LMFDB - Embedded newform 930.2.j.g.497.10

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			497.10
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.73204 - 0.00608872i) q^{3} -1.00000i q^{4} +(-2.02131 + 0.956187i) q^{5} +(-1.22043 + 1.22904i) q^{6} +(-1.11064 - 1.11064i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99993 - 0.0210918i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.73204 - 0.00608872i) q^{3} -1.00000i q^{4} +(-2.02131 + 0.956187i) q^{5} +(-1.22043 + 1.22904i) q^{6} +(-1.11064 - 1.11064i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99993 - 0.0210918i) q^{9} +(0.753158 - 2.10541i) q^{10} +2.70947i q^{11} +(-0.00608872 - 1.73204i) q^{12} +(0.120439 - 0.120439i) q^{13} +1.57068 q^{14} +(-3.49517 + 1.66846i) q^{15} -1.00000 q^{16} +(0.852346 - 0.852346i) q^{17} +(-2.10635 + 2.13618i) q^{18} +5.63716i q^{19} +(0.956187 + 2.02131i) q^{20} +(-1.93043 - 1.91690i) q^{21} +(-1.91589 - 1.91589i) q^{22} +(6.00623 + 6.00623i) q^{23} +(1.22904 + 1.22043i) q^{24} +(3.17141 - 3.86551i) q^{25} +0.170327i q^{26} +(5.19586 - 0.0547976i) q^{27} +(-1.11064 + 1.11064i) q^{28} -9.37974 q^{29} +(1.29168 - 3.65124i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.0164972 + 4.69291i) q^{33} +1.20540i q^{34} +(3.30692 + 1.18297i) q^{35} +(-0.0210918 - 2.99993i) q^{36} +(4.37896 + 4.37896i) q^{37} +(-3.98607 - 3.98607i) q^{38} +(0.207872 - 0.209339i) q^{39} +(-2.10541 - 0.753158i) q^{40} +12.3602i q^{41} +(2.72047 - 0.00956340i) q^{42} +(-6.77836 + 6.77836i) q^{43} +2.70947 q^{44} +(-6.04362 + 2.91112i) q^{45} -8.49409 q^{46} +(-1.75294 + 1.75294i) q^{47} +(-1.73204 + 0.00608872i) q^{48} -4.53298i q^{49} +(0.490799 + 4.97585i) q^{50} +(1.47111 - 1.48149i) q^{51} +(-0.120439 - 0.120439i) q^{52} +(0.0579639 + 0.0579639i) q^{53} +(-3.63528 + 3.71278i) q^{54} +(-2.59076 - 5.47669i) q^{55} -1.57068i q^{56} +(0.0343231 + 9.76379i) q^{57} +(6.63248 - 6.63248i) q^{58} +1.06847 q^{59} +(1.66846 + 3.49517i) q^{60} +7.56989 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-3.35525 - 3.30840i) q^{63} +1.00000i q^{64} +(-0.128283 + 0.358608i) q^{65} +(-3.33006 - 3.30673i) q^{66} +(5.10127 + 5.10127i) q^{67} +(-0.852346 - 0.852346i) q^{68} +(10.4396 + 10.3665i) q^{69} +(-3.17483 + 1.50186i) q^{70} -15.7810i q^{71} +(2.13618 + 2.10635i) q^{72} +(-3.90256 + 3.90256i) q^{73} -6.19279 q^{74} +(5.46948 - 6.71452i) q^{75} +5.63716 q^{76} +(3.00924 - 3.00924i) q^{77} +(0.00103707 + 0.295013i) q^{78} -7.85631i q^{79} +(2.02131 - 0.956187i) q^{80} +(8.99911 - 0.126548i) q^{81} +(-8.74002 - 8.74002i) q^{82} +(8.60592 + 8.60592i) q^{83} +(-1.91690 + 1.93043i) q^{84} +(-0.907855 + 2.53786i) q^{85} -9.58605i q^{86} +(-16.2461 + 0.0571106i) q^{87} +(-1.91589 + 1.91589i) q^{88} -5.43975 q^{89} +(2.21501 - 6.33196i) q^{90} -0.267529 q^{91} +(6.00623 - 6.00623i) q^{92} +(1.73204 - 0.00608872i) q^{93} -2.47903i q^{94} +(-5.39018 - 11.3945i) q^{95} +(1.22043 - 1.22904i) q^{96} +(-2.97219 - 2.97219i) q^{97} +(3.20530 + 3.20530i) q^{98} +(0.0571477 + 8.12821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * 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
$3$	1.73204	−	0.00608872i	0.999994	−	0.00351532i
$3$	1.73204	−	0.00608872i	0.999994	−	0.00351532i
$4$		−	1.00000i		−	0.500000i
$5$	−2.02131	+	0.956187i	−0.903959	+	0.427620i
$5$	−2.02131	+	0.956187i	−0.903959	+	0.427620i
$6$	−1.22043	+	1.22904i	−0.498239	+	0.501755i
$7$	−1.11064	−	1.11064i	−0.419781	−	0.419781i	0.465347	−	0.885128i	$-0.345929\pi$
$7$	−1.11064	−	1.11064i	−0.419781	−	0.419781i	−0.885128	+	0.465347i	$0.845929\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.99993	−	0.0210918i	0.999975	−	0.00703060i
$10$	0.753158	−	2.10541i	0.238169	−	0.665789i
$11$			2.70947i			0.816936i	0.912773	+	0.408468i	$0.133937\pi$
$11$			2.70947i			0.816936i	−0.912773	+	0.408468i	$0.866063\pi$
$12$	−0.00608872	−	1.73204i	−0.00175766	−	0.499997i
$13$	0.120439	−	0.120439i	0.0334039	−	0.0334039i	−0.690208	−	0.723611i	$-0.742481\pi$
$13$	0.120439	−	0.120439i	0.0334039	−	0.0334039i	0.723611	+	0.690208i	$0.242481\pi$
$14$	1.57068			0.419781
$15$	−3.49517	+	1.66846i	−0.902450	+	0.430795i
$16$	−1.00000			−0.250000
$17$	0.852346	−	0.852346i	0.206724	−	0.206724i	−0.596149	−	0.802874i	$-0.703303\pi$
$17$	0.852346	−	0.852346i	0.206724	−	0.206724i	0.802874	+	0.596149i	$0.203303\pi$
$18$	−2.10635	+	2.13618i	−0.496472	+	0.503503i
$19$			5.63716i			1.29325i	0.762807	+	0.646627i	$0.223821\pi$
$19$			5.63716i			1.29325i	−0.762807	+	0.646627i	$0.776179\pi$
$20$	0.956187	+	2.02131i	0.213810	+	0.451979i
$21$	−1.93043	−	1.91690i	−0.421254	−	0.418303i
$22$	−1.91589	−	1.91589i	−0.408468	−	0.408468i
$23$	6.00623	+	6.00623i	1.25239	+	1.25239i	0.954648	+	0.297738i	$0.0962323\pi$
$23$	6.00623	+	6.00623i	1.25239	+	1.25239i	0.297738	+	0.954648i	$0.403768\pi$
$24$	1.22904	+	1.22043i	0.250877	+	0.249120i
$25$	3.17141	−	3.86551i	0.634282	−	0.773101i
$26$			0.170327i			0.0334039i
$27$	5.19586	−	0.0547976i	0.999944	−	0.0105458i
$28$	−1.11064	+	1.11064i	−0.209890	+	0.209890i
$29$	−9.37974			−1.74177			−0.870887	−	0.491483i	$-0.836455\pi$
$29$	−9.37974			−1.74177			−0.870887	+	0.491483i	$0.836455\pi$
$30$	1.29168	−	3.65124i	0.235827	−	0.666622i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.0164972	+	4.69291i	0.00287180	+	0.816931i
$34$			1.20540i			0.206724i
$35$	3.30692	+	1.18297i	0.558971	+	0.199958i
$36$	−0.0210918	−	2.99993i	−0.00351530	−	0.499988i
$37$	4.37896	+	4.37896i	0.719897	+	0.719897i	0.968584	−	0.248687i	$-0.0799991\pi$
$37$	4.37896	+	4.37896i	0.719897	+	0.719897i	−0.248687	+	0.968584i	$0.579999\pi$
$38$	−3.98607	−	3.98607i	−0.646627	−	0.646627i
$39$	0.207872	−	0.209339i	0.0332862	−	0.0335211i
$40$	−2.10541	−	0.753158i	−0.332895	−	0.119085i
$41$			12.3602i			1.93035i	0.261611	+	0.965173i	$0.415746\pi$
$41$			12.3602i			1.93035i	−0.261611	+	0.965173i	$0.584254\pi$
$42$	2.72047	−	0.00956340i	0.419778	−	0.00147567i
$43$	−6.77836	+	6.77836i	−1.03369	+	1.03369i	−0.0342777	+	0.999412i	$0.510913\pi$
$43$	−6.77836	+	6.77836i	−1.03369	+	1.03369i	−0.999412	+	0.0342777i	$0.989087\pi$
$44$	2.70947			0.408468
$45$	−6.04362	+	2.91112i	−0.900930	+	0.433965i
$46$	−8.49409			−1.25239
$47$	−1.75294	+	1.75294i	−0.255692	+	0.255692i	−0.823299	−	0.567607i	$-0.807869\pi$
$47$	−1.75294	+	1.75294i	−0.255692	+	0.255692i	0.567607	+	0.823299i	$0.307869\pi$
$48$	−1.73204	+	0.00608872i	−0.249998	+	0.000878831i
$49$		−	4.53298i		−	0.647568i
$50$	0.490799	+	4.97585i	0.0694095	+	0.703692i
$51$	1.47111	−	1.48149i	0.205996	−	0.207450i
$52$	−0.120439	−	0.120439i	−0.0167019	−	0.0167019i
$53$	0.0579639	+	0.0579639i	0.00796195	+	0.00796195i	0.711077	−	0.703115i	$-0.248208\pi$
$53$	0.0579639	+	0.0579639i	0.00796195	+	0.00796195i	−0.703115	+	0.711077i	$0.748208\pi$
$54$	−3.63528	+	3.71278i	−0.494699	+	0.505245i
$55$	−2.59076	−	5.47669i	−0.349338	−	0.738477i
$56$		−	1.57068i		−	0.209890i
$57$	0.0343231	+	9.76379i	0.00454620	+	1.29325i
$58$	6.63248	−	6.63248i	0.870887	−	0.870887i
$59$	1.06847			0.139102			0.0695512	−	0.997578i	$-0.477843\pi$
$59$	1.06847			0.139102			0.0695512	+	0.997578i	$0.477843\pi$
$60$	1.66846	+	3.49517i	0.215397	+	0.451225i
$61$	7.56989			0.969225			0.484612	−	0.874729i	$-0.338961\pi$
$61$	7.56989			0.969225			0.484612	+	0.874729i	$0.338961\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−3.35525	−	3.30840i	−0.422722	−	0.416819i
$64$			1.00000i			0.125000i
$65$	−0.128283	+	0.358608i	−0.0159116	+	0.0444799i
$66$	−3.33006	−	3.30673i	−0.409902	−	0.407030i
$67$	5.10127	+	5.10127i	0.623219	+	0.623219i	0.946353	−	0.323134i	$-0.104737\pi$
$67$	5.10127	+	5.10127i	0.623219	+	0.623219i	−0.323134	+	0.946353i	$0.604737\pi$
$68$	−0.852346	−	0.852346i	−0.103362	−	0.103362i
$69$	10.4396	+	10.3665i	1.25678	+	1.24798i
$70$	−3.17483	+	1.50186i	−0.379465	+	0.179507i
$71$		−	15.7810i		−	1.87286i	−0.350854	−	0.936430i	$-0.614109\pi$
$71$		−	15.7810i		−	1.87286i	0.350854	−	0.936430i	$-0.385891\pi$
$72$	2.13618	+	2.10635i	0.251751	+	0.248236i
$73$	−3.90256	+	3.90256i	−0.456760	+	0.456760i	−0.897590	−	0.440831i	$-0.854684\pi$
$73$	−3.90256	+	3.90256i	−0.456760	+	0.456760i	0.440831	+	0.897590i	$0.354684\pi$
$74$	−6.19279			−0.719897
$75$	5.46948	−	6.71452i	0.631561	−	0.775326i
$76$	5.63716			0.646627
$77$	3.00924	−	3.00924i	0.342934	−	0.342934i
$78$	0.00103707	+	0.295013i	0.000117425	+	0.0334037i
$79$		−	7.85631i		−	0.883904i	−0.897039	−	0.441952i	$-0.854286\pi$
$79$		−	7.85631i		−	0.883904i	0.897039	−	0.441952i	$-0.145714\pi$
$80$	2.02131	−	0.956187i	0.225990	−	0.106905i
