LMFDB - Embedded newform 847.2.r.b.40.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(40,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([25, 21]))

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

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

chi := DirichletCharacter("847.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.r (of order $30$, degree $8$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			40.4
Character	$\chi$	$=$	847.40
Dual form			847.2.r.b.360.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.298749 + 0.671002i) q^{2} +(-0.246568 - 1.16001i) q^{3} +(0.977269 - 1.08537i) q^{4} +(-0.156952 + 0.0164963i) q^{5} +(0.704708 - 0.512000i) q^{6} +(2.62446 + 0.334983i) q^{7} +(2.41735 + 0.785445i) q^{8} +(1.45581 - 0.648167i) q^{9} +O(q^{10})$	\(q+(0.298749 + 0.671002i) q^{2} +(-0.246568 - 1.16001i) q^{3} +(0.977269 - 1.08537i) q^{4} +(-0.156952 + 0.0164963i) q^{5} +(0.704708 - 0.512000i) q^{6} +(2.62446 + 0.334983i) q^{7} +(2.41735 + 0.785445i) q^{8} +(1.45581 - 0.648167i) q^{9} +(-0.0579584 - 0.100387i) q^{10} +(-1.50000 - 0.866025i) q^{12} +(1.73394 + 1.25978i) q^{13} +(0.559281 + 1.86109i) q^{14} +(0.0578352 + 0.177998i) q^{15} +(-0.110182 - 1.04831i) q^{16} +(-4.02183 - 1.79064i) q^{17} +(0.869843 + 0.783210i) q^{18} +(4.11152 + 4.56631i) q^{19} +(-0.135480 + 0.186472i) q^{20} +(-0.258524 - 3.12700i) q^{21} +(-1.20321 + 2.08402i) q^{23} +(0.315083 - 2.99782i) q^{24} +(-4.86638 + 1.03438i) q^{25} +(-0.327302 + 1.53983i) q^{26} +(-3.20205 - 4.40724i) q^{27} +(2.92838 - 2.52113i) q^{28} +(2.00270 - 0.650718i) q^{29} +(-0.102159 + 0.0919845i) q^{30} +(-4.23837 - 0.445471i) q^{31} +(5.07295 - 2.92887i) q^{32} -3.23361i q^{34} +(-0.417440 - 0.00928232i) q^{35} +(0.719216 - 2.21352i) q^{36} +(6.76977 + 1.43896i) q^{37} +(-1.83569 + 4.12302i) q^{38} +(1.03382 - 2.32201i) q^{39} +(-0.392365 - 0.0833997i) q^{40} +(-1.98691 + 6.11509i) q^{41} +(2.02099 - 1.10766i) q^{42} -6.98850i q^{43} +(-0.217799 + 0.125747i) q^{45} +(-1.75784 - 0.184757i) q^{46} +(2.76122 - 2.48622i) q^{47} +(-1.18888 + 0.386292i) q^{48} +(6.77557 + 1.75830i) q^{49} +(-2.14790 - 2.95633i) q^{50} +(-1.08550 + 5.10688i) q^{51} +(3.06184 - 0.650815i) q^{52} +(0.0334735 - 0.318479i) q^{53} +(2.00066 - 3.46524i) q^{54} +(6.08113 + 2.87114i) q^{56} +(4.28320 - 5.89532i) q^{57} +(1.03494 + 1.14942i) q^{58} +(-10.0307 - 9.03168i) q^{59} +(0.249714 + 0.111180i) q^{60} +(-0.714026 - 6.79350i) q^{61} +(-0.967300 - 2.97704i) q^{62} +(4.03783 - 1.21342i) q^{63} +(1.77527 + 1.28981i) q^{64} +(-0.292926 - 0.169121i) q^{65} +(1.32743 + 2.29918i) q^{67} +(-5.87391 + 2.61523i) q^{68} +(2.71416 + 0.881884i) q^{69} +(-0.118481 - 0.282876i) q^{70} +(2.84336 - 2.06582i) q^{71} +(4.02830 - 0.423391i) q^{72} +(2.36295 - 2.62432i) q^{73} +(1.05692 + 4.97242i) q^{74} +(2.39978 + 5.39000i) q^{75} +8.97419 q^{76} +1.86693 q^{78} +(-0.613656 - 1.37829i) q^{79} +(0.0345865 + 0.162717i) q^{80} +(-1.12398 + 1.24831i) q^{81} +(-4.69683 + 0.493657i) q^{82} +(-7.67857 + 5.57881i) q^{83} +(-3.64659 - 2.77532i) q^{84} +(0.660773 + 0.214698i) q^{85} +(4.68930 - 2.08781i) q^{86} +(-1.24864 - 2.16271i) q^{87} +(-11.7448 - 6.78089i) q^{89} +(-0.149444 - 0.108577i) q^{90} +(4.12864 + 3.88708i) q^{91} +(1.08607 + 3.34257i) q^{92} +(0.528296 + 5.02640i) q^{93} +(2.49317 + 1.11003i) q^{94} +(-0.720639 - 0.648866i) q^{95} +(-4.64834 - 5.16251i) q^{96} +(-2.09121 + 2.87830i) q^{97} +(0.844377 + 5.07171i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 48 * q + 6 * q^3 - 4 * q^4 + 4 * q^9	$ 48 q + 6 q^{3} - 4 q^{4} + 4 q^{9} - 72 q^{12} - 8 q^{14} + 20 q^{15} - 12 q^{16} - 80 q^{23} - 14 q^{25} - 18 q^{26} - 6 q^{31} + 12 q^{36} - 16 q^{37} + 48 q^{38} - 16 q^{42} + 216 q^{45} + 18 q^{47} - 16 q^{49} + 2 q^{53} + 72 q^{56} + 6 q^{58} + 12 q^{59} - 28 q^{64} - 96 q^{67} + 58 q^{70} - 20 q^{71} + 78 q^{75} + 32 q^{78} - 30 q^{80} - 14 q^{81} - 54 q^{82} + 38 q^{86} - 264 q^{89} - 22 q^{91} + 20 q^{92} - 12 q^{93}+O(q^{100}) $ 48 * q + 6 * q^3 - 4 * q^4 + 4 * q^9 - 72 * q^12 - 8 * q^14 + 20 * q^15 - 12 * q^16 - 80 * q^23 - 14 * q^25 - 18 * q^26 - 6 * q^31 + 12 * q^36 - 16 * q^37 + 48 * q^38 - 16 * q^42 + 216 * q^45 + 18 * q^47 - 16 * q^49 + 2 * q^53 + 72 * q^56 + 6 * q^58 + 12 * q^59 - 28 * q^64 - 96 * q^67 + 58 * q^70 - 20 * q^71 + 78 * q^75 + 32 * q^78 - 30 * q^80 - 14 * q^81 - 54 * q^82 + 38 * q^86 - 264 * q^89 - 22 * q^91 + 20 * q^92 - 12 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.298749	+	0.671002i	0.211248	+	0.474470i	0.987828	−	0.155548i	$-0.0497142\pi$
$2$	0.298749	+	0.671002i	0.211248	+	0.474470i	−0.776581	+	0.630018i	$0.783048\pi$
$3$	−0.246568	−	1.16001i	−0.142356	−	0.669733i	−0.990220	−	0.139518i	$-0.955445\pi$
$3$	−0.246568	−	1.16001i	−0.142356	−	0.669733i	0.847864	−	0.530215i	$-0.177889\pi$
$4$	0.977269	−	1.08537i	0.488634	−	0.542683i
$5$	−0.156952	+	0.0164963i	−0.0701910	+	0.00737738i	−0.139559	−	0.990214i	$-0.544568\pi$
$5$	−0.156952	+	0.0164963i	−0.0701910	+	0.00737738i	0.0693678	+	0.997591i	$0.477902\pi$
$6$	0.704708	−	0.512000i	0.287696	−	0.209023i
$7$	2.62446	+	0.334983i	0.991952	+	0.126612i
$7$	2.62446	+	0.334983i	0.991952	+	0.126612i
$8$	2.41735	+	0.785445i	0.854662	+	0.277697i
$9$	1.45581	−	0.648167i	0.485269	−	0.216056i
$10$	−0.0579584	−	0.100387i	−0.0183280	−	0.0317451i
$11$		0			0
$11$		0			0
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	1.73394	+	1.25978i	0.480908	+	0.349400i	0.801677	−	0.597758i	$-0.203941\pi$
$13$	1.73394	+	1.25978i	0.480908	+	0.349400i	−0.320769	+	0.947157i	$0.603941\pi$
$14$	0.559281	+	1.86109i	0.149474	+	0.497398i
$15$	0.0578352	+	0.177998i	0.0149330	+	0.0459590i
$16$	−0.110182	−	1.04831i	−0.0275455	−	0.262077i
$17$	−4.02183	−	1.79064i	−0.975438	−	0.434293i	−0.143797	−	0.989607i	$-0.545931\pi$
$17$	−4.02183	−	1.79064i	−0.975438	−	0.434293i	−0.831641	+	0.555314i	$0.812598\pi$
$18$	0.869843	+	0.783210i	0.205024	+	0.184604i
$19$	4.11152	+	4.56631i	0.943248	+	1.04758i	0.998793	+	0.0491273i	$0.0156440\pi$
$19$	4.11152	+	4.56631i	0.943248	+	1.04758i	−0.0555440	+	0.998456i	$0.517689\pi$
$20$	−0.135480	+	0.186472i	−0.0302942	+	0.0416963i
$21$	−0.258524	−	3.12700i	−0.0564145	−	0.682367i
$22$		0			0
$23$	−1.20321	+	2.08402i	−0.250887	+	0.434549i	−0.963770	−	0.266734i	$-0.914055\pi$
$23$	−1.20321	+	2.08402i	−0.250887	+	0.434549i	0.712883	+	0.701282i	$0.247389\pi$
$24$	0.315083	−	2.99782i	0.0643161	−	0.611927i
$25$	−4.86638	+	1.03438i	−0.973275	+	0.206876i
$26$	−0.327302	+	1.53983i	−0.0641891	+	0.301986i
$27$	−3.20205	−	4.40724i	−0.616234	−	0.848173i
$28$	2.92838	−	2.52113i	0.553412	−	0.476449i
$29$	2.00270	−	0.650718i	0.371893	−	0.120835i	−0.117107	−	0.993119i	$-0.537362\pi$
$29$	2.00270	−	0.650718i	0.371893	−	0.120835i	0.488999	+	0.872284i	$0.337362\pi$
$30$	−0.102159	+	0.0919845i	−0.0186516	+	0.0167940i
$31$	−4.23837	−	0.445471i	−0.761234	−	0.0800090i	−0.284047	−	0.958810i	$-0.591677\pi$
$31$	−4.23837	−	0.445471i	−0.761234	−	0.0800090i	−0.477188	+	0.878801i	$0.658344\pi$
$32$	5.07295	−	2.92887i	0.896779	−	0.517755i
$33$		0			0
$34$		−	3.23361i		−	0.554560i
$35$	−0.417440	−	0.00928232i	−0.0705602	−	0.00156900i
$36$	0.719216	−	2.21352i	0.119869	−	0.368920i
$37$	6.76977	+	1.43896i	1.11294	+	0.236563i	0.727459	−	0.686151i	$-0.240701\pi$
$37$	6.76977	+	1.43896i	1.11294	+	0.236563i	0.385484	+	0.922714i	$0.374034\pi$
$38$	−1.83569	+	4.12302i	−0.297788	+	0.668843i
$39$	1.03382	−	2.32201i	0.165544	−	0.371819i
$40$	−0.392365	−	0.0833997i	−0.0620383	−	0.0131867i
$41$	−1.98691	+	6.11509i	−0.310304	+	0.955017i	0.667341	+	0.744753i	$0.267433\pi$
$41$	−1.98691	+	6.11509i	−0.310304	+	0.955017i	−0.977645	+	0.210265i	$0.932567\pi$
$42$	2.02099	−	1.10766i	0.311845	−	0.170915i
$43$		−	6.98850i		−	1.06574i	−0.846198	−	0.532868i	$-0.821114\pi$
$43$		−	6.98850i		−	1.06574i	0.846198	−	0.532868i	$-0.178886\pi$
$44$		0			0
$45$	−0.217799	+	0.125747i	−0.0324676	+	0.0187452i
$46$	−1.75784	−	0.184757i	−0.259180	−	0.0272409i
$47$	2.76122	−	2.48622i	0.402766	−	0.362652i	−0.442711	−	0.896665i	$-0.645983\pi$
$47$	2.76122	−	2.48622i	0.402766	−	0.362652i	0.845477	+	0.534012i	$0.179316\pi$
$48$	−1.18888	+	0.386292i	−0.171601	+	0.0557564i
$49$	6.77557	+	1.75830i	0.967939	+	0.251185i
$50$	−2.14790	−	2.95633i	−0.303759	−	0.418088i
$51$	−1.08550	+	5.10688i	−0.152001	+	0.715107i
$52$	3.06184	−	0.650815i	0.424601	−	0.0902518i
$53$	0.0334735	−	0.318479i	0.00459794	−	0.0437464i	−0.991982	−	0.126376i	$-0.959665\pi$
$53$	0.0334735	−	0.318479i	0.00459794	−	0.0437464i	0.996580	+	0.0826300i	$0.0263320\pi$
$54$	2.00066	−	3.46524i	0.272255	−	0.471559i
$55$		0			0
$56$	6.08113	+	2.87114i	0.812625	+	0.383672i
$57$	4.28320	−	5.89532i	0.567324	−	0.780854i
$58$	1.03494	+	1.14942i	0.135894	+	0.150926i
$59$	−10.0307	−	9.03168i	−1.30589	−	1.17582i	−0.972466	−	0.233046i	$-0.925131\pi$
$59$	−10.0307	−	9.03168i	−1.30589	−	1.17582i	−0.333420	−	0.942778i	$-0.608203\pi$
$60$	0.249714	+	0.111180i	0.0322380	+	0.0143533i
$61$	−0.714026	−	6.79350i	−0.0914216	−	0.869819i	−0.940098	−	0.340906i	$-0.889266\pi$
$61$	−0.714026	−	6.79350i	−0.0914216	−	0.869819i	0.848676	−	0.528913i	$-0.177400\pi$
$62$	−0.967300	−	2.97704i	−0.122847	−	0.378085i
$63$	4.03783	−	1.21342i	0.508719	−	0.152876i
$64$	1.77527	+	1.28981i	0.221909	+	0.161226i
$65$	−0.292926	−	0.169121i	−0.0363331	−	0.0209769i
$66$		0			0
$67$	1.32743	+	2.29918i	0.162171	+	0.280889i	0.935647	−	0.352937i	$-0.114817\pi$
