LMFDB - Embedded newform 690.3.k.b.553.13

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			553.13
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.66464 - 2.36274i) q^{10} -2.98698 q^{11} +(2.44949 - 2.44949i) q^{12} +(-7.61449 - 7.61449i) q^{13} -16.2860i q^{14} +(-2.89375 - 8.16249i) q^{15} -4.00000 q^{16} +(15.0931 - 15.0931i) q^{17} +(-3.00000 - 3.00000i) q^{18} -14.0712i q^{19} +(-4.30191 + 9.02738i) q^{20} -19.9462 q^{21} +(2.98698 - 2.98698i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(15.7468 + 19.4175i) q^{25} +15.2290 q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.2860 + 16.2860i) q^{28} +49.2034i q^{29} +(11.0562 + 5.26874i) q^{30} -5.90652 q^{31} +(4.00000 - 4.00000i) q^{32} +(-3.65829 - 3.65829i) q^{33} +30.1863i q^{34} +(54.2702 - 19.2398i) q^{35} +6.00000 q^{36} +(41.6945 - 41.6945i) q^{37} +(14.0712 + 14.0712i) q^{38} -18.6516i q^{39} +(-4.72547 - 13.3293i) q^{40} -20.3143 q^{41} +(19.9462 - 19.9462i) q^{42} +(-22.1189 - 22.1189i) q^{43} +5.97396i q^{44} +(6.45286 - 13.5411i) q^{45} -6.78233 q^{46} +(60.9689 - 60.9689i) q^{47} +(-4.89898 - 4.89898i) q^{48} -83.6170i q^{49} +(-35.1643 - 3.67068i) q^{50} +36.9705 q^{51} +(-15.2290 + 15.2290i) q^{52} +(63.5049 + 63.5049i) q^{53} -7.34847i q^{54} +(13.4823 + 6.42486i) q^{55} -32.5720 q^{56} +(17.2337 - 17.2337i) q^{57} +(-49.2034 - 49.2034i) q^{58} -15.2382i q^{59} +(-16.3250 + 5.78750i) q^{60} -12.0570 q^{61} +(5.90652 - 5.90652i) q^{62} +(-24.4290 - 24.4290i) q^{63} +8.00000i q^{64} +(17.9910 + 50.7478i) q^{65} +7.31658 q^{66} +(79.9748 - 79.9748i) q^{67} +(-30.1863 - 30.1863i) q^{68} +8.30662i q^{69} +(-35.0304 + 73.5100i) q^{70} +20.4797 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.611855 - 0.611855i) q^{73} +83.3890i q^{74} +(-4.49564 + 43.0673i) q^{75} -28.1424 q^{76} +(24.3230 - 24.3230i) q^{77} +(18.6516 + 18.6516i) q^{78} -127.031i q^{79} +(18.0548 + 8.60381i) q^{80} -9.00000 q^{81} +(20.3143 - 20.3143i) q^{82} +(-24.8801 - 24.8801i) q^{83} +39.8924i q^{84} +(-100.590 + 35.6611i) q^{85} +44.2378 q^{86} +(-60.2616 + 60.2616i) q^{87} +(-5.97396 - 5.97396i) q^{88} +87.9111i q^{89} +(7.08821 + 19.9939i) q^{90} +124.010 q^{91} +(6.78233 - 6.78233i) q^{92} +(-7.23398 - 7.23398i) q^{93} +121.938i q^{94} +(-30.2665 + 63.5131i) q^{95} +9.79796 q^{96} +(15.5564 - 15.5564i) q^{97} +(83.6170 + 83.6170i) q^{98} -8.96095i 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
$5$	−4.51369	−	2.15095i	−0.902738	−	0.430191i
$5$	−4.51369	−	2.15095i	−0.902738	−	0.430191i
$6$	−2.44949			−0.408248
$7$	−8.14300	+	8.14300i	−1.16329	+	1.16329i	−0.179535	+	0.983752i	$0.557459\pi$
$7$	−8.14300	+	8.14300i	−1.16329	+	1.16329i	−0.983752	+	0.179535i	$0.942541\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	6.66464	−	2.36274i	0.666464	−	0.236274i
$11$	−2.98698			−0.271544			−0.135772	−	0.990740i	$-0.543351\pi$
$11$	−2.98698			−0.271544			−0.135772	+	0.990740i	$0.543351\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−7.61449	−	7.61449i	−0.585730	−	0.585730i	0.350742	−	0.936472i	$-0.385929\pi$
$13$	−7.61449	−	7.61449i	−0.585730	−	0.585730i	−0.936472	+	0.350742i	$0.885929\pi$
$14$		−	16.2860i		−	1.16329i
$15$	−2.89375	−	8.16249i	−0.192917	−	0.544166i
$16$	−4.00000			−0.250000
$17$	15.0931	−	15.0931i	0.887831	−	0.887831i	−0.106483	−	0.994315i	$-0.533959\pi$
$17$	15.0931	−	15.0931i	0.887831	−	0.887831i	0.994315	+	0.106483i	$0.0339590\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	14.0712i		−	0.740591i	−0.928914	−	0.370295i	$-0.879256\pi$
$19$		−	14.0712i		−	0.740591i	0.928914	−	0.370295i	$-0.120744\pi$
$20$	−4.30191	+	9.02738i	−0.215095	+	0.451369i
$21$	−19.9462			−0.949819
$22$	2.98698	−	2.98698i	0.135772	−	0.135772i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	15.7468	+	19.4175i	0.629872	+	0.776699i
$26$	15.2290			0.585730
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	16.2860	+	16.2860i	0.581643	+	0.581643i
$29$			49.2034i			1.69667i	0.529462	+	0.848334i	$0.322394\pi$
$29$			49.2034i			1.69667i	−0.529462	+	0.848334i	$0.677606\pi$
$30$	11.0562	+	5.26874i	0.368541	+	0.175625i
$31$	−5.90652			−0.190533			−0.0952664	−	0.995452i	$-0.530370\pi$
$31$	−5.90652			−0.190533			−0.0952664	+	0.995452i	$0.530370\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−3.65829	−	3.65829i	−0.110857	−	0.110857i
$34$			30.1863i			0.887831i
$35$	54.2702	−	19.2398i	1.55058	−	0.549708i
$36$	6.00000			0.166667
$37$	41.6945	−	41.6945i	1.12688	−	1.12688i	0.136196	−	0.990682i	$-0.456512\pi$
$37$	41.6945	−	41.6945i	1.12688	−	1.12688i	0.990682	−	0.136196i	$-0.0434878\pi$
$38$	14.0712	+	14.0712i	0.370295	+	0.370295i
$39$		−	18.6516i		−	0.478246i
$40$	−4.72547	−	13.3293i	−0.118137	−	0.333232i
$41$	−20.3143			−0.495470			−0.247735	−	0.968828i	$-0.579686\pi$
$41$	−20.3143			−0.495470			−0.247735	+	0.968828i	$0.579686\pi$
$42$	19.9462	−	19.9462i	0.474910	−	0.474910i
$43$	−22.1189	−	22.1189i	−0.514393	−	0.514393i	0.401477	−	0.915869i	$-0.368497\pi$
$43$	−22.1189	−	22.1189i	−0.514393	−	0.514393i	−0.915869	+	0.401477i	$0.868497\pi$
$44$			5.97396i			0.135772i
$45$	6.45286	−	13.5411i	0.143397	−	0.300913i
$46$	−6.78233			−0.147442
$47$	60.9689	−	60.9689i	1.29721	−	1.29721i	0.366984	−	0.930227i	$-0.380391\pi$
$47$	60.9689	−	60.9689i	1.29721	−	1.29721i	0.930227	−	0.366984i	$-0.119609\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	83.6170i		−	1.70647i
$50$	−35.1643	−	3.67068i	−0.703285	−	0.0734135i
$51$	36.9705			0.724911
$52$	−15.2290	+	15.2290i	−0.292865	+	0.292865i
$53$	63.5049	+	63.5049i	1.19821	+	1.19821i	0.974703	+	0.223502i	$0.0717490\pi$
$53$	63.5049	+	63.5049i	1.19821	+	1.19821i	0.223502	+	0.974703i	$0.428251\pi$
$54$		−	7.34847i		−	0.136083i
$55$	13.4823	+	6.42486i	0.245133	+	0.116816i
$56$	−32.5720			−0.581643
$57$	17.2337	−	17.2337i	0.302345	−	0.302345i
$58$	−49.2034	−	49.2034i	−0.848334	−	0.848334i
$59$		−	15.2382i		−	0.258275i	−0.991627	−	0.129137i	$-0.958779\pi$
$59$		−	15.2382i		−	0.258275i	0.991627	−	0.129137i	$-0.0412208\pi$
$60$	−16.3250	+	5.78750i	−0.272083	+	0.0964583i
$61$	−12.0570			−0.197655			−0.0988275	−	0.995105i	$-0.531509\pi$
$61$	−12.0570			−0.197655			−0.0988275	+	0.995105i	$0.531509\pi$
$62$	5.90652	−	5.90652i	0.0952664	−	0.0952664i
$63$	−24.4290	−	24.4290i	−0.387762	−	0.387762i
$64$			8.00000i			0.125000i
$65$	17.9910	+	50.7478i	0.276785	+	0.780736i
$66$	7.31658			0.110857
$67$	79.9748	−	79.9748i	1.19365	−	1.19365i	0.217620	−	0.976033i	$-0.430171\pi$
$67$	79.9748	−	79.9748i	1.19365	−	1.19365i	0.976033	−	0.217620i	$-0.0698295\pi$
$68$	−30.1863	−	30.1863i	−0.443916	−	0.443916i
$69$			8.30662i			0.120386i
$70$	−35.0304	+	73.5100i	−0.500435	+	1.05014i
$71$	20.4797			0.288446			0.144223	−	0.989545i	$-0.453932\pi$
$71$	20.4797			0.288446			0.144223	+	0.989545i	$0.453932\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−0.611855	−	0.611855i	−0.00838158	−	0.00838158i	0.702904	−	0.711285i	$-0.251887\pi$
$73$	−0.611855	−	0.611855i	−0.00838158	−	0.00838158i	−0.711285	+	0.702904i	$0.751887\pi$
$74$			83.3890i			1.12688i
$75$	−4.49564	+	43.0673i	−0.0599419	+	0.574230i
$76$	−28.1424			−0.370295
$77$	24.3230	−	24.3230i	0.315883	−	0.315883i
$78$	18.6516	+	18.6516i	0.239123	+	0.239123i
$79$		−	127.031i		−	1.60799i	−0.594636	−	0.803995i	$-0.702704\pi$
$79$		−	127.031i		−	1.60799i	0.594636	−	0.803995i	$-0.297296\pi$
$80$	18.0548	+	8.60381i	0.225685	+	0.107548i
$81$	−9.00000			−0.111111
$82$	20.3143	−	20.3143i	0.247735	−	0.247735i
$83$	−24.8801	−	24.8801i	−0.299761	−	0.299761i	0.541159	−	0.840920i	$-0.317986\pi$
$83$	−24.8801	−	24.8801i	−0.299761	−	0.299761i	−0.840920	+	0.541159i	$0.817986\pi$
$84$			39.8924i			0.474910i
$85$	−100.590	+	35.6611i	−1.18342	+	0.419542i
$86$	44.2378			0.514393
$87$	−60.2616	+	60.2616i	−0.692662	+	0.692662i
$88$	−5.97396	−	5.97396i	−0.0678860	−	0.0678860i
$89$			87.9111i			0.987765i	0.869529	+	0.493883i	$0.164423\pi$
