LMFDB - Embedded newform 370.2.m.a.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, 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:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.a.159.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.686141 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 1.65831i) q^{5} +0.792287i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-1.18614 + 2.05446i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.686141 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 1.65831i) q^{5} +0.792287i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-1.18614 + 2.05446i) q^{9} +(2.18614 - 0.469882i) q^{10} +(-0.686141 - 0.396143i) q^{12} +(-2.68614 - 4.65253i) q^{13} -3.46410i q^{14} +(-1.68614 - 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18614 + 3.78651i) q^{17} +(-1.18614 - 2.05446i) q^{18} +(-0.686141 + 2.12819i) q^{20} +(-1.37228 + 2.37686i) q^{21} -8.74456 q^{23} +(0.686141 - 0.396143i) q^{24} +(-0.500000 + 4.97494i) q^{25} +5.37228 q^{26} +4.25639i q^{27} +(3.00000 + 1.73205i) q^{28} -4.40387i q^{29} +(1.31386 - 1.18843i) q^{30} +1.08724i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.18614 - 3.78651i) q^{34} +(7.37228 + 2.37686i) q^{35} +2.37228 q^{36} +(0.500000 - 6.06218i) q^{37} +(-3.68614 - 2.12819i) q^{39} +(-1.50000 - 1.65831i) q^{40} +(-2.87228 - 4.97494i) q^{41} +(-1.37228 - 2.37686i) q^{42} +8.11684 q^{43} +(5.18614 - 1.11469i) q^{45} +(4.37228 - 7.57301i) q^{46} +1.58457i q^{47} +0.792287i q^{48} +(2.50000 - 4.33013i) q^{49} +(-4.05842 - 2.92048i) q^{50} +3.46410i q^{51} +(-2.68614 + 4.65253i) q^{52} +(3.68614 + 2.12819i) q^{53} +(-3.68614 - 2.12819i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(3.81386 + 2.20193i) q^{58} +(-4.62772 - 2.67181i) q^{59} +(0.372281 + 1.73205i) q^{60} +(-6.55842 + 3.78651i) q^{61} +(-0.941578 - 0.543620i) q^{62} -8.21782i q^{63} +1.00000 q^{64} +(-3.68614 + 11.4333i) q^{65} +(10.1168 - 5.84096i) q^{67} +4.37228 q^{68} +(-6.00000 + 3.46410i) q^{69} +(-5.74456 + 5.19615i) q^{70} +(4.37228 + 7.57301i) q^{71} +(-1.18614 + 2.05446i) q^{72} +6.92820i q^{73} +(5.00000 + 3.46410i) q^{74} +(1.62772 + 3.61158i) q^{75} +(3.68614 - 2.12819i) q^{78} +(10.1168 - 5.84096i) q^{79} +(2.18614 - 0.469882i) q^{80} +(-1.87228 - 3.24289i) q^{81} +5.74456 q^{82} +(-0.255437 - 0.147477i) q^{83} +2.74456 q^{84} +(9.55842 - 2.05446i) q^{85} +(-4.05842 + 7.02939i) q^{86} +(-1.74456 - 3.02167i) q^{87} +(-11.1861 - 6.45832i) q^{89} +(-1.62772 + 5.04868i) q^{90} +(16.1168 + 9.30506i) q^{91} +(4.37228 + 7.57301i) q^{92} +(0.430703 + 0.746000i) q^{93} +(-1.37228 - 0.792287i) q^{94} +(-0.686141 - 0.396143i) q^{96} +5.11684 q^{97} +(2.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9	$ 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9} + 3 q^{10} + 3 q^{12} - 5 q^{13} - q^{15} - 2 q^{16} - 3 q^{17} + q^{18} + 3 q^{20} + 6 q^{21} - 12 q^{23} - 3 q^{24} - 2 q^{25} + 10 q^{26} + 12 q^{28} + 11 q^{30} - 2 q^{32} - 3 q^{34} + 18 q^{35} - 2 q^{36} + 2 q^{37} - 9 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} + 15 q^{45} + 6 q^{46} + 10 q^{49} + q^{50} - 5 q^{52} + 9 q^{53} - 9 q^{54} - 12 q^{56} + 21 q^{58} - 30 q^{59} - 10 q^{60} - 9 q^{61} - 21 q^{62} + 4 q^{64} - 9 q^{65} + 6 q^{67} + 6 q^{68} - 24 q^{69} + 6 q^{71} + q^{72} + 20 q^{74} + 18 q^{75} + 9 q^{78} + 6 q^{79} + 3 q^{80} + 4 q^{81} - 24 q^{83} - 12 q^{84} + 21 q^{85} + q^{86} + 16 q^{87} - 39 q^{89} - 18 q^{90} + 30 q^{91} + 6 q^{92} - 27 q^{93} + 6 q^{94} + 3 q^{96} - 14 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9 + 3 * q^10 + 3 * q^12 - 5 * q^13 - q^15 - 2 * q^16 - 3 * q^17 + q^18 + 3 * q^20 + 6 * q^21 - 12 * q^23 - 3 * q^24 - 2 * q^25 + 10 * q^26 + 12 * q^28 + 11 * q^30 - 2 * q^32 - 3 * q^34 + 18 * q^35 - 2 * q^36 + 2 * q^37 - 9 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 + 15 * q^45 + 6 * q^46 + 10 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 9 * q^54 - 12 * q^56 + 21 * q^58 - 30 * q^59 - 10 * q^60 - 9 * q^61 - 21 * q^62 + 4 * q^64 - 9 * q^65 + 6 * q^67 + 6 * q^68 - 24 * q^69 + 6 * q^71 + q^72 + 20 * q^74 + 18 * q^75 + 9 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 - 24 * q^83 - 12 * q^84 + 21 * q^85 + q^86 + 16 * q^87 - 39 * q^89 - 18 * q^90 + 30 * q^91 + 6 * q^92 - 27 * q^93 + 6 * q^94 + 3 * q^96 - 14 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.686141	−	0.396143i	0.396143	−	0.228714i	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	0.686141	−	0.396143i	0.396143	−	0.228714i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$6$			0.792287i			0.323450i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$	−1.18614	+	2.05446i	−0.395380	+	0.684819i
$10$	2.18614	−	0.469882i	0.691318	−	0.148590i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.686141	−	0.396143i	−0.198072	−	0.114357i
$13$	−2.68614	−	4.65253i	−0.745001	−	1.29038i	−0.950194	−	0.311659i	$-0.899115\pi$
$13$	−2.68614	−	4.65253i	−0.745001	−	1.29038i	0.205193	−	0.978722i	$-0.434218\pi$
$14$		−	3.46410i		−	0.925820i
$15$	−1.68614	−	0.543620i	−0.435360	−	0.140362i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.18614	+	3.78651i	−0.530217	+	0.918363i	0.469162	+	0.883112i	$0.344556\pi$
$17$	−2.18614	+	3.78651i	−0.530217	+	0.918363i	−0.999379	+	0.0352504i	$0.988777\pi$
$18$	−1.18614	−	2.05446i	−0.279576	−	0.484240i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.686141	+	2.12819i	−0.153426	+	0.475879i
$21$	−1.37228	+	2.37686i	−0.299456	+	0.518674i
$22$		0			0
$23$	−8.74456			−1.82337			−0.911684	−	0.410893i	$-0.865217\pi$
$23$	−8.74456			−1.82337			−0.911684	+	0.410893i	$0.865217\pi$
$24$	0.686141	−	0.396143i	0.140058	−	0.0808625i
$25$	−0.500000	+	4.97494i	−0.100000	+	0.994987i
$26$	5.37228			1.05359
$27$			4.25639i			0.819142i
$28$	3.00000	+	1.73205i	0.566947	+	0.327327i
$29$		−	4.40387i		−	0.817777i	−0.912584	−	0.408889i	$-0.865916\pi$
$29$		−	4.40387i		−	0.817777i	0.912584	−	0.408889i	$-0.134084\pi$
$30$	1.31386	−	1.18843i	0.239877	−	0.216977i
$31$			1.08724i			0.195274i	0.995222	+	0.0976371i	$0.0311284\pi$
$31$			1.08724i			0.195274i	−0.995222	+	0.0976371i	$0.968872\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−2.18614	−	3.78651i	−0.374920	−	0.649381i
$35$	7.37228	+	2.37686i	1.24614	+	0.401763i
$36$	2.37228			0.395380
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$38$		0			0
$39$	−3.68614	−	2.12819i	−0.590255	−	0.340784i
$40$	−1.50000	−	1.65831i	−0.237171	−	0.262202i
$41$	−2.87228	−	4.97494i	−0.448575	−	0.776955i	0.549719	−	0.835350i	$-0.314735\pi$
$41$	−2.87228	−	4.97494i	−0.448575	−	0.776955i	−0.998294	+	0.0583953i	$0.981402\pi$
$42$	−1.37228	−	2.37686i	−0.211748	−	0.366758i
$43$	8.11684			1.23781			0.618904	−	0.785467i	$-0.287577\pi$
$43$	8.11684			1.23781			0.618904	+	0.785467i	$0.287577\pi$
$44$		0			0
$45$	5.18614	−	1.11469i	0.773104	−	0.166168i
$46$	4.37228	−	7.57301i	0.644658	−	1.11658i
$47$			1.58457i			0.231134i	0.993300	+	0.115567i	$0.0368685\pi$
$47$			1.58457i			0.231134i	−0.993300	+	0.115567i	$0.963132\pi$
$48$			0.792287i			0.114357i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	−4.05842	−	2.92048i	−0.573948	−	0.413018i
$51$			3.46410i			0.485071i
$52$	−2.68614	+	4.65253i	−0.372501	+	0.645190i
$53$	3.68614	+	2.12819i	0.506330	+	0.292330i	0.731324	−	0.682030i	$-0.238903\pi$
$53$	3.68614	+	2.12819i	0.506330	+	0.292330i	−0.224994	+	0.974360i	$0.572236\pi$
$54$	−3.68614	−	2.12819i	−0.501620	−	0.289611i
$55$		0			0
$56$	−3.00000	+	1.73205i	−0.400892	+	0.231455i
$57$		0			0
$58$	3.81386	+	2.20193i	0.500784	+	0.289128i
$59$	−4.62772	−	2.67181i	−0.602478	−	0.347841i	0.167538	−	0.985866i	$-0.446418\pi$
$59$	−4.62772	−	2.67181i	−0.602478	−	0.347841i	−0.770016	+	0.638025i	$0.779752\pi$
$60$	0.372281	+	1.73205i	0.0480613	+	0.223607i
$61$	−6.55842	+	3.78651i	−0.839720	+	0.484813i	−0.857169	−	0.515035i	$-0.827779\pi$
$61$	−6.55842	+	3.78651i	−0.839720	+	0.484813i	0.0174491	+	0.999848i	$0.494445\pi$
$62$	−0.941578	−	0.543620i	−0.119581	−	0.0690398i
$63$		−	8.21782i		−	1.03535i
$64$	1.00000			0.125000
$65$	−3.68614	+	11.4333i	−0.457209	+	1.41812i
$66$		0			0
$67$	10.1168	−	5.84096i	1.23597	−	0.713587i	0.267701	−	0.963502i	$-0.413736\pi$