$67$	1.32743	+	2.29918i	0.162171	+	0.280889i	−0.773476	+	0.633826i	$0.781484\pi$
$68$	−5.87391	+	2.61523i	−0.712316	+	0.317143i
$69$	2.71416	+	0.881884i	0.326747	+	0.106166i
$70$	−0.118481	−	0.282876i	−0.0141612	−	0.0338102i
$71$	2.84336	−	2.06582i	0.337445	−	0.245168i	−0.406138	−	0.913812i	$-0.633125\pi$
$71$	2.84336	−	2.06582i	0.337445	−	0.245168i	0.743583	+	0.668644i	$0.233125\pi$
$72$	4.02830	−	0.423391i	0.474739	−	0.0498971i
$73$	2.36295	−	2.62432i	0.276563	−	0.307154i	−0.588821	−	0.808263i	$-0.700408\pi$
$73$	2.36295	−	2.62432i	0.276563	−	0.307154i	0.865384	+	0.501109i	$0.167075\pi$
$74$	1.05692	+	4.97242i	0.122864	+	0.578032i
$75$	2.39978	+	5.39000i	0.277103	+	0.622384i
$76$	8.97419			1.02941
$77$		0			0
$78$	1.86693			0.211388
$79$	−0.613656	−	1.37829i	−0.0690417	−	0.155070i	0.875728	−	0.482804i	$-0.160382\pi$
$79$	−0.613656	−	1.37829i	−0.0690417	−	0.155070i	−0.944770	+	0.327734i	$0.893715\pi$
$80$	0.0345865	+	0.162717i	0.00386689	+	0.0181923i
$81$	−1.12398	+	1.24831i	−0.124887	+	0.138701i
$82$	−4.69683	+	0.493657i	−0.518678	+	0.0545153i
$83$	−7.67857	+	5.57881i	−0.842832	+	0.612354i	−0.923160	−	0.384415i	$-0.874403\pi$
$83$	−7.67857	+	5.57881i	−0.842832	+	0.612354i	0.0803281	+	0.996768i	$0.474403\pi$
$84$	−3.64659	−	2.77532i	−0.397875	−	0.302813i
$85$	0.660773	+	0.214698i	0.0716709	+	0.0232873i
$86$	4.68930	−	2.08781i	0.505660	−	0.225134i
$87$	−1.24864	−	2.16271i	−0.133868	−	0.231867i
$88$		0			0
$89$	−11.7448	−	6.78089i	−1.24495	−	0.718773i	−0.274853	−	0.961486i	$-0.588629\pi$
$89$	−11.7448	−	6.78089i	−1.24495	−	0.718773i	−0.970098	+	0.242714i	$0.921962\pi$
$90$	−0.149444	−	0.108577i	−0.0157527	−	0.0114450i
$91$	4.12864	+	3.88708i	0.432799	+	0.407476i
$92$	1.08607	+	3.34257i	0.113230	+	0.348487i
$93$	0.528296	+	5.02640i	0.0547817	+	0.521213i
$94$	2.49317	+	1.11003i	0.257151	+	0.114491i
$95$	−0.720639	−	0.648866i	−0.0739360	−	0.0665723i
$96$	−4.64834	−	5.16251i	−0.474419	−	0.526896i
$97$	−2.09121	+	2.87830i	−0.212330	+	0.292247i	−0.901876	−	0.431994i	$-0.857810\pi$
$97$	−2.09121	+	2.87830i	−0.212330	+	0.292247i	0.689546	+	0.724242i	$0.257810\pi$
$98$	0.844377	+	5.07171i	0.0852949	+	0.512321i
$99$		0			0
$100$	−3.63307	+	6.29267i	−0.363307	+	0.629267i
$101$	−1.47717	+	14.0544i	−0.146984	+	1.39846i	0.633721	+	0.773562i	$0.281527\pi$
$101$	−1.47717	+	14.0544i	−0.146984	+	1.39846i	−0.780705	+	0.624900i	$0.785140\pi$
$102$	−3.75102	+	0.797304i	−0.371407	+	0.0789449i
$103$	−3.35893	+	15.8025i	−0.330966	+	1.55707i	0.426679	+	0.904403i	$0.359684\pi$
$103$	−3.35893	+	15.8025i	−0.330966	+	1.55707i	−0.757644	+	0.652668i	$0.773650\pi$
$104$	3.20205	+	4.40724i	0.313986	+	0.432165i
$105$	0.0921597	+	0.486524i	0.00899387	+	0.0474798i
$106$	0.223700	−	0.0726846i	0.0217277	−	0.00705975i
$107$	0.426160	−	0.383716i	0.0411984	−	0.0370952i	−0.648274	−	0.761407i	$-0.724509\pi$
$107$	0.426160	−	0.383716i	0.0411984	−	0.0370952i	0.689473	+	0.724312i	$0.257842\pi$
$108$	−7.91273	−	0.831661i	−0.761403	−	0.0800266i
$109$	−11.6766	+	6.74149i	−1.11842	+	0.645718i	−0.940996	−	0.338417i	$-0.890109\pi$
$109$	−11.6766	+	6.74149i	−1.11842	+	0.645718i	−0.177420	+	0.984135i	$0.556775\pi$
$110$		0			0
$111$		−	8.20781i		−	0.779050i
$112$	0.0619983	−	2.78816i	0.00585828	−	0.263456i
$113$	1.62186	−	4.99156i	0.152571	−	0.469567i	−0.845335	−	0.534236i	$-0.820599\pi$
$113$	1.62186	−	4.99156i	0.152571	−	0.469567i	0.997907	+	0.0646694i	$0.0205993\pi$
$114$	5.23538	+	1.11281i	0.490338	+	0.104225i
$115$	0.154468	−	0.346940i	0.0144042	−	0.0323523i
$116$	1.25091	−	2.80959i	0.116144	−	0.260864i
$117$	3.34082	+	0.710114i	0.308859	+	0.0656501i
$118$	3.06361	−	9.42883i	0.282028	−	0.867994i
$119$	−9.95530	−	6.04669i	−0.912601	−	0.554300i
$120$			0.475711i			0.0434263i
$121$		0			0
$122$	4.34514	−	2.50867i	0.393390	−	0.227124i
$123$	7.58349	+	0.797056i	0.683780	+	0.0718682i
$124$	−4.62553	+	4.16484i	−0.415385	+	0.374014i
$125$	1.49719	−	0.486465i	0.133912	−	0.0435108i
$126$	2.02051	+	2.34689i	0.180001	+	0.209077i
$127$	12.3232	+	16.9614i	1.09351	+	1.50508i	0.843720	+	0.536784i	$0.180361\pi$
$127$	12.3232	+	16.9614i	1.09351	+	1.50508i	0.249788	+	0.968301i	$0.419639\pi$
$128$	2.10068	−	9.88291i	0.185675	−	0.873534i
$129$	−8.10673	+	1.72314i	−0.713758	+	0.151714i
$130$	0.0259691	−	0.247079i	0.00227764	−	0.0216703i
$131$	−8.25344	+	14.2954i	−0.721106	+	1.24899i	0.239450	+	0.970909i	$0.423033\pi$
$131$	−8.25344	+	14.2954i	−0.721106	+	1.24899i	−0.960557	+	0.278084i	$0.910301\pi$
$132$		0			0
$133$	9.26089	+	13.3614i	0.803021	+	1.15858i
$134$	−1.14618	+	1.57759i	−0.0990152	+	0.136283i
$135$	0.575271	+	0.638903i	0.0495114	+	0.0549880i
$136$	−8.31573	−	7.48752i	−0.713068	−	0.642050i
$137$	−9.45466	−	4.20948i	−0.807766	−	0.359641i	−0.0390551	−	0.999237i	$-0.512435\pi$
$137$	−9.45466	−	4.20948i	−0.807766	−	0.359641i	−0.768711	+	0.639596i	$0.779101\pi$
$138$	0.219108	+	2.08467i	0.0186517	+	0.177459i
$139$	5.01277	+	15.4277i	0.425178	+	1.30856i	0.902824	+	0.430010i	$0.141490\pi$
$139$	5.01277	+	15.4277i	0.425178	+	1.30856i	−0.477647	+	0.878552i	$0.658510\pi$
$140$	−0.418026	+	0.444004i	−0.0353296	+	0.0375252i
$141$	−3.56487	−	2.59003i	−0.300216	−	0.218120i
$142$	2.23562	+	1.29074i	0.187609	+	0.108316i
$143$		0			0
$144$	−0.839883	−	1.45472i	−0.0699903	−	0.121227i
$145$	−0.303594	+	0.135169i	−0.0252121	+	0.0112251i
$146$	2.46686	+	0.801531i	0.204159	+	0.0663352i
$147$	0.369006	−	8.29328i	0.0304351	−	0.684018i
$148$	8.17768	−	5.94143i	0.672201	−	0.488383i
$149$	−16.3706	+	1.72061i	−1.34113	+	0.140958i	−0.747758	−	0.663971i	$-0.768870\pi$
$149$	−16.3706	+	1.72061i	−1.34113	+	0.140958i	−0.593370	+	0.804930i	$0.702203\pi$
$150$	−2.89977	+	3.22052i	−0.236765	+	0.262954i
$151$	−1.95287	−	9.18753i	−0.158922	−	0.747670i	−0.983353	−	0.181707i	$-0.941838\pi$
$151$	−1.95287	−	9.18753i	−0.158922	−	0.747670i	0.824430	−	0.565963i	$-0.191496\pi$
$152$	6.35241	+	14.2677i	0.515249	+	1.15727i
$153$	−7.01564			−0.567181
$154$		0			0
$155$	0.672570			0.0540221
$156$	−1.50990	−	3.39130i	−0.120889	−	0.271521i
$157$	0.264270	+	1.24329i	0.0210910	+	0.0992255i	0.987434	−	0.158031i	$-0.0505147\pi$
$157$	0.264270	+	1.24329i	0.0210910	+	0.0992255i	−0.966343	+	0.257257i	$0.917181\pi$
$158$	0.741509	−	0.823530i	0.0589913	−	0.0655165i
$159$	−0.377692	+	0.0396971i	−0.0299530	+	0.00314818i
$160$	−0.747893	+	0.543376i	−0.0591262	+	0.0429577i
$161$	−3.85589	+	5.06637i	−0.303887	+	0.399286i
$162$	−1.17341	−	0.381263i	−0.0921916	−	0.0299549i
$163$	13.8020	−	6.14505i	1.08106	−	0.481317i	0.212628	−	0.977133i	$-0.431798\pi$
$163$	13.8020	−	6.14505i	1.08106	−	0.481317i	0.868428	+	0.495816i	$0.165131\pi$
$164$	4.69537	+	8.13262i	0.366647	+	0.635051i
$165$		0			0
$166$	−6.03736	−	3.48567i	−0.468590	−	0.270541i
$167$	10.0740	+	7.31921i	0.779552	+	0.566377i	0.904844	−	0.425742i	$-0.139987\pi$
$167$	10.0740	+	7.31921i	0.779552	+	0.566377i	−0.125293	+	0.992120i	$0.539987\pi$
$168$	1.83114	−	7.76210i	0.141276	−	0.598859i
$169$	−2.59773	−	7.99498i	−0.199825	−	0.614999i
$170$	0.0533426	+	0.507521i	0.00409119	+	0.0389251i
$171$	8.94532	+	3.98271i	0.684066	+	0.304566i
$172$	−7.58508	−	6.82964i	−0.578357	−	0.520755i
$173$	−13.6911	−	15.2055i	−1.04092	−	1.15606i	−0.987522	−	0.157483i	$-0.949662\pi$
$173$	−13.6911	−	15.2055i	−1.04092	−	1.15606i	−0.0533959	−	0.998573i	$-0.517005\pi$
$174$	1.07815	−	1.48395i	0.0817345	−	0.112498i
$175$	−13.1181	+	1.08454i	−0.991636	+	0.0819832i
$176$		0			0
$177$	−8.00360	+	13.8626i	−0.601587	+	1.04198i
$178$	1.04123	−	9.90660i	0.0780432	−	0.742531i
$179$	−2.62121	+	0.557155i	−0.195918	+	0.0416437i	−0.304826	−	0.952408i	$-0.598598\pi$
$179$	−2.62121	+	0.557155i	−0.195918	+	0.0416437i	0.108907	+	0.994052i	$0.465265\pi$
$180$	−0.0763674	+	0.359280i	−0.00569209	+	0.0267792i
$181$	−3.93682	−	5.41856i	−0.292621	−	0.402759i	0.637242	−	0.770664i	$-0.280075\pi$
$181$	−3.93682	−	5.41856i	−0.292621	−	0.402759i	−0.929863	+	0.367905i	$0.880075\pi$
$182$	−1.37481	+	3.93159i	−0.101908	+	0.291429i
$183$	−7.70448	+	2.50334i	−0.569531	+	0.185052i
$184$	−4.54546	+	4.09275i	−0.335096	+	0.301722i
$185$	−1.08627	−	0.114171i	−0.0798639	−	0.00839403i
$186$	−3.21490	+	1.85612i	−0.235728	+	0.136097i
$187$		0			0
$188$		−	5.42664i		−	0.395779i
$189$	−6.92729	−	12.6392i	−0.503886	−	0.919370i
$190$	0.220100	−	0.677399i	0.0159678	−	0.0491437i
$191$	23.8702	+	5.07377i	1.72719	+	0.367125i	0.961226	−	0.275760i	$-0.0889296\pi$
$191$	23.8702	+	5.07377i	1.72719	+	0.367125i	0.765962	+	0.642886i	$0.222263\pi$
$192$	1.05847	−	2.37736i	0.0763884	−	0.171571i
$193$	−3.60987	+	8.10790i	−0.259844	+	0.583619i	−0.995608	−	0.0936188i	$-0.970157\pi$
$193$	−3.60987	+	8.10790i	−0.259844	+	0.583619i	0.735764	+	0.677238i	$0.236823\pi$
$194$	−2.55610	−	0.543315i	−0.183517	−	0.0390077i
$195$	−0.123956	+	0.381498i	−0.00887668	+	0.0273196i
$196$	8.52995	−	5.63565i	0.609282	−	0.402547i
$197$			14.5955i			1.03988i	0.854202	+	0.519942i	$0.174046\pi$
$197$			14.5955i			1.03988i	−0.854202	+	0.519942i	$0.825954\pi$
$198$		0			0
$199$	19.6730	−	11.3582i	1.39459	−	0.805164i	0.400767	−	0.916180i	$-0.368744\pi$
$199$	19.6730	−	11.3582i	1.39459	−	0.805164i	0.993819	+	0.111016i	$0.0354104\pi$
$200$	−12.5762	−	1.32181i	−0.889270	−	0.0934661i
$201$	2.33977	−	2.10674i	0.165035	−	0.148598i
$202$	−9.87181	+	3.20755i	−0.694578	+	0.225682i
$203$	5.47399	−	1.03691i	0.384199	−	0.0727769i
$204$	4.48201	+	6.16896i	0.313804	+	0.431914i
$205$	0.210974	−	0.992553i	0.0147350	−	0.0693229i
$206$	−11.6070	+	2.46715i	−0.808700	+	0.171894i
