LMFDB - Embedded newform 690.3.k.a.277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.7
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.91222 - 5.89021i) q^{10} -12.9969 q^{11} +(-2.44949 - 2.44949i) q^{12} +(10.2470 - 10.2470i) q^{13} +4.29989i q^{14} +(7.21400 - 4.79147i) q^{15} -4.00000 q^{16} +(-2.98774 - 2.98774i) q^{17} +(3.00000 - 3.00000i) q^{18} -26.4014i q^{19} +(1.97798 - 9.80243i) q^{20} -5.26627 q^{21} +(-12.9969 - 12.9969i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(23.0438 + 9.69452i) q^{25} +20.4940 q^{26} +(3.67423 + 3.67423i) q^{27} +(-4.29989 + 4.29989i) q^{28} +45.6115i q^{29} +(12.0055 + 2.42253i) q^{30} +37.4631 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.9179 - 15.9179i) q^{33} -5.97547i q^{34} +(-8.41107 - 12.6636i) q^{35} +6.00000 q^{36} +(-44.9599 - 44.9599i) q^{37} +(26.4014 - 26.4014i) q^{38} +25.0999i q^{39} +(11.7804 - 7.82444i) q^{40} +39.3742 q^{41} +(-5.26627 - 5.26627i) q^{42} +(29.7399 - 29.7399i) q^{43} -25.9939i q^{44} +(-2.96698 + 14.7036i) q^{45} +6.78233 q^{46} +(-10.2691 - 10.2691i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.7555i q^{49} +(13.3493 + 32.7383i) q^{50} +7.31843 q^{51} +(20.4940 + 20.4940i) q^{52} +(34.6215 - 34.6215i) q^{53} +7.34847i q^{54} +(63.7007 + 12.8539i) q^{55} -8.59979 q^{56} +(32.3350 + 32.3350i) q^{57} +(-45.6115 + 45.6115i) q^{58} -22.8736i q^{59} +(9.58295 + 14.4280i) q^{60} -70.3445 q^{61} +(37.4631 + 37.4631i) q^{62} +(6.44984 - 6.44984i) q^{63} -8.00000i q^{64} +(-60.3568 + 40.0884i) q^{65} +31.8358 q^{66} +(19.6879 + 19.6879i) q^{67} +(5.97547 - 5.97547i) q^{68} +8.30662i q^{69} +(4.25256 - 21.0747i) q^{70} +131.287 q^{71} +(6.00000 + 6.00000i) q^{72} +(49.0534 - 49.0534i) q^{73} -89.9197i q^{74} +(-40.0961 + 16.3494i) q^{75} +52.8028 q^{76} +(-27.9427 - 27.9427i) q^{77} +(-25.0999 + 25.0999i) q^{78} -59.2011i q^{79} +(19.6049 + 3.95597i) q^{80} -9.00000 q^{81} +(39.3742 + 39.3742i) q^{82} +(-31.0483 + 31.0483i) q^{83} -10.5325i q^{84} +(11.6887 + 17.5984i) q^{85} +59.4799 q^{86} +(-55.8625 - 55.8625i) q^{87} +(25.9939 - 25.9939i) q^{88} -169.901i q^{89} +(-17.6706 + 11.7367i) q^{90} +44.0609 q^{91} +(6.78233 + 6.78233i) q^{92} +(-45.8827 + 45.8827i) q^{93} -20.5382i q^{94} +(-26.1108 + 129.399i) q^{95} +9.79796 q^{96} +(8.17591 + 8.17591i) q^{97} +(39.7555 - 39.7555i) q^{98} +38.9908i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−4.90121	−	0.988992i	−0.980243	−	0.197798i
$5$	−4.90121	−	0.988992i	−0.980243	−	0.197798i
$6$	−2.44949			−0.408248
$7$	2.14995	+	2.14995i	0.307135	+	0.307135i	0.843797	−	0.536662i	$-0.180315\pi$
$7$	2.14995	+	2.14995i	0.307135	+	0.307135i	−0.536662	+	0.843797i	$0.680315\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−3.91222	−	5.89021i	−0.391222	−	0.589021i
$11$	−12.9969			−1.18154			−0.590770	−	0.806840i	$-0.701176\pi$
$11$	−12.9969			−1.18154			−0.590770	+	0.806840i	$0.701176\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	10.2470	−	10.2470i	0.788229	−	0.788229i	−0.192975	−	0.981204i	$-0.561814\pi$
$13$	10.2470	−	10.2470i	0.788229	−	0.788229i	0.981204	+	0.192975i	$0.0618136\pi$
$14$			4.29989i			0.307135i
$15$	7.21400	−	4.79147i	0.480933	−	0.319432i
$16$	−4.00000			−0.250000
$17$	−2.98774	−	2.98774i	−0.175749	−	0.175749i	0.613751	−	0.789500i	$-0.289660\pi$
$17$	−2.98774	−	2.98774i	−0.175749	−	0.175749i	−0.789500	+	0.613751i	$0.789660\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	26.4014i		−	1.38955i	−0.719228	−	0.694774i	$-0.755504\pi$
$19$		−	26.4014i		−	1.38955i	0.719228	−	0.694774i	$-0.244496\pi$
$20$	1.97798	−	9.80243i	0.0988992	−	0.490121i
$21$	−5.26627			−0.250775
$22$	−12.9969	−	12.9969i	−0.590770	−	0.590770i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	23.0438	+	9.69452i	0.921752	+	0.387781i
$26$	20.4940			0.788229
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−4.29989	+	4.29989i	−0.153568	+	0.153568i
$29$			45.6115i			1.57281i	0.617711	+	0.786406i	$0.288060\pi$
$29$			45.6115i			1.57281i	−0.617711	+	0.786406i	$0.711940\pi$
$30$	12.0055	+	2.42253i	0.400182	+	0.0807509i
$31$	37.4631			1.20849			0.604243	−	0.796800i	$-0.293476\pi$
$31$	37.4631			1.20849			0.604243	+	0.796800i	$0.293476\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	15.9179	−	15.9179i	0.482361	−	0.482361i
$34$		−	5.97547i		−	0.175749i
$35$	−8.41107	−	12.6636i	−0.240316	−	0.361818i
$36$	6.00000			0.166667
$37$	−44.9599	−	44.9599i	−1.21513	−	1.21513i	−0.969317	−	0.245815i	$-0.920945\pi$
$37$	−44.9599	−	44.9599i	−1.21513	−	1.21513i	−0.245815	−	0.969317i	$-0.579055\pi$
$38$	26.4014	−	26.4014i	0.694774	−	0.694774i
$39$			25.0999i			0.643586i
$40$	11.7804	−	7.82444i	0.294510	−	0.195611i
$41$	39.3742			0.960347			0.480173	−	0.877174i	$-0.340574\pi$
$41$	39.3742			0.960347			0.480173	+	0.877174i	$0.340574\pi$
$42$	−5.26627	−	5.26627i	−0.125387	−	0.125387i
$43$	29.7399	−	29.7399i	0.691627	−	0.691627i	−0.270963	−	0.962590i	$-0.587342\pi$
$43$	29.7399	−	29.7399i	0.691627	−	0.691627i	0.962590	+	0.270963i	$0.0873421\pi$
$44$		−	25.9939i		−	0.590770i
$45$	−2.96698	+	14.7036i	−0.0659328	+	0.326748i
$46$	6.78233			0.147442
$47$	−10.2691	−	10.2691i	−0.218491	−	0.218491i	0.589371	−	0.807862i	$-0.299376\pi$
$47$	−10.2691	−	10.2691i	−0.218491	−	0.218491i	−0.807862	+	0.589371i	$0.799376\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	39.7555i		−	0.811336i
$50$	13.3493	+	32.7383i	0.266985	+	0.654766i
$51$	7.31843			0.143499
$52$	20.4940	+	20.4940i	0.394114	+	0.394114i
$53$	34.6215	−	34.6215i	0.653235	−	0.653235i	−0.300535	−	0.953771i	$-0.597165\pi$
$53$	34.6215	−	34.6215i	0.653235	−	0.653235i	0.953771	+	0.300535i	$0.0971654\pi$
$54$			7.34847i			0.136083i
$55$	63.7007	+	12.8539i	1.15820	+	0.233707i
$56$	−8.59979			−0.153568
$57$	32.3350	+	32.3350i	0.567281	+	0.567281i
$58$	−45.6115	+	45.6115i	−0.786406	+	0.786406i
$59$		−	22.8736i		−	0.387688i	−0.981032	−	0.193844i	$-0.937904\pi$
$59$		−	22.8736i		−	0.387688i	0.981032	−	0.193844i	$-0.0620955\pi$
$60$	9.58295	+	14.4280i	0.159716	+	0.240467i
$61$	−70.3445			−1.15319			−0.576595	−	0.817030i	$-0.695619\pi$
$61$	−70.3445			−1.15319			−0.576595	+	0.817030i	$0.695619\pi$
$62$	37.4631	+	37.4631i	0.604243	+	0.604243i
$63$	6.44984	−	6.44984i	0.102378	−	0.102378i
$64$		−	8.00000i		−	0.125000i
$65$	−60.3568	+	40.0884i	−0.928566	+	0.616745i
$66$	31.8358			0.482361
$67$	19.6879	+	19.6879i	0.293849	+	0.293849i	0.838599	−	0.544750i	$-0.183375\pi$
$67$	19.6879	+	19.6879i	0.293849	+	0.293849i	−0.544750	+	0.838599i	$0.683375\pi$
$68$	5.97547	−	5.97547i	0.0878746	−	0.0878746i
$69$			8.30662i			0.120386i
$70$	4.25256	−	21.0747i	0.0607509	−	0.301067i
$71$	131.287			1.84911			0.924557	−	0.381044i	$-0.124436\pi$
$71$	131.287			1.84911			0.924557	+	0.381044i	$0.124436\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	49.0534	−	49.0534i	0.671964	−	0.671964i	−0.286205	−	0.958169i	$-0.592394\pi$
$73$	49.0534	−	49.0534i	0.671964	−	0.671964i	0.958169	+	0.286205i	$0.0923937\pi$
$74$		−	89.9197i		−	1.21513i
$75$	−40.0961	+	16.3494i	−0.534614	+	0.217993i
$76$	52.8028			0.694774
$77$	−27.9427	−	27.9427i	−0.362892	−	0.362892i
$78$	−25.0999	+	25.0999i	−0.321793	+	0.321793i
$79$		−	59.2011i		−	0.749381i	−0.927150	−	0.374691i	$-0.877749\pi$
$79$		−	59.2011i		−	0.749381i	0.927150	−	0.374691i	$-0.122251\pi$
$80$	19.6049	+	3.95597i	0.245061	+	0.0494496i
$81$	−9.00000			−0.111111
$82$	39.3742	+	39.3742i	0.480173	+	0.480173i
$83$	−31.0483	+	31.0483i	−0.374076	+	0.374076i	−0.868960	−	0.494883i	$-0.835211\pi$
$83$	−31.0483	+	31.0483i	−0.374076	+	0.374076i	0.494883	+	0.868960i	$0.335211\pi$
$84$		−	10.5325i		−	0.125387i
$85$	11.6887	+	17.5984i	0.137514	+	0.207040i
$86$	59.4799			0.691627
$87$	−55.8625	−	55.8625i	−0.642097	−	0.642097i
$88$	25.9939	−	25.9939i	0.295385	−	0.295385i
$89$		−	169.901i		−	1.90900i	−0.298219	−	0.954498i	$-0.596392\pi$
$89$		−	169.901i		−	1.90900i	0.298219	−	0.954498i	$-0.403608\pi$
