LMFDB - Embedded newform 370.2.g.d.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 $ x^10 + 3x^8 - 8x^7 - 26x^6 + 12x^5 + 24x^4 + 166x^3 + 113x^2 - 152x + 160
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$-1.66045 + 0.156295i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.d.327.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.05122 - 1.05122i) q^{3} -1.00000 q^{4} +(0.609231 - 2.15147i) q^{5} +(-1.05122 - 1.05122i) q^{6} +(-1.21846 + 1.21846i) q^{7} +1.00000i q^{8} +0.789858i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.05122 - 1.05122i) q^{3} -1.00000 q^{4} +(0.609231 - 2.15147i) q^{5} +(-1.05122 - 1.05122i) q^{6} +(-1.21846 + 1.21846i) q^{7} +1.00000i q^{8} +0.789858i q^{9} +(-2.15147 - 0.609231i) q^{10} -4.85196i q^{11} +(-1.05122 + 1.05122i) q^{12} -5.57745i q^{13} +(1.21846 + 1.21846i) q^{14} +(-1.62124 - 2.90212i) q^{15} +1.00000 q^{16} +1.00832 q^{17} +0.789858 q^{18} +(-1.94395 + 1.94395i) q^{19} +(-0.609231 + 2.15147i) q^{20} +2.56175i q^{21} -4.85196 q^{22} +3.14053i q^{23} +(1.05122 + 1.05122i) q^{24} +(-4.25768 - 2.62149i) q^{25} -5.57745 q^{26} +(3.98399 + 3.98399i) q^{27} +(1.21846 - 1.21846i) q^{28} +(4.77672 + 4.77672i) q^{29} +(-2.90212 + 1.62124i) q^{30} +(-1.71430 + 1.71430i) q^{31} -1.00000i q^{32} +(-5.10050 - 5.10050i) q^{33} -1.00832i q^{34} +(1.87916 + 3.36381i) q^{35} -0.789858i q^{36} +(3.78986 - 4.75783i) q^{37} +(1.94395 + 1.94395i) q^{38} +(-5.86315 - 5.86315i) q^{39} +(2.15147 + 0.609231i) q^{40} -0.412903i q^{41} +2.56175 q^{42} -1.47727i q^{43} +4.85196i q^{44} +(1.69936 + 0.481206i) q^{45} +3.14053 q^{46} +(8.35899 - 8.35899i) q^{47} +(1.05122 - 1.05122i) q^{48} +4.03070i q^{49} +(-2.62149 + 4.25768i) q^{50} +(1.05997 - 1.05997i) q^{51} +5.57745i q^{52} +(3.85196 + 3.85196i) q^{53} +(3.98399 - 3.98399i) q^{54} +(-10.4389 - 2.95597i) q^{55} +(-1.21846 - 1.21846i) q^{56} +4.08706i q^{57} +(4.77672 - 4.77672i) q^{58} +(-7.33529 + 7.33529i) q^{59} +(1.62124 + 2.90212i) q^{60} +(-0.457758 + 0.457758i) q^{61} +(1.71430 + 1.71430i) q^{62} +(-0.962411 - 0.962411i) q^{63} -1.00000 q^{64} +(-11.9997 - 3.39796i) q^{65} +(-5.10050 + 5.10050i) q^{66} +(5.29402 + 5.29402i) q^{67} -1.00832 q^{68} +(3.30140 + 3.30140i) q^{69} +(3.36381 - 1.87916i) q^{70} +7.15491 q^{71} -0.789858 q^{72} +(9.08993 - 9.08993i) q^{73} +(-4.75783 - 3.78986i) q^{74} +(-7.23154 + 1.72000i) q^{75} +(1.94395 - 1.94395i) q^{76} +(5.91193 + 5.91193i) q^{77} +(-5.86315 + 5.86315i) q^{78} +(-1.46413 + 1.46413i) q^{79} +(0.609231 - 2.15147i) q^{80} +6.00655 q^{81} -0.412903 q^{82} +(9.88040 + 9.88040i) q^{83} -2.56175i q^{84} +(0.614300 - 2.16937i) q^{85} -1.47727 q^{86} +10.0428 q^{87} +4.85196 q^{88} +(-7.09280 - 7.09280i) q^{89} +(0.481206 - 1.69936i) q^{90} +(6.79592 + 6.79592i) q^{91} -3.14053i q^{92} +3.60423i q^{93} +(-8.35899 - 8.35899i) q^{94} +(2.99805 + 5.36668i) q^{95} +(-1.05122 - 1.05122i) q^{96} +2.10245 q^{97} +4.03070 q^{98} +3.83236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) $ 10 * q - 2 * q^3 - 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7	$ 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 2 q^{10} + 2 q^{12} + 4 q^{14} - 6 q^{15} + 10 q^{16} - 24 q^{17} - 18 q^{18} - 8 q^{19} - 2 q^{20} - 8 q^{22} - 2 q^{24} - 28 q^{25} - 12 q^{26} + 28 q^{27} + 4 q^{28} + 32 q^{29} + 14 q^{30} - 26 q^{31} - 24 q^{33} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 6 q^{39} - 2 q^{40} - 40 q^{42} + 4 q^{45} + 4 q^{46} + 48 q^{47} - 2 q^{48} + 16 q^{51} - 2 q^{53} + 28 q^{54} + 18 q^{55} - 4 q^{56} + 32 q^{58} + 20 q^{59} + 6 q^{60} - 24 q^{61} + 26 q^{62} + 20 q^{63} - 10 q^{64} - 28 q^{65} - 24 q^{66} + 10 q^{67} + 24 q^{68} + 46 q^{69} + 22 q^{70} - 16 q^{71} + 18 q^{72} - 4 q^{73} + 2 q^{74} - 48 q^{75} + 8 q^{76} + 24 q^{77} - 6 q^{78} + 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} + 10 q^{85} + 12 q^{86} + 8 q^{88} + 2 q^{89} - 10 q^{90} + 16 q^{91} - 48 q^{94} + 28 q^{95} + 2 q^{96} - 4 q^{97} - 18 q^{98} - 28 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 2 * q^10 + 2 * q^12 + 4 * q^14 - 6 * q^15 + 10 * q^16 - 24 * q^17 - 18 * q^18 - 8 * q^19 - 2 * q^20 - 8 * q^22 - 2 * q^24 - 28 * q^25 - 12 * q^26 + 28 * q^27 + 4 * q^28 + 32 * q^29 + 14 * q^30 - 26 * q^31 - 24 * q^33 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 6 * q^39 - 2 * q^40 - 40 * q^42 + 4 * q^45 + 4 * q^46 + 48 * q^47 - 2 * q^48 + 16 * q^51 - 2 * q^53 + 28 * q^54 + 18 * q^55 - 4 * q^56 + 32 * q^58 + 20 * q^59 + 6 * q^60 - 24 * q^61 + 26 * q^62 + 20 * q^63 - 10 * q^64 - 28 * q^65 - 24 * q^66 + 10 * q^67 + 24 * q^68 + 46 * q^69 + 22 * q^70 - 16 * q^71 + 18 * q^72 - 4 * q^73 + 2 * q^74 - 48 * q^75 + 8 * q^76 + 24 * q^77 - 6 * q^78 + 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 + 10 * q^85 + 12 * q^86 + 8 * q^88 + 2 * q^89 - 10 * q^90 + 16 * q^91 - 48 * q^94 + 28 * q^95 + 2 * q^96 - 4 * q^97 - 18 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.05122	−	1.05122i	0.606924	−	0.606924i	−0.335217	−	0.942141i	$-0.608810\pi$
$3$	1.05122	−	1.05122i	0.606924	−	0.606924i	0.942141	+	0.335217i	$0.108810\pi$
$4$	−1.00000			−0.500000
$5$	0.609231	−	2.15147i	0.272456	−	0.962168i
$5$	0.609231	−	2.15147i	0.272456	−	0.962168i
$6$	−1.05122	−	1.05122i	−0.429160	−	0.429160i
$7$	−1.21846	+	1.21846i	−0.460535	+	0.460535i	−0.898831	−	0.438296i	$-0.855582\pi$
$7$	−1.21846	+	1.21846i	−0.460535	+	0.460535i	0.438296	+	0.898831i	$0.355582\pi$
$8$			1.00000i			0.353553i
$9$			0.789858i			0.263286i
$10$	−2.15147	−	0.609231i	−0.680356	−	0.192656i
$11$		−	4.85196i		−	1.46292i	−0.681884	−	0.731461i	$-0.738839\pi$
$11$		−	4.85196i		−	1.46292i	0.681884	−	0.731461i	$-0.261161\pi$
$12$	−1.05122	+	1.05122i	−0.303462	+	0.303462i
$13$		−	5.57745i		−	1.54691i	−0.633853	−	0.773454i	$-0.718528\pi$
$13$		−	5.57745i		−	1.54691i	0.633853	−	0.773454i	$-0.281472\pi$
$14$	1.21846	+	1.21846i	0.325648	+	0.325648i
$15$	−1.62124	−	2.90212i	−0.418603	−	0.749324i
$16$	1.00000			0.250000
$17$	1.00832			0.244553			0.122277	−	0.992496i	$-0.460980\pi$
$17$	1.00832			0.244553			0.122277	+	0.992496i	$0.460980\pi$
$18$	0.789858			0.186171
$19$	−1.94395	+	1.94395i	−0.445974	+	0.445974i	−0.894014	−	0.448040i	$-0.852122\pi$
$19$	−1.94395	+	1.94395i	−0.445974	+	0.445974i	0.448040	+	0.894014i	$0.352122\pi$
$20$	−0.609231	+	2.15147i	−0.136228	+	0.481084i
$21$			2.56175i			0.559020i
$22$	−4.85196			−1.03444
$23$			3.14053i			0.654846i	0.944878	+	0.327423i	$0.106180\pi$
$23$			3.14053i			0.654846i	−0.944878	+	0.327423i	$0.893820\pi$
$24$	1.05122	+	1.05122i	0.214580	+	0.214580i
$25$	−4.25768	−	2.62149i	−0.851535	−	0.524298i
$26$	−5.57745			−1.09383
$27$	3.98399	+	3.98399i	0.766719	+	0.766719i
$28$	1.21846	−	1.21846i	0.230268	−	0.230268i
$29$	4.77672	+	4.77672i	0.887014	+	0.887014i	0.994235	−	0.107221i	$-0.0341953\pi$
$29$	4.77672	+	4.77672i	0.887014	+	0.887014i	−0.107221	+	0.994235i	$0.534195\pi$
$30$	−2.90212	+	1.62124i	−0.529852	+	0.295997i
$31$	−1.71430	+	1.71430i	−0.307898	+	0.307898i	−0.844094	−	0.536196i	$-0.819861\pi$
$31$	−1.71430	+	1.71430i	−0.307898	+	0.307898i	0.536196	+	0.844094i	$0.319861\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.10050	−	5.10050i	−0.887882	−	0.887882i
$34$		−	1.00832i		−	0.172925i
$35$	1.87916	+	3.36381i	0.317637	+	0.568588i
$36$		−	0.789858i		−	0.131643i
$37$	3.78986	−	4.75783i	0.623049	−	0.782183i
$37$	3.78986	−	4.75783i	0.623049	−	0.782183i
$38$	1.94395	+	1.94395i	0.315351	+	0.315351i
$39$	−5.86315	−	5.86315i	−0.938856	−	0.938856i
$40$	2.15147	+	0.609231i	0.340178	+	0.0963279i
$41$		−	0.412903i		−	0.0644846i	−0.999480	−	0.0322423i	$-0.989735\pi$
$41$		−	0.412903i		−	0.0644846i	0.999480	−	0.0322423i	$-0.0102648\pi$
$42$	2.56175			0.395287
$43$		−	1.47727i		−	0.225281i	−0.993636	−	0.112641i	$-0.964069\pi$
$43$		−	1.47727i		−	0.225281i	0.993636	−	0.112641i	$-0.0359309\pi$
$44$			4.85196i			0.731461i
$45$	1.69936	+	0.481206i	0.253325	+	0.0717339i
$46$	3.14053			0.463046
$47$	8.35899	−	8.35899i	1.21928	−	1.21928i	0.251401	−	0.967883i	$-0.419109\pi$
$47$	8.35899	−	8.35899i	1.21928	−	1.21928i	0.967883	−	0.251401i	$-0.0808914\pi$
$48$	1.05122	−	1.05122i	0.151731	−	0.151731i
$49$			4.03070i			0.575814i
$50$	−2.62149	+	4.25768i	−0.370734	+	0.602126i
$51$	1.05997	−	1.05997i	0.148425	−	0.148425i
$52$			5.57745i			0.773454i
$53$	3.85196	+	3.85196i	0.529108	+	0.529108i	0.920306	−	0.391199i	$-0.127939\pi$
$53$	3.85196	+	3.85196i	0.529108	+	0.529108i	−0.391199	+	0.920306i	$0.627939\pi$
$54$	3.98399	−	3.98399i	0.542152	−	0.542152i
$55$	−10.4389	−	2.95597i	−1.40758	−	0.398582i
