LMFDB - Embedded newform 510.2.l.g.137.5

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			137.5
Character	$\chi$	$=$	510.137
Dual form			510.2.l.g.443.5

$q$-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 $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

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

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	0.984836	−	0.173485i	$-0.0555029\pi$
$7$	2.14663	+	2.14663i	0.811351	+	0.811351i	−0.173485	+	0.984836i	$0.555503\pi$
$8$	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	$0.325590\pi$
$11$			5.66219i			1.70721i	−0.520917	+	0.853607i	$0.674410\pi$
$12$	−1.10918	−	1.33031i	−0.320193	−	0.384027i
$13$	−2.16195	+	2.16195i	−0.599616	+	0.599616i	−0.940210	−	0.340594i	$-0.889372\pi$
$13$	−2.16195	+	2.16195i	−0.599616	+	0.599616i	0.340594	+	0.940210i	$0.389372\pi$
$14$	−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	$-0.849067\pi$
$19$		−	3.98054i		−	0.913199i	0.889672	−	0.456600i	$-0.150933\pi$
$20$	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	0.321545	−	0.946894i	$-0.395798\pi$
$23$	−2.99907	−	2.99907i	−0.625350	−	0.625350i	−0.946894	+	0.321545i	$0.895798\pi$
$24$	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	0.943700	−	0.330802i	$-0.107319\pi$
$37$	3.72812	+	3.72812i	0.612898	+	0.612898i	−0.330802	+	0.943700i	$0.607319\pi$
$38$	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	$-0.611028\pi$
$41$		−	12.0351i		−	1.87956i	0.341775	−	0.939782i	$-0.388972\pi$
$42$	−4.03855	+	3.36725i	−0.623162	+	0.519577i
$43$	7.34865	−	7.34865i	1.12066	−	1.12066i	0.129016	−	0.991642i	$-0.458818\pi$
$43$	7.34865	−	7.34865i	1.12066	−	1.12066i	0.991642	−	0.129016i	$-0.0411820\pi$
$44$	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	−0.625652	−	0.780103i	$-0.715167\pi$
$47$	1.05886	−	1.05886i	0.154451	−	0.154451i	0.780103	+	0.625652i	$0.215167\pi$
$48$	−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	0.597335	−	0.801992i	$-0.296226\pi$
$53$	−1.48993	−	1.48993i	−0.204657	−	0.204657i	−0.801992	+	0.597335i	$0.796226\pi$
$54$	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	0.921681	+	0.387950i	$0.126817\pi$
$67$	10.7198	+	10.7198i	1.30963	+	1.30963i	0.387950	+	0.921681i	$0.373183\pi$
$68$	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	$-0.981394\pi$
$71$		−	0.984495i		−	0.116838i	0.998292	−	0.0584191i	$-0.0186060\pi$
$72$	2.46819	−	1.70530i	0.290879	−	0.200972i
$73$	10.5383	−	10.5383i	1.23342	−	1.23342i	0.270772	−	0.962643i	$-0.412721\pi$
$73$	10.5383	−	10.5383i	1.23342	−	1.23342i	0.962643	−	0.270772i	$-0.0872791\pi$
$74$	−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	$0.0565680\pi$
$79$			3.14251i			0.353560i	−0.984250	+	0.176780i	$0.943432\pi$
$80$	−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	0.936360	−	0.351042i	$-0.114173\pi$
$83$	5.33250	+	5.33250i	0.585318	+	0.585318i	−0.351042	+	0.936360i	$0.614173\pi$
$84$	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	−0.912114	−	0.409936i	$-0.865551\pi$
$97$	−13.0207	−	13.0207i	−1.32205	−	1.32205i	−0.409936	−	0.912114i	$-0.634449\pi$
$98$	−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	$-0.776557\pi$
$101$		−	12.9788i		−	1.29144i	0.763574	−	0.645720i	$-0.223443\pi$
$102$	−1.10918	−	1.33031i	−0.109825	−	0.131720i
