LMFDB - Embedded newform 370.2.h.d.117.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			117.2
Root			$-1.66045 + 0.156295i$ of defining polynomial
Character	$\chi$	$=$	370.117
Dual form			370.2.h.d.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.05122	−	1.05122i	−0.606924	−	0.606924i	0.335217	−	0.942141i	$-0.391190\pi$
$3$	−1.05122	−	1.05122i	−0.606924	−	0.606924i	−0.942141	+	0.335217i	$0.891190\pi$
$4$	1.00000			0.500000
$5$	−2.15147	+	0.609231i	−0.962168	+	0.272456i
$5$	−2.15147	+	0.609231i	−0.962168	+	0.272456i
$6$	−1.05122	−	1.05122i	−0.429160	−	0.429160i
$7$	−1.21846	−	1.21846i	−0.460535	−	0.460535i	0.438296	−	0.898831i	$-0.355582\pi$
$7$	−1.21846	−	1.21846i	−0.460535	−	0.460535i	−0.898831	+	0.438296i	$0.855582\pi$
$8$	1.00000			0.353553
$9$		−	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
$13$	−5.57745			−1.54691			−0.773454	−	0.633853i	$-0.781472\pi$
$13$	−5.57745			−1.54691			−0.773454	+	0.633853i	$0.781472\pi$
$14$	−1.21846	−	1.21846i	−0.325648	−	0.325648i
$15$	2.90212	+	1.62124i	0.749324	+	0.418603i
$16$	1.00000			0.250000
$17$			1.00832i			0.244553i	0.992496	+	0.122277i	$0.0390195\pi$
$17$			1.00832i			0.244553i	−0.992496	+	0.122277i	$0.960980\pi$
$18$		−	0.789858i		−	0.186171i
$19$	1.94395	−	1.94395i	0.445974	−	0.445974i	−0.448040	−	0.894014i	$-0.647878\pi$
$19$	1.94395	−	1.94395i	0.445974	−	0.445974i	0.894014	+	0.448040i	$0.147878\pi$
$20$	−2.15147	+	0.609231i	−0.481084	+	0.136228i
$21$			2.56175i			0.559020i
$22$		−	4.85196i		−	1.03444i
$23$	3.14053			0.654846			0.327423	−	0.944878i	$-0.393820\pi$
$23$	3.14053			0.654846			0.327423	+	0.944878i	$0.393820\pi$
$24$	−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	0.107221	−	0.994235i	$-0.465805\pi$
$29$	−4.77672	−	4.77672i	−0.887014	−	0.887014i	−0.994235	+	0.107221i	$0.965805\pi$
$30$	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	$0.319861\pi$
$32$	1.00000			0.176777
$33$	−5.10050	+	5.10050i	−0.887882	+	0.887882i
$34$			1.00832i			0.172925i
$35$	3.36381	+	1.87916i	0.568588	+	0.317637i
$36$		−	0.789858i		−	0.131643i
$37$	4.75783	+	3.78986i	0.782183	+	0.623049i
$37$	4.75783	+	3.78986i	0.782183	+	0.623049i
$38$	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	$-0.0102648\pi$
$42$			2.56175i			0.395287i
$43$	−1.47727			−0.225281			−0.112641	−	0.993636i	$-0.535931\pi$
$43$	−1.47727			−0.225281			−0.112641	+	0.993636i	$0.535931\pi$
$44$		−	4.85196i		−	0.731461i
$45$	0.481206	+	1.69936i	0.0717339	+	0.253325i
$46$	3.14053			0.463046
$47$	8.35899	+	8.35899i	1.21928	+	1.21928i	0.967883	+	0.251401i	$0.0808914\pi$
$47$	8.35899	+	8.35899i	1.21928	+	1.21928i	0.251401	+	0.967883i	$0.419109\pi$
$48$	−1.05122	−	1.05122i	−0.151731	−	0.151731i
$49$		−	4.03070i		−	0.575814i
$50$	4.25768	−	2.62149i	0.602126	−	0.370734i
$51$	1.05997	−	1.05997i	0.148425	−	0.148425i
$52$	−5.57745			−0.773454
$53$	3.85196	−	3.85196i	0.529108	−	0.529108i	−0.391199	−	0.920306i	$-0.627939\pi$
$53$	3.85196	−	3.85196i	0.529108	−	0.529108i	0.920306	+	0.391199i	$0.127939\pi$
$54$	−3.98399	+	3.98399i	−0.542152	+	0.542152i
$55$	2.95597	+	10.4389i	0.398582	+	1.40758i
$56$	−1.21846	−	1.21846i	−0.162824	−	0.162824i
$57$	−4.08706			−0.541345
$58$	−4.77672	−	4.77672i	−0.627214	−	0.627214i
$59$	7.33529	−	7.33529i	0.954973	−	0.954973i	−0.0440560	−	0.999029i	$-0.514028\pi$
$59$	7.33529	−	7.33529i	0.954973	−	0.954973i	0.999029	+	0.0440560i	$0.0140280\pi$
$60$	2.90212	+	1.62124i	0.374662	+	0.209301i
$61$	−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	$-0.901195\pi$
$67$	−5.29402	+	5.29402i	−0.646767	+	0.646767i	0.305443	+	0.952210i	$0.401195\pi$
$68$			1.00832i			0.122277i
$69$	−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	$0.360427\pi$
$72$		−	0.789858i		−	0.0930856i
$73$	−9.08993	−	9.08993i	−1.06390	−	1.06390i	−0.997814	−	0.0660820i	$-0.978950\pi$
$73$	−9.08993	−	9.08993i	−1.06390	−	1.06390i	−0.0660820	−	0.997814i	$-0.521050\pi$
$74$	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	−0.619930	−	0.784657i	$-0.712839\pi$
$79$	1.46413	−	1.46413i	0.164727	−	0.164727i	0.784657	+	0.619930i	$0.212839\pi$
$80$	−2.15147	+	0.609231i	−0.240542	+	0.0681141i
$81$	6.00655			0.667395
$82$		−	0.412903i		−	0.0455975i
$83$	9.88040	−	9.88040i	1.08451	−	1.08451i	0.0884327	−	0.996082i	$-0.471814\pi$
$83$	9.88040	−	9.88040i	1.08451	−	1.08451i	0.996082	−	0.0884327i	$-0.0281858\pi$
$84$			2.56175i			0.279510i
$85$	−0.614300	−	2.16937i	−0.0666301	−	0.235302i
$86$	−1.47727			−0.159298
$87$			10.0428i			1.07670i
$88$		−	4.85196i		−	0.517221i
$89$	7.09280	+	7.09280i	0.751836	+	0.751836i	0.974822	−	0.222986i	$-0.0715804\pi$
$89$	7.09280	+	7.09280i	0.751836	+	0.751836i	−0.222986	+	0.974822i	$0.571580\pi$
$90$	0.481206	+	1.69936i	0.0507235	+	0.179128i
$91$	6.79592	+	6.79592i	0.712406	+	0.712406i
$92$	3.14053			0.327423
$93$	3.60423			0.373741
$94$	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
$97$			2.10245i			0.213471i	0.994287	+	0.106736i	$0.0340398\pi$
$97$			2.10245i			0.213471i	−0.994287	+	0.106736i	$0.965960\pi$
$98$		−	4.03070i		−	0.407162i
$99$	−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
$103$			3.38743i			0.333774i	0.985976	+	0.166887i	$0.0533714\pi$
$103$			3.38743i			0.333774i	−0.985976	+	0.166887i	$0.946629\pi$
$104$	−5.57745			−0.546914
$105$	−1.56070	−	5.51154i	−0.152309	−	0.537871i
$106$	3.85196	−	3.85196i	0.374136	−	0.374136i
$107$	−6.68246	−	6.68246i	−0.646018	−	0.646018i	0.306010	−	0.952028i	$-0.401006\pi$
$107$	−6.68246	−	6.68246i	−0.646018	−	0.646018i	−0.952028	+	0.306010i	$0.901006\pi$
$108$	−3.98399	+	3.98399i	−0.383359	+	0.383359i
