LMFDB - Embedded newform 930.2.j.h.683.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.20
Character	$\chi$	$=$	930.683
Dual form			930.2.j.h.497.20

$q$-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} +(1.73024 + 0.0792035i) q^{3} +1.00000i q^{4} +(1.29721 + 1.82133i) q^{5} +(1.16746 + 1.27947i) q^{6} +(2.17556 - 2.17556i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98745 + 0.274082i) q^{9} +(-0.370615 + 2.20514i) q^{10} -4.45544i q^{11} +(-0.0792035 + 1.73024i) q^{12} +(0.974917 + 0.974917i) q^{13} +3.07670 q^{14} +(2.10022 + 3.25409i) q^{15} -1.00000 q^{16} +(0.387611 + 0.387611i) q^{17} +(1.91864 + 2.30625i) q^{18} -7.08062i q^{19} +(-1.82133 + 1.29721i) q^{20} +(3.93654 - 3.59192i) q^{21} +(3.15047 - 3.15047i) q^{22} +(-4.52613 + 4.52613i) q^{23} +(-1.27947 + 1.16746i) q^{24} +(-1.63452 + 4.72529i) q^{25} +1.37874i q^{26} +(5.14730 + 0.710844i) q^{27} +(2.17556 + 2.17556i) q^{28} -6.82973 q^{29} +(-0.815908 + 3.78607i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.352887 - 7.70898i) q^{33} +0.548164i q^{34} +(6.78456 + 1.14027i) q^{35} +(-0.274082 + 2.98745i) q^{36} +(-2.48442 + 2.48442i) q^{37} +(5.00675 - 5.00675i) q^{38} +(1.60962 + 1.76406i) q^{39} +(-2.20514 - 0.370615i) q^{40} +9.64559i q^{41} +(5.32343 + 0.243686i) q^{42} +(-1.87101 - 1.87101i) q^{43} +4.45544 q^{44} +(3.37615 + 5.79669i) q^{45} -6.40091 q^{46} +(-9.31831 - 9.31831i) q^{47} +(-1.73024 - 0.0792035i) q^{48} -2.46609i q^{49} +(-4.49706 + 2.18551i) q^{50} +(0.639959 + 0.701359i) q^{51} +(-0.974917 + 0.974917i) q^{52} +(-10.1295 + 10.1295i) q^{53} +(3.13705 + 4.14233i) q^{54} +(8.11485 - 5.77962i) q^{55} +3.07670i q^{56} +(0.560810 - 12.2512i) q^{57} +(-4.82935 - 4.82935i) q^{58} -4.06326 q^{59} +(-3.25409 + 2.10022i) q^{60} +7.35980 q^{61} +(-0.707107 - 0.707107i) q^{62} +(7.09565 - 5.90309i) q^{63} -1.00000i q^{64} +(-0.510982 + 3.04032i) q^{65} +(5.70060 - 5.20154i) q^{66} +(-5.24191 + 5.24191i) q^{67} +(-0.387611 + 0.387611i) q^{68} +(-8.18977 + 7.47280i) q^{69} +(3.99111 + 5.60370i) q^{70} +12.5156i q^{71} +(-2.30625 + 1.91864i) q^{72} +(7.93503 + 7.93503i) q^{73} -3.51351 q^{74} +(-3.20236 + 8.04642i) q^{75} +7.08062 q^{76} +(-9.69306 - 9.69306i) q^{77} +(-0.109201 + 2.38555i) q^{78} -17.0708i q^{79} +(-1.29721 - 1.82133i) q^{80} +(8.84976 + 1.63761i) q^{81} +(-6.82046 + 6.82046i) q^{82} +(2.57771 - 2.57771i) q^{83} +(3.59192 + 3.93654i) q^{84} +(-0.203158 + 1.20878i) q^{85} -2.64601i q^{86} +(-11.8171 - 0.540939i) q^{87} +(3.15047 + 3.15047i) q^{88} -2.48762 q^{89} +(-1.71159 + 6.48618i) q^{90} +4.24197 q^{91} +(-4.52613 - 4.52613i) q^{92} +(-1.73024 - 0.0792035i) q^{93} -13.1781i q^{94} +(12.8962 - 9.18502i) q^{95} +(-1.16746 - 1.27947i) q^{96} +(10.2426 - 10.2426i) q^{97} +(1.74379 - 1.74379i) q^{98} +(1.22116 - 13.3104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.73024	+	0.0792035i	0.998954	+	0.0457282i
$3$	1.73024	+	0.0792035i	0.998954	+	0.0457282i
$4$			1.00000i			0.500000i
$5$	1.29721	+	1.82133i	0.580128	+	0.814525i
$5$	1.29721	+	1.82133i	0.580128	+	0.814525i
$6$	1.16746	+	1.27947i	0.476613	+	0.522341i
$7$	2.17556	−	2.17556i	0.822283	−	0.822283i	−0.164152	−	0.986435i	$-0.552489\pi$
$7$	2.17556	−	2.17556i	0.822283	−	0.822283i	0.986435	+	0.164152i	$0.0524888\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.98745	+	0.274082i	0.995818	+	0.0913607i
$10$	−0.370615	+	2.20514i	−0.117199	+	0.697327i
$11$		−	4.45544i		−	1.34337i	−0.740839	−	0.671683i	$-0.765572\pi$
$11$		−	4.45544i		−	1.34337i	0.740839	−	0.671683i	$-0.234428\pi$
$12$	−0.0792035	+	1.73024i	−0.0228641	+	0.499477i
$13$	0.974917	+	0.974917i	0.270393	+	0.270393i	0.829259	−	0.558865i	$-0.188763\pi$
$13$	0.974917	+	0.974917i	0.270393	+	0.270393i	−0.558865	+	0.829259i	$0.688763\pi$
$14$	3.07670			0.822283
$15$	2.10022	+	3.25409i	0.542274	+	0.840202i
$16$	−1.00000			−0.250000
$17$	0.387611	+	0.387611i	0.0940094	+	0.0940094i	0.752547	−	0.658538i	$-0.228825\pi$
$17$	0.387611	+	0.387611i	0.0940094	+	0.0940094i	−0.658538	+	0.752547i	$0.728825\pi$
$18$	1.91864	+	2.30625i	0.452229	+	0.543589i
$19$		−	7.08062i		−	1.62441i	−0.583375	−	0.812203i	$-0.698268\pi$
$19$		−	7.08062i		−	1.62441i	0.583375	−	0.812203i	$-0.301732\pi$
$20$	−1.82133	+	1.29721i	−0.407263	+	0.290064i
$21$	3.93654	−	3.59192i	0.859024	−	0.783821i
$22$	3.15047	−	3.15047i	0.671683	−	0.671683i
$23$	−4.52613	+	4.52613i	−0.943763	+	0.943763i	−0.998501	−	0.0547380i	$-0.982568\pi$
$23$	−4.52613	+	4.52613i	−0.943763	+	0.943763i	0.0547380	+	0.998501i	$0.482568\pi$
$24$	−1.27947	+	1.16746i	−0.261171	+	0.238306i
$25$	−1.63452	+	4.72529i	−0.326903	+	0.945058i
$26$			1.37874i			0.270393i
$27$	5.14730	+	0.710844i	0.990598	+	0.136802i
$28$	2.17556	+	2.17556i	0.411141	+	0.411141i
$29$	−6.82973			−1.26825			−0.634125	−	0.773231i	$-0.718639\pi$
$29$	−6.82973			−1.26825			−0.634125	+	0.773231i	$0.718639\pi$
$30$	−0.815908	+	3.78607i	−0.148964	+	0.691238i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.352887	−	7.70898i	0.0614297	−	1.34196i
$34$			0.548164i			0.0940094i
$35$	6.78456	+	1.14027i	1.14680	+	0.192741i
$36$	−0.274082	+	2.98745i	−0.0456803	+	0.497909i
$37$	−2.48442	+	2.48442i	−0.408437	+	0.408437i	−0.881193	−	0.472756i	$-0.843259\pi$
$37$	−2.48442	+	2.48442i	−0.408437	+	0.408437i	0.472756	+	0.881193i	$0.343259\pi$
$38$	5.00675	−	5.00675i	0.812203	−	0.812203i
$39$	1.60962	+	1.76406i	0.257746	+	0.282475i
$40$	−2.20514	−	0.370615i	−0.348663	−	0.0585994i
$41$			9.64559i			1.50639i	0.657798	+	0.753194i	$0.271488\pi$
$41$			9.64559i			1.50639i	−0.657798	+	0.753194i	$0.728512\pi$
$42$	5.32343	+	0.243686i	0.821423	+	0.0376015i
$43$	−1.87101	−	1.87101i	−0.285327	−	0.285327i	0.549902	−	0.835229i	$-0.314665\pi$
$43$	−1.87101	−	1.87101i	−0.285327	−	0.285327i	−0.835229	+	0.549902i	$0.814665\pi$
$44$	4.45544			0.671683
$45$	3.37615	+	5.79669i	0.503286	+	0.864120i
$46$	−6.40091			−0.943763
$47$	−9.31831	−	9.31831i	−1.35921	−	1.35921i	−0.874886	−	0.484328i	$-0.839064\pi$
$47$	−9.31831	−	9.31831i	−1.35921	−	1.35921i	−0.484328	−	0.874886i	$-0.660936\pi$
$48$	−1.73024	−	0.0792035i	−0.249738	−	0.0114320i
$49$		−	2.46609i		−	0.352298i
$50$	−4.49706	+	2.18551i	−0.635981	+	0.309077i
$51$	0.639959	+	0.701359i	0.0896122	+	0.0982099i
$52$	−0.974917	+	0.974917i	−0.135197	+	0.135197i
$53$	−10.1295	+	10.1295i	−1.39139	+	1.39139i	−0.569176	+	0.822216i	$0.692738\pi$
$53$	−10.1295	+	10.1295i	−1.39139	+	1.39139i	−0.822216	+	0.569176i	$0.807262\pi$
$54$	3.13705	+	4.14233i	0.426898	+	0.563700i
$55$	8.11485	−	5.77962i	1.09421	−	0.779324i
$56$			3.07670i			0.411141i
$57$	0.560810	−	12.2512i	0.0742811	−	1.62271i
$58$	−4.82935	−	4.82935i	−0.634125	−	0.634125i
$59$	−4.06326			−0.528992			−0.264496	−	0.964387i	$-0.585206\pi$
$59$	−4.06326			−0.528992			−0.264496	+	0.964387i	$0.585206\pi$
$60$	−3.25409	+	2.10022i	−0.420101	+	0.271137i
$61$	7.35980			0.942326			0.471163	−	0.882046i	$-0.343834\pi$
$61$	7.35980			0.942326			0.471163	+	0.882046i	$0.343834\pi$
$62$	−0.707107	−	0.707107i	−0.0898027	−	0.0898027i
$63$	7.09565	−	5.90309i	0.893968	−	0.743720i
$64$		−	1.00000i		−	0.125000i
$65$	−0.510982	+	3.04032i	−0.0633796	+	0.377105i
$66$	5.70060	−	5.20154i	0.701695	−	0.640266i
$67$	−5.24191	+	5.24191i	−0.640401	+	0.640401i	−0.950654	−	0.310253i	$-0.899586\pi$
$67$	−5.24191	+	5.24191i	−0.640401	+	0.640401i	0.310253	+	0.950654i	$0.399586\pi$
$68$	−0.387611	+	0.387611i	−0.0470047	+	0.0470047i
$69$	−8.18977	+	7.47280i	−0.985932	+	0.899619i
$70$	3.99111	+	5.60370i	0.477029	+	0.669770i
$71$			12.5156i			1.48533i	0.669661	+	0.742667i	$0.266439\pi$
$71$			12.5156i			1.48533i	−0.669661	+	0.742667i	$0.733561\pi$
$72$	−2.30625	+	1.91864i	−0.271795	+	0.226114i
$73$	7.93503	+	7.93503i	0.928725	+	0.928725i	0.997624	−	0.0688990i	$-0.0219486\pi$
$73$	7.93503	+	7.93503i	0.928725	+	0.928725i	−0.0688990	+	0.997624i	$0.521949\pi$
$74$	−3.51351			−0.408437
$75$	−3.20236	+	8.04642i	−0.369777	+	0.929120i
$76$	7.08062			0.812203
$77$	−9.69306	−	9.69306i	−1.10463	−	1.10463i
$78$	−0.109201	+	2.38555i	−0.0123646	+	0.270111i
$79$		−	17.0708i		−	1.92062i	−0.278936	−	0.960310i	$-0.589982\pi$
$79$		−	17.0708i		−	1.92062i	0.278936	−	0.960310i	$-0.410018\pi$
$80$	−1.29721	−	1.82133i	−0.145032	−	0.203631i
$81$	8.84976	+	1.63761i	0.983306	+	0.181957i
$82$	−6.82046	+	6.82046i	−0.753194	+	0.753194i
$83$	2.57771	−	2.57771i	0.282940	−	0.282940i	−0.551340	−	0.834280i	$-0.685883\pi$
