LMFDB - Embedded newform 287.2.c.b.204.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (of order $2$, degree $1$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 $ x^12 + 18x^10 + 113x^8 + 290x^6 + 258x^4 + 49*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.7
Root			$0.152182i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.b.204.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.152182 q^{2} -1.15218i q^{3} -1.97684 q^{4} +3.83685 q^{5} -0.175342i q^{6} +1.00000i q^{7} -0.605204 q^{8} +1.67248 q^{9} +O(q^{10})$	\(q+0.152182 q^{2} -1.15218i q^{3} -1.97684 q^{4} +3.83685 q^{5} -0.175342i q^{6} +1.00000i q^{7} -0.605204 q^{8} +1.67248 q^{9} +0.583900 q^{10} +2.58390i q^{11} +2.27768i q^{12} -6.41889i q^{13} +0.152182i q^{14} -4.42075i q^{15} +3.86158 q^{16} -4.32846i q^{17} +0.254521 q^{18} +1.25638i q^{19} -7.58484 q^{20} +1.15218 q^{21} +0.393223i q^{22} -2.31627 q^{23} +0.697305i q^{24} +9.72140 q^{25} -0.976841i q^{26} -5.38354i q^{27} -1.97684i q^{28} +8.41704i q^{29} -0.672759i q^{30} +4.14121 q^{31} +1.79807 q^{32} +2.97712 q^{33} -0.658714i q^{34} +3.83685i q^{35} -3.30622 q^{36} -7.00279 q^{37} +0.191198i q^{38} -7.39573 q^{39} -2.32208 q^{40} +(-3.89860 + 5.07946i) q^{41} +0.175342 q^{42} -4.86001 q^{43} -5.10796i q^{44} +6.41704 q^{45} -0.352495 q^{46} +10.9565i q^{47} -4.44924i q^{48} -1.00000 q^{49} +1.47942 q^{50} -4.98717 q^{51} +12.6891i q^{52} -5.30530i q^{53} -0.819279i q^{54} +9.91403i q^{55} -0.605204i q^{56} +1.44757 q^{57} +1.28092i q^{58} -2.16315 q^{59} +8.73911i q^{60} +4.40304 q^{61} +0.630218 q^{62} +1.67248i q^{63} -7.44953 q^{64} -24.6283i q^{65} +0.453065 q^{66} +12.7210i q^{67} +8.55668i q^{68} +2.66877i q^{69} +0.583900i q^{70} -7.94952i q^{71} -1.01219 q^{72} -16.8626 q^{73} -1.06570 q^{74} -11.2008i q^{75} -2.48366i q^{76} -2.58390 q^{77} -1.12550 q^{78} +5.18847i q^{79} +14.8163 q^{80} -1.18539 q^{81} +(-0.593297 + 0.773003i) q^{82} +10.0524 q^{83} -2.27768 q^{84} -16.6076i q^{85} -0.739606 q^{86} +9.69796 q^{87} -1.56379i q^{88} -3.97992i q^{89} +0.976558 q^{90} +6.41889 q^{91} +4.57890 q^{92} -4.77143i q^{93} +1.66738i q^{94} +4.82052i q^{95} -2.07171i q^{96} -1.35742i q^{97} -0.152182 q^{98} +4.32151i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.152182			0.107609			0.0538045	−	0.998551i	$-0.482865\pi$
$2$	0.152182			0.107609			0.0538045	+	0.998551i	$0.482865\pi$
$3$		−	1.15218i		−	0.665213i	−0.943066	−	0.332606i	$-0.892072\pi$
$3$		−	1.15218i		−	0.665213i	0.943066	−	0.332606i	$-0.107928\pi$
$4$	−1.97684			−0.988420
$5$	3.83685			1.71589			0.857945	−	0.513741i	$-0.171741\pi$
$5$	3.83685			1.71589			0.857945	+	0.513741i	$0.171741\pi$
$6$		−	0.175342i		−	0.0715829i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.605204			−0.213972
$9$	1.67248			0.557492
$10$	0.583900			0.184645
$11$			2.58390i			0.779075i	0.921011	+	0.389538i	$0.127365\pi$
$11$			2.58390i			0.779075i	−0.921011	+	0.389538i	$0.872635\pi$
$12$			2.27768i			0.657510i
$13$		−	6.41889i		−	1.78028i	−0.455687	−	0.890140i	$-0.650606\pi$
$13$		−	6.41889i		−	1.78028i	0.455687	−	0.890140i	$-0.349394\pi$
$14$			0.152182i			0.0406724i
$15$		−	4.42075i		−	1.14143i
$16$	3.86158			0.965395
$17$		−	4.32846i		−	1.04981i	−0.851162	−	0.524903i	$-0.824102\pi$
$17$		−	4.32846i		−	1.04981i	0.851162	−	0.524903i	$-0.175898\pi$
$18$	0.254521			0.0599912
$19$			1.25638i			0.288232i	0.989561	+	0.144116i	$0.0460339\pi$
$19$			1.25638i			0.288232i	−0.989561	+	0.144116i	$0.953966\pi$
$20$	−7.58484			−1.69602
$21$	1.15218			0.251427
$22$			0.393223i			0.0838355i
$23$	−2.31627			−0.482976			−0.241488	−	0.970404i	$-0.577635\pi$
$23$	−2.31627			−0.482976			−0.241488	+	0.970404i	$0.577635\pi$
$24$			0.697305i			0.142337i
$25$	9.72140			1.94428
$26$		−	0.976841i		−	0.191574i
$27$		−	5.38354i		−	1.03606i
$28$		−	1.97684i		−	0.373588i
$29$			8.41704i			1.56300i	0.623902	+	0.781502i	$0.285546\pi$
$29$			8.41704i			1.56300i	−0.623902	+	0.781502i	$0.714454\pi$
$30$		−	0.672759i		−	0.122828i
$31$	4.14121			0.743784			0.371892	−	0.928276i	$-0.378709\pi$
$31$	4.14121			0.743784			0.371892	+	0.928276i	$0.378709\pi$
$32$	1.79807			0.317857
$33$	2.97712			0.518251
$34$		−	0.658714i		−	0.112969i
$35$			3.83685i			0.648546i
$36$	−3.30622			−0.551037
$37$	−7.00279			−1.15125			−0.575626	−	0.817713i	$-0.695242\pi$
$37$	−7.00279			−1.15125			−0.575626	+	0.817713i	$0.695242\pi$
$38$			0.191198i			0.0310164i
$39$	−7.39573			−1.18427
$40$	−2.32208			−0.367152
$41$	−3.89860	+	5.07946i	−0.608859	+	0.793279i
$41$	−3.89860	+	5.07946i	−0.608859	+	0.793279i
$42$	0.175342			0.0270558
$43$	−4.86001			−0.741144			−0.370572	−	0.928804i	$-0.620838\pi$
$43$	−4.86001			−0.741144			−0.370572	+	0.928804i	$0.620838\pi$
$44$		−	5.10796i		−	0.770054i
$45$	6.41704			0.956595
$46$	−0.352495			−0.0519726
$47$			10.9565i			1.59817i	0.601221	+	0.799083i	$0.294681\pi$
$47$			10.9565i			1.59817i	−0.601221	+	0.799083i	$0.705319\pi$
$48$		−	4.44924i		−	0.642193i
$49$	−1.00000			−0.142857
$50$	1.47942			0.209222
$51$	−4.98717			−0.698344
$52$			12.6891i			1.75967i
$53$		−	5.30530i		−	0.728739i	−0.931254	−	0.364370i	$-0.881284\pi$
$53$		−	5.30530i		−	0.728739i	0.931254	−	0.364370i	$-0.118716\pi$
$54$		−	0.819279i		−	0.111490i
$55$			9.91403i			1.33681i
$56$		−	0.605204i		−	0.0808738i
$57$	1.44757			0.191736
$58$			1.28092i			0.168193i
$59$	−2.16315			−0.281618			−0.140809	−	0.990037i	$-0.544970\pi$
$59$	−2.16315			−0.281618			−0.140809	+	0.990037i	$0.544970\pi$
$60$			8.73911i			1.12821i
$61$	4.40304			0.563751			0.281875	−	0.959451i	$-0.409043\pi$
$61$	4.40304			0.563751			0.281875	+	0.959451i	$0.409043\pi$
$62$	0.630218			0.0800378
$63$			1.67248i			0.210712i
$64$	−7.44953			−0.931191
$65$		−	24.6283i		−	3.05477i
$66$	0.453065			0.0557684
$67$			12.7210i			1.55411i	0.629432	+	0.777056i	$0.283288\pi$
$67$			12.7210i			1.55411i	−0.629432	+	0.777056i	$0.716712\pi$
$68$			8.55668i			1.03765i
$69$			2.66877i			0.321282i
$70$			0.583900i			0.0697894i
$71$		−	7.94952i		−	0.943435i	−0.881750	−	0.471717i	$-0.843634\pi$
$71$		−	7.94952i		−	0.943435i	0.881750	−	0.471717i	$-0.156366\pi$
$72$	−1.01219			−0.119288
$73$	−16.8626			−1.97362			−0.986810	−	0.161884i	$-0.948243\pi$
$73$	−16.8626			−1.97362			−0.986810	+	0.161884i	$0.948243\pi$
$74$	−1.06570			−0.123885
