LMFDB - Embedded newform 841.2.e.k.267.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.2
Character	$\chi$	$=$	841.267
Dual form			841.2.e.k.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.323845 - 0.258258i) q^{2} +(-0.403828 - 0.0921712i) q^{3} +(-0.406863 - 1.78258i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.106974 + 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(-0.688047 + 1.42874i) q^{8} +(-2.54832 - 1.22721i) q^{9} +O(q^{10})$	\(q+(-0.323845 - 0.258258i) q^{2} +(-0.403828 - 0.0921712i) q^{3} +(-0.406863 - 1.78258i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.106974 + 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(-0.688047 + 1.42874i) q^{8} +(-2.54832 - 1.22721i) q^{9} +(-0.403828 + 0.0921712i) q^{10} +(1.04749 + 2.17513i) q^{11} +0.757359i q^{12} +(1.64736 - 0.793325i) q^{13} +(0.915973 - 0.730464i) q^{14} +(-0.323845 + 0.258258i) q^{15} +(-2.70291 + 1.30165i) q^{16} +4.82843i q^{17} +(0.508326 + 1.05555i) q^{18} +(-5.84957 + 1.33513i) q^{19} +(-1.64736 - 0.793325i) q^{20} +(0.508326 - 1.05555i) q^{21} +(0.222521 - 0.974928i) q^{22} +(-4.77397 - 5.98637i) q^{23} +(0.409542 - 0.513549i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-0.738371 - 0.168528i) q^{26} +(1.88751 + 1.50524i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(3.18289 + 2.53827i) q^{31} +(4.30354 + 0.982255i) q^{32} +(-0.222521 - 0.974928i) q^{33} +(1.24698 - 1.56366i) q^{34} +(1.76350 + 2.21135i) q^{35} +(-1.15078 + 5.04191i) q^{36} +(-1.73553 + 3.60388i) q^{37} +(2.23916 + 1.07832i) q^{38} +(-0.738371 + 0.168528i) q^{39} +(0.688047 + 1.42874i) q^{40} +12.4853i q^{41} +(-0.437223 + 0.210556i) q^{42} +(5.01483 - 3.99920i) q^{43} +(3.45117 - 2.75222i) q^{44} +(-2.54832 + 1.22721i) q^{45} +3.17157i q^{46} +(-2.27470 - 4.72346i) q^{47} +(1.21149 - 0.276514i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.718882 - 1.49277i) q^{50} +(0.445042 - 1.94986i) q^{51} +(-2.08442 - 2.61378i) q^{52} +(-4.66700 + 5.85223i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(2.35368 + 0.537213i) q^{55} +(-3.50673 - 2.79653i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.592127 + 0.472206i) q^{60} +(0.807657 + 0.184342i) q^{61} +(-0.375235 - 1.64401i) q^{62} +(4.98792 - 6.25465i) q^{63} +(2.60093 + 3.26147i) q^{64} +(0.406863 - 1.78258i) q^{65} +(-0.179721 + 0.373194i) q^{66} +(-5.09665 - 2.45442i) q^{67} +(8.60708 - 1.96451i) q^{68} +(1.37609 + 2.85749i) q^{69} -1.17157i q^{70} +(-2.85749 + 1.37609i) q^{71} +(3.50673 - 2.79653i) q^{72} +(-3.12733 + 2.49396i) q^{73} +(1.49277 - 0.718882i) q^{74} -1.65685i q^{75} +(4.75995 + 9.88414i) q^{76} +(-6.65722 + 1.51947i) q^{77} +(0.282642 + 0.136113i) q^{78} +(-0.179721 + 0.373194i) q^{79} +(-0.667563 + 2.92478i) q^{80} +(4.66700 + 5.85223i) q^{81} +(3.22442 - 4.04330i) q^{82} +(0.813727 + 3.56517i) q^{83} +(-2.08843 - 0.476670i) q^{84} +(3.77502 + 3.01048i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-3.50673 - 2.79653i) q^{89} +(1.14220 + 0.260699i) q^{90} +(1.15078 + 5.04191i) q^{91} +(-8.72886 + 10.9456i) q^{92} +(-1.05139 - 1.31840i) q^{93} +(-0.483220 + 2.11713i) q^{94} +(-2.60330 + 5.40581i) q^{95} +(-1.64736 - 0.793325i) q^{96} +(-12.1722 + 2.77824i) q^{97} +(0.179721 + 0.373194i) q^{98} -6.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	−0.323845	−	0.258258i	−0.228993	−	0.182616i	0.502271	−	0.864710i	$-0.332498\pi$
$2$	−0.323845	−	0.258258i	−0.228993	−	0.182616i	−0.731264	+	0.682094i	$0.761069\pi$
$3$	−0.403828	−	0.0921712i	−0.233150	−	0.0532151i	0.104349	−	0.994541i	$-0.466724\pi$
$3$	−0.403828	−	0.0921712i	−0.233150	−	0.0532151i	−0.337500	+	0.941326i	$0.609581\pi$
$4$	−0.406863	−	1.78258i	−0.203432	−	0.891292i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i	−0.622619	−	0.782526i	$-0.713931\pi$
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i	0.901452	+	0.432880i	$0.142503\pi$
$6$	0.106974	+	0.134141i	0.0436719	+	0.0547629i
$7$	−0.629384	+	2.75751i	−0.237885	+	1.04224i	0.705022	+	0.709185i	$0.250937\pi$
$7$	−0.629384	+	2.75751i	−0.237885	+	1.04224i	−0.942907	+	0.333056i	$0.891920\pi$
$8$	−0.688047	+	1.42874i	−0.243261	+	0.505137i
$9$	−2.54832	−	1.22721i	−0.849442	−	0.409070i
$10$	−0.403828	+	0.0921712i	−0.127702	+	0.0291471i
$11$	1.04749	+	2.17513i	0.315830	+	0.655827i	0.997092	−	0.0762129i	$-0.0242829\pi$
$11$	1.04749	+	2.17513i	0.315830	+	0.655827i	−0.681262	+	0.732040i	$0.738569\pi$
$12$			0.757359i			0.218631i
$13$	1.64736	−	0.793325i	0.456894	−	0.220029i	−0.191257	−	0.981540i	$-0.561257\pi$
$13$	1.64736	−	0.793325i	0.456894	−	0.220029i	0.648152	+	0.761511i	$0.275542\pi$
$14$	0.915973	−	0.730464i	0.244804	−	0.195225i
$15$	−0.323845	+	0.258258i	−0.0836165	+	0.0666819i
$16$	−2.70291	+	1.30165i	−0.675727	+	0.325413i
$17$			4.82843i			1.17107i	0.810649	+	0.585533i	$0.199115\pi$
$17$			4.82843i			1.17107i	−0.810649	+	0.585533i	$0.800885\pi$
$18$	0.508326	+	1.05555i	0.119814	+	0.248796i
$19$	−5.84957	+	1.33513i	−1.34198	+	0.306299i	−0.832425	−	0.554138i	$-0.813048\pi$
$19$	−5.84957	+	1.33513i	−1.34198	+	0.306299i	−0.509558	+	0.860436i	$0.670191\pi$
$20$	−1.64736	−	0.793325i	−0.368360	−	0.177393i
$21$	0.508326	−	1.05555i	0.110926	−	0.230340i
$22$	0.222521	−	0.974928i	0.0474416	−	0.207855i
$23$	−4.77397	−	5.98637i	−0.995442	−	1.24824i	−0.968605	−	0.248605i	$-0.920028\pi$
$23$	−4.77397	−	5.98637i	−0.995442	−	1.24824i	−0.0268366	−	0.999640i	$-0.508543\pi$
$24$	0.409542	−	0.513549i	0.0835974	−	0.104828i
$25$	0.890084	+	3.89971i	0.178017	+	0.779942i
$26$	−0.738371	−	0.168528i	−0.144806	−	0.0330511i
$27$	1.88751	+	1.50524i	0.363251	+	0.289683i
$28$	5.17157			0.977335
$29$		0			0
$29$		0			0
$30$	0.171573			0.0313248
$31$	3.18289	+	2.53827i	0.571664	+	0.455887i	0.866161	−	0.499766i	$-0.166581\pi$
$31$	3.18289	+	2.53827i	0.571664	+	0.455887i	−0.294497	+	0.955652i	$0.595152\pi$
$32$	4.30354	+	0.982255i	0.760766	+	0.173640i
$33$	−0.222521	−	0.974928i	−0.0387359	−	0.169713i
$34$	1.24698	−	1.56366i	0.213855	−	0.268166i
$35$	1.76350	+	2.21135i	0.298085	+	0.373787i
$36$	−1.15078	+	5.04191i	−0.191797	+	0.840318i
$37$	−1.73553	+	3.60388i	−0.285320	+	0.592473i	−0.993535	−	0.113523i	$-0.963786\pi$
$37$	−1.73553	+	3.60388i	−0.285320	+	0.592473i	0.708215	+	0.705997i	$0.249501\pi$
$38$	2.23916	+	1.07832i	0.363240	+	0.174927i
$39$	−0.738371	+	0.168528i	−0.118234	+	0.0269861i
$40$	0.688047	+	1.42874i	0.108790	+	0.225904i
$41$			12.4853i			1.94987i	0.222483	+	0.974937i	$0.428584\pi$
$41$			12.4853i			1.94987i	−0.222483	+	0.974937i	$0.571416\pi$
$42$	−0.437223	+	0.210556i	−0.0674650	+	0.0324894i
$43$	5.01483	−	3.99920i	0.764755	−	0.609872i	−0.161455	−	0.986880i	$-0.551619\pi$
$43$	5.01483	−	3.99920i	0.764755	−	0.609872i	0.926210	+	0.377008i	$0.123047\pi$
$44$	3.45117	−	2.75222i	0.520284	−	0.414912i
$45$	−2.54832	+	1.22721i	−0.379882	+	0.182941i
$46$			3.17157i			0.467623i
$47$	−2.27470	−	4.72346i	−0.331799	−	0.688987i	0.666608	−	0.745408i	$-0.267745\pi$
$47$	−2.27470	−	4.72346i	−0.331799	−	0.688987i	−0.998407	+	0.0564212i	$0.982031\pi$
$48$	1.21149	−	0.276514i	0.174863	−	0.0399113i
$49$	−0.900969	−	0.433884i	−0.128710	−	0.0619834i
$50$	0.718882	−	1.49277i	0.101665	−	0.211110i
$51$	0.445042	−	1.94986i	0.0623183	−	0.273034i
$52$	−2.08442	−	2.61378i	−0.289057	−	0.362466i
$53$	−4.66700	+	5.85223i	−0.641061	+	0.803865i	−0.991135	−	0.132857i	$-0.957585\pi$
$53$	−4.66700	+	5.85223i	−0.641061	+	0.803865i	0.350074	+	0.936722i	$0.386156\pi$
$54$	−0.222521	−	0.974928i	−0.0302813	−	0.132671i
$55$	2.35368	+	0.537213i	0.317371	+	0.0724378i
$56$	−3.50673	−	2.79653i	−0.468607	−	0.373702i
$57$	2.48528			0.329184
$58$		0			0
$59$	7.65685			0.996838			0.498419	−	0.866936i	$-0.333914\pi$
$59$	7.65685			0.996838			0.498419	+	0.866936i	$0.333914\pi$
$60$	0.592127	+	0.472206i	0.0764433	+	0.0609615i
$61$	0.807657	+	0.184342i	0.103410	+	0.0236026i	0.273913	−	0.961755i	$-0.411682\pi$
$61$	0.807657	+	0.184342i	0.103410	+	0.0236026i	−0.170503	+	0.985357i	$0.554539\pi$
$62$	−0.375235	−	1.64401i	−0.0476549	−	0.208790i
$63$	4.98792	−	6.25465i	0.628419	−	0.788012i
$64$	2.60093	+	3.26147i	0.325117	+	0.407683i
$65$	0.406863	−	1.78258i	0.0504652	−	0.221102i
$66$	−0.179721	+	0.373194i	−0.0221221	+	0.0459369i
$67$	−5.09665	−	2.45442i	−0.622655	−	0.299855i	0.0958296	−	0.995398i	$-0.469450\pi$
$67$	−5.09665	−	2.45442i	−0.622655	−	0.299855i	−0.718484	+	0.695543i	$0.755164\pi$
$68$	8.60708	−	1.96451i	1.04376	−	0.238232i
$69$	1.37609	+	2.85749i	0.165662	+	0.344001i
$70$		−	1.17157i		−	0.140030i
$71$	−2.85749	+	1.37609i	−0.339121	+	0.163312i	−0.595691	−	0.803213i	$-0.703122\pi$
$71$	−2.85749	+	1.37609i	−0.339121	+	0.163312i	0.256570	+	0.966526i	$0.417408\pi$
$72$	3.50673	−	2.79653i	0.413273	−	0.329574i
$73$	−3.12733	+	2.49396i	−0.366026	+	0.291896i	−0.789180	−	0.614162i	$-0.789494\pi$
$73$	−3.12733	+	2.49396i	−0.366026	+	0.291896i	0.423154	+	0.906058i	$0.360923\pi$
$74$	1.49277	−	0.718882i	0.173531	−	0.0835683i
$75$		−	1.65685i		−	0.191317i
$76$	4.75995	+	9.88414i	0.546004	+	1.13379i
$77$	−6.65722	+	1.51947i	−0.758661	+	0.173159i
$78$	0.282642	+	0.136113i	0.0320029	+	0.0154118i
$79$	−0.179721	+	0.373194i	−0.0202201	+	0.0419876i	−0.910834	−	0.412772i	$-0.864561\pi$
