LMFDB - Embedded newform 230.3.f.b.47.11

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			47.11
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(2.98334 - 2.98334i) q^{3} +2.00000i q^{4} +(4.43275 + 2.31317i) q^{5} +5.96668 q^{6} +(-2.75384 - 2.75384i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.80061i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(2.98334 - 2.98334i) q^{3} +2.00000i q^{4} +(4.43275 + 2.31317i) q^{5} +5.96668 q^{6} +(-2.75384 - 2.75384i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.80061i q^{9} +(2.11958 + 6.74591i) q^{10} +18.9804 q^{11} +(5.96668 + 5.96668i) q^{12} +(-10.4067 + 10.4067i) q^{13} -5.50767i q^{14} +(20.1253 - 6.32343i) q^{15} -4.00000 q^{16} +(-14.4765 - 14.4765i) q^{17} +(8.80061 - 8.80061i) q^{18} -6.41178i q^{19} +(-4.62633 + 8.86550i) q^{20} -16.4312 q^{21} +(18.9804 + 18.9804i) q^{22} +(-3.39116 + 3.39116i) q^{23} +11.9334i q^{24} +(14.2985 + 20.5074i) q^{25} -20.8133 q^{26} +(0.594854 + 0.594854i) q^{27} +(5.50767 - 5.50767i) q^{28} -47.3573i q^{29} +(26.4488 + 13.8019i) q^{30} -30.5899 q^{31} +(-4.00000 - 4.00000i) q^{32} +(56.6249 - 56.6249i) q^{33} -28.9529i q^{34} +(-5.83698 - 18.5771i) q^{35} +17.6012 q^{36} +(33.0572 + 33.0572i) q^{37} +(6.41178 - 6.41178i) q^{38} +62.0932i q^{39} +(-13.4918 + 4.23917i) q^{40} -29.3912 q^{41} +(-16.4312 - 16.4312i) q^{42} +(-48.4128 + 48.4128i) q^{43} +37.9608i q^{44} +(20.3573 - 39.0109i) q^{45} -6.78233 q^{46} +(31.5526 + 31.5526i) q^{47} +(-11.9334 + 11.9334i) q^{48} -33.8328i q^{49} +(-6.20884 + 34.8059i) q^{50} -86.3764 q^{51} +(-20.8133 - 20.8133i) q^{52} +(-67.5707 + 67.5707i) q^{53} +1.18971i q^{54} +(84.1353 + 43.9048i) q^{55} +11.0153 q^{56} +(-19.1285 - 19.1285i) q^{57} +(47.3573 - 47.3573i) q^{58} -14.7890i q^{59} +(12.6469 + 40.2507i) q^{60} -69.1934 q^{61} +(-30.5899 - 30.5899i) q^{62} +(-24.2354 + 24.2354i) q^{63} -8.00000i q^{64} +(-70.2025 + 22.0578i) q^{65} +113.250 q^{66} +(-64.7703 - 64.7703i) q^{67} +(28.9529 - 28.9529i) q^{68} +20.2340i q^{69} +(12.7402 - 24.4141i) q^{70} +48.8198 q^{71} +(17.6012 + 17.6012i) q^{72} +(41.0637 - 41.0637i) q^{73} +66.1143i q^{74} +(103.838 + 18.5231i) q^{75} +12.8236 q^{76} +(-52.2689 - 52.2689i) q^{77} +(-62.0932 + 62.0932i) q^{78} -25.2498i q^{79} +(-17.7310 - 9.25266i) q^{80} +82.7548 q^{81} +(-29.3912 - 29.3912i) q^{82} +(3.17366 - 3.17366i) q^{83} -32.8625i q^{84} +(-30.6841 - 97.6571i) q^{85} -96.8256 q^{86} +(-141.283 - 141.283i) q^{87} +(-37.9608 + 37.9608i) q^{88} -10.7109i q^{89} +(59.3682 - 18.6536i) q^{90} +57.3165 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-91.2601 + 91.2601i) q^{93} +63.1053i q^{94} +(14.8315 - 28.4218i) q^{95} -23.8667 q^{96} +(9.11145 + 9.11145i) q^{97} +(33.8328 - 33.8328i) q^{98} -167.039i 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

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

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
$3$	2.98334	−	2.98334i	0.994446	−	0.994446i	−0.00553876	−	0.999985i	$-0.501763\pi$
$3$	2.98334	−	2.98334i	0.994446	−	0.994446i	0.999985	+	0.00553876i	$0.00176305\pi$
$4$			2.00000i			0.500000i
$5$	4.43275	+	2.31317i	0.886550	+	0.462633i
$5$	4.43275	+	2.31317i	0.886550	+	0.462633i
$6$	5.96668			0.994446
$7$	−2.75384	−	2.75384i	−0.393405	−	0.393405i	0.482494	−	0.875899i	$-0.339731\pi$
$7$	−2.75384	−	2.75384i	−0.393405	−	0.393405i	−0.875899	+	0.482494i	$0.839731\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	8.80061i		−	0.977845i
$10$	2.11958	+	6.74591i	0.211958	+	0.674591i
$11$	18.9804			1.72549			0.862745	−	0.505639i	$-0.168743\pi$
$11$	18.9804			1.72549			0.862745	+	0.505639i	$0.168743\pi$
$12$	5.96668	+	5.96668i	0.497223	+	0.497223i
$13$	−10.4067	+	10.4067i	−0.800512	+	0.800512i	−0.983176	−	0.182663i	$-0.941528\pi$
$13$	−10.4067	+	10.4067i	−0.800512	+	0.800512i	0.182663	+	0.983176i	$0.441528\pi$
$14$		−	5.50767i		−	0.393405i
$15$	20.1253	−	6.32343i	1.34169	−	0.421562i
$16$	−4.00000			−0.250000
$17$	−14.4765	−	14.4765i	−0.851557	−	0.851557i	0.138768	−	0.990325i	$-0.455686\pi$
$17$	−14.4765	−	14.4765i	−0.851557	−	0.851557i	−0.990325	+	0.138768i	$0.955686\pi$
$18$	8.80061	−	8.80061i	0.488923	−	0.488923i
$19$		−	6.41178i		−	0.337462i	−0.985662	−	0.168731i	$-0.946033\pi$
$19$		−	6.41178i		−	0.337462i	0.985662	−	0.168731i	$-0.0539669\pi$
$20$	−4.62633	+	8.86550i	−0.231317	+	0.443275i
$21$	−16.4312			−0.782440
$22$	18.9804	+	18.9804i	0.862745	+	0.862745i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			11.9334i			0.497223i
$25$	14.2985	+	20.5074i	0.571941	+	0.820295i
$26$	−20.8133			−0.800512
$27$	0.594854	+	0.594854i	0.0220316	+	0.0220316i
$28$	5.50767	−	5.50767i	0.196703	−	0.196703i
$29$		−	47.3573i		−	1.63301i	−0.577339	−	0.816505i	$-0.695909\pi$
$29$		−	47.3573i		−	1.63301i	0.577339	−	0.816505i	$-0.304091\pi$
$30$	26.4488	+	13.8019i	0.881626	+	0.460064i
$31$	−30.5899			−0.986772			−0.493386	−	0.869811i	$-0.664241\pi$
$31$	−30.5899			−0.986772			−0.493386	+	0.869811i	$0.664241\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	56.6249	−	56.6249i	1.71591	−	1.71591i
$34$		−	28.9529i		−	0.851557i
$35$	−5.83698	−	18.5771i	−0.166771	−	0.530775i
$36$	17.6012			0.488923
$37$	33.0572	+	33.0572i	0.893437	+	0.893437i	0.994845	−	0.101408i	$-0.0323347\pi$
$37$	33.0572	+	33.0572i	0.893437	+	0.893437i	−0.101408	+	0.994845i	$0.532335\pi$
$38$	6.41178	−	6.41178i	0.168731	−	0.168731i
$39$			62.0932i			1.59213i
$40$	−13.4918	+	4.23917i	−0.337296	+	0.105979i
$41$	−29.3912			−0.716859			−0.358430	−	0.933557i	$-0.616688\pi$
$41$	−29.3912			−0.716859			−0.358430	+	0.933557i	$0.616688\pi$
$42$	−16.4312	−	16.4312i	−0.391220	−	0.391220i
$43$	−48.4128	+	48.4128i	−1.12588	+	1.12588i	−0.135039	+	0.990840i	$0.543116\pi$
$43$	−48.4128	+	48.4128i	−1.12588	+	1.12588i	−0.990840	+	0.135039i	$0.956884\pi$
$44$			37.9608i			0.862745i
$45$	20.3573	−	39.0109i	0.452384	−	0.866909i
$46$	−6.78233			−0.147442
$47$	31.5526	+	31.5526i	0.671333	+	0.671333i	0.958023	−	0.286691i	$-0.0925552\pi$
$47$	31.5526	+	31.5526i	0.671333	+	0.671333i	−0.286691	+	0.958023i	$0.592555\pi$
$48$	−11.9334	+	11.9334i	−0.248611	+	0.248611i
$49$		−	33.8328i		−	0.690465i
$50$	−6.20884	+	34.8059i	−0.124177	+	0.696118i
$51$	−86.3764			−1.69366
$52$	−20.8133	−	20.8133i	−0.400256	−	0.400256i
$53$	−67.5707	+	67.5707i	−1.27492	+	1.27492i	−0.331443	+	0.943475i	$0.607536\pi$
$53$	−67.5707	+	67.5707i	−1.27492	+	1.27492i	−0.943475	+	0.331443i	$0.892464\pi$
$54$			1.18971i			0.0220316i
$55$	84.1353	+	43.9048i	1.52973	+	0.798269i
$56$	11.0153			0.196703
$57$	−19.1285	−	19.1285i	−0.335588	−	0.335588i
$58$	47.3573	−	47.3573i	0.816505	−	0.816505i
$59$		−	14.7890i		−	0.250662i	−0.992115	−	0.125331i	$-0.960001\pi$
$59$		−	14.7890i		−	0.250662i	0.992115	−	0.125331i	$-0.0399993\pi$
$60$	12.6469	+	40.2507i	0.210781	+	0.670845i
$61$	−69.1934			−1.13432			−0.567159	−	0.823608i	$-0.691957\pi$
$61$	−69.1934			−1.13432			−0.567159	+	0.823608i	$0.691957\pi$
$62$	−30.5899	−	30.5899i	−0.493386	−	0.493386i
$63$	−24.2354	+	24.2354i	−0.384689	+	0.384689i
$64$		−	8.00000i		−	0.125000i
$65$	−70.2025	+	22.0578i	−1.08004	+	0.339351i
$66$	113.250			1.71591
$67$	−64.7703	−	64.7703i	−0.966721	−	0.966721i	0.0327431	−	0.999464i	$-0.489576\pi$
$67$	−64.7703	−	64.7703i	−0.966721	−	0.966721i	−0.999464	+	0.0327431i	$0.989576\pi$
$68$	28.9529	−	28.9529i	0.425779	−	0.425779i
$69$			20.2340i			0.293246i
$70$	12.7402	−	24.4141i	0.182002	−	0.348773i
$71$	48.8198			0.687602			0.343801	−	0.939042i	$-0.388285\pi$
$71$	48.8198			0.687602			0.343801	+	0.939042i	$0.388285\pi$
$72$	17.6012	+	17.6012i	0.244461	+	0.244461i
$73$	41.0637	−	41.0637i	0.562516	−	0.562516i	−0.367505	−	0.930021i	$-0.619788\pi$
$73$	41.0637	−	41.0637i	0.562516	−	0.562516i	0.930021	+	0.367505i	$0.119788\pi$
$74$			66.1143i			0.893437i
$75$	103.838	+	18.5231i	1.38450	+	0.246974i
$76$	12.8236			0.168731
$77$	−52.2689	−	52.2689i	−0.678817	−	0.678817i
$78$	−62.0932	+	62.0932i	−0.796066	+	0.796066i
$79$		−	25.2498i		−	0.319618i	−0.987148	−	0.159809i	$-0.948912\pi$