$90$	−17.6706	+	11.7367i	−0.196340	+	0.130407i
$91$	44.0609			0.484186
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	−45.8827	+	45.8827i	−0.493362	+	0.493362i
$94$		−	20.5382i		−	0.218491i
$95$	−26.1108	+	129.399i	−0.274850	+	1.36209i
$96$	9.79796			0.102062
$97$	8.17591	+	8.17591i	0.0842878	+	0.0842878i	0.747994	−	0.663706i	$-0.231017\pi$
$97$	8.17591	+	8.17591i	0.0842878	+	0.0842878i	−0.663706	+	0.747994i	$0.731017\pi$
$98$	39.7555	−	39.7555i	0.405668	−	0.405668i
$99$			38.9908i			0.393846i
$100$	−19.3890	+	46.0876i	−0.193890	+	0.460876i
$101$	−155.093			−1.53558			−0.767788	−	0.640704i	$-0.778643\pi$
$101$	−155.093			−1.53558			−0.767788	+	0.640704i	$0.778643\pi$
$102$	7.31843	+	7.31843i	0.0717493	+	0.0717493i
$103$	−46.5485	+	46.5485i	−0.451927	+	0.451927i	−0.895994	−	0.444067i	$-0.853535\pi$
$103$	−46.5485	+	46.5485i	−0.451927	+	0.451927i	0.444067	+	0.895994i	$0.353535\pi$
$104$			40.9879i			0.394114i
$105$	25.8111	+	5.20830i	0.245820	+	0.0496029i
$106$	69.2429			0.653235
$107$	13.6792	+	13.6792i	0.127843	+	0.127843i	0.768133	−	0.640290i	$-0.221186\pi$
$107$	13.6792	+	13.6792i	0.127843	+	0.127843i	−0.640290	+	0.768133i	$0.721186\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			105.153i			0.964702i	0.875978	+	0.482351i	$0.160217\pi$
$109$			105.153i			0.964702i	−0.875978	+	0.482351i	$0.839783\pi$
$110$	50.8469	+	76.5546i	0.462244	+	0.695951i
$111$	110.129			0.992151
$112$	−8.59979	−	8.59979i	−0.0767838	−	0.0767838i
$113$	−140.459	+	140.459i	−1.24300	+	1.24300i	−0.284254	+	0.958749i	$0.591746\pi$
$113$	−140.459	+	140.459i	−1.24300	+	1.24300i	−0.958749	+	0.284254i	$0.908254\pi$
$114$			64.6700i			0.567281i
$115$	−19.9747	+	13.2670i	−0.173693	+	0.115365i
$116$	−91.2230			−0.786406
$117$	−30.7409	−	30.7409i	−0.262743	−	0.262743i
$118$	22.8736	−	22.8736i	0.193844	−	0.193844i
$119$		−	12.8469i		−	0.107958i
$120$	−4.84505	+	24.0109i	−0.0403754	+	0.200091i
$121$	47.9202			0.396035
$122$	−70.3445	−	70.3445i	−0.576595	−	0.576595i
$123$	−48.2234	+	48.2234i	−0.392060	+	0.392060i
$124$			74.9261i			0.604243i
$125$	−103.355	−	70.3051i	−0.826838	−	0.562441i
$126$	12.8997			0.102378
$127$	−110.338	−	110.338i	−0.868803	−	0.868803i	0.123537	−	0.992340i	$-0.460576\pi$
$127$	−110.338	−	110.338i	−0.868803	−	0.868803i	−0.992340	+	0.123537i	$0.960576\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			72.8477i			0.564711i
$130$	−100.445	−	20.2684i	−0.772656	−	0.155910i
$131$	62.3911			0.476268			0.238134	−	0.971232i	$-0.423464\pi$
$131$	62.3911			0.476268			0.238134	+	0.971232i	$0.423464\pi$
$132$	31.8358	+	31.8358i	0.241181	+	0.241181i
$133$	56.7616	−	56.7616i	0.426779	−	0.426779i
$134$			39.3757i			0.293849i
$135$	−14.3744	−	21.6420i	−0.106477	−	0.160311i
$136$	11.9509			0.0878746
$137$	−3.75731	−	3.75731i	−0.0274256	−	0.0274256i	0.693261	−	0.720687i	$-0.256173\pi$
$137$	−3.75731	−	3.75731i	−0.0274256	−	0.0274256i	−0.720687	+	0.693261i	$0.756173\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	244.157i		−	1.75652i	−0.478179	−	0.878262i	$-0.658703\pi$
$139$		−	244.157i		−	1.75652i	0.478179	−	0.878262i	$-0.341297\pi$
$140$	25.3273	−	16.8221i	0.180909	−	0.120158i
$141$	25.1540			0.178397
$142$	131.287	+	131.287i	0.924557	+	0.924557i
$143$	−133.179	+	133.179i	−0.931323	+	0.931323i
$144$			12.0000i			0.0833333i
$145$	45.1094	−	223.552i	0.311100	−	1.54174i
$146$	98.1067			0.671964
$147$	48.6903	+	48.6903i	0.331226	+	0.331226i
$148$	89.9197	−	89.9197i	0.607566	−	0.607566i
$149$		−	209.038i		−	1.40294i	−0.712699	−	0.701470i	$-0.752527\pi$
$149$		−	209.038i		−	1.40294i	0.712699	−	0.701470i	$-0.247473\pi$
$150$	−56.4455	−	23.7466i	−0.376303	−	0.158311i
$151$	−97.4480			−0.645351			−0.322675	−	0.946510i	$-0.604582\pi$
$151$	−97.4480			−0.645351			−0.322675	+	0.946510i	$0.604582\pi$
$152$	52.8028	+	52.8028i	0.347387	+	0.347387i
$153$	−8.96321	+	8.96321i	−0.0585830	+	0.0585830i
$154$		−	55.8854i		−	0.362892i
$155$	−183.614	−	37.0507i	−1.18461	−	0.239037i
$156$	−50.1997			−0.321793
$157$	142.961	+	142.961i	0.910581	+	0.910581i	0.996318	−	0.0857369i	$-0.0273245\pi$
$157$	142.961	+	142.961i	0.910581	+	0.910581i	−0.0857369	+	0.996318i	$0.527324\pi$
$158$	59.2011	−	59.2011i	0.374691	−	0.374691i
$159$			84.8049i			0.533364i
$160$	15.6489	+	23.5608i	0.0978055	+	0.147255i
$161$	14.5817			0.0905693
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−102.695	+	102.695i	−0.630032	+	0.630032i	−0.948076	−	0.318044i	$-0.896974\pi$
$163$	−102.695	+	102.695i	−0.630032	+	0.630032i	0.318044	+	0.948076i	$0.396974\pi$
$164$			78.7484i			0.480173i
$165$	−93.7599	+	62.2744i	−0.568242	+	0.377421i
$166$	−62.0967			−0.374076
$167$	−169.393	−	169.393i	−1.01433	−	1.01433i	−0.999896	−	0.0144364i	$-0.995405\pi$
$167$	−169.393	−	169.393i	−1.01433	−	1.01433i	−0.0144364	−	0.999896i	$-0.504595\pi$
$168$	10.5325	−	10.5325i	0.0626937	−	0.0626937i
$169$		−	41.0011i		−	0.242610i
$170$	−5.90969	+	29.2871i	−0.0347629	+	0.172277i
$171$	−79.2042			−0.463183
$172$	59.4799	+	59.4799i	0.345813	+	0.345813i
$173$	91.2722	−	91.2722i	0.527585	−	0.527585i	−0.392267	−	0.919852i	$-0.628309\pi$
$173$	91.2722	−	91.2722i	0.527585	−	0.527585i	0.919852	+	0.392267i	$0.128309\pi$
$174$		−	111.725i		−	0.642097i
$175$	28.7002	+	70.3857i	0.164001	+	0.402204i
$176$	51.9877			0.295385
$177$	28.0143	+	28.0143i	0.158273	+	0.158273i
$178$	169.901	−	169.901i	0.954498	−	0.954498i
$179$		−	134.161i		−	0.749503i	−0.927125	−	0.374752i	$-0.877728\pi$
$179$		−	134.161i		−	0.749503i	0.927125	−	0.374752i	$-0.122272\pi$
$180$	−29.4073	−	5.93395i	−0.163374	−	0.0329664i
$181$	−102.342			−0.565424			−0.282712	−	0.959205i	$-0.591234\pi$
$181$	−102.342			−0.565424			−0.282712	+	0.959205i	$0.591234\pi$
$182$	44.0609	+	44.0609i	0.242093	+	0.242093i
$183$	86.1541	−	86.1541i	0.470787	−	0.470787i
$184$			13.5647i			0.0737210i
$185$	175.893	+	264.823i	0.950773	+	1.43148i
$186$	−91.7654			−0.493362
$187$	38.8314	+	38.8314i	0.207654	+	0.207654i
$188$	20.5382	−	20.5382i	0.109246	−	0.109246i
$189$			15.7988i			0.0835917i
$190$	−155.510	+	103.288i	−0.818472	+	0.543622i
$191$	139.686			0.731342			0.365671	−	0.930744i	$-0.380840\pi$
$191$	139.686			0.731342			0.365671	+	0.930744i	$0.380840\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−103.467	+	103.467i	−0.536099	+	0.536099i	−0.922381	−	0.386282i	$-0.873759\pi$
$193$	−103.467	+	103.467i	−0.536099	+	0.536099i	0.386282	+	0.922381i	$0.373759\pi$
$194$			16.3518i			0.0842878i
$195$	24.8236	−	123.020i	0.127300	−	0.630871i
$196$	79.5109			0.405668
$197$	−233.769	−	233.769i	−1.18664	−	1.18664i	−0.977990	−	0.208653i	$-0.933092\pi$
$197$	−233.769	−	233.769i	−1.18664	−	1.18664i	−0.208653	−	0.977990i	$-0.566908\pi$
$198$	−38.9908	+	38.9908i	−0.196923	+	0.196923i
$199$		−	164.360i		−	0.825929i	−0.910747	−	0.412965i	$-0.864493\pi$
$199$		−	164.360i		−	0.825929i	0.910747	−	0.412965i	$-0.135507\pi$
$200$	−65.4766	+	26.6985i	−0.327383	+	0.133493i
$201$	−48.2252			−0.239926
$202$	−155.093	−	155.093i	−0.767788	−	0.767788i
$203$	−98.0624	+	98.0624i	−0.483066	+	0.483066i
$204$			14.6369i			0.0717493i
$205$	−192.981	−	38.9408i	−0.941373	−	0.189955i
$206$	−93.0969			−0.451927
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	−40.9879	+	40.9879i	−0.197057	+	0.197057i
$209$			343.137i			1.64181i
$210$	20.6028	+	31.0194i	0.0981087	+	0.147712i
$211$	75.9698			0.360047			0.180023	−	0.983662i	$-0.442383\pi$
$211$	75.9698			0.360047			0.180023	+	0.983662i	$0.442383\pi$
$212$	69.2429	+	69.2429i	0.326618	+	0.326618i
$213$	−160.793	+	160.793i	−0.754897	+	0.754897i
$214$			27.3584i			0.127843i
$215$	−175.174	+	116.349i	−0.814765	+	0.541159i
$216$	−14.6969			−0.0680414
$217$	80.5436	+	80.5436i	0.371169	+	0.371169i
$218$	−105.153	+	105.153i	−0.482351	+	0.482351i
$219$			120.156i			0.548656i
$220$	−25.7077	+	127.401i	−0.116853	+	0.579098i
$221$	−61.2305			−0.277061
$222$	110.129	+	110.129i	0.496075	+	0.496075i