$75$		−	11.2008i		−	1.29336i
$76$		−	2.48366i		−	0.284895i
$77$	−2.58390			−0.294463
$78$	−1.12550			−0.127438
$79$			5.18847i			0.583748i	0.956457	+	0.291874i	$0.0942788\pi$
$79$			5.18847i			0.583748i	−0.956457	+	0.291874i	$0.905721\pi$
$80$	14.8163			1.65651
$81$	−1.18539			−0.131710
$82$	−0.593297	+	0.773003i	−0.0655187	+	0.0853639i
$83$	10.0524			1.10339			0.551695	−	0.834046i	$-0.313981\pi$
$83$	10.0524			1.10339			0.551695	+	0.834046i	$0.313981\pi$
$84$	−2.27768			−0.248515
$85$		−	16.6076i		−	1.80135i
$86$	−0.739606			−0.0797538
$87$	9.69796			1.03973
$88$		−	1.56379i		−	0.166700i
$89$		−	3.97992i		−	0.421870i	−0.977500	−	0.210935i	$-0.932349\pi$
$89$		−	3.97992i		−	0.421870i	0.977500	−	0.210935i	$-0.0676509\pi$
$90$	0.976558			0.102938
$91$	6.41889			0.672883
$92$	4.57890			0.477383
$93$		−	4.77143i		−	0.494774i
$94$			1.66738i			0.171977i
$95$			4.82052i			0.494575i
$96$		−	2.07171i		−	0.211443i
$97$		−	1.35742i		−	0.137826i	−0.997623	−	0.0689128i	$-0.978047\pi$
$97$		−	1.35742i		−	0.137826i	0.997623	−	0.0689128i	$-0.0219530\pi$
$98$	−0.152182			−0.0153727
$99$			4.32151i			0.434328i
$100$	−19.2177			−1.92177
$101$			10.5672i			1.05148i	0.850647	+	0.525738i	$0.176211\pi$
$101$			10.5672i			1.05148i	−0.850647	+	0.525738i	$0.823789\pi$
$102$	−0.758959			−0.0751481
$103$	−3.84101			−0.378466			−0.189233	−	0.981932i	$-0.560600\pi$
$103$	−3.84101			−0.378466			−0.189233	+	0.981932i	$0.560600\pi$
$104$			3.88474i			0.380930i
$105$	4.42075			0.431421
$106$		−	0.807372i		−	0.0784189i
$107$	−15.3995			−1.48872			−0.744361	−	0.667777i	$-0.767246\pi$
$107$	−15.3995			−1.48872			−0.744361	+	0.667777i	$0.767246\pi$
$108$			10.6424i			1.02407i
$109$		−	0.507168i		−	0.0485779i	−0.999705	−	0.0242889i	$-0.992268\pi$
$109$		−	0.507168i		−	0.0485779i	0.999705	−	0.0242889i	$-0.00773217\pi$
$110$			1.50874i			0.143853i
$111$			8.06849i			0.765827i
$112$			3.86158i			0.364885i
$113$	6.61352			0.622147			0.311074	−	0.950386i	$-0.399311\pi$
$113$	6.61352			0.622147			0.311074	+	0.950386i	$0.399311\pi$
$114$	0.220295			0.0206325
$115$	−8.88718			−0.828734
$116$		−	16.6391i		−	1.54491i
$117$		−	10.7354i		−	0.992492i
$118$	−0.329193			−0.0303047
$119$	4.32846			0.396789
$120$			2.67545i			0.244234i
$121$	4.32346			0.393042
$122$	0.670063			0.0606647
$123$	5.85246	+	4.49190i	0.527699	+	0.405021i
$124$	−8.18652			−0.735171
$125$	18.1153			1.62028
$126$			0.254521i			0.0226745i
$127$	−17.5573			−1.55796			−0.778981	−	0.627048i	$-0.784263\pi$
$127$	−17.5573			−1.55796			−0.778981	+	0.627048i	$0.784263\pi$
$128$	−4.72983			−0.418062
$129$			5.59961i			0.493018i
$130$		−	3.74799i		−	0.328720i
$131$	9.65598			0.843647			0.421824	−	0.906678i	$-0.361390\pi$
$131$	9.65598			0.843647			0.421824	+	0.906678i	$0.361390\pi$
$132$	−5.88530			−0.512249
$133$	−1.25638			−0.108942
$134$			1.93590i			0.167236i
$135$		−	20.6558i		−	1.77777i
$136$			2.61960i			0.224629i
$137$		−	8.77061i		−	0.749324i	−0.927162	−	0.374662i	$-0.877759\pi$
$137$		−	8.77061i		−	0.749324i	0.927162	−	0.374662i	$-0.122241\pi$
$138$			0.406138i			0.0345728i
$139$	−8.46040			−0.717602			−0.358801	−	0.933414i	$-0.616814\pi$
$139$	−8.46040			−0.717602			−0.358801	+	0.933414i	$0.616814\pi$
$140$		−	7.58484i		−	0.641036i
$141$	12.6239			1.06312
$142$		−	1.20977i		−	0.101522i
$143$	16.5858			1.38697
$144$	6.45840			0.538200
$145$			32.2949i			2.68194i
$146$	−2.56619			−0.212379
$147$			1.15218i			0.0950304i
$148$	13.8434			1.13792
$149$			8.49081i			0.695594i	0.937570	+	0.347797i	$0.113070\pi$
$149$			8.49081i			0.695594i	−0.937570	+	0.347797i	$0.886930\pi$
$150$		−	1.70457i		−	0.139177i
$151$		−	5.72234i		−	0.465677i	−0.972515	−	0.232839i	$-0.925199\pi$
$151$		−	5.72234i		−	0.465677i	0.972515	−	0.232839i	$-0.0748014\pi$
$152$		−	0.760364i		−	0.0616736i
$153$		−	7.23925i		−	0.585259i
$154$	−0.393223			−0.0316868
$155$	15.8892			1.27625
$156$	14.6202			1.17055
$157$		−	13.8365i		−	1.10427i	−0.833754	−	0.552136i	$-0.813813\pi$
$157$		−	13.8365i		−	1.10427i	0.833754	−	0.552136i	$-0.186187\pi$
$158$			0.789592i			0.0628166i
$159$	−6.11267			−0.484767
$160$	6.89893			0.545408
$161$		−	2.31627i		−	0.182548i
$162$	−0.180396			−0.0141732
$163$	16.7894			1.31505			0.657523	−	0.753435i	$-0.271604\pi$
$163$	16.7894			1.31505			0.657523	+	0.753435i	$0.271604\pi$
$164$	7.70691	−	10.0413i	0.601808	−	0.784093i
$165$	11.4228			0.889261
$166$	1.52979			0.118735
$167$		−	15.4256i		−	1.19367i	−0.802366	−	0.596833i	$-0.796426\pi$
$167$		−	15.4256i		−	1.19367i	0.802366	−	0.596833i	$-0.203574\pi$
$168$	−0.697305			−0.0537983
$169$	−28.2022			−2.16940
$170$		−	2.52739i		−	0.193842i
$171$			2.10126i			0.160687i
$172$	9.60746			0.732562
$173$	19.0284			1.44670			0.723351	−	0.690481i	$-0.242601\pi$
$173$	19.0284			1.44670			0.723351	+	0.690481i	$0.242601\pi$
$174$	1.47586			0.111884
$175$			9.72140i			0.734869i
$176$			9.97794i			0.752115i
$177$			2.49235i			0.187336i
$178$		−	0.605672i		−	0.0453970i
$179$		−	10.9490i		−	0.818369i	−0.912452	−	0.409185i	$-0.865813\pi$
$179$		−	10.9490i		−	0.818369i	0.912452	−	0.409185i	$-0.134187\pi$
$180$	−12.6855			−0.945518
$181$		−	6.01857i		−	0.447357i	−0.974663	−	0.223679i	$-0.928193\pi$
$181$		−	6.01857i		−	0.447357i	0.974663	−	0.223679i	$-0.0718066\pi$
$182$	0.976841			0.0724082
$183$		−	5.07310i		−	0.375014i
$184$	1.40182			0.103343
$185$	−26.8686			−1.97542
$186$		−	0.726126i		−	0.0532422i
$187$	11.1843			0.817878
$188$		−	21.6592i		−	1.57966i
$189$	5.38354			0.391595
$190$			0.733597i			0.0532208i
$191$		−	15.8546i		−	1.14720i	−0.819137	−	0.573598i	$-0.805547\pi$
$191$		−	15.8546i		−	1.14720i	0.819137	−	0.573598i	$-0.194453\pi$
$192$			8.58321i			0.619440i
$193$			10.4950i			0.755445i	0.925919	+	0.377722i	$0.123293\pi$
$193$			10.4950i			0.755445i	−0.925919	+	0.377722i	$0.876707\pi$
$194$		−	0.206576i		−	0.0148313i
$195$	−28.3763			−2.03207
$196$	1.97684			0.141203
$197$	−2.46364			−0.175527			−0.0877635	−	0.996141i	$-0.527972\pi$
$197$	−2.46364			−0.175527			−0.0877635	+	0.996141i	$0.527972\pi$
$198$			0.657657i			0.0467376i
$199$			12.4176i			0.880262i	0.897934	+	0.440131i	$0.145068\pi$
$199$			12.4176i			0.880262i	−0.897934	+	0.440131i	$0.854932\pi$
$200$	−5.88343			−0.416021
$201$	14.6569			1.03381
$202$			1.60814i			0.113148i
$203$	−8.41704			−0.590760
