LMFDB - Embedded newform 220.2.t.a.69.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(9,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.t (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.1
Character	$\chi$	$=$	220.69
Dual form			220.2.t.a.169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.93917 + 0.954994i) q^{3} +(-1.85993 - 1.24124i) q^{5} +(2.42366 + 0.787496i) q^{7} +(5.29965 - 3.85042i) q^{9} +(2.91878 - 1.57503i) q^{11} +(-2.27445 - 3.13052i) q^{13} +(6.65201 + 1.87199i) q^{15} +(3.92157 - 5.39758i) q^{17} +(0.918630 + 2.82725i) q^{19} -7.87561 q^{21} -2.50158i q^{23} +(1.91865 + 4.61723i) q^{25} +(-6.44992 + 8.87756i) q^{27} +(1.00077 - 3.08006i) q^{29} +(-3.01253 + 2.18873i) q^{31} +(-7.07465 + 7.41669i) q^{33} +(-3.53036 - 4.47303i) q^{35} +(1.94137 + 0.630791i) q^{37} +(9.67463 + 7.02903i) q^{39} +(-3.15408 - 9.70725i) q^{41} -6.30940i q^{43} +(-14.6363 + 0.583365i) q^{45} +(-2.75439 + 0.894954i) q^{47} +(-0.409123 - 0.297245i) q^{49} +(-6.37150 + 19.6095i) q^{51} +(5.35388 + 7.36899i) q^{53} +(-7.38370 - 0.693471i) q^{55} +(-5.40002 - 7.43249i) q^{57} +(2.44623 - 7.52871i) q^{59} +(5.03193 + 3.65591i) q^{61} +(15.8768 - 5.15867i) q^{63} +(0.344595 + 8.64567i) q^{65} -7.40503i q^{67} +(2.38899 + 7.35256i) q^{69} +(5.48190 + 3.98283i) q^{71} +(13.1880 + 4.28503i) q^{73} +(-10.0487 - 11.7385i) q^{75} +(8.31447 - 1.51881i) q^{77} +(-2.17071 + 1.57711i) q^{79} +(4.40654 - 13.5619i) q^{81} +(-1.51256 + 2.08185i) q^{83} +(-13.9935 + 5.17149i) q^{85} +10.0085i q^{87} -2.81308 q^{89} +(-3.04724 - 9.37844i) q^{91} +(6.76411 - 9.31000i) q^{93} +(1.80071 - 6.39872i) q^{95} +(3.85848 + 5.31074i) q^{97} +(9.40400 - 19.5856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) $ 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.93917	+	0.954994i	−1.69693	+	0.551366i	−0.988073	−	0.153986i	$-0.950789\pi$
$3$	−2.93917	+	0.954994i	−1.69693	+	0.551366i	−0.708857	+	0.705352i	$0.750789\pi$
$4$		0			0
$5$	−1.85993	−	1.24124i	−0.831784	−	0.555099i
$5$	−1.85993	−	1.24124i	−0.831784	−	0.555099i
$6$		0			0
$7$	2.42366	+	0.787496i	0.916059	+	0.297646i	0.728849	−	0.684674i	$-0.240056\pi$
$7$	2.42366	+	0.787496i	0.916059	+	0.297646i	0.187210	+	0.982320i	$0.440056\pi$
$8$		0			0
$9$	5.29965	−	3.85042i	1.76655	−	1.28347i
$10$		0			0
$11$	2.91878	−	1.57503i	0.880046	−	0.474889i
$11$	2.91878	−	1.57503i	0.880046	−	0.474889i
$12$		0			0
$13$	−2.27445	−	3.13052i	−0.630820	−	0.868249i	0.367264	−	0.930117i	$-0.380294\pi$
$13$	−2.27445	−	3.13052i	−0.630820	−	0.868249i	−0.998084	+	0.0618674i	$0.980294\pi$
$14$		0			0
$15$	6.65201	+	1.87199i	1.71754	+	0.483347i
$16$		0			0
$17$	3.92157	−	5.39758i	0.951121	−	1.30911i	9.26164e−5	−	1.00000i	$-0.499971\pi$
$17$	3.92157	−	5.39758i	0.951121	−	1.30911i	0.951028	−	0.309105i	$-0.100029\pi$
$18$		0			0
$19$	0.918630	+	2.82725i	0.210748	+	0.648616i	0.999428	+	0.0338123i	$0.0107648\pi$
$19$	0.918630	+	2.82725i	0.210748	+	0.648616i	−0.788680	+	0.614804i	$0.789235\pi$
$20$		0			0
$21$	−7.87561			−1.71860
$22$		0			0
$23$		−	2.50158i		−	0.521615i	−0.965391	−	0.260808i	$-0.916011\pi$
$23$		−	2.50158i		−	0.521615i	0.965391	−	0.260808i	$-0.0839888\pi$
$24$		0			0
$25$	1.91865	+	4.61723i	0.383730	+	0.923445i
$26$		0			0
$27$	−6.44992	+	8.87756i	−1.24129	+	1.70849i
$28$		0			0
$29$	1.00077	−	3.08006i	0.185839	−	0.571952i	−0.814123	−	0.580692i	$-0.802782\pi$
$29$	1.00077	−	3.08006i	0.185839	−	0.571952i	0.999962	+	0.00873982i	$0.00278201\pi$
$30$		0			0
$31$	−3.01253	+	2.18873i	−0.541066	+	0.393108i	−0.824481	−	0.565890i	$-0.808533\pi$
$31$	−3.01253	+	2.18873i	−0.541066	+	0.393108i	0.283415	+	0.958997i	$0.408533\pi$
$32$		0			0
$33$	−7.07465	+	7.41669i	−1.23154	+	1.29108i
$34$		0			0
$35$	−3.53036	−	4.47303i	−0.596740	−	0.756080i
$36$		0			0
$37$	1.94137	+	0.630791i	0.319160	+	0.103701i	0.464216	−	0.885722i	$-0.346336\pi$
$37$	1.94137	+	0.630791i	0.319160	+	0.103701i	−0.145056	+	0.989423i	$0.546336\pi$
$38$		0			0
$39$	9.67463	+	7.02903i	1.54918	+	1.12555i
$40$		0			0
$41$	−3.15408	−	9.70725i	−0.492584	−	1.51602i	−0.820688	−	0.571377i	$-0.806410\pi$
$41$	−3.15408	−	9.70725i	−0.492584	−	1.51602i	0.328104	−	0.944642i	$-0.393590\pi$
$42$		0			0
$43$		−	6.30940i		−	0.962175i	−0.876673	−	0.481087i	$-0.840242\pi$
$43$		−	6.30940i		−	0.962175i	0.876673	−	0.481087i	$-0.159758\pi$
$44$		0			0
$45$	−14.6363	+	0.583365i	−2.18184	+	0.0869629i
$46$		0			0
$47$	−2.75439	+	0.894954i	−0.401768	+	0.130542i	−0.502929	−	0.864328i	$-0.667744\pi$
$47$	−2.75439	+	0.894954i	−0.401768	+	0.130542i	0.101161	+	0.994870i	$0.467744\pi$
$48$		0			0
$49$	−0.409123	−	0.297245i	−0.0584462	−	0.0424636i
$50$		0			0
$51$	−6.37150	+	19.6095i	−0.892189	+	2.74588i
$52$		0			0
$53$	5.35388	+	7.36899i	0.735413	+	1.01221i	0.998869	+	0.0475374i	$0.0151373\pi$
$53$	5.35388	+	7.36899i	0.735413	+	1.01221i	−0.263457	+	0.964671i	$0.584863\pi$
$54$		0			0
$55$	−7.38370	−	0.693471i	−0.995619	−	0.0935076i
$56$		0			0
$57$	−5.40002	−	7.43249i	−0.715250	−	0.984457i
$58$		0			0
$59$	2.44623	−	7.52871i	0.318472	−	0.980155i	−0.655830	−	0.754908i	$-0.727681\pi$
$59$	2.44623	−	7.52871i	0.318472	−	0.980155i	0.974302	−	0.225246i	$-0.0723187\pi$
$60$		0			0
$61$	5.03193	+	3.65591i	0.644272	+	0.468091i	0.861315	−	0.508071i	$-0.169641\pi$
$61$	5.03193	+	3.65591i	0.644272	+	0.468091i	−0.217043	+	0.976162i	$0.569641\pi$
$62$		0			0
$63$	15.8768	−	5.15867i	2.00028	−	0.649932i
$64$		0			0
$65$	0.344595	+	8.64567i	0.0427418	+	1.07236i
$66$		0			0
$67$		−	7.40503i		−	0.904668i	−0.891849	−	0.452334i	$-0.850591\pi$
$67$		−	7.40503i		−	0.904668i	0.891849	−	0.452334i	$-0.149409\pi$
$68$		0			0
$69$	2.38899	+	7.35256i	0.287601	+	0.885144i
$70$		0			0
$71$	5.48190	+	3.98283i	0.650582	+	0.472675i	0.863469	−	0.504401i	$-0.168287\pi$
$71$	5.48190	+	3.98283i	0.650582	+	0.472675i	−0.212888	+	0.977077i	$0.568287\pi$
$72$		0			0
$73$	13.1880	+	4.28503i	1.54354	+	0.501525i	0.952349	−	0.305010i	$-0.0986598\pi$
$73$	13.1880	+	4.28503i	1.54354	+	0.501525i	0.591186	+	0.806535i	$0.298660\pi$
$74$		0			0
$75$	−10.0487	−	11.7385i	−1.16032	−	1.35545i
$76$		0			0
$77$	8.31447	−	1.51881i	0.947522	−	0.173084i
$78$		0			0
$79$	−2.17071	+	1.57711i	−0.244224	+	0.177439i	−0.703163	−	0.711029i	$-0.748230\pi$
$79$	−2.17071	+	1.57711i	−0.244224	+	0.177439i	0.458939	+	0.888468i	$0.348230\pi$
$80$		0			0
$81$	4.40654	−	13.5619i	0.489616	−	1.50688i
$82$		0			0
$83$	−1.51256	+	2.08185i	−0.166025	+	0.228513i	−0.883920	−	0.467637i	$-0.845105\pi$
$83$	−1.51256	+	2.08185i	−0.166025	+	0.228513i	0.717896	+	0.696150i	$0.245105\pi$
$84$		0			0
$85$	−13.9935	+	5.17149i	−1.51781	+	0.560927i