$103$	−3.45747	+	3.45747i	−0.340675	+	0.340675i	−0.856621	−	0.515946i	$-0.827440\pi$
$103$	−3.45747	+	3.45747i	−0.340675	+	0.340675i	0.515946	+	0.856621i	$0.327440\pi$
$104$	−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	−0.748475	−	0.663162i	$-0.769214\pi$
$107$	−0.882485	+	0.882485i	−0.0853130	+	0.0853130i	0.663162	+	0.748475i	$0.269214\pi$
$108$	−4.52421	+	2.55568i	−0.435343	+	0.245920i
$109$		−	13.5361i		−	1.29652i	−0.761420	−	0.648259i	$-0.775497\pi$
$109$		−	13.5361i		−	1.29652i	0.761420	−	0.648259i	$-0.224503\pi$
$110$	−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	0.629496	−	0.777004i	$-0.283261\pi$
$113$	−1.56803	−	1.56803i	−0.147508	−	0.147508i	−0.777004	+	0.629496i	$0.783261\pi$
$114$	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	0.934001	−	0.357270i	$-0.116292\pi$
$127$	6.49943	+	6.49943i	0.576731	+	0.576731i	−0.357270	+	0.934001i	$0.616292\pi$
$128$	−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	$-0.842392\pi$
$131$		−	10.8768i		−	0.950309i	0.879902	−	0.475155i	$-0.157608\pi$
$132$	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	−0.00820945	−	0.999966i	$-0.502613\pi$
$137$	11.6082	−	11.6082i	0.991757	−	0.991757i	0.999966	+	0.00820945i	$0.00261318\pi$
$138$	5.64227	−	4.70439i	0.480302	−	0.400465i
$139$			6.56323i			0.556686i	0.960482	+	0.278343i	$0.0897851\pi$
$139$			6.56323i			0.556686i	−0.960482	+	0.278343i	$0.910215\pi$
$140$	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	0.961757	−	0.273903i	$-0.0883147\pi$
$157$	8.61879	+	8.61879i	0.687855	+	0.687855i	−0.273903	+	0.961757i	$0.588315\pi$
$158$	−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	−0.953408	−	0.301684i	$-0.902451\pi$
$163$	−8.32065	+	8.32065i	−0.651724	+	0.651724i	0.301684	+	0.953408i	$0.402451\pi$
$164$	−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	−0.775688	−	0.631117i	$-0.782597\pi$
$167$	−1.86827	+	1.86827i	−0.144571	+	0.144571i	0.631117	+	0.775688i	$0.282597\pi$
$168$	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	0.999910	+	0.0134081i	$0.00426805\pi$
$173$	13.3281	+	13.3281i	1.01332	+	1.01332i	0.0134081	+	0.999910i	$0.495732\pi$
$174$	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	$0.176030\pi$
$191$			14.5183i			1.05051i	−0.850945	+	0.525255i	$0.823970\pi$
$192$	1.10918	+	1.33031i	0.0800481	+	0.0960067i
$193$	−6.63092	+	6.63092i	−0.477304	+	0.477304i	−0.904269	−	0.426964i	$-0.859583\pi$
$193$	−6.63092	+	6.63092i	−0.477304	+	0.477304i	0.426964	+	0.904269i	$0.359583\pi$
$194$	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	−0.776832	−	0.629708i	$-0.783175\pi$
$197$	−2.06498	+	2.06498i	−0.147124	+	0.147124i	0.629708	+	0.776832i	$0.283175\pi$
$198$	−13.9753	+	9.65574i	−0.993184	+	0.686204i
$199$			18.0953i			1.28274i	0.767230	+	0.641372i	$0.221635\pi$
$199$			18.0953i			1.28274i	−0.767230	+	0.641372i	$0.778365\pi$
$200$	−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	−0.999136	−	0.0415633i	$-0.986766\pi$
$223$	−14.2996	+	14.2996i	−0.957573	+	0.957573i	0.0415633	+	0.999136i	$0.486766\pi$
$224$	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	−0.478353	−	0.878168i	$-0.658766\pi$
$227$	6.02382	−	6.02382i	0.399815	−	0.399815i	0.878168	+	0.478353i	$0.158766\pi$
$228$	−5.29535	+	4.41514i	−0.350693	+	0.292400i
