LMFDB - Embedded newform 950.2.u.b.499.1

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			499.1
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	950.499
Dual form			950.2.u.b.99.1

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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	$-0.261910\pi$
$3$	1.85083	+	0.326352i	1.06858	+	0.188419i	0.388419	+	0.921483i	$0.373021\pi$
$4$	−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	0.683842	−	0.729630i	$-0.260308\pi$
$7$	4.38571	−	2.53209i	1.65764	−	0.957040i	0.973799	−	0.227410i	$-0.0730256\pi$
$8$	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	−0.739798	−	0.672829i	$-0.765079\pi$
$11$	0.705737	−	1.22237i	0.212788	−	0.368559i	0.952586	+	0.304270i	$0.0984124\pi$
$12$	−1.62760	+	0.939693i	−0.469846	+	0.271266i
$13$	−1.28558	+	0.226682i	−0.356554	+	0.0628702i	−0.349056	−	0.937102i	$-0.613498\pi$
$13$	−1.28558	+	0.226682i	−0.356554	+	0.0628702i	−0.00749804	+	0.999972i	$0.502387\pi$
$14$	−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	$-0.204677\pi$
$17$	−0.817150	−	2.24510i	−0.198188	−	0.544517i	−0.998481	+	0.0550919i	$0.982455\pi$
$18$		−	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	$-0.118720\pi$
$23$	1.96962	+	2.34730i	0.410693	+	0.489445i	−0.520556	+	0.853827i	$0.674275\pi$
$24$	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	0.949475	−	0.313841i	$-0.101616\pi$
$29$	7.94356	+	2.89122i	1.47508	+	0.536886i	0.525607	+	0.850727i	$0.323838\pi$
$30$		0			0
$31$	−0.184793	−	0.320070i	−0.0331897	−	0.0574863i	0.848953	−	0.528468i	$-0.177233\pi$
$31$	−0.184793	−	0.320070i	−0.0331897	−	0.0574863i	−0.882143	+	0.470981i	$0.843900\pi$
$32$	−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	−0.998509	−	0.0545825i	$-0.982617\pi$
$41$	−0.266044	+	1.50881i	−0.0415492	+	0.235637i	0.956960	+	0.290220i	$0.0937283\pi$
$42$	−6.11776	−	7.29086i	−0.943990	−	1.12500i
$43$	−0.487728	+	0.581252i	−0.0743779	+	0.0886401i	−0.801950	−	0.597391i	$-0.796204\pi$
$43$	−0.487728	+	0.581252i	−0.0743779	+	0.0886401i	0.727572	+	0.686031i	$0.240649\pi$
$44$	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	0.372314	+	0.928107i	$0.378565\pi$
$47$	−3.49276	+	9.59627i	−0.509471	+	1.39976i	−0.881785	+	0.471652i	$0.843658\pi$
$48$	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	$-0.258922\pi$
$53$	−1.07666	−	1.28312i	−0.147891	−	0.176250i	−0.834904	+	0.550395i	$0.814477\pi$
$54$	−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	−0.297797	−	0.954629i	$-0.596252\pi$
$59$	0.673648	−	0.245188i	0.0877015	−	0.0319207i	0.385498	+	0.922709i	$0.374030\pi$
$60$		0			0
$61$	7.47565	−	6.27282i	0.957159	−	0.803152i	−0.0233295	−	0.999728i	$-0.507427\pi$
$61$	7.47565	−	6.27282i	0.957159	−	0.803152i	0.980489	+	0.196576i	$0.0629822\pi$
$62$	−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	$-0.916216\pi$
$67$	−0.480105	+	1.31908i	−0.0586542	+	0.161151i	0.906905	+	0.421336i	$0.138439\pi$
$68$	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	0.305567	−	0.952171i	$-0.401154\pi$
$71$	−4.87939	−	4.09429i	−0.579076	−	0.485903i	−0.884644	+	0.466268i	$0.845598\pi$
$72$	0.342020	+	0.407604i	0.0403075	+	0.0480366i
$73$	4.49016	+	0.791737i	0.525534	+	0.0926658i	0.430120	−	0.902772i	$-0.358471\pi$
$73$	4.49016	+	0.791737i	0.525534	+	0.0926658i	0.0954141	+	0.995438i	$0.469582\pi$
$74$	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	−0.955056	−	0.296426i	$-0.904205\pi$
$79$	0.389185	−	2.20718i	0.0437868	−	0.248327i	0.998843	+	0.0480989i	$0.0153163\pi$
$80$		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	$-0.596475\pi$
$83$	3.45150	−	1.99273i	0.378852	−	0.218730i	0.677319	+	0.735690i	$0.263142\pi$
