LMFDB - Embedded newform 930.2.j.h.497.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			497.20
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.73024 - 0.0792035i) q^{3} -1.00000i q^{4} +(1.29721 - 1.82133i) q^{5} +(1.16746 - 1.27947i) q^{6} +(2.17556 + 2.17556i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98745 - 0.274082i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.986435	−	0.164152i	$-0.0524888\pi$
$7$	2.17556	+	2.17556i	0.822283	+	0.822283i	−0.164152	+	0.986435i	$0.552489\pi$
$8$	−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	$0.234428\pi$
$11$			4.45544i			1.34337i	−0.740839	+	0.671683i	$0.765572\pi$
$12$	−0.0792035	−	1.73024i	−0.0228641	−	0.499477i
$13$	0.974917	−	0.974917i	0.270393	−	0.270393i	−0.558865	−	0.829259i	$-0.688763\pi$
$13$	0.974917	−	0.974917i	0.270393	−	0.270393i	0.829259	+	0.558865i	$0.188763\pi$
$14$	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	−0.658538	−	0.752547i	$-0.728825\pi$
$17$	0.387611	−	0.387611i	0.0940094	−	0.0940094i	0.752547	+	0.658538i	$0.228825\pi$
$18$	1.91864	−	2.30625i	0.452229	−	0.543589i
$19$			7.08062i			1.62441i	0.583375	+	0.812203i	$0.301732\pi$
$19$			7.08062i			1.62441i	−0.583375	+	0.812203i	$0.698268\pi$
$20$	−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	0.0547380	−	0.998501i	$-0.482568\pi$
$23$	−4.52613	−	4.52613i	−0.943763	−	0.943763i	−0.998501	+	0.0547380i	$0.982568\pi$
$24$	−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	0.472756	−	0.881193i	$-0.343259\pi$
$37$	−2.48442	−	2.48442i	−0.408437	−	0.408437i	−0.881193	+	0.472756i	$0.843259\pi$
$38$	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	$-0.728512\pi$
$41$		−	9.64559i		−	1.50639i	0.657798	−	0.753194i	$-0.271488\pi$
$42$	5.32343	−	0.243686i	0.821423	−	0.0376015i
$43$	−1.87101	+	1.87101i	−0.285327	+	0.285327i	−0.835229	−	0.549902i	$-0.814665\pi$
$43$	−1.87101	+	1.87101i	−0.285327	+	0.285327i	0.549902	+	0.835229i	$0.314665\pi$
$44$	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	−0.484328	+	0.874886i	$0.660936\pi$
$47$	−9.31831	+	9.31831i	−1.35921	+	1.35921i	−0.874886	+	0.484328i	$0.839064\pi$
$48$	−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	−0.822216	−	0.569176i	$-0.807262\pi$
$53$	−10.1295	−	10.1295i	−1.39139	−	1.39139i	−0.569176	−	0.822216i	$-0.692738\pi$
$54$	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	0.310253	−	0.950654i	$-0.399586\pi$
$67$	−5.24191	−	5.24191i	−0.640401	−	0.640401i	−0.950654	+	0.310253i	$0.899586\pi$
$68$	−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	$-0.733561\pi$
$71$		−	12.5156i		−	1.48533i	0.669661	−	0.742667i	$-0.266439\pi$
$72$	−2.30625	−	1.91864i	−0.271795	−	0.226114i
$73$	7.93503	−	7.93503i	0.928725	−	0.928725i	−0.0688990	−	0.997624i	$-0.521949\pi$
$73$	7.93503	−	7.93503i	0.928725	−	0.928725i	0.997624	+	0.0688990i	$0.0219486\pi$
$74$	−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	$0.410018\pi$
$79$			17.0708i			1.92062i	−0.278936	+	0.960310i	$0.589982\pi$
$80$	−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	0.834280	−	0.551340i	$-0.185883\pi$
$83$	2.57771	+	2.57771i	0.282940	+	0.282940i	−0.551340	+	0.834280i	$0.685883\pi$
$84$	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	0.999167	+	0.0408129i	$0.0129948\pi$
$97$	10.2426	+	10.2426i	1.03998	+	1.03998i	0.0408129	+	0.999167i	$0.487005\pi$
