LMFDB - Embedded newform 690.3.k.a.553.7

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			553.7
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.7

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	−0.536662	−	0.843797i	$-0.680315\pi$
$7$	2.14995	−	2.14995i	0.307135	−	0.307135i	0.843797	+	0.536662i	$0.180315\pi$
$8$	−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	0.981204	−	0.192975i	$-0.0618136\pi$
$13$	10.2470	+	10.2470i	0.788229	+	0.788229i	−0.192975	+	0.981204i	$0.561814\pi$
$14$		−	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	−0.789500	−	0.613751i	$-0.789660\pi$
$17$	−2.98774	+	2.98774i	−0.175749	+	0.175749i	0.613751	+	0.789500i	$0.289660\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			26.4014i			1.38955i	0.719228	+	0.694774i	$0.244496\pi$
$19$			26.4014i			1.38955i	−0.719228	+	0.694774i	$0.755504\pi$
$20$	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	$-0.711940\pi$
$29$		−	45.6115i		−	1.57281i	0.617711	−	0.786406i	$-0.288060\pi$
$30$	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	−0.245815	+	0.969317i	$0.579055\pi$
$37$	−44.9599	+	44.9599i	−1.21513	+	1.21513i	−0.969317	+	0.245815i	$0.920945\pi$
$38$	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	0.962590	−	0.270963i	$-0.0873421\pi$
$43$	29.7399	+	29.7399i	0.691627	+	0.691627i	−0.270963	+	0.962590i	$0.587342\pi$
$44$			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	−0.807862	−	0.589371i	$-0.799376\pi$
$47$	−10.2691	+	10.2691i	−0.218491	+	0.218491i	0.589371	+	0.807862i	$0.299376\pi$
$48$	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	0.953771	−	0.300535i	$-0.0971654\pi$
$53$	34.6215	+	34.6215i	0.653235	+	0.653235i	−0.300535	+	0.953771i	$0.597165\pi$
$54$		−	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	$0.0620955\pi$
$59$			22.8736i			0.387688i	−0.981032	+	0.193844i	$0.937904\pi$
$60$	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	−0.544750	−	0.838599i	$-0.683375\pi$
$67$	19.6879	−	19.6879i	0.293849	−	0.293849i	0.838599	+	0.544750i	$0.183375\pi$
$68$	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	0.958169	−	0.286205i	$-0.0923937\pi$
$73$	49.0534	+	49.0534i	0.671964	+	0.671964i	−0.286205	+	0.958169i	$0.592394\pi$
$74$			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	$0.122251\pi$
$79$			59.2011i			0.749381i	−0.927150	+	0.374691i	$0.877749\pi$
$80$	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	0.494883	−	0.868960i	$-0.335211\pi$
$83$	−31.0483	−	31.0483i	−0.374076	−	0.374076i	−0.868960	+	0.494883i	$0.835211\pi$
$84$			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	$0.403608\pi$
$89$			169.901i			1.90900i	−0.298219	+	0.954498i	$0.596392\pi$
$90$	−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	−0.663706	−	0.747994i	$-0.731017\pi$
$97$	8.17591	−	8.17591i	0.0842878	−	0.0842878i	0.747994	+	0.663706i	$0.231017\pi$
$98$	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	0.444067	−	0.895994i	$-0.353535\pi$
$103$	−46.5485	−	46.5485i	−0.451927	−	0.451927i	−0.895994	+	0.444067i	$0.853535\pi$
$104$		−	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	−0.640290	−	0.768133i	$-0.721186\pi$
$107$	13.6792	−	13.6792i	0.127843	−	0.127843i	0.768133	+	0.640290i	$0.221186\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	105.153i		−	0.964702i	−0.875978	−	0.482351i	$-0.839783\pi$
$109$		−	105.153i		−	0.964702i	0.875978	−	0.482351i	$-0.160217\pi$
$110$	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	−0.958749	−	0.284254i	$-0.908254\pi$
$113$	−140.459	−	140.459i	−1.24300	−	1.24300i	−0.284254	−	0.958749i	$-0.591746\pi$
$114$		−	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	−0.992340	−	0.123537i	$-0.960576\pi$
