LMFDB - Embedded newform 275.3.q.d.24.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,18,0,30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.1
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	275.24
Dual form			275.3.q.d.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.224514 + 0.690983i) q^{2} +(-0.812299 - 1.11803i) q^{3} +(2.80902 + 2.04087i) q^{4} +(0.954915 - 0.310271i) q^{6} +(-8.05748 - 5.85410i) q^{7} +(-4.39201 + 3.19098i) q^{8} +(2.19098 - 6.74315i) q^{9} +(-10.3713 - 3.66547i) q^{11} -4.79837i q^{12} +(1.62460 - 5.00000i) q^{13} +(5.85410 - 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-4.72253 - 14.5344i) q^{17} +(4.16750 + 3.02786i) q^{18} +(-1.21885 - 1.67760i) q^{19} +13.7638i q^{21} +(4.86128 - 6.34346i) q^{22} -2.76393i q^{23} +(7.13525 + 2.31838i) q^{24} +(3.09017 + 2.24514i) q^{26} +(-21.1478 + 6.87132i) q^{27} +(-10.6861 - 32.8885i) q^{28} +(16.7082 - 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} -28.9402 q^{32} +(4.32650 + 14.5729i) q^{33} +11.1033 q^{34} +(19.9164 - 14.4701i) q^{36} +(23.6579 - 32.5623i) q^{37} +(1.43284 - 0.465558i) q^{38} +(-6.90983 + 2.24514i) q^{39} +(-41.2426 - 56.7656i) q^{41} +(-9.51057 - 3.09017i) q^{42} -23.0624 q^{43} +(-21.6525 - 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(16.0090 + 22.0344i) q^{47} +(8.07772 - 11.1180i) q^{48} +(15.5106 + 47.7369i) q^{49} +(-12.4139 + 17.0863i) q^{51} +(14.7679 - 10.7295i) q^{52} +(-10.8981 - 3.54102i) q^{53} -16.1554i q^{54} +54.0689 q^{56} +(-0.885544 + 2.72542i) q^{57} +(12.1392 + 16.7082i) q^{58} +(-1.83688 - 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-4.18774 - 3.04257i) q^{62} +(-57.1289 + 41.5066i) q^{63} +(-5.79431 + 17.8330i) q^{64} +(-11.0410 - 0.282294i) q^{66} +38.4934i q^{67} +(16.3973 - 50.4656i) q^{68} +(-3.09017 + 2.24514i) q^{69} +(23.5836 + 72.5828i) q^{71} +(11.8945 + 36.6074i) q^{72} +(83.2237 + 60.4656i) q^{73} +(17.1885 + 23.6579i) q^{74} -7.19991i q^{76} +(62.1087 + 90.2492i) q^{77} -5.27864i q^{78} +(3.74265 + 1.21606i) q^{79} +(-26.7639 - 19.4451i) q^{81} +(48.4836 - 15.7533i) q^{82} +(25.7238 + 79.1697i) q^{83} +(-28.0902 + 38.6628i) q^{84} +(5.17783 - 15.9357i) q^{86} -39.2833 q^{87} +(57.2474 - 16.9959i) q^{88} -123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(5.64083 - 7.76393i) q^{92} +(9.36408 - 3.04257i) q^{93} +(-18.8197 + 6.11488i) q^{94} +(23.5081 + 32.3562i) q^{96} +(73.6196 + 23.9205i) q^{97} -36.4677 q^{98} +(-47.4402 + 61.9044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{4} + 30 q^{6} + 22 q^{9} + 2 q^{11} + 20 q^{14} + 38 q^{16} - 50 q^{19} - 10 q^{24} - 20 q^{26} + 80 q^{29} - 116 q^{31} - 260 q^{34} + 52 q^{36} - 100 q^{39} - 160 q^{41} - 48 q^{44} + 60 q^{46}+ \cdots - 62 q^{99}+O(q^{100}) $ 8 * q + 18 * q^4 + 30 * q^6 + 22 * q^9 + 2 * q^11 + 20 * q^14 + 38 * q^16 - 50 * q^19 - 10 * q^24 - 20 * q^26 + 80 * q^29 - 116 * q^31 - 260 * q^34 + 52 * q^36 - 100 * q^39 - 160 * q^41 - 48 * q^44 + 60 * q^46 + 218 * q^49 - 390 * q^51 + 200 * q^56 - 46 * q^59 + 20 * q^61 + 298 * q^64 + 180 * q^66 + 20 * q^69 + 296 * q^71 + 540 * q^74 - 140 * q^79 - 232 * q^81 - 180 * q^84 + 350 * q^86 - 244 * q^89 - 160 * q^91 - 240 * q^94 + 680 * q^96 - 62 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	−0.224514	+	0.690983i	−0.112257	+	0.345492i	−0.991365	−	0.131131i	$-0.958139\pi$
$2$	−0.224514	+	0.690983i	−0.112257	+	0.345492i	0.879108	+	0.476623i	$0.158139\pi$
$3$	−0.812299	−	1.11803i	−0.270766	−	0.372678i	0.651882	−	0.758321i	$-0.273980\pi$
$3$	−0.812299	−	1.11803i	−0.270766	−	0.372678i	−0.922648	+	0.385643i	$0.873980\pi$
$4$	2.80902	+	2.04087i	0.702254	+	0.510218i
$5$		0			0
$5$		0			0
$6$	0.954915	−	0.310271i	0.159153	−	0.0517118i
$7$	−8.05748	−	5.85410i	−1.15107	−	0.836300i	−0.162446	−	0.986717i	$-0.551938\pi$
$7$	−8.05748	−	5.85410i	−1.15107	−	0.836300i	−0.988623	+	0.150417i	$0.951938\pi$
$8$	−4.39201	+	3.19098i	−0.549001	+	0.398873i
$9$	2.19098	−	6.74315i	0.243443	−	0.749239i
$10$		0			0
$11$	−10.3713	−	3.66547i	−0.942848	−	0.333224i
$11$	−10.3713	−	3.66547i	−0.942848	−	0.333224i
$12$		−	4.79837i		−	0.399864i
$13$	1.62460	−	5.00000i	0.124969	−	0.384615i	−0.868926	−	0.494941i	$-0.835190\pi$
$13$	1.62460	−	5.00000i	0.124969	−	0.384615i	0.993895	+	0.110326i	$0.0351895\pi$
$14$	5.85410	−	4.25325i	0.418150	−	0.303804i
$15$		0			0
$16$	3.07295	+	9.45756i	0.192059	+	0.591098i
$17$	−4.72253	−	14.5344i	−0.277796	−	0.854967i	−0.988466	−	0.151442i	$-0.951608\pi$
$17$	−4.72253	−	14.5344i	−0.277796	−	0.854967i	0.710670	−	0.703525i	$-0.248392\pi$
$18$	4.16750	+	3.02786i	0.231528	+	0.168215i
$19$	−1.21885	−	1.67760i	−0.0641498	−	0.0882947i	0.775737	−	0.631057i	$-0.217379\pi$
$19$	−1.21885	−	1.67760i	−0.0641498	−	0.0882947i	−0.839886	+	0.542762i	$0.817379\pi$
$20$		0			0
$21$			13.7638i			0.655420i
$22$	4.86128	−	6.34346i	0.220967	−	0.288339i
$23$		−	2.76393i		−	0.120171i	−0.998193	−	0.0600855i	$-0.980863\pi$
$23$		−	2.76393i		−	0.120171i	0.998193	−	0.0600855i	$-0.0191373\pi$
$24$	7.13525	+	2.31838i	0.297302	+	0.0965994i
$25$		0			0
$26$	3.09017	+	2.24514i	0.118853	+	0.0863515i
$27$	−21.1478	+	6.87132i	−0.783250	+	0.254493i
$28$	−10.6861	−	32.8885i	−0.381648	−	1.17459i
$29$	16.7082	−	22.9969i	0.576145	−	0.792996i	−0.417121	−	0.908851i	$-0.636961\pi$
$29$	16.7082	−	22.9969i	0.576145	−	0.792996i	0.993266	+	0.115855i	$0.0369609\pi$
$30$		0			0
$31$	−2.20163	+	6.77591i	−0.0710202	+	0.218578i	−0.980266	−	0.197681i	$-0.936659\pi$
$31$	−2.20163	+	6.77591i	−0.0710202	+	0.218578i	0.909246	+	0.416259i	$0.136659\pi$
$32$	−28.9402			−0.904382
$33$	4.32650	+	14.5729i	0.131106	+	0.441605i
$34$	11.1033			0.326568
$35$		0			0
$36$	19.9164	−	14.4701i	0.553234	−	0.401948i
$37$	23.6579	−	32.5623i	0.639403	−	0.880062i	−0.359181	−	0.933268i	$-0.616944\pi$
$37$	23.6579	−	32.5623i	0.639403	−	0.880062i	0.998584	+	0.0532056i	$0.0169439\pi$
$38$	1.43284	−	0.465558i	0.0377063	−	0.0122515i
$39$	−6.90983	+	2.24514i	−0.177175	+	0.0575677i
$40$		0			0
$41$	−41.2426	−	56.7656i	−1.00592	−	1.38453i	−0.921623	−	0.388087i	$-0.873136\pi$
$41$	−41.2426	−	56.7656i	−1.00592	−	1.38453i	−0.0842954	−	0.996441i	$-0.526864\pi$
$42$	−9.51057	−	3.09017i	−0.226442	−	0.0735755i
$43$	−23.0624			−0.536334			−0.268167	−	0.963372i	$-0.586418\pi$
$43$	−23.0624			−0.536334			−0.268167	+	0.963372i	$0.586418\pi$
$44$	−21.6525	−	31.4629i	−0.492102	−	0.715066i
$45$		0			0
$46$	1.90983	+	0.620541i	0.0415180	+	0.0134900i
$47$	16.0090	+	22.0344i	0.340616	+	0.468818i	0.944621	−	0.328163i	$-0.106429\pi$
$47$	16.0090	+	22.0344i	0.340616	+	0.468818i	−0.604005	+	0.796980i	$0.706429\pi$
$48$	8.07772	−	11.1180i	0.168286	−	0.231626i
$49$	15.5106	+	47.7369i	0.316544	+	0.974221i
$50$		0			0
$51$	−12.4139	+	17.0863i	−0.243410	+	0.335025i
$52$	14.7679	−	10.7295i	0.283998	−	0.206336i
$53$	−10.8981	−	3.54102i	−0.205625	−	0.0668117i	0.204393	−	0.978889i	$-0.434478\pi$
$53$	−10.8981	−	3.54102i	−0.205625	−	0.0668117i	−0.410019	+	0.912077i	$0.634478\pi$
$54$		−	16.1554i		−	0.299175i
$55$		0			0
$56$	54.0689			0.965516
$57$	−0.885544	+	2.72542i	−0.0155359	+	0.0478145i
$58$	12.1392	+	16.7082i	0.209297	+	0.288072i
$59$	−1.83688	−	1.33457i	−0.0311336	−	0.0226199i	0.572110	−	0.820177i	$-0.306125\pi$
$59$	−1.83688	−	1.33457i	−0.0311336	−	0.0226199i	−0.603243	+	0.797557i	$0.706125\pi$
$60$		0			0
$61$	21.5066	−	6.98791i	0.352567	−	0.114556i	−0.127379	−	0.991854i	$-0.540656\pi$
$61$	21.5066	−	6.98791i	0.352567	−	0.114556i	0.479946	+	0.877298i	$0.340656\pi$
$62$	−4.18774	−	3.04257i	−0.0675442	−	0.0490737i
$63$	−57.1289	+	41.5066i	−0.906808	+	0.658835i
$64$	−5.79431	+	17.8330i	−0.0905361	+	0.278641i
$65$		0			0
$66$	−11.0410	−	0.282294i	−0.167288	−	0.00427718i
$67$			38.4934i			0.574529i	0.957851	+	0.287264i	$0.0927458\pi$
$67$			38.4934i			0.574529i	−0.957851	+	0.287264i	$0.907254\pi$
$68$	16.3973	−	50.4656i	0.241136	−	0.742141i
$69$	−3.09017	+	2.24514i	−0.0447851	+	0.0325383i
$70$		0			0
$71$	23.5836	+	72.5828i	0.332163	+	1.02229i	0.968103	+	0.250554i	$0.0806129\pi$
$71$	23.5836	+	72.5828i	0.332163	+	1.02229i	−0.635939	+	0.771739i	$0.719387\pi$
$72$	11.8945	+	36.6074i	0.165201	+	0.508436i
$73$	83.2237	+	60.4656i	1.14005	+	0.828295i	0.987126	−	0.159943i	$-0.0511309\pi$
