LMFDB - Embedded newform 690.3.k.b.553.8

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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.8
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.85468 + 1.73590i) q^{10} +18.3249 q^{11} +(-2.44949 + 2.44949i) q^{12} +(7.21738 + 7.21738i) q^{13} +10.9455i q^{14} +(-2.12604 + 8.39523i) q^{15} -4.00000 q^{16} +(1.48954 - 1.48954i) q^{17} +(-3.00000 - 3.00000i) q^{18} +13.9116i q^{19} +(-8.59058 + 5.11878i) q^{20} -13.4055 q^{21} +(-18.3249 + 18.3249i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.8991 + 21.9866i) q^{25} -14.4348 q^{26} +(3.67423 - 3.67423i) q^{27} +(-10.9455 - 10.9455i) q^{28} -0.950775i q^{29} +(-6.26919 - 10.5213i) q^{30} +56.4791 q^{31} +(4.00000 - 4.00000i) q^{32} +(-22.4433 - 22.4433i) q^{33} +2.97907i q^{34} +(-37.5141 - 9.50020i) q^{35} +6.00000 q^{36} +(44.4969 - 44.4969i) q^{37} +(-13.9116 - 13.9116i) q^{38} -17.6789i q^{39} +(3.47181 - 13.7094i) q^{40} -44.8287 q^{41} +(13.4055 - 13.4055i) q^{42} +(31.1063 + 31.1063i) q^{43} -36.6498i q^{44} +(12.8859 - 7.67816i) q^{45} +6.78233 q^{46} +(25.7168 - 25.7168i) q^{47} +(4.89898 + 4.89898i) q^{48} -10.9024i q^{49} +(-10.0876 - 33.8857i) q^{50} -3.64860 q^{51} +(14.4348 - 14.4348i) q^{52} +(-17.7789 - 17.7789i) q^{53} +7.34847i q^{54} +(-46.9005 - 78.7108i) q^{55} +21.8911 q^{56} +(17.0382 - 17.0382i) q^{57} +(0.950775 + 0.950775i) q^{58} -0.459649i q^{59} +(16.7905 + 4.25208i) q^{60} +24.6543 q^{61} +(-56.4791 + 56.4791i) q^{62} +(16.4183 + 16.4183i) q^{63} +8.00000i q^{64} +(12.5287 - 49.4728i) q^{65} +44.8867 q^{66} +(-32.6237 + 32.6237i) q^{67} +(-2.97907 - 2.97907i) q^{68} +8.30662i q^{69} +(47.0143 - 28.0139i) q^{70} +46.7310 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.372008 - 0.372008i) q^{73} +88.9939i q^{74} +(41.5013 - 12.3547i) q^{75} +27.8232 q^{76} +(100.288 - 100.288i) q^{77} +(17.6789 + 17.6789i) q^{78} -65.5336i q^{79} +(10.2376 + 17.1812i) q^{80} -9.00000 q^{81} +(44.8287 - 44.8287i) q^{82} +(-85.4484 - 85.4484i) q^{83} +26.8110i q^{84} +(-10.2103 - 2.58569i) q^{85} -62.2125 q^{86} +(-1.16446 + 1.16446i) q^{87} +(36.6498 + 36.6498i) q^{88} +64.0437i q^{89} +(-5.20771 + 20.5640i) q^{90} +78.9980 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-69.1725 - 69.1725i) q^{93} +51.4335i q^{94} +(59.7544 - 35.6052i) q^{95} -9.79796 q^{96} +(49.4654 - 49.4654i) q^{97} +(10.9024 + 10.9024i) q^{98} +54.9747i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * 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
$5$	−2.55939	−	4.29529i	−0.511878	−	0.859058i
$5$	−2.55939	−	4.29529i	−0.511878	−	0.859058i
$6$	2.44949			0.408248
$7$	5.47277	−	5.47277i	0.781824	−	0.781824i	−0.198315	−	0.980138i	$-0.563547\pi$
$7$	5.47277	−	5.47277i	0.781824	−	0.781824i	0.980138	+	0.198315i	$0.0635468\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	6.85468	+	1.73590i	0.685468	+	0.173590i
$11$	18.3249			1.66590			0.832950	−	0.553348i	$-0.186650\pi$
$11$	18.3249			1.66590			0.832950	+	0.553348i	$0.186650\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	7.21738	+	7.21738i	0.555183	+	0.555183i	0.927932	−	0.372749i	$-0.121585\pi$
$13$	7.21738	+	7.21738i	0.555183	+	0.555183i	−0.372749	+	0.927932i	$0.621585\pi$
$14$			10.9455i			0.781824i
$15$	−2.12604	+	8.39523i	−0.141736	+	0.559682i
$16$	−4.00000			−0.250000
$17$	1.48954	−	1.48954i	0.0876198	−	0.0876198i	−0.661938	−	0.749558i	$-0.730266\pi$
$17$	1.48954	−	1.48954i	0.0876198	−	0.0876198i	0.749558	+	0.661938i	$0.230266\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			13.9116i			0.732190i	0.930578	+	0.366095i	$0.119305\pi$
$19$			13.9116i			0.732190i	−0.930578	+	0.366095i	$0.880695\pi$
$20$	−8.59058	+	5.11878i	−0.429529	+	0.255939i
$21$	−13.4055			−0.638357
$22$	−18.3249	+	18.3249i	−0.832950	+	0.832950i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−11.8991	+	21.9866i	−0.475963	+	0.879465i
$26$	−14.4348			−0.555183
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−10.9455	−	10.9455i	−0.390912	−	0.390912i
$29$		−	0.950775i		−	0.0327854i	−0.999866	−	0.0163927i	$-0.994782\pi$
$29$		−	0.950775i		−	0.0327854i	0.999866	−	0.0163927i	$-0.00521818\pi$
$30$	−6.26919	−	10.5213i	−0.208973	−	0.350709i
$31$	56.4791			1.82191			0.910954	−	0.412508i	$-0.135347\pi$
$31$	56.4791			1.82191			0.910954	+	0.412508i	$0.135347\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−22.4433	−	22.4433i	−0.680101	−	0.680101i
$34$			2.97907i			0.0876198i
$35$	−37.5141	−	9.50020i	−1.07183	−	0.271434i
$36$	6.00000			0.166667
$37$	44.4969	−	44.4969i	1.20262	−	1.20262i	0.229254	−	0.973367i	$-0.426372\pi$
$37$	44.4969	−	44.4969i	1.20262	−	1.20262i	0.973367	−	0.229254i	$-0.0736285\pi$
$38$	−13.9116	−	13.9116i	−0.366095	−	0.366095i
$39$		−	17.6789i		−	0.453305i
$40$	3.47181	−	13.7094i	0.0867952	−	0.342734i
$41$	−44.8287			−1.09338			−0.546692	−	0.837334i	$-0.684113\pi$
$41$	−44.8287			−1.09338			−0.546692	+	0.837334i	$0.684113\pi$
$42$	13.4055	−	13.4055i	0.319178	−	0.319178i
$43$	31.1063	+	31.1063i	0.723402	+	0.723402i	0.969296	−	0.245895i	$-0.0790818\pi$
$43$	31.1063	+	31.1063i	0.723402	+	0.723402i	−0.245895	+	0.969296i	$0.579082\pi$
$44$		−	36.6498i		−	0.832950i
$45$	12.8859	−	7.67816i	0.286353	−	0.170626i
$46$	6.78233			0.147442
$47$	25.7168	−	25.7168i	0.547165	−	0.547165i	−0.378455	−	0.925620i	$-0.623544\pi$
$47$	25.7168	−	25.7168i	0.547165	−	0.547165i	0.925620	+	0.378455i	$0.123544\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	10.9024i		−	0.222497i
$50$	−10.0876	−	33.8857i	−0.201751	−	0.677714i
$51$	−3.64860			−0.0715412
$52$	14.4348	−	14.4348i	0.277591	−	0.277591i
$53$	−17.7789	−	17.7789i	−0.335450	−	0.335450i	0.519202	−	0.854652i	$-0.326229\pi$
$53$	−17.7789	−	17.7789i	−0.335450	−	0.335450i	−0.854652	+	0.519202i	$0.826229\pi$
$54$			7.34847i			0.136083i
$55$	−46.9005	−	78.7108i	−0.852737	−	1.43111i
$56$	21.8911			0.390912
$57$	17.0382	−	17.0382i	0.298915	−	0.298915i
$58$	0.950775	+	0.950775i	0.0163927	+	0.0163927i
$59$		−	0.459649i		−	0.00779066i	−0.999992	−	0.00389533i	$-0.998760\pi$
$59$		−	0.459649i		−	0.00779066i	0.999992	−	0.00389533i	$-0.00123992\pi$
$60$	16.7905	+	4.25208i	0.279841	+	0.0708680i
$61$	24.6543			0.404169			0.202084	−	0.979368i	$-0.435228\pi$
$61$	24.6543			0.404169			0.202084	+	0.979368i	$0.435228\pi$
$62$	−56.4791	+	56.4791i	−0.910954	+	0.910954i
$63$	16.4183	+	16.4183i	0.260608	+	0.260608i
$64$			8.00000i			0.125000i
$65$	12.5287	−	49.4728i	0.192749	−	0.761120i
$66$	44.8867			0.680101
$67$	−32.6237	+	32.6237i	−0.486920	+	0.486920i	−0.907333	−	0.420413i	$-0.861885\pi$
$67$	−32.6237	+	32.6237i	−0.486920	+	0.486920i	0.420413	+	0.907333i	$0.361885\pi$
$68$	−2.97907	−	2.97907i	−0.0438099	−	0.0438099i
$69$			8.30662i			0.120386i
$70$	47.0143	−	28.0139i	0.671632	−	0.400198i
$71$	46.7310			0.658183			0.329092	−	0.944298i	$-0.393258\pi$
$71$	46.7310			0.658183			0.329092	+	0.944298i	$0.393258\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−0.372008	−	0.372008i	−0.00509599	−	0.00509599i	0.704554	−	0.709650i	$-0.251147\pi$
$73$	−0.372008	−	0.372008i	−0.00509599	−	0.00509599i	−0.709650	+	0.704554i	$0.751147\pi$
$74$			88.9939i			1.20262i
$75$	41.5013	−	12.3547i	0.553351	−	0.164729i
$76$	27.8232			0.366095
$77$	100.288	−	100.288i	1.30244	−	1.30244i
$78$	17.6789	+	17.6789i	0.226652	+	0.226652i
$79$		−	65.5336i		−	0.829539i	−0.909926	−	0.414770i	$-0.863862\pi$
$79$		−	65.5336i		−	0.829539i	0.909926	−	0.414770i	$-0.136138\pi$
$80$	10.2376	+	17.1812i	0.127969	+	0.214765i
$81$	−9.00000			−0.111111
$82$	44.8287	−	44.8287i	0.546692	−	0.546692i
$83$	−85.4484	−	85.4484i	−1.02950	−	1.02950i	−0.999551	−	0.0299470i	$-0.990466\pi$
$83$	−85.4484	−	85.4484i	−1.02950	−	1.02950i	−0.0299470	−	0.999551i	$-0.509534\pi$
$84$			26.8110i			0.319178i
$85$	−10.2103	−	2.58569i	−0.120121	−	0.0304199i
$86$	−62.2125			−0.723402
$87$	−1.16446	+	1.16446i	−0.0133846	+	0.0133846i
$88$	36.6498	+	36.6498i	0.416475	+	0.416475i
