LMFDB - Embedded newform 950.2.u.b.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.2
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	950.99
Dual form			950.2.u.b.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-1.85083 + 0.326352i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{6} +(-4.38571 - 2.53209i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.500000 - 0.181985i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(-1.85083 + 0.326352i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{6} +(-4.38571 - 2.53209i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.500000 - 0.181985i) q^{9} +(0.705737 + 1.22237i) q^{11} +(1.62760 + 0.939693i) q^{12} +(1.28558 + 0.226682i) q^{13} +(-3.87939 + 3.25519i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.817150 - 2.24510i) q^{17} -0.532089i q^{18} +(-2.23396 + 3.74292i) q^{19} +(8.94356 + 3.25519i) q^{21} +(1.39003 - 0.245100i) q^{22} +(-1.96962 + 2.34730i) q^{23} +(1.43969 - 1.20805i) q^{24} +(0.652704 - 1.13052i) q^{26} +(4.01676 - 2.31908i) q^{27} +(1.73205 + 4.75877i) q^{28} +(7.94356 - 2.89122i) q^{29} +(-0.184793 + 0.320070i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-1.70513 - 2.03209i) q^{33} +(-1.83022 - 1.53574i) q^{34} +(-0.500000 - 0.181985i) q^{36} +4.82295i q^{37} +(2.75314 + 3.37939i) q^{38} -2.45336 q^{39} +(-0.266044 - 1.50881i) q^{41} +(6.11776 - 7.29086i) q^{42} +(0.487728 + 0.581252i) q^{43} +(0.245100 - 1.39003i) q^{44} +(1.53209 + 2.65366i) q^{46} +(3.49276 + 9.59627i) q^{47} +(-0.642788 - 1.76604i) q^{48} +(9.32295 + 16.1478i) q^{49} +(-0.779715 + 4.42198i) q^{51} +(-0.839100 - 1.00000i) q^{52} +(1.07666 - 1.28312i) q^{53} +(-0.805407 - 4.56769i) q^{54} +5.06418 q^{56} +(2.91317 - 7.65657i) q^{57} -8.45336i q^{58} +(0.673648 + 0.245188i) q^{59} +(7.47565 + 6.27282i) q^{61} +(0.237565 + 0.283119i) q^{62} +(-2.65366 - 0.467911i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.49273 + 0.907278i) q^{66} +(0.480105 + 1.31908i) q^{67} +(-2.06910 + 1.19459i) q^{68} +(2.87939 - 4.98724i) q^{69} +(-4.87939 + 4.09429i) q^{71} +(-0.342020 + 0.407604i) q^{72} +(-4.49016 + 0.791737i) q^{73} +(4.53209 + 1.64955i) q^{74} +(4.11721 - 1.43128i) q^{76} -7.14796i q^{77} +(-0.839100 + 2.30541i) q^{78} +(0.389185 + 2.20718i) q^{79} +(-7.90033 + 6.62916i) q^{81} +(-1.50881 - 0.266044i) q^{82} +(-3.45150 - 1.99273i) q^{83} +(-4.75877 - 8.24243i) q^{84} +(0.713011 - 0.259515i) q^{86} +(-13.7587 + 7.94356i) q^{87} +(-1.22237 - 0.705737i) q^{88} +(1.84864 - 10.4842i) q^{89} +(-5.06418 - 4.24935i) q^{91} +(3.01763 - 0.532089i) q^{92} +(0.237565 - 0.652704i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(-0.524005 + 1.43969i) q^{97} +(18.3626 - 3.23783i) q^{98} +(0.575322 + 0.482753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^6 + 6 * q^9	$ 12 q - 6 q^{6} + 6 q^{9} - 12 q^{11} - 24 q^{14} - 36 q^{19} + 48 q^{21} + 6 q^{24} + 12 q^{26} + 36 q^{29} + 12 q^{31} + 24 q^{34} - 6 q^{36} + 24 q^{39} + 6 q^{41} + 30 q^{49} + 42 q^{51} - 18 q^{54} + 24 q^{56} + 6 q^{59} + 12 q^{61} + 6 q^{64} + 6 q^{66} + 12 q^{69} - 36 q^{71} + 36 q^{74} - 12 q^{76} - 12 q^{79} - 66 q^{81} - 12 q^{84} + 24 q^{86} - 24 q^{91} + 24 q^{94} - 42 q^{99}+O(q^{100}) $ 12 * q - 6 * q^6 + 6 * q^9 - 12 * q^11 - 24 * q^14 - 36 * q^19 + 48 * q^21 + 6 * q^24 + 12 * q^26 + 36 * q^29 + 12 * q^31 + 24 * q^34 - 6 * q^36 + 24 * q^39 + 6 * q^41 + 30 * q^49 + 42 * q^51 - 18 * q^54 + 24 * q^56 + 6 * q^59 + 12 * q^61 + 6 * q^64 + 6 * q^66 + 12 * q^69 - 36 * q^71 + 36 * q^74 - 12 * q^76 - 12 * q^79 - 66 * q^81 - 12 * q^84 + 24 * q^86 - 24 * q^91 + 24 * q^94 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	−1.85083	+	0.326352i	−1.06858	+	0.188419i	−0.680160	−	0.733064i	$-0.738090\pi$
$3$	−1.85083	+	0.326352i	−1.06858	+	0.188419i	−0.388419	+	0.921483i	$0.626979\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.326352	+	1.85083i	−0.133233	+	0.755599i
$7$	−4.38571	−	2.53209i	−1.65764	−	0.957040i	−0.973799	−	0.227410i	$-0.926974\pi$
$7$	−4.38571	−	2.53209i	−1.65764	−	0.957040i	−0.683842	−	0.729630i	$-0.739692\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.500000	−	0.181985i	0.166667	−	0.0606617i
$10$		0			0
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	0.952586	−	0.304270i	$-0.0984124\pi$
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	−0.739798	+	0.672829i	$0.765079\pi$
$12$	1.62760	+	0.939693i	0.469846	+	0.271266i
$13$	1.28558	+	0.226682i	0.356554	+	0.0628702i	0.349056	−	0.937102i	$-0.386502\pi$
$13$	1.28558	+	0.226682i	0.356554	+	0.0628702i	0.00749804	+	0.999972i	$0.497613\pi$
$14$	−3.87939	+	3.25519i	−1.03681	+	0.869986i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.817150	−	2.24510i	0.198188	−	0.544517i	−0.800293	−	0.599609i	$-0.795323\pi$
$17$	0.817150	−	2.24510i	0.198188	−	0.544517i	0.998481	+	0.0550919i	$0.0175452\pi$
$18$		−	0.532089i		−	0.125415i
$19$	−2.23396	+	3.74292i	−0.512505	+	0.858685i
$19$	−2.23396	+	3.74292i	−0.512505	+	0.858685i
$20$		0			0
$21$	8.94356	+	3.25519i	1.95165	+	0.710341i
$22$	1.39003	−	0.245100i	0.296356	−	0.0522555i
$23$	−1.96962	+	2.34730i	−0.410693	+	0.489445i	−0.931249	−	0.364382i	$-0.881280\pi$
$23$	−1.96962	+	2.34730i	−0.410693	+	0.489445i	0.520556	+	0.853827i	$0.325725\pi$
$24$	1.43969	−	1.20805i	0.293876	−	0.246591i
$25$		0			0
$26$	0.652704	−	1.13052i	0.128006	−	0.221712i
$27$	4.01676	−	2.31908i	0.773026	−	0.446307i
$28$	1.73205	+	4.75877i	0.327327	+	0.899323i
$29$	7.94356	−	2.89122i	1.47508	−	0.536886i	0.525607	−	0.850727i	$-0.323838\pi$
$29$	7.94356	−	2.89122i	1.47508	−	0.536886i	0.949475	+	0.313841i	$0.101616\pi$
$30$		0			0
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	−0.882143	−	0.470981i	$-0.843900\pi$
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	0.848953	+	0.528468i	$0.177233\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−1.70513	−	2.03209i	−0.296824	−	0.353741i
$34$	−1.83022	−	1.53574i	−0.313881	−	0.263377i
$35$		0			0
$36$	−0.500000	−	0.181985i	−0.0833333	−	0.0303309i
$37$			4.82295i			0.792888i	0.918059	+	0.396444i	$0.129756\pi$
$37$			4.82295i			0.792888i	−0.918059	+	0.396444i	$0.870244\pi$
$38$	2.75314	+	3.37939i	0.446618	+	0.548209i
$39$	−2.45336			−0.392853
$40$		0			0
$41$	−0.266044	−	1.50881i	−0.0415492	−	0.235637i	0.956960	−	0.290220i	$-0.0937283\pi$
$41$	−0.266044	−	1.50881i	−0.0415492	−	0.235637i	−0.998509	+	0.0545825i	$0.982617\pi$
$42$	6.11776	−	7.29086i	0.943990	−	1.12500i
$43$	0.487728	+	0.581252i	0.0743779	+	0.0886401i	0.801950	−	0.597391i	$-0.203796\pi$
$43$	0.487728	+	0.581252i	0.0743779	+	0.0886401i	−0.727572	+	0.686031i	$0.759351\pi$
$44$	0.245100	−	1.39003i	0.0369502	−	0.209555i
$45$		0			0
$46$	1.53209	+	2.65366i	0.225894	+	0.391260i
$47$	3.49276	+	9.59627i	0.509471	+	1.39976i	0.881785	+	0.471652i	$0.156342\pi$
$47$	3.49276	+	9.59627i	0.509471	+	1.39976i	−0.372314	+	0.928107i	$0.621435\pi$
$48$	−0.642788	−	1.76604i	−0.0927784	−	0.254907i
$49$	9.32295	+	16.1478i	1.33185	+	2.30683i
$50$		0			0
$51$	−0.779715	+	4.42198i	−0.109182	+	0.619202i
$52$	−0.839100	−	1.00000i	−0.116362	−	0.138675i
$53$	1.07666	−	1.28312i	0.147891	−	0.176250i	−0.687013	−	0.726645i	$-0.741078\pi$
$53$	1.07666	−	1.28312i	0.147891	−	0.176250i	0.834904	+	0.550395i	$0.185523\pi$
$54$	−0.805407	−	4.56769i	−0.109602	−	0.621584i
$55$		0			0
$56$	5.06418			0.676729
$57$	2.91317	−	7.65657i	0.385859	−	1.01414i
$58$		−	8.45336i		−	1.10998i
$59$	0.673648	+	0.245188i	0.0877015	+	0.0319207i	0.385498	−	0.922709i	$-0.374030\pi$
$59$	0.673648	+	0.245188i	0.0877015	+	0.0319207i	−0.297797	+	0.954629i	$0.596252\pi$
$60$		0			0
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	0.980489	−	0.196576i	$-0.0629822\pi$
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	−0.0233295	+	0.999728i	$0.507427\pi$
$62$	0.237565	+	0.283119i	0.0301707	+	0.0359561i
$63$	−2.65366	−	0.467911i	−0.334329	−	0.0589513i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−2.49273	+	0.907278i	−0.306833	+	0.111678i
$67$	0.480105	+	1.31908i	0.0586542	+	0.161151i	0.965559	−	0.260185i	$-0.0837835\pi$
$67$	0.480105	+	1.31908i	0.0586542	+	0.161151i	−0.906905	+	0.421336i	$0.861561\pi$
$68$	−2.06910	+	1.19459i	−0.250915	+	0.144866i
$69$	2.87939	−	4.98724i	0.346637	−	0.600393i
$70$		0			0
$71$	−4.87939	+	4.09429i	−0.579076	+	0.485903i	−0.884644	−	0.466268i	$-0.845598\pi$
$71$	−4.87939	+	4.09429i	−0.579076	+	0.485903i	0.305567	+	0.952171i	$0.401154\pi$
$72$	−0.342020	+	0.407604i	−0.0403075	+	0.0480366i
$73$	−4.49016	+	0.791737i	−0.525534	+	0.0926658i	−0.430120	−	0.902772i	$-0.641529\pi$
$73$	−4.49016	+	0.791737i	−0.525534	+	0.0926658i	−0.0954141	+	0.995438i	$0.530418\pi$