$109$	−11.6763	+	11.6763i	−1.11839	+	1.11839i	−0.126410	+	0.991978i	$0.540346\pi$
$109$	−11.6763	+	11.6763i	−1.11839	+	1.11839i	−0.991978	+	0.126410i	$0.959654\pi$
$110$	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
$113$		−	4.19525i		−	0.394656i	−0.980338	−	0.197328i	$-0.936774\pi$
$113$		−	4.19525i		−	0.394656i	0.980338	−	0.197328i	$-0.0632264\pi$
$114$	−4.08706			−0.382788
$115$	−6.75677	+	1.91331i	−0.630072	+	0.178417i
$116$	−4.77672	−	4.77672i	−0.443507	−	0.443507i
$117$			4.40539i			0.407279i
$118$	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
$125$	−7.56318	+	8.23397i	−0.676472	+	0.736469i
$126$	−0.962411	+	0.962411i	−0.0857384	+	0.0857384i
$127$	−8.69347	−	8.69347i	−0.771421	−	0.771421i	0.206934	−	0.978355i	$-0.433651\pi$
$127$	−8.69347	−	8.69347i	−0.771421	−	0.771421i	−0.978355	+	0.206934i	$0.933651\pi$
$128$	1.00000			0.0883883
$129$	1.55294	+	1.55294i	0.136729	+	0.136729i
$130$	11.9997	−	3.39796i	1.05245	−	0.298021i
$131$	−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
$133$	−4.73727			−0.410773
$134$	−5.29402	+	5.29402i	−0.457333	+	0.457333i
$135$	6.14427	−	10.9986i	0.528815	−	0.946610i
$136$			1.00832i			0.0864627i
$137$	−13.2365	−	13.2365i	−1.13087	−	1.13087i	−0.990032	−	0.140840i	$-0.955020\pi$
$137$	−13.2365	−	13.2365i	−1.13087	−	1.13087i	−0.140840	−	0.990032i	$-0.544980\pi$
$138$	−3.30140	−	3.30140i	−0.281034	−	0.281034i
$139$	15.1028			1.28100			0.640500	−	0.767958i	$-0.278727\pi$
$139$	15.1028			1.28100			0.640500	+	0.767958i	$0.278727\pi$
$140$	3.36381	+	1.87916i	0.284294	+	0.158818i
$141$		−	17.5743i		−	1.48003i
$142$	7.15491			0.600427
$143$			27.0616i			2.26300i
$144$		−	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
$148$	4.75783	+	3.78986i	0.391092	+	0.311524i
$149$		−	21.2958i		−	1.74462i	−0.488957	−	0.872308i	$-0.662622\pi$
$149$		−	21.2958i		−	1.74462i	0.488957	−	0.872308i	$-0.337378\pi$
$150$	−7.23154	−	1.72000i	−0.590453	−	0.140437i
$151$			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
$153$	0.796429			0.0643875
$154$	−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	0.869549	−	0.493847i	$-0.164410\pi$
$157$	4.70753	+	4.70753i	0.375702	+	0.375702i	−0.493847	+	0.869549i	$0.664410\pi$
$158$	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
$162$	6.00655			0.471919
$163$		−	7.46188i		−	0.584460i	−0.956348	−	0.292230i	$-0.905603\pi$
$163$		−	7.46188i		−	0.584460i	0.956348	−	0.292230i	$-0.0943972\pi$
$164$		−	0.412903i		−	0.0322423i
$165$	7.86620	−	14.0810i	0.612383	−	1.09620i
$166$	9.88040	−	9.88040i	0.766868	−	0.766868i
$167$		−	19.1080i		−	1.47862i	−0.673365	−	0.739310i	$-0.735152\pi$
$167$		−	19.1080i		−	1.47862i	0.673365	−	0.739310i	$-0.264848\pi$
$168$			2.56175i			0.197643i
$169$	18.1080			1.39292
$170$	−0.614300	−	2.16937i	−0.0471146	−	0.166383i
$171$	−1.53545	−	1.53545i	−0.117419	−	0.117419i
$172$	−1.47727			−0.112641
$173$	−15.1632	−	15.1632i	−1.15284	−	1.15284i	−0.985981	−	0.166858i	$-0.946638\pi$
$173$	−15.1632	−	15.1632i	−1.15284	−	1.15284i	−0.166858	−	0.985981i	$-0.553362\pi$
$174$			10.0428i			0.761342i
$175$	−8.38200	−	1.99363i	−0.633620	−	0.150704i
$176$		−	4.85196i		−	0.365730i
$177$	−15.4221			−1.15919
$178$	7.09280	+	7.09280i	0.531628	+	0.531628i
$179$	9.36945	+	9.36945i	0.700305	+	0.700305i	0.964476	−	0.264171i	$-0.0850982\pi$
$179$	9.36945	+	9.36945i	0.700305	+	0.700305i	−0.264171	+	0.964476i	$0.585098\pi$
$180$	0.481206	+	1.69936i	0.0358670	+	0.126663i
$181$	−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
$183$	0.962411			0.0711435
$184$	3.14053			0.231523
$185$	−12.5453	−	5.25516i	−0.922345	−	0.386367i
$186$	3.60423			0.264275
$187$	4.89233			0.357762
$188$	8.35899	+	8.35899i	0.609642	+	0.609642i
$189$	9.70868			0.706202
$190$	−2.99805	+	5.36668i	−0.217501	+	0.389340i
$191$	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
$193$	−13.5647			−0.976408			−0.488204	−	0.872729i	$-0.662348\pi$
$193$	−13.5647			−0.976408			−0.488204	+	0.872729i	$0.662348\pi$
$194$			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	0.973425	+	0.229006i	$0.0735474\pi$
$197$	16.8769	+	16.8769i	1.20243	+	1.20243i	0.229006	+	0.973425i	$0.426453\pi$
$198$	−3.83236			−0.272354
$199$	9.13039	+	9.13039i	0.647236	+	0.647236i	0.952324	−	0.305088i	$-0.0986858\pi$
$199$	9.13039	+	9.13039i	0.647236	+	0.647236i	−0.305088	+	0.952324i	$0.598686\pi$
$200$	4.25768	−	2.62149i	0.301063	−	0.185367i
$201$	11.1304			0.785077
$202$		−	6.66420i		−	0.468891i
$203$			11.6405i			0.817003i
$204$	1.05997	−	1.05997i	0.0742127	−	0.0742127i
$205$	0.251553	+	0.888349i	0.0175692	+	0.0620450i
$206$			3.38743i			0.236014i
$207$		−	2.48057i		−	0.172412i
$208$	−5.57745			−0.386727
$209$	−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
$217$	4.17762			0.283596
$218$	−11.6763	+	11.6763i	−0.790820	+	0.790820i
$219$			19.1111i			1.29141i
$220$	2.95597	+	10.4389i	0.199291	+	0.703788i
$221$		−	5.62386i		−	0.378302i
$222$	−1.01756	−	8.98554i	−0.0682941	−	0.603070i
$223$	2.45704	−	2.45704i	0.164536	−	0.164536i	−0.620037	−	0.784573i	$-0.712882\pi$
$223$	2.45704	−	2.45704i	0.164536	−	0.164536i	0.784573	+	0.620037i	$0.212882\pi$
$224$	−1.21846	−	1.21846i	−0.0814119	−	0.0814119i
$225$	−2.07060	−	3.36296i	−0.138040	−	0.224197i
$226$		−	4.19525i		−	0.279064i
$227$		−	19.5967i		−	1.30068i	−0.759643	−	0.650340i	$-0.774626\pi$
$227$		−	19.5967i		−	1.30068i	0.759643	−	0.650340i	$-0.225374\pi$
$228$	−4.08706			−0.270672
$229$		−	8.54964i		−	0.564976i	−0.959271	−	0.282488i	$-0.908840\pi$
$229$		−	8.54964i		−	0.564976i	0.959271	−	0.282488i	$-0.0911597\pi$