$89$			87.9111i			0.987765i	−0.869529	+	0.493883i	$0.835577\pi$
$90$	7.08821	+	19.9939i	0.0787579	+	0.222155i
$91$	124.010			1.36274
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−7.23398	−	7.23398i	−0.0777847	−	0.0777847i
$94$			121.938i			1.29721i
$95$	−30.2665	+	63.5131i	−0.318595	+	0.668559i
$96$	9.79796			0.102062
$97$	15.5564	−	15.5564i	0.160375	−	0.160375i	−0.622358	−	0.782733i	$-0.713825\pi$
$97$	15.5564	−	15.5564i	0.160375	−	0.160375i	0.782733	+	0.622358i	$0.213825\pi$
$98$	83.6170	+	83.6170i	0.853235	+	0.853235i
$99$		−	8.96095i		−	0.0905146i
$100$	38.8349	−	31.4936i	0.388349	−	0.314936i
$101$	−136.156			−1.34808			−0.674042	−	0.738693i	$-0.735443\pi$
$101$	−136.156			−1.34808			−0.674042	+	0.738693i	$0.735443\pi$
$102$	−36.9705	+	36.9705i	−0.362456	+	0.362456i
$103$	23.3277	+	23.3277i	0.226483	+	0.226483i	0.811222	−	0.584739i	$-0.198803\pi$
$103$	23.3277	+	23.3277i	0.226483	+	0.226483i	−0.584739	+	0.811222i	$0.698803\pi$
$104$		−	30.4579i		−	0.292865i
$105$	90.0310	+	42.9034i	0.857438	+	0.408603i
$106$	−127.010			−1.19821
$107$	107.221	−	107.221i	1.00207	−	1.00207i	0.00206949	−	0.999998i	$-0.499341\pi$
$107$	107.221	−	107.221i	1.00207	−	1.00207i	0.999998	−	0.00206949i	$-0.000658739\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	59.6007i		−	0.546796i	−0.961901	−	0.273398i	$-0.911852\pi$
$109$		−	59.6007i		−	0.546796i	0.961901	−	0.273398i	$-0.0881475\pi$
$110$	−19.9072	+	7.05745i	−0.180974	+	0.0641587i
$111$	102.130			0.920092
$112$	32.5720	−	32.5720i	0.290822	−	0.290822i
$113$	144.185	+	144.185i	1.27597	+	1.27597i	0.942901	+	0.333072i	$0.108085\pi$
$113$	144.185	+	144.185i	1.27597	+	1.27597i	0.333072	+	0.942901i	$0.391915\pi$
$114$			34.4673i			0.302345i
$115$	−8.01243	−	22.6009i	−0.0696733	−	0.196530i
$116$	98.4067			0.848334
$117$	22.8435	−	22.8435i	0.195243	−	0.195243i
$118$	15.2382	+	15.2382i	0.129137	+	0.129137i
$119$			245.807i			2.06560i
$120$	10.5375	−	22.1125i	0.0878123	−	0.184271i
$121$	−112.078			−0.926264
$122$	12.0570	−	12.0570i	0.0988275	−	0.0988275i
$123$	−24.8798	−	24.8798i	−0.202275	−	0.202275i
$124$			11.8130i			0.0952664i
$125$	−29.3101	−	121.515i	−0.234481	−	0.972121i
$126$	48.8580			0.387762
$127$	−19.3030	+	19.3030i	−0.151992	+	0.151992i	−0.779007	−	0.627015i	$-0.784276\pi$
$127$	−19.3030	+	19.3030i	−0.151992	+	0.151992i	0.627015	+	0.779007i	$0.284276\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	54.1800i		−	0.420000i
$130$	−68.7389	−	32.7568i	−0.528761	−	0.251975i
$131$	−50.6870			−0.386923			−0.193462	−	0.981108i	$-0.561972\pi$
$131$	−50.6870			−0.386923			−0.193462	+	0.981108i	$0.561972\pi$
$132$	−7.31658	+	7.31658i	−0.0554287	+	0.0554287i
$133$	114.582	+	114.582i	0.861519	+	0.861519i
$134$			159.950i			1.19365i
$135$	24.4875	−	8.68125i	0.181389	−	0.0643056i
$136$	60.3725			0.443916
$137$	113.943	−	113.943i	0.831703	−	0.831703i	−0.156047	−	0.987750i	$-0.549875\pi$
$137$	113.943	−	113.943i	0.831703	−	0.831703i	0.987750	+	0.156047i	$0.0498751\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$		−	205.743i		−	1.48017i	−0.672515	−	0.740084i	$-0.734786\pi$
$139$		−	205.743i		−	1.48017i	0.672515	−	0.740084i	$-0.265214\pi$
$140$	−38.4796	−	108.540i	−0.274854	−	0.775289i
$141$	149.343			1.05917
$142$	−20.4797	+	20.4797i	−0.144223	+	0.144223i
$143$	22.7443	+	22.7443i	0.159051	+	0.159051i
$144$		−	12.0000i		−	0.0833333i
$145$	105.834	−	222.089i	0.729891	−	1.53165i
$146$	1.22371			0.00838158
$147$	102.410	−	102.410i	0.696664	−	0.696664i
$148$	−83.3890	−	83.3890i	−0.563439	−	0.563439i
$149$			51.6051i			0.346343i	0.984892	+	0.173172i	$0.0554015\pi$
$149$			51.6051i			0.346343i	−0.984892	+	0.173172i	$0.944598\pi$
$150$	−38.5716	−	47.5629i	−0.257144	−	0.317086i
$151$	113.345			0.750629			0.375314	−	0.926898i	$-0.377535\pi$
$151$	113.345			0.750629			0.375314	+	0.926898i	$0.377535\pi$
$152$	28.1424	−	28.1424i	0.185148	−	0.185148i
$153$	45.2794	+	45.2794i	0.295944	+	0.295944i
$154$			48.6460i			0.315883i
$155$	26.6602	+	12.7046i	0.172001	+	0.0819654i
$156$	−37.3032			−0.239123
$157$	−160.914	+	160.914i	−1.02493	+	1.02493i	−0.0252486	+	0.999681i	$0.508038\pi$
$157$	−160.914	+	160.914i	−1.02493	+	1.02493i	−0.999681	+	0.0252486i	$0.991962\pi$
$158$	127.031	+	127.031i	0.803995	+	0.803995i
$159$			155.555i			0.978331i
$160$	−26.6586	+	9.45095i	−0.166616	+	0.0590684i
$161$	−55.2285			−0.343034
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−122.176	−	122.176i	−0.749545	−	0.749545i	0.224848	−	0.974394i	$-0.427811\pi$
$163$	−122.176	−	122.176i	−0.749545	−	0.749545i	−0.974394	+	0.224848i	$0.927811\pi$
$164$			40.6286i			0.247735i
$165$	8.64358	+	24.3812i	0.0523853	+	0.147765i
$166$	49.7603			0.299761
$167$	−126.535	+	126.535i	−0.757695	+	0.757695i	−0.975902	−	0.218207i	$-0.929979\pi$
$167$	−126.535	+	126.535i	−0.757695	+	0.757695i	0.218207	+	0.975902i	$0.429979\pi$
$168$	−39.8924	−	39.8924i	−0.237455	−	0.237455i
$169$		−	53.0392i		−	0.313841i
$170$	64.9293	−	136.251i	0.381937	−	0.801479i
$171$	42.2137			0.246864
$172$	−44.2378	+	44.2378i	−0.257196	+	0.257196i
$173$	−116.139	−	116.139i	−0.671324	−	0.671324i	0.286697	−	0.958021i	$-0.407443\pi$
$173$	−116.139	−	116.139i	−0.671324	−	0.671324i	−0.958021	+	0.286697i	$0.907443\pi$
$174$		−	120.523i		−	0.692662i
$175$	−286.343	−	29.8903i	−1.63624	−	0.170802i
$176$	11.9479			0.0678860
$177$	18.6629	−	18.6629i	0.105440	−	0.105440i
$178$	−87.9111	−	87.9111i	−0.493883	−	0.493883i
$179$		−	127.573i		−	0.712696i	−0.934353	−	0.356348i	$-0.884022\pi$
$179$		−	127.573i		−	0.712696i	0.934353	−	0.356348i	$-0.115978\pi$
$180$	−27.0821	−	12.9057i	−0.150456	−	0.0716984i
$181$	−321.120			−1.77414			−0.887072	−	0.461630i	$-0.847265\pi$
$181$	−321.120			−1.77414			−0.887072	+	0.461630i	$0.847265\pi$
$182$	−124.010	+	124.010i	−0.681371	+	0.681371i
$183$	−14.7667	−	14.7667i	−0.0806923	−	0.0806923i
$184$			13.5647i			0.0737210i
$185$	−277.879	+	98.5131i	−1.50205	+	0.532503i
$186$	14.4680			0.0777847
$187$	−45.0829	+	45.0829i	−0.241085	+	0.241085i
$188$	−121.938	−	121.938i	−0.648605	−	0.648605i
$189$		−	59.8386i		−	0.316606i
$190$	−33.2466	−	93.7797i	−0.174982	−	0.493577i
$191$	91.9988			0.481669			0.240835	−	0.970566i	$-0.422579\pi$
$191$	91.9988			0.481669			0.240835	+	0.970566i	$0.422579\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−73.1687	−	73.1687i	−0.379113	−	0.379113i	0.491669	−	0.870782i	$-0.336387\pi$
$193$	−73.1687	−	73.1687i	−0.379113	−	0.379113i	−0.870782	+	0.491669i	$0.836387\pi$
$194$			31.1128i			0.160375i
$195$	−40.1187	+	84.1876i	−0.205737	+	0.431731i
$196$	−167.234			−0.853235
$197$	71.2245	−	71.2245i	0.361546	−	0.361546i	−0.502836	−	0.864382i	$-0.667710\pi$
$197$	71.2245	−	71.2245i	0.361546	−	0.361546i	0.864382	+	0.502836i	$0.167710\pi$
$198$	8.96095	+	8.96095i	0.0452573	+	0.0452573i
$199$			272.364i			1.36866i	0.729171	+	0.684331i	$0.239906\pi$
$199$			272.364i			1.36866i	−0.729171	+	0.684331i	$0.760094\pi$
$200$	−7.34135	+	70.3285i	−0.0367068	+	0.351643i
$201$	195.897			0.974614
$202$	136.156	−	136.156i	0.674042	−	0.674042i
$203$	−400.663	−	400.663i	−1.97371	−	1.97371i
$204$		−	73.9410i		−	0.362456i
$205$	91.6924	+	43.6951i	0.447280	+	0.213147i
$206$	−46.6554			−0.226483
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	30.4579	+	30.4579i	0.146432	+	0.146432i
$209$			42.0305i			0.201103i
$210$	−132.934	+	47.1276i	−0.633021	+	0.224417i
$211$	317.005			1.50239			0.751197	−	0.660078i	$-0.229477\pi$
$211$	317.005			1.50239			0.751197	+	0.660078i	$0.229477\pi$
$212$	127.010	−	127.010i	0.599103	−	0.599103i
$213$	25.0824	+	25.0824i	0.117758	+	0.117758i
$214$			214.442i			1.00207i
$215$	52.2611	+	147.414i	0.243075	+	0.685649i
$216$	−14.6969			−0.0680414
$217$	48.0968	−	48.0968i	0.221644	−	0.221644i
$218$	59.6007	+	59.6007i	0.273398	+	0.273398i
$219$		−	1.49873i		−	0.00684353i
$220$	12.8497	−	26.9646i	0.0584078	−	0.122566i
$221$	−229.853			−1.04006
$222$	−102.130	+	102.130i	−0.460046	+	0.460046i
