LMFDB - Embedded newform 855.2.n.e.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, degree $2$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Character	$\chi$	$=$	855.647
Dual form			855.2.n.e.818.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95934 + 1.95934i) q^{2} -5.67802i q^{4} +(2.21856 - 0.279275i) q^{5} +(0.856099 + 0.856099i) q^{7} +(7.20648 + 7.20648i) q^{8} +O(q^{10})$	\(q+(-1.95934 + 1.95934i) q^{2} -5.67802i q^{4} +(2.21856 - 0.279275i) q^{5} +(0.856099 + 0.856099i) q^{7} +(7.20648 + 7.20648i) q^{8} +(-3.79972 + 4.89410i) q^{10} +5.46102i q^{11} +(2.07133 - 2.07133i) q^{13} -3.35477 q^{14} -16.8838 q^{16} +(4.51856 - 4.51856i) q^{17} +1.00000i q^{19} +(-1.58573 - 12.5970i) q^{20} +(-10.7000 - 10.7000i) q^{22} +(-1.88947 - 1.88947i) q^{23} +(4.84401 - 1.23918i) q^{25} +8.11687i q^{26} +(4.86094 - 4.86094i) q^{28} -0.00315126 q^{29} -0.931958 q^{31} +(18.6682 - 18.6682i) q^{32} +17.7068i q^{34} +(2.13839 + 1.66022i) q^{35} +(-0.220688 - 0.220688i) q^{37} +(-1.95934 - 1.95934i) q^{38} +(18.0006 + 13.9754i) q^{40} +8.50374i q^{41} +(1.78713 - 1.78713i) q^{43} +31.0078 q^{44} +7.40422 q^{46} +(-0.566821 + 0.566821i) q^{47} -5.53419i q^{49} +(-7.06309 + 11.9190i) q^{50} +(-11.7610 - 11.7610i) q^{52} +(6.18050 + 6.18050i) q^{53} +(1.52513 + 12.1156i) q^{55} +12.3389i q^{56} +(0.00617439 - 0.00617439i) q^{58} -14.2951 q^{59} +10.1461 q^{61} +(1.82602 - 1.82602i) q^{62} +39.3870i q^{64} +(4.01690 - 5.17384i) q^{65} +(9.71049 + 9.71049i) q^{67} +(-25.6565 - 25.6565i) q^{68} +(-7.44277 + 0.936904i) q^{70} +3.58566i q^{71} +(5.50695 - 5.50695i) q^{73} +0.864804 q^{74} +5.67802 q^{76} +(-4.67517 + 4.67517i) q^{77} -10.3405i q^{79} +(-37.4578 + 4.71523i) q^{80} +(-16.6617 - 16.6617i) q^{82} +(-1.80556 - 1.80556i) q^{83} +(8.76278 - 11.2866i) q^{85} +7.00319i q^{86} +(-39.3548 + 39.3548i) q^{88} -3.93092 q^{89} +3.54652 q^{91} +(-10.7284 + 10.7284i) q^{92} -2.22119i q^{94} +(0.279275 + 2.21856i) q^{95} +(5.28584 + 5.28584i) q^{97} +(10.8434 + 10.8434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7}+O(q^{10}) $ 36 * q + 4 * q^7	$ 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.95934	+	1.95934i	−1.38546	+	1.38546i	−0.550872	+	0.834590i	$0.685705\pi$
$2$	−1.95934	+	1.95934i	−1.38546	+	1.38546i	−0.834590	+	0.550872i	$0.814295\pi$
$3$		0			0
$3$		0			0
$4$		−	5.67802i		−	2.83901i
$5$	2.21856	−	0.279275i	0.992170	−	0.124896i
$5$	2.21856	−	0.279275i	0.992170	−	0.124896i
$6$		0			0
$7$	0.856099	+	0.856099i	0.323575	+	0.323575i	0.850137	−	0.526562i	$-0.176519\pi$
$7$	0.856099	+	0.856099i	0.323575	+	0.323575i	−0.526562	+	0.850137i	$0.676519\pi$
$8$	7.20648	+	7.20648i	2.54788	+	2.54788i
$9$		0			0
$10$	−3.79972	+	4.89410i	−1.20158	+	1.54765i
$11$			5.46102i			1.64656i	0.567635	+	0.823280i	$0.307858\pi$
$11$			5.46102i			1.64656i	−0.567635	+	0.823280i	$0.692142\pi$
$12$		0			0
$13$	2.07133	−	2.07133i	0.574483	−	0.574483i	−0.358895	−	0.933378i	$-0.616846\pi$
$13$	2.07133	−	2.07133i	0.574483	−	0.574483i	0.933378	+	0.358895i	$0.116846\pi$
$14$	−3.35477			−0.896601
$15$		0			0
$16$	−16.8838			−4.22096
$17$	4.51856	−	4.51856i	1.09591	−	1.09591i	0.101029	−	0.994883i	$-0.467786\pi$
$17$	4.51856	−	4.51856i	1.09591	−	1.09591i	0.994883	−	0.101029i	$-0.0322135\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.58573	−	12.5970i	−0.354579	−	2.81678i
$21$		0			0
$22$	−10.7000	−	10.7000i	−2.28125	−	2.28125i
$23$	−1.88947	−	1.88947i	−0.393982	−	0.393982i	0.482122	−	0.876104i	$-0.339866\pi$
$23$	−1.88947	−	1.88947i	−0.393982	−	0.393982i	−0.876104	+	0.482122i	$0.839866\pi$
$24$		0			0
$25$	4.84401	−	1.23918i	0.968802	−	0.247835i
$26$			8.11687i			1.59185i
$27$		0			0
$28$	4.86094	−	4.86094i	0.918632	−	0.918632i
$29$	−0.00315126			−0.000585175			−0.000292587	−	1.00000i	$-0.500093\pi$
$29$	−0.00315126			−0.000585175			−0.000292587		1.00000i	$0.500093\pi$
$30$		0			0
$31$	−0.931958			−0.167385			−0.0836923	−	0.996492i	$-0.526671\pi$
$31$	−0.931958			−0.167385			−0.0836923	+	0.996492i	$0.526671\pi$
$32$	18.6682	−	18.6682i	3.30010	−	3.30010i
$33$		0			0
$34$			17.7068i			3.03669i
$35$	2.13839	+	1.66022i	0.361454	+	0.280628i
$36$		0			0
$37$	−0.220688	−	0.220688i	−0.0362808	−	0.0362808i	0.688734	−	0.725014i	$-0.258167\pi$
$37$	−0.220688	−	0.220688i	−0.0362808	−	0.0362808i	−0.725014	+	0.688734i	$0.758167\pi$
$38$	−1.95934	−	1.95934i	−0.317847	−	0.317847i
$39$		0			0
$40$	18.0006	+	13.9754i	2.84614	+	2.20971i
$41$			8.50374i			1.32806i	0.747706	+	0.664030i	$0.231155\pi$
$41$			8.50374i			1.32806i	−0.747706	+	0.664030i	$0.768845\pi$
$42$		0			0
$43$	1.78713	−	1.78713i	0.272535	−	0.272535i	−0.557585	−	0.830120i	$-0.688272\pi$
$43$	1.78713	−	1.78713i	0.272535	−	0.272535i	0.830120	+	0.557585i	$0.188272\pi$
$44$	31.0078			4.67460
$45$		0			0
$46$	7.40422			1.09169
$47$	−0.566821	+	0.566821i	−0.0826793	+	0.0826793i	−0.747237	−	0.664558i	$-0.768620\pi$
$47$	−0.566821	+	0.566821i	−0.0826793	+	0.0826793i	0.664558	+	0.747237i	$0.268620\pi$
$48$		0			0
$49$		−	5.53419i		−	0.790599i
$50$	−7.06309	+	11.9190i	−0.998872	+	1.68560i
$51$		0			0
$52$	−11.7610	−	11.7610i	−1.63096	−	1.63096i
$53$	6.18050	+	6.18050i	0.848957	+	0.848957i	0.990003	−	0.141046i	$-0.0450464\pi$
$53$	6.18050	+	6.18050i	0.848957	+	0.848957i	−0.141046	+	0.990003i	$0.545046\pi$
$54$		0			0
$55$	1.52513	+	12.1156i	0.205648	+	1.63367i
$56$			12.3389i			1.64886i
$57$		0			0
$58$	0.00617439	−	0.00617439i	0.000810738	−	0.000810738i
$59$	−14.2951			−1.86107			−0.930534	−	0.366207i	$-0.880656\pi$
$59$	−14.2951			−1.86107			−0.930534	+	0.366207i	$0.880656\pi$
$60$		0			0
$61$	10.1461			1.29908			0.649541	−	0.760327i	$-0.274961\pi$
$61$	10.1461			1.29908			0.649541	+	0.760327i	$0.274961\pi$
$62$	1.82602	−	1.82602i	0.231905	−	0.231905i
$63$		0			0
$64$			39.3870i			4.92337i
$65$	4.01690	−	5.17384i	0.498235	−	0.641735i
$66$		0			0
$67$	9.71049	+	9.71049i	1.18633	+	1.18633i	0.978076	+	0.208250i	$0.0667767\pi$
$67$	9.71049	+	9.71049i	1.18633	+	1.18633i	0.208250	+	0.978076i	$0.433223\pi$
$68$	−25.6565	−	25.6565i	−3.11131	−	3.11131i
$69$		0			0
$70$	−7.44277	+	0.936904i	−0.889581	+	0.111981i
$71$			3.58566i			0.425540i	0.977102	+	0.212770i	$0.0682485\pi$
$71$			3.58566i			0.425540i	−0.977102	+	0.212770i	$0.931752\pi$
$72$		0			0
$73$	5.50695	−	5.50695i	0.644540	−	0.644540i	−0.307128	−	0.951668i	$-0.599368\pi$
$73$	5.50695	−	5.50695i	0.644540	−	0.644540i	0.951668	+	0.307128i	$0.0993681\pi$
$74$	0.864804			0.100531
$75$		0			0
$76$	5.67802			0.651313
$77$	−4.67517	+	4.67517i	−0.532785	+	0.532785i
$78$		0			0
$79$		−	10.3405i		−	1.16340i	−0.813403	−	0.581701i	$-0.802387\pi$
$79$		−	10.3405i		−	1.16340i	0.813403	−	0.581701i	$-0.197613\pi$
$80$	−37.4578	+	4.71523i	−4.18791	+	0.527179i
$81$		0			0