$230$	−6.75677	+	1.91331i	−0.445528	+	0.126160i
$231$	12.4295			0.817803
$232$	−4.77672	−	4.77672i	−0.313607	−	0.313607i
$233$	18.6855	+	18.6855i	1.22413	+	1.22413i	0.966150	+	0.257980i	$0.0830568\pi$
$233$	18.6855	+	18.6855i	1.22413	+	1.22413i	0.257980	+	0.966150i	$0.416943\pi$
$234$			4.40539i			0.287990i
$235$	−23.0767	−	12.8916i	−1.50536	−	0.840955i
$236$	7.33529	−	7.33529i	0.477487	−	0.477487i
$237$	−3.07825			−0.199954
$238$	1.22860	−	1.22860i	0.0796383	−	0.0796383i
$239$	14.5251	−	14.5251i	0.939550	−	0.939550i	−0.0587243	−	0.998274i	$-0.518703\pi$
$239$	14.5251	−	14.5251i	0.939550	−	0.939550i	0.998274	+	0.0587243i	$0.0187033\pi$
$240$	2.90212	+	1.62124i	0.187331	+	0.104651i
$241$	−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	$0.874929\pi$
$242$	−12.5415			−0.806200
$243$	5.63773	+	5.63773i	0.361661	+	0.361661i
$244$	−0.457758	+	0.457758i	−0.0293049	+	0.0293049i
$245$	2.45563	+	8.67194i	0.156884	+	0.554030i
$246$	−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
$253$		−	15.2377i		−	0.957988i
$254$	−8.69347	−	8.69347i	−0.545477	−	0.545477i
$255$	−1.63473	+	2.92626i	−0.102371	+	0.183250i
$256$	1.00000			0.0625000
$257$			14.1881i			0.885028i	0.896762	+	0.442514i	$0.145913\pi$
$257$			14.1881i			0.885028i	−0.896762	+	0.442514i	$0.854087\pi$
$258$	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	$-0.376545\pi$
$263$	−8.87946	−	8.87946i	−0.547531	−	0.547531i	−0.925726	+	0.378195i	$0.876545\pi$
$264$	−5.10050	+	5.10050i	−0.313914	+	0.313914i
$265$	−5.94066	+	10.6341i	−0.364932	+	0.653249i
$266$	−4.73727			−0.290461
$267$		−	14.9122i		−	0.912615i
$268$	−5.29402	+	5.29402i	−0.323384	+	0.323384i
$269$		−	13.1011i		−	0.798790i	−0.916779	−	0.399395i	$-0.869220\pi$
$269$		−	13.1011i		−	0.798790i	0.916779	−	0.399395i	$-0.130780\pi$
$270$	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	$0.568063\pi$
$272$			1.00832i			0.0611384i
$273$		−	14.2881i		−	0.864752i
$274$	−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
$277$	14.9569			0.898672			0.449336	−	0.893363i	$-0.351661\pi$
$277$	14.9569			0.898672			0.449336	+	0.893363i	$0.351661\pi$
$278$	15.1028			0.905804
$279$	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	$0.551487\pi$
$282$		−	17.5743i		−	1.04654i
$283$			9.08448i			0.540017i	0.962858	+	0.270008i	$0.0870264\pi$
$283$			9.08448i			0.540017i	−0.962858	+	0.270008i	$0.912974\pi$
$284$	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
$288$		−	0.789858i		−	0.0465428i
$289$	15.9833			0.940194
$290$	13.1871	+	7.36685i	0.774373	+	0.432597i
$291$	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	−0.897089	−	0.441850i	$-0.854322\pi$
$293$	−7.79244	+	7.79244i	−0.455239	+	0.455239i	0.441850	+	0.897089i	$0.354322\pi$
$294$	−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
$298$		−	21.2958i		−	1.23363i
$299$	−17.5162			−1.01299
$300$	−7.23154	−	1.72000i	−0.417513	−	0.0993041i
$301$	1.79999	+	1.79999i	0.103750	+	0.103750i
$302$			5.71666i			0.328957i
$303$	−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	$-0.785726\pi$
$307$	−2.77527	+	2.77527i	−0.158393	+	0.158393i	0.623461	+	0.781854i	$0.285726\pi$
$308$	−5.91193	+	5.91193i	−0.336864	+	0.336864i
$309$	3.56095	−	3.56095i	0.202575	−	0.202575i
$310$	2.64387	−	4.73268i	0.150162	−	0.268798i
$311$	−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
$313$	10.8979			0.615983			0.307991	−	0.951389i	$-0.400343\pi$
$313$	10.8979			0.615983			0.307991	+	0.951389i	$0.400343\pi$
$314$	4.70753	+	4.70753i	0.265661	+	0.265661i
$315$	1.48427	−	2.65693i	0.0836292	−	0.149701i
$316$	1.46413	−	1.46413i	0.0823636	−	0.0823636i
$317$	−1.04250	+	1.04250i	−0.0585527	+	0.0585527i	−0.735777	−	0.677224i	$-0.763183\pi$
$317$	−1.04250	+	1.04250i	−0.0585527	+	0.0585527i	0.677224	+	0.735777i	$0.263183\pi$
$318$	−8.09855			−0.454144
$319$	−23.1764	+	23.1764i	−1.29763	+	1.29763i
$320$	−2.15147	+	0.609231i	−0.120271	+	0.0340570i
$321$			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
$325$	−23.7470	+	14.6212i	−1.31725	+	0.811040i
$326$		−	7.46188i		−	0.413275i
$327$	24.5488			1.35755
$328$		−	0.412903i		−	0.0227987i
$329$		−	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
$333$	2.99345	−	3.75801i	0.164040	−	0.205938i
$334$		−	19.1080i		−	1.04554i
$335$	8.16466	−	14.6152i	0.446083	−	0.798515i
$336$			2.56175i			0.139755i
$337$	12.1788	−	12.1788i	0.663422	−	0.663422i	−0.292763	−	0.956185i	$-0.594575\pi$
$337$	12.1788	−	12.1788i	0.663422	−	0.663422i	0.956185	+	0.292763i	$0.0945746\pi$
$338$	18.1080			0.984945
$339$	−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
$347$	13.0029			0.698035			0.349017	−	0.937116i	$-0.386515\pi$
$347$	13.0029			0.698035			0.349017	+	0.937116i	$0.386515\pi$
$348$			10.0428i			0.538350i
$349$			21.6550i			1.15917i	0.814913	+	0.579584i	$0.196785\pi$
$349$			21.6550i			1.15917i	−0.814913	+	0.579584i	$0.803215\pi$
$350$	−8.38200	−	1.99363i	−0.448037	−	0.106564i
$351$	22.2205	−	22.2205i	1.18604	−	1.18604i
$352$		−	4.85196i		−	0.258610i
$353$			2.78988i			0.148490i	0.997240	+	0.0742452i	$0.0236547\pi$
$353$			2.78988i			0.148490i	−0.997240	+	0.0742452i	$0.976345\pi$
$354$	−15.4221			−0.819673
$355$	−15.3936	+	4.35899i	−0.817007	+	0.231351i
$356$	7.09280	+	7.09280i	0.375918	+	0.375918i
$357$	−2.58307			−0.136710
$358$	9.36945	+	9.36945i	0.495191	+	0.495191i
$359$		−	1.30687i		−	0.0689740i	−0.999405	−	0.0344870i	$-0.989020\pi$
$359$		−	1.30687i		−	0.0689740i	0.999405	−	0.0344870i	$-0.0109797\pi$
$360$	0.481206	+	1.69936i	0.0253618	+	0.0895640i
$361$			11.4421i			0.602215i
