LMFDB - Embedded newform 950.2.l.h.351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 105x^{8} + 394x^{6} + 1077x^{4} + 1443x^{2} + 1369 $ x^12 + 12x^10 + 105x^8 + 394x^6 + 1077x^4 + 1443*x^2 + 1369
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.2
Root			$0.838929 + 1.45307i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.h.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(1.28531 - 1.07851i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(0.237742 - 0.411781i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0320889 + 0.181985i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(1.28531 - 1.07851i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(0.237742 - 0.411781i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0320889 + 0.181985i) q^{9} +(2.79789 + 4.84609i) q^{11} +(-0.838929 + 1.45307i) q^{12} +(-1.88608 - 1.58261i) q^{13} +(0.446808 + 0.162625i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.498962 + 2.82975i) q^{17} -0.184793 q^{18} +(3.17997 + 2.98124i) q^{19} +(-0.138535 - 0.785674i) q^{21} +(-4.28662 + 3.59690i) q^{22} +(4.12150 - 1.50010i) q^{23} +(-1.57667 - 0.573861i) q^{24} +(1.23105 - 2.13224i) q^{26} +(2.67181 + 4.62772i) q^{27} +(-0.0825669 + 0.468260i) q^{28} +(1.51505 - 8.59227i) q^{29} +(-2.88192 + 4.99163i) q^{31} +(0.766044 + 0.642788i) q^{32} +(8.82271 + 3.21120i) q^{33} +(-2.70012 + 0.982762i) q^{34} +(-0.0320889 - 0.181985i) q^{36} +6.02691 q^{37} +(-2.38375 + 3.64935i) q^{38} -4.13105 q^{39} +(5.18173 - 4.34799i) q^{41} +(0.749681 - 0.272862i) q^{42} +(0.433776 + 0.157881i) q^{43} +(-4.28662 - 3.59690i) q^{44} +(2.19300 + 3.79839i) q^{46} +(0.456851 - 2.59093i) q^{47} +(0.291357 - 1.65237i) q^{48} +(3.38696 + 5.86638i) q^{49} +(3.69323 + 3.09899i) q^{51} +(2.31362 + 0.842088i) q^{52} +(-7.43135 + 2.70479i) q^{53} +(-4.09346 + 3.43482i) q^{54} -0.475484 q^{56} +(7.30255 + 0.402213i) q^{57} +8.72482 q^{58} +(-1.42203 - 8.06471i) q^{59} +(-2.98996 + 1.08826i) q^{61} +(-5.41624 - 1.97135i) q^{62} +(0.0673091 + 0.0564791i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.63037 + 9.24629i) q^{66} +(-0.0262550 + 0.148899i) q^{67} +(-1.43670 - 2.48844i) q^{68} +(3.67955 - 6.37316i) q^{69} +(-4.48601 - 1.63277i) q^{71} +(0.173648 - 0.0632028i) q^{72} +(-7.04620 + 5.91246i) q^{73} +(1.04656 + 5.93535i) q^{74} +(-4.00784 - 1.71384i) q^{76} +2.66070 q^{77} +(-0.717350 - 4.06829i) q^{78} +(9.48725 - 7.96075i) q^{79} +(7.90420 + 2.87689i) q^{81} +(5.18173 + 4.34799i) q^{82} +(-6.59560 + 11.4239i) q^{83} +(0.398897 + 0.690910i) q^{84} +(-0.0801585 + 0.454602i) q^{86} +(-7.31950 - 12.6777i) q^{87} +(2.79789 - 4.84609i) q^{88} +(-1.23909 - 1.03972i) q^{89} +(-1.10009 + 0.400399i) q^{91} +(-3.35987 + 2.81927i) q^{92} +(1.67933 + 9.52398i) q^{93} +2.63090 q^{94} +1.67786 q^{96} +(-0.873563 - 4.95422i) q^{97} +(-5.18912 + 4.35419i) q^{98} +(-0.971697 + 0.353669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.28531	−	1.07851i	0.742076	−	0.622676i	−0.191318	−	0.981528i	$-0.561276\pi$
$3$	1.28531	−	1.07851i	0.742076	−	0.622676i	0.933394	+	0.358852i	$0.116832\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	1.28531	+	1.07851i	0.524727	+	0.440298i
$7$	0.237742	−	0.411781i	0.0898579	−	0.155639i	−0.817593	−	0.575797i	$-0.804692\pi$
$7$	0.237742	−	0.411781i	0.0898579	−	0.155639i	0.907451	+	0.420158i	$0.138025\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.0320889	+	0.181985i	−0.0106963	+	0.0606617i
$10$		0			0
$11$	2.79789	+	4.84609i	0.843596	+	1.46115i	0.886835	+	0.462086i	$0.152899\pi$
$11$	2.79789	+	4.84609i	0.843596	+	1.46115i	−0.0432392	+	0.999065i	$0.513768\pi$
$12$	−0.838929	+	1.45307i	−0.242178	+	0.419465i
$13$	−1.88608	−	1.58261i	−0.523104	−	0.438936i	0.342608	−	0.939478i	$-0.388690\pi$
$13$	−1.88608	−	1.58261i	−0.523104	−	0.438936i	−0.865712	+	0.500542i	$0.833134\pi$
$14$	0.446808	+	0.162625i	0.119415	+	0.0434633i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.498962	+	2.82975i	0.121016	+	0.686316i	0.983595	+	0.180393i	$0.0577369\pi$
$17$	0.498962	+	2.82975i	0.121016	+	0.686316i	−0.862579	+	0.505923i	$0.831152\pi$
$18$	−0.184793			−0.0435560
$19$	3.17997	+	2.98124i	0.729535	+	0.683944i
$19$	3.17997	+	2.98124i	0.729535	+	0.683944i
$20$		0			0
$21$	−0.138535	−	0.785674i	−0.0302309	−	0.171448i
$22$	−4.28662	+	3.59690i	−0.913910	+	0.766862i
$23$	4.12150	−	1.50010i	0.859391	−	0.312793i	0.125528	−	0.992090i	$-0.459938\pi$
$23$	4.12150	−	1.50010i	0.859391	−	0.312793i	0.733863	+	0.679297i	$0.237715\pi$
$24$	−1.57667	−	0.573861i	−0.321837	−	0.117139i
$25$		0			0
$26$	1.23105	−	2.13224i	0.241429	−	0.418167i
$27$	2.67181	+	4.62772i	0.514191	+	0.890605i
$28$	−0.0825669	+	0.468260i	−0.0156037	+	0.0884928i
$29$	1.51505	−	8.59227i	0.281337	−	1.59554i	−0.436745	−	0.899586i	$-0.643869\pi$
$29$	1.51505	−	8.59227i	0.281337	−	1.59554i	0.718082	−	0.695958i	$-0.245020\pi$
$30$		0			0
$31$	−2.88192	+	4.99163i	−0.517608	+	0.896524i	0.482183	+	0.876071i	$0.339844\pi$
$31$	−2.88192	+	4.99163i	−0.517608	+	0.896524i	−0.999791	+	0.0204528i	$0.993489\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	8.82271	+	3.21120i	1.53584	+	0.558999i
$34$	−2.70012	+	0.982762i	−0.463066	+	0.168542i
$35$		0			0
$36$	−0.0320889	−	0.181985i	−0.00534815	−	0.0303309i
$37$	6.02691			0.990819			0.495409	−	0.868660i	$-0.335018\pi$
$37$	6.02691			0.990819			0.495409	+	0.868660i	$0.335018\pi$
$38$	−2.38375	+	3.64935i	−0.386696	+	0.592002i
$39$	−4.13105			−0.661498
$40$		0			0
$41$	5.18173	−	4.34799i	0.809250	−	0.679041i	−0.141179	−	0.989984i	$-0.545089\pi$
$41$	5.18173	−	4.34799i	0.809250	−	0.679041i	0.950429	+	0.310943i	$0.100645\pi$
$42$	0.749681	−	0.272862i	0.115678	−	0.0421035i
$43$	0.433776	+	0.157881i	0.0661502	+	0.0240767i	0.374883	−	0.927072i	$-0.377683\pi$
$43$	0.433776	+	0.157881i	0.0661502	+	0.0240767i	−0.308733	+	0.951149i	$0.599905\pi$
$44$	−4.28662	−	3.59690i	−0.646232	−	0.542253i
$45$		0			0
$46$	2.19300	+	3.79839i	0.323340	+	0.560042i
$47$	0.456851	−	2.59093i	0.0666386	−	0.377926i	−0.933190	−	0.359385i	$-0.882987\pi$
$47$	0.456851	−	2.59093i	0.0666386	−	0.377926i	0.999828	−	0.0185414i	$-0.00590226\pi$
$48$	0.291357	−	1.65237i	0.0420538	−	0.238499i
$49$	3.38696	+	5.86638i	0.483851	+	0.838055i
$50$		0			0
$51$	3.69323	+	3.09899i	0.517155	+	0.433945i
$52$	2.31362	+	0.842088i	0.320841	+	0.116777i
$53$	−7.43135	+	2.70479i	−1.02077	+	0.371531i	−0.797561	−	0.603238i	$-0.793877\pi$
$53$	−7.43135	+	2.70479i	−1.02077	+	0.371531i	−0.223213	+	0.974770i	$0.571655\pi$
$54$	−4.09346	+	3.43482i	−0.557049	+	0.467420i
$55$		0			0
$56$	−0.475484			−0.0635392
$57$	7.30255	+	0.402213i	0.967246	+	0.0532744i
$58$	8.72482			1.14562
$59$	−1.42203	−	8.06471i	−0.185132	−	1.04994i	−0.925786	−	0.378049i	$-0.876595\pi$
$59$	−1.42203	−	8.06471i	−0.185132	−	1.04994i	0.740653	−	0.671887i	$-0.234516\pi$
$60$		0			0
$61$	−2.98996	+	1.08826i	−0.382825	+	0.139337i	−0.526262	−	0.850323i	$-0.676407\pi$
$61$	−2.98996	+	1.08826i	−0.382825	+	0.139337i	0.143437	+	0.989659i	$0.454185\pi$
$62$	−5.41624	−	1.97135i	−0.687863	−	0.250362i
$63$	0.0673091	+	0.0564791i	0.00848015	+	0.00711569i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−1.63037	+	9.24629i	−0.200685	+	1.13814i
$67$	−0.0262550	+	0.148899i	−0.00320756	+	0.0181910i	−0.986370	−	0.164545i	$-0.947384\pi$
$67$	−0.0262550	+	0.148899i	−0.00320756	+	0.0181910i	0.983162	+	0.182736i	$0.0584954\pi$
$68$	−1.43670	−	2.48844i	−0.174226	−	0.301768i
$69$	3.67955	−	6.37316i	0.442965	−	0.767238i
$70$		0			0
$71$	−4.48601	−	1.63277i	−0.532392	−	0.193775i	0.0618143	−	0.998088i	$-0.480311\pi$
$71$	−4.48601	−	1.63277i	−0.532392	−	0.193775i	−0.594206	+	0.804313i	$0.702534\pi$
$72$	0.173648	−	0.0632028i	0.0204646	−	0.00744852i
$73$	−7.04620	+	5.91246i	−0.824695	+	0.692001i	−0.954066	−	0.299595i	$-0.903148\pi$
$73$	−7.04620	+	5.91246i	−0.824695	+	0.692001i	0.129372	+	0.991596i	$0.458704\pi$
$74$	1.04656	+	5.93535i	0.121660	+	0.689971i
$75$		0			0
$76$	−4.00784	−	1.71384i	−0.459731	−	0.196591i
$77$	2.66070			0.303215
$78$	−0.717350	−	4.06829i	−0.0812239	−	0.460643i
$79$	9.48725	−	7.96075i	1.06740	−	0.895654i	0.0725851	−	0.997362i	$-0.476875\pi$