$82$	−16.6617	−	16.6617i	−1.83998	−	1.83998i
$83$	−1.80556	−	1.80556i	−0.198185	−	0.198185i	0.601036	−	0.799222i	$-0.294755\pi$
$83$	−1.80556	−	1.80556i	−0.198185	−	0.198185i	−0.799222	+	0.601036i	$0.794755\pi$
$84$		0			0
$85$	8.76278	−	11.2866i	0.950457	−	1.22421i
$86$			7.00319i			0.755173i
$87$		0			0
$88$	−39.3548	+	39.3548i	−4.19523	+	4.19523i
$89$	−3.93092			−0.416676			−0.208338	−	0.978057i	$-0.566805\pi$
$89$	−3.93092			−0.416676			−0.208338	+	0.978057i	$0.566805\pi$
$90$		0			0
$91$	3.54652			0.371777
$92$	−10.7284	+	10.7284i	−1.11852	+	1.11852i
$93$		0			0
$94$		−	2.22119i		−	0.229098i
$95$	0.279275	+	2.21856i	0.0286530	+	0.227619i
$96$		0			0
$97$	5.28584	+	5.28584i	0.536696	+	0.536696i	0.922557	−	0.385861i	$-0.126096\pi$
$97$	5.28584	+	5.28584i	0.536696	+	0.536696i	−0.385861	+	0.922557i	$0.626096\pi$
$98$	10.8434	+	10.8434i	1.09534	+	1.09534i
$99$		0			0
$100$	−7.03606	−	27.5044i	−0.703606	−	2.75044i
$101$		−	9.69831i		−	0.965018i	−0.875891	−	0.482509i	$-0.839726\pi$
$101$		−	9.69831i		−	0.965018i	0.875891	−	0.482509i	$-0.160274\pi$
$102$		0			0
$103$	−0.356805	+	0.356805i	−0.0351571	+	0.0351571i	−0.724467	−	0.689310i	$-0.757914\pi$
$103$	−0.356805	+	0.356805i	−0.0351571	+	0.0351571i	0.689310	+	0.724467i	$0.257914\pi$
$104$	29.8540			2.92742
$105$		0			0
$106$	−24.2194			−2.35240
$107$	−7.10480	+	7.10480i	−0.686847	+	0.686847i	−0.961534	−	0.274687i	$-0.911426\pi$
$107$	−7.10480	+	7.10480i	−0.686847	+	0.686847i	0.274687	+	0.961534i	$0.411426\pi$
$108$		0			0
$109$			14.7261i			1.41050i	0.708957	+	0.705252i	$0.249166\pi$
$109$			14.7261i			1.41050i	−0.708957	+	0.705252i	$0.750834\pi$
$110$	−26.7268	−	20.7503i	−2.54830	−	1.97847i
$111$		0			0
$112$	−14.4542	−	14.4542i	−1.36580	−	1.36580i
$113$	6.28138	+	6.28138i	0.590902	+	0.590902i	0.937875	−	0.346973i	$-0.112790\pi$
$113$	6.28138	+	6.28138i	0.590902	+	0.590902i	−0.346973	+	0.937875i	$0.612790\pi$
$114$		0			0
$115$	−4.71958	−	3.66422i	−0.440103	−	0.341690i
$116$			0.0178929i			0.00166132i
$117$		0			0
$118$	28.0090	−	28.0090i	2.57844	−	2.57844i
$119$	7.73667			0.709220
$120$		0			0
$121$	−18.8228			−1.71116
$122$	−19.8797	+	19.8797i	−1.79983	+	1.79983i
$123$		0			0
$124$			5.29167i			0.475206i
$125$	10.4007	−	4.10200i	0.930263	−	0.366894i
$126$		0			0
$127$	−1.78545	−	1.78545i	−0.158433	−	0.158433i	0.623439	−	0.781872i	$-0.285735\pi$
$127$	−1.78545	−	1.78545i	−0.158433	−	0.158433i	−0.781872	+	0.623439i	$0.785735\pi$
$128$	−39.8360	−	39.8360i	−3.52104	−	3.52104i
$129$		0			0
$130$	2.26684	+	18.0078i	0.198815	+	1.57938i
$131$			8.23650i			0.719627i	0.933024	+	0.359813i	$0.117160\pi$
$131$			8.23650i			0.719627i	−0.933024	+	0.359813i	$0.882840\pi$
$132$		0			0
$133$	−0.856099	+	0.856099i	−0.0742332	+	0.0742332i
$134$	−38.0523			−3.28722
$135$		0			0
$136$	65.1259			5.58450
$137$	4.46768	−	4.46768i	0.381699	−	0.381699i	−0.490015	−	0.871714i	$-0.663009\pi$
$137$	4.46768	−	4.46768i	0.381699	−	0.381699i	0.871714	+	0.490015i	$0.163009\pi$
$138$		0			0
$139$			16.1737i			1.37183i	0.727681	+	0.685916i	$0.240598\pi$
$139$			16.1737i			1.37183i	−0.727681	+	0.685916i	$0.759402\pi$
$140$	9.42675	−	12.1418i	0.796706	−	1.02617i
$141$		0			0
$142$	−7.02553	−	7.02553i	−0.589569	−	0.589569i
$143$	11.3116	+	11.3116i	0.945921	+	0.945921i
$144$		0			0
$145$	−0.00699127		0.000880069i	−0.000580593		7.30857e-5i
$146$			21.5800i			1.78597i
$147$		0			0
$148$	−1.25307	+	1.25307i	−0.103002	+	0.103002i
$149$	4.25399			0.348501			0.174250	−	0.984701i	$-0.444250\pi$
$149$	4.25399			0.348501			0.174250	+	0.984701i	$0.444250\pi$
$150$		0			0
$151$	−9.26233			−0.753758			−0.376879	−	0.926263i	$-0.623003\pi$
$151$	−9.26233			−0.753758			−0.376879	+	0.926263i	$0.623003\pi$
$152$	−7.20648	+	7.20648i	−0.584523	+	0.584523i
$153$		0			0
$154$		−	18.3205i		−	1.47631i
$155$	−2.06760	+	0.260272i	−0.166074	+	0.0209056i
$156$		0			0
$157$	6.58572	+	6.58572i	0.525598	+	0.525598i	0.919257	−	0.393659i	$-0.128791\pi$
$157$	6.58572	+	6.58572i	0.525598	+	0.525598i	−0.393659	+	0.919257i	$0.628791\pi$
$158$	20.2606	+	20.2606i	1.61185	+	1.61185i
$159$		0			0
$160$	36.2030	−	46.6301i	2.86209	−	3.68643i
$161$		−	3.23514i		−	0.254965i
$162$		0			0
$163$	4.41965	−	4.41965i	0.346174	−	0.346174i	−0.512508	−	0.858682i	$-0.671284\pi$
$163$	4.41965	−	4.41965i	0.346174	−	0.346174i	0.858682	+	0.512508i	$0.171284\pi$
$164$	48.2844			3.77038
$165$		0			0
$166$	7.07539			0.549157
$167$	10.8918	−	10.8918i	0.842834	−	0.842834i	−0.146393	−	0.989227i	$-0.546766\pi$
$167$	10.8918	−	10.8918i	0.842834	−	0.842834i	0.989227	+	0.146393i	$0.0467663\pi$
$168$		0			0
$169$			4.41919i			0.339938i
$170$	4.94506	+	39.2836i	0.379269	+	3.01291i
$171$		0			0
$172$	−10.1474	−	10.1474i	−0.773729	−	0.773729i
$173$	−8.89772	−	8.89772i	−0.676481	−	0.676481i	0.282721	−	0.959202i	$-0.408763\pi$
$173$	−8.89772	−	8.89772i	−0.676481	−	0.676481i	−0.959202	+	0.282721i	$0.908763\pi$
$174$		0			0
$175$	5.20781	+	3.08609i	0.393673	+	0.233287i
$176$		−	92.2030i		−	6.95006i
$177$		0			0
$178$	7.70200	−	7.70200i	0.577289	−	0.577289i
$179$	11.7448			0.877850			0.438925	−	0.898524i	$-0.355359\pi$
$179$	11.7448			0.877850			0.438925	+	0.898524i	$0.355359\pi$
$180$		0			0
$181$	−10.0054			−0.743693			−0.371847	−	0.928294i	$-0.621275\pi$
$181$	−10.0054			−0.743693			−0.371847	+	0.928294i	$0.621275\pi$
$182$	−6.94884	+	6.94884i	−0.515082	+	0.515082i
$183$		0			0
$184$		−	27.2329i		−	2.00763i
$185$	−0.551241	−	0.427976i	−0.0405281	−	0.0314654i
$186$		0			0
$187$	24.6760	+	24.6760i	1.80449	+	1.80449i
$188$	3.21842	+	3.21842i	0.234727	+	0.234727i
$189$		0			0
$190$	−4.89410	−	3.79972i	−0.355056	−	0.275660i
$191$		−	11.8635i		−	0.858409i	−0.903207	−	0.429205i	$-0.858794\pi$
$191$		−	11.8635i		−	0.858409i	0.903207	−	0.429205i	$-0.141206\pi$
$192$		0			0
$193$	−4.39865	+	4.39865i	−0.316621	+	0.316621i	−0.847468	−	0.530847i	$-0.821874\pi$
$193$	−4.39865	+	4.39865i	−0.316621	+	0.316621i	0.530847	+	0.847468i	$0.321874\pi$
$194$	−20.7135			−1.48714
$195$		0			0
$196$	−31.4232			−2.24452
$197$	−16.3011	+	16.3011i	−1.16140	+	1.16140i	−0.177233	+	0.984169i	$0.556715\pi$
$197$	−16.3011	+	16.3011i	−1.16140	+	1.16140i	−0.984169	+	0.177233i	$0.943285\pi$
$198$		0			0
$199$		−	7.44767i		−	0.527951i	−0.964529	−	0.263976i	$-0.914966\pi$
$199$		−	7.44767i		−	0.527951i	0.964529	−	0.263976i	$-0.0850338\pi$
$200$	43.8384	+	25.9782i	3.09984	+	1.83693i
$201$		0			0
$202$	19.0023	+	19.0023i	1.33700	+	1.33700i
$203$	−0.00269779	−	0.00269779i	−0.000189348	−	0.000189348i
$204$		0			0
$205$	2.37488	+	18.8660i	0.165869	+	1.31766i
$206$		−	1.39820i		−	0.0974175i
$207$		0			0
$208$	−34.9720	+	34.9720i	−2.42487	+	2.42487i
$209$	−5.46102			−0.377747
$210$		0			0
$211$	−10.6136			−0.730673			−0.365337	−	0.930876i	$-0.619046\pi$