$84$	−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	0.911051	+	0.412293i	$0.135272\pi$
$89$	1.84864	+	10.4842i	0.195956	+	1.11132i	−0.715096	+	0.699026i	$0.753617\pi$
$90$		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	$-0.0863279\pi$
$97$	0.524005	+	1.43969i	0.0532047	+	0.146179i	−0.910244	+	0.414073i	$0.864106\pi$
$98$	−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	0.961081	+	0.276265i	$0.0890968\pi$
$101$	1.53209	+	8.68891i	0.152449	+	0.864579i	−0.808633	+	0.588314i	$0.799792\pi$
$102$	−3.88863	+	2.24510i	−0.385031	+	0.222298i
$103$	−6.19031	−	3.57398i	−0.609950	−	0.352155i	0.162996	−	0.986627i	$-0.447884\pi$
$103$	−6.19031	−	3.57398i	−0.609950	−	0.352155i	−0.772946	+	0.634472i	$0.781218\pi$
$104$	−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	$-0.816276\pi$
$107$	−8.11430	+	4.68479i	−0.784439	+	0.452896i	0.0535622	+	0.998565i	$0.482942\pi$
$108$	4.56769	−	0.805407i	0.439526	−	0.0775004i
$109$	−8.47565	−	7.11192i	−0.811820	−	0.681198i	0.139221	−	0.990261i	$-0.455540\pi$
$109$	−8.47565	−	7.11192i	−0.811820	−	0.681198i	−0.951041	+	0.309063i	$0.899985\pi$
$110$		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	$-0.473965\pi$
$127$	5.62738	−	0.992259i	0.499349	−	0.0880488i	0.417650	+	0.908608i	$0.362854\pi$
$128$	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	0.0970281	−	0.995282i	$-0.469066\pi$
$131$	9.28359	−	3.37895i	0.811111	−	0.295220i	0.714083	+	0.700062i	$0.246844\pi$
$132$			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	$-0.148171\pi$
$137$	3.46908	+	4.13429i	0.296383	+	0.353216i	−0.597217	+	0.802080i	$0.703727\pi$
$138$	3.70167	−	4.41147i	0.315107	−	0.375530i
$139$	0.406260	+	2.30401i	0.0344585	+	0.195424i	0.997178	−	0.0750794i	$-0.0239210\pi$
$139$	0.406260	+	2.30401i	0.0344585	+	0.195424i	−0.962719	+	0.270503i	$0.912810\pi$
$140$		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	−0.693932	−	0.720040i	$-0.744123\pi$
$149$	2.49525	−	14.1513i	0.204419	−	1.15932i	0.898351	−	0.439278i	$-0.144766\pi$
$150$		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	$-0.859581\pi$
$157$	−4.09429	+	4.87939i	−0.326760	+	0.389417i	0.577506	+	0.816386i	$0.304026\pi$
$158$	−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	$-0.274009\pi$
$163$	4.09754	+	2.36571i	0.320944	+	0.185297i	−0.330869	+	0.943677i	$0.607342\pi$
$164$	−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	0.999423	+	0.0339719i	$0.0108157\pi$
$167$	11.1050	+	13.2344i	0.859331	+	1.02411i	−0.140092	+	0.990138i	$0.544740\pi$
$168$	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	0.901171	+	0.433463i	$0.142709\pi$
$173$	6.43783	+	17.6878i	0.489459	+	1.34478i	−0.411712	+	0.911314i	$0.635069\pi$
$174$	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	0.483034	+	0.875602i	$0.339535\pi$
$179$	−6.91400	+	11.9754i	−0.516777	+	0.895083i	−0.999810	+	0.0194816i	$0.993798\pi$
$180$		0			0
$181$	−11.5175	−	4.19204i	−0.856092	−	0.311592i	−0.123570	−	0.992336i	$-0.539434\pi$
$181$	−11.5175	−	4.19204i	−0.856092	−	0.311592i	−0.732522	+	0.680744i	$0.761657\pi$
$182$	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	$-0.649480\pi$
$193$	−16.4316	−	2.89734i	−1.18277	−	0.208555i	−0.730239	+	0.683192i	$0.760591\pi$
$194$	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	$-0.513523\pi$
$197$	11.2501	−	6.49525i	0.801537	−	0.462768i	0.844008	+	0.536330i	$0.180190\pi$
$198$	−0.650411	−	0.375515i	−0.0462227	−	0.0266867i
$199$	16.1557	+	5.88019i	1.14525	+	0.416836i	0.843806	−	0.536649i	$-0.180310\pi$
$199$	16.1557	+	5.88019i	1.14525	+	0.416836i	0.301441	+	0.953485i	$0.402532\pi$