$86$		0			0
$87$			10.0085i			1.07303i
$88$		0			0
$89$	−2.81308			−0.298186			−0.149093	−	0.988823i	$-0.547635\pi$
$89$	−2.81308			−0.298186			−0.149093	+	0.988823i	$0.547635\pi$
$90$		0			0
$91$	−3.04724	−	9.37844i	−0.319438	−	0.983128i
$92$		0			0
$93$	6.76411	−	9.31000i	0.701405	−	0.965402i
$94$		0			0
$95$	1.80071	−	6.39872i	0.184749	−	0.656495i
$96$		0			0
$97$	3.85848	+	5.31074i	0.391769	+	0.539224i	0.958655	−	0.284573i	$-0.0918517\pi$
$97$	3.85848	+	5.31074i	0.391769	+	0.539224i	−0.566885	+	0.823797i	$0.691852\pi$
$98$		0			0
$99$	9.40400	−	19.5856i	0.945138	−	1.96843i
$100$		0			0
$101$	−4.38336	+	3.18469i	−0.436160	+	0.316889i	−0.784107	−	0.620625i	$-0.786879\pi$
$101$	−4.38336	+	3.18469i	−0.436160	+	0.316889i	0.347947	+	0.937514i	$0.386879\pi$
$102$		0			0
$103$	−11.7931	−	3.83182i	−1.16201	−	0.377561i	−0.336357	−	0.941735i	$-0.609195\pi$
$103$	−11.7931	−	3.83182i	−1.16201	−	0.377561i	−0.825656	+	0.564174i	$0.809195\pi$
$104$		0			0
$105$	14.6481	+	9.77552i	1.42950	+	0.953993i
$106$		0			0
$107$	−1.28491	+	0.417492i	−0.124217	+	0.0403605i	−0.370466	−	0.928846i	$-0.620802\pi$
$107$	−1.28491	+	0.417492i	−0.124217	+	0.0403605i	0.246249	+	0.969207i	$0.420802\pi$
$108$		0			0
$109$	2.88662			0.276488			0.138244	−	0.990398i	$-0.455854\pi$
$109$	2.88662			0.276488			0.138244	+	0.990398i	$0.455854\pi$
$110$		0			0
$111$	−6.30843			−0.598770
$112$		0			0
$113$	−13.1835	+	4.28357i	−1.24020	+	0.402964i	−0.854398	−	0.519619i	$-0.826074\pi$
$113$	−13.1835	+	4.28357i	−1.24020	+	0.402964i	−0.385798	+	0.922583i	$0.626074\pi$
$114$		0			0
$115$	−3.10506	+	4.65275i	−0.289548	+	0.433871i
$116$		0			0
$117$	−24.1076	−	7.83304i	−2.22875	−	0.724165i
$118$		0			0
$119$	13.7551	−	9.99369i	1.26093	−	0.916120i
$120$		0			0
$121$	6.03857	−	9.19433i	0.548961	−	0.835848i
$122$		0			0
$123$	18.5407	+	25.5191i	1.67176	+	2.30098i
$124$		0			0
$125$	2.16254	−	10.9692i	0.193423	−	0.981115i
$126$		0			0
$127$	−5.88900	+	8.10552i	−0.522565	+	0.719248i	−0.985975	−	0.166896i	$-0.946626\pi$
$127$	−5.88900	+	8.10552i	−0.522565	+	0.719248i	0.463410	+	0.886144i	$0.346626\pi$
$128$		0			0
$129$	6.02544	+	18.5444i	0.530510	+	1.63274i
$130$		0			0
$131$	−7.84327			−0.685270			−0.342635	−	0.939469i	$-0.611319\pi$
$131$	−7.84327			−0.685270			−0.342635	+	0.939469i	$0.611319\pi$
$132$		0			0
$133$			7.57573i			0.656899i
$134$		0			0
$135$	23.0156	−	8.50570i	1.98086	−	0.732054i
$136$		0			0
$137$	8.71352	−	11.9931i	0.744446	−	1.02464i	−0.253905	−	0.967229i	$-0.581715\pi$
$137$	8.71352	−	11.9931i	0.744446	−	1.02464i	0.998351	−	0.0574127i	$-0.0182851\pi$
$138$		0			0
$139$	−5.26594	+	16.2069i	−0.446651	+	1.37465i	0.434011	+	0.900907i	$0.357098\pi$
$139$	−5.26594	+	16.2069i	−0.446651	+	1.37465i	−0.880663	+	0.473744i	$0.842902\pi$
$140$		0			0
$141$	7.24093	−	5.26084i	0.609796	−	0.443043i
$142$		0			0
$143$	−11.5693	−	5.55497i	−0.967472	−	0.464530i
$144$		0			0
$145$	−5.68445	+	4.48648i	−0.472068	+	0.372582i
$146$		0			0
$147$	1.48635	+	0.482944i	0.122592	+	0.0398326i
$148$		0			0
$149$	−11.9307	−	8.66819i	−0.977404	−	0.710126i	−0.0202773	−	0.999794i	$-0.506455\pi$
$149$	−11.9307	−	8.66819i	−0.977404	−	0.710126i	−0.957127	+	0.289669i	$0.906455\pi$
$150$		0			0
$151$	2.49182	+	7.66902i	0.202781	+	0.624096i	0.999797	+	0.0201379i	$0.00641052\pi$
$151$	2.49182	+	7.66902i	0.202781	+	0.624096i	−0.797016	+	0.603958i	$0.793589\pi$
$152$		0			0
$153$		−	43.7050i		−	3.53334i
$154$		0			0
$155$	8.31982	−	0.331607i	0.668264	−	0.0266353i
$156$		0			0
$157$	18.9651	−	6.16215i	1.51358	−	0.491793i	0.569638	−	0.821896i	$-0.307083\pi$
$157$	18.9651	−	6.16215i	1.51358	−	0.491793i	0.943945	+	0.330103i	$0.107083\pi$
$158$		0			0
$159$	−22.7733	−	16.5458i	−1.80604	−	1.31217i
$160$		0			0
$161$	1.96998	−	6.06298i	0.155256	−	0.477830i
$162$		0			0
$163$	4.58820	+	6.31511i	0.359375	+	0.494638i	0.949975	−	0.312327i	$-0.101109\pi$
$163$	4.58820	+	6.31511i	0.359375	+	0.494638i	−0.590599	+	0.806965i	$0.701109\pi$
$164$		0			0
$165$	22.3642	−	5.01317i	1.74105	−	0.390274i
$166$		0			0
$167$	6.59279	+	9.07420i	0.510166	+	0.702183i	0.983947	−	0.178460i	$-0.0571114\pi$
$167$	6.59279	+	9.07420i	0.510166	+	0.702183i	−0.473782	+	0.880642i	$0.657111\pi$
$168$		0			0
$169$	−0.609775	+	1.87669i	−0.0469058	+	0.144361i
$170$		0			0
$171$	15.7545	+	11.4463i	1.20478	+	0.875323i
$172$		0			0
$173$	−10.1638	+	3.30242i	−0.772740	+	0.251078i	−0.668738	−	0.743499i	$-0.733165\pi$
$173$	−10.1638	+	3.30242i	−0.772740	+	0.251078i	−0.104003	+	0.994577i	$0.533165\pi$
$174$		0			0
$175$	1.01411	+	12.7015i	0.0766598	+	0.960146i
$176$		0			0
$177$			24.4643i			1.83885i
$178$		0			0
$179$	1.32476	+	4.07720i	0.0990174	+	0.304744i	0.988280	−	0.152653i	$-0.0487817\pi$
$179$	1.32476	+	4.07720i	0.0990174	+	0.304744i	−0.889262	+	0.457397i	$0.848782\pi$
$180$		0			0
$181$	3.72614	+	2.70720i	0.276962	+	0.201224i	0.717591	−	0.696465i	$-0.245245\pi$
$181$	3.72614	+	2.70720i	0.276962	+	0.201224i	−0.440629	+	0.897689i	$0.645245\pi$
$182$		0			0
$183$	−18.2811	−	5.93987i	−1.35137	−	0.439088i
$184$		0			0
$185$	−2.82785	−	3.58293i	−0.207908	−	0.263423i
$186$		0			0
$187$	2.94487	−	21.9309i	0.215350	−	1.60375i
$188$		0			0
$189$	−22.6235	+	16.4369i	−1.64562	+	1.19561i
$190$		0			0
$191$	−0.734771	+	2.26139i	−0.0531661	+	0.163629i	−0.974114	−	0.226057i	$-0.927416\pi$
$191$	−0.734771	+	2.26139i	−0.0531661	+	0.163629i	0.920948	+	0.389686i	$0.127416\pi$
$192$		0			0
$193$	−8.69425	+	11.9666i	−0.625826	+	0.861376i	−0.997761	−	0.0668833i	$-0.978694\pi$
$193$	−8.69425	+	11.9666i	−0.625826	+	0.861376i	0.371935	+	0.928259i	$0.378694\pi$
$194$		0			0
$195$	−9.26939	−	25.0820i	−0.663795	−	1.79616i
$196$		0			0
$197$			17.0562i			1.21520i	0.794242	+	0.607602i	$0.207868\pi$
$197$			17.0562i			1.21520i	−0.794242	+	0.607602i	$0.792132\pi$
$198$		0			0
$199$	−8.88040			−0.629515			−0.314757	−	0.949172i	$-0.601923\pi$
$199$	−8.88040			−0.629515			−0.314757	+	0.949172i	$0.601923\pi$
$200$		0			0
$201$	7.07176	+	21.7646i	0.498803	+	1.53516i
$202$		0			0
$203$	4.85107	−	6.67692i	0.340478	−	0.468628i
$204$		0			0
$205$	−6.18267	+	21.9697i	−0.431817	+	1.53443i
$206$		0			0
$207$	−9.63213	−	13.2575i	−0.669479	−	0.921459i
$208$		0			0
$209$	7.13428	+	6.80526i	0.493489	+	0.470730i
$210$		0			0
$211$	13.2271	−	9.61005i	0.910591	−	0.661583i	−0.0305732	−	0.999533i	$-0.509733\pi$
$211$	13.2271	−	9.61005i	0.910591	−	0.661583i	0.941164	+	0.337949i	$0.109733\pi$
$212$		0			0
$213$	−19.9158	−	6.47104i	−1.36461	−	0.443388i
$214$		0			0
$215$	−7.83148	+	11.7350i	−0.534102	+	0.800322i
$216$		0			0