$79$	−0.179721	+	0.373194i	−0.0202201	+	0.0419876i	0.890614	+	0.454760i	$0.150275\pi$
$80$	−0.667563	+	2.92478i	−0.0746358	+	0.327001i
$81$	4.66700	+	5.85223i	0.518555	+	0.650248i
$82$	3.22442	−	4.04330i	0.356078	−	0.446508i
$83$	0.813727	+	3.56517i	0.0893181	+	0.391328i	0.999751	−	0.0223293i	$-0.00710824\pi$
$83$	0.813727	+	3.56517i	0.0893181	+	0.391328i	−0.910433	+	0.413658i	$0.864251\pi$
$84$	−2.08843	−	0.476670i	−0.227866	−	0.0520090i
$85$	3.77502	+	3.01048i	0.409458	+	0.326532i
$86$	−2.65685			−0.286496
$87$		0			0
$88$	−3.82843			−0.408112
$89$	−3.50673	−	2.79653i	−0.371713	−	0.296431i	0.419760	−	0.907635i	$-0.362114\pi$
$89$	−3.50673	−	2.79653i	−0.371713	−	0.296431i	−0.791473	+	0.611204i	$0.790686\pi$
$90$	1.14220	+	0.260699i	0.120398	+	0.0274801i
$91$	1.15078	+	5.04191i	0.120635	+	0.528536i
$92$	−8.72886	+	10.9456i	−0.910046	+	1.14116i
$93$	−1.05139	−	1.31840i	−0.109024	−	0.136711i
$94$	−0.483220	+	2.11713i	−0.0498404	+	0.218365i
$95$	−2.60330	+	5.40581i	−0.267093	+	0.554625i
$96$	−1.64736	−	0.793325i	−0.168133	−	0.0809684i
$97$	−12.1722	+	2.77824i	−1.23590	+	0.282087i	−0.790064	−	0.613025i	$-0.789953\pi$
$97$	−12.1722	+	2.77824i	−1.23590	+	0.282087i	−0.445841	+	0.895112i	$0.647095\pi$
$98$	0.179721	+	0.373194i	0.0181545	+	0.0376982i
$99$		−	6.82843i		−	0.686283i
$100$	6.58942	−	3.17330i	0.658942	−	0.317330i
$101$	−10.6774	+	8.51491i	−1.06244	+	0.847265i	−0.988684	−	0.150011i	$-0.952069\pi$
$101$	−10.6774	+	8.51491i	−1.06244	+	0.847265i	−0.0737526	+	0.997277i	$0.523498\pi$
$102$	−0.647690	+	0.516516i	−0.0641309	+	0.0511427i
$103$	−0.746387	+	0.359441i	−0.0735437	+	0.0354168i	−0.470294	−	0.882510i	$-0.655852\pi$
$103$	−0.746387	+	0.359441i	−0.0735437	+	0.0354168i	0.396750	+	0.917927i	$0.370138\pi$
$104$			2.89949i			0.284319i
$105$	−0.508326	−	1.05555i	−0.0496076	−	0.103011i
$106$	3.02277	−	0.689927i	0.293597	−	0.0670117i
$107$	8.26330	+	3.97940i	0.798844	+	0.384703i	0.788338	−	0.615242i	$-0.210942\pi$
$107$	8.26330	+	3.97940i	0.798844	+	0.384703i	0.0105053	+	0.999945i	$0.496656\pi$
$108$	1.91526	−	3.97707i	0.184296	−	0.382694i
$109$	0.298878	−	1.30947i	0.0286273	−	0.125425i	−0.958595	−	0.284772i	$-0.908082\pi$
$109$	0.298878	−	1.30947i	0.0286273	−	0.125425i	0.987223	+	0.159348i	$0.0509391\pi$
$110$	−0.623490	−	0.781831i	−0.0594474	−	0.0745447i
$111$	1.03303	−	1.29538i	0.0980510	−	0.122952i
$112$	−1.88815	−	8.27254i	−0.178414	−	0.781681i
$113$	−9.08019	−	2.07250i	−0.854193	−	0.194964i	−0.227064	−	0.973880i	$-0.572913\pi$
$113$	−9.08019	−	2.07250i	−0.854193	−	0.194964i	−0.627128	+	0.778916i	$0.715770\pi$
$114$	−0.804846	−	0.641844i	−0.0753808	−	0.0601142i
$115$	−7.65685			−0.714005
$116$		0			0
$117$	−5.17157			−0.478112
$118$	−2.47964	−	1.97744i	−0.228269	−	0.182038i
$119$	−13.3144	−	3.03894i	−1.22053	−	0.278579i
$120$	−0.146164	−	0.640386i	−0.0133429	−	0.0584589i
$121$	3.22442	−	4.04330i	0.293129	−	0.367573i
$122$	−0.213948	−	0.268282i	−0.0193699	−	0.0242891i
$123$	1.15078	−	5.04191i	0.103763	−	0.454614i
$124$	3.22968	−	6.70650i	0.290034	−	0.602261i
$125$	8.10872	+	3.90495i	0.725266	+	0.349270i
$126$	−3.23063	+	0.737370i	−0.287807	+	0.0656901i
$127$	−6.79325	−	14.1063i	−0.602804	−	1.25174i	−0.949503	−	0.313759i	$-0.898412\pi$
$127$	−6.79325	−	14.1063i	−0.602804	−	1.25174i	0.346699	−	0.937976i	$-0.387303\pi$
$128$		−	10.5563i		−	0.933058i
$129$	−2.39374	+	1.15277i	−0.210757	+	0.101495i
$130$	−0.592127	+	0.472206i	−0.0519330	+	0.0414152i
$131$	1.02710	−	0.819084i	0.0897380	−	0.0715637i	−0.577593	−	0.816325i	$-0.696008\pi$
$131$	1.02710	−	0.819084i	0.0897380	−	0.0715637i	0.667331	+	0.744761i	$0.267437\pi$
$132$	−1.64736	+	0.793325i	−0.143384	+	0.0690501i
$133$		−	16.9706i		−	1.47153i
$134$	1.01665	+	2.11110i	0.0878254	+	0.182371i
$135$	2.35368	−	0.537213i	0.202573	−	0.0462359i
$136$	−6.89859	−	3.32218i	−0.591549	−	0.284875i
$137$	−5.20660	+	10.8116i	−0.444830	+	0.923700i	0.551174	+	0.834391i	$0.314180\pi$
$137$	−5.20660	+	10.8116i	−0.444830	+	0.923700i	−0.996004	+	0.0893090i	$0.971534\pi$
$138$	0.292328	−	1.28077i	0.0248846	−	0.109026i
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	0.999297	−	0.0375004i	$-0.0119395\pi$
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	−0.258925	+	0.965898i	$0.583368\pi$
$140$	3.22442	−	4.04330i	0.272513	−	0.341721i
$141$	0.483220	+	2.11713i	0.0406945	+	0.178294i
$142$	1.28077	+	0.292328i	0.107480	+	0.0245316i
$143$	3.45117	+	2.75222i	0.288601	+	0.230152i
$144$	8.48528			0.707107
$145$		0			0
$146$	1.65685			0.137122
$147$	0.323845	+	0.258258i	0.0267103	+	0.0213008i
$148$	7.13034	+	1.62745i	0.586110	+	0.133776i
$149$	−0.483220	−	2.11713i	−0.0395870	−	0.173442i	0.951270	−	0.308360i	$-0.0997801\pi$
$149$	−0.483220	−	2.11713i	−0.0395870	−	0.173442i	−0.990857	+	0.134918i	$0.956923\pi$
$150$	−0.427896	+	0.536564i	−0.0349375	+	0.0438103i
$151$	−8.81748	−	11.0568i	−0.717556	−	0.899787i	0.280641	−	0.959813i	$-0.409453\pi$
$151$	−8.81748	−	11.0568i	−0.717556	−	0.899787i	−0.998197	+	0.0600260i	$0.980882\pi$
$152$	2.11722	−	9.27616i	0.171730	−	0.752396i
$153$	5.92549	−	12.3044i	0.479047	−	0.994752i
$154$	2.54832	+	1.22721i	0.205350	+	0.0988913i
$155$	3.96900	−	0.905898i	0.318798	−	0.0727635i
$156$	0.600832	+	1.24764i	0.0481051	+	0.0998912i
$157$		−	8.48528i		−	0.677199i	−0.940931	−	0.338600i	$-0.890047\pi$
$157$		−	8.48528i		−	0.677199i	0.940931	−	0.338600i	$-0.109953\pi$
$158$	0.154582	−	0.0744427i	0.0122979	−	0.00592234i
$159$	2.42407	−	1.93313i	0.192241	−	0.153307i
$160$	3.45117	−	2.75222i	0.272839	−	0.217582i
$161$	19.5122	−	9.39656i	1.53777	−	0.740552i
$162$		−	3.10051i		−	0.243599i
$163$	−7.84074	−	16.2815i	−0.614134	−	1.27526i	−0.943598	−	0.331095i	$-0.892582\pi$
$163$	−7.84074	−	16.2815i	−0.614134	−	1.27526i	0.329463	−	0.944168i	$-0.393132\pi$
$164$	22.2561	−	5.07980i	1.73791	−	0.396666i
$165$	−0.900969	−	0.433884i	−0.0701403	−	0.0337778i
$166$	0.657212	−	1.36471i	0.0510095	−	0.105922i
$167$	−1.96451	+	8.60708i	−0.152018	+	0.666036i	0.840279	+	0.542155i	$0.182391\pi$
$167$	−1.96451	+	8.60708i	−0.152018	+	0.666036i	−0.992297	+	0.123881i	$0.960466\pi$
$168$	1.15836	+	1.45254i	0.0893694	+	0.112066i
$169$	−6.02095	+	7.55003i	−0.463150	+	0.580772i
$170$	−0.445042	−	1.94986i	−0.0341332	−	0.149547i
$171$	16.5451	+	3.77631i	1.26523	+	0.288781i
$172$	−9.16926	−	7.31224i	−0.699149	−	0.557553i
$173$	−23.6569			−1.79860			−0.899299	−	0.437335i	$-0.855922\pi$
$173$	−23.6569			−1.79860			−0.899299	+	0.437335i	$0.855922\pi$
$174$		0			0
$175$	−11.3137			−0.855236
$176$	−5.66252	−	4.51571i	−0.426829	−	0.340385i
$177$	−3.09205	−	0.705741i	−0.232413	−	0.0530468i
$178$	0.413414	+	1.81128i	0.0309867	+	0.135761i
$179$	−6.53747	+	8.19772i	−0.488633	+	0.612727i	−0.963623	−	0.267265i	$-0.913880\pi$
$179$	−6.53747	+	8.19772i	−0.488633	+	0.612727i	0.474990	+	0.879991i	$0.342452\pi$
$180$	3.22442	+	4.04330i	0.240334	+	0.301370i
$181$	3.18510	−	13.9548i	0.236747	−	1.03725i	−0.707163	−	0.707051i	$-0.750025\pi$
$181$	3.18510	−	13.9548i	0.236747	−	1.03725i	0.943910	−	0.330204i	$-0.107118\pi$
$182$	0.929438	−	1.93000i	0.0688945	−	0.143061i
$183$	−0.309164	−	0.148885i	−0.0228540	−	0.0110059i
$184$	11.8377	−	2.70188i	0.872687	−	0.199185i
$185$	1.73553	+	3.60388i	0.127599	+	0.264962i
$186$			0.698485i			0.0512154i
$187$	−10.5025	+	5.05772i	−0.768016	+	0.369857i
$188$	−7.49447	+	5.97664i	−0.546590	+	0.435891i
$189$	−5.33868	+	4.25745i	−0.388332	+	0.309684i
$190$	2.23916	−	1.07832i	0.162446	−	0.0782298i
$191$		−	2.68629i		−	0.194373i	−0.995266	−	0.0971866i	$-0.969016\pi$
$191$		−	2.68629i		−	0.194373i	0.995266	−	0.0971866i	$-0.0309844\pi$
$192$	−0.749717	−	1.55680i	−0.0541062	−	0.112353i
$193$	10.5569	−	2.40955i	0.759905	−	0.173443i	0.175026	−	0.984564i	$-0.443999\pi$
$193$	10.5569	−	2.40955i	0.759905	−	0.173443i	0.584879	+	0.811121i	$0.301142\pi$
$194$	4.65943	+	2.24386i	0.334527	+	0.161100i
$195$	−0.328606	+	0.682357i	−0.0235320	+	0.0488646i
$196$	−0.406863	+	1.78258i	−0.0290617	+	0.127327i
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	0.824266	−	0.566202i	$-0.191588\pi$
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	−0.735423	+	0.677609i	$0.763016\pi$
$198$	−1.76350	+	2.21135i	−0.125326	+	0.157154i
$199$	−3.66832	−	16.0720i	−0.260040	−	1.13931i	−0.921207	−	0.389072i	$-0.872796\pi$
$199$	−3.66832	−	16.0720i	−0.260040	−	1.13931i	0.661167	−	0.750239i	$-0.270062\pi$
$200$	−6.18411	−	1.41148i	−0.437283	−	0.0998069i
$201$	1.83195	+	1.46093i	0.129215	+	0.103046i
$202$	5.65685			0.398015
$203$		0			0
$204$	−3.65685			−0.256031
$205$	9.76139	+	7.78445i	0.681765	+	0.543689i
$206$	0.334542	+	0.0763571i	0.0233087	+	0.00532005i
$207$	4.81910	+	21.1139i	0.334951	+	1.46752i
$208$	−3.42002	+	4.28857i	−0.237136	+	0.297359i
$209$	−9.03143	−	11.3250i	−0.624717	−	0.783370i
$210$	−0.107985	+	0.473114i	−0.00745169	+	0.0326480i
$211$	7.54297	−	15.6631i	0.519280	−	1.07830i	−0.462208	−	0.886771i	$-0.652943\pi$
$211$	7.54297	−	15.6631i	0.519280	−	1.07830i	0.981488	−	0.191524i	$-0.0613429\pi$
$212$	12.3309	+	5.93826i	0.846891	+	0.407841i
$213$	1.28077	−	0.292328i	0.0877570	−	0.0200300i
$214$	−1.64832	−	3.42277i	−0.112677	−	0.233976i
$215$		−	6.41421i		−	0.437446i
$216$	−3.44929	+	1.66109i	−0.234695	+	0.113023i
$217$	−9.00257	+	7.17931i	−0.611134	+	0.487363i