$98$	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	$0.0175335\pi$
$101$			1.10660i			0.110110i	−0.998483	+	0.0550552i	$0.982467\pi$
$102$	−0.0434165	−	0.948455i	−0.00429888	−	0.0939110i
$103$	6.47834	−	6.47834i	0.638330	−	0.638330i	−0.311813	−	0.950143i	$-0.600936\pi$
$103$	6.47834	−	6.47834i	0.638330	−	0.638330i	0.950143	+	0.311813i	$0.100936\pi$
$104$	−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	−0.783380	−	0.621543i	$-0.786506\pi$
$107$	−1.67405	+	1.67405i	−0.161836	+	0.161836i	0.621543	+	0.783380i	$0.286506\pi$
$108$	−0.710844	−	5.14730i	−0.0684010	−	0.495299i
$109$		−	2.67214i		−	0.255945i	−0.991778	−	0.127972i	$-0.959153\pi$
$109$		−	2.67214i		−	0.255945i	0.991778	−	0.127972i	$-0.0408469\pi$
$110$	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	0.999897	+	0.0143368i	$0.00456370\pi$
$113$	10.7815	+	10.7815i	1.01423	+	1.01423i	0.0143368	+	0.999897i	$0.495436\pi$
$114$	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	0.497768	−	0.867310i	$-0.334153\pi$
$127$	−4.16452	−	4.16452i	−0.369542	−	0.369542i	−0.867310	+	0.497768i	$0.834153\pi$
$128$	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	$0.133708\pi$
$131$			9.33522i			0.815622i	−0.913066	+	0.407811i	$0.866292\pi$
$132$	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	−0.0763645	−	0.997080i	$-0.524331\pi$
$137$	10.7767	−	10.7767i	0.920715	−	0.920715i	0.997080	+	0.0763645i	$0.0243313\pi$
$138$	−11.0751	+	0.506975i	−0.942776	+	0.0431566i
$139$			0.244460i			0.0207348i	0.999946	+	0.0103674i	$0.00330011\pi$
$139$			0.244460i			0.0207348i	−0.999946	+	0.0103674i	$0.996700\pi$
$140$	−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	0.639212	−	0.769031i	$-0.279261\pi$
$157$	−1.62663	−	1.62663i	−0.129819	−	0.129819i	−0.769031	+	0.639212i	$0.779261\pi$
$158$	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	−0.211550	−	0.977367i	$-0.567851\pi$
$163$	9.77730	−	9.77730i	0.765817	−	0.765817i	0.977367	+	0.211550i	$0.0678512\pi$
$164$	−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	−0.605578	−	0.795786i	$-0.707058\pi$
$167$	2.45802	−	2.45802i	0.190207	−	0.190207i	0.795786	+	0.605578i	$0.207058\pi$
$168$	−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	0.993241	−	0.116070i	$-0.0370297\pi$
$173$	11.5374	+	11.5374i	0.877171	+	0.877171i	−0.116070	+	0.993241i	$0.537030\pi$
$174$	−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	$-0.948222\pi$
$191$		−	4.47635i		−	0.323897i	0.986799	−	0.161949i	$-0.0517779\pi$
$192$	0.0792035	+	1.73024i	0.00571602	+	0.124869i
$193$	−6.48726	+	6.48726i	−0.466963	+	0.466963i	−0.900929	−	0.433966i	$-0.857114\pi$
$193$	−6.48726	+	6.48726i	−0.466963	+	0.466963i	0.433966	+	0.900929i	$0.357114\pi$
$194$	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	−0.967657	−	0.252271i	$-0.918822\pi$
$197$	−10.0409	+	10.0409i	−0.715385	+	0.715385i	0.252271	+	0.967657i	$0.418822\pi$
$198$	10.2754	+	8.54840i	0.730239	+	0.607509i
$199$			10.0543i			0.712731i	0.934347	+	0.356366i	$0.115984\pi$
$199$			10.0543i			0.712731i	−0.934347	+	0.356366i	$0.884016\pi$
$200$	−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	−0.792275	−	0.610165i	$-0.791103\pi$
$223$	−2.71948	+	2.71948i	−0.182110	+	0.182110i	0.610165	+	0.792275i	$0.291103\pi$
$224$	−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	−0.681438	−	0.731875i	$-0.738645\pi$
