LMFDB - Embedded newform 690.3.k.a.553.19

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			553.19
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.45244 - 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 + 3.57605i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.45244 - 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 + 3.57605i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-6.72747 + 2.17742i) q^{10} +15.2817 q^{11} +(2.44949 - 2.44949i) q^{12} +(9.30559 + 9.30559i) q^{13} +7.15211i q^{14} +(-2.66678 - 8.23943i) q^{15} -4.00000 q^{16} +(7.64975 - 7.64975i) q^{17} +(3.00000 + 3.00000i) q^{18} +16.6289i q^{19} +(-4.55005 + 8.90489i) q^{20} -8.75951 q^{21} +(15.2817 - 15.2817i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(14.6485 + 20.2588i) q^{25} +18.6112 q^{26} +(-3.67423 + 3.67423i) q^{27} +(7.15211 + 7.15211i) q^{28} -28.4867i q^{29} +(-10.9062 - 5.57265i) q^{30} +46.8375 q^{31} +(-4.00000 + 4.00000i) q^{32} +(18.7162 + 18.7162i) q^{33} -15.2995i q^{34} +(24.0578 - 7.78657i) q^{35} +6.00000 q^{36} +(38.8008 - 38.8008i) q^{37} +(16.6289 + 16.6289i) q^{38} +22.7940i q^{39} +(4.35484 + 13.4549i) q^{40} +49.1688 q^{41} +(-8.75951 + 8.75951i) q^{42} +(-39.9675 - 39.9675i) q^{43} -30.5635i q^{44} +(6.82507 - 13.3573i) q^{45} -6.78233 q^{46} +(42.2681 - 42.2681i) q^{47} +(-4.89898 - 4.89898i) q^{48} +23.4237i q^{49} +(34.9074 + 5.61032i) q^{50} +18.7380 q^{51} +(18.6112 - 18.6112i) q^{52} +(40.9030 + 40.9030i) q^{53} +7.34847i q^{54} +(-68.0411 - 34.7664i) q^{55} +14.3042 q^{56} +(-20.3661 + 20.3661i) q^{57} +(-28.4867 - 28.4867i) q^{58} +115.558i q^{59} +(-16.4789 + 5.33357i) q^{60} -39.5522 q^{61} +(46.8375 - 46.8375i) q^{62} +(-10.7282 - 10.7282i) q^{63} +8.00000i q^{64} +(-20.2622 - 62.6031i) q^{65} +37.4325 q^{66} +(30.0611 - 30.0611i) q^{67} +(-15.2995 - 15.2995i) q^{68} -8.30662i q^{69} +(16.2712 - 31.8444i) q^{70} -109.516 q^{71} +(6.00000 - 6.00000i) q^{72} +(37.5852 + 37.5852i) q^{73} -77.6015i q^{74} +(-6.87121 + 42.7526i) q^{75} +33.2577 q^{76} +(-54.6484 + 54.6484i) q^{77} +(22.7940 + 22.7940i) q^{78} +116.711i q^{79} +(17.8098 + 9.10010i) q^{80} -9.00000 q^{81} +(49.1688 - 49.1688i) q^{82} +(97.5863 + 97.5863i) q^{83} +17.5190i q^{84} +(-51.4635 + 16.6567i) q^{85} -79.9350 q^{86} +(34.8890 - 34.8890i) q^{87} +(-30.5635 - 30.5635i) q^{88} -26.3345i q^{89} +(-6.53226 - 20.1824i) q^{90} -66.5546 q^{91} +(-6.78233 + 6.78233i) q^{92} +(57.3640 + 57.3640i) q^{93} -84.5362i q^{94} +(37.8311 - 74.0391i) q^{95} -9.79796 q^{96} +(-70.0462 + 70.0462i) q^{97} +(23.4237 + 23.4237i) q^{98} +45.8452i 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
$5$	−4.45244	−	2.27502i	−0.890489	−	0.455005i
$5$	−4.45244	−	2.27502i	−0.890489	−	0.455005i
$6$	2.44949			0.408248
$7$	−3.57605	+	3.57605i	−0.510865	+	0.510865i	−0.914791	−	0.403927i	$-0.867645\pi$
$7$	−3.57605	+	3.57605i	−0.510865	+	0.510865i	0.403927	+	0.914791i	$0.367645\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−6.72747	+	2.17742i	−0.672747	+	0.217742i
$11$	15.2817			1.38925			0.694625	−	0.719372i	$-0.255570\pi$
$11$	15.2817			1.38925			0.694625	+	0.719372i	$0.255570\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	9.30559	+	9.30559i	0.715815	+	0.715815i	0.967745	−	0.251931i	$-0.0810654\pi$
$13$	9.30559	+	9.30559i	0.715815	+	0.715815i	−0.251931	+	0.967745i	$0.581065\pi$
$14$			7.15211i			0.510865i
$15$	−2.66678	−	8.23943i	−0.177786	−	0.549296i
$16$	−4.00000			−0.250000
$17$	7.64975	−	7.64975i	0.449986	−	0.449986i	−0.445364	−	0.895350i	$-0.646926\pi$
$17$	7.64975	−	7.64975i	0.449986	−	0.449986i	0.895350	+	0.445364i	$0.146926\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			16.6289i			0.875203i	0.899169	+	0.437602i	$0.144172\pi$
$19$			16.6289i			0.875203i	−0.899169	+	0.437602i	$0.855828\pi$
$20$	−4.55005	+	8.90489i	−0.227502	+	0.445244i
$21$	−8.75951			−0.417119
$22$	15.2817	−	15.2817i	0.694625	−	0.694625i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	14.6485	+	20.2588i	0.585941	+	0.810354i
$26$	18.6112			0.715815
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	7.15211	+	7.15211i	0.255432	+	0.255432i
$29$		−	28.4867i		−	0.982301i	−0.871075	−	0.491150i	$-0.836577\pi$
$29$		−	28.4867i		−	0.982301i	0.871075	−	0.491150i	$-0.163423\pi$
$30$	−10.9062	−	5.57265i	−0.363541	−	0.185755i
$31$	46.8375			1.51089			0.755443	−	0.655214i	$-0.227422\pi$
$31$	46.8375			1.51089			0.755443	+	0.655214i	$0.227422\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	18.7162	+	18.7162i	0.567159	+	0.567159i
$34$		−	15.2995i		−	0.449986i
$35$	24.0578	−	7.78657i	0.687366	−	0.222473i
$36$	6.00000			0.166667
$37$	38.8008	−	38.8008i	1.04867	−	1.04867i	0.0499156	−	0.998753i	$-0.484105\pi$
$37$	38.8008	−	38.8008i	1.04867	−	1.04867i	0.998753	−	0.0499156i	$-0.0158952\pi$
$38$	16.6289	+	16.6289i	0.437602	+	0.437602i
$39$			22.7940i			0.584460i
$40$	4.35484	+	13.4549i	0.108871	+	0.336373i
$41$	49.1688			1.19924			0.599620	−	0.800285i	$-0.295319\pi$
$41$	49.1688			1.19924			0.599620	+	0.800285i	$0.295319\pi$
$42$	−8.75951	+	8.75951i	−0.208560	+	0.208560i
$43$	−39.9675	−	39.9675i	−0.929477	−	0.929477i	0.0681954	−	0.997672i	$-0.478276\pi$
$43$	−39.9675	−	39.9675i	−0.929477	−	0.929477i	−0.997672	+	0.0681954i	$0.978276\pi$
$44$		−	30.5635i		−	0.694625i
$45$	6.82507	−	13.3573i	0.151668	−	0.296830i
$46$	−6.78233			−0.147442
$47$	42.2681	−	42.2681i	0.899322	−	0.899322i	−0.0960544	−	0.995376i	$-0.530622\pi$
$47$	42.2681	−	42.2681i	0.899322	−	0.899322i	0.995376	+	0.0960544i	$0.0306223\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			23.4237i			0.478034i
$50$	34.9074	+	5.61032i	0.698147	+	0.112206i
$51$	18.7380			0.367412
$52$	18.6112	−	18.6112i	0.357907	−	0.357907i
$53$	40.9030	+	40.9030i	0.771756	+	0.771756i	0.978413	−	0.206658i	$-0.0662587\pi$
$53$	40.9030	+	40.9030i	0.771756	+	0.771756i	−0.206658	+	0.978413i	$0.566259\pi$
$54$			7.34847i			0.136083i
$55$	−68.0411	−	34.7664i	−1.23711	−	0.632115i
$56$	14.3042			0.255432
$57$	−20.3661	+	20.3661i	−0.357300	+	0.357300i
$58$	−28.4867	−	28.4867i	−0.491150	−	0.491150i
$59$			115.558i			1.95860i	0.202409	+	0.979301i	$0.435123\pi$
$59$			115.558i			1.95860i	−0.202409	+	0.979301i	$0.564877\pi$
$60$	−16.4789	+	5.33357i	−0.274648	+	0.0888928i
$61$	−39.5522			−0.648397			−0.324199	−	0.945989i	$-0.605095\pi$
$61$	−39.5522			−0.648397			−0.324199	+	0.945989i	$0.605095\pi$
$62$	46.8375	−	46.8375i	0.755443	−	0.755443i
$63$	−10.7282	−	10.7282i	−0.170288	−	0.170288i
$64$			8.00000i			0.125000i
$65$	−20.2622	−	62.6031i	−0.311726	−	0.963124i
$66$	37.4325			0.567159
$67$	30.0611	−	30.0611i	0.448673	−	0.448673i	−0.446240	−	0.894913i	$-0.647237\pi$
$67$	30.0611	−	30.0611i	0.448673	−	0.448673i	0.894913	+	0.446240i	$0.147237\pi$
$68$	−15.2995	−	15.2995i	−0.224993	−	0.224993i
$69$		−	8.30662i		−	0.120386i
$70$	16.2712	−	31.8444i	0.232446	−	0.454920i
$71$	−109.516			−1.54247			−0.771237	−	0.636548i	$-0.780362\pi$
$71$	−109.516			−1.54247			−0.771237	+	0.636548i	$0.780362\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	37.5852	+	37.5852i	0.514865	+	0.514865i	0.916013	−	0.401148i	$-0.131389\pi$
$73$	37.5852	+	37.5852i	0.514865	+	0.514865i	−0.401148	+	0.916013i	$0.631389\pi$
$74$		−	77.6015i		−	1.04867i
$75$	−6.87121	+	42.7526i	−0.0916162	+	0.570035i
$76$	33.2577			0.437602
$77$	−54.6484	+	54.6484i	−0.709719	+	0.709719i
$78$	22.7940	+	22.7940i	0.292230	+	0.292230i
$79$			116.711i			1.47736i	0.674057	+	0.738679i	$0.264550\pi$
$79$			116.711i			1.47736i	−0.674057	+	0.738679i	$0.735450\pi$
$80$	17.8098	+	9.10010i	0.222622	+	0.113751i
$81$	−9.00000			−0.111111
$82$	49.1688	−	49.1688i	0.599620	−	0.599620i
$83$	97.5863	+	97.5863i	1.17574	+	1.17574i	0.980819	+	0.194920i	$0.0624447\pi$
$83$	97.5863	+	97.5863i	1.17574	+	1.17574i	0.194920	+	0.980819i	$0.437555\pi$
$84$			17.5190i			0.208560i
$85$	−51.4635	+	16.6567i	−0.605453	+	0.195961i
$86$	−79.9350			−0.929477
$87$	34.8890	−	34.8890i	0.401023	−	0.401023i