$223$	235.175	−	235.175i	1.05460	−	1.05460i	0.0561774	−	0.998421i	$-0.482109\pi$
$223$	235.175	−	235.175i	1.05460	−	1.05460i	0.998421	−	0.0561774i	$-0.0178912\pi$
$224$		−	17.1996i		−	0.0767838i
$225$	29.0836	−	69.1314i	0.129260	−	0.307251i
$226$	−280.919			−1.24300
$227$	22.8432	+	22.8432i	0.100631	+	0.100631i	0.755630	−	0.654999i	$-0.227331\pi$
$227$	22.8432	+	22.8432i	0.100631	+	0.100631i	−0.654999	+	0.755630i	$0.727331\pi$
$228$	−64.6700	+	64.6700i	−0.283640	+	0.283640i
$229$		−	93.3450i		−	0.407620i	−0.979010	−	0.203810i	$-0.934667\pi$
$229$		−	93.3450i		−	0.407620i	0.979010	−	0.203810i	$-0.0653325\pi$
$230$	−33.2416	−	6.70767i	−0.144529	−	0.0291638i
$231$	68.4454			0.296300
$232$	−91.2230	−	91.2230i	−0.393203	−	0.393203i
$233$	−154.261	+	154.261i	−0.662063	+	0.662063i	−0.955866	−	0.293803i	$-0.905079\pi$
$233$	−154.261	+	154.261i	−0.662063	+	0.662063i	0.293803	+	0.955866i	$0.405079\pi$
$234$		−	61.4819i		−	0.262743i
$235$	40.1749	+	60.4870i	0.170957	+	0.257391i
$236$	45.7471			0.193844
$237$	72.5063	+	72.5063i	0.305934	+	0.305934i
$238$	12.8469	−	12.8469i	0.0539788	−	0.0539788i
$239$		−	9.07323i		−	0.0379633i	−0.999820	−	0.0189816i	$-0.993958\pi$
$239$		−	9.07323i		−	0.0379633i	0.999820	−	0.0189816i	$-0.00604241\pi$
$240$	−28.8560	+	19.1659i	−0.120233	+	0.0798579i
$241$	253.551			1.05208			0.526039	−	0.850460i	$-0.323677\pi$
$241$	253.551			1.05208			0.526039	+	0.850460i	$0.323677\pi$
$242$	47.9202	+	47.9202i	0.198017	+	0.198017i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	140.689i		−	0.576595i
$245$	−39.3178	+	194.850i	−0.160481	+	0.795306i
$246$	−96.4468			−0.392060
$247$	−270.535	−	270.535i	−1.09528	−	1.09528i
$248$	−74.9261	+	74.9261i	−0.302121	+	0.302121i
$249$		−	76.0526i		−	0.305432i
$250$	−33.0497	−	173.660i	−0.132199	−	0.694639i
$251$	139.932			0.557498			0.278749	−	0.960364i	$-0.410080\pi$
$251$	139.932			0.557498			0.278749	+	0.960364i	$0.410080\pi$
$252$	12.8997	+	12.8997i	0.0511892	+	0.0511892i
$253$	−44.0747	+	44.0747i	−0.174208	+	0.174208i
$254$		−	220.676i		−	0.868803i
$255$	−35.8692	−	7.23787i	−0.140663	−	0.0283838i
$256$	16.0000			0.0625000
$257$	−27.8299	−	27.8299i	−0.108287	−	0.108287i	0.650887	−	0.759175i	$-0.274397\pi$
$257$	−27.8299	−	27.8299i	−0.108287	−	0.108287i	−0.759175	+	0.650887i	$0.774397\pi$
$258$	−72.8477	+	72.8477i	−0.282355	+	0.282355i
$259$		−	193.323i		−	0.746420i
$260$	−80.1769	−	120.714i	−0.308373	−	0.464283i
$261$	136.835			0.524270
$262$	62.3911	+	62.3911i	0.238134	+	0.238134i
$263$	−224.271	+	224.271i	−0.852741	+	0.852741i	−0.990470	−	0.137729i	$-0.956020\pi$
$263$	−224.271	+	224.271i	−0.852741	+	0.852741i	0.137729	+	0.990470i	$0.456020\pi$
$264$			63.6717i			0.241181i
$265$	−203.928	+	135.447i	−0.769538	+	0.511120i
$266$	113.523			0.426779
$267$	208.085	+	208.085i	0.779344	+	0.779344i
$268$	−39.3757	+	39.3757i	−0.146924	+	0.146924i
$269$			458.186i			1.70329i	0.524117	+	0.851646i	$0.324395\pi$
$269$			458.186i			1.70329i	−0.524117	+	0.851646i	$0.675605\pi$
$270$	7.26758	−	36.0164i	0.0269170	−	0.133394i
$271$	334.255			1.23341			0.616706	−	0.787193i	$-0.288467\pi$
$271$	334.255			1.23341			0.616706	+	0.787193i	$0.288467\pi$
$272$	11.9509	+	11.9509i	0.0439373	+	0.0439373i
$273$	−53.9634	+	53.9634i	−0.197668	+	0.197668i
$274$		−	7.51462i		−	0.0274256i
$275$	−299.499	−	125.999i	−1.08909	−	0.458178i
$276$	−16.6132			−0.0601929
$277$	−200.494	−	200.494i	−0.723807	−	0.723807i	0.245572	−	0.969378i	$-0.421024\pi$
$277$	−200.494	−	200.494i	−0.723807	−	0.723807i	−0.969378	+	0.245572i	$0.921024\pi$
$278$	244.157	−	244.157i	0.878262	−	0.878262i
$279$		−	112.389i		−	0.402829i
$280$	42.1494	+	8.50513i	0.150534	+	0.0303754i
$281$	44.8143			0.159482			0.0797408	−	0.996816i	$-0.474591\pi$
$281$	44.8143			0.159482			0.0797408	+	0.996816i	$0.474591\pi$
$282$	25.1540	+	25.1540i	0.0891986	+	0.0891986i
$283$	76.0560	−	76.0560i	0.268749	−	0.268749i	−0.559847	−	0.828596i	$-0.689140\pi$
$283$	76.0560	−	76.0560i	0.268749	−	0.268749i	0.828596	+	0.559847i	$0.189140\pi$
$284$			262.574i			0.924557i
$285$	−126.502	−	190.460i	−0.443865	−	0.668280i
$286$	−266.358			−0.931323
$287$	84.6525	+	84.6525i	0.294956	+	0.294956i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	271.147i		−	0.938224i
$290$	268.661	−	178.442i	0.926418	−	0.615318i
$291$	−20.0268			−0.0688207
$292$	98.1067	+	98.1067i	0.335982	+	0.335982i
$293$	−144.599	+	144.599i	−0.493512	+	0.493512i	−0.909411	−	0.415899i	$-0.863467\pi$
$293$	−144.599	+	144.599i	−0.493512	+	0.493512i	0.415899	+	0.909411i	$0.363467\pi$
$294$			97.3806i			0.331226i
$295$	−22.6218	+	112.108i	−0.0766840	+	0.380028i
$296$	179.839			0.607566
$297$	−47.7538	−	47.7538i	−0.160787	−	0.160787i
$298$	209.038	−	209.038i	0.701470	−	0.701470i
$299$		−	69.4984i		−	0.232436i
$300$	−32.6989	−	80.1922i	−0.108996	−	0.267307i
$301$	127.879			0.424846
$302$	−97.4480	−	97.4480i	−0.322675	−	0.322675i
$303$	189.950	−	189.950i	0.626896	−	0.626896i
$304$			105.606i			0.347387i
$305$	344.774	+	69.5702i	1.13041	+	0.228099i
$306$	−17.9264			−0.0585830
$307$	168.960	+	168.960i	0.550360	+	0.550360i	0.926545	−	0.376185i	$-0.122764\pi$
$307$	168.960	+	168.960i	0.550360	+	0.550360i	−0.376185	+	0.926545i	$0.622764\pi$
$308$	55.8854	−	55.8854i	0.181446	−	0.181446i
$309$		−	114.020i		−	0.368997i
$310$	−146.564	−	220.665i	−0.472786	−	0.711823i
$311$	527.554			1.69631			0.848157	−	0.529745i	$-0.177712\pi$
$311$	527.554			1.69631			0.848157	+	0.529745i	$0.177712\pi$
$312$	−50.1997	−	50.1997i	−0.160897	−	0.160897i
$313$	−385.731	+	385.731i	−1.23237	+	1.23237i	−0.269316	+	0.963052i	$0.586798\pi$
$313$	−385.731	+	385.731i	−1.23237	+	1.23237i	−0.963052	+	0.269316i	$0.913202\pi$
$314$			285.922i			0.910581i
$315$	−37.9909	+	25.2332i	−0.120606	+	0.0801054i
$316$	118.402			0.374691
$317$	211.055	+	211.055i	0.665788	+	0.665788i	0.956738	−	0.290950i	$-0.0939714\pi$
$317$	211.055	+	211.055i	0.665788	+	0.665788i	−0.290950	+	0.956738i	$0.593971\pi$
$318$	−84.8049	+	84.8049i	−0.266682	+	0.266682i
$319$		−	592.810i		−	1.85834i
$320$	−7.91194	+	39.2097i	−0.0247248	+	0.122530i
$321$	−33.5070			−0.104383
$322$	14.5817	+	14.5817i	0.0452846	+	0.0452846i
$323$	−78.8804	+	78.8804i	−0.244212	+	0.244212i
$324$		−	18.0000i		−	0.0555556i
$325$	335.469	−	136.790i	1.03221	−	0.420891i
$326$	−205.390			−0.630032
$327$	−128.785	−	128.785i	−0.393838	−	0.393838i
$328$	−78.7484	+	78.7484i	−0.240087	+	0.240087i
$329$		−	44.1560i		−	0.134213i
$330$	−156.034	−	31.4854i	−0.472831	−	0.0954103i
$331$	136.580			0.412627			0.206313	−	0.978486i	$-0.433853\pi$
$331$	136.580			0.412627			0.206313	+	0.978486i	$0.433853\pi$
$332$	−62.0967	−	62.0967i	−0.187038	−	0.187038i
$333$	−134.880	+	134.880i	−0.405044	+	0.405044i
$334$		−	338.787i		−	1.01433i
$335$	−77.0232	−	115.966i	−0.229920	−	0.346166i
$336$	21.0651			0.0626937
$337$	−77.6053	−	77.6053i	−0.230283	−	0.230283i	0.582528	−	0.812811i	$-0.302064\pi$
$337$	−77.6053	−	77.6053i	−0.230283	−	0.230283i	−0.812811	+	0.582528i	$0.802064\pi$
$338$	41.0011	−	41.0011i	0.121305	−	0.121305i
$339$		−	344.054i		−	1.01491i
$340$	−35.1968	+	23.3774i	−0.103520	+	0.0687569i
$341$	−486.905			−1.42787
$342$	−79.2042	−	79.2042i	−0.231591	−	0.231591i
$343$	190.820	−	190.820i	0.556325	−	0.556325i
$344$			118.960i			0.345813i
$345$	8.21519	−	40.7125i	0.0238121	−	0.118007i
$346$	182.544			0.527585
$347$	−334.981	−	334.981i	−0.965362	−	0.965362i	0.0340576	−	0.999420i	$-0.489157\pi$
$347$	−334.981	−	334.981i	−0.965362	−	0.965362i	−0.999420	+	0.0340576i	$0.989157\pi$
$348$	111.725	−	111.725i	0.321049	−	0.321049i
$349$			462.956i			1.32652i	0.748389	+	0.663261i	$0.230828\pi$
$349$			462.956i			1.32652i	−0.748389	+	0.663261i	$0.769172\pi$
$350$	−41.6854	+	99.0859i	−0.119101	+	0.283102i
$351$	75.2996			0.214529
$352$	51.9877	+	51.9877i	0.147692	+	0.147692i
$353$	−419.637	+	419.637i	−1.18877	+	1.18877i	−0.211367	+	0.977407i	$0.567792\pi$