$207$	−0.400848	+	3.81381i	−0.0278609	+	0.265078i
$208$	1.12959	−	1.95651i	0.0783230	−	0.135659i
$209$		0			0
$210$	−0.298926	+	0.207188i	−0.0206278	+	0.0142973i
$211$	−2.28615	+	3.14662i	−0.157385	+	0.216622i	−0.880426	−	0.474183i	$-0.842744\pi$
$211$	−2.28615	+	3.14662i	−0.157385	+	0.216622i	0.723041	+	0.690805i	$0.242744\pi$
$212$	−0.312954	−	0.347570i	−0.0214938	−	0.0238712i
$213$	−3.09746	−	2.78897i	−0.212234	−	0.191097i
$214$	0.384789	+	0.171319i	0.0263037	+	0.0117111i
$215$	0.115284	+	1.09686i	0.00786233	+	0.0748051i
$216$	−4.27882	−	13.1689i	−0.291137	−	0.896028i
$217$	−10.9742	−	2.58890i	−0.744978	−	0.175746i
$218$	−8.01194	−	5.82101i	−0.542637	−	0.394249i
$219$	−3.62687	−	2.09398i	−0.245081	−	0.141498i
$220$		0			0
$221$	−4.71780	−	8.17147i	−0.317354	−	0.549672i
$222$	5.50746	−	2.45208i	0.369636	−	0.164573i
$223$	−18.4764	−	6.00336i	−1.23727	−	0.402014i	−0.383929	−	0.923363i	$-0.625429\pi$
$223$	−18.4764	−	6.00336i	−1.23727	−	0.402014i	−0.853344	+	0.521348i	$0.825429\pi$
$224$	14.2949	−	5.98734i	0.955115	−	0.400046i
$225$	−6.41405	+	4.66008i	−0.427604	+	0.310672i
$226$	3.83388	−	0.402957i	0.255026	−	0.0268043i
$227$	−9.73474	+	10.8115i	−0.646117	+	0.717586i	−0.973852	−	0.227184i	$-0.927048\pi$
$227$	−9.73474	+	10.8115i	−0.646117	+	0.717586i	0.327735	+	0.944770i	$0.393715\pi$
$228$	−2.21275	−	10.4102i	−0.146543	−	0.689429i
$229$	1.46462	+	3.28960i	0.0967851	+	0.217383i	0.955449	−	0.295156i	$-0.0953717\pi$
$229$	1.46462	+	3.28960i	0.0967851	+	0.217383i	−0.858664	+	0.512539i	$0.828705\pi$
$230$	0.278944			0.0183931
$231$		0			0
$232$	5.35234			0.351398
$233$	6.20951	+	13.9468i	0.406799	+	0.913684i	0.994513	+	0.104616i	$0.0333613\pi$
$233$	6.20951	+	13.9468i	0.406799	+	0.913684i	−0.587714	+	0.809069i	$0.699972\pi$
$234$	0.521581	+	2.45385i	0.0340968	+	0.160413i
$235$	−0.392366	+	0.435767i	−0.0255952	+	0.0284263i
$236$	−19.6054	+	2.06061i	−1.27620	+	0.134134i
$237$	−1.44753	+	1.05169i	−0.0940271	+	0.0683147i
$238$	1.08320	−	8.48648i	0.0702137	−	0.550097i
$239$	−5.70178	−	1.85262i	−0.368817	−	0.119836i	0.118744	−	0.992925i	$-0.462113\pi$
$239$	−5.70178	−	1.85262i	−0.368817	−	0.119836i	−0.487561	+	0.873089i	$0.662113\pi$
$240$	0.180225	−	0.0802414i	0.0116335	−	0.00517956i
$241$	2.05090	+	3.55227i	0.132110	+	0.228822i	0.924490	−	0.381207i	$-0.124491\pi$
$241$	2.05090	+	3.55227i	0.132110	+	0.228822i	−0.792380	+	0.610028i	$0.791158\pi$
$242$		0			0
$243$	−12.4282	−	7.17543i	−0.797270	−	0.460304i
$244$	−8.07123	−	5.86409i	−0.516708	−	0.375410i
$245$	−1.09244	−	0.164196i	−0.0697937	−	0.0104901i
$246$	1.73074	+	5.32666i	0.110348	+	0.339615i
$247$	1.37658	+	13.0973i	0.0875898	+	0.833362i
$248$	−9.89574	−	4.40587i	−0.628380	−	0.279773i
$249$	8.36476	+	7.53167i	0.530095	+	0.477300i
$250$	0.773703	+	0.859284i	0.0489332	+	0.0543459i
$251$	−4.11000	+	5.65692i	−0.259421	+	0.357062i	−0.918783	−	0.394764i	$-0.870826\pi$
$251$	−4.11000	+	5.65692i	−0.259421	+	0.357062i	0.659362	+	0.751826i	$0.270826\pi$
$252$	2.62904	−	5.56836i	0.165614	−	0.350774i
$253$		0			0
$254$	−7.69961	+	13.3361i	−0.483117	+	0.836783i
$255$	0.0861268	−	0.819442i	0.00539347	−	0.0513154i
$256$	11.5518	−	2.45542i	0.721990	−	0.153464i
$257$	−4.12886	+	19.4248i	−0.257551	+	1.21168i	0.639163	+	0.769072i	$0.279281\pi$
$257$	−4.12886	+	19.4248i	−0.257551	+	1.21168i	−0.896714	+	0.442611i	$0.854052\pi$
$258$	−3.57811	−	4.92485i	−0.222763	−	0.306608i
$259$	17.2850	+	6.04425i	1.07403	+	0.375571i
$260$	−0.469826	+	0.152656i	−0.0291374	+	0.00946731i
$261$	2.49378	−	2.24541i	0.154361	−	0.138987i
$262$	−12.0579	−	1.26734i	−0.744942	−	0.0782965i
$263$	5.55559	−	3.20752i	0.342572	−	0.197784i	−0.318837	−	0.947810i	$-0.603292\pi$
$263$	5.55559	−	3.20752i	0.342572	−	0.197784i	0.661409	+	0.750025i	$0.269959\pi$
$264$		0			0
$265$			0.0505381i			0.00310453i
$266$	−6.19883	+	10.2058i	−0.380075	+	0.625757i
$267$	−4.97000	+	15.2961i	−0.304159	+	0.936106i
$268$	3.79271	+	0.806165i	0.231676	+	0.0492443i
$269$	7.88977	−	17.7207i	0.481048	−	1.08045i	−0.496173	−	0.868224i	$-0.665262\pi$
$269$	7.88977	−	17.7207i	0.481048	−	1.08045i	0.977220	−	0.212227i	$-0.0680716\pi$
$270$	−0.256843	+	0.576880i	−0.0156310	+	0.0351078i
$271$	−11.2208	−	2.38505i	−0.681614	−	0.144882i	−0.145924	−	0.989296i	$-0.546615\pi$
$271$	−11.2208	−	2.38505i	−0.681614	−	0.144882i	−0.535691	+	0.844414i	$0.679949\pi$
$272$	−1.43401	+	4.41342i	−0.0869495	+	0.267603i
$273$	3.49106	−	5.74770i	0.211289	−	0.347866i
$274$		−	7.60168i		−	0.459234i
$275$		0			0
$276$	3.60963	−	2.08402i	0.217274	−	0.125443i
$277$	−4.70107	−	0.494103i	−0.282460	−	0.0296878i	−0.0377610	−	0.999287i	$-0.512023\pi$
$277$	−4.70107	−	0.494103i	−0.282460	−	0.0296878i	−0.244699	+	0.969599i	$0.578689\pi$
$278$	−8.85447	+	7.97260i	−0.531056	+	0.478165i
$279$	−6.45899	+	2.09865i	−0.386690	+	0.125643i
$280$	−1.00181	−	0.350315i	−0.0598695	−	0.0209353i
$281$	−12.4507	−	17.1369i	−0.742747	−	1.02230i	−0.998456	−	0.0555497i	$-0.982309\pi$
$281$	−12.4507	−	17.1369i	−0.742747	−	1.02230i	0.255709	−	0.966754i	$-0.417691\pi$
$282$	0.672913	−	3.16580i	0.0400714	−	0.188521i
$283$	28.3324	−	6.02223i	1.68418	−	0.357984i	0.736314	−	0.676640i	$-0.236565\pi$
$283$	28.3324	−	6.02223i	1.68418	−	0.357984i	0.947871	+	0.318656i	$0.103231\pi$
$284$	0.536552	−	5.10495i	0.0318385	−	0.302923i
$285$	−0.575006	+	0.995939i	−0.0340604	+	0.0589943i
$286$		0			0
$287$	−7.26303	+	15.3832i	−0.428723	+	0.908044i
$288$	5.48684	−	7.55198i	0.323315	−	0.445005i
$289$	1.59354	+	1.76981i	0.0937379	+	0.104106i
$290$	−0.181397	−	0.163330i	−0.0106520	−	0.00959110i
$291$	3.85449	+	1.71613i	0.225954	+	0.100601i
$292$	−0.539115	−	5.12934i	−0.0315493	−	0.300172i
$293$	−2.90190	−	8.93113i	−0.169531	−	0.521762i	0.829811	−	0.558045i	$-0.188448\pi$
$293$	−2.90190	−	8.93113i	−0.169531	−	0.521762i	−0.999342	+	0.0362829i	$0.988448\pi$
$294$	5.67505	−	2.23001i	0.330975	−	0.130057i
$295$	1.72333	+	1.25207i	0.100336	+	0.0728984i
$296$	15.2347	+	8.79575i	0.885498	+	0.511242i
$297$		0			0
$298$	−6.04523	−	10.4706i	−0.350191	−	0.606548i
$299$	−4.71170	+	2.09778i	−0.272484	+	0.121318i
$300$	8.19536	+	2.66284i	0.473160	+	0.153739i
$301$	2.34103	−	18.3410i	0.134935	−	1.05716i
$302$	5.58143	−	4.05515i	0.321175	−	0.233348i
$303$	16.6674	−	1.75182i	0.957519	−	0.100639i
$304$	4.33389	−	4.81328i	0.248566	−	0.276060i
$305$	0.224135	+	1.05447i	0.0128340	+	0.0603790i
$306$	−2.09592	−	4.70751i	−0.119816	−	0.269111i
$307$	3.76948			0.215136			0.107568	−	0.994198i	$-0.465694\pi$
$307$	3.76948			0.215136			0.107568	+	0.994198i	$0.465694\pi$
$308$		0			0
$309$	19.1593			1.08994
$310$	0.200930	+	0.451296i	0.0114120	+	0.0256319i
$311$	−1.79620	−	8.45046i	−0.101853	−	0.479182i	−0.999277	−	0.0380128i	$-0.987897\pi$
$311$	−1.79620	−	8.45046i	−0.101853	−	0.479182i	0.897424	−	0.441169i	$-0.145436\pi$
$312$	4.32292	−	4.80109i	0.244737	−	0.271808i
$313$	10.4409	−	1.09739i	0.590157	−	0.0620280i	0.195257	−	0.980752i	$-0.437446\pi$
$313$	10.4409	−	1.09739i	0.590157	−	0.0620280i	0.394900	+	0.918724i	$0.370779\pi$
$314$	−0.755301	+	0.548758i	−0.0426241	+	0.0309682i
$315$	−0.613729	+	0.257058i	−0.0345797	+	0.0144836i
$316$	−2.09566	−	0.680922i	−0.117890	−	0.0383049i
$317$	21.2717	−	9.47079i	1.19474	−	0.531932i	0.289642	−	0.957135i	$-0.406464\pi$
$317$	21.2717	−	9.47079i	1.19474	−	0.531932i	0.905098	+	0.425203i	$0.139797\pi$
$318$	−0.139472	−	0.241573i	−0.00782121	−	0.0135467i
$319$		0			0
$320$	−0.299909	−	0.173153i	−0.0167654	−	0.00967953i
$321$	−0.550192	−	0.399738i	−0.0307087	−	0.0223112i
$322$	−4.55149	−	1.07373i	−0.253645	−	0.0598368i
$323$	−8.35927	−	25.7272i	−0.465122	−	1.43150i
$324$	0.256440	+	2.43987i	0.0142467	+	0.135548i
$325$	−9.74108	−	4.33701i	−0.540338	−	0.240574i
$326$	8.24668	+	7.42534i	0.456741	+	0.411252i
$327$	10.6993	+	11.8828i	0.591672	+	0.657118i
$328$	−9.60614	+	13.2217i	−0.530410	+	0.730047i
$329$	8.07956	−	5.60001i	0.445441	−	0.308739i
$330$		0			0
$331$	−8.14766	+	14.1122i	−0.447836	+	0.775675i	−0.998245	−	0.0592204i	$-0.981139\pi$
$331$	−8.14766	+	14.1122i	−0.447836	+	0.775675i	0.550409	+	0.834895i	$0.314472\pi$
$332$	−1.44897	+	13.7861i	−0.0795227	+	0.756608i
$333$	10.7882	−	2.29310i	0.591188	−	0.125661i
$334$	−1.90160	+	8.94630i	−0.104051	+	0.489520i
$335$	−0.246271	−	0.338963i	−0.0134552	−	0.0185195i
$336$	−3.24958	+	0.615551i	−0.177279	+	0.0335811i
$337$	16.3536	−	5.31362i	0.890839	−	0.289451i	0.172389	−	0.985029i	$-0.444852\pi$
$337$	16.3536	−	5.31362i	0.890839	−	0.289451i	0.718451	+	0.695578i	$0.244852\pi$
$338$	4.58858	−	4.13158i	0.249586	−	0.224728i
$339$	−6.19016	−	0.650613i	−0.336204	−	0.0353364i
$340$	0.878779	−	0.507364i	0.0476585	−	0.0275157i
$341$		0			0
$342$			7.19216i			0.388908i
$343$	17.1932	+	6.88428i	0.928346	+	0.371716i
$344$	5.48908	−	16.8936i	0.295951	−	0.910844i
$345$	−0.440541	−	0.0936398i	−0.0237179	−	0.00504140i
$346$	6.11274	−	13.7294i	0.328623	−	0.738099i
$347$	1.21116	−	2.72030i	0.0650182	−	0.146033i	−0.878114	−	0.478452i	$-0.841198\pi$
$347$	1.21116	−	2.72030i	0.0650182	−	0.146033i	0.943132	+	0.332419i	$0.107865\pi$
$348$	−3.56759	−	0.758315i	−0.191243	−	0.0406500i
$349$	−5.55112	+	17.0846i	−0.297145	+	0.914517i	0.685348	+	0.728216i	$0.259650\pi$
$349$	−5.55112	+	17.0846i	−0.297145	+	0.914517i	−0.982493	+	0.186301i	$0.940350\pi$
$350$	−4.64675	−	8.47827i	−0.248379	−	0.453183i
$351$		−	11.6757i		−	0.623205i
$352$		0			0
$353$	27.2798	−	15.7500i	1.45195	−	0.838287i	0.453362	−	0.891326i	$-0.350224\pi$