$88$	−30.5635	−	30.5635i	−0.347312	−	0.347312i
$89$		−	26.3345i		−	0.295893i	−0.988995	−	0.147946i	$-0.952734\pi$
$89$		−	26.3345i		−	0.295893i	0.988995	−	0.147946i	$-0.0472663\pi$
$90$	−6.53226	−	20.1824i	−0.0725807	−	0.224249i
$91$	−66.5546			−0.731369
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	57.3640	+	57.3640i	0.616817	+	0.616817i
$94$		−	84.5362i		−	0.899322i
$95$	37.8311	−	74.0391i	0.398222	−	0.779359i
$96$	−9.79796			−0.102062
$97$	−70.0462	+	70.0462i	−0.722126	+	0.722126i	−0.969038	−	0.246912i	$-0.920584\pi$
$97$	−70.0462	+	70.0462i	−0.722126	+	0.722126i	0.246912	+	0.969038i	$0.420584\pi$
$98$	23.4237	+	23.4237i	0.239017	+	0.239017i
$99$			45.8452i			0.463083i
$100$	40.5177	−	29.2970i	0.405177	−	0.292970i
$101$	157.618			1.56057			0.780285	−	0.625424i	$-0.215074\pi$
$101$	157.618			1.56057			0.780285	+	0.625424i	$0.215074\pi$
$102$	18.7380	−	18.7380i	0.183706	−	0.183706i
$103$	−133.113	−	133.113i	−1.29236	−	1.29236i	−0.933325	−	0.359032i	$-0.883107\pi$
$103$	−133.113	−	133.113i	−1.29236	−	1.29236i	−0.359032	−	0.933325i	$-0.616893\pi$
$104$		−	37.2224i		−	0.357907i
$105$	39.0012	+	19.9281i	0.371440	+	0.189791i
$106$	81.8061			0.771756
$107$	−14.8025	+	14.8025i	−0.138341	+	0.138341i	−0.772886	−	0.634545i	$-0.781188\pi$
$107$	−14.8025	+	14.8025i	−0.138341	+	0.138341i	0.634545	+	0.772886i	$0.281188\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			0.102683i			0.000942049i	1.00000		0.000471024i	$0.000149932\pi$
$109$			0.102683i			0.000942049i	−1.00000		0.000471024i	$0.999850\pi$
$110$	−102.807	+	33.2748i	−0.934613	+	0.302498i
$111$	95.0421			0.856235
$112$	14.3042	−	14.3042i	0.127716	−	0.127716i
$113$	−54.9742	−	54.9742i	−0.486497	−	0.486497i	0.420702	−	0.907199i	$-0.361784\pi$
$113$	−54.9742	−	54.9742i	−0.486497	−	0.486497i	−0.907199	+	0.420702i	$0.861784\pi$
$114$			40.7322i			0.357300i
$115$	7.38399	+	22.8140i	0.0642086	+	0.198382i
$116$	−56.9734			−0.491150
$117$	−27.9168	+	27.9168i	−0.238605	+	0.238605i
$118$	115.558	+	115.558i	0.979301	+	0.979301i
$119$			54.7119i			0.459764i
$120$	−11.1453	+	21.8124i	−0.0928775	+	0.181770i
$121$	112.532			0.930014
$122$	−39.5522	+	39.5522i	−0.324199	+	0.324199i
$123$	60.2193	+	60.2193i	0.489587	+	0.489587i
$124$		−	93.6750i		−	0.755443i
$125$	−19.1324	−	123.527i	−0.153059	−	0.988217i
$126$	−21.4563			−0.170288
$127$	−159.860	+	159.860i	−1.25874	+	1.25874i	−0.307042	+	0.951696i	$0.599339\pi$
$127$	−159.860	+	159.860i	−1.25874	+	1.25874i	−0.951696	+	0.307042i	$0.900661\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	97.9000i		−	0.758914i
$130$	−82.8653	−	42.3409i	−0.637425	−	0.325699i
$131$	−249.753			−1.90651			−0.953257	−	0.302161i	$-0.902292\pi$
$131$	−249.753			−1.90651			−0.953257	+	0.302161i	$0.902292\pi$
$132$	37.4325	−	37.4325i	0.283579	−	0.283579i
$133$	−59.4657	−	59.4657i	−0.447111	−	0.447111i
$134$		−	60.1222i		−	0.448673i
$135$	24.7183	−	8.00035i	0.183099	−	0.0592619i
$136$	−30.5990			−0.224993
$137$	24.1535	−	24.1535i	0.176303	−	0.176303i	−0.613439	−	0.789742i	$-0.710214\pi$
$137$	24.1535	−	24.1535i	0.176303	−	0.176303i	0.789742	+	0.613439i	$0.210214\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$		−	107.895i		−	0.776221i	−0.921613	−	0.388111i	$-0.873128\pi$
$139$		−	107.895i		−	0.776221i	0.921613	−	0.388111i	$-0.126872\pi$
$140$	−15.5731	−	48.1156i	−0.111237	−	0.343683i
$141$	103.535			0.734293
$142$	−109.516	+	109.516i	−0.771237	+	0.771237i
$143$	142.206	+	142.206i	0.994445	+	0.994445i
$144$		−	12.0000i		−	0.0833333i
$145$	−64.8080	+	126.836i	−0.446952	+	0.874728i
$146$	75.1703			0.514865
$147$	−28.6880	+	28.6880i	−0.195157	+	0.195157i
$148$	−77.6015	−	77.6015i	−0.524335	−	0.524335i
$149$		−	149.146i		−	1.00098i	−0.865741	−	0.500492i	$-0.833153\pi$
$149$		−	149.146i		−	1.00098i	0.865741	−	0.500492i	$-0.166847\pi$
$150$	35.8814	+	49.6238i	0.239209	+	0.330826i
$151$	−87.3637			−0.578568			−0.289284	−	0.957243i	$-0.593417\pi$
$151$	−87.3637			−0.578568			−0.289284	+	0.957243i	$0.593417\pi$
$152$	33.2577	−	33.2577i	0.218801	−	0.218801i
$153$	22.9493	+	22.9493i	0.149995	+	0.149995i
$154$			109.297i			0.709719i
$155$	−208.541	−	106.556i	−1.34543	−	0.687461i
$156$	45.5879			0.292230
$157$	81.1651	−	81.1651i	0.516975	−	0.516975i	−0.399680	−	0.916655i	$-0.630879\pi$
$157$	81.1651	−	81.1651i	0.516975	−	0.516975i	0.916655	+	0.399680i	$0.130879\pi$
$158$	116.711	+	116.711i	0.738679	+	0.738679i
$159$			100.192i			0.630136i
$160$	26.9099	−	8.70968i	0.168187	−	0.0544355i
$161$	24.2540			0.150646
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−56.4577	−	56.4577i	−0.346366	−	0.346366i	0.512388	−	0.858754i	$-0.328761\pi$
$163$	−56.4577	−	56.4577i	−0.346366	−	0.346366i	−0.858754	+	0.512388i	$0.828761\pi$
$164$		−	98.3376i		−	0.599620i
$165$	−40.7531	−	125.913i	−0.246989	−	0.763109i
$166$	195.173			1.17574
$167$	161.337	−	161.337i	0.966088	−	0.966088i	−0.0333553	−	0.999444i	$-0.510619\pi$
$167$	161.337	−	161.337i	0.966088	−	0.966088i	0.999444	+	0.0333553i	$0.0106193\pi$
$168$	17.5190	+	17.5190i	0.104280	+	0.104280i
$169$			4.18809i			0.0247816i
$170$	−34.8068	+	68.1202i	−0.204746	+	0.400707i
$171$	−49.8866			−0.291734
$172$	−79.9350	+	79.9350i	−0.464738	+	0.464738i
$173$	−113.686	−	113.686i	−0.657146	−	0.657146i	0.297558	−	0.954704i	$-0.403828\pi$
$173$	−113.686	−	113.686i	−0.657146	−	0.657146i	−0.954704	+	0.297558i	$0.903828\pi$
$174$		−	69.7779i		−	0.401023i
$175$	−124.831	−	20.0628i	−0.713318	−	0.114645i
$176$	−61.1270			−0.347312
$177$	−141.528	+	141.528i	−0.799596	+	0.799596i
$178$	−26.3345	−	26.3345i	−0.147946	−	0.147946i
$179$			202.276i			1.13003i	0.825080	+	0.565016i	$0.191130\pi$
$179$			202.276i			1.13003i	−0.825080	+	0.565016i	$0.808870\pi$
$180$	−26.7147	−	13.6501i	−0.148415	−	0.0758342i
$181$	−119.692			−0.661281			−0.330640	−	0.943757i	$-0.607265\pi$
$181$	−119.692			−0.661281			−0.330640	+	0.943757i	$0.607265\pi$
$182$	−66.5546	+	66.5546i	−0.365685	+	0.365685i
$183$	−48.4414	−	48.4414i	−0.264707	−	0.264707i
$184$			13.5647i			0.0737210i
$185$	−261.031	+	84.4855i	−1.41098	+	0.456679i
$186$	114.728			0.616817
$187$	116.902	−	116.902i	0.625142	−	0.625142i
$188$	−84.5362	−	84.5362i	−0.449661	−	0.449661i
$189$		−	26.2785i		−	0.139040i
$190$	−36.2080	−	111.870i	−0.190568	−	0.588790i
$191$	354.419			1.85560			0.927798	−	0.373084i	$-0.121700\pi$
$191$	354.419			1.85560			0.927798	+	0.373084i	$0.121700\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	89.8493	+	89.8493i	0.465541	+	0.465541i	0.900466	−	0.434926i	$-0.143225\pi$
$193$	89.8493	+	89.8493i	0.465541	+	0.465541i	−0.434926	+	0.900466i	$0.643225\pi$
$194$			140.092i			0.722126i
$195$	51.8568	−	101.489i	0.265932	−	0.520455i
$196$	46.8473			0.239017
$197$	244.917	−	244.917i	1.24323	−	1.24323i	0.284582	−	0.958652i	$-0.408145\pi$
$197$	244.917	−	244.917i	1.24323	−	1.24323i	0.958652	−	0.284582i	$-0.0918548\pi$
$198$	45.8452	+	45.8452i	0.231542	+	0.231542i
$199$		−	201.091i		−	1.01051i	−0.862971	−	0.505253i	$-0.831399\pi$
$199$		−	201.091i		−	1.01051i	0.862971	−	0.505253i	$-0.168601\pi$
$200$	11.2206	−	69.8147i	0.0561032	−	0.349074i
$201$	73.6343			0.366340
$202$	157.618	−	157.618i	0.780285	−	0.780285i
$203$	101.870	+	101.870i	0.501823	+	0.501823i
$204$		−	37.4760i		−	0.183706i
$205$	−218.921	−	111.860i	−1.06791	−	0.545660i
$206$	−266.226			−1.29236
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	−37.2224	−	37.2224i	−0.178954	−	0.178954i
$209$			254.118i			1.21588i
$210$	58.9293	−	19.0731i	0.280616	−	0.0908244i
$211$	−56.8261			−0.269318			−0.134659	−	0.990892i	$-0.542994\pi$
$211$	−56.8261			−0.269318			−0.134659	+	0.990892i	$0.542994\pi$
$212$	81.8061	−	81.8061i	0.385878	−	0.385878i
$213$	−134.129	−	134.129i	−0.629712	−	0.629712i
$214$			29.6049i			0.138341i
$215$	87.0260	+	268.880i	0.404772	+	1.25061i
$216$	14.6969			0.0680414
$217$	−167.493	+	167.493i	−0.771859	+	0.771859i
$218$	0.102683	+	0.102683i	0.000471024	+	0.000471024i