$79$		−	25.2498i		−	0.319618i	0.987148	−	0.159809i	$-0.0510878\pi$
$80$	−17.7310	−	9.25266i	−0.221637	−	0.115658i
$81$	82.7548			1.02166
$82$	−29.3912	−	29.3912i	−0.358430	−	0.358430i
$83$	3.17366	−	3.17366i	0.0382368	−	0.0382368i	−0.687730	−	0.725967i	$-0.741393\pi$
$83$	3.17366	−	3.17366i	0.0382368	−	0.0382368i	0.725967	+	0.687730i	$0.241393\pi$
$84$		−	32.8625i		−	0.391220i
$85$	−30.6841	−	97.6571i	−0.360989	−	1.14891i
$86$	−96.8256			−1.12588
$87$	−141.283	−	141.283i	−1.62394	−	1.62394i
$88$	−37.9608	+	37.9608i	−0.431373	+	0.431373i
$89$		−	10.7109i		−	0.120347i	−0.998188	−	0.0601737i	$-0.980835\pi$
$89$		−	10.7109i		−	0.120347i	0.998188	−	0.0601737i	$-0.0191655\pi$
$90$	59.3682	−	18.6536i	0.659646	−	0.207262i
$91$	57.3165			0.629851
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−91.2601	+	91.2601i	−0.981291	+	0.981291i
$94$			63.1053i			0.671333i
$95$	14.8315	−	28.4218i	0.156121	−	0.299177i
$96$	−23.8667			−0.248611
$97$	9.11145	+	9.11145i	0.0939324	+	0.0939324i	0.752512	−	0.658579i	$-0.228842\pi$
$97$	9.11145	+	9.11145i	0.0939324	+	0.0939324i	−0.658579	+	0.752512i	$0.728842\pi$
$98$	33.8328	−	33.8328i	0.345232	−	0.345232i
$99$		−	167.039i		−	1.68726i
$100$	−41.0147	+	28.5971i	−0.410147	+	0.285971i
$101$	−76.1517			−0.753977			−0.376989	−	0.926218i	$-0.623040\pi$
$101$	−76.1517			−0.753977			−0.376989	+	0.926218i	$0.623040\pi$
$102$	−86.3764	−	86.3764i	−0.846828	−	0.846828i
$103$	−127.185	+	127.185i	−1.23481	+	1.23481i	−0.272709	+	0.962097i	$0.587919\pi$
$103$	−127.185	+	127.185i	−1.23481	+	1.23481i	−0.962097	+	0.272709i	$0.912081\pi$
$104$		−	41.6266i		−	0.400256i
$105$	−72.8356	−	38.0082i	−0.693672	−	0.361983i
$106$	−135.141			−1.27492
$107$	40.2038	+	40.2038i	0.375736	+	0.375736i	0.869561	−	0.493825i	$-0.164402\pi$
$107$	40.2038	+	40.2038i	0.375736	+	0.375736i	−0.493825	+	0.869561i	$0.664402\pi$
$108$	−1.18971	+	1.18971i	−0.0110158	+	0.0110158i
$109$		−	66.3610i		−	0.608816i	−0.952542	−	0.304408i	$-0.901541\pi$
$109$		−	66.3610i		−	0.608816i	0.952542	−	0.304408i	$-0.0984586\pi$
$110$	40.2305	+	128.040i	0.365732	+	1.16400i
$111$	197.241			1.77695
$112$	11.0153	+	11.0153i	0.0983513	+	0.0983513i
$113$	82.3748	−	82.3748i	0.728981	−	0.728981i	−0.241436	−	0.970417i	$-0.577618\pi$
$113$	82.3748	−	82.3748i	0.728981	−	0.728981i	0.970417	+	0.241436i	$0.0776184\pi$
$114$		−	38.2570i		−	0.335588i
$115$	−22.8765	+	7.18786i	−0.198926	+	0.0625031i
$116$	94.7146			0.816505
$117$	91.5849	+	91.5849i	0.782777	+	0.782777i
$118$	14.7890	−	14.7890i	0.125331	−	0.125331i
$119$			79.7317i			0.670014i
$120$	−27.6038	+	52.8975i	−0.230032	+	0.440813i
$121$	239.255			1.97732
$122$	−69.1934	−	69.1934i	−0.567159	−	0.567159i
$123$	−87.6840	+	87.6840i	−0.712878	+	0.712878i
$124$		−	61.1798i		−	0.493386i
$125$	15.9448	+	123.979i	0.127559	+	0.991831i
$126$	−48.4709			−0.384689
$127$	10.6359	+	10.6359i	0.0837475	+	0.0837475i	0.747740	−	0.663992i	$-0.231139\pi$
$127$	10.6359	+	10.6359i	0.0837475	+	0.0837475i	−0.663992	+	0.747740i	$0.731139\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			288.863i			2.23925i
$130$	−92.2602	−	48.1447i	−0.709694	−	0.370344i
$131$	44.6507			0.340845			0.170422	−	0.985371i	$-0.445487\pi$
$131$	44.6507			0.340845			0.170422	+	0.985371i	$0.445487\pi$
$132$	113.250	+	113.250i	0.857953	+	0.857953i
$133$	−17.6570	+	17.6570i	−0.132759	+	0.132759i
$134$		−	129.541i		−	0.966721i
$135$	1.26084	+	4.01284i	0.00933958	+	0.0297247i
$136$	57.9059			0.425779
$137$	83.3365	+	83.3365i	0.608296	+	0.608296i	0.942500	−	0.334205i	$-0.108468\pi$
$137$	83.3365	+	83.3365i	0.608296	+	0.608296i	−0.334205	+	0.942500i	$0.608468\pi$
$138$	−20.2340	+	20.2340i	−0.146623	+	0.146623i
$139$		−	50.7125i		−	0.364838i	−0.983221	−	0.182419i	$-0.941607\pi$
$139$		−	50.7125i		−	0.364838i	0.983221	−	0.182419i	$-0.0583927\pi$
$140$	37.1543	−	11.6740i	0.265388	−	0.0833855i
$141$	188.264			1.33521
$142$	48.8198	+	48.8198i	0.343801	+	0.343801i
$143$	−197.523	+	197.523i	−1.38128	+	1.38128i
$144$			35.2024i			0.244461i
$145$	109.545	−	209.923i	0.755484	−	1.44774i
$146$	82.1274			0.562516
$147$	−100.935	−	100.935i	−0.686630	−	0.686630i
$148$	−66.1143	+	66.1143i	−0.446718	+	0.446718i
$149$		−	99.2558i		−	0.666147i	−0.942901	−	0.333073i	$-0.891914\pi$
$149$		−	99.2558i		−	0.666147i	0.942901	−	0.333073i	$-0.108086\pi$
$150$	85.3147	+	122.361i	0.568765	+	0.815739i
$151$	233.791			1.54828			0.774141	−	0.633013i	$-0.218182\pi$
$151$	233.791			1.54828			0.774141	+	0.633013i	$0.218182\pi$
$152$	12.8236	+	12.8236i	0.0843655	+	0.0843655i
$153$	−127.402	+	127.402i	−0.832691	+	0.832691i
$154$		−	104.538i		−	0.678817i
$155$	−135.597	−	70.7595i	−0.874822	−	0.456513i
$156$	−124.186			−0.796066
$157$	4.54816	+	4.54816i	0.0289692	+	0.0289692i	0.721443	−	0.692474i	$-0.243479\pi$
$157$	4.54816	+	4.54816i	0.0289692	+	0.0289692i	−0.692474	+	0.721443i	$0.743479\pi$
$158$	25.2498	−	25.2498i	0.159809	−	0.159809i
$159$			403.172i			2.53568i
$160$	−8.47833	−	26.9837i	−0.0529896	−	0.168648i
$161$	18.6774			0.116009
$162$	82.7548	+	82.7548i	0.510832	+	0.510832i
$163$	64.1590	−	64.1590i	0.393613	−	0.393613i	−0.482360	−	0.875973i	$-0.660220\pi$
$163$	64.1590	−	64.1590i	0.393613	−	0.393613i	0.875973	+	0.482360i	$0.160220\pi$
$164$		−	58.7825i		−	0.358430i
$165$	381.987	−	120.021i	2.31507	−	0.727401i
$166$	6.34732			0.0382368
$167$	62.0741	+	62.0741i	0.371701	+	0.371701i	0.868097	−	0.496395i	$-0.165343\pi$
$167$	62.0741	+	62.0741i	0.371701	+	0.371701i	−0.496395	+	0.868097i	$0.665343\pi$
$168$	32.8625	−	32.8625i	0.195610	−	0.195610i
$169$		−	47.5972i		−	0.281640i
$170$	66.9730	−	128.341i	0.393959	−	0.754948i
$171$	−56.4275			−0.329986
$172$	−96.8256	−	96.8256i	−0.562940	−	0.562940i
$173$	69.2914	−	69.2914i	0.400528	−	0.400528i	−0.477891	−	0.878419i	$-0.658599\pi$
$173$	69.2914	−	69.2914i	0.400528	−	0.400528i	0.878419	+	0.477891i	$0.158599\pi$
$174$		−	282.566i		−	1.62394i
$175$	17.0981	−	95.8497i	0.0977035	−	0.547713i
$176$	−75.9216			−0.431373
$177$	−44.1207	−	44.1207i	−0.249270	−	0.249270i
$178$	10.7109	−	10.7109i	0.0601737	−	0.0601737i
$179$		−	0.945202i		−	0.00528046i	−0.999997	−	0.00264023i	$-0.999160\pi$
$179$		−	0.945202i		−	0.00528046i	0.999997	−	0.00264023i	$-0.000840412\pi$
$180$	78.0218	+	40.7145i	0.433454	+	0.226192i
$181$	225.068			1.24347			0.621734	−	0.783228i	$-0.286428\pi$
$181$	225.068			1.24347			0.621734	+	0.783228i	$0.286428\pi$
$182$	57.3165	+	57.3165i	0.314926	+	0.314926i
$183$	−206.427	+	206.427i	−1.12802	+	1.12802i
$184$		−	13.5647i		−	0.0737210i
$185$	70.0674	+	223.001i	0.378743	+	1.20541i
$186$	−182.520			−0.981291
$187$	−274.769	−	274.769i	−1.46935	−	1.46935i
$188$	−63.1053	+	63.1053i	−0.335666	+	0.335666i
$189$		−	3.27626i		−	0.0173347i
$190$	43.2533	−	13.5903i	0.227649	−	0.0715279i
$191$	−81.3359			−0.425842			−0.212921	−	0.977069i	$-0.568298\pi$
$191$	−81.3359			−0.425842			−0.212921	+	0.977069i	$0.568298\pi$
$192$	−23.8667	−	23.8667i	−0.124306	−	0.124306i
$193$	258.788	−	258.788i	1.34087	−	1.34087i	0.445673	−	0.895196i	$-0.352964\pi$
$193$	258.788	−	258.788i	1.34087	−	1.34087i	0.895196	−	0.445673i	$-0.147036\pi$
$194$			18.2229i			0.0939324i
$195$	−143.632	+	275.243i	−0.736573	+	1.41150i
$196$	67.6656			0.345232
$197$	141.860	+	141.860i	0.720102	+	0.720102i	0.968626	−	0.248524i	$-0.0799454\pi$
$197$	141.860	+	141.860i	0.720102	+	0.720102i	−0.248524	+	0.968626i	$0.579945\pi$
$198$	167.039	−	167.039i	0.843631	−	0.843631i
$199$		−	130.445i		−	0.655501i	−0.944764	−	0.327751i	$-0.893709\pi$
$199$		−	130.445i		−	0.655501i	0.944764	−	0.327751i	$-0.106291\pi$
$200$	−69.6118	−	12.4177i	−0.348059	−	0.0620884i
$201$	−386.463			−1.92270
$202$	−76.1517	−	76.1517i	−0.376989	−	0.376989i
$203$	−130.414	+	130.414i	−0.642434	+	0.642434i
$204$		−	172.753i		−	0.846828i
$205$	−130.284	−	67.9868i	−0.635531	−	0.331643i
$206$	−254.370			−1.23481
$207$	29.8443	+	29.8443i	0.144175	+	0.144175i
$208$	41.6266	−	41.6266i	0.200128	−	0.200128i
$209$		−	121.698i		−	0.582287i
$210$	−34.8274	−	110.844i	−0.165845	−	0.527827i