$204$	9.85885			0.690258
$205$	−14.9583	+	19.4891i	−1.04473	+	1.36118i
$206$	−0.584533			−0.0407263
$207$	−3.87391			−0.269255
$208$		−	24.7871i		−	1.71867i
$209$	−3.24635			−0.224555
$210$	0.672759			0.0464248
$211$		−	5.66414i		−	0.389935i	−0.980810	−	0.194968i	$-0.937540\pi$
$211$		−	5.66414i		−	0.389935i	0.980810	−	0.194968i	$-0.0624602\pi$
$212$			10.4877i			0.720301i
$213$	−9.15930			−0.627585
$214$	−2.34352			−0.160200
$215$	−18.6471			−1.27172
$216$			3.25814i			0.221688i
$217$			4.14121i			0.281124i
$218$		−	0.0771819i		−	0.00522742i
$219$			19.4288i			1.31288i
$220$		−	19.5985i		−	1.32133i
$221$	−27.7839			−1.86895
$222$			1.22788i			0.0824099i
$223$	−7.56057			−0.506293			−0.253147	−	0.967428i	$-0.581466\pi$
$223$	−7.56057			−0.506293			−0.253147	+	0.967428i	$0.581466\pi$
$224$			1.79807i			0.120139i
$225$	16.2588			1.08392
$226$	1.00646			0.0669487
$227$			12.7147i			0.843907i	0.906618	+	0.421953i	$0.138655\pi$
$227$			12.7147i			0.843907i	−0.906618	+	0.421953i	$0.861345\pi$
$228$	−2.86162			−0.189516
$229$			20.8381i			1.37702i	0.725226	+	0.688511i	$0.241735\pi$
$229$			20.8381i			1.37702i	−0.725226	+	0.688511i	$0.758265\pi$
$230$	−1.35247			−0.0891792
$231$			2.97712i			0.195880i
$232$		−	5.09402i		−	0.334439i
$233$			13.9497i			0.913876i	0.889499	+	0.456938i	$0.151054\pi$
$233$			13.9497i			0.913876i	−0.889499	+	0.456938i	$0.848946\pi$
$234$		−	1.63374i		−	0.106801i
$235$			42.0383i			2.74228i
$236$	4.27621			0.278357
$237$	5.97806			0.388317
$238$	0.658714			0.0426981
$239$		−	1.50855i		−	0.0975803i	−0.998809	−	0.0487902i	$-0.984463\pi$
$239$		−	1.50855i		−	0.0975803i	0.998809	−	0.0487902i	$-0.0155366\pi$
$240$		−	17.0711i		−	1.10193i
$241$	10.7896			0.695019			0.347509	−	0.937677i	$-0.387027\pi$
$241$	10.7896			0.695019			0.347509	+	0.937677i	$0.387027\pi$
$242$	0.657954			0.0422949
$243$		−	14.7848i		−	0.948448i
$244$	−8.70410			−0.557223
$245$	−3.83685			−0.245127
$246$	0.890640	+	0.683586i	0.0567852	+	0.0435839i
$247$	8.06454			0.513135
$248$	−2.50628			−0.159149
$249$		−	11.5821i		−	0.733988i
$250$	2.75682			0.174357
$251$	−0.343383			−0.0216741			−0.0108371	−	0.999941i	$-0.503450\pi$
$251$	−0.343383			−0.0216741			−0.0108371	+	0.999941i	$0.503450\pi$
$252$		−	3.30622i		−	0.208272i
$253$		−	5.98501i		−	0.376275i
$254$	−2.67191			−0.167651
$255$	−19.1350			−1.19828
$256$	14.1793			0.886204
$257$			4.73143i			0.295139i	0.989052	+	0.147569i	$0.0471450\pi$
$257$			4.73143i			0.295139i	−0.989052	+	0.147569i	$0.952855\pi$
$258$			0.852161i			0.0530532i
$259$		−	7.00279i		−	0.435132i
$260$			48.6863i			3.01939i
$261$			14.0773i			0.871363i
$262$	1.46947			0.0907840
$263$		−	9.33088i		−	0.575367i	−0.957726	−	0.287683i	$-0.907115\pi$
$263$		−	9.33088i		−	0.575367i	0.957726	−	0.287683i	$-0.0928851\pi$
$264$	−1.80177			−0.110891
$265$		−	20.3556i		−	1.25044i
$266$	−0.191198			−0.0117231
$267$	−4.58559			−0.280633
$268$		−	25.1473i		−	1.53612i
$269$	−6.96925			−0.424923			−0.212461	−	0.977169i	$-0.568148\pi$
$269$	−6.96925			−0.424923			−0.212461	+	0.977169i	$0.568148\pi$
$270$		−	3.14345i		−	0.191304i
$271$	−25.5806			−1.55391			−0.776956	−	0.629555i	$-0.783237\pi$
$271$	−25.5806			−1.55391			−0.776956	+	0.629555i	$0.783237\pi$
$272$		−	16.7147i		−	1.01348i
$273$		−	7.39573i		−	0.447610i
$274$		−	1.33473i		−	0.0806340i
$275$			25.1191i			1.51474i
$276$		−	5.27573i		−	0.317561i
$277$	−0.317474			−0.0190752			−0.00953758	−	0.999955i	$-0.503036\pi$
$277$	−0.317474			−0.0190752			−0.00953758	+	0.999955i	$0.503036\pi$
$278$	−1.28752			−0.0772204
$279$	6.92608			0.414654
$280$		−	2.32208i		−	0.138771i
$281$		−	9.27437i		−	0.553263i	−0.960976	−	0.276631i	$-0.910782\pi$
$281$		−	9.27437i		−	0.553263i	0.960976	−	0.276631i	$-0.0892181\pi$
$282$	1.92112			0.114401
$283$	9.60985			0.571247			0.285623	−	0.958342i	$-0.407799\pi$
$283$	9.60985			0.571247			0.285623	+	0.958342i	$0.407799\pi$
$284$			15.7149i			0.932510i
$285$	5.55412			0.328998
$286$	2.52406			0.149251
$287$	−5.07946	−	3.89860i	−0.299831	−	0.230127i
$288$	3.00723			0.177203
$289$	−1.73557			−0.102092
$290$			4.91470i			0.288601i
$291$	−1.56400			−0.0916833
$292$	33.3347			1.95077
$293$			18.9420i			1.10661i	0.832980	+	0.553303i	$0.186633\pi$
$293$			18.9420i			1.10661i	−0.832980	+	0.553303i	$0.813367\pi$
$294$			0.175342i			0.0102261i
$295$	−8.29969			−0.483226
$296$	4.23812			0.246336
$297$	13.9105			0.807171
$298$			1.29215i			0.0748522i
$299$			14.8679i			0.859833i
$300$			22.1422i			1.27838i
$301$		−	4.86001i		−	0.280126i
$302$		−	0.870838i		−	0.0501111i
$303$	12.1753			0.699455
$304$			4.85160i			0.278258i
$305$	16.8938			0.967335
$306$		−	1.10168i		−	0.0629791i
$307$	−16.6844			−0.952232			−0.476116	−	0.879383i	$-0.657956\pi$
$307$	−16.6844			−0.952232			−0.476116	+	0.879383i	$0.657956\pi$
$308$	5.10796			0.291053
$309$			4.42554i			0.251760i
$310$	2.41805			0.137336
$311$		−	20.5409i		−	1.16477i	−0.812913	−	0.582385i	$-0.802120\pi$
$311$		−	20.5409i		−	1.16477i	0.812913	−	0.582385i	$-0.197880\pi$
$312$	4.47593			0.253399
$313$			2.93531i			0.165914i	0.996553	+	0.0829569i	$0.0264364\pi$
$313$			2.93531i			0.165914i	−0.996553	+	0.0829569i	$0.973564\pi$
$314$		−	2.10567i		−	0.118830i
$315$			6.41704i			0.361559i
$316$		−	10.2568i		−	0.576989i
$317$		−	12.0542i		−	0.677033i	−0.940960	−	0.338516i	$-0.890075\pi$
$317$		−	12.0542i		−	0.677033i	0.940960	−	0.338516i	$-0.109925\pi$
$318$	−0.930240			−0.0521652
$319$	−21.7488			−1.21770
$320$	−28.5827			−1.59782
$321$			17.7430i			0.990317i
$322$		−	0.352495i		−	0.0196438i
$323$	5.43817			0.302588
$324$	2.34333			0.130185
$325$		−	62.4006i		−	3.46136i
$326$	2.55504			0.141511
$327$	−0.584350			−0.0323146
$328$	2.35945	−	3.07411i	0.130279	−	0.169739i
$329$	−10.9565			−0.604050
$330$	1.73834			0.0956925
$331$			17.2239i			0.946711i	0.880872	+	0.473355i	$0.156957\pi$
$331$			17.2239i			0.946711i	−0.880872	+	0.473355i	$0.843043\pi$
$332$	−19.8719			−1.09061
$333$	−11.7120			−0.641814
$334$		−	2.34749i		−	0.128449i
$335$			48.8084i			2.66669i
$336$	4.44924			0.242726
$337$	−9.49318			−0.517126			−0.258563	−	0.965994i	$-0.583249\pi$
$337$	−9.49318			−0.517126			−0.258563	+	0.965994i	$0.583249\pi$
$338$	−4.29187			−0.233447
$339$		−	7.61998i		−	0.413860i
$340$			32.8307i			1.78049i
$341$			10.7005i			0.579463i