$219$			92.0645i			0.420386i
$220$	−69.5327	+	136.082i	−0.316058	+	0.618556i
$221$	142.371			0.644213
$222$	95.0421	−	95.0421i	0.428117	−	0.428117i
$223$	50.8364	+	50.8364i	0.227966	+	0.227966i	0.811843	−	0.583876i	$-0.198465\pi$
$223$	50.8364	+	50.8364i	0.227966	+	0.227966i	−0.583876	+	0.811843i	$0.698465\pi$
$224$		−	28.6084i		−	0.127716i
$225$	−60.7765	+	43.9456i	−0.270118	+	0.195314i
$226$	−109.948			−0.486497
$227$	−75.8315	+	75.8315i	−0.334060	+	0.334060i	−0.854126	−	0.520066i	$-0.825907\pi$
$227$	−75.8315	+	75.8315i	−0.334060	+	0.334060i	0.520066	+	0.854126i	$0.325907\pi$
$228$	40.7322	+	40.7322i	0.178650	+	0.178650i
$229$			70.0263i			0.305792i	0.988242	+	0.152896i	$0.0488599\pi$
$229$			70.0263i			0.305792i	−0.988242	+	0.152896i	$0.951140\pi$
$230$	30.1979	+	15.4300i	0.131295	+	0.0670868i
$231$	−133.861			−0.579483
$232$	−56.9734	+	56.9734i	−0.245575	+	0.245575i
$233$	4.02362	+	4.02362i	0.0172687	+	0.0172687i	0.715688	−	0.698420i	$-0.246113\pi$
$233$	4.02362	+	4.02362i	0.0172687	+	0.0172687i	−0.698420	+	0.715688i	$0.746113\pi$
$234$			55.8336i			0.238605i
$235$	−284.357	+	92.0354i	−1.21003	+	0.391640i
$236$	231.115			0.979301
$237$	−142.942	+	142.942i	−0.603129	+	0.603129i
$238$	54.7119	+	54.7119i	0.229882	+	0.229882i
$239$			268.560i			1.12368i	0.827245	+	0.561842i	$0.189907\pi$
$239$			268.560i			1.12368i	−0.827245	+	0.561842i	$0.810093\pi$
$240$	10.6671	+	32.9577i	0.0444464	+	0.137324i
$241$	−265.941			−1.10349			−0.551745	−	0.834013i	$-0.686038\pi$
$241$	−265.941			−1.10349			−0.551745	+	0.834013i	$0.686038\pi$
$242$	112.532	−	112.532i	0.465007	−	0.465007i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			79.1045i			0.324199i
$245$	53.2894	−	104.293i	0.217508	−	0.425684i
$246$	120.439			0.489587
$247$	−154.741	+	154.741i	−0.626483	+	0.626483i
$248$	−93.6750	−	93.6750i	−0.377722	−	0.377722i
$249$			239.037i			0.959987i
$250$	−142.659	−	104.395i	−0.570638	−	0.417579i
$251$	167.641			0.667893			0.333947	−	0.942592i	$-0.391619\pi$
$251$	167.641			0.667893			0.333947	+	0.942592i	$0.391619\pi$
$252$	−21.4563	+	21.4563i	−0.0851442	+	0.0851442i
$253$	−51.8229	−	51.8229i	−0.204834	−	0.204834i
$254$			319.719i			1.25874i
$255$	−83.4299	−	42.6294i	−0.327176	−	0.167174i
$256$	16.0000			0.0625000
$257$	64.2388	−	64.2388i	0.249956	−	0.249956i	−0.570996	−	0.820953i	$-0.693443\pi$
$257$	64.2388	−	64.2388i	0.249956	−	0.249956i	0.820953	+	0.570996i	$0.193443\pi$
$258$	−97.9000	−	97.9000i	−0.379457	−	0.379457i
$259$			277.507i			1.07146i
$260$	−125.206	+	40.5244i	−0.481562	+	0.155863i
$261$	85.4602			0.327434
$262$	−249.753	+	249.753i	−0.953257	+	0.953257i
$263$	−26.1375	−	26.1375i	−0.0993820	−	0.0993820i	0.655668	−	0.755050i	$-0.272387\pi$
$263$	−26.1375	−	26.1375i	−0.0993820	−	0.0993820i	−0.755050	+	0.655668i	$0.772387\pi$
$264$		−	74.8650i		−	0.283579i
$265$	−89.0631	−	275.174i	−0.336087	−	1.03839i
$266$	−118.931			−0.447111
$267$	32.2530	−	32.2530i	0.120798	−	0.120798i
$268$	−60.1222	−	60.1222i	−0.224336	−	0.224336i
$269$			114.873i			0.427036i	0.976939	+	0.213518i	$0.0684922\pi$
$269$			114.873i			0.427036i	−0.976939	+	0.213518i	$0.931508\pi$
$270$	16.7180	−	32.7187i	0.0619183	−	0.121180i
$271$	263.414			0.972007			0.486004	−	0.873957i	$-0.338454\pi$
$271$	263.414			0.972007			0.486004	+	0.873957i	$0.338454\pi$
$272$	−30.5990	+	30.5990i	−0.112496	+	0.112496i
$273$	−81.5124	−	81.5124i	−0.298580	−	0.298580i
$274$		−	48.3070i		−	0.176303i
$275$	223.855	+	309.590i	0.814018	+	1.12578i
$276$	−16.6132			−0.0601929
$277$	−247.635	+	247.635i	−0.893990	+	0.893990i	−0.994896	−	0.100906i	$-0.967826\pi$
$277$	−247.635	+	247.635i	−0.893990	+	0.893990i	0.100906	+	0.994896i	$0.467826\pi$
$278$	−107.895	−	107.895i	−0.388111	−	0.388111i
$279$			140.512i			0.503629i
$280$	−63.6887	−	32.5425i	−0.227460	−	0.116223i
$281$	−503.134			−1.79051			−0.895257	−	0.445550i	$-0.853008\pi$
$281$	−503.134			−1.79051			−0.895257	+	0.445550i	$0.853008\pi$
$282$	103.535	−	103.535i	0.367147	−	0.367147i
$283$	−334.802	−	334.802i	−1.18304	−	1.18304i	−0.978951	−	0.204093i	$-0.934575\pi$
$283$	−334.802	−	334.802i	−1.18304	−	1.18304i	−0.204093	−	0.978951i	$-0.565425\pi$
$284$			219.031i			0.771237i
$285$	137.012	−	44.3456i	0.480745	−	0.155598i
$286$	284.411			0.994445
$287$	−175.830	+	175.830i	−0.612649	+	0.612649i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			171.963i			0.595026i
$290$	62.0275	+	191.644i	0.213888	+	0.660840i
$291$	−171.578			−0.589614
$292$	75.1703	−	75.1703i	0.257433	−	0.257433i
$293$	−103.910	−	103.910i	−0.354642	−	0.354642i	0.507192	−	0.861833i	$-0.330684\pi$
$293$	−103.910	−	103.910i	−0.354642	−	0.354642i	−0.861833	+	0.507192i	$0.830684\pi$
$294$			57.3760i			0.195157i
$295$	262.896	−	514.513i	0.891174	−	1.74411i
$296$	−155.203			−0.524335
$297$	−56.1487	+	56.1487i	−0.189053	+	0.189053i
$298$	−149.146	−	149.146i	−0.500492	−	0.500492i
$299$		−	63.1136i		−	0.211082i
$300$	85.5052	+	13.7424i	0.285017	+	0.0458081i
$301$	285.852			0.949674
$302$	−87.3637	+	87.3637i	−0.289284	+	0.289284i
$303$	193.041	+	193.041i	0.637100	+	0.637100i
$304$		−	66.5154i		−	0.218801i
$305$	176.104	+	89.9823i	0.577391	+	0.295024i
$306$	45.8985			0.149995
$307$	15.9914	−	15.9914i	0.0520893	−	0.0520893i	−0.680582	−	0.732672i	$-0.738273\pi$
$307$	15.9914	−	15.9914i	0.0520893	−	0.0520893i	0.732672	+	0.680582i	$0.238273\pi$
$308$	109.297	+	109.297i	0.354859	+	0.354859i
$309$		−	326.058i		−	1.05521i
$310$	−315.098	+	101.985i	−1.01644	+	0.328983i
$311$	430.485			1.38420			0.692098	−	0.721804i	$-0.256687\pi$
$311$	430.485			1.38420			0.692098	+	0.721804i	$0.256687\pi$
$312$	45.5879	−	45.5879i	0.146115	−	0.146115i
$313$	−215.563	−	215.563i	−0.688699	−	0.688699i	0.273246	−	0.961944i	$-0.411903\pi$
$313$	−215.563	−	215.563i	−0.688699	−	0.688699i	−0.961944	+	0.273246i	$0.911903\pi$
$314$		−	162.330i		−	0.516975i
$315$	23.3597	+	72.1734i	0.0741578	+	0.229122i
$316$	233.423			0.738679
$317$	−74.4937	+	74.4937i	−0.234996	+	0.234996i	−0.814774	−	0.579778i	$-0.803139\pi$
$317$	−74.4937	+	74.4937i	−0.234996	+	0.234996i	0.579778	+	0.814774i	$0.303139\pi$
$318$	100.192	+	100.192i	0.315068	+	0.315068i
$319$		−	435.327i		−	1.36466i
$320$	18.2002	−	35.6196i	0.0568756	−	0.111311i
$321$	−36.2585			−0.112955
$322$	24.2540	−	24.2540i	0.0753229	−	0.0753229i
$323$	127.207	+	127.207i	0.393829	+	0.393829i
$324$			18.0000i			0.0555556i
$325$	−52.2074	+	324.834i	−0.160638	+	0.999488i
$326$	−112.915			−0.346366
$327$	−0.125761	+	0.125761i	−0.000384590	+	0.000384590i
$328$	−98.3376	−	98.3376i	−0.299810	−	0.299810i
$329$			302.306i			0.918864i
$330$	−166.666	−	85.1598i	−0.505049	−	0.258060i
$331$	316.884			0.957354			0.478677	−	0.877991i	$-0.341116\pi$
$331$	316.884			0.957354			0.478677	+	0.877991i	$0.341116\pi$
$332$	195.173	−	195.173i	0.587870	−	0.587870i
$333$	116.402	+	116.402i	0.349556	+	0.349556i
$334$		−	322.673i		−	0.966088i
$335$	−202.235	+	65.4556i	−0.603687	+	0.195390i
$336$	35.0380			0.104280
$337$	81.9442	−	81.9442i	0.243158	−	0.243158i	−0.574997	−	0.818155i	$-0.694997\pi$
$337$	81.9442	−	81.9442i	0.243158	−	0.243158i	0.818155	+	0.574997i	$0.194997\pi$
$338$	4.18809	+	4.18809i	0.0123908	+	0.0123908i
$339$		−	134.659i		−	0.397223i
$340$	33.3134	+	102.927i	0.0979807	+	0.302726i
$341$	715.758			2.09900
$342$	−49.8866	+	49.8866i	−0.145867	+	0.145867i
$343$	−258.991	−	258.991i	−0.755076	−	0.755076i
$344$			159.870i			0.464738i
$345$	−18.8978	+	36.9848i	−0.0547762	+	0.107202i
$346$	−227.372			−0.657146
$347$	253.677	−	253.677i	0.731058	−	0.731058i	−0.239771	−	0.970829i	$-0.577072\pi$
$347$	253.677	−	253.677i	0.731058	−	0.731058i	0.970829	+	0.239771i	$0.0770724\pi$
$348$	−69.7779	−	69.7779i	−0.200511	−	0.200511i
$349$			162.699i			0.466186i	0.972454	+	0.233093i	$0.0748847\pi$
$349$			162.699i			0.466186i	−0.972454	+	0.233093i	$0.925115\pi$
$350$	−144.893	+	104.768i	−0.413981	+	0.299337i
$351$	−68.3819			−0.194820
$352$	−61.1270	+	61.1270i	−0.173656	+	0.173656i
