LMFDB - Embedded newform 441.2.u.e.127.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	441.127
Dual form			441.2.u.e.316.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47259 + 1.19074i) q^{2} +(3.44888 + 4.32476i) q^{4} +(-0.875748 - 3.83690i) q^{5} +(2.35340 + 1.20894i) q^{7} +(2.15666 + 9.44894i) q^{8} +O(q^{10})$	\(q+(2.47259 + 1.19074i) q^{2} +(3.44888 + 4.32476i) q^{4} +(-0.875748 - 3.83690i) q^{5} +(2.35340 + 1.20894i) q^{7} +(2.15666 + 9.44894i) q^{8} +(2.40338 - 10.5299i) q^{10} +(-2.55212 - 1.22904i) q^{11} +(0.616863 + 0.297065i) q^{13} +(4.37947 + 5.79148i) q^{14} +(-3.45689 + 15.1456i) q^{16} +(-1.04670 + 1.31252i) q^{17} -1.89493 q^{19} +(13.5733 - 17.0204i) q^{20} +(-4.84689 - 6.07781i) q^{22} +(-1.91858 - 2.40582i) q^{23} +(-9.45004 + 4.55090i) q^{25} +(1.17152 + 1.46904i) q^{26} +(2.88823 + 14.3473i) q^{28} +(0.771945 - 0.967989i) q^{29} -5.03952 q^{31} +(-14.4963 + 18.1778i) q^{32} +(-4.15091 + 1.99897i) q^{34} +(2.57759 - 10.0885i) q^{35} +(3.52916 - 4.42543i) q^{37} +(-4.68539 - 2.25636i) q^{38} +(34.3660 - 16.5498i) q^{40} +(0.933778 + 4.09115i) q^{41} +(1.44494 - 6.33069i) q^{43} +(-3.48667 - 15.2761i) q^{44} +(-1.87916 - 8.23315i) q^{46} +(-8.20432 - 3.95099i) q^{47} +(4.07695 + 5.69021i) q^{49} -28.7850 q^{50} +(0.842749 + 3.69232i) q^{52} +(5.02083 + 6.29592i) q^{53} +(-2.48068 + 10.8686i) q^{55} +(-6.34769 + 24.8444i) q^{56} +(3.06133 - 1.47426i) q^{58} +(2.50659 - 10.9821i) q^{59} +(-4.99461 + 6.26304i) q^{61} +(-12.4607 - 6.00075i) q^{62} +(-29.4951 + 14.2041i) q^{64} +(0.599595 - 2.62700i) q^{65} -7.46313 q^{67} -9.28623 q^{68} +(18.3860 - 21.8755i) q^{70} +(3.52116 + 4.41540i) q^{71} +(9.56936 - 4.60836i) q^{73} +(13.9957 - 6.73998i) q^{74} +(-6.53538 - 8.19511i) q^{76} +(-4.52032 - 5.97776i) q^{77} +6.83607 q^{79} +61.1397 q^{80} +(-2.56263 + 11.2276i) q^{82} +(-2.56700 + 1.23620i) q^{83} +(5.95263 + 2.86664i) q^{85} +(11.1109 - 13.9327i) q^{86} +(6.10903 - 26.7654i) q^{88} +(5.79090 - 2.78875i) q^{89} +(1.09259 + 1.44486i) q^{91} +(3.78765 - 16.5948i) q^{92} +(-15.5813 - 19.5384i) q^{94} +(1.65948 + 7.27066i) q^{95} -3.29836 q^{97} +(3.30509 + 18.9241i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) $ 60 * q - 12 * q^4 - 2 * q^7	$ 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) $ 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	2.47259	+	1.19074i	1.74839	+	0.841979i	0.979184	+	0.202974i	$0.0650607\pi$
$2$	2.47259	+	1.19074i	1.74839	+	0.841979i	0.769203	+	0.639005i	$0.220654\pi$
$3$		0			0
$3$		0			0
$4$	3.44888	+	4.32476i	1.72444	+	2.16238i
$5$	−0.875748	−	3.83690i	−0.391646	−	1.71591i	−0.658850	−	0.752275i	$-0.728957\pi$
$5$	−0.875748	−	3.83690i	−0.391646	−	1.71591i	0.267203	−	0.963640i	$-0.413900\pi$
$6$		0			0
$7$	2.35340	+	1.20894i	0.889500	+	0.456935i
$7$	2.35340	+	1.20894i	0.889500	+	0.456935i
$8$	2.15666	+	9.44894i	0.762494	+	3.34070i
$9$		0			0
$10$	2.40338	−	10.5299i	0.760014	−	3.32984i
$11$	−2.55212	−	1.22904i	−0.769493	−	0.370568i	0.00758624	−	0.999971i	$-0.497585\pi$
$11$	−2.55212	−	1.22904i	−0.769493	−	0.370568i	−0.777079	+	0.629403i	$0.783299\pi$
$12$		0			0
$13$	0.616863	+	0.297065i	0.171087	+	0.0823911i	0.517467	−	0.855703i	$-0.326875\pi$
$13$	0.616863	+	0.297065i	0.171087	+	0.0823911i	−0.346380	+	0.938094i	$0.612589\pi$
$14$	4.37947	+	5.79148i	1.17046	+	1.54784i
$15$		0			0
$16$	−3.45689	+	15.1456i	−0.864223	+	3.78641i
$17$	−1.04670	+	1.31252i	−0.253861	+	0.318332i	−0.892389	−	0.451267i	$-0.850972\pi$
$17$	−1.04670	+	1.31252i	−0.253861	+	0.318332i	0.638528	+	0.769599i	$0.279544\pi$
$18$		0			0
$19$	−1.89493			−0.434727			−0.217363	−	0.976091i	$-0.569746\pi$
$19$	−1.89493			−0.434727			−0.217363	+	0.976091i	$0.569746\pi$
$20$	13.5733	−	17.0204i	3.03509	−	3.80588i
$21$		0			0
$22$	−4.84689	−	6.07781i	−1.03336	−	1.29579i
$23$	−1.91858	−	2.40582i	−0.400052	−	0.501649i	0.540479	−	0.841357i	$-0.318243\pi$
$23$	−1.91858	−	2.40582i	−0.400052	−	0.501649i	−0.940531	+	0.339709i	$0.889672\pi$
$24$		0			0
$25$	−9.45004	+	4.55090i	−1.89001	+	0.910180i
$26$	1.17152	+	1.46904i	0.229755	+	0.288103i
$27$		0			0
$28$	2.88823	+	14.3473i	0.545823	+	2.71139i
$29$	0.771945	−	0.967989i	0.143347	−	0.179751i	−0.704975	−	0.709232i	$-0.749042\pi$
$29$	0.771945	−	0.967989i	0.143347	−	0.179751i	0.848322	+	0.529481i	$0.177613\pi$
$30$		0			0
$31$	−5.03952			−0.905125			−0.452562	−	0.891733i	$-0.649490\pi$
$31$	−5.03952			−0.905125			−0.452562	+	0.891733i	$0.649490\pi$
$32$	−14.4963	+	18.1778i	−2.56261	+	3.21341i
$33$		0			0
$34$	−4.15091	+	1.99897i	−0.711876	+	0.342821i
$35$	2.57759	−	10.0885i	0.435691	−	1.70526i
$36$		0			0
$37$	3.52916	−	4.42543i	0.580191	−	0.727536i	−0.401955	−	0.915660i	$-0.631669\pi$
$37$	3.52916	−	4.42543i	0.580191	−	0.727536i	0.982145	+	0.188123i	$0.0602405\pi$
$38$	−4.68539	−	2.25636i	−0.760070	−	0.366031i
$39$		0			0
$40$	34.3660	−	16.5498i	5.43374	−	2.61675i
$41$	0.933778	+	4.09115i	0.145832	+	0.638930i	0.994017	+	0.109230i	$0.0348384\pi$
$41$	0.933778	+	4.09115i	0.145832	+	0.638930i	−0.848185	+	0.529700i	$0.822304\pi$
$42$		0			0
$43$	1.44494	−	6.33069i	0.220351	−	0.965422i	−0.736863	−	0.676042i	$-0.763694\pi$
$43$	1.44494	−	6.33069i	0.220351	−	0.965422i	0.957214	−	0.289380i	$-0.0934490\pi$
$44$	−3.48667	−	15.2761i	−0.525635	−	2.30296i
$45$		0			0
$46$	−1.87916	−	8.23315i	−0.277067	−	1.21391i
$47$	−8.20432	−	3.95099i	−1.19672	−	0.576311i	−0.273983	−	0.961735i	$-0.588341\pi$
$47$	−8.20432	−	3.95099i	−1.19672	−	0.576311i	−0.922740	+	0.385423i	$0.874055\pi$
$48$		0			0
$49$	4.07695	+	5.69021i	0.582421	+	0.812887i
$50$	−28.7850			−4.07082
$51$		0			0
$52$	0.842749	+	3.69232i	0.116868	+	0.512033i
$53$	5.02083	+	6.29592i	0.689664	+	0.864812i	0.996204	−	0.0870461i	$-0.0277427\pi$
$53$	5.02083	+	6.29592i	0.689664	+	0.864812i	−0.306540	+	0.951858i	$0.599171\pi$
$54$		0			0
$55$	−2.48068	+	10.8686i	−0.334494	+	1.46552i
$56$	−6.34769	+	24.8444i	−0.848245	+	3.31997i
$57$		0			0
$58$	3.06133	−	1.47426i	0.401972	−	0.193580i
$59$	2.50659	−	10.9821i	0.326330	−	1.42974i	−0.499740	−	0.866176i	$-0.666571\pi$
$59$	2.50659	−	10.9821i	0.326330	−	1.42974i	0.826069	−	0.563569i	$-0.190572\pi$
$60$		0			0
$61$	−4.99461	+	6.26304i	−0.639494	+	0.801900i	−0.990940	−	0.134308i	$-0.957119\pi$
$61$	−4.99461	+	6.26304i	−0.639494	+	0.801900i	0.351446	+	0.936208i	$0.385690\pi$
$62$	−12.4607	−	6.00075i	−1.58251	−	0.762096i
$63$		0			0
$64$	−29.4951	+	14.2041i	−3.68689	+	1.77551i
$65$	0.599595	−	2.62700i	0.0743706	−	0.325839i
$66$		0			0
$67$	−7.46313			−0.911766			−0.455883	−	0.890040i	$-0.650676\pi$
$67$	−7.46313			−0.911766			−0.455883	+	0.890040i	$0.650676\pi$
$68$	−9.28623			−1.12612
$69$		0			0
$70$	18.3860	−	21.8755i	2.19755	−	2.61462i
$71$	3.52116	+	4.41540i	0.417885	+	0.524011i	0.945566	−	0.325432i	$-0.105510\pi$
$71$	3.52116	+	4.41540i	0.417885	+	0.524011i	−0.527681	+	0.849443i	$0.676938\pi$
$72$		0			0
$73$	9.56936	−	4.60836i	1.12001	−	0.539368i	0.220114	−	0.975474i	$-0.429357\pi$
$73$	9.56936	−	4.60836i	1.12001	−	0.539368i	0.899895	+	0.436106i	$0.143643\pi$
$74$	13.9957	−	6.73998i	1.62697	−	0.783507i
$75$		0			0
$76$	−6.53538	−	8.19511i	−0.749659	−	0.940043i
$77$	−4.52032	−	5.97776i	−0.515139	−	0.681228i
$78$		0			0
$79$	6.83607			0.769118			0.384559	−	0.923100i	$-0.374353\pi$
$79$	6.83607			0.769118			0.384559	+	0.923100i	$0.374353\pi$