$79$	9.48725	−	7.96075i	1.06740	−	0.895654i	0.994814	+	0.101708i	$0.0324307\pi$
$80$		0			0
$81$	7.90420	+	2.87689i	0.878244	+	0.319655i
$82$	5.18173	+	4.34799i	0.572226	+	0.480155i
$83$	−6.59560	+	11.4239i	−0.723961	+	1.25394i	0.235439	+	0.971889i	$0.424347\pi$
$83$	−6.59560	+	11.4239i	−0.723961	+	1.25394i	−0.959400	+	0.282048i	$0.908986\pi$
$84$	0.398897	+	0.690910i	0.0435232	+	0.0753844i
$85$		0			0
$86$	−0.0801585	+	0.454602i	−0.00864372	+	0.0490209i
$87$	−7.31950	−	12.6777i	−0.784733	−	1.35920i
$88$	2.79789	−	4.84609i	0.298256	−	0.516595i
$89$	−1.23909	−	1.03972i	−0.131343	−	0.110210i	0.574750	−	0.818329i	$-0.305099\pi$
$89$	−1.23909	−	1.03972i	−0.131343	−	0.110210i	−0.706093	+	0.708119i	$0.749544\pi$
$90$		0			0
$91$	−1.10009	+	0.400399i	−0.115320	+	0.0419732i
$92$	−3.35987	+	2.81927i	−0.350291	+	0.293929i
$93$	1.67933	+	9.52398i	0.174139	+	0.987591i
$94$	2.63090			0.271357
$95$		0			0
$96$	1.67786			0.171246
$97$	−0.873563	−	4.95422i	−0.0886969	−	0.503025i	−0.996497	−	0.0836230i	$-0.973351\pi$
$97$	−0.873563	−	4.95422i	−0.0886969	−	0.503025i	0.907801	−	0.419402i	$-0.137760\pi$
$98$	−5.18912	+	4.35419i	−0.524180	+	0.439839i
$99$	−0.971697	+	0.353669i	−0.0976593	+	0.0355451i
$100$		0			0
$101$	4.13640	+	3.47085i	0.411587	+	0.345362i	0.824952	−	0.565203i	$-0.191202\pi$
$101$	4.13640	+	3.47085i	0.411587	+	0.345362i	−0.413365	+	0.910565i	$0.635647\pi$
$102$	−2.41058	+	4.17525i	−0.238683	+	0.413412i
$103$	−6.53114	−	11.3123i	−0.643532	−	1.11463i	−0.984638	−	0.174605i	$-0.944135\pi$
$103$	−6.53114	−	11.3123i	−0.643532	−	1.11463i	0.341107	−	0.940025i	$-0.389198\pi$
$104$	−0.427539	+	2.42469i	−0.0419237	+	0.237761i
$105$		0			0
$106$	−3.95414	−	6.84877i	−0.384060	−	0.665211i
$107$	0.594412	−	1.02955i	0.0574640	−	0.0995305i	−0.835862	−	0.548939i	$-0.815032\pi$
$107$	0.594412	−	1.02955i	0.0574640	−	0.0995305i	0.893326	+	0.449409i	$0.148365\pi$
$108$	−4.09346	−	3.43482i	−0.393893	−	0.330516i
$109$	−10.9101	−	3.97094i	−1.04499	−	0.380347i	−0.238223	−	0.971210i	$-0.576565\pi$
$109$	−10.9101	−	3.97094i	−1.04499	−	0.380347i	−0.806771	+	0.590864i	$0.798787\pi$
$110$		0			0
$111$	7.74648	−	6.50007i	0.735263	−	0.616959i
$112$	−0.0825669	−	0.468260i	−0.00780183	−	0.0442464i
$113$	−12.6577			−1.19074			−0.595369	−	0.803452i	$-0.702994\pi$
$113$	−12.6577			−1.19074			−0.595369	+	0.803452i	$0.702994\pi$
$114$	0.871971	+	7.26145i	0.0816676	+	0.680097i
$115$		0			0
$116$	1.51505	+	8.59227i	0.140669	+	0.797772i
$117$	0.348533	−	0.292454i	0.0322219	−	0.0270374i
$118$	7.69526	−	2.80085i	0.708406	−	0.257839i
$119$	1.28386	+	0.467287i	0.117691	+	0.0428362i
$120$		0			0
$121$	−10.1564	+	17.5914i	−0.923308	+	1.59922i
$122$	−1.59092	−	2.75556i	−0.144035	−	0.249477i
$123$	1.97082	−	11.1771i	0.177703	−	1.00780i
$124$	1.00088	−	5.67627i	0.0898817	−	0.509744i
$125$		0			0
$126$	−0.0439329	+	0.0760940i	−0.00391385	+	0.00677899i
$127$	4.73081	+	3.96962i	0.419791	+	0.352247i	0.828084	−	0.560604i	$-0.189431\pi$
$127$	4.73081	+	3.96962i	0.419791	+	0.352247i	−0.408292	+	0.912851i	$0.633876\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	0.727814	−	0.264903i	0.0640805	−	0.0233234i
$130$		0			0
$131$	−3.39327	−	19.2442i	−0.296471	−	1.68137i	−0.661163	−	0.750243i	$-0.729937\pi$
$131$	−3.39327	−	19.2442i	−0.296471	−	1.68137i	0.364692	−	0.931128i	$-0.381174\pi$
$132$	−9.38893			−0.817201
$133$	1.98363	−	0.600685i	0.172002	−	0.0520860i
$134$	−0.151196			−0.0130614
$135$		0			0
$136$	2.20116	−	1.84699i	0.188748	−	0.158378i
$137$	12.5528	−	4.56885i	1.07246	−	0.390344i	0.255364	−	0.966845i	$-0.417805\pi$
$137$	12.5528	−	4.56885i	1.07246	−	0.390344i	0.817096	+	0.576501i	$0.195582\pi$
$138$	6.91528	+	2.51696i	0.588668	+	0.214258i
$139$	12.8285	+	10.7644i	1.08810	+	0.913021i	0.996568	−	0.0827819i	$-0.0263805\pi$
$139$	12.8285	+	10.7644i	1.08810	+	0.913021i	0.0915279	+	0.995803i	$0.470825\pi$
$140$		0			0
$141$	−2.20714	−	3.82288i	−0.185875	−	0.321944i
$142$	0.828981	−	4.70139i	0.0695666	−	0.394532i
$143$	2.39242	−	13.5681i	0.200064	−	1.13462i
$144$	0.0923963	+	0.160035i	0.00769969	+	0.0133363i
$145$		0			0
$146$	−7.04620	−	5.91246i	−0.583147	−	0.489319i
$147$	10.6802	+	3.88729i	0.880891	+	0.320618i
$148$	−5.66345	+	2.06133i	−0.465533	+	0.169440i
$149$	−10.2016	+	8.56016i	−0.835748	+	0.701276i	−0.956603	−	0.291395i	$-0.905881\pi$
$149$	−10.2016	+	8.56016i	−0.835748	+	0.701276i	0.120855	+	0.992670i	$0.461436\pi$
$150$		0			0
$151$	−13.1191			−1.06762			−0.533810	−	0.845604i	$-0.679240\pi$
$151$	−13.1191			−1.06762			−0.533810	+	0.845604i	$0.679240\pi$
$152$	0.991846	−	4.24455i	0.0804493	−	0.344279i
$153$	−0.530984			−0.0429275
$154$	0.462026	+	2.62028i	0.0372311	+	0.211148i
$155$		0			0
$156$	3.88192	−	1.41290i	0.310802	−	0.113123i
$157$	−5.52322	−	2.01029i	−0.440801	−	0.160438i	0.112079	−	0.993699i	$-0.464249\pi$
$157$	−5.52322	−	2.01029i	−0.440801	−	0.160438i	−0.552880	+	0.833261i	$0.686471\pi$
$158$	9.48725	+	7.96075i	0.754765	+	0.633323i
$159$	−6.63448	+	11.4913i	−0.526149	+	0.911316i
$160$		0			0
$161$	0.362139	−	2.05379i	0.0285405	−	0.161861i
$162$	−1.46064	+	8.28368i	−0.114758	+	0.650828i
$163$	−4.27049	−	7.39670i	−0.334490	−	0.579354i	0.648896	−	0.760877i	$-0.275231\pi$
$163$	−4.27049	−	7.39670i	−0.334490	−	0.579354i	−0.983387	+	0.181522i	$0.941898\pi$
$164$	−3.38213	+	5.85803i	−0.264100	+	0.457435i
$165$		0			0
$166$	−12.3957	−	4.51166i	−0.962091	−	0.350172i
$167$	−18.3978	+	6.69625i	−1.42367	+	0.518172i	−0.935109	−	0.354361i	$-0.884698\pi$
$167$	−18.3978	+	6.69625i	−1.42367	+	0.518172i	−0.488556	+	0.872532i	$0.662476\pi$
$168$	−0.611146	+	0.512812i	−0.0471509	+	0.0395643i
$169$	−1.20478	−	6.83266i	−0.0926756	−	0.525589i
$170$		0			0
$171$	−0.644583	+	0.483042i	−0.0492925	+	0.0369392i
$172$	−0.461615			−0.0351978
$173$	4.32608	+	24.5344i	0.328906	+	1.86532i	0.480669	+	0.876902i	$0.340394\pi$
$173$	4.32608	+	24.5344i	0.328906	+	1.86532i	−0.151763	+	0.988417i	$0.548495\pi$
$174$	11.2141	−	9.40977i	0.850141	−	0.713353i
$175$		0			0
$176$	5.25832	+	1.91387i	0.396360	+	0.144263i
$177$	−10.5256	−	8.83202i	−0.791152	−	0.663855i
$178$	0.808758	−	1.40081i	0.0606189	−	0.104995i
$179$	−0.0206472	−	0.0357621i	−0.00154325	−	0.00267298i	0.865253	−	0.501336i	$-0.167158\pi$
$179$	−0.0206472	−	0.0357621i	−0.00154325	−	0.00267298i	−0.866796	+	0.498663i	$0.833825\pi$
$180$		0			0
$181$	2.23778	−	12.6911i	0.166333	−	0.943321i	−0.781346	−	0.624098i	$-0.785467\pi$
$181$	2.23778	−	12.6911i	0.166333	−	0.943321i	0.947679	−	0.319224i	$-0.103422\pi$
$182$	−0.585344	−	1.01385i	−0.0433886	−	0.0751512i
$183$	−2.66934	+	4.62344i	−0.197324	+	0.341774i
$184$	−3.35987	−	2.81927i	−0.247693	−	0.207839i
$185$		0			0
$186$	−9.08768	+	3.30764i	−0.666341	+	0.242528i
$187$	−12.3172	+	10.3353i	−0.900722	+	0.755796i
$188$	0.456851	+	2.59093i	0.0333193	+	0.188963i
$189$	2.54081			0.184817
$190$		0			0
$191$	−17.4110			−1.25982			−0.629909	−	0.776669i	$-0.716908\pi$
$191$	−17.4110			−1.25982			−0.629909	+	0.776669i	$0.716908\pi$
$192$	0.291357	+	1.65237i	0.0210269	+	0.119249i
$193$	16.9959	−	14.2613i	1.22339	−	1.02655i	0.224752	−	0.974416i	$-0.427843\pi$
$193$	16.9959	−	14.2613i	1.22339	−	1.02655i	0.998640	−	0.0521318i	$-0.0166016\pi$
$194$	4.72726	−	1.72058i	0.339398	−	0.123531i
$195$		0			0
$196$	−5.18912	−	4.35419i	−0.370651	−	0.311013i
$197$	2.48552	−	4.30504i	0.177086	−	0.306721i	−0.763795	−	0.645458i	$-0.776666\pi$
$197$	2.48552	−	4.30504i	0.177086	−	0.306721i	0.940881	+	0.338737i	$0.110000\pi$
$198$	−0.517029	−	0.895521i	−0.0367437	−	0.0636419i
$199$	1.43717	−	8.15057i	0.101878	−	0.577779i	−0.890543	−	0.454898i	$-0.849676\pi$
$199$	1.43717	−	8.15057i	0.101878	−	0.577779i	0.992421	−	0.122881i	$-0.0392132\pi$
$200$		0			0
$201$	0.126843	+	0.219699i	0.00894682	+	0.0154963i
$202$	−2.69984	+	4.67626i	−0.189960	+	0.329021i
$203$	−3.17794	−	2.66661i	−0.223048	−	0.187159i
$204$	−4.53041	−	1.64894i	−0.317192	−	0.115449i
$205$		0			0
$206$	10.0063	−	8.39627i	0.697171	−	0.584996i
$207$	0.140742	+	0.798187i	0.00978224	+	0.0554779i
$208$	−2.46210			−0.170716
$209$	−5.55015	+	23.7516i	−0.383912	+	1.64293i
$210$		0			0
$211$	−2.81533	−	15.9665i	−0.193815	−	1.09918i	−0.914096	−	0.405499i	$-0.867098\pi$