$353$	19.9049	+	19.9049i	0.0563877	+	0.0563877i	0.734738	−	0.678351i	$-0.237305\pi$
$353$	19.9049	+	19.9049i	0.0563877	+	0.0563877i	−0.678351	+	0.734738i	$0.737305\pi$
$354$			283.057i			0.799596i
$355$	487.612	+	249.151i	1.37356	+	0.701833i
$356$	−52.6689			−0.147946
$357$	−67.0081	+	67.0081i	−0.187698	+	0.187698i
$358$	202.276	+	202.276i	0.565016	+	0.565016i
$359$			414.391i			1.15429i	0.816641	+	0.577146i	$0.195834\pi$
$359$			414.391i			1.15429i	−0.816641	+	0.577146i	$0.804166\pi$
$360$	−40.3648	+	13.0645i	−0.112124	+	0.0362903i
$361$	84.4810			0.234019
$362$	−119.692	+	119.692i	−0.330640	+	0.330640i
$363$	137.823	+	137.823i	0.379677	+	0.379677i
$364$			133.109i			0.365685i
$365$	−81.8387	−	252.853i	−0.224215	−	0.692748i
$366$	−96.8828			−0.264707
$367$	105.693	−	105.693i	0.287991	−	0.287991i	−0.548294	−	0.836286i	$-0.684723\pi$
$367$	105.693	−	105.693i	0.287991	−	0.287991i	0.836286	+	0.548294i	$0.184723\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$			147.506i			0.399746i
$370$	−176.545	+	345.516i	−0.477150	+	0.933828i
$371$	−292.543			−0.788526
$372$	114.728	−	114.728i	0.308408	−	0.308408i
$373$	−322.018	−	322.018i	−0.863319	−	0.863319i	0.128403	−	0.991722i	$-0.459015\pi$
$373$	−322.018	−	322.018i	−0.863319	−	0.863319i	−0.991722	+	0.128403i	$0.959015\pi$
$374$		−	233.803i		−	0.625142i
$375$	127.857	−	174.721i	0.340952	−	0.465924i
$376$	−169.072			−0.449661
$377$	265.086	−	265.086i	0.703145	−	0.703145i
$378$	−26.2785	−	26.2785i	−0.0695199	−	0.0695199i
$379$		−	46.2839i		−	0.122121i	−0.998134	−	0.0610605i	$-0.980552\pi$
$379$		−	46.2839i		−	0.122121i	0.998134	−	0.0610605i	$-0.0194483\pi$
$380$	−148.078	−	75.6621i	−0.389679	−	0.199111i
$381$	−391.575			−1.02776
$382$	354.419	−	354.419i	0.927798	−	0.927798i
$383$	−456.507	−	456.507i	−1.19192	−	1.19192i	−0.976527	−	0.215397i	$-0.930895\pi$
$383$	−456.507	−	456.507i	−1.19192	−	1.19192i	−0.215397	−	0.976527i	$-0.569105\pi$
$384$			19.5959i			0.0510310i
$385$	367.645	−	118.992i	0.954922	−	0.309071i
$386$	179.699			0.465541
$387$	119.902	−	119.902i	0.309826	−	0.309826i
$388$	140.092	+	140.092i	0.361063	+	0.361063i
$389$			423.277i			1.08812i	0.839048	+	0.544058i	$0.183113\pi$
$389$			423.277i			1.08812i	−0.839048	+	0.544058i	$0.816887\pi$
$390$	−49.6320	−	153.346i	−0.127262	−	0.393194i
$391$	−51.8832			−0.132693
$392$	46.8473	−	46.8473i	0.119509	−	0.119509i
$393$	−305.884	−	305.884i	−0.778331	−	0.778331i
$394$		−	489.834i		−	1.24323i
$395$	265.521	−	519.651i	0.672206	−	1.31557i
$396$	91.6905			0.231542
$397$	114.959	−	114.959i	0.289569	−	0.289569i	−0.547341	−	0.836910i	$-0.684360\pi$
$397$	114.959	−	114.959i	0.289569	−	0.289569i	0.836910	+	0.547341i	$0.184360\pi$
$398$	−201.091	−	201.091i	−0.505253	−	0.505253i
$399$		−	145.661i		−	0.365064i
$400$	−58.5941	−	81.0354i	−0.146485	−	0.202588i
$401$	−545.562			−1.36050			−0.680252	−	0.732978i	$-0.738130\pi$
$401$	−545.562			−1.36050			−0.680252	+	0.732978i	$0.738130\pi$
$402$	73.6343	−	73.6343i	0.183170	−	0.183170i
$403$	435.850	+	435.850i	1.08151	+	1.08151i
$404$		−	315.235i		−	0.780285i
$405$	40.0720	+	20.4752i	0.0989432	+	0.0505561i
$406$	203.740			0.501823
$407$	592.943	−	592.943i	1.45686	−	1.45686i
$408$	−37.4760	−	37.4760i	−0.0918529	−	0.0918529i
$409$		−	400.154i		−	0.978371i	−0.872180	−	0.489185i	$-0.837294\pi$
$409$		−	400.154i		−	0.978371i	0.872180	−	0.489185i	$-0.162706\pi$
$410$	−330.782	+	107.061i	−0.806785	+	0.261125i
$411$	59.1637			0.143951
$412$	−266.226	+	266.226i	−0.646179	+	0.646179i
$413$	−413.240	−	413.240i	−1.00058	−	1.00058i
$414$		−	20.3470i		−	0.0491473i
$415$	−212.486	−	656.509i	−0.512015	−	1.58195i
$416$	−74.4447			−0.178954
$417$	132.144	−	132.144i	0.316891	−	0.316891i
$418$	254.118	+	254.118i	0.607938	+	0.607938i
$419$			100.320i			0.239428i	0.992808	+	0.119714i	$0.0381978\pi$
$419$			100.320i			0.239428i	−0.992808	+	0.119714i	$0.961802\pi$
$420$	39.8562	−	78.0025i	0.0948957	−	0.185720i
$421$	115.474			0.274286			0.137143	−	0.990551i	$-0.456208\pi$
$421$	115.474			0.274286			0.137143	+	0.990551i	$0.456208\pi$
$422$	−56.8261	+	56.8261i	−0.134659	+	0.134659i
$423$	126.804	+	126.804i	0.299774	+	0.299774i
$424$		−	163.612i		−	0.385878i
$425$	267.033	+	42.9176i	0.628312	+	0.100983i
$426$	−268.257			−0.629712
$427$	141.441	−	141.441i	0.331243	−	0.331243i
$428$	29.6049	+	29.6049i	0.0691704	+	0.0691704i
$429$			348.331i			0.811961i
$430$	355.906	+	181.854i	0.827689	+	0.422916i
$431$	341.266			0.791801			0.395901	−	0.918293i	$-0.370432\pi$
$431$	341.266			0.791801			0.395901	+	0.918293i	$0.370432\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−364.495	−	364.495i	−0.841791	−	0.841791i	0.147301	−	0.989092i	$-0.452941\pi$
$433$	−364.495	−	364.495i	−0.841791	−	0.841791i	−0.989092	+	0.147301i	$0.952941\pi$
$434$			334.987i			0.771859i
$435$	−234.714	+	75.9679i	−0.539573	+	0.174639i
$436$	0.205367			0.000471024
$437$	56.3912	−	56.3912i	0.129042	−	0.129042i
$438$	92.0645	+	92.0645i	0.210193	+	0.210193i
$439$			745.512i			1.69821i	0.528228	+	0.849103i	$0.322857\pi$
$439$			745.512i			1.69821i	−0.528228	+	0.849103i	$0.677143\pi$
$440$	66.5495	+	205.615i	0.151249	+	0.467307i
$441$	−70.2710			−0.159345
$442$	142.371	−	142.371i	0.322106	−	0.322106i
$443$	426.726	+	426.726i	0.963264	+	0.963264i	0.999349	−	0.0360845i	$-0.0114886\pi$
$443$	426.726	+	426.726i	0.963264	+	0.963264i	−0.0360845	+	0.999349i	$0.511489\pi$
$444$		−	190.084i		−	0.428117i
$445$	−59.9116	+	117.253i	−0.134633	+	0.263489i
$446$	101.673			0.227966
$447$	182.666	−	182.666i	0.408650	−	0.408650i
$448$	−28.6084	−	28.6084i	−0.0638581	−	0.0638581i
$449$			183.403i			0.408470i	0.978922	+	0.204235i	$0.0654707\pi$
$449$			183.403i			0.408470i	−0.978922	+	0.204235i	$0.934529\pi$
$450$	−16.8310	+	104.722i	−0.0374021	+	0.232716i
$451$	751.385			1.66604
$452$	−109.948	+	109.948i	−0.243248	+	0.243248i
$453$	−106.998	−	106.998i	−0.236199	−	0.236199i
$454$			151.663i			0.334060i
$455$	296.331	+	151.413i	0.651276	+	0.332777i
$456$	81.4644			0.178650
$457$	−68.1150	+	68.1150i	−0.149048	+	0.149048i	−0.777693	−	0.628645i	$-0.783610\pi$
$457$	−68.1150	+	68.1150i	−0.149048	+	0.149048i	0.628645	+	0.777693i	$0.283610\pi$
$458$	70.0263	+	70.0263i	0.152896	+	0.152896i
$459$			56.2140i			0.122471i
$460$	45.6279	−	14.7680i	0.0991911	−	0.0321043i
$461$	−386.997			−0.839472			−0.419736	−	0.907646i	$-0.637877\pi$
$461$	−386.997			−0.839472			−0.419736	+	0.907646i	$0.637877\pi$
$462$	−133.861	+	133.861i	−0.289742	+	0.289742i
$463$	−111.577	−	111.577i	−0.240986	−	0.240986i	0.576272	−	0.817258i	$-0.304507\pi$
$463$	−111.577	−	111.577i	−0.240986	−	0.240986i	−0.817258	+	0.576272i	$0.804507\pi$
$464$			113.947i			0.245575i
$465$	−124.905	−	385.914i	−0.268614	−	0.829923i
$466$	8.04723			0.0172687
$467$	−8.27939	+	8.27939i	−0.0177289	+	0.0177289i	−0.715916	−	0.698187i	$-0.753991\pi$
$467$	−8.27939	+	8.27939i	−0.0177289	+	0.0177289i	0.698187	+	0.715916i	$0.253991\pi$
$468$	55.8336	+	55.8336i	0.119302	+	0.119302i
$469$			215.000i			0.458422i
$470$	−192.322	+	376.393i	−0.409196	+	0.800836i
$471$	198.813			0.422108
$472$	231.115	−	231.115i	0.489651	−	0.489651i
$473$	−610.773	−	610.773i	−1.29128	−	1.29128i
$474$			285.883i			0.603129i
$475$	−336.881	+	243.588i	−0.709224	+	0.512817i
$476$	109.424			0.229882
$477$	−122.709	+	122.709i	−0.257252	+	0.257252i
$478$	268.560	+	268.560i	0.561842	+	0.561842i
$479$		−	391.487i		−	0.817301i	−0.912691	−	0.408651i	$-0.865999\pi$
$479$		−	391.487i		−	0.817301i	0.912691	−	0.408651i	$-0.134001\pi$
$480$	43.6249	+	22.2906i	0.0908851	+	0.0464388i
$481$	722.128			1.50131
$482$	−265.941	+	265.941i	−0.551745	+	0.551745i
$483$	29.7049	+	29.7049i	0.0615009	+	0.0615009i
$484$		−	225.063i		−	0.465007i
$485$	471.234	−	152.520i	0.971616	−	0.314474i
$486$	−22.0454			−0.0453609
$487$	−282.428	+	282.428i	−0.579933	+	0.579933i	−0.934885	−	0.354951i	$-0.884497\pi$
$487$	−282.428	+	282.428i	−0.579933	+	0.579933i	0.354951	+	0.934885i	$0.384497\pi$