$211$	−10.6136			−0.730673			−0.365337	+	0.930876i	$0.619046\pi$
$212$	35.0930	−	35.0930i	2.41020	−	2.41020i
$213$		0			0
$214$		−	27.8414i		−	1.90320i
$215$	3.46576	−	4.46396i	0.236363	−	0.304439i
$216$		0			0
$217$	−0.797848	−	0.797848i	−0.0541614	−	0.0541614i
$218$	−28.8534	−	28.8534i	−1.95420	−	1.95420i
$219$		0			0
$220$	68.7926	−	8.65969i	4.63800	−	0.583836i
$221$		−	18.7189i		−	1.25917i
$222$		0			0
$223$	−0.989962	+	0.989962i	−0.0662928	+	0.0662928i	−0.739476	−	0.673183i	$-0.764927\pi$
$223$	−0.989962	+	0.989962i	−0.0662928	+	0.0662928i	0.673183	+	0.739476i	$0.264927\pi$
$224$	31.9636			2.13566
$225$		0			0
$226$	−24.6147			−1.63735
$227$	14.2824	−	14.2824i	0.947954	−	0.947954i	−0.0507573	−	0.998711i	$-0.516164\pi$
$227$	14.2824	−	14.2824i	0.947954	−	0.947954i	0.998711	+	0.0507573i	$0.0161635\pi$
$228$		0			0
$229$		−	16.3304i		−	1.07914i	−0.841941	−	0.539570i	$-0.818587\pi$
$229$		−	16.3304i		−	1.07914i	0.841941	−	0.539570i	$-0.181413\pi$
$230$	16.4267	−	2.06781i	1.08314	−	0.136348i
$231$		0			0
$232$	−0.0227095	−	0.0227095i	−0.00149095	−	0.00149095i
$233$	−20.8065	−	20.8065i	−1.36308	−	1.36308i	−0.869966	−	0.493112i	$-0.835859\pi$
$233$	−20.8065	−	20.8065i	−1.36308	−	1.36308i	−0.493112	−	0.869966i	$-0.664141\pi$
$234$		0			0
$235$	−1.09923	+	1.41582i	−0.0717057	+	0.0923582i
$236$			81.1680i			5.28359i
$237$		0			0
$238$	−15.1588	+	15.1588i	−0.982596	+	0.982596i
$239$	26.1069			1.68871			0.844356	−	0.535782i	$-0.179983\pi$
$239$	26.1069			1.68871			0.844356	+	0.535782i	$0.179983\pi$
$240$		0			0
$241$	3.05139			0.196557			0.0982787	−	0.995159i	$-0.468666\pi$
$241$	3.05139			0.196557			0.0982787	+	0.995159i	$0.468666\pi$
$242$	36.8802	−	36.8802i	2.37075	−	2.37075i
$243$		0			0
$244$		−	57.6100i		−	3.68810i
$245$	−1.54556	−	12.2779i	−0.0987422	−	0.784408i
$246$		0			0
$247$	2.07133	+	2.07133i	0.131796	+	0.131796i
$248$	−6.71614	−	6.71614i	−0.426475	−	0.426475i
$249$		0			0
$250$	−12.3412	+	28.4156i	−0.780527	+	1.79716i
$251$		−	6.35460i		−	0.401099i	−0.979684	−	0.200550i	$-0.935727\pi$
$251$		−	6.35460i		−	0.401099i	0.979684	−	0.200550i	$-0.0642728\pi$
$252$		0			0
$253$	10.3184	−	10.3184i	0.648714	−	0.648714i
$254$	6.99662			0.439007
$255$		0			0
$256$	77.3306			4.83316
$257$	0.321859	−	0.321859i	0.0200770	−	0.0200770i	−0.696997	−	0.717074i	$-0.745481\pi$
$257$	0.321859	−	0.321859i	0.0200770	−	0.0200770i	0.717074	+	0.696997i	$0.245481\pi$
$258$		0			0
$259$		−	0.377861i		−	0.0234791i
$260$	−29.3771	−	22.8080i	−1.82189	−	1.41449i
$261$		0			0
$262$	−16.1381	−	16.1381i	−0.997015	−	0.997015i
$263$	−16.0902	−	16.0902i	−0.992166	−	0.992166i	0.00780379	−	0.999970i	$-0.497516\pi$
$263$	−16.0902	−	16.0902i	−0.992166	−	0.992166i	−0.999970	+	0.00780379i	$0.997516\pi$
$264$		0			0
$265$	15.4379	+	11.9858i	0.948341	+	0.736279i
$266$		−	3.35477i		−	0.205694i
$267$		0			0
$268$	55.1363	−	55.1363i	3.36799	−	3.36799i
$269$	−5.57270			−0.339774			−0.169887	−	0.985464i	$-0.554340\pi$
$269$	−5.57270			−0.339774			−0.169887	+	0.985464i	$0.554340\pi$
$270$		0			0
$271$	−3.44302			−0.209149			−0.104574	−	0.994517i	$-0.533348\pi$
$271$	−3.44302			−0.209149			−0.104574	+	0.994517i	$0.533348\pi$
$272$	−76.2907	+	76.2907i	−4.62580	+	4.62580i
$273$		0			0
$274$			17.5074i			1.05766i
$275$	6.76717	+	26.4533i	0.408075	+	1.59519i
$276$		0			0
$277$	−9.24600	−	9.24600i	−0.555538	−	0.555538i	0.372496	−	0.928034i	$-0.378502\pi$
$277$	−9.24600	−	9.24600i	−0.555538	−	0.555538i	−0.928034	+	0.372496i	$0.878502\pi$
$278$	−31.6897	−	31.6897i	−1.90062	−	1.90062i
$279$		0			0
$280$	3.44595	+	27.3746i	0.205935	+	1.63595i
$281$			16.9578i			1.01162i	0.862646	+	0.505809i	$0.168806\pi$
$281$			16.9578i			1.01162i	−0.862646	+	0.505809i	$0.831194\pi$
$282$		0			0
$283$	1.28776	−	1.28776i	0.0765491	−	0.0765491i	−0.667796	−	0.744345i	$-0.732762\pi$
$283$	1.28776	−	1.28776i	0.0765491	−	0.0765491i	0.744345	+	0.667796i	$0.232762\pi$
$284$	20.3595			1.20811
$285$		0			0
$286$	−44.3264			−2.62108
$287$	−7.28004	+	7.28004i	−0.429727	+	0.429727i
$288$		0			0
$289$		−	23.8348i		−	1.40205i
$290$	0.0119739	−	0.0154226i	0.000703132	−	0.000905647i
$291$		0			0
$292$	−31.2685	−	31.2685i	−1.82985	−	1.82985i
$293$	−13.6994	−	13.6994i	−0.800330	−	0.800330i	0.182817	−	0.983147i	$-0.441478\pi$
$293$	−13.6994	−	13.6994i	−0.800330	−	0.800330i	−0.983147	+	0.182817i	$0.941478\pi$
$294$		0			0
$295$	−31.7146	+	3.99227i	−1.84649	+	0.232439i
$296$		−	3.18076i		−	0.184878i
$297$		0			0
$298$	−8.33501	+	8.33501i	−0.482834	+	0.482834i
$299$	−7.82743			−0.452672
$300$		0			0
$301$	3.05992			0.176371
$302$	18.1480	−	18.1480i	1.04430	−	1.04430i
$303$		0			0
$304$		−	16.8838i		−	0.968355i
$305$	22.5098	−	2.83356i	1.28891	−	0.162249i
$306$		0			0
$307$	4.58950	+	4.58950i	0.261937	+	0.261937i	0.825840	−	0.563904i	$-0.190701\pi$
$307$	4.58950	+	4.58950i	0.261937	+	0.261937i	−0.563904	+	0.825840i	$0.690701\pi$
$308$	26.5457	+	26.5457i	1.51258	+	1.51258i
$309$		0			0
$310$	3.54117	−	4.56110i	0.201125	−	0.259053i
$311$			15.4214i			0.874470i	0.899347	+	0.437235i	$0.144042\pi$
$311$			15.4214i			0.874470i	−0.899347	+	0.437235i	$0.855958\pi$
$312$		0			0
$313$	−3.50438	+	3.50438i	−0.198080	+	0.198080i	−0.799176	−	0.601097i	$-0.794731\pi$
$313$	−3.50438	+	3.50438i	−0.198080	+	0.198080i	0.601097	+	0.799176i	$0.294731\pi$
$314$	−25.8073			−1.45639
$315$		0			0
$316$	−58.7138			−3.30291
$317$	−3.39019	+	3.39019i	−0.190412	+	0.190412i	−0.795874	−	0.605462i	$-0.792988\pi$
$317$	−3.39019	+	3.39019i	−0.190412	+	0.190412i	0.605462	+	0.795874i	$0.292988\pi$
$318$		0			0
$319$		−	0.0172091i		−	0.000963526i
$320$	10.9998	+	87.3823i	0.614907	+	4.88482i
$321$		0			0
$322$	6.33874	+	6.33874i	0.353244	+	0.353244i
$323$	4.51856	+	4.51856i	0.251420	+	0.251420i
$324$		0			0
$325$	7.46680	−	12.6003i	0.414184	−	0.698938i
$326$			17.3192i			0.959222i
$327$		0			0
$328$	−61.2820	+	61.2820i	−3.38373	+	3.38373i
$329$	−0.970509			−0.0535059
$330$		0			0
$331$	−11.9188			−0.655119			−0.327559	−	0.944831i	$-0.606226\pi$
$331$	−11.9188			−0.655119			−0.327559	+	0.944831i	$0.606226\pi$
$332$	−10.2520	+	10.2520i	−0.562650	+	0.562650i
$333$		0			0
$334$			42.6815i			2.33543i
$335$	24.2552	+	18.8314i	1.32520	+	1.02887i
$336$		0			0
$337$	−20.4505	−	20.4505i	−1.11401	−	1.11401i	−0.992603	−	0.121407i	$-0.961260\pi$
$337$	−20.4505	−	20.4505i	−1.11401	−	1.11401i	−0.121407	−	0.992603i	$-0.538740\pi$
$338$	−8.65869	−	8.65869i	−0.470971	−	0.470971i
$339$		0			0
$340$	−64.0856	−	49.7552i	−3.47553	−	2.69836i
$341$		−	5.08944i		−	0.275609i
$342$		0			0
$343$	10.7305	−	10.7305i	0.579393	−	0.579393i
$344$	25.7578			1.38877
$345$		0			0
$346$	34.8673			1.87448
$347$	−14.3452	+	14.3452i	−0.770093	+	0.770093i	−0.978123	−	0.208029i	$-0.933295\pi$
$347$	−14.3452	+	14.3452i	−0.770093	+	0.770093i	0.208029	+	0.978123i	$0.433295\pi$