$67$	10.1168	−	5.84096i	1.23597	−	0.713587i	0.968268	+	0.249915i	$0.0804026\pi$
$68$	4.37228			0.530217
$69$	−6.00000	+	3.46410i	−0.722315	+	0.417029i
$70$	−5.74456	+	5.19615i	−0.686607	+	0.621059i
$71$	4.37228	+	7.57301i	0.518894	+	0.898751i	0.999759	+	0.0219565i	$0.00698952\pi$
$71$	4.37228	+	7.57301i	0.518894	+	0.898751i	−0.480865	+	0.876795i	$0.659677\pi$
$72$	−1.18614	+	2.05446i	−0.139788	+	0.242120i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	1.62772	+	3.61158i	0.187953	+	0.417029i
$76$		0			0
$77$		0			0
$78$	3.68614	−	2.12819i	0.417373	−	0.240971i
$79$	10.1168	−	5.84096i	1.13823	−	0.657160i	0.192241	−	0.981348i	$-0.438424\pi$
$79$	10.1168	−	5.84096i	1.13823	−	0.657160i	0.945993	+	0.324188i	$0.105091\pi$
$80$	2.18614	−	0.469882i	0.244418	−	0.0525344i
$81$	−1.87228	−	3.24289i	−0.208031	−	0.360321i
$82$	5.74456			0.634381
$83$	−0.255437	−	0.147477i	−0.0280379	−	0.0161877i	0.485916	−	0.874006i	$-0.338486\pi$
$83$	−0.255437	−	0.147477i	−0.0280379	−	0.0161877i	−0.513953	+	0.857818i	$0.671820\pi$
$84$	2.74456			0.299456
$85$	9.55842	−	2.05446i	1.03676	−	0.222837i
$86$	−4.05842	+	7.02939i	−0.437631	+	0.757999i
$87$	−1.74456	−	3.02167i	−0.187037	−	0.323957i
$88$		0			0
$89$	−11.1861	−	6.45832i	−1.18573	−	0.684581i	−0.228396	−	0.973568i	$-0.573348\pi$
$89$	−11.1861	−	6.45832i	−1.18573	−	0.684581i	−0.957333	+	0.288988i	$0.906681\pi$
$90$	−1.62772	+	5.04868i	−0.171577	+	0.532177i
$91$	16.1168	+	9.30506i	1.68950	+	0.975436i
$92$	4.37228	+	7.57301i	0.455842	+	0.789541i
$93$	0.430703	+	0.746000i	0.0446619	+	0.0773566i
$94$	−1.37228	−	0.792287i	−0.141540	−	0.0817182i
$95$		0			0
$96$	−0.686141	−	0.396143i	−0.0700289	−	0.0404312i
$97$	5.11684			0.519537			0.259768	−	0.965671i	$-0.416354\pi$
$97$	5.11684			0.519537			0.259768	+	0.965671i	$0.416354\pi$
$98$	2.50000	+	4.33013i	0.252538	+	0.437409i
$99$		0			0
$100$	4.55842	−	2.05446i	0.455842	−	0.205446i
$101$	−4.37228			−0.435058			−0.217529	−	0.976054i	$-0.569800\pi$
$101$	−4.37228			−0.435058			−0.217529	+	0.976054i	$0.569800\pi$
$102$	−3.00000	−	1.73205i	−0.297044	−	0.171499i
$103$	−7.48913			−0.737925			−0.368963	−	0.929444i	$-0.620287\pi$
$103$	−7.48913			−0.737925			−0.368963	+	0.929444i	$0.620287\pi$
$104$	−2.68614	−	4.65253i	−0.263398	−	0.456218i
$105$	6.00000	−	1.28962i	0.585540	−	0.125854i
$106$	−3.68614	+	2.12819i	−0.358030	+	0.206709i
$107$	−16.8030	+	9.70121i	−1.62441	+	0.937851i	−0.638684	+	0.769469i	$0.720521\pi$
$107$	−16.8030	+	9.70121i	−1.62441	+	0.937851i	−0.985722	+	0.168382i	$0.946146\pi$
$108$	3.68614	−	2.12819i	0.354699	−	0.204786i
$109$	6.55842	+	3.78651i	0.628183	+	0.362682i	0.780048	−	0.625720i	$-0.215195\pi$
$109$	6.55842	+	3.78651i	0.628183	+	0.362682i	−0.151865	+	0.988401i	$0.548528\pi$
$110$		0			0
$111$	−2.05842	−	4.35758i	−0.195377	−	0.413603i
$112$		−	3.46410i		−	0.327327i
$113$	−7.11684	+	12.3267i	−0.669496	+	1.15960i	0.308549	+	0.951209i	$0.400157\pi$
$113$	−7.11684	+	12.3267i	−0.669496	+	1.15960i	−0.978045	+	0.208393i	$0.933177\pi$
$114$		0			0
$115$	13.1168	+	14.5012i	1.22315	+	1.35225i
$116$	−3.81386	+	2.20193i	−0.354108	+	0.204444i
$117$	12.7446			1.17824
$118$	4.62772	−	2.67181i	0.426016	−	0.245960i
$119$		−	15.1460i		−	1.38843i
$120$	−1.68614	−	0.543620i	−0.153923	−	0.0496255i
$121$	−11.0000			−1.00000
$122$		−	7.57301i		−	0.685628i
$123$	−3.94158	−	2.27567i	−0.355400	−	0.205190i
$124$	0.941578	−	0.543620i	0.0845562	−	0.0488185i
$125$	9.00000	−	6.63325i	0.804984	−	0.593296i
$126$	7.11684	+	4.10891i	0.634019	+	0.366051i
$127$	15.0000	+	8.66025i	1.33103	+	0.768473i	0.985458	−	0.169917i	$-0.0543501\pi$
$127$	15.0000	+	8.66025i	1.33103	+	0.768473i	0.345576	+	0.938391i	$0.387683\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.56930	−	3.21543i	0.490349	−	0.283103i
$130$	−8.05842	−	8.90892i	−0.706770	−	0.781364i
$131$	−5.74456	−	3.31662i	−0.501905	−	0.289775i	0.227595	−	0.973756i	$-0.426914\pi$
$131$	−5.74456	−	3.31662i	−0.501905	−	0.289775i	−0.729500	+	0.683981i	$0.760247\pi$
$132$		0			0
$133$		0			0
$134$			11.6819i			1.00916i
$135$	7.05842	−	6.38458i	0.607492	−	0.549497i
$136$	−2.18614	+	3.78651i	−0.187460	+	0.324690i
$137$		−	5.98844i		−	0.511627i	−0.966726	−	0.255813i	$-0.917657\pi$
$137$		−	5.98844i		−	0.511627i	0.966726	−	0.255813i	$-0.0823433\pi$
$138$		−	6.92820i		−	0.589768i
$139$	3.62772	−	6.28339i	0.307699	−	0.532950i	−0.670160	−	0.742217i	$-0.733774\pi$
$139$	3.62772	−	6.28339i	0.307699	−	0.532950i	0.977859	+	0.209267i	$0.0671077\pi$
$140$	−1.62772	−	7.57301i	−0.137567	−	0.640036i
$141$	0.627719	+	1.08724i	0.0528634	+	0.0915622i
$142$	−8.74456			−0.733827
$143$		0			0
$144$	−1.18614	−	2.05446i	−0.0988451	−	0.171205i
$145$	−7.30298	+	6.60580i	−0.606480	+	0.548582i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$		−	3.96143i		−	0.326734i
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	−16.3723			−1.34127			−0.670635	−	0.741788i	$-0.733978\pi$
$149$	−16.3723			−1.34127			−0.670635	+	0.741788i	$0.733978\pi$
$150$	−3.94158	−	0.396143i	−0.321828	−	0.0323450i
$151$	5.43070	+	9.40625i	0.441944	+	0.765470i	0.997834	−	0.0657862i	$-0.0209555\pi$
$151$	5.43070	+	9.40625i	0.441944	+	0.765470i	−0.555889	+	0.831256i	$0.687622\pi$
$152$		0			0
$153$	−5.18614	−	8.98266i	−0.419275	−	0.726205i
$154$		0			0
$155$	1.80298	−	1.63086i	0.144819	−	0.130994i
$156$			4.25639i			0.340784i
$157$	−11.6168	−	6.70699i	−0.927125	−	0.535276i	−0.0412239	−	0.999150i	$-0.513126\pi$
$157$	−11.6168	−	6.70699i	−0.927125	−	0.535276i	−0.885901	+	0.463874i	$0.846459\pi$
$158$			11.6819i			0.929364i
$159$	3.37228			0.267439
$160$	−0.686141	+	2.12819i	−0.0542442	+	0.168249i
$161$	26.2337	−	15.1460i	2.06750	−	1.19367i
$162$	3.74456			0.294201
$163$	0.0584220	−	0.101190i	0.00457596	−	0.00792580i	−0.863728	−	0.503958i	$-0.831877\pi$
$163$	0.0584220	−	0.101190i	0.00457596	−	0.00792580i	0.868304	+	0.496032i	$0.165210\pi$
$164$	−2.87228	+	4.97494i	−0.224287	+	0.388477i
$165$		0			0
$166$	0.255437	−	0.147477i	0.0198258	−	0.0114464i
$167$	8.74456	+	15.1460i	0.676675	+	1.17203i	0.975976	+	0.217876i	$0.0699129\pi$
$167$	8.74456	+	15.1460i	0.676675	+	1.17203i	−0.299302	+	0.954158i	$0.596754\pi$
$168$	−1.37228	+	2.37686i	−0.105874	+	0.183379i
$169$	−7.93070	+	13.7364i	−0.610054	+	1.05664i
$170$	−3.00000	+	9.30506i	−0.230089	+	0.713666i
$171$		0			0
$172$	−4.05842	−	7.02939i	−0.309452	−	0.535986i
$173$	−21.0475	−	12.1518i	−1.60022	−	0.923885i	−0.991443	−	0.130540i	$-0.958329\pi$
$173$	−21.0475	−	12.1518i	−1.60022	−	0.923885i	−0.608772	−	0.793345i	$-0.708338\pi$
$174$	3.48913			0.264510
$175$	−7.11684	−	15.7908i	−0.537983	−	1.19368i
$176$		0			0
$177$	−4.23369			−0.318223
$178$	11.1861	−	6.45832i	0.838437	−	0.484072i
$179$		−	6.33830i		−	0.473746i	−0.971541	−	0.236873i	$-0.923877\pi$
$179$		−	6.33830i		−	0.473746i	0.971541	−	0.236873i	$-0.0761226\pi$
$180$	−3.55842	−	3.93398i	−0.265229	−	0.293222i
$181$	−11.9307	−	20.6646i	−0.886802	−	1.53599i	−0.843634	−	0.536919i	$-0.819588\pi$
$181$	−11.9307	−	20.6646i	−0.886802	−	1.53599i	−0.0431682	−	0.999068i	$-0.513745\pi$
$182$	−16.1168	+	9.30506i	−1.19466	+	0.689737i
$183$	−3.00000	+	5.19615i	−0.221766	+	0.384111i
$184$	−8.74456			−0.644658
$185$	−10.8030	+	8.26411i	−0.794251	+	0.607589i
$186$	−0.861407			−0.0631614
$187$		0			0
$188$	1.37228	−	0.792287i	0.100084	−	0.0577835i
$189$	−7.37228	−	12.7692i	−0.536255	−	0.928820i
$190$		0			0
$191$		−	1.38219i		−	0.100012i	−0.998749	−	0.0500060i	$-0.984076\pi$
$191$		−	1.38219i		−	0.100012i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$	0.686141	−	0.396143i	0.0495179	−	0.0285892i
$193$	−12.3723			−0.890576			−0.445288	−	0.895387i	$-0.646899\pi$
$193$	−12.3723			−0.890576			−0.445288	+	0.895387i	$0.646899\pi$
$194$	−2.55842	+	4.43132i	−0.183684	+	0.318150i
$195$	2.00000	+	9.30506i	0.143223	+	0.666349i
$196$	−5.00000			−0.357143
$197$	−11.8723	−	6.85446i	−0.845865	−	0.488360i	0.0133885	−	0.999910i	$-0.495738\pi$
$197$	−11.8723	−	6.85446i	−0.845865	−	0.488360i	−0.859254	+	0.511550i	$0.829072\pi$
$198$		0			0
$199$		−	20.9870i		−	1.48773i	−0.668331	−	0.743864i	$-0.732991\pi$
$199$		−	20.9870i		−	1.48773i	0.668331	−	0.743864i	$-0.267009\pi$
$200$	−0.500000	+	4.97494i	−0.0353553	+	0.351781i