$200$		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	0.236420	−	0.971651i	$-0.424026\pi$
$211$	15.1373	−	5.50952i	1.04209	−	0.379291i	0.805673	+	0.592360i	$0.201804\pi$
$212$	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	$-0.734117\pi$
$223$	2.62500	−	3.12836i	0.175783	−	0.209490i	0.846741	+	0.532005i	$0.178561\pi$
$224$	−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	−0.213921	+	0.976851i	$0.568624\pi$
$233$	−17.3828	+	20.7160i	−1.13878	+	1.35715i	−0.924863	+	0.380300i	$0.875821\pi$
$234$	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	−0.870610	−	0.491973i	$-0.836276\pi$
$239$	−0.142903	+	0.247516i	−0.00924366	+	0.0160105i	0.861367	+	0.507984i	$0.169609\pi$
$240$		0			0
$241$	0.538485	+	3.05390i	0.0346869	+	0.196719i	0.997227	−	0.0744203i	$-0.0237106\pi$
$241$	0.538485	+	3.05390i	0.0346869	+	0.196719i	−0.962540	+	0.271139i	$0.912600\pi$
$242$	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	−0.895287	−	0.445489i	$-0.853030\pi$
$251$	−9.69640	+	8.13625i	−0.612032	+	0.513555i	0.283256	+	0.959044i	$0.408585\pi$
$252$	−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	−0.0249253	+	0.999689i	$0.507935\pi$
$257$	−10.3950	+	28.5599i	−0.648419	+	1.78152i	−0.623494	+	0.781828i	$0.714287\pi$
$258$	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	$-0.680424\pi$
$263$	−21.5699	−	3.80335i	−1.33005	−	0.234524i	−0.793102	+	0.609088i	$0.791535\pi$
$264$	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	−0.976277	−	0.216527i	$-0.930527\pi$
$269$	0.248970	−	1.41198i	0.0151800	−	0.0860900i	0.991457	+	0.130437i	$0.0416381\pi$
$270$		0			0
$271$	12.3892	+	10.3958i	0.752589	+	0.631498i	0.936186	−	0.351504i	$-0.114330\pi$
$271$	12.3892	+	10.3958i	0.752589	+	0.631498i	−0.183597	+	0.983002i	$0.558774\pi$
$272$	−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	$-0.441641\pi$
$277$	−9.62046	−	5.55438i	−0.578038	−	0.333730i	−0.760353	+	0.649510i	$0.774974\pi$
$278$	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	−0.540519	−	0.841332i	$-0.681772\pi$
$281$	3.25490	−	2.73119i	0.194171	−	0.162929i	0.734690	+	0.678403i	$0.237328\pi$
$282$	18.9010	+	3.33275i	1.12554	+	0.198462i
$283$	−1.86608	−	5.12701i	−0.110927	−	0.304769i	0.871791	−	0.489878i	$-0.162959\pi$
$283$	−1.86608	−	5.12701i	−0.110927	−	0.304769i	−0.982718	+	0.185108i	$0.940736\pi$
$284$	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	$-0.159140\pi$
$293$	15.4269	+	8.90673i	0.901249	+	0.520337i	0.0236440	+	0.999720i	$0.492473\pi$
$294$	−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	$-0.749261\pi$
$307$	−28.2233	−	4.97653i	−1.61079	−	0.284026i	−0.905325	+	0.424720i	$0.860373\pi$
$308$	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	0.549929	−	0.835211i	$-0.314655\pi$
$311$	−7.90673	−	13.6949i	−0.448349	−	0.776564i	−0.998279	+	0.0586473i	$0.981321\pi$
$312$	−2.12467	−	1.22668i	−0.120286	−	0.0694472i
$313$	−4.49422	+	12.3478i	−0.254028	+	0.697937i	0.745478	+	0.666530i	$0.232221\pi$
$313$	−4.49422	+	12.3478i	−0.254028	+	0.697937i	−0.999507	+	0.0314071i	$0.990001\pi$
$314$	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	$-0.350284\pi$
$317$	21.0795	−	3.71688i	1.18394	−	0.208761i	0.730746	+	0.682650i	$0.239173\pi$
$318$	−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	−0.271164	−	0.962533i	$-0.587409\pi$
$331$	12.6989	−	21.9952i	0.697996	−	1.20897i	0.969160	−	0.246432i	$-0.0792582\pi$
$332$	−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	0.0710588	+	0.997472i	$0.477362\pi$
$337$	−16.9550	+	20.2062i	−0.923599	+	1.10070i	−0.994658	+	0.103230i	$0.967082\pi$
$338$	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	−0.113714	−	0.993514i	$-0.536275\pi$
