	0.141551i
$85$	−10.4038	+	2.78768i	−1.12845	+	0.302366i
$86$	−0.980422	−	1.93827i	−0.105722	−	0.209009i
$87$	4.26557	+	2.46273i	0.457317	+	0.264032i
$88$	2.33312	−	5.11818i	0.248711	−	0.545600i
$89$	−8.32774	−	2.23141i	−0.882739	−	0.236529i	−0.211151	−	0.977454i	$-0.567721\pi$
$89$	−8.32774	−	2.23141i	−0.882739	−	0.236529i	−0.671589	+	0.740924i	$0.734388\pi$
$90$	1.84853	−	5.63274i	0.194852	−	0.593743i
$91$	−2.49591	+	0.274075i	−0.261642	+	0.0287309i
$92$	−6.09272	+	8.28296i	−0.635210	+	0.863558i
$93$	1.19021	+	0.318917i	0.123419	+	0.0330701i
$94$	2.91592	+	13.9196i	0.300755	+	1.43570i
$95$	6.57464	−	11.3876i	0.674544	−	1.16834i
$96$	3.94072	+	4.05842i	0.402198	+	0.414211i
$97$	−9.59613	+	2.57127i	−0.974339	+	0.261073i	−0.710659	−	0.703537i	$-0.751603\pi$
$97$	−9.59613	+	2.57127i	−0.974339	+	0.261073i	−0.263680	+	0.964610i	$0.584936\pi$
$98$	9.19955	+	0.509278i	0.929295	+	0.0514448i
$99$	−1.40622	+	1.40622i	−0.141330	+	0.141330i
$100$	23.0307	−	10.0919i	2.30307	−	1.00919i
$101$	−1.12307	−	1.94521i	−0.111749	−	0.193556i	0.804726	−	0.593646i	$-0.202312\pi$
$101$	−1.12307	−	1.94521i	−0.111749	−	0.193556i	−0.916476	+	0.400090i	$0.868979\pi$
$102$	−1.98800	+	3.04162i	−0.196841	+	0.301165i
$103$	−8.58404			−0.845810			−0.422905	−	0.906174i	$-0.638990\pi$
$103$	−8.58404			−0.845810			−0.422905	+	0.906174i	$0.638990\pi$
$104$	−3.19184	+	9.68567i	−0.312986	+	0.949758i
$105$	2.91928			0.284892
$106$	2.94601	−	4.50736i	0.286141	−	0.437793i
$107$	−6.49784	−	11.2546i	−0.628170	−	1.08802i	−0.987919	−	0.154973i	$-0.950471\pi$
$107$	−6.49784	−	11.2546i	−0.628170	−	1.08802i	0.359749	−	0.933049i	$-0.382862\pi$
$108$	−0.802706	−	1.83185i	−0.0772405	−	0.176270i
$109$	4.52092	−	4.52092i	0.433025	−	0.433025i	−0.456631	−	0.889656i	$-0.650944\pi$
$109$	4.52092	−	4.52092i	0.433025	−	0.433025i	0.889656	+	0.456631i	$0.150944\pi$
$110$	−11.7716	−	0.651661i	−1.12237	−	0.0621335i
$111$	−9.75657	+	2.61427i	−0.926053	+	0.248135i
$112$	−1.29376	+	2.46693i	−0.122249	+	0.233103i
$113$	−4.52773	+	7.84226i	−0.425933	+	0.737738i	−0.996507	−	0.0835082i	$-0.973388\pi$
$113$	−4.52773	+	7.84226i	−0.425933	+	0.737738i	0.570574	+	0.821246i	$0.306721\pi$
$114$	−0.909545	−	4.34186i	−0.0851867	−	0.406652i
$115$	20.8174	+	5.57799i	1.94123	+	0.520151i
$116$	7.93534	+	5.83702i	0.736778	+	0.541954i
$117$	2.25599	−	2.81256i	0.208566	−	0.260022i
$118$	5.14131	−	15.6663i	0.473296	−	1.44220i
$119$	−1.72836	−	0.463113i	−0.158438	−	0.0424535i
$120$	4.91795	−	10.7886i	0.448945	−	0.984856i
$121$	−6.10124	−	3.52255i	−0.554658	−	0.320232i
$122$	−2.51450	−	4.97110i	−0.227653	−	0.450062i
$123$	6.57848	−	1.76270i	0.593162	−	0.158937i
$124$	2.29548	+	0.896686i	0.206140	+	0.0805248i
$125$	−22.4458	−	22.4458i	−2.00761	−	2.00761i
$126$	0.733830	−	0.656843i	0.0653747	−	0.0585163i
$127$	−3.83893	−	6.64922i	−0.340650	−	0.590023i	0.643904	−	0.765107i	$-0.277314\pi$
$127$	−3.83893	−	6.64922i	−0.340650	−	0.590023i	−0.984554	+	0.175084i	$0.943980\pi$
$128$	6.93734	+	8.93719i	0.613180	+	0.789943i
$129$			1.53592i			0.135230i
$130$	21.3436	−	1.15515i	1.87196	−	0.101314i
$131$	−11.8697			−1.03706			−0.518532	−	0.855058i	$-0.673521\pi$
$131$	−11.8697			−1.03706			−0.518532	+	0.855058i	$0.673521\pi$
$132$	−3.10569	+	2.48482i	−0.270315	+	0.216275i
$133$	1.89181	−	1.09223i	0.164040	−	0.0947087i
$134$	14.0144	−	12.5441i	1.21066	−	1.08365i
$135$	−2.96415	+	2.96415i	−0.255114	+	0.255114i
$136$	−4.62317	+	5.60719i	−0.396433	+	0.480813i
$137$	−0.266712	−	0.995383i	−0.0227867	−	0.0850413i	0.953596	−	0.301089i	$-0.0973501\pi$
$137$	−0.266712	−	0.995383i	−0.0227867	−	0.0850413i	−0.976383	+	0.216048i	$0.930683\pi$
$138$	6.48800	−	3.28179i	0.552295	−	0.279364i
$139$	−7.48663	+	12.9672i	−0.635007	+	1.09986i	0.351506	+	0.936186i	$0.385670\pi$
$139$	−7.48663	+	12.9672i	−0.635007	+	1.09986i	−0.986514	+	0.163679i	$0.947664\pi$
$140$	5.80287	+	0.644457i	0.490432	+	0.0544666i
$141$	2.60276	−	9.71365i	0.219192	−	0.818037i
$142$	−1.91064	+	5.82199i	−0.160337	+	0.488570i
$143$	−6.56392	−	2.88593i	−0.548903	−	0.241334i
$144$	−1.19121	−	3.81851i	−0.0992671	−	0.318209i
$145$	5.34390	−	19.9437i	0.443787	−	1.65623i
$146$	−12.1851	+	2.55256i	−1.00844	+	0.211251i
$147$	−5.64218	−	3.25751i	−0.465359	−	0.268675i
$148$	−19.9710	+	3.04273i	−1.64161	+	0.250111i
$149$	1.30181	+	4.85842i	0.106648	+	0.398017i	0.998527	−	0.0542577i	$-0.0172792\pi$
$149$	1.30181	+	4.85842i	0.106648	+	0.398017i	−0.891879	+	0.452275i	$0.850613\pi$
$150$	−17.7529	−	0.982781i	−1.44952	−	0.0802437i
$151$	11.3630	+	11.3630i	0.924708	+	0.924708i	0.997358	−	0.0726494i	$-0.0231454\pi$
$151$	11.3630	+	11.3630i	0.924708	+	0.924708i	−0.0726494	+	0.997358i	$0.523145\pi$
$152$	−0.849468	−	8.83144i	−0.0689010	−	0.716325i
$153$	2.22516	−	1.28470i	0.179894	−	0.103862i
$154$	−1.63946	−	1.07155i	−0.132112	−	0.0863480i
$155$		−	5.16531i		−	0.414888i
$156$	5.10530	−	5.09273i	0.408752	−	0.407744i
$157$		−	11.6585i		−	0.930447i	−0.885193	−	0.465223i	$-0.845974\pi$
$157$		−	11.6585i		−	0.930447i	0.885193	−	0.465223i	$-0.154026\pi$
$158$	13.1002	−	20.0431i	1.04219	−	1.59454i
$159$	−3.29745	+	1.90379i	−0.261505	+	0.150980i
$160$	12.1575	−	20.3596i	0.961132	−	1.60957i
$161$	2.53169	+	2.53169i	0.199525	+	0.199525i
$162$	−0.0781697	+	1.41205i	−0.00614159	+	0.110941i
$163$	1.98986	+	7.42627i	0.155858	+	0.581670i	0.999030	+	0.0440267i	$0.0140187\pi$
$163$	1.98986	+	7.42627i	0.155858	+	0.581670i	−0.843172	+	0.537643i	$0.819315\pi$
$164$	13.4657	−	2.05160i	1.05149	−	0.160203i
$165$	7.21961	+	4.16825i	0.562046	+	0.324498i
$166$	0.365202	+	1.74335i	0.0283452	+	0.135310i
$167$	−0.0946296	+	0.353163i	−0.00732266	+	0.0273285i	−0.969491	−	0.245129i	$-0.921170\pi$
$167$	−0.0946296	+	0.353163i	−0.00732266	+	0.0273285i	0.962168	+	0.272457i	$0.0878364\pi$
$168$	1.60370	−	1.14366i	0.123728	−	0.0882353i
$169$	12.4006	+	3.90202i	0.953890	+	0.300155i
$170$	14.4727	+	4.74960i	1.11001	+	0.364278i
$171$	−0.811863	+	3.02991i	−0.0620847	+	0.231703i
$172$	−0.339069	+	3.05307i	−0.0258537	+	0.232794i
$173$	−5.89187	+	10.2050i	−0.447950	+	0.775873i	−0.998252	−	0.0590928i	$-0.981179\pi$
$173$	−5.89187	+	10.2050i	−0.447950	+	0.775873i	0.550302	+	0.834966i	$0.314513\pi$
$174$	−3.14406	−	6.21571i	−0.238351	−	0.471212i
$175$	−2.26607	−	8.45710i	−0.171299	−	0.639297i
$176$	−6.72197	+	4.25365i	−0.506687	+	0.320631i
$177$	−8.24418	+	8.24418i	−0.619671	+	0.619671i
$178$	8.13179	+	9.08488i	0.609503	+	0.680941i
$179$	15.7071	−	9.06850i	1.17400	−	0.677811i	0.219384	−	0.975639i	$-0.429595\pi$
$179$	15.7071	−	9.06850i	1.17400	−	0.677811i	0.954620	+	0.297827i	$0.0962620\pi$
$180$	−6.54645	+	5.23772i	−0.487943	+	0.390396i
$181$	4.36074			0.324131			0.162065	−	0.986780i	$-0.448184\pi$
$181$	4.36074			0.324131			0.162065	+	0.986780i	$0.448184\pi$
$182$	3.16668	+	1.60669i	0.234730	+	0.119096i
$183$			3.93920i			0.291194i
$184$	13.6212	−	5.09119i	1.00417	−	0.375327i
$185$	21.1709	+	36.6691i	1.55651	+	2.69596i
$186$	−1.16221	−	1.29842i	−0.0852171	−	0.0952051i
$187$	−3.61313	−	3.61313i	−0.264218	−	0.264218i
$188$	7.31810	−	18.7340i	0.533727	−	1.36632i
$189$	−0.672672	+	0.180242i	−0.0489297	+	0.0131107i
$190$	−16.5938	+	8.39356i	−1.20384	+	0.608933i
$191$	7.43846	+	4.29459i	0.538228	+	0.310746i	0.744360	−	0.667778i	$-0.232754\pi$
$191$	7.43846	+	4.29459i	0.538228	+	0.310746i	−0.206133	+	0.978524i	$0.566088\pi$
$192$	−1.52488	−	7.85333i	−0.110049	−	0.566765i
$193$	22.0872	+	5.91824i	1.58987	+	0.426004i	0.941963	−	0.335717i	$-0.108978\pi$
$193$	22.0872	+	5.91824i	1.58987	+	0.426004i	0.647906	+	0.761721i	$0.275645\pi$
$194$	13.3492	+	4.38090i	0.958419	+	0.314530i
$195$	−13.8360	−	6.08323i	−0.990818	−	0.435629i
$196$	−10.4963	−	7.72078i	−0.749734	−	0.551484i
$197$	2.57369	+	0.689618i	0.183368	+	0.0491332i	0.349334	−	0.936998i	$-0.386408\pi$
$197$	2.57369	+	0.689618i	0.183368	+	0.0491332i	−0.165967	+	0.986131i	$0.553074\pi$
$198$	2.75269	−	0.576641i	0.195625	−	0.0409801i
