LMFDB - Embedded newform 950.2.l.b.351.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.b.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.673648 + 0.565258i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.386659 + 2.19285i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.673648 + 0.565258i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.386659 + 2.19285i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.439693 - 0.761570i) q^{12} +(-0.500000 - 0.419550i) q^{13} +(-0.500000 - 0.181985i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.673648 - 3.82045i) q^{17} +2.22668 q^{18} +(-4.21688 + 1.10359i) q^{19} +(0.0812519 + 0.460802i) q^{21} +(0.766044 - 0.642788i) q^{22} +(-4.25877 + 1.55007i) q^{23} +(-0.826352 - 0.300767i) q^{24} +(-0.326352 + 0.565258i) q^{26} +(-2.29813 - 3.98048i) q^{27} +(-0.0923963 + 0.524005i) q^{28} +(-0.773318 + 4.38571i) q^{29} +(-1.37939 + 2.38917i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.826352 - 0.300767i) q^{33} +(-3.64543 + 1.32683i) q^{34} +(-0.386659 - 2.19285i) q^{36} +0.958111 q^{37} +(1.81908 + 3.96118i) q^{38} +0.573978 q^{39} +(-4.78699 + 4.01676i) q^{41} +(0.439693 - 0.160035i) q^{42} +(-4.70574 - 1.71275i) q^{43} +(-0.766044 - 0.642788i) q^{44} +(2.26604 + 3.92490i) q^{46} +(-0.134285 + 0.761570i) q^{47} +(-0.152704 + 0.866025i) q^{48} +(3.35844 + 5.81699i) q^{49} +(2.61334 + 2.19285i) q^{51} +(0.613341 + 0.223238i) q^{52} +(-3.62449 + 1.31920i) q^{53} +(-3.52094 + 2.95442i) q^{54} +0.532089 q^{56} +(2.21688 - 3.12706i) q^{57} +4.45336 q^{58} +(1.08853 + 6.17334i) q^{59} +(-4.62449 + 1.68317i) q^{61} +(2.59240 + 0.943555i) q^{62} +(0.907604 + 0.761570i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.152704 + 0.866025i) q^{66} +(-0.233956 + 1.32683i) q^{67} +(1.93969 + 3.35965i) q^{68} +(1.99273 - 3.45150i) q^{69} +(-5.33275 - 1.94096i) q^{71} +(-2.09240 + 0.761570i) q^{72} +(-5.72668 + 4.80526i) q^{73} +(-0.166374 - 0.943555i) q^{74} +(3.58512 - 2.47929i) q^{76} +0.532089 q^{77} +(-0.0996702 - 0.565258i) q^{78} +(-0.543233 + 0.455827i) q^{79} +(-2.47906 - 0.902302i) q^{81} +(4.78699 + 4.01676i) q^{82} +(-5.28359 + 9.15144i) q^{83} +(-0.233956 - 0.405223i) q^{84} +(-0.869585 + 4.93166i) q^{86} +(-1.95811 - 3.39155i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.75877 + 3.15398i) q^{89} +(-0.326352 + 0.118782i) q^{91} +(3.47178 - 2.91317i) q^{92} +(-0.421274 - 2.38917i) q^{93} +0.773318 q^{94} +0.879385 q^{96} +(-0.0175410 - 0.0994798i) q^{97} +(5.14543 - 4.31753i) q^{98} +(-2.09240 + 0.761570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * 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
$3$	−0.673648	+	0.565258i	−0.388931	+	0.326352i	−0.816197	−	0.577774i	$-0.803921\pi$
$3$	−0.673648	+	0.565258i	−0.388931	+	0.326352i	0.427266	+	0.904126i	$0.359477\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	0.673648	+	0.565258i	0.275016	+	0.230766i
$7$	0.266044	−	0.460802i	0.100555	−	0.174167i	−0.811358	−	0.584549i	$-0.801271\pi$
$7$	0.266044	−	0.460802i	0.100555	−	0.174167i	0.911914	+	0.410382i	$0.134605\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.386659	+	2.19285i	−0.128886	+	0.730951i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.439693	−	0.761570i	0.126928	−	0.219846i
$13$	−0.500000	−	0.419550i	−0.138675	−	0.116362i	0.570812	−	0.821081i	$-0.306629\pi$
$13$	−0.500000	−	0.419550i	−0.138675	−	0.116362i	−0.709487	+	0.704719i	$0.751073\pi$
$14$	−0.500000	−	0.181985i	−0.133631	−	0.0486376i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.673648	−	3.82045i	−0.163384	−	0.926595i	−0.950715	−	0.310065i	$-0.899649\pi$
$17$	−0.673648	−	3.82045i	−0.163384	−	0.926595i	0.787332	−	0.616530i	$-0.211462\pi$
$18$	2.22668			0.524834
$19$	−4.21688	+	1.10359i	−0.967419	+	0.253181i
$19$	−4.21688	+	1.10359i	−0.967419	+	0.253181i
$20$		0			0
$21$	0.0812519	+	0.460802i	0.0177306	+	0.100555i
$22$	0.766044	−	0.642788i	0.163321	−	0.137043i
$23$	−4.25877	+	1.55007i	−0.888015	+	0.323211i	−0.745440	−	0.666573i	$-0.767761\pi$
$23$	−4.25877	+	1.55007i	−0.888015	+	0.323211i	−0.142575	+	0.989784i	$0.545538\pi$
$24$	−0.826352	−	0.300767i	−0.168678	−	0.0613939i
$25$		0			0
$26$	−0.326352	+	0.565258i	−0.0640029	+	0.110856i
$27$	−2.29813	−	3.98048i	−0.442276	−	0.766044i
$28$	−0.0923963	+	0.524005i	−0.0174613	+	0.0990277i
$29$	−0.773318	+	4.38571i	−0.143602	+	0.814405i	0.824878	+	0.565311i	$0.191244\pi$
$29$	−0.773318	+	4.38571i	−0.143602	+	0.814405i	−0.968479	+	0.249094i	$0.919867\pi$
$30$		0			0
$31$	−1.37939	+	2.38917i	−0.247745	+	0.429107i	−0.962900	−	0.269859i	$-0.913023\pi$
$31$	−1.37939	+	2.38917i	−0.247745	+	0.429107i	0.715155	+	0.698966i	$0.246356\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−0.826352	−	0.300767i	−0.143849	−	0.0523569i
$34$	−3.64543	+	1.32683i	−0.625186	+	0.227549i
$35$		0			0
$36$	−0.386659	−	2.19285i	−0.0644432	−	0.365476i
$37$	0.958111			0.157512			0.0787562	−	0.996894i	$-0.474905\pi$
$37$	0.958111			0.157512			0.0787562	+	0.996894i	$0.474905\pi$
$38$	1.81908	+	3.96118i	0.295093	+	0.642588i
$39$	0.573978			0.0919100
$40$		0			0
$41$	−4.78699	+	4.01676i	−0.747602	+	0.627313i	−0.934868	−	0.354997i	$-0.884482\pi$
$41$	−4.78699	+	4.01676i	−0.747602	+	0.627313i	0.187265	+	0.982309i	$0.440038\pi$
$42$	0.439693	−	0.160035i	0.0678460	−	0.0246939i
$43$	−4.70574	−	1.71275i	−0.717618	−	0.261192i	−0.0427039	−	0.999088i	$-0.513597\pi$
$43$	−4.70574	−	1.71275i	−0.717618	−	0.261192i	−0.674914	+	0.737896i	$0.735819\pi$
$44$	−0.766044	−	0.642788i	−0.115486	−	0.0969039i
$45$		0			0
$46$	2.26604	+	3.92490i	0.334110	+	0.578696i
$47$	−0.134285	+	0.761570i	−0.0195875	+	0.111086i	−0.993034	−	0.117829i	$-0.962407\pi$
$47$	−0.134285	+	0.761570i	−0.0195875	+	0.111086i	0.973446	+	0.228915i	$0.0735178\pi$
$48$	−0.152704	+	0.866025i	−0.0220409	+	0.125000i
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$		0			0
$51$	2.61334	+	2.19285i	0.365941	+	0.307061i
$52$	0.613341	+	0.223238i	0.0850551	+	0.0309575i
$53$	−3.62449	+	1.31920i	−0.497861	+	0.181207i	−0.578732	−	0.815518i	$-0.696452\pi$
$53$	−3.62449	+	1.31920i	−0.497861	+	0.181207i	0.0808705	+	0.996725i	$0.474230\pi$
$54$	−3.52094	+	2.95442i	−0.479140	+	0.402046i
$55$		0			0
$56$	0.532089			0.0711034
$57$	2.21688	−	3.12706i	0.293633	−	0.414189i
$58$	4.45336			0.584755
$59$	1.08853	+	6.17334i	0.141714	+	0.803700i	0.969947	+	0.243316i	$0.0782353\pi$
$59$	1.08853	+	6.17334i	0.141714	+	0.803700i	−0.828233	+	0.560384i	$0.810654\pi$
$60$		0			0
$61$	−4.62449	+	1.68317i	−0.592105	+	0.215508i	−0.620655	−	0.784084i	$-0.713133\pi$
$61$	−4.62449	+	1.68317i	−0.592105	+	0.215508i	0.0285502	+	0.999592i	$0.490911\pi$
$62$	2.59240	+	0.943555i	0.329235	+	0.119832i
$63$	0.907604	+	0.761570i	0.114347	+	0.0959488i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−0.152704	+	0.866025i	−0.0187965	+	0.106600i
$67$	−0.233956	+	1.32683i	−0.0285822	+	0.162098i	−0.995758	−	0.0920102i	$-0.970671\pi$
$67$	−0.233956	+	1.32683i	−0.0285822	+	0.162098i	0.967176	+	0.254108i	$0.0817819\pi$
$68$	1.93969	+	3.35965i	0.235222	+	0.407417i
$69$	1.99273	−	3.45150i	0.239896	−	0.415512i
$70$		0			0
$71$	−5.33275	−	1.94096i	−0.632881	−	0.230350i	0.00560389	−	0.999984i	$-0.498216\pi$
$71$	−5.33275	−	1.94096i	−0.632881	−	0.230350i	−0.638485	+	0.769635i	$0.720438\pi$
$72$	−2.09240	+	0.761570i	−0.246591	+	0.0897519i
$73$	−5.72668	+	4.80526i	−0.670257	+	0.562413i	−0.913142	−	0.407643i	$-0.866351\pi$
$73$	−5.72668	+	4.80526i	−0.670257	+	0.562413i	0.242884	+	0.970055i	$0.421906\pi$
$74$	−0.166374	−	0.943555i	−0.0193406	−	0.109686i
$75$		0			0
$76$	3.58512	−	2.47929i	0.411242	−	0.284395i
$77$	0.532089			0.0606372
$78$	−0.0996702	−	0.565258i	−0.0112854	−	0.0640029i
$79$	−0.543233	+	0.455827i	−0.0611185	+	0.0512845i	−0.672835	−	0.739792i	$-0.734924\pi$
$79$	−0.543233	+	0.455827i	−0.0611185	+	0.0512845i	0.611717	+	0.791077i	$0.290479\pi$
$80$		0			0
$81$	−2.47906	−	0.902302i	−0.275451	−	0.100256i
$82$	4.78699	+	4.01676i	0.528634	+	0.443577i
$83$	−5.28359	+	9.15144i	−0.579949	+	1.00450i	0.415536	+	0.909577i	$0.363594\pi$
$83$	−5.28359	+	9.15144i	−0.579949	+	1.00450i	−0.995485	+	0.0949240i	$0.969739\pi$
