LMFDB - Embedded newform 1290.2.c.c.1031.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1290,2,Mod(1031,1290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1290.1031");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1290 = 2 \cdot 3 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1290.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:	$10.3007018607$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1031.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	1290.1031
Dual form			1290.2.c.c.1031.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(1.00000 + 1.41421i) q^{6} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(1.00000 + 1.41421i) q^{6} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000 q^{10} -1.41421i q^{11} +(-1.00000 - 1.41421i) q^{12} +2.00000 q^{13} +(-1.00000 - 1.41421i) q^{15} +1.00000 q^{16} +7.07107i q^{17} +(1.00000 - 2.82843i) q^{18} -4.24264i q^{19} +1.00000 q^{20} +1.41421i q^{22} +2.82843i q^{23} +(1.00000 + 1.41421i) q^{24} +1.00000 q^{25} -2.00000 q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 1.41421i) q^{30} +8.00000 q^{31} -1.00000 q^{32} +(-2.00000 + 1.41421i) q^{33} -7.07107i q^{34} +(-1.00000 + 2.82843i) q^{36} +4.24264i q^{37} +4.24264i q^{38} +(-2.00000 - 2.82843i) q^{39} -1.00000 q^{40} +2.82843i q^{41} +(-5.00000 + 4.24264i) q^{43} -1.41421i q^{44} +(-1.00000 + 2.82843i) q^{45} -2.82843i q^{46} +2.82843i q^{47} +(-1.00000 - 1.41421i) q^{48} +7.00000 q^{49} -1.00000 q^{50} +(10.0000 - 7.07107i) q^{51} +2.00000 q^{52} -1.41421i q^{53} +(-5.00000 + 1.41421i) q^{54} -1.41421i q^{55} +(-6.00000 + 4.24264i) q^{57} -1.41421i q^{59} +(-1.00000 - 1.41421i) q^{60} -8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +(2.00000 - 1.41421i) q^{66} -4.00000 q^{67} +7.07107i q^{68} +(4.00000 - 2.82843i) q^{69} +12.0000 q^{71} +(1.00000 - 2.82843i) q^{72} +4.24264i q^{73} -4.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} -4.24264i q^{76} +(2.00000 + 2.82843i) q^{78} +8.00000 q^{79} +1.00000 q^{80} +(-7.00000 - 5.65685i) q^{81} -2.82843i q^{82} -14.1421i q^{83} +7.07107i q^{85} +(5.00000 - 4.24264i) q^{86} +1.41421i q^{88} +(1.00000 - 2.82843i) q^{90} +2.82843i q^{92} +(-8.00000 - 11.3137i) q^{93} -2.82843i q^{94} -4.24264i q^{95} +(1.00000 + 1.41421i) q^{96} +2.00000 q^{97} -7.00000 q^{98} +(4.00000 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 2 q^{20} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 10 q^{27} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 2 q^{36} - 4 q^{39} - 2 q^{40} - 10 q^{43} - 2 q^{45} - 2 q^{48} + 14 q^{49} - 2 q^{50} + 20 q^{51} + 4 q^{52} - 10 q^{54} - 12 q^{57} - 2 q^{60} - 16 q^{62} + 2 q^{64} + 4 q^{65} + 4 q^{66} - 8 q^{67} + 8 q^{69} + 24 q^{71} + 2 q^{72} - 2 q^{75} + 4 q^{78} + 16 q^{79} + 2 q^{80} - 14 q^{81} + 10 q^{86} + 2 q^{90} - 16 q^{93} + 2 q^{96} + 4 q^{97} - 14 q^{98} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 2 * q^20 + 2 * q^24 + 2 * q^25 - 4 * q^26 + 10 * q^27 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^36 - 4 * q^39 - 2 * q^40 - 10 * q^43 - 2 * q^45 - 2 * q^48 + 14 * q^49 - 2 * q^50 + 20 * q^51 + 4 * q^52 - 10 * q^54 - 12 * q^57 - 2 * q^60 - 16 * q^62 + 2 * q^64 + 4 * q^65 + 4 * q^66 - 8 * q^67 + 8 * q^69 + 24 * q^71 + 2 * q^72 - 2 * q^75 + 4 * q^78 + 16 * q^79 + 2 * q^80 - 14 * q^81 + 10 * q^86 + 2 * q^90 - 16 * q^93 + 2 * q^96 + 4 * q^97 - 14 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1290\mathbb{Z}\right)^\times$.

$n$	$431$	$517$	$691$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$	1.00000			0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	−1.00000			−0.316228
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−1.00000	−	1.41421i	−0.258199	−	0.365148i
$16$	1.00000			0.250000
$17$			7.07107i			1.71499i	0.514496	+	0.857493i	$0.327979\pi$
$17$			7.07107i			1.71499i	−0.514496	+	0.857493i	$0.672021\pi$
$18$	1.00000	−	2.82843i	0.235702	−	0.666667i
$19$		−	4.24264i		−	0.973329i	−0.873589	−	0.486664i	$-0.838214\pi$
$19$		−	4.24264i		−	0.973329i	0.873589	−	0.486664i	$-0.161786\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$			1.41421i			0.301511i
$23$			2.82843i			0.589768i	0.955533	+	0.294884i	$0.0952810\pi$
$23$			2.82843i			0.589768i	−0.955533	+	0.294884i	$0.904719\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$	1.00000			0.200000
$26$	−2.00000			−0.392232
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.00000	+	1.41421i	0.182574	+	0.258199i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000			−0.176777
$33$	−2.00000	+	1.41421i	−0.348155	+	0.246183i
$34$		−	7.07107i		−	1.21268i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$			4.24264i			0.697486i	0.937218	+	0.348743i	$0.113391\pi$
$37$			4.24264i			0.697486i	−0.937218	+	0.348743i	$0.886609\pi$
$38$			4.24264i			0.688247i
$39$	−2.00000	−	2.82843i	−0.320256	−	0.452911i
$40$	−1.00000			−0.158114
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		0			0
$43$	−5.00000	+	4.24264i	−0.762493	+	0.646997i
$43$	−5.00000	+	4.24264i	−0.762493	+	0.646997i
$44$		−	1.41421i		−	0.213201i
$45$	−1.00000	+	2.82843i	−0.149071	+	0.421637i
$46$		−	2.82843i		−	0.417029i
$47$			2.82843i			0.412568i	0.978492	+	0.206284i	$0.0661372\pi$
$47$			2.82843i			0.412568i	−0.978492	+	0.206284i	$0.933863\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$	7.00000			1.00000
$50$	−1.00000			−0.141421
$51$	10.0000	−	7.07107i	1.40028	−	0.990148i
$52$	2.00000			0.277350
$53$		−	1.41421i		−	0.194257i	−0.995272	−	0.0971286i	$-0.969034\pi$
$53$		−	1.41421i		−	0.194257i	0.995272	−	0.0971286i	$-0.0309658\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$		−	1.41421i		−	0.190693i
$56$		0			0
$57$	−6.00000	+	4.24264i	−0.794719	+	0.561951i
$58$		0			0
$59$		−	1.41421i		−	0.184115i	−0.995754	−	0.0920575i	$-0.970656\pi$
$59$		−	1.41421i		−	0.184115i	0.995754	−	0.0920575i	$-0.0293443\pi$
$60$	−1.00000	−	1.41421i	−0.129099	−	0.182574i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000			0.248069