$201$	4.62772	−	8.01544i	0.326414	−	0.565366i
$202$	2.18614	−	3.78651i	0.153816	−	0.266418i
$203$	7.62772	+	13.2116i	0.535361	+	0.927272i
$204$	3.00000	−	1.73205i	0.210042	−	0.121268i
$205$	−3.94158	+	12.2255i	−0.275292	+	0.853869i
$206$	3.74456	−	6.48577i	0.260896	−	0.451885i
$207$	10.3723	−	17.9653i	0.720923	−	1.24868i
$208$	5.37228			0.372501
$209$		0			0
$210$	−1.88316	+	5.84096i	−0.129950	+	0.403065i
$211$	7.48913			0.515573			0.257786	−	0.966202i	$-0.417007\pi$
$211$	7.48913			0.515573			0.257786	+	0.966202i	$0.417007\pi$
$212$		−	4.25639i		−	0.292330i
$213$	6.00000	+	3.46410i	0.411113	+	0.237356i
$214$		−	19.4024i		−	1.32632i
$215$	−12.1753	−	13.4603i	−0.830346	−	0.917982i
$216$			4.25639i			0.289611i
$217$	−1.88316	−	3.26172i	−0.127837	−	0.221420i
$218$	−6.55842	+	3.78651i	−0.444192	+	0.256455i
$219$	2.74456	+	4.75372i	0.185460	+	0.321227i
$220$		0			0
$221$	23.4891			1.58005
$222$	4.80298	+	0.396143i	0.322355	+	0.0265874i
$223$			1.28962i			0.0863594i	0.999067	+	0.0431797i	$0.0137488\pi$
$223$			1.28962i			0.0863594i	−0.999067	+	0.0431797i	$0.986251\pi$
$224$	3.00000	+	1.73205i	0.200446	+	0.115728i
$225$	−9.62772	−	6.92820i	−0.641848	−	0.461880i
$226$	−7.11684	−	12.3267i	−0.473405	−	0.819962i
$227$	2.31386	+	4.00772i	0.153576	+	0.266002i	0.932540	−	0.361067i	$-0.117588\pi$
$227$	2.31386	+	4.00772i	0.153576	+	0.266002i	−0.778963	+	0.627069i	$0.784254\pi$
$228$		0			0
$229$	9.93070	+	17.2005i	0.656239	+	1.13664i	0.981582	+	0.191044i	$0.0611872\pi$
$229$	9.93070	+	17.2005i	0.656239	+	1.13664i	−0.325342	+	0.945596i	$0.605479\pi$
$230$	−19.1168	+	4.10891i	−1.26053	+	0.270934i
$231$		0			0
$232$		−	4.40387i		−	0.289128i
$233$			11.3321i			0.742389i	0.928555	+	0.371194i	$0.121052\pi$
$233$			11.3321i			0.742389i	−0.928555	+	0.371194i	$0.878948\pi$
$234$	−6.37228	+	11.0371i	−0.416569	+	0.721519i
$235$	2.62772	−	2.37686i	0.171413	−	0.155049i
$236$			5.34363i			0.347841i
$237$	4.62772	−	8.01544i	0.300603	−	0.520659i
$238$	13.1168	+	7.57301i	0.850239	+	0.490886i
$239$	14.4891	+	8.36530i	0.937224	+	0.541106i	0.889089	−	0.457735i	$-0.151339\pi$
$239$	14.4891	+	8.36530i	0.937224	+	0.541106i	0.0481347	+	0.998841i	$0.484672\pi$
$240$	1.31386	−	1.18843i	0.0848093	−	0.0767129i
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.951180	−	0.308637i	$-0.900127\pi$
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.208302	+	0.978065i	$0.566794\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−13.6277	−	7.86797i	−0.874219	−	0.504730i
$244$	6.55842	+	3.78651i	0.419860	+	0.242406i
$245$	−10.9307	+	2.34941i	−0.698337	+	0.150098i
$246$	3.94158	−	2.27567i	0.251306	−	0.145091i
$247$		0			0
$248$			1.08724i			0.0690398i
$249$	−0.233688			−0.0148094
$250$	1.24456	+	11.1109i	0.0787131	+	0.702712i
$251$			11.3870i			0.718739i	0.933195	+	0.359370i	$0.117008\pi$
$251$			11.3870i			0.718739i	−0.933195	+	0.359370i	$0.882992\pi$
$252$	−7.11684	+	4.10891i	−0.448319	+	0.258837i
$253$		0			0
$254$	−15.0000	+	8.66025i	−0.941184	+	0.543393i
$255$	5.74456	−	5.19615i	0.359738	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.9307	−	24.1287i	0.868973	−	1.50511i	0.00592640	−	0.999982i	$-0.498114\pi$
$257$	13.9307	−	24.1287i	0.868973	−	1.50511i	0.863047	−	0.505124i	$-0.168553\pi$
$258$			6.43087i			0.400368i
$259$	9.00000	+	19.0526i	0.559233	+	1.18387i
$260$	11.7446	−	2.52434i	0.728367	−	0.156553i
$261$	9.04755	+	5.22360i	0.560029	+	0.323333i
$262$	5.74456	−	3.31662i	0.354900	−	0.204902i
$263$	−8.74456	+	5.04868i	−0.539213	+	0.311315i	−0.744760	−	0.667333i	$-0.767436\pi$
$263$	−8.74456	+	5.04868i	−0.539213	+	0.311315i	0.205547	+	0.978647i	$0.434103\pi$
$264$		0			0
$265$	−2.00000	−	9.30506i	−0.122859	−	0.571606i
$266$		0			0
$267$	−10.2337			−0.626292
$268$	−10.1168	−	5.84096i	−0.617985	−	0.356794i
$269$	−0.510875			−0.0311486			−0.0155743	−	0.999879i	$-0.504958\pi$
$269$	−0.510875			−0.0311486			−0.0155743	+	0.999879i	$0.504958\pi$
$270$	2.00000	+	9.30506i	0.121716	+	0.566288i
$271$	−6.31386	+	10.9359i	−0.383540	+	0.664310i	−0.991565	−	0.129607i	$-0.958628\pi$
$271$	−6.31386	+	10.9359i	−0.383540	+	0.664310i	0.608026	+	0.793917i	$0.291962\pi$
$272$	−2.18614	−	3.78651i	−0.132554	−	0.229591i
$273$	14.7446			0.892382
$274$	5.18614	+	2.99422i	0.313306	+	0.180887i
$275$		0			0
$276$	6.00000	+	3.46410i	0.361158	+	0.208514i
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	3.62772	+	6.28339i	0.217576	+	0.376853i
$279$	−2.23369	−	1.28962i	−0.133727	−	0.0772075i
$280$	7.37228	+	2.37686i	0.440578	+	0.142045i
$281$	11.8723	+	6.85446i	0.708241	+	0.408903i	0.810409	−	0.585864i	$-0.199245\pi$
$281$	11.8723	+	6.85446i	0.708241	+	0.408903i	−0.102168	+	0.994767i	$0.532578\pi$
$282$	−1.25544			−0.0747602
$283$	−10.0584	−	17.4217i	−0.597911	−	1.03561i	−0.993129	−	0.117025i	$-0.962664\pi$
$283$	−10.0584	−	17.4217i	−0.597911	−	1.03561i	0.395218	−	0.918587i	$-0.370669\pi$
$284$	4.37228	−	7.57301i	0.259447	−	0.449376i
$285$		0			0
$286$		0			0
$287$	17.2337	+	9.94987i	1.01727	+	0.587323i
$288$	2.37228			0.139788
$289$	−1.05842	−	1.83324i	−0.0622601	−	0.107838i
$290$	−2.06930	−	9.62747i	−0.121513	−	0.565344i
$291$	3.51087	−	2.02700i	0.205811	−	0.118825i
$292$	6.00000	−	3.46410i	0.351123	−	0.202721i
$293$	−2.01087	+	1.16098i	−0.117477	+	0.0678251i	−0.557587	−	0.830119i	$-0.688273\pi$
$293$	−2.01087	+	1.16098i	−0.117477	+	0.0678251i	0.440110	+	0.897944i	$0.354939\pi$
$294$	3.43070	+	1.98072i	0.200083	+	0.115518i
$295$	2.51087	+	11.6819i	0.146189	+	0.680148i
$296$	0.500000	−	6.06218i	0.0290619	−	0.352357i
$297$		0			0
$298$	8.18614	−	14.1788i	0.474210	−	0.821356i
$299$	23.4891	+	40.6844i	1.35841	+	2.35284i
$300$	2.31386	−	3.21543i	0.133591	−	0.185643i
$301$	−24.3505	+	14.0588i	−1.40354	+	0.810335i
$302$	−10.8614			−0.625004
$303$	−3.00000	+	1.73205i	−0.172345	+	0.0995037i
$304$		0			0
$305$	16.1168	+	5.19615i	0.922848	+	0.297531i
$306$	10.3723			0.592944
$307$			30.0897i			1.71731i	0.512555	+	0.858654i	$0.328699\pi$
$307$			30.0897i			1.71731i	−0.512555	+	0.858654i	$0.671301\pi$
$308$		0			0
$309$	−5.13859	+	2.96677i	−0.292324	+	0.168774i
$310$	0.510875	+	2.37686i	0.0290157	+	0.134997i
$311$	−20.9198	−	12.0781i	−1.18625	−	0.684884i	−0.228801	−	0.973473i	$-0.573481\pi$
$311$	−20.9198	−	12.0781i	−1.18625	−	0.684884i	−0.957453	+	0.288589i	$0.906814\pi$
$312$	−3.68614	−	2.12819i	−0.208687	−	0.120485i
$313$	11.6753	−	20.2222i	0.659925	−	1.14302i	−0.320710	−	0.947178i	$-0.603921\pi$
$313$	11.6753	−	20.2222i	0.659925	−	1.14302i	0.980635	−	0.195846i	$-0.0627453\pi$
$314$	11.6168	−	6.70699i	0.655576	−	0.378497i
$315$	−13.6277	+	12.3267i	−0.767835	+	0.694533i
$316$	−10.1168	−	5.84096i	−0.569117	−	0.328580i
$317$	17.3614	+	10.0236i	0.975114	+	0.562982i	0.900791	−	0.434252i	$-0.142987\pi$
$317$	17.3614	+	10.0236i	0.975114	+	0.562982i	0.0743224	+	0.997234i	$0.476321\pi$
$318$	−1.68614	+	2.92048i	−0.0945541	+	0.163772i
$319$		0			0
$320$	−1.50000	−	1.65831i	−0.0838525	−	0.0927025i
$321$	−7.68614	+	13.3128i	−0.428999	+	0.743047i
$322$			30.2921i			1.68811i
$323$		0			0
$324$	−1.87228	+	3.24289i	−0.104016	+	0.180160i
$325$	24.4891	−	11.0371i	1.35841	−	0.612229i
$326$	0.0584220	+	0.101190i	0.00323569	+	0.00560439i
$327$	6.00000			0.331801
$328$	−2.87228	−	4.97494i	−0.158595	−	0.274695i
$329$	−2.74456	−	4.75372i	−0.151313	−	0.262081i
$330$		0			0
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.335566	−	0.942017i	$-0.608928\pi$
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.983593	+	0.180400i	$0.942261\pi$
$332$			0.294954i			0.0161877i
$333$	11.8614	+	8.21782i	0.650001	+	0.450334i
$334$	−17.4891			−0.956962
$335$	−24.8614	−	8.01544i	−1.35832	−	0.437930i
$336$	−1.37228	−	2.37686i	−0.0748641	−	0.129668i
$337$	−9.55842	+	5.51856i	−0.520680	+	0.300615i	−0.737213	−	0.675660i	$-0.763859\pi$
$337$	−9.55842	+	5.51856i	−0.520680	+	0.300615i	0.216533	+	0.976275i	$0.430525\pi$
$338$	−7.93070	−	13.7364i	−0.431373	−	0.747161i
$339$			11.2772i			0.612492i
$340$	−6.55842	−	7.25061i	−0.355680	−	0.393219i
$341$		0			0
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$	8.11684			0.437631
$345$	14.7446	+	4.75372i	0.793821	+	0.255932i
$346$	21.0475	−	12.1518i	1.13152	−	0.653285i
$347$	8.74456			0.469433			0.234716	−	0.972064i	$-0.424584\pi$
