LMFDB - Embedded newform 275.3.x.e.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] 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([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,5,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	275.101
Dual form			275.3.x.e.226.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.690983 + 0.224514i) q^{2} +(1.11803 - 0.812299i) q^{3} +(-2.80902 - 2.04087i) q^{4} +(0.954915 - 0.310271i) q^{6} +(-5.85410 + 8.05748i) q^{7} +(-3.19098 - 4.39201i) q^{8} +(-2.19098 + 6.74315i) q^{9} +(-10.3713 - 3.66547i) q^{11} -4.79837 q^{12} +(5.00000 + 1.62460i) q^{13} +(-5.85410 + 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-14.5344 + 4.72253i) q^{17} +(-3.02786 + 4.16750i) q^{18} +(1.21885 + 1.67760i) q^{19} +13.7638i q^{21} +(-6.34346 - 4.86128i) q^{22} +2.76393 q^{23} +(-7.13525 - 2.31838i) q^{24} +(3.09017 + 2.24514i) q^{26} +(6.87132 + 21.1478i) q^{27} +(32.8885 - 10.6861i) q^{28} +(-16.7082 + 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} +28.9402i q^{32} +(-14.5729 + 4.32650i) q^{33} -11.1033 q^{34} +(19.9164 - 14.4701i) q^{36} +(-32.5623 - 23.6579i) q^{37} +(0.465558 + 1.43284i) q^{38} +(6.90983 - 2.24514i) q^{39} +(-41.2426 - 56.7656i) q^{41} +(-3.09017 + 9.51057i) q^{42} -23.0624i q^{43} +(21.6525 + 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(22.0344 - 16.0090i) q^{47} +(11.1180 + 8.07772i) q^{48} +(-15.5106 - 47.7369i) q^{49} +(-12.4139 + 17.0863i) q^{51} +(-10.7295 - 14.7679i) q^{52} +(3.54102 - 10.8981i) q^{53} +16.1554i q^{54} +54.0689 q^{56} +(2.72542 + 0.885544i) q^{57} +(-16.7082 + 12.1392i) q^{58} +(1.83688 + 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-3.04257 + 4.18774i) q^{62} +(-41.5066 - 57.1289i) q^{63} +(5.79431 - 17.8330i) q^{64} +(-11.0410 - 0.282294i) q^{66} +38.4934 q^{67} +(50.4656 + 16.3973i) q^{68} +(3.09017 - 2.24514i) q^{69} +(23.5836 + 72.5828i) q^{71} +(36.6074 - 11.8945i) q^{72} +(-60.4656 + 83.2237i) q^{73} +(-17.1885 - 23.6579i) q^{74} -7.19991i q^{76} +(90.2492 - 62.1087i) q^{77} +5.27864 q^{78} +(-3.74265 - 1.21606i) q^{79} +(-26.7639 - 19.4451i) q^{81} +(-15.7533 - 48.4836i) q^{82} +(-79.1697 + 25.7238i) q^{83} +(28.0902 - 38.6628i) q^{84} +(5.17783 - 15.9357i) q^{86} +39.2833i q^{87} +(16.9959 + 57.2474i) q^{88} +123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(-7.76393 - 5.64083i) q^{92} +(3.04257 + 9.36408i) q^{93} +(18.8197 - 6.11488i) q^{94} +(23.5081 + 32.3562i) q^{96} +(23.9205 - 73.6196i) q^{97} -36.4677i q^{98} +(47.4402 - 61.9044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 9 q^{4} + 15 q^{6} - 10 q^{7} - 15 q^{8} - 11 q^{9} + q^{11} + 30 q^{12} + 20 q^{13} - 10 q^{14} + 19 q^{16} - 30 q^{18} + 25 q^{19} + 35 q^{22} + 20 q^{23} + 5 q^{24} - 10 q^{26} - 15 q^{27}+ \cdots + 31 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 - 9 * q^4 + 15 * q^6 - 10 * q^7 - 15 * q^8 - 11 * q^9 + q^11 + 30 * q^12 + 20 * q^13 - 10 * q^14 + 19 * q^16 - 30 * q^18 + 25 * q^19 + 35 * q^22 + 20 * q^23 + 5 * q^24 - 10 * q^26 - 15 * q^27 + 60 * q^28 - 40 * q^29 - 58 * q^31 - 65 * q^33 + 130 * q^34 + 26 * q^36 - 90 * q^37 + 60 * q^38 + 50 * q^39 - 80 * q^41 + 10 * q^42 + 24 * q^44 + 30 * q^46 + 30 * q^47 + 40 * q^48 - 109 * q^49 - 195 * q^51 - 110 * q^52 - 120 * q^53 + 100 * q^56 - 45 * q^57 - 40 * q^58 + 23 * q^59 + 10 * q^61 - 200 * q^62 - 90 * q^63 - 149 * q^64 + 90 * q^66 + 230 * q^67 + 260 * q^68 - 10 * q^69 + 148 * q^71 + 95 * q^72 - 300 * q^73 - 270 * q^74 + 200 * q^77 + 200 * q^78 + 70 * q^79 - 116 * q^81 - 25 * q^82 - 225 * q^83 + 90 * q^84 + 175 * q^86 - 55 * q^88 + 122 * q^89 - 80 * q^91 - 40 * q^92 + 200 * q^93 + 120 * q^94 + 340 * q^96 + 165 * q^97 + 31 * 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 $

$2$	0.690983	+	0.224514i	0.345492	+	0.112257i	0.476623	−	0.879108i	$-0.341861\pi$
$2$	0.690983	+	0.224514i	0.345492	+	0.112257i	−0.131131	+	0.991365i	$0.541861\pi$
$3$	1.11803	−	0.812299i	0.372678	−	0.270766i	−0.385643	−	0.922648i	$-0.626020\pi$
$3$	1.11803	−	0.812299i	0.372678	−	0.270766i	0.758321	+	0.651882i	$0.226020\pi$
$4$	−2.80902	−	2.04087i	−0.702254	−	0.510218i
$5$		0			0
$5$		0			0
$6$	0.954915	−	0.310271i	0.159153	−	0.0517118i
$7$	−5.85410	+	8.05748i	−0.836300	+	1.15107i	0.150417	+	0.988623i	$0.451938\pi$
$7$	−5.85410	+	8.05748i	−0.836300	+	1.15107i	−0.986717	+	0.162446i	$0.948062\pi$
$8$	−3.19098	−	4.39201i	−0.398873	−	0.549001i
$9$	−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
$12$	−4.79837			−0.399864
$13$	5.00000	+	1.62460i	0.384615	+	0.124969i	0.494941	−	0.868926i	$-0.335190\pi$
$13$	5.00000	+	1.62460i	0.384615	+	0.124969i	−0.110326	+	0.993895i	$0.535190\pi$
$14$	−5.85410	+	4.25325i	−0.418150	+	0.303804i
$15$		0			0
$16$	3.07295	+	9.45756i	0.192059	+	0.591098i
$17$	−14.5344	+	4.72253i	−0.854967	+	0.277796i	−0.703525	−	0.710670i	$-0.748392\pi$
$17$	−14.5344	+	4.72253i	−0.854967	+	0.277796i	−0.151442	+	0.988466i	$0.548392\pi$
$18$	−3.02786	+	4.16750i	−0.168215	+	0.231528i
$19$	1.21885	+	1.67760i	0.0641498	+	0.0882947i	0.839886	−	0.542762i	$-0.182621\pi$
$19$	1.21885	+	1.67760i	0.0641498	+	0.0882947i	−0.775737	+	0.631057i	$0.782621\pi$
$20$		0			0
$21$			13.7638i			0.655420i
$22$	−6.34346	−	4.86128i	−0.288339	−	0.220967i
$23$	2.76393			0.120171			0.0600855	−	0.998193i	$-0.480863\pi$
$23$	2.76393			0.120171			0.0600855	+	0.998193i	$0.480863\pi$
$24$	−7.13525	−	2.31838i	−0.297302	−	0.0965994i
$25$		0			0
$26$	3.09017	+	2.24514i	0.118853	+	0.0863515i
$27$	6.87132	+	21.1478i	0.254493	+	0.783250i
$28$	32.8885	−	10.6861i	1.17459	−	0.381648i
$29$	−16.7082	+	22.9969i	−0.576145	+	0.792996i	−0.993266	−	0.115855i	$-0.963039\pi$
$29$	−16.7082	+	22.9969i	−0.576145	+	0.792996i	0.417121	+	0.908851i	$0.363039\pi$
$30$		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	$0.136659\pi$
$32$			28.9402i			0.904382i
$33$	−14.5729	+	4.32650i	−0.441605	+	0.131106i
$34$	−11.1033			−0.326568
$35$		0			0
$36$	19.9164	−	14.4701i	0.553234	−	0.401948i
$37$	−32.5623	−	23.6579i	−0.880062	−	0.639403i	0.0532056	−	0.998584i	$-0.483056\pi$
$37$	−32.5623	−	23.6579i	−0.880062	−	0.639403i	−0.933268	+	0.359181i	$0.883056\pi$
$38$	0.465558	+	1.43284i	0.0122515	+	0.0377063i
