LMFDB - Embedded newform 750.2.g.f.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.4
Root			$2.17199 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.301
Dual form			750.2.g.f.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.63137 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.63137 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.05464 - 1.49278i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(0.116478 + 0.0846260i) q^{13} +(-3.74686 + 2.72225i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.31485 + 7.12436i) q^{17} +1.00000 q^{18} +(-2.08298 - 6.41074i) q^{19} +(1.43117 - 4.40469i) q^{21} +(-0.784803 + 2.41537i) q^{22} +(-1.35699 + 0.985910i) q^{23} +1.00000 q^{24} -0.143974 q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.43117 - 4.40469i) q^{28} +(-0.696812 + 2.14457i) q^{29} +(0.310207 + 0.954718i) q^{31} +1.00000 q^{32} +(-0.784803 - 2.41537i) q^{33} +(-6.06035 - 4.40310i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(0.0719871 + 0.0523017i) q^{37} +(5.45330 + 3.96205i) q^{38} +(0.116478 - 0.0846260i) q^{39} +(-2.48680 - 1.80677i) q^{41} +(1.43117 + 4.40469i) q^{42} +9.02860 q^{43} +(-0.784803 - 2.41537i) q^{44} +(0.518324 - 1.59524i) q^{46} +(3.36376 - 10.3526i) q^{47} +(-0.809017 + 0.587785i) q^{48} +14.4496 q^{49} +7.49100 q^{51} +(0.116478 - 0.0846260i) q^{52} +(-1.53429 + 4.72205i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.43117 + 4.40469i) q^{56} -6.74065 q^{57} +(-0.696812 - 2.14457i) q^{58} +(-4.25029 - 3.08802i) q^{59} +(11.0841 - 8.05305i) q^{61} +(-0.812131 - 0.590048i) q^{62} +(-3.74686 - 2.72225i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.05464 + 1.49278i) q^{66} +(-2.36376 - 7.27491i) q^{67} +7.49100 q^{68} +(0.518324 + 1.59524i) q^{69} +(-3.17196 + 9.76228i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-1.59036 + 1.15547i) q^{73} -0.0889810 q^{74} -6.74065 q^{76} +(9.51580 - 6.91363i) q^{77} +(-0.0444905 + 0.136928i) q^{78} +(0.230908 - 0.710661i) q^{79} +(0.309017 + 0.951057i) q^{81} +3.07386 q^{82} +(-0.958745 - 2.95072i) q^{83} +(-3.74686 - 2.72225i) q^{84} +(-7.30429 + 5.30688i) q^{86} +(1.82428 + 1.32542i) q^{87} +(2.05464 + 1.49278i) q^{88} +(-0.593709 + 0.431355i) q^{89} +(0.539451 + 0.391934i) q^{91} +(0.518324 + 1.59524i) q^{92} +1.00385 q^{93} +(3.36376 + 10.3526i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-2.81837 + 8.67406i) q^{97} +(-11.6900 + 8.49326i) q^{98} -2.53967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	4.63137			1.75049			0.875247	−	0.483677i	$-0.160699\pi$
$7$	4.63137			1.75049			0.875247	+	0.483677i	$0.160699\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	2.05464	−	1.49278i	0.619497	−	0.450091i	−0.233249	−	0.972417i	$-0.574936\pi$
$11$	2.05464	−	1.49278i	0.619497	−	0.450091i	0.852746	+	0.522326i	$0.174936\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	0.116478	+	0.0846260i	0.0323051	+	0.0234710i	0.603821	−	0.797120i	$-0.293644\pi$
$13$	0.116478	+	0.0846260i	0.0323051	+	0.0234710i	−0.571516	+	0.820591i	$0.693644\pi$
$14$	−3.74686	+	2.72225i	−1.00139	+	0.727552i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.31485	+	7.12436i	0.561433	+	1.72791i	0.678320	+	0.734767i	$0.262708\pi$
$17$	2.31485	+	7.12436i	0.561433	+	1.72791i	−0.116887	+	0.993145i	$0.537292\pi$
$18$	1.00000			0.235702
$19$	−2.08298	−	6.41074i	−0.477867	−	1.47072i	−0.842051	−	0.539397i	$-0.818652\pi$
$19$	−2.08298	−	6.41074i	−0.477867	−	1.47072i	0.364184	−	0.931327i	$-0.381348\pi$
$20$		0			0
$21$	1.43117	−	4.40469i	0.312307	−	0.961183i
$22$	−0.784803	+	2.41537i	−0.167320	+	0.514959i
$23$	−1.35699	+	0.985910i	−0.282952	+	0.205576i	−0.720204	−	0.693763i	$-0.755952\pi$
$23$	−1.35699	+	0.985910i	−0.282952	+	0.205576i	0.437252	+	0.899339i	$0.355952\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−0.143974			−0.0282357
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.43117	−	4.40469i	0.270466	−	0.832409i
$29$	−0.696812	+	2.14457i	−0.129395	+	0.398236i	−0.994676	−	0.103050i	$-0.967140\pi$
$29$	−0.696812	+	2.14457i	−0.129395	+	0.398236i	0.865281	+	0.501287i	$0.167140\pi$
$30$		0			0
$31$	0.310207	+	0.954718i	0.0557148	+	0.171472i	0.975042	−	0.222023i	$-0.0712659\pi$
$31$	0.310207	+	0.954718i	0.0557148	+	0.171472i	−0.919327	+	0.393495i	$0.871266\pi$
$32$	1.00000			0.176777
$33$	−0.784803	−	2.41537i	−0.136617	−	0.420463i
$34$	−6.06035	−	4.40310i	−1.03934	−	0.755125i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	0.0719871	+	0.0523017i	0.0118346	+	0.00859835i	0.593687	−	0.804696i	$-0.297672\pi$
$37$	0.0719871	+	0.0523017i	0.0118346	+	0.00859835i	−0.581852	+	0.813295i	$0.697672\pi$
$38$	5.45330	+	3.96205i	0.884642	+	0.642730i
$39$	0.116478	−	0.0846260i	0.0186514	−	0.0135510i
$40$		0			0
$41$	−2.48680	−	1.80677i	−0.388373	−	0.282170i	0.376415	−	0.926451i	$-0.377157\pi$
$41$	−2.48680	−	1.80677i	−0.388373	−	0.282170i	−0.764789	+	0.644281i	$0.777157\pi$
$42$	1.43117	+	4.40469i	0.220835	+	0.679659i
$43$	9.02860			1.37685			0.688424	−	0.725308i	$-0.258303\pi$
$43$	9.02860			1.37685			0.688424	+	0.725308i	$0.258303\pi$
$44$	−0.784803	−	2.41537i	−0.118313	−	0.364131i
$45$		0			0
$46$	0.518324	−	1.59524i	0.0764226	−	0.235205i
$47$	3.36376	−	10.3526i	0.490655	−	1.51008i	−0.332965	−	0.942939i	$-0.608049\pi$
$47$	3.36376	−	10.3526i	0.490655	−	1.51008i	0.823620	−	0.567141i	$-0.191951\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	14.4496			2.06423
$50$		0			0
$51$	7.49100			1.04895
$52$	0.116478	−	0.0846260i	0.0161525	−	0.0117355i
$53$	−1.53429	+	4.72205i	−0.210751	+	0.648624i	0.788677	+	0.614807i	$0.210766\pi$
$53$	−1.53429	+	4.72205i	−0.210751	+	0.648624i	−0.999428	+	0.0338165i	$0.989234\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$		0			0
$56$	1.43117	+	4.40469i	0.191248	+	0.588602i
$57$	−6.74065			−0.892821
$58$	−0.696812	−	2.14457i	−0.0914959	−	0.281596i
$59$	−4.25029	−	3.08802i	−0.553341	−	0.402026i	0.275675	−	0.961251i	$-0.411099\pi$
$59$	−4.25029	−	3.08802i	−0.553341	−	0.402026i	−0.829016	+	0.559225i	$0.811099\pi$
$60$		0			0
$61$	11.0841	−	8.05305i	1.41917	−	1.03109i	0.427263	−	0.904127i	$-0.359478\pi$
$61$	11.0841	−	8.05305i	1.41917	−	1.03109i	0.991908	−	0.126960i	$-0.0405221\pi$
$62$	−0.812131	−	0.590048i	−0.103141	−	0.0749362i
$63$	−3.74686	−	2.72225i	−0.472060	−	0.342971i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	2.05464	+	1.49278i	0.252909	+	0.183749i
$67$	−2.36376	−	7.27491i	−0.288779	−	0.888771i	−0.985240	−	0.171177i	$-0.945243\pi$
$67$	−2.36376	−	7.27491i	−0.288779	−	0.888771i	0.696461	−	0.717595i	$-0.254757\pi$
$68$	7.49100			0.908417
$69$	0.518324	+	1.59524i	0.0623988	+	0.192044i
$70$		0			0
$71$	−3.17196	+	9.76228i	−0.376442	+	1.15857i	0.566059	+	0.824365i	$0.308468\pi$
$71$	−3.17196	+	9.76228i	−0.376442	+	1.15857i	−0.942501	+	0.334204i	$0.891532\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	−1.59036	+	1.15547i	−0.186138	+	0.135237i	−0.676952	−	0.736027i	$-0.736699\pi$
$73$	−1.59036	+	1.15547i	−0.186138	+	0.135237i	0.490814	+	0.871264i	$0.336699\pi$
$74$	−0.0889810			−0.0103438
$75$		0			0
$76$	−6.74065			−0.773206
$77$	9.51580	−	6.91363i	1.08443	−	0.787881i
$78$	−0.0444905	+	0.136928i	−0.00503756	+	0.0155040i
$79$	0.230908	−	0.710661i	0.0259792	−	0.0799556i	−0.937226	−	0.348722i	$-0.886616\pi$
$79$	0.230908	−	0.710661i	0.0259792	−	0.0799556i	0.963205	+	0.268766i	$0.0866158\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.07386			0.339451
$83$	−0.958745	−	2.95072i	−0.105236	−	0.323883i	0.884550	−	0.466446i	$-0.154466\pi$
$83$	−0.958745	−	2.95072i	−0.105236	−	0.323883i	−0.989786	+	0.142563i	$0.954466\pi$
$84$	−3.74686	−	2.72225i	−0.408816	−	0.297022i
$85$		0			0
$86$	−7.30429	+	5.30688i	−0.787642	+	0.572255i
$87$	1.82428	+	1.32542i	0.195583	+	0.142099i
$88$	2.05464	+	1.49278i	0.219025	+	0.159131i
$89$	−0.593709	+	0.431355i	−0.0629331	+	0.0457236i	−0.618807	−	0.785543i	$-0.712384\pi$
