LMFDB - Embedded newform 510.2.l.g.443.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			443.5
Character	$\chi$	$=$	510.443
Dual form			510.2.l.g.137.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.33031 + 1.10918i) q^{3} +1.00000i q^{4} +(1.95694 - 1.08185i) q^{5} +(-0.156362 - 1.72498i) q^{6} +(2.14663 - 2.14663i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539441 + 2.95110i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.33031 + 1.10918i) q^{3} +1.00000i q^{4} +(1.95694 - 1.08185i) q^{5} +(-0.156362 - 1.72498i) q^{6} +(2.14663 - 2.14663i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539441 + 2.95110i) q^{9} +(-2.14875 - 0.618778i) q^{10} -5.66219i q^{11} +(-1.10918 + 1.33031i) q^{12} +(-2.16195 - 2.16195i) q^{13} -3.03580 q^{14} +(3.80330 + 0.731396i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(1.70530 - 2.46819i) q^{18} +3.98054i q^{19} +(1.08185 + 1.95694i) q^{20} +(5.23669 - 0.474682i) q^{21} +(-4.00377 + 4.00377i) q^{22} +(-2.99907 + 2.99907i) q^{23} +(1.72498 - 0.156362i) q^{24} +(2.65919 - 4.23423i) q^{25} +3.05746i q^{26} +(-2.55568 + 4.52421i) q^{27} +(2.14663 + 2.14663i) q^{28} -0.0340765 q^{29} +(-2.17216 - 3.20651i) q^{30} -2.05514 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.28038 - 7.53246i) q^{33} +1.00000i q^{34} +(1.87848 - 6.52316i) q^{35} +(-2.95110 + 0.539441i) q^{36} +(3.72812 - 3.72812i) q^{37} +(2.81467 - 2.81467i) q^{38} +(-0.478069 - 5.27404i) q^{39} +(0.618778 - 2.14875i) q^{40} +12.0351i q^{41} +(-4.03855 - 3.36725i) q^{42} +(7.34865 + 7.34865i) q^{43} +5.66219 q^{44} +(4.24831 + 5.19152i) q^{45} +4.24133 q^{46} +(1.05886 + 1.05886i) q^{47} +(-1.33031 - 1.10918i) q^{48} -2.21607i q^{49} +(-4.87439 + 1.11372i) q^{50} +(-0.156362 - 1.72498i) q^{51} +(2.16195 - 2.16195i) q^{52} +(-1.48993 + 1.48993i) q^{53} +(5.00624 - 1.39196i) q^{54} +(-6.12565 - 11.0805i) q^{55} -3.03580i q^{56} +(-4.41514 + 5.29535i) q^{57} +(0.0240957 + 0.0240957i) q^{58} -7.73324 q^{59} +(-0.731396 + 3.80330i) q^{60} -3.85997 q^{61} +(1.45320 + 1.45320i) q^{62} +(7.49292 + 5.17695i) q^{63} -1.00000i q^{64} +(-6.56970 - 1.89188i) q^{65} +(-9.76715 + 0.885349i) q^{66} +(10.7198 - 10.7198i) q^{67} +(0.707107 - 0.707107i) q^{68} +(-7.31620 + 0.663181i) q^{69} +(-5.94086 + 3.28428i) q^{70} +0.984495i q^{71} +(2.46819 + 1.70530i) q^{72} +(10.5383 + 10.5383i) q^{73} -5.27235 q^{74} +(8.23407 - 2.68331i) q^{75} -3.98054 q^{76} +(-12.1546 - 12.1546i) q^{77} +(-3.39127 + 4.06736i) q^{78} -3.14251i q^{79} +(-1.95694 + 1.08185i) q^{80} +(-8.41801 + 3.18389i) q^{81} +(8.51009 - 8.51009i) q^{82} +(5.33250 - 5.33250i) q^{83} +(0.474682 + 5.23669i) q^{84} +(-2.14875 - 0.618778i) q^{85} -10.3926i q^{86} +(-0.0453322 - 0.0377969i) q^{87} +(-4.00377 - 4.00377i) q^{88} -9.37013 q^{89} +(0.666954 - 6.67497i) q^{90} -9.28182 q^{91} +(-2.99907 - 2.99907i) q^{92} +(-2.73396 - 2.27951i) q^{93} -1.49746i q^{94} +(4.30636 + 7.78967i) q^{95} +(0.156362 + 1.72498i) q^{96} +(-13.0207 + 13.0207i) q^{97} +(-1.56700 + 1.56700i) q^{98} +(16.7097 - 3.05442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7}+O(q^{10}) $ 28 * q + 4 * q^7	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.33031	+	1.10918i	0.768054	+	0.640385i
$3$	1.33031	+	1.10918i	0.768054	+	0.640385i
$4$			1.00000i			0.500000i
$5$	1.95694	−	1.08185i	0.875168	−	0.483819i
$5$	1.95694	−	1.08185i	0.875168	−	0.483819i
$6$	−0.156362	−	1.72498i	−0.0638344	−	0.704220i
$7$	2.14663	−	2.14663i	0.811351	−	0.811351i	−0.173485	−	0.984836i	$-0.555503\pi$
$7$	2.14663	−	2.14663i	0.811351	−	0.811351i	0.984836	+	0.173485i	$0.0555029\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.539441	+	2.95110i	0.179814	+	0.983701i
$10$	−2.14875	−	0.618778i	−0.679494	−	0.195675i
$11$		−	5.66219i		−	1.70721i	−0.520917	−	0.853607i	$-0.674410\pi$
$11$		−	5.66219i		−	1.70721i	0.520917	−	0.853607i	$-0.325590\pi$
$12$	−1.10918	+	1.33031i	−0.320193	+	0.384027i
$13$	−2.16195	−	2.16195i	−0.599616	−	0.599616i	0.340594	−	0.940210i	$-0.389372\pi$
$13$	−2.16195	−	2.16195i	−0.599616	−	0.599616i	−0.940210	+	0.340594i	$0.889372\pi$
$14$	−3.03580			−0.811351
$15$	3.80330	+	0.731396i	0.982007	+	0.188846i
$16$	−1.00000			−0.250000
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$18$	1.70530	−	2.46819i	0.401944	−	0.581757i
$19$			3.98054i			0.913199i	0.889672	+	0.456600i	$0.150933\pi$
$19$			3.98054i			0.913199i	−0.889672	+	0.456600i	$0.849067\pi$
$20$	1.08185	+	1.95694i	0.241909	+	0.437584i
$21$	5.23669	−	0.474682i	1.14274	−	0.103584i
$22$	−4.00377	+	4.00377i	−0.853607	+	0.853607i
$23$	−2.99907	+	2.99907i	−0.625350	+	0.625350i	−0.946894	−	0.321545i	$-0.895798\pi$
$23$	−2.99907	+	2.99907i	−0.625350	+	0.625350i	0.321545	+	0.946894i	$0.395798\pi$
$24$	1.72498	−	0.156362i	0.352110	−	0.0319172i
$25$	2.65919	−	4.23423i	0.531839	−	0.846846i
$26$			3.05746i			0.599616i
$27$	−2.55568	+	4.52421i	−0.491841	+	0.870685i
$28$	2.14663	+	2.14663i	0.405676	+	0.405676i
$29$	−0.0340765			−0.00632784			−0.00316392	−	0.999995i	$-0.501007\pi$
$29$	−0.0340765			−0.00632784			−0.00316392	+	0.999995i	$0.501007\pi$
$30$	−2.17216	−	3.20651i	−0.396580	−	0.585426i
$31$	−2.05514			−0.369113			−0.184557	−	0.982822i	$-0.559085\pi$
$31$	−2.05514			−0.369113			−0.184557	+	0.982822i	$0.559085\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.28038	−	7.53246i	1.09327	−	1.31123i
$34$			1.00000i			0.171499i
$35$	1.87848	−	6.52316i	0.317522	−	1.10262i
$36$	−2.95110	+	0.539441i	−0.491850	+	0.0899068i
$37$	3.72812	−	3.72812i	0.612898	−	0.612898i	−0.330802	−	0.943700i	$-0.607319\pi$
$37$	3.72812	−	3.72812i	0.612898	−	0.612898i	0.943700	+	0.330802i	$0.107319\pi$
$38$	2.81467	−	2.81467i	0.456600	−	0.456600i
$39$	−0.478069	−	5.27404i	−0.0765523	−	0.844523i
$40$	0.618778	−	2.14875i	0.0978373	−	0.339747i
$41$			12.0351i			1.87956i	0.341775	+	0.939782i	$0.388972\pi$
$41$			12.0351i			1.87956i	−0.341775	+	0.939782i	$0.611028\pi$
$42$	−4.03855	−	3.36725i	−0.623162	−	0.519577i
$43$	7.34865	+	7.34865i	1.12066	+	1.12066i	0.991642	+	0.129016i	$0.0411820\pi$
$43$	7.34865	+	7.34865i	1.12066	+	1.12066i	0.129016	+	0.991642i	$0.458818\pi$
$44$	5.66219			0.853607
$45$	4.24831	+	5.19152i	0.633300	+	0.773906i
$46$	4.24133			0.625350
$47$	1.05886	+	1.05886i	0.154451	+	0.154451i	0.780103	−	0.625652i	$-0.215167\pi$
$47$	1.05886	+	1.05886i	0.154451	+	0.154451i	−0.625652	+	0.780103i	$0.715167\pi$
$48$	−1.33031	−	1.10918i	−0.192013	−	0.160096i
$49$		−	2.21607i		−	0.316582i
$50$	−4.87439	+	1.11372i	−0.689342	+	0.157504i
$51$	−0.156362	−	1.72498i	−0.0218950	−	0.241545i
$52$	2.16195	−	2.16195i	0.299808	−	0.299808i
$53$	−1.48993	+	1.48993i	−0.204657	+	0.204657i	−0.801992	−	0.597335i	$-0.796226\pi$
$53$	−1.48993	+	1.48993i	−0.204657	+	0.204657i	0.597335	+	0.801992i	$0.296226\pi$
$54$	5.00624	−	1.39196i	0.681263	−	0.189422i
$55$	−6.12565	−	11.0805i	−0.825982	−	1.49410i
$56$		−	3.03580i		−	0.405676i
$57$	−4.41514	+	5.29535i	−0.584799	+	0.701386i
$58$	0.0240957	+	0.0240957i	0.00316392	+	0.00316392i
$59$	−7.73324			−1.00678			−0.503391	−	0.864059i	$-0.667914\pi$
$59$	−7.73324			−1.00678			−0.503391	+	0.864059i	$0.667914\pi$
$60$	−0.731396	+	3.80330i	−0.0944229	+	0.491003i
$61$	−3.85997			−0.494219			−0.247110	−	0.968988i	$-0.579481\pi$
$61$	−3.85997			−0.494219			−0.247110	+	0.968988i	$0.579481\pi$
$62$	1.45320	+	1.45320i	0.184557	+	0.184557i
$63$	7.49292	+	5.17695i	0.944019	+	0.652235i
$64$		−	1.00000i		−	0.125000i
$65$	−6.56970	−	1.89188i	−0.814871	−	0.234659i
$66$	−9.76715	+	0.885349i	−1.20225	+	0.108979i
$67$	10.7198	−	10.7198i	1.30963	−	1.30963i	0.387950	−	0.921681i	$-0.373183\pi$
$67$	10.7198	−	10.7198i	1.30963	−	1.30963i	0.921681	−	0.387950i	$-0.126817\pi$
$68$	0.707107	−	0.707107i	0.0857493	−	0.0857493i
$69$	−7.31620	+	0.663181i	−0.880767	+	0.0798376i
$70$	−5.94086	+	3.28428i	−0.710069	+	0.392547i
$71$			0.984495i			0.116838i	0.998292	+	0.0584191i	$0.0186060\pi$
$71$			0.984495i			0.116838i	−0.998292	+	0.0584191i	$0.981394\pi$
$72$	2.46819	+	1.70530i	0.290879	+	0.200972i
$73$	10.5383	+	10.5383i	1.23342	+	1.23342i	0.962643	+	0.270772i	$0.0872791\pi$
$73$	10.5383	+	10.5383i	1.23342	+	1.23342i	0.270772	+	0.962643i	$0.412721\pi$
$74$	−5.27235			−0.612898
$75$	8.23407	−	2.68331i	0.950788	−	0.309842i
$76$	−3.98054			−0.456600
$77$	−12.1546	−	12.1546i	−1.38515	−	1.38515i
$78$	−3.39127	+	4.06736i	−0.383985	+	0.460538i
$79$		−	3.14251i		−	0.353560i	−0.984250	−	0.176780i	$-0.943432\pi$
$79$		−	3.14251i		−	0.353560i	0.984250	−	0.176780i	$-0.0565680\pi$