$227$	0.759912	−	0.759912i	0.0504371	−	0.0504371i	0.731875	+	0.681438i	$0.238645\pi$
$228$	12.2512	−	0.560810i	0.811353	−	0.0371405i
$229$		−	3.91489i		−	0.258703i	−0.991599	−	0.129351i	$-0.958710\pi$
$229$		−	3.91489i		−	0.258703i	0.991599	−	0.129351i	$-0.0412895\pi$
$230$	−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	0.598404	−	0.801194i	$-0.295802\pi$
$233$	−3.09546	−	3.09546i	−0.202790	−	0.202790i	−0.801194	+	0.598404i	$0.795802\pi$
$234$	−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	$0.203558\pi$
$251$			18.9099i			1.19358i	−0.802396	+	0.596792i	$0.796442\pi$
$252$	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	−0.294773	−	0.955567i	$-0.595244\pi$
$257$	10.5933	−	10.5933i	0.660794	−	0.660794i	0.955567	+	0.294773i	$0.0952440\pi$
$258$	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	0.826235	−	0.563326i	$-0.190478\pi$
$263$	4.26368	+	4.26368i	0.262910	+	0.262910i	−0.563326	+	0.826235i	$0.690478\pi$
$264$	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	0.922953	−	0.384912i	$-0.125768\pi$
$277$	8.95479	+	8.95479i	0.538041	+	0.538041i	−0.384912	+	0.922953i	$0.625768\pi$
$278$	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	$0.0113330\pi$
$281$			1.19340i			0.0711924i	−0.999366	+	0.0355962i	$0.988667\pi$
$282$	1.04375	+	22.8012i	0.0621544	+	1.35779i
$283$	4.03370	−	4.03370i	0.239778	−	0.239778i	−0.576980	−	0.816758i	$-0.695769\pi$
$283$	4.03370	−	4.03370i	0.239778	−	0.239778i	0.816758	+	0.576980i	$0.195769\pi$
$284$	−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	0.989304	+	0.145868i	$0.0465973\pi$
$293$	19.4310	+	19.4310i	1.13517	+	1.13517i	0.145868	+	0.989304i	$0.453403\pi$
$294$	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	0.628810	−	0.777559i	$-0.283542\pi$
$307$	−2.60628	−	2.60628i	−0.148748	−	0.148748i	−0.777559	+	0.628810i	$0.783542\pi$
$308$	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	$0.205056\pi$
$311$			21.1821i			1.20112i	−0.799578	+	0.600562i	$0.794944\pi$
$312$	−2.38555	+	0.109201i	−0.135055	+	0.00618230i
$313$	6.20568	−	6.20568i	0.350766	−	0.350766i	−0.509629	−	0.860395i	$-0.670217\pi$
$313$	6.20568	−	6.20568i	0.350766	−	0.350766i	0.860395	+	0.509629i	$0.170217\pi$
$314$	−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	−0.684635	−	0.728886i	$-0.740038\pi$
$317$	0.787882	−	0.787882i	0.0442518	−	0.0442518i	0.728886	+	0.684635i	$0.240038\pi$
$318$	−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	0.999862	−	0.0166419i	$-0.00529751\pi$
$337$	18.0495	+	18.0495i	0.983220	+	0.983220i	−0.0166419	+	0.999862i	$0.505298\pi$
$338$	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	−0.922248	−	0.386598i	$-0.873650\pi$
$347$	−9.97805	+	9.97805i	−0.535650	+	0.535650i	0.386598	+	0.922248i	$0.373650\pi$
$348$	0.540939	+	11.8171i	0.0289974	+	0.633462i
$349$			9.44139i			0.505386i	0.967547	+	0.252693i	$0.0813163\pi$
$349$			9.44139i			0.505386i	−0.967547	+	0.252693i	$0.918684\pi$
$350$	−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	0.967090	−	0.254434i	$-0.0818891\pi$
$353$	13.3896	+	13.3896i	0.712656	+	0.712656i	−0.254434	+	0.967090i	$0.581889\pi$
$354$	−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	0.340123	−	0.940381i	$-0.389531\pi$
$367$	−11.4993	−	11.4993i	−0.600258	−	0.600258i	−0.940381	+	0.340123i	$0.889531\pi$
$368$	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	−0.151624	−	0.988438i	$-0.548450\pi$