$127$	−110.338	+	110.338i	−0.868803	+	0.868803i	0.123537	+	0.992340i	$0.460576\pi$
$128$	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	−0.720687	−	0.693261i	$-0.756173\pi$
$137$	−3.75731	+	3.75731i	−0.0274256	+	0.0274256i	0.693261	+	0.720687i	$0.256173\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			244.157i			1.75652i	0.478179	+	0.878262i	$0.341297\pi$
$139$			244.157i			1.75652i	−0.478179	+	0.878262i	$0.658703\pi$
$140$	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	$0.247473\pi$
$149$			209.038i			1.40294i	−0.712699	+	0.701470i	$0.752527\pi$
$150$	−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	−0.0857369	−	0.996318i	$-0.527324\pi$
$157$	142.961	−	142.961i	0.910581	−	0.910581i	0.996318	+	0.0857369i	$0.0273245\pi$
$158$	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	0.318044	−	0.948076i	$-0.396974\pi$
$163$	−102.695	−	102.695i	−0.630032	−	0.630032i	−0.948076	+	0.318044i	$0.896974\pi$
$164$		−	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	−0.0144364	+	0.999896i	$0.504595\pi$
$167$	−169.393	+	169.393i	−1.01433	+	1.01433i	−0.999896	+	0.0144364i	$0.995405\pi$
$168$	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	0.919852	−	0.392267i	$-0.128309\pi$
$173$	91.2722	+	91.2722i	0.527585	+	0.527585i	−0.392267	+	0.919852i	$0.628309\pi$
$174$			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	$0.122272\pi$
$179$			134.161i			0.749503i	−0.927125	+	0.374752i	$0.877728\pi$
$180$	−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	0.386282	−	0.922381i	$-0.373759\pi$
$193$	−103.467	−	103.467i	−0.536099	−	0.536099i	−0.922381	+	0.386282i	$0.873759\pi$
$194$		−	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	−0.208653	+	0.977990i	$0.566908\pi$
$197$	−233.769	+	233.769i	−1.18664	+	1.18664i	−0.977990	+	0.208653i	$0.933092\pi$
$198$	−38.9908	−	38.9908i	−0.196923	−	0.196923i
$199$			164.360i			0.825929i	0.910747	+	0.412965i	$0.135507\pi$
$199$			164.360i			0.825929i	−0.910747	+	0.412965i	$0.864493\pi$
$200$	−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	0.998421	+	0.0561774i	$0.0178912\pi$
$223$	235.175	+	235.175i	1.05460	+	1.05460i	0.0561774	+	0.998421i	$0.482109\pi$
$224$			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	−0.654999	−	0.755630i	$-0.727331\pi$
$227$	22.8432	−	22.8432i	0.100631	−	0.100631i	0.755630	+	0.654999i	$0.227331\pi$
$228$	−64.6700	−	64.6700i	−0.283640	−	0.283640i
$229$			93.3450i			0.407620i	0.979010	+	0.203810i	$0.0653325\pi$
$229$			93.3450i			0.407620i	−0.979010	+	0.203810i	$0.934667\pi$
$230$	−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	0.293803	−	0.955866i	$-0.405079\pi$
$233$	−154.261	−	154.261i	−0.662063	−	0.662063i	−0.955866	+	0.293803i	$0.905079\pi$
$234$			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	$0.00604241\pi$
$239$			9.07323i			0.0379633i	−0.999820	+	0.0189816i	$0.993958\pi$
$240$	−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	−0.759175	−	0.650887i	$-0.774397\pi$
$257$	−27.8299	+	27.8299i	−0.108287	+	0.108287i	0.650887	+	0.759175i	$0.274397\pi$
$258$	−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	0.137729	−	0.990470i	$-0.456020\pi$
$263$	−224.271	−	224.271i	−0.852741	−	0.852741i	−0.990470	+	0.137729i	$0.956020\pi$
$264$		−	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	$-0.675605\pi$
$269$		−	458.186i		−	1.70329i	0.524117	−	0.851646i	$-0.324395\pi$
$270$	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	−0.969378	−	0.245572i	$-0.921024\pi$
$277$	−200.494	+	200.494i	−0.723807	+	0.723807i	0.245572	+	0.969378i	$0.421024\pi$
$278$	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	0.828596	−	0.559847i	$-0.189140\pi$
