LMFDB - Embedded newform 230.3.f.b.93.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.4
Character	$\chi$	$=$	230.93
Dual form			230.3.f.b.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +(0.691863 + 7.03714i) q^{10} -14.8137 q^{11} +(-2.72079 + 2.72079i) q^{12} +(-4.91350 - 4.91350i) q^{13} -14.4378i q^{14} +(9.57330 - 0.941208i) q^{15} -4.00000 q^{16} +(-17.8271 + 17.8271i) q^{17} +(-5.29864 - 5.29864i) q^{18} -29.6011i q^{19} +(7.72900 + 6.34528i) q^{20} -19.6412 q^{21} +(-14.8137 + 14.8137i) q^{22} +(-3.39116 - 3.39116i) q^{23} +5.44159i q^{24} +(-4.86874 - 24.5213i) q^{25} -9.82700 q^{26} +(-19.4518 + 19.4518i) q^{27} +(-14.4378 - 14.4378i) q^{28} +11.0158i q^{29} +(8.63209 - 10.5145i) q^{30} +42.3661 q^{31} +(-4.00000 + 4.00000i) q^{32} +(20.1526 + 20.1526i) q^{33} +35.6542i q^{34} +(4.99449 + 50.8005i) q^{35} -10.5973 q^{36} +(14.7295 - 14.7295i) q^{37} +(-29.6011 - 29.6011i) q^{38} +13.3686i q^{39} +(14.0743 - 1.38373i) q^{40} +23.9580 q^{41} +(-19.6412 + 19.6412i) q^{42} +(0.419945 + 0.419945i) q^{43} +29.6275i q^{44} +(20.4766 + 16.8107i) q^{45} -6.78233 q^{46} +(53.0162 - 53.0162i) q^{47} +(5.44159 + 5.44159i) q^{48} -55.2252i q^{49} +(-29.3901 - 19.6526i) q^{50} +48.5039 q^{51} +(-9.82700 + 9.82700i) q^{52} +(-58.3755 - 58.3755i) q^{53} +38.9036i q^{54} +(46.9987 - 57.2477i) q^{55} -28.8756 q^{56} +(-40.2692 + 40.2692i) q^{57} +(11.0158 + 11.0158i) q^{58} -13.7747i q^{59} +(-1.88242 - 19.1466i) q^{60} +39.0198 q^{61} +(42.3661 - 42.3661i) q^{62} +(-38.2504 - 38.2504i) q^{63} +8.00000i q^{64} +(34.5770 - 3.39947i) q^{65} +40.3051 q^{66} +(-16.9106 + 16.9106i) q^{67} +(35.6542 + 35.6542i) q^{68} +9.22666i q^{69} +(55.7949 + 45.8060i) q^{70} +103.112 q^{71} +(-10.5973 + 10.5973i) q^{72} +(41.5993 + 41.5993i) q^{73} -29.4590i q^{74} +(-26.7353 + 39.9821i) q^{75} -59.2022 q^{76} +(-106.939 + 106.939i) q^{77} +(13.3686 + 13.3686i) q^{78} +155.484i q^{79} +(12.6906 - 15.4580i) q^{80} +5.23660 q^{81} +(23.9580 - 23.9580i) q^{82} +(12.7160 + 12.7160i) q^{83} +39.2823i q^{84} +(-12.3339 - 125.452i) q^{85} +0.839889 q^{86} +(14.9859 - 14.9859i) q^{87} +(29.6275 + 29.6275i) q^{88} -141.715i q^{89} +(37.2873 - 3.66593i) q^{90} -70.9402 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-57.6347 - 57.6347i) q^{93} -106.032i q^{94} +(114.393 + 93.9135i) q^{95} +10.8832 q^{96} +(-29.4379 + 29.4379i) q^{97} +(-55.2252 - 55.2252i) q^{98} +78.4927i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.36040	−	1.36040i	−0.453466	−	0.453466i	0.443038	−	0.896503i	$-0.353901\pi$
$3$	−1.36040	−	1.36040i	−0.453466	−	0.453466i	−0.896503	+	0.443038i	$0.853901\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−3.17264	+	3.86450i	−0.634528	+	0.772900i
$5$	−3.17264	+	3.86450i	−0.634528	+	0.772900i
$6$	−2.72079			−0.453466
$7$	7.21891	−	7.21891i	1.03127	−	1.03127i	0.0317775	−	0.999495i	$-0.489883\pi$
$7$	7.21891	−	7.21891i	1.03127	−	1.03127i	0.999495	−	0.0317775i	$-0.0101168\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		−	5.29864i		−	0.588738i
$10$	0.691863	+	7.03714i	0.0691863	+	0.703714i
$11$	−14.8137			−1.34670			−0.673352	−	0.739322i	$-0.735146\pi$
$11$	−14.8137			−1.34670			−0.673352	+	0.739322i	$0.735146\pi$
$12$	−2.72079	+	2.72079i	−0.226733	+	0.226733i
$13$	−4.91350	−	4.91350i	−0.377962	−	0.377962i	0.492405	−	0.870366i	$-0.336118\pi$
$13$	−4.91350	−	4.91350i	−0.377962	−	0.377962i	−0.870366	+	0.492405i	$0.836118\pi$
$14$		−	14.4378i		−	1.03127i
$15$	9.57330	−	0.941208i	0.638220	−	0.0627472i
$16$	−4.00000			−0.250000
$17$	−17.8271	+	17.8271i	−1.04865	+	1.04865i	−0.0499002	+	0.998754i	$0.515890\pi$
$17$	−17.8271	+	17.8271i	−1.04865	+	1.04865i	−0.998754	+	0.0499002i	$0.984110\pi$
$18$	−5.29864	−	5.29864i	−0.294369	−	0.294369i
$19$		−	29.6011i		−	1.55795i	−0.627054	−	0.778976i	$-0.715739\pi$
$19$		−	29.6011i		−	1.55795i	0.627054	−	0.778976i	$-0.284261\pi$
$20$	7.72900	+	6.34528i	0.386450	+	0.317264i
$21$	−19.6412			−0.935293
$22$	−14.8137	+	14.8137i	−0.673352	+	0.673352i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$			5.44159i			0.226733i
$25$	−4.86874	−	24.5213i	−0.194749	−	0.980853i
$26$	−9.82700			−0.377962
$27$	−19.4518	+	19.4518i	−0.720438	+	0.720438i
$28$	−14.4378	−	14.4378i	−0.515636	−	0.515636i
$29$			11.0158i			0.379856i	0.981798	+	0.189928i	$0.0608255\pi$
$29$			11.0158i			0.379856i	−0.981798	+	0.189928i	$0.939175\pi$
$30$	8.63209	−	10.5145i	0.287736	−	0.350484i
$31$	42.3661			1.36665			0.683325	−	0.730115i	$-0.260533\pi$
$31$	42.3661			1.36665			0.683325	+	0.730115i	$0.260533\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	20.1526	+	20.1526i	0.610684	+	0.610684i
$34$			35.6542i			1.04865i
$35$	4.99449	+	50.8005i	0.142700	+	1.45144i
$36$	−10.5973			−0.294369
$37$	14.7295	−	14.7295i	0.398095	−	0.398095i	−0.479466	−	0.877561i	$-0.659169\pi$
$37$	14.7295	−	14.7295i	0.398095	−	0.398095i	0.877561	+	0.479466i	$0.159169\pi$
$38$	−29.6011	−	29.6011i	−0.778976	−	0.778976i
$39$			13.3686i			0.342785i
$40$	14.0743	−	1.38373i	0.351857	−	0.0345931i
$41$	23.9580			0.584341			0.292171	−	0.956366i	$-0.405622\pi$
$41$	23.9580			0.584341			0.292171	+	0.956366i	$0.405622\pi$
$42$	−19.6412	+	19.6412i	−0.467646	+	0.467646i
$43$	0.419945	+	0.419945i	0.00976615	+	0.00976615i	0.711973	−	0.702207i	$-0.247802\pi$
$43$	0.419945	+	0.419945i	0.00976615	+	0.00976615i	−0.702207	+	0.711973i	$0.747802\pi$
$44$			29.6275i			0.673352i
$45$	20.4766	+	16.8107i	0.455036	+	0.373571i
$46$	−6.78233			−0.147442
$47$	53.0162	−	53.0162i	1.12800	−	1.12800i	0.137502	−	0.990502i	$-0.456093\pi$
$47$	53.0162	−	53.0162i	1.12800	−	1.12800i	0.990502	−	0.137502i	$-0.0439073\pi$
$48$	5.44159	+	5.44159i	0.113366	+	0.113366i
$49$		−	55.2252i		−	1.12705i
$50$	−29.3901	−	19.6526i	−0.587801	−	0.393052i
$51$	48.5039			0.951057
$52$	−9.82700	+	9.82700i	−0.188981	+	0.188981i
$53$	−58.3755	−	58.3755i	−1.10142	−	1.10142i	−0.994239	−	0.107186i	$-0.965816\pi$
$53$	−58.3755	−	58.3755i	−1.10142	−	1.10142i	−0.107186	−	0.994239i	$-0.534184\pi$
$54$			38.9036i			0.720438i
$55$	46.9987	−	57.2477i	0.854521	−	1.04087i
$56$	−28.8756			−0.515636
$57$	−40.2692	+	40.2692i	−0.706477	+	0.706477i
$58$	11.0158	+	11.0158i	0.189928	+	0.189928i
$59$		−	13.7747i		−	0.233469i	−0.993163	−	0.116735i	$-0.962757\pi$
$59$		−	13.7747i		−	0.233469i	0.993163	−	0.116735i	$-0.0372427\pi$
$60$	−1.88242	−	19.1466i	−0.0313736	−	0.319110i
$61$	39.0198			0.639670			0.319835	−	0.947473i	$-0.396373\pi$
$61$	39.0198			0.639670			0.319835	+	0.947473i	$0.396373\pi$
$62$	42.3661	−	42.3661i	0.683325	−	0.683325i
$63$	−38.2504	−	38.2504i	−0.607149	−	0.607149i
$64$			8.00000i			0.125000i
$65$	34.5770	−	3.39947i	0.531954	−	0.0522995i
$66$	40.3051			0.610684
$67$	−16.9106	+	16.9106i	−0.252397	+	0.252397i	−0.821953	−	0.569556i	$-0.807115\pi$
$67$	−16.9106	+	16.9106i	−0.252397	+	0.252397i	0.569556	+	0.821953i	$0.307115\pi$
$68$	35.6542	+	35.6542i	0.524327	+	0.524327i
$69$			9.22666i			0.133720i
$70$	55.7949	+	45.8060i	0.797071	+	0.654371i
$71$	103.112			1.45229			0.726143	−	0.687544i	$-0.241311\pi$
$71$	103.112			1.45229			0.726143	+	0.687544i	$0.241311\pi$
$72$	−10.5973	+	10.5973i	−0.147185	+	0.147185i
$73$	41.5993	+	41.5993i	0.569853	+	0.569853i	0.932087	−	0.362234i	$-0.117986\pi$
$73$	41.5993	+	41.5993i	0.569853	+	0.569853i	−0.362234	+	0.932087i	$0.617986\pi$
$74$		−	29.4590i		−	0.398095i
$75$	−26.7353	+	39.9821i	−0.356471	+	0.533095i
$76$	−59.2022			−0.778976
$77$	−106.939	+	106.939i	−1.38882	+	1.38882i
$78$	13.3686	+	13.3686i	0.171393	+	0.171393i
$79$			155.484i			1.96815i	0.177757	+	0.984074i	$0.443116\pi$
$79$			155.484i			1.96815i	−0.177757	+	0.984074i	$0.556884\pi$
$80$	12.6906	−	15.4580i	0.158632	−	0.193225i
$81$	5.23660			0.0646494
$82$	23.9580	−	23.9580i	0.292171	−	0.292171i
$83$	12.7160	+	12.7160i	0.153205	+	0.153205i	0.779548	−	0.626343i	$-0.215449\pi$
$83$	12.7160	+	12.7160i	0.153205	+	0.153205i	−0.626343	+	0.779548i	$0.715449\pi$
$84$			39.2823i			0.467646i