$218$	−0.434971	+	0.346878i	−0.0294600	+	0.0234935i
$219$	1.49277	−	0.718882i	0.100872	−	0.0485776i
$220$		−	4.41421i		−	0.297606i
$221$	3.83051	+	7.95414i	0.257668	+	0.535053i
$222$	−0.669085	+	0.152714i	−0.0449060	+	0.0102495i
$223$	7.95414	+	3.83051i	0.532648	+	0.256510i	0.680819	−	0.732452i	$-0.261624\pi$
$223$	7.95414	+	3.83051i	0.532648	+	0.256510i	−0.148170	+	0.988962i	$0.547338\pi$
$224$	−5.41716	+	11.2488i	−0.361949	+	0.751595i
$225$	2.51754	−	11.0301i	0.167836	−	0.735337i
$226$	2.40534	+	3.01620i	0.160001	+	0.200635i
$227$	12.5584	−	15.7478i	0.833531	−	1.04522i	−0.164734	−	0.986338i	$-0.552677\pi$
$227$	12.5584	−	15.7478i	0.833531	−	1.04522i	0.998265	−	0.0588772i	$-0.0187520\pi$
$228$	−1.01117	−	4.43022i	−0.0669664	−	0.293399i
$229$	19.9717	+	4.55840i	1.31977	+	0.301228i	0.823684	−	0.567049i	$-0.191915\pi$
$229$	19.9717	+	4.55840i	1.31977	+	0.301228i	0.496081	+	0.868276i	$0.334772\pi$
$230$	2.47964	+	1.97744i	0.163502	+	0.130389i
$231$	2.82843			0.186097
$232$		0			0
$233$	−4.31371			−0.282600			−0.141300	−	0.989967i	$-0.545128\pi$
$233$	−4.31371			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$234$	1.67479	+	1.33560i	0.109484	+	0.0873109i
$235$	−5.11120	−	1.16660i	−0.333418	−	0.0761004i
$236$	−3.11529	−	13.6490i	−0.202788	−	0.888474i
$237$	0.106974	−	0.134141i	0.00694870	−	0.00871340i
$238$	3.52699	+	4.42271i	0.228621	+	0.286681i
$239$	1.85652	−	8.13397i	0.120089	−	0.526143i	−0.878720	−	0.477338i	$-0.841602\pi$
$239$	1.85652	−	8.13397i	0.120089	−	0.526143i	0.998808	−	0.0488045i	$-0.0155411\pi$
$240$	0.539162	−	1.11958i	0.0348027	−	0.0722686i
$241$	3.88652	+	1.87165i	0.250353	+	0.120563i	0.554852	−	0.831949i	$-0.312775\pi$
$241$	3.88652	+	1.87165i	0.250353	+	0.120563i	−0.304499	+	0.952513i	$0.598489\pi$
$242$	−2.08843	+	0.476670i	−0.134249	+	0.0306415i
$243$	−4.48772	−	9.31885i	−0.287888	−	0.597805i
$244$		−	1.51472i		−	0.0969699i
$245$	−0.900969	+	0.433884i	−0.0575608	+	0.0277198i
$246$	−1.67479	+	1.33560i	−0.106781	+	0.0851547i
$247$	−8.57713	+	6.84003i	−0.545750	+	0.435221i
$248$	−5.81651	+	2.80109i	−0.369349	+	0.177869i
$249$		−	1.51472i		−	0.0959914i
$250$	−1.61748	−	3.35874i	−0.102299	−	0.212425i
$251$	−5.78028	+	1.31931i	−0.364848	+	0.0832742i	−0.401015	−	0.916072i	$-0.631342\pi$
$251$	−5.78028	+	1.31931i	−0.364848	+	0.0832742i	0.0361667	+	0.999346i	$0.488485\pi$
$252$	−13.1788	−	6.34660i	−0.830189	−	0.399798i
$253$	8.02046	−	16.6547i	0.504242	−	1.04707i
$254$	−1.44311	+	6.32268i	−0.0905488	+	0.396720i
$255$	−1.24698	−	1.56366i	−0.0780889	−	0.0979204i
$256$	2.47561	−	3.10431i	0.154725	−	0.194019i
$257$	5.30232	+	23.2310i	0.330750	+	1.44911i	0.817682	+	0.575670i	$0.195259\pi$
$257$	5.30232	+	23.2310i	0.330750	+	1.44911i	−0.486932	+	0.873440i	$0.661884\pi$
$258$	1.07291	+	0.244885i	0.0667967	+	0.0152459i
$259$	−8.84541	−	7.05398i	−0.549627	−	0.438313i
$260$	−3.34315			−0.207333
$261$		0			0
$262$	−0.544156			−0.0336181
$263$	−8.78985	−	7.00967i	−0.542005	−	0.432235i	0.313833	−	0.949478i	$-0.398387\pi$
$263$	−8.78985	−	7.00967i	−0.542005	−	0.432235i	−0.855838	+	0.517243i	$0.826958\pi$
$264$	1.54603	+	0.352871i	0.0951514	+	0.0217177i
$265$	1.66563	+	7.29761i	0.102319	+	0.448289i
$266$	−4.38278	+	5.49584i	−0.268726	+	0.336971i
$267$	1.15836	+	1.45254i	0.0708904	+	0.0888938i
$268$	−2.30157	+	10.0838i	−0.140591	+	0.615967i
$269$	−8.44157	+	17.5291i	−0.514692	+	1.06877i	0.468036	+	0.883710i	$0.344962\pi$
$269$	−8.44157	+	17.5291i	−0.514692	+	1.06877i	−0.982727	+	0.185059i	$0.940752\pi$
$270$	−0.900969	−	0.433884i	−0.0548312	−	0.0264053i
$271$	−14.1914	+	3.23909i	−0.862066	+	0.196761i	−0.630625	−	0.776088i	$-0.717201\pi$
$271$	−14.1914	+	3.23909i	−0.862066	+	0.196761i	−0.231441	+	0.972849i	$0.574344\pi$
$272$	−6.28493	−	13.0508i	−0.381080	−	0.791320i
$273$		−	2.14214i		−	0.129648i
$274$	4.47832	−	2.15665i	0.270545	−	0.130288i
$275$	−7.55003	+	6.02095i	−0.455284	+	0.363077i
$276$	4.53383	−	3.61561i	0.272905	−	0.217634i
$277$	−4.78749	+	2.30553i	−0.287652	+	0.138526i	−0.572146	−	0.820152i	$-0.693889\pi$
$277$	−4.78749	+	2.30553i	−0.287652	+	0.138526i	0.284494	+	0.958678i	$0.408175\pi$
$278$		−	5.79899i		−	0.347800i
$279$	−4.99605	−	10.3744i	−0.299106	−	0.621099i
$280$	−4.37283	+	0.998069i	−0.261326	+	0.0596460i
$281$	1.77542	+	0.854995i	0.105912	+	0.0510047i	0.486090	−	0.873909i	$-0.338423\pi$
$281$	1.77542	+	0.854995i	0.105912	+	0.0510047i	−0.380177	+	0.924914i	$0.624137\pi$
$282$	0.390276	−	0.810417i	0.0232406	−	0.0482596i
$283$	0.0763571	−	0.334542i	0.00453896	−	0.0198865i	−0.972608	−	0.232453i	$-0.925325\pi$
$283$	0.0763571	−	0.334542i	0.00453896	−	0.0198865i	0.977147	+	0.212566i	$0.0681821\pi$
$284$	3.61561	+	4.53383i	0.214547	+	0.269033i
$285$	1.54955	−	1.94307i	0.0917873	−	0.115098i
$286$	−0.406863	−	1.78258i	−0.0240583	−	0.105406i
$287$	−34.4283	−	7.85804i	−2.03224	−	0.463845i
$288$	−9.76139	−	7.78445i	−0.575195	−	0.458703i
$289$	−6.31371			−0.371395
$290$		0			0
$291$	5.17157			0.303163
$292$	5.71809	+	4.56002i	0.334626	+	0.266855i
$293$	−3.56517	−	0.813727i	−0.208279	−	0.0475384i	0.117108	−	0.993119i	$-0.462638\pi$
$293$	−3.56517	−	0.813727i	−0.208279	−	0.0475384i	−0.325388	+	0.945581i	$0.605495\pi$
$294$	−0.0381786	−	0.167271i	−0.00222662	−	0.00975545i
$295$	4.77397	−	5.98637i	0.277951	−	0.348540i
$296$	−3.95489	−	4.95927i	−0.229873	−	0.288252i
$297$	−1.29695	+	5.68230i	−0.0752565	+	0.329720i
$298$	−0.390276	+	0.810417i	−0.0226081	+	0.0469462i
$299$	−12.6136	−	6.07437i	−0.729461	−	0.351290i
$300$	−2.95348	+	0.674113i	−0.170519	+	0.0389199i
$301$	7.87158	+	16.3455i	0.453710	+	0.942139i
$302$			5.85786i			0.337082i
$303$	5.09665	−	2.45442i	0.292795	−	0.141003i
$304$	14.0730	−	11.2228i	0.807140	−	0.643673i
$305$	0.647690	−	0.516516i	0.0370866	−	0.0295756i
$306$	−5.09665	+	2.45442i	−0.291356	+	0.140310i
$307$			16.8995i			0.964505i	0.876032	+	0.482253i	$0.160181\pi$
$307$			16.8995i			0.964505i	−0.876032	+	0.482253i	$0.839819\pi$
$308$	5.41716	+	11.2488i	0.308671	+	0.640963i
$309$	0.334542	−	0.0763571i	0.0190315	−	0.00434380i
$310$	−1.51930	−	0.731654i	−0.0862902	−	0.0415552i
$311$	−10.9832	+	22.8069i	−0.622801	+	1.29326i	0.315988	+	0.948763i	$0.397664\pi$
$311$	−10.9832	+	22.8069i	−0.622801	+	1.29326i	−0.938788	+	0.344495i	$0.888050\pi$
$312$	0.267250	−	1.17090i	0.0151300	−	0.0662891i
$313$	2.60093	+	3.26147i	0.147013	+	0.184349i	0.849886	−	0.526967i	$-0.176671\pi$
$313$	2.60093	+	3.26147i	0.147013	+	0.184349i	−0.702872	+	0.711316i	$0.748099\pi$
$314$	−2.19139	+	2.74792i	−0.123667	+	0.155074i
$315$	−1.78017	−	7.79942i	−0.100301	−	0.439448i
$316$	0.738371	+	0.168528i	0.0415366	+	0.00948046i
$317$	15.2112	+	12.1305i	0.854346	+	0.681318i	0.949371	−	0.314157i	$-0.101722\pi$
$317$	15.2112	+	12.1305i	0.854346	+	0.681318i	−0.0950254	+	0.995475i	$0.530293\pi$
$318$	−1.28427			−0.0720184
$319$		0			0
$320$	4.17157			0.233198
$321$	−2.97017	−	2.36863i	−0.165779	−	0.132204i
$322$	−8.74565	−	1.99614i	−0.487376	−	0.111240i
$323$	−6.44656	−	28.2442i	−0.358696	−	1.57155i
$324$	8.53326	−	10.7004i	0.474070	−	0.594465i
$325$	4.56002	+	5.71809i	0.252945	+	0.317182i
$326$	−1.66563	+	7.29761i	−0.0922508	+	0.404177i
$327$	−0.241391	+	0.501253i	−0.0133489	+	0.0277194i
$328$	−17.8383	−	8.59046i	−0.984954	−	0.474329i
$329$	14.4566	−	3.29964i	0.797021	−	0.181915i
$330$	0.179721	+	0.373194i	0.00989329	+	0.0205436i
$331$			0.414214i			0.0227672i	0.999935	+	0.0113836i	$0.00362360\pi$
$331$			0.414214i			0.0227672i	−0.999935	+	0.0113836i	$0.996376\pi$
$332$	6.02414	−	2.90107i	0.330618	−	0.159217i
$333$	8.84541	−	7.05398i	0.484726	−	0.386556i
$334$	2.85904	−	2.28001i	0.156440	−	0.124757i
$335$	−5.09665	+	2.45442i	−0.278460	+	0.134099i
$336$			3.51472i			0.191744i
$337$	7.72269	+	16.0363i	0.420682	+	0.873555i	0.998358	+	0.0572886i	$0.0182455\pi$
$337$	7.72269	+	16.0363i	0.420682	+	0.873555i	−0.577676	+	0.816266i	$0.696040\pi$
$338$	3.89971	−	0.890084i	0.212116	−	0.0484142i
$339$	3.47582	+	1.67386i	0.188780	+	0.0909118i
$340$	3.83051	−	7.95414i	0.207739	−	0.431374i
$341$	−2.18703	+	9.58201i	−0.118434	+	0.518895i
$342$	−4.38278	−	5.49584i	−0.236994	−	0.297181i
$343$	−10.5810	+	13.2681i	−0.571319	+	0.716411i
$344$	2.26339	+	9.91655i	0.122034	+	0.534665i
$345$	3.09205	+	0.705741i	0.166471	+	0.0379958i
$346$	7.66116	+	6.10957i	0.411866	+	0.328453i
$347$	14.4853			0.777611			0.388805	−	0.921320i	$-0.372888\pi$
$347$	14.4853			0.777611			0.388805	+	0.921320i	$0.372888\pi$
$348$		0			0
$349$	23.1421			1.23877			0.619385	−	0.785087i	$-0.287382\pi$
$349$	23.1421			1.23877			0.619385	+	0.785087i	$0.287382\pi$
$350$	3.66389	+	2.92185i	0.195843	+	0.156180i
$351$	4.30354	+	0.982255i	0.229706	+	0.0524289i
$352$	2.37137	+	10.3897i	0.126395	+	0.553771i
$353$	4.34607	−	5.44981i	0.231318	−	0.290064i	−0.652603	−	0.757700i	$-0.726323\pi$
$353$	4.34607	−	5.44981i	0.231318	−	0.290064i	0.883921	+	0.467636i	$0.154894\pi$
$354$	0.819084	+	1.02710i	0.0435338	+	0.0545897i
$355$	−0.705741	+	3.09205i	−0.0374569	+	0.164109i
$356$	−3.55828	+	7.38885i	−0.188589	+	0.391609i
$357$	5.09665	+	2.45442i	0.269743	+	0.129902i
$358$	4.23425	−	0.966441i	0.223787	−	0.0510780i
$359$	7.84074	+	16.2815i	0.413819	+	0.859303i	0.998834	+	0.0482808i	$0.0153742\pi$
$359$	7.84074	+	16.2815i	0.413819	+	0.859303i	−0.585015	+	0.811022i	$0.698911\pi$