$347$	8.74456			0.469433			0.234716	+	0.972064i	$0.424584\pi$
$348$	−1.74456	+	3.02167i	−0.0935184	+	0.161979i
$349$	−3.18614	+	5.51856i	−0.170550	+	0.295402i	−0.938612	−	0.344974i	$-0.887888\pi$
$349$	−3.18614	+	5.51856i	−0.170550	+	0.295402i	0.768062	+	0.640375i	$0.221221\pi$
$350$	17.2337	+	1.73205i	0.921179	+	0.0925820i
$351$	19.8030	−	11.4333i	1.05701	−	0.610262i
$352$		0			0
$353$	13.6753	−	23.6863i	0.727861	−	1.26069i	−0.229925	−	0.973208i	$-0.573848\pi$
$353$	13.6753	−	23.6863i	0.727861	−	1.26069i	0.957786	−	0.287484i	$-0.0928187\pi$
$354$	2.11684	−	3.66648i	0.112509	−	0.194871i
$355$	6.00000	−	18.6101i	0.318447	−	0.987723i
$356$			12.9166i			0.684581i
$357$	−6.00000	−	10.3923i	−0.317554	−	0.550019i
$358$	5.48913	+	3.16915i	0.290109	+	0.167495i
$359$	−4.62772			−0.244242			−0.122121	−	0.992515i	$-0.538970\pi$
$359$	−4.62772			−0.244242			−0.122121	+	0.992515i	$0.538970\pi$
$360$	5.18614	−	1.11469i	0.273334	−	0.0587494i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	23.8614			1.25413
$363$	−7.54755	+	4.35758i	−0.396143	+	0.228714i
$364$		−	18.6101i		−	0.975436i
$365$	11.4891	−	10.3923i	0.601368	−	0.543958i
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	−1.88316	+	1.08724i	−0.0982999	+	0.0567535i	−0.548344	−	0.836253i	$-0.684742\pi$
$367$	−1.88316	+	1.08724i	−0.0982999	+	0.0567535i	0.450044	+	0.893006i	$0.351408\pi$
$368$	4.37228	−	7.57301i	0.227921	−	0.394771i
$369$	13.6277			0.709431
$370$	−1.75544	−	13.4877i	−0.0912608	−	0.701193i
$371$	−14.7446			−0.765500
$372$	0.430703	−	0.746000i	0.0223309	−	0.0386783i
$373$	−10.5000	+	6.06218i	−0.543669	+	0.313888i	−0.746565	−	0.665313i	$-0.768298\pi$
$373$	−10.5000	+	6.06218i	−0.543669	+	0.313888i	0.202895	+	0.979200i	$0.434965\pi$
$374$		0			0
$375$	3.54755	−	8.11663i	0.183195	−	0.419141i
$376$			1.58457i			0.0817182i
$377$	−20.4891	+	11.8294i	−1.05524	+	0.609245i
$378$	14.7446			0.758378
$379$	0.372281	−	0.644810i	0.0191228	−	0.0331217i	−0.856306	−	0.516469i	$-0.827246\pi$
$379$	0.372281	−	0.644810i	0.0191228	−	0.0331217i	0.875428	+	0.483348i	$0.160579\pi$
$380$		0			0
$381$	13.7228			0.703041
$382$	1.19702	+	0.691097i	0.0612446	+	0.0353596i
$383$	17.7446	+	30.7345i	0.906705	+	1.57046i	0.818612	+	0.574346i	$0.194744\pi$
$383$	17.7446	+	30.7345i	0.906705	+	1.57046i	0.0880925	+	0.996112i	$0.471923\pi$
$384$			0.792287i			0.0404312i
$385$		0			0
$386$	6.18614	−	10.7147i	0.314866	−	0.545364i
$387$	−9.62772	+	16.6757i	−0.489404	+	0.847673i
$388$	−2.55842	−	4.43132i	−0.129884	−	0.224966i
$389$	−24.0475	+	13.8839i	−1.21926	+	0.703940i	−0.964759	−	0.263133i	$-0.915244\pi$
$389$	−24.0475	+	13.8839i	−1.21926	+	0.703940i	−0.254500	+	0.967073i	$0.581911\pi$
$390$	−9.05842	−	2.92048i	−0.458691	−	0.147884i
$391$	19.1168	−	33.1113i	0.966780	−	1.67451i
$392$	2.50000	−	4.33013i	0.126269	−	0.218704i
$393$	−5.25544			−0.265102
$394$	11.8723	−	6.85446i	0.598117	−	0.345323i
$395$	−24.8614	−	8.01544i	−1.25091	−	0.403301i
$396$		0			0
$397$			3.02167i			0.151653i	0.997121	+	0.0758267i	$0.0241596\pi$
$397$			3.02167i			0.151653i	−0.997121	+	0.0758267i	$0.975840\pi$
$398$	18.1753	+	10.4935i	0.911044	+	0.525991i
$399$		0			0
$400$	−4.05842	−	2.92048i	−0.202921	−	0.146024i
$401$		−	13.2665i		−	0.662497i	−0.943543	−	0.331249i	$-0.892530\pi$
$401$		−	13.2665i		−	0.662497i	0.943543	−	0.331249i	$-0.107470\pi$
$402$	4.62772	+	8.01544i	0.230810	+	0.399774i
$403$	5.05842	−	2.92048i	0.251978	−	0.145480i
$404$	2.18614	+	3.78651i	0.108765	+	0.188386i
$405$	−2.56930	+	7.96916i	−0.127669	+	0.395991i
$406$	−15.2554			−0.757115
$407$		0			0
$408$			3.46410i			0.171499i
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.973247	−	0.229759i	$-0.0737939\pi$
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.287646	+	0.957737i	$0.407127\pi$
$410$	−8.61684	−	9.52628i	−0.425556	−	0.470469i
$411$	−2.37228	−	4.10891i	−0.117016	−	0.202678i
$412$	3.74456	+	6.48577i	0.184481	+	0.319531i
$413$	18.5109			0.910861
$414$	10.3723	+	17.9653i	0.509770	+	0.882947i
$415$	0.138593	+	0.644810i	0.00680328	+	0.0316525i
$416$	−2.68614	+	4.65253i	−0.131699	+	0.228109i
$417$		−	5.74839i		−	0.281500i
$418$		0			0
$419$	−14.4891	+	25.0959i	−0.707840	+	1.22602i	0.257817	+	0.966194i	$0.416997\pi$
$419$	−14.4891	+	25.0959i	−0.707840	+	1.22602i	−0.965657	+	0.259821i	$0.916336\pi$
$420$	−4.11684	−	4.55134i	−0.200881	−	0.222083i
$421$		−	19.2549i		−	0.938428i	−0.883084	−	0.469214i	$-0.844537\pi$
$421$		−	19.2549i		−	0.938428i	0.883084	−	0.469214i	$-0.155463\pi$
$422$	−3.74456	+	6.48577i	−0.182282	+	0.315722i
$423$	−3.25544	−	1.87953i	−0.158285	−	0.0913858i
$424$	3.68614	+	2.12819i	0.179015	+	0.103354i
$425$	−17.7446	−	12.7692i	−0.860738	−	0.619396i
$426$	−6.00000	+	3.46410i	−0.290701	+	0.167836i
$427$	13.1168	−	22.7190i	0.634769	−	1.09945i
$428$	16.8030	+	9.70121i	0.812203	+	0.468926i
$429$		0			0
$430$	17.7446	−	3.81396i	0.855719	−	0.183925i
$431$	−4.54755	+	2.62553i	−0.219048	+	0.126467i	−0.605509	−	0.795838i	$-0.707031\pi$
$431$	−4.54755	+	2.62553i	−0.219048	+	0.126467i	0.386462	+	0.922306i	$0.373697\pi$
$432$	−3.68614	−	2.12819i	−0.177350	−	0.102393i
$433$			8.86263i			0.425911i	0.977062	+	0.212955i	$0.0683089\pi$
$433$			8.86263i			0.425911i	−0.977062	+	0.212955i	$0.931691\pi$
$434$	3.76631			0.180789
$435$	−2.39403	+	7.42554i	−0.114785	+	0.356027i
$436$		−	7.57301i		−	0.362682i
$437$		0			0
$438$	−5.48913			−0.262281
$439$	−23.0584	+	13.3128i	−1.10052	+	0.635385i	−0.936357	−	0.351049i	$-0.885825\pi$
$439$	−23.0584	+	13.3128i	−1.10052	+	0.635385i	−0.164161	+	0.986434i	$0.552492\pi$
$440$		0			0
$441$	5.93070	+	10.2723i	0.282414	+	0.489156i
$442$	−11.7446	+	20.3422i	−0.558632	+	0.967579i
$443$		−	31.9692i		−	1.51890i	−0.650564	−	0.759451i	$-0.725468\pi$
$443$		−	31.9692i		−	1.51890i	0.650564	−	0.759451i	$-0.274532\pi$
$444$	−2.74456	+	3.96143i	−0.130251	+	0.188001i
$445$	6.06930	+	28.2376i	0.287712	+	1.33859i
$446$	−1.11684	−	0.644810i	−0.0528841	−	0.0305326i
$447$	−11.2337	+	6.48577i	−0.531335	+	0.306767i
$448$	−3.00000	+	1.73205i	−0.141737	+	0.0818317i
$449$	25.8030	−	14.8974i	1.21772	−	0.703050i	0.253289	−	0.967391i	$-0.418488\pi$
$449$	25.8030	−	14.8974i	1.21772	−	0.703050i	0.964429	+	0.264341i	$0.0851544\pi$
$450$	10.8139	−	4.87375i	0.509770	−	0.229751i
$451$		0			0
$452$	14.2337			0.669496
$453$	7.45245	+	4.30268i	0.350147	+	0.202157i
$454$	−4.62772			−0.217190
$455$	−8.74456	−	40.6844i	−0.409951	−	1.90731i
$456$		0			0
$457$	10.3030	+	17.8453i	0.481953	+	0.834768i	0.999785	−	0.0207147i	$-0.00659415\pi$
$457$	10.3030	+	17.8453i	0.481953	+	0.834768i	−0.517832	+	0.855482i	$0.673261\pi$
$458$	−19.8614			−0.928063
$459$	−16.1168	−	9.30506i	−0.752270	−	0.434323i
$460$	6.00000	−	18.6101i	0.279751	−	0.867702i
$461$	−0.861407	−	0.497333i	−0.0401197	−	0.0231631i	0.479806	−	0.877375i	$-0.340707\pi$
$461$	−0.861407	−	0.497333i	−0.0401197	−	0.0231631i	−0.519926	+	0.854211i	$0.674040\pi$
$462$		0			0
$463$	−13.7446	−	23.8063i	−0.638764	−	1.10637i	−0.985704	−	0.168484i	$-0.946113\pi$
$463$	−13.7446	−	23.8063i	−0.638764	−	1.10637i	0.346940	−	0.937887i	$-0.387221\pi$
$464$	3.81386	+	2.20193i	0.177054	+	0.102222i
$465$	0.591046	−	1.83324i	0.0274091	−	0.0850145i
$466$	−9.81386	−	5.66603i	−0.454618	−	0.262474i
$467$	−16.6277			−0.769439			−0.384720	−	0.923034i	$-0.625702\pi$
$467$	−16.6277			−0.769439			−0.384720	+	0.923034i	$0.625702\pi$
$468$	−6.37228	−	11.0371i	−0.294559	−	0.510191i
$469$	−20.2337	+	35.0458i	−0.934305	+	1.61826i
$470$	0.744563	+	3.46410i	0.0343441	+	0.159787i
$471$	−10.6277			−0.489699
$472$	−4.62772	−	2.67181i	−0.213008	−	0.122980i
$473$		0			0
$474$	4.62772	+	8.01544i	0.212558	+	0.368162i
$475$		0			0
$476$	−13.1168	+	7.57301i	−0.601210	+	0.347108i
$477$	−8.74456	+	5.04868i	−0.400386	+	0.231163i
$478$	−14.4891	+	8.36530i	−0.662717	+	0.382620i
$479$	−5.91983	−	3.41781i	−0.270484	−	0.156164i	0.358624	−	0.933482i	$-0.383246\pi$
$479$	−5.91983	−	3.41781i	−0.270484	−	0.156164i	−0.629108	+	0.777318i	$0.716579\pi$
$480$	0.372281	+	1.73205i	0.0169922	+	0.0790569i
$481$	−29.5475	+	13.9576i	−1.34725	+	0.636412i
$482$		−	20.7846i		−	0.946713i
$483$	12.0000	−	20.7846i	0.546019	−	0.945732i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−7.67527	−	8.48533i	−0.348516	−	0.385299i