$66$	2.00000	−	1.41421i	0.246183	−	0.174078i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$			7.07107i			0.857493i
$69$	4.00000	−	2.82843i	0.481543	−	0.340503i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	1.00000	−	2.82843i	0.117851	−	0.333333i
$73$			4.24264i			0.496564i	0.968688	+	0.248282i	$0.0798659\pi$
$73$			4.24264i			0.496564i	−0.968688	+	0.248282i	$0.920134\pi$
$74$		−	4.24264i		−	0.493197i
$75$	−1.00000	−	1.41421i	−0.115470	−	0.163299i
$76$		−	4.24264i		−	0.486664i
$77$		0			0
$78$	2.00000	+	2.82843i	0.226455	+	0.320256i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000			0.111803
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		−	2.82843i		−	0.312348i
$83$		−	14.1421i		−	1.55230i	−0.630548	−	0.776151i	$-0.717170\pi$
$83$		−	14.1421i		−	1.55230i	0.630548	−	0.776151i	$-0.282830\pi$
$84$		0			0
$85$			7.07107i			0.766965i
$86$	5.00000	−	4.24264i	0.539164	−	0.457496i
$87$		0			0
$88$			1.41421i			0.150756i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	1.00000	−	2.82843i	0.105409	−	0.298142i
$91$		0			0
$92$			2.82843i			0.294884i
$93$	−8.00000	−	11.3137i	−0.829561	−	1.17318i
$94$		−	2.82843i		−	0.291730i
$95$		−	4.24264i		−	0.435286i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−7.00000			−0.707107
$99$	4.00000	+	1.41421i	0.402015	+	0.142134i
$100$	1.00000			0.100000
$101$		−	14.1421i		−	1.40720i	−0.710599	−	0.703598i	$-0.751576\pi$
$101$		−	14.1421i		−	1.40720i	0.710599	−	0.703598i	$-0.248424\pi$
$102$	−10.0000	+	7.07107i	−0.990148	+	0.700140i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$			1.41421i			0.137361i
$107$		−	5.65685i		−	0.546869i	−0.961891	−	0.273434i	$-0.911840\pi$
$107$		−	5.65685i		−	0.546869i	0.961891	−	0.273434i	$-0.0881596\pi$
$108$	5.00000	−	1.41421i	0.481125	−	0.136083i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$			1.41421i			0.134840i
$111$	6.00000	−	4.24264i	0.569495	−	0.402694i
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	6.00000	−	4.24264i	0.561951	−	0.397360i
$115$			2.82843i			0.263752i
$116$		0			0
$117$	−2.00000	+	5.65685i	−0.184900	+	0.522976i
$118$			1.41421i			0.130189i
$119$		0			0
$120$	1.00000	+	1.41421i	0.0912871	+	0.129099i
$121$	9.00000			0.818182
$122$		0			0
$123$	4.00000	−	2.82843i	0.360668	−	0.255031i
$124$	8.00000			0.718421
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000			−0.0883883
$129$	11.0000	+	2.82843i	0.968496	+	0.249029i
$130$	−2.00000			−0.175412
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−2.00000	+	1.41421i	−0.174078	+	0.123091i
$133$		0			0
$134$	4.00000			0.345547
$135$	5.00000	−	1.41421i	0.430331	−	0.121716i
$136$		−	7.07107i		−	0.606339i
$137$	18.0000			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$138$	−4.00000	+	2.82843i	−0.340503	+	0.240772i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$		0			0
$141$	4.00000	−	2.82843i	0.336861	−	0.238197i
$142$	−12.0000			−1.00702
$143$		−	2.82843i		−	0.236525i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$		0			0
$146$		−	4.24264i		−	0.351123i
$147$	−7.00000	−	9.89949i	−0.577350	−	0.816497i
$148$			4.24264i			0.348743i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	+	1.41421i	0.0816497	+	0.115470i
$151$			12.7279i			1.03578i	0.855446	+	0.517892i	$0.173283\pi$
$151$			12.7279i			1.03578i	−0.855446	+	0.517892i	$0.826717\pi$
$152$			4.24264i			0.344124i
$153$	−20.0000	−	7.07107i	−1.61690	−	0.571662i
$154$		0			0
$155$	8.00000			0.642575
$156$	−2.00000	−	2.82843i	−0.160128	−	0.226455i
$157$		−	4.24264i		−	0.338600i	−0.985565	−	0.169300i	$-0.945849\pi$
$157$		−	4.24264i		−	0.338600i	0.985565	−	0.169300i	$-0.0541506\pi$
$158$	−8.00000			−0.636446
$159$	−2.00000	+	1.41421i	−0.158610	+	0.112154i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$			2.82843i			0.220863i
$165$	−2.00000	+	1.41421i	−0.155700	+	0.110096i
$166$			14.1421i			1.09764i
$167$			11.3137i			0.875481i	0.899101	+	0.437741i	$0.144221\pi$
$167$			11.3137i			0.875481i	−0.899101	+	0.437741i	$0.855779\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		−	7.07107i		−	0.542326i
$171$	12.0000	+	4.24264i	0.917663	+	0.324443i
$172$	−5.00000	+	4.24264i	−0.381246	+	0.323498i
$173$		−	9.89949i		−	0.752645i	−0.926489	−	0.376322i	$-0.877189\pi$
$173$		−	9.89949i		−	0.752645i	0.926489	−	0.376322i	$-0.122811\pi$
$174$		0			0
$175$		0			0
$176$		−	1.41421i		−	0.106600i
$177$	−2.00000	+	1.41421i	−0.150329	+	0.106299i
$178$		0			0
$179$	−24.0000			−1.79384			−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000			−1.79384			−0.896922	+	0.442189i	$0.854202\pi$
$180$	−1.00000	+	2.82843i	−0.0745356	+	0.210819i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$		−	2.82843i		−	0.208514i
$185$			4.24264i			0.311925i
$186$	8.00000	+	11.3137i	0.586588	+	0.829561i
$187$	10.0000			0.731272
$188$			2.82843i			0.206284i
$189$		0			0
$190$			4.24264i			0.307794i
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$	−2.00000			−0.143592
$195$	−2.00000	−	2.82843i	−0.143223	−	0.202548i
$196$	7.00000			0.500000
$197$			7.07107i			0.503793i	0.967754	+	0.251896i	$0.0810542\pi$
$197$			7.07107i			0.503793i	−0.967754	+	0.251896i	$0.918946\pi$
$198$	−4.00000	−	1.41421i	−0.284268	−	0.100504i
$199$			12.7279i			0.902258i	0.892459	+	0.451129i	$0.148979\pi$
$199$			12.7279i			0.902258i	−0.892459	+	0.451129i	$0.851021\pi$
$200$	−1.00000			−0.0707107
$201$	4.00000	+	5.65685i	0.282138	+	0.399004i
$202$			14.1421i			0.995037i
$203$		0			0
$204$	10.0000	−	7.07107i	0.700140	−	0.495074i
$205$			2.82843i			0.197546i
$206$	−14.0000			−0.975426
$207$	−8.00000	−	2.82843i	−0.556038	−	0.196589i
$208$	2.00000			0.138675
$209$	−6.00000			−0.415029
$210$		0			0
$211$		−	4.24264i		−	0.292075i	−0.989279	−	0.146038i	$-0.953348\pi$
$211$		−	4.24264i		−	0.292075i	0.989279	−	0.146038i	$-0.0466521\pi$
$212$		−	1.41421i		−	0.0971286i
$213$	−12.0000	−	16.9706i	−0.822226	−	1.16280i
$214$			5.65685i			0.386695i