$83$	2.57771	−	2.57771i	0.282940	−	0.282940i	0.834280	+	0.551340i	$0.185883\pi$
$84$	3.59192	+	3.93654i	0.391911	+	0.429512i
$85$	−0.203158	+	1.20878i	−0.0220356	+	0.131110i
$86$		−	2.64601i		−	0.285327i
$87$	−11.8171	−	0.540939i	−1.26692	−	0.0579948i
$88$	3.15047	+	3.15047i	0.335842	+	0.335842i
$89$	−2.48762			−0.263687			−0.131844	−	0.991271i	$-0.542090\pi$
$89$	−2.48762			−0.263687			−0.131844	+	0.991271i	$0.542090\pi$
$90$	−1.71159	+	6.48618i	−0.180417	+	0.683703i
$91$	4.24197			0.444680
$92$	−4.52613	−	4.52613i	−0.471881	−	0.471881i
$93$	−1.73024	−	0.0792035i	−0.179417	−	0.00821302i
$94$		−	13.1781i		−	1.35921i
$95$	12.8962	−	9.18502i	1.32312	−	0.942363i
$96$	−1.16746	−	1.27947i	−0.119153	−	0.130585i
$97$	10.2426	−	10.2426i	1.03998	−	1.03998i	0.0408129	−	0.999167i	$-0.487005\pi$
$97$	10.2426	−	10.2426i	1.03998	−	1.03998i	0.999167	−	0.0408129i	$-0.0129948\pi$
$98$	1.74379	−	1.74379i	0.176149	−	0.176149i
$99$	1.22116	−	13.3104i	0.122731	−	1.33775i
$100$	−4.72529	−	1.63452i	−0.472529	−	0.163452i
$101$		−	1.10660i		−	0.110110i	−0.998483	−	0.0550552i	$-0.982467\pi$
$101$		−	1.10660i		−	0.110110i	0.998483	−	0.0550552i	$-0.0175335\pi$
$102$	−0.0434165	+	0.948455i	−0.00429888	+	0.0939110i
$103$	6.47834	+	6.47834i	0.638330	+	0.638330i	0.950143	−	0.311813i	$-0.100936\pi$
$103$	6.47834	+	6.47834i	0.638330	+	0.638330i	−0.311813	+	0.950143i	$0.600936\pi$
$104$	−1.37874			−0.135197
$105$	11.6486	+	2.51030i	1.13679	+	0.244981i
$106$	−14.3253			−1.39139
$107$	−1.67405	−	1.67405i	−0.161836	−	0.161836i	0.621543	−	0.783380i	$-0.286506\pi$
$107$	−1.67405	−	1.67405i	−0.161836	−	0.161836i	−0.783380	+	0.621543i	$0.786506\pi$
$108$	−0.710844	+	5.14730i	−0.0684010	+	0.495299i
$109$			2.67214i			0.255945i	0.991778	+	0.127972i	$0.0408469\pi$
$109$			2.67214i			0.255945i	−0.991778	+	0.127972i	$0.959153\pi$
$110$	9.82487	+	1.65125i	0.936765	+	0.157441i
$111$	−4.49542	+	4.10187i	−0.426687	+	0.389332i
$112$	−2.17556	+	2.17556i	−0.205571	+	0.205571i
$113$	10.7815	−	10.7815i	1.01423	−	1.01423i	0.0143368	−	0.999897i	$-0.495436\pi$
$113$	10.7815	−	10.7815i	1.01423	−	1.01423i	0.999897	−	0.0143368i	$-0.00456370\pi$
$114$	9.05943	−	8.26633i	0.848494	−	0.774213i
$115$	−14.1149	−	2.37227i	−1.31622	−	0.221216i
$116$		−	6.82973i		−	0.634125i
$117$	2.64531	+	3.17973i	0.244559	+	0.293966i
$118$	−2.87316	−	2.87316i	−0.264496	−	0.264496i
$119$	1.68654			0.154605
$120$	−3.78607	−	0.815908i	−0.345619	−	0.0744818i
$121$	−8.85096			−0.804633
$122$	5.20417	+	5.20417i	0.471163	+	0.471163i
$123$	−0.763965	+	16.6892i	−0.0688844	+	1.50481i
$124$		−	1.00000i		−	0.0898027i
$125$	−10.7266	+	3.15267i	−0.959419	+	0.281983i
$126$	9.19150	+	0.843268i	0.818844	+	0.0751243i
$127$	−4.16452	+	4.16452i	−0.369542	+	0.369542i	−0.867310	−	0.497768i	$-0.834153\pi$
$127$	−4.16452	+	4.16452i	−0.369542	+	0.369542i	0.497768	+	0.867310i	$0.334153\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.08911	−	3.38549i	−0.271981	−	0.298076i
$130$	−2.51115	+	1.78851i	−0.220242	+	0.156863i
$131$		−	9.33522i		−	0.815622i	−0.913066	−	0.407811i	$-0.866292\pi$
$131$		−	9.33522i		−	0.815622i	0.913066	−	0.407811i	$-0.133708\pi$
$132$	7.70898	+	0.352887i	0.670980	+	0.0307148i
$133$	−15.4043	−	15.4043i	−1.33572	−	1.33572i
$134$	−7.41318			−0.640401
$135$	5.38242	+	10.2971i	0.463245	+	0.886230i
$136$	−0.548164			−0.0470047
$137$	10.7767	+	10.7767i	0.920715	+	0.920715i	0.997080	−	0.0763645i	$-0.0243313\pi$
$137$	10.7767	+	10.7767i	0.920715	+	0.920715i	−0.0763645	+	0.997080i	$0.524331\pi$
$138$	−11.0751	−	0.506975i	−0.942776	−	0.0431566i
$139$		−	0.244460i		−	0.0207348i	−0.999946	−	0.0103674i	$-0.996700\pi$
$139$		−	0.244460i		−	0.0207348i	0.999946	−	0.0103674i	$-0.00330011\pi$
$140$	−1.14027	+	6.78456i	−0.0963706	+	0.573400i
$141$	−15.3849	−	16.8609i	−1.29564	−	1.41995i
$142$	−8.84990	+	8.84990i	−0.742667	+	0.742667i
$143$	4.34369	−	4.34369i	0.363237	−	0.363237i
$144$	−2.98745	−	0.274082i	−0.248954	−	0.0228402i
$145$	−8.85957	−	12.4392i	−0.735747	−	1.03302i
$146$			11.2218i			0.928725i
$147$	0.195323	−	4.26692i	0.0161099	−	0.351930i
$148$	−2.48442	−	2.48442i	−0.204218	−	0.204218i
$149$	14.2761			1.16955			0.584773	−	0.811197i	$-0.301184\pi$
$149$	14.2761			1.16955			0.584773	+	0.811197i	$0.301184\pi$
$150$	−7.95409	+	3.42526i	−0.649449	+	0.279672i
$151$	−16.9541			−1.37971			−0.689853	−	0.723949i	$-0.742325\pi$
$151$	−16.9541			−1.37971			−0.689853	+	0.723949i	$0.742325\pi$
$152$	5.00675	+	5.00675i	0.406101	+	0.406101i
$153$	1.05173	+	1.26421i	0.0850274	+	0.102205i
$154$		−	13.7081i		−	1.10463i
$155$	−1.29721	−	1.82133i	−0.104194	−	0.146293i
$156$	−1.76406	+	1.60962i	−0.141238	+	0.128873i
$157$	−1.62663	+	1.62663i	−0.129819	+	0.129819i	−0.769031	−	0.639212i	$-0.779261\pi$
$157$	−1.62663	+	1.62663i	−0.129819	+	0.129819i	0.639212	+	0.769031i	$0.279261\pi$
$158$	12.0709	−	12.0709i	0.960310	−	0.960310i
$159$	−18.3287	+	16.7241i	−1.45356	+	1.32631i
$160$	0.370615	−	2.20514i	0.0292997	−	0.174332i
$161$			19.6937i			1.55208i
$162$	5.09976	+	7.41569i	0.400675	+	0.582632i
$163$	9.77730	+	9.77730i	0.765817	+	0.765817i	0.977367	−	0.211550i	$-0.0678512\pi$
$163$	9.77730	+	9.77730i	0.765817	+	0.765817i	−0.211550	+	0.977367i	$0.567851\pi$
$164$	−9.64559			−0.753194
$165$	14.4984	−	9.35740i	1.12870	−	0.728473i
$166$	3.64543			0.282940
$167$	2.45802	+	2.45802i	0.190207	+	0.190207i	0.795786	−	0.605578i	$-0.207058\pi$
$167$	2.45802	+	2.45802i	0.190207	+	0.190207i	−0.605578	+	0.795786i	$0.707058\pi$
$168$	−0.243686	+	5.32343i	−0.0188007	+	0.410711i
$169$		−	11.0991i		−	0.853775i
$170$	−0.998390	+	0.711081i	−0.0765730	+	0.0545375i
$171$	1.94067	−	21.1530i	0.148407	−	1.61761i
$172$	1.87101	−	1.87101i	0.142663	−	0.142663i
$173$	11.5374	−	11.5374i	0.877171	−	0.877171i	−0.116070	−	0.993241i	$-0.537030\pi$
$173$	11.5374	−	11.5374i	0.877171	−	0.877171i	0.993241	+	0.116070i	$0.0370297\pi$
$174$	−7.97343	−	8.73843i	−0.604464	−	0.662459i
$175$	6.72415	+	13.8361i	0.508298	+	1.04591i
$176$			4.45544i			0.335842i
$177$	−7.03042	−	0.321825i	−0.528439	−	0.0241898i
$178$	−1.75902	−	1.75902i	−0.131844	−	0.131844i
$179$	6.13492			0.458546			0.229273	−	0.973362i	$-0.426365\pi$
$179$	6.13492			0.458546			0.229273	+	0.973362i	$0.426365\pi$
$180$	−5.79669	+	3.37615i	−0.432060	+	0.251643i
$181$	−0.756752			−0.0562490			−0.0281245	−	0.999604i	$-0.508953\pi$
$181$	−0.756752			−0.0562490			−0.0281245	+	0.999604i	$0.508953\pi$
$182$	2.99953	+	2.99953i	0.222340	+	0.222340i
$183$	12.7342	+	0.582922i	0.941341	+	0.0430909i
$184$		−	6.40091i		−	0.471881i
$185$	−7.74777	−	1.30216i	−0.569628	−	0.0957366i
$186$	−1.16746	−	1.27947i	−0.0856022	−	0.0938152i
$187$	1.72698	−	1.72698i	0.126289	−	0.126289i
$188$	9.31831	−	9.31831i	0.679607	−	0.679607i
$189$	12.7447	−	9.65176i	0.927042	−	0.702062i
$190$	15.6138	+	2.62418i	1.13274	+	0.190378i
$191$			4.47635i			0.323897i	0.986799	+	0.161949i	$0.0517779\pi$
$191$			4.47635i			0.323897i	−0.986799	+	0.161949i	$0.948222\pi$
$192$	0.0792035	−	1.73024i	0.00571602	−	0.124869i
$193$	−6.48726	−	6.48726i	−0.466963	−	0.466963i	0.433966	−	0.900929i	$-0.357114\pi$
$193$	−6.48726	−	6.48726i	−0.466963	−	0.466963i	−0.900929	+	0.433966i	$0.857114\pi$
$194$	14.4852			1.03998
$195$	−1.12493	+	5.22000i	−0.0805576	+	0.373812i
$196$	2.46609			0.176149
$197$	−10.0409	−	10.0409i	−0.715385	−	0.715385i	0.252271	−	0.967657i	$-0.418822\pi$
$197$	−10.0409	−	10.0409i	−0.715385	−	0.715385i	−0.967657	+	0.252271i	$0.918822\pi$
$198$	10.2754	−	8.54840i	0.730239	−	0.607509i
$199$		−	10.0543i		−	0.712731i	−0.934347	−	0.356366i	$-0.884016\pi$
$199$		−	10.0543i		−	0.712731i	0.934347	−	0.356366i	$-0.115984\pi$
$200$	−2.18551	−	4.49706i	−0.154539	−	0.317990i
$201$	−9.48494	+	8.65458i	−0.669016	+	0.610447i
$202$	0.782481	−	0.782481i	0.0550552	−	0.0550552i
$203$	−14.8585	+	14.8585i	−1.04286	+	1.04286i
$204$	−0.701359	+	0.639959i	−0.0491050	+	0.0448061i
$205$	−17.5678	+	12.5123i	−1.22699	+	0.873898i
$206$			9.16176i			0.638330i
$207$	−14.7621	+	12.2811i	−1.02604	+	0.853593i
$208$	−0.974917	−	0.974917i	−0.0675983	−	0.0675983i
$209$	−31.5473			−2.18217
$210$	6.46174	+	10.0119i	0.445903	+	0.690883i
$211$	4.01722			0.276557			0.138279	−	0.990393i	$-0.455843\pi$
$211$	4.01722			0.276557			0.138279	+	0.990393i	$0.455843\pi$
$212$	−10.1295	−	10.1295i	−0.695696	−	0.695696i
$213$	−0.991283	+	21.6551i	−0.0679216	+	1.48378i
$214$		−	2.36746i		−	0.161836i
$215$	0.980652	−	5.83482i	0.0668799	−	0.397932i