$347$	16.4755	−	19.6348i	0.884452	−	1.05405i	0.998166	−	0.0605352i	$-0.0192807\pi$
$348$	−15.6458	+	2.75877i	−0.838701	+	0.147886i
$349$	−2.92127	−	5.05980i	−0.156372	−	0.270845i	0.777186	−	0.629271i	$-0.216647\pi$
$349$	−2.92127	−	5.05980i	−0.156372	−	0.270845i	−0.933558	+	0.358427i	$0.883313\pi$
$350$		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	$-0.536726\pi$
$353$	−19.4074	−	11.2049i	−1.03295	−	0.596375i	−0.917829	+	0.396977i	$0.870059\pi$
$354$	−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	−0.0923503	−	0.995727i	$-0.529438\pi$
$359$	9.03684	−	3.28914i	0.476946	−	0.173594i	0.569296	+	0.822132i	$0.307216\pi$
$360$		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	$-0.764263\pi$
$367$	−23.0052	+	4.05644i	−1.20086	+	0.211744i	−0.462791	+	0.886468i	$0.653152\pi$
$368$	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	$-0.432271\pi$
$373$	22.4663	−	12.9709i	1.16326	−	0.671608i	0.952083	+	0.305840i	$0.0989373\pi$
$374$	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	$-0.332454\pi$
$383$	13.2835	+	2.34224i	0.678756	+	0.119683i	0.176367	+	0.984324i	$0.443565\pi$
$384$	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	−0.335576	−	0.942013i	$-0.608931\pi$
$389$	−23.6313	−	8.60111i	−1.19816	−	0.436093i	−0.862581	+	0.505920i	$0.831153\pi$
$390$		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	$-0.163801\pi$
$397$	−2.24579	−	6.17024i	−0.112713	−	0.309676i	−0.983205	+	0.182507i	$0.941579\pi$
$398$		−	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	0.461185	−	0.887304i	$-0.347425\pi$
$401$	27.7310	−	10.0933i	1.38482	−	0.504034i	0.923636	+	0.383270i	$0.125202\pi$
$402$	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	0.782559	−	0.622576i	$-0.213914\pi$
$409$	19.8567	+	7.22724i	0.981850	+	0.357364i	0.199291	+	0.979940i	$0.436136\pi$
$410$		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	−0.984996	−	0.172578i	$-0.944790\pi$
$421$	−0.00774079	+	0.0439002i	−0.000377263	+	0.00213956i	0.984619	+	0.174718i	$0.0559013\pi$
$422$	−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	−0.993585	−	0.113084i	$-0.963927\pi$
$431$	−2.04694	−	11.6088i	−0.0985977	−	0.559175i	0.894988	−	0.446091i	$-0.147184\pi$
$432$	−2.98135	+	3.55303i	−0.143440	+	0.170945i
$433$	−17.7704	−	21.1780i	−0.853993	−	1.01775i	−0.999596	−	0.0284060i	$-0.990957\pi$
$433$	−17.7704	−	21.1780i	−0.853993	−	1.01775i	0.145604	−	0.989343i	$-0.453488\pi$
$434$	−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	0.686314	−	0.727305i	$-0.259227\pi$
$439$	35.1908	−	12.8084i	1.67956	−	0.611311i	0.993250	+	0.115994i	$0.0370052\pi$
$440$		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	$-0.389408\pi$
$443$	20.6693	−	3.64455i	0.982027	−	0.173158i	0.641539	+	0.767091i	$0.278296\pi$
$444$	−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	−0.999813	−	0.0193235i	$-0.993849\pi$
$449$	−10.9474	−	18.9615i	−0.516641	−	0.894849i	0.483172	−	0.875525i	$-0.339485\pi$
$450$		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	0.718040	−	0.696002i	$-0.245040\pi$
$461$	3.37733	+	2.83391i	0.157298	+	0.131988i	−0.560742	+	0.827991i	$0.689484\pi$
$462$	−13.2297	+	2.33275i	−0.615500	+	0.108529i
$463$	−23.0930	+	13.3327i	−1.07322	+	0.619625i	−0.929060	−	0.369929i	$-0.879382\pi$
$463$	−23.0930	+	13.3327i	−1.07322	+	0.619625i	−0.144162	+	0.989554i	$0.546049\pi$
$464$	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	$-0.578705\pi$
$467$	−26.0793	−	15.0569i	−1.20681	−	0.696750i	−0.962060	+	0.272837i	$0.912038\pi$
$468$	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	−0.774437	−	0.632651i	$-0.781967\pi$