$73$	83.2237	+	60.4656i	1.14005	+	0.828295i	0.152924	+	0.988238i	$0.451131\pi$
$74$	17.1885	+	23.6579i	0.232277	+	0.319701i
$75$		0			0
$76$		−	7.19991i		−	0.0947357i
$77$	62.1087	+	90.2492i	0.806606	+	1.17207i
$78$		−	5.27864i		−	0.0676749i
$79$	3.74265	+	1.21606i	0.0473753	+	0.0153932i	0.332609	−	0.943065i	$-0.392071\pi$
$79$	3.74265	+	1.21606i	0.0473753	+	0.0153932i	−0.285233	+	0.958458i	$0.592071\pi$
$80$		0			0
$81$	−26.7639	−	19.4451i	−0.330419	−	0.240063i
$82$	48.4836	−	15.7533i	0.591264	−	0.192113i
$83$	25.7238	+	79.1697i	0.309925	+	0.953852i	0.977793	+	0.209572i	$0.0672071\pi$
$83$	25.7238	+	79.1697i	0.309925	+	0.953852i	−0.667868	+	0.744280i	$0.732793\pi$
$84$	−28.0902	+	38.6628i	−0.334407	+	0.460271i
$85$		0			0
$86$	5.17783	−	15.9357i	0.0602073	−	0.185299i
$87$	−39.2833			−0.451533
$88$	57.2474	−	16.9959i	0.650539	−	0.193136i
$89$	−123.297			−1.38536			−0.692679	−	0.721246i	$-0.743570\pi$
$89$	−123.297			−1.38536			−0.692679	+	0.721246i	$0.743570\pi$
$90$		0			0
$91$	−42.3607	+	30.7768i	−0.465502	+	0.338207i
$92$	5.64083	−	7.76393i	0.0613133	−	0.0843906i
$93$	9.36408	−	3.04257i	0.100689	−	0.0327158i
$94$	−18.8197	+	6.11488i	−0.200209	+	0.0650519i
$95$		0			0
$96$	23.5081	+	32.3562i	0.244876	+	0.337043i
$97$	73.6196	+	23.9205i	0.758965	+	0.246603i	0.662835	−	0.748766i	$-0.269353\pi$
$97$	73.6196	+	23.9205i	0.758965	+	0.246603i	0.0961309	+	0.995369i	$0.469353\pi$
$98$	−36.4677			−0.372119
$99$	−47.4402	+	61.9044i	−0.479194	+	0.625297i
$100$		0			0
$101$	−107.159	−	34.8181i	−1.06098	−	0.344734i	−0.274012	−	0.961726i	$-0.588351\pi$
$101$	−107.159	−	34.8181i	−1.06098	−	0.344734i	−0.786969	+	0.616993i	$0.788351\pi$
$102$	−9.01922	−	12.4139i	−0.0884238	−	0.121705i
$103$	54.4347	−	74.9230i	0.528493	−	0.727408i	−0.458407	−	0.888742i	$-0.651580\pi$
$103$	54.4347	−	74.9230i	0.528493	−	0.727408i	0.986900	+	0.161335i	$0.0515799\pi$
$104$	8.81966	+	27.1441i	0.0848044	+	0.261001i
$105$		0			0
$106$	4.89357	−	6.73542i	0.0461657	−	0.0635417i
$107$	−68.6273	+	49.8607i	−0.641377	+	0.465988i	−0.860323	−	0.509749i	$-0.829738\pi$
$107$	−68.6273	+	49.8607i	−0.641377	+	0.465988i	0.218946	+	0.975737i	$0.429738\pi$
$108$	−73.4279	−	23.8582i	−0.679888	−	0.220909i
$109$		−	94.0766i		−	0.863088i	−0.902092	−	0.431544i	$-0.857969\pi$
$109$		−	94.0766i		−	0.863088i	0.902092	−	0.431544i	$-0.142031\pi$
$110$		0			0
$111$	−55.6231			−0.501109
$112$	30.6053	−	94.1935i	0.273262	−	0.841013i
$113$	4.99231	+	6.87132i	0.0441797	+	0.0608082i	0.830535	−	0.556966i	$-0.188035\pi$
$113$	4.99231	+	6.87132i	0.0441797	+	0.0608082i	−0.786356	+	0.617774i	$0.788035\pi$
$114$	−1.68441	−	1.22379i	−0.0147755	−	0.0107350i
$115$		0			0
$116$	93.8673	−	30.4993i	0.809200	−	0.262925i
$117$	−30.1563	−	21.9098i	−0.257746	−	0.187264i
$118$	1.33457	−	0.969623i	0.0113099	−	0.00821715i
$119$	−47.0344	+	144.757i	−0.395247	+	1.21645i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$			16.4296i			0.134669i
$123$	−29.9645	+	92.2214i	−0.243614	+	0.749767i
$124$	−20.0132	+	14.5404i	−0.161396	+	0.117261i
$125$		0			0
$126$	−15.8541	−	48.7939i	−0.125826	−	0.387253i
$127$	58.1734	+	179.039i	0.458059	+	1.40976i	0.867506	+	0.497426i	$0.165721\pi$
$127$	58.1734	+	179.039i	0.458059	+	1.40976i	−0.409448	+	0.912334i	$0.634279\pi$
$128$	−104.674	−	76.0501i	−0.817766	−	0.594141i
$129$	18.7336	+	25.7845i	0.145221	+	0.199880i
$130$		0			0
$131$		−	141.932i		−	1.08345i	−0.840556	−	0.541725i	$-0.817771\pi$
$131$		−	141.932i		−	1.08345i	0.840556	−	0.541725i	$-0.182229\pi$
$132$	−17.5883	+	49.7655i	−0.133245	+	0.377011i
$133$			20.6525i			0.155282i
$134$	−26.5983	−	8.64231i	−0.198495	−	0.0644949i
$135$		0			0
$136$	67.1205	+	48.7659i	0.493533	+	0.358573i
$137$	15.4617	−	5.02380i	0.112859	−	0.0366701i	−0.252043	−	0.967716i	$-0.581102\pi$
$137$	15.4617	−	5.02380i	0.112859	−	0.0366701i	0.364902	+	0.931046i	$0.381102\pi$
$138$	−0.857567	−	2.63932i	−0.00621425	−	0.0191255i
$139$	133.108	−	183.208i	0.957614	−	1.31804i	0.00955293	−	0.999954i	$-0.496959\pi$
$139$	133.108	−	183.208i	0.957614	−	1.31804i	0.948061	−	0.318088i	$-0.103041\pi$
$140$		0			0
$141$	11.6312	−	35.7971i	0.0824907	−	0.253880i
$142$	−55.4484			−0.390481
$143$	−35.1766	+	45.9017i	−0.245990	+	0.320991i
$144$	70.5066			0.489629
$145$		0			0
$146$	−60.4656	+	43.9308i	−0.414148	+	0.300896i
$147$	40.7721	−	56.1180i	0.277361	−	0.381755i
$148$	132.911	−	43.1854i	0.898047	−	0.291793i
$149$	63.8967	−	20.7613i	0.428837	−	0.139338i	−0.0866427	−	0.996239i	$-0.527614\pi$
$149$	63.8967	−	20.7613i	0.428837	−	0.139338i	0.515479	+	0.856902i	$0.327614\pi$
$150$		0			0
$151$	59.0871	+	81.3264i	0.391305	+	0.538585i	0.958535	−	0.284974i	$-0.0919850\pi$
$151$	59.0871	+	81.3264i	0.391305	+	0.538585i	−0.567230	+	0.823559i	$0.691985\pi$
$152$	10.7064	+	3.47871i	0.0704367	+	0.0228863i
$153$	−108.355			−0.708202
$154$	−76.3050	+	22.6538i	−0.495487	+	0.147103i
$155$		0			0
$156$	−23.9919	−	7.79543i	−0.153794	−	0.0499707i
$157$	−144.960	−	199.520i	−0.923309	−	1.27083i	−0.962413	−	0.271591i	$-0.912450\pi$
$157$	−144.960	−	199.520i	−0.923309	−	1.27083i	0.0391033	−	0.999235i	$-0.487550\pi$
$158$	−1.68055	+	2.31308i	−0.0106364	+	0.0146398i
$159$	4.89357	+	15.0609i	0.0307772	+	0.0947224i
$160$		0			0
$161$	−16.1803	+	22.2703i	−0.100499	+	0.138325i
$162$	19.4451	−	14.1277i	0.120032	−	0.0872081i
$163$	165.832	+	53.8820i	1.01737	+	0.330564i	0.769786	−	0.638302i	$-0.220363\pi$
$163$	165.832	+	53.8820i	1.01737	+	0.330564i	0.247586	+	0.968866i	$0.420363\pi$
$164$		−	243.627i		−	1.48553i
$165$		0			0
$166$	−60.4803			−0.364339
$167$	76.3120	−	234.864i	0.456958	−	1.40637i	−0.411863	−	0.911246i	$-0.635122\pi$
$167$	76.3120	−	234.864i	0.456958	−	1.40637i	0.868821	−	0.495126i	$-0.164878\pi$
$168$	−43.9201	−	60.4508i	−0.261429	−	0.359826i
$169$	114.363	+	83.0897i	0.676705	+	0.491655i
$170$		0			0
$171$	−13.9828	+	4.54328i	−0.0817706	+	0.0265689i
$172$	−64.7826	−	47.0673i	−0.376643	−	0.273647i
$173$	40.2469	−	29.2411i	0.232641	−	0.169024i	−0.465357	−	0.885123i	$-0.654074\pi$
$173$	40.2469	−	29.2411i	0.232641	−	0.169024i	0.697999	+	0.716099i	$0.254074\pi$
$174$	8.81966	−	27.1441i	0.0506877	−	0.156001i
$175$		0			0
$176$	2.79586	−	109.351i	0.0158856	−	0.621314i
$177$			3.13777i			0.0177275i
$178$	27.6819	−	85.1960i	0.155516	−	0.478629i
$179$	177.134	−	128.695i	0.989574	−	0.718967i	0.0297461	−	0.999557i	$-0.490530\pi$
$179$	177.134	−	128.695i	0.989574	−	0.718967i	0.959828	+	0.280590i	$0.0905301\pi$
$180$		0			0
$181$	12.0213	+	36.9977i	0.0664159	+	0.204407i	0.978757	−	0.205024i	$-0.0657272\pi$
$181$	12.0213	+	36.9977i	0.0664159	+	0.204407i	−0.912341	+	0.409431i	$0.865727\pi$
$182$	−11.7557	−	36.1803i	−0.0645918	−	0.198793i
$183$	−25.2825	−	18.3688i	−0.138156	−	0.100376i
$184$	8.81966	+	12.1392i	0.0479329	+	0.0659740i
$185$		0			0
$186$			7.15352i			0.0384598i
$187$	−4.29670	+	168.052i	−0.0229770	+	0.898672i
$188$			94.5673i			0.503018i
$189$	210.623	+	68.4356i	1.11441	+	0.362093i
$190$		0			0
$191$	−96.9230	−	70.4187i	−0.507450	−	0.368684i	0.304405	−	0.952543i	$-0.401542\pi$
$191$	−96.9230	−	70.4187i	−0.507450	−	0.368684i	−0.811855	+	0.583858i	$0.801542\pi$
$192$	24.6447	−	8.00754i	0.128358	−	0.0417059i
$193$	9.03061	+	27.7933i	0.0467907	+	0.144007i	0.971722	−	0.236127i	$-0.0758780\pi$
$193$	9.03061	+	27.7933i	0.0467907	+	0.144007i	−0.924932	+	0.380134i	$0.875878\pi$
$194$	−33.0573	+	45.4994i	−0.170398	+	0.234533i
$195$		0			0
$196$	−53.8551	+	165.749i	−0.274771	+	0.845657i
$197$	−282.037			−1.43166			−0.715830	−	0.698275i	$-0.753951\pi$
$197$	−282.037			−1.43166			−0.715830	+	0.698275i	$0.753951\pi$
$198$	−32.1239	−	46.6788i	−0.162242	−	0.235751i
$199$	−177.469			−0.891804			−0.445902	−	0.895082i	$-0.647117\pi$
$199$	−177.469			−0.891804			−0.445902	+	0.895082i	$0.647117\pi$
$200$		0			0
$201$	43.0370	−	31.2682i	0.214114	−	0.155563i
$202$	48.1174	−	66.2279i	0.238205	−	0.327861i
$203$	−269.252	+	87.4853i	−1.32636	+	0.430962i
$204$	−69.7417	+	22.6604i	−0.341871	+	0.111081i
$205$		0			0
$206$	39.5492	+	54.4347i	0.191986	+	0.264246i
$207$	−18.6376	−	6.05573i	−0.0900368	−	0.0292547i
$208$	52.2801			0.251347
$209$	6.49187	+	21.8666i	0.0310616	+	0.104625i
$210$		0			0