$74$	4.53209	+	1.64955i	0.526845	+	0.191756i
$75$		0			0
$76$	4.11721	−	1.43128i	0.472277	−	0.164179i
$77$		−	7.14796i		−	0.814585i
$78$	−0.839100	+	2.30541i	−0.0950093	+	0.261036i
$79$	0.389185	+	2.20718i	0.0437868	+	0.248327i	0.998843	−	0.0480989i	$-0.0153163\pi$
$79$	0.389185	+	2.20718i	0.0437868	+	0.248327i	−0.955056	+	0.296426i	$0.904205\pi$
$80$		0			0
$81$	−7.90033	+	6.62916i	−0.877814	+	0.736574i
$82$	−1.50881	−	0.266044i	−0.166621	−	0.0293797i
$83$	−3.45150	−	1.99273i	−0.378852	−	0.218730i	0.298467	−	0.954420i	$-0.403525\pi$
$83$	−3.45150	−	1.99273i	−0.378852	−	0.218730i	−0.677319	+	0.735690i	$0.736858\pi$
$84$	−4.75877	−	8.24243i	−0.519224	−	0.899323i
$85$		0			0
$86$	0.713011	−	0.259515i	0.0768860	−	0.0279842i
$87$	−13.7587	+	7.94356i	−1.47508	+	0.851639i
$88$	−1.22237	−	0.705737i	−0.130305	−	0.0752318i
$89$	1.84864	−	10.4842i	0.195956	−	1.11132i	−0.715096	−	0.699026i	$-0.753617\pi$
$89$	1.84864	−	10.4842i	0.195956	−	1.11132i	0.911051	−	0.412293i	$-0.135272\pi$
$90$		0			0
$91$	−5.06418	−	4.24935i	−0.530870	−	0.445453i
$92$	3.01763	−	0.532089i	0.314609	−	0.0554741i
$93$	0.237565	−	0.652704i	0.0246343	−	0.0676822i
$94$	10.2121			1.05330
$95$		0			0
$96$	−1.87939			−0.191814
$97$	−0.524005	+	1.43969i	−0.0532047	+	0.146179i	−0.963448	−	0.267895i	$-0.913672\pi$
$97$	−0.524005	+	1.43969i	−0.0532047	+	0.146179i	0.910244	+	0.414073i	$0.135894\pi$
$98$	18.3626	−	3.23783i	1.85491	−	0.327070i
$99$	0.575322	+	0.482753i	0.0578220	+	0.0485185i
$100$		0			0
$101$	1.53209	−	8.68891i	0.152449	−	0.864579i	−0.808633	−	0.588314i	$-0.799792\pi$
$101$	1.53209	−	8.68891i	0.152449	−	0.864579i	0.961081	−	0.276265i	$-0.0890968\pi$
$102$	3.88863	+	2.24510i	0.385031	+	0.222298i
$103$	6.19031	−	3.57398i	0.609950	−	0.352155i	−0.162996	−	0.986627i	$-0.552116\pi$
$103$	6.19031	−	3.57398i	0.609950	−	0.352155i	0.772946	+	0.634472i	$0.218782\pi$
$104$	−1.22668	+	0.446476i	−0.120286	+	0.0437805i
$105$		0			0
$106$	−0.837496	−	1.45059i	−0.0813448	−	0.140893i
$107$	8.11430	+	4.68479i	0.784439	+	0.452896i	0.838001	−	0.545669i	$-0.183724\pi$
$107$	8.11430	+	4.68479i	0.784439	+	0.452896i	−0.0535622	+	0.998565i	$0.517058\pi$
$108$	−4.56769	−	0.805407i	−0.439526	−	0.0775004i
$109$	−8.47565	+	7.11192i	−0.811820	+	0.681198i	−0.951041	−	0.309063i	$-0.899985\pi$
$109$	−8.47565	+	7.11192i	−0.811820	+	0.681198i	0.139221	+	0.990261i	$0.455540\pi$
$110$		0			0
$111$	−1.57398	−	8.92647i	−0.149395	−	0.847263i
$112$	1.73205	−	4.75877i	0.163663	−	0.449662i
$113$			13.2986i			1.25103i	0.780213	+	0.625514i	$0.215110\pi$
$113$			13.2986i			1.25103i	−0.780213	+	0.625514i	$0.784890\pi$
$114$	−6.19846	−	5.35619i	−0.580539	−	0.501653i
$115$		0			0
$116$	−7.94356	−	2.89122i	−0.737541	−	0.268443i
$117$	0.684040	−	0.120615i	0.0632395	−	0.0111508i
$118$	0.460802	−	0.549163i	0.0424203	−	0.0505546i
$119$	−9.26857	+	7.77725i	−0.849648	+	0.712940i
$120$		0			0
$121$	4.50387	−	7.80093i	0.409443	−	0.709176i
$122$	8.45134	−	4.87939i	0.765149	−	0.441759i
$123$	0.984808	+	2.70574i	0.0887971	+	0.243968i
$124$	0.347296	−	0.126406i	0.0311881	−	0.0113516i
$125$		0			0
$126$	−1.34730	+	2.33359i	−0.120027	+	0.207892i
$127$	−5.62738	−	0.992259i	−0.499349	−	0.0880488i	−0.0816999	−	0.996657i	$-0.526035\pi$
$127$	−5.62738	−	0.992259i	−0.499349	−	0.0880488i	−0.417650	+	0.908608i	$0.637146\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−1.09240	−	0.916629i	−0.0961801	−	0.0807047i
$130$		0			0
$131$	9.28359	+	3.37895i	0.811111	+	0.295220i	0.714083	−	0.700062i	$-0.246844\pi$
$131$	9.28359	+	3.37895i	0.811111	+	0.295220i	0.0970281	+	0.995282i	$0.469066\pi$
$132$			2.65270i			0.230888i
$133$	19.2749	−	10.7588i	1.67134	−	0.932904i
$134$	1.40373			0.121264
$135$		0			0
$136$	0.414878	+	2.35289i	0.0355755	+	0.201759i
$137$	−3.46908	+	4.13429i	−0.296383	+	0.353216i	−0.893600	−	0.448864i	$-0.851829\pi$
$137$	−3.46908	+	4.13429i	−0.296383	+	0.353216i	0.597217	+	0.802080i	$0.296273\pi$
$138$	−3.70167	−	4.41147i	−0.315107	−	0.375530i
$139$	0.406260	−	2.30401i	0.0344585	−	0.195424i	−0.962719	−	0.270503i	$-0.912810\pi$
$139$	0.406260	−	2.30401i	0.0344585	−	0.195424i	0.997178	+	0.0750794i	$0.0239210\pi$
$140$		0			0
$141$	−9.59627	−	16.6212i	−0.808151	−	1.39976i
$142$	2.17853	+	5.98545i	0.182818	+	0.502288i
$143$	0.630189	+	1.73143i	0.0526990	+	0.144789i
$144$	0.266044	+	0.460802i	0.0221704	+	0.0384002i
$145$		0			0
$146$	−0.791737	+	4.49016i	−0.0655246	+	0.371608i
$147$	−22.5251	−	26.8444i	−1.85784	−	2.21409i
$148$	3.10013	−	3.69459i	0.254829	−	0.303694i
$149$	2.49525	+	14.1513i	0.204419	+	1.15932i	0.898351	+	0.439278i	$0.144766\pi$
$149$	2.49525	+	14.1513i	0.204419	+	1.15932i	−0.693932	+	0.720040i	$0.744123\pi$
$150$		0			0
$151$	−20.8384			−1.69581			−0.847904	−	0.530150i	$-0.822135\pi$
$151$	−20.8384			−1.69581			−0.847904	+	0.530150i	$0.822135\pi$
$152$	0.0632028	−	4.35844i	0.00512642	−	0.353516i
$153$		−	1.27126i		−	0.102775i
$154$	−6.71688	−	2.44474i	−0.541262	−	0.197003i
$155$		0			0
$156$	1.87939	+	1.57699i	0.150471	+	0.126260i
$157$	4.09429	+	4.87939i	0.326760	+	0.389417i	0.904266	−	0.426969i	$-0.140419\pi$
$157$	4.09429	+	4.87939i	0.326760	+	0.389417i	−0.577506	+	0.816386i	$0.695974\pi$
$158$	2.20718	+	0.389185i	0.175594	+	0.0309619i
$159$	−1.57398	+	2.72621i	−0.124825	+	0.216202i
$160$		0			0
$161$	14.5817	−	5.30731i	1.14920	−	0.418275i
$162$	3.52730	+	9.69119i	0.277131	+	0.761412i
$163$	−4.09754	+	2.36571i	−0.320944	+	0.185297i	−0.651813	−	0.758380i	$-0.725991\pi$
$163$	−4.09754	+	2.36571i	−0.320944	+	0.185297i	0.330869	+	0.943677i	$0.392658\pi$
$164$	−0.766044	+	1.32683i	−0.0598180	+	0.103608i
$165$		0			0
$166$	−3.05303	+	2.56180i	−0.236961	+	0.198834i
$167$	−11.1050	+	13.2344i	−0.859331	+	1.02411i	0.140092	+	0.990138i	$0.455260\pi$
$167$	−11.1050	+	13.2344i	−0.859331	+	1.02411i	−0.999423	+	0.0339719i	$0.989184\pi$
$168$	−9.37295	+	1.65270i	−0.723139	+	0.127509i
$169$	−10.6147	−	3.86343i	−0.816514	−	0.297187i
$170$		0			0
$171$	−0.435822	+	2.27801i	−0.0333282	+	0.174203i
$172$		−	0.758770i		−	0.0578557i
$173$	−6.43783	+	17.6878i	−0.489459	+	1.34478i	0.411712	+	0.911314i	$0.364931\pi$
$173$	−6.43783	+	17.6878i	−0.489459	+	1.34478i	−0.901171	+	0.433463i	$0.857291\pi$
$174$	2.75877	+	15.6458i	0.209142	+	1.18610i
$175$		0			0
$176$	−1.08125	+	0.907278i	−0.0815024	+	0.0683887i
$177$	−1.32683	−	0.233956i	−0.0997305	−	0.0175852i
$178$	−9.21962	−	5.32295i	−0.691039	−	0.398972i
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	−0.999810	−	0.0194816i	$-0.993798\pi$
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	0.483034	−	0.875602i	$-0.339535\pi$
$180$		0			0
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.732522	−	0.680744i	$-0.761657\pi$
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.123570	+	0.992336i	$0.539434\pi$
$182$	−5.72513	+	3.30541i	−0.424375	+	0.245013i
$183$	−15.8833	−	9.17024i	−1.17413	−	0.677884i
$184$	0.532089	−	3.01763i	0.0392261	−	0.222462i
$185$		0			0
$186$	−0.532089	−	0.446476i	−0.0390147	−	0.0327372i
$187$	3.32104	−	0.585589i	0.242859	−	0.0428225i
$188$	3.49276	−	9.59627i	0.254735	−	0.699880i
$189$	−23.4884			−1.70853
$190$		0			0
$191$	−20.0993			−1.45433			−0.727166	−	0.686462i	$-0.759163\pi$
$191$	−20.0993			−1.45433			−0.727166	+	0.686462i	$0.759163\pi$
$192$	−0.642788	+	1.76604i	−0.0463892	+	0.127453i
$193$	16.4316	−	2.89734i	1.18277	−	0.208555i	0.452535	−	0.891747i	$-0.350520\pi$
$193$	16.4316	−	2.89734i	1.18277	−	0.208555i	0.730239	+	0.683192i	$0.239409\pi$
$194$	1.17365	+	0.984808i	0.0842630	+	0.0707051i
$195$		0			0
$196$	3.23783	−	18.3626i	0.231273	−	1.31162i
$197$	−11.2501	−	6.49525i	−0.801537	−	0.462768i	0.0424714	−	0.999098i	$-0.486477\pi$
$197$	−11.2501	−	6.49525i	−0.801537	−	0.462768i	−0.844008	+	0.536330i	$0.819810\pi$
$198$	0.650411	−	0.375515i	0.0462227	−	0.0266867i
$199$	16.1557	−	5.88019i	1.14525	−	0.416836i	0.301441	−	0.953485i	$-0.402532\pi$
$199$	16.1557	−	5.88019i	1.14525	−	0.416836i	0.843806	+	0.536649i	$0.180310\pi$
$200$		0			0
$201$	−1.31908	−	2.28471i	−0.0930406	−	0.161151i
$202$	−7.64090	−	4.41147i	−0.537612	−	0.310390i
$203$	−42.1590	−	7.43376i	−2.95898	−	0.521748i
$204$	3.43969	−	2.88624i	0.240827	−	0.202078i
$205$		0			0
$206$	−1.24123	−	7.03936i	−0.0864806	−	0.490456i
$207$	−0.557635	+	1.53209i	−0.0387583	+	0.106488i
$208$			1.30541i			0.0905137i
$209$	−6.15183	−	0.0892091i	−0.425531	−	0.00617072i
$210$		0			0
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.805673	−	0.592360i	$-0.201804\pi$
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.236420	+	0.971651i	$0.424026\pi$