$348$		0			0
$349$			12.3698i			0.662142i	0.943606	+	0.331071i	$0.107410\pi$
$349$			12.3698i			0.662142i	−0.943606	+	0.331071i	$0.892590\pi$
$350$	−16.2506	+	4.15715i	−0.868629	+	0.222209i
$351$		0			0
$352$	101.947	+	101.947i	5.43382	+	5.43382i
$353$	−0.436019	−	0.436019i	−0.0232070	−	0.0232070i	0.695408	−	0.718615i	$-0.255224\pi$
$353$	−0.436019	−	0.436019i	−0.0232070	−	0.0232070i	−0.718615	+	0.695408i	$0.755224\pi$
$354$		0			0
$355$	1.00139	+	7.95500i	0.0531480	+	0.422208i
$356$			22.3198i			1.18295i
$357$		0			0
$358$	−23.0121	+	23.0121i	−1.21623	+	1.21623i
$359$	−27.8172			−1.46814			−0.734068	−	0.679076i	$-0.762381\pi$
$359$	−27.8172			−1.46814			−0.734068	+	0.679076i	$0.762381\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	19.6039	−	19.6039i	1.03036	−	1.03036i
$363$		0			0
$364$		−	20.1372i		−	1.05548i
$365$	10.6795	−	13.7554i	0.558993	−	0.719993i
$366$		0			0
$367$	11.3323	+	11.3323i	0.591539	+	0.591539i	0.938047	−	0.346508i	$-0.112633\pi$
$367$	11.3323	+	11.3323i	0.591539	+	0.591539i	−0.346508	+	0.938047i	$0.612633\pi$
$368$	31.9015	+	31.9015i	1.66298	+	1.66298i
$369$		0			0
$370$	1.91862	−	0.241518i	0.0997442	−	0.0125559i
$371$			10.5822i			0.549403i
$372$		0			0
$373$	2.87926	−	2.87926i	0.149082	−	0.149082i	−0.628626	−	0.777708i	$-0.716382\pi$
$373$	2.87926	−	2.87926i	0.149082	−	0.149082i	0.777708	+	0.628626i	$0.216382\pi$
$374$	−96.6972			−5.00009
$375$		0			0
$376$	−8.16957			−0.421313
$377$	−0.00652730	+	0.00652730i	−0.000336173	+	0.000336173i
$378$		0			0
$379$		−	5.60842i		−	0.288085i	−0.989571	−	0.144043i	$-0.953990\pi$
$379$		−	5.60842i		−	0.288085i	0.989571	−	0.144043i	$-0.0460103\pi$
$380$	12.5970	−	1.58573i	0.646213	−	0.0813461i
$381$		0			0
$382$	23.2445	+	23.2445i	1.18929	+	1.18929i
$383$	−8.10307	−	8.10307i	−0.414047	−	0.414047i	0.469098	−	0.883146i	$-0.344579\pi$
$383$	−8.10307	−	8.10307i	−0.414047	−	0.414047i	−0.883146	+	0.469098i	$0.844579\pi$
$384$		0			0
$385$	−9.06649	+	11.6778i	−0.462071	+	0.595156i
$386$		−	17.2369i		−	0.877334i
$387$		0			0
$388$	30.0131	−	30.0131i	1.52368	−	1.52368i
$389$	−28.9704			−1.46886			−0.734429	−	0.678685i	$-0.762550\pi$
$389$	−28.9704			−1.46886			−0.734429	+	0.678685i	$0.762550\pi$
$390$		0			0
$391$	−17.0754			−0.863539
$392$	39.8820	−	39.8820i	2.01435	−	2.01435i
$393$		0			0
$394$		−	63.8786i		−	3.21816i
$395$	−2.88785	−	22.9411i	−0.145304	−	1.15429i
$396$		0			0
$397$	−8.89058	−	8.89058i	−0.446205	−	0.446205i	0.447886	−	0.894091i	$-0.352177\pi$
$397$	−8.89058	−	8.89058i	−0.446205	−	0.446205i	−0.894091	+	0.447886i	$0.852177\pi$
$398$	14.5925	+	14.5925i	0.731456	+	0.731456i
$399$		0			0
$400$	−81.7855	+	20.9220i	−4.08928	+	1.04610i
$401$		−	18.9793i		−	0.947780i	−0.880584	−	0.473890i	$-0.842849\pi$
$401$		−	18.9793i		−	0.947780i	0.880584	−	0.473890i	$-0.157151\pi$
$402$		0			0
$403$	−1.93039	+	1.93039i	−0.0961596	+	0.0961596i
$404$	−55.0672			−2.73969
$405$		0			0
$406$	0.0105718			0.000524669
$407$	1.20518	−	1.20518i	0.0597386	−	0.0597386i
$408$		0			0
$409$		−	31.4196i		−	1.55360i	−0.629747	−	0.776800i	$-0.716841\pi$
$409$		−	31.4196i		−	1.55360i	0.629747	−	0.776800i	$-0.283159\pi$
$410$	−41.6182	−	32.3118i	−2.05538	−	1.59577i
$411$		0			0
$412$	2.02595	+	2.02595i	0.0998112	+	0.0998112i
$413$	−12.2380	−	12.2380i	−0.602195	−	0.602195i
$414$		0			0
$415$	−4.50998	−	3.50149i	−0.221386	−	0.171881i
$416$		−	77.3360i		−	3.79171i
$417$		0			0
$418$	10.7000	−	10.7000i	0.523354	−	0.523354i
$419$	40.2224			1.96499			0.982496	−	0.186286i	$-0.0596450\pi$
$419$	40.2224			1.96499			0.982496	+	0.186286i	$0.0596450\pi$
$420$		0			0
$421$	20.0777			0.978529			0.489265	−	0.872135i	$-0.337265\pi$
$421$	20.0777			0.978529			0.489265	+	0.872135i	$0.337265\pi$
$422$	20.7957	−	20.7957i	1.01232	−	1.01232i
$423$		0			0
$424$			89.0794i			4.32608i
$425$	16.2887	−	27.4873i	0.790117	−	1.33333i
$426$		0			0
$427$	8.68610	+	8.68610i	0.420350	+	0.420350i
$428$	40.3412	+	40.3412i	1.94997	+	1.94997i
$429$		0			0
$430$	1.95581	+	15.5370i	0.0943178	+	0.749260i
$431$		−	35.5854i		−	1.71409i	−0.515245	−	0.857043i	$-0.672299\pi$
$431$		−	35.5854i		−	1.71409i	0.515245	−	0.857043i	$-0.327701\pi$
$432$		0			0
$433$	17.1114	−	17.1114i	0.822322	−	0.822322i	−0.164119	−	0.986441i	$-0.552478\pi$
$433$	17.1114	−	17.1114i	0.822322	−	0.822322i	0.986441	+	0.164119i	$0.0524780\pi$
$434$	3.12651			0.150077
$435$		0			0
$436$	83.6150			4.00443
$437$	1.88947	−	1.88947i	0.0903856	−	0.0903856i
$438$		0			0
$439$			18.1837i			0.867859i	0.900947	+	0.433930i	$0.142873\pi$
$439$			18.1837i			0.867859i	−0.900947	+	0.433930i	$0.857127\pi$
$440$	−76.3201	+	98.3016i	−3.63842	+	4.68635i
$441$		0			0
$442$	36.6766	+	36.6766i	1.74453	+	1.74453i
$443$	−16.9872	−	16.9872i	−0.807085	−	0.807085i	0.177106	−	0.984192i	$-0.443326\pi$
$443$	−16.9872	−	16.9872i	−0.807085	−	0.807085i	−0.984192	+	0.177106i	$0.943326\pi$
$444$		0			0
$445$	−8.72097	+	1.09781i	−0.413414	+	0.0520410i
$446$		−	3.87934i		−	0.183692i
$447$		0			0
$448$	−33.7191	+	33.7191i	−1.59308	+	1.59308i
$449$	−13.4830			−0.636304			−0.318152	−	0.948040i	$-0.603062\pi$
$449$	−13.4830			−0.636304			−0.318152	+	0.948040i	$0.603062\pi$
$450$		0			0
$451$	−46.4391			−2.18673
$452$	35.6658	−	35.6658i	1.67758	−	1.67758i
$453$		0			0
$454$			55.9680i			2.62671i
$455$	7.86817	−	0.990455i	0.368866	−	0.0464332i
$456$		0			0
$457$	22.2789	+	22.2789i	1.04216	+	1.04216i	0.999071	+	0.0430903i	$0.0137203\pi$
$457$	22.2789	+	22.2789i	1.04216	+	1.04216i	0.0430903	+	0.999071i	$0.486280\pi$
$458$	31.9967	+	31.9967i	1.49511	+	1.49511i
$459$		0			0
$460$	−20.8055	+	26.7979i	−0.970061	+	1.24946i
$461$		−	13.8272i		−	0.643996i	−0.946740	−	0.321998i	$-0.895646\pi$
$461$		−	13.8272i		−	0.643996i	0.946740	−	0.321998i	$-0.104354\pi$
$462$		0			0
$463$	−19.6128	+	19.6128i	−0.911482	+	0.911482i	−0.996389	−	0.0849064i	$-0.972941\pi$
$463$	−19.6128	+	19.6128i	−0.911482	+	0.911482i	0.0849064	+	0.996389i	$0.472941\pi$
$464$	0.0532054			0.00247000
$465$		0			0
$466$	81.5339			3.77698
$467$	14.5969	−	14.5969i	0.675463	−	0.675463i	−0.283507	−	0.958970i	$-0.591498\pi$
$467$	14.5969	−	14.5969i	0.675463	−	0.675463i	0.958970	+	0.283507i	$0.0914979\pi$
$468$		0			0
$469$			16.6263i			0.767730i
$470$	−0.620322	−	4.92784i	−0.0286133	−	0.227304i
$471$		0			0
$472$	−103.018	−	103.018i	−4.74177	−	4.74177i
$473$	9.75956	+	9.75956i	0.448745	+	0.448745i
$474$		0			0
$475$	1.23918	+	4.84401i	0.0568573	+	0.222258i
$476$		−	43.9289i		−	2.01348i
$477$		0			0
$478$	−51.1522	+	51.1522i	−2.33965	+	2.33965i
$479$	23.9892			1.09610			0.548048	−	0.836447i	$-0.315371\pi$
$479$	23.9892			1.09610			0.548048	+	0.836447i	$0.315371\pi$
$480$		0			0
$481$	−0.914233			−0.0416855
$482$	−5.97871	+	5.97871i	−0.272323	+	0.272323i