$223$	−16.1528	−	16.1528i	−0.0724339	−	0.0724339i	0.669962	−	0.742396i	$-0.266310\pi$
$223$	−16.1528	−	16.1528i	−0.0724339	−	0.0724339i	−0.742396	+	0.669962i	$0.766310\pi$
$224$			65.1440i			0.290822i
$225$	−58.2524	+	47.2404i	−0.258900	+	0.209957i
$226$	−288.370			−1.27597
$227$	219.388	−	219.388i	0.966466	−	0.966466i	−0.0329895	−	0.999456i	$-0.510503\pi$
$227$	219.388	−	219.388i	0.966466	−	0.966466i	0.999456	+	0.0329895i	$0.0105028\pi$
$228$	−34.4673	−	34.4673i	−0.151172	−	0.151172i
$229$			314.913i			1.37517i	0.726105	+	0.687583i	$0.241328\pi$
$229$			314.913i			1.37517i	−0.726105	+	0.687583i	$0.758672\pi$
$230$	30.6133	+	14.5885i	0.133101	+	0.0634282i
$231$	59.5790			0.257918
$232$	−98.4067	+	98.4067i	−0.424167	+	0.424167i
$233$	20.1806	+	20.1806i	0.0866119	+	0.0866119i	0.749085	−	0.662473i	$-0.230493\pi$
$233$	20.1806	+	20.1806i	0.0866119	+	0.0866119i	−0.662473	+	0.749085i	$0.730493\pi$
$234$			45.6869i			0.195243i
$235$	−406.336	+	144.054i	−1.72909	+	0.612994i
$236$	−30.4764			−0.129137
$237$	155.581	−	155.581i	0.656459	−	0.656459i
$238$	−245.807	−	245.807i	−1.03280	−	1.03280i
$239$		−	363.636i		−	1.52149i	−0.649051	−	0.760745i	$-0.724834\pi$
$239$		−	363.636i		−	1.52149i	0.649051	−	0.760745i	$-0.275166\pi$
$240$	11.5750	+	32.6500i	0.0482292	+	0.136041i
$241$	53.3378			0.221319			0.110659	−	0.993858i	$-0.464704\pi$
$241$	53.3378			0.221319			0.110659	+	0.993858i	$0.464704\pi$
$242$	112.078	−	112.078i	0.463132	−	0.463132i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			24.1139i			0.0988275i
$245$	−179.856	+	377.421i	−0.734108	+	1.54050i
$246$	49.7596			0.202275
$247$	−107.145	+	107.145i	−0.433786	+	0.433786i
$248$	−11.8130	−	11.8130i	−0.0476332	−	0.0476332i
$249$		−	60.9437i		−	0.244754i
$250$	150.825	+	92.2050i	0.603301	+	0.368820i
$251$	165.873			0.660850			0.330425	−	0.943832i	$-0.392808\pi$
$251$	165.873			0.660850			0.330425	+	0.943832i	$0.392808\pi$
$252$	−48.8580	+	48.8580i	−0.193881	+	0.193881i
$253$	−10.1294	−	10.1294i	−0.0400370	−	0.0400370i
$254$		−	38.6059i		−	0.151992i
$255$	−166.873	−	79.5218i	−0.654405	−	0.311850i
$256$	16.0000			0.0625000
$257$	−256.875	+	256.875i	−0.999515	+	0.999515i	−1.00000		0.000484450i	$-0.999846\pi$
$257$	−256.875	+	256.875i	−0.999515	+	0.999515i	0.000484450		1.00000i	$0.499846\pi$
$258$	54.1800	+	54.1800i	0.210000	+	0.210000i
$259$			679.037i			2.62176i
$260$	101.496	−	35.9821i	0.390368	−	0.138393i
$261$	−147.610			−0.565556
$262$	50.6870	−	50.6870i	0.193462	−	0.193462i
$263$	−29.0957	−	29.0957i	−0.110630	−	0.110630i	0.649625	−	0.760255i	$-0.274926\pi$
$263$	−29.0957	−	29.0957i	−0.110630	−	0.110630i	−0.760255	+	0.649625i	$0.774926\pi$
$264$		−	14.6332i		−	0.0554287i
$265$	−150.045	−	423.237i	−0.566209	−	1.59712i
$266$	−229.164			−0.861519
$267$	−107.669	+	107.669i	−0.403253	+	0.403253i
$268$	−159.950	−	159.950i	−0.596827	−	0.596827i
$269$		−	92.9336i		−	0.345478i	−0.984968	−	0.172739i	$-0.944738\pi$
$269$		−	92.9336i		−	0.345478i	0.984968	−	0.172739i	$-0.0552618\pi$
$270$	−15.8062	+	33.1687i	−0.0585415	+	0.122847i
$271$	−355.672			−1.31244			−0.656221	−	0.754568i	$-0.727846\pi$
$271$	−355.672			−1.31244			−0.656221	+	0.754568i	$0.727846\pi$
$272$	−60.3725	+	60.3725i	−0.221958	+	0.221958i
$273$	151.880	+	151.880i	0.556337	+	0.556337i
$274$			227.887i			0.831703i
$275$	−47.0354	−	57.9997i	−0.171038	−	0.210908i
$276$	16.6132			0.0601929
$277$	91.3940	−	91.3940i	0.329942	−	0.329942i	−0.522622	−	0.852564i	$-0.675046\pi$
$277$	91.3940	−	91.3940i	0.329942	−	0.329942i	0.852564	+	0.522622i	$0.175046\pi$
$278$	205.743	+	205.743i	0.740084	+	0.740084i
$279$		−	17.7196i		−	0.0635109i
$280$	147.020	+	70.0609i	0.525071	+	0.250217i
$281$	203.040			0.722564			0.361282	−	0.932457i	$-0.382339\pi$
$281$	203.040			0.722564			0.361282	+	0.932457i	$0.382339\pi$
$282$	−149.343	+	149.343i	−0.529584	+	0.529584i
$283$	−127.646	−	127.646i	−0.451046	−	0.451046i	0.444656	−	0.895702i	$-0.353326\pi$
$283$	−127.646	−	127.646i	−0.451046	−	0.451046i	−0.895702	+	0.444656i	$0.853326\pi$
$284$		−	40.9594i		−	0.144223i
$285$	−114.856	+	40.7186i	−0.403004	+	0.142872i
$286$	−45.4887			−0.159051
$287$	165.419	−	165.419i	0.576374	−	0.576374i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	166.605i		−	0.576489i
$290$	116.255	+	327.923i	0.400878	+	1.13077i
$291$	38.1052			0.130946
$292$	−1.22371	+	1.22371i	−0.00419079	+	0.00419079i
$293$	−19.7725	−	19.7725i	−0.0674828	−	0.0674828i	0.672560	−	0.740043i	$-0.265195\pi$
$293$	−19.7725	−	19.7725i	−0.0674828	−	0.0674828i	−0.740043	+	0.672560i	$0.765195\pi$
$294$			204.819i			0.696664i
$295$	−32.7767	+	68.7806i	−0.111107	+	0.233155i
$296$	166.778			0.563439
$297$	10.9749	−	10.9749i	0.0369524	−	0.0369524i
$298$	−51.6051	−	51.6051i	−0.173172	−	0.173172i
$299$		−	51.6440i		−	0.172722i
$300$	86.1345	+	8.99128i	0.287115	+	0.0299709i
$301$	360.228			1.19677
$302$	−113.345	+	113.345i	−0.375314	+	0.375314i
$303$	−166.757	−	166.757i	−0.550353	−	0.550353i
$304$			56.2849i			0.185148i
$305$	54.4214	+	25.9339i	0.178431	+	0.0850293i
$306$	−90.5588			−0.295944
$307$	22.7462	−	22.7462i	0.0740918	−	0.0740918i	−0.669090	−	0.743182i	$-0.733316\pi$
$307$	22.7462	−	22.7462i	0.0740918	−	0.0740918i	0.743182	+	0.669090i	$0.233316\pi$
$308$	−48.6460	−	48.6460i	−0.157942	−	0.157942i
$309$			57.1410i			0.184922i
$310$	−39.3648	+	13.9555i	−0.126983	+	0.0450179i
$311$	58.8069			0.189090			0.0945449	−	0.995521i	$-0.469860\pi$
$311$	58.8069			0.189090			0.0945449	+	0.995521i	$0.469860\pi$
$312$	37.3032	−	37.3032i	0.119562	−	0.119562i
$313$	−321.959	−	321.959i	−1.02862	−	1.02862i	−0.999578	−	0.0290452i	$-0.990753\pi$
$313$	−321.959	−	321.959i	−1.02862	−	1.02862i	−0.0290452	−	0.999578i	$-0.509247\pi$
$314$		−	321.828i		−	1.02493i
$315$	57.7193	+	162.811i	0.183236	+	0.516859i
$316$	−254.062			−0.803995
$317$	65.2518	−	65.2518i	0.205842	−	0.205842i	−0.596656	−	0.802497i	$-0.703504\pi$
$317$	65.2518	−	65.2518i	0.205842	−	0.205842i	0.802497	+	0.596656i	$0.203504\pi$
$318$	−155.555	−	155.555i	−0.489165	−	0.489165i
$319$		−	146.970i		−	0.460720i
$320$	17.2076	−	36.1095i	0.0537738	−	0.112842i
$321$	262.637			0.818185
$322$	55.2285	−	55.2285i	0.171517	−	0.171517i
$323$	−212.379	−	212.379i	−0.657520	−	0.657520i
$324$			18.0000i			0.0555556i
$325$	27.9503	−	267.758i	0.0860010	−	0.823870i
$326$	244.352			0.749545
$327$	72.9957	−	72.9957i	0.223228	−	0.223228i
$328$	−40.6286	−	40.6286i	−0.123868	−	0.123868i
$329$			992.940i			3.01806i
$330$	−33.0248	−	15.7376i	−0.100075	−	0.0476898i
$331$	−498.721			−1.50671			−0.753355	−	0.657614i	$-0.771566\pi$
$331$	−498.721			−1.50671			−0.753355	+	0.657614i	$0.771566\pi$
$332$	−49.7603	+	49.7603i	−0.149880	+	0.149880i
$333$	125.083	+	125.083i	0.375626	+	0.375626i
$334$		−	253.070i		−	0.757695i
$335$	−533.004	+	188.959i	−1.59106	+	0.564058i
$336$	79.7848			0.237455
$337$	253.715	−	253.715i	0.752863	−	0.752863i	−0.222149	−	0.975013i	$-0.571307\pi$
$337$	253.715	−	253.715i	0.752863	−	0.752863i	0.975013	+	0.222149i	$0.0713072\pi$
$338$	53.0392	+	53.0392i	0.156921	+	0.156921i
$339$			353.180i			1.04183i
$340$	71.3222	+	201.181i	0.209771	+	0.591708i
$341$	17.6427			0.0517380
$342$	−42.2137	+	42.2137i	−0.123432	+	0.123432i
$343$	281.887	+	281.887i	0.821827	+	0.821827i
$344$		−	88.4755i		−	0.257196i
$345$	17.8672	−	37.4935i	0.0517889	−	0.108677i
$346$	232.278			0.671324
$347$	350.383	−	350.383i	1.00975	−	1.00975i	0.00979723	−	0.999952i	$-0.496881\pi$
$347$	350.383	−	350.383i	1.00975	−	1.00975i	0.999952	−	0.00979723i	$-0.00311860\pi$
$348$	120.523	+	120.523i	0.346331	+	0.346331i
$349$		−	501.750i		−	1.43768i	−0.695176	−	0.718840i	$-0.744673\pi$
$349$		−	501.750i		−	1.43768i	0.695176	−	0.718840i	$-0.255327\pi$
$350$	316.233	−	256.453i	0.903523	−	0.732721i
$351$	55.9548			0.159415
$352$	−11.9479	+	11.9479i	−0.0339430	+	0.0339430i
$353$	83.9266	+	83.9266i	0.237752	+	0.237752i	0.815919	−	0.578166i	$-0.196232\pi$