$80$	−1.95694	+	1.08185i	−0.218792	+	0.120955i
$81$	−8.41801	+	3.18389i	−0.935334	+	0.353766i
$82$	8.51009	−	8.51009i	0.939782	−	0.939782i
$83$	5.33250	−	5.33250i	0.585318	−	0.585318i	−0.351042	−	0.936360i	$-0.614173\pi$
$83$	5.33250	−	5.33250i	0.585318	−	0.585318i	0.936360	+	0.351042i	$0.114173\pi$
$84$	0.474682	+	5.23669i	0.0517921	+	0.571369i
$85$	−2.14875	−	0.618778i	−0.233064	−	0.0671159i
$86$		−	10.3926i		−	1.12066i
$87$	−0.0453322	−	0.0377969i	−0.00486012	−	0.00405226i
$88$	−4.00377	−	4.00377i	−0.426804	−	0.426804i
$89$	−9.37013			−0.993231			−0.496616	−	0.867971i	$-0.665424\pi$
$89$	−9.37013			−0.993231			−0.496616	+	0.867971i	$0.665424\pi$
$90$	0.666954	−	6.67497i	0.0703031	−	0.703603i
$91$	−9.28182			−0.972999
$92$	−2.99907	−	2.99907i	−0.312675	−	0.312675i
$93$	−2.73396	−	2.27951i	−0.283499	−	0.236375i
$94$		−	1.49746i		−	0.154451i
$95$	4.30636	+	7.78967i	0.441823	+	0.799203i
$96$	0.156362	+	1.72498i	0.0159586	+	0.176055i
$97$	−13.0207	+	13.0207i	−1.32205	+	1.32205i	−0.409936	+	0.912114i	$0.634449\pi$
$97$	−13.0207	+	13.0207i	−1.32205	+	1.32205i	−0.912114	+	0.409936i	$0.865551\pi$
$98$	−1.56700	+	1.56700i	−0.158291	+	0.158291i
$99$	16.7097	−	3.05442i	1.67939	−	0.306980i
$100$	4.23423	+	2.65919i	0.423423	+	0.265919i
$101$			12.9788i			1.29144i	0.763574	+	0.645720i	$0.223443\pi$
$101$			12.9788i			1.29144i	−0.763574	+	0.645720i	$0.776557\pi$
$102$	−1.10918	+	1.33031i	−0.109825	+	0.131720i
$103$	−3.45747	−	3.45747i	−0.340675	−	0.340675i	0.515946	−	0.856621i	$-0.327440\pi$
$103$	−3.45747	−	3.45747i	−0.340675	−	0.340675i	−0.856621	+	0.515946i	$0.827440\pi$
$104$	−3.05746			−0.299808
$105$	9.73432	−	6.59424i	0.949973	−	0.643532i
$106$	2.10708			0.204657
$107$	−0.882485	−	0.882485i	−0.0853130	−	0.0853130i	0.663162	−	0.748475i	$-0.269214\pi$
$107$	−0.882485	−	0.882485i	−0.0853130	−	0.0853130i	−0.748475	+	0.663162i	$0.769214\pi$
$108$	−4.52421	−	2.55568i	−0.435343	−	0.245920i
$109$			13.5361i			1.29652i	0.761420	+	0.648259i	$0.224503\pi$
$109$			13.5361i			1.29652i	−0.761420	+	0.648259i	$0.775497\pi$
$110$	−3.50364	+	12.1666i	−0.334059	+	1.16004i
$111$	9.09469	−	0.824394i	0.863230	−	0.0782480i
$112$	−2.14663	+	2.14663i	−0.202838	+	0.202838i
$113$	−1.56803	+	1.56803i	−0.147508	+	0.147508i	−0.777004	−	0.629496i	$-0.783261\pi$
$113$	−1.56803	+	1.56803i	−0.147508	+	0.147508i	0.629496	+	0.777004i	$0.283261\pi$
$114$	6.86635	−	0.622404i	0.643093	−	0.0582935i
$115$	−2.62444	+	9.11354i	−0.244730	+	0.849842i
$116$		−	0.0340765i		−	0.00316392i
$117$	5.21388	−	7.54637i	0.482024	−	0.697662i
$118$	5.46822	+	5.46822i	0.503391	+	0.503391i
$119$	−3.03580			−0.278291
$120$	3.20651	−	2.17216i	0.292713	−	0.198290i
$121$	−21.0604			−1.91458
$122$	2.72941	+	2.72941i	0.247110	+	0.247110i
$123$	−13.3491	+	16.0104i	−1.20364	+	1.44361i
$124$		−	2.05514i		−	0.184557i
$125$	0.623062	−	11.1630i	0.0557284	−	0.998446i
$126$	−1.63763	−	8.95895i	−0.145892	−	0.798127i
$127$	6.49943	−	6.49943i	0.576731	−	0.576731i	−0.357270	−	0.934001i	$-0.616292\pi$
$127$	6.49943	−	6.49943i	0.576731	−	0.576731i	0.934001	+	0.357270i	$0.116292\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	1.62500	+	17.9269i	0.143073	+	1.57838i
$130$	3.30771	+	5.98324i	0.290106	+	0.524765i
$131$			10.8768i			0.950309i	0.879902	+	0.475155i	$0.157608\pi$
$131$			10.8768i			0.950309i	−0.879902	+	0.475155i	$0.842392\pi$
$132$	7.53246	+	6.28038i	0.655616	+	0.546637i
$133$	8.54477	+	8.54477i	0.740926	+	0.740926i
$134$	−15.1601			−1.30963
$135$	−0.106772	+	11.6185i	−0.00918947	+	0.999958i
$136$	−1.00000			−0.0857493
$137$	11.6082	+	11.6082i	0.991757	+	0.991757i	0.999966	−	0.00820945i	$-0.00261318\pi$
$137$	11.6082	+	11.6082i	0.991757	+	0.991757i	−0.00820945	+	0.999966i	$0.502613\pi$
$138$	5.64227	+	4.70439i	0.480302	+	0.400465i
$139$		−	6.56323i		−	0.556686i	−0.960482	−	0.278343i	$-0.910215\pi$
$139$		−	6.56323i		−	0.556686i	0.960482	−	0.278343i	$-0.0897851\pi$
$140$	6.52316	+	1.87848i	0.551308	+	0.158761i
$141$	0.234145	+	2.58308i	0.0197186	+	0.217535i
$142$	0.696143	−	0.696143i	0.0584191	−	0.0584191i
$143$	−12.2414	+	12.2414i	−1.02367	+	1.02367i
$144$	−0.539441	−	2.95110i	−0.0449534	−	0.245925i
$145$	−0.0666855	+	0.0368657i	−0.00553793	+	0.00306153i
$146$		−	14.9034i		−	1.23342i
$147$	2.45802	−	2.94806i	0.202734	−	0.243152i
$148$	3.72812	+	3.72812i	0.306449	+	0.306449i
$149$	−10.6505			−0.872526			−0.436263	−	0.899819i	$-0.643698\pi$
$149$	−10.6505			−0.872526			−0.436263	+	0.899819i	$0.643698\pi$
$150$	−7.71975	−	3.92498i	−0.630315	−	0.320473i
$151$	4.06863			0.331100			0.165550	−	0.986201i	$-0.447060\pi$
$151$	4.06863			0.331100			0.165550	+	0.986201i	$0.447060\pi$
$152$	2.81467	+	2.81467i	0.228300	+	0.228300i
$153$	1.70530	−	2.46819i	0.137865	−	0.199541i
$154$			17.1893i			1.38515i
$155$	−4.02177	+	2.22335i	−0.323036	+	0.178584i
$156$	5.27404	−	0.478069i	0.422261	−	0.0382761i
$157$	8.61879	−	8.61879i	0.687855	−	0.687855i	−0.273903	−	0.961757i	$-0.588315\pi$
$157$	8.61879	−	8.61879i	0.687855	−	0.687855i	0.961757	+	0.273903i	$0.0883147\pi$
$158$	−2.22209	+	2.22209i	−0.176780	+	0.176780i
$159$	−3.63466	+	0.329466i	−0.288247	+	0.0261283i
$160$	2.14875	+	0.618778i	0.169873	+	0.0489187i
$161$			12.8758i			1.01476i
$162$	8.20378	+	3.70108i	0.644550	+	0.290784i
$163$	−8.32065	−	8.32065i	−0.651724	−	0.651724i	0.301684	−	0.953408i	$-0.402451\pi$
$163$	−8.32065	−	8.32065i	−0.651724	−	0.651724i	−0.953408	+	0.301684i	$0.902451\pi$
$164$	−12.0351			−0.939782
$165$	4.14131	−	21.5350i	0.322400	−	1.67650i
$166$	−7.54129			−0.585318
$167$	−1.86827	−	1.86827i	−0.144571	−	0.144571i	0.631117	−	0.775688i	$-0.282597\pi$
$167$	−1.86827	−	1.86827i	−0.144571	−	0.144571i	−0.775688	+	0.631117i	$0.782597\pi$
$168$	3.36725	−	4.03855i	0.259789	−	0.311581i
$169$		−	3.65197i		−	0.280921i
$170$	1.08185	+	1.95694i	0.0829742	+	0.150090i
$171$	−11.7470	+	2.14727i	−0.898315	+	0.164206i
$172$	−7.34865	+	7.34865i	−0.560329	+	0.560329i
$173$	13.3281	−	13.3281i	1.01332	−	1.01332i	0.0134081	−	0.999910i	$-0.495732\pi$
$173$	13.3281	−	13.3281i	1.01332	−	1.01332i	0.999910	−	0.0134081i	$-0.00426805\pi$
$174$	0.00532825	+	0.0587812i	0.000403934	+	0.00445619i
$175$	−3.38102	−	14.7977i	−0.255581	−	1.11860i
$176$			5.66219i			0.426804i
$177$	−10.2876	−	8.57755i	−0.773263	−	0.644728i
$178$	6.62568	+	6.62568i	0.496616	+	0.496616i
$179$	−2.21788			−0.165772			−0.0828860	−	0.996559i	$-0.526414\pi$
$179$	−2.21788			−0.165772			−0.0828860	+	0.996559i	$0.526414\pi$
$180$	−5.19152	+	4.24831i	−0.386953	+	0.316650i
$181$	−24.1020			−1.79149			−0.895744	−	0.444569i	$-0.853357\pi$
$181$	−24.1020			−1.79149			−0.895744	+	0.444569i	$0.853357\pi$
$182$	6.56324	+	6.56324i	0.486499	+	0.486499i
$183$	−5.13496	−	4.28141i	−0.379587	−	0.316491i
$184$			4.24133i			0.312675i
$185$	3.26241	−	11.3290i	0.239857	−	0.832921i
$186$	0.321344	+	3.54507i	0.0235621	+	0.259937i
$187$	−4.00377	+	4.00377i	−0.292785	+	0.292785i
$188$	−1.05886	+	1.05886i	−0.0772255	+	0.0772255i
$189$	4.22572	+	15.1979i	0.307376	+	1.10549i
$190$	2.46307	−	8.55318i	0.178690	−	0.620513i
$191$		−	14.5183i		−	1.05051i	−0.850945	−	0.525255i	$-0.823970\pi$
$191$		−	14.5183i		−	1.05051i	0.850945	−	0.525255i	$-0.176030\pi$
$192$	1.10918	−	1.33031i	0.0800481	−	0.0960067i
$193$	−6.63092	−	6.63092i	−0.477304	−	0.477304i	0.426964	−	0.904269i	$-0.359583\pi$
$193$	−6.63092	−	6.63092i	−0.477304	−	0.477304i	−0.904269	+	0.426964i	$0.859583\pi$
$194$	18.4140			1.32205
$195$	−6.64128	−	9.80377i	−0.475592	−	0.702062i
$196$	2.21607			0.158291
$197$	−2.06498	−	2.06498i	−0.147124	−	0.147124i	0.629708	−	0.776832i	$-0.283175\pi$
$197$	−2.06498	−	2.06498i	−0.147124	−	0.147124i	−0.776832	+	0.629708i	$0.783175\pi$
$198$	−13.9753	−	9.65574i	−0.993184	−	0.686204i
$199$		−	18.0953i		−	1.28274i	−0.767230	−	0.641372i	$-0.778365\pi$
$199$		−	18.0953i		−	1.28274i	0.767230	−	0.641372i	$-0.221635\pi$
$200$	−1.11372	−	4.87439i	−0.0787518	−	0.344671i
$201$	26.1508	−	2.37045i	1.84453	−	0.167199i
$202$	9.17741	−	9.17741i	0.645720	−	0.645720i
$203$	−0.0731497	+	0.0731497i	−0.00513410	+	0.00513410i
$204$	1.72498	−	0.156362i	0.120773	−	0.0109475i
$205$	13.0202	+	23.5519i	0.909368	+	1.64493i
$206$			4.88960i			0.340675i
$207$	−10.4684	−	7.23274i	−0.727603	−	0.502710i
$208$	2.16195	+	2.16195i	0.149904	+	0.149904i
$209$	22.5386			1.55903
$210$	−11.5460	−	2.22037i	−0.796752	−	0.153220i
$211$	−9.80363			−0.674910			−0.337455	−	0.941342i	$-0.609566\pi$
$211$	−9.80363			−0.674910			−0.337455	+	0.941342i	$0.609566\pi$
