LMFDB - Embedded newform 51.3.j.a.37.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(7,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.j (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	51.37
Dual form			51.3.j.a.40.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.76539 + 1.14546i) q^{2} +(-1.69877 - 0.337906i) q^{3} +(3.50687 - 3.50687i) q^{4} +(-1.01802 - 1.52358i) q^{5} +(5.08482 - 1.01143i) q^{6} +(5.94423 - 8.89617i) q^{7} +(-1.09904 + 2.65331i) q^{8} +(2.77164 + 1.14805i) q^{9} +(4.56044 + 3.04719i) q^{10} +(-1.10464 - 5.55340i) q^{11} +(-7.14237 + 4.77238i) q^{12} +(-7.64701 - 7.64701i) q^{13} +(-6.24789 + 31.4103i) q^{14} +(1.21456 + 2.93221i) q^{15} +11.2415i q^{16} +(-13.7696 - 9.96991i) q^{17} -8.97971 q^{18} +(-10.0649 + 4.16901i) q^{19} +(-8.91309 - 1.77292i) q^{20} +(-13.1040 + 13.1040i) q^{21} +(9.41598 + 14.0920i) q^{22} +(35.7162 - 7.10439i) q^{23} +(2.76358 - 4.13598i) q^{24} +(8.28216 - 19.9949i) q^{25} +(29.9063 + 12.3876i) q^{26} +(-4.32044 - 2.88683i) q^{27} +(-10.3521 - 52.0434i) q^{28} +(16.5449 - 11.0549i) q^{29} +(-6.71748 - 6.71748i) q^{30} +(-8.38326 + 42.1455i) q^{31} +(-17.2729 - 41.7005i) q^{32} +9.80722i q^{33} +(49.4984 + 11.7982i) q^{34} -19.6054 q^{35} +(13.7459 - 5.69372i) q^{36} +(-40.0038 - 7.95725i) q^{37} +(23.0579 - 23.0579i) q^{38} +(10.4065 + 15.5745i) q^{39} +(5.16137 - 1.02666i) q^{40} +(-0.900494 + 1.34768i) q^{41} +(21.2275 - 51.2476i) q^{42} +(47.3255 + 19.6029i) q^{43} +(-23.3489 - 15.6013i) q^{44} +(-1.07245 - 5.39156i) q^{45} +(-90.6314 + 60.5579i) q^{46} +(22.5271 + 22.5271i) q^{47} +(3.79859 - 19.0968i) q^{48} +(-25.0565 - 60.4917i) q^{49} +64.7806i q^{50} +(20.0224 + 21.5894i) q^{51} -53.6342 q^{52} +(-76.5589 + 31.7117i) q^{53} +(15.2545 + 3.03430i) q^{54} +(-7.33651 + 7.33651i) q^{55} +(17.0713 + 25.5491i) q^{56} +(18.5066 - 3.68120i) q^{57} +(-33.0900 + 49.5227i) q^{58} +(-7.23788 + 17.4738i) q^{59} +(14.5422 + 6.02358i) q^{60} +(89.1552 + 59.5716i) q^{61} +(-25.0931 - 126.151i) q^{62} +(26.6885 - 17.8327i) q^{63} +(63.7368 + 63.7368i) q^{64} +(-3.86600 + 19.4357i) q^{65} +(-11.2338 - 27.1208i) q^{66} -111.776i q^{67} +(-83.2513 + 13.3249i) q^{68} -63.0742 q^{69} +(54.2167 - 22.4573i) q^{70} +(99.1067 + 19.7135i) q^{71} +(-6.09226 + 6.09226i) q^{72} +(-5.05783 - 7.56958i) q^{73} +(119.741 - 23.8180i) q^{74} +(-20.8259 + 31.1681i) q^{75} +(-20.6761 + 49.9164i) q^{76} +(-55.9703 - 23.1837i) q^{77} +(-46.6181 - 31.1492i) q^{78} +(-15.5295 - 78.0722i) q^{79} +(17.1274 - 11.4442i) q^{80} +(6.36396 + 6.36396i) q^{81} +(0.946495 - 4.75835i) q^{82} +(25.9811 + 62.7240i) q^{83} +91.9078i q^{84} +(-1.17222 + 31.1287i) q^{85} -153.328 q^{86} +(-31.8415 + 13.1892i) q^{87} +(15.9489 + 3.17244i) q^{88} +(26.7368 - 26.7368i) q^{89} +(9.14157 + 13.6813i) q^{90} +(-113.485 + 22.5735i) q^{91} +(100.338 - 150.166i) q^{92} +(28.4824 - 68.7627i) q^{93} +(-88.1002 - 36.4923i) q^{94} +(16.5981 + 11.0905i) q^{95} +(15.2518 + 76.6762i) q^{96} +(-10.4438 + 6.97830i) q^{97} +(138.582 + 138.582i) q^{98} +(3.31392 - 16.6602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) $ 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−2.76539	+	1.14546i	−1.38270	+	0.572731i	−0.945201	−	0.326490i	$-0.894134\pi$
$2$	−2.76539	+	1.14546i	−1.38270	+	0.572731i	−0.437495	+	0.899221i	$0.644134\pi$
$3$	−1.69877	−	0.337906i	−0.566257	−	0.112635i
$3$	−1.69877	−	0.337906i	−0.566257	−	0.112635i
$4$	3.50687	−	3.50687i	0.876718	−	0.876718i
$5$	−1.01802	−	1.52358i	−0.203605	−	0.304716i	0.715589	−	0.698522i	$-0.246158\pi$
$5$	−1.01802	−	1.52358i	−0.203605	−	0.304716i	−0.919194	+	0.393805i	$0.871158\pi$
$6$	5.08482	−	1.01143i	0.847470	−	0.168572i
$7$	5.94423	−	8.89617i	0.849176	−	1.27088i	−0.111655	−	0.993747i	$-0.535615\pi$
$7$	5.94423	−	8.89617i	0.849176	−	1.27088i	0.960831	−	0.277135i	$-0.0893848\pi$
$8$	−1.09904	+	2.65331i	−0.137379	+	0.331663i
$9$	2.77164	+	1.14805i	0.307960	+	0.127561i
$10$	4.56044	+	3.04719i	0.456044	+	0.304719i
$11$	−1.10464	−	5.55340i	−0.100422	−	0.504855i	−0.997956	−	0.0639093i	$-0.979643\pi$
$11$	−1.10464	−	5.55340i	−0.100422	−	0.504855i	0.897534	−	0.440946i	$-0.145357\pi$
$12$	−7.14237	+	4.77238i	−0.595197	+	0.397698i
$13$	−7.64701	−	7.64701i	−0.588232	−	0.588232i	0.348921	−	0.937152i	$-0.386548\pi$
$13$	−7.64701	−	7.64701i	−0.588232	−	0.588232i	−0.937152	+	0.348921i	$0.886548\pi$
$14$	−6.24789	+	31.4103i	−0.446278	+	2.24359i
$15$	1.21456	+	2.93221i	0.0809708	+	0.195481i
$16$			11.2415i			0.702597i
$17$	−13.7696	−	9.96991i	−0.809974	−	0.586466i
$17$	−13.7696	−	9.96991i	−0.809974	−	0.586466i
$18$	−8.97971			−0.498873
$19$	−10.0649	+	4.16901i	−0.529730	+	0.219422i	−0.631485	−	0.775388i	$-0.717554\pi$
$19$	−10.0649	+	4.16901i	−0.529730	+	0.219422i	0.101755	+	0.994810i	$0.467554\pi$
$20$	−8.91309	−	1.77292i	−0.445655	−	0.0886462i
$21$	−13.1040	+	13.1040i	−0.623998	+	0.623998i
$22$	9.41598	+	14.0920i	0.427999	+	0.640546i
$23$	35.7162	−	7.10439i	1.55288	−	0.308887i	0.657243	−	0.753678i	$-0.271722\pi$
$23$	35.7162	−	7.10439i	1.55288	−	0.308887i	0.895634	+	0.444792i	$0.146722\pi$
$24$	2.76358	−	4.13598i	0.115149	−	0.172333i
$25$	8.28216	−	19.9949i	0.331286	−	0.799796i
$26$	29.9063	+	12.3876i	1.15024	+	0.476447i
$27$	−4.32044	−	2.88683i	−0.160016	−	0.106920i
$28$	−10.3521	−	52.0434i	−0.369717	−	1.85869i
$29$	16.5449	−	11.0549i	0.570513	−	0.381205i	−0.236595	−	0.971608i	$-0.576031\pi$
$29$	16.5449	−	11.0549i	0.570513	−	0.381205i	0.807108	+	0.590404i	$0.201031\pi$
$30$	−6.71748	−	6.71748i	−0.223916	−	0.223916i
$31$	−8.38326	+	42.1455i	−0.270428	+	1.35953i	0.571793	+	0.820398i	$0.306248\pi$
$31$	−8.38326	+	42.1455i	−0.270428	+	1.35953i	−0.842220	+	0.539133i	$0.818752\pi$
$32$	−17.2729	−	41.7005i	−0.539778	−	1.30314i
$33$			9.80722i			0.297189i
$34$	49.4984	+	11.7982i	1.45583	+	0.347006i
$35$	−19.6054			−0.560155
$36$	13.7459	−	5.69372i	0.381829	−	0.158159i
$37$	−40.0038	−	7.95725i	−1.08118	−	0.215061i	−0.377812	−	0.925882i	$-0.623323\pi$
$37$	−40.0038	−	7.95725i	−1.08118	−	0.215061i	−0.703372	+	0.710821i	$0.748323\pi$
$38$	23.0579	−	23.0579i	0.606786	−	0.606786i
$39$	10.4065	+	15.5745i	0.266834	+	0.399346i
$40$	5.16137	−	1.02666i	0.129034	−	0.0256665i
$41$	−0.900494	+	1.34768i	−0.0219633	+	0.0328703i	−0.842289	−	0.539027i	$-0.818792\pi$
$41$	−0.900494	+	1.34768i	−0.0219633	+	0.0328703i	0.820326	+	0.571897i	$0.193792\pi$
$42$	21.2275	−	51.2476i	0.505416	−	1.22018i
$43$	47.3255	+	19.6029i	1.10059	+	0.455881i	0.857689	−	0.514169i	$-0.171900\pi$
$43$	47.3255	+	19.6029i	1.10059	+	0.455881i	0.242905	+	0.970050i	$0.421900\pi$
$44$	−23.3489	−	15.6013i	−0.530657	−	0.354574i
$45$	−1.07245	−	5.39156i	−0.0238322	−	0.119812i
$46$	−90.6314	+	60.5579i	−1.97025	+	1.31648i
$47$	22.5271	+	22.5271i	0.479300	+	0.479300i	0.904908	−	0.425608i	$-0.139940\pi$
$47$	22.5271	+	22.5271i	0.479300	+	0.479300i	−0.425608	+	0.904908i	$0.639940\pi$
$48$	3.79859	−	19.0968i	0.0791373	−	0.397850i
$49$	−25.0565	−	60.4917i	−0.511357	−	1.23453i
$50$			64.7806i			1.29561i
$51$	20.0224	+	21.5894i	0.392596	+	0.423322i
$52$	−53.6342			−1.03143
$53$	−76.5589	+	31.7117i	−1.44451	+	0.598334i	−0.960886	−	0.276944i	$-0.910678\pi$
$53$	−76.5589	+	31.7117i	−1.44451	+	0.598334i	−0.483620	+	0.875278i	$0.660678\pi$
$54$	15.2545	+	3.03430i	0.282490	+	0.0561908i
$55$	−7.33651	+	7.33651i	−0.133391	+	0.133391i
$56$	17.0713	+	25.5491i	0.304845	+	0.456233i
$57$	18.5066	−	3.68120i	0.324678	−	0.0645825i
$58$	−33.0900	+	49.5227i	−0.570518	+	0.853840i
$59$	−7.23788	+	17.4738i	−0.122676	+	0.296166i	−0.973273	−	0.229653i	$-0.926241\pi$
$59$	−7.23788	+	17.4738i	−0.122676	+	0.296166i	0.850597	+	0.525819i	$0.176241\pi$
$60$	14.5422	+	6.02358i	0.242370	+	0.100393i
$61$	89.1552	+	59.5716i	1.46156	+	0.976584i	0.995789	+	0.0916799i	$0.0292236\pi$
$61$	89.1552	+	59.5716i	1.46156	+	0.976584i	0.465773	+	0.884904i	$0.345776\pi$
$62$	−25.0931	−	126.151i	−0.404727	−	2.03470i
$63$	26.6885	−	17.8327i	0.423627	−	0.283059i
$64$	63.7368	+	63.7368i	0.995887	+	0.995887i
$65$	−3.86600	+	19.4357i	−0.0594769	+	0.299011i
$66$	−11.2338	−	27.1208i	−0.170209	−	0.410921i
$67$		−	111.776i		−	1.66829i	−0.551542	−	0.834147i	$-0.685960\pi$
$67$		−	111.776i		−	1.66829i	0.551542	−	0.834147i	$-0.314040\pi$
$68$	−83.2513	+	13.3249i	−1.22428	+	0.195954i
$69$	−63.0742			−0.914119
$70$	54.2167	−	22.4573i	0.774524	−	0.320818i
$71$	99.1067	+	19.7135i	1.39587	+	0.277656i	0.835000	−	0.550249i	$-0.185467\pi$
$71$	99.1067	+	19.7135i	1.39587	+	0.277656i	0.560869	+	0.827905i	$0.310467\pi$
$72$	−6.09226	+	6.09226i	−0.0846147	+	0.0846147i
$73$	−5.05783	−	7.56958i	−0.0692854	−	0.103693i	0.795209	−	0.606336i	$-0.207361\pi$
$73$	−5.05783	−	7.56958i	−0.0692854	−	0.103693i	−0.864494	+	0.502643i	$0.832361\pi$
$74$	119.741	−	23.8180i	1.61812	−	0.321864i
$75$	−20.8259	+	31.1681i	−0.277678	+	0.415575i
$76$	−20.6761	+	49.9164i	−0.272054	+	0.656795i
$77$	−55.9703	−	23.1837i	−0.726887	−	0.301086i
$78$	−46.6181	−	31.1492i	−0.597668	−	0.399349i