$80$	61.1397			6.83562
$81$		0			0
$82$	−2.56263	+	11.2276i	−0.282995	+	1.23988i
$83$	−2.56700	+	1.23620i	−0.281765	+	0.135691i	−0.569429	−	0.822040i	$-0.692836\pi$
$83$	−2.56700	+	1.23620i	−0.281765	+	0.135691i	0.287664	+	0.957731i	$0.407121\pi$
$84$		0			0
$85$	5.95263	+	2.86664i	0.645654	+	0.310930i
$86$	11.1109	−	13.9327i	1.19812	−	1.50240i
$87$		0			0
$88$	6.10903	−	26.7654i	0.651225	−	2.85320i
$89$	5.79090	−	2.78875i	0.613834	−	0.295607i	−0.101016	−	0.994885i	$-0.532209\pi$
$89$	5.79090	−	2.78875i	0.613834	−	0.295607i	0.714850	+	0.699278i	$0.246495\pi$
$90$		0			0
$91$	1.09259	+	1.44486i	0.114535	+	0.151462i
$92$	3.78765	−	16.5948i	0.394890	−	1.73013i
$93$		0			0
$94$	−15.5813	−	19.5384i	−1.60709	−	2.01523i
$95$	1.65948	+	7.27066i	0.170259	+	0.745954i
$96$		0			0
$97$	−3.29836			−0.334898			−0.167449	−	0.985881i	$-0.553553\pi$
$97$	−3.29836			−0.334898			−0.167449	+	0.985881i	$0.553553\pi$
$98$	3.30509	+	18.9241i	0.333864	+	1.91163i
$99$		0			0
$100$	−52.2736	−	25.1736i	−5.22736	−	2.51736i
$101$	2.50827	+	10.9894i	0.249582	+	1.09349i	0.931980	+	0.362509i	$0.118080\pi$
$101$	2.50827	+	10.9894i	0.249582	+	1.09349i	−0.682398	+	0.730981i	$0.739063\pi$
$102$		0			0
$103$	1.38468	+	6.06669i	0.136437	+	0.597769i	0.996201	+	0.0870783i	$0.0277530\pi$
$103$	1.38468	+	6.06669i	0.136437	+	0.597769i	−0.859765	+	0.510690i	$0.829390\pi$
$104$	−1.47659	+	6.46937i	−0.144792	+	0.634374i
$105$		0			0
$106$	4.91768	+	21.5457i	0.477647	+	2.09271i
$107$	9.39197	−	4.52293i	0.907956	−	0.437248i	0.0791998	−	0.996859i	$-0.474763\pi$
$107$	9.39197	−	4.52293i	0.907956	−	0.437248i	0.828756	+	0.559610i	$0.189049\pi$
$108$		0			0
$109$	16.2743	+	7.83728i	1.55879	+	0.750676i	0.997059	−	0.0766415i	$-0.0244197\pi$
$109$	16.2743	+	7.83728i	1.55879	+	0.750676i	0.561735	+	0.827317i	$0.310134\pi$
$110$	−19.0753	+	23.9197i	−1.81876	+	2.28065i
$111$		0			0
$112$	−26.4455	+	31.4645i	−2.49887	+	2.97312i
$113$	−9.06075	+	4.36343i	−0.852363	+	0.410477i	−0.808454	−	0.588559i	$-0.799695\pi$
$113$	−9.06075	+	4.36343i	−0.852363	+	0.410477i	−0.0439091	+	0.999036i	$0.513981\pi$
$114$		0			0
$115$	−7.55072	+	9.46830i	−0.704108	+	0.882924i
$116$	6.84866			0.635882
$117$		0			0
$118$	19.2745	−	24.1695i	1.77437	−	2.22498i
$119$	−4.05004	+	1.82348i	−0.371266	+	0.167158i
$120$		0			0
$121$	−1.85561	−	2.32686i	−0.168691	−	0.211532i
$122$	−19.8073	+	9.53868i	−1.79327	+	0.863591i
$123$		0			0
$124$	−17.3807	−	21.7947i	−1.56083	−	1.95722i
$125$	13.4682	+	16.8886i	1.20464	+	1.51057i
$126$		0			0
$127$	−0.210417	+	0.263855i	−0.0186715	+	0.0234133i	−0.791080	−	0.611713i	$-0.790481\pi$
$127$	−0.210417	+	0.263855i	−0.0186715	+	0.0234133i	0.772408	+	0.635127i	$0.219052\pi$
$128$	−43.3422			−3.83095
$129$		0			0
$130$	4.61062	−	5.78153i	0.404378	−	0.507074i
$131$	3.68434	−	16.1422i	0.321902	−	1.41035i	−0.512261	−	0.858830i	$-0.671192\pi$
$131$	3.68434	−	16.1422i	0.321902	−	1.41035i	0.834164	−	0.551517i	$-0.185951\pi$
$132$		0			0
$133$	−4.45952	−	2.29085i	−0.386689	−	0.198642i
$134$	−18.4533	−	8.88663i	−1.59412	−	0.767688i
$135$		0			0
$136$	−14.6592	−	7.05952i	−1.25702	−	0.605349i
$137$	−2.98481	+	13.0773i	−0.255009	+	1.11727i	0.671502	+	0.741002i	$0.265649\pi$
$137$	−2.98481	+	13.0773i	−0.255009	+	1.11727i	−0.926512	+	0.376266i	$0.877208\pi$
$138$		0			0
$139$	2.71321	+	11.8874i	0.230132	+	1.00827i	0.949530	+	0.313675i	$0.101560\pi$
$139$	2.71321	+	11.8874i	0.230132	+	1.00827i	−0.719399	+	0.694597i	$0.755583\pi$
$140$	52.5200	−	23.6465i	4.43875	−	1.99849i
$141$		0			0
$142$	3.44882	+	15.1103i	0.289418	+	1.26802i
$143$	−1.20920	−	1.51629i	−0.101119	−	0.126799i
$144$		0			0
$145$	−4.39011	−	2.11416i	−0.364579	−	0.175572i
$146$	29.1485			2.41235
$147$		0			0
$148$	31.3106			2.57371
$149$	−3.68545	−	1.77482i	−0.301923	−	0.145399i	0.276788	−	0.960931i	$-0.410730\pi$
$149$	−3.68545	−	1.77482i	−0.301923	−	0.145399i	−0.578712	+	0.815532i	$0.696444\pi$
$150$		0			0
$151$	−8.38061	−	10.5090i	−0.682004	−	0.855206i	0.313533	−	0.949577i	$-0.398487\pi$
$151$	−8.38061	−	10.5090i	−0.682004	−	0.855206i	−0.995537	+	0.0943709i	$0.969916\pi$
$152$	−4.08672	−	17.9051i	−0.331476	−	1.45229i
$153$		0			0
$154$	−4.05898	−	20.1631i	−0.327082	−	1.62479i
$155$	4.41335	+	19.3362i	0.354489	+	1.55312i
$156$		0			0
$157$	−2.59110	+	11.3524i	−0.206793	+	0.906018i	0.759892	+	0.650049i	$0.225252\pi$
$157$	−2.59110	+	11.3524i	−0.206793	+	0.906018i	−0.966685	+	0.255969i	$0.917606\pi$
$158$	16.9028	+	8.13997i	1.34472	+	0.647581i
$159$		0			0
$160$	82.4415	+	39.7018i	6.51758	+	3.13870i
$161$	−1.60669	−	7.98130i	−0.126625	−	0.629014i
$162$		0			0
$163$	−2.21088	+	9.68649i	−0.173169	+	0.758705i	0.811511	+	0.584337i	$0.198645\pi$
$163$	−2.21088	+	9.68649i	−0.173169	+	0.758705i	−0.984681	+	0.174368i	$0.944212\pi$
$164$	−14.4727	+	18.1482i	−1.13013	+	1.41714i
$165$		0			0
$166$	−7.81915			−0.606883
$167$	−8.77942	+	11.0090i	−0.679372	+	0.851906i	−0.995296	−	0.0968788i	$-0.969114\pi$
$167$	−8.77942	+	11.0090i	−0.679372	+	0.851906i	0.315924	+	0.948784i	$0.397686\pi$
$168$		0			0
$169$	−7.81310	−	9.79731i	−0.601007	−	0.753639i
$170$	11.3050	+	14.1761i	0.867056	+	1.08725i
$171$		0			0
$172$	32.3621	−	15.5848i	2.46759	−	1.18833i
$173$	−0.426398	−	0.534686i	−0.0324185	−	0.0406515i	0.765358	−	0.643605i	$-0.222562\pi$
$173$	−0.426398	−	0.534686i	−0.0324185	−	0.0406515i	−0.797776	+	0.602953i	$0.793991\pi$
$174$		0			0
$175$	−27.7414	−	0.714418i	−2.09706	−	0.0540049i
$176$	27.4369	−	34.4048i	2.06814	−	2.59336i
$177$		0			0
$178$	17.6392			1.32211
$179$	2.70299	−	3.38945i	0.202031	−	0.253339i	−0.670486	−	0.741922i	$-0.733915\pi$
$179$	2.70299	−	3.38945i	0.202031	−	0.253339i	0.872518	+	0.488583i	$0.162486\pi$
$180$		0			0
$181$	20.0307	−	9.64625i	1.48887	−	0.717000i	0.500031	−	0.866008i	$-0.333322\pi$
$181$	20.0307	−	9.64625i	1.48887	−	0.717000i	0.988836	+	0.149007i	$0.0476078\pi$
$182$	0.981080	+	4.87354i	0.0727225	+	0.361251i
$183$		0			0
$184$	18.5948	−	23.3171i	1.37082	−	1.71896i
$185$	−20.0706	−	9.66549i	−1.47562	−	0.710621i
$186$		0			0
$187$	4.28442	−	2.06327i	0.313308	−	0.150881i
$188$	−11.2086	−	49.1081i	−0.817472	−	3.58158i
$189$		0			0
$190$	−4.55423	+	19.9534i	−0.330398	+	1.44757i
$191$	2.21882	+	9.72129i	0.160548	+	0.703408i	0.989553	+	0.144167i	$0.0460502\pi$
$191$	2.21882	+	9.72129i	0.160548	+	0.703408i	−0.829005	+	0.559241i	$0.811093\pi$
$192$		0			0
$193$	−2.28325	−	10.0036i	−0.164352	−	0.720072i	−0.988188	−	0.153245i	$-0.951028\pi$
$193$	−2.28325	−	10.0036i	−0.164352	−	0.720072i	0.823836	−	0.566828i	$-0.191829\pi$
$194$	−8.15550	−	3.92748i	−0.585531	−	0.281977i
$195$		0			0
$196$	−10.5479	+	37.2566i	−0.753419	+	2.66119i
$197$	−2.06178			−0.146896			−0.0734480	−	0.997299i	$-0.523400\pi$
$197$	−2.06178			−0.146896			−0.0734480	+	0.997299i	$0.523400\pi$
$198$		0			0
$199$	0.765304	+	3.35301i	0.0542509	+	0.237689i	0.994783	−	0.102017i	$-0.0325296\pi$
$199$	0.765304	+	3.35301i	0.0542509	+	0.237689i	−0.940532	+	0.339706i	$0.889672\pi$
$200$	−63.3817	−	79.4781i	−4.48176	−	5.61995i
$201$		0			0
$202$	−6.88362	+	30.1591i	−0.484330	+	2.12199i
$203$	2.98693	−	1.34483i	0.209641	−	0.0943885i
$204$		0			0
$205$	14.8796	−	7.16563i	1.03923	−	0.500469i
$206$	−3.80008	+	16.6492i	−0.264764	+	1.16001i
$207$		0			0
$208$	−6.63167	+	8.31585i	−0.459824	+	0.576601i
$209$	4.83609	+	2.32894i	0.334519	+	0.161096i
$210$		0			0