$85$	−12.3339	−	125.452i	−0.145105	−	1.47591i
$86$	0.839889			0.00976615
$87$	14.9859	−	14.9859i	0.172252	−	0.172252i
$88$	29.6275	+	29.6275i	0.336676	+	0.336676i
$89$		−	141.715i		−	1.59230i	−0.605101	−	0.796149i	$-0.706867\pi$
$89$		−	141.715i		−	1.59230i	0.605101	−	0.796149i	$-0.293133\pi$
$90$	37.2873	−	3.66593i	0.414303	−	0.0407326i
$91$	−70.9402			−0.779563
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	−57.6347	−	57.6347i	−0.619728	−	0.619728i
$94$		−	106.032i		−	1.12800i
$95$	114.393	+	93.9135i	1.20414	+	0.988563i
$96$	10.8832			0.113366
$97$	−29.4379	+	29.4379i	−0.303483	+	0.303483i	−0.842375	−	0.538892i	$-0.818843\pi$
$97$	−29.4379	+	29.4379i	−0.303483	+	0.303483i	0.538892	+	0.842375i	$0.318843\pi$
$98$	−55.2252	−	55.2252i	−0.563523	−	0.563523i
$99$			78.4927i			0.792856i
$100$	−49.0427	+	9.73747i	−0.490427	+	0.0973747i
$101$	105.739			1.04692			0.523459	−	0.852051i	$-0.324641\pi$
$101$	105.739			1.04692			0.523459	+	0.852051i	$0.324641\pi$
$102$	48.5039	−	48.5039i	0.475529	−	0.475529i
$103$	−15.4223	−	15.4223i	−0.149732	−	0.149732i	0.628267	−	0.777998i	$-0.283765\pi$
$103$	−15.4223	−	15.4223i	−0.149732	−	0.149732i	−0.777998	+	0.628267i	$0.783765\pi$
$104$			19.6540i			0.188981i
$105$	62.3143	−	75.9033i	0.593469	−	0.722888i
$106$	−116.751			−1.10142
$107$	−38.0079	+	38.0079i	−0.355214	+	0.355214i	−0.862045	−	0.506831i	$-0.830817\pi$
$107$	−38.0079	+	38.0079i	−0.355214	+	0.355214i	0.506831	+	0.862045i	$0.330817\pi$
$108$	38.9036	+	38.9036i	0.360219	+	0.360219i
$109$		−	146.178i		−	1.34108i	−0.741873	−	0.670540i	$-0.766062\pi$
$109$		−	146.178i		−	1.34108i	0.741873	−	0.670540i	$-0.233938\pi$
$110$	−10.2491	−	104.246i	−0.0931735	−	0.947694i
$111$	−40.0760			−0.361045
$112$	−28.8756	+	28.8756i	−0.257818	+	0.257818i
$113$	2.38693	+	2.38693i	0.0211232	+	0.0211232i	0.717590	−	0.696466i	$-0.245245\pi$
$113$	2.38693	+	2.38693i	0.0211232	+	0.0211232i	−0.696466	+	0.717590i	$0.745245\pi$
$114$			80.5384i			0.706477i
$115$	23.8641	−	2.34622i	0.207514	−	0.0204019i
$116$	22.0317			0.189928
$117$	−26.0349	+	26.0349i	−0.222520	+	0.222520i
$118$	−13.7747	−	13.7747i	−0.116735	−	0.116735i
$119$			257.385i			2.16290i
$120$	−21.0290	−	17.2642i	−0.175242	−	0.143868i
$121$	98.4471			0.813612
$122$	39.0198	−	39.0198i	0.319835	−	0.319835i
$123$	−32.5924	−	32.5924i	−0.264979	−	0.264979i
$124$		−	84.7322i		−	0.683325i
$125$	110.209	+	58.9821i	0.881675	+	0.471856i
$126$	−76.5008			−0.607149
$127$	−134.874	+	134.874i	−1.06200	+	1.06200i	−0.0640551	+	0.997946i	$0.520403\pi$
$127$	−134.874	+	134.874i	−1.06200	+	1.06200i	−0.997946	+	0.0640551i	$0.979597\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	1.14258i		−	0.00885723i
$130$	31.1775	−	37.9765i	0.239827	−	0.292127i
$131$	−48.2924			−0.368644			−0.184322	−	0.982866i	$-0.559009\pi$
$131$	−48.2924			−0.368644			−0.184322	+	0.982866i	$0.559009\pi$
$132$	40.3051	−	40.3051i	0.305342	−	0.305342i
$133$	−213.687	−	213.687i	−1.60667	−	1.60667i
$134$			33.8212i			0.252397i
$135$	−13.4580	−	136.885i	−0.0996889	−	1.01396i
$136$	71.3085			0.524327
$137$	−3.29075	+	3.29075i	−0.0240200	+	0.0240200i	−0.719015	−	0.694995i	$-0.755407\pi$
$137$	−3.29075	+	3.29075i	−0.0240200	+	0.0240200i	0.694995	+	0.719015i	$0.255407\pi$
$138$	9.22666	+	9.22666i	0.0668598	+	0.0668598i
$139$			108.941i			0.783751i	0.920018	+	0.391876i	$0.128174\pi$
$139$			108.941i			0.783751i	−0.920018	+	0.391876i	$0.871826\pi$
$140$	101.601	−	9.98899i	0.725721	−	0.0713499i
$141$	−144.246			−1.02302
$142$	103.112	−	103.112i	0.726143	−	0.726143i
$143$	72.7874	+	72.7874i	0.509002	+	0.509002i
$144$			21.1946i			0.147185i
$145$	−42.5707	−	34.9492i	−0.293591	−	0.241029i
$146$	83.1985			0.569853
$147$	−75.1282	+	75.1282i	−0.511076	+	0.511076i
$148$	−29.4590	−	29.4590i	−0.199048	−	0.199048i
$149$		−	68.8768i		−	0.462260i	−0.972923	−	0.231130i	$-0.925758\pi$
$149$		−	68.8768i		−	0.462260i	0.972923	−	0.231130i	$-0.0742423\pi$
$150$	13.2468	+	66.7175i	0.0883121	+	0.444783i
$151$	138.399			0.916549			0.458275	−	0.888811i	$-0.348468\pi$
$151$	138.399			0.916549			0.458275	+	0.888811i	$0.348468\pi$
$152$	−59.2022	+	59.2022i	−0.389488	+	0.389488i
$153$	94.4596	+	94.4596i	0.617383	+	0.617383i
$154$			213.878i			1.38882i
$155$	−134.412	+	163.724i	−0.867177	+	1.05628i
$156$	26.7372			0.171393
$157$	−135.287	+	135.287i	−0.861699	+	0.861699i	−0.991535	−	0.129836i	$-0.958555\pi$
$157$	−135.287	+	135.287i	−0.861699	+	0.861699i	0.129836	+	0.991535i	$0.458555\pi$
$158$	155.484	+	155.484i	0.984074	+	0.984074i
$159$			158.828i			0.998916i
$160$	−2.76745	−	28.1486i	−0.0172966	−	0.175928i
$161$	−48.9610			−0.304106
$162$	5.23660	−	5.23660i	0.0323247	−	0.0323247i
$163$	−84.3740	−	84.3740i	−0.517632	−	0.517632i	0.399222	−	0.916854i	$-0.369280\pi$
$163$	−84.3740	−	84.3740i	−0.517632	−	0.517632i	−0.916854	+	0.399222i	$0.869280\pi$
$164$		−	47.9160i		−	0.292171i
$165$	−141.816	+	13.9428i	−0.859494	+	0.0845019i
$166$	25.4320			0.153205
$167$	217.730	−	217.730i	1.30378	−	1.30378i	0.377949	−	0.925826i	$-0.376629\pi$
$167$	217.730	−	217.730i	1.30378	−	1.30378i	0.925826	−	0.377949i	$-0.123371\pi$
$168$	39.2823	+	39.2823i	0.233823	+	0.233823i
$169$		−	120.715i		−	0.714290i
$170$	−137.786	−	113.118i	−0.810505	−	0.665400i
$171$	−156.846			−0.917225
$172$	0.839889	−	0.839889i	0.00488308	−	0.00488308i
$173$	−222.534	−	222.534i	−1.28632	−	1.28632i	−0.937003	−	0.349321i	$-0.886412\pi$
$173$	−222.534	−	222.534i	−1.28632	−	1.28632i	−0.349321	−	0.937003i	$-0.613588\pi$
$174$		−	29.9718i		−	0.172252i
$175$	−212.164	−	141.870i	−1.21237	−	0.810687i
$176$	59.2550			0.336676
$177$	−18.7390	+	18.7390i	−0.105870	+	0.105870i
$178$	−141.715	−	141.715i	−0.796149	−	0.796149i
$179$		−	194.058i		−	1.08412i	−0.840339	−	0.542061i	$-0.817644\pi$
$179$		−	194.058i		−	1.08412i	0.840339	−	0.542061i	$-0.182356\pi$
$180$	33.6214	−	40.9532i	0.186785	−	0.227518i
$181$	−0.412795			−0.00228064			−0.00114032	−	0.999999i	$-0.500363\pi$
$181$	−0.412795			−0.00228064			−0.00114032	+	0.999999i	$0.500363\pi$
$182$	−70.9402	+	70.9402i	−0.389781	+	0.389781i
$183$	−53.0825	−	53.0825i	−0.290068	−	0.290068i
$184$			13.5647i			0.0737210i
$185$	10.1908	+	103.654i	0.0550855	+	0.560290i
$186$	−115.269			−0.619728
$187$	264.086	−	264.086i	1.41223	−	1.41223i
$188$	−106.032	−	106.032i	−0.564002	−	0.564002i
$189$			280.842i			1.48594i
$190$	208.307	−	20.4799i	1.09635	−	0.107789i
$191$	−313.636			−1.64207			−0.821036	−	0.570877i	$-0.806603\pi$
$191$	−313.636			−1.64207			−0.821036	+	0.570877i	$0.806603\pi$
$192$	10.8832	−	10.8832i	0.0566832	−	0.0566832i
$193$	−11.9642	−	11.9642i	−0.0619909	−	0.0619909i	0.675432	−	0.737423i	$-0.263957\pi$
$193$	−11.9642	−	11.9642i	−0.0619909	−	0.0619909i	−0.737423	+	0.675432i	$0.763957\pi$
$194$			58.8757i			0.303483i
$195$	−51.6630	−	42.4138i	−0.264939	−	0.217507i
$196$	−110.450			−0.563523
$197$	−57.7317	+	57.7317i	−0.293054	+	0.293054i	−0.838286	−	0.545231i	$-0.816442\pi$
$197$	−57.7317	+	57.7317i	−0.293054	+	0.293054i	0.545231	+	0.838286i	$0.316442\pi$
$198$	78.4927	+	78.4927i	0.396428	+	0.396428i
$199$		−	263.722i		−	1.32524i	−0.748957	−	0.662619i	$-0.769445\pi$
$199$		−	263.722i		−	1.32524i	0.748957	−	0.662619i	$-0.230555\pi$
$200$	−39.3052	+	58.7801i	−0.196526	+	0.293901i
$201$	46.0102			0.228907
$202$	105.739	−	105.739i	0.523459	−	0.523459i
$203$	79.5222	+	79.5222i	0.391735	+	0.391735i
$204$		−	97.0078i		−	0.475529i
$205$	−76.0101	+	92.5857i	−0.370781	+	0.451638i
$206$	−30.8447			−0.149732
$207$	−17.9686	+	17.9686i	−0.0868047	+	0.0868047i
$208$	19.6540	+	19.6540i	0.0944904	+	0.0944904i
$209$			438.503i			2.09810i
$210$	−13.5890	−	138.218i	−0.0647095	−	0.658179i
$211$	321.514			1.52376			0.761881	−	0.647717i	$-0.224276\pi$
$211$	321.514			1.52376			0.761881	+	0.647717i	$0.224276\pi$
$212$	−116.751	+	116.751i	−0.550712	+	0.550712i
$213$	−140.274	−	140.274i	−0.658561	−	0.658561i
$214$			76.0158i			0.355214i
$215$	−2.95521	+	0.290544i	−0.0137452	+	0.00135137i