$217$	−9.02497	+	2.93239i	−0.612655	+	0.199064i
$218$		0			0
$219$	−42.8539			−2.89580
$220$		0			0
$221$	−25.8166			−1.73662
$222$		0			0
$223$	−27.3783	+	8.89573i	−1.83338	+	0.595702i	−0.834375	+	0.551198i	$0.814171\pi$
$223$	−27.3783	+	8.89573i	−1.83338	+	0.595702i	−0.999009	+	0.0445045i	$0.985829\pi$
$224$		0			0
$225$	27.9464	+	17.0821i	1.86310	+	1.13881i
$226$		0			0
$227$	16.9712	+	5.51427i	1.12642	+	0.365995i	0.812214	−	0.583360i	$-0.198262\pi$
$227$	16.9712	+	5.51427i	1.12642	+	0.365995i	0.314204	+	0.949355i	$0.398262\pi$
$228$		0			0
$229$	−9.02768	+	6.55899i	−0.596566	+	0.433430i	−0.844658	−	0.535306i	$-0.820196\pi$
$229$	−9.02768	+	6.55899i	−0.596566	+	0.433430i	0.248092	+	0.968736i	$0.420196\pi$
$230$		0			0
$231$	−22.9872	+	12.4043i	−1.51245	+	0.816144i
$232$		0			0
$233$	8.30542	+	11.4314i	0.544106	+	0.748898i	0.989198	−	0.146587i	$-0.0468289\pi$
$233$	8.30542	+	11.4314i	0.544106	+	0.748898i	−0.445092	+	0.895485i	$0.646829\pi$
$234$		0			0
$235$	6.23381	+	1.75430i	0.406649	+	0.114438i
$236$		0			0
$237$	4.87395	−	6.70842i	0.316597	−	0.435759i
$238$		0			0
$239$	−0.359831	−	1.10744i	−0.0232755	−	0.0716346i	0.938744	−	0.344615i	$-0.111991\pi$
$239$	−0.359831	−	1.10744i	−0.0232755	−	0.0716346i	−0.962020	+	0.272980i	$0.911991\pi$
$240$		0			0
$241$	21.3808			1.37726			0.688629	−	0.725114i	$-0.258213\pi$
$241$	21.3808			1.37726			0.688629	+	0.725114i	$0.258213\pi$
$242$		0			0
$243$			11.1493i			0.715225i
$244$		0			0
$245$	0.391986	+	1.06067i	0.0250431	+	0.0677640i
$246$		0			0
$247$	6.76138	−	9.30624i	0.430216	−	0.592142i
$248$		0			0
$249$	2.45750	−	7.56340i	0.155738	−	0.479311i
$250$		0			0
$251$	−3.77497	+	2.74267i	−0.238274	+	0.173116i	−0.700514	−	0.713639i	$-0.747046\pi$
$251$	−3.77497	+	2.74267i	−0.238274	+	0.173116i	0.462240	+	0.886755i	$0.347046\pi$
$252$		0			0
$253$	−3.94006	−	7.30156i	−0.247709	−	0.459045i
$254$		0			0
$255$	36.1906	−	28.5636i	2.26634	−	1.78872i
$256$		0			0
$257$	−7.78615	−	2.52987i	−0.485687	−	0.157809i	0.0559302	−	0.998435i	$-0.482188\pi$
$257$	−7.78615	−	2.52987i	−0.485687	−	0.157809i	−0.541617	+	0.840626i	$0.682188\pi$
$258$		0			0
$259$	4.20849	+	3.05765i	0.261503	+	0.189993i
$260$		0			0
$261$	−6.55578	−	20.1766i	−0.405793	−	1.24890i
$262$		0			0
$263$		−	18.9398i		−	1.16788i	−0.811798	−	0.583938i	$-0.801511\pi$
$263$		−	18.9398i		−	1.16788i	0.811798	−	0.583938i	$-0.198489\pi$
$264$		0			0
$265$	−0.811150	−	20.3512i	−0.0498285	−	1.25017i
$266$		0			0
$267$	8.26812	−	2.68648i	0.506001	−	0.164410i
$268$		0			0
$269$	3.28340	+	2.38553i	0.200192	+	0.145448i	0.683365	−	0.730077i	$-0.260516\pi$
$269$	3.28340	+	2.38553i	0.200192	+	0.145448i	−0.483173	+	0.875525i	$0.660516\pi$
$270$		0			0
$271$	8.92056	−	27.4547i	0.541885	−	1.66775i	−0.186397	−	0.982475i	$-0.559681\pi$
$271$	8.92056	−	27.4547i	0.541885	−	1.66775i	0.728282	−	0.685277i	$-0.240319\pi$
$272$		0			0
$273$	17.9127	+	24.6547i	1.08413	+	1.49217i
$274$		0			0
$275$	12.8724	+	10.4547i	0.776234	+	0.630445i
$276$		0			0
$277$	1.12402	+	1.54709i	0.0675360	+	0.0929553i	0.841449	−	0.540337i	$-0.181703\pi$
$277$	1.12402	+	1.54709i	0.0675360	+	0.0929553i	−0.773913	+	0.633292i	$0.781703\pi$
$278$		0			0
$279$	−7.53782	+	23.1990i	−0.451277	+	1.38889i
$280$		0			0
$281$	5.89269	+	4.28129i	0.351528	+	0.255400i	0.749510	−	0.661993i	$-0.230289\pi$
$281$	5.89269	+	4.28129i	0.351528	+	0.255400i	−0.397982	+	0.917393i	$0.630289\pi$
$282$		0			0
$283$	26.2405	−	8.52606i	1.55984	−	0.506822i	0.603072	−	0.797686i	$-0.293943\pi$
$283$	26.2405	−	8.52606i	1.55984	−	0.506822i	0.956764	+	0.290865i	$0.0939430\pi$
$284$		0			0
$285$	0.818139	+	20.5266i	0.0484624	+	1.21589i
$286$		0			0
$287$		−	26.0109i		−	1.53538i
$288$		0			0
$289$	−8.50185	−	26.1660i	−0.500109	−	1.53918i
$290$		0			0
$291$	−16.4125	−	11.9243i	−0.962115	−	0.699018i
$292$		0			0
$293$	21.3023	+	6.92153i	1.24449	+	0.404360i	0.855944	−	0.517068i	$-0.172977\pi$
$293$	21.3023	+	6.92153i	1.24449	+	0.404360i	0.388549	+	0.921428i	$0.372977\pi$
$294$		0			0
$295$	−13.8947	+	10.9665i	−0.808983	+	0.638494i
$296$		0			0
$297$	−4.84351	+	36.0705i	−0.281049	+	2.09302i
$298$		0			0
$299$	−7.83123	+	5.68972i	−0.452892	+	0.329045i
$300$		0			0
$301$	4.96863	−	15.2919i	0.286387	−	0.881409i
$302$		0			0
$303$	9.84206	−	13.5464i	0.565412	−	0.778222i
$304$		0			0
$305$	−4.82115	−	13.0455i	−0.276058	−	0.746986i
$306$		0			0
$307$			2.79397i			0.159460i	0.996816	+	0.0797302i	$0.0254059\pi$
$307$			2.79397i			0.159460i	−0.996816	+	0.0797302i	$0.974594\pi$
$308$		0			0
$309$	38.3214			2.18003
$310$		0			0
$311$	8.36032	+	25.7304i	0.474070	+	1.45904i	0.847208	+	0.531262i	$0.178282\pi$
$311$	8.36032	+	25.7304i	0.474070	+	1.45904i	−0.373138	+	0.927776i	$0.621718\pi$
$312$		0			0
$313$	5.19932	−	7.15625i	0.293883	−	0.404495i	−0.636387	−	0.771370i	$-0.719572\pi$
$313$	5.19932	−	7.15625i	0.293883	−	0.404495i	0.930271	+	0.366874i	$0.119572\pi$
$314$		0			0
$315$	−35.9328	−	10.1121i	−2.02458	−	0.569753i
$316$		0			0
$317$	−15.6310	−	21.5142i	−0.877923	−	1.20836i	−0.976992	−	0.213277i	$-0.931586\pi$
$317$	−15.6310	−	21.5142i	−0.877923	−	1.20836i	0.0990682	−	0.995081i	$-0.468414\pi$
$318$		0			0
$319$	−1.93014	−	10.5663i	−0.108067	−	0.591597i
$320$		0			0
$321$	3.37786	−	2.45416i	0.188534	−	0.136978i
$322$		0			0
$323$	18.8628	+	6.12889i	1.04955	+	0.341021i
$324$		0			0
$325$	10.0904	−	16.5080i	0.559716	−	0.915701i
$326$		0			0
$327$	−8.48426	+	2.75670i	−0.469181	+	0.152446i
$328$		0			0
$329$	−7.38048			−0.406899
$330$		0			0
$331$	11.3682			0.624850			0.312425	−	0.949942i	$-0.398859\pi$
$331$	11.3682			0.624850			0.312425	+	0.949942i	$0.398859\pi$
$332$		0			0
$333$	12.7174	−	4.13214i	0.696910	−	0.226440i
$334$		0			0
$335$	−9.19141	+	13.7728i	−0.502181	+	0.752489i
$336$		0			0
$337$	3.71550	+	1.20724i	0.202396	+	0.0657625i	0.408461	−	0.912776i	$-0.366066\pi$
$337$	3.71550	+	1.20724i	0.202396	+	0.0657625i	−0.206065	+	0.978538i	$0.566066\pi$
$338$		0			0
$339$	34.6576	−	25.1803i	1.88234	−	1.36760i
$340$		0			0
$341$	−5.34560	+	11.1332i	−0.289481	+	0.602899i
$342$		0			0
$343$	−11.2428	−	15.4744i	−0.607056	−	0.835542i
$344$		0			0
$345$	4.68294	−	16.6405i	0.252121	−	0.895896i
$346$		0			0
$347$	−9.59445	+	13.2056i	−0.515057	+	0.708915i	−0.984762	−	0.173908i	$-0.944360\pi$
$347$	−9.59445	+	13.2056i	−0.515057	+	0.708915i	0.469705	+	0.882824i	$0.344360\pi$
$348$		0			0
$349$	7.78393	+	23.9565i	0.416664	+	1.28236i	0.910754	+	0.412949i	$0.135501\pi$
$349$	7.78393	+	23.9565i	0.416664	+	1.28236i	−0.494090	+	0.869411i	$0.664499\pi$
$350$		0			0
$351$	42.4614			2.26642
$352$		0			0