$216$	−4.14233	+	3.13705i	−0.281850	+	0.213449i
$217$	−2.17556	+	2.17556i	−0.147686	+	0.147686i
$218$	−1.88949	+	1.88949i	−0.127972	+	0.127972i
$219$	13.1010	+	14.3580i	0.885284	+	0.970222i
$220$	5.77962	+	8.11485i	0.389662	+	0.547103i
$221$			0.755776i			0.0508390i
$222$	−6.07920	−	0.278282i	−0.408010	−	0.0186771i
$223$	−2.71948	−	2.71948i	−0.182110	−	0.182110i	0.610165	−	0.792275i	$-0.291103\pi$
$223$	−2.71948	−	2.71948i	−0.182110	−	0.182110i	−0.792275	+	0.610165i	$0.791103\pi$
$224$	−3.07670			−0.205571
$225$	−6.17816	+	13.6686i	−0.411877	+	0.911239i
$226$	15.2473			1.01423
$227$	0.759912	+	0.759912i	0.0504371	+	0.0504371i	0.731875	−	0.681438i	$-0.238645\pi$
$227$	0.759912	+	0.759912i	0.0504371	+	0.0504371i	−0.681438	+	0.731875i	$0.738645\pi$
$228$	12.2512	+	0.560810i	0.811353	+	0.0371405i
$229$			3.91489i			0.258703i	0.991599	+	0.129351i	$0.0412895\pi$
$229$			3.91489i			0.258703i	−0.991599	+	0.129351i	$0.958710\pi$
$230$	−8.30330	−	11.6582i	−0.547503	−	0.768719i
$231$	−16.0036	−	17.5390i	−1.05296	−	1.15398i
$232$	4.82935	−	4.82935i	0.317062	−	0.317062i
$233$	−3.09546	+	3.09546i	−0.202790	+	0.202790i	−0.801194	−	0.598404i	$-0.795802\pi$
$233$	−3.09546	+	3.09546i	−0.202790	+	0.202790i	0.598404	+	0.801194i	$0.295802\pi$
$234$	−0.377888	+	4.11893i	−0.0247033	+	0.269263i
$235$	4.88399	−	29.0595i	0.318597	−	1.89563i
$236$		−	4.06326i		−	0.264496i
$237$	1.35207	−	29.5366i	0.0878264	−	1.91861i
$238$	1.19256	+	1.19256i	0.0773023	+	0.0773023i
$239$	19.9202			1.28853			0.644265	−	0.764802i	$-0.277163\pi$
$239$	19.9202			1.28853			0.644265	+	0.764802i	$0.277163\pi$
$240$	−2.10022	−	3.25409i	−0.135569	−	0.210050i
$241$	−10.1524			−0.653971			−0.326986	−	0.945029i	$-0.606033\pi$
$241$	−10.1524			−0.653971			−0.326986	+	0.945029i	$0.606033\pi$
$242$	−6.25857	−	6.25857i	−0.402316	−	0.402316i
$243$	15.1825	+	3.53440i	0.973957	+	0.226732i
$244$			7.35980i			0.471163i
$245$	4.49157	−	3.19902i	0.286956	−	0.204378i
$246$	−12.3412	+	11.2608i	−0.786848	+	0.717964i
$247$	6.90302	−	6.90302i	0.439228	−	0.439228i
$248$	0.707107	−	0.707107i	0.0449013	−	0.0449013i
$249$	4.66421	−	4.25589i	0.295582	−	0.269706i
$250$	−9.81415	−	5.35560i	−0.620701	−	0.338718i
$251$		−	18.9099i		−	1.19358i	−0.802396	−	0.596792i	$-0.796442\pi$
$251$		−	18.9099i		−	1.19358i	0.802396	−	0.596792i	$-0.203558\pi$
$252$	5.90309	+	7.09565i	0.371860	+	0.446984i
$253$	20.1659	+	20.1659i	1.26782	+	1.26782i
$254$	−5.88953			−0.369542
$255$	−0.447251	+	2.07539i	−0.0280080	+	0.129966i
$256$	1.00000			0.0625000
$257$	10.5933	+	10.5933i	0.660794	+	0.660794i	0.955567	−	0.294773i	$-0.0952440\pi$
$257$	10.5933	+	10.5933i	0.660794	+	0.660794i	−0.294773	+	0.955567i	$0.595244\pi$
$258$	0.209573	−	4.57823i	0.0130475	−	0.285028i
$259$			10.8100i			0.671701i
$260$	−3.04032	−	0.510982i	−0.188553	−	0.0316898i
$261$	−20.4035	−	1.87191i	−1.26295	−	0.115868i
$262$	6.60100	−	6.60100i	0.407811	−	0.407811i
$263$	4.26368	−	4.26368i	0.262910	−	0.262910i	−0.563326	−	0.826235i	$-0.690478\pi$
$263$	4.26368	−	4.26368i	0.262910	−	0.262910i	0.826235	+	0.563326i	$0.190478\pi$
$264$	5.20154	+	5.70060i	0.320133	+	0.350848i
$265$	−31.5892	−	5.30916i	−1.94051	−	0.326139i
$266$		−	21.7849i		−	1.33572i
$267$	−4.30418	−	0.197029i	−0.263412	−	0.0120579i
$268$	−5.24191	−	5.24191i	−0.320201	−	0.320201i
$269$	−1.71396			−0.104502			−0.0522510	−	0.998634i	$-0.516640\pi$
$269$	−1.71396			−0.104502			−0.0522510	+	0.998634i	$0.516640\pi$
$270$	−3.47518	+	11.0871i	−0.211493	+	0.674738i
$271$	−25.3308			−1.53874			−0.769368	−	0.638806i	$-0.779429\pi$
$271$	−25.3308			−1.53874			−0.769368	+	0.638806i	$0.779429\pi$
$272$	−0.387611	−	0.387611i	−0.0235023	−	0.0235023i
$273$	7.33963	+	0.335979i	0.444214	+	0.0203344i
$274$			15.2406i			0.920715i
$275$	21.0532	+	7.28250i	1.26956	+	0.439151i
$276$	−7.47280	−	8.18977i	−0.449809	−	0.492966i
$277$	8.95479	−	8.95479i	0.538041	−	0.538041i	−0.384912	−	0.922953i	$-0.625768\pi$
$277$	8.95479	−	8.95479i	0.538041	−	0.538041i	0.922953	+	0.384912i	$0.125768\pi$
$278$	0.172859	−	0.172859i	0.0103674	−	0.0103674i
$279$	−2.98745	−	0.274082i	−0.178854	−	0.0164089i
$280$	−5.60370	+	3.99111i	−0.334885	+	0.238515i
$281$		−	1.19340i		−	0.0711924i	−0.999366	−	0.0355962i	$-0.988667\pi$
$281$		−	1.19340i		−	0.0711924i	0.999366	−	0.0355962i	$-0.0113330\pi$
$282$	1.04375	−	22.8012i	0.0621544	−	1.35779i
$283$	4.03370	+	4.03370i	0.239778	+	0.239778i	0.816758	−	0.576980i	$-0.195769\pi$
$283$	4.03370	+	4.03370i	0.239778	+	0.239778i	−0.576980	+	0.816758i	$0.695769\pi$
$284$	−12.5156			−0.742667
$285$	23.0409	−	14.8709i	1.36483	−	0.880873i
$286$	6.14290			0.363237
$287$	20.9845	+	20.9845i	1.23868	+	1.23868i
$288$	−1.91864	−	2.30625i	−0.113057	−	0.135897i
$289$		−	16.6995i		−	0.982324i
$290$	2.53120	−	15.0605i	0.148637	−	0.884384i
$291$	18.5334	−	16.9109i	1.08645	−	0.991335i
$292$	−7.93503	+	7.93503i	−0.464362	+	0.464362i
$293$	19.4310	−	19.4310i	1.13517	−	1.13517i	0.145868	−	0.989304i	$-0.453403\pi$
$293$	19.4310	−	19.4310i	1.13517	−	1.13517i	0.989304	−	0.145868i	$-0.0465973\pi$
$294$	3.15528	−	2.87905i	0.184020	−	0.167910i
$295$	−5.27089	−	7.40056i	−0.306883	−	0.430877i
$296$		−	3.51351i		−	0.204218i
$297$	3.16713	−	22.9335i	0.183775	−	1.33074i
$298$	10.0947	+	10.0947i	0.584773	+	0.584773i
$299$	−8.82520			−0.510374
$300$	−8.04642	−	3.20236i	−0.464560	−	0.184889i
$301$	−8.14098			−0.469238
$302$	−11.9884	−	11.9884i	−0.689853	−	0.689853i
$303$	0.0876463	−	1.91467i	0.00503515	−	0.109995i
$304$			7.08062i			0.406101i
$305$	9.54718	+	13.4047i	0.546670	+	0.767549i
$306$	−0.150242	+	1.63761i	−0.00858876	+	0.0936162i
$307$	−2.60628	+	2.60628i	−0.148748	+	0.148748i	−0.777559	−	0.628810i	$-0.783542\pi$
$307$	−2.60628	+	2.60628i	−0.148748	+	0.148748i	0.628810	+	0.777559i	$0.283542\pi$
$308$	9.69306	−	9.69306i	0.552313	−	0.552313i
$309$	10.6960	+	11.7222i	0.608473	+	0.666852i
$310$	0.370615	−	2.20514i	0.0210495	−	0.125244i
$311$		−	21.1821i		−	1.20112i	−0.799578	−	0.600562i	$-0.794944\pi$
$311$		−	21.1821i		−	1.20112i	0.799578	−	0.600562i	$-0.205056\pi$
$312$	−2.38555	−	0.109201i	−0.135055	−	0.00618230i
$313$	6.20568	+	6.20568i	0.350766	+	0.350766i	0.860395	−	0.509629i	$-0.170217\pi$
$313$	6.20568	+	6.20568i	0.350766	+	0.350766i	−0.509629	+	0.860395i	$0.670217\pi$
$314$	−2.30040			−0.129819
$315$	19.9560	+	5.26603i	1.12439	+	0.296707i
$316$	17.0708			0.960310
$317$	0.787882	+	0.787882i	0.0442518	+	0.0442518i	0.728886	−	0.684635i	$-0.240038\pi$
$317$	0.787882	+	0.787882i	0.0442518	+	0.0442518i	−0.684635	+	0.728886i	$0.740038\pi$
$318$	−24.7861	−	1.13461i	−1.38994	−	0.0636258i
$319$			30.4295i			1.70372i
$320$	1.82133	−	1.29721i	0.101816	−	0.0725160i
$321$	−2.76392	−	3.02910i	−0.154267	−	0.169068i
$322$	−13.9255	+	13.9255i	−0.776040	+	0.776040i
$323$	2.74452	−	2.74452i	0.152709	−	0.152709i
$324$	−1.63761	+	8.84976i	−0.0909786	+	0.491653i
$325$	−6.20028	+	3.01325i	−0.343930	+	0.167145i
$326$			13.8272i			0.765817i
$327$	−0.211643	+	4.62344i	−0.0117039	+	0.255677i
$328$	−6.82046	−	6.82046i	−0.376597	−	0.376597i
$329$	−40.5450			−2.23532
$330$	16.8686	+	3.63523i	0.928586	+	0.200113i
$331$	6.28831			0.345637			0.172818	−	0.984954i	$-0.444713\pi$
$331$	6.28831			0.345637			0.172818	+	0.984954i	$0.444713\pi$
$332$	2.57771	+	2.57771i	0.141470	+	0.141470i
$333$	−8.10304	+	6.74116i	−0.444044	+	0.369414i
$334$			3.47616i			0.190207i
$335$	−16.3471	−	2.74744i	−0.893138	−	0.150109i
$336$	−3.93654	+	3.59192i	−0.214756	+	0.195955i
$337$	18.0495	−	18.0495i	0.983220	−	0.983220i	−0.0166419	−	0.999862i	$-0.505298\pi$
$337$	18.0495	−	18.0495i	0.983220	−	0.983220i	0.999862	+	0.0166419i	$0.00529751\pi$
$338$	7.84823	−	7.84823i	0.426887	−	0.426887i
$339$	19.5084	−	17.8006i	1.05955	−	0.966794i
$340$	−1.20878	−	0.203158i	−0.0655552	−	0.0110178i
$341$			4.45544i			0.241276i
$342$	16.3297	−	13.5852i	0.883009	−	0.734603i
$343$	9.86378	+	9.86378i	0.532594	+	0.532594i
$344$	2.64601			0.142663
$345$	−24.2343	−	5.22255i	−1.30473	−	0.281173i
$346$	16.3163			0.877171
$347$	−9.97805	−	9.97805i	−0.535650	−	0.535650i	0.386598	−	0.922248i	$-0.373650\pi$
$347$	−9.97805	−	9.97805i	−0.535650	−	0.535650i	−0.922248	+	0.386598i	$0.873650\pi$
$348$	0.540939	−	11.8171i	0.0289974	−	0.633462i
$349$		−	9.44139i		−	0.505386i	−0.967547	−	0.252693i	$-0.918684\pi$
$349$		−	9.44139i		−	0.505386i	0.967547	−	0.252693i	$-0.0813163\pi$
$350$	−5.02892	+	14.5383i	−0.268807	+	0.777105i