$360$		−	4.48528i		−	0.236395i
$361$	15.3165	−	7.37602i	0.806130	−	0.388212i
$362$	−4.63543	+	3.69663i	−0.243633	+	0.194290i
$363$	−1.67479	+	1.33560i	−0.0879036	+	0.0701008i
$364$	8.51942	−	4.10274i	0.446539	−	0.215042i
$365$			4.00000i			0.209370i
$366$	0.0616703	+	0.128060i	0.00322356	+	0.00669379i
$367$	−17.5487	+	4.00538i	−0.916035	+	0.209079i	−0.654453	−	0.756102i	$-0.727101\pi$
$367$	−17.5487	+	4.00538i	−0.916035	+	0.209079i	−0.261582	+	0.965181i	$0.584244\pi$
$368$	20.6958	+	9.96655i	1.07884	+	0.519543i
$369$	15.3220	−	31.8166i	0.797634	−	1.65630i
$370$	0.368685	−	1.61531i	0.0191670	−	0.0839761i
$371$	−13.2003	−	16.5526i	−0.685323	−	0.859368i
$372$	−1.92238	+	2.41059i	−0.0996709	+	0.124983i
$373$	0.820277	+	3.59387i	0.0424723	+	0.186083i	0.991714	−	0.128464i	$-0.0410045\pi$
$373$	0.820277	+	3.59387i	0.0424723	+	0.186083i	−0.949242	+	0.314547i	$0.898147\pi$
$374$	4.70737	+	1.07443i	0.243412	+	0.0555573i
$375$	−2.91461	−	2.32432i	−0.150510	−	0.120027i
$376$	8.31371			0.428747
$377$		0			0
$378$	2.82843			0.145479
$379$	−21.0864	−	16.8159i	−1.08314	−	0.863773i	−0.0918872	−	0.995769i	$-0.529290\pi$
$379$	−21.0864	−	16.8159i	−1.08314	−	0.863773i	−0.991250	+	0.131996i	$0.957861\pi$
$380$	10.6955	+	2.44118i	0.548668	+	0.125230i
$381$	1.44311	+	6.32268i	0.0739328	+	0.323921i
$382$	−0.693756	+	0.869943i	−0.0354956	+	0.0445101i
$383$	12.7724	+	16.0160i	0.652637	+	0.818381i	0.992519	−	0.122087i	$-0.0389586\pi$
$383$	12.7724	+	16.0160i	0.652637	+	0.818381i	−0.339882	+	0.940468i	$0.610387\pi$
$384$	−0.972991	+	4.26295i	−0.0496528	+	0.217543i
$385$	−2.96274	+	6.15220i	−0.150995	+	0.313545i
$386$	−4.04110	−	1.94609i	−0.205687	−	0.0990534i
$387$	−17.6873	+	4.03700i	−0.899095	+	0.205212i
$388$	9.90488	+	20.5677i	0.502844	+	1.04417i
$389$			36.9706i			1.87448i	0.348682	+	0.937241i	$0.386629\pi$
$389$			36.9706i			1.87448i	−0.348682	+	0.937241i	$0.613371\pi$
$390$	0.282642	−	0.136113i	0.0143121	−	0.00689235i
$391$	28.9047	−	23.0508i	1.46178	−	1.16573i
$392$	1.23982	−	0.988722i	0.0626203	−	0.0499380i
$393$	−0.490268	+	0.236100i	−0.0247307	+	0.0119097i
$394$		−	0.828427i		−	0.0417356i
$395$	0.179721	+	0.373194i	0.00904272	+	0.0187774i
$396$	−12.1722	+	2.77824i	−0.611679	+	0.139612i
$397$	−27.6209	−	13.3015i	−1.38625	−	0.667584i	−0.415929	−	0.909397i	$-0.636544\pi$
$397$	−27.6209	−	13.3015i	−1.38625	−	0.667584i	−0.970323	+	0.241813i	$0.922258\pi$
$398$	−2.96274	+	6.15220i	−0.148509	+	0.308382i
$399$	−1.56420	+	6.85319i	−0.0783078	+	0.343089i
$400$	−7.48188	−	9.38198i	−0.374094	−	0.469099i
$401$	−4.57838	+	5.74110i	−0.228633	+	0.286697i	−0.882894	−	0.469572i	$-0.844408\pi$
$401$	−4.57838	+	5.74110i	−0.228633	+	0.286697i	0.654261	+	0.756269i	$0.272980\pi$
$402$	−0.215971	−	0.946229i	−0.0107716	−	0.0471936i
$403$	7.25702	+	1.65637i	0.361498	+	0.0825096i
$404$	19.5228	+	15.5689i	0.971294	+	0.774581i
$405$	7.48528			0.371947
$406$		0			0
$407$	−9.65685			−0.478672
$408$	2.47964	+	1.97744i	0.122760	+	0.0978980i
$409$	14.5952	+	3.33126i	0.721687	+	0.164720i	0.567562	−	0.823331i	$-0.307887\pi$
$409$	14.5952	+	3.33126i	0.721687	+	0.164720i	0.154125	+	0.988051i	$0.450744\pi$
$410$	−1.15078	−	5.04191i	−0.0568331	−	0.249002i
$411$	3.09910	−	3.88614i	0.152867	−	0.191689i
$412$	0.944412	+	1.18425i	0.0465278	+	0.0583440i
$413$	−4.81910	+	21.1139i	−0.237133	+	1.03895i
$414$	3.89218	−	8.08220i	0.191290	−	0.397218i
$415$	3.29471	+	1.58665i	0.161731	+	0.0778856i
$416$	7.86871	−	1.79598i	0.385795	−	0.0880552i
$417$	−2.51609	−	5.22471i	−0.123213	−	0.255855i
$418$			6.00000i			0.293470i
$419$	−23.8624	+	11.4915i	−1.16576	+	0.561398i	−0.913730	−	0.406322i	$-0.866811\pi$
$419$	−23.8624	+	11.4915i	−1.16576	+	0.561398i	−0.252025	+	0.967721i	$0.581097\pi$
$420$	−1.67479	+	1.33560i	−0.0817213	+	0.0651706i
$421$	19.6339	−	15.6575i	0.956898	−	0.763100i	−0.0146627	−	0.999892i	$-0.504667\pi$
$421$	19.6339	−	15.6575i	0.956898	−	0.763100i	0.971560	+	0.236792i	$0.0760960\pi$
$422$	−6.48789	+	3.12440i	−0.315825	+	0.152093i
$423$			14.8284i			0.720983i
$424$	−5.15023	−	10.6946i	−0.250117	−	0.519373i
$425$	−18.8295	+	4.29770i	−0.913364	+	0.208469i
$426$	−0.490268	−	0.236100i	−0.0237535	−	0.0114391i
$427$	−1.01665	+	2.11110i	−0.0491993	+	0.102163i
$428$	3.73158	−	16.3491i	0.180373	−	0.790264i
$429$	−1.14001	−	1.42952i	−0.0550400	−	0.0690180i
$430$	−1.65652	+	2.07721i	−0.0798846	+	0.100172i
$431$	−1.85652	−	8.13397i	−0.0894256	−	0.391799i	0.910331	−	0.413882i	$-0.135827\pi$
$431$	−1.85652	−	8.13397i	−0.0894256	−	0.391799i	−0.999756	+	0.0220827i	$0.992970\pi$
$432$	−7.06105	−	1.61164i	−0.339725	−	0.0775400i
$433$	−11.4362	−	9.12005i	−0.549588	−	0.438281i	0.308916	−	0.951089i	$-0.400034\pi$
$433$	−11.4362	−	9.12005i	−0.549588	−	0.438281i	−0.858503	+	0.512808i	$0.828605\pi$
$434$	4.76955			0.228946
$435$		0			0
$436$	−2.45584			−0.117614
$437$	35.9182	+	28.6438i	1.71820	+	1.37022i
$438$	−0.669085	−	0.152714i	−0.0319701	−	0.00729697i
$439$	−2.59389	−	11.3646i	−0.123800	−	0.542402i	−0.998348	−	0.0574631i	$-0.981699\pi$
$439$	−2.59389	−	11.3646i	−0.123800	−	0.542402i	0.874548	−	0.484939i	$-0.161158\pi$
$440$	−2.38699	+	2.99318i	−0.113795	+	0.142694i
$441$	1.76350	+	2.21135i	0.0839760	+	0.105303i
$442$	0.813727	−	3.56517i	0.0387050	−	0.169578i
$443$	−15.4709	+	32.1257i	−0.735046	+	1.52634i	0.111348	+	0.993781i	$0.464483\pi$
$443$	−15.4709	+	32.1257i	−0.735046	+	1.52634i	−0.846394	+	0.532557i	$0.821231\pi$
$444$	−2.72943	−	1.31442i	−0.129533	−	0.0623798i
$445$	−4.37283	+	0.998069i	−0.207292	+	0.0473130i
$446$	−1.58665	−	3.29471i	−0.0751300	−	0.156009i
$447$			0.899495i			0.0425447i
$448$	−10.6305	+	5.11939i	−0.502245	+	0.241868i
$449$	−0.804846	+	0.641844i	−0.0379831	+	0.0302905i	−0.642297	−	0.766456i	$-0.722019\pi$
$449$	−0.804846	+	0.641844i	−0.0379831	+	0.0302905i	0.604314	+	0.796746i	$0.293447\pi$
$450$	−3.66389	+	2.92185i	−0.172717	+	0.137738i
$451$	−27.1571	+	13.0782i	−1.27878	+	0.615828i
$452$			17.0294i			0.800997i
$453$	2.54163	+	5.27775i	0.119416	+	0.247970i
$454$	−8.13397	+	1.85652i	−0.381746	+	0.0871310i
$455$	4.65943	+	2.24386i	0.218437	+	0.105194i
$456$	−1.70999	+	3.55083i	−0.0800776	+	0.166283i
$457$	7.78168	−	34.0938i	0.364012	−	1.59484i	−0.378892	−	0.925441i	$-0.623695\pi$
$457$	7.78168	−	34.0938i	0.364012	−	1.59484i	0.742903	−	0.669399i	$-0.233448\pi$
$458$	−5.29049	−	6.63406i	−0.247208	−	0.309989i
$459$	−7.26793	+	9.11370i	−0.339238	+	0.425391i
$460$	3.11529	+	13.6490i	0.145251	+	0.636387i
$461$	−13.6490	−	3.11529i	−0.635697	−	0.145094i	−0.107486	−	0.994207i	$-0.534280\pi$
$461$	−13.6490	−	3.11529i	−0.635697	−	0.145094i	−0.528211	+	0.849113i	$0.677137\pi$
$462$	−0.915973	−	0.730464i	−0.0426149	−	0.0339842i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		0			0
$465$	−1.68629			−0.0781999
$466$	1.39697	+	1.11405i	0.0647136	+	0.0516073i
$467$	31.5441	+	7.19974i	1.45969	+	0.333164i	0.877377	−	0.479802i	$-0.159291\pi$
$467$	31.5441	+	7.19974i	1.45969	+	0.333164i	0.582311	+	0.812966i	$0.302149\pi$
$468$	2.10412	+	9.21877i	0.0972631	+	0.426138i
$469$	9.97584	−	12.5093i	0.460641	−	0.577626i
$470$	1.35395	+	1.69780i	0.0624532	+	0.0783139i
$471$	−0.782098	+	3.42660i	−0.0360372	+	0.157889i
$472$	−5.26828	+	10.9397i	−0.242492	+	0.503540i
$473$	13.9518	+	6.71881i	0.641502	+	0.308931i
$474$	−0.0692860	+	0.0158141i	−0.00318241	+	0.000726365i
$475$	−10.4132	−	21.6233i	−0.477791	−	0.992143i
$476$			24.9706i			1.14452i
$477$	19.0749	−	9.18600i	0.873381	−	0.420598i
$478$	−2.70189	+	2.15468i	−0.123581	+	0.0985529i
$479$	10.0852	−	8.04270i	0.460806	−	0.367481i	−0.365398	−	0.930851i	$-0.619067\pi$
$479$	10.0852	−	8.04270i	0.460806	−	0.367481i	0.826204	+	0.563371i	$0.190496\pi$
$480$	−1.64736	+	0.793325i	−0.0751912	+	0.0362102i
$481$			7.31371i			0.333476i
$482$	−0.775262	−	1.60985i	−0.0353122	−	0.0733266i
$483$	−8.74565	+	1.99614i	−0.397941	+	0.0908274i
$484$	−8.51942	−	4.10274i	−0.387246	−	0.186488i
$485$	−5.41716	+	11.2488i	−0.245981	+	0.510784i
$486$	−0.953340	+	4.17686i	−0.0432444	+	0.189466i
$487$	−17.7603	−	22.2707i	−0.804795	−	1.00918i	−0.999598	−	0.0283389i	$-0.990978\pi$
$487$	−17.7603	−	22.2707i	−0.804795	−	1.00918i	0.194803	−	0.980842i	$-0.437593\pi$
$488$	−0.819084	+	1.02710i	−0.0370782	+	0.0464946i
$489$	1.66563	+	7.29761i	0.0753225	+	0.330009i
$490$	0.403828	+	0.0921712i	0.0182431	+	0.00416387i
$491$	−9.97411	−	7.95408i	−0.450125	−	0.358963i	0.372035	−	0.928219i	$-0.378660\pi$
$491$	−9.97411	−	7.95408i	−0.450125	−	0.358963i	−0.822160	+	0.569256i	$0.807231\pi$
$492$	−9.45584			−0.426302
$493$		0			0
$494$	4.54416			0.204451
$495$	−5.33868	−	4.25745i	−0.239956	−	0.191358i
$496$	−11.9070	−	2.71769i	−0.534640	−	0.122028i
$497$	−1.99614	−	8.74565i	−0.0895390	−	0.392296i
$498$	−0.391188	+	0.490534i	−0.0175296	+	0.0219814i
$499$	9.33399	+	11.7045i	0.417847	+	0.523963i	0.945555	−	0.325462i	$-0.105520\pi$
$499$	9.33399	+	11.7045i	0.417847	+	0.523963i	−0.527708	+	0.849426i	$0.676948\pi$
$500$	3.66177	−	16.0433i	0.163759	−	0.717476i
$501$	1.58665	−	3.29471i	0.0708863	−	0.147197i
$502$	2.21264	+	1.06555i	0.0987549	+	0.0475579i
$503$	25.0829	−	5.72500i	1.11839	−	0.255265i	0.376916	−	0.926247i	$-0.376984\pi$
$503$	25.0829	−	5.72500i	1.11839	−	0.255265i	0.741474	+	0.670982i	$0.234127\pi$