$212$	−1.48993	−	1.48993i	−0.102329	−	0.102329i
$213$	−1.09198	+	1.30968i	−0.0748214	+	0.0897380i
$214$			1.24802i			0.0853130i
$215$	22.3310	+	6.43068i	1.52296	+	0.438569i
$216$	1.39196	+	5.00624i	0.0947111	+	0.340631i
$217$	−4.41162	+	4.41162i	−0.299481	+	0.299481i
$218$	9.57143	−	9.57143i	0.648259	−	0.648259i
$219$	2.33032	+	25.7081i	0.157469	+	1.73719i
$220$	11.0805	−	6.12565i	0.747050	−	0.412991i
$221$			3.05746i			0.205667i
$222$	−7.01385	−	5.84799i	−0.470739	−	0.392491i
$223$	−14.2996	−	14.2996i	−0.957573	−	0.957573i	0.0415633	−	0.999136i	$-0.486766\pi$
$223$	−14.2996	−	14.2996i	−0.957573	−	0.957573i	−0.999136	+	0.0415633i	$0.986766\pi$
$224$	3.03580			0.202838
$225$	13.9301	+	5.56343i	0.928675	+	0.370896i
$226$	2.21753			0.147508
$227$	6.02382	+	6.02382i	0.399815	+	0.399815i	0.878168	−	0.478353i	$-0.158766\pi$
$227$	6.02382	+	6.02382i	0.399815	+	0.399815i	−0.478353	+	0.878168i	$0.658766\pi$
$228$	−5.29535	−	4.41514i	−0.350693	−	0.292400i
$229$			7.78756i			0.514616i	0.966329	+	0.257308i	$0.0828355\pi$
$229$			7.78756i			0.514616i	−0.966329	+	0.257308i	$0.917164\pi$
$230$	8.30000	−	4.58849i	0.547286	−	0.302556i
$231$	−2.68774	−	29.6511i	−0.176840	−	1.95090i
$232$	−0.0240957	+	0.0240957i	−0.00158196	+	0.00158196i
$233$	−4.50357	+	4.50357i	−0.295038	+	0.295038i	−0.839067	−	0.544028i	$-0.816898\pi$
$233$	−4.50357	+	4.50357i	−0.295038	+	0.295038i	0.544028	+	0.839067i	$0.316898\pi$
$234$	−9.02286	+	1.64932i	−0.589843	+	0.107819i
$235$	3.21766	+	0.926594i	0.209897	+	0.0604443i
$236$		−	7.73324i		−	0.503391i
$237$	3.48560	−	4.18050i	0.226414	−	0.271553i
$238$	2.14663	+	2.14663i	0.139146	+	0.139146i
$239$	14.8781			0.962384			0.481192	−	0.876615i	$-0.340204\pi$
$239$	14.8781			0.962384			0.481192	+	0.876615i	$0.340204\pi$
$240$	−3.80330	−	0.731396i	−0.245502	−	0.0472114i
$241$	−21.6372			−1.39378			−0.696889	−	0.717179i	$-0.745433\pi$
$241$	−21.6372			−1.39378			−0.696889	+	0.717179i	$0.745433\pi$
$242$	14.8919	+	14.8919i	0.957290	+	0.957290i
$243$	−14.7301	−	5.10152i	−0.944933	−	0.327263i
$244$		−	3.85997i		−	0.247110i
$245$	−2.39746	−	4.33671i	−0.153168	−	0.277062i
$246$	20.7603	−	1.88182i	1.32363	−	0.119981i
$247$	8.60573	−	8.60573i	0.547569	−	0.547569i
$248$	−1.45320	+	1.45320i	−0.0922783	+	0.0922783i
$249$	13.0086	−	1.17917i	0.824384	−	0.0747268i
$250$	−8.33398	+	7.45284i	−0.527087	+	0.471359i
$251$		−	2.36545i		−	0.149306i	−0.997210	−	0.0746529i	$-0.976215\pi$
$251$		−	2.36545i		−	0.149306i	0.997210	−	0.0746529i	$-0.0237849\pi$
$252$	−5.17695	+	7.49292i	−0.326117	+	0.472009i
$253$	16.9813	+	16.9813i	1.06761	+	1.06761i
$254$	−9.19158			−0.576731
$255$	−2.17216	−	3.20651i	−0.136026	−	0.200800i
$256$	1.00000			0.0625000
$257$	−19.4702	−	19.4702i	−1.21452	−	1.21452i	−0.969525	−	0.244992i	$-0.921215\pi$
$257$	−19.4702	−	19.4702i	−1.21452	−	1.21452i	−0.244992	−	0.969525i	$-0.578785\pi$
$258$	11.5272	−	13.8253i	0.717653	−	0.860726i
$259$		−	16.0058i		−	0.994552i
$260$	1.89188	−	6.56970i	0.117330	−	0.407435i
$261$	−0.0183822	−	0.100563i	−0.00113783	−	0.00622470i
$262$	7.69105	−	7.69105i	0.475155	−	0.475155i
$263$	11.1382	−	11.1382i	0.686812	−	0.686812i	−0.274714	−	0.961526i	$-0.588583\pi$
$263$	11.1382	−	11.1382i	0.686812	−	0.686812i	0.961526	+	0.274714i	$0.0885832\pi$
$264$	−0.885349	−	9.76715i	−0.0544895	−	0.601127i
$265$	−1.30381	+	4.52757i	−0.0800925	+	0.278127i
$266$		−	12.0841i		−	0.740926i
$267$	−12.4652	−	10.3932i	−0.762855	−	0.636051i
$268$	10.7198	+	10.7198i	0.654815	+	0.654815i
$269$	19.0255			1.16001			0.580003	−	0.814614i	$-0.303051\pi$
$269$	19.0255			1.16001			0.580003	+	0.814614i	$0.303051\pi$
$270$	8.29099	−	8.13999i	0.504574	−	0.495384i
$271$	0.444681			0.0270125			0.0135062	−	0.999909i	$-0.495701\pi$
$271$	0.444681			0.0270125			0.0135062	+	0.999909i	$0.495701\pi$
$272$	0.707107	+	0.707107i	0.0428746	+	0.0428746i
$273$	−12.3477	−	10.2952i	−0.747316	−	0.623094i
$274$		−	16.4165i		−	0.991757i
$275$	−23.9750	−	15.0569i	−1.44575	−	0.907963i
$276$	−0.663181	−	7.31620i	−0.0399188	−	0.440383i
$277$	−6.98252	+	6.98252i	−0.419539	+	0.419539i	−0.885045	−	0.465506i	$-0.845872\pi$
$277$	−6.98252	+	6.98252i	−0.419539	+	0.419539i	0.465506	+	0.885045i	$0.345872\pi$
$278$	−4.64090	+	4.64090i	−0.278343	+	0.278343i
$279$	−1.10862	−	6.06492i	−0.0663716	−	0.363097i
$280$	−3.28428	−	5.94086i	−0.196274	−	0.355034i
$281$		−	5.68922i		−	0.339390i	−0.985497	−	0.169695i	$-0.945722\pi$
$281$		−	5.68922i		−	0.339390i	0.985497	−	0.169695i	$-0.0542783\pi$
$282$	1.66095	−	1.99208i	0.0989082	−	0.118627i
$283$	−2.10107	−	2.10107i	−0.124896	−	0.124896i	0.641896	−	0.766792i	$-0.278148\pi$
$283$	−2.10107	−	2.10107i	−0.124896	−	0.124896i	−0.766792	+	0.641896i	$0.778148\pi$
$284$	−0.984495			−0.0584191
$285$	−2.91136	+	15.1392i	−0.172454	+	0.896768i
$286$	17.3119			1.02367
$287$	25.8349	+	25.8349i	1.52499	+	1.52499i
$288$	−1.70530	+	2.46819i	−0.100486	+	0.145439i
$289$			1.00000i			0.0588235i
$290$	0.0732217	+	0.0210858i	0.00429973	+	0.00123820i
$291$	−31.7638	+	2.87925i	−1.86203	+	0.168785i
$292$	−10.5383	+	10.5383i	−0.616708	+	0.616708i
$293$	2.94684	−	2.94684i	0.172156	−	0.172156i	−0.615770	−	0.787926i	$-0.711155\pi$
$293$	2.94684	−	2.94684i	0.172156	−	0.172156i	0.787926	+	0.615770i	$0.211155\pi$
$294$	−3.82268	+	0.346509i	−0.222943	+	0.0202088i
$295$	−15.1334	+	8.36622i	−0.881103	+	0.487100i
$296$		−	5.27235i		−	0.306449i
$297$	25.6169	+	14.4707i	1.48645	+	0.839678i
$298$	7.53107	+	7.53107i	0.436263	+	0.436263i
$299$	12.9677			0.749940
$300$	2.68331	+	8.23407i	0.154921	+	0.475394i
$301$	31.5497			1.81850
$302$	−2.87696	−	2.87696i	−0.165550	−	0.165550i
$303$	−14.3958	+	17.2658i	−0.827019	+	0.991896i
$304$		−	3.98054i		−	0.228300i
$305$	−7.55372	+	4.17592i	−0.432525	+	0.239113i
$306$	−2.95110	+	0.539441i	−0.168703	+	0.0308378i
$307$	11.7953	−	11.7953i	0.673194	−	0.673194i	−0.285257	−	0.958451i	$-0.592079\pi$
$307$	11.7953	−	11.7953i	0.673194	−	0.673194i	0.958451	+	0.285257i	$0.0920790\pi$
$308$	12.1546	−	12.1546i	0.692575	−	0.692575i
$309$	−0.764547	−	8.43446i	−0.0434935	−	0.479820i
$310$	4.41597	+	1.27167i	0.250810	+	0.0722261i
$311$		−	27.1364i		−	1.53877i	−0.638788	−	0.769383i	$-0.720564\pi$
$311$		−	27.1364i		−	1.53877i	0.638788	−	0.769383i	$-0.279436\pi$
$312$	−4.06736	−	3.39127i	−0.230269	−	0.191993i
$313$	3.80475	+	3.80475i	0.215057	+	0.215057i	0.806412	−	0.591355i	$-0.201407\pi$
$313$	3.80475	+	3.80475i	0.215057	+	0.215057i	−0.591355	+	0.806412i	$0.701407\pi$
$314$	−12.1888			−0.687855
$315$	20.2639	+	2.02474i	1.14174	+	0.114081i
$316$	3.14251			0.176780
$317$	−19.4872	−	19.4872i	−1.09451	−	1.09451i	−0.995041	−	0.0994674i	$-0.968286\pi$
$317$	−19.4872	−	19.4872i	−1.09451	−	1.09451i	−0.0994674	−	0.995041i	$-0.531714\pi$
$318$	2.80306	+	2.33713i	0.157188	+	0.131059i
$319$			0.192947i			0.0108030i
$320$	−1.08185	−	1.95694i	−0.0604774	−	0.109396i
$321$	−0.195143	−	2.15281i	−0.0108918	−	0.120158i
$322$	9.10458	−	9.10458i	0.507378	−	0.507378i
$323$	2.81467	−	2.81467i	0.156612	−	0.156612i
$324$	−3.18389	−	8.41801i	−0.176883	−	0.467667i
$325$	−14.9032	+	3.40514i	−0.826682	+	0.188883i
$326$			11.7672i			0.651724i
$327$	−15.0139	+	18.0071i	−0.830271	+	0.995796i
$328$	8.51009	+	8.51009i	0.469891	+	0.469891i
$329$	4.54598			0.250628
$330$	−18.1559	+	12.2992i	−0.999448	+	0.677048i
$331$	−0.967661			−0.0531874			−0.0265937	−	0.999646i	$-0.508466\pi$
$331$	−0.967661			−0.0531874			−0.0265937	+	0.999646i	$0.508466\pi$
$332$	5.33250	+	5.33250i	0.292659	+	0.292659i
$333$	13.0131	+	8.99095i	0.713116	+	0.492701i
$334$			2.64214i			0.144571i
$335$	9.38071	−	32.5751i	0.512523	−	1.77977i
$336$	−5.23669	+	0.474682i	−0.285685	+	0.0258961i
$337$	7.53858	−	7.53858i	0.410652	−	0.410652i	−0.471313	−	0.881966i	$-0.656220\pi$
$337$	7.53858	−	7.53858i	0.410652	−	0.410652i	0.881966	+	0.471313i	$0.156220\pi$
$338$	−2.58233	+	2.58233i	−0.140460	+	0.140460i
$339$	−3.82519	+	0.346737i	−0.207756	+	0.0188321i
$340$	0.618778	−	2.14875i	0.0335579	−	0.116532i
$341$			11.6366i			0.630155i
$342$	9.82473	+	6.78803i	0.531260	+	0.367055i
$343$	10.2693	+	10.2693i	0.554492	+	0.554492i
$344$	10.3926			0.560329
$345$	−13.5999	+	9.21285i	−0.732192	+	0.496003i
$346$	−18.8488			−1.01332
$347$	18.6332	+	18.6332i	1.00028	+	1.00028i	1.00000		0.000281995i	$8.97618e-5\pi$
$347$	18.6332	+	18.6332i	1.00028	+	1.00028i	0.000281995		1.00000i	$0.499910\pi$
$348$	0.0377969	−	0.0453322i	0.00202613	−	0.00243006i
$349$			0.505066i			0.0270356i	0.999909	+	0.0135178i	$0.00430297\pi$