$351$	4.32518	+	5.71121i	0.230861	+	0.304842i
$352$	−3.15047	+	3.15047i	−0.167921	+	0.167921i
$353$	13.3896	−	13.3896i	0.712656	−	0.712656i	−0.254434	−	0.967090i	$-0.581889\pi$
$353$	13.3896	−	13.3896i	0.712656	−	0.712656i	0.967090	+	0.254434i	$0.0818891\pi$
$354$	−4.74369	−	5.19882i	−0.252124	−	0.276314i
$355$	−22.7952	+	16.2354i	−1.20984	+	0.861683i
$356$		−	2.48762i		−	0.131844i
$357$	2.91811	+	0.133580i	0.154443	+	0.00706979i
$358$	4.33805	+	4.33805i	0.229273	+	0.229273i
$359$	13.8690			0.731979			0.365990	−	0.930619i	$-0.380731\pi$
$359$	13.8690			0.731979			0.365990	+	0.930619i	$0.380731\pi$
$360$	−6.48618	−	1.71159i	−0.341851	−	0.0902085i
$361$	−31.1352			−1.63869
$362$	−0.535105	−	0.535105i	−0.0281245	−	0.0281245i
$363$	−15.3143	−	0.701027i	−0.803791	−	0.0367944i
$364$			4.24197i			0.222340i
$365$	−4.15898	+	24.7457i	−0.217691	+	1.29525i
$366$	8.59226	+	9.41664i	0.449125	+	0.492216i
$367$	−11.4993	+	11.4993i	−0.600258	+	0.600258i	−0.940381	−	0.340123i	$-0.889531\pi$
$367$	−11.4993	+	11.4993i	−0.600258	+	0.600258i	0.340123	+	0.940381i	$0.389531\pi$
$368$	4.52613	−	4.52613i	0.235941	−	0.235941i
$369$	−2.64368	+	28.8158i	−0.137625	+	1.50009i
$370$	−4.55774	−	6.39927i	−0.236946	−	0.332682i
$371$			44.0745i			2.28823i
$372$	0.0792035	−	1.73024i	0.00410651	−	0.0897087i
$373$	16.1616	+	16.1616i	0.836814	+	0.836814i	0.988438	−	0.151624i	$-0.0484503\pi$
$373$	16.1616	+	16.1616i	0.836814	+	0.836814i	−0.151624	+	0.988438i	$0.548450\pi$
$374$	2.44231			0.126289
$375$	−18.8093	+	4.60528i	−0.971310	+	0.237816i
$376$	13.1781			0.679607
$377$	−6.65843	−	6.65843i	−0.342926	−	0.342926i
$378$	15.8367	+	2.18706i	0.814552	+	0.112490i
$379$		−	3.26340i		−	0.167630i	−0.996481	−	0.0838148i	$-0.973290\pi$
$379$		−	3.26340i		−	0.167630i	0.996481	−	0.0838148i	$-0.0267104\pi$
$380$	9.18502	+	12.8962i	0.471181	+	0.661560i
$381$	−7.53547	+	6.87578i	−0.386054	+	0.352257i
$382$	−3.16525	+	3.16525i	−0.161949	+	0.161949i
$383$	−20.8788	+	20.8788i	−1.06686	+	1.06686i	−0.0692583	+	0.997599i	$0.522063\pi$
$383$	−20.8788	+	20.8788i	−1.06686	+	1.06686i	−0.997599	+	0.0692583i	$0.977937\pi$
$384$	1.27947	−	1.16746i	0.0652926	−	0.0595766i
$385$	5.08041	−	30.2282i	0.258922	−	1.54057i
$386$		−	9.17438i		−	0.466963i
$387$	−5.07675	−	6.10237i	−0.258066	−	0.310201i
$388$	10.2426	+	10.2426i	0.519990	+	0.519990i
$389$	−25.5691			−1.29640			−0.648201	−	0.761469i	$-0.724479\pi$
$389$	−25.5691			−1.29640			−0.648201	+	0.761469i	$0.724479\pi$
$390$	−4.48654	+	2.89566i	−0.227185	+	0.146627i
$391$	−3.50875			−0.177445
$392$	1.74379	+	1.74379i	0.0880745	+	0.0880745i
$393$	0.739382	−	16.1522i	0.0372969	−	0.814769i
$394$		−	14.2000i		−	0.715385i
$395$	31.0917	−	22.1444i	1.56439	−	1.11420i
$396$	13.3104	+	1.22116i	0.668874	+	0.0613654i
$397$	21.1945	−	21.1945i	1.06372	−	1.06372i	0.0658935	−	0.997827i	$-0.479010\pi$
$397$	21.1945	−	21.1945i	1.06372	−	1.06372i	0.997827	−	0.0658935i	$-0.0209898\pi$
$398$	7.10947	−	7.10947i	0.356366	−	0.356366i
$399$	−25.4330	−	27.8732i	−1.27324	−	1.39540i
$400$	1.63452	−	4.72529i	0.0817258	−	0.236264i
$401$			23.2465i			1.16087i	0.814305	+	0.580437i	$0.197118\pi$
$401$			23.2465i			1.16087i	−0.814305	+	0.580437i	$0.802882\pi$
$402$	−12.8266	−	0.587150i	−0.639731	−	0.0292844i
$403$	−0.974917	−	0.974917i	−0.0485641	−	0.0485641i
$404$	1.10660			0.0550552
$405$	8.49731	+	18.2427i	0.422235	+	0.906487i
$406$	−21.0130			−1.04286
$407$	11.0692	+	11.0692i	0.548680	+	0.548680i
$408$	−0.948455	−	0.0434165i	−0.0469555	−	0.00214944i
$409$			31.5271i			1.55891i	0.626456	+	0.779456i	$0.284505\pi$
$409$			31.5271i			1.55891i	−0.626456	+	0.779456i	$0.715495\pi$
$410$	−21.2699	−	3.57480i	−1.05044	−	0.176547i
$411$	17.7927	+	19.4998i	0.877650	+	0.961855i
$412$	−6.47834	+	6.47834i	−0.319165	+	0.319165i
$413$	−8.83986	+	8.83986i	−0.434981	+	0.434981i
$414$	−19.1224	−	1.75437i	−0.939816	−	0.0862228i
$415$	8.03868	+	1.35105i	0.394603	+	0.0663205i
$416$		−	1.37874i		−	0.0675983i
$417$	0.0193621	−	0.422975i	0.000948167	−	0.0207132i
$418$	−22.3073	−	22.3073i	−1.09109	−	1.09109i
$419$	0.356745			0.0174281			0.00871406	−	0.999962i	$-0.497226\pi$
$419$	0.356745			0.0174281			0.00871406	+	0.999962i	$0.497226\pi$
$420$	−2.51030	+	11.6486i	−0.122490	+	0.568393i
$421$	23.8321			1.16151			0.580753	−	0.814080i	$-0.302758\pi$
$421$	23.8321			1.16151			0.580753	+	0.814080i	$0.302758\pi$
$422$	2.84061	+	2.84061i	0.138279	+	0.138279i
$423$	−25.2840	−	30.3920i	−1.22935	−	1.47771i
$424$		−	14.3253i		−	0.695696i
$425$	−2.46513	+	1.19802i	−0.119576	+	0.0581123i
$426$	−16.0134	+	14.6115i	−0.775851	+	0.707929i
$427$	16.0117	−	16.0117i	0.774859	−	0.774859i
$428$	1.67405	−	1.67405i	0.0809182	−	0.0809182i
$429$	7.85965	−	7.17158i	0.379468	−	0.346247i
$430$	4.81927	−	3.43242i	0.232406	−	0.165526i
$431$			24.3243i			1.17166i	0.810433	+	0.585831i	$0.199232\pi$
$431$			24.3243i			1.17166i	−0.810433	+	0.585831i	$0.800768\pi$
$432$	−5.14730	−	0.710844i	−0.247650	−	0.0342005i
$433$	−4.98544	−	4.98544i	−0.239585	−	0.239585i	0.577093	−	0.816678i	$-0.304187\pi$
$433$	−4.98544	−	4.98544i	−0.239585	−	0.239585i	−0.816678	+	0.577093i	$0.804187\pi$
$434$	−3.07670			−0.147686
$435$	−14.3439	−	22.2245i	−0.687739	−	1.06559i
$436$	−2.67214			−0.127972
$437$	32.0478	+	32.0478i	1.53305	+	1.53305i
$438$	−0.888808	+	19.4164i	−0.0424689	+	0.927753i
$439$			36.3333i			1.73410i	0.498225	+	0.867048i	$0.333985\pi$
$439$			36.3333i			1.73410i	−0.498225	+	0.867048i	$0.666015\pi$
$440$	−1.65125	+	9.82487i	−0.0787205	+	0.468383i
$441$	0.675910	−	7.36732i	0.0321862	−	0.350825i
$442$	−0.534415	+	0.534415i	−0.0254195	+	0.0254195i
$443$	−0.742619	+	0.742619i	−0.0352829	+	0.0352829i	−0.724528	−	0.689245i	$-0.757942\pi$
$443$	−0.742619	+	0.742619i	−0.0352829	+	0.0352829i	0.689245	+	0.724528i	$0.257942\pi$
$444$	−4.10187	−	4.49542i	−0.194666	−	0.213343i
$445$	−3.22696	−	4.53079i	−0.152972	−	0.214780i
$446$		−	3.84593i		−	0.182110i
$447$	24.7011	+	1.13072i	1.16832	+	0.0534812i
$448$	−2.17556	−	2.17556i	−0.102785	−	0.102785i
$449$	−32.1988			−1.51956			−0.759778	−	0.650183i	$-0.774692\pi$
$449$	−32.1988			−1.51956			−0.759778	+	0.650183i	$0.774692\pi$
$450$	−14.0338	+	5.29653i	−0.661558	+	0.249681i
$451$	42.9754			2.02363
$452$	10.7815	+	10.7815i	0.507117	+	0.507117i
$453$	−29.3347	−	1.34283i	−1.37826	−	0.0630914i
$454$			1.07468i			0.0504371i
$455$	5.50271	+	7.72605i	0.257971	+	0.362203i
$456$	8.26633	+	9.05943i	0.387106	+	0.424247i
$457$	−9.79211	+	9.79211i	−0.458056	+	0.458056i	−0.898017	−	0.439961i	$-0.854992\pi$
$457$	−9.79211	+	9.79211i	−0.458056	+	0.458056i	0.439961	+	0.898017i	$0.354992\pi$
$458$	−2.76824	+	2.76824i	−0.129351	+	0.129351i
$459$	1.71962	+	2.27068i	0.0802649	+	0.105986i
$460$	2.37227	−	14.1149i	0.110608	−	0.658111i
$461$			27.9465i			1.30160i	0.759250	+	0.650799i	$0.225566\pi$
$461$			27.9465i			1.30160i	−0.759250	+	0.650799i	$0.774434\pi$
$462$	1.08573	−	23.7182i	0.0505126	−	1.10347i
$463$	29.4940	+	29.4940i	1.37070	+	1.37070i	0.859400	+	0.511303i	$0.170837\pi$
$463$	29.4940	+	29.4940i	1.37070	+	1.37070i	0.511303	+	0.859400i	$0.329163\pi$
$464$	6.82973			0.317062
$465$	−2.10022	−	3.25409i	−0.0973953	−	0.150905i
$466$	−4.37764			−0.202790
$467$	3.83696	+	3.83696i	0.177553	+	0.177553i	0.790288	−	0.612735i	$-0.209931\pi$
$467$	3.83696	+	3.83696i	0.177553	+	0.177553i	−0.612735	+	0.790288i	$0.709931\pi$
$468$	−3.17973	+	2.64531i	−0.146983	+	0.122280i
$469$			22.8081i			1.05318i
$470$	24.0017	−	17.0947i	1.10711	−	0.788518i
$471$	−2.94330	+	2.68563i	−0.135620	+	0.123747i
$472$	2.87316	−	2.87316i	0.132248	−	0.132248i
$473$	−8.33618	+	8.33618i	−0.383298	+	0.383298i
$474$	21.8416	−	19.9295i	1.00322	−	0.915392i
$475$	33.4580	+	11.5734i	1.53516	+	0.531024i
$476$			1.68654i			0.0773023i
$477$	−33.0377	+	27.4851i	−1.51269	+	1.25845i
$478$	14.0857	+	14.0857i	0.644265	+	0.644265i
$479$	23.4682			1.07229			0.536145	−	0.844126i	$-0.319880\pi$
$479$	23.4682			1.07229			0.536145	+	0.844126i	$0.319880\pi$
$480$	0.815908	−	3.78607i	0.0372409	−	0.172809i
$481$	−4.84421			−0.220877
$482$	−7.17881	−	7.17881i	−0.326986	−	0.326986i
$483$	−1.55981	+	34.0748i	−0.0709738	+	1.55046i
$484$		−	8.85096i		−	0.402316i
$485$	31.9420	+	5.36845i	1.45041	+	0.243769i
$486$	8.23645	+	13.2348i	0.373613	+	0.600344i
$487$	7.21655	−	7.21655i	0.327013	−	0.327013i	−0.524436	−	0.851450i	$-0.675724\pi$
$487$	7.21655	−	7.21655i	0.327013	−	0.327013i	0.851450	+	0.524436i	$0.175724\pi$