$199$	7.55025	−	13.0774i	0.535223	−	0.927034i	−0.463929	−	0.885872i	$-0.653561\pi$
$199$	7.55025	−	13.0774i	0.535223	−	0.927034i	0.999153	−	0.0411616i	$-0.0131058\pi$
$200$	−35.0718	−	5.87267i	−2.47995	−	0.415260i
$201$	−12.8464	+	3.44219i	−0.906116	+	0.242793i
$202$	−0.175580	+	3.17166i	−0.0123537	+	0.223157i
$203$	2.42544	−	2.42544i	0.170233	−	0.170233i
$204$	4.70674	−	2.06247i	0.329538	−	0.144402i
$205$	−14.2747	−	24.7245i	−0.996990	−	1.72684i
$206$	10.1617	+	6.64167i	0.707998	+	0.462747i
$207$	−5.14122			−0.357340
$208$	11.2725	−	8.99617i	0.781606	−	0.623772i
$209$	6.23813			0.431500
$210$	−3.45580	−	2.25871i	−0.238473	−	0.155866i
$211$	3.38488	+	5.86279i	0.233025	+	0.403611i	0.958697	−	0.284430i	$-0.0918043\pi$
$211$	3.38488	+	5.86279i	0.233025	+	0.403611i	−0.725672	+	0.688041i	$0.758471\pi$
$212$	−6.97489	+	3.05636i	−0.479037	+	0.209912i
$213$	3.06374	−	3.06374i	0.209924	−	0.209924i
$214$	−1.01587	+	18.3506i	−0.0694433	+	1.25442i
$215$	6.21911	−	1.66640i	0.424140	−	0.113648i
$216$	−0.467108	+	2.78959i	−0.0317826	+	0.189808i
$217$	0.429052	−	0.743140i	0.0291260	−	0.0504477i
$218$	−8.84974	+	1.85387i	−0.599380	+	0.125560i
$219$	8.50319	+	2.27842i	0.574593	+	0.153962i
$220$	13.4308	+	9.87935i	0.905506	+	0.666066i
$221$	7.22659	+	5.79652i	0.486113	+	0.389916i
$222$	13.5724	+	4.45415i	0.910922	+	0.298943i
$223$	−10.9771	−	2.94131i	−0.735081	−	0.196964i	−0.128190	−	0.991750i	$-0.540917\pi$
$223$	−10.9771	−	2.94131i	−0.735081	−	0.196964i	−0.606891	+	0.794785i	$0.707583\pi$
$224$	3.44027	−	1.91931i	0.229862	−	0.128239i
$225$	10.8880	+	6.28620i	0.725868	+	0.419080i
$226$	11.4276	−	5.78036i	0.760153	−	0.384504i
$227$	−28.8059	+	7.71851i	−1.91191	+	0.512296i	−0.918867	+	0.394567i	$0.870895\pi$
$227$	−28.8059	+	7.71851i	−1.91191	+	0.512296i	−0.993046	+	0.117729i	$0.962439\pi$
$228$	−2.28269	+	5.84357i	−0.151175	+	0.387000i
$229$	13.3996	+	13.3996i	0.885468	+	0.885468i	0.994084	−	0.108616i	$-0.0346419\pi$
$229$	13.3996	+	13.3996i	0.885468	+	0.885468i	−0.108616	+	0.994084i	$0.534642\pi$
$230$	−20.3275	−	22.7100i	−1.34036	−	1.49745i
$231$	0.692464	+	1.19938i	0.0455608	+	0.0789136i
$232$	−4.87752	−	13.0495i	−0.320225	−	0.856745i
$233$		−	17.5537i		−	1.14998i	−0.818159	−	0.574991i	$-0.805005\pi$
$233$		−	17.5537i		−	1.14998i	0.818159	−	0.574991i	$-0.194995\pi$
$234$	−4.84676	+	1.58397i	−0.316842	+	0.103547i
$235$	−42.1555			−2.74992
$236$	−18.2076	+	14.5676i	−1.18521	+	0.948272i
$237$	−14.6630	+	8.46567i	−0.952463	+	0.549905i
$238$	1.68769	+	1.88550i	0.109397	+	0.122219i
$239$	2.83532	−	2.83532i	0.183401	−	0.183401i	−0.609435	−	0.792836i	$-0.708604\pi$
$239$	2.83532	−	2.83532i	0.183401	−	0.183401i	0.792836	+	0.609435i	$0.208604\pi$
$240$	−14.1692	+	8.96623i	−0.914615	+	0.578768i
$241$	−2.26070	−	8.43706i	−0.145625	−	0.543479i	−0.999727	−	0.0233734i	$-0.992559\pi$
$241$	−2.26070	−	8.43706i	−0.145625	−	0.543479i	0.854102	−	0.520105i	$-0.174107\pi$
$242$	4.49709	+	8.89062i	0.289084	+	0.571510i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.869615	+	7.83026i	−0.0556714	+	0.501281i
$245$	−7.06851	+	26.3800i	−0.451591	+	1.68536i
$246$	−9.15137	−	3.00326i	−0.583470	−	0.191481i
$247$	−11.2423	+	1.23452i	−0.715331	+	0.0785503i
$248$	−2.02357	−	2.83755i	−0.128497	−	0.180184i
$249$	0.325981	−	1.21658i	0.0206582	−	0.0770974i
$250$	9.20422	+	43.9378i	0.582126	+	2.77887i
$251$	1.95463	+	1.12851i	0.123375	+	0.0712307i	0.560418	−	0.828210i	$-0.310641\pi$
$251$	1.95463	+	1.12851i	0.123375	+	0.0712307i	−0.437042	+	0.899441i	$0.643974\pi$
$252$	−1.37691	+	0.209782i	−0.0867374	+	0.0132151i
$253$	2.64625	+	9.87593i	0.166368	+	0.620894i
$254$	−0.600176	+	10.8415i	−0.0376584	+	0.680258i
$255$	−7.61608	−	7.61608i	−0.476937	−	0.476937i
$256$	−1.29743	−	15.9473i	−0.0810895	−	0.996707i
$257$	−5.29317	+	3.05601i	−0.330179	+	0.190629i	−0.655921	−	0.754830i	$-0.727719\pi$
$257$	−5.29317	+	3.05601i	−0.330179	+	0.190629i	0.325742	+	0.945459i	$0.394386\pi$
$258$	1.18838	−	1.81820i	0.0739851	−	0.113196i
$259$			7.03417i			0.437082i
$260$	−26.1600	−	15.1466i	−1.62238	−	0.939349i
$261$			4.92545i			0.304878i
$262$	14.0513	+	9.18389i	0.868090	+	0.567383i
$263$	−17.6089	+	10.1665i	−1.08581	+	0.626892i	−0.932457	−	0.361280i	$-0.882340\pi$
$263$	−17.6089	+	10.1665i	−1.08581	+	0.626892i	−0.153351	+	0.988172i	$0.549007\pi$
$264$	5.59903	−	0.538553i	0.344597	−	0.0331457i
$265$	11.2862	+	11.2862i	0.693307	+	0.693307i
$266$	−3.08458	−	0.170759i	−0.189128	−	0.0104699i
$267$	−2.23141	−	8.32774i	−0.136560	−	0.509650i
$268$	−26.2957	+	4.00634i	−1.60627	+	0.244726i
$269$	14.9329	+	8.62150i	0.910473	+	0.525662i	0.880583	−	0.473891i	$-0.157151\pi$
$269$	14.9329	+	8.62150i	0.910473	+	0.525662i	0.0298900	+	0.999553i	$0.490484\pi$
$270$	5.80236	−	1.21550i	0.353120	−	0.0739727i
$271$	0.581405	−	2.16983i	0.0353179	−	0.131808i	−0.946016	−	0.324120i	$-0.894932\pi$
$271$	0.581405	−	2.16983i	0.0353179	−	0.131808i	0.981334	+	0.192312i	$0.0615985\pi$
$272$	9.81126	−	3.06068i	0.594895	−	0.185581i
$273$	−1.48531	−	2.02448i	−0.0898950	−	0.122527i
$274$	−0.454420	+	1.38468i	−0.0274525	+	0.0836517i
$275$	6.47116	−	24.1507i	0.390226	−	1.45634i
$276$	−10.2196	−	1.13497i	−0.615148	−	0.0683173i
$277$	8.95128	−	15.5041i	0.537830	−	0.931550i	−0.461190	−	0.887301i	$-0.652577\pi$
$277$	8.95128	−	15.5041i	0.537830	−	0.931550i	0.999021	−	0.0442483i	$-0.0140893\pi$
$278$	18.8956	−	9.55786i	1.13328	−	0.573242i
$279$	0.318917	+	1.19021i	0.0190930	+	0.0712562i
$280$	−6.37074	−	5.25272i	−0.380725	−	0.313910i
$281$	13.2225	−	13.2225i	0.788790	−	0.788790i	−0.192506	−	0.981296i	$-0.561661\pi$
$281$	13.2225	−	13.2225i	0.788790	−	0.788790i	0.981296	+	0.192506i	$0.0616614\pi$
$282$	−10.5968	+	9.48508i	−0.631030	+	0.564828i
$283$	1.72989	−	0.998751i	0.102831	−	0.0593696i	−0.447702	−	0.894183i	$-0.647758\pi$
$283$	1.72989	−	0.998751i	0.102831	−	0.0593696i	0.550534	+	0.834813i	$0.314424\pi$
$284$	6.76639	−	5.41369i	0.401512	−	0.321244i
$285$	13.1493			0.778896
$286$	5.53738	+	8.49499i	0.327432	+	0.502319i
$287$		−	4.74287i		−	0.279963i
$288$	−1.54433	+	5.44197i	−0.0910008	+	0.320671i
$289$	−5.19911	−	9.00511i	−0.305830	−	0.529713i
$290$	−21.7569	+	19.4744i	−1.27761	+	1.14358i
$291$	−7.02485	−	7.02485i	−0.411804	−	0.411804i
$292$	16.3995	+	6.40616i	0.959707	+	0.374892i
$293$	4.65703	−	1.24785i	0.272067	−	0.0729001i	−0.120206	−	0.992749i	$-0.538356\pi$
$293$	4.65703	−	1.24785i	0.272067	−	0.0729001i	0.392273	+	0.919849i	$0.371689\pi$
$294$	4.15873	+	8.22168i	0.242542	+	0.479498i
$295$	42.3261	+	24.4370i	2.46432	+	1.42278i
$296$	25.9957	+	11.8501i	1.51097	+	0.688773i
$297$	−1.92093	−	0.514712i	−0.111464	−	0.0298666i
$298$	2.21800	−	6.75858i	0.128485	−	0.391514i
$299$	−6.72347	−	17.2746i	−0.388829	−	0.999018i
$300$	20.2552	+	14.8992i	1.16944	+	0.860206i
$301$	1.03317	+	0.276837i	0.0595510	+	0.0159566i
$302$	−4.65957	−	22.2432i	−0.268128	−	1.27995i
$303$	1.12307	−	1.94521i	0.0645185	−	0.111749i
$304$	−5.82750	+	11.1118i	−0.334230	+	0.637306i
$305$	15.9502	−	4.27386i	0.913308	−	0.244720i
$306$	−3.62812	−	0.200849i	−0.207406	−	0.0114818i
$307$	24.1719	−	24.1719i	1.37956	−	1.37956i	0.534218	−	0.845347i	$-0.320606\pi$
$307$	24.1719	−	24.1719i	1.37956	−	1.37956i	0.845347	−	0.534218i	$-0.179394\pi$
$308$	1.11169	+	2.53698i	0.0633445	+	0.144558i
$309$	−4.29202	−	7.43400i	−0.244164	−	0.422905i
$310$	−3.99652	+	6.11463i	−0.226987	+	0.347288i
$311$	−24.4435			−1.38606			−0.693031	−	0.720907i	$-0.743725\pi$
$311$	−24.4435			−1.38606			−0.693031	+	0.720907i	$0.743725\pi$
$312$	−9.98395	+	2.07862i	−0.565230	+	0.117678i
$313$	−17.1596			−0.969917			−0.484958	−	0.874537i	$-0.661165\pi$
$313$	−17.1596			−0.969917			−0.484958	+	0.874537i	$0.661165\pi$
$314$	−9.02042	+	13.8011i	−0.509052	+	0.778844i
$315$	1.45964	+	2.52817i	0.0822413	+	0.142446i
$316$	−31.0156	+	13.5909i	−1.74477	+	0.764548i
$317$	17.0262	−	17.0262i	0.956285	−	0.956285i	−0.0427985	−	0.999084i	$-0.513627\pi$
$317$	17.0262	−	17.0262i	0.956285	−	0.956285i	0.999084	+	0.0427985i	$0.0136273\pi$