$342$			0.319774i			0.0172914i
$343$		−	1.00000i		−	0.0539949i
$344$	2.94130			0.158584
$345$			10.2397i			0.551284i
$346$	2.89578			0.155678
$347$		−	22.8196i		−	1.22502i	−0.790464	−	0.612509i	$-0.790160\pi$
$347$		−	22.8196i		−	1.22502i	0.790464	−	0.612509i	$-0.209840\pi$
$348$	−19.1713			−1.02769
$349$	17.0917			0.914896			0.457448	−	0.889236i	$-0.348764\pi$
$349$	17.0917			0.914896			0.457448	+	0.889236i	$0.348764\pi$
$350$			1.47942i			0.0790785i
$351$	−34.5564			−1.84448
$352$			4.64604i			0.247635i
$353$	17.8996			0.952700			0.476350	−	0.879256i	$-0.341960\pi$
$353$	17.8996			0.952700			0.476350	+	0.879256i	$0.341960\pi$
$354$			0.379290i			0.0201591i
$355$		−	30.5011i		−	1.61883i
$356$			7.86766i			0.416985i
$357$		−	4.98717i		−	0.263949i
$358$		−	1.66625i		−	0.0880639i
$359$	0.886477			0.0467865			0.0233932	−	0.999726i	$-0.492553\pi$
$359$	0.886477			0.0467865			0.0233932	+	0.999726i	$0.492553\pi$
$360$	−3.88362			−0.204685
$361$	17.4215			0.916922
$362$		−	0.915919i		−	0.0481397i
$363$		−	4.98142i		−	0.261457i
$364$	−12.6891			−0.665091
$365$	−64.6993			−3.38652
$366$		−	0.772035i		−	0.0403549i
$367$	8.14133			0.424974			0.212487	−	0.977164i	$-0.431844\pi$
$367$	8.14133			0.424974			0.212487	+	0.977164i	$0.431844\pi$
$368$	−8.94447			−0.466263
$369$	−6.52031	+	8.49528i	−0.339434	+	0.442247i
$370$	−4.08893			−0.212573
$371$	5.30530			0.275438
$372$			9.43236i			0.489045i
$373$	22.9783			1.18977			0.594885	−	0.803811i	$-0.297198\pi$
$373$	22.9783			1.18977			0.594885	+	0.803811i	$0.297198\pi$
$374$	1.70205			0.0880110
$375$		−	20.8721i		−	1.07783i
$376$		−	6.63090i		−	0.341963i
$377$	54.0281			2.78259
$378$	0.819279			0.0421392
$379$	4.20559			0.216026			0.108013	−	0.994149i	$-0.465551\pi$
$379$	4.20559			0.216026			0.108013	+	0.994149i	$0.465551\pi$
$380$		−	9.52941i		−	0.488848i
$381$			20.2292i			1.03638i
$382$		−	2.41278i		−	0.123449i
$383$		−	19.1121i		−	0.976582i	−0.872681	−	0.488291i	$-0.837621\pi$
$383$		−	19.1121i		−	0.976582i	0.872681	−	0.488291i	$-0.162379\pi$
$384$			5.44962i			0.278100i
$385$	−9.91403			−0.505266
$386$			1.59715i			0.0812926i
$387$	−8.12825			−0.413182
$388$			2.68341i			0.136230i
$389$	7.90633			0.400867			0.200433	−	0.979707i	$-0.435765\pi$
$389$	7.90633			0.400867			0.200433	+	0.979707i	$0.435765\pi$
$390$	−4.31837			−0.218669
$391$			10.0259i			0.507031i
$392$	0.605204			0.0305674
$393$		−	11.1255i		−	0.561205i
$394$	−0.374922			−0.0188883
$395$			19.9074i			1.00165i
$396$		−	8.54294i		−	0.429299i
$397$			19.7418i			0.990811i	0.868662	+	0.495406i	$0.164981\pi$
$397$			19.7418i			0.990811i	−0.868662	+	0.495406i	$0.835019\pi$
$398$			1.88974i			0.0947241i
$399$			1.44757i			0.0724693i
$400$	37.5400			1.87700
$401$	16.5916			0.828545			0.414273	−	0.910153i	$-0.364036\pi$
$401$	16.5916			0.828545			0.414273	+	0.910153i	$0.364036\pi$
$402$	2.23051			0.111248
$403$		−	26.5820i		−	1.32414i
$404$		−	20.8897i		−	1.03930i
$405$	−4.54817			−0.226001
$406$	−1.28092			−0.0635711
$407$		−	18.0945i		−	0.896912i
$408$	3.01826			0.149426
$409$	1.34855			0.0666814			0.0333407	−	0.999444i	$-0.489385\pi$
$409$	1.34855			0.0666814			0.0333407	+	0.999444i	$0.489385\pi$
$410$	−2.27639	+	2.96590i	−0.112423	+	0.146475i
$411$	−10.1053			−0.498460
$412$	7.59306			0.374083
$413$		−	2.16315i		−	0.106442i
$414$	−0.589540			−0.0289743
$415$	38.5693			1.89329
$416$		−	11.5416i		−	0.565875i
$417$			9.74792i			0.477358i
$418$	−0.494036			−0.0241641
$419$	18.6352			0.910391			0.455196	−	0.890391i	$-0.349569\pi$
$419$	18.6352			0.910391			0.455196	+	0.890391i	$0.349569\pi$
$420$	−8.73911			−0.426425
$421$		−	11.7619i		−	0.573241i	−0.958044	−	0.286620i	$-0.907468\pi$
$421$		−	11.7619i		−	0.573241i	0.958044	−	0.286620i	$-0.0925319\pi$
$422$		−	0.861981i		−	0.0419606i
$423$			18.3244i			0.890965i
$424$			3.21079i			0.155930i
$425$		−	42.0787i		−	2.04112i
$426$	−1.39388			−0.0675338
$427$			4.40304i			0.213078i
$428$	30.4423			1.47148
$429$		−	19.1098i		−	0.922631i
$430$	−2.83776			−0.136849
$431$	0.347093			0.0167189			0.00835943	−	0.999965i	$-0.497339\pi$
$431$	0.347093			0.0167189			0.00835943	+	0.999965i	$0.497339\pi$
$432$		−	20.7890i		−	1.00021i
$433$	25.5193			1.22638			0.613189	−	0.789936i	$-0.289886\pi$
$433$	25.5193			1.22638			0.613189	+	0.789936i	$0.289886\pi$
$434$			0.630218i			0.0302515i
$435$	37.2096			1.78406
$436$			1.00259i			0.0480153i
$437$		−	2.91011i		−	0.139209i
$438$			2.95672i			0.141277i
$439$		−	38.1082i		−	1.81881i	−0.415916	−	0.909403i	$-0.636539\pi$
$439$		−	38.1082i		−	1.81881i	0.415916	−	0.909403i	$-0.363461\pi$
$440$		−	6.00001i		−	0.286039i
$441$	−1.67248			−0.0796417
$442$	−4.22822			−0.201116
$443$	−2.35616			−0.111945			−0.0559723	−	0.998432i	$-0.517826\pi$
$443$	−2.35616			−0.111945			−0.0559723	+	0.998432i	$0.517826\pi$
$444$		−	15.9501i		−	0.756959i
$445$		−	15.2703i		−	0.723883i
$446$	−1.15058			−0.0544817
$447$	9.78296			0.462718
$448$		−	7.44953i		−	0.351957i
$449$	27.2168			1.28444			0.642220	−	0.766520i	$-0.278013\pi$
$449$	27.2168			1.28444			0.642220	+	0.766520i	$0.278013\pi$
$450$	2.47430			0.116640
$451$	−13.1248	−	10.0736i	−0.618024	−	0.474347i
$452$	−13.0739			−0.614943
$453$	−6.59318			−0.309774
$454$			1.93496i			0.0908119i
$455$	24.6283			1.15459
$456$	−0.876078			−0.0410261
$457$			6.20255i			0.290143i	0.989421	+	0.145071i	$0.0463412\pi$
$457$			6.20255i			0.290143i	−0.989421	+	0.145071i	$0.953659\pi$
$458$			3.17119i			0.148180i
$459$	−23.3025			−1.08767
$460$	17.5685			0.819137
$461$	−21.3143			−0.992706			−0.496353	−	0.868121i	$-0.665328\pi$
$461$	−21.3143			−0.992706			−0.496353	+	0.868121i	$0.665328\pi$
$462$			0.453065i			0.0210785i
$463$			28.3635i			1.31817i	0.752071	+	0.659083i	$0.229055\pi$
$463$			28.3635i			1.31817i	−0.752071	+	0.659083i	$0.770945\pi$
$464$			32.5031i			1.50892i
$465$		−	18.3073i		−	0.848979i
$466$			2.12290i			0.0983413i
$467$	36.6502			1.69597			0.847984	−	0.530022i	$-0.177816\pi$
$467$	36.6502			1.69597			0.847984	+	0.530022i	$0.177816\pi$
$468$			21.2223i			0.981000i
$469$	−12.7210			−0.587399
$470$			6.39748i			0.295094i
$471$	−15.9422			−0.734576
$472$	1.30915			0.0602584
$473$		−	12.5578i		−	0.577407i
$474$	0.909754			0.0417864
$475$			12.2137i			0.560405i
$476$	−8.55668			−0.392195
$477$		−	8.87299i		−	0.406266i