$283$	76.0560	+	76.0560i	0.268749	+	0.268749i	−0.559847	+	0.828596i	$0.689140\pi$
$284$		−	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	0.415899	−	0.909411i	$-0.363467\pi$
$293$	−144.599	−	144.599i	−0.493512	−	0.493512i	−0.909411	+	0.415899i	$0.863467\pi$
$294$		−	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	−0.376185	−	0.926545i	$-0.622764\pi$
$307$	168.960	−	168.960i	0.550360	−	0.550360i	0.926545	+	0.376185i	$0.122764\pi$
$308$	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	−0.963052	−	0.269316i	$-0.913202\pi$
$313$	−385.731	−	385.731i	−1.23237	−	1.23237i	−0.269316	−	0.963052i	$-0.586798\pi$
$314$		−	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	−0.290950	−	0.956738i	$-0.593971\pi$
$317$	211.055	−	211.055i	0.665788	−	0.665788i	0.956738	+	0.290950i	$0.0939714\pi$
$318$	−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	−0.812811	−	0.582528i	$-0.802064\pi$
$337$	−77.6053	+	77.6053i	−0.230283	+	0.230283i	0.582528	+	0.812811i	$0.302064\pi$
$338$	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	−0.999420	−	0.0340576i	$-0.989157\pi$
$347$	−334.981	+	334.981i	−0.965362	+	0.965362i	0.0340576	+	0.999420i	$0.489157\pi$
$348$	111.725	+	111.725i	0.321049	+	0.321049i
$349$		−	462.956i		−	1.32652i	−0.748389	−	0.663261i	$-0.769172\pi$
$349$		−	462.956i		−	1.32652i	0.748389	−	0.663261i	$-0.230828\pi$
$350$	−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	−0.977407	−	0.211367i	$-0.932208\pi$
$353$	−419.637	−	419.637i	−1.18877	−	1.18877i	−0.211367	−	0.977407i	$-0.567792\pi$
$354$		−	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	$-0.885269\pi$
$359$		−	253.226i		−	0.705366i	0.935743	−	0.352683i	$-0.114731\pi$
$360$	−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	−0.501894	−	0.864929i	$-0.667363\pi$
$367$	133.234	−	133.234i	0.363035	−	0.363035i	0.864929	+	0.501894i	$0.167363\pi$
$368$	−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	0.462723	−	0.886503i	$-0.346872\pi$
$373$	−158.070	−	158.070i	−0.423780	−	0.423780i	−0.886503	+	0.462723i	$0.846872\pi$
$374$		−	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	$0.221368\pi$
$379$			485.673i			1.28146i	−0.767766	+	0.640730i	$0.778632\pi$
$380$	−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	0.982849	+	0.184410i	$0.0590375\pi$
$383$	447.060	+	447.060i	1.16726	+	1.16726i	0.184410	+	0.982849i	$0.440963\pi$
$384$		−	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	$0.105000\pi$
$389$			252.009i			0.647837i	−0.946085	+	0.323919i	$0.895000\pi$
$390$	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	0.421050	−	0.907038i	$-0.361662\pi$
$397$	527.251	−	527.251i	1.32809	−	1.32809i	0.907038	−	0.421050i	$-0.138338\pi$
$398$	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	$-0.695125\pi$
$409$		−	669.062i		−	1.63585i	0.575327	−	0.817924i	$-0.304875\pi$
$410$	−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	$0.0539372\pi$
$419$			141.319i			0.337278i	−0.985678	+	0.168639i	$0.946063\pi$
$420$	−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	0.915626	−	0.402032i	$-0.131696\pi$
$433$	222.386	+	222.386i	0.513593	+	0.513593i	−0.402032	+	0.915626i	$0.631696\pi$
$434$		−	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	$-0.921028\pi$
$439$		−	215.602i		−	0.491121i	0.969381	−	0.245561i	$-0.0789720\pi$
$440$	−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	0.949811	−	0.312823i	$-0.101275\pi$
$443$	282.186	+	282.186i	0.636988	+	0.636988i	−0.312823	+	0.949811i	$0.601275\pi$
$444$		−	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	$0.322208\pi$
$449$			761.526i			1.69605i	−0.529958	+	0.848024i	$0.677792\pi$