$486$	13.6277	−	7.86797i	0.618166	−	0.356898i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−6.55842	+	3.78651i	−0.296886	+	0.171407i
$489$		−	0.0925740i		−	0.00418634i
$490$	3.43070	−	10.6410i	0.154983	−	0.480710i
$491$	37.7228			1.70241			0.851203	−	0.524836i	$-0.175873\pi$
$491$	37.7228			1.70241			0.851203	+	0.524836i	$0.175873\pi$
$492$			4.55134i			0.205190i
$493$	16.6753	+	9.62747i	0.751016	+	0.433599i
$494$		0			0
$495$		0			0
$496$	−0.941578	−	0.543620i	−0.0422781	−	0.0244093i
$497$	−26.2337	−	15.1460i	−1.17674	−	0.679392i
$498$	0.116844	−	0.202380i	0.00523590	−	0.00906885i
$499$	12.0000	−	6.92820i	0.537194	−	0.310149i	−0.206747	−	0.978394i	$-0.566288\pi$
$499$	12.0000	−	6.92820i	0.537194	−	0.310149i	0.743941	+	0.668245i	$0.232954\pi$
$500$	−10.2446	−	4.47760i	−0.458151	−	0.200245i
$501$	12.0000	+	6.92820i	0.536120	+	0.309529i
$502$	−9.86141	−	5.69349i	−0.440136	−	0.254113i
$503$	−11.4891	+	19.8997i	−0.512275	+	0.887286i	0.487624	+	0.873054i	$0.337864\pi$
$503$	−11.4891	+	19.8997i	−0.512275	+	0.887286i	−0.999899	+	0.0142322i	$0.995470\pi$
$504$		−	8.21782i		−	0.366051i
$505$	6.55842	+	7.25061i	0.291846	+	0.322648i
$506$		0			0
$507$			12.5668i			0.558111i
$508$		−	17.3205i		−	0.768473i
$509$	9.30298	−	16.1132i	0.412348	−	0.714207i	−0.582798	−	0.812617i	$-0.698042\pi$
$509$	9.30298	−	16.1132i	0.412348	−	0.714207i	0.995146	+	0.0984099i	$0.0313756\pi$
$510$	1.62772	+	7.57301i	0.0720766	+	0.335339i
$511$	−12.0000	−	20.7846i	−0.530849	−	0.919457i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.9307	+	24.1287i	0.614457	+	1.06427i
$515$	11.2337	+	12.4193i	0.495015	+	0.547260i
$516$	−5.56930	−	3.21543i	−0.245175	−	0.141552i
$517$		0			0
$518$	−21.0000	−	1.73205i	−0.922687	−	0.0761019i
$519$	−19.2554			−0.845220
$520$	−3.68614	+	11.4333i	−0.161648	+	0.501382i
$521$	0.686141	+	1.18843i	0.0300604	+	0.0520661i	0.880664	−	0.473741i	$-0.157097\pi$
$521$	0.686141	+	1.18843i	0.0300604	+	0.0520661i	−0.850604	+	0.525807i	$0.823763\pi$
$522$	−9.04755	+	5.22360i	−0.396000	+	0.228631i
$523$	0.0584220	+	0.101190i	0.00255462	+	0.00442472i	0.867300	−	0.497786i	$-0.165854\pi$
$523$	0.0584220	+	0.101190i	0.00255462	+	0.00442472i	−0.864745	+	0.502211i	$0.832520\pi$
$524$			6.63325i			0.289775i
$525$	−11.1386	−	8.01544i	−0.486128	−	0.349823i
$526$		−	10.0974i		−	0.440265i
$527$	−4.11684	−	2.37686i	−0.179333	−	0.103538i
$528$		0			0
$529$	53.4674			2.32467
$530$	9.05842	+	2.92048i	0.393473	+	0.126858i
$531$	10.9783	−	6.33830i	0.476415	−	0.275059i
$532$		0			0
$533$	−15.4307	+	26.7268i	−0.668378	+	1.15766i
$534$	5.11684	−	8.86263i	0.221427	−	0.383524i
$535$	41.2921	+	13.3128i	1.78521	+	0.575562i
$536$	10.1168	−	5.84096i	0.436981	−	0.252291i
$537$	−2.51087	−	4.34896i	−0.108352	−	0.187672i
$538$	0.255437	−	0.442430i	0.0110127	−	0.0190745i
$539$		0			0
$540$	−9.05842	−	2.92048i	−0.389812	−	0.125678i
$541$			25.2983i			1.08766i	0.839196	+	0.543829i	$0.183026\pi$
$541$			25.2983i			1.08766i	−0.839196	+	0.543829i	$0.816974\pi$
$542$	−6.31386	−	10.9359i	−0.271203	−	0.469738i
$543$	−16.3723	−	9.45254i	−0.702602	−	0.405647i
$544$	4.37228			0.187460
$545$	−3.55842	−	16.5557i	−0.152426	−	0.709167i
$546$	−7.37228	+	12.7692i	−0.315505	+	0.546470i
$547$	−17.0951			−0.730933			−0.365467	−	0.930824i	$-0.619091\pi$
$547$	−17.0951			−0.730933			−0.365467	+	0.930824i	$0.619091\pi$
$548$	−5.18614	+	2.99422i	−0.221541	+	0.127907i
$549$		−	17.9653i		−	0.766741i
$550$		0			0
$551$		0			0
$552$	−6.00000	+	3.46410i	−0.255377	+	0.147442i
$553$	−20.2337	+	35.0458i	−0.860424	+	1.49030i
$554$	7.00000			0.297402
$555$	−4.13859	+	9.94987i	−0.175674	+	0.422349i
$556$	−7.25544			−0.307699
$557$	−10.7554	+	18.6290i	−0.455723	+	0.789335i	−0.998729	−	0.0503937i	$-0.983952\pi$
$557$	−10.7554	+	18.6290i	−0.455723	+	0.789335i	0.543007	+	0.839728i	$0.317286\pi$
$558$	2.23369	−	1.28962i	0.0945596	−	0.0545940i
$559$	−21.8030	−	37.7639i	−0.922168	−	1.59724i
$560$	−5.74456	+	5.19615i	−0.242752	+	0.219578i
$561$		0			0
$562$	−11.8723	+	6.85446i	−0.500802	+	0.289138i
$563$	26.2337			1.10562			0.552809	−	0.833308i	$-0.313556\pi$
$563$	26.2337			1.10562			0.552809	+	0.833308i	$0.313556\pi$
$564$	0.627719	−	1.08724i	0.0264317	−	0.0457811i
$565$	31.1168	−	6.68815i	1.30910	−	0.281373i
$566$	20.1168			0.845574
$567$	11.2337	+	6.48577i	0.471771	+	0.272377i
$568$	4.37228	+	7.57301i	0.183457	+	0.317757i
$569$			26.9754i			1.13087i	0.824793	+	0.565434i	$0.191291\pi$
$569$			26.9754i			1.13087i	−0.824793	+	0.565434i	$0.808709\pi$
$570$		0			0
$571$	−15.2337	+	26.3855i	−0.637510	+	1.10420i	0.348467	+	0.937321i	$0.386702\pi$
$571$	−15.2337	+	26.3855i	−0.637510	+	1.10420i	−0.985977	+	0.166879i	$0.946631\pi$
$572$		0			0
$573$	−0.547547	−	0.948380i	−0.0228741	−	0.0396191i
$574$	−17.2337	+	9.94987i	−0.719320	+	0.415300i
$575$	4.37228	−	43.5036i	0.182337	−	1.81423i
$576$	−1.18614	+	2.05446i	−0.0494225	+	0.0856023i
$577$	21.2337	−	36.7778i	0.883970	−	1.53108i	0.0370803	−	0.999312i	$-0.488194\pi$
$577$	21.2337	−	36.7778i	0.883970	−	1.53108i	0.846890	−	0.531769i	$-0.178472\pi$
$578$	2.11684			0.0880491
$579$	−8.48913	+	4.90120i	−0.352796	+	0.203687i
$580$	9.37228	+	3.02167i	0.389163	+	0.125468i
$581$	1.02175			0.0423893
$582$			4.05401i			0.168044i
$583$		0			0
$584$			6.92820i			0.286691i
$585$	−19.1168	−	21.1345i	−0.790384	−	0.873803i
$586$		−	2.32196i		−	0.0959192i
$587$	4.80298	+	8.31901i	0.198240	+	0.343362i	0.947958	−	0.318396i	$-0.103144\pi$
$587$	4.80298	+	8.31901i	0.198240	+	0.343362i	−0.749718	+	0.661758i	$0.769811\pi$
$588$	−3.43070	+	1.98072i	−0.141480	+	0.0816834i
$589$		0			0
$590$	−11.3723	−	3.66648i	−0.468189	−	0.150947i
$591$	−10.8614			−0.446779
$592$	5.00000	+	3.46410i	0.205499	+	0.142374i
$593$			5.69349i			0.233803i	0.993143	+	0.116902i	$0.0372963\pi$
$593$			5.69349i			0.233803i	−0.993143	+	0.116902i	$0.962704\pi$
$594$		0			0
$595$	−25.1168	+	22.7190i	−1.02969	+	0.931390i
$596$	8.18614	+	14.1788i	0.335317	+	0.580787i
$597$	−8.31386	−	14.4000i	−0.340264	−	0.589354i
$598$	−46.9783			−1.92108
$599$	9.68614	+	16.7769i	0.395765	+	0.685485i	0.993199	−	0.116433i	$-0.0371462\pi$
$599$	9.68614	+	16.7769i	0.395765	+	0.685485i	−0.597434	+	0.801918i	$0.703813\pi$
$600$	1.62772	+	3.61158i	0.0664513	+	0.147442i
$601$	−7.12772	+	12.3456i	−0.290746	+	0.503586i	−0.973986	−	0.226607i	$-0.927237\pi$
$601$	−7.12772	+	12.3456i	−0.290746	+	0.503586i	0.683241	+	0.730193i	$0.260570\pi$
$602$		−	28.1176i		−	1.14599i
$603$			27.7128i			1.12855i
$604$	5.43070	−	9.40625i	0.220972	−	0.382735i
$605$	16.5000	+	18.2414i	0.670820	+	0.741620i
$606$		−	3.46410i		−	0.140720i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$		0			0
$609$	10.4674	+	6.04334i	0.424159	+	0.244889i
$610$	−12.5584	+	11.3595i	−0.508476	+	0.459934i
$611$	7.37228	−	4.25639i	0.298251	−	0.172195i
$612$	−5.18614	+	8.98266i	−0.209637	+	0.363102i
$613$	−39.5584	−	22.8391i	−1.59775	−	0.922461i	−0.991920	−	0.126867i	$-0.959508\pi$
$613$	−39.5584	−	22.8391i	−1.59775	−	0.922461i	−0.605830	−	0.795594i	$-0.707159\pi$
$614$	−26.0584	−	15.0448i	−1.05163	−	0.607160i
$615$	2.13859	+	9.94987i	0.0862364	+	0.401218i
$616$		0			0
$617$	−11.4891	−	6.63325i	−0.462535	−	0.267045i	0.250575	−	0.968097i	$-0.419380\pi$
$617$	−11.4891	−	6.63325i	−0.462535	−	0.267045i	−0.713109	+	0.701053i	$0.752714\pi$
$618$		−	5.93354i		−	0.238682i
$619$	30.4674			1.22459			0.612294	−	0.790630i	$-0.290247\pi$
$619$	30.4674			1.22459			0.612294	+	0.790630i	$0.290247\pi$
$620$	−2.31386	−	0.746000i	−0.0929268	−	0.0299601i
$621$		−	37.2203i		−	1.49360i
$622$	20.9198	−	12.0781i	0.838809	−	0.484286i
$623$	44.7446			1.79265
$624$	3.68614	−	2.12819i	0.147564	−	0.0851960i
$625$	−24.5000	−	4.97494i	−0.980000	−	0.198997i
$626$	11.6753	+	20.2222i	0.466637	+	0.808240i
$627$		0			0
$628$			13.4140i			0.535276i
$629$	21.8614	+	15.1460i	0.871671	+	0.603912i
$630$	−3.86141	−	17.9653i	−0.153842	−	0.715755i
$631$	−36.1753	−	20.8858i	−1.44011	−	0.831451i	−0.442258	−	0.896888i	$-0.645822\pi$
$631$	−36.1753	−	20.8858i	−1.44011	−	0.831451i	−0.997857	+	0.0654374i	$0.979156\pi$
$632$	10.1168	−	5.84096i	0.402426	−	0.232341i
$633$	5.13859	−	2.96677i	0.204241	−	0.117918i
$634$	−17.3614	+	10.0236i	−0.689510	+	0.398089i