$488$	−5.20417	+	5.20417i	−0.235582	+	0.235582i
$489$	16.1427	+	17.6915i	0.729996	+	0.800035i
$490$	5.43807	+	0.913969i	0.245667	+	0.0412889i
$491$		−	29.1852i		−	1.31711i	−0.752534	−	0.658554i	$-0.771168\pi$
$491$		−	29.1852i		−	1.31711i	0.752534	−	0.658554i	$-0.228832\pi$
$492$	−16.6892	−	0.763965i	−0.752406	−	0.0344422i
$493$	−2.64728	−	2.64728i	−0.119227	−	0.119227i
$494$	9.76234			0.439228
$495$	25.8268	−	15.0422i	1.16083	−	0.676097i
$496$	1.00000			0.0449013
$497$	27.2285	+	27.2285i	1.22136	+	1.22136i
$498$	6.30746	+	0.288731i	0.282644	+	0.0129383i
$499$			11.3575i			0.508429i	0.967148	+	0.254215i	$0.0818170\pi$
$499$			11.3575i			0.508429i	−0.967148	+	0.254215i	$0.918183\pi$
$500$	−3.15267	−	10.7266i	−0.140992	−	0.479710i
$501$	4.05827	+	4.44764i	0.181310	+	0.198706i
$502$	13.3713	−	13.3713i	0.596792	−	0.596792i
$503$	20.1340	−	20.1340i	0.897732	−	0.897732i	−0.0975031	−	0.995235i	$-0.531086\pi$
$503$	20.1340	−	20.1340i	0.897732	−	0.897732i	0.995235	+	0.0975031i	$0.0310856\pi$
$504$	−0.843268	+	9.19150i	−0.0375622	+	0.409422i
$505$	2.01548	−	1.43548i	0.0896877	−	0.0638781i
$506$			28.5189i			1.26782i
$507$	0.879086	−	19.2040i	0.0390416	−	0.852882i
$508$	−4.16452	−	4.16452i	−0.184771	−	0.184771i
$509$	−44.2083			−1.95950			−0.979749	−	0.200227i	$-0.935832\pi$
$509$	−44.2083			−1.95950			−0.979749	+	0.200227i	$0.935832\pi$
$510$	−1.78377	+	1.15126i	−0.0789868	+	0.0509789i
$511$	34.5262			1.52735
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.03322	−	36.4461i	0.222222	−	1.60913i
$514$			14.9812i			0.660794i
$515$	−3.39549	+	20.2030i	−0.149623	+	0.890249i
$516$	3.38549	−	3.08911i	0.149038	−	0.135990i
$517$	−41.5172	+	41.5172i	−1.82592	+	1.82592i
$518$	−7.64383	+	7.64383i	−0.335851	+	0.335851i
$519$	20.8762	−	19.0486i	0.916365	−	0.836142i
$520$	−1.78851	−	2.51115i	−0.0784314	−	0.110121i
$521$		−	39.0652i		−	1.71148i	−0.517409	−	0.855738i	$-0.673104\pi$
$521$		−	39.0652i		−	1.71148i	0.517409	−	0.855738i	$-0.326896\pi$
$522$	−13.1038	−	15.7511i	−0.573539	−	0.689407i
$523$	2.56964	+	2.56964i	0.112363	+	0.112363i	0.761053	−	0.648690i	$-0.224683\pi$
$523$	2.56964	+	2.56964i	0.112363	+	0.112363i	−0.648690	+	0.761053i	$0.724683\pi$
$524$	9.33522			0.407811
$525$	10.5385	+	24.4724i	0.459938	+	1.06806i
$526$	6.02975			0.262910
$527$	−0.387611	−	0.387611i	−0.0168846	−	0.0168846i
$528$	−0.352887	+	7.70898i	−0.0153574	+	0.335490i
$529$		−	17.9717i		−	0.781376i
$530$	−18.5828	−	26.0911i	−0.807185	−	1.13332i
$531$	−12.1388	−	1.11367i	−0.526780	−	0.0483291i
$532$	15.4043	−	15.4043i	0.667860	−	0.667860i
$533$	−9.40365	+	9.40365i	−0.407317	+	0.407317i
$534$	−2.90420	−	3.18284i	−0.125677	−	0.137735i
$535$	0.877418	−	5.22059i	0.0379341	−	0.225706i
$536$		−	7.41318i		−	0.320201i
$537$	10.6149	+	0.485908i	0.458066	+	0.0209685i
$538$	−1.21195	−	1.21195i	−0.0522510	−	0.0522510i
$539$	−10.9875			−0.473265
$540$	−10.2971	+	5.38242i	−0.443115	+	0.231622i
$541$	−22.6591			−0.974190			−0.487095	−	0.873349i	$-0.661943\pi$
$541$	−22.6591			−0.974190			−0.487095	+	0.873349i	$0.661943\pi$
$542$	−17.9116	−	17.9116i	−0.769368	−	0.769368i
$543$	−1.30936	−	0.0599375i	−0.0561901	−	0.00257216i
$544$		−	0.548164i		−	0.0235023i
$545$	−4.86686	+	3.46632i	−0.208474	+	0.148481i
$546$	4.95233	+	5.42747i	0.211940	+	0.232274i
$547$	1.40675	−	1.40675i	0.0601483	−	0.0601483i	−0.676393	−	0.736541i	$-0.736458\pi$
$547$	1.40675	−	1.40675i	0.0601483	−	0.0601483i	0.736541	+	0.676393i	$0.236458\pi$
$548$	−10.7767	+	10.7767i	−0.460358	+	0.460358i
$549$	21.9871	+	2.01719i	0.938385	+	0.0860916i
$550$	9.73739	+	20.0364i	0.415204	+	0.854355i
$551$			48.3587i			2.06015i
$552$	0.506975	−	11.0751i	0.0215783	−	0.471388i
$553$	−37.1386	−	37.1386i	−1.57929	−	1.57929i
$554$	12.6640			0.538041
$555$	−13.3024	−	2.86670i	−0.564654	−	0.121684i
$556$	0.244460			0.0103674
$557$	7.62304	+	7.62304i	0.322998	+	0.322998i	0.849916	−	0.526918i	$-0.176652\pi$
$557$	7.62304	+	7.62304i	0.322998	+	0.322998i	−0.526918	+	0.849916i	$0.676652\pi$
$558$	−1.91864	−	2.30625i	−0.0812227	−	0.0976315i
$559$		−	3.64816i		−	0.154301i
$560$	−6.78456	−	1.14027i	−0.286700	−	0.0481853i
$561$	3.12486	−	2.85130i	0.131932	−	0.120382i
$562$	0.843863	−	0.843863i	0.0355962	−	0.0355962i
$563$	23.1894	−	23.1894i	0.977318	−	0.977318i	−0.0224305	−	0.999748i	$-0.507140\pi$
$563$	23.1894	−	23.1894i	0.977318	−	0.977318i	0.999748	+	0.0224305i	$0.00714044\pi$
$564$	16.8609	−	15.3849i	0.709974	−	0.647819i
$565$	33.6224	+	5.65087i	1.41450	+	0.237734i
$566$			5.70451i			0.239778i
$567$	22.8159	−	15.6904i	0.958176	−	0.658936i
$568$	−8.84990	−	8.84990i	−0.371333	−	0.371333i
$569$	−9.41142			−0.394547			−0.197274	−	0.980348i	$-0.563209\pi$
$569$	−9.41142			−0.394547			−0.197274	+	0.980348i	$0.563209\pi$
$570$	26.8077	+	5.77713i	1.12285	+	0.241977i
$571$	−44.1278			−1.84669			−0.923346	−	0.383969i	$-0.874557\pi$
$571$	−44.1278			−1.84669			−0.923346	+	0.383969i	$0.874557\pi$
$572$	4.34369	+	4.34369i	0.181619	+	0.181619i
$573$	−0.354542	+	7.74515i	−0.0148112	+	0.323558i
$574$			29.6766i			1.23868i
$575$	−13.9892	−	28.7853i	−0.583391	−	1.20043i
$576$	0.274082	−	2.98745i	0.0114201	−	0.124477i
$577$	6.40542	−	6.40542i	0.266661	−	0.266661i	−0.561092	−	0.827753i	$-0.689619\pi$
$577$	6.40542	−	6.40542i	0.266661	−	0.266661i	0.827753	+	0.561092i	$0.189619\pi$
$578$	11.8083	−	11.8083i	0.491162	−	0.491162i
$579$	−10.7107	−	11.7383i	−0.445122	−	0.487828i
$580$	12.4392	−	8.85957i	0.516511	−	0.367873i
$581$		−	11.2159i		−	0.465314i
$582$	25.0629	+	1.14728i	1.03889	+	0.0475564i
$583$	45.1313	+	45.1313i	1.86915	+	1.86915i
$584$	−11.2218			−0.464362
$585$	−2.35983	+	8.94276i	−0.0975671	+	0.369738i
$586$	27.4796			1.13517
$587$	13.2030	+	13.2030i	0.544944	+	0.544944i	0.924974	−	0.380030i	$-0.124086\pi$
$587$	13.2030	+	13.2030i	0.544944	+	0.544944i	−0.380030	+	0.924974i	$0.624086\pi$
$588$	4.26692	+	0.195323i	0.175965	+	0.00805497i
$589$			7.08062i			0.291752i
$590$	1.50591	−	8.96007i	0.0619972	−	0.368880i
$591$	−16.5779	−	18.1685i	−0.681924	−	0.747350i
$592$	2.48442	−	2.48442i	0.102109	−	0.102109i
$593$	−8.86519	+	8.86519i	−0.364050	+	0.364050i	−0.865302	−	0.501252i	$-0.832873\pi$
$593$	−8.86519	+	8.86519i	−0.364050	+	0.364050i	0.501252	+	0.865302i	$0.332873\pi$
$594$	18.4559	−	13.9769i	0.757256	−	0.573481i
$595$	2.18778	+	3.07175i	0.0896904	+	0.125929i
$596$			14.2761i			0.584773i
$597$	0.796337	−	17.3964i	0.0325919	−	0.711986i
$598$	−6.24036	−	6.24036i	−0.255187	−	0.255187i
$599$	−7.02020			−0.286838			−0.143419	−	0.989662i	$-0.545810\pi$
$599$	−7.02020			−0.286838			−0.143419	+	0.989662i	$0.545810\pi$
$600$	−3.42526	−	7.95409i	−0.139836	−	0.324724i
$601$	29.5451			1.20517			0.602585	−	0.798055i	$-0.294137\pi$
$601$	29.5451			1.20517			0.602585	+	0.798055i	$0.294137\pi$
$602$	−5.75654	−	5.75654i	−0.234619	−	0.234619i
$603$	−17.0967	+	14.2233i	−0.696231	+	0.579216i
$604$		−	16.9541i		−	0.689853i
$605$	−11.4815	−	16.1206i	−0.466790	−	0.655394i
$606$	1.41585	−	1.29190i	0.0575152	−	0.0524800i
$607$	−31.7105	+	31.7105i	−1.28709	+	1.28709i	−0.350541	+	0.936547i	$0.614002\pi$
$607$	−31.7105	+	31.7105i	−1.28709	+	1.28709i	−0.936547	+	0.350541i	$0.885998\pi$
$608$	−5.00675	+	5.00675i	−0.203051	+	0.203051i
$609$	−26.8855	+	24.5319i	−1.08946	+	0.994081i
$610$	−2.72765	+	16.2294i	−0.110440	+	0.657109i
$611$		−	18.1692i		−	0.735045i
$612$	−1.26421	+	1.05173i	−0.0511025	+	0.0425137i
$613$	16.7960	+	16.7960i	0.678384	+	0.678384i	0.959635	−	0.281250i	$-0.0907490\pi$
$613$	16.7960	+	16.7960i	0.678384	+	0.678384i	−0.281250	+	0.959635i	$0.590749\pi$
$614$	−3.68583			−0.148748
$615$	−31.3876	+	20.2579i	−1.26567	+	0.816876i
$616$	13.7081			0.552313
$617$	−13.2277	−	13.2277i	−0.532525	−	0.532525i	0.388798	−	0.921323i	$-0.372890\pi$
$617$	−13.2277	−	13.2277i	−0.532525	−	0.532525i	−0.921323	+	0.388798i	$0.872890\pi$
$618$	−0.725644	+	15.8520i	−0.0291897	+	0.637662i
$619$		−	26.8070i		−	1.07746i	−0.842477	−	0.538732i	$-0.818903\pi$
$619$		−	26.8070i		−	1.07746i	0.842477	−	0.538732i	$-0.181097\pi$
$620$	1.82133	−	1.29721i	0.0731465	−	0.0520970i
$621$	−26.5147	+	20.0800i	−1.06400	+	0.805781i
$622$	14.9780	−	14.9780i	0.600562	−	0.600562i
$623$	−5.41196	+	5.41196i	−0.216826	+	0.216826i
$624$	−1.60962	−	1.76406i	−0.0644365	−	0.0706188i
$625$	−19.6567	−	15.4471i	−0.786268	−	0.617885i
$626$			8.77616i			0.350766i
$627$	−54.5843	−	2.49866i	−2.17989	−	0.0997867i
$628$	−1.62663	−	1.62663i	−0.0649097	−	0.0649097i