$353$	−419.637	+	419.637i	−1.18877	+	1.18877i	−0.977407	+	0.211367i	$0.932208\pi$
$354$			56.0286i			0.158273i
$355$	−643.466	−	129.842i	−1.81258	−	0.365752i
$356$	339.801			0.954498
$357$	15.7342	+	15.7342i	0.0440735	+	0.0440735i
$358$	134.161	−	134.161i	0.374752	−	0.374752i
$359$			253.226i			0.705366i	0.935743	+	0.352683i	$0.114731\pi$
$359$			253.226i			0.705366i	−0.935743	+	0.352683i	$0.885269\pi$
$360$	−23.4733	−	35.3412i	−0.0652037	−	0.0981701i
$361$	−336.034			−0.930843
$362$	−102.342	−	102.342i	−0.282712	−	0.282712i
$363$	−58.6900	+	58.6900i	−0.161681	+	0.161681i
$364$			88.1218i			0.242093i
$365$	−288.934	+	191.908i	−0.791601	+	0.525774i
$366$	172.308			0.470787
$367$	133.234	+	133.234i	0.363035	+	0.363035i	0.864929	−	0.501894i	$-0.167363\pi$
$367$	133.234	+	133.234i	0.363035	+	0.363035i	−0.501894	+	0.864929i	$0.667363\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	118.123i		−	0.320116i
$370$	−88.9299	+	440.716i	−0.240351	+	1.19112i
$371$	148.869			0.401263
$372$	−91.7654	−	91.7654i	−0.246681	−	0.246681i
$373$	−158.070	+	158.070i	−0.423780	+	0.423780i	−0.886503	−	0.462723i	$-0.846872\pi$
$373$	−158.070	+	158.070i	−0.423780	+	0.423780i	0.462723	+	0.886503i	$0.346872\pi$
$374$			77.6628i			0.207654i
$375$	212.689	−	40.4774i	0.567170	−	0.107940i
$376$	41.0763			0.109246
$377$	467.380	+	467.380i	1.23974	+	1.23974i
$378$	−15.7988	+	15.7988i	−0.0417958	+	0.0417958i
$379$		−	485.673i		−	1.28146i	−0.767766	−	0.640730i	$-0.778632\pi$
$379$		−	485.673i		−	1.28146i	0.767766	−	0.640730i	$-0.221368\pi$
$380$	−258.798	−	52.2216i	−0.681047	−	0.137425i
$381$	270.272			0.709375
$382$	139.686	+	139.686i	0.365671	+	0.365671i
$383$	447.060	−	447.060i	1.16726	−	1.16726i	0.184410	−	0.982849i	$-0.440963\pi$
$383$	447.060	−	447.060i	1.16726	−	1.16726i	0.982849	−	0.184410i	$-0.0590375\pi$
$384$			19.5959i			0.0510310i
$385$	109.318	+	164.588i	0.283943	+	0.427502i
$386$	−206.934			−0.536099
$387$	−89.2198	−	89.2198i	−0.230542	−	0.230542i
$388$	−16.3518	+	16.3518i	−0.0421439	+	0.0421439i
$389$		−	252.009i		−	0.647837i	−0.946085	−	0.323919i	$-0.895000\pi$
$389$		−	252.009i		−	0.647837i	0.946085	−	0.323919i	$-0.105000\pi$
$390$	147.843	−	98.1962i	0.379086	−	0.251785i
$391$	−20.2638			−0.0518256
$392$	79.5109	+	79.5109i	0.202834	+	0.202834i
$393$	−76.4132	+	76.4132i	−0.194436	+	0.194436i
$394$		−	467.537i		−	1.18664i
$395$	−58.5494	+	290.157i	−0.148226	+	0.734575i
$396$	−77.9816			−0.196923
$397$	527.251	+	527.251i	1.32809	+	1.32809i	0.907038	+	0.421050i	$0.138338\pi$
$397$	527.251	+	527.251i	1.32809	+	1.32809i	0.421050	+	0.907038i	$0.361662\pi$
$398$	164.360	−	164.360i	0.412965	−	0.412965i
$399$			139.037i			0.348464i
$400$	−92.1752	−	38.7781i	−0.230438	−	0.0969452i
$401$	337.961			0.842796			0.421398	−	0.906876i	$-0.361540\pi$
$401$	337.961			0.842796			0.421398	+	0.906876i	$0.361540\pi$
$402$	−48.2252	−	48.2252i	−0.119963	−	0.119963i
$403$	383.883	−	383.883i	0.952563	−	0.952563i
$404$		−	310.186i		−	0.767788i
$405$	44.1109	+	8.90093i	0.108916	+	0.0219776i
$406$	−196.125			−0.483066
$407$	584.340	+	584.340i	1.43573	+	1.43573i
$408$	−14.6369	+	14.6369i	−0.0358746	+	0.0358746i
$409$			669.062i			1.63585i	0.575327	+	0.817924i	$0.304875\pi$
$409$			669.062i			1.63585i	−0.575327	+	0.817924i	$0.695125\pi$
$410$	−154.041	−	231.922i	−0.375709	−	0.565664i
$411$	9.20349			0.0223929
$412$	−93.0969	−	93.0969i	−0.225963	−	0.225963i
$413$	49.1770	−	49.1770i	0.119073	−	0.119073i
$414$		−	20.3470i		−	0.0491473i
$415$	182.881	−	121.468i	0.440677	−	0.292694i
$416$	−81.9758			−0.197057
$417$	299.030	+	299.030i	0.717098	+	0.717098i
$418$	−343.137	+	343.137i	−0.820903	+	0.820903i
$419$		−	141.319i		−	0.337278i	−0.985678	−	0.168639i	$-0.946063\pi$
$419$		−	141.319i		−	0.337278i	0.985678	−	0.168639i	$-0.0539372\pi$
$420$	−10.4166	+	51.6223i	−0.0248014	+	0.122910i
$421$	336.422			0.799103			0.399551	−	0.916711i	$-0.369166\pi$
$421$	336.422			0.799103			0.399551	+	0.916711i	$0.369166\pi$
$422$	75.9698	+	75.9698i	0.180023	+	0.180023i
$423$	−30.8072	+	30.8072i	−0.0728303	+	0.0728303i
$424$			138.486i			0.326618i
$425$	−39.8841	−	97.8134i	−0.0938449	−	0.230149i
$426$	−321.586			−0.754897
$427$	−151.237	−	151.237i	−0.354185	−	0.354185i
$428$	−27.3584	+	27.3584i	−0.0639214	+	0.0639214i
$429$		−	326.221i		−	0.760422i
$430$	−291.524	−	58.8252i	−0.677962	−	0.136803i
$431$	568.586			1.31922			0.659612	−	0.751606i	$-0.270720\pi$
$431$	568.586			1.31922			0.659612	+	0.751606i	$0.270720\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	222.386	−	222.386i	0.513593	−	0.513593i	−0.402032	−	0.915626i	$-0.631696\pi$
$433$	222.386	−	222.386i	0.513593	−	0.513593i	0.915626	+	0.402032i	$0.131696\pi$
$434$			161.087i			0.371169i
$435$	218.546	+	329.041i	0.502405	+	0.756417i
$436$	−210.305			−0.482351
$437$	−89.5315	−	89.5315i	−0.204878	−	0.204878i
$438$	−120.156	+	120.156i	−0.274328	+	0.274328i
$439$			215.602i			0.491121i	0.969381	+	0.245561i	$0.0789720\pi$
$439$			215.602i			0.491121i	−0.969381	+	0.245561i	$0.921028\pi$
$440$	−153.109	+	101.694i	−0.347975	+	0.231122i
$441$	−119.266			−0.270445
$442$	−61.2305	−	61.2305i	−0.138531	−	0.138531i
$443$	282.186	−	282.186i	0.636988	−	0.636988i	−0.312823	−	0.949811i	$-0.601275\pi$
$443$	282.186	−	282.186i	0.636988	−	0.636988i	0.949811	+	0.312823i	$0.101275\pi$
$444$			220.257i			0.496075i
$445$	−168.030	+	832.719i	−0.377596	+	1.87128i
$446$	470.351			1.05460
$447$	256.018	+	256.018i	0.572748	+	0.572748i
$448$	17.1996	−	17.1996i	0.0383919	−	0.0383919i
$449$		−	761.526i		−	1.69605i	−0.529958	−	0.848024i	$-0.677792\pi$
$449$		−	761.526i		−	1.69605i	0.529958	−	0.848024i	$-0.322208\pi$
$450$	98.2149	−	40.0478i	0.218255	−	0.0889951i
$451$	−511.744			−1.13469
$452$	−280.919	−	280.919i	−0.621502	−	0.621502i
$453$	119.349	−	119.349i	0.263463	−	0.263463i
$454$			45.6864i			0.100631i
$455$	−215.952	−	43.5759i	−0.474620	−	0.0957712i
$456$	−129.340			−0.283640
$457$	271.064	+	271.064i	0.593138	+	0.593138i	0.938478	−	0.345340i	$-0.112236\pi$
$457$	271.064	+	271.064i	0.593138	+	0.593138i	−0.345340	+	0.938478i	$0.612236\pi$
$458$	93.3450	−	93.3450i	0.203810	−	0.203810i
$459$		−	21.9553i		−	0.0478329i
$460$	−26.5340	−	39.9493i	−0.0576826	−	0.0868463i
$461$	29.2935			0.0635435			0.0317717	−	0.999495i	$-0.489885\pi$
$461$	29.2935			0.0635435			0.0317717	+	0.999495i	$0.489885\pi$
$462$	68.4454	+	68.4454i	0.148150	+	0.148150i
$463$	−233.316	+	233.316i	−0.503922	+	0.503922i	−0.912654	−	0.408733i	$-0.865971\pi$
$463$	−233.316	+	233.316i	−0.503922	+	0.503922i	0.408733	+	0.912654i	$0.365971\pi$
$464$		−	182.446i		−	0.393203i
$465$	270.258	−	179.503i	0.581201	−	0.386028i
$466$	−308.521			−0.662063
$467$	−407.377	−	407.377i	−0.872328	−	0.872328i	0.120398	−	0.992726i	$-0.461583\pi$
$467$	−407.377	−	407.377i	−0.872328	−	0.872328i	−0.992726	+	0.120398i	$0.961583\pi$
$468$	61.4819	−	61.4819i	0.131371	−	0.131371i
$469$			84.6557i			0.180503i
$470$	−20.3121	+	100.662i	−0.0432172	+	0.214174i
$471$	−350.182			−0.743486
$472$	45.7471	+	45.7471i	0.0969219	+	0.0969219i
$473$	−386.528	+	386.528i	−0.817184	+	0.817184i
$474$			145.013i			0.305934i
$475$	255.949	−	608.388i	0.538840	−	1.28082i
$476$	25.6939			0.0539788
$477$	−103.864	−	103.864i	−0.217745	−	0.217745i
$478$	9.07323	−	9.07323i	0.0189816	−	0.0189816i
$479$			703.739i			1.46918i	0.678509	+	0.734592i	$0.262626\pi$
$479$			703.739i			1.46918i	−0.678509	+	0.734592i	$0.737374\pi$
$480$	−48.0219	−	9.69011i	−0.100046	−	0.0201877i
$481$	−921.405			−1.91560
$482$	253.551	+	253.551i	0.526039	+	0.526039i
$483$	−17.8588	+	17.8588i	−0.0369747	+	0.0369747i
$484$			95.8404i			0.198017i
$485$	−31.9860	−	48.1578i	−0.0659505	−	0.0992944i
$486$	22.0454			0.0453609
$487$	407.800	+	407.800i	0.837372	+	0.837372i	0.988512	−	0.151141i	$-0.0482946\pi$
$487$	407.800	+	407.800i	0.837372	+	0.837372i	−0.151141	+	0.988512i	$0.548295\pi$
$488$	140.689	−	140.689i	0.288297	−	0.288297i
