LMFDB - Embedded newform 370.2.h.d.253.1

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			253.1
Root			$-0.287871 - 2.59703i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.d.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.70160 + 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 + 1.41373i) q^{5} +(-1.70160 + 1.70160i) q^{6} +(2.82745 - 2.82745i) q^{7} +1.00000 q^{8} -2.79087i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.70160 + 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 + 1.41373i) q^{5} +(-1.70160 + 1.70160i) q^{6} +(2.82745 - 2.82745i) q^{7} +1.00000 q^{8} -2.79087i q^{9} +(1.73245 + 1.41373i) q^{10} +2.94236i q^{11} +(-1.70160 + 1.70160i) q^{12} -0.738730 q^{13} +(2.82745 - 2.82745i) q^{14} +(-5.35353 + 0.542335i) q^{15} +1.00000 q^{16} +6.61833i q^{17} -2.79087i q^{18} +(-5.03108 - 5.03108i) q^{19} +(1.73245 + 1.41373i) q^{20} +9.62238i q^{21} +2.94236i q^{22} +6.39364 q^{23} +(-1.70160 + 1.70160i) q^{24} +(1.00275 + 4.89842i) q^{25} -0.738730 q^{26} +(-0.355853 - 0.355853i) q^{27} +(2.82745 - 2.82745i) q^{28} +(-2.49797 + 2.49797i) q^{29} +(-5.35353 + 0.542335i) q^{30} +(-1.48171 - 1.48171i) q^{31} +1.00000 q^{32} +(-5.00671 - 5.00671i) q^{33} +6.61833i q^{34} +(8.89567 - 0.901168i) q^{35} -2.79087i q^{36} +(-6.07917 - 0.209128i) q^{37} +(-5.03108 - 5.03108i) q^{38} +(1.25702 - 1.25702i) q^{39} +(1.73245 + 1.41373i) q^{40} -7.39769i q^{41} +9.62238i q^{42} +6.98494 q^{43} +2.94236i q^{44} +(3.94553 - 4.83504i) q^{45} +6.39364 q^{46} +(7.56618 - 7.56618i) q^{47} +(-1.70160 + 1.70160i) q^{48} -8.98899i q^{49} +(1.00275 + 4.89842i) q^{50} +(-11.2617 - 11.2617i) q^{51} -0.738730 q^{52} +(1.94236 + 1.94236i) q^{53} +(-0.355853 - 0.355853i) q^{54} +(-4.15969 + 5.09748i) q^{55} +(2.82745 - 2.82745i) q^{56} +17.1218 q^{57} +(-2.49797 + 2.49797i) q^{58} +(-8.34044 - 8.34044i) q^{59} +(-5.35353 + 0.542335i) q^{60} +(-2.31872 - 2.31872i) q^{61} +(-1.48171 - 1.48171i) q^{62} +(-7.89106 - 7.89106i) q^{63} +1.00000 q^{64} +(-1.27981 - 1.04436i) q^{65} +(-5.00671 - 5.00671i) q^{66} +(2.10003 + 2.10003i) q^{67} +6.61833i q^{68} +(-10.8794 + 10.8794i) q^{69} +(8.89567 - 0.901168i) q^{70} -2.52254 q^{71} -2.79087i q^{72} +(7.18876 - 7.18876i) q^{73} +(-6.07917 - 0.209128i) q^{74} +(-10.0414 - 6.62886i) q^{75} +(-5.03108 - 5.03108i) q^{76} +(8.31937 + 8.31937i) q^{77} +(1.25702 - 1.25702i) q^{78} +(-5.69610 - 5.69610i) q^{79} +(1.73245 + 1.41373i) q^{80} +9.58365 q^{81} -7.39769i q^{82} +(-2.72617 - 2.72617i) q^{83} +9.62238i q^{84} +(-9.35651 + 11.4659i) q^{85} +6.98494 q^{86} -8.50109i q^{87} +2.94236i q^{88} +(-4.25577 + 4.25577i) q^{89} +(3.94553 - 4.83504i) q^{90} +(-2.08872 + 2.08872i) q^{91} +6.39364 q^{92} +5.04255 q^{93} +(7.56618 - 7.56618i) q^{94} +(-1.60351 - 15.8287i) q^{95} +(-1.70160 + 1.70160i) q^{96} -3.40320i q^{97} -8.98899i q^{98} +8.21174 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.70160	+	1.70160i	−0.982418	+	0.982418i	−0.999848	−	0.0174300i	$-0.994452\pi$
$3$	−1.70160	+	1.70160i	−0.982418	+	0.982418i	0.0174300	+	0.999848i	$0.494452\pi$
$4$	1.00000			0.500000
$5$	1.73245	+	1.41373i	0.774774	+	0.632238i
$5$	1.73245	+	1.41373i	0.774774	+	0.632238i
$6$	−1.70160	+	1.70160i	−0.694674	+	0.694674i
$7$	2.82745	−	2.82745i	1.06868	−	1.06868i	0.0712163	−	0.997461i	$-0.477312\pi$
$7$	2.82745	−	2.82745i	1.06868	−	1.06868i	0.997461	−	0.0712163i	$-0.0226881\pi$
$8$	1.00000			0.353553
$9$		−	2.79087i		−	0.930291i
$10$	1.73245	+	1.41373i	0.547848	+	0.447060i
$11$			2.94236i			0.887153i	0.896236	+	0.443577i	$0.146291\pi$
$11$			2.94236i			0.887153i	−0.896236	+	0.443577i	$0.853709\pi$
$12$	−1.70160	+	1.70160i	−0.491209	+	0.491209i
$13$	−0.738730			−0.204887			−0.102443	−	0.994739i	$-0.532666\pi$
$13$	−0.738730			−0.204887			−0.102443	+	0.994739i	$0.532666\pi$
$14$	2.82745	−	2.82745i	0.755669	−	0.755669i
$15$	−5.35353	+	0.542335i	−1.38227	+	0.140030i
$16$	1.00000			0.250000
$17$			6.61833i			1.60518i	0.596531	+	0.802590i	$0.296545\pi$
$17$			6.61833i			1.60518i	−0.596531	+	0.802590i	$0.703455\pi$
$18$		−	2.79087i		−	0.657815i
$19$	−5.03108	−	5.03108i	−1.15421	−	1.15421i	−0.985700	−	0.168509i	$-0.946105\pi$
$19$	−5.03108	−	5.03108i	−1.15421	−	1.15421i	−0.168509	−	0.985700i	$-0.553895\pi$
$20$	1.73245	+	1.41373i	0.387387	+	0.316119i
$21$			9.62238i			2.09978i
$22$			2.94236i			0.627312i
$23$	6.39364			1.33317			0.666583	−	0.745431i	$-0.267756\pi$
$23$	6.39364			1.33317			0.666583	+	0.745431i	$0.267756\pi$
$24$	−1.70160	+	1.70160i	−0.347337	+	0.347337i
$25$	1.00275	+	4.89842i	0.200550	+	0.979683i
$26$	−0.738730			−0.144877
$27$	−0.355853	−	0.355853i	−0.0684839	−	0.0684839i
$28$	2.82745	−	2.82745i	0.534339	−	0.534339i
$29$	−2.49797	+	2.49797i	−0.463862	+	0.463862i	−0.899919	−	0.436057i	$-0.856375\pi$
$29$	−2.49797	+	2.49797i	−0.463862	+	0.463862i	0.436057	+	0.899919i	$0.356375\pi$
$30$	−5.35353	+	0.542335i	−0.977415	+	0.0990163i
$31$	−1.48171	−	1.48171i	−0.266123	−	0.266123i	0.561413	−	0.827536i	$-0.310258\pi$
$31$	−1.48171	−	1.48171i	−0.266123	−	0.266123i	−0.827536	+	0.561413i	$0.810258\pi$
$32$	1.00000			0.176777
$33$	−5.00671	−	5.00671i	−0.871556	−	0.871556i
$34$			6.61833i			1.13503i
$35$	8.89567	−	0.901168i	1.50364	−	0.152325i
$36$		−	2.79087i		−	0.465145i
$37$	−6.07917	−	0.209128i	−0.999409	−	0.0343805i
$37$	−6.07917	−	0.209128i	−0.999409	−	0.0343805i
$38$	−5.03108	−	5.03108i	−0.816149	−	0.816149i
$39$	1.25702	−	1.25702i	0.201284	−	0.201284i
$40$	1.73245	+	1.41373i	0.273924	+	0.223530i
$41$		−	7.39769i		−	1.15533i	−0.816276	−	0.577663i	$-0.803965\pi$
$41$		−	7.39769i		−	1.15533i	0.816276	−	0.577663i	$-0.196035\pi$
$42$			9.62238i			1.48477i
$43$	6.98494			1.06519			0.532597	−	0.846369i	$-0.321216\pi$
$43$	6.98494			1.06519			0.532597	+	0.846369i	$0.321216\pi$
$44$			2.94236i			0.443577i
$45$	3.94553	−	4.83504i	0.588165	−	0.720765i
$46$	6.39364			0.942691
$47$	7.56618	−	7.56618i	1.10364	−	1.10364i	0.109674	−	0.993968i	$-0.465019\pi$
$47$	7.56618	−	7.56618i	1.10364	−	1.10364i	0.993968	−	0.109674i	$-0.0349806\pi$
$48$	−1.70160	+	1.70160i	−0.245605	+	0.245605i
$49$		−	8.98899i		−	1.28414i
$50$	1.00275	+	4.89842i	0.141810	+	0.692741i
$51$	−11.2617	−	11.2617i	−1.57696	−	1.57696i
$52$	−0.738730			−0.102443
$53$	1.94236	+	1.94236i	0.266803	+	0.266803i	0.827811	−	0.561008i	$-0.189586\pi$
$53$	1.94236	+	1.94236i	0.266803	+	0.266803i	−0.561008	+	0.827811i	$0.689586\pi$
$54$	−0.355853	−	0.355853i	−0.0484254	−	0.0484254i
$55$	−4.15969	+	5.09748i	−0.560892	+	0.687344i
$56$	2.82745	−	2.82745i	0.377834	−	0.377834i
$57$	17.1218			2.26783
$58$	−2.49797	+	2.49797i	−0.328000	+	0.328000i
$59$	−8.34044	−	8.34044i	−1.08583	−	1.08583i	−0.995953	−	0.0898798i	$-0.971352\pi$
$59$	−8.34044	−	8.34044i	−1.08583	−	1.08583i	−0.0898798	−	0.995953i	$-0.528648\pi$
$60$	−5.35353	+	0.542335i	−0.691137	+	0.0700151i
$61$	−2.31872	−	2.31872i	−0.296882	−	0.296882i	0.542909	−	0.839791i	$-0.317323\pi$
$61$	−2.31872	−	2.31872i	−0.296882	−	0.296882i	−0.839791	+	0.542909i	$0.817323\pi$
$62$	−1.48171	−	1.48171i	−0.188177	−	0.188177i
$63$	−7.89106	−	7.89106i	−0.994180	−	0.994180i
$64$	1.00000			0.125000
$65$	−1.27981	−	1.04436i	−0.158741	−	0.129537i
$66$	−5.00671	−	5.00671i	−0.616283	−	0.616283i
$67$	2.10003	+	2.10003i	0.256560	+	0.256560i	0.823653	−	0.567093i	$-0.191932\pi$
$67$	2.10003	+	2.10003i	0.256560	+	0.256560i	−0.567093	+	0.823653i	$0.691932\pi$
$68$			6.61833i			0.802590i
$69$	−10.8794	+	10.8794i	−1.30973	+	1.30973i
$70$	8.89567	−	0.901168i	1.06324	−	0.107710i
$71$	−2.52254			−0.299370			−0.149685	−	0.988734i	$-0.547826\pi$
$71$	−2.52254			−0.299370			−0.149685	+	0.988734i	$0.547826\pi$
$72$		−	2.79087i		−	0.328907i
$73$	7.18876	−	7.18876i	0.841381	−	0.841381i	−0.147658	−	0.989038i	$-0.547173\pi$
$73$	7.18876	−	7.18876i	0.841381	−	0.841381i	0.989038	+	0.147658i	$0.0471735\pi$
$74$	−6.07917	−	0.209128i	−0.706689	−	0.0243107i
$75$	−10.0414	−	6.62886i	−1.15948	−	0.765434i
$76$	−5.03108	−	5.03108i	−0.577104	−	0.577104i
$77$	8.31937	+	8.31937i	0.948081	+	0.948081i
$78$	1.25702	−	1.25702i	0.142330	−	0.142330i