$84$	−0.233956	−	0.405223i	−0.0255266	−	0.0442134i
$85$		0			0
$86$	−0.869585	+	4.93166i	−0.0937698	+	0.531795i
$87$	−1.95811	−	3.39155i	−0.209932	−	0.363612i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.75877	+	3.15398i	0.398429	+	0.334322i	0.819886	−	0.572527i	$-0.194037\pi$
$89$	3.75877	+	3.15398i	0.398429	+	0.334322i	−0.421457	+	0.906848i	$0.638481\pi$
$90$		0			0
$91$	−0.326352	+	0.118782i	−0.0342110	+	0.0124518i
$92$	3.47178	−	2.91317i	0.361958	−	0.303719i
$93$	−0.421274	−	2.38917i	−0.0436841	−	0.247745i
$94$	0.773318			0.0797617
$95$		0			0
$96$	0.879385			0.0897519
$97$	−0.0175410	−	0.0994798i	−0.00178102	−	0.0101006i	0.983904	−	0.178696i	$-0.0571879\pi$
$97$	−0.0175410	−	0.0994798i	−0.00178102	−	0.0101006i	−0.985685	+	0.168596i	$0.946077\pi$
$98$	5.14543	−	4.31753i	0.519767	−	0.436136i
$99$	−2.09240	+	0.761570i	−0.210294	+	0.0765407i
$100$		0			0
$101$	−10.9816	−	9.21464i	−1.09271	−	0.916891i	−0.0957949	−	0.995401i	$-0.530539\pi$
$101$	−10.9816	−	9.21464i	−1.09271	−	0.916891i	−0.996913	+	0.0785100i	$0.974984\pi$
$102$	1.70574	−	2.95442i	0.168893	−	0.292531i
$103$	−3.09240	−	5.35619i	−0.304703	−	0.527761i	0.672492	−	0.740104i	$-0.265224\pi$
$103$	−3.09240	−	5.35619i	−0.304703	−	0.527761i	−0.977195	+	0.212343i	$0.931890\pi$
$104$	0.113341	−	0.642788i	0.0111140	−	0.0630305i
$105$		0			0
$106$	1.92855	+	3.34034i	0.187317	+	0.324443i
$107$	−4.89053	+	8.47065i	−0.472785	+	0.818888i	−0.999515	−	0.0311447i	$-0.990085\pi$
$107$	−4.89053	+	8.47065i	−0.472785	+	0.818888i	0.526730	+	0.850033i	$0.323418\pi$
$108$	3.52094	+	2.95442i	0.338803	+	0.284290i
$109$	12.0360	+	4.38073i	1.15284	+	0.419598i	0.846533	−	0.532336i	$-0.178686\pi$
$109$	12.0360	+	4.38073i	1.15284	+	0.419598i	0.306303	+	0.951934i	$0.400908\pi$
$110$		0			0
$111$	−0.645430	+	0.541580i	−0.0612615	+	0.0514045i
$112$	−0.0923963	−	0.524005i	−0.00873063	−	0.0495138i
$113$	5.47565			0.515106			0.257553	−	0.966264i	$-0.417084\pi$
$113$	5.47565			0.515106			0.257553	+	0.966264i	$0.417084\pi$
$114$	−3.46451	−	1.64019i	−0.324481	−	0.153618i
$115$		0			0
$116$	−0.773318	−	4.38571i	−0.0718008	−	0.407203i
$117$	1.11334	−	0.934204i	0.102928	−	0.0863672i
$118$	5.89053	−	2.14398i	0.542267	−	0.197369i
$119$	−1.93969	−	0.705990i	−0.177811	−	0.0647180i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	2.46064	+	4.26195i	0.222776	+	0.385859i
$123$	0.954241	−	5.41177i	0.0860410	−	0.487963i
$124$	0.479055	−	2.71686i	0.0430205	−	0.243981i
$125$		0			0
$126$	0.592396	−	1.02606i	0.0527749	−	0.0914087i
$127$	7.87804	+	6.61046i	0.699063	+	0.586584i	0.921507	−	0.388362i	$-0.126959\pi$
$127$	7.87804	+	6.61046i	0.699063	+	0.586584i	−0.222444	+	0.974946i	$0.571403\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	4.13816	−	1.50617i	0.364344	−	0.132610i
$130$		0			0
$131$	−1.46404	−	8.30299i	−0.127914	−	0.725435i	−0.979534	−	0.201277i	$-0.935491\pi$
$131$	−1.46404	−	8.30299i	−0.127914	−	0.725435i	0.851621	−	0.524159i	$-0.175620\pi$
$132$	0.879385			0.0765407
$133$	−0.613341	+	2.23675i	−0.0531834	+	0.193951i
$134$	1.34730			0.116389
$135$		0			0
$136$	2.97178	−	2.49362i	0.254828	−	0.213826i
$137$	7.49020	−	2.72621i	0.639931	−	0.232916i	−0.00161707	−	0.999999i	$-0.500515\pi$
$137$	7.49020	−	2.72621i	0.639931	−	0.232916i	0.641548	+	0.767083i	$0.278293\pi$
$138$	−3.74510	−	1.36310i	−0.318804	−	0.116035i
$139$	−4.83409	−	4.05629i	−0.410022	−	0.344050i	0.414330	−	0.910127i	$-0.364016\pi$
$139$	−4.83409	−	4.05629i	−0.410022	−	0.344050i	−0.824352	+	0.566077i	$0.808460\pi$
$140$		0			0
$141$	−0.340022	−	0.588936i	−0.0286351	−	0.0495974i
$142$	−0.985452	+	5.58878i	−0.0826973	+	0.469000i
$143$	0.113341	−	0.642788i	0.00947803	−	0.0537526i
$144$	1.11334	+	1.92836i	0.0927784	+	0.160697i
$145$		0			0
$146$	5.72668	+	4.80526i	0.473944	+	0.397686i
$147$	−5.55051	−	2.02022i	−0.457798	−	0.166625i
$148$	−0.900330	+	0.327693i	−0.0740067	+	0.0269362i
$149$	13.8589	−	11.6290i	1.13537	−	0.952685i	0.136089	−	0.990697i	$-0.456547\pi$
$149$	13.8589	−	11.6290i	1.13537	−	0.952685i	0.999277	+	0.0380115i	$0.0121024\pi$
$150$		0			0
$151$	10.2071			0.830640			0.415320	−	0.909675i	$-0.363670\pi$
$151$	10.2071			0.830640			0.415320	+	0.909675i	$0.363670\pi$
$152$	−3.06418	−	3.10013i	−0.248538	−	0.251454i
$153$	8.63816			0.698353
$154$	−0.0923963	−	0.524005i	−0.00744550	−	0.0422255i
$155$		0			0
$156$	−0.539363	+	0.196312i	−0.0431836	+	0.0157175i
$157$	14.9868	+	5.45475i	1.19608	+	0.435336i	0.861853	−	0.507158i	$-0.169304\pi$
$157$	14.9868	+	5.45475i	1.19608	+	0.435336i	0.334223	+	0.942494i	$0.391526\pi$
$158$	0.543233	+	0.455827i	0.0432173	+	0.0362636i
$159$	1.69594	−	2.93745i	0.134497	−	0.232955i
$160$		0			0
$161$	−0.418748	+	2.37484i	−0.0330020	+	0.187163i
$162$	−0.458111	+	2.59808i	−0.0359926	+	0.204124i
$163$	−8.26264	−	14.3113i	−0.647180	−	1.12095i	−0.983793	−	0.179306i	$-0.942615\pi$
$163$	−8.26264	−	14.3113i	−0.647180	−	1.12095i	0.336613	−	0.941643i	$-0.390718\pi$
$164$	3.12449	−	5.41177i	0.243981	−	0.422588i
$165$		0			0
$166$	9.92989	+	3.61419i	0.770709	+	0.280515i
$167$	−22.3516	+	8.13533i	−1.72962	+	0.629531i	−0.998604	−	0.0528278i	$-0.983177\pi$
$167$	−22.3516	+	8.13533i	−1.72962	+	0.629531i	−0.731018	+	0.682359i	$0.760954\pi$
$168$	−0.358441	+	0.300767i	−0.0276543	+	0.0232047i
$169$	−2.18345	−	12.3830i	−0.167958	−	0.952535i
$170$		0			0
$171$	−0.789515	−	9.67372i	−0.0603757	−	0.739768i
$172$	5.00774			0.381837
$173$	0.533433	+	3.02525i	0.0405562	+	0.230005i	0.998348	−	0.0574574i	$-0.0182993\pi$
$173$	0.533433	+	3.02525i	0.0405562	+	0.230005i	−0.957792	+	0.287463i	$0.907188\pi$
$174$	−3.00000	+	2.51730i	−0.227429	+	0.190836i
$175$		0			0
$176$	0.939693	+	0.342020i	0.0708320	+	0.0257807i
$177$	−4.22281	−	3.54336i	−0.317406	−	0.266335i
$178$	2.45336	−	4.24935i	0.183887	−	0.318502i
$179$	−7.98680	−	13.8335i	−0.596961	−	1.03397i	−0.993267	−	0.115848i	$-0.963041\pi$
$179$	−7.98680	−	13.8335i	−0.596961	−	1.03397i	0.396306	−	0.918119i	$-0.370292\pi$
$180$		0			0
$181$	−1.69728	+	9.62576i	−0.126158	+	0.715477i	0.854455	+	0.519525i	$0.173891\pi$
$181$	−1.69728	+	9.62576i	−0.126158	+	0.715477i	−0.980613	+	0.195952i	$0.937220\pi$
$182$	0.173648	+	0.300767i	0.0128717	+	0.0222944i
$183$	2.16385	−	3.74789i	0.159956	−	0.277052i
$184$	−3.47178	−	2.91317i	−0.255943	−	0.214762i
$185$		0			0
$186$	−2.27972	+	0.829748i	−0.167157	+	0.0608401i
$187$	2.97178	−	2.49362i	0.217318	−	0.182352i
$188$	−0.134285	−	0.761570i	−0.00979376	−	0.0555432i
$189$	−2.44562			−0.177893
$190$		0			0
$191$	7.52023			0.544145			0.272072	−	0.962277i	$-0.412291\pi$
$191$	7.52023			0.544145			0.272072	+	0.962277i	$0.412291\pi$
$192$	−0.152704	−	0.866025i	−0.0110204	−	0.0625000i
$193$	18.7986	−	15.7739i	1.35315	−	1.13543i	0.375121	−	0.926976i	$-0.377601\pi$
$193$	18.7986	−	15.7739i	1.35315	−	1.13543i	0.978032	−	0.208454i	$-0.0668432\pi$
$194$	−0.0949225	+	0.0345490i	−0.00681504	+	0.00248047i
$195$		0			0
$196$	−5.14543	−	4.31753i	−0.367531	−	0.308395i
$197$	−7.20187	+	12.4740i	−0.513112	+	0.888736i	0.486773	+	0.873529i	$0.338174\pi$
$197$	−7.20187	+	12.4740i	−0.513112	+	0.888736i	−0.999884	+	0.0152069i	$0.995159\pi$
$198$	1.11334	+	1.92836i	0.0791217	+	0.137043i
$199$	−0.771097	+	4.37311i	−0.0546616	+	0.310001i	−0.999864	−	0.0164832i	$-0.994753\pi$
$199$	−0.771097	+	4.37311i	−0.0546616	+	0.310001i	0.945203	+	0.326485i	$0.105864\pi$
$200$		0			0
$201$	−0.592396	−	1.02606i	−0.0417844	−	0.0723727i
$202$	−7.16772	+	12.4149i	−0.504319	+	0.873506i
$203$	1.81521	+	1.52314i	0.127403	+	0.106903i
$204$	−3.20574	−	1.16679i	−0.224446	−	0.0816918i
$205$		0			0
$206$	−4.73783	+	3.97551i	−0.330100	+	0.276987i
$207$	−1.75237	−	9.93821i	−0.121798	−	0.690753i
$208$	−0.652704			−0.0452569
$209$	−3.06418	−	3.10013i	−0.211954	−	0.214441i
$210$		0			0
$211$	−1.95218	−	11.0714i	−0.134394	−	0.762185i	−0.975280	−	0.220973i	$-0.929077\pi$
$211$	−1.95218	−	11.0714i	−0.134394	−	0.762185i	0.840886	−	0.541212i	$-0.182034\pi$
$212$	2.95471	−	2.47929i	0.202930	−	0.170279i
$213$	4.68954	−	1.70685i	0.321322	−	0.116952i
$214$	9.19119	+	3.34532i	0.628297	+	0.228681i
$215$		0			0
$216$	2.29813	−	3.98048i	0.156368	−	0.270838i
$217$	0.733956	+	1.27125i	0.0498241	+	0.0862980i