$211$	0.405845	−	0.195445i	0.0279395	−	0.0134550i	−0.419862	−	0.907588i	$-0.637921\pi$
$211$	0.405845	−	0.195445i	0.0279395	−	0.0134550i	0.447801	+	0.894133i	$0.352207\pi$
$212$	−9.91210	+	43.4277i	−0.680766	+	2.98263i
$213$		0			0
$214$	28.6081			1.95561
$215$	−25.5557			−1.74288
$216$		0			0
$217$	−11.8600	−	6.09246i	−0.805109	−	0.413583i
$218$	30.9075	+	38.7568i	2.09332	+	2.62494i
$219$		0			0
$220$	−55.5594	+	26.7560i	−3.74581	+	1.80389i
$221$	−1.03557	+	0.498704i	−0.0696600	+	0.0335465i
$222$		0			0
$223$	−14.1605	−	17.7567i	−0.948255	−	1.18907i	−0.981854	−	0.189639i	$-0.939268\pi$
$223$	−14.1605	−	17.7567i	−0.948255	−	1.18907i	0.0335985	−	0.999435i	$-0.489303\pi$
$224$	−56.0914	+	25.2545i	−3.74776	+	1.68738i
$225$		0			0
$226$	−27.5992			−1.83587
$227$	1.86150			0.123552			0.0617760	−	0.998090i	$-0.480324\pi$
$227$	1.86150			0.123552			0.0617760	+	0.998090i	$0.480324\pi$
$228$		0			0
$229$	5.74574	−	25.1737i	0.379689	−	1.66353i	−0.318735	−	0.947844i	$-0.603258\pi$
$229$	5.74574	−	25.1737i	0.379689	−	1.66353i	0.698424	−	0.715684i	$-0.253885\pi$
$230$	−29.9441	+	14.4203i	−1.97446	+	0.950848i
$231$		0			0
$232$	10.8113	+	5.20644i	0.709796	+	0.341820i
$233$	−2.88031	+	3.61180i	−0.188695	+	0.236617i	−0.867176	−	0.498002i	$-0.834067\pi$
$233$	−2.88031	+	3.61180i	−0.188695	+	0.236617i	0.678481	+	0.734618i	$0.262639\pi$
$234$		0			0
$235$	−7.97465	+	34.9392i	−0.520209	+	2.27918i
$236$	56.1397	−	27.0355i	3.65438	−	1.75986i
$237$		0			0
$238$	−12.1854	−	0.313807i	−0.789861	−	0.0203411i
$239$	−5.93196	+	25.9896i	−0.383706	+	1.68113i	0.302047	+	0.953293i	$0.402330\pi$
$239$	−5.93196	+	25.9896i	−0.383706	+	1.68113i	−0.685753	+	0.727834i	$0.740527\pi$
$240$		0			0
$241$	16.5343	+	20.7334i	1.06507	+	1.33555i	0.939148	+	0.343513i	$0.111617\pi$
$241$	16.5343	+	20.7334i	1.06507	+	1.33555i	0.125920	+	0.992040i	$0.459812\pi$
$242$	−1.81748	−	7.96291i	−0.116832	−	0.511875i
$243$		0			0
$244$	−44.3119			−2.83678
$245$	18.2624	−	20.6260i	1.16674	−	1.31775i
$246$		0			0
$247$	−1.16891	−	0.562918i	−0.0743760	−	0.0358176i
$248$	−10.8685	−	47.6181i	−0.690152	−	3.02376i
$249$		0			0
$250$	13.1915	+	57.7959i	0.834306	+	3.65533i
$251$	−3.37639	+	14.7929i	−0.213116	+	0.933721i	0.749319	+	0.662209i	$0.230381\pi$
$251$	−3.37639	+	14.7929i	−0.213116	+	0.933721i	−0.962435	+	0.271512i	$0.912476\pi$
$252$		0			0
$253$	1.93960	+	8.49795i	0.121942	+	0.534262i
$254$	−0.834458	+	0.401854i	−0.0523585	+	0.0252145i
$255$		0			0
$256$	−48.1774	−	23.2010i	−3.01109	−	1.45006i
$257$	8.93029	−	11.1982i	0.557056	−	0.698526i	−0.420954	−	0.907082i	$-0.638305\pi$
$257$	8.93029	−	11.1982i	0.557056	−	0.698526i	0.978011	+	0.208556i	$0.0668762\pi$
$258$		0			0
$259$	13.6556	−	6.14826i	0.848516	−	0.382034i
$260$	13.4290	−	6.46709i	0.832834	−	0.401072i
$261$		0			0
$262$	28.3309	−	35.5259i	1.75029	−	2.19480i
$263$	26.9900			1.66428			0.832138	−	0.554568i	$-0.187117\pi$
$263$	26.9900			1.66428			0.832138	+	0.554568i	$0.187117\pi$
$264$		0			0
$265$	19.7599	−	24.7781i	1.21384	−	1.52211i
$266$	−8.29878	−	10.9745i	−0.508831	−	0.672887i
$267$		0			0
$268$	−25.7394	−	32.2762i	−1.57228	−	1.97158i
$269$	−20.3932	+	9.82086i	−1.24340	+	0.598789i	−0.935734	−	0.352707i	$-0.885261\pi$
$269$	−20.3932	+	9.82086i	−1.24340	+	0.598789i	−0.307663	+	0.951495i	$0.599547\pi$
$270$		0			0
$271$	−15.7790	−	19.7862i	−0.958505	−	1.20193i	−0.979356	−	0.202144i	$-0.935209\pi$
$271$	−15.7790	−	19.7862i	−0.958505	−	1.20193i	0.0208509	−	0.999783i	$-0.493362\pi$
$272$	−16.2606	−	20.3901i	−0.985941	−	1.23633i
$273$		0			0
$274$	−22.9518	+	28.7807i	−1.38657	+	1.73871i
$275$	29.7108			1.79163
$276$		0			0
$277$	18.7045	−	23.4547i	1.12384	−	1.40925i	0.223157	−	0.974783i	$-0.428364\pi$
$277$	18.7045	−	23.4547i	1.12384	−	1.40925i	0.900686	−	0.434471i	$-0.143065\pi$
$278$	−7.44606	+	32.6233i	−0.446585	+	1.95662i
$279$		0			0
$280$	100.884	+	2.59805i	6.02899	+	0.155263i
$281$	−5.14470	−	2.47756i	−0.306907	−	0.147799i	0.274091	−	0.961704i	$-0.411623\pi$
$281$	−5.14470	−	2.47756i	−0.306907	−	0.147799i	−0.580998	+	0.813905i	$0.697337\pi$
$282$		0			0
$283$	19.7408	+	9.50666i	1.17347	+	0.565112i	0.916001	−	0.401175i	$-0.131398\pi$
$283$	19.7408	+	9.50666i	1.17347	+	0.565112i	0.257466	+	0.966287i	$0.417112\pi$
$284$	−6.95146	+	30.4563i	−0.412493	+	1.80725i
$285$		0			0
$286$	−1.18436	−	5.18902i	−0.0700326	−	0.306833i
$287$	−2.74838	+	10.7570i	−0.162232	+	0.634964i
$288$		0			0
$289$	3.15573	+	13.8262i	0.185631	+	0.813304i
$290$	−8.33753	−	10.4549i	−0.489597	−	0.613935i
$291$		0			0
$292$	52.9336	+	25.4915i	3.09771	+	1.49178i
$293$	11.1663			0.652341			0.326171	−	0.945311i	$-0.394242\pi$
$293$	11.1663			0.652341			0.326171	+	0.945311i	$0.394242\pi$
$294$		0			0
$295$	−44.3323			−2.58113
$296$	49.4268	+	23.8027i	2.87288	+	1.38350i
$297$		0			0
$298$	−6.99926	−	8.77680i	−0.405456	−	0.508426i
$299$	−0.468814	−	2.05401i	−0.0271122	−	0.118786i
$300$		0			0
$301$	11.0539	−	13.1518i	0.637137	−	0.758057i
$302$	−8.20843	−	35.9635i	−0.472342	−	2.06947i
$303$		0			0
$304$	6.55056	−	28.6999i	0.375701	−	1.64605i
$305$	28.4047	+	13.6790i	1.62645	+	0.783256i
$306$		0			0
$307$	−12.2679	−	5.90790i	−0.700165	−	0.337182i	0.0497079	−	0.998764i	$-0.484171\pi$
$307$	−12.2679	−	5.90790i	−0.700165	−	0.337182i	−0.749873	+	0.661582i	$0.769885\pi$
$308$	10.2623	−	40.1658i	0.584748	−	2.28866i
$309$		0			0
$310$	−12.1119	+	53.0656i	−0.687908	+	3.01392i
$311$	−0.382693	+	0.479882i	−0.0217005	+	0.0272116i	−0.792563	−	0.609790i	$-0.791254\pi$
$311$	−0.382693	+	0.479882i	−0.0217005	+	0.0272116i	0.770863	+	0.637001i	$0.219825\pi$
$312$		0			0
$313$	23.2650			1.31502			0.657509	−	0.753447i	$-0.271610\pi$
$313$	23.2650			1.31502			0.657509	+	0.753447i	$0.271610\pi$
$314$	−19.9244	+	24.9845i	−1.12440	+	1.40995i
$315$		0			0
$316$	23.5768	+	29.5643i	1.32630	+	1.66312i
$317$	−13.4523	−	16.8686i	−0.755555	−	0.947436i	0.244197	−	0.969726i	$-0.421476\pi$
$317$	−13.4523	−	16.8686i	−0.755555	−	0.947436i	−0.999752	+	0.0222902i	$0.992904\pi$
$318$		0			0
$319$	−3.15979	+	1.52167i	−0.176914	+	0.0851974i
$320$	80.3300	+	100.731i	4.49059	+	5.63102i
$321$		0			0
$322$	5.53093	−	21.6476i	0.308227	−	1.20638i
$323$	1.98341	−	2.48712i	0.110360	−	0.138387i
$324$		0			0
$325$	−7.18129			−0.398346
$326$	−17.0007	+	21.3182i	−0.941580	+	1.18070i
$327$		0			0
$328$	−36.6432	+	17.6464i	−2.02328	+	0.974361i
$329$	−14.5315	−	19.2167i	−0.801148	−	1.05945i
$330$		0			0
$331$	2.44153	−	3.06159i	0.134199	−	0.168280i	−0.710191	−	0.704009i	$-0.751392\pi$
$331$	2.44153	−	3.06159i	0.134199	−	0.168280i	0.844390	+	0.535729i	$0.179963\pi$
$332$	−14.1996	−	6.83815i	−0.779302	−	0.375292i
$333$		0			0
$334$	−34.8168	+	16.7669i	−1.90509	+	0.917444i
$335$	6.53582	+	28.6353i	0.357090	+	1.56451i
$336$		0			0
$337$	5.27506	−	23.1116i	0.287351	−	1.25897i	−0.600794	−	0.799404i	$-0.705149\pi$
$337$	5.27506	−	23.1116i	0.287351	−	1.25897i	0.888145	−	0.459563i	$-0.151994\pi$
$338$	−7.65257	−	33.5281i	−0.416245	−	1.82369i
$339$		0			0
$340$	8.13240	+	35.6304i	0.441041	+	1.93233i
$341$	12.8615	+	6.19375i	0.696487	+	0.335411i
$342$		0			0
$343$	2.71558	+	18.3201i	0.146628	+	0.989192i
$344$	62.9346			3.39321
$345$		0			0
$346$	−0.417638	−	1.82979i	−0.0224523	−	0.0983701i
$347$	−5.70055	−	7.14826i	−0.306021	−	0.383739i	0.604912	−	0.796292i	$-0.293208\pi$