$479$	−6.25671	+	5.25000i	−0.285876	+	0.239879i	0.488560	+	0.872530i	$0.337522\pi$
$480$		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	$-0.460883\pi$
$487$	23.0251	−	13.2935i	1.04337	−	0.602388i	0.920785	+	0.390070i	$0.127549\pi$
$488$	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	−0.322549	−	0.946553i	$-0.604540\pi$
$491$	6.74257	−	38.2390i	0.304288	−	1.72570i	0.626837	−	0.779151i	$-0.284349\pi$
$492$	−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	0.215717	−	0.976456i	$-0.430791\pi$
$499$	−15.8255	−	13.2791i	−0.708446	−	0.594456i	−0.924163	+	0.382000i	$0.875236\pi$
$500$		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	$-0.889412\pi$
$503$	−0.0251977	+	0.0692302i	−0.00112351	+	0.00308682i	0.939130	+	0.343563i	$0.111634\pi$
$504$	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	−0.861122	−	0.508398i	$-0.830238\pi$
$509$	−11.5057	+	9.65441i	−0.509980	+	0.427924i	0.351142	+	0.936322i	$0.385793\pi$
$510$		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	−0.369533	+	0.929217i	$0.620482\pi$
$521$	−22.5856	+	39.1194i	−0.989493	+	1.71385i	−0.619959	+	0.784634i	$0.712851\pi$
$522$	1.53839	−	4.22668i	0.0673333	−	0.184997i
$523$	−0.0573076	+	0.157451i	−0.00250589	+	0.00688487i	−0.940939	−	0.338575i	$-0.890055\pi$
$523$	−0.0573076	+	0.157451i	−0.00250589	+	0.00688487i	0.938433	+	0.345460i	$0.112277\pi$
$524$	−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	0.361749	−	0.932276i	$-0.382180\pi$
$541$	0.921274	+	0.335316i	0.0396087	+	0.0144164i	−0.322140	+	0.946692i	$0.604402\pi$
$542$	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	$-0.0144957\pi$
$547$	18.2582	+	21.7592i	0.780663	+	0.930358i	−0.218300	+	0.975882i	$0.570051\pi$
$548$	−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	$-0.827867\pi$
$557$	−35.0909	+	6.18748i	−1.48685	+	0.262172i	−0.629539	+	0.776969i	$0.716756\pi$
$558$	−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	$-0.724861\pi$
$563$	−7.47183	+	4.31386i	−0.314900	+	0.181808i	0.334217	+	0.942496i	$0.391528\pi$
$564$	−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	$-0.511700\pi$
$577$	19.4645	−	11.2378i	0.810317	−	0.467837i	0.847066	+	0.531488i	$0.178367\pi$
$578$	−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	$-0.138393\pi$
$587$	−1.41868	−	3.89780i	−0.0585554	−	0.160880i	−0.965521	+	0.260325i	$0.916170\pi$
$588$			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	$-0.290838\pi$
$593$	−6.69621	−	7.98024i	−0.274981	−	0.327709i	−0.885806	+	0.464057i	$0.846393\pi$
$594$	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	−0.560792	−	0.827957i	$-0.689503\pi$
$599$	−37.2645	−	13.5632i	−1.52258	−	0.554175i	−0.961792	+	0.273781i	$0.911726\pi$
$600$		0			0
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	0.513150	−	0.858299i	$-0.328478\pi$
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	−0.999884	+	0.0152517i	$0.995145\pi$
$602$	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	0.0709862	+	0.997477i	$0.477385\pi$
$613$	−22.8688	+	27.2540i	−0.923664	+	1.10078i	−0.994650	+	0.103302i	$0.967059\pi$
$614$	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	$-0.811019\pi$
$617$	4.11532	−	11.3068i	0.165677	−	0.455193i	0.994552	+	0.104240i	$0.0332411\pi$
$618$	−4.59462	+	12.6236i	−0.184823	+	0.507796i
$619$	−8.55644	+	14.8202i	−0.343912	+	0.595673i	−0.985156	−	0.171664i	$-0.945086\pi$
$619$	−8.55644	+	14.8202i	−0.343912	+	0.595673i	0.641243	+	0.767338i	$0.278419\pi$
$620$		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	−0.318771	−	0.947832i	$-0.603270\pi$
$631$	14.0496	−	11.7890i	0.559307	−	0.469314i	0.878078	+	0.478517i	$0.158826\pi$