$218$	2.22416	−	12.6138i	0.150639	−	0.854315i
$219$	1.14156	−	6.47410i	0.0771394	−	0.437479i
$220$		0			0
$221$	−1.26604	+	2.19285i	−0.0851634	+	0.147507i
$222$	0.645430	+	0.541580i	0.0433184	+	0.0363485i
$223$	−11.2811	−	4.10597i	−0.755436	−	0.274956i	−0.0645444	−	0.997915i	$-0.520559\pi$
$223$	−11.2811	−	4.10597i	−0.755436	−	0.274956i	−0.690891	+	0.722959i	$0.742782\pi$
$224$	−0.500000	+	0.181985i	−0.0334077	+	0.0121594i
$225$		0			0
$226$	−0.950837	−	5.39246i	−0.0632487	−	0.358701i
$227$	−25.8871			−1.71819			−0.859094	−	0.511817i	$-0.828973\pi$
$227$	−25.8871			−1.71819			−0.859094	+	0.511817i	$0.828973\pi$
$228$	−1.01367	+	3.69669i	−0.0671320	+	0.244819i
$229$	11.1138			0.734421			0.367211	−	0.930138i	$-0.380313\pi$
$229$	11.1138			0.734421			0.367211	+	0.930138i	$0.380313\pi$
$230$		0			0
$231$	−0.358441	+	0.300767i	−0.0235837	+	0.0197890i
$232$	−4.18479	+	1.52314i	−0.274745	+	0.0999990i
$233$	1.19207	+	0.433877i	0.0780949	+	0.0284242i	0.380772	−	0.924669i	$-0.375658\pi$
$233$	1.19207	+	0.433877i	0.0780949	+	0.0284242i	−0.302677	+	0.953093i	$0.597880\pi$
$234$	−1.11334	−	0.934204i	−0.0727814	−	0.0610708i
$235$		0			0
$236$	−3.13429	−	5.42874i	−0.204025	−	0.353381i
$237$	0.108288	−	0.614134i	0.00703408	−	0.0398923i
$238$	−0.358441	+	2.03282i	−0.0232343	+	0.131768i
$239$	−2.13429	−	3.69669i	−0.138055	−	0.239119i	0.788705	−	0.614772i	$-0.210752\pi$
$239$	−2.13429	−	3.69669i	−0.138055	−	0.239119i	−0.926761	+	0.375653i	$0.877419\pi$
$240$		0			0
$241$	22.5214	+	18.8977i	1.45073	+	1.21731i	0.932044	+	0.362344i	$0.118024\pi$
$241$	22.5214	+	18.8977i	1.45073	+	1.21731i	0.518687	+	0.854964i	$0.326421\pi$
$242$	−9.39693	−	3.42020i	−0.604057	−	0.219859i
$243$	15.1373	−	5.50952i	0.971057	−	0.353436i
$244$	3.76991	−	3.16333i	0.241344	−	0.202512i
$245$		0			0
$246$	−5.49525			−0.350364
$247$	2.57145	+	1.21740i	0.163618	+	0.0774611i
$248$	−2.75877			−0.175182
$249$	−1.61365	−	9.15144i	−0.102261	−	0.579949i
$250$		0			0
$251$	−9.14290	+	3.32774i	−0.577095	+	0.210045i	−0.614044	−	0.789272i	$-0.710458\pi$
$251$	−9.14290	+	3.32774i	−0.577095	+	0.210045i	0.0369491	+	0.999317i	$0.488236\pi$
$252$	−1.11334	−	0.405223i	−0.0701339	−	0.0255266i
$253$	−3.47178	−	2.91317i	−0.218269	−	0.183149i
$254$	5.14203	−	8.90625i	0.322639	−	0.558828i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	0.783585	−	4.44393i	0.0488787	−	0.277205i	−0.950566	−	0.310522i	$-0.899496\pi$
$257$	0.783585	−	4.44393i	0.0488787	−	0.277205i	0.999445	+	0.0333173i	$0.0106072\pi$
$258$	−2.20187	−	3.81374i	−0.137082	−	0.237433i
$259$	0.254900	−	0.441500i	0.0158387	−	0.0274335i
$260$		0			0
$261$	−9.31820	−	3.39155i	−0.576782	−	0.209932i
$262$	−7.92262	+	2.88360i	−0.489461	+	0.178149i
$263$	−23.0744	+	19.3618i	−1.42283	+	1.19390i	−0.473029	+	0.881047i	$0.656839\pi$
$263$	−23.0744	+	19.3618i	−1.42283	+	1.19390i	−0.949802	+	0.312850i	$0.898716\pi$
$264$	−0.152704	−	0.866025i	−0.00939826	−	0.0533002i
$265$		0			0
$266$	2.30928	+	0.215615i	0.141591	+	0.0132202i
$267$	−4.31490			−0.264068
$268$	−0.233956	−	1.32683i	−0.0142911	−	0.0810489i
$269$	−3.31315	+	2.78006i	−0.202006	+	0.169503i	−0.738179	−	0.674605i	$-0.764314\pi$
$269$	−3.31315	+	2.78006i	−0.202006	+	0.169503i	0.536173	+	0.844108i	$0.319870\pi$
$270$		0			0
$271$	25.3491	+	9.22632i	1.53985	+	0.560459i	0.966009	−	0.258509i	$-0.0832310\pi$
$271$	25.3491	+	9.22632i	1.53985	+	0.560459i	0.573840	+	0.818968i	$0.305453\pi$
$272$	−2.97178	−	2.49362i	−0.180191	−	0.151198i
$273$	0.152704	−	0.264490i	0.00924205	−	0.0160077i
$274$	−3.98545	−	6.90301i	−0.240770	−	0.417026i
$275$		0			0
$276$	−0.692066	+	3.92490i	−0.0416575	+	0.236251i
$277$	1.10220	+	1.90906i	0.0662246	+	0.114704i	0.897237	−	0.441550i	$-0.145571\pi$
$277$	1.10220	+	1.90906i	0.0662246	+	0.114704i	−0.831012	+	0.556255i	$0.812238\pi$
$278$	−3.15523	+	5.46502i	−0.189238	+	0.327770i
$279$	−4.70574	−	3.94858i	−0.281725	−	0.236395i
$280$		0			0
$281$	−17.8341	+	6.49108i	−1.06389	+	0.387225i	−0.813889	−	0.581020i	$-0.802654\pi$
$281$	−17.8341	+	6.49108i	−1.06389	+	0.387225i	−0.250003	+	0.968245i	$0.580432\pi$
$282$	−0.520945	+	0.437124i	−0.0310218	+	0.0260304i
$283$	−2.52481	−	14.3189i	−0.150085	−	0.851172i	−0.963143	−	0.268990i	$-0.913310\pi$
$283$	−2.52481	−	14.3189i	−0.150085	−	0.851172i	0.813058	−	0.582182i	$-0.197801\pi$
$284$	5.67499			0.336749
$285$		0			0
$286$	−0.652704			−0.0385952
$287$	0.577382	+	3.27449i	0.0340818	+	0.193287i
$288$	1.70574	−	1.43128i	0.100512	−	0.0843392i
$289$	1.83275	−	0.667066i	0.107809	−	0.0392392i
$290$		0			0
$291$	0.0680482	+	0.0570992i	0.00398905	+	0.00334721i
$292$	3.73783	−	6.47410i	0.218740	−	0.378868i
$293$	3.13088	+	5.42285i	0.182908	+	0.316806i	0.942870	−	0.333162i	$-0.108116\pi$
$293$	3.13088	+	5.42285i	0.182908	+	0.316806i	−0.759962	+	0.649968i	$0.774782\pi$
$294$	−1.02569	+	5.81699i	−0.0598196	+	0.339254i
$295$		0			0
$296$	0.479055	+	0.829748i	0.0278445	+	0.0482281i
$297$	2.29813	−	3.98048i	0.133351	−	0.230971i
$298$	−13.8589	−	11.6290i	−0.802825	−	0.673650i
$299$	2.77972	+	1.01173i	0.160755	+	0.0585101i
$300$		0			0
$301$	−2.04117	+	1.71275i	−0.117651	+	0.0987212i
$302$	−1.77244	−	10.0520i	−0.101993	−	0.578428i
$303$	12.6064			0.724217
$304$	−2.52094	+	3.55596i	−0.144586	+	0.203948i
$305$		0			0
$306$	−1.50000	−	8.50692i	−0.0857493	−	0.486308i
$307$	−5.95992	+	5.00097i	−0.340151	+	0.285420i	−0.796821	−	0.604216i	$-0.793486\pi$
$307$	−5.95992	+	5.00097i	−0.340151	+	0.285420i	0.456670	+	0.889636i	$0.349042\pi$
$308$	−0.500000	+	0.181985i	−0.0284901	+	0.0103696i
$309$	5.11081	+	1.86018i	0.290744	+	0.105822i
$310$		0			0
$311$	15.5189	−	26.8795i	0.879995	−	1.52420i	0.0286507	−	0.999589i	$-0.490879\pi$
$311$	15.5189	−	26.8795i	0.879995	−	1.52420i	0.851345	−	0.524607i	$-0.175788\pi$
$312$	0.286989	+	0.497079i	0.0162476	+	0.0281416i
$313$	1.60220	−	9.08651i	0.0905615	−	0.513600i	−0.905456	−	0.424440i	$-0.860471\pi$
$313$	1.60220	−	9.08651i	0.0905615	−	0.513600i	0.996017	−	0.0891594i	$-0.0284180\pi$
$314$	2.76945	−	15.7063i	0.156289	−	0.886359i
$315$		0			0
$316$	0.354570	−	0.614134i	0.0199461	−	0.0345477i
$317$	18.3897	+	15.4308i	1.03287	+	0.866677i	0.991189	−	0.132454i	$-0.0422856\pi$
$317$	18.3897	+	15.4308i	1.03287	+	0.866677i	0.0416766	+	0.999131i	$0.486730\pi$
$318$	−3.18732	−	1.16009i	−0.178736	−	0.0650546i
$319$	−4.18479	+	1.52314i	−0.234303	+	0.0852795i
$320$		0			0
$321$	−1.49360	−	8.47065i	−0.0833648	−	0.472785i
$322$	2.41147			0.134386
$323$	7.05690	+	15.3669i	0.392657	+	0.855040i
$324$	2.63816			0.146564
$325$		0			0
$326$	−12.6591	+	10.6222i	−0.701123	+	0.588312i
$327$	−10.5842	+	3.85235i	−0.585310	+	0.213035i
$328$	−5.87211	−	2.13727i	−0.324233	−	0.118011i
$329$	0.315207	+	0.264490i	0.0173780	+	0.0145818i
$330$		0			0
$331$	12.2724	+	21.2565i	0.674554	+	1.16836i	0.976599	+	0.215069i	$0.0689975\pi$
$331$	12.2724	+	21.2565i	0.674554	+	1.16836i	−0.302045	+	0.953294i	$0.597669\pi$
$332$	1.83497	−	10.4066i	0.100707	−	0.571138i
$333$	−0.370462	+	2.10100i	−0.0203012	+	0.115134i
$334$	11.8931	+	20.5994i	0.650759	+	1.12715i
$335$		0			0
$336$	0.358441	+	0.300767i	0.0195545	+	0.0164082i
$337$	28.8050	+	10.4842i	1.56911	+	0.571109i	0.972800	−	0.231647i	$-0.0744114\pi$
$337$	28.8050	+	10.4842i	1.56911	+	0.571109i	0.596308	+	0.802756i	$0.296634\pi$
$338$	−11.8157	+	4.30055i	−0.642688	+	0.233919i
$339$	−3.68866	+	3.09516i	−0.200341	+	0.168106i
$340$		0			0
$341$	−2.75877			−0.149396
$342$	−9.38965	+	2.45734i	−0.507734	+	0.132878i
$343$	7.29860			0.394087
$344$	−0.869585	−	4.93166i	−0.0468849	−	0.265897i
$345$		0			0
$346$	2.88666	−	1.05066i	0.155188	−	0.0564837i
$347$	7.29086	+	2.65366i	0.391394	+	0.142456i	0.530218	−	0.847861i	$-0.322110\pi$
$347$	7.29086	+	2.65366i	0.391394	+	0.142456i	−0.138824	+	0.990317i	$0.544332\pi$
$348$	3.00000	+	2.51730i	0.160817	+	0.134941i
$349$	6.37551	−	11.0427i	0.341273	−	0.591103i	−0.643396	−	0.765534i	$-0.722475\pi$
$349$	6.37551	−	11.0427i	0.341273	−	0.591103i	0.984669	+	0.174431i	$0.0558084\pi$
$350$		0			0
$351$	−0.520945	+	2.95442i	−0.0278060	+	0.157695i
$352$	0.173648	−	0.984808i	0.00925548	−	0.0524904i
