LMFDB - Embedded newform 304.2.m.a.227.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(75,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("304.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			227.9
Character	$\chi$	$=$	304.227
Dual form			304.2.m.a.75.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18010 + 0.779343i) q^{2} +(1.07779 + 1.07779i) q^{3} +(0.785249 - 1.83940i) q^{4} +(-1.37400 + 1.37400i) q^{5} +(-2.11187 - 0.431928i) q^{6} -4.00321 q^{7} +(0.506854 + 2.78264i) q^{8} -0.676721i q^{9} +O(q^{10})$	\(q+(-1.18010 + 0.779343i) q^{2} +(1.07779 + 1.07779i) q^{3} +(0.785249 - 1.83940i) q^{4} +(-1.37400 + 1.37400i) q^{5} +(-2.11187 - 0.431928i) q^{6} -4.00321 q^{7} +(0.506854 + 2.78264i) q^{8} -0.676721i q^{9} +(0.550634 - 2.69227i) q^{10} +(-2.44045 - 2.44045i) q^{11} +(2.82883 - 1.13616i) q^{12} +(-3.86163 + 3.86163i) q^{13} +(4.72416 - 3.11987i) q^{14} -2.96178 q^{15} +(-2.76677 - 2.88877i) q^{16} +0.770883 q^{17} +(0.527398 + 0.798595i) q^{18} +(-2.90179 + 3.25263i) q^{19} +(1.44840 + 3.60627i) q^{20} +(-4.31463 - 4.31463i) q^{21} +(4.78190 + 0.978013i) q^{22} +7.83638 q^{23} +(-2.45283 + 3.54540i) q^{24} +1.22424i q^{25} +(1.54756 - 7.56663i) q^{26} +(3.96275 - 3.96275i) q^{27} +(-3.14351 + 7.36349i) q^{28} +(-4.22402 + 4.22402i) q^{29} +(3.49518 - 2.30824i) q^{30} -6.35498 q^{31} +(5.51639 + 1.25276i) q^{32} -5.26059i q^{33} +(-0.909715 + 0.600782i) q^{34} +(5.50041 - 5.50041i) q^{35} +(-1.24476 - 0.531394i) q^{36} +(-1.65503 - 1.65503i) q^{37} +(0.889474 - 6.09990i) q^{38} -8.32409 q^{39} +(-4.51977 - 3.12694i) q^{40} +2.19975 q^{41} +(8.45425 + 1.72910i) q^{42} +(-7.25972 - 7.25972i) q^{43} +(-6.40531 + 2.57259i) q^{44} +(0.929815 + 0.929815i) q^{45} +(-9.24767 + 6.10723i) q^{46} -3.06973i q^{47} +(0.131491 - 6.09550i) q^{48} +9.02565 q^{49} +(-0.954102 - 1.44472i) q^{50} +(0.830853 + 0.830853i) q^{51} +(4.07074 + 10.1354i) q^{52} +(8.94960 + 8.94960i) q^{53} +(-1.58808 + 7.76476i) q^{54} +6.70635 q^{55} +(-2.02904 - 11.1395i) q^{56} +(-6.63320 + 0.378133i) q^{57} +(1.69278 - 8.27670i) q^{58} +(-8.06369 + 8.06369i) q^{59} +(-2.32573 + 5.44789i) q^{60} +(5.67621 + 5.67621i) q^{61} +(7.49948 - 4.95271i) q^{62} +2.70905i q^{63} +(-7.48620 + 2.82079i) q^{64} -10.6118i q^{65} +(4.09981 + 6.20800i) q^{66} +(6.75376 + 6.75376i) q^{67} +(0.605335 - 1.41796i) q^{68} +(8.44600 + 8.44600i) q^{69} +(-2.20430 + 10.7777i) q^{70} -5.29590i q^{71} +(1.88307 - 0.342999i) q^{72} +7.64027i q^{73} +(3.24292 + 0.663255i) q^{74} +(-1.31948 + 1.31948i) q^{75} +(3.70425 + 7.89167i) q^{76} +(9.76960 + 9.76960i) q^{77} +(9.82322 - 6.48732i) q^{78} -4.93934 q^{79} +(7.77072 + 0.167629i) q^{80} +6.51189 q^{81} +(-2.59592 + 1.71436i) q^{82} +(1.44386 - 1.44386i) q^{83} +(-11.3244 + 4.54826i) q^{84} +(-1.05919 + 1.05919i) q^{85} +(14.2250 + 2.90935i) q^{86} -9.10524 q^{87} +(5.55394 - 8.02784i) q^{88} -0.971859 q^{89} +(-1.82192 - 0.372625i) q^{90} +(15.4589 - 15.4589i) q^{91} +(6.15351 - 14.4142i) q^{92} +(-6.84936 - 6.84936i) q^{93} +(2.39238 + 3.62258i) q^{94} +(-0.482054 - 8.45619i) q^{95} +(4.59532 + 7.29575i) q^{96} +6.62675i q^{97} +(-10.6511 + 7.03408i) q^{98} +(-1.65150 + 1.65150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7	$ 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43} - 76 q^{44} + 4 q^{45} + 44 q^{49} + 96 q^{54} - 8 q^{55} + 24 q^{58} + 28 q^{61} + 20 q^{62} - 64 q^{64} + 12 q^{66} - 80 q^{74} + 12 q^{76} - 32 q^{77} - 16 q^{80} - 52 q^{81} + 68 q^{82} + 36 q^{83} - 56 q^{85} - 120 q^{87} - 8 q^{92} - 16 q^{93} + 48 q^{96} + 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.18010	+	0.779343i	−0.834453	+	0.551079i
$2$	−1.18010	+	0.779343i	−0.834453	+	0.551079i
$3$	1.07779	+	1.07779i	0.622265	+	0.622265i	0.946110	−	0.323845i	$-0.104976\pi$
$3$	1.07779	+	1.07779i	0.622265	+	0.622265i	−0.323845	+	0.946110i	$0.604976\pi$
$4$	0.785249	−	1.83940i	0.392624	−	0.919699i
$5$	−1.37400	+	1.37400i	−0.614472	+	0.614472i	−0.944108	−	0.329636i	$-0.893074\pi$
$5$	−1.37400	+	1.37400i	−0.614472	+	0.614472i	0.329636	+	0.944108i	$0.393074\pi$
$6$	−2.11187	−	0.431928i	−0.862167	−	0.176334i
$7$	−4.00321			−1.51307			−0.756535	−	0.653954i	$-0.773109\pi$
$7$	−4.00321			−1.51307			−0.756535	+	0.653954i	$0.773109\pi$
$8$	0.506854	+	2.78264i	0.179200	+	0.983813i
$9$		−	0.676721i		−	0.225574i
$10$	0.550634	−	2.69227i	0.174126	−	0.851371i
$11$	−2.44045	−	2.44045i	−0.735822	−	0.735822i	0.235945	−	0.971767i	$-0.424182\pi$
$11$	−2.44045	−	2.44045i	−0.735822	−	0.735822i	−0.971767	+	0.235945i	$0.924182\pi$
$12$	2.82883	−	1.13616i	0.816612	−	0.327980i
$13$	−3.86163	+	3.86163i	−1.07102	+	1.07102i	−0.0737474	+	0.997277i	$0.523496\pi$
$13$	−3.86163	+	3.86163i	−1.07102	+	1.07102i	−0.997277	+	0.0737474i	$0.976504\pi$
$14$	4.72416	−	3.11987i	1.26259	−	0.833820i
$15$	−2.96178			−0.764729
$16$	−2.76677	−	2.88877i	−0.691692	−	0.722192i
$17$	0.770883			0.186967			0.0934833	−	0.995621i	$-0.470200\pi$
$17$	0.770883			0.186967			0.0934833	+	0.995621i	$0.470200\pi$
$18$	0.527398	+	0.798595i	0.124309	+	0.188231i
$19$	−2.90179	+	3.25263i	−0.665717	+	0.746205i
$19$	−2.90179	+	3.25263i	−0.665717	+	0.746205i
$20$	1.44840	+	3.60627i	0.323873	+	0.806386i
$21$	−4.31463	−	4.31463i	−0.941529	−	0.941529i
$22$	4.78190	+	0.978013i	1.01950	+	0.208513i
$23$	7.83638			1.63400			0.816999	−	0.576639i	$-0.195636\pi$
$23$	7.83638			1.63400			0.816999	+	0.576639i	$0.195636\pi$
$24$	−2.45283	+	3.54540i	−0.500682	+	0.723702i
$25$			1.22424i			0.244848i
$26$	1.54756	−	7.56663i	0.303501	−	1.48394i
$27$	3.96275	−	3.96275i	0.762631	−	0.762631i
$28$	−3.14351	+	7.36349i	−0.594068	+	1.39157i
$29$	−4.22402	+	4.22402i	−0.784380	+	0.784380i	−0.980567	−	0.196186i	$-0.937144\pi$
$29$	−4.22402	+	4.22402i	−0.784380	+	0.784380i	0.196186	+	0.980567i	$0.437144\pi$
$30$	3.49518	−	2.30824i	0.638130	−	0.421426i
$31$	−6.35498			−1.14139			−0.570694	−	0.821163i	$-0.693326\pi$
$31$	−6.35498			−1.14139			−0.570694	+	0.821163i	$0.693326\pi$
$32$	5.51639	+	1.25276i	0.975170	+	0.221459i
$33$		−	5.26059i		−	0.915752i
$34$	−0.909715	+	0.600782i	−0.156015	+	0.103033i
$35$	5.50041	−	5.50041i	0.929739	−	0.929739i
$36$	−1.24476	−	0.531394i	−0.207460	−	0.0885657i
$37$	−1.65503	−	1.65503i	−0.272085	−	0.272085i	0.557854	−	0.829939i	$-0.311625\pi$
$37$	−1.65503	−	1.65503i	−0.272085	−	0.272085i	−0.829939	+	0.557854i	$0.811625\pi$
$38$	0.889474	−	6.09990i	0.144292	−	0.989535i
$39$	−8.32409			−1.33292
$40$	−4.51977	−	3.12694i	−0.714639	−	0.494412i
$41$	2.19975			0.343544			0.171772	−	0.985137i	$-0.445051\pi$
$41$	2.19975			0.343544			0.171772	+	0.985137i	$0.445051\pi$
$42$	8.45425	+	1.72910i	1.30452	+	0.266805i
$43$	−7.25972	−	7.25972i	−1.10710	−	1.10710i	−0.993530	−	0.113566i	$-0.963773\pi$
$43$	−7.25972	−	7.25972i	−1.10710	−	1.10710i	−0.113566	−	0.993530i	$-0.536227\pi$
$44$	−6.40531	+	2.57259i	−0.965636	+	0.387833i
$45$	0.929815	+	0.929815i	0.138609	+	0.138609i
$46$	−9.24767	+	6.10723i	−1.36349	+	0.900462i
$47$		−	3.06973i		−	0.447767i	−0.974616	−	0.223883i	$-0.928127\pi$
$47$		−	3.06973i		−	0.447767i	0.974616	−	0.223883i	$-0.0718735\pi$
$48$	0.131491	−	6.09550i	0.0189792	−	0.879810i
$49$	9.02565			1.28938
$50$	−0.954102	−	1.44472i	−0.134930	−	0.204314i
$51$	0.830853	+	0.830853i	0.116343	+	0.116343i
$52$	4.07074	+	10.1354i	0.564510	+	1.40553i
$53$	8.94960	+	8.94960i	1.22932	+	1.22932i	0.964220	+	0.265102i	$0.0854058\pi$
$53$	8.94960	+	8.94960i	1.22932	+	1.22932i	0.265102	+	0.964220i	$0.414594\pi$
$54$	−1.58808	+	7.76476i	−0.216110	+	1.05665i
$55$	6.70635			0.904284
$56$	−2.02904	−	11.1395i	−0.271142	−	1.48858i
$57$	−6.63320	+	0.378133i	−0.878589	+	0.0500849i
$58$	1.69278	−	8.27670i	0.222273	−	1.08678i
$59$	−8.06369	+	8.06369i	−1.04980	+	1.04980i	−0.0511094	+	0.998693i	$0.516276\pi$
$59$	−8.06369	+	8.06369i	−1.04980	+	1.04980i	−0.998693	+	0.0511094i	$0.983724\pi$
$60$	−2.32573	+	5.44789i	−0.300251	+	0.703320i
$61$	5.67621	+	5.67621i	0.726764	+	0.726764i	0.969974	−	0.243209i	$-0.0782002\pi$
$61$	5.67621	+	5.67621i	0.726764	+	0.726764i	−0.243209	+	0.969974i	$0.578200\pi$
$62$	7.49948	−	4.95271i	0.952435	−	0.628995i
$63$			2.70905i			0.341308i
$64$	−7.48620	+	2.82079i	−0.935775	+	0.352598i
$65$		−	10.6118i		−	1.31623i
$66$	4.09981	+	6.20800i	0.504651	+	0.764152i
$67$	6.75376	+	6.75376i	0.825103	+	0.825103i	0.986835	−	0.161732i	$-0.0517079\pi$
$67$	6.75376	+	6.75376i	0.825103	+	0.825103i	−0.161732	+	0.986835i	$0.551708\pi$
$68$	0.605335	−	1.41796i	0.0734076	−	0.171953i
$69$	8.44600	+	8.44600i	1.01678	+	1.01678i
$70$	−2.20430	+	10.7777i	−0.263464	+	1.28818i
$71$		−	5.29590i		−	0.628507i	−0.949339	−	0.314254i	$-0.898246\pi$
$71$		−	5.29590i		−	0.628507i	0.949339	−	0.314254i	$-0.101754\pi$