$318$	5.37649	+	0.297637i	0.301499	+	0.0166906i
$319$	9.46145	−	2.53519i	0.529740	−	0.141943i
$320$	−30.1445	+	14.6949i	−1.68513	+	0.821471i
$321$	6.49784	−	11.2546i	0.362674	−	0.628170i
$322$	−1.03816	−	4.95581i	−0.0578543	−	0.276177i
$323$	−7.78504	−	2.08600i	−0.433171	−	0.116068i
$324$	1.18507	−	1.61109i	0.0658374	−	0.0895049i
$325$	−6.88289	+	44.8049i	−0.381794	+	2.48533i
$326$	3.39030	−	10.3307i	0.187771	−	0.572166i
$327$	6.17569	+	1.65477i	0.341516	+	0.0915090i
$328$	−17.5279	−	7.99007i	−0.967816	−	0.441178i
$329$	−6.06497	−	3.50161i	−0.334373	−	0.193050i
$330$	−5.32142	−	10.5203i	−0.292935	−	0.579123i
$331$	−11.9421	+	3.19987i	−0.656395	+	0.175881i	−0.571619	−	0.820519i	$-0.693684\pi$
$331$	−11.9421	+	3.19987i	−0.656395	+	0.175881i	−0.0847764	+	0.996400i	$0.527018\pi$
$332$	0.916548	−	2.34632i	0.0503021	−	0.128771i
$333$	−7.14231	−	7.14231i	−0.391396	−	0.391396i
$334$	0.385271	−	0.344852i	0.0210811	−	0.0188695i
$335$	27.8756	+	48.2819i	1.52300	+	2.63792i
$336$	−2.78331	+	0.113035i	−0.151842	+	0.00616655i
$337$			12.1485i			0.661773i	0.943670	+	0.330887i	$0.107348\pi$
$337$			12.1485i			0.661773i	−0.943670	+	0.330887i	$0.892652\pi$
$338$	−11.6606	−	14.2138i	−0.634251	−	0.773127i
$339$	−9.05547			−0.491825
$340$	−13.4578	−	16.8204i	−0.729850	−	0.912214i
$341$	2.12217	−	1.22523i	0.114922	−	0.0663501i
$342$	3.30539	−	2.95862i	0.178735	−	0.159984i
$343$	−6.65520	+	6.65520i	−0.359347	+	0.359347i
$344$	2.76362	−	3.35184i	0.149004	−	0.180719i
$345$	5.57799	+	20.8174i	0.300309	+	1.12077i
$346$	14.8706	−	7.52190i	0.799447	−	0.404380i
$347$	11.4207	−	19.7812i	0.613095	−	1.06191i	−0.377620	−	0.925961i	$-0.623258\pi$
$347$	11.4207	−	19.7812i	0.613095	−	1.06191i	0.990715	−	0.135952i	$-0.0434092\pi$
$348$	−1.08734	+	9.79071i	−0.0582875	+	0.524837i
$349$	4.28348	−	15.9862i	0.229290	−	0.855721i	−0.751351	−	0.659903i	$-0.770597\pi$
$349$	4.28348	−	15.9862i	0.229290	−	0.855721i	0.980640	−	0.195818i	$-0.0627360\pi$
$350$	−3.86090	+	11.7647i	−0.206374	+	0.628851i
$351$	3.56375	+	0.547460i	0.190219	+	0.0292213i
$352$	11.2485	+	0.165514i	0.599549	+	0.00882191i
$353$	2.36680	−	8.83301i	0.125972	−	0.470134i	−0.873900	−	0.486105i	$-0.838417\pi$
$353$	2.36680	−	8.83301i	0.125972	−	0.470134i	0.999872	+	0.0159711i	$0.00508396\pi$
$354$	16.1381	−	3.38065i	0.857729	−	0.179679i
$355$	−15.7294	−	9.08140i	−0.834832	−	0.481991i
$356$	−2.59713	−	17.0463i	−0.137647	−	0.903453i
$357$	−0.463113	−	1.72836i	−0.0245105	−	0.0914745i
$358$	−25.6104	−	1.41776i	−1.35355	−	0.0749311i
$359$	9.99660	+	9.99660i	0.527600	+	0.527600i	0.919856	−	0.392256i	$-0.128305\pi$
$359$	9.99660	+	9.99660i	0.527600	+	0.527600i	−0.392256	+	0.919856i	$0.628305\pi$
$360$	11.8021	−	1.13521i	0.622027	−	0.0598309i
$361$	−7.93323	+	4.58025i	−0.417538	+	0.241066i
$362$	−5.16218	−	3.37400i	−0.271318	−	0.177334i
$363$		−	7.04510i		−	0.369772i
$364$	−2.50554	−	4.35212i	−0.131326	−	0.228113i
$365$		−	36.9023i		−	1.93156i
$366$	3.04785	−	4.66318i	0.159314	−	0.243748i
$367$	−3.87070	+	2.23475i	−0.202049	+	0.116653i	−0.597611	−	0.801786i	$-0.703883\pi$
$367$	−3.87070	+	2.23475i	−0.202049	+	0.116653i	0.395562	+	0.918439i	$0.370550\pi$
$368$	−20.0638	−	4.51215i	−1.04590	−	0.235212i
$369$	4.81578	+	4.81578i	0.250700	+	0.250700i
$370$	3.30984	−	59.7888i	0.172071	−	3.10827i
$371$	0.686284	+	2.56125i	0.0356301	+	0.132973i
$372$	0.371185	+	2.43628i	0.0192450	+	0.126315i
$373$	−20.7860	−	12.0008i	−1.07626	−	0.621379i	−0.146375	−	0.989229i	$-0.546761\pi$
$373$	−20.7860	−	12.0008i	−1.07626	−	0.621379i	−0.929885	+	0.367850i	$0.880094\pi$
$374$	1.48162	+	7.07274i	0.0766126	+	0.365723i
$375$	8.21572	−	30.6615i	0.424258	−	1.58335i
$376$	−23.1580	+	16.5149i	−1.19428	+	0.851691i
$377$	−16.5497	+	6.44130i	−0.852350	+	0.331744i
$378$	0.935758	+	0.307093i	0.0481302	+	0.0157952i
$379$	−3.53204	+	13.1818i	−0.181429	+	0.677101i	0.813938	+	0.580952i	$0.197319\pi$
$379$	−3.53204	+	13.1818i	−0.181429	+	0.677101i	−0.995367	+	0.0961498i	$0.969347\pi$
$380$	26.1379	+	2.90283i	1.34084	+	0.148912i
$381$	3.83893	−	6.64922i	0.196674	−	0.340650i
$382$	−5.48273	−	10.8392i	−0.280521	−	0.554581i
$383$	1.60993	+	6.00834i	0.0822635	+	0.307012i	0.994782	−	0.102024i	$-0.0325318\pi$
$383$	1.60993	+	6.00834i	0.0822635	+	0.307012i	−0.912518	+	0.409036i	$0.865865\pi$
$384$	−4.27116	+	10.4765i	−0.217962	+	0.534627i
$385$	4.10514	−	4.10514i	0.209217	−	0.209217i
$386$	−21.5674	−	24.0953i	−1.09775	−	1.22642i
$387$	−1.33015	+	0.767960i	−0.0676151	+	0.0390376i
$388$	−12.4131	−	15.5147i	−0.630177	−	0.787637i
$389$	14.3237			0.726243			0.363121	−	0.931742i	$-0.381711\pi$
$389$	14.3237			0.726243			0.363121	+	0.931742i	$0.381711\pi$
$390$	11.6722	+	17.9065i	0.591044	+	0.906731i
$391$		−	13.2098i		−	0.668050i
$392$	6.45162	+	17.2610i	0.325856	+	0.871811i
$393$	−5.93487	−	10.2795i	−0.299375	−	0.518532i
$394$	−2.51313	−	2.80768i	−0.126610	−	0.141449i
$395$	50.1871	+	50.1871i	2.52519	+	2.52519i
$396$	−3.70476	−	1.44720i	−0.186171	−	0.0727243i
$397$	22.8531	−	6.12346i	1.14696	−	0.307328i	0.365215	−	0.930923i	$-0.380995\pi$
$397$	22.8531	−	6.12346i	1.14696	−	0.307328i	0.781747	+	0.623595i	$0.214329\pi$
$398$	−19.0562	+	9.63909i	−0.955201	+	0.483164i
$399$	1.89181	+	1.09223i	0.0947087	+	0.0546801i
$400$	36.9738	+	34.0879i	1.84869	+	1.70439i
$401$	29.9488	+	8.02475i	1.49557	+	0.400737i	0.911614	−	0.411048i	$-0.134837\pi$
$401$	29.9488	+	8.02475i	1.49557	+	0.400737i	0.583956	+	0.811785i	$0.301504\pi$
$402$	17.8707	+	5.86474i	0.891310	+	0.292507i
$403$	−3.58208	+	2.62808i	−0.178436	+	0.130914i
$404$	2.66183	−	3.61872i	0.132431	−	0.180038i
$405$	−4.04911	−	1.08496i	−0.201202	−	0.0539119i
$406$	−4.74783	+	0.994588i	−0.235631	+	0.0493606i
$407$	−10.0436	+	17.3961i	−0.497845	+	0.862293i
$408$	−7.16756	−	1.20018i	−0.354847	−	0.0594180i
$409$	−10.8865	+	2.91704i	−0.538305	+	0.144238i	−0.517720	−	0.855550i	$-0.673219\pi$
$409$	−10.8865	+	2.91704i	−0.538305	+	0.144238i	−0.0205842	+	0.999788i	$0.506553\pi$
$410$	−2.23170	+	40.3133i	−0.110216	+	1.99093i
$411$	0.728671	−	0.728671i	0.0359427	−	0.0359427i
$412$	−6.89046	−	15.7246i	−0.339469	−	0.774698i
$413$	4.05968	+	7.03158i	0.199764	+	0.346001i
$414$	6.08611	+	3.97788i	0.299116	+	0.195502i
$415$	−5.27973			−0.259172
$416$	−20.3048	+	1.92778i	−0.995523	+	0.0945171i
$417$	−14.9733			−0.733243
$418$	−7.38462	−	4.82658i	−0.361193	−	0.236076i
$419$	−4.62020	−	8.00241i	−0.225711	−	0.390944i	0.730821	−	0.682569i	$-0.239137\pi$
$419$	−4.62020	−	8.00241i	−0.225711	−	0.390944i	−0.956533	+	0.291625i	$0.905804\pi$
$420$	2.34332	+	5.34767i	0.114342	+	0.260939i
$421$	9.69070	−	9.69070i	0.472296	−	0.472296i	−0.430361	−	0.902657i	$-0.641614\pi$
$421$	9.69070	−	9.69070i	0.472296	−	0.472296i	0.902657	+	0.430361i	$0.141614\pi$
$422$	0.529190	−	9.55925i	0.0257606	−	0.465337i
$423$	9.71365	−	2.60276i	0.472294	−	0.126551i
$424$	10.6216	+	1.77855i	0.515829	+	0.0863738i
$425$	−16.1517	+	27.9756i	−0.783474	+	1.35702i
$426$	−5.99731	+	1.25633i	−0.290571	+	0.0608695i
$427$	2.64979	+	0.710009i	0.128232	+	0.0343597i
$428$	15.4008	−	20.9372i	0.744427	−	1.01204i
$429$	−0.782668	−	7.12749i	−0.0377876	−	0.344119i
$430$	−8.65144	−	2.83920i	−0.417209	−	0.136918i
$431$	−26.1745	−	7.01344i	−1.26078	−	0.337825i	−0.434289	−	0.900773i	$-0.643000\pi$
$431$	−26.1745	−	7.01344i	−1.26078	−	0.337825i	−0.826492	+	0.562948i	$0.809667\pi$
$432$	2.71133	−	2.94087i	0.130449	−	0.141493i
$433$	10.7502	+	6.20662i	0.516621	+	0.298271i	0.735551	−	0.677469i	$-0.236923\pi$
$433$	10.7502	+	6.20662i	0.516621	+	0.298271i	−0.218930	+	0.975741i	$0.570257\pi$
$434$	−1.08289	+	0.547753i	−0.0519805	+	0.0262930i
$435$	19.9437	−	5.34390i	0.956227	−	0.256220i
$436$	11.9106	+	4.65266i	0.570414	+	0.222822i
$437$	11.4035	+	11.4035i	0.545503	+	0.545503i
$438$	−8.30311	−	9.27628i	−0.396738	−	0.443238i
$439$	−0.927728	−	1.60687i	−0.0442780	−	0.0766918i	0.843037	−	0.537856i	$-0.180765\pi$