$81$	8.99911	−	0.126548i	0.999901	−	0.0140609i
$82$	−8.74002	−	8.74002i	−0.965173	−	0.965173i
$83$	8.60592	+	8.60592i	0.944622	+	0.944622i	0.998545	−	0.0539231i	$-0.0171726\pi$
$83$	8.60592	+	8.60592i	0.944622	+	0.944622i	−0.0539231	+	0.998545i	$0.517173\pi$
$84$	−1.91690	+	1.93043i	−0.209151	+	0.210627i
$85$	−0.907855	+	2.53786i	−0.0984707	+	0.275270i
$86$		−	9.58605i		−	1.03369i
$87$	−16.2461	+	0.0571106i	−1.74176	+	0.00612290i
$88$	−1.91589	+	1.91589i	−0.204234	+	0.204234i
$89$	−5.43975			−0.576612			−0.288306	−	0.957538i	$-0.593092\pi$
$89$	−5.43975			−0.576612			−0.288306	+	0.957538i	$0.593092\pi$
$90$	2.21501	−	6.33196i	0.233483	−	0.667447i
$91$	−0.267529			−0.0280446
$92$	6.00623	−	6.00623i	0.626193	−	0.626193i
$93$	1.73204	−	0.00608872i	0.179604	−	0.000631371i
$94$		−	2.47903i		−	0.255692i
$95$	−5.39018	−	11.3945i	−0.553021	−	1.16905i
$96$	1.22043	−	1.22904i	0.124560	−	0.125439i
$97$	−2.97219	−	2.97219i	−0.301780	−	0.301780i	0.539930	−	0.841710i	$-0.318451\pi$
$97$	−2.97219	−	2.97219i	−0.301780	−	0.301780i	−0.841710	+	0.539930i	$0.818451\pi$
$98$	3.20530	+	3.20530i	0.323784	+	0.323784i
$99$	0.0571477	+	8.12821i	0.00574356	+	0.816916i
$100$	−3.86551	−	3.17141i	−0.386551	−	0.317141i
$101$		−	11.9110i		−	1.18519i	−0.805499	−	0.592597i	$-0.798103\pi$
$101$		−	11.9110i		−	1.18519i	0.805499	−	0.592597i	$-0.201897\pi$
$102$	0.00733933	+	2.08780i	0.000726702	+	0.206723i
$103$	4.74787	−	4.74787i	0.467822	−	0.467822i	−0.433386	−	0.901208i	$-0.642681\pi$
$103$	4.74787	−	4.74787i	0.467822	−	0.467822i	0.901208	+	0.433386i	$0.142681\pi$
$104$	0.170327			0.0167019
$105$	5.73492	+	2.02881i	0.559671	+	0.197992i
$106$	−0.0819733			−0.00796195
$107$	−11.4901	+	11.4901i	−1.11079	+	1.11079i	−0.117742	+	0.993044i	$0.537565\pi$
$107$	−11.4901	+	11.4901i	−1.11079	+	1.11079i	−0.993044	+	0.117742i	$0.962435\pi$
$108$	−0.0547976	−	5.19586i	−0.00527290	−	0.499972i
$109$		−	4.28732i		−	0.410651i	−0.978694	−	0.205326i	$-0.934175\pi$
$109$		−	4.28732i		−	0.410651i	0.978694	−	0.205326i	$-0.0658253\pi$
$110$	5.70455	+	2.04066i	0.543908	+	0.194569i
$111$	7.61120	+	7.55787i	0.722423	+	0.717362i
$112$	1.11064	+	1.11064i	0.104945	+	0.104945i
$113$	5.16233	+	5.16233i	0.485631	+	0.485631i	0.906924	−	0.421294i	$-0.138424\pi$
$113$	5.16233	+	5.16233i	0.485631	+	0.485631i	−0.421294	+	0.906924i	$0.638424\pi$
$114$	−6.92831	−	6.87977i	−0.648896	−	0.644350i
$115$	−17.8836	−	6.39739i	−1.66765	−	0.596560i
$116$			9.37974i			0.870887i
$117$	0.358769	−	0.363849i	0.0331682	−	0.0336379i
$118$	−0.755519	+	0.755519i	−0.0695512	+	0.0695512i
$119$	−1.89329			−0.173558
$120$	−3.65124	−	1.29168i	−0.333311	−	0.117914i
$121$	3.65876			0.332615
$122$	−5.35272	+	5.35272i	−0.484612	+	0.484612i
$123$	0.0752581	+	21.4084i	0.00678579	+	1.93033i
$124$		−	1.00000i		−	0.0898027i
$125$	−2.71427	+	10.8459i	−0.242771	+	0.970084i
$126$	4.71191	−	0.0331284i	0.419771	−	0.00295131i
$127$	−1.14523	−	1.14523i	−0.101622	−	0.101622i	0.654468	−	0.756090i	$-0.272893\pi$
$127$	−1.14523	−	1.14523i	−0.101622	−	0.101622i	−0.756090	+	0.654468i	$0.772893\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−11.6991	+	11.7817i	−1.03005	+	1.03732i
$130$	−0.162864	−	0.344284i	−0.0142842	−	0.0301957i
$131$			2.05800i			0.179809i	0.995950	+	0.0899043i	$0.0286561\pi$
$131$			2.05800i			0.179809i	−0.995950	+	0.0899043i	$0.971344\pi$
$132$	4.69291	−	0.0164972i	0.408466	−	0.00143590i
$133$	6.26083	−	6.26083i	0.542883	−	0.542883i
$134$	−7.21428			−0.623219
$135$	−10.4501	+	5.07898i	−0.899399	+	0.437129i
$136$	1.20540			0.103362
$137$	9.93566	−	9.93566i	0.848861	−	0.848861i	−0.141130	−	0.989991i	$-0.545074\pi$
$137$	9.93566	−	9.93566i	0.848861	−	0.848861i	0.989991	+	0.141130i	$0.0450735\pi$
$138$	−14.7121	+	0.0517181i	−1.25238	+	0.00440254i
$139$		−	6.17825i		−	0.524032i	−0.965064	−	0.262016i	$-0.915613\pi$
$139$		−	6.17825i		−	0.524032i	0.965064	−	0.262016i	$-0.0843873\pi$
$140$	1.18297	−	3.30692i	0.0999789	−	0.279486i
$141$	−3.02548	+	3.04683i	−0.254792	+	0.256589i
$142$	11.1589	+	11.1589i	0.936430	+	0.936430i
$143$	0.326327	+	0.326327i	0.0272888	+	0.0272888i
$144$	−2.99993	+	0.0210918i	−0.249994	+	0.00175765i
$145$	18.9594	−	8.96879i	1.57449	−	0.744817i
$146$		−	5.51905i		−	0.456760i
$147$	−0.0276000	−	7.85130i	−0.00227641	−	0.647564i
$148$	4.37896	−	4.37896i	0.359948	−	0.359948i
$149$	−15.4668			−1.26709			−0.633544	−	0.773707i	$-0.718400\pi$
$149$	−15.4668			−1.26709			−0.633544	+	0.773707i	$0.718400\pi$
$150$	0.880381	+	8.61539i	0.0718828	+	0.703444i
$151$	−4.45159			−0.362265			−0.181132	−	0.983459i	$-0.557976\pi$
$151$	−4.45159			−0.362265			−0.181132	+	0.983459i	$0.557976\pi$
$152$	−3.98607	+	3.98607i	−0.323313	+	0.323313i
$153$	2.53900	−	2.57495i	0.205266	−	0.208172i
$154$			4.25570i			0.342934i
$155$	−2.02131	+	0.956187i	−0.162356	+	0.0768028i
$156$	−0.209339	−	0.207872i	−0.0167605	−	0.0166431i
$157$	5.72384	+	5.72384i	0.456812	+	0.456812i	0.897607	−	0.440796i	$-0.145304\pi$
$157$	5.72384	+	5.72384i	0.456812	+	0.456812i	−0.440796	+	0.897607i	$0.645304\pi$
$158$	5.55525	+	5.55525i	0.441952	+	0.441952i
$159$	0.100749	+	0.100043i	0.00798989	+	0.00793391i
$160$	−0.753158	+	2.10541i	−0.0595423	+	0.166447i
$161$		−	13.3415i		−	1.05146i
$162$	−6.27385	+	6.45281i	−0.492920	+	0.506981i
$163$	14.2135	−	14.2135i	1.11328	−	1.11328i	0.120581	−	0.992704i	$-0.461524\pi$
$163$	14.2135	−	14.2135i	1.11328	−	1.11328i	0.992704	−	0.120581i	$-0.0384756\pi$
$164$	12.3602			0.965173
$165$	−4.52065	−	9.47007i	−0.351932	−	0.737244i
$166$	−12.1706			−0.944622
$167$	−8.59228	+	8.59228i	−0.664891	+	0.664891i	−0.956529	−	0.291638i	$-0.905800\pi$
$167$	−8.59228	+	8.59228i	−0.664891	+	0.664891i	0.291638	+	0.956529i	$0.405800\pi$
$168$	−0.00956340	−	2.72047i	−0.000737833	−	0.209889i
$169$			12.9710i			0.997768i
$170$	−1.15259	−	2.43649i	−0.0883994	−	0.186870i
$171$	0.118898	+	16.9111i	0.00909235	+	1.29322i
$172$	6.77836	+	6.77836i	0.516845	+	0.516845i
$173$	−5.62788	−	5.62788i	−0.427879	−	0.427879i	0.460026	−	0.887905i	$-0.347840\pi$
$173$	−5.62788	−	5.62788i	−0.427879	−	0.427879i	−0.887905	+	0.460026i	$0.847840\pi$
$174$	11.4473	−	11.5281i	0.867820	−	0.873943i
$175$	−7.81545	+	0.770887i	−0.590793	+	0.0582736i
$176$		−	2.70947i		−	0.204234i
$177$	1.85063	−	0.00650558i	0.139101	−	0.000488990i
$178$	3.84648	−	3.84648i	0.288306	−	0.288306i
$179$	−22.3130			−1.66775			−0.833876	−	0.551952i	$-0.813883\pi$
$179$	−22.3130			−1.66775			−0.833876	+	0.551952i	$0.813883\pi$
$180$	2.91112	+	6.04362i	0.216982	+	0.450465i
$181$	−12.4142			−0.922742			−0.461371	−	0.887207i	$-0.652642\pi$
$181$	−12.4142			−0.922742			−0.461371	+	0.887207i	$0.652642\pi$
$182$	0.189171	−	0.189171i	0.0140223	−	0.0140223i
$183$	13.1113	−	0.0460909i	0.969219	−	0.00340714i
$184$			8.49409i			0.626193i
$185$	−13.0384	−	4.66414i	−0.958599	−	0.342915i
$186$	−1.22043	+	1.22904i	−0.0894864	+	0.0901178i
$187$	2.30941	+	2.30941i	0.168881	+	0.168881i
$188$	1.75294	+	1.75294i	0.127846	+	0.127846i
$189$	−5.83157	−	5.70985i	−0.424184	−	0.415331i
$190$	11.8685	+	4.24567i	0.861034	+	0.308013i
$191$		−	12.7221i		−	0.920537i	−0.887780	−	0.460268i	$-0.847753\pi$
$191$		−	12.7221i		−	0.920537i	0.887780	−	0.460268i	$-0.152247\pi$
$192$	0.00608872	+	1.73204i	0.000439415	+	0.124999i
$193$	8.41038	−	8.41038i	0.605393	−	0.605393i	−0.336346	−	0.941739i	$-0.609191\pi$
$193$	8.41038	−	8.41038i	0.605393	−	0.605393i	0.941739	+	0.336346i	$0.109191\pi$
$194$	4.20331			0.301780
$195$	−0.220008	+	0.621905i	−0.0157551	+	0.0445355i
$196$	−4.53298			−0.323784
$197$	−2.94410	+	2.94410i	−0.209759	+	0.209759i	−0.804165	−	0.594406i	$-0.797387\pi$
$197$	−2.94410	+	2.94410i	−0.209759	+	0.209759i	0.594406	+	0.804165i	$0.297387\pi$
$198$	−5.78792	−	5.70711i	−0.411330	−	0.405586i
$199$		−	14.6680i		−	1.03979i	−0.854231	−	0.519894i	$-0.825971\pi$
$199$		−	14.6680i		−	1.03979i	0.854231	−	0.519894i	$-0.174029\pi$
$200$	4.97585	−	0.490799i	0.351846	−	0.0347048i
$201$	8.86666	+	8.80454i	0.625406	+	0.621024i
$202$	8.42238	+	8.42238i	0.592597	+	0.592597i
$203$	10.4175	+	10.4175i	0.731163	+	0.731163i
$204$	−1.48149	−	1.47111i	−0.103725	−	0.102998i
$205$	−11.8187	−	24.9839i	−0.825455	−	1.74495i
$206$			6.71451i			0.467822i
$207$	18.1449	+	17.8916i	1.26116	+	1.24355i
$208$	−0.120439	+	0.120439i	−0.00835097	+	0.00835097i
$209$	−15.2737			−1.05651
$210$	−5.48979	+	2.62061i	−0.378831	+	0.180839i
$211$	18.9811			1.30671			0.653357	−	0.757050i	$-0.273360\pi$
$211$	18.9811			1.30671			0.653357	+	0.757050i	$0.273360\pi$
$212$	0.0579639	−	0.0579639i	0.00398098	−	0.00398098i