$211$	309.896			1.46870			0.734351	−	0.678769i	$-0.237486\pi$
$211$	309.896			1.46870			0.734351	+	0.678769i	$0.237486\pi$
$212$	−135.141	−	135.141i	−0.637459	−	0.637459i
$213$	145.646	−	145.646i	0.683783	−	0.683783i
$214$			80.4076i			0.375736i
$215$	−326.589	+	102.615i	−1.51902	+	0.477279i
$216$	−2.37942			−0.0110158
$217$	84.2396	+	84.2396i	0.388201	+	0.388201i
$218$	66.3610	−	66.3610i	0.304408	−	0.304408i
$219$		−	245.014i		−	1.11878i
$220$	−87.8096	+	168.271i	−0.399135	+	0.764867i
$221$	301.304			1.36336
$222$	197.241	+	197.241i	0.888475	+	0.888475i
$223$	12.4564	−	12.4564i	0.0558584	−	0.0558584i	−0.678626	−	0.734484i	$-0.737424\pi$
$223$	12.4564	−	12.4564i	0.0558584	−	0.0558584i	0.734484	+	0.678626i	$0.237424\pi$
$224$			22.0307i			0.0983513i
$225$	180.477	−	125.836i	0.802121	−	0.559270i
$226$	164.750			0.728981
$227$	288.913	+	288.913i	1.27274	+	1.27274i	0.944643	+	0.328100i	$0.106408\pi$
$227$	288.913	+	288.913i	1.27274	+	1.27274i	0.328100	+	0.944643i	$0.393592\pi$
$228$	38.2570	−	38.2570i	0.167794	−	0.167794i
$229$		−	67.7128i		−	0.295689i	−0.989011	−	0.147845i	$-0.952766\pi$
$229$		−	67.7128i		−	0.295689i	0.989011	−	0.147845i	$-0.0472335\pi$
$230$	−30.0644	−	15.6887i	−0.130715	−	0.0682115i
$231$	−311.871			−1.35009
$232$	94.7146	+	94.7146i	0.408252	+	0.408252i
$233$	11.5652	−	11.5652i	0.0496362	−	0.0496362i	−0.681853	−	0.731489i	$-0.738826\pi$
$233$	11.5652	−	11.5652i	0.0496362	−	0.0496362i	0.731489	+	0.681853i	$0.238826\pi$
$234$			183.170i			0.782777i
$235$	66.8784	+	212.851i	0.284589	+	0.905751i
$236$	29.5781			0.125331
$237$	−75.3287	−	75.3287i	−0.317843	−	0.317843i
$238$	−79.7317	+	79.7317i	−0.335007	+	0.335007i
$239$			94.9543i			0.397298i	0.980071	+	0.198649i	$0.0636554\pi$
$239$			94.9543i			0.397298i	−0.980071	+	0.198649i	$0.936345\pi$
$240$	−80.5014	+	25.2937i	−0.335422	+	0.105391i
$241$	−20.8747			−0.0866171			−0.0433086	−	0.999062i	$-0.513790\pi$
$241$	−20.8747			−0.0866171			−0.0433086	+	0.999062i	$0.513790\pi$
$242$	239.255	+	239.255i	0.988658	+	0.988658i
$243$	241.532	−	241.532i	0.993958	−	0.993958i
$244$		−	138.387i		−	0.567159i
$245$	78.2608	−	149.972i	0.319432	−	0.612132i
$246$	−175.368			−0.712878
$247$	66.7252	+	66.7252i	0.270142	+	0.270142i
$248$	61.1798	−	61.1798i	0.246693	−	0.246693i
$249$		−	18.9362i		−	0.0760489i
$250$	−108.034	+	139.924i	−0.432136	+	0.559695i
$251$	−227.711			−0.907217			−0.453608	−	0.891201i	$-0.649863\pi$
$251$	−227.711			−0.907217			−0.453608	+	0.891201i	$0.649863\pi$
$252$	−48.4709	−	48.4709i	−0.192345	−	0.192345i
$253$	−64.3656	+	64.3656i	−0.254410	+	0.254410i
$254$			21.2719i			0.0837475i
$255$	−382.885	−	199.803i	−1.50151	−	0.783541i
$256$	16.0000			0.0625000
$257$	−218.548	−	218.548i	−0.850380	−	0.850380i	0.139800	−	0.990180i	$-0.455354\pi$
$257$	−218.548	−	218.548i	−0.850380	−	0.850380i	−0.990180	+	0.139800i	$0.955354\pi$
$258$	−288.863	+	288.863i	−1.11963	+	1.11963i
$259$		−	182.068i		−	0.702965i
$260$	−44.1156	−	140.405i	−0.169675	−	0.540019i
$261$	−416.773			−1.59683
$262$	44.6507	+	44.6507i	0.170422	+	0.170422i
$263$	51.6126	−	51.6126i	0.196246	−	0.196246i	−0.602143	−	0.798388i	$-0.705686\pi$
$263$	51.6126	−	51.6126i	0.196246	−	0.196246i	0.798388	+	0.602143i	$0.205686\pi$
$264$			226.500i			0.857953i
$265$	−455.826	+	143.222i	−1.72010	+	0.540459i
$266$	−35.3139			−0.132759
$267$	−31.9543	−	31.9543i	−0.119679	−	0.119679i
$268$	129.541	−	129.541i	0.483360	−	0.483360i
$269$			296.367i			1.10174i	0.834592	+	0.550869i	$0.185704\pi$
$269$			296.367i			1.10174i	−0.834592	+	0.550869i	$0.814296\pi$
$270$	−2.75199	+	5.27368i	−0.0101926	+	0.0195321i
$271$	22.4446			0.0828216			0.0414108	−	0.999142i	$-0.486815\pi$
$271$	22.4446			0.0828216			0.0414108	+	0.999142i	$0.486815\pi$
$272$	57.9059	+	57.9059i	0.212889	+	0.212889i
$273$	170.994	−	170.994i	0.626353	−	0.626353i
$274$			166.673i			0.608296i
$275$	271.392	+	389.238i	0.986879	+	1.41541i
$276$	−40.4680			−0.146623
$277$	−247.968	−	247.968i	−0.895191	−	0.895191i	0.0998150	−	0.995006i	$-0.468175\pi$
$277$	−247.968	−	247.968i	−0.895191	−	0.895191i	−0.995006	+	0.0998150i	$0.968175\pi$
$278$	50.7125	−	50.7125i	0.182419	−	0.182419i
$279$			269.210i			0.964910i
$280$	48.8282	+	25.4803i	0.174387	+	0.0910011i
$281$	−171.969			−0.611989			−0.305995	−	0.952033i	$-0.598989\pi$
$281$	−171.969			−0.611989			−0.305995	+	0.952033i	$0.598989\pi$
$282$	188.264	+	188.264i	0.667604	+	0.667604i
$283$	−221.860	+	221.860i	−0.783957	+	0.783957i	−0.980496	−	0.196539i	$-0.937030\pi$
$283$	−221.860	+	221.860i	−0.783957	+	0.783957i	0.196539	+	0.980496i	$0.437030\pi$
$284$			97.6395i			0.343801i
$285$	−40.5444	−	129.039i	−0.142261	−	0.452769i
$286$	−395.045			−1.38128
$287$	80.9386	+	80.9386i	0.282016	+	0.282016i
$288$	−35.2024	+	35.2024i	−0.122231	+	0.122231i
$289$			130.137i			0.450300i
$290$	319.468	−	100.378i	1.10161	−	0.346130i
$291$	54.3650			0.186821
$292$	82.1274	+	82.1274i	0.281258	+	0.281258i
$293$	296.237	−	296.237i	1.01105	−	1.01105i	0.0111087	−	0.999938i	$-0.496464\pi$
$293$	296.237	−	296.237i	1.01105	−	1.01105i	0.999938	−	0.0111087i	$-0.00353607\pi$
$294$		−	201.869i		−	0.686630i
$295$	34.2095	−	65.5561i	0.115964	−	0.222224i
$296$	−132.229			−0.446718
$297$	11.2906	+	11.2906i	0.0380154	+	0.0380154i
$298$	99.2558	−	99.2558i	0.333073	−	0.333073i
$299$		−	70.5814i		−	0.236058i
$300$	−37.0461	+	207.675i	−0.123487	+	0.692252i
$301$	266.642			0.885853
$302$	233.791	+	233.791i	0.774141	+	0.774141i
$303$	−227.186	+	227.186i	−0.749790	+	0.749790i
$304$			25.6471i			0.0843655i
$305$	−306.717	−	160.056i	−1.00563	−	0.524773i
$306$	−254.804			−0.832691
$307$	−190.590	−	190.590i	−0.620816	−	0.620816i	0.324924	−	0.945740i	$-0.394661\pi$
$307$	−190.590	−	190.590i	−0.620816	−	0.620816i	−0.945740	+	0.324924i	$0.894661\pi$
$308$	104.538	−	104.538i	0.339408	−	0.339408i
$309$			758.871i			2.45589i
$310$	−64.8379	−	206.357i	−0.209154	−	0.665668i
$311$	−89.9132			−0.289110			−0.144555	−	0.989497i	$-0.546175\pi$
$311$	−89.9132			−0.289110			−0.144555	+	0.989497i	$0.546175\pi$
$312$	−124.186	−	124.186i	−0.398033	−	0.398033i
$313$	194.964	−	194.964i	0.622890	−	0.622890i	−0.323380	−	0.946269i	$-0.604819\pi$
$313$	194.964	−	194.964i	0.622890	−	0.622890i	0.946269	+	0.323380i	$0.104819\pi$
$314$			9.09633i			0.0289692i
$315$	−163.490	+	51.3690i	−0.519016	+	0.163076i
$316$	50.4996			0.159809
$317$	−136.607	−	136.607i	−0.430937	−	0.430937i	0.458010	−	0.888947i	$-0.348562\pi$
$317$	−136.607	−	136.607i	−0.430937	−	0.430937i	−0.888947	+	0.458010i	$0.848562\pi$
$318$	−403.172	+	403.172i	−1.26784	+	1.26784i
$319$		−	898.860i		−	2.81774i
$320$	18.5053	−	35.4620i	0.0578291	−	0.110819i
$321$	239.883			0.747299
$322$	18.6774	+	18.6774i	0.0580044	+	0.0580044i
$323$	−92.8199	+	92.8199i	−0.287368	+	0.287368i
$324$			165.510i			0.510832i
$325$	−362.213	−	64.6133i	−1.11450	−	0.198810i
$326$	128.318			0.393613
$327$	−197.977	−	197.977i	−0.605435	−	0.605435i
$328$	58.7825	−	58.7825i	0.179215	−	0.179215i
$329$		−	173.782i		−	0.528211i
$330$	502.008	+	261.966i	1.52124	+	0.793835i
$331$	−258.496			−0.780955			−0.390477	−	0.920613i	$-0.627690\pi$
$331$	−258.496			−0.780955			−0.390477	+	0.920613i	$0.627690\pi$
$332$	6.34732	+	6.34732i	0.0191184	+	0.0191184i
$333$	290.923	−	290.923i	0.873643	−	0.873643i
$334$			124.148i			0.371701i
$335$	−137.286	−	436.935i	−0.409809	−	1.30428i
$336$	65.7250			0.195610
$337$	−342.054	−	342.054i	−1.01500	−	1.01500i	−0.999886	−	0.0151116i	$-0.995190\pi$
$337$	−342.054	−	342.054i	−1.01500	−	1.01500i	−0.0151116	−	0.999886i	$-0.504810\pi$
$338$	47.5972	−	47.5972i	0.140820	−	0.140820i
$339$		−	491.504i		−	1.44986i
$340$	195.314	−	61.3682i	0.574453	−	0.180495i
$341$	−580.609			−1.70266
$342$	−56.4275	−	56.4275i	−0.164993	−	0.164993i
$343$	−228.108	+	228.108i	−0.665037	+	0.665037i
$344$		−	193.651i		−	0.562940i
$345$	−46.8046	+	89.6922i	−0.135665	+	0.259977i
$346$	138.583			0.400528
$347$	−407.068	−	407.068i	−1.17311	−	1.17311i	−0.981465	−	0.191640i	$-0.938619\pi$
$347$	−407.068	−	407.068i	−1.17311	−	1.17311i	−0.191640	−	0.981465i	$-0.561381\pi$