$353$	−4.73009	−	8.19275i	−0.251757	−	0.436056i	0.712253	−	0.701923i	$-0.247675\pi$
$353$	−4.73009	−	8.19275i	−0.251757	−	0.436056i	−0.964010	+	0.265867i	$0.914342\pi$
$354$	−2.75624	+	4.77396i	−0.146493	+	0.253733i
$355$		0			0
$356$	−4.61081	−	1.67820i	−0.244373	−	0.0889444i
$357$	1.70574	−	0.620838i	0.0902772	−	0.0328582i
$358$	−12.2365	+	10.2676i	−0.646718	+	0.542661i
$359$	−0.181799	−	1.03104i	−0.00959501	−	0.0544160i	0.979634	−	0.200790i	$-0.0643509\pi$
$359$	−0.181799	−	1.03104i	−0.00959501	−	0.0544160i	−0.989229	+	0.146374i	$0.953240\pi$
$360$		0			0
$361$	16.5642	−	9.30742i	0.871799	−	0.489864i
$362$	9.77425			0.513723
$363$	1.52704	+	8.66025i	0.0801486	+	0.454545i
$364$	0.266044	−	0.223238i	0.0139445	−	0.0117008i
$365$		0			0
$366$	−4.06670	−	1.48016i	−0.212570	−	0.0773692i
$367$	−7.57192	−	6.35359i	−0.395251	−	0.331655i	0.423404	−	0.905941i	$-0.360835\pi$
$367$	−7.57192	−	6.35359i	−0.395251	−	0.331655i	−0.818655	+	0.574286i	$0.805280\pi$
$368$	−2.26604	+	3.92490i	−0.118126	+	0.204600i
$369$	−6.95723	−	12.0503i	−0.362179	−	0.627313i
$370$		0			0
$371$	−0.356381	+	2.02114i	−0.0185024	+	0.104932i
$372$	1.21301	+	2.10100i	0.0628917	+	0.108932i
$373$	−13.8610	+	24.0079i	−0.717694	+	1.24308i	0.244218	+	0.969720i	$0.421469\pi$
$373$	−13.8610	+	24.0079i	−0.717694	+	1.24308i	−0.961911	+	0.273361i	$0.911864\pi$
$374$	−2.97178	−	2.49362i	−0.153667	−	0.128942i
$375$		0			0
$376$	−0.726682	+	0.264490i	−0.0374757	+	0.0136401i
$377$	2.22668	−	1.86841i	0.114680	−	0.0962279i
$378$	0.424678	+	2.40847i	0.0218431	+	0.123878i
$379$	−13.0787			−0.671809			−0.335905	−	0.941896i	$-0.609042\pi$
$379$	−13.0787			−0.671809			−0.335905	+	0.941896i	$0.609042\pi$
$380$		0			0
$381$	−9.04364			−0.463320
$382$	−1.30587	−	7.40598i	−0.0668143	−	0.378923i
$383$	7.63041	−	6.40268i	0.389896	−	0.327162i	−0.426677	−	0.904404i	$-0.640316\pi$
$383$	7.63041	−	6.40268i	0.389896	−	0.327162i	0.816573	+	0.577243i	$0.195871\pi$
$384$	−0.826352	+	0.300767i	−0.0421696	+	0.0153485i
$385$		0			0
$386$	−18.7986	−	15.7739i	−0.956824	−	0.802870i
$387$	5.57532	−	9.65674i	0.283410	−	0.490880i
$388$	0.0505072	+	0.0874810i	0.00256411	+	0.00444118i
$389$	−4.18850	+	23.7542i	−0.212365	+	1.20438i	0.673055	+	0.739593i	$0.264982\pi$
$389$	−4.18850	+	23.7542i	−0.212365	+	1.20438i	−0.885420	+	0.464791i	$0.846129\pi$
$390$		0			0
$391$	8.79086	+	15.2262i	0.444573	+	0.770023i
$392$	−3.35844	+	5.81699i	−0.169627	+	0.293802i
$393$	5.67958	+	4.76573i	0.286497	+	0.240399i
$394$	13.5351	+	4.92637i	0.681888	+	0.248187i
$395$		0			0
$396$	1.70574	−	1.43128i	0.0857165	−	0.0719247i
$397$	−4.40538	−	24.9842i	−0.221100	−	1.25392i	−0.870002	−	0.493048i	$-0.835883\pi$
$397$	−4.40538	−	24.9842i	−0.221100	−	1.25392i	0.648902	−	0.760872i	$-0.275228\pi$
$398$	4.44057			0.222586
$399$	−0.851167	−	1.85348i	−0.0426116	−	0.0927901i
$400$		0			0
$401$	−4.30810	−	24.4324i	−0.215136	−	1.22010i	−0.880670	−	0.473730i	$-0.842907\pi$
$401$	−4.30810	−	24.4324i	−0.215136	−	1.22010i	0.665534	−	0.746367i	$-0.268204\pi$
$402$	−0.907604	+	0.761570i	−0.0452672	+	0.0379837i
$403$	1.69207	−	0.615862i	0.0842878	−	0.0306783i
$404$	13.4709	+	4.90301i	0.670203	+	0.243934i
$405$		0			0
$406$	1.18479	−	2.05212i	0.0588003	−	0.101845i
$407$	0.479055	+	0.829748i	0.0237459	+	0.0411291i
$408$	−0.592396	+	3.35965i	−0.0293280	+	0.166327i
$409$	−5.20692	+	29.5299i	−0.257466	+	1.46016i	0.532198	+	0.846620i	$0.321366\pi$
$409$	−5.20692	+	29.5299i	−0.257466	+	1.46016i	−0.789664	+	0.613540i	$0.789745\pi$
$410$		0			0
$411$	−3.50475	+	6.07040i	−0.172876	+	0.299431i
$412$	4.73783	+	3.97551i	0.233416	+	0.195859i
$413$	3.13429	+	1.14079i	0.154228	+	0.0561344i
$414$	−9.48293	+	3.45150i	−0.466060	+	0.169632i
$415$		0			0
$416$	0.113341	+	0.642788i	0.00555699	+	0.0315153i
$417$	5.54933			0.271752
$418$	−2.52094	+	3.55596i	−0.123303	+	0.173928i
$419$	−17.7196			−0.865658			−0.432829	−	0.901476i	$-0.642485\pi$
$419$	−17.7196			−0.865658			−0.432829	+	0.901476i	$0.642485\pi$
$420$		0			0
$421$	−9.22462	+	7.74038i	−0.449581	+	0.377243i	−0.839280	−	0.543699i	$-0.817023\pi$
$421$	−9.22462	+	7.74038i	−0.449581	+	0.377243i	0.389700	+	0.920942i	$0.372579\pi$
$422$	−10.5642	+	3.84505i	−0.514256	+	0.187174i
$423$	−1.61809	−	0.588936i	−0.0786742	−	0.0286351i
$424$	−2.95471	−	2.47929i	−0.143493	−	0.120405i
$425$		0			0
$426$	−2.49525	−	4.32190i	−0.120895	−	0.209397i
$427$	−0.454707	+	2.57877i	−0.0220048	+	0.124796i
$428$	1.69846	−	9.63246i	0.0820983	−	0.465603i
$429$	0.286989	+	0.497079i	0.0138560	+	0.0239992i
$430$		0			0
$431$	27.0913	+	22.7323i	1.30494	+	1.09498i	0.989269	+	0.146107i	$0.0466743\pi$
$431$	27.0913	+	22.7323i	1.30494	+	1.09498i	0.315672	+	0.948868i	$0.397770\pi$
$432$	−4.31908	−	1.57202i	−0.207802	−	0.0756336i
$433$	25.1805	−	9.16496i	1.21010	−	0.440440i	0.343360	−	0.939204i	$-0.388435\pi$
$433$	25.1805	−	9.16496i	1.21010	−	0.440440i	0.866738	+	0.498764i	$0.166213\pi$
$434$	1.12449	−	0.943555i	0.0539770	−	0.0452921i
$435$		0			0
$436$	−12.8084			−0.613411
$437$	16.2481	−	11.2364i	0.777252	−	0.537509i
$438$	−6.57398			−0.314117
$439$	4.14244	+	23.4929i	0.197708	+	1.12126i	0.908510	+	0.417864i	$0.137221\pi$
$439$	4.14244	+	23.4929i	0.197708	+	1.12126i	−0.710802	+	0.703392i	$0.751668\pi$
$440$		0			0
$441$	−14.0544	+	5.11538i	−0.669256	+	0.243589i
$442$	2.37939	+	0.866025i	0.113176	+	0.0411926i
$443$	25.8182	+	21.6640i	1.22666	+	1.02929i	0.998449	+	0.0556780i	$0.0177320\pi$
$443$	25.8182	+	21.6640i	1.22666	+	1.02929i	0.228211	+	0.973612i	$0.426712\pi$
$444$	0.421274	−	0.729669i	0.0199928	−	0.0346285i
$445$		0			0
$446$	−2.08466	+	11.8227i	−0.0987113	+	0.559820i
$447$	−2.76264	+	15.6677i	−0.130668	+	0.741057i
$448$	0.266044	+	0.460802i	0.0125694	+	0.0217709i
$449$	−6.45605	+	11.1822i	−0.304680	+	0.527721i	−0.977190	−	0.212367i	$-0.931883\pi$
$449$	−6.45605	+	11.1822i	−0.304680	+	0.527721i	0.672510	+	0.740088i	$0.265216\pi$
$450$		0			0
$451$	−5.87211	−	2.13727i	−0.276507	−	0.100640i
$452$	−5.14543	+	1.87278i	−0.242021	+	0.0880883i
$453$	−6.87598	+	5.76963i	−0.323062	+	0.271081i
$454$	4.49525	+	25.4938i	0.210973	+	1.19649i
$455$		0			0
$456$	3.81655	+	0.356347i	0.178726	+	0.0166875i
$457$	36.0779			1.68765			0.843827	−	0.536616i	$-0.180298\pi$
$457$	36.0779			1.68765			0.843827	+	0.536616i	$0.180298\pi$
$458$	−1.92989	−	10.9450i	−0.0901780	−	0.511425i
$459$	−13.6591	+	11.4613i	−0.637552	+	0.534970i
$460$		0			0
$461$	0.0530334	+	0.0193026i	0.00247001	+	0.000899011i	0.343255	−	0.939242i	$-0.388471\pi$
$461$	0.0530334	+	0.0193026i	0.00247001	+	0.000899011i	−0.340785	+	0.940141i	$0.610693\pi$
$462$	0.358441	+	0.300767i	0.0166762	+	0.0139930i
$463$	−14.0753	+	24.3792i	−0.654136	+	1.13300i	0.327974	+	0.944687i	$0.393634\pi$
$463$	−14.0753	+	24.3792i	−0.654136	+	1.13300i	−0.982110	+	0.188310i	$0.939699\pi$
$464$	2.22668	+	3.85673i	0.103371	+	0.179044i
$465$		0			0
$466$	0.220285	−	1.24930i	0.0102045	−	0.0578726i
$467$	−0.154048	−	0.266819i	−0.00712848	−	0.0123469i	0.862439	−	0.506161i	$-0.168936\pi$
$467$	−0.154048	−	0.266819i	−0.00712848	−	0.0123469i	−0.869568	+	0.493814i	$0.835602\pi$
$468$	−0.726682	+	1.25865i	−0.0335909	+	0.0581811i
$469$	0.549163	+	0.460802i	0.0253580	+	0.0212779i
$470$		0			0
$471$	−13.1792	+	4.79682i	−0.607264	+	0.221026i
$472$	−4.80200	+	4.02936i	−0.221030	+	0.185466i
$473$	−0.869585	−	4.93166i	−0.0399836	−	0.226758i
$474$	−0.623608			−0.0286433
$475$		0			0
$476$	2.06418			0.0946114
$477$	−1.49138	−	8.45805i	−0.0682857	−	0.387267i
$478$	−3.26991	+	2.74378i	−0.149562	+	0.125498i
$479$	−28.4021	+	10.3375i	−1.29773	+	0.472334i	−0.896256	−	0.443538i	$-0.853723\pi$
$479$	−28.4021	+	10.3375i	−1.29773	+	0.472334i	−0.401471	+	0.915872i	$0.631501\pi$
$480$		0			0
$481$	−0.479055	−	0.401975i	−0.0218430	−	0.0183285i
$482$	14.6998	−	25.4608i	0.669558	−	1.15971i
$483$	−1.06031	−	1.83651i	−0.0482457	−	0.0835639i
$484$	−1.73648	+	9.84808i	−0.0789310	+	0.447640i
$485$		0			0
$486$	−8.05438	−	13.9506i	−0.365354	−	0.632812i
$487$	14.9508	−	25.8956i	0.677487	−	1.17344i	−0.298248	−	0.954488i	$-0.596402\pi$
$487$	14.9508	−	25.8956i	0.677487	−	1.17344i	0.975735	−	0.218954i	$-0.0702644\pi$
$488$	−3.76991	−	3.16333i	−0.170656	−	0.143197i