$229$		−	7.78756i		−	0.514616i	−0.966329	−	0.257308i	$-0.917164\pi$
$229$		−	7.78756i		−	0.514616i	0.966329	−	0.257308i	$-0.0828355\pi$
$230$	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	0.544028	−	0.839067i	$-0.316898\pi$
$233$	−4.50357	−	4.50357i	−0.295038	−	0.295038i	−0.839067	+	0.544028i	$0.816898\pi$
$234$	−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	$0.0237849\pi$
$251$			2.36545i			0.149306i	−0.997210	+	0.0746529i	$0.976215\pi$
$252$	−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	−0.244992	+	0.969525i	$0.578785\pi$
$257$	−19.4702	+	19.4702i	−1.21452	+	1.21452i	−0.969525	+	0.244992i	$0.921215\pi$
$258$	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	0.961526	−	0.274714i	$-0.0885832\pi$
$263$	11.1382	+	11.1382i	0.686812	+	0.686812i	−0.274714	+	0.961526i	$0.588583\pi$
$264$	−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	0.465506	−	0.885045i	$-0.345872\pi$
$277$	−6.98252	−	6.98252i	−0.419539	−	0.419539i	−0.885045	+	0.465506i	$0.845872\pi$
$278$	−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	$0.0542783\pi$
$281$			5.68922i			0.339390i	−0.985497	+	0.169695i	$0.945722\pi$
$282$	1.66095	+	1.99208i	0.0989082	+	0.118627i
$283$	−2.10107	+	2.10107i	−0.124896	+	0.124896i	−0.766792	−	0.641896i	$-0.778148\pi$
$283$	−2.10107	+	2.10107i	−0.124896	+	0.124896i	0.641896	+	0.766792i	$0.278148\pi$
$284$	−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	0.787926	−	0.615770i	$-0.211155\pi$
$293$	2.94684	+	2.94684i	0.172156	+	0.172156i	−0.615770	+	0.787926i	$0.711155\pi$
$294$	−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	0.958451	−	0.285257i	$-0.0920790\pi$
$307$	11.7953	+	11.7953i	0.673194	+	0.673194i	−0.285257	+	0.958451i	$0.592079\pi$
$308$	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	$0.279436\pi$
$311$			27.1364i			1.53877i	−0.638788	+	0.769383i	$0.720564\pi$
$312$	−4.06736	+	3.39127i	−0.230269	+	0.191993i
$313$	3.80475	−	3.80475i	0.215057	−	0.215057i	−0.591355	−	0.806412i	$-0.701407\pi$
$313$	3.80475	−	3.80475i	0.215057	−	0.215057i	0.806412	+	0.591355i	$0.201407\pi$
$314$	−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	−0.0994674	+	0.995041i	$0.531714\pi$
$317$	−19.4872	+	19.4872i	−1.09451	+	1.09451i	−0.995041	+	0.0994674i	$0.968286\pi$
$318$	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	0.881966	−	0.471313i	$-0.156220\pi$
$337$	7.53858	+	7.53858i	0.410652	+	0.410652i	−0.471313	+	0.881966i	$0.656220\pi$
$338$	−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	0.000281995	−	1.00000i	$-0.499910\pi$
$347$	18.6332	−	18.6332i	1.00028	−	1.00028i	1.00000		0.000281995i	$-8.97618e-5\pi$
$348$	0.0377969	+	0.0453322i	0.00202613	+	0.00243006i
$349$		−	0.505066i		−	0.0270356i	−0.999909	−	0.0135178i	$-0.995697\pi$
$349$		−	0.505066i		−	0.0270356i	0.999909	−	0.0135178i	$-0.00430297\pi$
$350$	−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	0.426444	−	0.904514i	$-0.359766\pi$
$353$	−8.98211	−	8.98211i	−0.478069	−	0.478069i	−0.904514	+	0.426444i	$0.859766\pi$
$354$	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	0.859391	−	0.511319i	$-0.170843\pi$
$367$	6.66810	+	6.66810i	0.348072	+	0.348072i	−0.511319	+	0.859391i	$0.670843\pi$
$368$	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	−0.287506	−	0.957779i	$-0.592826\pi$