$89$			64.0437i			0.719592i	0.933031	+	0.359796i	$0.117154\pi$
$89$			64.0437i			0.719592i	−0.933031	+	0.359796i	$0.882846\pi$
$90$	−5.20771	+	20.5640i	−0.0578635	+	0.228489i
$91$	78.9980			0.868110
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	−69.1725	−	69.1725i	−0.743791	−	0.743791i
$94$			51.4335i			0.547165i
$95$	59.7544	−	35.6052i	0.628994	−	0.374791i
$96$	−9.79796			−0.102062
$97$	49.4654	−	49.4654i	0.509953	−	0.509953i	−0.404559	−	0.914512i	$-0.632575\pi$
$97$	49.4654	−	49.4654i	0.509953	−	0.509953i	0.914512	+	0.404559i	$0.132575\pi$
$98$	10.9024	+	10.9024i	0.111249	+	0.111249i
$99$			54.9747i			0.555300i
$100$	43.9733	+	23.7981i	0.439733	+	0.237981i
$101$	−122.832			−1.21616			−0.608078	−	0.793877i	$-0.708059\pi$
$101$	−122.832			−1.21616			−0.608078	+	0.793877i	$0.708059\pi$
$102$	3.64860	−	3.64860i	0.0357706	−	0.0357706i
$103$	40.9149	+	40.9149i	0.397232	+	0.397232i	0.877256	−	0.480024i	$-0.159372\pi$
$103$	40.9149	+	40.9149i	0.397232	+	0.397232i	−0.480024	+	0.877256i	$0.659372\pi$
$104$			28.8695i			0.277591i
$105$	34.3098	+	57.5805i	0.326760	+	0.548386i
$106$	35.5577			0.335450
$107$	124.288	−	124.288i	1.16157	−	1.16157i	0.177442	−	0.984131i	$-0.443218\pi$
$107$	124.288	−	124.288i	1.16157	−	1.16157i	0.984131	−	0.177442i	$-0.0567822\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			28.6845i			0.263161i	0.991306	+	0.131580i	$0.0420051\pi$
$109$			28.6845i			0.263161i	−0.991306	+	0.131580i	$0.957995\pi$
$110$	125.611	+	31.8103i	1.14192	+	0.289184i
$111$	−108.995			−0.981935
$112$	−21.8911	+	21.8911i	−0.195456	+	0.195456i
$113$	−124.706	−	124.706i	−1.10360	−	1.10360i	−0.993973	−	0.109624i	$-0.965035\pi$
$113$	−124.706	−	124.706i	−1.10360	−	1.10360i	−0.109624	−	0.993973i	$-0.534965\pi$
$114$			34.0763i			0.298915i
$115$	−5.88674	+	23.2454i	−0.0511890	+	0.202133i
$116$	−1.90155			−0.0163927
$117$	−21.6521	+	21.6521i	−0.185061	+	0.185061i
$118$	0.459649	+	0.459649i	0.00389533	+	0.00389533i
$119$		−	16.3038i		−	0.137006i
$120$	−21.0425	+	12.5384i	−0.175355	+	0.104487i
$121$	214.802			1.77522
$122$	−24.6543	+	24.6543i	−0.202084	+	0.202084i
$123$	54.9038	+	54.9038i	0.446372	+	0.446372i
$124$		−	112.958i		−	0.910954i
$125$	124.893	−	5.16236i	0.999147	−	0.0412989i
$126$	−32.8366			−0.260608
$127$	−18.1196	+	18.1196i	−0.142674	+	0.142674i	−0.774836	−	0.632162i	$-0.782168\pi$
$127$	−18.1196	+	18.1196i	−0.142674	+	0.142674i	0.632162	+	0.774836i	$0.282168\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	76.1945i		−	0.590655i
$130$	36.9441	+	62.0015i	0.284186	+	0.476934i
$131$	−88.8228			−0.678037			−0.339018	−	0.940780i	$-0.610095\pi$
$131$	−88.8228			−0.678037			−0.339018	+	0.940780i	$0.610095\pi$
$132$	−44.8867	+	44.8867i	−0.340050	+	0.340050i
$133$	76.1350	+	76.1350i	0.572443	+	0.572443i
$134$		−	65.2473i		−	0.486920i
$135$	−25.1857	−	6.37812i	−0.186561	−	0.0472453i
$136$	5.95814			0.0438099
$137$	84.4843	−	84.4843i	0.616674	−	0.616674i	−0.328003	−	0.944677i	$-0.606376\pi$
$137$	84.4843	−	84.4843i	0.616674	−	0.616674i	0.944677	+	0.328003i	$0.106376\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			1.42790i			0.0102727i	0.999987	+	0.00513633i	$0.00163495\pi$
$139$			1.42790i			0.0102727i	−0.999987	+	0.00513633i	$0.998365\pi$
$140$	−19.0004	+	75.0281i	−0.135717	+	0.535915i
$141$	−62.9930			−0.446759
$142$	−46.7310	+	46.7310i	−0.329092	+	0.329092i
$143$	132.258	+	132.258i	0.924879	+	0.924879i
$144$		−	12.0000i		−	0.0833333i
$145$	−4.08386	+	2.43340i	−0.0281645	+	0.0167821i
$146$	0.744015			0.00509599
$147$	−13.3526	+	13.3526i	−0.0908341	+	0.0908341i
$148$	−88.9939	−	88.9939i	−0.601310	−	0.601310i
$149$			267.416i			1.79474i	0.441280	+	0.897369i	$0.354525\pi$
$149$			267.416i			1.79474i	−0.441280	+	0.897369i	$0.645475\pi$
$150$	−29.1466	+	53.8560i	−0.194311	+	0.359040i
$151$	−160.559			−1.06331			−0.531653	−	0.846962i	$-0.678429\pi$
$151$	−160.559			−1.06331			−0.531653	+	0.846962i	$0.678429\pi$
$152$	−27.8232	+	27.8232i	−0.183047	+	0.183047i
$153$	4.46861	+	4.46861i	0.0292066	+	0.0292066i
$154$			200.576i			1.30244i
$155$	−144.552	−	242.594i	−0.932594	−	1.56513i
$156$	−35.3578			−0.226652
$157$	93.2547	−	93.2547i	0.593979	−	0.593979i	−0.344725	−	0.938704i	$-0.612028\pi$
$157$	93.2547	−	93.2547i	0.593979	−	0.593979i	0.938704	+	0.344725i	$0.112028\pi$
$158$	65.5336	+	65.5336i	0.414770	+	0.414770i
$159$			43.5491i			0.273894i
$160$	−27.4187	−	6.94362i	−0.171367	−	0.0433976i
$161$	−37.1181			−0.230547
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−213.296	−	213.296i	−1.30857	−	1.30857i	−0.922451	−	0.386115i	$-0.873817\pi$
$163$	−213.296	−	213.296i	−1.30857	−	1.30857i	−0.386115	−	0.922451i	$-0.626183\pi$
$164$			89.6575i			0.546692i
$165$	−38.9595	+	153.842i	−0.236118	+	0.932375i
$166$	170.897			1.02950
$167$	−13.9577	+	13.9577i	−0.0835792	+	0.0835792i	−0.747660	−	0.664081i	$-0.768823\pi$
$167$	−13.9577	+	13.9577i	−0.0835792	+	0.0835792i	0.664081	+	0.747660i	$0.268823\pi$
$168$	−26.8110	−	26.8110i	−0.159589	−	0.159589i
$169$		−	64.8190i		−	0.383544i
$170$	12.7960	−	7.62460i	0.0752705	−	0.0448506i
$171$	−41.7348			−0.244063
$172$	62.2125	−	62.2125i	0.361701	−	0.361701i
$173$	−187.546	−	187.546i	−1.08408	−	1.08408i	−0.996124	−	0.0879593i	$-0.971965\pi$
$173$	−187.546	−	187.546i	−1.08408	−	1.08408i	−0.0879593	−	0.996124i	$-0.528035\pi$
$174$		−	2.32891i		−	0.0133846i
$175$	55.2069	+	185.449i	0.315468	+	1.05971i
$176$	−73.2996			−0.416475
$177$	−0.562953	+	0.562953i	−0.00318052	+	0.00318052i
$178$	−64.0437	−	64.0437i	−0.359796	−	0.359796i
$179$			59.2046i			0.330752i	0.986231	+	0.165376i	$0.0528837\pi$
$179$			59.2046i			0.330752i	−0.986231	+	0.165376i	$0.947116\pi$
$180$	−15.3563	−	25.7718i	−0.0853129	−	0.143176i
$181$	218.953			1.20968			0.604842	−	0.796346i	$-0.293236\pi$
$181$	218.953			1.20968			0.604842	+	0.796346i	$0.293236\pi$
$182$	−78.9980	+	78.9980i	−0.434055	+	0.434055i
$183$	−30.1952	−	30.1952i	−0.165001	−	0.165001i
$184$		−	13.5647i		−	0.0737210i
$185$	−305.012	−	77.2424i	−1.64872	−	0.417527i
$186$	138.345			0.743791
$187$	27.2956	−	27.2956i	0.145966	−	0.145966i
$188$	−51.4335	−	51.4335i	−0.273583	−	0.273583i
$189$		−	40.2165i		−	0.212786i
$190$	−24.1492	+	95.3596i	−0.127101	+	0.501893i
$191$	−24.7100			−0.129371			−0.0646857	−	0.997906i	$-0.520604\pi$
$191$	−24.7100			−0.129371			−0.0646857	+	0.997906i	$0.520604\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	116.701	+	116.701i	0.604667	+	0.604667i	0.941548	−	0.336880i	$-0.109372\pi$
$193$	116.701	+	116.701i	0.604667	+	0.604667i	−0.336880	+	0.941548i	$0.609372\pi$
$194$			98.9308i			0.509953i
$195$	−75.9360	+	45.2471i	−0.389415	+	0.232037i
$196$	−21.8047			−0.111249
$197$	124.625	−	124.625i	0.632612	−	0.632612i	−0.316111	−	0.948722i	$-0.602377\pi$
$197$	124.625	−	124.625i	0.632612	−	0.632612i	0.948722	+	0.316111i	$0.102377\pi$
$198$	−54.9747	−	54.9747i	−0.277650	−	0.277650i
$199$			261.088i			1.31200i	0.754760	+	0.656001i	$0.227753\pi$
$199$			261.088i			1.31200i	−0.754760	+	0.656001i	$0.772247\pi$
$200$	−67.7714	+	20.1751i	−0.338857	+	0.100876i
$201$	79.9113			0.397569
$202$	122.832	−	122.832i	0.608078	−	0.608078i
$203$	−5.20337	−	5.20337i	−0.0256324	−	0.0256324i
$204$			7.29721i			0.0357706i
$205$	114.734	+	192.552i	0.559679	+	0.939280i
$206$	−81.8298			−0.397232
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	−28.8695	−	28.8695i	−0.138796	−	0.138796i
$209$			254.929i			1.21975i
$210$	−91.8903	−	23.2706i	−0.437573	−	0.110813i
$211$	−164.286			−0.778605			−0.389303	−	0.921110i	$-0.627284\pi$
$211$	−164.286			−0.778605			−0.389303	+	0.921110i	$0.627284\pi$
$212$	−35.5577	+	35.5577i	−0.167725	+	0.167725i
$213$	−57.2335	−	57.2335i	−0.268702	−	0.268702i
$214$			248.577i			1.16157i
$215$	53.9975	−	213.224i	0.251151	−	0.991737i
$216$	14.6969			0.0680414
$217$	309.097	−	309.097i	1.42441	−	1.42441i
$218$	−28.6845	−	28.6845i	−0.131580	−	0.131580i
$219$			0.911229i			0.00416086i
$220$	−157.422	+	93.8011i	−0.715553	+	0.426368i