$348$	282.566	−	282.566i	0.811970	−	0.811970i
$349$			533.516i			1.52870i	0.644803	+	0.764349i	$0.276940\pi$
$349$			533.516i			1.52870i	−0.644803	+	0.764349i	$0.723060\pi$
$350$	112.948	−	78.7516i	0.322708	−	0.225005i
$351$	−12.3809			−0.0352732
$352$	−75.9216	−	75.9216i	−0.215686	−	0.215686i
$353$	−257.393	+	257.393i	−0.729159	+	0.729159i	−0.970452	−	0.241293i	$-0.922429\pi$
$353$	−257.393	+	257.393i	−0.729159	+	0.729159i	0.241293	+	0.970452i	$0.422429\pi$
$354$		−	88.2415i		−	0.249270i
$355$	216.406	+	112.928i	0.609594	+	0.318108i
$356$	21.4219			0.0601737
$357$	237.866	+	237.866i	0.666293	+	0.666293i
$358$	0.945202	−	0.945202i	0.00264023	−	0.00264023i
$359$		−	195.229i		−	0.543813i	−0.962324	−	0.271906i	$-0.912346\pi$
$359$		−	195.229i		−	0.543813i	0.962324	−	0.271906i	$-0.0876541\pi$
$360$	37.3072	+	118.736i	0.103631	+	0.329823i
$361$	319.889			0.886119
$362$	225.068	+	225.068i	0.621734	+	0.621734i
$363$	713.779	−	713.779i	1.96633	−	1.96633i
$364$			114.633i			0.314926i
$365$	277.012	−	87.0379i	0.758937	−	0.238460i
$366$	−412.854			−1.12802
$367$	416.486	+	416.486i	1.13484	+	1.13484i	0.989362	+	0.145477i	$0.0464716\pi$
$367$	416.486	+	416.486i	1.13484	+	1.13484i	0.145477	+	0.989362i	$0.453528\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			258.661i			0.700977i
$370$	−152.933	+	293.068i	−0.413334	+	0.792076i
$371$	372.157			1.00312
$372$	−182.520	−	182.520i	−0.490645	−	0.490645i
$373$	−217.599	+	217.599i	−0.583375	+	0.583375i	−0.935829	−	0.352454i	$-0.885347\pi$
$373$	−217.599	+	217.599i	−0.583375	+	0.583375i	0.352454	+	0.935829i	$0.385347\pi$
$374$		−	549.538i		−	1.46935i
$375$	417.440	+	322.302i	1.11317	+	0.859472i
$376$	−126.211			−0.335666
$377$	492.831	+	492.831i	1.30724	+	1.30724i
$378$	3.27626	−	3.27626i	0.00866736	−	0.00866736i
$379$			118.665i			0.313102i	0.987670	+	0.156551i	$0.0500375\pi$
$379$			118.665i			0.313102i	−0.987670	+	0.156551i	$0.949963\pi$
$380$	56.8436	+	29.6630i	0.149588	+	0.0780605i
$381$	63.4611			0.166565
$382$	−81.3359	−	81.3359i	−0.212921	−	0.212921i
$383$	−297.633	+	297.633i	−0.777109	+	0.777109i	−0.979338	−	0.202229i	$-0.935182\pi$
$383$	−297.633	+	297.633i	−0.777109	+	0.777109i	0.202229	+	0.979338i	$0.435182\pi$
$384$		−	47.7334i		−	0.124306i
$385$	−110.788	−	352.601i	−0.287762	−	0.915848i
$386$	517.575			1.34087
$387$	426.062	+	426.062i	1.10094	+	1.10094i
$388$	−18.2229	+	18.2229i	−0.0469662	+	0.0469662i
$389$			706.167i			1.81534i	0.419684	+	0.907670i	$0.362141\pi$
$389$			706.167i			1.81534i	−0.419684	+	0.907670i	$0.637859\pi$
$390$	−418.875	+	131.612i	−1.07404	+	0.337466i
$391$	98.1842			0.251111
$392$	67.6656	+	67.6656i	0.172616	+	0.172616i
$393$	133.208	−	133.208i	0.338952	−	0.338952i
$394$			283.720i			0.720102i
$395$	58.4070	−	111.926i	0.147866	−	0.283357i
$396$	334.078			0.843631
$397$	−283.294	−	283.294i	−0.713588	−	0.713588i	0.253696	−	0.967284i	$-0.418354\pi$
$397$	−283.294	−	283.294i	−0.713588	−	0.713588i	−0.967284	+	0.253696i	$0.918354\pi$
$398$	130.445	−	130.445i	0.327751	−	0.327751i
$399$			105.353i			0.264044i
$400$	−57.1941	−	82.0295i	−0.142985	−	0.205074i
$401$	−453.040			−1.12977			−0.564887	−	0.825168i	$-0.691080\pi$
$401$	−453.040			−1.12977			−0.564887	+	0.825168i	$0.691080\pi$
$402$	−386.463	−	386.463i	−0.961351	−	0.961351i
$403$	318.339	−	318.339i	0.789923	−	0.789923i
$404$		−	152.303i		−	0.376989i
$405$	366.831	+	191.426i	0.905756	+	0.472656i
$406$	−260.828			−0.642434
$407$	627.438	+	627.438i	1.54162	+	1.54162i
$408$	172.753	−	172.753i	0.423414	−	0.423414i
$409$		−	368.025i		−	0.899816i	−0.893075	−	0.449908i	$-0.851457\pi$
$409$		−	368.025i		−	0.899816i	0.893075	−	0.449908i	$-0.148543\pi$
$410$	−62.2972	−	198.271i	−0.151944	−	0.483587i
$411$	497.242			1.20983
$412$	−254.370	−	254.370i	−0.617403	−	0.617403i
$413$	−40.7266	+	40.7266i	−0.0986116	+	0.0986116i
$414$			59.6886i			0.144175i
$415$	21.4092	−	6.72683i	0.0515885	−	0.0162092i
$416$	83.2533			0.200128
$417$	−151.292	−	151.292i	−0.362812	−	0.362812i
$418$	121.698	−	121.698i	0.291144	−	0.291144i
$419$			630.197i			1.50405i	0.659134	+	0.752026i	$0.270923\pi$
$419$			630.197i			1.50405i	−0.659134	+	0.752026i	$0.729077\pi$
$420$	76.0164	−	145.671i	0.180991	−	0.346836i
$421$	689.372			1.63746			0.818732	−	0.574176i	$-0.194677\pi$
$421$	689.372			1.63746			0.818732	+	0.574176i	$0.194677\pi$
$422$	309.896	+	309.896i	0.734351	+	0.734351i
$423$	277.682	−	277.682i	0.656459	−	0.656459i
$424$		−	270.283i		−	0.637459i
$425$	89.8821	−	503.867i	0.211487	−	1.18557i
$426$	291.292			0.683783
$427$	190.547	+	190.547i	0.446246	+	0.446246i
$428$	−80.4076	+	80.4076i	−0.187868	+	0.187868i
$429$			1178.55i			2.74721i
$430$	−429.204	−	223.974i	−0.998148	−	0.520869i
$431$	599.060			1.38993			0.694966	−	0.719043i	$-0.255420\pi$
$431$	599.060			1.38993			0.694966	+	0.719043i	$0.255420\pi$
$432$	−2.37942	−	2.37942i	−0.00550791	−	0.00550791i
$433$	345.916	−	345.916i	0.798883	−	0.798883i	−0.184037	−	0.982919i	$-0.558916\pi$
$433$	345.916	−	345.916i	0.798883	−	0.798883i	0.982919	+	0.184037i	$0.0589165\pi$
$434$			168.479i			0.388201i
$435$	−299.461	−	953.082i	−0.688415	−	2.19099i
$436$	132.722			0.304408
$437$	21.7434	+	21.7434i	0.0497560	+	0.0497560i
$438$	245.014	−	245.014i	0.559392	−	0.559392i
$439$			733.085i			1.66990i	0.550328	+	0.834949i	$0.314503\pi$
$439$			733.085i			1.66990i	−0.550328	+	0.834949i	$0.685497\pi$
$440$	−256.080	+	80.4610i	−0.582001	+	0.182866i
$441$	−297.749			−0.675168
$442$	301.304	+	301.304i	0.681682	+	0.681682i
$443$	−299.493	+	299.493i	−0.676057	+	0.676057i	−0.959106	−	0.283049i	$-0.908654\pi$
$443$	−299.493	+	299.493i	−0.676057	+	0.676057i	0.283049	+	0.959106i	$0.408654\pi$
$444$			394.483i			0.888475i
$445$	24.7761	−	47.4788i	0.0556767	−	0.106694i
$446$	24.9128			0.0558584
$447$	−296.114	−	296.114i	−0.662447	−	0.662447i
$448$	−22.0307	+	22.0307i	−0.0491756	+	0.0491756i
$449$		−	53.7628i		−	0.119739i	−0.998206	−	0.0598694i	$-0.980932\pi$
$449$		−	53.7628i		−	0.119739i	0.998206	−	0.0598694i	$-0.0190684\pi$
$450$	306.313	+	54.6416i	0.680696	+	0.121426i
$451$	−557.857			−1.23693
$452$	164.750	+	164.750i	0.364490	+	0.364490i
$453$	697.476	−	697.476i	1.53968	−	1.53968i
$454$			577.825i			1.27274i
$455$	254.070	+	132.582i	0.558395	+	0.291390i
$456$	76.5140			0.167794
$457$	−637.061	−	637.061i	−1.39401	−	1.39401i	−0.816110	−	0.577897i	$-0.803874\pi$
$457$	−637.061	−	637.061i	−1.39401	−	1.39401i	−0.577897	−	0.816110i	$-0.696126\pi$
$458$	67.7128	−	67.7128i	0.147845	−	0.147845i
$459$		−	17.2228i		−	0.0375224i
$460$	−14.3757	−	45.7530i	−0.0312516	−	0.0994631i
$461$	−508.755			−1.10359			−0.551795	−	0.833980i	$-0.686057\pi$
$461$	−508.755			−1.10359			−0.551795	+	0.833980i	$0.686057\pi$
$462$	−311.871	−	311.871i	−0.675046	−	0.675046i
$463$	617.632	−	617.632i	1.33398	−	1.33398i	0.432200	−	0.901778i	$-0.357737\pi$
$463$	617.632	−	617.632i	1.33398	−	1.33398i	0.901778	−	0.432200i	$-0.142263\pi$
$464$			189.429i			0.408252i
$465$	−615.633	+	193.433i	−1.32394	+	0.415986i
$466$	23.1305			0.0496362
$467$	−331.293	−	331.293i	−0.709407	−	0.709407i	0.257004	−	0.966410i	$-0.417265\pi$
$467$	−331.293	−	331.293i	−0.709407	−	0.709407i	−0.966410	+	0.257004i	$0.917265\pi$
$468$	−183.170	+	183.170i	−0.391389	+	0.391389i
$469$			356.733i			0.760626i
$470$	−145.973	+	279.730i	−0.310581	+	0.595170i
$471$	27.1374			0.0576166
$472$	29.5781	+	29.5781i	0.0626655	+	0.0626655i
$473$	−918.894	+	918.894i	−1.94269	+	1.94269i
$474$		−	150.657i		−	0.317843i
$475$	131.489	−	91.6790i	0.276818	−	0.193008i
$476$	−159.463			−0.335007
$477$	594.663	+	594.663i	1.24667	+	1.24667i
$478$	−94.9543	+	94.9543i	−0.198649	+	0.198649i
$479$		−	86.5041i		−	0.180593i	−0.995915	−	0.0902965i	$-0.971219\pi$
$479$		−	86.5041i		−	0.180593i	0.995915	−	0.0902965i	$-0.0287815\pi$
$480$	−105.795	−	55.2076i	−0.220406	−	0.115016i
$481$	−688.030			−1.43041
$482$	−20.8747	−	20.8747i	−0.0433086	−	0.0433086i
$483$	55.7211	−	55.7211i	0.115365	−	0.115365i
$484$			478.511i			0.988658i