$39$	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	$-0.526864\pi$
$42$	−3.09017	+	9.51057i	−0.0735755	+	0.226442i
$43$		−	23.0624i		−	0.536334i	−0.963372	−	0.268167i	$-0.913582\pi$
$43$		−	23.0624i		−	0.536334i	0.963372	−	0.268167i	$-0.0864180\pi$
$44$	21.6525	+	31.4629i	0.492102	+	0.715066i
$45$		0			0
$46$	1.90983	+	0.620541i	0.0415180	+	0.0134900i
$47$	22.0344	−	16.0090i	0.468818	−	0.340616i	−0.328163	−	0.944621i	$-0.606429\pi$
$47$	22.0344	−	16.0090i	0.468818	−	0.340616i	0.796980	+	0.604005i	$0.206429\pi$
$48$	11.1180	+	8.07772i	0.231626	+	0.168286i
$49$	−15.5106	−	47.7369i	−0.316544	−	0.974221i
$50$		0			0
$51$	−12.4139	+	17.0863i	−0.243410	+	0.335025i
$52$	−10.7295	−	14.7679i	−0.206336	−	0.283998i
$53$	3.54102	−	10.8981i	0.0668117	−	0.205625i	−0.912077	−	0.410019i	$-0.865522\pi$
$53$	3.54102	−	10.8981i	0.0668117	−	0.205625i	0.978889	+	0.204393i	$0.0655222\pi$
$54$			16.1554i			0.299175i
$55$		0			0
$56$	54.0689			0.965516
$57$	2.72542	+	0.885544i	0.0478145	+	0.0155359i
$58$	−16.7082	+	12.1392i	−0.288072	+	0.209297i
$59$	1.83688	+	1.33457i	0.0311336	+	0.0226199i	0.603243	−	0.797557i	$-0.293875\pi$
$59$	1.83688	+	1.33457i	0.0311336	+	0.0226199i	−0.572110	+	0.820177i	$0.693875\pi$
$60$		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	$0.340656\pi$
$62$	−3.04257	+	4.18774i	−0.0490737	+	0.0675442i
$63$	−41.5066	−	57.1289i	−0.658835	−	0.906808i
$64$	5.79431	−	17.8330i	0.0905361	−	0.278641i
$65$		0			0
$66$	−11.0410	−	0.282294i	−0.167288	−	0.00427718i
$67$	38.4934			0.574529			0.287264	−	0.957851i	$-0.407254\pi$
$67$	38.4934			0.574529			0.287264	+	0.957851i	$0.407254\pi$
$68$	50.4656	+	16.3973i	0.742141	+	0.241136i
$69$	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	$0.719387\pi$
$72$	36.6074	−	11.8945i	0.508436	−	0.165201i
$73$	−60.4656	+	83.2237i	−0.828295	+	1.14005i	0.159943	+	0.987126i	$0.448869\pi$
$73$	−60.4656	+	83.2237i	−0.828295	+	1.14005i	−0.988238	+	0.152924i	$0.951131\pi$
$74$	−17.1885	−	23.6579i	−0.232277	−	0.319701i
$75$		0			0
$76$		−	7.19991i		−	0.0947357i
$77$	90.2492	−	62.1087i	1.17207	−	0.806606i
$78$	5.27864			0.0676749
$79$	−3.74265	−	1.21606i	−0.0473753	−	0.0153932i	0.285233	−	0.958458i	$-0.407929\pi$
$79$	−3.74265	−	1.21606i	−0.0473753	−	0.0153932i	−0.332609	+	0.943065i	$0.607929\pi$
$80$		0			0
$81$	−26.7639	−	19.4451i	−0.330419	−	0.240063i
$82$	−15.7533	−	48.4836i	−0.192113	−	0.591264i
$83$	−79.1697	+	25.7238i	−0.953852	+	0.309925i	−0.744280	−	0.667868i	$-0.767207\pi$
$83$	−79.1697	+	25.7238i	−0.953852	+	0.309925i	−0.209572	+	0.977793i	$0.567207\pi$
$84$	28.0902	−	38.6628i	0.334407	−	0.460271i
$85$		0			0
$86$	5.17783	−	15.9357i	0.0602073	−	0.185299i
$87$			39.2833i			0.451533i
$88$	16.9959	+	57.2474i	0.193136	+	0.650539i
$89$	123.297			1.38536			0.692679	−	0.721246i	$-0.256430\pi$
$89$	123.297			1.38536			0.692679	+	0.721246i	$0.256430\pi$
$90$		0			0
$91$	−42.3607	+	30.7768i	−0.465502	+	0.338207i
$92$	−7.76393	−	5.64083i	−0.0843906	−	0.0613133i
$93$	3.04257	+	9.36408i	0.0327158	+	0.100689i
$94$	18.8197	−	6.11488i	0.200209	−	0.0650519i
$95$		0			0