$72$	1.88307	−	0.342999i	0.221922	−	0.0404228i
$73$			7.64027i			0.894226i	0.894478	+	0.447113i	$0.147548\pi$
$73$			7.64027i			0.894226i	−0.894478	+	0.447113i	$0.852452\pi$
$74$	3.24292	+	0.663255i	0.376982	+	0.0771018i
$75$	−1.31948	+	1.31948i	−0.152360	+	0.152360i
$76$	3.70425	+	7.89167i	0.424907	+	0.905237i
$77$	9.76960	+	9.76960i	1.11335	+	1.11335i
$78$	9.82322	−	6.48732i	1.11226	−	0.734545i
$79$	−4.93934			−0.555719			−0.277860	−	0.960622i	$-0.589625\pi$
$79$	−4.93934			−0.555719			−0.277860	+	0.960622i	$0.589625\pi$
$80$	7.77072	+	0.167629i	0.868793	+	0.0187415i
$81$	6.51189			0.723543
$82$	−2.59592	+	1.71436i	−0.286671	+	0.189320i
$83$	1.44386	−	1.44386i	0.158484	−	0.158484i	−0.623411	−	0.781895i	$-0.714254\pi$
$83$	1.44386	−	1.44386i	0.158484	−	0.158484i	0.781895	+	0.623411i	$0.214254\pi$
$84$	−11.3244	+	4.54826i	−1.23559	+	0.496256i
$85$	−1.05919	+	1.05919i	−0.114886	+	0.114886i
$86$	14.2250	+	2.90935i	1.53392	+	0.313723i
$87$	−9.10524			−0.976184
$88$	5.55394	−	8.02784i	0.592052	−	0.855770i
$89$	−0.971859			−0.103017			−0.0515084	−	0.998673i	$-0.516403\pi$
$89$	−0.971859			−0.103017			−0.0515084	+	0.998673i	$0.516403\pi$
$90$	−1.82192	−	0.372625i	−0.192047	−	0.0392782i
$91$	15.4589	−	15.4589i	1.62053	−	1.62053i
$92$	6.15351	−	14.4142i	0.641547	−	1.50279i
$93$	−6.84936	−	6.84936i	−0.710245	−	0.710245i
$94$	2.39238	+	3.62258i	0.246755	+	0.373640i
$95$	−0.482054	−	8.45619i	−0.0494577	−	0.867586i
$96$	4.59532	+	7.29575i	0.469008	+	0.744620i
$97$			6.62675i			0.672845i	0.941711	+	0.336422i	$0.109217\pi$
$97$			6.62675i			0.672845i	−0.941711	+	0.336422i	$0.890783\pi$
$98$	−10.6511	+	7.03408i	−1.07593	+	0.710549i
$99$	−1.65150	+	1.65150i	−0.165982	+	0.165982i
$100$	2.25186	+	0.961332i	0.225186	+	0.0961332i
$101$	−8.93505	+	8.93505i	−0.889070	+	0.889070i	−0.994434	−	0.105363i	$-0.966399\pi$
$101$	−8.93505	+	8.93505i	−0.889070	+	0.889070i	0.105363	+	0.994434i	$0.466399\pi$
$102$	−1.62801	−	0.332966i	−0.161197	−	0.0329685i
$103$		−	2.76517i		−	0.272460i	−0.990677	−	0.136230i	$-0.956501\pi$
$103$		−	2.76517i		−	0.272460i	0.990677	−	0.136230i	$-0.0434986\pi$
$104$	−12.7028	−	8.78826i	−1.24561	−	0.861760i
$105$	11.8566			1.15709
$106$	−17.5362	−	3.58657i	−1.70327	−	0.348359i
$107$	−2.29005	+	2.29005i	−0.221387	+	0.221387i	−0.809082	−	0.587695i	$-0.800035\pi$
$107$	−2.29005	+	2.29005i	−0.221387	+	0.221387i	0.587695	+	0.809082i	$0.300035\pi$
$108$	−4.17733	−	10.4008i	−0.401963	−	1.00082i
$109$	7.12660	−	7.12660i	0.682604	−	0.682604i	−0.277982	−	0.960586i	$-0.589666\pi$
$109$	7.12660	−	7.12660i	0.682604	−	0.682604i	0.960586	+	0.277982i	$0.0896655\pi$
$110$	−7.91413	+	5.22655i	−0.754583	+	0.498332i
$111$		−	3.56756i		−	0.338617i
$112$	11.0759	+	11.5643i	1.04658	+	1.09273i
$113$			4.01320i			0.377530i	0.982022	+	0.188765i	$0.0604485\pi$
$113$			4.01320i			0.377530i	−0.982022	+	0.188765i	$0.939552\pi$
$114$	7.53311	−	5.61577i	0.705540	−	0.525965i
$115$	−10.7672	+	10.7672i	−1.00405	+	1.00405i
$116$	4.45274	+	11.0865i	0.413427	+	1.02936i
$117$	2.61325	+	2.61325i	0.241595	+	0.241595i
$118$	3.23154	−	15.8003i	0.297487	−	1.45453i
$119$	−3.08600			−0.282893
$120$	−1.50119	−	8.24158i	−0.137039	−	0.752350i
$121$			0.911546i			0.0828678i
$122$	−11.1222	−	2.27475i	−1.00696	−	0.205946i
$123$	2.37088	+	2.37088i	0.213775	+	0.213775i
$124$	−4.99024	+	11.6893i	−0.448137	+	1.04973i
$125$	−8.55211	−	8.55211i	−0.764924	−	0.764924i
$126$	−2.11128	−	3.19694i	−0.188088	−	0.284806i
$127$	−21.0423			−1.86721			−0.933603	−	0.358309i	$-0.883354\pi$
$127$	−21.0423			−1.86721			−0.933603	+	0.358309i	$0.883354\pi$
$128$	6.63607	−	9.16311i	0.586551	−	0.809912i
$129$		−	15.6490i		−	1.37781i
$130$	8.27022	+	12.5229i	0.725346	+	1.09833i
$131$	5.90211	−	5.90211i	0.515669	−	0.515669i	−0.400589	−	0.916258i	$-0.631194\pi$
$131$	5.90211	−	5.90211i	0.515669	−	0.515669i	0.916258	+	0.400589i	$0.131194\pi$
$132$	−9.67632	−	4.13087i	−0.842216	−	0.359546i
$133$	11.6165	−	13.0209i	1.00728	−	1.12906i
$134$	−13.2336	−	2.70658i	−1.14321	−	0.233813i
$135$			10.8896i			0.937231i
$136$	0.390725	+	2.14509i	0.0335044	+	0.183940i
$137$		−	0.836629i		−	0.0714781i	−0.999361	−	0.0357390i	$-0.988621\pi$
$137$		−	0.836629i		−	0.0714781i	0.999361	−	0.0357390i	$-0.0113785\pi$
$138$	−16.5494	−	3.38475i	−1.40878	−	0.288129i
$139$	9.52338	+	9.52338i	0.807762	+	0.807762i	0.984295	−	0.176533i	$-0.0564881\pi$
$139$	9.52338	+	9.52338i	0.807762	+	0.807762i	−0.176533	+	0.984295i	$0.556488\pi$
$140$	−5.79825	−	14.4366i	−0.490042	−	1.22012i
$141$	3.30854	−	3.30854i	0.278629	−	0.278629i
$142$	4.12732	+	6.24966i	0.346357	+	0.524460i
$143$	18.8482			1.57617
$144$	−1.95489	+	1.87233i	−0.162908	+	0.156027i
$145$		−	11.6076i		−	0.963960i
$146$	−5.95439	−	9.01624i	−0.492789	−	0.746190i
$147$	9.72779	+	9.72779i	0.802335	+	0.802335i
$148$	−4.34386	+	1.74464i	−0.357063	+	0.143409i
$149$	6.00097	−	6.00097i	0.491619	−	0.491619i	−0.417197	−	0.908816i	$-0.636988\pi$
$149$	6.00097	−	6.00097i	0.491619	−	0.491619i	0.908816	+	0.417197i	$0.136988\pi$
$150$	0.528783	−	2.58543i	0.0431750	−	0.211100i
$151$		−	18.9950i		−	1.54579i	−0.634533	−	0.772895i	$-0.718808\pi$
$151$		−	18.9950i		−	1.54579i	0.634533	−	0.772895i	$-0.281192\pi$
$152$	−10.5217	−	6.42604i	−0.853422	−	0.521221i
$153$		−	0.521673i		−	0.0421747i
$154$	−19.1429	−	3.91519i	−1.54258	−	0.315495i
$155$	8.73175	−	8.73175i	0.701351	−	0.701351i
$156$	−6.53648	+	15.3113i	−0.523337	+	1.22589i
$157$	−0.417157	−	0.417157i	−0.0332928	−	0.0332928i	0.690264	−	0.723557i	$-0.257494\pi$
$157$	−0.417157	−	0.417157i	−0.0332928	−	0.0332928i	−0.723557	+	0.690264i	$0.757494\pi$
$158$	5.82889	−	3.84944i	0.463722	−	0.306245i
$159$			19.2917i			1.52993i
$160$	−9.30083	+	5.85824i	−0.735295	+	0.463134i
$161$	−31.3706			−2.47235
$162$	−7.68465	+	5.07499i	−0.603763	+	0.398729i
$163$	−6.53608	+	6.53608i	−0.511945	+	0.511945i	−0.915122	−	0.403177i	$-0.867906\pi$
$163$	−6.53608	+	6.53608i	−0.511945	+	0.511945i	0.403177	+	0.915122i	$0.367906\pi$
$164$	1.72735	−	4.04622i	0.134884	−	0.315957i
$165$	7.22806	+	7.22806i	0.562704	+	0.562704i
$166$	−0.578628	+	2.82915i	−0.0449103	+	0.219584i
$167$			6.23492i			0.482473i	0.970466	+	0.241236i	$0.0775529\pi$
$167$			6.23492i			0.482473i	−0.970466	+	0.241236i	$0.922447\pi$
$168$	9.81919	−	14.1930i	0.757567	−	1.09501i
$169$		−	16.8244i		−	1.29419i
$170$	0.424474	−	2.07543i	0.0325557	−	0.159178i
$171$	2.20112	+	1.96370i	0.168324	+	0.150168i
$172$	−19.0542	+	7.65283i	−1.45287	+	0.583523i
$173$	−9.89033	+	9.89033i	−0.751948	+	0.751948i	−0.974843	−	0.222895i	$-0.928449\pi$
$173$	−9.89033	+	9.89033i	−0.751948	+	0.751948i	0.222895	+	0.974843i	$0.428449\pi$
$174$	10.7450	−	7.09610i	0.814580	−	0.537954i
$175$		−	4.90088i		−	0.370472i
$176$	−0.297736	+	13.8020i	−0.0224427	+	1.04037i
$177$	−17.3820			−1.30651
$178$	1.14689	−	0.757412i	0.0859627	−	0.0567704i
$179$	−0.867301	−	0.867301i	−0.0648251	−	0.0648251i	0.673951	−	0.738776i	$-0.264596\pi$
$179$	−0.867301	−	0.867301i	−0.0648251	−	0.0648251i	−0.738776	+	0.673951i	$0.764596\pi$
$180$	2.44044	−	0.980164i	0.181899	−	0.0730571i
$181$	−12.5035	−	12.5035i	−0.929379	−	0.929379i	0.0682866	−	0.997666i	$-0.478247\pi$
$181$	−12.5035	−	12.5035i	−0.929379	−	0.929379i	−0.997666	+	0.0682866i	$0.978247\pi$
$182$	−6.19519	+	30.2908i	−0.459218	+	2.24530i
$183$			12.2356i			0.904479i
$184$	3.97190	+	21.8058i	0.292812	+	1.60755i
$185$	4.54802			0.334377
$186$	13.4209	+	2.74489i	0.984068	+	0.201265i
$187$	−1.88130	−	1.88130i	−0.137574	−	0.137574i
$188$	−5.64646	−	2.41050i	−0.411811	−	0.175804i
$189$	−15.8637	+	15.8637i	−1.15391	+	1.15391i
$190$	7.15914	+	9.60342i	0.519379	+	0.696705i
$191$		−	8.81392i		−	0.637753i	−0.947796	−	0.318876i	$-0.896695\pi$
$191$		−	8.81392i		−	0.637753i	0.947796	−	0.318876i	$-0.103305\pi$
$192$	−11.1088	−	5.02835i	−0.801709	−	0.362890i
$193$			6.79503i			0.489117i	0.969635	+	0.244558i	$0.0786430\pi$
$193$			6.79503i			0.489117i	−0.969635	+	0.244558i	$0.921357\pi$
$194$	−5.16451	−	7.82020i	−0.370790	−	0.561457i
$195$	11.4373	−	11.4373i	0.819043	−	0.819043i
$196$	7.08738	−	16.6018i	0.506242	−	1.18584i
$197$	5.37965	−	5.37965i	0.383284	−	0.383284i	−0.489000	−	0.872284i	$-0.662638\pi$
$197$	5.37965	−	5.37965i	0.383284	−	0.383284i	0.872284	+	0.489000i	$0.162638\pi$
$198$	0.661842	−	3.23601i	0.0470351	−	0.229973i
$199$	−2.55317			−0.180990			−0.0904949	−	0.995897i	$-0.528845\pi$
$199$	−2.55317			−0.180990			−0.0904949	+	0.995897i	$0.528845\pi$
$200$	−3.40662	+	0.620510i	−0.240884	+	0.0438767i
$201$			14.5583i			1.02686i
$202$	3.58074	−	17.5077i	0.251940	−	1.23184i
$203$	16.9096	−	16.9096i	1.18682	−	1.18682i
$204$	2.18070	−	0.875843i	0.152679	−	0.0613213i