$483$		0			0
$484$			106.876i			4.85800i
$485$	13.2032	+	10.2507i	0.599524	+	0.465462i
$486$		0			0
$487$	−8.65504	−	8.65504i	−0.392197	−	0.392197i	0.483273	−	0.875470i	$-0.339448\pi$
$487$	−8.65504	−	8.65504i	−0.392197	−	0.392197i	−0.875470	+	0.483273i	$0.839448\pi$
$488$	73.1180	+	73.1180i	3.30990	+	3.30990i
$489$		0			0
$490$	27.0849	+	21.0283i	1.22357	+	0.949964i
$491$			18.9837i			0.856723i	0.903607	+	0.428362i	$0.140909\pi$
$491$			18.9837i			0.856723i	−0.903607	+	0.428362i	$0.859091\pi$
$492$		0			0
$493$	−0.0142392	+	0.0142392i	−0.000641301	+	0.000641301i
$494$	−8.11687			−0.365195
$495$		0			0
$496$	15.7350			0.706524
$497$	−3.06968	+	3.06968i	−0.137694	+	0.137694i
$498$		0			0
$499$		−	5.06213i		−	0.226612i	−0.993560	−	0.113306i	$-0.963856\pi$
$499$		−	5.06213i		−	0.226612i	0.993560	−	0.113306i	$-0.0361440\pi$
$500$	−23.2912	−	59.0551i	−1.04161	−	2.64102i
$501$		0			0
$502$	12.4508	+	12.4508i	0.555707	+	0.555707i
$503$	−2.72862	−	2.72862i	−0.121663	−	0.121663i	0.643654	−	0.765317i	$-0.277418\pi$
$503$	−2.72862	−	2.72862i	−0.121663	−	0.121663i	−0.765317	+	0.643654i	$0.777418\pi$
$504$		0			0
$505$	−2.70849	−	21.5163i	−0.120526	−	0.957462i
$506$			40.4346i			1.79754i
$507$		0			0
$508$	−10.1378	+	10.1378i	−0.449794	+	0.449794i
$509$	−41.2272			−1.82736			−0.913681	−	0.406431i	$-0.866773\pi$
$509$	−41.2272			−1.82736			−0.913681	+	0.406431i	$0.866773\pi$
$510$		0			0
$511$	9.42898			0.417114
$512$	−71.8448	+	71.8448i	−3.17512	+	3.17512i
$513$		0			0
$514$			1.26126i			0.0556318i
$515$	−0.691947	+	0.891240i	−0.0304908	+	0.0392727i
$516$		0			0
$517$	−3.09542	−	3.09542i	−0.136136	−	0.136136i
$518$	0.740357	+	0.740357i	0.0325294	+	0.0325294i
$519$		0			0
$520$	66.2328	−	8.33747i	2.90450	−	0.365622i
$521$			10.2073i			0.447192i	0.974682	+	0.223596i	$0.0717796\pi$
$521$			10.2073i			0.447192i	−0.974682	+	0.223596i	$0.928220\pi$
$522$		0			0
$523$	18.9862	−	18.9862i	0.830207	−	0.830207i	−0.157338	−	0.987545i	$-0.550291\pi$
$523$	18.9862	−	18.9862i	0.830207	−	0.830207i	0.987545	+	0.157338i	$0.0502912\pi$
$524$	46.7670			2.04303
$525$		0			0
$526$	63.0524			2.74922
$527$	−4.21111	+	4.21111i	−0.183439	+	0.183439i
$528$		0			0
$529$		−	15.8598i		−	0.689557i
$530$	−53.7322	+	6.76387i	−2.33398	+	0.293804i
$531$		0			0
$532$	4.86094	+	4.86094i	0.210749	+	0.210749i
$533$	17.6140	+	17.6140i	0.762949	+	0.762949i
$534$		0			0
$535$	−13.7782	+	17.7466i	−0.595685	+	0.767253i
$536$			139.957i			6.04522i
$537$		0			0
$538$	10.9188	−	10.9188i	0.470744	−	0.470744i
$539$	30.2223			1.30177
$540$		0			0
$541$	−27.8880			−1.19900			−0.599499	−	0.800375i	$-0.704633\pi$
$541$	−27.8880			−1.19900			−0.599499	+	0.800375i	$0.704633\pi$
$542$	6.74604	−	6.74604i	0.289767	−	0.289767i
$543$		0			0
$544$		−	168.707i		−	7.23325i
$545$	4.11263	+	32.6707i	0.176166	+	1.39946i
$546$		0			0
$547$	−21.7647	−	21.7647i	−0.930590	−	0.930590i	0.0671524	−	0.997743i	$-0.478609\pi$
$547$	−21.7647	−	21.7647i	−0.930590	−	0.930590i	−0.997743	+	0.0671524i	$0.978609\pi$
$548$	−25.3675	−	25.3675i	−1.08365	−	1.08365i
$549$		0			0
$550$	−65.0901	−	38.5717i	−2.77545	−	1.64470i
$551$		−	0.00315126i		−	0.000134248i
$552$		0			0
$553$	8.85253	−	8.85253i	0.376448	−	0.376448i
$554$	36.2321			1.53935
$555$		0			0
$556$	91.8343			3.89464
$557$	16.7148	−	16.7148i	0.708230	−	0.708230i	−0.257933	−	0.966163i	$-0.583041\pi$
$557$	16.7148	−	16.7148i	0.708230	−	0.708230i	0.966163	+	0.257933i	$0.0830414\pi$
$558$		0			0
$559$		−	7.40347i		−	0.313134i
$560$	−36.1043	−	28.0309i	−1.52568	−	1.18452i
$561$		0			0
$562$	−33.2261	−	33.2261i	−1.40156	−	1.40156i
$563$	−27.3062	−	27.3062i	−1.15082	−	1.15082i	−0.986389	−	0.164431i	$-0.947421\pi$
$563$	−27.3062	−	27.3062i	−1.15082	−	1.15082i	−0.164431	−	0.986389i	$-0.552579\pi$
$564$		0			0
$565$	15.6898	+	12.1814i	0.660077	+	0.512474i
$566$			5.04630i			0.212112i
$567$		0			0
$568$	−25.8400	+	25.8400i	−1.08422	+	1.08422i
$569$	−41.7778			−1.75142			−0.875708	−	0.482841i	$-0.839605\pi$
$569$	−41.7778			−1.75142			−0.875708	+	0.482841i	$0.839605\pi$
$570$		0			0
$571$	−13.3703			−0.559528			−0.279764	−	0.960069i	$-0.590256\pi$
$571$	−13.3703			−0.559528			−0.279764	+	0.960069i	$0.590256\pi$
$572$	64.2273	−	64.2273i	2.68548	−	2.68548i
$573$		0			0
$574$		−	28.5281i		−	1.19074i
$575$	−11.4940	−	6.81123i	−0.479333	−	0.284048i
$576$		0			0
$577$	19.5122	+	19.5122i	0.812302	+	0.812302i	0.984979	−	0.172676i	$-0.0552415\pi$
$577$	19.5122	+	19.5122i	0.812302	+	0.812302i	−0.172676	+	0.984979i	$0.555242\pi$
$578$	46.7005	+	46.7005i	1.94249	+	1.94249i
$579$		0			0
$580$	0.00499704	+	0.0396965i	0.000207491	+	0.00164831i
$581$		−	3.09147i		−	0.128256i
$582$		0			0
$583$	−33.7519	+	33.7519i	−1.39786	+	1.39786i
$584$	79.3714			3.28441
$585$		0			0
$586$	53.6837			2.21765
$587$	−4.78568	+	4.78568i	−0.197526	+	0.197526i	−0.798939	−	0.601413i	$-0.794605\pi$
$587$	−4.78568	+	4.78568i	−0.197526	+	0.197526i	0.601413	+	0.798939i	$0.294605\pi$
$588$		0			0
$589$		−	0.931958i		−	0.0384007i
$590$	54.3174	−	69.9618i	2.23621	−	2.88028i
$591$		0			0
$592$	3.72605	+	3.72605i	0.153140	+	0.153140i
$593$	17.9505	+	17.9505i	0.737140	+	0.737140i	0.972024	−	0.234884i	$-0.0754709\pi$
$593$	17.9505	+	17.9505i	0.737140	+	0.737140i	−0.234884	+	0.972024i	$0.575471\pi$
$594$		0			0
$595$	17.1643	−	2.16066i	0.703666	−	0.0885783i
$596$		−	24.1542i		−	0.989396i
$597$		0			0
$598$	15.3366	−	15.3366i	0.627159	−	0.627159i
$599$	−7.40996			−0.302763			−0.151381	−	0.988475i	$-0.548372\pi$
$599$	−7.40996			−0.302763			−0.151381	+	0.988475i	$0.548372\pi$
$600$		0			0
$601$	−22.8129			−0.930559			−0.465279	−	0.885164i	$-0.654046\pi$
$601$	−22.8129			−0.930559			−0.465279	+	0.885164i	$0.654046\pi$
$602$	−5.99542	+	5.99542i	−0.244355	+	0.244355i
$603$		0			0
$604$			52.5917i			2.13992i
$605$	−41.7594	+	5.25673i	−1.69776	+	0.213716i
$606$		0			0
$607$	−8.40689	−	8.40689i	−0.341225	−	0.341225i	0.515603	−	0.856828i	$-0.327568\pi$
$607$	−8.40689	−	8.40689i	−0.341225	−	0.341225i	−0.856828	+	0.515603i	$0.827568\pi$
$608$	18.6682	+	18.6682i	0.757095	+	0.757095i
$609$		0			0
$610$	−38.5525	+	49.6563i	−1.56094	+	2.01053i
$611$			2.34815i			0.0949958i
$612$		0			0
$613$	0.704510	−	0.704510i	0.0284549	−	0.0284549i	−0.692736	−	0.721191i	$-0.743595\pi$
$613$	0.704510	−	0.704510i	0.0284549	−	0.0284549i	0.721191	+	0.692736i	$0.243595\pi$
$614$	−17.9848			−0.725807
$615$		0			0
$616$	−67.3831			−2.71494
$617$	−25.1156	+	25.1156i	−1.01112	+	1.01112i	−0.0111781	+	0.999938i	$0.503558\pi$
$617$	−25.1156	+	25.1156i	−1.01112	+	1.01112i	−0.999938	+	0.0111781i	$0.996442\pi$
$618$		0			0
$619$		−	4.40076i		−	0.176882i	−0.996081	−	0.0884408i	$-0.971812\pi$
$619$		−	4.40076i		−	0.176882i	0.996081	−	0.0884408i	$-0.0281884\pi$