$96$	23.5081	+	32.3562i	0.244876	+	0.337043i
$97$	23.9205	−	73.6196i	0.246603	−	0.758965i	−0.748766	−	0.662835i	$-0.769353\pi$
$97$	23.9205	−	73.6196i	0.246603	−	0.758965i	0.995369	−	0.0961309i	$-0.0306467\pi$
$98$		−	36.4677i		−	0.372119i
$99$	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	$0.788351\pi$
$102$	−12.4139	+	9.01922i	−0.121705	+	0.0884238i
$103$	74.9230	+	54.4347i	0.727408	+	0.528493i	0.888742	−	0.458407i	$-0.151580\pi$
$103$	74.9230	+	54.4347i	0.727408	+	0.528493i	−0.161335	+	0.986900i	$0.551580\pi$
$104$	−8.81966	−	27.1441i	−0.0848044	−	0.261001i
$105$		0			0
$106$	4.89357	−	6.73542i	0.0461657	−	0.0635417i
$107$	49.8607	+	68.6273i	0.465988	+	0.641377i	0.975737	−	0.218946i	$-0.0702619\pi$
$107$	49.8607	+	68.6273i	0.465988	+	0.641377i	−0.509749	+	0.860323i	$0.670262\pi$
$108$	23.8582	−	73.4279i	0.220909	−	0.679888i
$109$			94.0766i			0.863088i	0.902092	+	0.431544i	$0.142031\pi$
$109$			94.0766i			0.863088i	−0.902092	+	0.431544i	$0.857969\pi$
$110$		0			0
$111$	−55.6231			−0.501109
$112$	−94.1935	−	30.6053i	−0.841013	−	0.273262i
$113$	−6.87132	+	4.99231i	−0.0608082	+	0.0441797i	−0.617774	−	0.786356i	$-0.711965\pi$
$113$	−6.87132	+	4.99231i	−0.0608082	+	0.0441797i	0.556966	+	0.830535i	$0.311965\pi$
$114$	1.68441	+	1.22379i	0.0147755	+	0.0107350i
$115$		0			0
$116$	93.8673	−	30.4993i	0.809200	−	0.262925i
$117$	−21.9098	+	30.1563i	−0.187264	+	0.257746i
$118$	0.969623	+	1.33457i	0.00821715	+	0.0113099i
$119$	47.0344	−	144.757i	0.395247	−	1.21645i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$	16.4296			0.134669
$123$	−92.2214	−	29.9645i	−0.749767	−	0.243614i
$124$	20.0132	−	14.5404i	0.161396	−	0.117261i
$125$		0			0
$126$	−15.8541	−	48.7939i	−0.125826	−	0.387253i
$127$	179.039	−	58.1734i	1.40976	−	0.458059i	0.497426	−	0.867506i	$-0.334279\pi$
$127$	179.039	−	58.1734i	1.40976	−	0.458059i	0.912334	+	0.409448i	$0.134279\pi$
$128$	76.0501	−	104.674i	0.594141	−	0.817766i
$129$	−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	$-0.182229\pi$
$132$	49.7655	+	17.5883i	0.377011	+	0.133245i
$133$	−20.6525			−0.155282
$134$	26.5983	+	8.64231i	0.198495	+	0.0644949i
$135$		0			0
$136$	67.1205	+	48.7659i	0.493533	+	0.358573i
$137$	−5.02380	−	15.4617i	−0.0366701	−	0.112859i	0.931046	−	0.364902i	$-0.118898\pi$
$137$	−5.02380	−	15.4617i	−0.0366701	−	0.112859i	−0.967716	+	0.252043i	$0.918898\pi$
$138$	2.63932	−	0.857567i	0.0191255	−	0.00621425i
$139$	−133.108	+	183.208i	−0.957614	+	1.31804i	−0.00955293	+	0.999954i	$0.503041\pi$
$139$	−133.108	+	183.208i	−0.957614	+	1.31804i	−0.948061	+	0.318088i	$0.896959\pi$
$140$		0			0
$141$	11.6312	−	35.7971i	0.0824907	−	0.253880i
$142$			55.4484i			0.390481i
$143$	−45.9017	−	35.1766i	−0.320991	−	0.245990i
$144$	−70.5066			−0.489629
$145$		0			0
$146$	−60.4656	+	43.9308i	−0.414148	+	0.300896i
$147$	−56.1180	−	40.7721i	−0.381755	−	0.277361i
$148$	43.1854	+	132.911i	0.291793	+	0.898047i
$149$	−63.8967	+	20.7613i	−0.428837	+	0.139338i	−0.515479	−	0.856902i	$-0.672386\pi$
$149$	−63.8967	+	20.7613i	−0.428837	+	0.139338i	0.0866427	+	0.996239i	$0.472386\pi$