$221$	21.5011			0.0972900
$222$	108.995	−	108.995i	0.490968	−	0.490968i
$223$	−187.046	−	187.046i	−0.838771	−	0.838771i	0.149926	−	0.988697i	$-0.452097\pi$
$223$	−187.046	−	187.046i	−0.838771	−	0.838771i	−0.988697	+	0.149926i	$0.952097\pi$
$224$		−	43.7821i		−	0.195456i
$225$	−65.9599	−	35.6972i	−0.293155	−	0.158654i
$226$	249.413			1.10360
$227$	−218.115	+	218.115i	−0.960860	+	0.960860i	−0.999262	−	0.0384021i	$-0.987773\pi$
$227$	−218.115	+	218.115i	−0.960860	+	0.960860i	0.0384021	+	0.999262i	$0.487773\pi$
$228$	−34.0763	−	34.0763i	−0.149458	−	0.149458i
$229$			358.055i			1.56356i	0.623556	+	0.781779i	$0.285687\pi$
$229$			358.055i			1.56356i	−0.623556	+	0.781779i	$0.714313\pi$
$230$	−17.3586	−	29.1321i	−0.0754722	−	0.126661i
$231$	−245.654			−1.06344
$232$	1.90155	−	1.90155i	0.00819634	−	0.00819634i
$233$	40.1742	+	40.1742i	0.172422	+	0.172422i	0.788042	−	0.615621i	$-0.211095\pi$
$233$	40.1742	+	40.1742i	0.172422	+	0.172422i	−0.615621	+	0.788042i	$0.711095\pi$
$234$		−	43.3043i		−	0.185061i
$235$	−176.280	−	44.6419i	−0.750129	−	0.189965i
$236$	−0.919298			−0.00389533
$237$	−80.2619	+	80.2619i	−0.338658	+	0.338658i
$238$	16.3038	+	16.3038i	0.0685032	+	0.0685032i
$239$			42.3559i			0.177221i	0.996066	+	0.0886106i	$0.0282427\pi$
$239$			42.3559i			0.177221i	−0.996066	+	0.0886106i	$0.971757\pi$
$240$	8.50416	−	33.5809i	0.0354340	−	0.139921i
$241$	138.250			0.573652			0.286826	−	0.957983i	$-0.407400\pi$
$241$	138.250			0.573652			0.286826	+	0.957983i	$0.407400\pi$
$242$	−214.802	+	214.802i	−0.887612	+	0.887612i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	49.3086i		−	0.202084i
$245$	−46.8288	+	27.9034i	−0.191138	+	0.113891i
$246$	−109.808			−0.446372
$247$	−100.405	+	100.405i	−0.406499	+	0.406499i
$248$	112.958	+	112.958i	0.455477	+	0.455477i
$249$			209.305i			0.840582i
$250$	−119.731	+	130.056i	−0.478924	+	0.520223i
$251$	−167.580			−0.667649			−0.333824	−	0.942635i	$-0.608339\pi$
$251$	−167.580			−0.667649			−0.333824	+	0.942635i	$0.608339\pi$
$252$	32.8366	−	32.8366i	0.130304	−	0.130304i
$253$	−62.1428	−	62.1428i	−0.245624	−	0.245624i
$254$		−	36.2391i		−	0.142674i
$255$	9.33819	+	15.6718i	0.0366204	+	0.0614581i
$256$	16.0000			0.0625000
$257$	−137.640	+	137.640i	−0.535565	+	0.535565i	−0.922223	−	0.386658i	$-0.873629\pi$
$257$	−137.640	+	137.640i	−0.535565	+	0.535565i	0.386658	+	0.922223i	$0.373629\pi$
$258$	76.1945	+	76.1945i	0.295327	+	0.295327i
$259$		−	487.043i		−	1.88047i
$260$	−98.9456	−	25.0573i	−0.380560	−	0.0963744i
$261$	2.85233			0.0109285
$262$	88.8228	−	88.8228i	0.339018	−	0.339018i
$263$	−147.620	−	147.620i	−0.561293	−	0.561293i	0.368381	−	0.929675i	$-0.379912\pi$
$263$	−147.620	−	147.620i	−0.561293	−	0.561293i	−0.929675	+	0.368381i	$0.879912\pi$
$264$		−	89.7733i		−	0.340050i
$265$	−30.8624	+	121.868i	−0.116462	+	0.459881i
$266$	−152.270			−0.572443
$267$	78.4372	−	78.4372i	0.293772	−	0.293772i
$268$	65.2473	+	65.2473i	0.243460	+	0.243460i
$269$		−	43.0679i		−	0.160104i	−0.996791	−	0.0800518i	$-0.974491\pi$
$269$		−	43.0679i		−	0.160104i	0.996791	−	0.0800518i	$-0.0255086\pi$
$270$	31.5638	−	18.8076i	0.116903	−	0.0696577i
$271$	−455.005			−1.67898			−0.839492	−	0.543372i	$-0.817147\pi$
$271$	−455.005			−1.67898			−0.839492	+	0.543372i	$0.817147\pi$
$272$	−5.95814	+	5.95814i	−0.0219049	+	0.0219049i
$273$	−96.7524	−	96.7524i	−0.354405	−	0.354405i
$274$			168.969i			0.616674i
$275$	−218.049	+	402.903i	−0.792906	+	1.46510i
$276$	16.6132			0.0601929
$277$	75.2499	−	75.2499i	0.271660	−	0.271660i	−0.558108	−	0.829768i	$-0.688472\pi$
$277$	75.2499	−	75.2499i	0.271660	−	0.271660i	0.829768	+	0.558108i	$0.188472\pi$
$278$	−1.42790	−	1.42790i	−0.00513633	−	0.00513633i
$279$			169.437i			0.607303i
$280$	−56.0277	−	94.0285i	−0.200099	−	0.335816i
$281$	34.5423			0.122926			0.0614632	−	0.998109i	$-0.480423\pi$
$281$	34.5423			0.122926			0.0614632	+	0.998109i	$0.480423\pi$
$282$	62.9930	−	62.9930i	0.223379	−	0.223379i
$283$	84.0695	+	84.0695i	0.297065	+	0.297065i	0.839863	−	0.542798i	$-0.182635\pi$
$283$	84.0695	+	84.0695i	0.297065	+	0.297065i	−0.542798	+	0.839863i	$0.682635\pi$
$284$		−	93.4620i		−	0.329092i
$285$	−116.791	−	29.5766i	−0.409794	−	0.103778i
$286$	−264.515			−0.924879
$287$	−245.337	+	245.337i	−0.854833	+	0.854833i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			284.563i			0.984646i
$290$	1.65045	−	6.51726i	0.00569122	−	0.0224733i
$291$	−121.165			−0.416375
$292$	−0.744015	+	0.744015i	−0.00254800	+	0.00254800i
$293$	358.395	+	358.395i	1.22319	+	1.22319i	0.966491	+	0.256700i	$0.0826354\pi$
$293$	358.395	+	358.395i	1.22319	+	1.22319i	0.256700	+	0.966491i	$0.417365\pi$
$294$		−	26.7052i		−	0.0908341i
$295$	−1.97433	+	1.17642i	−0.00669263	+	0.00398786i
$296$	177.988			0.601310
$297$	67.3300	−	67.3300i	0.226700	−	0.226700i
$298$	−267.416	−	267.416i	−0.897369	−	0.897369i
$299$		−	48.9506i		−	0.163714i
$300$	−24.7094	−	83.0027i	−0.0823647	−	0.276676i
$301$	340.475			1.13115
$302$	160.559	−	160.559i	0.531653	−	0.531653i
$303$	150.438	+	150.438i	0.496494	+	0.496494i
$304$		−	55.6464i		−	0.183047i
$305$	−63.0999	−	105.897i	−0.206885	−	0.347205i
$306$	−8.93722			−0.0292066
$307$	−43.1449	+	43.1449i	−0.140537	+	0.140537i	−0.773875	−	0.633338i	$-0.781684\pi$
$307$	−43.1449	+	43.1449i	−0.140537	+	0.140537i	0.633338	+	0.773875i	$0.281684\pi$
$308$	−200.576	−	200.576i	−0.651220	−	0.651220i
$309$		−	100.221i		−	0.324338i
$310$	387.146	+	98.0424i	1.24886	+	0.316266i
$311$	188.459			0.605976			0.302988	−	0.952994i	$-0.402016\pi$
$311$	188.459			0.605976			0.302988	+	0.952994i	$0.402016\pi$
$312$	35.3578	−	35.3578i	0.113326	−	0.113326i
$313$	−140.266	−	140.266i	−0.448134	−	0.448134i	0.446600	−	0.894734i	$-0.352635\pi$
$313$	−140.266	−	140.266i	−0.448134	−	0.448134i	−0.894734	+	0.446600i	$0.852635\pi$
$314$			186.509i			0.593979i
$315$	28.5006	−	112.542i	0.0904781	−	0.357277i
$316$	−131.067			−0.414770
$317$	−127.294	+	127.294i	−0.401557	+	0.401557i	−0.878782	−	0.477224i	$-0.841643\pi$
$317$	−127.294	+	127.294i	−0.401557	+	0.401557i	0.477224	+	0.878782i	$0.341643\pi$
$318$	−43.5491	−	43.5491i	−0.136947	−	0.136947i
$319$		−	17.4229i		−	0.0546171i
$320$	34.3623	−	20.4751i	0.107382	−	0.0639847i
$321$	−304.443			−0.948421
$322$	37.1181	−	37.1181i	0.115274	−	0.115274i
$323$	20.7218	+	20.7218i	0.0641543	+	0.0641543i
$324$			18.0000i			0.0555556i
$325$	−244.566	+	72.8058i	−0.752510	+	0.224018i
$326$	426.592			1.30857
$327$	35.1312	−	35.1312i	0.107435	−	0.107435i
$328$	−89.6575	−	89.6575i	−0.273346	−	0.273346i
$329$		−	281.484i		−	0.855574i
$330$	−114.882	−	192.801i	−0.348128	−	0.584246i
$331$	432.406			1.30636			0.653182	−	0.757201i	$-0.273434\pi$
$331$	432.406			1.30636			0.653182	+	0.757201i	$0.273434\pi$
$332$	−170.897	+	170.897i	−0.514749	+	0.514749i
$333$	133.491	+	133.491i	0.400873	+	0.400873i
$334$		−	27.9154i		−	0.0835792i
$335$	223.625	+	56.6316i	0.667537	+	0.169049i
$336$	53.6219			0.159589
$337$	251.277	−	251.277i	0.745630	−	0.745630i	−0.228025	−	0.973655i	$-0.573227\pi$
$337$	251.277	−	251.277i	0.745630	−	0.745630i	0.973655	+	0.228025i	$0.0732269\pi$
$338$	64.8190	+	64.8190i	0.191772	+	0.191772i
$339$			305.467i			0.901083i
$340$	−5.17138	+	20.4206i	−0.0152100	+	0.0600605i
$341$	1034.97			3.03512
$342$	41.7348	−	41.7348i	0.122032	−	0.122032i
$343$	208.500	+	208.500i	0.607870	+	0.607870i
$344$			124.425i			0.361701i
$345$	35.6794	−	21.2599i	0.103418	−	0.0616228i
$346$	375.093			1.08408
$347$	151.537	−	151.537i	0.436707	−	0.436707i	−0.454195	−	0.890902i	$-0.650073\pi$
$347$	151.537	−	151.537i	0.436707	−	0.436707i	0.890902	+	0.454195i	$0.150073\pi$
$348$	2.32891	+	2.32891i	0.00669228	+	0.00669228i
$349$		−	642.693i		−	1.84153i	−0.390120	−	0.920764i	$-0.627566\pi$
$349$		−	642.693i		−	1.84153i	0.390120	−	0.920764i	$-0.372434\pi$
$350$	−240.655	−	130.242i	−0.687587	−	0.372119i
$351$	53.0367			0.151102
$352$	73.2996	−	73.2996i	0.208238	−	0.208238i
