LMFDB - Embedded newform 950.2.l.l.301.3

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.3
Character	$\chi$	$=$	950.301
Dual form			950.2.l.l.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.0808150 + 0.0294142i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0808150 + 0.0294142i) q^{6} +(-1.91879 - 3.32344i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29247 + 1.92361i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.0808150 + 0.0294142i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0808150 + 0.0294142i) q^{6} +(-1.91879 - 3.32344i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29247 + 1.92361i) q^{9} +(-1.81940 + 3.15129i) q^{11} +(-0.0430007 - 0.0744795i) q^{12} +(5.10468 + 1.85795i) q^{13} +(-0.666388 + 3.77928i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.33279 + 2.79655i) q^{17} +2.99260 q^{18} +(2.88277 - 3.26950i) q^{19} +(0.252823 + 0.212144i) q^{21} +(3.41935 - 1.24454i) q^{22} +(-0.631806 - 3.58315i) q^{23} +(-0.0149340 + 0.0846949i) q^{24} +(-2.71614 - 4.70450i) q^{26} +(0.257686 - 0.446326i) q^{27} +(2.93976 - 2.46675i) q^{28} +(0.814552 - 0.683490i) q^{29} +(0.846669 + 1.46647i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0543417 - 0.308187i) q^{33} +(-0.755483 - 4.28456i) q^{34} +(-2.29247 - 1.92361i) q^{36} +4.69909 q^{37} +(-4.30992 + 0.651573i) q^{38} -0.467184 q^{39} +(10.5664 - 3.84584i) q^{41} +(-0.0573104 - 0.325023i) q^{42} +(1.96605 - 11.1500i) q^{43} +(-3.41935 - 1.24454i) q^{44} +(-1.81921 + 3.15097i) q^{46} +(-4.24968 + 3.56591i) q^{47} +(0.0658810 - 0.0552807i) q^{48} +(-3.86350 + 6.69178i) q^{49} +(-0.351598 - 0.127971i) q^{51} +(-0.943306 + 5.34975i) q^{52} +(-0.464786 - 2.63593i) q^{53} +(-0.484292 + 0.176268i) q^{54} -3.83758 q^{56} +(-0.136801 + 0.349019i) q^{57} -1.06332 q^{58} +(8.09344 + 6.79121i) q^{59} +(1.77122 + 10.0451i) q^{61} +(0.294045 - 1.66761i) q^{62} +(10.7918 + 3.92788i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.239727 + 0.201155i) q^{66} +(4.86807 - 4.08479i) q^{67} +(-2.17533 + 3.76778i) q^{68} +(0.156455 + 0.270988i) q^{69} +(-0.369952 + 2.09810i) q^{71} +(0.519660 + 2.94714i) q^{72} +(6.51525 - 2.37136i) q^{73} +(-3.59971 - 3.02052i) q^{74} +(3.72042 + 2.27123i) q^{76} +13.9641 q^{77} +(0.357884 + 0.300300i) q^{78} +(7.31775 - 2.66344i) q^{79} +(1.55128 - 8.79777i) q^{81} +(-10.5664 - 3.84584i) q^{82} +(1.60303 + 2.77653i) q^{83} +(-0.165019 + 0.285821i) q^{84} +(-8.67318 + 7.27766i) q^{86} +(-0.0457236 + 0.0791956i) q^{87} +(1.81940 + 3.15129i) q^{88} +(-3.01370 - 1.09690i) q^{89} +(-3.62001 - 20.5301i) q^{91} +(3.41900 - 1.24441i) q^{92} +(-0.111559 - 0.0936089i) q^{93} +5.54757 q^{94} -0.0860015 q^{96} +(-13.7657 - 11.5508i) q^{97} +(7.26101 - 2.64279i) q^{98} +(-1.89093 - 10.7240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.0808150	+	0.0294142i	−0.0466585	+	0.0169823i	−0.365244	−	0.930912i	$-0.619014\pi$
$3$	−0.0808150	+	0.0294142i	−0.0466585	+	0.0169823i	0.318585	+	0.947894i	$0.396792\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	0.0808150	+	0.0294142i	0.0329926	+	0.0120083i
$7$	−1.91879	−	3.32344i	−0.725234	−	1.25614i	−0.958878	−	0.283820i	$-0.908398\pi$
$7$	−1.91879	−	3.32344i	−0.725234	−	1.25614i	0.233644	−	0.972322i	$-0.424935\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.29247	+	1.92361i	−0.764156	+	0.641203i
$10$		0			0
$11$	−1.81940	+	3.15129i	−0.548568	+	0.950148i	0.449805	+	0.893127i	$0.351494\pi$
$11$	−1.81940	+	3.15129i	−0.548568	+	0.950148i	−0.998373	+	0.0570213i	$0.981840\pi$
$12$	−0.0430007	−	0.0744795i	−0.0124132	−	0.0215004i
$13$	5.10468	+	1.85795i	1.41578	+	0.515303i	0.932821	−	0.360339i	$-0.117339\pi$
$13$	5.10468	+	1.85795i	1.41578	+	0.515303i	0.482961	+	0.875642i	$0.339561\pi$
$14$	−0.666388	+	3.77928i	−0.178100	+	1.01005i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.33279	+	2.79655i	0.808321	+	0.678262i	0.950206	−	0.311621i	$-0.100872\pi$
$17$	3.33279	+	2.79655i	0.808321	+	0.678262i	−0.141885	+	0.989883i	$0.545316\pi$
$18$	2.99260			0.705363
$19$	2.88277	−	3.26950i	0.661353	−	0.750075i
$19$	2.88277	−	3.26950i	0.661353	−	0.750075i
$20$		0			0
$21$	0.252823	+	0.212144i	0.0551706	+	0.0462936i
$22$	3.41935	−	1.24454i	0.729007	−	0.265337i
$23$	−0.631806	−	3.58315i	−0.131741	−	0.747138i	−0.977074	−	0.212899i	$-0.931709\pi$
$23$	−0.631806	−	3.58315i	−0.131741	−	0.747138i	0.845333	−	0.534239i	$-0.179402\pi$
$24$	−0.0149340	+	0.0846949i	−0.00304839	+	0.0172883i
$25$		0			0
$26$	−2.71614	−	4.70450i	−0.532679	−	0.922627i
$27$	0.257686	−	0.446326i	0.0495918	−	0.0858955i
$28$	2.93976	−	2.46675i	0.555561	−	0.466171i
$29$	0.814552	−	0.683490i	0.151258	−	0.126921i	−0.564018	−	0.825762i	$-0.690745\pi$
$29$	0.814552	−	0.683490i	0.151258	−	0.126921i	0.715277	+	0.698842i	$0.246301\pi$
$30$		0			0
$31$	0.846669	+	1.46647i	0.152066	+	0.263386i	0.931987	−	0.362492i	$-0.118074\pi$
$31$	0.846669	+	1.46647i	0.152066	+	0.263386i	−0.779921	+	0.625878i	$0.784741\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.0543417	−	0.308187i	0.00945968	−	0.0536485i
$34$	−0.755483	−	4.28456i	−0.129564	−	0.734795i
$35$		0			0
$36$	−2.29247	−	1.92361i	−0.382078	−	0.320601i
$37$	4.69909			0.772525			0.386263	−	0.922389i	$-0.373766\pi$
$37$	4.69909			0.772525			0.386263	+	0.922389i	$0.373766\pi$
$38$	−4.30992	+	0.651573i	−0.699162	+	0.105699i
$39$	−0.467184			−0.0748094
$40$		0			0
$41$	10.5664	−	3.84584i	1.65019	−	0.600620i	0.661413	−	0.750022i	$-0.269957\pi$
$41$	10.5664	−	3.84584i	1.65019	−	0.600620i	0.988777	+	0.149402i	$0.0477347\pi$
$42$	−0.0573104	−	0.325023i	−0.00884318	−	0.0501522i
$43$	1.96605	−	11.1500i	0.299820	−	1.70036i	−0.347120	−	0.937821i	$-0.612840\pi$
$43$	1.96605	−	11.1500i	0.299820	−	1.70036i	0.646940	−	0.762541i	$-0.276049\pi$
$44$	−3.41935	−	1.24454i	−0.515486	−	0.187621i
$45$		0			0
$46$	−1.81921	+	3.15097i	−0.268228	+	0.464585i
$47$	−4.24968	+	3.56591i	−0.619880	+	0.520141i	−0.897766	−	0.440473i	$-0.854811\pi$
$47$	−4.24968	+	3.56591i	−0.619880	+	0.520141i	0.277886	+	0.960614i	$0.410366\pi$
$48$	0.0658810	−	0.0552807i	0.00950910	−	0.00797908i
$49$	−3.86350	+	6.69178i	−0.551929	+	0.955969i
$50$		0			0
$51$	−0.351598	−	0.127971i	−0.0492335	−	0.0179195i
$52$	−0.943306	+	5.34975i	−0.130813	+	0.741877i
$53$	−0.464786	−	2.63593i	−0.0638433	−	0.362073i	−0.999946	−	0.0103477i	$-0.996706\pi$
$53$	−0.464786	−	2.63593i	−0.0638433	−	0.362073i	0.936103	−	0.351725i	$-0.114405\pi$
$54$	−0.484292	+	0.176268i	−0.0659038	+	0.0239870i
$55$		0			0
$56$	−3.83758			−0.512818
$57$	−0.136801	+	0.349019i	−0.0181198	+	0.0462287i
$58$	−1.06332			−0.139621
$59$	8.09344	+	6.79121i	1.05368	+	0.884140i	0.993475	−	0.114046i	$-0.0363813\pi$
$59$	8.09344	+	6.79121i	1.05368	+	0.884140i	0.0602014	+	0.998186i	$0.480826\pi$
$60$		0			0
$61$	1.77122	+	10.0451i	0.226781	+	1.28614i	0.859251	+	0.511555i	$0.170930\pi$
$61$	1.77122	+	10.0451i	0.226781	+	1.28614i	−0.632469	+	0.774585i	$0.717959\pi$
$62$	0.294045	−	1.66761i	0.0373438	−	0.211787i
$63$	10.7918	+	3.92788i	1.35963	+	0.494866i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.239727	+	0.201155i	−0.0295084	+	0.0247605i
$67$	4.86807	−	4.08479i	0.594729	−	0.499037i	−0.295017	−	0.955492i	$-0.595325\pi$
$67$	4.86807	−	4.08479i	0.594729	−	0.499037i	0.889747	+	0.456455i	$0.150881\pi$
$68$	−2.17533	+	3.76778i	−0.263797	+	0.456910i
$69$	0.156455	+	0.270988i	0.0188350	+	0.0326231i
$70$		0			0
$71$	−0.369952	+	2.09810i	−0.0439052	+	0.248999i	−0.998859	−	0.0477555i	$-0.984793\pi$
$71$	−0.369952	+	2.09810i	−0.0439052	+	0.248999i	0.954954	+	0.296754i	$0.0959043\pi$
$72$	0.519660	+	2.94714i	0.0612425	+	0.347324i
$73$	6.51525	−	2.37136i	0.762553	−	0.277546i	0.0686747	−	0.997639i	$-0.478123\pi$
$73$	6.51525	−	2.37136i	0.762553	−	0.277546i	0.693878	+	0.720093i	$0.255901\pi$
$74$	−3.59971	−	3.02052i	−0.418458	−	0.351128i
$75$		0			0
$76$	3.72042	+	2.27123i	0.426761	+	0.260528i
$77$	13.9641			1.59136
$78$	0.357884	+	0.300300i	0.0405224	+	0.0340023i
$79$	7.31775	−	2.66344i	0.823311	−	0.299661i	0.104200	−	0.994556i	$-0.466772\pi$
$79$	7.31775	−	2.66344i	0.823311	−	0.299661i	0.719111	+	0.694896i	$0.244549\pi$
$80$		0			0
$81$	1.55128	−	8.79777i	0.172365	−	0.977530i
$82$	−10.5664	−	3.84584i	−1.16686	−	0.424702i