$150$		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	$0.691985\pi$
$152$	3.47871	−	10.7064i	0.0228863	−	0.0704367i
$153$		−	108.355i		−	0.708202i
$154$	76.3050	−	22.6538i	0.495487	−	0.147103i
$155$		0			0
$156$	−23.9919	−	7.79543i	−0.153794	−	0.0499707i
$157$	−199.520	+	144.960i	−1.27083	+	0.923309i	−0.999235	−	0.0391033i	$-0.987550\pi$
$157$	−199.520	+	144.960i	−1.27083	+	0.923309i	−0.271591	+	0.962413i	$0.587550\pi$
$158$	−2.31308	−	1.68055i	−0.0146398	−	0.0106364i
$159$	−4.89357	−	15.0609i	−0.0307772	−	0.0947224i
$160$		0			0
$161$	−16.1803	+	22.2703i	−0.100499	+	0.138325i
$162$	−14.1277	−	19.4451i	−0.0872081	−	0.120032i
$163$	−53.8820	+	165.832i	−0.330564	+	1.01737i	0.638302	+	0.769786i	$0.279637\pi$
$163$	−53.8820	+	165.832i	−0.330564	+	1.01737i	−0.968866	+	0.247586i	$0.920363\pi$
$164$			243.627i			1.48553i
$165$		0			0
$166$	−60.4803			−0.364339
$167$	−234.864	−	76.3120i	−1.40637	−	0.456958i	−0.495126	−	0.868821i	$-0.664878\pi$
$167$	−234.864	−	76.3120i	−1.40637	−	0.456958i	−0.911246	+	0.411863i	$0.864878\pi$
$168$	60.4508	−	43.9201i	0.359826	−	0.261429i
$169$	−114.363	−	83.0897i	−0.676705	−	0.491655i
$170$		0			0
$171$	−13.9828	+	4.54328i	−0.0817706	+	0.0265689i
$172$	−47.0673	+	64.7826i	−0.273647	+	0.376643i
$173$	29.2411	+	40.2469i	0.169024	+	0.232641i	0.885123	−	0.465357i	$-0.154074\pi$
$173$	29.2411	+	40.2469i	0.169024	+	0.232641i	−0.716099	+	0.697999i	$0.754074\pi$
$174$	−8.81966	+	27.1441i	−0.0506877	+	0.156001i
$175$		0			0
$176$	2.79586	−	109.351i	0.0158856	−	0.621314i
$177$	3.13777			0.0177275
$178$	85.1960	+	27.6819i	0.478629	+	0.155516i
$179$	−177.134	+	128.695i	−0.989574	+	0.718967i	−0.959828	−	0.280590i	$-0.909470\pi$
$179$	−177.134	+	128.695i	−0.989574	+	0.718967i	−0.0297461	+	0.999557i	$0.509470\pi$
$180$		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	$0.865727\pi$
$182$	−36.1803	+	11.7557i	−0.198793	+	0.0645918i
$183$	18.3688	−	25.2825i	0.100376	−	0.138156i
$184$	−8.81966	−	12.1392i	−0.0479329	−	0.0659740i
$185$		0			0
$186$			7.15352i			0.0384598i
$187$	168.052	+	4.29670i	0.898672	+	0.0229770i
$188$	−94.5673			−0.503018
$189$	−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	$0.801542\pi$
$192$	−8.00754	−	24.6447i	−0.0417059	−	0.128358i
$193$	−27.7933	+	9.03061i	−0.144007	+	0.0467907i	−0.380134	−	0.924932i	$-0.624122\pi$
$193$	−27.7933	+	9.03061i	−0.144007	+	0.0467907i	0.236127	+	0.971722i	$0.424122\pi$
$194$	33.0573	−	45.4994i	0.170398	−	0.234533i
$195$		0			0
$196$	−53.8551	+	165.749i	−0.274771	+	0.845657i
$197$			282.037i			1.43166i	0.698275	+	0.715830i	$0.253951\pi$
$197$			282.037i			1.43166i	−0.698275	+	0.715830i	$0.746049\pi$
$198$	46.6788	−	32.1239i	0.235751	−	0.162242i
$199$	177.469			0.891804			0.445902	−	0.895082i	$-0.352883\pi$
$199$	177.469			0.891804			0.445902	+	0.895082i	$0.352883\pi$
$200$		0			0
$201$	43.0370	−	31.2682i	0.214114	−	0.155563i
$202$	−66.2279	−	48.1174i	−0.327861	−	0.238205i
$203$	−87.4853	−	269.252i	−0.430962	−	1.32636i
$204$	69.7417	−	22.6604i	0.341871	−	0.111081i
$205$		0			0
$206$	39.5492	+	54.4347i	0.191986	+	0.264246i
$207$	−6.05573	+	18.6376i	−0.0292547	+	0.0900368i
