LMFDB - Embedded newform 304.2.k.b.77.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (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:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.1
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41340 + 0.0478764i) q^{2} +(-1.10634 - 1.10634i) q^{3} +(1.99542 - 0.135337i) q^{4} +(-0.498475 + 0.498475i) q^{5} +(1.61667 + 1.51074i) q^{6} +1.73883i q^{7} +(-2.81385 + 0.286820i) q^{8} -0.552016i q^{9} +O(q^{10})$	\(q+(-1.41340 + 0.0478764i) q^{2} +(-1.10634 - 1.10634i) q^{3} +(1.99542 - 0.135337i) q^{4} +(-0.498475 + 0.498475i) q^{5} +(1.61667 + 1.51074i) q^{6} +1.73883i q^{7} +(-2.81385 + 0.286820i) q^{8} -0.552016i q^{9} +(0.680681 - 0.728411i) q^{10} +(-3.05310 + 3.05310i) q^{11} +(-2.35734 - 2.05788i) q^{12} +(0.508457 + 0.508457i) q^{13} +(-0.0832489 - 2.45766i) q^{14} +1.10297 q^{15} +(3.96337 - 0.540108i) q^{16} +1.46111 q^{17} +(0.0264286 + 0.780221i) q^{18} +(0.707107 + 0.707107i) q^{19} +(-0.927202 + 1.06213i) q^{20} +(1.92374 - 1.92374i) q^{21} +(4.16909 - 4.46144i) q^{22} +8.23755i q^{23} +(3.43040 + 2.79576i) q^{24} +4.50305i q^{25} +(-0.742998 - 0.694311i) q^{26} +(-3.92974 + 3.92974i) q^{27} +(0.235328 + 3.46969i) q^{28} +(2.19423 + 2.19423i) q^{29} +(-1.55894 + 0.0528061i) q^{30} +7.08512 q^{31} +(-5.57598 + 0.953143i) q^{32} +6.75555 q^{33} +(-2.06514 + 0.0699527i) q^{34} +(-0.866762 - 0.866762i) q^{35} +(-0.0747084 - 1.10150i) q^{36} +(0.912428 - 0.912428i) q^{37} +(-1.03328 - 0.965573i) q^{38} -1.12505i q^{39} +(1.25966 - 1.54560i) q^{40} -2.23712i q^{41} +(-2.62692 + 2.81112i) q^{42} +(-7.26655 + 7.26655i) q^{43} +(-5.67901 + 6.50541i) q^{44} +(0.275166 + 0.275166i) q^{45} +(-0.394384 - 11.6430i) q^{46} -1.81837 q^{47} +(-4.98238 - 3.78729i) q^{48} +3.97648 q^{49} +(-0.215590 - 6.36462i) q^{50} +(-1.61649 - 1.61649i) q^{51} +(1.08340 + 0.945770i) q^{52} +(-1.97547 + 1.97547i) q^{53} +(5.36617 - 5.74245i) q^{54} -3.04379i q^{55} +(-0.498730 - 4.89280i) q^{56} -1.56460i q^{57} +(-3.20639 - 2.99628i) q^{58} +(-2.91479 + 2.91479i) q^{59} +(2.20088 - 0.149273i) q^{60} +(0.410289 + 0.410289i) q^{61} +(-10.0141 + 0.339210i) q^{62} +0.959862 q^{63} +(7.83547 - 1.61413i) q^{64} -0.506906 q^{65} +(-9.54831 + 0.323431i) q^{66} +(-5.61894 - 5.61894i) q^{67} +(2.91552 - 0.197743i) q^{68} +(9.11355 - 9.11355i) q^{69} +(1.26658 + 1.18359i) q^{70} -15.9644i q^{71} +(0.158329 + 1.55329i) q^{72} -1.42531i q^{73} +(-1.24594 + 1.33331i) q^{74} +(4.98191 - 4.98191i) q^{75} +(1.50667 + 1.31527i) q^{76} +(-5.30882 - 5.30882i) q^{77} +(0.0538636 + 1.59015i) q^{78} -2.86784 q^{79} +(-1.70641 + 2.24487i) q^{80} +7.03923 q^{81} +(0.107105 + 3.16195i) q^{82} +(-7.59138 - 7.59138i) q^{83} +(3.57830 - 4.09901i) q^{84} +(-0.728326 + 0.728326i) q^{85} +(9.92267 - 10.6185i) q^{86} -4.85514i q^{87} +(7.71527 - 9.46665i) q^{88} +16.6536i q^{89} +(-0.402095 - 0.375747i) q^{90} +(-0.884119 + 0.884119i) q^{91} +(1.11485 + 16.4373i) q^{92} +(-7.83856 - 7.83856i) q^{93} +(2.57009 - 0.0870572i) q^{94} -0.704950 q^{95} +(7.22344 + 5.11443i) q^{96} -2.39980 q^{97} +(-5.62036 + 0.190379i) q^{98} +(1.68536 + 1.68536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * 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 $

$2$	−1.41340	+	0.0478764i	−0.999427	+	0.0338537i
$2$	−1.41340	+	0.0478764i	−0.999427	+	0.0338537i
$3$	−1.10634	−	1.10634i	−0.638747	−	0.638747i	0.311500	−	0.950246i	$-0.399169\pi$
$3$	−1.10634	−	1.10634i	−0.638747	−	0.638747i	−0.950246	+	0.311500i	$0.899169\pi$
$4$	1.99542	−	0.135337i	0.997708	−	0.0676687i
$5$	−0.498475	+	0.498475i	−0.222925	+	0.222925i	−0.809729	−	0.586804i	$-0.800386\pi$
$5$	−0.498475	+	0.498475i	−0.222925	+	0.222925i	0.586804	+	0.809729i	$0.300386\pi$
$6$	1.61667	+	1.51074i	0.660004	+	0.616757i
$7$			1.73883i			0.657215i	0.944467	+	0.328608i	$0.106579\pi$
$7$			1.73883i			0.657215i	−0.944467	+	0.328608i	$0.893421\pi$
$8$	−2.81385	+	0.286820i	−0.994845	+	0.101406i
$9$		−	0.552016i		−	0.184005i
$10$	0.680681	−	0.728411i	0.215250	−	0.230344i
$11$	−3.05310	+	3.05310i	−0.920545	+	0.920545i	−0.997068	−	0.0765227i	$-0.975618\pi$
$11$	−3.05310	+	3.05310i	−0.920545	+	0.920545i	0.0765227	+	0.997068i	$0.475618\pi$
$12$	−2.35734	−	2.05788i	−0.680506	−	0.594059i
$13$	0.508457	+	0.508457i	0.141021	+	0.141021i	0.774093	−	0.633072i	$-0.218206\pi$
$13$	0.508457	+	0.508457i	0.141021	+	0.141021i	−0.633072	+	0.774093i	$0.718206\pi$
$14$	−0.0832489	−	2.45766i	−0.0222492	−	0.656839i
$15$	1.10297			0.284785
$16$	3.96337	−	0.540108i	0.990842	−	0.135027i
$17$	1.46111			0.354371			0.177186	−	0.984177i	$-0.443301\pi$
$17$	1.46111			0.354371			0.177186	+	0.984177i	$0.443301\pi$
$18$	0.0264286	+	0.780221i	0.00622927	+	0.183900i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$20$	−0.927202	+	1.06213i	−0.207329	+	0.237499i
$21$	1.92374	−	1.92374i	0.419794	−	0.419794i
$22$	4.16909	−	4.46144i	0.888854	−	0.951181i
$23$			8.23755i			1.71765i	0.512271	+	0.858824i	$0.328804\pi$
$23$			8.23755i			1.71765i	−0.512271	+	0.858824i	$0.671196\pi$
$24$	3.43040	+	2.79576i	0.700227	+	0.570681i
$25$			4.50305i			0.900609i
$26$	−0.742998	−	0.694311i	−0.145714	−	0.136166i
$27$	−3.92974	+	3.92974i	−0.756280	+	0.756280i
$28$	0.235328	+	3.46969i	0.0444729	+	0.655709i
$29$	2.19423	+	2.19423i	0.407459	+	0.407459i	0.880851	−	0.473393i	$-0.156971\pi$
$29$	2.19423	+	2.19423i	0.407459	+	0.407459i	−0.473393	+	0.880851i	$0.656971\pi$
$30$	−1.55894	+	0.0528061i	−0.284622	+	0.00964103i
$31$	7.08512			1.27253			0.636263	−	0.771473i	$-0.280479\pi$
$31$	7.08512			1.27253			0.636263	+	0.771473i	$0.280479\pi$
$32$	−5.57598	+	0.953143i	−0.985703	+	0.168493i
$33$	6.75555			1.17599
$34$	−2.06514	+	0.0699527i	−0.354168	+	0.0119968i
$35$	−0.866762	−	0.866762i	−0.146510	−	0.146510i
$36$	−0.0747084	−	1.10150i	−0.0124514	−	0.183584i
$37$	0.912428	−	0.912428i	0.150002	−	0.150002i	−0.628117	−	0.778119i	$-0.716174\pi$
$37$	0.912428	−	0.912428i	0.150002	−	0.150002i	0.778119	+	0.628117i	$0.216174\pi$
$38$	−1.03328	−	0.965573i	−0.167620	−	0.156637i
$39$		−	1.12505i		−	0.180153i
$40$	1.25966	−	1.54560i	0.199170	−	0.244381i
$41$		−	2.23712i		−	0.349380i	−0.984624	−	0.174690i	$-0.944108\pi$
$41$		−	2.23712i		−	0.349380i	0.984624	−	0.174690i	$-0.0558923\pi$
$42$	−2.62692	+	2.81112i	−0.405342	+	0.433765i
$43$	−7.26655	+	7.26655i	−1.10814	+	1.10814i	−0.114744	+	0.993395i	$0.536605\pi$
$43$	−7.26655	+	7.26655i	−1.10814	+	1.10814i	−0.993395	+	0.114744i	$0.963395\pi$
$44$	−5.67901	+	6.50541i	−0.856143	+	0.980727i
$45$	0.275166	+	0.275166i	0.0410194	+	0.0410194i
$46$	−0.394384	−	11.6430i	−0.0581488	−	1.71666i
$47$	−1.81837			−0.265237			−0.132619	−	0.991167i	$-0.542339\pi$
$47$	−1.81837			−0.265237			−0.132619	+	0.991167i	$0.542339\pi$
$48$	−4.98238	−	3.78729i	−0.719145	−	0.546649i
$49$	3.97648			0.568068
$50$	−0.215590	−	6.36462i	−0.0304890	−	0.900093i
$51$	−1.61649	−	1.61649i	−0.226353	−	0.226353i
$52$	1.08340	+	0.945770i	0.150240	+	0.131155i
$53$	−1.97547	+	1.97547i	−0.271351	+	0.271351i	−0.829644	−	0.558293i	$-0.811457\pi$
$53$	−1.97547	+	1.97547i	−0.271351	+	0.271351i	0.558293	+	0.829644i	$0.311457\pi$
$54$	5.36617	−	5.74245i	0.730243	−	0.781449i
$55$		−	3.04379i		−	0.410425i
$56$	−0.498730	−	4.89280i	−0.0666456	−	0.653827i
$57$		−	1.56460i		−	0.207237i
$58$	−3.20639	−	2.99628i	−0.421019	−	0.393431i
$59$	−2.91479	+	2.91479i	−0.379473	+	0.379473i	−0.870912	−	0.491439i	$-0.836471\pi$
$59$	−2.91479	+	2.91479i	−0.379473	+	0.379473i	0.491439	+	0.870912i	$0.336471\pi$
$60$	2.20088	−	0.149273i	0.284132	−	0.0192710i
$61$	0.410289	+	0.410289i	0.0525321	+	0.0525321i	0.732885	−	0.680353i	$-0.238173\pi$
$61$	0.410289	+	0.410289i	0.0525321	+	0.0525321i	−0.680353	+	0.732885i	$0.738173\pi$
$62$	−10.0141	+	0.339210i	−1.27180	+	0.0430797i
$63$	0.959862			0.120931
$64$	7.83547	−	1.61413i	0.979434	−	0.201767i
$65$	−0.506906			−0.0628739
$66$	−9.54831	+	0.323431i	−1.17532	+	0.0398117i
$67$	−5.61894	−	5.61894i	−0.686463	−	0.686463i	0.274986	−	0.961448i	$-0.411327\pi$
$67$	−5.61894	−	5.61894i	−0.686463	−	0.686463i	−0.961448	+	0.274986i	$0.911327\pi$
$68$	2.91552	−	0.197743i	0.353559	−	0.0239798i
$69$	9.11355	−	9.11355i	1.09714	−	1.09714i
$70$	1.26658	+	1.18359i	0.151385	+	0.141466i
$71$		−	15.9644i		−	1.89462i	−0.320316	−	0.947311i	$-0.603789\pi$
$71$		−	15.9644i		−	1.89462i	0.320316	−	0.947311i	$-0.396211\pi$
$72$	0.158329	+	1.55329i	0.0186593	+	0.183057i
$73$		−	1.42531i		−	0.166820i	−0.996515	−	0.0834100i	$-0.973419\pi$
$73$		−	1.42531i		−	0.166820i	0.996515	−	0.0834100i	$-0.0265811\pi$
$74$	−1.24594	+	1.33331i	−0.144838	+	0.154994i