$353$	412.979	+	412.979i	1.16991	+	1.16991i	0.982230	+	0.187681i	$0.0600973\pi$
$353$	412.979	+	412.979i	1.16991	+	1.16991i	0.187681	+	0.982230i	$0.439903\pi$
$354$		−	1.12591i		−	0.00318052i
$355$	−119.603	−	200.723i	−0.336909	−	0.565418i
$356$	128.087			0.359796
$357$	−19.9680	+	19.9680i	−0.0559326	+	0.0559326i
$358$	−59.2046	−	59.2046i	−0.165376	−	0.165376i
$359$			149.819i			0.417324i	0.977988	+	0.208662i	$0.0669109\pi$
$359$			149.819i			0.417324i	−0.977988	+	0.208662i	$0.933089\pi$
$360$	41.1281	+	10.4154i	0.114245	+	0.0289317i
$361$	167.467			0.463898
$362$	−218.953	+	218.953i	−0.604842	+	0.604842i
$363$	−263.078	−	263.078i	−0.724732	−	0.724732i
$364$		−	157.996i		−	0.434055i
$365$	−0.645770	+	2.54999i	−0.00176923	+	0.00698628i
$366$	60.3905			0.165001
$367$	−257.690	+	257.690i	−0.702152	+	0.702152i	−0.964872	−	0.262720i	$-0.915380\pi$
$367$	−257.690	+	257.690i	−0.702152	+	0.702152i	0.262720	+	0.964872i	$0.415380\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	134.486i		−	0.364461i
$370$	382.255	−	227.770i	1.03312	−	0.615594i
$371$	−194.599			−0.524526
$372$	−138.345	+	138.345i	−0.371895	+	0.371895i
$373$	−274.503	−	274.503i	−0.735934	−	0.735934i	0.235854	−	0.971788i	$-0.424211\pi$
$373$	−274.503	−	274.503i	−0.735934	−	0.735934i	−0.971788	+	0.235854i	$0.924211\pi$
$374$			54.5912i			0.145966i
$375$	−159.285	−	146.640i	−0.424760	−	0.391040i
$376$	102.867			0.273583
$377$	6.86210	−	6.86210i	0.0182019	−	0.0182019i
$378$	40.2165	+	40.2165i	0.106393	+	0.106393i
$379$			543.361i			1.43367i	0.697243	+	0.716834i	$0.254410\pi$
$379$			543.361i			1.43367i	−0.697243	+	0.716834i	$0.745590\pi$
$380$	−71.2104	−	119.509i	−0.187396	−	0.314497i
$381$	44.3837			0.116493
$382$	24.7100	−	24.7100i	0.0646857	−	0.0646857i
$383$	322.889	+	322.889i	0.843053	+	0.843053i	0.989255	−	0.146202i	$-0.0467049\pi$
$383$	322.889	+	322.889i	0.843053	+	0.843053i	−0.146202	+	0.989255i	$0.546705\pi$
$384$			19.5959i			0.0510310i
$385$	−687.442	−	174.090i	−1.78556	−	0.452182i
$386$	−233.402			−0.604667
$387$	−93.3188	+	93.3188i	−0.241134	+	0.241134i
$388$	−98.9308	−	98.9308i	−0.254976	−	0.254976i
$389$		−	720.417i		−	1.85197i	−0.377557	−	0.925986i	$-0.623236\pi$
$389$		−	720.417i		−	1.85197i	0.377557	−	0.925986i	$-0.376764\pi$
$390$	30.6889	−	121.183i	0.0786894	−	0.310726i
$391$	−10.1025			−0.0258377
$392$	21.8047	−	21.8047i	0.0556243	−	0.0556243i
$393$	108.785	+	108.785i	0.276807	+	0.276807i
$394$			249.249i			0.632612i
$395$	−281.486	+	167.726i	−0.712623	+	0.424622i
$396$	109.949			0.277650
$397$	139.692	−	139.692i	0.351869	−	0.351869i	−0.508936	−	0.860804i	$-0.669961\pi$
$397$	139.692	−	139.692i	0.351869	−	0.351869i	0.860804	+	0.508936i	$0.169961\pi$
$398$	−261.088	−	261.088i	−0.656001	−	0.656001i
$399$		−	186.492i		−	0.467398i
$400$	47.5963	−	87.9465i	0.118991	−	0.219866i
$401$	410.867			1.02461			0.512303	−	0.858805i	$-0.328793\pi$
$401$	410.867			1.02461			0.512303	+	0.858805i	$0.328793\pi$
$402$	−79.9113	+	79.9113i	−0.198784	+	0.198784i
$403$	407.631	+	407.631i	1.01149	+	1.01149i
$404$			245.664i			0.608078i
$405$	23.0345	+	38.6576i	0.0568753	+	0.0954509i
$406$	10.4067			0.0256324
$407$	815.402	−	815.402i	2.00345	−	2.00345i
$408$	−7.29721	−	7.29721i	−0.0178853	−	0.0178853i
$409$		−	185.429i		−	0.453372i	−0.973968	−	0.226686i	$-0.927211\pi$
$409$		−	185.429i		−	0.453372i	0.973968	−	0.226686i	$-0.0727891\pi$
$410$	−307.287	−	77.8184i	−0.749480	−	0.189801i
$411$	−206.943			−0.503512
$412$	81.8298	−	81.8298i	0.198616	−	0.198616i
$413$	−2.51555	−	2.51555i	−0.00609092	−	0.00609092i
$414$			20.3470i			0.0491473i
$415$	−148.330	+	585.721i	−0.357422	+	1.41138i
$416$	57.7390			0.138796
$417$	1.74881	−	1.74881i	0.00419379	−	0.00419379i
$418$	−254.929	−	254.929i	−0.609877	−	0.609877i
$419$		−	203.166i		−	0.484884i	−0.970166	−	0.242442i	$-0.922052\pi$
$419$		−	203.166i		−	0.484884i	0.970166	−	0.242442i	$-0.0779484\pi$
$420$	115.161	−	68.6197i	0.274193	−	0.163380i
$421$	−622.636			−1.47895			−0.739473	−	0.673187i	$-0.764925\pi$
$421$	−622.636			−1.47895			−0.739473	+	0.673187i	$0.764925\pi$
$422$	164.286	−	164.286i	0.389303	−	0.389303i
$423$	77.1503	+	77.1503i	0.182388	+	0.182388i
$424$		−	71.1154i		−	0.167725i
$425$	15.0258	+	50.4740i	0.0353548	+	0.118762i
$426$	114.467			0.268702
$427$	134.927	−	134.927i	0.315989	−	0.315989i
$428$	−248.577	−	248.577i	−0.580787	−	0.580787i
$429$		−	323.964i		−	0.755161i
$430$	159.226	+	267.221i	0.370293	+	0.621444i
$431$	645.267			1.49714			0.748570	−	0.663056i	$-0.230741\pi$
$431$	645.267			1.49714			0.748570	+	0.663056i	$0.230741\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	332.543	+	332.543i	0.767998	+	0.767998i	0.977754	−	0.209756i	$-0.0672669\pi$
$433$	332.543	+	332.543i	0.767998	+	0.767998i	−0.209756	+	0.977754i	$0.567267\pi$
$434$			618.194i			1.42441i
$435$	7.98198	+	2.02139i	0.0183494	+	0.00464686i
$436$	57.3690			0.131580
$437$	47.1765	−	47.1765i	0.107955	−	0.107955i
$438$	−0.911229	−	0.911229i	−0.00208043	−	0.00208043i
$439$			42.1637i			0.0960448i	0.998846	+	0.0480224i	$0.0152919\pi$
$439$			42.1637i			0.0960448i	−0.998846	+	0.0480224i	$0.984708\pi$
$440$	63.6205	−	251.223i	0.144592	−	0.570961i
$441$	32.7071			0.0741657
$442$	−21.5011	+	21.5011i	−0.0486450	+	0.0486450i
$443$	−18.6195	−	18.6195i	−0.0420305	−	0.0420305i	0.685779	−	0.727810i	$-0.259462\pi$
$443$	−18.6195	−	18.6195i	−0.0420305	−	0.0420305i	−0.727810	+	0.685779i	$0.759462\pi$
$444$			217.990i			0.490968i
$445$	275.086	−	163.913i	0.618172	−	0.368343i
$446$	374.092			0.838771
$447$	327.517	−	327.517i	0.732699	−	0.732699i
$448$	43.7821	+	43.7821i	0.0977280	+	0.0977280i
$449$			256.938i			0.572245i	0.958193	+	0.286123i	$0.0923665\pi$
$449$			256.938i			0.572245i	−0.958193	+	0.286123i	$0.907633\pi$
$450$	101.657	−	30.2627i	0.225905	−	0.0672505i
$451$	−821.482			−1.82147
$452$	−249.413	+	249.413i	−0.551798	+	0.551798i
$453$	196.644	+	196.644i	0.434093	+	0.434093i
$454$		−	436.231i		−	0.960860i
$455$	−202.187	−	339.320i	−0.444366	−	0.745757i
$456$	68.1527			0.149458
$457$	−343.079	+	343.079i	−0.750719	+	0.750719i	−0.974613	−	0.223894i	$-0.928123\pi$
$457$	−343.079	+	343.079i	−0.750719	+	0.750719i	0.223894	+	0.974613i	$0.428123\pi$
$458$	−358.055	−	358.055i	−0.781779	−	0.781779i
$459$		−	10.9458i		−	0.0238471i
$460$	46.4907	+	11.7735i	0.101067	+	0.0255945i
$461$	−518.066			−1.12379			−0.561893	−	0.827210i	$-0.689927\pi$
$461$	−518.066			−1.12379			−0.561893	+	0.827210i	$0.689927\pi$
$462$	245.654	−	245.654i	0.531719	−	0.531719i
$463$	581.305	+	581.305i	1.25552	+	1.25552i	0.953211	+	0.302307i	$0.0977567\pi$
$463$	581.305	+	581.305i	1.25552	+	1.25552i	0.302307	+	0.953211i	$0.402243\pi$
$464$			3.80310i			0.00819634i
$465$	−120.077	+	474.156i	−0.258230	+	1.01969i
$466$	−80.3485			−0.172422
$467$	−175.982	+	175.982i	−0.376835	+	0.376835i	−0.869959	−	0.493124i	$-0.835855\pi$
$467$	−175.982	+	175.982i	−0.376835	+	0.376835i	0.493124	+	0.869959i	$0.335855\pi$
$468$	43.3043	+	43.3043i	0.0925305	+	0.0925305i
$469$			357.084i			0.761372i
$470$	220.922	−	131.638i	0.470047	−	0.280082i
$471$	−228.426			−0.484982
$472$	0.919298	−	0.919298i	0.00194766	−	0.00194766i
$473$	570.019	+	570.019i	1.20511	+	1.20511i
$474$		−	160.524i		−	0.338658i
$475$	−305.869	−	165.535i	−0.643936	−	0.348495i
$476$	−32.6075			−0.0685032
$477$	53.3366	−	53.3366i	0.111817	−	0.111817i
$478$	−42.3559	−	42.3559i	−0.0886106	−	0.0886106i
$479$		−	92.7211i		−	0.193572i	−0.995305	−	0.0967861i	$-0.969144\pi$
$479$		−	92.7211i		−	0.193572i	0.995305	−	0.0967861i	$-0.0308563\pi$
$480$	25.0768	+	42.0851i	0.0522433	+	0.0876773i
$481$	642.302			1.33535
$482$	−138.250	+	138.250i	−0.286826	+	0.286826i
$483$	45.4602	+	45.4602i	0.0941205	+	0.0941205i
$484$		−	429.604i		−	0.887612i
$485$	−339.069	−	85.8672i	−0.699112	−	0.177046i
$486$	−22.0454			−0.0453609
$487$	−359.308	+	359.308i	−0.737800	+	0.737800i	−0.972152	−	0.234352i	$-0.924703\pi$
$487$	−359.308	+	359.308i	−0.737800	+	0.737800i	0.234352	+	0.972152i	$0.424703\pi$