$216$	77.8073			0.360219
$217$	305.837	−	305.837i	1.40939	−	1.40939i
$218$	−146.178	−	146.178i	−0.670540	−	0.670540i
$219$		−	113.183i		−	0.516817i
$220$	−114.495	−	93.9973i	−0.520434	−	0.427261i
$221$	175.187			0.792702
$222$	−40.0760	+	40.0760i	−0.180522	+	0.180522i
$223$	−75.9702	−	75.9702i	−0.340674	−	0.340674i	0.515947	−	0.856621i	$-0.327440\pi$
$223$	−75.9702	−	75.9702i	−0.340674	−	0.340674i	−0.856621	+	0.515947i	$0.827440\pi$
$224$			57.7513i			0.257818i
$225$	−129.930	+	25.7977i	−0.577466	+	0.114656i
$226$	4.77385			0.0211232
$227$	−63.6613	+	63.6613i	−0.280446	+	0.280446i	−0.833287	−	0.552841i	$-0.813544\pi$
$227$	−63.6613	+	63.6613i	−0.280446	+	0.280446i	0.552841	+	0.833287i	$0.313544\pi$
$228$	80.5384	+	80.5384i	0.353239	+	0.353239i
$229$			103.156i			0.450462i	0.974305	+	0.225231i	$0.0723137\pi$
$229$			103.156i			0.450462i	−0.974305	+	0.225231i	$0.927686\pi$
$230$	21.5179	−	26.2103i	0.0935560	−	0.113958i
$231$	290.959			1.25956
$232$	22.0317	−	22.0317i	0.0949640	−	0.0949640i
$233$	−211.803	−	211.803i	−0.909026	−	0.909026i	0.0871679	−	0.996194i	$-0.472218\pi$
$233$	−211.803	−	211.803i	−0.909026	−	0.909026i	−0.996194	+	0.0871679i	$0.972218\pi$
$234$			52.0698i			0.222520i
$235$	36.6799	+	373.082i	0.156085	+	1.58758i
$236$	−27.5494			−0.116735
$237$	211.520	−	211.520i	0.892488	−	0.892488i
$238$	257.385	+	257.385i	1.08145	+	1.08145i
$239$			89.5138i			0.374535i	0.982309	+	0.187267i	$0.0599631\pi$
$239$			89.5138i			0.374535i	−0.982309	+	0.187267i	$0.940037\pi$
$240$	−38.2932	+	3.76483i	−0.159555	+	0.0156868i
$241$	175.324			0.727487			0.363744	−	0.931499i	$-0.381498\pi$
$241$	175.324			0.727487			0.363744	+	0.931499i	$0.381498\pi$
$242$	98.4471	−	98.4471i	0.406806	−	0.406806i
$243$	167.943	+	167.943i	0.691122	+	0.691122i
$244$		−	78.0397i		−	0.319835i
$245$	213.418	+	175.210i	0.871094	+	0.715142i
$246$	−65.1848			−0.264979
$247$	−145.445	+	145.445i	−0.588846	+	0.588846i
$248$	−84.7322	−	84.7322i	−0.341662	−	0.341662i
$249$		−	34.5976i		−	0.138946i
$250$	169.191	−	51.2274i	0.676766	−	0.204909i
$251$	326.776			1.30190			0.650948	−	0.759122i	$-0.274371\pi$
$251$	326.776			1.30190			0.650948	+	0.759122i	$0.274371\pi$
$252$	−76.5008	+	76.5008i	−0.303575	+	0.303575i
$253$	50.2359	+	50.2359i	0.198561	+	0.198561i
$254$			269.748i			1.06200i
$255$	−153.885	+	187.443i	−0.603472	+	0.735072i
$256$	16.0000			0.0625000
$257$	−44.9594	+	44.9594i	−0.174939	+	0.174939i	−0.789146	−	0.614206i	$-0.789476\pi$
$257$	−44.9594	+	44.9594i	−0.174939	+	0.174939i	0.614206	+	0.789146i	$0.289476\pi$
$258$	−1.14258	−	1.14258i	−0.00442861	−	0.00442861i
$259$		−	212.662i		−	0.821089i
$260$	−6.79894	−	69.1540i	−0.0261498	−	0.265977i
$261$	58.3689			0.223636
$262$	−48.2924	+	48.2924i	−0.184322	+	0.184322i
$263$	123.550	+	123.550i	0.469771	+	0.469771i	0.901840	−	0.432070i	$-0.142217\pi$
$263$	123.550	+	123.550i	0.469771	+	0.469771i	−0.432070	+	0.901840i	$0.642217\pi$
$264$		−	80.6103i		−	0.305342i
$265$	410.797	−	40.3879i	1.55018	−	0.152407i
$266$	−427.375			−1.60667
$267$	−192.788	+	192.788i	−0.722052	+	0.722052i
$268$	33.8212	+	33.8212i	0.126198	+	0.126198i
$269$		−	237.309i		−	0.882189i	−0.897461	−	0.441094i	$-0.854590\pi$
$269$		−	237.309i		−	0.882189i	0.897461	−	0.441094i	$-0.145410\pi$
$270$	−150.343	−	123.427i	−0.556827	−	0.457138i
$271$	26.2193			0.0967502			0.0483751	−	0.998829i	$-0.484596\pi$
$271$	26.2193			0.0967502			0.0483751	+	0.998829i	$0.484596\pi$
$272$	71.3085	−	71.3085i	0.262164	−	0.262164i
$273$	96.5068	+	96.5068i	0.353505	+	0.353505i
$274$			6.58149i			0.0240200i
$275$	72.1242	+	363.253i	0.262270	+	1.32092i
$276$	18.4533			0.0668598
$277$	−225.480	+	225.480i	−0.814007	+	0.814007i	−0.985232	−	0.171225i	$-0.945228\pi$
$277$	−225.480	+	225.480i	−0.814007	+	0.814007i	0.171225	+	0.985232i	$0.445228\pi$
$278$	108.941	+	108.941i	0.391876	+	0.391876i
$279$		−	224.483i		−	0.804598i
$280$	91.6119	−	111.590i	0.327185	−	0.398535i
$281$	−70.2491			−0.249997			−0.124998	−	0.992157i	$-0.539893\pi$
$281$	−70.2491			−0.249997			−0.124998	+	0.992157i	$0.539893\pi$
$282$	−144.246	+	144.246i	−0.511511	+	0.511511i
$283$	49.1215	+	49.1215i	0.173574	+	0.173574i	0.788548	−	0.614974i	$-0.210833\pi$
$283$	49.1215	+	49.1215i	0.173574	+	0.173574i	−0.614974	+	0.788548i	$0.710833\pi$
$284$		−	206.225i		−	0.726143i
$285$	−27.8608	−	283.380i	−0.0977571	−	0.994316i
$286$	145.575			0.509002
$287$	172.951	−	172.951i	0.602615	−	0.602615i
$288$	21.1946	+	21.1946i	0.0735923	+	0.0735923i
$289$		−	346.613i		−	1.19935i
$290$	−77.5199	+	7.62144i	−0.267310	+	0.0262808i
$291$	80.0943			0.275238
$292$	83.1985	−	83.1985i	0.284926	−	0.284926i
$293$	369.904	+	369.904i	1.26247	+	1.26247i	0.949891	+	0.312580i	$0.101193\pi$
$293$	369.904	+	369.904i	1.26247	+	1.26247i	0.312580	+	0.949891i	$0.398807\pi$
$294$			150.256i			0.511076i
$295$	53.2323	+	43.7021i	0.180448	+	0.148143i
$296$	−58.9181			−0.199048
$297$	288.154	−	288.154i	0.970217	−	0.970217i
$298$	−68.8768	−	68.8768i	−0.231130	−	0.231130i
$299$			33.3250i			0.111455i
$300$	79.9643	+	53.4706i	0.266548	+	0.178235i
$301$	6.06308			0.0201431
$302$	138.399	−	138.399i	0.458275	−	0.458275i
$303$	−143.847	−	143.847i	−0.474741	−	0.474741i
$304$			118.404i			0.389488i
$305$	−123.796	+	150.792i	−0.405888	+	0.494401i
$306$	188.919			0.617383
$307$	4.17039	−	4.17039i	0.0135843	−	0.0135843i	−0.700282	−	0.713866i	$-0.746942\pi$
$307$	4.17039	−	4.17039i	0.0135843	−	0.0135843i	0.713866	+	0.700282i	$0.246942\pi$
$308$	213.878	+	213.878i	0.694409	+	0.694409i
$309$			41.9610i			0.135796i
$310$	29.3115	+	298.136i	0.0945534	+	0.961730i
$311$	−385.664			−1.24008			−0.620039	−	0.784571i	$-0.712883\pi$
$311$	−385.664			−1.24008			−0.620039	+	0.784571i	$0.712883\pi$
$312$	26.7372	−	26.7372i	0.0856963	−	0.0856963i
$313$	−156.465	−	156.465i	−0.499888	−	0.499888i	0.411515	−	0.911403i	$-0.365000\pi$
$313$	−156.465	−	156.465i	−0.499888	−	0.499888i	−0.911403	+	0.411515i	$0.865000\pi$
$314$			270.574i			0.861699i
$315$	269.173	−	26.4640i	0.854519	−	0.0840128i
$316$	310.967			0.984074
$317$	−172.672	+	172.672i	−0.544708	+	0.544708i	−0.924905	−	0.380198i	$-0.875856\pi$
$317$	−172.672	+	172.672i	−0.544708	+	0.544708i	0.380198	+	0.924905i	$0.375856\pi$
$318$	158.828	+	158.828i	0.499458	+	0.499458i
$319$		−	163.186i		−	0.511554i
$320$	−30.9160	−	25.3811i	−0.0966125	−	0.0793160i
$321$	103.412			0.322155
$322$	−48.9610	+	48.9610i	−0.152053	+	0.152053i
$323$	527.702	+	527.702i	1.63375	+	1.63375i
$324$		−	10.4732i		−	0.0323247i
$325$	−96.5630	+	144.408i	−0.297117	+	0.444333i
$326$	−168.748			−0.517632
$327$	−198.860	+	198.860i	−0.608134	+	0.608134i
$328$	−47.9160	−	47.9160i	−0.146085	−	0.146085i
$329$		−	765.437i		−	2.32656i
$330$	−127.874	+	155.759i	−0.387496	+	0.471998i
$331$	594.585			1.79633			0.898165	−	0.439659i	$-0.144901\pi$
$331$	594.585			1.79633			0.898165	+	0.439659i	$0.144901\pi$
$332$	25.4320	−	25.4320i	0.0766024	−	0.0766024i
$333$	−78.0465	−	78.0465i	−0.234374	−	0.234374i
$334$		−	435.461i		−	1.30378i
$335$	−11.6998	−	119.002i	−0.0349248	−	0.355231i
$336$	78.5646			0.233823
$337$	−318.172	+	318.172i	−0.944130	+	0.944130i	−0.998520	−	0.0543895i	$-0.982679\pi$
$337$	−318.172	+	318.172i	−0.944130	+	0.944130i	0.0543895	+	0.998520i	$0.482679\pi$
$338$	−120.715	−	120.715i	−0.357145	−	0.357145i
$339$		−	6.49433i		−	0.0191573i
$340$	−250.904	+	24.6679i	−0.737953	+	0.0725525i
$341$	−627.601			−1.84047
$342$	−156.846	+	156.846i	−0.458613	+	0.458613i
$343$	−44.9394	−	44.9394i	−0.131019	−	0.131019i
$344$		−	1.67978i		−	0.00488308i
$345$	−35.6564	−	29.2728i	−0.103352	−	0.0848488i
$346$	−445.068			−1.28632
$347$	161.848	−	161.848i	0.466422	−	0.466422i	−0.434331	−	0.900753i	$-0.643015\pi$
$347$	161.848	−	161.848i	0.466422	−	0.466422i	0.900753	+	0.434331i	$0.143015\pi$
$348$	−29.9718	−	29.9718i	−0.0861258	−	0.0861258i
$349$		−	66.1242i		−	0.189468i	−0.995503	−	0.0947339i	$-0.969800\pi$