$83$	1.60303	+	2.77653i	0.175956	+	0.304764i	0.940492	−	0.339817i	$-0.110365\pi$
$83$	1.60303	+	2.77653i	0.175956	+	0.304764i	−0.764536	+	0.644581i	$0.777032\pi$
$84$	−0.165019	+	0.285821i	−0.0180050	+	0.0311856i
$85$		0			0
$86$	−8.67318	+	7.27766i	−0.935253	+	0.784770i
$87$	−0.0457236	+	0.0791956i	−0.00490209	+	0.00849066i
$88$	1.81940	+	3.15129i	0.193948	+	0.335928i
$89$	−3.01370	−	1.09690i	−0.319452	−	0.116271i	0.177317	−	0.984154i	$-0.443258\pi$
$89$	−3.01370	−	1.09690i	−0.319452	−	0.116271i	−0.496769	+	0.867883i	$0.665480\pi$
$90$		0			0
$91$	−3.62001	−	20.5301i	−0.379480	−	2.15214i
$92$	3.41900	−	1.24441i	0.356456	−	0.129739i
$93$	−0.111559	−	0.0936089i	−0.0115681	−	0.00970679i
$94$	5.54757			0.572188
$95$		0			0
$96$	−0.0860015			−0.00877749
$97$	−13.7657	−	11.5508i	−1.39770	−	1.17281i	−0.962110	−	0.272663i	$-0.912095\pi$
$97$	−13.7657	−	11.5508i	−1.39770	−	1.17281i	−0.435590	−	0.900145i	$-0.643460\pi$
$98$	7.26101	−	2.64279i	0.733472	−	0.266962i
$99$	−1.89093	−	10.7240i	−0.190046	−	1.07781i
$100$		0			0
$101$	9.90858	+	3.60643i	0.985941	+	0.358853i	0.784147	−	0.620575i	$-0.213101\pi$
$101$	9.90858	+	3.60643i	0.985941	+	0.358853i	0.201793	+	0.979428i	$0.435323\pi$
$102$	0.187081	+	0.324034i	0.0185238	+	0.0320842i
$103$	−6.65638	+	11.5292i	−0.655873	+	1.13601i	0.325801	+	0.945438i	$0.394366\pi$
$103$	−6.65638	+	11.5292i	−0.655873	+	1.13601i	−0.981674	+	0.190567i	$0.938967\pi$
$104$	4.16137	−	3.49180i	0.408056	−	0.342400i
$105$		0			0
$106$	−1.33830	+	2.31800i	−0.129987	+	0.225144i
$107$	−3.73596	−	6.47086i	−0.361168	−	0.625562i	0.626985	−	0.779031i	$-0.284289\pi$
$107$	−3.73596	−	6.47086i	−0.361168	−	0.625562i	−0.988153	+	0.153469i	$0.950955\pi$
$108$	0.484292	+	0.176268i	0.0466010	+	0.0169614i
$109$	−0.916418	+	5.19727i	−0.0877770	+	0.497808i	0.908946	+	0.416914i	$0.136888\pi$
$109$	−0.916418	+	5.19727i	−0.0877770	+	0.497808i	−0.996723	+	0.0808935i	$0.974223\pi$
$110$		0			0
$111$	−0.379757	+	0.138220i	−0.0360449	+	0.0131193i
$112$	2.93976	+	2.46675i	0.277781	+	0.233086i
$113$	5.35357			0.503621			0.251811	−	0.967777i	$-0.418974\pi$
$113$	5.35357			0.503621			0.251811	+	0.967777i	$0.418974\pi$
$114$	0.329141	−	0.179430i	0.0308269	−	0.0168052i
$115$		0			0
$116$	0.814552	+	0.683490i	0.0756292	+	0.0634605i
$117$	−15.2763	+	5.56011i	−1.41229	+	0.514032i
$118$	−1.83464	−	10.4047i	−0.168892	−	0.957833i
$119$	2.89922	−	16.4423i	0.265771	−	1.50726i
$120$		0			0
$121$	−1.12040	−	1.94059i	−0.101855	−	0.176417i
$122$	5.10002	−	8.83349i	0.461734	−	0.799747i
$123$	−0.740798	+	0.621603i	−0.0667955	+	0.0560481i
$124$	−1.29717	+	1.08846i	−0.116490	+	0.0977463i
$125$		0			0
$126$	−5.74217	−	9.94574i	−0.511554	−	0.886037i
$127$	2.70333	+	0.983931i	0.239882	+	0.0873098i	0.459163	−	0.888352i	$-0.348149\pi$
$127$	2.70333	+	0.983931i	0.239882	+	0.0873098i	−0.219282	+	0.975662i	$0.570371\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	0.169083	+	0.958918i	0.0148869	+	0.0844280i
$130$		0			0
$131$	7.45922	+	6.25903i	0.651715	+	0.546854i	0.907591	−	0.419856i	$-0.137919\pi$
$131$	7.45922	+	6.25903i	0.651715	+	0.546854i	−0.255876	+	0.966710i	$0.582364\pi$
$132$	0.312941			0.0272381
$133$	−16.3974	−	3.30724i	−1.42184	−	0.286774i
$134$	−6.35481			−0.548972
$135$		0			0
$136$	4.08828	−	1.48801i	0.350567	−	0.127596i
$137$	2.53551	+	14.3796i	0.216623	+	1.22853i	0.878067	+	0.478537i	$0.158833\pi$
$137$	2.53551	+	14.3796i	0.216623	+	1.22853i	−0.661444	+	0.749995i	$0.730056\pi$
$138$	0.0543362	−	0.308156i	0.00462541	−	0.0262320i
$139$	−8.54372	−	3.10966i	−0.724669	−	0.263758i	−0.0467625	−	0.998906i	$-0.514890\pi$
$139$	−8.54372	−	3.10966i	−0.724669	−	0.263758i	−0.677907	+	0.735148i	$0.737113\pi$
$140$		0			0
$141$	0.238550	−	0.413180i	0.0200895	−	0.0347960i
$142$	1.63203	−	1.36944i	0.136957	−	0.114921i
$143$	−15.1424	+	12.7059i	−1.26627	+	1.06252i
$144$	1.49630	−	2.59167i	0.124692	−	0.215973i
$145$		0			0
$146$	−6.51525	−	2.37136i	−0.539206	−	0.196255i
$147$	0.115395	−	0.654438i	0.00951762	−	0.0539771i
$148$	0.815988	+	4.62770i	0.0670738	+	0.380395i
$149$	5.02344	−	1.82838i	0.411536	−	0.149787i	−0.127951	−	0.991780i	$-0.540840\pi$
$149$	5.02344	−	1.82838i	0.411536	−	0.149787i	0.539488	+	0.841994i	$0.318618\pi$
$150$		0			0
$151$	11.9187			0.969930			0.484965	−	0.874533i	$-0.338832\pi$
$151$	11.9187			0.969930			0.484965	+	0.874533i	$0.338832\pi$
$152$	−1.39008	−	4.13130i	−0.112751	−	0.335093i
$153$	−13.0198			−1.05259
$154$	−10.6972	−	8.97598i	−0.862001	−	0.723305i
$155$		0			0
$156$	−0.0811257	−	0.460087i	−0.00649526	−	0.0368364i
$157$	2.80848	−	15.9277i	0.224141	−	1.27117i	−0.640178	−	0.768227i	$-0.721139\pi$
$157$	2.80848	−	15.9277i	0.224141	−	1.27117i	0.864320	−	0.502943i	$-0.167749\pi$
$158$	−7.31775	−	2.66344i	−0.582169	−	0.211892i
$159$	0.115096	+	0.199351i	0.00912768	+	0.0158096i
$160$		0			0
$161$	−10.6961	+	8.97508i	−0.842969	+	0.707335i
$162$	−6.84345	+	5.74234i	−0.537672	+	0.451160i
$163$	5.97258	−	10.3448i	0.467808	−	0.810268i	−0.531515	−	0.847049i	$-0.678377\pi$
$163$	5.97258	−	10.3448i	0.467808	−	0.810268i	0.999323	+	0.0367810i	$0.0117104\pi$
$164$	5.62225	+	9.73802i	0.439024	+	0.760412i
$165$		0			0
$166$	0.556727	−	3.15736i	0.0432104	−	0.245058i
$167$	4.03336	+	22.8743i	0.312110	+	1.77007i	0.587985	+	0.808872i	$0.299922\pi$
$167$	4.03336	+	22.8743i	0.312110	+	1.77007i	−0.275874	+	0.961194i	$0.588967\pi$
$168$	0.310134	−	0.112879i	0.0239273	−	0.00870884i
$169$	12.6472	+	10.6122i	0.972859	+	0.816326i
$170$		0			0
$171$	−0.319421	+	13.0405i	−0.0244267	+	0.997235i
$172$	11.3220			0.863296
$173$	4.25454	+	3.56998i	0.323467	+	0.271421i	0.790032	−	0.613066i	$-0.210064\pi$
$173$	4.25454	+	3.56998i	0.323467	+	0.271421i	−0.466565	+	0.884487i	$0.654509\pi$
$174$	0.0859323	−	0.0312768i	0.00651451	−	0.00237109i
$175$		0			0
$176$	0.631869	−	3.58351i	0.0476290	−	0.270117i
$177$	−0.853830	−	0.310769i	−0.0641778	−	0.0233588i
$178$	1.60356	+	2.77745i	0.120192	+	0.208178i
$179$	0.219888	−	0.380858i	0.0164352	−	0.0284667i	−0.857691	−	0.514166i	$-0.828102\pi$
$179$	0.219888	−	0.380858i	0.0164352	−	0.0284667i	0.874126	+	0.485699i	$0.161435\pi$
$180$		0			0
$181$	−1.72218	+	1.44508i	−0.128008	+	0.107412i	−0.704544	−	0.709660i	$-0.748849\pi$
$181$	−1.72218	+	1.44508i	−0.128008	+	0.107412i	0.576536	+	0.817072i	$0.304404\pi$
$182$	−10.4234	+	18.0539i	−0.772634	+	1.33824i
$183$	−0.438609	−	0.759693i	−0.0324229	−	0.0561582i
$184$	−3.41900	−	1.24441i	−0.252052	−	0.0917395i
$185$		0			0
$186$	0.0252883	+	0.143417i	0.00185423	+	0.0105159i
$187$	−14.8764	+	5.41456i	−1.08787	+	0.395952i
$188$	−4.24968	−	3.56591i	−0.309940	−	0.260071i
$189$	−1.97778			−0.143863
$190$		0			0
$191$	−3.39261			−0.245481			−0.122740	−	0.992439i	$-0.539168\pi$
$191$	−3.39261			−0.245481			−0.122740	+	0.992439i	$0.539168\pi$
$192$	0.0658810	+	0.0552807i	0.00475455	+	0.00398954i
$193$	−15.7460	+	5.73106i	−1.13342	+	0.412531i	−0.839533	−	0.543309i	$-0.817171\pi$
$193$	−15.7460	+	5.73106i	−1.13342	+	0.412531i	−0.293887	+	0.955840i	$0.594949\pi$
$194$	3.12044	+	17.6969i	0.224035	+	1.27056i
$195$		0			0
$196$	−7.26101	−	2.64279i	−0.518643	−	0.188771i
$197$	0.844789	+	1.46322i	0.0601887	+	0.104250i	0.894550	−	0.446969i	$-0.147496\pi$
$197$	0.844789	+	1.46322i	0.0601887	+	0.104250i	−0.834361	+	0.551218i	$0.814163\pi$
$198$	−5.44473	+	9.43055i	−0.386940	+	0.670200i
$199$	−9.70294	+	8.14174i	−0.687823	+	0.577152i	−0.918281	−	0.395930i	$-0.870422\pi$
$199$	−9.70294	+	8.14174i	−0.687823	+	0.577152i	0.230457	+	0.973082i	$0.425978\pi$
$200$		0			0
$201$	−0.273262	+	0.473303i	−0.0192744	+	0.0333842i
$202$	−5.27225	−	9.13180i	−0.370954	−	0.642511i
$203$	−3.83449	−	1.39564i	−0.269128	−	0.0979548i
$204$	0.0649726	−	0.368478i	0.00454899	−	0.0257986i
$205$		0			0
$206$	12.5099	−	4.55323i	0.871606	−	0.317239i
$207$	8.34097	+	6.99891i	0.579738	+	0.486458i
$208$	−5.43228			−0.376661
$209$	5.05823	+	15.0329i	0.349885	+	1.03985i
$210$		0			0
$211$	−6.40845	−	5.37733i	−0.441176	−	0.370191i	0.394973	−	0.918693i	$-0.370754\pi$
$211$	−6.40845	−	5.37733i	−0.441176	−	0.370191i	−0.836149	+	0.548502i	$0.815198\pi$
$212$	2.51518	−	0.915450i	0.172743	−	0.0628734i
$213$	−0.0318164	−	0.180440i	−0.00218003	−	0.0123635i