$79$	−15.5295	−	78.0722i	−0.196576	−	0.988256i	−0.945506	−	0.325606i	$-0.894432\pi$
$79$	−15.5295	−	78.0722i	−0.196576	−	0.988256i	0.748929	−	0.662650i	$-0.230568\pi$
$80$	17.1274	−	11.4442i	0.214093	−	0.143052i
$81$	6.36396	+	6.36396i	0.0785674	+	0.0785674i
$82$	0.946495	−	4.75835i	0.0115426	−	0.0580287i
$83$	25.9811	+	62.7240i	0.313026	+	0.755711i	0.999590	+	0.0286416i	$0.00911814\pi$
$83$	25.9811	+	62.7240i	0.313026	+	0.755711i	−0.686564	+	0.727069i	$0.740882\pi$
$84$			91.9078i			1.09414i
$85$	−1.17222	+	31.1287i	−0.0137909	+	0.366220i
$86$	−153.328			−1.78288
$87$	−31.8415	+	13.1892i	−0.365994	+	0.151600i
$88$	15.9489	+	3.17244i	0.181238	+	0.0360504i
$89$	26.7368	−	26.7368i	0.300414	−	0.300414i	−0.540762	−	0.841176i	$-0.681864\pi$
$89$	26.7368	−	26.7368i	0.300414	−	0.300414i	0.841176	+	0.540762i	$0.181864\pi$
$90$	9.14157	+	13.6813i	0.101573	+	0.152015i
$91$	−113.485	+	22.5735i	−1.24709	+	0.248061i
$92$	100.338	−	150.166i	1.09063	−	1.63224i
$93$	28.4824	−	68.7627i	0.306263	−	0.739384i
$94$	−88.1002	−	36.4923i	−0.937236	−	0.388216i
$95$	16.5981	+	11.0905i	0.174717	+	0.116742i
$96$	15.2518	+	76.6762i	0.158873	+	0.798710i
$97$	−10.4438	+	6.97830i	−0.107668	+	0.0719412i	−0.608238	−	0.793754i	$-0.708124\pi$
$97$	−10.4438	+	6.97830i	−0.107668	+	0.0719412i	0.500571	+	0.865696i	$0.333124\pi$
$98$	138.582	+	138.582i	1.41410	+	1.41410i
$99$	3.31392	−	16.6602i	0.0334740	−	0.168285i
$100$	−41.0751	−	99.1641i	−0.410751	−	0.991641i
$101$		−	98.5500i		−	0.975743i	−0.872915	−	0.487871i	$-0.837773\pi$
$101$		−	98.5500i		−	0.975743i	0.872915	−	0.487871i	$-0.162227\pi$
$102$	−80.0997	−	36.7682i	−0.785291	−	0.360473i
$103$	97.0494			0.942227			0.471114	−	0.882073i	$-0.343852\pi$
$103$	97.0494			0.942227			0.471114	+	0.882073i	$0.343852\pi$
$104$	28.6942	−	11.8855i	0.275906	−	0.114284i
$105$	33.3051	+	6.62480i	0.317191	+	0.0630933i
$106$	175.391	−	175.391i	1.65463	−	1.65463i
$107$	33.8465	+	50.6549i	0.316323	+	0.473410i	0.955226	−	0.295876i	$-0.0956117\pi$
$107$	33.8465	+	50.6549i	0.316323	+	0.473410i	−0.638903	+	0.769287i	$0.720612\pi$
$108$	−25.2750	+	5.02751i	−0.234028	+	0.0465510i
$109$	−9.72246	+	14.5507i	−0.0891969	+	0.133493i	−0.873385	−	0.487031i	$-0.838080\pi$
$109$	−9.72246	+	14.5507i	−0.0891969	+	0.133493i	0.784188	+	0.620524i	$0.213080\pi$
$110$	11.8846	−	28.6920i	0.108042	−	0.260837i
$111$	65.2685	+	27.0351i	0.588004	+	0.243559i
$112$	100.007	+	66.8224i	0.892917	+	0.596628i
$113$	33.5914	+	168.875i	0.297269	+	1.49447i	0.783913	+	0.620871i	$0.213221\pi$
$113$	33.5914	+	168.875i	0.297269	+	1.49447i	−0.486644	+	0.873601i	$0.661779\pi$
$114$	−46.9614	+	31.3786i	−0.411942	+	0.275251i
$115$	−47.1841	−	47.1841i	−0.410296	−	0.410296i
$116$	19.2525	−	96.7890i	0.165970	−	0.834388i
$117$	−12.4156	−	29.9739i	−0.106116	−	0.256187i
$118$		−	56.6125i		−	0.479767i
$119$	−170.544	+	63.2329i	−1.43314	+	0.531369i
$120$	−9.11490			−0.0759575
$121$	82.1694	−	34.0357i	0.679086	−	0.281286i
$122$	−314.786	−	62.6149i	−2.58021	−	0.513237i
$123$	1.98512	−	1.98512i	0.0161392	−	0.0161392i
$124$	118.400	+	177.198i	0.954837	+	1.42902i
$125$	−83.8250	+	16.6738i	−0.670600	+	0.133391i
$126$	−53.3775	+	79.8851i	−0.423631	+	0.634008i
$127$	−3.41321	+	8.24022i	−0.0268757	+	0.0648836i	−0.936748	−	0.350006i	$-0.886180\pi$
$127$	−3.41321	+	8.24022i	−0.0268757	+	0.0648836i	0.909872	+	0.414889i	$0.136180\pi$
$128$	−82.4632	−	34.1574i	−0.644244	−	0.266854i
$129$	−73.7713	−	49.2924i	−0.571870	−	0.382111i
$130$	−11.5719	−	58.1757i	−0.0890143	−	0.447505i
$131$	−42.6658	+	28.5084i	−0.325693	+	0.217621i	−0.707657	−	0.706556i	$-0.750248\pi$
$131$	−42.6658	+	28.5084i	−0.325693	+	0.217621i	0.381964	+	0.924177i	$0.375248\pi$
$132$	34.3927	+	34.3927i	0.260551	+	0.260551i
$133$	−22.7398	+	114.320i	−0.170976	+	0.859552i
$134$	128.035	+	309.104i	0.955484	+	2.30674i
$135$			9.52141i			0.0705290i
$136$	41.5865	−	25.5776i	0.305783	−	0.188070i
$137$	12.0176			0.0877195			0.0438597	−	0.999038i	$-0.486035\pi$
$137$	12.0176			0.0877195			0.0438597	+	0.999038i	$0.486035\pi$
$138$	174.425	−	72.2491i	1.26395	−	0.523544i
$139$	151.967	+	30.2282i	1.09329	+	0.217469i	0.708623	−	0.705587i	$-0.249317\pi$
$139$	151.967	+	30.2282i	1.09329	+	0.217469i	0.384666	+	0.923056i	$0.374317\pi$
$140$	−68.7537	+	68.7537i	−0.491098	+	0.491098i
$141$	−30.6563	−	45.8804i	−0.217421	−	0.325393i
$142$	−296.650	+	59.0073i	−2.08908	+	0.415545i
$143$	−34.0197	+	50.9142i	−0.237900	+	0.356043i
$144$	−12.9059	+	31.1575i	−0.0896240	+	0.216372i
$145$	−33.6862	−	13.9533i	−0.232319	−	0.0962295i
$146$	22.6575	+	15.1393i	0.155189	+	0.103694i
$147$	22.1247	+	111.228i	0.150508	+	0.756655i
$148$	−168.193	+	112.383i	−1.13644	+	0.759346i
$149$	−157.894	−	157.894i	−1.05969	−	1.05969i	−0.998101	−	0.0615911i	$-0.980383\pi$
$149$	−157.894	−	157.894i	−1.05969	−	1.05969i	−0.0615911	−	0.998101i	$-0.519617\pi$
$150$	21.8898	−	110.047i	0.145932	−	0.733649i
$151$	−58.3798	−	140.941i	−0.386621	−	0.933386i	−0.990651	−	0.136424i	$-0.956439\pi$
$151$	−58.3798	−	140.941i	−0.386621	−	0.933386i	0.604029	−	0.796962i	$-0.293561\pi$
$152$		−	31.2871i		−	0.205836i
$153$	−26.7183	−	43.4411i	−0.174629	−	0.283929i
$154$	181.336			1.17750
$155$	72.7464	−	30.1326i	0.469332	−	0.194404i
$156$	91.1122	+	18.1233i	0.584053	+	0.116175i
$157$	−24.8438	+	24.8438i	−0.158241	+	0.158241i	−0.781787	−	0.623546i	$-0.785691\pi$
$157$	−24.8438	+	24.8438i	−0.158241	+	0.158241i	0.623546	+	0.781787i	$0.285691\pi$
$158$	132.374	+	198.112i	0.837810	+	1.25387i
$159$	140.771	−	28.0012i	0.885355	−	0.176108i
$160$	−45.9499	+	68.7688i	−0.287187	+	0.429805i
$161$	149.103	−	359.967i	0.926108	−	2.23582i
$162$	−24.8885	−	10.3092i	−0.153633	−	0.0636368i
$163$	47.4788	+	31.7243i	0.291281	+	0.194628i	0.692621	−	0.721301i	$-0.256456\pi$
$163$	47.4788	+	31.7243i	0.291281	+	0.194628i	−0.401341	+	0.915929i	$0.631456\pi$
$164$	1.56824	+	7.88407i	0.00956244	+	0.0480736i
$165$	14.9421	−	9.98400i	0.0905582	−	0.0605091i
$166$	−143.696	−	143.696i	−0.865638	−	0.865638i
$167$	34.2808	−	172.341i	0.205274	−	1.03198i	−0.731445	−	0.681900i	$-0.761154\pi$
$167$	34.2808	−	172.341i	0.205274	−	1.03198i	0.936719	−	0.350082i	$-0.113846\pi$
$168$	−20.3671	−	49.1705i	−0.121233	−	0.292682i
$169$		−	52.0464i		−	0.307967i
$170$	−32.4151	−	87.4257i	−0.190677	−	0.514269i
$171$	−32.6824			−0.191125
$172$	234.710	−	97.2199i	1.36459	−	0.565232i
$173$	95.1890	+	18.9343i	0.550226	+	0.109447i	0.462371	−	0.886687i	$-0.346999\pi$
$173$	95.1890	+	18.9343i	0.550226	+	0.109447i	0.0878547	+	0.996133i	$0.471999\pi$
$174$	72.9464	−	72.9464i	0.419232	−	0.419232i
$175$	−128.647	−	192.534i	−0.735126	−	1.10019i
$176$	62.4288	−	12.4179i	0.354709	−	0.0705561i
$177$	18.2000	−	27.2382i	0.102825	−	0.153888i
$178$	−43.3118	+	104.564i	−0.243324	+	0.587437i
$179$	88.6200	+	36.7076i	0.495084	+	0.205070i	0.616233	−	0.787564i	$-0.288658\pi$
$179$	88.6200	+	36.7076i	0.495084	+	0.205070i	−0.121149	+	0.992634i	$0.538658\pi$
$180$	−22.6685	−	15.1466i	−0.125936	−	0.0841477i
$181$	55.4271	+	278.651i	0.306227	+	1.53951i	0.760912	+	0.648855i	$0.224752\pi$
$181$	55.4271	+	278.651i	0.306227	+	1.53951i	−0.454686	+	0.890652i	$0.650248\pi$
$182$	287.973	−	192.417i	1.58227	−	1.05724i
$183$	−131.325	−	131.325i	−0.717621	−	0.717621i
$184$	−20.4032	+	102.574i	−0.110887	+	0.557467i
$185$	28.6014	+	69.0498i	0.154602	+	0.373242i
$186$			222.781i			1.19775i
$187$	−40.1565	+	87.4811i	−0.214741	+	0.467813i
$188$	157.999			0.840423
$189$	−51.3634	+	21.2754i	−0.271764	+	0.112568i
$190$	−58.6040	−	11.6571i	−0.308442	−	0.0613530i
$191$	25.8379	−	25.8379i	0.135277	−	0.135277i	−0.636226	−	0.771503i	$-0.719505\pi$
$191$	25.8379	−	25.8379i	0.135277	−	0.135277i	0.771503	+	0.636226i	$0.219505\pi$
$192$	−86.7371	−	129.811i	−0.451755	−	0.676100i
$193$	25.1712	−	5.00686i	0.130421	−	0.0259423i	−0.129448	−	0.991586i	$-0.541321\pi$
$193$	25.1712	−	5.00686i	0.130421	−	0.0259423i	0.259869	+	0.965644i	$0.416321\pi$
$194$	20.8877	−	31.2607i	0.107669	−	0.161137i
$195$	13.1349	−	31.7104i	0.0673584	−	0.162618i
$196$	−300.007	−	124.267i	−1.53065	−	0.634015i
$197$	−114.459	−	76.4791i	−0.581011	−	0.388219i	0.230052	−	0.973178i	$-0.426110\pi$
$197$	−114.459	−	76.4791i	−0.581011	−	0.388219i	−0.811062	+	0.584960i	$0.801110\pi$
$198$	9.91936	+	49.8680i	0.0500978	+	0.251858i
$199$	−197.687	+	132.091i	−0.993405	+	0.663772i	−0.942247	−	0.334919i	$-0.891291\pi$
$199$	−197.687	+	132.091i	−0.993405	+	0.663772i	−0.0511576	+	0.998691i	$0.516291\pi$
$200$	43.9502	+	43.9502i	0.219751	+	0.219751i
$201$	−37.7697	+	189.881i	−0.187909	+	0.944683i
$202$	112.885	+	272.529i	0.558838	+	1.34916i
$203$		−	212.899i		−	1.04876i
$204$	145.927	+	5.49524i	0.715331	+	0.0269375i
$205$	2.97003			0.0144880
$206$	−268.379	+	111.166i	−1.30281	+	0.539643i
$207$	107.149	+	21.3132i	0.517626	+	0.102962i
$208$	85.9642	−	85.9642i	0.413290	−	0.413290i
$209$	34.2703	+	51.2891i	0.163973	+	0.245402i
$210$	−99.6901	+	19.8296i	−0.474715	+	0.0944266i
$211$	−38.1257	+	57.0591i	−0.180690	+	0.270422i	−0.910747	−	0.412964i	$-0.864493\pi$