$215$	−5.00000	+	4.24264i	−0.340997	+	0.289346i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$		0			0
$218$	4.00000			0.270914
$219$	6.00000	−	4.24264i	0.405442	−	0.286691i
$220$		−	1.41421i		−	0.0953463i
$221$			14.1421i			0.951303i
$222$	−6.00000	+	4.24264i	−0.402694	+	0.284747i
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−1.00000	+	2.82843i	−0.0666667	+	0.188562i
$226$	−6.00000			−0.399114
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	−6.00000	+	4.24264i	−0.397360	+	0.280976i
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		−	2.82843i		−	0.186501i
$231$		0			0
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	2.00000	−	5.65685i	0.130744	−	0.369800i
$235$			2.82843i			0.184506i
$236$		−	1.41421i		−	0.0920575i
$237$	−8.00000	−	11.3137i	−0.519656	−	0.734904i
$238$		0			0
$239$		−	1.41421i		−	0.0914779i	−0.998953	−	0.0457389i	$-0.985436\pi$
$239$		−	1.41421i		−	0.0914779i	0.998953	−	0.0457389i	$-0.0145642\pi$
$240$	−1.00000	−	1.41421i	−0.0645497	−	0.0912871i
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	−9.00000			−0.578542
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$		0			0
$245$	7.00000			0.447214
$246$	−4.00000	+	2.82843i	−0.255031	+	0.180334i
$247$		−	8.48528i		−	0.539906i
$248$	−8.00000			−0.508001
$249$	−20.0000	+	14.1421i	−1.26745	+	0.896221i
$250$	−1.00000			−0.0632456
$251$		−	26.8701i		−	1.69602i	−0.529978	−	0.848012i	$-0.677800\pi$
$251$		−	26.8701i		−	1.69602i	0.529978	−	0.848012i	$-0.322200\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	−8.00000			−0.501965
$255$	10.0000	−	7.07107i	0.626224	−	0.442807i
$256$	1.00000			0.0625000
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$	−11.0000	−	2.82843i	−0.684830	−	0.176090i
$259$		0			0
$260$	2.00000			0.124035
$261$		0			0
$262$	−12.0000			−0.741362
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$	2.00000	−	1.41421i	0.123091	−	0.0870388i
$265$		−	1.41421i		−	0.0868744i
$266$		0			0
$267$		0			0
$268$	−4.00000			−0.244339
$269$			19.7990i			1.20717i	0.797300	+	0.603583i	$0.206261\pi$
$269$			19.7990i			1.20717i	−0.797300	+	0.603583i	$0.793739\pi$
$270$	−5.00000	+	1.41421i	−0.304290	+	0.0860663i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$			7.07107i			0.428746i
$273$		0			0
$274$	−18.0000			−1.08742
$275$		−	1.41421i		−	0.0852803i
$276$	4.00000	−	2.82843i	0.240772	−	0.170251i
$277$		−	21.2132i		−	1.27458i	−0.770625	−	0.637289i	$-0.780056\pi$
$277$		−	21.2132i		−	1.27458i	0.770625	−	0.637289i	$-0.219944\pi$
$278$	−8.00000			−0.479808
$279$	−8.00000	+	22.6274i	−0.478947	+	1.35467i
$280$		0			0
$281$			2.82843i			0.168730i	0.996435	+	0.0843649i	$0.0268861\pi$
$281$			2.82843i			0.168730i	−0.996435	+	0.0843649i	$0.973114\pi$
$282$	−4.00000	+	2.82843i	−0.238197	+	0.168430i
$283$	−10.0000			−0.594438			−0.297219	−	0.954809i	$-0.596059\pi$
$283$	−10.0000			−0.594438			−0.297219	+	0.954809i	$0.596059\pi$
$284$	12.0000			0.712069
$285$	−6.00000	+	4.24264i	−0.355409	+	0.251312i
$286$			2.82843i			0.167248i
$287$		0			0
$288$	1.00000	−	2.82843i	0.0589256	−	0.166667i
$289$	−33.0000			−1.94118
$290$		0			0
$291$	−2.00000	−	2.82843i	−0.117242	−	0.165805i
$292$			4.24264i			0.248282i
$293$			24.0416i			1.40453i	0.711917	+	0.702264i	$0.247827\pi$
$293$			24.0416i			1.40453i	−0.711917	+	0.702264i	$0.752173\pi$
$294$	7.00000	+	9.89949i	0.408248	+	0.577350i
$295$		−	1.41421i		−	0.0823387i
$296$		−	4.24264i		−	0.246598i
$297$	−2.00000	−	7.07107i	−0.116052	−	0.410305i
$298$	6.00000			0.347571
$299$			5.65685i			0.327144i
$300$	−1.00000	−	1.41421i	−0.0577350	−	0.0816497i
$301$		0			0
$302$		−	12.7279i		−	0.732410i
$303$	−20.0000	+	14.1421i	−1.14897	+	0.812444i
$304$		−	4.24264i		−	0.243332i
$305$		0			0
$306$	20.0000	+	7.07107i	1.14332	+	0.404226i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$		0			0
$309$	−14.0000	−	19.7990i	−0.796432	−	1.12633i
$310$	−8.00000			−0.454369
$311$		−	26.8701i		−	1.52366i	−0.647776	−	0.761831i	$-0.724301\pi$
$311$		−	26.8701i		−	1.52366i	0.647776	−	0.761831i	$-0.275699\pi$
$312$	2.00000	+	2.82843i	0.113228	+	0.160128i
$313$			29.6985i			1.67866i	0.543624	+	0.839329i	$0.317052\pi$
$313$			29.6985i			1.67866i	−0.543624	+	0.839329i	$0.682948\pi$
$314$			4.24264i			0.239426i
$315$		0			0
$316$	8.00000			0.450035
$317$			15.5563i			0.873732i	0.899527	+	0.436866i	$0.143912\pi$
$317$			15.5563i			0.873732i	−0.899527	+	0.436866i	$0.856088\pi$
$318$	2.00000	−	1.41421i	0.112154	−	0.0793052i
$319$		0			0
$320$	1.00000			0.0559017
$321$	−8.00000	+	5.65685i	−0.446516	+	0.315735i
$322$		0			0
$323$	30.0000			1.66924
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$	2.00000			0.110940
$326$		0			0
$327$	4.00000	+	5.65685i	0.221201	+	0.312825i
$328$		−	2.82843i		−	0.156174i
$329$		0			0
$330$	2.00000	−	1.41421i	0.110096	−	0.0778499i
$331$			29.6985i			1.63238i	0.577786	+	0.816188i	$0.303917\pi$
$331$			29.6985i			1.63238i	−0.577786	+	0.816188i	$0.696083\pi$
$332$		−	14.1421i		−	0.776151i
$333$	−12.0000	−	4.24264i	−0.657596	−	0.232495i
$334$		−	11.3137i		−	0.619059i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	9.00000			0.489535
$339$	−6.00000	−	8.48528i	−0.325875	−	0.460857i
$340$			7.07107i			0.383482i
$341$		−	11.3137i		−	0.612672i
$342$	−12.0000	−	4.24264i	−0.648886	−	0.229416i
$343$		0			0
$344$	5.00000	−	4.24264i	0.269582	−	0.228748i
$345$	4.00000	−	2.82843i	0.215353	−	0.152277i
$346$			9.89949i			0.532200i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$	10.0000	−	2.82843i	0.533761	−	0.150970i
$352$			1.41421i			0.0753778i
$353$			24.0416i			1.27961i	0.768539	+	0.639803i	$0.220984\pi$
$353$			24.0416i			1.27961i	−0.768539	+	0.639803i	$0.779016\pi$
$354$	2.00000	−	1.41421i	0.106299	−	0.0751646i
$355$	12.0000			0.636894
$356$		0			0
$357$		0			0
$358$	24.0000			1.26844
$359$		−	18.3848i		−	0.970311i	−0.874428	−	0.485156i	$-0.838763\pi$
$359$		−	18.3848i		−	0.970311i	0.874428	−	0.485156i	$-0.161237\pi$
$360$	1.00000	−	2.82843i	0.0527046	−	0.149071i
$361$	1.00000			0.0526316
$362$	−20.0000			−1.05118