$79$	−5.69610	−	5.69610i	−0.640861	−	0.640861i	0.309906	−	0.950767i	$-0.399702\pi$
$79$	−5.69610	−	5.69610i	−0.640861	−	0.640861i	−0.950767	+	0.309906i	$0.899702\pi$
$80$	1.73245	+	1.41373i	0.193694	+	0.158059i
$81$	9.58365			1.06485
$82$		−	7.39769i		−	0.816939i
$83$	−2.72617	−	2.72617i	−0.299236	−	0.299236i	0.541479	−	0.840714i	$-0.317865\pi$
$83$	−2.72617	−	2.72617i	−0.299236	−	0.299236i	−0.840714	+	0.541479i	$0.817865\pi$
$84$			9.62238i			1.04989i
$85$	−9.35651	+	11.4659i	−1.01486	+	1.24365i
$86$	6.98494			0.753205
$87$		−	8.50109i		−	0.911413i
$88$			2.94236i			0.313656i
$89$	−4.25577	+	4.25577i	−0.451110	+	0.451110i	−0.895723	−	0.444613i	$-0.853341\pi$
$89$	−4.25577	+	4.25577i	−0.451110	+	0.451110i	0.444613	+	0.895723i	$0.353341\pi$
$90$	3.94553	−	4.83504i	0.415895	−	0.509658i
$91$	−2.08872	+	2.08872i	−0.218958	+	0.218958i
$92$	6.39364			0.666583
$93$	5.04255			0.522888
$94$	7.56618	−	7.56618i	0.780392	−	0.780392i
$95$	−1.60351	−	15.8287i	−0.164517	−	1.62399i
$96$	−1.70160	+	1.70160i	−0.173669	+	0.173669i
$97$		−	3.40320i		−	0.345542i	−0.984962	−	0.172771i	$-0.944728\pi$
$97$		−	3.40320i		−	0.345542i	0.984962	−	0.172771i	$-0.0552721\pi$
$98$		−	8.98899i		−	0.908026i
$99$	8.21174			0.825310
$100$	1.00275	+	4.89842i	0.100275	+	0.489842i
$101$		−	4.21918i		−	0.419825i	−0.977720	−	0.209912i	$-0.932682\pi$
$101$		−	4.21918i		−	0.419825i	0.977720	−	0.209912i	$-0.0673178\pi$
$102$	−11.2617	−	11.2617i	−1.11508	−	1.11508i
$103$			8.10234i			0.798347i	0.916875	+	0.399174i	$0.130703\pi$
$103$			8.10234i			0.798347i	−0.916875	+	0.399174i	$0.869297\pi$
$104$	−0.738730			−0.0724384
$105$	−13.6034	+	16.6703i	−1.32756	+	1.62685i
$106$	1.94236	+	1.94236i	0.188658	+	0.188658i
$107$	−11.7919	+	11.7919i	−1.13996	+	1.13996i	−0.151508	+	0.988456i	$0.548413\pi$
$107$	−11.7919	+	11.7919i	−1.13996	+	1.13996i	−0.988456	+	0.151508i	$0.951587\pi$
$108$	−0.355853	−	0.355853i	−0.0342419	−	0.0342419i
$109$	9.81489	+	9.81489i	0.940096	+	0.940096i	0.998304	−	0.0582084i	$-0.0185388\pi$
$109$	9.81489	+	9.81489i	0.940096	+	0.940096i	−0.0582084	+	0.998304i	$0.518539\pi$
$110$	−4.15969	+	5.09748i	−0.396611	+	0.486025i
$111$	10.7002	−	9.98845i	1.01561	−	0.948061i
$112$	2.82745	−	2.82745i	0.267169	−	0.267169i
$113$		−	5.85257i		−	0.550564i	−0.961364	−	0.275282i	$-0.911229\pi$
$113$		−	5.85257i		−	0.550564i	0.961364	−	0.275282i	$-0.0887712\pi$
$114$	17.1218			1.60360
$115$	11.0766	+	9.03886i	1.03290	+	0.842878i
$116$	−2.49797	+	2.49797i	−0.231931	+	0.231931i
$117$			2.06170i			0.190604i
$118$	−8.34044	−	8.34044i	−0.767799	−	0.767799i
$119$	18.7130	+	18.7130i	1.71542	+	1.71542i
$120$	−5.35353	+	0.542335i	−0.488708	+	0.0495082i
$121$	2.34255			0.212959
$122$	−2.31872	−	2.31872i	−0.209927	−	0.209927i
$123$	12.5879	+	12.5879i	1.13501	+	1.13501i
$124$	−1.48171	−	1.48171i	−0.133061	−	0.133061i
$125$	−5.18781	+	9.90387i	−0.464012	+	0.885829i
$126$	−7.89106	−	7.89106i	−0.702992	−	0.702992i
$127$	1.49192	−	1.49192i	0.132387	−	0.132387i	−0.637808	−	0.770195i	$-0.720159\pi$
$127$	1.49192	−	1.49192i	0.132387	−	0.132387i	0.770195	+	0.637808i	$0.220159\pi$
$128$	1.00000			0.0883883
$129$	−11.8856	+	11.8856i	−1.04647	+	1.04647i
$130$	−1.27981	−	1.04436i	−0.112247	−	0.0915966i
$131$	−11.9137	−	11.9137i	−1.04090	−	1.04090i	−0.999127	−	0.0417762i	$-0.986698\pi$
$131$	−11.9137	−	11.9137i	−1.04090	−	1.04090i	−0.0417762	−	0.999127i	$-0.513302\pi$
$132$	−5.00671	−	5.00671i	−0.435778	−	0.435778i
$133$	−28.4503			−2.46695
$134$	2.10003	+	2.10003i	0.181415	+	0.181415i
$135$	−0.113418	−	1.11957i	−0.00976143	−	0.0963576i
$136$			6.61833i			0.567517i
$137$	5.09297	−	5.09297i	0.435122	−	0.435122i	−0.455244	−	0.890367i	$-0.650448\pi$
$137$	5.09297	−	5.09297i	0.435122	−	0.435122i	0.890367	+	0.455244i	$0.150448\pi$
$138$	−10.8794	+	10.8794i	−0.926116	+	0.926116i
$139$	1.23936			0.105121			0.0525606	−	0.998618i	$-0.483262\pi$
$139$	1.23936			0.105121			0.0525606	+	0.998618i	$0.483262\pi$
$140$	8.89567	−	0.901168i	0.751821	−	0.0761626i
$141$			25.7492i			2.16847i
$142$	−2.52254			−0.211687
$143$		−	2.17361i		−	0.181766i
$144$		−	2.79087i		−	0.232573i
$145$	−7.85906	+	0.796156i	−0.652659	+	0.0661171i
$146$	7.18876	−	7.18876i	0.594946	−	0.594946i
$147$	15.2957	+	15.2957i	1.26156	+	1.26156i
$148$	−6.07917	−	0.209128i	−0.499704	−	0.0171903i
$149$		−	0.292738i		−	0.0239821i	−0.999928	−	0.0119910i	$-0.996183\pi$
$149$		−	0.292738i		−	0.0239821i	0.999928	−	0.0119910i	$-0.00381696\pi$
$150$	−10.0414	−	6.62886i	−0.819878	−	0.541244i
$151$			16.1449i			1.31386i	0.753954	+	0.656928i	$0.228144\pi$
$151$			16.1449i			1.31386i	−0.753954	+	0.656928i	$0.771856\pi$
$152$	−5.03108	−	5.03108i	−0.408074	−	0.408074i
$153$	18.4709			1.49328
$154$	8.31937	+	8.31937i	0.670394	+	0.670394i
$155$	−0.472251	−	4.66171i	−0.0379321	−	0.374438i
$156$	1.25702	−	1.25702i	0.100642	−	0.100642i
$157$	−3.24426	+	3.24426i	−0.258920	+	0.258920i	−0.824615	−	0.565695i	$-0.808608\pi$
$157$	−3.24426	+	3.24426i	−0.258920	+	0.258920i	0.565695	+	0.824615i	$0.308608\pi$
$158$	−5.69610	−	5.69610i	−0.453157	−	0.453157i
$159$	−6.61022			−0.524224
$160$	1.73245	+	1.41373i	0.136962	+	0.111765i
$161$	18.0777	−	18.0777i	1.42472	−	1.42472i
$162$	9.58365			0.752963
$163$		−	23.5099i		−	1.84144i	−0.390228	−	0.920718i	$-0.627604\pi$
$163$		−	23.5099i		−	1.84144i	0.390228	−	0.920718i	$-0.372396\pi$
$164$		−	7.39769i		−	0.577663i
$165$	−1.59574	−	15.7520i	−0.124228	−	1.22629i
$166$	−2.72617	−	2.72617i	−0.211592	−	0.211592i
$167$		−	11.4543i		−	0.886359i	−0.896433	−	0.443179i	$-0.853850\pi$
$167$		−	11.4543i		−	0.886359i	0.896433	−	0.443179i	$-0.146150\pi$
$168$			9.62238i			0.742383i
$169$	−12.4543			−0.958021
$170$	−9.35651	+	11.4659i	−0.717611	+	0.879395i
$171$	−14.0411	+	14.0411i	−1.07375	+	1.07375i
$172$	6.98494			0.532597
$173$	2.14087	−	2.14087i	0.162767	−	0.162767i	−0.621024	−	0.783791i	$-0.713283\pi$
$173$	2.14087	−	2.14087i	0.162767	−	0.162767i	0.783791	+	0.621024i	$0.213283\pi$
$174$		−	8.50109i		−	0.644466i
$175$	16.6853	+	11.0148i	1.26129	+	0.832642i
$176$			2.94236i			0.221788i
$177$	28.3841			2.13348
$178$	−4.25577	+	4.25577i	−0.318983	+	0.318983i
$179$	14.9428	−	14.9428i	1.11688	−	1.11688i	0.124682	−	0.992197i	$-0.460209\pi$
$179$	14.9428	−	14.9428i	1.11688	−	1.11688i	0.992197	−	0.124682i	$-0.0397909\pi$
$180$	3.94553	−	4.83504i	0.294082	−	0.360383i
$181$	12.0625			0.896602			0.448301	−	0.893883i	$-0.352029\pi$
$181$	12.0625			0.896602			0.448301	+	0.893883i	$0.352029\pi$
$182$	−2.08872	+	2.08872i	−0.154827	+	0.154827i
$183$	7.89106			0.583324
$184$	6.39364			0.471345
$185$	−10.2362	−	8.95659i	−0.752580	−	0.658501i
$186$	5.04255			0.369737
$187$	−19.4735			−1.42404
$188$	7.56618	−	7.56618i	0.551821	−	0.551821i
$189$	−2.01231			−0.146374
$190$	−1.60351	−	15.8287i	−0.116331	−	1.14833i
$191$	−10.7383	+	10.7383i	−0.776998	+	0.776998i	−0.979319	−	0.202321i	$-0.935151\pi$
$191$	−10.7383	+	10.7383i	−0.776998	+	0.776998i	0.202321	+	0.979319i	$0.435151\pi$
$192$	−1.70160	+	1.70160i	−0.122802	+	0.122802i
$193$	−9.09024			−0.654330			−0.327165	−	0.944967i	$-0.606093\pi$
$193$	−9.09024			−0.654330			−0.327165	+	0.944967i	$0.606093\pi$
$194$		−	3.40320i		−	0.244335i
$195$	3.95481	−	0.400639i	0.283210	−	0.0286903i
$196$		−	8.98899i		−	0.642071i
$197$	−7.91262	+	7.91262i	−0.563751	+	0.563751i	−0.930371	−	0.366620i	$-0.880515\pi$
$197$	−7.91262	+	7.91262i	−0.563751	+	0.563751i	0.366620	+	0.930371i	$0.380515\pi$
$198$	8.21174			0.583583
$199$	−9.14683	+	9.14683i	−0.648402	+	0.648402i	−0.952607	−	0.304205i	$-0.901609\pi$
$199$	−9.14683	+	9.14683i	−0.648402	+	0.648402i	0.304205	+	0.952607i	$0.401609\pi$
$200$	1.00275	+	4.89842i	0.0709052	+	0.346370i
$201$	−7.14683			−0.504098
$202$		−	4.21918i		−	0.296861i
$203$			14.1258i			0.991437i
$204$	−11.2617	−	11.2617i	−0.788479	−	0.788479i
$205$	10.4583	−	12.8161i	0.730441	−	0.895117i
$206$			8.10234i			0.564517i
$207$		−	17.8438i		−	1.24023i
$208$	−0.738730			−0.0512217
$209$	14.8032	−	14.8032i	1.02396	−	1.02396i
$210$	−13.6034	+	16.6703i	−0.938725	+	1.15036i
