LMFDB - Embedded newform 390.2.j.b.187.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(73,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 396x^{12} + 2412x^{10} + 7716x^{8} + 12984x^{6} + 10756x^{4} + 3648x^{2} + 256 $ x^16 + 32x^14 + 396x^12 + 2412x^10 + 7716x^8 + 12984x^6 + 10756x^4 + 3648*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.5
Root			$3.14581i$ of defining polynomial
Character	$\chi$	$=$	390.187
Dual form			390.2.j.b.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 - 0.227886i) q^{5} +(0.707107 - 0.707107i) q^{6} -4.05336i q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 - 0.227886i) q^{5} +(0.707107 - 0.707107i) q^{6} -4.05336i q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.22443 - 0.227886i) q^{10} +(1.63560 + 1.63560i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.18675 - 1.68659i) q^{13} -4.05336i q^{14} +(-1.73405 + 1.41177i) q^{15} +1.00000 q^{16} +(0.932546 - 0.932546i) q^{17} -1.00000i q^{18} +(-4.66558 - 4.66558i) q^{19} +(-2.22443 - 0.227886i) q^{20} +(-2.86616 - 2.86616i) q^{21} +(1.63560 + 1.63560i) q^{22} +(3.93804 + 3.93804i) q^{23} +(0.707107 - 0.707107i) q^{24} +(4.89614 + 1.01383i) q^{25} +(3.18675 - 1.68659i) q^{26} +(-0.707107 - 0.707107i) q^{27} -4.05336i q^{28} +6.86725i q^{29} +(-1.73405 + 1.41177i) q^{30} +(-6.67096 + 6.67096i) q^{31} +1.00000 q^{32} +2.31309 q^{33} +(0.932546 - 0.932546i) q^{34} +(-0.923704 + 9.01640i) q^{35} -1.00000i q^{36} +8.04614i q^{37} +(-4.66558 - 4.66558i) q^{38} +(1.06077 - 3.44598i) q^{39} +(-2.22443 - 0.227886i) q^{40} +(6.69985 - 6.69985i) q^{41} +(-2.86616 - 2.86616i) q^{42} +(-2.58651 - 2.58651i) q^{43} +(1.63560 + 1.63560i) q^{44} +(-0.227886 + 2.22443i) q^{45} +(3.93804 + 3.93804i) q^{46} -0.559306i q^{47} +(0.707107 - 0.707107i) q^{48} -9.42974 q^{49} +(4.89614 + 1.01383i) q^{50} -1.31882i q^{51} +(3.18675 - 1.68659i) q^{52} +(-6.34712 + 6.34712i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-3.26554 - 4.01100i) q^{55} -4.05336i q^{56} -6.59812 q^{57} +6.86725i q^{58} +(-2.29565 + 2.29565i) q^{59} +(-1.73405 + 1.41177i) q^{60} +6.48216 q^{61} +(-6.67096 + 6.67096i) q^{62} -4.05336 q^{63} +1.00000 q^{64} +(-7.47305 + 3.02549i) q^{65} +2.31309 q^{66} +7.13460 q^{67} +(0.932546 - 0.932546i) q^{68} +5.56923 q^{69} +(-0.923704 + 9.01640i) q^{70} +(5.56896 - 5.56896i) q^{71} -1.00000i q^{72} +7.36347 q^{73} +8.04614i q^{74} +(4.17898 - 2.74520i) q^{75} +(-4.66558 - 4.66558i) q^{76} +(6.62968 - 6.62968i) q^{77} +(1.06077 - 3.44598i) q^{78} +1.91721i q^{79} +(-2.22443 - 0.227886i) q^{80} -1.00000 q^{81} +(6.69985 - 6.69985i) q^{82} +0.718668i q^{83} +(-2.86616 - 2.86616i) q^{84} +(-2.28689 + 1.86186i) q^{85} +(-2.58651 - 2.58651i) q^{86} +(4.85588 + 4.85588i) q^{87} +(1.63560 + 1.63560i) q^{88} +(-4.02209 + 4.02209i) q^{89} +(-0.227886 + 2.22443i) q^{90} +(-6.83638 - 12.9171i) q^{91} +(3.93804 + 3.93804i) q^{92} +9.43416i q^{93} -0.559306i q^{94} +(9.31501 + 11.4414i) q^{95} +(0.707107 - 0.707107i) q^{96} -6.60149 q^{97} -9.42974 q^{98} +(1.63560 - 1.63560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 4 q^{11} + 4 q^{13} + 4 q^{15} + 16 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{21} + 4 q^{22} + 16 q^{23} - 16 q^{25} + 4 q^{26} + 4 q^{30} + 12 q^{31} + 16 q^{32} + 4 q^{34} - 12 q^{35} + 4 q^{38} - 4 q^{39} + 4 q^{41} - 8 q^{42} - 16 q^{43} + 4 q^{44} + 16 q^{46} - 80 q^{49} - 16 q^{50} + 4 q^{52} - 44 q^{53} - 20 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{60} - 32 q^{61} + 12 q^{62} + 16 q^{64} - 44 q^{65} - 32 q^{67} + 4 q^{68} - 16 q^{69} - 12 q^{70} + 16 q^{71} + 4 q^{76} - 32 q^{77} - 4 q^{78} - 16 q^{81} + 4 q^{82} - 8 q^{84} - 64 q^{85} - 16 q^{86} + 28 q^{87} + 4 q^{88} + 4 q^{89} + 76 q^{91} + 16 q^{92} + 40 q^{95} - 8 q^{97} - 80 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 4 * q^11 + 4 * q^13 + 4 * q^15 + 16 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 + 4 * q^26 + 4 * q^30 + 12 * q^31 + 16 * q^32 + 4 * q^34 - 12 * q^35 + 4 * q^38 - 4 * q^39 + 4 * q^41 - 8 * q^42 - 16 * q^43 + 4 * q^44 + 16 * q^46 - 80 * q^49 - 16 * q^50 + 4 * q^52 - 44 * q^53 - 20 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^60 - 32 * q^61 + 12 * q^62 + 16 * q^64 - 44 * q^65 - 32 * q^67 + 4 * q^68 - 16 * q^69 - 12 * q^70 + 16 * q^71 + 4 * q^76 - 32 * q^77 - 4 * q^78 - 16 * q^81 + 4 * q^82 - 8 * q^84 - 64 * q^85 - 16 * q^86 + 28 * q^87 + 4 * q^88 + 4 * q^89 + 76 * q^91 + 16 * q^92 + 40 * q^95 - 8 * q^97 - 80 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−2.22443	−	0.227886i	−0.994793	−	0.101914i
$5$	−2.22443	−	0.227886i	−0.994793	−	0.101914i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$		−	4.05336i		−	1.53203i	−0.642825	−	0.766013i	$-0.722238\pi$
$7$		−	4.05336i		−	1.53203i	0.642825	−	0.766013i	$-0.277762\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−2.22443	−	0.227886i	−0.703425	−	0.0720639i
$11$	1.63560	+	1.63560i	0.493152	+	0.493152i	0.909298	−	0.416146i	$-0.136619\pi$
$11$	1.63560	+	1.63560i	0.493152	+	0.493152i	−0.416146	+	0.909298i	$0.636619\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.18675	−	1.68659i	0.883846	−	0.467777i
$13$	3.18675	−	1.68659i	0.883846	−	0.467777i
$14$		−	4.05336i		−	1.08331i
$15$	−1.73405	+	1.41177i	−0.447729	+	0.364517i
$16$	1.00000			0.250000
$17$	0.932546	−	0.932546i	0.226176	−	0.226176i	−0.584917	−	0.811093i	$-0.698873\pi$
$17$	0.932546	−	0.932546i	0.226176	−	0.226176i	0.811093	+	0.584917i	$0.198873\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−4.66558	−	4.66558i	−1.07036	−	1.07036i	−0.997330	−	0.0730270i	$-0.976734\pi$
$19$	−4.66558	−	4.66558i	−1.07036	−	1.07036i	−0.0730270	−	0.997330i	$-0.523266\pi$
$20$	−2.22443	−	0.227886i	−0.497397	−	0.0509568i
$21$	−2.86616	−	2.86616i	−0.625447	−	0.625447i
$22$	1.63560	+	1.63560i	0.348711	+	0.348711i
$23$	3.93804	+	3.93804i	0.821139	+	0.821139i	0.986271	−	0.165133i	$-0.0528053\pi$
$23$	3.93804	+	3.93804i	0.821139	+	0.821139i	−0.165133	+	0.986271i	$0.552805\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	4.89614	+	1.01383i	0.979227	+	0.202766i
$26$	3.18675	−	1.68659i	0.624974	−	0.330768i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		−	4.05336i		−	0.766013i
$29$			6.86725i			1.27522i	0.770361	+	0.637608i	$0.220076\pi$
$29$			6.86725i			1.27522i	−0.770361	+	0.637608i	$0.779924\pi$
$30$	−1.73405	+	1.41177i	−0.316592	+	0.257752i
$31$	−6.67096	+	6.67096i	−1.19814	+	1.19814i	−0.223417	+	0.974723i	$0.571721\pi$
$31$	−6.67096	+	6.67096i	−1.19814	+	1.19814i	−0.974723	+	0.223417i	$0.928279\pi$
$32$	1.00000			0.176777
$33$	2.31309			0.402657
$34$	0.932546	−	0.932546i	0.159930	−	0.159930i
$35$	−0.923704	+	9.01640i	−0.156135	+	1.52405i
$36$		−	1.00000i		−	0.166667i
$37$			8.04614i			1.32278i	0.750043	+	0.661389i	$0.230033\pi$
$37$			8.04614i			1.32278i	−0.750043	+	0.661389i	$0.769967\pi$
$38$	−4.66558	−	4.66558i	−0.756857	−	0.756857i
$39$	1.06077	−	3.44598i	0.169860	−	0.551798i
$40$	−2.22443	−	0.227886i	−0.351713	−	0.0360319i
$41$	6.69985	−	6.69985i	1.04634	−	1.04634i	0.0474680	−	0.998873i	$-0.484885\pi$
$41$	6.69985	−	6.69985i	1.04634	−	1.04634i	0.998873	−	0.0474680i	$-0.0151152\pi$
$42$	−2.86616	−	2.86616i	−0.442258	−	0.442258i
$43$	−2.58651	−	2.58651i	−0.394439	−	0.394439i	0.481828	−	0.876266i	$-0.339973\pi$
$43$	−2.58651	−	2.58651i	−0.394439	−	0.394439i	−0.876266	+	0.481828i	$0.839973\pi$
$44$	1.63560	+	1.63560i	0.246576	+	0.246576i
$45$	−0.227886	+	2.22443i	−0.0339712	+	0.331598i
$46$	3.93804	+	3.93804i	0.580633	+	0.580633i
$47$		−	0.559306i		−	0.0815831i	−0.999168	−	0.0407916i	$-0.987012\pi$
$47$		−	0.559306i		−	0.0815831i	0.999168	−	0.0407916i	$-0.0129880\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	−9.42974			−1.34711
$50$	4.89614	+	1.01383i	0.692418	+	0.143377i
$51$		−	1.31882i		−	0.184672i
$52$	3.18675	−	1.68659i	0.441923	−	0.233889i
$53$	−6.34712	+	6.34712i	−0.871845	+	0.871845i	−0.992673	−	0.120829i	$-0.961445\pi$
$53$	−6.34712	+	6.34712i	−0.871845	+	0.871845i	0.120829	+	0.992673i	$0.461445\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−3.26554	−	4.01100i	−0.440326	−	0.540844i
$56$		−	4.05336i		−	0.541653i
$57$	−6.59812			−0.873943
$58$			6.86725i			0.901713i
$59$	−2.29565	+	2.29565i	−0.298868	+	0.298868i	−0.840570	−	0.541703i	$-0.817780\pi$
$59$	−2.29565	+	2.29565i	−0.298868	+	0.298868i	0.541703	+	0.840570i	$0.317780\pi$
$60$	−1.73405	+	1.41177i	−0.223864	+	0.182258i
$61$	6.48216			0.829956			0.414978	−	0.909832i	$-0.363789\pi$
$61$	6.48216			0.829956			0.414978	+	0.909832i	$0.363789\pi$