$208$			52.2801i			0.251347i
$209$	−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	$0.525128\pi$
$212$	−32.1885	+	23.3863i	−0.151832	+	0.110313i
$213$	85.3262	+	61.9931i	0.400593	+	0.291048i
$214$	19.0451	+	58.6147i	0.0889957	+	0.273901i
$215$		0			0
$216$	70.9549	−	97.6611i	0.328495	−	0.452135i
$217$	−41.7082	−	57.4064i	−0.192204	−	0.264546i
$218$	−21.1215	+	65.0053i	−0.0968876	+	0.298190i
$219$			142.163i			0.649146i
$220$		0			0
$221$	−80.3444			−0.363549
$222$	−38.4346	−	12.4882i	−0.173129	−	0.0562529i
$223$	215.220	−	156.366i	0.965111	−	0.701194i	0.0107791	−	0.999942i	$-0.496569\pi$
$223$	215.220	−	156.366i	0.965111	−	0.701194i	0.954332	+	0.298748i	$0.0965689\pi$
$224$	−233.185	−	169.419i	−1.04101	−	0.756335i
$225$		0			0
$226$	−5.86881	+	1.90689i	−0.0259682	+	0.00843758i
$227$	−149.606	+	205.915i	−0.659057	+	0.907114i	−0.999450	−	0.0331697i	$-0.989440\pi$
$227$	−149.606	+	205.915i	−0.659057	+	0.907114i	0.340393	+	0.940283i	$0.389440\pi$
$228$	−5.84848	−	8.04975i	−0.0256512	−	0.0353059i
$229$	−12.4245	+	38.2388i	−0.0542556	+	0.166982i	−0.974513	−	0.224333i	$-0.927980\pi$
$229$	−12.4245	+	38.2388i	−0.0542556	+	0.166982i	0.920257	+	0.391315i	$0.127980\pi$
$230$		0			0
$231$	50.4508	−	142.749i	0.218402	−	0.617961i
$232$	154.318			0.665164
$233$	219.639	+	71.3649i	0.942655	+	0.306287i	0.739728	−	0.672906i	$-0.234954\pi$
$233$	219.639	+	71.3649i	0.942655	+	0.306287i	0.202928	+	0.979194i	$0.434954\pi$
$234$	−21.9098	+	15.9184i	−0.0936318	+	0.0680275i
$235$		0			0
$236$	−2.43614	−	7.49767i	−0.0103226	−	0.0317698i
$237$	−5.17221	+	1.68055i	−0.0218237	+	0.00709094i
$238$	65.0000	−	89.4648i	0.273109	−	0.375903i
$239$	185.249	+	254.974i	0.775101	+	1.06684i	0.995806	+	0.0914947i	$0.0291645\pi$
$239$	185.249	+	254.974i	0.775101	+	1.06684i	−0.220704	+	0.975341i	$0.570836\pi$
$240$		0			0
$241$			270.933i			1.12420i	0.827069	+	0.562101i	$0.190007\pi$
$241$			270.933i			1.12420i	−0.827069	+	0.562101i	$0.809993\pi$
$242$	47.9712	+	73.6697i	0.198228	+	0.304420i
$243$	−245.843			−1.01170
$244$	−74.6738	−	24.2630i	−0.306040	−	0.0994384i
$245$		0			0
$246$	−56.9959	−	41.4100i	−0.231691	−	0.168333i
$247$	3.36881	+	10.3681i	0.0136389	+	0.0419762i
$248$	36.7852	−	11.9522i	0.148327	−	0.0481945i
$249$	−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	$0.0929391\pi$
$252$			245.186i			0.972959i
$253$	−28.6656	−	10.1311i	−0.113303	−	0.0400439i
$254$	136.774			0.538480
$255$		0			0
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	−326.261	−	237.042i	−1.26950	−	0.922344i	−0.270315	−	0.962772i	$-0.587128\pi$
$257$	−326.261	−	237.042i	−1.26950	−	0.922344i	−0.999182	+	0.0404281i	$0.987128\pi$
$258$	−7.15558	−	22.0226i	−0.0277348	−	0.0853590i
$259$	381.246	−	123.874i	1.47199	−	0.478279i
$260$		0			0
$261$	−118.464	−	163.052i	−0.453885	−	0.624719i
$262$	31.8657	−	98.0726i	0.121625	−	0.374323i
$263$		−	42.6636i		−	0.162219i	−0.996705	−	0.0811094i	$-0.974154\pi$
$263$		−	42.6636i		−	0.162219i	0.996705	−	0.0811094i	$-0.0258463\pi$
$264$	65.5041	+	50.1988i	0.248121	+	0.190147i
$265$		0			0