$211$	−38.1257	+	57.0591i	−0.180690	+	0.270422i	0.730057	+	0.683386i	$0.239493\pi$
$212$	−157.273	+	379.691i	−0.741855	+	1.79100i
$213$	−161.698	−	66.9776i	−0.759146	−	0.314449i
$214$	−151.622	−	101.311i	−0.708515	−	0.473415i
$215$	−18.3120	−	92.0605i	−0.0851720	−	0.428189i
$216$	12.4080	−	8.29073i	0.0574442	−	0.0383830i
$217$	325.101	+	325.101i	1.49816	+	1.49816i
$218$	10.2191	−	51.3751i	0.0468768	−	0.235665i
$219$	6.03428	+	14.5680i	0.0275538	+	0.0665208i
$220$			51.4565i			0.233893i
$221$	29.0560	+	181.536i	0.131475	+	0.821430i
$222$	−211.461			−0.952525
$223$	−279.797	+	115.896i	−1.25469	+	0.519711i	−0.908277	−	0.418370i	$-0.862602\pi$
$223$	−279.797	+	115.896i	−1.25469	+	0.519711i	−0.346417	+	0.938081i	$0.612602\pi$
$224$	−473.649	−	94.2146i	−2.11450	−	0.420601i
$225$	45.9103	−	45.9103i	0.204046	−	0.204046i
$226$	−286.334	−	428.529i	−1.26696	−	1.89614i
$227$	71.9272	−	14.3072i	0.316860	−	0.0630274i	−0.0340982	−	0.999418i	$-0.510856\pi$
$227$	71.9272	−	14.3072i	0.316860	−	0.0630274i	0.350958	+	0.936391i	$0.385856\pi$
$228$	51.9910	−	77.8100i	0.228031	−	0.341272i
$229$	−62.0965	+	149.914i	−0.271164	+	0.654648i	−0.999534	−	0.0305366i	$-0.990278\pi$
$229$	−62.0965	+	149.914i	−0.271164	+	0.654648i	0.728370	+	0.685184i	$0.240278\pi$
$230$	184.530	+	76.4348i	0.802304	+	0.332325i
$231$	87.2467	+	58.2964i	0.377691	+	0.252365i
$232$	11.1487	+	56.0484i	0.0480548	+	0.241588i
$233$	184.013	−	122.954i	0.789756	−	0.527698i	−0.0940412	−	0.995568i	$-0.529979\pi$
$233$	184.013	−	122.954i	0.789756	−	0.527698i	0.883797	+	0.467870i	$0.154979\pi$
$234$	68.6680	+	68.6680i	0.293453	+	0.293453i
$235$	11.3887	−	57.2550i	0.0484627	−	0.243638i
$236$	35.8960	+	86.6607i	0.152102	+	0.367206i
$237$			137.874i			0.581748i
$238$	399.189	−	370.215i	1.67726	−	1.55552i
$239$	282.155			1.18056			0.590282	−	0.807197i	$-0.299017\pi$
$239$	282.155			1.18056			0.590282	+	0.807197i	$0.299017\pi$
$240$	−32.9626	+	13.6536i	−0.137344	+	0.0568898i
$241$	315.661	+	62.7888i	1.30980	+	0.260534i	0.800124	−	0.599835i	$-0.204767\pi$
$241$	315.661	+	62.7888i	1.30980	+	0.260534i	0.509671	+	0.860369i	$0.329767\pi$
$242$	−188.244	+	188.244i	−0.777867	+	0.777867i
$243$	−8.66048	−	12.9613i	−0.0356398	−	0.0533388i
$244$	521.566	−	103.746i	2.13757	−	0.425189i
$245$	−66.6560	+	99.7577i	−0.272065	+	0.407174i
$246$	−3.21576	+	7.76352i	−0.0130722	+	0.0315590i
$247$	108.847	+	45.0858i	0.440675	+	0.182534i
$248$	−102.611	−	68.5627i	−0.413755	−	0.276462i
$249$	−22.9411	−	115.333i	−0.0921330	−	0.463184i
$250$	212.710	−	142.128i	0.850838	−	0.568512i
$251$	−129.692	−	129.692i	−0.516700	−	0.516700i	0.399871	−	0.916571i	$-0.369055\pi$
$251$	−129.692	−	129.692i	−0.516700	−	0.516700i	−0.916571	+	0.399871i	$0.869055\pi$
$252$	31.0562	−	156.130i	0.123239	−	0.619565i
$253$	−78.9071	−	190.499i	−0.311886	−	0.752959i
$254$		−	26.6971i		−	0.105107i
$255$	12.5099	−	52.4844i	0.0490585	−	0.205821i
$256$	−93.3807			−0.364768
$257$	−265.297	+	109.890i	−1.03228	+	0.427586i	−0.833536	−	0.552465i	$-0.813687\pi$
$257$	−265.297	+	109.890i	−1.03228	+	0.427586i	−0.198748	+	0.980051i	$0.563687\pi$
$258$	260.469	+	51.8105i	1.00957	+	0.200816i
$259$	−308.581	+	308.581i	−1.19143	+	1.19143i
$260$	54.6010	+	81.7161i	0.210004	+	0.314293i
$261$	58.5480	−	11.6459i	0.224322	−	0.0446204i
$262$	85.3323	−	127.709i	0.325696	−	0.487438i
$263$	−177.907	+	429.506i	−0.676454	+	1.63310i	0.0939730	+	0.995575i	$0.470043\pi$
$263$	−177.907	+	429.506i	−0.676454	+	1.63310i	−0.770427	+	0.637529i	$0.779957\pi$
$264$	−26.0216	−	10.7785i	−0.0985665	−	0.0408276i
$265$	126.254	+	84.3604i	0.476431	+	0.318341i
$266$	−68.0655	−	342.188i	−0.255885	−	1.28642i
$267$	−54.4543	+	36.3852i	−0.203949	+	0.136274i
$268$	−391.983	−	391.983i	−1.46262	−	1.46262i
$269$	−26.0248	+	130.835i	−0.0967463	+	0.486377i	0.901784	+	0.432186i	$0.142258\pi$
$269$	−26.0248	+	130.835i	−0.0967463	+	0.486377i	−0.998531	+	0.0541903i	$0.982742\pi$
$270$	−10.9064	−	26.3304i	−0.0403941	−	0.0975201i
$271$		−	161.290i		−	0.595167i	−0.954696	−	0.297584i	$-0.903819\pi$
$271$		−	161.290i		−	0.595167i	0.954696	−	0.297584i	$-0.0961807\pi$
$272$	112.077	−	154.791i	0.412049	−	0.569085i
$273$	200.412			0.734111
$274$	−33.2333	+	13.7657i	−0.121289	+	0.0502397i
$275$	−120.189	−	23.9070i	−0.437049	−	0.0869345i
$276$	−221.193	+	221.193i	−0.801425	+	0.801425i
$277$	−14.7816	−	22.1223i	−0.0533633	−	0.0798638i	0.803829	−	0.594861i	$-0.202793\pi$
$277$	−14.7816	−	22.1223i	−0.0533633	−	0.0798638i	−0.857192	+	0.514997i	$0.827793\pi$
$278$	−454.874	+	90.4800i	−1.63624	+	0.325468i
$279$	−71.6205	+	107.188i	−0.256704	+	0.384185i
$280$	21.5470	−	52.0192i	0.0769537	−	0.185783i
$281$	226.046	+	93.6314i	0.804435	+	0.333208i	0.746731	−	0.665126i	$-0.231622\pi$
$281$	226.046	+	93.6314i	0.804435	+	0.333208i	0.0577035	+	0.998334i	$0.481622\pi$
$282$	137.331	+	91.7616i	0.486989	+	0.325396i
$283$	−46.7209	−	234.882i	−0.165092	−	0.829971i	−0.971211	−	0.238219i	$-0.923436\pi$
$283$	−46.7209	−	234.882i	−0.165092	−	0.829971i	0.806120	−	0.591752i	$-0.201564\pi$
$284$	416.688	−	278.422i	1.46721	−	0.980358i
$285$	−24.4488	−	24.4488i	−0.0857854	−	0.0857854i
$286$	35.7577	−	179.766i	0.125027	−	0.628552i
$287$	6.63648	+	16.0219i	0.0231236	+	0.0558254i
$288$		−	135.409i		−	0.470170i
$289$	90.2016	+	274.563i	0.312116	+	0.950044i
$290$	109.138			0.376339
$291$	20.0996	−	8.32551i	0.0690707	−	0.0286100i
$292$	−44.2827	−	8.80838i	−0.151653	−	0.0301657i
$293$	−201.107	+	201.107i	−0.686372	+	0.686372i	−0.961428	−	0.275056i	$-0.911304\pi$
$293$	−201.107	+	201.107i	−0.686372	+	0.686372i	0.275056	+	0.961428i	$0.411304\pi$
$294$	−188.591	−	282.247i	−0.641467	−	0.960023i
$295$	33.9911	−	6.76124i	0.115224	−	0.0229195i
$296$	65.0786	−	97.3971i	0.219860	−	0.329044i
$297$	−11.2592	+	27.1821i	−0.0379097	+	0.0915221i
$298$	617.501	+	255.777i	2.07215	+	0.858313i
$299$	−327.449	−	218.795i	−1.09515	−	0.731755i
$300$	36.2690	+	182.336i	0.120897	+	0.607788i
$301$	455.705	−	304.492i	1.51397	−	1.01160i
$302$	322.886	+	322.886i	1.06916	+	1.06916i
$303$	−33.3007	+	167.414i	−0.109903	+	0.552521i
$304$	−46.8661	−	113.145i	−0.154165	−	0.372187i
$305$		−	196.481i		−	0.644199i
$306$	123.647	+	89.5269i	0.404074	+	0.292572i
$307$	−75.0263			−0.244385			−0.122193	−	0.992506i	$-0.538993\pi$
$307$	−75.0263			−0.244385			−0.122193	+	0.992506i	$0.538993\pi$
$308$	−277.583	+	114.979i	−0.901243	+	0.373307i
$309$	−164.865	−	32.7936i	−0.533542	−	0.106128i
$310$	−166.657	+	166.657i	−0.537602	+	0.537602i
$311$	26.6835	+	39.9347i	0.0857991	+	0.128407i	0.871887	−	0.489708i	$-0.162897\pi$
$311$	26.6835	+	39.9347i	0.0857991	+	0.128407i	−0.786088	+	0.618115i	$0.787897\pi$
$312$	−52.7610	+	10.4948i	−0.169106	+	0.0336372i
$313$	223.180	−	334.013i	0.713036	−	1.06713i	−0.281171	−	0.959658i	$-0.590723\pi$
$313$	223.180	−	334.013i	0.713036	−	1.06713i	0.994208	−	0.107477i	$-0.0342771\pi$
$314$	40.2452	−	97.1605i	0.128169	−	0.309428i
$315$	−54.3391	−	22.5080i	−0.172505	−	0.0714540i
$316$	−328.250	−	219.329i	−1.03876	−	0.694080i
$317$	−38.4930	−	193.517i	−0.121429	−	0.610465i	−0.992794	−	0.119830i	$-0.961765\pi$
$317$	−38.4930	−	193.517i	−0.121429	−	0.610465i	0.871365	−	0.490635i	$-0.163235\pi$
$318$	−357.214	+	238.683i	−1.12331	+	0.750574i
$319$	−79.6687	−	79.6687i	−0.249745	−	0.249745i
$320$	32.2226	−	161.994i	0.100696	−	0.506231i
$321$	−40.3809	−	97.4880i	−0.125797	−	0.303701i
$322$			1166.24i			3.62187i
$323$	180.154	+	42.9405i	0.557751	+	0.132943i
$324$	44.6352			0.137763
$325$	−216.235	+	89.5675i	−0.665339	+	0.275592i
$326$	−167.636	−	33.3449i	−0.514222	−	0.102285i
$327$	21.4330	−	21.4330i	0.0655443	−	0.0655443i
$328$	−2.58614	−	3.87044i	−0.00788458	−	0.0118001i
$329$	334.311	−	66.4987i	1.01614	−	0.202124i
$330$	−29.8845	+	44.7253i	−0.0905590	+	0.135531i
$331$	167.757	−	405.002i	0.506819	−	1.22357i	−0.438886	−	0.898543i	$-0.644627\pi$
$331$	167.757	−	405.002i	0.506819	−	1.22357i	0.945705	−	0.325027i	$-0.105373\pi$
$332$	311.078	+	128.853i	0.936981	+	0.388110i
$333$	−101.741	−	67.9810i	−0.305528	−	0.204147i
$334$	102.610	+	515.858i	0.307217	+	1.54448i
$335$	−170.299	+	113.790i	−0.508357	+	0.339673i
$336$	−147.309	−	147.309i	−0.438419	−	0.438419i
$337$	39.7297	−	199.734i	0.117892	−	0.592684i	−0.875998	−	0.482314i	$-0.839796\pi$
$337$	39.7297	−	199.734i	0.117892	−	0.592684i	0.993891	−	0.110370i	$-0.0352036\pi$
$338$	59.6172	+	143.929i	0.176382	+	0.425824i
$339$		−	298.231i		−	0.879738i
$340$	105.053	+	113.275i	0.308981	+	0.333162i
$341$	243.311			0.713523
$342$	90.3797	−	37.4365i	0.264268	−	0.109463i
$343$	−172.893	−	34.3905i	−0.504060	−	0.100264i
$344$	−104.025	+	104.025i	−0.302398	+	0.302398i
$345$	64.2111	+	96.0987i	0.186119	+	0.278547i
$346$	−284.923	+	56.6748i	−0.823478	+	0.163800i
$347$	222.155	−	332.478i	0.640215	−	0.958150i	−0.359472	−	0.933156i	$-0.617043\pi$
$347$	222.155	−	332.478i	0.640215	−	0.958150i	0.999688	−	0.0249943i	$-0.00795676\pi$
$348$	−65.4113	+	157.917i	−0.187963	+	0.453784i