$62$	−6.67096	+	6.67096i	−0.847213	+	0.847213i
$63$	−4.05336			−0.510676
$64$	1.00000			0.125000
$65$	−7.47305	+	3.02549i	−0.926917	+	0.375266i
$66$	2.31309			0.284722
$67$	7.13460			0.871630			0.435815	−	0.900036i	$-0.356460\pi$
$67$	7.13460			0.871630			0.435815	+	0.900036i	$0.356460\pi$
$68$	0.932546	−	0.932546i	0.113088	−	0.113088i
$69$	5.56923			0.670457
$70$	−0.923704	+	9.01640i	−0.110404	+	1.07767i
$71$	5.56896	−	5.56896i	0.660914	−	0.660914i	−0.294681	−	0.955596i	$-0.595213\pi$
$71$	5.56896	−	5.56896i	0.660914	−	0.660914i	0.955596	+	0.294681i	$0.0952135\pi$
$72$		−	1.00000i		−	0.117851i
$73$	7.36347			0.861829			0.430915	−	0.902393i	$-0.358191\pi$
$73$	7.36347			0.861829			0.430915	+	0.902393i	$0.358191\pi$
$74$			8.04614i			0.935345i
$75$	4.17898	−	2.74520i	0.482547	−	0.316989i
$76$	−4.66558	−	4.66558i	−0.535179	−	0.535179i
$77$	6.62968	−	6.62968i	0.755523	−	0.755523i
$78$	1.06077	−	3.44598i	0.120109	−	0.390180i
$79$			1.91721i			0.215703i	0.994167	+	0.107851i	$0.0343970\pi$
$79$			1.91721i			0.215703i	−0.994167	+	0.107851i	$0.965603\pi$
$80$	−2.22443	−	0.227886i	−0.248698	−	0.0254784i
$81$	−1.00000			−0.111111
$82$	6.69985	−	6.69985i	0.739875	−	0.739875i
$83$			0.718668i			0.0788840i	0.999222	+	0.0394420i	$0.0125580\pi$
$83$			0.718668i			0.0788840i	−0.999222	+	0.0394420i	$0.987442\pi$
$84$	−2.86616	−	2.86616i	−0.312724	−	0.312724i
$85$	−2.28689	+	1.86186i	−0.248048	+	0.201948i
$86$	−2.58651	−	2.58651i	−0.278910	−	0.278910i
$87$	4.85588	+	4.85588i	0.520605	+	0.520605i
$88$	1.63560	+	1.63560i	0.174356	+	0.174356i
$89$	−4.02209	+	4.02209i	−0.426340	+	0.426340i	−0.887380	−	0.461039i	$-0.847477\pi$
$89$	−4.02209	+	4.02209i	−0.426340	+	0.426340i	0.461039	+	0.887380i	$0.347477\pi$
$90$	−0.227886	+	2.22443i	−0.0240213	+	0.234475i
$91$	−6.83638	−	12.9171i	−0.716647	−	1.35408i
$92$	3.93804	+	3.93804i	0.410569	+	0.410569i
$93$			9.43416i			0.978277i
$94$		−	0.559306i		−	0.0576880i
$95$	9.31501	+	11.4414i	0.955700	+	1.17387i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−6.60149			−0.670280			−0.335140	−	0.942168i	$-0.608784\pi$
$97$	−6.60149			−0.670280			−0.335140	+	0.942168i	$0.608784\pi$
$98$	−9.42974			−0.952548
$99$	1.63560	−	1.63560i	0.164384	−	0.164384i
$100$	4.89614	+	1.01383i	0.489614	+	0.101383i
$101$			14.8793i			1.48055i	0.672306	+	0.740273i	$0.265304\pi$
$101$			14.8793i			1.48055i	−0.672306	+	0.740273i	$0.734696\pi$
$102$		−	1.31882i		−	0.130583i
$103$	5.70999	+	5.70999i	0.562622	+	0.562622i	0.930051	−	0.367429i	$-0.119762\pi$
$103$	5.70999	+	5.70999i	0.562622	+	0.562622i	−0.367429	+	0.930051i	$0.619762\pi$
$104$	3.18675	−	1.68659i	0.312487	−	0.165384i
$105$	5.72240	+	7.02872i	0.558449	+	0.685932i
$106$	−6.34712	+	6.34712i	−0.616487	+	0.616487i
$107$	−4.91690	−	4.91690i	−0.475335	−	0.475335i	0.428301	−	0.903636i	$-0.359112\pi$
$107$	−4.91690	−	4.91690i	−0.475335	−	0.475335i	−0.903636	+	0.428301i	$0.859112\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−12.9297	−	12.9297i	−1.23844	−	1.23844i	−0.960638	−	0.277803i	$-0.910394\pi$
$109$	−12.9297	−	12.9297i	−1.23844	−	1.23844i	−0.277803	−	0.960638i	$-0.589606\pi$
$110$	−3.26554	−	4.01100i	−0.311357	−	0.382434i
$111$	5.68948	+	5.68948i	0.540022	+	0.540022i
$112$		−	4.05336i		−	0.383007i
$113$	−5.41651	+	5.41651i	−0.509542	+	0.509542i	−0.914386	−	0.404844i	$-0.867326\pi$
$113$	−5.41651	+	5.41651i	−0.509542	+	0.509542i	0.404844	+	0.914386i	$0.367326\pi$
$114$	−6.59812			−0.617971
$115$	−7.86246	−	9.65731i	−0.733178	−	0.900548i
$116$			6.86725i			0.637608i
$117$	−1.68659	−	3.18675i	−0.155926	−	0.294615i
$118$	−2.29565	+	2.29565i	−0.211331	+	0.211331i
$119$	−3.77995	−	3.77995i	−0.346507	−	0.346507i
$120$	−1.73405	+	1.41177i	−0.158296	+	0.128876i
$121$		−	5.64961i		−	0.513601i
$122$	6.48216			0.586867
$123$		−	9.47502i		−	0.854334i
$124$	−6.67096	+	6.67096i	−0.599070	+	0.599070i
$125$	−10.6601	−	3.37095i	−0.953464	−	0.301507i
$126$	−4.05336			−0.361102
$127$	10.3854	−	10.3854i	0.921556	−	0.921556i	−0.0755835	−	0.997139i	$-0.524082\pi$
$127$	10.3854	−	10.3854i	0.921556	−	0.921556i	0.997139	+	0.0755835i	$0.0240819\pi$
$128$	1.00000			0.0883883
$129$	−3.65787			−0.322058
$130$	−7.47305	+	3.02549i	−0.655430	+	0.265353i
$131$	11.4500			1.00039			0.500195	−	0.865913i	$-0.333262\pi$
$131$	11.4500			1.00039			0.500195	+	0.865913i	$0.333262\pi$
$132$	2.31309			0.201329
$133$	−18.9113	+	18.9113i	−1.63982	+	1.63982i
$134$	7.13460			0.616335
$135$	1.41177	+	1.73405i	0.121506	+	0.149243i
$136$	0.932546	−	0.932546i	0.0799651	−	0.0799651i
$137$			20.7669i			1.77423i	0.461546	+	0.887116i	$0.347295\pi$
$137$			20.7669i			1.77423i	−0.461546	+	0.887116i	$0.652705\pi$
$138$	5.56923			0.474085
$139$		−	13.0183i		−	1.10420i	−0.833780	−	0.552098i	$-0.813828\pi$
$139$		−	13.0183i		−	1.10420i	0.833780	−	0.552098i	$-0.186172\pi$
$140$	−0.923704	+	9.01640i	−0.0780673	+	0.762025i
$141$	−0.395489	−	0.395489i	−0.0333062	−	0.0333062i
$142$	5.56896	−	5.56896i	0.467337	−	0.467337i
$143$	7.97086	+	2.45366i	0.666556	+	0.205186i
$144$		−	1.00000i		−	0.0833333i
$145$	1.56495	−	15.2757i	0.129962	−	1.26858i
$146$	7.36347			0.609405
$147$	−6.66783	+	6.66783i	−0.549954	+	0.549954i
$148$			8.04614i			0.661389i
$149$	−4.39862	−	4.39862i	−0.360349	−	0.360349i	0.503592	−	0.863941i	$-0.332011\pi$
$149$	−4.39862	−	4.39862i	−0.360349	−	0.360349i	−0.863941	+	0.503592i	$0.832011\pi$
$150$	4.17898	−	2.74520i	0.341212	−	0.224145i
$151$	−3.77985	−	3.77985i	−0.307600	−	0.307600i	0.536378	−	0.843978i	$-0.319792\pi$
$151$	−3.77985	−	3.77985i	−0.307600	−	0.307600i	−0.843978	+	0.536378i	$0.819792\pi$
$152$	−4.66558	−	4.66558i	−0.378428	−	0.378428i
$153$	−0.932546	−	0.932546i	−0.0753919	−	0.0753919i
$154$	6.62968	−	6.62968i	0.534235	−	0.534235i
$155$	16.3593	−	13.3188i	1.31401	−	1.06979i
$156$	1.06077	−	3.44598i	0.0849298	−	0.275899i
$157$	13.1242	+	13.1242i	1.04743	+	1.04743i	0.998818	+	0.0486112i	$0.0154795\pi$
$157$	13.1242	+	13.1242i	1.04743	+	1.04743i	0.0486112	+	0.998818i	$0.484520\pi$
$158$			1.91721i			0.152525i
$159$			8.97619i			0.711858i
$160$	−2.22443	−	0.227886i	−0.175856	−	0.0180160i
$161$	15.9623	−	15.9623i	1.25801	−	1.25801i
$162$	−1.00000			−0.0785674
$163$	9.96010			0.780135			0.390068	−	0.920786i	$-0.372452\pi$
$163$	9.96010			0.780135			0.390068	+	0.920786i	$0.372452\pi$
$164$	6.69985	−	6.69985i	0.523170	−	0.523170i
$165$	−5.14530	−	0.527121i	−0.400561	−	0.0410363i
$166$			0.718668i			0.0557794i
$167$		−	10.9823i		−	0.849833i	−0.905233	−	0.424916i	$-0.860304\pi$
$167$		−	10.9823i		−	0.849833i	0.905233	−	0.424916i	$-0.139696\pi$
$168$	−2.86616	−	2.86616i	−0.221129	−	0.221129i
$169$	7.31080	−	10.7495i	0.562369	−	0.826886i
$170$	−2.28689	+	1.86186i	−0.175397	+	0.142798i
$171$	−4.66558	+	4.66558i	−0.356786	+	0.356786i
$172$	−2.58651	−	2.58651i	−0.197219	−	0.197219i
$173$	−5.50754	−	5.50754i	−0.418730	−	0.418730i	0.466036	−	0.884766i	$-0.345682\pi$
$173$	−5.50754	−	5.50754i	−0.418730	−	0.418730i	−0.884766	+	0.466036i	$0.845682\pi$
$174$	4.85588	+	4.85588i	0.368123	+	0.368123i
$175$	4.10942	−	19.8458i	0.310643	−	1.50020i
$176$	1.63560	+	1.63560i	0.123288	+	0.123288i
$177$			3.24653i			0.244024i
$178$	−4.02209	+	4.02209i	−0.301468	+	0.301468i
$179$	−23.3767			−1.74726			−0.873628	−	0.486594i	$-0.838239\pi$
$179$	−23.3767			−1.74726			−0.873628	+	0.486594i	$0.838239\pi$
$180$	−0.227886	+	2.22443i	−0.0169856	+	0.165799i
$181$			15.3920i			1.14408i	0.820226	+	0.572039i	$0.193847\pi$
$181$			15.3920i			1.14408i	−0.820226	+	0.572039i	$0.806153\pi$
$182$	−6.83638	−	12.9171i	−0.506746	−	0.957477i
$183$	4.58358	−	4.58358i	0.338828	−	0.338828i
$184$	3.93804	+	3.93804i	0.290316	+	0.290316i
$185$	1.83360	−	17.8980i	0.134809	−	1.31589i
$186$			9.43416i			0.691746i
$187$	3.05055			0.223078
$188$		−	0.559306i		−	0.0407916i
$189$	−2.86616	+	2.86616i	−0.208482	+	0.208482i
$190$	9.31501	+	11.4414i	0.675782	+	0.830050i
$191$	−18.3221			−1.32574			−0.662870	−	0.748734i	$-0.730662\pi$
$191$	−18.3221			−1.32574			−0.662870	+	0.748734i	$0.730662\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	10.6298			0.765149			0.382575	−	0.923925i	$-0.375038\pi$
$193$	10.6298			0.765149			0.382575	+	0.923925i	$0.375038\pi$
$194$	−6.60149			−0.473960
$195$	−3.14490	+	7.42358i	−0.225211	+	0.531614i
$196$	−9.42974			−0.673553
$197$	−0.621588			−0.0442863			−0.0221432	−	0.999755i	$-0.507049\pi$
$197$	−0.621588			−0.0442863			−0.0221432	+	0.999755i	$0.507049\pi$
$198$	1.63560	−	1.63560i	0.116237	−	0.116237i
$199$	−5.48672			−0.388943			−0.194472	−	0.980908i	$-0.562299\pi$
$199$	−5.48672			−0.388943			−0.194472	+	0.980908i	$0.562299\pi$