$213$	−0.0960861	−	27.3333i	−0.00658371	−	1.87285i
$214$		−	16.2494i		−	1.11079i
$215$	7.21980	−	20.1826i	0.492387	−	1.37644i
$216$	3.71278	+	3.63528i	0.252623	+	0.247350i
$217$	−1.11064	−	1.11064i	−0.0753949	−	0.0753949i
$218$	3.03160	+	3.03160i	0.205326	+	0.205326i
$219$	−6.73562	+	6.78314i	−0.455151	+	0.458362i
$220$	−5.47669	+	2.59076i	−0.369238	+	0.174669i
$221$		−	0.205312i		−	0.0138108i
$222$	−10.7262	+	0.0377061i	−0.719892	+	0.00253067i
$223$	6.20254	−	6.20254i	0.415352	−	0.415352i	−0.468246	−	0.883598i	$-0.655114\pi$
$223$	6.20254	−	6.20254i	0.415352	−	0.415352i	0.883598	+	0.468246i	$0.155114\pi$
$224$	−1.57068			−0.104945
$225$	9.43247	−	11.6631i	0.628831	−	0.777542i
$226$	−7.30063			−0.485631
$227$	19.9921	−	19.9921i	1.32692	−	1.32692i	0.418875	−	0.908044i	$-0.362424\pi$
$227$	19.9921	−	19.9921i	1.32692	−	1.32692i	0.908044	−	0.418875i	$-0.137576\pi$
$228$	9.76379	−	0.0343231i	0.646623	−	0.00227310i
$229$			4.09903i			0.270872i	0.990786	+	0.135436i	$0.0432435\pi$
$229$			4.09903i			0.270872i	−0.990786	+	0.135436i	$0.956757\pi$
$230$	17.1692	−	8.12194i	1.13210	−	0.535545i
$231$	5.19380	−	5.23044i	0.341727	−	0.344138i
$232$	−6.63248	−	6.63248i	−0.435443	−	0.435443i
$233$	−6.35559	−	6.35559i	−0.416369	−	0.416369i	0.467581	−	0.883950i	$-0.345126\pi$
$233$	−6.35559	−	6.35559i	−0.416369	−	0.416369i	−0.883950	+	0.467581i	$0.845126\pi$
$234$	0.00359250	+	0.510968i	0.000234849	+	0.0334030i
$235$	1.86710	−	5.21937i	0.121796	−	0.340474i
$236$		−	1.06847i		−	0.0695512i
$237$	−0.0478349	−	13.6074i	−0.00310721	−	0.883898i
$238$	1.33876	−	1.33876i	0.0867789	−	0.0867789i
$239$	20.9423			1.35465			0.677323	−	0.735686i	$-0.263140\pi$
$239$	20.9423			1.35465			0.677323	+	0.735686i	$0.263140\pi$
$240$	3.49517	−	1.66846i	0.225612	−	0.107699i
$241$	23.1603			1.49189			0.745944	−	0.666008i	$-0.231998\pi$
$241$	23.1603			1.49189			0.745944	+	0.666008i	$0.231998\pi$
$242$	−2.58714	+	2.58714i	−0.166307	+	0.166307i
$243$	15.5860	−	0.273979i	0.999846	−	0.0175757i
$244$		−	7.56989i		−	0.484612i
$245$	4.33437	+	9.16256i	0.276913	+	0.585375i
$246$	−15.1913	−	15.0848i	−0.968560	−	0.961774i
$247$	0.678936	+	0.678936i	0.0431997	+	0.0431997i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	14.9582	+	14.8534i	0.947937	+	0.941296i
$250$	−5.74991	−	9.58846i	−0.363656	−	0.606427i
$251$		−	30.2525i		−	1.90952i	−0.297373	−	0.954761i	$-0.596110\pi$
$251$		−	30.2525i		−	1.90952i	0.297373	−	0.954761i	$-0.403890\pi$
$252$	−3.30840	+	3.35525i	−0.208410	+	0.211361i
$253$	−16.2737	+	16.2737i	−1.02312	+	1.02312i
$254$	1.61959			0.101622
$255$	−1.55699	+	4.40120i	−0.0975025	+	0.275614i
$256$	1.00000			0.0625000
$257$	4.86596	−	4.86596i	0.303531	−	0.303531i	−0.538863	−	0.842393i	$-0.681146\pi$
$257$	4.86596	−	4.86596i	0.303531	−	0.303531i	0.842393	+	0.538863i	$0.181146\pi$
$258$	−0.0583667	−	16.6034i	−0.00363375	−	1.03368i
$259$		−	9.72686i		−	0.604398i
$260$	0.358608	+	0.128283i	0.0222399	+	0.00795578i
$261$	−28.1385	+	0.197836i	−1.74173	+	0.0122457i
$262$	−1.45523	−	1.45523i	−0.0899043	−	0.0899043i
$263$	16.9917	+	16.9917i	1.04775	+	1.04775i	0.998801	+	0.0489530i	$0.0155885\pi$
$263$	16.9917	+	16.9917i	1.04775	+	1.04775i	0.0489530	+	0.998801i	$0.484412\pi$
$264$	−3.30673	+	3.33006i	−0.203515	+	0.204951i
$265$	−0.172587	−	0.0617388i	−0.0106020	−	0.00379259i
$266$			8.85415i			0.542883i
$267$	−9.42186	+	0.0331211i	−0.576609	+	0.00202698i
$268$	5.10127	−	5.10127i	0.311609	−	0.311609i
$269$	−1.95810			−0.119387			−0.0596936	−	0.998217i	$-0.519012\pi$
$269$	−1.95810			−0.119387			−0.0596936	+	0.998217i	$0.519012\pi$
$270$	3.79793	−	10.9807i	0.231135	−	0.668264i
$271$	−5.58554			−0.339298			−0.169649	−	0.985505i	$-0.554263\pi$
$271$	−5.58554			−0.339298			−0.169649	+	0.985505i	$0.554263\pi$
$272$	−0.852346	+	0.852346i	−0.0516811	+	0.0516811i
$273$	−0.463370	+	0.00162891i	−0.0280444	+	9.85859e-5i
$274$			14.0512i			0.848861i
$275$	10.4735	+	8.59285i	0.631575	+	0.518168i
$276$	10.3665	−	10.4396i	0.623988	−	0.628390i
$277$	−4.89103	−	4.89103i	−0.293874	−	0.293874i	0.544735	−	0.838608i	$-0.316630\pi$
$277$	−4.89103	−	4.89103i	−0.293874	−	0.293874i	−0.838608	+	0.544735i	$0.816630\pi$
$278$	4.36868	+	4.36868i	0.262016	+	0.262016i
$279$	2.99993	−	0.0210918i	0.179601	−	0.00126273i
$280$	1.50186	+	3.17483i	0.0897533	+	0.189732i
$281$		−	4.05643i		−	0.241987i	−0.992653	−	0.120993i	$-0.961392\pi$
$281$		−	4.05643i		−	0.241987i	0.992653	−	0.120993i	$-0.0386080\pi$
$282$	−0.0150941	−	4.29377i	−0.000898840	−	0.255690i
$283$	7.09487	−	7.09487i	0.421746	−	0.421746i	−0.464058	−	0.885805i	$-0.653607\pi$
$283$	7.09487	−	7.09487i	0.421746	−	0.421746i	0.885805	+	0.464058i	$0.153607\pi$
$284$	−15.7810			−0.936430
$285$	−9.40539	−	19.7029i	−0.557127	−	1.16710i
$286$	−0.461496			−0.0272888
$287$	13.7277	−	13.7277i	0.810323	−	0.810323i
$288$	2.10635	−	2.13618i	0.124118	−	0.125876i
$289$			15.5470i			0.914530i
$290$	−7.06442	+	19.7482i	−0.414837	+	1.15965i
$291$	−5.16605	−	5.12986i	−0.302839	−	0.300718i
$292$	3.90256	+	3.90256i	0.228380	+	0.228380i
$293$	13.6690	+	13.6690i	0.798554	+	0.798554i	0.982867	−	0.184314i	$-0.0590063\pi$
$293$	13.6690	+	13.6690i	0.798554	+	0.798554i	−0.184314	+	0.982867i	$0.559006\pi$
$294$	5.57122	+	5.53219i	0.324920	+	0.322644i
$295$	−2.15970	+	1.02165i	−0.125743	+	0.0594829i
$296$			6.19279i			0.359948i
$297$	0.148472	+	14.0780i	0.00861524	+	0.816891i
$298$	10.9367	−	10.9367i	0.633544	−	0.633544i
$299$	1.44677			0.0836691
$300$	−6.71452	−	5.46948i	−0.387663	−	0.315780i
$301$	15.0566			0.867847
$302$	3.14775	−	3.14775i	0.181132	−	0.181132i
$303$	−0.0725230	−	20.6304i	−0.00416634	−	1.18519i
$304$		−	5.63716i		−	0.323313i
$305$	−15.3011	+	7.23823i	−0.876139	+	0.414460i
$306$	0.0254240	+	3.61611i	0.00145340	+	0.206719i
$307$	6.23253	+	6.23253i	0.355709	+	0.355709i	0.862229	−	0.506519i	$-0.169068\pi$
$307$	6.23253	+	6.23253i	0.355709	+	0.355709i	−0.506519	+	0.862229i	$0.669068\pi$
$308$	−3.00924	−	3.00924i	−0.171467	−	0.171467i
$309$	8.19460	−	8.25242i	0.466175	−	0.469464i
$310$	0.753158	−	2.10541i	0.0427765	−	0.119579i
$311$		−	30.1255i		−	1.70826i	−0.520061	−	0.854129i	$-0.674091\pi$
$311$		−	30.1255i		−	1.70826i	0.520061	−	0.854129i	$-0.325909\pi$
$312$	0.295013	−	0.00103707i	0.0167018	−	5.87127e-5i
$313$	−11.1395	+	11.1395i	−0.629641	+	0.629641i	−0.947978	−	0.318337i	$-0.896876\pi$
$313$	−11.1395	+	11.1395i	−0.629641	+	0.629641i	0.318337	+	0.947978i	$0.396876\pi$
$314$	−8.09473			−0.456812
$315$	9.94546	+	3.47906i	0.560363	+	0.196023i
$316$	−7.85631			−0.441952
$317$	−12.6989	+	12.6989i	−0.713244	+	0.713244i	−0.967212	−	0.253969i	$-0.918264\pi$
$317$	−12.6989	+	12.6989i	−0.713244	+	0.713244i	0.253969	+	0.967212i	$0.418264\pi$
$318$	−0.141981		0.000499112i	−0.00796190		2.79888e-5i
$319$		−	25.4141i		−	1.42292i
$320$	−0.956187	−	2.02131i	−0.0534525	−	0.112995i
$321$	−19.8313	+	19.9712i	−1.10687	+	1.11468i
$322$	9.43384	+	9.43384i	0.525728	+	0.525728i
$323$	4.80481	+	4.80481i	0.267347	+	0.267347i
$324$	−0.126548	−	8.99911i	−0.00703043	−	0.499951i
$325$	−0.0835964	−	0.847522i	−0.00463709	−	0.0470121i
$326$			20.1009i			1.11328i
$327$	−0.0261043	−	7.42582i	−0.00144357	−	0.410649i
$328$	−8.74002	+	8.74002i	−0.482587	+	0.482587i
$329$	3.89375			0.214669
$330$	9.89293	+	3.49977i	0.544588	+	0.192656i
$331$	−33.5872			−1.84612			−0.923060	−	0.384656i	$-0.874320\pi$
$331$	−33.5872			−1.84612			−0.923060	+	0.384656i	$0.874320\pi$
$332$	8.60592	−	8.60592i	0.472311	−	0.472311i
$333$	13.2289	+	13.0442i	0.724940	+	0.714818i
$334$		−	12.1513i		−	0.664891i
$335$	−15.1890	−	5.43349i	−0.829865	−	0.296863i
$336$	1.93043	+	1.91690i	0.105313	+	0.104576i
$337$	−4.79406	−	4.79406i	−0.261149	−	0.261149i	0.564372	−	0.825521i	$-0.309118\pi$
$337$	−4.79406	−	4.79406i	−0.261149	−	0.261149i	−0.825521	+	0.564372i	$0.809118\pi$
$338$	−9.17187	−	9.17187i	−0.498884	−	0.498884i
$339$	8.97279	+	8.90992i	0.487335	+	0.483921i
$340$	2.53786	+	0.907855i	0.137635	+	0.0492354i
$341$			2.70947i			0.146726i
$342$	−12.0420	−	11.8739i	−0.651157	−	0.642065i
$343$	−12.8089	+	12.8089i	−0.691618	+	0.691618i
$344$	−9.58605			−0.516845
$345$	−31.0140	−	10.9717i	−1.66974	−	0.590694i
$346$	7.95902			0.427879
$347$	16.6890	−	16.6890i	0.895910	−	0.895910i	−0.0991609	−	0.995071i	$-0.531616\pi$
$347$	16.6890	−	16.6890i	0.895910	−	0.895910i	0.995071	+	0.0991609i	$0.0316159\pi$
$348$	0.0571106	+	16.2461i	0.00306145	+	0.870882i
$349$			19.9193i			1.06626i	0.846034	+	0.533129i	$0.178984\pi$
$349$			19.9193i			1.06626i	−0.846034	+	0.533129i	$0.821016\pi$