$349$		−	66.1242i		−	0.189468i	0.995503	−	0.0947339i	$-0.0302000\pi$
$350$	−354.034	+	70.2939i	−1.01153	+	0.200840i
$351$	191.153			0.544596
$352$	59.2550	−	59.2550i	0.168338	−	0.168338i
$353$	331.118	+	331.118i	0.938012	+	0.938012i	0.998188	−	0.0601762i	$-0.0191662\pi$
$353$	331.118	+	331.118i	0.938012	+	0.938012i	−0.0601762	+	0.998188i	$0.519166\pi$
$354$			37.4780i			0.105870i
$355$	−327.138	+	398.478i	−0.921515	+	1.12247i
$356$	−283.429			−0.796149
$357$	350.145	−	350.145i	0.980799	−	0.980799i
$358$	−194.058	−	194.058i	−0.542061	−	0.542061i
$359$		−	134.587i		−	0.374893i	−0.982275	−	0.187447i	$-0.939979\pi$
$359$		−	134.587i		−	0.374893i	0.982275	−	0.187447i	$-0.0600211\pi$
$360$	−7.33187	−	74.5746i	−0.0203663	−	0.207152i
$361$	−515.224			−1.42721
$362$	−0.412795	+	0.412795i	−0.00114032	+	0.00114032i
$363$	−133.927	−	133.927i	−0.368945	−	0.368945i
$364$			141.880i			0.389781i
$365$	−292.740	+	28.7810i	−0.802027	+	0.0788520i
$366$	−106.165			−0.290068
$367$	451.660	−	451.660i	1.23068	−	1.23068i	0.266979	−	0.963702i	$-0.413975\pi$
$367$	451.660	−	451.660i	1.23068	−	1.23068i	0.963702	−	0.266979i	$-0.0860254\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	126.945i		−	0.344024i
$370$	113.845	+	93.4629i	0.307688	+	0.252602i
$371$	−842.815			−2.27174
$372$	−115.269	+	115.269i	−0.309864	+	0.309864i
$373$	451.866	+	451.866i	1.21144	+	1.21144i	0.970554	+	0.240883i	$0.0774369\pi$
$373$	451.866	+	451.866i	1.21144	+	1.21144i	0.240883	+	0.970554i	$0.422563\pi$
$374$		−	528.173i		−	1.41223i
$375$	−69.6895	−	230.168i	−0.185839	−	0.613780i
$376$	−212.065			−0.564002
$377$	54.1263	−	54.1263i	0.143571	−	0.143571i
$378$	280.842	+	280.842i	0.742968	+	0.742968i
$379$		−	230.954i		−	0.609377i	−0.952452	−	0.304688i	$-0.901448\pi$
$379$		−	230.954i		−	0.609377i	0.952452	−	0.304688i	$-0.0985524\pi$
$380$	187.827	−	228.787i	0.494282	−	0.602071i
$381$	366.965			0.963162
$382$	−313.636	+	313.636i	−0.821036	+	0.821036i
$383$	183.834	+	183.834i	0.479985	+	0.479985i	0.905127	−	0.425142i	$-0.139776\pi$
$383$	183.834	+	183.834i	0.479985	+	0.479985i	−0.425142	+	0.905127i	$0.639776\pi$
$384$		−	21.7663i		−	0.0566832i
$385$	−73.9872	−	752.545i	−0.192174	−	1.95466i
$386$	−23.9285			−0.0619909
$387$	2.22514	−	2.22514i	0.00574971	−	0.00574971i
$388$	58.8757	+	58.8757i	0.151742	+	0.151742i
$389$			468.206i			1.20362i	0.798641	+	0.601808i	$0.205553\pi$
$389$			468.206i			1.20362i	−0.798641	+	0.601808i	$0.794447\pi$
$390$	−94.0768	+	9.24925i	−0.241223	+	0.0237160i
$391$	120.909			0.309231
$392$	−110.450	+	110.450i	−0.281761	+	0.281761i
$393$	65.6968	+	65.6968i	0.167168	+	0.167168i
$394$			115.463i			0.293054i
$395$	−600.867	−	493.294i	−1.52118	−	1.24884i
$396$	156.985			0.396428
$397$	53.6961	−	53.6961i	0.135255	−	0.135255i	−0.636238	−	0.771493i	$-0.719510\pi$
$397$	53.6961	−	53.6961i	0.135255	−	0.135255i	0.771493	+	0.636238i	$0.219510\pi$
$398$	−263.722	−	263.722i	−0.662619	−	0.662619i
$399$			581.399i			1.45714i
$400$	19.4749	+	98.0853i	0.0486874	+	0.245213i
$401$	248.645			0.620062			0.310031	−	0.950727i	$-0.399661\pi$
$401$	248.645			0.620062			0.310031	+	0.950727i	$0.399661\pi$
$402$	46.0102	−	46.0102i	0.114453	−	0.114453i
$403$	−208.166	−	208.166i	−0.516541	−	0.516541i
$404$		−	211.477i		−	0.523459i
$405$	−16.6138	+	20.2369i	−0.0410218	+	0.0499675i
$406$	159.044			0.391735
$407$	−218.199	+	218.199i	−0.536117	+	0.536117i
$408$	−97.0078	−	97.0078i	−0.237764	−	0.237764i
$409$		−	561.926i		−	1.37390i	−0.726703	−	0.686952i	$-0.758948\pi$
$409$		−	561.926i		−	1.37390i	0.726703	−	0.686952i	$-0.241052\pi$
$410$	16.5756	+	168.596i	0.0404284	+	0.411209i
$411$	8.95344			0.0217845
$412$	−30.8447	+	30.8447i	−0.0748658	+	0.0748658i
$413$	−99.4381	−	99.4381i	−0.240770	−	0.240770i
$414$			35.9371i			0.0868047i
$415$	−89.4842	+	8.79772i	−0.215625	+	0.0211993i
$416$	39.3080			0.0944904
$417$	148.204	−	148.204i	0.355404	−	0.355404i
$418$	438.503	+	438.503i	1.04905	+	1.04905i
$419$			453.494i			1.08233i	0.840918	+	0.541163i	$0.182016\pi$
$419$			453.494i			1.08233i	−0.840918	+	0.541163i	$0.817984\pi$
$420$	−151.807	−	124.629i	−0.361444	−	0.296735i
$421$	−62.8563			−0.149302			−0.0746512	−	0.997210i	$-0.523784\pi$
$421$	−62.8563			−0.149302			−0.0746512	+	0.997210i	$0.523784\pi$
$422$	321.514	−	321.514i	0.761881	−	0.761881i
$423$	−280.914	−	280.914i	−0.664099	−	0.664099i
$424$			233.502i			0.550712i
$425$	523.940	+	350.349i	1.23280	+	0.824351i
$426$	−280.547			−0.658561
$427$	281.681	−	281.681i	0.659674	−	0.659674i
$428$	76.0158	+	76.0158i	0.177607	+	0.177607i
$429$		−	198.039i		−	0.461630i
$430$	−2.66466	+	3.24575i	−0.00619689	+	0.00754826i
$431$	−175.877			−0.408068			−0.204034	−	0.978964i	$-0.565405\pi$
$431$	−175.877			−0.408068			−0.204034	+	0.978964i	$0.565405\pi$
$432$	77.8073	−	77.8073i	0.180109	−	0.180109i
$433$	−342.932	−	342.932i	−0.791991	−	0.791991i	0.189827	−	0.981818i	$-0.439207\pi$
$433$	−342.932	−	342.932i	−0.791991	−	0.791991i	−0.981818	+	0.189827i	$0.939207\pi$
$434$		−	611.674i		−	1.40939i
$435$	10.3682	+	105.458i	0.0238349	+	0.242432i
$436$	−292.356			−0.670540
$437$	−100.382	+	100.382i	−0.229707	+	0.229707i
$438$	−113.183	−	113.183i	−0.258409	−	0.258409i
$439$		−	55.4496i		−	0.126309i	−0.998004	−	0.0631544i	$-0.979884\pi$
$439$		−	55.4496i		−	0.126309i	0.998004	−	0.0631544i	$-0.0201161\pi$
$440$	−208.493	+	20.4982i	−0.473847	+	0.0465867i
$441$	−292.619			−0.663535
$442$	175.187	−	175.187i	0.396351	−	0.396351i
$443$	−154.793	−	154.793i	−0.349420	−	0.349420i	0.510473	−	0.859894i	$-0.329470\pi$
$443$	−154.793	−	154.793i	−0.349420	−	0.349420i	−0.859894	+	0.510473i	$0.829470\pi$
$444$			80.1520i			0.180522i
$445$	547.656	+	449.609i	1.23069	+	1.01036i
$446$	−151.940			−0.340674
$447$	−93.6997	+	93.6997i	−0.209619	+	0.209619i
$448$	57.7513	+	57.7513i	0.128909	+	0.128909i
$449$			658.321i			1.46619i	0.680124	+	0.733097i	$0.261926\pi$
$449$			658.321i			1.46619i	−0.680124	+	0.733097i	$0.738074\pi$
$450$	−104.132	+	155.727i	−0.231405	+	0.346061i
$451$	−354.908			−0.786935
$452$	4.77385	−	4.77385i	0.0105616	−	0.0105616i
$453$	−188.277	−	188.277i	−0.415623	−	0.415623i
$454$			127.323i			0.280446i
$455$	225.068	−	274.149i	0.494654	−	0.602524i
$456$	161.077			0.353239
$457$	−630.005	+	630.005i	−1.37857	+	1.37857i	−0.531522	+	0.847045i	$0.678380\pi$
$457$	−630.005	+	630.005i	−1.37857	+	1.37857i	−0.847045	+	0.531522i	$0.821620\pi$
$458$	103.156	+	103.156i	0.225231	+	0.225231i
$459$		−	693.540i		−	1.51098i
$460$	−4.69244	−	47.7282i	−0.0102010	−	0.103757i
$461$	−635.738			−1.37904			−0.689520	−	0.724266i	$-0.742179\pi$
$461$	−635.738			−1.37904			−0.689520	+	0.724266i	$0.742179\pi$
$462$	290.959	−	290.959i	0.629781	−	0.629781i
$463$	−30.8108	−	30.8108i	−0.0665460	−	0.0665460i	0.673051	−	0.739597i	$-0.264984\pi$
$463$	−30.8108	−	30.8108i	−0.0665460	−	0.0665460i	−0.739597	+	0.673051i	$0.764984\pi$
$464$		−	44.0633i		−	0.0949640i
$465$	405.584	−	39.8753i	0.872223	−	0.0857534i
$466$	−423.606			−0.909026
$467$	273.937	−	273.937i	0.586588	−	0.586588i	−0.350118	−	0.936706i	$-0.613858\pi$
$467$	273.937	−	273.937i	0.586588	−	0.586588i	0.936706	+	0.350118i	$0.113858\pi$
$468$	52.0698	+	52.0698i	0.111260	+	0.111260i
$469$			244.152i			0.520580i
$470$	409.762	+	336.402i	0.871834	+	0.715749i
$471$	368.087			0.781502
$472$	−27.5494	+	27.5494i	−0.0583673	+	0.0583673i
$473$	−6.22095	−	6.22095i	−0.0131521	−	0.0131521i
$474$		−	423.039i		−	0.892488i
$475$	−725.858	+	144.120i	−1.52812	+	0.303410i
$476$	514.769			1.08145
$477$	−309.311	+	309.311i	−0.648451	+	0.648451i
$478$	89.5138	+	89.5138i	0.187267	+	0.187267i
$479$		−	617.839i		−	1.28985i	−0.764245	−	0.644926i	$-0.776888\pi$
$479$		−	617.839i		−	1.28985i	0.764245	−	0.644926i	$-0.223112\pi$
$480$	−34.5284	+	42.0580i	−0.0719341	+	0.0876209i
$481$	−144.747			−0.300929
$482$	175.324	−	175.324i	0.363744	−	0.363744i
$483$	66.6064	+	66.6064i	0.137901	+	0.137901i
$484$		−	196.894i		−	0.406806i