$214$	−1.29748	+	7.35840i	−0.0886942	+	0.503010i
$215$		0			0
$216$	−0.257686	−	0.446326i	−0.0175333	−	0.0303686i
$217$	3.24916	−	5.62771i	0.220567	−	0.382034i
$218$	4.04276	−	3.39227i	0.273810	−	0.229754i
$219$	−0.456778	+	0.383282i	−0.0308662	+	0.0258998i
$220$		0			0
$221$	11.8170	+	20.4676i	0.794897	+	1.37680i
$222$	0.379757	+	0.138220i	0.0254876	+	0.00927673i
$223$	−0.0222983	+	0.126460i	−0.00149320	+	0.00846837i	−0.985545	−	0.169412i	$-0.945813\pi$
$223$	−0.0222983	+	0.126460i	−0.00149320	+	0.00846837i	0.984052	+	0.177881i	$0.0569241\pi$
$224$	−0.666388	−	3.77928i	−0.0445249	−	0.252514i
$225$		0			0
$226$	−4.10107	−	3.44121i	−0.272799	−	0.228906i
$227$	9.18019			0.609310			0.304655	−	0.952463i	$-0.401459\pi$
$227$	9.18019			0.609310			0.304655	+	0.952463i	$0.401459\pi$
$228$	−0.367472	−	0.0741163i	−0.0243364	−	0.00490847i
$229$	5.87648			0.388328			0.194164	−	0.980969i	$-0.437801\pi$
$229$	5.87648			0.388328			0.194164	+	0.980969i	$0.437801\pi$
$230$		0			0
$231$	−1.12851	+	0.410745i	−0.0742506	+	0.0270250i
$232$	−0.184644	−	1.04717i	−0.0121225	−	0.0687499i
$233$	−1.06889	+	6.06196i	−0.0700251	+	0.397132i	0.929569	+	0.368648i	$0.120179\pi$
$233$	−1.06889	+	6.06196i	−0.0700251	+	0.397132i	−0.999594	+	0.0284843i	$0.990932\pi$
$234$	15.2763	+	5.56011i	0.998641	+	0.363476i
$235$		0			0
$236$	−5.28262	+	9.14977i	−0.343869	+	0.595599i
$237$	−0.513040	+	0.430492i	−0.0333255	+	0.0279635i
$238$	−12.7899	+	10.7320i	−0.829043	+	0.695650i
$239$	1.02850	−	1.78141i	0.0665282	−	0.115230i	−0.830843	−	0.556507i	$-0.812141\pi$
$239$	1.02850	−	1.78141i	0.0665282	−	0.115230i	0.897371	+	0.441277i	$0.145474\pi$
$240$		0			0
$241$	−9.06713	−	3.30017i	−0.584065	−	0.212582i	0.0330518	−	0.999454i	$-0.489477\pi$
$241$	−9.06713	−	3.30017i	−0.584065	−	0.212582i	−0.617117	+	0.786871i	$0.711700\pi$
$242$	−0.389111	+	2.20676i	−0.0250130	+	0.141856i
$243$	0.401893	+	2.27925i	0.0257815	+	0.146214i
$244$	−9.58490	+	3.48862i	−0.613610	+	0.223336i
$245$		0			0
$246$	0.967043			0.0616564
$247$	20.7902	−	11.3337i	1.32285	−	0.721146i
$248$	1.69334			0.107527
$249$	−0.211218	−	0.177233i	−0.0133854	−	0.0112317i
$250$		0			0
$251$	−2.86001	−	16.2199i	−0.180522	−	1.02379i	−0.931575	−	0.363549i	$-0.881565\pi$
$251$	−2.86001	−	16.2199i	−0.180522	−	1.02379i	0.751053	−	0.660242i	$-0.229546\pi$
$252$	−1.99424	+	11.3099i	−0.125625	+	0.712455i
$253$	12.4410	+	4.52817i	0.782161	+	0.284683i
$254$	−1.43841	−	2.49140i	−0.0902539	−	0.156324i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−17.1843	+	14.4194i	−1.07193	+	0.899456i	−0.995226	−	0.0975982i	$-0.968884\pi$
$257$	−17.1843	+	14.4194i	−1.07193	+	0.899456i	−0.0767037	+	0.997054i	$0.524440\pi$
$258$	0.486855	−	0.843258i	0.0303103	−	0.0524990i
$259$	−9.01656	−	15.6171i	−0.560262	−	0.970402i
$260$		0			0
$261$	−0.552566	+	3.13376i	−0.0342030	+	0.193975i
$262$	−1.69087	−	9.58939i	−0.104462	−	0.592435i
$263$	−13.6565	+	4.97057i	−0.842098	+	0.306498i	−0.726814	−	0.686834i	$-0.759000\pi$
$263$	−13.6565	+	4.97057i	−0.842098	+	0.306498i	−0.115283	+	0.993333i	$0.536778\pi$
$264$	−0.239727	−	0.201155i	−0.0147542	−	0.0123802i
$265$		0			0
$266$	10.4353	+	13.0735i	0.639829	+	0.801590i
$267$	0.275817			0.0168797
$268$	4.86807	+	4.08479i	0.297365	+	0.249518i
$269$	−27.8282	+	10.1286i	−1.69672	+	0.617554i	−0.995445	−	0.0953391i	$-0.969606\pi$
$269$	−27.8282	+	10.1286i	−1.69672	+	0.617554i	−0.701272	+	0.712894i	$0.747384\pi$
$270$		0			0
$271$	2.06802	−	11.7283i	0.125623	−	0.712443i	−0.855313	−	0.518112i	$-0.826635\pi$
$271$	2.06802	−	11.7283i	0.125623	−	0.712443i	0.980936	−	0.194332i	$-0.0622538\pi$
$272$	−4.08828	−	1.48801i	−0.247888	−	0.0902239i
$273$	0.896428	+	1.55266i	0.0542543	+	0.0939712i
$274$	7.30071	−	12.6452i	0.441052	−	0.763925i
$275$		0			0
$276$	−0.239703	+	0.201135i	−0.0144284	+	0.0121069i
$277$	−5.66635	+	9.81441i	−0.340458	+	0.589691i	−0.984518	−	0.175284i	$-0.943916\pi$
$277$	−5.66635	+	9.81441i	−0.340458	+	0.589691i	0.644060	+	0.764975i	$0.277249\pi$
$278$	4.54602	+	7.87394i	0.272652	+	0.472247i
$279$	−4.76188	−	1.73318i	−0.285086	−	0.103763i
$280$		0			0
$281$	−1.11030	−	6.29682i	−0.0662348	−	0.375636i	−0.999849	−	0.0173573i	$-0.994475\pi$
$281$	−1.11030	−	6.29682i	−0.0662348	−	0.375636i	0.933615	−	0.358279i	$-0.116636\pi$
$282$	−0.448327	+	0.163178i	−0.0266975	+	0.00971708i
$283$	−4.69512	−	3.93967i	−0.279096	−	0.234189i	0.492484	−	0.870321i	$-0.336089\pi$
$283$	−4.69512	−	3.93967i	−0.279096	−	0.234189i	−0.771580	+	0.636132i	$0.780533\pi$
$284$	−2.13047			−0.126420
$285$		0			0
$286$	19.7669			1.16884
$287$	−33.0561	−	27.7373i	−1.95124	−	1.63728i
$288$	−2.81213	+	1.02353i	−0.165706	+	0.0603121i
$289$	0.334825	+	1.89888i	0.0196956	+	0.111699i
$290$		0			0
$291$	1.45224	+	0.528571i	0.0851316	+	0.0309854i
$292$	3.46669	+	6.00449i	0.202873	+	0.351386i
$293$	−4.85059	+	8.40147i	−0.283375	+	0.490819i	−0.972214	−	0.234095i	$-0.924787\pi$
$293$	−4.85059	+	8.40147i	−0.283375	+	0.490819i	0.688839	+	0.724914i	$0.258121\pi$
$294$	−0.509062	+	0.427154i	−0.0296891	+	0.0249121i
$295$		0			0
$296$	2.34954	−	4.06953i	0.136564	−	0.236537i
$297$	0.937667	+	1.62409i	0.0544090	+	0.0942391i
$298$	−5.02344	−	1.82838i	−0.291000	−	0.105915i
$299$	3.43215	−	19.4647i	0.198486	−	1.12567i
$300$		0			0
$301$	−40.8289	+	14.8605i	−2.35334	+	0.856544i
$302$	−9.13026	−	7.66120i	−0.525387	−	0.440852i
$303$	−0.906842			−0.0520967
$304$	−1.59068	+	4.05829i	−0.0912320	+	0.232759i
$305$		0			0
$306$	9.97373	+	8.36895i	0.570160	+	0.478421i
$307$	−2.66894	+	0.971416i	−0.152325	+	0.0554417i	−0.417057	−	0.908880i	$-0.636939\pi$
$307$	−2.66894	+	0.971416i	−0.152325	+	0.0554417i	0.264733	+	0.964322i	$0.414716\pi$
$308$	2.42485	+	13.7520i	0.138169	+	0.783593i
$309$	0.198813	−	1.12752i	0.0113101	−	0.0641426i
$310$		0			0
$311$	5.94935	+	10.3046i	0.337357	+	0.584319i	0.983935	−	0.178529i	$-0.0571338\pi$
$311$	5.94935	+	10.3046i	0.337357	+	0.584319i	−0.646578	+	0.762848i	$0.723800\pi$
$312$	−0.233592	+	0.404594i	−0.0132246	+	0.0229056i
$313$	21.0617	−	17.6728i	1.19048	−	0.998928i	0.190625	−	0.981663i	$-0.438949\pi$
$313$	21.0617	−	17.6728i	1.19048	−	0.998928i	0.999851	−	0.0172647i	$-0.00549579\pi$
$314$	−12.3896	+	10.3961i	−0.699183	+	0.586684i
$315$		0			0
$316$	3.89369	+	6.74407i	0.219037	+	0.379384i
$317$	−16.5860	−	6.03680i	−0.931561	−	0.339060i	−0.168733	−	0.985662i	$-0.553967\pi$
$317$	−16.5860	−	6.03680i	−0.931561	−	0.339060i	−0.762828	+	0.646601i	$0.776190\pi$
$318$	0.0399723	−	0.226694i	0.00224153	−	0.0127124i
$319$	0.671880	+	3.81042i	0.0376181	+	0.213343i
$320$		0			0
$321$	0.492257	+	0.413052i	0.0274751	+	0.0230543i
$322$	13.9627			0.778113
$323$	18.7510	−	2.83477i	1.04333	−	0.157731i
$324$	8.93349			0.496305
$325$		0			0
$326$	−11.2248	+	4.08548i	−0.621683	+	0.226274i
$327$	−0.0788133	−	0.446973i	−0.00435839	−	0.0247176i
$328$	1.95259	−	11.0737i	0.107814	−	0.611441i
$329$	20.0053	+	7.28134i	1.10293	+	0.401434i
$330$		0			0
$331$	14.5665	−	25.2299i	0.800647	−	1.38676i	−0.118544	−	0.992949i	$-0.537823\pi$
$331$	14.5665	−	25.2299i	0.800647	−	1.38676i	0.919191	−	0.393813i	$-0.128844\pi$
$332$	−2.45599	+	2.06082i	−0.134790	+	0.113102i
$333$	−10.7725	+	9.03921i	−0.590330	+	0.495346i
$334$	11.6136	−	20.1153i	0.635467	−	1.10066i
$335$		0			0
$336$	−0.310134	−	0.112879i	−0.0169192	−	0.00615808i
$337$	4.58649	−	26.0113i	0.249842	−	1.41693i	−0.559130	−	0.829080i	$-0.688865\pi$
$337$	4.58649	−	26.0113i	0.249842	−	1.41693i	0.808973	−	0.587846i	$-0.200024\pi$
$338$	−2.86688	−	16.2589i	−0.155938	−	0.884367i
$339$	−0.432648	+	0.157471i	−0.0234982	+	0.00855265i
$340$		0			0
$341$	−6.16170			−0.333675
$342$	8.62699	−	9.78432i	0.466494	−	0.529075i
$343$	2.78993			0.150642
$344$	−8.67318	−	7.27766i	−0.467626	−	0.392385i
$345$		0			0
$346$	−0.964426	−	5.46953i	−0.0518479	−	0.294044i
$347$	0.742771	−	4.21246i	0.0398740	−	0.226137i	−0.958358	−	0.285568i	$-0.907818\pi$
$347$	0.742771	−	4.21246i	0.0398740	−	0.226137i	0.998232	+	0.0594314i	$0.0189288\pi$
$348$	−0.0859323	−	0.0312768i	−0.00460645	−	0.00167661i
$349$	4.48031	+	7.76012i	0.239825	+	0.415390i	0.960664	−	0.277713i	$-0.0895765\pi$
$349$	4.48031	+	7.76012i	0.239825	+	0.415390i	−0.720839	+	0.693103i	$0.756243\pi$
$350$		0			0