$620$	1.47783	+	11.7399i	0.0593511	+	0.471485i
$621$		0			0
$622$	−30.2158	−	30.2158i	−1.21154	−	1.21154i
$623$	−3.36525	−	3.36525i	−0.134826	−	0.134826i
$624$		0			0
$625$	21.9289	−	12.0052i	0.877155	−	0.480206i
$626$		−	13.7326i		−	0.548863i
$627$		0			0
$628$	37.3938	−	37.3938i	1.49218	−	1.49218i
$629$	−1.99438			−0.0795212
$630$		0			0
$631$	−23.2493			−0.925540			−0.462770	−	0.886478i	$-0.653144\pi$
$631$	−23.2493			−0.925540			−0.462770	+	0.886478i	$0.653144\pi$
$632$	74.5189	−	74.5189i	2.96420	−	2.96420i
$633$		0			0
$634$		−	13.2851i		−	0.527618i
$635$	−4.45977	−	3.46250i	−0.176981	−	0.137405i
$636$		0			0
$637$	−11.4631	−	11.4631i	−0.454186	−	0.454186i
$638$	0.0337185	+	0.0337185i	0.00133493	+	0.00133493i
$639$		0			0
$640$	−99.5038	−	77.2534i	−3.93323	−	3.05371i
$641$			38.6951i			1.52836i	0.645001	+	0.764182i	$0.276857\pi$
$641$			38.6951i			1.52836i	−0.645001	+	0.764182i	$0.723143\pi$
$642$		0			0
$643$	−27.2947	+	27.2947i	−1.07640	+	1.07640i	−0.0795667	+	0.996830i	$0.525354\pi$
$643$	−27.2947	+	27.2947i	−1.07640	+	1.07640i	−0.996830	+	0.0795667i	$0.974646\pi$
$644$	−18.3692			−0.723848
$645$		0			0
$646$	−17.7068			−0.696664
$647$	6.91041	−	6.91041i	0.271676	−	0.271676i	−0.558098	−	0.829775i	$-0.688469\pi$
$647$	6.91041	−	6.91041i	0.271676	−	0.271676i	0.829775	+	0.558098i	$0.188469\pi$
$648$		0			0
$649$		−	78.0660i		−	3.06436i
$650$	10.0582	+	39.3182i	0.394516	+	1.54219i
$651$		0			0
$652$	−25.0949	−	25.0949i	−0.982791	−	0.982791i
$653$	−5.27855	−	5.27855i	−0.206566	−	0.206566i	0.596240	−	0.802806i	$-0.296661\pi$
$653$	−5.27855	−	5.27855i	−0.206566	−	0.206566i	−0.802806	+	0.596240i	$0.796661\pi$
$654$		0			0
$655$	2.30025	+	18.2732i	0.0898781	+	0.713992i
$656$		−	143.576i		−	5.60569i
$657$		0			0
$658$	1.90156	−	1.90156i	0.0741304	−	0.0741304i
$659$	−21.8569			−0.851424			−0.425712	−	0.904859i	$-0.639976\pi$
$659$	−21.8569			−0.851424			−0.425712	+	0.904859i	$0.639976\pi$
$660$		0			0
$661$	−0.641376			−0.0249466			−0.0124733	−	0.999922i	$-0.503970\pi$
$661$	−0.641376			−0.0249466			−0.0124733	+	0.999922i	$0.503970\pi$
$662$	23.3530	−	23.3530i	0.907642	−	0.907642i
$663$		0			0
$664$		−	26.0234i		−	1.00990i
$665$	−1.66022	+	2.13839i	−0.0643805	+	0.0829233i
$666$		0			0
$667$	0.00595422	+	0.00595422i	0.000230548	+	0.000230548i
$668$	−61.8439	−	61.8439i	−2.39281	−	2.39281i
$669$		0			0
$670$	−84.4213	+	10.6270i	−3.26148	+	0.410559i
$671$			55.4084i			2.13902i
$672$		0			0
$673$	24.8372	−	24.8372i	0.957402	−	0.957402i	−0.0417271	−	0.999129i	$-0.513286\pi$
$673$	24.8372	−	24.8372i	0.957402	−	0.957402i	0.999129	+	0.0417271i	$0.0132860\pi$
$674$	80.1389			3.08683
$675$		0			0
$676$	25.0922			0.965086
$677$	23.9517	−	23.9517i	0.920539	−	0.920539i	−0.0765287	−	0.997067i	$-0.524384\pi$
$677$	23.9517	−	23.9517i	0.920539	−	0.920539i	0.997067	+	0.0765287i	$0.0243837\pi$
$678$		0			0
$679$			9.05040i			0.347322i
$680$	144.486	−	18.1880i	5.54077	−	0.697479i
$681$		0			0
$682$	9.97194	+	9.97194i	0.381845	+	0.381845i
$683$	17.6124	+	17.6124i	0.673918	+	0.673918i	0.958617	−	0.284699i	$-0.0918936\pi$
$683$	17.6124	+	17.6124i	0.673918	+	0.673918i	−0.284699	+	0.958617i	$0.591894\pi$
$684$		0			0
$685$	8.66410	−	11.1595i	0.331038	−	0.426383i
$686$			42.0494i			1.60545i
$687$		0			0
$688$	−30.1736	+	30.1736i	−1.15036	+	1.15036i
$689$	25.6037			0.975424
$690$		0			0
$691$	5.81616			0.221257			0.110629	−	0.993862i	$-0.464714\pi$
$691$	5.81616			0.221257			0.110629	+	0.993862i	$0.464714\pi$
$692$	−50.5214	+	50.5214i	−1.92054	+	1.92054i
$693$		0			0
$694$		−	56.2144i		−	2.13387i
$695$	4.51689	+	35.8822i	0.171336	+	1.36109i
$696$		0			0
$697$	38.4247	+	38.4247i	1.45544	+	1.45544i
$698$	−24.2367	−	24.2367i	−0.917373	−	0.917373i
$699$		0			0
$700$	17.5229	−	29.5700i	0.662303	−	1.11764i
$701$		−	22.0006i		−	0.830952i	−0.909604	−	0.415476i	$-0.863615\pi$
$701$		−	22.0006i		−	0.830952i	0.909604	−	0.415476i	$-0.136385\pi$
$702$		0			0
$703$	0.220688	−	0.220688i	0.00832339	−	0.00832339i
$704$	−215.093			−8.10663
$705$		0			0
$706$	1.70862			0.0643047
$707$	8.30271	−	8.30271i	0.312256	−	0.312256i
$708$		0			0
$709$			3.92768i			0.147507i	0.997276	+	0.0737535i	$0.0234978\pi$
$709$			3.92768i			0.147507i	−0.997276	+	0.0737535i	$0.976502\pi$
$710$	−17.5486	−	13.6245i	−0.658587	−	0.511318i
$711$		0			0
$712$	−28.3281	−	28.3281i	−1.06164	−	1.06164i
$713$	1.76091	+	1.76091i	0.0659464	+	0.0659464i
$714$		0			0
$715$	28.2544	+	21.9364i	1.05666	+	0.820373i
$716$		−	66.6874i		−	2.49222i
$717$		0			0
$718$	54.5033	−	54.5033i	2.03405	−	2.03405i
$719$	18.9384			0.706285			0.353142	−	0.935570i	$-0.385113\pi$
$719$	18.9384			0.706285			0.353142	+	0.935570i	$0.385113\pi$
$720$		0			0
$721$	−0.610921			−0.0227519
$722$	1.95934	−	1.95934i	0.0729190	−	0.0729190i
$723$		0			0
$724$			56.8107i			2.11135i
$725$	−0.0152648	+	0.00390497i	−0.000566919	+	0.000145027i
$726$		0			0
$727$	−17.7527	−	17.7527i	−0.658411	−	0.658411i	0.296593	−	0.955004i	$-0.404150\pi$
$727$	−17.7527	−	17.7527i	−0.658411	−	0.658411i	−0.955004	+	0.296593i	$0.904150\pi$
$728$	25.5580	+	25.5580i	0.947241	+	0.947241i
$729$		0			0
$730$	6.02674	+	47.8764i	0.223060	+	1.77199i
$731$		−	16.1505i		−	0.597349i
$732$		0			0
$733$	−0.950125	+	0.950125i	−0.0350937	+	0.0350937i	−0.724436	−	0.689342i	$-0.757900\pi$
$733$	−0.950125	+	0.950125i	−0.0350937	+	0.0350937i	0.689342	+	0.724436i	$0.257900\pi$
$734$	−44.4075			−1.63911
$735$		0			0
$736$	−70.5460			−2.60036
$737$	−53.0292	+	53.0292i	−1.95336	+	1.95336i
$738$		0			0
$739$		−	36.9689i		−	1.35992i	−0.733248	−	0.679961i	$-0.761996\pi$
$739$		−	36.9689i		−	1.35992i	0.733248	−	0.679961i	$-0.238004\pi$
$740$	−2.43006	+	3.12996i	−0.0893306	+	0.115059i
$741$		0			0
$742$	−20.7342	−	20.7342i	−0.761176	−	0.761176i
$743$	−5.55417	−	5.55417i	−0.203763	−	0.203763i	0.597847	−	0.801610i	$-0.296023\pi$
$743$	−5.55417	−	5.55417i	−0.203763	−	0.203763i	−0.801610	+	0.597847i	$0.796023\pi$
$744$		0			0
$745$	9.43773	−	1.18803i	0.345772	−	0.0435262i
$746$			11.2829i			0.413096i
$747$		0			0
$748$	140.111	−	140.111i	5.12295	−	5.12295i
$749$	−12.1648			−0.444493
$750$		0			0
$751$	−7.76037			−0.283180			−0.141590	−	0.989925i	$-0.545221\pi$
$751$	−7.76037			−0.283180			−0.141590	+	0.989925i	$0.545221\pi$
$752$	9.57011	−	9.57011i	0.348986	−	0.348986i
$753$		0			0
$754$		−	0.0255784i		−	0.000931510i
$755$	−20.5490	+	2.58674i	−0.747856	+	0.0941410i
$756$		0			0
$757$	36.2585	+	36.2585i	1.31784	+	1.31784i	0.915484	+	0.402355i	$0.131808\pi$
$757$	36.2585	+	36.2585i	1.31784	+	1.31784i	0.402355	+	0.915484i	$0.368192\pi$
$758$	10.9888	+	10.9888i	0.399131	+	0.399131i
$759$		0			0
$760$	−13.9754	+	18.0006i	−0.506942	+	0.652950i
$761$		−	0.0245055i		−	0.000888325i	−1.00000		0.000444162i	$-0.999859\pi$