$373$	12.9451	−	12.9451i	0.670273	−	0.670273i	0.957779	+	0.287506i	$0.0928262\pi$
$374$	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	$-0.850074\pi$
$379$		−	17.6684i		−	0.907565i	0.891112	−	0.453783i	$-0.149926\pi$
$380$	−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	−0.936244	−	0.351351i	$-0.885722\pi$
$383$	−25.1987	−	25.1987i	−1.28760	−	1.28760i	−0.351351	−	0.936244i	$-0.614278\pi$
$384$	−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	−0.938839	−	0.344357i	$-0.888097\pi$
$397$	−25.5675	−	25.5675i	−1.28320	−	1.28320i	−0.344357	−	0.938839i	$-0.611903\pi$
$398$	−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	$0.125469\pi$
$401$			15.3809i			0.768086i	−0.923315	+	0.384043i	$0.874531\pi$
$402$	−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	$0.135413\pi$
$409$			16.6925i			0.825392i	−0.910869	+	0.412696i	$0.864587\pi$
$410$	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	$-0.743691\pi$
$431$		−	29.9359i		−	1.44196i	0.692955	−	0.720981i	$-0.256309\pi$
$432$	2.55568	+	4.52421i	0.122960	+	0.217671i
$433$	−2.82971	+	2.82971i	−0.135987	+	0.135987i	−0.771824	−	0.635837i	$-0.780655\pi$
$433$	−2.82971	+	2.82971i	−0.135987	+	0.135987i	0.635837	+	0.771824i	$0.280655\pi$
$434$	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	$0.162636\pi$
$439$			20.4911i			0.977986i	−0.872288	+	0.488993i	$0.837364\pi$
$440$	−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	0.832253	−	0.554396i	$-0.187051\pi$
$443$	5.84820	+	5.84820i	0.277856	+	0.277856i	−0.554396	+	0.832253i	$0.687051\pi$
$444$	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	0.659039	−	0.752109i	$-0.270963\pi$
$457$	−1.98962	−	1.98962i	−0.0930704	−	0.0930704i	−0.752109	+	0.659039i	$0.770963\pi$
$458$	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	$-0.801624\pi$
$461$		−	25.0630i		−	1.16730i	0.812006	−	0.583649i	$-0.198376\pi$
$462$	−19.0660	−	22.8670i	−0.887030	−	1.06387i
$463$	19.7164	−	19.7164i	0.916298	−	0.916298i	−0.0804595	−	0.996758i	$-0.525639\pi$
$463$	19.7164	−	19.7164i	0.916298	−	0.916298i	0.996758	+	0.0804595i	$0.0256388\pi$
$464$	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	−0.863941	−	0.503593i	$-0.832011\pi$
$467$	−7.78719	+	7.78719i	−0.360348	+	0.360348i	0.503593	+	0.863941i	$0.332011\pi$
$468$	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	0.419361	−	0.907820i	$-0.362254\pi$
$487$	−10.7794	−	10.7794i	−0.488459	−	0.488459i	−0.907820	+	0.419361i	$0.862254\pi$
$488$	−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	$-0.964221\pi$
$491$		−	4.97082i		−	0.224330i	0.993690	−	0.112165i	$-0.0357785\pi$
$492$	−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	$-0.955416\pi$
$499$		−	6.23712i		−	0.279212i	0.990207	−	0.139606i	$-0.0445836\pi$
$500$	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	0.572928	−	0.819606i	$-0.305807\pi$
$503$	−5.53239	−	5.53239i	−0.246677	−	0.246677i	−0.819606	+	0.572928i	$0.805807\pi$
$504$	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	$-0.600184\pi$
$521$		−	43.4084i		−	1.90176i	0.309565	−	0.950878i	$-0.399816\pi$
$522$	−0.0581107	−	0.0841071i	−0.00254344	−	0.00368127i
$523$	−31.2684	+	31.2684i	−1.36727	+	1.36727i	−0.502960	+	0.864310i	$0.667756\pi$
$523$	−31.2684	+	31.2684i	−1.36727	+	1.36727i	−0.864310	+	0.502960i	$0.832244\pi$