$205$	−3.02247	+	3.02247i	−0.211098	+	0.211098i
$206$	2.15501	+	3.26316i	0.150147	+	0.227355i
$207$		−	5.30304i		−	0.368587i
$208$	21.8396	+	0.471122i	1.51430	+	0.0326664i
$209$	15.0195	−	0.856205i	1.03892	−	0.0592250i
$210$	−13.9919	+	9.24037i	−0.965535	+	0.637646i
$211$	−7.16054	−	7.16054i	−0.492952	−	0.492952i	0.416283	−	0.909235i	$-0.363333\pi$
$211$	−7.16054	−	7.16054i	−0.492952	−	0.492952i	−0.909235	+	0.416283i	$0.863333\pi$
$212$	23.4895	−	9.43422i	1.61327	−	0.647945i
$213$	5.70789	−	5.70789i	0.391098	−	0.391098i
$214$	0.917741	−	4.48721i	0.0627355	−	0.306739i
$215$	19.9497			1.36056
$216$	13.0354	+	9.01837i	0.886949	+	0.613623i
$217$	25.4403			1.72700
$218$	−2.85600	+	13.9641i	−0.193433	+	0.945770i
$219$	−8.23463	+	8.23463i	−0.556445	+	0.556445i
$220$	5.26615	−	12.3356i	0.355044	−	0.831669i
$221$	−2.97687	+	2.97687i	−0.200246	+	0.200246i
$222$	2.78035	+	4.21005i	0.186605	+	0.282560i
$223$	0.364568			0.0244133			0.0122066	−	0.999925i	$-0.496114\pi$
$223$	0.364568			0.0244133			0.0122066	+	0.999925i	$0.496114\pi$
$224$	−22.0833	−	5.01506i	−1.47550	−	0.335083i
$225$	0.828468			0.0552312
$226$	−3.12766	−	4.73596i	−0.208049	−	0.315031i
$227$	12.1764	+	12.1764i	0.808178	+	0.808178i	0.984358	−	0.176180i	$-0.0563741\pi$
$227$	12.1764	+	12.1764i	0.808178	+	0.808178i	−0.176180	+	0.984358i	$0.556374\pi$
$228$	−4.51317	+	12.4980i	−0.298892	+	0.827702i
$229$	−3.93799	+	3.93799i	−0.260230	+	0.260230i	−0.825147	−	0.564917i	$-0.808908\pi$
$229$	−3.93799	+	3.93799i	−0.260230	+	0.260230i	0.564917	+	0.825147i	$0.308908\pi$
$230$	4.31498	−	21.0977i	0.284521	−	1.39114i
$231$			21.0592i			1.38560i
$232$	−13.8949	−	9.61297i	−0.912244	−	0.631122i
$233$		−	0.107442i		−	0.00703876i	−0.999994	−	0.00351938i	$-0.998880\pi$
$233$		−	0.107442i		−	0.00703876i	0.999994	−	0.00351938i	$-0.00112026\pi$
$234$	−5.12050	−	1.04726i	−0.334737	−	0.0684618i
$235$	4.21782	+	4.21782i	0.275140	+	0.275140i
$236$	8.50033	+	21.1643i	0.553324	+	1.37768i
$237$	−5.32359	−	5.32359i	−0.345804	−	0.345804i
$238$	3.64178	−	2.40506i	0.236061	−	0.155897i
$239$		−	5.60709i		−	0.362692i	−0.983419	−	0.181346i	$-0.941955\pi$
$239$		−	5.60709i		−	0.362692i	0.983419	−	0.181346i	$-0.0580455\pi$
$240$	8.19456	+	8.55590i	0.528957	+	0.552281i
$241$		−	25.7917i		−	1.66139i	−0.556727	−	0.830695i	$-0.687943\pi$
$241$		−	25.7917i		−	1.66139i	0.556727	−	0.830695i	$-0.312057\pi$
$242$	−0.710407	−	1.07571i	−0.0456667	−	0.0691493i
$243$	−4.86977	−	4.86977i	−0.312396	−	0.312396i
$244$	14.8980	−	5.98357i	0.953750	−	0.383059i
$245$	−12.4013	+	12.4013i	−0.792288	+	0.792288i
$246$	−4.64560	−	0.950135i	−0.296192	−	0.0605784i
$247$	−1.35481	−	23.7661i	−0.0862048	−	1.51220i
$248$	−3.22105	−	17.6836i	−0.204537	−	1.12291i
$249$	3.11236			0.197238
$250$	16.7573	+	3.42728i	1.05983	+	0.216760i
$251$	11.9794	+	11.9794i	0.756132	+	0.756132i	0.975616	−	0.219484i	$-0.0704374\pi$
$251$	11.9794	+	11.9794i	0.756132	+	0.756132i	−0.219484	+	0.975616i	$0.570437\pi$
$252$	4.98302	+	2.12728i	0.313901	+	0.134006i
$253$	−19.1243	−	19.1243i	−1.20233	−	1.20233i
$254$	24.8320	−	16.3992i	1.55810	−	1.02898i
$255$	−2.28319			−0.142979
$256$	−0.689979	+	15.9851i	−0.0431237	+	0.999070i
$257$			21.1739i			1.32079i	0.750917	+	0.660396i	$0.229612\pi$
$257$			21.1739i			1.32079i	−0.750917	+	0.660396i	$0.770388\pi$
$258$	12.1959	+	18.4673i	0.759284	+	1.14972i
$259$	6.62541	+	6.62541i	0.411683	+	0.411683i
$260$	−19.5193	−	8.33289i	−1.21053	−	0.516784i
$261$	2.85848	+	2.85848i	0.176935	+	0.176935i
$262$	−2.36528	+	11.5648i	−0.146128	+	0.714477i
$263$	−3.56210			−0.219648			−0.109824	−	0.993951i	$-0.535029\pi$
$263$	−3.56210			−0.219648			−0.109824	+	0.993951i	$0.535029\pi$
$264$	14.6384	−	2.66635i	0.900928	−	0.164103i
$265$	−24.5935			−1.51077
$266$	−3.56075	+	24.4192i	−0.218323	+	1.49724i
$267$	−1.04746	−	1.04746i	−0.0641037	−	0.0641037i
$268$	17.7262	−	7.11947i	1.08280	−	0.434891i
$269$	−6.71180	+	6.71180i	−0.409226	+	0.409226i	−0.881469	−	0.472243i	$-0.843445\pi$
$269$	−6.71180	+	6.71180i	−0.409226	+	0.409226i	0.472243	+	0.881469i	$0.343445\pi$
$270$	−8.48677	−	12.8508i	−0.516488	−	0.782076i
$271$			17.8380i			1.08358i	0.840514	+	0.541789i	$0.182253\pi$
$271$			17.8380i			1.08358i	−0.840514	+	0.541789i	$0.817747\pi$
$272$	−2.13286	−	2.22690i	−0.129323	−	0.135026i
$273$	33.3230			2.01680
$274$	0.652021	+	0.987302i	0.0393900	+	0.0596451i
$275$	2.98769	−	2.98769i	0.180164	−	0.180164i
$276$	22.1678	−	8.90334i	1.33434	−	0.535918i
$277$	−4.31985	+	4.31985i	−0.259555	+	0.259555i	−0.824873	−	0.565318i	$-0.808753\pi$
$277$	−4.31985	+	4.31985i	−0.259555	+	0.259555i	0.565318	+	0.824873i	$0.308753\pi$
$278$	−18.6605	−	3.81651i	−1.11918	−	0.228899i
$279$			4.30055i			0.257467i
$280$	18.0936	+	12.5178i	1.08130	+	0.748080i
$281$	−10.9456			−0.652961			−0.326480	−	0.945204i	$-0.605863\pi$
$281$	−10.9456			−0.652961			−0.326480	+	0.945204i	$0.605863\pi$
$282$	−1.32590	+	6.48288i	−0.0789565	+	0.386050i
$283$	12.7625	+	12.7625i	0.758651	+	0.758651i	0.976077	−	0.217426i	$-0.0697660\pi$
$283$	12.7625	+	12.7625i	0.758651	+	0.758651i	−0.217426	+	0.976077i	$0.569766\pi$
$284$	−9.74126	−	4.15860i	−0.578038	−	0.246767i
$285$	8.59447	−	9.63358i	0.509092	−	0.570644i
$286$	−22.2427	+	14.6892i	−1.31524	+	0.868592i
$287$	−8.80607			−0.519806
$288$	0.847769	−	3.73306i	0.0499553	−	0.219973i
$289$	−16.4057			−0.965043
$290$	9.04631	+	13.6981i	0.531218	+	0.804379i
$291$	−7.14227	+	7.14227i	−0.418687	+	0.418687i
$292$	14.0535	+	5.99951i	0.822418	+	0.351095i
$293$	−15.2720	−	15.2720i	−0.892202	−	0.892202i	0.102529	−	0.994730i	$-0.467307\pi$
$293$	−15.2720	−	15.2720i	−0.892202	−	0.892202i	−0.994730	+	0.102529i	$0.967307\pi$
$294$	−19.0610	−	3.89843i	−1.11166	−	0.227361i
$295$		−	22.1590i		−	1.29015i
$296$	3.76649	−	5.44420i	0.218923	−	0.316438i
$297$	−19.3417			−1.12232
$298$	−2.40490	+	11.7585i	−0.139312	+	0.681153i
$299$	−30.2612	+	30.2612i	−1.75005	+	1.75005i
$300$	1.39093	+	3.46316i	0.0803051	+	0.199946i
$301$	29.0621	+	29.0621i	1.67511	+	1.67511i
$302$	14.8036	+	22.4159i	0.851853	+	1.28989i
$303$	−19.2603			−1.10647
$304$	17.4247	−	0.616672i	0.999374	−	0.0353686i
$305$	−15.5982			−0.893153
$306$	0.406562	+	0.615623i	0.0232416	+	0.0351928i
$307$	−3.37715	−	3.37715i	−0.192744	−	0.192744i	0.604137	−	0.796881i	$-0.293518\pi$
$307$	−3.37715	−	3.37715i	−0.192744	−	0.192744i	−0.796881	+	0.604137i	$0.793518\pi$
$308$	25.6418	−	10.2986i	1.46107	−	0.586818i
$309$	2.98028	−	2.98028i	0.169542	−	0.169542i
$310$	−3.49927	+	17.1093i	−0.198745	+	0.971745i
$311$	−1.49807			−0.0849477			−0.0424738	−	0.999098i	$-0.513524\pi$
$311$	−1.49807			−0.0849477			−0.0424738	+	0.999098i	$0.513524\pi$
$312$	−4.21910	−	23.1630i	−0.238859	−	1.31134i
$313$		−	18.4107i		−	1.04064i	−0.853973	−	0.520318i	$-0.825813\pi$
$313$		−	18.4107i		−	1.04064i	0.853973	−	0.520318i	$-0.174187\pi$
$314$	0.817394	+	0.167177i	0.0461282	+	0.00943432i
$315$	−3.72224	−	3.72224i	−0.209725	−	0.209725i
$316$	−3.87861	+	9.08541i	−0.218189	+	0.511094i
$317$	16.6166	−	16.6166i	0.933283	−	0.933283i	−0.0646267	−	0.997910i	$-0.520586\pi$
$317$	16.6166	−	16.6166i	0.933283	−	0.933283i	0.997910	+	0.0646267i	$0.0205857\pi$
$318$	−15.0348	−	22.7660i	−0.843111	−	1.27665i
$319$	20.6170			1.15433
$320$	6.41028	−	14.1618i	0.358346	−	0.791669i
$321$	−4.93640			−0.275523
$322$	37.0203	−	24.4485i	2.06306	−	1.36246i
$323$	−2.23694	+	2.50740i	−0.124467	+	0.139515i
$324$	5.11345	−	11.9780i	0.284081	−	0.665442i
$325$	−4.72756	−	4.72756i	−0.262238	−	0.262238i
$326$	2.61935	−	12.8070i	0.145072	−	0.709317i
$327$	15.3620			0.849521
$328$	1.11495	+	6.12113i	0.0615630	+	0.337983i
$329$			12.2888i			0.677502i
$330$	−14.1629	−	2.89666i	−0.779644	−	0.159456i
$331$	−13.9808	+	13.9808i	−0.768453	+	0.768453i	−0.977834	−	0.209381i	$-0.932855\pi$
$331$	−13.9808	+	13.9808i	−0.768453	+	0.768453i	0.209381	+	0.977834i	$0.432855\pi$
$332$	−1.52204	−	3.78961i	−0.0835328	−	0.207982i
$333$	−1.11999	+	1.11999i	−0.0613751	+	0.0613751i
$334$	−4.85915	−	7.35780i	−0.265881	−	0.402601i
$335$	−18.5594			−1.01401
$336$	−0.526387	+	24.4016i	−0.0287168	+	1.33121i
$337$			17.8920i			0.974641i	0.873223	+	0.487320i	$0.162026\pi$
$337$			17.8920i			0.974641i	−0.873223	+	0.487320i	$0.837974\pi$
$338$	13.1120	+	19.8544i	0.713199	+	1.07994i
$339$	−4.32540	+	4.32540i	−0.234924	+	0.234924i
$340$	1.11655	+	2.78001i	0.0605534	+	0.150767i
$341$	15.5090	+	15.5090i	0.839858	+	0.839858i
$342$	−4.12793	−	0.601926i	−0.223213	−	0.0325484i
$343$	−8.10910			−0.437850
$344$	16.5216	−	23.8808i	0.890784	−	1.28757i
$345$	−23.2096			−1.24956
$346$	3.96357	−	19.3795i	0.213083	−	1.04185i
$347$	−0.120595	−	0.120595i	−0.00647386	−	0.00647386i	0.703862	−	0.710336i	$-0.251457\pi$