$75$	4.98191	−	4.98191i	0.575261	−	0.575261i
$76$	1.50667	+	1.31527i	0.172827	+	0.150872i
$77$	−5.30882	−	5.30882i	−0.604996	−	0.604996i
$78$	0.0538636	+	1.59015i	0.00609885	+	0.180050i
$79$	−2.86784			−0.322657			−0.161329	−	0.986901i	$-0.551578\pi$
$79$	−2.86784			−0.322657			−0.161329	+	0.986901i	$0.551578\pi$
$80$	−1.70641	+	2.24487i	−0.190782	+	0.250984i
$81$	7.03923			0.782137
$82$	0.107105	+	3.16195i	0.0118278	+	0.349179i
$83$	−7.59138	−	7.59138i	−0.833262	−	0.833262i	0.154699	−	0.987962i	$-0.450559\pi$
$83$	−7.59138	−	7.59138i	−0.833262	−	0.833262i	−0.987962	+	0.154699i	$0.950559\pi$
$84$	3.57830	−	4.09901i	0.390425	−	0.447239i
$85$	−0.728326	+	0.728326i	−0.0789981	+	0.0789981i
$86$	9.92267	−	10.6185i	1.06999	−	1.14502i
$87$		−	4.85514i		−	0.520526i
$88$	7.71527	−	9.46665i	0.822451	−	1.00915i
$89$			16.6536i			1.76528i	0.470053	+	0.882638i	$0.344235\pi$
$89$			16.6536i			1.76528i	−0.470053	+	0.882638i	$0.655765\pi$
$90$	−0.402095	−	0.375747i	−0.0423845	−	0.0396072i
$91$	−0.884119	+	0.884119i	−0.0926809	+	0.0926809i
$92$	1.11485	+	16.4373i	0.116231	+	1.71371i
$93$	−7.83856	−	7.83856i	−0.812821	−	0.812821i
$94$	2.57009	−	0.0870572i	0.265085	−	0.00897926i
$95$	−0.704950			−0.0723263
$96$	7.22344	+	5.11443i	0.737239	+	0.521990i
$97$	−2.39980			−0.243662			−0.121831	−	0.992551i	$-0.538877\pi$
$97$	−2.39980			−0.243662			−0.121831	+	0.992551i	$0.538877\pi$
$98$	−5.62036	+	0.190379i	−0.567742	+	0.0192312i
$99$	1.68536	+	1.68536i	0.169385	+	0.169385i
$100$	0.609430	+	8.98545i	0.0609430	+	0.898545i
$101$	−0.953182	+	0.953182i	−0.0948451	+	0.0948451i	−0.752937	−	0.658092i	$-0.771364\pi$
$101$	−0.953182	+	0.953182i	−0.0948451	+	0.0948451i	0.658092	+	0.752937i	$0.271364\pi$
$102$	2.36214	+	2.20735i	0.233886	+	0.218561i
$103$			10.4323i			1.02792i	0.857813	+	0.513962i	$0.171823\pi$
$103$			10.4323i			1.02792i	−0.857813	+	0.513962i	$0.828177\pi$
$104$	−1.57656	−	1.28488i	−0.154594	−	0.125993i
$105$			1.91787i			0.187165i
$106$	2.69755	−	2.88671i	0.262009	−	0.280382i
$107$	5.67099	−	5.67099i	0.548236	−	0.548236i	−0.377695	−	0.925930i	$-0.623283\pi$
$107$	5.67099	−	5.67099i	0.548236	−	0.548236i	0.925930	+	0.377695i	$0.123283\pi$
$108$	−7.30963	+	8.37331i	−0.703370	+	0.805722i
$109$	−8.67729	−	8.67729i	−0.831133	−	0.831133i	0.156538	−	0.987672i	$-0.449966\pi$
$109$	−8.67729	−	8.67729i	−0.831133	−	0.831133i	−0.987672	+	0.156538i	$0.949966\pi$
$110$	0.145726	+	4.30210i	0.0138944	+	0.410189i
$111$	−2.01891			−0.191627
$112$	0.939156	+	6.89162i	0.0887419	+	0.651196i
$113$	−10.6176			−0.998820			−0.499410	−	0.866366i	$-0.666450\pi$
$113$	−10.6176			−0.998820			−0.499410	+	0.866366i	$0.666450\pi$
$114$	0.0749076	+	2.21141i	0.00701574	+	0.207118i
$115$	−4.10621	−	4.10621i	−0.382906	−	0.382906i
$116$	4.67537	+	4.08144i	0.434097	+	0.378952i
$117$	0.280676	−	0.280676i	0.0259486	−	0.0259486i
$118$	3.98022	−	4.25932i	0.366409	−	0.392102i
$119$			2.54062i			0.232898i
$120$	−3.10358	+	0.316352i	−0.283317	+	0.0288789i
$121$		−	7.64287i		−	0.694807i
$122$	−0.599546	−	0.560260i	−0.0542804	−	0.0507236i
$123$	−2.47502	+	2.47502i	−0.223165	+	0.223165i
$124$	14.1378	−	0.958881i	1.26961	−	0.0861101i
$125$	−4.73703	−	4.73703i	−0.423693	−	0.423693i
$126$	−1.35667	+	0.0459547i	−0.120862	+	0.00409397i
$127$	11.3967			1.01129			0.505647	−	0.862741i	$-0.331254\pi$
$127$	11.3967			1.01129			0.505647	+	0.862741i	$0.331254\pi$
$128$	−10.9974	+	2.65655i	−0.972042	+	0.234808i
$129$	16.0786			1.41564
$130$	0.716462	−	0.0242688i	0.0628379	−	0.00212852i
$131$	9.18273	+	9.18273i	0.802298	+	0.802298i	0.983454	−	0.181156i	$-0.0579839\pi$
$131$	9.18273	+	9.18273i	0.802298	+	0.802298i	−0.181156	+	0.983454i	$0.557984\pi$
$132$	13.4801	−	0.914278i	1.17329	−	0.0795777i
$133$	−1.22954	+	1.22954i	−0.106614	+	0.106614i
$134$	8.21084	+	7.67281i	0.709308	+	0.662830i
$135$		−	3.91776i		−	0.337187i
$136$	−4.11134	+	0.419075i	−0.352544	+	0.0359354i
$137$			18.1025i			1.54660i	0.634041	+	0.773299i	$0.281395\pi$
$137$			18.1025i			1.54660i	−0.634041	+	0.773299i	$0.718605\pi$
$138$	−12.4448	+	13.3174i	−1.05937	+	1.13366i
$139$	−5.10508	+	5.10508i	−0.433007	+	0.433007i	−0.889650	−	0.456643i	$-0.849052\pi$
$139$	−5.10508	+	5.10508i	−0.433007	+	0.433007i	0.456643	+	0.889650i	$0.349052\pi$
$140$	−1.84686	−	1.61225i	−0.156088	−	0.136260i
$141$	2.01174	+	2.01174i	0.169419	+	0.169419i
$142$	0.764316	+	22.5641i	0.0641400	+	1.89354i
$143$	−3.10474			−0.259632
$144$	−0.298149	−	2.18784i	−0.0248457	−	0.182320i
$145$	−2.18754			−0.181665
$146$	0.0682388	+	2.01454i	0.00564748	+	0.166724i
$147$	−4.39934	−	4.39934i	−0.362852	−	0.362852i
$148$	1.69719	−	1.94416i	0.139508	−	0.159809i
$149$	7.11551	−	7.11551i	0.582925	−	0.582925i	−0.352781	−	0.935706i	$-0.614764\pi$
$149$	7.11551	−	7.11551i	0.582925	−	0.582925i	0.935706	+	0.352781i	$0.114764\pi$
$150$	−6.80293	+	7.27996i	−0.555457	+	0.594406i
$151$			4.21913i			0.343348i	0.985154	+	0.171674i	$0.0549176\pi$
$151$			4.21913i			0.343348i	−0.985154	+	0.171674i	$0.945082\pi$
$152$	−2.19250	−	1.78688i	−0.177835	−	0.144935i
$153$		−	0.806556i		−	0.0652062i
$154$	7.75767	+	7.24934i	0.625131	+	0.584168i
$155$	−3.53175	+	3.53175i	−0.283677	+	0.283677i
$156$	−0.152262	−	2.24495i	−0.0121907	−	0.179740i
$157$	2.99596	+	2.99596i	0.239104	+	0.239104i	0.816479	−	0.577375i	$-0.195923\pi$
$157$	2.99596	+	2.99596i	0.239104	+	0.239104i	−0.577375	+	0.816479i	$0.695923\pi$
$158$	4.05341	−	0.137302i	0.322472	−	0.0109232i
$159$	4.37108			0.346649
$160$	2.30437	−	3.25460i	0.182176	−	0.257299i
$161$	−14.3237			−1.12886
$162$	−9.94927	+	0.337013i	−0.781688	+	0.0264782i
$163$	3.68684	+	3.68684i	0.288775	+	0.288775i	0.836596	−	0.547821i	$-0.184542\pi$
$163$	3.68684	+	3.68684i	0.288775	+	0.288775i	−0.547821	+	0.836596i	$0.684542\pi$
$164$	−0.302766	−	4.46399i	−0.0236420	−	0.348579i
$165$	−3.36747	+	3.36747i	−0.262157	+	0.262157i
$166$	11.0931	+	10.3662i	0.860993	+	0.804575i
$167$		−	24.6861i		−	1.91027i	−0.296172	−	0.955135i	$-0.595710\pi$
$167$		−	24.6861i		−	1.91027i	0.296172	−	0.955135i	$-0.404290\pi$
$168$	−4.86134	+	5.96487i	−0.375060	+	0.460200i
$169$		−	12.4829i		−	0.960226i
$170$	0.994549	−	1.06429i	0.0762784	−	0.0816272i
$171$	0.390334	−	0.390334i	0.0298496	−	0.0298496i
$172$	−13.5164	+	15.4832i	−1.03061	+	1.18059i
$173$	4.09177	+	4.09177i	0.311091	+	0.311091i	0.845332	−	0.534241i	$-0.179402\pi$
$173$	4.09177	+	4.09177i	0.311091	+	0.311091i	−0.534241	+	0.845332i	$0.679402\pi$
$174$	0.232447	+	6.86227i	0.0176217	+	0.520227i
$175$	−7.83002			−0.591894
$176$	−10.4516	+	13.7496i	−0.787816	+	1.03641i
$177$	6.44951			0.484775
$178$	−0.797314	−	23.5382i	−0.0597612	−	1.76426i
$179$	9.35401	+	9.35401i	0.699152	+	0.699152i	0.964228	−	0.265076i	$-0.0853970\pi$
$179$	9.35401	+	9.35401i	0.699152	+	0.699152i	−0.265076	+	0.964228i	$0.585397\pi$
$180$	0.586311	+	0.511831i	0.0437011	+	0.0381496i
$181$	3.56370	−	3.56370i	0.264888	−	0.264888i	−0.562149	−	0.827036i	$-0.690025\pi$
$181$	3.56370	−	3.56370i	0.264888	−	0.264888i	0.827036	+	0.562149i	$0.190025\pi$
$182$	1.20729	−	1.29195i	0.0894902	−	0.0957653i
$183$		−	0.907839i		−	0.0671094i
$184$	−2.36269	−	23.1792i	−0.174180	−	1.70879i
$185$			0.909645i			0.0668784i
$186$	11.4543	+	10.7038i	0.839872	+	0.784838i
$187$	−4.46092	+	4.46092i	−0.326215	+	0.326215i
$188$	−3.62841	+	0.246094i	−0.264629	+	0.0179482i
$189$	−6.83315	−	6.83315i	−0.497038	−	0.497038i
$190$	0.996378	−	0.0337505i	0.0722849	−	0.00244852i
$191$	11.4263			0.826779			0.413389	−	0.910554i	$-0.364345\pi$
$191$	11.4263			0.826779			0.413389	+	0.910554i	$0.364345\pi$
$192$	−10.4545	−	6.88292i	−0.754488	−	0.496732i
$193$	−8.13588			−0.585633			−0.292817	−	0.956169i	$-0.594593\pi$
$193$	−8.13588			−0.585633			−0.292817	+	0.956169i	$0.594593\pi$
$194$	3.39188	−	0.114894i	0.243523	−	0.00824888i
$195$	0.560811	+	0.560811i	0.0401605	+	0.0401605i
$196$	7.93472	−	0.538166i	0.566766	−	0.0384404i
$197$	17.5406	−	17.5406i	1.24972	−	1.24972i	0.293872	−	0.955845i	$-0.405056\pi$
$197$	17.5406	−	17.5406i	1.24972	−	1.24972i	0.955845	−	0.293872i	$-0.0949441\pi$
$198$	−2.46279	−	2.30141i	−0.175023	−	0.163554i
$199$			7.87107i			0.557965i	0.960296	+	0.278983i	$0.0899972\pi$
$199$			7.87107i			0.557965i	−0.960296	+	0.278983i	$0.910003\pi$
$200$	−1.29156	−	12.6709i	−0.0913272	−	0.895967i
$201$			12.4329i			0.876951i
$202$	1.30159	−	1.39286i	0.0915799	−	0.0980016i
$203$	−3.81539	+	3.81539i	−0.267788	+	0.267788i
$204$	−3.44433	−	3.00679i	−0.241152	−	0.210517i
$205$	1.11515	+	1.11515i	0.0778853	+	0.0778853i
$206$	−0.499461	−	14.7450i	−0.0347991	−	1.02733i
$207$	4.54726			0.316057