$350$	4.98126	−	6.07146i	0.266260	−	0.324533i
$351$	0.619187	−	0.632386i	0.0330497	−	0.0337543i
$352$	1.91589	+	1.91589i	0.102117	+	0.102117i
$353$	−14.1451	−	14.1451i	−0.752867	−	0.752867i	0.222147	−	0.975013i	$-0.428694\pi$
$353$	−14.1451	−	14.1451i	−0.752867	−	0.752867i	−0.975013	+	0.222147i	$0.928694\pi$
$354$	−1.30399	+	1.31319i	−0.0693063	+	0.0697952i
$355$	15.0896	+	31.8983i	0.800872	+	1.69299i
$356$			5.43975i			0.288306i
$357$	−3.27926	+	0.0115277i	−0.173557	+	0.000610112i
$358$	15.7777	−	15.7777i	0.833876	−	0.833876i
$359$	−8.32324			−0.439284			−0.219642	−	0.975581i	$-0.570489\pi$
$359$	−8.32324			−0.439284			−0.219642	+	0.975581i	$0.570489\pi$
$360$	−6.33196	−	2.21501i	−0.333724	−	0.116741i
$361$	−12.7776			−0.672504
$362$	8.77818	−	8.77818i	0.461371	−	0.461371i
$363$	6.33712	−	0.0222772i	0.332613	−	0.00116925i
$364$			0.267529i			0.0140223i
$365$	4.15671	−	11.6199i	0.217572	−	0.608211i
$366$	−9.23853	+	9.30371i	−0.482906	+	0.486313i
$367$	1.16292	+	1.16292i	0.0607039	+	0.0607039i	0.736807	−	0.676103i	$-0.236333\pi$
$367$	1.16292	+	1.16292i	0.0607039	+	0.0607039i	−0.676103	+	0.736807i	$0.736333\pi$
$368$	−6.00623	−	6.00623i	−0.313096	−	0.313096i
$369$	0.260700	+	37.0798i	0.0135715	+	1.93030i
$370$	12.5176	−	5.92146i	0.650757	−	0.307842i
$371$		−	0.128754i		−	0.00668455i
$372$	−0.00608872	−	1.73204i	−0.000315685	−	0.0898021i
$373$	−4.28033	+	4.28033i	−0.221627	+	0.221627i	−0.809183	−	0.587556i	$-0.800090\pi$
$373$	−4.28033	+	4.28033i	−0.221627	+	0.221627i	0.587556	+	0.809183i	$0.300090\pi$
$374$	−3.26599			−0.168881
$375$	−4.63518	+	18.8020i	−0.239360	+	0.970931i
$376$	−2.47903			−0.127846
$377$	−1.12969	+	1.12969i	−0.0581820	+	0.0581820i
$378$	8.16102	−	0.0860692i	0.419758	−	0.00442692i
$379$			12.4876i			0.641444i	0.947173	+	0.320722i	$0.103926\pi$
$379$			12.4876i			0.641444i	−0.947173	+	0.320722i	$0.896074\pi$
$380$	−11.3945	+	5.39018i	−0.584524	+	0.276510i
$381$	−1.99055	−	1.97660i	−0.101979	−	0.101264i
$382$	8.99586	+	8.99586i	0.460268	+	0.460268i
$383$	−1.59874	−	1.59874i	−0.0816916	−	0.0816916i	0.665080	−	0.746772i	$-0.268397\pi$
$383$	−1.59874	−	1.59874i	−0.0816916	−	0.0816916i	−0.746772	+	0.665080i	$0.768397\pi$
$384$	−1.22904	−	1.22043i	−0.0627193	−	0.0622799i
$385$	−3.20521	+	8.96000i	−0.163353	+	0.456644i
$386$			11.8941i			0.605393i
$387$	−20.1916	+	20.4775i	−1.02640	+	1.04093i
$388$	−2.97219	+	2.97219i	−0.150890	+	0.150890i
$389$	−6.21736			−0.315233			−0.157616	−	0.987500i	$-0.550381\pi$
$389$	−6.21736			−0.315233			−0.157616	+	0.987500i	$0.550381\pi$
$390$	−0.284184	−	0.595322i	−0.0143902	−	0.0301453i
$391$	10.2388			0.517797
$392$	3.20530	−	3.20530i	0.161892	−	0.161892i
$393$	0.0125306	+	3.56454i	0.000632085	+	0.179807i
$394$		−	4.16359i		−	0.209759i
$395$	7.51210	+	15.8801i	0.377975	+	0.799013i
$396$	8.12821	−	0.0571477i	0.408458	−	0.00287178i
$397$	15.0580	+	15.0580i	0.755741	+	0.755741i	0.975544	−	0.219803i	$-0.0705416\pi$
$397$	15.0580	+	15.0580i	0.755741	+	0.755741i	−0.219803	+	0.975544i	$0.570542\pi$
$398$	10.3719	+	10.3719i	0.519894	+	0.519894i
$399$	10.8059	−	10.8821i	0.540971	−	0.544788i
$400$	−3.17141	+	3.86551i	−0.158571	+	0.193275i
$401$			3.70278i			0.184908i	0.995717	+	0.0924540i	$0.0294711\pi$
$401$			3.70278i			0.184908i	−0.995717	+	0.0924540i	$0.970529\pi$
$402$	−12.4954	+	0.0439257i	−0.623215	+	0.00219082i
$403$	0.120439	−	0.120439i	0.00599951	−	0.00599951i
$404$	−11.9110			−0.592597
$405$	−18.0690	+	8.86063i	−0.897857	+	0.440288i
$406$	−14.7325			−0.731163
$407$	−11.8647	+	11.8647i	−0.588110	+	0.588110i
$408$	2.08780	−	0.00733933i	0.103361	−	0.000363351i
$409$		−	11.8101i		−	0.583970i	−0.956423	−	0.291985i	$-0.905684\pi$
$409$		−	11.8101i		−	0.583970i	0.956423	−	0.291985i	$-0.0943157\pi$
$410$	26.0234	+	9.30922i	1.28520	+	0.459749i
$411$	17.1485	−	17.2695i	0.845872	−	0.851840i
$412$	−4.74787	−	4.74787i	−0.233911	−	0.233911i
$413$	−1.18668	−	1.18668i	−0.0583925	−	0.0583925i
$414$	−25.4817	+	0.179156i	−1.25235	+	0.00880503i
$415$	−25.6241	−	9.16638i	−1.25784	−	0.449960i
$416$		−	0.170327i		−	0.00835097i
$417$	−0.0376176	−	10.7010i	−0.00184214	−	0.524029i
$418$	10.8002	−	10.8002i	0.528253	−	0.528253i
$419$	4.51774			0.220706			0.110353	−	0.993892i	$-0.464802\pi$
$419$	4.51774			0.220706			0.110353	+	0.993892i	$0.464802\pi$
$420$	2.02881	−	5.73492i	0.0989958	−	0.279835i
$421$	−34.9059			−1.70121			−0.850604	−	0.525807i	$-0.823763\pi$
$421$	−34.9059			−1.70121			−0.850604	+	0.525807i	$0.823763\pi$
$422$	−13.4217	+	13.4217i	−0.653357	+	0.653357i
$423$	−5.22170	+	5.29565i	−0.253888	+	0.257483i
$424$			0.0819733i			0.00398098i
$425$	−0.591609	−	5.99789i	−0.0286973	−	0.290940i
$426$	19.3955	+	19.2596i	0.939716	+	0.933133i
$427$	−8.40739	−	8.40739i	−0.406862	−	0.406862i
$428$	11.4901	+	11.4901i	0.555393	+	0.555393i
$429$	0.567198	+	0.563225i	0.0273846	+	0.0271927i
$430$	9.16606	+	19.3764i	0.442026	+	0.934413i
$431$			7.18868i			0.346267i	0.984898	+	0.173133i	$0.0553892\pi$
$431$			7.18868i			0.346267i	−0.984898	+	0.173133i	$0.944611\pi$
$432$	−5.19586	+	0.0547976i	−0.249986	+	0.00263645i
$433$	−2.70121	+	2.70121i	−0.129812	+	0.129812i	−0.769028	−	0.639216i	$-0.779259\pi$
$433$	−2.70121	+	2.70121i	−0.129812	+	0.129812i	0.639216	+	0.769028i	$0.279259\pi$
$434$	1.57068			0.0753949
$435$	32.7838	−	15.6497i	1.57186	−	0.750347i
$436$	−4.28732			−0.205326
$437$	−33.8581	+	33.8581i	−1.61965	+	1.61965i
$438$	−0.0336039	−	9.55921i	−0.00160566	−	0.456757i
$439$			13.5187i			0.645211i	0.946533	+	0.322606i	$0.104559\pi$
$439$			13.5187i			0.645211i	−0.946533	+	0.322606i	$0.895441\pi$
$440$	2.04066	−	5.70455i	0.0972846	−	0.271954i
$441$	−0.0956087	−	13.5986i	−0.00455279	−	0.647552i
$442$	0.145177	+	0.145177i	0.00690539	+	0.00690539i
$443$	−5.99533	−	5.99533i	−0.284847	−	0.284847i	0.550192	−	0.835038i	$-0.314555\pi$
$443$	−5.99533	−	5.99533i	−0.284847	−	0.284847i	−0.835038	+	0.550192i	$0.814555\pi$
$444$	7.55787	−	7.61120i	0.358681	−	0.361212i
$445$	10.9954	−	5.20142i	0.521233	−	0.246571i
$446$			8.77171i			0.415352i
$447$	−26.7891	+	0.0941728i	−1.26708	+	0.00445422i
$448$	1.11064	−	1.11064i	0.0524726	−	0.0524726i
$449$	6.91133			0.326166			0.163083	−	0.986612i	$-0.447856\pi$
$449$	6.91133			0.326166			0.163083	+	0.986612i	$0.447856\pi$
$450$	1.57731	+	14.9168i	0.0743552	+	0.703187i
$451$	−33.4897			−1.57697
$452$	5.16233	−	5.16233i	0.242815	−	0.242815i
$453$	−7.71032	+	0.0271045i	−0.362263	+	0.00127348i
$454$			28.2730i			1.32692i
$455$	0.540759	−	0.255807i	0.0253512	−	0.0119924i
$456$	−6.87977	+	6.92831i	−0.322175	+	0.324448i
$457$	−7.97308	−	7.97308i	−0.372965	−	0.372965i	0.495591	−	0.868556i	$-0.334951\pi$
$457$	−7.97308	−	7.97308i	−0.372965	−	0.372965i	−0.868556	+	0.495591i	$0.834951\pi$
$458$	−2.89845	−	2.89845i	−0.135436	−	0.135436i
$459$	4.38197	−	4.47538i	0.204533	−	0.208893i
$460$	−6.39739	+	17.8836i	−0.298280	+	0.833825i
$461$		−	19.9386i		−	0.928632i	−0.885670	−	0.464316i	$-0.846300\pi$
$461$		−	19.9386i		−	0.928632i	0.885670	−	0.464316i	$-0.153700\pi$
$462$	0.0259118	+	7.37105i	0.00120552	+	0.342932i
$463$	5.79569	−	5.79569i	0.269348	−	0.269348i	−0.559489	−	0.828838i	$-0.689003\pi$
$463$	5.79569	−	5.79569i	0.269348	−	0.269348i	0.828838	+	0.559489i	$0.189003\pi$
$464$	9.37974			0.435443
$465$	−3.49517	+	1.66846i	−0.162085	+	0.0773731i
$466$	8.98817			0.416369
$467$	17.5385	−	17.5385i	0.811584	−	0.811584i	−0.173288	−	0.984871i	$-0.555439\pi$
$467$	17.5385	−	17.5385i	0.811584	−	0.811584i	0.984871	+	0.173288i	$0.0554390\pi$
$468$	−0.363849	−	0.358769i	−0.0168189	−	0.0165841i
$469$		−	11.3313i		−	0.523231i
$470$	2.37041	+	5.01089i	0.109339	+	0.231135i
$471$	9.94876	+	9.87906i	0.458415	+	0.455203i
$472$	0.755519	+	0.755519i	0.0347756	+	0.0347756i
$473$	−18.3658	−	18.3658i	−0.844459	−	0.844459i
$474$	9.65574	+	9.58809i	0.443503	+	0.440396i
$475$	21.7905	+	17.8778i	0.999816	+	0.820288i
$476$			1.89329i			0.0867789i
$477$	0.175110	+	0.172665i	0.00801773	+	0.00790578i
$478$	−14.8085	+	14.8085i	−0.677323	+	0.677323i
$479$	12.9831			0.593212			0.296606	−	0.955000i	$-0.404145\pi$
$479$	12.9831			0.593212			0.296606	+	0.955000i	$0.404145\pi$
$480$	−1.29168	+	3.65124i	−0.0589569	+	0.166656i
$481$	1.05480			0.0480947
$482$	−16.3768	+	16.3768i	−0.745944	+	0.745944i
$483$	−0.0812325	−	23.1080i	−0.00369620	−	1.05145i
$484$		−	3.65876i		−	0.166307i
$485$	8.84970	+	3.16576i	0.401844	+	0.143750i
$486$	−10.8273	+	11.2147i	−0.491135	+	0.508711i
$487$	−4.06854	−	4.06854i	−0.184363	−	0.184363i	0.608891	−	0.793254i	$-0.291615\pi$