$347$	−0.120595	−	0.120595i	−0.00647386	−	0.00647386i	−0.710336	+	0.703862i	$0.751457\pi$
$348$	−7.14988	+	16.7482i	−0.383274	+	0.897795i
$349$	−0.280410	−	0.280410i	−0.0150100	−	0.0150100i	0.699562	−	0.714572i	$-0.253379\pi$
$349$	−0.280410	−	0.280410i	−0.0150100	−	0.0150100i	−0.714572	+	0.699562i	$0.753379\pi$
$350$	3.81947	+	5.78350i	0.204159	+	0.309141i
$351$			30.6054i			1.63359i
$352$	−10.4052	−	16.5197i	−0.554597	−	0.880506i
$353$	16.6801			0.887792			0.443896	−	0.896078i	$-0.353596\pi$
$353$	16.6801			0.887792			0.443896	+	0.896078i	$0.353596\pi$
$354$	20.5124	−	13.5465i	1.09022	−	0.719990i
$355$	7.27657	+	7.27657i	0.386200	+	0.386200i
$356$	−0.763151	+	1.78764i	−0.0404469	+	0.0947445i
$357$	−3.32608	−	3.32608i	−0.176035	−	0.176035i
$358$	1.69942	+	0.347573i	0.0898173	+	0.0183698i
$359$	23.6765			1.24960			0.624800	−	0.780785i	$-0.285180\pi$
$359$	23.6765			1.24960			0.624800	+	0.780785i	$0.285180\pi$
$360$	−2.11606	+	3.05862i	−0.111526	+	0.161204i
$361$	−2.15922	−	18.8769i	−0.113643	−	0.993522i
$362$	24.4999	+	5.01081i	1.28768	+	0.263362i
$363$	−0.982458	+	0.982458i	−0.0515657	+	0.0515657i
$364$	−16.2960	−	40.5742i	−0.854142	−	2.12666i
$365$	−10.4977	−	10.4977i	−0.549477	−	0.549477i
$366$	−9.53571	−	14.4391i	−0.498439	−	0.754746i
$367$			8.49939i			0.443665i	0.975085	+	0.221832i	$0.0712038\pi$
$367$			8.49939i			0.443665i	−0.975085	+	0.221832i	$0.928796\pi$
$368$	−21.6814	−	22.6375i	−1.13022	−	1.18006i
$369$		−	1.48862i		−	0.0774944i
$370$	−5.36709	+	3.54447i	−0.279022	+	0.184268i
$371$	−35.8271	−	35.8271i	−1.86005	−	1.86005i
$372$	−17.9771	+	7.22025i	−0.932072	+	0.374352i
$373$	15.0345	+	15.0345i	0.778457	+	0.778457i	0.979568	−	0.201111i	$-0.0644553\pi$
$373$	15.0345	+	15.0345i	0.778457	+	0.778457i	−0.201111	+	0.979568i	$0.564455\pi$
$374$	3.68629	+	0.753934i	0.190613	+	0.0389850i
$375$		−	18.4348i		−	0.951971i
$376$	8.54197	−	1.55591i	0.440519	−	0.0802398i
$377$		−	32.6232i		−	1.68018i
$378$	6.35741	−	31.0839i	0.326990	−	1.59878i
$379$	−10.6125	+	10.6125i	−0.545128	+	0.545128i	−0.925028	−	0.379900i	$-0.875958\pi$
$379$	−10.6125	+	10.6125i	−0.545128	+	0.545128i	0.379900	+	0.925028i	$0.375958\pi$
$380$	−15.9328	−	5.75352i	−0.817337	−	0.295149i
$381$	−22.6793	−	22.6793i	−1.16190	−	1.16190i
$382$	6.86907	+	10.4013i	0.351452	+	0.532175i
$383$	−6.01982			−0.307599			−0.153799	−	0.988102i	$-0.549151\pi$
$383$	−6.01982			−0.307599			−0.153799	+	0.988102i	$0.549151\pi$
$384$	17.0283	−	2.72364i	0.868970	−	0.138990i
$385$	−26.8469			−1.36824
$386$	−5.29566	−	8.01878i	−0.269542	−	0.408145i
$387$	−4.91280	+	4.91280i	−0.249732	+	0.249732i
$388$	12.1892	+	5.20365i	0.618815	+	0.264175i
$389$	9.78130	−	9.78130i	0.495932	−	0.495932i	−0.414237	−	0.910169i	$-0.635952\pi$
$389$	9.78130	−	9.78130i	0.495932	−	0.495932i	0.910169	+	0.414237i	$0.135952\pi$
$390$	−4.58353	+	22.4107i	−0.232096	+	1.13481i
$391$	6.04093			0.305503
$392$	4.57469	+	25.1152i	0.231057	+	1.26851i
$393$	12.7225			0.641766
$394$	−2.15591	+	10.5411i	−0.108613	+	0.531053i
$395$	6.78666	−	6.78666i	0.341474	−	0.341474i
$396$	1.74093	+	4.33460i	0.0874849	+	0.217822i
$397$	−17.2798	−	17.2798i	−0.867247	−	0.867247i	0.124920	−	0.992167i	$-0.460133\pi$
$397$	−17.2798	−	17.2798i	−0.867247	−	0.867247i	−0.992167	+	0.124920i	$0.960133\pi$
$398$	3.01299	−	1.98980i	0.151027	−	0.0997396i
$399$	26.5541	−	1.51374i	1.32937	−	0.0757820i
$400$	3.53654	−	3.38719i	0.176827	−	0.169359i
$401$			21.0663i			1.05200i	0.850485	+	0.526000i	$0.176309\pi$
$401$			21.0663i			1.05200i	−0.850485	+	0.526000i	$0.823691\pi$
$402$	−11.3459	−	17.1802i	−0.565883	−	0.856871i
$403$	24.5406	−	24.5406i	1.22245	−	1.22245i
$404$	9.41887	+	23.4513i	0.468606	+	1.16675i
$405$	−8.94734	+	8.94734i	−0.444597	+	0.444597i
$406$	−6.77656	+	33.1333i	−0.336315	+	1.64438i
$407$			8.07800i			0.400412i
$408$	−1.89085	+	2.73309i	−0.0936108	+	0.135308i
$409$	30.6366			1.51488			0.757441	−	0.652904i	$-0.226449\pi$
$409$	30.6366			1.51488			0.757441	+	0.652904i	$0.226449\pi$
$410$	1.21126	−	5.92234i	0.0598198	−	0.292483i
$411$	0.901714	−	0.901714i	0.0444783	−	0.0444783i
$412$	−5.08624	−	2.17134i	−0.250581	−	0.106974i
$413$	32.2806	−	32.2806i	1.58842	−	1.58842i
$414$	4.13289	+	6.25809i	0.203120	+	0.307568i
$415$			3.96772i			0.194768i
$416$	−26.1400	+	16.4646i	−1.28162	+	0.807243i
$417$			20.5285i			1.00528i
$418$	−17.0572	+	12.7158i	−0.834295	+	0.621949i
$419$	−11.0415	+	11.0415i	−0.539415	+	0.539415i	−0.923357	−	0.383942i	$-0.874566\pi$
$419$	−11.0415	+	11.0415i	−0.539415	+	0.539415i	0.383942	+	0.923357i	$0.374566\pi$
$420$	9.31039	−	21.8090i	0.454301	−	1.06417i
$421$	−9.18271	−	9.18271i	−0.447538	−	0.447538i	0.446997	−	0.894535i	$-0.352493\pi$
$421$	−9.18271	−	9.18271i	−0.447538	−	0.447538i	−0.894535	+	0.446997i	$0.852493\pi$
$422$	14.0306	+	2.86960i	0.683001	+	0.139690i
$423$	−2.07735			−0.101004
$424$	−20.3674	+	29.4397i	−0.989129	+	1.42972i
$425$			0.943745i			0.0457784i
$426$	−2.28745	+	11.1842i	−0.110827	+	0.541879i
$427$	−22.7230	−	22.7230i	−1.09964	−	1.09964i
$428$	2.41405	+	6.01057i	0.116688	+	0.290532i
$429$	20.3145	+	20.3145i	0.980793	+	0.980793i
$430$	−23.5426	+	15.5477i	−1.13532	+	0.749776i
$431$	34.1955			1.64714			0.823570	−	0.567215i	$-0.191979\pi$
$431$	34.1955			1.64714			0.823570	+	0.567215i	$0.191979\pi$
$432$	−22.4115	−	0.483457i	−1.07827	−	0.0232604i
$433$			7.12873i			0.342585i	0.985220	+	0.171292i	$0.0547943\pi$
$433$			7.12873i			0.342585i	−0.985220	+	0.171292i	$0.945206\pi$
$434$	−30.0220	+	19.8267i	−1.44110	+	0.951713i
$435$	12.5106	−	12.5106i	0.599838	−	0.599838i
$436$	−7.51250	−	18.7048i	−0.359783	−	0.895798i
$437$	−22.7395	+	25.4888i	−1.08778	+	1.21930i
$438$	3.30005	−	16.1353i	0.157682	−	0.770972i
$439$			13.3329i			0.636347i	0.948033	+	0.318173i	$0.103069\pi$
$439$			13.3329i			0.636347i	−0.948033	+	0.318173i	$0.896931\pi$
$440$	3.39914	+	18.6614i	0.162048	+	0.889646i
$441$		−	6.10785i		−	0.290850i
$442$	1.19299	−	5.83299i	0.0567445	−	0.277447i
$443$	−6.00022	−	6.00022i	−0.285079	−	0.285079i	0.550052	−	0.835131i	$-0.314608\pi$
$443$	−6.00022	−	6.00022i	−0.285079	−	0.285079i	−0.835131	+	0.550052i	$0.814608\pi$
$444$	−6.56215	−	2.80142i	−0.311426	−	0.132949i
$445$	1.33534	−	1.33534i	0.0633010	−	0.0633010i
$446$	−0.430224	+	0.284123i	−0.0203717	+	0.0134536i
$447$	12.9356			0.611834
$448$	29.9688	−	11.2922i	1.41589	−	0.533506i
$449$		−	24.8792i		−	1.17412i	−0.809542	−	0.587061i	$-0.800285\pi$
$449$		−	24.8792i		−	1.17412i	0.809542	−	0.587061i	$-0.199715\pi$
$450$	−0.977671	+	0.645661i	−0.0460878	+	0.0304367i
$451$	−5.36838	−	5.36838i	−0.252787	−	0.252787i
$452$	7.38188	+	3.15136i	0.347214	+	0.148228i
$453$	20.4727	−	20.4727i	0.961891	−	0.961891i
$454$	−23.8590	−	4.87973i	−1.11976	−	0.229017i
$455$			42.4811i			1.99155i
$456$	−4.41427	−	18.2662i	−0.206717	−	0.855391i
$457$			35.0890i			1.64140i	0.571363	+	0.820698i	$0.306415\pi$
$457$			35.0890i			1.64140i	−0.571363	+	0.820698i	$0.693585\pi$
$458$	1.57816	−	7.71625i	0.0737425	−	0.360557i
$459$	3.05481	−	3.05481i	0.142587	−	0.142587i
$460$	11.3502	+	28.2601i	0.529207	+	1.31763i
$461$	3.40782	+	3.40782i	0.158718	+	0.158718i	0.781998	−	0.623280i	$-0.214200\pi$
$461$	3.40782	+	3.40782i	0.158718	+	0.158718i	−0.623280	+	0.781998i	$0.714200\pi$
$462$	−16.4124	−	24.8519i	−0.763573	−	1.15622i
$463$		−	5.08661i		−	0.236395i	−0.992990	−	0.118197i	$-0.962288\pi$
$463$		−	5.08661i		−	0.236395i	0.992990	−	0.118197i	$-0.0377115\pi$
$464$	23.8891	+	0.515332i	1.10902	+	0.0239237i
$465$	18.8221			0.872852
$466$	0.0837341	+	0.126792i	0.00387891	+	0.00587351i
$467$	−10.1565	+	10.1565i	−0.469989	+	0.469989i	−0.901911	−	0.431922i	$-0.857836\pi$
$467$	−10.1565	+	10.1565i	−0.469989	+	0.469989i	0.431922	+	0.901911i	$0.357836\pi$
$468$	6.85885	−	2.75475i	0.317050	−	0.127338i
$469$	−27.0367	−	27.0367i	−1.24844	−	1.24844i
$470$	−8.26456	−	1.69030i	−0.381216	−	0.0779677i
$471$		−	0.899219i		−	0.0414338i
$472$	−26.5255	−	18.3512i	−1.22093	−	0.844684i
$473$			35.4339i			1.62925i
$474$	10.4312	+	2.13344i	0.479123	+	0.0979921i
$475$	−3.98200	−	3.55249i	−0.182707	−	0.162999i
$476$	−2.42328	+	5.67639i	−0.111071	+	0.260177i
$477$	6.05638	−	6.05638i	0.277303	−	0.277303i
$478$	4.36985	+	6.61690i	0.199872	+	0.302650i
$479$			5.47969i			0.250373i	0.992133	+	0.125187i	$0.0399530\pi$
$479$			5.47969i			0.250373i	−0.992133	+	0.125187i	$0.960047\pi$
$480$	−16.3383	−	3.71040i	−0.745740	−	0.169356i
$481$	12.7822			0.582819
$482$	20.1006	+	30.4367i	0.915557	+	1.38635i
$483$	−33.8111	−	33.8111i	−1.53846	−	1.53846i
$484$	1.67670	+	0.715790i	0.0762134	+	0.0325359i
$485$	−9.10517	−	9.10517i	−0.413444	−	0.413444i
$486$	9.54201	+	1.95157i	0.432834	+	0.0885250i
$487$			40.0620i			1.81538i	0.419636	+	0.907692i	$0.362158\pi$