$629$	−1.92598			−0.0767938
$630$	10.3874	+	17.8347i	0.413843	+	0.710551i
$631$	5.81594			0.231529			0.115764	−	0.993277i	$-0.463068\pi$
$631$	5.81594			0.231529			0.115764	+	0.993277i	$0.463068\pi$
$632$	12.0709	+	12.0709i	0.480155	+	0.480155i
$633$	6.95076	+	0.318178i	0.276268	+	0.0126464i
$634$			1.11423i			0.0442518i
$635$	−12.9872	−	2.18275i	−0.515383	−	0.0866197i
$636$	−16.7241	−	18.3287i	−0.663155	−	0.726781i
$637$	2.40423	−	2.40423i	0.0952591	−	0.0952591i
$638$	−21.5169	+	21.5169i	−0.851862	+	0.851862i
$639$	−3.43031	+	37.3899i	−0.135701	+	1.47912i
$640$	2.20514	+	0.370615i	0.0871658	+	0.0146499i
$641$			2.98189i			0.117778i	0.998265	+	0.0588889i	$0.0187558\pi$
$641$			2.98189i			0.117778i	−0.998265	+	0.0588889i	$0.981244\pi$
$642$	0.187511	−	4.09628i	0.00740049	−	0.161667i
$643$	−0.965272	−	0.965272i	−0.0380666	−	0.0380666i	0.687817	−	0.725884i	$-0.258569\pi$
$643$	−0.965272	−	0.965272i	−0.0380666	−	0.0380666i	−0.725884	+	0.687817i	$0.758569\pi$
$644$	−19.6937			−0.776040
$645$	2.15890	−	10.0180i	0.0850066	−	0.394457i
$646$	3.88134			0.152709
$647$	24.2718	+	24.2718i	0.954221	+	0.954221i	0.998997	−	0.0447756i	$-0.0142573\pi$
$647$	24.2718	+	24.2718i	0.954221	+	0.954221i	−0.0447756	+	0.998997i	$0.514257\pi$
$648$	−7.41569	+	5.09976i	−0.291316	+	0.200337i
$649$			18.1036i			0.710630i
$650$	−6.51495	−	2.25358i	−0.255537	−	0.0883925i
$651$	−3.93654	+	3.59192i	−0.154285	+	0.140778i
$652$	−9.77730	+	9.77730i	−0.382908	+	0.382908i
$653$	10.5261	−	10.5261i	0.411917	−	0.411917i	−0.470489	−	0.882406i	$-0.655922\pi$
$653$	10.5261	−	10.5261i	0.411917	−	0.411917i	0.882406	+	0.470489i	$0.155922\pi$
$654$	−3.41892	+	3.11961i	−0.133690	+	0.121987i
$655$	17.0026	−	12.1097i	0.664345	−	0.473165i
$656$		−	9.64559i		−	0.376597i
$657$	21.5307	+	25.8804i	0.839992	+	1.00969i
$658$	−28.6696	−	28.6696i	−1.11766	−	1.11766i
$659$	3.92435			0.152871			0.0764354	−	0.997075i	$-0.475646\pi$
$659$	3.92435			0.152871			0.0764354	+	0.997075i	$0.475646\pi$
$660$	9.35740	+	14.4984i	0.364236	+	0.564349i
$661$	−25.5836			−0.995087			−0.497544	−	0.867439i	$-0.665765\pi$
$661$	−25.5836			−0.995087			−0.497544	+	0.867439i	$0.665765\pi$
$662$	4.44651	+	4.44651i	0.172818	+	0.172818i
$663$	−0.0598602	+	1.30767i	−0.00232478	+	0.0507858i
$664$			3.64543i			0.141470i
$665$	8.07383	−	48.0389i	0.313090	−	1.86287i
$666$	−10.4964	−	0.962989i	−0.406729	−	0.0373151i
$667$	30.9122	−	30.9122i	1.19693	−	1.19693i
$668$	−2.45802	+	2.45802i	−0.0951036	+	0.0951036i
$669$	−4.48996	−	4.92075i	−0.173592	−	0.190247i
$670$	−9.61642	−	13.5019i	−0.371515	−	0.521623i
$671$		−	32.7912i		−	1.26589i
$672$	−5.32343	−	0.243686i	−0.205356	−	0.00940037i
$673$	−5.33140	−	5.33140i	−0.205510	−	0.205510i	0.596846	−	0.802356i	$-0.296420\pi$
$673$	−5.33140	−	5.33140i	−0.205510	−	0.205510i	−0.802356	+	0.596846i	$0.796420\pi$
$674$	25.5259			0.983220
$675$	−11.7723	+	23.1606i	−0.453116	+	0.891452i
$676$	11.0991			0.426887
$677$	−0.550707	−	0.550707i	−0.0211654	−	0.0211654i	0.696445	−	0.717610i	$-0.254764\pi$
$677$	−0.550707	−	0.550707i	−0.0211654	−	0.0211654i	−0.717610	+	0.696445i	$0.754764\pi$
$678$	26.3814	+	1.20764i	1.01317	+	0.0463791i
$679$		−	44.5667i		−	1.71031i
$680$	−0.711081	−	0.998390i	−0.0272687	−	0.0382865i
$681$	1.25464	+	1.37502i	0.0480779	+	0.0526907i
$682$	−3.15047	+	3.15047i	−0.120638	+	0.120638i
$683$	−11.6004	+	11.6004i	−0.443879	+	0.443879i	−0.893313	−	0.449435i	$-0.851626\pi$
$683$	−11.6004	+	11.6004i	−0.443879	+	0.443879i	0.449435	+	0.893313i	$0.351626\pi$
$684$	21.1530	+	1.94067i	0.808806	+	0.0742034i
$685$	−5.64838	+	33.6076i	−0.215813	+	1.28408i
$686$			13.9495i			0.532594i
$687$	−0.310073	+	6.77369i	−0.0118300	+	0.258432i
$688$	1.87101	+	1.87101i	0.0713317	+	0.0713317i
$689$	−19.7508			−0.752446
$690$	−13.4433	−	20.8291i	−0.511778	−	0.792951i
$691$	21.7394			0.827006			0.413503	−	0.910503i	$-0.364305\pi$
$691$	21.7394			0.827006			0.413503	+	0.910503i	$0.364305\pi$
$692$	11.5374	+	11.5374i	0.438585	+	0.438585i
$693$	−26.3009	−	31.6143i	−0.999088	−	1.20093i
$694$		−	14.1111i		−	0.535650i
$695$	0.445244	−	0.317115i	0.0168891	−	0.0120289i
$696$	8.73843	−	7.97343i	0.331229	−	0.302232i
$697$	−3.73873	+	3.73873i	−0.141615	+	0.141615i
$698$	6.67607	−	6.67607i	0.252693	−	0.252693i
$699$	−5.60105	+	5.11071i	−0.211851	+	0.193305i
$700$	−13.8361	+	6.72415i	−0.522956	+	0.254149i
$701$		−	1.39715i		−	0.0527695i	−0.999652	−	0.0263848i	$-0.991600\pi$
$701$		−	1.39715i		−	0.0527695i	0.999652	−	0.0263848i	$-0.00839950\pi$
$702$	−0.980070	+	7.09679i	−0.0369904	+	0.267851i
$703$	17.5913	+	17.5913i	0.663467	+	0.663467i
$704$	−4.45544			−0.167921
$705$	10.7521	−	49.8931i	0.404947	−	1.87908i
$706$	18.9357			0.712656
$707$	−2.40746	−	2.40746i	−0.0905419	−	0.0905419i
$708$	0.321825	−	7.03042i	0.0120949	−	0.264219i
$709$		−	34.8156i		−	1.30753i	−0.756699	−	0.653763i	$-0.773189\pi$
$709$		−	34.8156i		−	1.30753i	0.756699	−	0.653763i	$-0.226811\pi$
$710$	−27.5988	−	4.63849i	−1.03576	−	0.174079i
$711$	4.67881	−	50.9983i	0.175469	−	1.91259i
$712$	1.75902	−	1.75902i	0.0659219	−	0.0659219i
$713$	4.52613	−	4.52613i	0.169505	−	0.169505i
$714$	1.96896	+	2.15787i	0.0736865	+	0.0807563i
$715$	13.5460	+	2.27665i	0.506590	+	0.0851420i
$716$			6.13492i			0.229273i
$717$	34.4667	+	1.57775i	1.28718	+	0.0589222i
$718$	9.80688	+	9.80688i	0.365990	+	0.365990i
$719$	−10.9732			−0.409232			−0.204616	−	0.978842i	$-0.565595\pi$
$719$	−10.9732			−0.409232			−0.204616	+	0.978842i	$0.565595\pi$
$720$	−3.37615	−	5.79669i	−0.125822	−	0.216030i
$721$	28.1880			1.04978
$722$	−22.0159	−	22.0159i	−0.819346	−	0.819346i
$723$	−17.5660	−	0.804103i	−0.653287	−	0.0299049i
$724$		−	0.756752i		−	0.0281245i
$725$	11.1633	−	32.2725i	0.414595	−	1.19857i
$726$	−10.3331	−	11.3245i	−0.383498	−	0.420293i
$727$	−16.5136	+	16.5136i	−0.612456	+	0.612456i	−0.943585	−	0.331130i	$-0.892570\pi$
$727$	−16.5136	+	16.5136i	−0.612456	+	0.612456i	0.331130	+	0.943585i	$0.392570\pi$
$728$	−2.99953	+	2.99953i	−0.111170	+	0.111170i
$729$	25.9894	+	7.31786i	0.962570	+	0.271032i
$730$	−20.4387	+	14.5570i	−0.756470	+	0.538779i
$731$		−	1.45045i		−	0.0536468i
$732$	−0.582922	+	12.7342i	−0.0215454	+	0.470670i
$733$	15.9328	+	15.9328i	0.588493	+	0.588493i	0.937223	−	0.348730i	$-0.113387\pi$
$733$	15.9328	+	15.9328i	0.588493	+	0.588493i	−0.348730	+	0.937223i	$0.613387\pi$
$734$	−16.2624			−0.600258
$735$	8.02486	−	5.17932i	0.296001	−	0.191042i
$736$	6.40091			0.235941
$737$	23.3550	+	23.3550i	0.860293	+	0.860293i
$738$	−22.2452	+	18.5065i	−0.818857	+	0.681232i
$739$			3.52497i			0.129668i	0.997896	+	0.0648341i	$0.0206518\pi$
$739$			3.52497i			0.129668i	−0.997896	+	0.0648341i	$0.979348\pi$
$740$	1.30216	−	7.74777i	0.0478683	−	0.284814i
$741$	12.4906	−	11.3971i	0.458854	−	0.418684i
$742$	−31.1654	+	31.1654i	−1.14412	+	1.14412i
$743$	−1.31841	+	1.31841i	−0.0483679	+	0.0483679i	−0.730877	−	0.682509i	$-0.760889\pi$
$743$	−1.31841	+	1.31841i	−0.0483679	+	0.0483679i	0.682509	+	0.730877i	$0.260889\pi$
$744$	1.27947	−	1.16746i	0.0469076	−	0.0428011i
$745$	18.5191	+	26.0016i	0.678486	+	0.952625i
$746$			22.8559i			0.836814i
$747$	8.40728	−	6.99428i	0.307606	−	0.255907i
$748$	1.72698	+	1.72698i	0.0631445	+	0.0631445i
$749$	−7.28398			−0.266151
$750$	−16.5566	−	10.0438i	−0.604563	−	0.366747i
$751$	−40.2008			−1.46695			−0.733474	−	0.679718i	$-0.762102\pi$
$751$	−40.2008			−1.46695			−0.733474	+	0.679718i	$0.762102\pi$
$752$	9.31831	+	9.31831i	0.339804	+	0.339804i
$753$	1.49773	−	32.7187i	0.0545804	−	1.19234i
$754$		−	9.41644i		−	0.342926i
$755$	−21.9930	−	30.8791i	−0.800406	−	1.12381i
$756$	9.65176	+	12.7447i	0.351031	+	0.463521i
$757$	−4.14240	+	4.14240i	−0.150558	+	0.150558i	−0.778367	−	0.627809i	$-0.783952\pi$
$757$	−4.14240	+	4.14240i	−0.150558	+	0.150558i	0.627809	+	0.778367i	$0.283952\pi$
$758$	2.30757	−	2.30757i	0.0838148	−	0.0838148i
$759$	33.2946	+	36.4890i	1.20852	+	1.32447i
$760$	−2.62418	+	15.6138i	−0.0951892	+	0.566371i
$761$			11.1300i			0.403461i	0.979441	+	0.201731i	$0.0646565\pi$
$761$			11.1300i			0.403461i	−0.979441	+	0.201731i	$0.935343\pi$
$762$	−10.1903	−	0.466471i	−0.369155	−	0.0168985i
$763$	5.81339	+	5.81339i	0.210459	+	0.210459i
$764$	−4.47635			−0.161949
$765$	−0.938229	+	3.55549i	−0.0339218	+	0.128549i
$766$	−29.5271			−1.06686
$767$	−3.96135	−	3.96135i	−0.143036	−	0.143036i
$768$	1.73024	+	0.0792035i	0.0624346	+	0.00285801i