$485$	19.3125	+	61.4650i	0.0398195	+	0.126732i
$486$	483.063			0.993958
$487$	184.538	+	184.538i	0.378929	+	0.378929i	0.870716	−	0.491787i	$-0.163656\pi$
$487$	184.538	+	184.538i	0.378929	+	0.378929i	−0.491787	+	0.870716i	$0.663656\pi$
$488$	138.387	−	138.387i	0.283579	−	0.283579i
$489$		−	382.816i		−	0.782854i
$490$	228.233	−	71.7114i	0.465782	−	0.146350i
$491$	654.719			1.33344			0.666720	−	0.745308i	$-0.267698\pi$
$491$	654.719			1.33344			0.666720	+	0.745308i	$0.267698\pi$
$492$	−175.368	−	175.368i	−0.356439	−	0.356439i
$493$	−685.566	+	685.566i	−1.39060	+	1.39060i
$494$			133.450i			0.270142i
$495$	386.389	−	740.442i	0.780584	−	1.49584i
$496$	122.360			0.246693
$497$	−134.442	−	134.442i	−0.270506	−	0.270506i
$498$	18.9362	−	18.9362i	0.0380245	−	0.0380245i
$499$			437.927i			0.877609i	0.898583	+	0.438804i	$0.144598\pi$
$499$			437.927i			0.877609i	−0.898583	+	0.438804i	$0.855402\pi$
$500$	−247.958	+	31.8897i	−0.495916	+	0.0637794i
$501$	370.376			0.739273
$502$	−227.711	−	227.711i	−0.453608	−	0.453608i
$503$	−322.632	+	322.632i	−0.641415	+	0.641415i	−0.950903	−	0.309488i	$-0.899842\pi$
$503$	−322.632	+	322.632i	−0.641415	+	0.641415i	0.309488	+	0.950903i	$0.399842\pi$
$504$		−	96.9417i		−	0.192345i
$505$	−337.561	−	176.152i	−0.668439	−	0.348815i
$506$	−128.731			−0.254410
$507$	−141.999	−	141.999i	−0.280076	−	0.280076i
$508$	−21.2719	+	21.2719i	−0.0418737	+	0.0418737i
$509$		−	980.067i		−	1.92548i	−0.270436	−	0.962738i	$-0.587168\pi$
$509$		−	980.067i		−	1.92548i	0.270436	−	0.962738i	$-0.412832\pi$
$510$	−183.082	−	582.688i	−0.358984	−	1.14253i
$511$	−226.165			−0.442593
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	3.81407	−	3.81407i	0.00743484	−	0.00743484i
$514$		−	437.095i		−	0.850380i
$515$	−857.979	+	269.579i	−1.66598	+	0.523455i
$516$	−577.727			−1.11963
$517$	598.881	+	598.881i	1.15838	+	1.15838i
$518$	182.068	−	182.068i	0.351483	−	0.351483i
$519$		−	413.439i		−	0.796607i
$520$	96.2893	−	184.520i	0.185172	−	0.354847i
$521$	−197.263			−0.378624			−0.189312	−	0.981917i	$-0.560626\pi$
$521$	−197.263			−0.378624			−0.189312	+	0.981917i	$0.560626\pi$
$522$	−416.773	−	416.773i	−0.798415	−	0.798415i
$523$	−284.732	+	284.732i	−0.544420	+	0.544420i	−0.924821	−	0.380401i	$-0.875786\pi$
$523$	−284.732	+	284.732i	−0.544420	+	0.544420i	0.380401	+	0.924821i	$0.375786\pi$
$524$			89.3014i			0.170422i
$525$	−234.943	−	336.962i	−0.447510	−	0.641831i
$526$	103.225			0.196246
$527$	442.834	+	442.834i	0.840292	+	0.840292i
$528$	−226.500	+	226.500i	−0.428977	+	0.428977i
$529$		−	23.0000i		−	0.0434783i
$530$	−599.048	−	312.604i	−1.13028	−	0.589820i
$531$	−130.153			−0.245109
$532$	−35.3139	−	35.3139i	−0.0663796	−	0.0663796i
$533$	305.865	−	305.865i	0.573855	−	0.573855i
$534$		−	63.9086i		−	0.119679i
$535$	85.2153	+	271.211i	0.159281	+	0.506937i
$536$	259.081			0.483360
$537$	−2.81986	−	2.81986i	−0.00525113	−	0.00525113i
$538$	−296.367	+	296.367i	−0.550869	+	0.550869i
$539$		−	642.159i		−	1.19139i
$540$	−8.02567	+	2.52169i	−0.0148624	+	0.00466979i
$541$	−926.910			−1.71333			−0.856664	−	0.515875i	$-0.827467\pi$
$541$	−926.910			−1.71333			−0.856664	+	0.515875i	$0.827467\pi$
$542$	22.4446	+	22.4446i	0.0414108	+	0.0414108i
$543$	671.453	−	671.453i	1.23656	−	1.23656i
$544$			115.812i			0.212889i
$545$	153.504	−	294.161i	0.281659	−	0.539746i
$546$	341.989			0.626353
$547$	735.910	+	735.910i	1.34536	+	1.34536i	0.890632	+	0.454725i	$0.150263\pi$
$547$	735.910	+	735.910i	1.34536	+	1.34536i	0.454725	+	0.890632i	$0.349737\pi$
$548$	−166.673	+	166.673i	−0.304148	+	0.304148i
$549$			608.944i			1.10919i
$550$	−117.846	+	660.630i	−0.214266	+	1.20114i
$551$	−303.644			−0.551079
$552$	−40.4680	−	40.4680i	−0.0733115	−	0.0733115i
$553$	−69.5338	+	69.5338i	−0.125739	+	0.125739i
$554$		−	495.936i		−	0.895191i
$555$	874.322	+	456.252i	1.57535	+	0.822076i
$556$	101.425			0.182419
$557$	−8.85338	−	8.85338i	−0.0158948	−	0.0158948i	0.699115	−	0.715009i	$-0.253578\pi$
$557$	−8.85338	−	8.85338i	−0.0158948	−	0.0158948i	−0.715009	+	0.699115i	$0.753578\pi$
$558$	−269.210	+	269.210i	−0.482455	+	0.482455i
$559$		−	1007.63i		−	1.80256i
$560$	23.3479	+	74.3086i	0.0416927	+	0.132694i
$561$	−1639.46			−2.92239
$562$	−171.969	−	171.969i	−0.305995	−	0.305995i
$563$	152.740	−	152.740i	0.271297	−	0.271297i	−0.558325	−	0.829622i	$-0.688556\pi$
$563$	152.740	−	152.740i	0.271297	−	0.271297i	0.829622	+	0.558325i	$0.188556\pi$
$564$			376.529i			0.667604i
$565$	555.693	−	174.600i	0.983528	−	0.309027i
$566$	−443.719			−0.783957
$567$	−227.893	−	227.893i	−0.401928	−	0.401928i
$568$	−97.6395	+	97.6395i	−0.171901	+	0.171901i
$569$			62.0659i			0.109079i	0.998512	+	0.0545394i	$0.0173691\pi$
$569$			62.0659i			0.109079i	−0.998512	+	0.0545394i	$0.982631\pi$
$570$	88.4947	−	169.584i	0.155254	−	0.297515i
$571$	415.564			0.727782			0.363891	−	0.931441i	$-0.381448\pi$
$571$	415.564			0.727782			0.363891	+	0.931441i	$0.381448\pi$
$572$	−395.045	−	395.045i	−0.690638	−	0.690638i
$573$	−242.652	+	242.652i	−0.423477	+	0.423477i
$574$			161.877i			0.282016i
$575$	−118.033	−	21.0552i	−0.205274	−	0.0366177i
$576$	−70.4049			−0.122231
$577$	96.4813	+	96.4813i	0.167212	+	0.167212i	0.785753	−	0.618541i	$-0.212276\pi$
$577$	96.4813	+	96.4813i	0.167212	+	0.167212i	−0.618541	+	0.785753i	$0.712276\pi$
$578$	−130.137	+	130.137i	−0.225150	+	0.225150i
$579$		−	1544.10i		−	2.66684i
$580$	419.846	+	219.090i	0.723872	+	0.377742i
$581$	−17.4795			−0.0300851
$582$	54.3650	+	54.3650i	0.0934107	+	0.0934107i
$583$	−1282.52	+	1282.52i	−2.19986	+	2.19986i
$584$			164.255i			0.281258i
$585$	194.122	+	617.824i	0.331832	+	1.05611i
$586$	592.474			1.01105
$587$	−233.441	−	233.441i	−0.397684	−	0.397684i	0.479731	−	0.877416i	$-0.340734\pi$
$587$	−233.441	−	233.441i	−0.397684	−	0.397684i	−0.877416	+	0.479731i	$0.840734\pi$
$588$	201.869	−	201.869i	0.343315	−	0.343315i
$589$			196.136i			0.332998i
$590$	99.7657	−	31.3466i	0.169094	−	0.0531299i
$591$	846.433			1.43220
$592$	−132.229	−	132.229i	−0.223359	−	0.223359i
$593$	74.2997	−	74.2997i	0.125295	−	0.125295i	−0.641679	−	0.766973i	$-0.721762\pi$
$593$	74.2997	−	74.2997i	0.125295	−	0.125295i	0.766973	+	0.641679i	$0.221762\pi$
$594$			22.5811i			0.0380154i
$595$	−184.433	+	353.430i	−0.309971	+	0.594001i
$596$	198.512			0.333073
$597$	−389.161	−	389.161i	−0.651860	−	0.651860i
$598$	70.5814	−	70.5814i	0.118029	−	0.118029i
$599$			199.713i			0.333410i	0.986007	+	0.166705i	$0.0533127\pi$
$599$			199.713i			0.333410i	−0.986007	+	0.166705i	$0.946687\pi$
$600$	−244.722	+	170.629i	−0.407869	+	0.284382i
$601$	865.420			1.43997			0.719983	−	0.693991i	$-0.244149\pi$
$601$	865.420			1.43997			0.719983	+	0.693991i	$0.244149\pi$
$602$	266.642	+	266.642i	0.442927	+	0.442927i
$603$	−570.018	+	570.018i	−0.945303	+	0.945303i
$604$			467.581i			0.774141i
$605$	1060.56	+	553.437i	1.75299	+	0.914772i
$606$	−454.373			−0.749790
$607$	524.328	+	524.328i	0.863802	+	0.863802i	0.991777	−	0.127976i	$-0.0408479\pi$
$607$	524.328	+	524.328i	0.863802	+	0.863802i	−0.127976	+	0.991777i	$0.540848\pi$
$608$	−25.6471	+	25.6471i	−0.0421827	+	0.0421827i
$609$			778.139i			1.27773i
$610$	−146.661	−	466.773i	−0.240428	−	0.765201i
$611$	−656.715			−1.07482
$612$	−254.804	−	254.804i	−0.416346	−	0.416346i
$613$	64.5323	−	64.5323i	0.105273	−	0.105273i	−0.652508	−	0.757781i	$-0.726283\pi$
$613$	64.5323	−	64.5323i	0.105273	−	0.105273i	0.757781	+	0.652508i	$0.226283\pi$
$614$		−	381.181i		−	0.620816i
$615$	−591.509	+	185.853i	−0.961803	+	0.302201i
$616$	209.076			0.339408
$617$	317.503	+	317.503i	0.514592	+	0.514592i	0.915930	−	0.401338i	$-0.131455\pi$
$617$	317.503	+	317.503i	0.514592	+	0.514592i	−0.401338	+	0.915930i	$0.631455\pi$
$618$	−758.871	+	758.871i	−1.22795	+	1.22795i
$619$		−	133.002i		−	0.214866i	−0.994212	−	0.107433i	$-0.965737\pi$
$619$		−	133.002i		−	0.214866i	0.994212	−	0.107433i	$-0.0342631\pi$
$620$	141.519	−	271.195i	0.228257	−	0.437411i
$621$	−4.03450			−0.00649678
$622$	−89.9132	−	89.9132i	−0.144555	−	0.144555i
$623$	−29.4961	+	29.4961i	−0.0473453	+	0.0473453i