$478$		−	0.229575i		−	0.0105005i
$479$			11.9606i			0.546492i	0.961944	+	0.273246i	$0.0880974\pi$
$479$			11.9606i			0.546492i	−0.961944	+	0.273246i	$0.911903\pi$
$480$		−	7.94882i		−	0.362812i
$481$			44.9502i			2.04955i
$482$	1.64198			0.0747903
$483$	−2.66877			−0.121433
$484$	−8.54680			−0.388491
$485$		−	5.20823i		−	0.236494i
$486$		−	2.24999i		−	0.102062i
$487$	6.52996			0.295901			0.147950	−	0.988995i	$-0.452732\pi$
$487$	6.52996			0.295901			0.147950	+	0.988995i	$0.452732\pi$
$488$	−2.66474			−0.120627
$489$		−	19.3444i		−	0.874785i
$490$	−0.583900			−0.0263779
$491$	−23.9296			−1.07993			−0.539963	−	0.841689i	$-0.681562\pi$
$491$	−23.9296			−1.07993			−0.539963	+	0.841689i	$0.681562\pi$
$492$	−11.5694	−	8.87976i	−0.521588	−	0.400331i
$493$	36.4328			1.64085
$494$	1.22728			0.0552179
$495$			16.5810i			0.745260i
$496$	15.9916			0.718045
$497$	7.94952			0.356585
$498$		−	1.76259i		−	0.0789838i
$499$			41.7463i			1.86882i	0.356200	+	0.934410i	$0.384072\pi$
$499$			41.7463i			1.86882i	−0.356200	+	0.934410i	$0.615928\pi$
$500$	−35.8111			−1.60152
$501$	−17.7731			−0.794042
$502$	−0.0522567			−0.00233233
$503$			6.57457i			0.293146i	0.989200	+	0.146573i	$0.0468243\pi$
$503$			6.57457i			0.293146i	−0.989200	+	0.146573i	$0.953176\pi$
$504$		−	1.01219i		−	0.0450865i
$505$			40.5447i			1.80422i
$506$		−	0.910812i		−	0.0404905i
$507$			32.4940i			1.44311i
$508$	34.7080			1.53992
$509$			6.70150i			0.297039i	0.988909	+	0.148519i	$0.0474507\pi$
$509$			6.70150i			0.297039i	−0.988909	+	0.148519i	$0.952549\pi$
$510$	−2.91201			−0.128946
$511$		−	16.8626i		−	0.745958i
$512$	11.6175			0.513425
$513$	6.76376			0.298627
$514$			0.720040i			0.0317596i
$515$	−14.7374			−0.649406
$516$		−	11.0695i		−	0.487309i
$517$	−28.3104			−1.24509
$518$		−	1.06570i		−	0.0468242i
$519$		−	21.9242i		−	0.962364i
$520$			14.9052i			0.653634i
$521$		−	31.2410i		−	1.36869i	−0.729158	−	0.684346i	$-0.760088\pi$
$521$		−	31.2410i		−	1.36869i	0.729158	−	0.684346i	$-0.239912\pi$
$522$			2.14231i			0.0937665i
$523$	−22.3471			−0.977172			−0.488586	−	0.872516i	$-0.662487\pi$
$523$	−22.3471			−0.977172			−0.488586	+	0.872516i	$0.662487\pi$
$524$	−19.0883			−0.833878
$525$	11.2008			0.488844
$526$		−	1.41999i		−	0.0619147i
$527$		−	17.9251i		−	0.780828i
$528$	11.4964			0.500317
$529$	−17.6349			−0.766734
$530$		−	3.09776i		−	0.134558i
$531$	−3.61782			−0.157000
$532$	2.48366			0.107680
$533$	32.6045	+	25.0247i	1.41226	+	1.08394i
$534$	−0.697844			−0.0301987
$535$	−59.0854			−2.55448
$536$		−	7.69877i		−	0.332536i
$537$	−12.6153			−0.544390
$538$	−1.06060			−0.0457255
$539$		−	2.58390i		−	0.111296i
$540$			40.8333i			1.75719i
$541$	−23.9496			−1.02967			−0.514837	−	0.857288i	$-0.672148\pi$
$541$	−23.9496			−1.02967			−0.514837	+	0.857288i	$0.672148\pi$
$542$	−3.89291			−0.167215
$543$	−6.93449			−0.297588
$544$		−	7.78288i		−	0.333688i
$545$		−	1.94593i		−	0.0833543i
$546$		−	1.12550i		−	0.0481669i
$547$		−	43.7723i		−	1.87157i	−0.352575	−	0.935784i	$-0.614694\pi$
$547$		−	43.7723i		−	1.87157i	0.352575	−	0.935784i	$-0.385306\pi$
$548$			17.3381i			0.740647i
$549$	7.36397			0.314287
$550$			3.82268i			0.163000i
$551$	−10.5750			−0.450509
$552$		−	1.61515i		−	0.0687453i
$553$	−5.18847			−0.220636
$554$	−0.0483139			−0.00205266
$555$			30.9576i			1.31408i
$556$	16.7249			0.709292
$557$			28.1854i			1.19426i	0.802146	+	0.597128i	$0.203691\pi$
$557$			28.1854i			1.19426i	−0.802146	+	0.597128i	$0.796309\pi$
$558$	1.05403			0.0446205
$559$			31.1959i			1.31944i
$560$			14.8163i			0.626103i
$561$		−	12.8864i		−	0.544063i
$562$		−	1.41139i		−	0.0595360i
$563$		−	0.653830i		−	0.0275557i	−0.999905	−	0.0137778i	$-0.995614\pi$
$563$		−	0.653830i		−	0.0275557i	0.999905	−	0.0137778i	$-0.00438576\pi$
$564$	−24.9553			−1.05081
$565$	25.3751			1.06754
$566$	1.46245			0.0614713
$567$		−	1.18539i		−	0.0497819i
$568$			4.81108i			0.201869i
$569$	0.872585			0.0365806			0.0182903	−	0.999833i	$-0.494178\pi$
$569$	0.872585			0.0365806			0.0182903	+	0.999833i	$0.494178\pi$
$570$	0.845238			0.0354031
$571$		−	33.2535i		−	1.39161i	−0.718228	−	0.695807i	$-0.755047\pi$
$571$		−	33.2535i		−	1.39161i	0.718228	−	0.695807i	$-0.244953\pi$
$572$	−32.7874			−1.37091
$573$	−18.2673			−0.763129
$574$	−0.773003	−	0.593297i	−0.0322645	−	0.0247637i
$575$	−22.5174			−0.939041
$576$	−12.4592			−0.519131
$577$		−	20.8403i		−	0.867594i	−0.901011	−	0.433797i	$-0.857173\pi$
$577$		−	20.8403i		−	0.867594i	0.901011	−	0.433797i	$-0.142827\pi$
$578$	−0.264123			−0.0109861
$579$	12.0921			0.502531
$580$		−	63.8419i		−	2.65089i
$581$			10.0524i			0.417042i
$582$	−0.238013			−0.00986595
$583$	13.7084			0.567743
$584$	10.2053			0.422299
$585$		−	41.1903i		−	1.70301i
$586$			2.88264i			0.119081i
$587$		−	12.8489i		−	0.530330i	−0.964203	−	0.265165i	$-0.914574\pi$
$587$		−	12.8489i		−	0.530330i	0.964203	−	0.265165i	$-0.0854264\pi$
$588$		−	2.27768i		−	0.0939300i
$589$			5.20292i			0.214383i
$590$	−1.26306			−0.0519995
$591$			2.83856i			0.116763i
$592$	−27.0418			−1.11141
$593$		−	17.8369i		−	0.732472i	−0.930522	−	0.366236i	$-0.880646\pi$
$593$		−	17.8369i		−	0.732472i	0.930522	−	0.366236i	$-0.119354\pi$
$594$	2.11693			0.0868589
$595$	16.6076			0.680847
$596$		−	16.7850i		−	0.687540i
$597$	14.3074			0.585561
$598$			2.26263i			0.0925257i
$599$	23.5371			0.961700			0.480850	−	0.876803i	$-0.340328\pi$
$599$	23.5371			0.961700			0.480850	+	0.876803i	$0.340328\pi$
$600$			6.77878i			0.276743i
$601$		−	27.4331i		−	1.11902i	−0.828824	−	0.559509i	$-0.810990\pi$
$601$		−	27.4331i		−	1.11902i	0.828824	−	0.559509i	$-0.189010\pi$
$602$		−	0.739606i		−	0.0301441i
$603$			21.2755i			0.866405i
$604$			11.3122i			0.460285i
$605$	16.5885			0.674417
$606$	1.85287			0.0752676
$607$	2.96417			0.120312			0.0601561	−	0.998189i	$-0.480840\pi$
$607$	2.96417			0.120312			0.0601561	+	0.998189i	$0.480840\pi$
$608$			2.25905i			0.0916167i
$609$			9.69796i			0.392981i
$610$	2.57093			0.104094
$611$	70.3284			2.84518
$612$			14.3108i			0.578481i
$613$	6.10886			0.246734			0.123367	−	0.992361i	$-0.460631\pi$
$613$	6.10886			0.246734			0.123367	+	0.992361i	$0.460631\pi$
$614$	−2.53907			−0.102469
$615$	22.4550	+	17.2347i	0.905474	+	0.694971i
$616$	1.56379			0.0630067
$617$	17.8438			0.718364			0.359182	−	0.933267i	$-0.383056\pi$
