LMFDB - Embedded newform 390.2.j.b.73.5

Newspace parameters

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
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			73.5
Root			$-3.14581i$ of defining polynomial
Character	$\chi$	$=$	390.73
Dual form			390.2.j.b.187.5

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 + 0.227886i) q^{5} +(0.707107 + 0.707107i) q^{6} +4.05336i q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	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	$0.277762\pi$
$7$			4.05336i			1.53203i	−0.642825	+	0.766013i	$0.722238\pi$
$8$	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	−0.416146	−	0.909298i	$-0.636619\pi$
$11$	1.63560	−	1.63560i	0.493152	−	0.493152i	0.909298	+	0.416146i	$0.136619\pi$
$12$	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	0.811093	−	0.584917i	$-0.198873\pi$
$17$	0.932546	+	0.932546i	0.226176	+	0.226176i	−0.584917	+	0.811093i	$0.698873\pi$
$18$			1.00000i			0.235702i
$19$	−4.66558	+	4.66558i	−1.07036	+	1.07036i	−0.0730270	+	0.997330i	$0.523266\pi$
$19$	−4.66558	+	4.66558i	−1.07036	+	1.07036i	−0.997330	+	0.0730270i	$0.976734\pi$
$20$	−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	−0.165133	−	0.986271i	$-0.552805\pi$
$23$	3.93804	−	3.93804i	0.821139	−	0.821139i	0.986271	+	0.165133i	$0.0528053\pi$
$24$	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	$-0.779924\pi$
$29$		−	6.86725i		−	1.27522i	0.770361	−	0.637608i	$-0.220076\pi$
$30$	−1.73405	−	1.41177i	−0.316592	−	0.257752i
$31$	−6.67096	−	6.67096i	−1.19814	−	1.19814i	−0.974723	−	0.223417i	$-0.928279\pi$
$31$	−6.67096	−	6.67096i	−1.19814	−	1.19814i	−0.223417	−	0.974723i	$-0.571721\pi$
$32$	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	$-0.769967\pi$
$37$		−	8.04614i		−	1.32278i	0.750043	−	0.661389i	$-0.230033\pi$
$38$	−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	0.998873	+	0.0474680i	$0.0151152\pi$
$41$	6.69985	+	6.69985i	1.04634	+	1.04634i	0.0474680	+	0.998873i	$0.484885\pi$
$42$	−2.86616	+	2.86616i	−0.442258	+	0.442258i
$43$	−2.58651	+	2.58651i	−0.394439	+	0.394439i	−0.876266	−	0.481828i	$-0.839973\pi$
$43$	−2.58651	+	2.58651i	−0.394439	+	0.394439i	0.481828	+	0.876266i	$0.339973\pi$
$44$	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	$0.0129880\pi$
$47$			0.559306i			0.0815831i	−0.999168	+	0.0407916i	$0.987012\pi$
$48$	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	0.120829	−	0.992673i	$-0.461445\pi$
$53$	−6.34712	−	6.34712i	−0.871845	−	0.871845i	−0.992673	+	0.120829i	$0.961445\pi$
$54$	−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	0.541703	−	0.840570i	$-0.317780\pi$
$59$	−2.29565	−	2.29565i	−0.298868	−	0.298868i	−0.840570	+	0.541703i	$0.817780\pi$
$60$	−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	0.955596	−	0.294681i	$-0.0952135\pi$
$71$	5.56896	+	5.56896i	0.660914	+	0.660914i	−0.294681	+	0.955596i	$0.595213\pi$
$72$			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	$-0.965603\pi$
$79$		−	1.91721i		−	0.215703i	0.994167	−	0.107851i	$-0.0343970\pi$
$80$	−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	$-0.987442\pi$
$83$		−	0.718668i		−	0.0788840i	0.999222	−	0.0394420i	$-0.0125580\pi$
$84$	−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	0.461039	−	0.887380i	$-0.347477\pi$
$89$	−4.02209	−	4.02209i	−0.426340	−	0.426340i	−0.887380	+	0.461039i	$0.847477\pi$
$90$	−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	$-0.734696\pi$
$101$		−	14.8793i		−	1.48055i	0.672306	−	0.740273i	$-0.265304\pi$
$102$			1.31882i			0.130583i
$103$	5.70999	−	5.70999i	0.562622	−	0.562622i	−0.367429	−	0.930051i	$-0.619762\pi$
$103$	5.70999	−	5.70999i	0.562622	−	0.562622i	0.930051	+	0.367429i	$0.119762\pi$
$104$	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	−0.903636	−	0.428301i	$-0.859112\pi$