$349$	−244.378	−	101.225i	−0.700222	−	0.290042i	0.00402941	−	0.999992i	$-0.498717\pi$
$349$	−244.378	−	101.225i	−0.700222	−	0.290042i	−0.704252	+	0.709950i	$0.748717\pi$
$350$	576.299	+	385.071i	1.64657	+	1.10020i
$351$	10.9629	+	55.1141i	0.0312333	+	0.157020i
$352$	−212.499	+	141.987i	−0.603691	+	0.403374i
$353$	−52.7998	−	52.7998i	−0.149574	−	0.149574i	0.628354	−	0.777928i	$-0.283729\pi$
$353$	−52.7998	−	52.7998i	−0.149574	−	0.149574i	−0.777928	+	0.628354i	$0.783729\pi$
$354$	−19.1297	+	96.1717i	−0.0540388	+	0.271671i
$355$	−70.8579	−	171.066i	−0.199600	−	0.481876i
$356$		−	187.525i		−	0.526757i
$357$	311.081	−	49.7904i	0.871375	−	0.139469i
$358$	−287.116			−0.802000
$359$	310.454	−	128.594i	0.864773	−	0.358201i	0.0942007	−	0.995553i	$-0.469970\pi$
$359$	310.454	−	128.594i	0.864773	−	0.358201i	0.770572	+	0.637352i	$0.219970\pi$
$360$	15.4841	+	3.07998i	0.0430114	+	0.00855551i
$361$	−171.344	+	171.344i	−0.474638	+	0.474638i
$362$	−472.461	−	707.088i	−1.30514	−	1.95328i
$363$	−151.088	+	30.0532i	−0.416220	+	0.0827912i
$364$	−318.814	+	477.139i	−0.875863	+	1.31082i
$365$	−6.38388	+	15.4120i	−0.0174901	+	0.0422248i
$366$	513.591	+	212.736i	1.40325	+	0.581247i
$367$	−40.6220	−	27.1427i	−0.110687	−	0.0739584i	0.498995	−	0.866605i	$-0.333703\pi$
$367$	−40.6220	−	27.1427i	−0.110687	−	0.0739584i	−0.609681	+	0.792647i	$0.708703\pi$
$368$	79.8643	+	401.505i	0.217023	+	1.09105i
$369$	−4.04305	+	2.70148i	−0.0109568	+	0.00732109i
$370$	−158.188	−	158.188i	−0.427535	−	0.427535i
$371$	−172.971	+	869.583i	−0.466228	+	2.34389i
$372$	−141.258	−	341.027i	−0.379725	−	0.916738i
$373$			467.685i			1.25385i	0.779081	+	0.626924i	$0.215686\pi$
$373$			467.685i			1.25385i	−0.779081	+	0.626924i	$0.784314\pi$
$374$	10.8422	−	287.917i	0.0289898	−	0.769832i
$375$	148.034			0.394756
$376$	−84.5294	+	35.0132i	−0.224812	+	0.0931202i
$377$	−211.056	−	41.9817i	−0.559830	−	0.111357i
$378$	117.670	−	117.670i	0.311296	−	0.311296i
$379$	−147.215	−	220.323i	−0.388430	−	0.581326i	0.584795	−	0.811181i	$-0.301175\pi$
$379$	−147.215	−	220.323i	−0.388430	−	0.581326i	−0.973225	+	0.229855i	$0.926175\pi$
$380$	97.1005	−	19.3145i	0.255528	−	0.0508276i
$381$	8.58268	−	12.8449i	0.0225267	−	0.0337136i
$382$	−41.8556	+	101.048i	−0.109570	+	0.264524i
$383$	−452.009	−	187.228i	−1.18018	−	0.488847i	−0.295636	−	0.955301i	$-0.595531\pi$
$383$	−452.009	−	187.228i	−1.18018	−	0.488847i	−0.884546	+	0.466454i	$0.845531\pi$
$384$	128.544	+	85.8904i	0.334750	+	0.223673i
$385$	21.6570	+	108.877i	0.0562518	+	0.282797i
$386$	−63.8729	+	42.6785i	−0.165474	+	0.110566i
$387$	108.664	+	108.664i	0.280786	+	0.280786i
$388$	−12.1529	+	61.0970i	−0.0313220	+	0.157466i
$389$	−42.6356	−	102.931i	−0.109603	−	0.264605i	0.859556	−	0.511042i	$-0.170740\pi$
$389$	−42.6356	−	102.931i	−0.109603	−	0.264605i	−0.969159	+	0.246437i	$0.920740\pi$
$390$			102.737i			0.263429i
$391$	−562.626	−	258.263i	−1.43894	−	0.660519i
$392$	188.041			0.479696
$393$	82.1125	−	34.0121i	0.208938	−	0.0865449i
$394$	404.128	+	80.3861i	1.02571	+	0.204026i
$395$	−103.140	+	103.140i	−0.261114	+	0.261114i
$396$	−46.8038	−	70.0468i	−0.118191	−	0.176886i
$397$	−260.711	+	51.8587i	−0.656703	+	0.130626i	−0.512184	−	0.858876i	$-0.671163\pi$
$397$	−260.711	+	51.8587i	−0.656703	+	0.130626i	−0.144519	+	0.989502i	$0.546163\pi$
$398$	395.378	−	591.726i	0.993413	−	1.48675i
$399$	77.2592	−	186.520i	0.193632	−	0.467469i
$400$	224.774	+	93.1043i	0.561934	+	0.232761i
$401$	183.395	+	122.540i	0.457343	+	0.305587i	0.762818	−	0.646613i	$-0.223815\pi$
$401$	183.395	+	122.540i	0.457343	+	0.305587i	−0.305475	+	0.952200i	$0.598815\pi$
$402$	−113.054	−	568.360i	−0.281228	−	1.41383i
$403$	386.394	−	258.180i	0.958794	−	0.640645i
$404$	−345.603	−	345.603i	−0.855452	−	0.855452i
$405$	3.21735	−	16.1747i	0.00794406	−	0.0399375i
$406$	243.868	+	588.749i	0.600660	+	1.45012i
$407$			230.947i			0.567438i
$408$	−79.2886	+	29.3981i	−0.194335	+	0.0720541i
$409$	139.981			0.342251			0.171126	−	0.985249i	$-0.445260\pi$
$409$	139.981			0.342251			0.171126	+	0.985249i	$0.445260\pi$
$410$	−8.21330	+	3.40206i	−0.0200324	+	0.00829770i
$411$	−20.4151	−	4.06081i	−0.0496717	−	0.00988033i
$412$	340.340	−	340.340i	0.826068	−	0.826068i
$413$	112.426	+	168.258i	0.272218	+	0.407403i
$414$	−320.721	+	63.7954i	−0.774688	+	0.154095i
$415$	69.1157	−	103.439i	0.166544	−	0.249251i
$416$	−186.798	+	450.970i	−0.449034	+	1.08406i
$417$	−247.943	−	102.701i	−0.594587	−	0.246286i
$418$	−153.520	−	102.579i	−0.367274	−	0.245404i
$419$	−71.1999	−	357.946i	−0.169928	−	0.854286i	−0.967851	−	0.251526i	$-0.919068\pi$
$419$	−71.1999	−	357.946i	−0.169928	−	0.854286i	0.797922	−	0.602760i	$-0.205932\pi$
$420$	140.029	−	93.5645i	0.333403	−	0.222773i
$421$	196.189	+	196.189i	0.466006	+	0.466006i	0.900618	−	0.434612i	$-0.143114\pi$
$421$	196.189	+	196.189i	0.466006	+	0.466006i	−0.434612	+	0.900618i	$0.643114\pi$
$422$	40.0733	−	201.462i	0.0949605	−	0.477398i
$423$	36.5747	+	88.2992i	0.0864651	+	0.208745i
$424$		−	237.986i		−	0.561288i
$425$	−313.389	+	192.749i	−0.737386	+	0.453526i
$426$	523.879			1.22976
$427$	1059.92	−	439.033i	2.48225	−	1.02818i
$428$	296.336	+	58.9449i	0.692374	+	0.137722i
$429$	74.9959	−	74.9959i	0.174816	−	0.174816i
$430$	156.092	+	233.608i	0.363004	+	0.543274i
$431$	443.882	−	88.2936i	1.02989	−	0.204858i	0.348906	−	0.937158i	$-0.386553\pi$
$431$	443.882	−	88.2936i	1.02989	−	0.204858i	0.680982	+	0.732300i	$0.261553\pi$
$432$	32.4524	−	48.5685i	0.0751213	−	0.112427i
$433$	185.595	−	448.067i	0.428627	−	1.03480i	−0.551096	−	0.834442i	$-0.685790\pi$
$433$	185.595	−	448.067i	0.428627	−	1.03480i	0.979723	−	0.200355i	$-0.0642096\pi$
$434$	−1271.42	−	526.641i	−2.92955	−	1.21346i
$435$	52.5102	+	35.0862i	0.120713	+	0.0806579i
$436$	16.9320	+	85.1229i	0.0388348	+	0.195236i
$437$	−329.861	+	220.406i	−0.754830	+	0.504361i
$438$	−33.3743	−	33.3743i	−0.0761970	−	0.0761970i
$439$	45.5906	−	229.199i	0.103851	−	0.522094i	−0.893481	−	0.449100i	$-0.851745\pi$
$439$	45.5906	−	229.199i	0.103851	−	0.522094i	0.997332	−	0.0729940i	$-0.0232554\pi$
$440$	−11.4029	−	27.5291i	−0.0259157	−	0.0625661i
$441$		−	196.427i		−	0.445413i
$442$	−288.294	−	468.736i	−0.652248	−	1.06049i
$443$	−47.6565			−0.107577			−0.0537884	−	0.998552i	$-0.517130\pi$
$443$	−47.6565			−0.107577			−0.0537884	+	0.998552i	$0.517130\pi$
$444$	323.697	−	134.080i	0.729047	−	0.301981i
$445$	−67.9545	−	13.5170i	−0.152707	−	0.0303753i
$446$	640.993	−	640.993i	1.43720	−	1.43720i
$447$	214.872	+	321.579i	0.480699	+	0.719417i
$448$	945.879	−	188.147i	2.11134	−	0.419971i
$449$	−39.5237	+	59.1513i	−0.0880260	+	0.131740i	−0.872869	−	0.487954i	$-0.837743\pi$
$449$	−39.5237	+	59.1513i	−0.0880260	+	0.131740i	0.784843	+	0.619694i	$0.212743\pi$
$450$	−74.3714	+	179.548i	−0.165270	+	0.398997i
$451$	8.47896	+	3.51210i	0.0188003	+	0.00778736i
$452$	710.025	+	474.424i	1.57085	+	1.04961i
$453$	51.5489	+	259.154i	0.113794	+	0.572083i
$454$	−182.519	+	121.955i	−0.402023	+	0.268623i
$455$	149.923	+	149.923i	0.329501	+	0.329501i
$456$	−10.5721	+	53.1496i	−0.0231844	+	0.116556i
$457$	65.9745	+	159.276i	0.144364	+	0.348526i	0.979478	−	0.201551i	$-0.0645982\pi$
$457$	65.9745	+	159.276i	0.144364	+	0.348526i	−0.835114	+	0.550077i	$0.814598\pi$
$458$		−	485.701i		−	1.06048i
$459$	30.7092	+	82.8248i	0.0669045	+	0.180446i
$460$	−330.937			−0.719429
$461$	−652.067	+	270.095i	−1.41446	+	0.585890i	−0.953463	−	0.301510i	$-0.902509\pi$
$461$	−652.067	+	270.095i	−1.41446	+	0.585890i	−0.461000	+	0.887400i	$0.652509\pi$
$462$	−308.048	−	61.2745i	−0.666770	−	0.132629i
$463$	−612.164	+	612.164i	−1.32217	+	1.32217i	−0.410150	+	0.912018i	$0.634524\pi$
$463$	−612.164	+	612.164i	−1.32217	+	1.32217i	−0.912018	+	0.410150i	$0.865476\pi$
$464$	124.275	+	185.990i	0.267833	+	0.400840i
$465$	−133.761	+	26.6068i	−0.287659	+	0.0572189i
$466$	−368.029	+	550.795i	−0.789763	+	1.18196i
$467$	−196.565	+	474.550i	−0.420911	+	1.01617i	0.561169	+	0.827701i	$0.310352\pi$
$467$	−196.565	+	474.550i	−0.420911	+	1.01617i	−0.982080	+	0.188467i	$0.939648\pi$
$468$	−148.655	−	61.5748i	−0.317638	−	0.131570i
$469$	−994.376	−	664.421i	−2.12021	−	1.41668i
$470$	34.0892	+	171.378i	0.0725302	+	0.364634i
$471$	50.5988	−	33.8090i	0.107428	−	0.0717814i
$472$	−38.4086	−	38.4086i	−0.0813741	−	0.0813741i
$473$	56.5850	−	284.472i	0.119630	−	0.601421i
$474$	−157.930	−	381.276i	−0.333185	−	0.804380i
$475$			235.775i			0.496368i
$476$	−376.325	+	819.825i	−0.790598	+	1.72232i
$477$	−248.600			−0.521174
$478$	−780.268	+	323.198i	−1.63236	+	0.676146i
$479$	815.305	+	162.174i	1.70210	+	0.338568i	0.948018	−	0.318216i	$-0.103084\pi$
$479$	815.305	+	162.174i	1.70210	+	0.338568i	0.754079	+	0.656784i	$0.228084\pi$
$480$	101.296	−	101.296i	0.211033	−	0.211033i
$481$	245.060	+	366.759i	0.509481	+	0.762493i
$482$	−944.847	+	187.942i	−1.96026	+	0.389921i
$483$	−374.928	+	561.119i	−0.776248	+	1.16174i
$484$	168.799	−	407.516i	0.348758	−	0.841976i
$485$	21.2640	+	8.80785i	0.0438433	+	0.0181605i