$349$			0.505066i			0.0270356i	−0.999909	+	0.0135178i	$0.995697\pi$
$350$	−8.07278	+	12.8543i	−0.431508	+	0.687089i
$351$	15.3064	−	4.25587i	0.816993	−	0.227161i
$352$	4.00377	−	4.00377i	0.213402	−	0.213402i
$353$	−8.98211	+	8.98211i	−0.478069	+	0.478069i	−0.904514	−	0.426444i	$-0.859766\pi$
$353$	−8.98211	+	8.98211i	−0.478069	+	0.478069i	0.426444	+	0.904514i	$0.359766\pi$
$354$	1.20918	+	13.3397i	0.0642673	+	0.708995i
$355$	1.06508	+	1.92659i	0.0565285	+	0.102253i
$356$		−	9.37013i		−	0.496616i
$357$	−4.03855	−	3.36725i	−0.213743	−	0.178214i
$358$	1.56828	+	1.56828i	0.0828860	+	0.0828860i
$359$	22.1944			1.17138			0.585688	−	0.810537i	$-0.300825\pi$
$359$	22.1944			1.17138			0.585688	+	0.810537i	$0.300825\pi$
$360$	6.67497	+	0.666954i	0.351802	+	0.0351515i
$361$	3.15527			0.166067
$362$	17.0427	+	17.0427i	0.895744	+	0.895744i
$363$	−28.0168	−	23.3598i	−1.47050	−	1.22607i
$364$		−	9.28182i		−	0.486499i
$365$	32.0237	+	9.22190i	1.67620	+	0.482696i
$366$	0.603552	+	6.65837i	0.0315482	+	0.348039i
$367$	6.66810	−	6.66810i	0.348072	−	0.348072i	−0.511319	−	0.859391i	$-0.670843\pi$
$367$	6.66810	−	6.66810i	0.348072	−	0.348072i	0.859391	+	0.511319i	$0.170843\pi$
$368$	2.99907	−	2.99907i	0.156337	−	0.156337i
$369$	−35.5167	+	6.49222i	−1.84893	+	0.337971i
$370$	−10.3177	+	5.70390i	−0.536389	+	0.296532i
$371$			6.39666i			0.332098i
$372$	2.27951	−	2.73396i	0.118187	−	0.141749i
$373$	12.9451	+	12.9451i	0.670273	+	0.670273i	0.957779	−	0.287506i	$-0.0928262\pi$
$373$	12.9451	+	12.9451i	0.670273	+	0.670273i	−0.287506	+	0.957779i	$0.592826\pi$
$374$	5.66219			0.292785
$375$	13.2106	−	14.1591i	0.682192	−	0.731173i
$376$	1.49746			0.0772255
$377$	0.0736715	+	0.0736715i	0.00379428	+	0.00379428i
$378$	7.75853	−	13.7346i	0.399056	−	0.706432i
$379$			17.6684i			0.907565i	0.891112	+	0.453783i	$0.149926\pi$
$379$			17.6684i			0.907565i	−0.891112	+	0.453783i	$0.850074\pi$
$380$	−7.78967	+	4.30636i	−0.399602	+	0.220912i
$381$	15.8553	−	1.43721i	0.812290	−	0.0736305i
$382$	−10.2660	+	10.2660i	−0.525255	+	0.525255i
$383$	−25.1987	+	25.1987i	−1.28760	+	1.28760i	−0.351351	+	0.936244i	$0.614278\pi$
$383$	−25.1987	+	25.1987i	−1.28760	+	1.28760i	−0.936244	+	0.351351i	$0.885722\pi$
$384$	−1.72498	+	0.156362i	−0.0880274	+	0.00797930i
$385$	−36.9354	−	10.6363i	−1.88240	−	0.542078i
$386$			9.37754i			0.477304i
$387$	−17.7225	+	25.6508i	−0.900883	+	1.30390i
$388$	−13.0207	−	13.0207i	−0.661025	−	0.661025i
$389$	−8.50060			−0.430998			−0.215499	−	0.976504i	$-0.569138\pi$
$389$	−8.50060			−0.430998			−0.215499	+	0.976504i	$0.569138\pi$
$390$	−2.23621	+	11.6284i	−0.113235	+	0.588827i
$391$	4.24133			0.214493
$392$	−1.56700	−	1.56700i	−0.0791455	−	0.0791455i
$393$	−12.0643	+	14.4695i	−0.608564	+	0.729889i
$394$			2.92033i			0.147124i
$395$	−3.39973	−	6.14968i	−0.171059	−	0.309424i
$396$	3.05442	+	16.7097i	0.153490	+	0.839694i
$397$	−25.5675	+	25.5675i	−1.28320	+	1.28320i	−0.344357	+	0.938839i	$0.611903\pi$
$397$	−25.5675	+	25.5675i	−1.28320	+	1.28320i	−0.938839	+	0.344357i	$0.888097\pi$
$398$	−12.7953	+	12.7953i	−0.641372	+	0.641372i
$399$	1.88949	+	20.8449i	0.0945930	+	1.04355i
$400$	−2.65919	+	4.23423i	−0.132960	+	0.211711i
$401$		−	15.3809i		−	0.768086i	−0.923315	−	0.384043i	$-0.874531\pi$
$401$		−	15.3809i		−	0.768086i	0.923315	−	0.384043i	$-0.125469\pi$
$402$	−20.1676	−	16.8152i	−1.00587	−	0.838668i
$403$	4.44309	+	4.44309i	0.221326	+	0.221326i
$404$	−12.9788			−0.645720
$405$	−13.0290	+	15.3377i	−0.647416	+	0.762137i
$406$	0.103449			0.00513410
$407$	−21.1093	−	21.1093i	−1.04635	−	1.04635i
$408$	−1.33031	−	1.10918i	−0.0658601	−	0.0549126i
$409$		−	16.6925i		−	0.825392i	−0.910869	−	0.412696i	$-0.864587\pi$
$409$		−	16.6925i		−	0.825392i	0.910869	−	0.412696i	$-0.135413\pi$
$410$	7.44704	−	25.8603i	0.367783	−	1.27715i
$411$	2.56691	+	28.3181i	0.126616	+	1.39683i
$412$	3.45747	−	3.45747i	0.170337	−	0.170337i
$413$	−16.6004	+	16.6004i	−0.816854	+	0.816854i
$414$	2.28795	+	12.5166i	0.112446	+	0.615157i
$415$	4.66638	−	16.2043i	0.229064	−	0.795439i
$416$		−	3.05746i		−	0.149904i
$417$	7.27980	−	8.73111i	0.356493	−	0.427565i
$418$	−15.9372	−	15.9372i	−0.779514	−	0.779514i
$419$	2.47877			0.121096			0.0605479	−	0.998165i	$-0.480715\pi$
$419$	2.47877			0.121096			0.0605479	+	0.998165i	$0.480715\pi$
$420$	6.59424	+	9.73432i	0.321766	+	0.474986i
$421$	31.1464			1.51798			0.758992	−	0.651100i	$-0.225692\pi$
$421$	31.1464			1.51798			0.758992	+	0.651100i	$0.225692\pi$
$422$	6.93222	+	6.93222i	0.337455	+	0.337455i
$423$	−2.55362	+	3.69601i	−0.124161	+	0.179706i
$424$			2.10708i			0.102329i
$425$	−4.87439	+	1.11372i	−0.236442	+	0.0540233i
$426$	1.69823	−	0.153937i	0.0822797	−	0.00745829i
$427$	−8.28595	+	8.28595i	−0.400985	+	0.400985i
$428$	0.882485	−	0.882485i	0.0426565	−	0.0426565i
$429$	−29.8626	+	2.70692i	−1.44178	+	0.130691i
$430$	−11.2432	−	20.3376i	−0.542196	−	0.980765i
$431$			29.9359i			1.44196i	0.692955	+	0.720981i	$0.256309\pi$
$431$			29.9359i			1.44196i	−0.692955	+	0.720981i	$0.743691\pi$
$432$	2.55568	−	4.52421i	0.122960	−	0.217671i
$433$	−2.82971	−	2.82971i	−0.135987	−	0.135987i	0.635837	−	0.771824i	$-0.280655\pi$
$433$	−2.82971	−	2.82971i	−0.135987	−	0.135987i	−0.771824	+	0.635837i	$0.780655\pi$
$434$	6.23898			0.299481
$435$	−0.129603	−	0.0249234i	−0.00621398	−	0.00119499i
$436$	−13.5361			−0.648259
$437$	−11.9379	−	11.9379i	−0.571069	−	0.571069i
$438$	16.5306	−	19.8261i	0.789861	−	0.947330i
$439$		−	20.4911i		−	0.977986i	−0.872288	−	0.488993i	$-0.837364\pi$
$439$		−	20.4911i		−	0.977986i	0.872288	−	0.488993i	$-0.162636\pi$
$440$	−12.1666	−	3.50364i	−0.580020	−	0.167029i
$441$	6.53986	−	1.19544i	0.311422	−	0.0569258i
$442$	2.16195	−	2.16195i	0.102833	−	0.102833i
$443$	5.84820	−	5.84820i	0.277856	−	0.277856i	−0.554396	−	0.832253i	$-0.687051\pi$
$443$	5.84820	−	5.84820i	0.277856	−	0.277856i	0.832253	+	0.554396i	$0.187051\pi$
$444$	0.824394	+	9.09469i	0.0391240	+	0.431615i
$445$	−18.3367	+	10.1371i	−0.869245	+	0.480544i
$446$			20.2227i			0.957573i
$447$	−14.1685	−	11.8134i	−0.670147	−	0.558753i
$448$	−2.14663	−	2.14663i	−0.101419	−	0.101419i
$449$	15.2235			0.718441			0.359221	−	0.933253i	$-0.383043\pi$
$449$	15.2235			0.718441			0.359221	+	0.933253i	$0.383043\pi$
$450$	−5.91614	−	13.7840i	−0.278889	−	0.649785i
$451$	68.1449			3.20882
$452$	−1.56803	−	1.56803i	−0.0737539	−	0.0737539i
$453$	5.41253	+	4.51284i	0.254303	+	0.212032i
$454$		−	8.51896i		−	0.399815i
$455$	−18.1639	+	10.0416i	−0.851538	+	0.470755i
$456$	0.622404	+	6.86635i	0.0291468	+	0.321546i
$457$	−1.98962	+	1.98962i	−0.0930704	+	0.0930704i	−0.752109	−	0.659039i	$-0.770963\pi$
$457$	−1.98962	+	1.98962i	−0.0930704	+	0.0930704i	0.659039	+	0.752109i	$0.270963\pi$
$458$	5.50663	−	5.50663i	0.257308	−	0.257308i
$459$	5.00624	−	1.39196i	0.233671	−	0.0649713i
$460$	−9.11354	−	2.62444i	−0.424921	−	0.122365i
$461$			25.0630i			1.16730i	0.812006	+	0.583649i	$0.198376\pi$
$461$			25.0630i			1.16730i	−0.812006	+	0.583649i	$0.801624\pi$
$462$	−19.0660	+	22.8670i	−0.887030	+	1.06387i
$463$	19.7164	+	19.7164i	0.916298	+	0.916298i	0.996758	−	0.0804595i	$-0.0256388\pi$
$463$	19.7164	+	19.7164i	0.916298	+	0.916298i	−0.0804595	+	0.996758i	$0.525639\pi$
$464$	0.0340765			0.00158196
$465$	−7.81629	−	1.50312i	−0.362472	−	0.0697055i
$466$	6.36901			0.295038
$467$	−7.78719	−	7.78719i	−0.360348	−	0.360348i	0.503593	−	0.863941i	$-0.332011\pi$
$467$	−7.78719	−	7.78719i	−0.360348	−	0.360348i	−0.863941	+	0.503593i	$0.832011\pi$
$468$	7.54637	+	5.21388i	0.348831	+	0.241012i
$469$		−	46.0229i		−	2.12514i
$470$	−1.62003	−	2.93043i	−0.0747263	−	0.135171i
$471$	21.0254	−	1.90586i	0.968801	−	0.0878175i
$472$	−5.46822	+	5.46822i	−0.251695	+	0.251695i
$473$	41.6095	−	41.6095i	1.91320	−	1.91320i
$474$	−5.42076	+	0.491367i	−0.248984	+	0.0225693i
$475$	16.8545	+	10.5850i	0.773339	+	0.485675i
$476$		−	3.03580i		−	0.139146i
$477$	−5.20066	−	3.59320i	−0.238122	−	0.164521i
$478$	−10.5204	−	10.5204i	−0.481192	−	0.481192i
$479$	−17.1808			−0.785009			−0.392504	−	0.919750i	$-0.628391\pi$
$479$	−17.1808			−0.785009			−0.392504	+	0.919750i	$0.628391\pi$
$480$	2.17216	+	3.20651i	0.0991451	+	0.146357i
$481$	−16.1200			−0.735008
$482$	15.2998	+	15.2998i	0.696889	+	0.696889i
$483$	−14.2816	+	17.1288i	−0.649835	+	0.779388i
$484$		−	21.0604i		−	0.957290i
$485$	−11.3942	+	39.5671i	−0.517383	+	1.79665i
$486$	6.80840	+	14.0230i	0.308835	+	0.636098i
$487$	−10.7794	+	10.7794i	−0.488459	+	0.488459i	−0.907820	−	0.419361i	$-0.862254\pi$