$353$	27.2798	−	15.7500i	1.45195	−	0.838287i	0.998592	+	0.0530398i	$0.0168910\pi$
$354$	−11.6929	−	1.22898i	−0.621472	−	0.0653194i
$355$	−0.412193	+	0.371140i	−0.0218769	+	0.0196981i
$356$	−18.8376	+	6.12071i	−0.998391	+	0.324397i
$357$	−4.55957	+	13.0392i	−0.241318	+	0.690107i
$358$	−1.15694	−	1.59239i	−0.0611460	−	0.0841602i
$359$	−3.46412	+	16.2974i	−0.182829	+	0.860144i	0.787113	+	0.616809i	$0.211575\pi$
$359$	−3.46412	+	16.2974i	−0.182829	+	0.860144i	−0.969942	+	0.243335i	$0.921758\pi$
$360$	−0.625264	+	0.132904i	−0.0329543	+	0.00700466i
$361$	−1.96052	+	18.6531i	−0.103185	+	0.981741i
$362$	2.45975	−	4.26040i	0.129281	−	0.223922i
$363$		0			0
$364$	8.25370	−	0.682372i	0.432611	−	0.0357660i
$365$	−0.327578	+	0.450873i	−0.0171462	+	0.0235998i
$366$	−3.98145	−	4.42185i	−0.208114	−	0.231134i
$367$	12.2148	+	10.9982i	0.637607	+	0.574104i	0.923234	−	0.384237i	$-0.125535\pi$
$367$	12.2148	+	10.9982i	0.637607	+	0.574104i	−0.285628	+	0.958341i	$0.592202\pi$
$368$	2.31727	+	1.03172i	0.120796	+	0.0537819i
$369$	1.07104	+	10.1903i	0.0557560	+	0.530483i
$370$	−0.247912	−	0.762995i	−0.0128883	−	0.0396662i
$371$	0.194535	−	0.824622i	0.0100997	−	0.0428122i
$372$	5.97177	+	4.33875i	0.309622	+	0.224953i
$373$	−18.7583	−	10.8301i	−0.971270	−	0.560763i	−0.0716470	−	0.997430i	$-0.522826\pi$
$373$	−18.7583	−	10.8301i	−0.971270	−	0.560763i	−0.899623	+	0.436667i	$0.856159\pi$
$374$		0			0
$375$	−0.933463	−	1.61680i	−0.0482038	−	0.0834914i
$376$	8.62763	−	3.84127i	0.444936	−	0.198098i
$377$	4.29232	+	1.39466i	0.221066	+	0.0718286i
$378$	6.41144	−	8.42419i	0.329769	−	0.433294i
$379$	−20.3745	+	14.8029i	−1.04657	+	0.760375i	−0.971557	−	0.236808i	$-0.923899\pi$
$379$	−20.3745	+	14.8029i	−1.04657	+	0.760375i	−0.0750099	+	0.997183i	$0.523899\pi$
$380$	−1.40852	+	0.148041i	−0.0722553	+	0.00759434i
$381$	16.6369	−	18.4772i	0.852336	−	0.946616i
$382$	3.72670	+	17.5328i	0.190675	+	0.897054i
$383$	8.43284	+	18.9405i	0.430898	+	0.967813i	0.990304	+	0.138919i	$0.0443628\pi$
$383$	8.43284	+	18.9405i	0.430898	+	0.967813i	−0.559405	+	0.828894i	$0.688971\pi$
$384$	−11.9822			−0.611466
$385$		0			0
$386$	−6.51886			−0.331801
$387$	−4.52971	−	10.1739i	−0.230258	−	0.517169i
$388$	1.08034	+	5.08260i	0.0548460	+	0.258030i
$389$	−17.2436	+	19.1510i	−0.874288	+	0.970995i	−0.999777	−	0.0211001i	$-0.993283\pi$
$389$	−17.2436	+	19.1510i	−0.874288	+	0.970995i	0.125490	+	0.992095i	$0.459950\pi$
$390$	−0.293018	+	0.0307974i	−0.0148375	+	0.00155949i
$391$	8.57083	−	6.22707i	0.433446	−	0.314917i
$392$	14.9979	+	9.57226i	0.757508	+	0.483472i
$393$	18.6178	+	6.04930i	0.939145	+	0.305147i
$394$	−9.79359	+	4.36039i	−0.493394	+	0.219673i
$395$	0.119051	+	0.206203i	0.00599012	+	0.0103752i
$396$		0			0
$397$	−23.5045	−	13.5703i	−1.17966	−	0.681074i	−0.223721	−	0.974653i	$-0.571820\pi$
$397$	−23.5045	−	13.5703i	−1.17966	−	0.681074i	−0.955935	+	0.293579i	$0.905154\pi$
$398$	13.4987	+	9.80739i	0.676629	+	0.491600i
$399$	13.2159	−	14.0372i	0.661623	−	0.702740i
$400$	1.62054	+	4.98750i	0.0810269	+	0.249375i
$401$	2.12189	+	20.1884i	0.105962	+	1.00816i	0.910289	+	0.413973i	$0.135859\pi$
$401$	2.12189	+	20.1884i	0.105962	+	1.00816i	−0.804327	+	0.594187i	$0.797474\pi$
$402$	2.11263	+	0.940603i	0.105368	+	0.0469130i
$403$	−6.78788	−	6.11183i	−0.338128	−	0.304452i
$404$	13.8105	+	15.3382i	0.687100	+	0.763102i
$405$	0.155819	−	0.214466i	0.00774270	−	0.0106569i
$406$	2.33112	+	3.36328i	0.115692	+	0.166917i
$407$		0			0
$408$	−6.63521	+	11.4925i	−0.328492	+	0.568965i
$409$	2.08964	−	19.8816i	0.103326	−	0.983083i	−0.812895	−	0.582410i	$-0.802110\pi$
$409$	2.08964	−	19.8816i	0.103326	−	0.983083i	0.916221	−	0.400673i	$-0.131224\pi$
$410$	0.729033	−	0.154961i	0.0360044	−	0.00765297i
$411$	−2.55183	+	12.0054i	−0.125873	+	0.592184i
$412$	13.8690	+	19.0890i	0.683275	+	0.940448i
$413$	−23.2997	−	27.0634i	−1.14650	−	1.33170i
$414$	−2.67883	+	0.870405i	−0.131657	+	0.0427781i
$415$	1.11314	−	1.00227i	0.0546417	−	0.0491996i
$416$	12.4859	+	1.31232i	0.612171	+	0.0643418i
$417$	16.6603	−	9.61885i	0.815860	−	0.471037i
$418$		0			0
$419$		−	0.494451i		−	0.0241555i	−0.999927	−	0.0120778i	$-0.996155\pi$
$419$		−	0.494451i		−	0.0241555i	0.999927	−	0.0120778i	$-0.00384456\pi$
$420$	0.618121	+	0.375437i	0.0301612	+	0.0183195i
$421$	−7.10649	+	21.8715i	−0.346349	+	1.06595i	0.614509	+	0.788910i	$0.289354\pi$
$421$	−7.10649	+	21.8715i	−0.346349	+	1.06595i	−0.960858	+	0.277043i	$0.910646\pi$
$422$	−2.79438	−	0.593963i	−0.136028	−	0.0289137i
$423$	2.40833	−	5.40919i	0.117097	−	0.263004i
$424$	0.331065	−	0.743583i	0.0160779	−	0.0361116i
$425$	21.4239	+	4.55380i	1.03921	+	0.220892i
$426$	0.946037	−	2.91160i	0.0458357	−	0.141068i
$427$	0.401776	−	18.0685i	0.0194433	−	0.874394i
$428$		−	0.837533i		−	0.0404837i
$429$		0			0
$430$	−0.701553	+	0.405042i	−0.0338319	+	0.0195329i
$431$	25.1363	+	2.64193i	1.21077	+	0.127257i	0.688318	−	0.725409i	$-0.258349\pi$
$431$	25.1363	+	2.64193i	1.21077	+	0.127257i	0.522456	+	0.852667i	$0.325016\pi$
$432$	−4.26734	+	3.84233i	−0.205313	+	0.184864i
$433$	5.07195	−	1.64798i	0.243743	−	0.0791967i	−0.184598	−	0.982814i	$-0.559098\pi$
$433$	5.07195	−	1.64798i	0.243743	−	0.0791967i	0.428341	+	0.903617i	$0.359098\pi$
$434$	−1.54138	−	8.13715i	−0.0739886	−	0.390596i
$435$	0.231653	+	0.318844i	0.0111069	+	0.0152874i
$436$	−4.09419	+	19.2617i	−0.196076	+	0.922466i
$437$	−14.4633	+	3.07427i	−0.691874	+	0.147062i
$438$	0.321536	−	3.05921i	0.0153636	−	0.146175i
$439$	11.1143	−	19.2506i	0.530457	−	0.918779i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	11.1143	−	19.2506i	0.530457	−	0.918779i	0.999368	−	0.0355336i	$-0.0113131\pi$
$440$		0			0
$441$	11.0036	−	1.83196i	0.523981	−	0.0872362i
$442$	4.07363	−	5.60688i	0.193763	−	0.266692i
$443$	15.9877	+	17.7561i	0.759597	+	0.843617i	0.991633	−	0.129090i	$-0.0412055\pi$
$443$	15.9877	+	17.7561i	0.759597	+	0.843617i	−0.232036	+	0.972707i	$0.574539\pi$
$444$	−8.90848	−	8.02123i	−0.422778	−	0.380671i
$445$	1.95524	+	0.870527i	0.0926871	+	0.0412669i
$446$	−1.49156	−	14.1912i	−0.0706273	−	0.671974i
$447$	6.03238	+	18.5658i	0.285322	+	0.878131i
$448$	4.22706	+	3.97974i	0.199710	+	0.188025i
$449$	−16.6818	−	12.1200i	−0.787263	−	0.571980i	0.119887	−	0.992788i	$-0.461747\pi$
$449$	−16.6818	−	12.1200i	−0.787263	−	0.571980i	−0.907150	+	0.420808i	$0.861747\pi$
$450$	−5.04312	−	2.91165i	−0.237735	−	0.137256i
$451$		0			0
$452$	−3.83269	−	6.63841i	−0.180274	−	0.312244i
$453$	−10.1761	+	4.53070i	−0.478116	+	0.212871i
$454$	−10.1628	−	3.30209i	−0.476964	−	0.154975i
$455$	−0.712121	−	0.541977i	−0.0333847	−	0.0254083i
$456$	14.9844	−	10.8868i	0.701711	−	0.509823i
$457$	1.06687	−	0.112132i	0.0499060	−	0.00524534i	−0.0795425	−	0.996831i	$-0.525346\pi$
$457$	1.06687	−	0.112132i	0.0499060	−	0.00524534i	0.129449	+	0.991586i	$0.458679\pi$
$458$	−1.76977	+	1.96553i	−0.0826961	+	0.0918433i
$459$	4.98634	+	23.4589i	0.232742	+	1.09497i
$460$	−0.225601	−	0.506707i	−0.0105187	−	0.0236253i
$461$	10.8005			0.503032			0.251516	−	0.967853i	$-0.419071\pi$
$461$	10.8005			0.503032			0.251516	+	0.967853i	$0.419071\pi$
$462$		0			0
$463$	−3.80564			−0.176863			−0.0884316	−	0.996082i	$-0.528185\pi$
$463$	−3.80564			−0.176863			−0.0884316	+	0.996082i	$0.528185\pi$
$464$	−0.902815	−	2.02776i	−0.0419121	−	0.0941362i
$465$	−0.165834	−	0.780188i	−0.00769037	−	0.0361804i
$466$	−7.50324	+	8.33319i	−0.347581	+	0.386028i
$467$	−1.51422	+	0.159151i	−0.0700697	+	0.00736463i	−0.139498	−	0.990222i	$-0.544549\pi$
$467$	−1.51422	+	0.159151i	−0.0700697	+	0.00736463i	0.0694287	+	0.997587i	$0.477882\pi$
$468$	4.03562	−	2.93205i	0.186546	−	0.135534i
$469$	2.71360	+	6.47876i	0.125302	+	0.299161i
$470$	−0.409620	−	0.133093i	−0.0188943	−	0.00613915i
$471$	1.37707	−	0.613112i	0.0634521	−	0.0282507i
$472$	−17.1538	−	29.7113i	−0.789569	−	1.36757i
$473$		0			0
$474$	−1.13814	−	0.657103i	−0.0522763	−	0.0301817i
$475$	−24.7315	−	17.9685i	−1.13476	−	0.824452i
$476$	−16.2919	+	4.89591i	−0.746737	+	0.224404i
$477$	−0.157697	−	0.485340i	−0.00722043	−	0.0222222i
$478$	−0.460291	−	4.37937i	−0.0210532	−	0.200308i
$479$	−3.33197	−	1.48349i	−0.152242	−	0.0677823i	0.329201	−	0.944260i	$-0.393220\pi$
$479$	−3.33197	−	1.48349i	−0.152242	−	0.0677823i	−0.481443	+	0.876477i	$0.659887\pi$
$480$	0.814729	+	0.733585i	0.0371871	+	0.0334834i
$481$	9.92558	+	11.0235i	0.452568	+	0.502627i
$482$	−1.77087	+	2.43740i	−0.0806611	+	0.111020i
$483$	6.82779	+	3.22367i	0.310675	+	0.146682i
$484$		0			0
$485$	0.280738	−	0.486253i	0.0127477	−	0.0220796i
$486$	1.10181	−	10.4830i	0.0499791	−	0.475519i
$487$	25.6191	−	5.44550i	1.16091	−	0.246759i	0.413110	−	0.910681i	$-0.364443\pi$
$487$	25.6191	−	5.44550i	1.16091	−	0.246759i	0.747802	+	0.663922i	$0.231109\pi$
$488$	3.60987	−	16.9831i	0.163411	−	0.768789i
$489$	−10.5314	−	14.4953i	−0.476249	−	0.655500i
$490$	−0.216191	−	0.782086i	−0.00976652	−	0.0353311i
$491$	−9.16179	+	2.97685i	−0.413466	+	0.134343i	−0.508361	−	0.861144i	$-0.669748\pi$
$491$	−9.16179	+	2.97685i	−0.413466	+	0.134343i	0.0948951	+	0.995487i	$0.469748\pi$
$492$	8.27620	−	7.45192i	0.373120	−	0.335959i
$493$	−9.21973	−	0.969033i	−0.415236	−	0.0436431i
$494$	−8.37707	+	4.83650i	−0.376902	+	0.217605i
$495$		0			0
$496$			4.49221i			0.201706i
$497$	8.15430	−	4.46919i	0.365771	−	0.200471i
$498$	−2.55480	+	7.86286i	−0.114483	+	0.352343i
$499$	6.51686	+	1.38520i	0.291735	+	0.0620101i	0.351454	−	0.936205i	$-0.385687\pi$
$499$	6.51686	+	1.38520i	0.291735	+	0.0620101i	−0.0597196	+	0.998215i	$0.519021\pi$