$200$	4.89614	+	1.01383i	0.346209	+	0.0716886i
$201$	5.04492	−	5.04492i	0.355841	−	0.355841i
$202$			14.8793i			1.04690i
$203$	27.8354			1.95366
$204$		−	1.31882i		−	0.0923358i
$205$	−16.4301	+	13.3765i	−1.14753	+	0.934256i
$206$	5.70999	+	5.70999i	0.397834	+	0.397834i
$207$	3.93804	−	3.93804i	0.273713	−	0.273713i
$208$	3.18675	−	1.68659i	0.220962	−	0.116944i
$209$		−	15.2621i		−	1.05570i
$210$	5.72240	+	7.02872i	0.394883	+	0.485027i
$211$	12.2985			0.846666			0.423333	−	0.905974i	$-0.360860\pi$
$211$	12.2985			0.846666			0.423333	+	0.905974i	$0.360860\pi$
$212$	−6.34712	+	6.34712i	−0.435922	+	0.435922i
$213$		−	7.87570i		−	0.539634i
$214$	−4.91690	−	4.91690i	−0.336112	−	0.336112i
$215$	5.16406	+	6.34292i	0.352186	+	0.432584i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	27.0398	+	27.0398i	1.83558	+	1.83558i
$218$	−12.9297	−	12.9297i	−0.875710	−	0.875710i
$219$	5.20676	−	5.20676i	0.351840	−	0.351840i
$220$	−3.26554	−	4.01100i	−0.220163	−	0.270422i
$221$	1.39897	−	4.54462i	0.0941047	−	0.305704i
$222$	5.68948	+	5.68948i	0.381853	+	0.381853i
$223$		−	10.5250i		−	0.704806i	−0.935848	−	0.352403i	$-0.885365\pi$
$223$		−	10.5250i		−	0.704806i	0.935848	−	0.352403i	$-0.114635\pi$
$224$		−	4.05336i		−	0.270827i
$225$	1.01383	−	4.89614i	0.0675887	−	0.326409i
$226$	−5.41651	+	5.41651i	−0.360301	+	0.360301i
$227$	−17.9899			−1.19403			−0.597015	−	0.802230i	$-0.703647\pi$
$227$	−17.9899			−1.19403			−0.597015	+	0.802230i	$0.703647\pi$
$228$	−6.59812			−0.436971
$229$	1.48156	−	1.48156i	0.0979041	−	0.0979041i	−0.656458	−	0.754362i	$-0.727946\pi$
$229$	1.48156	−	1.48156i	0.0979041	−	0.0979041i	0.754362	+	0.656458i	$0.227946\pi$
$230$	−7.86246	−	9.65731i	−0.518435	−	0.636784i
$231$		−	9.37579i		−	0.616882i
$232$			6.86725i			0.450857i
$233$	2.70461	+	2.70461i	0.177185	+	0.177185i	0.790127	−	0.612943i	$-0.210014\pi$
$233$	2.70461	+	2.70461i	0.177185	+	0.177185i	−0.612943	+	0.790127i	$0.710014\pi$
$234$	−1.68659	−	3.18675i	−0.110256	−	0.208325i
$235$	−0.127458	+	1.24413i	−0.00831444	+	0.0811584i
$236$	−2.29565	+	2.29565i	−0.149434	+	0.149434i
$237$	1.35567	+	1.35567i	0.0880602	+	0.0880602i
$238$	−3.77995	−	3.77995i	−0.245017	−	0.245017i
$239$	−3.98109	−	3.98109i	−0.257515	−	0.257515i	0.566528	−	0.824043i	$-0.308286\pi$
$239$	−3.98109	−	3.98109i	−0.257515	−	0.257515i	−0.824043	+	0.566528i	$0.808286\pi$
$240$	−1.73405	+	1.41177i	−0.111932	+	0.0911291i
$241$	−15.4622	−	15.4622i	−0.996011	−	0.996011i	0.00398120	−	0.999992i	$-0.498733\pi$
$241$	−15.4622	−	15.4622i	−0.996011	−	0.996011i	−0.999992	+	0.00398120i	$0.998733\pi$
$242$		−	5.64961i		−	0.363171i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	6.48216			0.414978
$245$	20.9758	+	2.14891i	1.34009	+	0.137289i
$246$		−	9.47502i		−	0.604105i
$247$	−22.7370	−	6.99911i	−1.44672	−	0.445343i
$248$	−6.67096	+	6.67096i	−0.423606	+	0.423606i
$249$	0.508175	+	0.508175i	0.0322043	+	0.0322043i
$250$	−10.6601	−	3.37095i	−0.674201	−	0.213198i
$251$		−	17.9961i		−	1.13590i	−0.823062	−	0.567951i	$-0.807736\pi$
$251$		−	17.9961i		−	1.13590i	0.823062	−	0.567951i	$-0.192264\pi$
$252$	−4.05336			−0.255338
$253$			12.8821i			0.809893i
$254$	10.3854	−	10.3854i	0.651638	−	0.651638i
$255$	−0.300540	+	2.93361i	−0.0188206	+	0.183710i
$256$	1.00000			0.0625000
$257$	1.36406	−	1.36406i	0.0850880	−	0.0850880i	−0.663282	−	0.748370i	$-0.730837\pi$
$257$	1.36406	−	1.36406i	0.0850880	−	0.0850880i	0.748370	+	0.663282i	$0.230837\pi$
$258$	−3.65787			−0.227729
$259$	32.6139			2.02653
$260$	−7.47305	+	3.02549i	−0.463459	+	0.187633i
$261$	6.86725			0.425072
$262$	11.4500			0.707382
$263$	−2.33074	+	2.33074i	−0.143719	+	0.143719i	−0.775306	−	0.631586i	$-0.782404\pi$
$263$	−2.33074	+	2.33074i	−0.143719	+	0.143719i	0.631586	+	0.775306i	$0.282404\pi$
$264$	2.31309			0.142361
$265$	15.5651	−	12.6723i	0.956158	−	0.778452i
$266$	−18.9113	+	18.9113i	−1.15952	+	1.15952i
$267$			5.68809i			0.348105i
$268$	7.13460			0.435815
$269$			12.4274i			0.757711i	0.925456	+	0.378855i	$0.123682\pi$
$269$			12.4274i			0.757711i	−0.925456	+	0.378855i	$0.876318\pi$
$270$	1.41177	+	1.73405i	0.0859174	+	0.105531i
$271$	3.48130	+	3.48130i	0.211474	+	0.211474i	0.804893	−	0.593419i	$-0.202222\pi$
$271$	3.48130	+	3.48130i	0.211474	+	0.211474i	−0.593419	+	0.804893i	$0.702222\pi$
$272$	0.932546	−	0.932546i	0.0565439	−	0.0565439i
$273$	−13.9678	−	4.29970i	−0.845369	−	0.260229i
$274$			20.7669i			1.25457i
$275$	6.34990	+	9.66635i	0.382914	+	0.582903i
$276$	5.56923			0.335228
$277$	−12.9182	+	12.9182i	−0.776178	+	0.776178i	−0.979179	−	0.203001i	$-0.934931\pi$
$277$	−12.9182	+	12.9182i	−0.776178	+	0.776178i	0.203001	+	0.979179i	$0.434931\pi$
$278$		−	13.0183i		−	0.780784i
$279$	6.67096	+	6.67096i	0.399380	+	0.399380i
$280$	−0.923704	+	9.01640i	−0.0552019	+	0.538833i
$281$	−17.4567	−	17.4567i	−1.04138	−	1.04138i	−0.999106	−	0.0422717i	$-0.986540\pi$
$281$	−17.4567	−	17.4567i	−1.04138	−	1.04138i	−0.0422717	−	0.999106i	$-0.513460\pi$
$282$	−0.395489	−	0.395489i	−0.0235510	−	0.0235510i
$283$	−7.63296	−	7.63296i	−0.453733	−	0.453733i	0.442859	−	0.896591i	$-0.353964\pi$
$283$	−7.63296	−	7.63296i	−0.453733	−	0.453733i	−0.896591	+	0.442859i	$0.853964\pi$
$284$	5.56896	−	5.56896i	0.330457	−	0.330457i
$285$	14.6770	+	1.50362i	0.869392	+	0.0890667i
$286$	7.97086	+	2.45366i	0.471327	+	0.145088i
$287$	−27.1569	−	27.1569i	−1.60302	−	1.60302i
$288$		−	1.00000i		−	0.0589256i
$289$			15.2607i			0.897689i
$290$	1.56495	−	15.2757i	0.0918970	−	0.897018i
$291$	−4.66796	+	4.66796i	−0.273641	+	0.273641i
$292$	7.36347			0.430915
$293$	0.359058			0.0209764			0.0104882	−	0.999945i	$-0.496661\pi$
$293$	0.359058			0.0209764			0.0104882	+	0.999945i	$0.496661\pi$
$294$	−6.66783	+	6.66783i	−0.388876	+	0.388876i
$295$	5.62964	−	4.58335i	0.327770	−	0.266853i
$296$			8.04614i			0.467672i
$297$		−	2.31309i		−	0.134219i
$298$	−4.39862	−	4.39862i	−0.254805	−	0.254805i
$299$	19.1915	+	5.90769i	1.10987	+	0.341651i
$300$	4.17898	−	2.74520i	0.241273	−	0.158494i
$301$	−10.4840	+	10.4840i	−0.604290	+	0.604290i
$302$	−3.77985	−	3.77985i	−0.217506	−	0.217506i
$303$	10.5213	+	10.5213i	0.604430	+	0.604430i
$304$	−4.66558	−	4.66558i	−0.267589	−	0.267589i
$305$	−14.4191	−	1.47719i	−0.825634	−	0.0845838i
$306$	−0.932546	−	0.932546i	−0.0533101	−	0.0533101i
$307$		−	4.45946i		−	0.254515i	−0.991870	−	0.127257i	$-0.959383\pi$
$307$		−	4.45946i		−	0.254515i	0.991870	−	0.127257i	$-0.0406174\pi$
$308$	6.62968	−	6.62968i	0.377761	−	0.377761i
$309$	8.07515			0.459379
$310$	16.3593	−	13.3188i	0.929144	−	0.756459i
$311$		−	17.3852i		−	0.985824i	−0.870079	−	0.492912i	$-0.835932\pi$
$311$		−	17.3852i		−	0.985824i	0.870079	−	0.492912i	$-0.164068\pi$
$312$	1.06077	−	3.44598i	0.0600544	−	0.195090i
$313$	4.06946	−	4.06946i	0.230019	−	0.230019i	−0.582681	−	0.812701i	$-0.697996\pi$
$313$	4.06946	−	4.06946i	0.230019	−	0.230019i	0.812701	+	0.582681i	$0.197996\pi$
$314$	13.1242	+	13.1242i	0.740644	+	0.740644i
$315$	9.01640	+	0.923704i	0.508017	+	0.0520448i
$316$			1.91721i			0.107851i
$317$	5.85556			0.328881			0.164440	−	0.986387i	$-0.447418\pi$
$317$	5.85556			0.328881			0.164440	+	0.986387i	$0.447418\pi$
$318$			8.97619i			0.503360i
$319$	−11.2321	+	11.2321i	−0.628876	+	0.628876i
$320$	−2.22443	−	0.227886i	−0.124349	−	0.0127392i
$321$	−6.95355			−0.388109
$322$	15.9623	−	15.9623i	0.889545	−	0.889545i
$323$	−8.70173			−0.484177
$324$	−1.00000			−0.0555556
$325$	17.3127	−	5.02697i	0.960336	−	0.278846i
$326$	9.96010			0.551639
$327$	−18.2854			−1.01118
$328$	6.69985	−	6.69985i	0.369937	−	0.369937i
$329$	−2.26707			−0.124988
$330$	−5.14530	−	0.527121i	−0.283239	−	0.0290170i
$331$	−22.6533	+	22.6533i	−1.24514	+	1.24514i	−0.287294	+	0.957842i	$0.592756\pi$
$331$	−22.6533	+	22.6533i	−1.24514	+	1.24514i	−0.957842	+	0.287294i	$0.907244\pi$
$332$			0.718668i			0.0394420i
$333$	8.04614			0.440926
$334$		−	10.9823i		−	0.600922i
$335$	−15.8704	−	1.62587i	−0.867091	−	0.0888310i
$336$	−2.86616	−	2.86616i	−0.156362	−	0.156362i
$337$	7.97905	−	7.97905i	0.434647	−	0.434647i	−0.455559	−	0.890206i	$-0.650561\pi$
$337$	7.97905	−	7.97905i	0.434647	−	0.434647i	0.890206	+	0.455559i	$0.150561\pi$
$338$	7.31080	−	10.7495i	0.397655	−	0.584697i
$339$			7.66010i			0.416039i
$340$	−2.28689	+	1.86186i	−0.124024	+	0.100974i
$341$	−21.8221			−1.18173
$342$	−4.66558	+	4.66558i	−0.252286	+	0.252286i
$343$			9.84862i			0.531775i
$344$	−2.58651	−	2.58651i	−0.139455	−	0.139455i
$345$	−12.3883	−	1.26915i	−0.666966	−	0.0683287i
$346$	−5.50754	−	5.50754i	−0.296087	−	0.296087i