$487$	−10.7794	+	10.7794i	−0.488459	+	0.488459i	0.419361	+	0.907820i	$0.362254\pi$
$488$	−2.72941	+	2.72941i	−0.123555	+	0.123555i
$489$	−1.83994	−	20.2981i	−0.0832047	−	0.917913i
$490$	−1.37126	+	4.76178i	−0.0619471	+	0.215115i
$491$			4.97082i			0.224330i	0.993690	+	0.112165i	$0.0357785\pi$
$491$			4.97082i			0.224330i	−0.993690	+	0.112165i	$0.964221\pi$
$492$	−16.0104	−	13.3491i	−0.721803	−	0.601822i
$493$	0.0240957	+	0.0240957i	0.00108522	+	0.00108522i
$494$	−12.1703			−0.547569
$495$	29.3954	−	24.0547i	1.32122	−	1.08118i
$496$	2.05514			0.0922783
$497$	2.11335	+	2.11335i	0.0947968	+	0.0947968i
$498$	−10.0322	−	8.36464i	−0.449555	−	0.374829i
$499$			6.23712i			0.279212i	0.990207	+	0.139606i	$0.0445836\pi$
$499$			6.23712i			0.279212i	−0.990207	+	0.139606i	$0.955416\pi$
$500$	11.1630	+	0.623062i	0.499223	+	0.0278642i
$501$	−0.413129	−	4.55763i	−0.0184572	−	0.203620i
$502$	−1.67262	+	1.67262i	−0.0746529	+	0.0746529i
$503$	−5.53239	+	5.53239i	−0.246677	+	0.246677i	−0.819606	−	0.572928i	$-0.805807\pi$
$503$	−5.53239	+	5.53239i	−0.246677	+	0.246677i	0.572928	+	0.819606i	$0.305807\pi$
$504$	8.95895	−	1.63763i	0.399063	−	0.0729460i
$505$	14.0412	+	25.3987i	0.624823	+	1.13023i
$506$		−	24.0152i		−	1.06761i
$507$	4.05069	−	4.85824i	0.179897	−	0.215762i
$508$	6.49943	+	6.49943i	0.288365	+	0.288365i
$509$	36.4655			1.61630			0.808152	−	0.588974i	$-0.200468\pi$
$509$	36.4655			1.61630			0.808152	+	0.588974i	$0.200468\pi$
$510$	−0.731396	+	3.80330i	−0.0323868	+	0.168413i
$511$	45.2438			2.00147
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−18.0088	−	10.1730i	−0.795109	−	0.449149i
$514$			27.5350i			1.21452i
$515$	−10.5065	−	3.02558i	−0.462973	−	0.133323i
$516$	−17.9269	+	1.62500i	−0.789190	+	0.0715366i
$517$	5.99548	−	5.99548i	0.263681	−	0.263681i
$518$	−11.3178	+	11.3178i	−0.497276	+	0.497276i
$519$	32.5138	−	2.94723i	1.42720	−	0.129369i
$520$	−5.98324	+	3.30771i	−0.262383	+	0.145053i
$521$			43.4084i			1.90176i	0.309565	+	0.950878i	$0.399816\pi$
$521$			43.4084i			1.90176i	−0.309565	+	0.950878i	$0.600184\pi$
$522$	−0.0581107	+	0.0841071i	−0.00254344	+	0.00368127i
$523$	−31.2684	−	31.2684i	−1.36727	−	1.36727i	−0.864310	−	0.502960i	$-0.832244\pi$
$523$	−31.2684	−	31.2684i	−1.36727	−	1.36727i	−0.502960	−	0.864310i	$-0.667756\pi$
$524$	−10.8768			−0.475155
$525$	11.9155	−	23.4356i	0.520033	−	1.02281i
$526$	−15.7518			−0.686812
$527$	1.45320	+	1.45320i	0.0633024	+	0.0633024i
$528$	−6.28038	+	7.53246i	−0.273319	+	0.327808i
$529$			5.01114i			0.217876i
$530$	4.12341	−	2.27954i	0.179110	−	0.0990171i
$531$	−4.17162	−	22.8216i	−0.181033	−	0.990372i
$532$	−8.54477	+	8.54477i	−0.370463	+	0.370463i
$533$	26.0192	−	26.0192i	1.12702	−	1.12702i
$534$	1.46513	+	16.1633i	0.0634023	+	0.699453i
$535$	−2.68168	−	0.772248i	−0.115939	−	0.0333872i
$536$		−	15.1601i		−	0.654815i
$537$	−2.95046	−	2.46003i	−0.127322	−	0.106158i
$538$	−13.4531	−	13.4531i	−0.580003	−	0.580003i
$539$	−12.5478			−0.540473
$540$	−11.6185	−	0.106772i	−0.499979	−	0.00459473i
$541$	11.8970			0.511491			0.255746	−	0.966744i	$-0.417679\pi$
$541$	11.8970			0.511491			0.255746	+	0.966744i	$0.417679\pi$
$542$	−0.314437	−	0.314437i	−0.0135062	−	0.0135062i
$543$	−32.0631	−	26.7335i	−1.37596	−	1.14724i
$544$		−	1.00000i		−	0.0428746i
$545$	14.6440	+	26.4892i	0.627280	+	1.13467i
$546$	1.45132	+	16.0109i	0.0621108	+	0.685205i
$547$	8.68865	−	8.68865i	0.371500	−	0.371500i	−0.496523	−	0.868023i	$-0.665390\pi$
$547$	8.68865	−	8.68865i	0.371500	−	0.371500i	0.868023	+	0.496523i	$0.165390\pi$
$548$	−11.6082	+	11.6082i	−0.495878	+	0.495878i
$549$	−2.08223	−	11.3912i	−0.0888674	−	0.486164i
$550$	6.30608	+	27.5997i	0.268892	+	1.17685i
$551$		−	0.135643i		−	0.00577858i
$552$	−4.70439	+	5.64227i	−0.200232	+	0.240151i
$553$	−6.74581	−	6.74581i	−0.286861	−	0.286861i
$554$	9.87478			0.419539
$555$	16.9059	−	11.4524i	0.717614	−	0.486127i
$556$	6.56323			0.278343
$557$	24.2419	+	24.2419i	1.02716	+	1.02716i	0.999621	+	0.0275434i	$0.00876845\pi$
$557$	24.2419	+	24.2419i	1.02716	+	1.02716i	0.0275434	+	0.999621i	$0.491232\pi$
$558$	−3.50463	+	5.07246i	−0.148363	+	0.214734i
$559$		−	31.7748i		−	1.34393i
$560$	−1.87848	+	6.52316i	−0.0793804	+	0.275654i
$561$	−9.76715	+	0.885349i	−0.412370	+	0.0373795i
$562$	−4.02288	+	4.02288i	−0.169695	+	0.169695i
$563$	9.05740	−	9.05740i	0.381724	−	0.381724i	−0.489999	−	0.871723i	$-0.663003\pi$
$563$	9.05740	−	9.05740i	0.381724	−	0.381724i	0.871723	+	0.489999i	$0.163003\pi$
$564$	−2.58308	+	0.234145i	−0.108767	+	0.00985929i
$565$	−1.37216	+	4.76491i	−0.0577271	+	0.200461i
$566$			2.97136i			0.124896i
$567$	−11.2357	+	24.9050i	−0.471856	+	1.04591i
$568$	0.696143	+	0.696143i	0.0292095	+	0.0292095i
$569$	−31.4725			−1.31939			−0.659697	−	0.751532i	$-0.729315\pi$
$569$	−31.4725			−1.31939			−0.659697	+	0.751532i	$0.729315\pi$
$570$	12.7637	−	8.64638i	0.534611	−	0.362157i
$571$	−34.8293			−1.45756			−0.728781	−	0.684747i	$-0.759913\pi$
$571$	−34.8293			−1.45756			−0.728781	+	0.684747i	$0.759913\pi$
$572$	−12.2414	−	12.2414i	−0.511837	−	0.511837i
$573$	16.1034	−	19.3139i	0.672731	−	0.806848i
$574$		−	36.5361i		−	1.52499i
$575$	4.72364	+	20.6739i	0.196990	+	0.862160i
$576$	2.95110	−	0.539441i	0.122963	−	0.0224767i
$577$	−2.40343	+	2.40343i	−0.100056	+	0.100056i	−0.755363	−	0.655307i	$-0.772539\pi$
$577$	−2.40343	+	2.40343i	−0.100056	+	0.100056i	0.655307	+	0.755363i	$0.272539\pi$
$578$	0.707107	−	0.707107i	0.0294118	−	0.0294118i
$579$	−1.46629	−	16.1761i	−0.0609368	−	0.672254i
$580$	−0.0368657	−	0.0666855i	−0.00153076	−	0.00276896i
$581$		−	22.8938i		−	0.949796i
$582$	24.4963	+	20.4245i	1.01541	+	0.846621i
$583$	8.43625	+	8.43625i	0.349394	+	0.349394i
$584$	14.9034			0.616708
$585$	2.03918	−	20.4084i	0.0843097	−	0.843784i
$586$	−4.16746			−0.172156
$587$	−31.0045	−	31.0045i	−1.27969	−	1.27969i	−0.940838	−	0.338857i	$-0.889960\pi$
$587$	−31.0045	−	31.0045i	−1.27969	−	1.27969i	−0.338857	−	0.940838i	$-0.610040\pi$
$588$	2.94806	+	2.45802i	0.121576	+	0.101367i
$589$		−	8.18056i		−	0.337074i
$590$	16.6168	+	4.78515i	0.684102	+	0.197002i
$591$	−0.456627	−	5.03750i	−0.0187831	−	0.207215i
$592$	−3.72812	+	3.72812i	−0.153225	+	0.153225i
$593$	−4.61831	+	4.61831i	−0.189651	+	0.189651i	−0.795545	−	0.605894i	$-0.792816\pi$
$593$	−4.61831	+	4.61831i	−0.189651	+	0.189651i	0.605894	+	0.795545i	$0.292816\pi$
$594$	−7.88156	−	28.3463i	−0.323384	−	1.16306i
$595$	−5.94086	+	3.28428i	−0.243552	+	0.134643i
$596$		−	10.6505i		−	0.436263i
$597$	20.0710	−	24.0724i	0.821451	−	0.985217i
$598$	−9.16953	−	9.16953i	−0.374970	−	0.374970i
$599$	−37.2695			−1.52279			−0.761395	−	0.648289i	$-0.775485\pi$
$599$	−37.2695			−1.52279			−0.761395	+	0.648289i	$0.775485\pi$
$600$	3.92498	−	7.71975i	0.160237	−	0.315157i
$601$	−8.21635			−0.335152			−0.167576	−	0.985859i	$-0.553594\pi$
$601$	−8.21635			−0.335152			−0.167576	+	0.985859i	$0.553594\pi$
$602$	−22.3090	−	22.3090i	−0.909248	−	0.909248i
$603$	37.4179	+	25.8525i	1.52377	+	1.05279i
$604$			4.06863i			0.165550i
$605$	−41.2138	+	22.7842i	−1.67558	+	0.926310i
$606$	22.3882	−	2.02939i	0.909458	−	0.0824383i
$607$	22.5216	−	22.5216i	0.914122	−	0.914122i	−0.0824715	−	0.996593i	$-0.526281\pi$
$607$	22.5216	−	22.5216i	0.914122	−	0.914122i	0.996593	+	0.0824715i	$0.0262814\pi$
$608$	−2.81467	+	2.81467i	−0.114150	+	0.114150i
$609$	−0.178448	+	0.0161755i	−0.00723107	+	0.000655465i
$610$	8.29411	+	2.38847i	0.335819	+	0.0967062i
$611$		−	4.57841i		−	0.185223i
$612$	2.46819	+	1.70530i	0.0997705	+	0.0689327i
$613$	17.0167	+	17.0167i	0.687298	+	0.687298i	0.961634	−	0.274336i	$-0.0884579\pi$
$613$	17.0167	+	17.0167i	0.687298	+	0.687298i	−0.274336	+	0.961634i	$0.588458\pi$
$614$	−16.6811			−0.673194
$615$	−8.80241	+	45.7730i	−0.354948	+	1.84574i
$616$	−17.1893			−0.692575
$617$	−28.0645	−	28.0645i	−1.12983	−	1.12983i	−0.990204	−	0.139630i	$-0.955409\pi$
$617$	−28.0645	−	28.0645i	−1.12983	−	1.12983i	−0.139630	−	0.990204i	$-0.544591\pi$
$618$	−5.42345	+	6.50468i	−0.218163	+	0.261657i
$619$		−	0.456432i		−	0.0183456i	−0.999958	−	0.00917278i	$-0.997080\pi$
$619$		−	0.456432i		−	0.0183456i	0.999958	−	0.00917278i	$-0.00291983\pi$
$620$	−2.22335	−	4.02177i	−0.0892920	−	0.161518i
$621$	−5.90377	−	21.2331i	−0.236910	−	0.852055i
$622$	−19.1883	+	19.1883i	−0.769383	+	0.769383i
$623$	−20.1142	+	20.1142i	−0.805860	+	0.805860i
$624$	0.478069	+	5.27404i	0.0191381	+	0.211131i
$625$	−10.8574	−	22.5193i	−0.434295	−	0.900771i
$626$		−	5.38072i		−	0.215057i
$627$	29.9833	+	24.9994i	1.19742	+	0.998378i