$211$	−12.2667			−0.844473			−0.422237	−	0.906486i	$-0.638755\pi$
$211$	−12.2667			−0.844473			−0.422237	+	0.906486i	$0.638755\pi$
$212$	1.94236	+	1.94236i	0.133402	+	0.133402i
$213$	4.29235	−	4.29235i	0.294107	−	0.294107i
$214$	−11.7919	+	11.7919i	−0.806076	+	0.806076i
$215$	12.1010	+	9.87480i	0.825284	+	0.673456i
$216$	−0.355853	−	0.355853i	−0.0242127	−	0.0242127i
$217$	−8.37893			−0.568799
$218$	9.81489	+	9.81489i	0.664748	+	0.664748i
$219$			24.4648i			1.65317i
$220$	−4.15969	+	5.09748i	−0.280446	+	0.343672i
$221$		−	4.88915i		−	0.328880i
$222$	10.7002	−	9.98845i	0.718147	−	0.670381i
$223$	−8.70510	−	8.70510i	−0.582937	−	0.582937i	0.352772	−	0.935709i	$-0.385239\pi$
$223$	−8.70510	−	8.70510i	−0.582937	−	0.582937i	−0.935709	+	0.352772i	$0.885239\pi$
$224$	2.82745	−	2.82745i	0.188917	−	0.188917i
$225$	13.6709	−	2.79855i	0.911390	−	0.186570i
$226$		−	5.85257i		−	0.389307i
$227$			22.3785i			1.48532i	0.669671	+	0.742658i	$0.266435\pi$
$227$			22.3785i			1.48532i	−0.669671	+	0.742658i	$0.733565\pi$
$228$	17.1218			1.13392
$229$			6.97332i			0.460810i	0.973095	+	0.230405i	$0.0740051\pi$
$229$			6.97332i			0.460810i	−0.973095	+	0.230405i	$0.925995\pi$
$230$	11.0766	+	9.03886i	0.730372	+	0.596005i
$231$	−28.3125			−1.86282
$232$	−2.49797	+	2.49797i	−0.164000	+	0.164000i
$233$	15.1891	−	15.1891i	0.995069	−	0.995069i	−0.00491851	−	0.999988i	$-0.501566\pi$
$233$	15.1891	−	15.1891i	0.995069	−	0.995069i	0.999988	+	0.00491851i	$0.00156562\pi$
$234$			2.06170i			0.134778i
$235$	23.8045	−	2.41150i	1.55284	−	0.157309i
$236$	−8.34044	−	8.34044i	−0.542916	−	0.542916i
$237$	19.3849			1.25919
$238$	18.7130	+	18.7130i	1.21298	+	1.21298i
$239$	1.35831	+	1.35831i	0.0878617	+	0.0878617i	0.749672	−	0.661810i	$-0.230211\pi$
$239$	1.35831	+	1.35831i	0.0878617	+	0.0878617i	−0.661810	+	0.749672i	$0.730211\pi$
$240$	−5.35353	+	0.542335i	−0.345569	+	0.0350076i
$241$	−9.55663	+	9.55663i	−0.615596	+	0.615596i	−0.944399	−	0.328802i	$-0.893355\pi$
$241$	−9.55663	+	9.55663i	−0.615596	+	0.615596i	0.328802	+	0.944399i	$0.393355\pi$
$242$	2.34255			0.150585
$243$	−15.2400	+	15.2400i	−0.977644	+	0.977644i
$244$	−2.31872	−	2.31872i	−0.148441	−	0.148441i
$245$	12.7080	−	15.5730i	0.811883	−	0.994920i
$246$	12.5879	+	12.5879i	0.802575	+	0.802575i
$247$	3.71661	+	3.71661i	0.236482	+	0.236482i
$248$	−1.48171	−	1.48171i	−0.0940886	−	0.0940886i
$249$	9.27768			0.587949
$250$	−5.18781	+	9.90387i	−0.328106	+	0.626376i
$251$	11.4900	+	11.4900i	0.725241	+	0.725241i	0.969668	−	0.244427i	$-0.0785998\pi$
$251$	11.4900	+	11.4900i	0.725241	+	0.725241i	−0.244427	+	0.969668i	$0.578600\pi$
$252$	−7.89106	−	7.89106i	−0.497090	−	0.497090i
$253$			18.8124i			1.18272i
$254$	1.49192	−	1.49192i	0.0936114	−	0.0936114i
$255$	−3.58935	−	35.4314i	−0.224774	−	2.21880i
$256$	1.00000			0.0625000
$257$			31.7662i			1.98152i	0.135622	+	0.990761i	$0.456697\pi$
$257$			31.7662i			1.98152i	−0.135622	+	0.990761i	$0.543303\pi$
$258$	−11.8856	+	11.8856i	−0.739963	+	0.739963i
$259$	−17.7799	+	16.5973i	−1.10479	+	1.03130i
$260$	−1.27981	−	1.04436i	−0.0793705	−	0.0647686i
$261$	6.97152	+	6.97152i	0.431526	+	0.431526i
$262$	−11.9137	−	11.9137i	−0.736030	−	0.736030i
$263$	−18.8716	+	18.8716i	−1.16367	+	1.16367i	−0.180007	+	0.983665i	$0.557612\pi$
$263$	−18.8716	+	18.8716i	−1.16367	+	1.16367i	−0.983665	+	0.180007i	$0.942388\pi$
$264$	−5.00671	−	5.00671i	−0.308141	−	0.308141i
$265$	0.619069	+	6.11099i	0.0380291	+	0.375395i
$266$	−28.4503			−1.74440
$267$		−	14.4832i		−	0.886358i
$268$	2.10003	+	2.10003i	0.128280	+	0.128280i
$269$		−	5.87409i		−	0.358150i	−0.983835	−	0.179075i	$-0.942690\pi$
$269$		−	5.87409i		−	0.358150i	0.983835	−	0.179075i	$-0.0573104\pi$
$270$	−0.113418	−	1.11957i	−0.00690238	−	0.0681351i
$271$	2.68158			0.162895			0.0814473	−	0.996678i	$-0.474046\pi$
$271$	2.68158			0.162895			0.0814473	+	0.996678i	$0.474046\pi$
$272$			6.61833i			0.401295i
$273$		−	7.10834i		−	0.430216i
$274$	5.09297	−	5.09297i	0.307678	−	0.307678i
$275$	−14.4129	+	2.95045i	−0.869130	+	0.177919i
$276$	−10.8794	+	10.8794i	−0.654863	+	0.654863i
$277$	−8.90912			−0.535297			−0.267649	−	0.963517i	$-0.586247\pi$
$277$	−8.90912			−0.535297			−0.267649	+	0.963517i	$0.586247\pi$
$278$	1.23936			0.0743319
$279$	−4.13526	+	4.13526i	−0.247571	+	0.247571i
$280$	8.89567	−	0.901168i	0.531618	−	0.0538551i
$281$	−3.03708	+	3.03708i	−0.181177	+	0.181177i	−0.791869	−	0.610692i	$-0.790892\pi$
$281$	−3.03708	+	3.03708i	−0.181177	+	0.181177i	0.610692	+	0.791869i	$0.290892\pi$
$282$			25.7492i			1.53334i
$283$		−	5.36256i		−	0.318771i	−0.987216	−	0.159386i	$-0.949049\pi$
$283$		−	5.36256i		−	0.318771i	0.987216	−	0.159386i	$-0.0509513\pi$
$284$	−2.52254			−0.149685
$285$	29.6625	+	24.2055i	1.75706	+	1.43381i
$286$		−	2.17361i		−	0.128528i
$287$	−20.9166	−	20.9166i	−1.23467	−	1.23467i
$288$		−	2.79087i		−	0.164454i
$289$	−26.8022			−1.57660
$290$	−7.85906	+	0.796156i	−0.461500	+	0.0467519i
$291$	5.79087	+	5.79087i	0.339467	+	0.339467i
$292$	7.18876	−	7.18876i	0.420690	−	0.420690i
$293$	13.2752	+	13.2752i	0.775544	+	0.775544i	0.979070	−	0.203525i	$-0.0652399\pi$
$293$	13.2752	+	13.2752i	0.775544	+	0.775544i	−0.203525	+	0.979070i	$0.565240\pi$
$294$	15.2957	+	15.2957i	0.892061	+	0.892061i
$295$	−2.65827	−	26.2405i	−0.154771	−	1.52778i
$296$	−6.07917	−	0.209128i	−0.353344	−	0.0121553i
$297$	1.04704	−	1.04704i	0.0607557	−	0.0607557i
$298$		−	0.292738i		−	0.0169579i
$299$	−4.72317			−0.273148
$300$	−10.0414	−	6.62886i	−0.579741	−	0.382717i
$301$	19.7496	−	19.7496i	1.13835	−	1.13835i
$302$			16.1449i			0.929036i
$303$	7.17936	+	7.17936i	0.412443	+	0.412443i
$304$	−5.03108	−	5.03108i	−0.288552	−	0.288552i
$305$	−0.739025	−	7.29510i	−0.0423164	−	0.417716i
$306$	18.4709			1.05591
$307$	3.46389	+	3.46389i	0.197694	+	0.197694i	0.799011	−	0.601316i	$-0.205357\pi$
$307$	3.46389	+	3.46389i	0.197694	+	0.197694i	−0.601316	+	0.799011i	$0.705357\pi$
$308$	8.31937	+	8.31937i	0.474040	+	0.474040i
$309$	−13.7869	−	13.7869i	−0.784311	−	0.784311i
$310$	−0.472251	−	4.66171i	−0.0268221	−	0.264768i
$311$	10.6674	+	10.6674i	0.604894	+	0.604894i	0.941607	−	0.336713i	$-0.109315\pi$
$311$	10.6674	+	10.6674i	0.604894	+	0.604894i	−0.336713	+	0.941607i	$0.609315\pi$
$312$	1.25702	−	1.25702i	0.0711648	−	0.0711648i
$313$	−23.2451			−1.31389			−0.656947	−	0.753937i	$-0.728152\pi$
$313$	−23.2451			−1.31389			−0.656947	+	0.753937i	$0.728152\pi$
$314$	−3.24426	+	3.24426i	−0.183084	+	0.183084i
$315$	−2.51505	−	24.8267i	−0.141707	−	1.39882i
$316$	−5.69610	−	5.69610i	−0.320430	−	0.320430i
$317$	7.42086	+	7.42086i	0.416797	+	0.416797i	0.884098	−	0.467301i	$-0.154774\pi$
$317$	7.42086	+	7.42086i	0.416797	+	0.416797i	−0.467301	+	0.884098i	$0.654774\pi$
$318$	−6.61022			−0.370682
$319$	−7.34992	−	7.34992i	−0.411517	−	0.411517i
$320$	1.73245	+	1.41373i	0.0968468	+	0.0790297i
$321$		−	40.1301i		−	2.23984i
$322$	18.0777	−	18.0777i	1.00743	−	1.00743i
$323$	33.2973	−	33.2973i	1.85271	−	1.85271i
$324$	9.58365			0.532425
$325$	−0.740762	−	3.61861i	−0.0410901	−	0.200724i
$326$		−	23.5099i		−	1.30209i
$327$	−33.4020			−1.84713
$328$		−	7.39769i		−	0.408469i
$329$		−	42.7861i		−	2.35887i
$330$	−1.59574	−	15.7520i	−0.0878427	−	0.867118i
$331$	13.2492	−	13.2492i	0.728243	−	0.728243i	−0.242027	−	0.970270i	$-0.577812\pi$
$331$	13.2492	−	13.2492i	0.728243	−	0.728243i	0.970270	+	0.242027i	$0.0778122\pi$
$332$	−2.72617	−	2.72617i	−0.149618	−	0.149618i
$333$	−0.583651	+	16.9662i	−0.0319839	+	0.929741i
$334$		−	11.4543i		−	0.626750i
$335$	0.669325	+	6.60708i	0.0365691	+	0.360983i
$336$			9.62238i			0.524944i
$337$	3.84828	+	3.84828i	0.209629	+	0.209629i	0.804110	−	0.594481i	$-0.202642\pi$
$337$	3.84828	+	3.84828i	0.209629	+	0.209629i	−0.594481	+	0.804110i	$0.702642\pi$
$338$	−12.4543			−0.677423
$339$	9.95872	+	9.95872i	0.540884	+	0.540884i
$340$	−9.35651	+	11.4659i	−0.507428	+	0.621826i
$341$	4.35971	−	4.35971i	0.236092	−	0.236092i
$342$	−14.0411	+	14.0411i	−0.759256	+	0.759256i
$343$	−5.62379	−	5.62379i	−0.303656	−	0.303656i
$344$	6.98494			0.376603
$345$	−34.2285	+	3.46749i	−1.84280	+	0.186683i