$632$	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	0.0348149	−	0.999394i	$-0.488916\pi$
$641$	−23.8837	−	20.0408i	−0.943350	−	0.791565i	−0.978165	+	0.207829i	$0.933360\pi$
$642$	11.3189	+	13.4893i	0.446721	+	0.532381i
$643$	31.4642	+	5.54798i	1.24083	+	0.218791i	0.755269	−	0.655414i	$-0.227506\pi$
$643$	31.4642	+	5.54798i	1.24083	+	0.218791i	0.485556	+	0.874206i	$0.338617\pi$
$644$	−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	$-0.672495\pi$
$653$	−0.810446	+	0.467911i	−0.0317152	+	0.0183108i	0.484059	+	0.875036i	$0.339162\pi$
$654$	−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	0.997814	+	0.0660804i	$0.0210494\pi$
$659$	2.12495	+	12.0512i	0.0827764	+	0.469448i	−0.915038	+	0.403368i	$0.867840\pi$
$660$		0			0
$661$	−9.15839	+	7.68480i	−0.356220	+	0.298904i	−0.803282	−	0.595599i	$-0.796915\pi$
$661$	−9.15839	+	7.68480i	−0.356220	+	0.298904i	0.447062	+	0.894503i	$0.352470\pi$
$662$	−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	$-0.000855397\pi$
$673$	38.8529	+	22.4317i	1.49767	+	0.864679i	0.497671	+	0.867366i	$0.334189\pi$
$674$	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	$-0.660880\pi$
$677$	0.819197	−	0.472964i	0.0314843	−	0.0181775i	0.515660	+	0.856794i	$0.327547\pi$
$678$	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	0.864058	−	0.503392i	$-0.167915\pi$
$691$	−0.103074	−	0.178529i	−0.00392111	−	0.00679156i	−0.867979	+	0.496600i	$0.834581\pi$
$692$	−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	−0.418396	−	0.908265i	$-0.637407\pi$
$701$	−4.10607	+	1.49449i	−0.155084	+	0.0564460i	0.263312	+	0.964711i	$0.415185\pi$
$702$		−	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	0.942863	−	0.333182i	$-0.108122\pi$
$709$	−1.52023	−	8.62165i	−0.0570934	−	0.323793i	−0.999956	+	0.00938924i	$0.997011\pi$
$710$		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	−0.754909	−	0.655830i	$-0.772319\pi$
$719$	4.79385	−	27.1873i	0.178781	−	1.01391i	0.933689	−	0.358085i	$-0.116570\pi$
$720$		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	$-0.955974\pi$
$727$	−18.4071	+	21.9368i	−0.682682	+	0.813589i	0.307768	+	0.951462i	$0.400418\pi$
$728$	−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	$-0.0941823\pi$
$733$	32.0095	+	18.4807i	1.18230	+	0.682600i	0.225753	+	0.974184i	$0.427516\pi$
$734$	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	0.613446	−	0.789737i	$-0.289783\pi$
$739$	43.2508	−	15.7420i	1.59101	−	0.579079i	0.977560	+	0.210658i	$0.0675607\pi$
$740$		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	0.987751	+	0.156036i	$0.0498715\pi$
$743$	9.03298	+	24.8179i	0.331388	+	0.910480i	−0.656364	+	0.754445i	$0.727906\pi$
$744$	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	0.762961	−	0.646444i	$-0.223745\pi$
$751$	25.5381	+	9.29510i	0.931898	+	0.339183i	0.168936	+	0.985627i	$0.445967\pi$
$752$	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	$-0.329729\pi$
$757$	19.1099	+	3.36959i	0.694560	+	0.122470i	0.184787	+	0.982779i	$0.440841\pi$
$758$	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	−0.416263	−	0.909244i	$-0.636660\pi$
$769$	−36.5933	−	13.3189i	−1.31959	−	0.480291i	−0.903327	+	0.428953i	$0.858883\pi$
$770$		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	$-0.594365\pi$
$773$	−6.66015	+	1.17436i	−0.239549	+	0.0422389i	0.0525847	+	0.998616i	$0.483254\pi$
$774$	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	$-0.366324\pi$
$787$	−5.02709	−	2.90239i	−0.179196	−	0.103459i	−0.586915	+	0.809649i	$0.699658\pi$
$788$	−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	−0.797888	−	0.602805i	$-0.794050\pi$