$353$		−	14.5640i		−	0.775166i	−0.921835	−	0.387583i	$-0.873310\pi$
$353$		−	14.5640i		−	0.775166i	0.921835	−	0.387583i	$-0.126690\pi$
$354$		0			0
$355$	−5.25228	−	14.2121i	−0.278762	−	0.754301i
$356$		0			0
$357$	−30.8848	+	42.5092i	−1.63460	+	2.24983i
$358$		0			0
$359$	−3.20734	+	9.87118i	−0.169277	+	0.520981i	−0.999326	−	0.0367094i	$-0.988312\pi$
$359$	−3.20734	+	9.87118i	−0.169277	+	0.520981i	0.830049	+	0.557691i	$0.188312\pi$
$360$		0			0
$361$	8.22185	−	5.97352i	0.432729	−	0.314396i
$362$		0			0
$363$	−8.96786	+	32.7905i	−0.470691	+	1.72105i
$364$		0			0
$365$	−19.2099	−	24.3393i	−1.00549	−	1.27398i
$366$		0			0
$367$	10.7297	+	3.48630i	0.560087	+	0.181983i	0.575360	−	0.817900i	$-0.304862\pi$
$367$	10.7297	+	3.48630i	0.560087	+	0.181983i	−0.0152735	+	0.999883i	$0.504862\pi$
$368$		0			0
$369$	−54.0925	−	39.3005i	−2.81595	−	2.04590i
$370$		0			0
$371$	7.17296	+	22.0761i	0.372402	+	1.14613i
$372$		0			0
$373$			31.7107i			1.64192i	0.570987	+	0.820959i	$0.306561\pi$
$373$			31.7107i			1.64192i	−0.570987	+	0.820959i	$0.693439\pi$
$374$		0			0
$375$	4.11946	+	34.3056i	0.212728	+	1.77153i
$376$		0			0
$377$	−11.9184	+	3.87252i	−0.613828	+	0.199445i
$378$		0			0
$379$	−13.6665	−	9.92929i	−0.702001	−	0.510033i	0.178582	−	0.983925i	$-0.442849\pi$
$379$	−13.6665	−	9.92929i	−0.702001	−	0.510033i	−0.880583	+	0.473891i	$0.842849\pi$
$380$		0			0
$381$	9.56806	−	29.4475i	0.490186	−	1.50864i
$382$		0			0
$383$	3.29186	+	4.53086i	0.168206	+	0.231516i	0.884796	−	0.465979i	$-0.154298\pi$
$383$	3.29186	+	4.53086i	0.168206	+	0.231516i	−0.716589	+	0.697495i	$0.754298\pi$
$384$		0			0
$385$	−17.3495	−	7.49538i	−0.884213	−	0.382000i
$386$		0			0
$387$	−24.2939	−	33.4376i	−1.23493	−	1.69973i
$388$		0			0
$389$	−6.26383	+	19.2781i	−0.317589	+	0.977437i	0.657087	+	0.753815i	$0.271788\pi$
$389$	−6.26383	+	19.2781i	−0.317589	+	0.977437i	−0.974676	+	0.223623i	$0.928212\pi$
$390$		0			0
$391$	−13.5025	−	9.81011i	−0.682849	−	0.496119i
$392$		0			0
$393$	23.0527	−	7.49028i	1.16285	−	0.377834i
$394$		0			0
$395$	5.99494	−	0.238943i	0.301638	−	0.0120225i
$396$		0			0
$397$		−	6.94622i		−	0.348621i	−0.984691	−	0.174311i	$-0.944230\pi$
$397$		−	6.94622i		−	0.348621i	0.984691	−	0.174311i	$-0.0557696\pi$
$398$		0			0
$399$	−7.23477	−	22.2663i	−0.362192	−	1.11471i
$400$		0			0
$401$	7.47076	+	5.42782i	0.373072	+	0.271053i	0.758484	−	0.651692i	$-0.225941\pi$
$401$	7.47076	+	5.42782i	0.373072	+	0.271053i	−0.385412	+	0.922745i	$0.625941\pi$
$402$		0			0
$403$	13.7037	+	4.45261i	0.682631	+	0.221800i
$404$		0			0
$405$	−25.0295	+	19.7546i	−1.24372	+	0.981615i
$406$		0			0
$407$	6.65996	−	1.21658i	0.330122	−	0.0603036i
$408$		0			0
$409$	−20.7732	+	15.0926i	−1.02717	+	0.746282i	−0.967740	−	0.251950i	$-0.918928\pi$
$409$	−20.7732	+	15.0926i	−1.02717	+	0.746282i	−0.0594294	+	0.998233i	$0.518928\pi$
$410$		0			0
$411$	−14.1571	+	43.5712i	−0.698320	+	2.14921i
$412$		0			0
$413$	11.8577	−	16.3207i	0.583477	−	0.803088i
$414$		0			0
$415$	5.39732	−	1.99465i	0.264944	−	0.0979136i
$416$		0			0
$417$		−	52.6638i		−	2.57896i
$418$		0			0
$419$	27.4748			1.34223			0.671116	−	0.741353i	$-0.265815\pi$
$419$	27.4748			1.34223			0.671116	+	0.741353i	$0.265815\pi$
$420$		0			0
$421$	−5.73707	−	17.6569i	−0.279608	−	0.860545i	−0.987963	−	0.154689i	$-0.950563\pi$
$421$	−5.73707	−	17.6569i	−0.279608	−	0.860545i	0.708355	−	0.705856i	$-0.249437\pi$
$422$		0			0
$423$	−11.1513	+	15.3485i	−0.542196	+	0.746269i
$424$		0			0
$425$	32.4460	+	7.75072i	1.57386	+	0.375965i
$426$		0			0
$427$	9.31668	+	12.8233i	0.450866	+	0.620564i
$428$		0			0
$429$	39.3090	+	5.27839i	1.89786	+	0.254843i
$430$		0			0
$431$	−2.41572	+	1.75512i	−0.116361	+	0.0845412i	−0.644444	−	0.764652i	$-0.722911\pi$
$431$	−2.41572	+	1.75512i	−0.116361	+	0.0845412i	0.528083	+	0.849193i	$0.322911\pi$
$432$		0			0
$433$	−1.20198	−	0.390545i	−0.0577632	−	0.0187684i	0.279993	−	0.960002i	$-0.409668\pi$
$433$	−1.20198	−	0.390545i	−0.0577632	−	0.0187684i	−0.337756	+	0.941234i	$0.609668\pi$
$434$		0			0
$435$	12.4230	−	18.6151i	0.595637	−	0.892528i
$436$		0			0
$437$	7.07259	−	2.29802i	0.338328	−	0.109929i
$438$		0			0
$439$	31.4150			1.49936			0.749679	−	0.661802i	$-0.230208\pi$
$439$	31.4150			1.49936			0.749679	+	0.661802i	$0.230208\pi$
$440$		0			0
$441$	−3.31273			−0.157749
$442$		0			0
$443$	−8.37709	+	2.72188i	−0.398008	+	0.129321i	−0.501180	−	0.865343i	$-0.667101\pi$
$443$	−8.37709	+	2.72188i	−0.398008	+	0.129321i	0.103172	+	0.994663i	$0.467101\pi$
$444$		0			0
$445$	5.23212	+	3.49171i	0.248026	+	0.165523i
$446$		0			0
$447$	43.3445	+	14.0835i	2.05013	+	0.666126i
$448$		0			0
$449$	−4.08516	+	2.96804i	−0.192791	+	0.140071i	−0.679993	−	0.733218i	$-0.738017\pi$
$449$	−4.08516	+	2.96804i	−0.192791	+	0.140071i	0.487203	+	0.873289i	$0.338017\pi$
$450$		0			0
$451$	−24.4953	−	23.3656i	−1.15344	−	1.10024i
$452$		0			0
$453$	−14.6477	−	20.1609i	−0.688210	−	0.947240i
$454$		0			0
$455$	−5.97325	+	21.2256i	−0.280030	+	0.995070i
$456$		0			0
$457$	−1.79587	+	2.47181i	−0.0840074	+	0.115626i	−0.848952	−	0.528469i	$-0.822766\pi$
$457$	−1.79587	+	2.47181i	−0.0840074	+	0.115626i	0.764945	+	0.644096i	$0.222766\pi$
$458$		0			0
$459$	22.6235	+	69.6279i	1.05597	+	3.24995i
$460$		0			0
$461$	−36.4179			−1.69615			−0.848076	−	0.529875i	$-0.822239\pi$
$461$	−36.4179			−1.69615			−0.848076	+	0.529875i	$0.822239\pi$
$462$		0			0
$463$		−	9.93257i		−	0.461606i	−0.973001	−	0.230803i	$-0.925865\pi$
$463$		−	9.93257i		−	0.461606i	0.973001	−	0.230803i	$-0.0741352\pi$
$464$		0			0
$465$	−24.1367	+	8.92003i	−1.11931	+	0.413656i
$466$		0			0
$467$	13.5492	−	18.6489i	0.626982	−	0.862966i	−0.370856	−	0.928690i	$-0.620936\pi$
$467$	13.5492	−	18.6489i	0.626982	−	0.862966i	0.997838	+	0.0657240i	$0.0209357\pi$
$468$		0			0
$469$	5.83143	−	17.9473i	0.269270	−	0.828729i
$470$		0			0
$471$	−49.8570	+	36.2232i	−2.29729	+	1.66908i
$472$		0			0
$473$	−9.93749	−	18.4158i	−0.456926	−	0.846758i
$474$		0			0
$475$	−11.2915	+	9.66603i	−0.518091	+	0.443508i
$476$		0			0
$477$	56.7474	+	18.4384i	2.59829	+	0.844235i
$478$		0			0
$479$	−1.85320	−	1.34643i	−0.0846747	−	0.0615198i	0.544642	−	0.838668i	$-0.316665\pi$
$479$	−1.85320	−	1.34643i	−0.0846747	−	0.0615198i	−0.629317	+	0.777149i	$0.716665\pi$
$480$		0			0
$481$	−2.44086	−	7.51221i	−0.111294	−	0.342527i
$482$		0			0
$483$			19.7015i			0.896447i
$484$		0			0
$485$	−0.584586	−	14.6669i	−0.0265447	−	0.665989i
$486$		0			0
$487$	−25.8390	+	8.39560i	−1.17088	+	0.380441i	−0.828970	−	0.559293i	$-0.811073\pi$
$487$	−25.8390	+	8.39560i	−1.17088	+	0.380441i	−0.341907	+	0.939734i	$0.611073\pi$
$488$		0			0