$346$	2.14087	−	2.14087i	0.115094	−	0.115094i
$347$	20.7126			1.11191			0.555956	−	0.831212i	$-0.312352\pi$
$347$	20.7126			1.11191			0.555956	+	0.831212i	$0.312352\pi$
$348$		−	8.50109i		−	0.455706i
$349$		−	29.0891i		−	1.55711i	−0.627579	−	0.778553i	$-0.715954\pi$
$349$		−	29.0891i		−	1.55711i	0.627579	−	0.778553i	$-0.284046\pi$
$350$	16.6853	+	11.0148i	0.891866	+	0.588767i
$351$	0.262879	+	0.262879i	0.0140314	+	0.0140314i
$352$			2.94236i			0.156828i
$353$			22.8767i			1.21760i	0.793323	+	0.608801i	$0.208349\pi$
$353$			22.8767i			1.21760i	−0.793323	+	0.608801i	$0.791651\pi$
$354$	28.3841			1.50860
$355$	−4.37017	−	3.56618i	−0.231945	−	0.189273i
$356$	−4.25577	+	4.25577i	−0.225555	+	0.225555i
$357$	−63.6841			−3.37052
$358$	14.9428	−	14.9428i	0.789752	−	0.789752i
$359$		−	25.7577i		−	1.35944i	−0.733472	−	0.679720i	$-0.762101\pi$
$359$		−	25.7577i		−	1.35944i	0.733472	−	0.679720i	$-0.237899\pi$
$360$	3.94553	−	4.83504i	0.207948	−	0.254829i
$361$			31.6235i			1.66440i
$362$	12.0625			0.633993
$363$	−3.98607	+	3.98607i	−0.209214	+	0.209214i
$364$	−2.08872	+	2.08872i	−0.109479	+	0.109479i
$365$	22.6171	−	2.29121i	1.18383	−	0.119927i
$366$	7.89106			0.412472
$367$	−17.7447	+	17.7447i	−0.926265	+	0.926265i	−0.997462	−	0.0711974i	$-0.977318\pi$
$367$	−17.7447	+	17.7447i	−0.926265	+	0.926265i	0.0711974	+	0.997462i	$0.477318\pi$
$368$	6.39364			0.333291
$369$	−20.6460			−1.07479
$370$	−10.2362	−	8.95659i	−0.532154	−	0.465631i
$371$	10.9838			0.570253
$372$	5.04255			0.261444
$373$	22.7050	−	22.7050i	1.17562	−	1.17562i	0.194773	−	0.980848i	$-0.437603\pi$
$373$	22.7050	−	22.7050i	1.17562	−	1.17562i	0.980848	−	0.194773i	$-0.0623969\pi$
$374$	−19.4735			−1.00695
$375$	−8.02484	−	25.6800i	−0.414401	−	1.32611i
$376$	7.56618	−	7.56618i	0.390196	−	0.390196i
$377$	1.84533	−	1.84533i	0.0950392	−	0.0950392i
$378$	−2.01231			−0.103502
$379$			27.5341i			1.41433i	0.707047	+	0.707166i	$0.250027\pi$
$379$			27.5341i			1.41433i	−0.707047	+	0.707166i	$0.749973\pi$
$380$	−1.60351	−	15.8287i	−0.0822583	−	0.811993i
$381$			5.07730i			0.260118i
$382$	−10.7383	+	10.7383i	−0.549420	+	0.549420i
$383$	4.93269			0.252049			0.126024	−	0.992027i	$-0.459778\pi$
$383$	4.93269			0.252049			0.126024	+	0.992027i	$0.459778\pi$
$384$	−1.70160	+	1.70160i	−0.0868343	+	0.0868343i
$385$	2.65156	+	26.1742i	0.135136	+	1.33396i
$386$	−9.09024			−0.462681
$387$		−	19.4941i		−	0.990939i
$388$		−	3.40320i		−	0.172771i
$389$	−4.25176	−	4.25176i	−0.215573	−	0.215573i	0.591057	−	0.806630i	$-0.298711\pi$
$389$	−4.25176	−	4.25176i	−0.215573	−	0.215573i	−0.806630	+	0.591057i	$0.798711\pi$
$390$	3.95481	−	0.400639i	0.200259	−	0.0202871i
$391$			42.3152i			2.13997i
$392$		−	8.98899i		−	0.454013i
$393$	40.5446			2.04520
$394$	−7.91262	+	7.91262i	−0.398632	+	0.398632i
$395$	−1.81546	−	17.9209i	−0.0913459	−	0.901699i
$396$	8.21174			0.412655
$397$	−6.85748	−	6.85748i	−0.344167	−	0.344167i	0.513764	−	0.857931i	$-0.328251\pi$
$397$	−6.85748	−	6.85748i	−0.344167	−	0.344167i	−0.857931	+	0.513764i	$0.828251\pi$
$398$	−9.14683	+	9.14683i	−0.458489	+	0.458489i
$399$	48.4110	−	48.4110i	2.42358	−	2.42358i
$400$	1.00275	+	4.89842i	0.0501376	+	0.244921i
$401$	4.52089	+	4.52089i	0.225763	+	0.225763i	0.810920	−	0.585157i	$-0.198967\pi$
$401$	4.52089	+	4.52089i	0.225763	+	0.225763i	−0.585157	+	0.810920i	$0.698967\pi$
$402$	−7.14683			−0.356451
$403$	1.09458	+	1.09458i	0.0545250	+	0.0545250i
$404$		−	4.21918i		−	0.209912i
$405$	16.6032	+	13.5487i	0.825018	+	0.673239i
$406$			14.1258i			0.701052i
$407$	0.615330	−	17.8871i	0.0305008	−	0.886629i
$408$	−11.2617	−	11.2617i	−0.557539	−	0.557539i
$409$	12.6409	−	12.6409i	0.625053	−	0.625053i	−0.321766	−	0.946819i	$-0.604277\pi$
$409$	12.6409	−	12.6409i	0.625053	−	0.625053i	0.946819	+	0.321766i	$0.104277\pi$
$410$	10.4583	−	12.8161i	0.516500	−	0.632943i
$411$			17.3324i			0.854944i
$412$			8.10234i			0.399174i
$413$	−47.1644			−2.32081
$414$		−	17.8438i		−	0.876976i
$415$	−0.868886	−	8.57700i	−0.0426519	−	0.421028i
$416$	−0.738730			−0.0362192
$417$	−2.10889	+	2.10889i	−0.103273	+	0.103273i
$418$	14.8032	−	14.8032i	0.724049	−	0.724049i
$419$			18.0818i			0.883353i	0.897174	+	0.441676i	$0.145616\pi$
$419$			18.0818i			0.883353i	−0.897174	+	0.441676i	$0.854384\pi$
$420$	−13.6034	+	16.6703i	−0.663779	+	0.813426i
$421$	−2.11385	−	2.11385i	−0.103023	−	0.103023i	0.653717	−	0.756739i	$-0.273209\pi$
$421$	−2.11385	−	2.11385i	−0.103023	−	0.103023i	−0.756739	+	0.653717i	$0.773209\pi$
$422$	−12.2667			−0.597133
$423$	−21.1162	−	21.1162i	−1.02671	−	1.02671i
$424$	1.94236	+	1.94236i	0.0943291	+	0.0943291i
$425$	−32.4193	+	6.63654i	−1.57257	+	0.321919i
$426$	4.29235	−	4.29235i	0.207965	−	0.207965i
$427$	−13.1122			−0.634542
$428$	−11.7919	+	11.7919i	−0.569982	+	0.569982i
$429$	3.69860	+	3.69860i	0.178570	+	0.178570i
$430$	12.1010	+	9.87480i	0.583564	+	0.476205i
$431$	−2.69254	−	2.69254i	−0.129695	−	0.129695i	0.639279	−	0.768975i	$-0.279233\pi$
$431$	−2.69254	−	2.69254i	−0.129695	−	0.129695i	−0.768975	+	0.639279i	$0.779233\pi$
$432$	−0.355853	−	0.355853i	−0.0171210	−	0.0171210i
$433$	−13.9527	−	13.9527i	−0.670524	−	0.670524i	0.287312	−	0.957837i	$-0.407238\pi$
$433$	−13.9527	−	13.9527i	−0.670524	−	0.670524i	−0.957837	+	0.287312i	$0.907238\pi$
$434$	−8.37893			−0.402201
$435$	12.0182	−	14.7277i	0.576230	−	0.706139i
$436$	9.81489	+	9.81489i	0.470048	+	0.470048i
$437$	−32.1669	−	32.1669i	−1.53875	−	1.53875i
$438$			24.4648i			1.16897i
$439$	−22.9884	+	22.9884i	−1.09718	+	1.09718i	−0.102437	+	0.994739i	$0.532664\pi$
$439$	−22.9884	+	22.9884i	−1.09718	+	1.09718i	−0.994739	+	0.102437i	$0.967336\pi$
$440$	−4.15969	+	5.09748i	−0.198305	+	0.243013i
$441$	−25.0871			−1.19463
$442$		−	4.88915i		−	0.232553i
$443$	−7.06197	+	7.06197i	−0.335524	+	0.335524i	−0.854680	−	0.519156i	$-0.826247\pi$
$443$	−7.06197	+	7.06197i	−0.335524	+	0.335524i	0.519156	+	0.854680i	$0.326247\pi$
$444$	10.7002	−	9.98845i	0.507807	−	0.474031i
$445$	−13.3894	+	1.35640i	−0.634718	+	0.0642996i
$446$	−8.70510	−	8.70510i	−0.412199	−	0.412199i
$447$	0.498123	+	0.498123i	0.0235604	+	0.0235604i
$448$	2.82745	−	2.82745i	0.133585	−	0.133585i
$449$	2.65135	+	2.65135i	0.125125	+	0.125125i	0.766896	−	0.641771i	$-0.221800\pi$
$449$	2.65135	+	2.65135i	0.125125	+	0.125125i	−0.641771	+	0.766896i	$0.721800\pi$
$450$	13.6709	−	2.79855i	0.644450	−	0.131925i
$451$	21.7666			1.02495
$452$		−	5.85257i		−	0.275282i
$453$	−27.4722	−	27.4722i	−1.29075	−	1.29075i
$454$			22.3785i			1.05028i
$455$	−6.57149	+	0.665720i	−0.308076	+	0.0312094i
$456$	17.1218			0.801799
$457$			6.35811i			0.297420i	0.988881	+	0.148710i	$0.0475121\pi$
$457$			6.35811i			0.297420i	−0.988881	+	0.148710i	$0.952488\pi$
$458$			6.97332i			0.325842i
$459$	2.35515	−	2.35515i	0.109929	−	0.109929i
$460$	11.0766	+	9.03886i	0.516451	+	0.421439i
$461$	13.5522	−	13.5522i	0.631188	−	0.631188i	−0.317178	−	0.948366i	$-0.602735\pi$
$461$	13.5522	−	13.5522i	0.631188	−	0.631188i	0.948366	+	0.317178i	$0.102735\pi$
$462$	−28.3125			−1.31721
$463$	6.65144			0.309119			0.154559	−	0.987983i	$-0.450604\pi$
$463$	6.65144			0.309119			0.154559	+	0.987983i	$0.450604\pi$
$464$	−2.49797	+	2.49797i	−0.115965	+	0.115965i
$465$	8.73595	+	7.12878i	0.405120	+	0.330589i
$466$	15.1891	−	15.1891i	0.703620	−	0.703620i
$467$			18.5636i			0.859019i	0.903062	+	0.429510i	$0.141314\pi$
$467$			18.5636i			0.859019i	−0.903062	+	0.429510i	$0.858686\pi$
$468$			2.06170i			0.0953021i
$469$	11.8755			0.548360
$470$	23.8045	−	2.41150i	1.09802	−	0.111234i
$471$		−	11.0409i		−	0.508736i
$472$	−8.34044	−	8.34044i	−0.383900	−	0.383900i
$473$			20.5522i			0.944990i
$474$	19.3849			0.890379
$475$	19.5994	−	29.6892i	0.899282	−	1.36224i
$476$	18.7130	+	18.7130i	0.857710	+	0.857710i
$477$	5.42086	−	5.42086i	0.248204	−	0.248204i
$478$	1.35831	+	1.35831i	0.0621276	+	0.0621276i
$479$	−3.71611	−	3.71611i	−0.169793	−	0.169793i	0.617095	−	0.786889i	$-0.288309\pi$
$479$	−3.71611	−	3.71611i	−0.169793	−	0.169793i	−0.786889	+	0.617095i	$0.788309\pi$
$480$	−5.35353	+	0.542335i	−0.244354	+	0.0247541i