$347$	13.0579	+	13.0579i	0.700985	+	0.700985i	0.964622	−	0.263637i	$-0.0849221\pi$
$347$	13.0579	+	13.0579i	0.700985	+	0.700985i	−0.263637	+	0.964622i	$0.584922\pi$
$348$	4.85588	+	4.85588i	0.260302	+	0.260302i
$349$	−21.5924	+	21.5924i	−1.15581	+	1.15581i	−0.170447	+	0.985367i	$0.554521\pi$
$349$	−21.5924	+	21.5924i	−1.15581	+	1.15581i	−0.985367	+	0.170447i	$0.945479\pi$
$350$	4.10942	−	19.8458i	0.219658	−	1.06080i
$351$	−3.44598	−	1.06077i	−0.183933	−	0.0566199i
$352$	1.63560	+	1.63560i	0.0871779	+	0.0871779i
$353$			0.516800i			0.0275065i	0.999905	+	0.0137533i	$0.00437794\pi$
$353$			0.516800i			0.0275065i	−0.999905	+	0.0137533i	$0.995622\pi$
$354$			3.24653i			0.172551i
$355$	−13.6568	+	11.1187i	−0.724829	+	0.590117i
$356$	−4.02209	+	4.02209i	−0.213170	+	0.213170i
$357$	−5.34565			−0.282922
$358$	−23.3767			−1.23550
$359$	0.362077	−	0.362077i	0.0191097	−	0.0191097i	−0.697487	−	0.716597i	$-0.745699\pi$
$359$	0.362077	−	0.362077i	0.0191097	−	0.0191097i	0.716597	+	0.697487i	$0.245699\pi$
$360$	−0.227886	+	2.22443i	−0.0120106	+	0.117238i
$361$			24.5352i			1.29133i
$362$			15.3920i			0.808985i
$363$	−3.99488	−	3.99488i	−0.209677	−	0.209677i
$364$	−6.83638	−	12.9171i	−0.358324	−	0.677038i
$365$	−16.3795	−	1.67803i	−0.857342	−	0.0878322i
$366$	4.58358	−	4.58358i	0.239588	−	0.239588i
$367$	5.81538	+	5.81538i	0.303560	+	0.303560i	0.842405	−	0.538845i	$-0.181139\pi$
$367$	5.81538	+	5.81538i	0.303560	+	0.303560i	−0.538845	+	0.842405i	$0.681139\pi$
$368$	3.93804	+	3.93804i	0.205285	+	0.205285i
$369$	−6.69985	−	6.69985i	−0.348780	−	0.348780i
$370$	1.83360	−	17.8980i	0.0953244	−	0.930475i
$371$	25.7272	+	25.7272i	1.33569	+	1.33569i
$372$			9.43416i			0.489138i
$373$	−10.4146	+	10.4146i	−0.539248	+	0.539248i	−0.923308	−	0.384060i	$-0.874525\pi$
$373$	−10.4146	+	10.4146i	−0.539248	+	0.539248i	0.384060	+	0.923308i	$0.374525\pi$
$374$	3.05055			0.157740
$375$	−9.92142	+	5.15417i	−0.512340	+	0.266160i
$376$		−	0.559306i		−	0.0288440i
$377$	11.5823	+	21.8842i	0.596517	+	1.12709i
$378$	−2.86616	+	2.86616i	−0.147419	+	0.147419i
$379$	23.6838	+	23.6838i	1.21656	+	1.21656i	0.968830	+	0.247726i	$0.0796832\pi$
$379$	23.6838	+	23.6838i	1.21656	+	1.21656i	0.247726	+	0.968830i	$0.420317\pi$
$380$	9.31501	+	11.4414i	0.477850	+	0.586934i
$381$		−	14.6872i		−	0.752447i
$382$	−18.3221			−0.937440
$383$		−	25.2587i		−	1.29066i	−0.763904	−	0.645330i	$-0.776720\pi$
$383$		−	25.2587i		−	1.29066i	0.763904	−	0.645330i	$-0.223280\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−16.2581	+	13.2364i	−0.828587	+	0.674591i
$386$	10.6298			0.541042
$387$	−2.58651	+	2.58651i	−0.131480	+	0.131480i
$388$	−6.60149			−0.335140
$389$	19.0841			0.967604			0.483802	−	0.875177i	$-0.339255\pi$
$389$	19.0841			0.967604			0.483802	+	0.875177i	$0.339255\pi$
$390$	−3.14490	+	7.42358i	−0.159248	+	0.375908i
$391$	7.34481			0.371443
$392$	−9.42974			−0.476274
$393$	8.09636	−	8.09636i	0.408407	−	0.408407i
$394$	−0.621588			−0.0313152
$395$	0.436904	−	4.26468i	0.0219830	−	0.214579i
$396$	1.63560	−	1.63560i	0.0821921	−	0.0821921i
$397$		−	13.5313i		−	0.679118i	−0.940585	−	0.339559i	$-0.889722\pi$
$397$		−	13.5313i		−	0.679118i	0.940585	−	0.339559i	$-0.110278\pi$
$398$	−5.48672			−0.275024
$399$			26.7446i			1.33890i
$400$	4.89614	+	1.01383i	0.244807	+	0.0506915i
$401$	−2.75570	−	2.75570i	−0.137613	−	0.137613i	0.634945	−	0.772558i	$-0.281023\pi$
$401$	−2.75570	−	2.75570i	−0.137613	−	0.137613i	−0.772558	+	0.634945i	$0.781023\pi$
$402$	5.04492	−	5.04492i	0.251618	−	0.251618i
$403$	−10.0075	+	32.5099i	−0.498509	+	1.61943i
$404$			14.8793i			0.740273i
$405$	2.22443	+	0.227886i	0.110533	+	0.0113237i
$406$	27.8354			1.38145
$407$	−13.1603	+	13.1603i	−0.652331	+	0.652331i
$408$		−	1.31882i		−	0.0652913i
$409$	−3.99155	−	3.99155i	−0.197369	−	0.197369i	0.601502	−	0.798871i	$-0.294569\pi$
$409$	−3.99155	−	3.99155i	−0.197369	−	0.197369i	−0.798871	+	0.601502i	$0.794569\pi$
$410$	−16.4301	+	13.3765i	−0.811426	+	0.660619i
$411$	14.6844	+	14.6844i	0.724328	+	0.724328i
$412$	5.70999	+	5.70999i	0.281311	+	0.281311i
$413$	9.30508	+	9.30508i	0.457873	+	0.457873i
$414$	3.93804	−	3.93804i	0.193544	−	0.193544i
$415$	0.163774	−	1.59862i	0.00803936	−	0.0784733i
$416$	3.18675	−	1.68659i	0.156243	−	0.0826921i
$417$	−9.20531	−	9.20531i	−0.450786	−	0.450786i
$418$		−	15.2621i		−	0.746491i
$419$			36.0580i			1.76155i	0.473538	+	0.880773i	$0.342977\pi$
$419$			36.0580i			1.76155i	−0.473538	+	0.880773i	$0.657023\pi$
$420$	5.72240	+	7.02872i	0.279225	+	0.342966i
$421$	−25.5839	+	25.5839i	−1.24688	+	1.24688i	−0.289791	+	0.957090i	$0.593586\pi$
$421$	−25.5839	+	25.5839i	−1.24688	+	1.24688i	−0.957090	+	0.289791i	$0.906414\pi$
$422$	12.2985			0.598683
$423$	−0.559306			−0.0271944
$424$	−6.34712	+	6.34712i	−0.308244	+	0.308244i
$425$	5.51131	−	3.62043i	0.267338	−	0.175617i
$426$		−	7.87570i		−	0.381579i
$427$		−	26.2745i		−	1.27151i
$428$	−4.91690	−	4.91690i	−0.237667	−	0.237667i
$429$	7.37125	−	3.90124i	0.355887	−	0.188354i
$430$	5.16406	+	6.34292i	0.249033	+	0.305883i
$431$	−19.5932	+	19.5932i	−0.943773	+	0.943773i	−0.998501	−	0.0547284i	$-0.982571\pi$
$431$	−19.5932	+	19.5932i	−0.943773	+	0.943773i	0.0547284	+	0.998501i	$0.482571\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−6.55103	−	6.55103i	−0.314823	−	0.314823i	0.531952	−	0.846775i	$-0.321459\pi$
$433$	−6.55103	−	6.55103i	−0.314823	−	0.314823i	−0.846775	+	0.531952i	$0.821459\pi$
$434$	27.0398	+	27.0398i	1.29795	+	1.29795i
$435$	−9.69495	−	11.9081i	−0.464837	−	0.570951i
$436$	−12.9297	−	12.9297i	−0.619221	−	0.619221i
$437$		−	36.7465i		−	1.75782i
$438$	5.20676	−	5.20676i	0.248789	−	0.248789i
$439$	1.85121			0.0883534			0.0441767	−	0.999024i	$-0.485934\pi$
$439$	1.85121			0.0883534			0.0441767	+	0.999024i	$0.485934\pi$
$440$	−3.26554	−	4.01100i	−0.155679	−	0.191217i
$441$			9.42974i			0.449035i
$442$	1.39897	−	4.54462i	0.0665421	−	0.216166i
$443$	−2.16126	+	2.16126i	−0.102685	+	0.102685i	−0.756583	−	0.653898i	$-0.773133\pi$
$443$	−2.16126	+	2.16126i	−0.102685	+	0.102685i	0.653898	+	0.756583i	$0.273133\pi$
$444$	5.68948	+	5.68948i	0.270011	+	0.270011i
$445$	9.86341	−	8.03026i	0.467570	−	0.380671i
$446$		−	10.5250i		−	0.498373i
$447$	−6.22059			−0.294224
$448$		−	4.05336i		−	0.191503i
$449$	8.96066	−	8.96066i	0.422880	−	0.422880i	−0.463314	−	0.886194i	$-0.653340\pi$
$449$	8.96066	−	8.96066i	0.422880	−	0.422880i	0.886194	+	0.463314i	$0.153340\pi$
$450$	1.01383	−	4.89614i	0.0477924	−	0.230806i
$451$	21.9166			1.03201
$452$	−5.41651	+	5.41651i	−0.254771	+	0.254771i
$453$	−5.34551			−0.251154
$454$	−17.9899			−0.844306
$455$	12.2634	+	30.2910i	0.574917	+	1.42006i
$456$	−6.59812			−0.308985
$457$	19.1156			0.894189			0.447094	−	0.894487i	$-0.352459\pi$
$457$	19.1156			0.894189			0.447094	+	0.894487i	$0.352459\pi$
$458$	1.48156	−	1.48156i	0.0692286	−	0.0692286i
$459$	−1.31882			−0.0615572
$460$	−7.86246	−	9.65731i	−0.366589	−	0.450274i
$461$	−23.8829	+	23.8829i	−1.11234	+	1.11234i	−0.119506	+	0.992834i	$0.538131\pi$
$461$	−23.8829	+	23.8829i	−1.11234	+	1.11234i	−0.992834	+	0.119506i	$0.961869\pi$
$462$		−	9.37579i		−	0.436201i
$463$	−0.610648			−0.0283792			−0.0141896	−	0.999899i	$-0.504517\pi$
$463$	−0.610648			−0.0283792			−0.0141896	+	0.999899i	$0.504517\pi$
$464$			6.86725i			0.318804i
$465$	2.14991	−	20.9856i	0.0996998	−	0.973183i
$466$	2.70461	+	2.70461i	0.125289	+	0.125289i
$467$	−24.0091	+	24.0091i	−1.11101	+	1.11101i	−0.117992	+	0.993015i	$0.537646\pi$
$467$	−24.0091	+	24.0091i	−1.11101	+	1.11101i	−0.993015	+	0.117992i	$0.962354\pi$
$468$	−1.68659	−	3.18675i	−0.0779629	−	0.147308i
$469$		−	28.9191i		−	1.33536i
$470$	−0.127458	+	1.24413i	−0.00587920	+	0.0573876i
$471$	18.5605			0.855222
$472$	−2.29565	+	2.29565i	−0.105666	+	0.105666i
$473$		−	8.46099i		−	0.389037i
$474$	1.35567	+	1.35567i	0.0622680	+	0.0622680i
$475$	−18.1132	−	27.5734i	−0.831091	−	1.26515i
$476$	−3.77995	−	3.77995i	−0.173253	−	0.173253i
$477$	6.34712	+	6.34712i	0.290615	+	0.290615i
$478$	−3.98109	−	3.98109i	−0.182091	−	0.182091i
$479$	0.400346	−	0.400346i	0.0182923	−	0.0182923i	−0.697901	−	0.716194i	$-0.745883\pi$
$479$	0.400346	−	0.400346i	0.0182923	−	0.0182923i	0.716194	+	0.697901i	$0.245883\pi$
$480$	−1.73405	+	1.41177i	−0.0791480	+	0.0644380i
$481$	13.5706	+	25.6411i	0.618765	+	1.16913i
$482$	−15.4622	−	15.4622i	−0.704286	−	0.704286i
$483$		−	22.5741i		−	1.02716i
$484$		−	5.64961i		−	0.256801i
$485$	14.6845	+	1.50439i	0.666790	+	0.0683107i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	4.51084			0.204406			0.102203	−	0.994764i	$-0.467411\pi$
$487$	4.51084			0.204406			0.102203	+	0.994764i	$0.467411\pi$