$208$	2.28982	+	1.74058i	0.158771	+	0.120687i
$209$	−4.31774			−0.298664
$210$	−0.0918207	−	2.71072i	−0.00633623	−	0.187058i
$211$	−2.62308	−	2.62308i	−0.180580	−	0.180580i	0.611028	−	0.791609i	$-0.290756\pi$
$211$	−2.62308	−	2.62308i	−0.180580	−	0.180580i	−0.791609	+	0.611028i	$0.790756\pi$
$212$	−3.67452	+	4.20923i	−0.252367	+	0.289091i
$213$	−17.6620	+	17.6620i	−1.21018	+	1.21018i
$214$	−7.74389	+	8.28691i	−0.529362	+	0.566481i
$215$		−	7.24439i		−	0.494063i
$216$	9.93057	−	12.1848i	0.675690	−	0.829072i
$217$			12.3198i			0.836323i
$218$	12.6799	+	11.8491i	0.858794	+	0.802520i
$219$	−1.57688	+	1.57688i	−0.106556	+	0.106556i
$220$	−0.411938	−	6.07363i	−0.0277729	−	0.409484i
$221$	0.742911	+	0.742911i	0.0499736	+	0.0499736i
$222$	2.85354	−	0.0966584i	0.191517	−	0.00648729i
$223$	20.7757			1.39124			0.695622	−	0.718408i	$-0.255129\pi$
$223$	20.7757			1.39124			0.695622	+	0.718408i	$0.255129\pi$
$224$	−1.65735	−	9.69567i	−0.110736	−	0.647819i
$225$	2.48575			0.165717
$226$	15.0070	−	0.508333i	0.998248	−	0.0338138i
$227$	6.57711	+	6.57711i	0.436538	+	0.436538i	0.890845	−	0.454307i	$-0.150113\pi$
$227$	6.57711	+	6.57711i	0.436538	+	0.436538i	−0.454307	+	0.890845i	$0.650113\pi$
$228$	−0.211749	−	3.12203i	−0.0140234	−	0.206762i
$229$	11.6107	−	11.6107i	0.767255	−	0.767255i	−0.210367	−	0.977622i	$-0.567466\pi$
$229$	11.6107	−	11.6107i	0.767255	−	0.767255i	0.977622	+	0.210367i	$0.0674660\pi$
$230$	6.00032	+	5.60714i	0.395650	+	0.369724i
$231$			11.7467i			0.772879i
$232$	−6.80358	−	5.54488i	−0.446677	−	0.364039i
$233$		−	9.10215i		−	0.596302i	−0.954519	−	0.298151i	$-0.903630\pi$
$233$		−	9.10215i		−	0.596302i	0.954519	−	0.298151i	$-0.0963699\pi$
$234$	−0.383271	+	0.410147i	−0.0250552	+	0.0268121i
$235$	0.906413	−	0.906413i	0.0591279	−	0.0591279i
$236$	−5.42174	+	6.21070i	−0.352925	+	0.404282i
$237$	3.17281	+	3.17281i	0.206096	+	0.206096i
$238$	−0.121636	−	3.59092i	−0.00788447	−	0.232765i
$239$	−0.489126			−0.0316389			−0.0158195	−	0.999875i	$-0.505036\pi$
$239$	−0.489126			−0.0316389			−0.0158195	+	0.999875i	$0.505036\pi$
$240$	4.37146	−	0.595722i	0.282177	−	0.0384537i
$241$	−28.2441			−1.81936			−0.909681	−	0.415308i	$-0.863674\pi$
$241$	−28.2441			−1.81936			−0.909681	+	0.415308i	$0.863674\pi$
$242$	0.365913	+	10.8025i	0.0235218	+	0.694408i
$243$	4.00144	+	4.00144i	0.256692	+	0.256692i
$244$	0.874224	+	0.763169i	0.0559664	+	0.0488569i
$245$	−1.98217	+	1.98217i	−0.126636	+	0.126636i
$246$	3.37971	−	3.61670i	0.215482	−	0.230592i
$247$			0.719067i			0.0457531i
$248$	−19.9364	+	2.03215i	−1.26597	+	0.129042i
$249$			16.7973i			1.06449i
$250$	6.92212	+	6.46854i	0.437793	+	0.409106i
$251$	3.15831	−	3.15831i	0.199351	−	0.199351i	−0.600371	−	0.799722i	$-0.704980\pi$
$251$	3.15831	−	3.15831i	0.199351	−	0.199351i	0.799722	+	0.600371i	$0.204980\pi$
$252$	1.91532	−	0.129905i	0.120654	−	0.00818325i
$253$	−25.1501	−	25.1501i	−1.58117	−	1.58117i
$254$	−16.1081	+	0.545633i	−1.01071	+	0.0342360i
$255$	1.61156			0.100919
$256$	15.4166	−	4.28130i	0.963535	−	0.267581i
$257$	26.6475			1.66223			0.831114	−	0.556102i	$-0.187704\pi$
$257$	26.6475			1.66223			0.831114	+	0.556102i	$0.187704\pi$
$258$	−22.7255	+	0.769785i	−1.41483	+	0.0479247i
$259$	1.58656	+	1.58656i	0.0985838	+	0.0985838i
$260$	−1.01149	+	0.0686033i	−0.0627298	+	0.00425460i
$261$	1.21125	−	1.21125i	0.0749746	−	0.0749746i
$262$	−13.4185	−	12.5393i	−0.828999	−	0.774678i
$263$			0.00967738i			0.000596733i	1.00000		0.000298366i	$9.49730e-5\pi$
$263$			0.00967738i			0.000596733i	−1.00000		0.000298366i	$0.999905\pi$
$264$	−19.0091	+	1.93762i	−1.16993	+	0.119252i
$265$		−	1.96944i		−	0.120982i
$266$	1.67897	−	1.79670i	0.102944	−	0.110163i
$267$	18.4246	−	18.4246i	1.12756	−	1.12756i
$268$	−11.9726	−	10.4517i	−0.731341	−	0.638437i
$269$	14.6835	+	14.6835i	0.895267	+	0.895267i	0.995013	−	0.0997462i	$-0.0318031\pi$
$269$	14.6835	+	14.6835i	0.895267	+	0.895267i	−0.0997462	+	0.995013i	$0.531803\pi$
$270$	0.187568	+	5.53737i	0.0114150	+	0.336994i
$271$	−20.1499			−1.22402			−0.612011	−	0.790849i	$-0.709639\pi$
$271$	−20.1499			−1.22402			−0.612011	+	0.790849i	$0.709639\pi$
$272$	5.79091	−	0.789157i	0.351126	−	0.0478497i
$273$	1.95628			0.118399
$274$	−0.866681	−	25.5861i	−0.0523581	−	1.54571i
$275$	−13.7483	−	13.7483i	−0.829051	−	0.829051i
$276$	16.9519	−	19.4187i	1.02039	−	1.16887i
$277$	−11.2116	+	11.2116i	−0.673642	+	0.673642i	−0.958554	−	0.284912i	$-0.908036\pi$
$277$	−11.2116	+	11.2116i	−0.673642	+	0.673642i	0.284912	+	0.958554i	$0.408036\pi$
$278$	6.97112	−	7.45995i	0.418100	−	0.447418i
$279$		−	3.91110i		−	0.234152i
$280$	2.68754	+	2.19033i	0.160611	+	0.130897i
$281$		−	8.52708i		−	0.508683i	−0.967114	−	0.254342i	$-0.918141\pi$
$281$		−	8.52708i		−	0.508683i	0.967114	−	0.254342i	$-0.0818587\pi$
$282$	−2.93972	−	2.74709i	−0.175058	−	0.163587i
$283$	17.4288	−	17.4288i	1.03603	−	1.03603i	0.0367072	−	0.999326i	$-0.488313\pi$
$283$	17.4288	−	17.4288i	1.03603	−	1.03603i	0.999326	−	0.0367072i	$-0.0116869\pi$
$284$	−2.16057	−	31.8555i	−0.128206	−	1.89028i
$285$	0.779915	+	0.779915i	0.0461982	+	0.0461982i
$286$	4.38825	−	0.148644i	0.259483	−	0.00878950i
$287$	3.88997			0.229618
$288$	0.526150	+	3.07803i	0.0310037	+	0.181375i
$289$	−14.8652			−0.874421
$290$	3.09187	−	0.104731i	0.181561	−	0.00615004i
$291$	2.65500	+	2.65500i	0.155639	+	0.155639i
$292$	−0.192898	−	2.84409i	−0.0112885	−	0.166438i
$293$	−22.7032	+	22.7032i	−1.32633	+	1.32633i	−0.417792	+	0.908543i	$0.637196\pi$
$293$	−22.7032	+	22.7032i	−1.32633	+	1.32633i	−0.908543	+	0.417792i	$0.862804\pi$
$294$	6.42867	+	6.00742i	0.374927	+	0.350360i
$295$		−	2.90590i		−	0.169188i
$296$	−2.30573	+	2.82914i	−0.134018	+	0.164440i
$297$		−	23.9958i		−	1.39238i
$298$	−9.71642	+	10.3977i	−0.562857	+	0.602325i
$299$	−4.18844	+	4.18844i	−0.242224	+	0.242224i
$300$	9.26674	−	10.6152i	0.535015	−	0.612870i
$301$	−12.6353	−	12.6353i	−0.728286	−	0.728286i
$302$	−0.201997	−	5.96333i	−0.0116236	−	0.343151i
$303$	2.10909			0.121164
$304$	3.18444	+	2.42061i	0.182640	+	0.138831i
$305$	−0.409037			−0.0234214
$306$	0.0386150	+	1.13999i	0.00220747	+	0.0651688i
$307$	−4.61588	−	4.61588i	−0.263442	−	0.263442i	0.563009	−	0.826451i	$-0.309644\pi$
$307$	−4.61588	−	4.61588i	−0.263442	−	0.263442i	−0.826451	+	0.563009i	$0.809644\pi$
$308$	−11.3118	−	9.87482i	−0.644549	−	0.562670i
$309$	11.5417	−	11.5417i	0.656583	−	0.656583i
$310$	4.82270	−	5.16088i	0.273911	−	0.293118i
$311$		−	11.6904i		−	0.662902i	−0.943472	−	0.331451i	$-0.892462\pi$
$311$		−	11.6904i		−	0.662902i	0.943472	−	0.331451i	$-0.107538\pi$
$312$	0.322687	+	3.16573i	0.0182686	+	0.179224i
$313$			21.6421i			1.22329i	0.791134	+	0.611643i	$0.209491\pi$
$313$			21.6421i			1.22329i	−0.791134	+	0.611643i	$0.790509\pi$
$314$	−4.37794	−	4.09106i	−0.247061	−	0.230872i
$315$	−0.478467	+	0.478467i	−0.0269585	+	0.0269585i
$316$	−5.72253	+	0.388126i	−0.321918	+	0.0218338i
$317$	10.2440	+	10.2440i	0.575359	+	0.575359i	0.933621	−	0.358262i	$-0.116630\pi$
$317$	10.2440	+	10.2440i	0.575359	+	0.575359i	−0.358262	+	0.933621i	$0.616630\pi$
$318$	−6.17810	+	0.209272i	−0.346451	+	0.0117354i
$319$	−13.3984			−0.750168
$320$	−3.10118	+	4.71039i	−0.173361	+	0.263319i
$321$	−12.5481			−0.700367
$322$	20.2451	−	0.685767i	1.12822	−	0.0382163i
$323$	1.03316	+	1.03316i	0.0574866	+	0.0574866i
$324$	14.0462	−	0.952670i	0.780344	−	0.0529261i
$325$	−2.28960	+	2.28960i	−0.127004	+	0.127004i
$326$	−5.38750	−	5.03447i	−0.298386	−	0.278834i
$327$			19.2001i			1.06177i
$328$	0.641650	+	6.29492i	0.0354292	+	0.347579i
$329$		−	3.16184i		−	0.174318i
$330$	4.59837	−	4.92082i	0.253132	−	0.270882i
$331$	−24.6498	+	24.6498i	−1.35488	+	1.35488i	−0.474760	+	0.880115i	$0.657465\pi$
$331$	−24.6498	+	24.6498i	−1.35488	+	1.35488i	−0.880115	+	0.474760i	$0.842535\pi$
$332$	−16.1754	−	14.1206i	−0.887738	−	0.774966i
$333$	−0.503675	−	0.503675i	−0.0276012	−	0.0276012i
$334$	1.18188	+	34.8914i	0.0646698	+	1.90917i
$335$	5.60180			0.306059
$336$	6.58545	−	8.66351i	0.359266	−	0.472633i
$337$	−13.4650			−0.733485			−0.366742	−	0.930323i	$-0.619527\pi$
$337$	−13.4650			−0.733485			−0.366742	+	0.930323i	$0.619527\pi$
$338$	0.597639	+	17.6434i	0.0325072	+	0.959676i
$339$	11.7467	+	11.7467i	0.637993	+	0.637993i
$340$	−1.35474	+	1.55188i	−0.0734713	+	0.0841627i
$341$	−21.6316	+	21.6316i	−1.17142	+	1.17142i
$342$	−0.533012	+	0.570388i	−0.0288220	+	0.0308430i
$343$			19.0862i			1.03056i
$344$	18.3628	−	22.5312i	0.990055	−	1.21480i
$345$			9.08575i			0.489160i
$346$	−5.97922	−	5.58742i	−0.321445	−	0.300381i
$347$	23.2413	−	23.2413i	1.24766	−	1.24766i	0.290903	−	0.956752i	$-0.406044\pi$