$351$	2.14466	−	1.79958i	0.114473	−	0.0960545i
$352$	−2.78748	+	2.33897i	−0.148573	+	0.124668i
$353$	−9.48952	+	16.4363i	−0.505076	+	0.874818i	0.494907	+	0.868946i	$0.335202\pi$
$353$	−9.48952	+	16.4363i	−0.505076	+	0.874818i	−0.999983	+	0.00587136i	$0.998131\pi$
$354$	0.454313	+	0.786894i	0.0241465	+	0.0418229i
$355$		0			0
$356$	0.556910	−	3.15839i	0.0295162	−	0.167395i
$357$	0.249338	+	1.41406i	0.0131963	+	0.0748402i
$358$	−0.413255	+	0.150413i	−0.0218412	+	0.00794955i
$359$	−3.57413	−	2.99905i	−0.188635	−	0.158284i	0.543579	−	0.839358i	$-0.317069\pi$
$359$	−3.57413	−	2.99905i	−0.188635	−	0.158284i	−0.732215	+	0.681074i	$0.761513\pi$
$360$		0			0
$361$	−2.37926	−	18.8504i	−0.125224	−	0.992128i
$362$	2.24814			0.118160
$363$	0.147626	+	0.123873i	0.00774836	+	0.00650165i
$364$	19.5896	−	7.13003i	1.02677	−	0.373715i
$365$		0			0
$366$	−0.152327	+	0.863892i	−0.00796228	+	0.0451563i
$367$	12.2595	+	4.46209i	0.639940	+	0.232919i	0.641552	−	0.767080i	$-0.278291\pi$
$367$	12.2595	+	4.46209i	0.639940	+	0.232919i	−0.00161191	+	0.999999i	$0.500513\pi$
$368$	1.81921	+	3.15097i	0.0948330	+	0.164256i
$369$	−16.8252	+	29.1420i	−0.875883	+	1.51707i
$370$		0			0
$371$	−7.86854	+	6.60249i	−0.408514	+	0.342784i
$372$	0.0728148	−	0.126119i	0.00377527	−	0.00653896i
$373$	−6.51467	−	11.2837i	−0.337317	−	0.584250i	0.646610	−	0.762821i	$-0.276186\pi$
$373$	−6.51467	−	11.2837i	−0.337317	−	0.584250i	−0.983927	+	0.178570i	$0.942853\pi$
$374$	14.8764	+	5.41456i	0.769239	+	0.279980i
$375$		0			0
$376$	0.963325	+	5.46329i	0.0496797	+	0.281748i
$377$	5.42791	−	1.97560i	0.279552	−	0.101749i
$378$	1.51507	+	1.27129i	0.0779268	+	0.0653883i
$379$	−21.4427			−1.10144			−0.550718	−	0.834692i	$-0.685646\pi$
$379$	−21.4427			−1.10144			−0.550718	+	0.834692i	$0.685646\pi$
$380$		0			0
$381$	−0.247411			−0.0126752
$382$	2.59889	+	2.18073i	0.132971	+	0.111576i
$383$	11.4828	−	4.17939i	0.586743	−	0.213557i	−0.0315534	−	0.999502i	$-0.510045\pi$
$383$	11.4828	−	4.17939i	0.586743	−	0.213557i	0.618296	+	0.785945i	$0.287823\pi$
$384$	−0.0149340	−	0.0846949i	−0.000762097	−	0.00432207i
$385$		0			0
$386$	15.7460	+	5.73106i	0.801449	+	0.291703i
$387$	16.9412	+	29.3430i	0.861168	+	1.49159i
$388$	8.98495	−	15.5624i	0.456142	−	0.790060i
$389$	8.31670	−	6.97854i	0.421673	−	0.353826i	−0.407126	−	0.913372i	$-0.633469\pi$
$389$	8.31670	−	6.97854i	0.421673	−	0.353826i	0.828799	+	0.559546i	$0.189025\pi$
$390$		0			0
$391$	7.91476	−	13.7088i	0.400267	−	0.693282i
$392$	3.86350	+	6.69178i	0.195136	+	0.337986i
$393$	−0.786921	−	0.286416i	−0.0396949	−	0.0144478i
$394$	0.293392	−	1.66391i	0.0147809	−	0.0838265i
$395$		0			0
$396$	10.2327	−	3.72441i	0.514215	−	0.187159i
$397$	23.2954	+	19.5472i	1.16916	+	0.981046i	0.999990	−	0.00454025i	$-0.00144521\pi$
$397$	23.2954	+	19.5472i	1.16916	+	0.981046i	0.169175	+	0.985586i	$0.445890\pi$
$398$	12.6663			0.634904
$399$	1.42244	−	0.215043i	0.0712109	−	0.0107656i
$400$		0			0
$401$	7.75243	+	6.50506i	0.387138	+	0.324847i	0.815497	−	0.578761i	$-0.196464\pi$
$401$	7.75243	+	6.50506i	0.387138	+	0.324847i	−0.428359	+	0.903609i	$0.640908\pi$
$402$	0.513564	−	0.186922i	0.0256142	−	0.00932282i
$403$	1.59734	+	9.05894i	0.0795690	+	0.451258i
$404$	−1.83103	+	10.3843i	−0.0910972	+	0.516638i
$405$		0			0
$406$	2.04029	+	3.53389i	0.101258	+	0.175384i
$407$	−8.54950	+	14.8082i	−0.423783	+	0.734014i
$408$	−0.286625	+	0.240507i	−0.0141901	+	0.0119069i
$409$	14.1505	−	11.8737i	0.699699	−	0.587117i	−0.221989	−	0.975049i	$-0.571255\pi$
$409$	14.1505	−	11.8737i	0.699699	−	0.587117i	0.921688	+	0.387932i	$0.126811\pi$
$410$		0			0
$411$	−0.627872	−	1.08751i	−0.0309707	−	0.0536427i
$412$	−12.5099	−	4.55323i	−0.616319	−	0.224322i
$413$	7.04055	−	39.9290i	0.346443	−	1.96478i
$414$	−1.89074	−	10.7229i	−0.0929250	−	0.527004i
$415$		0			0
$416$	4.16137	+	3.49180i	0.204028	+	0.171200i
$417$	0.781929			0.0382912
$418$	5.78817	−	14.7673i	0.283108	−	0.722291i
$419$	12.5375			0.612497			0.306248	−	0.951952i	$-0.400926\pi$
$419$	12.5375			0.612497			0.306248	+	0.951952i	$0.400926\pi$
$420$		0			0
$421$	−33.8406	+	12.3170i	−1.64929	+	0.600292i	−0.988627	−	0.150390i	$-0.951947\pi$
$421$	−33.8406	+	12.3170i	−1.64929	+	0.600292i	−0.660663	+	0.750682i	$0.729725\pi$
$422$	1.45268	+	8.23855i	0.0707153	+	0.401046i
$423$	2.88285	−	16.3495i	0.140169	−	0.794938i
$424$	−2.51518	−	0.915450i	−0.122148	−	0.0444582i
$425$		0			0
$426$	−0.0916117	+	0.158676i	−0.00443860	+	0.00768788i
$427$	29.9856	−	25.1609i	1.45111	−	1.21762i
$428$	5.72382	−	4.80285i	0.276671	−	0.232155i
$429$	0.849993	−	1.47223i	0.0410381	−	0.0710800i
$430$		0			0
$431$	−20.3899	−	7.42133i	−0.982148	−	0.357473i	−0.199473	−	0.979903i	$-0.563923\pi$
$431$	−20.3899	−	7.42133i	−0.982148	−	0.357473i	−0.782675	+	0.622431i	$0.786145\pi$
$432$	−0.0894935	+	0.507543i	−0.00430576	+	0.0244192i
$433$	−0.0791112	−	0.448662i	−0.00380184	−	0.0215613i	0.982848	−	0.184418i	$-0.0590402\pi$
$433$	−0.0791112	−	0.448662i	−0.00380184	−	0.0215613i	−0.986650	+	0.162857i	$0.947929\pi$
$434$	−6.10642	+	2.22256i	−0.293118	+	0.106686i
$435$		0			0
$436$	−5.27744			−0.252744
$437$	−13.5365	−	8.26371i	−0.647537	−	0.395307i
$438$	0.596281			0.0284914
$439$	−0.454717	−	0.381552i	−0.0217024	−	0.0182105i	0.631872	−	0.775073i	$-0.282287\pi$
$439$	−0.454717	−	0.381552i	−0.0217024	−	0.0182105i	−0.653574	+	0.756862i	$0.726731\pi$
$440$		0			0
$441$	−4.01542	−	22.7726i	−0.191210	−	1.08441i
$442$	4.10400	−	23.2749i	0.195207	−	1.10708i
$443$	−35.4197	−	12.8917i	−1.68284	−	0.612503i	−0.689145	−	0.724624i	$-0.742014\pi$
$443$	−35.4197	−	12.8917i	−1.68284	−	0.612503i	−0.993695	+	0.112120i	$0.964236\pi$
$444$	−0.202064	−	0.349986i	−0.00958955	−	0.0166096i
$445$		0			0
$446$	0.0983682	−	0.0825408i	0.00465787	−	0.00390842i
$447$	−0.352189	+	0.295521i	−0.0166579	+	0.0139777i
$448$	−1.91879	+	3.32344i	−0.0906543	+	0.157018i
$449$	10.2230	+	17.7068i	0.482455	+	0.835636i	0.999797	−	0.0201424i	$-0.00641195\pi$
$449$	10.2230	+	17.7068i	0.482455	+	0.835636i	−0.517342	+	0.855779i	$0.673079\pi$
$450$		0			0
$451$	−7.10505	+	40.2948i	−0.334564	+	1.89741i
$452$	0.929637	+	5.27223i	0.0437264	+	0.247985i
$453$	−0.963210	+	0.350580i	−0.0452555	+	0.0164717i
$454$	−7.03243	−	5.90091i	−0.330048	−	0.276943i
$455$		0			0
$456$	0.233859	+	0.292983i	0.0109514	+	0.0137202i
$457$	12.9647			0.606465			0.303233	−	0.952917i	$-0.401934\pi$
$457$	12.9647			0.606465			0.303233	+	0.952917i	$0.401934\pi$
$458$	−4.50164	−	3.77733i	−0.210348	−	0.176503i
$459$	2.10699	−	0.766880i	0.0983457	−	0.0357949i
$460$		0			0
$461$	0.488216	−	2.76881i	0.0227385	−	0.128956i	−0.971325	−	0.237754i	$-0.923589\pi$
$461$	0.488216	−	2.76881i	0.0227385	−	0.128956i	0.994064	+	0.108797i	$0.0347000\pi$
$462$	1.12851	+	0.410745i	0.0525031	+	0.0191096i
$463$	10.1939	+	17.6564i	0.473752	+	0.820563i	0.999548	−	0.0300475i	$-0.00956585\pi$
$463$	10.1939	+	17.6564i	0.473752	+	0.820563i	−0.525796	+	0.850611i	$0.676233\pi$
$464$	−0.531661	+	0.920864i	−0.0246817	+	0.0427500i
$465$		0			0
$466$	4.71537	−	3.95666i	0.218435	−	0.183289i
$467$	−12.6620	+	21.9312i	−0.585927	+	1.01485i	0.408833	+	0.912609i	$0.365936\pi$
$467$	−12.6620	+	21.9312i	−0.585927	+	1.01485i	−0.994759	+	0.102245i	$0.967397\pi$
$468$	−8.12834	−	14.0787i	−0.375732	−	0.650788i
$469$	−22.9164	−	8.34087i	−1.05818	−	0.385146i
$470$		0			0
$471$	0.241534	+	1.36981i	0.0111293	+	0.0631174i
$472$	9.92808	−	3.61353i	0.456977	−	0.166326i
$473$	31.5599	+	26.4819i	1.45112	+	1.21764i
$474$	0.669726			0.0307616
$475$		0			0
$476$	16.6960			0.765258
$477$	6.13601	+	5.14872i	0.280949	+	0.235744i
$478$	−1.93295	+	0.703536i	−0.0884110	+	0.0321790i
$479$	−6.76001	−	38.3379i	−0.308873	−	1.75170i	−0.604691	−	0.796460i	$-0.706703\pi$
$479$	−6.76001	−	38.3379i	−0.308873	−	1.75170i	0.295818	−	0.955244i	$-0.404408\pi$
$480$		0			0
$481$	23.9873	+	8.73067i	1.09373	+	0.398084i
$482$	4.82452	+	8.35632i	0.219751	+	0.380620i
$483$	0.600408	−	1.03994i	0.0273195	−	0.0473188i
$484$	1.71655	−	1.44036i	0.0780252	−	0.0654709i
$485$		0			0
$486$	1.15721	−	2.00434i	0.0524919	−	0.0909187i
$487$	−12.6902	−	21.9801i	−0.575050	−	0.996015i	−0.996036	−	0.0889482i	$-0.971649\pi$
$487$	−12.6902	−	21.9801i	−0.575050	−	0.996015i	0.420987	−	0.907067i	$-0.361684\pi$