$362$	−11.6623			−0.612955
$363$	13.1840	+	13.1840i	0.691978	+	0.691978i
$364$	6.79592	+	6.79592i	0.356203	+	0.356203i
$365$	25.0946	+	14.0189i	1.31351	+	0.733782i
$366$	0.962411			0.0503061
$367$	19.2822	+	19.2822i	1.00652	+	1.00652i	0.999979	+	0.00654459i	$0.00208322\pi$
$367$	19.2822	+	19.2822i	1.00652	+	1.00652i	0.00654459	+	0.999979i	$0.497917\pi$
$368$	3.14053			0.163711
$369$	−0.326134			−0.0169779
$370$	−12.5453	−	5.25516i	−0.652197	−	0.273203i
$371$	−9.38694			−0.487346
$372$	3.60423			0.186871
$373$	7.69384	+	7.69384i	0.398372	+	0.398372i	0.877658	−	0.479287i	$-0.159105\pi$
$373$	7.69384	+	7.69384i	0.398372	+	0.398372i	−0.479287	+	0.877658i	$0.659105\pi$
$374$	4.89233			0.252976
$375$	16.6063	−	0.705149i	0.857548	−	0.0364137i
$376$	8.35899	+	8.35899i	0.431082	+	0.431082i
$377$	26.6419	+	26.6419i	1.37213	+	1.37213i
$378$	9.70868			0.499360
$379$		−	16.7516i		−	0.860474i	−0.902716	−	0.430237i	$-0.858430\pi$
$379$		−	16.7516i		−	0.860474i	0.902716	−	0.430237i	$-0.141570\pi$
$380$	−2.99805	+	5.36668i	−0.153797	+	0.275305i
$381$			18.2776i			0.936388i
$382$	17.6354	+	17.6354i	0.902304	+	0.902304i
$383$	11.5317			0.589241			0.294620	−	0.955614i	$-0.404807\pi$
$383$	11.5317			0.589241			0.294620	+	0.955614i	$0.404807\pi$
$384$	−1.05122	−	1.05122i	−0.0536450	−	0.0536450i
$385$	9.11763	−	16.3211i	0.464677	−	0.831800i
$386$	−13.5647			−0.690425
$387$			1.16683i			0.0593134i
$388$			2.10245i			0.106736i
$389$	−19.8314	+	19.8314i	−1.00549	+	1.00549i	−0.00550900	+	0.999985i	$0.501754\pi$
$389$	−19.8314	+	19.8314i	−1.00549	+	1.00549i	−0.999985	+	0.00550900i	$0.998246\pi$
$390$	−16.1864	−	9.04240i	−0.819632	−	0.457880i
$391$			3.16666i			0.160145i
$392$		−	4.03070i		−	0.203581i
$393$	16.7485			0.844852
$394$	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	$-0.940664\pi$
$397$	−15.8870	+	15.8870i	−0.797343	+	0.797343i	0.185333	+	0.982676i	$0.440664\pi$
$398$	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	$0.407289\pi$
$402$	11.1304			0.555134
$403$	9.56144	−	9.56144i	0.476289	−	0.476289i
$404$		−	6.66420i		−	0.331556i
$405$	−12.9229	+	3.65938i	−0.642146	+	0.181836i
$406$			11.6405i			0.577708i
$407$	18.3882	−	23.0848i	0.911471	−	1.14427i
$408$	1.05997	−	1.05997i	0.0524763	−	0.0524763i
$409$	16.9289	+	16.9289i	0.837082	+	0.837082i	0.988474	−	0.151392i	$-0.0483755\pi$
$409$	16.9289	+	16.9289i	0.837082	+	0.837082i	−0.151392	+	0.988474i	$0.548376\pi$
$410$	0.251553	+	0.888349i	0.0124233	+	0.0438725i
$411$			27.8291i			1.37271i
$412$			3.38743i			0.166887i
$413$	−17.8755			−0.879598
$414$		−	2.48057i		−	0.121913i
$415$	−15.2380	+	27.2769i	−0.748003	+	1.33897i
$416$	−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	$-0.707907\pi$
$419$		−	32.5124i		−	1.58834i	0.607698	−	0.794169i	$-0.292093\pi$
$420$	−1.56070	−	5.51154i	−0.0761543	−	0.268936i
$421$	−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	$0.470503\pi$
$422$	−10.0888			−0.491114
$423$	6.60241	−	6.60241i	0.321020	−	0.321020i
$424$	3.85196	−	3.85196i	0.187068	−	0.187068i
$425$	2.64330	+	4.29310i	0.128219	+	0.208246i
$426$	−7.52141	−	7.52141i	−0.364413	−	0.364413i
$427$	1.11552			0.0539838
$428$	−6.68246	−	6.68246i	−0.323009	−	0.323009i
$429$	28.4478	−	28.4478i	1.37347	−	1.37347i
$430$	3.17830	−	0.899997i	0.153271	−	0.0434017i
$431$	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	0.0495314	−	0.998773i	$-0.484227\pi$
$433$	21.8138	−	21.8138i	1.04830	−	1.04830i	0.998773	−	0.0495314i	$-0.0157728\pi$
$434$	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
$438$			19.1111i			0.913164i
$439$	−12.9479	−	12.9479i	−0.617971	−	0.617971i	0.327040	−	0.945011i	$-0.393949\pi$
$439$	−12.9479	−	12.9479i	−0.617971	−	0.617971i	−0.945011	+	0.327040i	$0.893949\pi$
$440$	2.95597	+	10.4389i	0.140920	+	0.497653i
$441$	−3.18368			−0.151604
$442$		−	5.62386i		−	0.267500i
$443$	2.00074	+	2.00074i	0.0950579	+	0.0950579i	0.753037	−	0.657979i	$-0.228588\pi$
$443$	2.00074	+	2.00074i	0.0950579	+	0.0950579i	−0.657979	+	0.753037i	$0.728588\pi$
$444$	−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	−0.985586	−	0.169174i	$-0.945890\pi$
$449$	−17.2995	+	17.2995i	−0.816412	+	0.816412i	0.169174	+	0.985586i	$0.445890\pi$
$450$	−2.07060	−	3.36296i	−0.0976091	−	0.158531i
$451$	−2.00339			−0.0943359
$452$		−	4.19525i		−	0.197328i
$453$	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
$457$		−	24.4123i		−	1.14196i	−0.820965	−	0.570979i	$-0.806564\pi$
$457$		−	24.4123i		−	1.14196i	0.820965	−	0.570979i	$-0.193436\pi$
$458$		−	8.54964i		−	0.399498i
$459$	−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	$0.904516\pi$
$462$	12.4295			0.578274
$463$	−9.45035			−0.439195			−0.219597	−	0.975591i	$-0.570474\pi$
$463$	−9.45035			−0.439195			−0.219597	+	0.975591i	$0.570474\pi$
$464$	−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
$467$			5.91129i			0.273542i	0.990603	+	0.136771i	$0.0436724\pi$
$467$			5.91129i			0.273542i	−0.990603	+	0.136771i	$0.956328\pi$
$468$			4.40539i			0.203639i
$469$	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
$473$			7.16765i			0.329569i
$474$	−3.07825			−0.141389
$475$	3.18067	−	13.3728i	0.145939	−	0.613585i
$476$	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	−0.962839	−	0.270075i	$-0.912951\pi$
$479$	−15.1619	+	15.1619i	−0.692764	+	0.692764i	0.270075	+	0.962839i	$0.412951\pi$
$480$	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
$483$			8.04526i			0.366072i
$484$	−12.5415			−0.570069
$485$	−1.28088	−	4.52336i	−0.0581616	−	0.205395i
$486$	5.63773	+	5.63773i	0.255733	+	0.255733i