$487$			40.0620i			1.81538i	−0.419636	+	0.907692i	$0.637842\pi$
$488$	−12.9179	+	18.6719i	−0.584764	+	0.845236i
$489$	−14.0891			−0.637131
$490$	4.96983	−	24.2995i	0.224514	−	1.09774i
$491$	−22.1640	−	22.1640i	−1.00025	−	1.00025i	−1.00000		0.000247972i	$-0.999921\pi$
$491$	−22.1640	−	22.1640i	−1.00025	−	1.00025i	−0.000247972	−	1.00000i	$-0.500079\pi$
$492$	6.22273	−	2.49926i	0.280542	−	0.112675i
$493$	−3.25622	+	3.25622i	−0.146653	+	0.146653i
$494$	20.1208	+	26.9904i	0.905276	+	1.21436i
$495$		−	4.53833i		−	0.203983i
$496$	17.5828	+	18.3581i	0.789489	+	0.824302i
$497$			21.2006i			0.950975i
$498$	−3.67288	+	2.42560i	−0.164586	+	0.108694i
$499$	6.12304	−	6.12304i	0.274105	−	0.274105i	−0.556645	−	0.830750i	$-0.687912\pi$
$499$	6.12304	−	6.12304i	0.274105	−	0.274105i	0.830750	+	0.556645i	$0.187912\pi$
$500$	−22.4463	+	9.01520i	−1.00383	+	0.403172i
$501$	−6.71996	+	6.71996i	−0.300226	+	0.300226i
$502$	−23.4729	−	4.80076i	−1.04765	−	0.214269i
$503$	−22.7361			−1.01375			−0.506876	−	0.862019i	$-0.669200\pi$
$503$	−22.7361			−1.01375			−0.506876	+	0.862019i	$0.669200\pi$
$504$	−7.53832	+	1.37309i	−0.335784	+	0.0611625i
$505$		−	24.5535i		−	1.09262i
$506$	37.4728	+	7.66408i	1.66587	+	0.340710i
$507$	18.1333	−	18.1333i	0.805326	−	0.805326i
$508$	−16.5235	+	38.7053i	−0.733111	+	1.71727i
$509$	−10.5574	+	10.5574i	−0.467948	+	0.467948i	−0.901249	−	0.433301i	$-0.857349\pi$
$509$	−10.5574	+	10.5574i	−0.467948	+	0.467948i	0.433301	+	0.901249i	$0.357349\pi$
$510$	2.69438	−	1.77939i	0.119309	−	0.0787925i
$511$		−	30.5856i		−	1.35303i
$512$	−11.6436	−	19.4017i	−0.514581	−	0.857442i
$513$	1.39029	+	24.3884i	0.0613828	+	1.07677i
$514$	−16.5017	−	24.9872i	−0.727861	−	1.10214i
$515$	3.79934	+	3.79934i	0.167419	+	0.167419i
$516$	−28.7847	−	12.2883i	−1.26717	−	0.540963i
$517$	−7.49152	+	7.49152i	−0.329477	+	0.329477i
$518$	−12.9821	−	2.65515i	−0.570400	−	0.116660i
$519$	−21.3195			−0.935821
$520$	29.5288	−	5.37862i	1.29492	−	0.235868i
$521$	25.0157			1.09596			0.547979	−	0.836492i	$-0.315397\pi$
$521$	25.0157			1.09596			0.547979	+	0.836492i	$0.315397\pi$
$522$	−5.60101	−	1.14554i	−0.245150	−	0.0501390i
$523$	−0.0726825	+	0.0726825i	−0.00317819	+	0.00317819i	−0.708694	−	0.705516i	$-0.750715\pi$
$523$	−0.0726825	+	0.0726825i	−0.00317819	+	0.00317819i	0.705516	+	0.708694i	$0.250715\pi$
$524$	−6.22170	−	15.4909i	−0.271796	−	0.676725i
$525$	5.28214	−	5.28214i	0.230531	−	0.230531i
$526$	4.20361	−	2.77610i	0.183286	−	0.121044i
$527$	−4.89895			−0.213401
$528$	−15.1966	+	14.5548i	−0.661349	+	0.633418i
$529$	38.4088			1.66995
$530$	29.0227	−	19.1668i	1.26067	−	0.832553i
$531$	5.45686	+	5.45686i	0.236808	+	0.236808i
$532$	−14.8289	−	31.5920i	−0.642914	−	1.36969i
$533$	−8.49464	+	8.49464i	−0.367944	+	0.367944i
$534$	2.05244	+	0.419773i	0.0888178	+	0.0181654i
$535$		−	6.29306i		−	0.272073i
$536$	−15.3701	+	22.2165i	−0.663888	+	0.959605i
$537$		−	1.86954i		−	0.0806767i
$538$	2.68977	−	13.1514i	0.115964	−	0.566995i
$539$	−22.0266	−	22.0266i	−0.948753	−	0.948753i
$540$	20.0304	+	8.55108i	0.861971	+	0.367980i
$541$	26.1537	+	26.1537i	1.12444	+	1.12444i	0.991066	+	0.133371i	$0.0425801\pi$
$541$	26.1537	+	26.1537i	1.12444	+	1.12444i	0.133371	+	0.991066i	$0.457420\pi$
$542$	−13.9019	−	21.0505i	−0.597137	−	0.904196i
$543$		−	26.9524i		−	1.15664i
$544$	4.25249	+	0.965732i	0.182324	+	0.0414054i
$545$			19.5839i			0.838883i
$546$	−39.3244	+	25.9701i	−1.68293	+	1.11142i
$547$	−14.2992	−	14.2992i	−0.611388	−	0.611388i	0.331919	−	0.943308i	$-0.392304\pi$
$547$	−14.2992	−	14.2992i	−0.611388	−	0.611388i	−0.943308	+	0.331919i	$0.892304\pi$
$548$	−1.53889	−	0.656962i	−0.0657383	−	0.0280640i
$549$	3.84121	−	3.84121i	0.163939	−	0.163939i
$550$	−1.19732	+	5.85419i	−0.0510540	+	0.249623i
$551$	−1.48195	−	25.9964i	−0.0631333	−	1.10748i
$552$	−19.2213	+	27.7831i	−0.818113	+	1.18253i
$553$	19.7732			0.840842
$554$	1.73119	−	8.46448i	0.0735512	−	0.359621i
$555$	4.90183	+	4.90183i	0.208071	+	0.208071i
$556$	24.9955	−	10.0391i	1.06005	−	0.425751i
$557$	21.0678	+	21.0678i	0.892670	+	0.892670i	0.994774	−	0.102103i	$-0.0325573\pi$
$557$	21.0678	+	21.0678i	0.892670	+	0.892670i	−0.102103	+	0.994774i	$0.532557\pi$
$558$	−3.35160	−	5.07505i	−0.141885	−	0.214844i
$559$	56.0687			2.37146
$560$	−31.1078	−	0.671053i	−1.31454	−	0.0283572i
$561$		−	4.05530i		−	0.171215i
$562$	12.9169	−	8.53039i	0.544865	−	0.359833i
$563$	−6.74038	−	6.74038i	−0.284073	−	0.284073i	0.550658	−	0.834731i	$-0.314377\pi$
$563$	−6.74038	−	6.74038i	−0.284073	−	0.284073i	−0.834731	+	0.550658i	$0.814377\pi$
$564$	−3.48770	−	8.68375i	−0.146858	−	0.365652i
$565$	−5.51415	−	5.51415i	−0.231982	−	0.231982i
$566$	−25.0073	−	5.11459i	−1.05114	−	0.214982i
$567$	−26.0684			−1.09477
$568$	14.7366	−	2.68425i	0.618334	−	0.112628i
$569$	−34.0576			−1.42777			−0.713885	−	0.700263i	$-0.753066\pi$
$569$	−34.0576			−1.42777			−0.713885	+	0.700263i	$0.753066\pi$
$570$	−2.63443	+	18.0666i	−0.110344	+	0.756726i
$571$	−4.22887	−	4.22887i	−0.176973	−	0.176973i	0.613062	−	0.790035i	$-0.289938\pi$
$571$	−4.22887	−	4.22887i	−0.176973	−	0.176973i	−0.790035	+	0.613062i	$0.789938\pi$
$572$	14.8005	−	34.6694i	0.618841	−	1.44960i
$573$	9.49959	−	9.49959i	0.396851	−	0.396851i
$574$	10.3920	−	6.86295i	0.433754	−	0.286454i
$575$			9.59360i			0.400081i
$576$	1.90888	+	5.06607i	0.0795369	+	0.211086i
$577$	−36.3517			−1.51334			−0.756671	−	0.653795i	$-0.773176\pi$
$577$	−36.3517			−1.51334			−0.756671	+	0.653795i	$0.773176\pi$
$578$	19.3603	−	12.7857i	0.805284	−	0.531815i
$579$	−7.32364	+	7.32364i	−0.304360	+	0.304360i
$580$	−21.3510	−	9.11486i	−0.886553	−	0.378474i
$581$	−5.78006	+	5.78006i	−0.239797	+	0.239797i
$582$	2.86228	−	13.9948i	0.118645	−	0.580105i
$583$		−	43.6820i		−	1.80913i
$584$	−21.2601	+	3.87250i	−0.879751	+	0.160245i
$585$	−7.18121			−0.296907
$586$	29.9246	+	6.12030i	1.23617	+	0.252827i
$587$	26.7919	+	26.7919i	1.10582	+	1.10582i	0.993694	+	0.112124i	$0.0357654\pi$
$587$	26.7919	+	26.7919i	1.10582	+	1.10582i	0.112124	+	0.993694i	$0.464235\pi$
$588$	25.5320	−	10.2545i	1.05292	−	0.422890i
$589$	18.4408	−	20.6704i	0.759841	−	0.851709i
$590$	17.2695	+	26.1498i	0.710974	+	1.07657i
$591$	11.5963			0.477009
$592$	−0.201914	+	9.36007i	−0.00829862	+	0.384696i
$593$	−5.90642			−0.242548			−0.121274	−	0.992619i	$-0.538698\pi$
$593$	−5.90642			−0.242548			−0.121274	+	0.992619i	$0.538698\pi$
$594$	22.8251	−	15.0738i	0.936525	−	0.618487i
$595$	4.24017	−	4.24017i	0.173830	−	0.173830i
$596$	−6.32592	−	15.7504i	−0.259120	−	0.645163i
$597$	−2.75180	−	2.75180i	−0.112623	−	0.112623i
$598$	12.1272	−	59.2950i	0.495920	−	2.42475i
$599$			34.2515i			1.39948i	0.714398	+	0.699739i	$0.246700\pi$
$599$			34.2515i			1.39948i	−0.714398	+	0.699739i	$0.753300\pi$
$600$	−4.34042	−	3.00285i	−0.177197	−	0.122591i
$601$	−6.25234			−0.255038			−0.127519	−	0.991836i	$-0.540701\pi$
$601$	−6.25234			−0.255038			−0.127519	+	0.991836i	$0.540701\pi$
$602$	−56.9455	−	11.6467i	−2.32092	−	0.474685i
$603$	4.57041	−	4.57041i	0.186121	−	0.186121i
$604$	−34.9394	−	14.9158i	−1.42166	−	0.606915i
$605$	−1.25247	−	1.25247i	−0.0509200	−	0.0509200i
$606$	22.7290	−	15.0104i	0.923301	−	0.609754i
$607$	34.1961			1.38798			0.693988	−	0.719987i	$-0.255852\pi$
$607$	34.1961			1.38798			0.693988	+	0.719987i	$0.255852\pi$
$608$	−20.0822	+	14.3075i	−0.814440	+	0.580247i
$609$	36.4501			1.47703
$610$	18.4074	−	12.1564i	0.745294	−	0.492198i
$611$	11.8542	+	11.8542i	0.479569	+	0.479569i
$612$	−0.959563	−	0.409643i	−0.0387881	−	0.0165588i
$613$	5.80803	−	5.80803i	0.234584	−	0.234584i	−0.580019	−	0.814603i	$-0.696955\pi$
$613$	5.80803	−	5.80803i	0.234584	−	0.234584i	0.814603	+	0.580019i	$0.196955\pi$
$614$	6.61732	+	1.35340i	0.267053	+	0.0546188i
$615$	−6.51519			−0.262718
$616$	−22.2336	+	32.1371i	−0.895815	+	1.29484i
$617$			33.1368i			1.33404i	0.745041	+	0.667019i	$0.232430\pi$
$617$			33.1368i			1.33404i	−0.745041	+	0.667019i	$0.767570\pi$
$618$	−1.19435	+	5.83967i	−0.0480439	+	0.234906i
$619$	−3.63801	−	3.63801i	−0.146224	−	0.146224i	0.630205	−	0.776429i	$-0.282971\pi$
$619$	−3.63801	−	3.63801i	−0.146224	−	0.146224i	−0.776429	+	0.630205i	$0.782971\pi$
$620$	−9.20457	−	22.9178i	−0.369664	−	0.920400i
$621$	31.0536	−	31.0536i	1.24614	−	1.24614i
$622$	1.76786	−	1.16751i	0.0708849	−	0.0468129i
$623$	3.89055			0.155872
$624$	23.0308	+	24.0464i	0.921971	+	0.962625i
$625$	17.3800			0.695202
$626$	14.3483	+	21.7264i	0.573472	+	0.868362i
$627$	17.1108	+	15.2651i	0.683338	+	0.609631i
$628$	−1.09489	+	0.439746i	−0.0436909	+	0.0175478i
$629$	−1.27583	−	1.27583i	−0.0508708	−	0.0508708i
$630$	7.29350	+	1.49170i	0.290580	+	0.0594306i
$631$	8.04038			0.320083			0.160041	−	0.987110i	$-0.448837\pi$