$488$	79.1045	+	79.1045i	0.162099	+	0.162099i
$489$		−	138.292i		−	0.282807i
$490$	−51.0032	−	157.582i	−0.104088	−	0.321596i
$491$	15.3095			0.0311802			0.0155901	−	0.999878i	$-0.495037\pi$
$491$	15.3095			0.0311802			0.0155901	+	0.999878i	$0.495037\pi$
$492$	120.439	−	120.439i	0.244794	−	0.244794i
$493$	−217.916	−	217.916i	−0.442021	−	0.442021i
$494$			309.483i			0.626483i
$495$	104.299	−	204.123i	0.210705	−	0.412370i
$496$	−187.350			−0.377722
$497$	391.634	−	391.634i	0.787996	−	0.787996i
$498$	239.037	+	239.037i	0.479993	+	0.479993i
$499$			823.731i			1.65076i	0.564575	+	0.825382i	$0.309040\pi$
$499$			823.731i			1.65076i	−0.564575	+	0.825382i	$0.690960\pi$
$500$	−247.054	+	38.2647i	−0.494109	+	0.0765294i
$501$	395.193			0.788808
$502$	167.641	−	167.641i	0.333947	−	0.333947i
$503$	−230.664	−	230.664i	−0.458577	−	0.458577i	0.439611	−	0.898188i	$-0.355116\pi$
$503$	−230.664	−	230.664i	−0.458577	−	0.458577i	−0.898188	+	0.439611i	$0.855116\pi$
$504$			42.9127i			0.0851442i
$505$	−701.784	−	358.584i	−1.38967	−	0.710067i
$506$	−103.646			−0.204834
$507$	−5.12934	+	5.12934i	−0.0101170	+	0.0101170i
$508$	319.719	+	319.719i	0.629369	+	0.629369i
$509$		−	879.412i		−	1.72772i	−0.503728	−	0.863862i	$-0.668039\pi$
$509$		−	879.412i		−	1.72772i	0.503728	−	0.863862i	$-0.331961\pi$
$510$	−126.059	+	40.8005i	−0.247175	+	0.0800009i
$511$	−268.813			−0.526053
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−61.0983	−	61.0983i	−0.119100	−	0.119100i
$514$		−	128.478i		−	0.249956i
$515$	289.842	+	895.512i	0.562801	+	1.73886i
$516$	−195.800			−0.379457
$517$	645.931	−	645.931i	1.24938	−	1.24938i
$518$	277.507	+	277.507i	0.535728	+	0.535728i
$519$		−	278.473i		−	0.536557i
$520$	−84.6818	+	165.731i	−0.162850	+	0.318713i
$521$	−207.118			−0.397540			−0.198770	−	0.980046i	$-0.563695\pi$
$521$	−207.118			−0.397540			−0.198770	+	0.980046i	$0.563695\pi$
$522$	85.4602	−	85.4602i	0.163717	−	0.163717i
$523$	222.354	+	222.354i	0.425151	+	0.425151i	0.886973	−	0.461822i	$-0.152804\pi$
$523$	222.354	+	222.354i	0.425151	+	0.425151i	−0.461822	+	0.886973i	$0.652804\pi$
$524$			499.507i			0.953257i
$525$	−128.314	−	177.458i	−0.244407	−	0.338014i
$526$	−52.2749			−0.0993820
$527$	358.295	−	358.295i	0.679877	−	0.679877i
$528$	−74.8650	−	74.8650i	−0.141790	−	0.141790i
$529$			23.0000i			0.0434783i
$530$	−364.237	−	186.111i	−0.687240	−	0.351153i
$531$	−346.673			−0.652867
$532$	−118.931	+	118.931i	−0.223555	+	0.223555i
$533$	457.545	+	457.545i	0.858433	+	0.858433i
$534$		−	64.5060i		−	0.120798i
$535$	99.5832	−	32.2312i	0.186137	−	0.0602452i
$536$	−120.244			−0.224336
$537$	−247.736	+	247.736i	−0.461333	+	0.461333i
$538$	114.873	+	114.873i	0.213518	+	0.213518i
$539$			357.955i			0.664109i
$540$	−16.0007	−	49.4366i	−0.0296309	−	0.0915493i
$541$	209.995			0.388160			0.194080	−	0.980986i	$-0.437828\pi$
$541$	209.995			0.388160			0.194080	+	0.980986i	$0.437828\pi$
$542$	263.414	−	263.414i	0.486004	−	0.486004i
$543$	−146.592	−	146.592i	−0.269967	−	0.269967i
$544$			61.1980i			0.112496i
$545$	0.233607	−	0.457192i	0.000428637	−	0.000838884i
$546$	−163.025			−0.298580
$547$	−56.6666	+	56.6666i	−0.103595	+	0.103595i	−0.757005	−	0.653409i	$-0.773338\pi$
$547$	−56.6666	+	56.6666i	−0.103595	+	0.103595i	0.653409	+	0.757005i	$0.273338\pi$
$548$	−48.3070	−	48.3070i	−0.0881514	−	0.0881514i
$549$		−	118.657i		−	0.216132i
$550$	533.446	+	85.7355i	0.969901	+	0.155883i
$551$	473.702			0.859713
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	−417.366	−	417.366i	−0.754731	−	0.754731i
$554$			495.271i			0.893990i
$555$	−423.169	−	216.223i	−0.762468	−	0.389591i
$556$	−215.789			−0.388111
$557$	−51.0912	+	51.0912i	−0.0917256	+	0.0917256i	−0.751481	−	0.659755i	$-0.770660\pi$
$557$	−51.0912	+	51.0912i	−0.0917256	+	0.0917256i	0.659755	+	0.751481i	$0.270660\pi$
$558$	140.512	+	140.512i	0.251814	+	0.251814i
$559$		−	743.842i		−	1.33067i
$560$	−96.2312	+	31.1463i	−0.171841	+	0.0556184i
$561$	286.349			0.510426
$562$	−503.134	+	503.134i	−0.895257	+	0.895257i
$563$	−189.263	−	189.263i	−0.336169	−	0.336169i	0.518755	−	0.854923i	$-0.326396\pi$
$563$	−189.263	−	189.263i	−0.336169	−	0.336169i	−0.854923	+	0.518755i	$0.826396\pi$
$564$		−	207.071i		−	0.367147i
$565$	119.702	+	369.837i	0.211862	+	0.654579i
$566$	−669.603			−1.18304
$567$	32.1845	−	32.1845i	0.0567628	−	0.0567628i
$568$	219.031	+	219.031i	0.385618	+	0.385618i
$569$		−	743.025i		−	1.30584i	−0.757426	−	0.652921i	$-0.773543\pi$
$569$		−	743.025i		−	1.30584i	0.757426	−	0.652921i	$-0.226457\pi$
$570$	92.6668	−	181.358i	0.162573	−	0.318172i
$571$	630.678			1.10452			0.552258	−	0.833673i	$-0.313766\pi$
$571$	630.678			1.10452			0.552258	+	0.833673i	$0.313766\pi$
$572$	284.411	−	284.411i	0.497223	−	0.497223i
$573$	434.072	+	434.072i	0.757544	+	0.757544i
$574$			351.661i			0.612649i
$575$	19.0255	−	118.377i	0.0330879	−	0.205872i
$576$	−24.0000			−0.0416667
$577$	87.5513	−	87.5513i	0.151735	−	0.151735i	−0.627157	−	0.778893i	$-0.715782\pi$
$577$	87.5513	−	87.5513i	0.151735	−	0.151735i	0.778893	+	0.627157i	$0.215782\pi$
$578$	171.963	+	171.963i	0.297513	+	0.297513i
$579$			220.085i			0.380112i
$580$	253.671	+	129.616i	0.437364	+	0.223476i
$581$	−697.948			−1.20129
$582$	−171.578	+	171.578i	−0.294807	+	0.294807i
$583$	625.070	+	625.070i	1.07216	+	1.07216i
$584$		−	150.341i		−	0.257433i
$585$	187.809	−	60.7865i	0.321041	−	0.103909i
$586$	−207.820			−0.354642
$587$	−358.680	+	358.680i	−0.611039	+	0.611039i	−0.943217	−	0.332178i	$-0.892217\pi$
$587$	−358.680	+	358.680i	−0.611039	+	0.611039i	0.332178	+	0.943217i	$0.392217\pi$
$588$	57.3760	+	57.3760i	0.0975783	+	0.0975783i
$589$			778.854i			1.32233i
$590$	−251.617	−	777.410i	−0.426470	−	1.31764i
$591$	599.922			1.01510
$592$	−155.203	+	155.203i	−0.262167	+	0.262167i
$593$	388.968	+	388.968i	0.655933	+	0.655933i	0.954415	−	0.298482i	$-0.0964804\pi$
$593$	388.968	+	388.968i	0.655933	+	0.655933i	−0.298482	+	0.954415i	$0.596480\pi$
$594$			112.297i			0.189053i
$595$	124.471	−	243.602i	0.209195	−	0.409414i
$596$	−298.293			−0.500492
$597$	246.285	−	246.285i	0.412538	−	0.412538i
$598$	−63.1136	−	63.1136i	−0.105541	−	0.105541i
$599$		−	430.104i		−	0.718036i	−0.933331	−	0.359018i	$-0.883112\pi$
$599$		−	430.104i		−	0.718036i	0.933331	−	0.359018i	$-0.116888\pi$
$600$	99.2477	−	71.7628i	0.165413	−	0.119605i
$601$	613.240			1.02037			0.510183	−	0.860066i	$-0.329578\pi$
$601$	613.240			1.02037			0.510183	+	0.860066i	$0.329578\pi$
$602$	285.852	−	285.852i	0.474837	−	0.474837i
$603$	90.1833	+	90.1833i	0.149558	+	0.149558i
$604$			174.727i			0.289284i
$605$	−501.041	−	256.013i	−0.828168	−	0.423161i
$606$	386.083			0.637100
$607$	−332.149	+	332.149i	−0.547198	+	0.547198i	−0.925629	−	0.378432i	$-0.876464\pi$
$607$	−332.149	+	332.149i	−0.547198	+	0.547198i	0.378432	+	0.925629i	$0.376464\pi$
$608$	−66.5154	−	66.5154i	−0.109400	−	0.109400i
$609$			249.530i			0.409737i
$610$	266.086	−	86.1218i	0.436207	−	0.141183i
$611$	786.660			1.28750
$612$	45.8985	−	45.8985i	0.0749976	−	0.0749976i
$613$	−766.001	−	766.001i	−1.24959	−	1.24959i	−0.955900	−	0.293693i	$-0.905116\pi$
$613$	−766.001	−	766.001i	−1.24959	−	1.24959i	−0.293693	−	0.955900i	$-0.594884\pi$
$614$		−	31.9828i		−	0.0520893i
$615$	−131.123	−	405.123i	−0.213207	−	0.658737i
$616$	218.593			0.354859
$617$	255.443	−	255.443i	0.414008	−	0.414008i	−0.469124	−	0.883132i	$-0.655430\pi$
$617$	255.443	−	255.443i	0.414008	−	0.414008i	0.883132	+	0.469124i	$0.155430\pi$
$618$	−326.058	−	326.058i	−0.527603	−	0.527603i
$619$			750.831i			1.21297i	0.795093	+	0.606487i	$0.207422\pi$
$619$			750.831i			1.21297i	−0.795093	+	0.606487i	$0.792578\pi$
$620$	−213.113	+	417.083i	−0.343730	+	0.672714i
$621$	24.9199			0.0401286
$622$	430.485	−	430.485i	0.692098	−	0.692098i
$623$	94.1735	+	94.1735i	0.151161	+	0.151161i
$624$		−	91.1758i		−	0.146115i
$625$	−195.842	+	593.524i	−0.313346	+	0.949639i
$626$	−431.125			−0.688699
$627$	−311.230	+	311.230i	−0.496379	+	0.496379i