$212$	−1.64955	+	0.290859i	−0.113291	+	0.0199763i
$213$	7.69475	−	9.17024i	0.527236	−	0.628335i
$214$	7.17752	−	6.02265i	0.490645	−	0.411700i
$215$		0			0
$216$	−2.31908	+	4.01676i	−0.157793	+	0.273306i
$217$	1.62089	−	0.935822i	0.110033	−	0.0635278i
$218$	3.78417	+	10.3969i	0.256296	+	0.704169i
$219$	8.05216	−	2.93075i	0.544114	−	0.198041i
$220$		0			0
$221$	1.55943	−	2.70101i	0.104899	−	0.181690i
$222$	−8.92647	−	1.57398i	−0.599106	−	0.105638i
$223$	−2.62500	−	3.12836i	−0.175783	−	0.209490i	0.670958	−	0.741495i	$-0.265883\pi$
$223$	−2.62500	−	3.12836i	−0.175783	−	0.209490i	−0.846741	+	0.532005i	$0.821439\pi$
$224$	−3.87939	−	3.25519i	−0.259202	−	0.217497i
$225$		0			0
$226$	12.4966	+	4.54839i	0.831261	+	0.302554i
$227$			13.6604i			0.906676i	0.891339	+	0.453338i	$0.149767\pi$
$227$			13.6604i			0.906676i	−0.891339	+	0.453338i	$0.850233\pi$
$228$	−7.15317	+	3.99273i	−0.473730	+	0.264425i
$229$	5.22163			0.345055			0.172527	−	0.985005i	$-0.444807\pi$
$229$	5.22163			0.345055			0.172527	+	0.985005i	$0.444807\pi$
$230$		0			0
$231$	2.33275	+	13.2297i	0.153484	+	0.870449i
$232$	−5.43372	+	6.47565i	−0.356741	+	0.425147i
$233$	17.3828	+	20.7160i	1.13878	+	1.35715i	0.924863	+	0.380300i	$0.124179\pi$
$233$	17.3828	+	20.7160i	1.13878	+	1.35715i	0.213921	+	0.976851i	$0.431376\pi$
$234$	0.120615	−	0.684040i	0.00788483	−	0.0447171i
$235$		0			0
$236$	−0.358441	−	0.620838i	−0.0233325	−	0.0404131i
$237$	−1.44063	−	3.95811i	−0.0935793	−	0.257107i
$238$	4.13819	+	11.3696i	0.268239	+	0.736981i
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	0.861367	−	0.507984i	$-0.169609\pi$
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	−0.870610	+	0.491973i	$0.836276\pi$
$240$		0			0
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	−0.962540	−	0.271139i	$-0.912600\pi$
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	0.997227	+	0.0744203i	$0.0237106\pi$
$242$	−5.79006	−	6.90033i	−0.372199	−	0.443570i
$243$	3.51471	−	4.18866i	0.225468	−	0.268703i
$244$	−1.69459	−	9.61051i	−0.108485	−	0.615250i
$245$		0			0
$246$	2.87939			0.183583
$247$	−3.72037	+	4.30541i	−0.236721	+	0.273947i
$248$		−	0.369585i		−	0.0234687i
$249$	7.03849	+	2.56180i	0.446046	+	0.162347i
$250$		0			0
$251$	−9.69640	−	8.13625i	−0.612032	−	0.513555i	0.283256	−	0.959044i	$-0.408585\pi$
$251$	−9.69640	−	8.13625i	−0.612032	−	0.513555i	−0.895287	+	0.445489i	$0.853030\pi$
$252$	1.73205	+	2.06418i	0.109109	+	0.130031i
$253$	−4.25930	−	0.751030i	−0.267780	−	0.0472168i
$254$	−2.85710	+	4.94864i	−0.179270	+	0.310505i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	10.3950	+	28.5599i	0.648419	+	1.78152i	0.623494	+	0.781828i	$0.285713\pi$
$257$	10.3950	+	28.5599i	0.648419	+	1.78152i	0.0249253	+	0.999689i	$0.492065\pi$
$258$	−1.23497	+	0.713011i	−0.0768860	+	0.0443901i
$259$	12.2121	−	21.1520i	0.758825	−	1.31432i
$260$		0			0
$261$	3.44562	−	2.89122i	0.213279	−	0.178962i
$262$	6.35035	−	7.56805i	0.392326	−	0.467556i
$263$	21.5699	−	3.80335i	1.33005	−	0.234524i	0.536952	−	0.843613i	$-0.319576\pi$
$263$	21.5699	−	3.80335i	1.33005	−	0.234524i	0.793102	+	0.609088i	$0.208465\pi$
$264$	2.49273	+	0.907278i	0.153417	+	0.0558391i
$265$		0			0
$266$	−3.51754	−	21.7922i	−0.215674	−	1.33616i
$267$			20.0077i			1.22445i
$268$	0.480105	−	1.31908i	0.0293271	−	0.0805755i
$269$	0.248970	+	1.41198i	0.0151800	+	0.0860900i	0.991457	−	0.130437i	$-0.0416381\pi$
$269$	0.248970	+	1.41198i	0.0151800	+	0.0860900i	−0.976277	+	0.216527i	$0.930527\pi$
$270$		0			0
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	−0.183597	−	0.983002i	$-0.558774\pi$
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	0.936186	+	0.351504i	$0.114330\pi$
$272$	2.35289	+	0.414878i	0.142665	+	0.0251557i
$273$	10.7597	+	6.21213i	0.651209	+	0.375975i
$274$	2.69846	+	4.67388i	0.163020	+	0.282359i
$275$		0			0
$276$	−5.41147	+	1.96962i	−0.325732	+	0.118557i
$277$	9.62046	−	5.55438i	0.578038	−	0.333730i	−0.182315	−	0.983240i	$-0.558359\pi$
$277$	9.62046	−	5.55438i	0.578038	−	0.333730i	0.760353	+	0.649510i	$0.225026\pi$
$278$	−2.02611	−	1.16978i	−0.121518	−	0.0701586i
$279$	−0.0341483	+	0.193665i	−0.00204440	+	0.0115944i
$280$		0			0
$281$	3.25490	+	2.73119i	0.194171	+	0.162929i	0.734690	−	0.678403i	$-0.237328\pi$
$281$	3.25490	+	2.73119i	0.194171	+	0.162929i	−0.540519	+	0.841332i	$0.681772\pi$
$282$	−18.9010	+	3.33275i	−1.12554	+	0.198462i
$283$	1.86608	−	5.12701i	0.110927	−	0.304769i	−0.871791	−	0.489878i	$-0.837041\pi$
$283$	1.86608	−	5.12701i	0.110927	−	0.304769i	0.982718	+	0.185108i	$0.0592637\pi$
$284$	6.36959			0.377965
$285$		0			0
$286$	1.84255			0.108952
$287$	−2.65366	+	7.29086i	−0.156640	+	0.430366i
$288$	0.524005	−	0.0923963i	0.0308773	−	0.00544450i
$289$	8.65002	+	7.25822i	0.508824	+	0.426954i
$290$		0			0
$291$	0.500000	−	2.83564i	0.0293105	−	0.166228i
$292$	3.94858	+	2.27972i	0.231073	+	0.133410i
$293$	−15.4269	+	8.90673i	−0.901249	+	0.520337i	−0.877605	−	0.479384i	$-0.840860\pi$
$293$	−15.4269	+	8.90673i	−0.901249	+	0.520337i	−0.0236440	+	0.999720i	$0.507527\pi$
$294$	−32.9295	+	11.9854i	−1.92049	+	0.699000i
$295$		0			0
$296$	−2.41147	−	4.17680i	−0.140164	−	0.242771i
$297$	5.66955	+	3.27332i	0.328981	+	0.189937i
$298$	14.1513	+	2.49525i	0.819762	+	0.144546i
$299$	−3.06418	+	2.57115i	−0.177206	+	0.148693i
$300$		0			0
$301$	−0.667252	−	3.78417i	−0.0384597	−	0.218116i
$302$	−7.12716	+	19.5817i	−0.410122	+	1.12680i
$303$			16.5817i			0.952595i
$304$	−4.07398	−	1.55007i	−0.233659	−	0.0889024i
$305$		0			0
$306$	−1.19459	−	0.434796i	−0.0682903	−	0.0248556i
$307$	28.2233	−	4.97653i	1.61079	−	0.284026i	0.705464	−	0.708746i	$-0.250739\pi$
$307$	28.2233	−	4.97653i	1.61079	−	0.284026i	0.905325	+	0.424720i	$0.139627\pi$
$308$	−4.59462	+	5.47565i	−0.261803	+	0.312004i
$309$	−10.2909	+	8.63506i	−0.585427	+	0.491231i
$310$		0			0
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	−0.998279	−	0.0586473i	$-0.981321\pi$
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	0.549929	+	0.835211i	$0.314655\pi$
$312$	2.12467	−	1.22668i	0.120286	−	0.0694472i
$313$	4.49422	+	12.3478i	0.254028	+	0.697937i	0.999507	+	0.0314071i	$0.00999883\pi$
$313$	4.49422	+	12.3478i	0.254028	+	0.697937i	−0.745478	+	0.666530i	$0.767779\pi$
$314$	5.98545	−	2.17853i	0.337779	−	0.122941i
$315$		0			0
$316$	1.12061	−	1.94096i	0.0630395	−	0.109188i
$317$	−21.0795	−	3.71688i	−1.18394	−	0.208761i	−0.453196	−	0.891411i	$-0.649716\pi$
$317$	−21.0795	−	3.71688i	−1.18394	−	0.208761i	−0.730746	+	0.682650i	$0.760827\pi$
$318$	2.02347	+	2.41147i	0.113470	+	0.135229i
$319$	9.14022	+	7.66955i	0.511754	+	0.429412i
$320$		0			0
$321$	−16.5471	−	6.02265i	−0.923569	−	0.336152i
$322$		−	15.5175i		−	0.864759i
$323$	6.57775	+	8.07398i	0.365996	+	0.449248i
$324$	10.3131			0.572953
$325$		0			0
$326$	0.821604	+	4.65955i	0.0455044	+	0.258069i
$327$	13.3660	−	15.9290i	0.739143	−	0.880877i
$328$	0.984808	+	1.17365i	0.0543769	+	0.0648039i
$329$	8.98040	−	50.9304i	0.495105	−	2.80788i
$330$		0			0
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	0.969160	+	0.246432i	$0.0792582\pi$
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	−0.271164	+	0.962533i	$0.587409\pi$
$332$	1.36310	+	3.74510i	0.0748101	+	0.205539i
$333$	0.877705	+	2.41147i	0.0480979	+	0.132148i
$334$	8.63816	+	14.9617i	0.472659	+	0.818669i
$335$		0			0
$336$	−1.65270	+	9.37295i	−0.0901624	+	0.511336i
$337$	16.9550	+	20.2062i	0.923599	+	1.10070i	0.994658	+	0.103230i	$0.0329178\pi$
$337$	16.9550	+	20.2062i	0.923599	+	1.10070i	−0.0710588	+	0.997472i	$0.522638\pi$
$338$	−7.26087	+	8.65317i	−0.394939	+	0.470670i
$339$	−4.34002	−	24.6135i	−0.235718	−	1.33682i
$340$		0			0
$341$	−0.521660			−0.0282495
$342$	1.99157	+	1.18866i	0.107692	+	0.0642755i
$343$		−	58.9769i		−	3.18445i
$344$	−0.713011	−	0.259515i	−0.0384430	−	0.0139921i
$345$		0			0
$346$	14.4192	+	12.0992i	0.775182	+	0.650455i
$347$	−16.4755	−	19.6348i	−0.884452	−	1.05405i	−0.998166	−	0.0605352i	$-0.980719\pi$
$347$	−16.4755	−	19.6348i	−0.884452	−	1.05405i	0.113714	−	0.993514i	$-0.463725\pi$
$348$	15.6458	+	2.75877i	0.838701	+	0.147886i
$349$	−2.92127	+	5.05980i	−0.156372	+	0.270845i	−0.933558	−	0.358427i	$-0.883313\pi$
$349$	−2.92127	+	5.05980i	−0.156372	+	0.270845i	0.777186	+	0.629271i	$0.216647\pi$
$350$		0			0
$351$	5.68954	−	2.07082i	0.303685	−	0.110532i
$352$	0.482753	+	1.32635i	0.0257308	+	0.0706948i
$353$	19.4074	−	11.2049i	1.03295	−	0.596375i	0.115122	−	0.993351i	$-0.463274\pi$
$353$	19.4074	−	11.2049i	1.03295	−	0.596375i	0.917829	+	0.396977i	$0.129941\pi$
$354$	−0.673648	+	1.16679i	−0.0358040	+	0.0620143i
$355$		0			0
$356$	−8.15523	+	6.84305i	−0.432226	+	0.362681i