$450$	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	−0.345340	−	0.938478i	$-0.612236\pi$
$457$	271.064	−	271.064i	0.593138	−	0.593138i	0.938478	+	0.345340i	$0.112236\pi$
$458$	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	0.408733	−	0.912654i	$-0.365971\pi$
$463$	−233.316	−	233.316i	−0.503922	−	0.503922i	−0.912654	+	0.408733i	$0.865971\pi$
$464$			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	−0.992726	−	0.120398i	$-0.961583\pi$
$467$	−407.377	+	407.377i	−0.872328	+	0.872328i	0.120398	+	0.992726i	$0.461583\pi$
$468$	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	$-0.737374\pi$
$479$		−	703.739i		−	1.46918i	0.678509	−	0.734592i	$-0.262626\pi$
$480$	−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	−0.151141	−	0.988512i	$-0.548295\pi$
$487$	407.800	−	407.800i	0.837372	−	0.837372i	0.988512	+	0.151141i	$0.0482946\pi$
$488$	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	$0.152493\pi$
$499$			460.033i			0.921910i	−0.887424	+	0.460955i	$0.847507\pi$
$500$	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	0.699614	−	0.714521i	$-0.253355\pi$
$503$	−7.49816	−	7.49816i	−0.0149069	−	0.0149069i	−0.714521	+	0.699614i	$0.753355\pi$
$504$		−	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	$0.158319\pi$
$509$			485.709i			0.954241i	−0.878838	+	0.477120i	$0.841681\pi$
$510$	−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	0.969497	−	0.245103i	$-0.0788219\pi$
$523$	378.858	+	378.858i	0.724393	+	0.724393i	−0.245103	+	0.969497i	$0.578822\pi$
$524$		−	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	−0.172038	−	0.985090i	$-0.555035\pi$
$547$	444.740	−	444.740i	0.813052	−	0.813052i	0.985090	+	0.172038i	$0.0550352\pi$
$548$	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	−0.0487058	+	0.998813i	$0.515510\pi$
$557$	−583.468	+	583.468i	−1.04752	+	1.04752i	−0.998813	+	0.0487058i	$0.984490\pi$
$558$	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	0.672070	−	0.740488i	$-0.265405\pi$
$563$	−38.5193	−	38.5193i	−0.0684179	−	0.0684179i	−0.740488	+	0.672070i	$0.765405\pi$
$564$		−	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	$-0.979800\pi$
$569$		−	72.1680i		−	0.126833i	0.997987	−	0.0634165i	$-0.0201997\pi$
$570$	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	−0.268202	−	0.963363i	$-0.586429\pi$
$577$	401.108	−	401.108i	0.695161	−	0.695161i	0.963363	+	0.268202i	$0.0864293\pi$
$578$	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	−0.935400	−	0.353593i	$-0.884960\pi$
$587$	−341.521	+	341.521i	−0.581807	+	0.581807i	0.353593	+	0.935400i	$0.384960\pi$
$588$	−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	0.703005	−	0.711185i	$-0.251841\pi$
$593$	−4.85045	−	4.85045i	−0.00817952	−	0.00817952i	−0.711185	+	0.703005i	$0.751841\pi$
$594$			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	$0.153465\pi$
$599$			555.468i			0.927326i	−0.886012	+	0.463663i	$0.846535\pi$
$600$	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	−0.258308	−	0.966063i	$-0.583165\pi$
$607$	429.607	−	429.607i	0.707755	−	0.707755i	0.966063	+	0.258308i	$0.0831648\pi$
$608$	−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	0.952138	−	0.305670i	$-0.0988803\pi$
$613$	396.285	+	396.285i	0.646468	+	0.646468i	−0.305670	+	0.952138i	$0.598880\pi$
$614$		−	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	−0.368299	+	0.929707i	$0.620060\pi$
$617$	−800.870	+	800.870i	−1.29801	+	1.29801i	−0.929707	+	0.368299i	$0.879940\pi$
$618$	114.020	+	114.020i	0.184498	+	0.184498i
$619$		−	480.925i		−	0.776939i	−0.921462	−	0.388469i	$-0.873004\pi$
$619$		−	480.925i		−	0.776939i	0.921462	−	0.388469i	$-0.126996\pi$