$487$		−	21.5964i		−	0.978624i	−0.872109	−	0.489312i	$-0.837248\pi$
$487$		−	21.5964i		−	0.978624i	0.872109	−	0.489312i	$-0.162752\pi$
$488$	−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
$495$	8.24522	−	2.33479i	0.370595	−	0.104941i
$496$	−1.71430	+	1.71430i	−0.0769744	+	0.0769744i
$497$	−8.71798	−	8.71798i	−0.391055	−	0.391055i
$498$	−20.7730			−0.930861
$499$	8.86811	+	8.86811i	0.396991	+	0.396991i	0.877170	−	0.480179i	$-0.159428\pi$
$499$	8.86811	+	8.86811i	0.396991	+	0.396991i	−0.480179	+	0.877170i	$0.659428\pi$
$500$	−7.56318	+	8.23397i	−0.338236	+	0.368234i
$501$	−20.0868	+	20.0868i	−0.897411	+	0.897411i
$502$	6.65372	−	6.65372i	0.296970	−	0.296970i
$503$	27.8555			1.24202			0.621008	−	0.783804i	$-0.286723\pi$
$503$	27.8555			1.24202			0.621008	+	0.783804i	$0.286723\pi$
$504$	−0.962411	+	0.962411i	−0.0428692	+	0.0428692i
$505$	4.06004	+	14.3378i	0.180669	+	0.638026i
$506$		−	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	$-0.816153\pi$
$509$	−37.8029			−1.67558			−0.837791	+	0.545990i	$0.816153\pi$
$510$	−1.63473	+	2.92626i	−0.0723870	+	0.129577i
$511$			22.1515i			0.979924i
$512$	1.00000			0.0441942
$513$			15.4894i			0.683873i
$514$			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
$518$	−1.17944	−	10.4150i	−0.0518217	−	0.457610i
$519$			31.8799i			1.39937i
$520$	11.9997	−	3.39796i	0.526224	−	0.149010i
$521$			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
$523$	−34.6818			−1.51653			−0.758265	−	0.651946i	$-0.773953\pi$
$523$	−34.6818			−1.51653			−0.758265	+	0.651946i	$0.773953\pi$
$524$	−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
$532$	−4.73727			−0.205387
$533$			2.30295i			0.0997517i
$534$		−	14.9122i		−	0.645316i
$535$	18.4483	+	10.3060i	0.797590	+	0.445566i
$536$	−5.29402	+	5.29402i	−0.228667	+	0.228667i
$537$		−	19.6988i		−	0.850065i
$538$		−	13.1011i		−	0.564830i
$539$	−19.5568			−0.842371
$540$	6.14427	−	10.9986i	0.264407	−	0.473305i
$541$	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	$0.691191\pi$
$542$	−6.98656			−0.300098
$543$	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
$547$	−34.2347			−1.46377			−0.731885	−	0.681428i	$-0.761359\pi$
$547$	−34.2347			−1.46377			−0.731885	+	0.681428i	$0.761359\pi$
$548$	−13.2365	−	13.2365i	−0.565436	−	0.565436i
$549$	0.361563	+	0.361563i	0.0154311	+	0.0154311i
$550$	−12.7194	−	20.6581i	−0.542355	−	0.880863i
$551$	−18.5714			−0.791170
$552$	−3.30140	−	3.30140i	−0.140517	−	0.140517i
$553$	−3.56797			−0.151725
$554$	14.9569			0.635457
$555$	7.66352	+	18.7122i	0.325298	+	0.794289i
$556$	15.1028			0.640500
$557$	21.2394			0.899943			0.449971	−	0.893043i	$-0.351434\pi$
$557$	21.2394			0.899943			0.449971	+	0.893043i	$0.351434\pi$
$558$	1.35405	+	1.35405i	0.0573217	+	0.0573217i
$559$	8.23939			0.348489
$560$	3.36381	+	1.87916i	0.142147	+	0.0794092i
$561$	−5.14293	−	5.14293i	−0.217135	−	0.217135i
$562$	13.8446	+	13.8446i	0.583998	+	0.583998i
$563$	−20.2289			−0.852546			−0.426273	−	0.904594i	$-0.640174\pi$
$563$	−20.2289			−0.852546			−0.426273	+	0.904594i	$0.640174\pi$
$564$		−	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
$568$	7.15491			0.300213
$569$	2.40147	+	2.40147i	0.100675	+	0.100675i	0.755650	−	0.654975i	$-0.227321\pi$
$569$	2.40147	+	2.40147i	0.100675	+	0.100675i	−0.654975	+	0.755650i	$0.727321\pi$
$570$	8.79321	−	2.48997i	0.368307	−	0.104293i
$571$	−7.39594			−0.309510			−0.154755	−	0.987953i	$-0.549459\pi$
$571$	−7.39594			−0.309510			−0.154755	+	0.987953i	$0.549459\pi$
$572$			27.0616i			1.13150i
$573$		−	37.0774i		−	1.54893i
$574$	−0.503106	+	0.503106i	−0.0209993	+	0.0209993i
$575$	13.3714	−	8.23286i	0.557624	−	0.343334i
$576$		−	0.789858i		−	0.0329107i
$577$		−	38.1791i		−	1.58942i	−0.606993	−	0.794708i	$-0.707624\pi$
$577$		−	38.1791i		−	1.58942i	0.606993	−	0.794708i	$-0.292376\pi$
$578$	15.9833			0.664817
$579$	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
$587$	21.8152			0.900410			0.450205	−	0.892925i	$-0.351351\pi$
$587$	21.8152			0.900410			0.450205	+	0.892925i	$0.351351\pi$
$588$	−4.23717	+	4.23717i	−0.174738	+	0.174738i
$589$			6.66505i			0.274629i
$590$	−11.3128	+	20.2506i	−0.465740	+	0.833702i
$591$		−	35.4828i		−	1.45957i
$592$	4.75783	+	3.78986i	0.195546	+	0.155762i
$593$	−4.84337	+	4.84337i	−0.198893	+	0.198893i	−0.799526	−	0.600632i	$-0.794916\pi$
$593$	−4.84337	+	4.84337i	−0.198893	+	0.198893i	0.600632	+	0.799526i	$0.294916\pi$
$594$	19.3302	+	19.3302i	0.793126	+	0.793126i
$595$	−1.89480	+	3.39180i	−0.0776791	+	0.139050i
$596$		−	21.2958i		−	0.872308i
$597$		−	19.1962i		−	0.785647i
$598$	−17.5162			−0.716289
$599$			29.5415i			1.20703i	0.797350	+	0.603517i	$0.206234\pi$
$599$			29.5415i			1.20703i	−0.797350	+	0.603517i	$0.793766\pi$
$600$	−7.23154	−	1.72000i	−0.295226	−	0.0702186i
$601$	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
$605$	26.9828	−	7.64069i	1.09701	−	0.310638i
$606$	−7.00556	+	7.00556i	−0.284582	+	0.284582i
$607$	35.5553			1.44314			0.721572	−	0.692340i	$-0.243420\pi$
$607$	35.5553			1.44314			0.721572	+	0.692340i	$0.243420\pi$
$608$	1.94395	−	1.94395i	0.0788378	−	0.0788378i
$609$	12.2368	−	12.2368i	0.495859	−	0.495859i
$610$	0.705973	−	1.26373i	0.0285840	−	0.0511671i
$611$	−46.6219	−	46.6219i	−1.88612	−	1.88612i
$612$	0.796429			0.0321937
$613$	23.4695	+	23.4695i	0.947925	+	0.947925i	0.998710	−	0.0507843i	$-0.0161721\pi$
$613$	23.4695	+	23.4695i	0.947925	+	0.947925i	−0.0507843	+	0.998710i	$0.516172\pi$
$614$	−2.77527	+	2.77527i	−0.112001	+	0.112001i
$615$	0.669415	−	1.19829i	0.0269934	−	0.0483198i
$616$	−5.91193	+	5.91193i	−0.238198	+	0.238198i