$363$	−9.00000	−	12.7279i	−0.472377	−	0.668043i
$364$		0			0
$365$			4.24264i			0.222070i
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$			2.82843i			0.147442i
$369$	−8.00000	−	2.82843i	−0.416463	−	0.147242i
$370$		−	4.24264i		−	0.220564i
$371$		0			0
$372$	−8.00000	−	11.3137i	−0.414781	−	0.586588i
$373$			29.6985i			1.53773i	0.639412	+	0.768865i	$0.279178\pi$
$373$			29.6985i			1.53773i	−0.639412	+	0.768865i	$0.720822\pi$
$374$	−10.0000			−0.517088
$375$	−1.00000	−	1.41421i	−0.0516398	−	0.0730297i
$376$		−	2.82843i		−	0.145865i
$377$		0			0
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		−	4.24264i		−	0.217643i
$381$	−8.00000	−	11.3137i	−0.409852	−	0.579619i
$382$	12.0000			0.613973
$383$	24.0000			1.22634			0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000			1.22634			0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$		0			0
$386$	10.0000			0.508987
$387$	−7.00000	−	18.3848i	−0.355830	−	0.934551i
$388$	2.00000			0.101535
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$	2.00000	+	2.82843i	0.101274	+	0.143223i
$391$	−20.0000			−1.01144
$392$	−7.00000			−0.353553
$393$	−12.0000	−	16.9706i	−0.605320	−	0.856052i
$394$		−	7.07107i		−	0.356235i
$395$	8.00000			0.402524
$396$	4.00000	+	1.41421i	0.201008	+	0.0710669i
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$		−	12.7279i		−	0.637993i
$399$		0			0
$400$	1.00000			0.0500000
$401$			11.3137i			0.564980i	0.959270	+	0.282490i	$0.0911603\pi$
$401$			11.3137i			0.564980i	−0.959270	+	0.282490i	$0.908840\pi$
$402$	−4.00000	−	5.65685i	−0.199502	−	0.282138i
$403$	16.0000			0.797017
$404$		−	14.1421i		−	0.703598i
$405$	−7.00000	−	5.65685i	−0.347833	−	0.281091i
$406$		0			0
$407$	6.00000			0.297409
$408$	−10.0000	+	7.07107i	−0.495074	+	0.350070i
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		−	2.82843i		−	0.139686i
$411$	−18.0000	−	25.4558i	−0.887875	−	1.25564i
$412$	14.0000			0.689730
$413$		0			0
$414$	8.00000	+	2.82843i	0.393179	+	0.139010i
$415$		−	14.1421i		−	0.694210i
$416$	−2.00000			−0.0980581
$417$	−8.00000	−	11.3137i	−0.391762	−	0.554035i
$418$	6.00000			0.293470
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$			4.24264i			0.206529i
$423$	−8.00000	−	2.82843i	−0.388973	−	0.137523i
$424$			1.41421i			0.0686803i
$425$			7.07107i			0.342997i
$426$	12.0000	+	16.9706i	0.581402	+	0.822226i
$427$		0			0
$428$		−	5.65685i		−	0.273434i
$429$	−4.00000	+	2.82843i	−0.193122	+	0.136558i
$430$	5.00000	−	4.24264i	0.241121	−	0.204598i
$431$		−	35.3553i		−	1.70301i	−0.524349	−	0.851503i	$-0.675691\pi$
$431$		−	35.3553i		−	1.70301i	0.524349	−	0.851503i	$-0.324309\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$		−	4.24264i		−	0.203888i	−0.994790	−	0.101944i	$-0.967494\pi$
$433$		−	4.24264i		−	0.203888i	0.994790	−	0.101944i	$-0.0325063\pi$
$434$		0			0
$435$		0			0
$436$	−4.00000			−0.191565
$437$	12.0000			0.574038
$438$	−6.00000	+	4.24264i	−0.286691	+	0.202721i
$439$	−40.0000			−1.90910			−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000			−1.90910			−0.954548	+	0.298057i	$0.903661\pi$
$440$			1.41421i			0.0674200i
$441$	−7.00000	+	19.7990i	−0.333333	+	0.942809i
$442$		−	14.1421i		−	0.672673i
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	6.00000	−	4.24264i	0.284747	−	0.201347i
$445$		0			0
$446$		0			0
$447$	6.00000	+	8.48528i	0.283790	+	0.401340i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	1.00000	−	2.82843i	0.0471405	−	0.133333i
$451$	4.00000			0.188353
$452$	6.00000			0.282216
$453$	18.0000	−	12.7279i	0.845714	−	0.598010i
$454$	18.0000			0.844782
$455$		0			0
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$		−	29.6985i		−	1.38924i	−0.719379	−	0.694618i	$-0.755573\pi$
$457$		−	29.6985i		−	1.38924i	0.719379	−	0.694618i	$-0.244427\pi$
$458$	16.0000			0.747631
$459$	10.0000	+	35.3553i	0.466760	+	1.65025i
$460$			2.82843i			0.131876i
$461$			2.82843i			0.131733i	0.997828	+	0.0658665i	$0.0209811\pi$
$461$			2.82843i			0.131733i	−0.997828	+	0.0658665i	$0.979019\pi$
$462$		0			0
$463$		−	25.4558i		−	1.18303i	−0.806293	−	0.591517i	$-0.798529\pi$
$463$		−	25.4558i		−	1.18303i	0.806293	−	0.591517i	$-0.201471\pi$
$464$		0			0
$465$	−8.00000	−	11.3137i	−0.370991	−	0.524661i
$466$	18.0000			0.833834
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−2.00000	+	5.65685i	−0.0924500	+	0.261488i
$469$		0			0
$470$		−	2.82843i		−	0.130466i
$471$	−6.00000	+	4.24264i	−0.276465	+	0.195491i
$472$			1.41421i			0.0650945i
$473$	6.00000	+	7.07107i	0.275880	+	0.325128i
$474$	8.00000	+	11.3137i	0.367452	+	0.519656i
$475$		−	4.24264i		−	0.194666i
$476$		0			0
$477$	4.00000	+	1.41421i	0.183147	+	0.0647524i
$478$			1.41421i			0.0646846i
$479$			41.0122i			1.87389i	0.349470	+	0.936947i	$0.386362\pi$
$479$			41.0122i			1.87389i	−0.349470	+	0.936947i	$0.613638\pi$
$480$	1.00000	+	1.41421i	0.0456435	+	0.0645497i
$481$			8.48528i			0.386896i
$482$		−	8.48528i		−	0.386494i
$483$		0			0
$484$	9.00000			0.409091
$485$	2.00000			0.0908153
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$		0			0
$489$		0			0
$490$	−7.00000			−0.316228
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	4.00000	−	2.82843i	0.180334	−	0.127515i
$493$		0			0
$494$			8.48528i			0.381771i
$495$	4.00000	+	1.41421i	0.179787	+	0.0635642i
$496$	8.00000			0.359211
$497$		0			0
$498$	20.0000	−	14.1421i	0.896221	−	0.633724i
$499$			4.24264i			0.189927i	0.995481	+	0.0949633i	$0.0302734\pi$
$499$			4.24264i			0.189927i	−0.995481	+	0.0949633i	$0.969727\pi$
$500$	1.00000			0.0447214
$501$	16.0000	−	11.3137i	0.714827	−	0.505459i
$502$			26.8701i			1.19927i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$		−	14.1421i		−	0.629317i
$506$	−4.00000			−0.177822
$507$	9.00000	+	12.7279i	0.399704	+	0.565267i
$508$	8.00000			0.354943
$509$			11.3137i			0.501471i	0.968056	+	0.250736i	$0.0806725\pi$
$509$			11.3137i			0.501471i	−0.968056	+	0.250736i	$0.919328\pi$
$510$	−10.0000	+	7.07107i	−0.442807	+	0.313112i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−6.00000	−	21.2132i	−0.264906	−	0.936586i