$628$	8.61879	+	8.61879i	0.343927	+	0.343927i
$629$	−5.27235			−0.210222
$630$	−12.8970	−	15.7604i	−0.513829	−	0.627910i
$631$	25.7180			1.02382			0.511908	−	0.859040i	$-0.328939\pi$
$631$	25.7180			1.02382			0.511908	+	0.859040i	$0.328939\pi$
$632$	−2.22209	−	2.22209i	−0.0883899	−	0.0883899i
$633$	−13.0419	−	10.8740i	−0.518367	−	0.432202i
$634$			27.5590i			1.09451i
$635$	5.68754	−	19.7504i	0.225703	−	0.783770i
$636$	−0.329466	−	3.63466i	−0.0130642	−	0.144124i
$637$	−4.79103	+	4.79103i	−0.189828	+	0.189828i
$638$	0.136434	−	0.136434i	0.00540149	−	0.00540149i
$639$	−2.90535	+	0.531077i	−0.114934	+	0.0210091i
$640$	−0.618778	+	2.14875i	−0.0244593	+	0.0849367i
$641$			18.5681i			0.733394i	0.930340	+	0.366697i	$0.119511\pi$
$641$			18.5681i			0.733394i	−0.930340	+	0.366697i	$0.880489\pi$
$642$	−1.38428	+	1.66025i	−0.0546332	+	0.0655250i
$643$	1.35994	+	1.35994i	0.0536309	+	0.0536309i	0.733414	−	0.679783i	$-0.237926\pi$
$643$	1.35994	+	1.35994i	0.0536309	+	0.0536309i	−0.679783	+	0.733414i	$0.737926\pi$
$644$	−12.8758			−0.507378
$645$	22.5743	+	33.3239i	0.888863	+	1.31213i
$646$	−3.98054			−0.156612
$647$	−2.31050	−	2.31050i	−0.0908351	−	0.0908351i	0.660229	−	0.751064i	$-0.270459\pi$
$647$	−2.31050	−	2.31050i	−0.0908351	−	0.0908351i	−0.751064	+	0.660229i	$0.770459\pi$
$648$	−3.70108	+	8.20378i	−0.145392	+	0.322275i
$649$			43.7870i			1.71879i
$650$	12.9460	+	8.13036i	0.507782	+	0.318899i
$651$	−10.7621	+	0.975537i	−0.421800	+	0.0382343i
$652$	8.32065	−	8.32065i	0.325862	−	0.325862i
$653$	22.0517	−	22.0517i	0.862949	−	0.862949i	−0.128730	−	0.991680i	$-0.541090\pi$
$653$	22.0517	−	22.0517i	0.862949	−	0.862949i	0.991680	+	0.128730i	$0.0410901\pi$
$654$	23.3494	−	2.11652i	0.913034	−	0.0827625i
$655$	11.7671	+	21.2852i	0.459777	+	0.831680i
$656$		−	12.0351i		−	0.469891i
$657$	−25.4148	+	36.7844i	−0.991527	+	1.43510i
$658$	−3.21449	−	3.21449i	−0.125314	−	0.125314i
$659$	14.1385			0.550758			0.275379	−	0.961336i	$-0.411197\pi$
$659$	14.1385			0.550758			0.275379	+	0.961336i	$0.411197\pi$
$660$	21.5350	+	4.14131i	0.838248	+	0.161200i
$661$	7.85692			0.305599			0.152799	−	0.988257i	$-0.451171\pi$
$661$	7.85692			0.305599			0.152799	+	0.988257i	$0.451171\pi$
$662$	0.684239	+	0.684239i	0.0265937	+	0.0265937i
$663$	−3.39127	+	4.06736i	−0.131706	+	0.157963i
$664$		−	7.54129i		−	0.292659i
$665$	25.9657	+	7.47739i	1.00691	+	0.289961i
$666$	−2.84412	−	15.5592i	−0.110208	−	0.602909i
$667$	0.102198	−	0.102198i	0.00395711	−	0.00395711i
$668$	1.86827	−	1.86827i	0.0722856	−	0.0722856i
$669$	−3.16205	−	34.8837i	−0.122252	−	1.34868i
$670$	−29.6673	+	16.4009i	−1.14615	+	0.633624i
$671$			21.8559i			0.843738i
$672$	4.03855	+	3.36725i	0.155790	+	0.129894i
$673$	−15.3690	−	15.3690i	−0.592431	−	0.592431i	0.345857	−	0.938287i	$-0.387588\pi$
$673$	−15.3690	−	15.3690i	−0.592431	−	0.592431i	−0.938287	+	0.345857i	$0.887588\pi$
$674$	−10.6612			−0.410652
$675$	12.3605	+	22.8521i	0.475756	+	0.879577i
$676$	3.65197			0.140460
$677$	18.5051	+	18.5051i	0.711207	+	0.711207i	0.966788	−	0.255581i	$-0.0822667\pi$
$677$	18.5051	+	18.5051i	0.711207	+	0.711207i	−0.255581	+	0.966788i	$0.582267\pi$
$678$	2.95000	+	2.45964i	0.113294	+	0.0944619i
$679$			55.9013i			2.14529i
$680$	−1.95694	+	1.08185i	−0.0750451	+	0.0414871i
$681$	1.33204	+	14.6950i	0.0510439	+	0.563115i
$682$	8.22830	−	8.22830i	0.315078	−	0.315078i
$683$	−21.0301	+	21.0301i	−0.804696	+	0.804696i	−0.983826	−	0.179129i	$-0.942672\pi$
$683$	−21.0301	+	21.0301i	−0.804696	+	0.804696i	0.179129	+	0.983826i	$0.442672\pi$
$684$	−2.14727	−	11.7470i	−0.0821029	−	0.449157i
$685$	35.2749	+	10.1582i	1.34778	+	0.388123i
$686$		−	14.5230i		−	0.554492i
$687$	−8.63780	+	10.3599i	−0.329553	+	0.395253i
$688$	−7.34865	−	7.34865i	−0.280165	−	0.280165i
$689$	6.44229			0.245432
$690$	16.1310	+	3.10209i	0.614098	+	0.118095i
$691$	12.9720			0.493478			0.246739	−	0.969082i	$-0.420641\pi$
$691$	12.9720			0.493478			0.246739	+	0.969082i	$0.420641\pi$
$692$	13.3281	+	13.3281i	0.506659	+	0.506659i
$693$	29.3129	−	42.4263i	1.11350	−	1.61164i
$694$		−	26.3513i		−	1.00028i
$695$	−7.10044	−	12.8438i	−0.269335	−	0.487193i
$696$	−0.0587812	+	0.00532825i	−0.00222810	+	0.000201967i
$697$	8.51009	−	8.51009i	0.322342	−	0.322342i
$698$	0.357135	−	0.357135i	0.0135178	−	0.0135178i
$699$	−10.9864	+	0.995868i	−0.415544	+	0.0376672i
$700$	14.7977	−	3.38102i	0.559299	−	0.127791i
$701$			2.11308i			0.0798098i	0.999203	+	0.0399049i	$0.0127055\pi$
$701$			2.11308i			0.0798098i	−0.999203	+	0.0399049i	$0.987295\pi$
$702$	−13.8326	−	7.81387i	−0.522077	−	0.294916i
$703$	14.8399	+	14.8399i	0.559699	+	0.559699i
$704$	−5.66219			−0.213402
$705$	3.25272	+	4.80162i	0.122505	+	0.180839i
$706$	12.7026			0.478069
$707$	27.8608	+	27.8608i	1.04781	+	1.04781i
$708$	8.57755	−	10.2876i	0.322364	−	0.386631i
$709$		−	7.85717i		−	0.295082i	−0.989056	−	0.147541i	$-0.952864\pi$
$709$		−	7.85717i		−	0.295082i	0.989056	−	0.147541i	$-0.0471359\pi$
$710$	0.609184	−	2.11543i	0.0228623	−	0.0793907i
$711$	9.27386	−	1.69520i	0.347797	−	0.0635748i
$712$	−6.62568	+	6.62568i	−0.248308	+	0.248308i
$713$	6.16350	−	6.16350i	0.230825	−	0.230825i
$714$	0.474682	+	5.23669i	0.0177645	+	0.195978i
$715$	−10.7122	+	37.1989i	−0.400614	+	1.39116i
$716$		−	2.21788i		−	0.0828860i
$717$	19.7924	+	16.5025i	0.739162	+	0.616296i
$718$	−15.6938	−	15.6938i	−0.585688	−	0.585688i
$719$	21.8812			0.816032			0.408016	−	0.912975i	$-0.366221\pi$
$719$	21.8812			0.816032			0.408016	+	0.912975i	$0.366221\pi$
$720$	−4.24831	−	5.19152i	−0.158325	−	0.193477i
$721$	−14.8439			−0.552814
$722$	−2.23111	−	2.23111i	−0.0830333	−	0.0830333i
$723$	−28.7842	−	23.9996i	−1.07050	−	0.892554i
$724$		−	24.1020i		−	0.895744i
$725$	−0.0906159	+	0.144288i	−0.00336539	+	0.00535871i
$726$	3.29304	+	36.3287i	0.122216	+	1.34828i
$727$	−19.2980	+	19.2980i	−0.715723	+	0.715723i	−0.967726	−	0.252003i	$-0.918911\pi$
$727$	−19.2980	+	19.2980i	−0.715723	+	0.715723i	0.252003	+	0.967726i	$0.418911\pi$
$728$	−6.56324	+	6.56324i	−0.243250	+	0.243250i
$729$	−13.9370	−	23.1249i	−0.516185	−	0.856477i
$730$	−16.1233	−	29.1650i	−0.596750	−	1.07945i
$731$		−	10.3926i		−	0.384383i
$732$	4.28141	−	5.13496i	0.158245	−	0.189793i
$733$	−26.8443	−	26.8443i	−0.991518	−	0.991518i	0.00844679	−	0.999964i	$-0.497311\pi$
$733$	−26.8443	−	26.8443i	−0.991518	−	0.991518i	−0.999964	+	0.00844679i	$0.997311\pi$
$734$	−9.43011			−0.348072
$735$	1.62083	−	8.42838i	0.0597851	−	0.310886i
$736$	−4.24133			−0.156337
$737$	−60.6974	−	60.6974i	−2.23582	−	2.23582i
$738$	29.7048	+	20.5234i	1.09345	+	0.755478i
$739$		−	25.3809i		−	0.933652i	−0.884349	−	0.466826i	$-0.845397\pi$
$739$		−	25.3809i		−	0.933652i	0.884349	−	0.466826i	$-0.154603\pi$
$740$	11.3290	+	3.26241i	0.416461	+	0.119929i
$741$	20.9936	−	1.90297i	0.771218	−	0.0699075i
$742$	4.52312	−	4.52312i	0.166049	−	0.166049i
$743$	−4.30942	+	4.30942i	−0.158097	+	0.158097i	−0.781723	−	0.623626i	$-0.785659\pi$
$743$	−4.30942	+	4.30942i	−0.158097	+	0.158097i	0.623626	+	0.781723i	$0.285659\pi$
$744$	−3.54507	+	0.321344i	−0.129968	+	0.0117811i
$745$	−20.8424	+	11.5223i	−0.763607	+	0.422145i
$746$		−	18.3072i		−	0.670273i
$747$	18.6133	+	12.8602i	0.681025	+	0.470529i
$748$	−4.00377	−	4.00377i	−0.146392	−	0.146392i
$749$	−3.78874			−0.138438
$750$	−19.3533	+	0.670691i	−0.706683	+	0.0244902i
$751$	−47.0434			−1.71664			−0.858319	−	0.513117i	$-0.828491\pi$
$751$	−47.0434			−1.71664			−0.858319	+	0.513117i	$0.828491\pi$
$752$	−1.05886	−	1.05886i	−0.0386128	−	0.0386128i
$753$	2.62371	−	3.14678i	0.0956132	−	0.114675i
$754$		−	0.104187i		−	0.00379428i
$755$	7.96205	−	4.40165i	0.289768	−	0.160193i
$756$	−15.1979	+	4.22572i	−0.552744	+	0.153688i
$757$	37.3380	−	37.3380i	1.35707	−	1.35707i	0.479566	−	0.877506i	$-0.340794\pi$
$757$	37.3380	−	37.3380i	1.35707	−	1.35707i	0.877506	−	0.479566i	$-0.159206\pi$
$758$	12.4935	−	12.4935i	0.453783	−	0.453783i
$759$	3.75506	+	41.4257i	0.136300	+	1.50366i
$760$	8.55318	+	2.46307i	0.310257	+	0.0893450i
$761$		−	34.2864i		−	1.24288i	−0.783461	−	0.621441i	$-0.786548\pi$
$761$		−	34.2864i		−	1.24288i	0.783461	−	0.621441i	$-0.213452\pi$
$762$	−12.2276	−	10.1951i	−0.442960	−	0.369330i
$763$	29.0569	+	29.0569i	1.05193	+	1.05193i
$764$	14.5183			0.525255
$765$	0.666954	−	6.67497i	0.0241138	−	0.241334i
$766$	35.6364			1.28760
$767$	16.7188	+	16.7188i	0.603683	+	0.603683i
$768$	1.33031	+	1.10918i	0.0480034	+	0.0400241i
$769$			17.4620i			0.629697i	0.949142	+	0.314848i	$0.101954\pi$