$347$	−5.70055	−	7.14826i	−0.306021	−	0.383739i	−0.910933	+	0.412554i	$0.864637\pi$
$348$		0			0
$349$	−4.88389	+	21.3977i	−0.261429	+	1.14539i	0.658274	+	0.752778i	$0.271287\pi$
$349$	−4.88389	+	21.3977i	−0.261429	+	1.14539i	−0.919703	+	0.392616i	$0.871570\pi$
$350$	−67.7426	−	34.7992i	−3.62099	−	1.86010i
$351$		0			0
$352$	59.3375	−	28.5754i	3.16270	−	1.52307i
$353$	−3.55404	+	15.5713i	−0.189162	+	0.828775i	0.787897	+	0.615807i	$0.211170\pi$
$353$	−3.55404	+	15.5713i	−0.189162	+	0.828775i	−0.977059	+	0.212968i	$0.931687\pi$
$354$		0			0
$355$	13.8578	−	17.3771i	0.735495	−	0.922282i
$356$	32.0327	+	15.4262i	1.69773	+	0.817585i
$357$		0			0
$358$	10.7193	−	5.16217i	0.566535	−	0.272829i
$359$	2.42315	−	10.6165i	0.127889	−	0.560318i	−0.869863	−	0.493294i	$-0.835793\pi$
$359$	2.42315	−	10.6165i	0.127889	−	0.560318i	0.997751	−	0.0670234i	$-0.0213502\pi$
$360$		0			0
$361$	−15.4092			−0.811013
$362$	61.0138			3.20681
$363$		0			0
$364$	−2.48046	+	9.70833i	−0.130011	+	0.508855i
$365$	−26.0622	−	32.6809i	−1.36416	−	1.71060i
$366$		0			0
$367$	1.98518	−	0.956014i	0.103626	−	0.0499035i	−0.381353	−	0.924430i	$-0.624542\pi$
$367$	1.98518	−	0.956014i	0.103626	−	0.0499035i	0.484979	+	0.874526i	$0.338827\pi$
$368$	43.0700	−	20.7414i	2.24518	−	1.08122i
$369$		0			0
$370$	−38.1173	−	47.7976i	−1.98163	−	2.48488i
$371$	4.20464	+	20.8867i	0.218294	+	1.08438i
$372$		0			0
$373$	2.93614			0.152027			0.0760137	−	0.997107i	$-0.475781\pi$
$373$	2.93614			0.152027			0.0760137	+	0.997107i	$0.475781\pi$
$374$	13.0504			0.674822
$375$		0			0
$376$	19.6388	−	86.0430i	1.01279	−	4.43733i
$377$	0.763740	−	0.367798i	0.0393346	−	0.0189426i
$378$		0			0
$379$	−4.94887	−	2.38325i	−0.254206	−	0.122419i	0.302441	−	0.953168i	$-0.402198\pi$
$379$	−4.94887	−	2.38325i	−0.254206	−	0.122419i	−0.556648	+	0.830749i	$0.687913\pi$
$380$	−25.7205	+	32.2525i	−1.31943	+	1.65452i
$381$		0			0
$382$	−6.08927	+	26.6788i	−0.311554	+	1.36501i
$383$	−19.7434	+	9.50792i	−1.00884	+	0.485832i	−0.863930	−	0.503613i	$-0.832004\pi$
$383$	−19.7434	+	9.50792i	−1.00884	+	0.485832i	−0.144911	+	0.989445i	$0.546290\pi$
$384$		0			0
$385$	−18.9774	+	22.5790i	−0.967178	+	1.15073i
$386$	6.26608	−	27.4535i	0.318935	−	1.39735i
$387$		0			0
$388$	−11.3756	−	14.2646i	−0.577511	−	0.724176i
$389$	−2.86238	−	12.5409i	−0.145129	−	0.635850i	−0.994198	−	0.107568i	$-0.965694\pi$
$389$	−2.86238	−	12.5409i	−0.145129	−	0.635850i	0.849069	−	0.528282i	$-0.177164\pi$
$390$		0			0
$391$	5.16585			0.261248
$392$	−44.9739	+	50.7947i	−2.27152	+	2.56552i
$393$		0			0
$394$	−5.09795	−	2.45504i	−0.256831	−	0.123683i
$395$	−5.98668	−	26.2293i	−0.301222	−	1.31974i
$396$		0			0
$397$	−3.33904	−	14.6293i	−0.167582	−	0.734223i	−0.986959	−	0.160969i	$-0.948538\pi$
$397$	−3.33904	−	14.6293i	−0.167582	−	0.734223i	0.819378	−	0.573254i	$-0.194319\pi$
$398$	−2.10028	+	9.20191i	−0.105277	+	0.461250i
$399$		0			0
$400$	−36.2585	−	158.859i	−1.81292	−	7.94294i
$401$	30.2929	−	14.5883i	1.51276	−	0.728505i	0.520633	−	0.853780i	$-0.325696\pi$
$401$	30.2929	−	14.5883i	1.51276	−	0.728505i	0.992122	+	0.125276i	$0.0399816\pi$
$402$		0			0
$403$	−3.10869	−	1.49707i	−0.154855	−	0.0745743i
$404$	−38.8759	+	48.7489i	−1.93415	+	2.42535i
$405$		0			0
$406$	8.98680	+	0.231435i	0.446007	+	0.0114859i
$407$	−14.4459	+	6.95676i	−0.716054	+	0.344834i
$408$		0			0
$409$	1.41986	−	1.78045i	0.0702077	−	0.0880377i	−0.745487	−	0.666520i	$-0.767783\pi$
$409$	1.41986	−	1.78045i	0.0702077	−	0.0880377i	0.815695	+	0.578482i	$0.196355\pi$
$410$	45.3235			2.23837
$411$		0			0
$412$	−21.4614	+	26.9117i	−1.05733	+	1.32584i
$413$	19.1756	−	22.8149i	0.943570	−	1.12265i
$414$		0			0
$415$	6.99124	+	8.76674i	0.343186	+	0.430342i
$416$	−14.3422	+	6.90685i	−0.703186	+	0.338636i
$417$		0			0
$418$	9.18452	+	11.5170i	0.449229	+	0.563316i
$419$	−13.8313	−	17.3440i	−0.675705	−	0.847307i	0.319246	−	0.947672i	$-0.396571\pi$
$419$	−13.8313	−	17.3440i	−0.675705	−	0.847307i	−0.994951	+	0.100365i	$0.967999\pi$
$420$		0			0
$421$	−2.37084	+	2.97293i	−0.115547	+	0.144892i	−0.836242	−	0.548361i	$-0.815252\pi$
$421$	−2.37084	+	2.97293i	−0.115547	+	0.144892i	0.720694	+	0.693253i	$0.243823\pi$
$422$	1.23621			0.0601779
$423$		0			0
$424$	−48.6616	+	61.0197i	−2.36322	+	2.96338i
$425$	3.91819	−	17.1667i	0.190060	−	0.832708i
$426$		0			0
$427$	−19.3259	+	8.70126i	−0.935246	+	0.421083i
$428$	51.9523	+	25.0189i	2.51121	+	1.20934i
$429$		0			0
$430$	−63.1887	−	30.4301i	−3.04723	−	1.46747i
$431$	4.72673	−	20.7092i	0.227679	−	0.997526i	−0.723848	−	0.689960i	$-0.757628\pi$
$431$	4.72673	−	20.7092i	0.227679	−	0.997526i	0.951527	−	0.307566i	$-0.0995146\pi$
$432$		0			0
$433$	5.83276	+	25.5550i	0.280305	+	1.22809i	0.897404	+	0.441210i	$0.145450\pi$
$433$	5.83276	+	25.5550i	0.280305	+	1.22809i	−0.617100	+	0.786885i	$0.711692\pi$
$434$	−22.0704	−	29.1863i	−1.05941	−	1.40099i
$435$		0			0
$436$	22.2337	+	97.4121i	1.06480	+	4.66520i
$437$	3.63557	+	4.55887i	0.173913	+	0.218080i
$438$		0			0
$439$	13.8619	+	6.67556i	0.661594	+	0.318607i	0.734378	−	0.678741i	$-0.237474\pi$
$439$	13.8619	+	6.67556i	0.661594	+	0.318607i	−0.0727836	+	0.997348i	$0.523188\pi$
$440$	−108.046			−5.15091
$441$		0			0
$442$	−3.15437			−0.150038
$443$	13.7467	+	6.62008i	0.653128	+	0.314530i	0.730943	−	0.682438i	$-0.239080\pi$
$443$	13.7467	+	6.62008i	0.653128	+	0.314530i	−0.0778158	+	0.996968i	$0.524795\pi$
$444$		0			0
$445$	−15.7715	−	19.7769i	−0.747642	−	0.937513i
$446$	−13.8695	−	60.7664i	−0.656742	−	2.87737i
$447$		0			0
$448$	−86.5856	−	2.22982i	−4.09078	−	0.105349i
$449$	−1.26563	−	5.54511i	−0.0597290	−	0.261690i	0.936243	−	0.351353i	$-0.114278\pi$
$449$	−1.26563	−	5.54511i	−0.0597290	−	0.261690i	−0.995972	+	0.0896628i	$0.971421\pi$
$450$		0			0
$451$	2.64505	−	11.5887i	0.124551	−	0.545693i
$452$	−50.1202	−	24.1366i	−2.35745	−	1.13529i
$453$		0			0
$454$	4.60273	+	2.21656i	0.216017	+	0.104028i
$455$	4.58695	−	5.45749i	0.215040	−	0.255851i
$456$		0			0
$457$	5.21373	−	22.8428i	0.243888	−	1.06854i	−0.693555	−	0.720404i	$-0.743957\pi$
$457$	5.21373	−	22.8428i	0.243888	−	1.06854i	0.937443	−	0.348139i	$-0.113186\pi$
$458$	44.1822	−	55.4027i	2.06450	−	2.58880i
$459$		0			0
$460$	−66.9896			−3.12341
$461$	−4.74375	+	5.94848i	−0.220939	+	0.277048i	−0.879931	−	0.475101i	$-0.842411\pi$
$461$	−4.74375	+	5.94848i	−0.220939	+	0.277048i	0.658993	+	0.752149i	$0.270983\pi$
$462$		0			0
$463$	−15.4888	−	19.4223i	−0.719824	−	0.902631i	0.278504	−	0.960435i	$-0.410161\pi$
$463$	−15.4888	−	19.4223i	−0.719824	−	0.902631i	−0.998328	+	0.0578044i	$0.981590\pi$
$464$	11.9923	+	15.0378i	0.556727	+	0.698114i
$465$		0			0
$466$	−11.4225	+	5.50081i	−0.529139	+	0.254820i
$467$	−5.30089	−	6.64710i	−0.245296	−	0.307591i	0.643908	−	0.765103i	$-0.277312\pi$
$467$	−5.30089	−	6.64710i	−0.245296	−	0.307591i	−0.889203	+	0.457512i	$0.848741\pi$
$468$		0			0
$469$	−17.5637	−	9.02244i	−0.811016	−	0.416617i
$470$	−61.3215	+	76.8948i	−2.82855	+	3.54689i
$471$		0			0
$472$	109.175			5.02518
$473$	−11.4683	+	14.3808i	−0.527313	+	0.661230i
$474$		0			0
$475$	17.9072	−	8.62363i	0.821637	−	0.395679i
$476$	−21.8542	−	11.2265i	−1.00169	−	0.514564i
$477$		0			0
$478$	−45.6141	+	57.1983i	−2.08634	+	2.61619i
$479$	−18.2193	−	8.77393i	−0.832459	−	0.400891i	−0.0314222	−	0.999506i	$-0.510004\pi$
$479$	−18.2193	−	8.77393i	−0.832459	−	0.400891i	−0.801037	+	0.598615i	$0.795718\pi$