$347$	23.2413	−	23.2413i	1.24766	−	1.24766i	0.956752	−	0.290903i	$-0.0939558\pi$
$348$	−0.657082	−	9.68802i	−0.0352233	−	0.519332i
$349$	18.9477	+	18.9477i	1.01425	+	1.01425i	0.999897	+	0.0143493i	$0.00456768\pi$
$349$	18.9477	+	18.9477i	1.01425	+	1.01425i	0.0143493	+	0.999897i	$0.495432\pi$
$350$	11.0670	−	0.374873i	0.591555	−	0.0200378i
$351$	−3.99621			−0.213302
$352$	14.1140	−	19.9341i	0.752278	−	1.06249i
$353$	21.7770			1.15908			0.579538	−	0.814945i	$-0.303233\pi$
$353$	21.7770			1.15908			0.579538	+	0.814945i	$0.303233\pi$
$354$	−9.11575	+	0.308779i	−0.484497	+	0.0164114i
$355$	7.95783	+	7.95783i	0.422358	+	0.422358i
$356$	2.25385	+	33.2308i	0.119454	+	1.76123i
$357$	2.81079	−	2.81079i	0.148763	−	0.148763i
$358$	−13.6688	−	12.7732i	−0.722420	−	0.675082i
$359$		−	11.2750i		−	0.595070i	−0.954711	−	0.297535i	$-0.903836\pi$
$359$		−	11.2750i		−	0.595070i	0.954711	−	0.297535i	$-0.0961645\pi$
$360$	−0.853199	−	0.695353i	−0.0449675	−	0.0366483i
$361$			1.00000i			0.0526316i
$362$	−4.86632	+	5.20756i	−0.255768	+	0.273703i
$363$	−8.45563	+	8.45563i	−0.443805	+	0.443805i
$364$	−1.64453	+	1.88384i	−0.0861968	+	0.0987400i
$365$	0.710482	+	0.710482i	0.0371883	+	0.0371883i
$366$	0.0434641	+	1.28314i	0.00227190	+	0.0670709i
$367$	28.8399			1.50543			0.752716	−	0.658346i	$-0.228744\pi$
$367$	28.8399			1.50543			0.752716	+	0.658346i	$0.228744\pi$
$368$	4.44917	+	32.6484i	0.231929	+	1.70192i
$369$	−1.23493			−0.0642877
$370$	−0.0435505	−	1.28569i	−0.00226408	−	0.0668401i
$371$	−3.43500	−	3.43500i	−0.178336	−	0.178336i
$372$	−16.7020	−	14.5803i	−0.865961	−	0.755956i
$373$	−8.34178	+	8.34178i	−0.431921	+	0.431921i	−0.889281	−	0.457361i	$-0.848795\pi$
$373$	−8.34178	+	8.34178i	−0.431921	+	0.431921i	0.457361	+	0.889281i	$0.348795\pi$
$374$	6.09150	−	6.51865i	0.314984	−	0.337071i
$375$			10.4815i			0.541265i
$376$	5.11662	−	0.521545i	0.263870	−	0.0268966i
$377$			2.23134i			0.114920i
$378$	9.98514	+	9.33085i	0.513580	+	0.479927i
$379$	19.8348	−	19.8348i	1.01885	−	1.01885i	0.0190276	−	0.999819i	$-0.493943\pi$
$379$	19.8348	−	19.8348i	1.01885	−	1.01885i	0.999819	−	0.0190276i	$-0.00605705\pi$
$380$	−1.40667	+	0.0954060i	−0.0721605	+	0.00489423i
$381$	−12.6086	−	12.6086i	−0.645960	−	0.645960i
$382$	−16.1500	+	0.547051i	−0.826305	+	0.0279895i
$383$	−18.6397			−0.952446			−0.476223	−	0.879324i	$-0.657995\pi$
$383$	−18.6397			−0.952446			−0.476223	+	0.879324i	$0.657995\pi$
$384$	15.1059	+	9.22782i	0.770871	+	0.470905i
$385$	5.29263			0.269737
$386$	11.4993	−	0.389517i	0.585297	−	0.0198259i
$387$	4.01126	+	4.01126i	0.203904	+	0.203904i
$388$	−4.78859	+	0.324782i	−0.243104	+	0.0164883i
$389$	−6.76041	+	6.76041i	−0.342767	+	0.342767i	−0.857406	−	0.514640i	$-0.827926\pi$
$389$	−6.76041	+	6.76041i	−0.342767	+	0.342767i	0.514640	+	0.857406i	$0.327926\pi$
$390$	−0.819502	−	0.765802i	−0.0414971	−	0.0387779i
$391$			12.0360i			0.608685i
$392$	−11.1892	+	1.14053i	−0.565140	+	0.0576055i
$393$		−	20.3185i		−	1.02493i
$394$	−23.9522	+	25.6317i	−1.20669	+	1.29131i
$395$	1.42955	−	1.42955i	0.0719283	−	0.0719283i
$396$	3.59109	+	3.13491i	0.180459	+	0.157535i
$397$	27.1460	+	27.1460i	1.36242	+	1.36242i	0.870824	+	0.491595i	$0.163586\pi$
$397$	27.1460	+	27.1460i	1.36242	+	1.36242i	0.491595	+	0.870824i	$0.336414\pi$
$398$	−0.376839	−	11.1250i	−0.0188892	−	0.557646i
$399$	2.72058			0.136199
$400$	2.43213	+	17.8472i	0.121607	+	0.892361i
$401$	0.201895			0.0100822			0.00504108	−	0.999987i	$-0.498395\pi$
$401$	0.201895			0.0100822			0.00504108	+	0.999987i	$0.498395\pi$
$402$	−0.595244	−	17.5727i	−0.0296881	−	0.876449i
$403$	3.60248	+	3.60248i	0.179452	+	0.179452i
$404$	−1.77299	+	2.03099i	−0.0882097	+	0.101046i
$405$	−3.50888	+	3.50888i	−0.174358	+	0.174358i
$406$	5.21002	−	5.57535i	0.258569	−	0.276700i
$407$			5.57147i			0.276168i
$408$	5.01218	+	4.08490i	0.248140	+	0.202233i
$409$			10.4518i			0.516809i	0.966037	+	0.258404i	$0.0831967\pi$
$409$			10.4518i			0.516809i	−0.966037	+	0.258404i	$0.916803\pi$
$410$	−1.62954	−	1.52276i	−0.0804774	−	0.0752040i
$411$	20.0275	−	20.0275i	0.987884	−	0.987884i
$412$	1.41188	+	20.8168i	0.0695582	+	1.02557i
$413$	−5.06832	−	5.06832i	−0.249396	−	0.249396i
$414$	−6.42711	+	0.217707i	−0.315875	+	0.0106997i
$415$	7.56822			0.371509
$416$	−3.31978	−	2.35051i	−0.162765	−	0.115243i
$417$	11.2959			0.553164
$418$	6.10271	−	0.206718i	0.298493	−	0.0101109i
$419$	−9.18590	−	9.18590i	−0.448760	−	0.448760i	0.446182	−	0.894942i	$-0.352783\pi$
$419$	−9.18590	−	9.18590i	−0.448760	−	0.448760i	−0.894942	+	0.446182i	$0.852783\pi$
$420$	0.259559	+	3.82695i	0.0126652	+	0.186736i
$421$	1.24332	−	1.24332i	0.0605957	−	0.0605957i	−0.676160	−	0.736755i	$-0.736357\pi$
$421$	1.24332	−	1.24332i	0.0605957	−	0.0605957i	0.736755	+	0.676160i	$0.236357\pi$
$422$	3.83305	+	3.58189i	0.186590	+	0.174363i
$423$			1.00377i			0.0488051i
$424$	4.99206	−	6.12526i	0.242436	−	0.297469i
$425$			6.57944i			0.319150i
$426$	24.1180	−	25.8092i	1.16852	−	1.25046i
$427$	−0.713422	+	0.713422i	−0.0345249	+	0.0345249i
$428$	10.5485	−	12.0835i	0.509881	−	0.584077i
$429$	3.43491	+	3.43491i	0.165839	+	0.165839i
$430$	0.346835	+	10.2392i	0.0167259	+	0.493780i
$431$	33.1220			1.59543			0.797716	−	0.603033i	$-0.206041\pi$
$431$	33.1220			1.59543			0.797716	+	0.603033i	$0.206041\pi$
$432$	−13.4525	+	17.6975i	−0.647235	+	0.851472i
$433$	−15.0777			−0.724587			−0.362293	−	0.932064i	$-0.618006\pi$
$433$	−15.0777			−0.724587			−0.362293	+	0.932064i	$0.618006\pi$
$434$	−0.589828	−	17.4129i	−0.0283127	−	0.835844i
$435$	2.42016	+	2.42016i	0.116038	+	0.116038i
$436$	−18.4892	−	16.1404i	−0.885470	−	0.772987i
$437$	−5.82483	+	5.82483i	−0.278639	+	0.278639i
$438$	2.15327	−	2.30426i	0.102887	−	0.110102i
$439$			11.3253i			0.540528i	0.962786	+	0.270264i	$0.0871110\pi$
$439$			11.3253i			0.540528i	−0.962786	+	0.270264i	$0.912889\pi$
$440$	0.873018	+	8.56476i	0.0416195	+	0.408309i
$441$		−	2.19508i		−	0.104528i
$442$	−1.08560	−	1.01446i	−0.0516368	−	0.0482532i
$443$	12.0384	−	12.0384i	0.571959	−	0.571959i	−0.360716	−	0.932676i	$-0.617468\pi$
$443$	12.0384	−	12.0384i	0.571959	−	0.571959i	0.932676	+	0.360716i	$0.117468\pi$
$444$	−4.02857	+	0.273234i	−0.191188	+	0.0129671i
$445$	−8.30139	−	8.30139i	−0.393524	−	0.393524i
$446$	−29.3644	+	0.994666i	−1.39045	+	0.0470988i
$447$	−15.7444			−0.744683
$448$	2.80670	+	13.6245i	0.132604	+	0.643699i
$449$	−12.6844			−0.598612			−0.299306	−	0.954157i	$-0.596755\pi$
$449$	−12.6844			−0.598612			−0.299306	+	0.954157i	$0.596755\pi$
$450$	−3.51337	+	0.119009i	−0.165622	+	0.00561014i
$451$	6.83016	+	6.83016i	0.321620	+	0.321620i
$452$	−21.1865	+	1.43696i	−0.996531	+	0.0675888i
$453$	4.66780	−	4.66780i	0.219312	−	0.219312i
$454$	−9.61099	−	8.98122i	−0.451066	−	0.421509i
$455$		−	0.881422i		−	0.0413217i
$456$	0.448759	+	4.40255i	0.0210151	+	0.206168i
$457$		−	29.4134i		−	1.37590i	−0.725757	−	0.687951i	$-0.758510\pi$
$457$		−	29.4134i		−	1.37590i	0.725757	−	0.687951i	$-0.241490\pi$
$458$	−15.8547	+	16.9664i	−0.740841	+	0.792790i
$459$	−5.74178	+	5.74178i	−0.268004	+	0.268004i
$460$	−8.74932	−	7.63788i	−0.407939	−	0.356118i
$461$	28.8222	+	28.8222i	1.34239	+	1.34239i	0.893679	+	0.448707i	$0.148115\pi$
$461$	28.8222	+	28.8222i	1.34239	+	1.34239i	0.448707	+	0.893679i	$0.351885\pi$
$462$	−0.562392	−	16.6029i	−0.0261648	−	0.772436i
$463$	−35.2834			−1.63976			−0.819880	−	0.572536i	$-0.805960\pi$
$463$	−35.2834			−1.63976			−0.819880	+	0.572536i	$0.805960\pi$
$464$	9.88167	+	7.51142i	0.458745	+	0.348709i
$465$	7.81465			0.362396
$466$	0.435778	+	12.8650i	0.0201870	+	0.595960i
$467$	−1.87213	−	1.87213i	−0.0866320	−	0.0866320i	0.662463	−	0.749095i	$-0.269511\pi$
$467$	−1.87213	−	1.87213i	−0.0866320	−	0.0866320i	−0.749095	+	0.662463i	$0.769511\pi$
$468$	0.522080	−	0.598052i	0.0241332	−	0.0276450i
$469$	9.77037	−	9.77037i	0.451154	−	0.451154i
$470$	−1.23773	+	1.32452i	−0.0570923	+	0.0610957i
$471$		−	6.62911i		−	0.305453i
$472$	7.36575	−	9.03779i	0.339036	−	0.415998i
$473$		−	44.3711i		−	2.04018i
$474$	−4.63636	−	4.33256i	−0.212955	−	0.199001i
$475$	−3.18413	+	3.18413i	−0.146098	+	0.146098i
$476$	0.343840	+	5.06959i	0.0157599	+	0.232364i
$477$	1.09049	+	1.09049i	0.0499301	+	0.0499301i
$478$	0.691332	−	0.0234176i	0.0316208	−	0.00107110i
$479$	−19.8235			−0.905761			−0.452880	−	0.891571i	$-0.649604\pi$
$479$	−19.8235			−0.905761			−0.452880	+	0.891571i	$0.649604\pi$
$480$	−6.15012	+	1.05128i	−0.280713	+	0.0479844i
$481$	0.927861			0.0423068
$482$	39.9203	−	1.35223i	1.81832	−	0.0615922i
$483$	15.8469	+	15.8469i	0.721059	+	0.721059i
$484$	−1.03437	−	15.2507i	−0.0470166	−	0.693214i