$769$			17.4620i			0.629697i	−0.949142	+	0.314848i	$0.898046\pi$
$770$	18.5962	+	33.6383i	0.670162	+	1.21224i
$771$	−4.30542	−	47.4973i	−0.155056	−	1.71057i
$772$	6.63092	−	6.63092i	0.238652	−	0.238652i
$773$	8.19837	−	8.19837i	0.294875	−	0.294875i	−0.544128	−	0.839002i	$-0.683139\pi$
$773$	8.19837	−	8.19837i	0.294875	−	0.294875i	0.839002	+	0.544128i	$0.183139\pi$
$774$	30.6695	−	5.60617i	1.10239	−	0.201510i
$775$	−5.46500	+	8.70191i	−0.196309	+	0.312582i
$776$			18.4140i			0.661025i
$777$	17.7533	−	21.2926i	0.636896	−	0.763869i
$778$	6.01083	+	6.01083i	0.215499	+	0.215499i
$779$	−47.9062			−1.71642
$780$	9.80377	−	6.64128i	0.351031	−	0.237796i
$781$	5.57440			0.199468
$782$	−2.99907	−	2.99907i	−0.107247	−	0.107247i
$783$	0.0870885	−	0.154169i	0.00311229	−	0.00550956i
$784$			2.21607i			0.0791455i
$785$	7.54217	−	26.1907i	0.269191	−	0.934785i
$786$	18.7622	−	1.70071i	0.669226	−	0.0606624i
$787$	12.4410	−	12.4410i	0.443472	−	0.443472i	−0.449705	−	0.893177i	$-0.648471\pi$
$787$	12.4410	−	12.4410i	0.443472	−	0.443472i	0.893177	+	0.449705i	$0.148471\pi$
$788$	2.06498	−	2.06498i	0.0735619	−	0.0735619i
$789$	27.1715	−	2.46298i	0.967333	−	0.0876844i
$790$	−1.94451	+	6.75245i	−0.0691826	+	0.240241i
$791$			6.73197i			0.239361i
$792$	9.65574	−	13.9753i	0.343102	−	0.496592i
$793$	8.34506	+	8.34506i	0.296342	+	0.296342i
$794$	36.1579			1.28320
$795$	−6.75636	+	4.57691i	−0.239624	+	0.162326i
$796$	18.0953			0.641372
$797$	3.79713	+	3.79713i	0.134501	+	0.134501i	0.771152	−	0.636651i	$-0.219681\pi$
$797$	3.79713	+	3.79713i	0.134501	+	0.134501i	−0.636651	+	0.771152i	$0.719681\pi$
$798$	13.4035	−	16.0756i	0.474478	−	0.569071i
$799$		−	1.49746i		−	0.0529763i
$800$	4.87439	−	1.11372i	0.172336	−	0.0393759i
$801$	−5.05463	−	27.6522i	−0.178597	−	0.977042i
$802$	−10.8759	+	10.8759i	−0.384043	+	0.384043i
$803$	59.6699	−	59.6699i	2.10571	−	2.10571i
$804$	2.37045	+	26.1508i	0.0835994	+	0.922267i
$805$	13.9297	+	25.1971i	0.490958	+	0.888083i
$806$		−	6.28349i		−	0.221326i
$807$	25.3098	+	21.1027i	0.890947	+	0.742851i
$808$	9.17741	+	9.17741i	0.322860	+	0.322860i
$809$	8.78612			0.308904			0.154452	−	0.988000i	$-0.450639\pi$
$809$	8.78612			0.308904			0.154452	+	0.988000i	$0.450639\pi$
$810$	20.0583	−	1.63250i	0.704776	−	0.0573603i
$811$	7.20157			0.252881			0.126441	−	0.991974i	$-0.459645\pi$
$811$	7.20157			0.252881			0.126441	+	0.991974i	$0.459645\pi$
$812$	−0.0731497	−	0.0731497i	−0.00256705	−	0.00256705i
$813$	0.591563	+	0.493231i	0.0207470	+	0.0172984i
$814$			29.8531i			1.04635i
$815$	−25.2847	−	7.28127i	−0.885684	−	0.255052i
$816$	0.156362	+	1.72498i	0.00547375	+	0.0603863i
$817$	−29.2516	+	29.2516i	−1.02339	+	1.02339i
$818$	−11.8034	+	11.8034i	−0.412696	+	0.412696i
$819$	−5.00699	−	27.3916i	−0.174958	−	0.957140i
$820$	−23.5519	+	13.0202i	−0.822467	+	0.454684i
$821$		−	33.0127i		−	1.15215i	−0.817397	−	0.576075i	$-0.804583\pi$
$821$		−	33.0127i		−	1.15215i	0.817397	−	0.576075i	$-0.195417\pi$
$822$	18.2088	−	21.8390i	0.635106	−	0.761723i
$823$	15.9237	+	15.9237i	0.555066	+	0.555066i	0.927899	−	0.372833i	$-0.121614\pi$
$823$	15.9237	+	15.9237i	0.555066	+	0.555066i	−0.372833	+	0.927899i	$0.621614\pi$
$824$	−4.88960			−0.170337
$825$	−15.1934	−	46.6228i	−0.528966	−	1.62320i
$826$	23.4765			0.816854
$827$	−8.99763	−	8.99763i	−0.312878	−	0.312878i	0.533145	−	0.846024i	$-0.321010\pi$
$827$	−8.99763	−	8.99763i	−0.312878	−	0.312878i	−0.846024	+	0.533145i	$0.821010\pi$
$828$	7.23274	−	10.4684i	0.251355	−	0.363802i
$829$			24.2421i			0.841964i	0.907069	+	0.420982i	$0.138314\pi$
$829$			24.2421i			0.841964i	−0.907069	+	0.420982i	$0.861686\pi$
$830$	−14.7578	+	8.15856i	−0.512251	+	0.283188i
$831$	−17.0338	+	1.54404i	−0.590895	+	0.0535620i
$832$	−2.16195	+	2.16195i	−0.0749520	+	0.0749520i
$833$	−1.56700	+	1.56700i	−0.0542933	+	0.0542933i
$834$	−11.3214	+	1.02624i	−0.392029	+	0.0355357i
$835$	−5.67728	−	1.63489i	−0.196470	−	0.0565779i
$836$			22.5386i			0.779514i
$837$	5.25227	−	9.29787i	0.181545	−	0.321381i
$838$	−1.75275	−	1.75275i	−0.0605479	−	0.0605479i
$839$	−0.491093			−0.0169544			−0.00847720	−	0.999964i	$-0.502698\pi$
$839$	−0.491093			−0.0169544			−0.00847720	+	0.999964i	$0.502698\pi$
$840$	2.22037	−	11.5460i	0.0766101	−	0.398376i
$841$	−28.9988			−0.999960
$842$	−22.0239	−	22.0239i	−0.758992	−	0.758992i
$843$	6.31036	−	7.56841i	0.217341	−	0.260670i
$844$		−	9.80363i		−	0.337455i
$845$	−3.95089	−	7.14667i	−0.135915	−	0.245853i
$846$	4.41915	−	0.807790i	0.151934	−	0.0277724i
$847$	−45.2089	+	45.2089i	−1.55340	+	1.55340i
$848$	1.48993	−	1.48993i	0.0511643	−	0.0511643i
$849$	−0.464607	−	5.12553i	−0.0159453	−	0.175908i
$850$	4.23423	+	2.65919i	0.145233	+	0.0912096i
$851$			22.3618i			0.766552i
$852$	−1.30968	−	1.09198i	−0.0448690	−	0.0374107i
$853$	−13.2372	−	13.2372i	−0.453232	−	0.453232i	0.443194	−	0.896426i	$-0.353845\pi$
$853$	−13.2372	−	13.2372i	−0.453232	−	0.453232i	−0.896426	+	0.443194i	$0.853845\pi$
$854$	11.7181			0.400985
$855$	−20.6651	+	16.9106i	−0.706731	+	0.578329i
$856$	−1.24802			−0.0426565
$857$	−26.9943	−	26.9943i	−0.922109	−	0.922109i	0.0750694	−	0.997178i	$-0.476082\pi$
$857$	−26.9943	−	26.9943i	−0.922109	−	0.922109i	−0.997178	+	0.0750694i	$0.976082\pi$
$858$	23.0302	+	19.2020i	0.786236	+	0.655545i
$859$			36.7774i			1.25483i	0.778686	+	0.627414i	$0.215887\pi$
$859$			36.7774i			1.25483i	−0.778686	+	0.627414i	$0.784113\pi$
$860$	−6.43068	+	22.3310i	−0.219285	+	0.761480i
$861$	5.71284	+	63.0239i	0.194693	+	2.14785i
$862$	21.1679	−	21.1679i	0.720981	−	0.720981i
$863$	20.9039	−	20.9039i	0.711575	−	0.711575i	−0.255289	−	0.966865i	$-0.582171\pi$
$863$	20.9039	−	20.9039i	0.711575	−	0.711575i	0.966865	+	0.255289i	$0.0821707\pi$
$864$	−5.00624	+	1.39196i	−0.170316	+	0.0473556i
$865$	11.6632	−	40.5013i	0.396561	−	1.37709i
$866$			4.00182i			0.135987i
$867$	−1.10918	+	1.33031i	−0.0376697	+	0.0451796i
$868$	−4.41162	−	4.41162i	−0.149740	−	0.149740i
$869$	−17.7935			−0.603602
$870$	0.0740196	+	0.109267i	0.00250950	+	0.00370449i
$871$	−46.3512			−1.57055
$872$	9.57143	+	9.57143i	0.324130	+	0.324130i
$873$	−45.4493	−	31.4015i	−1.53822	−	1.06278i
$874$			16.8828i			0.571069i
$875$	−22.6253	−	25.3003i	−0.764875	−	0.855306i
$876$	−25.7081	+	2.33032i	−0.868596	+	0.0787343i
$877$	25.2158	−	25.2158i	0.851475	−	0.851475i	−0.138839	−	0.990315i	$-0.544337\pi$
$877$	25.2158	−	25.2158i	0.851475	−	0.851475i	0.990315	+	0.138839i	$0.0443372\pi$
$878$	−14.4894	+	14.4894i	−0.488993	+	0.488993i
$879$	7.18878	−	0.651631i	0.242472	−	0.0219790i
$880$	6.12565	+	11.0805i	0.206496	+	0.373525i
$881$		−	11.9943i		−	0.404097i	−0.979375	−	0.202049i	$-0.935240\pi$
$881$		−	11.9943i		−	0.404097i	0.979375	−	0.202049i	$-0.0647599\pi$
$882$	−5.46968	−	3.77907i	−0.184174	−	0.127248i
$883$	27.2734	+	27.2734i	0.917824	+	0.917824i	0.996871	−	0.0790470i	$-0.0251877\pi$
$883$	27.2734	+	27.2734i	0.917824	+	0.917824i	−0.0790470	+	0.996871i	$0.525188\pi$
$884$	−3.05746			−0.102833
$885$	−29.4118	−	5.65606i	−0.988666	−	0.190126i
$886$	−8.27060			−0.277856
$887$	21.5152	+	21.5152i	0.722408	+	0.722408i	0.969095	−	0.246687i	$-0.0793420\pi$
$887$	21.5152	+	21.5152i	0.722408	+	0.722408i	−0.246687	+	0.969095i	$0.579342\pi$
$888$	5.84799	−	7.01385i	0.196246	−	0.235370i
$889$		−	27.9038i		−	0.935863i
$890$	20.1340	+	5.79802i	0.674894	+	0.194350i
$891$	18.0278	+	47.6643i	0.603954	+	1.59682i
$892$	14.2996	−	14.2996i	0.478786	−	0.478786i
$893$	−4.21485	+	4.21485i	−0.141045	+	0.141045i
$894$	1.66534	+	18.3720i	0.0556972	+	0.614450i
$895$	−4.34025	+	2.39942i	−0.145078	+	0.0802037i
$896$			3.03580i			0.101419i
$897$	17.2510	+	14.3835i	0.575994	+	0.480250i
$898$	−10.7646	−	10.7646i	−0.359221	−	0.359221i
$899$	0.0700318			0.00233569
$900$	−5.56343	+	13.9301i	−0.185448	+	0.464337i
$901$	2.10708			0.0701969
$902$	−48.1857	−	48.1857i	−1.60441	−	1.60441i
$903$	41.9709	+	34.9943i	1.39670	+	1.16454i
$904$			2.21753i			0.0737539i
$905$	−47.1661	+	26.0748i	−1.56785	+	0.866756i
$906$	−0.636178	−	7.01830i	−0.0211356	−	0.233167i
$907$	16.3295	−	16.3295i	0.542211	−	0.542211i	−0.381966	−	0.924177i	$-0.624753\pi$
$907$	16.3295	−	16.3295i	0.542211	−	0.542211i	0.924177	+	0.381966i	$0.124753\pi$
$908$	−6.02382	+	6.02382i	−0.199907	+	0.199907i
$909$	−38.3018	+	7.00131i	−1.27039	+	0.232219i
$910$	19.9443	+	5.74338i	0.661146	+	0.190391i
$911$		−	27.8382i		−	0.922319i	−0.887317	−	0.461160i	$-0.847434\pi$
$911$		−	27.8382i		−	0.922319i	0.887317	−	0.461160i	$-0.152566\pi$
$912$	4.41514	−	5.29535i	0.146200	−	0.175347i