$620$	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	−0.995319	−	0.0966483i	$-0.969188\pi$
$643$	−702.135	−	702.135i	−1.09197	−	1.09197i	−0.0966483	−	0.995319i	$-0.530812\pi$
$644$		−	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	−0.994433	−	0.105371i	$-0.966397\pi$
$647$	−575.223	+	575.223i	−0.889062	+	0.889062i	0.105371	+	0.994433i	$0.466397\pi$
$648$	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	0.479069	−	0.877777i	$-0.340974\pi$
$653$	−260.357	−	260.357i	−0.398708	−	0.398708i	−0.877777	+	0.479069i	$0.840974\pi$
$654$			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	$0.103620\pi$
$659$			421.514i			0.639626i	−0.947481	+	0.319813i	$0.896380\pi$
$660$	−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	0.479328	−	0.877636i	$-0.340880\pi$
$673$	−268.061	−	268.061i	−0.398308	−	0.398308i	−0.877636	+	0.479328i	$0.840880\pi$
$674$			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	−0.504991	−	0.863124i	$-0.668504\pi$
$677$	242.456	−	242.456i	0.358133	−	0.358133i	0.863124	+	0.504991i	$0.168504\pi$
$678$	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	0.0661774	−	0.997808i	$-0.478920\pi$
$683$	−636.304	−	636.304i	−0.931630	−	0.931630i	−0.997808	+	0.0661774i	$0.978920\pi$
$684$			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	$-0.887017\pi$
$709$		−	492.812i		−	0.695080i	0.937665	−	0.347540i	$-0.112983\pi$
$710$	−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	$0.0148235\pi$
$719$			66.9427i			0.0931052i	−0.998916	+	0.0465526i	$0.985176\pi$
$720$	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	−0.865212	−	0.501406i	$-0.832816\pi$
$727$	−264.488	+	264.488i	−0.363807	+	0.363807i	0.501406	+	0.865212i	$0.332816\pi$
$728$	−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	0.707479	−	0.706735i	$-0.249832\pi$
$733$	0.545555	+	0.545555i	0.000744277	+	0.000744277i	−0.706735	+	0.707479i	$0.749832\pi$
$734$		−	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	$0.152809\pi$
$739$			682.594i			0.923673i	−0.886965	+	0.461836i	$0.847191\pi$
$740$	−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	0.393609	−	0.919278i	$-0.371227\pi$
$743$	−390.572	−	390.572i	−0.525670	−	0.525670i	−0.919278	+	0.393609i	$0.871227\pi$
$744$			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	0.0250588	−	0.999686i	$-0.492023\pi$
$757$	775.732	−	775.732i	1.02474	−	1.02474i	0.999686	−	0.0250588i	$-0.00797731\pi$
$758$	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	$-0.791012\pi$
$769$		−	938.784i		−	1.22079i	0.792099	−	0.610393i	$-0.208988\pi$
$770$	−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	0.996845	−	0.0793776i	$-0.0252933\pi$
$773$	709.202	+	709.202i	0.917467	+	0.917467i	−0.0793776	+	0.996845i	$0.525293\pi$
$774$			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	−0.715918	−	0.698184i	$-0.753992\pi$
$787$	−13.9567	+	13.9567i	−0.0177341	+	0.0177341i	0.698184	+	0.715918i	$0.253992\pi$
$788$	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	−0.945972	−	0.324249i	$-0.894888\pi$
$797$	−495.513	+	495.513i	−0.621723	+	0.621723i	0.324249	+	0.945972i	$0.394888\pi$
$798$	−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	$0.0830131\pi$
$809$			417.197i			0.515694i	−0.966186	+	0.257847i	$0.916987\pi$
$810$	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	0.876964	−	0.480556i	$-0.159565\pi$
$823$	326.244	+	326.244i	0.396409	+	0.396409i	−0.480556	+	0.876964i	$0.659565\pi$
$824$			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	−0.815321	−	0.579009i	$-0.803439\pi$
$827$	−195.429	+	195.429i	−0.236311	+	0.236311i	0.579009	+	0.815321i	$0.303439\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	1340.21i		−	1.61666i	−0.588733	−	0.808328i	$-0.700373\pi$