$486$	38.7963	+	25.9229i	0.0798278	+	0.0533393i
$487$	155.236	+	780.422i	0.318759	+	1.60251i	0.725004	+	0.688745i	$0.241838\pi$
$487$	155.236	+	780.422i	0.318759	+	1.60251i	−0.406245	+	0.913764i	$0.633162\pi$
$488$	−256.046	+	171.085i	−0.524685	+	0.350584i
$489$	−69.9356	−	69.9356i	−0.143018	−	0.143018i
$490$	70.0611	−	352.221i	0.142982	−	0.718818i
$491$	257.166	+	620.853i	0.523759	+	1.26447i	0.935552	+	0.353189i	$0.114903\pi$
$491$	257.166	+	620.853i	0.523759	+	1.26447i	−0.411793	+	0.911277i	$0.635097\pi$
$492$		−	13.9231i		−	0.0282991i
$493$	−338.032	−	12.7294i	−0.685664	−	0.0258203i
$494$	−352.648			−0.713862
$495$	−28.7569	+	11.9115i	−0.0580947	+	0.0240636i
$496$	−473.780	−	94.2408i	−0.955202	−	0.190002i
$497$	764.488	−	764.488i	1.53821	−	1.53821i
$498$	195.551	+	292.662i	0.392672	+	0.587675i
$499$	10.6279	−	2.11403i	0.0212985	−	0.00423653i	−0.184430	−	0.982846i	$-0.559044\pi$
$499$	10.6279	−	2.11403i	0.0212985	−	0.00423653i	0.205728	+	0.978609i	$0.434044\pi$
$500$	−235.491	+	352.437i	−0.470981	+	0.704873i
$501$	−116.470	+	281.184i	−0.232476	+	0.561246i
$502$	507.205	+	210.091i	1.01037	+	0.418509i
$503$	−367.862	−	245.798i	−0.731336	−	0.488663i	0.133291	−	0.991077i	$-0.457445\pi$
$503$	−367.862	−	245.798i	−0.731336	−	0.488663i	−0.864627	+	0.502414i	$0.832445\pi$
$504$	17.9840	+	90.4115i	0.0356825	+	0.179388i
$505$	−150.149	+	100.326i	−0.297325	+	0.198666i
$506$	436.418	+	436.418i	0.862486	+	0.862486i
$507$	−17.5868	+	88.4149i	−0.0346880	+	0.174388i
$508$	16.9277	+	40.8671i	0.0333223	+	0.0804471i
$509$		−	124.505i		−	0.244607i	−0.992493	−	0.122304i	$-0.960972\pi$
$509$		−	124.505i		−	0.244607i	0.992493	−	0.122304i	$-0.0390281\pi$
$510$	25.5240	+	159.469i	0.0500471	+	0.312685i
$511$	−97.4052			−0.190617
$512$	588.087	−	243.594i	1.14861	−	0.475769i
$513$	55.5199	+	11.0436i	0.108226	+	0.0215275i
$514$	607.776	−	607.776i	1.18244	−	1.18244i
$515$	−98.7987	−	147.863i	−0.191842	−	0.287112i
$516$	−431.569	+	85.8443i	−0.836373	+	0.166365i
$517$	100.218	−	149.986i	0.193845	−	0.290109i
$518$	499.879	−	1206.82i	0.965018	−	2.32976i
$519$	−155.306	−	64.3299i	−0.299241	−	0.123950i
$520$	−47.3200	−	31.6182i	−0.0909999	−	0.0608042i
$521$	−51.0680	−	256.736i	−0.0980191	−	0.492775i	−0.998342	−	0.0575537i	$-0.981670\pi$
$521$	−51.0680	−	256.736i	−0.0980191	−	0.492775i	0.900323	−	0.435222i	$-0.143330\pi$
$522$	−148.568	+	99.2701i	−0.284613	+	0.190173i
$523$	687.886	+	687.886i	1.31527	+	1.31527i	0.917474	+	0.397795i	$0.130224\pi$
$523$	687.886	+	687.886i	1.31527	+	1.31527i	0.397795	+	0.917474i	$0.369776\pi$
$524$	−49.6483	+	249.599i	−0.0947487	+	0.476334i
$525$	153.483	+	370.541i	0.292349	+	0.705793i
$526$		−	1391.54i		−	2.64551i
$527$	535.621	−	496.744i	1.01636	−	0.942589i
$528$	−110.248			−0.208804
$529$	736.441	−	305.044i	1.39214	−	0.576642i
$530$	−445.774	−	88.6699i	−0.841083	−	0.167302i
$531$	−40.1216	+	40.1216i	−0.0755585	+	0.0755585i
$532$	321.162	+	480.653i	0.603688	+	0.903483i
$533$	17.1918	−	3.41967i	0.0322549	−	0.00641589i
$534$	108.910	−	162.995i	0.203950	−	0.305233i
$535$	42.7203	−	103.136i	0.0798510	−	0.192777i
$536$	296.575	+	122.845i	0.553312	+	0.229189i
$537$	−138.141	−	92.3031i	−0.257246	−	0.171887i
$538$	−77.8983	−	391.621i	−0.144792	−	0.727920i
$539$	−308.257	+	205.970i	−0.571905	+	0.382135i
$540$	33.3904	+	33.3904i	0.0618340	+	0.0618340i
$541$	96.3014	−	484.140i	0.178006	−	0.894898i	−0.783768	−	0.621054i	$-0.786705\pi$
$541$	96.3014	−	484.140i	0.178006	−	0.894898i	0.961774	−	0.273844i	$-0.0882952\pi$
$542$	184.752	+	446.031i	0.340871	+	0.822935i
$543$		−	492.093i		−	0.906248i
$544$	−177.910	+	746.407i	−0.327040	+	1.37207i
$545$	32.0669			0.0588383
$546$	−554.218	+	229.565i	−1.01505	+	0.420448i
$547$	−101.427	−	20.1751i	−0.185424	−	0.0368831i	0.101505	−	0.994835i	$-0.467634\pi$
$547$	−101.427	−	20.1751i	−0.185424	−	0.0368831i	−0.286929	+	0.957952i	$0.592634\pi$
$548$	42.1441	−	42.1441i	0.0769053	−	0.0769053i
$549$	178.715	+	267.466i	0.325528	+	0.487187i
$550$	359.753	−	71.5593i	0.654096	−	0.130108i
$551$	−120.434	+	180.242i	−0.218574	+	0.327118i
$552$	69.3207	−	167.355i	0.125581	−	0.303180i
$553$	−786.855	−	325.926i	−1.42288	−	0.589378i
$554$	66.2172	+	44.2449i	0.119526	+	0.0798645i
$555$	−25.2548	−	126.964i	−0.0455041	−	0.228764i
$556$	638.936	−	426.923i	1.14917	−	0.767848i
$557$	−463.495	−	463.495i	−0.832127	−	0.832127i	0.155680	−	0.987808i	$-0.450243\pi$
$557$	−463.495	−	463.495i	−0.832127	−	0.832127i	−0.987808	+	0.155680i	$0.950243\pi$
$558$	75.2792	−	378.454i	0.134909	−	0.678233i
$559$	−211.996	−	511.802i	−0.379241	−	0.915568i
$560$		−	220.395i		−	0.393563i
$561$	97.7772	−	135.041i	0.174291	−	0.240715i
$562$	−732.357			−1.30313
$563$	668.501	−	276.902i	1.18739	−	0.491833i	0.300486	−	0.953786i	$-0.402851\pi$
$563$	668.501	−	276.902i	1.18739	−	0.491833i	0.886904	+	0.461953i	$0.152851\pi$
$564$	−268.405	−	53.3890i	−0.475895	−	0.0946614i
$565$	223.099	−	223.099i	0.394865	−	0.394865i
$566$	398.250	+	596.023i	0.703622	+	1.05304i
$567$	94.4438	−	18.7860i	0.166567	−	0.0331323i
$568$	−161.228	+	241.294i	−0.283852	+	0.424814i
$569$	−390.523	+	942.806i	−0.686332	+	1.65695i	0.0657114	+	0.997839i	$0.479068\pi$
$569$	−390.523	+	942.806i	−0.686332	+	1.65695i	−0.752043	+	0.659113i	$0.770932\pi$
$570$	95.6158	+	39.6054i	0.167747	+	0.0694831i
$571$	833.078	+	556.645i	1.45898	+	0.974860i	0.996081	+	0.0884494i	$0.0281912\pi$
$571$	833.078	+	556.645i	1.45898	+	0.974860i	0.462900	+	0.886410i	$0.346809\pi$
$572$	59.2465	+	297.852i	0.103578	+	0.520721i
$573$	−52.6235	+	35.1619i	−0.0918385	+	0.0613645i
$574$	−36.7049	−	36.7049i	−0.0639459	−	0.0639459i
$575$	153.756	−	772.981i	0.267401	−	1.34431i
$576$	103.482	+	249.828i	0.179657	+	0.433730i
$577$			577.755i			1.00131i	0.865647	+	0.500655i	$0.166907\pi$
$577$			577.755i			1.00131i	−0.865647	+	0.500655i	$0.833093\pi$
$578$	−563.944	−	655.950i	−0.975682	−	1.13486i
$579$	−44.4519			−0.0767735
$580$	−167.066	+	69.2008i	−0.288044	+	0.119312i
$581$	712.441	+	141.713i	1.22623	+	0.243913i
$582$	−46.0466	+	46.0466i	−0.0791178	+	0.0791178i
$583$	260.678	+	390.132i	0.447132	+	0.669180i
$584$	25.6431	−	5.10074i	0.0439095	−	0.00873414i
$585$	−33.0283	+	49.4304i	−0.0564587	+	0.0844964i
$586$	325.779	−	786.500i	0.555937	−	1.34215i
$587$	−181.745	−	75.2813i	−0.309617	−	0.128247i	0.222464	−	0.974941i	$-0.428590\pi$
$587$	−181.745	−	75.2813i	−0.309617	−	0.128247i	−0.532081	+	0.846693i	$0.678590\pi$
$588$	467.652	+	312.475i	0.795327	+	0.531420i
$589$	−91.3284	−	459.139i	−0.155057	−	0.779523i
$590$	−86.2538	+	57.6330i	−0.146193	+	0.0976830i
$591$	168.597	+	168.597i	0.285274	+	0.285274i
$592$	89.4518	−	449.705i	0.151101	−	0.759636i
$593$	−397.065	−	958.600i	−0.669587	−	1.61653i	−0.782303	−	0.622898i	$-0.785955\pi$
$593$	−397.065	−	958.600i	−0.669587	−	1.61653i	0.112716	−	0.993627i	$-0.464045\pi$
$594$		−	88.0660i		−	0.148259i
$595$	269.958	+	195.464i	0.453711	+	0.328512i
$596$	−1107.43			−1.85810
$597$	380.460	−	157.592i	0.637286	−	0.263973i
$598$	1156.15	+	229.972i	1.93336	+	0.384568i
$599$	−507.791	+	507.791i	−0.847731	+	0.847731i	−0.989850	−	0.142118i	$-0.954609\pi$
$599$	−507.791	+	507.791i	−0.847731	+	0.847731i	0.142118	+	0.989850i	$0.454609\pi$
$600$	−59.8102	−	89.5123i	−0.0996837	−	0.149187i
$601$	−959.570	+	190.870i	−1.59662	+	0.317588i	−0.911645	−	0.410978i	$-0.865187\pi$
$601$	−959.570	+	190.870i	−1.59662	+	0.317588i	−0.684976	+	0.728565i	$0.740187\pi$
$602$	−911.417	+	1364.03i	−1.51398	+	2.26583i
$603$	128.324	−	309.802i	0.212810	−	0.513768i
$604$	−698.994	−	289.533i	−1.15728	−	0.479359i
$605$	−135.507	−	90.5426i	−0.223978	−	0.149657i
$606$	−99.6768	−	501.109i	−0.164483	−	0.826913i
$607$	−332.737	+	222.327i	−0.548166	+	0.366273i	−0.798601	−	0.601861i	$-0.794426\pi$
$607$	−332.737	+	222.327i	−0.548166	+	0.366273i	0.250435	+	0.968133i	$0.419426\pi$
$608$	347.699	+	347.699i	0.571874	+	0.571874i
$609$	−71.9400	+	361.667i	−0.118128	+	0.593870i
$610$	225.061	+	543.346i	0.368953	+	0.890731i
$611$		−	344.530i		−	0.563879i
$612$	−246.040	−	58.6450i	−0.402027	−	0.0958251i
$613$	−124.279			−0.202739			−0.101370	−	0.994849i	$-0.532322\pi$
$613$	−124.279			−0.202739			−0.101370	+	0.994849i	$0.532322\pi$
$614$	207.477	−	85.9398i	0.337910	−	0.139967i
$615$	−5.04540	−	1.00359i	−0.00820390	−	0.00163186i
$616$	123.027	−	123.027i	0.199719	−	0.199719i
$617$	111.245	+	166.490i	0.180300	+	0.269839i	0.910600	−	0.413288i	$-0.135620\pi$
$617$	111.245	+	166.490i	0.180300	+	0.269839i	−0.730300	+	0.683127i	$0.760620\pi$
$618$	493.479	−	98.1590i	0.798509	−	0.158833i
$619$	211.859	−	317.069i	0.342259	−	0.512227i	−0.619912	−	0.784671i	$-0.712832\pi$
$619$	211.859	−	317.069i	0.342259	−	0.512227i	0.962172	+	0.272444i	$0.0878318\pi$
$620$	149.442	−	360.784i	0.241035	−	0.581909i
$621$	−174.819	−	72.4123i	−0.281512	−	0.116606i
$622$	−119.534	−	79.8701i	−0.192177	−	0.128408i
$623$	−78.9255	−	396.786i	−0.126686	−	0.636895i
$624$	−175.081	+	116.986i	−0.280579	+	0.187477i
$625$	−271.846	−	271.846i	−0.434954	−	0.434954i