$489$		−	251.551i		−	0.514419i
$490$	−234.168	+	155.532i	−0.477893	+	0.317413i
$491$	−198.942			−0.405178			−0.202589	−	0.979264i	$-0.564936\pi$
$491$	−198.942			−0.405178			−0.202589	+	0.979264i	$0.564936\pi$
$492$	−96.4468	−	96.4468i	−0.196030	−	0.196030i
$493$	136.275	−	136.275i	0.276420	−	0.276420i
$494$		−	541.069i		−	1.09528i
$495$	38.5616	−	191.102i	0.0779022	−	0.386065i
$496$	−149.852			−0.302121
$497$	282.260	+	282.260i	0.567928	+	0.567928i
$498$	76.0526	−	76.0526i	0.152716	−	0.152716i
$499$		−	460.033i		−	0.921910i	−0.887424	−	0.460955i	$-0.847507\pi$
$499$		−	460.033i		−	0.921910i	0.887424	−	0.460955i	$-0.152493\pi$
$500$	140.610	−	206.709i	0.281220	−	0.413419i
$501$	414.928			0.828199
$502$	139.932	+	139.932i	0.278749	+	0.278749i
$503$	−7.49816	+	7.49816i	−0.0149069	+	0.0149069i	−0.714521	−	0.699614i	$-0.753355\pi$
$503$	−7.49816	+	7.49816i	−0.0149069	+	0.0149069i	0.699614	+	0.714521i	$0.253355\pi$
$504$			25.7994i			0.0511892i
$505$	760.145	+	153.386i	1.50524	+	0.303735i
$506$	−88.1495			−0.174208
$507$	50.2158	+	50.2158i	0.0990450	+	0.0990450i
$508$	220.676	−	220.676i	0.434402	−	0.434402i
$509$		−	485.709i		−	0.954241i	−0.878838	−	0.477120i	$-0.841681\pi$
$509$		−	485.709i		−	0.954241i	0.878838	−	0.477120i	$-0.158319\pi$
$510$	−28.6313	−	43.1070i	−0.0561398	−	0.0845236i
$511$	210.924			0.412768
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	97.0050	−	97.0050i	0.189094	−	0.189094i
$514$		−	55.6598i		−	0.108287i
$515$	274.180	−	182.108i	0.532388	−	0.353607i
$516$	−145.695			−0.282355
$517$	133.466	+	133.466i	0.258156	+	0.258156i
$518$	193.323	−	193.323i	0.373210	−	0.373210i
$519$			223.570i			0.430771i
$520$	40.5367	−	200.890i	0.0779552	−	0.386328i
$521$	−125.674			−0.241217			−0.120609	−	0.992700i	$-0.538485\pi$
$521$	−125.674			−0.241217			−0.120609	+	0.992700i	$0.538485\pi$
$522$	136.835	+	136.835i	0.262135	+	0.262135i
$523$	378.858	−	378.858i	0.724393	−	0.724393i	−0.245103	−	0.969497i	$-0.578822\pi$
$523$	378.858	−	378.858i	0.724393	−	0.724393i	0.969497	+	0.245103i	$0.0788219\pi$
$524$			124.782i			0.238134i
$525$	−121.355	−	51.0540i	−0.231152	−	0.0972458i
$526$	−448.542			−0.852741
$527$	−111.930	−	111.930i	−0.212390	−	0.212390i
$528$	−63.6717	+	63.6717i	−0.120590	+	0.120590i
$529$		−	23.0000i		−	0.0434783i
$530$	−339.374	−	68.4807i	−0.640329	−	0.129209i
$531$	−68.6207			−0.129229
$532$	113.523	+	113.523i	0.213390	+	0.213390i
$533$	403.467	−	403.467i	0.756973	−	0.756973i
$534$			416.170i			0.779344i
$535$	−53.5160	−	80.5732i	−0.100030	−	0.150604i
$536$	−78.7514			−0.146924
$537$	164.313	+	164.313i	0.305983	+	0.305983i
$538$	−458.186	+	458.186i	−0.851646	+	0.851646i
$539$			516.699i			0.958625i
$540$	43.2840	−	28.7488i	0.0801555	−	0.0532386i
$541$	377.104			0.697050			0.348525	−	0.937300i	$-0.386683\pi$
$541$	377.104			0.697050			0.348525	+	0.937300i	$0.386683\pi$
$542$	334.255	+	334.255i	0.616706	+	0.616706i
$543$	125.343	−	125.343i	0.230833	−	0.230833i
$544$			23.9019i			0.0439373i
$545$	103.995	−	515.375i	0.190817	−	0.945643i
$546$	−107.927			−0.197668
$547$	444.740	+	444.740i	0.813052	+	0.813052i	0.985090	−	0.172038i	$-0.0550352\pi$
$547$	444.740	+	444.740i	0.813052	+	0.813052i	−0.172038	+	0.985090i	$0.555035\pi$
$548$	7.51462	−	7.51462i	0.0137128	−	0.0137128i
$549$			211.034i			0.384396i
$550$	−173.499	−	425.498i	−0.315454	−	0.773632i
$551$	1204.21			2.18550
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	127.279	−	127.279i	0.230161	−	0.230161i
$554$		−	400.989i		−	0.723807i
$555$	−539.764	−	108.916i	−0.972549	−	0.196246i
$556$	488.314			0.878262
$557$	−583.468	−	583.468i	−1.04752	−	1.04752i	−0.998813	−	0.0487058i	$-0.984490\pi$
$557$	−583.468	−	583.468i	−1.04752	−	1.04752i	−0.0487058	−	0.998813i	$-0.515510\pi$
$558$	112.389	−	112.389i	0.201414	−	0.201414i
$559$		−	609.489i		−	1.09032i
$560$	33.6443	+	50.6545i	0.0600791	+	0.0904545i
$561$	−95.1171			−0.169549
$562$	44.8143	+	44.8143i	0.0797408	+	0.0797408i
$563$	−38.5193	+	38.5193i	−0.0684179	+	0.0684179i	−0.740488	−	0.672070i	$-0.765405\pi$
$563$	−38.5193	+	38.5193i	−0.0684179	+	0.0684179i	0.672070	+	0.740488i	$0.265405\pi$
$564$			50.3080i			0.0891986i
$565$	827.335	−	549.508i	1.46431	−	0.972581i
$566$	152.112			0.268749
$567$	−19.3495	−	19.3495i	−0.0341261	−	0.0341261i
$568$	−262.574	+	262.574i	−0.462278	+	0.462278i
$569$			72.1680i			0.126833i	0.997987	+	0.0634165i	$0.0201997\pi$
$569$			72.1680i			0.126833i	−0.997987	+	0.0634165i	$0.979800\pi$
$570$	63.9581	−	316.961i	0.112207	−	0.556073i
$571$	−653.227			−1.14401			−0.572003	−	0.820252i	$-0.693833\pi$
$571$	−653.227			−1.14401			−0.572003	+	0.820252i	$0.693833\pi$
$572$	−266.358	−	266.358i	−0.465662	−	0.465662i
$573$	−171.080	+	171.080i	−0.298569	+	0.298569i
$574$			169.305i			0.294956i
$575$	111.021	−	45.2696i	0.193080	−	0.0787297i
$576$	−24.0000			−0.0416667
$577$	401.108	+	401.108i	0.695161	+	0.695161i	0.963363	−	0.268202i	$-0.0864293\pi$
$577$	401.108	+	401.108i	0.695161	+	0.695161i	−0.268202	+	0.963363i	$0.586429\pi$
$578$	271.147	−	271.147i	0.469112	−	0.469112i
$579$		−	253.442i		−	0.437723i
$580$	447.104	+	90.2189i	0.770868	+	0.155550i
$581$	−133.505			−0.229784
$582$	−20.0268	−	20.0268i	−0.0344103	−	0.0344103i
$583$	−449.973	+	449.973i	−0.771823	+	0.771823i
$584$			196.213i			0.335982i
$585$	120.265	+	181.070i	0.205582	+	0.309522i
$586$	−289.198			−0.493512
$587$	−341.521	−	341.521i	−0.581807	−	0.581807i	0.353593	−	0.935400i	$-0.384960\pi$
$587$	−341.521	−	341.521i	−0.581807	−	0.581807i	−0.935400	+	0.353593i	$0.884960\pi$
$588$	−97.3806	+	97.3806i	−0.165613	+	0.165613i
$589$		−	989.077i		−	1.67925i
$590$	−134.730	+	89.4865i	−0.228356	+	0.151672i
$591$	572.614			0.968890
$592$	179.839	+	179.839i	0.303783	+	0.303783i
$593$	−4.85045	+	4.85045i	−0.00817952	+	0.00817952i	−0.711185	−	0.703005i	$-0.751841\pi$
$593$	−4.85045	+	4.85045i	−0.00817952	+	0.00817952i	0.703005	+	0.711185i	$0.251841\pi$
$594$		−	95.5075i		−	0.160787i
$595$	−12.7055	+	62.9656i	−0.0213538	+	0.105825i
$596$	418.076			0.701470
$597$	201.299	+	201.299i	0.337184	+	0.337184i
$598$	69.4984	−	69.4984i	0.116218	−	0.116218i
$599$		−	555.468i		−	0.927326i	−0.886012	−	0.463663i	$-0.846535\pi$
$599$		−	555.468i		−	0.927326i	0.886012	−	0.463663i	$-0.153465\pi$
$600$	47.4933	−	112.891i	0.0791555	−	0.188152i
$601$	705.957			1.17464			0.587319	−	0.809356i	$-0.300183\pi$
$601$	705.957			1.17464			0.587319	+	0.809356i	$0.300183\pi$
$602$	127.879	+	127.879i	0.212423	+	0.212423i
$603$	59.0636	−	59.0636i	0.0979495	−	0.0979495i
$604$		−	194.896i		−	0.322675i
$605$	−234.867	−	47.3927i	−0.388210	−	0.0783351i
$606$	379.899			0.626896
$607$	429.607	+	429.607i	0.707755	+	0.707755i	0.966063	−	0.258308i	$-0.0831648\pi$
$607$	429.607	+	429.607i	0.707755	+	0.707755i	−0.258308	+	0.966063i	$0.583165\pi$
$608$	−105.606	+	105.606i	−0.173693	+	0.173693i
$609$		−	240.203i		−	0.394422i
$610$	275.203	+	414.344i	0.451153	+	0.679252i
$611$	−210.454			−0.344442
$612$	−17.9264	−	17.9264i	−0.0292915	−	0.0292915i
$613$	396.285	−	396.285i	0.646468	−	0.646468i	−0.305670	−	0.952138i	$-0.598880\pi$
$613$	396.285	−	396.285i	0.646468	−	0.646468i	0.952138	+	0.305670i	$0.0988803\pi$
$614$			337.921i			0.550360i
$615$	284.046	−	188.661i	0.461863	−	0.306765i
$616$	111.771			0.181446
$617$	−800.870	−	800.870i	−1.29801	−	1.29801i	−0.929707	−	0.368299i	$-0.879940\pi$
$617$	−800.870	−	800.870i	−1.29801	−	1.29801i	−0.368299	−	0.929707i	$-0.620060\pi$
$618$	114.020	−	114.020i	0.184498	−	0.184498i
$619$			480.925i			0.776939i	0.921462	+	0.388469i	$0.126996\pi$
$619$			480.925i			0.776939i	−0.921462	+	0.388469i	$0.873004\pi$
$620$	74.1013	−	367.229i	0.119518	−	0.592305i
$621$	24.9199			0.0401286
$622$	527.554	+	527.554i	0.848157	+	0.848157i
$623$	365.277	−	365.277i	0.586320	−	0.586320i
$624$		−	100.399i		−	0.160897i
$625$	437.032	+	446.797i	0.699252	+	0.714875i
$626$	−771.462			−1.23237