$504$	5.50438	+	11.4300i	0.245184	+	0.509131i
$505$			13.6569i			0.607722i
$506$	−6.89859	+	3.32218i	−0.306680	+	0.147689i
$507$	3.12733	−	2.49396i	0.138889	−	0.110761i
$508$	−22.3818	+	17.8489i	−0.993033	+	0.791917i
$509$	24.7634	−	11.9254i	1.09762	−	0.528585i	0.204709	−	0.978823i	$-0.434375\pi$
$509$	24.7634	−	11.9254i	1.09762	−	0.528585i	0.892909	+	0.450238i	$0.148661\pi$
$510$			0.828427i			0.0366834i
$511$	−4.90883	−	10.1933i	−0.217154	−	0.450925i
$512$	−22.1868	+	5.06399i	−0.980527	+	0.223799i
$513$	−13.0508	−	6.28493i	−0.576206	−	0.277486i
$514$	4.28246	−	8.89261i	0.188891	−	0.392236i
$515$	−0.184342	+	0.807657i	−0.00812310	+	0.0355896i
$516$	3.02883	+	3.79803i	0.133337	+	0.167199i
$517$	7.89142	−	9.89553i	0.347064	−	0.435205i
$518$	1.04280	+	4.56880i	0.0458179	+	0.200741i
$519$	9.55331	+	2.18048i	0.419344	+	0.0957125i
$520$	2.26692	+	1.80781i	0.0994109	+	0.0792775i
$521$	0.857864			0.0375837			0.0187919	−	0.999823i	$-0.494018\pi$
$521$	0.857864			0.0375837			0.0187919	+	0.999823i	$0.494018\pi$
$522$		0			0
$523$	27.3137			1.19435			0.597173	−	0.802113i	$-0.296291\pi$
$523$	27.3137			1.19435			0.597173	+	0.802113i	$0.296291\pi$
$524$	−1.87798	−	1.49764i	−0.0820397	−	0.0654245i
$525$	4.56880	+	1.04280i	0.199399	+	0.0455114i
$526$	1.03625	+	4.54010i	0.0451825	+	0.197958i
$527$	−12.2558	+	15.3683i	−0.533873	+	0.669456i
$528$	1.87047	+	2.34549i	0.0814017	+	0.102075i
$529$	−7.92785	+	34.7342i	−0.344689	+	1.51018i
$530$	1.34526	−	2.79346i	0.0584343	−	0.121340i
$531$	−19.5122	−	9.39656i	−0.846755	−	0.407776i
$532$	−30.2515	+	6.90470i	−1.31157	+	0.299357i
$533$	9.90488	+	20.5677i	0.429028	+	0.890886i
$534$		−	0.769553i		−	0.0333018i
$535$	8.26330	−	3.97940i	0.357254	−	0.172044i
$536$	7.01347	−	5.59305i	0.302936	−	0.241583i
$537$	3.39561	−	2.70791i	0.146531	−	0.116855i
$538$	7.26080	−	3.49661i	0.313035	−	0.150750i
$539$		−	2.41421i		−	0.103988i
$540$	−1.91526	−	3.97707i	−0.0824195	−	0.171146i
$541$	21.1139	−	4.81910i	0.907756	−	0.207189i	0.256942	−	0.966427i	$-0.417285\pi$
$541$	21.1139	−	4.81910i	0.907756	−	0.207189i	0.650814	+	0.759237i	$0.274428\pi$
$542$	5.43234	+	2.61607i	0.233339	+	0.112370i
$543$	−2.57247	+	5.34178i	−0.110395	+	0.229238i
$544$	−4.74275	+	20.7793i	−0.203344	+	0.890906i
$545$	−0.837438	−	1.05011i	−0.0358719	−	0.0449819i
$546$	−0.553224	+	0.693720i	−0.0236758	+	0.0296885i
$547$	0.845355	+	3.70374i	0.0361448	+	0.158361i	0.989780	−	0.142606i	$-0.0455480\pi$
$547$	0.845355	+	3.70374i	0.0361448	+	0.158361i	−0.953635	+	0.300966i	$0.902691\pi$
$548$	21.3910	+	4.88236i	0.913779	+	0.208564i
$549$	−1.83195	−	1.46093i	−0.0781855	−	0.0623509i
$550$	4.00000			0.170561
$551$		0			0
$552$	−5.02944			−0.214067
$553$	−0.915973	−	0.730464i	−0.0389511	−	0.0310625i
$554$	2.14583	+	0.489771i	0.0911674	+	0.0208084i
$555$	−0.368685	−	1.61531i	−0.0156498	−	0.0685662i
$556$	15.9601	−	20.0133i	0.676858	−	0.848753i
$557$	−3.31304	−	4.15442i	−0.140378	−	0.176029i	0.706673	−	0.707541i	$-0.250195\pi$
$557$	−3.31304	−	4.15442i	−0.140378	−	0.176029i	−0.847051	+	0.531512i	$0.821624\pi$
$558$	−1.06133	+	4.64997i	−0.0449295	+	0.196849i
$559$	5.08855	−	10.5665i	0.215223	−	0.446915i
$560$	−7.64497	−	3.68163i	−0.323059	−	0.155577i
$561$	4.70737	−	1.07443i	0.198745	−	0.0453623i
$562$	−0.354151	−	0.735401i	−0.0149389	−	0.0310210i
$563$		−	9.24264i		−	0.389531i	−0.980850	−	0.194765i	$-0.937605\pi$
$563$		−	9.24264i		−	0.389531i	0.980850	−	0.194765i	$-0.0623946\pi$
$564$	3.57735	−	1.72276i	0.150634	−	0.0725414i
$565$	−7.28175	+	5.80700i	−0.306346	+	0.244302i
$566$	−0.111126	+	0.0886201i	−0.00467098	+	0.00372498i
$567$	−19.0749	+	9.18600i	−0.801072	+	0.385776i
$568$		−	5.02944i		−	0.211030i
$569$	12.2976	+	25.5363i	0.515543	+	1.07054i	0.982501	+	0.186257i	$0.0596358\pi$
$569$	12.2976	+	25.5363i	0.515543	+	1.07054i	−0.466958	+	0.884280i	$0.654650\pi$
$570$	−1.00363	+	0.229071i	−0.0420373	+	0.00959474i
$571$	27.5943	+	13.2887i	1.15479	+	0.556116i	0.910468	−	0.413579i	$-0.135721\pi$
$571$	27.5943	+	13.2887i	1.15479	+	0.556116i	0.244319	+	0.969695i	$0.421436\pi$
$572$	3.50191	−	7.27178i	0.146422	−	0.304048i
$573$	−0.247599	+	1.08480i	−0.0103436	+	0.0453182i
$574$	9.12005	+	11.4362i	0.380663	+	0.477337i
$575$	19.0959	−	23.9455i	0.796353	−	0.998595i
$576$	−2.62552	−	11.5032i	−0.109397	−	0.479299i
$577$	−9.55331	−	2.18048i	−0.397709	−	0.0907746i	0.0189882	−	0.999820i	$-0.493955\pi$
$577$	−9.55331	−	2.18048i	−0.397709	−	0.0907746i	−0.416698	+	0.909045i	$0.636813\pi$
$578$	2.04466	+	1.63057i	0.0850468	+	0.0678226i
$579$	−4.48528			−0.186402
$580$		0			0
$581$	−10.3431			−0.429106
$582$	−1.67479	−	1.33560i	−0.0694222	−	0.0553624i
$583$	−17.6180	−	4.02119i	−0.729663	−	0.166541i
$584$	−1.41148	−	6.18411i	−0.0584076	−	0.255900i
$585$	−3.22442	+	4.04330i	−0.133313	+	0.167170i
$586$	0.944412	+	1.18425i	0.0390133	+	0.0489211i
$587$	0.813727	−	3.56517i	0.0335861	−	0.147150i	−0.955355	−	0.295462i	$-0.904527\pi$
$587$	0.813727	−	3.56517i	0.0335861	−	0.147150i	0.988941	+	0.148311i	$0.0473837\pi$
$588$	0.328606	−	0.682357i	0.0135515	−	0.0281399i
$589$	−22.0074	−	10.5982i	−0.906800	−	0.436692i
$590$	−3.09205	+	0.705741i	−0.127298	+	0.0290549i
$591$	−0.359441	−	0.746387i	−0.0147854	−	0.0307023i
$592$		−	12.0000i		−	0.493197i
$593$	−2.26568	+	1.09110i	−0.0930405	+	0.0448059i	−0.479825	−	0.877364i	$-0.659300\pi$
$593$	−2.26568	+	1.09110i	−0.0930405	+	0.0448059i	0.386785	+	0.922170i	$0.373586\pi$
$594$	1.88751	−	1.50524i	0.0774454	−	0.0617606i
$595$	−10.6774	+	8.51491i	−0.437729	+	0.349077i
$596$	−3.57735	+	1.72276i	−0.146534	+	0.0705671i
$597$			6.82843i			0.279469i
$598$	2.51609	+	5.22471i	0.102890	+	0.213654i
$599$	42.7701	−	9.76201i	1.74754	−	0.398865i	0.775067	−	0.631879i	$-0.217716\pi$
$599$	42.7701	−	9.76201i	1.74754	−	0.398865i	0.972473	+	0.233014i	$0.0748588\pi$
$600$	2.36722	+	1.13999i	0.0966414	+	0.0465400i
$601$	9.90488	−	20.5677i	0.404029	−	0.838974i	−0.595341	−	0.803473i	$-0.702983\pi$
$601$	9.90488	−	20.5677i	0.404029	−	0.838974i	0.999370	−	0.0355009i	$-0.0113027\pi$
$602$	1.67218	−	7.32631i	0.0681531	−	0.298598i
$603$	9.97584	+	12.5093i	0.406247	+	0.509418i
$604$	−16.1221	+	20.2165i	−0.656000	+	0.822597i
$605$	−1.15078	−	5.04191i	−0.0467860	−	0.204983i
$606$	−2.28440	−	0.521399i	−0.0927973	−	0.0211804i
$607$	13.8602	+	11.0532i	0.562570	+	0.448635i	0.863025	−	0.505161i	$-0.168567\pi$
$607$	13.8602	+	11.0532i	0.562570	+	0.448635i	−0.300455	+	0.953796i	$0.597138\pi$
$608$	−26.4853			−1.07412
$609$		0			0
$610$	−0.343146			−0.0138936
$611$	−7.49447	−	5.97664i	−0.303194	−	0.241789i
$612$	−24.3445	−	5.55647i	−0.984068	−	0.224607i
$613$	−2.00269	−	8.77435i	−0.0808878	−	0.354393i	0.918246	−	0.396011i	$-0.129606\pi$
$613$	−2.00269	−	8.77435i	−0.0808878	−	0.354393i	−0.999134	+	0.0416183i	$0.986749\pi$
$614$	4.36443	−	5.47282i	0.176134	−	0.220865i
$615$	−3.22442	−	4.04330i	−0.130021	−	0.163042i
$616$	2.40955	−	10.5569i	0.0970836	−	0.425351i
$617$	10.1154	−	21.0049i	0.407232	−	0.845626i	−0.591980	−	0.805952i	$-0.701654\pi$
$617$	10.1154	−	21.0049i	0.407232	−	0.845626i	0.999213	−	0.0396741i	$-0.0126320\pi$
$618$	−0.128060	−	0.0616703i	−0.00515132	−	0.00248074i
$619$	35.5012	−	8.10292i	1.42692	−	0.325684i	0.561806	−	0.827269i	$-0.310107\pi$
$619$	35.5012	−	8.10292i	1.42692	−	0.325684i	0.865109	+	0.501585i	$0.167249\pi$
$620$	−3.22968	−	6.70650i	−0.129707	−	0.269339i
$621$		−	18.4853i		−	0.741789i
$622$	9.44691	−	4.54939i	0.378787	−	0.182414i
$623$	9.91854	−	7.90977i	0.397378	−	0.316898i
$624$	1.77638	−	1.41662i	0.0711122	−	0.0567101i
$625$	−9.91066	+	4.77272i	−0.396426	+	0.190909i
$626$		−	1.72792i		−	0.0690617i
$627$	2.60330	+	5.40581i	0.103966	+	0.215887i
$628$	−15.1257	+	3.45235i	−0.603582	+	0.137764i
$629$	−17.4011	−	8.37990i	−0.693825	−	0.334129i
$630$	−1.43776	+	2.98555i	−0.0572819	+	0.118947i
$631$	−6.93633	+	30.3900i	−0.276131	+	1.20981i	0.626510	+	0.779413i	$0.284483\pi$
$631$	−6.93633	+	30.3900i	−0.276131	+	1.20981i	−0.902641	+	0.430395i	$0.858374\pi$
$632$	−0.409542	−	0.513549i	−0.0162907	−	0.0204279i
$633$	−4.48976	+	5.62998i	−0.178452	+	0.223771i
$634$	−1.79327	−	7.85682i	−0.0712198	−	0.312034i
$635$	−15.2643	−	3.48398i	−0.605745	−	0.138257i
$636$	−4.43224	−	3.53459i	−0.175750	−	0.140156i
$637$	−1.82843			−0.0724449
$638$		0			0
$639$	8.97056			0.354870
$640$	−8.25329	−	6.58178i	−0.326240	−	0.260168i
$641$	−21.2524	−	4.85073i	−0.839421	−	0.191592i	−0.218866	−	0.975755i	$-0.570236\pi$
$641$	−21.2524	−	4.85073i	−0.839421	−	0.191592i	−0.620555	+	0.784163i	$0.713093\pi$
$642$	0.350157	+	1.53414i	0.0138196	+	0.0605477i
$643$	−9.67327	+	12.1299i	−0.381476	+	0.478356i	−0.935086	−	0.354420i	$-0.884678\pi$
$643$	−9.67327	+	12.1299i	−0.381476	+	0.478356i	0.553610	+	0.832776i	$0.313250\pi$
$644$	−24.6889	−	30.9589i	−0.972880	−	1.21995i
$645$	−0.591206	+	2.59024i	−0.0232787	+	0.101991i
$646$	−5.20660	+	10.8116i	−0.204851	+	0.425378i
$647$	25.5363	+	12.2976i	1.00394	+	0.483470i	0.862272	−	0.506445i	$-0.169041\pi$
$647$	25.5363	+	12.2976i	1.00394	+	0.483470i	0.141663	+	0.989915i	$0.454755\pi$
$648$	−11.5725	+	2.64134i	−0.454609	+	0.103761i
$649$	8.02046	+	16.6547i	0.314831	+	0.653753i
$650$		−	3.02944i		−	0.118824i
$651$	4.29722	−	2.06943i	0.168421	−	0.0811074i