$488$	9.58490	+	3.48862i	0.433888	+	0.157922i
$489$	−0.178389	+	1.01169i	−0.00806703	+	0.0457504i
$490$		0			0
$491$	20.7422	−	7.54953i	0.936080	−	0.340705i	0.171464	−	0.985190i	$-0.445150\pi$
$491$	20.7422	−	7.54953i	0.936080	−	0.340705i	0.764617	+	0.644485i	$0.222928\pi$
$492$	−0.740798	−	0.621603i	−0.0333978	−	0.0280241i
$493$	4.62614			0.208351
$494$	−23.2114	−	4.68156i	−1.04433	−	0.210633i
$495$		0			0
$496$	−1.29717	−	1.08846i	−0.0582448	−	0.0488731i
$497$	7.68278	−	2.79630i	0.344620	−	0.125431i
$498$	0.0478793	+	0.271537i	0.00214552	+	0.0121679i
$499$	−1.77767	+	10.0817i	−0.0795794	+	0.451317i	0.918816	+	0.394687i	$0.129147\pi$
$499$	−1.77767	+	10.0817i	−0.0795794	+	0.451317i	−0.998395	+	0.0566307i	$0.981964\pi$
$500$		0			0
$501$	−0.998785	−	1.72995i	−0.0446224	−	0.0772883i
$502$	−8.23506	+	14.2635i	−0.367549	+	0.636613i
$503$	16.1430	−	13.5456i	0.719779	−	0.603967i	−0.207545	−	0.978225i	$-0.566547\pi$
$503$	16.1430	−	13.5456i	0.719779	−	0.603967i	0.927324	+	0.374259i	$0.122103\pi$
$504$	8.79752	−	7.38200i	0.391873	−	0.328820i
$505$		0			0
$506$	−6.61974	−	11.4657i	−0.294283	−	0.509713i
$507$	−1.33423	−	0.485620i	−0.0592553	−	0.0215672i
$508$	−0.499555	+	2.83312i	−0.0221642	+	0.125699i
$509$	0.753952	+	4.27588i	0.0334184	+	0.189525i	0.996947	−	0.0780800i	$-0.0248789\pi$
$509$	0.753952	+	4.27588i	0.0334184	+	0.189525i	−0.963529	+	0.267605i	$0.913768\pi$
$510$		0			0
$511$	−20.3825	−	17.1029i	−0.901667	−	0.756588i
$512$	−1.00000			−0.0441942
$513$	−0.716412	−	2.12916i	−0.0316303	−	0.0940048i
$514$	22.4326			0.989458
$515$		0			0
$516$	−0.914989	+	0.333029i	−0.0402801	+	0.0146608i
$517$	−3.50534	−	19.8798i	−0.154165	−	0.874311i
$518$	−3.13142	+	17.7592i	−0.137587	+	0.780292i
$519$	−0.448839	−	0.163364i	−0.0197018	−	0.00717088i
$520$		0			0
$521$	13.6133	−	23.5788i	0.596407	−	1.03301i	−0.396939	−	0.917845i	$-0.629928\pi$
$521$	13.6133	−	23.5788i	0.596407	−	1.03301i	0.993347	−	0.115163i	$-0.0367391\pi$
$522$	2.43763	−	2.04541i	0.106692	−	0.0895254i
$523$	22.4219	−	18.8142i	0.980439	−	0.822686i	−0.00371632	−	0.999993i	$-0.501183\pi$
$523$	22.4219	−	18.8142i	0.980439	−	0.822686i	0.984156	+	0.177307i	$0.0567385\pi$
$524$	−4.86866	+	8.43277i	−0.212689	+	0.368387i
$525$		0			0
$526$	13.6565	+	4.97057i	0.595453	+	0.216727i
$527$	−1.27929	+	7.25520i	−0.0557267	+	0.316042i
$528$	0.0543417	+	0.308187i	0.00236492	+	0.0134121i
$529$	9.17315	−	3.33875i	0.398832	−	0.145163i
$530$		0			0
$531$	−31.6176			−1.37209
$532$	0.409610	−	16.7226i	0.0177589	−	0.725017i
$533$	61.0833			2.64581
$534$	−0.211288	−	0.177292i	−0.00914332	−	0.00767216i
$535$		0			0
$536$	−1.10350	−	6.25827i	−0.0476640	−	0.270316i
$537$	−0.00656763	+	0.0372469i	−0.000283414	+	0.00160732i
$538$	27.8282	+	10.1286i	1.19976	+	0.436677i
$539$	−14.0585	−	24.3500i	−0.605541	−	1.04883i
$540$		0			0
$541$	−16.7891	+	14.0878i	−0.721822	+	0.605680i	−0.927889	−	0.372858i	$-0.878378\pi$
$541$	−16.7891	+	14.0878i	−0.721822	+	0.605680i	0.206067	+	0.978538i	$0.433934\pi$
$542$	−9.12300	+	7.65510i	−0.391866	+	0.328815i
$543$	0.0966718	−	0.167441i	0.00414859	−	0.00718556i
$544$	2.17533	+	3.76778i	0.0932663	+	0.161542i
$545$		0			0
$546$	0.311326	−	1.76562i	0.0133235	−	0.0755615i
$547$	−3.51251	−	19.9205i	−0.150184	−	0.851737i	−0.963057	−	0.269296i	$-0.913209\pi$
$547$	−3.51251	−	19.9205i	−0.150184	−	0.851737i	0.812873	−	0.582441i	$-0.197902\pi$
$548$	−13.7209	+	4.99398i	−0.586126	+	0.213332i
$549$	−23.3833	−	19.6209i	−0.997973	−	0.837399i
$550$		0			0
$551$	0.113495	−	4.63352i	0.00483507	−	0.197395i
$552$	0.312910			0.0133183
$553$	−22.8930	−	19.2095i	−0.973509	−	0.816871i
$554$	10.6493	−	3.87601i	0.452444	−	0.164676i
$555$		0			0
$556$	1.57882	−	8.95391i	0.0669567	−	0.379730i
$557$	22.0400	+	8.02192i	0.933866	+	0.339900i	0.763741	−	0.645523i	$-0.223361\pi$
$557$	22.0400	+	8.02192i	0.933866	+	0.339900i	0.170125	+	0.985422i	$0.445583\pi$
$558$	2.53374	+	4.38857i	0.107262	+	0.185783i
$559$	30.7522	−	53.2644i	1.30068	−	2.25284i
$560$		0			0
$561$	1.04297	−	0.875155i	0.0440342	−	0.0369491i
$562$	−3.19698	+	5.53733i	−0.134856	+	0.233578i
$563$	10.0610	+	17.4261i	0.424019	+	0.734422i	0.996328	−	0.0856154i	$-0.0272856\pi$
$563$	10.0610	+	17.4261i	0.424019	+	0.734422i	−0.572309	+	0.820038i	$0.693952\pi$
$564$	0.448327	+	0.163178i	0.0188780	+	0.00687101i
$565$		0			0
$566$	1.06430	+	6.03592i	0.0447357	+	0.253709i
$567$	−32.2154	+	11.7255i	−1.35292	+	0.492423i
$568$	1.63203	+	1.36944i	0.0684786	+	0.0574604i
$569$	22.2047			0.930871			0.465436	−	0.885082i	$-0.345898\pi$
$569$	22.2047			0.930871			0.465436	+	0.885082i	$0.345898\pi$
$570$		0			0
$571$	23.9839			1.00370			0.501848	−	0.864956i	$-0.332654\pi$
$571$	23.9839			1.00370			0.501848	+	0.864956i	$0.332654\pi$
$572$	−15.1424	−	12.7059i	−0.633134	−	0.531262i
$573$	0.274174	−	0.0997912i	0.0114538	−	0.00416884i
$574$	7.49320	+	42.4961i	0.312760	+	1.77375i
$575$		0			0
$576$	2.81213	+	1.02353i	0.117172	+	0.0426471i
$577$	3.40913	+	5.90479i	0.141924	+	0.245820i	0.928221	−	0.372029i	$-0.121338\pi$
$577$	3.40913	+	5.90479i	0.141924	+	0.245820i	−0.786297	+	0.617849i	$0.788004\pi$
$578$	0.964089	−	1.66985i	0.0401008	−	0.0694566i
$579$	1.10393	−	0.926311i	0.0458780	−	0.0384962i
$580$		0			0
$581$	6.15176	−	10.6552i	0.255218	−	0.442050i
$582$	−0.772719	−	1.33839i	−0.0320302	−	0.0554780i
$583$	9.15221	+	3.33113i	0.379046	+	0.137961i
$584$	1.20397	−	6.82805i	0.0498206	−	0.282547i
$585$		0			0
$586$	9.11613	−	3.31800i	0.376584	−	0.137065i
$587$	−22.2281	−	18.6516i	−0.917453	−	0.769835i	0.0560690	−	0.998427i	$-0.482143\pi$
$587$	−22.2281	−	18.6516i	−0.917453	−	0.769835i	−0.973522	+	0.228592i	$0.926588\pi$
$588$	0.664534			0.0274049
$589$	7.23539	+	1.45932i	0.298129	+	0.0601304i
$590$		0			0
$591$	−0.111311	−	0.0934010i	−0.00457872	−	0.00384200i
$592$	−4.41570	+	1.60718i	−0.181484	+	0.0660548i
$593$	−3.47902	−	19.7305i	−0.142866	−	0.810236i	−0.969056	−	0.246843i	$-0.920607\pi$
$593$	−3.47902	−	19.7305i	−0.142866	−	0.810236i	0.826189	−	0.563393i	$-0.190504\pi$
$594$	0.325648	−	1.84684i	0.0133615	−	0.0757769i
$595$		0			0
$596$	2.67292	+	4.62963i	0.109487	+	0.189637i
$597$	0.544660	−	0.943379i	0.0222914	−	0.0386099i
$598$	−15.1408	+	12.7047i	−0.619155	+	0.519533i
$599$	−25.3636	+	21.2826i	−1.03633	+	0.869583i	−0.991590	−	0.129416i	$-0.958690\pi$
$599$	−25.3636	+	21.2826i	−1.03633	+	0.869583i	−0.0447378	+	0.998999i	$0.514245\pi$
$600$		0			0
$601$	19.6224	+	33.9870i	0.800415	+	1.38636i	0.919343	+	0.393457i	$0.128721\pi$
$601$	19.6224	+	33.9870i	0.800415	+	1.38636i	−0.118927	+	0.992903i	$0.537946\pi$
$602$	40.8289	+	14.8605i	1.66406	+	0.605668i
$603$	−3.30234	+	18.7285i	−0.134482	+	0.762684i
$604$	2.06966	+	11.7376i	0.0842133	+	0.477598i
$605$		0			0
$606$	0.694681	+	0.582907i	0.0282195	+	0.0236790i
$607$	9.56175			0.388099			0.194050	−	0.980992i	$-0.437838\pi$
$607$	9.56175			0.388099			0.194050	+	0.980992i	$0.437838\pi$
$608$	3.82715	−	2.08636i	0.155212	−	0.0846130i
$609$	0.350936			0.0142206
$610$		0			0
$611$	−28.3185	+	10.3071i	−1.14565	+	0.416981i
$612$	−2.26086	−	12.8220i	−0.0913899	−	0.518298i
$613$	−0.401235	+	2.27551i	−0.0162057	+	0.0919072i	−0.991838	−	0.127505i	$-0.959303\pi$
$613$	−0.401235	+	2.27551i	−0.0162057	+	0.0919072i	0.975632	+	0.219413i	$0.0704141\pi$
$614$	2.66894	+	0.971416i	0.107710	+	0.0392032i
$615$		0			0
$616$	6.98207	−	12.0933i	0.281316	−	0.487253i
$617$	28.4155	−	23.8435i	1.14397	−	0.959902i	0.144405	−	0.989519i	$-0.453873\pi$
$617$	28.4155	−	23.8435i	1.14397	−	0.959902i	0.999561	+	0.0296168i	$0.00942869\pi$
$618$	−0.877058	+	0.735939i	−0.0352804	+	0.0296038i
$619$	−15.6980	+	27.1897i	−0.630956	+	1.09285i	0.356401	+	0.934333i	$0.384004\pi$
$619$	−15.6980	+	27.1897i	−0.630956	+	1.09285i	−0.987357	+	0.158515i	$0.949330\pi$
$620$		0			0
$621$	−1.76206	−	0.641338i	−0.0707090	−	0.0257360i
$622$	2.06619	−	11.7179i	0.0828466	−	0.469846i
$623$	2.13719	+	12.1206i	0.0856245	+	0.485601i
$624$	0.439010	−	0.159786i	0.0175745	−	0.00639658i
$625$		0			0
$626$	−27.4941			−1.09888
$627$	−0.850963	−	1.06610i	−0.0339842	−	0.0425761i
$628$	16.1734			0.645390
$629$	15.6611	+	13.1412i	0.624449	+	0.523975i
$630$		0			0