$626$	−234.582	+	1179.32i	−0.374731	+	1.88390i
$627$	−40.8864	−	98.7085i	−0.0652096	−	0.157430i
$628$			174.248i			0.277465i
$629$	471.502	+	508.403i	0.749606	+	0.808271i
$630$	176.051			0.279446
$631$	−325.555	+	134.849i	−0.515935	+	0.213707i	−0.625430	−	0.780280i	$-0.715077\pi$
$631$	−325.555	+	134.849i	−0.515935	+	0.213707i	0.109495	+	0.993987i	$0.465077\pi$
$632$	224.217	+	44.5995i	0.354774	+	0.0705689i
$633$	84.0473	−	84.0473i	0.132776	−	0.132776i
$634$	328.115	+	491.059i	0.517532	+	0.774541i
$635$	16.0294	−	3.18844i	0.0252431	−	0.00502117i
$636$	395.471	−	591.864i	0.621810	−	0.930604i
$637$	−270.974	+	654.188i	−0.425390	+	1.02698i
$638$	311.572	+	129.058i	0.488358	+	0.202284i
$639$	252.056	+	168.418i	0.394454	+	0.263565i
$640$	31.9080	+	160.412i	0.0498563	+	0.250644i
$641$	−464.966	+	310.680i	−0.725376	+	0.484681i	−0.862617	−	0.505857i	$-0.831176\pi$
$641$	−464.966	+	310.680i	−0.725376	+	0.484681i	0.137241	+	0.990538i	$0.456176\pi$
$642$	223.338	+	223.338i	0.347878	+	0.347878i
$643$	−200.678	+	1008.88i	−0.312097	+	1.56902i	0.432583	+	0.901594i	$0.357602\pi$
$643$	−200.678	+	1008.88i	−0.312097	+	1.56902i	−0.744680	+	0.667422i	$0.767398\pi$
$644$	−739.474	−	1785.25i	−1.14825	−	2.77212i
$645$			162.577i			0.252058i
$646$	−547.382	+	87.6118i	−0.847340	+	0.135622i
$647$	−239.057			−0.369485			−0.184742	−	0.982787i	$-0.559145\pi$
$647$	−239.057			−0.369485			−0.184742	+	0.982787i	$0.559145\pi$
$648$	−23.8797	+	9.89132i	−0.0368515	+	0.0152644i
$649$	105.034	+	20.8926i	0.161840	+	0.0321920i
$650$	495.378	−	495.378i	0.762120	−	0.762120i
$651$	−442.419	−	662.126i	−0.679599	−	1.01709i
$652$	277.755	−	55.2489i	0.426005	−	0.0847376i
$653$	258.571	−	386.978i	0.395973	−	0.592616i	−0.578894	−	0.815403i	$-0.696515\pi$
$653$	258.571	−	386.978i	0.395973	−	0.592616i	0.974867	+	0.222787i	$0.0715154\pi$
$654$	−34.7199	+	83.8213i	−0.0530886	+	0.128167i
$655$	86.8697	+	35.9826i	0.132625	+	0.0549353i
$656$	−15.1500	−	10.1229i	−0.0230946	−	0.0154313i
$657$	−5.32822	−	26.7868i	−0.00810993	−	0.0407714i
$658$	−848.330	+	566.836i	−1.28925	+	0.861453i
$659$	371.262	+	371.262i	0.563372	+	0.563372i	0.930264	−	0.366892i	$-0.119578\pi$
$659$	371.262	+	371.262i	0.563372	+	0.563372i	−0.366892	+	0.930264i	$0.619578\pi$
$660$	17.3875	−	87.4127i	0.0263446	−	0.132443i
$661$	−180.420	−	435.573i	−0.272950	−	0.658960i	0.726657	−	0.687001i	$-0.241073\pi$
$661$	−180.420	−	435.573i	−0.272950	−	0.658960i	−0.999607	+	0.0280407i	$0.991073\pi$
$662$			1312.15i			1.98209i
$663$	11.9828	−	318.206i	0.0180736	−	0.479949i
$664$	−194.980			−0.293645
$665$	197.326	−	81.7352i	0.296731	−	0.122910i
$666$	359.223	+	71.4539i	0.539374	+	0.107288i
$667$	512.381	−	512.381i	0.768188	−	0.768188i
$668$	−484.160	−	724.597i	−0.724790	−	1.08473i
$669$	514.472	−	102.335i	0.769016	−	0.152967i
$670$	340.602	−	509.747i	0.508361	−	0.760816i
$671$	232.341	−	560.920i	0.346261	−	0.835947i
$672$	772.785	+	320.098i	1.14998	+	0.476336i
$673$	−216.306	−	144.531i	−0.321405	−	0.214756i	0.384392	−	0.923170i	$-0.374411\pi$
$673$	−216.306	−	144.531i	−0.321405	−	0.214756i	−0.705797	+	0.708414i	$0.749411\pi$
$674$	118.920	+	597.853i	0.176440	+	0.887022i
$675$	−93.5044	+	62.4777i	−0.138525	+	0.0925595i
$676$	−182.520	−	182.520i	−0.270000	−	0.270000i
$677$	0.136553	−	0.686499i	0.000201703	−	0.00101403i	−0.980684	−	0.195597i	$-0.937335\pi$
$677$	0.136553	−	0.686499i	0.000201703	−	0.00101403i	0.980886	+	0.194583i	$0.0623355\pi$
$678$	341.612	+	824.725i	0.503853	+	1.21641i
$679$			134.390i			0.197924i
$680$	−81.3056	−	37.3218i	−0.119567	−	0.0548850i
$681$	−127.022			−0.186523
$682$	−672.851	+	278.704i	−0.986585	+	0.408657i
$683$	−674.620	−	134.190i	−0.987731	−	0.196472i	−0.325313	−	0.945606i	$-0.605470\pi$
$683$	−674.620	−	134.190i	−0.987731	−	0.196472i	−0.662418	+	0.749134i	$0.730470\pi$
$684$	−114.613	+	114.613i	−0.167563	+	0.167563i
$685$	−12.2342	−	18.3098i	−0.0178601	−	0.0267296i
$686$	517.509	−	102.939i	0.754386	−	0.150057i
$687$	156.145	−	233.687i	0.227285	−	0.340156i
$688$	−220.367	+	532.012i	−0.320300	+	0.773274i
$689$	827.946	+	342.947i	1.20166	+	0.497745i
$690$	−287.646	−	192.199i	−0.416878	−	0.278549i
$691$	73.8905	+	371.473i	0.106933	+	0.537587i	0.996700	+	0.0811728i	$0.0258666\pi$
$691$	73.8905	+	371.473i	0.106933	+	0.537587i	−0.889767	+	0.456414i	$0.849133\pi$
$692$	400.216	−	267.416i	0.578347	−	0.386439i
$693$	−128.513	−	128.513i	−0.185445	−	0.185445i
$694$	−233.504	+	1173.90i	−0.336460	+	1.69150i
$695$	−108.651	−	262.307i	−0.156333	−	0.377421i
$696$		−	98.9805i		−	0.142213i
$697$	25.8357	−	9.57917i	0.0370670	−	0.0137434i
$698$	791.748			1.13431
$699$	−354.143	+	146.691i	−0.506642	+	0.209858i
$700$	−1126.34	−	224.043i	−1.60906	−	0.320062i
$701$	−47.7250	+	47.7250i	−0.0680813	+	0.0680813i	−0.740328	−	0.672246i	$-0.765330\pi$
$701$	−47.7250	+	47.7250i	−0.0680813	+	0.0680813i	0.672246	+	0.740328i	$0.265330\pi$
$702$	−93.4477	−	139.854i	−0.133116	−	0.199223i
$703$	435.807	−	86.6875i	0.619925	−	0.123311i
$704$	283.550	−	424.362i	0.402770	−	0.602787i
$705$	−38.6937	+	93.4148i	−0.0548847	+	0.132503i
$706$	206.492	+	85.5318i	0.292482	+	0.121150i
$707$	−876.718	−	585.804i	−1.24005	−	0.828578i
$708$	−31.6959	−	159.346i	−0.0447682	−	0.225065i
$709$	136.937	−	91.4983i	0.193141	−	0.129053i	−0.455240	−	0.890369i	$-0.650447\pi$
$709$	136.937	−	91.4983i	0.193141	−	0.129053i	0.648381	+	0.761316i	$0.275447\pi$
$710$	391.899	+	391.899i	0.551971	+	0.551971i
$711$	46.5886	−	234.217i	0.0655255	−	0.329419i
$712$	41.5563	+	100.326i	0.0583656	+	0.140907i
$713$			1564.83i			2.19472i
$714$	−803.228	+	494.022i	−1.12497	+	0.691907i
$715$	112.205			0.156930
$716$	439.508	−	182.050i	0.613838	−	0.254260i
$717$	−479.316	−	95.3419i	−0.668502	−	0.132973i
$718$	−711.226	+	711.226i	−0.990565	+	0.990565i
$719$	548.289	+	820.572i	0.762571	+	1.14127i	0.986032	+	0.166555i	$0.0532645\pi$
$719$	548.289	+	820.572i	0.762571	+	1.14127i	−0.223461	+	0.974713i	$0.571736\pi$
$720$	60.6095	−	12.0560i	0.0841798	−	0.0167444i
$721$	576.884	−	863.368i	0.800117	−	1.19746i
$722$	277.566	−	670.103i	0.384440	−	0.928120i
$723$	−515.018	−	213.327i	−0.712335	−	0.295059i
$724$	1171.57	+	782.817i	1.61819	+	1.08124i
$725$	−84.0150	−	422.372i	−0.115883	−	0.582582i
$726$	383.392	−	256.174i	0.528088	−	0.352857i
$727$	244.476	+	244.476i	0.336281	+	0.336281i	0.854966	−	0.518685i	$-0.173578\pi$
$727$	244.476	+	244.476i	0.336281	+	0.336281i	−0.518685	+	0.854966i	$0.673578\pi$
$728$	64.8293	−	325.919i	0.0890512	−	0.447691i
$729$	10.3325	+	24.9447i	0.0141735	+	0.0342178i
$730$		−	49.9328i		−	0.0684011i
$731$	−456.213	−	741.755i	−0.624094	−	1.01471i
$732$	−921.078			−1.25830
$733$	−440.763	+	182.570i	−0.601314	+	0.249072i	−0.662510	−	0.749053i	$-0.730509\pi$
$733$	−440.763	+	182.570i	−0.601314	+	0.249072i	0.0611957	+	0.998126i	$0.480509\pi$
$734$	143.427	+	28.5293i	0.195404	+	0.0388683i
$735$	146.942	−	146.942i	0.199921	−	0.199921i
$736$	−913.179	−	1366.67i	−1.24073	−	1.85689i
$737$	−620.736	+	123.472i	−0.842247	+	0.167533i
$738$	8.08617	−	12.1018i	0.0109569	−	0.0163981i
$739$	−301.663	+	728.278i	−0.408204	+	0.985491i	0.577406	+	0.816457i	$0.304065\pi$
$739$	−301.663	+	728.278i	−0.408204	+	0.985491i	−0.985610	+	0.169034i	$0.945935\pi$
$740$	342.450	+	141.848i	0.462771	+	0.191686i
$741$	−169.671	−	113.370i	−0.228975	−	0.152996i
$742$	−517.742	−	2602.87i	−0.697766	−	3.50791i
$743$	−671.111	+	448.422i	−0.903245	+	0.603529i	−0.918095	−	0.396361i	$-0.870273\pi$
$743$	−671.111	+	448.422i	−0.903245	+	0.603529i	0.0148497	+	0.999890i	$0.495273\pi$
$744$	151.145	+	151.145i	0.203152	+	0.203152i
$745$	−79.8245	+	401.305i	−0.107147	+	0.538664i
$746$	−535.716	−	1293.33i	−0.718118	−	1.73369i
$747$			203.676i			0.272659i
$748$	165.961	+	447.609i	0.221873	+	0.598408i
$749$	651.827			0.870262
$750$	−409.371	+	169.567i	−0.545828	+	0.226089i
$751$	−564.672	−	112.320i	−0.751894	−	0.149561i	−0.195758	−	0.980652i	$-0.562717\pi$
$751$	−564.672	−	112.320i	−0.751894	−	0.149561i	−0.556136	+	0.831091i	$0.687717\pi$
$752$	−253.239	+	253.239i	−0.336755	+	0.336755i
$753$	176.493	+	264.140i	0.234386	+	0.350784i
$754$	631.741	−	125.661i	0.837853	−	0.166659i
$755$	−155.304	+	232.428i	−0.205700	+	0.307852i
$756$	−105.515	+	254.735i	−0.139570	+	0.336951i
$757$	772.341	+	319.914i	1.02027	+	0.422608i	0.829190	−	0.558967i	$-0.188802\pi$
$757$	772.341	+	319.914i	1.02027	+	0.422608i	0.191076	+	0.981575i	$0.438802\pi$
$758$	659.478	+	440.649i	0.870024	+	0.581331i
$759$	69.6743	+	350.276i	0.0917975	+	0.461497i
$760$	−47.6684	+	31.8510i	−0.0627216	+	0.0419092i
$761$	−990.680	−	990.680i	−1.30181	−	1.30181i	−0.927168	−	0.374646i	$-0.877764\pi$
$761$	−990.680	−	990.680i	−1.30181	−	1.30181i	−0.374646	−	0.927168i	$-0.622236\pi$
$762$	−9.02113	+	45.3523i	−0.0118388	+	0.0595174i
$763$	71.6529	+	172.985i	0.0939094	+	0.226717i
$764$		−	181.221i		−	0.237200i
$765$	−38.9863	+	84.9317i	−0.0509624	+	0.111022i
$766$	1464.45			1.91181
$767$	188.970	−	78.2741i	0.246376	−	0.102052i