$489$	13.6557	+	4.97027i	0.617532	+	0.224763i
$490$		0			0
$491$	−2.98680	+	2.50622i	−0.134792	+	0.113104i	−0.707691	−	0.706522i	$-0.750263\pi$
$491$	−2.98680	+	2.50622i	−0.134792	+	0.113104i	0.572899	+	0.819626i	$0.305819\pi$
$492$	0.954241	+	5.41177i	0.0430205	+	0.243981i
$493$	17.2763			0.778086
$494$	0.752374	−	2.74378i	0.0338509	−	0.123449i
$495$		0			0
$496$	0.479055	+	2.71686i	0.0215102	+	0.121991i
$497$	−2.31315	+	1.94096i	−0.103759	+	0.0870640i
$498$	−8.73220	+	3.17826i	−0.391299	+	0.142421i
$499$	22.9231	+	8.34332i	1.02618	+	0.373498i	0.799625	−	0.600500i	$-0.205032\pi$
$499$	22.9231	+	8.34332i	1.02618	+	0.373498i	0.226554	+	0.973999i	$0.427254\pi$
$500$		0			0
$501$	10.4586	−	18.1148i	0.467255	−	0.809309i
$502$	4.86484	+	8.42615i	0.217128	+	0.376077i
$503$	2.36777	−	13.4283i	0.105574	−	0.598739i	−0.885416	−	0.464800i	$-0.846126\pi$
$503$	2.36777	−	13.4283i	0.105574	−	0.598739i	0.990990	−	0.133939i	$-0.0427626\pi$
$504$	−0.205737	+	1.16679i	−0.00916426	+	0.0519731i
$505$		0			0
$506$	−2.26604	+	3.92490i	−0.100738	+	0.174483i
$507$	8.47044	+	7.10754i	0.376185	+	0.315657i
$508$	−9.66385	−	3.51735i	−0.428764	−	0.156057i
$509$	7.18004	−	2.61332i	0.318250	−	0.115833i	−0.177956	−	0.984038i	$-0.556948\pi$
$509$	7.18004	−	2.61332i	0.318250	−	0.115833i	0.496206	+	0.868205i	$0.334726\pi$
$510$		0			0
$511$	0.690722	+	3.91728i	0.0305558	+	0.173290i
$512$	−1.00000			−0.0441942
$513$	14.0838	+	14.2490i	0.621814	+	0.629110i
$514$	−4.51249			−0.199037
$515$		0			0
$516$	−3.37346	+	2.83067i	−0.148508	+	0.124613i
$517$	−0.726682	+	0.264490i	−0.0319594	+	0.0116323i
$518$	−0.479055	−	0.174362i	−0.0210485	−	0.00766102i
$519$	−2.06939	−	1.73643i	−0.0908362	−	0.0762207i
$520$		0			0
$521$	−6.52734	−	11.3057i	−0.285968	−	0.495311i	0.686875	−	0.726775i	$-0.258982\pi$
$521$	−6.52734	−	11.3057i	−0.285968	−	0.495311i	−0.972843	+	0.231464i	$0.925648\pi$
$522$	−1.72193	+	9.76557i	−0.0753670	+	0.427427i
$523$	−3.08688	+	17.5065i	−0.134980	+	0.765508i	0.839894	+	0.542750i	$0.182617\pi$
$523$	−3.08688	+	17.5065i	−0.134980	+	0.765508i	−0.974874	+	0.222758i	$0.928494\pi$
$524$	4.21554	+	7.30152i	0.184157	+	0.318969i
$525$		0			0
$526$	23.0744	+	19.3618i	1.00609	+	0.844213i
$527$	10.0569	+	3.66041i	0.438086	+	0.159450i
$528$	−0.826352	+	0.300767i	−0.0359623	+	0.0130892i
$529$	−1.88460	+	1.58137i	−0.0819391	+	0.0687551i
$530$		0			0
$531$	−13.9581			−0.605730
$532$	−0.188663	−	2.31164i	−0.00817958	−	0.100222i
$533$	4.07873			0.176669
$534$	0.749275	+	4.24935i	0.0324243	+	0.183887i
$535$		0			0
$536$	−1.26604	+	0.460802i	−0.0546848	+	0.0199036i
$537$	13.1998	+	4.80434i	0.569614	+	0.207322i
$538$	3.31315	+	2.78006i	0.142840	+	0.119857i
$539$	−3.35844	+	5.81699i	−0.144658	+	0.250555i
$540$		0			0
$541$	−6.67008	+	37.8279i	−0.286769	+	1.62635i	0.412127	+	0.911126i	$0.364786\pi$
$541$	−6.67008	+	37.8279i	−0.286769	+	1.62635i	−0.698896	+	0.715223i	$0.746325\pi$
$542$	4.68433	−	26.5661i	0.201209	−	1.14111i
$543$	−4.29767	−	7.44378i	−0.184431	−	0.319443i
$544$	−1.93969	+	3.35965i	−0.0831636	+	0.144044i
$545$		0			0
$546$	−0.286989	−	0.104455i	−0.0122820	−	0.00447028i
$547$	−25.3888	+	9.24076i	−1.08555	+	0.395106i	−0.821969	−	0.569532i	$-0.807124\pi$
$547$	−25.3888	+	9.24076i	−1.08555	+	0.395106i	−0.263577	+	0.964638i	$0.584902\pi$
$548$	−6.10607	+	5.12360i	−0.260838	+	0.218869i
$549$	−1.90286	−	10.7916i	−0.0812119	−	0.460576i
$550$		0			0
$551$	−1.57903	−	19.3474i	−0.0672690	−	0.824228i
$552$	3.98545			0.169632
$553$	0.0655219	+	0.371593i	0.00278628	+	0.0158018i
$554$	1.68866	−	1.41696i	0.0717444	−	0.0602007i
$555$		0			0
$556$	5.92989	+	2.15830i	0.251483	+	0.0915325i
$557$	−9.20052	−	7.72016i	−0.389839	−	0.327113i	0.426712	−	0.904388i	$-0.359672\pi$
$557$	−9.20052	−	7.72016i	−0.389839	−	0.327113i	−0.816550	+	0.577274i	$0.804116\pi$
$558$	−3.07145	+	5.31991i	−0.130025	+	0.225210i
$559$	1.63429	+	2.83067i	0.0691229	+	0.119724i
$560$		0			0
$561$	−0.592396	+	3.35965i	−0.0250110	+	0.141844i
$562$	9.48932	+	16.4360i	0.400283	+	0.693310i
$563$	−7.37939	+	12.7815i	−0.311004	+	0.538675i	−0.978580	−	0.205867i	$-0.933999\pi$
$563$	−7.37939	+	12.7815i	−0.311004	+	0.538675i	0.667576	+	0.744542i	$0.267332\pi$
$564$	0.520945	+	0.437124i	0.0219357	+	0.0184063i
$565$		0			0
$566$	−13.6630	+	4.97291i	−0.574297	+	0.209027i
$567$	−1.07532	+	0.902302i	−0.0451593	+	0.0378931i
$568$	−0.985452	−	5.58878i	−0.0413487	−	0.234500i
$569$	−41.7570			−1.75055			−0.875273	−	0.483630i	$-0.839318\pi$
$569$	−41.7570			−1.75055			−0.875273	+	0.483630i	$0.839318\pi$
$570$		0			0
$571$	29.2431			1.22379			0.611893	−	0.790941i	$-0.290408\pi$
$571$	29.2431			1.22379			0.611893	+	0.790941i	$0.290408\pi$
$572$	0.113341	+	0.642788i	0.00473902	+	0.0268763i
$573$	−5.06599	+	4.25087i	−0.211635	+	0.177583i
$574$	3.12449	−	1.13722i	0.130413	−	0.0474666i
$575$		0			0
$576$	−1.70574	−	1.43128i	−0.0710724	−	0.0596368i
$577$	0.612159	−	1.06029i	0.0254845	−	0.0441405i	−0.853002	−	0.521908i	$-0.825220\pi$
$577$	0.612159	−	1.06029i	0.0254845	−	0.0441405i	0.878486	+	0.477767i	$0.158554\pi$
$578$	−0.975185	−	1.68907i	−0.0405624	−	0.0702561i
$579$	−3.74732	+	21.2521i	−0.155733	+	0.883208i
$580$		0			0
$581$	2.81134	+	4.86938i	0.116634	+	0.202016i
$582$	0.0444153	−	0.0769295i	0.00184107	−	0.00318883i
$583$	−2.95471	−	2.47929i	−0.122371	−	0.102682i
$584$	−7.02481	−	2.55682i	−0.290689	−	0.105802i
$585$		0			0
$586$	4.79679	−	4.02498i	0.198154	−	0.166271i
$587$	−4.82904	−	27.3868i	−0.199316	−	1.13038i	−0.906137	−	0.422984i	$-0.860983\pi$
$587$	−4.82904	−	27.3868i	−0.199316	−	1.13038i	0.706821	−	0.707392i	$-0.250128\pi$
$588$	5.90673			0.243589
$589$	3.18004	−	11.5971i	0.131031	−	0.477850i
$590$		0			0
$591$	−2.19950	−	12.4740i	−0.0904754	−	0.513112i
$592$	0.733956	−	0.615862i	0.0301654	−	0.0253118i
$593$	28.4628	−	10.3596i	1.16883	−	0.425418i	0.316583	−	0.948565i	$-0.397464\pi$
$593$	28.4628	−	10.3596i	1.16883	−	0.425418i	0.852242	+	0.523147i	$0.175242\pi$
$594$	−4.31908	−	1.57202i	−0.177214	−	0.0645006i
$595$		0			0
$596$	−9.04576	+	15.6677i	−0.370529	+	0.641775i
$597$	−1.95249	−	3.38180i	−0.0799099	−	0.138408i
$598$	0.513671	−	2.91317i	0.0210056	−	0.119128i
$599$	−2.09105	+	11.8589i	−0.0854381	+	0.484543i	0.911823	+	0.410583i	$0.134675\pi$
$599$	−2.09105	+	11.8589i	−0.0854381	+	0.484543i	−0.997261	+	0.0739602i	$0.976436\pi$
$600$		0			0
$601$	−7.05572	+	12.2209i	−0.287809	+	0.498500i	−0.973286	−	0.229594i	$-0.926260\pi$
$601$	−7.05572	+	12.2209i	−0.287809	+	0.498500i	0.685478	+	0.728094i	$0.259593\pi$
$602$	2.04117	+	1.71275i	0.0831920	+	0.0698064i
$603$	−2.81908	−	1.02606i	−0.114802	−	0.0417844i
$604$	−9.59152	+	3.49103i	−0.390273	+	0.142048i
$605$		0			0
$606$	−2.18907	−	12.4149i	−0.0889250	−	0.504319i
$607$	−5.31727			−0.215821			−0.107911	−	0.994161i	$-0.534416\pi$
$607$	−5.31727			−0.215821			−0.107911	+	0.994161i	$0.534416\pi$
$608$	3.93969	+	1.86516i	0.159776	+	0.0756422i
$609$	−2.08378			−0.0844390
$610$		0			0
$611$	0.386659	−	0.324446i	0.0156426	−	0.0131257i
$612$	−8.11721	+	2.95442i	−0.328119	+	0.119425i
$613$	−39.5531	−	14.3961i	−1.59753	−	0.581455i	−0.618614	−	0.785695i	$-0.712305\pi$
$613$	−39.5531	−	14.3961i	−1.59753	−	0.581455i	−0.978921	+	0.204241i	$0.934528\pi$
$614$	5.95992	+	5.00097i	0.240523	+	0.201823i
$615$		0			0
$616$	0.266044	+	0.460802i	0.0107192	+	0.0185663i
$617$	−2.70867	+	15.3617i	−0.109047	+	0.618437i	0.880479	+	0.474085i	$0.157221\pi$
$617$	−2.70867	+	15.3617i	−0.109047	+	0.618437i	−0.989526	+	0.144352i	$0.953890\pi$
$618$	0.944440	−	5.35619i	0.0379910	−	0.215457i
$619$	−11.1853	−	19.3734i	−0.449574	−	0.778684i	0.548785	−	0.835964i	$-0.315091\pi$
$619$	−11.1853	−	19.3734i	−0.449574	−	0.778684i	−0.998358	+	0.0572796i	$0.981757\pi$
$620$		0			0
$621$	15.9572	+	13.3897i	0.640342	+	0.537311i
$622$	−29.1660	−	10.6155i	−1.16945	−	0.425644i
$623$	2.45336	−	0.892951i	0.0982919	−	0.0357753i
$624$	0.439693	−	0.368946i	0.0176018	−	0.0147697i
$625$		0			0
$626$	−9.22668			−0.368772
$627$	3.81655	+	0.356347i	0.152418	+	0.0142311i
$628$	−15.9486			−0.636419
$629$	−0.645430	−	3.66041i	−0.0257350	−	0.145950i
$630$		0			0
$631$	−4.58260	+	1.66793i	−0.182430	+	0.0663992i	−0.431620	−	0.902055i	$-0.642058\pi$