$631$	4.22758	+	23.9758i	0.168297	+	0.954462i	0.945599	+	0.325334i	$0.105477\pi$
$631$	4.22758	+	23.9758i	0.168297	+	0.954462i	−0.777302	+	0.629128i	$0.783412\pi$
$632$	1.35226	−	7.66908i	0.0537902	−	0.305059i
$633$	0.676069	+	0.246069i	0.0268713	+	0.00978036i
$634$	8.82521	+	15.2857i	0.350494	+	0.607073i
$635$		0			0
$636$	−0.176337	+	0.147964i	−0.00699221	+	0.00586716i
$637$	−32.1549	+	26.9812i	−1.27402	+	1.06903i
$638$	1.93460	−	3.35083i	0.0765917	−	0.132661i
$639$	−3.18782	−	5.52147i	−0.126108	−	0.218426i
$640$		0			0
$641$	−1.64443	+	9.32600i	−0.0649509	+	0.368355i	0.934957	+	0.354762i	$0.115438\pi$
$641$	−1.64443	+	9.32600i	−0.0649509	+	0.368355i	−0.999908	+	0.0135931i	$0.995673\pi$
$642$	−0.111586	−	0.632833i	−0.00440393	−	0.0249759i
$643$	−3.51571	+	1.27961i	−0.138646	+	0.0504631i	−0.410411	−	0.911901i	$-0.634615\pi$
$643$	−3.51571	+	1.27961i	−0.138646	+	0.0504631i	0.271765	+	0.962364i	$0.412393\pi$
$644$	−10.6961	−	8.97508i	−0.421485	−	0.353668i
$645$		0			0
$646$	−16.1862	−	9.88134i	−0.636839	−	0.388776i
$647$	32.1985			1.26585			0.632926	−	0.774212i	$-0.281854\pi$
$647$	32.1985			1.26585			0.632926	+	0.774212i	$0.281854\pi$
$648$	−6.84345	−	5.74234i	−0.268836	−	0.225580i
$649$	−36.1262	+	13.1489i	−1.41808	+	0.516138i
$650$		0			0
$651$	−0.0970458	+	0.550374i	−0.00380353	+	0.0215709i
$652$	11.2248	+	4.08548i	0.439596	+	0.160000i
$653$	−7.68376	−	13.3087i	−0.300689	−	0.520808i	0.675603	−	0.737265i	$-0.263883\pi$
$653$	−7.68376	−	13.3087i	−0.300689	−	0.520808i	−0.976292	+	0.216457i	$0.930550\pi$
$654$	−0.226934	+	0.393061i	−0.00887382	+	0.0153699i
$655$		0			0
$656$	−8.61378	+	7.22782i	−0.336312	+	0.282199i
$657$	−10.3744	+	17.9691i	−0.404745	+	0.701040i
$658$	−10.6446	−	18.4370i	−0.414970	−	0.718750i
$659$	19.3778	+	7.05295i	0.754853	+	0.274744i	0.690646	−	0.723193i	$-0.257326\pi$
$659$	19.3778	+	7.05295i	0.754853	+	0.274744i	0.0642067	+	0.997937i	$0.479548\pi$
$660$		0			0
$661$	3.02307	+	17.1447i	0.117584	+	0.666850i	0.985439	+	0.170032i	$0.0543871\pi$
$661$	3.02307	+	17.1447i	0.117584	+	0.666850i	−0.867855	+	0.496818i	$0.834502\pi$
$662$	−27.3761	+	9.96407i	−1.06400	+	0.387265i
$663$	−1.55703	−	1.30650i	−0.0604700	−	0.0507403i
$664$	3.20606			0.124419
$665$		0			0
$666$	14.0625			0.544911
$667$	−2.96369	−	2.48683i	−0.114754	−	0.0962903i
$668$	−21.8264	+	7.94416i	−0.844489	+	0.307369i
$669$	−0.00191768	−	0.0108757i	−7.41420e−5	−	0.000420480i
$670$		0			0
$671$	−34.8775	−	12.6944i	−1.34643	−	0.490060i
$672$	0.165019	+	0.285821i	0.00636573	+	0.0110258i
$673$	21.9641	−	38.0429i	0.846654	−	1.46645i	−0.0375234	−	0.999296i	$-0.511947\pi$
$673$	21.9641	−	38.0429i	0.846654	−	1.46645i	0.884177	−	0.467152i	$-0.154720\pi$
$674$	−20.2332	+	16.9777i	−0.779354	+	0.653956i
$675$		0			0
$676$	−8.25485	+	14.2978i	−0.317494	+	0.549916i
$677$	−5.62776	−	9.74756i	−0.216292	−	0.374629i	0.737379	−	0.675479i	$-0.236063\pi$
$677$	−5.62776	−	9.74756i	−0.216292	−	0.374629i	−0.953672	+	0.300850i	$0.902730\pi$
$678$	0.432648	+	0.157471i	0.0166158	+	0.00604764i
$679$	−11.9749	+	67.9132i	−0.459556	+	2.60627i
$680$		0			0
$681$	−0.741896	+	0.270028i	−0.0284295	+	0.0103475i
$682$	4.72014	+	3.96067i	0.180743	+	0.151662i
$683$	−26.1364			−1.00008			−0.500040	−	0.866002i	$-0.666682\pi$
$683$	−26.1364			−1.00008			−0.500040	+	0.866002i	$0.666682\pi$
$684$	−12.8979	+	1.94990i	−0.493163	+	0.0745563i
$685$		0			0
$686$	−2.13721	−	1.79333i	−0.0815990	−	0.0684697i
$687$	−0.474907	+	0.172852i	−0.0181188	+	0.00659472i
$688$	1.96605	+	11.1500i	0.0749549	+	0.425090i
$689$	2.52485	−	14.3191i	0.0961891	−	0.545516i
$690$		0			0
$691$	12.7785	+	22.1330i	0.486116	+	0.841977i	0.999873	−	0.0159586i	$-0.00508000\pi$
$691$	12.7785	+	22.1330i	0.486116	+	0.841977i	−0.513757	+	0.857936i	$0.671747\pi$
$692$	−2.77695	+	4.80983i	−0.105564	+	0.182842i
$693$	−32.0123	+	26.8615i	−1.21605	+	1.02039i
$694$	−3.27671	+	2.74949i	−0.124382	+	0.104369i
$695$		0			0
$696$	0.0457236	+	0.0791956i	0.00173315	+	0.00300190i
$697$	45.9706	+	16.7319i	1.74126	+	0.633767i
$698$	1.55599	−	8.82448i	0.0588953	−	0.334012i
$699$	−0.0919259	−	0.521337i	−0.00347696	−	0.0197188i
$700$		0			0
$701$	−20.9395	−	17.5703i	−0.790875	−	0.663623i	0.155087	−	0.987901i	$-0.450434\pi$
$701$	−20.9395	−	17.5703i	−0.790875	−	0.663623i	−0.945962	+	0.324278i	$0.894879\pi$
$702$	−2.79965			−0.105666
$703$	13.5464	−	15.3637i	0.510912	−	0.579452i
$704$	3.63879			0.137142
$705$		0			0
$706$	17.8345	−	6.49121i	0.671209	−	0.244300i
$707$	−7.02673	−	39.8505i	−0.264267	−	1.49873i
$708$	0.157781	−	0.894822i	0.00592979	−	0.0336295i
$709$	−33.1490	−	12.0653i	−1.24494	−	0.453120i	−0.366249	−	0.930517i	$-0.619358\pi$
$709$	−33.1490	−	12.0653i	−1.24494	−	0.453120i	−0.878688	+	0.477397i	$0.841580\pi$
$710$		0			0
$711$	−11.6523	+	20.1823i	−0.436994	+	0.756897i
$712$	−2.45679	+	2.06150i	−0.0920723	+	0.0772578i
$713$	4.71966	−	3.96027i	0.176753	−	0.148313i
$714$	0.717939	−	1.24351i	0.0268682	−	0.0465371i
$715$		0			0
$716$	0.413255	+	0.150413i	0.0154441	+	0.00562118i
$717$	−0.0307192	+	0.174217i	−0.00114723	+	0.00650627i
$718$	0.810189	+	4.59481i	0.0302360	+	0.171477i
$719$	24.8968	−	9.06170i	0.928494	−	0.337944i	0.166882	−	0.985977i	$-0.446630\pi$
$719$	24.8968	−	9.06170i	0.928494	−	0.337944i	0.761613	+	0.648033i	$0.224408\pi$
$720$		0			0
$721$	51.0888			1.90265
$722$	−10.2942	+	15.9696i	−0.383111	+	0.594328i
$723$	0.829832			0.0308618
$724$	−1.72218	−	1.44508i	−0.0640042	−	0.0537059i
$725$		0			0
$726$	−0.0334641	−	0.189785i	−0.00124197	−	0.00704356i
$727$	6.25227	−	35.4584i	0.231884	−	1.31508i	−0.617194	−	0.786811i	$-0.711731\pi$
$727$	6.25227	−	35.4584i	0.231884	−	1.31508i	0.849078	−	0.528268i	$-0.177158\pi$
$728$	−19.5896	−	7.13003i	−0.726039	−	0.264256i
$729$	13.3007	+	23.0375i	0.492619	+	0.853241i
$730$		0			0
$731$	37.7340	−	31.6626i	1.39564	−	1.17108i
$732$	0.671988	−	0.563865i	0.0248374	−	0.0208411i
$733$	−23.0029	+	39.8422i	−0.849633	+	1.47161i	0.0319037	+	0.999491i	$0.489843\pi$
$733$	−23.0029	+	39.8422i	−0.849633	+	1.47161i	−0.881536	+	0.472116i	$0.843490\pi$
$734$	−6.52314	−	11.2984i	−0.240773	−	0.417032i
$735$		0			0
$736$	0.631806	−	3.58315i	0.0232887	−	0.132077i
$737$	4.01541	+	22.7725i	0.147910	+	0.838837i
$738$	31.6210	−	11.5091i	1.16398	−	0.423655i
$739$	22.1707	+	18.6035i	0.815564	+	0.684339i	0.951929	−	0.306319i	$-0.0990975\pi$
$739$	22.1707	+	18.6035i	0.815564	+	0.684339i	−0.136365	+	0.990659i	$0.543542\pi$
$740$		0			0
$741$	−1.34679	+	1.52746i	−0.0494754	+	0.0561126i
$742$	10.2716			0.377084
$743$	−39.1676	−	32.8655i	−1.43692	−	1.20572i	−0.941477	−	0.337079i	$-0.890561\pi$
$743$	−39.1676	−	32.8655i	−1.43692	−	1.20572i	−0.495443	−	0.868640i	$-0.664994\pi$
$744$	−0.136847	+	0.0498082i	−0.00501706	+	0.00182606i
$745$		0			0
$746$	−2.26252	+	12.8314i	−0.0828368	+	0.469791i
$747$	−9.01586	−	3.28150i	−0.329873	−	0.120064i
$748$	−7.91556	−	13.7101i	−0.289421	−	0.501293i
$749$	−14.3370	+	24.8324i	−0.523863	+	0.907358i
$750$		0			0
$751$	14.2455	−	11.9534i	0.519825	−	0.436185i	−0.344745	−	0.938696i	$-0.612035\pi$
$751$	14.2455	−	11.9534i	0.519825	−	0.436185i	0.864571	+	0.502511i	$0.167590\pi$
$752$	2.77378	−	4.80434i	0.101150	−	0.175196i
$753$	0.708227	+	1.22669i	0.0258092	+	0.0447029i
$754$	−5.42791	−	1.97560i	−0.197673	−	0.0719471i
$755$		0			0
$756$	−0.343438	−	1.94774i	−0.0124907	−	0.0708385i
$757$	−41.2095	+	14.9990i	−1.49778	+	0.545149i	−0.955486	−	0.295037i	$-0.904668\pi$
$757$	−41.2095	+	14.9990i	−1.49778	+	0.545149i	−0.542298	+	0.840186i	$0.682446\pi$
$758$	16.4260	+	13.7831i	0.596620	+	0.500624i
$759$	−1.13861			−0.0413291
$760$		0			0
$761$	27.5848			0.999950			0.499975	−	0.866040i	$-0.333343\pi$
$761$	27.5848			0.999950			0.499975	+	0.866040i	$0.333343\pi$
$762$	0.189528	+	0.159033i	0.00686587	+	0.00576115i
$763$	19.0312	−	6.92680i	0.688976	−	0.250767i
$764$	−0.589121	−	3.34107i	−0.0213137	−	0.120876i
$765$		0			0
$766$	−11.4828	−	4.17939i	−0.414890	−	0.151008i
$767$	28.6967	+	49.7041i	1.03618	+	1.79471i
$768$	−0.0430007	+	0.0744795i	−0.00155166	+	0.00268755i
$769$	−7.43025	+	6.23472i	−0.267942	+	0.224830i	−0.766852	−	0.641824i	$-0.778178\pi$
$769$	−7.43025	+	6.23472i	−0.267942	+	0.224830i	0.498911	+	0.866653i	$0.333734\pi$
$770$		0			0