$481$	4.49086	+	0.154489i	0.204766	+	0.00704411i
$482$	−9.55663	+	9.55663i	−0.435292	+	0.435292i
$483$			61.5220i			2.79935i
$484$	2.34255			0.106479
$485$	4.81119	−	5.89586i	0.218465	−	0.267717i
$486$	−15.2400	+	15.2400i	−0.691299	+	0.691299i
$487$		−	0.818395i		−	0.0370850i	−0.999828	−	0.0185425i	$-0.994097\pi$
$487$		−	0.818395i		−	0.0370850i	0.999828	−	0.0185425i	$-0.00590260\pi$
$488$	−2.31872	−	2.31872i	−0.104964	−	0.104964i
$489$	40.0044	+	40.0044i	1.80906	+	1.80906i
$490$	12.7080	−	15.5730i	0.574088	−	0.703515i
$491$	5.21815			0.235492			0.117746	−	0.993044i	$-0.462433\pi$
$491$	5.21815			0.235492			0.117746	+	0.993044i	$0.462433\pi$
$492$	12.5879	+	12.5879i	0.567506	+	0.567506i
$493$	−16.5324	−	16.5324i	−0.744582	−	0.744582i
$494$	3.71661	+	3.71661i	0.167218	+	0.167218i
$495$	14.2264	+	11.6092i	0.639429	+	0.521793i
$496$	−1.48171	−	1.48171i	−0.0665307	−	0.0665307i
$497$	−7.13237	+	7.13237i	−0.319930	+	0.319930i
$498$	9.27768			0.415743
$499$	−17.1758	+	17.1758i	−0.768894	+	0.768894i	−0.977912	−	0.209018i	$-0.932973\pi$
$499$	−17.1758	+	17.1758i	−0.768894	+	0.768894i	0.209018	+	0.977912i	$0.432973\pi$
$500$	−5.18781	+	9.90387i	−0.232006	+	0.442914i
$501$	19.4906	+	19.4906i	0.870775	+	0.870775i
$502$	11.4900	+	11.4900i	0.512823	+	0.512823i
$503$	26.2211			1.16914			0.584569	−	0.811344i	$-0.301263\pi$
$503$	26.2211			1.16914			0.584569	+	0.811344i	$0.301263\pi$
$504$	−7.89106	−	7.89106i	−0.351496	−	0.351496i
$505$	5.96478	−	7.30952i	0.265429	−	0.325269i
$506$			18.8124i			0.836311i
$507$	21.1922	−	21.1922i	0.941178	−	0.941178i
$508$	1.49192	−	1.49192i	0.0661933	−	0.0661933i
$509$	−5.42333			−0.240385			−0.120192	−	0.992751i	$-0.538351\pi$
$509$	−5.42333			−0.240385			−0.120192	+	0.992751i	$0.538351\pi$
$510$	−3.58935	−	35.4314i	−0.158939	−	1.56893i
$511$		−	40.6518i		−	1.79833i
$512$	1.00000			0.0441942
$513$			3.58064i			0.158089i
$514$			31.7662i			1.40115i
$515$	−11.4545	+	14.0369i	−0.504745	+	0.618539i
$516$	−11.8856	+	11.8856i	−0.523233	+	0.523233i
$517$	22.2624	+	22.2624i	0.979099	+	0.979099i
$518$	−17.7799	+	16.5973i	−0.781202	+	0.729242i
$519$			7.28579i			0.319811i
$520$	−1.27981	−	1.04436i	−0.0561234	−	0.0457983i
$521$			20.3630i			0.892120i	0.895003	+	0.446060i	$0.147173\pi$
$521$			20.3630i			0.892120i	−0.895003	+	0.446060i	$0.852827\pi$
$522$	6.97152	+	6.97152i	0.305135	+	0.305135i
$523$	−3.41343			−0.149259			−0.0746293	−	0.997211i	$-0.523777\pi$
$523$	−3.41343			−0.149259			−0.0746293	+	0.997211i	$0.523777\pi$
$524$	−11.9137	−	11.9137i	−0.520452	−	0.520452i
$525$	−47.1344	+	9.64886i	−2.05712	+	0.421111i
$526$	−18.8716	+	18.8716i	−0.822841	+	0.822841i
$527$	9.80643	−	9.80643i	0.427175	−	0.427175i
$528$	−5.00671	−	5.00671i	−0.217889	−	0.217889i
$529$	17.8786			0.777331
$530$	0.619069	+	6.11099i	0.0268906	+	0.265444i
$531$	−23.2771	+	23.2771i	−1.01014	+	1.01014i
$532$	−28.4503			−1.23348
$533$			5.46490i			0.236711i
$534$		−	14.4832i		−	0.626750i
$535$	−37.0993	+	3.75832i	−1.60394	+	0.162486i
$536$	2.10003	+	2.10003i	0.0907077	+	0.0907077i
$537$			50.8533i			2.19448i
$538$		−	5.87409i		−	0.253250i
$539$	26.4488			1.13923
$540$	−0.113418	−	1.11957i	−0.00488072	−	0.0481788i
$541$	1.72146	−	1.72146i	0.0740112	−	0.0740112i	−0.669132	−	0.743143i	$-0.733334\pi$
$541$	1.72146	−	1.72146i	0.0740112	−	0.0740112i	0.743143	+	0.669132i	$0.233334\pi$
$542$	2.68158			0.115184
$543$	−20.5256	+	20.5256i	−0.880838	+	0.880838i
$544$			6.61833i			0.283758i
$545$	3.12821	+	30.8794i	0.133998	+	1.32273i
$546$		−	7.10834i		−	0.304209i
$547$	38.3283			1.63880			0.819400	−	0.573223i	$-0.194307\pi$
$547$	38.3283			1.63880			0.819400	+	0.573223i	$0.194307\pi$
$548$	5.09297	−	5.09297i	0.217561	−	0.217561i
$549$	−6.47125	+	6.47125i	−0.276186	+	0.276186i
$550$	−14.4129	+	2.95045i	−0.614567	+	0.125808i
$551$	25.1350			1.07079
$552$	−10.8794	+	10.8794i	−0.463058	+	0.463058i
$553$	−32.2109			−1.36975
$554$	−8.90912			−0.378512
$555$	32.6584	−	2.17737i	1.38627	−	0.0924242i
$556$	1.23936			0.0525606
$557$	−14.2458			−0.603613			−0.301806	−	0.953369i	$-0.597590\pi$
$557$	−14.2458			−0.603613			−0.301806	+	0.953369i	$0.597590\pi$
$558$	−4.13526	+	4.13526i	−0.175059	+	0.175059i
$559$	−5.15998			−0.218244
$560$	8.89567	−	0.901168i	0.375910	−	0.0380813i
$561$	33.1360	−	33.1360i	1.39900	−	1.39900i
$562$	−3.03708	+	3.03708i	−0.128112	+	0.128112i
$563$	−4.87106			−0.205291			−0.102645	−	0.994718i	$-0.532731\pi$
$563$	−4.87106			−0.205291			−0.102645	+	0.994718i	$0.532731\pi$
$564$			25.7492i			1.08424i
$565$	8.27394	−	10.1393i	0.348087	−	0.426563i
$566$		−	5.36256i		−	0.225405i
$567$	27.0973	−	27.0973i	1.13798	−	1.13798i
$568$	−2.52254			−0.105843
$569$	15.2311	−	15.2311i	0.638521	−	0.638521i	−0.311669	−	0.950191i	$-0.600888\pi$
$569$	15.2311	−	15.2311i	0.638521	−	0.638521i	0.950191	+	0.311669i	$0.100888\pi$
$570$	29.6625	+	24.2055i	1.24243	+	1.01386i
$571$	10.5691			0.442302			0.221151	−	0.975240i	$-0.429019\pi$
$571$	10.5691			0.442302			0.221151	+	0.975240i	$0.429019\pi$
$572$		−	2.17361i		−	0.0908830i
$573$		−	36.5446i		−	1.52667i
$574$	−20.9166	−	20.9166i	−0.873044	−	0.873044i
$575$	6.41123	+	31.3187i	0.267367	+	1.30608i
$576$		−	2.79087i		−	0.116286i
$577$		−	27.8591i		−	1.15979i	−0.814691	−	0.579895i	$-0.803094\pi$
$577$		−	27.8591i		−	1.15979i	0.814691	−	0.579895i	$-0.196906\pi$
$578$	−26.8022			−1.11483
$579$	15.4679	−	15.4679i	0.642826	−	0.642826i
$580$	−7.85906	+	0.796156i	−0.326330	+	0.0330586i
$581$	−15.4162			−0.639573
$582$	5.79087	+	5.79087i	0.240039	+	0.240039i
$583$	−5.71510	+	5.71510i	−0.236695	+	0.236695i
$584$	7.18876	−	7.18876i	0.297473	−	0.297473i
$585$	−2.91468	+	3.57179i	−0.120507	+	0.147675i
$586$	13.2752	+	13.2752i	0.548393	+	0.548393i
$587$	−1.53471			−0.0633441			−0.0316720	−	0.999498i	$-0.510083\pi$
$587$	−1.53471			−0.0633441			−0.0316720	+	0.999498i	$0.510083\pi$
$588$	15.2957	+	15.2957i	0.630782	+	0.630782i
$589$			14.9092i			0.614322i
$590$	−2.65827	−	26.2405i	−0.109439	−	1.08030i
$591$		−	26.9282i		−	1.10768i
$592$	−6.07917	−	0.209128i	−0.249852	−	0.00859513i
$593$	33.9424	+	33.9424i	1.39385	+	1.39385i	0.816495	+	0.577353i	$0.195914\pi$
$593$	33.9424	+	33.9424i	1.39385	+	1.39385i	0.577353	+	0.816495i	$0.304086\pi$
$594$	1.04704	−	1.04704i	0.0429608	−	0.0429608i
$595$	5.96423	+	58.8744i	0.244509	+	2.41362i
$596$		−	0.292738i		−	0.0119910i
$597$		−	31.1285i		−	1.27400i
$598$	−4.72317			−0.193145
$599$			3.02066i			0.123421i	0.998094	+	0.0617105i	$0.0196555\pi$
$599$			3.02066i			0.123421i	−0.998094	+	0.0617105i	$0.980344\pi$
$600$	−10.0414	−	6.62886i	−0.409939	−	0.270622i
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$	19.7496	−	19.7496i	0.804933	−	0.804933i
$603$	5.86093	−	5.86093i	0.238675	−	0.238675i
$604$			16.1449i			0.656928i
$605$	4.05834	+	3.31172i	0.164995	+	0.134641i
$606$	7.17936	+	7.17936i	0.291641	+	0.291641i
$607$	−2.50292			−0.101590			−0.0507951	−	0.998709i	$-0.516176\pi$
$607$	−2.50292			−0.101590			−0.0507951	+	0.998709i	$0.516176\pi$
$608$	−5.03108	−	5.03108i	−0.204037	−	0.204037i
$609$	−24.0364	−	24.0364i	−0.974006	−	0.974006i
$610$	−0.739025	−	7.29510i	−0.0299222	−	0.295370i
$611$	−5.58936	+	5.58936i	−0.226122	+	0.226122i
$612$	18.4709			0.746642
$613$	26.8961	−	26.8961i	1.08632	−	1.08632i	0.0904205	−	0.995904i	$-0.471179\pi$
$613$	26.8961	−	26.8961i	1.08632	−	1.08632i	0.995904	−	0.0904205i	$-0.0288211\pi$
$614$	3.46389	+	3.46389i	0.139791	+	0.139791i
$615$	4.01203	+	39.6037i	0.161780	+	1.59698i
$616$	8.31937	+	8.31937i	0.335197	+	0.335197i
$617$	−4.81845	−	4.81845i	−0.193983	−	0.193983i	0.603432	−	0.797415i	$-0.293800\pi$
$617$	−4.81845	−	4.81845i	−0.193983	−	0.193983i	−0.797415	+	0.603432i	$0.793800\pi$
$618$	−13.7869	−	13.7869i	−0.554591	−	0.554591i
$619$	−10.4774			−0.421121			−0.210560	−	0.977581i	$-0.567529\pi$
$619$	−10.4774			−0.421121			−0.210560	+	0.977581i	$0.567529\pi$
$620$	−0.472251	−	4.66171i	−0.0189661	−	0.187219i
$621$	−2.27519	−	2.27519i	−0.0913003	−	0.0913003i
$622$	10.6674	+	10.6674i	0.427725	+	0.427725i
$623$			24.0660i			0.964183i
$624$	1.25702	−	1.25702i	0.0503211	−	0.0503211i