$357$	14.6165	−	17.4192i	0.773585	−	0.921923i
$358$	−13.6179	+	2.40121i	−0.719730	+	0.126908i
$359$	9.03684	+	3.28914i	0.476946	+	0.173594i	0.569296	−	0.822132i	$-0.307216\pi$
$359$	9.03684	+	3.28914i	0.476946	+	0.173594i	−0.0923503	+	0.995727i	$0.529438\pi$
$360$		0			0
$361$	−9.01889	−	16.7230i	−0.474678	−	0.880159i
$362$			12.2567i			0.644198i
$363$	−5.79006	+	15.9081i	−0.303900	+	0.834957i
$364$	1.14796	+	6.51038i	0.0601692	+	0.341237i
$365$		0			0
$366$	−14.0496	+	11.7890i	−0.734386	+	0.616223i
$367$	23.0052	+	4.05644i	1.20086	+	0.211744i	0.738071	−	0.674723i	$-0.235737\pi$
$367$	23.0052	+	4.05644i	1.20086	+	0.211744i	0.462791	+	0.886468i	$0.346848\pi$
$368$	−2.65366	−	1.53209i	−0.138331	−	0.0798657i
$369$	−0.407604	−	0.705990i	−0.0212190	−	0.0367524i
$370$		0			0
$371$	−7.97090	+	2.90117i	−0.413829	+	0.150621i
$372$	−0.601535	+	0.347296i	−0.0311881	+	0.0180065i
$373$	−22.4663	−	12.9709i	−1.16326	−	0.671608i	−0.211176	−	0.977448i	$-0.567729\pi$
$373$	−22.4663	−	12.9709i	−1.16326	−	0.671608i	−0.952083	+	0.305840i	$0.901063\pi$
$374$	0.585589	−	3.32104i	0.0302801	−	0.171727i
$375$		0			0
$376$	−7.82295	−	6.56423i	−0.403438	−	0.338524i
$377$	10.8674	−	1.91622i	0.559701	−	0.0986904i
$378$	−8.03352	+	22.0719i	−0.413200	+	1.13526i
$379$	−9.47834			−0.486870			−0.243435	−	0.969917i	$-0.578274\pi$
$379$	−9.47834			−0.486870			−0.243435	+	0.969917i	$0.578274\pi$
$380$		0			0
$381$	10.7392			0.550184
$382$	−6.87435	+	18.8871i	−0.351722	+	0.966349i
$383$	−13.2835	+	2.34224i	−0.678756	+	0.119683i	−0.502390	−	0.864641i	$-0.667546\pi$
$383$	−13.2835	+	2.34224i	−0.678756	+	0.119683i	−0.176367	+	0.984324i	$0.556435\pi$
$384$	1.43969	+	1.20805i	0.0734690	+	0.0616478i
$385$		0			0
$386$	2.89734	−	16.4316i	0.147471	−	0.836347i
$387$	0.349643	+	0.201867i	0.0177734	+	0.0102615i
$388$	1.32683	−	0.766044i	0.0673595	−	0.0388900i
$389$	−23.6313	+	8.60111i	−1.19816	+	0.436093i	−0.862581	−	0.505920i	$-0.831153\pi$
$389$	−23.6313	+	8.60111i	−1.19816	+	0.436093i	−0.335576	+	0.942013i	$0.608931\pi$
$390$		0			0
$391$	3.66044	+	6.34008i	0.185117	+	0.320631i
$392$	−16.1478	−	9.32295i	−0.815588	−	0.470880i
$393$	−18.2851	−	3.22416i	−0.922361	−	0.162637i
$394$	−9.95130	+	8.35014i	−0.501339	+	0.420674i
$395$		0			0
$396$	−0.130415	−	0.739620i	−0.00655360	−	0.0371673i
$397$	2.24579	−	6.17024i	0.112713	−	0.309676i	−0.870492	−	0.492183i	$-0.836199\pi$
$397$	2.24579	−	6.17024i	0.112713	−	0.309676i	0.983205	+	0.182507i	$0.0584213\pi$
$398$		−	17.1925i		−	0.861784i
$399$	−32.1634	+	26.2031i	−1.61019	+	1.31179i
$400$		0			0
$401$	27.7310	+	10.0933i	1.38482	+	0.504034i	0.923636	−	0.383270i	$-0.125202\pi$
$401$	27.7310	+	10.0933i	1.38482	+	0.504034i	0.461185	+	0.887304i	$0.347425\pi$
$402$	−2.59808	+	0.458111i	−0.129580	+	0.0228485i
$403$	−0.310119	+	0.369585i	−0.0154481	+	0.0184103i
$404$	−6.75877	+	5.67128i	−0.336261	+	0.282157i
$405$		0			0
$406$	−21.4047	+	37.0740i	−1.06230	+	1.83995i
$407$	−5.89544	+	3.40373i	−0.292226	+	0.168717i
$408$	−1.53574	−	4.21941i	−0.0760304	−	0.208892i
$409$	19.8567	−	7.22724i	0.981850	−	0.357364i	0.199291	−	0.979940i	$-0.436136\pi$
$409$	19.8567	−	7.22724i	0.981850	−	0.357364i	0.782559	+	0.622576i	$0.213914\pi$
$410$		0			0
$411$	5.07145	−	8.78401i	0.250156	−	0.433283i
$412$	−7.03936	−	1.24123i	−0.346804	−	0.0611510i
$413$	−2.33359	−	2.78106i	−0.114828	−	0.136847i
$414$	1.24897	+	1.04801i	0.0613835	+	0.0515069i
$415$		0			0
$416$	1.22668	+	0.446476i	0.0601430	+	0.0218903i
$417$			4.39693i			0.215318i
$418$	−2.18788	+	5.75031i	−0.107013	+	0.281257i
$419$	27.8830			1.36217			0.681087	−	0.732202i	$-0.261508\pi$
$419$	27.8830			1.36217			0.681087	+	0.732202i	$0.261508\pi$
$420$		0			0
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	0.984619	−	0.174718i	$-0.0559013\pi$
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	−0.984996	+	0.172578i	$0.944790\pi$
$422$	10.3545	−	12.3400i	0.504050	−	0.600703i
$423$	3.49276	+	4.16250i	0.169824	+	0.202388i
$424$	−0.290859	+	1.64955i	−0.0141254	+	0.0801090i
$425$		0			0
$426$	−5.98545	−	10.3671i	−0.289996	−	0.502288i
$427$	−16.9027	−	46.4397i	−0.817978	−	2.24738i
$428$	−3.20459	−	8.80453i	−0.154900	−	0.425583i
$429$	−1.73143	−	2.99892i	−0.0835942	−	0.144789i
$430$		0			0
$431$	−2.04694	+	11.6088i	−0.0985977	+	0.559175i	0.894988	+	0.446091i	$0.147184\pi$
$431$	−2.04694	+	11.6088i	−0.0985977	+	0.559175i	−0.993585	+	0.113084i	$0.963927\pi$
$432$	2.98135	+	3.55303i	0.143440	+	0.170945i
$433$	17.7704	−	21.1780i	0.853993	−	1.01775i	−0.145604	−	0.989343i	$-0.546512\pi$
$433$	17.7704	−	21.1780i	0.853993	−	1.01775i	0.999596	−	0.0284060i	$-0.00904313\pi$
$434$	−0.325008	−	1.84321i	−0.0156009	−	0.0884769i
$435$		0			0
$436$	11.0642			0.529878
$437$	−4.38571	−	12.6159i	−0.209797	−	0.603499i
$438$		−	8.56893i		−	0.409439i
$439$	35.1908	+	12.8084i	1.67956	+	0.611311i	0.993250	−	0.115994i	$-0.0370052\pi$
$439$	35.1908	+	12.8084i	1.67956	+	0.611311i	0.686314	+	0.727305i	$0.259227\pi$
$440$		0			0
$441$	7.60014	+	6.37727i	0.361911	+	0.303680i
$442$	−2.00476	−	2.38919i	−0.0953569	−	0.113642i
$443$	−20.6693	−	3.64455i	−0.982027	−	0.173158i	−0.340489	−	0.940249i	$-0.610592\pi$
$443$	−20.6693	−	3.64455i	−0.982027	−	0.173158i	−0.641539	+	0.767091i	$0.721704\pi$
$444$	−4.53209	+	7.84981i	−0.215083	+	0.372535i
$445$		0			0
$446$	−3.83750	+	1.39673i	−0.181711	+	0.0661373i
$447$	−9.23659	−	25.3773i	−0.436876	−	1.20031i
$448$	−4.38571	+	2.53209i	−0.207205	+	0.119630i
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	0.483172	+	0.875525i	$0.339485\pi$
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	−0.999813	+	0.0193235i	$0.993849\pi$
$450$		0			0
$451$	1.65657	−	1.39003i	0.0780050	−	0.0654540i
$452$	8.54818	−	10.1873i	0.402072	−	0.479171i
$453$	38.5685	−	6.80066i	1.81210	−	0.319523i
$454$	12.8366	+	4.67215i	0.602452	+	0.219275i
$455$		0			0
$456$	1.30541	+	8.08737i	0.0611313	+	0.378726i
$457$		−	13.0496i		−	0.610436i	−0.952283	−	0.305218i	$-0.901271\pi$
$457$		−	13.0496i		−	0.610436i	0.952283	−	0.305218i	$-0.0987293\pi$
$458$	1.78590	−	4.90673i	0.0834497	−	0.229276i
$459$	−1.92427	−	10.9131i	−0.0898171	−	0.509378i
$460$		0			0
$461$	3.37733	−	2.83391i	0.157298	−	0.131988i	−0.560742	−	0.827991i	$-0.689484\pi$
$461$	3.37733	−	2.83391i	0.157298	−	0.131988i	0.718040	+	0.696002i	$0.245040\pi$
$462$	13.2297	+	2.33275i	0.615500	+	0.108529i
$463$	23.0930	+	13.3327i	1.07322	+	0.619625i	0.929060	−	0.369929i	$-0.120618\pi$
$463$	23.0930	+	13.3327i	1.07322	+	0.619625i	0.144162	+	0.989554i	$0.453951\pi$
$464$	4.22668	+	7.32083i	0.196219	+	0.339861i
$465$		0			0
$466$	25.4119	−	9.24919i	1.17719	−	0.428460i
$467$	26.0793	−	15.0569i	1.20681	−	0.696750i	0.244747	−	0.969587i	$-0.421295\pi$
$467$	26.0793	−	15.0569i	1.20681	−	0.696750i	0.962060	+	0.272837i	$0.0879618\pi$
$468$	−0.601535	−	0.347296i	−0.0278060	−	0.0160538i
$469$	1.23442	−	7.00076i	0.0570003	−	0.323265i
$470$		0			0
$471$	−9.17024	−	7.69475i	−0.422543	−	0.354555i
$472$	−0.705990	+	0.124485i	−0.0324958	+	0.00572989i
$473$	−0.366298	+	1.00640i	−0.0168424	+	0.0462742i
$474$	−4.21213			−0.193470
$475$		0			0
$476$	12.0993			0.554569
$477$	0.304824	−	0.837496i	0.0139569	−	0.0383463i
$478$	−0.281465	+	0.0496299i	−0.0128739	+	0.00227002i
$479$	−6.25671	−	5.25000i	−0.285876	−	0.239879i	0.488560	−	0.872530i	$-0.337522\pi$
$479$	−6.25671	−	5.25000i	−0.285876	−	0.239879i	−0.774437	+	0.632651i	$0.781967\pi$
$480$		0			0
$481$	−1.09327	+	6.20026i	−0.0498490	+	0.282708i
$482$	−2.68556	−	1.55051i	−0.122324	−	0.0706237i
$483$	−25.2563	+	14.5817i	−1.14920	+	0.663491i
$484$	−8.46451	+	3.08083i	−0.384750	+	0.140038i
$485$		0			0
$486$	−2.73396	−	4.73535i	−0.124015	−	0.214800i
$487$	−23.0251	−	13.2935i	−1.04337	−	0.602388i	−0.122582	−	0.992458i	$-0.539117\pi$
$487$	−23.0251	−	13.2935i	−1.04337	−	0.602388i	−0.920785	+	0.390070i	$0.872451\pi$
$488$	−9.61051	−	1.69459i	−0.435047	−	0.0767106i
$489$	6.81180	−	5.71578i	0.308040	−	0.258477i
$490$		0			0
$491$	6.74257	+	38.2390i	0.304288	+	1.72570i	0.626837	+	0.779151i	$0.284349\pi$
$491$	6.74257	+	38.2390i	0.304288	+	1.72570i	−0.322549	+	0.946553i	$0.604540\pi$
$492$	0.984808	−	2.70574i	0.0443986	−	0.121984i
$493$		−	20.1967i		−	0.909611i
$494$	2.77332	+	4.96854i	0.124777	+	0.223545i
$495$		0			0
$496$	−0.347296	−	0.126406i	−0.0155941	−	0.00567578i
$497$	31.7667	−	5.60132i	1.42493	−	0.251253i
$498$	4.81461	−	5.73783i	0.215748	−	0.257118i
$499$	−15.8255	+	13.2791i	−0.708446	+	0.594456i	−0.924163	−	0.382000i	$-0.875236\pi$
$499$	−15.8255	+	13.2791i	−0.708446	+	0.594456i	0.215717	+	0.976456i	$0.430791\pi$
$500$		0			0