$485$	−20.3670	−	207.158i	−0.0419937	−	0.427130i
$486$	335.885			0.691122
$487$	182.634	−	182.634i	0.375019	−	0.375019i	−0.494283	−	0.869301i	$-0.664569\pi$
$487$	182.634	−	182.634i	0.375019	−	0.375019i	0.869301	+	0.494283i	$0.164569\pi$
$488$	−78.0397	−	78.0397i	−0.159917	−	0.159917i
$489$			229.564i			0.469456i
$490$	388.628	−	38.2083i	0.793118	−	0.0779761i
$491$	−31.9547			−0.0650808			−0.0325404	−	0.999470i	$-0.510360\pi$
$491$	−31.9547			−0.0650808			−0.0325404	+	0.999470i	$0.510360\pi$
$492$	−65.1848	+	65.1848i	−0.132489	+	0.132489i
$493$	−196.381	−	196.381i	−0.398338	−	0.398338i
$494$			290.890i			0.588846i
$495$	−303.335	−	249.029i	−0.612799	−	0.503089i
$496$	−169.464			−0.341662
$497$	744.358	−	744.358i	1.49770	−	1.49770i
$498$	−34.5976	−	34.5976i	−0.0694731	−	0.0694731i
$499$			138.737i			0.278030i	0.990290	+	0.139015i	$0.0443936\pi$
$499$			138.737i			0.278030i	−0.990290	+	0.139015i	$0.955606\pi$
$500$	117.964	−	220.419i	0.235928	−	0.440838i
$501$	−592.400			−1.18243
$502$	326.776	−	326.776i	0.650948	−	0.650948i
$503$	159.071	+	159.071i	0.316245	+	0.316245i	0.847323	−	0.531078i	$-0.178213\pi$
$503$	159.071	+	159.071i	0.316245	+	0.316245i	−0.531078	+	0.847323i	$0.678213\pi$
$504$			153.002i			0.303575i
$505$	−335.471	+	408.627i	−0.664298	+	0.809163i
$506$	100.472			0.198561
$507$	−164.220	+	164.220i	−0.323906	+	0.323906i
$508$	269.748	+	269.748i	0.531001	+	0.531001i
$509$			128.670i			0.252790i	0.991980	+	0.126395i	$0.0403406\pi$
$509$			128.670i			0.252790i	−0.991980	+	0.126395i	$0.959659\pi$
$510$	33.5581	+	341.329i	0.0658001	+	0.669272i
$511$	600.602			1.17535
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	575.795	+	575.795i	1.12241	+	1.12241i
$514$			89.9188i			0.174939i
$515$	108.529	−	10.6701i	0.210736	−	0.0207187i
$516$	−2.28516			−0.00442861
$517$	−785.368	+	785.368i	−1.51909	+	1.51909i
$518$	−212.662	−	212.662i	−0.410545	−	0.410545i
$519$			605.469i			1.16661i
$520$	−75.9529	−	62.3550i	−0.146063	−	0.119914i
$521$	452.310			0.868157			0.434078	−	0.900875i	$-0.357074\pi$
$521$	452.310			0.868157			0.434078	+	0.900875i	$0.357074\pi$
$522$	58.3689	−	58.3689i	0.111818	−	0.111818i
$523$	66.3514	+	66.3514i	0.126867	+	0.126867i	0.767689	−	0.640822i	$-0.221406\pi$
$523$	66.3514	+	66.3514i	0.126867	+	0.126867i	−0.640822	+	0.767689i	$0.721406\pi$
$524$			96.5848i			0.184322i
$525$	95.6276	+	481.627i	0.182148	+	0.917385i
$526$	247.099			0.469771
$527$	−755.266	+	755.266i	−1.43314	+	1.43314i
$528$	−80.6103	−	80.6103i	−0.152671	−	0.152671i
$529$			23.0000i			0.0434783i
$530$	370.409	−	451.184i	0.698884	−	0.851291i
$531$	−72.9871			−0.137452
$532$	−427.375	+	427.375i	−0.803336	+	0.803336i
$533$	−117.718	−	117.718i	−0.220859	−	0.220859i
$534$			385.576i			0.722052i
$535$	−26.2962	−	267.467i	−0.0491519	−	0.499938i
$536$	67.6424			0.126198
$537$	−263.996	+	263.996i	−0.491612	+	0.491612i
$538$	−237.309	−	237.309i	−0.441094	−	0.441094i
$539$			818.093i			1.51780i
$540$	−273.770	+	26.9160i	−0.506982	+	0.0498444i
$541$	−598.507			−1.10630			−0.553148	−	0.833083i	$-0.686574\pi$
$541$	−598.507			−1.10630			−0.553148	+	0.833083i	$0.686574\pi$
$542$	26.2193	−	26.2193i	0.0483751	−	0.0483751i
$543$	0.561565	+	0.561565i	0.00103419	+	0.00103419i
$544$		−	142.617i		−	0.262164i
$545$	564.904	+	463.769i	1.03652	+	0.850953i
$546$	193.014			0.353505
$547$	87.9130	−	87.9130i	0.160718	−	0.160718i	−0.622166	−	0.782885i	$-0.713747\pi$
$547$	87.9130	−	87.9130i	0.160718	−	0.160718i	0.782885	+	0.622166i	$0.213747\pi$
$548$	6.58149	+	6.58149i	0.0120100	+	0.0120100i
$549$		−	206.752i		−	0.376598i
$550$	435.377	+	291.128i	0.791594	+	0.529325i
$551$	326.080			0.591797
$552$	18.4533	−	18.4533i	0.0334299	−	0.0334299i
$553$	1122.42	+	1122.42i	2.02970	+	2.02970i
$554$			450.960i			0.814007i
$555$	127.147	−	154.874i	0.229093	−	0.279052i
$556$	217.883			0.391876
$557$	688.697	−	688.697i	1.23644	−	1.23644i	0.274995	−	0.961446i	$-0.411324\pi$
$557$	688.697	−	688.697i	1.23644	−	1.23644i	0.961446	−	0.274995i	$-0.0886762\pi$
$558$	−224.483	−	224.483i	−0.402299	−	0.402299i
$559$		−	4.12680i		−	0.00738246i
$560$	−19.9780	−	203.202i	−0.0356750	−	0.362860i
$561$	−718.525			−1.28079
$562$	−70.2491	+	70.2491i	−0.124998	+	0.124998i
$563$	51.4275	+	51.4275i	0.0913454	+	0.0913454i	0.751303	−	0.659958i	$-0.229426\pi$
$563$	51.4275	+	51.4275i	0.0913454	+	0.0913454i	−0.659958	+	0.751303i	$0.729426\pi$
$564$			288.492i			0.511511i
$565$	−16.7971	+	1.65143i	−0.0297294	+	0.00292288i
$566$	98.2430			0.173574
$567$	37.8025	−	37.8025i	0.0666712	−	0.0666712i
$568$	−206.225	−	206.225i	−0.363071	−	0.363071i
$569$		−	632.828i		−	1.11218i	−0.831124	−	0.556088i	$-0.812302\pi$
$569$		−	632.828i		−	1.11218i	0.831124	−	0.556088i	$-0.187698\pi$
$570$	−311.241	−	255.519i	−0.546036	−	0.448279i
$571$	696.211			1.21928			0.609642	−	0.792677i	$-0.291313\pi$
$571$	696.211			1.21928			0.609642	+	0.792677i	$0.291313\pi$
$572$	145.575	−	145.575i	0.254501	−	0.254501i
$573$	426.669	+	426.669i	0.744623	+	0.744623i
$574$		−	345.901i		−	0.602615i
$575$	−66.6452	+	99.6665i	−0.115905	+	0.173333i
$576$	42.3891			0.0735923
$577$	−75.3419	+	75.3419i	−0.130575	+	0.130575i	−0.769374	−	0.638799i	$-0.779432\pi$
$577$	−75.3419	+	75.3419i	−0.130575	+	0.130575i	0.638799	+	0.769374i	$0.279432\pi$
$578$	−346.613	−	346.613i	−0.599676	−	0.599676i
$579$			32.5522i			0.0562215i
$580$	−69.8985	+	85.1413i	−0.120515	+	0.146795i
$581$	183.591			0.315992
$582$	80.0943	−	80.0943i	0.137619	−	0.137619i
$583$	864.760	+	864.760i	1.48329	+	1.48329i
$584$		−	166.397i		−	0.284926i
$585$	−18.0126	−	183.211i	−0.0307907	−	0.313181i
$586$	739.808			1.26247
$587$	537.340	−	537.340i	0.915401	−	0.915401i	−0.0812898	−	0.996691i	$-0.525904\pi$
$587$	537.340	−	537.340i	0.915401	−	0.915401i	0.996691	+	0.0812898i	$0.0259039\pi$
$588$	150.256	+	150.256i	0.255538	+	0.255538i
$589$		−	1254.08i		−	2.12917i
$590$	96.9343	−	9.53019i	0.164295	−	0.0161529i
$591$	157.076			0.265780
$592$	−58.9181	+	58.9181i	−0.0995238	+	0.0995238i
$593$	−100.376	−	100.376i	−0.169268	−	0.169268i	0.617390	−	0.786657i	$-0.288190\pi$
$593$	−100.376	−	100.376i	−0.169268	−	0.169268i	−0.786657	+	0.617390i	$0.788190\pi$
$594$		−	576.309i		−	0.970217i
$595$	−994.663	−	816.589i	−1.67170	−	1.37242i
$596$	−137.754			−0.231130
$597$	−358.767	+	358.767i	−0.600949	+	0.600949i
$598$	33.3250	+	33.3250i	0.0557274	+	0.0557274i
$599$			57.7918i			0.0964805i	0.998836	+	0.0482403i	$0.0153613\pi$
$599$			57.7918i			0.0964805i	−0.998836	+	0.0482403i	$0.984639\pi$
$600$	133.435	−	26.4936i	0.222392	−	0.0441561i
$601$	855.388			1.42327			0.711637	−	0.702547i	$-0.247954\pi$
$601$	855.388			1.42327			0.711637	+	0.702547i	$0.247954\pi$
$602$	6.06308	−	6.06308i	0.0100716	−	0.0100716i
$603$	89.6032	+	89.6032i	0.148596	+	0.148596i
$604$		−	276.798i		−	0.458275i
$605$	−312.337	+	380.449i	−0.516259	+	0.628841i
$606$	−287.693			−0.474741
$607$	171.294	−	171.294i	0.282198	−	0.282198i	−0.551787	−	0.833985i	$-0.686054\pi$
$607$	171.294	−	171.294i	0.282198	−	0.282198i	0.833985	+	0.551787i	$0.186054\pi$
$608$	118.404	+	118.404i	0.194744	+	0.194744i
$609$		−	216.364i		−	0.355277i
$610$	26.9964	+	274.588i	0.0442564	+	0.450144i
$611$	−520.990			−0.852684
$612$	188.919	−	188.919i	0.308691	−	0.308691i
$613$	−107.859	−	107.859i	−0.175952	−	0.175952i	0.613636	−	0.789589i	$-0.289706\pi$
$613$	−107.859	−	107.859i	−0.175952	−	0.175952i	−0.789589	+	0.613636i	$0.789706\pi$
$614$		−	8.34078i		−	0.0135843i
$615$	229.357	−	22.5495i	0.372938	−	0.0366658i
$616$	427.756			0.694409
$617$	234.765	−	234.765i	0.380495	−	0.380495i	−0.490786	−	0.871280i	$-0.663290\pi$
$617$	234.765	−	234.765i	0.380495	−	0.380495i	0.871280	+	0.490786i	$0.163290\pi$
$618$	41.9610	+	41.9610i	0.0678981	+	0.0678981i
$619$		−	35.0950i		−	0.0566964i	−0.999598	−	0.0283482i	$-0.990975\pi$
$619$		−	35.0950i		−	0.0566964i	0.999598	−	0.0283482i	$-0.00902472\pi$
$620$	327.448	+	268.825i	0.528142	+	0.433588i
$621$	131.929			0.212446