$488$	6.48216			0.293434
$489$	7.04286	−	7.04286i	0.318489	−	0.318489i
$490$	20.9758	+	2.14891i	0.947588	+	0.0970777i
$491$		−	13.4933i		−	0.608944i	−0.952521	−	0.304472i	$-0.901520\pi$
$491$		−	13.4933i		−	0.608944i	0.952521	−	0.304472i	$-0.0984800\pi$
$492$		−	9.47502i		−	0.427167i
$493$	6.40402	+	6.40402i	0.288423	+	0.288423i
$494$	−22.7370	−	6.99911i	−1.02299	−	0.314905i
$495$	−4.01100	+	3.26554i	−0.180281	+	0.146775i
$496$	−6.67096	+	6.67096i	−0.299535	+	0.299535i
$497$	−22.5730	−	22.5730i	−1.01254	−	1.01254i
$498$	0.508175	+	0.508175i	0.0227719	+	0.0227719i
$499$	8.38741	+	8.38741i	0.375472	+	0.375472i	0.869466	−	0.493993i	$-0.164463\pi$
$499$	8.38741	+	8.38741i	0.375472	+	0.375472i	−0.493993	+	0.869466i	$0.664463\pi$
$500$	−10.6601	−	3.37095i	−0.476732	−	0.150754i
$501$	−7.76563	−	7.76563i	−0.346943	−	0.346943i
$502$		−	17.9961i		−	0.803204i
$503$	−9.71446	+	9.71446i	−0.433146	+	0.433146i	−0.889697	−	0.456551i	$-0.849085\pi$
$503$	−9.71446	+	9.71446i	−0.433146	+	0.433146i	0.456551	+	0.889697i	$0.349085\pi$
$504$	−4.05336			−0.180551
$505$	3.39078	−	33.0979i	0.150888	−	1.47284i
$506$			12.8821i			0.572681i
$507$	−2.43155	−	12.7706i	−0.107989	−	0.567161i
$508$	10.3854	−	10.3854i	0.460778	−	0.460778i
$509$	−4.00130	−	4.00130i	−0.177354	−	0.177354i	0.612847	−	0.790202i	$-0.290024\pi$
$509$	−4.00130	−	4.00130i	−0.177354	−	0.177354i	−0.790202	+	0.612847i	$0.790024\pi$
$510$	−0.300540	+	2.93361i	−0.0133081	+	0.129903i
$511$		−	29.8468i		−	1.32035i
$512$	1.00000			0.0441942
$513$			6.59812i			0.291314i
$514$	1.36406	−	1.36406i	0.0601663	−	0.0601663i
$515$	−11.4002	−	14.0027i	−0.502354	−	0.617032i
$516$	−3.65787			−0.161029
$517$	0.914801	−	0.914801i	0.0402329	−	0.0402329i
$518$	32.6139			1.43297
$519$	−7.78883			−0.341892
$520$	−7.47305	+	3.02549i	−0.327715	+	0.132676i
$521$	11.8398			0.518712			0.259356	−	0.965782i	$-0.416490\pi$
$521$	11.8398			0.518712			0.259356	+	0.965782i	$0.416490\pi$
$522$	6.86725			0.300571
$523$	11.9564	−	11.9564i	0.522816	−	0.522816i	−0.395605	−	0.918421i	$-0.629465\pi$
$523$	11.9564	−	11.9564i	0.522816	−	0.522816i	0.918421	+	0.395605i	$0.129465\pi$
$524$	11.4500			0.500195
$525$	−11.1273	−	16.9389i	−0.485635	−	0.739275i
$526$	−2.33074	+	2.33074i	−0.101625	+	0.101625i
$527$			12.4419i			0.541980i
$528$	2.31309			0.100664
$529$			8.01635i			0.348537i
$530$	15.5651	−	12.6723i	0.676106	−	0.550449i
$531$	2.29565	+	2.29565i	0.0996226	+	0.0996226i
$532$	−18.9113	+	18.9113i	−0.819908	+	0.819908i
$533$	10.0508	−	32.6507i	0.435350	−	1.41426i
$534$			5.68809i			0.246148i
$535$	9.81679	+	12.0578i	0.424417	+	0.521303i
$536$	7.13460			0.308168
$537$	−16.5298	+	16.5298i	−0.713315	+	0.713315i
$538$			12.4274i			0.535782i
$539$	−15.4233	−	15.4233i	−0.664329	−	0.664329i
$540$	1.41177	+	1.73405i	0.0607528	+	0.0746215i
$541$	17.5003	+	17.5003i	0.752395	+	0.752395i	0.974926	−	0.222530i	$-0.0714316\pi$
$541$	17.5003	+	17.5003i	0.752395	+	0.752395i	−0.222530	+	0.974926i	$0.571432\pi$
$542$	3.48130	+	3.48130i	0.149535	+	0.149535i
$543$	10.8838	+	10.8838i	0.467068	+	0.467068i
$544$	0.932546	−	0.932546i	0.0399826	−	0.0399826i
$545$	25.8147	+	31.7077i	1.10578	+	1.35821i
$546$	−13.9678	−	4.29970i	−0.597766	−	0.184010i
$547$	−15.1432	−	15.1432i	−0.647478	−	0.647478i	0.304905	−	0.952383i	$-0.401375\pi$
$547$	−15.1432	−	15.1432i	−0.647478	−	0.647478i	−0.952383	+	0.304905i	$0.901375\pi$
$548$			20.7669i			0.887116i
$549$		−	6.48216i		−	0.276652i
$550$	6.34990	+	9.66635i	0.270761	+	0.412175i
$551$	32.0397	−	32.0397i	1.36494	−	1.36494i
$552$	5.56923			0.237042
$553$	7.77113			0.330462
$554$	−12.9182	+	12.9182i	−0.548841	+	0.548841i
$555$	−11.3593	−	13.9524i	−0.482174	−	0.592245i
$556$		−	13.0183i		−	0.552098i
$557$			21.9240i			0.928952i	0.885586	+	0.464476i	$0.153757\pi$
$557$			21.9240i			0.928952i	−0.885586	+	0.464476i	$0.846243\pi$
$558$	6.67096	+	6.67096i	0.282404	+	0.282404i
$559$	−12.6049	−	3.88017i	−0.533132	−	0.164114i
$560$	−0.923704	+	9.01640i	−0.0390336	+	0.381012i
$561$	2.15706	−	2.15706i	0.0910712	−	0.0910712i
$562$	−17.4567	−	17.4567i	−0.736365	−	0.736365i
$563$	−22.7318	−	22.7318i	−0.958032	−	0.958032i	0.0411219	−	0.999154i	$-0.486907\pi$
$563$	−22.7318	−	22.7318i	−0.958032	−	0.958032i	−0.999154	+	0.0411219i	$0.986907\pi$
$564$	−0.395489	−	0.395489i	−0.0166531	−	0.0166531i
$565$	13.2830	−	10.8143i	0.558818	−	0.454960i
$566$	−7.63296	−	7.63296i	−0.320837	−	0.320837i
$567$			4.05336i			0.170225i
$568$	5.56896	−	5.56896i	0.233668	−	0.233668i
$569$	−14.5679			−0.610717			−0.305358	−	0.952238i	$-0.598776\pi$
$569$	−14.5679			−0.610717			−0.305358	+	0.952238i	$0.598776\pi$
$570$	14.6770	+	1.50362i	0.614753	+	0.0629797i
$571$			7.78560i			0.325817i	0.986641	+	0.162909i	$0.0520876\pi$
$571$			7.78560i			0.325817i	−0.986641	+	0.162909i	$0.947912\pi$
$572$	7.97086	+	2.45366i	0.333278	+	0.102593i
$573$	−12.9557	+	12.9557i	−0.541231	+	0.541231i
$574$	−27.1569	−	27.1569i	−1.13351	−	1.13351i
$575$	15.2887	+	23.2737i	0.637582	+	0.970580i
$576$		−	1.00000i		−	0.0416667i
$577$	−2.68505			−0.111780			−0.0558901	−	0.998437i	$-0.517800\pi$
$577$	−2.68505			−0.111780			−0.0558901	+	0.998437i	$0.517800\pi$
$578$			15.2607i			0.634762i
$579$	7.51640	−	7.51640i	0.312371	−	0.312371i
$580$	1.56495	−	15.2757i	0.0649810	−	0.634288i
$581$	2.91302			0.120852
$582$	−4.66796	+	4.66796i	−0.193493	+	0.193493i
$583$	−20.7627			−0.859905
$584$	7.36347			0.304703
$585$	3.02549	+	7.47305i	0.125089	+	0.308972i
$586$	0.359058			0.0148325
$587$	20.4677			0.844792			0.422396	−	0.906411i	$-0.361189\pi$
$587$	20.4677			0.844792			0.422396	+	0.906411i	$0.361189\pi$
$588$	−6.66783	+	6.66783i	−0.274977	+	0.274977i
$589$	62.2478			2.56487
$590$	5.62964	−	4.58335i	0.231769	−	0.188693i
$591$	−0.439529	+	0.439529i	−0.0180798	+	0.0180798i
$592$			8.04614i			0.330694i
$593$	−1.45240			−0.0596428			−0.0298214	−	0.999555i	$-0.509494\pi$
$593$	−1.45240			−0.0596428			−0.0298214	+	0.999555i	$0.509494\pi$
$594$		−	2.31309i		−	0.0949072i
$595$	7.54681	+	9.26960i	0.309389	+	0.380017i
$596$	−4.39862	−	4.39862i	−0.180174	−	0.180174i
$597$	−3.87970	+	3.87970i	−0.158785	+	0.158785i
$598$	19.1915	+	5.90769i	0.784797	+	0.241583i
$599$			9.73974i			0.397955i	0.980004	+	0.198978i	$0.0637621\pi$
$599$			9.73974i			0.397955i	−0.980004	+	0.198978i	$0.936238\pi$
$600$	4.17898	−	2.74520i	0.170606	−	0.112073i
$601$	−5.83608			−0.238059			−0.119029	−	0.992891i	$-0.537978\pi$
$601$	−5.83608			−0.238059			−0.119029	+	0.992891i	$0.537978\pi$
$602$	−10.4840	+	10.4840i	−0.427298	+	0.427298i
$603$		−	7.13460i		−	0.290543i
$604$	−3.77985	−	3.77985i	−0.153800	−	0.153800i
$605$	−1.28747	+	12.5671i	−0.0523430	+	0.510927i
$606$	10.5213	+	10.5213i	0.427397	+	0.427397i
$607$	−25.1205	−	25.1205i	−1.01961	−	1.01961i	−0.999804	−	0.0198060i	$-0.993695\pi$
$607$	−25.1205	−	25.1205i	−1.01961	−	1.01961i	−0.0198060	−	0.999804i	$-0.506305\pi$
$608$	−4.66558	−	4.66558i	−0.189214	−	0.189214i
$609$	19.6826	−	19.6826i	0.797580	−	0.797580i
$610$	−14.4191	−	1.47719i	−0.583812	−	0.0598098i
$611$	−0.943322	−	1.78237i	−0.0381627	−	0.0721070i
$612$	−0.932546	−	0.932546i	−0.0376959	−	0.0376959i
$613$		−	46.0466i		−	1.85980i	−0.367808	−	0.929902i	$-0.619892\pi$
$613$		−	46.0466i		−	1.85980i	0.367808	−	0.929902i	$-0.380108\pi$
$614$		−	4.45946i		−	0.179969i
$615$	−2.15922	+	21.0765i	−0.0870683	+	0.849885i
$616$	6.62968	−	6.62968i	0.267118	−	0.267118i
$617$	25.5757			1.02964			0.514819	−	0.857299i	$-0.327859\pi$
$617$	25.5757			1.02964			0.514819	+	0.857299i	$0.327859\pi$
$618$	8.07515			0.324830
$619$	2.22356	−	2.22356i	0.0893725	−	0.0893725i	−0.661007	−	0.750380i	$-0.729871\pi$
$619$	2.22356	−	2.22356i	0.0893725	−	0.0893725i	0.750380	+	0.661007i	$0.229871\pi$
$620$	16.3593	−	13.3188i	0.657004	−	0.534897i
$621$		−	5.56923i		−	0.223486i
$622$		−	17.3852i		−	0.697083i
$623$	16.3030	+	16.3030i	0.653165	+	0.653165i
$624$	1.06077	−	3.44598i	0.0424649	−	0.137950i
$625$	22.9443	+	9.92770i	0.917772	+	0.397108i
$626$	4.06946	−	4.06946i	0.162648	−	0.162648i
$627$	−10.7919	−	10.7919i	−0.430987	−	0.430987i
$628$	13.1242	+	13.1242i	0.523714	+	0.523714i
$629$	7.50339	+	7.50339i	0.299180	+	0.299180i
$630$	9.01640	+	0.923704i	0.359222	+	0.0368013i
$631$	−11.3678	−	11.3678i	−0.452546	−	0.452546i	0.443653	−	0.896199i	$-0.353682\pi$
$631$	−11.3678	−	11.3678i	−0.452546	−	0.452546i	−0.896199	+	0.443653i	$0.853682\pi$
$632$			1.91721i			0.0762624i
$633$	8.69637	−	8.69637i	0.345650	−	0.345650i
$634$	5.85556			0.232554
$635$	−25.4683	+	20.7349i	−1.01068	+	0.822838i
$636$			8.97619i			0.355929i
