LMFDB - Embedded newform 378.2.bf.a.101.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(5,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 + 0.766044i) q^{2} +(0.0131187 - 1.73200i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(3.23672 - 2.71593i) q^{5} +(1.31836 + 1.12336i) q^{6} +(1.66664 - 2.05482i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.99966 - 0.0454431i) q^{9} +4.22523i q^{10} +(-0.952616 + 1.13528i) q^{11} +(-1.70797 + 0.287839i) q^{12} +(-0.0656487 + 0.180368i) q^{13} +(0.502790 + 2.59754i) q^{14} +(-4.66153 - 5.64163i) q^{15} +(-0.939693 + 0.342020i) q^{16} -2.02023 q^{17} +(1.96295 - 2.26866i) q^{18} +2.77145i q^{19} +(-3.23672 - 2.71593i) q^{20} +(-3.53709 - 2.91358i) q^{21} +(-0.257348 - 1.45949i) q^{22} +(-3.18022 + 8.73758i) q^{23} +(0.877362 - 1.49340i) q^{24} +(2.23183 - 12.6573i) q^{25} +(-0.0959719 - 0.166228i) q^{26} +(-0.118059 + 5.19481i) q^{27} +(-2.31302 - 1.28451i) q^{28} +(-1.08284 - 2.97507i) q^{29} +(7.31811 + 0.0554294i) q^{30} +(8.59947 - 1.51632i) q^{31} +(0.342020 - 0.939693i) q^{32} +(1.95381 + 1.66482i) q^{33} +(1.29858 - 1.54759i) q^{34} +(-0.186307 - 11.1774i) q^{35} +(0.476132 + 2.96198i) q^{36} +(0.880053 - 1.52430i) q^{37} +(-2.12305 - 1.78145i) q^{38} +(0.311537 + 0.116070i) q^{39} +(4.16104 - 0.733704i) q^{40} +(8.23124 + 2.99593i) q^{41} +(4.50553 - 0.836757i) q^{42} +(0.731893 - 4.15077i) q^{43} +(1.28346 + 0.741003i) q^{44} +(-9.83246 + 7.99976i) q^{45} +(-4.64917 - 8.05260i) q^{46} +(-1.78435 + 10.1195i) q^{47} +(0.580052 + 1.63204i) q^{48} +(-1.44461 - 6.84931i) q^{49} +(8.26149 + 9.84566i) q^{50} +(-0.0265028 + 3.49905i) q^{51} +(0.189028 + 0.0333307i) q^{52} +(0.697789 + 0.402869i) q^{53} +(-3.90357 - 3.42960i) q^{54} +6.26182i q^{55} +(2.47077 - 0.946209i) q^{56} +(4.80016 + 0.0363577i) q^{57} +(2.97507 + 1.08284i) q^{58} +(-12.1899 - 4.43676i) q^{59} +(-4.74645 + 5.57037i) q^{60} +(0.731264 + 0.128942i) q^{61} +(-4.36607 + 7.56225i) q^{62} +(-5.09273 + 6.08803i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.277381 + 0.762098i) q^{65} +(-2.53122 + 0.426580i) q^{66} +(2.31335 - 1.94113i) q^{67} +(0.350810 + 1.98954i) q^{68} +(15.0918 + 5.62277i) q^{69} +(8.68211 + 7.04195i) q^{70} +(-1.21869 + 0.703610i) q^{71} +(-2.57506 - 1.53918i) q^{72} +(4.52619 - 2.61320i) q^{73} +(0.601992 + 1.65396i) q^{74} +(-21.8932 - 4.03158i) q^{75} +(2.72935 - 0.481257i) q^{76} +(0.745138 + 3.84957i) q^{77} +(-0.289167 + 0.164043i) q^{78} +(5.61542 + 4.71190i) q^{79} +(-2.11262 + 3.65916i) q^{80} +(8.99587 + 0.272627i) q^{81} +(-7.58595 + 4.37975i) q^{82} +(3.70712 - 1.34928i) q^{83} +(-2.25511 + 3.98930i) q^{84} +(-6.53893 + 5.48681i) q^{85} +(2.70923 + 3.22873i) q^{86} +(-5.16703 + 1.83645i) q^{87} +(-1.39263 + 0.506876i) q^{88} -11.2356 q^{89} +(0.192008 - 12.6742i) q^{90} +(0.261212 + 0.435506i) q^{91} +(9.15708 + 1.61464i) q^{92} +(-2.51345 - 14.9142i) q^{93} +(-6.60506 - 7.87160i) q^{94} +(7.52706 + 8.97040i) q^{95} +(-1.62306 - 0.604707i) q^{96} +(-11.9147 - 2.10087i) q^{97} +(6.17546 + 3.29602i) q^{98} +(2.90911 - 3.36217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	0.0131187	−	1.73200i	0.00757407	−	0.999971i
$3$	0.0131187	−	1.73200i	0.00757407	−	0.999971i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	3.23672	−	2.71593i	1.44750	−	1.21460i	0.513127	−	0.858313i	$-0.328487\pi$
$5$	3.23672	−	2.71593i	1.44750	−	1.21460i	0.934377	−	0.356287i	$-0.115958\pi$
$6$	1.31836	+	1.12336i	0.538217	+	0.458609i
$7$	1.66664	−	2.05482i	0.629931	−	0.776651i
$7$	1.66664	−	2.05482i	0.629931	−	0.776651i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.99966	−	0.0454431i	−0.999885	−	0.0151477i
$10$			4.22523i			1.33614i
$11$	−0.952616	+	1.13528i	−0.287224	+	0.342301i	−0.890293	−	0.455389i	$-0.849500\pi$
$11$	−0.952616	+	1.13528i	−0.287224	+	0.342301i	0.603068	+	0.797690i	$0.293945\pi$
$12$	−1.70797	+	0.287839i	−0.493047	+	0.0830921i
$13$	−0.0656487	+	0.180368i	−0.0182077	+	0.0500252i	−0.948464	−	0.316886i	$-0.897363\pi$
$13$	−0.0656487	+	0.180368i	−0.0182077	+	0.0500252i	0.930256	+	0.366912i	$0.119585\pi$
$14$	0.502790	+	2.59754i	0.134376	+	0.694221i
$15$	−4.66153	−	5.64163i	−1.20360	−	1.45666i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.02023			−0.489979			−0.244989	−	0.969526i	$-0.578785\pi$
$17$	−2.02023			−0.489979			−0.244989	+	0.969526i	$0.578785\pi$
$18$	1.96295	−	2.26866i	0.462672	−	0.534728i
$19$			2.77145i			0.635814i	0.948122	+	0.317907i	$0.102980\pi$
$19$			2.77145i			0.635814i	−0.948122	+	0.317907i	$0.897020\pi$
$20$	−3.23672	−	2.71593i	−0.723752	−	0.607300i
$21$	−3.53709	−	2.91358i	−0.771857	−	0.635796i
$22$	−0.257348	−	1.45949i	−0.0548667	−	0.311165i
$23$	−3.18022	+	8.73758i	−0.663122	+	1.82191i	−0.100950	+	0.994891i	$0.532188\pi$
$23$	−3.18022	+	8.73758i	−0.663122	+	1.82191i	−0.562171	+	0.827021i	$0.690034\pi$
$24$	0.877362	−	1.49340i	0.179091	−	0.304839i
$25$	2.23183	−	12.6573i	0.446366	−	2.53147i
$26$	−0.0959719	−	0.166228i	−0.0188216	−	0.0326001i
$27$	−0.118059	+	5.19481i	−0.0227205	+	0.999742i
$28$	−2.31302	−	1.28451i	−0.437119	−	0.242749i
$29$	−1.08284	−	2.97507i	−0.201078	−	0.552457i	0.797637	−	0.603138i	$-0.206083\pi$
$29$	−1.08284	−	2.97507i	−0.201078	−	0.552457i	−0.998715	+	0.0506810i	$0.983861\pi$
$30$	7.31811	+	0.0554294i	1.33610	+	0.0101200i
$31$	8.59947	−	1.51632i	1.54451	−	0.272339i	0.664498	−	0.747290i	$-0.268645\pi$
$31$	8.59947	−	1.51632i	1.54451	−	0.272339i	0.880012	+	0.474951i	$0.157534\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	1.95381	+	1.66482i	0.340115	+	0.289809i
$34$	1.29858	−	1.54759i	0.222705	−	0.265409i
$35$	−0.186307	−	11.1774i	−0.0314917	−	1.88932i
$36$	0.476132	+	2.96198i	0.0793553	+	0.493663i
$37$	0.880053	−	1.52430i	0.144680	−	0.250593i	−0.784574	−	0.620036i	$-0.787118\pi$
$37$	0.880053	−	1.52430i	0.144680	−	0.250593i	0.929253	+	0.369443i	$0.120451\pi$
$38$	−2.12305	−	1.78145i	−0.344405	−	0.288990i
$39$	0.311537	+	0.116070i	0.0498858	+	0.0185860i
$40$	4.16104	−	0.733704i	0.657919	−	0.116009i
$41$	8.23124	+	2.99593i	1.28550	+	0.467885i	0.892249	−	0.451544i	$-0.149127\pi$
$41$	8.23124	+	2.99593i	1.28550	+	0.467885i	0.393255	+	0.919429i	$0.371349\pi$
$42$	4.50553	−	0.836757i	0.695219	−	0.129114i
$43$	0.731893	−	4.15077i	0.111613	−	0.632987i	−0.876759	−	0.480930i	$-0.840299\pi$
$43$	0.731893	−	4.15077i	0.111613	−	0.632987i	0.988372	−	0.152057i	$-0.0485898\pi$
$44$	1.28346	+	0.741003i	0.193488	+	0.111710i
$45$	−9.83246	+	7.99976i	−1.46574	+	1.19253i
$46$	−4.64917	−	8.05260i	−0.685483	−	1.18729i
$47$	−1.78435	+	10.1195i	−0.260274	+	1.47609i	0.521890	+	0.853013i	$0.325227\pi$
$47$	−1.78435	+	10.1195i	−0.260274	+	1.47609i	−0.782164	+	0.623073i	$0.785884\pi$
$48$	0.580052	+	1.63204i	0.0837233	+	0.235564i
$49$	−1.44461	−	6.84931i	−0.206373	−	0.978473i
$50$	8.26149	+	9.84566i	1.16835	+	1.39239i
$51$	−0.0265028	+	3.49905i	−0.00371113	+	0.489965i
$52$	0.189028	+	0.0333307i	0.0262134	+	0.00462214i
$53$	0.697789	+	0.402869i	0.0958487	+	0.0553383i	0.547158	−	0.837029i	$-0.315710\pi$
$53$	0.697789	+	0.402869i	0.0958487	+	0.0553383i	−0.451309	+	0.892368i	$0.649043\pi$
$54$	−3.90357	−	3.42960i	−0.531208	−	0.466709i
$55$			6.26182i			0.844344i
$56$	2.47077	−	0.946209i	0.330170	−	0.126443i
$57$	4.80016	+	0.0363577i	0.635796	+	0.00481570i
$58$	2.97507	+	1.08284i	0.390646	+	0.142183i
$59$	−12.1899	−	4.43676i	−1.58699	−	0.577616i	−0.610279	−	0.792186i	$-0.708943\pi$
$59$	−12.1899	−	4.43676i	−1.58699	−	0.577616i	−0.976709	+	0.214570i	$0.931165\pi$
$60$	−4.74645	+	5.57037i	−0.612764	+	0.719131i
$61$	0.731264	+	0.128942i	0.0936287	+	0.0165093i	0.220266	−	0.975440i	$-0.429307\pi$
$61$	0.731264	+	0.128942i	0.0936287	+	0.0165093i	−0.126638	+	0.991949i	$0.540418\pi$
$62$	−4.36607	+	7.56225i	−0.554491	+	0.960406i
$63$	−5.09273	+	6.08803i	−0.641624	+	0.767020i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	0.277381	+	0.762098i	0.0344049	+	0.0945266i
$66$	−2.53122	+	0.426580i	−0.311571	+	0.0525084i
$67$	2.31335	−	1.94113i	0.282621	−	0.237147i	−0.490446	−	0.871472i	$-0.663166\pi$
$67$	2.31335	−	1.94113i	0.282621	−	0.237147i	0.773067	+	0.634325i	$0.218722\pi$
$68$	0.350810	+	1.98954i	0.0425420	+	0.241268i
$69$	15.0918	+	5.62277i	1.81684	+	0.676902i
$70$	8.68211	+	7.04195i	1.03771	+	0.841674i
$71$	−1.21869	+	0.703610i	−0.144632	+	0.0835032i	−0.570570	−	0.821249i	$-0.693278\pi$
$71$	−1.21869	+	0.703610i	−0.144632	+	0.0835032i	0.425938	+	0.904752i	$0.359944\pi$
$72$	−2.57506	−	1.53918i	−0.303473	−	0.181394i
$73$	4.52619	−	2.61320i	0.529750	−	0.305851i	−0.211165	−	0.977451i	$-0.567726\pi$
$73$	4.52619	−	2.61320i	0.529750	−	0.305851i	0.740915	+	0.671599i	$0.234392\pi$
$74$	0.601992	+	1.65396i	0.0699801	+	0.192269i
$75$	−21.8932	−	4.03158i	−2.52801	−	0.465527i
$76$	2.72935	−	0.481257i	0.313077	−	0.0552040i
$77$	0.745138	+	3.84957i	0.0849164	+	0.438699i
$78$	−0.289167	+	0.164043i	−0.0327417	+	0.0185742i
$79$	5.61542	+	4.71190i	0.631784	+	0.530130i	0.901483	−	0.432815i	$-0.142480\pi$
$79$	5.61542	+	4.71190i	0.631784	+	0.530130i	−0.269699	+	0.962945i	$0.586924\pi$
$80$	−2.11262	+	3.65916i	−0.236198	+	0.409106i
$81$	8.99587	+	0.272627i	0.999541	+	0.0302919i