$89$	−0.593709	+	0.431355i	−0.0629331	+	0.0457236i	0.555874	+	0.831267i	$0.312384\pi$
$90$		0			0
$91$	0.539451	+	0.391934i	0.0565498	+	0.0410859i
$92$	0.518324	+	1.59524i	0.0540390	+	0.166315i
$93$	1.00385			0.104094
$94$	3.36376	+	10.3526i	0.346945	+	1.06779i
$95$		0			0
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−2.81837	+	8.67406i	−0.286162	+	0.880717i	0.699886	+	0.714255i	$0.253234\pi$
$97$	−2.81837	+	8.67406i	−0.286162	+	0.880717i	−0.986048	+	0.166462i	$0.946766\pi$
$98$	−11.6900	+	8.49326i	−1.18086	+	0.857948i
$99$	−2.53967			−0.255247
$100$		0			0
$101$	−2.88013			−0.286583			−0.143292	−	0.989680i	$-0.545769\pi$
$101$	−2.88013			−0.286583			−0.143292	+	0.989680i	$0.545769\pi$
$102$	−6.06035	+	4.40310i	−0.600064	+	0.435972i
$103$	−3.45214	+	10.6246i	−0.340149	+	1.04687i	0.623981	+	0.781440i	$0.285514\pi$
$103$	−3.45214	+	10.6246i	−0.340149	+	1.04687i	−0.964130	+	0.265432i	$0.914486\pi$
$104$	−0.0444905	+	0.136928i	−0.00436265	+	0.0134269i
$105$		0			0
$106$	−1.53429	−	4.72205i	−0.149023	−	0.458646i
$107$	14.0538			1.35863			0.679316	−	0.733846i	$-0.262277\pi$
$107$	14.0538			1.35863			0.679316	+	0.733846i	$0.262277\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−5.43552	−	3.94914i	−0.520628	−	0.378259i	0.296212	−	0.955122i	$-0.404276\pi$
$109$	−5.43552	−	3.94914i	−0.520628	−	0.378259i	−0.816841	+	0.576863i	$0.804276\pi$
$110$		0			0
$111$	0.0719871	−	0.0523017i	0.00683272	−	0.00496426i
$112$	−3.74686	−	2.72225i	−0.354045	−	0.257229i
$113$	−0.807092	−	0.586387i	−0.0759248	−	0.0551626i	0.549175	−	0.835707i	$-0.314942\pi$
$113$	−0.807092	−	0.586387i	−0.0759248	−	0.0551626i	−0.625100	+	0.780545i	$0.714942\pi$
$114$	5.45330	−	3.96205i	0.510748	−	0.371080i
$115$		0			0
$116$	1.82428	+	1.32542i	0.169380	+	0.123062i
$117$	−0.0444905	−	0.136928i	−0.00411315	−	0.0126590i
$118$	5.25365			0.483638
$119$	10.7209	+	32.9956i	0.982784	+	3.02470i
$120$		0			0
$121$	−1.40604	+	4.32736i	−0.127822	+	0.393396i
$122$	−4.23374	+	13.0301i	−0.383305	+	1.17969i
$123$	−2.48680	+	1.80677i	−0.224227	+	0.162911i
$124$	1.00385			0.0901484
$125$		0			0
$126$	4.63137			0.412595
$127$	−9.32123	+	6.77227i	−0.827125	+	0.600942i	−0.918745	−	0.394852i	$-0.870796\pi$
$127$	−9.32123	+	6.77227i	−0.827125	+	0.600942i	0.0916192	+	0.995794i	$0.470796\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	2.78999	−	8.58671i	0.245645	−	0.756017i
$130$		0			0
$131$	−0.551316	−	1.69677i	−0.0481687	−	0.148248i	0.924079	−	0.382201i	$-0.124834\pi$
$131$	−0.551316	−	1.69677i	−0.0481687	−	0.148248i	−0.972248	+	0.233953i	$0.924834\pi$
$132$	−2.53967			−0.221050
$133$	−9.64703	−	29.6905i	−0.836504	−	2.57449i
$134$	6.18841	+	4.49614i	0.534597	+	0.388407i
$135$		0			0
$136$	−6.06035	+	4.40310i	−0.519670	+	0.377563i
$137$	−12.9632	−	9.41828i	−1.10752	−	0.804658i	−0.125246	−	0.992126i	$-0.539972\pi$
$137$	−12.9632	−	9.41828i	−1.10752	−	0.804658i	−0.982271	+	0.187467i	$0.939972\pi$
$138$	−1.35699	−	0.985910i	−0.115515	−	0.0839262i
$139$	2.99660	−	2.17716i	0.254168	−	0.184664i	−0.453404	−	0.891305i	$-0.649790\pi$
$139$	2.99660	−	2.17716i	0.254168	−	0.184664i	0.707572	+	0.706641i	$0.249790\pi$
$140$		0			0
$141$	−8.80644	−	6.39825i	−0.741636	−	0.538830i
$142$	−3.17196	−	9.76228i	−0.266185	−	0.819232i
$143$	0.365648			0.0305770
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$		0			0
$146$	0.607465	−	1.86958i	0.0502741	−	0.154728i
$147$	4.46517	−	13.7424i	0.368281	−	1.13345i
$148$	0.0719871	−	0.0523017i	0.00591731	−	0.00429918i
$149$	1.88534			0.154453			0.0772267	−	0.997014i	$-0.475393\pi$
$149$	1.88534			0.154453			0.0772267	+	0.997014i	$0.475393\pi$
$150$		0			0
$151$	−6.15090			−0.500553			−0.250276	−	0.968174i	$-0.580522\pi$
$151$	−6.15090			−0.500553			−0.250276	+	0.968174i	$0.580522\pi$
$152$	5.45330	−	3.96205i	0.442321	−	0.321365i
$153$	2.31485	−	7.12436i	0.187144	−	0.575971i
$154$	−3.63471	+	11.1865i	−0.292893	+	0.901433i
$155$		0			0
$156$	−0.0444905	−	0.136928i	−0.00356209	−	0.0109630i
$157$	−23.4830			−1.87414			−0.937072	−	0.349137i	$-0.886475\pi$
$157$	−23.4830			−1.87414			−0.937072	+	0.349137i	$0.886475\pi$
$158$	0.230908	+	0.710661i	0.0183700	+	0.0565372i
$159$	4.01682	+	2.91839i	0.318554	+	0.231443i
$160$		0			0
$161$	−6.28472	+	4.56611i	−0.495305	+	0.359860i
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	12.7641	+	9.27366i	0.999762	+	0.726369i	0.962037	−	0.272919i	$-0.0879891\pi$
$163$	12.7641	+	9.27366i	0.999762	+	0.726369i	0.0377245	+	0.999288i	$0.487989\pi$
$164$	−2.48680	+	1.80677i	−0.194187	+	0.141085i
$165$		0			0
$166$	2.51003	+	1.82364i	0.194816	+	0.141542i
$167$	−1.24837	−	3.84208i	−0.0966016	−	0.297309i	0.891066	−	0.453873i	$-0.149958\pi$
$167$	−1.24837	−	3.84208i	−0.0966016	−	0.297309i	−0.987668	+	0.156564i	$0.949958\pi$
$168$	4.63137			0.357318
$169$	−4.01082	−	12.3440i	−0.308524	−	0.949540i
$170$		0			0
$171$	−2.08298	+	6.41074i	−0.159289	+	0.490241i
$172$	2.78999	−	8.58671i	0.212735	−	0.654730i
$173$	−16.3094	+	11.8495i	−1.23998	+	0.900899i	−0.997597	−	0.0692809i	$-0.977930\pi$
$173$	−16.3094	+	11.8495i	−1.23998	+	0.900899i	−0.242384	+	0.970180i	$0.577930\pi$
$174$	−2.25493			−0.170946
$175$		0			0
$176$	−2.53967			−0.191435
$177$	−4.25029	+	3.08802i	−0.319472	+	0.232110i
$178$	0.226777	−	0.697947i	0.0169976	−	0.0523134i
$179$	−2.39818	+	7.38084i	−0.179248	+	0.551670i	−0.999802	−	0.0198998i	$-0.993665\pi$
$179$	−2.39818	+	7.38084i	−0.179248	+	0.551670i	0.820554	+	0.571570i	$0.193665\pi$
$180$		0			0
$181$	3.64358	+	11.2138i	0.270825	+	0.833515i	0.990294	+	0.138990i	$0.0443855\pi$
$181$	3.64358	+	11.2138i	0.270825	+	0.833515i	−0.719469	+	0.694525i	$0.755615\pi$
$182$	−0.666798			−0.0494264
$183$	−4.23374	−	13.0301i	−0.312967	−	0.963214i
$184$	−1.35699	−	0.985910i	−0.100039	−	0.0726822i
$185$		0			0
$186$	−0.812131	+	0.590048i	−0.0595484	+	0.0432644i
$187$	15.3913	+	11.1824i	1.12552	+	0.817741i
$188$	−8.80644	−	6.39825i	−0.642276	−	0.466641i
$189$	−3.74686	+	2.72225i	−0.272544	+	0.198015i
$190$		0			0
$191$	−3.95155	−	2.87097i	−0.285924	−	0.207736i	0.435573	−	0.900153i	$-0.356546\pi$
$191$	−3.95155	−	2.87097i	−0.285924	−	0.207736i	−0.721497	+	0.692417i	$0.756546\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	−18.7342			−1.34852			−0.674258	−	0.738496i	$-0.735536\pi$
$193$	−18.7342			−1.34852			−0.674258	+	0.738496i	$0.735536\pi$
$194$	−2.81837	−	8.67406i	−0.202347	−	0.622761i
$195$		0			0
$196$	4.46517	−	13.7424i	0.318941	−	0.981598i
$197$	−0.387674	+	1.19314i	−0.0276206	+	0.0850075i	−0.963917	−	0.266204i	$-0.914230\pi$
$197$	−0.387674	+	1.19314i	−0.0276206	+	0.0850075i	0.936296	+	0.351212i	$0.114230\pi$
$198$	2.05464	−	1.49278i	0.146017	−	0.106087i
$199$	19.3703			1.37312			0.686562	−	0.727071i	$-0.259119\pi$
$199$	19.3703			1.37312			0.686562	+	0.727071i	$0.259119\pi$
$200$		0			0
$201$	−7.64929			−0.539539
$202$	2.33007	−	1.69290i	0.163943	−	0.119112i
$203$	−3.22720	+	9.93229i	−0.226505	+	0.697110i
$204$	2.31485	−	7.12436i	0.162072	−	0.498805i
$205$		0			0
$206$	−3.45214	−	10.6246i	−0.240522	−	0.740250i
$207$	1.67733			0.116583
$208$	−0.0444905	−	0.136928i	−0.00308486	−	0.00949423i
$209$	−13.8496	−	10.0623i	−0.957997	−	0.696026i
$210$		0			0
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	−0.552455	−	0.833543i	$-0.686309\pi$
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	0.622029	+	0.782994i	$0.286309\pi$
$212$	4.01682	+	2.91839i	0.275876	+	0.200436i
$213$	8.30429	+	6.03342i	0.569001	+	0.413403i
$214$	−11.3698	+	8.26061i	−0.777221	+	0.564684i
$215$		0			0
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	1.43668	+	4.42165i	0.0975283	+	0.300161i
$218$	6.71867			0.455046
$219$	0.607465	+	1.86958i	0.0410487	+	0.126335i
$220$		0			0
$221$	−0.333278	+	1.02573i	−0.0224187	+	0.0689978i
$222$	−0.0274966	+	0.0846260i	−0.00184545	+	0.00567972i