$211$	93.5354	+	30.3915i	0.443296	+	0.144036i	0.522156	−	0.852850i	$-0.325128\pi$
$211$	93.5354	+	30.3915i	0.443296	+	0.144036i	−0.0788599	+	0.996886i	$0.525128\pi$
$212$	−23.3863	−	32.1885i	−0.110313	−	0.151832i
$213$	61.9931	−	85.3262i	0.291048	−	0.400593i
$214$	−19.0451	−	58.6147i	−0.0889957	−	0.273901i
$215$		0			0
$216$	70.9549	−	97.6611i	0.328495	−	0.452135i
$217$	57.4064	−	41.7082i	0.264546	−	0.192204i
$218$	65.0053	+	21.1215i	0.298190	+	0.0968876i
$219$		−	142.163i		−	0.649146i
$220$		0			0
$221$	−80.3444			−0.363549
$222$	12.4882	−	38.4346i	0.0562529	−	0.173129i
$223$	−156.366	−	215.220i	−0.701194	−	0.965111i	−0.999942	−	0.0107791i	$-0.996569\pi$
$223$	−156.366	−	215.220i	−0.701194	−	0.965111i	0.298748	−	0.954332i	$-0.403431\pi$
$224$	233.185	+	169.419i	1.04101	+	0.756335i
$225$		0			0
$226$	−5.86881	+	1.90689i	−0.0259682	+	0.00843758i
$227$	−205.915	−	149.606i	−0.907114	−	0.659057i	0.0331697	−	0.999450i	$-0.489440\pi$
$227$	−205.915	−	149.606i	−0.907114	−	0.659057i	−0.940283	+	0.340393i	$0.889440\pi$
$228$	−8.04975	+	5.84848i	−0.0353059	+	0.0256512i
$229$	12.4245	−	38.2388i	0.0542556	−	0.166982i	−0.920257	−	0.391315i	$-0.872020\pi$
$229$	12.4245	−	38.2388i	0.0542556	−	0.166982i	0.974513	+	0.224333i	$0.0720204\pi$
$230$		0			0
$231$	50.4508	−	142.749i	0.218402	−	0.617961i
$232$			154.318i			0.665164i
$233$	71.3649	−	219.639i	0.306287	−	0.942655i	−0.672906	−	0.739728i	$-0.734954\pi$
$233$	71.3649	−	219.639i	0.306287	−	0.942655i	0.979194	−	0.202928i	$-0.0650457\pi$
$234$	21.9098	−	15.9184i	0.0936318	−	0.0680275i
$235$		0			0
$236$	−2.43614	−	7.49767i	−0.0103226	−	0.0317698i
$237$	−1.68055	−	5.17221i	−0.00709094	−	0.0218237i
$238$	−89.4648	−	65.0000i	−0.375903	−	0.273109i
$239$	−185.249	−	254.974i	−0.775101	−	1.06684i	−0.995806	−	0.0914947i	$-0.970836\pi$
$239$	−185.249	−	254.974i	−0.775101	−	1.06684i	0.220704	−	0.975341i	$-0.429164\pi$
$240$		0			0
$241$			270.933i			1.12420i	0.827069	+	0.562101i	$0.190007\pi$
$241$			270.933i			1.12420i	−0.827069	+	0.562101i	$0.809993\pi$
$242$	−73.6697	+	47.9712i	−0.304420	+	0.198228i
$243$			245.843i			1.01170i
$244$	74.6738	+	24.2630i	0.306040	+	0.0994384i
$245$		0			0
$246$	−56.9959	−	41.4100i	−0.231691	−	0.168333i
$247$	−10.3681	+	3.36881i	−0.0419762	+	0.0136389i
$248$	−11.9522	−	36.7852i	−0.0481945	−	0.148327i
$249$	67.6190	−	93.0696i	0.271562	−	0.373773i
$250$		0			0
$251$	3.44080	−	10.5897i	0.0137084	−	0.0421900i	−0.943968	−	0.330036i	$-0.892939\pi$
$251$	3.44080	−	10.5897i	0.0137084	−	0.0421900i	0.957677	+	0.287846i	$0.0929391\pi$
$252$	−245.186			−0.972959
$253$	−10.1311	+	28.6656i	−0.0400439	+	0.113303i
$254$	−136.774			−0.538480
$255$		0			0
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	237.042	−	326.261i	0.922344	−	1.26950i	−0.0404281	−	0.999182i	$-0.512872\pi$
$257$	237.042	−	326.261i	0.922344	−	1.26950i	0.962772	−	0.270315i	$-0.0871278\pi$
$258$	−22.0226	+	7.15558i	−0.0853590	+	0.0277348i
$259$	−381.246	+	123.874i	−1.47199	+	0.478279i
$260$		0			0
$261$	−118.464	−	163.052i	−0.453885	−	0.624719i
$262$	98.0726	+	31.8657i	0.374323	+	0.121625i
$263$	−42.6636			−0.162219			−0.0811094	−	0.996705i	$-0.525846\pi$
$263$	−42.6636			−0.162219			−0.0811094	+	0.996705i	$0.525846\pi$
$264$	−65.5041	−	50.1988i	−0.248121	−	0.190147i
$265$		0			0
$266$	−14.2705	−	4.63677i	−0.0536485	−	0.0174315i
$267$	100.154	+	137.850i	0.375108	+	0.516292i
$268$	−78.5601	+	108.129i	−0.293135	+	0.403465i
$269$	126.695	+	389.927i	0.470985	+	1.44954i	0.851296	+	0.524685i	$0.175817\pi$
$269$	126.695	+	389.927i	0.470985	+	1.44954i	−0.380311	+	0.924859i	$0.624183\pi$
$270$		0			0
$271$	−136.400	+	187.739i	−0.503322	+	0.692763i	−0.982775	−	0.184804i	$-0.940835\pi$
$271$	−136.400	+	187.739i	−0.503322	+	0.692763i	0.479454	+	0.877567i	$0.340835\pi$
$272$	122.948	−	89.3272i	0.452016	−	0.328409i
$273$	68.8191	+	22.3607i	0.252085	+	0.0819073i
$274$			11.8117i			0.0431082i
$275$		0			0
$276$	−13.2624			−0.0480521
$277$	94.6507	−	291.305i	0.341699	−	1.05164i	−0.621628	−	0.783313i	$-0.713528\pi$
$277$	94.6507	−	291.305i	0.341699	−	1.05164i	0.963327	−	0.268330i	$-0.0864716\pi$
$278$	96.7089	+	133.108i	0.347874	+	0.478807i
$279$	40.8673	+	29.6918i	0.146478	+	0.106422i
$280$		0			0
$281$	−123.114	+	40.0022i	−0.438128	+	0.142356i	−0.519772	−	0.854305i	$-0.673983\pi$
$281$	−123.114	+	40.0022i	−0.438128	+	0.142356i	0.0816438	+	0.996662i	$0.473983\pi$
$282$	22.1238	+	16.0739i	0.0784533	+	0.0569997i
$283$	341.320	−	247.984i	1.20608	−	0.876268i	0.211210	−	0.977441i	$-0.432260\pi$
$283$	341.320	−	247.984i	1.20608	−	0.876268i	0.994869	+	0.101173i	$0.0322596\pi$
$284$	−81.8854	+	252.017i	−0.288329	+	0.887385i
$285$		0			0
$286$	−23.8197	−	34.6120i	−0.0832855	−	0.121021i
$287$			698.827i			2.43494i
$288$	−63.4076	+	195.148i	−0.220165	+	0.677599i
$289$	44.8582	−	32.5914i	0.155219	−	0.112773i
$290$		0			0
$291$	−33.0573	−	101.740i	−0.113599	−	0.349621i
$292$	110.374	+	339.698i	0.377995	+	1.16335i
$293$	−52.1646	−	37.8998i	−0.178036	−	0.129351i	0.495198	−	0.868780i	$-0.335095\pi$
$293$	−52.1646	−	37.8998i	−0.178036	−	0.129351i	−0.673234	+	0.739429i	$0.735095\pi$
$294$	29.6227	+	40.7721i	0.100757	+	0.138681i
$295$		0			0
$296$			218.506i			0.738196i
$297$	244.517	+	6.25174i	0.823289	+	0.0210496i
$298$			48.8127i			0.163801i
$299$	−13.8197	−	4.49028i	−0.0462196	−	0.0150177i
$300$		0			0
$301$	185.825	+	135.010i	0.617358	+	0.448537i
$302$	−69.4610	+	22.5693i	−0.230003	+	0.0747326i
$303$	48.1174	+	148.090i	0.158803	+	0.488746i
$304$	12.1205	−	16.6825i	0.0398702	−	0.0548766i
$305$		0			0
$306$	24.3272	−	74.8714i	0.0795006	−	0.244678i
$307$	−356.512			−1.16128			−0.580639	−	0.814161i	$-0.697197\pi$
$307$	−356.512			−1.16128			−0.580639	+	0.814161i	$0.697197\pi$
$308$	−9.72257	+	380.267i	−0.0315668	+	1.23463i
$309$	−127.984			−0.414187
$310$		0			0
$311$	449.177	−	326.346i	1.44430	−	1.04935i	0.457178	−	0.889375i	$-0.348860\pi$
$311$	449.177	−	326.346i	1.44430	−	1.04935i	0.987122	−	0.159970i	$-0.0511397\pi$
$312$	23.1838	−	31.9098i	0.0743072	−	0.102275i
$313$	315.170	−	102.405i	1.00693	−	0.327172i	0.241300	−	0.970451i	$-0.422426\pi$
$313$	315.170	−	102.405i	1.00693	−	0.327172i	0.765632	+	0.643279i	$0.222426\pi$
$314$	170.410	−	55.3696i	0.542708	−	0.176336i
$315$		0			0
$316$	8.03134	+	11.0542i	0.0254156	+	0.0349816i
$317$	491.628	+	159.740i	1.55088	+	0.503910i	0.954352	−	0.298685i	$-0.0965479\pi$
$317$	491.628	+	159.740i	1.55088	+	0.503910i	0.596524	+	0.802595i	$0.296548\pi$
$318$	−11.5055			−0.0361807
$319$	−257.580	+	177.265i	−0.807462	+	0.555688i
$320$		0			0
$321$	111.492	+	36.2259i	0.347327	+	0.112853i
$322$	−11.7557	−	16.1803i	−0.0365084	−	0.0502495i
$323$	−18.6269	+	25.6378i	−0.0576685	+	0.0793739i
$324$	−35.4953	−	109.243i	−0.109554	−	0.337171i
$325$		0			0
$326$	−74.4630	+	102.490i	−0.228414	+	0.314385i
$327$	−105.181	+	76.4183i	−0.321654	+	0.233695i
$328$	362.276	+	117.711i	1.10450	+	0.358874i
$329$		−	271.260i		−	0.824499i
$330$		0			0
$331$	208.884			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$331$	208.884			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$332$	−89.3165	+	274.888i	−0.269026	+	0.827976i
$333$	−167.739	−	230.872i	−0.503719	−	0.693310i
$334$	145.154	+	105.461i	0.434593	+	0.315750i
$335$		0			0
$336$	−130.172	+	42.2955i	−0.387417	+	0.125880i
$337$	109.159	+	79.3090i	0.323915	+	0.235338i	0.737844	−	0.674971i	$-0.235844\pi$
$337$	109.159	+	79.3090i	0.323915	+	0.235338i	−0.413929	+	0.910309i	$0.635844\pi$
$338$	−83.0897	+	60.3682i	−0.245828	+	0.178604i
$339$	3.62712	−	11.1631i	0.0106995	−	0.0329296i
$340$		0			0
$341$	47.6707	−	62.2051i	0.139797	−	0.182420i
$342$		−	10.6819i		−	0.0312336i
$343$	3.67320	−	11.3050i	0.0107090	−	0.0329590i
$344$	101.290	−	73.5917i	0.294448	−	0.213929i
$345$		0			0
$346$	11.1691	+	34.3750i	0.0322806	+	0.0993496i
$347$	29.2880	+	90.1393i	0.0844036	+	0.259767i	0.984348	−	0.176238i	$-0.0563928\pi$
$347$	29.2880	+	90.1393i	0.0844036	+	0.259767i	−0.899944	+	0.436005i	$0.856393\pi$
$348$	−110.348	−	80.1722i	−0.317091	−	0.230380i
$349$	100.997	+	139.010i	0.289389	+	0.398310i	0.928816	−	0.370542i	$-0.120828\pi$
$349$	100.997	+	139.010i	0.289389	+	0.398310i	−0.639426	+	0.768852i	$0.720828\pi$