$627$	−420.256	−	420.256i	−0.670264	−	0.670264i
$628$	−285.922	+	285.922i	−0.455290	+	0.455290i
$629$			268.656i			0.427117i
$630$	−63.2241	−	12.7577i	−0.100356	−	0.0202503i
$631$	−205.865			−0.326251			−0.163126	−	0.986605i	$-0.552158\pi$
$631$	−205.865			−0.326251			−0.163126	+	0.986605i	$0.552158\pi$
$632$	118.402	+	118.402i	0.187345	+	0.187345i
$633$	−93.0437	+	93.0437i	−0.146988	+	0.146988i
$634$			422.110i			0.665788i
$635$	431.667	+	649.913i	0.679790	+	1.02349i
$636$	−169.610			−0.266682
$637$	−407.373	−	407.373i	−0.639518	−	0.639518i
$638$	592.810	−	592.810i	0.929169	−	0.929169i
$639$		−	393.861i		−	0.616371i
$640$	−47.1216	+	31.2978i	−0.0736276	+	0.0489028i
$641$	652.976			1.01868			0.509342	−	0.860564i	$-0.329889\pi$
$641$	652.976			1.01868			0.509342	+	0.860564i	$0.329889\pi$
$642$	−33.5070	−	33.5070i	−0.0521916	−	0.0521916i
$643$	−702.135	+	702.135i	−1.09197	+	1.09197i	−0.0966483	+	0.995319i	$0.530812\pi$
$643$	−702.135	+	702.135i	−1.09197	+	1.09197i	−0.995319	+	0.0966483i	$0.969188\pi$
$644$			29.1633i			0.0452846i
$645$	72.0458	−	357.042i	0.111699	−	0.553554i
$646$	−157.761			−0.244212
$647$	−575.223	−	575.223i	−0.889062	−	0.889062i	0.105371	−	0.994433i	$-0.466397\pi$
$647$	−575.223	−	575.223i	−0.889062	−	0.889062i	−0.994433	+	0.105371i	$0.966397\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			297.286i			0.458068i
$650$	472.258	+	198.679i	0.726551	+	0.305660i
$651$	−197.291			−0.303058
$652$	−205.390	−	205.390i	−0.315016	−	0.315016i
$653$	−260.357	+	260.357i	−0.398708	+	0.398708i	−0.877777	−	0.479069i	$-0.840974\pi$
$653$	−260.357	+	260.357i	−0.398708	+	0.398708i	0.479069	+	0.877777i	$0.340974\pi$
$654$		−	257.570i		−	0.393838i
$655$	−305.792	−	61.7043i	−0.466858	−	0.0942050i
$656$	−157.497			−0.240087
$657$	−147.160	−	147.160i	−0.223988	−	0.223988i
$658$	44.1560	−	44.1560i	0.0671063	−	0.0671063i
$659$		−	421.514i		−	0.639626i	−0.947481	−	0.319813i	$-0.896380\pi$
$659$		−	421.514i		−	0.639626i	0.947481	−	0.319813i	$-0.103620\pi$
$660$	−124.549	−	187.520i	−0.188710	−	0.284121i
$661$	−190.516			−0.288224			−0.144112	−	0.989561i	$-0.546033\pi$
$661$	−190.516			−0.288224			−0.144112	+	0.989561i	$0.546033\pi$
$662$	136.580	+	136.580i	0.206313	+	0.206313i
$663$	74.9917	−	74.9917i	0.113110	−	0.113110i
$664$		−	124.193i		−	0.187038i
$665$	−334.338	+	222.064i	−0.502764	+	0.333931i
$666$	−269.759			−0.405044
$667$	154.676	+	154.676i	0.231898	+	0.231898i
$668$	338.787	−	338.787i	0.507166	−	0.507166i
$669$			576.060i			0.861076i
$670$	38.9423	−	192.989i	0.0581228	−	0.288043i
$671$	914.263			1.36254
$672$	21.0651	+	21.0651i	0.0313469	+	0.0313469i
$673$	−268.061	+	268.061i	−0.398308	+	0.398308i	−0.877636	−	0.479328i	$-0.840880\pi$
$673$	−268.061	+	268.061i	−0.398308	+	0.398308i	0.479328	+	0.877636i	$0.340880\pi$
$674$		−	155.211i		−	0.230283i
$675$	49.0483	+	120.288i	0.0726642	+	0.178205i
$676$	82.0021			0.121305
$677$	242.456	+	242.456i	0.358133	+	0.358133i	0.863124	−	0.504991i	$-0.168504\pi$
$677$	242.456	+	242.456i	0.358133	+	0.358133i	−0.504991	+	0.863124i	$0.668504\pi$
$678$	344.054	−	344.054i	0.507454	−	0.507454i
$679$			35.1556i			0.0517755i
$680$	−58.5741	−	11.8194i	−0.0861384	−	0.0173815i
$681$	−55.9541			−0.0821647
$682$	−486.905	−	486.905i	−0.713937	−	0.713937i
$683$	−636.304	+	636.304i	−0.931630	+	0.931630i	−0.997808	−	0.0661774i	$-0.978920\pi$
$683$	−636.304	+	636.304i	−0.931630	+	0.931630i	0.0661774	+	0.997808i	$0.478920\pi$
$684$		−	158.408i		−	0.231591i
$685$	14.6994	+	22.1313i	0.0214590	+	0.0323085i
$686$	381.639			0.556325
$687$	114.324	+	114.324i	0.166410	+	0.166410i
$688$	−118.960	+	118.960i	−0.172907	+	0.172907i
$689$		−	709.531i		−	1.02980i
$690$	48.9277	−	32.4974i	0.0709097	−	0.0470976i
$691$	−761.609			−1.10218			−0.551092	−	0.834445i	$-0.685789\pi$
$691$	−761.609			−1.10218			−0.551092	+	0.834445i	$0.685789\pi$
$692$	182.544	+	182.544i	0.263792	+	0.263792i
$693$	−83.8282	+	83.8282i	−0.120964	+	0.120964i
$694$		−	669.961i		−	0.965362i
$695$	−241.469	+	1196.67i	−0.347438	+	1.72182i
$696$	223.450			0.321049
$697$	−117.640	−	117.640i	−0.168780	−	0.168780i
$698$	−462.956	+	462.956i	−0.663261	+	0.663261i
$699$		−	377.860i		−	0.540572i
$700$	−140.771	+	57.4004i	−0.201102	+	0.0820006i
$701$	−752.904			−1.07404			−0.537022	−	0.843569i	$-0.680451\pi$
$701$	−752.904			−1.07404			−0.537022	+	0.843569i	$0.680451\pi$
$702$	75.2996	+	75.2996i	0.107264	+	0.107264i
$703$	−1187.00	+	1187.00i	−1.68848	+	1.68848i
$704$			103.975i			0.147692i
$705$	−123.285	−	24.8771i	−0.174873	−	0.0352867i
$706$	−839.274			−1.18877
$707$	−333.442	−	333.442i	−0.471630	−	0.471630i
$708$	−56.0286	+	56.0286i	−0.0791364	+	0.0791364i
$709$			492.812i			0.695080i	0.937665	+	0.347540i	$0.112983\pi$
$709$			492.812i			0.695080i	−0.937665	+	0.347540i	$0.887017\pi$
$710$	−513.624	−	773.308i	−0.723414	−	1.08917i
$711$	−177.603			−0.249794
$712$	339.801	+	339.801i	0.477249	+	0.477249i
$713$	127.043	−	127.043i	0.178181	−	0.178181i
$714$			31.4685i			0.0440735i
$715$	784.453	−	521.027i	1.09714	−	0.728709i
$716$	268.322			0.374752
$717$	11.1124	+	11.1124i	0.0154984	+	0.0154984i
$718$	−253.226	+	253.226i	−0.352683	+	0.352683i
$719$		−	66.9427i		−	0.0931052i	−0.998916	−	0.0465526i	$-0.985176\pi$
$719$		−	66.9427i		−	0.0931052i	0.998916	−	0.0465526i	$-0.0148235\pi$
$720$	11.8679	−	58.8146i	0.0164832	−	0.0816869i
$721$	−200.153			−0.277605
$722$	−336.034	−	336.034i	−0.465422	−	0.465422i
$723$	−310.535	+	310.535i	−0.429509	+	0.429509i
$724$		−	204.684i		−	0.282712i
$725$	−442.182	+	1051.06i	−0.609906	+	1.44974i
$726$	−117.380			−0.161681
$727$	−264.488	−	264.488i	−0.363807	−	0.363807i	0.501406	−	0.865212i	$-0.332816\pi$
$727$	−264.488	−	264.488i	−0.363807	−	0.363807i	−0.865212	+	0.501406i	$0.832816\pi$
$728$	−88.1218	+	88.1218i	−0.121046	+	0.121046i
$729$			27.0000i			0.0370370i
$730$	−480.842	−	97.0268i	−0.658688	−	0.132913i
$731$	−177.710			−0.243106
$732$	172.308	+	172.308i	0.235394	+	0.235394i
$733$	0.545555	−	0.545555i	0.000744277	−	0.000744277i	−0.706735	−	0.707479i	$-0.749832\pi$
$733$	0.545555	−	0.545555i	0.000744277	−	0.000744277i	0.707479	+	0.706735i	$0.249832\pi$
$734$			266.467i			0.363035i
$735$	−190.487	−	286.796i	−0.259166	−	0.390198i
$736$	−27.1293			−0.0368605
$737$	−255.882	−	255.882i	−0.347194	−	0.347194i
$738$	118.123	−	118.123i	0.160058	−	0.160058i
$739$		−	682.594i		−	0.923673i	−0.886965	−	0.461836i	$-0.847191\pi$
$739$		−	682.594i		−	0.923673i	0.886965	−	0.461836i	$-0.152809\pi$
$740$	−529.646	+	351.786i	−0.715738	+	0.475386i
$741$	662.672			0.894294
$742$	148.869	+	148.869i	0.200632	+	0.200632i
$743$	−390.572	+	390.572i	−0.525670	+	0.525670i	−0.919278	−	0.393609i	$-0.871227\pi$
$743$	−390.572	+	390.572i	−0.525670	+	0.525670i	0.393609	+	0.919278i	$0.371227\pi$
$744$		−	183.531i		−	0.246681i
$745$	−206.737	+	1024.54i	−0.277499	+	1.37522i
$746$	−316.140			−0.423780
$747$	93.1450	+	93.1450i	0.124692	+	0.124692i
$748$	−77.6628	+	77.6628i	−0.103827	+	0.103827i
$749$			58.8190i			0.0785301i
$750$	253.166	+	172.212i	0.337555	+	0.229615i
$751$	−39.5226			−0.0526266			−0.0263133	−	0.999654i	$-0.508377\pi$
$751$	−39.5226			−0.0526266			−0.0263133	+	0.999654i	$0.508377\pi$
$752$	41.0763	+	41.0763i	0.0546228	+	0.0546228i
$753$	−171.381	+	171.381i	−0.227598	+	0.227598i
$754$			934.760i			1.23974i
$755$	477.613	+	96.3753i	0.632601	+	0.127649i
$756$	−31.5976			−0.0417958
$757$	775.732	+	775.732i	1.02474	+	1.02474i	0.999686	+	0.0250588i	$0.00797731\pi$
$757$	775.732	+	775.732i	1.02474	+	1.02474i	0.0250588	+	0.999686i	$0.492023\pi$
$758$	485.673	−	485.673i	0.640730	−	0.640730i
$759$		−	107.961i		−	0.142241i
$760$	−206.576	−	311.019i	−0.271811	−	0.409236i
$761$	−993.258			−1.30520			−0.652600	−	0.757702i	$-0.726322\pi$
$761$	−993.258			−1.30520			−0.652600	+	0.757702i	$0.726322\pi$
$762$	270.272	+	270.272i	0.354687	+	0.354687i
$763$	−226.072	+	226.072i	−0.296294	+	0.296294i