$631$	−4.58260	+	1.66793i	−0.182430	+	0.0663992i	0.249190	+	0.968455i	$0.419836\pi$
$632$	−0.666374	−	0.242540i	−0.0265069	−	0.00964774i
$633$	7.57326	+	6.35472i	0.301010	+	0.252578i
$634$	12.0030	−	20.7898i	0.476700	−	0.825668i
$635$		0			0
$636$	−0.588993	+	3.34034i	−0.0233551	+	0.132453i
$637$	0.761297	−	4.31753i	0.0301637	−	0.171067i
$638$	2.22668	+	3.85673i	0.0881552	+	0.152689i
$639$	6.31820	−	10.9434i	0.249944	−	0.432916i
$640$		0			0
$641$	1.32635	+	0.482753i	0.0523877	+	0.0190676i	0.368081	−	0.929794i	$-0.380015\pi$
$641$	1.32635	+	0.482753i	0.0523877	+	0.0190676i	−0.315693	+	0.948861i	$0.602237\pi$
$642$	−8.08260	+	2.94182i	−0.318995	+	0.116105i
$643$	−6.26083	+	5.25346i	−0.246903	+	0.207176i	−0.757837	−	0.652444i	$-0.773744\pi$
$643$	−6.26083	+	5.25346i	−0.246903	+	0.207176i	0.510934	+	0.859620i	$0.329300\pi$
$644$	−0.418748	−	2.37484i	−0.0165010	−	0.0935817i
$645$		0			0
$646$	13.9081	−	9.61814i	0.547206	−	0.378421i
$647$	−31.3773			−1.23357			−0.616785	−	0.787132i	$-0.711565\pi$
$647$	−31.3773			−1.23357			−0.616785	+	0.787132i	$0.711565\pi$
$648$	−0.458111	−	2.59808i	−0.0179963	−	0.102062i
$649$	−4.80200	+	4.02936i	−0.188495	+	0.158166i
$650$		0			0
$651$	−1.21301	−	0.441500i	−0.0475417	−	0.0173037i
$652$	12.6591	+	10.6222i	0.495769	+	0.415999i
$653$	−19.4440	+	33.6780i	−0.760904	+	1.31792i	0.181482	+	0.983394i	$0.441911\pi$
$653$	−19.4440	+	33.6780i	−0.760904	+	1.31792i	−0.942385	+	0.334530i	$0.891423\pi$
$654$	5.63176	+	9.75449i	0.220219	+	0.381431i
$655$		0			0
$656$	−1.08512	+	6.15403i	−0.0423669	+	0.240275i
$657$	−8.32295	−	14.4158i	−0.324709	−	0.562413i
$658$	0.205737	−	0.356347i	0.00802047	−	0.0138919i
$659$	9.69047	+	8.13127i	0.377487	+	0.316749i	0.811715	−	0.584054i	$-0.198534\pi$
$659$	9.69047	+	8.13127i	0.377487	+	0.316749i	−0.434228	+	0.900803i	$0.642979\pi$
$660$		0			0
$661$	−41.7708	+	15.2033i	−1.62470	+	0.591342i	−0.984269	−	0.176676i	$-0.943466\pi$
$661$	−41.7708	+	15.2033i	−1.62470	+	0.591342i	−0.640429	+	0.768018i	$0.721243\pi$
$662$	18.8025	−	15.7771i	0.730779	−	0.613196i
$663$	−0.386659	−	2.19285i	−0.0150166	−	0.0851634i
$664$	−10.5672			−0.410086
$665$		0			0
$666$	2.13341			0.0826679
$667$	−3.50475	−	19.8764i	−0.135704	−	0.769618i
$668$	18.2212	−	15.2894i	0.705000	−	0.591565i
$669$	9.92040	−	3.61073i	0.383545	−	0.139599i
$670$		0			0
$671$	−3.76991	−	3.16333i	−0.145536	−	0.122119i
$672$	0.233956	−	0.405223i	0.00902503	−	0.0156318i
$673$	9.75196	+	16.8909i	0.375911	+	0.651096i	0.990463	−	0.137780i	$-0.0439967\pi$
$673$	9.75196	+	16.8909i	0.375911	+	0.651096i	−0.614552	+	0.788876i	$0.710663\pi$
$674$	5.32295	−	30.1879i	0.205032	−	1.16280i
$675$		0			0
$676$	6.28699	+	10.8894i	0.241807	+	0.418822i
$677$	−3.51455	+	6.08738i	−0.135075	+	0.233957i	−0.925626	−	0.378439i	$-0.876461\pi$
$677$	−3.51455	+	6.08738i	−0.135075	+	0.233957i	0.790551	+	0.612396i	$0.209794\pi$
$678$	3.68866	+	3.09516i	0.141662	+	0.118869i
$679$	−0.0505072	−	0.0183831i	−0.00193829	−	0.000705479i
$680$		0			0
$681$	17.4388	−	14.6329i	0.668257	−	0.560734i
$682$	0.479055	+	2.71686i	0.0183440	+	0.104034i
$683$	−0.386821			−0.0148013			−0.00740065	−	0.999973i	$-0.502356\pi$
$683$	−0.386821			−0.0148013			−0.00740065	+	0.999973i	$0.502356\pi$
$684$	4.05051	+	8.82029i	0.154875	+	0.337252i
$685$		0			0
$686$	−1.26739	−	7.18772i	−0.0483891	−	0.274428i
$687$	−7.48680	+	6.28217i	−0.285639	+	0.239680i
$688$	−4.70574	+	1.71275i	−0.179405	+	0.0652979i
$689$	2.36571	+	0.861050i	0.0901266	+	0.0328034i
$690$		0			0
$691$	21.2260	−	36.7645i	0.807474	−	1.39859i	−0.107134	−	0.994245i	$-0.534168\pi$
$691$	21.2260	−	36.7645i	0.807474	−	1.39859i	0.914608	−	0.404341i	$-0.132499\pi$
$692$	−1.53596	−	2.66036i	−0.0583884	−	0.101132i
$693$	−0.205737	+	1.16679i	−0.00781530	+	0.0443228i
$694$	1.34730	−	7.64090i	0.0511427	−	0.290044i
$695$		0			0
$696$	1.95811	−	3.39155i	0.0742220	−	0.128556i
$697$	18.5706	+	15.5826i	0.703411	+	0.590232i
$698$	−11.9820	−	4.36111i	−0.453527	−	0.165070i
$699$	−1.04829	+	0.381545i	−0.0396498	+	0.0144313i
$700$		0			0
$701$	−5.96497	−	33.8291i	−0.225294	−	1.27771i	−0.862122	−	0.506700i	$-0.830865\pi$
$701$	−5.96497	−	33.8291i	−0.225294	−	1.27771i	0.636828	−	0.771006i	$-0.280246\pi$
$702$	3.00000			0.113228
$703$	−4.04024	+	1.05736i	−0.152381	+	0.0398792i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	−7.24691	+	6.08088i	−0.272741	+	0.228857i
$707$	−7.16772	+	2.60884i	−0.269570	+	0.0981154i
$708$	5.18004	+	1.88538i	0.194678	+	0.0708570i
$709$	−7.38144	−	6.19377i	−0.277216	−	0.232612i	0.493570	−	0.869706i	$-0.335692\pi$
$709$	−7.38144	−	6.19377i	−0.277216	−	0.232612i	−0.770786	+	0.637094i	$0.780136\pi$
$710$		0			0
$711$	−0.789515	−	1.36748i	−0.0296091	−	0.0512845i
$712$	−0.852044	+	4.83218i	−0.0319317	+	0.181094i
$713$	2.17112	−	12.3130i	0.0813092	−	0.461127i
$714$	−0.907604	−	1.57202i	−0.0339662	−	0.0588312i
$715$		0			0
$716$	12.2365	+	10.2676i	0.457299	+	0.383719i
$717$	3.52734	+	1.28385i	0.131731	+	0.0479462i
$718$	−0.983803	+	0.358075i	−0.0367152	+	0.0133632i
$719$	35.3542	−	29.6657i	1.31849	−	1.10634i	0.331864	−	0.943327i	$-0.392322\pi$
$719$	35.3542	−	29.6657i	1.31849	−	1.10634i	0.986624	−	0.163015i	$-0.0521220\pi$
$720$		0			0
$721$	−3.29086			−0.122558
$722$	−12.0424	−	14.6963i	−0.448170	−	0.546940i
$723$	−25.8536			−0.961505
$724$	−1.69728	−	9.62576i	−0.0630790	−	0.357739i
$725$		0			0
$726$	8.26352	−	3.00767i	0.306688	−	0.111625i
$727$	−3.10132	−	1.12879i	−0.115022	−	0.0418644i	0.283868	−	0.958863i	$-0.408382\pi$
$727$	−3.10132	−	1.12879i	−0.115022	−	0.0418644i	−0.398890	+	0.916999i	$0.630604\pi$
$728$	−0.266044	−	0.223238i	−0.00986026	−	0.00827374i
$729$	−3.12567	+	5.41381i	−0.115765	+	0.200512i
$730$		0			0
$731$	−3.37346	+	19.1318i	−0.124772	+	0.707616i
$732$	−0.751497	+	4.26195i	−0.0277761	+	0.157526i
$733$	−21.6766	−	37.5450i	−0.800645	−	1.38676i	−0.919192	−	0.393809i	$-0.871157\pi$
$733$	−21.6766	−	37.5450i	−0.800645	−	1.38676i	0.118547	−	0.992948i	$-0.462176\pi$
$734$	−4.94222	+	8.56017i	−0.182421	+	0.315962i
$735$		0			0
$736$	4.25877	+	1.55007i	0.156980	+	0.0571362i
$737$	−1.26604	+	0.460802i	−0.0466353	+	0.0169739i
$738$	−10.6591	+	8.94405i	−0.392367	+	0.329235i
$739$	−0.427204	−	2.42279i	−0.0157150	−	0.0891239i	0.975942	−	0.218032i	$-0.0699638\pi$
$739$	−0.427204	−	2.42279i	−0.0157150	−	0.0891239i	−0.991657	+	0.128908i	$0.958853\pi$
$740$		0			0
$741$	−2.42040	+	0.633436i	−0.0889155	+	0.0232699i
$742$	2.05232			0.0753430
$743$	−1.46017	−	8.28104i	−0.0535685	−	0.303802i	0.946238	−	0.323471i	$-0.104850\pi$
$743$	−1.46017	−	8.28104i	−0.0535685	−	0.303802i	−0.999807	+	0.0196692i	$0.993739\pi$
$744$	1.85844	−	1.55942i	0.0681337	−	0.0571710i
$745$		0			0
$746$	26.0501	+	9.48146i	0.953762	+	0.347141i
$747$	−18.0248	−	15.1246i	−0.659493	−	0.553381i
$748$	−1.93969	+	3.35965i	−0.0709222	+	0.122841i
$749$	2.60220	+	4.50714i	0.0950822	+	0.164687i
$750$		0			0
$751$	−1.14502	+	6.49373i	−0.0417823	+	0.236959i	−0.998546	−	0.0539072i	$-0.982832\pi$
$751$	−1.14502	+	6.49373i	−0.0417823	+	0.236959i	0.956764	+	0.290867i	$0.0939436\pi$
$752$	0.386659	+	0.669713i	0.0141000	+	0.0244219i
$753$	4.27807	−	7.40983i	0.155901	−	0.270029i
$754$	−2.22668	−	1.86841i	−0.0810910	−	0.0680434i
$755$		0			0
$756$	2.29813	−	0.836452i	0.0835823	−	0.0304215i
$757$	1.98751	−	1.66772i	0.0722373	−	0.0606143i	−0.605954	−	0.795500i	$-0.707208\pi$
$757$	1.98751	−	1.66772i	0.0722373	−	0.0606143i	0.678191	+	0.734885i	$0.262764\pi$
$758$	2.27110	+	12.8800i	0.0824900	+	0.467824i
$759$	3.98545			0.144663
$760$		0			0
$761$	35.9454			1.30302			0.651510	−	0.758640i	$-0.274136\pi$
$761$	35.9454			1.30302			0.651510	+	0.758640i	$0.274136\pi$
$762$	1.57041	+	8.90625i	0.0568900	+	0.322639i
$763$	5.22075	−	4.38073i	0.189004	−	0.158593i
$764$	−7.06670	+	2.57207i	−0.255664	+	0.0930542i
$765$		0			0
$766$	−7.63041	−	6.40268i	−0.275698	−	0.231338i
$767$	2.04576	−	3.54336i	0.0738681	−	0.127943i
$768$	0.439693	+	0.761570i	0.0158660	+	0.0274808i
$769$	3.00815	−	17.0601i	0.108477	−	0.615202i	−0.881298	−	0.472561i	$-0.843330\pi$
$769$	3.00815	−	17.0601i	0.108477	−	0.615202i	0.989775	−	0.142641i	$-0.0455593\pi$