$768$	158.632	+	31.5539i	0.206553	+	0.0410859i
$769$	−235.285	+	235.285i	−0.305962	+	0.305962i	−0.843341	−	0.537379i	$-0.819415\pi$
$769$	−235.285	+	235.285i	−0.305962	+	0.305962i	0.537379	+	0.843341i	$0.319415\pi$
$770$	−184.604	−	276.280i	−0.239746	−	0.358805i
$771$	487.811	−	97.0317i	0.632699	−	0.125852i
$772$	70.7137	−	105.831i	0.0915980	−	0.137086i
$773$	558.885	−	1349.27i	0.723008	−	1.74549i	0.0584106	−	0.998293i	$-0.481397\pi$
$773$	558.885	−	1349.27i	0.723008	−	1.74549i	0.664597	−	0.747202i	$-0.268603\pi$
$774$	−424.970	−	176.028i	−0.549056	−	0.227427i
$775$	773.263	+	516.678i	0.997759	+	0.666681i
$776$	−7.03750	−	35.3799i	−0.00906894	−	0.0455926i
$777$	628.480	−	419.937i	0.808854	−	0.540459i
$778$	235.808	+	235.808i	0.303095	+	0.303095i
$779$	3.44485	−	17.3184i	0.00442215	−	0.0222316i
$780$	−65.1421	−	157.267i	−0.0835155	−	0.201624i
$781$		−	572.156i		−	0.732594i
$782$	1851.71	+	69.7306i	2.36792	+	0.0891695i
$783$	−103.395			−0.132050
$784$	680.021	−	281.674i	0.867373	−	0.359278i
$785$	63.1432	+	12.5600i	0.0804372	+	0.0159999i
$786$	−188.114	+	188.114i	−0.239330	+	0.239330i
$787$	−364.195	−	545.056i	−0.462764	−	0.692575i	0.524546	−	0.851382i	$-0.324235\pi$
$787$	−364.195	−	545.056i	−0.462764	−	0.692575i	−0.987310	+	0.158808i	$0.949235\pi$
$788$	−669.596	+	133.191i	−0.849741	+	0.169024i
$789$	447.356	−	669.516i	0.566992	−	0.848563i
$790$	167.079	−	403.365i	0.211493	−	0.510589i
$791$	1702.02	+	704.999i	2.15173	+	0.891276i
$792$	40.5625	+	27.1030i	0.0512153	+	0.0342210i
$793$	−226.226	−	1137.32i	−0.285279	−	1.43419i
$794$	661.566	−	442.044i	0.833206	−	0.556731i
$795$	−185.971	−	185.971i	−0.233926	−	0.233926i
$796$	−230.040	+	1156.49i	−0.288995	+	1.45288i
$797$	555.221	+	1340.42i	0.696639	+	1.68184i	0.730956	+	0.682425i	$0.239075\pi$
$797$	555.221	+	1340.42i	0.696639	+	1.68184i	−0.0343165	+	0.999411i	$0.510925\pi$
$798$			604.299i			0.757267i
$799$	−85.5951	−	534.782i	−0.107128	−	0.669314i
$800$	−976.854			−1.22107
$801$	104.800	−	43.4096i	0.130837	−	0.0541943i
$802$	−647.523	−	128.800i	−0.807385	−	0.160599i
$803$	−36.4498	+	36.4498i	−0.0453921	+	0.0453921i
$804$	533.436	+	798.343i	0.663478	+	0.992964i
$805$	−700.231	+	139.285i	−0.869852	+	0.173024i
$806$	−772.794	+	1156.57i	−0.958802	+	1.43495i
$807$	88.4202	−	213.465i	0.109567	−	0.264517i
$808$	261.483	+	108.310i	0.323618	+	0.134047i
$809$	−205.527	−	137.329i	−0.254051	−	0.169751i	0.422023	−	0.906585i	$-0.361320\pi$
$809$	−205.527	−	137.329i	−0.254051	−	0.169751i	−0.676074	+	0.736834i	$0.736320\pi$
$810$	9.63028	+	48.4147i	0.0118892	+	0.0597712i
$811$	742.611	−	496.197i	0.915674	−	0.611834i	−0.00592294	−	0.999982i	$-0.501885\pi$
$811$	742.611	−	496.197i	0.915674	−	0.611834i	0.921597	+	0.388149i	$0.126885\pi$
$812$	−746.610	−	746.610i	−0.919471	−	0.919471i
$813$	−54.5010	+	273.995i	−0.0670369	+	0.337017i
$814$	−264.541	−	638.659i	−0.324989	−	0.784594i
$815$		−	104.634i		−	0.128385i
$816$	−242.698	+	225.083i	−0.297424	+	0.275837i
$817$	−558.050			−0.683048
$818$	−387.102	+	160.343i	−0.473229	+	0.196018i
$819$	−340.454	−	67.7206i	−0.415695	−	0.0826869i
$820$	10.4155	−	10.4155i	0.0127019	−	0.0127019i
$821$	−105.448	−	157.815i	−0.128439	−	0.192222i	0.761677	−	0.647957i	$-0.224376\pi$
$821$	−105.448	−	157.815i	−0.128439	−	0.192222i	−0.890116	+	0.455735i	$0.849376\pi$
$822$	61.1072	−	12.1550i	0.0743397	−	0.0147871i
$823$	−311.015	+	465.467i	−0.377904	+	0.565574i	−0.970856	−	0.239664i	$-0.922963\pi$
$823$	−311.015	+	465.467i	−0.377904	+	0.565574i	0.592952	+	0.805238i	$0.297963\pi$
$824$	−106.661	+	257.502i	−0.129443	+	0.312502i
$825$	196.094	+	81.2250i	0.237690	+	0.0984545i
$826$	−503.635	−	336.518i	−0.609727	−	0.407407i
$827$	12.0743	+	60.7016i	0.0146001	+	0.0733998i	0.987398	−	0.158254i	$-0.0505864\pi$
$827$	12.0743	+	60.7016i	0.0146001	+	0.0733998i	−0.972798	+	0.231654i	$0.925586\pi$
$828$	450.499	−	301.014i	0.544081	−	0.363543i
$829$	454.439	+	454.439i	0.548178	+	0.548178i	0.925913	−	0.377736i	$-0.123297\pi$
$829$	454.439	+	454.439i	0.548178	+	0.548178i	−0.377736	+	0.925913i	$0.623297\pi$
$830$	−72.6465	+	365.219i	−0.0875259	+	0.440022i
$831$	17.6353	+	42.5755i	0.0212218	+	0.0512340i
$832$		−	974.792i		−	1.17162i
$833$	−258.080	+	1082.76i	−0.309820	+	1.29983i
$834$	803.300			0.963189
$835$	−297.474	+	123.218i	−0.356257	+	0.147566i
$836$	300.046	+	59.6828i	0.358907	+	0.0713909i
$837$	157.886	−	157.886i	0.188633	−	0.188633i
$838$	606.909	+	908.304i	0.724235	+	1.08389i
$839$	804.501	−	160.025i	0.958881	−	0.190733i	0.309248	−	0.950981i	$-0.399923\pi$
$839$	804.501	−	160.025i	0.958881	−	0.190733i	0.649633	+	0.760248i	$0.274923\pi$
$840$	−54.1811	+	81.0877i	−0.0645013	+	0.0965330i
$841$	−170.315	+	411.178i	−0.202515	+	0.488915i
$842$	−767.265	−	317.812i	−0.911241	−	0.377448i
$843$	−352.362	−	235.441i	−0.417985	−	0.279289i
$844$	66.3971	+	333.801i	0.0786696	+	0.395499i
$845$	−79.2970	+	52.9845i	−0.0938426	+	0.0627036i
$846$	−202.287	−	202.287i	−0.239110	−	0.239110i
$847$	185.647	−	933.309i	0.219181	−	1.10190i
$848$	−356.489	−	860.640i	−0.420388	−	1.01491i
$849$			414.797i			0.488572i
$850$	645.857	−	892.001i	0.759832	−	1.04941i
$851$	−1485.32			−1.74538
$852$	−801.937	+	332.173i	−0.941241	+	0.389875i
$853$	131.809	+	26.2184i	0.154524	+	0.0307367i	0.271746	−	0.962369i	$-0.412399\pi$
$853$	131.809	+	26.2184i	0.154524	+	0.0307367i	−0.117222	+	0.993106i	$0.537399\pi$
$854$	−2428.19	+	2428.19i	−2.84332	+	2.84332i
$855$	33.2715	+	49.7944i	0.0389141	+	0.0582390i
$856$	−171.602	+	34.1337i	−0.200469	+	0.0398758i
$857$	126.005	−	188.580i	0.147031	−	0.220047i	−0.750643	−	0.660708i	$-0.770256\pi$
$857$	126.005	−	188.580i	0.147031	−	0.220047i	0.897673	+	0.440661i	$0.145256\pi$
$858$	−121.488	+	293.298i	−0.141594	+	0.341839i
$859$	291.424	+	120.712i	0.339259	+	0.140526i	0.545807	−	0.837911i	$-0.316223\pi$
$859$	291.424	+	120.712i	0.339259	+	0.140526i	−0.206548	+	0.978436i	$0.566223\pi$
$860$	−387.063	−	258.627i	−0.450073	−	0.300729i
$861$	−5.85996	−	29.4600i	−0.00680600	−	0.0342160i
$862$	−1126.37	+	752.616i	−1.30669	+	0.873105i
$863$	−80.2596	−	80.2596i	−0.0930007	−	0.0930007i	0.659076	−	0.752076i	$-0.270948\pi$
$863$	−80.2596	−	80.2596i	−0.0930007	−	0.0930007i	−0.752076	+	0.659076i	$0.770948\pi$
$864$	−45.7555	+	230.028i	−0.0529578	+	0.266237i
$865$	−68.0569	−	164.304i	−0.0786785	−	0.189947i
$866$			1451.67i			1.67630i
$867$	−60.4554	−	496.899i	−0.0697294	−	0.573124i
$868$	2280.18			2.62693
$869$	−416.412	+	172.484i	−0.479185	+	0.198485i
$870$	−185.401	−	36.8786i	−0.213105	−	0.0423892i
$871$	−854.751	+	854.751i	−0.981344	+	0.981344i
$872$	−27.9221	−	41.7884i	−0.0320208	−	0.0479224i
$873$	−36.9578	+	7.35136i	−0.0423342	+	0.00842080i
$874$	659.727	−	987.351i	0.754836	−	1.12969i
$875$	−349.942	+	844.835i	−0.399934	+	0.965525i
$876$	72.2498	+	29.9268i	0.0824769	+	0.0341631i
$877$	1266.64	+	846.340i	1.44428	+	0.965040i	0.997520	+	0.0703879i	$0.0224237\pi$
$877$	1266.64	+	846.340i	1.44428	+	0.965040i	0.446764	+	0.894652i	$0.352576\pi$
$878$	136.463	+	686.048i	0.155425	+	0.781376i
$879$	409.590	−	273.679i	0.465972	−	0.311353i
$880$	−82.4738	−	82.4738i	−0.0937202	−	0.0937202i
$881$	197.802	−	994.419i	0.224520	−	1.12874i	−0.689879	−	0.723925i	$-0.742336\pi$
$881$	197.802	−	994.419i	0.224520	−	1.12874i	0.914399	−	0.404814i	$-0.132664\pi$
$882$	225.000	+	543.198i	0.255102	+	0.615871i
$883$		−	1200.42i		−	1.35948i	−0.733452	−	0.679741i	$-0.762092\pi$
$883$		−	1200.42i		−	1.35948i	0.733452	−	0.679741i	$-0.237908\pi$
$884$	738.520	+	534.728i	0.835429	+	0.604896i
$885$	−60.0277			−0.0678279
$886$	131.789	−	54.5887i	0.148746	−	0.0616126i
$887$	−1297.21	−	258.031i	−1.46247	−	0.290903i	−0.601219	−	0.799084i	$-0.705318\pi$
$887$	−1297.21	−	258.031i	−1.46247	−	0.290903i	−0.861251	+	0.508181i	$0.830318\pi$
$888$	−143.465	+	143.465i	−0.161559	+	0.161559i
$889$	53.0175	+	79.3463i	0.0596372	+	0.0892534i
$890$	203.404	−	40.4596i	0.228544	−	0.0454602i
$891$	28.3118	−	42.3715i	0.0317753	−	0.0475550i
$892$	−574.780	+	1387.64i	−0.644373	+	1.55565i
$893$	−320.648	−	132.817i	−0.359069	−	0.148731i
$894$	−962.563	−	643.164i	−1.07669	−	0.719423i
$895$	−34.2903	−	172.389i	−0.0383132	−	0.192614i
$896$	−794.050	+	530.567i	−0.886217	+	0.592151i
$897$	482.329	+	482.329i	0.537714	+	0.537714i
$898$	41.5427	−	208.849i	0.0462614	−	0.232572i
$899$	327.215	+	789.968i	0.363977	+	0.878719i
$900$		−	322.003i		−	0.357781i
$901$	1370.34	+	326.629i	1.52092	+	0.362518i
$902$	−27.4706			−0.0304552
$903$	−877.027	+	363.276i	−0.971237	+	0.402300i
$904$	−484.996	−	96.4717i	−0.536500	−	0.106716i
$905$	368.121	−	368.121i	0.406764	−	0.406764i
$906$	−439.404	−	657.614i	−0.484993	−	0.725843i
$907$	505.346	−	100.520i	0.557162	−	0.110826i	0.0915258	−	0.995803i	$-0.470826\pi$
$907$	505.346	−	100.520i	0.557162	−	0.110826i	0.465636	+	0.884976i	$0.345826\pi$
$908$	202.066	−	302.413i	0.222540	−	0.333054i
$909$	113.140	−	273.145i	0.124467	−	0.300490i
$910$	−586.326	−	242.864i	−0.644315	−	0.266884i