$373$	16.1616	−	16.1616i	0.836814	−	0.836814i	0.988438	+	0.151624i	$0.0484503\pi$
$374$	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	$0.0267104\pi$
$379$			3.26340i			0.167630i	−0.996481	+	0.0838148i	$0.973290\pi$
$380$	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	−0.997599	−	0.0692583i	$-0.977937\pi$
$383$	−20.8788	−	20.8788i	−1.06686	−	1.06686i	−0.0692583	−	0.997599i	$-0.522063\pi$
$384$	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	0.997827	+	0.0658935i	$0.0209898\pi$
$397$	21.1945	+	21.1945i	1.06372	+	1.06372i	0.0658935	+	0.997827i	$0.479010\pi$
$398$	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	$-0.802882\pi$
$401$		−	23.2465i		−	1.16087i	0.814305	−	0.580437i	$-0.197118\pi$
$402$	−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	$-0.715495\pi$
$409$		−	31.5271i		−	1.55891i	0.626456	−	0.779456i	$-0.284505\pi$
$410$	−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	$-0.800768\pi$
$431$		−	24.3243i		−	1.17166i	0.810433	−	0.585831i	$-0.199232\pi$
$432$	−5.14730	+	0.710844i	−0.247650	+	0.0342005i
$433$	−4.98544	+	4.98544i	−0.239585	+	0.239585i	−0.816678	−	0.577093i	$-0.804187\pi$
$433$	−4.98544	+	4.98544i	−0.239585	+	0.239585i	0.577093	+	0.816678i	$0.304187\pi$
$434$	−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	$-0.666015\pi$
$439$		−	36.3333i		−	1.73410i	0.498225	−	0.867048i	$-0.333985\pi$
$440$	−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	0.689245	−	0.724528i	$-0.257942\pi$
$443$	−0.742619	−	0.742619i	−0.0352829	−	0.0352829i	−0.724528	+	0.689245i	$0.757942\pi$
$444$	−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	0.439961	−	0.898017i	$-0.354992\pi$
$457$	−9.79211	−	9.79211i	−0.458056	−	0.458056i	−0.898017	+	0.439961i	$0.854992\pi$
$458$	−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	$-0.774434\pi$
$461$		−	27.9465i		−	1.30160i	0.759250	−	0.650799i	$-0.225566\pi$
$462$	1.08573	+	23.7182i	0.0505126	+	1.10347i
$463$	29.4940	−	29.4940i	1.37070	−	1.37070i	0.511303	−	0.859400i	$-0.329163\pi$
$463$	29.4940	−	29.4940i	1.37070	−	1.37070i	0.859400	−	0.511303i	$-0.170837\pi$
$464$	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	−0.612735	−	0.790288i	$-0.709931\pi$
$467$	3.83696	−	3.83696i	0.177553	−	0.177553i	0.790288	+	0.612735i	$0.209931\pi$
$468$	−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	0.851450	−	0.524436i	$-0.175724\pi$
$487$	7.21655	+	7.21655i	0.327013	+	0.327013i	−0.524436	+	0.851450i	$0.675724\pi$
$488$	−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	$0.228832\pi$
$491$			29.1852i			1.31711i	−0.752534	+	0.658554i	$0.771168\pi$
$492$	−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	$-0.918183\pi$
$499$		−	11.3575i		−	0.508429i	0.967148	−	0.254215i	$-0.0818170\pi$
$500$	−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	0.995235	−	0.0975031i	$-0.0310856\pi$
$503$	20.1340	+	20.1340i	0.897732	+	0.897732i	−0.0975031	+	0.995235i	$0.531086\pi$
$504$	−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	$0.326896\pi$
$521$			39.0652i			1.71148i	−0.517409	+	0.855738i	$0.673104\pi$
$522$	−13.1038	+	15.7511i	−0.573539	+	0.689407i
$523$	2.56964	−	2.56964i	0.112363	−	0.112363i	−0.648690	−	0.761053i	$-0.724683\pi$
$523$	2.56964	−	2.56964i	0.112363	−	0.112363i	0.761053	+	0.648690i	$0.224683\pi$