$770$		0			0
$771$	1.98411	+	3.43658i	0.0714559	+	0.123765i
$772$	−12.2699	+	21.2521i	−0.441604	+	0.764880i
$773$	−27.6236	−	23.1790i	−0.993552	−	0.833689i	−0.00747402	−	0.999972i	$-0.502379\pi$
$773$	−27.6236	−	23.1790i	−0.993552	−	0.833689i	−0.986078	+	0.166283i	$0.946824\pi$
$774$	−10.4782	−	3.81374i	−0.376630	−	0.137082i
$775$		0			0
$776$	0.0773815	−	0.0649308i	0.00277783	−	0.00233088i
$777$	0.0778483	+	0.441500i	0.00279279	+	0.0158387i
$778$	24.1206			0.864766
$779$	15.7533	−	22.2211i	0.564421	−	0.796153i
$780$		0			0
$781$	−0.985452	−	5.58878i	−0.0352622	−	0.199982i
$782$	13.4684	−	11.3013i	0.481628	−	0.404134i
$783$	19.2344	−	7.00076i	0.687382	−	0.250187i
$784$	6.31180	+	2.29731i	0.225422	+	0.0820467i
$785$		0			0
$786$	3.70708	−	6.42085i	0.132227	−	0.229024i
$787$	−5.79544	−	10.0380i	−0.206585	−	0.357816i	0.744051	−	0.668122i	$-0.232902\pi$
$787$	−5.79544	−	10.0380i	−0.206585	−	0.357816i	−0.950637	+	0.310306i	$0.899568\pi$
$788$	2.50118	−	14.1849i	0.0891009	−	0.505316i
$789$	4.59967	−	26.0860i	0.163753	−	0.928687i
$790$		0			0
$791$	1.45677	−	2.52319i	0.0517967	−	0.0897145i
$792$	−1.70574	−	1.43128i	−0.0606107	−	0.0508584i
$793$	3.01842	+	1.09861i	0.107187	+	0.0390129i
$794$	−23.8396	+	8.67691i	−0.846036	+	0.307932i
$795$		0			0
$796$	−0.771097	−	4.37311i	−0.0273308	−	0.155001i
$797$	−45.0634			−1.59623			−0.798113	−	0.602508i	$-0.794168\pi$
$797$	−45.0634			−1.59623			−0.798113	+	0.602508i	$0.794168\pi$
$798$	−1.67752	+	1.16009i	−0.0593835	+	0.0410667i
$799$	3.00000			0.106132
$800$		0			0
$801$	−8.36959	+	7.02292i	−0.295725	+	0.248143i
$802$	−23.3131	+	8.48529i	−0.823216	+	0.299626i
$803$	−7.02481	−	2.55682i	−0.247900	−	0.0902283i
$804$	0.907604	+	0.761570i	0.0320087	+	0.0268585i
$805$		0			0
$806$	−0.900330	−	1.55942i	−0.0317128	−	0.0549281i
$807$	0.660444	−	3.74557i	0.0232487	−	0.131850i
$808$	2.48932	−	14.1176i	0.0875741	−	0.496657i
$809$	2.82841	+	4.89895i	0.0994416	+	0.172238i	0.911454	−	0.411403i	$-0.134961\pi$
$809$	2.82841	+	4.89895i	0.0994416	+	0.172238i	−0.812012	+	0.583641i	$0.801628\pi$
$810$		0			0
$811$	21.2781	+	17.8545i	0.747176	+	0.626955i	0.934754	−	0.355295i	$-0.115619\pi$
$811$	21.2781	+	17.8545i	0.747176	+	0.626955i	−0.187578	+	0.982250i	$0.560064\pi$
$812$	−2.22668	−	0.810446i	−0.0781412	−	0.0284411i
$813$	−22.2916	+	8.11349i	−0.781802	+	0.284553i
$814$	0.733956	−	0.615862i	0.0257251	−	0.0215859i
$815$		0			0
$816$	3.41147			0.119425
$817$	21.7337	+	2.02925i	0.760366	+	0.0709945i
$818$	29.9855			1.04842
$819$	−0.134285	−	0.761570i	−0.00469231	−	0.0266114i
$820$		0			0
$821$	−36.1450	+	13.1557i	−1.26147	+	0.459137i	−0.884262	−	0.466991i	$-0.845338\pi$
$821$	−36.1450	+	13.1557i	−1.26147	+	0.459137i	−0.377208	+	0.926129i	$0.623116\pi$
$822$	6.58677	+	2.39739i	0.229740	+	0.0836185i
$823$	−7.16044	−	6.00833i	−0.249597	−	0.209437i	0.509402	−	0.860529i	$-0.329867\pi$
$823$	−7.16044	−	6.00833i	−0.249597	−	0.209437i	−0.758999	+	0.651092i	$0.774311\pi$
$824$	3.09240	−	5.35619i	0.107729	−	0.186592i
$825$		0			0
$826$	0.579193	−	3.28476i	0.0201527	−	0.114292i
$827$	−7.95652	+	45.1237i	−0.276675	+	1.56910i	0.456914	+	0.889511i	$0.348955\pi$
$827$	−7.95652	+	45.1237i	−0.276675	+	1.56910i	−0.733590	+	0.679593i	$0.762157\pi$
$828$	5.04576	+	8.73951i	0.175352	+	0.303719i
$829$	20.7699	−	35.9745i	0.721369	−	1.24945i	−0.239082	−	0.970999i	$-0.576847\pi$
$829$	20.7699	−	35.9745i	0.721369	−	1.24945i	0.960451	−	0.278448i	$-0.0898201\pi$
$830$		0			0
$831$	−1.82160	−	0.663010i	−0.0631907	−	0.0229996i
$832$	0.613341	−	0.223238i	0.0212638	−	0.00773938i
$833$	19.9611	−	16.7494i	0.691611	−	0.580331i
$834$	−0.963630	−	5.46502i	−0.0333678	−	0.189238i
$835$		0			0
$836$	3.93969	+	1.86516i	0.136257	+	0.0645079i
$837$	12.6800			0.438286
$838$	3.07697	+	17.4504i	0.106292	+	0.602813i
$839$	−18.0458	+	15.1422i	−0.623009	+	0.522766i	−0.898748	−	0.438466i	$-0.855522\pi$
$839$	−18.0458	+	15.1422i	−0.623009	+	0.522766i	0.275739	+	0.961233i	$0.411077\pi$
$840$		0			0
$841$	8.61468	+	3.13549i	0.297058	+	0.108120i
$842$	9.22462	+	7.74038i	0.317901	+	0.266751i
$843$	8.34477	−	14.4536i	0.287409	−	0.497807i
$844$	5.62108	+	9.73600i	0.193486	+	0.335127i
$845$		0			0
$846$	−0.299011	+	1.69577i	−0.0102802	+	0.0583019i
$847$	−2.66044	−	4.60802i	−0.0914140	−	0.158334i
$848$	−1.92855	+	3.34034i	−0.0662266	+	0.114708i
$849$	9.79473	+	8.21875i	0.336154	+	0.282067i
$850$		0			0
$851$	−4.08037	+	1.48513i	−0.139873	+	0.0509098i
$852$	−3.82295	+	3.20783i	−0.130972	+	0.109899i
$853$	2.73025	+	15.4840i	0.0934819	+	0.530162i	0.995202	+	0.0978418i	$0.0311939\pi$
$853$	2.73025	+	15.4840i	0.0934819	+	0.530162i	−0.901720	+	0.432320i	$0.857695\pi$
$854$	2.61856			0.0896051
$855$		0			0
$856$	−9.78106			−0.334310
$857$	−0.454403	−	2.57705i	−0.0155221	−	0.0880302i	0.976063	−	0.217490i	$-0.0697869\pi$
$857$	−0.454403	−	2.57705i	−0.0155221	−	0.0880302i	−0.991585	+	0.129460i	$0.958676\pi$
$858$	0.439693	−	0.368946i	0.0150109	−	0.0125956i
$859$	20.7729	−	7.56072i	0.708762	−	0.257968i	0.0376150	−	0.999292i	$-0.488024\pi$
$859$	20.7729	−	7.56072i	0.708762	−	0.257968i	0.671147	+	0.741324i	$0.265802\pi$
$860$		0			0
$861$	−2.23989	−	1.87949i	−0.0763351	−	0.0640527i
$862$	17.6826	−	30.6271i	0.602271	−	1.04316i
$863$	1.59920	+	2.76990i	0.0544375	+	0.0942885i	0.891960	−	0.452114i	$-0.149330\pi$
$863$	1.59920	+	2.76990i	0.0544375	+	0.0942885i	−0.837522	+	0.546403i	$0.815997\pi$
$864$	−0.798133	+	4.52644i	−0.0271530	+	0.153993i
$865$		0			0
$866$	−13.3983	−	23.2065i	−0.455292	−	0.788588i
$867$	−0.857563	+	1.48534i	−0.0291244	+	0.0504449i
$868$	−1.12449	−	0.943555i	−0.0381675	−	0.0320263i
$869$	−0.666374	−	0.242540i	−0.0226052	−	0.00822762i
$870$		0			0
$871$	0.673648	−	0.565258i	0.0228257	−	0.0191530i
$872$	2.22416	+	12.6138i	0.0753194	+	0.427158i
$873$	0.224927			0.00761262
$874$	−13.8871	−	14.0501i	−0.469739	−	0.475251i
$875$		0			0
$876$	1.14156	+	6.47410i	0.0385697	+	0.218740i
$877$	−41.5001	+	34.8227i	−1.40136	+	1.17588i	−0.440865	+	0.897574i	$0.645328\pi$
$877$	−41.5001	+	34.8227i	−1.40136	+	1.17588i	−0.960493	+	0.278305i	$0.910227\pi$
$878$	22.4167	−	8.15901i	0.756527	−	0.275353i
$879$	−5.17442	−	1.88333i	−0.174529	−	0.0635233i
$880$		0			0
$881$	25.2670	−	43.7637i	0.851266	−	1.47444i	−0.0288001	−	0.999585i	$-0.509169\pi$
$881$	25.2670	−	43.7637i	0.851266	−	1.47444i	0.880066	−	0.474851i	$-0.157498\pi$
$882$	7.47818	+	12.9526i	0.251803	+	0.436136i
$883$	7.84224	−	44.4756i	0.263913	−	1.49672i	−0.508201	−	0.861238i	$-0.669689\pi$
$883$	7.84224	−	44.4756i	0.263913	−	1.49672i	0.772114	−	0.635484i	$-0.219199\pi$
$884$	0.439693	−	2.49362i	0.0147885	−	0.0838695i
$885$		0			0
$886$	16.8516	−	29.1879i	0.566142	−	0.980586i
$887$	41.4051	+	34.7430i	1.39025	+	1.16656i	0.965239	+	0.261368i	$0.0841735\pi$
$887$	41.4051	+	34.7430i	1.39025	+	1.16656i	0.425009	+	0.905189i	$0.360271\pi$
$888$	−0.791737	−	0.288169i	−0.0265689	−	0.00967030i
$889$	5.14203	−	1.87154i	0.172458	−	0.0627696i
$890$		0			0
$891$	−0.458111	−	2.59808i	−0.0153473	−	0.0870388i
$892$	12.0051			0.401959
$893$	−0.274196	−	3.35965i	−0.00917561	−	0.112426i
$894$	15.9094			0.532090
$895$		0			0
$896$	0.407604	−	0.342020i	0.0136171	−	0.0114261i
$897$	−2.44444	+	0.889704i	−0.0816175	+	0.0297063i
$898$	12.1334	+	4.41620i	0.404897	+	0.147370i
$899$	−9.41147	−	7.89716i	−0.313890	−	0.263385i
$900$		0			0
$901$	7.48158	+	12.9585i	0.249248	+	0.431710i
$902$	−1.08512	+	6.15403i	−0.0361306	+	0.204907i
$903$	0.406889	−	2.30758i	0.0135404	−	0.0767914i
$904$	2.73783	+	4.74205i	0.0910587	+	0.157718i
$905$		0			0
$906$	6.87598	+	5.76963i	0.228439	+	0.191683i
$907$	20.3243	+	7.39744i	0.674857	+	0.245628i	0.656638	−	0.754206i	$-0.271978\pi$
$907$	20.3243	+	7.39744i	0.674857	+	0.245628i	0.0182193	+	0.999834i	$0.494200\pi$
$908$	24.3259	−	8.85392i	0.807285	−	0.293828i
$909$	24.4525	−	20.5181i	0.811038	−	0.680541i
$910$		0			0
$911$	−38.0529			−1.26075			−0.630375	−	0.776291i	$-0.717099\pi$
$911$	−38.0529			−1.26075			−0.630375	+	0.776291i	$0.717099\pi$
$912$	−0.311804	−	3.82045i	−0.0103249	−	0.126508i
$913$	−10.5672			−0.349722
$914$	−6.26486	−	35.5298i	−0.207223	−	1.17522i
$915$		0			0