$211$	−2.81533	−	15.9665i	−0.193815	−	1.09918i	0.720280	−	0.693683i	$-0.244013\pi$
$212$	6.05809	−	5.08334i	0.416071	−	0.349125i
$213$	−7.52689	+	2.73956i	−0.515734	+	0.187712i
$214$	1.11713	+	0.406602i	0.0763654	+	0.0277947i
$215$		0			0
$216$	2.67181	−	4.62772i	0.181794	−	0.314876i
$217$	1.37031	+	2.37344i	0.0930224	+	0.161120i
$218$	2.01610	−	11.4339i	0.136547	−	0.774399i
$219$	−2.67995	+	15.1987i	−0.181094	+	1.02704i
$220$		0			0
$221$	3.53730	−	6.12679i	0.237945	−	0.412133i
$222$	7.74648	+	6.50007i	0.519909	+	0.436256i
$223$	22.3444	+	8.13268i	1.49629	+	0.544605i	0.955097	−	0.296294i	$-0.0957509\pi$
$223$	22.3444	+	8.13268i	1.49629	+	0.544605i	0.541192	+	0.840899i	$0.317973\pi$
$224$	0.446808	−	0.162625i	0.0298536	−	0.0108658i
$225$		0			0
$226$	−2.19799	−	12.4654i	−0.146208	−	0.829187i
$227$	1.49007			0.0988996			0.0494498	−	0.998777i	$-0.484253\pi$
$227$	1.49007			0.0988996			0.0494498	+	0.998777i	$0.484253\pi$
$228$	−6.99971	+	2.11966i	−0.463567	+	0.140378i
$229$	17.9170			1.18399			0.591995	−	0.805942i	$-0.298341\pi$
$229$	17.9170			1.18399			0.591995	+	0.805942i	$0.298341\pi$
$230$		0			0
$231$	3.41984	−	2.86958i	0.225009	−	0.188805i
$232$	−8.19865	+	2.98406i	−0.538267	+	0.195913i
$233$	−18.6245	−	6.77876i	−1.22013	−	0.444091i	−0.349924	−	0.936778i	$-0.613793\pi$
$233$	−18.6245	−	6.77876i	−1.22013	−	0.444091i	−0.870207	+	0.492687i	$0.836015\pi$
$234$	0.348533	+	0.292454i	0.0227843	+	0.0191183i
$235$		0			0
$236$	4.09456	+	7.09199i	0.266533	+	0.461649i
$237$	3.60838	−	20.4641i	0.234389	−	1.32929i
$238$	−0.237248	+	1.34550i	−0.0153785	+	0.0872158i
$239$	−12.6431	−	21.8985i	−0.817816	−	1.41650i	−0.907288	−	0.420510i	$-0.861851\pi$
$239$	−12.6431	−	21.8985i	−0.817816	−	1.41650i	0.0894720	−	0.995989i	$-0.471482\pi$
$240$		0			0
$241$	6.91515	+	5.80250i	0.445444	+	0.373772i	0.837742	−	0.546066i	$-0.183875\pi$
$241$	6.91515	+	5.80250i	0.445444	+	0.373772i	−0.392298	+	0.919838i	$0.628320\pi$
$242$	−19.0878	−	6.94738i	−1.22701	−	0.446594i
$243$	−1.80198	+	0.655868i	−0.115597	+	0.0420740i
$244$	2.43744	−	2.04525i	0.156041	−	0.130934i
$245$		0			0
$246$	11.3495			0.723616
$247$	−1.27954	−	10.6555i	−0.0814149	−	0.677993i
$248$	5.76384			0.366004
$249$	3.84335	+	21.7967i	0.243562	+	1.38131i
$250$		0			0
$251$	15.9786	−	5.81575i	1.00856	−	0.367087i	0.215682	−	0.976464i	$-0.430802\pi$
$251$	15.9786	−	5.81575i	1.00856	−	0.367087i	0.792881	+	0.609377i	$0.208580\pi$
$252$	−0.0825669	−	0.0300519i	−0.00520122	−	0.00189309i
$253$	18.8011	+	15.7760i	1.18202	+	0.991829i
$254$	−3.08782	+	5.34825i	−0.193747	+	0.335579i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.80992	−	21.6071i	0.237656	−	1.34782i	−0.599291	−	0.800531i	$-0.704551\pi$
$257$	3.80992	−	21.6071i	0.237656	−	1.34782i	0.836947	−	0.547284i	$-0.184338\pi$
$258$	0.387262	+	0.670757i	0.0241099	+	0.0417595i
$259$	1.43285	−	2.48177i	0.0890329	−	0.154210i
$260$		0			0
$261$	1.51505	+	0.551433i	0.0937791	+	0.0341328i
$262$	18.3626	−	6.68343i	1.13444	−	0.412904i
$263$	21.0249	−	17.6420i	1.29645	−	1.08785i	0.305703	−	0.952127i	$-0.401109\pi$
$263$	21.0249	−	17.6420i	1.29645	−	1.08785i	0.990747	−	0.135723i	$-0.0433359\pi$
$264$	−1.63037	−	9.24629i	−0.100342	−	0.569070i
$265$		0			0
$266$	0.936013	+	1.84919i	0.0573906	+	0.113381i
$267$	−2.71396			−0.166092
$268$	−0.0262550	−	0.148899i	−0.00160378	−	0.00909548i
$269$	12.1089	−	10.1606i	0.738291	−	0.619500i	−0.194087	−	0.980984i	$-0.562174\pi$
$269$	12.1089	−	10.1606i	0.738291	−	0.619500i	0.932378	+	0.361484i	$0.117730\pi$
$270$		0			0
$271$	21.6087	+	7.86493i	1.31264	+	0.477760i	0.901091	−	0.433629i	$-0.142767\pi$
$271$	21.6087	+	7.86493i	1.31264	+	0.477760i	0.411544	+	0.911390i	$0.364989\pi$
$272$	2.20116	+	1.84699i	0.133465	+	0.111990i
$273$	−0.982124	+	1.70109i	−0.0594408	+	0.102955i
$274$	6.67922	+	11.5687i	0.403506	+	0.698893i
$275$		0			0
$276$	−1.27789	+	7.24729i	−0.0769201	+	0.436236i
$277$	−2.55383	−	4.42336i	−0.153445	−	0.265774i	0.779047	−	0.626966i	$-0.215703\pi$
$277$	−2.55383	−	4.42336i	−0.153445	−	0.265774i	−0.932492	+	0.361192i	$0.882370\pi$
$278$	−8.37318	+	14.5028i	−0.502190	+	0.869819i
$279$	−0.815925	−	0.684642i	−0.0488482	−	0.0409885i
$280$		0			0
$281$	−27.6841	+	10.0762i	−1.65150	+	0.601095i	−0.988993	−	0.147964i	$-0.952728\pi$
$281$	−27.6841	+	10.0762i	−1.65150	+	0.601095i	−0.662503	+	0.749059i	$0.730506\pi$
$282$	3.38153	−	2.83744i	0.201367	−	0.168967i
$283$	−3.71376	−	21.0618i	−0.220760	−	1.25199i	−0.870627	−	0.491944i	$-0.836286\pi$
$283$	−3.71376	−	21.0618i	−0.220760	−	1.25199i	0.649867	−	0.760048i	$-0.274825\pi$
$284$	4.77391			0.283280
$285$		0			0
$286$	13.7774			0.814673
$287$	−0.558504	−	3.16743i	−0.0329675	−	0.186968i
$288$	−0.141559	+	0.118782i	−0.00834146	+	0.00699932i
$289$	8.21624	−	2.99047i	0.483308	−	0.175910i
$290$		0			0
$291$	−6.46596	−	5.42559i	−0.379042	−	0.318054i
$292$	4.59908	−	7.96584i	0.269141	−	0.466165i
$293$	−9.90800	−	17.1612i	−0.578831	−	1.00257i	−0.995614	−	0.0935590i	$-0.970176\pi$
$293$	−9.90800	−	17.1612i	−0.578831	−	1.00257i	0.416782	−	0.909006i	$-0.363158\pi$
$294$	−1.97363	+	11.1930i	−0.115104	+	0.652789i
$295$		0			0
$296$	−3.01346	−	5.21946i	−0.175154	−	0.303375i
$297$	−14.9509	+	25.8957i	−0.867539	+	1.50262i
$298$	−10.2016	−	8.56016i	−0.590963	−	0.495877i
$299$	−10.1475	−	3.69340i	−0.586847	−	0.213595i
$300$		0			0
$301$	0.168139	−	0.141086i	0.00969138	−	0.00813203i
$302$	−2.27811	−	12.9198i	−0.131091	−	0.743452i
$303$	9.05990			0.520478
$304$	4.35230	+	0.239718i	0.249622	+	0.0137488i
$305$		0			0
$306$	−0.0922044	−	0.522917i	−0.00527097	−	0.0298932i
$307$	3.52240	−	2.95565i	0.201034	−	0.168688i	−0.536713	−	0.843765i	$-0.680334\pi$
$307$	3.52240	−	2.95565i	0.201034	−	0.168688i	0.737747	+	0.675077i	$0.235890\pi$
$308$	−2.50024	+	0.910014i	−0.142465	+	0.0518528i
$309$	−20.5949	−	7.49593i	−1.17160	−	0.426429i
$310$		0			0
$311$	7.18969	−	12.4529i	0.407690	−	0.706140i	−0.586940	−	0.809630i	$-0.699668\pi$
$311$	7.18969	−	12.4529i	0.407690	−	0.706140i	0.994630	+	0.103490i	$0.0330011\pi$
$312$	2.06553	+	3.57760i	0.116937	+	0.202542i
$313$	−2.62811	+	14.9047i	−0.148550	+	0.842466i	0.815899	+	0.578195i	$0.196243\pi$
$313$	−2.62811	+	14.9047i	−0.148550	+	0.842466i	−0.964448	+	0.264271i	$0.914869\pi$
$314$	1.02065	−	5.78839i	0.0575986	−	0.326658i
$315$		0			0
$316$	−6.19236	+	10.7255i	−0.348348	+	0.603356i
$317$	1.09244	+	0.916667i	0.0613576	+	0.0514851i	0.672951	−	0.739687i	$-0.265027\pi$
$317$	1.09244	+	0.916667i	0.0613576	+	0.0514851i	−0.611593	+	0.791172i	$0.709471\pi$
$318$	−12.4687	−	4.53825i	−0.699213	−	0.254493i
$319$	45.8778	−	16.6982i	2.56867	−	0.934918i
$320$		0			0
$321$	−0.346372	−	1.96437i	−0.0193326	−	0.109641i
$322$	2.08547			0.116219
$323$	−6.84949	+	10.4860i	−0.381116	+	0.583459i
$324$	−8.41147			−0.467304
$325$		0			0
$326$	6.54277	−	5.49003i	0.362370	−	0.304065i
$327$	−18.3055	+	6.66267i	−1.01230	+	0.368446i
$328$	−6.35633	−	2.31352i	−0.350970	−	0.127743i
$329$	−0.958283	−	0.804095i	−0.0528318	−	0.0443312i
$330$		0			0
$331$	−2.41089	−	4.17579i	−0.132515	−	0.229522i	0.792131	−	0.610352i	$-0.208972\pi$
$331$	−2.41089	−	4.17579i	−0.132515	−	0.229522i	−0.924645	+	0.380829i	$0.875638\pi$
$332$	2.29063	−	12.9908i	0.125715	−	0.712963i
$333$	−0.193397	+	1.09681i	−0.0105981	+	0.0601048i
$334$	−9.78927	−	16.9555i	−0.535645	−	0.927764i
$335$		0			0
$336$	−0.611146	−	0.512812i	−0.0333407	−	0.0279762i
$337$	−20.3231	−	7.39701i	−1.10707	−	0.402941i	−0.277152	−	0.960826i	$-0.589391\pi$
$337$	−20.3231	−	7.39701i	−1.10707	−	0.402941i	−0.829918	+	0.557885i	$0.811613\pi$
$338$	6.51965	−	2.37296i	0.354622	−	0.129072i
$339$	−16.2691	+	13.6514i	−0.883618	+	0.741444i
$340$		0			0
$341$	−32.2532			−1.74661
$342$	−0.587635	−	0.550911i	−0.0317756	−	0.0297899i
$343$	6.54927			0.353627
$344$	−0.0801585	−	0.454602i	−0.00432186	−	0.0245105i
$345$		0			0
$346$	−23.4105	+	8.52072i	−1.25856	+	0.458077i
$347$	−15.5263	−	5.65111i	−0.833496	−	0.303368i	−0.110203	−	0.993909i	$-0.535150\pi$
$347$	−15.5263	−	5.65111i	−0.833496	−	0.303368i	−0.723293	+	0.690542i	$0.757372\pi$
$348$	11.2141	+	9.40977i	0.601140	+	0.504417i
$349$	−3.82195	+	6.61982i	−0.204584	+	0.354351i	−0.950000	−	0.312249i	$-0.898918\pi$