$501$	16.2344	−	28.1188i	0.725301	−	1.25626i
$502$	−10.9619	+	6.32888i	−0.489255	+	0.282472i
$503$	0.0251977	+	0.0692302i	0.00112351	+	0.00308682i	0.940253	−	0.340476i	$-0.110588\pi$
$503$	0.0251977	+	0.0692302i	0.00112351	+	0.00308682i	−0.939130	+	0.343563i	$0.888366\pi$
$504$	2.53209	−	0.921605i	0.112788	−	0.0410515i
$505$		0			0
$506$	−2.16250	+	3.74557i	−0.0961350	+	0.166511i
$507$	20.9068	+	3.68644i	0.928506	+	0.163721i
$508$	3.67301	+	4.37733i	0.162964	+	0.194212i
$509$	−11.5057	−	9.65441i	−0.509980	−	0.427924i	0.351142	−	0.936322i	$-0.385793\pi$
$509$	−11.5057	−	9.65441i	−0.509980	−	0.427924i	−0.861122	+	0.508398i	$0.830238\pi$
$510$		0			0
$511$	21.6973	+	7.89716i	0.959831	+	0.349350i
$512$			1.00000i			0.0441942i
$513$	−0.293144	+	20.2151i	−0.0129426	+	0.892520i
$514$	30.3928			1.34057
$515$		0			0
$516$	0.247626	+	1.40436i	0.0109011	+	0.0618234i
$517$	−9.26525	+	11.0419i	−0.407485	+	0.485622i
$518$	−15.6996	−	18.7101i	−0.689802	−	0.822073i
$519$	6.14290	−	34.8381i	0.269644	−	1.52922i
$520$		0			0
$521$	−22.5856	−	39.1194i	−0.989493	−	1.71385i	−0.619959	−	0.784634i	$-0.712851\pi$
$521$	−22.5856	−	39.1194i	−0.989493	−	1.71385i	−0.369533	−	0.929217i	$-0.620482\pi$
$522$	−1.53839	−	4.22668i	−0.0673333	−	0.184997i
$523$	0.0573076	+	0.157451i	0.00250589	+	0.00688487i	0.940939	−	0.338575i	$-0.109945\pi$
$523$	0.0573076	+	0.157451i	0.00250589	+	0.00688487i	−0.938433	+	0.345460i	$0.887723\pi$
$524$	−4.93969	−	8.55580i	−0.215791	−	0.373762i
$525$		0			0
$526$	3.80335	−	21.5699i	0.165834	−	0.940490i
$527$	0.567586	+	0.676423i	0.0247244	+	0.0294654i
$528$	1.70513	−	2.03209i	0.0742060	−	0.0884353i
$529$	2.36349	+	13.4040i	0.102761	+	0.582784i
$530$		0			0
$531$	0.381445			0.0165533
$532$	−21.6810	−	4.14796i	−0.939991	−	0.179837i
$533$		−	2.00000i		−	0.0866296i
$534$	18.8011	+	6.84305i	0.813604	+	0.296128i
$535$		0			0
$536$	−1.07532	−	0.902302i	−0.0464468	−	0.0389735i
$537$	16.7049	+	19.9081i	0.720868	+	0.859097i
$538$	1.41198	+	0.248970i	0.0608748	+	0.0107339i
$539$	−13.1591	+	22.7922i	−0.566803	+	0.981731i
$540$		0			0
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	−0.322140	−	0.946692i	$-0.604402\pi$
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	0.361749	+	0.932276i	$0.382180\pi$
$542$	−5.53147	−	15.1976i	−0.237597	−	0.652792i
$543$	19.9490	−	11.5175i	0.856092	−	0.494265i
$544$	1.19459	−	2.06910i	0.0512177	−	0.0887117i
$545$		0			0
$546$	9.51754	−	7.98617i	0.407313	−	0.341776i
$547$	−18.2582	+	21.7592i	−0.780663	+	0.930358i	−0.998963	−	0.0455238i	$-0.985504\pi$
$547$	−18.2582	+	21.7592i	−0.780663	+	0.930358i	0.218300	+	0.975882i	$0.429949\pi$
$548$	5.31493	−	0.937166i	0.227043	−	0.0400338i
$549$	4.87939	+	1.77595i	0.208247	+	0.0757957i
$550$		0			0
$551$	−6.92396	+	36.1910i	−0.294971	+	1.54179i
$552$			5.75877i			0.245110i
$553$	3.88192	−	10.6655i	0.165076	−	0.453543i
$554$	−1.92902	−	10.9400i	−0.0819560	−	0.464796i
$555$		0			0
$556$	−1.79220	+	1.50384i	−0.0760064	+	0.0637769i
$557$	35.0909	+	6.18748i	1.48685	+	0.262172i	0.857312	−	0.514797i	$-0.172133\pi$
$557$	35.0909	+	6.18748i	1.48685	+	0.262172i	0.629539	+	0.776969i	$0.283244\pi$
$558$	0.170306	+	0.0983261i	0.00720962	+	0.00416247i
$559$	0.495252	+	0.857802i	0.0209469	+	0.0362812i
$560$		0			0
$561$	−5.95558	+	2.16766i	−0.251445	+	0.0915185i
$562$	3.67972	−	2.12449i	0.155219	−	0.0896160i
$563$	7.47183	+	4.31386i	0.314900	+	0.181808i	0.649117	−	0.760688i	$-0.275139\pi$
$563$	7.47183	+	4.31386i	0.314900	+	0.181808i	−0.334217	+	0.942496i	$0.608472\pi$
$564$	−3.33275	+	18.9010i	−0.140334	+	0.795874i
$565$		0			0
$566$	−4.17958	−	3.50708i	−0.175681	−	0.147414i
$567$	51.4342	−	9.06923i	2.16003	−	0.380872i
$568$	2.17853	−	5.98545i	0.0914089	−	0.251144i
$569$	−22.3310			−0.936164			−0.468082	−	0.883685i	$-0.655055\pi$
$569$	−22.3310			−0.936164			−0.468082	+	0.883685i	$0.655055\pi$
$570$		0			0
$571$	−9.56448			−0.400261			−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448			−0.400261			−0.200131	+	0.979769i	$0.564137\pi$
$572$	0.630189	−	1.73143i	0.0263495	−	0.0723947i
$573$	37.2004	−	6.55943i	1.55407	−	0.274024i
$574$	5.94356	+	4.98724i	0.248080	+	0.208163i
$575$		0			0
$576$	0.0923963	−	0.524005i	0.00384984	−	0.0218336i
$577$	−19.4645	−	11.2378i	−0.810317	−	0.467837i	0.0367489	−	0.999325i	$-0.488300\pi$
$577$	−19.4645	−	11.2378i	−0.810317	−	0.467837i	−0.847066	+	0.531488i	$0.821633\pi$
$578$	9.77898	−	5.64590i	0.406752	−	0.234838i
$579$	−29.4666	+	10.7250i	−1.22459	+	0.445715i
$580$		0			0
$581$	10.0915	+	17.4790i	0.418667	+	0.725152i
$582$	−2.49362	−	1.43969i	−0.103364	−	0.0596772i
$583$	2.32829	+	0.410540i	0.0964279	+	0.0170028i
$584$	3.49273	−	2.93075i	0.144530	−	0.121275i
$585$		0			0
$586$	3.09327	+	17.5428i	0.127782	+	0.724687i
$587$	1.41868	−	3.89780i	0.0585554	−	0.160880i	−0.906966	−	0.421205i	$-0.861607\pi$
$587$	1.41868	−	3.89780i	0.0585554	−	0.160880i	0.965521	+	0.260325i	$0.0838297\pi$
$588$			35.0428i			1.44514i
$589$	−0.785178	−	1.40669i	−0.0323527	−	0.0579615i
$590$		0			0
$591$	22.9418	+	8.35014i	0.943700	+	0.343479i
$592$	−4.74968	+	0.837496i	−0.195211	+	0.0344209i
$593$	6.69621	−	7.98024i	0.274981	−	0.327709i	−0.610825	−	0.791766i	$-0.709162\pi$
$593$	6.69621	−	7.98024i	0.274981	−	0.327709i	0.885806	+	0.464057i	$0.153607\pi$
$594$	5.01501	−	4.20810i	0.205769	−	0.172660i
$595$		0			0
$596$	7.18479	−	12.4444i	0.294301	−	0.509744i
$597$	−27.9825	+	16.1557i	−1.14525	+	0.661209i
$598$	1.36808	+	3.75877i	0.0559450	+	0.153708i
$599$	−37.2645	+	13.5632i	−1.52258	+	0.554175i	−0.961792	−	0.273781i	$-0.911726\pi$
$599$	−37.2645	+	13.5632i	−1.52258	+	0.554175i	−0.560792	+	0.827957i	$0.689503\pi$
$600$		0			0
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	−0.999884	−	0.0152517i	$-0.995145\pi$
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	0.513150	+	0.858299i	$0.328478\pi$
$602$	−3.78417	−	0.667252i	−0.154231	−	0.0271951i
$603$	0.480105	+	0.572167i	0.0195514	+	0.0233004i
$604$	15.9632	+	13.3947i	0.649532	+	0.545022i
$605$		0			0
$606$	15.5817	+	5.67128i	0.632964	+	0.230380i
$607$		−	29.9317i		−	1.21489i	−0.794362	−	0.607445i	$-0.792194\pi$
$607$		−	29.9317i		−	1.21489i	0.794362	−	0.607445i	$-0.207806\pi$
$608$	−2.84997	+	3.29813i	−0.115581	+	0.133757i
$609$	80.4552			3.26021
$610$		0			0
$611$	2.31490	+	13.1285i	0.0936509	+	0.531121i
$612$	−0.817150	+	0.973841i	−0.0330313	+	0.0393652i
$613$	22.8688	+	27.2540i	0.923664	+	1.10078i	0.994650	+	0.103302i	$0.0329409\pi$
$613$	22.8688	+	27.2540i	0.923664	+	1.10078i	−0.0709862	+	0.997477i	$0.522615\pi$
$614$	4.97653	−	28.2233i	0.200836	−	1.13900i
$615$		0			0
$616$	3.57398	+	6.19031i	0.144000	+	0.249415i
$617$	−4.11532	−	11.3068i	−0.165677	−	0.455193i	0.828876	−	0.559433i	$-0.188981\pi$
$617$	−4.11532	−	11.3068i	−0.165677	−	0.455193i	−0.994552	+	0.104240i	$0.966759\pi$
$618$	4.59462	+	12.6236i	0.184823	+	0.507796i
$619$	−8.55644	−	14.8202i	−0.343912	−	0.595673i	0.641243	−	0.767338i	$-0.278419\pi$
$619$	−8.55644	−	14.8202i	−0.343912	−	0.595673i	−0.985156	+	0.171664i	$0.945086\pi$
$620$		0			0
$621$	−2.46791	+	13.9962i	−0.0990339	+	0.561649i
$622$	10.1647	+	12.1138i	0.407567	+	0.485719i
$623$	−34.6544	+	41.2995i	−1.38840	+	1.65463i
$624$	−0.426022	−	2.41609i	−0.0170545	−	0.0967211i
$625$		0			0
$626$	13.1402			0.525189
$627$	11.4151	−	1.84255i	0.455876	−	0.0735843i
$628$		−	6.36959i		−	0.254174i
$629$	10.8280	+	3.94107i	0.431741	+	0.157141i
$630$		0			0
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	0.878078	−	0.478517i	$-0.158826\pi$
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	−0.318771	+	0.947832i	$0.603270\pi$
$632$	−1.44063	−	1.71688i	−0.0573054	−	0.0682939i
$633$	−29.8146	−	5.25712i	−1.18502	−	0.208952i
$634$	−10.7023	+	18.5370i	−0.425044	+	0.736198i
$635$		0			0
$636$	2.95811	−	1.07666i	0.117297	−	0.0426925i
$637$	8.32494	+	22.8726i	0.329846	+	0.906245i
$638$	10.3332	−	5.96585i	0.409094	−	0.236190i
$639$	−1.69459	+	2.93512i	−0.0670371	+	0.116112i
$640$		0			0
$641$	−23.8837	+	20.0408i	−0.943350	+	0.791565i	−0.978165	−	0.207829i	$-0.933360\pi$
$641$	−23.8837	+	20.0408i	−0.943350	+	0.791565i	0.0348149	+	0.999394i	$0.488916\pi$
$642$	−11.3189	+	13.4893i	−0.446721	+	0.532381i
$643$	−31.4642	+	5.54798i	−1.24083	+	0.218791i	−0.755269	−	0.655414i	$-0.772494\pi$
$643$	−31.4642	+	5.54798i	−1.24083	+	0.218791i	−0.485556	+	0.874206i	$0.661383\pi$
$644$	−14.5817	−	5.30731i	−0.574600	−	0.209137i
$645$		0			0
$646$	9.83678	−	3.41960i	0.387023	−	0.134542i
$647$			2.99588i			0.117780i	0.998264	+	0.0588901i	$0.0187562\pi$
$647$			2.99588i			0.117780i	−0.998264	+	0.0588901i	$0.981244\pi$
$648$	3.52730	−	9.69119i	0.138566	−	0.380706i