$829$		−	1340.21i		−	1.61666i	0.588733	−	0.808328i	$-0.299627\pi$
$830$	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	$-0.873523\pi$
$839$		−	649.331i		−	0.773934i	0.922094	−	0.386967i	$-0.126477\pi$
$840$	−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	0.156890	−	0.987616i	$-0.449853\pi$
$853$	−708.610	−	708.610i	−0.830726	−	0.830726i	−0.987616	+	0.156890i	$0.949853\pi$
$854$			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	−0.999922	−	0.0125131i	$-0.996017\pi$
$857$	−846.209	+	846.209i	−0.987409	+	0.987409i	0.0125131	+	0.999922i	$0.496017\pi$
$858$	326.221	+	326.221i	0.380211	+	0.380211i
$859$			97.8764i			0.113942i	0.998376	+	0.0569711i	$0.0181443\pi$
$859$			97.8764i			0.113942i	−0.998376	+	0.0569711i	$0.981856\pi$
$860$	−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	0.776443	−	0.630187i	$-0.217022\pi$
$863$	126.219	+	126.219i	0.146256	+	0.146256i	−0.630187	+	0.776443i	$0.717022\pi$
$864$			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	−0.887510	−	0.460788i	$-0.847567\pi$
$877$	−374.235	+	374.235i	−0.426722	+	0.426722i	0.460788	+	0.887510i	$0.347567\pi$
$878$	−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	0.723186	−	0.690653i	$-0.242677\pi$
$883$	28.7262	+	28.7262i	0.0325325	+	0.0325325i	−0.690653	+	0.723186i	$0.742677\pi$
$884$			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	−0.0733156	−	0.997309i	$-0.523358\pi$
$887$	819.582	−	819.582i	0.923993	−	0.923993i	0.997309	+	0.0733156i	$0.0233581\pi$
$888$	−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	−0.972072	−	0.234683i	$-0.924595\pi$
$907$	−668.812	+	668.812i	−0.737389	+	0.737389i	0.234683	+	0.972072i	$0.424595\pi$
$908$	−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	$0.273014\pi$
$919$			1390.15i			1.51268i	−0.654181	+	0.756338i	$0.726986\pi$
$920$	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	$-0.811477\pi$
$929$		−	1037.21i		−	1.11648i	0.829680	−	0.558239i	$-0.188523\pi$
$930$	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	−0.945658	−	0.325163i	$-0.894581\pi$
$937$	−581.404	+	581.404i	−0.620496	+	0.620496i	0.325163	+	0.945658i	$0.394581\pi$
$938$	−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	−0.850750	−	0.525570i	$-0.823852\pi$
$947$	−307.946	+	307.946i	−0.325181	+	0.325181i	0.525570	+	0.850750i	$0.323852\pi$
$948$	−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	0.854377	−	0.519654i	$-0.173939\pi$
$953$	318.991	+	318.991i	0.334723	+	0.334723i	−0.519654	+	0.854377i	$0.673939\pi$
$954$			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	−0.796918	−	0.604087i	$-0.793538\pi$
$967$	−186.468	+	186.468i	−0.192831	+	0.192831i	0.604087	+	0.796918i	$0.293538\pi$
$968$	−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	−0.479410	−	0.877591i	$-0.659149\pi$
$977$	389.022	−	389.022i	0.398181	−	0.398181i	0.877591	+	0.479410i	$0.159149\pi$
$978$	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	0.929839	−	0.367966i	$-0.119946\pi$
$983$	552.321	+	552.321i	0.561873	+	0.561873i	−0.367966	+	0.929839i	$0.619946\pi$
$984$			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	−0.572821	−	0.819681i	$-0.694151\pi$
$997$	246.119	−	246.119i	0.246860	−	0.246860i	0.819681	+	0.572821i	$0.194151\pi$
$998$	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.553.7	yes	40
5.2	odd	4	inner	690.3.k.a.277.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.7	✓	40	5.2	odd	4	inner
690.3.k.a.553.7	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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

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