$622$	−385.664	+	385.664i	−0.620039	+	0.620039i
$623$	−1023.02	−	1023.02i	−1.64209	−	1.64209i
$624$		−	53.4745i		−	0.0856963i
$625$	−577.591	+	238.776i	−0.924145	+	0.382041i
$626$	−312.930			−0.499888
$627$	596.538	−	596.538i	0.951416	−	0.951416i
$628$	270.574	+	270.574i	0.430850	+	0.430850i
$629$			525.170i			0.834929i
$630$	242.709	−	295.637i	0.385253	−	0.469266i
$631$	−826.767			−1.31025			−0.655124	−	0.755521i	$-0.727384\pi$
$631$	−826.767			−1.31025			−0.655124	+	0.755521i	$0.727384\pi$
$632$	310.967	−	310.967i	0.492037	−	0.492037i
$633$	−437.386	−	437.386i	−0.690974	−	0.690974i
$634$			345.345i			0.544708i
$635$	−93.3144	−	949.128i	−0.146952	−	1.49469i
$636$	317.655			0.499458
$637$	−271.349	+	271.349i	−0.425980	+	0.425980i
$638$	−163.186	−	163.186i	−0.255777	−	0.255777i
$639$		−	546.355i		−	0.855016i
$640$	−56.2971	+	5.53490i	−0.0879642	+	0.00864829i
$641$	52.1713			0.0813904			0.0406952	−	0.999172i	$-0.487043\pi$
$641$	52.1713			0.0813904			0.0406952	+	0.999172i	$0.487043\pi$
$642$	103.412	−	103.412i	0.161077	−	0.161077i
$643$	241.431	+	241.431i	0.375476	+	0.375476i	0.869467	−	0.493991i	$-0.164463\pi$
$643$	241.431	+	241.431i	0.375476	+	0.375476i	−0.493991	+	0.869467i	$0.664463\pi$
$644$			97.9220i			0.152053i
$645$	4.41551	+	3.62500i	0.00684575	+	0.00562016i
$646$	1055.40			1.63375
$647$	−320.910	+	320.910i	−0.495998	+	0.495998i	−0.910190	−	0.414192i	$-0.864064\pi$
$647$	−320.910	+	320.910i	−0.495998	+	0.495998i	0.414192	+	0.910190i	$0.364064\pi$
$648$	−10.4732	−	10.4732i	−0.0161624	−	0.0161624i
$649$			204.055i			0.314414i
$650$	47.8451	+	240.971i	0.0736078	+	0.370725i
$651$	−832.119			−1.27822
$652$	−168.748	+	168.748i	−0.258816	+	0.258816i
$653$	358.411	+	358.411i	0.548869	+	0.548869i	0.926114	−	0.377245i	$-0.123128\pi$
$653$	358.411	+	358.411i	0.548869	+	0.548869i	−0.377245	+	0.926114i	$0.623128\pi$
$654$			397.720i			0.608134i
$655$	153.214	−	186.626i	0.233915	−	0.284925i
$656$	−95.8320			−0.146085
$657$	220.420	−	220.420i	0.335494	−	0.335494i
$658$	−765.437	−	765.437i	−1.16328	−	1.16328i
$659$			654.343i			0.992934i	0.868056	+	0.496467i	$0.165370\pi$
$659$			654.343i			0.992934i	−0.868056	+	0.496467i	$0.834630\pi$
$660$	27.8856	+	283.633i	0.0422510	+	0.429747i
$661$	205.380			0.310711			0.155355	−	0.987859i	$-0.450348\pi$
$661$	205.380			0.310711			0.155355	+	0.987859i	$0.450348\pi$
$662$	594.585	−	594.585i	0.898165	−	0.898165i
$663$	−238.324	−	238.324i	−0.359463	−	0.359463i
$664$		−	50.8640i		−	0.0766024i
$665$	1503.75	−	147.842i	2.26128	−	0.222319i
$666$	−156.093			−0.234374
$667$	37.3565	−	37.3565i	0.0560067	−	0.0560067i
$668$	−435.461	−	435.461i	−0.651888	−	0.651888i
$669$			206.699i			0.308967i
$670$	−130.702	−	107.302i	−0.195078	−	0.160153i
$671$	−578.030			−0.861446
$672$	78.5646	−	78.5646i	0.116912	−	0.116912i
$673$	−181.364	−	181.364i	−0.269486	−	0.269486i	0.559407	−	0.828893i	$-0.311029\pi$
$673$	−181.364	−	181.364i	−0.269486	−	0.269486i	−0.828893	+	0.559407i	$0.811029\pi$
$674$			636.344i			0.944130i
$675$	571.690	+	382.279i	0.846949	+	0.566339i
$676$	−241.430			−0.357145
$677$	49.6207	−	49.6207i	0.0732950	−	0.0732950i	−0.669509	−	0.742804i	$-0.733495\pi$
$677$	49.6207	−	49.6207i	0.0732950	−	0.0732950i	0.742804	+	0.669509i	$0.233495\pi$
$678$	−6.49433	−	6.49433i	−0.00957866	−	0.00957866i
$679$			425.018i			0.625947i
$680$	−226.236	+	275.572i	−0.332700	+	0.405253i
$681$	173.209			0.254345
$682$	−627.601	+	627.601i	−0.920236	+	0.920236i
$683$	−665.906	−	665.906i	−0.974972	−	0.974972i	0.0247224	−	0.999694i	$-0.492130\pi$
$683$	−665.906	−	665.906i	−0.974972	−	0.974972i	−0.999694	+	0.0247224i	$0.992130\pi$
$684$			313.691i			0.458613i
$685$	−2.27675	−	23.1574i	−0.00332372	−	0.0338065i
$686$	−89.8789			−0.131019
$687$	140.333	−	140.333i	0.204269	−	0.204269i
$688$	−1.67978	−	1.67978i	−0.00244154	−	0.00244154i
$689$			573.656i			0.832593i
$690$	−64.9293	+	6.38358i	−0.0941004	+	0.00925157i
$691$	868.900			1.25745			0.628727	−	0.777626i	$-0.283576\pi$
$691$	868.900			1.25745			0.628727	+	0.777626i	$0.283576\pi$
$692$	−445.068	+	445.068i	−0.643162	+	0.643162i
$693$	566.632	+	566.632i	0.817651	+	0.817651i
$694$		−	323.697i		−	0.466422i
$695$	−421.004	−	345.632i	−0.605761	−	0.497312i
$696$	−59.9436			−0.0861258
$697$	−427.102	+	427.102i	−0.612772	+	0.612772i
$698$	−66.1242	−	66.1242i	−0.0947339	−	0.0947339i
$699$			576.272i			0.824424i
$700$	−283.740	+	424.328i	−0.405344	+	0.606183i
$701$	769.630			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$701$	769.630			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$702$	191.153	−	191.153i	0.272298	−	0.272298i
$703$	−436.010	−	436.010i	−0.620213	−	0.620213i
$704$		−	118.510i		−	0.168338i
$705$	457.640	−	557.439i	0.649135	−	0.790693i
$706$	662.236			0.938012
$707$	763.318	−	763.318i	1.07966	−	1.07966i
$708$	37.4780	+	37.4780i	0.0529351	+	0.0529351i
$709$			1193.36i			1.68316i	0.540133	+	0.841580i	$0.318374\pi$
$709$			1193.36i			1.68316i	−0.540133	+	0.841580i	$0.681626\pi$
$710$	71.3396	+	725.615i	0.100478	+	1.02199i
$711$	823.853			1.15872
$712$	−283.429	+	283.429i	−0.398075	+	0.398075i
$713$	−143.671	−	143.671i	−0.201501	−	0.201501i
$714$		−	700.291i		−	0.980799i
$715$	−512.215	+	50.3589i	−0.716384	+	0.0704320i
$716$	−388.116			−0.542061
$717$	121.774	−	121.774i	0.169839	−	0.169839i
$718$	−134.587	−	134.587i	−0.187447	−	0.187447i
$719$			1266.00i			1.76078i	0.474252	+	0.880389i	$0.342719\pi$
$719$			1266.00i			1.76078i	−0.474252	+	0.880389i	$0.657281\pi$
$720$	−81.9064	−	67.2427i	−0.113759	−	0.0933926i
$721$	−222.665			−0.308828
$722$	−515.224	+	515.224i	−0.713607	+	0.713607i
$723$	−238.511	−	238.511i	−0.329890	−	0.329890i
$724$			0.825590i			0.00114032i
$725$	270.123	−	53.6331i	0.372583	−	0.0739768i
$726$	−267.854			−0.368945
$727$	−712.318	+	712.318i	−0.979805	+	0.979805i	−0.999800	−	0.0199952i	$-0.993635\pi$
$727$	−712.318	+	712.318i	−0.979805	+	0.979805i	0.0199952	+	0.999800i	$0.493635\pi$
$728$	141.880	+	141.880i	0.194891	+	0.194891i
$729$		−	504.066i		−	0.691449i
$730$	−263.959	+	321.521i	−0.361587	+	0.440439i
$731$	−14.9728			−0.0204826
$732$	−106.165	+	106.165i	−0.145034	+	0.145034i
$733$	−785.498	−	785.498i	−1.07162	−	1.07162i	−0.997229	−	0.0743915i	$-0.976299\pi$
$733$	−785.498	−	785.498i	−1.07162	−	1.07162i	−0.0743915	−	0.997229i	$-0.523701\pi$
$734$		−	903.320i		−	1.23068i
$735$	−51.9784	−	528.688i	−0.0707190	−	0.719303i
$736$	27.1293			0.0368605
$737$	250.509	−	250.509i	0.339904	−	0.339904i
$738$	−126.945	−	126.945i	−0.172012	−	0.172012i
$739$		−	176.725i		−	0.239141i	−0.992826	−	0.119570i	$-0.961848\pi$
$739$		−	176.725i		−	0.239141i	0.992826	−	0.119570i	$-0.0381517\pi$
$740$	207.307	−	20.3816i	0.280145	−	0.0275427i
$741$	395.726			0.534043
$742$	−842.815	+	842.815i	−1.13587	+	1.13587i
$743$	−433.606	−	433.606i	−0.583588	−	0.583588i	0.352300	−	0.935887i	$-0.385400\pi$
$743$	−433.606	−	433.606i	−0.583588	−	0.583588i	−0.935887	+	0.352300i	$0.885400\pi$
$744$			230.539i			0.309864i
$745$	266.174	+	218.521i	0.357281	+	0.293317i
$746$	903.732			1.21144
$747$	67.3775	−	67.3775i	0.0901975	−	0.0901975i
$748$	−528.173	−	528.173i	−0.706114	−	0.706114i
$749$			548.751i			0.732645i
$750$	−299.857	−	160.478i	−0.399809	−	0.213971i
$751$	197.940			0.263569			0.131785	−	0.991278i	$-0.457929\pi$
$751$	197.940			0.263569			0.131785	+	0.991278i	$0.457929\pi$
$752$	−212.065	+	212.065i	−0.282001	+	0.282001i
$753$	−444.545	−	444.545i	−0.590365	−	0.590365i
$754$		−	108.253i		−	0.143571i
$755$	−439.090	+	534.843i	−0.581576	+	0.708401i
$756$	561.684			0.742968
$757$	−660.110	+	660.110i	−0.872008	+	0.872008i	−0.992691	−	0.120683i	$-0.961491\pi$
$757$	−660.110	+	660.110i	−0.872008	+	0.872008i	0.120683	+	0.992691i	$0.461491\pi$
$758$	−230.954	−	230.954i	−0.304688	−	0.304688i
$759$		−	136.681i		−	0.180081i
$760$	−40.9598	−	416.614i	−0.0538944	−	0.548176i
$761$	886.095			1.16438			0.582191	−	0.813052i	$-0.302196\pi$