$524$	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	0.736541	−	0.676393i	$-0.236458\pi$
$547$	1.40675	+	1.40675i	0.0601483	+	0.0601483i	−0.676393	+	0.736541i	$0.736458\pi$
$548$	−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	−0.526918	−	0.849916i	$-0.676652\pi$
$557$	7.62304	−	7.62304i	0.322998	−	0.322998i	0.849916	+	0.526918i	$0.176652\pi$
$558$	−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	0.999748	−	0.0224305i	$-0.00714044\pi$
$563$	23.1894	+	23.1894i	0.977318	+	0.977318i	−0.0224305	+	0.999748i	$0.507140\pi$
$564$	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	0.827753	−	0.561092i	$-0.189619\pi$
$577$	6.40542	+	6.40542i	0.266661	+	0.266661i	−0.561092	+	0.827753i	$0.689619\pi$
$578$	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	−0.380030	−	0.924974i	$-0.624086\pi$
$587$	13.2030	−	13.2030i	0.544944	−	0.544944i	0.924974	+	0.380030i	$0.124086\pi$
$588$	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	0.501252	−	0.865302i	$-0.332873\pi$
$593$	−8.86519	−	8.86519i	−0.364050	−	0.364050i	−0.865302	+	0.501252i	$0.832873\pi$
$594$	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	−0.936547	−	0.350541i	$-0.885998\pi$
$607$	−31.7105	−	31.7105i	−1.28709	−	1.28709i	−0.350541	−	0.936547i	$-0.614002\pi$
$608$	−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	−0.281250	−	0.959635i	$-0.590749\pi$
$613$	16.7960	−	16.7960i	0.678384	−	0.678384i	0.959635	+	0.281250i	$0.0907490\pi$
$614$	−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	−0.921323	−	0.388798i	$-0.872890\pi$
$617$	−13.2277	+	13.2277i	−0.532525	+	0.532525i	0.388798	+	0.921323i	$0.372890\pi$
$618$	−0.725644	−	15.8520i	−0.0291897	−	0.637662i
$619$			26.8070i			1.07746i	0.842477	+	0.538732i	$0.181097\pi$
$619$			26.8070i			1.07746i	−0.842477	+	0.538732i	$0.818903\pi$
$620$	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	$-0.981244\pi$
$641$		−	2.98189i		−	0.117778i	0.998265	−	0.0588889i	$-0.0187558\pi$
$642$	0.187511	+	4.09628i	0.00740049	+	0.161667i
$643$	−0.965272	+	0.965272i	−0.0380666	+	0.0380666i	−0.725884	−	0.687817i	$-0.758569\pi$
$643$	−0.965272	+	0.965272i	−0.0380666	+	0.0380666i	0.687817	+	0.725884i	$0.258569\pi$
$644$	−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	−0.0447756	−	0.998997i	$-0.514257\pi$
$647$	24.2718	−	24.2718i	0.954221	−	0.954221i	0.998997	+	0.0447756i	$0.0142573\pi$
$648$	−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	0.882406	−	0.470489i	$-0.155922\pi$
$653$	10.5261	+	10.5261i	0.411917	+	0.411917i	−0.470489	+	0.882406i	$0.655922\pi$
$654$	−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	−0.802356	−	0.596846i	$-0.796420\pi$
$673$	−5.33140	+	5.33140i	−0.205510	+	0.205510i	0.596846	+	0.802356i	$0.296420\pi$
$674$	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	−0.717610	−	0.696445i	$-0.754764\pi$
$677$	−0.550707	+	0.550707i	−0.0211654	+	0.0211654i	0.696445	+	0.717610i	$0.254764\pi$
$678$	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	0.449435	−	0.893313i	$-0.351626\pi$
$683$	−11.6004	−	11.6004i	−0.443879	−	0.443879i	−0.893313	+	0.449435i	$0.851626\pi$
$684$	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	$0.00839950\pi$
$701$			1.39715i			0.0527695i	−0.999652	+	0.0263848i	$0.991600\pi$
$702$	−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	$0.226811\pi$
$709$			34.8156i			1.30753i	−0.756699	+	0.653763i	$0.773189\pi$