$771$	0.964617	−	1.67077i	0.0347398	−	0.0601711i
$772$	−8.37825	−	14.5116i	−0.301540	−	0.522283i
$773$	−29.8529	−	10.8656i	−1.07373	−	0.390807i	−0.256162	−	0.966634i	$-0.582458\pi$
$773$	−29.8529	−	10.8656i	−1.07373	−	0.390807i	−0.817572	+	0.575827i	$0.804680\pi$
$774$	5.88361	−	33.3676i	0.211482	−	1.19937i
$775$		0			0
$776$	−16.8862	+	6.14607i	−0.606178	+	0.220631i
$777$	1.18804	+	0.996883i	0.0426207	+	0.0357630i
$778$	−10.8567			−0.389231
$779$	17.8864	−	45.6334i	0.640848	−	1.63499i
$780$		0			0
$781$	−5.93863	−	4.98310i	−0.212501	−	0.178309i
$782$	−14.8749	+	5.41402i	−0.531925	+	0.193605i
$783$	−0.0951604	−	0.539682i	−0.00340076	−	0.0192866i
$784$	1.34178	−	7.60961i	0.0479207	−	0.271772i
$785$		0			0
$786$	0.418712	+	0.725231i	0.0149350	+	0.0258681i
$787$	−20.4662	+	35.4486i	−0.729543	+	1.26361i	0.227534	+	0.973770i	$0.426934\pi$
$787$	−20.4662	+	35.4486i	−0.729543	+	1.26361i	−0.957077	+	0.289835i	$0.906400\pi$
$788$	−1.29429	+	1.08604i	−0.0461072	+	0.0386886i
$789$	0.957446	−	0.803393i	0.0340860	−	0.0286015i
$790$		0			0
$791$	−10.2724	−	17.7923i	−0.365243	−	0.632620i
$792$	−10.2327	−	3.72441i	−0.363605	−	0.132341i
$793$	−9.62176	+	54.5677i	−0.341679	+	1.93776i
$794$	−5.28065	−	29.9480i	−0.187403	−	1.06282i
$795$		0			0
$796$	−9.70294	−	8.14174i	−0.343912	−	0.288576i
$797$	45.3730			1.60720			0.803598	−	0.595173i	$-0.202916\pi$
$797$	45.3730			1.60720			0.803598	+	0.595173i	$0.202916\pi$
$798$	−1.22788	−	0.749592i	−0.0434664	−	0.0265353i
$799$	−24.1355			−0.853854
$800$		0			0
$801$	9.01882	−	3.28258i	0.318665	−	0.115984i
$802$	−1.75733	−	9.96633i	−0.0620536	−	0.351923i
$803$	−4.38100	+	24.8459i	−0.154602	+	0.876791i
$804$	−0.513564	−	0.186922i	−0.0181120	−	0.00659223i
$805$		0			0
$806$	4.59935	−	7.96630i	0.162005	−	0.280601i
$807$	1.95101	−	1.63709i	0.0686788	−	0.0576284i
$808$	8.07755	−	6.77787i	0.284167	−	0.238445i
$809$	9.87479	−	17.1036i	0.347179	−	0.601332i	−0.638568	−	0.769565i	$-0.720473\pi$
$809$	9.87479	−	17.1036i	0.347179	−	0.601332i	0.985747	+	0.168233i	$0.0538062\pi$
$810$		0			0
$811$	−38.2589	−	13.9251i	−1.34345	−	0.488976i	−0.432553	−	0.901608i	$-0.642387\pi$
$811$	−38.2589	−	13.9251i	−1.34345	−	0.488976i	−0.910898	+	0.412632i	$0.864610\pi$
$812$	0.708585	−	4.01859i	0.0248665	−	0.141025i
$813$	0.177852	+	1.00865i	0.00623755	+	0.0353749i
$814$	16.0678	−	5.84820i	0.563176	−	0.204979i
$815$		0			0
$816$	0.374163			0.0130983
$817$	−30.7873	−	38.5710i	−1.07711	−	1.34943i
$818$	−18.4722			−0.645865
$819$	47.7906	+	40.1011i	1.66994	+	1.40125i
$820$		0			0
$821$	−1.97582	−	11.2055i	−0.0689567	−	0.391073i	−0.999679	−	0.0253456i	$-0.991931\pi$
$821$	−1.97582	−	11.2055i	−0.0689567	−	0.391073i	0.930722	−	0.365727i	$-0.119180\pi$
$822$	−0.218058	+	1.23667i	−0.00760564	+	0.0431337i
$823$	−14.9582	−	5.44433i	−0.521409	−	0.189777i	0.0678893	−	0.997693i	$-0.478374\pi$
$823$	−14.9582	−	5.44433i	−0.521409	−	0.189777i	−0.589298	+	0.807915i	$0.700596\pi$
$824$	6.65638	+	11.5292i	0.231886	+	0.401638i
$825$		0			0
$826$	−31.0592	+	26.0618i	−1.08069	+	0.906805i
$827$	−30.7586	+	25.8095i	−1.06958	+	0.897484i	−0.995014	−	0.0997322i	$-0.968201\pi$
$827$	−30.7586	+	25.8095i	−1.06958	+	0.897484i	−0.0745654	+	0.997216i	$0.523757\pi$
$828$	−5.44418	+	9.42960i	−0.189198	+	0.327701i
$829$	0.218144	+	0.377836i	0.00757644	+	0.0131228i	0.869789	−	0.493424i	$-0.164255\pi$
$829$	0.218144	+	0.377836i	0.00757644	+	0.0131228i	−0.862212	+	0.506547i	$0.830922\pi$
$830$		0			0
$831$	0.169243	−	0.959823i	0.00587096	−	0.0332959i
$832$	−0.943306	−	5.34975i	−0.0327033	−	0.185469i
$833$	−31.5901	+	11.4979i	−1.09453	+	0.398377i
$834$	−0.598992	−	0.502614i	−0.0207414	−	0.0174041i
$835$		0			0
$836$	−13.9262	+	7.59183i	−0.481648	+	0.262569i
$837$	0.872700			0.0301649
$838$	−9.60428	−	8.05895i	−0.331774	−	0.278392i
$839$	0.618007	−	0.224936i	0.0213360	−	0.00776566i	−0.331330	−	0.943515i	$-0.607497\pi$
$839$	0.618007	−	0.224936i	0.0213360	−	0.00776566i	0.352666	+	0.935749i	$0.385275\pi$
$840$		0			0
$841$	−4.83946	+	27.4459i	−0.166878	+	0.946412i
$842$	33.8406	+	12.3170i	1.16622	+	0.424471i
$843$	0.274945	+	0.476218i	0.00946960	+	0.0164018i
$844$	4.18282	−	7.24486i	0.143979	−	0.249378i
$845$		0			0
$846$	−12.7176	+	10.6714i	−0.437241	+	0.366889i
$847$	−4.29962	+	7.44717i	−0.147737	+	0.255888i
$848$	1.33830	+	2.31800i	0.0459573	+	0.0796005i
$849$	0.495318	+	0.180281i	0.0169993	+	0.00618723i
$850$		0			0
$851$	−2.96891	−	16.8375i	−0.101773	−	0.577183i
$852$	0.172174	−	0.0626661i	0.00589857	−	0.00214691i
$853$	−9.62499	−	8.07632i	−0.329553	−	0.276528i	0.462965	−	0.886377i	$-0.346786\pi$
$853$	−9.62499	−	8.07632i	−0.329553	−	0.276528i	−0.792518	+	0.609849i	$0.791230\pi$
$854$	−39.1434			−1.33946
$855$		0			0
$856$	−7.47191			−0.255385
$857$	−33.2359	−	27.8882i	−1.13532	−	0.952643i	−0.136041	−	0.990703i	$-0.543438\pi$
$857$	−33.2359	−	27.8882i	−1.13532	−	0.952643i	−0.999275	+	0.0380598i	$0.987882\pi$
$858$	−1.59746	+	0.581430i	−0.0545365	+	0.0198497i
$859$	−6.32528	−	35.8724i	−0.215816	−	1.22395i	−0.879486	−	0.475926i	$-0.842113\pi$
$859$	−6.32528	−	35.8724i	−0.215816	−	1.22395i	0.663670	−	0.748026i	$-0.268998\pi$
$860$		0			0
$861$	3.48730	+	1.26927i	0.118847	+	0.0432567i
$862$	10.8493	+	18.7915i	0.369527	+	0.640040i
$863$	−9.94203	+	17.2201i	−0.338431	+	0.586179i	−0.984138	−	0.177406i	$-0.943229\pi$
$863$	−9.94203	+	17.2201i	−0.338431	+	0.586179i	0.645707	+	0.763585i	$0.276563\pi$
$864$	0.394798	−	0.331275i	0.0134313	−	0.0112702i
$865$		0			0
$866$	−0.227792	+	0.394547i	−0.00774068	+	0.0134072i
$867$	−0.0829131	−	0.143610i	−0.00281588	−	0.00487724i
$868$	6.10642	+	2.22256i	0.207265	+	0.0754384i
$869$	−4.92061	+	27.9062i	−0.166920	+	0.946652i
$870$		0			0
$871$	32.4393	−	11.8069i	1.09916	−	0.400062i
$872$	4.04276	+	3.39227i	0.136905	+	0.114877i
$873$	53.7768			1.82007
$874$	5.05772	+	15.0314i	0.171080	+	0.508446i
$875$		0			0
$876$	−0.456778	−	0.383282i	−0.0154331	−	0.0129499i
$877$	−9.98104	+	3.63280i	−0.337036	+	0.122671i	−0.504993	−	0.863123i	$-0.668505\pi$
$877$	−9.98104	+	3.63280i	−0.337036	+	0.122671i	0.167958	+	0.985794i	$0.446283\pi$
$878$	0.103076	+	0.584572i	0.00347864	+	0.0197284i
$879$	0.144877	−	0.821641i	0.00488659	−	0.0277133i
$880$		0			0
$881$	−10.5068	−	18.1983i	−0.353982	−	0.613116i	0.632961	−	0.774184i	$-0.281839\pi$
$881$	−10.5068	−	18.1983i	−0.353982	−	0.613116i	−0.986943	+	0.161068i	$0.948506\pi$
$882$	−11.5619	+	20.0258i	−0.389310	+	0.674305i
$883$	−26.8463	+	22.5267i	−0.903450	+	0.758085i	−0.970862	−	0.239641i	$-0.922970\pi$
$883$	−26.8463	+	22.5267i	−0.903450	+	0.758085i	0.0674116	+	0.997725i	$0.478526\pi$
$884$	−18.1047	+	15.1916i	−0.608926	+	0.510950i
$885$		0			0
$886$	18.8464	+	32.6429i	0.633158	+	1.09666i
$887$	5.34637	+	1.94592i	0.179514	+	0.0653376i	0.430213	−	0.902727i	$-0.358438\pi$
$887$	5.34637	+	1.94592i	0.179514	+	0.0653376i	−0.250700	+	0.968065i	$0.580661\pi$
$888$	−0.0701762	+	0.397989i	−0.00235496	+	0.0133556i
$889$	−1.91708	−	10.8723i	−0.0642968	−	0.364645i
$890$		0			0
$891$	24.9019	+	20.8952i	0.834244	+	0.700014i
$892$	−0.128411			−0.00429951
$893$	−0.592129	+	24.1740i	−0.0198149	+	0.808953i
$894$	0.459749			0.0153763
$895$		0			0
$896$	3.60614	−	1.31253i	0.120473	−	0.0438485i
$897$	0.295170	+	1.67399i	0.00985544	+	0.0558930i
$898$	3.55042	−	20.1354i	0.118479	−	0.671928i
$899$	1.69198	+	0.615829i	0.0564306	+	0.0205390i
$900$		0			0
$901$	5.82247	−	10.0848i	0.193975	−	0.335974i
$902$	31.3438	−	26.3005i	1.04363	−	0.875712i
$903$	2.86247	−	2.40190i	0.0952571	−	0.0799302i
$904$	2.67678	−	4.63632i	0.0890285	−	0.154202i
$905$		0			0
$906$	0.963210	+	0.350580i	0.0320005	+	0.0116472i
$907$	−10.1428	+	57.5230i	−0.336788	+	1.91002i	0.0720304	+	0.997402i	$0.477052\pi$
$907$	−10.1428	+	57.5230i	−0.336788	+	1.91002i	−0.408818	+	0.912616i	$0.634059\pi$
$908$	1.59412	+	9.04072i	0.0529028	+	0.300027i
$909$	−29.6525	+	10.7926i	−0.983510	+	0.357968i
$910$		0			0
$911$	−10.1271			−0.335525			−0.167763	−	0.985827i	$-0.553654\pi$
$911$	−10.1271			−0.335525			−0.167763	+	0.985827i	$0.553654\pi$
$912$	0.00917952	−	0.374759i	0.000303964	−	0.0124095i
$913$	−11.6662			−0.386095
$914$	−9.93157	−	8.33358i	−0.328507	−	0.275650i
$915$		0			0