$617$	−4.77446	+	4.77446i	−0.192212	+	0.192212i	−0.796651	−	0.604439i	$-0.793397\pi$
$617$	−4.77446	+	4.77446i	−0.192212	+	0.192212i	0.604439	+	0.796651i	$0.293397\pi$
$618$	3.56095	−	3.56095i	0.143242	−	0.143242i
$619$	−16.3058			−0.655385			−0.327692	−	0.944784i	$-0.606271\pi$
$619$	−16.3058			−0.655385			−0.327692	+	0.944784i	$0.606271\pi$
$620$	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
$623$		−	17.2846i		−	0.692494i
$624$	5.86315	+	5.86315i	0.234714	+	0.234714i
$625$	11.2556	−	22.3229i	0.450224	−	0.892916i
$626$	10.8979			0.435566
$627$			19.8303i			0.791945i
$628$	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
$635$	24.0001	+	13.4074i	0.952415	+	0.532058i
$636$	−8.09855			−0.321128
$637$			22.4810i			0.890731i
$638$	−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	$0.479319\pi$
$642$			14.0495i			0.554490i
$643$		−	31.8234i		−	1.25499i	−0.778620	−	0.627496i	$-0.784080\pi$
$643$		−	31.8234i		−	1.25499i	0.778620	−	0.627496i	$-0.215920\pi$
$644$	−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
$647$	−26.7710			−1.05248			−0.526239	−	0.850337i	$-0.676398\pi$
$647$	−26.7710			−1.05248			−0.526239	+	0.850337i	$0.676398\pi$
$648$	6.00655			0.235960
$649$	−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
$652$		−	7.46188i		−	0.292230i
$653$			12.7656i			0.499558i	0.968303	+	0.249779i	$0.0803580\pi$
$653$			12.7656i			0.499558i	−0.968303	+	0.249779i	$0.919642\pi$
$654$	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
$658$		−	20.3702i		−	0.794114i
$659$	26.8508			1.04596			0.522980	−	0.852345i	$-0.324820\pi$
$659$	26.8508			1.04596			0.522980	+	0.852345i	$0.324820\pi$
$660$	7.86620	−	14.0810i	0.306191	−	0.548101i
$661$	−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
$668$		−	19.1080i		−	0.739310i
$669$	−5.16581			−0.199722
$670$	8.16466	−	14.6152i	0.315428	−	0.564635i
$671$	2.22102	+	2.22102i	0.0857416	+	0.0857416i
$672$			2.56175i			0.0988217i
$673$	−21.2991	+	21.2991i	−0.821019	+	0.821019i	−0.986254	−	0.165236i	$-0.947162\pi$
$673$	−21.2991	+	21.2991i	−0.821019	+	0.821019i	0.165236	+	0.986254i	$0.447162\pi$
$674$	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	$-0.926281\pi$
$677$	−19.3523	+	19.3523i	−0.743770	+	0.743770i	0.229531	+	0.973301i	$0.426281\pi$
$678$	−4.41015	+	4.41015i	−0.169371	+	0.169371i
$679$	2.56175	−	2.56175i	0.0983110	−	0.0983110i
$680$	−0.614300	−	2.16937i	−0.0235573	−	0.0831916i
$681$	−20.6005	+	20.6005i	−0.789414	+	0.789414i
$682$	8.31773	+	8.31773i	0.318502	+	0.318502i
$683$	−23.3423			−0.893169			−0.446584	−	0.894742i	$-0.647360\pi$
$683$	−23.3423			−0.893169			−0.446584	+	0.894742i	$0.647360\pi$
$684$	−1.53545	−	1.53545i	−0.0587093	−	0.0587093i
$685$	36.5421	+	20.4139i	1.39620	+	0.779976i
$686$	−13.4405	+	13.4405i	−0.513160	+	0.513160i
$687$	−8.98758	+	8.98758i	−0.342898	+	0.342898i
$688$	−1.47727			−0.0563203
$689$	−21.4841	+	21.4841i	−0.818480	+	0.818480i
$690$	9.11419	+	5.09156i	0.346971	+	0.193832i
$691$		−	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
$695$	−32.4932	+	9.20107i	−1.23254	+	0.349017i
$696$			10.0428i			0.380671i
$697$	0.416338			0.0157699
$698$			21.6550i			0.819655i
$699$		−	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
$703$	16.6163	−	1.88170i	0.626697	−	0.0709697i
$704$		−	4.85196i		−	0.182865i
$705$	10.7068	+	37.8107i	0.403243	+	1.42403i
$706$			2.78988i			0.104999i
$707$	−8.12007	+	8.12007i	−0.305387	+	0.305387i
$708$	−15.4221			−0.579596
$709$	29.5655	−	29.5655i	1.11036	−	1.11036i	0.117254	−	0.993102i	$-0.462591\pi$
$709$	29.5655	−	29.5655i	1.11036	−	1.11036i	0.993102	−	0.117254i	$-0.0374090\pi$
$710$	−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
$717$	−30.5382			−1.14047
$718$		−	1.30687i		−	0.0487720i
$719$			0.762333i			0.0284302i	0.999899	+	0.0142151i	$0.00452496\pi$
$719$			0.762333i			0.0284302i	−0.999899	+	0.0142151i	$0.995475\pi$
$720$	0.481206	+	1.69936i	0.0179335	+	0.0633313i
$721$	4.12746	−	4.12746i	0.153715	−	0.153715i
$722$			11.4421i			0.425830i
$723$			17.6544i			0.656574i
$724$	−11.6623			−0.433424
$725$	−32.8598	−	7.81560i	−1.22038	−	0.290264i
$726$	13.1840	+	13.1840i	0.489302	+	0.489302i
$727$	−3.28968			−0.122007			−0.0610037	−	0.998138i	$-0.519430\pi$
$727$	−3.28968			−0.122007			−0.0610037	+	0.998138i	$0.519430\pi$
$728$	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
$732$	0.962411			0.0355718
$733$	1.10605	+	1.10605i	0.0408531	+	0.0408531i	0.727238	−	0.686385i	$-0.240804\pi$
$733$	1.10605	+	1.10605i	0.0408531	+	0.0408531i	−0.686385	+	0.727238i	$0.740804\pi$
$734$	19.2822	+	19.2822i	0.711719	+	0.711719i
$735$	6.53474	−	11.6976i	0.241037	−	0.431471i
$736$	3.14053			0.115761
$737$	25.6864	+	25.6864i	0.946169	+	0.946169i
$738$	−0.326134			−0.0120052
$739$	15.8878			0.584443			0.292221	−	0.956351i	$-0.405606\pi$
$739$	15.8878			0.584443			0.292221	+	0.956351i	$0.405606\pi$
$740$	−12.5453	−	5.25516i	−0.461173	−	0.193183i
$741$	22.7954			0.837410
$742$	−9.38694			−0.344605
$743$	7.35293	+	7.35293i	0.269753	+	0.269753i	0.829001	−	0.559248i	$-0.188910\pi$
$743$	7.35293	+	7.35293i	0.269753	+	0.269753i	−0.559248	+	0.829001i	$0.688910\pi$
$744$	3.60423			0.132137
$745$	12.9740	+	45.8172i	0.475332	+	1.67861i
$746$	7.69384	+	7.69384i	0.281691	+	0.281691i
$747$	−7.80411	−	7.80411i	−0.285537	−	0.285537i
$748$	4.89233			0.178881
$749$			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
$753$	−13.9891			−0.509791
$754$	26.6419	+	26.6419i	0.970241	+	0.970241i
$755$	−3.48277	−	12.2992i	−0.126751	−	0.447615i
$756$	9.70868			0.353101