$625$	−22.9890	+	9.82379i	−0.919559	+	0.392952i
$626$	−23.2451			−0.929063
$627$			50.3783i			2.01191i
$628$	−3.24426	+	3.24426i	−0.129460	+	0.129460i
$629$	1.38408	−	40.2339i	0.0551869	−	1.60423i
$630$	−2.51505	−	24.8267i	−0.100202	−	0.989118i
$631$	−20.7491	−	20.7491i	−0.826008	−	0.826008i	0.160954	−	0.986962i	$-0.448543\pi$
$631$	−20.7491	−	20.7491i	−0.826008	−	0.826008i	−0.986962	+	0.160954i	$0.948543\pi$
$632$	−5.69610	−	5.69610i	−0.226578	−	0.226578i
$633$	20.8730	−	20.8730i	0.829626	−	0.829626i
$634$	7.42086	+	7.42086i	0.294720	+	0.294720i
$635$	4.69384	−	0.475506i	0.186269	−	0.0188699i
$636$	−6.61022			−0.262112
$637$			6.64044i			0.263104i
$638$	−7.34992	−	7.34992i	−0.290986	−	0.290986i
$639$			7.04009i			0.278502i
$640$	1.73245	+	1.41373i	0.0684810	+	0.0558825i
$641$	−31.3975			−1.24013			−0.620064	−	0.784552i	$-0.712893\pi$
$641$	−31.3975			−1.24013			−0.620064	+	0.784552i	$0.712893\pi$
$642$		−	40.1301i		−	1.58381i
$643$			39.2482i			1.54780i	0.633309	+	0.773899i	$0.281696\pi$
$643$			39.2482i			1.54780i	−0.633309	+	0.773899i	$0.718304\pi$
$644$	18.0777	−	18.0777i	0.712362	−	0.712362i
$645$	−37.3940	+	3.78817i	−1.47239	+	0.149159i
$646$	33.2973	−	33.2973i	1.31007	−	1.31007i
$647$	33.5881			1.32048			0.660242	−	0.751053i	$-0.270454\pi$
$647$	33.5881			1.32048			0.660242	+	0.751053i	$0.270454\pi$
$648$	9.58365			0.376481
$649$	24.5405	−	24.5405i	0.963300	−	0.963300i
$650$	−0.740762	−	3.61861i	−0.0290551	−	0.141933i
$651$	14.2576	−	14.2576i	0.558798	−	0.558798i
$652$		−	23.5099i		−	0.920718i
$653$			32.2571i			1.26232i	0.775653	+	0.631159i	$0.217421\pi$
$653$			32.2571i			1.26232i	−0.775653	+	0.631159i	$0.782579\pi$
$654$	−33.4020			−1.30612
$655$	−3.79714	−	37.4825i	−0.148366	−	1.46456i
$656$		−	7.39769i		−	0.288831i
$657$	−20.0629	−	20.0629i	−0.782728	−	0.782728i
$658$		−	42.7861i		−	1.66797i
$659$	28.7104			1.11840			0.559199	−	0.829033i	$-0.311109\pi$
$659$	28.7104			1.11840			0.559199	+	0.829033i	$0.311109\pi$
$660$	−1.59574	−	15.7520i	−0.0621141	−	0.613145i
$661$	5.46781	+	5.46781i	0.212673	+	0.212673i	0.805402	−	0.592729i	$-0.201949\pi$
$661$	5.46781	+	5.46781i	0.212673	+	0.212673i	−0.592729	+	0.805402i	$0.701949\pi$
$662$	13.2492	−	13.2492i	0.514945	−	0.514945i
$663$	8.31937	+	8.31937i	0.323098	+	0.323098i
$664$	−2.72617	−	2.72617i	−0.105796	−	0.105796i
$665$	−49.2887	−	40.2210i	−1.91133	−	1.55970i
$666$	−0.583651	+	16.9662i	−0.0226160	+	0.657426i
$667$	−15.9711	+	15.9711i	−0.618405	+	0.618405i
$668$		−	11.4543i		−	0.443179i
$669$	29.6252			1.14538
$670$	0.669325	+	6.60708i	0.0258583	+	0.255254i
$671$	6.82250	−	6.82250i	0.263380	−	0.263380i
$672$			9.62238i			0.371191i
$673$	15.3921	+	15.3921i	0.593323	+	0.593323i	0.938528	−	0.345204i	$-0.112190\pi$
$673$	15.3921	+	15.3921i	0.593323	+	0.593323i	−0.345204	+	0.938528i	$0.612190\pi$
$674$	3.84828	+	3.84828i	0.148230	+	0.148230i
$675$	1.38628	−	2.09995i	0.0533580	−	0.0808269i
$676$	−12.4543			−0.479011
$677$	8.46595	+	8.46595i	0.325373	+	0.325373i	0.850824	−	0.525451i	$-0.176103\pi$
$677$	8.46595	+	8.46595i	0.325373	+	0.325373i	−0.525451	+	0.850824i	$0.676103\pi$
$678$	9.95872	+	9.95872i	0.382462	+	0.382462i
$679$	−9.62238	−	9.62238i	−0.369273	−	0.369273i
$680$	−9.35651	+	11.4659i	−0.358806	+	0.439697i
$681$	−38.0793	−	38.0793i	−1.45920	−	1.45920i
$682$	4.35971	−	4.35971i	0.166942	−	0.166942i
$683$	−42.2105			−1.61514			−0.807570	−	0.589772i	$-0.799218\pi$
$683$	−42.2105			−1.61514			−0.807570	+	0.589772i	$0.799218\pi$
$684$	−14.0411	+	14.0411i	−0.536875	+	0.536875i
$685$	16.0234	−	1.62324i	0.612222	−	0.0620207i
$686$	−5.62379	−	5.62379i	−0.214717	−	0.214717i
$687$	−11.8658	−	11.8658i	−0.452708	−	0.452708i
$688$	6.98494			0.266298
$689$	−1.43488	−	1.43488i	−0.0546644	−	0.0546644i
$690$	−34.2285	+	3.46749i	−1.30306	+	0.132005i
$691$		−	7.77112i		−	0.295627i	−0.989015	−	0.147814i	$-0.952776\pi$
$691$		−	7.77112i		−	0.295627i	0.989015	−	0.147814i	$-0.0472236\pi$
$692$	2.14087	−	2.14087i	0.0813835	−	0.0813835i
$693$	23.2183	−	23.2183i	0.881991	−	0.881991i
$694$	20.7126			0.786240
$695$	2.14713	+	1.75212i	0.0814452	+	0.0664616i
$696$		−	8.50109i		−	0.322233i
$697$	48.9603			1.85451
$698$		−	29.0891i		−	1.10104i
$699$			51.6914i			1.95515i
$700$	16.6853	+	11.0148i	0.630644	+	0.416321i
$701$	−36.6175	+	36.6175i	−1.38302	+	1.38302i	−0.543828	+	0.839197i	$0.683026\pi$
$701$	−36.6175	+	36.6175i	−1.38302	+	1.38302i	−0.839197	+	0.543828i	$0.816974\pi$
$702$	0.262879	+	0.262879i	0.00992172	+	0.00992172i
$703$	29.5326	+	31.6369i	1.11384	+	1.19321i
$704$			2.94236i			0.110894i
$705$	−36.4024	+	44.6092i	−1.37099	+	1.68008i
$706$			22.8767i			0.860975i
$707$	−11.9296	−	11.9296i	−0.448657	−	0.448657i
$708$	28.3841			1.06674
$709$	33.4953	+	33.4953i	1.25794	+	1.25794i	0.952074	+	0.305869i	$0.0989469\pi$
$709$	33.4953	+	33.4953i	1.25794	+	1.25794i	0.305869	+	0.952074i	$0.401053\pi$
$710$	−4.37017	−	3.56618i	−0.164010	−	0.133836i
$711$	−15.8971	+	15.8971i	−0.596187	+	0.596187i
$712$	−4.25577	+	4.25577i	−0.159492	+	0.159492i
$713$	−9.47351	−	9.47351i	−0.354786	−	0.354786i
$714$	−63.6841			−2.38332
$715$	3.07288	−	3.76566i	0.114919	−	0.140828i
$716$	14.9428	−	14.9428i	0.558439	−	0.558439i
$717$	−4.62259			−0.172634
$718$		−	25.7577i		−	0.961269i
$719$		−	7.36568i		−	0.274693i	−0.990523	−	0.137347i	$-0.956143\pi$
$719$		−	7.36568i		−	0.274693i	0.990523	−	0.137347i	$-0.0438574\pi$
$720$	3.94553	−	4.83504i	0.147041	−	0.180191i
$721$	22.9090	+	22.9090i	0.853175	+	0.853175i
$722$			31.6235i			1.17691i
$723$		−	32.5231i		−	1.20955i
$724$	12.0625			0.448301
$725$	−14.7410	−	9.73127i	−0.547465	−	0.361410i
$726$	−3.98607	+	3.98607i	−0.147937	+	0.147937i
$727$	−49.6628			−1.84189			−0.920945	−	0.389692i	$-0.872581\pi$
$727$	−49.6628			−1.84189			−0.920945	+	0.389692i	$0.872581\pi$
$728$	−2.08872	+	2.08872i	−0.0774133	+	0.0774133i
$729$		−	23.1136i		−	0.856060i
$730$	22.6171	−	2.29121i	0.837096	−	0.0848014i
$731$			46.2286i			1.70983i
$732$	7.89106			0.291662
$733$	−1.72578	+	1.72578i	−0.0637431	+	0.0637431i	−0.738260	−	0.674517i	$-0.764352\pi$
$733$	−1.72578	+	1.72578i	−0.0637431	+	0.0637431i	0.674517	+	0.738260i	$0.264352\pi$
$734$	−17.7447	+	17.7447i	−0.654968	+	0.654968i
$735$	4.87504	+	48.1228i	0.179819	+	1.77504i
$736$	6.39364			0.235673
$737$	−6.17905	+	6.17905i	−0.227608	+	0.227608i
$738$	−20.6460			−0.759990
$739$	−34.0153			−1.25127			−0.625636	−	0.780115i	$-0.715160\pi$
$739$	−34.0153			−1.25127			−0.625636	+	0.780115i	$0.715160\pi$
$740$	−10.2362	−	8.95659i	−0.376290	−	0.329251i
$741$	−12.6483			−0.464649
$742$	10.9838			0.403229
$743$	11.8640	−	11.8640i	0.435249	−	0.435249i	−0.455160	−	0.890410i	$-0.650418\pi$
$743$	11.8640	−	11.8640i	0.435249	−	0.435249i	0.890410	+	0.455160i	$0.150418\pi$
$744$	5.04255			0.184869
$745$	0.413852	−	0.507154i	0.0151624	−	0.0185807i
$746$	22.7050	−	22.7050i	0.831290	−	0.831290i
$747$	−7.60838	+	7.60838i	−0.278376	+	0.278376i
$748$	−19.4735			−0.712020
$749$			66.6820i			2.43651i
$750$	−8.02484	−	25.6800i	−0.293026	−	0.937700i
$751$		−	18.1038i		−	0.660617i	−0.943873	−	0.330308i	$-0.892847\pi$
$751$		−	18.1038i		−	0.660617i	0.943873	−	0.330308i	$-0.107153\pi$
$752$	7.56618	−	7.56618i	0.275910	−	0.275910i
$753$	−39.1026			−1.42498
$754$	1.84533	−	1.84533i	0.0672028	−	0.0672028i
$755$	−22.8245	+	27.9702i	−0.830669	+	1.01794i
$756$	−2.01231			−0.0731871
$757$			25.2565i			0.917964i	0.888445	+	0.458982i	$0.151786\pi$
$757$			25.2565i			0.917964i	−0.888445	+	0.458982i	$0.848214\pi$
$758$			27.5341i			1.00008i
$759$	−32.0111	−	32.0111i	−1.16193	−	1.16193i
$760$	−1.60351	−	15.8287i	−0.0581654	−	0.574166i
$761$		−	45.4777i		−	1.64856i	−0.566179	−	0.824282i	$-0.691579\pi$
$761$		−	45.4777i		−	1.64856i	0.566179	−	0.824282i	$-0.308421\pi$
$762$			5.07730i			0.183931i
$763$	55.5023			2.00932
$764$	−10.7383	+	10.7383i	−0.388499	+	0.388499i
$765$	31.9999	+	26.1128i	1.15696	+	0.944111i
$766$	4.93269			0.178225
$767$	6.16133	+	6.16133i	0.222473	+	0.222473i
$768$	−1.70160	+	1.70160i	−0.0614011	+	0.0614011i