$624$		−	248.373i		−	0.398033i
$625$	−216.104	+	586.450i	−0.345767	+	0.938321i
$626$	389.929			0.622890
$627$	−363.066	−	363.066i	−0.579053	−	0.579053i
$628$	−9.09633	+	9.09633i	−0.0144846	+	0.0144846i
$629$		−	957.102i		−	1.52163i
$630$	−214.859	−	112.121i	−0.341046	−	0.177970i
$631$	488.775			0.774603			0.387302	−	0.921953i	$-0.373407\pi$
$631$	488.775			0.774603			0.387302	+	0.921953i	$0.373407\pi$
$632$	50.4996	+	50.4996i	0.0799045	+	0.0799045i
$633$	924.525	−	924.525i	1.46055	−	1.46055i
$634$		−	273.214i		−	0.430937i
$635$	22.5437	+	71.7491i	0.0355020	+	0.112991i
$636$	−806.345			−1.26784
$637$	352.086	+	352.086i	0.552726	+	0.552726i
$638$	898.860	−	898.860i	1.40887	−	1.40887i
$639$		−	429.644i		−	0.672369i
$640$	53.9673	−	16.9567i	0.0843239	−	0.0264948i
$641$	−838.305			−1.30781			−0.653904	−	0.756578i	$-0.726870\pi$
$641$	−838.305			−1.30781			−0.653904	+	0.756578i	$0.726870\pi$
$642$	239.883	+	239.883i	0.373649	+	0.373649i
$643$	−323.327	+	323.327i	−0.502841	+	0.502841i	−0.912320	−	0.409479i	$-0.865711\pi$
$643$	−323.327	+	323.327i	−0.502841	+	0.502841i	0.409479	+	0.912320i	$0.365711\pi$
$644$			37.3548i			0.0580044i
$645$	−668.189	+	1280.46i	−1.03595	+	1.98521i
$646$	−185.640			−0.287368
$647$	−329.025	−	329.025i	−0.508539	−	0.508539i	0.405539	−	0.914078i	$-0.367084\pi$
$647$	−329.025	−	329.025i	−0.508539	−	0.508539i	−0.914078	+	0.405539i	$0.867084\pi$
$648$	−165.510	+	165.510i	−0.255416	+	0.255416i
$649$		−	280.702i		−	0.432515i
$650$	−297.600	−	426.826i	−0.457846	−	0.656656i
$651$	502.630			0.772090
$652$	128.318	+	128.318i	0.196807	+	0.196807i
$653$	302.416	−	302.416i	0.463118	−	0.463118i	−0.436558	−	0.899676i	$-0.643803\pi$
$653$	302.416	−	302.416i	0.463118	−	0.463118i	0.899676	+	0.436558i	$0.143803\pi$
$654$		−	395.954i		−	0.605435i
$655$	197.925	+	103.284i	0.302176	+	0.157686i
$656$	117.565			0.179215
$657$	−361.385	−	361.385i	−0.550054	−	0.550054i
$658$	173.782	−	173.782i	0.264106	−	0.264106i
$659$			253.982i			0.385405i	0.981257	+	0.192703i	$0.0617252\pi$
$659$			253.982i			0.385405i	−0.981257	+	0.192703i	$0.938275\pi$
$660$	240.042	+	763.974i	0.363701	+	1.15754i
$661$	−166.313			−0.251608			−0.125804	−	0.992055i	$-0.540151\pi$
$661$	−166.313			−0.251608			−0.125804	+	0.992055i	$0.540151\pi$
$662$	−258.496	−	258.496i	−0.390477	−	0.390477i
$663$	898.890	−	898.890i	1.35579	−	1.35579i
$664$			12.6946i			0.0191184i
$665$	−119.112	+	37.4254i	−0.179116	+	0.0562788i
$666$	581.846			0.873643
$667$	160.596	+	160.596i	0.240774	+	0.240774i
$668$	−124.148	+	124.148i	−0.185851	+	0.185851i
$669$		−	74.3234i		−	0.111096i
$670$	299.649	−	574.221i	0.447237	−	0.857046i
$671$	−1313.32			−1.95725
$672$	65.7250	+	65.7250i	0.0978050	+	0.0978050i
$673$	−595.984	+	595.984i	−0.885564	+	0.885564i	−0.994093	−	0.108529i	$-0.965386\pi$
$673$	−595.984	+	595.984i	−0.885564	+	0.885564i	0.108529	+	0.994093i	$0.465386\pi$
$674$		−	684.108i		−	1.01500i
$675$	−3.69335	+	20.7044i	−0.00547164	+	0.0306732i
$676$	95.1944			0.140820
$677$	422.053	+	422.053i	0.623417	+	0.623417i	0.946404	−	0.322987i	$-0.104687\pi$
$677$	422.053	+	422.053i	0.623417	+	0.623417i	−0.322987	+	0.946404i	$0.604687\pi$
$678$	491.504	−	491.504i	0.724932	−	0.724932i
$679$		−	50.1828i		−	0.0739070i
$680$	256.682	+	133.946i	0.377474	+	0.196979i
$681$	1723.85			2.53135
$682$	−580.609	−	580.609i	−0.851332	−	0.851332i
$683$	270.331	−	270.331i	0.395799	−	0.395799i	−0.480949	−	0.876748i	$-0.659708\pi$
$683$	270.331	−	270.331i	0.395799	−	0.395799i	0.876748	+	0.480949i	$0.159708\pi$
$684$		−	112.855i		−	0.164993i
$685$	176.639	+	562.181i	0.257867	+	0.820702i
$686$	−456.216			−0.665037
$687$	−202.010	−	202.010i	−0.294047	−	0.294047i
$688$	193.651	−	193.651i	0.281470	−	0.281470i
$689$		−	1406.37i		−	2.04118i
$690$	−136.497	+	42.8876i	−0.197821	+	0.0621560i
$691$	−133.773			−0.193593			−0.0967967	−	0.995304i	$-0.530860\pi$
$691$	−133.773			−0.193593			−0.0967967	+	0.995304i	$0.530860\pi$
$692$	138.583	+	138.583i	0.200264	+	0.200264i
$693$	−459.998	+	459.998i	−0.663778	+	0.663778i
$694$		−	814.135i		−	1.17311i
$695$	117.306	−	224.796i	0.168786	−	0.323447i
$696$	565.131			0.811970
$697$	425.481	+	425.481i	0.610447	+	0.610447i
$698$	−533.516	+	533.516i	−0.764349	+	0.764349i
$699$		−	69.0061i		−	0.0987211i
$700$	191.699	+	34.1962i	0.273856	+	0.0488518i
$701$	−691.481			−0.986421			−0.493211	−	0.869910i	$-0.664177\pi$
$701$	−691.481			−0.986421			−0.493211	+	0.869910i	$0.664177\pi$
$702$	−12.3809	−	12.3809i	−0.0176366	−	0.0176366i
$703$	211.955	−	211.955i	0.301501	−	0.301501i
$704$		−	151.843i		−	0.215686i
$705$	834.528	+	435.487i	1.18373	+	0.617711i
$706$	−514.787			−0.729159
$707$	209.709	+	209.709i	0.296619	+	0.296619i
$708$	88.2415	−	88.2415i	0.124635	−	0.124635i
$709$			912.048i			1.28639i	0.765704	+	0.643193i	$0.222391\pi$
$709$			912.048i			1.28639i	−0.765704	+	0.643193i	$0.777609\pi$
$710$	103.478	+	329.334i	0.145743	+	0.463851i
$711$	−222.214			−0.312537
$712$	21.4219	+	21.4219i	0.0300869	+	0.0300869i
$713$	103.735	−	103.735i	0.145492	−	0.145492i
$714$			475.733i			0.666293i
$715$	−1332.47	+	418.665i	−1.86359	+	0.585546i
$716$	1.89040			0.00264023
$717$	283.281	+	283.281i	0.395092	+	0.395092i
$718$	195.229	−	195.229i	0.271906	−	0.271906i
$719$		−	318.675i		−	0.443220i	−0.975135	−	0.221610i	$-0.928869\pi$
$719$		−	318.675i		−	0.443220i	0.975135	−	0.221610i	$-0.0711312\pi$
$720$	−81.4291	+	156.044i	−0.113096	+	0.216727i
$721$	700.493			0.971557
$722$	319.889	+	319.889i	0.443060	+	0.443060i
$723$	−62.2764	+	62.2764i	−0.0861360	+	0.0861360i
$724$			450.136i			0.621734i
$725$	971.173	−	677.139i	1.33955	−	0.933985i
$726$	1427.56			1.96633
$727$	−482.245	−	482.245i	−0.663336	−	0.663336i	0.292829	−	0.956165i	$-0.405403\pi$
$727$	−482.245	−	482.245i	−0.663336	−	0.663336i	−0.956165	+	0.292829i	$0.905403\pi$
$728$	−114.633	+	114.633i	−0.157463	+	0.157463i
$729$		−	696.349i		−	0.955211i
$730$	364.050	+	189.974i	0.498699	+	0.260239i
$731$	1401.69			1.91750
$732$	−412.854	−	412.854i	−0.564009	−	0.564009i
$733$	−389.589	+	389.589i	−0.531499	+	0.531499i	−0.921018	−	0.389519i	$-0.872641\pi$
$733$	−389.589	+	389.589i	−0.531499	+	0.531499i	0.389519	+	0.921018i	$0.372641\pi$
$734$			832.971i			1.13484i
$735$	−213.939	−	680.896i	−0.291074	−	0.926389i
$736$	27.1293			0.0368605
$737$	−1229.37	−	1229.37i	−1.66807	−	1.66807i
$738$	−258.661	+	258.661i	−0.350489	+	0.350489i
$739$			866.857i			1.17301i	0.809944	+	0.586507i	$0.199497\pi$
$739$			866.857i			1.17301i	−0.809944	+	0.586507i	$0.800503\pi$
$740$	−446.002	+	140.135i	−0.602705	+	0.189371i
$741$	398.127			0.537284
$742$	372.157	+	372.157i	0.501559	+	0.501559i
$743$	128.175	−	128.175i	0.172510	−	0.172510i	−0.615571	−	0.788081i	$-0.711075\pi$
$743$	128.175	−	128.175i	0.172510	−	0.172510i	0.788081	+	0.615571i	$0.211075\pi$
$744$		−	365.040i		−	0.490645i
$745$	229.595	−	439.976i	0.308181	−	0.590572i
$746$	−435.198			−0.583375
$747$	−27.9301	−	27.9301i	−0.0373897	−	0.0373897i
$748$	549.538	−	549.538i	0.734677	−	0.734677i
$749$		−	221.429i		−	0.295633i
$750$	95.1377	+	739.742i	0.126850	+	0.986322i
$751$	−240.027			−0.319609			−0.159805	−	0.987149i	$-0.551086\pi$
$751$	−240.027			−0.319609			−0.159805	+	0.987149i	$0.551086\pi$
$752$	−126.211	−	126.211i	−0.167833	−	0.167833i
$753$	−679.340	+	679.340i	−0.902178	+	0.902178i
$754$			985.662i			1.30724i
$755$	1036.33	+	540.796i	1.37263	+	0.716287i
$756$	6.55252			0.00866736
$757$	−89.0481	−	89.0481i	−0.117633	−	0.117633i	0.645840	−	0.763473i	$-0.276507\pi$
$757$	−89.0481	−	89.0481i	−0.117633	−	0.117633i	−0.763473	+	0.645840i	$0.776507\pi$
$758$	−118.665	+	118.665i	−0.156551	+	0.156551i
$759$			384.049i			0.505993i
$760$	27.1806	+	86.5066i	0.0357639	+	0.113824i
$761$	−495.606			−0.651257			−0.325628	−	0.945498i	$-0.605576\pi$
$761$	−495.606			−0.651257			−0.325628	+	0.945498i	$0.605576\pi$
$762$	63.4611	+	63.4611i	0.0832823	+	0.0832823i
$763$	−182.747	+	182.747i	−0.239511	+	0.239511i
$764$		−	162.672i		−	0.212921i
$765$	−859.441	+	270.039i	−1.12345	+	0.352992i