$353$	83.9266	+	83.9266i	0.237752	+	0.237752i	−0.578166	+	0.815919i	$0.696232\pi$
$354$			37.3259i			0.105440i
$355$	−92.4390	−	44.0509i	−0.260391	−	0.124087i
$356$	175.822			0.493883
$357$	−301.051	+	301.051i	−0.843279	+	0.843279i
$358$	127.573	+	127.573i	0.356348	+	0.356348i
$359$		−	68.1546i		−	0.189846i	−0.995485	−	0.0949228i	$-0.969740\pi$
$359$		−	68.1546i		−	0.189846i	0.995485	−	0.0949228i	$-0.0302604\pi$
$360$	39.9879	−	14.1764i	0.111077	−	0.0393789i
$361$	163.001			0.451525
$362$	321.120	−	321.120i	0.887072	−	0.887072i
$363$	−137.267	−	137.267i	−0.378146	−	0.378146i
$364$		−	248.019i		−	0.681371i
$365$	1.44565	+	4.07780i	0.00396069	+	0.0111720i
$366$	29.5334			0.0806923
$367$	91.7002	−	91.7002i	0.249864	−	0.249864i	−0.571051	−	0.820915i	$-0.693464\pi$
$367$	91.7002	−	91.7002i	0.249864	−	0.249864i	0.820915	+	0.571051i	$0.193464\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	60.9428i		−	0.165157i
$370$	179.366	−	376.392i	0.484772	−	1.01728i
$371$	−1034.24			−2.78771
$372$	−14.4680	+	14.4680i	−0.0388924	+	0.0388924i
$373$	23.7795	+	23.7795i	0.0637519	+	0.0637519i	0.738264	−	0.674512i	$-0.235646\pi$
$373$	23.7795	+	23.7795i	0.0637519	+	0.0637519i	−0.674512	+	0.738264i	$0.735646\pi$
$374$		−	90.1659i		−	0.241085i
$375$	112.928	−	184.722i	0.301140	−	0.492593i
$376$	243.876			0.648605
$377$	374.658	−	374.658i	0.993789	−	0.993789i
$378$	59.8386	+	59.8386i	0.158303	+	0.158303i
$379$		−	178.495i		−	0.470964i	−0.971879	−	0.235482i	$-0.924333\pi$
$379$		−	178.495i		−	0.470964i	0.971879	−	0.235482i	$-0.0756669\pi$
$380$	127.026	+	60.5331i	0.334280	+	0.159298i
$381$	−47.2824			−0.124101
$382$	−91.9988	+	91.9988i	−0.240835	+	0.240835i
$383$	111.563	+	111.563i	0.291288	+	0.291288i	0.837589	−	0.546301i	$-0.183964\pi$
$383$	111.563	+	111.563i	0.291288	+	0.291288i	−0.546301	+	0.837589i	$0.683964\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−162.104	+	57.4689i	−0.421050	+	0.149270i
$386$	146.337			0.379113
$387$	66.3566	−	66.3566i	0.171464	−	0.171464i
$388$	−31.1128	−	31.1128i	−0.0801876	−	0.0801876i
$389$			765.523i			1.96792i	0.178377	+	0.983962i	$0.442915\pi$
$389$			765.523i			1.96792i	−0.178377	+	0.983962i	$0.557085\pi$
$390$	−44.0688	−	124.306i	−0.112997	−	0.318734i
$391$	102.367			0.261807
$392$	167.234	−	167.234i	0.426618	−	0.426618i
$393$	−62.0786	−	62.0786i	−0.157961	−	0.157961i
$394$			142.449i			0.361546i
$395$	−273.238	+	573.380i	−0.691742	+	1.45159i
$396$	−17.9219			−0.0452573
$397$	−68.4982	+	68.4982i	−0.172540	+	0.172540i	−0.788094	−	0.615555i	$-0.788932\pi$
$397$	−68.4982	+	68.4982i	−0.172540	+	0.172540i	0.615555	+	0.788094i	$0.288932\pi$
$398$	−272.364	−	272.364i	−0.684331	−	0.684331i
$399$			280.668i			0.703427i
$400$	−62.9872	−	77.6699i	−0.157468	−	0.194175i
$401$	603.687			1.50545			0.752727	−	0.658333i	$-0.228738\pi$
$401$	603.687			1.50545			0.752727	+	0.658333i	$0.228738\pi$
$402$	−195.897	+	195.897i	−0.487307	+	0.487307i
$403$	44.9751	+	44.9751i	0.111601	+	0.111601i
$404$			272.313i			0.674042i
$405$	40.6232	+	19.3586i	0.100304	+	0.0477990i
$406$	801.326			1.97371
$407$	−124.541	+	124.541i	−0.305997	+	0.305997i
$408$	73.9410	+	73.9410i	0.181228	+	0.181228i
$409$			410.613i			1.00394i	0.864884	+	0.501972i	$0.167392\pi$
$409$			410.613i			1.00394i	−0.864884	+	0.501972i	$0.832608\pi$
$410$	−135.387	+	47.9973i	−0.330213	+	0.117067i
$411$	279.103			0.679082
$412$	46.6554	−	46.6554i	0.113241	−	0.113241i
$413$	124.085	+	124.085i	0.300448	+	0.300448i
$414$		−	20.3470i		−	0.0491473i
$415$	58.7852	+	165.817i	0.141651	+	0.399560i
$416$	−60.9159			−0.146432
$417$	251.983	−	251.983i	0.604276	−	0.604276i
$418$	−42.0305	−	42.0305i	−0.100551	−	0.100551i
$419$		−	426.786i		−	1.01858i	−0.860594	−	0.509292i	$-0.829907\pi$
$419$		−	426.786i		−	1.01858i	0.860594	−	0.509292i	$-0.170093\pi$
$420$	85.8067	−	180.062i	0.204302	−	0.428719i
$421$	589.186			1.39949			0.699746	−	0.714392i	$-0.253297\pi$
$421$	589.186			1.39949			0.699746	+	0.714392i	$0.253297\pi$
$422$	−317.005	+	317.005i	−0.751197	+	0.751197i
$423$	182.907	+	182.907i	0.432404	+	0.432404i
$424$			254.020i			0.599103i
$425$	530.739	+	55.4020i	1.24880	+	0.130358i
$426$	−50.1648			−0.117758
$427$	98.1798	−	98.1798i	0.229929	−	0.229929i
$428$	−214.442	−	214.442i	−0.501034	−	0.501034i
$429$			55.7120i			0.129865i
$430$	−199.676	−	95.1534i	−0.464362	−	0.221287i
$431$	507.800			1.17819			0.589095	−	0.808064i	$-0.299484\pi$
$431$	507.800			1.17819			0.589095	+	0.808064i	$0.299484\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	97.8860	+	97.8860i	0.226065	+	0.226065i	0.811046	−	0.584982i	$-0.198898\pi$
$433$	97.8860	+	97.8860i	0.226065	+	0.226065i	−0.584982	+	0.811046i	$0.698898\pi$
$434$			96.1936i			0.221644i
$435$	401.622	−	142.382i	0.923269	−	0.327315i
$436$	−119.201			−0.273398
$437$	47.7178	−	47.7178i	0.109194	−	0.109194i
$438$	1.49873	+	1.49873i	0.00342176	+	0.00342176i
$439$			45.5200i			0.103690i	0.998655	+	0.0518451i	$0.0165102\pi$
$439$			45.5200i			0.103690i	−0.998655	+	0.0518451i	$0.983490\pi$
$440$	14.1149	+	39.8143i	0.0320793	+	0.0904872i
$441$	250.851			0.568823
$442$	229.853	−	229.853i	0.520029	−	0.520029i
$443$	−204.022	−	204.022i	−0.460547	−	0.460547i	0.438288	−	0.898835i	$-0.355585\pi$
$443$	−204.022	−	204.022i	−0.460547	−	0.460547i	−0.898835	+	0.438288i	$0.855585\pi$
$444$		−	204.260i		−	0.460046i
$445$	189.093	−	396.803i	0.424927	−	0.891693i
$446$	32.3055			0.0724339
$447$	−63.2031	+	63.2031i	−0.141394	+	0.141394i
$448$	−65.1440	−	65.1440i	−0.145411	−	0.145411i
$449$		−	699.112i		−	1.55704i	−0.627618	−	0.778521i	$-0.715970\pi$
$449$		−	699.112i		−	1.55704i	0.627618	−	0.778521i	$-0.284030\pi$
$450$	11.0120	−	105.493i	0.0244712	−	0.234428i
$451$	60.6784			0.134542
$452$	288.370	−	288.370i	0.637987	−	0.637987i
$453$	138.819	+	138.819i	0.306443	+	0.306443i
$454$			438.776i			0.966466i
$455$	−559.741	−	266.739i	−1.23020	−	0.586239i
$456$	68.9346			0.151172
$457$	175.228	−	175.228i	0.383432	−	0.383432i	−0.488905	−	0.872337i	$-0.662604\pi$
$457$	175.228	−	175.228i	0.383432	−	0.383432i	0.872337	+	0.488905i	$0.162604\pi$
$458$	−314.913	−	314.913i	−0.687583	−	0.687583i
$459$			110.911i			0.241637i
$460$	−45.2018	+	16.0249i	−0.0982648	+	0.0348367i
$461$	233.765			0.507083			0.253542	−	0.967324i	$-0.418405\pi$
$461$	233.765			0.507083			0.253542	+	0.967324i	$0.418405\pi$
$462$	−59.5790	+	59.5790i	−0.128959	+	0.128959i
$463$	295.945	+	295.945i	0.639190	+	0.639190i	0.950356	−	0.311166i	$-0.100719\pi$
$463$	295.945	+	295.945i	0.639190	+	0.639190i	−0.311166	+	0.950356i	$0.600719\pi$
$464$		−	196.813i		−	0.424167i
$465$	17.0920	+	48.2119i	0.0367570	+	0.103681i
$466$	−40.3611			−0.0866119
$467$	−40.8201	+	40.8201i	−0.0874092	+	0.0874092i	−0.749459	−	0.662050i	$-0.769687\pi$
$467$	−40.8201	+	40.8201i	−0.0874092	+	0.0874092i	0.662050	+	0.749459i	$0.269687\pi$
$468$	−45.6869	−	45.6869i	−0.0976216	−	0.0976216i
$469$			1302.47i			2.77712i
$470$	262.283	−	550.390i	0.558048	−	1.17104i
$471$	−394.157			−0.836852
$472$	30.4764	−	30.4764i	0.0645687	−	0.0645687i
$473$	66.0687	+	66.0687i	0.139680	+	0.139680i
$474$			311.162i			0.656459i
$475$	273.228	−	221.577i	0.575216	−	0.466477i
$476$	491.614			1.03280
$477$	−190.515	+	190.515i	−0.399402	+	0.399402i
$478$	363.636	+	363.636i	0.760745	+	0.760745i
$479$		−	145.106i		−	0.302935i	−0.988462	−	0.151467i	$-0.951600\pi$
$479$		−	145.106i		−	0.302935i	0.988462	−	0.151467i	$-0.0483999\pi$
$480$	−44.2250	−	21.0750i	−0.0921353	−	0.0439062i
$481$	−634.964			−1.32009
$482$	−53.3378	+	53.3378i	−0.110659	+	0.110659i
$483$	−67.6409	−	67.6409i	−0.140043	−	0.140043i
$484$			224.156i			0.463132i
$485$	−103.678	+	36.7556i	−0.213769	+	0.0757848i
$486$	22.0454			0.0453609
$487$	−9.52353	+	9.52353i	−0.0195555	+	0.0195555i	−0.716817	−	0.697261i	$-0.754402\pi$
$487$	−9.52353	+	9.52353i	−0.0195555	+	0.0195555i	0.697261	+	0.716817i	$0.254402\pi$