$635$	−8.13859	−	37.8651i	−0.322970	−	1.50263i
$636$	−1.68614	−	2.92048i	−0.0668598	−	0.115805i
$637$	−26.8614			−1.06429
$638$		0			0
$639$	−20.7446			−0.820642
$640$	2.18614	−	0.469882i	0.0864148	−	0.0185737i
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$	−7.68614	−	13.3128i	−0.303348	−	0.525414i
$643$	−20.8614			−0.822694			−0.411347	−	0.911479i	$-0.634941\pi$
$643$	−20.8614			−0.822694			−0.411347	+	0.911479i	$0.634941\pi$
$644$	−26.2337	−	15.1460i	−1.03375	−	0.596837i
$645$	−13.6861	−	4.41248i	−0.538891	−	0.173741i
$646$		0			0
$647$	0.255437	+	0.442430i	0.0100423	+	0.0173937i	0.871003	−	0.491278i	$-0.163470\pi$
$647$	0.255437	+	0.442430i	0.0100423	+	0.0173937i	−0.860961	+	0.508672i	$0.830137\pi$
$648$	−1.87228	−	3.24289i	−0.0735502	−	0.127393i
$649$		0			0
$650$	−2.68614	+	26.7268i	−0.105359	+	1.04831i
$651$	−2.58422	−	1.49200i	−0.101284	−	0.0584761i
$652$	−0.116844			−0.00457596
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$	3.11684	+	14.5012i	0.121785	+	0.566609i
$656$	5.74456			0.224287
$657$	−14.2337	−	8.21782i	−0.555309	−	0.320608i
$658$	5.48913			0.213988
$659$	−23.4891	−	40.6844i	−0.915006	−	1.58484i	−0.806892	−	0.590699i	$-0.798852\pi$
$659$	−23.4891	−	40.6844i	−0.915006	−	1.58484i	−0.108115	−	0.994138i	$-0.534481\pi$
$660$		0			0
$661$	0.207890	−	0.120025i	0.00808599	−	0.00466845i	−0.495952	−	0.868350i	$-0.665181\pi$
$661$	0.207890	−	0.120025i	0.00808599	−	0.00466845i	0.504038	+	0.863682i	$0.331847\pi$
$662$	24.0000	−	13.8564i	0.932786	−	0.538545i
$663$	16.1168	−	9.30506i	0.625926	−	0.361379i
$664$	−0.255437	−	0.147477i	−0.00991289	−	0.00572321i
$665$		0			0
$666$	−13.0475	+	6.16337i	−0.505582	+	0.238826i
$667$			38.5099i			1.49111i
$668$	8.74456	−	15.1460i	0.338337	−	0.586017i
$669$	0.510875	+	0.884861i	0.0197516	+	0.0342107i
$670$	19.3723	−	17.5229i	0.748417	−	0.676968i
$671$		0			0
$672$	2.74456			0.105874
$673$	6.00000	−	3.46410i	0.231283	−	0.133531i	−0.379881	−	0.925035i	$-0.624035\pi$
$673$	6.00000	−	3.46410i	0.231283	−	0.133531i	0.611164	+	0.791504i	$0.290702\pi$
$674$		−	11.0371i		−	0.425134i
$675$	−21.1753	−	2.12819i	−0.815036	−	0.0819142i
$676$	15.8614			0.610054
$677$		−	28.0627i		−	1.07854i	−0.842134	−	0.539268i	$-0.818701\pi$
$677$		−	28.0627i		−	1.07854i	0.842134	−	0.539268i	$-0.181299\pi$
$678$	−9.76631	−	5.63858i	−0.375073	−	0.216548i
$679$	−15.3505	+	8.86263i	−0.589099	+	0.340117i
$680$	9.55842	−	2.05446i	0.366549	−	0.0787848i
$681$	3.17527	+	1.83324i	0.121676	+	0.0702499i
$682$		0			0
$683$	14.0584	−	24.3499i	0.537931	−	0.931723i	−0.461085	−	0.887356i	$-0.652540\pi$
$683$	14.0584	−	24.3499i	0.537931	−	0.931723i	0.999015	−	0.0443670i	$-0.0141271\pi$
$684$		0			0
$685$	−9.93070	+	8.98266i	−0.379433	+	0.343210i
$686$	6.00000	+	3.46410i	0.229081	+	0.132260i
$687$	13.6277	+	7.86797i	0.519930	+	0.300182i
$688$	−4.05842	+	7.02939i	−0.154726	+	0.267993i
$689$		−	22.8665i		−	0.871145i
$690$	−11.4891	+	10.3923i	−0.437384	+	0.395628i
$691$	4.74456	−	8.21782i	0.180492	−	0.312621i	−0.761556	−	0.648099i	$-0.775564\pi$
$691$	4.74456	−	8.21782i	0.180492	−	0.312621i	0.942048	+	0.335478i	$0.108898\pi$
$692$			24.3036i			0.923885i
$693$		0			0
$694$	−4.37228	+	7.57301i	−0.165970	+	0.287468i
$695$	−15.8614	+	3.40920i	−0.601657	+	0.129318i
$696$	−1.74456	−	3.02167i	−0.0661275	−	0.114536i
$697$	25.1168			0.951368
$698$	−3.18614	−	5.51856i	−0.120597	−	0.208880i
$699$	4.48913	+	7.77539i	0.169794	+	0.294092i
$700$	−10.1168	+	14.0588i	−0.382381	+	0.531372i
$701$	21.2554	+	12.2718i	0.802807	+	0.463501i	0.844452	−	0.535632i	$-0.179926\pi$
$701$	21.2554	+	12.2718i	0.802807	+	0.463501i	−0.0416449	+	0.999132i	$0.513260\pi$
$702$			22.8665i			0.863041i
$703$		0			0
$704$		0			0
$705$	0.861407	−	2.67181i	0.0324425	−	0.100626i
$706$	13.6753	+	23.6863i	0.514675	+	0.891444i
$707$	13.1168	−	7.57301i	0.493310	−	0.284812i
$708$	2.11684	+	3.66648i	0.0795559	+	0.137795i
$709$			2.17448i			0.0816644i	0.999166	+	0.0408322i	$0.0130009\pi$
$709$			2.17448i			0.0816644i	−0.999166	+	0.0408322i	$0.986999\pi$
$710$	13.1168	+	14.5012i	0.492266	+	0.544221i
$711$			27.7128i			1.03931i
$712$	−11.1861	−	6.45832i	−0.419218	−	0.242036i
$713$		−	9.50744i		−	0.356057i
$714$	12.0000			0.449089
$715$		0			0
$716$	−5.48913	+	3.16915i	−0.205138	+	0.118437i
$717$	13.2554			0.495033
$718$	2.31386	−	4.00772i	0.0863525	−	0.149567i
$719$	6.17527	−	10.6959i	0.230299	−	0.398889i	−0.727597	−	0.686004i	$-0.759363\pi$
$719$	6.17527	−	10.6959i	0.230299	−	0.398889i	0.957896	+	0.287116i	$0.0926964\pi$
$720$	−1.62772	+	5.04868i	−0.0606615	+	0.188153i
$721$	22.4674	−	12.9715i	0.836729	−	0.483086i
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$	−8.23369	+	14.2612i	−0.306214	+	0.530378i
$724$	−11.9307	+	20.6646i	−0.443401	+	0.767993i
$725$	21.9090	+	2.20193i	0.813678	+	0.0817777i
$726$		−	8.71516i		−	0.323450i
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	16.1168	+	9.30506i	0.597330	+	0.344869i
$729$	−1.23369			−0.0456921
$730$	3.25544	+	15.1460i	0.120489	+	0.560580i
$731$	−17.7446	+	30.7345i	−0.656306	+	1.13676i
$732$	6.00000			0.221766
$733$	32.2337	−	18.6101i	1.19058	−	0.687381i	0.232141	−	0.972682i	$-0.425427\pi$
$733$	32.2337	−	18.6101i	1.19058	−	0.687381i	0.958438	+	0.285301i	$0.0920937\pi$
$734$		−	2.17448i		−	0.0802616i
$735$	−6.56930	+	5.94215i	−0.242312	+	0.219180i
$736$	4.37228	+	7.57301i	0.161164	+	0.279145i
$737$		0			0
$738$	−6.81386	+	11.8020i	−0.250822	+	0.434436i
$739$	24.9783			0.918840			0.459420	−	0.888219i	$-0.348057\pi$
$739$	24.9783			0.918840			0.459420	+	0.888219i	$0.348057\pi$
$740$	12.5584	+	5.22360i	0.461657	+	0.192023i
$741$		0			0
$742$	7.37228	−	12.7692i	0.270645	−	0.468771i
$743$	15.6060	−	9.01011i	0.572527	−	0.330549i	−0.185631	−	0.982620i	$-0.559433\pi$
$743$	15.6060	−	9.01011i	0.572527	−	0.330549i	0.758158	+	0.652071i	$0.226099\pi$
$744$	0.430703	+	0.746000i	0.0157903	+	0.0273497i
$745$	24.5584	+	27.1504i	0.899751	+	0.994712i
$746$		−	12.1244i		−	0.443904i
$747$	0.605969	−	0.349857i	0.0221713	−	0.0128006i
$748$		0			0
$749$	33.6060	−	58.2072i	1.22794	−	2.12685i
$750$	5.25544	+	7.13058i	0.191901	+	0.260372i
$751$	32.3505			1.18049			0.590244	−	0.807225i	$-0.299032\pi$
$751$	32.3505			1.18049			0.590244	+	0.807225i	$0.299032\pi$
$752$	−1.37228	−	0.792287i	−0.0500420	−	0.0288917i
$753$	4.51087	+	7.81306i	0.164385	+	0.284724i
$754$		−	23.6588i		−	0.861603i
$755$	7.45245	−	23.1152i	0.271223	−	0.841248i
$756$	−7.37228	+	12.7692i	−0.268127	+	0.464410i
$757$	3.61684	−	6.26456i	0.131456	−	0.227689i	−0.792782	−	0.609506i	$-0.791368\pi$
$757$	3.61684	−	6.26456i	0.131456	−	0.227689i	0.924238	+	0.381816i	$0.124701\pi$
$758$	0.372281	+	0.644810i	0.0135219	+	0.0234206i
$759$		0			0
$760$		0			0
$761$	1.67527	−	2.90165i	0.0607283	−	0.105185i	−0.834063	−	0.551669i	$-0.813991\pi$
$761$	1.67527	−	2.90165i	0.0607283	−	0.105185i	0.894791	+	0.446485i	$0.147324\pi$
$762$	−6.86141	+	11.8843i	−0.248563	+	0.430523i
$763$	−26.2337			−0.949723
$764$	−1.19702	+	0.691097i	−0.0433065	+	0.0250030i
$765$	−7.11684	+	22.0742i	−0.257310	+	0.798095i
$766$	−35.4891			−1.28227
$767$			28.7075i			1.03657i
$768$	−0.686141	−	0.396143i	−0.0247590	−	0.0142946i
$769$		−	39.7995i		−	1.43521i	−0.696452	−	0.717603i	$-0.745239\pi$
$769$		−	39.7995i		−	1.43521i	0.696452	−	0.717603i	$-0.254761\pi$
$770$		0			0
$771$		−	22.0742i		−	0.794984i
$772$	6.18614	+	10.7147i	0.222644	+	0.385631i
$773$	47.1060	−	27.1966i	1.69428	−	0.978195i	0.743298	−	0.668960i	$-0.233260\pi$
$773$	47.1060	−	27.1966i	1.69428	−	0.978195i	0.950986	−	0.309235i	$-0.100073\pi$
$774$	−9.62772	−	16.6757i	−0.346061	−	0.599396i
$775$	−5.40895	−	0.543620i	−0.194295	−	0.0195274i
$776$	5.11684			0.183684
$777$	13.7228	+	9.50744i	0.492303	+	0.341078i
$778$		−	27.7677i		−	0.995521i
$779$		0			0
$780$	7.05842	−	6.38458i	0.252732	−	0.228605i
$781$		0			0
$782$	19.1168	+	33.1113i	0.683617	+	1.18406i
$783$	18.7446			0.669876
$784$	2.50000	+	4.33013i	0.0892857	+	0.154647i
$785$	6.30298	+	29.3248i	0.224963	+	1.04665i
$786$	2.62772	−	4.55134i	0.0937276	−	0.162341i
$787$			29.2048i			1.04104i	0.853850	+	0.520520i	$0.174262\pi$
$787$			29.2048i			1.04104i	−0.853850	+	0.520520i	$0.825738\pi$
$788$			13.7089i			0.488360i