$514$	−6.00000			−0.264649
$515$	14.0000			0.616914
$516$	11.0000	+	2.82843i	0.484248	+	0.124515i
$517$	4.00000			0.175920
$518$		0			0
$519$	−14.0000	+	9.89949i	−0.614532	+	0.434540i
$520$	−2.00000			−0.0877058
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$			8.48528i			0.371035i	0.982641	+	0.185518i	$0.0593962\pi$
$523$			8.48528i			0.371035i	−0.982641	+	0.185518i	$0.940604\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	−18.0000			−0.784837
$527$			56.5685i			2.46416i
$528$	−2.00000	+	1.41421i	−0.0870388	+	0.0615457i
$529$	15.0000			0.652174
$530$			1.41421i			0.0614295i
$531$	4.00000	+	1.41421i	0.173585	+	0.0613716i
$532$		0			0
$533$			5.65685i			0.245026i
$534$		0			0
$535$		−	5.65685i		−	0.244567i
$536$	4.00000			0.172774
$537$	24.0000	+	33.9411i	1.03568	+	1.46467i
$538$		−	19.7990i		−	0.853595i
$539$		−	9.89949i		−	0.426401i
$540$	5.00000	−	1.41421i	0.215166	−	0.0608581i
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	−20.0000			−0.859074
$543$	−20.0000	−	28.2843i	−0.858282	−	1.21379i
$544$		−	7.07107i		−	0.303170i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	38.0000			1.62476			0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000			1.62476			0.812381	+	0.583127i	$0.198171\pi$
$548$	18.0000			0.768922
$549$		0			0
$550$			1.41421i			0.0603023i
$551$		0			0
$552$	−4.00000	+	2.82843i	−0.170251	+	0.120386i
$553$		0			0
$554$			21.2132i			0.901263i
$555$	6.00000	−	4.24264i	0.254686	−	0.180090i
$556$	8.00000			0.339276
$557$		−	1.41421i		−	0.0599222i	−0.999551	−	0.0299611i	$-0.990462\pi$
$557$		−	1.41421i		−	0.0599222i	0.999551	−	0.0299611i	$-0.00953833\pi$
$558$	8.00000	−	22.6274i	0.338667	−	0.957895i
$559$	−10.0000	+	8.48528i	−0.422955	+	0.358889i
$560$		0			0
$561$	−10.0000	−	14.1421i	−0.422200	−	0.597081i
$562$		−	2.82843i		−	0.119310i
$563$		−	22.6274i		−	0.953632i	−0.879003	−	0.476816i	$-0.841791\pi$
$563$		−	22.6274i		−	0.953632i	0.879003	−	0.476816i	$-0.158209\pi$
$564$	4.00000	−	2.82843i	0.168430	−	0.119098i
$565$	6.00000			0.252422
$566$	10.0000			0.420331
$567$		0			0
$568$	−12.0000			−0.503509
$569$			11.3137i			0.474295i	0.971474	+	0.237148i	$0.0762125\pi$
$569$			11.3137i			0.474295i	−0.971474	+	0.237148i	$0.923787\pi$
$570$	6.00000	−	4.24264i	0.251312	−	0.177705i
$571$			38.1838i			1.59794i	0.601370	+	0.798970i	$0.294622\pi$
$571$			38.1838i			1.59794i	−0.601370	+	0.798970i	$0.705378\pi$
$572$		−	2.82843i		−	0.118262i
$573$	12.0000	+	16.9706i	0.501307	+	0.708955i
$574$		0			0
$575$			2.82843i			0.117954i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$		−	21.2132i		−	0.883117i	−0.897232	−	0.441559i	$-0.854426\pi$
$577$		−	21.2132i		−	0.883117i	0.897232	−	0.441559i	$-0.145574\pi$
$578$	33.0000			1.37262
$579$	10.0000	+	14.1421i	0.415586	+	0.587727i
$580$		0			0
$581$		0			0
$582$	2.00000	+	2.82843i	0.0829027	+	0.117242i
$583$	−2.00000			−0.0828315
$584$		−	4.24264i		−	0.175562i
$585$	−2.00000	+	5.65685i	−0.0826898	+	0.233882i
$586$		−	24.0416i		−	0.993151i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	−7.00000	−	9.89949i	−0.288675	−	0.408248i
$589$		−	33.9411i		−	1.39852i
$590$			1.41421i			0.0582223i
$591$	10.0000	−	7.07107i	0.411345	−	0.290865i
$592$			4.24264i			0.174371i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	2.00000	+	7.07107i	0.0820610	+	0.290129i
$595$		0			0
$596$	−6.00000			−0.245770
$597$	18.0000	−	12.7279i	0.736691	−	0.520919i
$598$		−	5.65685i		−	0.231326i
$599$		−	9.89949i		−	0.404482i	−0.979336	−	0.202241i	$-0.935178\pi$
$599$		−	9.89949i		−	0.404482i	0.979336	−	0.202241i	$-0.0648225\pi$
$600$	1.00000	+	1.41421i	0.0408248	+	0.0577350i
$601$		−	8.48528i		−	0.346122i	−0.984911	−	0.173061i	$-0.944634\pi$
$601$		−	8.48528i		−	0.346122i	0.984911	−	0.173061i	$-0.0553658\pi$
$602$		0			0
$603$	4.00000	−	11.3137i	0.162893	−	0.460730i
$604$			12.7279i			0.517892i
$605$	9.00000			0.365902
$606$	20.0000	−	14.1421i	0.812444	−	0.574485i
$607$		−	25.4558i		−	1.03322i	−0.856221	−	0.516610i	$-0.827194\pi$
$607$		−	25.4558i		−	1.03322i	0.856221	−	0.516610i	$-0.172806\pi$
$608$			4.24264i			0.172062i
$609$		0			0
$610$		0			0
$611$			5.65685i			0.228852i
$612$	−20.0000	−	7.07107i	−0.808452	−	0.285831i
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$	10.0000			0.403567
$615$	4.00000	−	2.82843i	0.161296	−	0.114053i
$616$		0			0
$617$			7.07107i			0.284670i	0.989819	+	0.142335i	$0.0454611\pi$
$617$			7.07107i			0.284670i	−0.989819	+	0.142335i	$0.954539\pi$
$618$	14.0000	+	19.7990i	0.563163	+	0.796432i
$619$	8.00000			0.321547			0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000			0.321547			0.160774	+	0.986991i	$0.448601\pi$
$620$	8.00000			0.321288
$621$	4.00000	+	14.1421i	0.160514	+	0.567504i
$622$			26.8701i			1.07739i
$623$		0			0
$624$	−2.00000	−	2.82843i	−0.0800641	−	0.113228i
$625$	1.00000			0.0400000
$626$		−	29.6985i		−	1.18699i
$627$	6.00000	+	8.48528i	0.239617	+	0.338869i
$628$		−	4.24264i		−	0.169300i
$629$	−30.0000			−1.19618
$630$		0			0
$631$			12.7279i			0.506691i	0.967376	+	0.253345i	$0.0815309\pi$
$631$			12.7279i			0.506691i	−0.967376	+	0.253345i	$0.918469\pi$
$632$	−8.00000			−0.318223
$633$	−6.00000	+	4.24264i	−0.238479	+	0.168630i
$634$		−	15.5563i		−	0.617822i
$635$	8.00000			0.317470
$636$	−2.00000	+	1.41421i	−0.0793052	+	0.0560772i
$637$	14.0000			0.554700
$638$		0			0
$639$	−12.0000	+	33.9411i	−0.474713	+	1.34269i
$640$	−1.00000			−0.0395285
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$	8.00000	−	5.65685i	0.315735	−	0.223258i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	11.0000	+	2.82843i	0.433125	+	0.111369i
$646$	−30.0000			−1.18033
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$	7.00000	+	5.65685i	0.274986	+	0.222222i
$649$	−2.00000			−0.0785069
$650$	−2.00000			−0.0784465
$651$		0			0
$652$		0			0
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−4.00000	−	5.65685i	−0.156412	−	0.221201i
$655$	12.0000			0.468879