$628$	−162.330	−	162.330i	−0.258488	−	0.258488i
$629$		−	593.632i		−	0.943772i
$630$	95.5331	+	48.8137i	0.151640	+	0.0774820i
$631$	695.761			1.10263			0.551316	−	0.834297i	$-0.314126\pi$
$631$	695.761			1.10263			0.551316	+	0.834297i	$0.314126\pi$
$632$	233.423	−	233.423i	0.369340	−	0.369340i
$633$	−69.5975	−	69.5975i	−0.109949	−	0.109949i
$634$			148.987i			0.234996i
$635$	1075.45	−	348.082i	1.69362	−	0.548160i
$636$	200.383			0.315068
$637$	−217.971	+	217.971i	−0.342184	+	0.342184i
$638$	−435.327	−	435.327i	−0.682330	−	0.682330i
$639$		−	328.547i		−	0.514158i
$640$	−17.4194	−	53.8198i	−0.0272177	−	0.0840934i
$641$	−108.436			−0.169168			−0.0845838	−	0.996416i	$-0.526956\pi$
$641$	−108.436			−0.169168			−0.0845838	+	0.996416i	$0.526956\pi$
$642$	−36.2585	+	36.2585i	−0.0564774	+	0.0564774i
$643$	748.186	+	748.186i	1.16359	+	1.16359i	0.983685	+	0.179901i	$0.0575778\pi$
$643$	748.186	+	748.186i	1.16359	+	1.16359i	0.179901	+	0.983685i	$0.442422\pi$
$644$		−	48.5080i		−	0.0753229i
$645$	−222.725	+	435.894i	−0.345310	+	0.675805i
$646$	254.413			0.393829
$647$	175.618	−	175.618i	0.271435	−	0.271435i	−0.558243	−	0.829678i	$-0.688524\pi$
$647$	175.618	−	175.618i	0.271435	−	0.271435i	0.829678	+	0.558243i	$0.188524\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			1765.92i			2.72099i
$650$	272.626	+	377.041i	0.419425	+	0.580063i
$651$	−410.273			−0.630220
$652$	−112.915	+	112.915i	−0.173183	+	0.173183i
$653$	−752.118	−	752.118i	−1.15179	−	1.15179i	−0.986194	−	0.165595i	$-0.947046\pi$
$653$	−752.118	−	752.118i	−1.15179	−	1.15179i	−0.165595	−	0.986194i	$-0.552954\pi$
$654$			0.251522i			0.000384590i
$655$	1112.01	+	568.195i	1.69773	+	0.867473i
$656$	−196.675			−0.299810
$657$	−112.755	+	112.755i	−0.171622	+	0.171622i
$658$	302.306	+	302.306i	0.459432	+	0.459432i
$659$			651.736i			0.988977i	0.869184	+	0.494488i	$0.164645\pi$
$659$			651.736i			0.988977i	−0.869184	+	0.494488i	$0.835355\pi$
$660$	−251.826	+	81.5062i	−0.381554	+	0.123494i
$661$	−104.721			−0.158428			−0.0792141	−	0.996858i	$-0.525241\pi$
$661$	−104.721			−0.158428			−0.0792141	+	0.996858i	$0.525241\pi$
$662$	316.884	−	316.884i	0.478677	−	0.478677i
$663$	174.368	+	174.368i	0.262999	+	0.262999i
$664$		−	390.345i		−	0.587870i
$665$	129.482	+	400.054i	0.194709	+	0.601585i
$666$	232.805			0.349556
$667$	−96.6032	+	96.6032i	−0.144832	+	0.144832i
$668$	−322.673	−	322.673i	−0.483044	−	0.483044i
$669$			124.523i			0.186134i
$670$	−136.779	+	267.691i	−0.204148	+	0.399538i
$671$	−604.427			−0.900786
$672$	35.0380	−	35.0380i	0.0521399	−	0.0521399i
$673$	175.443	+	175.443i	0.260688	+	0.260688i	0.825333	−	0.564646i	$-0.190987\pi$
$673$	175.443	+	175.443i	0.260688	+	0.260688i	−0.564646	+	0.825333i	$0.690987\pi$
$674$		−	163.888i		−	0.243158i
$675$	−128.258	−	20.6136i	−0.190012	−	0.0305387i
$676$	8.37618			0.0123908
$677$	366.104	−	366.104i	0.540775	−	0.540775i	−0.382981	−	0.923756i	$-0.625103\pi$
$677$	366.104	−	366.104i	0.540775	−	0.540775i	0.923756	+	0.382981i	$0.125103\pi$
$678$	−134.659	−	134.659i	−0.198612	−	0.198612i
$679$		−	500.978i		−	0.737818i
$680$	136.240	+	69.6135i	0.200354	+	0.102373i
$681$	−185.749			−0.272758
$682$	715.758	−	715.758i	1.04950	−	1.04950i
$683$	−397.528	−	397.528i	−0.582032	−	0.582032i	0.353429	−	0.935461i	$-0.385016\pi$
$683$	−397.528	−	397.528i	−0.582032	−	0.582032i	−0.935461	+	0.353429i	$0.885016\pi$
$684$			99.7732i			0.145867i
$685$	−162.492	+	52.5923i	−0.237214	+	0.0767770i
$686$	−517.982			−0.755076
$687$	−85.7644	+	85.7644i	−0.124839	+	0.124839i
$688$	159.870	+	159.870i	0.232369	+	0.232369i
$689$			761.254i			1.10487i
$690$	18.0870	+	55.8826i	0.0262131	+	0.0809892i
$691$	−827.604			−1.19769			−0.598846	−	0.800865i	$-0.704374\pi$
$691$	−827.604			−1.19769			−0.598846	+	0.800865i	$0.704374\pi$
$692$	−227.372	+	227.372i	−0.328573	+	0.328573i
$693$	−163.945	−	163.945i	−0.236573	−	0.236573i
$694$		−	507.354i		−	0.731058i
$695$	−245.463	+	480.395i	−0.353184	+	0.691216i
$696$	−139.556			−0.200511
$697$	376.129	−	376.129i	0.539640	−	0.539640i
$698$	162.699	+	162.699i	0.233093	+	0.233093i
$699$			9.85581i			0.0140999i
$700$	−40.1256	+	249.661i	−0.0573223	+	0.356659i
$701$	−1107.02			−1.57920			−0.789600	−	0.613621i	$-0.789712\pi$
$701$	−1107.02			−1.57920			−0.789600	+	0.613621i	$0.789712\pi$
$702$	−68.3819	+	68.3819i	−0.0974101	+	0.0974101i
$703$	645.212	+	645.212i	0.917798	+	0.917798i
$704$			122.254i			0.173656i
$705$	−460.985	−	235.545i	−0.653880	−	0.334107i
$706$	39.8097			0.0563877
$707$	−563.649	+	563.649i	−0.797241	+	0.797241i
$708$	283.057	+	283.057i	0.399798	+	0.399798i
$709$		−	369.641i		−	0.521356i	−0.965426	−	0.260678i	$-0.916054\pi$
$709$		−	369.641i		−	0.521356i	0.965426	−	0.260678i	$-0.0839460\pi$
$710$	736.763	−	238.461i	1.03769	−	0.335861i
$711$	−350.134			−0.492453
$712$	−52.6689	+	52.6689i	−0.0739732	+	0.0739732i
$713$	−158.834	−	158.834i	−0.222768	−	0.222768i
$714$			134.016i			0.187698i
$715$	−309.641	−	956.684i	−0.433065	−	1.33802i
$716$	404.551			0.565016
$717$	−328.918	+	328.918i	−0.458742	+	0.458742i
$718$	414.391	+	414.391i	0.577146	+	0.577146i
$719$		−	700.854i		−	0.974762i	−0.873189	−	0.487381i	$-0.837952\pi$
$719$		−	700.854i		−	0.974762i	0.873189	−	0.487381i	$-0.162048\pi$
$720$	−27.3003	+	53.4293i	−0.0379171	+	0.0742074i
$721$	952.037			1.32044
$722$	84.4810	−	84.4810i	0.117010	−	0.117010i
$723$	−325.710	−	325.710i	−0.450498	−	0.450498i
$724$			239.384i			0.330640i
$725$	577.108	−	417.288i	0.796011	−	0.575570i
$726$	275.645			0.379677
$727$	−160.008	+	160.008i	−0.220093	+	0.220093i	−0.808538	−	0.588445i	$-0.799740\pi$
$727$	−160.008	+	160.008i	−0.220093	+	0.220093i	0.588445	+	0.808538i	$0.299740\pi$
$728$	133.109	+	133.109i	0.182842	+	0.182842i
$729$		−	27.0000i		−	0.0370370i
$730$	−334.692	−	171.014i	−0.458482	−	0.234266i
$731$	−611.483			−0.836502
$732$	−96.8828	+	96.8828i	−0.132354	+	0.132354i
$733$	−104.240	−	104.240i	−0.142210	−	0.142210i	0.632417	−	0.774628i	$-0.282063\pi$
$733$	−104.240	−	104.240i	−0.142210	−	0.142210i	−0.774628	+	0.632417i	$0.782063\pi$
$734$		−	211.386i		−	0.287991i
$735$	192.998	−	62.4659i	0.262582	−	0.0849876i
$736$	27.1293			0.0368605
$737$	459.386	−	459.386i	0.623319	−	0.623319i
$738$	147.506	+	147.506i	0.199873	+	0.199873i
$739$		−	761.948i		−	1.03105i	−0.856874	−	0.515526i	$-0.827597\pi$
$739$		−	761.948i		−	1.03105i	0.856874	−	0.515526i	$-0.172403\pi$
$740$	168.971	+	522.062i	0.228339	+	0.705489i
$741$	−379.037			−0.511521
$742$	−292.543	+	292.543i	−0.394263	+	0.394263i
$743$	−222.730	−	222.730i	−0.299772	−	0.299772i	0.541153	−	0.840924i	$-0.317988\pi$
$743$	−222.730	−	222.730i	−0.299772	−	0.299772i	−0.840924	+	0.541153i	$0.817988\pi$
$744$		−	229.456i		−	0.308408i
$745$	−339.312	+	664.066i	−0.455452	+	0.891364i
$746$	−644.036			−0.863319
$747$	−292.759	+	292.759i	−0.391913	+	0.391913i
$748$	−233.803	−	233.803i	−0.312571	−	0.312571i
$749$		−	105.869i		−	0.141347i
$750$	−46.8645	−	302.578i	−0.0624860	−	0.403438i
$751$	−276.810			−0.368589			−0.184294	−	0.982871i	$-0.559000\pi$
$751$	−276.810			−0.368589			−0.184294	+	0.982871i	$0.559000\pi$
$752$	−169.072	+	169.072i	−0.224830	+	0.224830i
$753$	205.318	+	205.318i	0.272666	+	0.272666i
$754$		−	530.172i		−	0.703145i
$755$	388.982	+	198.755i	0.515208	+	0.263251i
$756$	−52.5571			−0.0695199
$757$	−762.159	+	762.159i	−1.00681	+	1.00681i	−0.00683824	+	0.999977i	$0.502177\pi$
$757$	−762.159	+	762.159i	−1.00681	+	1.00681i	−0.999977	+	0.00683824i	$0.997823\pi$
$758$	−46.2839	−	46.2839i	−0.0610605	−	0.0610605i
$759$		−	126.940i		−	0.167246i
$760$	−223.740	+	72.4160i	−0.294395	+	0.0952842i
$761$	458.239			0.602153			0.301077	−	0.953600i	$-0.402654\pi$
$761$	458.239			0.602153			0.301077	+	0.953600i	$0.402654\pi$
$762$	−391.575	+	391.575i	−0.513878	+	0.513878i
$763$	−0.367201	−	0.367201i	−0.000481260	−	0.000481260i
$764$		−	708.837i		−	0.927798i
$765$	−49.9702	−	154.390i	−0.0653205	−	0.201818i
$766$	−913.014			−1.19192