$761$	886.095			1.16438			0.582191	+	0.813052i	$0.302196\pi$
$762$	366.965	−	366.965i	0.481581	−	0.481581i
$763$	−1055.24	−	1055.24i	−1.38302	−	1.38302i
$764$			627.271i			0.821036i
$765$	−664.725	+	65.3531i	−0.868922	+	0.0854288i
$766$	367.668			0.479985
$767$	−67.6819	+	67.6819i	−0.0882424	+	0.0882424i
$768$	−21.7663	−	21.7663i	−0.0283416	−	0.0283416i
$769$			666.097i			0.866185i	0.901349	+	0.433093i	$0.142578\pi$
$769$			666.097i			0.866185i	−0.901349	+	0.433093i	$0.857422\pi$
$770$	−826.532	−	678.558i	−1.07342	−	0.881244i
$771$	122.325			0.158658
$772$	−23.9285	+	23.9285i	−0.0309955	+	0.0309955i
$773$	686.942	+	686.942i	0.888670	+	0.888670i	0.994395	−	0.105725i	$-0.0337165\pi$
$773$	686.942	+	686.942i	0.888670	+	0.888670i	−0.105725	+	0.994395i	$0.533716\pi$
$774$		−	4.45027i		−	0.00574971i
$775$	−206.269	−	1038.87i	−0.266154	−	1.34048i
$776$	117.751			0.151742
$777$	−289.305	+	289.305i	−0.372336	+	0.372336i
$778$	468.206	+	468.206i	0.601808	+	0.601808i
$779$		−	709.183i		−	0.910376i
$780$	−84.8276	+	103.326i	−0.108753	+	0.132469i
$781$	−1527.48			−1.95580
$782$	120.909	−	120.909i	0.154616	−	0.154616i
$783$	−214.278	−	214.278i	−0.273663	−	0.273663i
$784$			220.901i			0.281761i
$785$	−93.5999	−	952.032i	−0.119236	−	1.21278i
$786$	131.394			0.167168
$787$	−202.388	+	202.388i	−0.257164	+	0.257164i	−0.823900	−	0.566736i	$-0.808206\pi$
$787$	−202.388	+	202.388i	−0.257164	+	0.257164i	0.566736	+	0.823900i	$0.308206\pi$
$788$	115.463	+	115.463i	0.146527	+	0.146527i
$789$		−	336.153i		−	0.426050i
$790$	−1094.16	+	107.573i	−1.38501	+	0.136169i
$791$	34.4620			0.0435676
$792$	156.985	−	156.985i	0.198214	−	0.198214i
$793$	−191.724	−	191.724i	−0.241771	−	0.241771i
$794$		−	107.392i		−	0.135255i
$795$	−613.790	−	503.903i	−0.772063	−	0.633840i
$796$	−527.445			−0.662619
$797$	374.756	−	374.756i	0.470208	−	0.470208i	−0.431774	−	0.901982i	$-0.642112\pi$
$797$	374.756	−	374.756i	0.470208	−	0.470208i	0.901982	+	0.431774i	$0.142112\pi$
$798$	581.399	+	581.399i	0.728571	+	0.728571i
$799$			1890.25i			2.36577i
$800$	117.560	+	78.6104i	0.146950	+	0.0982630i
$801$	−750.895			−0.937447
$802$	248.645	−	248.645i	0.310031	−	0.310031i
$803$	−616.241	−	616.241i	−0.767423	−	0.767423i
$804$		−	92.0205i		−	0.114453i
$805$	155.336	−	189.210i	0.192963	−	0.235043i
$806$	−416.332			−0.516541
$807$	−322.834	+	322.834i	−0.400042	+	0.400042i
$808$	−211.477	−	211.477i	−0.261729	−	0.261729i
$809$		−	928.234i		−	1.14738i	−0.819071	−	0.573692i	$-0.805510\pi$
$809$		−	928.234i		−	1.14738i	0.819071	−	0.573692i	$-0.194490\pi$
$810$	3.62301	+	36.8507i	0.00447285	+	0.0454947i
$811$	−111.016			−0.136888			−0.0684440	−	0.997655i	$-0.521803\pi$
$811$	−111.016			−0.136888			−0.0684440	+	0.997655i	$0.521803\pi$
$812$	159.044	−	159.044i	0.195868	−	0.195868i
$813$	−35.6686	−	35.6686i	−0.0438729	−	0.0438729i
$814$			436.399i			0.536117i
$815$	593.751	−	58.3752i	0.728529	−	0.0716261i
$816$	−194.016			−0.237764
$817$	12.4308	−	12.4308i	0.0152152	−	0.0152152i
$818$	−561.926	−	561.926i	−0.686952	−	0.686952i
$819$			375.887i			0.458958i
$820$	185.171	+	152.020i	0.225819	+	0.185390i
$821$	−151.544			−0.184585			−0.0922923	−	0.995732i	$-0.529419\pi$
$821$	−151.544			−0.184585			−0.0922923	+	0.995732i	$0.529419\pi$
$822$	8.95344	−	8.95344i	0.0108923	−	0.0108923i
$823$	720.489	+	720.489i	0.875442	+	0.875442i	0.993059	−	0.117617i	$-0.0375255\pi$
$823$	720.489	+	720.489i	0.875442	+	0.875442i	−0.117617	+	0.993059i	$0.537525\pi$
$824$			61.6894i			0.0748658i
$825$	396.050	−	592.285i	0.480061	−	0.717922i
$826$	−198.876			−0.240770
$827$	449.514	−	449.514i	0.543548	−	0.543548i	−0.381019	−	0.924567i	$-0.624427\pi$
$827$	449.514	−	449.514i	0.543548	−	0.543548i	0.924567	+	0.381019i	$0.124427\pi$
$828$	35.9371	+	35.9371i	0.0434023	+	0.0434023i
$829$			321.318i			0.387598i	0.981041	+	0.193799i	$0.0620809\pi$
$829$			321.318i			0.387598i	−0.981041	+	0.193799i	$0.937919\pi$
$830$	−80.6865	+	98.2819i	−0.0972126	+	0.118412i
$831$	613.485			0.738249
$832$	39.3080	−	39.3080i	0.0472452	−	0.0472452i
$833$	984.507	+	984.507i	1.18188	+	1.18188i
$834$		−	296.407i		−	0.355404i
$835$	150.640	+	1532.20i	0.180407	+	1.83497i
$836$	877.006			1.04905
$837$	−824.098	+	824.098i	−0.984586	+	0.984586i
$838$	453.494	+	453.494i	0.541163	+	0.541163i
$839$			439.686i			0.524060i	0.965060	+	0.262030i	$0.0843919\pi$
$839$			439.686i			0.524060i	−0.965060	+	0.262030i	$0.915608\pi$
$840$	−276.435	+	27.1780i	−0.329089	+	0.0323547i
$841$	719.652			0.855709
$842$	−62.8563	+	62.8563i	−0.0746512	+	0.0746512i
$843$	95.5667	+	95.5667i	0.113365	+	0.113365i
$844$		−	643.028i		−	0.761881i
$845$	466.503	+	382.985i	0.552075	+	0.453237i
$846$	−561.827			−0.664099
$847$	710.680	−	710.680i	0.839056	−	0.839056i
$848$	233.502	+	233.502i	0.275356	+	0.275356i
$849$		−	133.649i		−	0.157420i
$850$	874.289	−	173.591i	1.02858	−	0.204225i
$851$	−99.9005			−0.117392
$852$	−280.547	+	280.547i	−0.329281	+	0.329281i
$853$	649.971	+	649.971i	0.761983	+	0.761983i	0.976681	−	0.214698i	$-0.0688767\pi$
$853$	649.971	+	649.971i	0.761983	+	0.761983i	−0.214698	+	0.976681i	$0.568877\pi$
$854$		−	563.361i		−	0.659674i
$855$	497.614	−	606.130i	0.582005	−	0.708924i
$856$	152.032			0.177607
$857$	−451.584	+	451.584i	−0.526935	+	0.526935i	−0.919657	−	0.392722i	$-0.871533\pi$
$857$	−451.584	+	451.584i	−0.526935	+	0.526935i	0.392722	+	0.919657i	$0.371533\pi$
$858$	−198.039	−	198.039i	−0.230815	−	0.230815i
$859$		−	1259.30i		−	1.46601i	−0.680225	−	0.733003i	$-0.738118\pi$
$859$		−	1259.30i		−	1.46601i	0.680225	−	0.733003i	$-0.261882\pi$
$860$	0.581088	+	5.91042i	0.000675684	+	0.00687258i
$861$	−470.563			−0.546530
$862$	−175.877	+	175.877i	−0.204034	+	0.204034i
$863$	267.447	+	267.447i	0.309904	+	0.309904i	0.844872	−	0.534968i	$-0.179676\pi$
$863$	267.447	+	267.447i	0.309904	+	0.309904i	−0.534968	+	0.844872i	$0.679676\pi$
$864$		−	155.615i		−	0.180109i
$865$	1566.00	−	153.963i	1.81041	−	0.177992i
$866$	−685.864			−0.791991
$867$	−471.531	+	471.531i	−0.543865	+	0.543865i
$868$	−611.674	−	611.674i	−0.704694	−	0.704694i
$869$		−	2303.30i		−	2.65051i
$870$	115.826	+	95.0896i	0.133133	+	0.109298i
$871$	166.180			0.190793
$872$	−292.356	+	292.356i	−0.335270	+	0.335270i
$873$	155.981	+	155.981i	0.178672	+	0.178672i
$874$			200.764i			0.229707i
$875$	1221.38	−	369.806i	1.39586	−	0.422635i
$876$	−226.366			−0.258409
$877$	−278.861	+	278.861i	−0.317972	+	0.317972i	−0.847988	−	0.530016i	$-0.822186\pi$
$877$	−278.861	+	278.861i	−0.317972	+	0.317972i	0.530016	+	0.847988i	$0.322186\pi$
$878$	−55.4496	−	55.4496i	−0.0631544	−	0.0631544i
$879$		−	1006.43i		−	1.14497i
$880$	−187.995	+	228.991i	−0.213630	+	0.260217i
$881$	−1222.79			−1.38796			−0.693979	−	0.719995i	$-0.744144\pi$
$881$	−1222.79			−1.38796			−0.693979	+	0.719995i	$0.744144\pi$
$882$	−292.619	+	292.619i	−0.331767	+	0.331767i
$883$	−160.195	−	160.195i	−0.181421	−	0.181421i	0.610554	−	0.791975i	$-0.290947\pi$
$883$	−160.195	−	160.195i	−0.181421	−	0.181421i	−0.791975	+	0.610554i	$0.790947\pi$
$884$		−	350.374i		−	0.396351i
$885$	−12.9648	−	131.869i	−0.0146495	−	0.149005i
$886$	−309.587			−0.349420
$887$	982.564	−	982.564i	1.10774	−	1.10774i	0.114291	−	0.993447i	$-0.463540\pi$
$887$	982.564	−	982.564i	1.10774	−	1.10774i	0.993447	−	0.114291i	$-0.0364597\pi$
$888$	80.1520	+	80.1520i	0.0902612	+	0.0902612i
$889$			1947.29i			2.19043i
$890$	997.265	−	98.0470i	1.12052	−	0.110165i
$891$	−77.5737			−0.0870636
$892$	−151.940	+	151.940i	−0.170337	+	0.170337i
$893$	−1569.34	−	1569.34i	−1.75737	−	1.75737i
$894$			187.399i			0.209619i
$895$	749.937	+	615.675i	0.837918	+	0.687905i
$896$	115.503			0.128909
$897$	45.3352	−	45.3352i	0.0505409	−	0.0505409i
$898$	658.321	+	658.321i	0.733097	+	0.733097i
$899$			466.698i			0.519130i
$900$	51.5954	+	259.859i	0.0573282	+	0.288733i
$901$	2081.34			2.31003
$902$	−354.908	+	354.908i	−0.393468	+	0.393468i
$903$	−8.24820	−	8.24820i	−0.00913421	−	0.00913421i
$904$		−	9.54770i		−	0.0105616i