$656$			2.82843i			0.110432i
$657$	−12.0000	−	4.24264i	−0.468165	−	0.165521i
$658$		0			0
$659$		−	18.3848i		−	0.716169i	−0.933689	−	0.358085i	$-0.883430\pi$
$659$		−	18.3848i		−	0.716169i	0.933689	−	0.358085i	$-0.116570\pi$
$660$	−2.00000	+	1.41421i	−0.0778499	+	0.0550482i
$661$	−10.0000			−0.388955			−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000			−0.388955			−0.194477	+	0.980907i	$0.562301\pi$
$662$		−	29.6985i		−	1.15426i
$663$	20.0000	−	14.1421i	0.776736	−	0.549235i
$664$			14.1421i			0.548821i
$665$		0			0
$666$	12.0000	+	4.24264i	0.464991	+	0.164399i
$667$		0			0
$668$			11.3137i			0.437741i
$669$		0			0
$670$	4.00000			0.154533
$671$		0			0
$672$		0			0
$673$		−	29.6985i		−	1.14479i	−0.819977	−	0.572396i	$-0.806014\pi$
$673$		−	29.6985i		−	1.14479i	0.819977	−	0.572396i	$-0.193986\pi$
$674$	−2.00000			−0.0770371
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$	−9.00000			−0.346154
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	6.00000	+	8.48528i	0.230429	+	0.325875i
$679$		0			0
$680$		−	7.07107i		−	0.271163i
$681$	18.0000	+	25.4558i	0.689761	+	0.975470i
$682$			11.3137i			0.433224i
$683$			45.2548i			1.73163i	0.500366	+	0.865814i	$0.333199\pi$
$683$			45.2548i			1.73163i	−0.500366	+	0.865814i	$0.666801\pi$
$684$	12.0000	+	4.24264i	0.458831	+	0.162221i
$685$	18.0000			0.687745
$686$		0			0
$687$	16.0000	+	22.6274i	0.610438	+	0.863290i
$688$	−5.00000	+	4.24264i	−0.190623	+	0.161749i
$689$		−	2.82843i		−	0.107754i
$690$	−4.00000	+	2.82843i	−0.152277	+	0.107676i
$691$			38.1838i			1.45258i	0.687389	+	0.726289i	$0.258757\pi$
$691$			38.1838i			1.45258i	−0.687389	+	0.726289i	$0.741243\pi$
$692$		−	9.89949i		−	0.376322i
$693$		0			0
$694$	12.0000			0.455514
$695$	8.00000			0.303457
$696$		0			0
$697$	−20.0000			−0.757554
$698$		0			0
$699$	18.0000	+	25.4558i	0.680823	+	0.962828i
$700$		0			0
$701$		−	5.65685i		−	0.213656i	−0.994277	−	0.106828i	$-0.965931\pi$
$701$		−	5.65685i		−	0.213656i	0.994277	−	0.106828i	$-0.0340695\pi$
$702$	−10.0000	+	2.82843i	−0.377426	+	0.106752i
$703$	18.0000			0.678883
$704$		−	1.41421i		−	0.0533002i
$705$	4.00000	−	2.82843i	0.150649	−	0.106525i
$706$		−	24.0416i		−	0.904819i
$707$		0			0
$708$	−2.00000	+	1.41421i	−0.0751646	+	0.0531494i
$709$	50.0000			1.87779			0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000			1.87779			0.938895	+	0.344204i	$0.111851\pi$
$710$	−12.0000			−0.450352
$711$	−8.00000	+	22.6274i	−0.300023	+	0.848594i
$712$		0			0
$713$			22.6274i			0.847403i
$714$		0			0
$715$		−	2.82843i		−	0.105777i
$716$	−24.0000			−0.896922
$717$	−2.00000	+	1.41421i	−0.0746914	+	0.0528148i
$718$			18.3848i			0.686114i
$719$		−	18.3848i		−	0.685636i	−0.939402	−	0.342818i	$-0.888619\pi$
$719$		−	18.3848i		−	0.685636i	0.939402	−	0.342818i	$-0.111381\pi$
$720$	−1.00000	+	2.82843i	−0.0372678	+	0.105409i
$721$		0			0
$722$	−1.00000			−0.0372161
$723$	12.0000	−	8.48528i	0.446285	−	0.315571i
$724$	20.0000			0.743294
$725$		0			0
$726$	9.00000	+	12.7279i	0.334021	+	0.472377i
$727$		−	25.4558i		−	0.944105i	−0.881570	−	0.472052i	$-0.843513\pi$
$727$		−	25.4558i		−	0.944105i	0.881570	−	0.472052i	$-0.156487\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		−	4.24264i		−	0.157027i
$731$	−30.0000	−	35.3553i	−1.10959	−	1.30766i
$732$		0			0
$733$		−	29.6985i		−	1.09694i	−0.836171	−	0.548469i	$-0.815211\pi$
$733$		−	29.6985i		−	1.09694i	0.836171	−	0.548469i	$-0.184789\pi$
$734$	−8.00000			−0.295285
$735$	−7.00000	−	9.89949i	−0.258199	−	0.365148i
$736$		−	2.82843i		−	0.104257i
$737$			5.65685i			0.208373i
$738$	8.00000	+	2.82843i	0.294484	+	0.104116i
$739$		−	38.1838i		−	1.40461i	−0.711875	−	0.702306i	$-0.752154\pi$
$739$		−	38.1838i		−	1.40461i	0.711875	−	0.702306i	$-0.247846\pi$
$740$			4.24264i			0.155963i
$741$	−12.0000	+	8.48528i	−0.440831	+	0.311715i
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	8.00000	+	11.3137i	0.293294	+	0.414781i
$745$	−6.00000			−0.219823
$746$		−	29.6985i		−	1.08734i
$747$	40.0000	+	14.1421i	1.46352	+	0.517434i
$748$	10.0000			0.365636
$749$		0			0
$750$	1.00000	+	1.41421i	0.0365148	+	0.0516398i
$751$		−	46.6690i		−	1.70298i	−0.524373	−	0.851489i	$-0.675700\pi$
$751$		−	46.6690i		−	1.70298i	0.524373	−	0.851489i	$-0.324300\pi$
$752$			2.82843i			0.103142i
$753$	−38.0000	+	26.8701i	−1.38480	+	0.979199i
$754$		0			0
$755$			12.7279i			0.463217i
$756$		0			0
$757$		−	46.6690i		−	1.69622i	−0.529824	−	0.848108i	$-0.677742\pi$
$757$		−	46.6690i		−	1.69622i	0.529824	−	0.848108i	$-0.322258\pi$
$758$	16.0000			0.581146
$759$	−4.00000	−	5.65685i	−0.145191	−	0.205331i
$760$			4.24264i			0.153897i
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$	8.00000	+	11.3137i	0.289809	+	0.409852i
$763$		0			0
$764$	−12.0000			−0.434145
$765$	−20.0000	−	7.07107i	−0.723102	−	0.255655i
$766$	−24.0000			−0.867155
$767$		−	2.82843i		−	0.102129i
$768$	−1.00000	−	1.41421i	−0.0360844	−	0.0510310i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	−6.00000	−	8.48528i	−0.216085	−	0.305590i
$772$	−10.0000			−0.359908
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$	7.00000	+	18.3848i	0.251610	+	0.660827i
$775$	8.00000			0.287368
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	12.0000			0.430221
$779$	12.0000			0.429945
$780$	−2.00000	−	2.82843i	−0.0716115	−	0.101274i
$781$		−	16.9706i		−	0.607254i
$782$	20.0000			0.715199
$783$		0			0
$784$	7.00000			0.250000
$785$		−	4.24264i		−	0.151426i
$786$	12.0000	+	16.9706i	0.428026	+	0.605320i
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$			7.07107i			0.251896i
$789$	−18.0000	−	25.4558i	−0.640817	−	0.906252i
$790$	−8.00000			−0.284627
$791$		0			0
$792$	−4.00000	−	1.41421i	−0.142134	−	0.0502519i
$793$		0			0
$794$	34.0000			1.20661
$795$	−2.00000	+	1.41421i	−0.0709327	+	0.0501570i
$796$			12.7279i			0.451129i
$797$		−	26.8701i		−	0.951786i	−0.879503	−	0.475893i	$-0.842125\pi$
$797$		−	26.8701i		−	0.951786i	0.879503	−	0.475893i	$-0.157875\pi$
$798$		0			0
$799$	−20.0000			−0.707549