$637$	−30.0503	+	15.9042i	−1.19063	+	0.630145i
$638$	−11.2321	+	11.2321i	−0.444682	+	0.444682i
$639$	−5.56896	−	5.56896i	−0.220305	−	0.220305i
$640$	−2.22443	−	0.227886i	−0.0879281	−	0.00900798i
$641$		−	27.2559i		−	1.07654i	−0.842772	−	0.538271i	$-0.819078\pi$
$641$		−	27.2559i		−	1.07654i	0.842772	−	0.538271i	$-0.180922\pi$
$642$	−6.95355			−0.274435
$643$		−	12.3529i		−	0.487153i	−0.969882	−	0.243576i	$-0.921679\pi$
$643$		−	12.3529i		−	0.487153i	0.969882	−	0.243576i	$-0.0783207\pi$
$644$	15.9623	−	15.9623i	0.629003	−	0.629003i
$645$	8.13666	+	0.833578i	0.320381	+	0.0328221i
$646$	−8.70173			−0.342365
$647$	6.52838	−	6.52838i	0.256657	−	0.256657i	−0.567036	−	0.823693i	$-0.691910\pi$
$647$	6.52838	−	6.52838i	0.256657	−	0.256657i	0.823693	+	0.567036i	$0.191910\pi$
$648$	−1.00000			−0.0392837
$649$	−7.50953			−0.294775
$650$	17.3127	−	5.02697i	0.679060	−	0.197174i
$651$	38.2401			1.49875
$652$	9.96010			0.390068
$653$	13.6586	−	13.6586i	0.534500	−	0.534500i	−0.387408	−	0.921908i	$-0.626630\pi$
$653$	13.6586	−	13.6586i	0.534500	−	0.534500i	0.921908	+	0.387408i	$0.126630\pi$
$654$	−18.2854			−0.715014
$655$	−25.4696	−	2.60929i	−0.995181	−	0.101953i
$656$	6.69985	−	6.69985i	0.261585	−	0.261585i
$657$		−	7.36347i		−	0.287276i
$658$	−2.26707			−0.0883795
$659$		−	49.7146i		−	1.93661i	−0.249776	−	0.968304i	$-0.580357\pi$
$659$		−	49.7146i		−	1.93661i	0.249776	−	0.968304i	$-0.419643\pi$
$660$	−5.14530	−	0.527121i	−0.200280	−	0.0205181i
$661$	−24.9427	−	24.9427i	−0.970157	−	0.970157i	0.0294100	−	0.999567i	$-0.490637\pi$
$661$	−24.9427	−	24.9427i	−0.970157	−	0.970157i	−0.999567	+	0.0294100i	$0.990637\pi$
$662$	−22.6533	+	22.6533i	−0.880444	+	0.880444i
$663$	−2.22431	−	4.20275i	−0.0863851	−	0.163221i
$664$			0.718668i			0.0278897i
$665$	46.3763	−	37.7571i	1.79840	−	1.46416i
$666$	8.04614			0.311782
$667$	−27.0435	+	27.0435i	−1.04713	+	1.04713i
$668$		−	10.9823i		−	0.424916i
$669$	−7.44230	−	7.44230i	−0.287736	−	0.287736i
$670$	−15.8704	−	1.62587i	−0.613126	−	0.0628130i
$671$	10.6022	+	10.6022i	0.409295	+	0.409295i
$672$	−2.86616	−	2.86616i	−0.110565	−	0.110565i
$673$	5.37765	+	5.37765i	0.207293	+	0.207293i	0.803116	−	0.595823i	$-0.203174\pi$
$673$	5.37765	+	5.37765i	0.207293	+	0.207293i	−0.595823	+	0.803116i	$0.703174\pi$
$674$	7.97905	−	7.97905i	0.307342	−	0.307342i
$675$	−2.74520	−	4.17898i	−0.105663	−	0.160849i
$676$	7.31080	−	10.7495i	0.281185	−	0.413443i
$677$	−10.8097	−	10.8097i	−0.415449	−	0.415449i	0.468183	−	0.883632i	$-0.344909\pi$
$677$	−10.8097	−	10.8097i	−0.415449	−	0.415449i	−0.883632	+	0.468183i	$0.844909\pi$
$678$			7.66010i			0.294184i
$679$			26.7582i			1.02689i
$680$	−2.28689	+	1.86186i	−0.0876983	+	0.0713992i
$681$	−12.7208	+	12.7208i	−0.487461	+	0.487461i
$682$	−21.8221			−0.835610
$683$	29.1338			1.11477			0.557386	−	0.830253i	$-0.311804\pi$
$683$	29.1338			1.11477			0.557386	+	0.830253i	$0.311804\pi$
$684$	−4.66558	+	4.66558i	−0.178393	+	0.178393i
$685$	4.73248	−	46.1943i	0.180819	−	1.76499i
$686$			9.84862i			0.376022i
$687$		−	2.09524i		−	0.0799383i
$688$	−2.58651	−	2.58651i	−0.0986096	−	0.0986096i
$689$	−9.52170	+	30.9317i	−0.362748	+	1.17841i
$690$	−12.3883	−	1.26915i	−0.471616	−	0.0483157i
$691$	−23.8730	+	23.8730i	−0.908172	+	0.908172i	−0.996125	−	0.0879526i	$-0.971968\pi$
$691$	−23.8730	+	23.8730i	−0.908172	+	0.908172i	0.0879526	+	0.996125i	$0.471968\pi$
$692$	−5.50754	−	5.50754i	−0.209365	−	0.209365i
$693$	−6.62968	−	6.62968i	−0.251841	−	0.251841i
$694$	13.0579	+	13.0579i	0.495671	+	0.495671i
$695$	−2.96668	+	28.9582i	−0.112533	+	1.09845i
$696$	4.85588	+	4.85588i	0.184061	+	0.184061i
$697$		−	12.4958i		−	0.473313i
$698$	−21.5924	+	21.5924i	−0.817284	+	0.817284i
$699$	3.82490			0.144671
$700$	4.10942	−	19.8458i	0.155322	−	0.750101i
$701$			13.7155i			0.518027i	0.965874	+	0.259013i	$0.0833974\pi$
$701$			13.7155i			0.518027i	−0.965874	+	0.259013i	$0.916603\pi$
$702$	−3.44598	−	1.06077i	−0.130060	−	0.0400363i
$703$	37.5399	−	37.5399i	1.41584	−	1.41584i
$704$	1.63560	+	1.63560i	0.0616441	+	0.0616441i
$705$	0.789609	+	0.969862i	0.0297384	+	0.0365271i
$706$			0.516800i			0.0194500i
$707$	60.3112			2.26824
$708$			3.24653i			0.122012i
$709$	36.2581	−	36.2581i	1.36170	−	1.36170i	0.489949	−	0.871751i	$-0.337015\pi$
$709$	36.2581	−	36.2581i	1.36170	−	1.36170i	0.871751	−	0.489949i	$-0.162985\pi$
$710$	−13.6568	+	11.1187i	−0.512532	+	0.417276i
$711$	1.91721			0.0719008
$712$	−4.02209	+	4.02209i	−0.150734	+	0.150734i
$713$	−52.5410			−1.96768
$714$	−5.34565			−0.200056
$715$	−17.1714	−	7.27444i	−0.642175	−	0.272048i
$716$	−23.3767			−0.873628
$717$	−5.63011			−0.210260
$718$	0.362077	−	0.362077i	0.0135126	−	0.0135126i
$719$	23.5875			0.879666			0.439833	−	0.898080i	$-0.355038\pi$
$719$	23.5875			0.879666			0.439833	+	0.898080i	$0.355038\pi$
$720$	−0.227886	+	2.22443i	−0.00849281	+	0.0828994i
$721$	23.1447	−	23.1447i	0.861952	−	0.861952i
$722$			24.5352i			0.913107i
$723$	−21.8669			−0.813239
$724$			15.3920i			0.572039i
$725$	−6.96222	+	33.6230i	−0.258570	+	1.24873i
$726$	−3.99488	−	3.99488i	−0.148264	−	0.148264i
$727$	16.9055	−	16.9055i	0.626991	−	0.626991i	−0.320319	−	0.947310i	$-0.603790\pi$
$727$	16.9055	−	16.9055i	0.626991	−	0.626991i	0.947310	+	0.320319i	$0.103790\pi$
$728$	−6.83638	−	12.9171i	−0.253373	−	0.478738i
$729$			1.00000i			0.0370370i
$730$	−16.3795	−	1.67803i	−0.606232	−	0.0621068i
$731$	−4.82407			−0.178425
$732$	4.58358	−	4.58358i	0.169414	−	0.169414i
$733$			41.5404i			1.53433i	0.641449	+	0.767165i	$0.278333\pi$
$733$			41.5404i			1.53433i	−0.641449	+	0.767165i	$0.721667\pi$
$734$	5.81538	+	5.81538i	0.214650	+	0.214650i
$735$	16.3516	−	13.3126i	0.603138	−	0.491042i
$736$	3.93804	+	3.93804i	0.145158	+	0.145158i
$737$	11.6694	+	11.6694i	0.429846	+	0.429846i
$738$	−6.69985	−	6.69985i	−0.246625	−	0.246625i
$739$	−16.5636	+	16.5636i	−0.609303	+	0.609303i	−0.942764	−	0.333461i	$-0.891783\pi$
$739$	−16.5636	+	16.5636i	−0.609303	+	0.609303i	0.333461	+	0.942764i	$0.391783\pi$
$740$	1.83360	−	17.8980i	0.0674046	−	0.657945i
$741$	−21.0266	+	11.1284i	−0.772431	+	0.408811i
$742$	25.7272	+	25.7272i	0.944475	+	0.944475i
$743$		−	8.59040i		−	0.315151i	−0.987507	−	0.157576i	$-0.949632\pi$
$743$		−	8.59040i		−	0.315151i	0.987507	−	0.157576i	$-0.0503678\pi$
$744$			9.43416i			0.345873i
$745$	8.78202	+	10.7868i	0.321748	+	0.395197i
$746$	−10.4146	+	10.4146i	−0.381306	+	0.381306i
$747$	0.718668			0.0262947
$748$	3.05055			0.111539
$749$	−19.9300	+	19.9300i	−0.728226	+	0.728226i
$750$	−9.92142	+	5.15417i	−0.362279	+	0.188204i
$751$		−	28.0811i		−	1.02469i	−0.858779	−	0.512347i	$-0.828776\pi$
$751$		−	28.0811i		−	1.02469i	0.858779	−	0.512347i	$-0.171224\pi$
$752$		−	0.559306i		−	0.0203958i
$753$	−12.7251	−	12.7251i	−0.463730	−	0.463730i
$754$	11.5823	+	21.8842i	0.421801	+	0.796976i
$755$	7.54662	+	9.26937i	0.274650	+	0.337347i
$756$	−2.86616	+	2.86616i	−0.104241	+	0.104241i
$757$	28.5156	+	28.5156i	1.03642	+	1.03642i	0.999311	+	0.0371063i	$0.0118140\pi$
$757$	28.5156	+	28.5156i	1.03642	+	1.03642i	0.0371063	+	0.999311i	$0.488186\pi$
$758$	23.6838	+	23.6838i	0.860235	+	0.860235i
$759$	9.10905	+	9.10905i	0.330637	+	0.330637i
$760$	9.31501	+	11.4414i	0.337891	+	0.415025i
$761$	−6.51275	−	6.51275i	−0.236087	−	0.236087i	0.579141	−	0.815228i	$-0.303388\pi$
$761$	−6.51275	−	6.51275i	−0.236087	−	0.236087i	−0.815228	+	0.579141i	$0.803388\pi$
$762$		−	14.6872i		−	0.532061i
$763$	−52.4088	+	52.4088i	−1.89733	+	1.89733i
$764$	−18.3221			−0.662870
$765$	1.86186	+	2.28689i	0.0673158	+	0.0826828i
$766$		−	25.2587i		−	0.912635i
$767$	−3.44383	+	11.1875i	−0.124350	+	0.403957i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	1.48463	+	1.48463i	0.0535371	+	0.0535371i	0.733368	−	0.679831i	$-0.237947\pi$
$769$	1.48463	+	1.48463i	0.0535371	+	0.0535371i	−0.679831	+	0.733368i	$0.737947\pi$
$770$	−16.2581	+	13.2364i	−0.585899	+	0.477008i
$771$		−	1.92908i		−	0.0694741i
$772$	10.6298			0.382575
$773$			31.8123i			1.14421i	0.820181	+	0.572104i	$0.193872\pi$
$773$			31.8123i			1.14421i	−0.820181	+	0.572104i	$0.806128\pi$
$774$	−2.58651	+	2.58651i	−0.0929701	+	0.0929701i
$775$	−39.4251	+	25.8987i	−1.41619	+	0.930309i
$776$	−6.60149			−0.236980
$777$	23.0615	−	23.0615i	0.827327	−	0.827327i
$778$	19.0841			0.684199
$779$	−62.5173			−2.23992
$780$	−3.14490	+	7.42358i	−0.112605	+	0.265807i
$781$	18.2172			0.651863
$782$	7.34481			0.262650
$783$	4.85588	−	4.85588i	0.173535	−	0.173535i
$784$	−9.42974			−0.336776
$785$	−26.2031	−	32.1847i	−0.935228	−	1.14872i
$786$	8.09636	−	8.09636i	0.288788	−	0.288788i