$764$			279.373i			0.365671i
$765$	52.7951	−	35.0660i	0.0690132	−	0.0458380i
$766$	894.121			1.16726
$767$	−234.385	−	234.385i	−0.305587	−	0.305587i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			938.784i			1.22079i	0.792099	+	0.610393i	$0.208988\pi$
$769$			938.784i			1.22079i	−0.792099	+	0.610393i	$0.791012\pi$
$770$	−55.2703	+	273.906i	−0.0717796	+	0.355723i
$771$	68.1690			0.0884163
$772$	−206.934	−	206.934i	−0.268049	−	0.268049i
$773$	709.202	−	709.202i	0.917467	−	0.917467i	−0.0793776	−	0.996845i	$-0.525293\pi$
$773$	709.202	−	709.202i	0.917467	−	0.917467i	0.996845	+	0.0793776i	$0.0252933\pi$
$774$		−	178.440i		−	0.230542i
$775$	863.291	+	363.187i	1.11392	+	0.468628i
$776$	−32.7036			−0.0421439
$777$	236.771	+	236.771i	0.304725	+	0.304725i
$778$	252.009	−	252.009i	0.323919	−	0.323919i
$779$		−	1039.53i		−	1.33445i
$780$	246.040	+	49.6471i	0.315435	+	0.0636502i
$781$	−1706.33			−2.18480
$782$	−20.2638	−	20.2638i	−0.0259128	−	0.0259128i
$783$	−167.587	+	167.587i	−0.214032	+	0.214032i
$784$			159.022i			0.202834i
$785$	−559.296	−	842.071i	−0.712479	−	1.07270i
$786$	−152.826			−0.194436
$787$	−13.9567	−	13.9567i	−0.0177341	−	0.0177341i	0.698184	−	0.715918i	$-0.253992\pi$
$787$	−13.9567	−	13.9567i	−0.0177341	−	0.0177341i	−0.715918	+	0.698184i	$0.753992\pi$
$788$	467.537	−	467.537i	0.593321	−	0.593321i
$789$		−	549.349i		−	0.696260i
$790$	−348.707	+	231.608i	−0.441401	+	0.293174i
$791$	−603.961			−0.763540
$792$	−77.9816	−	77.9816i	−0.0984616	−	0.0984616i
$793$	−720.819	+	720.819i	−0.908977	+	0.908977i
$794$			1054.50i			1.32809i
$795$	83.8714	−	415.647i	0.105499	−	0.522826i
$796$	328.720			0.412965
$797$	−495.513	−	495.513i	−0.621723	−	0.621723i	0.324249	−	0.945972i	$-0.394888\pi$
$797$	−495.513	−	495.513i	−0.621723	−	0.621723i	−0.945972	+	0.324249i	$0.894888\pi$
$798$	−139.037	+	139.037i	−0.174232	+	0.174232i
$799$			61.3626i			0.0767992i
$800$	−53.3971	−	130.953i	−0.0667463	−	0.163692i
$801$	−509.702			−0.636332
$802$	337.961	+	337.961i	0.421398	+	0.421398i
$803$	−637.543	+	637.543i	−0.793952	+	0.793952i
$804$		−	96.4504i		−	0.119963i
$805$	−71.4678	−	14.4211i	−0.0887799	−	0.0179145i
$806$	767.766			0.952563
$807$	−561.161	−	561.161i	−0.695366	−	0.695366i
$808$	310.186	−	310.186i	0.383894	−	0.383894i
$809$		−	417.197i		−	0.515694i	−0.966186	−	0.257847i	$-0.916987\pi$
$809$		−	417.197i		−	0.515694i	0.966186	−	0.257847i	$-0.0830131\pi$
$810$	35.2100	+	53.0119i	0.0434691	+	0.0654467i
$811$	−3.41357			−0.00420909			−0.00210454	−	0.999998i	$-0.500670\pi$
$811$	−3.41357			−0.00420909			−0.00210454	+	0.999998i	$0.500670\pi$
$812$	−196.125	−	196.125i	−0.241533	−	0.241533i
$813$	−409.377	+	409.377i	−0.503539	+	0.503539i
$814$			1168.68i			1.43573i
$815$	604.896	−	401.767i	0.742204	−	0.492965i
$816$	−29.2737			−0.0358746
$817$	−785.176	−	785.176i	−0.961048	−	0.961048i
$818$	−669.062	+	669.062i	−0.817924	+	0.817924i
$819$		−	132.183i		−	0.161395i
$820$	77.8816	−	385.963i	0.0949776	−	0.470687i
$821$	1209.69			1.47344			0.736718	−	0.676200i	$-0.236375\pi$
$821$	1209.69			1.47344			0.736718	+	0.676200i	$0.236375\pi$
$822$	9.20349	+	9.20349i	0.0111965	+	0.0111965i
$823$	326.244	−	326.244i	0.396409	−	0.396409i	−0.480556	−	0.876964i	$-0.659565\pi$
$823$	326.244	−	326.244i	0.396409	−	0.396409i	0.876964	+	0.480556i	$0.159565\pi$
$824$		−	186.194i		−	0.225963i
$825$	521.126	−	212.493i	0.631668	−	0.257567i
$826$	98.3540			0.119073
$827$	−195.429	−	195.429i	−0.236311	−	0.236311i	0.579009	−	0.815321i	$-0.303439\pi$
$827$	−195.429	−	195.429i	−0.236311	−	0.236311i	−0.815321	+	0.579009i	$0.803439\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$			1340.21i			1.61666i	0.588733	+	0.808328i	$0.299627\pi$
$829$			1340.21i			1.61666i	−0.588733	+	0.808328i	$0.700373\pi$
$830$	304.349	+	61.4131i	0.366686	+	0.0739917i
$831$	491.109			0.590986
$832$	−81.9758	−	81.9758i	−0.0985286	−	0.0985286i
$833$	−118.779	+	118.779i	−0.142592	+	0.142592i
$834$			598.060i			0.717098i
$835$	662.705	+	997.762i	0.793658	+	1.19493i
$836$	−686.275			−0.820903
$837$	137.648	+	137.648i	0.164454	+	0.164454i
$838$	141.319	−	141.319i	0.168639	−	0.168639i
$839$			649.331i			0.773934i	0.922094	+	0.386967i	$0.126477\pi$
$839$			649.331i			0.773934i	−0.922094	+	0.386967i	$0.873523\pi$
$840$	−62.0389	+	41.2057i	−0.0738558	+	0.0490544i
$841$	−1239.41			−1.47373
$842$	336.422	+	336.422i	0.399551	+	0.399551i
$843$	−54.8861	+	54.8861i	−0.0651081	+	0.0651081i
$844$			151.940i			0.180023i
$845$	−40.5497	+	200.955i	−0.0479878	+	0.237816i
$846$	−61.6145			−0.0728303
$847$	103.026	+	103.026i	0.121636	+	0.121636i
$848$	−138.486	+	138.486i	−0.163309	+	0.163309i
$849$			186.298i			0.219433i
$850$	57.9293	−	137.697i	0.0681522	−	0.161997i
$851$	−304.933			−0.358323
$852$	−321.586	−	321.586i	−0.377449	−	0.377449i
$853$	−708.610	+	708.610i	−0.830726	+	0.830726i	−0.987616	−	0.156890i	$-0.949853\pi$
$853$	−708.610	+	708.610i	−0.830726	+	0.830726i	0.156890	+	0.987616i	$0.449853\pi$
$854$		−	302.474i		−	0.354185i
$855$	388.197	+	78.3324i	0.454031	+	0.0916168i
$856$	−54.7167			−0.0639214
$857$	−846.209	−	846.209i	−0.987409	−	0.987409i	0.0125131	−	0.999922i	$-0.496017\pi$
$857$	−846.209	−	846.209i	−0.987409	−	0.987409i	−0.999922	+	0.0125131i	$0.996017\pi$
$858$	326.221	−	326.221i	0.380211	−	0.380211i
$859$		−	97.8764i		−	0.113942i	−0.998376	−	0.0569711i	$-0.981856\pi$
$859$		−	97.8764i		−	0.113942i	0.998376	−	0.0569711i	$-0.0181443\pi$
$860$	−232.699	−	350.349i	−0.270580	−	0.407382i
$861$	−207.355			−0.240831
$862$	568.586	+	568.586i	0.659612	+	0.659612i
$863$	126.219	−	126.219i	0.146256	−	0.146256i	−0.630187	−	0.776443i	$-0.717022\pi$
$863$	126.219	−	126.219i	0.146256	−	0.146256i	0.776443	+	0.630187i	$0.217022\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−537.612	+	357.077i	−0.621517	+	0.412806i
$866$	444.772			0.513593
$867$	332.086	+	332.086i	0.383029	+	0.383029i
$868$	−161.087	+	161.087i	−0.185584	+	0.185584i
$869$			769.433i			0.885423i
$870$	−110.495	+	547.588i	−0.127006	+	0.629411i
$871$	403.482			0.463240
$872$	−210.305	−	210.305i	−0.241176	−	0.241176i
$873$	24.5277	−	24.5277i	0.0280959	−	0.0280959i
$874$		−	179.063i		−	0.204878i
$875$	−71.0550	−	373.359i	−0.0812057	−	0.426696i
$876$	−240.311			−0.274328
$877$	−374.235	−	374.235i	−0.426722	−	0.426722i	0.460788	−	0.887510i	$-0.347567\pi$
$877$	−374.235	−	374.235i	−0.426722	−	0.426722i	−0.887510	+	0.460788i	$0.847567\pi$
$878$	−215.602	+	215.602i	−0.245561	+	0.245561i
$879$		−	354.194i		−	0.402951i
$880$	−254.803	−	51.4155i	−0.289549	−	0.0584267i
$881$	473.542			0.537506			0.268753	−	0.963209i	$-0.413389\pi$
$881$	473.542			0.537506			0.268753	+	0.963209i	$0.413389\pi$
$882$	−119.266	−	119.266i	−0.135223	−	0.135223i
$883$	28.7262	−	28.7262i	0.0325325	−	0.0325325i	−0.690653	−	0.723186i	$-0.742677\pi$
$883$	28.7262	−	28.7262i	0.0325325	−	0.0325325i	0.723186	+	0.690653i	$0.242677\pi$
$884$		−	122.461i		−	0.138531i
$885$	−109.598	−	165.010i	−0.123840	−	0.186452i
$886$	564.371			0.636988
$887$	819.582	+	819.582i	0.923993	+	0.923993i	0.997309	−	0.0733156i	$-0.0233581\pi$
$887$	819.582	+	819.582i	0.923993	+	0.923993i	−0.0733156	+	0.997309i	$0.523358\pi$
$888$	−220.257	+	220.257i	−0.248038	+	0.248038i
$889$		−	474.442i		−	0.533680i
$890$	−1000.75	+	664.689i	−1.12444	+	0.746841i
$891$	116.972			0.131282
$892$	470.351	+	470.351i	0.527299	+	0.527299i
$893$	−271.118	+	271.118i	−0.303604	+	0.303604i
$894$			512.037i			0.572748i
$895$	−132.684	+	657.552i	−0.148251	+	0.734695i
$896$	34.3992			0.0383919
$897$	85.1178	+	85.1178i	0.0948916	+	0.0948916i
$898$	761.526	−	761.526i	0.848024	−	0.848024i
$899$			1708.75i			1.90072i
$900$	138.263	+	58.1671i	0.153625	+	0.0646302i
$901$	−206.880			−0.229611
$902$	−511.744	−	511.744i	−0.567344	−	0.567344i
$903$	−156.619	+	156.619i	−0.173443	+	0.173443i
$904$		−	561.837i		−	0.621502i
$905$	501.599	+	101.215i	0.554253	+	0.111840i