$107$	−4.91690	+	4.91690i	−0.475335	+	0.475335i	0.428301	+	0.903636i	$0.359112\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−12.9297	+	12.9297i	−1.23844	+	1.23844i	−0.277803	+	0.960638i	$0.589606\pi$
$109$	−12.9297	+	12.9297i	−1.23844	+	1.23844i	−0.960638	+	0.277803i	$0.910394\pi$
$110$	−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	0.404844	−	0.914386i	$-0.367326\pi$
$113$	−5.41651	−	5.41651i	−0.509542	−	0.509542i	−0.914386	+	0.404844i	$0.867326\pi$
$114$	−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	0.997139	−	0.0755835i	$-0.0240819\pi$
$127$	10.3854	+	10.3854i	0.921556	+	0.921556i	−0.0755835	+	0.997139i	$0.524082\pi$
$128$	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	$-0.652705\pi$
$137$		−	20.7669i		−	1.77423i	0.461546	−	0.887116i	$-0.347295\pi$
$138$	5.56923			0.474085
$139$			13.0183i			1.10420i	0.833780	+	0.552098i	$0.186172\pi$
$139$			13.0183i			1.10420i	−0.833780	+	0.552098i	$0.813828\pi$
$140$	−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	−0.863941	−	0.503592i	$-0.832011\pi$
$149$	−4.39862	+	4.39862i	−0.360349	+	0.360349i	0.503592	+	0.863941i	$0.332011\pi$
$150$	4.17898	+	2.74520i	0.341212	+	0.224145i
$151$	−3.77985	+	3.77985i	−0.307600	+	0.307600i	−0.843978	−	0.536378i	$-0.819792\pi$
$151$	−3.77985	+	3.77985i	−0.307600	+	0.307600i	0.536378	+	0.843978i	$0.319792\pi$
$152$	−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	0.0486112	−	0.998818i	$-0.484520\pi$
$157$	13.1242	−	13.1242i	1.04743	−	1.04743i	0.998818	−	0.0486112i	$-0.0154795\pi$
$158$		−	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	$0.139696\pi$
$167$			10.9823i			0.849833i	−0.905233	+	0.424916i	$0.860304\pi$
$168$	−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	−0.884766	−	0.466036i	$-0.845682\pi$
$173$	−5.50754	+	5.50754i	−0.418730	+	0.418730i	0.466036	+	0.884766i	$0.345682\pi$
$174$	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	$-0.806153\pi$
$181$		−	15.3920i		−	1.14408i	0.820226	−	0.572039i	$-0.193847\pi$
$182$	−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	$0.114635\pi$
$223$			10.5250i			0.704806i	−0.935848	+	0.352403i	$0.885365\pi$
$224$			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	0.754362	−	0.656458i	$-0.227946\pi$
$229$	1.48156	+	1.48156i	0.0979041	+	0.0979041i	−0.656458	+	0.754362i	$0.727946\pi$
$230$	−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	−0.612943	−	0.790127i	$-0.710014\pi$
$233$	2.70461	−	2.70461i	0.177185	−	0.177185i	0.790127	+	0.612943i	$0.210014\pi$
$234$	−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	−0.824043	−	0.566528i	$-0.808286\pi$
$239$	−3.98109	+	3.98109i	−0.257515	+	0.257515i	0.566528	+	0.824043i	$0.308286\pi$
$240$	−1.73405	−	1.41177i	−0.111932	−	0.0911291i
$241$	−15.4622	+	15.4622i	−0.996011	+	0.996011i	−0.999992	−	0.00398120i	$-0.998733\pi$
$241$	−15.4622	+	15.4622i	−0.996011	+	0.996011i	0.00398120	+	0.999992i	$0.498733\pi$
$242$			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	$0.192264\pi$
$251$			17.9961i			1.13590i	−0.823062	+	0.567951i	$0.807736\pi$
$252$	−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	0.748370	−	0.663282i	$-0.230837\pi$
$257$	1.36406	+	1.36406i	0.0850880	+	0.0850880i	−0.663282	+	0.748370i	$0.730837\pi$
$258$	−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	0.631586	−	0.775306i	$-0.282404\pi$
$263$	−2.33074	−	2.33074i	−0.143719	−	0.143719i	−0.775306	+	0.631586i	$0.782404\pi$
$264$	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	$-0.876318\pi$
$269$		−	12.4274i		−	0.757711i	0.925456	−	0.378855i	$-0.123682\pi$
$270$	1.41177	−	1.73405i	0.0859174	−	0.105531i
$271$	3.48130	−	3.48130i	0.211474	−	0.211474i	−0.593419	−	0.804893i	$-0.702222\pi$