$916$	1.02044	+	5.78720i	0.0337163	+	0.191214i
$917$	6.48884	−	36.8000i	0.214280	−	1.21524i
$918$	−2.10699	−	0.766880i	−0.0695409	−	0.0253108i
$919$	−6.04486	−	10.4700i	−0.199401	−	0.345373i	0.748933	−	0.662646i	$-0.230566\pi$
$919$	−6.04486	−	10.4700i	−0.199401	−	0.345373i	−0.948335	+	0.317272i	$0.897233\pi$
$920$		0			0
$921$	0.187117	−	0.157010i	0.00616572	−	0.00517365i
$922$	−2.15375	+	1.80721i	−0.0709300	+	0.0595174i
$923$	−5.78665	+	10.0228i	−0.190470	+	0.329904i
$924$	−0.600468	−	1.04004i	−0.0197540	−	0.0342149i
$925$		0			0
$926$	3.54032	−	20.0781i	0.116342	−	0.659808i
$927$	−6.91811	−	39.2346i	−0.227221	−	1.28863i
$928$	0.999196	−	0.363677i	0.0328002	−	0.0119383i
$929$	16.9263	+	14.2029i	0.555334	+	0.465981i	0.876743	−	0.480960i	$-0.159712\pi$
$929$	16.9263	+	14.2029i	0.555334	+	0.465981i	−0.321408	+	0.946941i	$0.604156\pi$
$930$		0			0
$931$	10.7412	+	31.9226i	0.352028	+	1.04622i
$932$	−6.15548			−0.201629
$933$	−0.783898	−	0.657768i	−0.0256637	−	0.0215344i
$934$	23.7967	−	8.66130i	0.778653	−	0.283407i
$935$		0			0
$936$	−2.82294	+	16.0097i	−0.0922707	+	0.523293i
$937$	−9.08162	−	3.30544i	−0.296684	−	0.107984i	0.189390	−	0.981902i	$-0.439349\pi$
$937$	−9.08162	−	3.30544i	−0.296684	−	0.107984i	−0.486073	+	0.873918i	$0.661571\pi$
$938$	12.1935	+	21.1198i	0.398133	+	0.689587i
$939$	−1.18226	+	2.04774i	−0.0385817	+	0.0668255i
$940$		0			0
$941$	−32.1824	+	27.0043i	−1.04912	+	0.880314i	−0.993001	−	0.118110i	$-0.962317\pi$
$941$	−32.1824	+	27.0043i	−1.04912	+	0.880314i	−0.0561173	+	0.998424i	$0.517872\pi$
$942$	0.695469	−	1.20459i	0.0226596	−	0.0392476i
$943$	−20.4561	−	35.4311i	−0.666143	−	1.15379i
$944$	−9.92808	−	3.61353i	−0.323131	−	0.117610i
$945$		0			0
$946$	−7.15404	−	40.5726i	−0.232598	−	1.31913i
$947$	28.8476	−	10.4997i	0.937421	−	0.341193i	0.172274	−	0.985049i	$-0.444888\pi$
$947$	28.8476	−	10.4997i	0.937421	−	0.341193i	0.765147	+	0.643856i	$0.222666\pi$
$948$	−0.513040	−	0.430492i	−0.0166628	−	0.0139817i
$949$	37.6641			1.22263
$950$		0			0
$951$	1.51796			0.0492233
$952$	−12.7899	−	10.7320i	−0.414522	−	0.347825i
$953$	−24.7298	+	9.00090i	−0.801076	+	0.291568i	−0.709932	−	0.704270i	$-0.751274\pi$
$953$	−24.7298	+	9.00090i	−0.801076	+	0.291568i	−0.0911437	+	0.995838i	$0.529052\pi$
$954$	−1.39092	−	7.88830i	−0.0450327	−	0.255393i
$955$		0			0
$956$	1.93295	+	0.703536i	0.0625160	+	0.0227540i
$957$	−0.166379	−	0.288176i	−0.00537826	−	0.00931542i
$958$	−19.4647	+	33.7138i	−0.628875	+	1.08924i
$959$	42.9246	−	36.0180i	1.38611	−	1.16308i
$960$		0			0
$961$	14.0663	−	24.3636i	0.453752	−	0.785921i
$962$	−12.7634	−	22.1068i	−0.411508	−	0.712753i
$963$	21.0120	+	7.64773i	0.677101	+	0.246445i
$964$	1.67554	−	9.50245i	0.0539655	−	0.306053i
$965$		0			0
$966$	−1.12840	+	0.410703i	−0.0363056	+	0.0132142i
$967$	−14.7609	−	12.3858i	−0.474677	−	0.398301i	0.373820	−	0.927501i	$-0.378048\pi$
$967$	−14.7609	−	12.3858i	−0.474677	−	0.398301i	−0.848497	+	0.529200i	$0.822492\pi$
$968$	−2.24080			−0.0720221
$969$	−1.43198	+	0.780637i	−0.0460017	+	0.0250777i
$970$		0			0
$971$	18.9271	+	15.8817i	0.607398	+	0.509668i	0.893814	−	0.448438i	$-0.148019\pi$
$971$	18.9271	+	15.8817i	0.607398	+	0.509668i	−0.286416	+	0.958105i	$0.592464\pi$
$972$	−2.17484	+	0.791575i	−0.0697579	+	0.0253898i
$973$	6.05883	+	34.3613i	0.194237	+	1.10157i
$974$	−4.40727	+	24.9949i	−0.141218	+	0.800888i
$975$		0			0
$976$	−5.10002	−	8.83349i	−0.163248	−	0.282753i
$977$	−27.3110	+	47.3041i	−0.873757	+	1.51339i	−0.0156762	+	0.999877i	$0.504990\pi$
$977$	−27.3110	+	47.3041i	−0.873757	+	1.51339i	−0.858081	+	0.513515i	$0.828343\pi$
$978$	0.786958	−	0.660336i	0.0251641	−	0.0211152i
$979$	8.93976	−	7.50135i	0.285716	−	0.239744i
$980$		0			0
$981$	−7.89665	−	13.6774i	−0.252121	−	0.436686i
$982$	−20.7422	−	7.54953i	−0.661909	−	0.240915i
$983$	−0.0238366	+	0.135184i	−0.000760268	+	0.00431169i	−0.985186	−	0.171492i	$-0.945141\pi$
$983$	−0.0238366	+	0.135184i	−0.000760268	+	0.00431169i	0.984425	+	0.175804i	$0.0562524\pi$
$984$	0.167925	+	0.952352i	0.00535326	+	0.0303599i
$985$		0			0
$986$	−3.54383	−	2.97363i	−0.112859	−	0.0946996i
$987$	−1.83090			−0.0582783
$988$	14.7717	+	18.5063i	0.469950	+	0.588762i
$989$	−41.1944			−1.30990
$990$		0			0
$991$	30.7282	−	11.1841i	0.976112	−	0.355276i	0.195785	−	0.980647i	$-0.437275\pi$
$991$	30.7282	−	11.1841i	0.976112	−	0.355276i	0.780327	+	0.625371i	$0.215052\pi$
$992$	0.294045	+	1.66761i	0.00933594	+	0.0529467i
$993$	−0.435072	+	2.46742i	−0.0138066	+	0.0783011i
$994$	−7.68278	−	2.79630i	−0.243683	−	0.0886933i
$995$		0			0
$996$	0.137863	−	0.238786i	0.00436836	−	0.00756622i
$997$	14.3103	−	12.0078i	0.453211	−	0.380289i	−0.387415	−	0.921906i	$-0.626632\pi$
$997$	14.3103	−	12.0078i	0.453211	−	0.380289i	0.840626	+	0.541616i	$0.182187\pi$
$998$	7.84215	−	6.58034i	0.248239	−	0.208297i
$999$	1.21089	−	2.09733i	0.0383109	−	0.0663564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.301.3		30
5.2	odd	4		190.2.p.a.149.8	yes	60
5.3	odd	4		190.2.p.a.149.3	yes	60
5.4	even	2		950.2.l.m.301.3		30
19.6	even	9	inner	950.2.l.l.101.3		30
95.44	even	18		950.2.l.m.101.3		30
95.63	odd	36		190.2.p.a.139.8	yes	60
95.82	odd	36		190.2.p.a.139.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.139.3	✓	60	95.82	odd	36
190.2.p.a.139.8	yes	60	95.63	odd	36
190.2.p.a.149.3	yes	60	5.3	odd	4
190.2.p.a.149.8	yes	60	5.2	odd	4
950.2.l.l.101.3		30	19.6	even	9	inner
950.2.l.l.301.3		30	1.1	even	1	trivial
950.2.l.m.101.3		30	95.44	even	18
950.2.l.m.301.3		30	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.0808150 + 0.0294142i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0808150 + 0.0294142i) q^{6} +(-1.91879 - 3.32344i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29247 + 1.92361i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.0808150 + 0.0294142i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.0808150 + 0.0294142i) q^{6} +(-1.91879 - 3.32344i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.29247 + 1.92361i) q^{9} +(-1.81940 + 3.15129i) q^{11} +(-0.0430007 - 0.0744795i) q^{12} +(5.10468 + 1.85795i) q^{13} +(-0.666388 + 3.77928i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.33279 + 2.79655i) q^{17} +2.99260 q^{18} +(2.88277 - 3.26950i) q^{19} +(0.252823 + 0.212144i) q^{21} +(3.41935 - 1.24454i) q^{22} +(-0.631806 - 3.58315i) q^{23} +(-0.0149340 + 0.0846949i) q^{24} +(-2.71614 - 4.70450i) q^{26} +(0.257686 - 0.446326i) q^{27} +(2.93976 - 2.46675i) q^{28} +(0.814552 - 0.683490i) q^{29} +(0.846669 + 1.46647i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0543417 - 0.308187i) q^{33} +(-0.755483 - 4.28456i) q^{34} +(-2.29247 - 1.92361i) q^{36} +4.69909 q^{37} +(-4.30992 + 0.651573i) q^{38} -0.467184 q^{39} +(10.5664 - 3.84584i) q^{41} +(-0.0573104 - 0.325023i) q^{42} +(1.96605 - 11.1500i) q^{43} +(-3.41935 - 1.24454i) q^{44} +(-1.81921 + 3.15097i) q^{46} +(-4.24968 + 3.56591i) q^{47} +(0.0658810 - 0.0552807i) q^{48} +(-3.86350 + 6.69178i) q^{49} +(-0.351598 - 0.127971i) q^{51} +(-0.943306 + 5.34975i) q^{52} +(-0.464786 - 2.63593i) q^{53} +(-0.484292 + 0.176268i) q^{54} -3.83758 q^{56} +(-0.136801 + 0.349019i) q^{57} -1.06332 q^{58} +(8.09344 + 6.79121i) q^{59} +(1.77122 + 10.0451i) q^{61} +(0.294045 - 1.66761i) q^{62} +(10.7918 + 3.92788i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.239727 + 0.201155i) q^{66} +(4.86807 - 4.08479i) q^{67} +(-2.17533 + 3.76778i) q^{68} +(0.156455 + 0.270988i) q^{69} +(-0.369952 + 2.09810i) q^{71} +(0.519660 + 2.94714i) q^{72} +(6.51525 - 2.37136i) q^{73} +(-3.59971 - 3.02052i) q^{74} +(3.72042 + 2.27123i) q^{76} +13.9641 q^{77} +(0.357884 + 0.300300i) q^{78} +(7.31775 - 2.66344i) q^{79} +(1.55128 - 8.79777i) q^{81} +(-10.5664 - 3.84584i) q^{82} +(1.60303 + 2.77653i) q^{83} +(-0.165019 + 0.285821i) q^{84} +(-8.67318 + 7.27766i) q^{86} +(-0.0457236 + 0.0791956i) q^{87} +(1.81940 + 3.15129i) q^{88} +(-3.01370 - 1.09690i) q^{89} +(-3.62001 - 20.5301i) q^{91} +(3.41900 - 1.24441i) q^{92} +(-0.111559 - 0.0936089i) q^{93} +5.54757 q^{94} -0.0860015 q^{96} +(-13.7657 - 11.5508i) q^{97} +(7.26101 - 2.64279i) q^{98} +(-1.89093 - 10.7240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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