$488$	49.3086	+	49.3086i	0.101042	+	0.101042i
$489$			522.467i			1.06844i
$490$	18.9255	−	74.7322i	0.0386234	−	0.152515i
$491$	215.844			0.439601			0.219801	−	0.975545i	$-0.429459\pi$
$491$	215.844			0.439601			0.219801	+	0.975545i	$0.429459\pi$
$492$	109.808	−	109.808i	0.223186	−	0.223186i
$493$	−1.41621	−	1.41621i	−0.00287264	−	0.00287264i
$494$		−	200.811i		−	0.406499i
$495$	236.132	−	140.702i	0.477035	−	0.284246i
$496$	−225.917			−0.455477
$497$	255.748	−	255.748i	0.514583	−	0.514583i
$498$	−209.305	−	209.305i	−0.420291	−	0.420291i
$499$			236.340i			0.473626i	0.971555	+	0.236813i	$0.0761029\pi$
$499$			236.340i			0.473626i	−0.971555	+	0.236813i	$0.923897\pi$
$500$	−10.3247	−	249.787i	−0.0206494	−	0.499573i
$501$	34.1893			0.0682421
$502$	167.580	−	167.580i	0.333824	−	0.333824i
$503$	158.114	+	158.114i	0.314342	+	0.314342i	0.846589	−	0.532247i	$-0.178652\pi$
$503$	158.114	+	158.114i	0.314342	+	0.314342i	−0.532247	+	0.846589i	$0.678652\pi$
$504$			65.6732i			0.130304i
$505$	314.374	+	527.599i	0.622523	+	1.04475i
$506$	124.286			0.245624
$507$	−79.3867	+	79.3867i	−0.156581	+	0.156581i
$508$	36.2391	+	36.2391i	0.0713368	+	0.0713368i
$509$		−	895.884i		−	1.76009i	−0.474894	−	0.880043i	$-0.657514\pi$
$509$		−	895.884i		−	1.76009i	0.474894	−	0.880043i	$-0.342486\pi$
$510$	−25.0100	−	6.33363i	−0.0490392	−	0.0124189i
$511$	−4.07182			−0.00796834
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	51.1145	+	51.1145i	0.0996384	+	0.0996384i
$514$		−	275.281i		−	0.535565i
$515$	71.0243	−	280.458i	0.137911	−	0.544579i
$516$	−152.389			−0.295327
$517$	471.257	−	471.257i	0.911523	−	0.911523i
$518$	487.043	+	487.043i	0.940237	+	0.940237i
$519$			459.393i			0.885150i
$520$	124.003	−	73.8883i	0.238467	−	0.142093i
$521$	624.757			1.19915			0.599575	−	0.800319i	$-0.295336\pi$
$521$	624.757			1.19915			0.599575	+	0.800319i	$0.295336\pi$
$522$	−2.85233	+	2.85233i	−0.00546423	+	0.00546423i
$523$	−604.436	−	604.436i	−1.15571	−	1.15571i	−0.985389	−	0.170321i	$-0.945520\pi$
$523$	−604.436	−	604.436i	−1.15571	−	1.15571i	−0.170321	−	0.985389i	$-0.554480\pi$
$524$			177.646i			0.339018i
$525$	159.513	−	294.742i	0.303834	−	0.561413i
$526$	295.240			0.561293
$527$	84.1277	−	84.1277i	0.159635	−	0.159635i
$528$	89.7733	+	89.7733i	0.170025	+	0.170025i
$529$			23.0000i			0.0434783i
$530$	−91.0060	−	152.731i	−0.171709	−	0.288171i
$531$	1.37895			0.00259689
$532$	152.270	−	152.270i	0.286222	−	0.286222i
$533$	−323.546	−	323.546i	−0.607028	−	0.607028i
$534$			156.874i			0.293772i
$535$	−851.957	−	215.753i	−1.59244	−	0.403276i
$536$	−130.495			−0.243460
$537$	72.5105	−	72.5105i	0.135029	−	0.135029i
$538$	43.0679	+	43.0679i	0.0800518	+	0.0800518i
$539$		−	199.785i		−	0.370658i
$540$	−12.7562	+	50.3714i	−0.0236227	+	0.0932804i
$541$	1001.87			1.85188			0.925938	−	0.377675i	$-0.123276\pi$
$541$	1001.87			1.85188			0.925938	+	0.377675i	$0.123276\pi$
$542$	455.005	−	455.005i	0.839492	−	0.839492i
$543$	−268.161	−	268.161i	−0.493851	−	0.493851i
$544$		−	11.9163i		−	0.0219049i
$545$	123.208	−	73.4148i	0.226070	−	0.134706i
$546$	193.505			0.354405
$547$	408.706	−	408.706i	0.747177	−	0.747177i	−0.226771	−	0.973948i	$-0.572817\pi$
$547$	408.706	−	408.706i	0.747177	−	0.747177i	0.973948	+	0.226771i	$0.0728170\pi$
$548$	−168.969	−	168.969i	−0.308337	−	0.308337i
$549$			73.9629i			0.134723i
$550$	−184.854	−	620.952i	−0.336098	−	1.12900i
$551$	13.2268			0.0240051
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	−358.650	−	358.650i	−0.648554	−	0.648554i
$554$			150.500i			0.271660i
$555$	278.960	+	468.165i	0.502631	+	0.843540i
$556$	2.85580			0.00513633
$557$	749.003	−	749.003i	1.34471	−	1.34471i	0.453402	−	0.891306i	$-0.350210\pi$
$557$	749.003	−	749.003i	1.34471	−	1.34471i	0.891306	−	0.453402i	$-0.149790\pi$
$558$	−169.437	−	169.437i	−0.303651	−	0.303651i
$559$			449.011i			0.803240i
$560$	150.056	+	38.0008i	0.267958	+	0.0678586i
$561$	−66.8603			−0.119181
$562$	−34.5423	+	34.5423i	−0.0614632	+	0.0614632i
$563$	−428.420	−	428.420i	−0.760959	−	0.760959i	0.215537	−	0.976496i	$-0.430850\pi$
$563$	−428.420	−	428.420i	−0.760959	−	0.760959i	−0.976496	+	0.215537i	$0.930850\pi$
$564$			125.986i			0.223379i
$565$	−216.478	+	854.823i	−0.383148	+	1.51296i
$566$	−168.139			−0.297065
$567$	−49.2549	+	49.2549i	−0.0868693	+	0.0868693i
$568$	93.4620	+	93.4620i	0.164546	+	0.164546i
$569$			800.840i			1.40745i	0.710472	+	0.703725i	$0.248481\pi$
$569$			800.840i			1.40745i	−0.710472	+	0.703725i	$0.751519\pi$
$570$	146.368	−	87.2145i	0.256786	−	0.153008i
$571$	675.867			1.18366			0.591828	−	0.806064i	$-0.298407\pi$
$571$	675.867			1.18366			0.591828	+	0.806064i	$0.298407\pi$
$572$	264.515	−	264.515i	0.462440	−	0.462440i
$573$	30.2634	+	30.2634i	0.0528157	+	0.0528157i
$574$		−	490.674i		−	0.854833i
$575$	114.912	−	34.2086i	0.199847	−	0.0594932i
$576$	−24.0000			−0.0416667
$577$	−639.279	+	639.279i	−1.10794	+	1.10794i	−0.114515	+	0.993422i	$0.536531\pi$
$577$	−639.279	+	639.279i	−1.10794	+	1.10794i	−0.993422	+	0.114515i	$0.963469\pi$
$578$	−284.563	−	284.563i	−0.492323	−	0.492323i
$579$		−	285.857i		−	0.493709i
$580$	4.86681	+	8.16771i	0.00839104	+	0.0140823i
$581$	−935.278			−1.60977
$582$	121.165	−	121.165i	0.208187	−	0.208187i
$583$	−325.796	−	325.796i	−0.558826	−	0.558826i
$584$		−	1.48803i		−	0.00254800i
$585$	148.418	+	37.5860i	0.253707	+	0.0642496i
$586$	−716.790			−1.22319
$587$	−578.249	+	578.249i	−0.985092	+	0.985092i	−0.999890	−	0.0147984i	$-0.995289\pi$
$587$	−578.249	+	578.249i	−0.985092	+	0.985092i	0.0147984	+	0.999890i	$0.495289\pi$
$588$	26.7052	+	26.7052i	0.0454170	+	0.0454170i
$589$			785.715i			1.33398i
$590$	0.797906	−	3.15075i	0.00135238	−	0.00534025i
$591$	−305.267			−0.516525
$592$	−177.988	+	177.988i	−0.300655	+	0.300655i
$593$	118.071	+	118.071i	0.199109	+	0.199109i	0.799618	−	0.600509i	$-0.205035\pi$
$593$	118.071	+	118.071i	0.199109	+	0.199109i	−0.600509	+	0.799618i	$0.705035\pi$
$594$			134.660i			0.226700i
$595$	−70.0294	+	41.7277i	−0.117697	+	0.0701305i
$596$	534.832			0.897369
$597$	319.767	−	319.767i	0.535623	−	0.535623i
$598$	48.9506	+	48.9506i	0.0818572	+	0.0818572i
$599$			262.366i			0.438006i	0.975724	+	0.219003i	$0.0702805\pi$
$599$			262.366i			0.438006i	−0.975724	+	0.219003i	$0.929720\pi$
$600$	107.712	+	58.2933i	0.179520	+	0.0971555i
$601$	−409.994			−0.682186			−0.341093	−	0.940030i	$-0.610797\pi$
$601$	−409.994			−0.682186			−0.341093	+	0.940030i	$0.610797\pi$
$602$	−340.475	+	340.475i	−0.565573	+	0.565573i
$603$	−97.8710	−	97.8710i	−0.162307	−	0.162307i
$604$			321.118i			0.531653i
$605$	−549.762	−	922.637i	−0.908697	−	1.52502i
$606$	−300.875			−0.496494
$607$	590.141	−	590.141i	0.972226	−	0.972226i	−0.0273990	−	0.999625i	$-0.508722\pi$
$607$	590.141	−	590.141i	0.972226	−	0.972226i	0.999625	+	0.0273990i	$0.00872246\pi$
$608$	55.6464	+	55.6464i	0.0915237	+	0.0915237i
$609$			12.7456i			0.0209287i
$610$	168.997	+	42.7975i	0.277045	+	0.0701598i
$611$	371.215			0.607554
$612$	8.93722	−	8.93722i	0.0146033	−	0.0146033i
$613$	−29.4751	−	29.4751i	−0.0480834	−	0.0480834i	0.682656	−	0.730740i	$-0.260825\pi$
$613$	−29.4751	−	29.4751i	−0.0480834	−	0.0480834i	−0.730740	+	0.682656i	$0.760825\pi$
$614$		−	86.2897i		−	0.140537i
$615$	95.3077	−	376.348i	0.154972	−	0.611947i
$616$	401.152			0.651220
$617$	−97.0052	+	97.0052i	−0.157221	+	0.157221i	−0.781334	−	0.624113i	$-0.785460\pi$
$617$	−97.0052	+	97.0052i	−0.157221	+	0.157221i	0.624113	+	0.781334i	$0.285460\pi$
$618$	100.221	+	100.221i	0.162169	+	0.162169i
$619$		−	464.849i		−	0.750968i	−0.926829	−	0.375484i	$-0.877476\pi$
$619$		−	464.849i		−	0.750968i	0.926829	−	0.375484i	$-0.122524\pi$
$620$	−485.189	+	289.104i	−0.782563	+	0.466297i
$621$	−24.9199			−0.0401286
$622$	−188.459	+	188.459i	−0.302988	+	0.302988i
$623$	350.496	+	350.496i	0.562594	+	0.562594i
$624$			70.7156i			0.113326i
$625$	−341.824	−	523.241i	−0.546919	−	0.837186i
$626$	280.532			0.448134