$769$		−	7.80274i		−	0.281374i	−0.990054	−	0.140687i	$-0.955069\pi$
$769$		−	7.80274i		−	0.281374i	0.990054	−	0.140687i	$-0.0449311\pi$
$770$	24.9670	−	17.7822i	0.899747	−	0.640825i
$771$	17.4900	+	19.1680i	0.629886	+	0.690320i
$772$	6.48726	−	6.48726i	0.233482	−	0.233482i
$773$	−0.245237	+	0.245237i	−0.00882054	+	0.00882054i	−0.711503	−	0.702683i	$-0.751985\pi$
$773$	−0.245237	+	0.245237i	−0.00882054	+	0.00882054i	0.702683	+	0.711503i	$0.251985\pi$
$774$	0.725224	−	7.90483i	0.0260676	−	0.284133i
$775$	1.63452	−	4.72529i	0.0587136	−	0.169737i
$776$			14.4852i			0.519990i
$777$	−0.856191	+	18.7039i	−0.0307157	+	0.670998i
$778$	−18.0801	−	18.0801i	−0.648201	−	0.648201i
$779$	68.2968			2.44699
$780$	−5.22000	−	1.12493i	−0.186906	−	0.0402788i
$781$	55.7627			1.99535
$782$	−2.48106	−	2.48106i	−0.0887225	−	0.0887225i
$783$	−35.1547	−	4.85488i	−1.25633	−	0.173499i
$784$			2.46609i			0.0880745i
$785$	−5.07272	−	0.852565i	−0.181053	−	0.0304293i
$786$	11.9441	−	10.8985i	0.426033	−	0.388736i
$787$	6.35269	−	6.35269i	0.226449	−	0.226449i	−0.584758	−	0.811207i	$-0.698811\pi$
$787$	6.35269	−	6.35269i	0.226449	−	0.226449i	0.811207	+	0.584758i	$0.198811\pi$
$788$	10.0409	−	10.0409i	0.357693	−	0.357693i
$789$	7.71488	−	7.03948i	0.274657	−	0.250612i
$790$	37.6436	+	6.32671i	1.33930	+	0.225094i
$791$		−	46.9113i		−	1.66797i
$792$	8.54840	+	10.2754i	0.303754	+	0.365120i
$793$	7.17520	+	7.17520i	0.254799	+	0.254799i
$794$	29.9735			1.06372
$795$	−54.2364	−	11.6881i	−1.92357	−	0.414534i
$796$	10.0543			0.356366
$797$	−13.5471	−	13.5471i	−0.479863	−	0.479863i	0.425225	−	0.905088i	$-0.360195\pi$
$797$	−13.5471	−	13.5471i	−0.479863	−	0.479863i	−0.905088	+	0.425225i	$0.860195\pi$
$798$	1.72544	−	37.6932i	0.0610801	−	1.33432i
$799$		−	7.22375i		−	0.255558i
$800$	4.49706	−	2.18551i	0.158995	−	0.0772693i
$801$	−7.43166	−	0.681813i	−0.262585	−	0.0240907i
$802$	−16.4378	+	16.4378i	−0.580437	+	0.580437i
$803$	35.3540	−	35.3540i	1.24762	−	1.24762i
$804$	−8.65458	−	9.48494i	−0.305223	−	0.334508i
$805$	−35.8688	+	25.5468i	−1.26421	+	0.900405i
$806$		−	1.37874i		−	0.0485641i
$807$	−2.96556	−	0.135752i	−0.104393	−	0.00477869i
$808$	0.782481	+	0.782481i	0.0275276	+	0.0275276i
$809$	−24.2925			−0.854078			−0.427039	−	0.904233i	$-0.640443\pi$
$809$	−24.2925			−0.854078			−0.427039	+	0.904233i	$0.640443\pi$
$810$	−6.89103	+	18.9080i	−0.242126	+	0.664361i
$811$	−28.6019			−1.00435			−0.502174	−	0.864766i	$-0.667466\pi$
$811$	−28.6019			−1.00435			−0.502174	+	0.864766i	$0.667466\pi$
$812$	−14.8585	−	14.8585i	−0.521430	−	0.521430i
$813$	−43.8283	−	2.00629i	−1.53713	−	0.0703636i
$814$			15.6542i			0.548680i
$815$	−5.12456	+	30.4909i	−0.179506	+	1.06805i
$816$	−0.639959	−	0.701359i	−0.0224030	−	0.0245525i
$817$	−13.2479	+	13.2479i	−0.463486	+	0.463486i
$818$	−22.2930	+	22.2930i	−0.779456	+	0.779456i
$819$	12.6727	+	1.16265i	0.442820	+	0.0406262i
$820$	−12.5123	−	17.5678i	−0.436949	−	0.613496i
$821$		−	42.2466i		−	1.47442i	−0.675665	−	0.737209i	$-0.736143\pi$
$821$		−	42.2466i		−	1.47442i	0.675665	−	0.737209i	$-0.263857\pi$
$822$	−1.20711	+	26.3698i	−0.0421026	+	0.919752i
$823$	−35.3675	−	35.3675i	−1.23283	−	1.23283i	−0.962871	−	0.269960i	$-0.912989\pi$
$823$	−35.3675	−	35.3675i	−1.23283	−	1.23283i	−0.269960	−	0.962871i	$-0.587011\pi$
$824$	−9.16176			−0.319165
$825$	35.8504	+	14.2679i	1.24815	+	0.496746i
$826$	−12.5014			−0.434981
$827$	2.53444	+	2.53444i	0.0881310	+	0.0881310i	0.749798	−	0.661667i	$-0.230151\pi$
$827$	2.53444	+	2.53444i	0.0881310	+	0.0881310i	−0.661667	+	0.749798i	$0.730151\pi$
$828$	−12.2811	−	14.7621i	−0.426797	−	0.513019i
$829$		−	6.31396i		−	0.219293i	−0.993971	−	0.109646i	$-0.965028\pi$
$829$		−	6.31396i		−	0.219293i	0.993971	−	0.109646i	$-0.0349719\pi$
$830$	4.72887	+	6.63954i	0.164141	+	0.230462i
$831$	16.2032	−	14.7847i	0.562082	−	0.512875i
$832$	0.974917	−	0.974917i	0.0337992	−	0.0337992i
$833$	0.955881	−	0.955881i	0.0331193	−	0.0331193i
$834$	0.312779	−	0.285397i	0.0108307	−	0.00988249i
$835$	−1.28832	+	7.66542i	−0.0445841	+	0.265273i
$836$		−	31.5473i		−	1.09109i
$837$	−5.14730	−	0.710844i	−0.177917	−	0.0245704i
$838$	0.252257	+	0.252257i	0.00871406	+	0.00871406i
$839$	−3.73215			−0.128848			−0.0644240	−	0.997923i	$-0.520521\pi$
$839$	−3.73215			−0.128848			−0.0644240	+	0.997923i	$0.520521\pi$
$840$	−10.0119	+	6.46174i	−0.345442	+	0.222951i
$841$	17.6453			0.608457
$842$	16.8519	+	16.8519i	0.580753	+	0.580753i
$843$	0.0945217	−	2.06487i	0.00325550	−	0.0711180i
$844$			4.01722i			0.138279i
$845$	20.2151	−	14.3978i	0.695421	−	0.495299i
$846$	3.61187	−	39.3689i	0.124179	−	1.35353i
$847$	−19.2558	+	19.2558i	−0.661636	+	0.661636i
$848$	10.1295	−	10.1295i	0.347848	−	0.347848i
$849$	6.65978	+	7.29874i	0.228563	+	0.250492i
$850$	−2.59023	−	0.895984i	−0.0888443	−	0.0307320i
$851$		−	22.4896i		−	0.770935i
$852$	−21.6551	−	0.991283i	−0.741890	−	0.0339608i
$853$	−27.2015	−	27.2015i	−0.931363	−	0.931363i	0.0664281	−	0.997791i	$-0.478840\pi$
$853$	−27.2015	−	27.2015i	−0.931363	−	0.931363i	−0.997791	+	0.0664281i	$0.978840\pi$
$854$	22.6439			0.774859
$855$	41.0442	−	23.9052i	1.40368	−	0.817541i
$856$	2.36746			0.0809182
$857$	−31.3069	−	31.3069i	−1.06942	−	1.06942i	−0.997403	−	0.0720192i	$-0.977056\pi$
$857$	−31.3069	−	31.3069i	−1.06942	−	1.06942i	−0.0720192	−	0.997403i	$-0.522944\pi$
$858$	10.6287	+	0.486539i	0.362857	+	0.0166102i
$859$			47.7582i			1.62949i	0.579821	+	0.814744i	$0.303123\pi$
$859$			47.7582i			1.62949i	−0.579821	+	0.814744i	$0.696877\pi$
$860$	5.83482	+	0.980652i	0.198966	+	0.0334399i
$861$	34.6462	+	37.9703i	1.18074	+	1.29402i
$862$	−17.1999	+	17.1999i	−0.585831	+	0.585831i
$863$	−7.12312	+	7.12312i	−0.242474	+	0.242474i	−0.817873	−	0.575399i	$-0.804847\pi$
$863$	−7.12312	+	7.12312i	−0.242474	+	0.242474i	0.575399	+	0.817873i	$0.304847\pi$
$864$	−3.13705	−	4.14233i	−0.106725	−	0.140925i
$865$	35.9798	+	6.04708i	1.22335	+	0.205607i
$866$		−	7.05048i		−	0.239585i
$867$	1.32266	−	28.8942i	0.0449199	−	0.981297i
$868$	−2.17556	−	2.17556i	−0.0738432	−	0.0738432i
$869$	−76.0581			−2.58010
$870$	5.57243	−	25.8578i	0.188923	−	0.876662i
$871$	−10.2209			−0.346321
$872$	−1.88949	−	1.88949i	−0.0639862	−	0.0639862i
$873$	33.4066	−	27.7920i	1.13064	−	0.940617i
$874$			45.3224i			1.53305i
$875$	−16.4776	+	30.1952i	−0.557044	+	1.02078i
$876$	−14.3580	+	13.1010i	−0.485111	+	0.442642i
$877$	9.24394	−	9.24394i	0.312146	−	0.312146i	−0.533595	−	0.845740i	$-0.679159\pi$
$877$	9.24394	−	9.24394i	0.312146	−	0.312146i	0.845740	+	0.533595i	$0.179159\pi$
$878$	−25.6915	+	25.6915i	−0.867048	+	0.867048i
$879$	35.1593	−	32.0813i	1.18589	−	1.08207i
$880$	−8.11485	+	5.77962i	−0.273551	+	0.194831i
$881$		−	2.89093i		−	0.0973979i	−0.998814	−	0.0486989i	$-0.984493\pi$
$881$		−	2.89093i		−	0.0973979i	0.998814	−	0.0486989i	$-0.0155075\pi$
$882$	5.68742	−	4.73154i	0.191505	−	0.159319i
$883$	−6.33199	−	6.33199i	−0.213088	−	0.213088i	0.592490	−	0.805578i	$-0.298145\pi$
$883$	−6.33199	−	6.33199i	−0.213088	−	0.213088i	−0.805578	+	0.592490i	$0.798145\pi$
$884$	−0.755776			−0.0254195
$885$	−8.53375	−	13.2222i	−0.286859	−	0.444460i
$886$	−1.05022			−0.0352829
$887$	−12.8228	−	12.8228i	−0.430547	−	0.430547i	0.458267	−	0.888814i	$-0.348470\pi$
$887$	−12.8228	−	12.8228i	−0.430547	−	0.430547i	−0.888814	+	0.458267i	$0.848470\pi$
$888$	0.278282	−	6.07920i	0.00933853	−	0.204005i
$889$			18.1203i			0.607736i
$890$	0.921951	−	5.48556i	0.0309039	−	0.183876i
$891$	7.29630	−	39.4296i	0.244435	−	1.32094i
$892$	2.71948	−	2.71948i	0.0910551	−	0.0910551i
$893$	−65.9794	+	65.9794i	−2.20792	+	2.20792i
$894$	16.6668	+	18.2659i	0.557421	+	0.610902i
$895$	7.95825	+	11.1737i	0.266015	+	0.373497i
$896$		−	3.07670i		−	0.102785i
$897$	−15.2697	−	0.698987i	−0.509841	−	0.0233385i
$898$	−22.7680	−	22.7680i	−0.759778	−	0.759778i
$899$	6.82973			0.227784
$900$	−13.6686	−	6.17816i	−0.455620	−	0.205939i
$901$	−7.85259			−0.261608
$902$	30.3882	+	30.3882i	1.01182	+	1.01182i
$903$	−14.0858	−	0.644794i	−0.468747	−	0.0214574i
$904$			15.2473i			0.507117i
$905$	−0.981663	−	1.37830i	−0.0326316	−	0.0458162i
$906$	−19.7932	−	21.6923i	−0.657586	−	0.720677i
$907$	21.3977	−	21.3977i	0.710499	−	0.710499i	−0.256141	−	0.966640i	$-0.582451\pi$
$907$	21.3977	−	21.3977i	0.710499	−	0.710499i	0.966640	+	0.256141i	$0.0824510\pi$
$908$	−0.759912	+	0.759912i	−0.0252186	+	0.0252186i
$909$	0.303298	−	3.30590i	0.0100598	−	0.109650i
$910$	−1.57214	+	9.35415i	−0.0521159	+	0.310087i