$350$		0			0
$351$			116.902i			0.333054i
$352$	300.149	+	106.080i	0.852695	+	0.301362i
$353$		−	119.644i		−	0.338936i	−0.985536	−	0.169468i	$-0.945795\pi$
$353$		−	119.644i		−	0.338936i	0.985536	−	0.169468i	$-0.0542049\pi$
$354$	−2.16814	−	0.704473i	−0.00612470	−	0.00199004i
$355$		0			0
$356$	−346.343	−	251.633i	−0.972873	−	0.706834i
$357$	200.049	−	65.0000i	0.560363	−	0.182073i
$358$	49.1572	+	151.290i	0.137311	+	0.422598i
$359$	−274.681	+	378.066i	−0.765127	+	1.05311i	0.231643	+	0.972801i	$0.425590\pi$
$359$	−274.681	+	378.066i	−0.765127	+	1.05311i	−0.996770	+	0.0803065i	$0.974410\pi$
$360$		0			0
$361$	110.226	−	339.242i	0.305336	−	0.939728i
$362$	−28.2637			−0.0780766
$363$	8.54517	−	166.999i	0.0235404	−	0.460053i
$364$	−181.803			−0.499460
$365$		0			0
$366$	18.3688	−	13.3457i	0.0501880	−	0.0364637i
$367$	193.279	−	266.026i	0.526647	−	0.724867i	−0.459968	−	0.887936i	$-0.652139\pi$
$367$	193.279	−	266.026i	0.526647	−	0.724867i	0.986615	+	0.163068i	$0.0521391\pi$
$368$	26.1401	−	8.49342i	0.0710328	−	0.0230800i
$369$	−473.141	+	153.733i	−1.28223	+	0.416620i
$370$		0			0
$371$	67.0820	+	92.3305i	0.180814	+	0.248869i
$372$	32.5133	+	10.5642i	0.0874015	+	0.0283985i
$373$	−214.135			−0.574088			−0.287044	−	0.957917i	$-0.592673\pi$
$373$	−214.135			−0.574088			−0.287044	+	0.957917i	$0.592673\pi$
$374$	−115.156	−	40.6989i	−0.307904	−	0.108821i
$375$		0			0
$376$	−140.623	−	45.6912i	−0.373997	−	0.121519i
$377$	−87.8402	−	120.902i	−0.232998	−	0.320694i
$378$	−94.5756	+	130.172i	−0.250200	+	0.344371i
$379$	−98.9630	−	304.577i	−0.261116	−	0.803633i	−0.992563	−	0.121734i	$-0.961154\pi$
$379$	−98.9630	−	304.577i	−0.261116	−	0.803633i	0.731447	−	0.681899i	$-0.238846\pi$
$380$		0			0
$381$	152.918	−	210.474i	0.401359	−	0.552424i
$382$	70.4187	−	51.1622i	0.184342	−	0.133932i
$383$	−520.759	−	169.205i	−1.35968	−	0.441788i	−0.463746	−	0.885968i	$-0.653495\pi$
$383$	−520.759	−	169.205i	−1.35968	−	0.441788i	−0.895937	+	0.444181i	$0.853495\pi$
$384$			178.805i			0.465637i
$385$		0			0
$386$	−21.2322			−0.0550058
$387$	−50.5293	+	155.513i	−0.130567	+	0.401843i
$388$	157.980	+	217.441i	0.407166	+	0.560415i
$389$	272.259	+	197.808i	0.699895	+	0.508504i	0.879898	−	0.475162i	$-0.157611\pi$
$389$	272.259	+	197.808i	0.699895	+	0.508504i	−0.180003	+	0.983666i	$0.557611\pi$
$390$		0			0
$391$	−40.1722	+	13.0527i	−0.102742	+	0.0333830i
$392$	−220.450	−	160.167i	−0.562373	−	0.408588i
$393$	−158.685	+	115.291i	−0.403778	+	0.293362i
$394$	63.3212	−	194.883i	0.160714	−	0.494626i
$395$		0			0
$396$	−259.599	+	77.0713i	−0.655554	+	0.194624i
$397$		−	115.374i		−	0.290614i	−0.989387	−	0.145307i	$-0.953583\pi$
$397$		−	115.374i		−	0.290614i	0.989387	−	0.145307i	$-0.0464170\pi$
$398$	39.8443	−	122.628i	0.100111	−	0.308111i
$399$	23.0902	−	16.7760i	0.0578701	−	0.0420451i
$400$		0			0
$401$	19.7138	+	60.6729i	0.0491617	+	0.151304i	0.972624	−	0.232386i	$-0.0746532\pi$
$401$	19.7138	+	60.6729i	0.0491617	+	0.151304i	−0.923462	+	0.383690i	$0.874653\pi$
$402$	11.9434	+	36.7579i	0.0297099	+	0.0914377i
$403$	30.3028	+	22.0163i	0.0751930	+	0.0546309i
$404$	−229.952	−	316.502i	−0.569189	−	0.783422i
$405$		0			0
$406$		−	205.690i		−	0.506626i
$407$	−364.720	+	250.997i	−0.896118	+	0.616700i
$408$		−	114.656i		−	0.281019i
$409$	581.745	+	189.020i	1.42236	+	0.462152i	0.916351	−	0.400377i	$-0.131121\pi$
$409$	581.745	+	189.020i	1.42236	+	0.462152i	0.506008	+	0.862529i	$0.331121\pi$
$410$		0			0
$411$	−18.1763	−	13.2058i	−0.0442245	−	0.0321310i
$412$	305.816	−	99.3657i	0.742272	−	0.241179i
$413$	6.98791	+	21.5066i	0.0169199	+	0.0520740i
$414$	8.36881	−	11.5187i	0.0202145	−	0.0278229i
$415$		0			0
$416$	−47.0163	+	144.701i	−0.113020	+	0.347839i
$417$	−312.957			−0.750495
$418$	−16.5669	−	0.423579i	−0.0396338	−	0.00101335i
$419$	−146.156			−0.348821			−0.174410	−	0.984673i	$-0.555802\pi$
$419$	−146.156			−0.348821			−0.174410	+	0.984673i	$0.555802\pi$
$420$		0			0
$421$	−480.079	+	348.798i	−1.14033	+	0.828498i	−0.987165	−	0.159702i	$-0.948947\pi$
$421$	−480.079	+	348.798i	−1.14033	+	0.828498i	−0.153165	+	0.988201i	$0.548947\pi$
$422$	−42.0000	+	57.8081i	−0.0995261	+	0.136986i
$423$	183.657	−	59.6738i	0.434177	−	0.141073i
$424$	59.1641	−	19.2236i	0.139538	−	0.0453386i
$425$		0			0
$426$	45.0407	+	61.9931i	0.105729	+	0.145524i
$427$	−214.197	−	69.5967i	−0.501632	−	0.162990i
$428$	−294.535			−0.688165
$429$	79.8936	+	2.04270i	0.186232	+	0.00476153i
$430$		0			0
$431$	165.807	+	53.8738i	0.384702	+	0.124997i	0.494982	−	0.868903i	$-0.335175\pi$
$431$	165.807	+	53.8738i	0.384702	+	0.124997i	−0.110280	+	0.993901i	$0.535175\pi$
$432$	−129.972	−	178.891i	−0.300861	−	0.414100i
$433$	364.804	−	502.109i	0.842503	−	1.15961i	−0.142962	−	0.989728i	$-0.545663\pi$
$433$	364.804	−	502.109i	0.842503	−	1.15961i	0.985465	−	0.169878i	$-0.0543373\pi$
$434$	15.9311	+	49.0309i	0.0367076	+	0.112975i
$435$		0			0
$436$	191.998	−	264.263i	0.440363	−	0.606107i
$437$	−4.63677	+	3.36881i	−0.0106105	+	0.00770895i
$438$	98.2323	+	31.9176i	0.224275	+	0.0728712i
$439$		−	676.778i		−	1.54164i	−0.637055	−	0.770818i	$-0.719848\pi$
$439$		−	676.778i		−	1.54164i	0.637055	−	0.770818i	$-0.280152\pi$
$440$		0			0
$441$	355.880			0.806985
$442$	18.0384	−	55.5166i	0.0408110	−	0.125603i
$443$	152.417	+	209.784i	0.344056	+	0.473552i	0.945621	−	0.325272i	$-0.105456\pi$
$443$	152.417	+	209.784i	0.344056	+	0.473552i	−0.601565	+	0.798824i	$0.705456\pi$
$444$	−156.246	−	113.519i	−0.351906	−	0.255674i
$445$		0			0
$446$	183.820	−	59.7266i	0.412152	−	0.133916i
$447$	−75.1150	−	54.5743i	−0.168043	−	0.122090i
$448$	151.084	−	109.769i	0.337241	−	0.245020i
$449$	−124.349	+	382.707i	−0.276947	+	0.852354i	0.711751	+	0.702432i	$0.247902\pi$
$449$	−124.349	+	382.707i	−0.276947	+	0.852354i	−0.988698	+	0.149923i	$0.952098\pi$
$450$		0			0
$451$	219.668	+	739.908i	0.487069	+	1.64059i
$452$			29.4903i			0.0652441i
$453$	42.9293	−	132.123i	0.0947666	−	0.291662i
$454$	149.606	−	108.695i	0.329528	−	0.239416i
$455$		0			0
$456$	−4.80746	−	14.7959i	−0.0105427	−	0.0324470i
$457$	−79.0234	−	243.209i	−0.172918	−	0.532186i	0.826614	−	0.562769i	$-0.190264\pi$
$457$	−79.0234	−	243.209i	−0.172918	−	0.532186i	−0.999532	+	0.0305823i	$0.990264\pi$
$458$	23.6329	+	17.1703i	0.0516002	+	0.0374897i
$459$	199.742	+	274.921i	0.435167	+	0.598956i
$460$		0			0
$461$		−	446.274i		−	0.968056i	−0.875053	−	0.484028i	$-0.839173\pi$
$461$		−	446.274i		−	0.968056i	0.875053	−	0.484028i	$-0.160827\pi$
$462$	87.3102	+	66.9098i	0.188983	+	0.144826i
$463$			73.1308i			0.157950i	0.996877	+	0.0789750i	$0.0251647\pi$
$463$			73.1308i			0.157950i	−0.996877	+	0.0789750i	$0.974835\pi$
$464$	268.838	+	87.3507i	0.579392	+	0.188256i
$465$		0			0
$466$	135.744	+	98.6239i	0.291297	+	0.211639i
$467$	10.5706	−	3.43459i	0.0226351	−	0.00735458i	−0.297678	−	0.954666i	$-0.596212\pi$
$467$	10.5706	−	3.43459i	0.0226351	−	0.00735458i	0.320313	+	0.947312i	$0.396212\pi$
$468$	−39.9944	−	123.090i	−0.0854582	−	0.263013i
$469$	225.344	−	310.160i	0.480479	−	0.661322i
$470$		0			0
$471$	−105.319	+	324.139i	−0.223608	+	0.688194i
$472$	12.3262			0.0261148
$473$	239.187	+	84.5344i	0.505682	+	0.178720i
$474$	3.95122			0.00833590
$475$		0			0
$476$	−427.551	+	310.634i	−0.898217	+	0.652593i
$477$	−47.7553	+	65.7295i	−0.100116	+	0.137798i
$478$	217.774	−	70.7589i	0.455593	−	0.148031i
$479$	545.546	−	177.259i	1.13893	−	0.370060i	0.321965	−	0.946752i	$-0.395657\pi$
$479$	545.546	−	177.259i	1.13893	−	0.370060i	0.816962	+	0.576692i	$0.195657\pi$
$480$		0			0
$481$	−124.377	−	171.190i	−0.258580	−	0.355905i
$482$	−187.210	−	60.8282i	−0.388402	−	0.126199i
$483$	38.0423			0.0787624
$484$	109.239	+	405.678i	0.225700	+	0.838178i
$485$		0			0
$486$	−169.873	−	55.1952i	−0.349533	−	0.113570i
$487$	−370.800	−	510.363i	−0.761397	−	1.04797i	−0.997097	−	0.0761466i	$-0.975738\pi$
$487$	−370.800	−	510.363i	−0.761397	−	1.04797i	0.235700	−	0.971826i	$-0.424262\pi$
$488$	−72.1588	+	99.3181i	−0.147866	+	0.203521i
$489$	−74.4630	−	229.174i	−0.152276	−	0.468658i
$490$		0			0
$491$	−256.297	+	352.763i	−0.521990	+	0.718458i	−0.985883	−	0.167433i	$-0.946452\pi$
$491$	−256.297	+	352.763i	−0.521990	+	0.718458i	0.463893	+	0.885891i	$0.346452\pi$