$82$	−7.58595	+	4.37975i	−0.837728	+	0.483663i
$83$	3.70712	−	1.34928i	0.406909	−	0.148103i	−0.130453	−	0.991455i	$-0.541643\pi$
$83$	3.70712	−	1.34928i	0.406909	−	0.148103i	0.537362	+	0.843352i	$0.319421\pi$
$84$	−2.25511	+	3.98930i	−0.246053	+	0.435268i
$85$	−6.53893	+	5.48681i	−0.709246	+	0.595128i
$86$	2.70923	+	3.22873i	0.292143	+	0.348163i
$87$	−5.16703	+	1.83645i	−0.553964	+	0.196888i
$88$	−1.39263	+	0.506876i	−0.148455	+	0.0540332i
$89$	−11.2356			−1.19097			−0.595483	−	0.803368i	$-0.703039\pi$
$89$	−11.2356			−1.19097			−0.595483	+	0.803368i	$0.703039\pi$
$90$	0.192008	−	12.6742i	0.0202394	−	1.33598i
$91$	0.261212	+	0.435506i	0.0273825	+	0.0456534i
$92$	9.15708	+	1.61464i	0.954692	+	0.168338i
$93$	−2.51345	−	14.9142i	−0.260633	−	1.54653i
$94$	−6.60506	−	7.87160i	−0.681260	−	0.811894i
$95$	7.52706	+	8.97040i	0.772260	+	0.920344i
$96$	−1.62306	−	0.604707i	−0.165653	−	0.0617176i
$97$	−11.9147	−	2.10087i	−1.20975	−	0.213311i	−0.467841	−	0.883813i	$-0.654968\pi$
$97$	−11.9147	−	2.10087i	−1.20975	−	0.213311i	−0.741908	+	0.670501i	$0.766079\pi$
$98$	6.17546	+	3.29602i	0.623815	+	0.332948i
$99$	2.90911	−	3.36217i	0.292377	−	0.337911i
$100$	−12.8526			−1.28526
$101$	13.6235	−	4.95855i	1.35559	−	0.493394i	0.440902	−	0.897555i	$-0.354659\pi$
$101$	13.6235	−	4.95855i	1.35559	−	0.493394i	0.914688	+	0.404161i	$0.132437\pi$
$102$	−2.66339	−	2.26945i	−0.263715	−	0.224709i
$103$	0.186351	+	0.222084i	0.0183617	+	0.0218826i	0.775147	−	0.631781i	$-0.217676\pi$
$103$	0.186351	+	0.222084i	0.0183617	+	0.0218826i	−0.756785	+	0.653663i	$0.773231\pi$
$104$	−0.147038	+	0.123379i	−0.0144182	+	0.0120983i
$105$	−19.3617	+	0.176052i	−1.88950	+	0.0171809i
$106$	−0.757146	+	0.275578i	−0.0735405	+	0.0267665i
$107$	−5.30878	+	3.06502i	−0.513219	+	0.296307i	−0.734156	−	0.678981i	$-0.762422\pi$
$107$	−5.30878	+	3.06502i	−0.513219	+	0.296307i	0.220937	+	0.975288i	$0.429088\pi$
$108$	5.13639	−	0.785804i	0.494249	−	0.0756140i
$109$	−2.96141	+	5.12932i	−0.283652	+	0.491300i	−0.972281	−	0.233814i	$-0.924879\pi$
$109$	−2.96141	+	5.12932i	−0.283652	+	0.491300i	0.688629	+	0.725114i	$0.258213\pi$
$110$	−4.79684	−	4.02502i	−0.457360	−	0.383771i
$111$	−2.62854	−	1.54425i	−0.249490	−	0.146574i
$112$	−0.863340	+	2.50093i	−0.0815779	+	0.236316i
$113$	6.06834	−	1.07001i	0.570862	−	0.100658i	0.119236	−	0.992866i	$-0.461955\pi$
$113$	6.06834	−	1.07001i	0.570862	−	0.100658i	0.451625	+	0.892208i	$0.350844\pi$
$114$	−3.11333	+	3.65376i	−0.291590	+	0.342206i
$115$	13.4372	+	36.9183i	1.25302	+	3.44265i
$116$	−2.74184	+	1.58300i	−0.254573	+	0.146978i
$117$	0.205120	−	0.538059i	0.0189633	−	0.0497436i
$118$	11.2343	−	6.48610i	1.03420	−	0.597094i
$119$	−3.36701	+	4.15123i	−0.308653	+	0.380542i
$120$	−1.21619	−	7.21656i	−0.111022	−	0.658778i
$121$	1.52874	+	8.66991i	0.138976	+	0.788174i
$122$	−0.568822	+	0.477298i	−0.0514987	+	0.0432126i
$123$	5.29693	−	14.2172i	0.477608	−	1.28192i
$124$	−2.98656	−	8.20552i	−0.268201	−	0.736877i
$125$	−16.5895	−	28.7339i	−1.48381	−	2.57004i
$126$	−1.39016	−	7.81457i	−0.123845	−	0.696177i
$127$	−5.08797	+	8.81262i	−0.451484	+	0.781993i	−0.998478	−	0.0551430i	$-0.982439\pi$
$127$	−5.08797	+	8.81262i	−0.451484	+	0.781993i	0.546994	+	0.837136i	$0.315772\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−7.17954	−	1.32209i	−0.632124	−	0.116404i
$130$	−0.762098	−	0.277381i	−0.0668404	−	0.0243279i
$131$	13.7618	+	5.00889i	1.20238	+	0.437629i	0.864053	−	0.503401i	$-0.167918\pi$
$131$	13.7618	+	5.00889i	1.20238	+	0.437629i	0.338323	+	0.941030i	$0.390140\pi$
$132$	1.30026	−	2.21323i	0.113173	−	0.192637i
$133$	5.69485	+	4.61902i	0.493806	+	0.400519i
$134$			3.01986i			0.260877i
$135$	13.7266	+	17.1348i	1.18140	+	1.47473i
$136$	−1.74957	−	1.01012i	−0.150025	−	0.0866169i
$137$	3.78164	+	0.666805i	0.323087	+	0.0569690i	0.332840	−	0.942983i	$-0.391993\pi$
$137$	3.78164	+	0.666805i	0.323087	+	0.0569690i	−0.00975248	+	0.999952i	$0.503104\pi$
$138$	−14.0081	+	7.94673i	−1.19245	+	0.676471i
$139$	3.42887	+	4.08637i	0.290833	+	0.346602i	0.891601	−	0.452822i	$-0.149583\pi$
$139$	3.42887	+	4.08637i	0.290833	+	0.346602i	−0.600768	+	0.799424i	$0.705138\pi$
$140$	−10.9752	+	2.12441i	−0.927574	+	0.179545i
$141$	17.5036	+	3.22325i	1.47407	+	0.271446i
$142$	0.244361	−	1.38584i	0.0205063	−	0.116297i
$143$	−0.142231	−	0.246351i	−0.0118940	−	0.0206009i
$144$	2.83430	−	0.983240i	0.236191	−	0.0819367i
$145$	−11.5849	−	6.68855i	−0.962075	−	0.555454i
$146$	−0.907553	+	5.14699i	−0.0751097	+	0.425968i
$147$	−11.8820	+	2.41221i	−0.980008	+	0.198956i
$148$	−1.65396	−	0.601992i	−0.135955	−	0.0494834i
$149$	13.5995	−	2.39795i	1.11411	−	0.196448i	0.413858	−	0.910342i	$-0.364181\pi$
$149$	13.5995	−	2.39795i	1.11411	−	0.196448i	0.700254	+	0.713894i	$0.253070\pi$
$150$	17.1611	−	14.1797i	1.40120	−	1.15777i
$151$	0.812197	+	0.681514i	0.0660956	+	0.0554608i	0.675237	−	0.737601i	$-0.264041\pi$
$151$	0.812197	+	0.681514i	0.0660956	+	0.0554608i	−0.609141	+	0.793062i	$0.708486\pi$
$152$	−1.38573	+	2.40015i	−0.112397	+	0.194678i
$153$	6.06001	+	0.0918057i	0.489923	+	0.00742205i
$154$	−3.42791	−	1.90365i	−0.276229	−	0.153400i
$155$	23.7158	−	28.2634i	1.90490	−	2.27017i
$156$	0.0602086	−	0.326959i	0.00482055	−	0.0261777i
$157$	−0.586436	+	1.61122i	−0.0468027	+	0.128589i	−0.960892	−	0.276924i	$-0.910685\pi$
$157$	−0.586436	+	1.61122i	−0.0468027	+	0.128589i	0.914089	+	0.405513i	$0.132907\pi$
$158$	−7.21904	+	1.27291i	−0.574316	+	0.101267i
$159$	0.706923	−	1.20329i	0.0560627	−	0.0954268i
$160$	−1.44511	−	3.97042i	−0.114246	−	0.313889i
$161$	12.6539	+	21.0972i	0.997268	+	1.66269i
$162$	−5.99128	+	6.71599i	−0.470719	+	0.527658i
$163$	−7.02330	−	12.1647i	−0.550108	−	0.952814i	−0.998266	−	0.0588602i	$-0.981253\pi$
$163$	−7.02330	−	12.1647i	−0.550108	−	0.952814i	0.448159	−	0.893954i	$-0.352080\pi$
$164$	1.52107	−	8.62643i	0.118776	−	0.673611i
$165$	10.8455	+	0.0821468i	0.844320	+	0.00639512i
$166$	−1.34928	+	3.70712i	−0.104724	+	0.287728i
$167$	−4.12751	−	23.4083i	−0.319396	−	1.81139i	−0.546437	−	0.837500i	$-0.684016\pi$
$167$	−4.12751	−	23.4083i	−0.319396	−	1.81139i	0.227041	−	0.973885i	$-0.427095\pi$
$168$	−1.60642	−	4.29178i	−0.123938	−	0.331118i
$169$	9.93035	+	8.33256i	0.763873	+	0.640966i
$170$		−	8.53596i		−	0.654679i
$171$	0.125943	−	8.31340i	0.00963112	−	0.635741i
$172$	−4.21481			−0.321376
$173$	−11.0999	+	4.04005i	−0.843912	+	0.307159i	−0.727556	−	0.686049i	$-0.759344\pi$
$173$	−11.0999	+	4.04005i	−0.843912	+	0.307159i	−0.116357	+	0.993208i	$0.537122\pi$
$174$	1.91450	−	5.13862i	0.145138	−	0.389558i
$175$	−22.2889	−	25.6813i	−1.68489	−	1.94132i
$176$	0.506876	−	1.39263i	0.0382072	−	0.104973i
$177$	−7.84438	+	21.0547i	−0.589620	+	1.58257i
$178$	7.22208	−	8.60693i	0.541317	−	0.645117i
$179$			16.2690i			1.21600i	0.793937	+	0.608000i	$0.208028\pi$
$179$			16.2690i			1.21600i	−0.793937	+	0.608000i	$0.791972\pi$
$180$	9.58562	+	8.29393i	0.714470	+	0.618193i
$181$	9.64937	+	5.57107i	0.717232	+	0.414094i	0.813733	−	0.581239i	$-0.197432\pi$
$181$	9.64937	+	5.57107i	0.717232	+	0.414094i	−0.0965009	+	0.995333i	$0.530765\pi$
$182$	−0.501521	−	0.0798375i	−0.0371752	−	0.00591795i
$183$	0.232920	−	1.26486i	0.0172179	−	0.0935010i
$184$	−7.12294	+	5.97686i	−0.525110	+	0.440620i
$185$	−1.29140	−	7.32387i	−0.0949454	−	0.538462i
$186$	13.0405	+	7.66124i	0.956179	+	0.561749i
$187$	1.92451	−	2.29354i	0.140734	−	0.167720i
$188$	10.2756			0.749428
$189$	10.4777	+	8.90048i	0.762138	+	0.647415i
$190$	−11.7100			−0.849535
$191$	−7.42197	+	8.84516i	−0.537035	+	0.640013i	−0.964520	−	0.264009i	$-0.914955\pi$
$191$	−7.42197	+	8.84516i	−0.537035	+	0.640013i	0.427485	+	0.904022i	$0.359400\pi$
$192$	1.50652	−	0.854639i	0.108723	−	0.0616783i
$193$	−2.03633	−	11.5486i	−0.146578	−	0.831286i	−0.966087	−	0.258219i	$-0.916865\pi$
$193$	−2.03633	−	11.5486i	−0.146578	−	0.831286i	0.819508	−	0.573067i	$-0.194247\pi$
$194$	9.26795	−	7.77674i	0.665400	−	0.558337i
$195$	1.32359	−	0.470426i	0.0947845	−	0.0336879i
$196$	−6.49440	+	2.61203i	−0.463886	+	0.186574i
$197$	−14.6216	−	8.44177i	−1.04174	−	0.601451i	−0.121417	−	0.992602i	$-0.538744\pi$
$197$	−14.6216	−	8.44177i	−1.04174	−	0.601451i	−0.920327	+	0.391150i	$0.872077\pi$
$198$	0.705631	+	4.38967i	0.0501470	+	0.311960i
$199$			17.7181i			1.25600i	0.778212	+	0.628001i	$0.216127\pi$
$199$			17.7181i			1.25600i	−0.778212	+	0.628001i	$0.783873\pi$
$200$	8.26149	−	9.84566i	0.584176	−	0.696193i
$201$	−3.33169	−	4.03219i	−0.235000	−	0.284409i
$202$	−4.95855	+	13.6235i	−0.348882	+	0.958546i
$203$	−7.91795	−	2.73334i	−0.555731	−	0.191843i
$204$	3.45049	−	0.581503i	0.241583	−	0.0407134i
$205$	34.7789	−	12.6585i	2.42907	−	0.884107i
$206$	−0.289911			−0.0201990
$207$	9.93663	−	26.0652i	0.690643	−	1.81166i
$208$		−	0.191944i		−	0.0133089i
$209$	−3.14638	−	2.64013i	−0.217640	−	0.182621i
$210$	12.3106	−	14.9450i	0.849510	−	1.03131i
$211$	−3.30791	−	18.7601i	−0.227726	−	1.29150i	−0.857406	−	0.514641i	$-0.827925\pi$
$211$	−3.30791	−	18.7601i	−0.227726	−	1.29150i	0.629680	−	0.776855i	$-0.283186\pi$
$212$	0.275578	−	0.757146i	0.0189268	−	0.0520010i
$213$	1.20267	+	2.12000i	0.0824053	+	0.145260i
$214$	1.06447	−	6.03692i	0.0727658	−	0.412675i