$627$	312.223	−	312.223i	0.497963	−	0.497963i
$628$	−186.509	−	186.509i	−0.296989	−	0.296989i
$629$		−	132.560i		−	0.210747i
$630$	84.0416	+	141.043i	0.133399	+	0.223877i
$631$	−1003.19			−1.58984			−0.794920	−	0.606714i	$-0.792487\pi$
$631$	−1003.19			−1.58984			−0.794920	+	0.606714i	$0.792487\pi$
$632$	131.067	−	131.067i	0.207385	−	0.207385i
$633$	201.208	+	201.208i	0.317864	+	0.317864i
$634$		−	254.587i		−	0.401557i
$635$	124.204	+	31.4538i	0.195596	+	0.0495336i
$636$	87.0982			0.136947
$637$	78.6864	−	78.6864i	0.123527	−	0.123527i
$638$	17.4229	+	17.4229i	0.0273086	+	0.0273086i
$639$			140.193i			0.219394i
$640$	−13.8872	+	54.8374i	−0.0216988	+	0.0856835i
$641$	−118.638			−0.185082			−0.0925410	−	0.995709i	$-0.529499\pi$
$641$	−118.638			−0.185082			−0.0925410	+	0.995709i	$0.529499\pi$
$642$	304.443	−	304.443i	0.474210	−	0.474210i
$643$	−790.836	−	790.836i	−1.22992	−	1.22992i	−0.963995	−	0.265920i	$-0.914324\pi$
$643$	−790.836	−	790.836i	−1.22992	−	1.22992i	−0.265920	−	0.963995i	$-0.585676\pi$
$644$			74.2362i			0.115274i
$645$	−327.278	+	195.011i	−0.507407	+	0.302343i
$646$	−41.4437			−0.0641543
$647$	−672.665	+	672.665i	−1.03967	+	1.03967i	−0.0404870	+	0.999180i	$0.512891\pi$
$647$	−672.665	+	672.665i	−1.03967	+	1.03967i	−0.999180	+	0.0404870i	$0.987109\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	8.42302i		−	0.0129785i
$650$	171.760	−	317.372i	0.264246	−	0.488264i
$651$	−757.130			−1.16303
$652$	−426.592	+	426.592i	−0.654283	+	0.654283i
$653$	702.904	+	702.904i	1.07642	+	1.07642i	0.996827	+	0.0795956i	$0.0253629\pi$
$653$	702.904	+	702.904i	1.07642	+	1.07642i	0.0795956	+	0.996827i	$0.474637\pi$
$654$			70.2624i			0.107435i
$655$	227.332	+	381.520i	0.347072	+	0.582473i
$656$	179.315			0.273346
$657$	1.11602	−	1.11602i	0.00169866	−	0.00169866i
$658$	281.484	+	281.484i	0.427787	+	0.427787i
$659$		−	1097.53i		−	1.66545i	−0.553683	−	0.832727i	$-0.686778\pi$
$659$		−	1097.53i		−	1.66545i	0.553683	−	0.832727i	$-0.313222\pi$
$660$	307.684	+	77.9189i	0.466187	+	0.118059i
$661$	−620.423			−0.938613			−0.469306	−	0.883035i	$-0.655496\pi$
$661$	−620.423			−0.938613			−0.469306	+	0.883035i	$0.655496\pi$
$662$	−432.406	+	432.406i	−0.653182	+	0.653182i
$663$	−26.3333	−	26.3333i	−0.0397185	−	0.0397185i
$664$		−	341.793i		−	0.514749i
$665$	132.163	−	521.881i	0.198741	−	0.784783i
$666$	−266.982			−0.400873
$667$	−3.22424	+	3.22424i	−0.00483394	+	0.00483394i
$668$	27.9154	+	27.9154i	0.0417896	+	0.0417896i
$669$			458.167i			0.684854i
$670$	−280.256	+	166.993i	−0.418293	+	0.249244i
$671$	451.788			0.673305
$672$	−53.6219	+	53.6219i	−0.0797946	+	0.0797946i
$673$	−512.487	−	512.487i	−0.761496	−	0.761496i	0.215097	−	0.976593i	$-0.430993\pi$
$673$	−512.487	−	512.487i	−0.761496	−	0.761496i	−0.976593	+	0.215097i	$0.930993\pi$
$674$			502.555i			0.745630i
$675$	37.0641	+	124.504i	0.0549098	+	0.184450i
$676$	−129.638			−0.191772
$677$	−141.059	+	141.059i	−0.208359	+	0.208359i	−0.803570	−	0.595211i	$-0.797069\pi$
$677$	−141.059	+	141.059i	−0.208359	+	0.208359i	0.595211	+	0.803570i	$0.297069\pi$
$678$	−305.467	−	305.467i	−0.450542	−	0.450542i
$679$		−	541.425i		−	0.797386i
$680$	−15.2492	−	25.5920i	−0.0224253	−	0.0376352i
$681$	534.271			0.784539
$682$	−1034.97	+	1034.97i	−1.51756	+	1.51756i
$683$	−606.606	−	606.606i	−0.888150	−	0.888150i	0.106196	−	0.994345i	$-0.466133\pi$
$683$	−606.606	−	606.606i	−0.888150	−	0.888150i	−0.994345	+	0.106196i	$0.966133\pi$
$684$			83.4696i			0.122032i
$685$	−579.113	−	146.657i	−0.845420	−	0.214097i
$686$	−416.999			−0.607870
$687$	438.526	−	438.526i	0.638320	−	0.638320i
$688$	−124.425	−	124.425i	−0.180850	−	0.180850i
$689$		−	256.633i		−	0.372472i
$690$	−14.4195	+	56.9392i	−0.0208978	+	0.0825206i
$691$	646.171			0.935125			0.467563	−	0.883960i	$-0.345132\pi$
$691$	646.171			0.935125			0.467563	+	0.883960i	$0.345132\pi$
$692$	−375.093	+	375.093i	−0.542042	+	0.542042i
$693$	300.864	+	300.864i	0.434147	+	0.434147i
$694$			303.075i			0.436707i
$695$	6.13324	−	3.65455i	0.00882481	−	0.00525834i
$696$	−4.65783			−0.00669228
$697$	−66.7740	+	66.7740i	−0.0958020	+	0.0958020i
$698$	642.693	+	642.693i	0.920764	+	0.920764i
$699$		−	98.4064i		−	0.140782i
$700$	370.897	−	110.414i	0.529853	−	0.157734i
$701$	−439.029			−0.626290			−0.313145	−	0.949705i	$-0.601383\pi$
$701$	−439.029			−0.626290			−0.313145	+	0.949705i	$0.601383\pi$
$702$	−53.0367	+	53.0367i	−0.0755508	+	0.0755508i
$703$	619.024	+	619.024i	0.880546	+	0.880546i
$704$			146.599i			0.208238i
$705$	161.223	+	270.573i	0.228686	+	0.383792i
$706$	−825.957			−1.16991
$707$	−672.230	+	672.230i	−0.950820	+	0.950820i
$708$	1.12591	+	1.12591i	0.00159026	+	0.00159026i
$709$		−	101.093i		−	0.142585i	−0.997455	−	0.0712927i	$-0.977288\pi$
$709$		−	101.093i		−	0.142585i	0.997455	−	0.0712927i	$-0.0227124\pi$
$710$	320.326	+	81.1205i	0.451163	+	0.114254i
$711$	196.601			0.276513
$712$	−128.087	+	128.087i	−0.179898	+	0.179898i
$713$	−191.530	−	191.530i	−0.268626	−	0.268626i
$714$		−	39.9359i		−	0.0559326i
$715$	229.587	−	906.584i	0.321100	−	1.26795i
$716$	118.409			0.165376
$717$	51.8751	−	51.8751i	0.0723502	−	0.0723502i
$718$	−149.819	−	149.819i	−0.208662	−	0.208662i
$719$			1336.70i			1.85911i	0.368680	+	0.929556i	$0.379810\pi$
$719$			1336.70i			1.85911i	−0.368680	+	0.929556i	$0.620190\pi$
$720$	−51.5435	+	30.7127i	−0.0715882	+	0.0426565i
$721$	447.835			0.621131
$722$	−167.467	+	167.467i	−0.231949	+	0.231949i
$723$	−169.321	−	169.321i	−0.234192	−	0.234192i
$724$		−	437.906i		−	0.604842i
$725$	20.9043	+	11.3133i	0.0288336	+	0.0156046i
$726$	526.155			0.724732
$727$	−512.751	+	512.751i	−0.705297	+	0.705297i	−0.965542	−	0.260246i	$-0.916196\pi$
$727$	−512.751	+	512.751i	−0.705297	+	0.705297i	0.260246	+	0.965542i	$0.416196\pi$
$728$	157.996	+	157.996i	0.217028	+	0.217028i
$729$		−	27.0000i		−	0.0370370i
$730$	−1.90422	−	3.19576i	−0.00260852	−	0.00437776i
$731$	92.6678			0.126769
$732$	−60.3905	+	60.3905i	−0.0825006	+	0.0825006i
$733$	163.456	+	163.456i	0.222995	+	0.222995i	0.809759	−	0.586763i	$-0.199598\pi$
$733$	163.456	+	163.456i	0.222995	+	0.222995i	−0.586763	+	0.809759i	$0.699598\pi$
$734$		−	515.380i		−	0.702152i
$735$	91.5279	+	23.1789i	0.124528	+	0.0315359i
$736$	−27.1293			−0.0368605
$737$	−597.826	+	597.826i	−0.811161	+	0.811161i
$738$	134.486	+	134.486i	0.182231	+	0.182231i
$739$		−	622.996i		−	0.843026i	−0.906822	−	0.421513i	$-0.861499\pi$
$739$		−	622.996i		−	0.843026i	0.906822	−	0.421513i	$-0.138501\pi$
$740$	−154.485	+	610.025i	−0.208763	+	0.824358i
$741$	245.942			0.331905
$742$	194.599	−	194.599i	0.262263	−	0.262263i
$743$	499.375	+	499.375i	0.672106	+	0.672106i	0.958201	−	0.286095i	$-0.0923572\pi$
$743$	499.375	+	499.375i	0.672106	+	0.672106i	−0.286095	+	0.958201i	$0.592357\pi$
$744$		−	276.690i		−	0.371895i
$745$	1148.63	−	684.422i	1.54179	−	0.918687i
$746$	549.007			0.735934
$747$	256.345	−	256.345i	0.343166	−	0.343166i
$748$	−54.5912	−	54.5912i	−0.0729829	−	0.0729829i
$749$		−	1360.40i		−	1.81629i
$750$	305.925	−	12.6451i	0.407900	−	0.0168602i
$751$	−1496.23			−1.99231			−0.996157	−	0.0875833i	$-0.972086\pi$
$751$	−1496.23			−1.99231			−0.996157	+	0.0875833i	$0.972086\pi$
$752$	−102.867	+	102.867i	−0.136791	+	0.136791i
$753$	205.243	+	205.243i	0.272566	+	0.272566i
$754$			13.7242i			0.0182019i
$755$	410.933	+	689.648i	0.544282	+	0.913442i
$756$	−80.4329			−0.106393
$757$	−810.088	+	810.088i	−1.07013	+	1.07013i	−0.0727809	+	0.997348i	$0.523187\pi$
$757$	−810.088	+	810.088i	−1.07013	+	1.07013i	−0.997348	+	0.0727809i	$0.976813\pi$
$758$	−543.361	−	543.361i	−0.716834	−	0.716834i
$759$			152.218i			0.200551i
$760$	190.719	+	48.2984i	0.250946	+	0.0635506i
$761$	374.404			0.491989			0.245995	−	0.969271i	$-0.420885\pi$
$761$	374.404			0.491989			0.245995	+	0.969271i	$0.420885\pi$
$762$	−44.3837	+	44.3837i	−0.0582463	+	0.0582463i
$763$	156.984	+	156.984i	0.205745	+	0.205745i
$764$			49.4199i			0.0646857i