$787$			24.7509i			0.882275i	0.897440	+	0.441137i	$0.145425\pi$
$787$			24.7509i			0.882275i	−0.897440	+	0.441137i	$0.854575\pi$
$788$	−0.621588			−0.0221432
$789$			3.29616i			0.117346i
$790$	0.436904	−	4.26468i	0.0155444	−	0.151731i
$791$	21.9551	+	21.9551i	0.780632	+	0.780632i
$792$	1.63560	−	1.63560i	0.0581186	−	0.0581186i
$793$	20.6570	−	10.9328i	0.733553	−	0.388234i
$794$		−	13.5313i		−	0.480209i
$795$	2.04555	−	19.9669i	0.0725481	−	0.708152i
$796$	−5.48672			−0.194472
$797$	36.1651	−	36.1651i	1.28103	−	1.28103i	0.340954	−	0.940080i	$-0.389250\pi$
$797$	36.1651	−	36.1651i	1.28103	−	1.28103i	0.940080	−	0.340954i	$-0.110750\pi$
$798$			26.7446i			0.946748i
$799$	−0.521578	−	0.521578i	−0.0184521	−	0.0184521i
$800$	4.89614	+	1.01383i	0.173105	+	0.0358443i
$801$	4.02209	+	4.02209i	0.142113	+	0.142113i
$802$	−2.75570	−	2.75570i	−0.0973070	−	0.0973070i
$803$	12.0437	+	12.0437i	0.425013	+	0.425013i
$804$	5.04492	−	5.04492i	0.177921	−	0.177921i
$805$	−39.1446	+	31.8694i	−1.37966	+	1.12325i
$806$	−10.0075	+	32.5099i	−0.352499	+	1.14511i
$807$	8.78748	+	8.78748i	0.309334	+	0.309334i
$808$			14.8793i			0.523452i
$809$		−	33.9567i		−	1.19385i	−0.802295	−	0.596927i	$-0.796388\pi$
$809$		−	33.9567i		−	1.19385i	0.802295	−	0.596927i	$-0.203612\pi$
$810$	2.22443	+	0.227886i	0.0781583	+	0.00800710i
$811$	14.9372	−	14.9372i	0.524515	−	0.524515i	−0.394417	−	0.918932i	$-0.629053\pi$
$811$	14.9372	−	14.9372i	0.524515	−	0.524515i	0.918932	+	0.394417i	$0.129053\pi$
$812$	27.8354			0.976832
$813$	4.92331			0.172668
$814$	−13.1603	+	13.1603i	−0.461268	+	0.461268i
$815$	−22.1555	−	2.26977i	−0.776074	−	0.0795065i
$816$		−	1.31882i		−	0.0461679i
$817$			24.1351i			0.844380i
$818$	−3.99155	−	3.99155i	−0.139561	−	0.139561i
$819$	−12.9171	+	6.83638i	−0.451359	+	0.238882i
$820$	−16.4301	+	13.3765i	−0.573765	+	0.467128i
$821$	−19.0135	+	19.0135i	−0.663574	+	0.663574i	−0.956221	−	0.292646i	$-0.905464\pi$
$821$	−19.0135	+	19.0135i	−0.663574	+	0.663574i	0.292646	+	0.956221i	$0.405464\pi$
$822$	14.6844	+	14.6844i	0.512177	+	0.512177i
$823$	−37.2505	−	37.2505i	−1.29847	−	1.29847i	−0.929402	−	0.369069i	$-0.879677\pi$
$823$	−37.2505	−	37.2505i	−1.29847	−	1.29847i	−0.369069	−	0.929402i	$-0.620323\pi$
$824$	5.70999	+	5.70999i	0.198917	+	0.198917i
$825$	11.3252	+	2.34508i	0.394293	+	0.0816453i
$826$	9.30508	+	9.30508i	0.323765	+	0.323765i
$827$		−	51.9149i		−	1.80526i	−0.430421	−	0.902628i	$-0.641635\pi$
$827$		−	51.9149i		−	1.80526i	0.430421	−	0.902628i	$-0.358365\pi$
$828$	3.93804	−	3.93804i	0.136856	−	0.136856i
$829$	−3.53681			−0.122838			−0.0614192	−	0.998112i	$-0.519563\pi$
$829$	−3.53681			−0.122838			−0.0614192	+	0.998112i	$0.519563\pi$
$830$	0.163774	−	1.59862i	0.00568469	−	0.0554890i
$831$			18.2691i			0.633747i
$832$	3.18675	−	1.68659i	0.110481	−	0.0584721i
$833$	−8.79366	+	8.79366i	−0.304682	+	0.304682i
$834$	−9.20531	−	9.20531i	−0.318754	−	0.318754i
$835$	−2.50270	+	24.4292i	−0.0866096	+	0.845408i
$836$		−	15.2621i		−	0.527849i
$837$	9.43416			0.326092
$838$			36.0580i			1.24560i
$839$	−30.0357	+	30.0357i	−1.03695	+	1.03695i	−0.0376553	+	0.999291i	$0.511989\pi$
$839$	−30.0357	+	30.0357i	−1.03695	+	1.03695i	−0.999291	+	0.0376553i	$0.988011\pi$
$840$	5.72240	+	7.02872i	0.197442	+	0.242514i
$841$	−18.1591			−0.626174
$842$	−25.5839	+	25.5839i	−0.881678	+	0.881678i
$843$	−24.6875			−0.850281
$844$	12.2985			0.423333
$845$	−18.7120	+	22.2455i	−0.643712	+	0.765268i
$846$	−0.559306			−0.0192293
$847$	−22.8999			−0.786851
$848$	−6.34712	+	6.34712i	−0.217961	+	0.217961i
$849$	−10.7946			−0.370471
$850$	5.51131	−	3.62043i	0.189037	−	0.124180i
$851$	−31.6860	+	31.6860i	−1.08618	+	1.08618i
$852$		−	7.87570i		−	0.269817i
$853$	−20.8885			−0.715210			−0.357605	−	0.933873i	$-0.616407\pi$
$853$	−20.8885			−0.715210			−0.357605	+	0.933873i	$0.616407\pi$
$854$		−	26.2745i		−	0.899096i
$855$	11.4414	−	9.31501i	0.391289	−	0.318567i
$856$	−4.91690	−	4.91690i	−0.168056	−	0.168056i
$857$	21.4086	−	21.4086i	0.731304	−	0.731304i	−0.239574	−	0.970878i	$-0.577008\pi$
$857$	21.4086	−	21.4086i	0.731304	−	0.731304i	0.970878	+	0.239574i	$0.0770077\pi$
$858$	7.37125	−	3.90124i	0.251650	−	0.133186i
$859$			41.5479i			1.41760i	0.705411	+	0.708799i	$0.250763\pi$
$859$			41.5479i			1.41760i	−0.705411	+	0.708799i	$0.749237\pi$
$860$	5.16406	+	6.34292i	0.176093	+	0.216292i
$861$	−38.4057			−1.30886
$862$	−19.5932	+	19.5932i	−0.667348	+	0.667348i
$863$		−	0.908974i		−	0.0309418i	−0.999880	−	0.0154709i	$-0.995075\pi$
$863$		−	0.908974i		−	0.0309418i	0.999880	−	0.0154709i	$-0.00492474\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	10.9960	+	13.5062i	0.373876	+	0.459224i
$866$	−6.55103	−	6.55103i	−0.222613	−	0.222613i
$867$	10.7910	+	10.7910i	0.366480	+	0.366480i
$868$	27.0398	+	27.0398i	0.917791	+	0.917791i
$869$	−3.13579	+	3.13579i	−0.106374	+	0.106374i
$870$	−9.69495	−	11.9081i	−0.328689	−	0.403723i
$871$	22.7362	−	12.0332i	0.770387	−	0.407728i
$872$	−12.9297	−	12.9297i	−0.437855	−	0.437855i
$873$			6.60149i			0.223427i
$874$		−	36.7465i		−	1.24297i
$875$	−13.6637	+	43.2090i	−0.461917	+	1.46073i
$876$	5.20676	−	5.20676i	0.175920	−	0.175920i
$877$	32.4962			1.09732			0.548660	−	0.836046i	$-0.315138\pi$
$877$	32.4962			1.09732			0.548660	+	0.836046i	$0.315138\pi$
$878$	1.85121			0.0624753
$879$	0.253892	−	0.253892i	0.00856357	−	0.00856357i
$880$	−3.26554	−	4.01100i	−0.110081	−	0.135211i
$881$		−	2.59766i		−	0.0875173i	−0.999042	−	0.0437587i	$-0.986067\pi$
$881$		−	2.59766i		−	0.0875173i	0.999042	−	0.0437587i	$-0.0139333\pi$
$882$			9.42974i			0.317516i
$883$	6.30884	+	6.30884i	0.212309	+	0.212309i	0.805248	−	0.592938i	$-0.202032\pi$
$883$	6.30884	+	6.30884i	0.212309	+	0.212309i	−0.592938	+	0.805248i	$0.702032\pi$
$884$	1.39897	−	4.54462i	0.0470523	−	0.152852i
$885$	0.739839	−	7.22167i	0.0248694	−	0.242754i
$886$	−2.16126	+	2.16126i	−0.0726090	+	0.0726090i
$887$	12.4134	+	12.4134i	0.416802	+	0.416802i	0.884100	−	0.467298i	$-0.154772\pi$
$887$	12.4134	+	12.4134i	0.416802	+	0.416802i	−0.467298	+	0.884100i	$0.654772\pi$
$888$	5.68948	+	5.68948i	0.190926	+	0.190926i
$889$	−42.0958	−	42.0958i	−1.41185	−	1.41185i
$890$	9.86341	−	8.03026i	0.330622	−	0.269175i
$891$	−1.63560	−	1.63560i	−0.0547947	−	0.0547947i
$892$		−	10.5250i		−	0.352403i
$893$	−2.60948	+	2.60948i	−0.0873231	+	0.0873231i
$894$	−6.22059			−0.208048
$895$	51.9997	+	5.32722i	1.73816	+	0.178069i
$896$		−	4.05336i		−	0.135413i
$897$	17.7478	−	9.39304i	0.592581	−	0.313624i
$898$	8.96066	−	8.96066i	0.299021	−	0.299021i
$899$	−45.8111	−	45.8111i	−1.52789	−	1.52789i
$900$	1.01383	−	4.89614i	0.0337944	−	0.163205i
$901$			11.8380i			0.394380i
$902$	21.9166			0.729742
$903$			14.8267i			0.493401i
$904$	−5.41651	+	5.41651i	−0.180150	+	0.180150i
$905$	3.50762	−	34.2384i	0.116597	−	1.13812i
$906$	−5.34551			−0.177593
$907$	22.6107	−	22.6107i	0.750776	−	0.750776i	−0.223848	−	0.974624i	$-0.571862\pi$
$907$	22.6107	−	22.6107i	0.750776	−	0.750776i	0.974624	+	0.223848i	$0.0718621\pi$
$908$	−17.9899			−0.597015
$909$	14.8793			0.493515
$910$	12.2634	+	30.2910i	0.406528	+	1.00414i
$911$	−41.9633			−1.39031			−0.695153	−	0.718862i	$-0.744663\pi$
$911$	−41.9633			−1.39031			−0.695153	+	0.718862i	$0.744663\pi$
$912$	−6.59812			−0.218486
$913$	−1.17545	+	1.17545i	−0.0389019	+	0.0389019i
$914$	19.1156			0.632287
$915$	−11.2404	+	9.15130i	−0.371595	+	0.302533i
$916$	1.48156	−	1.48156i	0.0489520	−	0.0489520i
$917$		−	46.4109i		−	1.53262i
$918$	−1.31882			−0.0435275
$919$		−	22.7484i		−	0.750399i	−0.926944	−	0.375199i	$-0.877574\pi$
$919$		−	22.7484i		−	0.750399i	0.926944	−	0.375199i	$-0.122426\pi$
$920$	−7.86246	−	9.65731i	−0.259218	−	0.318392i
$921$	−3.15331	−	3.15331i	−0.103905	−	0.103905i
$922$	−23.8829	+	23.8829i	−0.786543	+	0.786543i
$923$	8.35433	−	27.1395i	0.274986	−	0.893307i
$924$		−	9.37579i		−	0.308441i
$925$	−8.15742	+	39.3950i	−0.268214	+	1.29530i
$926$	−0.610648			−0.0200671
$927$	5.70999	−	5.70999i	0.187541	−	0.187541i
$928$			6.86725i			0.225428i
$929$	20.7250	+	20.7250i	0.679964	+	0.679964i	0.959992	−	0.280028i	$-0.0903437\pi$
$929$	20.7250	+	20.7250i	0.679964	+	0.679964i	−0.280028	+	0.959992i	$0.590344\pi$
$930$	2.14991	−	20.9856i	0.0704984	−	0.688144i
$931$	43.9952	+	43.9952i	1.44188	+	1.44188i
$932$	2.70461	+	2.70461i	0.0885925	+	0.0885925i
$933$	−12.2932	−	12.2932i	−0.402461	−	0.402461i
$934$	−24.0091	+	24.0091i	−0.785600	+	0.785600i
$935$	−6.78571	−	0.695177i	−0.221917	−	0.0227347i
$936$	−1.68659	−	3.18675i	−0.0551281	−	0.104162i
$937$	−7.53592	−	7.53592i	−0.246188	−	0.246188i	0.573216	−	0.819404i	$-0.305695\pi$