$906$	238.698			0.263463
$907$	−668.812	−	668.812i	−0.737389	−	0.737389i	0.234683	−	0.972072i	$-0.424595\pi$
$907$	−668.812	−	668.812i	−0.737389	−	0.737389i	−0.972072	+	0.234683i	$0.924595\pi$
$908$	−45.6864	+	45.6864i	−0.0503154	+	0.0503154i
$909$			465.280i			0.511859i
$910$	−172.376	−	259.528i	−0.189424	−	0.285195i
$911$	−1115.81			−1.22482			−0.612410	−	0.790540i	$-0.709800\pi$
$911$	−1115.81			−1.22482			−0.612410	+	0.790540i	$0.709800\pi$
$912$	−129.340	−	129.340i	−0.141820	−	0.141820i
$913$	403.533	−	403.533i	0.441986	−	0.441986i
$914$			542.128i			0.593138i
$915$	−507.465	+	337.054i	−0.554607	+	0.368365i
$916$	186.690			0.203810
$917$	134.138	+	134.138i	0.146279	+	0.146279i
$918$	21.9553	−	21.9553i	0.0239164	−	0.0239164i
$919$		−	1390.15i		−	1.51268i	−0.654181	−	0.756338i	$-0.726986\pi$
$919$		−	1390.15i		−	1.51268i	0.654181	−	0.756338i	$-0.273014\pi$
$920$	13.4153	−	66.4833i	0.0145819	−	0.0722645i
$921$	−413.867			−0.449367
$922$	29.2935	+	29.2935i	0.0317717	+	0.0317717i
$923$	1345.30	−	1345.30i	1.45752	−	1.45752i
$924$			136.891i			0.148150i
$925$	−600.181	−	1471.91i	−0.648844	−	1.59125i
$926$	−466.631			−0.503922
$927$	139.645	+	139.645i	0.150642	+	0.150642i
$928$	182.446	−	182.446i	0.196601	−	0.196601i
$929$			1037.21i			1.11648i	0.829680	+	0.558239i	$0.188523\pi$
$929$			1037.21i			1.11648i	−0.829680	+	0.558239i	$0.811477\pi$
$930$	449.762	+	90.7552i	0.483615	+	0.0975863i
$931$	−1049.60			−1.12739
$932$	−308.521	−	308.521i	−0.331031	−	0.331031i
$933$	−646.119	+	646.119i	−0.692517	+	0.692517i
$934$		−	814.754i		−	0.872328i
$935$	−151.917	−	228.725i	−0.162478	−	0.244626i
$936$	122.964			0.131371
$937$	−581.404	−	581.404i	−0.620496	−	0.620496i	0.325163	−	0.945658i	$-0.394581\pi$
$937$	−581.404	−	581.404i	−0.620496	−	0.620496i	−0.945658	+	0.325163i	$0.894581\pi$
$938$	−84.6557	+	84.6557i	−0.0902513	+	0.0902513i
$939$		−	944.845i		−	1.00622i
$940$	−120.974	+	80.3498i	−0.128696	+	0.0854785i
$941$	1214.11			1.29024			0.645118	−	0.764083i	$-0.276808\pi$
$941$	1214.11			1.29024			0.645118	+	0.764083i	$0.276808\pi$
$942$	−350.182	−	350.182i	−0.371743	−	0.371743i
$943$	133.524	−	133.524i	0.141595	−	0.141595i
$944$			91.4943i			0.0969219i
$945$	15.6249	−	77.4334i	0.0165343	−	0.0819401i
$946$	−773.056			−0.817184
$947$	−307.946	−	307.946i	−0.325181	−	0.325181i	0.525570	−	0.850750i	$-0.323852\pi$
$947$	−307.946	−	307.946i	−0.325181	−	0.325181i	−0.850750	+	0.525570i	$0.823852\pi$
$948$	−145.013	+	145.013i	−0.152967	+	0.152967i
$949$		−	1005.30i		−	1.05932i
$950$	864.338	−	352.439i	0.909829	−	0.370989i
$951$	−516.977			−0.543614
$952$	25.6939	+	25.6939i	0.0269894	+	0.0269894i
$953$	318.991	−	318.991i	0.334723	−	0.334723i	−0.519654	−	0.854377i	$-0.673939\pi$
$953$	318.991	−	318.991i	0.334723	−	0.334723i	0.854377	+	0.519654i	$0.173939\pi$
$954$		−	207.729i		−	0.217745i
$955$	−684.632	−	138.149i	−0.716892	−	0.144658i
$956$	18.1465			0.0189816
$957$	726.041	+	726.041i	0.758663	+	0.758663i
$958$	−703.739	+	703.739i	−0.734592	+	0.734592i
$959$		−	16.1560i		−	0.0168467i
$960$	−38.3318	−	57.7120i	−0.0399289	−	0.0601167i
$961$	442.480			0.460437
$962$	−921.405	−	921.405i	−0.957802	−	0.957802i
$963$	41.0375	−	41.0375i	0.0426143	−	0.0426143i
$964$			507.102i			0.526039i
$965$	609.443	−	404.786i	0.631547	−	0.419468i
$966$	−35.7176			−0.0369747
$967$	−186.468	−	186.468i	−0.192831	−	0.192831i	0.604087	−	0.796918i	$-0.293538\pi$
$967$	−186.468	−	186.468i	−0.192831	−	0.192831i	−0.796918	+	0.604087i	$0.793538\pi$
$968$	−95.8404	+	95.8404i	−0.0990087	+	0.0990087i
$969$		−	193.217i		−	0.199398i
$970$	16.1718	−	80.1438i	0.0166720	−	0.0826225i
$971$	−1246.50			−1.28373			−0.641864	−	0.766819i	$-0.721839\pi$
$971$	−1246.50			−1.28373			−0.641864	+	0.766819i	$0.721839\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	524.925	−	524.925i	0.539491	−	0.539491i
$974$			815.600i			0.837372i
$975$	−243.331	+	578.396i	−0.249571	+	0.593227i
$976$	281.378			0.288297
$977$	389.022	+	389.022i	0.398181	+	0.398181i	0.877591	−	0.479410i	$-0.159149\pi$
$977$	389.022	+	389.022i	0.398181	+	0.398181i	−0.479410	+	0.877591i	$0.659149\pi$
$978$	251.551	−	251.551i	0.257210	−	0.257210i
$979$			2208.19i			2.25555i
$980$	−389.700	−	78.6357i	−0.397653	−	0.0802405i
$981$	315.458			0.321567
$982$	−198.942	−	198.942i	−0.202589	−	0.202589i
$983$	552.321	−	552.321i	0.561873	−	0.561873i	−0.367966	−	0.929839i	$-0.619946\pi$
$983$	552.321	−	552.321i	0.561873	−	0.561873i	0.929839	+	0.367966i	$0.119946\pi$
$984$		−	192.894i		−	0.196030i
$985$	914.555	+	1376.95i	0.928482	+	1.39791i
$986$	272.550			0.276420
$987$	54.0798	+	54.0798i	0.0547921	+	0.0547921i
$988$	541.069	−	541.069i	0.547641	−	0.547641i
$989$		−	201.706i		−	0.203950i
$990$	229.664	−	152.541i	0.231984	−	0.154081i
$991$	−1165.66			−1.17625			−0.588125	−	0.808770i	$-0.700134\pi$
$991$	−1165.66			−1.17625			−0.588125	+	0.808770i	$0.700134\pi$
$992$	−149.852	−	149.852i	−0.151061	−	0.151061i
$993$	−167.275	+	167.275i	−0.168454	+	0.168454i
$994$			564.521i			0.567928i
$995$	−162.551	+	805.563i	−0.163368	+	0.809611i
$996$	152.105			0.152716
$997$	246.119	+	246.119i	0.246860	+	0.246860i	0.819681	−	0.572821i	$-0.194151\pi$
$997$	246.119	+	246.119i	0.246860	+	0.246860i	−0.572821	+	0.819681i	$0.694151\pi$
$998$	460.033	−	460.033i	0.460955	−	0.460955i
$999$		−	330.386i		−	0.330717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.7	✓	40
5.3	odd	4	inner	690.3.k.a.553.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.7	✓	40	1.1	even	1	trivial
690.3.k.a.553.7	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.91222 - 5.89021i) q^{10} -12.9969 q^{11} +(-2.44949 - 2.44949i) q^{12} +(10.2470 - 10.2470i) q^{13} +4.29989i q^{14} +(7.21400 - 4.79147i) q^{15} -4.00000 q^{16} +(-2.98774 - 2.98774i) q^{17} +(3.00000 - 3.00000i) q^{18} -26.4014i q^{19} +(1.97798 - 9.80243i) q^{20} -5.26627 q^{21} +(-12.9969 - 12.9969i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(23.0438 + 9.69452i) q^{25} +20.4940 q^{26} +(3.67423 + 3.67423i) q^{27} +(-4.29989 + 4.29989i) q^{28} +45.6115i q^{29} +(12.0055 + 2.42253i) q^{30} +37.4631 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.9179 - 15.9179i) q^{33} -5.97547i q^{34} +(-8.41107 - 12.6636i) q^{35} +6.00000 q^{36} +(-44.9599 - 44.9599i) q^{37} +(26.4014 - 26.4014i) q^{38} +25.0999i q^{39} +(11.7804 - 7.82444i) q^{40} +39.3742 q^{41} +(-5.26627 - 5.26627i) q^{42} +(29.7399 - 29.7399i) q^{43} -25.9939i q^{44} +(-2.96698 + 14.7036i) q^{45} +6.78233 q^{46} +(-10.2691 - 10.2691i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.7555i q^{49} +(13.3493 + 32.7383i) q^{50} +7.31843 q^{51} +(20.4940 + 20.4940i) q^{52} +(34.6215 - 34.6215i) q^{53} +7.34847i q^{54} +(63.7007 + 12.8539i) q^{55} -8.59979 q^{56} +(32.3350 + 32.3350i) q^{57} +(-45.6115 + 45.6115i) q^{58} -22.8736i q^{59} +(9.58295 + 14.4280i) q^{60} -70.3445 q^{61} +(37.4631 + 37.4631i) q^{62} +(6.44984 - 6.44984i) q^{63} -8.00000i q^{64} +(-60.3568 + 40.0884i) q^{65} +31.8358 q^{66} +(19.6879 + 19.6879i) q^{67} +(5.97547 - 5.97547i) q^{68} +8.30662i q^{69} +(4.25256 - 21.0747i) q^{70} +131.287 q^{71} +(6.00000 + 6.00000i) q^{72} +(49.0534 - 49.0534i) q^{73} -89.9197i q^{74} +(-40.0961 + 16.3494i) q^{75} +52.8028 q^{76} +(-27.9427 - 27.9427i) q^{77} +(-25.0999 + 25.0999i) q^{78} -59.2011i q^{79} +(19.6049 + 3.95597i) q^{80} -9.00000 q^{81} +(39.3742 + 39.3742i) q^{82} +(-31.0483 + 31.0483i) q^{83} -10.5325i q^{84} +(11.6887 + 17.5984i) q^{85} +59.4799 q^{86} +(-55.8625 - 55.8625i) q^{87} +(25.9939 - 25.9939i) q^{88} -169.901i q^{89} +(-17.6706 + 11.7367i) q^{90} +44.0609 q^{91} +(6.78233 + 6.78233i) q^{92} +(-45.8827 + 45.8827i) q^{93} -20.5382i q^{94} +(-26.1108 + 129.399i) q^{95} +9.79796 q^{96} +(8.17591 + 8.17591i) q^{97} +(39.7555 - 39.7555i) q^{98} +38.9908i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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