$649$	0.175708	+	0.996487i	0.00689713	+	0.0391155i
$650$		0			0
$651$	−2.69459	+	2.26103i	−0.105609	+	0.0886168i
$652$	4.65955	+	0.821604i	0.182482	+	0.0321765i
$653$	0.810446	+	0.467911i	0.0317152	+	0.0183108i	0.515774	−	0.856725i	$-0.327505\pi$
$653$	0.810446	+	0.467911i	0.0317152	+	0.0183108i	−0.484059	+	0.875036i	$0.660838\pi$
$654$	−10.3969	−	18.0080i	−0.406552	−	0.704169i
$655$		0			0
$656$	1.43969	−	0.524005i	0.0562106	−	0.0204590i
$657$	−2.10100	+	1.21301i	−0.0819677	+	0.0473241i
$658$	−44.7874	−	25.8580i	−1.74600	−	1.00805i
$659$	2.12495	−	12.0512i	0.0827764	−	0.469448i	−0.915038	−	0.403368i	$-0.867840\pi$
$659$	2.12495	−	12.0512i	0.0827764	−	0.469448i	0.997814	−	0.0660804i	$-0.0210494\pi$
$660$		0			0
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	0.447062	−	0.894503i	$-0.352470\pi$
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	−0.803282	+	0.595599i	$0.796915\pi$
$662$	25.0120	−	4.41029i	0.972119	−	0.171411i
$663$	−2.00476	+	5.50805i	−0.0778586	+	0.213915i
$664$	3.98545			0.154666
$665$		0			0
$666$	2.56624			0.0994397
$667$	−8.85921	+	24.3405i	−0.343030	+	0.942468i
$668$	17.0138	−	3.00000i	0.658285	−	0.116073i
$669$	5.87939	+	4.93339i	0.227310	+	0.190736i
$670$		0			0
$671$	−2.39187	+	13.5650i	−0.0923373	+	0.523671i
$672$	8.24243	+	4.75877i	0.317959	+	0.183574i
$673$	−38.8529	+	22.4317i	−1.49767	+	0.864679i	−0.999996	−	0.00268731i	$-0.999145\pi$
$673$	−38.8529	+	22.4317i	−1.49767	+	0.864679i	−0.497671	+	0.867366i	$0.665811\pi$
$674$	24.7866	−	9.02158i	0.954743	−	0.347498i
$675$		0			0
$676$	5.64796	+	9.78255i	0.217229	+	0.376252i
$677$	−0.819197	−	0.472964i	−0.0314843	−	0.0181775i	0.484175	−	0.874971i	$-0.339120\pi$
$677$	−0.819197	−	0.472964i	−0.0314843	−	0.0181775i	−0.515660	+	0.856794i	$0.672453\pi$
$678$	−24.6135	−	4.34002i	−0.945275	−	0.166678i
$679$	5.94356	−	4.98724i	0.228093	−	0.191393i
$680$		0			0
$681$	−4.45811	−	25.2832i	−0.170835	−	0.968854i
$682$	−0.178418	+	0.490200i	−0.00683198	+	0.0187707i
$683$			5.92221i			0.226607i	0.993560	+	0.113303i	$0.0361432\pi$
$683$			5.92221i			0.226607i	−0.993560	+	0.113303i	$0.963857\pi$
$684$	1.79813	−	1.46491i	0.0687533	−	0.0560123i
$685$		0			0
$686$	−55.4201	−	20.1713i	−2.11595	−	0.770143i
$687$	−9.66436	+	1.70409i	−0.368718	+	0.0650150i
$688$	−0.487728	+	0.581252i	−0.0185945	+	0.0221600i
$689$	1.67499	−	1.40549i	0.0638121	−	0.0535447i
$690$		0			0
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	−0.867979	−	0.496600i	$-0.834581\pi$
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	0.864058	+	0.503392i	$0.167915\pi$
$692$	16.3012	−	9.41147i	0.619677	−	0.357771i
$693$	−1.30082	−	3.57398i	−0.0494141	−	0.135764i
$694$	−24.0856	+	8.76644i	−0.914276	+	0.332769i
$695$		0			0
$696$	7.94356	−	13.7587i	0.301100	−	0.521520i
$697$	−3.60483	−	0.635630i	−0.136543	−	0.0240762i
$698$	3.75552	+	4.47565i	0.142148	+	0.169406i
$699$	−38.9334	−	32.6690i	−1.47259	−	1.23565i
$700$		0			0
$701$	−4.10607	−	1.49449i	−0.155084	−	0.0564460i	0.263312	−	0.964711i	$-0.415185\pi$
$701$	−4.10607	−	1.49449i	−0.155084	−	0.0564460i	−0.418396	+	0.908265i	$0.637407\pi$
$702$		−	6.05468i		−	0.228519i
$703$	−18.0519	−	10.7743i	−0.680840	−	0.406359i
$704$	1.41147			0.0531969
$705$		0			0
$706$	−3.89141	−	22.0693i	−0.146455	−	0.830588i
$707$	−28.7204	+	34.2276i	−1.08014	+	1.28726i
$708$	0.866025	+	1.03209i	0.0325472	+	0.0387883i
$709$	−1.52023	+	8.62165i	−0.0570934	+	0.323793i	−0.999956	−	0.00938924i	$-0.997011\pi$
$709$	−1.52023	+	8.62165i	−0.0570934	+	0.323793i	0.942863	+	0.333182i	$0.108122\pi$
$710$		0			0
$711$	0.596267	+	1.03276i	0.0223617	+	0.0387317i
$712$	3.64111	+	10.0039i	0.136456	+	0.374911i
$713$	−0.387329	−	1.06418i	−0.0145056	−	0.0398538i
$714$	−11.3696	−	19.6927i	−0.425496	−	0.736981i
$715$		0			0
$716$	−2.40121	+	13.6179i	−0.0897373	+	0.508926i
$717$	0.345268	+	0.411474i	0.0128943	+	0.0153668i
$718$	6.18156	−	7.36690i	0.230694	−	0.274930i
$719$	4.79385	+	27.1873i	0.178781	+	1.01391i	0.933689	+	0.358085i	$0.116570\pi$
$719$	4.79385	+	27.1873i	0.178781	+	1.01391i	−0.754909	+	0.655830i	$0.772319\pi$
$720$		0			0
$721$	−36.1985			−1.34810
$722$	−18.7991	+	2.75537i	−0.699632	+	0.102544i
$723$			5.82800i			0.216746i
$724$	11.5175	+	4.19204i	0.428046	+	0.155796i
$725$		0			0
$726$	12.9684	+	10.8818i	0.481302	+	0.403860i
$727$	18.4071	+	21.9368i	0.682682	+	0.813589i	0.990450	−	0.137872i	$-0.0440264\pi$
$727$	18.4071	+	21.9368i	0.682682	+	0.813589i	−0.307768	+	0.951462i	$0.599582\pi$
$728$	6.51038	+	1.14796i	0.241291	+	0.0425461i
$729$	10.3316	−	17.8948i	0.382651	−	0.662770i
$730$		0			0
$731$	1.70352	−	0.620029i	0.0630068	−	0.0229326i
$732$	6.27282	+	17.2344i	0.231850	+	0.637003i
$733$	−32.0095	+	18.4807i	−1.18230	+	0.682600i	−0.956545	−	0.291584i	$-0.905818\pi$
$733$	−32.0095	+	18.4807i	−1.18230	+	0.682600i	−0.225753	+	0.974184i	$0.572484\pi$
$734$	11.6800	−	20.2304i	0.431118	−	0.746719i
$735$		0			0
$736$	−2.34730	+	1.96962i	−0.0865225	+	0.0726010i
$737$	−1.27358	+	1.51779i	−0.0469128	+	0.0559085i
$738$	−0.802823	+	0.141559i	−0.0295523	+	0.00521087i
$739$	43.2508	+	15.7420i	1.59101	+	0.579079i	0.977560	−	0.210658i	$-0.0675607\pi$
$739$	43.2508	+	15.7420i	1.59101	+	0.579079i	0.613446	+	0.789737i	$0.289783\pi$
$740$		0			0
$741$	5.48070	−	9.18274i	0.201339	−	0.337336i
$742$			8.48246i			0.311401i
$743$	−9.03298	+	24.8179i	−0.331388	+	0.910480i	0.656364	+	0.754445i	$0.272094\pi$
$743$	−9.03298	+	24.8179i	−0.331388	+	0.910480i	−0.987751	+	0.156036i	$0.950129\pi$
$744$	0.120615	+	0.684040i	0.00442195	+	0.0250781i
$745$		0			0
$746$	−19.8726	+	16.6751i	−0.727587	+	0.610518i
$747$	−2.08840	−	0.368241i	−0.0764105	−	0.0134732i
$748$	−2.92047	−	1.68614i	−0.106783	−	0.0616513i
$749$	−23.7246	−	41.0923i	−0.866879	−	1.50148i
$750$		0			0
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.168936	−	0.985627i	$-0.445967\pi$
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.762961	+	0.646444i	$0.223745\pi$
$752$	−8.84397	+	5.10607i	−0.322506	+	0.186199i
$753$	20.6017	+	11.8944i	0.750768	+	0.433456i
$754$	1.91622	−	10.8674i	0.0697847	−	0.395769i
$755$		0			0
$756$	17.9932	+	15.0981i	0.654406	+	0.549112i
$757$	−19.1099	+	3.36959i	−0.694560	+	0.122470i	−0.509773	−	0.860309i	$-0.670271\pi$
$757$	−19.1099	+	3.36959i	−0.694560	+	0.122470i	−0.184787	+	0.982779i	$0.559159\pi$
$758$	−3.24178	+	8.90673i	−0.117747	+	0.323507i
$759$	8.12836			0.295041
$760$		0			0
$761$	40.2645			1.45959			0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645			1.45959			0.729793	+	0.683669i	$0.239617\pi$
$762$	3.67301	−	10.0915i	0.133059	−	0.365577i
$763$	55.1797	−	9.72967i	1.99764	−	0.352238i
$764$	15.3969	+	12.9196i	0.557041	+	0.467413i
$765$		0			0
$766$	−2.34224	+	13.2835i	−0.0846287	+	0.479953i
$767$	0.810446	+	0.467911i	0.0292635	+	0.0168953i
$768$	1.62760	−	0.939693i	0.0587308	−	0.0339082i
$769$	−36.5933	+	13.3189i	−1.31959	+	0.480291i	−0.903327	−	0.428953i	$-0.858883\pi$
$769$	−36.5933	+	13.3189i	−1.31959	+	0.480291i	−0.416263	+	0.909244i	$0.636660\pi$
$770$		0			0
$771$	−28.5599	−	49.4672i	−1.02856	−	1.78152i
$772$	−14.4497	−	8.34255i	−0.520057	−	0.300255i
$773$	6.66015	+	1.17436i	0.239549	+	0.0422389i	0.292133	−	0.956378i	$-0.405635\pi$
$773$	6.66015	+	1.17436i	0.239549	+	0.0422389i	−0.0525847	+	0.998616i	$0.516746\pi$
$774$	0.309278	−	0.259515i	0.0111168	−	0.00932807i
$775$		0			0
$776$	−0.266044	−	1.50881i	−0.00955044	−	0.0541632i
$777$	−15.6996	+	43.1343i	−0.563221	+	1.54744i
$778$			25.1480i			0.901598i
$779$	6.24170	+	2.37484i	0.223632	+	0.0850874i
$780$		0			0
$781$	−8.44831	−	3.07493i	−0.302304	−	0.110030i
$782$	7.20967	−	1.27126i	0.257817	−	0.0454601i
$783$	25.2024	−	30.0351i	0.900661	−	1.07337i
$784$	−14.2836	+	11.9854i	−0.510128	+	0.428048i
$785$		0			0
$786$	−9.28359	+	16.0796i	−0.331135	+	0.573542i
$787$	5.02709	−	2.90239i	0.179196	−	0.103459i	−0.407719	−	0.913108i	$-0.633676\pi$
$787$	5.02709	−	2.90239i	0.179196	−	0.103459i	0.586915	+	0.809649i	$0.300342\pi$
$788$	4.44301	+	12.2071i	0.158276	+	0.434859i
$789$	−38.6810	+	14.0787i	−1.37708	+	0.501216i
$790$		0			0
$791$	33.6732	−	58.3238i	1.19728	−	2.07375i
$792$	−0.739620	−	0.130415i	−0.0262812	−	0.00463409i
$793$	8.18858	+	9.75877i	0.290785	+	0.346544i
$794$	−5.03003	−	4.22070i	−0.178509	−	0.149787i
$795$		0			0
$796$	−16.1557	−	5.88019i	−0.572623	−	0.208418i
$797$		−	39.2181i		−	1.38918i	−0.719407	−	0.694589i	$-0.755586\pi$
$797$		−	39.2181i		−	1.38918i	0.719407	−	0.694589i	$-0.244414\pi$
$798$	13.6223	+	39.1857i	0.482224	+	1.38716i
$799$	24.3987			0.863163
$800$		0			0
$801$	−0.983641	−	5.57851i	−0.0347552	−	0.197107i