$215$	−8.90427	−	15.4226i	−0.607266	−	1.05182i
$216$	−2.69965	+	4.43981i	−0.183688	+	0.302091i
$217$	11.2165	−	20.1976i	0.761424	−	1.37110i
$218$	−2.02573	−	5.56564i	−0.137200	−	0.376953i
$219$	−4.46668	−	7.87364i	−0.301830	−	0.532052i
$220$	6.16669	−	1.08735i	0.415758	−	0.0733094i
$221$	0.132626	−	0.364386i	0.00892137	−	0.0245113i
$222$	2.87255	−	1.02095i	0.192793	−	0.0685218i
$223$	−9.50125	+	11.3231i	−0.636251	+	0.758254i	−0.983773	−	0.179418i	$-0.942579\pi$
$223$	−9.50125	+	11.3231i	−0.636251	+	0.758254i	0.347522	+	0.937672i	$0.387023\pi$
$224$	−1.36088	−	2.26892i	−0.0909275	−	0.151599i
$225$	−7.26991	+	37.8662i	−0.484661	+	2.52442i
$226$	−3.08098	+	5.33641i	−0.204944	+	0.354973i
$227$	15.6341	+	13.1186i	1.03767	+	0.870710i	0.991744	−	0.128235i	$-0.0409310\pi$
$227$	15.6341	+	13.1186i	1.03767	+	0.870710i	0.0459282	+	0.998945i	$0.485375\pi$
$228$	−0.797733	−	4.73354i	−0.0528312	−	0.313487i
$229$	18.6863	−	3.29490i	1.23483	−	0.217733i	0.482130	−	0.876100i	$-0.339863\pi$
$229$	18.6863	−	3.29490i	1.23483	−	0.217733i	0.752697	+	0.658367i	$0.228752\pi$
$230$	−36.9183	−	13.4372i	−2.43432	−	0.886021i
$231$	6.67723	−	1.24008i	0.439330	−	0.0815912i
$232$	0.549771	−	3.11790i	0.0360942	−	0.204700i
$233$	−2.02806	−	1.17090i	−0.132862	−	0.0767082i	0.432096	−	0.901828i	$-0.357774\pi$
$233$	−2.02806	−	1.17090i	−0.132862	−	0.0767082i	−0.564958	+	0.825120i	$0.691108\pi$
$234$	0.280329	+	0.502989i	0.0183257	+	0.0328814i
$235$	21.7085	+	37.6002i	1.41611	+	2.45277i
$236$	−2.25260	+	12.7751i	−0.146632	+	0.831590i
$237$	8.23468	−	9.66410i	0.534900	−	0.627751i
$238$	−1.01575	−	5.24764i	−0.0658416	−	0.340154i
$239$	−6.44557	−	7.68153i	−0.416929	−	0.496877i	0.516175	−	0.856483i	$-0.327355\pi$
$239$	−6.44557	−	7.68153i	−0.416929	−	0.496877i	−0.933104	+	0.359606i	$0.882911\pi$
$240$	6.30995	+	3.70706i	0.407306	+	0.239290i
$241$	−15.7343	−	2.77437i	−1.01353	−	0.178713i	−0.357873	−	0.933770i	$-0.616498\pi$
$241$	−15.7343	−	2.77437i	−1.01353	−	0.178713i	−0.655659	+	0.755057i	$0.727609\pi$
$242$	−7.62419	−	4.40183i	−0.490101	−	0.282960i
$243$	0.590205	−	15.5773i	0.0378616	−	0.999283i
$244$		−	0.742545i		−	0.0475365i
$245$	−23.2780	−	18.2458i	−1.48718	−	1.16568i
$246$	7.48622	+	13.1963i	0.477304	+	0.841368i
$247$	−0.499882	−	0.181942i	−0.0318067	−	0.0115767i
$248$	8.20552	+	2.98656i	0.521051	+	0.189647i
$249$	−2.28832	−	6.43843i	−0.145017	−	0.408019i
$250$	32.6750	+	5.76148i	2.06655	+	0.364388i
$251$	−7.40412	+	12.8243i	−0.467344	+	0.809464i	−0.999304	−	0.0373059i	$-0.988122\pi$
$251$	−7.40412	+	12.8243i	−0.467344	+	0.809464i	0.531960	+	0.846770i	$0.321456\pi$
$252$	6.87988	+	3.95818i	0.433392	+	0.249342i
$253$	−6.89010	−	11.9340i	−0.433177	−	0.750285i
$254$	−3.48037	−	9.56225i	−0.218378	−	0.599989i
$255$	9.41738	+	11.3974i	0.589739	+	0.713733i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.69526	+	9.61431i	0.105748	+	0.599724i	0.990919	+	0.134459i	$0.0429298\pi$
$257$	1.69526	+	9.61431i	0.105748	+	0.599724i	−0.885172	+	0.465265i	$0.845959\pi$
$258$	5.62770	−	4.65002i	0.350366	−	0.289498i
$259$	−1.66543	−	4.34881i	−0.103485	−	0.270222i
$260$	0.702353	−	0.405504i	0.0435581	−	0.0251483i
$261$	3.11294	+	8.97339i	0.192686	+	0.555439i
$262$	−12.6830	+	7.32251i	−0.783556	+	0.452386i
$263$	−0.998249	−	2.74267i	−0.0615547	−	0.169120i	0.905103	−	0.425193i	$-0.139794\pi$
$263$	−0.998249	−	2.74267i	−0.0615547	−	0.169120i	−0.966658	+	0.256072i	$0.917571\pi$
$264$	0.859641	+	2.41869i	0.0529072	+	0.148860i
$265$	3.35271	−	0.591173i	0.205955	−	0.0363155i
$266$	−7.19895	+	1.39346i	−0.441396	+	0.0854384i
$267$	−0.147396	+	19.4600i	−0.00902046	+	1.19093i
$268$	−2.31335	−	1.94113i	−0.141310	−	0.118573i
$269$	−1.69834	+	2.94161i	−0.103550	+	0.179353i	−0.913145	−	0.407636i	$-0.866353\pi$
$269$	−1.69834	+	2.94161i	−0.103550	+	0.179353i	0.809595	+	0.586989i	$0.199687\pi$
$270$	−21.9493	−	0.498827i	−1.33579	−	0.0303576i
$271$	−0.721049	+	0.416298i	−0.0438006	+	0.0252883i	−0.521740	−	0.853104i	$-0.674717\pi$
$271$	−0.721049	+	0.416298i	−0.0438006	+	0.0252883i	0.477940	+	0.878393i	$0.341384\pi$
$272$	1.89840	−	0.690961i	0.115107	−	0.0418957i
$273$	0.757723	−	0.446707i	0.0458595	−	0.0270359i
$274$	−2.94159	+	2.46829i	−0.177708	+	0.149115i
$275$	12.2436	+	14.5913i	0.738316	+	0.879891i
$276$	2.91669	−	15.8389i	0.175564	−	0.953389i
$277$	−9.48668	+	3.45287i	−0.570000	+	0.207463i	−0.610910	−	0.791700i	$-0.709196\pi$
$277$	−9.48668	+	3.45287i	−0.570000	+	0.207463i	0.0409105	+	0.999163i	$0.486974\pi$
$278$	−5.33438			−0.319935
$279$	−25.8644	+	4.15765i	−1.54846	+	0.248912i
$280$	5.42734	−	9.77303i	0.324345	−	0.584051i
$281$	−3.30648	−	0.583022i	−0.197248	−	0.0347802i	0.0741512	−	0.997247i	$-0.476375\pi$
$281$	−3.30648	−	0.583022i	−0.197248	−	0.0347802i	−0.271399	+	0.962467i	$0.587486\pi$
$282$	−13.7203	+	11.3367i	−0.817030	+	0.675091i
$283$	−18.0057	−	21.4584i	−1.07033	−	1.27557i	−0.959493	−	0.281732i	$-0.909091\pi$
$283$	−18.0057	−	21.4584i	−1.07033	−	1.27557i	−0.110837	−	0.993839i	$-0.535353\pi$
$284$	0.904544	+	1.07799i	0.0536748	+	0.0639671i
$285$	15.6355	−	12.9192i	0.926166	−	0.765267i
$286$	0.280141	+	0.0493963i	0.0165651	+	0.00292087i
$287$	19.8746	−	11.9206i	1.17316	−	0.703652i
$288$	−1.06865	+	2.80321i	−0.0629705	+	0.165181i
$289$	−12.9187			−0.759921
$290$	12.5704	−	4.57524i	0.738157	−	0.268667i
$291$	−3.79502	+	20.6086i	−0.222468	+	1.20810i
$292$	−3.35946	−	4.00365i	−0.196598	−	0.234296i
$293$	−13.5604	+	11.3785i	−0.792204	+	0.664738i	−0.946290	−	0.323319i	$-0.895201\pi$
$293$	−13.5604	+	11.3785i	−0.792204	+	0.664738i	0.154086	+	0.988058i	$0.450757\pi$
$294$	5.78972	−	10.6527i	0.337664	−	0.621276i
$295$	−51.5051	+	18.7463i	−2.99874	+	1.09145i
$296$	1.52430	−	0.880053i	0.0885979	−	0.0511520i
$297$	−5.78512	−	5.08269i	−0.335686	−	0.294927i
$298$	−6.90463	+	11.9592i	−0.399975	+	0.692776i
$299$	−1.36721	−	1.14722i	−0.0790675	−	0.0663455i
$300$	−0.168609	+	22.2607i	−0.00973464	+	1.28522i
$301$	−7.30931	−	8.42177i	−0.421302	−	0.485423i
$302$	−1.04414	+	0.184110i	−0.0600835	+	0.0105943i
$303$	−8.40949	−	23.6610i	−0.483113	−	1.35929i
$304$	−0.947892	−	2.60431i	−0.0543653	−	0.149368i
$305$	2.71709	−	1.56871i	0.155580	−	0.0898242i
$306$	−3.96563	+	4.58322i	−0.226700	+	0.262006i
$307$	−17.4229	+	10.0591i	−0.994379	+	0.574105i	−0.906580	−	0.422034i	$-0.861316\pi$
$307$	−17.4229	+	10.0591i	−0.994379	+	0.574105i	−0.0877984	+	0.996138i	$0.527983\pi$
$308$	3.66169	−	1.40229i	0.208644	−	0.0799028i
$309$	0.387095	−	0.319847i	0.0220211	−	0.0181954i
$310$	6.40680	+	36.3348i	0.363882	+	2.06368i
$311$	−5.67510	+	4.76198i	−0.321806	+	0.270027i	−0.789351	−	0.613942i	$-0.789583\pi$
$311$	−5.67510	+	4.76198i	−0.321806	+	0.270027i	0.467545	+	0.883969i	$0.345138\pi$
$312$	0.211764	+	0.256288i	0.0119888	+	0.0145094i
$313$	2.33310	+	6.41014i	0.131875	+	0.362322i	0.988002	−	0.154443i	$-0.0493583\pi$
$313$	2.33310	+	6.41014i	0.131875	+	0.362322i	−0.856127	+	0.516765i	$0.827136\pi$
$314$	−0.857312	−	1.48491i	−0.0483809	−	0.0837982i
$315$	0.0509237	+	33.5367i	0.00286923	+	1.88958i
$316$	3.66520	−	6.34832i	0.206184	−	0.357121i
$317$	−24.9555	−	4.40033i	−1.40164	−	0.247147i	−0.578823	−	0.815453i	$-0.696488\pi$
$317$	−24.9555	−	4.40033i	−1.40164	−	0.247147i	−0.822817	+	0.568306i	$0.807599\pi$
$318$	0.467369	+	1.31499i	0.0262088	+	0.0737411i
$319$	4.40907	+	1.60477i	0.246861	+	0.0898500i
$320$	3.97042	+	1.44511i	0.221953	+	0.0807844i
$321$	5.23898	+	9.23501i	0.292411	+	0.515448i
$322$	−24.2952	−	3.86757i	−1.35392	−	0.215531i
$323$		−	5.59898i		−	0.311536i
$324$	−1.29363	−	8.90654i	−0.0718684	−	0.494808i
$325$	2.13647	+	1.23349i	0.118510	+	0.0684216i
$326$	13.8332	+	2.43917i	0.766150	+	0.135093i
$327$	8.84514	+	5.19646i	0.489137	+	0.287365i
$328$	5.63050	+	6.71017i	0.310892	+	0.370507i
$329$	17.8200	+	20.5322i	0.982448	+	1.13197i
$330$	−7.03427	+	8.25532i	−0.387224	+	0.454441i
$331$	−2.02011	+	11.4566i	−0.111035	+	0.629711i	0.877602	+	0.479390i	$0.159142\pi$
$331$	−2.02011	+	11.4566i	−0.111035	+	0.629711i	−0.988637	+	0.150321i	$0.951969\pi$
$332$	−1.97252	−	3.41650i	−0.108256	−	0.187505i
$333$	−2.70912	+	4.53237i	−0.148459	+	0.248372i
$334$	20.5849	+	11.8847i	1.12635	+	0.650301i
$335$	2.21569	−	12.5658i	0.121056	−	0.686542i
$336$	4.32029	+	1.52811i	0.235691	+	0.0833655i
$337$	17.7791	+	6.47105i	0.968487	+	0.352500i	0.777354	−	0.629064i	$-0.216562\pi$
$337$	17.7791	+	6.47105i	0.968487	+	0.352500i	0.191133	+	0.981564i	$0.438784\pi$
$338$	−12.7662	+	2.25103i	−0.694391	+	0.122440i
$339$	−1.77365	−	10.5244i	−0.0963317	−	0.571608i
$340$	6.53893	+	5.48681i	0.354623	+	0.297564i
$341$	−6.47054	+	11.2073i	−0.350399	+	0.606909i
$342$	6.28748	+	5.44023i	0.339988	+	0.294174i
$343$	−16.4818	−	8.44694i	−0.889933	−	0.456092i
$344$	2.70923	−	3.22873i	0.146072	−	0.174081i
$345$	64.1189	−	22.7889i	3.45204	−	1.22691i
$346$	4.04005	−	11.0999i	0.217194	−	0.596736i
$347$	4.75433	−	0.838316i	0.255226	−	0.0450032i	−0.0445713	−	0.999006i	$-0.514192\pi$
$347$	4.75433	−	0.838316i	0.255226	−	0.0450032i	0.299797	+	0.954003i	$0.403081\pi$
$348$	2.70579	+	4.76964i	0.145046	+	0.255679i
$349$	−1.22982	−	3.37891i	−0.0658310	−	0.180869i	0.902415	−	0.430867i	$-0.141792\pi$