$761$		−	0.0245055i		−	0.000888325i	1.00000		0.000444162i	$-0.000141381\pi$
$762$		0			0
$763$	−12.6070	+	12.6070i	−0.456404	+	0.456404i
$764$	−67.3609			−2.43703
$765$		0			0
$766$	31.7533			1.14729
$767$	−29.6099	+	29.6099i	−1.06915	+	1.06915i
$768$		0			0
$769$			10.2039i			0.367962i	0.982930	+	0.183981i	$0.0588985\pi$
$769$			10.2039i			0.367962i	−0.982930	+	0.183981i	$0.941102\pi$
$770$	−5.11645	−	40.6451i	−0.184384	−	1.46475i
$771$		0			0
$772$	24.9756	+	24.9756i	0.898891	+	0.898891i
$773$	−7.14926	−	7.14926i	−0.257141	−	0.257141i	0.566749	−	0.823890i	$-0.308201\pi$
$773$	−7.14926	−	7.14926i	−0.257141	−	0.257141i	−0.823890	+	0.566749i	$0.808201\pi$
$774$		0			0
$775$	−4.51441	+	1.15486i	−0.162163	+	0.0414838i
$776$			76.1846i			2.73487i
$777$		0			0
$778$	56.7629	−	56.7629i	2.03505	−	2.03505i
$779$	−8.50374			−0.304678
$780$		0			0
$781$	−19.5814			−0.700677
$782$	33.4564	−	33.4564i	1.19640	−	1.19640i
$783$		0			0
$784$			93.4384i			3.33709i
$785$	16.4500	+	12.7716i	0.587127	+	0.455837i
$786$		0			0
$787$	0.540208	+	0.540208i	0.0192563	+	0.0192563i	0.716669	−	0.697413i	$-0.245666\pi$
$787$	0.540208	+	0.540208i	0.0192563	+	0.0192563i	−0.697413	+	0.716669i	$0.745666\pi$
$788$	92.5577	+	92.5577i	3.29723	+	3.29723i
$789$		0			0
$790$	50.6077	+	39.2911i	1.80054	+	1.39792i
$791$			10.7550i			0.382402i
$792$		0			0
$793$	21.0160	−	21.0160i	0.746301	−	0.746301i
$794$	34.8393			1.23640
$795$		0			0
$796$	−42.2880			−1.49886
$797$	7.49435	−	7.49435i	0.265463	−	0.265463i	−0.561806	−	0.827269i	$-0.689893\pi$
$797$	7.49435	−	7.49435i	0.265463	−	0.265463i	0.827269	+	0.561806i	$0.189893\pi$
$798$		0			0
$799$			5.12243i			0.181219i
$800$	67.2958	−	113.562i	2.37927	−	4.01503i
$801$		0			0
$802$	37.1868	+	37.1868i	1.31311	+	1.31311i
$803$	30.0736	+	30.0736i	1.06127	+	1.06127i
$804$		0			0
$805$	−0.903495	−	7.17736i	−0.0318440	−	0.252969i
$806$		−	7.56458i		−	0.266451i
$807$		0			0
$808$	69.8907	−	69.8907i	2.45875	−	2.45875i
$809$	0.284214			0.00999244			0.00499622	−	0.999988i	$-0.498410\pi$
$809$	0.284214			0.00999244			0.00499622	+	0.999988i	$0.498410\pi$
$810$		0			0
$811$	−52.1330			−1.83064			−0.915319	−	0.402729i	$-0.868062\pi$
$811$	−52.1330			−1.83064			−0.915319	+	0.402729i	$0.868062\pi$
$812$	−0.0153181	+	0.0153181i	−0.000537560	+	0.000537560i
$813$		0			0
$814$			4.72271i			0.165531i
$815$	8.57097	−	11.0396i	0.300228	−	0.386699i
$816$		0			0
$817$	1.78713	+	1.78713i	0.0625238	+	0.0625238i
$818$	61.5617	+	61.5617i	2.15245	+	2.15245i
$819$		0			0
$820$	107.122	−	13.4846i	3.74085	−	0.470903i
$821$		−	44.7223i		−	1.56082i	−0.625268	−	0.780410i	$-0.715011\pi$
$821$		−	44.7223i		−	1.56082i	0.625268	−	0.780410i	$-0.284989\pi$
$822$		0			0
$823$	22.2411	−	22.2411i	0.775275	−	0.775275i	−0.203748	−	0.979023i	$-0.565312\pi$
$823$	22.2411	−	22.2411i	0.775275	−	0.775275i	0.979023	+	0.203748i	$0.0653123\pi$
$824$	−5.14262			−0.179152
$825$		0			0
$826$	47.9569			1.66863
$827$	31.8846	−	31.8846i	1.10874	−	1.10874i	0.115420	−	0.993317i	$-0.463179\pi$
$827$	31.8846	−	31.8846i	1.10874	−	1.10874i	0.993317	−	0.115420i	$-0.0368214\pi$
$828$		0			0
$829$			12.4914i			0.433845i	0.976189	+	0.216923i	$0.0696019\pi$
$829$			12.4914i			0.433845i	−0.976189	+	0.216923i	$0.930398\pi$
$830$	15.6972	−	1.97598i	0.544857	−	0.0685872i
$831$		0			0
$832$	81.5834	+	81.5834i	2.82840	+	2.82840i
$833$	−25.0066	−	25.0066i	−0.866427	−	0.866427i
$834$		0			0
$835$	21.1223	−	27.2059i	0.730968	−	0.941501i
$836$			31.0078i			1.07243i
$837$		0			0
$838$	−78.8092	+	78.8092i	−2.72242	+	2.72242i
$839$	41.0921			1.41866			0.709329	−	0.704878i	$-0.248998\pi$
$839$	41.0921			1.41866			0.709329	+	0.704878i	$0.248998\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−39.3391	+	39.3391i	−1.35571	+	1.35571i
$843$		0			0
$844$			60.2644i			2.07439i
$845$	1.23417	+	9.80424i	0.0424567	+	0.337276i
$846$		0			0
$847$	−16.1141	−	16.1141i	−0.553689	−	0.553689i
$848$	−104.351	−	104.351i	−3.58342	−	3.58342i
$849$		0			0
$850$	21.9418	+	85.7719i	0.752598	+	2.94195i
$851$			0.833965i			0.0285880i
$852$		0			0
$853$	−9.99395	+	9.99395i	−0.342186	+	0.342186i	−0.857189	−	0.515002i	$-0.827791\pi$
$853$	−9.99395	+	9.99395i	−0.342186	+	0.342186i	0.515002	+	0.857189i	$0.327791\pi$
$854$	−34.0380			−1.16476
$855$		0			0
$856$	−102.401			−3.50000
$857$	−39.1772	+	39.1772i	−1.33827	+	1.33827i	−0.440529	+	0.897738i	$0.645209\pi$
$857$	−39.1772	+	39.1772i	−1.33827	+	1.33827i	−0.897738	+	0.440529i	$0.854791\pi$
$858$		0			0
$859$		−	8.77759i		−	0.299488i	−0.988725	−	0.149744i	$-0.952155\pi$
$859$		−	8.77759i		−	0.299488i	0.988725	−	0.149744i	$-0.0478449\pi$
$860$	−25.3464	−	19.6786i	−0.864306	−	0.671035i
$861$		0			0
$862$	69.7238	+	69.7238i	2.37480	+	2.37480i
$863$	−1.10409	−	1.10409i	−0.0375838	−	0.0375838i	0.688065	−	0.725649i	$-0.258460\pi$
$863$	−1.10409	−	1.10409i	−0.0375838	−	0.0375838i	−0.725649	+	0.688065i	$0.758460\pi$
$864$		0			0
$865$	−22.2250	−	17.2552i	−0.755674	−	0.586695i
$866$			67.0541i			2.27859i
$867$		0			0
$868$	−4.53019	+	4.53019i	−0.153765	+	0.153765i
$869$	56.4700			1.91561
$870$		0			0
$871$	40.2273			1.36305
$872$	−106.123	+	106.123i	−3.59379	+	3.59379i
$873$		0			0
$874$			7.40422i			0.250452i
$875$	12.4157	+	5.39227i	0.419727	+	0.182292i
$876$		0			0
$877$	−2.44257	−	2.44257i	−0.0824796	−	0.0824796i	0.664663	−	0.747143i	$-0.268575\pi$
$877$	−2.44257	−	2.44257i	−0.0824796	−	0.0824796i	−0.747143	+	0.664663i	$0.768575\pi$
$878$	−35.6280	−	35.6280i	−1.20239	−	1.20239i
$879$		0			0
$880$	−25.7500	−	204.558i	−0.868032	−	6.89565i
$881$			23.1978i			0.781553i	0.920486	+	0.390776i	$0.127793\pi$
$881$			23.1978i			0.781553i	−0.920486	+	0.390776i	$0.872207\pi$
$882$		0			0
$883$	−29.7481	+	29.7481i	−1.00110	+	1.00110i	−0.00110247	+	0.999999i	$0.500351\pi$
$883$	−29.7481	+	29.7481i	−1.00110	+	1.00110i	−0.999999	+	0.00110247i	$0.999649\pi$
$884$	−106.286			−3.57479
$885$		0			0
$886$	66.5673			2.23637
$887$	−14.0783	+	14.0783i	−0.472704	+	0.472704i	−0.902789	−	0.430085i	$-0.858484\pi$
$887$	−14.0783	+	14.0783i	−0.472704	+	0.472704i	0.430085	+	0.902789i	$0.358484\pi$
$888$		0			0
$889$		−	3.05705i		−	0.102530i
$890$	14.9364	−	19.2383i	0.500668	−	0.644870i
$891$		0			0
$892$	5.62102	+	5.62102i	0.188206	+	0.188206i
$893$	−0.566821	−	0.566821i	−0.0189679	−	0.0189679i
$894$		0			0
$895$	26.0566	−	3.28004i	0.870976	−	0.109640i
$896$		−	68.2071i		−	2.27864i
$897$		0			0
$898$	26.4178	−	26.4178i	0.881575	−	0.881575i
$899$	0.00293684			9.79493e−5
$900$		0			0
$901$	55.8540			1.86077
$902$	90.9899	−	90.9899i	3.02963	−	3.02963i
$903$		0			0
$904$			90.5333i			3.01109i
$905$	−22.1975	+	2.79425i	−0.737870	+	0.0928840i
$906$		0			0
$907$	24.0296	+	24.0296i	0.797891	+	0.797891i	0.982763	−	0.184871i	$-0.0591869\pi$