$802$	18.9691	−	22.6065i	0.669823	−	0.798264i
$803$	−4.13667	−	4.92989i	−0.145980	−	0.173972i
$804$	−0.458111	+	2.59808i	−0.0161563	+	0.0916271i
$805$		0			0
$806$	0.241230	+	0.417822i	0.00849695	+	0.0147171i
$807$	−0.921605	−	2.53209i	−0.0324420	−	0.0891338i
$808$	3.01763	+	8.29086i	0.106160	+	0.291671i
$809$	3.50134	+	6.06451i	0.123101	+	0.213217i	0.920989	−	0.389589i	$-0.127383\pi$
$809$	3.50134	+	6.06451i	0.123101	+	0.213217i	−0.797888	+	0.602805i	$0.794050\pi$
$810$		0			0
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	−0.498717	−	0.866765i	$-0.666195\pi$
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	0.765092	−	0.643921i	$-0.222694\pi$
$812$	27.5173	+	32.7939i	0.965668	+	1.15084i
$813$	−19.5376	+	23.2841i	−0.685215	+	0.816607i
$814$	1.18210	+	6.70405i	0.0414327	+	0.234977i
$815$		0			0
$816$	−4.49020			−0.157188
$817$	−3.26514	+	0.527036i	−0.114233	+	0.0184387i
$818$		−	21.1310i		−	0.738830i
$819$	−3.30541	−	1.20307i	−0.115500	−	0.0420387i
$820$		0			0
$821$	9.48751	+	7.96097i	0.331116	+	0.277840i	0.793155	−	0.609020i	$-0.208437\pi$
$821$	9.48751	+	7.96097i	0.331116	+	0.277840i	−0.462038	+	0.886860i	$0.652882\pi$
$822$	−6.51973	−	7.76991i	−0.227402	−	0.271007i
$823$	12.6334	+	2.22762i	0.440374	+	0.0776498i	0.389439	−	0.921052i	$-0.372669\pi$
$823$	12.6334	+	2.22762i	0.440374	+	0.0776498i	0.0509347	+	0.998702i	$0.483780\pi$
$824$	−3.57398	+	6.19031i	−0.124505	+	0.215650i
$825$		0			0
$826$	−3.41147	+	1.24168i	−0.118700	+	0.0432034i
$827$	−8.58353	−	23.5831i	−0.298479	−	0.820063i	−0.994755	−	0.102289i	$-0.967383\pi$
$827$	−8.58353	−	23.5831i	−0.298479	−	0.820063i	0.696276	−	0.717774i	$-0.254839\pi$
$828$	1.41198	−	0.815207i	0.0490697	−	0.0283304i
$829$	14.1634	−	24.5318i	0.491917	−	0.852024i	−0.508040	−	0.861333i	$-0.669630\pi$
$829$	14.1634	−	24.5318i	0.491917	−	0.852024i	0.999957	+	0.00930899i	$0.00296319\pi$
$830$		0			0
$831$	−15.9932	+	13.4199i	−0.554798	+	0.465531i
$832$	0.839100	−	1.00000i	0.0290905	−	0.0346688i
$833$	43.8717	−	7.73577i	1.52006	−	0.268028i
$834$	4.13176	+	1.50384i	0.143071	+	0.0520736i
$835$		0			0
$836$	4.65523	+	4.02266i	0.161004	+	0.139126i
$837$			1.71419i			0.0592512i
$838$	9.53655	−	26.2015i	0.329435	−	0.905114i
$839$	5.26682	+	29.8696i	0.181831	+	1.03121i	0.929960	+	0.367660i	$0.119841\pi$
$839$	5.26682	+	29.8696i	0.181831	+	1.03121i	−0.748129	+	0.663553i	$0.769048\pi$
$840$		0			0
$841$	32.5257	−	27.2923i	1.12158	−	0.941115i
$842$	−0.0439002	−	0.00774079i	−0.00151290	−	0.000266765i
$843$	−6.91560	−	3.99273i	−0.238186	−	0.137517i
$844$	−8.05438	−	13.9506i	−0.277243	−	0.480199i
$845$		0			0
$846$	5.10607	−	1.85846i	0.175550	−	0.0638950i
$847$	−39.5053	+	22.8084i	−1.35742	+	0.783706i
$848$	1.45059	+	0.837496i	0.0498133	+	0.0287597i
$849$	−1.78059	+	10.0982i	−0.0611098	+	0.346571i
$850$		0			0
$851$	−11.3209	−	9.49935i	−0.388075	−	0.325634i
$852$	−11.7890	+	2.07873i	−0.403886	+	0.0712160i
$853$	14.9231	−	41.0009i	0.510958	−	1.40385i	−0.369283	−	0.929317i	$-0.620397\pi$
$853$	14.9231	−	41.0009i	0.510958	−	1.40385i	0.880240	−	0.474528i	$-0.157381\pi$
$854$	−49.4201			−1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	−10.7770	+	29.6095i	−0.368135	+	1.01144i	0.607935	+	0.793987i	$0.291998\pi$
$857$	−10.7770	+	29.6095i	−0.368135	+	1.01144i	−0.976070	+	0.217456i	$0.930224\pi$
$858$	−3.41025	+	0.601319i	−0.116424	+	0.0205287i
$859$	14.3234	+	12.0188i	0.488709	+	0.410075i	0.853563	−	0.520989i	$-0.174437\pi$
$859$	14.3234	+	12.0188i	0.488709	+	0.410075i	−0.364855	+	0.931065i	$0.618881\pi$
$860$		0			0
$861$	2.53209	−	14.3602i	0.0862934	−	0.489394i
$862$	10.2086	+	5.89393i	0.347706	+	0.200748i
$863$	−9.20264	+	5.31315i	−0.313262	+	0.180862i	−0.648385	−	0.761313i	$-0.724555\pi$
$863$	−9.20264	+	5.31315i	−0.313262	+	0.180862i	0.335123	+	0.942174i	$0.391222\pi$
$864$	4.35844	−	1.58634i	0.148277	−	0.0539685i
$865$		0			0
$866$	−13.8229	−	23.9420i	−0.469723	−	0.813584i
$867$	−18.3785	−	10.6108i	−0.624166	−	0.360362i
$868$	−1.84321	−	0.325008i	−0.0625626	−	0.0110315i
$869$	−2.42333	+	2.03342i	−0.0822060	+	0.0689790i
$870$		0			0
$871$	0.318201	+	1.80460i	0.0107818	+	0.0611467i
$872$	3.78417	−	10.3969i	0.128148	−	0.352084i
$873$			0.815207i			0.0275906i
$874$	−13.3550	−	0.193665i	−0.451741	−	0.00655080i
$875$		0			0
$876$	−8.05216	−	2.93075i	−0.272057	−	0.0990207i
$877$	−44.2164	+	7.79654i	−1.49308	+	0.263270i	−0.859792	−	0.510645i	$-0.829407\pi$
$877$	−44.2164	+	7.79654i	−1.49308	+	0.263270i	−0.633289	+	0.773915i	$0.718296\pi$
$878$	24.0719	−	28.6878i	0.812388	−	0.968166i
$879$	25.6459	−	21.5195i	0.865015	−	0.725833i
$880$		0			0
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	−0.673431	−	0.739250i	$-0.735180\pi$
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	0.976925	+	0.213583i	$0.0685134\pi$
$882$	8.59208	−	4.96064i	0.289310	−	0.167033i
$883$	−15.9375	−	43.7879i	−0.536340	−	1.47358i	−0.851404	−	0.524511i	$-0.824248\pi$
$883$	−15.9375	−	43.7879i	−0.536340	−	1.47358i	0.315064	−	0.949070i	$-0.397974\pi$
$884$	−2.93077	+	1.06671i	−0.0985725	+	0.0358774i
$885$		0			0
$886$	−10.4941	+	18.1763i	−0.352555	+	0.610643i
$887$	6.97210	+	1.22937i	0.234100	+	0.0412782i	0.289467	−	0.957188i	$-0.406522\pi$
$887$	6.97210	+	1.22937i	0.234100	+	0.0412782i	−0.0553671	+	0.998466i	$0.517633\pi$
$888$	5.82634	+	6.94356i	0.195519	+	0.233011i
$889$	22.1676	+	18.6008i	0.743476	+	0.623850i
$890$		0			0
$891$	−13.6789	−	4.97870i	−0.458259	−	0.166793i
$892$			4.08378i			0.136735i
$893$	−43.7207	−	8.36453i	−1.46306	−	0.279908i
$894$	−27.0060			−0.903215
$895$		0			0
$896$	0.879385	+	4.98724i	0.0293782	+	0.166612i
$897$	4.83218	−	5.75877i	0.161342	−	0.192280i
$898$	14.0737	+	16.7724i	0.469647	+	0.559704i
$899$	−0.542518	+	3.07677i	−0.0180940	+	0.102616i
$900$		0			0
$901$	−2.00093	−	3.46572i	−0.0666608	−	0.115460i
$902$	−0.739620	−	2.03209i	−0.0246266	−	0.0676612i
$903$	2.46994	+	6.78611i	0.0821945	+	0.225828i
$904$	−6.64930	−	11.5169i	−0.221152	−	0.383047i
$905$		0			0
$906$	6.80066	−	38.5685i	0.225937	−	1.28135i
$907$	9.71610	+	11.5792i	0.322618	+	0.384481i	0.902840	−	0.429978i	$-0.141479\pi$
$907$	9.71610	+	11.5792i	0.322618	+	0.384481i	−0.580222	+	0.814458i	$0.697034\pi$
$908$	8.78076	−	10.4645i	0.291400	−	0.347277i
$909$	−0.815207	−	4.62327i	−0.0270387	−	0.153344i
$910$		0			0
$911$	−12.8366			−0.425294			−0.212647	−	0.977129i	$-0.568208\pi$
$911$	−12.8366			−0.425294			−0.212647	+	0.977129i	$0.568208\pi$
$912$	8.04612	+	1.53936i	0.266434	+	0.0509734i
$913$		−	5.62536i		−	0.186172i
$914$	−12.2626	−	4.46324i	−0.405612	−	0.147631i
$915$		0			0
$916$	−4.00000	−	3.35640i	−0.132164	−	0.110899i
$917$	−32.1593	−	38.3259i	−1.06199	−	1.26563i
$918$	−10.9131	−	1.92427i	−0.360185	−	0.0635103i
$919$	−10.3396	+	17.9086i	−0.341070	+	0.590751i	−0.984632	−	0.174643i	$-0.944123\pi$
$919$	−10.3396	+	17.9086i	−0.341070	+	0.590751i	0.643561	+	0.765395i	$0.277456\pi$
$920$		0			0
$921$	−50.6125	+	18.4215i	−1.66774	+	0.607007i
$922$	−1.50789	−	4.14290i	−0.0496598	−	0.136439i
$923$	−7.20092	+	4.15745i	−0.237021	+	0.136844i
$924$	6.71688	−	11.6340i	0.220969	−	0.382730i
$925$		0			0
$926$	20.4270	−	17.1403i	0.671271	−	0.563264i
$927$	2.44474	−	2.91353i	0.0802960	−	0.0956930i
$928$	8.32494	−	1.46791i	0.273279	−	0.0481865i
$929$	−17.1493	−	6.24183i	−0.562650	−	0.204788i	0.0450079	−	0.998987i	$-0.485669\pi$
$929$	−17.1493	−	6.24183i	−0.562650	−	0.204788i	−0.607658	+	0.794199i	$0.707891\pi$
$930$		0			0
$931$	−81.2670	−	1.17847i	−2.66342	−	0.0386229i
$932$		−	27.0428i		−	0.885817i
$933$	10.1647	−	27.9273i	0.332777	−	0.914297i
$934$	−5.22921	−	29.6563i	−0.171105	−	0.970384i
$935$		0			0
$936$	−0.532089	+	0.446476i	−0.0173919	+	0.0145935i
$937$	−4.67479	−	0.824292i	−0.152719	−	0.0269285i	0.0967660	−	0.995307i	$-0.469150\pi$
$937$	−4.67479	−	0.824292i	−0.152719	−	0.0269285i	−0.249485	+	0.968379i	$0.580261\pi$
$938$	−6.15636	−	3.55438i	−0.201012	−	0.116055i
$939$	−12.3478	−	21.3870i	−0.402954	−	0.697937i
$940$		0			0
$941$	−44.1857	+	16.0823i	−1.44041	+	0.524268i	−0.939897	−	0.341459i	$-0.889079\pi$
$941$	−44.1857	+	16.0823i	−1.44041	+	0.524268i	−0.500517	+	0.865727i	$0.666857\pi$
$942$	−10.3671	+	5.98545i	−0.337779	+	0.195017i
$943$	4.06564	+	2.34730i	0.132395	+	0.0764385i
$944$	−0.124485	+	0.705990i	−0.00405165	+	0.0229780i
$945$		0			0
$946$	0.820422	+	0.688416i	0.0266742	+	0.0223823i
$947$	−36.4338	+	6.42427i	−1.18394	+	0.208761i	−0.730745	−	0.682651i	$-0.760827\pi$
$947$	−36.4338	+	6.42427i	−1.18394	+	0.208761i	−0.453195	+	0.891411i	$0.649716\pi$
$948$	−1.44063	+	3.95811i	−0.0467896	+	0.128553i
$949$	−5.95191			−0.193207
$950$		0			0