$349$	−1.22982	−	3.37891i	−0.0658310	−	0.180869i	−0.968246	+	0.249998i	$0.919570\pi$
$350$	34.0001	−	0.566722i	1.81738	−	0.0302926i
$351$	−0.929229	−	0.362327i	−0.0495986	−	0.0193396i
$352$	0.741003	+	1.28346i	0.0394956	+	0.0684084i
$353$	−4.45378	+	25.2586i	−0.237051	+	1.34438i	0.601202	+	0.799097i	$0.294689\pi$
$353$	−4.45378	+	25.2586i	−0.237051	+	1.34438i	−0.838252	+	0.545283i	$0.816422\pi$
$354$	−11.0866	−	19.5428i	−0.589244	−	1.03869i
$355$	−2.03359	+	5.58726i	−0.107932	+	0.296541i
$356$	1.95103	+	11.0649i	0.103405	+	0.586436i
$357$	7.14576	+	5.88612i	0.378194	+	0.311527i
$358$	−12.4628	−	10.4575i	−0.658677	−	0.552696i
$359$		−	29.6158i		−	1.56306i	−0.623866	−	0.781531i	$-0.714439\pi$
$359$		−	29.6158i		−	1.56306i	0.623866	−	0.781531i	$-0.285561\pi$
$360$	−12.5150	+	2.01177i	−0.659600	+	0.106030i
$361$	11.3191			0.595740
$362$	−10.4702	+	3.81084i	−0.550301	+	0.200293i
$363$	15.0363	−	2.53404i	0.789204	−	0.133003i
$364$	0.383531	−	0.332869i	0.0201025	−	0.0174471i
$365$	7.55274	−	20.7510i	0.395328	−	1.08616i
$366$	0.819219	+	0.991462i	0.0428213	+	0.0518246i
$367$	−6.18402	+	7.36983i	−0.322803	+	0.384702i	−0.902904	−	0.429843i	$-0.858569\pi$
$367$	−6.18402	+	7.36983i	−0.322803	+	0.384702i	0.580100	+	0.814545i	$0.303013\pi$
$368$		−	9.29834i		−	0.484710i
$369$	−24.5548	−	9.36080i	−1.27827	−	0.487304i
$370$	6.44051	+	3.71843i	0.334826	+	0.193312i
$371$	1.99079	−	0.762396i	0.103357	−	0.0395816i
$372$	−14.2511	+	5.06509i	−0.738888	+	0.262613i
$373$	7.57470	−	6.35593i	0.392203	−	0.329097i	−0.425268	−	0.905068i	$-0.639820\pi$
$373$	7.57470	−	6.35593i	0.392203	−	0.329097i	0.817471	+	0.575970i	$0.195376\pi$
$374$	0.519903	+	2.94852i	0.0268835	+	0.152464i
$375$	−49.9848	+	28.3561i	−2.58120	+	1.46430i
$376$	−6.60506	+	7.87160i	−0.340630	+	0.405947i
$377$	0.607695			0.0312979
$378$	−13.5531	+	2.30524i	−0.697095	+	0.118569i
$379$	7.39121			0.379661			0.189831	−	0.981817i	$-0.439206\pi$
$379$	7.39121			0.379661			0.189831	+	0.981817i	$0.439206\pi$
$380$	7.52706	−	8.97040i	0.386130	−	0.460172i
$381$	15.1967	+	8.92797i	0.778551	+	0.457394i
$382$	−2.00504	−	11.3711i	−0.102587	−	0.581797i
$383$	−0.000148338	0	0.000124470i	−7.57972e−6	0	6.36014e-6i	−0.642791	−	0.766041i	$-0.722224\pi$
$383$	−0.000148338	0	0.000124470i	−7.57972e−6	0	6.36014e-6i	0.642784	+	0.766048i	$0.277779\pi$
$384$	−0.313678	+	1.70341i	−0.0160073	+	0.0869268i
$385$	12.8670	+	10.4362i	0.655761	+	0.531879i
$386$	10.1557	+	5.86337i	0.516909	+	0.298438i
$387$	−2.38405	+	12.4176i	−0.121188	+	0.631224i
$388$			12.0985i			0.614206i
$389$	15.0683	−	17.9578i	0.763996	−	0.910495i	−0.234098	−	0.972213i	$-0.575214\pi$
$389$	15.0683	−	17.9578i	0.763996	−	0.910495i	0.998094	+	0.0617185i	$0.0196581\pi$
$390$	−0.490422	+	1.31632i	−0.0248335	+	0.0666542i
$391$	6.42479	−	17.6520i	0.324916	−	0.892699i
$392$	2.17359	−	6.65398i	0.109783	−	0.336077i
$393$	8.85594	−	23.7698i	0.446723	−	1.19903i
$394$	15.8653	−	5.77451i	0.799284	−	0.290916i
$395$	30.9727			1.55841
$396$	−3.81625	−	2.28108i	−0.191774	−	0.114629i
$397$			3.65680i			0.183529i	0.995781	+	0.0917647i	$0.0292508\pi$
$397$			3.65680i			0.183529i	−0.995781	+	0.0917647i	$0.970749\pi$
$398$	−13.5728	−	11.3890i	−0.680345	−	0.570878i
$399$	8.07485	−	9.80288i	0.404248	−	0.490758i
$400$	2.23183	+	12.6573i	0.111592	+	0.632867i
$401$	5.50118	−	15.1144i	0.274716	−	0.754775i	−0.723224	−	0.690614i	$-0.757340\pi$
$401$	5.50118	−	15.1144i	0.274716	−	0.754775i	0.997940	−	0.0641615i	$-0.0204373\pi$
$402$	5.23041	+	0.0396166i	0.260869	+	0.00197590i
$403$	−0.291048	+	1.65062i	−0.0144981	+	0.0822230i
$404$	−7.24892	−	12.5555i	−0.360647	−	0.624659i
$405$	29.8575	−	23.5497i	1.48363	−	1.17019i
$406$	7.18342	−	4.30855i	0.356507	−	0.213830i
$407$	0.892155	+	2.45118i	0.0442225	+	0.121500i
$408$	−1.77248	+	3.01701i	−0.0877507	+	0.149364i
$409$	6.23813	−	1.09995i	0.308455	−	0.0543890i	−0.0172778	−	0.999851i	$-0.505500\pi$
$409$	6.23813	−	1.09995i	0.308455	−	0.0543890i	0.325733	+	0.945462i	$0.394389\pi$
$410$	−12.6585	+	34.7789i	−0.625158	+	1.71761i
$411$	1.20452	−	6.54105i	0.0594144	−	0.322646i
$412$	0.186351	−	0.222084i	0.00918085	−	0.0109413i
$413$	−29.4329	+	17.6536i	−1.44830	+	0.868677i
$414$	13.5800	+	24.3663i	0.667420	+	1.19754i
$415$	8.33434	−	14.4355i	0.409117	−	0.708611i
$416$	0.147038	+	0.123379i	0.00720911	+	0.00604916i
$417$	7.12259	−	5.88521i	0.348795	−	0.288200i
$418$	4.04491	−	0.713227i	0.197843	−	0.0348851i
$419$	6.48313	+	2.35967i	0.316722	+	0.115277i	0.495489	−	0.868614i	$-0.334989\pi$
$419$	6.48313	+	2.35967i	0.316722	+	0.115277i	−0.178768	+	0.983891i	$0.557211\pi$
$420$	3.53549	+	19.0369i	0.172514	+	0.928907i
$421$	0.923275	−	5.23615i	0.0449977	−	0.255194i	−0.954008	−	0.299782i	$-0.903086\pi$
$421$	0.923275	−	5.23615i	0.0449977	−	0.255194i	0.999005	+	0.0445873i	$0.0141973\pi$
$422$	16.4973	+	9.52473i	0.803077	+	0.463657i
$423$	5.81229	−	30.2740i	0.282603	−	1.47197i
$424$	0.402869	+	0.697789i	0.0195650	+	0.0338876i
$425$	−4.50882	+	25.5708i	−0.218710	+	1.24037i
$426$	−2.39707	−	0.441414i	−0.116139	−	0.0213866i
$427$	1.48371	−	1.28772i	0.0718016	−	0.0623171i
$428$	3.94032	+	4.69589i	0.190462	+	0.226984i
$429$	−0.428547	+	0.243113i	−0.0206904	+	0.0117376i
$430$	17.5380	+	3.09242i	0.845757	+	0.149130i
$431$	14.1802	+	8.18697i	0.683038	+	0.394352i	0.800999	−	0.598666i	$-0.204302\pi$
$431$	14.1802	+	8.18697i	0.683038	+	0.394352i	−0.117961	+	0.993018i	$0.537636\pi$
$432$	−1.66579	−	4.92190i	−0.0801454	−	0.236805i
$433$			38.7574i			1.86256i	0.364302	+	0.931281i	$0.381308\pi$
$433$			38.7574i			1.86256i	−0.364302	+	0.931281i	$0.618692\pi$
$434$	8.26242	+	21.5751i	0.396609	+	1.03564i
$435$	−11.7366	+	19.9773i	−0.562725	+	0.957840i
$436$	5.56564	+	2.02573i	0.266546	+	0.0970147i
$437$	−24.2158	−	8.81382i	−1.15840	−	0.421622i
$438$	8.90269	+	1.63941i	0.425387	+	0.0783338i
$439$	−27.1835	−	4.79319i	−1.29740	−	0.228766i	−0.518046	−	0.855353i	$-0.673340\pi$
$439$	−27.1835	−	4.79319i	−1.29740	−	0.228766i	−0.779352	+	0.626586i	$0.784452\pi$
$440$	−3.13091	+	5.42290i	−0.149260	+	0.258527i
$441$	4.02207	+	20.6112i	0.191527	+	0.981487i
$442$	0.193886	+	0.335820i	0.00922221	+	0.0159733i
$443$	0.362239	+	0.995244i	0.0172105	+	0.0472855i	0.948000	−	0.318269i	$-0.103102\pi$
$443$	0.362239	+	0.995244i	0.0172105	+	0.0472855i	−0.930790	+	0.365555i	$0.880879\pi$
$444$	−1.06435	+	2.85676i	−0.0505117	+	0.135576i
$445$	−36.3663	+	30.5150i	−1.72393	+	1.44655i
$446$	−2.56675	−	14.5568i	−0.121539	−	0.689283i
$447$	−3.97485	−	23.5858i	−0.188004	−	1.11557i
$448$	2.61285	+	0.415942i	0.123446	+	0.0196514i
$449$	−35.4815	+	20.4852i	−1.67447	+	0.966758i	−0.709391	+	0.704815i	$0.751030\pi$
$449$	−35.4815	+	20.4852i	−1.67447	+	0.966758i	−0.965083	+	0.261943i	$0.915637\pi$
$450$	−24.3342	−	29.9090i	−1.14713	−	1.40992i
$451$	−11.2424	+	6.49082i	−0.529386	+	0.305641i
$452$	−2.10751	−	5.79034i	−0.0991291	−	0.272355i
$453$	1.19104	−	1.39778i	0.0559598	−	0.0656737i
$454$	−20.0988	+	3.54396i	−0.943284	+	0.166326i
$455$	2.02827	+	0.700175i	0.0950869	+	0.0328247i
$456$	4.13888	+	2.43156i	0.193821	+	0.113868i
$457$	−13.9424	−	11.6991i	−0.652199	−	0.547260i	0.255538	−	0.966799i	$-0.417747\pi$
$457$	−13.9424	−	11.6991i	−0.652199	−	0.547260i	−0.907737	+	0.419539i	$0.862192\pi$
$458$	−9.48729	+	16.4325i	−0.443312	+	0.767839i
$459$	0.238507	−	10.4947i	0.0111325	−	0.489852i
$460$	34.0241	−	19.6438i	1.58638	−	0.915898i
$461$	20.2961	−	7.38716i	0.945282	−	0.344054i	0.177032	−	0.984205i	$-0.443350\pi$
$461$	20.2961	−	7.38716i	0.945282	−	0.344054i	0.768249	+	0.640151i	$0.221128\pi$
$462$	−3.34209	+	5.91216i	−0.155488	+	0.275059i
$463$	6.16101	−	5.16970i	0.286326	−	0.240256i	−0.488300	−	0.872676i	$-0.662383\pi$
$463$	6.16101	−	5.16970i	0.286326	−	0.240256i	0.774626	+	0.632420i	$0.217938\pi$
$464$	2.03507	+	2.42530i	0.0944757	+	0.112592i
$465$	−48.6412	−	41.4466i	−2.25568	−	1.92204i
$466$	2.20057	−	0.800942i	0.101939	−	0.0371029i
$467$	1.20533			0.0557760			0.0278880	−	0.999611i	$-0.491122\pi$
$467$	1.20533			0.0557760			0.0278880	+	0.999611i	$0.491122\pi$
$468$	−0.565504	−	0.108571i	−0.0261404	−	0.00501868i
$469$	−0.133158	−	7.98870i	−0.00614866	−	0.368884i
$470$	−42.7574	−	7.53928i	−1.97225	−	0.347761i
$471$	2.78294	+	1.03684i	0.128231	+	0.0477753i
$472$	−8.33837	−	9.93729i	−0.383805	−	0.457401i
$473$	4.01509	+	4.78500i	0.184614	+	0.220014i
$474$	2.10998	+	12.5201i	0.0969146	+	0.575067i
$475$	35.0792	+	6.18541i	1.60954	+	0.283806i
$476$	4.67284	+	2.59500i	0.214179	+	0.118942i
$477$	−2.07482	−	1.24018i	−0.0949995	−	0.0567838i
$478$	10.0275			0.458649
$479$	−22.7928	+	8.29591i	−1.04143	+	0.379050i	−0.805423	−	0.592701i	$-0.798062\pi$
$479$	−22.7928	+	8.29591i	−1.04143	+	0.379050i	−0.236009	+	0.971751i	$0.575839\pi$
$480$	−6.89573	+	2.45085i	−0.314746	+	0.111866i
$481$	0.217160	+	0.258802i	0.00990166	+	0.0118003i
$482$	12.2391	−	10.2698i	0.557475	−	0.467777i
$483$	36.7064	−	21.6398i	1.67020	−	0.984646i
$484$	8.27273	−	3.01103i	0.376033	−	0.136865i
$485$	−44.2702	+	25.5594i	−2.01020	+	1.16059i
$486$	11.5535	+	10.4650i	0.524078	+	0.474702i
$487$	14.7237	−	25.5022i	0.667196	−	1.15562i	−0.311490	−	0.950250i	$-0.600828\pi$