$439$	−0.927728	−	1.60687i	−0.0442780	−	0.0766918i	−0.887315	+	0.461164i	$0.847432\pi$
$440$	−8.25536	−	22.0868i	−0.393559	−	1.05295i
$441$		−	6.51503i		−	0.310239i
$442$	−4.06984	−	12.4532i	−0.193583	−	0.592340i
$443$	36.2868			1.72404			0.862019	−	0.506875i	$-0.169200\pi$
$443$	36.2868			1.72404			0.862019	+	0.506875i	$0.169200\pi$
$444$	−12.6206	−	15.7741i	−0.598947	−	0.748604i
$445$	−31.2990	+	18.0705i	−1.48371	+	0.856622i
$446$	10.7188	+	11.9751i	0.507550	+	0.567038i
$447$	−3.55661	+	3.55661i	−0.168222	+	0.168222i
$448$	−5.55756	−	0.389754i	−0.262570	−	0.0184141i
$449$	−3.89754	−	14.5458i	−0.183936	−	0.686459i	−0.994856	−	0.101301i	$-0.967699\pi$
$449$	−3.89754	−	14.5458i	−0.183936	−	0.686459i	0.810920	−	0.585157i	$-0.198967\pi$
$450$	−8.02533	−	15.8658i	−0.378318	−	0.747923i
$451$	6.77204	−	11.7295i	0.318883	−	0.552322i
$452$	−18.0003	−	1.99908i	−0.846661	−	0.0940287i
$453$	−4.15915	+	15.5222i	−0.195414	+	0.729294i
$454$	40.0720	+	13.1507i	1.88067	+	0.617192i
$455$	−6.58585	+	8.21065i	−0.308749	+	0.384921i
$456$	7.22352	−	5.15138i	0.338272	−	0.241236i
$457$	−2.22777	+	8.31414i	−0.104211	+	0.388919i	−0.998254	−	0.0590603i	$-0.981190\pi$
$457$	−2.22777	+	8.31414i	−0.104211	+	0.388919i	0.894044	+	0.447980i	$0.147856\pi$
$458$	−5.49469	−	26.2298i	−0.256750	−	1.22564i
$459$	2.22516	+	1.28470i	0.103862	+	0.0599645i
$460$	6.49219	+	42.6117i	0.302700	+	1.98678i
$461$	−2.91598	−	10.8826i	−0.135811	−	0.506852i	−0.999993	−	0.00367400i	$-0.998831\pi$
$461$	−2.91598	−	10.8826i	−0.135811	−	0.506852i	0.864183	−	0.503178i	$-0.167836\pi$
$462$	0.108259	−	1.95559i	0.00503668	−	0.0909823i
$463$	7.71267	+	7.71267i	0.358438	+	0.358438i	0.863237	−	0.504799i	$-0.168433\pi$
$463$	7.71267	+	7.71267i	0.358438	+	0.358438i	−0.504799	+	0.863237i	$0.668433\pi$
$464$	−4.32278	+	19.2217i	−0.200680	+	0.892347i
$465$	4.47329	−	2.58265i	0.207444	−	0.119768i
$466$	−13.5817	+	20.7799i	−0.629161	+	0.962609i
$467$			2.76029i			0.127731i	0.997959	+	0.0638654i	$0.0203428\pi$
$467$			2.76029i			0.127731i	−0.997959	+	0.0638654i	$0.979657\pi$
$468$	6.96308	+	1.87496i	0.321869	+	0.0866701i
$469$			9.26185i			0.427672i
$470$	49.9032	+	32.6167i	2.30186	+	1.50449i
$471$	10.0965	−	5.82923i	0.465223	−	0.268597i
$472$	32.8252	−	3.15735i	1.51090	−	0.145329i
$473$	2.15984	+	2.15984i	0.0993095	+	0.0993095i
$474$	23.9079	+	1.32352i	1.09813	+	0.0607912i
$475$	−10.2071	−	38.0933i	−0.468332	−	1.74784i
$476$	−0.539014	−	3.53783i	−0.0247057	−	0.162156i
$477$	−3.29745	−	1.90379i	−0.150980	−	0.0871684i
$478$	−5.55016	+	1.16266i	−0.253859	+	0.0531790i
$479$	6.97917	−	26.0466i	0.318887	−	1.19010i	−0.601430	−	0.798926i	$-0.705402\pi$
$479$	6.97917	−	26.0466i	0.318887	−	1.19010i	0.920316	−	0.391175i	$-0.127931\pi$
$480$	23.7107	+	0.348885i	1.08224	+	0.0159243i
$481$	14.6579	−	33.3387i	0.668344	−	1.52012i
$482$	−3.85175	+	11.7368i	−0.175442	+	0.534599i
$483$	−0.926663	+	3.45835i	−0.0421646	+	0.157361i
$484$	1.55527	−	14.0041i	0.0706942	−	0.636550i
$485$	−20.8227	+	36.0660i	−0.945512	+	1.63767i
$486$	−1.26196	+	0.638329i	−0.0572435	+	0.0289552i
$487$	−11.2172	−	41.8630i	−0.508298	−	1.89699i	−0.436816	−	0.899551i	$-0.643894\pi$
$487$	−11.2172	−	41.8630i	−0.508298	−	1.89699i	−0.0714815	−	0.997442i	$-0.522773\pi$
$488$	7.08789	−	8.59652i	0.320854	−	0.389146i
$489$	−5.43640	+	5.43640i	−0.245843	+	0.245843i
$490$	28.7785	−	25.7593i	1.30008	−	1.16369i
$491$	−34.6718	+	20.0177i	−1.56471	+	0.903388i	−0.567945	+	0.823066i	$0.692261\pi$
$491$	−34.6718	+	20.0177i	−1.56471	+	0.903388i	−0.996769	+	0.0803219i	$0.974405\pi$
$492$	8.50959	+	10.6358i	0.383642	+	0.479501i
$493$	−12.6554			−0.569972
$494$	14.2637	+	7.23702i	0.641753	+	0.325609i
$495$			8.33649i			0.374697i
$496$	0.200002	+	4.92474i	0.00898033	+	0.221127i
$497$	−1.50868	−	2.61311i	−0.0676735	−	0.117214i
$498$	−1.32719	+	1.18795i	−0.0594726	+	0.0532333i
$499$	17.9893	+	17.9893i	0.805310	+	0.805310i	0.983920	−	0.178610i	$-0.0571599\pi$
$499$	17.9893	+	17.9893i	0.805310	+	0.805310i	−0.178610	+	0.983920i	$0.557160\pi$
$500$	23.0998	−	59.1346i	1.03306	−	2.64458i
$501$	−0.353163	+	0.0946296i	−0.0157781	+	0.00422774i
$502$	−1.44072	−	2.84825i	−0.0643023	−	0.127124i
$503$	−14.4061	−	8.31735i	−0.642335	−	0.370852i	0.143178	−	0.989697i	$-0.454268\pi$
$503$	−14.4061	−	8.31735i	−0.642335	−	0.370852i	−0.785513	+	0.618845i	$0.787601\pi$
$504$	1.79229	+	0.817011i	0.0798348	+	0.0363926i
$505$	−9.09484	−	2.43695i	−0.404715	−	0.108443i
$506$	4.50863	−	13.7385i	0.200433	−	0.610749i
$507$	2.82104	+	12.6902i	0.125287	+	0.563593i
$508$	9.09882	−	12.3697i	0.403695	−	0.548817i
$509$	8.72657	+	2.33828i	0.386798	+	0.103642i	0.446977	−	0.894545i	$-0.352500\pi$
$509$	8.72657	+	2.33828i	0.386798	+	0.103642i	−0.0601790	+	0.998188i	$0.519167\pi$
$510$	3.12309	+	14.9086i	0.138293	+	0.660162i
$511$	3.06526	−	5.30919i	0.135599	−	0.234865i
$512$	−10.8029	+	19.8821i	−0.477426	+	0.878672i
$513$	−3.02991	+	0.811863i	−0.133774	+	0.0358446i
$514$	8.63050	+	0.477775i	0.380675	+	0.0210738i
$515$	−25.4444	+	25.4444i	−1.12121	+	1.12121i
$516$	−2.81357	+	1.23289i	−0.123861	+	0.0542751i
$517$	−9.99946	−	17.3196i	−0.439776	−	0.761714i
$518$	5.44250	−	8.32697i	0.239130	−	0.365866i
$519$	−11.7837			−0.517249
$520$	19.2487	+	38.1709i	0.844111	+	1.67391i
$521$	−5.78549			−0.253467			−0.126734	−	0.991937i	$-0.540449\pi$
$521$	−5.78549			−0.253467			−0.126734	+	0.991937i	$0.540449\pi$
$522$	3.81094	−	5.83069i	0.166800	−	0.255202i
$523$	−0.497104	−	0.861009i	−0.0217368	−	0.0376493i	0.854952	−	0.518707i	$-0.173586\pi$
$523$	−0.497104	−	0.861009i	−0.0217368	−	0.0376493i	−0.876689	+	0.481057i	$0.840253\pi$
$524$	−9.52792	−	21.7436i	−0.416229	−	0.949872i
$525$	6.19103	−	6.19103i	0.270199	−	0.270199i
$526$	28.7112	+	1.58942i	1.25187	+	0.0693021i
$527$	−3.05813	+	0.819422i	−0.133214	+	0.0356946i
$528$	−7.04476	−	3.69457i	−0.306584	−	0.160785i
$529$	−1.71608	+	2.97233i	−0.0746120	+	0.129232i
$530$	−4.62809	−	22.0929i	−0.201031	−	0.959655i
$531$	−11.2618	−	3.01758i	−0.488719	−	0.130952i
$532$	3.51937	+	2.58875i	0.152584	+	0.112237i
$533$	−9.88327	+	22.4790i	−0.428092	+	0.973675i
$534$	−3.80185	+	11.5848i	−0.164522	+	0.501322i
$535$	−52.6209	−	14.0997i	−2.27500	−	0.609585i
$536$	34.2283	+	15.6029i	1.47844	+	0.673944i
$537$	15.7071	+	9.06850i	0.677811	+	0.391334i
$538$	−11.0067	−	21.7599i	−0.474533	−	0.938137i
$539$	−12.5149	+	3.35336i	−0.539055	+	0.144439i
$540$	−7.80922	−	3.05053i	−0.336055	−	0.131274i
$541$	−30.9436	−	30.9436i	−1.33037	−	1.33037i	−0.905038	−	0.425331i	$-0.860158\pi$
$541$	−30.9436	−	30.9436i	−1.33037	−	1.33037i	−0.425331	−	0.905038i	$-0.639842\pi$
$542$	−2.36711	+	2.11878i	−0.101676	+	0.0910093i
$543$	2.18037	+	3.77651i	0.0935685	+	0.162065i
$544$	−13.9826	−	3.96801i	−0.599498	−	0.170127i
$545$		−	26.8014i		−	1.14804i
$546$	0.191904	+	3.54577i	0.00821272	+	0.151745i
$547$	19.9479			0.852912			0.426456	−	0.904508i	$-0.359762\pi$
$547$	19.9479			0.852912			0.426456	+	0.904508i	$0.359762\pi$
$548$	1.60930	−	1.28758i	0.0687458	−	0.0550025i
$549$	−3.41145	+	1.96960i	−0.145597	+	0.0840605i
$550$	−26.3464	+	23.5824i	−1.12342	+	1.00556i
$551$	10.9249	−	10.9249i	0.465417	−	0.465417i
$552$	11.2197	+	9.25071i	0.477542	+	0.393736i
$553$	3.05174	+	11.3892i	0.129773	+	0.484320i
$554$	−22.5923	+	11.4277i	−0.959854	+	0.485517i
$555$	−21.1709	+	36.6691i	−0.898654	+	1.55651i
$556$	−29.7635	−	3.30548i	−1.26225	−	0.140184i
$557$	6.32702	−	23.6127i	0.268084	−	1.00050i	−0.692251	−	0.721657i	$-0.743381\pi$
$557$	6.32702	−	23.6127i	0.268084	−	1.00050i	0.960335	−	0.278848i	$-0.0899524\pi$
$558$	0.543365	−	1.65571i	0.0230025	−	0.0700919i
$559$	−4.31988	−	3.46502i	−0.182711	−	0.146555i
$560$	3.47746	+	11.1473i	0.146949	+	0.471059i
$561$	1.32250	−	4.93563i	0.0558359	−	0.208382i
$562$	−25.8832	+	5.42210i	−1.09182	+	0.228717i
$563$	13.2449	+	7.64697i	0.558208	+	0.322281i	0.752426	−	0.658677i	$-0.228884\pi$
$563$	13.2449	+	7.64697i	0.558208	+	0.322281i	−0.194218	+	0.980958i	$0.562217\pi$
$564$	19.8832	−	3.02934i	0.837233	−	0.127558i