$617$	17.8438			0.718364			0.359182	+	0.933267i	$0.383056\pi$
$618$			0.673488i			0.0270917i
$619$	−35.7481			−1.43684			−0.718418	−	0.695611i	$-0.755134\pi$
$619$	−35.7481			−1.43684			−0.718418	+	0.695611i	$0.755134\pi$
$620$	−31.4104			−1.26147
$621$			12.4697i			0.500394i
$622$		−	3.12596i		−	0.125340i
$623$	3.97992			0.159452
$624$	−28.5592			−1.14328
$625$	20.8986			0.835946
$626$			0.446702i			0.0178538i
$627$			3.74039i			0.149377i
$628$			27.3525i			1.09149i
$629$			30.3113i			1.20859i
$630$			0.976558i			0.0389070i
$631$	6.11265			0.243341			0.121670	−	0.992571i	$-0.461175\pi$
$631$	6.11265			0.243341			0.121670	+	0.992571i	$0.461175\pi$
$632$		−	3.14008i		−	0.124906i
$633$	−6.52612			−0.259390
$634$		−	1.83444i		−	0.0728548i
$635$	−67.3648			−2.67329
$636$	12.0838			0.479153
$637$			6.41889i			0.254326i
$638$	−3.30978			−0.131035
$639$		−	13.2954i		−	0.525957i
$640$	−18.1476			−0.717348
$641$			3.78746i			0.149596i	0.997199	+	0.0747978i	$0.0238311\pi$
$641$			3.78746i			0.149596i	−0.997199	+	0.0747978i	$0.976169\pi$
$642$			2.70016i			0.106567i
$643$		−	13.4051i		−	0.528645i	−0.964434	−	0.264322i	$-0.914852\pi$
$643$		−	13.4051i		−	0.528645i	0.964434	−	0.264322i	$-0.0851483\pi$
$644$			4.57890i			0.180434i
$645$			21.4849i			0.845966i
$646$	0.827593			0.0325612
$647$	25.5383			1.00402			0.502008	−	0.864863i	$-0.332595\pi$
$647$	25.5383			1.00402			0.502008	+	0.864863i	$0.332595\pi$
$648$	0.717405			0.0281823
$649$		−	5.58937i		−	0.219402i
$650$		−	9.49626i		−	0.372474i
$651$	4.77143			0.187007
$652$	−33.1899			−1.29982
$653$			30.8321i			1.20655i	0.797531	+	0.603277i	$0.206139\pi$
$653$			30.8321i			1.20655i	−0.797531	+	0.603277i	$0.793861\pi$
$654$	−0.0889276			−0.00347734
$655$	37.0485			1.44761
$656$	−15.0547	+	19.6147i	−0.587789	+	0.765827i
$657$	−28.2023			−1.10028
$658$	−1.66738			−0.0650012
$659$		−	22.1897i		−	0.864387i	−0.901781	−	0.432193i	$-0.857740\pi$
$659$		−	22.1897i		−	0.864387i	0.901781	−	0.432193i	$-0.142260\pi$
$660$	−22.5810			−0.878964
$661$	−48.6668			−1.89292			−0.946460	−	0.322821i	$-0.895369\pi$
$661$	−48.6668			−1.89292			−0.946460	+	0.322821i	$0.895369\pi$
$662$			2.62117i			0.101875i
$663$			32.0121i			1.24325i
$664$	−6.08372			−0.236094
$665$	−4.82052			−0.186932
$666$	−1.78236			−0.0690650
$667$		−	19.4961i		−	0.754894i
$668$			30.4939i			1.17984i
$669$			8.71116i			0.336793i
$670$			7.42776i			0.286959i
$671$			11.3770i			0.439204i
$672$	2.07171			0.0799178
$673$		−	14.9842i		−	0.577600i	−0.957389	−	0.288800i	$-0.906744\pi$
$673$		−	14.9842i		−	0.577600i	0.957389	−	0.288800i	$-0.0932563\pi$
$674$	−1.44469			−0.0556474
$675$		−	52.3356i		−	2.01440i
$676$	55.7512			2.14428
$677$	11.5573			0.444182			0.222091	−	0.975026i	$-0.428712\pi$
$677$	11.5573			0.444182			0.222091	+	0.975026i	$0.428712\pi$
$678$		−	1.15962i		−	0.0445351i
$679$	1.35742			0.0520932
$680$			10.0510i			0.385439i
$681$	14.6497			0.561377
$682$			1.62842i			0.0623555i
$683$		−	32.5413i		−	1.24516i	−0.782556	−	0.622580i	$-0.786085\pi$
$683$		−	32.5413i		−	1.24516i	0.782556	−	0.622580i	$-0.213915\pi$
$684$		−	4.15385i		−	0.158827i
$685$		−	33.6515i		−	1.28576i
$686$		−	0.152182i		−	0.00581034i
$687$	24.0093			0.916013
$688$	−18.7673			−0.715497
$689$	−34.0542			−1.29736
$690$			1.55829i			0.0593231i
$691$			38.5148i			1.46517i	0.680675	+	0.732585i	$0.261686\pi$
$691$			38.5148i			1.46517i	−0.680675	+	0.732585i	$0.738314\pi$
$692$	−37.6161			−1.42995
$693$	−4.32151			−0.164161
$694$		−	3.47273i		−	0.131823i
$695$	−32.4613			−1.23133
$696$	−5.86924			−0.222473
$697$	21.9863	+	16.8749i	0.832789	+	0.639184i
$698$	2.60105			0.0984511
$699$	16.0726			0.607922
$700$		−	19.2177i		−	0.726359i
$701$	−23.3722			−0.882754			−0.441377	−	0.897322i	$-0.645510\pi$
$701$	−23.3722			−0.882754			−0.441377	+	0.897322i	$0.645510\pi$
$702$	−5.25886			−0.198483
$703$		−	8.79814i		−	0.331828i
$704$		−	19.2488i		−	0.725467i
$705$	48.4358			1.82420
$706$	2.72400			0.102519
$707$	−10.5672			−0.397420
$708$		−	4.92697i		−	0.185167i
$709$			51.2637i			1.92525i	0.270842	+	0.962624i	$0.412698\pi$
$709$			51.2637i			1.92525i	−0.270842	+	0.962624i	$0.587302\pi$
$710$		−	4.64172i		−	0.174201i
$711$			8.67759i			0.325435i
$712$			2.40866i			0.0902684i
$713$	−9.59217			−0.359230
$714$		−	0.758959i		−	0.0284033i
$715$	63.6371			2.37989
$716$			21.6445i			0.808893i
$717$	−1.73813			−0.0649117
$718$	0.134906			0.00503465
$719$		−	30.5814i		−	1.14049i	−0.821474	−	0.570246i	$-0.806848\pi$
$719$		−	30.5814i		−	1.14049i	0.821474	−	0.570246i	$-0.193152\pi$
$720$	24.7799			0.923492
$721$		−	3.84101i		−	0.143047i
$722$	2.65124			0.0986691
$723$		−	12.4316i		−	0.462335i
$724$			11.8978i			0.442177i
$725$			81.8254i			3.03892i
$726$		−	0.758082i		−	0.0281351i
$727$			8.80979i			0.326737i	0.986565	+	0.163369i	$0.0522360\pi$
$727$			8.80979i			0.326737i	−0.986565	+	0.163369i	$0.947764\pi$
$728$	−3.88474			−0.143978
$729$	−20.5910			−0.762630
$730$	−9.84607			−0.364420
$731$			21.0364i			0.778058i
$732$			10.0287i			0.370672i
$733$	−9.38730			−0.346728			−0.173364	−	0.984858i	$-0.555464\pi$
$733$	−9.38730			−0.346728			−0.173364	+	0.984858i	$0.555464\pi$
$734$	1.23897			0.0457310
$735$			4.42075i			0.163062i
$736$	−4.16482			−0.153517
$737$	−32.8697			−1.21077
$738$	−0.992275	+	1.29283i	−0.0365261	+	0.0475897i
$739$	−21.5329			−0.792099			−0.396049	−	0.918229i	$-0.629619\pi$
$739$	−21.5329			−0.792099			−0.396049	+	0.918229i	$0.629619\pi$
$740$	53.1150			1.95255
$741$		−	9.29182i		−	0.341344i
$742$	0.807372			0.0296396
$743$	−31.6510			−1.16116			−0.580580	−	0.814203i	$-0.697174\pi$
$743$	−31.6510			−1.16116			−0.580580	+	0.814203i	$0.697174\pi$
$744$			2.88769i			0.105868i
$745$			32.5780i			1.19356i
$746$	3.49688			0.128030
$747$	16.8123			0.615131
$748$	−22.1096			−0.808407
$749$		−	15.3995i		−	0.562684i
$750$		−	3.17636i		−	0.115984i
$751$		−	15.7820i		−	0.575893i	−0.957646	−	0.287947i	$-0.907027\pi$
$751$		−	15.7820i		−	0.575893i	0.957646	−	0.287947i	$-0.0929725\pi$
$752$			42.3093i			1.54286i
$753$			0.395639i			0.0144179i
$754$	8.22210			0.299431
$755$		−	21.9557i		−	0.799051i
$756$	−10.6424			−0.387061
$757$		−	22.9352i		−	0.833593i	−0.909000	−	0.416797i	$-0.863153\pi$
$757$		−	22.9352i		−	0.833593i	0.909000	−	0.416797i	$-0.136847\pi$
$758$	0.640015			0.0232464