$789$	−4.00000	+	6.92820i	−0.142404	+	0.246651i
$790$	19.3723	−	17.5229i	0.689235	−	0.623436i
$791$		−	49.3069i		−	1.75315i
$792$		0			0
$793$	35.2337	+	20.3422i	1.25118	+	0.722372i
$794$	−2.61684	−	1.51084i	−0.0928683	−	0.0536175i
$795$	−5.05842	−	5.59230i	−0.179404	−	0.198338i
$796$	−18.1753	+	10.4935i	−0.644205	+	0.371932i
$797$	−6.68614	+	11.5807i	−0.236835	+	0.410211i	−0.959804	−	0.280670i	$-0.909443\pi$
$797$	−6.68614	+	11.5807i	−0.236835	+	0.410211i	0.722969	+	0.690880i	$0.242777\pi$
$798$		0			0
$799$	−6.00000	−	3.46410i	−0.212265	−	0.122551i
$800$	4.55842	−	2.05446i	0.161165	−	0.0726360i
$801$	26.5367	−	15.3210i	0.937627	−	0.541339i
$802$	11.4891	+	6.63325i	0.405695	+	0.234228i
$803$		0			0
$804$	−9.25544			−0.326414
$805$	−64.4674	−	20.7846i	−2.27218	−	0.732561i
$806$			5.84096i			0.205739i
$807$	−0.350532	+	0.202380i	−0.0123393	+	0.00712410i
$808$	−4.37228			−0.153816
$809$	−30.4307	+	17.5692i	−1.06989	+	0.617699i	−0.928150	−	0.372205i	$-0.878602\pi$
$809$	−30.4307	+	17.5692i	−1.06989	+	0.617699i	−0.141736	+	0.989904i	$0.545268\pi$
$810$	−5.61684	−	6.20965i	−0.197356	−	0.218185i
$811$	12.1168	+	20.9870i	0.425480	+	0.736953i	0.996465	−	0.0840075i	$-0.0267720\pi$
$811$	12.1168	+	20.9870i	0.425480	+	0.736953i	−0.570985	+	0.820960i	$0.693439\pi$
$812$	7.62772	−	13.2116i	0.267680	−	0.463636i
$813$			10.0048i			0.350883i
$814$		0			0
$815$	−0.255437	+	0.0549029i	−0.00894758	+	0.00192316i
$816$	−3.00000	−	1.73205i	−0.105021	−	0.0606339i
$817$		0			0
$818$	−25.5000	+	14.7224i	−0.891587	+	0.514758i
$819$	−38.2337	+	22.0742i	−1.33599	+	0.771336i
$820$	12.5584	−	2.69927i	0.438559	−	0.0942625i
$821$	−1.11684	−	1.93443i	−0.0389781	−	0.0675121i	0.845878	−	0.533376i	$-0.179077\pi$
$821$	−1.11684	−	1.93443i	−0.0389781	−	0.0675121i	−0.884856	+	0.465864i	$0.845744\pi$
$822$	4.74456			0.165486
$823$	13.1168	+	7.57301i	0.457224	+	0.263979i	0.710876	−	0.703317i	$-0.248298\pi$
$823$	13.1168	+	7.57301i	0.457224	+	0.263979i	−0.253652	+	0.967296i	$0.581632\pi$
$824$	−7.48913			−0.260896
$825$		0			0
$826$	−9.25544	+	16.0309i	−0.322038	+	0.557786i
$827$	−20.2337	−	35.0458i	−0.703594	−	1.21866i	−0.967196	−	0.254030i	$-0.918244\pi$
$827$	−20.2337	−	35.0458i	−0.703594	−	1.21866i	0.263602	−	0.964631i	$-0.415089\pi$
$828$	−20.7446			−0.720923
$829$	32.2337	+	18.6101i	1.11952	+	0.646356i	0.941279	−	0.337630i	$-0.109625\pi$
$829$	32.2337	+	18.6101i	1.11952	+	0.646356i	0.178243	+	0.983986i	$0.442959\pi$
$830$	−0.627719	−	0.202380i	−0.0217884	−	0.00702470i
$831$	−4.80298	−	2.77300i	−0.166614	−	0.0961945i
$832$	−2.68614	−	4.65253i	−0.0931252	−	0.161298i
$833$	10.9307	+	18.9325i	0.378726	+	0.655973i
$834$	4.97825	+	2.87419i	0.172383	+	0.0995252i
$835$	12.0000	−	37.2203i	0.415277	−	1.28806i
$836$		0			0
$837$	−4.62772			−0.159957
$838$	−14.4891	−	25.0959i	−0.500519	−	0.866924i
$839$	7.19702	−	12.4656i	0.248469	−	0.430360i	−0.714633	−	0.699500i	$-0.753406\pi$
$839$	7.19702	−	12.4656i	0.248469	−	0.430360i	0.963101	+	0.269140i	$0.0867394\pi$
$840$	6.00000	−	1.28962i	0.207020	−	0.0444961i
$841$	9.60597			0.331240
$842$	16.6753	+	9.62747i	0.574668	+	0.331785i
$843$	10.8614			0.374087
$844$	−3.74456	−	6.48577i	−0.128893	−	0.223250i
$845$	34.6753	−	7.45299i	1.19287	−	0.256391i
$846$	3.25544	−	1.87953i	0.111924	−	0.0646195i
$847$	33.0000	−	19.0526i	1.13389	−	0.654654i
$848$	−3.68614	+	2.12819i	−0.126583	+	0.0730825i
$849$	−13.8030	−	7.96916i	−0.473717	−	0.273501i
$850$	19.9307	−	8.98266i	0.683617	−	0.308103i
$851$	−4.37228	+	53.0111i	−0.149880	+	1.81720i
$852$		−	6.92820i		−	0.237356i
$853$	−16.6168	+	28.7812i	−0.568950	+	0.985450i	0.427720	+	0.903911i	$0.359317\pi$
$853$	−16.6168	+	28.7812i	−0.568950	+	0.985450i	−0.996670	+	0.0815390i	$0.974016\pi$
$854$	13.1168	+	22.7190i	0.448849	+	0.777430i
$855$		0			0
$856$	−16.8030	+	9.70121i	−0.574314	+	0.331580i
$857$	−9.86141			−0.336859			−0.168430	−	0.985714i	$-0.553870\pi$
$857$	−9.86141			−0.336859			−0.168430	+	0.985714i	$0.553870\pi$
$858$		0			0
$859$		−	3.46410i		−	0.118194i	−0.998252	−	0.0590968i	$-0.981178\pi$
$859$		−	3.46410i		−	0.118194i	0.998252	−	0.0590968i	$-0.0188221\pi$
$860$	−5.56930	+	17.2742i	−0.189911	+	0.589046i
$861$	15.7663			0.537314
$862$		−	5.25106i		−	0.178852i
$863$	−33.6060	−	19.4024i	−1.14396	−	0.660466i	−0.196552	−	0.980493i	$-0.562975\pi$
$863$	−33.6060	−	19.4024i	−1.14396	−	0.660466i	−0.947408	+	0.320027i	$0.896308\pi$
$864$	3.68614	−	2.12819i	0.125405	−	0.0724026i
$865$	11.4198	+	53.1311i	0.388286	+	1.80651i
$866$	−7.67527	−	4.43132i	−0.260816	−	0.150582i
$867$	−1.45245	−	0.838574i	−0.0493279	−	0.0284795i
$868$	−1.88316	+	3.26172i	−0.0639185	+	0.110710i
$869$		0			0
$870$	−5.23369	−	5.78606i	−0.177439	−	0.196166i
$871$	−54.3505	−	31.3793i	−1.84160	−	1.06325i
$872$	6.55842	+	3.78651i	0.222096	+	0.128227i
$873$	−6.06930	+	10.5123i	−0.205415	+	0.355788i
$874$		0			0
$875$	−15.5109	+	35.4882i	−0.524363	+	1.19972i
$876$	2.74456	−	4.75372i	0.0927302	−	0.160613i
$877$		−	43.7060i		−	1.47585i	−0.674884	−	0.737924i	$-0.735806\pi$
$877$		−	43.7060i		−	1.47585i	0.674884	−	0.737924i	$-0.264194\pi$
$878$		−	26.6256i		−	0.898570i
$879$	−0.919829	+	1.59319i	−0.0310250	+	0.0537370i
$880$		0			0
$881$	0.558422	+	0.967215i	0.0188137	+	0.0325863i	0.875279	−	0.483618i	$-0.160678\pi$
$881$	0.558422	+	0.967215i	0.0188137	+	0.0325863i	−0.856465	+	0.516205i	$0.827344\pi$
$882$	−11.8614			−0.399394
$883$	3.82473	+	6.62463i	0.128713	+	0.222937i	0.923178	−	0.384373i	$-0.125582\pi$
$883$	3.82473	+	6.62463i	0.128713	+	0.222937i	−0.794465	+	0.607309i	$0.792249\pi$
$884$	−11.7446	−	20.3422i	−0.395012	−	0.684182i
$885$	6.35053	+	7.02078i	0.213471	+	0.236001i
$886$	27.6861	+	15.9846i	0.930134	+	0.537013i
$887$		−	11.3870i		−	0.382337i	−0.981557	−	0.191169i	$-0.938772\pi$
$887$		−	11.3870i		−	0.382337i	0.981557	−	0.191169i	$-0.0612277\pi$
$888$	−2.05842	−	4.35758i	−0.0690761	−	0.146231i
$889$	−60.0000			−2.01234
$890$	−27.4891	−	8.86263i	−0.921438	−	0.297076i
$891$		0			0
$892$	1.11684	−	0.644810i	0.0373947	−	0.0215898i
$893$		0			0
$894$		−	12.9715i		−	0.433833i
$895$	−10.5109	+	9.50744i	−0.351340	+	0.317799i
$896$		−	3.46410i		−	0.115728i
$897$	32.2337	+	18.6101i	1.07625	+	0.621374i
$898$			29.7947i			0.994263i
$899$	4.78806			0.159691
$900$	−1.18614	+	11.8020i	−0.0395380	+	0.393398i
$901$	−16.1168	+	9.30506i	−0.536930	+	0.309997i
$902$		0			0
$903$	−11.1386	+	19.2926i	−0.370669	+	0.642018i
$904$	−7.11684	+	12.3267i	−0.236703	+	0.409981i
$905$	−16.3723	+	50.7817i	−0.544233	+	1.68804i
$906$	−7.45245	+	4.30268i	−0.247591	+	0.142947i
$907$	24.7446	+	42.8588i	0.821630	+	1.42310i	0.904468	+	0.426541i	$0.140268\pi$
$907$	24.7446	+	42.8588i	0.821630	+	1.42310i	−0.0828383	+	0.996563i	$0.526399\pi$
$908$	2.31386	−	4.00772i	0.0767881	−	0.133001i
$909$	5.18614	−	8.98266i	0.172013	−	0.297936i
$910$	39.6060	+	12.7692i	1.31293	+	0.423294i
$911$			33.6636i			1.11532i	0.830068	+	0.557662i	$0.188302\pi$
$911$			33.6636i			1.11532i	−0.830068	+	0.557662i	$0.811698\pi$
$912$		0			0
$913$		0			0
$914$	−20.6060			−0.681585
$915$	13.1168	−	2.81929i	0.433629	−	0.0932029i
$916$	9.93070	−	17.2005i	0.328120	−	0.568320i
$917$	22.9783			0.758809
$918$	16.1168	−	9.30506i	0.531935	−	0.307113i
$919$		−	3.46410i		−	0.114270i	−0.998366	−	0.0571351i	$-0.981803\pi$
$919$		−	3.46410i		−	0.114270i	0.998366	−	0.0571351i	$-0.0181966\pi$
$920$	13.1168	+	14.5012i	0.432450	+	0.478091i
$921$	11.9198	+	20.6457i	0.392772	+	0.680301i
$922$	0.861407	−	0.497333i	0.0283689	−	0.0163788i
$923$	23.4891	−	40.6844i	0.773154	−	1.33914i
$924$		0			0
$925$	29.9090	+	5.51856i	0.983400	+	0.181449i
$926$	27.4891			0.903349
$927$	8.88316	−	15.3861i	0.291761	−	0.505345i
$928$	−3.81386	+	2.20193i	−0.125196	+	0.0722820i
$929$	3.98913	+	6.90937i	0.130879	+	0.226689i	0.924016	−	0.382355i	$-0.124887\pi$
$929$	3.98913	+	6.90937i	0.130879	+	0.226689i	−0.793137	+	0.609044i	$0.791553\pi$
$930$	1.29211	+	1.42848i	0.0423700	+	0.0468417i
$931$		0			0
$932$	9.81386	−	5.66603i	0.321464	−	0.185597i
$933$	−19.1386			−0.626569
$934$	8.31386	−	14.4000i	0.272038	−	0.471183i
$935$		0			0
$936$	12.7446			0.416569
$937$	−51.5584	−	29.7673i	−1.68434	−	0.972454i	−0.958717	−	0.284362i	$-0.908218\pi$