$485$	1.19624	−	1.19624i	0.0543184	−	0.0543184i
$486$	−5.84722	−	5.46407i	−0.265235	−	0.247855i
$487$		−	18.8682i		−	0.855000i	−0.904015	−	0.427500i	$-0.859394\pi$
$487$		−	18.8682i		−	0.855000i	0.904015	−	0.427500i	$-0.140606\pi$
$488$	−1.27217	−	1.03681i	−0.0575884	−	0.0469342i
$489$		−	8.15780i		−	0.368909i
$490$	2.70671	−	2.89651i	0.122277	−	0.130851i
$491$	−19.7364	+	19.7364i	−0.890689	+	0.890689i	−0.994588	−	0.103899i	$-0.966868\pi$
$491$	−19.7364	+	19.7364i	−0.890689	+	0.890689i	0.103899	+	0.994588i	$0.466868\pi$
$492$	−4.60373	+	5.27366i	−0.207552	+	0.237755i
$493$	3.20601	+	3.20601i	0.144392	+	0.144392i
$494$	−0.0344263	−	1.01633i	−0.00154891	−	0.0457269i
$495$	−1.68022			−0.0755203
$496$	28.0809	−	3.82673i	1.26087	−	0.171825i
$497$	27.7593			1.24517
$498$	−0.804195	−	23.7414i	−0.0360369	−	1.06388i
$499$	−23.8601	−	23.8601i	−1.06813	−	1.06813i	−0.997503	−	0.0706228i	$-0.977501\pi$
$499$	−23.8601	−	23.8601i	−1.06813	−	1.06813i	−0.0706228	−	0.997503i	$-0.522499\pi$
$500$	−10.0934	−	8.81125i	−0.451392	−	0.394051i
$501$	−27.3113	+	27.3113i	−1.22018	+	1.22018i
$502$	−4.31275	+	4.61517i	−0.192488	+	0.205985i
$503$		−	10.8772i		−	0.484992i	−0.970152	−	0.242496i	$-0.922034\pi$
$503$		−	10.8772i		−	0.484992i	0.970152	−	0.242496i	$-0.0779661\pi$
$504$	−2.70090	+	0.275307i	−0.120308	+	0.0122631i
$505$		−	0.950274i		−	0.0422866i
$506$	36.7513	+	34.3431i	1.63379	+	1.52674i
$507$	−13.8104	+	13.8104i	−0.613341	+	0.613341i
$508$	22.7411	−	1.54240i	1.00898	−	0.0684328i
$509$	18.6405	+	18.6405i	0.826224	+	0.826224i	0.986992	−	0.160769i	$-0.0513973\pi$
$509$	18.6405	+	18.6405i	0.826224	+	0.826224i	−0.160769	+	0.986992i	$0.551397\pi$
$510$	−2.27778	+	0.0771555i	−0.100862	+	0.00341650i
$511$	2.47837			0.109637
$512$	−21.5848	+	6.78929i	−0.953924	+	0.300047i
$513$	−5.55750			−0.245369
$514$	−37.6637	+	1.27579i	−1.66128	+	0.0562726i
$515$	−5.20023	−	5.20023i	−0.229150	−	0.229150i
$516$	32.0835	−	2.17603i	1.41240	−	0.0957945i
$517$	5.55168	−	5.55168i	0.244163	−	0.244163i
$518$	−2.31840	−	2.16648i	−0.101865	−	0.0951898i
$519$		−	9.05379i		−	0.397417i
$520$	1.42636	−	0.145390i	0.0625498	−	0.00637580i
$521$		−	23.0027i		−	1.00777i	−0.863772	−	0.503883i	$-0.831904\pi$
$521$		−	23.0027i		−	1.00777i	0.863772	−	0.503883i	$-0.168096\pi$
$522$	−1.65400	+	1.76998i	−0.0723934	+	0.0774698i
$523$	−15.2768	+	15.2768i	−0.668009	+	0.668009i	−0.957255	−	0.289246i	$-0.906596\pi$
$523$	−15.2768	+	15.2768i	−0.668009	+	0.668009i	0.289246	+	0.957255i	$0.406596\pi$
$524$	19.5661	+	17.0806i	0.854750	+	0.746169i
$525$	8.66268	+	8.66268i	0.378070	+	0.378070i
$526$	−0.000463318	−	0.0136780i	−2.02016e−5	−	0.000596391i
$527$	10.3521			0.450946
$528$	26.7747	−	3.64873i	1.16522	−	0.158791i
$529$	−44.8573			−1.95032
$530$	0.0942898	+	2.78361i	0.00409569	+	0.120912i
$531$	1.60901	+	1.60901i	0.0698251	+	0.0698251i
$532$	−2.28704	+	2.61984i	−0.0991556	+	0.113584i
$533$	1.13748	−	1.13748i	0.0492697	−	0.0492697i
$534$	−25.1592	+	26.9234i	−1.08875	+	1.16509i
$535$			5.65370i			0.244431i
$536$	17.4225	+	14.1992i	0.752535	+	0.613313i
$537$		−	20.6975i		−	0.893162i
$538$	−21.4566	−	20.0507i	−0.925062	−	0.864445i
$539$	−12.1406	+	12.1406i	−0.522932	+	0.522932i
$540$	−0.530219	−	7.81755i	−0.0228170	−	0.336414i
$541$	24.3853	+	24.3853i	1.04841	+	1.04841i	0.998767	+	0.0496401i	$0.0158074\pi$
$541$	24.3853	+	24.3853i	1.04841	+	1.04841i	0.0496401	+	0.998767i	$0.484193\pi$
$542$	28.4800	−	0.964707i	1.22332	−	0.0414377i
$543$	−7.88533			−0.338392
$544$	−8.14711	+	1.39265i	−0.349305	+	0.0597092i
$545$	8.65082			0.370560
$546$	−2.76501	+	0.0936595i	−0.118331	+	0.00400825i
$547$	−23.1698	−	23.1698i	−0.990669	−	0.990669i	0.00928761	−	0.999957i	$-0.497044\pi$
$547$	−23.1698	−	23.1698i	−0.990669	−	0.990669i	−0.999957	+	0.00928761i	$0.997044\pi$
$548$	2.44994	+	36.1219i	0.104656	+	1.54305i
$549$	0.226486	−	0.226486i	0.00966619	−	0.00966619i
$550$	20.0901	+	18.7736i	0.856643	+	0.800510i
$551$			3.10311i			0.132197i
$552$	−23.0302	+	28.2581i	−0.980230	+	1.20274i
$553$		−	4.98668i		−	0.212055i
$554$	15.3098	−	16.3833i	0.650451	−	0.696061i
$555$	1.00638	−	1.00638i	0.0427184	−	0.0427184i
$556$	−9.49585	+	10.8777i	−0.402714	+	0.461316i
$557$	−4.72880	−	4.72880i	−0.200366	−	0.200366i	0.599791	−	0.800157i	$-0.295250\pi$
$557$	−4.72880	−	4.72880i	−0.200366	−	0.200366i	−0.800157	+	0.599791i	$0.795250\pi$
$558$	0.187250	+	5.52796i	0.00792691	+	0.234017i
$559$	−7.38946			−0.312541
$560$	−3.90344	−	2.96715i	−0.164951	−	0.125385i
$561$	9.87060			0.416737
$562$	0.408246	+	12.0522i	0.0172208	+	0.508391i
$563$	−6.69065	−	6.69065i	−0.281977	−	0.281977i	0.551920	−	0.833897i	$-0.313895\pi$
$563$	−6.69065	−	6.69065i	−0.281977	−	0.281977i	−0.833897	+	0.551920i	$0.813895\pi$
$564$	4.28653	+	3.74200i	0.180495	+	0.157567i
$565$	5.29261	−	5.29261i	0.222662	−	0.222662i
$566$	−23.7995	+	25.4683i	−1.00037	+	1.07051i
$567$			12.2400i			0.514032i
$568$	4.57889	+	44.9213i	0.192126	+	1.88485i
$569$		−	3.92656i		−	0.164610i	−0.996607	−	0.0823051i	$-0.973772\pi$
$569$		−	3.92656i		−	0.164610i	0.996607	−	0.0823051i	$-0.0262282\pi$
$570$	−1.13967	−	1.06500i	−0.0477357	−	0.0446077i
$571$	11.1018	−	11.1018i	0.464595	−	0.464595i	−0.435563	−	0.900158i	$-0.643451\pi$
$571$	11.1018	−	11.1018i	0.464595	−	0.464595i	0.900158	+	0.435563i	$0.143451\pi$
$572$	−6.19525	+	0.420187i	−0.259036	+	0.0175689i
$573$	−12.6414	−	12.6414i	−0.528102	−	0.528102i
$574$	−5.49809	+	0.186238i	−0.229486	+	0.00777341i
$575$	−37.0941			−1.54693
$576$	−0.891027	−	4.32531i	−0.0371261	−	0.180221i
$577$	16.1342			0.671676			0.335838	−	0.941920i	$-0.390980\pi$
$577$	16.1342			0.671676			0.335838	+	0.941920i	$0.390980\pi$
$578$	21.0105	−	0.711690i	0.873920	−	0.0296024i
$579$	9.00106	+	9.00106i	0.374071	+	0.374071i
$580$	−4.36505	+	0.296056i	−0.181249	+	0.0122930i
$581$	13.2001	−	13.2001i	0.547633	−	0.547633i
$582$	−3.87969	−	3.62547i	−0.160818	−	0.150280i
$583$		−	12.0626i		−	0.499582i
$584$	0.408807	+	4.01061i	0.0169166	+	0.165960i
$585$			0.279820i			0.0115691i
$586$	31.0018	−	33.1757i	1.28067	−	1.37048i
$587$	27.6260	−	27.6260i	1.14025	−	1.14025i	0.151842	−	0.988405i	$-0.451480\pi$
$587$	27.6260	−	27.6260i	1.14025	−	1.14025i	0.988405	−	0.151842i	$-0.0485205\pi$
$588$	−9.37391	−	8.18312i	−0.386574	−	0.337466i
$589$	5.00994	+	5.00994i	0.206431	+	0.206431i
$590$	0.139124	+	4.10721i	0.00572764	+	0.169091i
$591$	−38.8118			−1.59651
$592$	3.12348	−	4.10910i	0.128374	−	0.168883i
$593$	24.1250			0.990695			0.495348	−	0.868695i	$-0.335041\pi$
$593$	24.1250			0.990695			0.495348	+	0.868695i	$0.335041\pi$
$594$	1.14883	+	33.9158i	0.0471372	+	1.39158i
$595$	−1.26643	−	1.26643i	−0.0519187	−	0.0519187i
$596$	13.2354	−	15.1614i	0.542143	−	0.621035i
$597$	8.70809	−	8.70809i	0.356399	−	0.356399i
$598$	5.71943	−	6.12048i	0.233885	−	0.250285i
$599$			9.29055i			0.379602i	0.981823	+	0.189801i	$0.0607842\pi$
$599$			9.29055i			0.379602i	−0.981823	+	0.189801i	$0.939216\pi$
$600$	−12.5894	+	15.4472i	−0.513961	+	0.630631i
$601$		−	4.35242i		−	0.177539i	−0.996052	−	0.0887694i	$-0.971707\pi$
$601$		−	4.35242i		−	0.177539i	0.996052	−	0.0887694i	$-0.0282934\pi$
$602$	18.4637	+	17.2538i	0.752524	+	0.703213i
$603$	−3.10175	+	3.10175i	−0.126313	+	0.126313i
$604$	0.571006	+	8.41892i	0.0232339	+	0.342561i
$605$	3.80978	+	3.80978i	0.154890	+	0.154890i
$606$	−2.98099	+	0.100976i	−0.121095	+	0.00410185i
$607$	−0.511748			−0.0207712			−0.0103856	−	0.999946i	$-0.503306\pi$
$607$	−0.511748			−0.0207712			−0.0103856	+	0.999946i	$0.503306\pi$
$608$	−4.61678	−	3.26884i	−0.187235	−	0.132569i
$609$	8.44225			0.342097
$610$	0.578134	−	0.0195832i	0.0234080	−	0.000792902i
$611$	−0.924565	−	0.924565i	−0.0374039	−	0.0374039i
$612$	−0.109157	−	1.60941i	−0.00441242	−	0.0650567i
$613$	22.9106	−	22.9106i	0.925352	−	0.925352i	−0.0720495	−	0.997401i	$-0.522954\pi$
$613$	22.9106	−	22.9106i	0.925352	−	0.925352i	0.997401	+	0.0720495i	$0.0229540\pi$
$614$	6.74509	+	6.30311i	0.272210	+	0.254373i
$615$		−	2.46747i		−	0.0994980i
$616$	16.4609	+	13.4155i	0.663228	+	0.540527i
$617$		−	22.7467i		−	0.915746i	−0.889018	−	0.457873i	$-0.848611\pi$
$617$		−	22.7467i		−	0.915746i	0.889018	−	0.457873i	$-0.151389\pi$
$618$	−15.7605	+	16.8656i	−0.633979	+	0.678435i
$619$	24.2352	−	24.2352i	0.974097	−	0.974097i	−0.0255764	−	0.999673i	$-0.508142\pi$
$619$	24.2352	−	24.2352i	0.974097	−	0.974097i	0.999673	+	0.0255764i	$0.00814210\pi$
$620$	−6.56934	+	7.52530i	−0.263831	+	0.302223i
$621$	−32.3715	−	32.3715i	−1.29902	−	1.29902i
$622$	0.559695	+	16.5233i	0.0224417	+	0.662522i
$623$	−28.9577			−1.16017