$56$	−1.21846	−	1.21846i	−0.162824	−	0.162824i
$57$			4.08706i			0.541345i
$58$	4.77672	−	4.77672i	0.627214	−	0.627214i
$59$	−7.33529	+	7.33529i	−0.954973	+	0.954973i	−0.999029	−	0.0440560i	$-0.985972\pi$
$59$	−7.33529	+	7.33529i	−0.954973	+	0.954973i	0.0440560	+	0.999029i	$0.485972\pi$
$60$	1.62124	+	2.90212i	0.209301	+	0.374662i
$61$	−0.457758	+	0.457758i	−0.0586099	+	0.0586099i	−0.735804	−	0.677194i	$-0.763196\pi$
$61$	−0.457758	+	0.457758i	−0.0586099	+	0.0586099i	0.677194	+	0.735804i	$0.263196\pi$
$62$	1.71430	+	1.71430i	0.217717	+	0.217717i
$63$	−0.962411	−	0.962411i	−0.121252	−	0.121252i
$64$	−1.00000			−0.125000
$65$	−11.9997	−	3.39796i	−1.48839	−	0.421465i
$66$	−5.10050	+	5.10050i	−0.627828	+	0.627828i
$67$	5.29402	+	5.29402i	0.646767	+	0.646767i	0.952210	−	0.305443i	$-0.0988046\pi$
$67$	5.29402	+	5.29402i	0.646767	+	0.646767i	−0.305443	+	0.952210i	$0.598805\pi$
$68$	−1.00832			−0.122277
$69$	3.30140	+	3.30140i	0.397442	+	0.397442i
$70$	3.36381	−	1.87916i	0.402053	−	0.224603i
$71$	7.15491			0.849131			0.424566	−	0.905397i	$-0.360427\pi$
$71$	7.15491			0.849131			0.424566	+	0.905397i	$0.360427\pi$
$72$	−0.789858			−0.0930856
$73$	9.08993	−	9.08993i	1.06390	−	1.06390i	0.0660820	−	0.997814i	$-0.478950\pi$
$73$	9.08993	−	9.08993i	1.06390	−	1.06390i	0.997814	−	0.0660820i	$-0.0210499\pi$
$74$	−4.75783	−	3.78986i	−0.553087	−	0.440562i
$75$	−7.23154	+	1.72000i	−0.835026	+	0.198608i
$76$	1.94395	−	1.94395i	0.222987	−	0.222987i
$77$	5.91193	+	5.91193i	0.673727	+	0.673727i
$78$	−5.86315	+	5.86315i	−0.663871	+	0.663871i
$79$	−1.46413	+	1.46413i	−0.164727	+	0.164727i	−0.784657	−	0.619930i	$-0.787161\pi$
$79$	−1.46413	+	1.46413i	−0.164727	+	0.164727i	0.619930	+	0.784657i	$0.287161\pi$
$80$	0.609231	−	2.15147i	0.0681141	−	0.240542i
$81$	6.00655			0.667395
$82$	−0.412903			−0.0455975
$83$	9.88040	+	9.88040i	1.08451	+	1.08451i	0.996082	+	0.0884327i	$0.0281858\pi$
$83$	9.88040	+	9.88040i	1.08451	+	1.08451i	0.0884327	+	0.996082i	$0.471814\pi$
$84$		−	2.56175i		−	0.279510i
$85$	0.614300	−	2.16937i	0.0666301	−	0.235302i
$86$	−1.47727			−0.159298
$87$	10.0428			1.07670
$88$	4.85196			0.517221
$89$	−7.09280	−	7.09280i	−0.751836	−	0.751836i	0.222986	−	0.974822i	$-0.428420\pi$
$89$	−7.09280	−	7.09280i	−0.751836	−	0.751836i	−0.974822	+	0.222986i	$0.928420\pi$
$90$	0.481206	−	1.69936i	0.0507235	−	0.179128i
$91$	6.79592	+	6.79592i	0.712406	+	0.712406i
$92$		−	3.14053i		−	0.327423i
$93$			3.60423i			0.373741i
$94$	−8.35899	−	8.35899i	−0.862164	−	0.862164i
$95$	2.99805	+	5.36668i	0.307593	+	0.550610i
$96$	−1.05122	−	1.05122i	−0.107290	−	0.107290i
$97$	2.10245			0.213471			0.106736	−	0.994287i	$-0.465960\pi$
$97$	2.10245			0.213471			0.106736	+	0.994287i	$0.465960\pi$
$98$	4.03070			0.407162
$99$	3.83236			0.385166
$100$	4.25768	+	2.62149i	0.425768	+	0.262149i
$101$		−	6.66420i		−	0.663113i	−0.943435	−	0.331556i	$-0.892426\pi$
$101$		−	6.66420i		−	0.663113i	0.943435	−	0.331556i	$-0.107574\pi$
$102$	−1.05997	−	1.05997i	−0.104953	−	0.104953i
$103$	−3.38743			−0.333774			−0.166887	−	0.985976i	$-0.553371\pi$
$103$	−3.38743			−0.333774			−0.166887	+	0.985976i	$0.553371\pi$
$104$	5.57745			0.546914
$105$	5.51154	+	1.56070i	0.537871	+	0.152309i
$106$	3.85196	−	3.85196i	0.374136	−	0.374136i
$107$	−6.68246	+	6.68246i	−0.646018	+	0.646018i	−0.952028	−	0.306010i	$-0.901006\pi$
$107$	−6.68246	+	6.68246i	−0.646018	+	0.646018i	0.306010	+	0.952028i	$0.401006\pi$
$108$	−3.98399	−	3.98399i	−0.383359	−	0.383359i
$109$	11.6763	−	11.6763i	1.11839	−	1.11839i	0.126410	−	0.991978i	$-0.459654\pi$
$109$	11.6763	−	11.6763i	1.11839	−	1.11839i	0.991978	−	0.126410i	$-0.0403456\pi$
$110$	−2.95597	+	10.4389i	−0.281840	+	0.995307i
$111$	−1.01756	−	8.98554i	−0.0965825	−	0.852869i
$112$	−1.21846	+	1.21846i	−0.115134	+	0.115134i
$113$	4.19525			0.394656			0.197328	−	0.980338i	$-0.436774\pi$
$113$	4.19525			0.394656			0.197328	+	0.980338i	$0.436774\pi$
$114$	4.08706			0.382788
$115$	6.75677	+	1.91331i	0.630072	+	0.178417i
$116$	−4.77672	−	4.77672i	−0.443507	−	0.443507i
$117$	4.40539			0.407279
$118$	7.33529	+	7.33529i	0.675268	+	0.675268i
$119$	−1.22860	+	1.22860i	−0.112625	+	0.112625i
$120$	2.90212	−	1.62124i	0.264926	−	0.147998i
$121$	−12.5415			−1.14014
$122$	0.457758	+	0.457758i	0.0414434	+	0.0414434i
$123$	−0.434053	−	0.434053i	−0.0391373	−	0.0391373i
$124$	1.71430	−	1.71430i	0.153949	−	0.153949i
$125$	−8.23397	+	7.56318i	−0.736469	+	0.676472i
$126$	−0.962411	+	0.962411i	−0.0857384	+	0.0857384i
$127$	−8.69347	+	8.69347i	−0.771421	+	0.771421i	−0.978355	−	0.206934i	$-0.933651\pi$
$127$	−8.69347	+	8.69347i	−0.771421	+	0.771421i	0.206934	+	0.978355i	$0.433651\pi$
$128$			1.00000i			0.0883883i
$129$	−1.55294	−	1.55294i	−0.136729	−	0.136729i
$130$	−3.39796	+	11.9997i	−0.298021	+	1.05245i
$131$	−7.96621	+	7.96621i	−0.696011	+	0.696011i	−0.963548	−	0.267537i	$-0.913790\pi$
$131$	−7.96621	+	7.96621i	−0.696011	+	0.696011i	0.267537	+	0.963548i	$0.413790\pi$
$132$	5.10050	+	5.10050i	0.443941	+	0.443941i
$133$		−	4.73727i		−	0.410773i
$134$	5.29402	−	5.29402i	0.457333	−	0.457333i
$135$	10.9986	−	6.14427i	0.946610	−	0.528815i
$136$			1.00832i			0.0864627i
$137$	−13.2365	+	13.2365i	−1.13087	+	1.13087i	−0.140840	+	0.990032i	$0.544980\pi$
$137$	−13.2365	+	13.2365i	−1.13087	+	1.13087i	−0.990032	+	0.140840i	$0.955020\pi$
$138$	3.30140	−	3.30140i	0.281034	−	0.281034i
$139$	−15.1028			−1.28100			−0.640500	−	0.767958i	$-0.721273\pi$
$139$	−15.1028			−1.28100			−0.640500	+	0.767958i	$0.721273\pi$
$140$	−1.87916	−	3.36381i	−0.158818	−	0.284294i
$141$		−	17.5743i		−	1.48003i
$142$		−	7.15491i		−	0.600427i
$143$	−27.0616			−2.26300
$144$			0.789858i			0.0658215i
$145$	13.1871	−	7.36685i	1.09513	−	0.611784i
$146$	−9.08993	−	9.08993i	−0.752288	−	0.752288i
$147$	4.23717	+	4.23717i	0.349476	+	0.349476i
$148$	−3.78986	+	4.75783i	−0.311524	+	0.391092i
$149$			21.2958i			1.74462i	0.488957	+	0.872308i	$0.337378\pi$
$149$			21.2958i			1.74462i	−0.488957	+	0.872308i	$0.662622\pi$
$150$	1.72000	+	7.23154i	0.140437	+	0.590453i
$151$			5.71666i			0.465215i	0.972571	+	0.232608i	$0.0747258\pi$
$151$			5.71666i			0.465215i	−0.972571	+	0.232608i	$0.925274\pi$
$152$	−1.94395	−	1.94395i	−0.157676	−	0.157676i
$153$			0.796429i			0.0643875i
$154$	5.91193	−	5.91193i	0.476397	−	0.476397i
$155$	2.64387	+	4.73268i	0.212361	+	0.380138i
$156$	5.86315	+	5.86315i	0.469428	+	0.469428i
$157$	4.70753	−	4.70753i	0.375702	−	0.375702i	−0.493847	−	0.869549i	$-0.664410\pi$
$157$	4.70753	−	4.70753i	0.375702	−	0.375702i	0.869549	+	0.493847i	$0.164410\pi$
$158$	1.46413	+	1.46413i	0.116480	+	0.116480i
$159$	8.09855			0.642256
$160$	−2.15147	−	0.609231i	−0.170089	−	0.0481639i
$161$	−3.82662	−	3.82662i	−0.301580	−	0.301580i
$162$		−	6.00655i		−	0.471919i
$163$	7.46188			0.584460			0.292230	−	0.956348i	$-0.405603\pi$
$163$	7.46188			0.584460			0.292230	+	0.956348i	$0.405603\pi$
$164$			0.412903i			0.0322423i
$165$	−14.0810	+	7.86620i	−1.09620	+	0.612383i
$166$	9.88040	−	9.88040i	0.766868	−	0.766868i
$167$	−19.1080			−1.47862			−0.739310	−	0.673365i	$-0.764848\pi$
$167$	−19.1080			−1.47862			−0.739310	+	0.673365i	$0.764848\pi$
$168$	−2.56175			−0.197643
$169$	−18.1080			−1.39292
$170$	−2.16937	−	0.614300i	−0.166383	−	0.0471146i
$171$	−1.53545	−	1.53545i	−0.117419	−	0.117419i
$172$			1.47727i			0.112641i
$173$	15.1632	−	15.1632i	1.15284	−	1.15284i	0.166858	−	0.985981i	$-0.446638\pi$
$173$	15.1632	−	15.1632i	1.15284	−	1.15284i	0.985981	−	0.166858i	$-0.0533621\pi$
$174$		−	10.0428i		−	0.761342i
$175$	8.38200	−	1.99363i	0.633620	−	0.150704i
$176$		−	4.85196i		−	0.365730i
$177$			15.4221i			1.15919i
$178$	−7.09280	+	7.09280i	−0.531628	+	0.531628i
$179$	−9.36945	−	9.36945i	−0.700305	−	0.700305i	0.264171	−	0.964476i	$-0.414902\pi$
$179$	−9.36945	−	9.36945i	−0.700305	−	0.700305i	−0.964476	+	0.264171i	$0.914902\pi$
$180$	−1.69936	−	0.481206i	−0.126663	−	0.0358670i
$181$	−11.6623			−0.866849			−0.433424	−	0.901190i	$-0.642695\pi$
$181$	−11.6623			−0.866849			−0.433424	+	0.901190i	$0.642695\pi$
$182$	6.79592	−	6.79592i	0.503747	−	0.503747i
$183$			0.962411i			0.0711435i
$184$	−3.14053			−0.231523
$185$	−7.92745	−	11.0524i	−0.582838	−	0.812588i
$186$	3.60423			0.264275
$187$		−	4.89233i		−	0.357762i
$188$	−8.35899	+	8.35899i	−0.609642	+	0.609642i
$189$	−9.70868			−0.706202
$190$	5.36668	−	2.99805i	0.389340	−	0.217501i
$191$	17.6354	+	17.6354i	1.27605	+	1.27605i	0.942859	+	0.333191i	$0.108125\pi$
$191$	17.6354	+	17.6354i	1.27605	+	1.27605i	0.333191	+	0.942859i	$0.391875\pi$
$192$	−1.05122	+	1.05122i	−0.0758655	+	0.0758655i
$193$		−	13.5647i		−	0.976408i	−0.872729	−	0.488204i	$-0.837652\pi$