$266$	−14.2705	−	4.63677i	−0.0536485	−	0.0174315i
$267$	137.850	−	100.154i	0.516292	−	0.375108i
$268$	−108.129	−	78.5601i	−0.403465	−	0.293135i
$269$	−126.695	−	389.927i	−0.470985	−	1.44954i	−0.851296	−	0.524685i	$-0.824183\pi$
$269$	−126.695	−	389.927i	−0.470985	−	1.44954i	0.380311	−	0.924859i	$-0.375817\pi$
$270$		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	$0.340835\pi$
$272$	−89.3272	−	122.948i	−0.328409	−	0.452016i
$273$	−22.3607	+	68.8191i	−0.0819073	+	0.252085i
$274$		−	11.8117i		−	0.0431082i
$275$		0			0
$276$	−13.2624			−0.0480521
$277$	−291.305	−	94.6507i	−1.05164	−	0.341699i	−0.268330	−	0.963327i	$-0.586472\pi$
$277$	−291.305	−	94.6507i	−1.05164	−	0.341699i	−0.783313	+	0.621628i	$0.786472\pi$
$278$	−133.108	+	96.7089i	−0.478807	+	0.347874i
$279$	−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	$0.473983\pi$
$282$	16.0739	−	22.1238i	0.0569997	−	0.0784533i
$283$	247.984	+	341.320i	0.876268	+	1.20608i	0.977441	+	0.211210i	$0.0677404\pi$
$283$	247.984	+	341.320i	0.876268	+	1.20608i	−0.101173	+	0.994869i	$0.532260\pi$
$284$	81.8854	−	252.017i	0.288329	−	0.887385i
$285$		0			0
$286$	−23.8197	−	34.6120i	−0.0832855	−	0.121021i
$287$	698.827			2.43494
$288$	−195.148	−	63.4076i	−0.677599	−	0.220165i
$289$	−44.8582	+	32.5914i	−0.155219	+	0.112773i
$290$		0			0
$291$	−33.0573	−	101.740i	−0.113599	−	0.349621i
$292$	339.698	−	110.374i	1.16335	−	0.377995i
$293$	37.8998	−	52.1646i	0.129351	−	0.178036i	−0.739429	−	0.673234i	$-0.764905\pi$
$293$	37.8998	−	52.1646i	0.129351	−	0.178036i	0.868780	+	0.495198i	$0.164905\pi$
$294$	−29.6227	−	40.7721i	−0.100757	−	0.138681i
$295$		0			0
$296$			218.506i			0.738196i
$297$	6.25174	−	244.517i	0.0210496	−	0.823289i
$298$	−48.8127			−0.163801
$299$	13.8197	+	4.49028i	0.0462196	+	0.0150177i
$300$		0			0
$301$	185.825	+	135.010i	0.617358	+	0.448537i
$302$	22.5693	+	69.4610i	0.0747326	+	0.230003i
$303$	−148.090	+	48.1174i	−0.488746	+	0.158803i
$304$	−12.1205	+	16.6825i	−0.0398702	+	0.0548766i
$305$		0			0
$306$	24.3272	−	74.8714i	0.0795006	−	0.244678i
$307$			356.512i			1.16128i	0.814161	+	0.580639i	$0.197197\pi$
$307$			356.512i			1.16128i	−0.814161	+	0.580639i	$0.802803\pi$
$308$	−380.267	−	9.72257i	−1.23463	−	0.0315668i
$309$	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	$-0.0511397\pi$
$312$	−31.9098	−	23.1838i	−0.102275	−	0.0743072i
$313$	102.405	+	315.170i	0.327172	+	1.00693i	0.970451	+	0.241300i	$0.0775736\pi$
$313$	102.405	+	315.170i	0.327172	+	1.00693i	−0.643279	+	0.765632i	$0.722426\pi$
$314$	−170.410	+	55.3696i	−0.542708	+	0.176336i
$315$		0			0
$316$	8.03134	+	11.0542i	0.0254156	+	0.0349816i
$317$	159.740	−	491.628i	0.503910	−	1.55088i	−0.298685	−	0.954352i	$-0.596548\pi$
$317$	159.740	−	491.628i	0.503910	−	1.55088i	0.802595	−	0.596524i	$-0.203452\pi$
$318$		−	11.5055i		−	0.0361807i
$319$	257.580	−	177.265i	0.807462	−	0.555688i
$320$		0			0
$321$	111.492	+	36.2259i	0.347327	+	0.112853i
$322$	−16.1803	+	11.7557i	−0.0502495	+	0.0365084i
$323$	−25.6378	−	18.6269i	−0.0793739	−	0.0576685i
$324$	35.4953	+	109.243i	0.109554	+	0.337171i
$325$		0			0