$757$		−	33.6937i		−	1.22462i	−0.790618	−	0.612309i	$-0.790241\pi$
$757$		−	33.6937i		−	1.22462i	0.790618	−	0.612309i	$-0.209759\pi$
$758$		−	16.7516i		−	0.608447i
$759$	−16.0183	+	16.0183i	−0.581426	+	0.581426i
$760$	−2.99805	+	5.36668i	−0.108751	+	0.194670i
$761$			8.01511i			0.290548i	0.989391	+	0.145274i	$0.0464063\pi$
$761$			8.01511i			0.290548i	−0.989391	+	0.145274i	$0.953594\pi$
$762$			18.2776i			0.662126i
$763$	28.4543			1.03011
$764$	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	0.635941	−	0.771737i	$-0.280612\pi$
$769$	−3.76573	−	3.76573i	−0.135796	−	0.135796i	−0.771737	+	0.635941i	$0.780612\pi$
$770$	9.11763	−	16.3211i	0.328577	−	0.588171i
$771$	14.9148	−	14.9148i	0.537145	−	0.537145i
$772$	−13.5647			−0.488204
$773$	27.2082	−	27.2082i	0.978611	−	0.978611i	−0.0211650	−	0.999776i	$-0.506738\pi$
$773$	27.2082	−	27.2082i	0.978611	−	0.978611i	0.999776	+	0.0211650i	$0.00673753\pi$
$774$			1.16683i			0.0419409i
$775$	−2.80492	+	11.7930i	−0.100756	+	0.423616i
$776$			2.10245i			0.0754735i
$777$	−9.70868	+	12.1884i	−0.348297	+	0.437256i
$778$	−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
$782$			3.16666i			0.113239i
$783$	38.0608			1.36018
$784$		−	4.03070i		−	0.143954i
$785$	−12.9961	−	7.26015i	−0.463851	−	0.259126i
$786$	16.7485			0.597400
$787$	−8.43368	−	8.43368i	−0.300628	−	0.300628i	0.540631	−	0.841260i	$-0.318185\pi$
$787$	−8.43368	−	8.43368i	−0.300628	−	0.300628i	−0.841260	+	0.540631i	$0.818185\pi$
$788$	16.8769	+	16.8769i	0.601215	+	0.601215i
$789$			18.6686i			0.664620i
$790$	−2.25804	+	4.04202i	−0.0803374	+	0.143809i
$791$	−5.11175	+	5.11175i	−0.181753	+	0.181753i
$792$	−3.83236			−0.136177
$793$	2.55312	−	2.55312i	0.0906640	−	0.0906640i
$794$	−15.8870	+	15.8870i	−0.563807	+	0.563807i
$795$	17.4238	−	4.93389i	0.617959	−	0.174987i
$796$	9.13039	+	9.13039i	0.323618	+	0.323618i
$797$	−10.2289			−0.362327			−0.181163	−	0.983453i	$-0.557986\pi$
$797$	−10.2289			−0.362327			−0.181163	+	0.983453i	$0.557986\pi$
$798$	4.97993	+	4.97993i	0.176288	+	0.176288i
$799$	−8.42854	+	8.42854i	−0.298180	+	0.298180i
$800$	4.25768	−	2.62149i	0.150532	−	0.0926836i
$801$	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
$808$		−	6.66420i		−	0.234446i
$809$	−14.1279	−	14.1279i	−0.496711	−	0.496711i	0.413701	−	0.910413i	$-0.364236\pi$
$809$	−14.1279	−	14.1279i	−0.496711	−	0.496711i	−0.910413	+	0.413701i	$0.864236\pi$
$810$	−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	$0.280958\pi$
$812$			11.6405i			0.408501i
$813$	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
$820$	0.251553	+	0.888349i	0.00878462	+	0.0310225i
$821$	−9.97250			−0.348043			−0.174021	−	0.984742i	$-0.555676\pi$
$821$	−9.97250			−0.348043			−0.174021	+	0.984742i	$0.555676\pi$
$822$			27.8291i			0.970651i
$823$	−37.3136	+	37.3136i	−1.30067	+	1.30067i	−0.372732	+	0.927939i	$0.621579\pi$
$823$	−37.3136	+	37.3136i	−1.30067	+	1.30067i	−0.927939	+	0.372732i	$0.878421\pi$
$824$			3.38743i			0.118007i
$825$	−8.34536	+	35.0872i	−0.290548	+	1.22158i
$826$	−17.8755			−0.621970
$827$		−	20.4583i		−	0.711404i	−0.934599	−	0.355702i	$-0.884242\pi$
$827$		−	20.4583i		−	0.711404i	0.934599	−	0.355702i	$-0.115758\pi$
$828$		−	2.48057i		−	0.0862058i
$829$	29.2865	+	29.2865i	1.01716	+	1.01716i	0.999850	+	0.0173134i	$0.00551130\pi$
$829$	29.2865	+	29.2865i	1.01716	+	1.01716i	0.0173134	+	0.999850i	$0.494489\pi$
$830$	−15.2380	+	27.2769i	−0.528918	+	0.946794i
$831$	−15.7230	−	15.7230i	−0.545426	−	0.545426i
$832$	−5.57745			−0.193363
$833$	4.06423			0.140817
$834$	−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
$837$		−	13.6595i		−	0.472142i
$838$		−	32.5124i		−	1.12312i
$839$	−43.3795			−1.49763			−0.748814	−	0.662780i	$-0.769376\pi$
$839$	−43.3795			−1.49763			−0.748814	+	0.662780i	$0.769376\pi$
$840$	−1.56070	−	5.51154i	−0.0538492	−	0.190166i
$841$			16.6340i			0.573588i
$842$	−18.5316	+	18.5316i	−0.638640	+	0.638640i
$843$		−	29.1075i		−	1.00252i
$844$	−10.0888			−0.347270
$845$	−38.9589	+	11.0320i	−1.34023	+	0.379511i
$846$	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
$853$			6.00476i			0.205599i	0.994702	+	0.102800i	$0.0327800\pi$
$853$			6.00476i			0.205599i	−0.994702	+	0.102800i	$0.967220\pi$
$854$	1.11552			0.0381723
$855$	4.23892	+	2.36803i	0.144968	+	0.0809850i
$856$	−6.68246	−	6.68246i	−0.228402	−	0.228402i
$857$			0.245134i			0.00837363i	0.999991	+	0.00418681i	$0.00133271\pi$
$857$			0.245134i			0.00837363i	−0.999991	+	0.00418681i	$0.998667\pi$
$858$	28.4478	−	28.4478i	0.971191	−	0.971191i
$859$	19.6130	−	19.6130i	0.669187	−	0.669187i	−0.288341	−	0.957528i	$-0.593104\pi$
$859$	19.6130	−	19.6130i	0.669187	−	0.669187i	0.957528	+	0.288341i	$0.0931037\pi$
$860$	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	0.191306	−	0.981530i	$-0.438728\pi$
$863$	34.4543	−	34.4543i	1.17284	−	1.17284i	0.981530	−	0.191306i	$-0.0612722\pi$
$864$	−3.98399	+	3.98399i	−0.135538	+	0.135538i
$865$	41.8612	+	23.3854i	1.42332	+	0.795126i
$866$	21.8138	−	21.8138i	0.741263	−	0.741263i
$867$	−16.8020	−	16.8020i	−0.570626	−	0.570626i
$868$	4.17762			0.141798
$869$	−7.10389	−	7.10389i	−0.240983	−	0.240983i
$870$	−6.11838	−	21.6068i	−0.207433	−	0.732539i
$871$	29.5271	−	29.5271i	1.00049	−	1.00049i
$872$	−11.6763	+	11.6763i	−0.395410	+	0.395410i
$873$	1.66063			0.0562039
$874$	6.10505	−	6.10505i	0.206506	−	0.206506i
$875$	19.2482	−	0.817330i	0.650709	−	0.0276308i
$876$			19.1111i			0.645704i
$877$	−4.63548	−	4.63548i	−0.156529	−	0.156529i	0.624498	−	0.781027i	$-0.285304\pi$
$877$	−4.63548	−	4.63548i	−0.156529	−	0.156529i	−0.781027	+	0.624498i	$0.785304\pi$