$349$	−3.82195	+	6.61982i	−0.204584	+	0.354351i	0.745416	+	0.666600i	$0.232251\pi$
$350$		0			0
$351$	2.28461	−	12.9567i	0.121943	−	0.691576i
$352$	−0.971697	+	5.51077i	−0.0517916	+	0.293725i
$353$	−4.85621	−	8.41121i	−0.258470	−	0.447684i	0.707362	−	0.706851i	$-0.249885\pi$
$353$	−4.85621	−	8.41121i	−0.258470	−	0.447684i	−0.965832	+	0.259168i	$0.916552\pi$
$354$	6.87009	−	11.8994i	0.365141	−	0.632443i
$355$		0			0
$356$	1.51997	+	0.553223i	0.0805581	+	0.0293208i
$357$	2.15414	−	0.784042i	0.114009	−	0.0414959i
$358$	0.0316334	−	0.0265436i	0.00167188	−	0.00140287i
$359$	−0.602693	−	3.41804i	−0.0318089	−	0.180397i	0.964764	−	0.263117i	$-0.0847505\pi$
$359$	−0.602693	−	3.41804i	−0.0318089	−	0.180397i	−0.996573	+	0.0827196i	$0.973639\pi$
$360$		0			0
$361$	1.22441	+	18.9605i	0.0644424	+	0.997921i
$362$	12.8869			0.677319
$363$	5.91827	+	33.5642i	0.310629	+	1.76166i
$364$	0.896799	−	0.752504i	0.0470050	−	0.0394419i
$365$		0			0
$366$	−5.01672	−	1.82594i	−0.262228	−	0.0954433i
$367$	21.9465	+	18.4153i	1.14560	+	0.961271i	0.999608	−	0.0280151i	$-0.00891864\pi$
$367$	21.9465	+	18.4153i	1.14560	+	0.961271i	0.145991	+	0.989286i	$0.453363\pi$
$368$	2.19300	−	3.79839i	0.114318	−	0.198005i
$369$	0.624993	+	1.08252i	0.0325358	+	0.0563537i
$370$		0			0
$371$	−0.652962	+	3.70313i	−0.0339001	+	0.192257i
$372$	−4.83545	−	8.37525i	−0.250707	−	0.434236i
$373$	−4.96377	+	8.59750i	−0.257014	+	0.445162i	−0.965441	−	0.260623i	$-0.916072\pi$
$373$	−4.96377	+	8.59750i	−0.257014	+	0.445162i	0.708426	+	0.705785i	$0.249405\pi$
$374$	−12.3172	−	10.3353i	−0.636907	−	0.534428i
$375$		0			0
$376$	−2.47224	+	0.899821i	−0.127496	+	0.0464047i
$377$	−16.4557	+	13.8080i	−0.847511	+	0.711146i
$378$	0.441207	+	2.50221i	0.0226932	+	0.128700i
$379$	6.49171			0.333457			0.166728	−	0.986003i	$-0.446680\pi$
$379$	6.49171			0.333457			0.166728	+	0.986003i	$0.446680\pi$
$380$		0			0
$381$	10.3618			0.530853
$382$	−3.02339	−	17.1465i	−0.154690	−	0.877292i
$383$	7.26922	−	6.09960i	0.371440	−	0.311675i	−0.437891	−	0.899028i	$-0.644274\pi$
$383$	7.26922	−	6.09960i	0.371440	−	0.311675i	0.809331	+	0.587353i	$0.199830\pi$
$384$	−1.57667	+	0.573861i	−0.0804591	+	0.0292847i
$385$		0			0
$386$	16.9959	+	14.2613i	0.865069	+	0.725879i
$387$	−0.0426515	+	0.0738745i	−0.00216810	+	0.00375525i
$388$	2.51532	+	4.35667i	0.127696	+	0.221176i
$389$	2.98830	−	16.9475i	0.151513	−	0.859271i	−0.810393	−	0.585887i	$-0.800746\pi$
$389$	2.98830	−	16.9475i	0.151513	−	0.859271i	0.961905	−	0.273383i	$-0.0881428\pi$
$390$		0			0
$391$	6.30138	+	10.9143i	0.318675	+	0.551961i
$392$	3.38696	−	5.86638i	0.171067	−	0.296297i
$393$	−25.1164	−	21.0751i	−1.26695	−	1.06310i
$394$	4.67124	+	1.70019i	0.235334	+	0.0856545i
$395$		0			0
$396$	0.792135	−	0.664680i	0.0398063	−	0.0334014i
$397$	5.37254	+	30.4692i	0.269640	+	1.52920i	0.755489	+	0.655161i	$0.227399\pi$
$397$	5.37254	+	30.4692i	0.269640	+	1.52920i	−0.485849	+	0.874043i	$0.661490\pi$
$398$	8.27631			0.414854
$399$	1.90174	−	2.91143i	0.0952063	−	0.145754i
$400$		0			0
$401$	3.78096	+	21.4429i	0.188812	+	1.07081i	0.920959	+	0.389659i	$0.127407\pi$
$401$	3.78096	+	21.4429i	0.188812	+	1.07081i	−0.732147	+	0.681147i	$0.761482\pi$
$402$	−0.194335	+	0.163066i	−0.00969254	+	0.00813301i
$403$	13.3353	−	4.85366i	0.664279	−	0.241778i
$404$	−5.07404	−	1.84680i	−0.252443	−	0.0918817i
$405$		0			0
$406$	2.07425	−	3.59271i	0.102943	−	0.178303i
$407$	16.8627	+	29.2070i	0.835851	+	1.44774i
$408$	0.837187	−	4.74792i	0.0414469	−	0.235057i
$409$	−4.32980	+	24.5555i	−0.214095	+	1.21419i	0.668376	+	0.743824i	$0.266990\pi$
$409$	−4.32980	+	24.5555i	−0.214095	+	1.21419i	−0.882471	+	0.470367i	$0.844121\pi$
$410$		0			0
$411$	11.2068	−	19.4107i	0.552790	−	0.957460i
$412$	10.0063	+	8.39627i	0.492974	+	0.413654i
$413$	−3.65897	−	1.33176i	−0.180046	−	0.0655314i
$414$	−0.761621	+	0.277208i	−0.0374317	+	0.0136240i
$415$		0			0
$416$	−0.427539	−	2.42469i	−0.0209618	−	0.118880i
$417$	28.0980			1.37597
$418$	−24.3545	−	1.34141i	−1.19122	−	0.0656106i
$419$	−20.5082			−1.00189			−0.500945	−	0.865479i	$-0.667014\pi$
$419$	−20.5082			−1.00189			−0.500945	+	0.865479i	$0.667014\pi$
$420$		0			0
$421$	−21.5897	+	18.1159i	−1.05222	+	0.882916i	−0.993325	−	0.115348i	$-0.963202\pi$
$421$	−21.5897	+	18.1159i	−1.05222	+	0.882916i	−0.0588935	+	0.998264i	$0.518757\pi$
$422$	15.2351	−	5.54512i	0.741633	−	0.269932i
$423$	0.456851	+	0.166280i	0.0222129	+	0.00808482i
$424$	6.05809	+	5.08334i	0.294207	+	0.246869i
$425$		0			0
$426$	−4.00497	−	6.93682i	−0.194042	−	0.336090i
$427$	−0.262715	+	1.48993i	−0.0127137	+	0.0721028i
$428$	−0.206437	+	1.17076i	−0.00997852	+	0.0565910i
$429$	−11.5582	−	20.0195i	−0.558037	−	0.966548i
$430$		0			0
$431$	4.08645	+	3.42894i	0.196837	+	0.165166i	0.735879	−	0.677113i	$-0.236769\pi$
$431$	4.08645	+	3.42894i	0.196837	+	0.165166i	−0.539042	+	0.842279i	$0.681214\pi$
$432$	5.02137	+	1.82763i	0.241591	+	0.0879318i
$433$	28.8835	−	10.5127i	1.38805	−	0.505210i	0.463443	−	0.886127i	$-0.346614\pi$
$433$	28.8835	−	10.5127i	1.38805	−	0.505210i	0.924609	+	0.380917i	$0.124392\pi$
$434$	−2.09943	+	1.76163i	−0.100776	+	0.0845610i
$435$		0			0
$436$	11.6102			0.556030
$437$	17.5784	+	7.51689i	0.840888	+	0.359582i
$438$	−15.4332			−0.737427
$439$	−1.25836	−	7.13650i	−0.0600581	−	0.340607i	0.939942	−	0.341335i	$-0.110879\pi$
$439$	−1.25836	−	7.13650i	−0.0600581	−	0.340607i	−1.00000		0.000728694i	$0.999768\pi$
$440$		0			0
$441$	−1.17628	+	0.428130i	−0.0560132	+	0.0203872i
$442$	6.64796	+	2.41966i	0.316211	+	0.115091i
$443$	0.217696	+	0.182669i	0.0103431	+	0.00867885i	0.647944	−	0.761688i	$-0.275629\pi$
$443$	0.217696	+	0.182669i	0.0103431	+	0.00867885i	−0.637601	+	0.770366i	$0.720073\pi$
$444$	−5.05615	+	8.75752i	−0.239954	+	0.415613i
$445$		0			0
$446$	−4.12907	+	23.4171i	−0.195517	+	1.10883i
$447$	−3.88007	+	22.0050i	−0.183521	+	1.04080i
$448$	0.237742	+	0.411781i	0.0112322	+	0.0194548i
$449$	−18.8885	+	32.7159i	−0.891405	+	1.54396i	−0.0532142	+	0.998583i	$0.516947\pi$
$449$	−18.8885	+	32.7159i	−0.891405	+	1.54396i	−0.838191	+	0.545376i	$0.816387\pi$
$450$		0			0
$451$	35.5686	+	12.9459i	1.67486	+	0.609600i
$452$	11.8944	−	4.32919i	0.559464	−	0.203628i
$453$	−16.8622	+	14.1491i	−0.792256	+	0.664781i
$454$	0.258748	+	1.46744i	0.0121437	+	0.0688702i
$455$		0			0
$456$	−3.30295	−	6.52530i	−0.154675	−	0.305575i
$457$	−4.61342			−0.215807			−0.107903	−	0.994161i	$-0.534414\pi$
$457$	−4.61342			−0.215807			−0.107903	+	0.994161i	$0.534414\pi$
$458$	3.11126	+	17.6448i	0.145379	+	0.824488i
$459$	−11.7622	+	9.86963i	−0.549011	+	0.460675i
$460$		0			0
$461$	22.5856	+	8.22050i	1.05192	+	0.382867i	0.809386	−	0.587277i	$-0.199800\pi$
$461$	22.5856	+	8.22050i	1.05192	+	0.382867i	0.242531	+	0.970144i	$0.422022\pi$
$462$	3.41984	+	2.86958i	0.159105	+	0.133505i
$463$	−17.2972	+	29.9596i	−0.803869	+	1.39234i	0.113183	+	0.993574i	$0.463895\pi$
$463$	−17.2972	+	29.9596i	−0.803869	+	1.39234i	−0.917052	+	0.398768i	$0.869438\pi$
$464$	−4.36241	−	7.55591i	−0.202520	−	0.350774i
$465$		0			0
$466$	3.44167	−	19.5187i	0.159432	−	0.904184i
$467$	18.2440	+	31.5995i	0.844232	+	1.46225i	0.886287	+	0.463137i	$0.153276\pi$
$467$	18.2440	+	31.5995i	0.844232	+	1.46225i	−0.0420547	+	0.999115i	$0.513390\pi$
$468$	−0.227489	+	0.394022i	−0.0105157	+	0.0182137i
$469$	0.0550720	+	0.0462109i	0.00254299	+	0.00213382i
$470$		0			0
$471$	−9.26717	+	3.37297i	−0.427009	+	0.155418i
$472$	−6.27323	+	5.26387i	−0.288749	+	0.242289i
$473$	0.448550	+	2.54385i	0.0206243	+	0.116966i
$474$	20.7798			0.954449
$475$		0			0
$476$	−1.36626			−0.0626223
$477$	−0.253768	−	1.43919i	−0.0116192	−	0.0658959i
$478$	19.3704	−	16.2537i	0.885981	−	0.743427i
$479$	−8.32833	+	3.03127i	−0.380531	+	0.138502i	−0.525202	−	0.850978i	$-0.676010\pi$
$479$	−8.32833	+	3.03127i	−0.380531	+	0.138502i	0.144670	+	0.989480i	$0.453788\pi$
$480$		0			0
$481$	−11.3672	−	9.53824i	−0.518301	−	0.434906i
$482$	−4.51354	+	7.81768i	−0.205586	+	0.356086i
$483$	−1.74956	−	3.03033i	−0.0796079	−	0.137885i
$484$	3.52728	−	20.0042i	0.160331	−	0.909281i
$485$		0			0
$486$	−0.958815	−	1.66072i	−0.0434927	−	0.0753316i
$487$	4.48323	−	7.76519i	0.203155	−	0.351874i	−0.746389	−	0.665510i	$-0.768214\pi$