$271$	3.48130	−	3.48130i	0.211474	−	0.211474i	0.804893	+	0.593419i	$0.202222\pi$
$272$	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	0.203001	−	0.979179i	$-0.434931\pi$
$277$	−12.9182	−	12.9182i	−0.776178	−	0.776178i	−0.979179	+	0.203001i	$0.934931\pi$
$278$			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	−0.0422717	+	0.999106i	$0.513460\pi$
$281$	−17.4567	+	17.4567i	−1.04138	+	1.04138i	−0.999106	+	0.0422717i	$0.986540\pi$
$282$	−0.395489	+	0.395489i	−0.0235510	+	0.0235510i
$283$	−7.63296	+	7.63296i	−0.453733	+	0.453733i	−0.896591	−	0.442859i	$-0.853964\pi$
$283$	−7.63296	+	7.63296i	−0.453733	+	0.453733i	0.442859	+	0.896591i	$0.353964\pi$
$284$	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	$0.0406174\pi$
$307$			4.45946i			0.254515i	−0.991870	+	0.127257i	$0.959383\pi$
$308$	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	$0.164068\pi$
$311$			17.3852i			0.985824i	−0.870079	+	0.492912i	$0.835932\pi$
$312$	1.06077	+	3.44598i	0.0600544	+	0.195090i
$313$	4.06946	+	4.06946i	0.230019	+	0.230019i	0.812701	−	0.582681i	$-0.197996\pi$
$313$	4.06946	+	4.06946i	0.230019	+	0.230019i	−0.582681	+	0.812701i	$0.697996\pi$
$314$	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	−0.957842	−	0.287294i	$-0.907244\pi$
$331$	−22.6533	−	22.6533i	−1.24514	−	1.24514i	−0.287294	−	0.957842i	$-0.592756\pi$
$332$		−	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	0.890206	−	0.455559i	$-0.150561\pi$
$337$	7.97905	+	7.97905i	0.434647	+	0.434647i	−0.455559	+	0.890206i	$0.650561\pi$
$338$	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	−0.263637	−	0.964622i	$-0.584922\pi$
$347$	13.0579	−	13.0579i	0.700985	−	0.700985i	0.964622	+	0.263637i	$0.0849221\pi$
$348$	4.85588	−	4.85588i	0.260302	−	0.260302i
$349$	−21.5924	−	21.5924i	−1.15581	−	1.15581i	−0.985367	−	0.170447i	$-0.945479\pi$
$349$	−21.5924	−	21.5924i	−1.15581	−	1.15581i	−0.170447	−	0.985367i	$-0.554521\pi$
$350$	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	$-0.995622\pi$
$353$		−	0.516800i		−	0.0275065i	0.999905	−	0.0137533i	$-0.00437794\pi$
$354$		−	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	0.716597	−	0.697487i	$-0.245699\pi$
$359$	0.362077	+	0.362077i	0.0191097	+	0.0191097i	−0.697487	+	0.716597i	$0.745699\pi$
$360$	−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	−0.538845	−	0.842405i	$-0.681139\pi$
$367$	5.81538	−	5.81538i	0.303560	−	0.303560i	0.842405	+	0.538845i	$0.181139\pi$
$368$	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	0.384060	−	0.923308i	$-0.374525\pi$
$373$	−10.4146	−	10.4146i	−0.539248	−	0.539248i	−0.923308	+	0.384060i	$0.874525\pi$
$374$	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	0.247726	−	0.968830i	$-0.420317\pi$
$379$	23.6838	−	23.6838i	1.21656	−	1.21656i	0.968830	−	0.247726i	$-0.0796832\pi$
$380$	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	$0.223280\pi$
$383$			25.2587i			1.29066i	−0.763904	+	0.645330i	$0.776720\pi$
$384$	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	$0.110278\pi$
$397$			13.5313i			0.679118i	−0.940585	+	0.339559i	$0.889722\pi$
$398$	−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	−0.772558	−	0.634945i	$-0.781023\pi$
$401$	−2.75570	+	2.75570i	−0.137613	+	0.137613i	0.634945	+	0.772558i	$0.281023\pi$
$402$	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	−0.798871	−	0.601502i	$-0.794569\pi$
$409$	−3.99155	+	3.99155i	−0.197369	+	0.197369i	0.601502	+	0.798871i	$0.294569\pi$
$410$	−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	$-0.657023\pi$
$419$		−	36.0580i		−	1.76155i	0.473538	−	0.880773i	$-0.342977\pi$
$420$	5.72240	−	7.02872i	0.279225	−	0.342966i
$421$	−25.5839	−	25.5839i	−1.24688	−	1.24688i	−0.957090	−	0.289791i	$-0.906414\pi$