$937$	−7.53592	−	7.53592i	−0.246188	−	0.246188i	−0.819404	+	0.573216i	$0.805695\pi$
$938$		−	28.9191i		−	0.944242i
$939$		−	5.75508i		−	0.187810i
$940$	−0.127458	+	1.24413i	−0.00415722	+	0.0405792i
$941$	25.2802	−	25.2802i	0.824111	−	0.824111i	−0.162584	−	0.986695i	$-0.551983\pi$
$941$	25.2802	−	25.2802i	0.824111	−	0.824111i	0.986695	+	0.162584i	$0.0519828\pi$
$942$	18.5605			0.604733
$943$	52.7686			1.71838
$944$	−2.29565	+	2.29565i	−0.0747169	+	0.0747169i
$945$	7.02872	−	5.72240i	0.228644	−	0.186150i
$946$		−	8.46099i		−	0.275090i
$947$			58.3795i			1.89708i	0.316661	+	0.948539i	$0.397438\pi$
$947$			58.3795i			1.89708i	−0.316661	+	0.948539i	$0.602562\pi$
$948$	1.35567	+	1.35567i	0.0440301	+	0.0440301i
$949$	23.4656	−	12.4192i	0.761725	−	0.403144i
$950$	−18.1132	−	27.5734i	−0.587670	−	0.894600i
$951$	4.14051	−	4.14051i	0.134265	−	0.134265i
$952$	−3.77995	−	3.77995i	−0.122509	−	0.122509i
$953$	14.5508	+	14.5508i	0.471347	+	0.471347i	0.902350	−	0.431003i	$-0.141840\pi$
$953$	14.5508	+	14.5508i	0.471347	+	0.471347i	−0.431003	+	0.902350i	$0.641840\pi$
$954$	6.34712	+	6.34712i	0.205496	+	0.205496i
$955$	40.7561	+	4.17535i	1.31884	+	0.135111i
$956$	−3.98109	−	3.98109i	−0.128758	−	0.128758i
$957$			15.8846i			0.513475i
$958$	0.400346	−	0.400346i	0.0129346	−	0.0129346i
$959$	84.1756			2.71817
$960$	−1.73405	+	1.41177i	−0.0559661	+	0.0455646i
$961$		−	58.0034i		−	1.87108i
$962$	13.5706	+	25.6411i	0.437533	+	0.826701i
$963$	−4.91690	+	4.91690i	−0.158445	+	0.158445i
$964$	−15.4622	−	15.4622i	−0.498005	−	0.498005i
$965$	−23.6452	−	2.42238i	−0.761165	−	0.0779792i
$966$		−	22.5741i		−	0.726310i
$967$	18.8283			0.605476			0.302738	−	0.953074i	$-0.402099\pi$
$967$	18.8283			0.605476			0.302738	+	0.953074i	$0.402099\pi$
$968$		−	5.64961i		−	0.181585i
$969$	−6.15305	+	6.15305i	−0.197665	+	0.197665i
$970$	14.6845	+	1.50439i	0.471492	+	0.0483030i
$971$	−35.3403			−1.13413			−0.567063	−	0.823675i	$-0.691920\pi$
$971$	−35.3403			−1.13413			−0.567063	+	0.823675i	$0.691920\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−52.7677			−1.69166
$974$	4.51084			0.144537
$975$	8.68732	−	15.7965i	0.278217	−	0.505894i
$976$	6.48216			0.207489
$977$	−4.38707			−0.140355			−0.0701774	−	0.997535i	$-0.522357\pi$
$977$	−4.38707			−0.140355			−0.0701774	+	0.997535i	$0.522357\pi$
$978$	7.04286	−	7.04286i	0.225206	−	0.225206i
$979$	−13.1571			−0.420502
$980$	20.9758	+	2.14891i	0.670046	+	0.0686443i
$981$	−12.9297	+	12.9297i	−0.412814	+	0.412814i
$982$		−	13.4933i		−	0.430588i
$983$	40.6617			1.29691			0.648454	−	0.761254i	$-0.275416\pi$
$983$	40.6617			1.29691			0.648454	+	0.761254i	$0.275416\pi$
$984$		−	9.47502i		−	0.302053i
$985$	1.38268	+	0.141651i	0.0440557	+	0.00451338i
$986$	6.40402	+	6.40402i	0.203946	+	0.203946i
$987$	−1.60306	+	1.60306i	−0.0510260	+	0.0510260i
$988$	−22.7370	−	6.99911i	−0.723360	−	0.222671i
$989$		−	20.3715i		−	0.647777i
$990$	−4.01100	+	3.26554i	−0.127478	+	0.103786i
$991$	40.6647			1.29176			0.645879	−	0.763440i	$-0.276491\pi$
$991$	40.6647			1.29176			0.645879	+	0.763440i	$0.276491\pi$
$992$	−6.67096	+	6.67096i	−0.211803	+	0.211803i
$993$			32.0366i			1.01665i
$994$	−22.5730	−	22.5730i	−0.715973	−	0.715973i
$995$	12.2048	+	1.25035i	0.386918	+	0.0396386i
$996$	0.508175	+	0.508175i	0.0161021	+	0.0161021i
$997$	1.66789	+	1.66789i	0.0528225	+	0.0528225i	0.733025	−	0.680202i	$-0.238108\pi$
$997$	1.66789	+	1.66789i	0.0528225	+	0.0528225i	−0.680202	+	0.733025i	$0.738108\pi$
$998$	8.38741	+	8.38741i	0.265499	+	0.265499i
$999$	5.68948	−	5.68948i	0.180007	−	0.180007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.j.b.187.5	yes	16
3.2	odd	2		1170.2.m.i.577.8		16
5.2	odd	4		1950.2.t.e.343.4		16
5.3	odd	4		390.2.t.b.343.7	yes	16
5.4	even	2		1950.2.j.e.1357.4		16
13.8	odd	4		390.2.t.b.307.7	yes	16
15.8	even	4		1170.2.w.i.343.4		16
39.8	even	4		1170.2.w.i.307.4		16
65.8	even	4	inner	390.2.j.b.73.5	✓	16
65.34	odd	4		1950.2.t.e.307.4		16
65.47	even	4		1950.2.j.e.1243.1		16
195.8	odd	4		1170.2.m.i.73.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.b.73.5	✓	16	65.8	even	4	inner
390.2.j.b.187.5	yes	16	1.1	even	1	trivial
390.2.t.b.307.7	yes	16	13.8	odd	4
390.2.t.b.343.7	yes	16	5.3	odd	4
1170.2.m.i.73.8		16	195.8	odd	4
1170.2.m.i.577.8		16	3.2	odd	2
1170.2.w.i.307.4		16	39.8	even	4
1170.2.w.i.343.4		16	15.8	even	4
1950.2.j.e.1243.1		16	65.47	even	4
1950.2.j.e.1357.4		16	5.4	even	2
1950.2.t.e.307.4		16	65.34	odd	4
1950.2.t.e.343.4		16	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 - 0.227886i) q^{5} +(0.707107 - 0.707107i) q^{6} -4.05336i q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 - 0.227886i) q^{5} +(0.707107 - 0.707107i) q^{6} -4.05336i q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.22443 - 0.227886i) q^{10} +(1.63560 + 1.63560i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.18675 - 1.68659i) q^{13} -4.05336i q^{14} +(-1.73405 + 1.41177i) q^{15} +1.00000 q^{16} +(0.932546 - 0.932546i) q^{17} -1.00000i q^{18} +(-4.66558 - 4.66558i) q^{19} +(-2.22443 - 0.227886i) q^{20} +(-2.86616 - 2.86616i) q^{21} +(1.63560 + 1.63560i) q^{22} +(3.93804 + 3.93804i) q^{23} +(0.707107 - 0.707107i) q^{24} +(4.89614 + 1.01383i) q^{25} +(3.18675 - 1.68659i) q^{26} +(-0.707107 - 0.707107i) q^{27} -4.05336i q^{28} +6.86725i q^{29} +(-1.73405 + 1.41177i) q^{30} +(-6.67096 + 6.67096i) q^{31} +1.00000 q^{32} +2.31309 q^{33} +(0.932546 - 0.932546i) q^{34} +(-0.923704 + 9.01640i) q^{35} -1.00000i q^{36} +8.04614i q^{37} +(-4.66558 - 4.66558i) q^{38} +(1.06077 - 3.44598i) q^{39} +(-2.22443 - 0.227886i) q^{40} +(6.69985 - 6.69985i) q^{41} +(-2.86616 - 2.86616i) q^{42} +(-2.58651 - 2.58651i) q^{43} +(1.63560 + 1.63560i) q^{44} +(-0.227886 + 2.22443i) q^{45} +(3.93804 + 3.93804i) q^{46} -0.559306i q^{47} +(0.707107 - 0.707107i) q^{48} -9.42974 q^{49} +(4.89614 + 1.01383i) q^{50} -1.31882i q^{51} +(3.18675 - 1.68659i) q^{52} +(-6.34712 + 6.34712i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-3.26554 - 4.01100i) q^{55} -4.05336i q^{56} -6.59812 q^{57} +6.86725i q^{58} +(-2.29565 + 2.29565i) q^{59} +(-1.73405 + 1.41177i) q^{60} +6.48216 q^{61} +(-6.67096 + 6.67096i) q^{62} -4.05336 q^{63} +1.00000 q^{64} +(-7.47305 + 3.02549i) q^{65} +2.31309 q^{66} +7.13460 q^{67} +(0.932546 - 0.932546i) q^{68} +5.56923 q^{69} +(-0.923704 + 9.01640i) q^{70} +(5.56896 - 5.56896i) q^{71} -1.00000i q^{72} +7.36347 q^{73} +8.04614i q^{74} +(4.17898 - 2.74520i) q^{75} +(-4.66558 - 4.66558i) q^{76} +(6.62968 - 6.62968i) q^{77} +(1.06077 - 3.44598i) q^{78} +1.91721i q^{79} +(-2.22443 - 0.227886i) q^{80} -1.00000 q^{81} +(6.69985 - 6.69985i) q^{82} +0.718668i q^{83} +(-2.86616 - 2.86616i) q^{84} +(-2.28689 + 1.86186i) q^{85} +(-2.58651 - 2.58651i) q^{86} +(4.85588 + 4.85588i) q^{87} +(1.63560 + 1.63560i) q^{88} +(-4.02209 + 4.02209i) q^{89} +(-0.227886 + 2.22443i) q^{90} +(-6.83638 - 12.9171i) q^{91} +(3.93804 + 3.93804i) q^{92} +9.43416i q^{93} -0.559306i q^{94} +(9.31501 + 11.4414i) q^{95} +(0.707107 - 0.707107i) q^{96} -6.60149 q^{97} -9.42974 q^{98} +(1.63560 - 1.63560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 4 q^{11} + 4 q^{13} + 4 q^{15} + 16 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{21} + 4 q^{22} + 16 q^{23} - 16 q^{25} + 4 q^{26} + 4 q^{30} + 12 q^{31} + 16 q^{32} + 4 q^{34} - 12 q^{35} + 4 q^{38} - 4 q^{39} + 4 q^{41} - 8 q^{42} - 16 q^{43} + 4 q^{44} + 16 q^{46} - 80 q^{49} - 16 q^{50} + 4 q^{52} - 44 q^{53} - 20 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{60} - 32 q^{61} + 12 q^{62} + 16 q^{64} - 44 q^{65} - 32 q^{67} + 4 q^{68} - 16 q^{69} - 12 q^{70} + 16 q^{71} + 4 q^{76} - 32 q^{77} - 4 q^{78} - 16 q^{81} + 4 q^{82} - 8 q^{84} - 64 q^{85} - 16 q^{86} + 28 q^{87} + 4 q^{88} + 4 q^{89} + 76 q^{91} + 16 q^{92} + 40 q^{95} - 8 q^{97} - 80 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 4 * q^11 + 4 * q^13 + 4 * q^15 + 16 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 + 4 * q^26 + 4 * q^30 + 12 * q^31 + 16 * q^32 + 4 * q^34 - 12 * q^35 + 4 * q^38 - 4 * q^39 + 4 * q^41 - 8 * q^42 - 16 * q^43 + 4 * q^44 + 16 * q^46 - 80 * q^49 - 16 * q^50 + 4 * q^52 - 44 * q^53 - 20 * q^55 - 16 * q^57 + 12 * q^59 + 4 * q^60 - 32 * q^61 + 12 * q^62 + 16 * q^64 - 44 * q^65 - 32 * q^67 + 4 * q^68 - 16 * q^69 - 12 * q^70 + 16 * q^71 + 4 * q^76 - 32 * q^77 - 4 * q^78 - 16 * q^81 + 4 * q^82 - 8 * q^84 - 64 * q^85 - 16 * q^86 + 28 * q^87 + 4 * q^88 + 4 * q^89 + 76 * q^91 + 16 * q^92 + 40 * q^95 - 8 * q^97 - 80 * q^98 + 4 * q^99

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