$489$	−19.5164	−	14.1795i	−0.882561	−	0.641218i
$490$		0			0
$491$	−6.78689	+	20.8879i	−0.306288	+	0.942658i	0.672905	+	0.739729i	$0.265046\pi$
$491$	−6.78689	+	20.8879i	−0.306288	+	0.942658i	−0.979193	+	0.202929i	$0.934954\pi$
$492$		0			0
$493$	−12.7003	−	17.4804i	−0.571991	−	0.787278i
$494$		0			0
$495$	−41.8012	+	24.7552i	−1.87882	+	1.11266i
$496$		0			0
$497$	10.1498	+	13.9700i	0.455281	+	0.626641i
$498$		0			0
$499$	1.55830	−	4.79596i	0.0697591	−	0.214697i	−0.910099	−	0.414390i	$-0.863995\pi$
$499$	1.55830	−	4.79596i	0.0697591	−	0.214697i	0.979858	+	0.199694i	$0.0639948\pi$
$500$		0			0
$501$	−28.0431	−	20.3745i	−1.25288	−	0.910267i
$502$		0			0
$503$	−24.3567	+	7.91397i	−1.08601	+	0.352867i	−0.796704	−	0.604370i	$-0.793425\pi$
$503$	−24.3567	+	7.91397i	−1.08601	+	0.352867i	−0.289307	+	0.957236i	$0.593425\pi$
$504$		0			0
$505$	12.1057	−	0.482503i	0.538696	−	0.0214711i
$506$		0			0
$507$		−	6.09826i		−	0.270833i
$508$		0			0
$509$	7.17001	+	22.0670i	0.317805	+	0.978103i	0.974584	+	0.224020i	$0.0719183\pi$
$509$	7.17001	+	22.0670i	0.317805	+	0.978103i	−0.656779	+	0.754083i	$0.728082\pi$
$510$		0			0
$511$	28.5888	+	20.7710i	1.26469	+	0.918853i
$512$		0			0
$513$	−31.0242	−	10.0804i	−1.36975	−	0.445059i
$514$		0			0
$515$	17.1782	+	21.7650i	0.756960	+	0.959081i
$516$		0			0
$517$	−6.62987	+	6.95041i	−0.291581	+	0.305679i
$518$		0			0
$519$	26.7194	−	19.4128i	1.17285	−	0.852125i
$520$		0			0
$521$	−0.608668	+	1.87329i	−0.0266662	+	0.0820703i	−0.963504	−	0.267694i	$-0.913738\pi$
$521$	−0.608668	+	1.87329i	−0.0266662	+	0.0820703i	0.936838	+	0.349764i	$0.113738\pi$
$522$		0			0
$523$	2.36781	−	3.25902i	0.103537	−	0.142507i	−0.754104	−	0.656755i	$-0.771929\pi$
$523$	2.36781	−	3.25902i	0.103537	−	0.142507i	0.857642	+	0.514248i	$0.171929\pi$
$524$		0			0
$525$	−15.1105	−	36.3635i	−0.659478	−	1.58703i
$526$		0			0
$527$			24.8436i			1.08221i
$528$		0			0
$529$	16.7421			0.727918
$530$		0			0
$531$	−16.0246	−	49.3186i	−0.695407	−	2.14024i
$532$		0			0
$533$	−23.2149	+	31.9526i	−1.00555	+	1.38402i
$534$		0			0
$535$	2.90805	+	0.818375i	0.125726	+	0.0353815i
$536$		0			0
$537$	−7.78740	−	10.7184i	−0.336051	−	0.462535i
$538$		0			0
$539$	−1.66231	−	0.223214i	−0.0716008	−	0.00961450i
$540$		0			0
$541$	8.78812	−	6.38494i	0.377831	−	0.274510i	−0.382620	−	0.923906i	$-0.624978\pi$
$541$	8.78812	−	6.38494i	0.377831	−	0.274510i	0.760451	+	0.649396i	$0.224978\pi$
$542$		0			0
$543$	−13.5371	−	4.39847i	−0.580933	−	0.188756i
$544$		0			0
$545$	−5.36890	−	3.58298i	−0.229978	−	0.153478i
$546$		0			0
$547$	−36.5009	+	11.8598i	−1.56066	+	0.507090i	−0.956985	−	0.290137i	$-0.906299\pi$
$547$	−36.5009	+	11.8598i	−1.56066	+	0.507090i	−0.603679	+	0.797228i	$0.706299\pi$
$548$		0			0
$549$	40.7442			1.73892
$550$		0			0
$551$	9.62744			0.410143
$552$		0			0
$553$	−6.50304	+	2.11297i	−0.276538	+	0.0898525i
$554$		0			0
$555$	11.7332	+	7.83027i	0.498047	+	0.332376i
$556$		0			0
$557$	−33.7158	−	10.9549i	−1.42858	−	0.464175i	−0.510265	−	0.860017i	$-0.670453\pi$
$557$	−33.7158	−	10.9549i	−1.42858	−	0.464175i	−0.918318	+	0.395843i	$0.870453\pi$
$558$		0			0
$559$	−19.7517	+	14.3504i	−0.835407	+	0.606959i
$560$		0			0
$561$	12.2884	+	67.2711i	0.518818	+	2.84019i
$562$		0			0
$563$	−13.5471	−	18.6460i	−0.570943	−	0.785836i	0.421723	−	0.906725i	$-0.361426\pi$
$563$	−13.5471	−	18.6460i	−0.570943	−	0.785836i	−0.992666	+	0.120889i	$0.961426\pi$
$564$		0			0
$565$	29.8372	+	8.39671i	1.25526	+	0.353252i
$566$		0			0
$567$	21.3599	−	29.3994i	0.897033	−	1.23466i
$568$		0			0
$569$	−5.77011	−	17.7586i	−0.241896	−	0.744478i	−0.996132	−	0.0878746i	$-0.971993\pi$
$569$	−5.77011	−	17.7586i	−0.241896	−	0.744478i	0.754236	−	0.656603i	$-0.228007\pi$
$570$		0			0
$571$	38.4165			1.60768			0.803841	−	0.594845i	$-0.202786\pi$
$571$	38.4165			1.60768			0.803841	+	0.594845i	$0.202786\pi$
$572$		0			0
$573$		−	7.34831i		−	0.306980i
$574$		0			0
$575$	11.5504	−	4.79965i	0.481683	−	0.200159i
$576$		0			0
$577$	7.58138	−	10.4349i	0.315617	−	0.434409i	−0.621506	−	0.783410i	$-0.713479\pi$
$577$	7.58138	−	10.4349i	0.315617	−	0.434409i	0.937123	+	0.349000i	$0.113479\pi$
$578$		0			0
$579$	14.1258	−	43.4749i	0.587050	−	1.80675i
$580$		0			0
$581$	−5.30538	+	3.85458i	−0.220104	+	0.159915i
$582$		0			0
$583$	27.2332	+	13.0760i	1.12788	+	0.541551i
$584$		0			0
$585$	35.1157	+	44.4922i	1.45186	+	1.83953i
$586$		0			0
$587$	−30.4450	−	9.89218i	−1.25660	−	0.408294i	−0.396318	−	0.918113i	$-0.629712\pi$
$587$	−30.4450	−	9.89218i	−1.25660	−	0.408294i	−0.860281	+	0.509820i	$0.829712\pi$
$588$		0			0
$589$	−8.95549	−	6.50655i	−0.369005	−	0.268098i
$590$		0			0
$591$	−16.2886	−	50.1310i	−0.670022	−	2.06212i
$592$		0			0
$593$			16.0380i			0.658603i	0.944225	+	0.329302i	$0.106813\pi$
$593$			16.0380i			0.658603i	−0.944225	+	0.329302i	$0.893187\pi$
$594$		0			0
$595$	−37.9881	+	1.51411i	−1.55736	+	0.0620725i
$596$		0			0
$597$	26.1010	−	8.48072i	1.06824	−	0.347093i
$598$		0			0
$599$	−10.0703	−	7.31647i	−0.411460	−	0.298943i	0.362733	−	0.931893i	$-0.381844\pi$
$599$	−10.0703	−	7.31647i	−0.411460	−	0.298943i	−0.774193	+	0.632950i	$0.781844\pi$
$600$		0			0
$601$	−8.18645	+	25.1953i	−0.333932	+	1.02774i	0.633313	+	0.773896i	$0.281694\pi$
$601$	−8.18645	+	25.1953i	−0.333932	+	1.02774i	−0.967246	+	0.253842i	$0.918306\pi$
$602$		0			0
$603$	−28.5125	−	39.2441i	−1.16112	−	1.59814i
$604$		0			0
$605$	−22.6437	+	9.60545i	−0.920596	+	0.390517i
$606$		0			0
$607$	14.8950	+	20.5013i	0.604571	+	0.832121i	0.996117	−	0.0880375i	$-0.0280595\pi$
$607$	14.8950	+	20.5013i	0.604571	+	0.832121i	−0.391546	+	0.920159i	$0.628060\pi$
$608$		0			0
$609$	−7.88169	+	24.2573i	−0.319382	+	0.982957i
$610$		0			0
$611$	9.06639	+	6.58712i	0.366787	+	0.266486i
$612$		0			0
$613$	−12.5884	+	4.09023i	−0.508443	+	0.165203i	−0.551994	−	0.833848i	$-0.686133\pi$
$613$	−12.5884	+	4.09023i	−0.508443	+	0.165203i	0.0435512	+	0.999051i	$0.486133\pi$
$614$		0			0
$615$	−2.80905	−	70.4772i	−0.113272	−	2.84192i
$616$		0			0
$617$			44.4014i			1.78753i	0.448534	+	0.893766i	$0.351946\pi$
$617$			44.4014i			1.78753i	−0.448534	+	0.893766i	$0.648054\pi$
$618$		0			0
$619$	7.52798	+	23.1687i	0.302575	+	0.931231i	0.980571	+	0.196165i	$0.0628488\pi$
$619$	7.52798	+	23.1687i	0.302575	+	0.931231i	−0.677996	+	0.735066i	$0.737151\pi$
$620$		0			0
$621$	22.2079	+	16.1350i	0.891172	+	0.647475i
$622$		0			0
$623$	−6.81796	−	2.21529i	−0.273156	−	0.0887538i
$624$		0			0
$625$	−17.6376	+	17.7177i	−0.705503	+	0.708707i
$626$		0			0
$627$	−27.4679	−	13.1886i	−1.09696	−	0.526703i
$628$		0			0
$629$	11.0180	−	8.00503i	0.439316	−	0.319181i