$492$	−272.383	+	197.898i	−0.553623	+	0.402231i
$493$	−413.152	−	134.241i	−0.838036	−	0.272294i
$494$		−	7.92055i		−	0.0160335i
$495$		0			0
$496$	−70.8491			−0.142841
$497$	234.883	−	722.895i	0.472602	−	1.45452i
$498$	49.1281	+	67.6190i	0.0986508	+	0.135781i
$499$	−376.446	−	273.504i	−0.754401	−	0.548105i	0.142787	−	0.989753i	$-0.454394\pi$
$499$	−376.446	−	273.504i	−0.754401	−	0.548105i	−0.897188	+	0.441649i	$0.854394\pi$
$500$		0			0
$501$	−324.574	+	105.461i	−0.647853	+	0.210500i
$502$	6.54479	+	4.75507i	0.0130374	+	0.00947225i
$503$	−371.704	+	270.059i	−0.738974	+	0.536896i	−0.892390	−	0.451265i	$-0.850973\pi$
$503$	−371.704	+	270.059i	−0.738974	+	0.536896i	0.153415	+	0.988162i	$0.450973\pi$
$504$	118.464	−	364.595i	0.235048	−	0.723402i
$505$		0			0
$506$	−17.5329	−	13.4363i	−0.0346500	−	0.0265539i
$507$		−	195.356i		−	0.385317i
$508$	−201.986	+	621.649i	−0.397610	+	1.22372i
$509$	−194.705	+	141.462i	−0.382525	+	0.277920i	−0.762385	−	0.647123i	$-0.775972\pi$
$509$	−194.705	+	141.462i	−0.382525	+	0.277920i	0.379861	+	0.925044i	$0.375972\pi$
$510$		0			0
$511$	−316.602	−	974.400i	−0.619573	−	1.90685i
$512$	−155.662	−	479.078i	−0.304027	−	0.935699i
$513$	37.3032	+	27.1024i	0.0727158	+	0.0528311i
$514$	172.221	+	237.042i	0.335061	+	0.461172i
$515$		0			0
$516$			110.662i			0.214461i
$517$	−85.2675	−	287.207i	−0.164928	−	0.555525i
$518$		−	291.246i		−	0.562251i
$519$	−65.3851	−	21.2449i	−0.125983	−	0.0409343i
$520$		0			0
$521$	564.504	+	410.136i	1.08350	+	0.787210i	0.978290	−	0.207240i	$-0.0664480\pi$
$521$	564.504	+	410.136i	1.08350	+	0.787210i	0.105212	+	0.994450i	$0.466448\pi$
$522$	139.263	−	45.2492i	0.266787	−	0.0866843i
$523$	−114.868	−	353.526i	−0.219632	−	0.675959i	−0.998792	−	0.0491334i	$-0.984354\pi$
$523$	−114.868	−	353.526i	−0.219632	−	0.675959i	0.779160	−	0.626825i	$-0.215646\pi$
$524$	289.665	−	398.689i	0.552795	−	0.760857i
$525$		0			0
$526$	9.57857	−	29.4798i	0.0182102	−	0.0560452i
$527$	108.881			0.206606
$528$	−124.529	+	85.7001i	−0.235851	+	0.162311i
$529$	521.361			0.985559
$530$		0			0
$531$	−13.0238	+	9.46234i	−0.0245269	+	0.0178199i
$532$	−42.1490	+	58.0132i	−0.0792275	+	0.109047i
$533$	−350.831	+	113.992i	−0.658219	+	0.213868i
$534$	−117.738	+	38.2554i	−0.220483	+	0.0716393i
$535$		0			0
$536$	−122.832	−	169.064i	−0.229164	−	0.315417i
$537$	−287.771	−	93.5025i	−0.535887	−	0.174120i
$538$	−297.878			−0.553676
$539$	14.1120	−	551.948i	0.0261819	−	1.02402i
$540$		0			0
$541$	−64.3657	−	20.9137i	−0.118975	−	0.0386575i	0.248924	−	0.968523i	$-0.419923\pi$
$541$	−64.3657	−	20.9137i	−0.118975	−	0.0386575i	−0.367900	+	0.929866i	$0.619923\pi$
$542$	−99.1005	−	136.400i	−0.182842	−	0.251661i
$543$	31.5998	−	43.4934i	0.0581949	−	0.0800984i
$544$	136.671	+	420.630i	0.251233	+	0.773217i
$545$		0			0
$546$	−30.9017	+	42.5325i	−0.0565965	+	0.0778984i
$547$	−600.625	+	436.380i	−1.09804	+	0.797769i	−0.980738	−	0.195328i	$-0.937423\pi$
$547$	−600.625	+	436.380i	−1.09804	+	0.797769i	−0.117297	+	0.993097i	$0.537423\pi$
$548$	53.6850	+	17.4433i	0.0979653	+	0.0318309i
$549$		−	160.333i		−	0.292045i
$550$		0			0
$551$	−58.9443			−0.106977
$552$	6.40786	−	19.7214i	0.0116084	−	0.0357271i
$553$	−23.0374	−	31.7082i	−0.0416589	−	0.0573385i
$554$	180.036	+	130.804i	0.324975	+	0.236108i
$555$		0			0
$556$	747.807	−	242.977i	1.34498	−	0.437010i
$557$	607.429	+	441.323i	1.09054	+	0.792322i	0.979490	−	0.201494i	$-0.0645795\pi$
$557$	607.429	+	441.323i	1.09054	+	0.792322i	0.111047	+	0.993815i	$0.464579\pi$
$558$	−29.6918	+	21.5724i	−0.0532111	+	0.0386601i
$559$	−37.4671	+	115.312i	−0.0670252	+	0.206282i
$560$		0			0
$561$	191.378	−	131.704i	0.341137	−	0.234767i
$562$		−	94.0507i		−	0.167350i
$563$	322.214	−	991.673i	0.572316	−	1.76141i	−0.0728240	−	0.997345i	$-0.523201\pi$
$563$	322.214	−	991.673i	0.572316	−	1.76141i	0.645140	−	0.764064i	$-0.276799\pi$
$564$	105.729	−	76.8170i	0.187464	−	0.136200i
$565$		0			0
$566$	94.7214	+	291.522i	0.167352	+	0.515057i
$567$	101.816	+	313.358i	0.179570	+	0.552659i
$568$	−335.190	−	243.530i	−0.590123	−	0.428750i
$569$	136.967	+	188.518i	0.240714	+	0.331315i	0.912232	−	0.409673i	$-0.134357\pi$
$569$	136.967	+	188.518i	0.240714	+	0.331315i	−0.671518	+	0.740988i	$0.734357\pi$
$570$		0			0
$571$		−	196.324i		−	0.343825i	−0.985112	−	0.171912i	$-0.945005\pi$
$571$		−	196.324i		−	0.343825i	0.985112	−	0.171912i	$-0.0549946\pi$
$572$	−192.491	+	57.1478i	−0.336523	+	0.0999088i
$573$			165.564i			0.288943i
$574$	−482.877	−	156.896i	−0.841250	−	0.273339i
$575$		0			0
$576$	107.556	+	78.1438i	0.186729	+	0.135666i
$577$	135.382	−	43.9884i	0.234631	−	0.0762364i	−0.189341	−	0.981911i	$-0.560635\pi$
$577$	135.382	−	43.9884i	0.234631	−	0.0762364i	0.423973	+	0.905675i	$0.360635\pi$
$578$	12.4488	+	38.3134i	0.0215377	+	0.0662862i
$579$	23.7384	−	32.6730i	0.0409989	−	0.0564301i
$580$		0			0
$581$	256.199	−	788.498i	0.440961	−	1.35714i
$582$	77.7223			0.133544
$583$	100.049	+	76.6718i	0.171610	+	0.131513i
$584$	−558.464			−0.956274
$585$		0			0
$586$	37.8998	−	27.5358i	0.0646754	−	0.0469894i
$587$	140.838	−	193.847i	0.239929	−	0.330233i	−0.672024	−	0.740530i	$-0.734575\pi$
$587$	140.838	−	193.847i	0.239929	−	0.330233i	0.911952	+	0.410296i	$0.134575\pi$
$588$	229.059	−	74.4259i	0.389557	−	0.126575i
$589$	14.0507	−	4.56535i	0.0238552	−	0.00775102i
$590$		0			0
$591$	229.098	+	315.327i	0.387645	+	0.533548i
$592$	380.660	+	123.684i	0.643006	+	0.208925i
$593$	598.782			1.00975			0.504875	−	0.863192i	$-0.331538\pi$
$593$	598.782			1.00975			0.504875	+	0.863192i	$0.331538\pi$
$594$	−59.2173	+	167.553i	−0.0996924	+	0.282076i
$595$		0			0
$596$	221.858	+	72.0860i	0.372245	+	0.120950i
$597$	144.158	+	198.416i	0.241471	+	0.332356i
$598$	6.20541	−	8.54102i	0.0103769	−	0.0142826i
$599$	−93.8359	−	288.797i	−0.156654	−	0.482132i	0.841670	−	0.539992i	$-0.181573\pi$
$599$	−93.8359	−	288.797i	−0.156654	−	0.482132i	−0.998325	+	0.0578592i	$0.981573\pi$
$600$		0			0
$601$	−107.416	+	147.845i	−0.178729	+	0.245999i	−0.888977	−	0.457953i	$-0.848583\pi$
$601$	−107.416	+	147.845i	−0.178729	+	0.245999i	0.710248	+	0.703952i	$0.248583\pi$
$602$	−135.010	+	98.0902i	−0.224268	+	0.162940i
$603$	259.567	+	84.3384i	0.430459	+	0.139865i
$604$			349.036i			0.577874i
$605$		0			0
$606$	−113.131			−0.186685
$607$	−249.940	+	769.237i	−0.411763	+	1.26728i	0.503351	+	0.864082i	$0.332100\pi$
$607$	−249.940	+	769.237i	−0.411763	+	1.26728i	−0.915114	+	0.403195i	$0.867900\pi$
$608$	35.2737	+	48.5501i	0.0580160	+	0.0798522i
$609$	316.525	+	229.969i	0.519745	+	0.377617i
$610$		0			0
$611$	136.180	−	44.2477i	0.222881	−	0.0724185i
$612$	−304.371	−	221.138i	−0.497338	−	0.361337i
$613$	−965.666	+	701.597i	−1.57531	+	1.14453i	−0.653478	+	0.756946i	$0.726691\pi$
$613$	−965.666	+	701.597i	−1.57531	+	1.14453i	−0.921834	+	0.387585i	$0.873309\pi$
$614$	80.0420	−	246.344i	0.130362	−	0.401212i
$615$		0			0
$616$	−560.766	−	198.188i	−0.910334	−	0.321733i
$617$		−	107.900i		−	0.174878i	−0.996170	−	0.0874390i	$-0.972132\pi$
$617$		−	107.900i		−	0.174878i	0.996170	−	0.0874390i	$-0.0278683\pi$
$618$	28.7341	−	88.4346i	0.0464954	−	0.143098i
$619$	−457.719	+	332.552i	−0.739449	+	0.537241i	−0.892539	−	0.450971i	$-0.851078\pi$
$619$	−457.719	+	332.552i	−0.739449	+	0.537241i	0.153089	+	0.988212i	$0.451078\pi$
$620$		0			0
$621$	18.9919	+	58.4510i	0.0305827	+	0.0941239i
$622$	124.653	+	383.643i	0.200407	+	0.616790i
$623$	993.462	+	721.792i	1.59464	+	1.15857i
$624$	−42.4671	−	58.4510i	−0.0680563	−	0.0936714i
$625$		0			0
$626$			240.768i			0.384614i
$627$	19.1742	−	25.0203i	0.0305809	−	0.0399048i
$628$		−	856.298i		−	1.36353i
$629$	−585.000	−	190.078i	−0.930048	−	0.302191i
$630$		0			0
$631$	−558.872	−	406.044i	−0.885693	−	0.643494i	0.0490585	−	0.998796i	$-0.484378\pi$
$631$	−558.872	−	406.044i	−0.885693	−	0.643494i	−0.934751	+	0.355302i	$0.884378\pi$
$632$	−20.3182	+	6.60177i	−0.0321490	+	0.0104458i
$633$	−42.0000	−	129.263i	−0.0663507	−	0.204207i
$634$	−220.755	+	303.843i	−0.348193	+	0.479247i
$635$		0			0
$636$	−16.9911	+	52.2933i	−0.0267156	+	0.0822222i
$637$	263.883			0.414259
$638$	−64.6564	−	217.782i	−0.101342	−	0.341351i
$639$	541.108			0.846805
$640$		0			0