$652$	−25.8330	+	20.6011i	−1.01170	+	0.806802i
$653$	1.45254	−	1.15836i	0.0568422	−	0.0453301i	−0.594657	−	0.803980i	$-0.702712\pi$
$653$	1.45254	−	1.15836i	0.0568422	−	0.0453301i	0.651499	+	0.758650i	$0.274141\pi$
$654$	0.207626	−	0.0999874i	0.00811882	−	0.00390982i
$655$		−	1.31371i		−	0.0513308i
$656$	−16.2515	−	33.7465i	−0.634514	−	1.31758i
$657$	11.0301	−	2.51754i	0.430323	−	0.0982185i
$658$	−5.53387	−	2.66497i	−0.215733	−	0.103891i
$659$	−5.02688	+	10.4384i	−0.195820	+	0.406624i	−0.975639	−	0.219380i	$-0.929596\pi$
$659$	−5.02688	+	10.4384i	−0.195820	+	0.406624i	0.779820	+	0.626004i	$0.215311\pi$
$660$	−0.406863	+	1.78258i	−0.0158371	+	0.0693870i
$661$	6.66279	+	8.35488i	0.259153	+	0.324967i	0.894337	−	0.447393i	$-0.147647\pi$
$661$	6.66279	+	8.35488i	0.259153	+	0.324967i	−0.635185	+	0.772360i	$0.719076\pi$
$662$	0.106974	−	0.134141i	0.00415766	−	0.00521354i
$663$	−0.813727	−	3.56517i	−0.0316025	−	0.138460i
$664$	−5.65360	−	1.29040i	−0.219402	−	0.0500771i
$665$	−13.2681	−	10.5810i	−0.514516	−	0.410313i
$666$	−4.68629			−0.181590
$667$		0			0
$668$	16.1421			0.624558
$669$	−2.85904	−	2.28001i	−0.110537	−	0.0881503i
$670$	2.28440	+	0.521399i	0.0882540	+	0.0201434i
$671$	0.445042	+	1.94986i	0.0171807	+	0.0752733i
$672$	3.22442	−	4.04330i	0.124385	−	0.155974i
$673$	−14.7315	−	18.4727i	−0.567856	−	0.712069i	0.412132	−	0.911124i	$-0.364784\pi$
$673$	−14.7315	−	18.4727i	−0.567856	−	0.712069i	−0.979988	+	0.199055i	$0.936213\pi$
$674$	1.64055	−	7.18774i	0.0631918	−	0.276861i
$675$	−4.18995	+	8.70053i	−0.161271	+	0.334883i
$676$	15.9083	+	7.66102i	0.611857	+	0.294655i
$677$	−21.4484	+	4.89546i	−0.824330	+	0.188148i	−0.613822	−	0.789444i	$-0.710369\pi$
$677$	−21.4484	+	4.89546i	−0.824330	+	0.188148i	−0.210507	+	0.977592i	$0.567512\pi$
$678$	−0.693337	−	1.43973i	−0.0266275	−	0.0552925i
$679$		−	35.3137i		−	1.35522i
$680$	−6.89859	+	3.32218i	−0.264549	+	0.127400i
$681$	−6.52293	+	5.20187i	−0.249959	+	0.199336i
$682$	3.18289	−	2.53827i	0.121879	−	0.0971954i
$683$	11.6861	−	5.62772i	0.447155	−	0.215339i	−0.196735	−	0.980457i	$-0.563034\pi$
$683$	11.6861	−	5.62772i	0.447155	−	0.215339i	0.643890	+	0.765118i	$0.277319\pi$
$684$		−	31.0294i		−	1.18644i
$685$	5.20660	+	10.8116i	0.198934	+	0.413091i
$686$	6.85319	−	1.56420i	0.261656	−	0.0597213i
$687$	−7.64497	−	3.68163i	−0.291674	−	0.140463i
$688$	−8.34907	+	17.3370i	−0.318305	+	0.660968i
$689$	−3.04549	+	13.3431i	−0.116024	+	0.508333i
$690$	−0.819084	−	1.02710i	−0.0311820	−	0.0391010i
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.250298	−	0.968169i	$-0.419471\pi$
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.888198	−	0.459460i	$-0.151957\pi$
$692$	9.62511	+	42.1703i	0.365892	+	1.60308i
$693$	18.8295	+	4.29770i	0.715273	+	0.163256i
$694$	−4.69099	−	3.74094i	−0.178068	−	0.142004i
$695$	14.0000			0.531050
$696$		0			0
$697$	−60.2843			−2.28343
$698$	−7.49447	−	5.97664i	−0.283670	−	0.226219i
$699$	1.74200	+	0.397600i	0.0658884	+	0.0150386i
$700$	4.60313	+	20.1676i	0.173982	+	0.762265i
$701$	−13.7870	+	17.2884i	−0.520729	+	0.652974i	−0.970764	−	0.240037i	$-0.922840\pi$
$701$	−13.7870	+	17.2884i	−0.520729	+	0.652974i	0.450034	+	0.893011i	$0.351412\pi$
$702$	−1.14001	−	1.42952i	−0.0430267	−	0.0539538i
$703$	5.34050	−	23.3983i	0.201421	−	0.882482i
$704$	−4.36967	+	9.07372i	−0.164688	+	0.341979i
$705$	1.95652	+	0.942210i	0.0736868	+	0.0354857i
$706$	−2.81491	+	0.642485i	−0.105941	+	0.0241802i
$707$	−16.7598	−	34.8021i	−0.630317	−	1.30887i
$708$			5.79899i			0.217939i
$709$	0.772909	−	0.372213i	0.0290272	−	0.0139788i	−0.419314	−	0.907841i	$-0.637729\pi$
$709$	0.772909	−	0.372213i	0.0290272	−	0.0139788i	0.448341	+	0.893863i	$0.352015\pi$
$710$	1.02710	−	0.819084i	0.0385463	−	0.0307397i
$711$	0.915973	−	0.730464i	0.0343517	−	0.0273945i
$712$	6.40832	−	3.08608i	0.240162	−	0.115656i
$713$		−	31.1716i		−	1.16738i
$714$	−1.01665	−	2.11110i	−0.0380473	−	0.0790060i
$715$	4.30354	−	0.982255i	0.160943	−	0.0367343i
$716$	17.2730	+	8.31823i	0.645522	+	0.310867i
$717$	−1.49943	+	3.11361i	−0.0559974	+	0.116280i
$718$	1.66563	−	7.29761i	0.0621608	−	0.272344i
$719$	5.07654	+	6.36578i	0.189323	+	0.237403i	0.867429	−	0.497560i	$-0.165771\pi$
$719$	5.07654	+	6.36578i	0.189323	+	0.237403i	−0.678107	+	0.734964i	$0.737199\pi$
$720$	5.29049	−	6.63406i	0.197165	−	0.247237i
$721$	−0.521399	−	2.28440i	−0.0194179	−	0.0850754i
$722$	−6.86508	−	1.56691i	−0.255492	−	0.0583144i
$723$	−1.39697	−	1.11405i	−0.0519540	−	0.0414319i
$724$	−26.1716			−0.972659
$725$		0			0
$726$	0.887302			0.0329309
$727$	16.6637	+	13.2889i	0.618023	+	0.492857i	0.881735	−	0.471744i	$-0.156375\pi$
$727$	16.6637	+	13.2889i	0.618023	+	0.492857i	−0.263712	+	0.964601i	$0.584947\pi$
$728$	−7.99539	−	1.82490i	−0.296329	−	0.0676352i
$729$	−4.04356	−	17.7160i	−0.149761	−	0.656147i
$730$	1.03303	−	1.29538i	0.0382342	−	0.0479442i
$731$	19.3098	+	24.2138i	0.714200	+	0.895578i
$732$	−0.139613	+	0.611686i	−0.00516026	+	0.0226086i
$733$	21.3709	−	44.3771i	0.789351	−	1.63910i	0.0204043	−	0.999792i	$-0.493505\pi$
$733$	21.3709	−	44.3771i	0.789351	−	1.63910i	0.768947	−	0.639313i	$-0.220781\pi$
$734$	6.71748	+	3.23497i	0.247947	+	0.119405i
$735$	0.403828	−	0.0921712i	0.0148954	−	0.00339979i
$736$	−14.6648	−	30.4518i	−0.540553	−	1.12247i
$737$		−	13.6569i		−	0.503057i
$738$	−13.1788	+	6.34660i	−0.485120	+	0.233622i
$739$	−7.87388	+	6.27921i	−0.289645	+	0.230984i	−0.757522	−	0.652809i	$-0.773590\pi$
$739$	−7.87388	+	6.27921i	−0.289645	+	0.230984i	0.467877	+	0.883793i	$0.345019\pi$
$740$	5.71809	−	4.56002i	0.210201	−	0.167630i
$741$	4.09414	−	1.97164i	0.150402	−	0.0724298i
$742$			8.76955i			0.321940i
$743$	−5.35549	−	11.1208i	−0.196474	−	0.407982i	0.779335	−	0.626607i	$-0.215557\pi$
$743$	−5.35549	−	11.1208i	−0.196474	−	0.407982i	−0.975809	+	0.218625i	$0.929843\pi$
$744$	2.60705	−	0.595043i	0.0955792	−	0.0218153i
$745$	−1.95652	−	0.942210i	−0.0716813	−	0.0345199i
$746$	0.662502	−	1.37570i	0.0242559	−	0.0503680i
$747$	2.30157	−	10.0838i	0.0842099	−	0.368948i
$748$	13.2889	+	16.6637i	0.485890	+	0.609286i
$749$	−16.1740	+	20.2816i	−0.590986	+	0.741073i
$750$	0.343607	+	1.50544i	0.0125468	+	0.0549709i
$751$	−2.61894	−	0.597756i	−0.0955665	−	0.0218124i	0.174470	−	0.984662i	$-0.444179\pi$
$751$	−2.61894	−	0.597756i	−0.0955665	−	0.0218124i	−0.270037	+	0.962850i	$0.587036\pi$
$752$	12.2966	+	9.80620i	0.448410	+	0.357595i
$753$	2.45584			0.0894959
$754$		0			0
$755$	−14.1421			−0.514685
$756$	9.76139	+	7.78445i	0.355018	+	0.283118i
$757$	41.4201	+	9.45386i	1.50544	+	0.343607i	0.894138	−	0.447792i	$-0.147789\pi$
$757$	41.4201	+	9.45386i	1.50544	+	0.343607i	0.611301	+	0.791398i	$0.290647\pi$
$758$	2.48591	+	10.8915i	0.0902923	+	0.395596i
$759$	−4.77397	+	5.98637i	−0.173284	+	0.217291i
$760$	−5.93233	−	7.43891i	−0.215188	−	0.269838i
$761$	7.47625	−	32.7556i	0.271014	−	1.18739i	−0.637805	−	0.770198i	$-0.720157\pi$
$761$	7.47625	−	32.7556i	0.271014	−	1.18739i	0.908819	−	0.417192i	$-0.136986\pi$
$762$	1.16554	−	2.42027i	0.0422230	−	0.0876770i
$763$	3.42277	+	1.64832i	0.123913	+	0.0596732i
$764$	−4.78854	+	1.09295i	−0.173243	+	0.0395417i
$765$	−5.92549	−	12.3044i	−0.214236	−	0.444867i
$766$		−	8.48528i		−	0.306586i
$767$	12.6136	−	6.07437i	0.455449	−	0.219333i
$768$	−1.28585	+	1.02543i	−0.0463990	+	0.0370020i
$769$	−10.2519	+	8.17563i	−0.369694	+	0.294821i	−0.790660	−	0.612255i	$-0.790262\pi$
$769$	−10.2519	+	8.17563i	−0.369694	+	0.294821i	0.420966	+	0.907076i	$0.361691\pi$
$770$	2.54832	−	1.22721i	0.0918353	−	0.0442255i
$771$		−	9.87006i		−	0.355461i
$772$	−8.59046	−	17.8383i	−0.309177	−	0.642014i
$773$	35.5705	−	8.11874i	1.27938	−	0.292011i	0.471769	−	0.881722i	$-0.343616\pi$
$773$	35.5705	−	8.11874i	1.27938	−	0.292011i	0.807614	+	0.589712i	$0.200759\pi$
$774$	6.77053	+	3.26051i	0.243362	+	0.117197i
$775$	−7.06548	+	14.6716i	−0.253800	+	0.527020i
$776$	4.40569	−	19.3026i	0.158155	−	0.692923i
$777$	2.92185	+	3.66389i	0.104821	+	0.131441i
$778$	9.54794	−	11.9727i	0.342310	−	0.429244i
$779$	−16.6694	−	73.0335i	−0.597244	−	2.61670i
$780$	1.35006	+	0.308142i	0.0483398	+	0.0110332i
$781$	−5.98637	−	4.77397i	−0.214209	−	0.170826i
$782$	−15.3137			−0.547617
$783$		0			0
$784$	3.00000			0.107143
$785$	−6.63406	−	5.29049i	−0.236780	−	0.188826i
$786$	0.219746	+	0.0501555i	0.00783807	+	0.00178899i
$787$	9.36441	+	41.0281i	0.333805	+	1.46250i	0.811698	+	0.584077i	$0.198544\pi$
$787$	9.36441	+	41.0281i	0.333805	+	1.46250i	−0.477893	+	0.878418i	$0.658599\pi$
$788$	2.28001	−	2.85904i	0.0812220	−	0.101849i
$789$	2.90350	+	3.64088i	0.103367	+	0.129619i
$790$	0.0381786	−	0.167271i	0.00135833	−	0.00595124i
$791$	11.4299	−	23.7344i	0.406399	−	0.843896i
$792$	9.75608	+	4.69828i	0.346667	+	0.166946i
$793$	1.47674	−	0.337057i	0.0524406	−	0.0119692i
$794$	5.50967	+	11.4409i	0.195531	+	0.406024i
$795$		−	3.10051i		−	0.109964i
$796$	−27.1571	+	13.0782i	−0.962559	+	0.463544i
$797$	−43.5794	+	34.7534i	−1.54366	+	1.23103i	−0.672423	+	0.740167i	$0.734746\pi$
$797$	−43.5794	+	34.7534i	−1.54366	+	1.23103i	−0.871238	+	0.490861i	$0.836682\pi$
$798$	2.27645	−	1.81541i	0.0805854	−	0.0642647i
$799$	22.8069	−	10.9832i	0.806849	−	0.388558i
$800$			17.6569i			0.624264i
$801$	5.50438	+	11.4300i	0.194488	+	0.403858i