$630$		0			0
$631$	11.4559	−	35.2578i	0.456054	−	1.40359i	−0.413840	−	0.910350i	$-0.635813\pi$
$631$	11.4559	−	35.2578i	0.456054	−	1.40359i	0.869894	−	0.493239i	$-0.164187\pi$
$632$		0			0
$633$	−29.6991	+	40.8774i	−1.18043	+	1.62473i
$634$		0			0
$635$	21.0140	−	7.76600i	0.833915	−	0.308184i
$636$		0			0
$637$			1.95684i			0.0775327i
$638$		0			0
$639$	44.3877			1.75595
$640$		0			0
$641$	1.45105	+	4.46587i	0.0573130	+	0.176391i	0.975615	−	0.219490i	$-0.0704393\pi$
$641$	1.45105	+	4.46587i	0.0573130	+	0.176391i	−0.918302	+	0.395881i	$0.870439\pi$
$642$		0			0
$643$	13.3418	−	18.3635i	0.526151	−	0.724184i	−0.460387	−	0.887718i	$-0.652289\pi$
$643$	13.3418	−	18.3635i	0.526151	−	0.724184i	0.986538	+	0.163534i	$0.0522894\pi$
$644$		0			0
$645$	11.8112	−	41.9702i	0.465064	−	1.65258i
$646$		0			0
$647$	24.2603	+	33.3915i	0.953772	+	1.31275i	0.949832	+	0.312762i	$0.101254\pi$
$647$	24.2603	+	33.3915i	0.953772	+	1.31275i	0.00393989	+	0.999992i	$0.498746\pi$
$648$		0			0
$649$	−4.71793	−	25.8275i	−0.185195	−	1.01382i
$650$		0			0
$651$	23.7255	−	17.2376i	0.929876	−	0.675594i
$652$		0			0
$653$	17.9886	+	5.84485i	0.703948	+	0.228727i	0.639050	−	0.769165i	$-0.279328\pi$
$653$	17.9886	+	5.84485i	0.703948	+	0.228727i	0.0648983	+	0.997892i	$0.479328\pi$
$654$		0			0
$655$	14.5879	+	9.73538i	0.569997	+	0.380393i
$656$		0			0
$657$	86.3908	−	28.0701i	3.37043	−	1.09512i
$658$		0			0
$659$	2.31523			0.0901884			0.0450942	−	0.998983i	$-0.485641\pi$
$659$	2.31523			0.0901884			0.0450942	+	0.998983i	$0.485641\pi$
$660$		0			0
$661$	32.8374			1.27723			0.638613	−	0.769528i	$-0.279508\pi$
$661$	32.8374			1.27723			0.638613	+	0.769528i	$0.279508\pi$
$662$		0			0
$663$	75.8795	−	24.6547i	2.94691	−	0.957511i
$664$		0			0
$665$	9.40329	−	14.0903i	0.364644	−	0.546398i
$666$		0			0
$667$	−7.70500	−	2.50351i	−0.298339	−	0.0969362i
$668$		0			0
$669$	71.9740	−	52.2921i	2.78267	−	2.02173i
$670$		0			0
$671$	20.4453	+	2.74537i	0.789280	+	0.105984i
$672$		0			0
$673$	8.77015	+	12.0711i	0.338064	+	0.465306i	0.943875	−	0.330303i	$-0.107151\pi$
$673$	8.77015	+	12.0711i	0.338064	+	0.465306i	−0.605811	+	0.795609i	$0.707151\pi$
$674$		0			0
$675$	−53.3648	−	12.7478i	−2.05401	−	0.490664i
$676$		0			0
$677$	−9.24875	+	12.7298i	−0.355458	+	0.489246i	−0.948876	−	0.315648i	$-0.897778\pi$
$677$	−9.24875	+	12.7298i	−0.355458	+	0.489246i	0.593418	+	0.804894i	$0.297778\pi$
$678$		0			0
$679$	5.16947	+	15.9100i	0.198386	+	0.610570i
$680$		0			0
$681$	−55.1473			−2.11325
$682$		0			0
$683$			17.4983i			0.669554i	0.942297	+	0.334777i	$0.108661\pi$
$683$			17.4983i			0.669554i	−0.942297	+	0.334777i	$0.891339\pi$
$684$		0			0
$685$	−31.0928	+	11.4908i	−1.18800	+	0.439040i
$686$		0			0
$687$	20.2701	−	27.8994i	0.773352	−	1.06443i
$688$		0			0
$689$	10.8916	−	33.5208i	0.414936	−	1.27704i
$690$		0			0
$691$	−10.0626	+	7.31089i	−0.382799	+	0.278120i	−0.762498	−	0.646990i	$-0.776027\pi$
$691$	−10.0626	+	7.31089i	−0.382799	+	0.278120i	0.379699	+	0.925110i	$0.376027\pi$
$692$		0			0
$693$	38.2158	−	40.0634i	1.45170	−	1.52188i
$694$		0			0
$695$	29.9109	−	23.6073i	1.13459	−	0.895478i
$696$		0			0
$697$	−64.7646	−	21.0433i	−2.45313	−	0.797072i
$698$		0			0
$699$	−35.3280	−	25.6673i	−1.33623	−	0.970826i
$700$		0			0
$701$	−5.73978	−	17.6652i	−0.216789	−	0.667207i	−0.999022	−	0.0442210i	$-0.985919\pi$
$701$	−5.73978	−	17.6652i	−0.216789	−	0.667207i	0.782233	−	0.622986i	$-0.214081\pi$
$702$		0			0
$703$			6.06822i			0.228867i
$704$		0			0
$705$	−19.9976	+	0.797053i	−0.753152	+	0.0300188i
$706$		0			0
$707$	−13.1317	+	4.26675i	−0.493869	+	0.160468i
$708$		0			0
$709$	18.3733	+	13.3490i	0.690025	+	0.501332i	0.876668	−	0.481096i	$-0.159761\pi$
$709$	18.3733	+	13.3490i	0.690025	+	0.501332i	−0.186644	+	0.982428i	$0.559761\pi$
$710$		0			0
$711$	−5.43146	+	16.7163i	−0.203696	+	0.626910i
$712$		0			0
$713$	5.47528	+	7.53608i	0.205051	+	0.282228i
$714$		0			0
$715$	14.6230	+	24.6921i	0.546868	+	0.923431i
$716$		0			0
$717$	2.11521	+	2.91133i	0.0789938	+	0.108726i
$718$		0			0
$719$	−15.2380	+	46.8979i	−0.568283	+	1.74900i	0.0897051	+	0.995968i	$0.471408\pi$
$719$	−15.2380	+	46.8979i	−0.568283	+	1.74900i	−0.657988	+	0.753028i	$0.728592\pi$
$720$		0			0
$721$	−25.5651	−	18.5741i	−0.952093	−	0.691736i
$722$		0			0
$723$	−62.8418	+	20.4185i	−2.33711	+	0.759374i
$724$		0			0
$725$	16.1415	−	1.28876i	0.599479	−	0.0478635i
$726$		0			0
$727$			26.3470i			0.977157i	0.872520	+	0.488578i	$0.162484\pi$
$727$			26.3470i			0.977157i	−0.872520	+	0.488578i	$0.837516\pi$
$728$		0			0
$729$	2.57215	+	7.91625i	0.0952647	+	0.293195i
$730$		0			0
$731$	−34.0555	−	24.7428i	−1.25959	−	0.915144i
$732$		0			0
$733$	6.09574	+	1.98063i	0.225151	+	0.0731561i	0.419420	−	0.907792i	$-0.362233\pi$
$733$	6.09574	+	1.98063i	0.225151	+	0.0731561i	−0.194269	+	0.980948i	$0.562233\pi$
$734$		0			0
$735$	−2.16505	−	2.74316i	−0.0798591	−	0.101183i
$736$		0			0
$737$	−11.6631	−	21.6137i	−0.429617	−	0.796149i
$738$		0			0
$739$	−26.2699	+	19.0862i	−0.966355	+	0.702098i	−0.954618	−	0.297833i	$-0.903736\pi$
$739$	−26.2699	+	19.0862i	−0.966355	+	0.702098i	−0.0117373	+	0.999931i	$0.503736\pi$
$740$		0			0
$741$	−10.9854	+	33.8097i	−0.403560	+	1.24203i
$742$		0			0
$743$	1.59684	−	2.19785i	0.0585822	−	0.0806315i	−0.778721	−	0.627371i	$-0.784131\pi$
$743$	1.59684	−	2.19785i	0.0585822	−	0.0806315i	0.837303	+	0.546739i	$0.184131\pi$
$744$		0			0
$745$	11.4310	+	30.9311i	0.418799	+	1.13323i
$746$		0			0
$747$			16.8571i			0.616768i
$748$		0			0
$749$	−3.44296			−0.125803
$750$		0			0
$751$	−16.4305	−	50.5680i	−0.599559	−	1.84525i	−0.530583	−	0.847633i	$-0.678027\pi$
$751$	−16.4305	−	50.5680i	−0.599559	−	1.84525i	−0.0689758	−	0.997618i	$-0.521973\pi$
$752$		0			0
$753$	8.47603	−	11.6663i	0.308884	−	0.425142i
$754$		0			0
$755$	4.88449	−	17.3567i	0.177765	−	0.631677i
$756$		0			0
$757$	−14.8575	−	20.4496i	−0.540005	−	0.743253i	0.448609	−	0.893728i	$-0.351920\pi$
$757$	−14.8575	−	20.4496i	−0.540005	−	0.743253i	−0.988614	+	0.150475i	$0.951920\pi$
$758$		0			0
$759$	18.5534	+	17.6978i	0.673447	+	0.642389i
$760$		0			0
$761$	4.29290	−	3.11897i	0.155617	−	0.113063i	−0.507252	−	0.861798i	$-0.669339\pi$
$761$	4.29290	−	3.11897i	0.155617	−	0.113063i	0.662869	+	0.748735i	$0.269339\pi$
$762$		0			0
$763$	6.99619	+	2.27320i	0.253279	+	0.0822954i
$764$		0			0
$765$	−54.2483	+	81.2880i	−1.96135	+	2.93898i
$766$		0			0
$767$	−29.1326	+	9.46575i	−1.05192	+	0.341788i
$768$		0			0
$769$	−16.8073			−0.606086			−0.303043	−	0.952977i	$-0.598003\pi$
$769$	−16.8073			−0.606086			−0.303043	+	0.952977i	$0.598003\pi$
$770$		0			0