$223$	−17.7058	+	12.8640i	−1.18567	+	0.861437i	−0.992800	−	0.119788i	$-0.961779\pi$
$223$	−17.7058	+	12.8640i	−1.18567	+	0.861437i	−0.192867	+	0.981225i	$0.561779\pi$
$224$	4.63137			0.309446
$225$		0			0
$226$	0.997621			0.0663607
$227$	−11.7335	+	8.52486i	−0.778777	+	0.565815i	−0.904612	−	0.426237i	$-0.859839\pi$
$227$	−11.7335	+	8.52486i	−0.778777	+	0.565815i	0.125835	+	0.992051i	$0.459839\pi$
$228$	−2.08298	+	6.41074i	−0.137948	+	0.424562i
$229$	1.45262	−	4.47071i	0.0959920	−	0.295433i	−0.891519	−	0.452983i	$-0.850360\pi$
$229$	1.45262	−	4.47071i	0.0959920	−	0.295433i	0.987511	+	0.157550i	$0.0503597\pi$
$230$		0			0
$231$	−3.63471	−	11.1865i	−0.239146	−	0.736017i
$232$	−2.25493			−0.148044
$233$	−3.65218	−	11.2403i	−0.239262	−	0.736374i	−0.996527	−	0.0832661i	$-0.973465\pi$
$233$	−3.65218	−	11.2403i	−0.239262	−	0.736374i	0.757265	−	0.653108i	$-0.226535\pi$
$234$	0.116478	+	0.0846260i	0.00761438	+	0.00553217i
$235$		0			0
$236$	−4.25029	+	3.08802i	−0.276671	+	0.201013i
$237$	−0.604525	−	0.439213i	−0.0392681	−	0.0285299i
$238$	−28.0677	−	20.3924i	−1.81936	−	1.32184i
$239$	−7.85849	+	5.70953i	−0.508324	+	0.369319i	−0.812187	−	0.583397i	$-0.801723\pi$
$239$	−7.85849	+	5.70953i	−0.508324	+	0.369319i	0.303864	+	0.952716i	$0.401723\pi$
$240$		0			0
$241$	−5.40451	−	3.92661i	−0.348135	−	0.252935i	0.399951	−	0.916537i	$-0.369027\pi$
$241$	−5.40451	−	3.92661i	−0.348135	−	0.252935i	−0.748086	+	0.663601i	$0.769027\pi$
$242$	−1.40604	−	4.32736i	−0.0903839	−	0.278173i
$243$	1.00000			0.0641500
$244$	−4.23374	−	13.0301i	−0.271037	−	0.834168i
$245$		0			0
$246$	0.949874	−	2.92341i	0.0605618	−	0.186390i
$247$	0.299895	−	0.922982i	0.0190819	−	0.0587279i
$248$	−0.812131	+	0.590048i	−0.0515704	+	0.0374681i
$249$	−3.10257			−0.196617
$250$		0			0
$251$	−19.6023			−1.23729			−0.618644	−	0.785672i	$-0.712317\pi$
$251$	−19.6023			−1.23729			−0.618644	+	0.785672i	$0.712317\pi$
$252$	−3.74686	+	2.72225i	−0.236030	+	0.171486i
$253$	−1.31637	+	4.05138i	−0.0827597	+	0.254708i
$254$	3.56039	−	10.9578i	0.223399	−	0.687551i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.46931			0.590679			0.295340	−	0.955392i	$-0.404567\pi$
$257$	9.46931			0.590679			0.295340	+	0.955392i	$0.404567\pi$
$258$	2.78999	+	8.58671i	0.173697	+	0.534585i
$259$	0.333399	+	0.242229i	0.0207164	+	0.0150514i
$260$		0			0
$261$	1.82428	−	1.32542i	0.112920	−	0.0820412i
$262$	1.44336	+	1.04866i	0.0891713	+	0.0647867i
$263$	17.1079	+	12.4296i	1.05492	+	0.766441i	0.973141	−	0.230210i	$-0.0739412\pi$
$263$	17.1079	+	12.4296i	1.05492	+	0.766441i	0.0817747	+	0.996651i	$0.473941\pi$
$264$	2.05464	−	1.49278i	0.126454	−	0.0918745i
$265$		0			0
$266$	25.2563	+	18.3497i	1.54856	+	1.12509i
$267$	0.226777	+	0.697947i	0.0138785	+	0.0427137i
$268$	−7.64929			−0.467255
$269$	−0.603355	−	1.85694i	−0.0367872	−	0.113219i	0.930977	−	0.365079i	$-0.118958\pi$
$269$	−0.603355	−	1.85694i	−0.0367872	−	0.113219i	−0.967764	+	0.251859i	$0.918958\pi$
$270$		0			0
$271$	−4.91521	+	15.1274i	−0.298577	+	0.918927i	0.683419	+	0.730027i	$0.260492\pi$
$271$	−4.91521	+	15.1274i	−0.298577	+	0.918927i	−0.981996	+	0.188900i	$0.939508\pi$
$272$	2.31485	−	7.12436i	0.140358	−	0.431978i
$273$	0.539451	−	0.391934i	0.0326491	−	0.0237209i
$274$	16.0233			0.968006
$275$		0			0
$276$	1.67733			0.100963
$277$	1.61033	−	1.16998i	0.0967555	−	0.0702970i	−0.538356	−	0.842718i	$-0.680954\pi$
$277$	1.61033	−	1.16998i	0.0967555	−	0.0702970i	0.635111	+	0.772421i	$0.280954\pi$
$278$	−1.14460	+	3.52272i	−0.0686485	+	0.211278i
$279$	0.310207	−	0.954718i	0.0185716	−	0.0571575i
$280$		0			0
$281$	−7.78302	−	23.9537i	−0.464296	−	1.42896i	−0.859866	−	0.510521i	$-0.829453\pi$
$281$	−7.78302	−	23.9537i	−0.464296	−	1.42896i	0.395569	−	0.918436i	$-0.370547\pi$
$282$	10.8854			0.648214
$283$	3.47958	+	10.7090i	0.206839	+	0.636586i	0.999633	+	0.0270957i	$0.00862588\pi$
$283$	3.47958	+	10.7090i	0.206839	+	0.636586i	−0.792794	+	0.609490i	$0.791374\pi$
$284$	8.30429	+	6.03342i	0.492769	+	0.358018i
$285$		0			0
$286$	−0.295815	+	0.214922i	−0.0174919	+	0.0127086i
$287$	−11.5173	−	8.36781i	−0.679845	−	0.493936i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−31.6448	+	22.9913i	−1.86146	+	1.35243i
$290$		0			0
$291$	7.37859	+	5.36086i	0.432541	+	0.314259i
$292$	0.607465	+	1.86958i	0.0355492	+	0.109409i
$293$	20.0482			1.17123			0.585613	−	0.810591i	$-0.300854\pi$
$293$	20.0482			1.17123			0.585613	+	0.810591i	$0.300854\pi$
$294$	4.46517	+	13.7424i	0.260414	+	0.801472i
$295$		0			0
$296$	−0.0274966	+	0.0846260i	−0.00159821	+	0.00491878i
$297$	−0.784803	+	2.41537i	−0.0455389	+	0.140154i
$298$	−1.52528	+	1.10818i	−0.0883569	+	0.0641950i
$299$	−0.241492			−0.0139659
$300$		0			0
$301$	41.8148			2.41016
$302$	4.97618	−	3.61541i	0.286347	−	0.208043i
$303$	−0.890008	+	2.73916i	−0.0511296	+	0.157361i
$304$	−2.08298	+	6.41074i	−0.119467	+	0.367681i
$305$		0			0
$306$	2.31485	+	7.12436i	0.132331	+	0.407273i
$307$	−14.4493			−0.824668			−0.412334	−	0.911033i	$-0.635286\pi$
$307$	−14.4493			−0.824668			−0.412334	+	0.911033i	$0.635286\pi$
$308$	−3.63471	−	11.1865i	−0.207107	−	0.637410i
$309$	9.03781	+	6.56635i	0.514143	+	0.373547i
$310$		0			0
$311$	19.0778	−	13.8608i	1.08180	−	0.785977i	0.103807	−	0.994597i	$-0.466897\pi$
$311$	19.0778	−	13.8608i	1.08180	−	0.785977i	0.977997	+	0.208621i	$0.0668975\pi$
$312$	0.116478	+	0.0846260i	0.00659425	+	0.00479100i
$313$	22.2420	+	16.1598i	1.25719	+	0.913405i	0.998616	−	0.0525858i	$-0.0167463\pi$
$313$	22.2420	+	16.1598i	1.25719	+	0.913405i	0.258577	+	0.965991i	$0.416746\pi$
$314$	18.9981	−	13.8029i	1.07213	−	0.778945i
$315$		0			0
$316$	−0.604525	−	0.439213i	−0.0340072	−	0.0247077i
$317$	1.86824	+	5.74985i	0.104931	+	0.322944i	0.989714	−	0.143059i	$-0.0456938\pi$
$317$	1.86824	+	5.74985i	0.104931	+	0.322944i	−0.884783	+	0.466002i	$0.845694\pi$
$318$	−4.96506			−0.278427
$319$	1.76968	+	5.44650i	0.0990829	+	0.304946i
$320$		0			0
$321$	4.34286	−	13.3660i	0.242395	−	0.746015i
$322$	2.40055	−	7.38813i	0.133777	−	0.411724i
$323$	40.8507	−	29.6798i	2.27299	−	1.65143i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−15.7773			−0.873824
$327$	−5.43552	+	3.94914i	−0.300585	+	0.218388i
$328$	0.949874	−	2.92341i	0.0524480	−	0.161418i
$329$	15.5788	−	47.9467i	0.858888	−	2.64339i
$330$		0			0
$331$	5.23211	+	16.1028i	0.287583	+	0.885089i	0.985613	+	0.169020i	$0.0540603\pi$
$331$	5.23211	+	16.1028i	0.287583	+	0.885089i	−0.698030	+	0.716069i	$0.745940\pi$
$332$	−3.10257			−0.170275
$333$	−0.0274966	−	0.0846260i	−0.00150681	−	0.00463747i
$334$	3.26827	+	2.37454i	0.178832	+	0.129929i
$335$		0			0
$336$	−3.74686	+	2.72225i	−0.204408	+	0.148511i
$337$	18.3341	+	13.3205i	0.998724	+	0.725616i	0.961814	−	0.273703i	$-0.0882485\pi$
$337$	18.3341	+	13.3205i	0.998724	+	0.725616i	0.0369100	+	0.999319i	$0.488249\pi$
$338$	10.5005	+	7.62902i	0.571149	+	0.414964i
$339$	−0.807092	+	0.586387i	−0.0438352	+	0.0318482i
$340$		0			0
$341$	2.06255	+	1.49853i	0.111693	+	0.0811500i
$342$	−2.08298	−	6.41074i	−0.112634	−	0.346653i
$343$	34.5018			1.86292
$344$	2.78999	+	8.58671i	0.150426	+	0.462964i
$345$		0			0
$346$	6.22964	−	19.1729i	0.334908	−	1.03074i
$347$	−3.16805	+	9.75025i	−0.170070	+	0.523421i	−0.999374	−	0.0353763i	$-0.988737\pi$
$347$	−3.16805	+	9.75025i	−0.170070	+	0.523421i	0.829304	+	0.558797i	$0.188737\pi$
$348$	1.82428	−	1.32542i	0.0977916	−	0.0710497i
$349$	1.38746			0.0742691			0.0371346	−	0.999310i	$-0.488177\pi$
$349$	1.38746			0.0742691			0.0371346	+	0.999310i	$0.488177\pi$
$350$		0			0
$351$	−0.143974			−0.00768478
$352$	2.05464	−	1.49278i	0.109513	−	0.0795656i
$353$	3.99189	−	12.2858i	0.212467	−	0.653906i	−0.786857	−	0.617136i	$-0.788293\pi$
$353$	3.99189	−	12.2858i	0.212467	−	0.653906i	0.999324	−	0.0367706i	$-0.0117071\pi$
$354$	1.62347	−	4.99652i	0.0862863	−	0.265562i
$355$		0			0
$356$	0.226777	+	0.697947i	0.0120191	+	0.0369911i