$488$	−24.1139	−	24.1139i	−0.0494137	−	0.0494137i
$489$		−	299.269i		−	0.612001i
$490$	−197.565	−	557.278i	−0.403194	−	1.13730i
$491$	−436.381			−0.888759			−0.444379	−	0.895839i	$-0.646576\pi$
$491$	−436.381			−0.888759			−0.444379	+	0.895839i	$0.646576\pi$
$492$	−49.7596	+	49.7596i	−0.101137	+	0.101137i
$493$	742.633	+	742.633i	1.50635	+	1.50635i
$494$		−	214.290i		−	0.433786i
$495$	−19.2746	+	40.4469i	−0.0389385	+	0.0817110i
$496$	23.6261			0.0476332
$497$	−166.766	+	166.766i	−0.335546	+	0.335546i
$498$	60.9437	+	60.9437i	0.122377	+	0.122377i
$499$		−	521.427i		−	1.04494i	−0.852656	−	0.522472i	$-0.825010\pi$
$499$		−	521.427i		−	1.04494i	0.852656	−	0.522472i	$-0.174990\pi$
$500$	−243.030	+	58.6202i	−0.486060	+	0.117240i
$501$	−309.946			−0.618655
$502$	−165.873	+	165.873i	−0.330425	+	0.330425i
$503$	−487.805	−	487.805i	−0.969791	−	0.969791i	0.0297662	−	0.999557i	$-0.490524\pi$
$503$	−487.805	−	487.805i	−0.969791	−	0.969791i	−0.999557	+	0.0297662i	$0.990524\pi$
$504$		−	97.7161i		−	0.193881i
$505$	614.568	+	292.866i	1.21697	+	0.579933i
$506$	20.2587			0.0400370
$507$	64.9595	−	64.9595i	0.128125	−	0.128125i
$508$	38.6059	+	38.6059i	0.0759959	+	0.0759959i
$509$			57.1963i			0.112370i	0.998420	+	0.0561850i	$0.0178937\pi$
$509$			57.1963i			0.112370i	−0.998420	+	0.0561850i	$0.982106\pi$
$510$	246.395	−	87.3515i	0.483128	−	0.171277i
$511$	9.96468			0.0195004
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	51.7010	+	51.7010i	0.100782	+	0.100782i
$514$		−	513.751i		−	0.999515i
$515$	−55.1172	−	155.471i	−0.107024	−	0.301885i
$516$	−108.360			−0.210000
$517$	−182.113	+	182.113i	−0.352250	+	0.352250i
$518$	−679.037	−	679.037i	−1.31088	−	1.31088i
$519$		−	284.481i		−	0.548134i
$520$	−65.5136	+	137.478i	−0.125988	+	0.264380i
$521$	−216.280			−0.415124			−0.207562	−	0.978222i	$-0.566553\pi$
$521$	−216.280			−0.415124			−0.207562	+	0.978222i	$0.566553\pi$
$522$	147.610	−	147.610i	0.282778	−	0.282778i
$523$	733.496	+	733.496i	1.40248	+	1.40248i	0.792143	+	0.610335i	$0.208965\pi$
$523$	733.496	+	733.496i	1.40248	+	1.40248i	0.610335	+	0.792143i	$0.291035\pi$
$524$			101.374i			0.193462i
$525$	−314.089	−	387.305i	−0.598265	−	0.737724i
$526$	58.1915			0.110630
$527$	−89.1479	+	89.1479i	−0.169161	+	0.169161i
$528$	14.6332	+	14.6332i	0.0277143	+	0.0277143i
$529$			23.0000i			0.0434783i
$530$	573.283	+	273.192i	1.08167	+	0.515457i
$531$	45.7147			0.0860916
$532$	229.164	−	229.164i	0.430760	−	0.430760i
$533$	154.683	+	154.683i	0.290212	+	0.290212i
$534$		−	215.337i		−	0.403253i
$535$	−714.591	+	253.335i	−1.33568	+	0.473524i
$536$	319.899			0.596827
$537$	156.244	−	156.244i	0.290957	−	0.290957i
$538$	92.9336	+	92.9336i	0.172739	+	0.172739i
$539$			249.763i			0.463381i
$540$	−17.3625	−	48.9749i	−0.0321528	−	0.0906943i
$541$	740.869			1.36944			0.684721	−	0.728805i	$-0.259924\pi$
$541$	740.869			1.36944			0.684721	+	0.728805i	$0.259924\pi$
$542$	355.672	−	355.672i	0.656221	−	0.656221i
$543$	−393.290	−	393.290i	−0.724292	−	0.724292i
$544$		−	120.745i		−	0.221958i
$545$	−128.198	+	269.019i	−0.235226	+	0.493613i
$546$	−303.760			−0.556337
$547$	−353.243	+	353.243i	−0.645782	+	0.645782i	−0.951971	−	0.306189i	$-0.900946\pi$
$547$	−353.243	+	353.243i	−0.645782	+	0.645782i	0.306189	+	0.951971i	$0.400946\pi$
$548$	−227.887	−	227.887i	−0.415851	−	0.415851i
$549$		−	36.1709i		−	0.0658850i
$550$	105.035	+	10.9642i	0.190973	+	0.0199350i
$551$	692.351			1.25654
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	1034.42	+	1034.42i	1.87055	+	1.87055i
$554$			182.788i			0.329942i
$555$	−460.984	−	219.677i	−0.830602	−	0.395815i
$556$	−411.487			−0.740084
$557$	−666.199	+	666.199i	−1.19605	+	1.19605i	−0.220708	+	0.975340i	$0.570837\pi$
$557$	−666.199	+	666.199i	−1.19605	+	1.19605i	−0.975340	+	0.220708i	$0.929163\pi$
$558$	17.7196	+	17.7196i	0.0317555	+	0.0317555i
$559$			336.848i			0.602590i
$560$	−217.081	+	76.9591i	−0.387644	+	0.137427i
$561$	−110.430			−0.196845
$562$	−203.040	+	203.040i	−0.361282	+	0.361282i
$563$	−629.280	−	629.280i	−1.11773	−	1.11773i	−0.992074	−	0.125652i	$-0.959898\pi$
$563$	−629.280	−	629.280i	−1.11773	−	1.11773i	−0.125652	−	0.992074i	$-0.540102\pi$
$564$		−	298.685i		−	0.529584i
$565$	−340.671	−	960.942i	−0.602958	−	1.70078i
$566$	255.292			0.451046
$567$	73.2870	−	73.2870i	0.129254	−	0.129254i
$568$	40.9594	+	40.9594i	0.0721116	+	0.0721116i
$569$			379.634i			0.667194i	0.942716	+	0.333597i	$0.108263\pi$
$569$			379.634i			0.667194i	−0.942716	+	0.333597i	$0.891737\pi$
$570$	74.1376	−	155.575i	0.130066	−	0.272938i
$571$	719.736			1.26048			0.630242	−	0.776399i	$-0.282956\pi$
$571$	719.736			1.26048			0.630242	+	0.776399i	$0.282956\pi$
$572$	45.4887	−	45.4887i	0.0795257	−	0.0795257i
$573$	112.675	+	112.675i	0.196641	+	0.196641i
$574$			330.839i			0.576374i
$575$	−12.4479	+	119.248i	−0.0216485	+	0.207388i
$576$	−24.0000			−0.0416667
$577$	391.579	−	391.579i	0.678647	−	0.678647i	−0.281047	−	0.959694i	$-0.590682\pi$
$577$	391.579	−	391.579i	0.678647	−	0.678647i	0.959694	+	0.281047i	$0.0906818\pi$
$578$	166.605	+	166.605i	0.288245	+	0.288245i
$579$		−	179.226i		−	0.309544i
$580$	−444.177	−	211.668i	−0.765823	−	0.364945i
$581$	405.198			0.697415
$582$	−38.1052	+	38.1052i	−0.0654729	+	0.0654729i
$583$	−189.688	−	189.688i	−0.325365	−	0.325365i
$584$		−	2.44742i		−	0.00419079i
$585$	−152.244	+	53.9731i	−0.260245	+	0.0922617i
$586$	39.5449			0.0674828
$587$	−525.796	+	525.796i	−0.895734	+	0.895734i	−0.995055	−	0.0993214i	$-0.968333\pi$
$587$	−525.796	+	525.796i	−0.895734	+	0.895734i	0.0993214	+	0.995055i	$0.468333\pi$
$588$	−204.819	−	204.819i	−0.348332	−	0.348332i
$589$			83.1119i			0.141107i
$590$	−36.0039	−	101.557i	−0.0610236	−	0.172131i
$591$	174.464			0.295201
$592$	−166.778	+	166.778i	−0.281720	+	0.281720i
$593$	376.688	+	376.688i	0.635225	+	0.635225i	0.949374	−	0.314149i	$-0.101719\pi$
$593$	376.688	+	376.688i	0.635225	+	0.635225i	−0.314149	+	0.949374i	$0.601719\pi$
$594$			21.9497i			0.0369524i
$595$	528.719	−	1109.50i	0.888604	−	1.86470i
$596$	103.210			0.173172
$597$	−333.576	+	333.576i	−0.558754	+	0.558754i
$598$	51.6440	+	51.6440i	0.0863611	+	0.0863611i
$599$			1066.37i			1.78025i	0.455713	+	0.890127i	$0.349384\pi$
$599$			1066.37i			1.78025i	−0.455713	+	0.890127i	$0.650616\pi$
$600$	−95.1258	+	77.1432i	−0.158543	+	0.128572i
$601$	−199.265			−0.331555			−0.165777	−	0.986163i	$-0.553013\pi$
$601$	−199.265			−0.331555			−0.165777	+	0.986163i	$0.553013\pi$
$602$	−360.228	+	360.228i	−0.598386	+	0.598386i
$603$	239.924	+	239.924i	0.397885	+	0.397885i
$604$		−	226.690i		−	0.375314i
$605$	505.885	+	241.074i	0.836174	+	0.398470i
$606$	333.514			0.550353
$607$	210.101	−	210.101i	0.346131	−	0.346131i	−0.512536	−	0.858666i	$-0.671294\pi$
$607$	210.101	−	210.101i	0.346131	−	0.346131i	0.858666	+	0.512536i	$0.171294\pi$
$608$	−56.2849	−	56.2849i	−0.0925738	−	0.0925738i
$609$		−	981.420i		−	1.61153i
$610$	−80.3553	+	28.4874i	−0.131730	+	0.0467007i
$611$	−928.494			−1.51963
$612$	90.5588	−	90.5588i	0.147972	−	0.147972i
$613$	105.165	+	105.165i	0.171557	+	0.171557i	0.787663	−	0.616106i	$-0.211291\pi$
$613$	105.165	+	105.165i	0.171557	+	0.171557i	−0.616106	+	0.787663i	$0.711291\pi$
$614$			45.4924i			0.0740918i
$615$	58.7844	+	165.815i	0.0955845	+	0.269618i
$616$	97.2920			0.157942
$617$	−224.661	+	224.661i	−0.364118	+	0.364118i	−0.865326	−	0.501209i	$-0.832889\pi$
$617$	−224.661	+	224.661i	−0.364118	+	0.364118i	0.501209	+	0.865326i	$0.332889\pi$
$618$	−57.1410	−	57.1410i	−0.0924611	−	0.0924611i
$619$		−	975.230i		−	1.57549i	−0.616000	−	0.787746i	$-0.711248\pi$
$619$		−	975.230i		−	1.57549i	0.616000	−	0.787746i	$-0.288752\pi$
$620$	25.4093	−	53.3204i	0.0409827	−	0.0860006i
$621$	−24.9199			−0.0401286
$622$	−58.8069	+	58.8069i	−0.0945449	+	0.0945449i
$623$	−715.860	−	715.860i	−1.14905	−	1.14905i
$624$			74.6064i			0.119562i
$625$	−129.077	+	611.526i	−0.206523	+	0.978442i
$626$	643.918			1.02862