$487$	14.7237	−	25.5022i	0.667196	−	1.15562i	0.978685	−	0.205367i	$-0.0658388\pi$
$488$	0.568822	+	0.477298i	0.0257494	+	0.0216063i
$489$	−21.1614	+	12.0048i	−0.956953	+	0.542875i
$490$	28.9400	−	6.10381i	1.30737	−	0.275742i
$491$	29.4534	−	5.19343i	1.32921	−	0.234376i	0.536464	−	0.843923i	$-0.319760\pi$
$491$	29.4534	−	5.19343i	1.32921	−	0.234376i	0.792750	+	0.609547i	$0.208649\pi$
$492$	−14.9210	−	2.74767i	−0.672692	−	0.123874i
$493$	2.18758	+	6.01034i	0.0985239	+	0.270692i
$494$	0.460694	−	0.265982i	0.0207276	−	0.0119671i
$495$	0.284557	−	18.7833i	0.0127899	−	0.844247i
$496$	−7.56225	+	4.36607i	−0.339555	+	0.196042i
$497$	−0.585322	+	3.67686i	−0.0262553	+	0.164930i
$498$	6.40303	+	2.38559i	0.286927	+	0.106901i
$499$	1.81466	+	10.2914i	0.0812353	+	0.460708i	0.998106	+	0.0615232i	$0.0195958\pi$
$499$	1.81466	+	10.2914i	0.0812353	+	0.460708i	−0.916870	+	0.399185i	$0.869293\pi$
$500$	−25.4166	+	21.3271i	−1.13667	+	0.953776i
$501$	−40.5973	+	6.84176i	−1.81375	+	0.305667i
$502$	−5.06472	−	13.9152i	−0.226049	−	0.621066i
$503$	−16.2725	−	28.1848i	−0.725554	−	1.25670i	−0.958746	−	0.284265i	$-0.908250\pi$
$503$	−16.2725	−	28.1848i	−0.725554	−	1.25670i	0.233192	−	0.972431i	$-0.425083\pi$
$504$	−7.45445	+	2.72602i	−0.332048	+	0.121427i
$505$	30.6284	−	53.0499i	1.36294	−	2.36069i
$506$	13.5709	+	2.39291i	0.603298	+	0.106378i
$507$	14.5623	−	17.0901i	0.646733	−	0.758997i
$508$	9.56225	+	3.48037i	0.424256	+	0.154417i
$509$	6.61041	+	2.40599i	0.293001	+	0.106644i	0.484339	−	0.874881i	$-0.339060\pi$
$509$	6.61041	+	2.40599i	0.293001	+	0.106644i	−0.191337	+	0.981524i	$0.561282\pi$
$510$	−14.7843	−	0.111980i	−0.654660	−	0.00495858i
$511$	2.17388	−	13.6558i	0.0961666	−	0.604096i
$512$			1.00000i			0.0441942i
$513$	−14.3972	−	0.327195i	−0.635650	−	0.0144460i
$514$	−8.45468	−	4.88131i	−0.372920	−	0.215305i
$515$	1.20633	+	0.212709i	0.0531573	+	0.00937306i
$516$	−0.0552926	+	7.30005i	−0.00243412	+	0.321367i
$517$	−9.78874	−	11.6658i	−0.430508	−	0.513060i
$518$	4.40190	+	1.51957i	0.193408	+	0.0667660i
$519$	6.85175	+	19.2781i	0.300758	+	0.846215i
$520$	−0.140830	+	0.798687i	−0.00617580	+	0.0350247i
$521$	−11.1713	−	19.3493i	−0.489424	−	0.847706i	0.510502	−	0.859876i	$-0.329459\pi$
$521$	−11.1713	−	19.3493i	−0.489424	−	0.847706i	−0.999926	+	0.0121699i	$0.996126\pi$
$522$	−8.87498	−	3.38333i	−0.388447	−	0.148085i
$523$	17.6613	+	10.1967i	0.772274	+	0.445873i	0.833685	−	0.552240i	$-0.186227\pi$
$523$	17.6613	+	10.1967i	0.772274	+	0.445873i	−0.0614113	+	0.998113i	$0.519560\pi$
$524$	2.54308	−	14.4225i	0.111095	−	0.630051i
$525$	−44.7724	+	38.2676i	−1.95403	+	1.67013i
$526$	2.74267	+	0.998249i	0.119586	+	0.0435257i
$527$	−17.3729	+	3.06332i	−0.756778	+	0.133440i
$528$	−2.40539	−	0.896180i	−0.104681	−	0.0390012i
$529$	−48.6125	−	40.7908i	−2.11359	−	1.77351i
$530$	−1.70221	+	2.94832i	−0.0739395	+	0.128067i
$531$	36.3638	+	13.8627i	1.57806	+	0.601589i
$532$	3.55994	−	6.41041i	0.154343	−	0.277927i
$533$	−1.08074	+	1.28798i	−0.0468121	+	0.0557884i
$534$	−14.8125	−	12.6216i	−0.640999	−	0.546188i
$535$	−8.85862	+	24.3389i	−0.382992	+	1.05226i
$536$	2.97399	−	0.524394i	0.128457	−	0.0226504i
$537$	28.1779	+	0.213427i	1.21596	+	0.00921006i
$538$	−1.16173	−	3.19184i	−0.0500859	−	0.137610i
$539$	9.15207	+	4.88472i	0.394207	+	0.210400i
$540$	14.4909	−	16.4935i	0.623587	−	0.709767i
$541$	−8.68856	−	15.0490i	−0.373550	−	0.647008i	0.616559	−	0.787309i	$-0.288526\pi$
$541$	−8.68856	−	15.0490i	−0.373550	−	0.647008i	−0.990109	+	0.140301i	$0.955193\pi$
$542$	0.144579	−	0.819946i	0.00621018	−	0.0352197i
$543$	9.77568	−	16.6396i	0.419515	−	0.714075i
$544$	−0.690961	+	1.89840i	−0.0296247	+	0.0813932i
$545$	4.34560	+	24.6451i	0.186145	+	1.05568i
$546$	−0.144858	+	0.867587i	−0.00619935	+	0.0371293i
$547$	−23.2533	−	19.5118i	−0.994239	−	0.834266i	−0.00806345	−	0.999967i	$-0.502567\pi$
$547$	−23.2533	−	19.5118i	−0.994239	−	0.834266i	−0.986176	+	0.165702i	$0.947011\pi$
$548$		−	3.83997i		−	0.164036i
$549$	−2.18768	−	0.420011i	−0.0933679	−	0.0179256i
$550$	−19.0476			−0.812194
$551$	8.24526	−	3.00103i	0.351260	−	0.127848i
$552$	10.2585	+	12.4154i	0.436630	+	0.528433i
$553$	19.0410	−	3.68566i	0.809706	−	0.156730i
$554$	3.45287	−	9.48668i	0.146698	−	0.403051i
$555$	−12.7019	+	2.14062i	−0.539166	+	0.0908643i
$556$	3.42887	−	4.08637i	0.145417	−	0.173301i
$557$			1.01885i			0.0431699i	0.999767	+	0.0215850i	$0.00687124\pi$
$557$			1.01885i			0.0431699i	−0.999767	+	0.0215850i	$0.993129\pi$
$558$	13.4403	−	22.4857i	0.568975	−	0.951897i
$559$	0.700620	+	0.404503i	0.0296331	+	0.0171087i
$560$	3.99796	+	10.4396i	0.168944	+	0.441152i
$561$	−3.94716	−	3.36334i	−0.166649	−	0.142000i
$562$	2.57199	−	2.15815i	0.108493	−	0.0910362i
$563$	−3.56773	−	20.2336i	−0.150362	−	0.852745i	−0.962904	−	0.269843i	$-0.913028\pi$
$563$	−3.56773	−	20.2336i	−0.150362	−	0.852745i	0.812542	−	0.582902i	$-0.198083\pi$
$564$	0.134803	−	17.7974i	0.00567622	−	0.749407i
$565$	16.7354	−	19.9445i	0.704065	−	0.839072i
$566$	28.0120			1.17743
$567$	15.5531	−	18.0306i	0.653169	−	0.757212i
$568$	−1.40722			−0.0590456
$569$	8.77632	−	10.4592i	0.367922	−	0.438473i	−0.550041	−	0.835138i	$-0.685388\pi$
$569$	8.77632	−	10.4592i	0.367922	−	0.438473i	0.917964	+	0.396665i	$0.129832\pi$
$570$	−0.153620	+	20.2818i	−0.00643443	+	0.849510i
$571$	−1.00699	−	5.71090i	−0.0421410	−	0.238994i	0.956460	−	0.291862i	$-0.0942748\pi$
$571$	−1.00699	−	5.71090i	−0.0421410	−	0.238994i	−0.998601	+	0.0528682i	$0.983164\pi$
$572$	−0.217911	+	0.182849i	−0.00911130	+	0.00764529i
$573$	15.2225	+	12.9709i	0.635927	+	0.541867i
$574$	−3.64345	+	22.8873i	−0.152075	+	0.955297i
$575$	103.497	+	59.7539i	4.31612	+	2.49191i
$576$	−1.46047	−	2.62050i	−0.0608530	−	0.109187i
$577$		−	16.9442i		−	0.705395i	−0.935737	−	0.352697i	$-0.885265\pi$
$577$		−	16.9442i		−	0.705395i	0.935737	−	0.352697i	$-0.114735\pi$
$578$	8.30395	−	9.89626i	0.345399	−	0.411630i
$579$	−20.0289	+	3.37542i	−0.832372	+	0.140278i
$580$	−4.57524	+	12.5704i	−0.189976	+	0.521956i
$581$	3.40590	−	9.86624i	0.141301	−	0.409321i
$582$	−13.3477	−	16.1541i	−0.553281	−	0.669610i
$583$	−1.12209	+	0.408409i	−0.0464724	+	0.0169146i
$584$	5.22639			0.216270
$585$	−0.797415	−	2.29864i	−0.0329691	−	0.0950369i
$586$		−	17.7018i		−	0.731254i
$587$	6.70387	+	5.62522i	0.276698	+	0.232178i	0.770567	−	0.637359i	$-0.219973\pi$
$587$	6.70387	+	5.62522i	0.276698	+	0.232178i	−0.493869	+	0.869537i	$0.664418\pi$
$588$	4.43885	+	11.2826i	0.183055	+	0.465286i
$589$	4.20240	+	23.8330i	0.173157	+	0.982022i
$590$	18.7463	−	51.5051i	0.771774	−	2.12043i
$591$	−14.8130	+	25.2138i	−0.609324	+	1.03716i
$592$	−0.305639	+	1.73337i	−0.0125617	+	0.0712409i
$593$	22.5781	+	39.1064i	0.927172	+	1.60591i	0.788030	+	0.615637i	$0.211101\pi$
$593$	22.5781	+	39.1064i	0.927172	+	1.60591i	0.139142	+	0.990272i	$0.455566\pi$
$594$	7.61217	−	1.16457i	0.312331	−	0.0477828i
$595$	0.376384	+	22.5809i	0.0154303	+	0.925727i
$596$	−4.72305	−	12.9765i	−0.193463	−	0.531537i
$597$	30.6878	+	0.232438i	1.25597	+	0.00951305i
$598$	1.75765	−	0.309920i	0.0718755	−	0.0126736i
$599$	−4.63202	+	12.7264i	−0.189259	+	0.519985i	−0.997639	−	0.0686759i	$-0.978123\pi$
$599$	−4.63202	+	12.7264i	−0.189259	+	0.519985i	0.808380	+	0.588661i	$0.200345\pi$
$600$	−16.9443	−	14.4381i	−0.691749	−	0.589432i
$601$	−18.2122	+	21.7044i	−0.742891	+	0.885343i	−0.996638	−	0.0819276i	$-0.973892\pi$
$601$	−18.2122	+	21.7044i	−0.742891	+	0.885343i	0.253747	+	0.967271i	$0.418337\pi$
$602$	11.1498	−	0.185848i	0.454431	−	0.00757458i
$603$	−7.02747	+	5.71760i	−0.286181	+	0.232839i
$604$	0.530124	−	0.918201i	0.0215704	−	0.0373611i
$605$	28.4949	+	23.9101i	1.15848	+	0.972084i
$606$	23.5309	+	8.76694i	0.955877	+	0.356132i
$607$	19.9225	−	3.51287i	0.808629	−	0.142583i	0.245975	−	0.969276i	$-0.420892\pi$
$607$	19.9225	−	3.51287i	0.808629	−	0.142583i	0.562653	+	0.826693i	$0.309781\pi$
$608$	2.60431	+	0.947892i	0.105619	+	0.0384421i
$609$	−4.83802	+	13.6780i	−0.196046	+	0.554262i
$610$	−0.544808	+	3.08976i	−0.0220586	+	0.125101i
$611$	−1.70810	−	0.986174i	−0.0691024	−	0.0398963i
$612$	−0.961899	−	5.98389i	−0.0388824	−	0.241884i
$613$	10.2502	+	17.7539i	0.414003	+	0.717075i	0.995323	−	0.0966001i	$-0.0307968\pi$
$613$	10.2502	+	17.7539i	0.414003	+	0.717075i	−0.581320	+	0.813675i	$0.697463\pi$
$614$	3.49350	−	19.8126i	0.140986	−	0.799572i
$615$	−21.4683	−	60.4032i	−0.865684	−	2.43569i
$616$	−1.27948	+	3.70639i	−0.0515515	+	0.149335i
$617$	−30.2178	−	36.0122i	−1.21652	−	1.44980i	−0.855945	−	0.517067i	$-0.827024\pi$
$617$	−30.2178	−	36.0122i	−1.21652	−	1.44980i	−0.360579	−	0.932729i	$-0.617421\pi$
$618$	−0.00380324	+	0.502125i	−0.000152989	+	0.0201984i
$619$	13.6419	+	2.40543i	0.548313	+	0.0966824i	0.440940	−	0.897536i	$-0.354645\pi$
$619$	13.6419	+	2.40543i	0.548313	+	0.0966824i	0.107373	+	0.994219i	$0.465756\pi$
$620$	−31.9523	−	18.4476i	−1.28323	−	0.740875i
$621$	−45.0146	−	17.5522i	−1.80638	−	0.704345i
$622$		−	7.40832i		−	0.297047i
$623$	−18.7256	+	23.0871i	−0.750227	+	0.924965i
$624$	−0.332447	−	0.00251805i	−0.0133085	−	0.000100803i
$625$	−71.3474	−	25.9683i	−2.85389	−	1.03873i
$626$	−6.41014	−	2.33310i	−0.256201	−	0.0932494i
$627$	−4.61398	+	5.41490i	−0.184265	+	0.216250i