$357$	34.6936			1.83618
$358$	−2.39818	−	7.38084i	−0.126748	−	0.390089i
$359$	−7.98876	−	5.80417i	−0.421630	−	0.306332i	0.356663	−	0.934233i	$-0.383914\pi$
$359$	−7.98876	−	5.80417i	−0.421630	−	0.306332i	−0.778294	+	0.627901i	$0.783914\pi$
$360$		0			0
$361$	−21.3875	+	15.5389i	−1.12566	+	0.817837i
$362$	−9.53902	−	6.93051i	−0.501360	−	0.364259i
$363$	3.68107	+	2.67445i	0.193206	+	0.140372i
$364$	0.539451	−	0.391934i	0.0282749	−	0.0205429i
$365$		0			0
$366$	11.0841	+	8.05305i	0.579374	+	0.420940i
$367$	1.64372	+	5.05886i	0.0858016	+	0.264070i	0.984748	−	0.173989i	$-0.0556659\pi$
$367$	1.64372	+	5.05886i	0.0858016	+	0.264070i	−0.898946	+	0.438060i	$0.855666\pi$
$368$	1.67733			0.0874369
$369$	0.949874	+	2.92341i	0.0494485	+	0.152187i
$370$		0			0
$371$	−7.10585	+	21.8696i	−0.368918	+	1.13541i
$372$	0.310207	−	0.954718i	0.0160835	−	0.0494998i
$373$	7.83499	−	5.69246i	0.405681	−	0.294744i	−0.366170	−	0.930548i	$-0.619331\pi$
$373$	7.83499	−	5.69246i	0.405681	−	0.294744i	0.771851	+	0.635804i	$0.219331\pi$
$374$	−19.0247			−0.983744
$375$		0			0
$376$	10.8854			0.561369
$377$	−0.262649	+	0.190826i	−0.0135271	+	0.00982803i
$378$	1.43117	−	4.40469i	0.0736116	−	0.226553i
$379$	−6.95968	+	21.4197i	−0.357495	+	1.10026i	0.597054	+	0.802201i	$0.296338\pi$
$379$	−6.95968	+	21.4197i	−0.357495	+	1.10026i	−0.954549	+	0.298055i	$0.903662\pi$
$380$		0			0
$381$	3.56039	+	10.9578i	0.182404	+	0.561383i
$382$	4.88438			0.249907
$383$	−2.22851	−	6.85864i	−0.113871	−	0.350460i	0.877839	−	0.478957i	$-0.158985\pi$
$383$	−2.22851	−	6.85864i	−0.113871	−	0.350460i	−0.991710	+	0.128497i	$0.958985\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$		0			0
$386$	15.1563	−	11.0117i	0.771434	−	0.560479i
$387$	−7.30429	−	5.30688i	−0.371298	−	0.269764i
$388$	7.37859	+	5.36086i	0.374591	+	0.272157i
$389$	−10.7139	+	7.78411i	−0.543217	+	0.394670i	−0.825278	−	0.564726i	$-0.808982\pi$
$389$	−10.7139	+	7.78411i	−0.543217	+	0.394670i	0.282062	+	0.959396i	$0.408982\pi$
$390$		0			0
$391$	−10.1652	−	7.38545i	−0.514076	−	0.373498i
$392$	4.46517	+	13.7424i	0.225525	+	0.694095i
$393$	−1.78409			−0.0899957
$394$	−0.387674	−	1.19314i	−0.0195307	−	0.0601094i
$395$		0			0
$396$	−0.784803	+	2.41537i	−0.0394378	+	0.121377i
$397$	−9.04265	+	27.8304i	−0.453838	+	1.39677i	0.418657	+	0.908144i	$0.362501\pi$
$397$	−9.04265	+	27.8304i	−0.453838	+	1.39677i	−0.872494	+	0.488624i	$0.837499\pi$
$398$	−15.6709	+	11.3856i	−0.785511	+	0.570707i
$399$	−31.2184			−1.56288
$400$		0			0
$401$	27.4005			1.36832			0.684158	−	0.729334i	$-0.260170\pi$
$401$	27.4005			1.36832			0.684158	+	0.729334i	$0.260170\pi$
$402$	6.18841	−	4.49614i	0.308650	−	0.224247i
$403$	−0.0446618	+	0.137455i	−0.00222476	+	0.00684711i
$404$	−0.890008	+	2.73916i	−0.0442796	+	0.136279i
$405$		0			0
$406$	−3.22720	−	9.93229i	−0.160163	−	0.492931i
$407$	0.225983			0.0112016
$408$	2.31485	+	7.12436i	0.114602	+	0.352709i
$409$	−8.09226	−	5.87937i	−0.400137	−	0.290716i	0.369460	−	0.929247i	$-0.379543\pi$
$409$	−8.09226	−	5.87937i	−0.400137	−	0.290716i	−0.769597	+	0.638530i	$0.779543\pi$
$410$		0			0
$411$	−12.9632	+	9.41828i	−0.639425	+	0.464570i
$412$	9.03781	+	6.56635i	0.445261	+	0.323501i
$413$	−19.6847	−	14.3018i	−0.968620	−	0.703744i
$414$	−1.35699	+	0.985910i	−0.0666924	+	0.0484548i
$415$		0			0
$416$	0.116478	+	0.0846260i	0.00571079	+	0.00414913i
$417$	−1.14460	−	3.52272i	−0.0560513	−	0.172508i
$418$	17.1191			0.837320
$419$	−2.48795	−	7.65713i	−0.121544	−	0.374075i	0.871711	−	0.490020i	$-0.163010\pi$
$419$	−2.48795	−	7.65713i	−0.121544	−	0.374075i	−0.993256	+	0.115945i	$0.963010\pi$
$420$		0			0
$421$	3.10662	−	9.56120i	0.151408	−	0.465984i	−0.846372	−	0.532593i	$-0.821218\pi$
$421$	3.10662	−	9.56120i	0.151408	−	0.465984i	0.997779	+	0.0666083i	$0.0212178\pi$
$422$	−0.386023	+	1.18806i	−0.0187913	+	0.0578337i
$423$	−8.80644	+	6.39825i	−0.428184	+	0.311094i
$424$	−4.96506			−0.241125
$425$		0			0
$426$	−10.2647			−0.497325
$427$	51.3345	−	37.2967i	2.48425	−	1.80491i
$428$	4.34286	−	13.3660i	0.209920	−	0.646068i
$429$	0.112991	−	0.347752i	0.00545528	−	0.0167896i
$430$		0			0
$431$	7.09793	+	21.8452i	0.341895	+	1.05225i	0.963225	+	0.268697i	$0.0865929\pi$
$431$	7.09793	+	21.8452i	0.341895	+	1.05225i	−0.621329	+	0.783549i	$0.713407\pi$
$432$	1.00000			0.0481125
$433$	5.56121	+	17.1156i	0.267254	+	0.822525i	0.991165	+	0.132631i	$0.0423426\pi$
$433$	5.56121	+	17.1156i	0.267254	+	0.822525i	−0.723911	+	0.689893i	$0.757657\pi$
$434$	−3.76128	−	2.73273i	−0.180547	−	0.131175i
$435$		0			0
$436$	−5.43552	+	3.94914i	−0.260314	+	0.189129i
$437$	9.14699	+	6.64567i	0.437560	+	0.317906i
$438$	−1.59036	−	1.15547i	−0.0759905	−	0.0552103i
$439$	21.1610	−	15.3743i	1.00996	−	0.733777i	0.0457572	−	0.998953i	$-0.485430\pi$
$439$	21.1610	−	15.3743i	1.00996	−	0.733777i	0.964200	+	0.265176i	$0.0854299\pi$
$440$		0			0
$441$	−11.6900	−	8.49326i	−0.556665	−	0.404441i
$442$	−0.333278	−	1.02573i	−0.0158524	−	0.0487888i
$443$	−40.5689			−1.92749			−0.963743	−	0.266833i	$-0.914023\pi$
$443$	−40.5689			−1.92749			−0.963743	+	0.266833i	$0.914023\pi$
$444$	−0.0274966	−	0.0846260i	−0.00130493	−	0.00401617i
$445$		0			0
$446$	6.76301	−	20.8144i	0.320238	−	0.985590i
$447$	0.582604	−	1.79307i	0.0275562	−	0.0848093i
$448$	−3.74686	+	2.72225i	−0.177022	+	0.128614i
$449$	−23.1589			−1.09294			−0.546468	−	0.837480i	$-0.684028\pi$
$449$	−23.1589			−1.09294			−0.546468	+	0.837480i	$0.684028\pi$
$450$		0			0
$451$	−7.80660			−0.367598
$452$	−0.807092	+	0.586387i	−0.0379624	+	0.0275813i
$453$	−1.90073	+	5.84985i	−0.0893042	+	0.274850i
$454$	4.48178	−	13.7935i	0.210340	−	0.647361i
$455$		0			0
$456$	−2.08298	−	6.41074i	−0.0975443	−	0.300210i
$457$	−38.3997			−1.79626			−0.898131	−	0.439728i	$-0.855075\pi$
$457$	−38.3997			−1.79626			−0.898131	+	0.439728i	$0.855075\pi$
$458$	1.45262	+	4.47071i	0.0678766	+	0.208903i
$459$	−6.06035	−	4.40310i	−0.282873	−	0.205519i
$460$		0			0
$461$	26.3670	−	19.1567i	1.22803	−	0.892217i	0.231290	−	0.972885i	$-0.425705\pi$
$461$	26.3670	−	19.1567i	1.22803	−	0.892217i	0.996741	+	0.0806677i	$0.0257053\pi$
$462$	9.51580	+	6.91363i	0.442715	+	0.321651i
$463$	2.05311	+	1.49167i	0.0954160	+	0.0693238i	0.634470	−	0.772947i	$-0.281218\pi$
$463$	2.05311	+	1.49167i	0.0954160	+	0.0693238i	−0.539054	+	0.842271i	$0.681218\pi$
$464$	1.82428	−	1.32542i	0.0846900	−	0.0615309i
$465$		0			0
$466$	9.56154	+	6.94686i	0.442930	+	0.321807i
$467$	0.462456	+	1.42329i	0.0213999	+	0.0658622i	0.961186	−	0.275901i	$-0.0889761\pi$
$467$	0.462456	+	1.42329i	0.0213999	+	0.0658622i	−0.939786	+	0.341763i	$0.888976\pi$
$468$	−0.143974			−0.00665521
$469$	−10.9475	−	33.6928i	−0.505506	−	1.55579i
$470$		0			0
$471$	−7.25663	+	22.3336i	−0.334368	+	1.02908i
$472$	1.62347	−	4.99652i	0.0747262	−	0.229983i
$473$	18.5505	−	13.4777i	0.852954	−	0.619707i
$474$	0.747233			0.0343216
$475$		0			0
$476$	34.6936			1.59018
$477$	4.01682	−	2.91839i	0.183917	−	0.133624i
$478$	3.00168	−	9.23821i	0.137294	−	0.422546i
$479$	7.50880	−	23.1097i	0.343086	−	1.05591i	−0.619514	−	0.784985i	$-0.712670\pi$
$479$	7.50880	−	23.1097i	0.343086	−	1.05591i	0.962600	−	0.270925i	$-0.0873295\pi$
$480$		0			0
$481$	0.00395881	+	0.0121840i	0.000180506	+	0.000555541i
$482$	6.68035			0.304281
$483$	2.40055	+	7.38813i	0.109229	+	0.336171i
$484$	3.68107	+	2.67445i	0.167321	+	0.121566i
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	8.09143	+	5.87877i	0.366658	+	0.266392i	0.755824	−	0.654775i	$-0.227237\pi$
$487$	8.09143	+	5.87877i	0.366658	+	0.266392i	−0.389166	+	0.921168i	$0.627237\pi$
$488$	11.0841	+	8.05305i	0.501753	+	0.364545i
$489$	12.7641	−	9.27366i	0.577213	−	0.419370i
$490$		0			0
$491$	−3.38163	−	2.45690i	−0.152611	−	0.110878i	0.508860	−	0.860850i	$-0.330067\pi$
$491$	−3.38163	−	2.45690i	−0.152611	−	0.110878i	−0.661470	+	0.749971i	$0.730067\pi$