$487$	4.48323	−	7.76519i	0.203155	−	0.351874i	0.949543	+	0.313636i	$0.101547\pi$
$488$	2.43744	+	2.04525i	0.110338	+	0.0925842i
$489$	−13.4663	−	4.90134i	−0.608967	−	0.221646i
$490$		0			0
$491$	−24.0360	+	20.1686i	−1.08473	+	0.910195i	−0.996305	−	0.0858884i	$-0.972627\pi$
$491$	−24.0360	+	20.1686i	−1.08473	+	0.910195i	−0.0884230	+	0.996083i	$0.528183\pi$
$492$	1.97082	+	11.1771i	0.0888513	+	0.503900i
$493$	25.0699			1.12909
$494$	10.2714	−	3.11040i	0.462133	−	0.139944i
$495$		0			0
$496$	1.00088	+	5.67627i	0.0449409	+	0.254872i
$497$	−1.73886	+	1.45907i	−0.0779984	+	0.0654484i
$498$	−20.7982	+	7.56992i	−0.931989	+	0.339216i
$499$	−22.0882	−	8.03943i	−0.988802	−	0.359894i	−0.203546	−	0.979065i	$-0.565246\pi$
$499$	−22.0882	−	8.03943i	−0.988802	−	0.359894i	−0.785256	+	0.619171i	$0.787469\pi$
$500$		0			0
$501$	−16.4250	+	28.4489i	−0.733815	+	1.27100i
$502$	8.50206	+	14.7260i	0.379466	+	0.657254i
$503$	3.20180	−	18.1583i	0.142761	−	0.809639i	−0.826376	−	0.563118i	$-0.809602\pi$
$503$	3.20180	−	18.1583i	0.142761	−	0.809639i	0.969138	−	0.246521i	$-0.0792873\pi$
$504$	0.0152577	−	0.0865309i	0.000679634	−	0.00385439i
$505$		0			0
$506$	−12.2716	+	21.2550i	−0.545537	+	0.944898i
$507$	−8.91759	−	7.48275i	−0.396044	−	0.332321i
$508$	−5.80319	−	2.11219i	−0.257475	−	0.0937133i
$509$	17.0220	−	6.19551i	0.754488	−	0.274611i	0.0639951	−	0.997950i	$-0.479616\pi$
$509$	17.0220	−	6.19551i	0.754488	−	0.274611i	0.690493	+	0.723339i	$0.257394\pi$
$510$		0			0
$511$	0.759463	+	4.30713i	0.0335967	+	0.190536i
$512$	1.00000			0.0441942
$513$	−5.30006	+	22.6813i	−0.234003	+	1.00141i
$514$	21.9405			0.967752
$515$		0			0
$516$	−0.593319	+	0.497854i	−0.0261194	+	0.0219168i
$517$	13.8341	−	5.03520i	0.608423	−	0.221448i
$518$	2.69288	+	0.980127i	0.118318	+	0.0430643i
$519$	32.0209	+	26.8687i	1.40556	+	1.17941i
$520$		0			0
$521$	−2.01668	−	3.49299i	−0.0883524	−	0.153031i	0.818462	−	0.574560i	$-0.194827\pi$
$521$	−2.01668	−	3.49299i	−0.0883524	−	0.153031i	−0.906815	+	0.421529i	$0.861494\pi$
$522$	−0.279970	+	1.58779i	−0.0122539	+	0.0694955i
$523$	2.15741	−	12.2353i	0.0943371	−	0.535012i	−0.900611	−	0.434625i	$-0.856881\pi$
$523$	2.15741	−	12.2353i	0.0943371	−	0.535012i	0.994948	−	0.100387i	$-0.0320081\pi$
$524$	9.77052	+	16.9230i	0.426827	+	0.739286i
$525$		0			0
$526$	21.0249	+	17.6420i	0.916728	+	0.769226i
$527$	−15.5630	−	5.66448i	−0.677937	−	0.246749i
$528$	8.82271	−	3.21120i	0.383959	−	0.139750i
$529$	−2.88261	+	2.41879i	−0.125331	+	0.105165i
$530$		0			0
$531$	1.51329			0.0656712
$532$	−1.65856	+	1.24290i	−0.0719075	+	0.0538866i
$533$	−16.6543			−0.721378
$534$	−0.471274	−	2.67273i	−0.0203940	−	0.115660i
$535$		0			0
$536$	0.142078	−	0.0517122i	0.00613684	−	0.00223363i
$537$	−0.0651078	−	0.0236973i	−0.00280961	−	0.00102261i
$538$	12.1089	+	10.1606i	0.522051	+	0.438053i
$539$	−18.9527	+	32.8270i	−0.816350	+	1.41396i
$540$		0			0
$541$	−0.859303	+	4.87335i	−0.0369443	+	0.209522i	−0.997692	−	0.0679020i	$-0.978369\pi$
$541$	−0.859303	+	4.87335i	−0.0369443	+	0.209522i	0.960748	+	0.277424i	$0.0894806\pi$
$542$	−3.99313	+	22.6462i	−0.171520	+	0.972736i
$543$	−10.8112	−	18.7255i	−0.463952	−	0.803588i
$544$	−1.43670	+	2.48844i	−0.0615981	+	0.106691i
$545$		0			0
$546$	−1.84579	−	0.671812i	−0.0789925	−	0.0287509i
$547$	−21.9471	+	7.98811i	−0.938392	+	0.341547i	−0.765531	−	0.643399i	$-0.777524\pi$
$547$	−21.9471	+	7.98811i	−0.938392	+	0.341547i	−0.172861	+	0.984946i	$0.555301\pi$
$548$	−10.2332	+	8.58664i	−0.437139	+	0.366803i
$549$	−0.102102	−	0.579049i	−0.00435760	−	0.0247132i
$550$		0			0
$551$	30.4334	−	22.8064i	1.29651	−	0.971586i
$552$	−7.35909			−0.313224
$553$	−1.02257	−	5.79927i	−0.0434840	−	0.246610i
$554$	3.91269	−	3.28314i	0.166234	−	0.139487i
$555$		0			0
$556$	−15.7364	−	5.72759i	−0.667373	−	0.242904i
$557$	−24.9853	−	20.9651i	−1.05866	−	0.888321i	−0.0646825	−	0.997906i	$-0.520603\pi$
$557$	−24.9853	−	20.9651i	−1.05866	−	0.888321i	−0.993977	+	0.109585i	$0.965048\pi$
$558$	0.532557	−	0.922416i	0.0225449	−	0.0390490i
$559$	−0.568270	−	0.984273i	−0.0240353	−	0.0416303i
$560$		0			0
$561$	−4.68471	+	26.5683i	−0.197789	+	1.12172i
$562$	−14.7304	−	25.5138i	−0.621365	−	1.07624i
$563$	9.64564	−	16.7067i	0.406515	−	0.704105i	−0.587981	−	0.808875i	$-0.700077\pi$
$563$	9.64564	−	16.7067i	0.406515	−	0.704105i	0.994497	+	0.104769i	$0.0334105\pi$
$564$	3.38153	+	2.83744i	0.142388	+	0.119478i
$565$		0			0
$566$	20.0969	−	7.31468i	0.844736	−	0.307459i
$567$	3.06381	−	2.57084i	0.128668	−	0.107965i
$568$	0.828981	+	4.70139i	0.0347833	+	0.197266i
$569$	7.98732			0.334846			0.167423	−	0.985885i	$-0.446455\pi$
$569$	7.98732			0.334846			0.167423	+	0.985885i	$0.446455\pi$
$570$		0			0
$571$	20.2098			0.845756			0.422878	−	0.906187i	$-0.361020\pi$
$571$	20.2098			0.845756			0.422878	+	0.906187i	$0.361020\pi$
$572$	2.39242	+	13.5681i	0.100032	+	0.567309i
$573$	−22.3786	+	18.7779i	−0.934881	+	0.784458i
$574$	3.02233	−	1.10004i	0.126150	−	0.0459147i
$575$		0			0
$576$	−0.141559	−	0.118782i	−0.00589830	−	0.00494926i
$577$	−12.3892	+	21.4587i	−0.515769	+	0.893338i	0.484063	+	0.875033i	$0.339160\pi$
$577$	−12.3892	+	21.4587i	−0.515769	+	0.893338i	−0.999832	+	0.0183054i	$0.994173\pi$
$578$	4.37177	+	7.57213i	0.181842	+	0.314959i
$579$	6.46421	−	36.6604i	0.268644	−	1.52355i
$580$		0			0
$581$	3.13610	+	5.43188i	0.130107	+	0.225353i
$582$	4.22036	−	7.30987i	0.174939	−	0.303004i
$583$	−33.8998	−	28.4453i	−1.40398	−	1.17808i
$584$	8.64344	+	3.14595i	0.357668	+	0.130181i
$585$		0			0
$586$	15.1799	−	12.7375i	0.627077	−	0.526180i
$587$	−6.54499	−	37.1185i	−0.270141	−	1.53204i	−0.753986	−	0.656890i	$-0.771871\pi$
$587$	−6.54499	−	37.1185i	−0.270141	−	1.53204i	0.483846	−	0.875153i	$-0.339240\pi$
$588$	−11.3657			−0.468712
$589$	−24.0457	+	7.28154i	−0.990785	+	0.300031i
$590$		0			0
$591$	−1.44834	−	8.21397i	−0.0595769	−	0.337878i
$592$	4.61688	−	3.87403i	0.189753	−	0.159221i
$593$	24.9353	−	9.07572i	1.02397	−	0.372695i	0.225189	−	0.974315i	$-0.427700\pi$
$593$	24.9353	−	9.07572i	1.02397	−	0.372695i	0.798783	+	0.601620i	$0.205478\pi$
$594$	−28.0985	−	10.2270i	−1.15289	−	0.419619i
$595$		0			0
$596$	6.65862	−	11.5331i	0.272748	−	0.472413i
$597$	−6.94324	−	12.0260i	−0.284168	−	0.492193i
$598$	1.87519	−	10.6347i	0.0766821	−	0.434886i
$599$	0.468352	−	2.65616i	0.0191363	−	0.108528i	−0.973743	−	0.227648i	$-0.926896\pi$
$599$	0.468352	−	2.65616i	0.0191363	−	0.108528i	0.992880	+	0.119121i	$0.0380075\pi$
$600$		0			0
$601$	0.233471	−	0.404383i	0.00952347	−	0.0164951i	−0.861224	−	0.508225i	$-0.830302\pi$
$601$	0.233471	−	0.404383i	0.00952347	−	0.0164951i	0.870748	+	0.491730i	$0.163635\pi$
$602$	0.168139	+	0.141086i	0.00685284	+	0.00575022i
$603$	−0.0262550	−	0.00955603i	−0.00106919	−	0.000389152i
$604$	12.3280	−	4.48701i	0.501617	−	0.182574i
$605$		0			0
$606$	1.57324	+	8.92226i	0.0639083	+	0.362442i
$607$	5.91389			0.240038			0.120019	−	0.992772i	$-0.461705\pi$
$607$	5.91389			0.240038			0.120019	+	0.992772i	$0.461705\pi$
$608$	0.519693	+	4.32781i	0.0210763	+	0.175516i
$609$	−6.96061			−0.282058
$610$		0			0
$611$	−4.96208	+	4.16368i	−0.200744	+	0.168444i
$612$	0.498962	−	0.181607i	0.0201693	−	0.00734103i
$613$	34.9761	+	12.7303i	1.41267	+	0.514170i	0.931912	−	0.362683i	$-0.118139\pi$
$613$	34.9761	+	12.7303i	1.41267	+	0.514170i	0.480758	+	0.876853i	$0.340362\pi$
$614$	3.52240	+	2.95565i	0.142153	+	0.119280i
$615$		0			0
$616$	−1.33035	−	2.30424i	−0.0536014	−	0.0928403i
$617$	−7.22223	+	40.9593i	−0.290756	+	1.64896i	0.393212	+	0.919448i	$0.371364\pi$
$617$	−7.22223	+	40.9593i	−0.290756	+	1.64896i	−0.683968	+	0.729512i	$0.739747\pi$
$618$	3.80578	−	21.5837i	0.153091	−	0.868223i
$619$	0.842548	+	1.45934i	0.0338649	+	0.0586557i	0.882461	−	0.470385i	$-0.155885\pi$
$619$	0.842548	+	1.45934i	0.0338649	+	0.0586557i	−0.848596	+	0.529041i	$0.822552\pi$
$620$		0			0
$621$	17.9539	+	15.0651i	0.720466	+	0.604543i
$622$	13.5122	+	4.91804i	0.541790	+	0.197195i
$623$	−0.722719	+	0.263048i	−0.0289551	+	0.0105388i
$624$	−3.16457	+	2.65539i	−0.126684	+	0.106301i
$625$		0			0
$626$	−15.1347			−0.604903
$627$	18.4826	+	36.5141i	0.738123	+	1.45823i
$628$	5.87768			0.234545