$913$	−30.1936	−	30.1936i	−0.999262	−	0.999262i
$914$	2.81374			0.0930704
$915$	−14.6806	−	2.82317i	−0.485327	−	0.0933312i
$916$	−7.78756			−0.257308
$917$	23.3485	+	23.3485i	0.771035	+	0.771035i
$918$	−4.52421	−	2.55568i	−0.149321	−	0.0843500i
$919$		−	0.365834i		−	0.0120678i	−0.999982	−	0.00603388i	$-0.998079\pi$
$919$		−	0.365834i		−	0.0120678i	0.999982	−	0.00603388i	$-0.00192066\pi$
$920$	4.58849	+	8.30000i	0.151278	+	0.273643i
$921$	28.7745	−	2.60828i	0.948152	−	0.0859458i
$922$	17.7222	−	17.7222i	0.583649	−	0.583649i
$923$	2.12843	−	2.12843i	0.0700580	−	0.0700580i
$924$	29.6511	−	2.68774i	0.975450	−	0.0884202i
$925$	−5.87191	−	25.6995i	−0.193067	−	0.844993i
$926$		−	27.8832i		−	0.916298i
$927$	8.33825	−	12.0685i	0.273864	−	0.396380i
$928$	−0.0240957	−	0.0240957i	−0.000790980	−	0.000790980i
$929$	46.1994			1.51575			0.757877	−	0.652397i	$-0.226237\pi$
$929$	46.1994			1.51575			0.757877	+	0.652397i	$0.226237\pi$
$930$	4.46409	+	6.58982i	0.146383	+	0.216089i
$931$	8.82118			0.289102
$932$	−4.50357	−	4.50357i	−0.147519	−	0.147519i
$933$	30.0992	−	36.0998i	0.985403	−	1.18185i
$934$			11.0127i			0.360348i
$935$	−3.50364	+	12.1666i	−0.114581	+	0.397891i
$936$	−1.64932	−	9.02286i	−0.0539096	−	0.294921i
$937$	−19.9576	+	19.9576i	−0.651986	+	0.651986i	−0.953471	−	0.301485i	$-0.902518\pi$
$937$	−19.9576	+	19.9576i	−0.651986	+	0.651986i	0.301485	+	0.953471i	$0.402518\pi$
$938$	−32.5431	+	32.5431i	−1.06257	+	1.06257i
$939$	0.841339	+	9.28164i	0.0274561	+	0.302895i
$940$	−0.926594	+	3.21766i	−0.0302222	+	0.104948i
$941$			0.736098i			0.0239961i	0.999928	+	0.0119980i	$0.00381919\pi$
$941$			0.736098i			0.0239961i	−0.999928	+	0.0119980i	$0.996181\pi$
$942$	−16.2149	−	13.5196i	−0.528309	−	0.440492i
$943$	−36.0941	−	36.0941i	−1.17538	−	1.17538i
$944$	7.73324			0.251695
$945$	24.7114	+	25.1698i	0.803861	+	0.818773i
$946$	−58.8446			−1.91320
$947$	−3.73870	−	3.73870i	−0.121491	−	0.121491i	0.643747	−	0.765238i	$-0.277379\pi$
$947$	−3.73870	−	3.73870i	−0.121491	−	0.121491i	−0.765238	+	0.643747i	$0.777379\pi$
$948$	4.18050	+	3.48560i	0.135776	+	0.113207i
$949$		−	45.5665i		−	1.47915i
$950$	−4.43320	−	19.4027i	−0.143832	−	0.629507i
$951$	−4.30917	−	47.5387i	−0.139735	−	1.54155i
$952$	−2.14663	+	2.14663i	−0.0695728	+	0.0695728i
$953$	−5.41752	+	5.41752i	−0.175491	+	0.175491i	−0.789387	−	0.613896i	$-0.789601\pi$
$953$	−5.41752	+	5.41752i	−0.175491	+	0.175491i	0.613896	+	0.789387i	$0.289601\pi$
$954$	1.13664	+	6.21820i	0.0368002	+	0.201322i
$955$	−15.7067	−	28.4114i	−0.508256	−	0.919373i
$956$			14.8781i			0.481192i
$957$	−0.214013	+	0.256680i	−0.00691807	+	0.00829727i
$958$	12.1486	+	12.1486i	0.392504	+	0.392504i
$959$	49.8372			1.60933
$960$	0.731396	−	3.80330i	0.0236057	−	0.122751i
$961$	−26.7764			−0.863755
$962$	11.3985	+	11.3985i	0.367504	+	0.367504i
$963$	2.12825	−	3.08035i	0.0685820	−	0.0992629i
$964$		−	21.6372i		−	0.696889i
$965$	−20.1500	−	5.80261i	−0.648650	−	0.186793i
$966$	22.2105	−	2.01328i	0.714611	−	0.0647763i
$967$	29.5836	−	29.5836i	0.951345	−	0.951345i	−0.0475254	−	0.998870i	$-0.515133\pi$
$967$	29.5836	−	29.5836i	0.951345	−	0.951345i	0.998870	+	0.0475254i	$0.0151335\pi$
$968$	−14.8919	+	14.8919i	−0.478645	+	0.478645i
$969$	6.86635	−	0.622404i	0.220579	−	0.0199945i
$970$	36.0351	−	19.9212i	1.15702	−	0.639633i
$971$			41.2664i			1.32430i	0.749370	+	0.662152i	$0.230357\pi$
$971$			41.2664i			1.32430i	−0.749370	+	0.662152i	$0.769643\pi$
$972$	5.10152	−	14.7301i	0.163631	−	0.472467i
$973$	−14.0888	−	14.0888i	−0.451668	−	0.451668i
$974$	15.2443			0.488459
$975$	−23.6028	−	12.0005i	−0.755894	−	0.384322i
$976$	3.85997			0.123555
$977$	6.88321	+	6.88321i	0.220213	+	0.220213i	0.808588	−	0.588375i	$-0.200232\pi$
$977$	6.88321	+	6.88321i	0.220213	+	0.220213i	−0.588375	+	0.808588i	$0.700232\pi$
$978$	−13.0519	+	15.6540i	−0.417354	+	0.500559i
$979$			53.0554i			1.69566i
$980$	4.33671	−	2.39746i	0.138531	−	0.0765841i
$981$	−39.9463	+	7.30190i	−1.27539	+	0.233132i
$982$	3.51490	−	3.51490i	0.112165	−	0.112165i
$983$	−42.5852	+	42.5852i	−1.35826	+	1.35826i	−0.482188	+	0.876068i	$0.660158\pi$
$983$	−42.5852	+	42.5852i	−1.35826	+	1.35826i	−0.876068	+	0.482188i	$0.839842\pi$
$984$	1.88182	+	20.7603i	0.0599904	+	0.661813i
$985$	−6.27504	−	1.80703i	−0.199939	−	0.0575768i
$986$		−	0.0340765i		−	0.00108522i
$987$	6.04756	+	5.04231i	0.192496	+	0.160499i
$988$	8.60573	+	8.60573i	0.273785	+	0.273785i
$989$	−44.0783			−1.40161
$990$	−37.7949	−	3.77642i	−1.20120	−	0.120022i
$991$	−43.5198			−1.38245			−0.691226	−	0.722638i	$-0.742929\pi$
$991$	−43.5198			−1.38245			−0.691226	+	0.722638i	$0.742929\pi$
$992$	−1.45320	−	1.45320i	−0.0461392	−	0.0461392i
$993$	−1.28729	−	1.07331i	−0.0408508	−	0.0340605i
$994$		−	2.98873i		−	0.0947968i
$995$	−19.5765	−	35.4114i	−0.620616	−	1.12262i
$996$	1.17917	+	13.0086i	0.0373634	+	0.412192i
$997$	0.505387	−	0.505387i	0.0160058	−	0.0160058i	−0.699059	−	0.715064i	$-0.746397\pi$
$997$	0.505387	−	0.505387i	0.0160058	−	0.0160058i	0.715064	+	0.699059i	$0.246397\pi$
$998$	4.41031	−	4.41031i	0.139606	−	0.139606i
$999$	7.33892	+	26.3947i	0.232193	+	0.835090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.443.5	yes	28
3.2	odd	2	inner	510.2.l.g.443.13	yes	28
5.2	odd	4	inner	510.2.l.g.137.13	yes	28
15.2	even	4	inner	510.2.l.g.137.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.5	✓	28	15.2	even	4	inner
510.2.l.g.137.13	yes	28	5.2	odd	4	inner
510.2.l.g.443.5	yes	28	1.1	even	1	trivial
510.2.l.g.443.13	yes	28	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.33031 + 1.10918i) q^{3} +1.00000i q^{4} +(1.95694 - 1.08185i) q^{5} +(-0.156362 - 1.72498i) q^{6} +(2.14663 - 2.14663i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539441 + 2.95110i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.33031 + 1.10918i) q^{3} +1.00000i q^{4} +(1.95694 - 1.08185i) q^{5} +(-0.156362 - 1.72498i) q^{6} +(2.14663 - 2.14663i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539441 + 2.95110i) q^{9} +(-2.14875 - 0.618778i) q^{10} -5.66219i q^{11} +(-1.10918 + 1.33031i) q^{12} +(-2.16195 - 2.16195i) q^{13} -3.03580 q^{14} +(3.80330 + 0.731396i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(1.70530 - 2.46819i) q^{18} +3.98054i q^{19} +(1.08185 + 1.95694i) q^{20} +(5.23669 - 0.474682i) q^{21} +(-4.00377 + 4.00377i) q^{22} +(-2.99907 + 2.99907i) q^{23} +(1.72498 - 0.156362i) q^{24} +(2.65919 - 4.23423i) q^{25} +3.05746i q^{26} +(-2.55568 + 4.52421i) q^{27} +(2.14663 + 2.14663i) q^{28} -0.0340765 q^{29} +(-2.17216 - 3.20651i) q^{30} -2.05514 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.28038 - 7.53246i) q^{33} +1.00000i q^{34} +(1.87848 - 6.52316i) q^{35} +(-2.95110 + 0.539441i) q^{36} +(3.72812 - 3.72812i) q^{37} +(2.81467 - 2.81467i) q^{38} +(-0.478069 - 5.27404i) q^{39} +(0.618778 - 2.14875i) q^{40} +12.0351i q^{41} +(-4.03855 - 3.36725i) q^{42} +(7.34865 + 7.34865i) q^{43} +5.66219 q^{44} +(4.24831 + 5.19152i) q^{45} +4.24133 q^{46} +(1.05886 + 1.05886i) q^{47} +(-1.33031 - 1.10918i) q^{48} -2.21607i q^{49} +(-4.87439 + 1.11372i) q^{50} +(-0.156362 - 1.72498i) q^{51} +(2.16195 - 2.16195i) q^{52} +(-1.48993 + 1.48993i) q^{53} +(5.00624 - 1.39196i) q^{54} +(-6.12565 - 11.0805i) q^{55} -3.03580i q^{56} +(-4.41514 + 5.29535i) q^{57} +(0.0240957 + 0.0240957i) q^{58} -7.73324 q^{59} +(-0.731396 + 3.80330i) q^{60} -3.85997 q^{61} +(1.45320 + 1.45320i) q^{62} +(7.49292 + 5.17695i) q^{63} -1.00000i q^{64} +(-6.56970 - 1.89188i) q^{65} +(-9.76715 + 0.885349i) q^{66} +(10.7198 - 10.7198i) q^{67} +(0.707107 - 0.707107i) q^{68} +(-7.31620 + 0.663181i) q^{69} +(-5.94086 + 3.28428i) q^{70} +0.984495i q^{71} +(2.46819 + 1.70530i) q^{72} +(10.5383 + 10.5383i) q^{73} -5.27235 q^{74} +(8.23407 - 2.68331i) q^{75} -3.98054 q^{76} +(-12.1546 - 12.1546i) q^{77} +(-3.39127 + 4.06736i) q^{78} -3.14251i q^{79} +(-1.95694 + 1.08185i) q^{80} +(-8.41801 + 3.18389i) q^{81} +(8.51009 - 8.51009i) q^{82} +(5.33250 - 5.33250i) q^{83} +(0.474682 + 5.23669i) q^{84} +(-2.14875 - 0.618778i) q^{85} -10.3926i q^{86} +(-0.0453322 - 0.0377969i) q^{87} +(-4.00377 - 4.00377i) q^{88} -9.37013 q^{89} +(0.666954 - 6.67497i) q^{90} -9.28182 q^{91} +(-2.99907 - 2.99907i) q^{92} +(-2.73396 - 2.27951i) q^{93} -1.49746i q^{94} +(4.30636 + 7.78967i) q^{95} +(0.156362 + 1.72498i) q^{96} +(-13.0207 + 13.0207i) q^{97} +(-1.56700 + 1.56700i) q^{98} +(16.7097 - 3.05442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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