$631$	8.04038			0.320083			0.160041	+	0.987110i	$0.448837\pi$
$632$	−2.50352	−	13.7444i	−0.0995849	−	0.546724i
$633$		−	15.4352i		−	0.613493i
$634$	−6.65915	+	32.5593i	−0.264468	+	1.29309i
$635$	28.9122	−	28.9122i	1.14735	−	1.14735i
$636$	35.4850	+	15.1487i	1.40707	+	0.600687i
$637$	−34.8538	+	34.8538i	−1.38096	+	1.38096i
$638$	−24.3300	+	16.0677i	−0.963233	+	0.636126i
$639$	−3.58384			−0.141775
$640$	3.47217	+	21.7081i	0.137249	+	0.858088i
$641$			4.50914i			0.178100i	0.996027	+	0.0890501i	$0.0283831\pi$
$641$			4.50914i			0.178100i	−0.996027	+	0.0890501i	$0.971617\pi$
$642$	5.82542	−	3.84715i	0.229911	−	0.151835i
$643$	−9.49870	+	9.49870i	−0.374592	+	0.374592i	−0.869147	−	0.494554i	$-0.835331\pi$
$643$	−9.49870	+	9.49870i	−0.374592	+	0.374592i	0.494554	+	0.869147i	$0.335331\pi$
$644$	−24.6337	+	57.7031i	−0.970706	+	2.27382i
$645$	21.5017	+	21.5017i	0.846629	+	0.846629i
$646$	0.685680	−	4.70231i	0.0269777	−	0.185010i
$647$	31.7571			1.24850			0.624250	−	0.781225i	$-0.285405\pi$
$647$	31.7571			1.24850			0.624250	+	0.781225i	$0.285405\pi$
$648$	3.30058	+	18.1203i	0.129659	+	0.711831i
$649$	39.3580			1.54494
$650$	9.26336	+	1.89458i	0.363339	+	0.0743115i
$651$	27.4194	+	27.4194i	1.07465	+	1.07465i
$652$	6.89000	+	17.1549i	0.269833	+	0.671838i
$653$	19.7023	+	19.7023i	0.771009	+	0.771009i	0.978283	−	0.207274i	$-0.0664591\pi$
$653$	19.7023	+	19.7023i	0.771009	+	0.771009i	−0.207274	+	0.978283i	$0.566459\pi$
$654$	−18.1286	+	11.9723i	−0.708886	+	0.468153i
$655$			16.2190i			0.633729i
$656$	−6.08621	−	6.35458i	−0.237627	−	0.248105i
$657$	5.17033			0.201714
$658$	−9.57717	−	14.5019i	−0.373357	−	0.565344i
$659$	3.40326	+	3.40326i	0.132572	+	0.132572i	0.770279	−	0.637707i	$-0.220117\pi$
$659$	3.40326	+	3.40326i	0.132572	+	0.132572i	−0.637707	+	0.770279i	$0.720117\pi$
$660$	18.9711	−	7.61946i	0.738450	−	0.296587i
$661$	−7.77011	−	7.77011i	−0.302222	−	0.302222i	0.539660	−	0.841883i	$-0.318553\pi$
$661$	−7.77011	−	7.77011i	−0.302222	−	0.302222i	−0.841883	+	0.539660i	$0.818553\pi$
$662$	5.60282	−	27.3945i	0.217760	−	1.06472i
$663$	−6.41690			−0.249212
$664$	4.74956	+	3.28591i	0.184319	+	0.127518i
$665$	1.92976	+	33.8518i	0.0748330	+	1.31272i
$666$	0.448839	−	2.19455i	0.0173921	−	0.0850372i
$667$	−33.1010	+	33.1010i	−1.28168	+	1.28168i
$668$	11.4685	+	4.89597i	0.443730	+	0.189431i
$669$	0.392929	+	0.392929i	0.0151915	+	0.0151915i
$670$	21.9018	−	14.4641i	0.846140	−	0.558797i
$671$		−	27.7050i		−	1.06954i
$672$	−18.3960	−	29.2064i	−0.709641	−	1.12666i
$673$		−	19.7481i		−	0.761232i	−0.924733	−	0.380616i	$-0.875712\pi$
$673$		−	19.7481i		−	0.761232i	0.924733	−	0.380616i	$-0.124288\pi$
$674$	−13.9440	−	21.1143i	−0.537104	−	0.813292i
$675$	4.85135	+	4.85135i	0.186729	+	0.186729i
$676$	−30.9468	−	13.2114i	−1.19026	−	0.508129i
$677$	−8.64520	−	8.64520i	−0.332262	−	0.332262i	0.521183	−	0.853445i	$-0.325491\pi$
$677$	−8.64520	−	8.64520i	−0.332262	−	0.332262i	−0.853445	+	0.521183i	$0.825491\pi$
$678$	1.73341	−	8.47536i	0.0665714	−	0.325494i
$679$		−	26.5282i		−	1.01806i
$680$	−3.48422	−	2.41050i	−0.133614	−	0.0924386i
$681$			26.2474i			1.00580i
$682$	−30.3889	−	6.21525i	−1.16365	−	0.237994i
$683$	7.82187	−	7.82187i	0.299295	−	0.299295i	−0.541442	−	0.840738i	$-0.682122\pi$
$683$	7.82187	−	7.82187i	0.299295	−	0.299295i	0.840738	+	0.541442i	$0.182122\pi$
$684$	5.34046	−	2.50675i	0.204198	−	0.0958478i
$685$	1.14953	+	1.14953i	0.0439213	+	0.0439213i
$686$	9.56951	−	6.31977i	0.365366	−	0.241290i
$687$	−8.48869			−0.323864
$688$	−0.885690	+	41.0576i	−0.0337666	+	1.56531i
$689$	−69.1202			−2.63327
$690$	27.3896	−	18.0883i	1.04270	−	0.688609i
$691$	−23.2422	+	23.2422i	−0.884173	+	0.884173i	−0.993956	−	0.109782i	$-0.964985\pi$
$691$	−23.2422	+	23.2422i	−0.884173	+	0.884173i	0.109782	+	0.993956i	$0.464985\pi$
$692$	10.4259	+	25.9586i	0.396333	+	0.986799i
$693$	6.61129	−	6.61129i	0.251142	−	0.251142i
$694$	0.236298	+	0.0483286i	0.00896975	+	0.00183453i
$695$	−26.1703			−0.992695
$696$	−4.61503	−	25.3366i	−0.174932	−	0.960382i
$697$	1.69575			0.0642312
$698$	0.549446	+	0.112375i	0.0207968	+	0.00425345i
$699$	0.115800	−	0.115800i	0.00437997	−	0.00437997i
$700$	−9.01467	−	3.84841i	−0.340722	−	0.145456i
$701$	−4.21154	−	4.21154i	−0.159068	−	0.159068i	0.623086	−	0.782153i	$-0.285879\pi$
$701$	−4.21154	−	4.21154i	−0.159068	−	0.159068i	−0.782153	+	0.623086i	$0.785879\pi$
$702$	−23.8521	−	36.1172i	−0.900238	−	1.36316i
$703$	10.1857	−	0.580649i	0.384162	−	0.0218996i
$704$	25.1536	+	11.3857i	0.948013	+	0.429114i
$705$			9.09188i			0.342420i
$706$	−19.6841	+	12.9995i	−0.740821	+	0.489243i
$707$	35.7688	−	35.7688i	1.34523	−	1.34523i
$708$	−13.6492	+	31.9724i	−0.512968	+	1.20160i
$709$	30.2765	−	30.2765i	1.13706	−	1.13706i	0.148083	−	0.988975i	$-0.452690\pi$
$709$	30.2765	−	30.2765i	1.13706	−	1.13706i	0.988975	−	0.148083i	$-0.0473102\pi$
$710$	−14.2580	−	2.91610i	−0.535093	−	0.109439i
$711$			3.34255i			0.125356i
$712$	−0.492590	−	2.70434i	−0.0184606	−	0.101349i
$713$	−49.8000			−1.86503
$714$	6.51724	+	1.33293i	0.243902	+	0.0498837i
$715$	−25.8975	+	25.8975i	−0.968510	+	0.968510i
$716$	−2.27636	+	0.914264i	−0.0850715	+	0.0341677i
$717$	6.04329	−	6.04329i	0.225691	−	0.225691i
$718$	−27.9406	+	18.4522i	−1.04273	+	0.688628i
$719$			34.3034i			1.27930i	0.768665	+	0.639651i	$0.220921\pi$
$719$			34.3034i			1.27930i	−0.768665	+	0.639651i	$0.779079\pi$
$720$	0.113438	−	5.25861i	0.00422759	−	0.195977i
$721$			11.0695i			0.412251i
$722$	17.2597	+	20.5938i	0.642338	+	0.766421i
$723$	27.7982	−	27.7982i	1.03382	−	1.03382i
$724$	−32.8173	+	13.1806i	−1.21965	+	0.489852i
$725$	−5.17120	−	5.17120i	−0.192054	−	0.192054i
$726$	0.393722	−	1.92507i	0.0146124	−	0.0714459i
$727$	49.1242			1.82192			0.910958	−	0.412499i	$-0.135344\pi$
$727$	49.1242			1.82192			0.910958	+	0.412499i	$0.135344\pi$
$728$	50.8520	+	35.1812i	1.88470	+	1.30390i
$729$		−	30.0329i		−	1.11233i
$730$	20.5697	+	4.20699i	0.761318	+	0.155708i
$731$	−5.59639	−	5.59639i	−0.206990	−	0.206990i
$732$	22.5061	+	9.60797i	0.831849	+	0.355121i
$733$	−15.2256	−	15.2256i	−0.562372	−	0.562372i	0.367609	−	0.929981i	$-0.380177\pi$
$733$	−15.2256	−	15.2256i	−0.562372	−	0.562372i	−0.929981	+	0.367609i	$0.880177\pi$
$734$	−6.62394	−	10.0301i	−0.244494	−	0.370217i
$735$	−26.7320			−0.986025
$736$	43.2285	+	9.81710i	1.59343	+	0.361863i
$737$		−	32.9644i		−	1.21426i
$738$	1.16015	+	1.75671i	0.0427055	+	0.0646655i
$739$	−37.2945	+	37.2945i	−1.37190	+	1.37190i	−0.514278	+	0.857623i	$0.671940\pi$
$739$	−37.2945	+	37.2945i	−1.37190	+	1.37190i	−0.857623	+	0.514278i	$0.828060\pi$
$740$	3.57133	−	8.36562i	0.131285	−	0.307526i
$741$	24.1548	−	27.0752i	0.887348	−	0.994632i
$742$	70.2010	+	14.3578i	2.57716	+	0.527091i
$743$			24.9289i			0.914553i	0.889325	+	0.457276i	$0.151175\pi$
$743$			24.9289i			0.914553i	−0.889325	+	0.457276i	$0.848825\pi$
$744$	15.5877	−	22.5309i	0.571473	−	0.826024i
$745$			16.4907i			0.604172i
$746$	−29.4592	−	6.02511i	−1.07858	−	0.220595i
$747$	−0.977088	−	0.977088i	−0.0357498	−	0.0357498i
$748$	−4.93774	+	1.98317i	−0.180542	+	0.0725118i
$749$	9.16753	−	9.16753i	0.334974	−	0.334974i
$750$	14.3671	+	21.7549i	0.524611	+	0.794375i
$751$	−23.5788			−0.860404			−0.430202	−	0.902733i	$-0.641558\pi$
$751$	−23.5788			−0.860404			−0.430202	+	0.902733i	$0.641558\pi$
$752$	−8.86776	+	8.49325i	−0.323374	+	0.309717i
$753$			25.8226i			0.941028i
$754$	25.4247	+	38.4985i	0.925912	+	1.40203i
$755$	26.0992	+	26.0992i	0.949846	+	0.949846i
$756$	16.7227	+	41.6366i	0.608199	+	1.51431i
$757$	4.74247	−	4.74247i	0.172368	−	0.172368i	−0.615651	−	0.788019i	$-0.711107\pi$
$757$	4.74247	−	4.74247i	0.172368	−	0.172368i	0.788019	+	0.615651i	$0.211107\pi$
$758$	4.25298	−	20.7945i	0.154475	−	0.755292i
$759$		−	41.2240i		−	1.49634i
$760$	23.2862	−	5.62744i	0.844680	−	0.204129i
$761$		−	51.4004i		−	1.86326i	−0.363402	−	0.931632i	$-0.618385\pi$
$761$		−	51.4004i		−	1.86326i	0.363402	−	0.931632i	$-0.381615\pi$
$762$	44.4387	+	9.08878i	1.60984	+	0.329252i
$763$	−28.5292	+	28.5292i	−1.03283	+	1.03283i
$764$	−16.2123	−	6.92112i	−0.586540	−	0.250397i
$765$	0.716779	+	0.716779i	0.0259152	+	0.0259152i
$766$	7.10397	−	4.69151i	0.256677	−	0.169511i
$767$		−	62.2780i		−	2.24873i
$768$	−17.9723	+	16.4850i	−0.648520	+	0.594851i
$769$	3.83126			0.138159			0.0690794	−	0.997611i	$-0.477994\pi$
$769$	3.83126			0.138159			0.0690794	+	0.997611i	$0.477994\pi$
$770$	31.6819	−	20.9229i	1.14174	−	0.754011i
$771$	−22.8211	+	22.8211i	−0.821882	+	0.821882i
$772$	12.4988	+	5.33579i	0.449840	+	0.192039i
$773$	27.6605	+	27.6605i	0.994880	+	0.994880i	0.999987	−	0.00510728i	$-0.00162571\pi$
$773$	27.6605	+	27.6605i	0.994880	+	0.994880i	−0.00510728	+	0.999987i	$0.501626\pi$