$565$	9.82478	+	36.6666i	0.413331	+	1.54257i
$566$	−2.82058	−	0.156144i	−0.118558	−	0.00656323i
$567$	−0.492430	−	0.492430i	−0.0206801	−	0.0206801i
$568$	−12.1987	+	1.17335i	−0.511845	+	0.0492327i
$569$	−9.58404	+	5.53335i	−0.401784	+	0.231970i	−0.687253	−	0.726418i	$-0.741184\pi$
$569$	−9.58404	+	5.53335i	−0.401784	+	0.231970i	0.285470	+	0.958388i	$0.407850\pi$
$570$	−15.5660	−	10.1739i	−0.651986	−	0.426138i
$571$			1.98113i			0.0829079i	0.999140	+	0.0414539i	$0.0131990\pi$
$571$			1.98113i			0.0829079i	−0.999140	+	0.0414539i	$0.986801\pi$
$572$	0.0176883	−	14.3407i	0.000739585	−	0.599613i
$573$			8.58919i			0.358819i
$574$	−3.66967	+	5.61455i	−0.153169	+	0.234347i
$575$	55.9777	−	32.3188i	2.33443	−	1.34779i
$576$	6.03874	−	5.24725i	0.251614	−	0.218635i
$577$	8.67410	+	8.67410i	0.361107	+	0.361107i	0.864221	−	0.503113i	$-0.167812\pi$
$577$	8.67410	+	8.67410i	0.361107	+	0.361107i	−0.503113	+	0.864221i	$0.667812\pi$
$578$	−0.812825	+	14.6828i	−0.0338091	+	0.610724i
$579$	5.91824	+	22.0872i	0.245954	+	0.917911i
$580$	40.8234	−	6.21973i	1.69510	−	0.258260i
$581$	−0.759602	−	0.438556i	−0.0315136	−	0.0181944i
$582$	2.88065	+	13.7512i	0.119407	+	0.570006i
$583$	−1.95980	+	7.31408i	−0.0811667	+	0.302918i
$584$	−14.4569	−	20.2722i	−0.598231	−	0.838869i
$585$	−1.64978	−	15.0240i	−0.0682099	−	0.621164i
$586$	−6.47843	−	2.12607i	−0.267621	−	0.0878269i
$587$	11.9092	−	44.4458i	0.491546	−	1.83448i	−0.0570250	−	0.998373i	$-0.518161\pi$
$587$	11.9092	−	44.4458i	0.491546	−	1.83448i	0.548572	−	0.836104i	$-0.315172\pi$
$588$	1.43825	−	12.9504i	0.0593125	−	0.534067i
$589$	1.93258	−	3.34732i	0.0796305	−	0.137924i
$590$	−31.1977	−	61.6769i	−1.28439	−	2.53920i
$591$	0.689618	+	2.57369i	0.0283671	+	0.105867i
$592$	−21.6047	−	34.1415i	−0.887947	−	1.40321i
$593$	−3.17599	+	3.17599i	−0.130422	+	0.130422i	−0.769305	−	0.638882i	$-0.779397\pi$
$593$	−3.17599	+	3.17599i	−0.130422	+	0.130422i	0.638882	+	0.769305i	$0.279397\pi$
$594$	1.87573	+	2.09558i	0.0769621	+	0.0859825i
$595$	−6.49586	+	3.75039i	−0.266304	+	0.153751i
$596$	−7.85491	+	6.28460i	−0.321750	+	0.257427i
$597$	15.1005			0.618023
$598$	−5.40661	+	25.6516i	−0.221093	+	1.04897i
$599$		−	1.13724i		−	0.0464662i	−0.999730	−	0.0232331i	$-0.992604\pi$
$599$		−	1.13724i		−	0.0464662i	0.999730	−	0.0232331i	$-0.00739599\pi$
$600$	−12.4500	−	33.3094i	−0.508271	−	1.35985i
$601$	−12.6630	−	21.9329i	−0.516533	−	0.894661i	−0.999816	−	0.0191971i	$-0.993889\pi$
$601$	−12.6630	−	21.9329i	−0.516533	−	0.894661i	0.483283	−	0.875464i	$-0.339444\pi$
$602$	−1.00886	−	1.12710i	−0.0411180	−	0.0459373i
$603$	−9.40423	−	9.40423i	−0.382970	−	0.382970i
$604$	−11.6941	+	29.9364i	−0.475827	+	1.21810i
$605$	−28.5264	+	7.64362i	−1.15976	+	0.310757i
$606$	−2.83452	+	1.43377i	−0.115145	+	0.0582430i
$607$	−10.5590	−	6.09626i	−0.428578	−	0.247440i	0.270163	−	0.962815i	$-0.412922\pi$
$607$	−10.5590	−	6.09626i	−0.428578	−	0.247440i	−0.698741	+	0.715375i	$0.746256\pi$
$608$	15.4960	−	8.64515i	0.628445	−	0.350607i
$609$	3.31321	+	0.887773i	0.134258	+	0.0359744i
$610$	−22.1885	−	7.28173i	−0.898385	−	0.294829i
$611$	21.4485	+	29.2343i	0.867712	+	1.18269i
$612$	4.13952	+	3.04492i	0.167330	+	0.123084i
$613$	19.3336	+	5.18041i	0.780875	+	0.209235i	0.627170	−	0.778882i	$-0.284213\pi$
$613$	19.3336	+	5.18041i	0.780875	+	0.209235i	0.153704	+	0.988117i	$0.450880\pi$
$614$	−47.3168	+	9.91206i	−1.90955	+	0.400018i
$615$	14.2747	−	24.7245i	0.575612	−	0.996990i
$616$	0.646911	−	3.86338i	0.0260648	−	0.155660i
$617$	11.4362	−	3.06431i	0.460403	−	0.123365i	−0.0211600	−	0.999776i	$-0.506736\pi$
$617$	11.4362	−	3.06431i	0.460403	−	0.123365i	0.481563	+	0.876412i	$0.340069\pi$
$618$	−0.671012	+	12.1211i	−0.0269921	+	0.487582i
$619$	20.6410	−	20.6410i	0.829631	−	0.829631i	−0.157835	−	0.987466i	$-0.550451\pi$
$619$	20.6410	−	20.6410i	0.829631	−	0.829631i	0.987466	+	0.157835i	$0.0504514\pi$
$620$	9.46206	−	4.14623i	0.380005	−	0.166516i
$621$	−2.57061	−	4.45243i	−0.103155	−	0.178670i
$622$	28.9359	+	18.9125i	1.16022	+	0.758321i
$623$	−6.00403			−0.240547
$624$	13.4272	+	5.26417i	0.537516	+	0.210736i
$625$	−70.2033			−2.80813
$626$	20.3133	+	13.2768i	0.811882	+	0.530646i
$627$	3.11906	+	5.40238i	0.124563	+	0.215750i
$628$	21.3565	−	9.35832i	0.852218	−	0.373438i
$629$	18.3514	−	18.3514i	0.731719	−	0.731719i
$630$	0.228199	−	4.12217i	0.00909166	−	0.164231i
$631$	26.0022	−	6.96728i	1.03513	−	0.277363i	0.299038	−	0.954241i	$-0.403334\pi$
$631$	26.0022	−	6.96728i	1.03513	−	0.277363i	0.736095	+	0.676878i	$0.236668\pi$
$632$	47.2315	+	7.90876i	1.87877	+	0.314594i
$633$	−3.38488	+	5.86279i	−0.134537	+	0.233025i
$634$	−33.3289	+	6.98184i	−1.32366	+	0.277284i
$635$	−31.0885	−	8.33013i	−1.23371	−	0.330571i
$636$	−6.13433	−	4.51225i	−0.243242	−	0.178922i
$637$	21.8906	−	8.52008i	0.867339	−	0.337578i
$638$	−13.1619	−	4.31942i	−0.521084	−	0.171007i
$639$	4.18515	+	1.12141i	0.165562	+	0.0443622i
$640$	47.0545	+	5.92785i	1.85999	+	0.234319i
$641$	−1.73439	−	1.00135i	−0.0685041	−	0.0395509i	0.465357	−	0.885123i	$-0.345926\pi$
$641$	−1.73439	−	1.00135i	−0.0685041	−	0.0395509i	−0.533861	+	0.845572i	$0.679259\pi$
$642$	−16.4000	+	8.29552i	−0.647256	+	0.327398i
$643$	0.00823808	−	0.00220739i	0.000324878	−	8.70508e-5i	−0.258657	−	0.965969i	$-0.583280\pi$
$643$	0.00823808	−	0.00220739i	0.000324878	−	8.70508e-5i	0.258981	+	0.965882i	$0.416613\pi$
$644$	−2.60547	+	6.66988i	−0.102670	+	0.262830i
$645$	4.55270	+	4.55270i	0.179262	+	0.179262i
$646$	7.60186	+	8.49284i	0.299091	+	0.334146i
$647$	5.39467	+	9.34384i	0.212086	+	0.367344i	0.952367	−	0.304953i	$-0.0986408\pi$
$647$	5.39467	+	9.34384i	0.212086	+	0.367344i	−0.740281	+	0.672298i	$0.765308\pi$
$648$	−2.64941	+	0.990268i	−0.104079	+	0.0389014i
$649$			23.1862i			0.910139i
$650$	42.8144	−	47.7140i	1.67932	−	1.87150i
$651$	0.858105			0.0336318
$652$	−12.0065	+	9.60623i	−0.470211	+	0.376209i
$653$	−37.9051	+	21.8845i	−1.48334	+	0.856408i	−0.999821	−	0.0189241i	$-0.993976\pi$
$653$	−37.9051	+	21.8845i	−1.48334	+	0.856408i	−0.483522	+	0.875332i	$0.660643\pi$
$654$	−6.03037	−	6.73716i	−0.235806	−	0.263444i
$655$	−35.1837	+	35.1837i	−1.37474	+	1.37474i
$656$	14.5672	+	23.0203i	0.568754	+	0.898791i
$657$	2.27842	+	8.50319i	0.0888898	+	0.331741i
$658$	4.47036	+	8.83777i	0.174273	+	0.344532i
$659$	−13.5277	+	23.4306i	−0.526964	+	0.912728i	0.472542	+	0.881308i	$0.343336\pi$
$659$	−13.5277	+	23.4306i	−0.526964	+	0.912728i	−0.999506	+	0.0314205i	$0.989997\pi$
$660$	−1.84036	+	16.5711i	−0.0716358	+	0.645029i
$661$	1.15261	−	4.30161i	0.0448314	−	0.167313i	−0.939881	−	0.341503i	$-0.889064\pi$
$661$	1.15261	−	4.30161i	0.0448314	−	0.167313i	0.984712	+	0.174190i	$0.0557307\pi$
$662$	16.6127	+	5.45188i	0.645670	+	0.211893i
$663$	−1.40664	+	9.15667i	−0.0546295	+	0.355616i
$664$	−2.90040	+	2.06839i	−0.112557	+	0.0802692i
$665$	2.37005	−	8.84515i	0.0919066	−	0.343000i
$666$	2.92881	+	13.9811i	0.113489	+	0.541758i
$667$	21.9302	+	12.6614i	0.849142	+	0.490252i
$668$	−0.722899	+	0.110139i	−0.0279698	+	0.00426140i
$669$	−2.94131	−	10.9771i	−0.113717	−	0.424399i
$670$	4.35805	−	78.7235i	0.168366	−	3.04135i
$671$	5.53937	+	5.53937i	0.213845	+	0.213845i
$672$	3.38231	+	2.01970i	0.130475	+	0.0779117i
$673$	18.0139	−	10.4003i	0.694384	−	0.400903i	−0.110868	−	0.993835i	$-0.535363\pi$
$673$	18.0139	−	10.4003i	0.694384	−	0.400903i	0.805252	+	0.592932i	$0.202030\pi$
$674$	9.39961	−	14.3813i	0.362059	−	0.553947i
$675$			12.5724i			0.483912i
$676$	2.80612	+	25.8481i	0.107928	+	0.994159i
$677$			50.5831i			1.94407i	0.234843	+	0.972033i	$0.424542\pi$
$677$			50.5831i			1.94407i	−0.234843	+	0.972033i	$0.575458\pi$
$678$	10.7197	+	7.00642i	0.411689	+	0.269080i
$679$	−5.99159	+	3.45925i	−0.229936	+	0.132754i
$680$	2.91680	+	30.3244i	0.111854	+	1.16289i
$681$	−21.0874	−	21.0874i	−0.808070	−	0.808070i
$682$	−3.46018	−	0.191552i	−0.132497	−	0.00733491i
$683$	9.13311	+	34.0852i	0.349469	+	1.30424i	0.887304	+	0.461185i	$0.152576\pi$