$629$	3.00720	+	17.0547i	0.119905	+	0.680014i
$630$		0			0
$631$	6.04729	−	2.20104i	0.240739	−	0.0876218i	−0.218833	−	0.975762i	$-0.570225\pi$
$631$	6.04729	−	2.20104i	0.240739	−	0.0876218i	0.459572	+	0.888140i	$0.348003\pi$
$632$	−11.6378	−	4.23583i	−0.462928	−	0.168492i
$633$	−20.8386	−	17.4857i	−0.828260	−	0.694993i
$634$	−0.713040	+	1.23502i	−0.0283184	+	0.0490490i
$635$		0			0
$636$	2.30413	−	13.0674i	0.0913648	−	0.518155i
$637$	2.89611	−	16.4247i	0.114748	−	0.650769i
$638$	24.4111	+	42.2812i	0.966444	+	1.67393i
$639$	0.441092	−	0.763993i	0.0174493	−	0.0302231i
$640$		0			0
$641$	19.4415	+	7.07614i	0.767894	+	0.279491i	0.696115	−	0.717930i	$-0.254910\pi$
$641$	19.4415	+	7.07614i	0.767894	+	0.279491i	0.0717787	+	0.997421i	$0.477132\pi$
$642$	1.87438	−	0.682220i	0.0739760	−	0.0269251i
$643$	20.3821	−	17.1026i	0.803791	−	0.674460i	−0.145327	−	0.989384i	$-0.546423\pi$
$643$	20.3821	−	17.1026i	0.803791	−	0.674460i	0.949117	+	0.314923i	$0.101979\pi$
$644$	0.362139	+	2.05379i	0.0142703	+	0.0809306i
$645$		0			0
$646$	−11.5161	−	4.92455i	−0.453097	−	0.193754i
$647$	28.0058			1.10102			0.550511	−	0.834828i	$-0.314433\pi$
$647$	28.0058			1.10102			0.550511	+	0.834828i	$0.314433\pi$
$648$	−1.46064	−	8.28368i	−0.0573792	−	0.325414i
$649$	35.1036	−	29.4555i	1.37794	−	1.15623i
$650$		0			0
$651$	4.32104	+	1.57273i	0.169355	+	0.0616402i
$652$	6.54277	+	5.49003i	0.256235	+	0.215006i
$653$	−24.6974	+	42.7772i	−0.966484	+	1.67400i	−0.260910	+	0.965363i	$0.584023\pi$
$653$	−24.6974	+	42.7772i	−0.966484	+	1.67400i	−0.705574	+	0.708636i	$0.749311\pi$
$654$	−9.74017	−	16.8705i	−0.380871	−	0.659688i
$655$		0			0
$656$	1.17460	−	6.66150i	0.0458605	−	0.260088i
$657$	−0.849875	−	1.47203i	−0.0331568	−	0.0574292i
$658$	0.625475	−	1.08335i	0.0243835	−	0.0422335i
$659$	−34.8775	−	29.2657i	−1.35863	−	1.14003i	−0.976401	−	0.215964i	$-0.930711\pi$
$659$	−34.8775	−	29.2657i	−1.35863	−	1.14003i	−0.382233	−	0.924066i	$-0.624845\pi$
$660$		0			0
$661$	−13.0816	+	4.76133i	−0.508817	+	0.185194i	−0.583655	−	0.812002i	$-0.698378\pi$
$661$	−13.0816	+	4.76133i	−0.508817	+	0.185194i	0.0748387	+	0.997196i	$0.476156\pi$
$662$	3.69370	−	3.09938i	0.143560	−	0.120461i
$663$	−2.06124	−	11.6899i	−0.0800518	−	0.453996i
$664$	13.1912			0.511918
$665$		0			0
$666$	−1.11373			−0.0431561
$667$	−6.64501	−	37.6857i	−0.257296	−	1.45920i
$668$	14.9980	−	12.5848i	0.580291	−	0.486922i
$669$	37.4907	−	13.6455i	1.44947	−	0.527565i
$670$		0			0
$671$	−13.6394	−	11.4448i	−0.526542	−	0.441821i
$672$	0.398897	−	0.690910i	0.0153878	−	0.0266524i
$673$	19.5575	+	33.8746i	0.753888	+	1.30577i	0.945925	+	0.324384i	$0.105157\pi$
$673$	19.5575	+	33.8746i	0.753888	+	1.30577i	−0.192038	+	0.981388i	$0.561510\pi$
$674$	3.75556	−	21.2988i	0.144659	−	0.820400i
$675$		0			0
$676$	3.46903	+	6.00854i	0.133424	+	0.231098i
$677$	4.29810	−	7.44452i	0.165189	−	0.286116i	−0.771533	−	0.636189i	$-0.780510\pi$
$677$	4.29810	−	7.44452i	0.165189	−	0.286116i	0.936723	+	0.350073i	$0.113843\pi$
$678$	−16.2691	−	13.6514i	−0.624812	−	0.524280i
$679$	−2.24774	−	0.818109i	−0.0862602	−	0.0313962i
$680$		0			0
$681$	1.91521	−	1.60705i	0.0733911	−	0.0615824i
$682$	−5.60071	−	31.7632i	−0.214462	−	1.21628i
$683$	−5.34403			−0.204484			−0.102242	−	0.994760i	$-0.532602\pi$
$683$	−5.34403			−0.204484			−0.102242	+	0.994760i	$0.532602\pi$
$684$	0.440500	−	0.674372i	0.0168429	−	0.0257852i
$685$		0			0
$686$	1.13727	+	6.44977i	0.0434211	+	0.246253i
$687$	23.0290	−	19.3236i	0.878611	−	0.737242i
$688$	0.433776	−	0.157881i	0.0165375	−	0.00601917i
$689$	18.2967	+	6.65946i	0.697050	+	0.253705i
$690$		0			0
$691$	11.1783	−	19.3614i	0.425243	−	0.736542i	−0.571200	−	0.820811i	$-0.693522\pi$
$691$	11.1783	−	19.3614i	0.425243	−	0.736542i	0.996443	+	0.0842688i	$0.0268554\pi$
$692$	−12.4565	−	21.5752i	−0.473524	−	0.820167i
$693$	−0.0853790	+	0.484208i	−0.00324328	+	0.0183935i
$694$	2.86914	−	16.2717i	0.108911	−	0.617666i
$695$		0			0
$696$	−7.31950	+	12.6777i	−0.277445	+	0.480549i
$697$	14.8892	+	12.4935i	0.563969	+	0.473226i
$698$	−7.18292	−	2.61437i	−0.271878	−	0.0989554i
$699$	−31.2492	+	11.3738i	−1.18195	+	0.430196i
$700$		0			0
$701$	−6.61580	−	37.5201i	−0.249875	−	1.41711i	−0.808892	−	0.587957i	$-0.799933\pi$
$701$	−6.61580	−	37.5201i	−0.249875	−	1.41711i	0.559017	−	0.829156i	$-0.311179\pi$
$702$	13.1565			0.496562
$703$	19.1654	+	17.9677i	0.722837	+	0.677664i
$704$	−5.59578			−0.210899
$705$		0			0
$706$	7.44015	−	6.24303i	0.280014	−	0.234960i
$707$	2.41262	−	0.878123i	0.0907360	−	0.0330252i
$708$	12.9116	+	4.69942i	0.485246	+	0.176615i
$709$	−27.1169	−	22.7538i	−1.01840	−	0.854535i	−0.0289703	−	0.999580i	$-0.509223\pi$
$709$	−27.1169	−	22.7538i	−1.01840	−	0.854535i	−0.989425	+	0.145045i	$0.953667\pi$
$710$		0			0
$711$	1.14430	+	1.98199i	0.0429147	+	0.0743305i
$712$	−0.280879	+	1.59294i	−0.0105264	+	0.0596980i
$713$	−4.38986	+	24.8962i	−0.164402	+	0.932368i
$714$	1.14619	+	1.98526i	0.0428952	+	0.0742966i
$715$		0			0
$716$	0.0316334	+	0.0265436i	0.00118220	+	0.000991980i
$717$	−39.8681	−	14.5108i	−1.48890	−	0.541916i
$718$	3.26146	−	1.18707i	0.121717	−	0.0443012i
$719$	−21.7324	+	18.2357i	−0.810482	+	0.680075i	−0.950723	−	0.310042i	$-0.899657\pi$
$719$	−21.7324	+	18.2357i	−0.810482	+	0.680075i	0.140241	+	0.990117i	$0.455212\pi$
$720$		0			0
$721$	−6.21090			−0.231306
$722$	−18.4598	+	4.49826i	−0.687004	+	0.167408i
$723$	15.1462			0.563292
$724$	2.23778	+	12.6911i	0.0831665	+	0.471661i
$725$		0			0
$726$	−32.0266	+	11.6567i	−1.18862	+	0.432621i
$727$	21.5033	+	7.82658i	0.797515	+	0.290272i	0.708456	−	0.705755i	$-0.249392\pi$
$727$	21.5033	+	7.82658i	0.797515	+	0.290272i	0.0890587	+	0.996026i	$0.471614\pi$
$728$	0.896799	+	0.752504i	0.0332376	+	0.0278896i
$729$	−14.2260	+	24.6401i	−0.526888	+	0.912596i
$730$		0			0
$731$	−0.230328	+	1.30625i	−0.00851898	+	0.0483136i
$732$	0.927053	−	5.25758i	0.0342649	−	0.194326i
$733$	−9.72391	−	16.8423i	−0.359161	−	0.622085i	0.628660	−	0.777680i	$-0.283604\pi$
$733$	−9.72391	−	16.8423i	−0.359161	−	0.622085i	−0.987821	+	0.155595i	$0.950270\pi$
$734$	−14.3246	+	24.8109i	−0.528729	+	0.915786i
$735$		0			0
$736$	4.12150	+	1.50010i	0.151920	+	0.0552945i
$737$	−0.795038	+	0.289370i	−0.0292856	+	0.0106591i
$738$	−0.957545	+	0.803475i	−0.0352477	+	0.0295763i
$739$	2.82258	+	16.0077i	0.103830	+	0.588852i	0.991681	+	0.128720i	$0.0410868\pi$
$739$	2.82258	+	16.0077i	0.103830	+	0.588852i	−0.887851	+	0.460132i	$0.847802\pi$
$740$		0			0
$741$	−13.1366	−	12.3157i	−0.482586	−	0.452427i
$742$	−3.76026			−0.138043
$743$	−4.21706	−	23.9162i	−0.154709	−	0.877398i	−0.959051	−	0.283232i	$-0.908593\pi$
$743$	−4.21706	−	23.9162i	−0.154709	−	0.877398i	0.804342	−	0.594166i	$-0.202518\pi$
$744$	7.40834	−	6.21634i	0.271603	−	0.227902i
$745$		0			0
$746$	−9.32883	−	3.39542i	−0.341553	−	0.124315i
$747$	−1.86734	−	1.56688i	−0.0683223	−	0.0573292i
$748$	8.03947	−	13.9248i	0.293952	−	0.509140i
$749$	−0.282633	−	0.489535i	−0.0103272	−	0.0178872i
$750$		0			0
$751$	−2.31768	+	13.1442i	−0.0845733	+	0.479639i	0.912875	+	0.408240i	$0.133857\pi$
$751$	−2.31768	+	13.1442i	−0.0845733	+	0.479639i	−0.997448	+	0.0713987i	$0.977254\pi$
$752$	−1.31545	−	2.27843i	−0.0479695	−	0.0830856i
$753$	14.2652	−	24.7081i	0.519855	−	0.900415i
$754$	−16.4557	−	13.8080i	−0.599280	−	0.502856i
$755$		0			0
$756$	−2.38758	+	0.869008i	−0.0868354	+	0.0316055i
$757$	7.41565	−	6.22247i	0.269526	−	0.226159i	−0.498000	−	0.867177i	$-0.665932\pi$
$757$	7.41565	−	6.22247i	0.269526	−	0.226159i	0.767526	+	0.641018i	$0.221487\pi$
$758$	1.12727	+	6.39309i	0.0409444	+	0.232207i
$759$	41.1799			1.49473
$760$		0			0
$761$	14.3031			0.518486			0.259243	−	0.965812i	$-0.416527\pi$
$761$	14.3031			0.518486			0.259243	+	0.965812i	$0.416527\pi$
$762$	1.79931	+	10.2044i	0.0651822	+	0.369667i
$763$	−4.22893	+	3.54850i	−0.153098	+	0.128464i
$764$	16.3610	−	5.95492i	0.591921	−	0.215442i
$765$		0			0
$766$	7.26922	+	6.09960i	0.262647	+	0.220387i
$767$	−10.0812	+	17.4612i	−0.364012	+	0.630487i
$768$	−0.838929	−	1.45307i	−0.0302722	−	0.0524331i
$769$	6.79200	−	38.5194i	0.244926	−	1.38904i	−0.575739	−	0.817634i	$-0.695285\pi$
$769$	6.79200	−	38.5194i	0.244926	−	1.38904i	0.820665	−	0.571410i	$-0.193603\pi$