$767$	−1075.33	+	1075.33i	−1.40200	+	1.40200i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	493.914i		−	0.642281i	−0.947032	−	0.321141i	$-0.895934\pi$
$769$		−	493.914i		−	0.642281i	0.947032	−	0.321141i	$-0.104066\pi$
$770$	248.653	−	486.638i	0.322926	−	0.631997i
$771$	157.352			0.204088
$772$	179.699	−	179.699i	0.232770	−	0.232770i
$773$	−429.285	−	429.285i	−0.555349	−	0.555349i	0.372631	−	0.927980i	$-0.378456\pi$
$773$	−429.285	−	429.285i	−0.555349	−	0.555349i	−0.927980	+	0.372631i	$0.878456\pi$
$774$		−	239.805i		−	0.309826i
$775$	686.100	+	948.873i	0.885290	+	1.22435i
$776$	280.185			0.361063
$777$	−339.876	+	339.876i	−0.437420	+	0.437420i
$778$	423.277	+	423.277i	0.544058	+	0.544058i
$779$			817.621i			1.04958i
$780$	−202.978	−	103.714i	−0.260228	−	0.132966i
$781$	−1673.59			−2.14288
$782$	−51.8832	+	51.8832i	−0.0663467	+	0.0663467i
$783$	104.667	+	104.667i	0.133674	+	0.133674i
$784$		−	93.6947i		−	0.119509i
$785$	−546.036	+	176.730i	−0.695587	+	0.225134i
$786$	−611.768			−0.778331
$787$	599.373	−	599.373i	0.761592	−	0.761592i	−0.215018	−	0.976610i	$-0.568981\pi$
$787$	599.373	−	599.373i	0.761592	−	0.761592i	0.976610	+	0.215018i	$0.0689809\pi$
$788$	−489.834	−	489.834i	−0.621617	−	0.621617i
$789$		−	64.0234i		−	0.0811450i
$790$	−254.130	−	785.172i	−0.321683	−	0.993889i
$791$	393.181			0.497068
$792$	91.6905	−	91.6905i	0.115771	−	0.115771i
$793$	−368.057	−	368.057i	−0.464132	−	0.464132i
$794$		−	229.918i		−	0.289569i
$795$	227.938	−	446.097i	0.286715	−	0.561129i
$796$	−402.182			−0.505253
$797$	−453.375	+	453.375i	−0.568853	+	0.568853i	−0.931807	−	0.362954i	$-0.881768\pi$
$797$	−453.375	+	453.375i	−0.568853	+	0.568853i	0.362954	+	0.931807i	$0.381768\pi$
$798$	−145.661	−	145.661i	−0.182532	−	0.182532i
$799$		−	646.681i		−	0.809363i
$800$	−139.629	−	22.4413i	−0.174537	−	0.0280516i
$801$	79.0034			0.0986310
$802$	−545.562	+	545.562i	−0.680252	+	0.680252i
$803$	574.367	+	574.367i	0.715276	+	0.715276i
$804$		−	147.269i		−	0.183170i
$805$	−107.990	−	55.1784i	−0.134148	−	0.0685446i
$806$	871.701			1.08151
$807$	−140.690	+	140.690i	−0.174337	+	0.174337i
$808$	−315.235	−	315.235i	−0.390143	−	0.390143i
$809$		−	495.664i		−	0.612687i	−0.951921	−	0.306344i	$-0.900894\pi$
$809$		−	495.664i		−	0.612687i	0.951921	−	0.306344i	$-0.0991057\pi$
$810$	60.5472	−	19.5968i	0.0747497	−	0.0241936i
$811$	−360.435			−0.444432			−0.222216	−	0.974997i	$-0.571329\pi$
$811$	−360.435			−0.444432			−0.222216	+	0.974997i	$0.571329\pi$
$812$	203.740	−	203.740i	0.250911	−	0.250911i
$813$	322.615	+	322.615i	0.396820	+	0.396820i
$814$		−	1185.89i		−	1.45686i
$815$	122.932	+	379.817i	0.150837	+	0.466033i
$816$	−74.9520			−0.0918529
$817$	664.614	−	664.614i	0.813481	−	0.813481i
$818$	−400.154	−	400.154i	−0.489185	−	0.489185i
$819$		−	199.664i		−	0.243790i
$820$	−223.721	+	437.843i	−0.272830	+	0.533955i
$821$	−1487.19			−1.81144			−0.905720	−	0.423876i	$-0.860669\pi$
$821$	−1487.19			−1.81144			−0.905720	+	0.423876i	$0.860669\pi$
$822$	59.1637	−	59.1637i	0.0719753	−	0.0719753i
$823$	−474.095	−	474.095i	−0.576057	−	0.576057i	0.357758	−	0.933814i	$-0.383541\pi$
$823$	−474.095	−	474.095i	−0.576057	−	0.576057i	−0.933814	+	0.357758i	$0.883541\pi$
$824$			532.451i			0.646179i
$825$	−105.004	+	653.335i	−0.127278	+	0.791921i
$826$	−826.480			−1.00058
$827$	−120.262	+	120.262i	−0.145420	+	0.145420i	−0.776069	−	0.630649i	$-0.782789\pi$
$827$	−120.262	+	120.262i	−0.145420	+	0.145420i	0.630649	+	0.776069i	$0.282789\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$			124.989i			0.150771i	0.997154	+	0.0753853i	$0.0240187\pi$
$829$			124.989i			0.150771i	−0.997154	+	0.0753853i	$0.975981\pi$
$830$	−868.996	−	444.023i	−1.04698	−	0.534967i
$831$	−606.580			−0.729940
$832$	−74.4447	+	74.4447i	−0.0894768	+	0.0894768i
$833$	179.185	+	179.185i	0.215108	+	0.215108i
$834$		−	264.287i		−	0.316891i
$835$	−1085.39	+	351.298i	−1.29987	+	0.420716i
$836$	508.236			0.607938
$837$	−172.092	+	172.092i	−0.205606	+	0.205606i
$838$	100.320	+	100.320i	0.119714	+	0.119714i
$839$		−	489.898i		−	0.583907i	−0.956432	−	0.291954i	$-0.905695\pi$
$839$		−	489.898i		−	0.583907i	0.956432	−	0.291954i	$-0.0943053\pi$
$840$	−38.1463	−	117.859i	−0.0454122	−	0.140308i
$841$	29.5068			0.0350854
$842$	115.474	−	115.474i	0.137143	−	0.137143i
$843$	−616.211	−	616.211i	−0.730974	−	0.730974i
$844$			113.652i			0.134659i
$845$	9.52801	−	18.6472i	0.0112758	−	0.0220677i
$846$	253.609			0.299774
$847$	−402.420	+	402.420i	−0.475112	+	0.475112i
$848$	−163.612	−	163.612i	−0.192939	−	0.192939i
$849$		−	820.093i		−	0.965952i
$850$	309.950	−	224.115i	0.364647	−	0.263665i
$851$	−263.160			−0.309236
$852$	−268.257	+	268.257i	−0.314856	+	0.314856i
$853$	−223.302	−	223.302i	−0.261785	−	0.261785i	0.563994	−	0.825779i	$-0.309264\pi$
$853$	−223.302	−	223.302i	−0.261785	−	0.261785i	−0.825779	+	0.563994i	$0.809264\pi$
$854$		−	282.882i		−	0.331243i
$855$	222.117	+	113.493i	0.259786	+	0.132741i
$856$	59.2099			0.0691704
$857$	−573.623	+	573.623i	−0.669338	+	0.669338i	−0.957563	−	0.288225i	$-0.906935\pi$
$857$	−573.623	+	573.623i	−0.669338	+	0.669338i	0.288225	+	0.957563i	$0.406935\pi$
$858$	348.331	+	348.331i	0.405981	+	0.405981i
$859$			1232.45i			1.43475i	0.696686	+	0.717376i	$0.254657\pi$
$859$			1232.45i			1.43475i	−0.696686	+	0.717376i	$0.745343\pi$
$860$	537.760	−	174.052i	0.625303	−	0.202386i
$861$	−430.695			−0.500226
$862$	341.266	−	341.266i	0.395901	−	0.395901i
$863$	−426.752	−	426.752i	−0.494498	−	0.494498i	0.415222	−	0.909720i	$-0.363704\pi$
$863$	−426.752	−	426.752i	−0.494498	−	0.494498i	−0.909720	+	0.415222i	$0.863704\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	247.543	+	764.821i	0.286176	+	0.884186i
$866$	−728.991			−0.841791
$867$	−210.610	+	210.610i	−0.242918	+	0.242918i
$868$	334.987	+	334.987i	0.385929	+	0.385929i
$869$			1783.55i			2.05242i
$870$	−158.747	+	310.682i	−0.182467	+	0.357106i
$871$	559.472			0.642333
$872$	0.205367	−	0.205367i	0.000235512	−	0.000235512i
$873$	−210.139	−	210.139i	−0.240709	−	0.240709i
$874$		−	112.782i		−	0.129042i
$875$	510.158	+	373.321i	0.583038	+	0.426653i
$876$	184.129			0.210193
$877$	−606.515	+	606.515i	−0.691579	+	0.691579i	−0.962579	−	0.271000i	$-0.912646\pi$
$877$	−606.515	+	606.515i	−0.691579	+	0.691579i	0.271000	+	0.962579i	$0.412646\pi$
$878$	745.512	+	745.512i	0.849103	+	0.849103i
$879$		−	254.526i		−	0.289564i
$880$	272.164	+	139.065i	0.309278	+	0.158029i
$881$	−1194.70			−1.35607			−0.678035	−	0.735030i	$-0.737168\pi$
$881$	−1194.70			−1.35607			−0.678035	+	0.735030i	$0.737168\pi$
$882$	−70.2710	+	70.2710i	−0.0796723	+	0.0796723i
$883$	−993.400	−	993.400i	−1.12503	−	1.12503i	−0.990974	−	0.134054i	$-0.957201\pi$
$883$	−993.400	−	993.400i	−1.12503	−	1.12503i	−0.134054	−	0.990974i	$-0.542799\pi$
$884$		−	284.742i		−	0.322106i
$885$	952.129	−	308.167i	1.07585	−	0.348211i
$886$	853.452			0.963264
$887$	1102.52	−	1102.52i	1.24298	−	1.24298i	0.284217	−	0.958760i	$-0.408266\pi$
$887$	1102.52	−	1102.52i	1.24298	−	1.24298i	0.958760	−	0.284217i	$-0.0917337\pi$
$888$	−190.084	−	190.084i	−0.214059	−	0.214059i
$889$		−	1143.33i		−	1.28609i
$890$	57.3412	+	177.164i	0.0644283	+	0.199061i
$891$	−137.536			−0.154361
$892$	101.673	−	101.673i	0.113983	−	0.113983i
$893$	702.871	+	702.871i	0.787089	+	0.787089i
$894$		−	365.333i		−	0.408650i
$895$	460.182	−	900.621i	0.514170	−	1.00628i
$896$	−57.2169			−0.0638581
$897$	77.2981	−	77.2981i	0.0861740	−	0.0861740i
$898$	183.403	+	183.403i	0.204235	+	0.204235i
$899$		−	1334.25i		−	1.48414i
$900$	87.8911	+	121.553i	0.0976568	+	0.135059i
$901$	625.796			0.694558
$902$	751.385	−	751.385i	0.833021	−	0.833021i
$903$	350.096	+	350.096i	0.387703	+	0.387703i
$904$			219.897i			0.243248i
$905$	532.921	+	272.302i	0.588863	+	0.300886i
$906$	−213.996			−0.236199
$907$	−884.694	+	884.694i	−0.975407	+	0.975407i	−0.999705	−	0.0242975i	$-0.992265\pi$
$907$	−884.694	+	884.694i	−0.975407	+	0.975407i	0.0242975	+	0.999705i	$0.492265\pi$