$641$	−624.756	+	453.912i	−0.974659	+	0.708131i	−0.956509	−	0.291704i	$-0.905778\pi$
$641$	−624.756	+	453.912i	−0.974659	+	0.708131i	−0.0181501	+	0.999835i	$0.505778\pi$
$642$	−50.0630	+	68.9058i	−0.0779797	+	0.107330i
$643$	−898.264	+	291.864i	−1.39699	+	0.453909i	−0.908216	−	0.418502i	$-0.862555\pi$
$643$	−898.264	+	291.864i	−1.39699	+	0.453909i	−0.488773	+	0.872411i	$0.662555\pi$
$644$	−90.9017	+	29.5358i	−0.141152	+	0.0458630i
$645$		0			0
$646$	−13.5333	−	18.6269i	−0.0209493	−	0.0288343i
$647$	927.614	+	301.400i	1.43372	+	0.465843i	0.919932	−	0.392077i	$-0.128243\pi$
$647$	927.614	+	301.400i	1.43372	+	0.465843i	0.513784	+	0.857920i	$0.328243\pi$
$648$	179.597			0.277155
$649$	14.1591	+	20.5743i	0.0218167	+	0.0317016i
$650$		0			0
$651$	−93.2624	−	30.3028i	−0.143260	−	0.0465481i
$652$	355.858	+	489.796i	0.545794	+	0.751221i
$653$	141.396	−	194.615i	0.216533	−	0.298032i	−0.686908	−	0.726744i	$-0.741033\pi$
$653$	141.396	−	194.615i	0.216533	−	0.298032i	0.903441	+	0.428712i	$0.141033\pi$
$654$	−29.1892	−	89.8351i	−0.0446318	−	0.137363i
$655$		0			0
$656$	410.128	−	564.493i	0.625195	−	0.860507i
$657$	590.070	−	428.711i	0.898128	−	0.652528i
$658$	187.436	+	60.9017i	0.284857	+	0.0925558i
$659$			937.713i			1.42293i	0.702720	+	0.711467i	$0.251969\pi$
$659$			937.713i			1.42293i	−0.702720	+	0.711467i	$0.748031\pi$
$660$		0			0
$661$	133.305			0.201672			0.100836	−	0.994903i	$-0.467848\pi$
$661$	133.305			0.201672			0.100836	+	0.994903i	$0.467848\pi$
$662$	−46.8973	+	144.335i	−0.0708418	+	0.218029i
$663$	65.2637	+	89.8278i	0.0984370	+	0.135487i
$664$	−365.608	−	265.630i	−0.550615	−	0.400045i
$665$		0			0
$666$	197.188	−	64.0704i	0.296079	−	0.0962018i
$667$	−63.5618	−	46.1803i	−0.0952950	−	0.0692359i
$668$	693.689	−	503.995i	1.03846	−	0.754483i
$669$	−113.607	+	349.646i	−0.169816	+	0.522639i
$670$		0			0
$671$	−248.666	−	6.35781i	−0.370590	−	0.00947513i
$672$		−	398.328i		−	0.592750i
$673$	−279.506	+	860.230i	−0.415313	+	1.27820i	0.496657	+	0.867947i	$0.334561\pi$
$673$	−279.506	+	860.230i	−0.415313	+	1.27820i	−0.911971	+	0.410256i	$0.865439\pi$
$674$	−79.3090	+	57.6214i	−0.117669	+	0.0854917i
$675$		0			0
$676$	151.673	+	466.801i	0.224368	+	0.690534i
$677$	−186.763	−	574.798i	−0.275869	−	0.849037i	−0.988988	−	0.147995i	$-0.952718\pi$
$677$	−186.763	−	574.798i	−0.275869	−	0.849037i	0.713119	−	0.701043i	$-0.247282\pi$
$678$	6.89920	+	5.01256i	0.0101758	+	0.00739316i
$679$	−453.156	−	623.716i	−0.667387	−	0.918580i
$680$		0			0
$681$			351.744i			0.516512i
$682$	32.2800	+	46.9055i	0.0473313	+	0.0687764i
$683$			1261.32i			1.84673i	0.383919	+	0.923367i	$0.374574\pi$
$683$			1261.32i			1.84673i	−0.383919	+	0.923367i	$0.625426\pi$
$684$	−48.5501	−	15.7749i	−0.0709797	−	0.0230627i
$685$		0			0
$686$	6.98684	+	5.07624i	0.0101849	+	0.00739977i
$687$	−52.8447	+	17.1703i	−0.0769210	+	0.0249931i
$688$	−70.8695	−	218.114i	−0.103008	−	0.317026i
$689$	−35.4102	+	48.7380i	−0.0513936	+	0.0707372i
$690$		0			0
$691$	−132.915	+	409.071i	−0.192352	+	0.591999i	0.807645	+	0.589669i	$0.200742\pi$
$691$	−132.915	+	409.071i	−0.192352	+	0.591999i	−0.999997	+	0.00232993i	$0.999258\pi$
$692$	172.732			0.249612
$693$	744.643	−	221.074i	1.07452	−	0.319010i
$694$	−68.8603			−0.0992224
$695$		0			0
$696$	172.533	−	125.352i	0.247892	−	0.180104i
$697$	−630.287	+	867.516i	−0.904286	+	1.24464i
$698$	−118.729	+	38.5774i	−0.170099	+	0.0552685i
$699$	−303.533	+	98.6239i	−0.434239	+	0.141093i
$700$		0			0
$701$	−299.098	−	411.673i	−0.426674	−	0.587266i	0.540512	−	0.841336i	$-0.318231\pi$
$701$	−299.098	−	411.673i	−0.426674	−	0.587266i	−0.967186	+	0.254070i	$0.918231\pi$
$702$	−80.7772	−	26.2461i	−0.115067	−	0.0373876i
$703$	−83.4619			−0.118722
$704$	125.461	−	163.713i	0.178212	−	0.232548i
$705$		0			0
$706$	82.6722	+	26.8618i	0.117099	+	0.0380479i
$707$	659.603	+	907.866i	0.932961	+	1.28411i
$708$	−6.40378	+	8.81404i	−0.00904488	+	0.0124492i
$709$	227.956	+	701.577i	0.321518	+	0.989531i	0.972988	+	0.230856i	$0.0741527\pi$
$709$	227.956	+	701.577i	0.321518	+	0.989531i	−0.651470	+	0.758674i	$0.725847\pi$
$710$		0			0
$711$	16.4001	−	22.5729i	0.0230663	−	0.0317481i
$712$	541.521	−	393.438i	0.760563	−	0.552582i
$713$	18.7282	+	6.08514i	0.0262667	+	0.00853457i
$714$			152.824i			0.214039i
$715$		0			0
$716$	760.222			1.06176
$717$	−134.591	+	414.230i	−0.187715	+	0.577726i
$718$	−199.567	−	274.681i	−0.277949	−	0.382564i
$719$	−425.782	−	309.349i	−0.592187	−	0.430249i	0.250910	−	0.968010i	$-0.419270\pi$
$719$	−425.782	−	309.349i	−0.592187	−	0.430249i	−0.843097	+	0.537762i	$0.819270\pi$
$720$		0			0
$721$	−877.214	+	285.024i	−1.21666	+	0.395318i
$722$	209.663	+	152.329i	0.290392	+	0.210982i
$723$	302.912	−	220.078i	0.418965	−	0.304396i
$724$	−41.7395	+	128.461i	−0.0576513	+	0.177432i
$725$		0			0
$726$	113.475	+	43.3983i	0.156302	+	0.0597772i
$727$			756.122i			1.04006i	0.854149	+	0.520029i	$0.174079\pi$
$727$			756.122i			1.04006i	−0.854149	+	0.520029i	$0.825921\pi$
$728$	87.8402	−	270.344i	0.120660	−	0.371352i
$729$	33.9853	−	24.6918i	0.0466191	−	0.0338707i
$730$		0			0
$731$	108.913	+	335.199i	0.148991	+	0.458548i
$732$	−33.5306	−	103.197i	−0.0458068	−	0.140979i
$733$	344.620	+	250.381i	0.470149	+	0.341584i	0.797500	−	0.603320i	$-0.206156\pi$
$733$	344.620	+	250.381i	0.470149	+	0.341584i	−0.327350	+	0.944903i	$0.606156\pi$
$734$	140.426	+	193.279i	0.191316	+	0.263323i
$735$		0			0
$736$			79.9888i			0.108680i
$737$	141.096	−	399.228i	0.191447	−	0.541693i
$738$		−	361.448i		−	0.489767i
$739$	−184.618	−	59.9862i	−0.249822	−	0.0811721i	0.181429	−	0.983404i	$-0.441928\pi$
$739$	−184.618	−	59.9862i	−0.249822	−	0.0811721i	−0.431251	+	0.902232i	$0.641928\pi$
$740$		0			0
$741$	12.1885	+	8.85544i	0.0164487	+	0.0119507i
$742$	−78.8597	+	25.6231i	−0.106280	+	0.0345324i
$743$	68.7477	+	211.584i	0.0925272	+	0.284769i	0.986601	−	0.163150i	$-0.0521653\pi$
$743$	68.7477	+	211.584i	0.0925272	+	0.284769i	−0.894074	+	0.447919i	$0.852165\pi$
$744$	−31.4183	+	43.2436i	−0.0422289	+	0.0581231i
$745$		0			0
$746$	48.0763	−	147.964i	0.0644454	−	0.198343i
$747$	590.214			0.790112
$748$	−355.041	+	463.291i	−0.474654	+	0.619373i
$749$	844.853			1.12797
$750$		0			0
$751$	1186.49	−	862.033i	1.57987	−	1.14785i	0.663037	−	0.748587i	$-0.269267\pi$
$751$	1186.49	−	862.033i	1.57987	−	1.14785i	0.916838	−	0.399260i	$-0.130733\pi$
$752$	−159.197	+	219.116i	−0.211699	+	0.291378i
$753$	−14.6346	+	4.75507i	−0.0194351	+	0.00631483i
$754$	103.262	−	33.5520i	0.136953	−	0.0444986i
$755$		0			0
$756$	451.976	+	622.091i	0.597851	+	0.822872i
$757$	−1264.41	−	410.832i	−1.67029	−	0.542710i	−0.687301	−	0.726373i	$-0.741205\pi$
$757$	−1264.41	−	410.832i	−1.67029	−	0.542710i	−0.982989	+	0.183663i	$0.941205\pi$
$758$	232.676			0.306961
$759$	40.2786	−	11.9581i	0.0530680	−	0.0157551i
$760$		0			0
$761$	654.725	+	212.733i	0.860348	+	0.279544i	0.705774	−	0.708437i	$-0.250599\pi$
$761$	654.725	+	212.733i	0.860348	+	0.279544i	0.154574	+	0.987981i	$0.450599\pi$
$762$	111.101	+	152.918i	0.145802	+	0.200680i
$763$	−550.734	+	758.020i	−0.721801	+	0.993473i
$764$	−128.543	−	395.614i	−0.168250	−	0.517820i
$765$		0			0
$766$	233.835	−	321.847i	0.305268	−	0.420165i
$767$	−9.65706	+	7.01626i	−0.0125907	+	0.00914767i
$768$	−24.9722	−	8.11397i	−0.0325159	−	0.0105651i
$769$			695.838i			0.904860i	0.891800	+	0.452430i	$0.149443\pi$
$769$			695.838i			0.904860i	−0.891800	+	0.452430i	$0.850557\pi$
$770$		0			0
$771$	−557.320			−0.722853
$772$	−31.3555	+	96.5023i	−0.0406159	+	0.125003i
$773$	−48.7939	−	67.1591i	−0.0631228	−	0.0868811i	0.776288	−	0.630378i	$-0.217100\pi$
$773$	−48.7939	−	67.1591i	−0.0631228	−	0.0868811i	−0.839411	+	0.543497i	$0.817100\pi$
$774$	−96.1124	−	69.8298i	−0.124176	−	0.0902193i
$775$		0			0
$776$	−399.668	+	129.860i	−0.515036	+	0.167345i
$777$	448.182	+	325.623i	0.576810	+	0.419077i
$778$	−197.808	+	143.716i	−0.254252	+	0.184725i
$779$	−44.9615	+	138.377i	−0.0577169	+	0.177634i
$780$		0			0
$781$	21.4571	−	839.225i	0.0274738	−	1.07455i
$782$		−	30.6888i		−	0.0392440i
$783$	−195.322	+	601.140i	−0.249454	+	0.767739i
$784$	−403.811	+	293.386i	−0.515065	+	0.374217i
$785$		0			0
$786$	−44.0373	−	135.533i	−0.0560271	−	0.172434i