$770$		0			0
$771$	−18.4065	−	31.8810i	−0.662893	−	1.14816i
$772$	−11.0933	+	19.2141i	−0.399256	+	0.691532i
$773$	−6.08567	−	5.10649i	−0.218886	−	0.183668i	0.526751	−	0.850020i	$-0.323410\pi$
$773$	−6.08567	−	5.10649i	−0.218886	−	0.183668i	−0.745637	+	0.666352i	$0.767855\pi$
$774$	−0.0801585	−	0.0291753i	−0.00288124	−	0.00104869i
$775$		0			0
$776$	−3.85370	+	3.23364i	−0.138340	+	0.116081i
$777$	−0.834941	−	4.73519i	−0.0299534	−	0.169874i
$778$	17.2089			0.616969
$779$	29.4401	+	1.62152i	1.05480	+	0.0580969i
$780$		0			0
$781$	−4.63880	−	26.3079i	−0.165989	−	0.941372i
$782$	−9.65428	+	8.10090i	−0.345236	+	0.289688i
$783$	43.8105	−	15.9457i	1.56566	−	0.569854i
$784$	6.36540	+	2.31682i	0.227336	+	0.0827434i
$785$		0			0
$786$	16.3935	−	28.3945i	0.584738	−	1.01280i
$787$	−18.1555	−	31.4462i	−0.647173	−	1.12094i	−0.983795	−	0.179297i	$-0.942618\pi$
$787$	−18.1555	−	31.4462i	−0.647173	−	1.12094i	0.336622	−	0.941640i	$-0.390716\pi$
$788$	−0.863210	+	4.89551i	−0.0307506	+	0.174395i
$789$	7.99659	−	45.3509i	0.284686	−	1.61454i
$790$		0			0
$791$	−3.00927	+	5.21221i	−0.106997	+	0.185325i
$792$	0.792135	+	0.664680i	0.0281473	+	0.0236184i
$793$	7.36157	+	2.67939i	0.261417	+	0.0951480i
$794$	−29.0733	+	10.5818i	−1.03177	+	0.375535i
$795$		0			0
$796$	1.43717	+	8.15057i	0.0509390	+	0.288889i
$797$	−0.408428			−0.0144673			−0.00723363	−	0.999974i	$-0.502303\pi$
$797$	−0.408428			−0.0144673			−0.00723363	+	0.999974i	$0.502303\pi$
$798$	3.19743	+	1.36729i	0.113188	+	0.0484015i
$799$	7.55964			0.267441
$800$		0			0
$801$	0.228974	−	0.192132i	0.00809041	−	0.00678866i
$802$	−20.4605	+	7.44703i	−0.722487	+	0.262964i
$803$	−48.3668	−	17.6041i	−1.70683	−	0.621234i
$804$	−0.194335	−	0.163066i	−0.00685366	−	0.00575090i
$805$		0			0
$806$	7.09557	+	12.2899i	0.249931	+	0.432893i
$807$	4.60548	−	26.1190i	0.162121	−	0.919432i
$808$	0.937645	−	5.31765i	0.0329862	−	0.187074i
$809$	−9.00584	−	15.5986i	−0.316628	−	0.548416i	0.663154	−	0.748483i	$-0.269217\pi$
$809$	−9.00584	−	15.5986i	−0.316628	−	0.548416i	−0.979782	+	0.200067i	$0.935884\pi$
$810$		0			0
$811$	−10.5463	−	8.84937i	−0.370329	−	0.310743i	0.438562	−	0.898701i	$-0.355488\pi$
$811$	−10.5463	−	8.84937i	−0.370329	−	0.310743i	−0.808892	+	0.587957i	$0.799932\pi$
$812$	3.89832	+	1.41887i	0.136804	+	0.0497927i
$813$	36.2564	−	13.1962i	1.27157	−	0.462812i
$814$	−25.8351	+	21.6782i	−0.905519	+	0.759821i
$815$		0			0
$816$	4.82117			0.168775
$817$	0.908711	+	1.79525i	0.0317918	+	0.0628078i
$818$	−24.9343			−0.871807
$819$	−0.0375661	−	0.213048i	−0.00131266	−	0.00744449i
$820$		0			0
$821$	24.0012	−	8.73571i	0.837646	−	0.304878i	0.112653	−	0.993634i	$-0.464065\pi$
$821$	24.0012	−	8.73571i	0.837646	−	0.304878i	0.724993	+	0.688756i	$0.241843\pi$
$822$	21.0619	+	7.66589i	0.734617	+	0.267379i
$823$	5.50144	+	4.61625i	0.191768	+	0.160912i	0.733616	−	0.679564i	$-0.237831\pi$
$823$	5.50144	+	4.61625i	0.191768	+	0.160912i	−0.541848	+	0.840476i	$0.682275\pi$
$824$	−6.53114	+	11.3123i	−0.227523	+	0.394081i
$825$		0			0
$826$	0.676150	−	3.83464i	0.0235263	−	0.133424i
$827$	3.70010	−	20.9843i	0.128665	−	0.729695i	−0.850398	−	0.526139i	$-0.823639\pi$
$827$	3.70010	−	20.9843i	0.128665	−	0.729695i	0.979063	−	0.203556i	$-0.0652499\pi$
$828$	−0.405250	−	0.701914i	−0.0140834	−	0.0243932i
$829$	−11.6453	+	20.1702i	−0.404457	+	0.700540i	−0.994258	−	0.107009i	$-0.965873\pi$
$829$	−11.6453	+	20.1702i	−0.404457	+	0.700540i	0.589801	+	0.807548i	$0.299206\pi$
$830$		0			0
$831$	−8.05309	−	2.93109i	−0.279359	−	0.101678i
$832$	2.31362	−	0.842088i	0.0802102	−	0.0291941i
$833$	−14.9104	+	12.5113i	−0.516616	+	0.433493i
$834$	4.87917	+	27.6711i	0.168952	+	0.958173i
$835$		0			0
$836$	−2.90809	−	24.2175i	−0.100578	−	0.837579i
$837$	−30.7998			−1.06460
$838$	−3.56121	−	20.1966i	−0.123020	−	0.697680i
$839$	−2.17636	+	1.82619i	−0.0751365	+	0.0630470i	−0.679582	−	0.733599i	$-0.737839\pi$
$839$	−2.17636	+	1.82619i	−0.0751365	+	0.0630470i	0.604446	+	0.796646i	$0.293395\pi$
$840$		0			0
$841$	−44.2806	−	16.1168i	−1.52692	−	0.555752i
$842$	−21.5897	−	18.1159i	−0.744031	−	0.624316i
$843$	−24.7155	+	42.8086i	−0.851248	+	1.47441i
$844$	8.10642	+	14.0407i	0.279035	+	0.483302i
$845$		0			0
$846$	−0.0844226	+	0.478785i	−0.00290251	+	0.0164610i
$847$	4.82920	+	8.36441i	0.165933	+	0.287405i
$848$	−3.95414	+	6.84877i	−0.135786	+	0.235188i
$849$	−27.4886	−	23.0657i	−0.943406	−	0.791612i
$850$		0			0
$851$	24.8399	−	9.04098i	0.851501	−	0.309921i
$852$	6.13598	−	5.14870i	0.210215	−	0.176391i
$853$	5.55302	+	31.4927i	0.190132	+	1.07829i	0.919183	+	0.393831i	$0.128851\pi$
$853$	5.55302	+	31.4927i	0.190132	+	1.07829i	−0.729051	+	0.684459i	$0.760038\pi$
$854$	−1.51292			−0.0517709
$855$		0			0
$856$	−1.18882			−0.0406332
$857$	6.03375	+	34.2191i	0.206109	+	1.16890i	0.895685	+	0.444689i	$0.146686\pi$
$857$	6.03375	+	34.2191i	0.206109	+	1.16890i	−0.689576	+	0.724213i	$0.742203\pi$
$858$	17.7082	−	14.8590i	0.604549	−	0.507277i
$859$	45.7819	−	16.6633i	1.56206	−	0.568543i	0.590853	−	0.806780i	$-0.298792\pi$
$859$	45.7819	−	16.6633i	1.56206	−	0.568543i	0.971207	+	0.238236i	$0.0765693\pi$
$860$		0			0
$861$	−4.13395	−	3.46880i	−0.140885	−	0.118216i
$862$	−2.66724	+	4.61980i	−0.0908466	+	0.157351i
$863$	10.3143	+	17.8649i	0.351103	+	0.608128i	0.986443	−	0.164104i	$-0.0524733\pi$
$863$	10.3143	+	17.8649i	0.351103	+	0.608128i	−0.635340	+	0.772233i	$0.719140\pi$
$864$	−0.927912	+	5.26245i	−0.0315682	+	0.179032i
$865$		0			0
$866$	15.3686	+	26.6192i	0.522246	+	0.904557i
$867$	7.33521	−	12.7050i	0.249117	−	0.431483i
$868$	−2.09943	−	1.76163i	−0.0712593	−	0.0597936i
$869$	65.1228	+	23.7028i	2.20914	+	0.804061i
$870$		0			0
$871$	0.285168	−	0.239284i	0.00966255	−	0.00810784i
$872$	2.01610	+	11.4339i	0.0682737	+	0.387199i
$873$	0.929627			0.0314631
$874$	−4.35024	+	18.6166i	−0.147149	+	0.629717i
$875$		0			0
$876$	−2.67995	−	15.1987i	−0.0905470	−	0.513518i
$877$	24.5431	−	20.5941i	0.828760	−	0.695412i	−0.126246	−	0.991999i	$-0.540293\pi$
$877$	24.5431	−	20.5941i	0.828760	−	0.695412i	0.955006	+	0.296587i	$0.0958484\pi$
$878$	6.80957	−	2.47848i	0.229812	−	0.0836447i
$879$	−31.2433	−	11.3716i	−1.05381	−	0.383556i
$880$		0			0
$881$	25.0768	−	43.4343i	0.844860	−	1.46334i	−0.0408828	−	0.999164i	$-0.513017\pi$
$881$	25.0768	−	43.4343i	0.844860	−	1.46334i	0.885743	−	0.464176i	$-0.153650\pi$
$882$	−0.625884	−	1.08406i	−0.0210746	−	0.0365023i
$883$	−4.12538	+	23.3962i	−0.138830	+	0.787344i	0.833286	+	0.552842i	$0.186457\pi$
$883$	−4.12538	+	23.3962i	−0.138830	+	0.787344i	−0.972116	+	0.234501i	$0.924654\pi$
$884$	−1.22849	+	6.96713i	−0.0413187	+	0.234330i
$885$		0			0
$886$	−0.142091	+	0.246109i	−0.00477364	+	0.00826819i
$887$	−16.9333	−	14.2087i	−0.568564	−	0.477082i	0.312605	−	0.949883i	$-0.398798\pi$
$887$	−16.9333	−	14.2087i	−0.568564	−	0.477082i	−0.881169	+	0.472801i	$0.843243\pi$
$888$	−9.50246	−	3.45861i	−0.318882	−	0.116063i
$889$	2.75932	−	1.00431i	0.0925447	−	0.0336835i
$890$		0			0
$891$	8.17341	+	46.3537i	0.273819	+	1.55291i
$892$	−23.7784			−0.796159
$893$	9.17696	−	6.87710i	0.307095	−	0.230133i
$894$	−22.3444			−0.747310
$895$		0			0
$896$	−0.364242	+	0.305635i	−0.0121685	+	0.0102105i
$897$	−17.0261	+	6.19700i	−0.568485	+	0.206912i
$898$	−35.4988	−	12.9205i	−1.18461	−	0.431163i
$899$	38.5232	+	32.3248i	1.28482	+	1.07809i
$900$		0			0
$901$	−11.3618	−	19.6793i	−0.378518	−	0.655612i
$902$	−6.57282	+	37.2763i	−0.218851	+	1.24117i
$903$	0.0639500	−	0.362678i	0.00212812	−	0.0120692i
$904$	6.32886	+	10.9619i	0.210495	+	0.364588i
$905$		0			0
$906$	−16.8622	−	14.1491i	−0.560209	−	0.470071i
$907$	21.1427	+	7.69531i	0.702031	+	0.255518i	0.668278	−	0.743912i	$-0.267032\pi$
$907$	21.1427	+	7.69531i	0.702031	+	0.255518i	0.0337533	+	0.999430i	$0.489254\pi$
$908$	−1.40021	+	0.509635i	−0.0464676	+	0.0169128i
$909$	−0.764375	+	0.641387i	−0.0253527	+	0.0212735i
$910$		0			0
$911$	−9.88173			−0.327396			−0.163698	−	0.986510i	$-0.552342\pi$
$911$	−9.88173			−0.327396			−0.163698	+	0.986510i	$0.552342\pi$
$912$	5.85261	−	4.38587i	0.193799	−	0.145231i
$913$	−73.8151			−2.44292
$914$	−0.801112	−	4.54333i	−0.0264984	−	0.150280i
$915$		0			0