$683$	9.13311	+	34.0852i	0.349469	+	1.30424i	−0.537835	+	0.843050i	$0.680758\pi$
$684$	−6.20202	+	0.944922i	−0.237140	+	0.0361300i
$685$	−3.74104	−	2.15989i	−0.142938	−	0.0825252i
$686$	13.0276	−	2.72907i	0.497397	−	0.104196i
$687$	−4.90458	+	18.3041i	−0.187121	+	0.698346i
$688$	−5.86493	+	1.82960i	−0.223598	+	0.0697527i
$689$	2.08450	−	13.5692i	0.0794130	−	0.516946i
$690$	9.50370	−	28.9592i	0.361800	−	1.10246i
$691$	0.678727	−	2.53304i	0.0258200	−	0.0963615i	−0.951813	−	0.306678i	$-0.900783\pi$
$691$	0.678727	−	2.53304i	0.0258200	−	0.0963615i	0.977633	+	0.210316i	$0.0674493\pi$
$692$	−23.4235	−	2.60137i	−0.890426	−	0.0988892i
$693$	−0.692464	+	1.19938i	−0.0263045	+	0.0455608i
$694$	−28.8249	+	14.5803i	−1.09418	+	0.553461i
$695$	16.2453	+	60.6283i	0.616220	+	2.29976i
$696$	8.86248	−	10.7488i	0.335931	−	0.407433i
$697$	−12.3737	+	12.3737i	−0.468685	+	0.468685i
$698$	−17.4396	+	15.6100i	−0.660099	+	0.590848i
$699$	15.2020	−	8.77686i	0.574991	−	0.331971i
$700$	13.6731	−	10.9397i	0.516796	−	0.413481i
$701$	−6.34129			−0.239507			−0.119754	−	0.992804i	$-0.538210\pi$
$701$	−6.34129			−0.239507			−0.119754	+	0.992804i	$0.538210\pi$
$702$	−3.79514	−	3.40543i	−0.143238	−	0.128530i
$703$			31.6840i			1.19498i
$704$	−13.1878	−	8.89918i	−0.497034	−	0.335400i
$705$	−21.0778	−	36.5077i	−0.793834	−	1.37496i
$706$	−9.63609	+	8.62517i	−0.362659	+	0.324612i
$707$	−1.10606	−	1.10606i	−0.0415978	−	0.0415978i
$708$	−21.7197	−	8.48442i	−0.816278	−	0.318864i
$709$	−11.0654	+	2.96497i	−0.415570	+	0.111352i	−0.460545	−	0.887636i	$-0.652346\pi$
$709$	−11.0654	+	2.96497i	−0.415570	+	0.111352i	0.0449746	+	0.998988i	$0.485679\pi$
$710$	11.5938	+	22.9207i	0.435109	+	0.860198i
$711$	−14.6630	−	8.46567i	−0.549905	−	0.317488i
$712$	−10.1147	+	22.1887i	−0.379064	+	0.831556i
$713$	6.11915	+	1.63962i	0.229164	+	0.0614043i
$714$	−0.789044	+	2.40433i	−0.0295292	+	0.0899798i
$715$	−28.0108	+	10.9021i	−1.04755	+	0.407716i
$716$	29.2203	+	21.4937i	1.09201	+	0.803256i
$717$	3.87312	+	1.03780i	0.144644	+	0.0387573i
$718$	−4.09925	−	19.5684i	−0.152983	−	0.730288i
$719$	26.0436	−	45.1088i	0.971262	−	1.68227i	0.279505	−	0.960144i	$-0.409830\pi$
$719$	26.0436	−	45.1088i	0.971262	−	1.68227i	0.691757	−	0.722131i	$-0.256837\pi$
$720$	−14.8496	−	7.78774i	−0.553411	−	0.290232i
$721$	−5.77424	+	1.54720i	−0.215044	+	0.0576209i
$722$	12.9351	+	0.716074i	0.481395	+	0.0266495i
$723$	6.17636	−	6.17636i	0.229701	−	0.229701i
$724$	3.50039	+	7.98820i	0.130091	+	0.296879i
$725$	−30.9624	−	53.6285i	−1.14991	−	1.99171i
$726$	−5.45095	+	8.33990i	−0.202304	+	0.309523i
$727$	22.1920			0.823057			0.411529	−	0.911397i	$-0.364995\pi$
$727$	22.1920			0.823057			0.411529	+	0.911397i	$0.364995\pi$
$728$	−0.401300	+	7.09058i	−0.0148732	+	0.262794i
$729$	1.00000			0.0370370
$730$	−28.5522	+	43.6845i	−1.05676	+	1.61684i
$731$	−1.97319	−	3.41767i	−0.0729812	−	0.126407i
$732$	−7.21601	+	3.16202i	−0.266711	+	0.116872i
$733$	9.37264	−	9.37264i	0.346186	−	0.346186i	−0.512500	−	0.858687i	$-0.671281\pi$
$733$	9.37264	−	9.37264i	0.346186	−	0.346186i	0.858687	+	0.512500i	$0.171281\pi$
$734$	6.31117	+	0.349380i	0.232950	+	0.0128958i
$735$	−26.3800	+	7.06851i	−0.973043	+	0.260726i
$736$	20.2601	+	20.8652i	0.746797	+	0.769102i
$737$	−13.2244	+	22.9053i	−0.487127	+	0.843728i
$738$	−1.97478	−	9.42695i	−0.0726928	−	0.347011i
$739$	−20.3466	−	5.45186i	−0.748463	−	0.200550i	−0.135627	−	0.990760i	$-0.543305\pi$
$739$	−20.3466	−	5.45186i	−0.748463	−	0.200550i	−0.612836	+	0.790210i	$0.709971\pi$
$740$	−50.1781	+	68.2163i	−1.84458	+	2.50768i
$741$	−6.69027	−	9.11886i	−0.245773	−	0.334990i
$742$	1.16928	−	3.56297i	0.0429256	−	0.130801i
$743$	−35.3311	−	9.46694i	−1.29617	−	0.347308i	−0.456171	−	0.889892i	$-0.650779\pi$
$743$	−35.3311	−	9.46694i	−1.29617	−	0.347308i	−0.840001	+	0.542584i	$0.817446\pi$
$744$	1.44560	−	3.17124i	0.0529984	−	0.116263i
$745$	18.2599	+	10.5423i	0.668990	+	0.386241i
$746$	15.3209	+	30.2890i	0.560939	+	1.10896i
$747$	1.21658	−	0.325981i	0.0445122	−	0.0119270i
$748$	3.71842	−	9.51898i	0.135959	−	0.348048i
$749$	−6.39946	−	6.39946i	−0.233831	−	0.233831i
$750$	−33.4492	+	29.9400i	−1.22139	+	1.09325i
$751$	10.3852	+	17.9877i	0.378961	+	0.656380i	0.990911	−	0.134516i	$-0.0429481\pi$
$751$	10.3852	+	17.9877i	0.378961	+	0.656380i	−0.611950	+	0.790896i	$0.709615\pi$
$752$	40.1921	−	1.63227i	1.46566	−	0.0595227i
$753$			2.25701i			0.0822501i
$754$	24.5751	+	5.17970i	0.894971	+	0.188634i
$755$	67.3634			2.45160
$756$	−0.870133	−	1.08755i	−0.0316464	−	0.0395538i
$757$	−0.213188	+	0.123084i	−0.00774847	+	0.00447358i	−0.503869	−	0.863780i	$-0.668091\pi$
$757$	−0.213188	+	0.123084i	−0.00774847	+	0.00447358i	0.496121	+	0.868254i	$0.334757\pi$
$758$	14.3802	−	12.8716i	0.522313	−	0.467517i
$759$	−7.22968	+	7.22968i	−0.262421	+	0.262421i
$760$	−28.6957	−	23.6598i	−1.04090	−	0.858231i
$761$	−7.95725	−	29.6969i	−0.288450	−	1.07651i	−0.946281	−	0.323345i	$-0.895193\pi$
$761$	−7.95725	−	29.6969i	−0.288450	−	1.07651i	0.657831	−	0.753165i	$-0.271474\pi$
$762$	−9.68913	+	4.90100i	−0.351000	+	0.177544i
$763$	2.22623	−	3.85595i	0.0805951	−	0.139595i
$764$	−1.89614	+	17.0734i	−0.0686001	+	0.617694i
$765$	2.78768	−	10.4038i	0.100789	−	0.376149i
$766$	2.74297	−	8.35823i	0.0991076	−	0.301995i
$767$	−4.58852	−	41.7861i	−0.165682	−	1.50881i
$768$	13.1621	−	9.09726i	0.474945	−	0.328269i
$769$	−13.9243	+	51.9662i	−0.502124	+	1.87395i	−0.0163491	+	0.999866i	$0.505204\pi$
$769$	−13.9243	+	51.9662i	−0.502124	+	1.87395i	−0.485774	+	0.874084i	$0.661462\pi$
$770$	−8.03585	+	1.68337i	−0.289592	+	0.0606646i
$771$	−5.29317	−	3.05601i	−0.190629	−	0.110060i
$772$	6.88820	+	45.2109i	0.247912	+	1.62718i
$773$	1.67429	+	6.24853i	0.0602199	+	0.224744i	0.989477	−	0.144690i	$-0.0462184\pi$
$773$	1.67429	+	6.24853i	0.0602199	+	0.224744i	−0.929257	+	0.369434i	$0.879552\pi$
$774$	2.16880	+	0.120062i	0.0779559	+	0.00431556i
$775$	−10.9543	−	10.9543i	−0.393490	−	0.393490i
$776$	2.69038	+	27.9703i	0.0965789	+	1.00408i
$777$	−6.09177	+	3.51709i	−0.218541	+	0.126175i
$778$	−16.9563	−	11.0826i	−0.607912	−	0.397331i
$779$		−	21.3633i		−	0.765420i
$780$	0.0372850	−	30.2285i	0.00133502	−	1.08235i
$781$		−	8.61658i		−	0.308326i
$782$	−10.2207	+	15.6376i	−0.365493	+	0.559200i
$783$	−4.26557	+	2.46273i	−0.152439	+	0.0880107i
$784$	5.71786	−	25.4251i	0.204209	−	0.908039i
$785$	−34.5575	−	34.5575i	−1.23341	−	1.23341i
$786$	−0.927854	+	16.7607i	−0.0330955	+	0.597834i
$787$	−7.39790	−	27.6093i	−0.263707	−	0.984166i	−0.963037	−	0.269368i	$-0.913185\pi$
$787$	−7.39790	−	27.6093i	−0.263707	−	0.984166i	0.699331	−	0.714798i	$-0.253481\pi$
$788$	0.802642	+	5.26816i	0.0285929	+	0.187671i
$789$	−17.6089	−	10.1665i	−0.626892	−	0.361936i
$790$	−20.5800	−	98.2418i	−0.732202	−	3.49528i
$791$	−1.63217	+	6.09136i	−0.0580334	+	0.216584i
$792$	3.26592	+	4.57963i	0.116049	+	0.162730i
$793$	−11.0793	−	8.88679i	−0.393436	−	0.315579i
$794$	−31.7910	−	10.4331i	−1.12822	−	0.370255i
$795$	−4.13105	+	15.4173i	−0.146513	+	0.546794i
$796$	30.0165	+	3.33358i	1.06391	+	0.118156i
$797$	−10.7845	+	18.6794i	−0.382008	+	0.661657i	−0.991349	−	0.131251i	$-0.958101\pi$
$797$	−10.7845	+	18.6794i	−0.382008	+	0.661657i	0.609341	+	0.792908i	$0.291434\pi$
$798$	−1.39441	−	2.75671i	−0.0493616	−	0.0975864i
$799$	6.68753	+	24.9582i	0.236588	+	0.882958i
$800$	−17.3946	−	68.9603i	−0.614991	−	2.43811i
$801$	6.09633	−	6.09633i	0.215403	−	0.215403i
$802$	−29.2440	−	32.6716i	−1.03264	−	1.15368i
$803$	15.1613	−	8.75338i	0.535031	−	0.308900i
$804$	−16.6175	−	20.7696i	−0.586052	−	0.732487i
$805$	15.0086			0.528985
$806$	6.27382	−	0.339551i	0.220986	−	0.0119602i
$807$			17.2430i			0.606982i
$808$	−5.95093	+	2.22427i	−0.209353	+	0.0782497i
$809$	−8.10164	−	14.0325i	−0.284839	−	0.493355i	0.687731	−	0.725965i	$-0.258607\pi$
$809$	−8.10164	−	14.0325i	−0.284839	−	0.493355i	−0.972570	+	0.232610i	$0.925273\pi$
$810$	3.95383	+	4.41724i	0.138923	+	0.155206i