$759$	−6.89582			−0.250303
$760$		−	2.91740i		−	0.105825i
$761$	10.1148			0.366662			0.183331	−	0.983051i	$-0.441312\pi$
$761$	10.1148			0.366662			0.183331	+	0.983051i	$0.441312\pi$
$762$			3.07853i			0.111523i
$763$	0.507168			0.0183607
$764$			31.3419i			1.13391i
$765$		−	27.7759i		−	1.00424i
$766$		−	2.90852i		−	0.105089i
$767$			13.8850i			0.501360i
$768$		−	16.3371i		−	0.589514i
$769$	−15.6290			−0.563595			−0.281797	−	0.959474i	$-0.590931\pi$
$769$	−15.6290			−0.563595			−0.281797	+	0.959474i	$0.590931\pi$
$770$	−1.50874			−0.0543711
$771$	5.45147			0.196330
$772$		−	20.7469i		−	0.746697i
$773$		−	40.6026i		−	1.46037i	−0.683248	−	0.730186i	$-0.739433\pi$
$773$		−	40.6026i		−	1.46037i	0.683248	−	0.730186i	$-0.260567\pi$
$774$	−1.23697			−0.0444621
$775$	40.2584			1.44612
$776$			0.821519i			0.0294908i
$777$	−8.06849			−0.289456
$778$	1.20320			0.0431369
$779$	−6.38171	−	4.89811i	−0.228649	−	0.175493i
$780$	56.0954			2.00854
$781$	20.5408			0.735006
$782$			1.52576i			0.0545611i
$783$	45.3135			1.61937
$784$	−3.86158			−0.137914
$785$		−	53.0885i		−	1.89481i
$786$		−	1.69309i		−	0.0603907i
$787$	−34.4656			−1.22857			−0.614283	−	0.789086i	$-0.710555\pi$
$787$	−34.4656			−1.22857			−0.614283	+	0.789086i	$0.710555\pi$
$788$	4.87022			0.173494
$789$	−10.7509			−0.382741
$790$			3.02954i			0.107786i
$791$			6.61352i			0.235150i
$792$		−	2.61540i		−	0.0929340i
$793$		−	28.2626i		−	1.00363i
$794$			3.00434i			0.106620i
$795$	−23.4534			−0.831806
$796$		−	24.5477i		−	0.870069i
$797$	−31.2074			−1.10542			−0.552712	−	0.833373i	$-0.686407\pi$
$797$	−31.2074			−1.10542			−0.552712	+	0.833373i	$0.686407\pi$
$798$			0.220295i			0.00779835i
$799$	47.4247			1.67776
$800$	17.4798			0.618003
$801$		−	6.65631i		−	0.235189i
$802$	2.52494			0.0891589
$803$		−	43.5713i		−	1.53760i
$804$	−28.9743			−1.02184
$805$		−	8.88718i		−	0.313232i
$806$		−	4.04530i		−	0.142490i
$807$			8.02985i			0.282664i
$808$		−	6.39531i		−	0.224986i
$809$		−	35.0454i		−	1.23213i	−0.787695	−	0.616065i	$-0.788726\pi$
$809$		−	35.0454i		−	1.23213i	0.787695	−	0.616065i	$-0.211274\pi$
$810$	−0.692151			−0.0243197
$811$	37.5838			1.31974			0.659872	−	0.751378i	$-0.270610\pi$
$811$	37.5838			1.31974			0.659872	+	0.751378i	$0.270610\pi$
$812$	16.6391			0.583919
$813$			29.4735i			1.03368i
$814$		−	2.75366i		−	0.0965158i
$815$	64.4183			2.25647
$816$	−19.2584			−0.674178
$817$		−	6.10600i		−	0.213622i
$818$	0.205225			0.00717552
$819$	10.7354			0.375127
$820$	29.5702	−	38.5269i	1.03264	−	1.34542i
$821$	−12.6805			−0.442551			−0.221275	−	0.975211i	$-0.571022\pi$
$821$	−12.6805			−0.442551			−0.221275	+	0.975211i	$0.571022\pi$
$822$	−1.53785			−0.0536387
$823$			44.7359i			1.55940i	0.626156	+	0.779698i	$0.284627\pi$
$823$			44.7359i			1.55940i	−0.626156	+	0.779698i	$0.715373\pi$
$824$	2.32459			0.0809810
$825$	28.9418			1.00762
$826$		−	0.329193i		−	0.0114541i
$827$			6.07233i			0.211156i	0.994411	+	0.105578i	$0.0336692\pi$
$827$			6.07233i			0.211156i	−0.994411	+	0.105578i	$0.966331\pi$
$828$	7.65810			0.266137
$829$	−8.80019			−0.305643			−0.152822	−	0.988254i	$-0.548836\pi$
$829$	−8.80019			−0.305643			−0.152822	+	0.988254i	$0.548836\pi$
$830$	5.86957			0.203736
$831$			0.365788i			0.0126890i
$832$			47.8177i			1.65778i
$833$			4.32846i			0.149972i
$834$			1.48346i			0.0513680i
$835$		−	59.1855i		−	2.04820i
$836$	6.41752			0.221954
$837$		−	22.2944i		−	0.770607i
$838$	2.83595			0.0979663
$839$			12.1219i			0.418494i	0.977863	+	0.209247i	$0.0671013\pi$
$839$			12.1219i			0.418494i	−0.977863	+	0.209247i	$0.932899\pi$
$840$	−2.67545			−0.0923119
$841$	−41.8465			−1.44298
$842$		−	1.78995i		−	0.0616859i
$843$	−10.6858			−0.368037
$844$			11.1971i			0.385420i
$845$	−108.207			−3.72245
$846$			2.78865i			0.0958758i
$847$			4.32346i			0.148556i
$848$		−	20.4868i		−	0.703521i
$849$		−	11.0723i		−	0.380000i
$850$		−	6.40363i		−	0.219643i
$851$	16.2204			0.556027
$852$	18.1065			0.620317
$853$	−29.3580			−1.00520			−0.502599	−	0.864520i	$-0.667623\pi$
$853$	−29.3580			−1.00520			−0.502599	+	0.864520i	$0.667623\pi$
$854$			0.670063i			0.0229291i
$855$			8.06221i			0.275722i
$856$	9.31982			0.318545
$857$	15.3461			0.524212			0.262106	−	0.965039i	$-0.415583\pi$
$857$	15.3461			0.524212			0.262106	+	0.965039i	$0.415583\pi$
$858$		−	2.90817i		−	0.0992834i
$859$	36.7415			1.25360			0.626802	−	0.779179i	$-0.284364\pi$
$859$	36.7415			1.25360			0.626802	+	0.779179i	$0.284364\pi$
$860$	36.8624			1.25700
$861$	−4.49190	+	5.85246i	−0.153083	+	0.199451i
$862$	0.0528213			0.00179910
$863$	−56.8877			−1.93648			−0.968240	−	0.250024i	$-0.919562\pi$
$863$	−56.8877			−1.93648			−0.968240	+	0.250024i	$0.919562\pi$
$864$		−	9.68000i		−	0.329320i
$865$	73.0090			2.48238
$866$	3.88358			0.131969
$867$			1.99970i			0.0679132i
$868$		−	8.18652i		−	0.277868i
$869$	−13.4065			−0.454784
$870$	5.66264			0.191981
$871$	81.6544			2.76675
$872$			0.306940i			0.0103943i
$873$		−	2.27026i		−	0.0768367i
$874$		−	0.442866i		−	0.0149802i
$875$			18.1153i			0.612409i
$876$		−	38.4076i		−	1.29767i
$877$	−52.5985			−1.77612			−0.888062	−	0.459723i	$-0.847949\pi$
$877$	−52.5985			−1.77612			−0.888062	+	0.459723i	$0.847949\pi$
$878$		−	5.79939i		−	0.195720i
$879$	21.8247			0.736128
$880$			38.2838i			1.29055i
$881$	30.7563			1.03621			0.518104	−	0.855318i	$-0.326638\pi$
$881$	30.7563			1.03621			0.518104	+	0.855318i	$0.326638\pi$
$882$	−0.254521			−0.00857017
$883$			43.9228i			1.47812i	0.673640	+	0.739059i	$0.264730\pi$
$883$			43.9228i			1.47812i	−0.673640	+	0.739059i	$0.735270\pi$
$884$	54.9244			1.84731
$885$			9.56275i			0.321448i
$886$	−0.358566			−0.0120463
$887$			24.1037i			0.809325i	0.914466	+	0.404662i	$0.132611\pi$
$887$			24.1037i			0.809325i	−0.914466	+	0.404662i	$0.867389\pi$
$888$		−	4.88308i		−	0.163866i
$889$		−	17.5573i		−	0.588854i
$890$		−	2.32387i		−	0.0778963i
$891$		−	3.06294i		−	0.102612i
$892$	14.9460			0.500431
$893$	−13.7655			−0.460643
$894$	1.48879			0.0497926
$895$		−	42.0098i		−	1.40423i
$896$		−	4.72983i		−	0.158012i
$897$	17.1305			0.571972
$898$	4.14191			0.138217
$899$			34.8567i			1.16254i
$900$	−32.1411			−1.07137
$901$	−22.9638			−0.765035
$902$	−1.99736	−	1.53302i	−0.0665049	−	0.0510440i
$903$	−5.59961			−0.186343
$904$	−4.00253			−0.133122
$905$		−	23.0924i		−	0.767616i