$480$		0			0
$481$	3.49165	−	1.68149i	0.159206	−	0.0766694i
$482$	16.1946	+	70.9532i	0.737644	+	3.23183i
$483$		0			0
$484$	3.66333	−	16.0501i	0.166515	−	0.729549i
$485$	2.88853	+	12.6555i	0.131162	+	0.574656i
$486$		0			0
$487$	4.84068	+	21.2084i	0.219352	+	0.961045i	0.957958	+	0.286908i	$0.0926273\pi$
$487$	4.84068	+	21.2084i	0.219352	+	0.961045i	−0.738606	+	0.674137i	$0.764516\pi$
$488$	−69.9508	−	33.6865i	−3.16652	−	1.52492i
$489$		0			0
$490$	69.7157	−	29.2541i	3.14943	−	1.32156i
$491$	2.15969			0.0974655			0.0487328	−	0.998812i	$-0.484482\pi$
$491$	2.15969			0.0974655			0.0487328	+	0.998812i	$0.484482\pi$
$492$		0			0
$493$	0.462508	+	2.02638i	0.0208303	+	0.0912636i
$494$	−2.21995	−	2.78373i	−0.0998804	−	0.125246i
$495$		0			0
$496$	17.4211	−	76.3267i	0.782230	−	3.42717i
$497$	2.94876	+	14.6480i	0.132270	+	0.657054i
$498$		0			0
$499$	13.9450	−	6.71555i	0.624263	−	0.300629i	−0.0948825	−	0.995488i	$-0.530248\pi$
$499$	13.9450	−	6.71555i	0.624263	−	0.300629i	0.719146	+	0.694859i	$0.244533\pi$
$500$	−26.5889	+	116.494i	−1.18909	+	5.20976i
$501$		0			0
$502$	−25.9629	+	32.5565i	−1.15878	+	1.45307i
$503$	−34.6690	−	16.6957i	−1.54581	−	0.744424i	−0.549941	−	0.835203i	$-0.685350\pi$
$503$	−34.6690	−	16.6957i	−1.54581	−	0.744424i	−0.995871	+	0.0907792i	$0.971064\pi$
$504$		0			0
$505$	39.9688	−	19.2480i	1.77859	−	0.856523i
$506$	−5.32299	+	23.3215i	−0.236636	+	1.03677i
$507$		0			0
$508$	−1.86681			−0.0828263
$509$	−37.6784			−1.67007			−0.835033	−	0.550201i	$-0.814551\pi$
$509$	−37.6784			−1.67007			−0.835033	+	0.550201i	$0.814551\pi$
$510$		0			0
$511$	28.0917	+	0.723439i	1.24270	+	0.0320030i
$512$	−37.4499	−	46.9607i	−1.65507	−	2.07539i
$513$		0			0
$514$	35.4151	−	17.0550i	1.56209	−	0.752265i
$515$	22.0647	−	10.6258i	0.972285	−	0.468228i
$516$		0			0
$517$	16.0825	+	20.1668i	0.707307	+	0.886935i
$518$	41.0857	+	1.05807i	1.80520	+	0.0464888i
$519$		0			0
$520$	26.1155			1.14524
$521$	−43.2588			−1.89520			−0.947601	−	0.319455i	$-0.896500\pi$
$521$	−43.2588			−1.89520			−0.947601	+	0.319455i	$0.896500\pi$
$522$		0			0
$523$	0.199073	−	0.872195i	0.00870485	−	0.0381384i	−0.970389	−	0.241548i	$-0.922345\pi$
$523$	0.199073	−	0.872195i	0.00870485	−	0.0381384i	0.979094	+	0.203409i	$0.0652022\pi$
$524$	82.5177	−	39.7384i	3.60480	−	1.73598i
$525$		0			0
$526$	66.7353	+	32.1380i	2.90980	+	1.40129i
$527$	5.27485	−	6.61445i	0.229776	−	0.288130i
$528$		0			0
$529$	3.01094	−	13.1918i	0.130911	−	0.573557i
$530$	78.3623	−	37.7373i	3.40384	−	1.63920i
$531$		0			0
$532$	−5.47298	−	27.1872i	−0.237284	−	1.17871i
$533$	−0.639326	+	2.80107i	−0.0276923	+	0.121328i
$534$		0			0
$535$	−25.5790	−	32.0751i	−1.10588	−	1.38673i
$536$	−16.0954	−	70.5186i	−0.695216	−	3.04594i
$537$		0			0
$538$	−62.1182			−2.67811
$539$	−3.41139	−	19.5328i	−0.146939	−	0.841338i
$540$		0			0
$541$	−11.4806	−	5.52875i	−0.493589	−	0.237700i	0.170494	−	0.985359i	$-0.445464\pi$
$541$	−11.4806	−	5.52875i	−0.493589	−	0.237700i	−0.664083	+	0.747659i	$0.731178\pi$
$542$	−15.4548	−	67.7119i	−0.663840	−	2.90847i
$543$		0			0
$544$	−8.68541	−	38.0532i	−0.372384	−	1.63152i
$545$	15.8187	−	69.3063i	0.677599	−	2.96876i
$546$		0			0
$547$	2.54649	+	11.1569i	0.108880	+	0.477034i	0.999741	+	0.0227583i	$0.00724483\pi$
$547$	2.54649	+	11.1569i	0.108880	+	0.477034i	−0.890861	+	0.454276i	$0.849898\pi$
$548$	−66.8503	+	32.1934i	−2.85570	+	1.37523i
$549$		0			0
$550$	73.4628	+	35.3778i	3.13246	+	1.50852i
$551$	−1.46278	+	1.83427i	−0.0623166	+	0.0781426i
$552$		0			0
$553$	16.0880	+	8.26437i	0.684131	+	0.351437i
$554$	74.1769	−	35.7217i	3.15147	−	1.51767i
$555$		0			0
$556$	−42.0524	+	52.7320i	−1.78342	+	2.23634i
$557$	7.50584			0.318033			0.159016	−	0.987276i	$-0.449168\pi$
$557$	7.50584			0.318033			0.159016	+	0.987276i	$0.449168\pi$
$558$		0			0
$559$	2.77196	−	3.47593i	0.117241	−	0.147016i
$560$	143.886	+	73.9139i	6.08029	+	3.12343i
$561$		0			0
$562$	−9.77063	−	12.2520i	−0.412149	−	0.516819i
$563$	5.34777	−	2.57535i	0.225382	−	0.108538i	−0.317786	−	0.948163i	$-0.602939\pi$
$563$	5.34777	−	2.57535i	0.225382	−	0.108538i	0.543167	+	0.839625i	$0.317225\pi$
$564$		0			0
$565$	24.6770	+	30.9439i	1.03817	+	1.30182i
$566$	37.4910	+	47.0122i	1.57586	+	1.97607i
$567$		0			0
$568$	−34.1269	+	42.7938i	−1.43193	+	1.79559i
$569$	−4.77238			−0.200069			−0.100034	−	0.994984i	$-0.531895\pi$
$569$	−4.77238			−0.200069			−0.100034	+	0.994984i	$0.531895\pi$
$570$		0			0
$571$	14.0341	−	17.5982i	0.587308	−	0.736461i	−0.396032	−	0.918237i	$-0.629613\pi$
$571$	14.0341	−	17.5982i	0.587308	−	0.736461i	0.983340	+	0.181776i	$0.0581844\pi$
$572$	2.38720	−	10.4590i	0.0998139	−	0.437313i
$573$		0			0
$574$	−19.6044	+	23.3250i	−0.818270	+	0.973567i
$575$	29.0793	+	14.0039i	1.21269	+	0.584001i
$576$		0			0
$577$	2.96870	+	1.42965i	0.123589	+	0.0595172i	0.494656	−	0.869089i	$-0.335294\pi$
$577$	2.96870	+	1.42965i	0.123589	+	0.0595172i	−0.371068	+	0.928606i	$0.621008\pi$
$578$	−8.66050	+	37.9441i	−0.360229	+	1.57827i
$579$		0			0
$580$	−5.99770	−	26.2776i	−0.249041	−	1.09112i
$581$	−7.53567	−	0.194064i	−0.312632	−	0.00805113i
$582$		0			0
$583$	−5.07584	−	22.2387i	−0.210220	−	0.921034i
$584$	64.1820	+	80.4817i	2.65587	+	3.33036i
$585$		0			0
$586$	27.6097	+	13.2961i	1.14054	+	0.549257i
$587$	11.4304			0.471782			0.235891	−	0.971780i	$-0.424199\pi$
$587$	11.4304			0.471782			0.235891	+	0.971780i	$0.424199\pi$
$588$		0			0
$589$	9.54954			0.393482
$590$	−109.616	−	52.7881i	−4.51281	−	2.17325i
$591$		0			0
$592$	54.8260	+	68.7496i	2.25333	+	2.82559i
$593$	8.47449	+	37.1292i	0.348006	+	1.52471i	0.781701	+	0.623653i	$0.214352\pi$
$593$	8.47449	+	37.1292i	0.348006	+	1.52471i	−0.433696	+	0.901059i	$0.642791\pi$
$594$		0			0
$595$	10.5433	+	13.9427i	0.432234	+	0.571594i
$596$	−5.03500	−	22.0598i	−0.206242	−	0.903604i
$597$		0			0
$598$	1.28660	−	5.63696i	0.0526129	−	0.230512i
$599$	−31.0294	−	14.9429i	−1.26782	−	0.610552i	−0.325592	−	0.945510i	$-0.605564\pi$
$599$	−31.0294	−	14.9429i	−1.26782	−	0.610552i	−0.942233	+	0.334958i	$0.891278\pi$
$600$		0			0
$601$	−18.8350	−	9.07048i	−0.768298	−	0.369993i	0.00831957	−	0.999965i	$-0.497352\pi$
$601$	−18.8350	−	9.07048i	−0.768298	−	0.369993i	−0.776617	+	0.629973i	$0.783066\pi$
$602$	42.9922	−	19.3567i	1.75223	−	0.788921i
$603$		0			0
$604$	16.5450	−	72.4882i	0.673205	−	2.94950i
$605$	−7.30288	+	9.15752i	−0.296904	+	0.372306i
$606$		0			0
$607$	−38.3632			−1.55712			−0.778558	−	0.627573i	$-0.784048\pi$
$607$	−38.3632			−1.55712			−0.778558	+	0.627573i	$0.784048\pi$
$608$	27.4695	−	34.4456i	1.11403	−	1.39696i
$609$		0			0
$610$	53.9451	+	67.6451i	2.18418	+	2.73887i
$611$	−3.88723	−	4.87444i	−0.157261	−	0.197199i
$612$		0			0
$613$	−20.6282	+	9.93400i	−0.833164	+	0.401231i	−0.801301	−	0.598262i	$-0.795858\pi$
$613$	−20.6282	+	9.93400i	−0.833164	+	0.401231i	−0.0318630	+	0.999492i	$0.510144\pi$
$614$	−23.2987	−	29.2156i	−0.940259	−	1.17905i
$615$		0			0
$616$	46.7347	−	55.6042i	1.88299	−	2.24036i
$617$	−6.98233	+	8.75557i	−0.281098	+	0.352486i	−0.902257	−	0.431199i	$-0.858091\pi$
$617$	−6.98233	+	8.75557i	−0.281098	+	0.352486i	0.621159	+	0.783685i	$0.286662\pi$
$618$		0			0
$619$	−16.0790			−0.646268			−0.323134	−	0.946353i	$-0.604737\pi$
$619$	−16.0790			−0.646268			−0.323134	+	0.946353i	$0.604737\pi$
$620$	−68.4030	+	85.7747i	−2.74713	+	3.44479i