$802$	2.96537	−	0.676826i	0.104711	−	0.0238996i
$803$	−8.70053	−	4.18995i	−0.307035	−	0.147860i
$804$	1.85888	−	3.86000i	0.0655575	−	0.136132i
$805$	4.81910	−	21.1139i	0.169851	−	0.744166i
$806$	−1.92238	−	2.41059i	−0.0677130	−	0.0849094i
$807$	5.02463	−	6.30068i	0.176875	−	0.221795i
$808$	−4.81910	−	21.1139i	−0.169535	−	0.742783i
$809$	19.7757	+	4.51367i	0.695277	+	0.158692i	0.555532	−	0.831495i	$-0.312515\pi$
$809$	19.7757	+	4.51367i	0.695277	+	0.158692i	0.139745	+	0.990188i	$0.455372\pi$
$810$	−2.42407	−	1.93313i	−0.0851732	−	0.0679234i
$811$	−5.17157			−0.181598			−0.0907992	−	0.995869i	$-0.528942\pi$
$811$	−5.17157			−0.181598			−0.0907992	+	0.995869i	$0.528942\pi$
$812$		0			0
$813$	6.02944			0.211462
$814$	3.12733	+	2.49396i	0.109613	+	0.0874132i
$815$	−17.6180	−	4.02119i	−0.617131	−	0.140856i
$816$	1.33513	+	5.84957i	0.0467387	+	0.204776i
$817$	−23.9952	+	30.0890i	−0.839485	+	1.05268i
$818$	−3.86627	−	4.84814i	−0.135181	−	0.169511i
$819$	3.25491	−	14.2607i	0.113736	−	0.498308i
$820$	9.90488	−	20.5677i	0.345894	−	0.718255i
$821$	13.9518	+	6.71881i	0.486920	+	0.234488i	0.661202	−	0.750207i	$-0.270046\pi$
$821$	13.9518	+	6.71881i	0.486920	+	0.234488i	−0.174283	+	0.984696i	$0.555761\pi$
$822$	−2.00725	+	0.458143i	−0.0700110	+	0.0159796i
$823$	0.991108	+	2.05806i	0.0345479	+	0.0717394i	0.917528	−	0.397670i	$-0.130181\pi$
$823$	0.991108	+	2.05806i	0.0345479	+	0.0717394i	−0.882981	+	0.469409i	$0.844467\pi$
$824$		−	1.31371i		−	0.0457652i
$825$	3.60388	−	1.73553i	0.125471	−	0.0604236i
$826$	7.01347	−	5.59305i	0.244030	−	0.194607i
$827$	−10.2424	+	8.16803i	−0.356163	+	0.284030i	−0.785182	−	0.619265i	$-0.787431\pi$
$827$	−10.2424	+	8.16803i	−0.356163	+	0.284030i	0.429019	+	0.903295i	$0.358859\pi$
$828$	35.6765	−	17.1809i	1.23985	−	0.597078i
$829$		−	9.79899i		−	0.340333i	−0.985415	−	0.170166i	$-0.945569\pi$
$829$		−	9.79899i		−	0.340333i	0.985415	−	0.170166i	$-0.0544306\pi$
$830$	−0.657212	−	1.36471i	−0.0228122	−	0.0473699i
$831$	2.14583	−	0.489771i	0.0744379	−	0.0169900i
$832$	6.87207	+	3.30941i	0.238246	+	0.114733i
$833$	2.09498	−	4.35026i	0.0725866	−	0.150728i
$834$	−0.534500	+	2.34180i	−0.0185082	+	0.0810898i
$835$	5.50443	+	6.90234i	0.190489	+	0.238865i
$836$	−16.5133	+	20.7070i	−0.571125	+	0.716167i
$837$	2.18703	+	9.58201i	0.0755948	+	0.331203i
$838$	10.6955	+	2.44118i	0.369470	+	0.0843292i
$839$	−17.2559	−	13.7611i	−0.595738	−	0.475085i	0.278597	−	0.960408i	$-0.410131\pi$
$839$	−17.2559	−	13.7611i	−0.595738	−	0.475085i	−0.874335	+	0.485323i	$0.838702\pi$
$840$	1.85786			0.0641024
$841$		0			0
$842$	−10.4020			−0.358477
$843$	−0.638157	−	0.508913i	−0.0219793	−	0.0175279i
$844$	−30.9898	−	7.07323i	−1.06671	−	0.243471i
$845$	2.14885	+	9.41474i	0.0739228	+	0.323877i
$846$	3.82956	−	4.80212i	0.131663	−	0.165100i
$847$	9.12005	+	11.4362i	0.313368	+	0.392952i
$848$	4.99690	−	21.8928i	0.171594	−	0.751803i
$849$	−0.0616703	+	0.128060i	−0.00211652	+	0.00439500i
$850$	7.20775	+	3.47107i	0.247224	+	0.119057i
$851$	29.8595	−	6.81524i	1.02357	−	0.233623i
$852$	−1.04220	−	2.16415i	−0.0357051	−	0.0741424i
$853$			10.9706i			0.375625i	0.982205	+	0.187812i	$0.0601397\pi$
$853$			10.9706i			0.375625i	−0.982205	+	0.187812i	$0.939860\pi$
$854$	0.874447	−	0.421111i	0.0299230	−	0.0144101i
$855$	13.2681	−	10.5810i	0.453760	−	0.361862i
$856$	−11.3711	+	9.06813i	−0.388655	+	0.309942i
$857$	10.6570	−	5.13216i	0.364038	−	0.175311i	−0.242918	−	0.970047i	$-0.578105\pi$
$857$	10.6570	−	5.13216i	0.364038	−	0.175311i	0.606956	+	0.794735i	$0.292390\pi$
$858$			0.757359i			0.0258558i
$859$	2.48525	+	5.16068i	0.0847957	+	0.176080i	0.939055	−	0.343767i	$-0.111703\pi$
$859$	2.48525	+	5.16068i	0.0847957	+	0.176080i	−0.854259	+	0.519847i	$0.825989\pi$
$860$	−11.4339	+	2.60971i	−0.389892	+	0.0889903i
$861$	13.1788	+	6.34660i	0.449134	+	0.216291i
$862$	−1.49943	+	3.11361i	−0.0510709	+	0.106050i
$863$	−10.0385	+	43.9816i	−0.341715	+	1.49715i	0.453737	+	0.891136i	$0.350091\pi$
$863$	−10.0385	+	43.9816i	−0.341715	+	1.49715i	−0.795452	+	0.606016i	$0.792767\pi$
$864$	6.64444	+	8.33186i	0.226048	+	0.283456i
$865$	−14.7498	+	18.4957i	−0.501508	+	0.628872i
$866$	1.34823	+	5.90697i	0.0458146	+	0.200727i
$867$	2.54965	+	0.581942i	0.0865908	+	0.0197638i
$868$	16.4605	+	13.1268i	0.558707	+	0.445554i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−10.3431			−0.350464
$872$	1.66526	+	1.32800i	0.0563927	+	0.0449717i
$873$	34.4283	+	7.85804i	1.16522	+	0.265954i
$874$	−4.23445	−	18.5523i	−0.143232	−	0.627542i
$875$	−15.8715	+	19.9022i	−0.536553	+	0.672816i
$876$	−1.88882	−	2.36851i	−0.0638174	−	0.0800245i
$877$	1.97106	−	8.63578i	0.0665580	−	0.291610i	−0.930684	−	0.365823i	$-0.880788\pi$
$877$	1.97106	−	8.63578i	0.0665580	−	0.291610i	0.997242	+	0.0742136i	$0.0236447\pi$
$878$	−2.09498	+	4.35026i	−0.0707020	+	0.146814i
$879$	1.36471	+	0.657212i	0.0460307	+	0.0221672i
$880$	−7.06105	+	1.61164i	−0.238028	+	0.0543283i
$881$	6.07437	+	12.6136i	0.204651	+	0.424962i	0.977881	−	0.209164i	$-0.0670743\pi$
$881$	6.07437	+	12.6136i	0.204651	+	0.424962i	−0.773230	+	0.634126i	$0.781360\pi$
$882$		−	1.17157i		−	0.0394489i
$883$	−41.8287	+	20.1437i	−1.40765	+	0.677888i	−0.974697	−	0.223529i	$-0.928242\pi$
$883$	−41.8287	+	20.1437i	−1.40765	+	0.677888i	−0.432952	+	0.901417i	$0.642528\pi$
$884$	12.6204	−	10.0645i	0.424471	−	0.338504i
$885$	−2.47964	+	1.97744i	−0.0833520	+	0.0664710i
$886$	13.3069	−	6.40827i	0.447054	−	0.215290i
$887$		−	36.8995i		−	1.23896i	−0.785011	−	0.619482i	$-0.787343\pi$
$887$		−	36.8995i		−	1.23896i	0.785011	−	0.619482i	$-0.212657\pi$
$888$	1.13999	+	2.36722i	0.0382557	+	0.0794387i
$889$	43.1740	−	9.85418i	1.44801	−	0.330499i
$890$	1.67388	+	0.806097i	0.0561085	+	0.0270204i
$891$	−7.84074	+	16.2815i	−0.262675	+	0.545450i
$892$	3.59196	−	15.7374i	0.120268	−	0.526928i
$893$	19.6124	+	24.5932i	0.656304	+	0.822979i
$894$	0.232302	−	0.291297i	0.00776933	−	0.00974243i
$895$	2.33319	+	10.2224i	0.0779901	+	0.341697i
$896$	29.1093	+	6.64400i	0.972472	+	0.221960i
$897$	4.53383	+	3.61561i	0.151380	+	0.120722i
$898$	0.426407			0.0142294
$899$		0			0
$900$	−20.6863			−0.689543
$901$	−28.2571	−	22.5343i	−0.941379	−	0.750725i
$902$	12.1722	+	2.77824i	0.405292	+	0.0925052i
$903$	−1.67218	−	7.32631i	−0.0556467	−	0.243804i
$904$	9.20867	−	11.5473i	0.306276	−	0.384058i
$905$	−8.92445	−	11.1909i	−0.296659	−	0.371998i
$906$	0.539926	−	2.36557i	0.0179379	−	0.0785909i
$907$	−14.8754	+	30.8891i	−0.493929	+	1.02565i	0.493814	+	0.869567i	$0.335602\pi$
$907$	−14.8754	+	30.8891i	−0.493929	+	1.02565i	−0.987743	+	0.156087i	$0.950112\pi$
$908$	−33.1813	−	15.9793i	−1.10116	−	0.530290i
$909$	37.6589	−	8.59541i	1.24907	−	0.285092i
$910$	−0.929438	−	1.93000i	−0.0308106	−	0.0639788i
$911$		−	46.5563i		−	1.54248i	−0.636544	−	0.771240i	$-0.719637\pi$
$911$		−	46.5563i		−	1.54248i	0.636544	−	0.771240i	$-0.280363\pi$
$912$	−6.71748	+	3.23497i	−0.222438	+	0.107121i
$913$	−6.90234	+	5.50443i	−0.228434	+	0.182170i
$914$	−11.3250	+	9.03143i	−0.374599	+	0.298733i
$915$	−0.309164	+	0.148885i	−0.0102206	+	0.00492200i
$916$		−	37.4558i		−	1.23758i
$917$	1.61219	+	3.34776i	0.0532393	+	0.110553i
$918$	4.70737	−	1.07443i	0.155366	−	0.0354613i
$919$	18.1474	+	8.73935i	0.598629	+	0.288284i	0.708555	−	0.705655i	$-0.249347\pi$
$919$	18.1474	+	8.73935i	0.598629	+	0.288284i	−0.109927	+	0.993940i	$0.535062\pi$
$920$	5.26828	−	10.9397i	0.173690	−	0.360671i
$921$	1.55765	−	6.82450i	0.0513262	−	0.224875i
$922$	3.61561	+	4.53383i	0.119074	+	0.149314i
$923$	−3.61561	+	4.53383i	−0.119009	+	0.149233i
$924$	−1.15078	−	5.04191i	−0.0378580	−	0.165867i
$925$	−15.5988	−	3.56033i	−0.512887	−	0.117063i
$926$	−8.41998	−	6.71471i	−0.276698	−	0.220659i
$927$	2.34315			0.0769590
$928$		0			0
$929$	41.3137			1.35546			0.677729	−	0.735311i	$-0.262964\pi$
$929$	41.3137			1.35546			0.677729	+	0.735311i	$0.262964\pi$
$930$	0.546097	+	0.435498i	0.0179072	+	0.0142805i
$931$	5.84957	+	1.33513i	0.191712	+	0.0437570i
$932$	1.75509	+	7.68955i	0.0574899	+	0.251880i
$933$	6.53747	−	8.19772i	0.214027	−	0.268381i
$934$	−8.35602	−	10.4781i	−0.273417	−	0.342855i
$935$	−2.59389	+	11.3646i	−0.0848294	+	0.371662i
$936$	3.55828	−	7.38885i	0.116306	−	0.241512i
$937$	25.7924	+	12.4210i	0.842601	+	0.405775i	0.804826	−	0.593511i	$-0.202259\pi$
$937$	25.7924	+	12.4210i	0.842601	+	0.405775i	0.0377754	+	0.999286i	$0.487973\pi$
$938$	−6.46125	+	1.47474i	−0.210967	+	0.0481519i
$939$	−0.749717	−	1.55680i	−0.0244661	−	0.0508044i
$940$			9.58579i			0.312654i
$941$	20.3601	−	9.80490i	0.663720	−	0.319630i	−0.0715187	−	0.997439i	$-0.522785\pi$
$941$	20.3601	−	9.80490i	0.663720	−	0.319630i	0.735238	+	0.677809i	$0.237070\pi$
$942$	1.13822	−	0.907704i	0.0370854	−	0.0295746i
$943$	74.7415	−	59.6044i	2.43392	−	1.94099i
$944$	−20.6958	+	9.96655i	−0.673590	+	0.324384i
$945$			6.82843i			0.222129i
$946$	−2.78302	−	5.77901i	−0.0904839	−	0.187892i
$947$	−38.3973	+	8.76394i	−1.24775	+	0.284790i	−0.794868	−	0.606783i	$-0.792460\pi$
$947$	−38.3973	+	8.76394i	−1.24775	+	0.284790i	−0.452878	+	0.891573i	$0.649603\pi$
$948$	−0.282642	−	0.136113i	−0.00917977	−	0.00442075i
$949$	−3.17330	+	6.58942i	−0.103010	+	0.213902i
$950$	−2.21211	+	9.69188i	−0.0717703	+	0.314446i
$951$	−5.02463	−	6.30068i	−0.162935	−	0.204314i