$809$	3.50134	−	6.06451i	0.123101	−	0.213217i	0.920989	+	0.389589i	$0.127383\pi$
$810$		0			0
$811$	7.58584	+	43.0214i	0.266375	+	1.51069i	0.765092	+	0.643921i	$0.222694\pi$
$811$	7.58584	+	43.0214i	0.266375	+	1.51069i	−0.498717	+	0.866765i	$0.666195\pi$
$812$	−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	−0.462038	−	0.886860i	$-0.652882\pi$
$821$	9.48751	−	7.96097i	0.331116	−	0.277840i	0.793155	+	0.609020i	$0.208437\pi$
$822$	6.51973	−	7.76991i	0.227402	−	0.271007i
$823$	−12.6334	+	2.22762i	−0.440374	+	0.0776498i	−0.389439	−	0.921052i	$-0.627331\pi$
$823$	−12.6334	+	2.22762i	−0.440374	+	0.0776498i	−0.0509347	+	0.998702i	$0.516220\pi$
$824$	−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	−0.696276	−	0.717774i	$-0.745161\pi$
$827$	8.58353	−	23.5831i	0.298479	−	0.820063i	0.994755	−	0.102289i	$-0.0326167\pi$
$828$	−1.41198	−	0.815207i	−0.0490697	−	0.0283304i
$829$	14.1634	+	24.5318i	0.491917	+	0.852024i	0.999957	−	0.00930899i	$-0.00296319\pi$
$829$	14.1634	+	24.5318i	0.491917	+	0.852024i	−0.508040	+	0.861333i	$0.669630\pi$
$830$		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	−0.748129	−	0.663553i	$-0.769048\pi$
$839$	5.26682	−	29.8696i	0.181831	−	1.03121i	0.929960	−	0.367660i	$-0.119841\pi$
$840$		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	−0.880240	−	0.474528i	$-0.842619\pi$
$853$	−14.9231	−	41.0009i	−0.510958	−	1.40385i	0.369283	−	0.929317i	$-0.379603\pi$
$854$	−49.4201			−1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	10.7770	+	29.6095i	0.368135	+	1.01144i	0.976070	+	0.217456i	$0.0697757\pi$
$857$	10.7770	+	29.6095i	0.368135	+	1.01144i	−0.607935	+	0.793987i	$0.708002\pi$
$858$	3.41025	+	0.601319i	0.116424	+	0.0205287i
$859$	14.3234	−	12.0188i	0.488709	−	0.410075i	−0.364855	−	0.931065i	$-0.618881\pi$
$859$	14.3234	−	12.0188i	0.488709	−	0.410075i	0.853563	+	0.520989i	$0.174437\pi$
$860$		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	$-0.275445\pi$
$863$	9.20264	+	5.31315i	0.313262	+	0.180862i	−0.335123	+	0.942174i	$0.608778\pi$
$864$	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	$-0.170593\pi$
$877$	44.2164	+	7.79654i	1.49308	+	0.263270i	0.633289	+	0.773915i	$0.281704\pi$
$878$	−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	0.976925	−	0.213583i	$-0.0685134\pi$
$881$	9.00821	+	15.6027i	0.303494	+	0.525667i	−0.673431	+	0.739250i	$0.735180\pi$
$882$	−8.59208	−	4.96064i	−0.289310	−	0.167033i
$883$	15.9375	−	43.7879i	0.536340	−	1.47358i	−0.315064	−	0.949070i	$-0.602026\pi$
$883$	15.9375	−	43.7879i	0.536340	−	1.47358i	0.851404	−	0.524511i	$-0.175752\pi$
$884$	−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	$-0.593478\pi$
$887$	−6.97210	+	1.22937i	−0.234100	+	0.0412782i	0.0553671	+	0.998466i	$0.482367\pi$
$888$	−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	$-0.858521\pi$
$907$	−9.71610	+	11.5792i	−0.322618	+	0.384481i	0.580222	+	0.814458i	$0.302966\pi$
$908$	−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	0.643561	−	0.765395i	$-0.277456\pi$
$919$	−10.3396	−	17.9086i	−0.341070	−	0.590751i	−0.984632	+	0.174643i	$0.944123\pi$
$920$		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	−0.607658	−	0.794199i	$-0.707891\pi$
$929$	−17.1493	+	6.24183i	−0.562650	+	0.204788i	0.0450079	+	0.998987i	$0.485669\pi$
$930$		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	$-0.530850\pi$
$937$	4.67479	−	0.824292i	0.152719	−	0.0269285i	0.249485	+	0.968379i	$0.419739\pi$
$938$	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	−0.500517	−	0.865727i	$-0.666857\pi$
$941$	−44.1857	−	16.0823i	−1.44041	−	0.524268i	−0.939897	+	0.341459i	$0.889079\pi$