$193$		−	13.5647i		−	0.976408i	0.872729	−	0.488204i	$-0.162348\pi$
$194$		−	2.10245i		−	0.150947i
$195$	−16.1864	+	9.04240i	−1.15913	+	0.647540i
$196$		−	4.03070i		−	0.287907i
$197$	16.8769	−	16.8769i	1.20243	−	1.20243i	0.229006	−	0.973425i	$-0.426453\pi$
$197$	16.8769	−	16.8769i	1.20243	−	1.20243i	0.973425	−	0.229006i	$-0.0735474\pi$
$198$		−	3.83236i		−	0.272354i
$199$	−9.13039	−	9.13039i	−0.647236	−	0.647236i	0.305088	−	0.952324i	$-0.401314\pi$
$199$	−9.13039	−	9.13039i	−0.647236	−	0.647236i	−0.952324	+	0.305088i	$0.901314\pi$
$200$	2.62149	−	4.25768i	0.185367	−	0.301063i
$201$	11.1304			0.785077
$202$	−6.66420			−0.468891
$203$	−11.6405			−0.817003
$204$	−1.05997	+	1.05997i	−0.0742127	+	0.0742127i
$205$	−0.888349	−	0.251553i	−0.0620450	−	0.0175692i
$206$			3.38743i			0.236014i
$207$	−2.48057			−0.172412
$208$		−	5.57745i		−	0.386727i
$209$	9.43199	+	9.43199i	0.652425	+	0.652425i
$210$	1.56070	−	5.51154i	0.107698	−	0.380333i
$211$	−10.0888			−0.694540			−0.347270	−	0.937765i	$-0.612891\pi$
$211$	−10.0888			−0.694540			−0.347270	+	0.937765i	$0.612891\pi$
$212$	−3.85196	−	3.85196i	−0.264554	−	0.264554i
$213$	7.52141	−	7.52141i	0.515358	−	0.515358i
$214$	6.68246	+	6.68246i	0.456804	+	0.456804i
$215$	−3.17830	−	0.899997i	−0.216758	−	0.0613793i
$216$	−3.98399	+	3.98399i	−0.271076	+	0.271076i
$217$		−	4.17762i		−	0.283596i
$218$	−11.6763	−	11.6763i	−0.790820	−	0.790820i
$219$		−	19.1111i		−	1.29141i
$220$	10.4389	+	2.95597i	0.703788	+	0.199291i
$221$		−	5.62386i		−	0.378302i
$222$	−8.98554	+	1.01756i	−0.603070	+	0.0682941i
$223$	2.45704	+	2.45704i	0.164536	+	0.164536i	0.784573	−	0.620037i	$-0.212882\pi$
$223$	2.45704	+	2.45704i	0.164536	+	0.164536i	−0.620037	+	0.784573i	$0.712882\pi$
$224$	1.21846	+	1.21846i	0.0814119	+	0.0814119i
$225$	2.07060	−	3.36296i	0.138040	−	0.224197i
$226$		−	4.19525i		−	0.279064i
$227$	−19.5967			−1.30068			−0.650340	−	0.759643i	$-0.725374\pi$
$227$	−19.5967			−1.30068			−0.650340	+	0.759643i	$0.725374\pi$
$228$		−	4.08706i		−	0.270672i
$229$			8.54964i			0.564976i	0.959271	+	0.282488i	$0.0911597\pi$
$229$			8.54964i			0.564976i	−0.959271	+	0.282488i	$0.908840\pi$
$230$	1.91331	−	6.75677i	0.126160	−	0.445528i
$231$	12.4295			0.817803
$232$	−4.77672	+	4.77672i	−0.313607	+	0.313607i
$233$	−18.6855	+	18.6855i	−1.22413	+	1.22413i	−0.257980	+	0.966150i	$0.583057\pi$
$233$	−18.6855	+	18.6855i	−1.22413	+	1.22413i	−0.966150	+	0.257980i	$0.916943\pi$
$234$		−	4.40539i		−	0.287990i
$235$	−12.8916	−	23.0767i	−0.840955	−	1.50536i
$236$	7.33529	−	7.33529i	0.477487	−	0.477487i
$237$			3.07825i			0.199954i
$238$	1.22860	+	1.22860i	0.0796383	+	0.0796383i
$239$	−14.5251	+	14.5251i	−0.939550	+	0.939550i	−0.998274	−	0.0587243i	$-0.981297\pi$
$239$	−14.5251	+	14.5251i	−0.939550	+	0.939550i	0.0587243	+	0.998274i	$0.481297\pi$
$240$	−1.62124	−	2.90212i	−0.104651	−	0.187331i
$241$	−8.39707	−	8.39707i	−0.540903	−	0.540903i	0.382891	−	0.923794i	$-0.374929\pi$
$241$	−8.39707	−	8.39707i	−0.540903	−	0.540903i	−0.923794	+	0.382891i	$0.874929\pi$
$242$			12.5415i			0.806200i
$243$	−5.63773	+	5.63773i	−0.361661	+	0.361661i
$244$	0.457758	−	0.457758i	0.0293049	−	0.0293049i
$245$	8.67194	+	2.45563i	0.554030	+	0.156884i
$246$	−0.434053	+	0.434053i	−0.0276742	+	0.0276742i
$247$	10.8423	+	10.8423i	0.689880	+	0.689880i
$248$	−1.71430	−	1.71430i	−0.108858	−	0.108858i
$249$	20.7730			1.31644
$250$	7.56318	+	8.23397i	0.478338	+	0.520762i
$251$	6.65372	−	6.65372i	0.419979	−	0.419979i	−0.465217	−	0.885197i	$-0.654024\pi$
$251$	6.65372	−	6.65372i	0.419979	−	0.419979i	0.885197	+	0.465217i	$0.154024\pi$
$252$	0.962411	+	0.962411i	0.0606262	+	0.0606262i
$253$	15.2377			0.957988
$254$	8.69347	+	8.69347i	0.545477	+	0.545477i
$255$	−1.63473	−	2.92626i	−0.102371	−	0.183250i
$256$	1.00000			0.0625000
$257$	14.1881			0.885028			0.442514	−	0.896762i	$-0.354087\pi$
$257$	14.1881			0.885028			0.442514	+	0.896762i	$0.354087\pi$
$258$	−1.55294	+	1.55294i	−0.0966817	+	0.0966817i
$259$	1.17944	+	10.4150i	0.0732870	+	0.647159i
$260$	11.9997	+	3.39796i	0.744193	+	0.210732i
$261$	−3.77293	+	3.77293i	−0.233538	+	0.233538i
$262$	7.96621	+	7.96621i	0.492154	+	0.492154i
$263$	8.87946	−	8.87946i	0.547531	−	0.547531i	−0.378195	−	0.925726i	$-0.623455\pi$
$263$	8.87946	−	8.87946i	0.547531	−	0.547531i	0.925726	+	0.378195i	$0.123455\pi$
$264$	5.10050	−	5.10050i	0.313914	−	0.313914i
$265$	10.6341	−	5.94066i	0.653249	−	0.364932i
$266$	−4.73727			−0.290461
$267$	−14.9122			−0.912615
$268$	−5.29402	−	5.29402i	−0.323384	−	0.323384i
$269$			13.1011i			0.798790i	0.916779	+	0.399395i	$0.130780\pi$
$269$			13.1011i			0.798790i	−0.916779	+	0.399395i	$0.869220\pi$
$270$	−6.14427	−	10.9986i	−0.373929	−	0.669354i
$271$	−6.98656			−0.424403			−0.212202	−	0.977226i	$-0.568063\pi$
$271$	−6.98656			−0.424403			−0.212202	+	0.977226i	$0.568063\pi$
$272$	1.00832			0.0611384
$273$	14.2881			0.864752
$274$	13.2365	+	13.2365i	0.799648	+	0.799648i
$275$	−12.7194	+	20.6581i	−0.767006	+	1.24573i
$276$	−3.30140	−	3.30140i	−0.198721	−	0.198721i
$277$		−	14.9569i		−	0.898672i	−0.893363	−	0.449336i	$-0.851661\pi$
$277$		−	14.9569i		−	0.898672i	0.893363	−	0.449336i	$-0.148339\pi$
$278$			15.1028i			0.905804i
$279$	−1.35405	−	1.35405i	−0.0810651	−	0.0810651i
$280$	−3.36381	+	1.87916i	−0.201026	+	0.112302i
$281$	13.8446	+	13.8446i	0.825898	+	0.825898i	0.986947	−	0.161048i	$-0.0514875\pi$
$281$	13.8446	+	13.8446i	0.825898	+	0.825898i	−0.161048	+	0.986947i	$0.551487\pi$
$282$	−17.5743			−1.04654
$283$	−9.08448			−0.540017			−0.270008	−	0.962858i	$-0.587026\pi$
$283$	−9.08448			−0.540017			−0.270008	+	0.962858i	$0.587026\pi$
$284$	−7.15491			−0.424566
$285$	8.79321	+	2.48997i	0.520865	+	0.147493i
$286$			27.0616i			1.60019i
$287$	0.503106	+	0.503106i	0.0296974	+	0.0296974i
$288$	0.789858			0.0465428
$289$	−15.9833			−0.940194
$290$	−7.36685	−	13.1871i	−0.432597	−	0.774373i
$291$	2.21014	−	2.21014i	0.129561	−	0.129561i
$292$	−9.08993	+	9.08993i	−0.531948	+	0.531948i
$293$	−7.79244	−	7.79244i	−0.455239	−	0.455239i	0.441850	−	0.897089i	$-0.354322\pi$
$293$	−7.79244	−	7.79244i	−0.455239	−	0.455239i	−0.897089	+	0.441850i	$0.854322\pi$
$294$	4.23717	−	4.23717i	0.247117	−	0.247117i
$295$	11.3128	+	20.2506i	0.658656	+	1.17903i
$296$	4.75783	+	3.78986i	0.276543	+	0.220281i
$297$	19.3302	−	19.3302i	1.12165	−	1.12165i
$298$	21.2958			1.23363
$299$	17.5162			1.01299
$300$	7.23154	−	1.72000i	0.417513	−	0.0993041i
$301$	1.79999	+	1.79999i	0.103750	+	0.103750i
$302$	5.71666			0.328957
$303$	−7.00556	−	7.00556i	−0.402459	−	0.402459i
$304$	−1.94395	+	1.94395i	−0.111493	+	0.111493i
$305$	0.705973	+	1.26373i	0.0404239	+	0.0723612i
$306$	0.796429			0.0455288
$307$	2.77527	+	2.77527i	0.158393	+	0.158393i	0.781854	−	0.623461i	$-0.214274\pi$
$307$	2.77527	+	2.77527i	0.158393	+	0.158393i	−0.623461	+	0.781854i	$0.714274\pi$
$308$	−5.91193	−	5.91193i	−0.336864	−	0.336864i
$309$	−3.56095	+	3.56095i	−0.202575	+	0.202575i
$310$	4.73268	−	2.64387i	0.268798	−	0.150162i
$311$	−2.34988	+	2.34988i	−0.133249	+	0.133249i	−0.770586	−	0.637336i	$-0.780036\pi$
$311$	−2.34988	+	2.34988i	−0.133249	+	0.133249i	0.637336	+	0.770586i	$0.280036\pi$
$312$	5.86315	−	5.86315i	0.331936	−	0.331936i
$313$			10.8979i			0.615983i	0.951389	+	0.307991i	$0.0996568\pi$
$313$			10.8979i			0.615983i	−0.951389	+	0.307991i	$0.900343\pi$
$314$	−4.70753	−	4.70753i	−0.265661	−	0.265661i
$315$	−2.65693	+	1.48427i	−0.149701	+	0.0836292i
$316$	1.46413	−	1.46413i	0.0823636	−	0.0823636i
$317$	1.04250	+	1.04250i	0.0585527	+	0.0585527i	0.735777	−	0.677224i	$-0.236817\pi$
$317$	1.04250	+	1.04250i	0.0585527	+	0.0585527i	−0.677224	+	0.735777i	$0.736817\pi$
$318$		−	8.09855i		−	0.454144i
$319$	23.1764	−	23.1764i	1.29763	−	1.29763i
$320$	−0.609231	+	2.15147i	−0.0340570	+	0.120271i
$321$			14.0495i			0.784168i
$322$	−3.82662	+	3.82662i	−0.213249	+	0.213249i
$323$	−1.96013	+	1.96013i	−0.109064	+	0.109064i
$324$	−6.00655			−0.333697
$325$	−14.6212	+	23.7470i	−0.811040	+	1.31725i
$326$		−	7.46188i		−	0.413275i
$327$		−	24.5488i		−	1.35755i
$328$	0.412903			0.0227987
$329$			20.3702i			1.12305i
$330$	7.86620	+	14.0810i	0.433020	+	0.775132i
$331$	15.4412	+	15.4412i	0.848726	+	0.848726i	0.989974	−	0.141248i	$-0.0451116\pi$
$331$	15.4412	+	15.4412i	0.848726	+	0.848726i	−0.141248	+	0.989974i	$0.545112\pi$
$332$	−9.88040	−	9.88040i	−0.542257	−	0.542257i
$333$	3.75801	+	2.99345i	0.205938	+	0.164040i
$334$			19.1080i			1.04554i
$335$	14.6152	−	8.16466i	0.798515	−	0.446083i
$336$			2.56175i			0.139755i
$337$	−12.1788	−	12.1788i	−0.663422	−	0.663422i	0.292763	−	0.956185i	$-0.405425\pi$