$771$	25.3008			0.911187
$772$		0			0
$773$	26.7708	−	8.69835i	0.962878	−	0.312858i	0.214940	−	0.976627i	$-0.431044\pi$
$773$	26.7708	−	8.69835i	0.962878	−	0.312858i	0.747937	+	0.663769i	$0.231044\pi$
$774$		0			0
$775$	−15.8859	−	9.71012i	−0.570637	−	0.348798i
$776$		0			0
$777$	−15.2895	−	4.96786i	−0.548508	−	0.178221i
$778$		0			0
$779$	24.5474	−	17.8348i	0.879503	−	0.638996i
$780$		0			0
$781$	22.2735	+	2.99087i	0.797010	+	0.107022i
$782$		0			0
$783$	20.8885	+	28.7505i	0.746494	+	1.02746i
$784$		0			0
$785$	−42.9225	−	12.0791i	−1.53197	−	0.431123i
$786$		0			0
$787$	−20.5959	+	28.3478i	−0.734164	+	1.01049i	0.264769	+	0.964312i	$0.414704\pi$
$787$	−20.5959	+	28.3478i	−0.734164	+	1.01049i	−0.998933	+	0.0461781i	$0.985296\pi$
$788$		0			0
$789$	18.0874	+	55.6672i	0.643927	+	1.98180i
$790$		0			0
$791$	−35.3256			−1.25603
$792$		0			0
$793$		−	24.0677i		−	0.854670i
$794$		0			0
$795$	21.8194	+	59.0411i	0.773855	+	2.09397i
$796$		0			0
$797$	9.55280	−	13.1483i	0.338378	−	0.465737i	−0.605589	−	0.795778i	$-0.707062\pi$
$797$	9.55280	−	13.1483i	0.338378	−	0.465737i	0.943967	+	0.330041i	$0.107062\pi$
$798$		0			0
$799$	−5.97093	+	18.3766i	−0.211236	+	0.650119i
$800$		0			0
$801$	−14.9084	+	10.8316i	−0.526761	+	0.382714i
$802$		0			0
$803$	45.2419	−	8.26435i	1.59655	−	0.291643i
$804$		0			0
$805$	−11.1896	+	8.83148i	−0.394383	+	0.311269i
$806$		0			0
$807$	−11.9286	−	3.87585i	−0.419908	−	0.136436i
$808$		0			0
$809$	19.9311	+	14.4808i	0.700740	+	0.509118i	0.880173	−	0.474653i	$-0.157426\pi$
$809$	19.9311	+	14.4808i	0.700740	+	0.509118i	−0.179433	+	0.983770i	$0.557426\pi$
$810$		0			0
$811$	3.46777	+	10.6727i	0.121770	+	0.374769i	0.993299	−	0.115575i	$-0.0368711\pi$
$811$	3.46777	+	10.6727i	0.121770	+	0.374769i	−0.871529	+	0.490344i	$0.836871\pi$
$812$		0			0
$813$			89.2130i			3.12884i
$814$		0			0
$815$	−0.695143	−	17.4407i	−0.0243498	−	0.610921i
$816$		0			0
$817$	17.8383	−	5.79601i	0.624082	−	0.202777i
$818$		0			0
$819$	−52.2603	−	37.9693i	−1.82612	−	1.32676i
$820$		0			0
$821$	−8.07088	+	24.8396i	−0.281676	+	0.866909i	0.705700	+	0.708511i	$0.250633\pi$
$821$	−8.07088	+	24.8396i	−0.281676	+	0.866909i	−0.987375	+	0.158398i	$0.949367\pi$
$822$		0			0
$823$	−7.90219	−	10.8764i	−0.275453	−	0.379128i	0.648768	−	0.760986i	$-0.275284\pi$
$823$	−7.90219	−	10.8764i	−0.275453	−	0.379128i	−0.924221	+	0.381858i	$0.875284\pi$
$824$		0			0
$825$	−47.8183	−	18.4352i	−1.66482	−	0.641832i
$826$		0			0
$827$	12.3622	+	17.0152i	0.429877	+	0.591675i	0.967925	−	0.251239i	$-0.0808381\pi$
$827$	12.3622	+	17.0152i	0.429877	+	0.591675i	−0.538048	+	0.842914i	$0.680838\pi$
$828$		0			0
$829$	12.6673	−	38.9860i	0.439955	−	1.35404i	−0.447968	−	0.894049i	$-0.647852\pi$
$829$	12.6673	−	38.9860i	0.439955	−	1.35404i	0.887923	−	0.459992i	$-0.152148\pi$
$830$		0			0
$831$	−4.78115	−	3.47371i	−0.165856	−	0.120502i
$832$		0			0
$833$	−3.20881	+	1.04261i	−0.111179	+	0.0361241i
$834$		0			0
$835$	−0.998853	−	25.0606i	−0.0345667	−	0.867257i
$836$		0			0
$837$		−	40.8610i		−	1.41236i
$838$		0			0
$839$	−11.8987	−	36.6203i	−0.410787	−	1.26427i	−0.915965	−	0.401258i	$-0.868573\pi$
$839$	−11.8987	−	36.6203i	−0.410787	−	1.26427i	0.505178	−	0.863015i	$-0.331427\pi$
$840$		0			0
$841$	14.9763	+	10.8809i	0.516424	+	0.375204i
$842$		0			0
$843$	−21.4082	−	6.95595i	−0.737338	−	0.239576i
$844$		0			0
$845$	3.46356	−	2.73364i	0.119150	−	0.0940400i
$846$		0			0
$847$	21.8760	−	17.5286i	0.751667	−	0.602290i
$848$		0			0
$849$	−68.9830	+	50.1191i	−2.36749	+	1.72008i
$850$		0			0
$851$	1.57797	−	4.85650i	0.0540922	−	0.166479i
$852$		0			0
$853$	22.9081	−	31.5302i	0.784357	−	1.07957i	−0.210431	−	0.977609i	$-0.567487\pi$
$853$	22.9081	−	31.5302i	0.784357	−	1.07957i	0.994788	−	0.101966i	$-0.0325132\pi$
$854$		0			0
$855$	−15.0946	−	40.8445i	−0.516225	−	1.39685i
$856$		0			0
$857$		−	39.8974i		−	1.36287i	−0.731879	−	0.681435i	$-0.761356\pi$
$857$		−	39.8974i		−	1.36287i	0.731879	−	0.681435i	$-0.238644\pi$
$858$		0			0
$859$	−6.92193			−0.236173			−0.118087	−	0.993003i	$-0.537676\pi$
$859$	−6.92193			−0.236173			−0.118087	+	0.993003i	$0.537676\pi$
$860$		0			0
$861$	24.8403	+	76.4506i	0.846555	+	2.60543i
$862$		0			0
$863$	6.84574	−	9.42235i	0.233032	−	0.320741i	−0.676447	−	0.736491i	$-0.736481\pi$
$863$	6.84574	−	9.42235i	0.233032	−	0.320741i	0.909479	+	0.415751i	$0.136481\pi$
$864$		0			0
$865$	23.0030	+	6.47346i	0.782127	+	0.220104i
$866$		0			0
$867$	49.9768	+	68.7871i	1.69730	+	2.33613i
$868$		0			0
$869$	−3.85183	+	8.02218i	−0.130664	+	0.272134i
$870$		0			0
$871$	−23.1816	+	16.8424i	−0.785477	+	0.570683i
$872$		0			0
$873$	40.8972	+	13.2883i	1.38416	+	0.449741i
$874$		0			0
$875$	13.8795	−	24.8827i	0.469212	−	0.841188i
$876$		0			0
$877$	7.53904	−	2.44958i	0.254575	−	0.0827166i	−0.178949	−	0.983858i	$-0.557270\pi$
$877$	7.53904	−	2.44958i	0.254575	−	0.0827166i	0.433525	+	0.901142i	$0.357270\pi$
$878$		0			0
$879$	−69.2211			−2.33477
$880$		0			0
$881$	−3.48465			−0.117401			−0.0587005	−	0.998276i	$-0.518696\pi$
$881$	−3.48465			−0.117401			−0.0587005	+	0.998276i	$0.518696\pi$
$882$		0			0
$883$	48.1792	−	15.6544i	1.62136	−	0.526811i	0.649097	−	0.760706i	$-0.275147\pi$
$883$	48.1792	−	15.6544i	1.62136	−	0.526811i	0.972262	+	0.233894i	$0.0751469\pi$
$884$		0			0
$885$	30.3660	−	45.5018i	1.02074	−	1.52953i
$886$		0			0
$887$	−19.9744	−	6.49007i	−0.670674	−	0.217915i	−0.0461663	−	0.998934i	$-0.514700\pi$
$887$	−19.9744	−	6.49007i	−0.670674	−	0.217915i	−0.624508	+	0.781019i	$0.714700\pi$
$888$		0			0
$889$	−20.6560	+	15.0075i	−0.692781	+	0.503335i
$890$		0			0
$891$	−8.49870	−	46.5248i	−0.284717	−	1.55864i
$892$		0			0
$893$	−5.06052	−	6.96521i	−0.169344	−	0.233082i
$894$		0			0
$895$	2.59682	−	9.22764i	0.0868021	−	0.308446i
$896$		0			0
$897$	17.5837	−	24.2018i	0.587101	−	0.808076i
$898$		0			0
$899$	3.72656	+	11.4692i	0.124288	+	0.382519i
$900$		0			0
$901$	60.7703			2.02455
$902$		0			0
$903$			49.6904i			1.65359i
$904$		0			0
$905$	−3.57006	−	9.66021i	−0.118673	−	0.321116i
$906$		0			0
$907$	2.04047	−	2.80847i	0.0677528	−	0.0932537i	−0.773796	−	0.633435i	$-0.781644\pi$
$907$	2.04047	−	2.80847i	0.0677528	−	0.0932537i	0.841549	+	0.540181i	$0.181644\pi$
$908$		0			0
$909$	−10.9678	+	33.7555i	−0.363780	+	1.11960i
$910$		0			0
$911$	29.7841	−	21.6394i	0.986790	−	0.716945i	0.0275744	−	0.999620i	$-0.491222\pi$
$911$	29.7841	−	21.6394i	0.986790	−	0.716945i	0.959216	+	0.282675i	$0.0912217\pi$
$912$		0			0
$913$	−1.13584	+	8.45879i	−0.0375908	+	0.279945i
$914$		0			0
$915$	26.6286	+	33.7389i	0.880314	+	1.11537i
$916$		0			0
$917$	−19.0095	−	6.17654i	−0.627747	−	0.203967i