$524$	−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	0.868023	−	0.496523i	$-0.165390\pi$
$547$	8.68865	+	8.68865i	0.371500	+	0.371500i	−0.496523	+	0.868023i	$0.665390\pi$
$548$	−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	0.0275434	−	0.999621i	$-0.491232\pi$
$557$	24.2419	−	24.2419i	1.02716	−	1.02716i	0.999621	−	0.0275434i	$-0.00876845\pi$
$558$	−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	0.871723	−	0.489999i	$-0.163003\pi$
$563$	9.05740	+	9.05740i	0.381724	+	0.381724i	−0.489999	+	0.871723i	$0.663003\pi$
$564$	−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	0.655307	−	0.755363i	$-0.272539\pi$
$577$	−2.40343	−	2.40343i	−0.100056	−	0.100056i	−0.755363	+	0.655307i	$0.772539\pi$
$578$	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	−0.338857	+	0.940838i	$0.610040\pi$
$587$	−31.0045	+	31.0045i	−1.27969	+	1.27969i	−0.940838	+	0.338857i	$0.889960\pi$
$588$	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	0.605894	−	0.795545i	$-0.292816\pi$
$593$	−4.61831	−	4.61831i	−0.189651	−	0.189651i	−0.795545	+	0.605894i	$0.792816\pi$
$594$	−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	0.996593	−	0.0824715i	$-0.0262814\pi$
$607$	22.5216	+	22.5216i	0.914122	+	0.914122i	−0.0824715	+	0.996593i	$0.526281\pi$
$608$	−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	−0.274336	−	0.961634i	$-0.588458\pi$
$613$	17.0167	−	17.0167i	0.687298	−	0.687298i	0.961634	+	0.274336i	$0.0884579\pi$
$614$	−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	−0.139630	+	0.990204i	$0.544591\pi$
$617$	−28.0645	+	28.0645i	−1.12983	+	1.12983i	−0.990204	+	0.139630i	$0.955409\pi$
$618$	−5.42345	−	6.50468i	−0.218163	−	0.261657i
$619$			0.456432i			0.0183456i	0.999958	+	0.00917278i	$0.00291983\pi$
$619$			0.456432i			0.0183456i	−0.999958	+	0.00917278i	$0.997080\pi$
$620$	−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	$-0.880489\pi$
$641$		−	18.5681i		−	0.733394i	0.930340	−	0.366697i	$-0.119511\pi$
$642$	−1.38428	−	1.66025i	−0.0546332	−	0.0655250i
$643$	1.35994	−	1.35994i	0.0536309	−	0.0536309i	−0.679783	−	0.733414i	$-0.737926\pi$
$643$	1.35994	−	1.35994i	0.0536309	−	0.0536309i	0.733414	+	0.679783i	$0.237926\pi$
$644$	−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	−0.751064	−	0.660229i	$-0.770459\pi$
$647$	−2.31050	+	2.31050i	−0.0908351	+	0.0908351i	0.660229	+	0.751064i	$0.270459\pi$
$648$	−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	0.991680	−	0.128730i	$-0.0410901\pi$
$653$	22.0517	+	22.0517i	0.862949	+	0.862949i	−0.128730	+	0.991680i	$0.541090\pi$
$654$	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	−0.938287	−	0.345857i	$-0.887588\pi$
$673$	−15.3690	+	15.3690i	−0.592431	+	0.592431i	0.345857	+	0.938287i	$0.387588\pi$
$674$	−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	−0.255581	−	0.966788i	$-0.582267\pi$
$677$	18.5051	−	18.5051i	0.711207	−	0.711207i	0.966788	+	0.255581i	$0.0822667\pi$
$678$	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	0.179129	−	0.983826i	$-0.442672\pi$
$683$	−21.0301	−	21.0301i	−0.804696	−	0.804696i	−0.983826	+	0.179129i	$0.942672\pi$
$684$	−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	$-0.987295\pi$
$701$		−	2.11308i		−	0.0798098i	0.999203	−	0.0399049i	$-0.0127055\pi$