$906$	−1.00336			−0.0333345
$907$	−25.4769			−0.845947			−0.422973	−	0.906142i	$-0.639014\pi$
$907$	−25.4769			−0.845947			−0.422973	+	0.906142i	$0.639014\pi$
$908$		−	25.1350i		−	0.834134i
$909$			17.6734i			0.586189i
$910$	3.74799			0.124245
$911$	−57.5479			−1.90665			−0.953324	−	0.301949i	$-0.902363\pi$
$911$	−57.5479			−1.90665			−0.953324	+	0.301949i	$0.902363\pi$
$912$	5.58992			0.185101
$913$			25.9743i			0.859623i
$914$			0.943917i			0.0312220i
$915$		−	19.4647i		−	0.643483i
$916$		−	41.1937i		−	1.36108i
$917$			9.65598i			0.318869i
$918$	−3.54622			−0.117043
$919$		−	40.3901i		−	1.33235i	−0.745797	−	0.666173i	$-0.767931\pi$
$919$		−	40.3901i		−	1.33235i	0.745797	−	0.666173i	$-0.232069\pi$
$920$	5.37856			0.177326
$921$			19.2235i			0.633437i
$922$	−3.24365			−0.106824
$923$	−51.0271			−1.67958
$924$		−	5.88530i		−	0.193612i
$925$	−68.0770			−2.23836
$926$			4.31642i			0.141846i
$927$	−6.42400			−0.210992
$928$			15.1344i			0.496812i
$929$		−	5.25733i		−	0.172488i	−0.996274	−	0.0862438i	$-0.972514\pi$
$929$		−	5.25733i		−	0.172488i	0.996274	−	0.0862438i	$-0.0274864\pi$
$930$		−	2.78604i		−	0.0913577i
$931$		−	1.25638i		−	0.0411761i
$932$		−	27.5764i		−	0.903293i
$933$	−23.6669			−0.774820
$934$	5.57750			0.182501
$935$	42.9125			1.40339
$936$			6.49713i			0.212365i
$937$			13.2644i			0.433330i	0.976246	+	0.216665i	$0.0695179\pi$
$937$			13.2644i			0.433330i	−0.976246	+	0.216665i	$0.930482\pi$
$938$	−1.93590			−0.0632094
$939$	3.38202			0.110368
$940$		−	83.1031i		−	2.71052i
$941$	20.8432			0.679468			0.339734	−	0.940521i	$-0.389663\pi$
$941$	20.8432			0.679468			0.339734	+	0.940521i	$0.389663\pi$
$942$	−2.42611			−0.0790470
$943$	9.03021	−	11.7654i	0.294064	−	0.383135i
$944$	−8.35318			−0.271873
$945$	20.6558			0.671934
$946$		−	1.91107i		−	0.0621342i
$947$	52.5092			1.70632			0.853160	−	0.521649i	$-0.174683\pi$
$947$	52.5092			1.70632			0.853160	+	0.521649i	$0.174683\pi$
$948$	−11.8177			−0.383820
$949$			108.239i			3.51360i
$950$			1.85871i			0.0603046i
$951$	−13.8887			−0.450371
$952$	−2.61960			−0.0849018
$953$	20.5614			0.666049			0.333025	−	0.942918i	$-0.391931\pi$
$953$	20.5614			0.666049			0.333025	+	0.942918i	$0.391931\pi$
$954$		−	1.35031i		−	0.0437179i
$955$		−	60.8315i		−	1.96846i
$956$			2.98217i			0.0964504i
$957$			25.0586i			0.810028i
$958$			1.82018i			0.0588075i
$959$	8.77061			0.283218
$960$			32.9325i			1.06289i
$961$	−13.8504			−0.446786
$962$			6.84061i			0.220550i
$963$	−25.7552			−0.829951
$964$	−21.3293			−0.686971
$965$			40.2676i			1.29626i
$966$	−0.406138			−0.0130673
$967$		−	26.8053i		−	0.862000i	−0.902352	−	0.431000i	$-0.858161\pi$
$967$		−	26.8053i		−	0.862000i	0.902352	−	0.431000i	$-0.141839\pi$
$968$	−2.61658			−0.0841000
$969$		−	6.26577i		−	0.201285i
$970$		−	0.792600i		−	0.0254488i
$971$			36.0958i			1.15837i	0.815196	+	0.579185i	$0.196629\pi$
$971$			36.0958i			1.15837i	−0.815196	+	0.579185i	$0.803371\pi$
$972$			29.2273i			0.937465i
$973$		−	8.46040i		−	0.271228i
$974$	0.993744			0.0318416
$975$	−71.8969			−2.30254
$976$	17.0027			0.544242
$977$			4.43052i			0.141745i	0.997485	+	0.0708724i	$0.0225783\pi$
$977$			4.43052i			0.141745i	−0.997485	+	0.0708724i	$0.977422\pi$
$978$		−	2.94387i		−	0.0941347i
$979$	10.2837			0.328669
$980$	7.58484			0.242289
$981$		−	0.848226i		−	0.0270818i
$982$	−3.64165			−0.116210
$983$	39.9452			1.27406			0.637028	−	0.770841i	$-0.280164\pi$
$983$	39.9452			1.27406			0.637028	+	0.770841i	$0.280164\pi$
$984$	−3.54194	−	2.71851i	−0.112913	−	0.0866630i
$985$	−9.45261			−0.301185
$986$	5.54442			0.176570
$987$			12.6239i			0.401822i
$988$	−15.9423			−0.507193
$989$	11.2571			0.357955
$990$			2.52333i			0.0801966i
$991$		−	20.0542i		−	0.637044i	−0.947916	−	0.318522i	$-0.896814\pi$
$991$		−	20.0542i		−	0.637044i	0.947916	−	0.318522i	$-0.103186\pi$
$992$	7.44619			0.236417
$993$	19.8451			0.629764
$994$	1.20977			0.0383717
$995$			47.6445i			1.51043i
$996$			22.8960i			0.725489i
$997$			5.20641i			0.164889i	0.996596	+	0.0824443i	$0.0262727\pi$
$997$			5.20641i			0.164889i	−0.996596	+	0.0824443i	$0.973727\pi$
$998$			6.35304i			0.201102i
$999$			37.6998i			1.19277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.b.204.7	✓	12
41.40	even	2	inner	287.2.c.b.204.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.b.204.7	✓	12	1.1	even	1	trivial
287.2.c.b.204.8	yes	12	41.40	even	2	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.152182 q^{2} -1.15218i q^{3} -1.97684 q^{4} +3.83685 q^{5} -0.175342i q^{6} +1.00000i q^{7} -0.605204 q^{8} +1.67248 q^{9} +O(q^{10})\)	\(q+0.152182 q^{2} -1.15218i q^{3} -1.97684 q^{4} +3.83685 q^{5} -0.175342i q^{6} +1.00000i q^{7} -0.605204 q^{8} +1.67248 q^{9} +0.583900 q^{10} +2.58390i q^{11} +2.27768i q^{12} -6.41889i q^{13} +0.152182i q^{14} -4.42075i q^{15} +3.86158 q^{16} -4.32846i q^{17} +0.254521 q^{18} +1.25638i q^{19} -7.58484 q^{20} +1.15218 q^{21} +0.393223i q^{22} -2.31627 q^{23} +0.697305i q^{24} +9.72140 q^{25} -0.976841i q^{26} -5.38354i q^{27} -1.97684i q^{28} +8.41704i q^{29} -0.672759i q^{30} +4.14121 q^{31} +1.79807 q^{32} +2.97712 q^{33} -0.658714i q^{34} +3.83685i q^{35} -3.30622 q^{36} -7.00279 q^{37} +0.191198i q^{38} -7.39573 q^{39} -2.32208 q^{40} +(-3.89860 + 5.07946i) q^{41} +0.175342 q^{42} -4.86001 q^{43} -5.10796i q^{44} +6.41704 q^{45} -0.352495 q^{46} +10.9565i q^{47} -4.44924i q^{48} -1.00000 q^{49} +1.47942 q^{50} -4.98717 q^{51} +12.6891i q^{52} -5.30530i q^{53} -0.819279i q^{54} +9.91403i q^{55} -0.605204i q^{56} +1.44757 q^{57} +1.28092i q^{58} -2.16315 q^{59} +8.73911i q^{60} +4.40304 q^{61} +0.630218 q^{62} +1.67248i q^{63} -7.44953 q^{64} -24.6283i q^{65} +0.453065 q^{66} +12.7210i q^{67} +8.55668i q^{68} +2.66877i q^{69} +0.583900i q^{70} -7.94952i q^{71} -1.01219 q^{72} -16.8626 q^{73} -1.06570 q^{74} -11.2008i q^{75} -2.48366i q^{76} -2.58390 q^{77} -1.12550 q^{78} +5.18847i q^{79} +14.8163 q^{80} -1.18539 q^{81} +(-0.593297 + 0.773003i) q^{82} +10.0524 q^{83} -2.27768 q^{84} -16.6076i q^{85} -0.739606 q^{86} +9.69796 q^{87} -1.56379i q^{88} -3.97992i q^{89} +0.976558 q^{90} +6.41889 q^{91} +4.57890 q^{92} -4.77143i q^{93} +1.66738i q^{94} +4.82052i q^{95} -2.07171i q^{96} -1.35742i q^{97} -0.152182 q^{98} +4.32151i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more