$628$	1.68857	+	0.297741i	0.0673814	+	0.0118812i
$629$	−1.77791	+	3.07944i	−0.0708900	+	0.122785i
$630$	−25.7233	−	21.5180i	−1.02484	−	0.857297i
$631$	−7.38376	−	12.7890i	−0.293943	−	0.509124i	0.680796	−	0.732473i	$-0.261634\pi$
$631$	−7.38376	−	12.7890i	−0.293943	−	0.509124i	−0.974738	+	0.223350i	$0.928301\pi$
$632$	2.50715	+	6.88833i	0.0997290	+	0.274003i
$633$	−32.5358	+	5.48319i	−1.29318	+	0.217937i
$634$	19.4119	−	16.2885i	0.770946	−	0.646901i
$635$	7.46612	+	42.3425i	0.296284	+	1.68031i
$636$	−1.30776	−	0.487235i	−0.0518561	−	0.0193201i
$637$	1.33024	+	0.189087i	0.0527059	+	0.00749189i
$638$	−4.06342	+	2.34602i	−0.160873	+	0.0928798i
$639$	3.68762	−	2.05521i	0.145880	−	0.0813027i
$640$	−3.65916	+	2.11262i	−0.144641	+	0.0835085i
$641$	8.51140	+	23.3849i	0.336180	+	0.923648i	0.986467	+	0.163959i	$0.0524265\pi$
$641$	8.51140	+	23.3849i	0.336180	+	0.923648i	−0.650287	+	0.759689i	$0.725351\pi$
$642$	−10.4420	−	1.92286i	−0.412112	−	0.0758893i
$643$	−1.86065	+	0.328082i	−0.0733767	+	0.0129383i	−0.210216	−	0.977655i	$-0.567417\pi$
$643$	−1.86065	+	0.328082i	−0.0733767	+	0.0129383i	0.136839	+	0.990593i	$0.456306\pi$
$644$	18.5794	−	16.1252i	0.732130	−	0.635421i
$645$	−26.8289	+	15.2199i	−1.05639	+	0.599282i
$646$	4.28907	+	3.59896i	0.168751	+	0.141599i
$647$	12.9150	−	22.3694i	0.507740	−	0.879431i	−0.492220	−	0.870471i	$-0.663815\pi$
$647$	12.9150	−	22.3694i	0.507740	−	0.879431i	0.999960	−	0.00896015i	$-0.00285214\pi$
$648$	7.65434	+	4.73404i	0.300691	+	0.185971i
$649$	16.6492	−	9.61245i	0.653540	−	0.377322i
$650$	−2.31820	+	0.843756i	−0.0909273	+	0.0330948i
$651$	−34.8351	−	19.6919i	−1.36529	−	0.771787i
$652$	−10.7603	+	9.02898i	−0.421407	+	0.353602i
$653$	−23.1505	−	27.5897i	−0.905948	−	1.07967i	−0.996485	−	0.0837739i	$-0.973303\pi$
$653$	−23.1505	−	27.5897i	−0.905948	−	1.07967i	0.0905366	−	0.995893i	$-0.471142\pi$
$654$	−9.66627	+	3.43555i	−0.377981	+	0.134341i
$655$	58.1469	−	21.1637i	2.27199	−	0.826936i
$656$	−8.75951			−0.342001
$657$	−13.6958	+	7.63300i	−0.534322	+	0.297792i
$658$	−27.1830	+	0.453094i	−1.05970	+	0.0176634i
$659$	5.93475	+	1.04646i	0.231185	+	0.0407642i	0.288040	−	0.957618i	$-0.406996\pi$
$659$	5.93475	+	1.04646i	0.231185	+	0.0407642i	−0.0568553	+	0.998382i	$0.518107\pi$
$660$	−1.80240	−	10.6950i	−0.0701583	−	0.416302i
$661$	9.68662	+	11.5441i	0.376766	+	0.449012i	0.920791	−	0.390057i	$-0.127545\pi$
$661$	9.68662	+	11.5441i	0.376766	+	0.449012i	−0.544025	+	0.839069i	$0.683100\pi$
$662$	−7.47776	−	8.91164i	−0.290631	−	0.346361i
$663$	−0.629377	−	0.234488i	−0.0244430	−	0.00910677i
$664$	3.88510	+	0.685048i	0.150771	+	0.0265850i
$665$	30.9775	−	0.516341i	1.20126	−	0.0200229i
$666$	−1.73061	−	4.98866i	−0.0670596	−	0.193307i
$667$	29.4386			1.13987
$668$	−22.3359	+	8.12960i	−0.864202	+	0.314544i
$669$	19.4871	+	16.6047i	0.753413	+	0.641976i
$670$	8.20173	+	9.77445i	0.316861	+	0.377620i
$671$	−0.842998	+	0.707359i	−0.0325436	+	0.0273073i
$672$	−3.94763	+	2.32728i	−0.152283	+	0.0897767i
$673$	−24.9408	+	9.07770i	−0.961396	+	0.349919i	−0.774580	−	0.632476i	$-0.782039\pi$
$673$	−24.9408	+	9.07770i	−0.961396	+	0.349919i	−0.186815	+	0.982395i	$0.559817\pi$
$674$	−16.3853	+	9.46004i	−0.631137	+	0.364387i
$675$	65.4890	+	13.0882i	2.52067	+	0.503767i
$676$	6.48158	−	11.2264i	0.249291	−	0.431786i
$677$	31.2281	+	26.2035i	1.20019	+	1.00708i	0.999625	+	0.0274018i	$0.00872336\pi$
$677$	31.2281	+	26.2035i	1.20019	+	1.00708i	0.200568	+	0.979680i	$0.435721\pi$
$678$	9.20225	+	5.40626i	0.353410	+	0.207626i
$679$	−24.1744	+	20.9811i	−0.927728	+	0.805181i
$680$	−8.40628	+	1.48225i	−0.322366	+	0.0568419i
$681$	22.9265	−	26.9062i	0.878545	−	1.03105i
$682$	−4.42611	−	12.1606i	−0.169484	−	0.465655i
$683$	−9.45309	+	5.45774i	−0.361712	+	0.208835i	−0.669832	−	0.742513i	$-0.733634\pi$
$683$	−9.45309	+	5.45774i	−0.361712	+	0.208835i	0.308119	+	0.951348i	$0.400300\pi$
$684$	−8.20897	+	1.31958i	−0.313878	+	0.0504553i
$685$	14.0511	−	8.11240i	0.536864	−	0.309959i
$686$	17.0650	−	7.19619i	0.651545	−	0.274752i
$687$	−5.46164	−	32.4080i	−0.208374	−	1.23644i
$688$	0.731893	+	4.15077i	0.0279032	+	0.158247i
$689$	−0.118474	+	0.0994112i	−0.00451349	+	0.00378727i
$690$	−23.7575	+	63.7663i	−0.904433	+	2.42754i
$691$	15.5905	+	42.8346i	0.593091	+	1.62950i	0.764735	+	0.644345i	$0.222870\pi$
$691$	15.5905	+	42.8346i	0.593091	+	1.62950i	−0.171644	+	0.985159i	$0.554908\pi$
$692$	5.90615	+	10.2298i	0.224518	+	0.388877i
$693$	−2.06022	−	11.5812i	−0.0782614	−	0.439935i
$694$	−2.41384	+	4.18089i	−0.0916279	+	0.158704i
$695$	22.1966	+	3.91386i	0.841965	+	0.148461i
$696$	−5.39300	−	0.993106i	−0.204421	−	0.0376436i
$697$	−16.6290	−	6.05248i	−0.629870	−	0.229254i
$698$	3.37891	+	1.22982i	0.127894	+	0.0465495i
$699$	−2.05460	+	3.49724i	−0.0777123	+	0.132278i
$700$	−21.4207	+	26.4098i	−0.809626	+	0.998198i
$701$		−	29.1414i		−	1.10066i	−0.834948	−	0.550329i	$-0.814502\pi$
$701$		−	29.1414i		−	1.10066i	0.834948	−	0.550329i	$-0.185498\pi$
$702$	0.874855	−	0.478931i	0.0330193	−	0.0180761i
$703$	4.22451	+	2.43902i	0.159330	+	0.0919895i
$704$	−1.45949	−	0.257348i	−0.0550067	−	0.00969916i
$705$	65.4084	−	37.1059i	2.46342	−	1.39749i
$706$	−16.4864	−	19.6477i	−0.620473	−	0.739451i
$707$	12.5166	−	36.2580i	0.470733	−	1.36362i
$708$	22.0970	+	4.06910i	0.830456	+	0.152926i
$709$	−2.83478	+	16.0769i	−0.106463	+	0.603779i	0.884164	+	0.467178i	$0.154729\pi$
$709$	−2.83478	+	16.0769i	−0.106463	+	0.603779i	−0.990626	+	0.136602i	$0.956382\pi$
$710$	−2.97292	−	5.14924i	−0.111572	−	0.193248i
$711$	−16.6302	−	14.3892i	−0.623681	−	0.539639i
$712$	−9.73028	−	5.61778i	−0.364657	−	0.210535i
$713$	−14.0993	+	79.9608i	−0.528021	+	2.99456i
$714$	−9.10224	+	1.69045i	−0.340643	+	0.0632633i
$715$	−1.12943	−	0.411080i	−0.0422385	−	0.0153735i
$716$	16.0218	−	2.82508i	0.598763	−	0.105578i
$717$	−13.3890	+	11.0630i	−0.500021	+	0.413154i
$718$	22.6870	+	19.0367i	0.846672	+	0.710442i
$719$	12.5282	−	21.6995i	0.467223	−	0.809254i	−0.532076	−	0.846697i	$-0.678588\pi$
$719$	12.5282	−	21.6995i	0.467223	−	0.809254i	0.999299	+	0.0374427i	$0.0119212\pi$
$720$	6.50341	−	10.8802i	0.242368	−	0.405482i
$721$	0.766925	−	0.0127833i	0.0285618	−	0.000476075i
$722$	−7.27575	+	8.67090i	−0.270775	+	0.322698i
$723$	−5.01163	+	27.2153i	−0.186385	+	1.01215i
$724$	3.81084	−	10.4702i	0.141629	−	0.389121i
$725$	−40.0732	+	7.06598i	−1.48828	+	0.262424i
$726$	−7.72399	+	13.1474i	−0.286664	+	0.487944i
$727$	−6.29728	−	17.3016i	−0.233553	−	0.641682i	0.766447	−	0.642308i	$-0.222023\pi$
$727$	−6.29728	−	17.3016i	−0.233553	−	0.641682i	−1.00000		0.000625865i	$0.999801\pi$
$728$	0.00846357	+	0.507765i	0.000313681	+	0.0188190i
$729$	−26.9721	−	1.22659i	−0.998968	−	0.0454292i
$730$	11.0414	+	19.1242i	0.408659	+	0.707818i
$731$	−1.47860	+	8.38554i	−0.0546879	+	0.310150i
$732$	−1.28609	−	0.00974119i	−0.0475352	−	0.000360045i
$733$	−8.13587	+	22.3531i	−0.300505	+	0.825631i	0.693907	+	0.720065i	$0.255888\pi$
$733$	−8.13587	+	22.3531i	−0.300505	+	0.825631i	−0.994412	+	0.105567i	$0.966334\pi$
$734$	−1.67060	−	9.47447i	−0.0616631	−	0.349709i
$735$	−31.9072	+	40.0782i	−1.17691	+	1.47831i
$736$	7.12294	+	5.97686i	0.262555	+	0.220310i
$737$			4.47546i			0.164856i
$738$	22.9543	−	12.7930i	0.844959	−	0.470918i
$739$	29.5625			1.08747			0.543737	−	0.839256i	$-0.317009\pi$
$739$	29.5625			1.08747			0.543737	+	0.839256i	$0.317009\pi$
$740$	−6.98836	+	2.54355i	−0.256897	+	0.0935029i
$741$	−0.321682	+	0.863409i	−0.0118173	+	0.0317181i
$742$	−0.695625	+	2.01509i	−0.0255372	+	0.0739764i
$743$	6.04653	−	16.6127i	0.221826	−	0.609461i	−0.777997	−	0.628267i	$-0.783764\pi$
$743$	6.04653	−	16.6127i	0.221826	−	0.609461i	0.999823	+	0.0188063i	$0.00598660\pi$
$744$	5.28038	−	14.1728i	0.193588	−	0.519600i
$745$	37.5050	−	44.6967i	1.37408	−	1.63756i
$746$			9.88807i			0.362028i
$747$	−11.1814	+	3.87891i	−0.409106	+	0.141922i
$748$	−2.59288	−	1.49700i	−0.0948051	−	0.0547358i
$749$	−2.54974	+	16.0169i	−0.0931656	+	0.585245i
$750$	10.4075	−	56.5175i	0.380030	−	2.06373i
$751$	−21.3533	+	17.9176i	−0.779195	+	0.653822i	−0.943046	−	0.332663i	$-0.892053\pi$
$751$	−21.3533	+	17.9176i	−0.779195	+	0.653822i	0.163851	+	0.986485i	$0.447608\pi$
$752$	−1.78435	−	10.1195i	−0.0650684	−	0.369021i
$753$	22.1146	+	12.9922i	0.805901	+	0.473462i
$754$	−0.390619	+	0.465521i	−0.0142255	+	0.0169533i
$755$	4.47979			0.163036
$756$	6.94584	−	11.8640i	0.252618	−	0.431491i
$757$	−38.8826			−1.41321			−0.706607	−	0.707606i	$-0.749775\pi$
$757$	−38.8826			−1.41321			−0.706607	+	0.707606i	$0.749775\pi$
$758$	−4.75098	+	5.66200i	−0.172563	+	0.205653i
$759$	−20.7601	+	11.7771i	−0.753544	+	0.427482i
$760$	2.03342	+	11.5321i	0.0737601	+	0.418314i
$761$	14.8724	−	12.4794i	0.539124	−	0.452379i	−0.332114	−	0.943239i	$-0.607762\pi$
$761$	14.8724	−	12.4794i	0.539124	−	0.452379i	0.871238	+	0.490860i	$0.163317\pi$
$762$	−16.6075	+	5.90257i	−0.601626	+	0.213827i
$763$	5.60424	+	14.6339i	0.202887	+	0.529784i
$764$	9.99959	+	5.77327i	0.361773	+	0.208870i
$765$	19.8639	−	16.1614i	0.718180	−	0.584317i
$766$		0	0.000193642i		0	6.99656e-6i
$767$	1.60050	−	1.90740i	0.0577907	−	0.0688723i
$768$	−1.10326	−	1.33522i	−0.0398104	−	0.0481807i