$951$	40.2276			1.30447
$952$	4.13819	−	11.3696i	0.134120	−	0.368490i
$953$	−37.1364	+	6.54814i	−1.20296	+	0.212115i	−0.738980	−	0.673728i	$-0.764692\pi$
$953$	−37.1364	+	6.54814i	−1.20296	+	0.212115i	−0.463985	+	0.885843i	$0.653581\pi$
$954$	−0.682733	−	0.572881i	−0.0221043	−	0.0185477i
$955$		0			0
$956$	−0.0496299	+	0.281465i	−0.00160514	+	0.00910322i
$957$	−19.4200	−	11.2121i	−0.627759	−	0.362437i
$958$	−7.07331	+	4.08378i	−0.228528	+	0.131941i
$959$	25.6827	−	9.34775i	0.829339	−	0.301855i
$960$		0			0
$961$	15.4317	+	26.7285i	0.497797	+	0.862209i
$962$	5.45242	+	3.14796i	0.175793	+	0.101494i
$963$	4.90971	+	0.865715i	0.158213	+	0.0278973i
$964$	−2.37551	+	1.99329i	−0.0765102	+	0.0641997i
$965$		0			0
$966$	5.06418	+	28.7204i	0.162937	+	0.924063i
$967$	13.8564	−	38.0702i	0.445592	−	1.22425i	−0.490172	−	0.871626i	$-0.663066\pi$
$967$	13.8564	−	38.0702i	0.445592	−	1.22425i	0.935764	−	0.352628i	$-0.114712\pi$
$968$			9.00774i			0.289520i
$969$	−14.8093	−	12.7969i	−0.475743	−	0.411096i
$970$		0			0
$971$	13.2289	+	4.81493i	0.424536	+	0.154518i	0.545448	−	0.838145i	$-0.316360\pi$
$971$	13.2289	+	4.81493i	0.424536	+	0.154518i	−0.120912	+	0.992663i	$0.538582\pi$
$972$	−5.38484	+	0.949493i	−0.172719	+	0.0304550i
$973$	−7.61570	+	9.07604i	−0.244148	+	0.290964i
$974$	−20.3669	+	17.0899i	−0.652597	+	0.547594i
$975$		0			0
$976$	−4.87939	+	8.45134i	−0.156185	+	0.270521i
$977$	−30.4890	+	17.6028i	−0.975429	+	0.563164i	−0.900887	−	0.434054i	$-0.857083\pi$
$977$	−30.4890	+	17.6028i	−0.975429	+	0.563164i	−0.0745421	+	0.997218i	$0.523750\pi$
$978$	−3.04130	−	8.35591i	−0.0972502	−	0.267193i
$979$	14.1202	−	5.13933i	0.451284	−	0.164254i
$980$		0			0
$981$	−2.94356	+	5.09840i	−0.0939807	+	0.162779i
$982$	38.2390	+	6.74257i	1.22026	+	0.215164i
$983$	−14.4240	−	17.1898i	−0.460054	−	0.548271i	0.485287	−	0.874355i	$-0.338715\pi$
$983$	−14.4240	−	17.1898i	−0.460054	−	0.548271i	−0.945341	+	0.326084i	$0.894271\pi$
$984$	−2.20574	−	1.85083i	−0.0703163	−	0.0590024i
$985$		0			0
$986$	−18.9786	−	6.90766i	−0.604403	−	0.219985i
$987$			97.1944i			3.09373i
$988$	5.61743	−	0.906726i	0.178714	−	0.0288468i
$989$	−2.32501			−0.0739309
$990$		0			0
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	0.963639	+	0.267209i	$0.0861014\pi$
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	−0.814133	+	0.580678i	$0.802787\pi$
$992$	−0.237565	+	0.283119i	−0.00754269	+	0.00898902i
$993$	−30.6818	−	36.5651i	−0.973657	−	1.16036i
$994$	5.60132	−	31.7667i	0.177663	−	1.00758i
$995$		0			0
$996$	−3.74510	−	6.48670i	−0.118668	−	0.205539i
$997$	−9.55850	−	26.2618i	−0.302721	−	0.831718i	−0.994025	−	0.109154i	$-0.965186\pi$
$997$	−9.55850	−	26.2618i	−0.302721	−	0.831718i	0.691304	−	0.722564i	$-0.257037\pi$
$998$	7.06569	+	19.4128i	0.223660	+	0.614502i
$999$	11.1848	+	19.3726i	0.353871	+	0.612923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.b.99.2		12
5.2	odd	4		950.2.l.d.251.1		6
5.3	odd	4		38.2.e.a.23.1	yes	6
5.4	even	2	inner	950.2.u.b.99.1		12
15.8	even	4		342.2.u.c.289.1		6
19.5	even	9	inner	950.2.u.b.499.1		12
20.3	even	4		304.2.u.c.289.1		6
95.3	even	36		722.2.e.l.245.1		6
95.8	even	12		722.2.e.l.389.1		6
95.13	even	36		722.2.c.l.429.1		6
95.18	even	4		722.2.e.k.99.1		6
95.23	odd	36		722.2.c.k.653.3		6
95.24	even	18	inner	950.2.u.b.499.2		12
95.28	odd	36		722.2.a.l.1.1		3
95.33	even	36		722.2.e.k.423.1		6
95.43	odd	36		38.2.e.a.5.1	✓	6
95.48	even	36		722.2.a.k.1.3		3
95.53	even	36		722.2.c.l.653.1		6
95.62	odd	36		950.2.l.d.651.1		6
95.63	odd	36		722.2.c.k.429.3		6
95.68	odd	12		722.2.e.b.389.1		6
95.73	odd	36		722.2.e.b.245.1		6
95.78	even	36		722.2.e.a.415.1		6
95.83	odd	12		722.2.e.m.595.1		6
95.88	even	12		722.2.e.a.595.1		6
95.93	odd	36		722.2.e.m.415.1		6
285.143	odd	36		6498.2.a.bq.1.3		3
285.218	even	36		6498.2.a.bl.1.3		3
285.233	even	36		342.2.u.c.271.1		6
380.43	even	36		304.2.u.c.81.1		6
380.123	even	36		5776.2.a.bn.1.3		3
380.143	odd	36		5776.2.a.bo.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	95.43	odd	36
38.2.e.a.23.1	yes	6	5.3	odd	4
304.2.u.c.81.1		6	380.43	even	36
304.2.u.c.289.1		6	20.3	even	4
342.2.u.c.271.1		6	285.233	even	36
342.2.u.c.289.1		6	15.8	even	4
722.2.a.k.1.3		3	95.48	even	36
722.2.a.l.1.1		3	95.28	odd	36
722.2.c.k.429.3		6	95.63	odd	36
722.2.c.k.653.3		6	95.23	odd	36
722.2.c.l.429.1		6	95.13	even	36
722.2.c.l.653.1		6	95.53	even	36
722.2.e.a.415.1		6	95.78	even	36
722.2.e.a.595.1		6	95.88	even	12
722.2.e.b.245.1		6	95.73	odd	36
722.2.e.b.389.1		6	95.68	odd	12
722.2.e.k.99.1		6	95.18	even	4
722.2.e.k.423.1		6	95.33	even	36
722.2.e.l.245.1		6	95.3	even	36
722.2.e.l.389.1		6	95.8	even	12
722.2.e.m.415.1		6	95.93	odd	36
722.2.e.m.595.1		6	95.83	odd	12
950.2.l.d.251.1		6	5.2	odd	4
950.2.l.d.651.1		6	95.62	odd	36
950.2.u.b.99.1		12	5.4	even	2	inner
950.2.u.b.99.2		12	1.1	even	1	trivial
950.2.u.b.499.1		12	19.5	even	9	inner
950.2.u.b.499.2		12	95.24	even	18	inner
5776.2.a.bn.1.3		3	380.123	even	36
5776.2.a.bo.1.1		3	380.143	odd	36
6498.2.a.bl.1.3		3	285.218	even	36
6498.2.a.bq.1.3		3	285.143	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-1.85083 + 0.326352i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{6} +(-4.38571 - 2.53209i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.500000 - 0.181985i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(-1.85083 + 0.326352i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{6} +(-4.38571 - 2.53209i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.500000 - 0.181985i) q^{9} +(0.705737 + 1.22237i) q^{11} +(1.62760 + 0.939693i) q^{12} +(1.28558 + 0.226682i) q^{13} +(-3.87939 + 3.25519i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.817150 - 2.24510i) q^{17} -0.532089i q^{18} +(-2.23396 + 3.74292i) q^{19} +(8.94356 + 3.25519i) q^{21} +(1.39003 - 0.245100i) q^{22} +(-1.96962 + 2.34730i) q^{23} +(1.43969 - 1.20805i) q^{24} +(0.652704 - 1.13052i) q^{26} +(4.01676 - 2.31908i) q^{27} +(1.73205 + 4.75877i) q^{28} +(7.94356 - 2.89122i) q^{29} +(-0.184793 + 0.320070i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-1.70513 - 2.03209i) q^{33} +(-1.83022 - 1.53574i) q^{34} +(-0.500000 - 0.181985i) q^{36} +4.82295i q^{37} +(2.75314 + 3.37939i) q^{38} -2.45336 q^{39} +(-0.266044 - 1.50881i) q^{41} +(6.11776 - 7.29086i) q^{42} +(0.487728 + 0.581252i) q^{43} +(0.245100 - 1.39003i) q^{44} +(1.53209 + 2.65366i) q^{46} +(3.49276 + 9.59627i) q^{47} +(-0.642788 - 1.76604i) q^{48} +(9.32295 + 16.1478i) q^{49} +(-0.779715 + 4.42198i) q^{51} +(-0.839100 - 1.00000i) q^{52} +(1.07666 - 1.28312i) q^{53} +(-0.805407 - 4.56769i) q^{54} +5.06418 q^{56} +(2.91317 - 7.65657i) q^{57} -8.45336i q^{58} +(0.673648 + 0.245188i) q^{59} +(7.47565 + 6.27282i) q^{61} +(0.237565 + 0.283119i) q^{62} +(-2.65366 - 0.467911i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.49273 + 0.907278i) q^{66} +(0.480105 + 1.31908i) q^{67} +(-2.06910 + 1.19459i) q^{68} +(2.87939 - 4.98724i) q^{69} +(-4.87939 + 4.09429i) q^{71} +(-0.342020 + 0.407604i) q^{72} +(-4.49016 + 0.791737i) q^{73} +(4.53209 + 1.64955i) q^{74} +(4.11721 - 1.43128i) q^{76} -7.14796i q^{77} +(-0.839100 + 2.30541i) q^{78} +(0.389185 + 2.20718i) q^{79} +(-7.90033 + 6.62916i) q^{81} +(-1.50881 - 0.266044i) q^{82} +(-3.45150 - 1.99273i) q^{83} +(-4.75877 - 8.24243i) q^{84} +(0.713011 - 0.259515i) q^{86} +(-13.7587 + 7.94356i) q^{87} +(-1.22237 - 0.705737i) q^{88} +(1.84864 - 10.4842i) q^{89} +(-5.06418 - 4.24935i) q^{91} +(3.01763 - 0.532089i) q^{92} +(0.237565 - 0.652704i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(-0.524005 + 1.43969i) q^{97} +(18.3626 - 3.23783i) q^{98} +(0.575322 + 0.482753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^6 + 6 * q^9	\( 12 q - 6 q^{6} + 6 q^{9} - 12 q^{11} - 24 q^{14} - 36 q^{19} + 48 q^{21} + 6 q^{24} + 12 q^{26} + 36 q^{29} + 12 q^{31} + 24 q^{34} - 6 q^{36} + 24 q^{39} + 6 q^{41} + 30 q^{49} + 42 q^{51} - 18 q^{54} + 24 q^{56} + 6 q^{59} + 12 q^{61} + 6 q^{64} + 6 q^{66} + 12 q^{69} - 36 q^{71} + 36 q^{74} - 12 q^{76} - 12 q^{79} - 66 q^{81} - 12 q^{84} + 24 q^{86} - 24 q^{91} + 24 q^{94} - 42 q^{99}+O(q^{100}) \) 12 * q - 6 * q^6 + 6 * q^9 - 12 * q^11 - 24 * q^14 - 36 * q^19 + 48 * q^21 + 6 * q^24 + 12 * q^26 + 36 * q^29 + 12 * q^31 + 24 * q^34 - 6 * q^36 + 24 * q^39 + 6 * q^41 + 30 * q^49 + 42 * q^51 - 18 * q^54 + 24 * q^56 + 6 * q^59 + 12 * q^61 + 6 * q^64 + 6 * q^66 + 12 * q^69 - 36 * q^71 + 36 * q^74 - 12 * q^76 - 12 * q^79 - 66 * q^81 - 12 * q^84 + 24 * q^86 - 24 * q^91 + 24 * q^94 - 42 * q^99

Introduction

L-functions

Modular forms

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