$702$	−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	$0.0471359\pi$
$709$			7.85717i			0.295082i	−0.989056	+	0.147541i	$0.952864\pi$
$710$	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	0.252003	−	0.967726i	$-0.418911\pi$
$727$	−19.2980	−	19.2980i	−0.715723	−	0.715723i	−0.967726	+	0.252003i	$0.918911\pi$
$728$	−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	−0.999964	−	0.00844679i	$-0.997311\pi$
$733$	−26.8443	+	26.8443i	−0.991518	+	0.991518i	0.00844679	+	0.999964i	$0.497311\pi$
$734$	−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	$0.154603\pi$
$739$			25.3809i			0.933652i	−0.884349	+	0.466826i	$0.845397\pi$
$740$	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	0.623626	−	0.781723i	$-0.285659\pi$
$743$	−4.30942	−	4.30942i	−0.158097	−	0.158097i	−0.781723	+	0.623626i	$0.785659\pi$
$744$	−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	0.877506	+	0.479566i	$0.159206\pi$
$757$	37.3380	+	37.3380i	1.35707	+	1.35707i	0.479566	+	0.877506i	$0.340794\pi$
$758$	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	$0.213452\pi$
$761$			34.2864i			1.24288i	−0.783461	+	0.621441i	$0.786548\pi$
$762$	−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	$-0.898046\pi$
$769$		−	17.4620i		−	0.629697i	0.949142	−	0.314848i	$-0.101954\pi$
$770$	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	0.839002	−	0.544128i	$-0.183139\pi$
$773$	8.19837	+	8.19837i	0.294875	+	0.294875i	−0.544128	+	0.839002i	$0.683139\pi$
$774$	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	0.893177	−	0.449705i	$-0.148471\pi$
$787$	12.4410	+	12.4410i	0.443472	+	0.443472i	−0.449705	+	0.893177i	$0.648471\pi$
$788$	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	−0.636651	−	0.771152i	$-0.719681\pi$
$797$	3.79713	−	3.79713i	0.134501	−	0.134501i	0.771152	+	0.636651i	$0.219681\pi$
$798$	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	$0.195417\pi$
$821$			33.0127i			1.15215i	−0.817397	+	0.576075i	$0.804583\pi$
$822$	18.2088	+	21.8390i	0.635106	+	0.761723i
$823$	15.9237	−	15.9237i	0.555066	−	0.555066i	−0.372833	−	0.927899i	$-0.621614\pi$
$823$	15.9237	−	15.9237i	0.555066	−	0.555066i	0.927899	+	0.372833i	$0.121614\pi$
$824$	−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	−0.846024	−	0.533145i	$-0.821010\pi$
$827$	−8.99763	+	8.99763i	−0.312878	+	0.312878i	0.533145	+	0.846024i	$0.321010\pi$
$828$	7.23274	+	10.4684i	0.251355	+	0.363802i
$829$		−	24.2421i		−	0.841964i	−0.907069	−	0.420982i	$-0.861686\pi$
$829$		−	24.2421i		−	0.841964i	0.907069	−	0.420982i	$-0.138314\pi$
$830$	−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	−0.896426	−	0.443194i	$-0.853845\pi$
$853$	−13.2372	+	13.2372i	−0.453232	+	0.453232i	0.443194	+	0.896426i	$0.353845\pi$
$854$	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	−0.997178	−	0.0750694i	$-0.976082\pi$
$857$	−26.9943	+	26.9943i	−0.922109	+	0.922109i	0.0750694	+	0.997178i	$0.476082\pi$
$858$	23.0302	−	19.2020i	0.786236	−	0.655545i
$859$		−	36.7774i		−	1.25483i	−0.778686	−	0.627414i	$-0.784113\pi$
$859$		−	36.7774i		−	1.25483i	0.778686	−	0.627414i	$-0.215887\pi$
$860$	−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	0.966865	−	0.255289i	$-0.0821707\pi$
$863$	20.9039	+	20.9039i	0.711575	+	0.711575i	−0.255289	+	0.966865i	$0.582171\pi$