$916$	−10.4436	+	3.80115i	−0.345065	+	0.125593i
$917$	−4.21554	−	1.53433i	−0.139209	−	0.0506680i
$918$	13.6591	+	11.4613i	0.450817	+	0.378281i
$919$	10.7255	−	18.5771i	0.353802	−	0.612802i	−0.633111	−	0.774061i	$-0.718222\pi$
$919$	10.7255	−	18.5771i	0.353802	−	0.612802i	0.986912	+	0.161259i	$0.0515555\pi$
$920$		0			0
$921$	1.18805	−	6.73779i	0.0391477	−	0.222018i
$922$	0.00980018	−	0.0555796i	0.000322752	−	0.00183042i
$923$	1.85204	+	3.20783i	0.0609608	+	0.105587i
$924$	0.233956	−	0.405223i	0.00769657	−	0.0133309i
$925$		0			0
$926$	26.4530	+	9.62809i	0.869298	+	0.316399i
$927$	12.9410	−	4.71015i	0.425039	−	0.154702i
$928$	3.41147	−	2.86257i	0.111987	−	0.0939684i
$929$	3.81093	+	21.6128i	0.125032	+	0.709094i	0.981289	+	0.192543i	$0.0616734\pi$
$929$	3.81093	+	21.6128i	0.125032	+	0.709094i	−0.856256	+	0.516551i	$0.827215\pi$
$930$		0			0
$931$	−20.5817	−	20.8232i	−0.674539	−	0.682453i
$932$	−1.26857			−0.0415534
$933$	4.73958	+	26.8795i	0.155167	+	0.879995i
$934$	−0.236015	+	0.198040i	−0.00772265	+	0.00648007i
$935$		0			0
$936$	1.36571	+	0.497079i	0.0446398	+	0.0162476i
$937$	−36.9365	−	30.9934i	−1.20666	−	1.01251i	−0.999414	−	0.0342223i	$-0.989105\pi$
$937$	−36.9365	−	30.9934i	−1.20666	−	1.01251i	−0.207249	−	0.978288i	$-0.566451\pi$
$938$	0.358441	−	0.620838i	0.0117035	−	0.0202711i
$939$	4.05690	+	7.02676i	0.132392	+	0.229310i
$940$		0			0
$941$	2.49004	−	14.1217i	0.0811729	−	0.460354i	−0.916944	−	0.399016i	$-0.869352\pi$
$941$	2.49004	−	14.1217i	0.0811729	−	0.460354i	0.998117	−	0.0613388i	$-0.0195370\pi$
$942$	7.01249	+	12.1460i	0.228479	+	0.395738i
$943$	14.1604	−	24.5266i	0.461128	−	0.798696i
$944$	4.80200	+	4.02936i	0.156292	+	0.131144i
$945$		0			0
$946$	−4.70574	+	1.71275i	−0.152997	+	0.0556862i
$947$	−17.9984	+	15.1025i	−0.584870	+	0.490764i	−0.886542	−	0.462648i	$-0.846900\pi$
$947$	−17.9984	+	15.1025i	−0.584870	+	0.490764i	0.301673	+	0.953412i	$0.402455\pi$
$948$	0.108288	+	0.614134i	0.00351704	+	0.0199461i
$949$	4.87939			0.158392
$950$		0			0
$951$	−21.1105			−0.684555
$952$	−0.358441	−	2.03282i	−0.0116171	−	0.0658840i
$953$	32.6798	−	27.4216i	1.05860	−	0.888273i	0.0646307	−	0.997909i	$-0.479413\pi$
$953$	32.6798	−	27.4216i	1.05860	−	0.888273i	0.993972	+	0.109636i	$0.0349686\pi$
$954$	−8.07057	+	2.93745i	−0.261294	+	0.0951034i
$955$		0			0
$956$	3.26991	+	2.74378i	0.105757	+	0.0887403i
$957$	1.95811	−	3.39155i	0.0632967	−	0.109633i
$958$	15.1125	+	26.1756i	0.488262	+	0.845694i
$959$	0.736482	−	4.17680i	0.0237822	−	0.134876i
$960$		0			0
$961$	11.6946	+	20.2556i	0.377245	+	0.653407i
$962$	−0.312681	+	0.541580i	−0.0100812	+	0.0174612i
$963$	−16.6839	−	13.9995i	−0.537632	−	0.451127i
$964$	−27.6266	−	10.0553i	−0.889793	−	0.323858i
$965$		0			0
$966$	−1.62449	+	1.36310i	−0.0522670	+	0.0438572i
$967$	3.13434	+	17.7757i	0.100794	+	0.571629i	0.992817	+	0.119640i	$0.0381742\pi$
$967$	3.13434	+	17.7757i	0.100794	+	0.571629i	−0.892024	+	0.451989i	$0.850715\pi$
$968$	10.0000			0.321412
$969$	−13.4402	−	6.36295i	−0.431760	−	0.204407i
$970$		0			0
$971$	−3.87346	−	21.9675i	−0.124305	−	0.704969i	−0.981718	−	0.190340i	$-0.939041\pi$
$971$	−3.87346	−	21.9675i	−0.124305	−	0.704969i	0.857413	−	0.514629i	$-0.172070\pi$
$972$	−12.3400	+	10.3545i	−0.395806	+	0.332121i
$973$	−3.15523	+	1.14841i	−0.101152	+	0.0368163i
$974$	−28.0984	−	10.2270i	−0.900330	−	0.327693i
$975$		0			0
$976$	−2.46064	+	4.26195i	−0.0787631	+	0.136422i
$977$	−3.72921	−	6.45918i	−0.119308	−	0.206647i	0.800186	−	0.599752i	$-0.204734\pi$
$977$	−3.72921	−	6.45918i	−0.119308	−	0.206647i	−0.919494	+	0.393105i	$0.871401\pi$
$978$	2.52347	−	14.3113i	0.0806917	−	0.457625i
$979$	−0.852044	+	4.83218i	−0.0272314	+	0.154437i
$980$		0			0
$981$	−14.2601	+	24.6992i	−0.455290	+	0.788586i
$982$	2.98680	+	2.50622i	0.0953125	+	0.0799767i
$983$	6.57620	+	2.39354i	0.209748	+	0.0763421i	0.444758	−	0.895651i	$-0.353290\pi$
$983$	6.57620	+	2.39354i	0.209748	+	0.0763421i	−0.235009	+	0.971993i	$0.575512\pi$
$984$	5.16385	−	1.87949i	0.164617	−	0.0599159i
$985$		0			0
$986$	−3.00000	−	17.0138i	−0.0955395	−	0.541831i
$987$	−0.361844			−0.0115176
$988$	−2.83275	−	0.264490i	−0.0901217	−	0.00841456i
$989$	22.6955			0.721676
$990$		0			0
$991$	7.77900	−	6.52736i	0.247108	−	0.207348i	−0.510818	−	0.859689i	$-0.670657\pi$
$991$	7.77900	−	6.52736i	0.247108	−	0.207348i	0.757926	+	0.652341i	$0.226213\pi$
$992$	2.59240	−	0.943555i	0.0823087	−	0.0299579i
$993$	−20.2827	−	7.38230i	−0.643652	−	0.234270i
$994$	2.31315	+	1.94096i	0.0733686	+	0.0615636i
$995$		0			0
$996$	4.64631	+	8.04764i	0.147224	+	0.254999i
$997$	−9.49928	+	53.8731i	−0.300845	+	1.70618i	0.341598	+	0.939846i	$0.389032\pi$
$997$	−9.49928	+	53.8731i	−0.300845	+	1.70618i	−0.642444	+	0.766333i	$0.722079\pi$
$998$	4.23601	−	24.0236i	0.134089	−	0.760455i
$999$	−2.20187	−	3.81374i	−0.0696640	−	0.120662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.b.351.1	✓	6
5.2	odd	4		950.2.u.d.199.2		12
5.3	odd	4		950.2.u.d.199.1		12
5.4	even	2		950.2.l.e.351.1	yes	6
19.17	even	9	inner	950.2.l.b.701.1	yes	6
95.17	odd	36		950.2.u.d.549.1		12
95.74	even	18		950.2.l.e.701.1	yes	6
95.93	odd	36		950.2.u.d.549.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.b.351.1	✓	6	1.1	even	1	trivial
950.2.l.b.701.1	yes	6	19.17	even	9	inner
950.2.l.e.351.1	yes	6	5.4	even	2
950.2.l.e.701.1	yes	6	95.74	even	18
950.2.u.d.199.1		12	5.3	odd	4
950.2.u.d.199.2		12	5.2	odd	4
950.2.u.d.549.1		12	95.17	odd	36
950.2.u.d.549.2		12	95.93	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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.673648 + 0.565258i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.386659 + 2.19285i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.673648 + 0.565258i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{6} +(0.266044 - 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.386659 + 2.19285i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.439693 - 0.761570i) q^{12} +(-0.500000 - 0.419550i) q^{13} +(-0.500000 - 0.181985i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.673648 - 3.82045i) q^{17} +2.22668 q^{18} +(-4.21688 + 1.10359i) q^{19} +(0.0812519 + 0.460802i) q^{21} +(0.766044 - 0.642788i) q^{22} +(-4.25877 + 1.55007i) q^{23} +(-0.826352 - 0.300767i) q^{24} +(-0.326352 + 0.565258i) q^{26} +(-2.29813 - 3.98048i) q^{27} +(-0.0923963 + 0.524005i) q^{28} +(-0.773318 + 4.38571i) q^{29} +(-1.37939 + 2.38917i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.826352 - 0.300767i) q^{33} +(-3.64543 + 1.32683i) q^{34} +(-0.386659 - 2.19285i) q^{36} +0.958111 q^{37} +(1.81908 + 3.96118i) q^{38} +0.573978 q^{39} +(-4.78699 + 4.01676i) q^{41} +(0.439693 - 0.160035i) q^{42} +(-4.70574 - 1.71275i) q^{43} +(-0.766044 - 0.642788i) q^{44} +(2.26604 + 3.92490i) q^{46} +(-0.134285 + 0.761570i) q^{47} +(-0.152704 + 0.866025i) q^{48} +(3.35844 + 5.81699i) q^{49} +(2.61334 + 2.19285i) q^{51} +(0.613341 + 0.223238i) q^{52} +(-3.62449 + 1.31920i) q^{53} +(-3.52094 + 2.95442i) q^{54} +0.532089 q^{56} +(2.21688 - 3.12706i) q^{57} +4.45336 q^{58} +(1.08853 + 6.17334i) q^{59} +(-4.62449 + 1.68317i) q^{61} +(2.59240 + 0.943555i) q^{62} +(0.907604 + 0.761570i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.152704 + 0.866025i) q^{66} +(-0.233956 + 1.32683i) q^{67} +(1.93969 + 3.35965i) q^{68} +(1.99273 - 3.45150i) q^{69} +(-5.33275 - 1.94096i) q^{71} +(-2.09240 + 0.761570i) q^{72} +(-5.72668 + 4.80526i) q^{73} +(-0.166374 - 0.943555i) q^{74} +(3.58512 - 2.47929i) q^{76} +0.532089 q^{77} +(-0.0996702 - 0.565258i) q^{78} +(-0.543233 + 0.455827i) q^{79} +(-2.47906 - 0.902302i) q^{81} +(4.78699 + 4.01676i) q^{82} +(-5.28359 + 9.15144i) q^{83} +(-0.233956 - 0.405223i) q^{84} +(-0.869585 + 4.93166i) q^{86} +(-1.95811 - 3.39155i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.75877 + 3.15398i) q^{89} +(-0.326352 + 0.118782i) q^{91} +(3.47178 - 2.91317i) q^{92} +(-0.421274 - 2.38917i) q^{93} +0.773318 q^{94} +0.879385 q^{96} +(-0.0175410 - 0.0994798i) q^{97} +(5.14543 - 4.31753i) q^{98} +(-2.09240 + 0.761570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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