$765$	7.75708	−	30.6309i	0.0101400	−	0.0400404i
$766$	−645.779			−0.843053
$767$	3.31746	−	3.31746i	0.00432524	−	0.00432524i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			1015.53i			1.32058i	0.751009	+	0.660291i	$0.229567\pi$
$769$			1015.53i			1.32058i	−0.751009	+	0.660291i	$0.770433\pi$
$770$	861.532	−	513.351i	1.11887	−	0.666690i
$771$	337.149			0.437287
$772$	233.402	−	233.402i	0.302334	−	0.302334i
$773$	477.540	+	477.540i	0.617774	+	0.617774i	0.944960	−	0.327186i	$-0.106100\pi$
$773$	477.540	+	477.540i	0.617774	+	0.617774i	−0.327186	+	0.944960i	$0.606100\pi$
$774$		−	186.638i		−	0.241134i
$775$	−672.049	+	1241.79i	−0.867160	+	1.60230i
$776$	197.862			0.254976
$777$	−596.503	+	596.503i	−0.767700	+	0.767700i
$778$	720.417	+	720.417i	0.925986	+	0.925986i
$779$		−	623.640i		−	0.800564i
$780$	90.4943	+	151.872i	0.116018	+	0.194708i
$781$	856.341			1.09647
$782$	10.1025	−	10.1025i	0.0129188	−	0.0129188i
$783$	−3.49337	−	3.49337i	−0.00446152	−	0.00446152i
$784$			43.6094i			0.0556243i
$785$	−639.231	−	161.881i	−0.814307	−	0.206218i
$786$	−217.571			−0.276807
$787$	65.3834	−	65.3834i	0.0830793	−	0.0830793i	−0.664346	−	0.747425i	$-0.731290\pi$
$787$	65.3834	−	65.3834i	0.0830793	−	0.0830793i	0.747425	+	0.664346i	$0.231290\pi$
$788$	−249.249	−	249.249i	−0.316306	−	0.316306i
$789$			361.594i			0.458294i
$790$	113.760	−	449.212i	0.144000	−	0.568623i
$791$	−1364.98			−1.72564
$792$	−109.949	+	109.949i	−0.138825	+	0.138825i
$793$	177.939	+	177.939i	0.224388	+	0.224388i
$794$			279.384i			0.351869i
$795$	187.056	−	111.459i	0.235291	−	0.140200i
$796$	522.177			0.656001
$797$	−879.060	+	879.060i	−1.10296	+	1.10296i	−0.108910	+	0.994052i	$0.534736\pi$
$797$	−879.060	+	879.060i	−1.10296	+	1.10296i	−0.994052	+	0.108910i	$0.965264\pi$
$798$	186.492	+	186.492i	0.233699	+	0.233699i
$799$		−	76.6121i		−	0.0958850i
$800$	40.3503	+	135.543i	0.0504378	+	0.169429i
$801$	−192.131			−0.239864
$802$	−410.867	+	410.867i	−0.512303	+	0.512303i
$803$	−6.81700	−	6.81700i	−0.00848942	−	0.00848942i
$804$		−	159.823i		−	0.198784i
$805$	94.9996	+	159.433i	0.118012	+	0.198054i
$806$	−815.262			−1.01149
$807$	−52.7472	+	52.7472i	−0.0653620	+	0.0653620i
$808$	−245.664	−	245.664i	−0.304039	−	0.304039i
$809$		−	1215.51i		−	1.50249i	−0.660024	−	0.751244i	$-0.729454\pi$
$809$		−	1215.51i		−	1.50249i	0.660024	−	0.751244i	$-0.270546\pi$
$810$	−61.6921	−	15.6231i	−0.0761631	−	0.0192878i
$811$	−1299.32			−1.60212			−0.801062	−	0.598581i	$-0.795731\pi$
$811$	−1299.32			−1.60212			−0.801062	+	0.598581i	$0.795731\pi$
$812$	−10.4067	+	10.4067i	−0.0128162	+	0.0128162i
$813$	557.265	+	557.265i	0.685442	+	0.685442i
$814$			1630.80i			2.00345i
$815$	−370.262	+	1462.08i	−0.454309	+	1.79396i
$816$	14.5944			0.0178853
$817$	−432.738	+	432.738i	−0.529667	+	0.529667i
$818$	185.429	+	185.429i	0.226686	+	0.226686i
$819$			236.994i			0.289370i
$820$	385.105	−	229.468i	0.469640	−	0.279839i
$821$	396.264			0.482660			0.241330	−	0.970443i	$-0.422416\pi$
$821$	396.264			0.482660			0.241330	+	0.970443i	$0.422416\pi$
$822$	206.943	−	206.943i	0.251756	−	0.251756i
$823$	24.9125	+	24.9125i	0.0302703	+	0.0302703i	0.722080	−	0.691810i	$-0.243186\pi$
$823$	24.9125	+	24.9125i	0.0302703	+	0.0302703i	−0.691810	+	0.722080i	$0.743186\pi$
$824$			163.660i			0.198616i
$825$	760.508	−	226.399i	0.921828	−	0.274423i
$826$	5.03110			0.00609092
$827$	−525.121	+	525.121i	−0.634971	+	0.634971i	−0.949311	−	0.314340i	$-0.898217\pi$
$827$	−525.121	+	525.121i	−0.634971	+	0.634971i	0.314340	+	0.949311i	$0.398217\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$			259.009i			0.312435i	0.987723	+	0.156218i	$0.0499301\pi$
$829$			259.009i			0.312435i	−0.987723	+	0.156218i	$0.950070\pi$
$830$	−437.391	−	734.051i	−0.526977	−	0.884399i
$831$	−184.324			−0.221810
$832$	−57.7390	+	57.7390i	−0.0693978	+	0.0693978i
$833$	−16.2395	−	16.2395i	−0.0194951	−	0.0194951i
$834$			3.49762i			0.00419379i
$835$	95.6757	+	24.2293i	0.114582	+	0.0290171i
$836$	509.858			0.609877
$837$	207.518	−	207.518i	0.247930	−	0.247930i
$838$	203.166	+	203.166i	0.242442	+	0.242442i
$839$			537.629i			0.640798i	0.947283	+	0.320399i	$0.103817\pi$
$839$			537.629i			0.640798i	−0.947283	+	0.320399i	$0.896183\pi$
$840$	−46.5413	+	183.781i	−0.0554063	+	0.218786i
$841$	840.096			0.998925
$842$	622.636	−	622.636i	0.739473	−	0.739473i
$843$	−42.3056	−	42.3056i	−0.0501845	−	0.0501845i
$844$			328.571i			0.389303i
$845$	−278.416	+	165.897i	−0.329487	+	0.196328i
$846$	−154.301			−0.182388
$847$	1175.56	−	1175.56i	1.38791	−	1.38791i
$848$	71.1154	+	71.1154i	0.0838625	+	0.0838625i
$849$		−	205.927i		−	0.242553i
$850$	−65.4998	−	35.4482i	−0.0770586	−	0.0417037i
$851$	−301.793			−0.354633
$852$	−114.467	+	114.467i	−0.134351	+	0.134351i
$853$	−195.388	−	195.388i	−0.229060	−	0.229060i	0.583240	−	0.812300i	$-0.301785\pi$
$853$	−195.388	−	195.388i	−0.229060	−	0.229060i	−0.812300	+	0.583240i	$0.801785\pi$
$854$			269.854i			0.315989i
$855$	106.816	+	179.263i	0.124930	+	0.209665i
$856$	497.153			0.580787
$857$	−379.526	+	379.526i	−0.442855	+	0.442855i	−0.892970	−	0.450116i	$-0.851383\pi$
$857$	−379.526	+	379.526i	−0.442855	+	0.442855i	0.450116	+	0.892970i	$0.351383\pi$
$858$	323.964	+	323.964i	0.377580	+	0.377580i
$859$		−	258.507i		−	0.300939i	−0.988615	−	0.150470i	$-0.951921\pi$
$859$		−	258.507i		−	0.300939i	0.988615	−	0.150470i	$-0.0480786\pi$
$860$	−426.447	−	107.995i	−0.495869	−	0.125576i
$861$	600.951			0.697969
$862$	−645.267	+	645.267i	−0.748570	+	0.748570i
$863$	856.478	+	856.478i	0.992443	+	0.992443i	0.999972	−	0.00752867i	$-0.00239647\pi$
$863$	856.478	+	856.478i	0.992443	+	0.992443i	−0.00752867	+	0.999972i	$0.502396\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−325.563	+	1285.57i	−0.376373	+	1.48621i
$866$	−665.086			−0.767998
$867$	348.517	−	348.517i	0.401980	−	0.401980i
$868$	−618.194	−	618.194i	−0.712205	−	0.712205i
$869$		−	1200.90i		−	1.38193i
$870$	−10.0034	+	5.96059i	−0.0114981	+	0.00685126i
$871$	−470.915			−0.540660
$872$	−57.3690	+	57.3690i	−0.0657902	+	0.0657902i
$873$	148.396	+	148.396i	0.169984	+	0.169984i
$874$			94.3531i			0.107955i
$875$	655.260	−	711.765i	0.748868	−	0.813445i
$876$	1.82246			0.00208043
$877$	−766.900	+	766.900i	−0.874458	+	0.874458i	−0.992954	−	0.118497i	$-0.962193\pi$
$877$	−766.900	+	766.900i	−0.874458	+	0.874458i	0.118497	+	0.992954i	$0.462193\pi$
$878$	−42.1637	−	42.1637i	−0.0480224	−	0.0480224i
$879$		−	877.885i		−	0.998732i
$880$	187.602	+	314.843i	0.213184	+	0.357776i
$881$	243.225			0.276079			0.138039	−	0.990427i	$-0.455920\pi$
$881$	243.225			0.276079			0.138039	+	0.990427i	$0.455920\pi$
$882$	−32.7071	+	32.7071i	−0.0370829	+	0.0370829i
$883$	−526.787	−	526.787i	−0.596588	−	0.596588i	0.342815	−	0.939403i	$-0.388620\pi$
$883$	−526.787	−	526.787i	−0.596588	−	0.596588i	−0.939403	+	0.342815i	$0.888620\pi$
$884$		−	43.0022i		−	0.0486450i
$885$	3.85886	+	0.977232i	0.00436029	+	0.00110422i
$886$	37.2390			0.0420305
$887$	531.370	−	531.370i	0.599064	−	0.599064i	−0.340999	−	0.940064i	$-0.610765\pi$
$887$	531.370	−	531.370i	0.599064	−	0.599064i	0.940064	+	0.340999i	$0.110765\pi$
$888$	−217.990	−	217.990i	−0.245484	−	0.245484i
$889$			198.328i			0.223091i
$890$	−111.174	+	438.999i	−0.124914	+	0.493258i
$891$	−164.924			−0.185100
$892$	−374.092	+	374.092i	−0.419386	+	0.419386i
$893$	357.762	+	357.762i	0.400629	+	0.400629i
$894$			655.033i			0.732699i
$895$	254.301	−	151.527i	0.284135	−	0.169304i
$896$	−87.5643			−0.0977280
$897$	−59.9520	+	59.9520i	−0.0668361	+	0.0668361i
$898$	−256.938	−	256.938i	−0.286123	−	0.286123i
$899$		−	53.6990i		−	0.0597319i
$900$	−71.3944	+	131.920i	−0.0793271	+	0.146578i
$901$	−52.9645			−0.0587841
$902$	821.482	−	821.482i	0.910734	−	0.910734i
$903$	−416.995	−	416.995i	−0.461788	−	0.461788i
$904$		−	498.826i		−	0.551798i
$905$	−560.385	−	940.466i	−0.619210	−	1.03919i
$906$	−393.288			−0.434093
$907$	433.552	−	433.552i	0.478007	−	0.478007i	−0.426487	−	0.904494i	$-0.640249\pi$