$500$	0.935159	−	2.10040i	0.0418216	−	0.0939329i
$501$	6.00643	−	13.4907i	0.268347	−	0.602718i
$502$	−5.02367	−	1.06781i	−0.224217	−	0.0476588i
$503$	8.25742	−	25.4137i	0.368180	−	1.13314i	−0.579785	−	0.814769i	$-0.696864\pi$
$503$	8.25742	−	25.4137i	0.368180	−	1.13314i	0.947966	−	0.318373i	$-0.103136\pi$
$504$	10.7139	+	0.238238i	0.477236	+	0.0106120i
$505$		−	2.23023i		−	0.0992438i
$506$		0			0
$507$	−8.63375	+	4.98470i	−0.383438	+	0.221378i
$508$	30.4525	+	3.20068i	1.35111	+	0.142007i
$509$	0.491916	−	0.442923i	0.0218038	−	0.0196322i	−0.658157	−	0.752881i	$-0.728664\pi$
$509$	0.491916	−	0.442923i	0.0218038	−	0.0196322i	0.679961	+	0.733249i	$0.261997\pi$
$510$	0.575578	−	0.187017i	0.0254870	−	0.00828123i
$511$	7.08058	−	6.09589i	0.313226	−	0.269666i
$512$	−6.77892	−	9.33038i	−0.299589	−	0.412349i
$513$	6.95953	−	32.7420i	0.307271	−	1.44559i
$514$	−14.2675	+	3.03266i	−0.629314	+	0.133765i
$515$	0.266508	−	2.53565i	0.0117437	−	0.111734i
$516$	−6.05222	+	10.4827i	−0.266434	+	0.461477i
$517$		0			0
$518$	1.10817	+	13.4040i	0.0486901	+	0.588936i
$519$	−14.2628	+	19.6311i	−0.626068	+	0.861708i
$520$	−0.575271	−	0.638903i	−0.0252273	−	0.0280177i
$521$	−5.09465	−	4.58724i	−0.223201	−	0.200971i	0.549942	−	0.835203i	$-0.314650\pi$
$521$	−5.09465	−	4.58724i	−0.223201	−	0.200971i	−0.773143	+	0.634232i	$0.781316\pi$
$522$	2.25169	+	1.00252i	0.0985536	+	0.0438789i
$523$	1.01765	+	9.68227i	0.0444986	+	0.423376i	0.993981	+	0.109555i	$0.0349426\pi$
$523$	1.01765	+	9.68227i	0.0444986	+	0.423376i	−0.949482	+	0.313821i	$0.898391\pi$
$524$	7.44990	+	22.9284i	0.325450	+	1.00163i
$525$	4.49258	+	14.9497i	0.196072	+	0.652460i
$526$	3.81198	+	2.76957i	0.166210	+	0.120759i
$527$	16.2484	+	9.38099i	0.707789	+	0.408642i
$528$		0			0
$529$	8.60457	+	14.9036i	0.374112	+	0.647981i
$530$	−0.0339112	+	0.0150982i	−0.00147301	+	0.000655825i
$531$	−20.4568	−	6.64682i	−0.887749	−	0.288447i
$532$	23.5524	+	3.00620i	1.02113	+	0.130335i
$533$	−11.1489	+	8.10011i	−0.482910	+	0.350855i
$534$	−11.7485	+	1.23482i	−0.508407	+	0.0534357i
$535$	−0.0605567	+	0.0672551i	−0.00261810	+	0.00290769i
$536$	1.40299	+	6.60054i	0.0605998	+	0.285100i
$537$	1.29261	+	2.90325i	0.0557803	+	0.125285i
$538$	14.2477			0.614262
$539$		0			0
$540$	1.25564			0.0540340
$541$	−6.08809	−	13.6741i	−0.261748	−	0.587895i	0.734089	−	0.679053i	$-0.237610\pi$
$541$	−6.08809	−	13.6741i	−0.261748	−	0.587895i	−0.995836	+	0.0911589i	$0.970943\pi$
$542$	−1.75183	−	8.24171i	−0.0752475	−	0.354012i
$543$	−5.31490	+	5.90279i	−0.228084	+	0.253313i
$544$	−25.6471	+	2.69562i	−1.09961	+	0.115574i
$545$	1.72146	−	1.25071i	0.0737391	−	0.0535746i
$546$	4.89967	+	0.625388i	0.209687	+	0.0267641i
$547$	5.15639	+	1.67541i	0.220471	+	0.0716354i	0.417170	−	0.908829i	$-0.363022\pi$
$547$	5.15639	+	1.67541i	0.220471	+	0.0716354i	−0.196699	+	0.980464i	$0.563022\pi$
$548$	−13.8086	+	6.14797i	−0.589873	+	0.262628i
$549$	−5.44281	−	9.42722i	−0.232293	−	0.402344i
$550$		0			0
$551$	11.2055	+	6.46952i	0.477372	+	0.275611i
$552$	5.86840	+	4.26365i	0.249776	+	0.181473i
$553$	−1.14881	−	3.82284i	−0.0488524	−	0.162564i
$554$	−1.07290	−	3.30204i	−0.0455831	−	0.140290i
$555$	0.135399	+	1.28823i	0.00574735	+	0.0546824i
$556$	21.6436	+	9.63633i	0.917891	+	0.408671i
$557$	−18.8714	−	16.9919i	−0.799606	−	0.719968i	0.164242	−	0.986420i	$-0.447482\pi$
$557$	−18.8714	−	16.9919i	−0.799606	−	0.719968i	−0.963848	+	0.266452i	$0.914149\pi$
$558$	−3.33782	−	3.70703i	−0.141301	−	0.156931i
$559$	8.80396	−	12.1176i	0.372368	−	0.512520i
$560$	0.0362635	+	0.438629i	0.00153241	+	0.0185355i
$561$		0			0
$562$	7.77928	−	13.4741i	0.328149	−	0.568371i
$563$	−1.55611	+	14.8054i	−0.0655821	+	0.623972i	0.911528	+	0.411238i	$0.134904\pi$
$563$	−1.55611	+	14.8054i	−0.0655821	+	0.623972i	−0.977110	+	0.212734i	$0.931763\pi$
$564$	−6.29497	+	1.33804i	−0.265066	+	0.0563415i
$565$	−0.172211	+	0.810190i	−0.00724498	+	0.0340850i
$566$	12.5052	+	17.2119i	0.525633	+	0.723472i
$567$	−3.36801	+	2.89962i	−0.141443	+	0.121773i
$568$	8.49599	−	2.76052i	0.356484	−	0.115829i
$569$	−25.0703	+	22.5734i	−1.05100	+	0.946326i	−0.998631	−	0.0523018i	$-0.983344\pi$
$569$	−25.0703	+	22.5734i	−1.05100	+	0.946326i	−0.0523701	+	0.998628i	$0.516678\pi$
$570$	−0.840060	−	0.0882938i	−0.0351862	−	0.00369822i
$571$	10.0725	−	5.81536i	0.421521	−	0.243365i	−0.274207	−	0.961671i	$-0.588415\pi$
$571$	10.0725	−	5.81536i	0.421521	−	0.243365i	0.695728	+	0.718305i	$0.255082\pi$
$572$		0			0
$573$		−	28.9407i		−	1.20902i
$574$	−12.4920	−	0.277776i	−0.521406	−	0.0115941i
$575$	3.69960	−	11.3862i	0.154284	−	0.474838i
$576$	3.42047	+	0.727042i	0.142519	+	0.0302934i
$577$	6.50528	−	14.6111i	0.270818	−	0.608268i	−0.726024	−	0.687669i	$-0.758634\pi$
$577$	6.50528	−	14.6111i	0.270818	−	0.608268i	0.996843	+	0.0794010i	$0.0253008\pi$
$578$	−0.711476	+	1.59800i	−0.0295935	+	0.0664681i
$579$	10.2953	+	2.18834i	0.427859	+	0.0909442i
$580$	−0.149985	+	0.461606i	−0.00622779	+	0.0191672i
$581$	−22.0209	+	12.0692i	−0.913581	+	0.500713i
$582$			3.09906i			0.128460i
$583$		0			0
$584$	7.77335	−	4.48794i	0.321663	−	0.185712i
$585$	−0.536063	−	0.0563425i	−0.0221635	−	0.00232948i
$586$	5.12586	−	4.61535i	0.211747	−	0.190658i
$587$	21.6657	−	7.03960i	0.894237	−	0.290555i	0.174381	−	0.984678i	$-0.444208\pi$
$587$	21.6657	−	7.03960i	0.894237	−	0.290555i	0.719856	+	0.694123i	$0.244208\pi$
$588$	−8.64063	−	8.50527i	−0.356334	−	0.350751i
$589$	−15.3920	−	21.1853i	−0.634217	−	0.872925i
$590$	−0.325299	+	1.53041i	−0.0133923	+	0.0630060i
$591$	16.9309	−	3.59877i	0.696444	−	0.148034i
$592$	0.762569	−	7.25536i	0.0313414	−	0.298194i
$593$	13.2417	−	22.9354i	0.543773	−	0.941842i	−0.454910	−	0.890537i	$-0.650329\pi$
$593$	13.2417	−	22.9354i	0.543773	−	0.941842i	0.998683	−	0.0513049i	$-0.0163380\pi$
$594$		0			0
$595$	1.66225	+	0.784815i	0.0681457	+	0.0321743i
$596$	−14.1309	+	19.4496i	−0.578825	+	0.796685i
$597$	−18.0264	−	20.0204i	−0.737772	−	0.819379i
$598$	−2.81523	−	2.53485i	−0.115123	−	0.103658i
$599$	8.65878	+	3.85514i	0.353788	+	0.157517i	0.575933	−	0.817497i	$-0.304639\pi$
$599$	8.65878	+	3.85514i	0.353788	+	0.157517i	−0.222145	+	0.975014i	$0.571306\pi$
$600$	1.56757	+	14.9144i	0.0639957	+	0.608879i
$601$	−13.3729	−	41.1575i	−0.545491	−	1.67885i	−0.719819	−	0.694162i	$-0.755775\pi$
$601$	−13.3729	−	41.1575i	−0.545491	−	1.67885i	0.174328	−	0.984688i	$-0.444225\pi$
$602$	13.0062	−	3.90854i	0.530095	−	0.159300i
$603$	3.42273	+	2.48676i	0.139384	+	0.101269i
$604$	−11.8803	−	6.85910i	−0.483403	−	0.279093i
$605$		0			0
$606$	6.15486	+	10.6605i	0.250024	+	0.433054i
$607$	−1.95797	+	0.871744i	−0.0794715	+	0.0353830i	−0.446087	−	0.894989i	$-0.647183\pi$
$607$	−1.95797	+	0.871744i	−0.0794715	+	0.0353830i	0.366616	+	0.930372i	$0.380516\pi$
$608$	34.2317	+	11.1225i	1.38828	+	0.451079i
$609$	−2.55254	−	6.09422i	−0.103434	−	0.246950i
$610$	−0.640594	+	0.465419i	−0.0259369	+	0.0188443i
$611$	7.91987	−	0.832412i	0.320404	−	0.0336758i
$612$	−6.85617	+	7.61455i	−0.277144	+	0.307800i
$613$	−7.17430	−	33.7525i	−0.289767	−	1.36325i	−0.846426	−	0.532507i	$-0.821250\pi$
$613$	−7.17430	−	33.7525i	−0.289767	−	1.36325i	0.556658	−	0.830742i	$-0.312083\pi$
$614$	1.12613	+	2.52933i	0.0454469	+	0.102075i
$615$	−1.20339			−0.0485254
$616$		0			0
$617$	−19.3537			−0.779150			−0.389575	−	0.920995i	$-0.627378\pi$
$617$	−19.3537			−0.779150			−0.389575	+	0.920995i	$0.627378\pi$
$618$	5.72384	+	12.8560i	0.230247	+	0.517142i
$619$	−0.274777	−	1.29273i	−0.0110442	−	0.0519590i	0.972280	−	0.233818i	$-0.0751219\pi$
$619$	−0.274777	−	1.29273i	−0.0110442	−	0.0519590i	−0.983325	+	0.181859i	$0.941789\pi$
$620$	0.657281	−	0.729985i	0.0263970	−	0.0293169i
$621$	13.0375	−	1.37030i	0.523177	−	0.0549882i
$622$	5.13367	−	3.72983i	0.205841	−	0.149552i
$623$	−28.5524	−	21.7305i	−1.14393	−	0.870613i
$624$	−2.54809	−	0.827925i	−0.102005	−	0.0331435i
$625$	22.4979	−	10.0167i	0.899916	−	0.400669i
$626$	3.85557	+	6.67805i	0.154100	+	0.266908i
$627$		0			0
$628$	1.60769	+	0.928200i	0.0641538	+	0.0370392i
$629$	−24.6502	−	17.9094i	−0.982869	−	0.714096i
$630$	−0.355837	−	0.335017i	−0.0141769	−	0.0133474i
$631$	−6.96406	−	21.4332i	−0.277235	−	0.853241i	−0.988619	−	0.150438i	$-0.951931\pi$
$631$	−6.96406	−	21.4332i	−0.277235	−	0.853241i	0.711384	−	0.702803i	$-0.248069\pi$
$632$	−0.400848	−	3.81381i	−0.0159449	−	0.151705i
$633$	4.21380	+	1.87611i	0.167484	+	0.0745685i
$634$	12.7098	+	11.4440i	0.504772	+	0.454499i
$635$	−2.21395	−	2.45884i	−0.0878580	−	0.0975762i
$636$	−0.326021	+	0.448729i	−0.0129276	+	0.0177933i
$637$	9.53335	+	11.5845i	0.377725	+	0.458995i
$638$		0			0
$639$	2.80039	−	4.85041i	0.110782	−	0.191879i
$640$	−0.166674	+	1.58580i	−0.00658836	+	0.0626841i
$641$	−30.8586	+	6.55921i	−1.21884	+	0.259073i	−0.772049	−	0.635564i	$-0.780768\pi$
$641$	−30.8586	+	6.55921i	−1.21884	+	0.259073i	−0.446794	+	0.894637i	$0.647434\pi$
$642$	0.103855	−	0.488602i	0.00409885	−	0.0192836i
$643$	−18.7211	−	25.7673i	−0.738287	−	1.01616i	−0.998715	−	0.0506715i	$-0.983864\pi$
$643$	−18.7211	−	25.7673i	−0.738287	−	1.01616i	0.260429	−	0.965493i	$-0.416136\pi$
$644$	1.73064	+	9.13626i	0.0681966	+	0.360019i
$645$	1.24394	−	0.404181i	0.0489802	−	0.0159146i
$646$	14.7657	−	13.2951i	0.580947	−	0.523087i
$647$	28.6473	+	3.01095i	1.12624	+	0.118373i	0.649278	−	0.760551i	$-0.275071\pi$
$647$	28.6473	+	3.01095i	1.12624	+	0.118373i	0.476962	+	0.878924i	$0.341738\pi$
$648$	−3.69754	+	2.13478i	−0.145253	+	0.0838619i