$937$	−51.5584	−	29.7673i	−1.68434	−	0.972454i	−0.725623	−	0.688092i	$-0.758448\pi$
$938$	−20.2337	−	35.0458i	−0.660653	−	1.14429i
$939$		−	18.5003i		−	0.603735i
$940$	−3.37228	−	1.08724i	−0.109992	−	0.0354619i
$941$	−7.93070	+	13.7364i	−0.258534	+	0.447793i	−0.965849	−	0.259105i	$-0.916573\pi$
$941$	−7.93070	+	13.7364i	−0.258534	+	0.447793i	0.707316	+	0.706898i	$0.249906\pi$
$942$	5.31386	−	9.20387i	0.173135	−	0.299878i
$943$	25.1168	+	43.5036i	0.817917	+	1.41667i
$944$	4.62772	−	2.67181i	0.150619	−	0.0869602i
$945$	−10.1168	+	31.3793i	−0.329101	+	1.02077i
$946$		0			0
$947$	−5.56930	+	9.64630i	−0.180978	+	0.313463i	−0.942214	−	0.335012i	$-0.891260\pi$
$947$	−5.56930	+	9.64630i	−0.180978	+	0.313463i	0.761236	+	0.648475i	$0.224593\pi$
$948$	−9.25544			−0.300603
$949$	32.2337	−	18.6101i	1.04635	−	0.604110i
$950$		0			0
$951$	15.8832			0.515047
$952$		−	15.1460i		−	0.490886i
$953$	−11.4891	−	6.63325i	−0.372169	−	0.214872i	0.302236	−	0.953233i	$-0.402267\pi$
$953$	−11.4891	−	6.63325i	−0.372169	−	0.214872i	−0.674406	+	0.738361i	$0.735600\pi$
$954$		−	10.0974i		−	0.326914i
$955$	−2.29211	+	2.07329i	−0.0741709	+	0.0670901i
$956$		−	16.7306i		−	0.541106i
$957$		0			0
$958$	5.91983	−	3.41781i	0.191261	−	0.110425i
$959$	10.3723	+	17.9653i	0.334938	+	0.580130i
$960$	−1.68614	−	0.543620i	−0.0544200	−	0.0175453i
$961$	29.8179			0.961868
$962$	2.68614	−	32.5677i	0.0866047	−	1.05003i
$963$		−	46.0280i		−	1.48323i
$964$	18.0000	+	10.3923i	0.579741	+	0.334714i
$965$	18.5584	+	20.5171i	0.597417	+	0.660469i
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	−0.116844	−	0.202380i	−0.00375745	−	0.00650809i	0.864141	−	0.503251i	$-0.167863\pi$
$967$	−0.116844	−	0.202380i	−0.00375745	−	0.00650809i	−0.867898	+	0.496742i	$0.834529\pi$
$968$	−11.0000			−0.353553
$969$		0			0
$970$	11.1861	−	2.40431i	0.359165	−	0.0771978i
$971$	−14.4891	+	25.0959i	−0.464978	+	0.805366i	−0.999201	−	0.0399782i	$-0.987271\pi$
$971$	−14.4891	+	25.0959i	−0.464978	+	0.805366i	0.534222	+	0.845344i	$0.320604\pi$
$972$			15.7359i			0.504730i
$973$			25.1336i			0.805745i
$974$	1.00000	−	1.73205i	0.0320421	−	0.0554985i
$975$	12.4307	−	17.2742i	0.398101	−	0.553218i
$976$		−	7.57301i		−	0.242406i
$977$	10.8832	−	18.8502i	0.348183	−	0.603071i	−0.637744	−	0.770249i	$-0.720132\pi$
$977$	10.8832	−	18.8502i	0.348183	−	0.603071i	0.985927	+	0.167178i	$0.0534654\pi$
$978$	0.0801714	+	0.0462870i	0.00256360	+	0.00148009i
$979$		0			0
$980$	7.50000	+	8.29156i	0.239579	+	0.264864i
$981$	−15.5584	+	8.98266i	−0.496742	+	0.286794i
$982$	−18.8614	+	32.6689i	−0.601892	+	1.04251i
$983$	−43.3723	−	25.0410i	−1.38336	−	0.798684i	−0.390805	−	0.920473i	$-0.627803\pi$
$983$	−43.3723	−	25.0410i	−1.38336	−	0.798684i	−0.992556	+	0.121790i	$0.961137\pi$
$984$	−3.94158	−	2.27567i	−0.125653	−	0.0725457i
$985$	6.44158	+	29.9696i	0.205246	+	0.954912i
$986$	−16.6753	+	9.62747i	−0.531049	+	0.306601i
$987$	−3.76631	−	2.17448i	−0.119883	−	0.0692145i
$988$		0			0
$989$	−70.9783			−2.25698
$990$		0			0
$991$		−	16.2333i		−	0.515667i	−0.966189	−	0.257833i	$-0.916991\pi$
$991$		−	16.2333i		−	0.515667i	0.966189	−	0.257833i	$-0.0830086\pi$
$992$	0.941578	−	0.543620i	0.0298951	−	0.0172600i
$993$	−21.9565			−0.696769
$994$	26.2337	−	15.1460i	0.832082	−	0.480403i
$995$	−34.8030	+	31.4805i	−1.10333	+	0.997998i
$996$	0.116844	+	0.202380i	0.00370234	+	0.00641265i
$997$	7.94158	−	13.7552i	0.251512	−	0.435632i	−0.712430	−	0.701743i	$-0.752405\pi$
$997$	7.94158	−	13.7552i	0.251512	−	0.435632i	0.963942	+	0.266111i	$0.0857388\pi$
$998$			13.8564i			0.438617i
$999$	25.8030	+	2.12819i	0.816370	+	0.0673331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.a.249.2	yes	4
5.4	even	2		370.2.m.b.249.1	yes	4
37.11	even	6		370.2.m.b.159.1	yes	4
185.159	even	6	inner	370.2.m.a.159.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.a.159.2	✓	4	185.159	even	6	inner
370.2.m.a.249.2	yes	4	1.1	even	1	trivial
370.2.m.b.159.1	yes	4	37.11	even	6
370.2.m.b.249.1	yes	4	5.4	even	2

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.686141 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 1.65831i) q^{5} +0.792287i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-1.18614 + 2.05446i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.686141 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 1.65831i) q^{5} +0.792287i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-1.18614 + 2.05446i) q^{9} +(2.18614 - 0.469882i) q^{10} +(-0.686141 - 0.396143i) q^{12} +(-2.68614 - 4.65253i) q^{13} -3.46410i q^{14} +(-1.68614 - 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18614 + 3.78651i) q^{17} +(-1.18614 - 2.05446i) q^{18} +(-0.686141 + 2.12819i) q^{20} +(-1.37228 + 2.37686i) q^{21} -8.74456 q^{23} +(0.686141 - 0.396143i) q^{24} +(-0.500000 + 4.97494i) q^{25} +5.37228 q^{26} +4.25639i q^{27} +(3.00000 + 1.73205i) q^{28} -4.40387i q^{29} +(1.31386 - 1.18843i) q^{30} +1.08724i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.18614 - 3.78651i) q^{34} +(7.37228 + 2.37686i) q^{35} +2.37228 q^{36} +(0.500000 - 6.06218i) q^{37} +(-3.68614 - 2.12819i) q^{39} +(-1.50000 - 1.65831i) q^{40} +(-2.87228 - 4.97494i) q^{41} +(-1.37228 - 2.37686i) q^{42} +8.11684 q^{43} +(5.18614 - 1.11469i) q^{45} +(4.37228 - 7.57301i) q^{46} +1.58457i q^{47} +0.792287i q^{48} +(2.50000 - 4.33013i) q^{49} +(-4.05842 - 2.92048i) q^{50} +3.46410i q^{51} +(-2.68614 + 4.65253i) q^{52} +(3.68614 + 2.12819i) q^{53} +(-3.68614 - 2.12819i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(3.81386 + 2.20193i) q^{58} +(-4.62772 - 2.67181i) q^{59} +(0.372281 + 1.73205i) q^{60} +(-6.55842 + 3.78651i) q^{61} +(-0.941578 - 0.543620i) q^{62} -8.21782i q^{63} +1.00000 q^{64} +(-3.68614 + 11.4333i) q^{65} +(10.1168 - 5.84096i) q^{67} +4.37228 q^{68} +(-6.00000 + 3.46410i) q^{69} +(-5.74456 + 5.19615i) q^{70} +(4.37228 + 7.57301i) q^{71} +(-1.18614 + 2.05446i) q^{72} +6.92820i q^{73} +(5.00000 + 3.46410i) q^{74} +(1.62772 + 3.61158i) q^{75} +(3.68614 - 2.12819i) q^{78} +(10.1168 - 5.84096i) q^{79} +(2.18614 - 0.469882i) q^{80} +(-1.87228 - 3.24289i) q^{81} +5.74456 q^{82} +(-0.255437 - 0.147477i) q^{83} +2.74456 q^{84} +(9.55842 - 2.05446i) q^{85} +(-4.05842 + 7.02939i) q^{86} +(-1.74456 - 3.02167i) q^{87} +(-11.1861 - 6.45832i) q^{89} +(-1.62772 + 5.04868i) q^{90} +(16.1168 + 9.30506i) q^{91} +(4.37228 + 7.57301i) q^{92} +(0.430703 + 0.746000i) q^{93} +(-1.37228 - 0.792287i) q^{94} +(-0.686141 - 0.396143i) q^{96} +5.11684 q^{97} +(2.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9	\( 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9} + 3 q^{10} + 3 q^{12} - 5 q^{13} - q^{15} - 2 q^{16} - 3 q^{17} + q^{18} + 3 q^{20} + 6 q^{21} - 12 q^{23} - 3 q^{24} - 2 q^{25} + 10 q^{26} + 12 q^{28} + 11 q^{30} - 2 q^{32} - 3 q^{34} + 18 q^{35} - 2 q^{36} + 2 q^{37} - 9 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} + 15 q^{45} + 6 q^{46} + 10 q^{49} + q^{50} - 5 q^{52} + 9 q^{53} - 9 q^{54} - 12 q^{56} + 21 q^{58} - 30 q^{59} - 10 q^{60} - 9 q^{61} - 21 q^{62} + 4 q^{64} - 9 q^{65} + 6 q^{67} + 6 q^{68} - 24 q^{69} + 6 q^{71} + q^{72} + 20 q^{74} + 18 q^{75} + 9 q^{78} + 6 q^{79} + 3 q^{80} + 4 q^{81} - 24 q^{83} - 12 q^{84} + 21 q^{85} + q^{86} + 16 q^{87} - 39 q^{89} - 18 q^{90} + 30 q^{91} + 6 q^{92} - 27 q^{93} + 6 q^{94} + 3 q^{96} - 14 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9 + 3 * q^10 + 3 * q^12 - 5 * q^13 - q^15 - 2 * q^16 - 3 * q^17 + q^18 + 3 * q^20 + 6 * q^21 - 12 * q^23 - 3 * q^24 - 2 * q^25 + 10 * q^26 + 12 * q^28 + 11 * q^30 - 2 * q^32 - 3 * q^34 + 18 * q^35 - 2 * q^36 + 2 * q^37 - 9 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 + 15 * q^45 + 6 * q^46 + 10 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 9 * q^54 - 12 * q^56 + 21 * q^58 - 30 * q^59 - 10 * q^60 - 9 * q^61 - 21 * q^62 + 4 * q^64 - 9 * q^65 + 6 * q^67 + 6 * q^68 - 24 * q^69 + 6 * q^71 + q^72 + 20 * q^74 + 18 * q^75 + 9 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 - 24 * q^83 - 12 * q^84 + 21 * q^85 + q^86 + 16 * q^87 - 39 * q^89 - 18 * q^90 + 30 * q^91 + 6 * q^92 - 27 * q^93 + 6 * q^94 + 3 * q^96 - 14 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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