$621$		0			0
$622$	−1.51766	+	0.730865i	−0.0608525	+	0.0293050i
$623$	16.9997	+	0.437789i	0.681078	+	0.0175396i
$624$		0			0
$625$	20.3072	−	25.4644i	0.812286	−	1.01857i
$626$	57.5249	+	27.7025i	2.29916	+	1.10722i
$627$		0			0
$628$	−58.0326	+	27.9470i	−2.31575	+	1.11521i
$629$	2.11448	+	9.26416i	0.0843100	+	0.369386i
$630$		0			0
$631$	1.07631	−	4.71563i	0.0428473	−	0.187726i	−0.948975	−	0.315350i	$-0.897878\pi$
$631$	1.07631	−	4.71563i	0.0428473	−	0.187726i	0.991823	+	0.127624i	$0.0407351\pi$
$632$	14.7431	+	64.5937i	0.586448	+	2.56940i
$633$		0			0
$634$	−13.1759	−	57.7273i	−0.523281	−	2.29264i
$635$	1.19666	+	0.576280i	0.0474879	+	0.0228690i
$636$		0			0
$637$	0.824554	+	4.72120i	0.0326700	+	0.187061i
$638$	−9.62479			−0.381049
$639$		0			0
$640$	37.9569	+	166.300i	1.50038	+	6.57358i
$641$	11.4974	+	14.4173i	0.454120	+	0.569448i	0.955203	−	0.295951i	$-0.0956364\pi$
$641$	11.4974	+	14.4173i	0.454120	+	0.569448i	−0.501083	+	0.865399i	$0.667065\pi$
$642$		0			0
$643$	−9.36365	+	41.0248i	−0.369266	+	1.61786i	0.359532	+	0.933133i	$0.382936\pi$
$643$	−9.36365	+	41.0248i	−0.369266	+	1.61786i	−0.728798	+	0.684728i	$0.759921\pi$
$644$	28.9759	−	34.4751i	1.14181	−	1.35851i
$645$		0			0
$646$	7.86569	−	3.78792i	0.309471	−	0.149034i
$647$	−3.01636	+	13.2155i	−0.118585	+	0.519556i	0.880388	+	0.474254i	$0.157282\pi$
$647$	−3.01636	+	13.2155i	−0.118585	+	0.519556i	−0.998973	+	0.0453018i	$0.985575\pi$
$648$		0			0
$649$	−19.8945	+	24.9469i	−0.780926	+	0.979250i
$650$	−17.7564	−	8.55104i	−0.696464	−	0.335399i
$651$		0			0
$652$	−49.5168	+	23.8460i	−1.93923	+	0.933882i
$653$	−6.95691	+	30.4802i	−0.272245	+	1.19278i	0.635111	+	0.772421i	$0.280954\pi$
$653$	−6.95691	+	30.4802i	−0.272245	+	1.19278i	−0.907356	+	0.420363i	$0.861903\pi$
$654$		0			0
$655$	−65.1624			−2.54611
$656$	−65.1910			−2.54528
$657$		0			0
$658$	−13.0484	−	64.8184i	−0.508681	−	2.52688i
$659$	−28.4112	−	35.6265i	−1.10674	−	1.38781i	−0.913587	−	0.406642i	$-0.866700\pi$
$659$	−28.4112	−	35.6265i	−1.10674	−	1.38781i	−0.193155	−	0.981168i	$-0.561872\pi$
$660$		0			0
$661$	−22.1213	+	10.6531i	−0.860418	+	0.414356i	−0.811434	−	0.584444i	$-0.801313\pi$
$661$	−22.1213	+	10.6531i	−0.860418	+	0.414356i	−0.0489843	+	0.998800i	$0.515598\pi$
$662$	9.68246	−	4.66283i	0.376320	−	0.181226i
$663$		0			0
$664$	−17.2170	−	21.5894i	−0.668148	−	0.837831i
$665$	−4.88434	+	19.1169i	−0.189407	+	0.741323i
$666$		0			0
$667$	−3.80985			−0.147518
$668$	−77.8906			−3.01368
$669$		0			0
$670$	−17.9367	+	78.5858i	−0.692955	+	3.03604i
$671$	20.4443	−	9.84547i	0.789245	−	0.380080i
$672$		0			0
$673$	−10.6995	−	5.15259i	−0.412434	−	0.198618i	0.216149	−	0.976360i	$-0.430650\pi$
$673$	−10.6995	−	5.15259i	−0.412434	−	0.198618i	−0.628583	+	0.777743i	$0.716365\pi$
$674$	40.5629	−	50.8643i	1.56242	−	1.95922i
$675$		0			0
$676$	15.4246	−	67.5795i	0.593253	−	2.59921i
$677$	18.8060	−	9.05651i	0.722774	−	0.348070i	−0.0360633	−	0.999350i	$-0.511482\pi$
$677$	18.8060	−	9.05651i	0.722774	−	0.348070i	0.758838	+	0.651280i	$0.225768\pi$
$678$		0			0
$679$	−7.76235	−	3.98751i	−0.297892	−	0.153026i
$680$	−14.2489	+	62.4284i	−0.546420	+	2.39402i
$681$		0			0
$682$	24.4260	+	30.6293i	0.935320	+	1.17285i
$683$	1.52378	+	6.67611i	0.0583057	+	0.255454i	0.995678	−	0.0928759i	$-0.0296060\pi$
$683$	1.52378	+	6.67611i	0.0583057	+	0.255454i	−0.937372	+	0.348330i	$0.886749\pi$
$684$		0			0
$685$	52.7902			2.01701
$686$	−15.0999	+	48.5317i	−0.576516	+	1.85295i
$687$		0			0
$688$	90.8873	+	43.7690i	3.46505	+	1.66868i
$689$	1.22686	+	5.37524i	0.0467397	+	0.204780i
$690$		0			0
$691$	−8.28218	−	36.2866i	−0.315069	−	1.38041i	−0.846086	−	0.533046i	$-0.821047\pi$
$691$	−8.28218	−	36.2866i	−0.315069	−	1.38041i	0.531017	−	0.847361i	$-0.321810\pi$
$692$	0.841793	−	3.68814i	0.0320002	−	0.140202i
$693$		0			0
$694$	−5.58343	−	24.4626i	−0.211944	−	0.928587i
$695$	43.2345	−	20.8207i	1.63998	−	0.789772i
$696$		0			0
$697$	−6.34707	−	3.05659i	−0.240413	−	0.115777i
$698$	−37.5550	+	47.0924i	−1.42148	+	1.78247i
$699$		0			0
$700$	−92.5871	−	122.439i	−3.49946	−	4.62775i
$701$	−33.6552	+	16.2075i	−1.27114	+	0.612149i	−0.943098	−	0.332514i	$-0.892103\pi$
$701$	−33.6552	+	16.2075i	−1.27114	+	0.612149i	−0.328042	+	0.944663i	$0.606389\pi$
$702$		0			0
$703$	−6.68751	+	8.38588i	−0.252224	+	0.316279i
$704$	92.7324			3.49498
$705$		0			0
$706$	−27.3290	+	34.2695i	−1.02854	+	1.28975i
$707$	−7.38257	+	28.8948i	−0.277650	+	1.08670i
$708$		0			0
$709$	−10.6635	−	13.3716i	−0.400476	−	0.502182i	0.540176	−	0.841552i	$-0.318357\pi$
$709$	−10.6635	−	13.3716i	−0.400476	−	0.502182i	−0.940653	+	0.339370i	$0.889786\pi$
$710$	54.9563	−	26.4656i	2.06247	−	0.993234i
$711$		0			0
$712$	38.8397	+	48.7034i	1.45558	+	1.82524i
$713$	9.66873	+	12.1242i	0.362097	+	0.454055i
$714$		0			0
$715$	−4.75891	+	5.96748i	−0.177973	+	0.223171i
$716$	23.9808			0.896206
$717$		0			0
$718$	18.6329	−	23.3650i	0.695375	−	0.871972i
$719$	9.49358	−	41.5941i	0.354051	−	1.55120i	−0.413678	−	0.910423i	$-0.635756\pi$
$719$	9.49358	−	41.5941i	0.354051	−	1.55120i	0.767729	−	0.640775i	$-0.221387\pi$
$720$		0			0
$721$	−4.07553	+	15.9513i	−0.151781	+	0.594058i
$722$	−38.1008	−	18.3484i	−1.41796	−	0.682856i
$723$		0			0
$724$	110.801	+	53.3589i	4.11789	+	1.98307i
$725$	−2.88969	+	12.6606i	−0.107321	+	0.470202i
$726$		0			0
$727$	5.75885	+	25.2312i	0.213584	+	0.935773i	0.962109	+	0.272666i	$0.0879054\pi$
$727$	5.75885	+	25.2312i	0.213584	+	0.935773i	−0.748525	+	0.663107i	$0.769237\pi$
$728$	−11.2961	+	13.4399i	−0.418660	+	0.498115i
$729$		0			0
$730$	−25.5267	−	111.840i	−0.944787	−	4.13938i
$731$	6.79672	+	8.52281i	0.251386	+	0.315228i
$732$		0			0
$733$	−40.2065	−	19.3624i	−1.48506	−	0.715168i	−0.496789	−	0.867871i	$-0.665488\pi$
$733$	−40.2065	−	19.3624i	−1.48506	−	0.715168i	−0.988272	+	0.152703i	$0.951202\pi$
$734$	6.04691			0.223196
$735$		0			0
$736$	71.5449			2.63718
$737$	19.0468	+	9.17245i	0.701597	+	0.337871i
$738$		0			0
$739$	−5.91278	−	7.41439i	−0.217505	−	0.272743i	0.661094	−	0.750303i	$-0.270093\pi$
$739$	−5.91278	−	7.41439i	−0.217505	−	0.272743i	−0.878599	+	0.477561i	$0.841521\pi$
$740$	−27.4202	−	120.136i	−1.00798	−	4.41627i
$741$		0			0
$742$	−14.4742	+	56.6508i	−0.531364	+	2.07972i
$743$	5.17087	+	22.6551i	0.189701	+	0.831134i	0.976774	+	0.214274i	$0.0687385\pi$
$743$	5.17087	+	22.6551i	0.189701	+	0.831134i	−0.787073	+	0.616860i	$0.788404\pi$
$744$		0			0
$745$	−3.58228	+	15.6950i	−0.131245	+	0.575020i
$746$	7.25987	+	3.49617i	0.265803	+	0.128004i
$747$		0			0
$748$	23.6996	+	11.4131i	0.866542	+	0.417305i
$749$	27.5710	+	0.710028i	1.00742	+	0.0259438i
$750$		0			0
$751$	−2.46916	+	10.8181i	−0.0901008	+	0.394757i	−0.999789	−	0.0205343i	$-0.993463\pi$
$751$	−2.46916	+	10.8181i	−0.0901008	+	0.394757i	0.909688	+	0.415292i	$0.136320\pi$
$752$	88.2017	−	110.601i	3.21638	−	4.03322i
$753$		0			0
$754$	2.32637			0.0847214
$755$	−32.9825	+	41.3588i	−1.20036	+	1.50520i
$756$		0			0
$757$	−6.10895	−	7.66038i	−0.222034	−	0.278421i	0.658321	−	0.752737i	$-0.271267\pi$
$757$	−6.10895	−	7.66038i	−0.222034	−	0.278421i	−0.880355	+	0.474316i	$0.842695\pi$
$758$	−9.39872	−	11.7856i	−0.341377	−	0.428073i
$759$		0			0
$760$	−65.1211	+	31.3607i	−2.36219	+	1.13757i
$761$	34.0417	+	42.6869i	1.23401	+	1.54740i	0.729472	+	0.684011i	$0.239766\pi$
$761$	34.0417	+	42.6869i	1.23401	+	1.54740i	0.504539	+	0.863389i	$0.331663\pi$