$421$	−25.5839	−	25.5839i	−1.24688	−	1.24688i	−0.289791	−	0.957090i	$-0.593586\pi$
$422$	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	0.0547284	−	0.998501i	$-0.482571\pi$
$431$	−19.5932	−	19.5932i	−0.943773	−	0.943773i	−0.998501	+	0.0547284i	$0.982571\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−6.55103	+	6.55103i	−0.314823	+	0.314823i	−0.846775	−	0.531952i	$-0.821459\pi$
$433$	−6.55103	+	6.55103i	−0.314823	+	0.314823i	0.531952	+	0.846775i	$0.321459\pi$
$434$	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	0.653898	−	0.756583i	$-0.273133\pi$
$443$	−2.16126	−	2.16126i	−0.102685	−	0.102685i	−0.756583	+	0.653898i	$0.773133\pi$
$444$	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	0.886194	−	0.463314i	$-0.153340\pi$
$449$	8.96066	+	8.96066i	0.422880	+	0.422880i	−0.463314	+	0.886194i	$0.653340\pi$
$450$	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	−0.992834	−	0.119506i	$-0.961869\pi$
$461$	−23.8829	−	23.8829i	−1.11234	−	1.11234i	−0.119506	−	0.992834i	$-0.538131\pi$
$462$			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	−0.993015	−	0.117992i	$-0.962354\pi$
$467$	−24.0091	−	24.0091i	−1.11101	−	1.11101i	−0.117992	−	0.993015i	$-0.537646\pi$
$468$	−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	0.716194	−	0.697901i	$-0.245883\pi$
$479$	0.400346	+	0.400346i	0.0182923	+	0.0182923i	−0.697901	+	0.716194i	$0.745883\pi$
$480$	−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	$0.0984800\pi$
$491$			13.4933i			0.608944i	−0.952521	+	0.304472i	$0.901520\pi$
$492$			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	−0.493993	−	0.869466i	$-0.664463\pi$
$499$	8.38741	−	8.38741i	0.375472	−	0.375472i	0.869466	+	0.493993i	$0.164463\pi$
$500$	−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	0.456551	−	0.889697i	$-0.349085\pi$
$503$	−9.71446	−	9.71446i	−0.433146	−	0.433146i	−0.889697	+	0.456551i	$0.849085\pi$
$504$	−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	−0.790202	−	0.612847i	$-0.790024\pi$
$509$	−4.00130	+	4.00130i	−0.177354	+	0.177354i	0.612847	+	0.790202i	$0.290024\pi$
$510$	−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	0.918421	−	0.395605i	$-0.129465\pi$
$523$	11.9564	+	11.9564i	0.522816	+	0.522816i	−0.395605	+	0.918421i	$0.629465\pi$
$524$	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	−0.222530	−	0.974926i	$-0.571432\pi$
$541$	17.5003	−	17.5003i	0.752395	−	0.752395i	0.974926	+	0.222530i	$0.0714316\pi$
$542$	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	−0.952383	−	0.304905i	$-0.901375\pi$
$547$	−15.1432	+	15.1432i	−0.647478	+	0.647478i	0.304905	+	0.952383i	$0.401375\pi$
$548$		−	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	$-0.846243\pi$
$557$		−	21.9240i		−	0.928952i	0.885586	−	0.464476i	$-0.153757\pi$
$558$	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	−0.999154	−	0.0411219i	$-0.986907\pi$
$563$	−22.7318	+	22.7318i	−0.958032	+	0.958032i	0.0411219	+	0.999154i	$0.486907\pi$
$564$	−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	$-0.947912\pi$
$571$		−	7.78560i		−	0.325817i	0.986641	−	0.162909i	$-0.0520876\pi$
$572$	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	$-0.936238\pi$
$599$		−	9.73974i		−	0.397955i	0.980004	−	0.198978i	$-0.0637621\pi$
$600$	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	−0.0198060	+	0.999804i	$0.506305\pi$
$607$	−25.1205	+	25.1205i	−1.01961	+	1.01961i	−0.999804	+	0.0198060i	$0.993695\pi$
$608$	−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	$0.380108\pi$
$613$			46.0466i			1.85980i	−0.367808	+	0.929902i	$0.619892\pi$
$614$			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	0.750380	−	0.661007i	$-0.229871\pi$
$619$	2.22356	+	2.22356i	0.0893725	+	0.0893725i	−0.661007	+	0.750380i	$0.729871\pi$