$907$	433.552	−	433.552i	0.478007	−	0.478007i	0.904494	+	0.426487i	$0.140249\pi$
$908$	436.231	+	436.231i	0.480430	+	0.480430i
$909$		−	368.495i		−	0.405386i
$910$	541.506	+	137.133i	0.595062	+	0.150696i
$911$	1084.05			1.18996			0.594980	−	0.803740i	$-0.297160\pi$
$911$	1084.05			1.18996			0.594980	+	0.803740i	$0.297160\pi$
$912$	−68.1527	+	68.1527i	−0.0747288	+	0.0747288i
$913$	−1565.83	−	1565.83i	−1.71504	−	1.71504i
$914$		−	686.158i		−	0.750719i
$915$	−52.4160	+	206.979i	−0.0572853	+	0.226206i
$916$	716.110			0.781779
$917$	−486.107	+	486.107i	−0.530105	+	0.530105i
$918$	10.9458	+	10.9458i	0.0119235	+	0.0119235i
$919$		−	1372.71i		−	1.49370i	−0.664993	−	0.746849i	$-0.731566\pi$
$919$		−	1372.71i		−	1.49370i	0.664993	−	0.746849i	$-0.268434\pi$
$920$	−58.2642	+	34.7172i	−0.0633306	+	0.0377361i
$921$	105.683			0.114748
$922$	518.066	−	518.066i	0.561893	−	0.561893i
$923$	337.275	+	337.275i	0.365412	+	0.365412i
$924$			491.308i			0.531719i
$925$	448.866	+	1507.81i	0.485261	+	1.63007i
$926$	−1162.61			−1.25552
$927$	−122.745	+	122.745i	−0.132411	+	0.132411i
$928$	−3.80310	−	3.80310i	−0.00409817	−	0.00409817i
$929$			668.265i			0.719338i	0.933080	+	0.359669i	$0.117110\pi$
$929$			668.265i			0.719338i	−0.933080	+	0.359669i	$0.882890\pi$
$930$	−354.079	−	594.232i	−0.380730	−	0.638960i
$931$	151.669			0.162910
$932$	80.3485	−	80.3485i	0.0862108	−	0.0862108i
$933$	−230.814	−	230.814i	−0.247389	−	0.247389i
$934$		−	351.964i		−	0.376835i
$935$	−187.103	−	47.3825i	−0.200110	−	0.0506765i
$936$	−86.6085			−0.0925305
$937$	−97.7256	+	97.7256i	−0.104296	+	0.104296i	−0.757329	−	0.653033i	$-0.773496\pi$
$937$	−97.7256	+	97.7256i	−0.104296	+	0.104296i	0.653033	+	0.757329i	$0.273496\pi$
$938$	−357.084	−	357.084i	−0.380686	−	0.380686i
$939$			343.580i			0.365900i
$940$	−89.2837	+	352.560i	−0.0949827	+	0.375064i
$941$	−1812.51			−1.92615			−0.963076	−	0.269229i	$-0.913231\pi$
$941$	−1812.51			−1.92615			−0.963076	+	0.269229i	$0.913231\pi$
$942$	228.426	−	228.426i	0.242491	−	0.242491i
$943$	152.022	+	152.022i	0.161211	+	0.161211i
$944$			1.83860i			0.00194766i
$945$	−172.741	+	102.930i	−0.182795	+	0.108920i
$946$	−1140.04			−1.20511
$947$	−200.460	+	200.460i	−0.211679	+	0.211679i	−0.804980	−	0.593302i	$-0.797824\pi$
$947$	−200.460	+	200.460i	−0.211679	+	0.211679i	0.593302	+	0.804980i	$0.297824\pi$
$948$	160.524	+	160.524i	0.169329	+	0.169329i
$949$		−	5.36984i		−	0.00565842i
$950$	471.405	−	140.334i	0.496215	−	0.147720i
$951$	311.804			0.327870
$952$	32.6075	−	32.6075i	0.0342516	−	0.0342516i
$953$	639.096	+	639.096i	0.670615	+	0.670615i	0.957858	−	0.287243i	$-0.0927388\pi$
$953$	639.096	+	639.096i	0.670615	+	0.670615i	−0.287243	+	0.957858i	$0.592739\pi$
$954$			106.673i			0.111817i
$955$	63.2423	+	106.136i	0.0662224	+	0.111138i
$956$	84.7117			0.0886106
$957$	−21.3386	+	21.3386i	−0.0222973	+	0.0222973i
$958$	92.7211	+	92.7211i	0.0967861	+	0.0967861i
$959$		−	924.726i		−	0.964260i
$960$	−67.1619	−	17.0083i	−0.0699603	−	0.0177170i
$961$	2228.89			2.31935
$962$	−642.302	+	642.302i	−0.667674	+	0.667674i
$963$	372.865	+	372.865i	0.387191	+	0.387191i
$964$		−	276.500i		−	0.286826i
$965$	202.581	−	799.947i	0.209929	−	0.828960i
$966$	−90.9204			−0.0941205
$967$	610.583	−	610.583i	0.631420	−	0.631420i	−0.317004	−	0.948424i	$-0.602677\pi$
$967$	610.583	−	610.583i	0.631420	−	0.631420i	0.948424	+	0.317004i	$0.102677\pi$
$968$	429.604	+	429.604i	0.443806	+	0.443806i
$969$		−	50.7579i		−	0.0523818i
$970$	424.937	−	253.202i	0.438079	−	0.261033i
$971$	504.845			0.519923			0.259962	−	0.965619i	$-0.416290\pi$
$971$	504.845			0.519923			0.259962	+	0.965619i	$0.416290\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	7.81456	+	7.81456i	0.00803141	+	0.00803141i
$974$		−	718.617i		−	0.737800i
$975$	388.699	+	210.362i	0.398666	+	0.215756i
$976$	−98.6172			−0.101042
$977$	489.671	−	489.671i	0.501198	−	0.501198i	−0.410612	−	0.911810i	$-0.634685\pi$
$977$	489.671	−	489.671i	0.501198	−	0.501198i	0.911810	+	0.410612i	$0.134685\pi$
$978$	−522.467	−	522.467i	−0.534220	−	0.534220i
$979$			1173.59i			1.19877i
$980$	55.8067	+	93.6577i	0.0569457	+	0.0955690i
$981$	−86.0536			−0.0877203
$982$	−215.844	+	215.844i	−0.219801	+	0.219801i
$983$	−737.262	−	737.262i	−0.750012	−	0.750012i	0.224469	−	0.974481i	$-0.427935\pi$
$983$	−737.262	−	737.262i	−0.750012	−	0.750012i	−0.974481	+	0.224469i	$0.927935\pi$
$984$			219.615i			0.223186i
$985$	−854.261	−	216.336i	−0.867270	−	0.219631i
$986$	2.83243			0.00287264
$987$	−344.746	+	344.746i	−0.349287	+	0.349287i
$988$	200.811	+	200.811i	0.203250	+	0.203250i
$989$		−	210.973i		−	0.213319i
$990$	−95.4308	+	376.834i	−0.0963948	+	0.380640i
$991$	−325.586			−0.328543			−0.164271	−	0.986415i	$-0.552527\pi$
$991$	−325.586			−0.328543			−0.164271	+	0.986415i	$0.552527\pi$
$992$	225.917	−	225.917i	0.227738	−	0.227738i
$993$	−529.587	−	529.587i	−0.533320	−	0.533320i
$994$			511.496i			0.514583i
$995$	1121.45	−	668.227i	1.12709	−	0.671584i
$996$	418.610			0.420291
$997$	217.426	−	217.426i	0.218081	−	0.218081i	−0.589609	−	0.807689i	$-0.700718\pi$
$997$	217.426	−	217.426i	0.218081	−	0.218081i	0.807689	+	0.589609i	$0.200718\pi$
$998$	−236.340	−	236.340i	−0.236813	−	0.236813i
$999$		−	326.984i		−	0.327312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.8	yes	48
5.2	odd	4	inner	690.3.k.b.277.8	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.8	✓	48	5.2	odd	4	inner
690.3.k.b.553.8	yes	48	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.55939 - 4.29529i) q^{5} +2.44949 q^{6} +(5.47277 - 5.47277i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.85468 + 1.73590i) q^{10} +18.3249 q^{11} +(-2.44949 + 2.44949i) q^{12} +(7.21738 + 7.21738i) q^{13} +10.9455i q^{14} +(-2.12604 + 8.39523i) q^{15} -4.00000 q^{16} +(1.48954 - 1.48954i) q^{17} +(-3.00000 - 3.00000i) q^{18} +13.9116i q^{19} +(-8.59058 + 5.11878i) q^{20} -13.4055 q^{21} +(-18.3249 + 18.3249i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.8991 + 21.9866i) q^{25} -14.4348 q^{26} +(3.67423 - 3.67423i) q^{27} +(-10.9455 - 10.9455i) q^{28} -0.950775i q^{29} +(-6.26919 - 10.5213i) q^{30} +56.4791 q^{31} +(4.00000 - 4.00000i) q^{32} +(-22.4433 - 22.4433i) q^{33} +2.97907i q^{34} +(-37.5141 - 9.50020i) q^{35} +6.00000 q^{36} +(44.4969 - 44.4969i) q^{37} +(-13.9116 - 13.9116i) q^{38} -17.6789i q^{39} +(3.47181 - 13.7094i) q^{40} -44.8287 q^{41} +(13.4055 - 13.4055i) q^{42} +(31.1063 + 31.1063i) q^{43} -36.6498i q^{44} +(12.8859 - 7.67816i) q^{45} +6.78233 q^{46} +(25.7168 - 25.7168i) q^{47} +(4.89898 + 4.89898i) q^{48} -10.9024i q^{49} +(-10.0876 - 33.8857i) q^{50} -3.64860 q^{51} +(14.4348 - 14.4348i) q^{52} +(-17.7789 - 17.7789i) q^{53} +7.34847i q^{54} +(-46.9005 - 78.7108i) q^{55} +21.8911 q^{56} +(17.0382 - 17.0382i) q^{57} +(0.950775 + 0.950775i) q^{58} -0.459649i q^{59} +(16.7905 + 4.25208i) q^{60} +24.6543 q^{61} +(-56.4791 + 56.4791i) q^{62} +(16.4183 + 16.4183i) q^{63} +8.00000i q^{64} +(12.5287 - 49.4728i) q^{65} +44.8867 q^{66} +(-32.6237 + 32.6237i) q^{67} +(-2.97907 - 2.97907i) q^{68} +8.30662i q^{69} +(47.0143 - 28.0139i) q^{70} +46.7310 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.372008 - 0.372008i) q^{73} +88.9939i q^{74} +(41.5013 - 12.3547i) q^{75} +27.8232 q^{76} +(100.288 - 100.288i) q^{77} +(17.6789 + 17.6789i) q^{78} -65.5336i q^{79} +(10.2376 + 17.1812i) q^{80} -9.00000 q^{81} +(44.8287 - 44.8287i) q^{82} +(-85.4484 - 85.4484i) q^{83} +26.8110i q^{84} +(-10.2103 - 2.58569i) q^{85} -62.2125 q^{86} +(-1.16446 + 1.16446i) q^{87} +(36.6498 + 36.6498i) q^{88} +64.0437i q^{89} +(-5.20771 + 20.5640i) q^{90} +78.9980 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-69.1725 - 69.1725i) q^{93} +51.4335i q^{94} +(59.7544 - 35.6052i) q^{95} -9.79796 q^{96} +(49.4654 - 49.4654i) q^{97} +(10.9024 + 10.9024i) q^{98} +54.9747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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