$649$		0			0
$650$		−	7.83196i		−	0.307195i
$651$	−0.297267	+	13.3685i	−0.0116508	+	0.523955i
$652$	6.81863	−	20.9856i	0.267038	−	0.821859i
$653$	3.76796	+	0.800905i	0.147452	+	0.0313418i	0.281046	−	0.959694i	$-0.409319\pi$
$653$	3.76796	+	0.800905i	0.147452	+	0.0313418i	−0.133594	+	0.991036i	$0.542652\pi$
$654$	−4.77695	+	10.7292i	−0.186794	+	0.419545i
$655$	1.05957	−	2.37984i	0.0414009	−	0.0929880i
$656$	6.62944	+	1.40913i	0.258836	+	0.0550173i
$657$	1.73900	−	5.35210i	0.0678449	−	0.208805i
$658$	6.17139	+	3.74840i	0.240586	+	0.146128i
$659$			20.3920i			0.794361i	0.917741	+	0.397180i	$0.130011\pi$
$659$			20.3920i			0.794361i	−0.917741	+	0.397180i	$0.869989\pi$
$660$		0			0
$661$	−23.7738	+	13.7258i	−0.924695	+	0.533873i	−0.885130	−	0.465344i	$-0.845931\pi$
$661$	−23.7738	+	13.7258i	−0.924695	+	0.533873i	−0.0395649	+	0.999217i	$0.512597\pi$
$662$	−11.9034	−	1.25110i	−0.462639	−	0.0486253i
$663$	−8.31573	+	7.48752i	−0.322956	+	0.290791i
$664$	−22.9436	+	7.45484i	−0.890386	+	0.289304i
$665$	−1.67393	−	1.94433i	−0.0649122	−	0.0753977i
$666$	4.76163	+	6.55382i	0.184509	+	0.253955i
$667$	−1.05356	+	4.95663i	−0.0407941	+	0.191921i
$668$	17.7891	−	3.78118i	0.688279	−	0.146298i
$669$	−2.40826	+	22.9131i	−0.0931088	+	0.885871i
$670$	0.153871	−	0.266513i	0.00594457	−	0.0102963i
$671$		0			0
$672$	−10.4700	−	15.1059i	−0.403890	−	0.582723i
$673$	10.9460	−	15.0658i	0.421935	−	0.580744i	−0.544143	−	0.838992i	$-0.683145\pi$
$673$	10.9460	−	15.0658i	0.421935	−	0.580744i	0.966079	+	0.258248i	$0.0831452\pi$
$674$	8.45109	+	9.38589i	0.325524	+	0.361531i
$675$	20.1411	+	18.1351i	0.775232	+	0.698022i
$676$	−11.2162	−	4.99376i	−0.431391	−	0.192068i
$677$	−0.0507341	−	0.482703i	−0.00194987	−	0.0185518i	0.993504	−	0.113800i	$-0.0363022\pi$
$677$	−0.0507341	−	0.482703i	−0.00194987	−	0.0185518i	−0.995454	+	0.0952480i	$0.969636\pi$
$678$	−1.41275	−	4.34798i	−0.0542562	−	0.166983i
$679$	−6.45248	+	6.85347i	−0.247623	+	0.263012i
$680$	1.42869	+	1.03800i	0.0547876	+	0.0398056i
$681$	14.9418	+	8.62663i	0.572569	+	0.330573i
$682$		0			0
$683$	0.275482	+	0.477149i	0.0105410	+	0.0182576i	0.871248	−	0.490843i	$-0.163311\pi$
$683$	0.275482	+	0.477149i	0.0105410	+	0.0182576i	−0.860707	+	0.509101i	$0.829978\pi$
$684$	13.0647	−	5.81677i	0.499541	−	0.222410i
$685$	1.55337	+	0.504720i	0.0593511	+	0.0192844i
$686$	0.517094	+	13.5934i	0.0197427	+	0.518997i
$687$	3.45484	−	2.51009i	0.131810	−	0.0957659i
$688$	−7.32611	+	0.770005i	−0.279305	+	0.0293562i
$689$	0.459254	−	0.510053i	0.0174962	−	0.0194315i
$690$	−0.0687787	−	0.323579i	−0.00261836	−	0.0123184i
$691$	−6.43716	−	14.4581i	−0.244881	−	0.550012i	0.748729	−	0.662876i	$-0.230664\pi$
$691$	−6.43716	−	14.4581i	−0.244881	−	0.550012i	−0.993610	+	0.112864i	$0.963998\pi$
$692$	−29.8835			−1.13600
$693$		0			0
$694$	2.18716			0.0830234
$695$	−1.04126	−	2.33872i	−0.0394974	−	0.0887126i
$696$	−1.31971	−	6.20877i	−0.0500236	−	0.235343i
$697$	18.9409	−	21.0360i	0.717439	−	0.796797i
$698$	−13.1222	+	1.37920i	−0.496682	+	0.0522034i
$699$	14.6474	−	10.6419i	0.554014	−	0.402515i
$700$	−11.6428	+	15.2978i	−0.440056	+	0.578204i
$701$	−39.6978	−	12.8986i	−1.49937	−	0.487174i	−0.559534	−	0.828808i	$-0.689020\pi$
$701$	−39.6978	−	12.8986i	−1.49937	−	0.487174i	−0.939833	+	0.341634i	$0.889020\pi$
$702$	7.83445	−	3.48812i	0.295692	−	0.131651i
$703$	21.2633	+	36.8292i	0.801962	+	1.38904i
$704$		0			0
$705$	0.602239	+	0.347703i	0.0226816	+	0.0130952i
$706$	18.7181	+	13.5995i	0.704464	+	0.511823i
$707$	−8.58475	+	36.3903i	−0.322863	+	1.36860i
$708$	7.22438	+	22.2344i	0.271509	+	0.835618i
$709$	−1.70867	−	16.2569i	−0.0641706	−	0.610542i	−0.978596	−	0.205789i	$-0.934024\pi$
$709$	−1.70867	−	16.2569i	−0.0641706	−	0.610542i	0.914426	−	0.404753i	$-0.132643\pi$
$710$	−0.372178	−	0.165704i	−0.0139676	−	0.00621877i
$711$	−1.78673	−	1.60878i	−0.0670076	−	0.0603340i
$712$	−23.0654	−	25.6167i	−0.864412	−	0.960026i
$713$	6.02803	−	8.29687i	0.225751	−	0.310720i
$714$	−10.1115	+	0.835964i	−0.378413	+	0.0312852i
$715$		0			0
$716$	−1.95691	+	3.38946i	−0.0731330	+	0.126670i
$717$	−0.743183	+	7.07092i	−0.0277547	+	0.264068i
$718$	−11.9705	+	2.54441i	−0.446735	+	0.0949565i
$719$	−0.657195	+	3.09186i	−0.0245092	+	0.115307i	−0.988702	−	0.149897i	$-0.952106\pi$
$719$	−0.657195	+	3.09186i	−0.0245092	+	0.115307i	0.964192	+	0.265204i	$0.0854392\pi$
$720$	0.155819	+	0.214466i	0.00580703	+	0.00799269i
$721$	−14.1090	+	40.3480i	−0.525446	+	1.50264i
$722$	−13.1020	+	4.25709i	−0.487605	+	0.158432i
$723$	3.61498	−	3.25494i	0.134443	−	0.121053i
$724$	−9.72845	−	1.02250i	−0.361555	−	0.0380010i
$725$	−9.07282	+	5.23819i	−0.336956	+	0.194542i
$726$		0			0
$727$			11.6758i			0.433033i	0.976279	+	0.216516i	$0.0694695\pi$
$727$			11.6758i			0.433033i	−0.976279	+	0.216516i	$0.930531\pi$
$728$	6.92729	+	12.6392i	0.256742	+	0.468442i
$729$	−6.81641	+	20.9787i	−0.252460	+	0.776991i
$730$	−0.400401	−	0.0851078i	−0.0148195	−	0.00314998i
$731$	−12.5139	+	28.1066i	−0.462841	+	1.03956i
$732$	−4.81231	+	10.8086i	−0.177868	+	0.399498i
$733$	−1.90961	−	0.405900i	−0.0705331	−	0.0149923i	0.172510	−	0.985008i	$-0.444812\pi$
$733$	−1.90961	−	0.405900i	−0.0705331	−	0.0149923i	−0.243043	+	0.970016i	$0.578146\pi$
$734$	−3.73068	+	11.4819i	−0.137702	+	0.423803i
$735$	0.0788923	+	1.30773i	0.00290999	+	0.0482365i
$736$			14.0962i			0.519592i
$737$		0			0
$738$	−6.51771	+	3.76300i	−0.239920	+	0.138518i
$739$	−48.4207	−	5.08922i	−1.78118	−	0.187210i	−0.844070	−	0.536233i	$-0.819847\pi$
$739$	−48.4207	−	5.08922i	−1.78118	−	0.187210i	−0.937114	+	0.349023i	$0.886513\pi$
$740$	−1.18549	+	1.06742i	−0.0435795	+	0.0392392i
$741$	14.8536	−	4.82623i	0.545660	−	0.177296i
$742$	0.611440	−	0.115822i	0.0224467	−	0.00425196i
$743$	7.30716	+	10.0574i	0.268074	+	0.368972i	0.921738	−	0.387813i	$-0.126769\pi$
$743$	7.30716	+	10.0574i	0.268074	+	0.368972i	−0.653665	+	0.756784i	$0.726769\pi$
$744$	−2.67088	+	12.5655i	−0.0979193	+	0.460674i
$745$	2.54101	−	0.540108i	0.0930953	−	0.0197880i
$746$	1.66300	−	15.8224i	0.0608867	−	0.579299i
$747$	−7.56252	+	13.0987i	−0.276698	+	0.479255i
$748$		0			0
$749$	1.24698	−	0.864291i	0.0455636	−	0.0315805i
$750$	0.806008	−	1.10938i	0.0294313	−	0.0405087i
$751$	6.54745	+	7.27168i	0.238920	+	0.265347i	0.850666	−	0.525707i	$-0.176199\pi$
$751$	6.54745	+	7.27168i	0.238920	+	0.265347i	−0.611746	+	0.791054i	$0.709532\pi$
$752$	−2.91056	−	2.62068i	−0.106137	−	0.0955665i
$753$	7.57549	+	3.37282i	0.276066	+	0.122913i
$754$	0.346509	+	3.29681i	0.0126191	+	0.120063i
$755$	0.458067	+	1.40979i	0.0166708	+	0.0513073i
$756$	−20.4880	−	4.83329i	−0.745143	−	0.175785i
$757$	−19.5973	−	14.2382i	−0.712274	−	0.517497i	0.171632	−	0.985161i	$-0.445096\pi$
$757$	−19.5973	−	14.2382i	−0.712274	−	0.517497i	−0.883907	+	0.467664i	$0.845096\pi$
$758$	−16.0197	−	9.24895i	−0.581860	−	0.335937i
$759$		0			0
$760$	−1.23239	−	2.13456i	−0.0447034	−	0.0774286i
$761$	36.0963	−	16.0711i	1.30849	−	0.582578i	0.370370	−	0.928884i	$-0.379231\pi$
$761$	36.0963	−	16.0711i	1.30849	−	0.582578i	0.938121	+	0.346307i	$0.112564\pi$
$762$	17.3685	+	5.64337i	0.629195	+	0.204438i
$763$	−32.9031	+	13.7813i	−1.19117	+	0.498917i
$764$	28.8345	−	20.9495i	1.04320	−	0.757926i
$765$	1.10112	−	0.115732i	0.0398110	−	0.00418431i
$766$	−10.1898	+	11.3169i	−0.368172	+	0.408897i
$767$	−6.01468	−	28.2968i	−0.217177	−	1.02174i
$768$	−5.69663	−	12.7948i	−0.205559	−	0.461694i
$769$	−37.5601			−1.35445			−0.677226	−	0.735775i	$-0.736818\pi$
$769$	−37.5601			−1.35445			−0.677226	+	0.735775i	$0.736818\pi$
$770$		0			0
$771$	23.5510			0.848167
$772$	5.27223	+	11.8416i	0.189752	+	0.426189i
$773$	−6.90141	−	32.4686i	−0.248226	−	1.16781i	−0.908859	−	0.417104i	$-0.863045\pi$
$773$	−6.90141	−	32.4686i	−0.248226	−	1.16781i	0.660633	−	0.750709i	$-0.270288\pi$
$774$	5.47346	−	6.07890i	0.196740	−	0.218501i
$775$	21.0863	−	2.21626i	0.757442	−	0.0796104i
$776$	−7.31593	+	5.31534i	−0.262627	+	0.190809i
$777$	2.74947	−	21.5411i	0.0986369	−	0.772781i
$778$	−18.0019	−	5.84917i	−0.645399	−	0.209703i
$779$	−36.0927	+	16.0695i	−1.29315	+	0.575749i
$780$	0.292926	+	0.507364i	0.0104885	+	0.0181665i
$781$		0			0
$782$	6.73891	+	3.89071i	0.240983	+	0.139132i
$783$	−9.28061	−	6.74276i	−0.331662	−	0.240967i
$784$	1.09670	−	7.29663i	0.0391677	−	0.260594i
$785$	−0.0619874	−	0.190778i	−0.00221242	−	0.00680914i
$786$	1.50297	+	14.2998i	0.0536092	+	0.510058i
$787$	22.1730	+	9.87207i	0.790383	+	0.351901i	0.761901	−	0.647693i	$-0.224266\pi$
$787$	22.1730	+	9.87207i	0.790383	+	0.351901i	0.0284818	+	0.999594i	$0.490933\pi$
$788$	15.8414	+	14.2637i	0.564327	+	0.508123i
$789$	−5.09059	−	5.65367i	−0.181230	−	0.201276i
$790$	−0.102796	+	0.141487i	−0.00365732	+	0.00503387i
$791$	5.92859	−	12.5569i	0.210796	−	0.446471i
$792$		0			0
$793$	7.32023	−	12.6790i	0.259949	−	0.450245i
$794$	2.08376	−	19.8257i	0.0739499	−	0.703587i
$795$	0.0586247	−	0.0124611i	0.00207920	−	0.000441948i
$796$	6.89800	−	32.4525i	0.244493	−	1.15025i
$797$	9.42061	+	12.9664i	0.333695	+	0.459292i	0.942587	−	0.333961i	$-0.108386\pi$
$797$	9.42061	+	12.9664i	0.333695	+	0.459292i	−0.608892	+	0.793254i	$0.708386\pi$
$798$	13.3673	+	4.67429i	0.473196	+	0.165468i
$799$	−15.5571	+	5.05481i	−0.550370	+	0.178826i
$800$	−21.6573	+	19.5003i	−0.765701	+	0.689440i
$801$	−21.4934	−	2.25904i	−0.759431	−	0.0798194i
$802$	−12.9125	+	7.45506i	−0.455958	+	0.263247i
$803$		0			0
$804$		−	4.59835i		−	0.162171i
$805$	0.521613	−	0.858785i	0.0183844	−	0.0302682i