$907$	24.0296	+	24.0296i	0.797891	+	0.797891i	−0.184871	+	0.982763i	$0.559187\pi$
$908$	−81.0955	−	81.0955i	−2.69125	−	2.69125i
$909$		0			0
$910$	−13.4758	+	17.3571i	−0.446718	+	0.575381i
$911$		−	17.0444i		−	0.564708i	−0.959310	−	0.282354i	$-0.908885\pi$
$911$		−	17.0444i		−	0.564708i	0.959310	−	0.282354i	$-0.0911152\pi$
$912$		0			0
$913$	9.86018	−	9.86018i	0.326324	−	0.326324i
$914$	−87.3037			−2.88775
$915$		0			0
$916$	−92.7240			−3.06369
$917$	−7.05126	+	7.05126i	−0.232853	+	0.232853i
$918$		0			0
$919$			1.11772i			0.0368700i	0.999830	+	0.0184350i	$0.00586838\pi$
$919$			1.11772i			0.0368700i	−0.999830	+	0.0184350i	$0.994132\pi$
$920$	−7.60545	−	60.4177i	−0.250744	−	1.99191i
$921$		0			0
$922$	27.0921	+	27.0921i	0.892232	+	0.892232i
$923$	7.42709	+	7.42709i	0.244466	+	0.244466i
$924$		0			0
$925$	−1.34248	−	0.795543i	−0.0441406	−	0.0261573i
$926$		−	76.8561i		−	2.52565i
$927$		0			0
$928$	−0.0588284	+	0.0588284i	−0.00193114	+	0.00193114i
$929$	−19.8873			−0.652480			−0.326240	−	0.945287i	$-0.605782\pi$
$929$	−19.8873			−0.652480			−0.326240	+	0.945287i	$0.605782\pi$
$930$		0			0
$931$	5.53419			0.181376
$932$	−118.140	+	118.140i	−3.86979	+	3.86979i
$933$		0			0
$934$			57.2005i			1.87166i
$935$	61.6365	+	47.8537i	2.01573	+	1.56498i
$936$		0			0
$937$	−39.2123	−	39.2123i	−1.28101	−	1.28101i	−0.940094	−	0.340915i	$-0.889263\pi$
$937$	−39.2123	−	39.2123i	−1.28101	−	1.28101i	−0.340915	−	0.940094i	$-0.610737\pi$
$938$	−32.5765	−	32.5765i	−1.06366	−	1.06366i
$939$		0			0
$940$	8.03908	+	6.24143i	0.262206	+	0.203573i
$941$		−	8.07378i		−	0.263198i	−0.991303	−	0.131599i	$-0.957989\pi$
$941$		−	8.07378i		−	0.263198i	0.991303	−	0.131599i	$-0.0420111\pi$
$942$		0			0
$943$	16.0676	−	16.0676i	0.523232	−	0.523232i
$944$	241.357			7.85549
$945$		0			0
$946$	−38.2446			−1.24344
$947$	−11.0278	+	11.0278i	−0.358354	+	0.358354i	−0.863206	−	0.504852i	$-0.831547\pi$
$947$	−11.0278	+	11.0278i	−0.358354	+	0.358354i	0.504852	+	0.863206i	$0.331547\pi$
$948$		0			0
$949$		−	22.8134i		−	0.740555i
$950$	−11.9190	−	7.06309i	−0.386704	−	0.229157i
$951$		0			0
$952$	55.7542	+	55.7542i	1.80700	+	1.80700i
$953$	5.75111	+	5.75111i	0.186297	+	0.186297i	0.794093	−	0.607796i	$-0.207946\pi$
$953$	5.75111	+	5.75111i	0.186297	+	0.186297i	−0.607796	+	0.794093i	$0.707946\pi$
$954$		0			0
$955$	−3.31316	−	26.3198i	−0.107211	−	0.851688i
$956$		−	148.235i		−	4.79427i
$957$		0			0
$958$	−47.0030	+	47.0030i	−1.51860	+	1.51860i
$959$	7.64954			0.247017
$960$		0			0
$961$	−30.1315			−0.971982
$962$	1.79129	−	1.79129i	0.0577536	−	0.0577536i
$963$		0			0
$964$		−	17.3258i		−	0.558028i
$965$	−8.53023	+	10.9871i	−0.274598	+	0.353687i
$966$		0			0
$967$	13.1593	+	13.1593i	0.423174	+	0.423174i	0.886295	−	0.463121i	$-0.153271\pi$
$967$	13.1593	+	13.1593i	0.423174	+	0.423174i	−0.463121	+	0.886295i	$0.653271\pi$
$968$	−135.646	−	135.646i	−4.35982	−	4.35982i
$969$		0			0
$970$	−45.9541	+	5.78476i	−1.47550	+	0.185737i
$971$			46.3083i			1.48610i	0.669234	+	0.743052i	$0.266622\pi$
$971$			46.3083i			1.48610i	−0.669234	+	0.743052i	$0.733378\pi$
$972$		0			0
$973$	−13.8462	+	13.8462i	−0.443890	+	0.443890i
$974$	33.9163			1.08675
$975$		0			0
$976$	−171.306			−5.48337
$977$	−13.3358	+	13.3358i	−0.426650	+	0.426650i	−0.887485	−	0.460836i	$-0.847550\pi$
$977$	−13.3358	+	13.3358i	−0.426650	+	0.426650i	0.460836	+	0.887485i	$0.347550\pi$
$978$		0			0
$979$		−	21.4668i		−	0.686083i
$980$	−69.7143	+	8.77572i	−2.22694	+	0.280330i
$981$		0			0
$982$	−37.1955	−	37.1955i	−1.18696	−	1.18696i
$983$	−16.7647	−	16.7647i	−0.534709	−	0.534709i	0.387261	−	0.921970i	$-0.373421\pi$
$983$	−16.7647	−	16.7647i	−0.534709	−	0.534709i	−0.921970	+	0.387261i	$0.873421\pi$
$984$		0			0
$985$	−31.6124	+	40.7173i	−1.00725	+	1.29736i
$986$		−	0.0557988i		−	0.00177699i
$987$		0			0
$988$	11.7610	−	11.7610i	0.374169	−	0.374169i
$989$	−6.75346			−0.214748
$990$		0			0
$991$	21.0394			0.668337			0.334169	−	0.942513i	$-0.391544\pi$
$991$	21.0394			0.668337			0.334169	+	0.942513i	$0.391544\pi$
$992$	−17.3980	+	17.3980i	−0.552386	+	0.552386i
$993$		0			0
$994$		−	12.0291i		−	0.381540i
$995$	−2.07995	−	16.5231i	−0.0659387	−	0.523817i
$996$		0			0
$997$	21.0315	+	21.0315i	0.666075	+	0.666075i	0.956805	−	0.290730i	$-0.0938982\pi$
$997$	21.0315	+	21.0315i	0.666075	+	0.666075i	−0.290730	+	0.956805i	$0.593898\pi$
$998$	9.91842	+	9.91842i	0.313962	+	0.313962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.e.647.1	✓	36
3.2	odd	2	inner	855.2.n.e.647.18	yes	36
5.3	odd	4	inner	855.2.n.e.818.18	yes	36
15.8	even	4	inner	855.2.n.e.818.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.e.647.1	✓	36	1.1	even	1	trivial
855.2.n.e.647.18	yes	36	3.2	odd	2	inner
855.2.n.e.818.1	yes	36	15.8	even	4	inner
855.2.n.e.818.18	yes	36	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95934 + 1.95934i) q^{2} -5.67802i q^{4} +(2.21856 - 0.279275i) q^{5} +(0.856099 + 0.856099i) q^{7} +(7.20648 + 7.20648i) q^{8} +O(q^{10})\)	\(q+(-1.95934 + 1.95934i) q^{2} -5.67802i q^{4} +(2.21856 - 0.279275i) q^{5} +(0.856099 + 0.856099i) q^{7} +(7.20648 + 7.20648i) q^{8} +(-3.79972 + 4.89410i) q^{10} +5.46102i q^{11} +(2.07133 - 2.07133i) q^{13} -3.35477 q^{14} -16.8838 q^{16} +(4.51856 - 4.51856i) q^{17} +1.00000i q^{19} +(-1.58573 - 12.5970i) q^{20} +(-10.7000 - 10.7000i) q^{22} +(-1.88947 - 1.88947i) q^{23} +(4.84401 - 1.23918i) q^{25} +8.11687i q^{26} +(4.86094 - 4.86094i) q^{28} -0.00315126 q^{29} -0.931958 q^{31} +(18.6682 - 18.6682i) q^{32} +17.7068i q^{34} +(2.13839 + 1.66022i) q^{35} +(-0.220688 - 0.220688i) q^{37} +(-1.95934 - 1.95934i) q^{38} +(18.0006 + 13.9754i) q^{40} +8.50374i q^{41} +(1.78713 - 1.78713i) q^{43} +31.0078 q^{44} +7.40422 q^{46} +(-0.566821 + 0.566821i) q^{47} -5.53419i q^{49} +(-7.06309 + 11.9190i) q^{50} +(-11.7610 - 11.7610i) q^{52} +(6.18050 + 6.18050i) q^{53} +(1.52513 + 12.1156i) q^{55} +12.3389i q^{56} +(0.00617439 - 0.00617439i) q^{58} -14.2951 q^{59} +10.1461 q^{61} +(1.82602 - 1.82602i) q^{62} +39.3870i q^{64} +(4.01690 - 5.17384i) q^{65} +(9.71049 + 9.71049i) q^{67} +(-25.6565 - 25.6565i) q^{68} +(-7.44277 + 0.936904i) q^{70} +3.58566i q^{71} +(5.50695 - 5.50695i) q^{73} +0.864804 q^{74} +5.67802 q^{76} +(-4.67517 + 4.67517i) q^{77} -10.3405i q^{79} +(-37.4578 + 4.71523i) q^{80} +(-16.6617 - 16.6617i) q^{82} +(-1.80556 - 1.80556i) q^{83} +(8.76278 - 11.2866i) q^{85} +7.00319i q^{86} +(-39.3548 + 39.3548i) q^{88} -3.93092 q^{89} +3.54652 q^{91} +(-10.7284 + 10.7284i) q^{92} -2.22119i q^{94} +(0.279275 + 2.21856i) q^{95} +(5.28584 + 5.28584i) q^{97} +(10.8434 + 10.8434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7}+O(q^{10}) \) 36 * q + 4 * q^7	\( 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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