$864$	−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	0.990315	−	0.138839i	$-0.0443372\pi$
$877$	25.2158	+	25.2158i	0.851475	+	0.851475i	−0.138839	+	0.990315i	$0.544337\pi$
$878$	−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	$0.0647599\pi$
$881$			11.9943i			0.404097i	−0.979375	+	0.202049i	$0.935240\pi$
$882$	−5.46968	+	3.77907i	−0.184174	+	0.127248i
$883$	27.2734	−	27.2734i	0.917824	−	0.917824i	−0.0790470	−	0.996871i	$-0.525188\pi$
$883$	27.2734	−	27.2734i	0.917824	−	0.917824i	0.996871	+	0.0790470i	$0.0251877\pi$
$884$	−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	−0.246687	−	0.969095i	$-0.579342\pi$
$887$	21.5152	−	21.5152i	0.722408	−	0.722408i	0.969095	+	0.246687i	$0.0793420\pi$
$888$	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	0.924177	−	0.381966i	$-0.124753\pi$
$907$	16.3295	+	16.3295i	0.542211	+	0.542211i	−0.381966	+	0.924177i	$0.624753\pi$
$908$	−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	$0.152566\pi$
$911$			27.8382i			0.922319i	−0.887317	+	0.461160i	$0.847434\pi$
$912$	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	$0.00192066\pi$
$919$			0.365834i			0.0120678i	−0.999982	+	0.00603388i	$0.998079\pi$
$920$	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	0.301485	−	0.953471i	$-0.402518\pi$
$937$	−19.9576	−	19.9576i	−0.651986	−	0.651986i	−0.953471	+	0.301485i	$0.902518\pi$
$938$	−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	$-0.996181\pi$
$941$		−	0.736098i		−	0.0239961i	0.999928	−	0.0119980i	$-0.00381919\pi$
$942$	−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	−0.765238	−	0.643747i	$-0.777379\pi$
$947$	−3.73870	+	3.73870i	−0.121491	+	0.121491i	0.643747	+	0.765238i	$0.277379\pi$
$948$	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	0.613896	−	0.789387i	$-0.289601\pi$
$953$	−5.41752	−	5.41752i	−0.175491	−	0.175491i	−0.789387	+	0.613896i	$0.789601\pi$
$954$	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	0.998870	−	0.0475254i	$-0.0151335\pi$
$967$	29.5836	+	29.5836i	0.951345	+	0.951345i	−0.0475254	+	0.998870i	$0.515133\pi$
$968$	−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	$-0.769643\pi$
$971$		−	41.2664i		−	1.32430i	0.749370	−	0.662152i	$-0.230357\pi$
$972$	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	−0.588375	−	0.808588i	$-0.700232\pi$
$977$	6.88321	−	6.88321i	0.220213	−	0.220213i	0.808588	+	0.588375i	$0.200232\pi$
$978$	−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	−0.876068	−	0.482188i	$-0.839842\pi$
$983$	−42.5852	−	42.5852i	−1.35826	−	1.35826i	−0.482188	−	0.876068i	$-0.660158\pi$
$984$	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	0.715064	−	0.699059i	$-0.246397\pi$
$997$	0.505387	+	0.505387i	0.0160058	+	0.0160058i	−0.699059	+	0.715064i	$0.746397\pi$
$998$	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.137.5	✓	28
3.2	odd	2	inner	510.2.l.g.137.13	yes	28
5.3	odd	4	inner	510.2.l.g.443.13	yes	28
15.8	even	4	inner	510.2.l.g.443.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.5	✓	28	1.1	even	1	trivial
510.2.l.g.137.13	yes	28	3.2	odd	2	inner
510.2.l.g.443.5	yes	28	15.8	even	4	inner
510.2.l.g.443.13	yes	28	5.3	odd	4	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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