$627$	−51.4766	+	51.4766i	−0.0820999	+	0.0820999i
$628$	321.828	+	321.828i	0.512465	+	0.512465i
$629$		−	1258.60i		−	2.00096i
$630$	−220.530	−	105.091i	−0.350048	−	0.166812i
$631$	−847.237			−1.34269			−0.671344	−	0.741146i	$-0.734283\pi$
$631$	−847.237			−1.34269			−0.671344	+	0.741146i	$0.734283\pi$
$632$	254.062	−	254.062i	0.401997	−	0.401997i
$633$	388.250	+	388.250i	0.613350	+	0.613350i
$634$			130.504i			0.205842i
$635$	128.647	−	45.6078i	0.202594	−	0.0718233i
$636$	311.109			0.489165
$637$	−636.701	+	636.701i	−0.999530	+	0.999530i
$638$	146.970	+	146.970i	0.230360	+	0.230360i
$639$			61.4391i			0.0961488i
$640$	18.9019	+	53.3171i	0.0295342	+	0.0833080i
$641$	−927.911			−1.44760			−0.723799	−	0.690010i	$-0.757606\pi$
$641$	−927.911			−1.44760			−0.723799	+	0.690010i	$0.757606\pi$
$642$	−262.637	+	262.637i	−0.409092	+	0.409092i
$643$	424.937	+	424.937i	0.660867	+	0.660867i	0.955584	−	0.294718i	$-0.0952256\pi$
$643$	424.937	+	424.937i	0.660867	+	0.660867i	−0.294718	+	0.955584i	$0.595226\pi$
$644$			110.457i			0.171517i
$645$	−116.539	+	244.552i	−0.180680	+	0.379150i
$646$	424.758			0.657520
$647$	−67.6741	+	67.6741i	−0.104597	+	0.104597i	−0.757468	−	0.652872i	$-0.773564\pi$
$647$	−67.6741	+	67.6741i	−0.104597	+	0.104597i	0.652872	+	0.757468i	$0.273564\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			45.5163i			0.0701330i
$650$	239.808	+	295.708i	0.368935	+	0.454936i
$651$	117.813			0.180972
$652$	−244.352	+	244.352i	−0.374773	+	0.374773i
$653$	412.106	+	412.106i	0.631097	+	0.631097i	0.948343	−	0.317246i	$-0.102758\pi$
$653$	412.106	+	412.106i	0.631097	+	0.631097i	−0.317246	+	0.948343i	$0.602758\pi$
$654$			145.991i			0.223228i
$655$	228.785	+	109.025i	0.349290	+	0.166451i
$656$	81.2571			0.123868
$657$	1.83557	−	1.83557i	0.00279386	−	0.00279386i
$658$	−992.940	−	992.940i	−1.50903	−	1.50903i
$659$		−	677.303i		−	1.02777i	−0.857858	−	0.513887i	$-0.828205\pi$
$659$		−	677.303i		−	1.02777i	0.857858	−	0.513887i	$-0.171795\pi$
$660$	48.7624	−	17.2872i	0.0738824	−	0.0261927i
$661$	−136.925			−0.207148			−0.103574	−	0.994622i	$-0.533028\pi$
$661$	−136.925			−0.207148			−0.103574	+	0.994622i	$0.533028\pi$
$662$	498.721	−	498.721i	0.753355	−	0.753355i
$663$	−281.511	−	281.511i	−0.424602	−	0.424602i
$664$		−	99.5206i		−	0.149880i
$665$	−270.727	−	763.648i	−0.407109	−	1.14834i
$666$	−250.167			−0.375626
$667$	−166.857	+	166.857i	−0.250160	+	0.250160i
$668$	253.070	+	253.070i	0.378847	+	0.378847i
$669$		−	39.5660i		−	0.0591420i
$670$	344.044	−	721.963i	0.513499	−	1.07756i
$671$	36.0139			0.0536720
$672$	−79.7848	+	79.7848i	−0.118727	+	0.118727i
$673$	519.433	+	519.433i	0.771817	+	0.771817i	0.978424	−	0.206607i	$-0.0662423\pi$
$673$	519.433	+	519.433i	0.771817	+	0.771817i	−0.206607	+	0.978424i	$0.566242\pi$
$674$			507.430i			0.752863i
$675$	−129.202	−	13.4869i	−0.191410	−	0.0199806i
$676$	−106.078			−0.156921
$677$	706.858	−	706.858i	1.04410	−	1.04410i	0.0451224	−	0.998981i	$-0.485632\pi$
$677$	706.858	−	706.858i	1.04410	−	1.04410i	0.998981	−	0.0451224i	$-0.0143678\pi$
$678$	−353.180	−	353.180i	−0.520914	−	0.520914i
$679$			253.351i			0.373124i
$680$	−272.503	−	129.859i	−0.400740	−	0.190968i
$681$	537.388			0.789116
$682$	−17.6427	+	17.6427i	−0.0258690	+	0.0258690i
$683$	−317.830	−	317.830i	−0.465344	−	0.465344i	0.435059	−	0.900402i	$-0.356728\pi$
$683$	−317.830	−	317.830i	−0.465344	−	0.465344i	−0.900402	+	0.435059i	$0.856728\pi$
$684$		−	84.4273i		−	0.123432i
$685$	−759.391	+	269.218i	−1.10860	+	0.393019i
$686$	−563.773			−0.821827
$687$	−385.688	+	385.688i	−0.561410	+	0.561410i
$688$	88.4755	+	88.4755i	0.128598	+	0.128598i
$689$		−	967.114i		−	1.40365i
$690$	19.6264	+	55.3607i	0.0284440	+	0.0802329i
$691$	791.492			1.14543			0.572715	−	0.819755i	$-0.305890\pi$
$691$	791.492			1.14543			0.572715	+	0.819755i	$0.305890\pi$
$692$	−232.278	+	232.278i	−0.335662	+	0.335662i
$693$	72.9690	+	72.9690i	0.105294	+	0.105294i
$694$			700.766i			1.00975i
$695$	−442.544	+	928.662i	−0.636754	+	1.33620i
$696$	−241.046			−0.346331
$697$	−306.606	+	306.606i	−0.439894	+	0.439894i
$698$	501.750	+	501.750i	0.718840	+	0.718840i
$699$			49.4321i			0.0707183i
$700$	−59.7807	+	572.686i	−0.0854009	+	0.818122i
$701$	672.284			0.959036			0.479518	−	0.877532i	$-0.340812\pi$
$701$	672.284			0.959036			0.479518	+	0.877532i	$0.340812\pi$
$702$	−55.9548	+	55.9548i	−0.0797077	+	0.0797077i
$703$	−586.693	−	586.693i	−0.834556	−	0.834556i
$704$		−	23.8959i		−	0.0339430i
$705$	−674.087	−	321.229i	−0.956152	−	0.455644i
$706$	−167.853			−0.237752
$707$	1108.72	−	1108.72i	1.56821	−	1.56821i
$708$	−37.3259	−	37.3259i	−0.0527201	−	0.0527201i
$709$		−	1080.93i		−	1.52459i	−0.647232	−	0.762293i	$-0.724074\pi$
$709$		−	1080.93i		−	1.52459i	0.647232	−	0.762293i	$-0.275926\pi$
$710$	136.490	−	48.3881i	0.192239	−	0.0681523i
$711$	381.094			0.535997
$712$	−175.822	+	175.822i	−0.246941	+	0.246941i
$713$	−20.0300	−	20.0300i	−0.0280925	−	0.0280925i
$714$		−	602.102i		−	0.843279i
$715$	−53.7389	−	151.583i	−0.0751593	−	0.212004i
$716$	−255.145			−0.356348
$717$	445.361	−	445.361i	0.621146	−	0.621146i
$718$	68.1546	+	68.1546i	0.0949228	+	0.0949228i
$719$		−	44.1508i		−	0.0614059i	−0.999529	−	0.0307029i	$-0.990225\pi$
$719$		−	44.1508i		−	0.0614059i	0.999529	−	0.0307029i	$-0.00977458\pi$
$720$	−25.8114	+	54.1643i	−0.0358492	+	0.0752282i
$721$	−379.915			−0.526928
$722$	−163.001	+	163.001i	−0.225763	+	0.225763i
$723$	65.3252	+	65.3252i	0.0903529	+	0.0903529i
$724$			642.240i			0.887072i
$725$	−955.405	+	774.795i	−1.31780	+	1.06868i
$726$	274.534			0.378146
$727$	−577.116	+	577.116i	−0.793832	+	0.793832i	−0.982115	−	0.188283i	$-0.939708\pi$
$727$	−577.116	+	577.116i	−0.793832	+	0.793832i	0.188283	+	0.982115i	$0.439708\pi$
$728$	248.019	+	248.019i	0.340686	+	0.340686i
$729$		−	27.0000i		−	0.0370370i
$730$	−5.52345	−	2.63214i	−0.00756637	−	0.00360568i
$731$	−667.686			−0.913388
$732$	−29.5334	+	29.5334i	−0.0403462	+	0.0403462i
$733$	−427.263	−	427.263i	−0.582896	−	0.582896i	0.352802	−	0.935698i	$-0.385229\pi$
$733$	−427.263	−	427.263i	−0.582896	−	0.582896i	−0.935698	+	0.352802i	$0.885229\pi$
$734$			183.400i			0.249864i
$735$	−682.523	+	241.967i	−0.928603	+	0.329207i
$736$	27.1293			0.0368605
$737$	−238.883	+	238.883i	−0.324129	+	0.324129i
$738$	60.9428	+	60.9428i	0.0825784	+	0.0825784i
$739$		−	326.041i		−	0.441192i	−0.975365	−	0.220596i	$-0.929200\pi$
$739$		−	326.041i		−	0.441192i	0.975365	−	0.220596i	$-0.0708003\pi$
$740$	197.026	+	555.758i	0.266252	+	0.751024i
$741$	−262.451			−0.354185
$742$	1034.24	−	1034.24i	1.39386	−	1.39386i
$743$	786.240	+	786.240i	1.05820	+	1.05820i	0.998199	+	0.0599978i	$0.0191094\pi$
$743$	786.240	+	786.240i	1.05820	+	1.05820i	0.0599978	+	0.998199i	$0.480891\pi$
$744$		−	28.9359i		−	0.0388924i
$745$	111.000	−	232.930i	0.148994	−	0.312657i
$746$	−47.5589			−0.0637519
$747$	74.6404	−	74.6404i	0.0999202	−	0.0999202i
$748$	90.1659	+	90.1659i	0.120543	+	0.120543i
$749$			1746.21i			2.33138i
$750$	71.7948	+	297.650i	0.0957264	+	0.396867i
$751$	−856.133			−1.13999			−0.569995	−	0.821648i	$-0.693055\pi$
$751$	−856.133			−1.13999			−0.569995	+	0.821648i	$0.693055\pi$
$752$	−243.876	+	243.876i	−0.324303	+	0.324303i
$753$	203.153	+	203.153i	0.269791	+	0.269791i
$754$			749.317i			0.993789i
$755$	−511.604	−	243.800i	−0.677621	−	0.322914i
$756$	−119.677			−0.158303
$757$	534.371	−	534.371i	0.705906	−	0.705906i	−0.259765	−	0.965672i	$-0.583645\pi$
$757$	534.371	−	534.371i	0.705906	−	0.705906i	0.965672	+	0.259765i	$0.0836452\pi$
$758$	178.495	+	178.495i	0.235482	+	0.235482i
$759$		−	24.8117i		−	0.0326900i
$760$	−187.559	+	66.4932i	−0.246789	+	0.0874911i
$761$	84.8082			0.111443			0.0557216	−	0.998446i	$-0.482254\pi$
$761$	84.8082			0.111443			0.0557216	+	0.998446i	$0.482254\pi$
$762$	47.2824	−	47.2824i	0.0620504	−	0.0620504i
$763$	485.329	+	485.329i	0.636080	+	0.636080i
$764$		−	183.998i		−	0.240835i