$492$	0.949874	+	2.92341i	0.0428236	+	0.131798i
$493$	−16.8917			−0.760764
$494$	0.299895	+	0.922982i	0.0134929	+	0.0415269i
$495$		0			0
$496$	0.310207	−	0.954718i	0.0139287	−	0.0428681i
$497$	−14.6905	+	45.2127i	−0.658959	+	2.02807i
$498$	2.51003	−	1.82364i	0.112477	−	0.0817194i
$499$	1.70548			0.0763476			0.0381738	−	0.999271i	$-0.487846\pi$
$499$	1.70548			0.0763476			0.0381738	+	0.999271i	$0.487846\pi$
$500$		0			0
$501$	−4.03980			−0.180485
$502$	15.8586	−	11.5220i	0.707804	−	0.514250i
$503$	−9.56125	+	29.4265i	−0.426315	+	1.31206i	0.475414	+	0.879762i	$0.342298\pi$
$503$	−9.56125	+	29.4265i	−0.426315	+	1.31206i	−0.901729	+	0.432301i	$0.857702\pi$
$504$	1.43117	−	4.40469i	0.0637495	−	0.196201i
$505$		0			0
$506$	−1.31637	−	4.05138i	−0.0585199	−	0.180106i
$507$	−12.9793			−0.576430
$508$	3.56039	+	10.9578i	0.157967	+	0.486172i
$509$	29.2182	+	21.2283i	1.29507	+	0.940926i	0.999895	−	0.0145162i	$-0.00462080\pi$
$509$	29.2182	+	21.2283i	1.29507	+	0.940926i	0.295179	+	0.955442i	$0.404621\pi$
$510$		0			0
$511$	−7.36556	+	5.35139i	−0.325833	+	0.236732i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	5.45330	+	3.96205i	0.240769	+	0.174929i
$514$	−7.66083	+	5.56592i	−0.337905	+	0.245502i
$515$		0			0
$516$	−7.30429	−	5.30688i	−0.321553	−	0.233622i
$517$	−8.54286	−	26.2922i	−0.375714	−	1.15633i
$518$	−0.412104			−0.0181068
$519$	6.22964	+	19.1729i	0.273451	+	0.841595i
$520$		0			0
$521$	1.38131	−	4.25122i	0.0605161	−	0.186249i	−0.916228	−	0.400657i	$-0.868782\pi$
$521$	1.38131	−	4.25122i	0.0605161	−	0.186249i	0.976744	+	0.214407i	$0.0687820\pi$
$522$	−0.696812	+	2.14457i	−0.0304986	+	0.0938652i
$523$	24.7955	−	18.0150i	1.08423	−	0.787741i	0.105817	−	0.994386i	$-0.466254\pi$
$523$	24.7955	−	18.0150i	1.08423	−	0.787741i	0.978416	+	0.206644i	$0.0662543\pi$
$524$	−1.78409			−0.0779385
$525$		0			0
$526$	−21.1465			−0.922030
$527$	−6.08368	+	4.42005i	−0.265009	+	0.192540i
$528$	−0.784803	+	2.41537i	−0.0341541	+	0.105116i
$529$	−6.23799	+	19.1986i	−0.271217	+	0.834720i
$530$		0			0
$531$	1.62347	+	4.99652i	0.0704525	+	0.216830i
$532$	−31.2184			−1.35349
$533$	−0.136757	−	0.420896i	−0.00592362	−	0.0182310i
$534$	−0.593709	−	0.431355i	−0.0256923	−	0.0186666i
$535$		0			0
$536$	6.18841	−	4.49614i	0.267298	−	0.194204i
$537$	6.27852	+	4.56161i	0.270938	+	0.196848i
$538$	1.57960	+	1.14765i	0.0681016	+	0.0494787i
$539$	29.6887	−	21.5701i	1.27878	−	0.929090i
$540$		0			0
$541$	−11.9065	−	8.65055i	−0.511899	−	0.371916i	0.301645	−	0.953420i	$-0.402464\pi$
$541$	−11.9065	−	8.65055i	−0.511899	−	0.371916i	−0.813543	+	0.581504i	$0.802464\pi$
$542$	−4.91521	−	15.1274i	−0.211126	−	0.649780i
$543$	11.7909			0.505995
$544$	2.31485	+	7.12436i	0.0992482	+	0.305455i
$545$		0			0
$546$	−0.206052	+	0.634163i	−0.00881821	+	0.0271397i
$547$	3.29653	−	10.1457i	0.140950	−	0.433798i	−0.855518	−	0.517773i	$-0.826761\pi$
$547$	3.29653	−	10.1457i	0.140950	−	0.433798i	0.996468	+	0.0839742i	$0.0267613\pi$
$548$	−12.9632	+	9.41828i	−0.553759	+	0.402329i
$549$	−13.7007			−0.584730
$550$		0			0
$551$	15.1997			0.647529
$552$	−1.35699	+	0.985910i	−0.0577573	+	0.0419631i
$553$	1.06942	−	3.29134i	0.0454764	−	0.139962i
$554$	−0.615092	+	1.89306i	−0.0261328	+	0.0804284i
$555$		0			0
$556$	−1.14460	−	3.52272i	−0.0485418	−	0.149396i
$557$	−16.1652			−0.684942			−0.342471	−	0.939528i	$-0.611264\pi$
$557$	−16.1652			−0.684942			−0.342471	+	0.939528i	$0.611264\pi$
$558$	0.310207	+	0.954718i	0.0131321	+	0.0404164i
$559$	1.05163	+	0.764054i	0.0444792	+	0.0323160i
$560$		0			0
$561$	15.3913	−	11.1824i	0.649821	−	0.472123i
$562$	20.3762	+	14.8042i	0.859519	+	0.624477i
$563$	−35.1746	−	25.5559i	−1.48243	−	1.07705i	−0.976762	−	0.214326i	$-0.931245\pi$
$563$	−35.1746	−	25.5559i	−1.48243	−	1.07705i	−0.505672	−	0.862726i	$-0.668755\pi$
$564$	−8.80644	+	6.39825i	−0.370818	+	0.269415i
$565$		0			0
$566$	−9.10965	−	6.61855i	−0.382907	−	0.278198i
$567$	1.43117	+	4.40469i	0.0601036	+	0.184980i
$568$	−10.2647			−0.430696
$569$	3.71683	+	11.4392i	0.155818	+	0.479558i	0.998243	−	0.0592558i	$-0.0188728\pi$
$569$	3.71683	+	11.4392i	0.155818	+	0.479558i	−0.842425	+	0.538813i	$0.818873\pi$
$570$		0			0
$571$	5.80332	−	17.8608i	0.242861	−	0.747450i	−0.753120	−	0.657884i	$-0.771452\pi$
$571$	5.80332	−	17.8608i	0.242861	−	0.747450i	0.995981	−	0.0895664i	$-0.0285481\pi$
$572$	0.112991	−	0.347752i	0.00472441	−	0.0145402i
$573$	−3.95155	+	2.87097i	−0.165078	+	0.119936i
$574$	14.2362			0.594206
$575$		0			0
$576$	1.00000			0.0416667
$577$	−17.1796	+	12.4817i	−0.715195	+	0.519619i	−0.884845	−	0.465885i	$-0.845736\pi$
$577$	−17.1796	+	12.4817i	−0.715195	+	0.519619i	0.169651	+	0.985504i	$0.445736\pi$
$578$	12.0872	−	37.2007i	0.502762	−	1.54734i
$579$	−5.78918	+	17.8173i	−0.240590	+	0.740460i
$580$		0			0
$581$	−4.44031	−	13.6659i	−0.184215	−	0.566955i
$582$	−9.12044			−0.378055
$583$	3.89659	+	11.9925i	0.161380	+	0.496678i
$584$	−1.59036	−	1.15547i	−0.0658097	−	0.0478135i
$585$		0			0
$586$	−16.2193	+	11.7840i	−0.670013	+	0.486793i
$587$	−26.3964	−	19.1781i	−1.08950	−	0.791566i	−0.110183	−	0.993911i	$-0.535144\pi$
$587$	−26.3964	−	19.1781i	−1.08950	−	0.791566i	−0.979314	+	0.202345i	$0.935144\pi$
$588$	−11.6900	−	8.49326i	−0.482086	−	0.350256i
$589$	5.47429	−	3.97731i	0.225564	−	0.163882i
$590$		0			0
$591$	1.01494	+	0.737399i	0.0417492	+	0.0303326i
$592$	−0.0274966	−	0.0846260i	−0.00113011	−	0.00347811i
$593$	0.911868			0.0374460			0.0187230	−	0.999825i	$-0.494040\pi$
$593$	0.911868			0.0374460			0.0187230	+	0.999825i	$0.494040\pi$
$594$	−0.784803	−	2.41537i	−0.0322008	−	0.0991040i
$595$		0			0
$596$	0.582604	−	1.79307i	0.0238644	−	0.0734470i
$597$	5.98575	−	18.4222i	0.244980	−	0.753972i
$598$	0.195371	−	0.141946i	0.00798933	−	0.00580459i
$599$	−35.5516			−1.45260			−0.726300	−	0.687378i	$-0.758762\pi$
$599$	−35.5516			−1.45260			−0.726300	+	0.687378i	$0.758762\pi$
$600$		0			0
$601$	−42.8608			−1.74833			−0.874164	−	0.485630i	$-0.838590\pi$
$601$	−42.8608			−1.74833			−0.874164	+	0.485630i	$0.838590\pi$
$602$	−33.8289	+	24.5781i	−1.37876	+	1.00173i
$603$	−2.36376	+	7.27491i	−0.0962598	+	0.296257i
$604$	−1.90073	+	5.84985i	−0.0773397	+	0.238027i
$605$		0			0
$606$	−0.890008	−	2.73916i	−0.0361541	−	0.111271i
$607$	47.7389			1.93766			0.968831	−	0.247724i	$-0.0796827\pi$
$607$	47.7389			1.93766			0.968831	+	0.247724i	$0.0796827\pi$
$608$	−2.08298	−	6.41074i	−0.0844758	−	0.259990i
$609$	8.44891	+	6.13849i	0.342367	+	0.248744i
$610$		0			0
$611$	1.26790	−	0.921184i	0.0512938	−	0.0372671i
$612$	−6.06035	−	4.40310i	−0.244975	−	0.177985i
$613$	−19.8234	−	14.4025i	−0.800660	−	0.581713i	0.110448	−	0.993882i	$-0.464771\pi$
$613$	−19.8234	−	14.4025i	−0.800660	−	0.581713i	−0.911108	+	0.412169i	$0.864771\pi$
$614$	11.6898	−	8.49311i	0.471761	−	0.342754i
$615$		0			0
$616$	9.51580	+	6.91363i	0.383402	+	0.278558i
$617$	0.809796	+	2.49230i	0.0326012	+	0.100336i	0.966033	−	0.258419i	$-0.0832014\pi$
$617$	0.809796	+	2.49230i	0.0326012	+	0.100336i	−0.933432	+	0.358755i	$0.883201\pi$
$618$	−11.1713			−0.449378
$619$	−2.08751	−	6.42470i	−0.0839041	−	0.258230i	0.900299	−	0.435271i	$-0.143348\pi$
$619$	−2.08751	−	6.42470i	−0.0839041	−	0.258230i	−0.984204	+	0.177041i	$0.943348\pi$
$620$		0			0
$621$	0.518324	−	1.59524i	0.0207996	−	0.0640146i
$622$	−7.28708	+	22.4273i	−0.292185	+	0.899254i
$623$	−2.74969	+	1.99777i	−0.110164	+	0.0800388i
$624$	−0.143974			−0.00576358
$625$		0			0
$626$	−27.4927			−1.09883
$627$	−13.8496	+	10.0623i	−0.553100	+	0.401851i
$628$	−7.25663	+	22.3336i	−0.289571	+	0.891208i
$629$	−0.205977	+	0.633933i	−0.00821285	+	0.0252766i
$630$		0			0
$631$	−9.31855	−	28.6796i	−0.370966	−	1.14172i	−0.946160	−	0.323699i	$-0.895074\pi$
$631$	−9.31855	−	28.6796i	−0.370966	−	1.14172i	0.575194	−	0.818017i	$-0.304926\pi$
$632$	0.747233			0.0297234
$633$	−0.386023	−	1.18806i	−0.0153430	−	0.0472210i
$634$	−4.89111	−	3.55360i	−0.194251	−	0.141132i