$487$	−4.06854	−	4.06854i	−0.184363	−	0.184363i	−0.793254	+	0.608891i	$0.791615\pi$
$488$	5.35272	+	5.35272i	0.242306	+	0.242306i
$489$	24.5317	−	24.7048i	1.10936	−	1.11719i
$490$	−9.54378	−	3.41405i	−0.431144	−	0.154231i
$491$			40.3334i			1.82022i	0.414367	+	0.910110i	$0.364003\pi$
$491$			40.3334i			1.82022i	−0.414367	+	0.910110i	$0.635997\pi$
$492$	21.4084	−	0.0752581i	0.965167	−	0.00339290i
$493$	−7.99478	+	7.99478i	−0.360067	+	0.360067i
$494$	−0.960160			−0.0431997
$495$	−7.88761	−	16.3750i	−0.354522	−	0.736002i
$496$	−1.00000			−0.0449013
$497$	−17.5269	+	17.5269i	−0.786191	+	0.786191i
$498$	−21.0800	+	0.0741034i	−0.944616	+	0.00332065i
$499$			33.6843i			1.50791i	0.656924	+	0.753957i	$0.271857\pi$
$499$			33.6843i			1.50791i	−0.656924	+	0.753957i	$0.728143\pi$
$500$	10.8459	+	2.71427i	0.485042	+	0.121386i
$501$	−14.8299	+	14.9345i	−0.662549	+	0.667224i
$502$	21.3918	+	21.3918i	0.954761	+	0.954761i
$503$	24.9786	+	24.9786i	1.11374	+	1.11374i	0.992640	+	0.121099i	$0.0386419\pi$
$503$	24.9786	+	24.9786i	1.11374	+	1.11374i	0.121099	+	0.992640i	$0.461358\pi$
$504$	−0.0331284	−	4.71191i	−0.00147566	−	0.209885i
$505$	11.3892	+	24.0760i	0.506812	+	1.07137i
$506$		−	23.0145i		−	1.02312i
$507$	0.0789767	+	22.4663i	0.00350748	+	0.997762i
$508$	−1.14523	+	1.14523i	−0.0508112	+	0.0508112i
$509$	23.8231			1.05594			0.527970	−	0.849263i	$-0.322953\pi$
$509$	23.8231			1.05594			0.527970	+	0.849263i	$0.322953\pi$
$510$	−2.01116	−	4.21308i	−0.0890558	−	0.186558i
$511$	8.66864			0.383478
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.308903	+	29.2899i	0.0136384	+	1.29318i
$514$			6.88151i			0.303531i
$515$	−5.05708	+	14.1368i	−0.222842	+	0.622942i
$516$	11.7817	+	11.6991i	0.518659	+	0.515025i
$517$	−4.74953	−	4.74953i	−0.208884	−	0.208884i
$518$	6.87793	+	6.87793i	0.302199	+	0.302199i
$519$	−9.78197	−	9.71344i	−0.429381	−	0.426373i
$520$	−0.344284	+	0.162864i	−0.0150979	+	0.00714208i
$521$			21.7076i			0.951027i	0.879708	+	0.475514i	$0.157738\pi$
$521$			21.7076i			0.951027i	−0.879708	+	0.475514i	$0.842262\pi$
$522$	19.7570	−	20.0368i	0.864743	−	0.876988i
$523$	3.85110	−	3.85110i	0.168397	−	0.168397i	−0.617878	−	0.786274i	$-0.712007\pi$
$523$	3.85110	−	3.85110i	0.168397	−	0.168397i	0.786274	+	0.617878i	$0.212007\pi$
$524$	2.05800			0.0899043
$525$	−13.5320	+	1.38279i	−0.590584	+	0.0603500i
$526$	−24.0299			−1.04775
$527$	0.852346	−	0.852346i	0.0371288	−	0.0371288i
$528$	−0.0164972	−	4.69291i	−0.000717949	−	0.204233i
$529$			49.1496i			2.13694i
$530$	0.165694	−	0.0783818i	0.00719727	−	0.00340469i
$531$	3.20532	−	0.0225359i	0.139099	−	0.000977973i
$532$	−6.26083	−	6.26083i	−0.271442	−	0.271442i
$533$	1.48866	+	1.48866i	0.0644810	+	0.0644810i
$534$	6.63884	−	6.68568i	0.287291	−	0.289318i
$535$	12.2384	−	34.2117i	0.529110	−	1.47910i
$536$			7.21428i			0.311609i
$537$	−38.6470	+	0.135858i	−1.66774	+	0.00586269i
$538$	1.38458	−	1.38458i	0.0596936	−	0.0596936i
$539$	12.2820			0.529022
$540$	5.07898	+	10.4501i	0.218565	+	0.449699i
$541$	−29.0743			−1.25000			−0.625000	−	0.780625i	$-0.714901\pi$
$541$	−29.0743			−1.25000			−0.625000	+	0.780625i	$0.714901\pi$
$542$	3.94958	−	3.94958i	0.169649	−	0.169649i
$543$	−21.5019	+	0.0755867i	−0.922736	+	0.00324374i
$544$		−	1.20540i		−	0.0516811i
$545$	4.09948	+	8.66602i	0.175603	+	0.371212i
$546$	0.326500	−	0.328804i	0.0139729	−	0.0140715i
$547$	3.34876	+	3.34876i	0.143183	+	0.143183i	0.775065	−	0.631882i	$-0.217717\pi$
$547$	3.34876	+	3.34876i	0.143183	+	0.143183i	−0.631882	+	0.775065i	$0.717717\pi$
$548$	−9.93566	−	9.93566i	−0.424431	−	0.424431i
$549$	22.7091	−	0.159663i	0.969201	−	0.00681423i
$550$	−13.4819	+	1.32981i	−0.574872	+	0.0567032i
$551$		−	52.8751i		−	2.25256i
$552$	0.0517181	+	14.7121i	0.00220127	+	0.626189i
$553$	−8.72550	+	8.72550i	−0.371046	+	0.371046i
$554$	6.91697			0.293874
$555$	−22.6114	−	7.99910i	−0.959799	−	0.339543i
$556$	−6.17825			−0.262016
$557$	30.4377	−	30.4377i	1.28969	−	1.28969i	0.354709	−	0.934977i	$-0.384580\pi$
$557$	30.4377	−	30.4377i	1.28969	−	1.28969i	0.934977	−	0.354709i	$-0.115420\pi$
$558$	−2.10635	+	2.13618i	−0.0891691	+	0.0904318i
$559$			1.63276i			0.0690585i
$560$	−3.30692	−	1.18297i	−0.139743	−	0.0499895i
$561$	4.01405	+	3.98592i	0.169473	+	0.168286i
$562$	2.86833	+	2.86833i	0.120993	+	0.120993i
$563$	−8.90858	−	8.90858i	−0.375452	−	0.375452i	0.494006	−	0.869458i	$-0.335532\pi$
$563$	−8.90858	−	8.90858i	−0.375452	−	0.375452i	−0.869458	+	0.494006i	$0.835532\pi$
$564$	3.04683	+	3.02548i	0.128295	+	0.127396i
$565$	−15.3708	−	5.49853i	−0.646656	−	0.231325i
$566$			10.0337i			0.421746i
$567$	−10.1353	−	9.85419i	−0.425642	−	0.413837i
$568$	11.1589	−	11.1589i	0.468215	−	0.468215i
$569$	−0.145735			−0.00610954			−0.00305477	−	0.999995i	$-0.500972\pi$
$569$	−0.145735			−0.00610954			−0.00305477	+	0.999995i	$0.500972\pi$
$570$	20.5826	+	7.28141i	0.862112	+	0.304985i
$571$	34.5504			1.44589			0.722946	−	0.690905i	$-0.242788\pi$
$571$	34.5504			1.44589			0.722946	+	0.690905i	$0.242788\pi$
$572$	0.326327	−	0.326327i	0.0136444	−	0.0136444i
$573$	−0.0774611	−	22.0351i	−0.00323598	−	0.920531i
$574$			19.4139i			0.810323i
$575$	42.2654	−	4.16890i	1.76259	−	0.173855i
$576$	0.0210918	+	2.99993i	0.000878825	+	0.124997i
$577$	20.0214	+	20.0214i	0.833502	+	0.833502i	0.987994	−	0.154492i	$-0.0493740\pi$
$577$	20.0214	+	20.0214i	0.833502	+	0.833502i	−0.154492	+	0.987994i	$0.549374\pi$
$578$	−10.9934	−	10.9934i	−0.457265	−	0.457265i
$579$	14.5159	−	14.6183i	0.603261	−	0.607517i
$580$	−8.96879	−	18.9594i	−0.372409	−	0.787246i
$581$		−	19.1161i		−	0.793068i
$582$	7.28031	−	0.0255928i	0.301779	−	0.00106086i
$583$	−0.157051	+	0.157051i	−0.00650441	+	0.00650441i
$584$	−5.51905			−0.228380
$585$	−0.377276	+	1.07850i	−0.0155984	+	0.0445906i
$586$	−19.3309			−0.798554
$587$	−0.473651	+	0.473651i	−0.0195497	+	0.0195497i	−0.716814	−	0.697264i	$-0.754400\pi$
$587$	−0.473651	+	0.473651i	−0.0195497	+	0.0195497i	0.697264	+	0.716814i	$0.254400\pi$
$588$	−7.85130	+	0.0276000i	−0.323782	+	0.00113821i
$589$			5.63716i			0.232275i
$590$	0.804723	−	2.24956i	0.0331299	−	0.0926129i
$591$	−5.08138	+	5.11723i	−0.209020	+	0.210495i
$592$	−4.37896	−	4.37896i	−0.179974	−	0.179974i
$593$	−20.6378	−	20.6378i	−0.847492	−	0.847492i	0.142328	−	0.989820i	$-0.454541\pi$
$593$	−20.6378	−	20.6378i	−0.847492	−	0.847492i	−0.989820	+	0.142328i	$0.954541\pi$
$594$	−10.0597	−	9.84970i	−0.412753	−	0.404138i
$595$	3.82693	−	1.81034i	0.156889	−	0.0742167i
$596$			15.4668i			0.633544i
$597$	−0.0893094	−	25.4056i	−0.00365519	−	1.03978i
$598$	−1.02302	+	1.02302i	−0.0418345	+	0.0418345i
$599$	−5.59941			−0.228786			−0.114393	−	0.993436i	$-0.536492\pi$
$599$	−5.59941			−0.228786			−0.114393	+	0.993436i	$0.536492\pi$
$600$	8.61539	−	0.880381i	0.351722	−	0.0359414i
$601$	−27.3476			−1.11553			−0.557766	−	0.829998i	$-0.688341\pi$
$601$	−27.3476			−1.11553			−0.557766	+	0.829998i	$0.688341\pi$
$602$	−10.6466	+	10.6466i	−0.433923	+	0.433923i
$603$	15.4110	+	15.1958i	0.627585	+	0.618822i
$604$			4.45159i			0.181132i
$605$	−7.39551	+	3.49846i	−0.300670	+	0.142233i
$606$	14.6392	+	14.5366i	0.594676	+	0.590510i
$607$	6.88434	+	6.88434i	0.279427	+	0.279427i	0.832880	−	0.553453i	$-0.186690\pi$
$607$	6.88434	+	6.88434i	0.279427	+	0.279427i	−0.553453	+	0.832880i	$0.686690\pi$
$608$	3.98607	+	3.98607i	0.161657	+	0.161657i
$609$	18.1069	+	17.9801i	0.733729	+	0.728589i
$610$	5.70132	−	15.9377i	0.230840	−	0.645299i
$611$			0.422245i			0.0170822i
$612$	−2.57495	−	2.53900i	−0.104086	−	0.102633i
$613$	−13.6123	+	13.6123i	−0.549794	+	0.549794i	−0.926381	−	0.376587i	$-0.877098\pi$
$613$	−13.6123	+	13.6123i	−0.549794	+	0.549794i	0.376587	+	0.926381i	$0.377098\pi$
$614$	−8.81412			−0.355709
$615$	−20.6226	−	43.2012i	−0.831584	−	1.74204i
$616$	4.25570			0.171467
$617$	−7.85935	+	7.85935i	−0.316406	+	0.316406i	−0.847385	−	0.530979i	$-0.821824\pi$
$617$	−7.85935	+	7.85935i	−0.316406	+	0.316406i	0.530979	+	0.847385i	$0.321824\pi$
$618$	0.0408827	+	11.6298i	0.00164455	+	0.467819i
$619$		−	17.0857i		−	0.686733i	−0.939202	−	0.343366i	$-0.888433\pi$
$619$		−	17.0857i		−	0.686733i	0.939202	−	0.343366i	$-0.111567\pi$
$620$	0.956187	+	2.02131i	0.0384014	+	0.0811779i
$621$	31.5367	+	30.8784i	1.26552	+	1.23911i
$622$	21.3019	+	21.3019i	0.854129	+	0.854129i
$623$	6.04158	+	6.04158i	0.242051	+	0.242051i
$624$	−0.207872	+	0.209339i	−0.00832156	+	0.00838027i
$625$	−4.88429	−	24.5182i	−0.195372	−	0.980729i
$626$		−	15.7536i		−	0.629641i
$627$	−26.4547	+	0.0929974i	−1.05650	+	0.00371396i
$628$	5.72384	−	5.72384i	0.228406	−	0.228406i