$918$		0			0
$919$	−8.18817	−	5.94906i	−0.270103	−	0.196241i	0.444486	−	0.895786i	$-0.353386\pi$
$919$	−8.18817	−	5.94906i	−0.270103	−	0.196241i	−0.714589	+	0.699544i	$0.753386\pi$
$920$		0			0
$921$	−2.66823	−	8.21196i	−0.0879211	−	0.270593i
$922$		0			0
$923$		−	26.2199i		−	0.863040i
$924$		0			0
$925$	0.812314	+	10.1740i	0.0267087	+	0.334520i
$926$		0			0
$927$	−77.2537	+	25.1012i	−2.53734	+	0.824433i
$928$		0			0
$929$	−22.6722	−	16.4723i	−0.743850	−	0.540439i	0.150064	−	0.988676i	$-0.452052\pi$
$929$	−22.6722	−	16.4723i	−0.743850	−	0.540439i	−0.893915	+	0.448237i	$0.852052\pi$
$930$		0			0
$931$	0.464555	−	1.42975i	0.0152252	−	0.0468583i
$932$		0			0
$933$	−49.1448	−	67.6420i	−1.60893	−	2.21450i
$934$		0			0
$935$	−32.6988	+	37.1346i	−1.06936	+	1.21443i
$936$		0			0
$937$	30.3728	+	41.8046i	0.992238	+	1.36570i	0.929969	+	0.367638i	$0.119834\pi$
$937$	30.3728	+	41.8046i	0.992238	+	1.36570i	0.0622687	+	0.998059i	$0.480166\pi$
$938$		0			0
$939$	−8.44751	+	25.9988i	−0.275674	+	0.848438i
$940$		0			0
$941$	33.3629	+	24.2396i	1.08760	+	0.790188i	0.978992	−	0.203897i	$-0.0653608\pi$
$941$	33.3629	+	24.2396i	1.08760	+	0.790188i	0.108608	+	0.994085i	$0.465361\pi$
$942$		0			0
$943$	−24.2835	+	7.89017i	−0.790778	+	0.256939i
$944$		0			0
$945$	62.4802	−	2.49030i	2.03248	−	0.0810096i
$946$		0			0
$947$		−	25.1201i		−	0.816292i	−0.912917	−	0.408146i	$-0.866175\pi$
$947$		−	25.1201i		−	0.816292i	0.912917	−	0.408146i	$-0.133825\pi$
$948$		0			0
$949$	−16.5811	−	51.0313i	−0.538244	−	1.65655i
$950$		0			0
$951$	66.4880	+	48.3064i	2.15602	+	1.56644i
$952$		0			0
$953$	−5.02344	−	1.63222i	−0.162725	−	0.0528726i	0.226521	−	0.974006i	$-0.427265\pi$
$953$	−5.02344	−	1.63222i	−0.162725	−	0.0528726i	−0.389247	+	0.921134i	$0.627265\pi$
$954$		0			0
$955$	4.17355	−	3.29399i	0.135053	−	0.106591i
$956$		0			0
$957$	15.7637	+	29.2127i	0.509569	+	0.944314i
$958$		0			0
$959$	30.5632	−	22.2054i	0.986936	−	0.717051i
$960$		0			0
$961$	−5.29474	+	16.2955i	−0.170798	+	0.525662i
$962$		0			0
$963$	−5.20205	+	7.16001i	−0.167634	+	0.230728i
$964$		0			0
$965$	31.0241	−	11.4654i	0.998701	−	0.369083i
$966$		0			0
$967$		−	18.4071i		−	0.591931i	−0.955199	−	0.295966i	$-0.904359\pi$
$967$		−	18.4071i		−	0.591931i	0.955199	−	0.295966i	$-0.0956414\pi$
$968$		0			0
$969$	−61.2940			−1.96905
$970$		0			0
$971$	−3.31247	−	10.1947i	−0.106302	−	0.327165i	0.883732	−	0.467994i	$-0.155023\pi$
$971$	−3.31247	−	10.1947i	−0.106302	−	0.327165i	−0.990034	+	0.140829i	$0.955023\pi$
$972$		0			0
$973$	−25.5257	+	35.1332i	−0.818318	+	1.12632i
$974$		0			0
$975$	−13.8924	+	58.1562i	−0.444913	+	1.86249i
$976$		0			0
$977$	1.51542	+	2.08579i	0.0484825	+	0.0667304i	0.832570	−	0.553920i	$-0.186869\pi$
$977$	1.51542	+	2.08579i	0.0484825	+	0.0667304i	−0.784087	+	0.620650i	$0.786869\pi$
$978$		0			0
$979$	−8.21077	+	4.43068i	−0.262417	+	0.141605i
$980$		0			0
$981$	15.2981	−	11.1147i	0.488430	−	0.354865i
$982$		0			0
$983$	40.6977	+	13.2235i	1.29806	+	0.421764i	0.874905	−	0.484295i	$-0.160924\pi$
$983$	40.6977	+	13.2235i	1.29806	+	0.421764i	0.423151	+	0.906059i	$0.360924\pi$
$984$		0			0
$985$	21.1708	−	31.7233i	0.674558	−	1.01079i
$986$		0			0
$987$	21.6925	−	7.04831i	0.690479	−	0.224350i
$988$		0			0
$989$	−15.7835			−0.501885
$990$		0			0
$991$	−45.3709			−1.44125			−0.720627	−	0.693323i	$-0.756146\pi$
$991$	−45.3709			−1.44125			−0.720627	+	0.693323i	$0.756146\pi$
$992$		0			0
$993$	−33.4129	+	10.8565i	−1.06033	+	0.344521i
$994$		0			0
$995$	16.5169	+	11.0227i	0.523620	+	0.349443i
$996$		0			0
$997$	−33.9867	−	11.0429i	−1.07637	−	0.349733i	−0.283403	−	0.959001i	$-0.591464\pi$
$997$	−33.9867	−	11.0429i	−1.07637	−	0.349733i	−0.792965	+	0.609268i	$0.791464\pi$
$998$		0			0
$999$	−18.1216	+	13.1661i	−0.573342	+	0.416557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.t.a.69.1	✓	24
4.3	odd	2		880.2.cd.d.289.6		24
5.2	odd	4		1100.2.n.f.201.6		24
5.3	odd	4		1100.2.n.f.201.1		24
5.4	even	2	inner	220.2.t.a.69.6	yes	24
11.2	odd	10		2420.2.b.h.969.12		12
11.4	even	5	inner	220.2.t.a.169.6	yes	24
11.9	even	5		2420.2.b.i.969.12		12
20.19	odd	2		880.2.cd.d.289.1		24
44.15	odd	10		880.2.cd.d.609.1		24
55.4	even	10	inner	220.2.t.a.169.1	yes	24
55.9	even	10		2420.2.b.i.969.1		12
55.24	odd	10		2420.2.b.h.969.1		12
55.37	odd	20		1100.2.n.f.301.6		24
55.48	odd	20		1100.2.n.f.301.1		24
220.59	odd	10		880.2.cd.d.609.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.69.1	✓	24	1.1	even	1	trivial
220.2.t.a.69.6	yes	24	5.4	even	2	inner
220.2.t.a.169.1	yes	24	55.4	even	10	inner
220.2.t.a.169.6	yes	24	11.4	even	5	inner
880.2.cd.d.289.1		24	20.19	odd	2
880.2.cd.d.289.6		24	4.3	odd	2
880.2.cd.d.609.1		24	44.15	odd	10
880.2.cd.d.609.6		24	220.59	odd	10
1100.2.n.f.201.1		24	5.3	odd	4
1100.2.n.f.201.6		24	5.2	odd	4
1100.2.n.f.301.1		24	55.48	odd	20
1100.2.n.f.301.6		24	55.37	odd	20
2420.2.b.h.969.1		12	55.24	odd	10
2420.2.b.h.969.12		12	11.2	odd	10
2420.2.b.i.969.1		12	55.9	even	10
2420.2.b.i.969.12		12	11.9	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.93917 + 0.954994i) q^{3} +(-1.85993 - 1.24124i) q^{5} +(2.42366 + 0.787496i) q^{7} +(5.29965 - 3.85042i) q^{9} +(2.91878 - 1.57503i) q^{11} +(-2.27445 - 3.13052i) q^{13} +(6.65201 + 1.87199i) q^{15} +(3.92157 - 5.39758i) q^{17} +(0.918630 + 2.82725i) q^{19} -7.87561 q^{21} -2.50158i q^{23} +(1.91865 + 4.61723i) q^{25} +(-6.44992 + 8.87756i) q^{27} +(1.00077 - 3.08006i) q^{29} +(-3.01253 + 2.18873i) q^{31} +(-7.07465 + 7.41669i) q^{33} +(-3.53036 - 4.47303i) q^{35} +(1.94137 + 0.630791i) q^{37} +(9.67463 + 7.02903i) q^{39} +(-3.15408 - 9.70725i) q^{41} -6.30940i q^{43} +(-14.6363 + 0.583365i) q^{45} +(-2.75439 + 0.894954i) q^{47} +(-0.409123 - 0.297245i) q^{49} +(-6.37150 + 19.6095i) q^{51} +(5.35388 + 7.36899i) q^{53} +(-7.38370 - 0.693471i) q^{55} +(-5.40002 - 7.43249i) q^{57} +(2.44623 - 7.52871i) q^{59} +(5.03193 + 3.65591i) q^{61} +(15.8768 - 5.15867i) q^{63} +(0.344595 + 8.64567i) q^{65} -7.40503i q^{67} +(2.38899 + 7.35256i) q^{69} +(5.48190 + 3.98283i) q^{71} +(13.1880 + 4.28503i) q^{73} +(-10.0487 - 11.7385i) q^{75} +(8.31447 - 1.51881i) q^{77} +(-2.17071 + 1.57711i) q^{79} +(4.40654 - 13.5619i) q^{81} +(-1.51256 + 2.08185i) q^{83} +(-13.9935 + 5.17149i) q^{85} +10.0085i q^{87} -2.81308 q^{89} +(-3.04724 - 9.37844i) q^{91} +(6.76411 - 9.31000i) q^{93} +(1.80071 - 6.39872i) q^{95} +(3.85848 + 5.31074i) q^{97} +(9.40400 - 19.5856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) \) 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

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