$620$	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	−0.896199	−	0.443653i	$-0.853682\pi$
$631$	−11.3678	+	11.3678i	−0.452546	+	0.452546i	0.443653	+	0.896199i	$0.353682\pi$
$632$		−	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	$0.180922\pi$
$641$			27.2559i			1.07654i	−0.842772	+	0.538271i	$0.819078\pi$
$642$	−6.95355			−0.274435
$643$			12.3529i			0.487153i	0.969882	+	0.243576i	$0.0783207\pi$
$643$			12.3529i			0.487153i	−0.969882	+	0.243576i	$0.921679\pi$
$644$	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	0.823693	−	0.567036i	$-0.191910\pi$
$647$	6.52838	+	6.52838i	0.256657	+	0.256657i	−0.567036	+	0.823693i	$0.691910\pi$
$648$	−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	0.921908	−	0.387408i	$-0.126630\pi$
$653$	13.6586	+	13.6586i	0.534500	+	0.534500i	−0.387408	+	0.921908i	$0.626630\pi$
$654$	−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	$0.419643\pi$
$659$			49.7146i			1.93661i	−0.249776	+	0.968304i	$0.580357\pi$
$660$	−5.14530	+	0.527121i	−0.200280	+	0.0205181i
$661$	−24.9427	+	24.9427i	−0.970157	+	0.970157i	−0.999567	−	0.0294100i	$-0.990637\pi$
$661$	−24.9427	+	24.9427i	−0.970157	+	0.970157i	0.0294100	+	0.999567i	$0.490637\pi$
$662$	−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	−0.595823	−	0.803116i	$-0.703174\pi$
$673$	5.37765	−	5.37765i	0.207293	−	0.207293i	0.803116	+	0.595823i	$0.203174\pi$
$674$	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	−0.883632	−	0.468183i	$-0.844909\pi$
$677$	−10.8097	+	10.8097i	−0.415449	+	0.415449i	0.468183	+	0.883632i	$0.344909\pi$
$678$		−	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	0.0879526	−	0.996125i	$-0.471968\pi$
$691$	−23.8730	−	23.8730i	−0.908172	−	0.908172i	−0.996125	+	0.0879526i	$0.971968\pi$
$692$	−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	$-0.916603\pi$
$701$		−	13.7155i		−	0.518027i	0.965874	−	0.259013i	$-0.0833974\pi$
$702$	−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	0.871751	+	0.489949i	$0.162985\pi$
$709$	36.2581	+	36.2581i	1.36170	+	1.36170i	0.489949	+	0.871751i	$0.337015\pi$
$710$	−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	0.947310	−	0.320319i	$-0.103790\pi$
$727$	16.9055	+	16.9055i	0.626991	+	0.626991i	−0.320319	+	0.947310i	$0.603790\pi$
$728$	−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	$-0.721667\pi$
$733$		−	41.5404i		−	1.53433i	0.641449	−	0.767165i	$-0.278333\pi$
$734$	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	0.333461	−	0.942764i	$-0.391783\pi$
$739$	−16.5636	−	16.5636i	−0.609303	−	0.609303i	−0.942764	+	0.333461i	$0.891783\pi$
$740$	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	$0.0503678\pi$
$743$			8.59040i			0.315151i	−0.987507	+	0.157576i	$0.949632\pi$
$744$		−	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	$0.171224\pi$
$751$			28.0811i			1.02469i	−0.858779	+	0.512347i	$0.828776\pi$
$752$			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	0.0371063	−	0.999311i	$-0.488186\pi$
$757$	28.5156	−	28.5156i	1.03642	−	1.03642i	0.999311	−	0.0371063i	$-0.0118140\pi$
$758$	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	−0.815228	−	0.579141i	$-0.803388\pi$
$761$	−6.51275	+	6.51275i	−0.236087	+	0.236087i	0.579141	+	0.815228i	$0.303388\pi$
$762$			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	−0.679831	−	0.733368i	$-0.737947\pi$
$769$	1.48463	−	1.48463i	0.0535371	−	0.0535371i	0.733368	+	0.679831i	$0.237947\pi$
$770$	−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	$-0.806128\pi$
$773$		−	31.8123i		−	1.14421i	0.820181	−	0.572104i	$-0.193872\pi$
$774$	−2.58651	−	2.58651i	−0.0929701	−	0.0929701i
$775$	−39.4251	−	25.8987i	−1.41619	−

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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