$629$	7.46478			0.297640
$630$	−9.49257	+	4.57243i	−0.378193	+	0.182170i
$631$	25.6532			1.02124			0.510619	−	0.859807i	$-0.329416\pi$
$631$	25.6532			1.02124			0.510619	+	0.859807i	$0.329416\pi$
$632$	5.55525	−	5.55525i	0.220976	−	0.220976i
$633$	32.8761	−	0.115571i	1.30671	−	0.00459352i
$634$		−	17.9590i		−	0.713244i
$635$	3.40991	+	1.21981i	0.135318	+	0.0484066i
$636$	0.100043	−	0.100749i	0.00396696	−	0.00399495i
$637$	−0.545949	−	0.545949i	−0.0216313	−	0.0216313i
$638$	17.9705	+	17.9705i	0.711459	+	0.711459i
$639$	−0.332850	−	47.3418i	−0.0131673	−	1.87281i
$640$	2.10541	+	0.753158i	0.0832237	+	0.0297712i
$641$		−	16.1733i		−	0.638807i	−0.947619	−	0.319404i	$-0.896517\pi$
$641$		−	16.1733i		−	0.638807i	0.947619	−	0.319404i	$-0.103483\pi$
$642$	−0.0989380	−	28.1446i	−0.00390477	−	1.11078i
$643$	−17.2738	+	17.2738i	−0.681213	+	0.681213i	−0.960274	−	0.279060i	$-0.909977\pi$
$643$	−17.2738	+	17.2738i	−0.681213	+	0.681213i	0.279060	+	0.960274i	$0.409977\pi$
$644$	−13.3415			−0.525728
$645$	12.3821	−	35.0010i	0.487545	−	1.37816i
$646$	−6.79503			−0.267347
$647$	27.3602	−	27.3602i	1.07564	−	1.07564i	0.0787470	−	0.996895i	$-0.474908\pi$
$647$	27.3602	−	27.3602i	1.07564	−	1.07564i	0.996895	−	0.0787470i	$-0.0250919\pi$
$648$	6.45281	+	6.27385i	0.253490	+	0.246460i
$649$			2.89498i			0.113638i
$650$	0.658400	+	0.540177i	0.0258246	+	0.0211875i
$651$	−1.93043	−	1.91690i	−0.0756594	−	0.0751294i
$652$	−14.2135	−	14.2135i	−0.556642	−	0.556642i
$653$	−28.0015	−	28.0015i	−1.09578	−	1.09578i	−0.994898	−	0.100884i	$-0.967833\pi$
$653$	−28.0015	−	28.0015i	−1.09578	−	1.09578i	−0.100884	−	0.994898i	$-0.532167\pi$
$654$	5.26930	+	5.23239i	0.206046	+	0.204603i
$655$	−1.96784	−	4.15987i	−0.0768897	−	0.162539i
$656$		−	12.3602i		−	0.482587i
$657$	−11.6251	+	11.7897i	−0.453537	+	0.459960i
$658$	−2.75329	+	2.75329i	−0.107335	+	0.107335i
$659$	−25.8325			−1.00629			−0.503145	−	0.864202i	$-0.667824\pi$
$659$	−25.8325			−1.00629			−0.503145	+	0.864202i	$0.667824\pi$
$660$	−9.47007	+	4.52065i	−0.368622	+	0.175966i
$661$	9.74125			0.378891			0.189445	−	0.981891i	$-0.439331\pi$
$661$	9.74125			0.378891			0.189445	+	0.981891i	$0.439331\pi$
$662$	23.7497	−	23.7497i	0.923060	−	0.923060i
$663$	−0.00125009	−	0.355609i	−4.85493e−5	−	0.0138107i
$664$			12.1706i			0.472311i
$665$	−6.66857	+	18.6416i	−0.258596	+	0.722891i
$666$	−18.5779	+	0.130617i	−0.719879	+	0.00506131i
$667$	−56.3369	−	56.3369i	−2.18137	−	2.18137i
$668$	8.59228	+	8.59228i	0.332445	+	0.332445i
$669$	10.7053	−	10.7808i	0.413890	−	0.416810i
$670$	14.5823	−	6.89820i	0.563364	−	0.266501i
$671$			20.5104i			0.791795i
$672$	−2.72047	+	0.00956340i	−0.104945	+	0.000368916i
$673$	−28.8522	+	28.8522i	−1.11217	+	1.11217i	−0.119314	+	0.992857i	$0.538070\pi$
$673$	−28.8522	+	28.8522i	−1.11217	+	1.11217i	−0.992857	+	0.119314i	$0.961930\pi$
$674$	6.77982			0.261149
$675$	16.2664	−	20.2584i	0.626094	−	0.779747i
$676$	12.9710			0.498884
$677$	−15.0187	+	15.0187i	−0.577215	+	0.577215i	−0.934135	−	0.356920i	$-0.883827\pi$
$677$	−15.0187	+	15.0187i	−0.577215	+	0.577215i	0.356920	+	0.934135i	$0.383827\pi$
$678$	−12.6450	+	0.0444515i	−0.485628	+	0.00170715i
$679$			6.60205i			0.253363i
$680$	−2.43649	+	1.15259i	−0.0934351	+	0.0441997i
$681$	34.5053	−	34.7488i	1.32225	−	1.33158i
$682$	−1.91589	−	1.91589i	−0.0733631	−	0.0733631i
$683$	9.36926	+	9.36926i	0.358505	+	0.358505i	0.863262	−	0.504757i	$-0.168418\pi$
$683$	9.36926	+	9.36926i	0.358505	+	0.358505i	−0.504757	+	0.863262i	$0.668418\pi$
$684$	16.9111	−	0.118898i	0.646611	−	0.00454618i
$685$	−10.5827	+	29.5834i	−0.404345	+	1.13033i
$686$		−	18.1146i		−	0.691618i
$687$	0.0249579	+	7.09969i	0.000952202	+	0.270870i
$688$	6.77836	−	6.77836i	0.258423	−	0.258423i
$689$	0.0139623			0.000531920
$690$	29.6883	−	14.1721i	1.13022	−	0.539522i
$691$	13.5136			0.514081			0.257040	−	0.966401i	$-0.417253\pi$
$691$	13.5136			0.514081			0.257040	+	0.966401i	$0.417253\pi$
$692$	−5.62788	+	5.62788i	−0.213940	+	0.213940i
$693$	8.96402	−	9.09096i	0.340515	−	0.345337i
$694$			23.6018i			0.895910i
$695$	5.90756	+	12.4882i	0.224087	+	0.473703i
$696$	−11.5281	−	11.4473i	−0.436972	−	0.433910i
$697$	10.5352	+	10.5352i	0.399049	+	0.399049i
$698$	−14.0851	−	14.0851i	−0.533129	−	0.533129i
$699$	−11.0468	−	10.9694i	−0.417830	−	0.414903i
$700$	0.770887	+	7.81545i	0.0291368	+	0.295396i
$701$			13.1874i			0.498083i	0.968493	+	0.249041i	$0.0801155\pi$
$701$			13.1874i			0.498083i	−0.968493	+	0.249041i	$0.919884\pi$
$702$	0.00933350	+	0.884996i	0.000352270	+	0.0334020i
$703$	−24.6849	+	24.6849i	−0.931009	+	0.931009i
$704$	−2.70947			−0.102117
$705$	3.20211	−	9.05152i	0.120598	−	0.340900i
$706$	20.0042			0.752867
$707$	−13.2288	+	13.2288i	−0.497522	+	0.497522i
$708$	−0.00650558	−	1.85063i	−0.000244495	−	0.0695507i
$709$		−	31.6160i		−	1.18736i	−0.804700	−	0.593681i	$-0.797674\pi$
$709$		−	31.6160i		−	1.18736i	0.804700	−	0.593681i	$-0.202326\pi$
$710$	−33.2255	−	11.8856i	−1.24693	−	0.446058i
$711$	−0.165704	−	23.5683i	−0.00621438	−	0.883882i
$712$	−3.84648	−	3.84648i	−0.144153	−	0.144153i
$713$	6.00623	+	6.00623i	0.224935	+	0.224935i
$714$	2.31063	−	2.32694i	0.0864733	−	0.0870834i
$715$	−0.971639	−	0.347579i	−0.0363372	−	0.0129987i
$716$			22.3130i			0.833876i
$717$	36.2729	−	0.127512i	1.35464	−	0.00476202i
$718$	5.88542	−	5.88542i	0.219642	−	0.219642i
$719$	−13.1043			−0.488708			−0.244354	−	0.969686i	$-0.578576\pi$
$719$	−13.1043			−0.488708			−0.244354	+	0.969686i	$0.578576\pi$
$720$	6.04362	−	2.91112i	0.225232	−	0.108491i
$721$	−10.5463			−0.392765
$722$	9.03512	−	9.03512i	0.336252	−	0.336252i
$723$	40.1146	−	0.141017i	1.49188	−	0.00524447i
$724$			12.4142i			0.461371i
$725$	−29.7470	+	36.2575i	−1.10478	+	1.34657i
$726$	−4.46527	+	4.49678i	−0.165722	+	0.166891i
$727$	0.608842	+	0.608842i	0.0225807	+	0.0225807i	0.718307	−	0.695726i	$-0.244917\pi$
$727$	0.608842	+	0.608842i	0.0225807	+	0.0225807i	−0.695726	+	0.718307i	$0.744917\pi$
$728$	−0.189171	−	0.189171i	−0.00701115	−	0.00701115i
$729$	26.9940	−	0.569441i	0.999778	−	0.0210904i
$730$	5.27724	+	11.1557i	0.195319	+	0.412892i
$731$			11.5550i			0.427378i
$732$	−0.0460909	−	13.1113i	−0.00170357	−	0.484609i
$733$	−16.4184	+	16.4184i	−0.606426	+	0.606426i	−0.942010	−	0.335584i	$-0.891066\pi$
$733$	−16.4184	+	16.4184i	−0.606426	+	0.606426i	0.335584	+	0.942010i	$0.391066\pi$
$734$	−1.64462			−0.0607039
$735$	7.56310	+	15.8435i	0.278969	+	0.584398i
$736$	8.49409			0.313096
$737$	−13.8217	+	13.8217i	−0.509130	+	0.509130i
$738$	−26.4037	−	26.0351i	−0.971935	−	0.958364i
$739$		−	35.9006i		−	1.32062i	−0.750991	−	0.660312i	$-0.770424\pi$
$739$		−	35.9006i		−	1.32062i	0.750991	−	0.660312i	$-0.229576\pi$
$740$	−4.66414	+	13.0384i	−0.171457	+	0.479300i
$741$	1.18008	+	1.17181i	0.0433513	+	0.0430475i
$742$	0.0910425	+	0.0910425i	0.00334227	+	0.00334227i
$743$	−1.93927	−	1.93927i	−0.0711450	−	0.0711450i	0.670639	−	0.741784i	$-0.266020\pi$
$743$	−1.93927	−	1.93927i	−0.0711450	−	0.0711450i	−0.741784	+	0.670639i	$0.766020\pi$
$744$	1.22904	+	1.22043i	0.0450589	+	0.0447432i
$745$	31.2632	−	14.7891i	1.14539	−	0.541832i
$746$		−	6.05331i		−	0.221627i
$747$	25.9986	+	25.6356i	0.951240	+	0.937957i
$748$	2.30941	−	2.30941i	0.0844403	−	0.0844403i
$749$	25.5225			0.932573
$750$	−10.0175	−	16.5726i	−0.365786	−	0.605145i
$751$	−3.28109			−0.119729			−0.0598643	−	0.998207i	$-0.519067\pi$
$751$	−3.28109			−0.119729			−0.0598643	+	0.998207i	$0.519067\pi$
$752$	1.75294	−	1.75294i	0.0639230	−	0.0639230i
$753$	−0.184199	−	52.3986i	−0.00671259	−	1.90951i
$754$		−	1.59762i		−	0.0581820i
$755$	8.99805	−	4.25655i	0.327472	−	0.154912i
$756$	−5.70985	+	5.83157i	−0.207665	+	0.212092i
$757$	−13.7472	−	13.7472i	−0.499650	−	0.499650i	0.411679	−	0.911329i	$-0.364942\pi$
$757$	−13.7472	−	13.7472i	−0.499650	−	0.499650i	−0.911329	+	0.411679i	$0.864942\pi$
$758$	−8.83005	−	8.83005i	−0.320722	−	0.320722i
$759$	−28.0876	+	28.2858i	−1.01952	+	1.02671i
$760$	4.24567	−	11.8685i	0.154007	−	0.430517i
$761$		−	11.9167i		−	0.431981i	−0.976395	−	0.215991i	$-0.930702\pi$
$761$		−	11.9167i		−	0.431981i	0.976395	−	0.215991i	$-0.0692981\pi$
$762$	2.80520	−	0.00986125i	0.101622	−	0.000357235i
$763$	−4.76166	+	4.76166i	−0.172384	+	0.172384i
$764$	−12.7221			−0.460268
$765$	−2.66997	+	7.63254i	−0.0965330	+	0.275955i
$766$	2.26095			0.0816916
$767$	0.128685	−	0.128685i	0.00464656	−	0.00464656i
$768$	1.73204	−	0.00608872i	0.0624996	−	0.000219708i
$769$		−	6.78944i		−	0.244834i	−0.992479	−	0.122417i	$-0.960936\pi$
$769$		−	6.78944i		−	0.244834i	0.992479	−	0.122417i	$-0.0390645\pi$