$766$	−595.266			−0.777109
$767$	153.905	+	153.905i	0.200658	+	0.200658i
$768$	47.7334	−	47.7334i	0.0621529	−	0.0621529i
$769$		−	379.943i		−	0.494074i	−0.969006	−	0.247037i	$-0.920543\pi$
$769$		−	379.943i		−	0.494074i	0.969006	−	0.247037i	$-0.0794569\pi$
$770$	241.813	−	463.390i	0.314043	−	0.601805i
$771$	−1304.00			−1.69131
$772$	517.575	+	517.575i	0.670435	+	0.670435i
$773$	−503.888	+	503.888i	−0.651860	+	0.651860i	−0.953441	−	0.301581i	$-0.902486\pi$
$773$	−503.888	+	503.888i	−0.651860	+	0.651860i	0.301581	+	0.953441i	$0.402486\pi$
$774$			852.124i			1.10094i
$775$	−437.391	−	627.319i	−0.564375	−	0.809443i
$776$	−36.4458			−0.0469662
$777$	−543.170	−	543.170i	−0.699061	−	0.699061i
$778$	−706.167	+	706.167i	−0.907670	+	0.907670i
$779$			188.450i			0.241913i
$780$	−550.487	−	287.264i	−0.705752	−	0.368287i
$781$	926.618			1.18645
$782$	98.1842	+	98.1842i	0.125555	+	0.125555i
$783$	28.1707	−	28.1707i	0.0359779	−	0.0359779i
$784$			135.331i			0.172616i
$785$	9.64021	+	30.6815i	0.0122805	+	0.0390847i
$786$	266.416			0.338952
$787$	−897.787	−	897.787i	−1.14077	−	1.14077i	−0.988309	−	0.152462i	$-0.951280\pi$
$787$	−897.787	−	897.787i	−1.14077	−	1.14077i	−0.152462	−	0.988309i	$-0.548720\pi$
$788$	−283.720	+	283.720i	−0.360051	+	0.360051i
$789$		−	307.956i		−	0.390311i
$790$	170.333	−	53.5191i	0.215612	−	0.0677457i
$791$	−453.693			−0.573569
$792$	334.078	+	334.078i	0.421816	+	0.421816i
$793$	720.072	−	720.072i	0.908035	−	0.908035i
$794$		−	566.589i		−	0.713588i
$795$	−932.604	+	1787.16i	−1.17309	+	2.24800i
$796$	260.889			0.327751
$797$	−244.863	−	244.863i	−0.307231	−	0.307231i	0.536603	−	0.843835i	$-0.319707\pi$
$797$	−244.863	−	244.863i	−0.307231	−	0.307231i	−0.843835	+	0.536603i	$0.819707\pi$
$798$	−105.353	+	105.353i	−0.132022	+	0.132022i
$799$		−	913.542i		−	1.14336i
$800$	24.8354	−	139.224i	0.0310442	−	0.174029i
$801$	−94.2627			−0.117681
$802$	−453.040	−	453.040i	−0.564887	−	0.564887i
$803$	779.405	−	779.405i	0.970616	−	0.970616i
$804$		−	772.927i		−	0.961351i
$805$	82.7923	+	43.2040i	0.102848	+	0.0536695i
$806$	636.678			0.789923
$807$	884.164	+	884.164i	1.09562	+	1.09562i
$808$	152.303	−	152.303i	0.188494	−	0.188494i
$809$		−	1234.87i		−	1.52641i	−0.646154	−	0.763207i	$-0.723624\pi$
$809$		−	1234.87i		−	1.52641i	0.646154	−	0.763207i	$-0.276376\pi$
$810$	175.406	+	558.257i	0.216550	+	0.689206i
$811$	1142.77			1.40909			0.704546	−	0.709658i	$-0.251151\pi$
$811$	1142.77			1.40909			0.704546	+	0.709658i	$0.251151\pi$
$812$	−260.828	−	260.828i	−0.321217	−	0.321217i
$813$	66.9600	−	66.9600i	0.0823616	−	0.0823616i
$814$			1254.88i			1.54162i
$815$	432.811	−	135.990i	0.531056	−	0.166859i
$816$	345.506			0.423414
$817$	310.412	+	310.412i	0.379941	+	0.379941i
$818$	368.025	−	368.025i	0.449908	−	0.449908i
$819$		−	504.420i		−	0.615897i
$820$	135.974	−	260.568i	0.165821	−	0.317766i
$821$	−210.621			−0.256542			−0.128271	−	0.991739i	$-0.540943\pi$
$821$	−210.621			−0.256542			−0.128271	+	0.991739i	$0.540943\pi$
$822$	497.242	+	497.242i	0.604917	+	0.604917i
$823$	527.137	−	527.137i	0.640507	−	0.640507i	−0.310173	−	0.950680i	$-0.600387\pi$
$823$	527.137	−	527.137i	0.640507	−	0.640507i	0.950680	+	0.310173i	$0.100387\pi$
$824$		−	508.740i		−	0.617403i
$825$	1970.88	+	351.575i	2.38895	+	0.426152i
$826$	−81.4532			−0.0986116
$827$	447.555	+	447.555i	0.541179	+	0.541179i	0.923874	−	0.382696i	$-0.125004\pi$
$827$	447.555	+	447.555i	0.541179	+	0.541179i	−0.382696	+	0.923874i	$0.625004\pi$
$828$	−59.6886	+	59.6886i	−0.0720877	+	0.0720877i
$829$		−	598.650i		−	0.722135i	−0.932540	−	0.361068i	$-0.882412\pi$
$829$		−	598.650i		−	0.722135i	0.932540	−	0.361068i	$-0.117588\pi$
$830$	28.1361	+	14.6824i	0.0338989	+	0.0176896i
$831$	−1479.54			−1.78044
$832$	83.2533	+	83.2533i	0.100064	+	0.100064i
$833$	−489.779	+	489.779i	−0.587970	+	0.587970i
$834$		−	302.585i		−	0.362812i
$835$	131.571	+	418.747i	0.157570	+	0.501493i
$836$	243.396			0.291144
$837$	−18.1965	−	18.1965i	−0.0217402	−	0.0217402i
$838$	−630.197	+	630.197i	−0.752026	+	0.752026i
$839$		−	156.758i		−	0.186839i	−0.995627	−	0.0934197i	$-0.970220\pi$
$839$		−	156.758i		−	0.186839i	0.995627	−	0.0934197i	$-0.0297798\pi$
$840$	221.688	−	69.6548i	0.263914	−	0.0829223i
$841$	−1401.71			−1.66672
$842$	689.372	+	689.372i	0.818732	+	0.818732i
$843$	−513.041	+	513.041i	−0.608590	+	0.608590i
$844$			619.793i			0.734351i
$845$	110.100	−	210.986i	0.130296	−	0.249688i
$846$	555.365			0.656459
$847$	−658.870	−	658.870i	−0.777886	−	0.777886i
$848$	270.283	−	270.283i	0.318730	−	0.318730i
$849$			1323.77i			1.55921i
$850$	593.749	−	413.985i	0.698528	−	0.487041i
$851$	−224.205			−0.263460
$852$	291.292	+	291.292i	0.341892	+	0.341892i
$853$	593.173	−	593.173i	0.695396	−	0.695396i	−0.268018	−	0.963414i	$-0.586369\pi$
$853$	593.173	−	593.173i	0.695396	−	0.695396i	0.963414	+	0.268018i	$0.0863686\pi$
$854$			381.094i			0.446246i
$855$	−250.129	−	130.526i	−0.292549	−	0.152662i
$856$	−160.815			−0.187868
$857$	591.419	+	591.419i	0.690104	+	0.690104i	0.962255	−	0.272151i	$-0.0877350\pi$
$857$	591.419	+	591.419i	0.690104	+	0.690104i	−0.272151	+	0.962255i	$0.587735\pi$
$858$	−1178.55	+	1178.55i	−1.37360	+	1.37360i
$859$			1358.37i			1.58134i	0.612245	+	0.790668i	$0.290266\pi$
$859$			1358.37i			1.58134i	−0.612245	+	0.790668i	$0.709734\pi$
$860$	−205.230	−	653.177i	−0.238639	−	0.759508i
$861$	482.934			0.560899
$862$	599.060	+	599.060i	0.694966	+	0.694966i
$863$	−158.479	+	158.479i	−0.183637	+	0.183637i	−0.792939	−	0.609301i	$-0.791450\pi$
$863$	−158.479	+	158.479i	−0.183637	+	0.183637i	0.609301	+	0.792939i	$0.291450\pi$
$864$		−	4.75883i		−	0.00550791i
$865$	467.434	−	146.869i	0.540386	−	0.169791i
$866$	691.833			0.798883
$867$	388.241	+	388.241i	0.447799	+	0.447799i
$868$	−168.479	+	168.479i	−0.194100	+	0.194100i
$869$		−	479.251i		−	0.551498i
$870$	653.621	−	1252.54i	0.751288	−	1.43970i
$871$	1348.08			1.54774
$872$	132.722	+	132.722i	0.152204	+	0.152204i
$873$	80.1863	−	80.1863i	0.0918514	−	0.0918514i
$874$			43.4868i			0.0497560i
$875$	297.508	−	385.327i	0.340009	−	0.440374i
$876$	490.027			0.559392
$877$	181.929	+	181.929i	0.207444	+	0.207444i	0.803180	−	0.595736i	$-0.203140\pi$
$877$	181.929	+	181.929i	0.207444	+	0.207444i	−0.595736	+	0.803180i	$0.703140\pi$
$878$	−733.085	+	733.085i	−0.834949	+	0.834949i
$879$		−	1767.55i		−	2.01086i
$880$	−336.541	−	175.619i	−0.382433	−	0.199567i
$881$	−1022.72			−1.16086			−0.580429	−	0.814311i	$-0.697115\pi$
$881$	−1022.72			−1.16086			−0.580429	+	0.814311i	$0.697115\pi$
$882$	−297.749	−	297.749i	−0.337584	−	0.337584i
$883$	630.164	−	630.164i	0.713662	−	0.713662i	−0.253637	−	0.967299i	$-0.581627\pi$
$883$	630.164	−	630.164i	0.713662	−	0.713662i	0.967299	+	0.253637i	$0.0816270\pi$
$884$			602.607i			0.681682i
$885$	−93.5176	−	297.635i	−0.105670	−	0.336310i
$886$	−598.987			−0.676057
$887$	−596.476	−	596.476i	−0.672464	−	0.672464i	0.285819	−	0.958283i	$-0.407734\pi$
$887$	−596.476	−	596.476i	−0.672464	−	0.672464i	−0.958283	+	0.285819i	$0.907734\pi$
$888$	−394.483	+	394.483i	−0.444237	+	0.444237i
$889$		−	58.5792i		−	0.0658934i
$890$	72.2550	−	22.7027i	0.0811854	−	0.0255087i
$891$	1570.72			1.76287
$892$	24.9128	+	24.9128i	0.0279292	+	0.0279292i
$893$	202.308	−	202.308i	0.226549	−	0.226549i
$894$		−	592.227i		−	0.662447i
$895$	2.18641	−	4.18984i	0.00244291	−	0.00468139i
$896$	−44.0614			−0.0491756
$897$	−210.568	−	210.568i	−0.234747	−	0.234747i
$898$	53.7628	−	53.7628i	0.0598694	−	0.0598694i
$899$			1448.66i			1.61141i
$900$	251.671	+	360.955i	0.279635	+	0.401061i
$901$	1956.37			2.17133
$902$	−557.857	−	557.857i	−0.618467	−	0.618467i
$903$	795.482	−	795.482i	0.880933	−	0.880933i
$904$			329.499i			0.364490i
$905$	997.669	+	520.619i	1.10240	+	0.575270i
$906$	1394.95			1.53968
$907$	−294.399	−	294.399i	−0.324586	−	0.324586i	0.525937	−	0.850523i	$-0.323715\pi$
$907$	−294.399	−	294.399i	−0.324586	−	0.324586i	−0.850523	+	0.525937i	$0.823715\pi$
$908$	−577.825	+	577.825i	−0.636371	+	0.636371i
$909$			670.181i			0.737273i