$916$	−16.8365	+	6.12798i	−0.556293	+	0.202474i
$917$	−8.73110	−	3.17786i	−0.288326	−	0.104942i
$918$	−11.7622	−	9.86963i	−0.388209	−	0.325746i
$919$	−10.8786	+	18.8423i	−0.358852	+	0.621549i	−0.987769	−	0.155923i	$-0.950165\pi$
$919$	−10.8786	+	18.8423i	−0.358852	+	0.621549i	0.628918	+	0.777472i	$0.283498\pi$
$920$		0			0
$921$	1.33971	−	7.59787i	0.0441449	−	0.250358i
$922$	−4.17366	+	23.6700i	−0.137452	+	0.779529i
$923$	5.87692	+	10.1791i	0.193441	+	0.335050i
$924$	−2.23214	+	3.86618i	−0.0734320	+	0.127188i
$925$		0			0
$926$	−32.5081	−	11.8320i	−1.06828	−	0.388823i
$927$	2.26824	−	0.825572i	0.0744988	−	0.0271153i
$928$	6.68360	−	5.60820i	0.219400	−	0.184098i
$929$	6.70803	+	38.0432i	0.220083	+	1.24816i	0.871864	+	0.489748i	$0.162911\pi$
$929$	6.70803	+	38.0432i	0.220083	+	1.24816i	−0.651781	+	0.758408i	$0.725978\pi$
$930$		0			0
$931$	−6.71868	+	28.7523i	−0.220196	+	0.942317i
$932$	19.8198			0.649218
$933$	−4.18953	−	23.7600i	−0.137159	−	0.777868i
$934$	−27.9514	+	23.4540i	−0.914599	+	0.767440i
$935$		0			0
$936$	−0.427539	−	0.155611i	−0.0139746	−	0.00508632i
$937$	−14.4425	−	12.1187i	−0.471815	−	0.395899i	0.375641	−	0.926765i	$-0.377422\pi$
$937$	−14.4425	−	12.1187i	−0.471815	−	0.395899i	−0.847456	+	0.530866i	$0.821867\pi$
$938$	−0.0359457	+	0.0622598i	−0.00117367	+	0.00203285i
$939$	12.6969	+	21.9917i	0.414348	+	0.717672i
$940$		0			0
$941$	6.07196	−	34.4358i	0.197940	−	1.12257i	−0.710229	−	0.703971i	$-0.751409\pi$
$941$	6.07196	−	34.4358i	0.197940	−	1.12257i	0.908169	−	0.418604i	$-0.137480\pi$
$942$	−4.93096	−	8.54067i	−0.160659	−	0.278270i
$943$	14.8340	−	25.6933i	0.483063	−	0.836690i
$944$	−6.27323	−	5.26387i	−0.204176	−	0.171324i
$945$		0			0
$946$	−2.42731	+	0.883470i	−0.0789188	+	0.0287241i
$947$	−32.5448	+	27.3083i	−1.05756	+	0.887401i	−0.993869	−	0.110568i	$-0.964733\pi$
$947$	−32.5448	+	27.3083i	−1.05756	+	0.887401i	−0.0636950	+	0.997969i	$0.520288\pi$
$948$	3.60838	+	20.4641i	0.117195	+	0.664644i
$949$	22.6468			0.735145
$950$		0			0
$951$	2.39276			0.0775906
$952$	−0.237248	−	1.34550i	−0.00768925	−	0.0436079i
$953$	15.0751	−	12.6495i	0.488330	−	0.409757i	−0.365097	−	0.930969i	$-0.618964\pi$
$953$	15.0751	−	12.6495i	0.488330	−	0.409757i	0.853427	+	0.521212i	$0.174520\pi$
$954$	1.37326	−	0.499825i	0.0444609	−	0.0161824i
$955$		0			0
$956$	19.3704	+	16.2537i	0.626483	+	0.525682i
$957$	40.9583	−	70.9419i	1.32399	−	2.29323i
$958$	−4.43141	−	7.67543i	−0.143172	−	0.247982i
$959$	1.10296	−	6.25522i	0.0356166	−	0.201992i
$960$		0			0
$961$	−1.11092	−	1.92418i	−0.0358363	−	0.0620702i
$962$	7.41943	−	12.8508i	0.239212	−	0.414327i
$963$	0.168289	+	0.141211i	0.00542304	+	0.00455047i
$964$	−8.48268	−	3.08744i	−0.273209	−	0.0994399i
$965$		0			0
$966$	2.68049	−	2.24920i	0.0862432	−	0.0723667i
$967$	−7.25972	−	41.1719i	−0.233457	−	1.32400i	−0.845839	−	0.533438i	$-0.820900\pi$
$967$	−7.25972	−	41.1719i	−0.233457	−	1.32400i	0.612383	−	0.790562i	$-0.290211\pi$
$968$	20.3128			0.652877
$969$	2.50553	+	20.8651i	0.0804891	+	0.670283i
$970$		0			0
$971$	−1.11254	−	6.30953i	−0.0357031	−	0.202483i	0.961738	−	0.273969i	$-0.0883367\pi$
$971$	−1.11254	−	6.30953i	−0.0357031	−	0.202483i	−0.997442	+	0.0714869i	$0.977226\pi$
$972$	1.46899	−	1.23263i	0.0471179	−	0.0395366i
$973$	7.48242	−	2.72338i	0.239875	−	0.0873074i
$974$	8.42572	+	3.06671i	0.269978	+	0.0982638i
$975$		0			0
$976$	−1.59092	+	2.75556i	−0.0509242	+	0.0882033i
$977$	25.7352	+	44.5748i	0.823344	+	1.42607i	0.903179	+	0.429265i	$0.141227\pi$
$977$	25.7352	+	44.5748i	0.823344	+	1.42607i	−0.0798351	+	0.996808i	$0.525439\pi$
$978$	2.48847	−	14.1128i	0.0795726	−	0.451279i
$979$	1.57174	−	8.91375i	0.0502329	−	0.284885i
$980$		0			0
$981$	1.07274	−	1.85805i	0.0342501	−	0.0593228i
$982$	−24.0360	−	20.1686i	−0.767018	−	0.643605i
$983$	−14.4447	−	5.25745i	−0.460715	−	0.167687i	0.101227	−	0.994863i	$-0.467723\pi$
$983$	−14.4447	−	5.25745i	−0.460715	−	0.167687i	−0.561942	+	0.827177i	$0.689945\pi$
$984$	−10.6650	+	3.88175i	−0.339988	+	0.123746i
$985$		0			0
$986$	4.35335	+	24.6891i	0.138639	+	0.786260i
$987$	−2.09892			−0.0668092
$988$	4.84676	+	9.57526i	0.154196	+	0.304630i
$989$	2.02464			0.0643799
$990$		0			0
$991$	−36.3462	+	30.4981i	−1.15457	+	0.968803i	−0.999817	−	0.0191497i	$-0.993904\pi$
$991$	−36.3462	+	30.4981i	−1.15457	+	0.968803i	−0.154758	+	0.987952i	$0.549460\pi$
$992$	−5.41624	+	1.97135i	−0.171966	+	0.0625904i
$993$	−7.60237	−	2.76704i	−0.241254	−	0.0878092i
$994$	−1.73886	−	1.45907i	−0.0551532	−	0.0462790i
$995$		0			0
$996$	−11.0665	−	19.1677i	−0.350655	−	0.607352i
$997$	0.122338	−	0.693816i	0.00387450	−	0.0219734i	−0.982809	−	0.184624i	$-0.940893\pi$
$997$	0.122338	−	0.693816i	0.00387450	−	0.0219734i	0.986684	+	0.162651i	$0.0520044\pi$
$998$	4.08173	−	23.1486i	0.129205	−	0.732757i
$999$	16.1028	+	27.8909i	0.509470	+	0.882428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.h.351.2		12
5.2	odd	4		950.2.u.e.199.1		24
5.3	odd	4		950.2.u.e.199.4		24
5.4	even	2		190.2.k.b.161.1	yes	12
19.17	even	9	inner	950.2.l.h.701.2		12
95.17	odd	36		950.2.u.e.549.4		24
95.44	even	18		3610.2.a.bc.1.2		6
95.74	even	18		190.2.k.b.131.1	✓	12
95.89	odd	18		3610.2.a.be.1.5		6
95.93	odd	36		950.2.u.e.549.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.131.1	✓	12	95.74	even	18
190.2.k.b.161.1	yes	12	5.4	even	2
950.2.l.h.351.2		12	1.1	even	1	trivial
950.2.l.h.701.2		12	19.17	even	9	inner
950.2.u.e.199.1		24	5.2	odd	4
950.2.u.e.199.4		24	5.3	odd	4
950.2.u.e.549.1		24	95.93	odd	36
950.2.u.e.549.4		24	95.17	odd	36
3610.2.a.bc.1.2		6	95.44	even	18
3610.2.a.be.1.5		6	95.89	odd	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.28531 - 1.07851i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(0.237742 - 0.411781i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0320889 + 0.181985i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.28531 - 1.07851i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(0.237742 - 0.411781i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0320889 + 0.181985i) q^{9} +(2.79789 + 4.84609i) q^{11} +(-0.838929 + 1.45307i) q^{12} +(-1.88608 - 1.58261i) q^{13} +(0.446808 + 0.162625i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.498962 + 2.82975i) q^{17} -0.184793 q^{18} +(3.17997 + 2.98124i) q^{19} +(-0.138535 - 0.785674i) q^{21} +(-4.28662 + 3.59690i) q^{22} +(4.12150 - 1.50010i) q^{23} +(-1.57667 - 0.573861i) q^{24} +(1.23105 - 2.13224i) q^{26} +(2.67181 + 4.62772i) q^{27} +(-0.0825669 + 0.468260i) q^{28} +(1.51505 - 8.59227i) q^{29} +(-2.88192 + 4.99163i) q^{31} +(0.766044 + 0.642788i) q^{32} +(8.82271 + 3.21120i) q^{33} +(-2.70012 + 0.982762i) q^{34} +(-0.0320889 - 0.181985i) q^{36} +6.02691 q^{37} +(-2.38375 + 3.64935i) q^{38} -4.13105 q^{39} +(5.18173 - 4.34799i) q^{41} +(0.749681 - 0.272862i) q^{42} +(0.433776 + 0.157881i) q^{43} +(-4.28662 - 3.59690i) q^{44} +(2.19300 + 3.79839i) q^{46} +(0.456851 - 2.59093i) q^{47} +(0.291357 - 1.65237i) q^{48} +(3.38696 + 5.86638i) q^{49} +(3.69323 + 3.09899i) q^{51} +(2.31362 + 0.842088i) q^{52} +(-7.43135 + 2.70479i) q^{53} +(-4.09346 + 3.43482i) q^{54} -0.475484 q^{56} +(7.30255 + 0.402213i) q^{57} +8.72482 q^{58} +(-1.42203 - 8.06471i) q^{59} +(-2.98996 + 1.08826i) q^{61} +(-5.41624 - 1.97135i) q^{62} +(0.0673091 + 0.0564791i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.63037 + 9.24629i) q^{66} +(-0.0262550 + 0.148899i) q^{67} +(-1.43670 - 2.48844i) q^{68} +(3.67955 - 6.37316i) q^{69} +(-4.48601 - 1.63277i) q^{71} +(0.173648 - 0.0632028i) q^{72} +(-7.04620 + 5.91246i) q^{73} +(1.04656 + 5.93535i) q^{74} +(-4.00784 - 1.71384i) q^{76} +2.66070 q^{77} +(-0.717350 - 4.06829i) q^{78} +(9.48725 - 7.96075i) q^{79} +(7.90420 + 2.87689i) q^{81} +(5.18173 + 4.34799i) q^{82} +(-6.59560 + 11.4239i) q^{83} +(0.398897 + 0.690910i) q^{84} +(-0.0801585 + 0.454602i) q^{86} +(-7.31950 - 12.6777i) q^{87} +(2.79789 - 4.84609i) q^{88} +(-1.23909 - 1.03972i) q^{89} +(-1.10009 + 0.400399i) q^{91} +(-3.35987 + 2.81927i) q^{92} +(1.67933 + 9.52398i) q^{93} +2.63090 q^{94} +1.67786 q^{96} +(-0.873563 - 4.95422i) q^{97} +(-5.18912 + 4.35419i) q^{98} +(-0.971697 + 0.353669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more