$800$	−1.00000			−0.0353553
$801$		0			0
$802$		−	11.3137i		−	0.399501i
$803$	6.00000			0.211735
$804$	4.00000	+	5.65685i	0.141069	+	0.199502i
$805$		0			0
$806$	−16.0000			−0.563576
$807$	28.0000	−	19.7990i	0.985647	−	0.696957i
$808$			14.1421i			0.497519i
$809$		−	31.1127i		−	1.09386i	−0.837177	−	0.546932i	$-0.815796\pi$
$809$		−	31.1127i		−	1.09386i	0.837177	−	0.546932i	$-0.184204\pi$
$810$	7.00000	+	5.65685i	0.245955	+	0.198762i
$811$		−	4.24264i		−	0.148979i	−0.997222	−	0.0744896i	$-0.976267\pi$
$811$		−	4.24264i		−	0.148979i	0.997222	−	0.0744896i	$-0.0237328\pi$
$812$		0			0
$813$	−20.0000	−	28.2843i	−0.701431	−	0.991973i
$814$	−6.00000			−0.210300
$815$		0			0
$816$	10.0000	−	7.07107i	0.350070	−	0.247537i
$817$	18.0000	+	21.2132i	0.629740	+	0.742156i
$818$		0			0
$819$		0			0
$820$			2.82843i			0.0987730i
$821$			28.2843i			0.987128i	0.869710	+	0.493564i	$0.164306\pi$
$821$			28.2843i			0.987128i	−0.869710	+	0.493564i	$0.835694\pi$
$822$	18.0000	+	25.4558i	0.627822	+	0.887875i
$823$	2.00000			0.0697156			0.0348578	−	0.999392i	$-0.488902\pi$
$823$	2.00000			0.0697156			0.0348578	+	0.999392i	$0.488902\pi$
$824$	−14.0000			−0.487713
$825$	−2.00000	+	1.41421i	−0.0696311	+	0.0492366i
$826$		0			0
$827$		−	31.1127i		−	1.08189i	−0.841057	−	0.540947i	$-0.818066\pi$
$827$		−	31.1127i		−	1.08189i	0.841057	−	0.540947i	$-0.181934\pi$
$828$	−8.00000	−	2.82843i	−0.278019	−	0.0982946i
$829$			25.4558i			0.884118i	0.896986	+	0.442059i	$0.145752\pi$
$829$			25.4558i			0.884118i	−0.896986	+	0.442059i	$0.854248\pi$
$830$			14.1421i			0.490881i
$831$	−30.0000	+	21.2132i	−1.04069	+	0.735878i
$832$	2.00000			0.0693375
$833$			49.4975i			1.71499i
$834$	8.00000	+	11.3137i	0.277017	+	0.391762i
$835$			11.3137i			0.391527i
$836$	−6.00000			−0.207514
$837$	40.0000	−	11.3137i	1.38260	−	0.391059i
$838$	−24.0000			−0.829066
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$	4.00000	−	2.82843i	0.137767	−	0.0974162i
$844$		−	4.24264i		−	0.146038i
$845$	−9.00000			−0.309609
$846$	8.00000	+	2.82843i	0.275046	+	0.0972433i
$847$		0			0
$848$		−	1.41421i		−	0.0485643i
$849$	10.0000	+	14.1421i	0.343199	+	0.485357i
$850$		−	7.07107i		−	0.242536i
$851$	−12.0000			−0.411355
$852$	−12.0000	−	16.9706i	−0.411113	−	0.581402i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		0			0
$855$	12.0000	+	4.24264i	0.410391	+	0.145095i
$856$			5.65685i			0.193347i
$857$		−	35.3553i		−	1.20772i	−0.797092	−	0.603858i	$-0.793630\pi$
$857$		−	35.3553i		−	1.20772i	0.797092	−	0.603858i	$-0.206370\pi$
$858$	4.00000	−	2.82843i	0.136558	−	0.0965609i
$859$		−	12.7279i		−	0.434271i	−0.976141	−	0.217136i	$-0.930329\pi$
$859$		−	12.7279i		−	0.434271i	0.976141	−	0.217136i	$-0.0696714\pi$
$860$	−5.00000	+	4.24264i	−0.170499	+	0.144673i
$861$		0			0
$862$			35.3553i			1.20421i
$863$	−42.0000			−1.42970			−0.714848	−	0.699280i	$-0.753504\pi$
$863$	−42.0000			−1.42970			−0.714848	+	0.699280i	$0.753504\pi$
$864$	−5.00000	+	1.41421i	−0.170103	+	0.0481125i
$865$		−	9.89949i		−	0.336593i
$866$			4.24264i			0.144171i
$867$	33.0000	+	46.6690i	1.12074	+	1.58496i
$868$		0			0
$869$		−	11.3137i		−	0.383791i
$870$		0			0
$871$	−8.00000			−0.271070
$872$	4.00000			0.135457
$873$	−2.00000	+	5.65685i	−0.0676897	+	0.191456i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	6.00000	−	4.24264i	0.202721	−	0.143346i
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	40.0000			1.34993
$879$	34.0000	−	24.0416i	1.14679	−	0.810904i
$880$		−	1.41421i		−	0.0476731i
$881$			53.7401i			1.81055i	0.424826	+	0.905275i	$0.360335\pi$
$881$			53.7401i			1.81055i	−0.424826	+	0.905275i	$0.639665\pi$
$882$	7.00000	−	19.7990i	0.235702	−	0.666667i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$			14.1421i			0.475651i
$885$	−2.00000	+	1.41421i	−0.0672293	+	0.0475383i
$886$		−	28.2843i		−	0.950229i
$887$	−6.00000			−0.201460			−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000			−0.201460			−0.100730	+	0.994914i	$0.532118\pi$
$888$	−6.00000	+	4.24264i	−0.201347	+	0.142374i
$889$		0			0
$890$		0			0
$891$	−8.00000	+	9.89949i	−0.268010	+	0.331646i
$892$		0			0
$893$	12.0000			0.401565
$894$	−6.00000	−	8.48528i	−0.200670	−	0.283790i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	8.00000	−	5.65685i	0.267112	−	0.188877i
$898$	−6.00000			−0.200223
$899$		0			0
$900$	−1.00000	+	2.82843i	−0.0333333	+	0.0942809i
$901$	10.0000			0.333148
$902$	−4.00000			−0.133185
$903$		0			0
$904$	−6.00000			−0.199557
$905$	20.0000			0.664822
$906$	−18.0000	+	12.7279i	−0.598010	+	0.422857i
$907$	−58.0000			−1.92586			−0.962929	−	0.269754i	$-0.913058\pi$
$907$	−58.0000			−1.92586			−0.962929	+	0.269754i	$0.913058\pi$
$908$	−18.0000			−0.597351
$909$	40.0000	+	14.1421i	1.32672	+	0.469065i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−6.00000	+	4.24264i	−0.198680	+	0.140488i
$913$	−20.0000			−0.661903
$914$			29.6985i			0.982339i
$915$		0			0
$916$	−16.0000			−0.528655
$917$		0			0
$918$	−10.0000	−	35.3553i	−0.330049	−	1.16690i
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$		−	2.82843i		−	0.0932505i
$921$	10.0000	+	14.1421i	0.329511	+	0.465999i
$922$		−	2.82843i		−	0.0931493i
$923$	24.0000			0.789970
$924$		0			0
$925$			4.24264i			0.139497i
$926$			25.4558i			0.836531i
$927$	−14.0000	+	39.5980i	−0.459820	+	1.30057i
$928$		0			0
$929$	36.0000			1.18112			0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000			1.18112			0.590561	+	0.806993i	$0.298907\pi$
$930$	8.00000	+	11.3137i	0.262330	+	0.370991i
$931$		−	29.6985i		−	0.973329i
$932$	−18.0000			−0.589610
$933$	−38.0000	+	26.8701i	−1.24406	+	0.879686i
$934$	12.0000			0.392652
$935$	10.0000			0.327035
$936$	2.00000	−	5.65685i	0.0653720	−	0.184900i
$937$			29.6985i			0.970207i	0.874457	+	0.485104i	$0.161218\pi$
$937$			29.6985i			0.970207i	−0.874457	+	0.485104i	$0.838782\pi$
$938$		0			0
$939$	42.0000	−	29.6985i	1.37062	−	0.969173i
$940$			2.82843i			0.0922531i
$941$			19.7990i			0.645429i	0.946496	+	0.322714i	$0.104595\pi$