$769$	−7.44636	+	20.4587i	−0.268523	+	0.737760i	0.730001	+	0.683446i	$0.239519\pi$
$769$	−7.44636	+	20.4587i	−0.268523	+	0.737760i	−0.998524	+	0.0543139i	$0.982703\pi$
$770$	−16.2653	+	3.14838i	−0.586162	+	0.113460i
$771$	16.6742	−	2.81007i	0.600508	−	0.101202i
$772$	−11.0195	+	4.01078i	−0.396602	+	0.144351i
$773$	9.52504			0.342592			0.171296	−	0.985220i	$-0.445205\pi$
$773$	9.52504			0.342592			0.171296	+	0.985220i	$0.445205\pi$
$774$	−7.98002	−	9.80819i	−0.286836	−	0.352548i
$775$		−	112.231i		−	4.03144i
$776$	−9.26795	−	7.77674i	−0.332700	−	0.279169i
$777$	−7.55399	+	2.82747i	−0.270998	+	0.101435i
$778$	4.07069	+	23.0860i	0.145941	+	0.827675i
$779$	−8.30306	+	22.8125i	−0.297488	+	0.817342i
$780$	−0.693119	−	1.22180i	−0.0248177	−	0.0437473i
$781$	0.362145	−	2.05383i	0.0129586	−	0.0734917i
$782$	9.39242	+	16.2681i	0.335872	+	0.581748i
$783$	15.5828	−	5.27390i	0.556883	−	0.188474i
$784$	3.70009	+	5.94216i	0.132146	+	0.212220i
$785$	2.47783	+	6.80778i	0.0884375	+	0.242980i
$786$	12.5162	+	22.0630i	0.446439	+	0.786960i
$787$	47.7032	−	8.41137i	1.70044	−	0.299833i	0.762590	−	0.646882i	$-0.223927\pi$
$787$	47.7032	−	8.41137i	1.70044	−	0.299833i	0.937847	+	0.347049i	$0.112816\pi$
$788$	−5.77451	+	15.8653i	−0.205708	+	0.565179i
$789$	−4.76340	+	1.69299i	−0.169582	+	0.0602720i
$790$	−19.9089	+	23.7265i	−0.708325	+	0.844149i
$791$	7.91507	−	14.2527i	0.281427	−	0.506768i
$792$	4.20045	−	1.45717i	0.149256	−	0.0517782i
$793$	−0.0712634	+	0.123432i	−0.00253064	+	0.00438320i
$794$	−2.80127	−	2.35054i	−0.0994133	−	0.0834177i
$795$	−0.979929	−	5.81465i	−0.0347545	−	0.206224i
$796$	17.4489	−	3.07671i	0.618460	−	0.109051i
$797$	−3.46019	−	1.25941i	−0.122566	−	0.0446105i	0.280009	−	0.959997i	$-0.409663\pi$
$797$	−3.46019	−	1.25941i	−0.122566	−	0.0446105i	−0.402575	+	0.915387i	$0.631885\pi$
$798$	2.31903	+	12.4869i	0.0820928	+	0.442030i
$799$	3.60480	−	20.4438i	0.127529	−	0.723251i
$800$	−11.1307	−	6.42630i	−0.393529	−	0.227204i
$801$	33.7028	+	0.510578i	1.19083	+	0.0180404i
$802$	8.04218	+	13.9295i	0.283979	+	0.491867i
$803$	−1.34500	+	7.62788i	−0.0474640	+	0.269182i
$804$	−3.39239	+	3.98126i	−0.119640	+	0.140408i
$805$	98.2557	+	33.9186i	3.46306	+	1.19547i
$806$	−1.07736	−	1.28395i	−0.0379485	−	0.0452253i
$807$	5.07259	+	2.98012i	0.178564	+	0.104905i
$808$	14.2776	+	2.51752i	0.502283	+	0.0885661i
$809$	−40.2522	−	23.2396i	−1.41519	−	0.817061i	−0.419321	−	0.907838i	$-0.637732\pi$
$809$	−40.2522	−	23.2396i	−1.41519	−	0.817061i	−0.995871	+	0.0907769i	$0.971065\pi$
$810$	−1.15191	+	38.0096i	−0.0404741	+	1.33552i
$811$			32.7012i			1.14830i	0.818752	+	0.574148i	$0.194666\pi$
$811$			32.7012i			1.14830i	−0.818752	+	0.574148i	$0.805334\pi$
$812$	−1.31687	+	8.27230i	−0.0462132	+	0.290301i
$813$	0.711569	+	1.25432i	0.0249558	+	0.0439909i
$814$	−2.45118	−	0.892155i	−0.0859137	−	0.0312700i
$815$	−55.7709	−	20.2990i	−1.95357	−	0.711042i
$816$	−1.17184	−	3.29709i	−0.0410226	−	0.115421i
$817$	11.5037	+	2.02841i	0.402462	+	0.0709650i
$818$	−3.16718	+	5.48572i	−0.110738	+	0.191804i
$819$	−0.763756	−	1.31824i	−0.0266878	−	0.0460630i
$820$	−18.5055	−	32.0524i	−0.646239	−	1.11932i
$821$	−3.46512	−	9.52035i	−0.120934	−	0.332262i	0.864424	−	0.502764i	$-0.167683\pi$
$821$	−3.46512	−	9.52035i	−0.120934	−	0.332262i	−0.985357	+	0.170501i	$0.945461\pi$
$822$	4.23649	+	5.12722i	0.147765	+	0.178832i
$823$	7.47413	−	6.27154i	0.260532	−	0.218612i	−0.503160	−	0.864193i	$-0.667829\pi$
$823$	7.47413	−	6.27154i	0.260532	−	0.218612i	0.763692	+	0.645581i	$0.223385\pi$
$824$	0.0503424	+	0.285506i	0.00175376	+	0.00994608i
$825$	25.4328	−	21.0145i	0.885457	−	0.731630i
$826$	5.39569	−	33.8944i	0.187740	−	1.17934i
$827$	−23.3228	+	13.4654i	−0.811014	+	0.468239i	−0.847308	−	0.531102i	$-0.821778\pi$
$827$	−23.3228	+	13.4654i	−0.811014	+	0.468239i	0.0362936	+	0.999341i	$0.488445\pi$
$828$	−27.3947	−	5.25949i	−0.952032	−	0.182780i
$829$	8.52058	−	4.91936i	0.295932	−	0.170856i	−0.344682	−	0.938720i	$-0.612013\pi$
$829$	8.52058	−	4.91936i	0.295932	−	0.170856i	0.640614	+	0.767863i	$0.278680\pi$
$830$	5.70102	+	15.6634i	0.197885	+	0.543686i
$831$	5.85592	+	16.4762i	0.203140	+	0.571555i
$832$	−0.189028	+	0.0333307i	−0.00655336	+	0.00115553i
$833$	2.91845	+	13.8372i	0.101118	+	0.479431i
$834$	−0.0699800	+	9.23916i	−0.00242321	+	0.319926i
$835$	−76.9347	−	64.5559i	−2.66244	−	2.23405i
$836$	−2.05365	+	3.55703i	−0.0710271	+	0.123023i
$837$	6.86174	+	44.8516i	0.237177	+	1.55030i
$838$	−5.97489	+	3.44960i	−0.206399	+	0.119165i
$839$	−2.27935	+	0.829616i	−0.0786920	+	0.0286415i	−0.381066	−	0.924548i	$-0.624443\pi$
$839$	−2.27935	+	0.829616i	−0.0786920	+	0.0286415i	0.302374	+	0.953189i	$0.402221\pi$
$840$	−16.8557	−	9.52836i	−0.581577	−	0.328760i
$841$	14.5368	−	12.1978i	0.501268	−	0.420614i
$842$	3.41766	+	4.07300i	0.117780	+	0.140365i
$843$	−1.05317	+	5.71918i	−0.0362731	+	0.196979i
$844$	−17.9006	+	6.51530i	−0.616166	+	0.224266i
$845$	54.7724			1.88423
$846$	19.4552	+	23.9122i	0.668883	+	0.822120i
$847$	20.3630	+	11.3083i	0.699681	+	0.388559i
$848$	−0.793497	−	0.139915i	−0.0272488	−	0.00480470i
$849$	−37.4022	+	30.9045i	−1.28364	+	1.06064i
$850$	−16.6901	−	19.8905i	−0.572467	−	0.682240i
$851$	10.5199	+	12.5371i	0.360618	+	0.429767i
$852$	1.87895	−	1.55253i	0.0643718	−	0.0531888i
$853$	−14.7314	−	2.59755i	−0.504394	−	0.0889383i	−0.0843394	−	0.996437i	$-0.526878\pi$
$853$	−14.7314	−	2.59755i	−0.504394	−	0.0889383i	−0.420055	+	0.907499i	$0.637989\pi$
$854$	0.0327417	+	1.96432i	0.00112040	+	0.0672175i
$855$	−22.1709	−	27.2502i	−0.758230	−	0.931936i
$856$	−6.13005			−0.209521
$857$	−31.0969	+	11.3183i	−1.06225	+	0.386627i	−0.813273	−	0.581883i	$-0.802316\pi$
$857$	−31.0969	+	11.3183i	−1.06225	+	0.386627i	−0.248976	+	0.968510i	$0.580094\pi$
$858$	0.0892296	−	0.484556i	0.00304625	−	0.0165425i
$859$	−35.4023	−	42.1908i	−1.20791	−	1.43953i	−0.866179	−	0.499734i	$-0.833431\pi$
$859$	−35.4023	−	42.1908i	−1.20791	−	1.43953i	−0.341731	−	0.939798i	$-0.611013\pi$
$860$	−13.6421	+	11.4471i	−0.465193	+	0.390343i
$861$	−20.3858	−	34.5793i	−0.694746	−	1.17846i
$862$	−15.3865	+	5.60021i	−0.524065	+	0.190744i
$863$	−41.9339	+	24.2106i	−1.42745	+	0.824137i	−0.996919	−	0.0784397i	$-0.975006\pi$
$863$	−41.9339	+	24.2106i	−1.42745	+	0.824137i	−0.430529	+	0.902577i	$0.641673\pi$
$864$	4.84115	+	1.88767i	0.164699	+	0.0642198i
$865$	−24.9549	+	43.2231i	−0.848491	+	1.46963i
$866$	−29.6899	−	24.9128i	−1.00890	−	0.846571i
$867$	−0.169475	+	22.3751i	−0.00575569	+	0.759899i
$868$	−21.8384	−	7.53880i	−0.741245	−	0.255883i
$869$	−10.6987	+	1.88646i	−0.362928	+	0.0639939i
$870$	−7.75941	−	21.8319i	−0.263069	−	0.740171i
$871$	0.198250	+	0.544688i	0.00671745	+	0.0184560i
$872$	−5.12932	+	2.96141i	−0.173701	+	0.100286i
$873$	35.6444	+	6.84334i	1.20638	+	0.231612i
$874$	22.3174	−	12.8849i	0.754897	−	0.435840i
$875$	−86.6919	−	13.8006i	−2.93072	−	0.466544i
$876$	−6.97839	+	5.76607i	−0.235778	+	0.194817i
$877$	1.46757	+	8.32301i	0.0495563	+	0.281048i	0.999509	−	0.0313473i	$-0.00997979\pi$
$877$	1.46757	+	8.32301i	0.0495563	+	0.281048i	−0.949952	+	0.312395i	$0.898869\pi$
$878$	21.1450	−	17.7428i	0.713610	−	0.598790i
$879$	19.5297	+	23.6358i	0.658719	+	0.797216i
$880$	−2.14167	−	5.88419i	−0.0721957	−	0.198356i
$881$	2.95687	+	5.12145i	0.0996194	+	0.172546i	0.911527	−	0.411240i	$-0.134904\pi$
$881$	2.95687	+	5.12145i	0.0996194	+	0.172546i	−0.811908	+	0.583786i	$0.801571\pi$
$882$	−18.3745	−	10.1676i	−0.618700	−	0.342359i
$883$	−16.4041	+	28.4128i	−0.552043	+	0.956166i	0.446084	+	0.894991i	$0.352818\pi$
$883$	−16.4041	+	28.4128i	−0.552043	+	0.956166i	−0.998127	+	0.0611754i	$0.980515\pi$
$884$	−0.381881	−	0.0673359i	−0.0128440	−	0.00226475i
$885$	31.7930	+	89.4528i	1.06871	+	3.00692i
$886$	−0.995244	−	0.362239i	−0.0334359	−	0.0121697i
$887$	−21.9818	−	8.00072i	−0.738076	−	0.268638i	−0.0544968	−	0.998514i	$-0.517355\pi$
$887$	−21.9818	−	8.00072i	−0.738076	−	0.268638i	−0.683579	+	0.729876i	$0.739578\pi$
$888$	−1.50426	−	2.65163i	−0.0504795	−	0.0889828i
$889$	9.62856	+	25.1424i	0.322932	+	0.843247i
$890$		−	47.4728i		−	1.59129i
$891$	−8.87911	+	9.95315i	−0.297462	+	0.333443i
$892$	12.8010	+	7.39066i	0.428609	+	0.247458i
$893$	−28.0458	−	4.94523i	−0.938517	−	0.165486i
$894$	20.6227	+	12.1157i	0.689727	+	0.405210i
$895$	44.1853	+	52.6580i	1.47695	+	1.76016i
$896$	−1.99814	+	1.73420i	−0.0667531	+	0.0579355i
$897$	−2.00493	+	2.35295i	−0.0669425	+	0.0785628i
$898$	7.11445	−	40.3480i	0.237412	−	1.34643i
$899$	−13.8230	−	23.9421i	−0.461022	−	0.798514i
$900$	38.5534	+	0.584062i	1.28511	+	0.0194687i
$901$	−1.40970	−	0.813890i	−0.0469639	−	0.0271146i
$902$	2.25424	−	12.7844i	0.0750580	−	0.425675i
$903$	−14.6824	+	12.5492i	−0.488600	+	0.417613i
$904$	5.79034	+	2.10751i	0.192584	+	0.0700948i
$905$	46.3629	−	8.17503i	1.54116	−	0.271747i
$906$	0.305181	+	1.81087i	0.0101390	+	0.0601620i
$907$	−14.9754	−	12.5659i	−0.497251	−	0.417243i	0.359365	−	0.933197i	$-0.382993\pi$
$907$	−14.9754	−	12.5659i	−0.497251	−	0.417243i	−0.856617	+	0.515954i	$0.827438\pi$
$908$	10.2044	−	17.6746i	0.338646	−	0.586552i
$909$	−41.0912	+	14.2548i	−1.36291	+	0.472804i
$910$	−1.84011	+	1.10368i	−0.0609992	+	0.0365867i