$787$	−33.5185	−	103.159i	−0.0425903	−	0.131079i	0.927500	−	0.373822i	$-0.121953\pi$
$787$	−33.5185	−	103.159i	−0.0425903	−	0.131079i	−0.970091	+	0.242743i	$0.921953\pi$
$788$	−792.246	−	575.601i	−1.00539	−	0.730458i
$789$	34.6556	+	47.6993i	0.0439234	+	0.0604554i
$790$		0			0
$791$		−	84.5910i		−	0.106942i
$792$	10.8219	−	423.266i	0.0136641	−	0.534427i
$793$		−	118.885i		−	0.149919i
$794$	79.7214	+	25.9030i	0.100405	+	0.0326235i
$795$		0			0
$796$	−498.514	−	362.191i	−0.626273	−	0.455014i
$797$	−949.759	+	308.596i	−1.19167	+	0.387196i	−0.836689	−	0.547678i	$-0.815512\pi$
$797$	−949.759	+	308.596i	−1.19167	+	0.387196i	−0.354979	+	0.934874i	$0.615512\pi$
$798$	6.40786	+	19.7214i	0.00802990	+	0.0247135i
$799$	244.656	−	336.740i	0.306202	−	0.421451i
$800$		0			0
$801$	−270.141	+	831.409i	−0.337255	+	1.03796i
$802$	−46.3500			−0.0577930
$803$	−641.505	−	932.162i	−0.798886	−	1.16085i
$804$	184.706			0.229734
$805$		0			0
$806$	−22.0163	+	15.9958i	−0.0273155	+	0.0198458i
$807$	333.038	−	458.387i	0.412686	−	0.568014i
$808$	581.748	−	189.021i	0.719985	−	0.233937i
$809$	−71.6823	+	23.2910i	−0.0886060	+	0.0287898i	−0.352985	−	0.935629i	$-0.614833\pi$
$809$	−71.6823	+	23.2910i	−0.0886060	+	0.0287898i	0.264379	+	0.964419i	$0.414833\pi$
$810$		0			0
$811$	−583.402	−	802.984i	−0.719361	−	0.990115i	−0.999545	−	0.0301690i	$-0.990395\pi$
$811$	−583.402	−	802.984i	−0.719361	−	0.990115i	0.280184	−	0.959946i	$-0.409605\pi$
$812$	−934.880	−	303.761i	−1.15133	−	0.374090i
$813$	320.696			0.394460
$814$	−91.5499	−	308.368i	−0.112469	−	0.378830i
$815$		0			0
$816$	−199.742	−	64.9000i	−0.244781	−	0.0795343i
$817$	28.1095	+	38.6894i	0.0344058	+	0.0473555i
$818$	−261.220	+	359.538i	−0.319339	+	0.439533i
$819$	114.721	+	353.076i	0.140075	+	0.431106i
$820$		0			0
$821$	−733.079	+	1009.00i	−0.892910	+	1.22898i	0.0797652	+	0.996814i	$0.474583\pi$
$821$	−733.079	+	1009.00i	−0.892910	+	1.22898i	−0.972675	+	0.232171i	$0.925417\pi$
$822$	13.2058	−	9.59460i	0.0160655	−	0.0116723i
$823$	−508.800	−	165.319i	−0.618227	−	0.200874i	−0.0168738	−	0.999858i	$-0.505371\pi$
$823$	−508.800	−	165.319i	−0.618227	−	0.200874i	−0.601353	+	0.798984i	$0.705371\pi$
$824$			502.763i			0.610149i
$825$		0			0
$826$	−16.4296			−0.0198905
$827$	17.3822	−	53.4969i	0.0210184	−	0.0646879i	−0.939997	−	0.341182i	$-0.889173\pi$
$827$	17.3822	−	53.4969i	0.0210184	−	0.0646879i	0.961016	+	0.276494i	$0.0891727\pi$
$828$	−39.9944	−	55.0476i	−0.0483024	−	0.0664826i
$829$	−660.320	−	479.751i	−0.796526	−	0.578710i	0.113367	−	0.993553i	$-0.463836\pi$
$829$	−660.320	−	479.751i	−0.796526	−	0.578710i	−0.909893	+	0.414843i	$0.863836\pi$
$830$		0			0
$831$	−402.574	+	130.804i	−0.484445	+	0.157406i
$832$	79.7518	+	57.9431i	0.0958555	+	0.0696431i
$833$	620.579	−	450.877i	0.744993	−	0.541269i
$834$	70.2631	−	216.248i	0.0842483	−	0.259290i
$835$		0			0
$836$	−26.3911	+	74.6726i	−0.0315682	+	0.0893213i
$837$		−	158.423i		−	0.189275i
$838$	32.8141	−	100.991i	0.0391576	−	0.120515i
$839$	49.8216	−	36.1975i	0.0593821	−	0.0431436i	−0.557698	−	0.830044i	$-0.688315\pi$
$839$	49.8216	−	36.1975i	0.0593821	−	0.0431436i	0.617080	+	0.786900i	$0.288315\pi$
$840$		0			0
$841$	10.1913	+	31.3657i	0.0121181	+	0.0372958i
$842$	−133.229	−	410.036i	−0.158229	−	0.486979i
$843$	144.729	+	105.152i	0.171683	+	0.124735i
$844$	200.717	+	276.264i	0.237817	+	0.327327i
$845$		0			0
$846$			140.301i			0.165841i
$847$	−313.344	−	1163.66i	−0.369945	−	1.37386i
$848$		−	113.951i		−	0.134376i
$849$	−554.508	−	180.171i	−0.653131	−	0.212215i
$850$		0			0
$851$	−90.0000	−	65.3888i	−0.105758	−	0.0768376i
$852$	348.280	−	113.163i	0.408779	−	0.132820i
$853$	437.746	+	1347.24i	0.513184	+	1.57942i	0.786562	+	0.617511i	$0.211859\pi$
$853$	437.746	+	1347.24i	0.513184	+	1.57942i	−0.273379	+	0.961907i	$0.588141\pi$
$854$	96.1803	−	132.381i	0.112623	−	0.155013i
$855$		0			0
$856$	142.307	−	437.977i	0.166247	−	0.511656i
$857$	1249.64			1.45815			0.729077	−	0.684432i	$-0.239950\pi$
$857$	1249.64			1.45815			0.729077	+	0.684432i	$0.239950\pi$
$858$	−19.3487	+	54.7465i	−0.0225509	+	0.0638071i
$859$	345.229			0.401896			0.200948	−	0.979602i	$-0.435598\pi$
$859$	345.229			0.401896			0.200948	+	0.979602i	$0.435598\pi$
$860$		0			0
$861$	781.312	−	567.656i	0.907447	−	0.659299i
$862$	−74.4518	+	102.474i	−0.0863710	+	0.118879i
$863$	385.456	−	125.242i	0.446647	−	0.145124i	−0.0770535	−	0.997027i	$-0.524551\pi$
$863$	385.456	−	125.242i	0.446647	−	0.145124i	0.523700	+	0.851903i	$0.324551\pi$
$864$	612.021	−	198.858i	0.708358	−	0.230159i
$865$		0			0
$866$	265.045	+	364.804i	0.306057	+	0.421251i
$867$	−72.8765	−	23.6790i	−0.0840560	−	0.0273114i
$868$	246.377			0.283844
$869$	−34.3588	−	26.3307i	−0.0395383	−	0.0303000i
$870$		0			0
$871$	192.467	+	62.5364i	0.220973	+	0.0717983i
$872$	300.197	+	413.185i	0.344262	+	0.473836i
$873$	322.599	−	444.019i	0.369529	−	0.508613i
$874$	−1.28677	−	3.96027i	−0.00147228	−	0.00453121i
$875$		0			0
$876$	290.136	−	399.338i	0.331206	−	0.455866i
$877$	287.759	−	209.069i	0.328117	−	0.238391i	−0.411514	−	0.911403i	$-0.635000\pi$
$877$	287.759	−	209.069i	0.328117	−	0.238391i	0.739631	+	0.673012i	$0.235000\pi$
$878$	467.642	+	151.946i	0.532622	+	0.173059i
$879$			89.1077i			0.101374i
$880$		0			0
$881$	−883.370			−1.00269			−0.501345	−	0.865248i	$-0.667161\pi$
$881$	−883.370			−1.00269			−0.501345	+	0.865248i	$0.667161\pi$
$882$	−79.9001	+	245.907i	−0.0905897	+	0.278806i
$883$	−490.062	−	674.512i	−0.554996	−	0.763887i	0.435683	−	0.900100i	$-0.356507\pi$
$883$	−490.062	−	674.512i	−0.554996	−	0.763887i	−0.990680	+	0.136213i	$0.956507\pi$
$884$	−225.689	−	163.973i	−0.255304	−	0.185489i
$885$		0			0
$886$	−179.177	+	58.2180i	−0.202231	+	0.0657088i
$887$	−74.7934	−	54.3406i	−0.0843217	−	0.0612633i	0.544826	−	0.838549i	$-0.316596\pi$
$887$	−74.7934	−	54.3406i	−0.0843217	−	0.0612633i	−0.629147	+	0.777286i	$0.716596\pi$
$888$	244.297	−	177.492i	0.275109	−	0.199879i
$889$	579.384	−	1783.16i	0.651725	−	2.00580i
$890$		0			0
$891$	206.302	+	299.774i	0.231540	+	0.336447i
$892$		−	923.680i		−	1.03552i
$893$	17.4525	−	53.7132i	0.0195437	−	0.0601492i
$894$	54.5743	−	39.6505i	0.0610451	−	0.0443518i
$895$		0			0
$896$	398.204	+	1225.54i	0.444424	+	1.36780i
$897$	6.20541	+	19.0983i	0.00691796	+	0.0212913i
$898$	−236.526	−	171.846i	−0.263392	−	0.191365i
$899$	119.039	+	163.844i	0.132413	+	0.182251i
$900$		0			0
$901$			175.121i			0.194363i
$902$	−560.583	−	14.3328i	−0.621489	−	0.0158900i
$903$		−	317.426i		−	0.351524i
$904$	−43.8525	−	14.2486i	−0.0485095	−	0.0157617i
$905$		0			0
$906$	81.6563	+	59.3268i	0.0901284	+	0.0654821i
$907$	−1399.68	+	454.784i	−1.54320	+	0.501415i	−0.952256	−	0.305299i	$-0.901243\pi$
$907$	−1399.68	+	454.784i	−1.54320	+	0.501415i	−0.590941	+	0.806715i	$0.701243\pi$
$908$	−273.092	−	840.491i	−0.300762	−	0.925651i
$909$	−469.567	+	646.304i	−0.516576	+	0.711005i
$910$		0			0
$911$	54.3525	−	167.280i	0.0596625	−	0.183622i	−0.916783	−	0.399385i	$-0.869224\pi$
$911$	54.3525	−	167.280i	0.0596625	−	0.183622i	0.976446	+	0.215763i	$0.0692237\pi$
$912$	−28.4971			−0.0312468
$913$	23.4043	−	915.384i	0.0256345	−	1.00261i
$914$	185.795			0.203277
$915$		0			0
$916$	112.941	−	82.0566i	0.123298	−	0.0895814i
$917$	−830.884	+	1143.61i	−0.906089	+	1.24713i
$918$	−234.810	+	76.2945i	−0.255785	+	0.0831095i
$919$	1636.12	−	531.609i	1.78033	−	0.578465i	0.781371	−	0.624066i	$-0.214521\pi$
$919$	1636.12	−	531.609i	1.78033	−	0.578465i	0.998960	+	0.0456019i	$0.0145206\pi$
$920$		0			0
$921$	289.595	+	398.593i	0.314435	+	0.432783i
$922$	308.368	+	100.195i	0.334455	+	0.108671i
$923$	401.228			0.434700
$924$	433.050	−	298.021i	0.468668	−	0.322533i
$925$		0			0
$926$	−50.5322	−	16.4189i	−0.0545704	−	0.0177310i
$927$	−385.952	−	531.217i	−0.416345	−	0.573049i
$928$	−483.539	+	665.535i	−0.521055	+	0.717171i
$929$	−288.957	−	889.317i	−0.311040	−	0.957284i	−0.977354	−	0.211612i	$-0.932129\pi$
$929$	−288.957	−	889.317i	−0.311040	−	0.957284i	0.666313	−	0.745672i	$-0.267871\pi$
$930$		0			0
$931$	61.1782	−	84.2046i	0.0657123	−	0.0904453i
$932$	648.720	−	471.322i	0.696051	−	0.505711i
$933$	−729.733	−	237.105i	−0.782136	−	0.254131i
$934$			8.07520i			0.00864583i
$935$		0			0
$936$	202.361			0.216197