$337$	−12.1788	−	12.1788i	−0.663422	−	0.663422i	−0.956185	+	0.292763i	$0.905425\pi$
$338$			18.1080i			0.984945i
$339$	4.41015	−	4.41015i	0.239526	−	0.239526i
$340$	−0.614300	+	2.16937i	−0.0333151	+	0.117651i
$341$	8.31773	+	8.31773i	0.450430	+	0.450430i
$342$	−1.53545	+	1.53545i	−0.0830275	+	0.0830275i
$343$	−13.4405	−	13.4405i	−0.725718	−	0.725718i
$344$	1.47727			0.0796489
$345$	9.11419	−	5.09156i	0.490691	−	0.274120i
$346$	−15.1632	−	15.1632i	−0.815180	−	0.815180i
$347$		−	13.0029i		−	0.698035i	−0.937116	−	0.349017i	$-0.886515\pi$
$347$		−	13.0029i		−	0.698035i	0.937116	−	0.349017i	$-0.113485\pi$
$348$	−10.0428			−0.538350
$349$		−	21.6550i		−	1.15917i	−0.814913	−	0.579584i	$-0.803215\pi$
$349$		−	21.6550i		−	1.15917i	0.814913	−	0.579584i	$-0.196785\pi$
$350$	−1.99363	−	8.38200i	−0.106564	−	0.448037i
$351$	22.2205	−	22.2205i	1.18604	−	1.18604i
$352$	−4.85196			−0.258610
$353$	−2.78988			−0.148490			−0.0742452	−	0.997240i	$-0.523655\pi$
$353$	−2.78988			−0.148490			−0.0742452	+	0.997240i	$0.523655\pi$
$354$	15.4221			0.819673
$355$	4.35899	−	15.3936i	0.231351	−	0.817007i
$356$	7.09280	+	7.09280i	0.375918	+	0.375918i
$357$			2.58307i			0.136710i
$358$	−9.36945	+	9.36945i	−0.495191	+	0.495191i
$359$			1.30687i			0.0689740i	0.999405	+	0.0344870i	$0.0109797\pi$
$359$			1.30687i			0.0689740i	−0.999405	+	0.0344870i	$0.989020\pi$
$360$	−0.481206	+	1.69936i	−0.0253618	+	0.0895640i
$361$			11.4421i			0.602215i
$362$			11.6623i			0.612955i
$363$	−13.1840	+	13.1840i	−0.691978	+	0.691978i
$364$	−6.79592	−	6.79592i	−0.356203	−	0.356203i
$365$	−14.0189	−	25.0946i	−0.733782	−	1.31351i
$366$	0.962411			0.0503061
$367$	19.2822	−	19.2822i	1.00652	−	1.00652i	0.00654459	−	0.999979i	$-0.497917\pi$
$367$	19.2822	−	19.2822i	1.00652	−	1.00652i	0.999979	−	0.00654459i	$-0.00208322\pi$
$368$			3.14053i			0.163711i
$369$	0.326134			0.0169779
$370$	−11.0524	+	7.92745i	−0.574587	+	0.412129i
$371$	−9.38694			−0.487346
$372$		−	3.60423i		−	0.186871i
$373$	−7.69384	+	7.69384i	−0.398372	+	0.398372i	−0.877658	−	0.479287i	$-0.840895\pi$
$373$	−7.69384	+	7.69384i	−0.398372	+	0.398372i	0.479287	+	0.877658i	$0.340895\pi$
$374$	−4.89233			−0.252976
$375$	−0.705149	+	16.6063i	−0.0364137	+	0.857548i
$376$	8.35899	+	8.35899i	0.431082	+	0.431082i
$377$	26.6419	−	26.6419i	1.37213	−	1.37213i
$378$			9.70868i			0.499360i
$379$			16.7516i			0.860474i	0.902716	+	0.430237i	$0.141570\pi$
$379$			16.7516i			0.860474i	−0.902716	+	0.430237i	$0.858430\pi$
$380$	−2.99805	−	5.36668i	−0.153797	−	0.275305i
$381$			18.2776i			0.936388i
$382$	17.6354	−	17.6354i	0.902304	−	0.902304i
$383$			11.5317i			0.589241i	0.955614	+	0.294620i	$0.0951932\pi$
$383$			11.5317i			0.589241i	−0.955614	+	0.294620i	$0.904807\pi$
$384$	1.05122	+	1.05122i	0.0536450	+	0.0536450i
$385$	16.3211	−	9.11763i	0.831800	−	0.464677i
$386$	−13.5647			−0.690425
$387$	1.16683			0.0593134
$388$	−2.10245			−0.106736
$389$	19.8314	−	19.8314i	1.00549	−	1.00549i	0.00550900	−	0.999985i	$-0.498246\pi$
$389$	19.8314	−	19.8314i	1.00549	−	1.00549i	0.999985	−	0.00550900i	$-0.00175358\pi$
$390$	9.04240	+	16.1864i	0.457880	+	0.819632i
$391$			3.16666i			0.160145i
$392$	−4.03070			−0.203581
$393$			16.7485i			0.844852i
$394$	−16.8769	−	16.8769i	−0.850247	−	0.850247i
$395$	2.25804	+	4.04202i	0.113614	+	0.203376i
$396$	−3.83236			−0.192583
$397$	15.8870	+	15.8870i	0.797343	+	0.797343i	0.982676	−	0.185333i	$-0.0593362\pi$
$397$	15.8870	+	15.8870i	0.797343	+	0.797343i	−0.185333	+	0.982676i	$0.559336\pi$
$398$	−9.13039	+	9.13039i	−0.457665	+	0.457665i
$399$	−4.97993	−	4.97993i	−0.249308	−	0.249308i
$400$	−4.25768	−	2.62149i	−0.212884	−	0.131074i
$401$	−13.4312	+	13.4312i	−0.670721	+	0.670721i	−0.957882	−	0.287161i	$-0.907289\pi$
$401$	−13.4312	+	13.4312i	−0.670721	+	0.670721i	0.287161	+	0.957882i	$0.407289\pi$
$402$		−	11.1304i		−	0.555134i
$403$	9.56144	+	9.56144i	0.476289	+	0.476289i
$404$			6.66420i			0.331556i
$405$	3.65938	−	12.9229i	0.181836	−	0.642146i
$406$			11.6405i			0.577708i
$407$	−23.0848	−	18.3882i	−1.14427	−	0.911471i
$408$	1.05997	+	1.05997i	0.0524763	+	0.0524763i
$409$	−16.9289	−	16.9289i	−0.837082	−	0.837082i	0.151392	−	0.988474i	$-0.451624\pi$
$409$	−16.9289	−	16.9289i	−0.837082	−	0.837082i	−0.988474	+	0.151392i	$0.951624\pi$
$410$	−0.251553	+	0.888349i	−0.0124233	+	0.0438725i
$411$			27.8291i			1.37271i
$412$	3.38743			0.166887
$413$		−	17.8755i		−	0.879598i
$414$			2.48057i			0.121913i
$415$	27.2769	−	15.2380i	1.33897	−	0.748003i
$416$	−5.57745			−0.273457
$417$	−15.8764	+	15.8764i	−0.777470	+	0.777470i
$418$	9.43199	−	9.43199i	0.461334	−	0.461334i
$419$			32.5124i			1.58834i	0.607698	+	0.794169i	$0.292093\pi$
$419$			32.5124i			1.58834i	−0.607698	+	0.794169i	$0.707907\pi$
$420$	−5.51154	−	1.56070i	−0.268936	−	0.0761543i
$421$	−18.5316	+	18.5316i	−0.903173	+	0.903173i	−0.995709	−	0.0925362i	$-0.970503\pi$
$421$	−18.5316	+	18.5316i	−0.903173	+	0.903173i	0.0925362	+	0.995709i	$0.470503\pi$
$422$			10.0888i			0.491114i
$423$	6.60241	+	6.60241i	0.321020	+	0.321020i
$424$	−3.85196	+	3.85196i	−0.187068	+	0.187068i
$425$	−4.29310	−	2.64330i	−0.208246	−	0.128219i
$426$	−7.52141	−	7.52141i	−0.364413	−	0.364413i
$427$		−	1.11552i		−	0.0539838i
$428$	6.68246	−	6.68246i	0.323009	−	0.323009i
$429$	−28.4478	+	28.4478i	−1.37347	+	1.37347i
$430$	−0.899997	+	3.17830i	−0.0434017	+	0.153271i
$431$	25.9149	−	25.9149i	1.24828	−	1.24828i	0.291796	−	0.956481i	$-0.405747\pi$
$431$	25.9149	−	25.9149i	1.24828	−	1.24828i	0.956481	−	0.291796i	$-0.0942529\pi$
$432$	3.98399	+	3.98399i	0.191680	+	0.191680i
$433$	21.8138	+	21.8138i	1.04830	+	1.04830i	0.998773	+	0.0495314i	$0.0157728\pi$
$433$	21.8138	+	21.8138i	1.04830	+	1.04830i	0.0495314	+	0.998773i	$0.484227\pi$
$434$	−4.17762			−0.200532
$435$	6.11838	−	21.6068i	0.293354	−	1.03597i
$436$	−11.6763	+	11.6763i	−0.559194	+	0.559194i
$437$	−6.10505	−	6.10505i	−0.292044	−	0.292044i
$438$	−19.1111			−0.913164
$439$	12.9479	+	12.9479i	0.617971	+	0.617971i	0.945011	−	0.327040i	$-0.106051\pi$
$439$	12.9479	+	12.9479i	0.617971	+	0.617971i	−0.327040	+	0.945011i	$0.606051\pi$
$440$	2.95597	−	10.4389i	0.140920	−	0.497653i
$441$	−3.18368			−0.151604
$442$	−5.62386			−0.267500
$443$	−2.00074	+	2.00074i	−0.0950579	+	0.0950579i	−0.753037	−	0.657979i	$-0.771412\pi$
$443$	−2.00074	+	2.00074i	−0.0950579	+	0.0950579i	0.657979	+	0.753037i	$0.271412\pi$
$444$	1.01756	+	8.98554i	0.0482912	+	0.426435i
$445$	−19.5811	+	10.9388i	−0.928235	+	0.518550i
$446$	2.45704	−	2.45704i	0.116344	−	0.116344i
$447$	22.3866	+	22.3866i	1.05885	+	1.05885i
$448$	1.21846	−	1.21846i	0.0575669	−	0.0575669i
$449$	17.2995	−	17.2995i	0.816412	−	0.816412i	−0.169174	−	0.985586i	$-0.554110\pi$
$449$	17.2995	−	17.2995i	0.816412	−	0.816412i	0.985586	+	0.169174i	$0.0541100\pi$
$450$	−3.36296	−	2.07060i	−0.158531	−	0.0976091i
$451$	−2.00339			−0.0943359
$452$	−4.19525			−0.197328
$453$	6.00949	+	6.00949i	0.282350	+	0.282350i
$454$			19.5967i			0.919720i
$455$	18.7615	−	10.4809i	0.879553	−	0.491354i
$456$	−4.08706			−0.191394
$457$	−24.4123			−1.14196			−0.570979	−	0.820965i	$-0.693436\pi$
$457$	−24.4123			−1.14196			−0.570979	+	0.820965i	$0.693436\pi$
$458$	8.54964			0.399498
$459$	4.01713	+	4.01713i	0.187504	+	0.187504i
$460$	−6.75677	−	1.91331i	−0.315036	−	0.0892085i
$461$	−14.1676	−	14.1676i	−0.659853	−	0.659853i	0.295492	−	0.955345i	$-0.404516\pi$
$461$	−14.1676	−	14.1676i	−0.659853	−	0.659853i	−0.955345	+	0.295492i	$0.904516\pi$
$462$		−	12.4295i		−	0.578274i
$463$		−	9.45035i		−	0.439195i	−0.975591	−	0.219597i	$-0.929526\pi$
$463$		−	9.45035i		−	0.439195i	0.975591	−	0.219597i	$-0.0704744\pi$
$464$	4.77672	+	4.77672i	0.221753	+	0.221753i
$465$	7.75441	+	2.19581i	0.359602	+	0.101828i
$466$	18.6855	+	18.6855i	0.865591	+	0.865591i
$467$	5.91129			0.273542			0.136771	−	0.990603i	$-0.456328\pi$
$467$	5.91129			0.273542			0.136771	+	0.990603i	$0.456328\pi$
$468$	−4.40539			−0.203639
$469$	−12.9011			−0.595718
$470$	−23.0767	+	12.8916i	−1.06445	+	0.594645i
$471$		−	9.89733i		−	0.456045i
$472$	−7.33529	−	7.33529i	−0.337634	−	0.337634i
$473$	−7.16765			−0.329569
$474$	3.07825			0.141389
$475$	13.3728	−	3.18067i	0.613585	−	0.145939i
$476$	1.22860	−	1.22860i	0.0563127	−	0.0563127i
$477$	−3.04250	+	3.04250i	−0.139307	+	0.139307i
$478$	14.5251	+	14.5251i	0.664362	+	0.664362i
$479$	15.1619	−	15.1619i	0.692764	−	0.692764i	−0.270075	−	0.962839i	$-0.587049\pi$
$479$	15.1619	−	15.1619i	0.692764	−	0.692764i	0.962839	+	0.270075i	$0.0870485\pi$
$480$	−2.90212	+	1.62124i	−0.132463	+	0.0739992i