$774$	1.96882	−	9.62633i	0.0707676	−	0.346011i
$775$		−	7.78001i		−	0.279466i
$776$	−18.4399	+	3.35879i	−0.661953	+	0.120574i
$777$			14.2817i			0.512352i
$778$	−3.91988	+	19.1659i	−0.140534	+	0.687129i
$779$	−6.38323	+	7.15499i	−0.228703	+	0.256354i
$780$	−12.0566	−	30.0189i	−0.431697	−	1.07485i
$781$	−12.9243	+	12.9243i	−0.462470	+	0.462470i
$782$	−7.12887	+	4.70796i	−0.254928	+	0.168356i
$783$			33.4774i			1.19639i
$784$	−24.9719	−	26.0730i	−0.891853	−	0.931180i
$785$	1.14635			0.0409150
$786$	−15.0138	+	9.91520i	−0.535523	+	0.353663i
$787$	4.34463	+	4.34463i	0.154869	+	0.154869i	0.780289	−	0.625419i	$-0.215072\pi$
$787$	4.34463	+	4.34463i	0.154869	+	0.154869i	−0.625419	+	0.780289i	$0.715072\pi$
$788$	−5.67096	−	14.1197i	−0.202020	−	0.502993i
$789$	−3.83921	−	3.83921i	−0.136679	−	0.136679i
$790$	−2.71977	+	13.2980i	−0.0967650	+	0.473123i
$791$		−	16.0657i		−	0.571230i
$792$	−5.43260	−	3.75846i	−0.193039	−	0.133551i
$793$	−43.8389			−1.55676
$794$	33.8586	+	6.92490i	1.20160	+	0.245756i
$795$	−26.5068	−	26.5068i	−0.940098	−	0.940098i
$796$	−2.00488	+	4.69630i	−0.0710610	+	0.166456i
$797$	26.1675	−	26.1675i	0.926899	−	0.926899i	−0.0706057	−	0.997504i	$-0.522493\pi$
$797$	26.1675	−	26.1675i	0.926899	−	0.926899i	0.997504	+	0.0706057i	$0.0224932\pi$
$798$	−30.1566	+	22.4811i	−1.06753	+	0.795822i
$799$		−	2.36641i		−	0.0837174i
$800$	−1.53368	+	6.75338i	−0.0542237	+	0.238768i
$801$			0.657677i			0.0232379i
$802$	−16.4179	−	24.8602i	−0.579735	−	0.877845i
$803$	18.6457	−	18.6457i	0.657991	−	0.657991i
$804$	26.7785	+	11.4319i	0.944407	+	0.403172i
$805$	43.1033	−	43.1033i	1.51919	−	1.51919i
$806$	−9.83469	+	48.0858i	−0.346412	+	1.69375i
$807$	−14.4679			−0.509293
$808$	−29.3918	−	20.3343i	−1.03400	−	0.715357i
$809$			37.4714i			1.31742i	0.752395	+	0.658712i	$0.228898\pi$
$809$			37.4714i			1.31742i	−0.752395	+	0.658712i	$0.771102\pi$
$810$	3.58567	−	17.5318i	0.125987	−	0.616003i
$811$	−7.02259	+	7.02259i	−0.246597	+	0.246597i	−0.819572	−	0.572976i	$-0.805789\pi$
$811$	−7.02259	+	7.02259i	−0.246597	+	0.246597i	0.572976	+	0.819572i	$0.305789\pi$
$812$	−17.8252	−	44.3817i	−0.625543	−	1.55749i
$813$	−19.2256	+	19.2256i	−0.674273	+	0.674273i
$814$	−6.29554	−	9.53281i	−0.220658	−	0.334125i
$815$		−	17.9612i		−	0.629152i
$816$	0.101365	−	4.69892i	0.00354847	−	0.164495i
$817$	44.6794	−	2.54700i	1.56313	−	0.0891082i
$818$	−36.1541	+	23.8764i	−1.26410	+	0.834819i
$819$	−10.4614	−	10.4614i	−0.365550	−	0.365550i
$820$	3.18613	+	7.93290i	0.111264	+	0.277029i
$821$	−25.4236	+	25.4236i	−0.887290	+	0.887290i	−0.994262	−	0.106972i	$-0.965885\pi$
$821$	−25.4236	+	25.4236i	−0.887290	+	0.887290i	0.106972	+	0.994262i	$0.465885\pi$
$822$	−0.361364	+	1.76685i	−0.0126040	+	0.0616261i
$823$	−39.4688			−1.37579			−0.687897	−	0.725808i	$-0.741466\pi$
$823$	−39.4688			−1.37579			−0.687897	+	0.725808i	$0.741466\pi$
$824$	7.69447	−	1.40153i	0.268049	−	0.0488248i
$825$	6.44022			0.224220
$826$	−12.9365	+	63.2518i	−0.450119	+	2.20081i
$827$	9.50078	−	9.50078i	0.330375	−	0.330375i	−0.522354	−	0.852729i	$-0.674946\pi$
$827$	9.50078	−	9.50078i	0.330375	−	0.330375i	0.852729	+	0.522354i	$0.174946\pi$
$828$	−9.75440	−	4.16421i	−0.338989	−	0.144716i
$829$	−33.9168	+	33.9168i	−1.17798	+	1.17798i	−0.197720	+	0.980259i	$0.563354\pi$
$829$	−33.9168	+	33.9168i	−1.17798	+	1.17798i	−0.980259	+	0.197720i	$0.936646\pi$
$830$	−3.09222	−	4.68229i	−0.107332	−	0.162525i
$831$	−9.31182			−0.323023
$832$	18.0161	−	39.8018i	0.624596	−	1.37988i
$833$	6.95772			0.241071
$834$	−15.9987	−	24.2256i	−0.553991	−	0.838862i
$835$	−8.56680	−	8.56680i	−0.296466	−	0.296466i
$836$	10.2192	−	28.2992i	0.353437	−	0.978749i
$837$	−25.1832	+	25.1832i	−0.870458	+	0.870458i
$838$	4.42492	−	21.6352i	0.152856	−	0.747377i
$839$		−	36.5254i		−	1.26100i	−0.776190	−	0.630499i	$-0.782850\pi$
$839$		−	36.5254i		−	1.26100i	0.776190	−	0.630499i	$-0.217150\pi$
$840$	6.00957	+	32.9927i	0.207350	+	1.13836i
$841$		−	6.68463i		−	0.230504i
$842$	17.9930	+	3.67999i	0.620078	+	0.126821i
$843$	−11.7971	−	11.7971i	−0.406314	−	0.406314i
$844$	−18.7939	+	7.54828i	−0.646912	+	0.259822i
$845$	23.1168	+	23.1168i	0.795242	+	0.795242i
$846$	2.45147	−	1.61897i	0.0842834	−	0.0556614i
$847$		−	3.64910i		−	0.125385i
$848$	1.09186	−	50.6148i	0.0374945	−	1.73812i
$849$			27.5107i			0.944164i
$850$	−0.735501	−	1.11371i	−0.0252275	−	0.0381999i
$851$	−12.9694	−	12.9694i	−0.444586	−	0.444586i
$852$	−6.01696	−	14.9812i	−0.206138	−	0.513247i
$853$	−32.1854	+	32.1854i	−1.10201	+	1.10201i	−0.107838	+	0.994168i	$0.534393\pi$
$853$	−32.1854	+	32.1854i	−1.10201	+	1.10201i	−0.994168	+	0.107838i	$0.965607\pi$
$854$	44.5244	+	9.10630i	1.52359	+	0.311611i
$855$	−5.72248	+	0.326216i	−0.195705	+	0.0111564i
$856$	−7.53311	−	5.21167i	−0.257476	−	0.178131i
$857$	3.04400			0.103981			0.0519905	−	0.998648i	$-0.483443\pi$
$857$	3.04400			0.103981			0.0519905	+	0.998648i	$0.483443\pi$
$858$	−39.8050	−	8.14107i	−1.35892	−	0.277932i
$859$	−3.14985	−	3.14985i	−0.107472	−	0.107472i	0.651326	−	0.758798i	$-0.274213\pi$
$859$	−3.14985	−	3.14985i	−0.107472	−	0.107472i	−0.758798	+	0.651326i	$0.774213\pi$
$860$	15.6655	−	36.6955i	0.534189	−	1.25131i
$861$	−9.49113	−	9.49113i	−0.323457	−	0.323457i
$862$	−40.3539	+	26.6500i	−1.37446	+	0.907703i
$863$	−11.5197			−0.392134			−0.196067	−	0.980590i	$-0.562817\pi$
$863$	−11.5197			−0.392134			−0.196067	+	0.980590i	$0.562817\pi$
$864$	26.8244	−	16.8957i	0.912586	−	0.574803i
$865$		−	27.1787i		−	0.924102i
$866$	−5.55572	−	8.41258i	−0.188791	−	0.285871i
$867$	−17.6820	−	17.6820i	−0.600512	−	0.600512i
$868$	19.9770	−	46.7948i	0.678062	−	1.58832i
$869$	12.0542	+	12.0542i	0.408910	+	0.408910i
$870$	−5.01365	+	24.5138i	−0.169979	+	0.831095i
$871$	−52.1611			−1.76741
$872$	23.4429	+	16.2186i	0.793878	+	0.549232i
$873$	4.48446			0.151776
$874$	6.97026	−	47.8012i	0.235772	−	1.61690i
$875$	34.2359	+	34.2359i	1.15738	+	1.15738i
$876$	8.68053	+	21.6130i	0.293288	+	0.730236i
$877$	−14.6976	+	14.6976i	−0.496304	+	0.496304i	−0.910285	−	0.413981i	$-0.864138\pi$
$877$	−14.6976	+	14.6976i	−0.496304	+	0.496304i	0.413981	+	0.910285i	$0.364138\pi$
$878$	−10.3909	−	15.7341i	−0.350677	−	0.531001i
$879$		−	32.9202i		−	1.11037i
$880$	−18.5549	−	19.3731i	−0.625486	−	0.653067i
$881$	21.0495			0.709174			0.354587	−	0.935023i	$-0.384621\pi$
$881$	21.0495			0.709174			0.354587	+	0.935023i	$0.384621\pi$
$882$	4.76011	+	7.20784i	0.160281	+	0.242701i
$883$	14.6536	−	14.6536i	0.493134	−	0.493134i	−0.416158	−	0.909292i	$-0.636624\pi$
$883$	14.6536	−	14.6536i	0.493134	−	0.493134i	0.909292	+	0.416158i	$0.136624\pi$
$884$	3.13806	+	7.81323i	0.105544	+	0.262787i
$885$	23.8829	−	23.8829i	0.802814	−	0.802814i
$886$	11.7571	+	2.40460i	0.394986	+	0.0807841i
$887$			32.4528i			1.08966i	0.838547	+	0.544830i	$0.183406\pi$
$887$			32.4528i			1.08966i	−0.838547	+	0.544830i	$0.816594\pi$
$888$	9.92723	−	1.80823i	0.333136	−	0.0606802i
$889$	84.2368			2.82521
$890$	−0.535138	+	2.61651i	−0.0179379	+	0.0877055i
$891$	−15.8919	−	15.8919i	−0.532399	−	0.532399i
$892$	0.286276	−	0.670585i	0.00958524	−	0.0224528i
$893$	9.98471	+	8.90773i	0.334126	+	0.298086i
$894$	−15.2653	+	10.0813i	−0.510547	+	0.337169i
$895$	2.38335			0.0796665
$896$	−26.5655	+	36.6818i	−0.887492	+	1.22545i
$897$	−65.2307			−2.17799
$898$	19.3894	+	29.3598i	0.647034	+	0.979750i
$899$	26.8435	−	26.8435i	0.895282	−	0.895282i
$900$	0.650553	−	1.52388i	0.0216851	−	0.0507961i
$901$	6.89910	+	6.89910i	0.229842	+	0.229842i
$902$	10.5190	+	2.15139i	0.350245	+	0.0716334i
$903$			62.6460i			2.08473i
$904$	−11.1673	+	2.03411i	−0.371419	+	0.0676534i
$905$	34.3597			1.14216
$906$	−8.20447	+	40.1150i	−0.272575	+	1.33273i
$907$	−3.07200	+	3.07200i	−0.102004	+	0.102004i	−0.756267	−	0.654263i	$-0.772979\pi$
$907$	−3.07200	+	3.07200i	−0.102004	+	0.102004i	0.654263	+	0.756267i	$0.272979\pi$
$908$	31.9588	−	12.8358i	1.06059	−	0.425970i
$909$	6.04653	+	6.04653i	0.200551	+	0.200551i
$910$	−33.1074	−	50.1318i	−1.09750	−	1.66185i
$911$	−33.6220			−1.11395			−0.556973	−	0.830531i	$-0.688037\pi$
$911$	−33.6220			−1.11395			−0.556973	+	0.830531i	$0.688037\pi$
$912$	19.4449	+	18.1156i	0.643884	+	0.599867i
$913$	−7.04731			−0.233232
$914$	−27.3464	−	41.4084i	−0.904538	−	1.36967i
$915$	−16.8117	−	16.8117i	−0.555777	−	0.555777i
$916$	4.15123	+	10.3358i	0.137161	+	0.341506i
$917$	−23.6273	+	23.6273i	−0.780244	+	0.780244i
$918$	−1.22422	+	5.98572i	−0.0404054	+	0.197558i
$919$	−29.3209			−0.967208			−0.483604	−	0.875287i	$-0.660673\pi$
$919$	−29.3209			−0.967208			−0.483604	+	0.875287i	$0.660673\pi$
$920$	−35.4187	−	24.5039i	−1.16772	−	0.807868i
$921$		−	7.27974i		−	0.239876i