$878$	−12.9479	−	12.9479i	−0.436971	−	0.436971i
$879$	16.3832			0.552591
$880$	2.95597	+	10.4389i	0.0996456	+	0.351894i
$881$		−	20.6076i		−	0.694288i	−0.937812	−	0.347144i	$-0.887152\pi$
$881$		−	20.6076i		−	0.694288i	0.937812	−	0.347144i	$-0.112848\pi$
$882$	−3.18368			−0.107200
$883$			27.2177i			0.915950i	0.888965	+	0.457975i	$0.151425\pi$
$883$			27.2177i			0.915950i	−0.888965	+	0.457975i	$0.848575\pi$
$884$		−	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	$-0.666797\pi$
$887$	10.8845	−	10.8845i	0.365465	−	0.365465i	0.865820	+	0.500355i	$0.166797\pi$
$888$	−1.01756	−	8.98554i	−0.0341471	−	0.301535i
$889$			21.1853i			0.710533i
$890$	−19.5811	−	10.9388i	−0.656361	−	0.366670i
$891$		−	29.1436i		−	0.976346i
$892$	2.45704	−	2.45704i	0.0822679	−	0.0822679i
$893$	32.4990			1.08754
$894$	−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
$902$	−2.00339			−0.0667055
$903$		−	3.78439i		−	0.125937i
$904$		−	4.19525i		−	0.139532i
$905$	25.0910	−	7.10501i	0.834054	−	0.236178i
$906$	6.00949	−	6.00949i	0.199652	−	0.199652i
$907$			35.7043i			1.18554i	0.805371	+	0.592771i	$0.201966\pi$
$907$			35.7043i			1.18554i	−0.805371	+	0.592771i	$0.798034\pi$
$908$		−	19.5967i		−	0.650340i
$909$	−5.26377			−0.174588
$910$	−18.7615	−	10.4809i	−0.621938	−	0.347440i
$911$	−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	$0.990617\pi$
$912$	−4.08706			−0.135336
$913$	−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
$917$	19.4130			0.641075
$918$	−4.01713	−	4.01713i	−0.132585	−	0.132585i
$919$	22.4493	+	22.4493i	0.740535	+	0.740535i	0.972681	−	0.232146i	$-0.0745748\pi$
$919$	22.4493	+	22.4493i	0.740535	+	0.740535i	−0.232146	+	0.972681i	$0.574575\pi$
$920$	−6.75677	+	1.91331i	−0.222764	+	0.0630799i
$921$	5.83485			0.192265
$922$	−14.1676	−	14.1676i	−0.466587	−	0.466587i
$923$	−39.9062			−1.31353
$924$	12.4295			0.408901
$925$	30.1924	+	3.66338i	0.992719	+	0.120451i
$926$	−9.45035			−0.310558
$927$	2.67559			0.0878778
$928$	−4.77672	−	4.77672i	−0.156803	−	0.156803i
$929$	−49.8210			−1.63457			−0.817286	−	0.576232i	$-0.804523\pi$
$929$	−49.8210			−1.63457			−0.817286	+	0.576232i	$0.804523\pi$
$930$	−7.75441	+	2.19581i	−0.254277	+	0.0720034i
$931$	−7.83550	−	7.83550i	−0.256798	−	0.256798i
$932$	18.6855	+	18.6855i	0.612065	+	0.612065i
$933$	4.94050			0.161745
$934$			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	0.658998	−	0.752145i	$-0.270980\pi$
$937$	−2.85125	−	2.85125i	−0.0931464	−	0.0931464i	−0.752145	+	0.658998i	$0.770980\pi$
$938$	12.9011			0.421236
$939$	−11.4561	−	11.4561i	−0.373855	−	0.373855i
$940$	−23.0767	−	12.8916i	−0.752679	−	0.420477i
$941$	45.3259			1.47758			0.738792	−	0.673934i	$-0.235397\pi$
$941$	45.3259			1.47758			0.738792	+	0.673934i	$0.235397\pi$
$942$		−	9.89733i		−	0.322473i
$943$		−	1.29673i		−	0.0422275i
$944$	7.33529	−	7.33529i	0.238743	−	0.238743i
$945$	−20.8880	+	5.91483i	−0.679485	+	0.192409i
$946$			7.16765i			0.233040i
$947$			35.8239i			1.16412i	0.813146	+	0.582060i	$0.197753\pi$
$947$			35.8239i			1.16412i	−0.813146	+	0.582060i	$0.802247\pi$
$948$	−3.07825			−0.0999769
$949$	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	0.960794	+	0.277263i	$0.0894273\pi$
$953$	38.2197	+	38.2197i	1.23806	+	1.23806i	0.277263	+	0.960794i	$0.410573\pi$
$954$	−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
$957$	48.7273			1.57513
$958$	−15.1619	+	15.1619i	−0.489858	+	0.489858i
$959$			32.2564i			1.04161i
$960$	2.90212	+	1.62124i	0.0936654	+	0.0523253i
$961$			25.1223i			0.810398i
$962$	−26.5366	−	21.1378i	−0.855574	−	0.681509i
$963$	−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
$967$		−	12.1533i		−	0.390823i	−0.980721	−	0.195411i	$-0.937396\pi$
$967$		−	12.1533i		−	0.390823i	0.980721	−	0.195411i	$-0.0626042\pi$
$968$	−12.5415			−0.403100
$969$		−	4.12107i		−	0.132388i
$970$	−1.28088	−	4.52336i	−0.0411265	−	0.145236i
$971$	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
$975$	40.3336	+	9.59321i	1.29171	+	0.307229i
$976$	−0.457758	+	0.457758i	−0.0146525	+	0.0146525i
$977$	−51.9854			−1.66316			−0.831580	−	0.555405i	$-0.812563\pi$
$977$	−51.9854			−1.66316			−0.831580	+	0.555405i	$0.812563\pi$
$978$	−7.84411	+	7.84411i	−0.250827	+	0.250827i
$979$	34.4140	−	34.4140i	1.09988	−	1.09988i
$980$	2.45563	+	8.67194i	0.0784422	+	0.277015i
$981$	9.22263	+	9.22263i	0.294456	+	0.294456i
$982$	36.1012			1.15204
$983$	−29.0021	−	29.0021i	−0.925025	−	0.925025i	0.0723544	−	0.997379i	$-0.476949\pi$
$983$	−29.0021	−	29.0021i	−0.925025	−	0.925025i	−0.997379	+	0.0723544i	$0.976949\pi$
$984$	−0.434053	+	0.434053i	−0.0138371	+	0.0138371i
$985$	−46.5922	−	26.0283i	−1.48455	−	0.829331i
$986$	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
$993$		−	32.4643i		−	1.03022i
$994$	−8.71798	−	8.71798i	−0.276518	−	0.276518i
$995$	−25.2063	−	14.0813i	−0.799094	−	0.446407i
$996$	−20.7730			−0.658218
$997$			15.7013i			0.497264i	0.968598	+	0.248632i	$0.0799810\pi$
$997$			15.7013i			0.497264i	−0.968598	+	0.248632i	$0.920019\pi$
$998$	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.h.d.117.2	yes	10
5.3	odd	4		370.2.g.d.43.4	✓	10
37.31	odd	4		370.2.g.d.327.4	yes	10
185.68	even	4	inner	370.2.h.d.253.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.4	✓	10	5.3	odd	4
370.2.g.d.327.4	yes	10	37.31	odd	4
370.2.h.d.117.2	yes	10	1.1	even	1	trivial
370.2.h.d.253.2	yes	10	185.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

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Database

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