$770$	−4.06925	−	8.60211i	−0.146646	−	0.309998i
$771$	8.39842	−	8.45767i	0.302462	−	0.304596i
$772$	−8.41038	−	8.41038i	−0.302696	−	0.302696i
$773$	2.30473	+	2.30473i	0.0828952	+	0.0828952i	0.747339	−	0.664443i	$-0.231331\pi$
$773$	2.30473	+	2.30473i	0.0828952	+	0.0828952i	−0.664443	+	0.747339i	$0.731331\pi$
$774$	−0.202187	−	28.7574i	−0.00726746	−	1.03366i
$775$	3.17141	−	3.86551i	0.113920	−	0.138853i
$776$		−	4.20331i		−	0.150890i
$777$	−0.0592241	−	16.8473i	−0.00212465	−	0.604394i
$778$	4.39634	−	4.39634i	0.157616	−	0.157616i
$779$	−69.6767			−2.49643
$780$	0.621905	+	0.220008i	0.0222678	+	0.00787755i
$781$	42.7582			1.53001
$782$	−7.23990	+	7.23990i	−0.258898	+	0.258898i
$783$	−48.7358	+	0.513987i	−1.74168	+	0.0183684i
$784$			4.53298i			0.161892i
$785$	−17.0427	−	6.09660i	−0.608281	−	0.217597i
$786$	−2.52937	−	2.51165i	−0.0902198	−	0.0895877i
$787$	38.2415	+	38.2415i	1.36316	+	1.36316i	0.869856	+	0.493305i	$0.164211\pi$
$787$	38.2415	+	38.2415i	1.36316	+	1.36316i	0.493305	+	0.869856i	$0.335789\pi$
$788$	2.94410	+	2.94410i	0.104879	+	0.104879i
$789$	29.5338	+	29.3269i	1.05143	+	1.04406i
$790$	−16.5408	−	5.91704i	−0.588494	−	0.210519i
$791$		−	11.4669i		−	0.407717i
$792$	−5.70711	+	5.78792i	−0.202793	+	0.205665i
$793$	0.911712	−	0.911712i	0.0323759	−	0.0323759i
$794$	−21.2953			−0.755741
$795$	−0.299304	−	0.105883i	−0.0106152	−	0.00375529i
$796$	−14.6680			−0.519894
$797$	26.9645	−	26.9645i	0.955132	−	0.955132i	−0.0439037	−	0.999036i	$-0.513979\pi$
$797$	26.9645	−	26.9645i	0.955132	−	0.955132i	0.999036	+	0.0439037i	$0.0139795\pi$
$798$	0.0539105	+	15.3358i	0.00190841	+	0.542880i
$799$			2.98821i			0.105715i
$800$	−0.490799	−	4.97585i	−0.0173524	−	0.175923i
$801$	−16.3188	+	0.114734i	−0.576598	+	0.00405393i
$802$	−2.61826	−	2.61826i	−0.0924540	−	0.0924540i
$803$	−10.5739	−	10.5739i	−0.373144	−	0.373144i
$804$	8.80454	−	8.86666i	0.310512	−	0.312703i
$805$	12.7569	+	26.9673i	0.449623	+	0.950472i
$806$			0.170327i			0.00599951i
$807$	−3.39150	+	0.0119223i	−0.119386	+	0.000419684i
$808$	8.42238	−	8.42238i	0.296298	−	0.296298i
$809$	10.1513			0.356900			0.178450	−	0.983949i	$-0.442892\pi$
$809$	10.1513			0.356900			0.178450	+	0.983949i	$0.442892\pi$
$810$	6.51131	−	19.0421i	0.228784	−	0.669072i
$811$	38.3970			1.34830			0.674151	−	0.738594i	$-0.264510\pi$
$811$	38.3970			1.34830			0.674151	+	0.738594i	$0.264510\pi$
$812$	10.4175	−	10.4175i	0.365582	−	0.365582i
$813$	−9.67439	+	0.0340088i	−0.339296	+	0.00119274i
$814$		−	16.7792i		−	0.588110i
$815$	−15.1391	+	42.3206i	−0.530300	+	1.48243i
$816$	−1.47111	+	1.48149i	−0.0514991	+	0.0518624i
$817$	−38.2107	−	38.2107i	−1.33682	−	1.33682i
$818$	8.35097	+	8.35097i	0.291985	+	0.291985i
$819$	−0.802566	+	0.00564266i	−0.0280439	+	0.000197170i
$820$	−24.9839	+	11.8187i	−0.872477	+	0.412727i
$821$		−	0.682885i		−	0.0238329i	−0.999929	−	0.0119164i	$-0.996207\pi$
$821$		−	0.682885i		−	0.0238329i	0.999929	−	0.0119164i	$-0.00379321\pi$
$822$	0.0855535	+	24.3372i	0.00298402	+	0.848856i
$823$	−4.32786	+	4.32786i	−0.150860	+	0.150860i	−0.778502	−	0.627642i	$-0.784020\pi$
$823$	−4.32786	+	4.32786i	−0.150860	+	0.150860i	0.627642	+	0.778502i	$0.284020\pi$
$824$	6.71451			0.233911
$825$	18.1928	+	14.8194i	0.633392	+	0.515945i
$826$	1.67821			0.0583925
$827$	−12.3055	+	12.3055i	−0.427903	+	0.427903i	−0.887914	−	0.460010i	$-0.847846\pi$
$827$	−12.3055	+	12.3055i	−0.427903	+	0.427903i	0.460010	+	0.887914i	$0.347846\pi$
$828$	17.8916	−	18.1449i	0.621775	−	0.630580i
$829$			48.9864i			1.70137i	0.525678	+	0.850684i	$0.323812\pi$
$829$			48.9864i			1.70137i	−0.525678	+	0.850684i	$0.676188\pi$
$830$	24.6006	−	11.6374i	0.853899	−	0.403939i
$831$	−8.50125	−	8.44169i	−0.294905	−	0.292839i
$832$	0.120439	+	0.120439i	0.00417548	+	0.00417548i
$833$	−3.86366	−	3.86366i	−0.133868	−	0.133868i
$834$	7.59333	+	7.54013i	0.262936	+	0.261093i
$835$	9.15186	−	25.5835i	0.316713	−	0.885354i
$836$			15.2737i			0.528253i
$837$	5.19586	−	0.0547976i	0.179595	−	0.00189408i
$838$	−3.19452	+	3.19452i	−0.110353	+	0.110353i
$839$	20.1390			0.695274			0.347637	−	0.937629i	$-0.386984\pi$
$839$	20.1390			0.695274			0.347637	+	0.937629i	$0.386984\pi$
$840$	2.62061	+	5.48979i	0.0904197	+	0.189416i
$841$	58.9795			2.03378
$842$	24.6822	−	24.6822i	0.850604	−	0.850604i
$843$	−0.0246985	−	7.02591i	−0.000850661	−	0.241985i
$844$		−	18.9811i		−	0.653357i
$845$	−12.4027	−	26.2184i	−0.426666	−	0.901941i
$846$	−0.0522871	−	7.43689i	−0.00179767	−	0.255686i
$847$	−4.06355	−	4.06355i	−0.139625	−	0.139625i
$848$	−0.0579639	−	0.0579639i	−0.00199049	−	0.00199049i
$849$	12.2454	−	12.3318i	0.420261	−	0.423226i
$850$	4.65948	+	3.82282i	0.159819	+	0.131122i
$851$			52.6021i			1.80318i
$852$	−27.3333	+	0.0960861i	−0.936424	+	0.00329185i
$853$	11.7571	−	11.7571i	0.402557	−	0.402557i	−0.476576	−	0.879133i	$-0.658122\pi$
$853$	11.7571	−	11.7571i	0.402557	−	0.402557i	0.879133	+	0.476576i	$0.158122\pi$
$854$	11.8898			0.406862
$855$	−16.4105	−	34.0689i	−0.561226	−	1.16513i
$856$	−16.2494			−0.555393
$857$	−28.6796	+	28.6796i	−0.979676	+	0.979676i	−0.999798	−	0.0201218i	$-0.993595\pi$
$857$	−28.6796	+	28.6796i	−0.979676	+	0.979676i	0.0201218	+	0.999798i	$0.493595\pi$
$858$	−0.799330	+	0.00280992i	−0.0272887	+	9.59291e-5i
$859$		−	21.3434i		−	0.728226i	−0.931355	−	0.364113i	$-0.881372\pi$
$859$		−	21.3434i		−	0.728226i	0.931355	−	0.364113i	$-0.118628\pi$
$860$	−20.1826	−	7.21980i	−0.688220	−	0.246193i
$861$	23.6934	−	23.8606i	0.807469	−	0.813166i
$862$	−5.08317	−	5.08317i	−0.173133	−	0.173133i
$863$	24.1749	+	24.1749i	0.822923	+	0.822923i	0.986526	−	0.163603i	$-0.0523118\pi$
$863$	24.1749	+	24.1749i	0.822923	+	0.822923i	−0.163603	+	0.986526i	$0.552312\pi$
$864$	3.63528	−	3.71278i	0.123675	−	0.126311i
$865$	16.7570	+	5.99439i	0.569755	+	0.203816i
$866$		−	3.82009i		−	0.129812i
$867$	0.0946614	+	26.9281i	0.00321487	+	0.914525i
$868$	−1.11064	+	1.11064i	−0.0376974	+	0.0376974i
$869$	21.2864			0.722093
$870$	−12.1156	+	34.2477i	−0.410758	+	1.16111i
$871$	1.22879			0.0416358
$872$	3.03160	−	3.03160i	0.102663	−	0.102663i
$873$	−8.97904	−	8.85367i	−0.303895	−	0.299651i
$874$		−	47.8826i		−	1.61965i
$875$	15.0604	−	9.03124i	0.509133	−	0.305312i
$876$	6.78314	+	6.73562i	0.229181	+	0.227576i
$877$	27.7279	+	27.7279i	0.936304	+	0.936304i	0.998089	−	0.0617854i	$-0.0196794\pi$
$877$	27.7279	+	27.7279i	0.936304	+	0.936304i	−0.0617854	+	0.998089i	$0.519679\pi$
$878$	−9.55915	−	9.55915i	−0.322606	−	0.322606i
$879$	23.7585	+	23.5921i	0.801356	+	0.795742i
$880$	2.59076	+	5.47669i	0.0873346	+	0.184619i
$881$			13.2873i			0.447662i	0.974628	+	0.223831i	$0.0718563\pi$
$881$			13.2873i			0.447662i	−0.974628	+	0.223831i	$0.928144\pi$
$882$	9.68326	+	9.54805i	0.326052	+	0.321500i
$883$	17.6127	−	17.6127i	0.592714	−	0.592714i	−0.345650	−	0.938364i	$-0.612342\pi$
$883$	17.6127	−	17.6127i	0.592714	−	0.592714i	0.938364	+	0.345650i	$0.112342\pi$
$884$	−0.205312			−0.00690539
$885$	−3.73447	+	1.78269i	−0.125533	+	0.0599246i
$886$	8.47867			0.284847
$887$	19.7879	−	19.7879i	0.664413	−	0.664413i	−0.292004	−	0.956417i	$-0.594322\pi$
$887$	19.7879	−	19.7879i	0.664413	−	0.664413i	0.956417	+	0.292004i	$0.0943222\pi$
$888$	0.0377061	+	10.7262i	0.00126533	+	0.359946i
$889$			2.54386i			0.0853182i
$890$	−4.09699	+	11.4529i	−0.137331	+	0.383902i
$891$	0.342877	+	24.3828i	0.0114868	+	0.816856i
$892$	−6.20254	−	6.20254i	−0.207676	−	0.207676i
$893$	−9.88158	−	9.88158i	−0.330674	−	0.330674i
$894$	18.8761	−	19.0093i	0.631313	−	0.635767i
$895$	45.1016	−	21.3354i	1.50758	−	0.713164i
$896$			1.57068i			0.0524726i
$897$	2.50587	−	0.00880899i	0.0836685	−	0.000294124i
$898$	−4.88705	+	4.88705i	−0.163083	+	0.163083i
$899$	−9.37974			−0.312832
$900$	−11.6631	−	9.43247i	−0.388771	−	0.314416i
$901$	0.0988105			0.00329186
$902$	23.6808	−	23.6808i	0.788485	−	0.788485i
$903$	26.0786	−	0.0916752i	0.867841	−	0.00305076i
$904$			7.30063i			0.242815i
$905$	25.0930	−	11.8703i	0.834120	−	0.394583i
$906$	5.43286	−	5.47119i	0.180495	−	0.181768i
$907$	7.84127	+	7.84127i	0.260365	+	0.260365i	0.825202	−	0.564837i	$-0.191061\pi$
$907$	7.84127	+	7.84127i	0.260365	+	0.260365i	−0.564837	+	0.825202i	$0.691061\pi$
$908$	−19.9921	−	19.9921i	−0.663459	−	0.663459i
$909$	−0.251226	−	35.7323i	−0.00833262	−	1.18516i
$910$	−0.201491	+	0.563257i	−0.00667937	+	0.0186718i
$911$		−	22.3664i		−	0.741031i	−0.928826	−	0.370515i	$-0.879181\pi$
$911$		−	22.3664i		−	0.741031i	0.928826	−	0.370515i	$-0.120819\pi$
$912$	−0.0343231	−	9.76379i	−0.00113655	−	0.323311i