$765$	−106.983	−	301.771i	−0.139847	−	0.394472i
$766$	−223.127			−0.291288
$767$	−116.031	+	116.031i	−0.151279	+	0.151279i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	662.469i		−	0.861468i	−0.902479	−	0.430734i	$-0.858255\pi$
$769$		−	662.469i		−	0.861468i	0.902479	−	0.430734i	$-0.141745\pi$
$770$	104.635	−	219.573i	0.135890	−	0.285160i
$771$	−629.214			−0.816101
$772$	−146.337	+	146.337i	−0.189556	+	0.189556i
$773$	608.097	+	608.097i	0.786671	+	0.786671i	0.980947	−	0.194276i	$-0.0622358\pi$
$773$	608.097	+	608.097i	0.786671	+	0.786671i	−0.194276	+	0.980947i	$0.562236\pi$
$774$			132.713i			0.171464i
$775$	−93.0087	−	114.690i	−0.120011	−	0.147987i
$776$	62.2255			0.0801876
$777$	−831.647	+	831.647i	−1.07033	+	1.07033i
$778$	−765.523	−	765.523i	−0.983962	−	0.983962i
$779$			285.847i			0.366941i
$780$	168.375	+	80.2375i	0.215866	+	0.102869i
$781$	−61.1725			−0.0783258
$782$	−102.367	+	102.367i	−0.130904	+	0.130904i
$783$	−180.785	−	180.785i	−0.230887	−	0.230887i
$784$			334.468i			0.426618i
$785$	1072.43	−	380.197i	1.36616	−	0.484328i
$786$	124.157			0.157961
$787$	437.028	−	437.028i	0.555309	−	0.555309i	−0.372659	−	0.927968i	$-0.621554\pi$
$787$	437.028	−	437.028i	0.555309	−	0.555309i	0.927968	+	0.372659i	$0.121554\pi$
$788$	−142.449	−	142.449i	−0.180773	−	0.180773i
$789$		−	71.2697i		−	0.0903292i
$790$	−300.141	−	846.618i	−0.379926	−	1.07167i
$791$	−2348.20			−2.96864
$792$	17.9219	−	17.9219i	0.0226287	−	0.0226287i
$793$	91.8075	+	91.8075i	0.115772	+	0.115772i
$794$		−	136.996i		−	0.172540i
$795$	334.591	−	702.125i	0.420869	−	0.883176i
$796$	544.728			0.684331
$797$	987.986	−	987.986i	1.23963	−	1.23963i	0.279479	−	0.960152i	$-0.409838\pi$
$797$	987.986	−	987.986i	1.23963	−	1.23963i	0.960152	−	0.279479i	$-0.0901619\pi$
$798$	−280.668	−	280.668i	−0.351714	−	0.351714i
$799$		−	1840.42i		−	2.30341i
$800$	140.657	+	14.6827i	0.175821	+	0.0183534i
$801$	−263.733			−0.329255
$802$	−603.687	+	603.687i	−0.752727	+	0.752727i
$803$	1.82760	+	1.82760i	0.00227597	+	0.00227597i
$804$		−	391.795i		−	0.487307i
$805$	249.285	+	118.794i	0.309670	+	0.147570i
$806$	−89.9502			−0.111601
$807$	113.820	−	113.820i	0.141041	−	0.141041i
$808$	−272.313	−	272.313i	−0.337021	−	0.337021i
$809$		−	15.8355i		−	0.0195741i	−0.999952	−	0.00978707i	$-0.996885\pi$
$809$		−	15.8355i		−	0.0195741i	0.999952	−	0.00978707i	$-0.00311537\pi$
$810$	−59.9818	+	21.2646i	−0.0740516	+	0.0262526i
$811$	833.392			1.02761			0.513805	−	0.857907i	$-0.328235\pi$
$811$	833.392			1.02761			0.513805	+	0.857907i	$0.328235\pi$
$812$	−801.326	+	801.326i	−0.986855	+	0.986855i
$813$	−435.608	−	435.608i	−0.535803	−	0.535803i
$814$		−	249.081i		−	0.305997i
$815$	288.669	+	814.259i	0.354196	+	0.999090i
$816$	−147.882			−0.181228
$817$	−311.240	+	311.240i	−0.380954	+	0.380954i
$818$	−410.613	−	410.613i	−0.501972	−	0.501972i
$819$			372.029i			0.454248i
$820$	87.3901	−	183.385i	0.106573	−	0.223640i
$821$	−720.880			−0.878051			−0.439025	−	0.898475i	$-0.644676\pi$
$821$	−720.880			−0.878051			−0.439025	+	0.898475i	$0.644676\pi$
$822$	−279.103	+	279.103i	−0.339541	+	0.339541i
$823$	473.318	+	473.318i	0.575112	+	0.575112i	0.933553	−	0.358440i	$-0.116691\pi$
$823$	473.318	+	473.318i	0.575112	+	0.575112i	−0.358440	+	0.933553i	$0.616691\pi$
$824$			93.3108i			0.113241i
$825$	13.4284	−	128.641i	0.0162769	−	0.155929i
$826$	−248.170			−0.300448
$827$	1030.31	−	1030.31i	1.24584	−	1.24584i	0.288296	−	0.957541i	$-0.406911\pi$
$827$	1030.31	−	1030.31i	1.24584	−	1.24584i	0.957541	−	0.288296i	$-0.0930886\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			6.82816i			0.00823662i	0.999992	+	0.00411831i	$0.00131090\pi$
$829$			6.82816i			0.00823662i	−0.999992	+	0.00411831i	$0.998689\pi$
$830$	−224.603	−	107.032i	−0.270605	−	0.128954i
$831$	223.869			0.269397
$832$	60.9159	−	60.9159i	0.0732162	−	0.0732162i
$833$	−1262.04	−	1262.04i	−1.51506	−	1.51506i
$834$			503.966i			0.604276i
$835$	843.311	−	298.969i	1.00995	−	0.358047i
$836$	84.0610			0.100551
$837$	21.7019	−	21.7019i	0.0259282	−	0.0259282i
$838$	426.786	+	426.786i	0.509292	+	0.509292i
$839$		−	628.504i		−	0.749111i	−0.927204	−	0.374556i	$-0.877795\pi$
$839$		−	628.504i		−	0.749111i	0.927204	−	0.374556i	$-0.122205\pi$
$840$	94.2553	+	265.869i	0.112209	+	0.316510i
$841$	−1579.97			−1.87868
$842$	−589.186	+	589.186i	−0.699746	+	0.699746i
$843$	248.673	+	248.673i	0.294985	+	0.294985i
$844$		−	634.010i		−	0.751197i
$845$	−114.085	+	239.402i	−0.135012	+	0.283316i
$846$	−365.813			−0.432404
$847$	912.651	−	912.651i	1.07751	−	1.07751i
$848$	−254.020	−	254.020i	−0.299551	−	0.299551i
$849$		−	312.667i		−	0.368277i
$850$	−586.141	+	475.337i	−0.689578	+	0.559220i
$851$	282.786			0.332298
$852$	50.1648	−	50.1648i	0.0588789	−	0.0588789i
$853$	−862.767	−	862.767i	−1.01145	−	1.01145i	−0.999934	−	0.0115168i	$-0.996334\pi$
$853$	−862.767	−	862.767i	−1.01145	−	1.01145i	−0.0115168	−	0.999934i	$-0.503666\pi$
$854$			196.360i			0.229929i
$855$	−190.539	−	90.7996i	−0.222853	−	0.106198i
$856$	428.885			0.501034
$857$	−860.819	+	860.819i	−1.00446	+	1.00446i	−0.00446575	+	0.999990i	$0.501421\pi$
$857$	−860.819	+	860.819i	−1.00446	+	1.00446i	−0.999990	+	0.00446575i	$0.998579\pi$
$858$	−55.7120	−	55.7120i	−0.0649324	−	0.0649324i
$859$			1096.93i			1.27698i	0.769629	+	0.638491i	$0.220441\pi$
$859$			1096.93i			1.27698i	−0.769629	+	0.638491i	$0.779559\pi$
$860$	294.829	−	104.522i	0.342824	−	0.121537i
$861$	405.193			0.470607
$862$	−507.800	+	507.800i	−0.589095	+	0.589095i
$863$	546.027	+	546.027i	0.632708	+	0.632708i	0.948746	−	0.316039i	$-0.102353\pi$
$863$	546.027	+	546.027i	0.632708	+	0.632708i	−0.316039	+	0.948746i	$0.602353\pi$
$864$			29.3939i			0.0340207i
$865$	274.406	+	774.025i	0.317232	+	0.894827i
$866$	−195.772			−0.226065
$867$	204.049	−	204.049i	0.235351	−	0.235351i
$868$	−96.1936	−	96.1936i	−0.110822	−	0.110822i
$869$			379.440i			0.436640i
$870$	−259.240	+	544.004i	−0.297977	+	0.625292i
$871$	−1217.93			−1.39832
$872$	119.201	−	119.201i	0.136699	−	0.136699i
$873$	46.6692	+	46.6692i	0.0534584	+	0.0534584i
$874$			95.4357i			0.109194i
$875$	1228.17	+	750.826i	1.40362	+	0.858087i
$876$	−2.99747			−0.00342176
$877$	170.933	−	170.933i	0.194906	−	0.194906i	−0.602906	−	0.797812i	$-0.705991\pi$
$877$	170.933	−	170.933i	0.194906	−	0.194906i	0.797812	+	0.602906i	$0.205991\pi$
$878$	−45.5200	−	45.5200i	−0.0518451	−	0.0518451i
$879$		−	48.4324i		−	0.0550995i
$880$	−53.9293	−	25.6994i	−0.0612832	−	0.0292039i
$881$	−1519.20			−1.72441			−0.862204	−	0.506562i	$-0.830916\pi$
$881$	−1519.20			−1.72441			−0.862204	+	0.506562i	$0.830916\pi$
$882$	−250.851	+	250.851i	−0.284412	+	0.284412i
$883$	1208.76	+	1208.76i	1.36893	+	1.36893i	0.861975	+	0.506950i	$0.169227\pi$
$883$	1208.76	+	1208.76i	1.36893	+	1.36893i	0.506950	+	0.861975i	$0.330773\pi$
$884$			459.706i			0.520029i
$885$	−124.382	+	44.0956i	−0.140544	+	0.0498255i
$886$	408.045			0.460547
$887$	608.850	−	608.850i	0.686415	−	0.686415i	−0.275023	−	0.961438i	$-0.588685\pi$
$887$	608.850	−	608.850i	0.686415	−	0.686415i	0.961438	+	0.275023i	$0.0886855\pi$
$888$	204.260	+	204.260i	0.230023	+	0.230023i
$889$		−	314.368i		−	0.353620i
$890$	207.711	+	585.896i	0.233383	+	0.658310i
$891$	26.8828			0.0301715
$892$	−32.3055	+	32.3055i	−0.0362170	+	0.0362170i
$893$	−857.907	−	857.907i	−0.960702	−	0.960702i
$894$		−	126.406i		−	0.141394i
$895$	−274.403	+	575.823i	−0.306595	+	0.643378i
$896$	130.288			0.145411
$897$	63.2507	−	63.2507i	0.0705136	−	0.0705136i
$898$	699.112	+	699.112i	0.778521	+	0.778521i
$899$		−	290.621i		−	0.323271i
$900$	94.4808	+	116.505i	0.104979	+	0.129450i
$901$	1916.98			2.12761
$902$	−60.6784	+	60.6784i	−0.0672710	+	0.0672710i
$903$	441.188	+	441.188i	0.488580	+	0.488580i
$904$			576.740i			0.637987i
$905$	1449.44	+	690.715i	1.60159	+	0.763221i
$906$	−277.637			−0.306443
$907$	−455.417	+	455.417i	−0.502114	+	0.502114i	−0.912094	−	0.409980i	$-0.865536\pi$