$911$	−515.920	−	344.727i	−0.566322	−	0.378405i	0.239200	−	0.970970i	$-0.423115\pi$
$911$	−515.920	−	344.727i	−0.566322	−	0.378405i	−0.805522	+	0.592566i	$0.798115\pi$
$912$	41.3824	+	208.043i	0.0453754	+	0.228118i
$913$	319.632	−	213.571i	0.350090	−	0.233922i
$914$	−364.890	−	364.890i	−0.399224	−	0.399224i
$915$	−66.3921	+	333.776i	−0.0725597	+	0.364782i
$916$	307.966	+	743.495i	0.336207	+	0.811676i
$917$			549.023i			0.598716i
$918$	−179.796	−	193.867i	−0.195856	−	0.211184i
$919$	−125.245			−0.136284			−0.0681420	−	0.997676i	$-0.521707\pi$
$919$	−125.245			−0.136284			−0.0681420	+	0.997676i	$0.521707\pi$
$920$	177.051	−	73.3368i	0.192446	−	0.0797139i
$921$	127.452	+	25.3519i	0.138385	+	0.0275265i
$922$	1493.84	−	1493.84i	1.62021	−	1.62021i
$923$	−607.120	−	908.620i	−0.657769	−	0.984420i
$924$	510.401	−	101.525i	0.552382	−	0.109876i
$925$	−490.423	+	733.969i	−0.530186	+	0.793480i
$926$	991.662	−	2394.08i	1.07091	−	2.58540i
$927$	268.986	+	111.418i	0.290168	+	0.120192i
$928$	−746.774	−	498.979i	−0.804714	−	0.537692i
$929$	309.673	+	1556.83i	0.333340	+	1.67581i	0.676427	+	0.736510i	$0.263528\pi$
$929$	309.673	+	1556.83i	0.333340	+	1.67581i	−0.343086	+	0.939304i	$0.611472\pi$
$930$	339.426	−	226.797i	0.364974	−	0.243868i
$931$	504.381	+	504.381i	0.541763	+	0.541763i
$932$	214.128	−	1076.49i	0.229751	−	1.15504i
$933$	−31.8350	−	76.8564i	−0.0341211	−	0.0823755i
$934$		−	1537.48i		−	1.64612i
$935$	174.165	−	27.8762i	0.186273	−	0.0298141i
$936$	93.1751			0.0995461
$937$	−1418.74	+	587.661i	−1.51413	+	0.627173i	−0.976405	−	0.215948i	$-0.930716\pi$
$937$	−1418.74	+	587.661i	−1.51413	+	0.627173i	−0.537724	+	0.843121i	$0.680716\pi$
$938$	3510.91	+	698.363i	3.74297	+	0.744523i
$939$	−491.997	+	491.997i	−0.523959	+	0.523959i
$940$	−160.847	−	240.725i	−0.171114	−	0.256091i
$941$	150.395	−	29.9154i	0.159825	−	0.0317911i	−0.114529	−	0.993420i	$-0.536536\pi$
$941$	150.395	−	29.9154i	0.159825	−	0.0317911i	0.274354	+	0.961629i	$0.411536\pi$
$942$	−101.198	+	151.454i	−0.107429	+	0.160779i
$943$	−22.5877	+	54.5316i	−0.0239530	+	0.0578278i
$944$	−196.432	−	81.3649i	−0.208085	−	0.0861916i
$945$	84.7041	+	56.5975i	0.0896340	+	0.0598915i
$946$	169.372	+	851.492i	0.179041	+	0.900097i
$947$	50.1805	−	33.5295i	0.0529889	−	0.0354061i	−0.528794	−	0.848750i	$-0.677355\pi$
$947$	50.1805	−	33.5295i	0.0529889	−	0.0354061i	0.581783	+	0.813344i	$0.302355\pi$
$948$	483.508	+	483.508i	0.510029	+	0.510029i
$949$	−19.2074	+	96.5620i	−0.0202396	+	0.101751i
$950$	−270.071	−	652.009i	−0.284285	−	0.686325i
$951$			341.749i			0.359357i
$952$	19.6571	−	521.999i	0.0206482	−	0.548319i
$953$	777.736			0.816093			0.408046	−	0.912961i	$-0.366210\pi$
$953$	777.736			0.816093			0.408046	+	0.912961i	$0.366210\pi$
$954$	687.476	−	284.762i	0.720625	−	0.298493i
$955$	−65.6698	−	13.0625i	−0.0687642	−	0.0136780i
$956$	989.481	−	989.481i	1.03502	−	1.03502i
$957$	108.418	+	162.259i	0.113290	+	0.169550i
$958$	−2440.40	+	485.426i	−2.54739	+	0.506707i
$959$	71.4352	−	106.910i	0.0744893	−	0.111481i
$960$	−109.477	+	264.302i	−0.114039	+	0.275315i
$961$	−818.114	−	338.874i	−0.851315	−	0.352626i
$962$	−1097.80	−	733.524i	−1.14116	−	0.762499i
$963$	35.6560	+	179.255i	0.0370259	+	0.186142i
$964$	1327.17	−	886.790i	1.37674	−	0.919906i
$965$	−33.2532	−	33.2532i	−0.0344593	−	0.0344593i
$966$	394.081	−	1981.18i	0.407951	−	2.05091i
$967$	324.490	+	783.389i	0.335564	+	0.810123i	0.998130	+	0.0611199i	$0.0194672\pi$
$967$	324.490	+	783.389i	0.335564	+	0.810123i	−0.662566	+	0.749003i	$0.730533\pi$
$968$			255.427i			0.263871i
$969$	−291.530	−	133.821i	−0.300856	−	0.138102i
$970$	−68.8924			−0.0710231
$971$	1004.73	−	416.171i	1.03473	−	0.428601i	0.200315	−	0.979732i	$-0.435804\pi$
$971$	1004.73	−	416.171i	1.03473	−	0.428601i	0.834419	+	0.551131i	$0.185804\pi$
$972$	−75.8250	−	15.0825i	−0.0780092	−	0.0155170i
$973$	1172.24	−	1172.24i	1.20477	−	1.20477i
$974$	−1323.23	−	1980.35i	−1.35855	−	2.03322i
$975$	397.599	−	79.0874i	0.407794	−	0.0811152i
$976$	−669.677	+	1002.24i	−0.686145	+	1.02689i
$977$	−287.786	+	694.777i	−0.294561	+	0.711133i	0.705436	+	0.708773i	$0.250751\pi$
$977$	−287.786	+	694.777i	−0.294561	+	0.711133i	−0.999997	+	0.00235960i	$0.999249\pi$
$978$	273.508	+	113.291i	0.279661	+	0.115839i
$979$	−178.015	−	118.946i	−0.181834	−	0.121497i
$980$	116.084	+	583.592i	0.118453	+	0.595502i
$981$	−43.6521	+	29.1674i	−0.0444975	+	0.0297323i
$982$	−1422.33	−	1422.33i	−1.44840	−	1.44840i
$983$	68.4864	−	344.305i	0.0696708	−	0.350259i	−0.930188	−	0.367084i	$-0.880356\pi$
$983$	68.4864	−	344.305i	0.0696708	−	0.350259i	0.999858	+	0.0168255i	$0.00535599\pi$
$984$	3.08542	+	7.44885i	0.00313559	+	0.00756997i
$985$			252.245i			0.256087i
$986$	949.373	−	352.002i	0.962853	−	0.357000i
$987$	−590.388			−0.598165
$988$	539.822	−	223.602i	0.546378	−	0.226317i
$989$	1829.55	+	363.921i	1.84990	+	0.367969i
$990$	65.8798	−	65.8798i	0.0665452	−	0.0665452i
$991$	−365.475	−	546.972i	−0.368794	−	0.551940i	0.599938	−	0.800046i	$-0.295192\pi$
$991$	−365.475	−	546.972i	−0.368794	−	0.551940i	−0.968733	+	0.248106i	$0.920192\pi$
$992$	1902.29	−	378.389i	1.91763	−	0.381441i
$993$	−421.833	+	631.318i	−0.424807	+	0.635769i
$994$	−1238.42	+	2989.80i	−1.24589	+	3.00785i
$995$	402.502	+	166.722i	0.404524	+	0.167559i
$996$	−484.909	−	324.006i	−0.486857	−	0.325307i
$997$	29.0007	+	145.796i	0.0290880	+	0.146235i	0.992600	−	0.121430i	$-0.0387479\pi$
$997$	29.0007	+	145.796i	0.0290880	+	0.146235i	−0.963512	+	0.267665i	$0.913748\pi$
$998$	−26.9688	+	18.0200i	−0.0270229	+	0.0180561i
$999$	149.863	+	149.863i	0.150013	+	0.150013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.j.a.37.2	✓	48
3.2	odd	2		153.3.p.c.37.5		48
17.6	odd	16	inner	51.3.j.a.40.2	yes	48
51.23	even	16		153.3.p.c.91.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.j.a.37.2	✓	48	1.1	even	1	trivial
51.3.j.a.40.2	yes	48	17.6	odd	16	inner
153.3.p.c.37.5		48	3.2	odd	2
153.3.p.c.91.5		48	51.23	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.j (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76539 + 1.14546i) q^{2} +(-1.69877 - 0.337906i) q^{3} +(3.50687 - 3.50687i) q^{4} +(-1.01802 - 1.52358i) q^{5} +(5.08482 - 1.01143i) q^{6} +(5.94423 - 8.89617i) q^{7} +(-1.09904 + 2.65331i) q^{8} +(2.77164 + 1.14805i) q^{9} +(4.56044 + 3.04719i) q^{10} +(-1.10464 - 5.55340i) q^{11} +(-7.14237 + 4.77238i) q^{12} +(-7.64701 - 7.64701i) q^{13} +(-6.24789 + 31.4103i) q^{14} +(1.21456 + 2.93221i) q^{15} +11.2415i q^{16} +(-13.7696 - 9.96991i) q^{17} -8.97971 q^{18} +(-10.0649 + 4.16901i) q^{19} +(-8.91309 - 1.77292i) q^{20} +(-13.1040 + 13.1040i) q^{21} +(9.41598 + 14.0920i) q^{22} +(35.7162 - 7.10439i) q^{23} +(2.76358 - 4.13598i) q^{24} +(8.28216 - 19.9949i) q^{25} +(29.9063 + 12.3876i) q^{26} +(-4.32044 - 2.88683i) q^{27} +(-10.3521 - 52.0434i) q^{28} +(16.5449 - 11.0549i) q^{29} +(-6.71748 - 6.71748i) q^{30} +(-8.38326 + 42.1455i) q^{31} +(-17.2729 - 41.7005i) q^{32} +9.80722i q^{33} +(49.4984 + 11.7982i) q^{34} -19.6054 q^{35} +(13.7459 - 5.69372i) q^{36} +(-40.0038 - 7.95725i) q^{37} +(23.0579 - 23.0579i) q^{38} +(10.4065 + 15.5745i) q^{39} +(5.16137 - 1.02666i) q^{40} +(-0.900494 + 1.34768i) q^{41} +(21.2275 - 51.2476i) q^{42} +(47.3255 + 19.6029i) q^{43} +(-23.3489 - 15.6013i) q^{44} +(-1.07245 - 5.39156i) q^{45} +(-90.6314 + 60.5579i) q^{46} +(22.5271 + 22.5271i) q^{47} +(3.79859 - 19.0968i) q^{48} +(-25.0565 - 60.4917i) q^{49} +64.7806i q^{50} +(20.0224 + 21.5894i) q^{51} -53.6342 q^{52} +(-76.5589 + 31.7117i) q^{53} +(15.2545 + 3.03430i) q^{54} +(-7.33651 + 7.33651i) q^{55} +(17.0713 + 25.5491i) q^{56} +(18.5066 - 3.68120i) q^{57} +(-33.0900 + 49.5227i) q^{58} +(-7.23788 + 17.4738i) q^{59} +(14.5422 + 6.02358i) q^{60} +(89.1552 + 59.5716i) q^{61} +(-25.0931 - 126.151i) q^{62} +(26.6885 - 17.8327i) q^{63} +(63.7368 + 63.7368i) q^{64} +(-3.86600 + 19.4357i) q^{65} +(-11.2338 - 27.1208i) q^{66} -111.776i q^{67} +(-83.2513 + 13.3249i) q^{68} -63.0742 q^{69} +(54.2167 - 22.4573i) q^{70} +(99.1067 + 19.7135i) q^{71} +(-6.09226 + 6.09226i) q^{72} +(-5.05783 - 7.56958i) q^{73} +(119.741 - 23.8180i) q^{74} +(-20.8259 + 31.1681i) q^{75} +(-20.6761 + 49.9164i) q^{76} +(-55.9703 - 23.1837i) q^{77} +(-46.6181 - 31.1492i) q^{78} +(-15.5295 - 78.0722i) q^{79} +(17.1274 - 11.4442i) q^{80} +(6.36396 + 6.36396i) q^{81} +(0.946495 - 4.75835i) q^{82} +(25.9811 + 62.7240i) q^{83} +91.9078i q^{84} +(-1.17222 + 31.1287i) q^{85} -153.328 q^{86} +(-31.8415 + 13.1892i) q^{87} +(15.9489 + 3.17244i) q^{88} +(26.7368 - 26.7368i) q^{89} +(9.14157 + 13.6813i) q^{90} +(-113.485 + 22.5735i) q^{91} +(100.338 - 150.166i) q^{92} +(28.4824 - 68.7627i) q^{93} +(-88.1002 - 36.4923i) q^{94} +(16.5981 + 11.0905i) q^{95} +(15.2518 + 76.6762i) q^{96} +(-10.4438 + 6.97830i) q^{97} +(138.582 + 138.582i) q^{98} +(3.31392 - 16.6602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) \) 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

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