$635$		0			0
$636$	4.01682	−	2.91839i	0.159277	−	0.115722i
$637$	1.68305	+	1.22281i	0.0666850	+	0.0484495i
$638$	−4.63307	−	3.36612i	−0.183425	−	0.133266i
$639$	8.30429	−	6.03342i	0.328513	−	0.238678i
$640$		0			0
$641$	−16.6059	−	12.0649i	−0.655892	−	0.476534i	0.209381	−	0.977834i	$-0.432855\pi$
$641$	−16.6059	−	12.0649i	−0.655892	−	0.476534i	−0.865273	+	0.501301i	$0.832855\pi$
$642$	4.34286	+	13.3660i	0.171399	+	0.527512i
$643$	−33.4413			−1.31880			−0.659399	−	0.751793i	$-0.729189\pi$
$643$	−33.4413			−1.31880			−0.659399	+	0.751793i	$0.729189\pi$
$644$	2.40055	+	7.38813i	0.0945949	+	0.291133i
$645$		0			0
$646$	−15.6036	+	48.0228i	−0.613914	+	1.88943i
$647$	5.58881	−	17.2006i	0.219719	−	0.676224i	−0.779066	−	0.626942i	$-0.784306\pi$
$647$	5.58881	−	17.2006i	0.219719	−	0.676224i	0.998785	−	0.0492828i	$-0.0156936\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	−13.3426			−0.523742
$650$		0			0
$651$	4.64920			0.182217
$652$	12.7641	−	9.27366i	0.499881	−	0.363185i
$653$	9.57766	−	29.4770i	0.374803	−	1.15352i	−0.568809	−	0.822470i	$-0.692596\pi$
$653$	9.57766	−	29.4770i	0.374803	−	1.15352i	0.943612	−	0.331055i	$-0.107404\pi$
$654$	2.07618	−	6.38984i	0.0811852	−	0.249862i
$655$		0			0
$656$	0.949874	+	2.92341i	0.0370864	+	0.114140i
$657$	1.96580			0.0766930
$658$	15.5788	+	47.9467i	0.607326	+	1.86916i
$659$	17.4953	+	12.7110i	0.681519	+	0.495152i	0.873861	−	0.486176i	$-0.161608\pi$
$659$	17.4953	+	12.7110i	0.681519	+	0.495152i	−0.192343	+	0.981328i	$0.561608\pi$
$660$		0			0
$661$	29.7396	−	21.6071i	1.15674	−	0.840418i	0.167374	−	0.985893i	$-0.446471\pi$
$661$	29.7396	−	21.6071i	1.15674	−	0.840418i	0.989362	+	0.145476i	$0.0464713\pi$
$662$	−13.6978	−	9.95207i	−0.532382	−	0.386798i
$663$	0.872534	+	0.633933i	0.0338864	+	0.0246199i
$664$	2.51003	−	1.82364i	0.0974080	−	0.0707710i
$665$		0			0
$666$	0.0719871	+	0.0523017i	0.00278945	+	0.00202665i
$667$	−1.16878	−	3.59715i	−0.0452555	−	0.139282i
$668$	−4.03980			−0.156305
$669$	6.76301	+	20.8144i	0.261473	+	0.804731i
$670$		0			0
$671$	10.7523	−	33.0923i	0.415089	−	1.27751i
$672$	1.43117	−	4.40469i	0.0552087	−	0.169915i
$673$	−24.9448	+	18.1235i	−0.961552	+	0.698608i	−0.953511	−	0.301360i	$-0.902560\pi$
$673$	−24.9448	+	18.1235i	−0.961552	+	0.698608i	−0.00804101	+	0.999968i	$0.502560\pi$
$674$	−22.6622			−0.872917
$675$		0			0
$676$	−12.9793			−0.499203
$677$	20.8808	−	15.1708i	0.802515	−	0.583061i	−0.109136	−	0.994027i	$-0.534808\pi$
$677$	20.8808	−	15.1708i	0.802515	−	0.583061i	0.911651	+	0.410966i	$0.134808\pi$
$678$	0.308282	−	0.948794i	0.0118395	−	0.0364382i
$679$	−13.0529	+	40.1728i	−0.500925	+	1.54169i
$680$		0			0
$681$	4.48178	+	13.7935i	0.171742	+	0.528568i
$682$	−2.54945			−0.0976235
$683$	6.45234	+	19.8582i	0.246892	+	0.759855i	0.995320	+	0.0966385i	$0.0308091\pi$
$683$	6.45234	+	19.8582i	0.246892	+	0.759855i	−0.748428	+	0.663216i	$0.769191\pi$
$684$	5.45330	+	3.96205i	0.208512	+	0.151493i
$685$		0			0
$686$	−27.9126	+	20.2797i	−1.06571	+	0.774281i
$687$	−3.80302	−	2.76305i	−0.145094	−	0.105417i
$688$	−7.30429	−	5.30688i	−0.278473	−	0.202323i
$689$	−0.578318	+	0.420173i	−0.0220322	+	0.0160073i
$690$		0			0
$691$	−16.7033	−	12.1357i	−0.635424	−	0.461662i	0.222851	−	0.974852i	$-0.428464\pi$
$691$	−16.7033	−	12.1357i	−0.635424	−	0.461662i	−0.858275	+	0.513190i	$0.828464\pi$
$692$	6.22964	+	19.1729i	0.236815	+	0.728843i
$693$	−11.7622			−0.446808
$694$	−3.16805	−	9.75025i	−0.120258	−	0.370115i
$695$		0			0
$696$	−0.696812	+	2.14457i	−0.0264126	+	0.0812896i
$697$	7.11551	−	21.8993i	0.269519	−	0.829494i
$698$	−1.12248	+	0.815529i	−0.0424865	+	0.0308682i
$699$	−11.8187			−0.447025
$700$		0			0
$701$	−12.3050			−0.464752			−0.232376	−	0.972626i	$-0.574650\pi$
$701$	−12.3050			−0.464752			−0.232376	+	0.972626i	$0.574650\pi$
$702$	0.116478	−	0.0846260i	0.00439617	−	0.00319400i
$703$	0.185345	−	0.570434i	0.00699043	−	0.0215143i
$704$	−0.784803	+	2.41537i	−0.0295784	+	0.0910328i
$705$		0			0
$706$	3.99189	+	12.2858i	0.150237	+	0.462382i
$707$	−13.3389			−0.501662
$708$	1.62347	+	4.99652i	0.0610137	+	0.187781i
$709$	19.9814	+	14.5173i	0.750417	+	0.545210i	0.895956	−	0.444143i	$-0.146492\pi$
$709$	19.9814	+	14.5173i	0.750417	+	0.545210i	−0.145539	+	0.989353i	$0.546492\pi$
$710$		0			0
$711$	−0.604525	+	0.439213i	−0.0226714	+	0.0164718i
$712$	−0.593709	−	0.431355i	−0.0222502	−	0.0161657i
$713$	−1.36221	−	0.989705i	−0.0510153	−	0.0370648i
$714$	−28.0677	+	20.3924i	−1.05041	+	0.763166i
$715$		0			0
$716$	6.27852	+	4.56161i	0.234639	+	0.170475i
$717$	3.00168	+	9.23821i	0.112100	+	0.345007i
$718$	9.87465			0.368519
$719$	−6.49650	−	19.9942i	−0.242279	−	0.745657i	−0.996072	−	0.0885457i	$-0.971778\pi$
$719$	−6.49650	−	19.9942i	−0.242279	−	0.745657i	0.753793	−	0.657111i	$-0.228222\pi$
$720$		0			0
$721$	−15.9881	+	49.2064i	−0.595429	+	1.83254i
$722$	8.16929	−	25.1425i	0.304029	−	0.935706i
$723$	−5.40451	+	3.92661i	−0.200996	+	0.146032i
$724$	11.7909			0.438205
$725$		0			0
$726$	−4.55005			−0.168868
$727$	−7.01519	+	5.09683i	−0.260179	+	0.189031i	−0.710226	−	0.703974i	$-0.751407\pi$
$727$	−7.01519	+	5.09683i	−0.260179	+	0.189031i	0.450047	+	0.893005i	$0.351407\pi$
$728$	−0.206052	+	0.634163i	−0.00763680	+	0.0235036i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	20.8998	+	64.3230i	0.773008	+	2.37907i
$732$	−13.7007			−0.506391
$733$	−10.4873	−	32.2766i	−0.387357	−	1.19216i	−0.934756	−	0.355291i	$-0.884382\pi$
$733$	−10.4873	−	32.2766i	−0.387357	−	1.19216i	0.547398	−	0.836872i	$-0.315618\pi$
$734$	−4.30332	−	3.12654i	−0.158838	−	0.115403i
$735$		0			0
$736$	−1.35699	+	0.985910i	−0.0500193	+	0.0363411i
$737$	−15.7165	−	11.4187i	−0.578926	−	0.420614i
$738$	−2.48680	−	1.80677i	−0.0915405	−	0.0665080i
$739$	13.2781	−	9.64708i	0.488442	−	0.354874i	−0.316143	−	0.948712i	$-0.602388\pi$
$739$	13.2781	−	9.64708i	0.488442	−	0.354874i	0.804585	+	0.593838i	$0.202388\pi$
$740$		0			0
$741$	−0.785135	−	0.570434i	−0.0288427	−	0.0209554i
$742$	−7.10585	−	21.8696i	−0.260864	−	0.802857i
$743$	−3.98742			−0.146284			−0.0731422	−	0.997322i	$-0.523303\pi$
$743$	−3.98742			−0.146284			−0.0731422	+	0.997322i	$0.523303\pi$
$744$	0.310207	+	0.954718i	0.0113727	+	0.0350017i
$745$		0			0
$746$	−2.99270	+	9.21059i	−0.109571	+	0.337224i
$747$	−0.958745	+	2.95072i	−0.0350787	+	0.107961i
$748$	15.3913	−	11.1824i	0.562762	−	0.408870i
$749$	65.0883			2.37828
$750$		0			0
$751$	37.5827			1.37141			0.685706	−	0.727879i	$-0.259494\pi$
$751$	37.5827			1.37141			0.685706	+	0.727879i	$0.259494\pi$
$752$	−8.80644	+	6.39825i	−0.321138	+	0.233320i
$753$	−6.05745	+	18.6429i	−0.220746	+	0.679385i
$754$	0.100323	−	0.308763i	0.00365355	−	0.0112445i
$755$		0			0
$756$	1.43117	+	4.40469i	0.0520512	+	0.160197i
$757$	31.2749			1.13671			0.568353	−	0.822785i	$-0.307581\pi$
$757$	31.2749			1.13671			0.568353	+	0.822785i	$0.307581\pi$
$758$	−6.95968	−	21.4197i	−0.252787	−	0.777999i
$759$	3.44631	+	2.50389i	0.125093	+	0.0908855i
$760$		0			0
$761$	−24.2292	+	17.6035i	−0.878306	+	0.638127i	−0.932803	−	0.360387i	$-0.882645\pi$
$761$	−24.2292	+	17.6035i	−0.878306	+	0.638127i	0.0544967	+	0.998514i	$0.482645\pi$
$762$	−9.32123	−	6.77227i	−0.337673	−	0.245333i
$763$	−25.1739	−	18.2899i	−0.911357	−	0.662139i
$764$	−3.95155	+	2.87097i	−0.142962	+	0.103868i
$765$		0			0
$766$	5.83431	+	4.23887i	0.210802	+	0.153157i
$767$	−0.233738	−	0.719370i	−0.00843978	−	0.0259750i
$768$	1.00000			0.0360844
$769$	−11.4039	−	35.0975i	−0.411234	−	1.26565i	−0.915576	−	0.402145i	$-0.868265\pi$
$769$	−11.4039	−	35.0975i	−0.411234	−	1.26565i	0.504342	−	0.863504i	$-0.331735\pi$
$770$		0			0
$771$	2.92618	−	9.00585i	0.105384	−	0.324338i
$772$	−5.78918	+	17.8173i	−0.208357	+	0.641257i
$773$	35.7898	−	26.0028i	1.28727	−	0.935256i	0.287523	−	0.957774i	$-0.407168\pi$
$773$	35.7898	−	26.0028i	1.28727	−	0.935256i	0.999746	+	0.0225174i	$0.00716813\pi$