$937$	−277.333	+	853.544i	−0.295980	+	0.910933i	0.686910	+	0.726742i	$0.258967\pi$
$937$	−277.333	+	853.544i	−0.295980	+	0.910933i	−0.982890	+	0.184191i	$0.941033\pi$
$938$	163.722	+	225.344i	0.174544	+	0.240239i
$939$	−370.504	−	269.187i	−0.394573	−	0.286674i
$940$		0			0
$941$	437.800	−	142.250i	0.465250	−	0.151169i	−0.0670056	−	0.997753i	$-0.521345\pi$
$941$	437.800	−	142.250i	0.465250	−	0.151169i	0.532256	+	0.846584i	$0.321345\pi$
$942$	−200.329	−	145.548i	−0.212664	−	0.154509i
$943$	−156.896	+	113.992i	−0.166380	+	0.120882i
$944$	6.97716	−	21.4735i	0.00739106	−	0.0227473i
$945$		0			0
$946$	−112.113	+	146.295i	−0.118512	+	0.154646i
$947$		−	1781.44i		−	1.88114i	−0.339600	−	0.940570i	$-0.610292\pi$
$947$		−	1781.44i		−	1.88114i	0.339600	−	0.940570i	$-0.389708\pi$
$948$	5.83511	−	17.9586i	0.00615518	−	0.0189437i
$949$	437.533	−	317.886i	0.461046	−	0.334970i
$950$		0			0
$951$	−220.755	−	679.413i	−0.232129	−	0.714419i
$952$	−255.342	−	785.861i	−0.268216	−	0.825484i
$953$	650.194	+	472.394i	0.682260	+	0.495691i	0.874107	−	0.485734i	$-0.161448\pi$
$953$	650.194	+	472.394i	0.682260	+	0.495691i	−0.191847	+	0.981425i	$0.561448\pi$
$954$	−34.6962	−	47.7553i	−0.0363692	−	0.0500579i
$955$		0			0
$956$		−	1094.30i		−	1.14466i
$957$	407.420	+	143.992i	0.425726	+	0.150462i
$958$			416.760i			0.435031i
$959$	−153.992	−	50.0350i	−0.160575	−	0.0521741i
$960$		0			0
$961$	736.400	+	535.026i	0.766285	+	0.556738i
$962$	146.214	−	47.5078i	0.151989	−	0.0493844i
$963$	185.857	+	572.008i	0.192998	+	0.593986i
$964$	−552.938	+	761.054i	−0.573587	+	0.789475i
$965$		0			0
$966$	−8.54102	+	26.2866i	−0.00884164	+	0.0272118i
$967$	915.454			0.946695			0.473347	−	0.880876i	$-0.343046\pi$
$967$	915.454			0.946695			0.473347	+	0.880876i	$0.343046\pi$
$968$	−656.030	−	33.5683i	−0.677716	−	0.0346780i
$969$	43.7945			0.0451956
$970$		0			0
$971$	−596.366	+	433.285i	−0.614177	+	0.446226i	−0.850883	−	0.525356i	$-0.823932\pi$
$971$	−596.366	+	433.285i	−0.614177	+	0.446226i	0.236706	+	0.971581i	$0.423932\pi$
$972$	−501.733	+	690.577i	−0.516187	+	0.710470i
$973$	−2145.04	+	696.964i	−2.20456	+	0.716305i
$974$	435.902	−	141.633i	0.447538	−	0.145414i
$975$		0			0
$976$	132.177	+	181.926i	0.135427	+	0.186400i
$977$	−181.942	−	59.1165i	−0.186225	−	0.0605082i	0.214420	−	0.976742i	$-0.431214\pi$
$977$	−181.942	−	59.1165i	−0.186225	−	0.0605082i	−0.400645	+	0.916233i	$0.631214\pi$
$978$	175.073			0.179011
$979$	1278.75	+	451.941i	1.30618	+	0.461635i
$980$		0			0
$981$	−634.373	−	206.120i	−0.646659	−	0.210112i
$982$	−186.211	−	256.297i	−0.189624	−	0.260995i
$983$	561.257	−	772.503i	0.570963	−	0.785863i	−0.421705	−	0.906733i	$-0.638568\pi$
$983$	561.257	−	772.503i	0.570963	−	0.785863i	0.992668	+	0.120870i	$0.0385683\pi$
$984$	−162.672	−	500.654i	−0.165317	−	0.508794i
$985$		0			0
$986$	185.517	−	255.342i	0.188151	−	0.258967i
$987$	−303.278	+	220.344i	−0.307273	+	0.223247i
$988$	−35.9996	−	11.6970i	−0.0364368	−	0.0118390i
$989$			63.7429i			0.0644518i
$990$		0			0
$991$	−1076.02			−1.08580			−0.542898	−	0.839799i	$-0.682673\pi$
$991$	−1076.02			−1.08580			−0.542898	+	0.839799i	$0.682673\pi$
$992$	63.7156	−	196.096i	0.0642294	−	0.197678i
$993$	−169.676	−	233.539i	−0.170872	−	0.235185i
$994$	446.774	+	324.600i	0.449471	+	0.326560i
$995$		0			0
$996$	379.886	−	123.432i	0.381411	−	0.123928i
$997$	−390.120	−	283.439i	−0.391294	−	0.284292i	0.374692	−	0.927150i	$-0.377749\pi$
$997$	−390.120	−	283.439i	−0.391294	−	0.284292i	−0.765986	+	0.642858i	$0.777749\pi$
$998$	273.504	−	198.712i	0.274052	−	0.199111i
$999$	−276.565	+	851.181i	−0.276842	+	0.852033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.d.24.1		8
5.2	odd	4		11.3.d.a.2.1	✓	4
5.3	odd	4		275.3.x.e.101.1		4
5.4	even	2	inner	275.3.q.d.24.2		8
11.6	odd	10	inner	275.3.q.d.149.2		8
15.2	even	4		99.3.k.a.46.1		4
20.7	even	4		176.3.n.a.145.1		4
55.2	even	20		121.3.d.c.118.1		4
55.7	even	20		121.3.b.b.120.3		4
55.17	even	20		11.3.d.a.6.1	yes	4
55.27	odd	20		121.3.d.d.94.1		4
55.28	even	20		275.3.x.e.226.1		4
55.32	even	4		121.3.d.d.112.1		4
55.37	odd	20		121.3.b.b.120.2		4
55.39	odd	10	inner	275.3.q.d.149.1		8
55.42	odd	20		121.3.d.a.118.1		4
55.47	odd	20		121.3.d.c.40.1		4
55.52	even	20		121.3.d.a.40.1		4
165.17	odd	20		99.3.k.a.28.1		4
165.62	odd	20		1089.3.c.e.604.2		4
165.92	even	20		1089.3.c.e.604.3		4
220.127	odd	20		176.3.n.a.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	5.2	odd	4
11.3.d.a.6.1	yes	4	55.17	even	20
99.3.k.a.28.1		4	165.17	odd	20
99.3.k.a.46.1		4	15.2	even	4
121.3.b.b.120.2		4	55.37	odd	20
121.3.b.b.120.3		4	55.7	even	20
121.3.d.a.40.1		4	55.52	even	20
121.3.d.a.118.1		4	55.42	odd	20
121.3.d.c.40.1		4	55.47	odd	20
121.3.d.c.118.1		4	55.2	even	20
121.3.d.d.94.1		4	55.27	odd	20
121.3.d.d.112.1		4	55.32	even	4
176.3.n.a.17.1		4	220.127	odd	20
176.3.n.a.145.1		4	20.7	even	4
275.3.q.d.24.1		8	1.1	even	1	trivial
275.3.q.d.24.2		8	5.4	even	2	inner
275.3.q.d.149.1		8	55.39	odd	10	inner
275.3.q.d.149.2		8	11.6	odd	10	inner
275.3.x.e.101.1		4	5.3	odd	4
275.3.x.e.226.1		4	55.28	even	20
1089.3.c.e.604.2		4	165.62	odd	20
1089.3.c.e.604.3		4	165.92	even	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.224514 + 0.690983i) q^{2} +(-0.812299 - 1.11803i) q^{3} +(2.80902 + 2.04087i) q^{4} +(0.954915 - 0.310271i) q^{6} +(-8.05748 - 5.85410i) q^{7} +(-4.39201 + 3.19098i) q^{8} +(2.19098 - 6.74315i) q^{9} +(-10.3713 - 3.66547i) q^{11} -4.79837i q^{12} +(1.62460 - 5.00000i) q^{13} +(5.85410 - 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-4.72253 - 14.5344i) q^{17} +(4.16750 + 3.02786i) q^{18} +(-1.21885 - 1.67760i) q^{19} +13.7638i q^{21} +(4.86128 - 6.34346i) q^{22} -2.76393i q^{23} +(7.13525 + 2.31838i) q^{24} +(3.09017 + 2.24514i) q^{26} +(-21.1478 + 6.87132i) q^{27} +(-10.6861 - 32.8885i) q^{28} +(16.7082 - 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} -28.9402 q^{32} +(4.32650 + 14.5729i) q^{33} +11.1033 q^{34} +(19.9164 - 14.4701i) q^{36} +(23.6579 - 32.5623i) q^{37} +(1.43284 - 0.465558i) q^{38} +(-6.90983 + 2.24514i) q^{39} +(-41.2426 - 56.7656i) q^{41} +(-9.51057 - 3.09017i) q^{42} -23.0624 q^{43} +(-21.6525 - 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(16.0090 + 22.0344i) q^{47} +(8.07772 - 11.1180i) q^{48} +(15.5106 + 47.7369i) q^{49} +(-12.4139 + 17.0863i) q^{51} +(14.7679 - 10.7295i) q^{52} +(-10.8981 - 3.54102i) q^{53} -16.1554i q^{54} +54.0689 q^{56} +(-0.885544 + 2.72542i) q^{57} +(12.1392 + 16.7082i) q^{58} +(-1.83688 - 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-4.18774 - 3.04257i) q^{62} +(-57.1289 + 41.5066i) q^{63} +(-5.79431 + 17.8330i) q^{64} +(-11.0410 - 0.282294i) q^{66} +38.4934i q^{67} +(16.3973 - 50.4656i) q^{68} +(-3.09017 + 2.24514i) q^{69} +(23.5836 + 72.5828i) q^{71} +(11.8945 + 36.6074i) q^{72} +(83.2237 + 60.4656i) q^{73} +(17.1885 + 23.6579i) q^{74} -7.19991i q^{76} +(62.1087 + 90.2492i) q^{77} -5.27864i q^{78} +(3.74265 + 1.21606i) q^{79} +(-26.7639 - 19.4451i) q^{81} +(48.4836 - 15.7533i) q^{82} +(25.7238 + 79.1697i) q^{83} +(-28.0902 + 38.6628i) q^{84} +(5.17783 - 15.9357i) q^{86} -39.2833 q^{87} +(57.2474 - 16.9959i) q^{88} -123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(5.64083 - 7.76393i) q^{92} +(9.36408 - 3.04257i) q^{93} +(-18.8197 + 6.11488i) q^{94} +(23.5081 + 32.3562i) q^{96} +(73.6196 + 23.9205i) q^{97} -36.4677 q^{98} +(-47.4402 + 61.9044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{4} + 30 q^{6} + 22 q^{9} + 2 q^{11} + 20 q^{14} + 38 q^{16} - 50 q^{19} - 10 q^{24} - 20 q^{26} + 80 q^{29} - 116 q^{31} - 260 q^{34} + 52 q^{36} - 100 q^{39} - 160 q^{41} - 48 q^{44} + 60 q^{46}+ \cdots - 62 q^{99}+O(q^{100}) \) 8 * q + 18 * q^4 + 30 * q^6 + 22 * q^9 + 2 * q^11 + 20 * q^14 + 38 * q^16 - 50 * q^19 - 10 * q^24 - 20 * q^26 + 80 * q^29 - 116 * q^31 - 260 * q^34 + 52 * q^36 - 100 * q^39 - 160 * q^41 - 48 * q^44 + 60 * q^46 + 218 * q^49 - 390 * q^51 + 200 * q^56 - 46 * q^59 + 20 * q^61 + 298 * q^64 + 180 * q^66 + 20 * q^69 + 296 * q^71 + 540 * q^74 - 140 * q^79 - 232 * q^81 - 180 * q^84 + 350 * q^86 - 244 * q^89 - 160 * q^91 - 240 * q^94 + 680 * q^96 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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