$762$		0			0
$763$	28.8251	+	38.1188i	1.04354	+	1.37999i
$764$	−34.3898	+	43.1234i	−1.24418	+	1.56015i
$765$		0			0
$766$	−60.1388			−2.17290
$767$	4.80861	−	6.02981i	0.173629	−	0.217724i
$768$		0			0
$769$	14.1289	−	6.80411i	0.509501	−	0.245363i	−0.161428	−	0.986884i	$-0.551610\pi$
$769$	14.1289	−	6.80411i	0.509501	−	0.245363i	0.670929	+	0.741522i	$0.265896\pi$
$770$	−73.8091	+	33.2317i	−2.65990	+	1.19759i
$771$		0			0
$772$	35.3883	−	44.3756i	1.27365	−	1.59711i
$773$	47.8163	+	23.0271i	1.71983	+	0.828228i	0.989395	+	0.145251i	$0.0463988\pi$
$773$	47.8163	+	23.0271i	1.71983	+	0.828228i	0.730439	+	0.682978i	$0.239315\pi$
$774$		0			0
$775$	47.6237	−	22.9344i	1.71069	−	0.823826i
$776$	−7.11344	−	31.1660i	−0.255358	−	1.11880i
$777$		0			0
$778$	7.85544	−	34.4169i	0.281631	−	1.23391i
$779$	−1.76944	−	7.75244i	−0.0633969	−	0.277760i
$780$		0			0
$781$	−3.55974	−	15.5963i	−0.127378	−	0.558078i
$782$	12.7730	+	6.15117i	0.456763	+	0.219965i
$783$		0			0
$784$	−100.275	+	42.0775i	−3.58126	+	1.50277i
$785$	45.8271			1.63564
$786$		0			0
$787$	2.25980	+	9.90083i	0.0805532	+	0.352927i	0.999101	−	0.0423823i	$-0.0134947\pi$
$787$	2.25980	+	9.90083i	0.0805532	+	0.352927i	−0.918548	+	0.395309i	$0.870638\pi$
$788$	−7.11084	−	8.91671i	−0.253313	−	0.317645i
$789$		0			0
$790$	16.4297	−	71.9830i	0.584541	−	2.56104i
$791$	−26.5986	−	0.684988i	−0.945738	−	0.0243554i
$792$		0			0
$793$	−4.94152	+	2.37971i	−0.175479	+	0.0845060i
$794$	9.16357	−	40.1482i	0.325203	−	1.42481i
$795$		0			0
$796$	−11.8615	+	14.8739i	−0.420421	+	0.527191i
$797$	6.05860	+	2.91767i	0.214607	+	0.103349i	0.538099	−	0.842882i	$-0.319143\pi$
$797$	6.05860	+	2.91767i	0.214607	+	0.103349i	−0.323492	+	0.946231i	$0.604857\pi$
$798$		0			0
$799$	13.7732	−	6.63280i	0.487259	−	0.234652i
$800$	54.2654	−	237.752i	1.91857	−	8.40581i
$801$		0			0
$802$	92.2728			3.25827
$803$	−30.0860			−1.06171
$804$		0			0
$805$	−29.2164	+	13.1543i	−1.02974	+	0.463629i
$806$	−5.90392	−	7.40328i	−0.207957	−	0.260769i
$807$		0			0
$808$	−98.4291	+	47.4009i	−3.46272	+	1.66756i
$809$	−3.75475	+	1.80819i	−0.132010	+	0.0635727i	−0.498723	−	0.866761i	$-0.666197\pi$
$809$	−3.75475	+	1.80819i	−0.132010	+	0.0635727i	0.366713	+	0.930334i	$0.380483\pi$
$810$		0			0
$811$	28.4813	+	35.7144i	1.00011	+	1.25410i	0.967034	+	0.254649i	$0.0819599\pi$
$811$	28.4813	+	35.7144i	1.00011	+	1.25410i	0.0330792	+	0.999453i	$0.489469\pi$
$812$	16.1176	+	8.27959i	0.565617	+	0.290557i
$813$		0			0
$814$	−44.0024			−1.54228
$815$	39.1023			1.36969
$816$		0			0
$817$	−2.73806	+	11.9962i	−0.0957925	+	0.419694i
$818$	5.63079	−	2.71165i	0.196876	−	0.0948105i
$819$		0			0
$820$	82.3074	+	39.6372i	2.87430	+	1.38419i
$821$	−28.9935	+	36.3567i	−1.01188	+	1.26886i	−0.0490377	+	0.998797i	$0.515615\pi$
$821$	−28.9935	+	36.3567i	−1.01188	+	1.26886i	−0.962843	+	0.270061i	$0.912956\pi$
$822$		0			0
$823$	−4.91698	+	21.5427i	−0.171395	+	0.750932i	0.814030	+	0.580823i	$0.197269\pi$
$823$	−4.91698	+	21.5427i	−0.171395	+	0.750932i	−0.985425	+	0.170109i	$0.945588\pi$
$824$	−54.3375	+	26.1676i	−1.89294	+	0.911590i
$825$		0			0
$826$	74.5800	−	33.5788i	2.59497	−	1.16835i
$827$	5.90842	−	25.8865i	0.205456	−	0.900162i	−0.762091	−	0.647470i	$-0.775827\pi$
$827$	5.90842	−	25.8865i	0.205456	−	0.900162i	0.967547	−	0.252692i	$-0.0813158\pi$
$828$		0			0
$829$	19.7709	+	24.7919i	0.686670	+	0.861057i	0.995950	−	0.0899139i	$-0.0286592\pi$
$829$	19.7709	+	24.7919i	0.686670	+	0.861057i	−0.309279	+	0.950971i	$0.600088\pi$
$830$	6.84760	+	30.0013i	0.237684	+	1.04136i
$831$		0			0
$832$	−22.4140			−0.777065
$833$	−11.7358	−	0.604860i	−0.406622	−	0.0209571i
$834$		0			0
$835$	49.9292	+	24.0446i	1.72787	+	0.832099i
$836$	6.60699	+	28.9471i	0.228507	+	1.00116i
$837$		0			0
$838$	−13.5472	−	59.3540i	−0.467979	−	2.05035i
$839$	5.20039	−	22.7844i	0.179538	−	0.786605i	−0.802306	−	0.596913i	$-0.796394\pi$
$839$	5.20039	−	22.7844i	0.179538	−	0.786605i	0.981844	−	0.189692i	$-0.0607491\pi$
$840$		0			0
$841$	6.11200	+	26.7784i	0.210759	+	0.923394i
$842$	−9.40210	+	4.52781i	−0.324018	+	0.156039i
$843$		0			0
$844$	2.24496	+	1.08112i	0.0772747	+	0.0372135i
$845$	−30.7490	+	38.5581i	−1.05780	+	1.32644i
$846$		0			0
$847$	−1.55396	−	7.71932i	−0.0533946	−	0.265239i
$848$	−112.712	+	54.2793i	−3.87055	+	1.86396i
$849$		0			0
$850$	30.1292	−	37.7808i	1.03342	−	1.29587i
$851$	−17.4178			−0.597074
$852$		0			0
$853$	12.3003	−	15.4241i	0.421155	−	0.528112i	−0.525313	−	0.850909i	$-0.676052\pi$
$853$	12.3003	−	15.4241i	0.421155	−	0.528112i	0.946468	+	0.322797i	$0.104623\pi$
$854$	−58.1460	−	1.49742i	−1.98972	−	0.0512406i
$855$		0			0
$856$	62.9922	+	78.9897i	2.15303	+	2.69981i
$857$	5.86440	−	2.82415i	0.200324	−	0.0964710i	−0.331032	−	0.943619i	$-0.607397\pi$
$857$	5.86440	−	2.82415i	0.200324	−	0.0964710i	0.531356	+	0.847148i	$0.321683\pi$
$858$		0			0
$859$	15.3960	+	19.3060i	0.525305	+	0.658712i	0.971726	−	0.236111i	$-0.0758729\pi$
$859$	15.3960	+	19.3060i	0.525305	+	0.658712i	−0.446421	+	0.894823i	$0.647302\pi$
$860$	−88.1383	−	110.522i	−3.00549	−	3.76877i
$861$		0			0
$862$	36.3465	−	45.5771i	1.23797	−	1.55236i
$863$	−8.19858			−0.279083			−0.139542	−	0.990216i	$-0.544563\pi$
$863$	−8.19858			−0.279083			−0.139542	+	0.990216i	$0.544563\pi$
$864$		0			0
$865$	−1.67812	+	2.10430i	−0.0570579	+	0.0715483i
$866$	−16.0073	+	70.1324i	−0.543949	+	2.38320i
$867$		0			0
$868$	−14.5553	−	72.3037i	−0.494038	−	2.45415i
$869$	−17.4465	−	8.40178i	−0.591831	−	0.285011i
$870$		0			0
$871$	−4.60372	−	2.21704i	−0.155991	−	0.0751214i
$872$	−38.9559	+	170.677i	−1.31921	+	5.77986i
$873$		0			0
$874$	3.56088	+	15.6012i	0.120449	+	0.527720i
$875$	11.2788	+	56.0279i	0.381294	+	1.89409i
$876$		0			0
$877$	−4.11637	−	18.0350i	−0.139000	−	0.608998i	−0.995656	−	0.0931099i	$-0.970319\pi$
$877$	−4.11637	−	18.0350i	−0.139000	−	0.608998i	0.856656	−	0.515888i	$-0.172538\pi$
$878$	26.3261	+	33.0119i	0.888463	+	1.11410i
$879$		0			0
$880$	−156.036	−	75.1428i	−5.25996	−	2.53306i
$881$	11.8580			0.399506			0.199753	−	0.979846i	$-0.435986\pi$
$881$	11.8580			0.399506			0.199753	+	0.979846i	$0.435986\pi$
$882$		0			0
$883$	4.89214			0.164634			0.0823168	−	0.996606i	$-0.473768\pi$
$883$	4.89214			0.164634			0.0823168	+	0.996606i	$0.473768\pi$
$884$	−5.72833	−	2.75862i	−0.192665	−	0.0927824i
$885$		0			0
$886$	26.1073	+	32.7375i	0.877092	+	1.09984i
$887$	6.68883	+	29.3057i	0.224589	+	0.983988i	0.953975	+	0.299886i	$0.0969486\pi$
$887$	6.68883	+	29.3057i	0.224589	+	0.983988i	−0.729386	+	0.684102i	$0.760194\pi$
$888$		0			0
$889$	−0.814178	+	0.366574i	−0.0273067	+	0.0122945i
$890$	−15.4475	−	67.6799i	−0.517801	−	2.26863i
$891$		0			0
$892$	27.9555	−	122.481i	0.936020	−	4.10097i
$893$	15.5466	+	7.48685i	0.520247	+	0.250538i
$894$		0			0
$895$	−15.3721	−	7.40282i	−0.513833	−	0.247449i
$896$	−102.001	−	52.3980i	−3.40763	−	1.75049i
$897$		0			0
$898$	3.47337	−	15.2178i	0.115908	−	0.507826i
$899$	−3.89024	+	4.87820i	−0.129747	+	0.162697i
$900$		0			0
$901$	−13.5188			−0.450376
$902$	20.3393	−	25.5047i	0.677224	−	0.849213i
$903$		0			0
$904$	−60.7707	−	76.2040i	−2.02120	−	2.53451i
$905$	−54.5535	−	68.4080i	−1.81342	−	2.27396i
$906$		0			0
$907$	28.3682	−	13.6614i	0.941951	−	0.453620i	0.101094	−	0.994877i	$-0.467766\pi$
$907$	28.3682	−	13.6614i	0.941951	−	0.453620i	0.840857	+	0.541257i	$0.182052\pi$