$774$	9.02860			0.324526
$775$		0			0
$776$	−9.12044			−0.327405
$777$	0.333399	−	0.242229i	0.0119606	−	0.00868990i
$778$	4.09235	−	12.5950i	0.146718	−	0.451551i
$779$	−6.40277	+	19.7057i	−0.229403	+	0.706030i
$780$		0			0
$781$	8.05574	+	24.7930i	0.288257	+	0.887164i
$782$	12.5649			0.449319
$783$	−0.696812	−	2.14457i	−0.0249020	−	0.0766406i
$784$	−11.6900	−	8.49326i	−0.417499	−	0.303331i
$785$		0			0
$786$	1.44336	−	1.04866i	0.0514830	−	0.0374046i
$787$	−32.4011	−	23.5408i	−1.15497	−	0.839138i	−0.165840	−	0.986153i	$-0.553034\pi$
$787$	−32.4011	−	23.5408i	−1.15497	−	0.839138i	−0.989134	+	0.147015i	$0.953034\pi$
$788$	1.01494	+	0.737399i	0.0361559	+	0.0262688i
$789$	17.1079	−	12.4296i	0.609056	−	0.442505i
$790$		0			0
$791$	−3.73794	−	2.71577i	−0.132906	−	0.0965618i
$792$	−0.784803	−	2.41537i	−0.0278867	−	0.0858266i
$793$	1.97254			0.0700471
$794$	−9.04265	−	27.8304i	−0.320912	−	0.987664i
$795$		0			0
$796$	5.98575	−	18.4222i	0.212159	−	0.652959i
$797$	13.7445	−	42.3012i	0.486854	−	1.49838i	−0.342423	−	0.939546i	$-0.611247\pi$
$797$	13.7445	−	42.3012i	0.486854	−	1.49838i	0.829277	−	0.558838i	$-0.188753\pi$
$798$	25.2563	−	18.3497i	0.894062	−	0.649574i
$799$	81.5422			2.88476
$800$		0			0
$801$	0.733865			0.0259299
$802$	−22.1675	+	16.1056i	−0.782761	+	0.568709i
$803$	−1.54276	+	4.74813i	−0.0544429	+	0.167558i
$804$	−2.36376	+	7.27491i	−0.0833634	+	0.256566i
$805$		0			0
$806$	−0.0446618	−	0.137455i	−0.00157314	−	0.00484164i
$807$	−1.95250			−0.0687312
$808$	−0.890008	−	2.73916i	−0.0313104	−	0.0963635i
$809$	27.7120	+	20.1339i	0.974301	+	0.707871i	0.956428	−	0.291969i	$-0.0943105\pi$
$809$	27.7120	+	20.1339i	0.974301	+	0.707871i	0.0178730	+	0.999840i	$0.494311\pi$
$810$		0			0
$811$	−8.61506	+	6.25921i	−0.302516	+	0.219790i	−0.728678	−	0.684856i	$-0.759865\pi$
$811$	−8.61506	+	6.25921i	−0.302516	+	0.219790i	0.426163	+	0.904646i	$0.359865\pi$
$812$	8.44891	+	6.13849i	0.296499	+	0.215419i
$813$	12.8682	+	9.34928i	0.451307	+	0.327893i
$814$	−0.182824	+	0.132829i	−0.00640798	+	0.00465567i
$815$		0			0
$816$	−6.06035	−	4.40310i	−0.212155	−	0.154139i
$817$	−18.8063	−	57.8800i	−0.657951	−	2.02496i
$818$	10.0026			0.349732
$819$	−0.206052	−	0.634163i	−0.00720004	−	0.0221594i
$820$		0			0
$821$	−4.55450	+	14.0173i	−0.158953	+	0.489208i	−0.998540	−	0.0540178i	$-0.982797\pi$
$821$	−4.55450	+	14.0173i	−0.158953	+	0.489208i	0.839587	+	0.543226i	$0.182797\pi$
$822$	4.95149	−	15.2391i	0.172703	−	0.531525i
$823$	−2.29161	+	1.66495i	−0.0798805	+	0.0580365i	−0.627009	−	0.779012i	$-0.715721\pi$
$823$	−2.29161	+	1.66495i	−0.0798805	+	0.0580365i	0.547128	+	0.837049i	$0.315721\pi$
$824$	−11.1713			−0.389172
$825$		0			0
$826$	24.3316			0.846605
$827$	−17.6459	+	12.8205i	−0.613609	+	0.445813i	−0.850683	−	0.525678i	$-0.823812\pi$
$827$	−17.6459	+	12.8205i	−0.613609	+	0.445813i	0.237074	+	0.971492i	$0.423812\pi$
$828$	0.518324	−	1.59524i	0.0180130	−	0.0554383i
$829$	−12.5472	+	38.6164i	−0.435784	+	1.34120i	0.456497	+	0.889725i	$0.349104\pi$
$829$	−12.5472	+	38.6164i	−0.435784	+	1.34120i	−0.892281	+	0.451480i	$0.850896\pi$
$830$		0			0
$831$	−0.615092	−	1.89306i	−0.0213373	−	0.0656695i
$832$	−0.143974			−0.00499141
$833$	33.4486	+	102.944i	1.15892	+	3.56680i
$834$	2.99660	+	2.17716i	0.103764	+	0.0753888i
$835$		0			0
$836$	−13.8496	+	10.0623i	−0.478999	+	0.348013i
$837$	−0.812131	−	0.590048i	−0.0280714	−	0.0203950i
$838$	6.51354	+	4.73236i	0.225007	+	0.163477i
$839$	−23.3715	+	16.9804i	−0.806875	+	0.586229i	−0.912923	−	0.408132i	$-0.866180\pi$
$839$	−23.3715	+	16.9804i	−0.806875	+	0.586229i	0.106048	+	0.994361i	$0.466180\pi$
$840$		0			0
$841$	19.3479	+	14.0571i	0.667168	+	0.484726i
$842$	3.10662	+	9.56120i	0.107061	+	0.329501i
$843$	−25.1864			−0.867465
$844$	−0.386023	−	1.18806i	−0.0132875	−	0.0408946i
$845$		0			0
$846$	3.36376	−	10.3526i	0.115648	−	0.355929i
$847$	−6.51191	+	20.0416i	−0.223752	+	0.688637i
$848$	4.01682	−	2.91839i	0.137938	−	0.100218i
$849$	11.2601			0.386447
$850$		0			0
$851$	−0.149251			−0.00511624
$852$	8.30429	−	6.03342i	0.284500	−	0.206702i
$853$	7.66646	−	23.5949i	0.262495	−	0.807875i	−0.729765	−	0.683698i	$-0.760371\pi$
$853$	7.66646	−	23.5949i	0.262495	−	0.807875i	0.992260	−	0.124178i	$-0.0396292\pi$
$854$	−19.6080	+	60.3473i	−0.670973	+	2.06504i
$855$		0			0
$856$	4.34286	+	13.3660i	0.148436	+	0.456839i
$857$	−20.0312			−0.684251			−0.342126	−	0.939654i	$-0.611147\pi$
$857$	−20.0312			−0.684251			−0.342126	+	0.939654i	$0.611147\pi$
$858$	0.112991	+	0.347752i	0.00385746	+	0.0118720i
$859$	25.7151	+	18.6831i	0.877387	+	0.637459i	0.932559	−	0.361018i	$-0.117571\pi$
$859$	25.7151	+	18.6831i	0.877387	+	0.637459i	−0.0551721	+	0.998477i	$0.517571\pi$
$860$		0			0
$861$	−11.5173	+	8.36781i	−0.392509	+	0.285174i
$862$	−18.5826	−	13.5011i	−0.632927	−	0.459848i
$863$	−19.3354	−	14.0480i	−0.658184	−	0.478199i	0.207865	−	0.978157i	$-0.433348\pi$
$863$	−19.3354	−	14.0480i	−0.658184	−	0.478199i	−0.866049	+	0.499959i	$0.833348\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$		0			0
$866$	−14.5594	−	10.5780i	−0.494749	−	0.359456i
$867$	12.0872	+	37.2007i	0.410504	+	1.26340i
$868$	4.64920			0.157804
$869$	−0.586431	−	1.80485i	−0.0198933	−	0.0612253i
$870$		0			0
$871$	0.340321	−	1.04740i	0.0115313	−	0.0354898i
$872$	2.07618	−	6.38984i	0.0703085	−	0.216387i
$873$	7.37859	−	5.36086i	0.249728	−	0.181438i
$874$	−11.3063			−0.382441
$875$		0			0
$876$	1.96580			0.0664181
$877$	3.80586	−	2.76512i	0.128515	−	0.0933715i	−0.521671	−	0.853147i	$-0.674691\pi$
$877$	3.80586	−	2.76512i	0.128515	−	0.0933715i	0.650186	+	0.759775i	$0.274691\pi$
$878$	−8.08277	+	24.8762i	−0.272780	+	0.839531i
$879$	6.19522	−	19.0669i	0.208960	−	0.643112i
$880$		0			0
$881$	−13.7902	−	42.4420i	−0.464605	−	1.42991i	−0.859478	−	0.511172i	$-0.829211\pi$
$881$	−13.7902	−	42.4420i	−0.464605	−	1.42991i	0.394873	−	0.918736i	$-0.370789\pi$
$882$	14.4496			0.486543
$883$	9.95182	+	30.6286i	0.334905	+	1.03073i	0.966769	+	0.255653i	$0.0822904\pi$
$883$	9.95182	+	30.6286i	0.334905	+	1.03073i	−0.631863	+	0.775080i	$0.717710\pi$
$884$	0.872534	+	0.633933i	0.0293465	+	0.0213215i
$885$		0			0
$886$	32.8209	−	23.8458i	1.10264	−	0.801115i
$887$	34.8080	+	25.2895i	1.16874	+	0.849137i	0.990857	−	0.134915i	$-0.0430761\pi$
$887$	34.8080	+	25.2895i	1.16874	+	0.849137i	0.177880	+	0.984052i	$0.443076\pi$
$888$	0.0719871	+	0.0523017i	0.00241573	+	0.00175513i
$889$	−43.1701	+	31.3649i	−1.44788	+	1.05194i
$890$		0			0
$891$	2.05464	+	1.49278i	0.0688330	+	0.0500101i
$892$	6.76301	+	20.8144i	0.226442	+	0.696917i
$893$	−73.3744			−2.45538
$894$	0.582604	+	1.79307i	0.0194852	+	0.0599692i
$895$		0			0
$896$	1.43117	−	4.40469i	0.0478121	−	0.147151i
$897$	−0.0746253	+	0.229673i	−0.00249167	+	0.00766856i
$898$	18.7360	−	13.6125i	0.625227	−	0.454254i
$899$	−2.26361			−0.0754957
$900$		0			0
$901$	−37.1933			−1.23909
$902$	6.31567	−	4.58860i	0.210289	−	0.152784i
$903$	12.9215	−	39.7682i	0.430000	−	1.32340i
$904$	0.308282	−	0.948794i	0.0102533	−	0.0315564i
$905$		0			0
$906$	−1.90073	−	5.84985i	−0.0631476	−	0.194348i
$907$	39.3398			1.30626			0.653129	−	0.757247i	$-0.273456\pi$
$907$	39.3398			1.30626			0.653129	+	0.757247i	$0.273456\pi$
$908$	4.48178	+	13.7935i	0.148733	+	0.457754i
$909$	2.33007	+	1.69290i	0.0772836	+	0.0561498i
$910$		0			0
$911$	11.0045	−	7.99523i	0.364595	−	0.264894i	−0.390371	−	0.920658i	$-0.627653\pi$
$911$	11.0045	−	7.99523i	0.364595	−	0.264894i	0.754966	+	0.655764i	$0.227653\pi$
$912$	5.45330	+	3.96205i	0.180577	+	0.131197i
$913$	−6.37465	−	4.63146i	−0.210970	−	0.153279i
$914$	31.0660	−	22.5708i	1.02757	−	0.746575i
$915$		0			0
$916$	−3.80302	−	2.76305i	−0.125655	−	0.0912938i
$917$	−2.55335	−	7.85839i	−0.0843189	−	0.259507i
$918$	7.49100			0.247240
$919$	−4.38951	−	13.5095i	−0.144797	−	0.445638i	0.852188	−	0.523235i	$-0.175275\pi$