$907$	−455.417	+	455.417i	−0.502114	+	0.502114i	0.409980	+	0.912094i	$0.365536\pi$
$908$	−438.776	−	438.776i	−0.483233	−	0.483233i
$909$		−	408.469i		−	0.449361i
$910$	826.480	−	293.002i	0.908220	−	0.321980i
$911$	987.462			1.08393			0.541966	−	0.840400i	$-0.317680\pi$
$911$	987.462			1.08393			0.541966	+	0.840400i	$0.317680\pi$
$912$	−68.9346	+	68.9346i	−0.0755862	+	0.0755862i
$913$	74.3165	+	74.3165i	0.0813982	+	0.0813982i
$914$			350.457i			0.383432i
$915$	34.8898	+	98.4147i	0.0381309	+	0.107557i
$916$	629.826			0.687583
$917$	412.744	−	412.744i	0.450103	−	0.450103i
$918$	−110.911	−	110.911i	−0.120819	−	0.120819i
$919$			434.013i			0.472267i	0.971721	+	0.236133i	$0.0758802\pi$
$919$			434.013i			0.472267i	−0.971721	+	0.236133i	$0.924120\pi$
$920$	29.1770	−	61.2267i	0.0317141	−	0.0665507i
$921$	55.7165			0.0604957
$922$	−233.765	+	233.765i	−0.253542	+	0.253542i
$923$	−155.942	−	155.942i	−0.168952	−	0.168952i
$924$		−	119.158i		−	0.128959i
$925$	1466.16	+	153.047i	1.58503	+	0.165456i
$926$	−591.890			−0.639190
$927$	−69.9831	+	69.9831i	−0.0754942	+	0.0754942i
$928$	196.813	+	196.813i	0.212083	+	0.212083i
$929$		−	1022.10i		−	1.10022i	−0.835094	−	0.550108i	$-0.814587\pi$
$929$		−	1022.10i		−	1.10022i	0.835094	−	0.550108i	$-0.185413\pi$
$930$	−65.3039	−	31.1199i	−0.0702192	−	0.0334623i
$931$	−1176.59			−1.26380
$932$	40.3611	−	40.3611i	0.0433060	−	0.0433060i
$933$	72.0235	+	72.0235i	0.0771956	+	0.0771956i
$934$		−	81.6402i		−	0.0874092i
$935$	300.462	−	106.519i	0.321349	−	0.113924i
$936$	91.3738			0.0976216
$937$	227.682	−	227.682i	0.242990	−	0.242990i	−0.575096	−	0.818086i	$-0.695035\pi$
$937$	227.682	−	227.682i	0.242990	−	0.242990i	0.818086	+	0.575096i	$0.195035\pi$
$938$	−1302.47	−	1302.47i	−1.38856	−	1.38856i
$939$		−	788.636i		−	0.839867i
$940$	288.107	+	812.672i	0.306497	+	0.864545i
$941$	−449.052			−0.477207			−0.238604	−	0.971117i	$-0.576690\pi$
$941$	−449.052			−0.477207			−0.238604	+	0.971117i	$0.576690\pi$
$942$	394.157	−	394.157i	0.418426	−	0.418426i
$943$	−68.8891	−	68.8891i	−0.0730531	−	0.0730531i
$944$			60.9529i			0.0645687i
$945$	−128.710	+	270.093i	−0.136201	+	0.285813i
$946$	−132.137			−0.139680
$947$	−686.063	+	686.063i	−0.724460	+	0.724460i	−0.969510	−	0.245051i	$-0.921195\pi$
$947$	−686.063	+	686.063i	−0.724460	+	0.724460i	0.245051	+	0.969510i	$0.421195\pi$
$948$	−311.162	−	311.162i	−0.328230	−	0.328230i
$949$			9.31793i			0.00981868i
$950$	−51.6509	+	494.804i	−0.0543694	+	0.520847i
$951$	159.834			0.168069
$952$	−491.614	+	491.614i	−0.516401	+	0.516401i
$953$	−462.432	−	462.432i	−0.485239	−	0.485239i	0.421561	−	0.906800i	$-0.361482\pi$
$953$	−462.432	−	462.432i	−0.485239	−	0.485239i	−0.906800	+	0.421561i	$0.861482\pi$
$954$		−	381.029i		−	0.399402i
$955$	−415.254	−	197.885i	−0.434821	−	0.207210i
$956$	−727.272			−0.760745
$957$	180.000	−	180.000i	0.188088	−	0.188088i
$958$	145.106	+	145.106i	0.151467	+	0.151467i
$959$			1855.68i			1.93502i
$960$	65.2999	−	23.1500i	0.0680207	−	0.0241146i
$961$	−926.113			−0.963697
$962$	634.964	−	634.964i	0.660046	−	0.660046i
$963$	321.664	+	321.664i	0.334022	+	0.334022i
$964$		−	106.676i		−	0.110659i
$965$	172.878	+	487.643i	0.179149	+	0.505330i
$966$	135.282			0.140043
$967$	−40.1752	+	40.1752i	−0.0415463	+	0.0415463i	−0.727575	−	0.686028i	$-0.759353\pi$
$967$	−40.1752	+	40.1752i	−0.0415463	+	0.0415463i	0.686028	+	0.727575i	$0.259353\pi$
$968$	−224.156	−	224.156i	−0.231566	−	0.231566i
$969$		−	520.220i		−	0.536863i
$970$	66.9221	−	140.433i	0.0689919	−	0.144777i
$971$	−233.865			−0.240850			−0.120425	−	0.992722i	$-0.538426\pi$
$971$	−233.865			−0.240850			−0.120425	+	0.992722i	$0.538426\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	1675.37	+	1675.37i	1.72186	+	1.72186i
$974$		−	19.0471i		−	0.0195555i
$975$	362.167	−	293.703i	0.371453	−	0.301234i
$976$	48.2278			0.0494137
$977$	456.792	−	456.792i	0.467545	−	0.467545i	−0.433573	−	0.901118i	$-0.642747\pi$
$977$	456.792	−	456.792i	0.467545	−	0.467545i	0.901118	+	0.433573i	$0.142747\pi$
$978$	299.269	+	299.269i	0.306001	+	0.306001i
$979$		−	262.589i		−	0.268222i
$980$	754.843	+	359.713i	0.770248	+	0.367054i
$981$	178.802			0.182265
$982$	436.381	−	436.381i	0.444379	−	0.444379i
$983$	1238.59	+	1238.59i	1.26001	+	1.26001i	0.951088	+	0.308922i	$0.0999681\pi$
$983$	1238.59	+	1238.59i	1.26001	+	1.26001i	0.308922	+	0.951088i	$0.400032\pi$
$984$		−	99.5192i		−	0.101137i
$985$	−474.686	+	168.285i	−0.481915	+	0.170848i
$986$	−1485.27			−1.50635
$987$	−1216.10	+	1216.10i	−1.23212	+	1.23212i
$988$	214.290	+	214.290i	0.216893	+	0.216893i
$989$		−	150.018i		−	0.151686i
$990$	−21.1724	−	59.7215i	−0.0213862	−	0.0603248i
$991$	−17.7654			−0.0179267			−0.00896337	−	0.999960i	$-0.502853\pi$
$991$	−17.7654			−0.0179267			−0.00896337	+	0.999960i	$0.502853\pi$
$992$	−23.6261	+	23.6261i	−0.0238166	+	0.0238166i
$993$	−610.806	−	610.806i	−0.615112	−	0.615112i
$994$		−	333.532i		−	0.335546i
$995$	585.842	−	1229.37i	0.588786	−	1.23554i
$996$	−121.887			−0.122377
$997$	319.432	−	319.432i	0.320393	−	0.320393i	−0.528525	−	0.848918i	$-0.677255\pi$
$997$	319.432	−	319.432i	0.320393	−	0.320393i	0.848918	+	0.528525i	$0.177255\pi$
$998$	521.427	+	521.427i	0.522472	+	0.522472i
$999$			306.391i			0.306697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.13	yes	48
5.2	odd	4	inner	690.3.k.b.277.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.13	✓	48	5.2	odd	4	inner
690.3.k.b.553.13	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.66464 - 2.36274i) q^{10} -2.98698 q^{11} +(2.44949 - 2.44949i) q^{12} +(-7.61449 - 7.61449i) q^{13} -16.2860i q^{14} +(-2.89375 - 8.16249i) q^{15} -4.00000 q^{16} +(15.0931 - 15.0931i) q^{17} +(-3.00000 - 3.00000i) q^{18} -14.0712i q^{19} +(-4.30191 + 9.02738i) q^{20} -19.9462 q^{21} +(2.98698 - 2.98698i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(15.7468 + 19.4175i) q^{25} +15.2290 q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.2860 + 16.2860i) q^{28} +49.2034i q^{29} +(11.0562 + 5.26874i) q^{30} -5.90652 q^{31} +(4.00000 - 4.00000i) q^{32} +(-3.65829 - 3.65829i) q^{33} +30.1863i q^{34} +(54.2702 - 19.2398i) q^{35} +6.00000 q^{36} +(41.6945 - 41.6945i) q^{37} +(14.0712 + 14.0712i) q^{38} -18.6516i q^{39} +(-4.72547 - 13.3293i) q^{40} -20.3143 q^{41} +(19.9462 - 19.9462i) q^{42} +(-22.1189 - 22.1189i) q^{43} +5.97396i q^{44} +(6.45286 - 13.5411i) q^{45} -6.78233 q^{46} +(60.9689 - 60.9689i) q^{47} +(-4.89898 - 4.89898i) q^{48} -83.6170i q^{49} +(-35.1643 - 3.67068i) q^{50} +36.9705 q^{51} +(-15.2290 + 15.2290i) q^{52} +(63.5049 + 63.5049i) q^{53} -7.34847i q^{54} +(13.4823 + 6.42486i) q^{55} -32.5720 q^{56} +(17.2337 - 17.2337i) q^{57} +(-49.2034 - 49.2034i) q^{58} -15.2382i q^{59} +(-16.3250 + 5.78750i) q^{60} -12.0570 q^{61} +(5.90652 - 5.90652i) q^{62} +(-24.4290 - 24.4290i) q^{63} +8.00000i q^{64} +(17.9910 + 50.7478i) q^{65} +7.31658 q^{66} +(79.9748 - 79.9748i) q^{67} +(-30.1863 - 30.1863i) q^{68} +8.30662i q^{69} +(-35.0304 + 73.5100i) q^{70} +20.4797 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.611855 - 0.611855i) q^{73} +83.3890i q^{74} +(-4.49564 + 43.0673i) q^{75} -28.1424 q^{76} +(24.3230 - 24.3230i) q^{77} +(18.6516 + 18.6516i) q^{78} -127.031i q^{79} +(18.0548 + 8.60381i) q^{80} -9.00000 q^{81} +(20.3143 - 20.3143i) q^{82} +(-24.8801 - 24.8801i) q^{83} +39.8924i q^{84} +(-100.590 + 35.6611i) q^{85} +44.2378 q^{86} +(-60.2616 + 60.2616i) q^{87} +(-5.97396 - 5.97396i) q^{88} +87.9111i q^{89} +(7.08821 + 19.9939i) q^{90} +124.010 q^{91} +(6.78233 - 6.78233i) q^{92} +(-7.23398 - 7.23398i) q^{93} +121.938i q^{94} +(-30.2665 + 63.5131i) q^{95} +9.79796 q^{96} +(15.5564 - 15.5564i) q^{97} +(83.6170 + 83.6170i) q^{98} -8.96095i 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

Fields

Representations

Groups

Database

Properties

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