$910$	121.487	+	386.652i	0.133502	+	0.424892i
$911$	957.759			1.05133			0.525663	−	0.850693i	$-0.323817\pi$
$911$	957.759			1.05133			0.525663	+	0.850693i	$0.323817\pi$
$912$	76.5140	+	76.5140i	0.0838969	+	0.0838969i
$913$	60.2373	−	60.2373i	0.0659773	−	0.0659773i
$914$		−	1274.12i		−	1.39401i
$915$	−1392.54	+	437.540i	−1.52190	+	0.478185i
$916$	135.426			0.147845
$917$	−122.961	−	122.961i	−0.134090	−	0.134090i
$918$	17.2228	−	17.2228i	0.0187612	−	0.0187612i
$919$		−	1187.09i		−	1.29172i	−0.763458	−	0.645858i	$-0.776500\pi$
$919$		−	1187.09i		−	1.29172i	0.763458	−	0.645858i	$-0.223500\pi$
$920$	31.3773	−	60.1287i	0.0341058	−	0.0653573i
$921$	−1137.19			−1.23474
$922$	−508.755	−	508.755i	−0.551795	−	0.551795i
$923$	−508.051	+	508.051i	−0.550434	+	0.550434i
$924$		−	623.743i		−	0.675046i
$925$	−205.247	+	1150.58i	−0.221888	+	1.24387i
$926$	1235.26			1.33398
$927$	1119.30	+	1119.30i	1.20745	+	1.20745i
$928$	−189.429	+	189.429i	−0.204126	+	0.204126i
$929$			1141.79i			1.22905i	0.788897	+	0.614525i	$0.210652\pi$
$929$			1141.79i			1.22905i	−0.788897	+	0.614525i	$0.789348\pi$
$930$	−809.066	−	422.199i	−0.869963	−	0.453978i
$931$	−216.928			−0.233006
$932$	23.1305	+	23.1305i	0.0248181	+	0.0248181i
$933$	−268.241	+	268.241i	−0.287504	+	0.287504i
$934$		−	662.586i		−	0.709407i
$935$	−582.396	−	1853.57i	−0.622884	−	1.98243i
$936$	−366.340			−0.391389
$937$	−1171.70	−	1171.70i	−1.25048	−	1.25048i	−0.955503	−	0.294982i	$-0.904687\pi$
$937$	−1171.70	−	1171.70i	−1.25048	−	1.25048i	−0.294982	−	0.955503i	$-0.595313\pi$
$938$	−356.733	+	356.733i	−0.380313	+	0.380313i
$939$		−	1163.29i		−	1.23886i
$940$	−425.703	+	133.757i	−0.452875	+	0.142295i
$941$	−1068.70			−1.13570			−0.567851	−	0.823131i	$-0.692225\pi$
$941$	−1068.70			−1.13570			−0.567851	+	0.823131i	$0.692225\pi$
$942$	27.1374	+	27.1374i	0.0288083	+	0.0288083i
$943$	99.6705	−	99.6705i	0.105695	−	0.105695i
$944$			59.1562i			0.0626655i
$945$	7.57854	−	14.5228i	0.00801962	−	0.0153681i
$946$	−1837.79			−1.94269
$947$	395.119	+	395.119i	0.417232	+	0.417232i	0.884249	−	0.467016i	$-0.154671\pi$
$947$	395.119	+	395.119i	0.417232	+	0.417232i	−0.467016	+	0.884249i	$0.654671\pi$
$948$	150.657	−	150.657i	0.158921	−	0.158921i
$949$			854.672i			0.900602i
$950$	223.168	+	39.8097i	0.234913	+	0.0419049i
$951$	−815.091			−0.857088
$952$	−159.463	−	159.463i	−0.167503	−	0.167503i
$953$	−1155.41	+	1155.41i	−1.21239	+	1.21239i	−0.242158	+	0.970237i	$0.577855\pi$
$953$	−1155.41	+	1155.41i	−1.21239	+	1.21239i	−0.970237	+	0.242158i	$0.922145\pi$
$954$			1189.33i			1.24667i
$955$	−360.541	−	188.143i	−0.377530	−	0.197009i
$956$	−189.909			−0.198649
$957$	−2681.60	−	2681.60i	−2.80209	−	2.80209i
$958$	86.5041	−	86.5041i	0.0902965	−	0.0902965i
$959$		−	458.990i		−	0.478613i
$960$	−50.5875	−	161.003i	−0.0526953	−	0.167711i
$961$	−25.2570			−0.0262820
$962$	−688.030	−	688.030i	−0.715207	−	0.715207i
$963$	353.818	−	353.818i	0.367412	−	0.367412i
$964$		−	41.7494i		−	0.0433086i
$965$	1745.76	−	548.522i	1.80908	−	0.568417i
$966$	111.442			0.115365
$967$	523.186	+	523.186i	0.541040	+	0.541040i	0.923834	−	0.382794i	$-0.125038\pi$
$967$	523.186	+	523.186i	0.541040	+	0.541040i	−0.382794	+	0.923834i	$0.625038\pi$
$968$	−478.511	+	478.511i	−0.494329	+	0.494329i
$969$			553.826i			0.571544i
$970$	−42.1526	+	80.7775i	−0.0434563	+	0.0832758i
$971$	719.506			0.740995			0.370497	−	0.928834i	$-0.379187\pi$
$971$	719.506			0.740995			0.370497	+	0.928834i	$0.379187\pi$
$972$	483.063	+	483.063i	0.496979	+	0.496979i
$973$	−139.654	+	139.654i	−0.143529	+	0.143529i
$974$			369.076i			0.378929i
$975$	−1273.37	+	887.841i	−1.30602	+	0.910606i
$976$	276.773			0.283579
$977$	−1241.69	−	1241.69i	−1.27092	−	1.27092i	−0.945608	−	0.325309i	$-0.894532\pi$
$977$	−1241.69	−	1241.69i	−1.27092	−	1.27092i	−0.325309	−	0.945608i	$-0.605468\pi$
$978$	382.816	−	382.816i	0.391427	−	0.391427i
$979$		−	203.298i		−	0.207658i
$980$	299.944	+	156.522i	0.306066	+	0.159716i
$981$	−584.017			−0.595328
$982$	654.719	+	654.719i	0.666720	+	0.666720i
$983$	617.791	−	617.791i	0.628475	−	0.628475i	−0.319209	−	0.947684i	$-0.603417\pi$
$983$	617.791	−	617.791i	0.628475	−	0.628475i	0.947684	+	0.319209i	$0.103417\pi$
$984$		−	350.736i		−	0.356439i
$985$	300.684	+	956.976i	0.305263	+	0.971549i
$986$	−1371.13			−1.39060
$987$	−518.449	−	518.449i	−0.525278	−	0.525278i
$988$	−133.450	+	133.450i	−0.135071	+	0.135071i
$989$		−	328.352i		−	0.332004i
$990$	1126.83	−	354.053i	1.13821	−	0.357629i
$991$	649.198			0.655094			0.327547	−	0.944835i	$-0.393778\pi$
$991$	649.198			0.655094			0.327547	+	0.944835i	$0.393778\pi$
$992$	122.360	+	122.360i	0.123346	+	0.123346i
$993$	−771.181	+	771.181i	−0.776617	+	0.776617i
$994$		−	268.883i		−	0.270506i
$995$	301.740	−	578.229i	0.303257	−	0.581134i
$996$	37.8724			0.0380245
$997$	−568.461	−	568.461i	−0.570172	−	0.570172i	0.362005	−	0.932176i	$-0.382092\pi$
$997$	−568.461	−	568.461i	−0.570172	−	0.570172i	−0.932176	+	0.362005i	$0.882092\pi$
$998$	−437.927	+	437.927i	−0.438804	+	0.438804i
$999$			39.3284i			0.0393678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.11	✓	24
5.3	odd	4	inner	230.3.f.b.93.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.11	✓	24	1.1	even	1	trivial
230.3.f.b.93.11	yes	24	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(2.98334 - 2.98334i) q^{3} +2.00000i q^{4} +(4.43275 + 2.31317i) q^{5} +5.96668 q^{6} +(-2.75384 - 2.75384i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.80061i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(2.98334 - 2.98334i) q^{3} +2.00000i q^{4} +(4.43275 + 2.31317i) q^{5} +5.96668 q^{6} +(-2.75384 - 2.75384i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.80061i q^{9} +(2.11958 + 6.74591i) q^{10} +18.9804 q^{11} +(5.96668 + 5.96668i) q^{12} +(-10.4067 + 10.4067i) q^{13} -5.50767i q^{14} +(20.1253 - 6.32343i) q^{15} -4.00000 q^{16} +(-14.4765 - 14.4765i) q^{17} +(8.80061 - 8.80061i) q^{18} -6.41178i q^{19} +(-4.62633 + 8.86550i) q^{20} -16.4312 q^{21} +(18.9804 + 18.9804i) q^{22} +(-3.39116 + 3.39116i) q^{23} +11.9334i q^{24} +(14.2985 + 20.5074i) q^{25} -20.8133 q^{26} +(0.594854 + 0.594854i) q^{27} +(5.50767 - 5.50767i) q^{28} -47.3573i q^{29} +(26.4488 + 13.8019i) q^{30} -30.5899 q^{31} +(-4.00000 - 4.00000i) q^{32} +(56.6249 - 56.6249i) q^{33} -28.9529i q^{34} +(-5.83698 - 18.5771i) q^{35} +17.6012 q^{36} +(33.0572 + 33.0572i) q^{37} +(6.41178 - 6.41178i) q^{38} +62.0932i q^{39} +(-13.4918 + 4.23917i) q^{40} -29.3912 q^{41} +(-16.4312 - 16.4312i) q^{42} +(-48.4128 + 48.4128i) q^{43} +37.9608i q^{44} +(20.3573 - 39.0109i) q^{45} -6.78233 q^{46} +(31.5526 + 31.5526i) q^{47} +(-11.9334 + 11.9334i) q^{48} -33.8328i q^{49} +(-6.20884 + 34.8059i) q^{50} -86.3764 q^{51} +(-20.8133 - 20.8133i) q^{52} +(-67.5707 + 67.5707i) q^{53} +1.18971i q^{54} +(84.1353 + 43.9048i) q^{55} +11.0153 q^{56} +(-19.1285 - 19.1285i) q^{57} +(47.3573 - 47.3573i) q^{58} -14.7890i q^{59} +(12.6469 + 40.2507i) q^{60} -69.1934 q^{61} +(-30.5899 - 30.5899i) q^{62} +(-24.2354 + 24.2354i) q^{63} -8.00000i q^{64} +(-70.2025 + 22.0578i) q^{65} +113.250 q^{66} +(-64.7703 - 64.7703i) q^{67} +(28.9529 - 28.9529i) q^{68} +20.2340i q^{69} +(12.7402 - 24.4141i) q^{70} +48.8198 q^{71} +(17.6012 + 17.6012i) q^{72} +(41.0637 - 41.0637i) q^{73} +66.1143i q^{74} +(103.838 + 18.5231i) q^{75} +12.8236 q^{76} +(-52.2689 - 52.2689i) q^{77} +(-62.0932 + 62.0932i) q^{78} -25.2498i q^{79} +(-17.7310 - 9.25266i) q^{80} +82.7548 q^{81} +(-29.3912 - 29.3912i) q^{82} +(3.17366 - 3.17366i) q^{83} -32.8625i q^{84} +(-30.6841 - 97.6571i) q^{85} -96.8256 q^{86} +(-141.283 - 141.283i) q^{87} +(-37.9608 + 37.9608i) q^{88} -10.7109i q^{89} +(59.3682 - 18.6536i) q^{90} +57.3165 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-91.2601 + 91.2601i) q^{93} +63.1053i q^{94} +(14.8315 - 28.4218i) q^{95} -23.8667 q^{96} +(9.11145 + 9.11145i) q^{97} +(33.8328 - 33.8328i) q^{98} -167.039i 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

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