$908$	151.663	+	151.663i	0.167030	+	0.167030i
$909$			472.853i			0.520190i
$910$	447.744	−	144.917i	0.492026	−	0.159250i
$911$	−225.502			−0.247532			−0.123766	−	0.992311i	$-0.539497\pi$
$911$	−225.502			−0.247532			−0.123766	+	0.992311i	$0.539497\pi$
$912$	81.4644	−	81.4644i	0.0893250	−	0.0893250i
$913$	1491.29	+	1491.29i	1.63340	+	1.63340i
$914$			136.230i			0.149048i
$915$	105.477	+	325.888i	0.115276	+	0.356162i
$916$	140.053			0.152896
$917$	893.132	−	893.132i	0.973971	−	0.973971i
$918$	56.2140	+	56.2140i	0.0612353	+	0.0612353i
$919$		−	262.008i		−	0.285101i	−0.989787	−	0.142551i	$-0.954470\pi$
$919$		−	262.008i		−	0.285101i	0.989787	−	0.142551i	$-0.0455304\pi$
$920$	30.8599	−	60.3959i	0.0335434	−	0.0656477i
$921$	39.1708			0.0425307
$922$	−386.997	+	386.997i	−0.419736	+	0.419736i
$923$	−1019.11	−	1019.11i	−1.10413	−	1.10413i
$924$			267.721i			0.289742i
$925$	1354.43	+	217.685i	1.46425	+	0.235335i
$926$	−223.153			−0.240986
$927$	399.338	−	399.338i	0.430786	−	0.430786i
$928$	113.947	+	113.947i	0.122788	+	0.122788i
$929$			837.652i			0.901671i	0.892607	+	0.450836i	$0.148874\pi$
$929$			837.652i			0.901671i	−0.892607	+	0.450836i	$0.851126\pi$
$930$	−510.820	−	261.009i	−0.549268	−	0.280655i
$931$	−389.509			−0.418377
$932$	8.04723	−	8.04723i	0.00863437	−	0.00863437i
$933$	527.234	+	527.234i	0.565096	+	0.565096i
$934$			16.5588i			0.0177289i
$935$	−786.452	+	254.544i	−0.841125	+	0.272239i
$936$	111.667			0.119302
$937$	198.243	−	198.243i	0.211572	−	0.211572i	−0.593363	−	0.804935i	$-0.702200\pi$
$937$	198.243	−	198.243i	0.211572	−	0.211572i	0.804935	+	0.593363i	$0.202200\pi$
$938$	215.000	+	215.000i	0.229211	+	0.229211i
$939$		−	528.019i		−	0.562320i
$940$	184.071	+	568.715i	0.195820	+	0.605016i
$941$	601.841			0.639576			0.319788	−	0.947489i	$-0.396388\pi$
$941$	601.841			0.639576			0.319788	+	0.947489i	$0.396388\pi$
$942$	198.813	−	198.813i	0.211054	−	0.211054i
$943$	−166.740	−	166.740i	−0.176818	−	0.176818i
$944$		−	462.230i		−	0.489651i
$945$	−59.7843	+	117.004i	−0.0632638	+	0.123813i
$946$	−1221.55			−1.29128
$947$	−861.408	+	861.408i	−0.909618	+	0.909618i	−0.996241	−	0.0866233i	$-0.972392\pi$
$947$	−861.408	+	861.408i	−0.909618	+	0.909618i	0.0866233	+	0.996241i	$0.472392\pi$
$948$	285.883	+	285.883i	0.301565	+	0.301565i
$949$			699.504i			0.737096i
$950$	−93.2932	+	580.470i	−0.0982034	+	0.611021i
$951$	−182.472			−0.191873
$952$	109.424	−	109.424i	0.114941	−	0.114941i
$953$	−500.153	−	500.153i	−0.524819	−	0.524819i	0.394204	−	0.919023i	$-0.371020\pi$
$953$	−500.153	−	500.153i	−0.524819	−	0.524819i	−0.919023	+	0.394204i	$0.871020\pi$
$954$			245.418i			0.257252i
$955$	−1578.03	−	806.311i	−1.65239	−	0.844305i
$956$	537.121			0.561842
$957$	533.164	−	533.164i	0.557120	−	0.557120i
$958$	−391.487	−	391.487i	−0.408651	−	0.408651i
$959$			172.748i			0.180134i
$960$	65.9155	−	21.3343i	0.0686619	−	0.0222232i
$961$	1232.75			1.28278
$962$	722.128	−	722.128i	0.750653	−	0.750653i
$963$	−44.4074	−	44.4074i	−0.0461136	−	0.0461136i
$964$			531.882i			0.551745i
$965$	−195.640	−	604.459i	−0.202735	−	0.626382i
$966$	59.4099			0.0615009
$967$	−820.417	+	820.417i	−0.848415	+	0.848415i	−0.989935	−	0.141521i	$-0.954801\pi$
$967$	−820.417	+	820.417i	−0.848415	+	0.848415i	0.141521	+	0.989935i	$0.454801\pi$
$968$	−225.063	−	225.063i	−0.232504	−	0.232504i
$969$			311.591i			0.321560i
$970$	318.714	−	623.754i	0.328571	−	0.643045i
$971$	247.015			0.254392			0.127196	−	0.991878i	$-0.459402\pi$
$971$	247.015			0.254392			0.127196	+	0.991878i	$0.459402\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	385.837	+	385.837i	0.396544	+	0.396544i
$974$			564.855i			0.579933i
$975$	−461.779	+	333.898i	−0.473620	+	0.342459i
$976$	158.209			0.162099
$977$	327.784	−	327.784i	0.335501	−	0.335501i	−0.519170	−	0.854671i	$-0.673759\pi$
$977$	327.784	−	327.784i	0.335501	−	0.335501i	0.854671	+	0.519170i	$0.173759\pi$
$978$	−138.292	−	138.292i	−0.141403	−	0.141403i
$979$		−	402.437i		−	0.411069i
$980$	−208.585	−	106.579i	−0.212842	−	0.108754i
$981$	−0.308050			−0.000314016
$982$	15.3095	−	15.3095i	0.0155901	−	0.0155901i
$983$	−565.846	−	565.846i	−0.575632	−	0.575632i	0.358065	−	0.933697i	$-0.383437\pi$
$983$	−565.846	−	565.846i	−0.575632	−	0.575632i	−0.933697	+	0.358065i	$0.883437\pi$
$984$		−	240.877i		−	0.244794i
$985$	−1647.67	+	533.287i	−1.67276	+	0.541408i
$986$	−435.833			−0.442021
$987$	−370.248	+	370.248i	−0.375125	+	0.375125i
$988$	309.483	+	309.483i	0.313242	+	0.313242i
$989$			271.073i			0.274088i
$990$	−99.8243	−	308.422i	−0.100833	−	0.311538i
$991$	1093.78			1.10371			0.551856	−	0.833939i	$-0.313920\pi$
$991$	1093.78			1.10371			0.551856	+	0.833939i	$0.313920\pi$
$992$	−187.350	+	187.350i	−0.188861	+	0.188861i
$993$	388.102	+	388.102i	0.390838	+	0.390838i
$994$		−	783.268i		−	0.787996i
$995$	−457.487	+	895.346i	−0.459786	+	0.899845i
$996$	478.073			0.479993
$997$	652.866	−	652.866i	0.654831	−	0.654831i	−0.299321	−	0.954152i	$-0.596760\pi$
$997$	652.866	−	652.866i	0.654831	−	0.654831i	0.954152	+	0.299321i	$0.0967603\pi$
$998$	823.731	+	823.731i	0.825382	+	0.825382i
$999$			285.126i			0.285412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.19	yes	40
5.2	odd	4	inner	690.3.k.a.277.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.19	✓	40	5.2	odd	4	inner
690.3.k.a.553.19	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.45244 - 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 + 3.57605i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.45244 - 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 + 3.57605i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-6.72747 + 2.17742i) q^{10} +15.2817 q^{11} +(2.44949 - 2.44949i) q^{12} +(9.30559 + 9.30559i) q^{13} +7.15211i q^{14} +(-2.66678 - 8.23943i) q^{15} -4.00000 q^{16} +(7.64975 - 7.64975i) q^{17} +(3.00000 + 3.00000i) q^{18} +16.6289i q^{19} +(-4.55005 + 8.90489i) q^{20} -8.75951 q^{21} +(15.2817 - 15.2817i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(14.6485 + 20.2588i) q^{25} +18.6112 q^{26} +(-3.67423 + 3.67423i) q^{27} +(7.15211 + 7.15211i) q^{28} -28.4867i q^{29} +(-10.9062 - 5.57265i) q^{30} +46.8375 q^{31} +(-4.00000 + 4.00000i) q^{32} +(18.7162 + 18.7162i) q^{33} -15.2995i q^{34} +(24.0578 - 7.78657i) q^{35} +6.00000 q^{36} +(38.8008 - 38.8008i) q^{37} +(16.6289 + 16.6289i) q^{38} +22.7940i q^{39} +(4.35484 + 13.4549i) q^{40} +49.1688 q^{41} +(-8.75951 + 8.75951i) q^{42} +(-39.9675 - 39.9675i) q^{43} -30.5635i q^{44} +(6.82507 - 13.3573i) q^{45} -6.78233 q^{46} +(42.2681 - 42.2681i) q^{47} +(-4.89898 - 4.89898i) q^{48} +23.4237i q^{49} +(34.9074 + 5.61032i) q^{50} +18.7380 q^{51} +(18.6112 - 18.6112i) q^{52} +(40.9030 + 40.9030i) q^{53} +7.34847i q^{54} +(-68.0411 - 34.7664i) q^{55} +14.3042 q^{56} +(-20.3661 + 20.3661i) q^{57} +(-28.4867 - 28.4867i) q^{58} +115.558i q^{59} +(-16.4789 + 5.33357i) q^{60} -39.5522 q^{61} +(46.8375 - 46.8375i) q^{62} +(-10.7282 - 10.7282i) q^{63} +8.00000i q^{64} +(-20.2622 - 62.6031i) q^{65} +37.4325 q^{66} +(30.0611 - 30.0611i) q^{67} +(-15.2995 - 15.2995i) q^{68} -8.30662i q^{69} +(16.2712 - 31.8444i) q^{70} -109.516 q^{71} +(6.00000 - 6.00000i) q^{72} +(37.5852 + 37.5852i) q^{73} -77.6015i q^{74} +(-6.87121 + 42.7526i) q^{75} +33.2577 q^{76} +(-54.6484 + 54.6484i) q^{77} +(22.7940 + 22.7940i) q^{78} +116.711i q^{79} +(17.8098 + 9.10010i) q^{80} -9.00000 q^{81} +(49.1688 - 49.1688i) q^{82} +(97.5863 + 97.5863i) q^{83} +17.5190i q^{84} +(-51.4635 + 16.6567i) q^{85} -79.9350 q^{86} +(34.8890 - 34.8890i) q^{87} +(-30.5635 - 30.5635i) q^{88} -26.3345i q^{89} +(-6.53226 - 20.1824i) q^{90} -66.5546 q^{91} +(-6.78233 + 6.78233i) q^{92} +(57.3640 + 57.3640i) q^{93} -84.5362i q^{94} +(37.8311 - 74.0391i) q^{95} -9.79796 q^{96} +(-70.0462 + 70.0462i) q^{97} +(23.4237 + 23.4237i) q^{98} +45.8452i 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

Related objects

Downloads

Learn more