$919$	−4.38951	−	13.5095i	−0.144797	−	0.445638i	−0.996985	+	0.0775974i	$0.975275\pi$
$920$		0			0
$921$	−4.46509	+	13.7421i	−0.147130	+	0.452819i
$922$	−10.0713	+	30.9962i	−0.331680	+	1.02081i
$923$	−1.19560	+	0.868657i	−0.0393538	+	0.0285922i
$924$	−11.7622			−0.386947
$925$		0			0
$926$	−2.53778			−0.0833966
$927$	9.03781	−	6.56635i	0.296841	−	0.215667i
$928$	−0.696812	+	2.14457i	−0.0228740	+	0.0703989i
$929$	2.50600	−	7.71269i	0.0822193	−	0.253045i	−0.901493	−	0.432793i	$-0.857528\pi$
$929$	2.50600	−	7.71269i	0.0822193	−	0.253045i	0.983713	+	0.179748i	$0.0575282\pi$
$930$		0			0
$931$	−30.0981	−	92.6326i	−0.986427	−	3.03591i
$932$	−11.8187			−0.387135
$933$	−7.28708	−	22.4273i	−0.238568	−	0.734238i
$934$	−1.21073	−	0.879644i	−0.0396161	−	0.0287828i
$935$		0			0
$936$	0.116478	−	0.0846260i	0.00380719	−	0.00276609i
$937$	−8.51533	−	6.18675i	−0.278184	−	0.202112i	0.439941	−	0.898027i	$-0.354999\pi$
$937$	−8.51533	−	6.18675i	−0.278184	−	0.202112i	−0.718125	+	0.695914i	$0.754999\pi$
$938$	28.6608	+	20.8233i	0.935808	+	0.679904i
$939$	22.2420	−	16.1598i	0.725841	−	0.527354i
$940$		0			0
$941$	40.0792	+	29.1193i	1.30655	+	0.949261i	0.999997	−	0.00259412i	$-0.000825736\pi$
$941$	40.0792	+	29.1193i	1.30655	+	0.949261i	0.306549	+	0.951855i	$0.400826\pi$
$942$	−7.25663	−	22.3336i	−0.236434	−	0.727668i
$943$	5.15587			0.167898
$944$	1.62347	+	4.99652i	0.0528394	+	0.162623i
$945$		0			0
$946$	−7.08567	+	21.8074i	−0.230375	+	0.709021i
$947$	3.26983	−	10.0635i	0.106255	−	0.327020i	−0.883768	−	0.467926i	$-0.845001\pi$
$947$	3.26983	−	10.0635i	0.106255	−	0.327020i	0.990023	+	0.140906i	$0.0450014\pi$
$948$	−0.604525	+	0.439213i	−0.0196340	+	0.0142650i
$949$	−0.283024			−0.00918735
$950$		0			0
$951$	6.04575			0.196047
$952$	−28.0677	+	20.3924i	−0.909680	+	0.660921i
$953$	−8.03886	+	24.7411i	−0.260404	+	0.801442i	0.732312	+	0.680969i	$0.238441\pi$
$953$	−8.03886	+	24.7411i	−0.260404	+	0.801442i	−0.992717	+	0.120473i	$0.961559\pi$
$954$	−1.53429	+	4.72205i	−0.0496744	+	0.152882i
$955$		0			0
$956$	3.00168	+	9.23821i	0.0970812	+	0.298785i
$957$	5.72679			0.185121
$958$	7.50880	+	23.1097i	0.242598	+	0.746641i
$959$	−60.0372	−	43.6196i	−1.93870	−	1.40855i
$960$		0			0
$961$	24.2643	−	17.6290i	0.782718	−	0.568678i
$962$	−0.0103643	−	0.00753010i	−0.000334158	−	0.000242780i
$963$	−11.3698	−	8.26061i	−0.366385	−	0.266195i
$964$	−5.40451	+	3.92661i	−0.174068	+	0.126468i
$965$		0			0
$966$	−6.28472	−	4.56611i	−0.202207	−	0.146912i
$967$	9.13183	+	28.1049i	0.293660	+	0.903793i	0.983668	+	0.179991i	$0.0576069\pi$
$967$	9.13183	+	28.1049i	0.293660	+	0.903793i	−0.690008	+	0.723802i	$0.742393\pi$
$968$	−4.55005			−0.146244
$969$	−15.6036	−	48.0228i	−0.501259	−	1.54272i
$970$		0			0
$971$	11.0850	−	34.1161i	0.355734	−	1.09484i	−0.599849	−	0.800114i	$-0.704773\pi$
$971$	11.0850	−	34.1161i	0.355734	−	1.09484i	0.955583	−	0.294723i	$-0.0952275\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	13.8784	−	10.0832i	0.444920	−	0.323253i
$974$	−10.0016			−0.320470
$975$		0			0
$976$	−13.7007			−0.438548
$977$	−17.4959	+	12.7115i	−0.559743	+	0.406677i	−0.831365	−	0.555727i	$-0.812440\pi$
$977$	−17.4959	+	12.7115i	−0.559743	+	0.406677i	0.271622	+	0.962404i	$0.412440\pi$
$978$	−4.87545	+	15.0051i	−0.155900	+	0.479810i
$979$	−0.575939	+	1.77256i	−0.0184071	+	0.0566512i
$980$		0			0
$981$	2.07618	+	6.38984i	0.0662875	+	0.204012i
$982$	4.17992			0.133387
$983$	−4.51722	−	13.9026i	−0.144077	−	0.443424i	0.852814	−	0.522215i	$-0.174894\pi$
$983$	−4.51722	−	13.9026i	−0.144077	−	0.443424i	−0.996891	+	0.0787911i	$0.974894\pi$
$984$	−2.48680	−	1.80677i	−0.0792764	−	0.0575977i
$985$		0			0
$986$	13.6657	−	9.92869i	0.435204	−	0.316194i
$987$	−40.7859	−	29.6327i	−1.29823	−	0.943219i
$988$	−0.785135	−	0.570434i	−0.0249785	−	0.0181479i
$989$	−12.2517	+	8.90139i	−0.389582	+	0.283048i
$990$		0			0
$991$	10.5772	+	7.68477i	0.335995	+	0.244115i	0.742970	−	0.669325i	$-0.233416\pi$
$991$	10.5772	+	7.68477i	0.335995	+	0.244115i	−0.406975	+	0.913439i	$0.633416\pi$
$992$	0.310207	+	0.954718i	0.00984907	+	0.0303123i
$993$	16.9315			0.537304
$994$	−14.6905	−	45.2127i	−0.465955	−	1.43406i
$995$		0			0
$996$	−0.958745	+	2.95072i	−0.0303790	+	0.0934970i
$997$	−3.76901	+	11.5998i	−0.119366	+	0.367370i	−0.992833	−	0.119514i	$-0.961866\pi$
$997$	−3.76901	+	11.5998i	−0.119366	+	0.367370i	0.873467	+	0.486884i	$0.161866\pi$
$998$	−1.37976	+	1.00245i	−0.0436755	+	0.0317321i
$999$	−0.0889810			−0.00281523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.301.4		16
5.2	odd	4		150.2.h.b.139.1	yes	16
5.3	odd	4		750.2.h.d.199.3		16
5.4	even	2		750.2.g.g.301.1		16
15.2	even	4		450.2.l.c.289.4		16
25.3	odd	20		3750.2.c.k.1249.1		16
25.4	even	10		3750.2.a.u.1.1		8
25.9	even	10		750.2.g.g.451.1		16
25.12	odd	20		750.2.h.d.49.4		16
25.13	odd	20		150.2.h.b.109.1	✓	16
25.16	even	5	inner	750.2.g.f.451.4		16
25.21	even	5		3750.2.a.v.1.8		8
25.22	odd	20		3750.2.c.k.1249.16		16
75.38	even	20		450.2.l.c.109.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.1	✓	16	25.13	odd	20
150.2.h.b.139.1	yes	16	5.2	odd	4
450.2.l.c.109.4		16	75.38	even	20
450.2.l.c.289.4		16	15.2	even	4
750.2.g.f.301.4		16	1.1	even	1	trivial
750.2.g.f.451.4		16	25.16	even	5	inner
750.2.g.g.301.1		16	5.4	even	2
750.2.g.g.451.1		16	25.9	even	10
750.2.h.d.49.4		16	25.12	odd	20
750.2.h.d.199.3		16	5.3	odd	4
3750.2.a.u.1.1		8	25.4	even	10
3750.2.a.v.1.8		8	25.21	even	5
3750.2.c.k.1249.1		16	25.3	odd	20
3750.2.c.k.1249.16		16	25.22	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.63137 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} +4.63137 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.05464 - 1.49278i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(0.116478 + 0.0846260i) q^{13} +(-3.74686 + 2.72225i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.31485 + 7.12436i) q^{17} +1.00000 q^{18} +(-2.08298 - 6.41074i) q^{19} +(1.43117 - 4.40469i) q^{21} +(-0.784803 + 2.41537i) q^{22} +(-1.35699 + 0.985910i) q^{23} +1.00000 q^{24} -0.143974 q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.43117 - 4.40469i) q^{28} +(-0.696812 + 2.14457i) q^{29} +(0.310207 + 0.954718i) q^{31} +1.00000 q^{32} +(-0.784803 - 2.41537i) q^{33} +(-6.06035 - 4.40310i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(0.0719871 + 0.0523017i) q^{37} +(5.45330 + 3.96205i) q^{38} +(0.116478 - 0.0846260i) q^{39} +(-2.48680 - 1.80677i) q^{41} +(1.43117 + 4.40469i) q^{42} +9.02860 q^{43} +(-0.784803 - 2.41537i) q^{44} +(0.518324 - 1.59524i) q^{46} +(3.36376 - 10.3526i) q^{47} +(-0.809017 + 0.587785i) q^{48} +14.4496 q^{49} +7.49100 q^{51} +(0.116478 - 0.0846260i) q^{52} +(-1.53429 + 4.72205i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.43117 + 4.40469i) q^{56} -6.74065 q^{57} +(-0.696812 - 2.14457i) q^{58} +(-4.25029 - 3.08802i) q^{59} +(11.0841 - 8.05305i) q^{61} +(-0.812131 - 0.590048i) q^{62} +(-3.74686 - 2.72225i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.05464 + 1.49278i) q^{66} +(-2.36376 - 7.27491i) q^{67} +7.49100 q^{68} +(0.518324 + 1.59524i) q^{69} +(-3.17196 + 9.76228i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-1.59036 + 1.15547i) q^{73} -0.0889810 q^{74} -6.74065 q^{76} +(9.51580 - 6.91363i) q^{77} +(-0.0444905 + 0.136928i) q^{78} +(0.230908 - 0.710661i) q^{79} +(0.309017 + 0.951057i) q^{81} +3.07386 q^{82} +(-0.958745 - 2.95072i) q^{83} +(-3.74686 - 2.72225i) q^{84} +(-7.30429 + 5.30688i) q^{86} +(1.82428 + 1.32542i) q^{87} +(2.05464 + 1.49278i) q^{88} +(-0.593709 + 0.431355i) q^{89} +(0.539451 + 0.391934i) q^{91} +(0.518324 + 1.59524i) q^{92} +1.00385 q^{93} +(3.36376 + 10.3526i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-2.81837 + 8.67406i) q^{97} +(-11.6900 + 8.49326i) q^{98} -2.53967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

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