$624$	−0.607651	−	4.45900i	−0.0243255	−	0.178503i
$625$	−17.7926			−0.711706
$626$	−1.03615	−	30.5890i	−0.0414128	−	1.22258i
$627$	4.77689	+	4.77689i	0.190771	+	0.190771i
$628$	6.38365	+	5.57272i	0.254735	+	0.222376i
$629$	1.33316	−	1.33316i	0.0531565	−	0.0531565i
$630$	0.653359	−	0.699174i	0.0260304	−	0.0278557i
$631$			35.9959i			1.43298i	0.697600	+	0.716488i	$0.254251\pi$
$631$			35.9959i			1.43298i	−0.697600	+	0.716488i	$0.745749\pi$
$632$	8.06966	−	0.822553i	0.320994	−	0.0327194i
$633$			5.80405i			0.230690i
$634$	−14.9693	−	13.9884i	−0.594508	−	0.555552i
$635$	−5.68096	+	5.68096i	−0.225442	+	0.225442i
$636$	8.72213	−	0.591571i	0.345855	−	0.0234573i
$637$	2.02187	+	2.02187i	0.0801093	+	0.0801093i
$638$	18.9374	−	0.641469i	0.749738	−	0.0253960i
$639$	−8.81259			−0.348621
$640$	4.15770	−	6.80615i	0.164348	−	0.269037i
$641$	21.0547			0.831611			0.415806	−	0.909454i	$-0.363500\pi$
$641$	21.0547			0.831611			0.415806	+	0.909454i	$0.363500\pi$
$642$	17.7355	−	0.600759i	0.699966	−	0.0237101i
$643$	6.15052	+	6.15052i	0.242553	+	0.242553i	0.817905	−	0.575353i	$-0.195135\pi$
$643$	6.15052	+	6.15052i	0.242553	+	0.242553i	−0.575353	+	0.817905i	$0.695135\pi$
$644$	−28.5817	+	1.93853i	−1.12628	+	0.0763888i
$645$	−8.01477	+	8.01477i	−0.315581	+	0.315581i
$646$	−1.50974	−	1.41081i	−0.0593998	−	0.0555075i
$647$			18.1000i			0.711584i	0.934565	+	0.355792i	$0.115789\pi$
$647$			18.1000i			0.711584i	−0.934565	+	0.355792i	$0.884211\pi$
$648$	−19.8073	+	2.01899i	−0.778105	+	0.0793133i
$649$		−	17.7983i		−	0.698645i
$650$	3.12652	−	3.34575i	0.122632	−	0.131231i
$651$	13.6299	−	13.6299i	0.534199	−	0.534199i
$652$	7.85574	+	6.85780i	0.307654	+	0.268572i
$653$	2.48100	+	2.48100i	0.0970890	+	0.0970890i	0.753983	−	0.656894i	$-0.228130\pi$
$653$	2.48100	+	2.48100i	0.0970890	+	0.0970890i	−0.656894	+	0.753983i	$0.728130\pi$
$654$	−0.919231	−	27.1375i	−0.0359448	−	1.06116i
$655$	−9.15471			−0.357704
$656$	−1.20829	−	8.86653i	−0.0471757	−	0.346180i
$657$	−0.786795			−0.0306958
$658$	0.151378	+	4.46895i	0.00590131	+	0.174218i
$659$	2.70017	+	2.70017i	0.105184	+	0.105184i	0.757740	−	0.652556i	$-0.226303\pi$
$659$	2.70017	+	2.70017i	0.105184	+	0.105184i	−0.652556	+	0.757740i	$0.726303\pi$
$660$	−6.26376	+	7.17525i	−0.243817	+	0.279296i
$661$	24.4617	−	24.4617i	0.951451	−	0.951451i	−0.0474237	−	0.998875i	$-0.515101\pi$
$661$	24.4617	−	24.4617i	0.951451	−	0.951451i	0.998875	+	0.0474237i	$0.0151011\pi$
$662$	33.6599	−	36.0202i	1.30823	−	1.39997i
$663$		−	1.64383i		−	0.0638409i
$664$	23.5383	+	19.1836i	0.913464	+	0.744469i
$665$		−	1.22579i		−	0.0475340i
$666$	0.736010	+	0.687782i	0.0285198	+	0.0266510i
$667$	−18.0751	+	18.0751i	−0.699871	+	0.699871i
$668$	−3.34095	−	49.2591i	−0.129265	−	1.90589i
$669$	−22.9850	−	22.9850i	−0.888653	−	0.888653i
$670$	−7.91760	+	0.268194i	−0.305884	+	0.0103612i
$671$	−2.50531			−0.0967163
$672$	−8.89312	+	12.5603i	−0.343060	+	0.484525i
$673$	−30.2515			−1.16611			−0.583055	−	0.812432i	$-0.698143\pi$
$673$	−30.2515			−1.16611			−0.583055	+	0.812432i	$0.698143\pi$
$674$	19.0315	−	0.644655i	0.733064	−	0.0248312i
$675$	−17.6958	−	17.6958i	−0.681112	−	0.681112i
$676$	−1.68941	−	24.9087i	−0.0649772	−	0.958025i
$677$	8.32477	−	8.32477i	0.319947	−	0.319947i	−0.528800	−	0.848747i	$-0.677358\pi$
$677$	8.32477	−	8.32477i	0.319947	−	0.319947i	0.848747	+	0.528800i	$0.177358\pi$
$678$	−17.1652	−	16.0404i	−0.659226	−	0.616029i
$679$		−	4.17283i		−	0.160139i
$680$	1.84050	−	2.25830i	0.0705800	−	0.0866017i
$681$		−	14.5531i		−	0.557674i
$682$	29.5385	−	31.6098i	1.13109	−	1.21040i
$683$	16.8657	−	16.8657i	0.645350	−	0.645350i	−0.306516	−	0.951866i	$-0.599163\pi$
$683$	16.8657	−	16.8657i	0.645350	−	0.645350i	0.951866	+	0.306516i	$0.0991632\pi$
$684$	0.726053	−	0.831706i	0.0277613	−	0.0318011i
$685$	−9.02362	−	9.02362i	−0.344775	−	0.344775i
$686$	−0.913779	−	26.9765i	−0.0348882	−	1.02997i
$687$	−25.6908			−0.980163
$688$	−24.8753	+	32.7248i	−0.948362	+	1.24762i
$689$	−2.00888			−0.0765322
$690$	−0.434993	−	12.8418i	−0.0165599	−	0.488880i
$691$	17.3544	+	17.3544i	0.660191	+	0.660191i	0.955425	−	0.295234i	$-0.0953975\pi$
$691$	17.3544	+	17.3544i	0.660191	+	0.660191i	−0.295234	+	0.955425i	$0.595398\pi$
$692$	8.71855	+	7.61101i	0.331429	+	0.289327i
$693$	−2.93056	+	2.93056i	−0.111323	+	0.111323i
$694$	−31.7365	+	33.9620i	−1.20470	+	1.28918i
$695$		−	5.08951i		−	0.193056i
$696$	1.39255	+	13.6616i	0.0527844	+	0.517842i
$697$		−	3.26868i		−	0.123810i
$698$	−27.6879	−	25.8736i	−1.04800	−	0.979329i
$699$	−10.0701	+	10.0701i	−0.380886	+	0.380886i
$700$	−15.6242	+	1.05969i	−0.590537	+	0.0400527i
$701$	−8.41548	−	8.41548i	−0.317848	−	0.317848i	0.530092	−	0.847940i	$-0.322157\pi$
$701$	−8.41548	−	8.41548i	−0.317848	−	0.317848i	−0.847940	+	0.530092i	$0.822157\pi$
$702$	5.64826	−	0.191324i	0.213180	−	0.00722107i
$703$	1.29037			0.0486672
$704$	−18.9944	+	28.8506i	−0.715878	+	1.08735i
$705$	−2.00561			−0.0755355
$706$	−30.7797	+	1.04261i	−1.15841	+	0.0392390i
$707$	−1.65742	−	1.65742i	−0.0623337	−	0.0623337i
$708$	12.8694	−	0.872859i	0.483663	−	0.0328040i
$709$	20.7227	−	20.7227i	0.778258	−	0.778258i	−0.201277	−	0.979534i	$-0.564509\pi$
$709$	20.7227	−	20.7227i	0.778258	−	0.778258i	0.979534	+	0.201277i	$0.0645091\pi$
$710$	−11.6286	−	10.8666i	−0.436414	−	0.407817i
$711$			1.58309i			0.0593707i
$712$	−4.77657	−	46.8606i	−0.179010	−	1.75618i
$713$			58.3640i			2.18575i
$714$	−3.83821	+	4.10735i	−0.143641	+	0.153714i
$715$	1.54764	−	1.54764i	0.0578783	−	0.0578783i
$716$	19.9311	+	17.3992i	0.744860	+	0.650239i
$717$	0.541140	+	0.541140i	0.0202093	+	0.0202093i
$718$	0.539805	+	15.9361i	0.0201453	+	0.594729i
$719$	27.1243			1.01157			0.505784	−	0.862660i	$-0.331203\pi$
$719$	27.1243			1.01157			0.505784	+	0.862660i	$0.331203\pi$
$720$	1.23920	+	0.941965i	0.0461824	+	0.0351050i
$721$	−18.1400			−0.675567
$722$	−0.0478764	−	1.41340i	−0.00178178	−	0.0526014i
$723$	31.2476	+	31.2476i	1.16211	+	1.16211i
$724$	6.62876	−	7.59336i	0.246356	−	0.282205i
$725$	−9.88073	+	9.88073i	−0.366961	+	0.366961i
$726$	11.5464	−	12.3560i	0.428527	−	0.458575i
$727$		−	41.3302i		−	1.53285i	−0.642331	−	0.766427i	$-0.722033\pi$
$727$		−	41.3302i		−	1.53285i	0.642331	−	0.766427i	$-0.277967\pi$
$728$	2.23419	−	2.74136i	0.0828047	−	0.101602i
$729$		−	29.9716i		−	1.11006i
$730$	−1.03821	−	0.970182i	−0.0384260	−	0.0359080i
$731$	−10.6172	+	10.6172i	−0.392692	+	0.392692i
$732$	−0.122864	−	1.81152i	−0.00454120	−	0.0669556i
$733$	−29.9108	−	29.9108i	−1.10478	−	1.10478i	−0.993826	−	0.110953i	$-0.964610\pi$
$733$	−29.9108	−	29.9108i	−1.10478	−	1.10478i	−0.110953	−	0.993826i	$-0.535390\pi$
$734$	−40.7624	+	1.38075i	−1.50457	+	0.0509645i
$735$	4.38592			0.161777
$736$	−7.85156	−	45.9324i	−0.289412	−	1.69309i
$737$	34.3104			1.26384
$738$	1.74545	−	0.0591239i	0.0642509	−	0.00217638i
$739$	3.69323	+	3.69323i	0.135858	+	0.135858i	0.771765	−	0.635908i	$-0.219374\pi$
$739$	3.69323	+	3.69323i	0.135858	+	0.135858i	−0.635908	+	0.771765i	$0.719374\pi$
$740$	0.123109	+	1.81512i	0.00452557	+	0.0667251i
$741$	0.795533	−	0.795533i	0.0292246	−	0.0292246i
$742$	5.01949	+	4.69058i	0.184271	+	0.172197i
$743$		−	45.8019i		−	1.68031i	−0.542349	−	0.840154i	$-0.682465\pi$
$743$		−	45.8019i		−	1.68031i	0.542349	−	0.840154i	$-0.317535\pi$
$744$	24.3048	+	19.8083i	0.891056	+	0.726206i
$745$			7.09380i			0.259897i
$746$	11.3909	−	12.1897i	0.417051	−	0.446295i
$747$	−4.19056	+	4.19056i	−0.153325	+	0.153325i
$748$	−8.29765	+	9.50511i	−0.303392	+	0.347541i
$749$	9.86089	+	9.86089i	0.360309	+	0.360309i
$750$	−0.501819	−	14.8146i	−0.0183238	−	0.540954i
$751$	−19.1263			−0.697929			−0.348965	−	0.937136i	$-0.613467\pi$
$751$	−19.1263			−0.697929			−0.348965	+	0.937136i	$0.613467\pi$
$752$	−7.20688	+	0.982119i	−0.262808	+	0.0358142i
$753$	−6.98834			−0.254669
$754$	−0.106829	−	3.15379i	−0.00389047	−	0.114854i
$755$	−2.10313	−	2.10313i	−0.0765408	−	0.0765408i
$756$	−14.5598	−	12.7102i	−0.529533	−	0.462265i
$757$	−8.77302	+	8.77302i	−0.318861	+	0.318861i	−0.848329	−	0.529469i	$-0.822391\pi$
$757$	−8.77302	+	8.77302i	−0.318861	+	0.318861i	0.529469	+	0.848329i	$0.322391\pi$
$758$	−27.0850	+	28.9842i	−0.983771	+	1.05275i
$759$			55.6492i			2.01994i
$760$	1.98362	−	0.202193i	0.0719535	−	0.00733432i
$761$			40.2885i			1.46046i	0.683203	+	0.730228i	$0.260586\pi$
$761$			40.2885i			1.46046i	−0.683203	+	0.730228i	$0.739414\pi$
$762$	18.4247	+	17.2174i	0.667458	+	0.623722i
$763$	15.0883	−	15.0883i	0.546234	−	0.546234i
$764$	22.8002	−	1.54641i	0.824883	−	0.0559470i
$765$	0.402048	+	0.402048i	0.0145361	+	0.0145361i
$766$	26.3455	−	0.892404i	0.951901	−	0.0322439i