$922$	−6.67741	−	1.36569i	−0.219909	−	0.0449766i
$923$	20.4508	+	20.4508i	0.673147	+	0.673147i
$924$	38.7363	+	16.5367i	1.27433	+	0.544019i
$925$	2.02615	−	2.02615i	0.0666193	−	0.0666193i
$926$	3.96421	+	6.00268i	0.130272	+	0.197260i
$927$	−1.87124			−0.0614597
$928$	−28.5930	+	18.0097i	−0.938612	+	0.591196i
$929$	−20.0624			−0.658227			−0.329114	−	0.944290i	$-0.606750\pi$
$929$	−20.0624			−0.658227			−0.329114	+	0.944290i	$0.606750\pi$
$930$	−22.2118	+	14.6688i	−0.728354	+	0.481010i
$931$	−26.1906	+	29.3571i	−0.858361	+	0.962141i
$932$	−0.197628	−	0.0843686i	−0.00647354	−	0.00276359i
$933$	−1.61461	−	1.61461i	−0.0528599	−	0.0528599i
$934$	4.07025	−	19.9011i	0.133183	−	0.651185i
$935$	5.16981			0.169071
$936$	−5.94720	+	8.59627i	−0.194390	+	0.280978i
$937$		−	22.1788i		−	0.724549i	−0.932072	−	0.362274i	$-0.882000\pi$
$937$		−	22.1788i		−	0.724549i	0.932072	−	0.362274i	$-0.118000\pi$
$938$	52.9767	+	10.8350i	1.72975	+	0.353775i
$939$	19.8430	−	19.8430i	0.647551	−	0.647551i
$940$	11.0703	−	4.44621i	0.361073	−	0.145019i
$941$	8.50754	−	8.50754i	0.277338	−	0.277338i	−0.554708	−	0.832045i	$-0.687170\pi$
$941$	8.50754	−	8.50754i	0.277338	−	0.277338i	0.832045	+	0.554708i	$0.187170\pi$
$942$	0.700800	+	1.06116i	0.0228333	+	0.0345746i
$943$	17.2381			0.561350
$944$	45.6045	+	0.983774i	1.48430	+	0.0320191i
$945$		−	43.5935i		−	1.41810i
$946$	−27.6152	−	41.8154i	−0.897846	−	1.35953i
$947$	−15.8585	+	15.8585i	−0.515333	+	0.515333i	−0.916156	−	0.400823i	$-0.868724\pi$
$947$	−15.8585	+	15.8585i	−0.515333	+	0.515333i	0.400823	+	0.916156i	$0.368724\pi$
$948$	−13.9725	+	5.61186i	−0.453807	+	0.182265i
$949$	−29.5039	−	29.5039i	−0.957738	−	0.957738i
$950$	7.46774	+	1.08893i	0.242285	+	0.0353295i
$951$	35.8186			1.16150
$952$	−1.56415	−	8.58724i	−0.0506945	−	0.278314i
$953$	−37.2019			−1.20509			−0.602543	−	0.798086i	$-0.705846\pi$
$953$	−37.2019			−1.20509			−0.602543	+	0.798086i	$0.705846\pi$
$954$	−2.42711	+	11.8671i	−0.0785805	+	0.384212i
$955$	12.1103	+	12.1103i	0.391881	+	0.391881i
$956$	−10.3137	−	4.40296i	−0.333568	−	0.142402i
$957$	22.2208	+	22.2208i	0.718298	+	0.718298i
$958$	−4.27056	−	6.46655i	−0.137975	−	0.208925i
$959$			3.34920i			0.108151i
$960$	22.1725	−	8.35455i	0.715614	−	0.269642i
$961$	9.38577			0.302767
$962$	−15.0842	+	9.96173i	−0.486335	+	0.321179i
$963$	1.54972	+	1.54972i	0.0499391	+	0.0499391i
$964$	−47.4412	−	20.2529i	−1.52798	−	0.652302i
$965$	−9.33638	−	9.33638i	−0.300549	−	0.300549i
$966$	66.2507	+	13.5499i	2.13158	+	0.435959i
$967$	54.2359			1.74411			0.872054	−	0.489409i	$-0.162788\pi$
$967$	54.2359			1.74411			0.872054	+	0.489409i	$0.162788\pi$
$968$	−2.53651	+	0.462020i	−0.0815264	+	0.0148499i
$969$	−5.11342	+	0.291496i	−0.164267	+	0.00936421i
$970$	17.8410	+	3.64891i	0.572840	+	0.117160i
$971$	26.3041	−	26.3041i	0.844137	−	0.844137i	−0.145257	−	0.989394i	$-0.546401\pi$
$971$	26.3041	−	26.3041i	0.844137	−	0.844137i	0.989394	+	0.145257i	$0.0464008\pi$
$972$	−12.7814	+	5.13346i	−0.409964	+	0.164656i
$973$	−38.1240	−	38.1240i	−1.22220	−	1.22220i
$974$	−31.2221	−	47.2770i	−1.00042	−	1.51485i
$975$		−	10.1907i		−	0.326363i
$976$	0.692501	−	32.1020i	0.0221664	−	1.02756i
$977$		−	53.5665i		−	1.71374i	−0.515529	−	0.856872i	$-0.672404\pi$
$977$		−	53.5665i		−	1.71374i	0.515529	−	0.856872i	$-0.327596\pi$
$978$	16.6265	−	10.9802i	0.531656	−	0.351109i
$979$	2.37177	+	2.37177i	0.0758021	+	0.0758021i
$980$	13.0728	+	32.5489i	0.417595	+	1.03974i
$981$	−4.82272	−	4.82272i	−0.153978	−	0.153978i
$982$	43.4290	+	8.88227i	1.38588	+	0.283445i
$983$		−	11.9694i		−	0.381765i	−0.981613	−	0.190882i	$-0.938865\pi$
$983$		−	11.9694i		−	0.381765i	0.981613	−	0.190882i	$-0.0611349\pi$
$984$	−5.39563	+	7.79901i	−0.172006	+	0.248623i
$985$			14.7833i			0.471035i
$986$	1.30494	−	6.38037i	0.0415577	−	0.203192i
$987$	−13.2448	+	13.2448i	−0.421586	+	0.421586i
$988$	−44.7792	−	16.1703i	−1.42462	−	0.514445i
$989$	−56.8899	−	56.8899i	−1.80899	−	1.80899i
$990$	3.53691	+	5.35566i	0.112411	+	0.170214i
$991$	−2.57961			−0.0819439			−0.0409720	−	0.999160i	$-0.513045\pi$
$991$	−2.57961			−0.0819439			−0.0409720	+	0.999160i	$0.513045\pi$
$992$	−35.0566	−	7.96127i	−1.11305	−	0.252770i
$993$	−30.1368			−0.956362
$994$	−16.5225	−	25.0187i	−0.524062	−	0.793544i
$995$	3.50807	−	3.50807i	0.111213	−	0.111213i
$996$	2.44398	−	5.72487i	0.0774404	−	0.181399i
$997$	−4.59126	+	4.59126i	−0.145407	+	0.145407i	−0.776063	−	0.630656i	$-0.782786\pi$
$997$	−4.59126	+	4.59126i	−0.145407	+	0.145407i	0.630656	+	0.776063i	$0.282786\pi$
$998$	−2.45382	+	11.9977i	−0.0776743	+	0.379781i
$999$	−13.1169			−0.415000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.m.a.227.9	yes	76
4.3	odd	2		1216.2.m.a.303.11		76
16.5	even	4		1216.2.m.a.911.28		76
16.11	odd	4	inner	304.2.m.a.75.30	yes	76
19.18	odd	2	inner	304.2.m.a.227.30	yes	76
76.75	even	2		1216.2.m.a.303.28		76
304.37	odd	4		1216.2.m.a.911.11		76
304.75	even	4	inner	304.2.m.a.75.9	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.9	✓	76	304.75	even	4	inner
304.2.m.a.75.30	yes	76	16.11	odd	4	inner
304.2.m.a.227.9	yes	76	1.1	even	1	trivial
304.2.m.a.227.30	yes	76	19.18	odd	2	inner
1216.2.m.a.303.11		76	4.3	odd	2
1216.2.m.a.303.28		76	76.75	even	2
1216.2.m.a.911.11		76	304.37	odd	4
1216.2.m.a.911.28		76	16.5	even	4

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18010 + 0.779343i) q^{2} +(1.07779 + 1.07779i) q^{3} +(0.785249 - 1.83940i) q^{4} +(-1.37400 + 1.37400i) q^{5} +(-2.11187 - 0.431928i) q^{6} -4.00321 q^{7} +(0.506854 + 2.78264i) q^{8} -0.676721i q^{9} +O(q^{10})\)	\(q+(-1.18010 + 0.779343i) q^{2} +(1.07779 + 1.07779i) q^{3} +(0.785249 - 1.83940i) q^{4} +(-1.37400 + 1.37400i) q^{5} +(-2.11187 - 0.431928i) q^{6} -4.00321 q^{7} +(0.506854 + 2.78264i) q^{8} -0.676721i q^{9} +(0.550634 - 2.69227i) q^{10} +(-2.44045 - 2.44045i) q^{11} +(2.82883 - 1.13616i) q^{12} +(-3.86163 + 3.86163i) q^{13} +(4.72416 - 3.11987i) q^{14} -2.96178 q^{15} +(-2.76677 - 2.88877i) q^{16} +0.770883 q^{17} +(0.527398 + 0.798595i) q^{18} +(-2.90179 + 3.25263i) q^{19} +(1.44840 + 3.60627i) q^{20} +(-4.31463 - 4.31463i) q^{21} +(4.78190 + 0.978013i) q^{22} +7.83638 q^{23} +(-2.45283 + 3.54540i) q^{24} +1.22424i q^{25} +(1.54756 - 7.56663i) q^{26} +(3.96275 - 3.96275i) q^{27} +(-3.14351 + 7.36349i) q^{28} +(-4.22402 + 4.22402i) q^{29} +(3.49518 - 2.30824i) q^{30} -6.35498 q^{31} +(5.51639 + 1.25276i) q^{32} -5.26059i q^{33} +(-0.909715 + 0.600782i) q^{34} +(5.50041 - 5.50041i) q^{35} +(-1.24476 - 0.531394i) q^{36} +(-1.65503 - 1.65503i) q^{37} +(0.889474 - 6.09990i) q^{38} -8.32409 q^{39} +(-4.51977 - 3.12694i) q^{40} +2.19975 q^{41} +(8.45425 + 1.72910i) q^{42} +(-7.25972 - 7.25972i) q^{43} +(-6.40531 + 2.57259i) q^{44} +(0.929815 + 0.929815i) q^{45} +(-9.24767 + 6.10723i) q^{46} -3.06973i q^{47} +(0.131491 - 6.09550i) q^{48} +9.02565 q^{49} +(-0.954102 - 1.44472i) q^{50} +(0.830853 + 0.830853i) q^{51} +(4.07074 + 10.1354i) q^{52} +(8.94960 + 8.94960i) q^{53} +(-1.58808 + 7.76476i) q^{54} +6.70635 q^{55} +(-2.02904 - 11.1395i) q^{56} +(-6.63320 + 0.378133i) q^{57} +(1.69278 - 8.27670i) q^{58} +(-8.06369 + 8.06369i) q^{59} +(-2.32573 + 5.44789i) q^{60} +(5.67621 + 5.67621i) q^{61} +(7.49948 - 4.95271i) q^{62} +2.70905i q^{63} +(-7.48620 + 2.82079i) q^{64} -10.6118i q^{65} +(4.09981 + 6.20800i) q^{66} +(6.75376 + 6.75376i) q^{67} +(0.605335 - 1.41796i) q^{68} +(8.44600 + 8.44600i) q^{69} +(-2.20430 + 10.7777i) q^{70} -5.29590i q^{71} +(1.88307 - 0.342999i) q^{72} +7.64027i q^{73} +(3.24292 + 0.663255i) q^{74} +(-1.31948 + 1.31948i) q^{75} +(3.70425 + 7.89167i) q^{76} +(9.76960 + 9.76960i) q^{77} +(9.82322 - 6.48732i) q^{78} -4.93934 q^{79} +(7.77072 + 0.167629i) q^{80} +6.51189 q^{81} +(-2.59592 + 1.71436i) q^{82} +(1.44386 - 1.44386i) q^{83} +(-11.3244 + 4.54826i) q^{84} +(-1.05919 + 1.05919i) q^{85} +(14.2250 + 2.90935i) q^{86} -9.10524 q^{87} +(5.55394 - 8.02784i) q^{88} -0.971859 q^{89} +(-1.82192 - 0.372625i) q^{90} +(15.4589 - 15.4589i) q^{91} +(6.15351 - 14.4142i) q^{92} +(-6.84936 - 6.84936i) q^{93} +(2.39238 + 3.62258i) q^{94} +(-0.482054 - 8.45619i) q^{95} +(4.59532 + 7.29575i) q^{96} +6.62675i q^{97} +(-10.6511 + 7.03408i) q^{98} +(-1.65150 + 1.65150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7	\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43} - 76 q^{44} + 4 q^{45} + 44 q^{49} + 96 q^{54} - 8 q^{55} + 24 q^{58} + 28 q^{61} + 20 q^{62} - 64 q^{64} + 12 q^{66} - 80 q^{74} + 12 q^{76} - 32 q^{77} - 16 q^{80} - 52 q^{81} + 68 q^{82} + 36 q^{83} - 56 q^{85} - 120 q^{87} - 8 q^{92} - 16 q^{93} + 48 q^{96} + 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

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