$913$	−23.3175	+	23.3175i	−0.771696	+	0.771696i
$914$	11.2756			0.372965
$915$	−26.4581	+	12.6301i	−0.874677	+	0.417537i
$916$	4.09903			0.135436
$917$	2.28569	−	2.28569i	0.0754802	−	0.0754802i
$918$	0.0660529	+	6.26309i	0.00218007	+	0.206713i
$919$		−	17.0089i		−	0.561071i	−0.959844	−	0.280535i	$-0.909488\pi$
$919$		−	17.0089i		−	0.561071i	0.959844	−	0.280535i	$-0.0905120\pi$
$920$	−8.12194	−	17.1692i	−0.267773	−	0.566052i
$921$	10.8329	+	10.7570i	0.356957	+	0.354456i
$922$	14.0987	+	14.0987i	0.464316	+	0.464316i
$923$	−1.90065	−	1.90065i	−0.0625608	−	0.0625608i
$924$	−5.23044	−	5.19380i	−0.172069	−	0.170863i
$925$	30.8144	−	3.03942i	1.01317	−	0.0999354i
$926$			8.19634i			0.269348i
$927$	14.1431	−	14.3434i	0.464521	−	0.471099i
$928$	−6.63248	+	6.63248i	−0.217722	+	0.217722i
$929$	−52.5241			−1.72326			−0.861630	−	0.507537i	$-0.830556\pi$
$929$	−52.5241			−1.72326			−0.861630	+	0.507537i	$0.830556\pi$
$930$	1.29168	−	3.65124i	0.0423559	−	0.119729i
$931$	25.5531			0.837470
$932$	−6.35559	+	6.35559i	−0.208184	+	0.208184i
$933$	−0.183425	−	52.1785i	−0.00600508	−	1.70825i
$934$			24.8031i			0.811584i
$935$	−6.87626	−	2.45981i	−0.224878	−	0.0804443i
$936$	0.510968	−	0.00359250i	0.0167015	−	0.000117425i
$937$	−6.40958	−	6.40958i	−0.209392	−	0.209392i	0.594617	−	0.804009i	$-0.297304\pi$
$937$	−6.40958	−	6.40958i	−0.209392	−	0.209392i	−0.804009	+	0.594617i	$0.797304\pi$
$938$	8.01244	+	8.01244i	0.261615	+	0.261615i
$939$	−19.2262	+	19.3618i	−0.627423	+	0.631850i
$940$	−5.21937	−	1.86710i	−0.170237	−	0.0608980i
$941$			16.6319i			0.542183i	0.962554	+	0.271091i	$0.0873846\pi$
$941$			16.6319i			0.542183i	−0.962554	+	0.271091i	$0.912615\pi$
$942$	−14.0204	+	0.0492865i	−0.456809	+	0.00160584i
$943$	−74.2385	+	74.2385i	−2.41754	+	2.41754i
$944$	−1.06847			−0.0347756
$945$	17.2471	+	5.96532i	0.561049	+	0.194052i
$946$	25.9731			0.844459
$947$	−1.14638	+	1.14638i	−0.0372524	+	0.0372524i	−0.725488	−	0.688235i	$-0.758386\pi$
$947$	−1.14638	+	1.14638i	−0.0372524	+	0.0372524i	0.688235	+	0.725488i	$0.258386\pi$
$948$	−13.6074	+	0.0478349i	−0.441949	+	0.00155360i
$949$			0.940042i			0.0305151i
$950$	−28.0497	+	2.76672i	−0.910052	+	0.0897641i
$951$	−21.9178	+	22.0724i	−0.710732	+	0.715746i
$952$	−1.33876	−	1.33876i	−0.0433894	−	0.0433894i
$953$	21.7711	+	21.7711i	0.705233	+	0.705233i	0.965529	−	0.260296i	$-0.0838200\pi$
$953$	21.7711	+	21.7711i	0.705233	+	0.705233i	−0.260296	+	0.965529i	$0.583820\pi$
$954$	−0.245914	+	0.00172897i	−0.00796175	+	5.59773e-5i
$955$	12.1647	+	25.7153i	0.393640	+	0.832127i
$956$		−	20.9423i		−	0.677323i
$957$	−0.154740	−	44.0183i	−0.00500202	−	1.42291i
$958$	−9.18043	+	9.18043i	−0.296606	+	0.296606i
$959$	−22.0698			−0.712671
$960$	−1.66846	−	3.49517i	−0.0538494	−	0.112806i
$961$	1.00000			0.0322581
$962$	−0.745855	+	0.745855i	−0.0240473	+	0.0240473i
$963$	−34.2270	+	34.7117i	−1.10295	+	1.11857i
$964$		−	23.1603i		−	0.745944i
$965$	−8.95811	+	25.0419i	−0.288372	+	0.806128i
$966$	16.3972	+	16.2824i	0.527572	+	0.523876i
$967$	−22.4276	−	22.4276i	−0.721222	−	0.721222i	0.247632	−	0.968854i	$-0.420348\pi$
$967$	−22.4276	−	22.4276i	−0.721222	−	0.721222i	−0.968854	+	0.247632i	$0.920348\pi$
$968$	2.58714	+	2.58714i	0.0831537	+	0.0831537i
$969$	8.35138	+	8.29287i	0.268285	+	0.266405i
$970$	−8.49621	+	4.01916i	−0.272797	+	0.129047i
$971$		−	42.8935i		−	1.37652i	−0.725466	−	0.688258i	$-0.758376\pi$
$971$		−	42.8935i		−	1.37652i	0.725466	−	0.688258i	$-0.241624\pi$
$972$	−0.273979	−	15.5860i	−0.00878787	−	0.499923i
$973$	−6.86178	+	6.86178i	−0.219979	+	0.219979i
$974$	5.75378			0.184363
$975$	−0.149953	−	1.46743i	−0.00480233	−	0.0469955i
$976$	−7.56989			−0.242306
$977$	−11.0944	+	11.0944i	−0.354942	+	0.354942i	−0.861945	−	0.507003i	$-0.830753\pi$
$977$	−11.0944	+	11.0944i	−0.354942	+	0.354942i	0.507003	+	0.861945i	$0.330753\pi$
$978$	0.122389	+	34.8155i	0.00391355	+	1.11328i
$979$		−	14.7388i		−	0.471055i
$980$	9.16256	−	4.33437i	0.292687	−	0.138456i
$981$	−0.0904274	−	12.8617i	−0.00288713	−	0.410641i
$982$	−28.5200	−	28.5200i	−0.910110	−	0.910110i
$983$	1.92745	+	1.92745i	0.0614760	+	0.0614760i	0.737176	−	0.675700i	$-0.236159\pi$
$983$	1.92745	+	1.92745i	0.0614760	+	0.0614760i	−0.675700	+	0.737176i	$0.736159\pi$
$984$	−15.0848	+	15.1913i	−0.480887	+	0.484280i
$985$	3.13584	−	8.76607i	0.0999162	−	0.279310i
$986$		−	11.3063i		−	0.360067i
$987$	6.74412	−	0.0237079i	0.214668	−	0.000754632i
$988$	0.678936	−	0.678936i	0.0215998	−	0.0215998i
$989$	−81.4248			−2.58916
$990$	17.1563	+	6.00151i	0.545262	+	0.190740i
$991$	17.1483			0.544735			0.272368	−	0.962193i	$-0.412193\pi$
$991$	17.1483			0.544735			0.272368	+	0.962193i	$0.412193\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−58.1744	+	0.204503i	−1.84611	+	0.00648971i
$994$		−	24.7868i		−	0.786191i
$995$	14.0254	+	29.6487i	0.444634	+	0.939926i
$996$	14.8534	−	14.9582i	0.470648	−	0.473968i
$997$	−17.9033	−	17.9033i	−0.567002	−	0.567002i	0.364285	−	0.931287i	$-0.381313\pi$
$997$	−17.9033	−	17.9033i	−0.567002	−	0.567002i	−0.931287	+	0.364285i	$0.881313\pi$
$998$	−23.8184	−	23.8184i	−0.753957	−	0.753957i
$999$	22.9924	+	22.5125i	0.727449	+	0.712265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.10	✓	40
3.2	odd	2	inner	930.2.j.g.497.16	yes	40
5.3	odd	4	inner	930.2.j.g.683.16	yes	40
15.8	even	4	inner	930.2.j.g.683.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.10	✓	40	1.1	even	1	trivial
930.2.j.g.497.16	yes	40	3.2	odd	2	inner
930.2.j.g.683.10	yes	40	15.8	even	4	inner
930.2.j.g.683.16	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.73204 - 0.00608872i) q^{3} -1.00000i q^{4} +(-2.02131 + 0.956187i) q^{5} +(-1.22043 + 1.22904i) q^{6} +(-1.11064 - 1.11064i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99993 - 0.0210918i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.73204 - 0.00608872i) q^{3} -1.00000i q^{4} +(-2.02131 + 0.956187i) q^{5} +(-1.22043 + 1.22904i) q^{6} +(-1.11064 - 1.11064i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99993 - 0.0210918i) q^{9} +(0.753158 - 2.10541i) q^{10} +2.70947i q^{11} +(-0.00608872 - 1.73204i) q^{12} +(0.120439 - 0.120439i) q^{13} +1.57068 q^{14} +(-3.49517 + 1.66846i) q^{15} -1.00000 q^{16} +(0.852346 - 0.852346i) q^{17} +(-2.10635 + 2.13618i) q^{18} +5.63716i q^{19} +(0.956187 + 2.02131i) q^{20} +(-1.93043 - 1.91690i) q^{21} +(-1.91589 - 1.91589i) q^{22} +(6.00623 + 6.00623i) q^{23} +(1.22904 + 1.22043i) q^{24} +(3.17141 - 3.86551i) q^{25} +0.170327i q^{26} +(5.19586 - 0.0547976i) q^{27} +(-1.11064 + 1.11064i) q^{28} -9.37974 q^{29} +(1.29168 - 3.65124i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.0164972 + 4.69291i) q^{33} +1.20540i q^{34} +(3.30692 + 1.18297i) q^{35} +(-0.0210918 - 2.99993i) q^{36} +(4.37896 + 4.37896i) q^{37} +(-3.98607 - 3.98607i) q^{38} +(0.207872 - 0.209339i) q^{39} +(-2.10541 - 0.753158i) q^{40} +12.3602i q^{41} +(2.72047 - 0.00956340i) q^{42} +(-6.77836 + 6.77836i) q^{43} +2.70947 q^{44} +(-6.04362 + 2.91112i) q^{45} -8.49409 q^{46} +(-1.75294 + 1.75294i) q^{47} +(-1.73204 + 0.00608872i) q^{48} -4.53298i q^{49} +(0.490799 + 4.97585i) q^{50} +(1.47111 - 1.48149i) q^{51} +(-0.120439 - 0.120439i) q^{52} +(0.0579639 + 0.0579639i) q^{53} +(-3.63528 + 3.71278i) q^{54} +(-2.59076 - 5.47669i) q^{55} -1.57068i q^{56} +(0.0343231 + 9.76379i) q^{57} +(6.63248 - 6.63248i) q^{58} +1.06847 q^{59} +(1.66846 + 3.49517i) q^{60} +7.56989 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-3.35525 - 3.30840i) q^{63} +1.00000i q^{64} +(-0.128283 + 0.358608i) q^{65} +(-3.33006 - 3.30673i) q^{66} +(5.10127 + 5.10127i) q^{67} +(-0.852346 - 0.852346i) q^{68} +(10.4396 + 10.3665i) q^{69} +(-3.17483 + 1.50186i) q^{70} -15.7810i q^{71} +(2.13618 + 2.10635i) q^{72} +(-3.90256 + 3.90256i) q^{73} -6.19279 q^{74} +(5.46948 - 6.71452i) q^{75} +5.63716 q^{76} +(3.00924 - 3.00924i) q^{77} +(0.00103707 + 0.295013i) q^{78} -7.85631i q^{79} +(2.02131 - 0.956187i) q^{80} +(8.99911 - 0.126548i) q^{81} +(-8.74002 - 8.74002i) q^{82} +(8.60592 + 8.60592i) q^{83} +(-1.91690 + 1.93043i) q^{84} +(-0.907855 + 2.53786i) q^{85} -9.58605i q^{86} +(-16.2461 + 0.0571106i) q^{87} +(-1.91589 + 1.91589i) q^{88} -5.43975 q^{89} +(2.21501 - 6.33196i) q^{90} -0.267529 q^{91} +(6.00623 - 6.00623i) q^{92} +(1.73204 - 0.00608872i) q^{93} -2.47903i q^{94} +(-5.39018 - 11.3945i) q^{95} +(1.22043 - 1.22904i) q^{96} +(-2.97219 - 2.97219i) q^{97} +(3.20530 + 3.20530i) q^{98} +(0.0571477 + 8.12821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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