$767$	−2.96409			−0.107027
$768$	−21.7926	−	12.3194i	−0.786371	−	0.444539i
$769$	28.8691			1.04105			0.520523	−	0.853848i	$-0.325737\pi$
$769$	28.8691			1.04105			0.520523	+	0.853848i	$0.325737\pi$
$770$	−7.48061	+	0.253392i	−0.269583	+	0.00913161i
$771$	−29.4813	−	29.4813i	−1.06174	−	1.06174i
$772$	−16.2345	+	1.10109i	−0.584291	+	0.0396290i
$773$	22.1239	−	22.1239i	0.795741	−	0.795741i	−0.186680	−	0.982421i	$-0.559773\pi$
$773$	22.1239	−	22.1239i	0.795741	−	0.795741i	0.982421	+	0.186680i	$0.0597727\pi$
$774$	−5.86157	−	5.47748i	−0.210690	−	0.196884i
$775$			31.9046i			1.14605i
$776$	6.75266	−	0.688309i	0.242406	−	0.0247088i
$777$		−	3.51055i		−	0.125940i
$778$	9.23152	−	9.87885i	0.330966	−	0.354174i
$779$	1.58188	−	1.58188i	0.0566768	−	0.0566768i
$780$	1.19495	+	1.04315i	0.0427861	+	0.0373509i
$781$	48.7408	+	48.7408i	1.74408	+	1.74408i
$782$	−0.576239	−	17.0117i	−0.0206063	−	0.608336i
$783$	−17.2455			−0.616305
$784$	15.7602	−	2.14773i	0.562866	−	0.0767046i
$785$	−2.98682			−0.106604
$786$	0.972775	+	28.7182i	0.0346977	+	1.02434i
$787$	−15.7724	−	15.7724i	−0.562225	−	0.562225i	0.367714	−	0.929939i	$-0.380141\pi$
$787$	−15.7724	−	15.7724i	−0.562225	−	0.562225i	−0.929939	+	0.367714i	$0.880141\pi$
$788$	32.6269	−	37.3747i	1.16229	−	1.33142i
$789$	0.0107065	−	0.0107065i	0.000381161	−	0.000381161i
$790$	−1.95208	+	2.08897i	−0.0694520	+	0.0743221i
$791$		−	18.4622i		−	0.656440i
$792$	−5.22575	−	4.25896i	−0.185689	−	0.151335i
$793$			0.417228i			0.0148162i
$794$	−39.6679	−	37.0686i	−1.40776	−	1.31552i
$795$	−2.17887	+	2.17887i	−0.0772767	+	0.0772767i
$796$	1.06525	+	15.7061i	0.0377568	+	0.556686i
$797$	−1.52923	−	1.52923i	−0.0541679	−	0.0541679i	0.679504	−	0.733672i	$-0.262195\pi$
$797$	−1.52923	−	1.52923i	−0.0541679	−	0.0541679i	−0.733672	+	0.679504i	$0.762195\pi$
$798$	−3.84527	+	0.130251i	−0.136121	+	0.00461085i
$799$	−2.65684			−0.0939923
$800$	−4.29204	−	25.1089i	−0.151747	−	0.887733i
$801$	9.19305			0.324820
$802$	−0.285359	+	0.00966601i	−0.0100764	+	0.000341319i
$803$	4.35162	+	4.35162i	0.153565	+	0.153565i
$804$	1.68264	+	24.8089i	0.0593421	+	0.874941i
$805$	7.14000	−	7.14000i	0.251652	−	0.251652i
$806$	−5.26423	−	4.91928i	−0.185425	−	0.173274i
$807$		−	32.4899i		−	1.14370i
$808$	2.40872	−	2.95550i	0.0847383	−	0.103974i
$809$			1.75910i			0.0618465i	0.999522	+	0.0309233i	$0.00984475\pi$
$809$			1.75910i			0.0618465i	−0.999522	+	0.0309233i	$0.990155\pi$
$810$	4.79147	−	5.12745i	0.168355	−	0.180160i
$811$	−22.8111	+	22.8111i	−0.801005	+	0.801005i	−0.983253	−	0.182248i	$-0.941663\pi$
$811$	−22.8111	+	22.8111i	−0.801005	+	0.801005i	0.182248	+	0.983253i	$0.441663\pi$
$812$	−7.09693	+	8.12966i	−0.249053	+	0.285295i
$813$	22.2927	+	22.2927i	0.781840	+	0.781840i
$814$	−0.266742	−	7.87474i	−0.00934931	−	0.276009i
$815$	−3.67559			−0.128750
$816$	−7.27981	−	5.53365i	−0.254844	−	0.193717i
$817$	−10.2765			−0.359528
$818$	−0.500395	−	14.7726i	−0.0174959	−	0.516513i
$819$	0.488048	+	0.488048i	0.0170538	+	0.0170538i
$820$	2.37611	+	2.07426i	0.0829772	+	0.0724364i
$821$	−24.4235	+	24.4235i	−0.852387	+	0.852387i	−0.990427	−	0.138040i	$-0.955920\pi$
$821$	−24.4235	+	24.4235i	−0.852387	+	0.852387i	0.138040	+	0.990427i	$0.455920\pi$
$822$	−27.3481	+	29.2658i	−0.953875	+	1.02076i
$823$			31.1432i			1.08558i	0.839868	+	0.542791i	$0.182633\pi$
$823$			31.1432i			1.08558i	−0.839868	+	0.542791i	$0.817367\pi$
$824$	−2.99218	−	29.3549i	−0.104238	−	1.02263i
$825$			30.4205i			1.05911i
$826$	7.40623	+	6.92092i	0.257696	+	0.240810i
$827$	−8.75102	+	8.75102i	−0.304303	+	0.304303i	−0.842695	−	0.538392i	$-0.819032\pi$
$827$	−8.75102	+	8.75102i	−0.304303	+	0.304303i	0.538392	+	0.842695i	$0.319032\pi$
$828$	9.07368	−	0.615414i	0.315332	−	0.0213871i
$829$	7.14743	+	7.14743i	0.248240	+	0.248240i	0.820248	−	0.572008i	$-0.193835\pi$
$829$	7.14743	+	7.14743i	0.248240	+	0.248240i	−0.572008	+	0.820248i	$0.693835\pi$
$830$	−10.6969	+	0.362339i	−0.371296	+	0.0125770i
$831$	24.8078			0.860573
$832$	4.80471	+	3.16328i	0.166574	+	0.109667i
$833$	5.81007			0.201307
$834$	−15.9657	+	0.540808i	−0.552847	+	0.0187267i
$835$	12.3054	+	12.3054i	0.425846	+	0.425846i
$836$	−8.61568	+	0.584351i	−0.297980	+	0.0202102i
$837$	−27.8427	+	27.8427i	−0.962385	+	0.962385i
$838$	13.4232	+	12.5436i	0.463695	+	0.433311i
$839$			17.3145i			0.597761i	0.954290	+	0.298881i	$0.0966133\pi$
$839$			17.3145i			0.597761i	−0.954290	+	0.298881i	$0.903387\pi$
$840$	−0.550082	−	5.39659i	−0.0189796	−	0.186200i
$841$		−	19.3707i		−	0.667955i
$842$	−1.69779	+	1.81684i	−0.0585096	+	0.0626124i
$843$	−9.43387	+	9.43387i	−0.324920	+	0.324920i
$844$	−5.58914	−	4.87913i	−0.192386	−	0.167947i
$845$	6.22243	+	6.22243i	0.214058	+	0.214058i
$846$	−0.0480570	−	1.41873i	−0.00165223	−	0.0487771i
$847$	13.2896			0.456638
$848$	−6.76254	+	8.89647i	−0.232226	+	0.305506i
$849$	−38.5644			−1.32353
$850$	−0.315000	−	9.29940i	−0.0108044	−	0.318967i
$851$	7.51617	+	7.51617i	0.257651	+	0.257651i
$852$	−32.8528	+	37.6334i	−1.12552	+	1.28930i
$853$	20.9166	−	20.9166i	0.716171	−	0.716171i	−0.251648	−	0.967819i	$-0.580972\pi$
$853$	20.9166	−	20.9166i	0.716171	−	0.716171i	0.967819	+	0.251648i	$0.0809724\pi$
$854$	0.974196	−	1.04251i	0.0333363	−	0.0356739i
$855$			0.389144i			0.0133084i
$856$	−14.3308	+	17.5839i	−0.489815	+	0.601004i
$857$			51.5798i			1.76193i	0.473180	+	0.880966i	$0.343106\pi$
$857$			51.5798i			1.76193i	−0.473180	+	0.880966i	$0.656894\pi$
$858$	−5.01936	−	4.69045i	−0.171358	−	0.160129i
$859$	33.4783	−	33.4783i	1.14226	−	1.14226i	0.154229	−	0.988035i	$-0.450711\pi$
$859$	33.4783	−	33.4783i	1.14226	−	1.14226i	0.988035	−	0.154229i	$-0.0492894\pi$
$860$	−0.980436	−	14.4556i	−0.0334326	−	0.492931i
$861$	−4.30363	−	4.30363i	−0.146667	−	0.146667i
$862$	−46.8148	+	1.58576i	−1.59452	+	0.0540113i
$863$	28.5808			0.972902			0.486451	−	0.873708i	$-0.338291\pi$
$863$	28.5808			0.972902			0.486451	+	0.873708i	$0.338291\pi$
$864$	18.1666	−	25.6578i	0.618039	−	0.872895i
$865$	−4.07929			−0.138700
$866$	21.3108	−	0.721865i	0.724171	−	0.0245300i
$867$	16.4459	+	16.4459i	0.558534	+	0.558534i
$868$	1.66733	+	24.5831i	0.0565929	+	0.834406i
$869$	8.75581	−	8.75581i	0.297021	−	0.297021i
$870$	−3.53654	−	3.30480i	−0.119900	−	0.112043i
$871$		−	5.71398i		−	0.193611i
$872$	26.9054	+	21.9277i	0.911131	+	0.742567i
$873$			1.32473i			0.0448352i
$874$	7.95396	−	8.51170i	0.269047	−	0.287913i
$875$	8.23688	−	8.23688i	0.278457	−	0.278457i
$876$	−2.93312	+	3.35994i	−0.0991010	+	0.113522i
$877$	23.9304	+	23.9304i	0.808074	+	0.808074i	0.984342	−	0.176268i	$-0.0564027\pi$
$877$	23.9304	+	23.9304i	0.808074	+	0.808074i	−0.176268	+	0.984342i	$0.556403\pi$
$878$	−0.542216	−	16.0072i	−0.0182989	−	0.540218i
$879$	50.2350			1.69438
$880$	−1.64398	−	12.0637i	−0.0554184	−	0.406666i
$881$	−30.5604			−1.02961			−0.514804	−	0.857308i	$-0.672135\pi$
$881$	−30.5604			−1.02961			−0.514804	+	0.857308i	$0.672135\pi$
$882$	0.105093	+	3.10253i	0.00353865	+	0.104468i
$883$	26.2790	+	26.2790i	0.884360	+	0.884360i	0.993974	−	0.109614i	$-0.0349615\pi$
$883$	26.2790	+	26.2790i	0.884360	+	0.884360i	−0.109614	+	0.993974i	$0.534962\pi$
$884$	1.58296	+	1.38187i	0.0532407	+	0.0464774i
$885$	−3.21492	+	3.21492i	−0.108068	+	0.108068i
$886$	−16.4387	+	17.5914i	−0.552268	+	0.590994i
$887$		−	52.6179i		−	1.76674i	−0.468679	−	0.883368i	$-0.655270\pi$
$887$		−	52.6179i		−	1.76674i	0.468679	−	0.883368i	$-0.344730\pi$
$888$	5.68092	−	0.579064i	0.190639	−	0.0194321i
$889$			19.8169i			0.664637i
$890$	12.1307	+	11.3358i	0.406620	+	0.379976i
$891$	−21.4915	+	21.4915i	−0.719992	+	0.719992i
$892$	41.4562	−	2.81173i	1.38806	−	0.0941436i
$893$	−1.28578	−	1.28578i	−0.0430271	−	0.0430271i
$894$	22.2531	−	0.753784i	0.744256	−	0.0252103i
$895$	−9.32548			−0.311716
$896$	−4.61929	−	19.1226i	−0.154320	−	0.638841i
$897$	9.26769			0.309439
$898$	17.9281	−	0.607281i	0.598269	−	0.0202652i
$899$	15.5464	+	15.5464i	0.518501	+	0.518501i
$900$	4.96011	−	0.336415i	0.165337	−	0.0112138i
$901$	−2.88637	+	2.88637i	−0.0961590	+	0.0961590i
$902$	−9.98077	−	9.32676i	−0.332323	−	0.310547i
$903$			27.9579i			0.930380i
$904$	29.8763	−	3.04534i	0.993671	−	0.101286i
$905$			3.55283i			0.118100i
$906$	−6.37401	+	6.82096i	−0.211762	+	0.226611i
$907$	11.5897	−	11.5897i	0.384831	−	0.384831i	−0.488008	−	0.872839i	$-0.662276\pi$
$907$	11.5897	−	11.5897i	0.384831	−	0.384831i	0.872839	+	0.488008i	$0.162276\pi$
$908$	14.0142	+	12.2339i	0.465077	+	0.405997i
$909$	0.526172	+	0.526172i	0.0174520	+	0.0174520i
$910$	0.0421993	+	1.24580i	0.00139889	+	0.0412980i
$911$	−47.2576			−1.56571			−0.782857	−	0.622202i	$-0.786238\pi$