$952$	13.5028	−	16.9320i	0.437629	−	0.548770i
$953$	−2.14230	−	9.38604i	−0.0693960	−	0.304044i	0.928305	−	0.371821i	$-0.121266\pi$
$953$	−2.14230	−	9.38604i	−0.0693960	−	0.304044i	−0.997700	+	0.0677772i	$0.978409\pi$
$954$	−8.54968	−	1.95141i	−0.276806	−	0.0631792i
$955$	−2.10023	−	1.67488i	−0.0679618	−	0.0541977i
$956$	−15.2548			−0.493377
$957$		0			0
$958$	−5.34315			−0.172629
$959$	−26.5362	−	21.1619i	−0.856900	−	0.683355i
$960$	−1.68460	−	0.384499i	−0.0543702	−	0.0124096i
$961$	−3.21018	−	14.0647i	−0.103554	−	0.453700i
$962$	1.88882	−	2.36851i	0.0608981	−	0.0763638i
$963$	−16.1740	−	20.2816i	−0.521201	−	0.653565i
$964$	1.75509	−	7.68955i	0.0565276	−	0.247664i
$965$	4.69828	−	9.75608i	0.151243	−	0.314059i
$966$	3.34776	+	1.61219i	0.107712	+	0.0518715i
$967$	−26.0865	+	5.95407i	−0.838885	+	0.191470i	−0.620317	−	0.784352i	$-0.712996\pi$
$967$	−26.0865	+	5.95407i	−0.838885	+	0.191470i	−0.218569	+	0.975822i	$0.570139\pi$
$968$	3.55828	+	7.38885i	0.114368	+	0.237487i
$969$			12.0000i			0.385496i
$970$	4.65943	−	2.24386i	0.149605	−	0.0720460i
$971$	−3.39561	+	2.70791i	−0.108970	+	0.0869009i	−0.676459	−	0.736480i	$-0.736486\pi$
$971$	−3.39561	+	2.70791i	−0.108970	+	0.0869009i	0.567489	+	0.823381i	$0.307915\pi$
$972$	−14.7858	+	11.7912i	−0.474253	+	0.378204i
$973$	−35.6765	+	17.1809i	−1.14374	+	0.550795i
$974$			11.7990i			0.378064i
$975$	−1.31442	−	2.72943i	−0.0420952	−	0.0874117i
$976$	−2.42297	+	0.553027i	−0.0775574	+	0.0177020i
$977$	−37.6861	−	18.1487i	−1.20569	−	0.580628i	−0.280394	−	0.959885i	$-0.590465\pi$
$977$	−37.6861	−	18.1487i	−1.20569	−	0.580628i	−0.925291	+	0.379257i	$0.876179\pi$
$978$	1.34526	−	2.79346i	0.0430166	−	0.0893250i
$979$	2.40955	−	10.5569i	0.0770096	−	0.337401i
$980$	1.14001	+	1.42952i	0.0364161	+	0.0456644i
$981$	−2.36863	+	2.97017i	−0.0756246	+	0.0948302i
$982$	1.17586	+	5.15178i	0.0375232	+	0.164400i
$983$	−31.0710	−	7.09176i	−0.991011	−	0.226192i	−0.303868	−	0.952714i	$-0.598278\pi$
$983$	−31.0710	−	7.09176i	−0.991011	−	0.226192i	−0.687143	+	0.726522i	$0.741135\pi$
$984$	6.41181	+	5.11325i	0.204401	+	0.163004i
$985$	2.00000			0.0637253
$986$		0			0
$987$	−6.14214			−0.195506
$988$	15.6827	+	12.5065i	0.498932	+	0.397885i
$989$	−47.8813	−	10.9286i	−1.52254	−	0.347509i
$990$	0.629384	+	2.75751i	0.0200031	+	0.0876395i
$991$	4.47140	−	5.60696i	0.142039	−	0.178111i	−0.705724	−	0.708487i	$-0.749378\pi$
$991$	4.47140	−	5.60696i	0.142039	−	0.178111i	0.847762	+	0.530376i	$0.177949\pi$
$992$	11.2045	+	14.0500i	0.355742	+	0.446086i
$993$	0.0381786	−	0.167271i	0.00121156	−	0.00530819i
$994$	−1.61219	+	3.34776i	−0.0511357	+	0.106184i
$995$	−14.8527	−	7.15270i	−0.470863	−	0.226756i
$996$	−2.70011	+	0.616283i	−0.0855564	+	0.0195277i
$997$	−12.2721	−	25.4832i	−0.388661	−	0.807063i	−0.999878	−	0.0155999i	$-0.995034\pi$
$997$	−12.2721	−	25.4832i	−0.388661	−	0.807063i	0.611217	−	0.791463i	$-0.290680\pi$
$998$		−	6.20101i		−	0.196290i
$999$	−8.70053	+	4.18995i	−0.275272	+	0.132564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.267.2		24
29.2	odd	28		841.2.d.f.778.1		12
29.3	odd	28		841.2.d.f.605.2		12
29.4	even	14	inner	841.2.e.k.270.2		24
29.5	even	14	inner	841.2.e.k.63.2		24
29.6	even	14	inner	841.2.e.k.651.3		24
29.7	even	7	inner	841.2.e.k.236.3		24
29.8	odd	28		841.2.d.j.645.1		12
29.9	even	14	inner	841.2.e.k.196.3		24
29.10	odd	28		841.2.d.j.571.1		12
29.11	odd	28		841.2.a.d.1.1		2
29.12	odd	4		841.2.d.j.574.2		12
29.13	even	14		841.2.b.a.840.3		4
29.14	odd	28		841.2.d.f.190.2		12
29.15	odd	28		841.2.d.j.190.1		12
29.16	even	7		841.2.b.a.840.2		4
29.17	odd	4		841.2.d.f.574.1		12
29.18	odd	28		29.2.a.a.1.2	✓	2
29.19	odd	28		841.2.d.f.571.2		12
29.20	even	7	inner	841.2.e.k.196.2		24
29.21	odd	28		841.2.d.f.645.2		12
29.22	even	14	inner	841.2.e.k.236.2		24
29.23	even	7	inner	841.2.e.k.651.2		24
29.24	even	7	inner	841.2.e.k.63.3		24
29.25	even	7	inner	841.2.e.k.270.3		24
29.26	odd	28		841.2.d.j.605.1		12
29.27	odd	28		841.2.d.j.778.2		12
29.28	even	2	inner	841.2.e.k.267.3		24
87.11	even	28		7569.2.a.c.1.2		2
87.47	even	28		261.2.a.d.1.1		2
116.47	even	28		464.2.a.h.1.2		2
145.18	even	28		725.2.b.b.349.2		4
145.47	even	28		725.2.b.b.349.3		4
145.134	odd	28		725.2.a.b.1.1		2
203.76	even	28		1421.2.a.j.1.2		2
232.163	even	28		1856.2.a.w.1.1		2
232.221	odd	28		1856.2.a.r.1.2		2
319.76	even	28		3509.2.a.j.1.1		2
348.47	odd	28		4176.2.a.bq.1.1		2
377.337	odd	28		4901.2.a.g.1.1		2
435.134	even	28		6525.2.a.o.1.2		2
493.424	odd	28		8381.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.2	✓	2	29.18	odd	28
261.2.a.d.1.1		2	87.47	even	28
464.2.a.h.1.2		2	116.47	even	28
725.2.a.b.1.1		2	145.134	odd	28
725.2.b.b.349.2		4	145.18	even	28
725.2.b.b.349.3		4	145.47	even	28
841.2.a.d.1.1		2	29.11	odd	28
841.2.b.a.840.2		4	29.16	even	7
841.2.b.a.840.3		4	29.13	even	14
841.2.d.f.190.2		12	29.14	odd	28
841.2.d.f.571.2		12	29.19	odd	28
841.2.d.f.574.1		12	29.17	odd	4
841.2.d.f.605.2		12	29.3	odd	28
841.2.d.f.645.2		12	29.21	odd	28
841.2.d.f.778.1		12	29.2	odd	28
841.2.d.j.190.1		12	29.15	odd	28
841.2.d.j.571.1		12	29.10	odd	28
841.2.d.j.574.2		12	29.12	odd	4
841.2.d.j.605.1		12	29.26	odd	28
841.2.d.j.645.1		12	29.8	odd	28
841.2.d.j.778.2		12	29.27	odd	28
841.2.e.k.63.2		24	29.5	even	14	inner
841.2.e.k.63.3		24	29.24	even	7	inner
841.2.e.k.196.2		24	29.20	even	7	inner
841.2.e.k.196.3		24	29.9	even	14	inner
841.2.e.k.236.2		24	29.22	even	14	inner
841.2.e.k.236.3		24	29.7	even	7	inner
841.2.e.k.267.2		24	1.1	even	1	trivial
841.2.e.k.267.3		24	29.28	even	2	inner
841.2.e.k.270.2		24	29.4	even	14	inner
841.2.e.k.270.3		24	29.25	even	7	inner
841.2.e.k.651.2		24	29.23	even	7	inner
841.2.e.k.651.3		24	29.6	even	14	inner
1421.2.a.j.1.2		2	203.76	even	28
1856.2.a.r.1.2		2	232.221	odd	28
1856.2.a.w.1.1		2	232.163	even	28
3509.2.a.j.1.1		2	319.76	even	28
4176.2.a.bq.1.1		2	348.47	odd	28
4901.2.a.g.1.1		2	377.337	odd	28
6525.2.a.o.1.2		2	435.134	even	28
7569.2.a.c.1.2		2	87.11	even	28
8381.2.a.e.1.2		2	493.424	odd	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.323845 - 0.258258i) q^{2} +(-0.403828 - 0.0921712i) q^{3} +(-0.406863 - 1.78258i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.106974 + 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(-0.688047 + 1.42874i) q^{8} +(-2.54832 - 1.22721i) q^{9} +O(q^{10})\)	\(q+(-0.323845 - 0.258258i) q^{2} +(-0.403828 - 0.0921712i) q^{3} +(-0.406863 - 1.78258i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.106974 + 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(-0.688047 + 1.42874i) q^{8} +(-2.54832 - 1.22721i) q^{9} +(-0.403828 + 0.0921712i) q^{10} +(1.04749 + 2.17513i) q^{11} +0.757359i q^{12} +(1.64736 - 0.793325i) q^{13} +(0.915973 - 0.730464i) q^{14} +(-0.323845 + 0.258258i) q^{15} +(-2.70291 + 1.30165i) q^{16} +4.82843i q^{17} +(0.508326 + 1.05555i) q^{18} +(-5.84957 + 1.33513i) q^{19} +(-1.64736 - 0.793325i) q^{20} +(0.508326 - 1.05555i) q^{21} +(0.222521 - 0.974928i) q^{22} +(-4.77397 - 5.98637i) q^{23} +(0.409542 - 0.513549i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-0.738371 - 0.168528i) q^{26} +(1.88751 + 1.50524i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(3.18289 + 2.53827i) q^{31} +(4.30354 + 0.982255i) q^{32} +(-0.222521 - 0.974928i) q^{33} +(1.24698 - 1.56366i) q^{34} +(1.76350 + 2.21135i) q^{35} +(-1.15078 + 5.04191i) q^{36} +(-1.73553 + 3.60388i) q^{37} +(2.23916 + 1.07832i) q^{38} +(-0.738371 + 0.168528i) q^{39} +(0.688047 + 1.42874i) q^{40} +12.4853i q^{41} +(-0.437223 + 0.210556i) q^{42} +(5.01483 - 3.99920i) q^{43} +(3.45117 - 2.75222i) q^{44} +(-2.54832 + 1.22721i) q^{45} +3.17157i q^{46} +(-2.27470 - 4.72346i) q^{47} +(1.21149 - 0.276514i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.718882 - 1.49277i) q^{50} +(0.445042 - 1.94986i) q^{51} +(-2.08442 - 2.61378i) q^{52} +(-4.66700 + 5.85223i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(2.35368 + 0.537213i) q^{55} +(-3.50673 - 2.79653i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.592127 + 0.472206i) q^{60} +(0.807657 + 0.184342i) q^{61} +(-0.375235 - 1.64401i) q^{62} +(4.98792 - 6.25465i) q^{63} +(2.60093 + 3.26147i) q^{64} +(0.406863 - 1.78258i) q^{65} +(-0.179721 + 0.373194i) q^{66} +(-5.09665 - 2.45442i) q^{67} +(8.60708 - 1.96451i) q^{68} +(1.37609 + 2.85749i) q^{69} -1.17157i q^{70} +(-2.85749 + 1.37609i) q^{71} +(3.50673 - 2.79653i) q^{72} +(-3.12733 + 2.49396i) q^{73} +(1.49277 - 0.718882i) q^{74} -1.65685i q^{75} +(4.75995 + 9.88414i) q^{76} +(-6.65722 + 1.51947i) q^{77} +(0.282642 + 0.136113i) q^{78} +(-0.179721 + 0.373194i) q^{79} +(-0.667563 + 2.92478i) q^{80} +(4.66700 + 5.85223i) q^{81} +(3.22442 - 4.04330i) q^{82} +(0.813727 + 3.56517i) q^{83} +(-2.08843 - 0.476670i) q^{84} +(3.77502 + 3.01048i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-3.50673 - 2.79653i) q^{89} +(1.14220 + 0.260699i) q^{90} +(1.15078 + 5.04191i) q^{91} +(-8.72886 + 10.9456i) q^{92} +(-1.05139 - 1.31840i) q^{93} +(-0.483220 + 2.11713i) q^{94} +(-2.60330 + 5.40581i) q^{95} +(-1.64736 - 0.793325i) q^{96} +(-12.1722 + 2.77824i) q^{97} +(0.179721 + 0.373194i) q^{98} -6.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

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