$911$		−	6.03619i		−	0.199988i	−0.994988	−	0.0999940i	$-0.968118\pi$
$911$		−	6.03619i		−	0.199988i	0.994988	−	0.0999940i	$-0.0318824\pi$
$912$	−0.560810	+	12.2512i	−0.0185703	+	0.405677i
$913$	−11.4848	−	11.4848i	−0.380092	−	0.380092i
$914$	−13.8481			−0.458056
$915$	15.4572	+	23.9494i	0.510999	+	0.791744i
$916$	−3.91489			−0.129351
$917$	−20.3093	−	20.3093i	−0.670672	−	0.670672i
$918$	−0.389659	+	2.82157i	−0.0128607	+	0.0931255i
$919$		−	10.5455i		−	0.347863i	−0.984758	−	0.173932i	$-0.944353\pi$
$919$		−	10.5455i		−	0.347863i	0.984758	−	0.173932i	$-0.0556471\pi$
$920$	11.6582	−	8.30330i	0.384359	−	0.273752i
$921$	−4.71591	+	4.30306i	−0.155395	+	0.141791i
$922$	−19.7611	+	19.7611i	−0.650799	+	0.650799i
$923$	−12.2017	+	12.2017i	−0.401624	+	0.401624i
$924$	17.5390	−	16.0036i	0.576992	−	0.526479i
$925$	−7.67879	−	15.8005i	−0.252477	−	0.519516i
$926$			41.7108i			1.37070i
$927$	17.5782	+	21.1293i	0.577342	+	0.693979i
$928$	4.82935	+	4.82935i	0.158531	+	0.158531i
$929$	12.8856			0.422762			0.211381	−	0.977404i	$-0.432204\pi$
$929$	12.8856			0.422762			0.211381	+	0.977404i	$0.432204\pi$
$930$	0.815908	−	3.78607i	0.0267547	−	0.124150i
$931$	−17.4614			−0.572275
$932$	−3.09546	−	3.09546i	−0.101395	−	0.101395i
$933$	1.67769	−	36.6500i	0.0549252	−	1.19987i
$934$			5.42628i			0.177553i
$935$	5.38564	+	0.905158i	0.176129	+	0.0296018i
$936$	−4.11893	−	0.377888i	−0.134631	−	0.0123517i
$937$	0.422297	−	0.422297i	0.0137959	−	0.0137959i	−0.700175	−	0.713971i	$-0.746895\pi$
$937$	0.422297	−	0.422297i	0.0137959	−	0.0137959i	0.713971	+	0.700175i	$0.246895\pi$
$938$	−16.1278	+	16.1278i	−0.526591	+	0.526591i
$939$	10.2458	+	11.2288i	0.334359	+	0.366439i
$940$	29.0595	+	4.88399i	0.947817	+	0.159298i
$941$			43.1125i			1.40543i	0.711472	+	0.702714i	$0.248029\pi$
$941$			43.1125i			1.40543i	−0.711472	+	0.702714i	$0.751971\pi$
$942$	−3.98025	−	0.182200i	−0.129684	−	0.00593640i
$943$	−43.6572	−	43.6572i	−1.42167	−	1.42167i
$944$	4.06326			0.132248
$945$	34.1116	+	10.6921i	1.10965	+	0.347814i
$946$	−11.7891			−0.383298
$947$	−15.6903	−	15.6903i	−0.509867	−	0.509867i	0.404618	−	0.914486i	$-0.367404\pi$
$947$	−15.6903	−	15.6903i	−0.509867	−	0.509867i	−0.914486	+	0.404618i	$0.867404\pi$
$948$	29.5366	+	1.35207i	0.959305	+	0.0439132i
$949$			15.4720i			0.502242i
$950$	15.4747	+	31.8420i	0.502067	+	1.03309i
$951$	1.30082	+	1.42563i	0.0421820	+	0.0462291i
$952$	−1.19256	+	1.19256i	−0.0386511	+	0.0386511i
$953$	3.86517	−	3.86517i	0.125205	−	0.125205i	−0.641728	−	0.766933i	$-0.721782\pi$
$953$	3.86517	−	3.86517i	0.125205	−	0.125205i	0.766933	+	0.641728i	$0.221782\pi$
$954$	−42.7960	−	3.92629i	−1.38557	−	0.127118i
$955$	−8.15292	+	5.80674i	−0.263822	+	0.187902i
$956$			19.9202i			0.644265i
$957$	−2.41012	+	52.6503i	−0.0779082	+	1.70194i
$958$	16.5945	+	16.5945i	0.536145	+	0.536145i
$959$	46.8906			1.51418
$960$	3.25409	−	2.10022i	0.105025	−	0.0677843i
$961$	1.00000			0.0322581
$962$	−3.42538	−	3.42538i	−0.110439	−	0.110439i
$963$	−4.54232	−	5.45997i	−0.146374	−	0.175945i
$964$		−	10.1524i		−	0.326986i
$965$	3.40016	−	20.2308i	0.109455	−	0.651252i
$966$	−25.1975	+	22.9916i	−0.810715	+	0.739741i
$967$	12.9177	−	12.9177i	0.415406	−	0.415406i	−0.468211	−	0.883617i	$-0.655101\pi$
$967$	12.9177	−	12.9177i	0.415406	−	0.415406i	0.883617	+	0.468211i	$0.155101\pi$
$968$	6.25857	−	6.25857i	0.201158	−	0.201158i
$969$	4.96606	−	4.53130i	0.159533	−	0.145566i
$970$	18.7903	+	26.3825i	0.603321	+	0.847090i
$971$		−	4.39480i		−	0.141036i	−0.997511	−	0.0705179i	$-0.977535\pi$
$971$		−	4.39480i		−	0.141036i	0.997511	−	0.0705179i	$-0.0224652\pi$
$972$	−3.53440	+	15.1825i	−0.113366	+	0.486979i
$973$	−0.531837	−	0.531837i	−0.0170499	−	0.0170499i
$974$	10.2057			0.327013
$975$	−10.9666	+	4.72255i	−0.351213	+	0.151243i
$976$	−7.35980			−0.235582
$977$	−23.7046	−	23.7046i	−0.758377	−	0.758377i	0.217650	−	0.976027i	$-0.430161\pi$
$977$	−23.7046	−	23.7046i	−0.758377	−	0.758377i	−0.976027	+	0.217650i	$0.930161\pi$
$978$	−1.09516	+	23.9243i	−0.0350194	+	0.765016i
$979$			11.0835i			0.354229i
$980$	3.19902	+	4.49157i	0.102189	+	0.143478i
$981$	−0.732386	+	7.98290i	−0.0233833	+	0.254874i
$982$	20.6370	−	20.6370i	0.658554	−	0.658554i
$983$	−12.9330	+	12.9330i	−0.412500	+	0.412500i	−0.882609	−	0.470108i	$-0.844215\pi$
$983$	−12.9330	+	12.9330i	−0.412500	+	0.412500i	0.470108	+	0.882609i	$0.344215\pi$
$984$	−11.2608	−	12.3412i	−0.358982	−	0.393424i
$985$	5.26273	−	31.3130i	0.167685	−	0.997714i
$986$		−	3.74382i		−	0.119227i
$987$	−70.1525	−	3.21131i	−2.23298	−	0.102217i
$988$	6.90302	+	6.90302i	0.219614	+	0.219614i
$989$	16.9369			0.538561
$990$	28.8988	+	7.62587i	0.918463	+	0.242366i
$991$	−45.2479			−1.43735			−0.718674	−	0.695347i	$-0.755251\pi$
$991$	−45.2479			−1.43735			−0.718674	+	0.695347i	$0.755251\pi$
$992$	0.707107	+	0.707107i	0.0224507	+	0.0224507i
$993$	10.8803	+	0.498056i	0.345275	+	0.0158053i
$994$			38.5069i			1.22136i
$995$	18.3123	−	13.0425i	0.580538	−	0.413475i
$996$	4.25589	+	4.66421i	0.134853	+	0.147791i
$997$	15.5663	−	15.5663i	0.492988	−	0.492988i	−0.416258	−	0.909246i	$-0.636659\pi$
$997$	15.5663	−	15.5663i	0.492988	−	0.492988i	0.909246	+	0.416258i	$0.136659\pi$
$998$	−8.03093	+	8.03093i	−0.254215	+	0.254215i
$999$	−14.5541	+	11.0220i	−0.460472	+	0.348722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.683.20	yes	40
3.2	odd	2	inner	930.2.j.h.683.6	yes	40
5.2	odd	4	inner	930.2.j.h.497.6	✓	40
15.2	even	4	inner	930.2.j.h.497.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.6	✓	40	5.2	odd	4	inner
930.2.j.h.497.20	yes	40	15.2	even	4	inner
930.2.j.h.683.6	yes	40	3.2	odd	2	inner
930.2.j.h.683.20	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.73024 + 0.0792035i) q^{3} +1.00000i q^{4} +(1.29721 + 1.82133i) q^{5} +(1.16746 + 1.27947i) q^{6} +(2.17556 - 2.17556i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98745 + 0.274082i) q^{9} +(-0.370615 + 2.20514i) q^{10} -4.45544i q^{11} +(-0.0792035 + 1.73024i) q^{12} +(0.974917 + 0.974917i) q^{13} +3.07670 q^{14} +(2.10022 + 3.25409i) q^{15} -1.00000 q^{16} +(0.387611 + 0.387611i) q^{17} +(1.91864 + 2.30625i) q^{18} -7.08062i q^{19} +(-1.82133 + 1.29721i) q^{20} +(3.93654 - 3.59192i) q^{21} +(3.15047 - 3.15047i) q^{22} +(-4.52613 + 4.52613i) q^{23} +(-1.27947 + 1.16746i) q^{24} +(-1.63452 + 4.72529i) q^{25} +1.37874i q^{26} +(5.14730 + 0.710844i) q^{27} +(2.17556 + 2.17556i) q^{28} -6.82973 q^{29} +(-0.815908 + 3.78607i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.352887 - 7.70898i) q^{33} +0.548164i q^{34} +(6.78456 + 1.14027i) q^{35} +(-0.274082 + 2.98745i) q^{36} +(-2.48442 + 2.48442i) q^{37} +(5.00675 - 5.00675i) q^{38} +(1.60962 + 1.76406i) q^{39} +(-2.20514 - 0.370615i) q^{40} +9.64559i q^{41} +(5.32343 + 0.243686i) q^{42} +(-1.87101 - 1.87101i) q^{43} +4.45544 q^{44} +(3.37615 + 5.79669i) q^{45} -6.40091 q^{46} +(-9.31831 - 9.31831i) q^{47} +(-1.73024 - 0.0792035i) q^{48} -2.46609i q^{49} +(-4.49706 + 2.18551i) q^{50} +(0.639959 + 0.701359i) q^{51} +(-0.974917 + 0.974917i) q^{52} +(-10.1295 + 10.1295i) q^{53} +(3.13705 + 4.14233i) q^{54} +(8.11485 - 5.77962i) q^{55} +3.07670i q^{56} +(0.560810 - 12.2512i) q^{57} +(-4.82935 - 4.82935i) q^{58} -4.06326 q^{59} +(-3.25409 + 2.10022i) q^{60} +7.35980 q^{61} +(-0.707107 - 0.707107i) q^{62} +(7.09565 - 5.90309i) q^{63} -1.00000i q^{64} +(-0.510982 + 3.04032i) q^{65} +(5.70060 - 5.20154i) q^{66} +(-5.24191 + 5.24191i) q^{67} +(-0.387611 + 0.387611i) q^{68} +(-8.18977 + 7.47280i) q^{69} +(3.99111 + 5.60370i) q^{70} +12.5156i q^{71} +(-2.30625 + 1.91864i) q^{72} +(7.93503 + 7.93503i) q^{73} -3.51351 q^{74} +(-3.20236 + 8.04642i) q^{75} +7.08062 q^{76} +(-9.69306 - 9.69306i) q^{77} +(-0.109201 + 2.38555i) q^{78} -17.0708i q^{79} +(-1.29721 - 1.82133i) q^{80} +(8.84976 + 1.63761i) q^{81} +(-6.82046 + 6.82046i) q^{82} +(2.57771 - 2.57771i) q^{83} +(3.59192 + 3.93654i) q^{84} +(-0.203158 + 1.20878i) q^{85} -2.64601i q^{86} +(-11.8171 - 0.540939i) q^{87} +(3.15047 + 3.15047i) q^{88} -2.48762 q^{89} +(-1.71159 + 6.48618i) q^{90} +4.24197 q^{91} +(-4.52613 - 4.52613i) q^{92} +(-1.73024 - 0.0792035i) q^{93} -13.1781i q^{94} +(12.8962 - 9.18502i) q^{95} +(-1.16746 - 1.27947i) q^{96} +(10.2426 - 10.2426i) q^{97} +(1.74379 - 1.74379i) q^{98} +(1.22116 - 13.3104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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