$481$	−26.5366	−	21.1378i	−1.20996	−	0.963799i
$482$	−8.39707	+	8.39707i	−0.382476	+	0.382476i
$483$	−8.04526			−0.366072
$484$	12.5415			0.570069
$485$	1.28088	−	4.52336i	0.0581616	−	0.205395i
$486$	5.63773	+	5.63773i	0.255733	+	0.255733i
$487$	−21.5964			−0.978624			−0.489312	−	0.872109i	$-0.662752\pi$
$487$	−21.5964			−0.978624			−0.489312	+	0.872109i	$0.662752\pi$
$488$	−0.457758	−	0.457758i	−0.0207217	−	0.0207217i
$489$	7.84411	−	7.84411i	0.354723	−	0.354723i
$490$	2.45563	−	8.67194i	0.110934	−	0.391759i
$491$	36.1012			1.62922			0.814612	−	0.580006i	$-0.196950\pi$
$491$	36.1012			1.62922			0.814612	+	0.580006i	$0.196950\pi$
$492$	0.434053	+	0.434053i	0.0195686	+	0.0195686i
$493$	4.81646	+	4.81646i	0.216922	+	0.216922i
$494$	10.8423	−	10.8423i	0.487819	−	0.487819i
$495$	2.33479	−	8.24522i	0.104941	−	0.370595i
$496$	−1.71430	+	1.71430i	−0.0769744	+	0.0769744i
$497$	−8.71798	+	8.71798i	−0.391055	+	0.391055i
$498$		−	20.7730i		−	0.930861i
$499$	−8.86811	−	8.86811i	−0.396991	−	0.396991i	0.480179	−	0.877170i	$-0.340572\pi$
$499$	−8.86811	−	8.86811i	−0.396991	−	0.396991i	−0.877170	+	0.480179i	$0.840572\pi$
$500$	8.23397	−	7.56318i	0.368234	−	0.338236i
$501$	−20.0868	+	20.0868i	−0.897411	+	0.897411i
$502$	−6.65372	−	6.65372i	−0.296970	−	0.296970i
$503$			27.8555i			1.24202i	0.783804	+	0.621008i	$0.213277\pi$
$503$			27.8555i			1.24202i	−0.783804	+	0.621008i	$0.786723\pi$
$504$	0.962411	−	0.962411i	0.0428692	−	0.0428692i
$505$	−14.3378	−	4.06004i	−0.638026	−	0.180669i
$506$		−	15.2377i		−	0.677400i
$507$	−19.0356	+	19.0356i	−0.845399	+	0.845399i
$508$	8.69347	−	8.69347i	0.385710	−	0.385710i
$509$	37.8029			1.67558			0.837791	−	0.545990i	$-0.183847\pi$
$509$	37.8029			1.67558			0.837791	+	0.545990i	$0.183847\pi$
$510$	−2.92626	+	1.63473i	−0.129577	+	0.0723870i
$511$			22.1515i			0.979924i
$512$		−	1.00000i		−	0.0441942i
$513$	−15.4894			−0.683873
$514$		−	14.1881i		−	0.625809i
$515$	−2.06373	+	7.28797i	−0.0909387	+	0.321146i
$516$	1.55294	+	1.55294i	0.0683643	+	0.0683643i
$517$	−40.5575	−	40.5575i	−1.78372	−	1.78372i
$518$	10.4150	−	1.17944i	0.457610	−	0.0518217i
$519$		−	31.8799i		−	1.39937i
$520$	3.39796	−	11.9997i	0.149010	−	0.526224i
$521$			24.2905i			1.06419i	0.846685	+	0.532094i	$0.178595\pi$
$521$			24.2905i			1.06419i	−0.846685	+	0.532094i	$0.821405\pi$
$522$	3.77293	+	3.77293i	0.165136	+	0.165136i
$523$		−	34.6818i		−	1.51653i	−0.651946	−	0.758265i	$-0.726047\pi$
$523$		−	34.6818i		−	1.51653i	0.651946	−	0.758265i	$-0.273953\pi$
$524$	7.96621	−	7.96621i	0.348005	−	0.348005i
$525$	6.71560	−	10.9071i	0.293093	−	0.476025i
$526$	−8.87946	−	8.87946i	−0.387163	−	0.387163i
$527$	−1.72856	+	1.72856i	−0.0752975	+	0.0752975i
$528$	−5.10050	−	5.10050i	−0.221971	−	0.221971i
$529$	13.1371			0.571177
$530$	−5.94066	−	10.6341i	−0.258046	−	0.461917i
$531$	−5.79383	−	5.79383i	−0.251431	−	0.251431i
$532$			4.73727i			0.205387i
$533$	−2.30295			−0.0997517
$534$			14.9122i			0.645316i
$535$	10.3060	+	18.4483i	0.445566	+	0.797590i
$536$	−5.29402	+	5.29402i	−0.228667	+	0.228667i
$537$	−19.6988			−0.850065
$538$	13.1011			0.564830
$539$	19.5568			0.842371
$540$	−10.9986	+	6.14427i	−0.473305	+	0.264407i
$541$	6.04272	+	6.04272i	0.259797	+	0.259797i	0.824971	−	0.565175i	$-0.191191\pi$
$541$	6.04272	+	6.04272i	0.259797	+	0.259797i	−0.565175	+	0.824971i	$0.691191\pi$
$542$			6.98656i			0.300098i
$543$	−12.2596	+	12.2596i	−0.526111	+	0.526111i
$544$		−	1.00832i		−	0.0432313i
$545$	−18.0077	−	32.2349i	−0.771366	−	1.38079i
$546$		−	14.2881i		−	0.611472i
$547$			34.2347i			1.46377i	0.681428	+	0.731885i	$0.261359\pi$
$547$			34.2347i			1.46377i	−0.681428	+	0.731885i	$0.738641\pi$
$548$	13.2365	−	13.2365i	0.565436	−	0.565436i
$549$	−0.361563	−	0.361563i	−0.0154311	−	0.0154311i
$550$	20.6581	+	12.7194i	0.880863	+	0.542355i
$551$	−18.5714			−0.791170
$552$	−3.30140	+	3.30140i	−0.140517	+	0.140517i
$553$		−	3.56797i		−	0.151725i
$554$	−14.9569			−0.635457
$555$	−19.9521	−	3.28502i	−0.846918	−	0.139441i
$556$	15.1028			0.640500
$557$		−	21.2394i		−	0.899943i	−0.893043	−	0.449971i	$-0.851434\pi$
$557$		−	21.2394i		−	0.899943i	0.893043	−	0.449971i	$-0.148566\pi$
$558$	−1.35405	+	1.35405i	−0.0573217	+	0.0573217i
$559$	−8.23939			−0.348489
$560$	1.87916	+	3.36381i	0.0794092	+	0.142147i
$561$	−5.14293	−	5.14293i	−0.217135	−	0.217135i
$562$	13.8446	−	13.8446i	0.583998	−	0.583998i
$563$		−	20.2289i		−	0.852546i	−0.904594	−	0.426273i	$-0.859826\pi$
$563$		−	20.2289i		−	0.852546i	0.904594	−	0.426273i	$-0.140174\pi$
$564$			17.5743i			0.740013i
$565$	2.55588	−	9.02597i	0.107527	−	0.379725i
$566$			9.08448i			0.381849i
$567$	−7.31876	+	7.31876i	−0.307359	+	0.307359i
$568$			7.15491i			0.300213i
$569$	−2.40147	−	2.40147i	−0.100675	−	0.100675i	0.654975	−	0.755650i	$-0.272679\pi$
$569$	−2.40147	−	2.40147i	−0.100675	−	0.100675i	−0.755650	+	0.654975i	$0.772679\pi$
$570$	2.48997	−	8.79321i	0.104293	−	0.368307i
$571$	−7.39594			−0.309510			−0.154755	−	0.987953i	$-0.549459\pi$
$571$	−7.39594			−0.309510			−0.154755	+	0.987953i	$0.549459\pi$
$572$	27.0616			1.13150
$573$	37.0774			1.54893
$574$	0.503106	−	0.503106i	0.0209993	−	0.0209993i
$575$	8.23286	−	13.3714i	0.343334	−	0.557624i
$576$		−	0.789858i		−	0.0329107i
$577$	−38.1791			−1.58942			−0.794708	−	0.606993i	$-0.792376\pi$
$577$	−38.1791			−1.58942			−0.794708	+	0.606993i	$0.792376\pi$
$578$			15.9833i			0.664817i
$579$	−14.2595	−	14.2595i	−0.592606	−	0.592606i
$580$	−13.1871	+	7.36685i	−0.547565	+	0.305892i
$581$	−24.0778			−0.998915
$582$	−2.21014	−	2.21014i	−0.0916134	−	0.0916134i
$583$	18.6896	−	18.6896i	0.774043	−	0.774043i
$584$	9.08993	+	9.08993i	0.376144	+	0.376144i
$585$	2.68390	−	9.47809i	0.110966	−	0.391871i
$586$	−7.79244	+	7.79244i	−0.321903	+	0.321903i
$587$		−	21.8152i		−	0.900410i	−0.892925	−	0.450205i	$-0.851351\pi$
$587$		−	21.8152i		−	0.900410i	0.892925	−	0.450205i	$-0.148649\pi$
$588$	−4.23717	−	4.23717i	−0.174738	−	0.174738i
$589$		−	6.66505i		−	0.274629i
$590$	20.2506	−	11.3128i	0.833702	−	0.465740i
$591$		−	35.4828i		−	1.45957i
$592$	3.78986	−	4.75783i	0.155762	−	0.195546i
$593$	−4.84337	−	4.84337i	−0.198893	−	0.198893i	0.600632	−	0.799526i	$-0.294916\pi$
$593$	−4.84337	−	4.84337i	−0.198893	−	0.198893i	−0.799526	+	0.600632i	$0.794916\pi$
$594$	−19.3302	−	19.3302i	−0.793126	−	0.793126i
$595$	1.89480	+	3.39180i	0.0776791	+	0.139050i
$596$		−	21.2958i		−	0.872308i
$597$	−19.1962			−0.785647
$598$		−	17.5162i		−	0.716289i
$599$		−	29.5415i		−	1.20703i	−0.797350	−	0.603517i	$-0.793766\pi$
$599$		−	29.5415i		−	1.20703i	0.797350	−	0.603517i	$-0.206234\pi$
$600$	−1.72000	−	7.23154i	−0.0702186	−	0.295226i
$601$	6.21588			0.253551			0.126776	−	0.991931i	$-0.459537\pi$
$601$	6.21588			0.253551			0.126776	+	0.991931i	$0.459537\pi$
$602$	1.79999	−	1.79999i	0.0733623	−	0.0733623i
$603$	−4.18152	+	4.18152i	−0.170285	+	0.170285i
$604$		−	5.71666i		−	0.232608i
$605$	−7.64069	+	26.9828i	−0.310638	+	1.09701i
$606$	−7.00556	+	7.00556i	−0.284582	+	0.284582i
$607$		−	35.5553i		−	1.44314i	−0.692340	−	0.721572i	$-0.743420\pi$
$607$		−	35.5553i		−	1.44314i	0.692340	−	0.721572i	$-0.256580\pi$
$608$	1.94395	+	1.94395i	0.0788378	+	0.0788378i
$609$	−12.2368	+	12.2368i	−0.495859	+	0.495859i
$610$	1.26373	−	0.705973i	0.0511671	−	0.0285840i
$611$	−46.6219	−	46.6219i	−1.88612	−	1.88612i
$612$		−	0.796429i		−	0.0321937i
$613$	−23.4695	+	23.4695i	−0.947925	+	0.947925i	−0.998710	−	0.0507843i	$-0.983828\pi$
$613$	−23.4695	+	23.4695i	−0.947925	+	0.947925i	0.0507843	+	0.998710i	$0.483828\pi$
$614$	2.77527	−	2.77527i	0.112001	−	0.112001i
$615$	−1.19829	+	0.669415i	−0.0483198	+	0.0269934i
$616$	−5.91193	+	5.91193i	−0.238198	+	0.238198i
$617$	4.77446	+	4.77446i	0.192212	+	0.192212i	0.796651	−	0.604439i	$-0.206603\pi$
$617$	4.77446	+	4.77446i	0.192212	+	0.192212i	−0.604439	+	0.796651i	$0.706603\pi$
$618$	3.56095	+	3.56095i	0.143242	+	0.143242i
$619$	16.3058			0.655385			0.327692	−	0.944784i	$-0.393729\pi$
$619$	16.3058			0.655385			0.327692	+	0.944784i	$0.393729\pi$
$620$	−2.64387	−	4.73268i	−0.106180	−	0.190069i
$621$	−12.5118	+	12.5118i	−0.502083	+	0.502083i
$622$	2.34988	+	2.34988i	0.0942216	+	0.0942216i
$623$	17.2846			0.692494
$624$	−5.86315	−	5.86315i	−0.234714	−	0.234714i
$625$	11.2556	+	22.3229i	0.450224	+	0.892916i
$626$	10.8979			0.435566
$627$	19.8303			0.791945
$628$	−4.70753	+	4.70753i	−0.187851	+	0.187851i
$629$	3.82139	−	4.79742i	0.152369	−	0.191286i
$630$	1.48427	+	2.65693i	0.0591348	+	0.105855i
$631$	12.0883	−	12.0883i	0.481228	−	0.481228i	−0.424296	−	0.905524i	$-0.639478\pi$
$631$	12.0883	−	12.0883i	0.481228	−	0.481228i	0.905524	+	0.424296i	$0.139478\pi$