$811$	23.3509	+	23.3509i	0.819962	+	0.819962i	0.986102	−	0.166141i	$-0.0531306\pi$
$811$	23.3509	+	23.3509i	0.819962	+	0.819962i	−0.166141	+	0.986102i	$0.553131\pi$
$812$	6.38995	+	2.49612i	0.224243	+	0.0875966i
$813$	2.16983	−	0.581405i	0.0760994	−	0.0203908i
$814$	25.3493	−	12.8223i	0.888493	−	0.449421i
$815$	27.9108	+	16.1143i	0.977674	+	0.564460i
$816$	7.55626	+	6.96646i	0.264522	+	0.243875i
$817$	4.65371	+	1.24696i	0.162813	+	0.0436255i
$818$	15.1443	+	4.97001i	0.529509	+	0.173772i
$819$	1.01060	−	2.29856i	0.0353131	−	0.0803181i
$820$	33.8332	−	45.9956i	1.18151	−	1.60624i
$821$	−38.1381	−	10.2191i	−1.33103	−	0.356648i	−0.477931	−	0.878397i	$-0.658613\pi$
$821$	−38.1381	−	10.2191i	−1.33103	−	0.356648i	−0.853099	+	0.521749i	$0.825280\pi$
$822$	−1.42638	+	0.298802i	−0.0497507	+	0.0104219i
$823$	−12.4827	+	21.6206i	−0.435119	+	0.753648i	−0.997305	−	0.0733626i	$-0.976627\pi$
$823$	−12.4827	+	21.6206i	−0.435119	+	0.753648i	0.562187	+	0.827010i	$0.309960\pi$
$824$	−4.00967	+	23.9459i	−0.139683	+	0.834197i
$825$	24.1507	−	6.47116i	0.840820	−	0.225297i
$826$	0.634688	−	11.4650i	0.0220836	−	0.398917i
$827$	5.54733	−	5.54733i	0.192900	−	0.192900i	−0.604048	−	0.796948i	$-0.706447\pi$
$827$	5.54733	−	5.54733i	0.192900	−	0.192900i	0.796948	+	0.604048i	$0.206447\pi$
$828$	−4.12689	−	9.41793i	−0.143419	−	0.327296i
$829$	9.15893	+	15.8637i	0.318103	+	0.550970i	0.980092	−	0.198543i	$-0.0636209\pi$
$829$	9.15893	+	15.8637i	0.318103	+	0.550970i	−0.661989	+	0.749513i	$0.730288\pi$
$830$	6.25007	+	4.08504i	0.216943	+	0.141794i
$831$	17.9026			0.621033
$832$	25.5281	+	13.4282i	0.885028	+	0.465538i
$833$	16.7397			0.579995
$834$	17.7252	+	11.5851i	0.613772	+	0.401161i
$835$	0.766331	+	1.32732i	0.0265200	+	0.0459340i
$836$	5.00738	+	11.4273i	0.173184	+	0.395221i
$837$	−0.871296	+	0.871296i	−0.0301164	+	0.0301164i
$838$	−0.722319	+	13.0479i	−0.0249521	+	0.450733i
$839$	−31.3808	+	8.40845i	−1.08338	+	0.290292i	−0.755982	−	0.654593i	$-0.772840\pi$
$839$	−31.3808	+	8.40845i	−1.08338	+	0.290292i	−0.327403	+	0.944885i	$0.606173\pi$
$840$	1.36362	−	8.14358i	0.0470492	−	0.280980i
$841$	−2.36995	+	4.10487i	−0.0817224	+	0.141547i
$842$	−18.9696	+	3.97381i	−0.653737	+	0.136947i
$843$	18.0623	+	4.83978i	0.622099	+	0.166691i
$844$	−8.02266	+	10.9067i	−0.276151	+	0.375423i
$845$	48.3234	−	25.1910i	1.66237	−	0.866597i
$846$	−13.5127	−	4.43455i	−0.464577	−	0.152463i
$847$	−4.73904	−	1.26982i	−0.162835	−	0.0436316i
$848$	−11.1976	−	10.3236i	−0.384526	−	0.354513i
$849$	1.72989	+	0.998751i	0.0593696	+	0.0342770i
$850$	40.7656	−	20.6202i	1.39825	−	0.707268i
$851$	−50.1607	+	13.4405i	−1.71949	+	0.460735i
$852$	8.07159	+	3.15302i	0.276528	+	0.108021i
$853$	29.3721	+	29.3721i	1.00568	+	1.00568i	0.999984	+	0.00569706i	$0.00181344\pi$
$853$	29.3721	+	29.3721i	1.00568	+	1.00568i	0.00569706	+	0.999984i	$0.498187\pi$
$854$	−2.58744	−	2.89070i	−0.0885403	−	0.0989178i
$855$	6.57464	+	11.3876i	0.224848	+	0.389448i
$856$	−34.4309	+	12.8692i	−1.17682	+	0.439860i
$857$		−	1.98662i		−	0.0678615i	−0.999424	−	0.0339308i	$-0.989197\pi$
$857$		−	1.98662i		−	0.0678615i	0.999424	−	0.0339308i	$-0.0108026\pi$
$858$	−4.58819	+	9.04300i	−0.156638	+	0.308723i
$859$	23.3326			0.796099			0.398049	−	0.917364i	$-0.369687\pi$
$859$	23.3326			0.796099			0.398049	+	0.917364i	$0.369687\pi$
$860$	8.04472	+	10.0548i	0.274323	+	0.342866i
$861$	4.10745	−	2.37144i	0.139981	−	0.0808183i
$862$	25.5586	+	28.5542i	0.870529	+	0.972561i
$863$	10.8333	−	10.8333i	0.368770	−	0.368770i	−0.498258	−	0.867029i	$-0.666027\pi$
$863$	10.8333	−	10.8333i	0.368770	−	0.368770i	0.867029	+	0.498258i	$0.166027\pi$
$864$	−5.48505	+	1.38355i	−0.186605	+	0.0470694i
$865$	12.7848	+	47.7136i	0.434697	+	1.62231i
$866$	−7.92373	−	15.6650i	−0.269259	−	0.532318i
$867$	5.19911	−	9.00511i	0.176571	−	0.305830i
$868$	1.70572	+	0.189435i	0.0578960	+	0.00642983i
$869$	−8.71476	+	32.5239i	−0.295628	+	1.10330i
$870$	−27.7438	−	9.10485i	−0.940603	−	0.308683i
$871$	19.3000	−	43.8969i	0.653955	−	1.48739i
$872$	−10.4997	−	14.7233i	−0.355566	−	0.498592i
$873$	2.57127	−	9.59613i	0.0870245	−	0.324780i
$874$	−4.67617	−	22.3224i	−0.158174	−	0.755068i
$875$	−19.1443	−	11.0530i	−0.647195	−	0.373658i
$876$	2.65184	+	17.4055i	0.0895975	+	0.588076i
$877$	−0.773421	−	2.88645i	−0.0261166	−	0.0974684i	0.951637	−	0.307224i	$-0.0994000\pi$
$877$	−0.773421	−	2.88645i	−0.0261166	−	0.0974684i	−0.977754	+	0.209755i	$0.932733\pi$
$878$	−0.145040	+	2.62000i	−0.00489488	+	0.0884207i
$879$	3.40918	+	3.40918i	0.114989	+	0.114989i
$880$	−7.31645	+	32.5334i	−0.246638	+	1.09670i
$881$	24.4004	−	14.0876i	0.822069	−	0.474622i	−0.0290604	−	0.999578i	$-0.509252\pi$
$881$	24.4004	−	14.0876i	0.822069	−	0.474622i	0.851129	+	0.524956i	$0.175918\pi$
$882$	−5.04082	+	7.71241i	−0.169733	+	0.259690i
$883$		−	0.751658i		−	0.0252953i	−0.999920	−	0.0126477i	$-0.995974\pi$
$883$		−	0.751658i		−	0.0252953i	0.999920	−	0.0126477i	$-0.00402598\pi$
$884$	−4.81751	+	17.8909i	−0.162031	+	0.601736i
$885$			48.8740i			1.64288i
$886$	−42.9559	−	28.0759i	−1.44313	−	0.943229i
$887$	24.4654	−	14.1251i	0.821467	−	0.474274i	−0.0294551	−	0.999566i	$-0.509377\pi$
$887$	24.4654	−	14.1251i	0.821467	−	0.474274i	0.850922	+	0.525292i	$0.176044\pi$
$888$	2.73536	+	28.4380i	0.0917927	+	0.954316i
$889$	−3.78081	−	3.78081i	−0.126804	−	0.126804i
$890$	51.0328	+	2.82513i	1.71062	+	0.0946984i
$891$	−0.514712	−	1.92093i	−0.0172435	−	0.0643536i
$892$	−3.42337	−	22.4694i	−0.114623	−	0.752330i
$893$	−27.3184	−	15.7723i	−0.914176	−	0.527800i
$894$	6.96210	−	1.45844i	0.232847	−	0.0487776i
$895$	19.6778	−	73.4386i	0.657757	−	2.45478i
$896$	6.27741	+	4.76140i	0.209714	+	0.159067i
$897$	11.5985	−	14.4600i	0.387264	−	0.482806i
$898$	−6.64056	+	20.2348i	−0.221598	+	0.675242i
$899$	1.57081	−	5.86234i	0.0523894	−	0.195520i
$900$	−2.77548	+	24.9912i	−0.0925158	+	0.833039i
$901$	4.89158	−	8.47246i	0.162962	−	0.282259i
$902$	−17.0921	+	8.64558i	−0.569103	+	0.287866i
$903$	0.276837	+	1.03317i	0.00921256	+	0.0343818i
$904$	19.7618	+	16.2937i	0.657266	+	0.541920i
$905$	12.9259	−	12.9259i	0.429671	−	0.429671i
$906$	16.9334	−	15.1569i	0.562574	−	0.503554i
$907$	44.9766	−	25.9673i	1.49342	−	0.862229i	0.493452	−	0.869773i	$-0.335735\pi$
$907$	44.9766	−	25.9673i	1.49342	−	0.862229i	0.999972	+	0.00754401i	$0.00240136\pi$
$908$	−37.2618	−	46.5723i	−1.23658	−	1.54555i
$909$	2.24613			0.0744996
$910$	14.1490	−	4.62405i	0.469035	−	0.153286i
$911$		−	11.9647i		−	0.396409i	−0.980161	−	0.198204i	$-0.936489\pi$
$911$		−	11.9647i		−	0.396409i	0.980161	−	0.198204i	$-0.0635110\pi$
$912$	−12.5369	+	0.509142i	−0.415137	+	0.0168594i
$913$	−1.25237	−	2.16917i	−0.0414475	−	0.0717891i
$914$	9.07005	−	8.11851i	0.300010	−	0.268536i
$915$	11.6764	+	11.6764i	0.386010	+	0.386010i
$916$	−13.7900	+	35.3018i	−0.455635	+	1.16641i
$917$	−7.98444	+	2.13943i	−0.263670	+	0.0706500i
$918$	−1.64012	−	3.24247i	−0.0541320	−	0.107017i
$919$	28.7810	+	16.6167i	0.949398	+	0.548135i	0.892894	−	0.450267i	$-0.148671\pi$
$919$	28.7810	+	16.6167i	0.949398	+	0.548135i	0.0565042	+	0.998402i	$0.482005\pi$
$920$	25.2843	−	55.4664i	0.833597	−	1.82867i
$921$	33.0195	+	8.84754i	1.08803	+	0.291536i
$922$	−4.96820	+	15.1388i	−0.163619	+	0.498571i
$923$	1.70521	+	15.5287i	0.0561276	+	0.511135i
$924$	−1.64124	+	2.23124i	−0.0539929	+	0.0734024i
$925$	122.664	+	32.8676i	4.03315	+	1.08068i
$926$	−3.16269	−	15.0976i	−0.103933	−	0.496139i
$927$	4.29202	−	7.43400i	0.140968	−	0.244164i
$928$	19.9896	−	19.4098i	0.656189	−	0.637159i
$929$	−6.66660	+	1.78631i	−0.218724	+	0.0586070i	−0.366517	−	0.930411i	$-0.619450\pi$
$929$	−6.66660	+	1.78631i	−0.218724	+	0.0586070i	0.147793	+	0.989018i	$0.452783\pi$
$930$	−7.29368	−	0.403771i	−0.239169	−	0.0132402i
$931$	−14.4507	+	14.4507i	−0.473601	+	0.473601i
$932$	32.1557	−	14.0905i	1.05330	−	0.461549i
$933$	−12.2217	−	21.1687i	−0.400122	−	0.693031i
$934$	2.13570	−	3.26759i	0.0698821	−	0.106919i
$935$	−21.4197			−0.700500