$710$	−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	0.331130	−	0.943585i	$-0.392570\pi$
$727$	−16.5136	−	16.5136i	−0.612456	−	0.612456i	−0.943585	+	0.331130i	$0.892570\pi$
$728$	−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	−0.348730	−	0.937223i	$-0.613387\pi$
$733$	15.9328	−	15.9328i	0.588493	−	0.588493i	0.937223	+	0.348730i	$0.113387\pi$
$734$	−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	$-0.979348\pi$
$739$		−	3.52497i		−	0.129668i	0.997896	−	0.0648341i	$-0.0206518\pi$
$740$	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	0.682509	−	0.730877i	$-0.260889\pi$
$743$	−1.31841	−	1.31841i	−0.0483679	−	0.0483679i	−0.730877	+	0.682509i	$0.760889\pi$
$744$	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	0.627809	−	0.778367i	$-0.283952\pi$
$757$	−4.14240	−	4.14240i	−0.150558	−	0.150558i	−0.778367	+	0.627809i	$0.783952\pi$
$758$	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	$-0.935343\pi$
$761$		−	11.1300i		−	0.403461i	0.979441	−	0.201731i	$-0.0646565\pi$
$762$	−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	$0.0449311\pi$
$769$			7.80274i			0.281374i	−0.990054	+	0.140687i	$0.955069\pi$
$770$	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	0.702683	−	0.711503i	$-0.251985\pi$
$773$	−0.245237	−	0.245237i	−0.00882054	−	0.00882054i	−0.711503	+	0.702683i	$0.751985\pi$
$774$	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	0.811207	−	0.584758i	$-0.198811\pi$
$787$	6.35269	+	6.35269i	0.226449	+	0.226449i	−0.584758	+	0.811207i	$0.698811\pi$
$788$	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	−0.905088	−	0.425225i	$-0.860195\pi$
$797$	−13.5471	+	13.5471i	−0.479863	+	0.479863i	0.425225	+	0.905088i	$0.360195\pi$
$798$	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	$0.263857\pi$
$821$			42.2466i			1.47442i	−0.675665	+	0.737209i	$0.736143\pi$
$822$	−1.20711	−	26.3698i	−0.0421026	−	0.919752i
$823$	−35.3675	+	35.3675i	−1.23283	+	1.23283i	−0.269960	+	0.962871i	$0.587011\pi$
$823$	−35.3675	+	35.3675i	−1.23283	+	1.23283i	−0.962871	+	0.269960i	$0.912989\pi$
$824$	−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	−0.661667	−	0.749798i	$-0.730151\pi$
$827$	2.53444	−	2.53444i	0.0881310	−	0.0881310i	0.749798	+	0.661667i	$0.230151\pi$
$828$	−12.2811	+	14.7621i	−0.426797	+	0.513019i
$829$			6.31396i			0.219293i	0.993971	+	0.109646i	$0.0349719\pi$
$829$			6.31396i			0.219293i	−0.993971	+	0.109646i	$0.965028\pi$
$830$	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	−0.997791	−	0.0664281i	$-0.978840\pi$
$853$	−27.2015	+	27.2015i	−0.931363	+	0.931363i	0.0664281	+	0.997791i	$0.478840\pi$
$854$	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	−0.0720192	+	0.997403i	$0.522944\pi$
$857$	−31.3069	+	31.3069i	−1.06942	+	1.06942i	−0.997403	+	0.0720192i	$0.977056\pi$
$858$	10.6287	−	0.486539i	0.362857	−	0.0166102i
$859$		−	47.7582i		−	1.62949i	−0.579821	−	0.814744i	$-0.696877\pi$
$859$		−	47.7582i		−	1.62949i	0.579821	−	0.814744i	$-0.303123\pi$
$860$	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	0.575399	−	0.817873i	$-0.304847\pi$
$863$	−7.12312	−	7.12312i	−0.242474	−	0.242474i	−0.817873	+	0.575399i	$0.804847\pi$
$864$	−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	0.845740	−	0.533595i	$-0.179159\pi$
$877$	9.24394	+	9.24394i	0.312146	+	0.312146i	−0.533595	+	0.845740i	$0.679159\pi$