$769$	5.30402	−	5.30402i	0.191268	−	0.191268i	−0.604976	−	0.796244i	$-0.706817\pi$
$769$	5.30402	−	5.30402i	0.191268	−	0.191268i	0.796244	+	0.604976i	$0.206817\pi$
$770$	2.65156	+	26.1742i	0.0955555	+	0.943253i
$771$	−54.0533	−	54.0533i	−1.94668	−	1.94668i
$772$	−9.09024			−0.327165
$773$	−21.8164	−	21.8164i	−0.784681	−	0.784681i	0.195935	−	0.980617i	$-0.437226\pi$
$773$	−21.8164	−	21.8164i	−0.784681	−	0.784681i	−0.980617	+	0.195935i	$0.937226\pi$
$774$		−	19.4941i		−	0.700700i
$775$	5.77224	−	8.74381i	0.207345	−	0.314087i
$776$		−	3.40320i		−	0.122168i
$777$	2.01231	−	58.4961i	0.0721913	−	2.09853i
$778$	−4.25176	−	4.25176i	−0.152433	−	0.152433i
$779$	−37.2184	+	37.2184i	−1.33349	+	1.33349i
$780$	3.95481	−	0.400639i	0.141605	−	0.0143452i
$781$		−	7.42221i		−	0.265588i
$782$			42.3152i			1.51319i
$783$	1.77782			0.0635341
$784$		−	8.98899i		−	0.321036i
$785$	−10.2070	+	1.03401i	−0.364304	+	0.0369055i
$786$	40.5446			1.44618
$787$	−29.6710	+	29.6710i	−1.05766	+	1.05766i	−0.0594240	+	0.998233i	$0.518926\pi$
$787$	−29.6710	+	29.6710i	−1.05766	+	1.05766i	−0.998233	+	0.0594240i	$0.981074\pi$
$788$	−7.91262	+	7.91262i	−0.281875	+	0.281875i
$789$		−	64.2237i		−	2.28643i
$790$	−1.81546	−	17.9209i	−0.0645913	−	0.637597i
$791$	−16.5479	−	16.5479i	−0.588375	−	0.588375i
$792$	8.21174			0.291791
$793$	1.71291	+	1.71291i	0.0608271	+	0.0608271i
$794$	−6.85748	−	6.85748i	−0.243363	−	0.243363i
$795$	−11.4519	−	9.34504i	−0.406155	−	0.331434i
$796$	−9.14683	+	9.14683i	−0.324201	+	0.324201i
$797$	−12.5492			−0.444515			−0.222257	−	0.974988i	$-0.571343\pi$
$797$	−12.5492			−0.444515			−0.222257	+	0.974988i	$0.571343\pi$
$798$	48.4110	−	48.4110i	1.71373	−	1.71373i
$799$	50.0755	+	50.0755i	1.77154	+	1.77154i
$800$	1.00275	+	4.89842i	0.0354526	+	0.173185i
$801$	11.8773	+	11.8773i	0.419664	+	0.419664i
$802$	4.52089	+	4.52089i	0.159638	+	0.159638i
$803$	21.1519	+	21.1519i	0.746434	+	0.746434i
$804$	−7.14683			−0.252049
$805$	56.8757	−	5.76175i	2.00460	−	0.203075i
$806$	1.09458	+	1.09458i	0.0385550	+	0.0385550i
$807$	9.99535	+	9.99535i	0.351853	+	0.351853i
$808$		−	4.21918i		−	0.148430i
$809$	−19.1078	+	19.1078i	−0.671796	+	0.671796i	−0.958130	−	0.286334i	$-0.907563\pi$
$809$	−19.1078	+	19.1078i	−0.671796	+	0.671796i	0.286334	+	0.958130i	$0.407563\pi$
$810$	16.6032	+	13.5487i	0.583376	+	0.476052i
$811$	9.22121			0.323801			0.161900	−	0.986807i	$-0.448238\pi$
$811$	9.22121			0.323801			0.161900	+	0.986807i	$0.448238\pi$
$812$			14.1258i			0.495719i
$813$	−4.56298	+	4.56298i	−0.160031	+	0.160031i
$814$	0.615330	−	17.8871i	0.0215673	−	0.626941i
$815$	33.2366	−	40.7297i	1.16423	−	1.42670i
$816$	−11.2617	−	11.2617i	−0.394239	−	0.394239i
$817$	−35.1418	−	35.1418i	−1.22946	−	1.22946i
$818$	12.6409	−	12.6409i	0.441979	−	0.441979i
$819$	5.82936	+	5.82936i	0.203694	+	0.203694i
$820$	10.4583	−	12.8161i	0.365220	−	0.447558i
$821$	1.92924			0.0673310			0.0336655	−	0.999433i	$-0.489282\pi$
$821$	1.92924			0.0673310			0.0336655	+	0.999433i	$0.489282\pi$
$822$			17.3324i			0.604536i
$823$	−14.9775	−	14.9775i	−0.522084	−	0.522084i	0.396116	−	0.918200i	$-0.370358\pi$
$823$	−14.9775	−	14.9775i	−0.522084	−	0.522084i	−0.918200	+	0.396116i	$0.870358\pi$
$824$			8.10234i			0.282258i
$825$	19.5045	−	29.5454i	0.679058	−	1.02864i
$826$	−47.1644			−1.64106
$827$		−	46.1448i		−	1.60461i	−0.596913	−	0.802306i	$-0.703606\pi$
$827$		−	46.1448i		−	1.60461i	0.596913	−	0.802306i	$-0.296394\pi$
$828$		−	17.8438i		−	0.620116i
$829$	−10.2967	+	10.2967i	−0.357619	+	0.357619i	−0.862935	−	0.505315i	$-0.831376\pi$
$829$	−10.2967	+	10.2967i	−0.357619	+	0.357619i	0.505315	+	0.862935i	$0.331376\pi$
$830$	−0.868886	−	8.57700i	−0.0301595	−	0.297712i
$831$	15.1597	−	15.1597i	0.525885	−	0.525885i
$832$	−0.738730			−0.0256108
$833$	59.4921			2.06128
$834$	−2.10889	+	2.10889i	−0.0730250	+	0.0730250i
$835$	16.1932	−	19.8439i	0.560390	−	0.686728i
$836$	14.8032	−	14.8032i	0.511980	−	0.511980i
$837$			1.05454i			0.0364502i
$838$			18.0818i			0.624625i
$839$	32.5351			1.12324			0.561619	−	0.827396i	$-0.310179\pi$
$839$	32.5351			1.12324			0.561619	+	0.827396i	$0.310179\pi$
$840$	−13.6034	+	16.6703i	−0.469363	+	0.575179i
$841$			16.5203i			0.569664i
$842$	−2.11385	−	2.11385i	−0.0728482	−	0.0728482i
$843$		−	10.3358i		−	0.355983i
$844$	−12.2667			−0.422237
$845$	−21.5764	−	17.6070i	−0.742250	−	0.605698i
$846$	−21.1162	−	21.1162i	−0.725992	−	0.725992i
$847$	6.62344	−	6.62344i	0.227584	−	0.227584i
$848$	1.94236	+	1.94236i	0.0667008	+	0.0667008i
$849$	9.12492	+	9.12492i	0.313166	+	0.313166i
$850$	−32.4193	+	6.63654i	−1.11197	+	0.227631i
$851$	−38.8680	−	1.33709i	−1.33238	−	0.0458349i
$852$	4.29235	−	4.29235i	0.147053	−	0.147053i
$853$		−	42.8714i		−	1.46789i	−0.679209	−	0.733945i	$-0.737677\pi$
$853$		−	42.8714i		−	1.46789i	0.679209	−	0.733945i	$-0.262323\pi$
$854$	−13.1122			−0.448689
$855$	−44.1757	+	4.47519i	−1.51078	+	0.153048i
$856$	−11.7919	+	11.7919i	−0.403038	+	0.403038i
$857$			3.29400i			0.112521i	0.998416	+	0.0562604i	$0.0179177\pi$
$857$			3.29400i			0.112521i	−0.998416	+	0.0562604i	$0.982082\pi$
$858$	3.69860	+	3.69860i	0.126268	+	0.126268i
$859$	−18.0550	−	18.0550i	−0.616030	−	0.616030i	0.328481	−	0.944511i	$-0.393463\pi$
$859$	−18.0550	−	18.0550i	−0.616030	−	0.616030i	−0.944511	+	0.328481i	$0.893463\pi$
$860$	12.1010	+	9.87480i	0.412642	+	0.336728i
$861$	71.1834			2.42592
$862$	−2.69254	−	2.69254i	−0.0917083	−	0.0917083i
$863$	−18.6224	−	18.6224i	−0.633913	−	0.633913i	0.315134	−	0.949047i	$-0.397950\pi$
$863$	−18.6224	−	18.6224i	−0.633913	−	0.633913i	−0.949047	+	0.315134i	$0.897950\pi$
$864$	−0.355853	−	0.355853i	−0.0121063	−	0.0121063i
$865$	6.73554	−	0.682339i	0.229015	−	0.0232002i
$866$	−13.9527	−	13.9527i	−0.474132	−	0.474132i
$867$	45.6066	−	45.6066i	1.54888	−	1.54888i
$868$	−8.37893			−0.284399
$869$	16.7599	−	16.7599i	0.568542	−	0.568542i
$870$	12.0182	−	14.7277i	0.407456	−	0.499316i
$871$	−1.55136	−	1.55136i	−0.0525658	−	0.0525658i
$872$	9.81489	+	9.81489i	0.332374	+	0.332374i
$873$	−9.49788			−0.321455
$874$	−32.1669	−	32.1669i	−1.08806	−	1.08806i
$875$	13.3344	+	42.6710i	0.450786	+	1.44254i
$876$			24.4648i			0.826587i
$877$	25.3664	−	25.3664i	0.856561	−	0.856561i	−0.134370	−	0.990931i	$-0.542901\pi$
$877$	25.3664	−	25.3664i	0.856561	−	0.856561i	0.990931	+	0.134370i	$0.0429011\pi$
$878$	−22.9884	+	22.9884i	−0.775821	+	0.775821i
$879$	−45.1780			−1.52382
$880$	−4.15969	+	5.09748i	−0.140223	+	0.171836i
$881$			28.4586i			0.958796i	0.877598	+	0.479398i	$0.159145\pi$
$881$			28.4586i			0.958796i	−0.877598	+	0.479398i	$0.840855\pi$
$882$	−25.0871			−0.844728
$883$		−	17.5471i		−	0.590508i	−0.955419	−	0.295254i	$-0.904596\pi$
$883$		−	17.5471i		−	0.590508i	0.955419	−	0.295254i	$-0.0954042\pi$
$884$		−	4.88915i		−	0.164440i
$885$	49.1740	+	40.1274i	1.65297	+	1.34887i
$886$	−7.06197	+	7.06197i	−0.237251	+	0.237251i
$887$	25.1122	+	25.1122i	0.843184	+	0.843184i	0.989272	−	0.146088i	$-0.0466683\pi$
$887$	25.1122	+	25.1122i	0.843184	+	0.843184i	−0.146088	+	0.989272i	$0.546668\pi$
$888$	10.7002	−	9.98845i	0.359074	−	0.335190i
$889$		−	8.43667i		−	0.282957i
$890$	−13.3894	+	1.35640i	−0.448813	+	0.0454667i
$891$			28.1985i			0.944685i
$892$	−8.70510	−	8.70510i	−0.291468	−	0.291468i
$893$	−76.1321			−2.54767
$894$	0.498123	+	0.498123i	0.0166597	+	0.0166597i
$895$	47.0127	−	4.76259i	1.57146	−	0.159196i
$896$	2.82745	−	2.82745i	0.0944586	−	0.0944586i
$897$	8.03694	−	8.03694i	0.268346	−	0.268346i
$898$	2.65135	+	2.65135i	0.0884768	+	0.0884768i
$899$	7.40254			0.246888
$900$	13.6709	−	2.79855i	0.455695	−	0.0932850i
$901$	−12.8551	+	12.8551i	−0.428267	+	0.428267i
$902$	21.7666			0.724750
$903$			67.2117i			2.23667i
$904$		−	5.85257i		−	0.194654i
$905$	20.8977	+	17.0532i	0.694664	+	0.566866i
$906$	−27.4722	−	27.4722i	−0.912702	−	0.912702i
$907$		−	57.0816i		−	1.89536i	−0.319215	−	0.947682i	$-0.603419\pi$
$907$		−	57.0816i		−	1.89536i	0.319215	−	0.947682i	$-0.396581\pi$
$908$			22.3785i			0.742658i
$909$	−11.7752			−0.390559
$910$	−6.57149	+	0.665720i	−0.217843	+	0.0220684i