$911$	−47.2576			−1.56571			−0.782857	+	0.622202i	$0.786238\pi$
$912$	−0.845055	−	6.20110i	−0.0279826	−	0.205339i
$913$	46.3545			1.53411
$914$	1.40821	+	41.5730i	0.0465794	+	1.37511i
$915$	0.452535	+	0.452535i	0.0149603	+	0.0149603i
$916$	21.5968	−	24.7395i	0.713577	−	0.817416i
$917$	−15.9672	+	15.9672i	−0.527283	+	0.527283i
$918$	7.84056	−	8.39035i	0.258777	−	0.276923i
$919$			26.7465i			0.882286i	0.897437	+	0.441143i	$0.145427\pi$
$919$			26.7465i			0.882286i	−0.897437	+	0.441143i	$0.854573\pi$
$920$	12.7320	+	10.3765i	0.419761	+	0.342103i
$921$			10.2135i			0.336546i
$922$	−42.1173	−	39.3575i	−1.38706	−	1.29617i
$923$	8.11719	−	8.11719i	0.267181	−	0.267181i
$924$	1.58977	+	23.4396i	0.0522997	+	0.771107i
$925$	4.10871	+	4.10871i	0.135093	+	0.135093i
$926$	49.8697	−	1.68924i	1.63882	−	0.0555120i
$927$	5.75879			0.189144
$928$	−14.3264	−	10.1436i	−0.470287	−	0.332979i
$929$	−41.7545			−1.36992			−0.684961	−	0.728580i	$-0.740181\pi$
$929$	−41.7545			−1.36992			−0.684961	+	0.728580i	$0.740181\pi$
$930$	−11.0453	+	0.374138i	−0.362188	+	0.0122685i
$931$	2.81179	+	2.81179i	0.0921528	+	0.0921528i
$932$	−1.23186	−	18.1626i	−0.0403509	−	0.594935i
$933$	−12.9336	+	12.9336i	−0.423426	+	0.423426i
$934$	2.73571	+	2.55645i	0.0895151	+	0.0836495i
$935$		−	4.44731i		−	0.145443i
$936$	−0.709277	+	0.870284i	−0.0231835	+	0.0284461i
$937$			51.6397i			1.68699i	0.537133	+	0.843497i	$0.319507\pi$
$937$			51.6397i			1.68699i	−0.537133	+	0.843497i	$0.680493\pi$
$938$	−13.3417	+	14.2772i	−0.435622	+	0.466168i
$939$	23.9436	−	23.9436i	0.781369	−	0.781369i
$940$	1.68600	−	1.93134i	0.0549913	−	0.0629935i
$941$	16.9364	+	16.9364i	0.552110	+	0.552110i	0.927049	−	0.374939i	$-0.122336\pi$
$941$	16.9364	+	16.9364i	0.552110	+	0.552110i	−0.374939	+	0.927049i	$0.622336\pi$
$942$	0.317378	+	9.36961i	0.0103407	+	0.305278i
$943$	18.4284			0.600111
$944$	−9.97808	+	13.1267i	−0.324759	+	0.427237i
$945$	6.81231			0.221604
$946$	2.12433	+	62.7142i	0.0690679	+	2.03901i
$947$	29.4810	+	29.4810i	0.958004	+	0.958004i	0.999153	−	0.0411494i	$-0.0131020\pi$
$947$	29.4810	+	29.4810i	0.958004	+	0.958004i	−0.0411494	+	0.999153i	$0.513102\pi$
$948$	6.76048	+	5.90168i	0.219570	+	0.191678i
$949$	0.724709	−	0.724709i	0.0235251	−	0.0235251i
$950$	4.34802	−	4.65291i	0.141068	−	0.150960i
$951$		−	22.6667i		−	0.735018i
$952$	−0.728699	−	7.14891i	−0.0236173	−	0.231698i
$953$			8.99500i			0.291377i	0.989331	+	0.145688i	$0.0465397\pi$
$953$			8.99500i			0.291377i	−0.989331	+	0.145688i	$0.953460\pi$
$954$	−1.59351	−	1.48909i	−0.0515918	−	0.0482112i
$955$	−5.69573	+	5.69573i	−0.184309	+	0.184309i
$956$	−0.976009	+	0.0661970i	−0.0315664	+	0.00214096i
$957$	14.8232	+	14.8232i	0.479167	+	0.479167i
$958$	28.0187	−	0.949080i	0.905242	−	0.0306634i
$959$	−31.4771			−1.01645
$960$	8.64226	−	1.78033i	0.278928	−	0.0574601i
$961$	19.1989			0.619321
$962$	−1.31144	+	0.0444226i	−0.0422826	+	0.00143224i
$963$	−3.13048	−	3.13048i	−0.100878	−	0.100878i
$964$	−56.3587	+	3.82248i	−1.81519	+	0.123114i
$965$	4.05553	−	4.05553i	0.130552	−	0.130552i
$966$	−23.1567	−	21.6393i	−0.745056	−	0.696235i
$967$			26.8387i			0.863076i	0.902095	+	0.431538i	$0.142029\pi$
$967$			26.8387i			0.863076i	−0.902095	+	0.431538i	$0.857971\pi$
$968$	2.19213	+	21.5059i	0.0704576	+	0.691225i
$969$		−	2.28606i		−	0.0734387i
$970$	−1.63350	+	1.74804i	−0.0524484	+	0.0561261i
$971$	−21.3167	+	21.3167i	−0.684087	+	0.684087i	−0.960918	−	0.276832i	$-0.910716\pi$
$971$	−21.3167	+	21.3167i	−0.684087	+	0.684087i	0.276832	+	0.960918i	$0.410716\pi$
$972$	8.52608	+	7.44299i	0.273474	+	0.238734i
$973$	−8.87686	−	8.87686i	−0.284579	−	0.284579i
$974$	0.903342	+	26.6684i	0.0289449	+	0.854510i
$975$	5.06617			0.162247
$976$	1.84773	+	1.40452i	0.0591442	+	0.0449577i
$977$	−55.5506			−1.77722			−0.888611	−	0.458662i	$-0.848329\pi$
$977$	−55.5506			−1.77722			−0.888611	+	0.458662i	$0.848329\pi$
$978$	0.390566	+	11.5303i	0.0124889	+	0.368697i
$979$	−50.8451	−	50.8451i	−1.62502	−	1.62502i
$980$	−3.68700	+	4.22352i	−0.117777	+	0.134915i
$981$	−4.79000	+	4.79000i	−0.152933	+	0.152933i
$982$	26.9505	−	28.8403i	0.860025	−	0.920332i
$983$		−	9.08993i		−	0.289924i	−0.989437	−	0.144962i	$-0.953694\pi$
$983$		−	9.08993i		−	0.289924i	0.989437	−	0.144962i	$-0.0463060\pi$
$984$	6.25444	−	7.67421i	0.199384	−	0.244645i
$985$			17.4871i			0.557186i
$986$	−4.68488	−	4.37789i	−0.149197	−	0.139421i
$987$	−3.49807	+	3.49807i	−0.111345	+	0.111345i
$988$	0.0973165	+	1.43484i	0.00309605	+	0.0456482i
$989$	−59.8586	−	59.8586i	−1.90339	−	1.90339i
$990$	2.37483	−	0.0804430i	0.0754771	−	0.00255665i
$991$	30.7572			0.977035			0.488518	−	0.872554i	$-0.337538\pi$
$991$	30.7572			0.977035			0.488518	+	0.872554i	$0.337538\pi$
$992$	−39.5065	+	6.75313i	−1.25433	+	0.214412i
$993$	54.5422			1.73084
$994$	−39.2351	+	1.32901i	−1.24446	+	0.0421538i
$995$	−3.92353	−	3.92353i	−0.124384	−	0.124384i
$996$	2.27330	+	33.5176i	0.0720324	+	1.06205i
$997$	−5.70755	+	5.70755i	−0.180760	+	0.180760i	−0.791687	−	0.610927i	$-0.790797\pi$
$997$	−5.70755	+	5.70755i	−0.180760	+	0.180760i	0.610927	+	0.791687i	$0.290797\pi$
$998$	34.8663	+	32.5816i	1.10367	+	1.03135i
$999$			7.17122i			0.226887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.1	✓	68
4.3	odd	2		1216.2.k.b.913.25		68
16.5	even	4	inner	304.2.k.b.229.1	yes	68
16.11	odd	4		1216.2.k.b.305.25		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.1	✓	68	1.1	even	1	trivial
304.2.k.b.229.1	yes	68	16.5	even	4	inner
1216.2.k.b.305.25		68	16.11	odd	4
1216.2.k.b.913.25		68	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41340 + 0.0478764i) q^{2} +(-1.10634 - 1.10634i) q^{3} +(1.99542 - 0.135337i) q^{4} +(-0.498475 + 0.498475i) q^{5} +(1.61667 + 1.51074i) q^{6} +1.73883i q^{7} +(-2.81385 + 0.286820i) q^{8} -0.552016i q^{9} +O(q^{10})\)	\(q+(-1.41340 + 0.0478764i) q^{2} +(-1.10634 - 1.10634i) q^{3} +(1.99542 - 0.135337i) q^{4} +(-0.498475 + 0.498475i) q^{5} +(1.61667 + 1.51074i) q^{6} +1.73883i q^{7} +(-2.81385 + 0.286820i) q^{8} -0.552016i q^{9} +(0.680681 - 0.728411i) q^{10} +(-3.05310 + 3.05310i) q^{11} +(-2.35734 - 2.05788i) q^{12} +(0.508457 + 0.508457i) q^{13} +(-0.0832489 - 2.45766i) q^{14} +1.10297 q^{15} +(3.96337 - 0.540108i) q^{16} +1.46111 q^{17} +(0.0264286 + 0.780221i) q^{18} +(0.707107 + 0.707107i) q^{19} +(-0.927202 + 1.06213i) q^{20} +(1.92374 - 1.92374i) q^{21} +(4.16909 - 4.46144i) q^{22} +8.23755i q^{23} +(3.43040 + 2.79576i) q^{24} +4.50305i q^{25} +(-0.742998 - 0.694311i) q^{26} +(-3.92974 + 3.92974i) q^{27} +(0.235328 + 3.46969i) q^{28} +(2.19423 + 2.19423i) q^{29} +(-1.55894 + 0.0528061i) q^{30} +7.08512 q^{31} +(-5.57598 + 0.953143i) q^{32} +6.75555 q^{33} +(-2.06514 + 0.0699527i) q^{34} +(-0.866762 - 0.866762i) q^{35} +(-0.0747084 - 1.10150i) q^{36} +(0.912428 - 0.912428i) q^{37} +(-1.03328 - 0.965573i) q^{38} -1.12505i q^{39} +(1.25966 - 1.54560i) q^{40} -2.23712i q^{41} +(-2.62692 + 2.81112i) q^{42} +(-7.26655 + 7.26655i) q^{43} +(-5.67901 + 6.50541i) q^{44} +(0.275166 + 0.275166i) q^{45} +(-0.394384 - 11.6430i) q^{46} -1.81837 q^{47} +(-4.98238 - 3.78729i) q^{48} +3.97648 q^{49} +(-0.215590 - 6.36462i) q^{50} +(-1.61649 - 1.61649i) q^{51} +(1.08340 + 0.945770i) q^{52} +(-1.97547 + 1.97547i) q^{53} +(5.36617 - 5.74245i) q^{54} -3.04379i q^{55} +(-0.498730 - 4.89280i) q^{56} -1.56460i q^{57} +(-3.20639 - 2.99628i) q^{58} +(-2.91479 + 2.91479i) q^{59} +(2.20088 - 0.149273i) q^{60} +(0.410289 + 0.410289i) q^{61} +(-10.0141 + 0.339210i) q^{62} +0.959862 q^{63} +(7.83547 - 1.61413i) q^{64} -0.506906 q^{65} +(-9.54831 + 0.323431i) q^{66} +(-5.61894 - 5.61894i) q^{67} +(2.91552 - 0.197743i) q^{68} +(9.11355 - 9.11355i) q^{69} +(1.26658 + 1.18359i) q^{70} -15.9644i q^{71} +(0.158329 + 1.55329i) q^{72} -1.42531i q^{73} +(-1.24594 + 1.33331i) q^{74} +(4.98191 - 4.98191i) q^{75} +(1.50667 + 1.31527i) q^{76} +(-5.30882 - 5.30882i) q^{77} +(0.0538636 + 1.59015i) q^{78} -2.86784 q^{79} +(-1.70641 + 2.24487i) q^{80} +7.03923 q^{81} +(0.107105 + 3.16195i) q^{82} +(-7.59138 - 7.59138i) q^{83} +(3.57830 - 4.09901i) q^{84} +(-0.728326 + 0.728326i) q^{85} +(9.92267 - 10.6185i) q^{86} -4.85514i q^{87} +(7.71527 - 9.46665i) q^{88} +16.6536i q^{89} +(-0.402095 - 0.375747i) q^{90} +(-0.884119 + 0.884119i) q^{91} +(1.11485 + 16.4373i) q^{92} +(-7.83856 - 7.83856i) q^{93} +(2.57009 - 0.0870572i) q^{94} -0.704950 q^{95} +(7.22344 + 5.11443i) q^{96} -2.39980 q^{97} +(-5.62036 + 0.190379i) q^{98} +(1.68536 + 1.68536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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