$878$	−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	$0.0155075\pi$
$881$			2.89093i			0.0973979i	−0.998814	+	0.0486989i	$0.984493\pi$
$882$	5.68742	+	4.73154i	0.191505	+	0.159319i
$883$	−6.33199	+	6.33199i	−0.213088	+	0.213088i	−0.805578	−	0.592490i	$-0.798145\pi$
$883$	−6.33199	+	6.33199i	−0.213088	+	0.213088i	0.592490	+	0.805578i	$0.298145\pi$
$884$	−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	−0.888814	−	0.458267i	$-0.848470\pi$
$887$	−12.8228	+	12.8228i	−0.430547	+	0.430547i	0.458267	+	0.888814i	$0.348470\pi$
$888$	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	0.966640	−	0.256141i	$-0.0824510\pi$
$907$	21.3977	+	21.3977i	0.710499	+	0.710499i	−0.256141	+	0.966640i	$0.582451\pi$
$908$	−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	$0.0318824\pi$
$911$			6.03619i			0.199988i	−0.994988	+	0.0999940i	$0.968118\pi$
$912$	−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	$0.0556471\pi$
$919$			10.5455i			0.347863i	−0.984758	+	0.173932i	$0.944353\pi$
$920$	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	0.713971	−	0.700175i	$-0.246895\pi$
$937$	0.422297	+	0.422297i	0.0137959	+	0.0137959i	−0.700175	+	0.713971i	$0.746895\pi$
$938$	−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	$-0.751971\pi$
$941$		−	43.1125i		−	1.40543i	0.711472	−	0.702714i	$-0.248029\pi$
$942$	−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	−0.914486	−	0.404618i	$-0.867404\pi$
$947$	−15.6903	+	15.6903i	−0.509867	+	0.509867i	0.404618	+	0.914486i	$0.367404\pi$
$948$	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	0.766933	−	0.641728i	$-0.221782\pi$
$953$	3.86517	+	3.86517i	0.125205	+	0.125205i	−0.641728	+	0.766933i	$0.721782\pi$
$954$	−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	0.883617	−	0.468211i	$-0.155101\pi$
$967$	12.9177	+	12.9177i	0.415406	+	0.415406i	−0.468211	+	0.883617i	$0.655101\pi$
$968$	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	$0.0224652\pi$
$971$			4.39480i			0.141036i	−0.997511	+	0.0705179i	$0.977535\pi$
$972$	−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	−0.976027	−	0.217650i	$-0.930161\pi$
$977$	−23.7046	+	23.7046i	−0.758377	+	0.758377i	0.217650	+	0.976027i	$0.430161\pi$
$978$	−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	0.470108	−	0.882609i	$-0.344215\pi$
$983$	−12.9330	−	12.9330i	−0.412500	−	0.412500i	−0.882609	+	0.470108i	$0.844215\pi$
$984$	−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	0.909246	−	0.416258i	$-0.136659\pi$
$997$	15.5663	+	15.5663i	0.492988	+	0.492988i	−0.416258	+	0.909246i	$0.636659\pi$
$998$	−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.497.20	yes	40
3.2	odd	2	inner	930.2.j.h.497.6	✓	40
5.3	odd	4	inner	930.2.j.h.683.6	yes	40
15.8	even	4	inner	930.2.j.h.683.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.6	✓	40	3.2	odd	2	inner
930.2.j.h.497.20	yes	40	1.1	even	1	trivial
930.2.j.h.683.6	yes	40	5.3	odd	4	inner
930.2.j.h.683.20	yes	40	15.8	even	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.73024 - 0.0792035i) q^{3} -1.00000i q^{4} +(1.29721 - 1.82133i) q^{5} +(1.16746 - 1.27947i) q^{6} +(2.17556 + 2.17556i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98745 - 0.274082i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) 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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