$942$	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	$-0.239173\pi$
$947$	36.4338	+	6.42427i	1.18394	+	0.208761i	0.453195	+	0.891411i	$0.350284\pi$
$948$	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	$-0.235308\pi$
$953$	37.1364	+	6.54814i	1.20296	+	0.212115i	0.463985	+	0.885843i	$0.346419\pi$
$954$	−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	−0.935764	−	0.352628i	$-0.885288\pi$
$967$	−13.8564	−	38.0702i	−0.445592	−	1.22425i	0.490172	−	0.871626i	$-0.336934\pi$
$968$			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	−0.120912	−	0.992663i	$-0.538582\pi$
$971$	13.2289	−	4.81493i	0.424536	−	0.154518i	0.545448	+	0.838145i	$0.316360\pi$
$972$	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	$-0.142917\pi$
$977$	30.4890	+	17.6028i	0.975429	+	0.563164i	0.0745421	+	0.997218i	$0.476250\pi$
$978$	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	$-0.661285\pi$
$983$	14.4240	−	17.1898i	0.460054	−	0.548271i	0.945341	+	0.326084i	$0.105729\pi$
$984$	−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	−0.814133	−	0.580678i	$-0.802787\pi$
$991$	4.70645	−	26.6916i	0.149505	−	0.847887i	0.963639	−	0.267209i	$-0.0861014\pi$
$992$	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	−0.691304	−	0.722564i	$-0.742963\pi$
$997$	9.55850	−	26.2618i	0.302721	−	0.831718i	0.994025	−	0.109154i	$-0.0348143\pi$
$998$	−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.499.1		12
5.2	odd	4		950.2.l.d.651.1		6
5.3	odd	4		38.2.e.a.5.1	✓	6
5.4	even	2	inner	950.2.u.b.499.2		12
15.8	even	4		342.2.u.c.271.1		6
19.4	even	9	inner	950.2.u.b.99.2		12
20.3	even	4		304.2.u.c.81.1		6
95.3	even	36		722.2.c.l.653.1		6
95.4	even	18	inner	950.2.u.b.99.1		12
95.8	even	12		722.2.e.a.415.1		6
95.13	even	36		722.2.e.l.389.1		6
95.18	even	4		722.2.e.k.423.1		6
95.23	odd	36		38.2.e.a.23.1	yes	6
95.28	odd	36		722.2.e.m.595.1		6
95.33	even	36		722.2.c.l.429.1		6
95.42	odd	36		950.2.l.d.251.1		6
95.43	odd	36		722.2.c.k.429.3		6
95.48	even	36		722.2.e.a.595.1		6
95.53	even	36		722.2.e.k.99.1		6
95.63	odd	36		722.2.e.b.389.1		6
95.68	odd	12		722.2.e.m.415.1		6
95.73	odd	36		722.2.c.k.653.3		6
95.78	even	36		722.2.a.k.1.3		3
95.83	odd	12		722.2.e.b.245.1		6
95.88	even	12		722.2.e.l.245.1		6
95.93	odd	36		722.2.a.l.1.1		3
285.23	even	36		342.2.u.c.289.1		6
285.173	odd	36		6498.2.a.bq.1.3		3
285.188	even	36		6498.2.a.bl.1.3		3
380.23	even	36		304.2.u.c.289.1		6
380.283	even	36		5776.2.a.bn.1.3		3
380.363	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	5.3	odd	4
38.2.e.a.23.1	yes	6	95.23	odd	36
304.2.u.c.81.1		6	20.3	even	4
304.2.u.c.289.1		6	380.23	even	36
342.2.u.c.271.1		6	15.8	even	4
342.2.u.c.289.1		6	285.23	even	36
722.2.a.k.1.3		3	95.78	even	36
722.2.a.l.1.1		3	95.93	odd	36
722.2.c.k.429.3		6	95.43	odd	36
722.2.c.k.653.3		6	95.73	odd	36
722.2.c.l.429.1		6	95.33	even	36
722.2.c.l.653.1		6	95.3	even	36
722.2.e.a.415.1		6	95.8	even	12
722.2.e.a.595.1		6	95.48	even	36
722.2.e.b.245.1		6	95.83	odd	12
722.2.e.b.389.1		6	95.63	odd	36
722.2.e.k.99.1		6	95.53	even	36
722.2.e.k.423.1		6	95.18	even	4
722.2.e.l.245.1		6	95.88	even	12
722.2.e.l.389.1		6	95.13	even	36
722.2.e.m.415.1		6	95.68	odd	12
722.2.e.m.595.1		6	95.28	odd	36
950.2.l.d.251.1		6	95.42	odd	36
950.2.l.d.651.1		6	5.2	odd	4
950.2.u.b.99.1		12	95.4	even	18	inner
950.2.u.b.99.2		12	19.4	even	9	inner
950.2.u.b.499.1		12	1.1	even	1	trivial
950.2.u.b.499.2		12	5.4	even	2	inner
5776.2.a.bn.1.3		3	380.283	even	36
5776.2.a.bo.1.1		3	380.363	odd	36
6498.2.a.bl.1.3		3	285.188	even	36
6498.2.a.bq.1.3		3	285.173	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

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