$941$			19.7990i			0.645429i	−0.946496	+	0.322714i	$0.895405\pi$
$942$	6.00000	−	4.24264i	0.195491	−	0.138233i
$943$	−8.00000			−0.260516
$944$		−	1.41421i		−	0.0460287i
$945$		0			0
$946$	−6.00000	−	7.07107i	−0.195077	−	0.229900i
$947$		−	39.5980i		−	1.28676i	−0.765546	−	0.643381i	$-0.777531\pi$
$947$		−	39.5980i		−	1.28676i	0.765546	−	0.643381i	$-0.222469\pi$
$948$	−8.00000	−	11.3137i	−0.259828	−	0.367452i
$949$			8.48528i			0.275444i
$950$			4.24264i			0.137649i
$951$	22.0000	−	15.5563i	0.713399	−	0.504449i
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	−4.00000	−	1.41421i	−0.129505	−	0.0457869i
$955$	−12.0000			−0.388311
$956$		−	1.41421i		−	0.0457389i
$957$		0			0
$958$		−	41.0122i		−	1.32504i
$959$		0			0
$960$	−1.00000	−	1.41421i	−0.0322749	−	0.0456435i
$961$	33.0000			1.06452
$962$		−	8.48528i		−	0.273576i
$963$	16.0000	+	5.65685i	0.515593	+	0.182290i
$964$			8.48528i			0.273293i
$965$	−10.0000			−0.321911
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−9.00000			−0.289271
$969$	−30.0000	−	42.4264i	−0.963739	−	1.36293i
$970$	−2.00000			−0.0642161
$971$		−	18.3848i		−	0.589996i	−0.955498	−	0.294998i	$-0.904681\pi$
$971$		−	18.3848i		−	0.589996i	0.955498	−	0.294998i	$-0.0953189\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$		0			0
$974$	16.0000			0.512673
$975$	−2.00000	−	2.82843i	−0.0640513	−	0.0905822i
$976$		0			0
$977$		−	1.41421i		−	0.0452447i	−0.999744	−	0.0226224i	$-0.992798\pi$
$977$		−	1.41421i		−	0.0452447i	0.999744	−	0.0226224i	$-0.00720153\pi$
$978$		0			0
$979$		0			0
$980$	7.00000			0.223607
$981$	4.00000	−	11.3137i	0.127710	−	0.361219i
$982$	−24.0000			−0.765871
$983$	−30.0000			−0.956851			−0.478426	−	0.878128i	$-0.658792\pi$
$983$	−30.0000			−0.956851			−0.478426	+	0.878128i	$0.658792\pi$
$984$	−4.00000	+	2.82843i	−0.127515	+	0.0901670i
$985$			7.07107i			0.225303i
$986$		0			0
$987$		0			0
$988$		−	8.48528i		−	0.269953i
$989$	−12.0000	−	14.1421i	−0.381578	−	0.449694i
$990$	−4.00000	−	1.41421i	−0.127128	−	0.0449467i
$991$		−	12.7279i		−	0.404316i	−0.979353	−	0.202158i	$-0.935205\pi$
$991$		−	12.7279i		−	0.404316i	0.979353	−	0.202158i	$-0.0647954\pi$
$992$	−8.00000			−0.254000
$993$	42.0000	−	29.6985i	1.33283	−	0.942453i
$994$		0			0
$995$			12.7279i			0.403502i
$996$	−20.0000	+	14.1421i	−0.633724	+	0.448111i
$997$		−	12.7279i		−	0.403097i	−0.979479	−	0.201549i	$-0.935403\pi$
$997$		−	12.7279i		−	0.403097i	0.979479	−	0.201549i	$-0.0645974\pi$
$998$		−	4.24264i		−	0.134298i
$999$	6.00000	+	21.2132i	0.189832	+	0.671156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1290.2.c.c.1031.1	✓	2
3.2	odd	2		1290.2.c.f.1031.1	yes	2
43.42	odd	2		1290.2.c.f.1031.2	yes	2
129.128	even	2	inner	1290.2.c.c.1031.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1290.2.c.c.1031.1	✓	2	1.1	even	1	trivial
1290.2.c.c.1031.2	yes	2	129.128	even	2	inner
1290.2.c.f.1031.1	yes	2	3.2	odd	2
1290.2.c.f.1031.2	yes	2	43.42	odd	2

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:	\( N \)	\(=\)	\( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1290.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(1.00000 + 1.41421i) q^{6} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(1.00000 + 1.41421i) q^{6} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000 q^{10} -1.41421i q^{11} +(-1.00000 - 1.41421i) q^{12} +2.00000 q^{13} +(-1.00000 - 1.41421i) q^{15} +1.00000 q^{16} +7.07107i q^{17} +(1.00000 - 2.82843i) q^{18} -4.24264i q^{19} +1.00000 q^{20} +1.41421i q^{22} +2.82843i q^{23} +(1.00000 + 1.41421i) q^{24} +1.00000 q^{25} -2.00000 q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 1.41421i) q^{30} +8.00000 q^{31} -1.00000 q^{32} +(-2.00000 + 1.41421i) q^{33} -7.07107i q^{34} +(-1.00000 + 2.82843i) q^{36} +4.24264i q^{37} +4.24264i q^{38} +(-2.00000 - 2.82843i) q^{39} -1.00000 q^{40} +2.82843i q^{41} +(-5.00000 + 4.24264i) q^{43} -1.41421i q^{44} +(-1.00000 + 2.82843i) q^{45} -2.82843i q^{46} +2.82843i q^{47} +(-1.00000 - 1.41421i) q^{48} +7.00000 q^{49} -1.00000 q^{50} +(10.0000 - 7.07107i) q^{51} +2.00000 q^{52} -1.41421i q^{53} +(-5.00000 + 1.41421i) q^{54} -1.41421i q^{55} +(-6.00000 + 4.24264i) q^{57} -1.41421i q^{59} +(-1.00000 - 1.41421i) q^{60} -8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +(2.00000 - 1.41421i) q^{66} -4.00000 q^{67} +7.07107i q^{68} +(4.00000 - 2.82843i) q^{69} +12.0000 q^{71} +(1.00000 - 2.82843i) q^{72} +4.24264i q^{73} -4.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} -4.24264i q^{76} +(2.00000 + 2.82843i) q^{78} +8.00000 q^{79} +1.00000 q^{80} +(-7.00000 - 5.65685i) q^{81} -2.82843i q^{82} -14.1421i q^{83} +7.07107i q^{85} +(5.00000 - 4.24264i) q^{86} +1.41421i q^{88} +(1.00000 - 2.82843i) q^{90} +2.82843i q^{92} +(-8.00000 - 11.3137i) q^{93} -2.82843i q^{94} -4.24264i q^{95} +(1.00000 + 1.41421i) q^{96} +2.00000 q^{97} -7.00000 q^{98} +(4.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 2 q^{20} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 10 q^{27} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 2 q^{36} - 4 q^{39} - 2 q^{40} - 10 q^{43} - 2 q^{45} - 2 q^{48} + 14 q^{49} - 2 q^{50} + 20 q^{51} + 4 q^{52} - 10 q^{54} - 12 q^{57} - 2 q^{60} - 16 q^{62} + 2 q^{64} + 4 q^{65} + 4 q^{66} - 8 q^{67} + 8 q^{69} + 24 q^{71} + 2 q^{72} - 2 q^{75} + 4 q^{78} + 16 q^{79} + 2 q^{80} - 14 q^{81} + 10 q^{86} + 2 q^{90} - 16 q^{93} + 2 q^{96} + 4 q^{97} - 14 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 2 * q^20 + 2 * q^24 + 2 * q^25 - 4 * q^26 + 10 * q^27 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^36 - 4 * q^39 - 2 * q^40 - 10 * q^43 - 2 * q^45 - 2 * q^48 + 14 * q^49 - 2 * q^50 + 20 * q^51 + 4 * q^52 - 10 * q^54 - 12 * q^57 - 2 * q^60 - 16 * q^62 + 2 * q^64 + 4 * q^65 + 4 * q^66 - 8 * q^67 + 8 * q^69 + 24 * q^71 + 2 * q^72 - 2 * q^75 + 4 * q^78 + 16 * q^79 + 2 * q^80 - 14 * q^81 + 10 * q^86 + 2 * q^90 - 16 * q^93 + 2 * q^96 + 4 * q^97 - 14 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more