$632$	−1.46413	−	1.46413i	−0.0582398	−	0.0582398i
$633$	−10.6056	+	10.6056i	−0.421533	+	0.421533i
$634$	1.04250	−	1.04250i	0.0414030	−	0.0414030i
$635$	13.4074	+	24.0001i	0.532058	+	0.952415i
$636$	−8.09855			−0.321128
$637$	22.4810			0.890731
$638$	−23.1764	−	23.1764i	−0.917564	−	0.917564i
$639$			5.65136i			0.223564i
$640$	2.15147	+	0.609231i	0.0850445	+	0.0240820i
$641$	3.28760			0.129853			0.0649263	−	0.997890i	$-0.479319\pi$
$641$	3.28760			0.129853			0.0649263	+	0.997890i	$0.479319\pi$
$642$	14.0495			0.554490
$643$	31.8234			1.25499			0.627496	−	0.778620i	$-0.284080\pi$
$643$	31.8234			1.25499			0.627496	+	0.778620i	$0.284080\pi$
$644$	3.82662	+	3.82662i	0.150790	+	0.150790i
$645$	−4.28720	+	2.39501i	−0.168809	+	0.0943033i
$646$	1.96013	+	1.96013i	0.0771202	+	0.0771202i
$647$			26.7710i			1.05248i	0.850337	+	0.526239i	$0.176398\pi$
$647$			26.7710i			1.05248i	−0.850337	+	0.526239i	$0.823602\pi$
$648$			6.00655i			0.235960i
$649$	35.5905	+	35.5905i	1.39705	+	1.39705i
$650$	23.7470	+	14.6212i	0.931433	+	0.573492i
$651$	−4.39162	−	4.39162i	−0.172121	−	0.172121i
$652$	−7.46188			−0.292230
$653$	−12.7656			−0.499558			−0.249779	−	0.968303i	$-0.580358\pi$
$653$	−12.7656			−0.499558			−0.249779	+	0.968303i	$0.580358\pi$
$654$	−24.5488			−0.959936
$655$	12.2858	+	21.9923i	0.480047	+	0.859312i
$656$		−	0.412903i		−	0.0161211i
$657$	7.17975	+	7.17975i	0.280109	+	0.280109i
$658$	20.3702			0.794114
$659$	−26.8508			−1.04596			−0.522980	−	0.852345i	$-0.675180\pi$
$659$	−26.8508			−1.04596			−0.522980	+	0.852345i	$0.675180\pi$
$660$	14.0810	−	7.86620i	0.548101	−	0.306191i
$661$	−0.244360	+	0.244360i	−0.00950449	+	0.00950449i	−0.711843	−	0.702339i	$-0.752139\pi$
$661$	−0.244360	+	0.244360i	−0.00950449	+	0.00950449i	0.702339	+	0.711843i	$0.252139\pi$
$662$	15.4412	−	15.4412i	0.600140	−	0.600140i
$663$	−5.91193	−	5.91193i	−0.229600	−	0.229600i
$664$	−9.88040	+	9.88040i	−0.383434	+	0.383434i
$665$	−10.1921	−	2.88609i	−0.395233	−	0.111918i
$666$	2.99345	−	3.75801i	0.115994	−	0.145620i
$667$	−15.0014	+	15.0014i	−0.580857	+	0.580857i
$668$	19.1080			0.739310
$669$	5.16581			0.199722
$670$	−8.16466	−	14.6152i	−0.315428	−	0.564635i
$671$	2.22102	+	2.22102i	0.0857416	+	0.0857416i
$672$	2.56175			0.0988217
$673$	−21.2991	−	21.2991i	−0.821019	−	0.821019i	0.165236	−	0.986254i	$-0.447162\pi$
$673$	−21.2991	−	21.2991i	−0.821019	−	0.821019i	−0.986254	+	0.165236i	$0.947162\pi$
$674$	−12.1788	+	12.1788i	−0.469110	+	0.469110i
$675$	−6.51855	−	27.4065i	−0.250899	−	1.05488i
$676$	18.1080			0.696461
$677$	19.3523	+	19.3523i	0.743770	+	0.743770i	0.973301	−	0.229531i	$-0.0737193\pi$
$677$	19.3523	+	19.3523i	0.743770	+	0.743770i	−0.229531	+	0.973301i	$0.573719\pi$
$678$	−4.41015	−	4.41015i	−0.169371	−	0.169371i
$679$	−2.56175	+	2.56175i	−0.0983110	+	0.0983110i
$680$	2.16937	+	0.614300i	0.0831916	+	0.0235573i
$681$	−20.6005	+	20.6005i	−0.789414	+	0.789414i
$682$	8.31773	−	8.31773i	0.318502	−	0.318502i
$683$		−	23.3423i		−	0.893169i	−0.894742	−	0.446584i	$-0.852640\pi$
$683$		−	23.3423i		−	0.893169i	0.894742	−	0.446584i	$-0.147360\pi$
$684$	1.53545	+	1.53545i	0.0587093	+	0.0587093i
$685$	20.4139	+	36.5421i	0.779976	+	1.39620i
$686$	−13.4405	+	13.4405i	−0.513160	+	0.513160i
$687$	8.98758	+	8.98758i	0.342898	+	0.342898i
$688$		−	1.47727i		−	0.0563203i
$689$	21.4841	−	21.4841i	0.818480	−	0.818480i
$690$	−5.09156	−	9.11419i	−0.193832	−	0.346971i
$691$		−	19.1059i		−	0.726822i	−0.931629	−	0.363411i	$-0.881612\pi$
$691$		−	19.1059i		−	0.726822i	0.931629	−	0.363411i	$-0.118388\pi$
$692$	−15.1632	+	15.1632i	−0.576419	+	0.576419i
$693$	−4.66958	+	4.66958i	−0.177383	+	0.177383i
$694$	−13.0029			−0.493585
$695$	−9.20107	+	32.4932i	−0.349017	+	1.23254i
$696$			10.0428i			0.380671i
$697$		−	0.416338i		−	0.0157699i
$698$	−21.6550			−0.819655
$699$			39.2854i			1.48591i
$700$	−8.38200	+	1.99363i	−0.316810	+	0.0753522i
$701$	35.3393	+	35.3393i	1.33475	+	1.33475i	0.901067	+	0.433679i	$0.142785\pi$
$701$	35.3393	+	35.3393i	1.33475	+	1.33475i	0.433679	+	0.901067i	$0.357215\pi$
$702$	−22.2205	−	22.2205i	−0.838659	−	0.838659i
$703$	1.88170	+	16.6163i	0.0709697	+	0.626697i
$704$			4.85196i			0.182865i
$705$	−37.8107	−	10.7068i	−1.42403	−	0.403243i
$706$			2.78988i			0.104999i
$707$	8.12007	+	8.12007i	0.305387	+	0.305387i
$708$		−	15.4221i		−	0.579596i
$709$	−29.5655	+	29.5655i	−1.11036	+	1.11036i	−0.117254	+	0.993102i	$0.537409\pi$
$709$	−29.5655	+	29.5655i	−1.11036	+	1.11036i	−0.993102	+	0.117254i	$0.962591\pi$
$710$	−15.3936	−	4.35899i	−0.577711	−	0.163590i
$711$	−1.15645	−	1.15645i	−0.0433703	−	0.0433703i
$712$	7.09280	−	7.09280i	0.265814	−	0.265814i
$713$	−5.38382	−	5.38382i	−0.201626	−	0.201626i
$714$	2.58307			0.0966688
$715$	−16.4868	+	58.2223i	−0.616570	+	2.17739i
$716$	9.36945	+	9.36945i	0.350153	+	0.350153i
$717$			30.5382i			1.14047i
$718$	1.30687			0.0487720
$719$		−	0.762333i		−	0.0284302i	−0.999899	−	0.0142151i	$-0.995475\pi$
$719$		−	0.762333i		−	0.0284302i	0.999899	−	0.0142151i	$-0.00452496\pi$
$720$	1.69936	+	0.481206i	0.0633313	+	0.0179335i
$721$	4.12746	−	4.12746i	0.153715	−	0.153715i
$722$	11.4421			0.425830
$723$	−17.6544			−0.656574
$724$	11.6623			0.433424
$725$	−7.81560	−	32.8598i	−0.290264	−	1.22038i
$726$	13.1840	+	13.1840i	0.489302	+	0.489302i
$727$			3.28968i			0.122007i	0.998138	+	0.0610037i	$0.0194302\pi$
$727$			3.28968i			0.122007i	−0.998138	+	0.0610037i	$0.980570\pi$
$728$	−6.79592	+	6.79592i	−0.251873	+	0.251873i
$729$			29.8727i			1.10640i
$730$	−25.0946	+	14.0189i	−0.928794	+	0.518862i
$731$		−	1.48956i		−	0.0550933i
$732$		−	0.962411i		−	0.0355718i
$733$	−1.10605	+	1.10605i	−0.0408531	+	0.0408531i	−0.727238	−	0.686385i	$-0.759196\pi$
$733$	−1.10605	+	1.10605i	−0.0408531	+	0.0408531i	0.686385	+	0.727238i	$0.259196\pi$
$734$	−19.2822	−	19.2822i	−0.711719	−	0.711719i
$735$	11.6976	−	6.53474i	0.431471	−	0.241037i
$736$	3.14053			0.115761
$737$	25.6864	−	25.6864i	0.946169	−	0.946169i
$738$		−	0.326134i		−	0.0120052i
$739$	−15.8878			−0.584443			−0.292221	−	0.956351i	$-0.594394\pi$
$739$	−15.8878			−0.584443			−0.292221	+	0.956351i	$0.594394\pi$
$740$	7.92745	+	11.0524i	0.291419	+	0.406294i
$741$	22.7954			0.837410
$742$			9.38694i			0.344605i
$743$	−7.35293	+	7.35293i	−0.269753	+	0.269753i	−0.829001	−	0.559248i	$-0.811090\pi$
$743$	−7.35293	+	7.35293i	−0.269753	+	0.269753i	0.559248	+	0.829001i	$0.311090\pi$
$744$	−3.60423			−0.132137
$745$	45.8172	+	12.9740i	1.67861	+	0.475332i
$746$	7.69384	+	7.69384i	0.281691	+	0.281691i
$747$	−7.80411	+	7.80411i	−0.285537	+	0.285537i
$748$			4.89233i			0.178881i
$749$		−	16.2847i		−	0.595028i
$750$	16.6063	+	0.705149i	0.606378	+	0.0257484i
$751$		−	33.7019i		−	1.22980i	−0.788605	−	0.614900i	$-0.789196\pi$
$751$		−	33.7019i		−	1.22980i	0.788605	−	0.614900i	$-0.210804\pi$
$752$	8.35899	−	8.35899i	0.304821	−	0.304821i
$753$		−	13.9891i		−	0.509791i
$754$	−26.6419	−	26.6419i	−0.970241	−	0.970241i
$755$	12.2992	+	3.48277i	0.447615	+	0.126751i
$756$	9.70868			0.353101
$757$	−33.6937			−1.22462			−0.612309	−	0.790618i	$-0.709759\pi$
$757$	−33.6937			−1.22462			−0.612309	+	0.790618i	$0.709759\pi$
$758$	16.7516			0.608447
$759$	16.0183	−	16.0183i	0.581426	−	0.581426i
$760$	−5.36668	+	2.99805i	−0.194670	+	0.108751i
$761$			8.01511i			0.290548i	0.989391	+	0.145274i	$0.0464063\pi$
$761$			8.01511i			0.290548i	−0.989391	+	0.145274i	$0.953594\pi$
$762$	18.2776			0.662126
$763$			28.4543i			1.03011i
$764$	−17.6354	−	17.6354i	−0.638025	−	0.638025i
$765$	1.71350	+	0.485209i	0.0619516	+	0.0175428i
$766$	11.5317			0.416656
$767$	40.9122	+	40.9122i	1.47725	+	1.47725i
$768$	1.05122	−	1.05122i	0.0379328	−	0.0379328i
$769$	3.76573	+	3.76573i	0.135796	+	0.135796i	0.771737	−	0.635941i	$-0.219388\pi$
$769$	3.76573	+	3.76573i	0.135796	+	0.135796i	−0.635941	+	0.771737i	$0.719388\pi$
$770$	−9.11763	−	16.3211i	−0.328577	−	0.588171i
$771$	14.9148	−	14.9148i	0.537145	−	0.537145i
$772$			13.5647i			0.488204i
$773$	27.2082	+	27.2082i	0.978611	+	0.978611i	0.999776	−	0.0211650i	$-0.00673753\pi$
$773$	27.2082	+	27.2082i	0.978611	+	0.978611i	−0.0211650	+	0.999776i	$0.506738\pi$
$774$		−	1.16683i		−	0.0419409i
$775$	11.7930	−	2.80492i	0.423616	−	0.100756i
$776$			2.10245i			0.0754735i
$777$	12.1884	+	9.70868i	0.437256	+	0.348297i
$778$	−19.8314	−	19.8314i	−0.710992	−	0.710992i
$779$	0.802664	+	0.802664i	0.0287584	+	0.0287584i
$780$	16.1864	−	9.04240i	0.579567	−	0.323770i
$781$		−	34.7153i		−	1.24221i
$782$	3.16666			0.113239
$783$			38.0608i			1.36018i
$784$			4.03070i			0.143954i