$908$	6.42008	+	8.05053i	0.213058	+	0.267166i
$909$		0			0
$910$	17.8401	−	8.03230i	0.591394	−	0.266268i
$911$	13.1486	−	16.4878i	0.435633	−	0.546267i	−0.514753	−	0.857338i	$-0.672117\pi$
$911$	13.1486	−	16.4878i	0.435633	−	0.546267i	0.950386	+	0.311072i	$0.100688\pi$
$912$		0			0
$913$	8.07064			0.267099
$914$	40.0912	−	50.2728i	1.32610	−	1.66288i
$915$		0			0
$916$	128.687	−	61.9722i	4.25193	−	2.04762i
$917$	28.1855	−	33.5348i	0.930769	−	1.10742i
$918$		0			0
$919$	−16.4670	+	20.6490i	−0.543196	+	0.681146i	−0.975353	−	0.220652i	$-0.929181\pi$
$919$	−16.4670	+	20.6490i	−0.543196	+	0.681146i	0.432156	+	0.901799i	$0.357753\pi$
$920$	−105.750	−	50.9264i	−3.48647	−	1.67899i
$921$		0			0
$922$	−18.8124	+	9.05960i	−0.619555	+	0.298362i
$923$	0.860412	+	3.76971i	0.0283208	+	0.124082i
$924$		0			0
$925$	−13.2110	+	57.8813i	−0.434376	+	1.90313i
$926$	−15.1705	−	66.4665i	−0.498535	−	2.18422i
$927$		0			0
$928$	6.40555	+	28.0645i	0.210272	+	0.921264i
$929$	8.93342	+	4.30211i	0.293096	+	0.141148i	0.574654	−	0.818397i	$-0.305137\pi$
$929$	8.93342	+	4.30211i	0.293096	+	0.141148i	−0.281558	+	0.959544i	$0.590851\pi$
$930$		0			0
$931$	−7.72553	−	10.7825i	−0.253194	−	0.353384i
$932$	−25.5540			−0.837048
$933$		0			0
$934$	−5.19198	−	22.7475i	−0.169887	−	0.744322i
$935$	−11.6686	−	14.6320i	−0.381605	−	0.478517i
$936$		0			0
$937$	4.00013	−	17.5257i	0.130678	−	0.572540i	−0.866612	−	0.498982i	$-0.833707\pi$
$937$	4.00013	−	17.5257i	0.130678	−	0.572540i	0.997291	−	0.0735580i	$-0.0234354\pi$
$938$	−32.6845	−	43.2226i	−1.06719	−	1.41127i
$939$		0			0
$940$	−178.607	+	86.0127i	−5.82553	+	2.80543i
$941$	5.39394	−	23.6324i	0.175837	−	0.770394i	−0.807686	−	0.589613i	$-0.799280\pi$
$941$	5.39394	−	23.6324i	0.175837	−	0.770394i	0.983523	−	0.180781i	$-0.0578625\pi$
$942$		0			0
$943$	8.05105	−	10.0957i	0.262178	−	0.328761i
$944$	157.665	+	75.9277i	5.13157	+	2.47124i
$945$		0			0
$946$	−45.4802	+	21.9021i	−1.47869	+	0.712099i
$947$	−10.7101	+	46.9240i	−0.348031	+	1.52483i	0.433612	+	0.901100i	$0.357239\pi$
$947$	−10.7101	+	46.9240i	−0.348031	+	1.52483i	−0.781643	+	0.623726i	$0.785618\pi$
$948$		0			0
$949$	7.27197			0.236058
$950$	54.5456			1.76969
$951$		0			0
$952$	−25.9645	−	34.3359i	−0.841514	−	1.11283i
$953$	17.0198	+	21.3421i	0.551325	+	0.691339i	0.976928	−	0.213571i	$-0.0685094\pi$
$953$	17.0198	+	21.3421i	0.551325	+	0.691339i	−0.425603	+	0.904910i	$0.639938\pi$
$954$		0			0
$955$	35.3565	−	17.0268i	1.14411	−	0.550974i
$956$	−132.857	+	63.9807i	−4.29691	+	2.06928i
$957$		0			0
$958$	−34.6013	−	43.3887i	−1.11792	−	1.40183i
$959$	−22.8340	+	27.1676i	−0.737350	+	0.877288i
$960$		0			0
$961$	−5.60321			−0.180749
$962$	10.6356			0.342907
$963$		0			0
$964$	−32.6419	+	143.014i	−1.05133	+	4.60616i
$965$	−36.3832	+	17.5212i	−1.17122	+	0.564028i
$966$		0			0
$967$	−48.5633	−	23.3868i	−1.56169	−	0.752070i	−0.564390	−	0.825508i	$-0.690889\pi$
$967$	−48.5633	−	23.3868i	−1.56169	−	0.752070i	−0.997300	+	0.0734377i	$0.976603\pi$
$968$	17.9844	−	22.5517i	0.578041	−	0.724840i
$969$		0			0
$970$	−7.92721	+	34.7314i	−0.254527	+	1.11516i
$971$	26.3489	−	12.6890i	0.845578	−	0.407209i	0.0396437	−	0.999214i	$-0.487378\pi$
$971$	26.3489	−	12.6890i	0.845578	−	0.407209i	0.805934	+	0.592005i	$0.201663\pi$
$972$		0			0
$973$	−7.98578	+	31.2558i	−0.256013	+	1.00201i
$974$	−13.2846	+	58.2037i	−0.425667	+	1.86497i
$975$		0			0
$976$	−77.5919	−	97.2971i	−2.48366	−	3.11441i
$977$	6.04450	+	26.4827i	0.193381	+	0.847256i	0.974770	+	0.223212i	$0.0716542\pi$
$977$	6.04450	+	26.4827i	0.193381	+	0.847256i	−0.781389	+	0.624044i	$0.785489\pi$
$978$		0			0
$979$	−18.2065			−0.581883
$980$	152.187	+	7.84369i	4.86145	+	0.250557i
$981$		0			0
$982$	5.34004	+	2.57163i	0.170407	+	0.0820639i
$983$	2.55456	+	11.1922i	0.0814777	+	0.356977i	0.999189	−	0.0402714i	$-0.0128222\pi$
$983$	2.55456	+	11.1922i	0.0814777	+	0.356977i	−0.917711	+	0.397249i	$0.869965\pi$
$984$		0			0
$985$	1.80560	+	7.91087i	0.0575313	+	0.252061i
$986$	−1.26929	+	5.56114i	−0.0404225	+	0.177103i
$987$		0			0
$988$	−1.59695	−	6.99669i	−0.0508057	−	0.222594i
$989$	−18.0028	+	8.66967i	−0.572455	+	0.275680i
$990$		0			0
$991$	−24.5370	−	11.8164i	−0.779443	−	0.375360i	0.00147054	−	0.999999i	$-0.499532\pi$
$991$	−24.5370	−	11.8164i	−0.779443	−	0.375360i	−0.780914	+	0.624639i	$0.785246\pi$
$992$	73.0545	−	91.6074i	2.31948	−	2.90854i
$993$		0			0
$994$	−10.1509	+	39.7298i	−0.321967	+	1.26015i
$995$	12.1950	−	5.87279i	0.386607	−	0.186180i
$996$		0			0
$997$	−1.44582	+	1.81300i	−0.0457896	+	0.0574183i	−0.804199	−	0.594360i	$-0.797405\pi$
$997$	−1.44582	+	1.81300i	−0.0457896	+	0.0574183i	0.758409	+	0.651778i	$0.225977\pi$
$998$	42.4767			1.34458
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.e.127.10	yes	60
3.2	odd	2	inner	441.2.u.e.127.1	✓	60
49.22	even	7	inner	441.2.u.e.316.10	yes	60
147.71	odd	14	inner	441.2.u.e.316.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.u.e.127.1	✓	60	3.2	odd	2	inner
441.2.u.e.127.10	yes	60	1.1	even	1	trivial
441.2.u.e.316.1	yes	60	147.71	odd	14	inner
441.2.u.e.316.10	yes	60	49.22	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47259 + 1.19074i) q^{2} +(3.44888 + 4.32476i) q^{4} +(-0.875748 - 3.83690i) q^{5} +(2.35340 + 1.20894i) q^{7} +(2.15666 + 9.44894i) q^{8} +O(q^{10})\)	\(q+(2.47259 + 1.19074i) q^{2} +(3.44888 + 4.32476i) q^{4} +(-0.875748 - 3.83690i) q^{5} +(2.35340 + 1.20894i) q^{7} +(2.15666 + 9.44894i) q^{8} +(2.40338 - 10.5299i) q^{10} +(-2.55212 - 1.22904i) q^{11} +(0.616863 + 0.297065i) q^{13} +(4.37947 + 5.79148i) q^{14} +(-3.45689 + 15.1456i) q^{16} +(-1.04670 + 1.31252i) q^{17} -1.89493 q^{19} +(13.5733 - 17.0204i) q^{20} +(-4.84689 - 6.07781i) q^{22} +(-1.91858 - 2.40582i) q^{23} +(-9.45004 + 4.55090i) q^{25} +(1.17152 + 1.46904i) q^{26} +(2.88823 + 14.3473i) q^{28} +(0.771945 - 0.967989i) q^{29} -5.03952 q^{31} +(-14.4963 + 18.1778i) q^{32} +(-4.15091 + 1.99897i) q^{34} +(2.57759 - 10.0885i) q^{35} +(3.52916 - 4.42543i) q^{37} +(-4.68539 - 2.25636i) q^{38} +(34.3660 - 16.5498i) q^{40} +(0.933778 + 4.09115i) q^{41} +(1.44494 - 6.33069i) q^{43} +(-3.48667 - 15.2761i) q^{44} +(-1.87916 - 8.23315i) q^{46} +(-8.20432 - 3.95099i) q^{47} +(4.07695 + 5.69021i) q^{49} -28.7850 q^{50} +(0.842749 + 3.69232i) q^{52} +(5.02083 + 6.29592i) q^{53} +(-2.48068 + 10.8686i) q^{55} +(-6.34769 + 24.8444i) q^{56} +(3.06133 - 1.47426i) q^{58} +(2.50659 - 10.9821i) q^{59} +(-4.99461 + 6.26304i) q^{61} +(-12.4607 - 6.00075i) q^{62} +(-29.4951 + 14.2041i) q^{64} +(0.599595 - 2.62700i) q^{65} -7.46313 q^{67} -9.28623 q^{68} +(18.3860 - 21.8755i) q^{70} +(3.52116 + 4.41540i) q^{71} +(9.56936 - 4.60836i) q^{73} +(13.9957 - 6.73998i) q^{74} +(-6.53538 - 8.19511i) q^{76} +(-4.52032 - 5.97776i) q^{77} +6.83607 q^{79} +61.1397 q^{80} +(-2.56263 + 11.2276i) q^{82} +(-2.56700 + 1.23620i) q^{83} +(5.95263 + 2.86664i) q^{85} +(11.1109 - 13.9327i) q^{86} +(6.10903 - 26.7654i) q^{88} +(5.79090 - 2.78875i) q^{89} +(1.09259 + 1.44486i) q^{91} +(3.78765 - 16.5948i) q^{92} +(-15.5813 - 19.5384i) q^{94} +(1.65948 + 7.27066i) q^{95} -3.29836 q^{97} +(3.30509 + 18.9241i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) 60 * q - 12 * q^4 - 2 * q^7	\( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

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