$905$	1.30965	−	1.59525i	0.00144713	−	0.00176270i
$906$	−376.555			−0.415623
$907$	290.205	−	290.205i	0.319961	−	0.319961i	−0.528791	−	0.848752i	$-0.677354\pi$
$907$	290.205	−	290.205i	0.319961	−	0.319961i	0.848752	+	0.528791i	$0.177354\pi$
$908$	127.323	+	127.323i	0.140223	+	0.140223i
$909$		−	560.272i		−	0.616360i
$910$	−49.0809	−	499.216i	−0.0539351	−	0.548589i
$911$	−1529.66			−1.67910			−0.839551	−	0.543280i	$-0.817182\pi$
$911$	−1529.66			−1.67910			−0.839551	+	0.543280i	$0.817182\pi$
$912$	161.077	−	161.077i	0.176619	−	0.176619i
$913$	−188.372	−	188.372i	−0.206321	−	0.206321i
$914$			1260.01i			1.37857i
$915$	373.549	−	36.7258i	0.408250	−	0.0401375i
$916$	206.312			0.225231
$917$	−348.618	+	348.618i	−0.380173	+	0.380173i
$918$	−693.540	−	693.540i	−0.755490	−	0.755490i
$919$			44.0845i			0.0479701i	0.999712	+	0.0239850i	$0.00763540\pi$
$919$			44.0845i			0.0479701i	−0.999712	+	0.0239850i	$0.992365\pi$
$920$	−52.4206	−	43.0358i	−0.0569790	−	0.0467780i
$921$	−11.3468			−0.0123201
$922$	−635.738	+	635.738i	−0.689520	+	0.689520i
$923$	−506.642	−	506.642i	−0.548908	−	0.548908i
$924$		−	581.918i		−	0.629781i
$925$	−432.902	−	289.473i	−0.468002	−	0.312944i
$926$	−61.6216			−0.0665460
$927$	−81.7175	+	81.7175i	−0.0881526	+	0.0881526i
$928$	−44.0633	−	44.0633i	−0.0474820	−	0.0474820i
$929$			973.596i			1.04800i	0.851717	+	0.524002i	$0.175562\pi$
$929$			973.596i			1.04800i	−0.851717	+	0.524002i	$0.824438\pi$
$930$	365.708	−	445.459i	0.393235	−	0.478988i
$931$	−1634.73			−1.75588
$932$	−423.606	+	423.606i	−0.454513	+	0.454513i
$933$	524.657	+	524.657i	0.562333	+	0.562333i
$934$		−	547.873i		−	0.586588i
$935$	182.712	+	1858.41i	0.195414	+	1.98761i
$936$	104.140			0.111260
$937$	423.335	−	423.335i	0.451798	−	0.451798i	−0.444153	−	0.895951i	$-0.646495\pi$
$937$	423.335	−	423.335i	0.451798	−	0.451798i	0.895951	+	0.444153i	$0.146495\pi$
$938$	244.152	+	244.152i	0.260290	+	0.260290i
$939$			425.708i			0.453364i
$940$	746.164	−	73.3598i	0.793792	−	0.0780424i
$941$	−1808.69			−1.92210			−0.961049	−	0.276377i	$-0.910866\pi$
$941$	−1808.69			−1.92210			−0.961049	+	0.276377i	$0.910866\pi$
$942$	368.087	−	368.087i	0.390751	−	0.390751i
$943$	−81.2455	−	81.2455i	−0.0861564	−	0.0861564i
$944$			55.0987i			0.0583673i
$945$	−1085.31	−	891.009i	−1.14848	−	0.942867i
$946$	−12.4419			−0.0131521
$947$	964.707	−	964.707i	1.01870	−	1.01870i	0.0188762	−	0.999822i	$-0.493991\pi$
$947$	964.707	−	964.707i	1.01870	−	1.01870i	0.999822	−	0.0188762i	$-0.00600883\pi$
$948$	−423.039	−	423.039i	−0.446244	−	0.446244i
$949$		−	408.796i		−	0.430765i
$950$	−581.738	+	869.978i	−0.612356	+	0.915766i
$951$	469.806			0.494012
$952$	514.769	−	514.769i	0.540724	−	0.540724i
$953$	713.688	+	713.688i	0.748886	+	0.748886i	0.974270	−	0.225384i	$-0.0723638\pi$
$953$	713.688	+	713.688i	0.748886	+	0.748886i	−0.225384	+	0.974270i	$0.572364\pi$
$954$			618.622i			0.648451i
$955$	995.052	−	1212.05i	1.04194	−	1.26916i
$956$	179.028			0.187267
$957$	−221.997	+	221.997i	−0.231972	+	0.231972i
$958$	−617.839	−	617.839i	−0.644926	−	0.644926i
$959$			47.5112i			0.0495424i
$960$	7.52966	+	76.5864i	0.00784340	+	0.0797775i
$961$	833.888			0.867730
$962$	−144.747	+	144.747i	−0.150465	+	0.150465i
$963$	201.390	+	201.390i	0.209128	+	0.209128i
$964$		−	350.649i		−	0.363744i
$965$	84.1941	−	8.27762i	0.0872478	−	0.00857784i
$966$	133.213			0.137901
$967$	448.530	−	448.530i	0.463836	−	0.463836i	−0.436074	−	0.899911i	$-0.643631\pi$
$967$	448.530	−	448.530i	0.463836	−	0.463836i	0.899911	+	0.436074i	$0.143631\pi$
$968$	−196.894	−	196.894i	−0.203403	−	0.203403i
$969$		−	1435.77i		−	1.48170i
$970$	−227.525	−	186.791i	−0.234562	−	0.192568i
$971$	1066.76			1.09862			0.549311	−	0.835618i	$-0.314890\pi$
$971$	1066.76			1.09862			0.549311	+	0.835618i	$0.314890\pi$
$972$	335.885	−	335.885i	0.345561	−	0.345561i
$973$	786.438	+	786.438i	0.808261	+	0.808261i
$974$		−	365.268i		−	0.375019i
$975$	327.816	−	65.0883i	0.336222	−	0.0667572i
$976$	−156.079			−0.159917
$977$	526.975	−	526.975i	0.539381	−	0.539381i	−0.383966	−	0.923347i	$-0.625442\pi$
$977$	526.975	−	526.975i	0.539381	−	0.539381i	0.923347	+	0.383966i	$0.125442\pi$
$978$	229.564	+	229.564i	0.234728	+	0.234728i
$979$			2099.32i			2.14435i
$980$	350.419	−	426.836i	0.357571	−	0.435547i
$981$	−774.544			−0.789545
$982$	−31.9547	+	31.9547i	−0.0325404	+	0.0325404i
$983$	−566.331	−	566.331i	−0.576125	−	0.576125i	0.357708	−	0.933833i	$-0.383558\pi$
$983$	−566.331	−	566.331i	−0.576125	−	0.576125i	−0.933833	+	0.357708i	$0.883558\pi$
$984$			130.370i			0.132489i
$985$	−39.9424	−	406.266i	−0.0405507	−	0.412453i
$986$	−392.761			−0.398338
$987$	−1041.30	+	1041.30i	−1.05501	+	1.05501i
$988$	290.890	+	290.890i	0.294423	+	0.294423i
$989$		−	2.84820i		−	0.00287988i
$990$	−552.364	+	54.3062i	−0.557944	+	0.0548548i
$991$	71.4593			0.0721083			0.0360541	−	0.999350i	$-0.488521\pi$
$991$	71.4593			0.0721083			0.0360541	+	0.999350i	$0.488521\pi$
$992$	−169.464	+	169.464i	−0.170831	+	0.170831i
$993$	−808.871	−	808.871i	−0.814573	−	0.814573i
$994$		−	1488.72i		−	1.49770i
$995$	1019.15	+	836.695i	1.02428	+	0.840900i
$996$	−69.1952			−0.0694731
$997$	694.965	−	694.965i	0.697056	−	0.697056i	−0.266718	−	0.963775i	$-0.585939\pi$
$997$	694.965	−	694.965i	0.697056	−	0.697056i	0.963775	+	0.266718i	$0.0859393\pi$
$998$	138.737	+	138.737i	0.139015	+	0.139015i
$999$			573.032i			0.573606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.93.4	yes	24
5.2	odd	4	inner	230.3.f.b.47.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.4	✓	24	5.2	odd	4	inner
230.3.f.b.93.4	yes	24	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +(0.691863 + 7.03714i) q^{10} -14.8137 q^{11} +(-2.72079 + 2.72079i) q^{12} +(-4.91350 - 4.91350i) q^{13} -14.4378i q^{14} +(9.57330 - 0.941208i) q^{15} -4.00000 q^{16} +(-17.8271 + 17.8271i) q^{17} +(-5.29864 - 5.29864i) q^{18} -29.6011i q^{19} +(7.72900 + 6.34528i) q^{20} -19.6412 q^{21} +(-14.8137 + 14.8137i) q^{22} +(-3.39116 - 3.39116i) q^{23} +5.44159i q^{24} +(-4.86874 - 24.5213i) q^{25} -9.82700 q^{26} +(-19.4518 + 19.4518i) q^{27} +(-14.4378 - 14.4378i) q^{28} +11.0158i q^{29} +(8.63209 - 10.5145i) q^{30} +42.3661 q^{31} +(-4.00000 + 4.00000i) q^{32} +(20.1526 + 20.1526i) q^{33} +35.6542i q^{34} +(4.99449 + 50.8005i) q^{35} -10.5973 q^{36} +(14.7295 - 14.7295i) q^{37} +(-29.6011 - 29.6011i) q^{38} +13.3686i q^{39} +(14.0743 - 1.38373i) q^{40} +23.9580 q^{41} +(-19.6412 + 19.6412i) q^{42} +(0.419945 + 0.419945i) q^{43} +29.6275i q^{44} +(20.4766 + 16.8107i) q^{45} -6.78233 q^{46} +(53.0162 - 53.0162i) q^{47} +(5.44159 + 5.44159i) q^{48} -55.2252i q^{49} +(-29.3901 - 19.6526i) q^{50} +48.5039 q^{51} +(-9.82700 + 9.82700i) q^{52} +(-58.3755 - 58.3755i) q^{53} +38.9036i q^{54} +(46.9987 - 57.2477i) q^{55} -28.8756 q^{56} +(-40.2692 + 40.2692i) q^{57} +(11.0158 + 11.0158i) q^{58} -13.7747i q^{59} +(-1.88242 - 19.1466i) q^{60} +39.0198 q^{61} +(42.3661 - 42.3661i) q^{62} +(-38.2504 - 38.2504i) q^{63} +8.00000i q^{64} +(34.5770 - 3.39947i) q^{65} +40.3051 q^{66} +(-16.9106 + 16.9106i) q^{67} +(35.6542 + 35.6542i) q^{68} +9.22666i q^{69} +(55.7949 + 45.8060i) q^{70} +103.112 q^{71} +(-10.5973 + 10.5973i) q^{72} +(41.5993 + 41.5993i) q^{73} -29.4590i q^{74} +(-26.7353 + 39.9821i) q^{75} -59.2022 q^{76} +(-106.939 + 106.939i) q^{77} +(13.3686 + 13.3686i) q^{78} +155.484i q^{79} +(12.6906 - 15.4580i) q^{80} +5.23660 q^{81} +(23.9580 - 23.9580i) q^{82} +(12.7160 + 12.7160i) q^{83} +39.2823i q^{84} +(-12.3339 - 125.452i) q^{85} +0.839889 q^{86} +(14.9859 - 14.9859i) q^{87} +(29.6275 + 29.6275i) q^{88} -141.715i q^{89} +(37.2873 - 3.66593i) q^{90} -70.9402 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-57.6347 - 57.6347i) q^{93} -106.032i q^{94} +(114.393 + 93.9135i) q^{95} +10.8832 q^{96} +(-29.4379 + 29.4379i) q^{97} +(-55.2252 - 55.2252i) q^{98} +78.4927i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more