$936$	−6.79211	−	7.60705i	−0.222007	−	0.248644i
$937$	38.0185			1.24201			0.621005	−	0.783807i	$-0.286725\pi$
$937$	38.0185			1.24201			0.621005	+	0.783807i	$0.286725\pi$
$938$	7.16610	−	10.9641i	0.233981	−	0.357989i
$939$	−8.57979	−	14.8606i	−0.279991	−	0.484958i
$940$	−33.8385	−	77.2224i	−1.10369	−	2.51872i
$941$	24.9793	−	24.9793i	0.814301	−	0.814301i	−0.170974	−	0.985276i	$-0.554691\pi$
$941$	24.9793	−	24.9793i	0.814301	−	0.814301i	0.985276	+	0.170974i	$0.0546915\pi$
$942$	−16.4623	−	0.911339i	−0.536372	−	0.0296930i
$943$	33.8214	−	9.06243i	1.10138	−	0.295113i
$944$	−41.3010	−	21.6600i	−1.34423	−	0.704972i
$945$	−1.45964	+	2.52817i	−0.0474820	+	0.0822413i
$946$	−0.885674	−	4.22791i	−0.0287958	−	0.137461i
$947$	−16.0409	−	4.29814i	−0.521258	−	0.139671i	−0.0114096	−	0.999935i	$-0.503632\pi$
$947$	−16.0409	−	4.29814i	−0.521258	−	0.139671i	−0.509848	+	0.860264i	$0.670299\pi$
$948$	−27.2779	−	20.0649i	−0.885944	−	0.651677i
$949$	−25.5913	+	18.7757i	−0.830729	+	0.609484i
$950$	−17.3906	+	52.9918i	−0.564227	+	1.71928i
$951$	23.2582	+	6.23201i	0.754198	+	0.202087i
$952$	−2.09922	+	4.60509i	−0.0680362	+	0.149252i
$953$	2.43645	+	1.40669i	0.0789244	+	0.0455670i	0.538943	−	0.842342i	$-0.318824\pi$
$953$	2.43645	+	1.40669i	0.0789244	+	0.0455670i	−0.460018	+	0.887909i	$0.652157\pi$
$954$	2.43048	+	4.80499i	0.0786898	+	0.155567i
$955$	34.7786	−	9.31889i	1.12541	−	0.301552i
$956$	7.46980	+	2.91794i	0.241590	+	0.0943729i
$957$	6.92626	+	6.92626i	0.223894	+	0.223894i
$958$	−28.4147	+	25.4337i	−0.918038	+	0.821727i
$959$	−0.358819	−	0.621493i	−0.0115869	−	0.0200691i
$960$	−27.7984	−	18.7585i	−0.897191	−	0.605427i
$961$			29.4817i			0.951022i
$962$	−43.1468	+	28.1248i	−1.39111	+	0.906781i
$963$	12.9957			0.418780
$964$	13.6407	−	10.9137i	0.439338	−	0.351508i
$965$	83.0123	−	47.9272i	2.67226	−	1.54283i
$966$	3.77278	−	3.37698i	0.121387	−	0.108652i
$967$	−1.15374	+	1.15374i	−0.0371019	+	0.0371019i	−0.725414	−	0.688312i	$-0.758352\pi$
$967$	−1.15374	+	1.15374i	−0.0371019	+	0.0371019i	0.688312	+	0.725414i	$0.258352\pi$
$968$	−12.6764	+	15.3745i	−0.407435	+	0.494156i
$969$	−2.08600	−	7.78504i	−0.0670118	−	0.250092i
$970$	52.5548	−	26.5835i	1.68743	−	0.853545i
$971$	−24.7483	+	42.8653i	−0.794211	+	1.37561i	0.129128	+	0.991628i	$0.458782\pi$
$971$	−24.7483	+	42.8653i	−0.794211	+	1.37561i	−0.923339	+	0.383986i	$0.874551\pi$
$972$	1.98778	+	0.220759i	0.0637580	+	0.00708086i
$973$	−2.69881	+	10.0721i	−0.0865198	+	0.322896i
$974$	−19.1116	+	58.2358i	−0.612376	+	1.86600i
$975$	−42.2436	+	16.4417i	−1.35288	+	0.526555i
$976$	−15.0419	+	4.69240i	−0.481479	+	0.150200i
$977$	−10.1712	+	37.9594i	−0.325405	+	1.21443i	0.588498	+	0.808498i	$0.299719\pi$
$977$	−10.1712	+	37.9594i	−0.325405	+	1.21443i	−0.913904	+	0.405931i	$0.866947\pi$
$978$	10.6418	−	2.22928i	0.340288	−	0.0712845i
$979$	−14.8485	−	8.57277i	−0.474560	−	0.273987i
$980$	−53.9981	+	8.22700i	−1.72491	+	0.262802i
$981$	1.65477	+	6.17569i	0.0528327	+	0.197174i
$982$	56.5322	+	3.12956i	1.80401	+	0.0998684i
$983$	−38.0927	−	38.0927i	−1.21497	−	1.21497i	−0.969372	−	0.245596i	$-0.921016\pi$
$983$	−38.0927	−	38.0927i	−1.21497	−	1.21497i	−0.245596	−	0.969372i	$-0.578984\pi$
$984$	−1.84435	−	19.1746i	−0.0587957	−	0.611265i
$985$	9.67294	−	5.58467i	0.308205	−	0.177943i
$986$	14.9813	+	9.79180i	0.477103	+	0.311834i
$987$		−	7.00323i		−	0.222915i
$988$	−11.2857	−	19.6032i	−0.359046	−	0.623662i
$989$			7.89651i			0.251094i
$990$	6.45013	−	9.86864i	0.204999	−	0.313646i
$991$	11.1398	−	6.43154i	0.353866	−	0.204305i	−0.312521	−	0.949911i	$-0.601173\pi$
$991$	11.1398	−	6.43154i	0.353866	−	0.204305i	0.666387	+	0.745606i	$0.267840\pi$
$992$	3.57362	−	5.98459i	0.113463	−	0.190011i
$993$	−8.74219	−	8.74219i	−0.277425	−	0.277425i
$994$	−0.235866	+	4.26066i	−0.00748121	+	0.135140i
$995$	−16.3834	−	61.1436i	−0.519388	−	1.93838i
$996$	2.49025	−	0.379407i	0.0789066	−	0.0120220i
$997$	−17.4212	−	10.0581i	−0.551736	−	0.318545i	0.198086	−	0.980185i	$-0.436527\pi$
$997$	−17.4212	−	10.0581i	−0.551736	−	0.318545i	−0.749822	+	0.661640i	$0.769861\pi$
$998$	−7.37677	−	35.2142i	−0.233508	−	1.11469i
$999$	2.61427	−	9.75657i	0.0827117	−	0.308684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.115.4	yes	56
3.2	odd	2		936.2.ed.e.739.11		56
8.3	odd	2	inner	312.2.bt.d.115.14	yes	56
13.6	odd	12	inner	312.2.bt.d.19.14	yes	56
24.11	even	2		936.2.ed.e.739.1		56
39.32	even	12		936.2.ed.e.19.1		56
104.19	even	12	inner	312.2.bt.d.19.4	✓	56
312.227	odd	12		936.2.ed.e.19.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.4	✓	56	104.19	even	12	inner
312.2.bt.d.19.14	yes	56	13.6	odd	12	inner
312.2.bt.d.115.4	yes	56	1.1	even	1	trivial
312.2.bt.d.115.14	yes	56	8.3	odd	2	inner
936.2.ed.e.19.1		56	39.32	even	12
936.2.ed.e.19.11		56	312.227	odd	12
936.2.ed.e.739.1		56	24.11	even	2
936.2.ed.e.739.11		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18379 - 0.773723i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.802706 + 1.83185i) q^{4} +(2.96415 - 2.96415i) q^{5} +(0.0781697 - 1.41205i) q^{6} +(0.672672 - 0.180242i) q^{7} +(0.467108 - 2.78959i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.80236 + 1.21550i) q^{10} +(1.92093 + 0.514712i) q^{11} +(-1.18507 + 1.61109i) q^{12} +(-3.56375 - 0.547460i) q^{13} +(-0.935758 - 0.307093i) q^{14} +(4.04911 + 1.08496i) q^{15} +(-2.71133 + 2.94087i) q^{16} +(-2.22516 - 1.28470i) q^{17} +(1.26196 - 0.638329i) q^{18} +(3.02991 - 0.811863i) q^{19} +(7.80922 + 3.05053i) q^{20} +(0.492430 + 0.492430i) q^{21} +(-1.87573 - 2.09558i) q^{22} +(2.57061 + 4.45243i) q^{23} +(2.64941 - 0.990268i) q^{24} -12.5724i q^{25} +(3.79514 + 3.40543i) q^{26} -1.00000 q^{27} +(0.870133 + 1.08755i) q^{28} +(4.26557 - 2.46273i) q^{29} +(-3.95383 - 4.41724i) q^{30} +(0.871296 - 0.871296i) q^{31} +(5.48505 - 1.38355i) q^{32} +(0.514712 + 1.92093i) q^{33} +(1.64012 + 3.24247i) q^{34} +(1.45964 - 2.52817i) q^{35} +(-1.98778 - 0.220759i) q^{36} +(-2.61427 + 9.75657i) q^{37} +(-4.21493 - 1.38324i) q^{38} +(-1.30776 - 3.36002i) q^{39} +(-6.88419 - 9.65335i) q^{40} +(1.76270 - 6.57848i) q^{41} +(-0.201928 - 0.963937i) q^{42} +(1.33015 + 0.767960i) q^{43} +(0.599070 + 3.93201i) q^{44} +(1.08496 + 4.04911i) q^{45} +(0.401888 - 7.25967i) q^{46} +(-7.11089 - 7.11089i) q^{47} +(-3.90253 - 0.877641i) q^{48} +(-5.64218 + 3.25751i) q^{49} +(-9.72755 + 14.8831i) q^{50} -2.56939i q^{51} +(-1.85778 - 6.96769i) q^{52} +3.80757i q^{53} +(1.18379 + 0.773723i) q^{54} +(7.21961 - 4.16825i) q^{55} +(-0.188591 - 1.96067i) q^{56} +(2.21805 + 2.21805i) q^{57} +(-6.95500 - 0.385021i) q^{58} +(3.01758 + 11.2618i) q^{59} +(1.26277 + 8.28825i) q^{60} +(3.41145 + 1.96960i) q^{61} +(-1.70557 + 0.357288i) q^{62} +(-0.180242 + 0.672672i) q^{63} +(-7.56362 - 2.60608i) q^{64} +(-12.1862 + 8.94073i) q^{65} +(0.876958 - 2.67222i) q^{66} +(-3.44219 + 12.8464i) q^{67} +(0.567218 - 5.10739i) q^{68} +(-2.57061 + 4.45243i) q^{69} +(-3.68400 + 1.86346i) q^{70} +(-1.12141 - 4.18515i) q^{71} +(2.18230 + 1.79932i) q^{72} +(6.22477 - 6.22477i) q^{73} +(10.6436 - 9.52699i) q^{74} +(10.8880 - 6.28620i) q^{75} +(3.91934 + 4.89865i) q^{76} +1.38493 q^{77} +(-1.05162 + 4.98940i) q^{78} +16.9313i q^{79} +(0.680406 + 16.7540i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.17658 + 6.42369i) q^{82} +(-0.890596 - 0.890596i) q^{83} +(-0.506780 + 1.29733i) q^{84} +(-10.4038 + 2.78768i) q^{85} +(-0.980422 - 1.93827i) q^{86} +(4.26557 + 2.46273i) q^{87} +(2.33312 - 5.11818i) q^{88} +(-8.32774 - 2.23141i) q^{89} +(1.84853 - 5.63274i) q^{90} +(-2.49591 + 0.274075i) q^{91} +(-6.09272 + 8.28296i) q^{92} +(1.19021 + 0.318917i) q^{93} +(2.91592 + 13.9196i) q^{94} +(6.57464 - 11.3876i) q^{95} +(3.94072 + 4.05842i) q^{96} +(-9.59613 + 2.57127i) q^{97} +(9.19955 + 0.509278i) q^{98} +(-1.40622 + 1.40622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) \) 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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