$911$	−22.4319	+	22.4319i	−0.743203	+	0.743203i	−0.973193	−	0.229990i	$-0.926131\pi$
$911$	−22.4319	+	22.4319i	−0.743203	+	0.743203i	0.229990	+	0.973193i	$0.426131\pi$
$912$	17.1218			0.566958
$913$	8.02135	−	8.02135i	0.265468	−	0.265468i
$914$			6.35811i			0.210308i
$915$	13.6709	+	11.1558i	0.451944	+	0.368800i
$916$			6.97332i			0.230405i
$917$	−67.3708			−2.22478
$918$	2.35515	−	2.35515i	0.0777315	−	0.0777315i
$919$	33.5651	−	33.5651i	1.10721	−	1.10721i	0.113694	−	0.993516i	$-0.463732\pi$
$919$	33.5651	−	33.5651i	1.10721	−	1.10721i	0.993516	−	0.113694i	$-0.0362684\pi$
$920$	11.0766	+	9.03886i	0.365186	+	0.298002i
$921$	−11.7883			−0.388437
$922$	13.5522	−	13.5522i	0.446317	−	0.446317i
$923$	1.86348			0.0613370
$924$	−28.3125			−0.931412
$925$	−5.07149	−	29.9880i	−0.166750	−	0.985999i
$926$	6.65144			0.218580
$927$	22.6126			0.742695
$928$	−2.49797	+	2.49797i	−0.0820000	+	0.0820000i
$929$	−58.2060			−1.90968			−0.954838	−	0.297127i	$-0.903972\pi$
$929$	−58.2060			−1.90968			−0.954838	+	0.297127i	$0.903972\pi$
$930$	8.73595	+	7.12878i	0.286463	+	0.233762i
$931$	−45.2243	+	45.2243i	−1.48217	+	1.48217i
$932$	15.1891	−	15.1891i	0.497535	−	0.497535i
$933$	−36.3033			−1.18852
$934$			18.5636i			0.607418i
$935$	−33.7368	−	27.5302i	−1.10331	−	0.900333i
$936$			2.06170i			0.0673888i
$937$	23.5283	−	23.5283i	0.768637	−	0.768637i	−0.209229	−	0.977867i	$-0.567095\pi$
$937$	23.5283	−	23.5283i	0.768637	−	0.768637i	0.977867	+	0.209229i	$0.0670955\pi$
$938$	11.8755			0.387749
$939$	39.5539	−	39.5539i	1.29079	−	1.29079i
$940$	23.8045	−	2.41150i	0.776418	−	0.0786545i
$941$	23.9226			0.779853			0.389926	−	0.920846i	$-0.372500\pi$
$941$	23.9226			0.779853			0.389926	+	0.920846i	$0.372500\pi$
$942$		−	11.0409i		−	0.359731i
$943$		−	47.2982i		−	1.54024i
$944$	−8.34044	−	8.34044i	−0.271458	−	0.271458i
$945$	−3.48623	−	2.84486i	−0.113407	−	0.0925434i
$946$			20.5522i			0.668209i
$947$			44.9073i			1.45929i	0.683826	+	0.729645i	$0.260315\pi$
$947$			44.9073i			1.45929i	−0.683826	+	0.729645i	$0.739685\pi$
$948$	19.3849			0.629593
$949$	−5.31055	+	5.31055i	−0.172388	+	0.172388i
$950$	19.5994	−	29.6892i	0.635889	−	0.963246i
$951$	−25.2547			−0.818938
$952$	18.7130	+	18.7130i	0.606492	+	0.606492i
$953$	−6.57978	+	6.57978i	−0.213140	+	0.213140i	−0.805600	−	0.592460i	$-0.798157\pi$
$953$	−6.57978	+	6.57978i	−0.213140	+	0.213140i	0.592460	+	0.805600i	$0.298157\pi$
$954$	5.42086	−	5.42086i	0.175507	−	0.175507i
$955$	−33.7846	+	3.42253i	−1.09325	+	0.110750i
$956$	1.35831	+	1.35831i	0.0439309	+	0.0439309i
$957$	25.0132			0.808563
$958$	−3.71611	−	3.71611i	−0.120062	−	0.120062i
$959$		−	28.8003i		−	0.930010i
$960$	−5.35353	+	0.542335i	−0.172784	+	0.0175038i
$961$		−	26.6091i		−	0.858357i
$962$	4.49086	+	0.154489i	0.144791	+	0.00498094i
$963$	32.9096	+	32.9096i	1.06050	+	1.06050i
$964$	−9.55663	+	9.55663i	−0.307798	+	0.307798i
$965$	−15.7484	−	12.8511i	−0.506958	−	0.413692i
$966$			61.5220i			1.97944i
$967$			37.1279i			1.19395i	0.802259	+	0.596977i	$0.203631\pi$
$967$			37.1279i			1.19395i	−0.802259	+	0.596977i	$0.796369\pi$
$968$	2.34255			0.0752923
$969$			113.317i			3.64028i
$970$	4.81119	−	5.89586i	0.154478	−	0.189305i
$971$	−12.7942			−0.410586			−0.205293	−	0.978701i	$-0.565815\pi$
$971$	−12.7942			−0.410586			−0.205293	+	0.978701i	$0.565815\pi$
$972$	−15.2400	+	15.2400i	−0.488822	+	0.488822i
$973$	3.50423	−	3.50423i	0.112341	−	0.112341i
$974$		−	0.818395i		−	0.0262231i
$975$	7.41789	+	4.89693i	0.237563	+	0.156827i
$976$	−2.31872	−	2.31872i	−0.0742204	−	0.0742204i
$977$	−27.6004			−0.883015			−0.441507	−	0.897258i	$-0.645556\pi$
$977$	−27.6004			−0.883015			−0.441507	+	0.897258i	$0.645556\pi$
$978$	40.0044	+	40.0044i	1.27920	+	1.27920i
$979$	−12.5220	−	12.5220i	−0.400204	−	0.400204i
$980$	12.7080	−	15.5730i	0.405942	−	0.497460i
$981$	27.3921	−	27.3921i	0.874562	−	0.874562i
$982$	5.21815			0.166518
$983$	−3.23105	+	3.23105i	−0.103054	+	0.103054i	−0.756754	−	0.653700i	$-0.773216\pi$
$983$	−3.23105	+	3.23105i	−0.103054	+	0.103054i	0.653700	+	0.756754i	$0.273216\pi$
$984$	12.5879	+	12.5879i	0.401288	+	0.401288i
$985$	−24.8945	+	2.52192i	−0.793205	+	0.0803550i
$986$	−16.5324	−	16.5324i	−0.526499	−	0.526499i
$987$	72.8047	+	72.8047i	2.31740	+	2.31740i
$988$	3.71661	+	3.71661i	0.118241	+	0.118241i
$989$	44.6592			1.42008
$990$	14.2264	+	11.6092i	0.452145	+	0.368963i
$991$	−19.0174	−	19.0174i	−0.604108	−	0.604108i	0.337292	−	0.941400i	$-0.390489\pi$
$991$	−19.0174	−	19.0174i	−0.604108	−	0.604108i	−0.941400	+	0.337292i	$0.890489\pi$
$992$	−1.48171	−	1.48171i	−0.0470443	−	0.0470443i
$993$			45.0897i			1.43088i
$994$	−7.13237	+	7.13237i	−0.226225	+	0.226225i
$995$	−28.7775	+	2.91528i	−0.912309	+	0.0924207i
$996$	9.27768			0.293974
$997$			28.6699i			0.907984i	0.891006	+	0.453992i	$0.150001\pi$
$997$			28.6699i			0.907984i	−0.891006	+	0.453992i	$0.849999\pi$
$998$	−17.1758	+	17.1758i	−0.543690	+	0.543690i
$999$	2.08887	+	2.23771i	0.0660889	+	0.0707979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.d.253.1	yes	10
5.2	odd	4		370.2.g.d.327.5	yes	10
37.6	odd	4		370.2.g.d.43.5	✓	10
185.117	even	4	inner	370.2.h.d.117.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.5	✓	10	37.6	odd	4
370.2.g.d.327.5	yes	10	5.2	odd	4
370.2.h.d.117.1	yes	10	185.117	even	4	inner
370.2.h.d.253.1	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.70160 + 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 + 1.41373i) q^{5} +(-1.70160 + 1.70160i) q^{6} +(2.82745 - 2.82745i) q^{7} +1.00000 q^{8} -2.79087i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.70160 + 1.70160i) q^{3} +1.00000 q^{4} +(1.73245 + 1.41373i) q^{5} +(-1.70160 + 1.70160i) q^{6} +(2.82745 - 2.82745i) q^{7} +1.00000 q^{8} -2.79087i q^{9} +(1.73245 + 1.41373i) q^{10} +2.94236i q^{11} +(-1.70160 + 1.70160i) q^{12} -0.738730 q^{13} +(2.82745 - 2.82745i) q^{14} +(-5.35353 + 0.542335i) q^{15} +1.00000 q^{16} +6.61833i q^{17} -2.79087i q^{18} +(-5.03108 - 5.03108i) q^{19} +(1.73245 + 1.41373i) q^{20} +9.62238i q^{21} +2.94236i q^{22} +6.39364 q^{23} +(-1.70160 + 1.70160i) q^{24} +(1.00275 + 4.89842i) q^{25} -0.738730 q^{26} +(-0.355853 - 0.355853i) q^{27} +(2.82745 - 2.82745i) q^{28} +(-2.49797 + 2.49797i) q^{29} +(-5.35353 + 0.542335i) q^{30} +(-1.48171 - 1.48171i) q^{31} +1.00000 q^{32} +(-5.00671 - 5.00671i) q^{33} +6.61833i q^{34} +(8.89567 - 0.901168i) q^{35} -2.79087i q^{36} +(-6.07917 - 0.209128i) q^{37} +(-5.03108 - 5.03108i) q^{38} +(1.25702 - 1.25702i) q^{39} +(1.73245 + 1.41373i) q^{40} -7.39769i q^{41} +9.62238i q^{42} +6.98494 q^{43} +2.94236i q^{44} +(3.94553 - 4.83504i) q^{45} +6.39364 q^{46} +(7.56618 - 7.56618i) q^{47} +(-1.70160 + 1.70160i) q^{48} -8.98899i q^{49} +(1.00275 + 4.89842i) q^{50} +(-11.2617 - 11.2617i) q^{51} -0.738730 q^{52} +(1.94236 + 1.94236i) q^{53} +(-0.355853 - 0.355853i) q^{54} +(-4.15969 + 5.09748i) q^{55} +(2.82745 - 2.82745i) q^{56} +17.1218 q^{57} +(-2.49797 + 2.49797i) q^{58} +(-8.34044 - 8.34044i) q^{59} +(-5.35353 + 0.542335i) q^{60} +(-2.31872 - 2.31872i) q^{61} +(-1.48171 - 1.48171i) q^{62} +(-7.89106 - 7.89106i) q^{63} +1.00000 q^{64} +(-1.27981 - 1.04436i) q^{65} +(-5.00671 - 5.00671i) q^{66} +(2.10003 + 2.10003i) q^{67} +6.61833i q^{68} +(-10.8794 + 10.8794i) q^{69} +(8.89567 - 0.901168i) q^{70} -2.52254 q^{71} -2.79087i q^{72} +(7.18876 - 7.18876i) q^{73} +(-6.07917 - 0.209128i) q^{74} +(-10.0414 - 6.62886i) q^{75} +(-5.03108 - 5.03108i) q^{76} +(8.31937 + 8.31937i) q^{77} +(1.25702 - 1.25702i) q^{78} +(-5.69610 - 5.69610i) q^{79} +(1.73245 + 1.41373i) q^{80} +9.58365 q^{81} -7.39769i q^{82} +(-2.72617 - 2.72617i) q^{83} +9.62238i q^{84} +(-9.35651 + 11.4659i) q^{85} +6.98494 q^{86} -8.50109i q^{87} +2.94236i q^{88} +(-4.25577 + 4.25577i) q^{89} +(3.94553 - 4.83504i) q^{90} +(-2.08872 + 2.08872i) q^{91} +6.39364 q^{92} +5.04255 q^{93} +(7.56618 - 7.56618i) q^{94} +(-1.60351 - 15.8287i) q^{95} +(-1.70160 + 1.70160i) q^{96} -3.40320i q^{97} -8.98899i q^{98} +8.21174 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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