$806$	2.07318	−	6.38059i	0.0730246	−	0.224747i
$807$	−22.5016	−	4.78286i	−0.792093	−	0.168365i
$808$	−14.6098	+	32.8141i	−0.513970	+	1.15440i
$809$	−14.2521	+	32.0108i	−0.501079	+	1.12544i	0.469121	+	0.883134i	$0.344571\pi$
$809$	−14.2521	+	32.0108i	−0.501079	+	1.12544i	−0.970200	+	0.242307i	$0.922096\pi$
$810$	0.190458	+	0.0404831i	0.00669202	+	0.00142243i
$811$	0.593494	−	1.82659i	0.0208404	−	0.0641401i	−0.940095	−	0.340911i	$-0.889264\pi$
$811$	0.593494	−	1.82659i	0.0208404	−	0.0641401i	0.960936	+	0.276771i	$0.0892644\pi$
$812$	4.22413	−	6.95463i	0.148238	−	0.244060i
$813$			13.6043i			0.477124i
$814$		0			0
$815$	−2.06488	+	1.19216i	−0.0723296	+	0.0417595i
$816$	5.47320	+	0.575256i	0.191600	+	0.0201380i
$817$	31.9117	−	28.7334i	1.11645	−	1.00525i
$818$	13.9649	−	4.53747i	0.488271	−	0.158649i
$819$	8.52998	+	2.98279i	0.298062	+	0.104227i
$820$	−0.871106	−	1.19897i	−0.0304203	−	0.0418700i
$821$	5.84990	−	27.5216i	0.204163	−	0.960511i	−0.750050	−	0.661382i	$-0.769970\pi$
$821$	5.84990	−	27.5216i	0.204163	−	0.960511i	0.954213	−	0.299130i	$-0.0966963\pi$
$822$	−8.81803	+	1.87433i	−0.307564	+	0.0653747i
$823$	0.133101	−	1.26637i	0.00463961	−	0.0441429i	−0.991957	−	0.126574i	$-0.959602\pi$
$823$	0.133101	−	1.26637i	0.00463961	−	0.0441429i	0.996597	+	0.0824313i	$0.0262685\pi$
$824$	−20.5317	+	35.5620i	−0.715257	+	1.23886i
$825$		0			0
$826$	11.1988	−	23.7193i	0.389657	−	0.825301i
$827$	−8.94706	+	12.3146i	−0.311120	+	0.428220i	−0.935730	−	0.352717i	$-0.885258\pi$
$827$	−8.94706	+	12.3146i	−0.311120	+	0.428220i	0.624610	+	0.780937i	$0.285258\pi$
$828$	3.74765	+	4.16219i	0.130240	+	0.144646i
$829$	1.28167	+	1.15402i	0.0445141	+	0.0400807i	0.691087	−	0.722771i	$-0.257132\pi$
$829$	1.28167	+	1.15402i	0.0445141	+	0.0400807i	−0.646573	+	0.762852i	$0.723799\pi$
$830$	1.00508	+	0.447489i	0.0348867	+	0.0155326i
$831$	0.585969	+	5.57513i	0.0203271	+	0.193399i
$832$	1.45333	+	4.47290i	0.0503852	+	0.155070i
$833$	−24.1018	−	19.2042i	−0.835076	−	0.665385i
$834$	11.4315	+	8.30549i	0.395842	+	0.287596i
$835$	−1.70188	−	0.982580i	−0.0588959	−	0.0340036i
$836$		0			0
$837$	11.6082	+	20.1059i	0.401237	+	0.694963i
$838$	0.331778	−	0.147717i	0.0114611	−	0.00510280i
$839$	−14.9999	−	4.87378i	−0.517856	−	0.168262i	0.0384162	−	0.999262i	$-0.487769\pi$
$839$	−14.9999	−	4.87378i	−0.517856	−	0.168262i	−0.556272	+	0.831000i	$0.687769\pi$
$840$	−0.159355	+	1.24848i	−0.00549827	+	0.0430768i
$841$	−19.8741	+	14.4394i	−0.685314	+	0.497910i
$842$	−16.7989	+	1.76564i	−0.578928	+	0.0608478i
$843$	−16.8091	+	18.6684i	−0.578935	+	0.642973i
$844$	1.18105	+	5.55641i	0.0406534	+	0.191259i
$845$	0.539606	+	1.21197i	0.0185630	+	0.0416932i
$846$	4.34906			0.149524
$847$		0			0
$848$	−0.337553			−0.0115916
$849$	−13.9717	−	31.3810i	−0.479508	−	1.07699i
$850$	3.34478	+	15.7360i	0.114725	+	0.539739i
$851$	−11.1443	+	12.3770i	−0.382021	+	0.424277i
$852$	−6.05410	+	0.636311i	−0.207410	+	0.0217997i
$853$	10.3274	−	7.50329i	0.353603	−	0.256908i	−0.396776	−	0.917916i	$-0.629871\pi$
$853$	10.3274	−	7.50329i	0.353603	−	0.256908i	0.750379	+	0.661008i	$0.229871\pi$
$854$	12.2440	−	5.12835i	0.418981	−	0.175488i
$855$	−1.46969	−	0.477530i	−0.0502622	−	0.0163312i
$856$	1.33157	−	0.592851i	0.0455120	−	0.0202632i
$857$	1.62935	+	2.82212i	0.0556576	+	0.0964017i	0.892512	−	0.451024i	$-0.148941\pi$
$857$	1.62935	+	2.82212i	0.0556576	+	0.0964017i	−0.836854	+	0.547426i	$0.815608\pi$
$858$		0			0
$859$	7.53736	+	4.35170i	0.257171	+	0.148478i	0.623044	−	0.782187i	$-0.285896\pi$
$859$	7.53736	+	4.35170i	0.257171	+	0.148478i	−0.365872	+	0.930665i	$0.619229\pi$
$860$	1.30316	+	0.946799i	0.0444373	+	0.0322856i
$861$	19.6355	+	4.63218i	0.669178	+	0.157864i
$862$	5.73672	+	17.6558i	0.195393	+	0.601359i
$863$	−4.35943	−	41.4772i	−0.148397	−	1.41190i	−0.774705	−	0.632323i	$-0.782101\pi$
$863$	−4.35943	−	41.4772i	−0.148397	−	1.41190i	0.626308	−	0.779576i	$-0.284565\pi$
$864$	−29.1520	−	12.9793i	−0.991772	−	0.441565i
$865$	2.39969	+	2.16069i	0.0815918	+	0.0734656i
$866$	2.62104	+	2.91096i	0.0890666	+	0.0989184i
$867$	1.66008	−	2.28491i	0.0563793	−	0.0775995i
$868$	−13.5347	+	9.38099i	−0.459396	+	0.318412i
$869$		0			0
$870$	−0.144738	+	0.250694i	−0.00490709	+	0.00849933i
$871$	−0.594774	+	5.65890i	−0.0201531	+	0.191744i
$872$	−33.5215	+	7.12522i	−1.13518	+	0.241290i
$873$	−1.17878	+	5.54571i	−0.0398955	+	0.187694i
$874$	−6.38375	−	8.78648i	−0.215934	−	0.297207i
$875$	4.09226	−	0.775176i	0.138344	−	0.0262057i
$876$	−5.81716	+	1.89011i	−0.196544	+	0.0638609i
$877$	−2.60146	+	2.34236i	−0.0878451	+	0.0790960i	−0.711883	−	0.702298i	$-0.752158\pi$
$877$	−2.60146	+	2.34236i	−0.0878451	+	0.0790960i	0.624038	+	0.781394i	$0.285491\pi$
$878$	16.2376	+	1.70664i	0.547991	+	0.0575962i
$879$	−9.64469	+	5.56836i	−0.325307	+	0.187816i
$880$		0			0
$881$			24.6580i			0.830750i	0.909650	+	0.415375i	$0.136350\pi$
$881$			24.6580i			0.830750i	−0.909650	+	0.415375i	$0.863650\pi$
$882$	4.51657	+	6.83614i	0.152081	+	0.230185i
$883$	8.98986	−	27.6680i	0.302533	−	0.931101i	−0.678053	−	0.735013i	$-0.737176\pi$
$883$	8.98986	−	27.6680i	0.302533	−	0.931101i	0.980586	−	0.196088i	$-0.0628238\pi$
$884$	−13.4796	−	2.86518i	−0.453368	−	0.0963663i
$885$	1.02750	−	2.30780i	0.0345390	−	0.0775758i
$886$	−7.13807	+	16.0324i	−0.239808	+	0.538618i
$887$	−41.8454	−	8.89451i	−1.40503	−	0.298648i	−0.557844	−	0.829946i	$-0.688371\pi$
$887$	−41.8454	−	8.89451i	−1.40503	−	0.298648i	−0.847185	+	0.531297i	$0.821705\pi$
$888$	6.44678	−	19.8411i	0.216340	−	0.665825i
$889$	26.6600	+	48.6427i	0.894146	+	1.63142i
$890$			1.57204i			0.0526948i
$891$		0			0
$892$	−24.5723	+	14.1868i	−0.822741	+	0.475009i
$893$	22.7057	+	2.38646i	0.759817	+	0.0798600i
$894$	−10.6555	+	9.59426i	−0.356373	+	0.320880i
$895$	0.402213	−	0.130687i	0.0134445	−	0.00436838i
$896$	8.82375	−	25.2336i	0.294781	−	0.842996i
$897$	3.59520	+	4.94837i	0.120040	+	0.165221i
$898$	3.14889	−	14.8144i	0.105080	−	0.494362i
$899$	−8.77808	+	1.86584i	−0.292765	+	0.0622292i
$900$	−1.21035	+	11.5158i	−0.0403451	+	0.383858i
$901$	−0.704904	+	1.22093i	−0.0234838	+	0.0406751i
$902$		0			0
$903$	−21.8530	+	1.80669i	−0.727223	+	0.0601229i
$904$	7.84119	−	10.7925i	0.260794	−	0.358952i
$905$	0.707277	+	0.785511i	0.0235107	+	0.0261113i
$906$	−6.08022	−	5.47465i	−0.202002	−	0.181883i
$907$	19.6384	+	8.74357i	0.652082	+	0.290325i	0.705991	−	0.708220i	$-0.250502\pi$
$907$	19.6384	+	8.74357i	0.652082	+	0.290325i	−0.0539098	+	0.998546i	$0.517168\pi$
$908$	2.22101	+	21.1315i	0.0737069	+	0.701274i
$909$	6.95910	+	21.4179i	0.230819	+	0.710387i
$910$	0.150922	−	0.639750i	0.00500302	−	0.0212075i
$911$	23.2995	+	16.9281i	0.771948	+	0.560853i	0.902552	−	0.430582i	$-0.141692\pi$
$911$	23.2995	+	16.9281i	0.771948	+	0.560853i	−0.130604	+	0.991435i	$0.541692\pi$
$912$	−6.65205	−	3.84056i	−0.220271	−	0.127174i
$913$		0			0
$914$	0.393968	+	0.682372i	0.0130313	+	0.0225709i
$915$	1.16794	−	0.519999i	0.0386108	−	0.0171906i
$916$	5.00176	+	1.62517i	0.165263	+	0.0536971i
$917$	−26.4495	+	34.7529i	−0.873440	+	1.14764i
$918$	−14.2513	+	10.3542i	−0.470363	+	0.341738i
$919$	14.0424	−	1.47592i	0.463216	−	0.0486860i	0.129954	−	0.991520i	$-0.458517\pi$
$919$	14.0424	−	1.47592i	0.463216	−	0.0486860i	0.333262	+	0.942834i	$0.391850\pi$
$920$	0.645904	−	0.717349i	0.0212948	−	0.0236503i
$921$	−0.929433	−	4.37264i	−0.0306259	−	0.144083i
$922$	3.22666	+	7.24719i	0.106264	+	0.238674i
$923$	7.53269			0.247942
$924$		0			0
$925$	−34.4327			−1.13214
$926$	−1.13693	−	2.55360i	−0.0373620	−	0.0839164i
$927$	5.35273	+	25.1826i	0.175807	+	0.827105i
$928$	8.25374	−	9.16670i	0.270942	−	0.300912i
$929$	21.7276	−	2.28367i	0.712861	−	0.0749247i	0.258846	−	0.965919i	$-0.416658\pi$
$929$	21.7276	−	2.28367i	0.712861	−	0.0749247i	0.454015	+	0.890994i	$0.349991\pi$
$930$	0.473965	−	0.344356i	0.0155419	−	0.0112919i
$931$	19.8290	+	38.1687i	0.649869	+	1.25093i
$932$	21.2057	+	6.89016i	0.694617	+	0.225695i
$933$	−9.35974	+	4.16723i	−0.306424	+	0.136429i
$934$	−0.559163	−	0.968498i	−0.0182964	−	0.0316902i
$935$		0			0
$936$	7.51819	+	4.34063i	0.245740	+	0.141878i
$937$	9.99780	+	7.26383i	0.326614	+	0.237299i	0.738992	−	0.673714i	$-0.235302\pi$
$937$	9.99780	+	7.26383i	0.326614	+	0.237299i	−0.412379	+	0.911013i	$0.635302\pi$
$938$	−3.53658	+	3.75636i	−0.115473	+	0.122649i
$939$	−3.84738	−	11.8410i	−0.125554	−	0.386417i
$940$	0.0895196	+	0.851722i	0.00291981	+	0.0277801i
$941$	9.47789	+	4.21983i	0.308970	+	0.137562i	0.555364	−	0.831607i	$-0.312579\pi$
$941$	9.47789	+	4.21983i	0.308970	+	0.137562i	−0.246394	+	0.969170i	$0.579246\pi$
$942$	0.822798	+	0.740851i	0.0268082	+	0.0241382i
$943$	−10.3533	−	11.4985i	−0.337150	−	0.374443i
$944$	−8.36280	+	11.5104i	−0.272186	+	0.374632i
$945$	1.29575	+	1.86948i	0.0421508	+	0.0608142i
$946$		0			0
$947$	22.3602	−	38.7290i	0.726609	−	1.25852i	−0.231699	−	0.972787i	$-0.574428\pi$
$947$	22.3602	−	38.7290i	0.726609	−	1.25852i	0.958308	−	0.285736i	$-0.0922382\pi$
$948$	−0.273154	+	2.59888i	−0.00887162	+	0.0844078i
$949$	7.40328	−	1.57362i	0.240321	−	0.0510817i
$950$	4.66838	−	21.9630i	0.151462	−	0.712573i
$951$	−16.2311	−	22.3403i	−0.526331	−	0.724432i
$952$	−19.3161	−	22.4363i	−0.626039	−	0.727165i
$953$	−2.40200	+	0.780456i	−0.0778083	+	0.0252814i	−0.347662	−	0.937620i	$-0.613024\pi$
$953$	−2.40200	+	0.780456i	−0.0778083	+	0.0252814i	0.269854	+	0.962901i	$0.413024\pi$
$954$	0.278553	−	0.250810i	0.00901847	−	0.00812027i
$955$	−3.83018	−	0.402568i	−0.123942	−	0.0130268i