$785$	−7.26015	−	12.9961i	−0.259126	−	0.463851i
$786$	16.7485			0.597400
$787$	−8.43368	+	8.43368i	−0.300628	+	0.300628i	−0.841260	−	0.540631i	$-0.818185\pi$
$787$	−8.43368	+	8.43368i	−0.300628	+	0.300628i	0.540631	+	0.841260i	$0.318185\pi$
$788$	−16.8769	+	16.8769i	−0.601215	+	0.601215i
$789$		−	18.6686i		−	0.664620i
$790$	4.04202	−	2.25804i	0.143809	−	0.0803374i
$791$	−5.11175	+	5.11175i	−0.181753	+	0.181753i
$792$			3.83236i			0.136177i
$793$	2.55312	+	2.55312i	0.0906640	+	0.0906640i
$794$	15.8870	−	15.8870i	0.563807	−	0.563807i
$795$	4.93389	−	17.4238i	0.174987	−	0.617959i
$796$	9.13039	+	9.13039i	0.323618	+	0.323618i
$797$			10.2289i			0.362327i	0.983453	+	0.181163i	$0.0579863\pi$
$797$			10.2289i			0.362327i	−0.983453	+	0.181163i	$0.942014\pi$
$798$	−4.97993	+	4.97993i	−0.176288	+	0.176288i
$799$	8.42854	−	8.42854i	0.298180	−	0.298180i
$800$	−2.62149	+	4.25768i	−0.0926836	+	0.150532i
$801$	5.60230	−	5.60230i	0.197948	−	0.197948i
$802$	13.4312	+	13.4312i	0.474272	+	0.474272i
$803$	−44.1040	−	44.1040i	−1.55640	−	1.55640i
$804$	−11.1304			−0.392539
$805$	−10.5642	+	5.90157i	−0.372338	+	0.208003i
$806$	9.56144	−	9.56144i	0.336787	−	0.336787i
$807$	13.7722	+	13.7722i	0.484805	+	0.484805i
$808$	6.66420			0.234446
$809$	14.1279	+	14.1279i	0.496711	+	0.496711i	0.910413	−	0.413701i	$-0.135764\pi$
$809$	14.1279	+	14.1279i	0.496711	+	0.496711i	−0.413701	+	0.910413i	$0.635764\pi$
$810$	−12.9229	−	3.65938i	−0.454066	−	0.128577i
$811$	36.1729			1.27020			0.635102	−	0.772428i	$-0.280958\pi$
$811$	36.1729			1.27020			0.635102	+	0.772428i	$0.280958\pi$
$812$	11.6405			0.408501
$813$	−7.34444	+	7.34444i	−0.257581	+	0.257581i
$814$	−18.3882	+	23.0848i	−0.644508	+	0.809123i
$815$	4.54601	−	16.0540i	0.159240	−	0.562349i
$816$	1.05997	−	1.05997i	0.0371064	−	0.0371064i
$817$	2.87174	+	2.87174i	0.100470	+	0.100470i
$818$	−16.9289	+	16.9289i	−0.591906	+	0.591906i
$819$	−5.36781	+	5.36781i	−0.187566	+	0.187566i
$820$	0.888349	+	0.251553i	0.0310225	+	0.00878462i
$821$	−9.97250			−0.348043			−0.174021	−	0.984742i	$-0.555676\pi$
$821$	−9.97250			−0.348043			−0.174021	+	0.984742i	$0.555676\pi$
$822$	27.8291			0.970651
$823$	−37.3136	−	37.3136i	−1.30067	−	1.30067i	−0.927939	−	0.372732i	$-0.878421\pi$
$823$	−37.3136	−	37.3136i	−1.30067	−	1.30067i	−0.372732	−	0.927939i	$-0.621579\pi$
$824$		−	3.38743i		−	0.118007i
$825$	8.34536	+	35.0872i	0.290548	+	1.22158i
$826$	−17.8755			−0.621970
$827$	−20.4583			−0.711404			−0.355702	−	0.934599i	$-0.615758\pi$
$827$	−20.4583			−0.711404			−0.355702	+	0.934599i	$0.615758\pi$
$828$	2.48057			0.0862058
$829$	−29.2865	−	29.2865i	−1.01716	−	1.01716i	−0.999850	−	0.0173134i	$-0.994489\pi$
$829$	−29.2865	−	29.2865i	−1.01716	−	1.01716i	−0.0173134	−	0.999850i	$-0.505511\pi$
$830$	−15.2380	−	27.2769i	−0.528918	−	0.946794i
$831$	−15.7230	−	15.7230i	−0.545426	−	0.545426i
$832$			5.57745i			0.193363i
$833$			4.06423i			0.140817i
$834$	15.8764	+	15.8764i	0.549754	+	0.549754i
$835$	−11.6412	+	41.1103i	−0.402860	+	1.42268i
$836$	−9.43199	−	9.43199i	−0.326212	−	0.326212i
$837$	−13.6595			−0.472142
$838$	32.5124			1.12312
$839$	43.3795			1.49763			0.748814	−	0.662780i	$-0.230624\pi$
$839$	43.3795			1.49763			0.748814	+	0.662780i	$0.230624\pi$
$840$	−1.56070	+	5.51154i	−0.0538492	+	0.190166i
$841$			16.6340i			0.573588i
$842$	18.5316	+	18.5316i	0.638640	+	0.638640i
$843$	29.1075			1.00252
$844$	10.0888			0.347270
$845$	−11.0320	+	38.9589i	−0.379511	+	1.34023i
$846$	6.60241	−	6.60241i	0.226996	−	0.226996i
$847$	15.2814	−	15.2814i	0.525074	−	0.525074i
$848$	3.85196	+	3.85196i	0.132277	+	0.132277i
$849$	−9.54983	+	9.54983i	−0.327749	+	0.327749i
$850$	−2.64330	+	4.29310i	−0.0906644	+	0.147252i
$851$	14.9421	+	11.9022i	0.512209	+	0.408001i
$852$	−7.52141	+	7.52141i	−0.257679	+	0.257679i
$853$	−6.00476			−0.205599			−0.102800	−	0.994702i	$-0.532780\pi$
$853$	−6.00476			−0.205599			−0.102800	+	0.994702i	$0.532780\pi$
$854$	−1.11552			−0.0381723
$855$	−4.23892	+	2.36803i	−0.144968	+	0.0809850i
$856$	−6.68246	−	6.68246i	−0.228402	−	0.228402i
$857$	0.245134			0.00837363			0.00418681	−	0.999991i	$-0.498667\pi$
$857$	0.245134			0.00837363			0.00418681	+	0.999991i	$0.498667\pi$
$858$	28.4478	+	28.4478i	0.971191	+	0.971191i
$859$	−19.6130	+	19.6130i	−0.669187	+	0.669187i	−0.957528	−	0.288341i	$-0.906896\pi$
$859$	−19.6130	+	19.6130i	−0.669187	+	0.669187i	0.288341	+	0.957528i	$0.406896\pi$
$860$	3.17830	+	0.899997i	0.108379	+	0.0306897i
$861$	1.05775			0.0360482
$862$	−25.9149	−	25.9149i	−0.882665	−	0.882665i
$863$	34.4543	+	34.4543i	1.17284	+	1.17284i	0.981530	+	0.191306i	$0.0612722\pi$
$863$	34.4543	+	34.4543i	1.17284	+	1.17284i	0.191306	+	0.981530i	$0.438728\pi$
$864$	3.98399	−	3.98399i	0.135538	−	0.135538i
$865$	−23.3854	−	41.8612i	−0.795126	−	1.42332i
$866$	21.8138	−	21.8138i	0.741263	−	0.741263i
$867$	−16.8020	+	16.8020i	−0.570626	+	0.570626i
$868$			4.17762i			0.141798i
$869$	7.10389	+	7.10389i	0.240983	+	0.240983i
$870$	−21.6068	−	6.11838i	−0.732539	−	0.207433i
$871$	29.5271	−	29.5271i	1.00049	−	1.00049i
$872$	11.6763	+	11.6763i	0.395410	+	0.395410i
$873$			1.66063i			0.0562039i
$874$	−6.10505	+	6.10505i	−0.206506	+	0.206506i
$875$	0.817330	−	19.2482i	0.0276308	−	0.650709i
$876$			19.1111i			0.645704i
$877$	−4.63548	+	4.63548i	−0.156529	+	0.156529i	−0.781027	−	0.624498i	$-0.785304\pi$
$877$	−4.63548	+	4.63548i	−0.156529	+	0.156529i	0.624498	+	0.781027i	$0.285304\pi$
$878$	12.9479	−	12.9479i	0.436971	−	0.436971i
$879$	−16.3832			−0.552591
$880$	−10.4389	−	2.95597i	−0.351894	−	0.0996456i
$881$		−	20.6076i		−	0.694288i	−0.937812	−	0.347144i	$-0.887152\pi$
$881$		−	20.6076i		−	0.694288i	0.937812	−	0.347144i	$-0.112848\pi$
$882$			3.18368i			0.107200i
$883$	−27.2177			−0.915950			−0.457975	−	0.888965i	$-0.651425\pi$
$883$	−27.2177			−0.915950			−0.457975	+	0.888965i	$0.651425\pi$
$884$			5.62386i			0.189151i
$885$	33.1801	+	9.39559i	1.11534	+	0.315829i
$886$	2.00074	+	2.00074i	0.0672161	+	0.0672161i
$887$	−10.8845	−	10.8845i	−0.365465	−	0.365465i	0.500355	−	0.865820i	$-0.333203\pi$
$887$	−10.8845	−	10.8845i	−0.365465	−	0.365465i	−0.865820	+	0.500355i	$0.833203\pi$
$888$	8.98554	−	1.01756i	0.301535	−	0.0341471i
$889$		−	21.1853i		−	0.710533i
$890$	10.9388	+	19.5811i	0.366670	+	0.656361i
$891$		−	29.1436i		−	0.976346i
$892$	−2.45704	−	2.45704i	−0.0822679	−	0.0822679i
$893$			32.4990i			1.08754i
$894$	22.3866	−	22.3866i	0.748720	−	0.748720i
$895$	−25.8663	+	14.4500i	−0.864614	+	0.483009i
$896$	−1.21846	−	1.21846i	−0.0407060	−	0.0407060i
$897$	18.4134	−	18.4134i	0.614806	−	0.614806i
$898$	−17.2995	−	17.2995i	−0.577291	−	0.577291i
$899$	−16.3775			−0.546219
$900$	−2.07060	+	3.36296i	−0.0690201	+	0.112099i
$901$	3.88401	+	3.88401i	0.129395	+	0.129395i
$902$			2.00339i			0.0667055i
$903$	3.78439			0.125937
$904$			4.19525i			0.139532i
$905$	−7.10501	+	25.0910i	−0.236178	+	0.834054i
$906$	6.00949	−	6.00949i	0.199652	−	0.199652i
$907$	35.7043			1.18554			0.592771	−	0.805371i	$-0.298034\pi$
$907$	35.7043			1.18554			0.592771	+	0.805371i	$0.298034\pi$
$908$	19.5967			0.650340
$909$	5.26377			0.174588
$910$	−10.4809	−	18.7615i	−0.347440	−	0.621938i
$911$	−29.2800	−	29.2800i	−0.970091	−	0.970091i	0.0294748	−	0.999566i	$-0.490617\pi$
$911$	−29.2800	−	29.2800i	−0.970091	−	0.970091i	−0.999566	+	0.0294748i	$0.990617\pi$
$912$			4.08706i			0.135336i
$913$	47.9393	−	47.9393i	1.58656	−	1.58656i
$914$			24.4123i			0.807486i
$915$	2.07060	+	0.586331i	0.0684520	+	0.0193835i
$916$		−	8.54964i		−	0.282488i
$917$		−	19.4130i		−	0.641075i
$918$	4.01713	−	4.01713i	0.132585	−	0.132585i
$919$	−22.4493	−	22.4493i	−0.740535	−	0.740535i	0.232146	−	0.972681i	$-0.425425\pi$
$919$	−22.4493	−	22.4493i	−0.740535	−	0.740535i	−0.972681	+	0.232146i	$0.925425\pi$
$920$	−1.91331	+	6.75677i	−0.0630799	+	0.222764i
$921$	5.83485			0.192265
$922$	−14.1676	+	14.1676i	−0.466587	+	0.466587i
$923$		−	39.9062i		−	1.31353i
$924$	−12.4295			−0.408901
$925$	−28.6086	+	10.3222i	−0.940645	+	0.339393i
$926$	−9.45035			−0.310558
$927$		−	2.67559i		−	0.0878778i
$928$	4.77672	−	4.77672i	0.156803	−	0.156803i
$929$	49.8210			1.63457			0.817286	−	0.576232i	$-0.195477\pi$
$929$	49.8210			1.63457			0.817286	+	0.576232i	$0.195477\pi$
$930$	2.19581	−	7.75441i	0.0720034	−	0.254277i
$931$	−7.83550	−	7.83550i	−0.256798	−	0.256798i
$932$	18.6855	−	18.6855i	0.612065	−	0.612065i
$933$			4.94050i			0.161745i
$934$		−	5.91129i		−	0.193423i
$935$	−10.5257	−	2.98056i	−0.344228	−	0.0974747i
$936$			4.40539i			0.143995i
$937$	−2.85125	+	2.85125i	−0.0931464	+	0.0931464i	−0.752145	−	0.658998i	$-0.770980\pi$