$911$	−21.0797	+	25.1218i	−0.698401	+	0.832322i	−0.992344	−	0.123501i	$-0.960588\pi$
$911$	−21.0797	+	25.1218i	−0.698401	+	0.832322i	0.293943	+	0.955823i	$0.405032\pi$
$912$	−4.52311	+	1.60758i	−0.149775	+	0.0532325i
$913$	−1.99964	+	5.49397i	−0.0661785	+	0.181824i
$914$	17.9240	−	3.16049i	0.592875	−	0.104540i
$915$	−2.68137	−	4.72658i	−0.0886432	−	0.156256i
$916$	−6.48969	−	17.8303i	−0.214425	−	0.589129i
$917$	33.2284	−	19.9301i	1.09730	−	0.658150i
$918$	7.88613	+	6.92859i	0.260281	+	0.228678i
$919$	15.1520	+	26.2440i	0.499817	+	0.865708i	1.00000		0.000211285i	$-6.72541e-5\pi$
$919$	15.1520	+	26.2440i	0.499817	+	0.865708i	−0.500183	+	0.865920i	$0.666734\pi$
$920$	−6.82223	+	38.6908i	−0.224922	+	1.27560i
$921$	17.1939	+	30.3085i	0.566557	+	0.998698i
$922$	−7.38716	+	20.2961i	−0.243283	+	0.668415i
$923$	−0.0469036	−	0.266004i	−0.00154385	−	0.00875562i
$924$	−2.38073	−	6.36045i	−0.0783202	−	0.209244i
$925$	−17.3294	−	14.5411i	−0.569787	−	0.478108i
$926$			8.04262i			0.264297i
$927$	−0.548896	−	0.674645i	−0.0180281	−	0.0221583i
$928$	−3.16600			−0.103929
$929$	8.35853	−	3.04226i	0.274234	−	0.0998132i	−0.201242	−	0.979542i	$-0.564498\pi$
$929$	8.35853	−	3.04226i	0.274234	−	0.0998132i	0.475477	+	0.879728i	$0.342276\pi$
$930$	63.0159	−	10.6199i	2.06637	−	0.348241i
$931$	18.9825	−	4.00366i	0.622128	−	0.131215i
$932$	−0.800942	+	2.20057i	−0.0262357	+	0.0720821i
$933$	8.17330	+	9.89176i	0.267582	+	0.323842i
$934$	−0.774771	+	0.923336i	−0.0253513	+	0.0302125i
$935$		−	12.6504i		−	0.413711i
$936$	0.446669	−	0.363413i	0.0145998	−	0.0118785i
$937$	−48.4864	−	27.9936i	−1.58398	−	0.914511i	−0.994270	−	0.106896i	$-0.965909\pi$
$937$	−48.4864	−	27.9936i	−1.58398	−	0.914511i	−0.589710	−	0.807615i	$-0.700758\pi$
$938$	6.20529	+	5.03303i	0.202610	+	0.164334i
$939$	11.1330	−	3.95684i	0.363311	−	0.129126i
$940$	33.2593	−	27.9079i	1.08480	−	0.910256i
$941$	4.15836	+	23.5832i	0.135559	+	0.768792i	0.974469	+	0.224522i	$0.0720820\pi$
$941$	4.15836	+	23.5832i	0.135559	+	0.768792i	−0.838910	+	0.544270i	$0.816807\pi$
$942$	−2.58311	+	1.46538i	−0.0841622	+	0.0477448i
$943$	−52.3543	+	62.3935i	−1.70489	+	2.03181i
$944$	12.9722			0.422209
$945$	58.0863	+	0.351757i	1.88955	+	0.0114427i
$946$	−6.24637			−0.203087
$947$	23.5070	−	28.0145i	0.763874	−	0.910350i	−0.234212	−	0.972185i	$-0.575251\pi$
$947$	23.5070	−	28.0145i	0.763874	−	0.910350i	0.998086	+	0.0618357i	$0.0196955\pi$
$948$	−10.9472	−	6.43142i	−0.355549	−	0.208883i
$949$	0.174199	+	0.987933i	0.00565475	+	0.0320697i
$950$	−27.2868	+	22.8963i	−0.885299	+	0.742854i
$951$	−7.94875	+	43.1652i	−0.257756	+	1.39973i
$952$	−4.99153	+	1.91156i	−0.161776	+	0.0619542i
$953$	−12.4873	−	7.20957i	−0.404505	−	0.233541i	0.283921	−	0.958848i	$-0.408365\pi$
$953$	−12.4873	−	7.20957i	−0.404505	−	0.233541i	−0.688426	+	0.725307i	$0.741698\pi$
$954$	2.28370	−	0.792234i	0.0739375	−	0.0256495i
$955$			48.7868i			1.57870i
$956$	−6.44557	+	7.68153i	−0.208465	+	0.248439i
$957$	2.83731	−	7.61547i	0.0917171	−	0.246173i
$958$	8.29591	−	22.7928i	0.268029	−	0.736403i
$959$	7.67280	−	6.65928i	0.247768	−	0.215039i
$960$	2.55503	−	6.85782i	0.0824632	−	0.221335i
$961$	42.5212	−	15.4765i	1.37165	−	0.499240i
$962$	−0.337841			−0.0108924
$963$	16.0638	−	8.95277i	0.517648	−	0.288499i
$964$			15.9770i			0.514584i
$965$	−37.9562	−	31.8490i	−1.22185	−	1.02526i
$966$	−7.01736	+	42.0286i	−0.225780	+	1.35225i
$967$	9.54019	+	54.1051i	0.306792	+	1.73990i	0.614948	+	0.788568i	$0.289177\pi$
$967$	9.54019	+	54.1051i	0.306792	+	1.73990i	−0.308156	+	0.951336i	$0.599712\pi$
$968$	−3.01103	+	8.27273i	−0.0967781	+	0.265896i
$969$	−9.69744	−	0.0734512i	−0.311527	−	0.00235959i
$970$	8.87668	−	50.3422i	0.285013	−	1.61639i
$971$	−8.64777	−	14.9784i	−0.277520	−	0.480679i	0.693248	−	0.720700i	$-0.256179\pi$
$971$	−8.64777	−	14.9784i	−0.277520	−	0.480679i	−0.970768	+	0.240020i	$0.922846\pi$
$972$	−15.4431	+	2.12373i	−0.495338	+	0.0681186i
$973$	14.1115	−	0.235214i	0.452394	−	0.00754062i
$974$	10.0716	+	27.6715i	0.322715	+	0.886654i
$975$	2.16443	−	3.68418i	0.0693173	−	0.117988i
$976$	−0.731264	+	0.128942i	−0.0234072	+	0.00412732i
$977$	0.499523	−	1.37243i	0.0159811	−	0.0439078i	−0.931446	−	0.363881i	$-0.881452\pi$
$977$	0.499523	−	1.37243i	0.0159811	−	0.0439078i	0.947427	+	0.319973i	$0.103674\pi$
$978$	4.40611	−	23.9271i	0.140892	−	0.765105i
$979$	10.7032	−	12.7555i	0.342075	−	0.407669i
$980$	−13.9265	+	26.0927i	−0.444864	+	0.833502i
$981$	9.11632	−	15.2516i	0.291062	−	0.486947i
$982$	−14.9539	+	25.9009i	−0.477198	+	0.826531i
$983$	−38.9049	−	32.6451i	−1.24087	−	1.04122i	−0.997455	−	0.0712946i	$-0.977287\pi$
$983$	−38.9049	−	32.6451i	−1.24087	−	1.04122i	−0.243418	−	0.969922i	$-0.578269\pi$
$984$	11.6959	−	9.66401i	0.372851	−	0.308077i
$985$	−70.2531	+	12.3875i	−2.23845	+	0.394699i
$986$	−6.01034	−	2.18758i	−0.191408	−	0.0696669i
$987$	35.7955	−	30.5949i	1.13938	−	0.973847i
$988$	−0.0923744	+	0.523881i	−0.00293882	+	0.0166669i
$989$	33.9402	+	19.5954i	1.07923	+	0.623096i
$990$	14.2059	+	12.2917i	0.451495	+	0.390655i
$991$	−6.21607	−	10.7665i	−0.197460	−	0.342011i	0.750244	−	0.661161i	$-0.229936\pi$
$991$	−6.21607	−	10.7665i	−0.197460	−	0.342011i	−0.947704	+	0.319150i	$0.896603\pi$
$992$	1.51632	−	8.59947i	0.0481432	−	0.273033i
$993$	19.8163	+	3.64912i	0.628852	+	0.115801i
$994$	−2.44040	−	2.81182i	−0.0774047	−	0.0891855i
$995$	48.1211	+	57.3484i	1.52554	+	1.81807i
$996$	−5.94325	+	3.37158i	−0.188319	+	0.106833i
$997$	23.1878	+	4.08863i	0.734364	+	0.129488i	0.528309	−	0.849052i	$-0.322826\pi$
$997$	23.1878	+	4.08863i	0.734364	+	0.129488i	0.206055	+	0.978540i	$0.433937\pi$
$998$	−9.05014	−	5.22510i	−0.286477	−	0.165398i
$999$	7.81453	+	4.75166i	0.247241	+	0.150336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.8	yes	144
7.5	odd	6		378.2.ba.a.47.15	✓	144
27.23	odd	18		378.2.ba.a.185.15	yes	144
189.131	even	18	inner	378.2.bf.a.131.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.15	✓	144	7.5	odd	6
378.2.ba.a.185.15	yes	144	27.23	odd	18
378.2.bf.a.101.8	yes	144	1.1	even	1	trivial
378.2.bf.a.131.8	yes	144	189.131	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(0.0131187 - 1.73200i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(3.23672 - 2.71593i) q^{5} +(1.31836 + 1.12336i) q^{6} +(1.66664 - 2.05482i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.99966 - 0.0454431i) q^{9} +4.22523i q^{10} +(-0.952616 + 1.13528i) q^{11} +(-1.70797 + 0.287839i) q^{12} +(-0.0656487 + 0.180368i) q^{13} +(0.502790 + 2.59754i) q^{14} +(-4.66153 - 5.64163i) q^{15} +(-0.939693 + 0.342020i) q^{16} -2.02023 q^{17} +(1.96295 - 2.26866i) q^{18} +2.77145i q^{19} +(-3.23672 - 2.71593i) q^{20} +(-3.53709 - 2.91358i) q^{21} +(-0.257348 - 1.45949i) q^{22} +(-3.18022 + 8.73758i) q^{23} +(0.877362 - 1.49340i) q^{24} +(2.23183 - 12.6573i) q^{25} +(-0.0959719 - 0.166228i) q^{26} +(-0.118059 + 5.19481i) q^{27} +(-2.31302 - 1.28451i) q^{28} +(-1.08284 - 2.97507i) q^{29} +(7.31811 + 0.0554294i) q^{30} +(8.59947 - 1.51632i) q^{31} +(0.342020 - 0.939693i) q^{32} +(1.95381 + 1.66482i) q^{33} +(1.29858 - 1.54759i) q^{34} +(-0.186307 - 11.1774i) q^{35} +(0.476132 + 2.96198i) q^{36} +(0.880053 - 1.52430i) q^{37} +(-2.12305 - 1.78145i) q^{38} +(0.311537 + 0.116070i) q^{39} +(4.16104 - 0.733704i) q^{40} +(8.23124 + 2.99593i) q^{41} +(4.50553 - 0.836757i) q^{42} +(0.731893 - 4.15077i) q^{43} +(1.28346 + 0.741003i) q^{44} +(-9.83246 + 7.99976i) q^{45} +(-4.64917 - 8.05260i) q^{46} +(-1.78435 + 10.1195i) q^{47} +(0.580052 + 1.63204i) q^{48} +(-1.44461 - 6.84931i) q^{49} +(8.26149 + 9.84566i) q^{50} +(-0.0265028 + 3.49905i) q^{51} +(0.189028 + 0.0333307i) q^{52} +(0.697789 + 0.402869i) q^{53} +(-3.90357 - 3.42960i) q^{54} +6.26182i q^{55} +(2.47077 - 0.946209i) q^{56} +(4.80016 + 0.0363577i) q^{57} +(2.97507 + 1.08284i) q^{58} +(-12.1899 - 4.43676i) q^{59} +(-4.74645 + 5.57037i) q^{60} +(0.731264 + 0.128942i) q^{61} +(-4.36607 + 7.56225i) q^{62} +(-5.09273 + 6.08803i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.277381 + 0.762098i) q^{65} +(-2.53122 + 0.426580i) q^{66} +(2.31335 - 1.94113i) q^{67} +(0.350810 + 1.98954i) q^{68} +(15.0918 + 5.62277i) q^{69} +(8.68211 + 7.04195i) q^{70} +(-1.21869 + 0.703610i) q^{71} +(-2.57506 - 1.53918i) q^{72} +(4.52619 - 2.61320i) q^{73} +(0.601992 + 1.65396i) q^{74} +(-21.8932 - 4.03158i) q^{75} +(2.72935 - 0.481257i) q^{76} +(0.745138 + 3.84957i) q^{77} +(-0.289167 + 0.164043i) q^{78} +(5.61542 + 4.71190i) q^{79} +(-2.11262 + 3.65916i) q^{80} +(8.99587 + 0.272627i) q^{81} +(-7.58595 + 4.37975i) q^{82} +(3.70712 - 1.34928i) q^{83} +(-2.25511 + 3.98930i) q^{84} +(-6.53893 + 5.48681i) q^{85} +(2.70923 + 3.22873i) q^{86} +(-5.16703 + 1.83645i) q^{87} +(-1.39263 + 0.506876i) q^{88} -11.2356 q^{89} +(0.192008 - 12.6742i) q^{90} +(0.261212 + 0.435506i) q^{91} +(9.15708 + 1.61464i) q^{92} +(-2.51345 - 14.9142i) q^{93} +(-6.60506 - 7.87160i) q^{94} +(7.52706 + 8.97040i) q^{95} +(-1.62306 - 0.604707i) q^{96} +(-11.9147 - 2.10087i) q^{97} +(6.17546 + 3.29602i) q^{98} +(2.90911 - 3.36217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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