$956$	−7.58294	+	4.37801i	−0.245250	+	0.141595i
$957$		0			0
$958$		−	2.67895i		−	0.0865529i
$959$	−23.4033	−	14.2148i	−0.755731	−	0.459019i
$960$	−0.126911	+	0.390592i	−0.00409604	+	0.0126063i
$961$	−12.5572	−	2.66912i	−0.405071	−	0.0861006i
$962$	−4.43151	+	9.95334i	−0.142878	+	0.320909i
$963$	0.371694	−	0.834839i	0.0119777	−	0.0269023i
$964$	5.85979	+	1.24554i	0.188731	+	0.0401161i
$965$	0.432825	−	1.33210i	0.0139331	−	0.0428818i
$966$	−0.123290	+	5.54453i	−0.00396678	+	0.178392i
$967$			31.8090i			1.02291i	0.859311	+	0.511454i	$0.170893\pi$
$967$			31.8090i			1.02291i	−0.859311	+	0.511454i	$0.829107\pi$
$968$		0			0
$969$	−27.7827	+	16.0403i	−0.892508	+	0.515290i
$970$	0.410147	+	0.0431082i	0.0131690	+	0.00138412i
$971$	30.4127	−	27.3837i	0.975991	−	0.878786i	−0.0166527	−	0.999861i	$-0.505301\pi$
$971$	30.4127	−	27.3837i	0.975991	−	0.878786i	0.992643	+	0.121075i	$0.0386343\pi$
$972$	−19.9337	+	6.47684i	−0.639373	+	0.207745i
$973$	7.98779	+	42.1686i	0.256077	+	1.35186i
$974$	11.3076	+	15.5636i	0.362320	+	0.498691i
$975$	−2.62914	+	12.3691i	−0.0841998	+	0.396129i
$976$	−7.04302	+	1.49704i	−0.225442	+	0.0479191i
$977$	4.16586	−	39.6356i	0.133278	−	1.26805i	−0.699575	−	0.714559i	$-0.746627\pi$
$977$	4.16586	−	39.6356i	0.133278	−	1.26805i	0.832853	−	0.553495i	$-0.186706\pi$
$978$	6.58011	−	11.3971i	0.210409	−	0.364439i
$979$		0			0
$980$	−1.24583	+	1.02524i	−0.0397964	+	0.0327501i
$981$	−12.6293	+	17.3827i	−0.403222	+	0.554987i
$982$	−4.73455	−	5.25825i	−0.151086	−	0.167798i
$983$	−12.7443	−	11.4750i	−0.406479	−	0.365995i	0.440381	−	0.897811i	$-0.354843\pi$
$983$	−12.7443	−	11.4750i	−0.406479	−	0.365995i	−0.846860	+	0.531816i	$0.821510\pi$
$984$	17.7059	+	7.88317i	0.564443	+	0.251306i
$985$	−0.240771	−	2.29079i	−0.00767161	−	0.0729905i
$986$	−2.10417	−	6.47596i	−0.0670103	−	0.206237i
$987$	−8.48824	−	7.99160i	−0.270184	−	0.254375i
$988$	15.5607	+	11.3055i	0.495051	+	0.359676i
$989$	14.5642	+	8.40863i	0.463114	+	0.267379i
$990$		0			0
$991$	−12.5921	−	21.8102i	−0.400002	−	0.692823i	0.593724	−	0.804669i	$-0.297657\pi$
$991$	−12.5921	−	21.8102i	−0.400002	−	0.692823i	−0.993726	+	0.111845i	$0.964324\pi$
$992$	−22.8058	+	10.1538i	−0.724084	+	0.322383i
$993$	18.3792	+	5.97177i	0.583247	+	0.189508i
$994$	5.43493	+	4.13639i	0.172386	+	0.131198i
$995$	−2.90035	+	2.10723i	−0.0919474	+	0.0668037i
$996$	16.3492	−	1.71837i	0.518046	−	0.0544488i
$997$	28.5692	−	31.7293i	0.904795	−	1.00488i	−0.0951605	−	0.995462i	$-0.530336\pi$
$997$	28.5692	−	31.7293i	0.904795	−	1.00488i	0.999956	−	0.00941490i	$-0.00299690\pi$
$998$	1.01743	+	4.78665i	0.0322063	+	0.151519i
$999$	−15.3353	−	34.4436i	−0.485187	−	1.08975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.r.b.40.4		48
7.3	odd	6	inner	847.2.r.b.766.3		48
11.2	odd	10	inner	847.2.r.b.215.3		48
11.3	even	5	inner	847.2.r.b.481.4		48
11.4	even	5	inner	847.2.r.b.838.3		48
11.5	even	5		77.2.i.a.54.3	yes	12
11.6	odd	10		77.2.i.a.54.4	yes	12
11.7	odd	10	inner	847.2.r.b.838.4		48
11.8	odd	10	inner	847.2.r.b.481.3		48
11.9	even	5	inner	847.2.r.b.215.4		48
11.10	odd	2	inner	847.2.r.b.40.3		48
33.5	odd	10		693.2.bg.a.208.4		12
33.17	even	10		693.2.bg.a.208.3		12
44.27	odd	10		1232.2.bn.a.593.1		12
44.39	even	10		1232.2.bn.a.593.2		12
77.3	odd	30	inner	847.2.r.b.360.3		48
77.5	odd	30		539.2.b.b.538.7		12
77.6	even	10		539.2.i.c.362.4		12
77.10	even	6	inner	847.2.r.b.766.4		48
77.16	even	15		539.2.b.b.538.8		12
77.17	even	30		77.2.i.a.10.3	✓	12
77.24	even	30	inner	847.2.r.b.94.3		48
77.27	odd	10		539.2.i.c.362.3		12
77.31	odd	30	inner	847.2.r.b.94.4		48
77.38	odd	30		77.2.i.a.10.4	yes	12
77.39	odd	30		539.2.i.c.472.3		12
77.52	even	30	inner	847.2.r.b.360.4		48
77.59	odd	30	inner	847.2.r.b.717.3		48
77.60	even	15		539.2.i.c.472.4		12
77.61	even	30		539.2.b.b.538.5		12
77.72	odd	30		539.2.b.b.538.6		12
77.73	even	30	inner	847.2.r.b.717.4		48
231.17	odd	30		693.2.bg.a.10.4		12
231.38	even	30		693.2.bg.a.10.3		12
308.115	even	30		1232.2.bn.a.241.2		12
308.171	odd	30		1232.2.bn.a.241.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.3	✓	12	77.17	even	30
77.2.i.a.10.4	yes	12	77.38	odd	30
77.2.i.a.54.3	yes	12	11.5	even	5
77.2.i.a.54.4	yes	12	11.6	odd	10
539.2.b.b.538.5		12	77.61	even	30
539.2.b.b.538.6		12	77.72	odd	30
539.2.b.b.538.7		12	77.5	odd	30
539.2.b.b.538.8		12	77.16	even	15
539.2.i.c.362.3		12	77.27	odd	10
539.2.i.c.362.4		12	77.6	even	10
539.2.i.c.472.3		12	77.39	odd	30
539.2.i.c.472.4		12	77.60	even	15
693.2.bg.a.10.3		12	231.38	even	30
693.2.bg.a.10.4		12	231.17	odd	30
693.2.bg.a.208.3		12	33.17	even	10
693.2.bg.a.208.4		12	33.5	odd	10
847.2.r.b.40.3		48	11.10	odd	2	inner
847.2.r.b.40.4		48	1.1	even	1	trivial
847.2.r.b.94.3		48	77.24	even	30	inner
847.2.r.b.94.4		48	77.31	odd	30	inner
847.2.r.b.215.3		48	11.2	odd	10	inner
847.2.r.b.215.4		48	11.9	even	5	inner
847.2.r.b.360.3		48	77.3	odd	30	inner
847.2.r.b.360.4		48	77.52	even	30	inner
847.2.r.b.481.3		48	11.8	odd	10	inner
847.2.r.b.481.4		48	11.3	even	5	inner
847.2.r.b.717.3		48	77.59	odd	30	inner
847.2.r.b.717.4		48	77.73	even	30	inner
847.2.r.b.766.3		48	7.3	odd	6	inner
847.2.r.b.766.4		48	77.10	even	6	inner
847.2.r.b.838.3		48	11.4	even	5	inner
847.2.r.b.838.4		48	11.7	odd	10	inner
1232.2.bn.a.241.1		12	308.171	odd	30
1232.2.bn.a.241.2		12	308.115	even	30
1232.2.bn.a.593.1		12	44.27	odd	10
1232.2.bn.a.593.2		12	44.39	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.r (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.298749 + 0.671002i) q^{2} +(-0.246568 - 1.16001i) q^{3} +(0.977269 - 1.08537i) q^{4} +(-0.156952 + 0.0164963i) q^{5} +(0.704708 - 0.512000i) q^{6} +(2.62446 + 0.334983i) q^{7} +(2.41735 + 0.785445i) q^{8} +(1.45581 - 0.648167i) q^{9} +O(q^{10})\)	\(q+(0.298749 + 0.671002i) q^{2} +(-0.246568 - 1.16001i) q^{3} +(0.977269 - 1.08537i) q^{4} +(-0.156952 + 0.0164963i) q^{5} +(0.704708 - 0.512000i) q^{6} +(2.62446 + 0.334983i) q^{7} +(2.41735 + 0.785445i) q^{8} +(1.45581 - 0.648167i) q^{9} +(-0.0579584 - 0.100387i) q^{10} +(-1.50000 - 0.866025i) q^{12} +(1.73394 + 1.25978i) q^{13} +(0.559281 + 1.86109i) q^{14} +(0.0578352 + 0.177998i) q^{15} +(-0.110182 - 1.04831i) q^{16} +(-4.02183 - 1.79064i) q^{17} +(0.869843 + 0.783210i) q^{18} +(4.11152 + 4.56631i) q^{19} +(-0.135480 + 0.186472i) q^{20} +(-0.258524 - 3.12700i) q^{21} +(-1.20321 + 2.08402i) q^{23} +(0.315083 - 2.99782i) q^{24} +(-4.86638 + 1.03438i) q^{25} +(-0.327302 + 1.53983i) q^{26} +(-3.20205 - 4.40724i) q^{27} +(2.92838 - 2.52113i) q^{28} +(2.00270 - 0.650718i) q^{29} +(-0.102159 + 0.0919845i) q^{30} +(-4.23837 - 0.445471i) q^{31} +(5.07295 - 2.92887i) q^{32} -3.23361i q^{34} +(-0.417440 - 0.00928232i) q^{35} +(0.719216 - 2.21352i) q^{36} +(6.76977 + 1.43896i) q^{37} +(-1.83569 + 4.12302i) q^{38} +(1.03382 - 2.32201i) q^{39} +(-0.392365 - 0.0833997i) q^{40} +(-1.98691 + 6.11509i) q^{41} +(2.02099 - 1.10766i) q^{42} -6.98850i q^{43} +(-0.217799 + 0.125747i) q^{45} +(-1.75784 - 0.184757i) q^{46} +(2.76122 - 2.48622i) q^{47} +(-1.18888 + 0.386292i) q^{48} +(6.77557 + 1.75830i) q^{49} +(-2.14790 - 2.95633i) q^{50} +(-1.08550 + 5.10688i) q^{51} +(3.06184 - 0.650815i) q^{52} +(0.0334735 - 0.318479i) q^{53} +(2.00066 - 3.46524i) q^{54} +(6.08113 + 2.87114i) q^{56} +(4.28320 - 5.89532i) q^{57} +(1.03494 + 1.14942i) q^{58} +(-10.0307 - 9.03168i) q^{59} +(0.249714 + 0.111180i) q^{60} +(-0.714026 - 6.79350i) q^{61} +(-0.967300 - 2.97704i) q^{62} +(4.03783 - 1.21342i) q^{63} +(1.77527 + 1.28981i) q^{64} +(-0.292926 - 0.169121i) q^{65} +(1.32743 + 2.29918i) q^{67} +(-5.87391 + 2.61523i) q^{68} +(2.71416 + 0.881884i) q^{69} +(-0.118481 - 0.282876i) q^{70} +(2.84336 - 2.06582i) q^{71} +(4.02830 - 0.423391i) q^{72} +(2.36295 - 2.62432i) q^{73} +(1.05692 + 4.97242i) q^{74} +(2.39978 + 5.39000i) q^{75} +8.97419 q^{76} +1.86693 q^{78} +(-0.613656 - 1.37829i) q^{79} +(0.0345865 + 0.162717i) q^{80} +(-1.12398 + 1.24831i) q^{81} +(-4.69683 + 0.493657i) q^{82} +(-7.67857 + 5.57881i) q^{83} +(-3.64659 - 2.77532i) q^{84} +(0.660773 + 0.214698i) q^{85} +(4.68930 - 2.08781i) q^{86} +(-1.24864 - 2.16271i) q^{87} +(-11.7448 - 6.78089i) q^{89} +(-0.149444 - 0.108577i) q^{90} +(4.12864 + 3.88708i) q^{91} +(1.08607 + 3.34257i) q^{92} +(0.528296 + 5.02640i) q^{93} +(2.49317 + 1.11003i) q^{94} +(-0.720639 - 0.648866i) q^{95} +(-4.64834 - 5.16251i) q^{96} +(-2.09121 + 2.87830i) q^{97} +(0.844377 + 5.07171i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 48 * q + 6 * q^3 - 4 * q^4 + 4 * q^9	\( 48 q + 6 q^{3} - 4 q^{4} + 4 q^{9} - 72 q^{12} - 8 q^{14} + 20 q^{15} - 12 q^{16} - 80 q^{23} - 14 q^{25} - 18 q^{26} - 6 q^{31} + 12 q^{36} - 16 q^{37} + 48 q^{38} - 16 q^{42} + 216 q^{45} + 18 q^{47} - 16 q^{49} + 2 q^{53} + 72 q^{56} + 6 q^{58} + 12 q^{59} - 28 q^{64} - 96 q^{67} + 58 q^{70} - 20 q^{71} + 78 q^{75} + 32 q^{78} - 30 q^{80} - 14 q^{81} - 54 q^{82} + 38 q^{86} - 264 q^{89} - 22 q^{91} + 20 q^{92} - 12 q^{93}+O(q^{100}) \) 48 * q + 6 * q^3 - 4 * q^4 + 4 * q^9 - 72 * q^12 - 8 * q^14 + 20 * q^15 - 12 * q^16 - 80 * q^23 - 14 * q^25 - 18 * q^26 - 6 * q^31 + 12 * q^36 - 16 * q^37 + 48 * q^38 - 16 * q^42 + 216 * q^45 + 18 * q^47 - 16 * q^49 + 2 * q^53 + 72 * q^56 + 6 * q^58 + 12 * q^59 - 28 * q^64 - 96 * q^67 + 58 * q^70 - 20 * q^71 + 78 * q^75 + 32 * q^78 - 30 * q^80 - 14 * q^81 - 54 * q^82 + 38 * q^86 - 264 * q^89 - 22 * q^91 + 20 * q^92 - 12 * q^93

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