$937$	−2.85125	+	2.85125i	−0.0931464	+	0.0931464i	0.658998	+	0.752145i	$0.270980\pi$
$938$			12.9011i			0.421236i
$939$	11.4561	+	11.4561i	0.373855	+	0.373855i
$940$	12.8916	+	23.0767i	0.420477	+	0.752679i
$941$	45.3259			1.47758			0.738792	−	0.673934i	$-0.235397\pi$
$941$	45.3259			1.47758			0.738792	+	0.673934i	$0.235397\pi$
$942$	−9.89733			−0.322473
$943$	1.29673			0.0422275
$944$	−7.33529	+	7.33529i	−0.238743	+	0.238743i
$945$	−5.91483	+	20.8880i	−0.192409	+	0.679485i
$946$			7.16765i			0.233040i
$947$	35.8239			1.16412			0.582060	−	0.813146i	$-0.302247\pi$
$947$	35.8239			1.16412			0.582060	+	0.813146i	$0.302247\pi$
$948$		−	3.07825i		−	0.0999769i
$949$	−50.6987	−	50.6987i	−1.64575	−	1.64575i
$950$	−3.18067	−	13.3728i	−0.103195	−	0.433870i
$951$	2.19180			0.0710741
$952$	−1.22860	−	1.22860i	−0.0398191	−	0.0398191i
$953$	−38.2197	+	38.2197i	−1.23806	+	1.23806i	−0.277263	+	0.960794i	$0.589427\pi$
$953$	−38.2197	+	38.2197i	−1.23806	+	1.23806i	−0.960794	+	0.277263i	$0.910573\pi$
$954$	3.04250	+	3.04250i	0.0985046	+	0.0985046i
$955$	48.6860	−	27.1980i	1.57544	−	0.880107i
$956$	14.5251	−	14.5251i	0.469775	−	0.469775i
$957$		−	48.7273i		−	1.57513i
$958$	−15.1619	−	15.1619i	−0.489858	−	0.489858i
$959$		−	32.2564i		−	1.04161i
$960$	1.62124	+	2.90212i	0.0523253	+	0.0936654i
$961$			25.1223i			0.810398i
$962$	−21.1378	+	26.5366i	−0.681509	+	0.855574i
$963$	−5.27819	−	5.27819i	−0.170087	−	0.170087i
$964$	8.39707	+	8.39707i	0.270452	+	0.270452i
$965$	−29.1841	−	8.26403i	−0.939469	−	0.266029i
$966$			8.04526i			0.258852i
$967$	−12.1533			−0.390823			−0.195411	−	0.980721i	$-0.562604\pi$
$967$	−12.1533			−0.390823			−0.195411	+	0.980721i	$0.562604\pi$
$968$		−	12.5415i		−	0.403100i
$969$			4.12107i			0.132388i
$970$	−4.52336	−	1.28088i	−0.145236	−	0.0411265i
$971$	17.0273			0.546432			0.273216	−	0.961953i	$-0.411913\pi$
$971$	17.0273			0.546432			0.273216	+	0.961953i	$0.411913\pi$
$972$	5.63773	−	5.63773i	0.180830	−	0.180830i
$973$	18.4021	−	18.4021i	0.589946	−	0.589946i
$974$			21.5964i			0.691992i
$975$	9.59321	+	40.3336i	0.307229	+	1.29171i
$976$	−0.457758	+	0.457758i	−0.0146525	+	0.0146525i
$977$			51.9854i			1.66316i	0.555405	+	0.831580i	$0.312563\pi$
$977$			51.9854i			1.66316i	−0.555405	+	0.831580i	$0.687437\pi$
$978$	−7.84411	−	7.84411i	−0.250827	−	0.250827i
$979$	−34.4140	+	34.4140i	−1.09988	+	1.09988i
$980$	−8.67194	−	2.45563i	−0.277015	−	0.0784422i
$981$	9.22263	+	9.22263i	0.294456	+	0.294456i
$982$		−	36.1012i		−	1.15204i
$983$	29.0021	−	29.0021i	0.925025	−	0.925025i	−0.0723544	−	0.997379i	$-0.523051\pi$
$983$	29.0021	−	29.0021i	0.925025	−	0.925025i	0.997379	+	0.0723544i	$0.0230513\pi$
$984$	0.434053	−	0.434053i	0.0138371	−	0.0138371i
$985$	−26.0283	−	46.5922i	−0.829331	−	1.48455i
$986$	4.81646	−	4.81646i	0.153387	−	0.153387i
$987$	21.4137	+	21.4137i	0.681605	+	0.681605i
$988$	−10.8423	−	10.8423i	−0.344940	−	0.344940i
$989$	4.63940			0.147524
$990$	−8.24522	−	2.33479i	−0.262050	−	0.0742045i
$991$	−33.1692	+	33.1692i	−1.05366	+	1.05366i	−0.0551795	+	0.998476i	$0.517573\pi$
$991$	−33.1692	+	33.1692i	−1.05366	+	1.05366i	−0.998476	+	0.0551795i	$0.982427\pi$
$992$	1.71430	+	1.71430i	0.0544292	+	0.0544292i
$993$	32.4643			1.03022
$994$	8.71798	+	8.71798i	0.276518	+	0.276518i
$995$	−25.2063	+	14.0813i	−0.799094	+	0.446407i
$996$	−20.7730			−0.658218
$997$	15.7013			0.497264			0.248632	−	0.968598i	$-0.420019\pi$
$997$	15.7013			0.497264			0.248632	+	0.968598i	$0.420019\pi$
$998$	−8.86811	+	8.86811i	−0.280715	+	0.280715i
$999$	34.0539	−	3.85640i	1.07742	−	0.122011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.d.43.4	✓	10
5.2	odd	4		370.2.h.d.117.2	yes	10
37.31	odd	4		370.2.h.d.253.2	yes	10
185.142	even	4	inner	370.2.g.d.327.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.4	✓	10	1.1	even	1	trivial
370.2.g.d.327.4	yes	10	185.142	even	4	inner
370.2.h.d.117.2	yes	10	5.2	odd	4
370.2.h.d.253.2	yes	10	37.31	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.05122 - 1.05122i) q^{3} -1.00000 q^{4} +(0.609231 - 2.15147i) q^{5} +(-1.05122 - 1.05122i) q^{6} +(-1.21846 + 1.21846i) q^{7} +1.00000i q^{8} +0.789858i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.05122 - 1.05122i) q^{3} -1.00000 q^{4} +(0.609231 - 2.15147i) q^{5} +(-1.05122 - 1.05122i) q^{6} +(-1.21846 + 1.21846i) q^{7} +1.00000i q^{8} +0.789858i q^{9} +(-2.15147 - 0.609231i) q^{10} -4.85196i q^{11} +(-1.05122 + 1.05122i) q^{12} -5.57745i q^{13} +(1.21846 + 1.21846i) q^{14} +(-1.62124 - 2.90212i) q^{15} +1.00000 q^{16} +1.00832 q^{17} +0.789858 q^{18} +(-1.94395 + 1.94395i) q^{19} +(-0.609231 + 2.15147i) q^{20} +2.56175i q^{21} -4.85196 q^{22} +3.14053i q^{23} +(1.05122 + 1.05122i) q^{24} +(-4.25768 - 2.62149i) q^{25} -5.57745 q^{26} +(3.98399 + 3.98399i) q^{27} +(1.21846 - 1.21846i) q^{28} +(4.77672 + 4.77672i) q^{29} +(-2.90212 + 1.62124i) q^{30} +(-1.71430 + 1.71430i) q^{31} -1.00000i q^{32} +(-5.10050 - 5.10050i) q^{33} -1.00832i q^{34} +(1.87916 + 3.36381i) q^{35} -0.789858i q^{36} +(3.78986 - 4.75783i) q^{37} +(1.94395 + 1.94395i) q^{38} +(-5.86315 - 5.86315i) q^{39} +(2.15147 + 0.609231i) q^{40} -0.412903i q^{41} +2.56175 q^{42} -1.47727i q^{43} +4.85196i q^{44} +(1.69936 + 0.481206i) q^{45} +3.14053 q^{46} +(8.35899 - 8.35899i) q^{47} +(1.05122 - 1.05122i) q^{48} +4.03070i q^{49} +(-2.62149 + 4.25768i) q^{50} +(1.05997 - 1.05997i) q^{51} +5.57745i q^{52} +(3.85196 + 3.85196i) q^{53} +(3.98399 - 3.98399i) q^{54} +(-10.4389 - 2.95597i) q^{55} +(-1.21846 - 1.21846i) q^{56} +4.08706i q^{57} +(4.77672 - 4.77672i) q^{58} +(-7.33529 + 7.33529i) q^{59} +(1.62124 + 2.90212i) q^{60} +(-0.457758 + 0.457758i) q^{61} +(1.71430 + 1.71430i) q^{62} +(-0.962411 - 0.962411i) q^{63} -1.00000 q^{64} +(-11.9997 - 3.39796i) q^{65} +(-5.10050 + 5.10050i) q^{66} +(5.29402 + 5.29402i) q^{67} -1.00832 q^{68} +(3.30140 + 3.30140i) q^{69} +(3.36381 - 1.87916i) q^{70} +7.15491 q^{71} -0.789858 q^{72} +(9.08993 - 9.08993i) q^{73} +(-4.75783 - 3.78986i) q^{74} +(-7.23154 + 1.72000i) q^{75} +(1.94395 - 1.94395i) q^{76} +(5.91193 + 5.91193i) q^{77} +(-5.86315 + 5.86315i) q^{78} +(-1.46413 + 1.46413i) q^{79} +(0.609231 - 2.15147i) q^{80} +6.00655 q^{81} -0.412903 q^{82} +(9.88040 + 9.88040i) q^{83} -2.56175i q^{84} +(0.614300 - 2.16937i) q^{85} -1.47727 q^{86} +10.0428 q^{87} +4.85196 q^{88} +(-7.09280 - 7.09280i) q^{89} +(0.481206 - 1.69936i) q^{90} +(6.79592 + 6.79592i) q^{91} -3.14053i q^{92} +3.60423i q^{93} +(-8.35899 - 8.35899i) q^{94} +(2.99805 + 5.36668i) q^{95} +(-1.05122 - 1.05122i) q^{96} +2.10245 q^{97} +4.03070 q^{98} +3.83236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) 10 * q - 2 * q^3 - 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7	\( 10 q - 2 q^{3} - 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 2 q^{10} + 2 q^{12} + 4 q^{14} - 6 q^{15} + 10 q^{16} - 24 q^{17} - 18 q^{18} - 8 q^{19} - 2 q^{20} - 8 q^{22} - 2 q^{24} - 28 q^{25} - 12 q^{26} + 28 q^{27} + 4 q^{28} + 32 q^{29} + 14 q^{30} - 26 q^{31} - 24 q^{33} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 6 q^{39} - 2 q^{40} - 40 q^{42} + 4 q^{45} + 4 q^{46} + 48 q^{47} - 2 q^{48} + 16 q^{51} - 2 q^{53} + 28 q^{54} + 18 q^{55} - 4 q^{56} + 32 q^{58} + 20 q^{59} + 6 q^{60} - 24 q^{61} + 26 q^{62} + 20 q^{63} - 10 q^{64} - 28 q^{65} - 24 q^{66} + 10 q^{67} + 24 q^{68} + 46 q^{69} + 22 q^{70} - 16 q^{71} + 18 q^{72} - 4 q^{73} + 2 q^{74} - 48 q^{75} + 8 q^{76} + 24 q^{77} - 6 q^{78} + 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} + 10 q^{85} + 12 q^{86} + 8 q^{88} + 2 q^{89} - 10 q^{90} + 16 q^{91} - 48 q^{94} + 28 q^{95} + 2 q^{96} - 4 q^{97} - 18 q^{98} - 28 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 2 * q^10 + 2 * q^12 + 4 * q^14 - 6 * q^15 + 10 * q^16 - 24 * q^17 - 18 * q^18 - 8 * q^19 - 2 * q^20 - 8 * q^22 - 2 * q^24 - 28 * q^25 - 12 * q^26 + 28 * q^27 + 4 * q^28 + 32 * q^29 + 14 * q^30 - 26 * q^31 - 24 * q^33 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 6 * q^39 - 2 * q^40 - 40 * q^42 + 4 * q^45 + 4 * q^46 + 48 * q^47 - 2 * q^48 + 16 * q^51 - 2 * q^53 + 28 * q^54 + 18 * q^55 - 4 * q^56 + 32 * q^58 + 20 * q^59 + 6 * q^60 - 24 * q^61 + 26 * q^62 + 20 * q^63 - 10 * q^64 - 28 * q^65 - 24 * q^66 + 10 * q^67 + 24 * q^68 + 46 * q^69 + 22 * q^70 - 16 * q^71 + 18 * q^72 - 4 * q^73 + 2 * q^74 - 48 * q^75 + 8 * q^76 + 24 * q^77 - 6 * q^78 + 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 + 10 * q^85 + 12 * q^86 + 8 * q^88 + 2 * q^89 - 10 * q^90 + 16 * q^91 - 48 * q^94 + 28 * q^95 + 2 * q^96 - 4 * q^97 - 18 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more