$326$	−74.4630	+	102.490i	−0.228414	+	0.314385i
$327$	76.4183	+	105.181i	0.233695	+	0.321654i
$328$	−117.711	+	362.276i	−0.358874	+	1.10450i
$329$			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	$0.397816\pi$
$332$	274.888	+	89.3165i	0.827976	+	0.269026i
$333$	230.872	−	167.739i	0.693310	−	0.503719i
$334$	−145.154	−	105.461i	−0.434593	−	0.315750i
$335$		0			0
$336$	−130.172	+	42.2955i	−0.387417	+	0.125880i
$337$	79.3090	−	109.159i	0.235338	−	0.323915i	−0.674971	−	0.737844i	$-0.735844\pi$
$337$	79.3090	−	109.159i	0.235338	−	0.323915i	0.910309	+	0.413929i	$0.135844\pi$
$338$	−60.3682	−	83.0897i	−0.178604	−	0.245828i
$339$	−3.62712	+	11.1631i	−0.0106995	+	0.0329296i
$340$		0			0
$341$	47.6707	−	62.2051i	0.139797	−	0.182420i
$342$	−10.6819			−0.0312336
$343$	11.3050	+	3.67320i	0.0329590	+	0.0107090i
$344$	−101.290	+	73.5917i	−0.294448	+	0.213929i
$345$		0			0
$346$	11.1691	+	34.3750i	0.0322806	+	0.0993496i
$347$	90.1393	−	29.2880i	0.259767	−	0.0844036i	−0.176238	−	0.984348i	$-0.556393\pi$
$347$	90.1393	−	29.2880i	0.259767	−	0.0844036i	0.436005	+	0.899944i	$0.356393\pi$
$348$	80.1722	−	110.348i	0.230380	−	0.317091i
$349$	−100.997	−	139.010i	−0.289389	−	0.398310i	0.639426	−	0.768852i	$-0.279172\pi$
$349$	−100.997	−	139.010i	−0.289389	−	0.398310i	−0.928816	+	0.370542i	$0.879172\pi$
$350$		0			0
$351$			116.902i			0.333054i
$352$	106.080	−	300.149i	0.301362	−	0.852695i
$353$	119.644			0.338936			0.169468	−	0.985536i	$-0.445795\pi$
$353$	119.644			0.338936			0.169468	+	0.985536i	$0.445795\pi$
$354$	2.16814	+	0.704473i	0.00612470	+	0.00199004i
$355$		0			0
$356$	−346.343	−	251.633i	−0.972873	−	0.706834i
$357$	−65.0000	−	200.049i	−0.182073	−	0.560363i
$358$	−151.290	+	49.1572i	−0.422598	+	0.137311i
$359$	274.681	−	378.066i	0.765127	−	1.05311i	−0.231643	−	0.972801i	$-0.574410\pi$
$359$	274.681	−	378.066i	0.765127	−	1.05311i	0.996770	−	0.0803065i	$-0.0255899\pi$
$360$		0			0
$361$	110.226	−	339.242i	0.305336	−	0.939728i
$362$			28.2637i			0.0780766i
$363$	166.999	+	8.54517i	0.460053	+	0.0235404i
$364$	181.803			0.499460
$365$		0			0
$366$	18.3688	−	13.3457i	0.0501880	−	0.0364637i
$367$	−266.026	−	193.279i	−0.724867	−	0.526647i	0.163068	−	0.986615i	$-0.447861\pi$
$367$	−266.026	−	193.279i	−0.724867	−	0.526647i	−0.887936	+	0.459968i	$0.847861\pi$
$368$	8.49342	+	26.1401i	0.0230800	+	0.0710328i
$369$	473.141	−	153.733i	1.28223	−	0.416620i
$370$		0			0
$371$	67.0820	+	92.3305i	0.180814	+	0.248869i
$372$	10.5642	−	32.5133i	0.0283985	−	0.0874015i
$373$		−	214.135i		−	0.574088i	−0.957917	−	0.287044i	$-0.907327\pi$
$373$		−	214.135i		−	0.574088i	0.957917	−	0.287044i	$-0.0926726\pi$
$374$	115.156	+	40.6989i	0.307904	+	0.108821i
$375$		0			0
$376$	−140.623	−	45.6912i	−0.373997	−	0.121519i
$377$	−120.902	+	87.8402i	−0.320694	+	0.232998i
$378$	−130.172	−	94.5756i	−0.344371	−	0.250200i
$379$	98.9630	+	304.577i	0.261116	+	0.803633i	0.992563	+	0.121734i	$0.0388456\pi$
$379$	98.9630	+	304.577i	0.261116	+	0.803633i	−0.731447	+	0.681899i	$0.761154\pi$
$380$		0			0
$381$	152.918	−	210.474i	0.401359	−	0.552424i
$382$	−51.1622	−	70.4187i	−0.133932	−	0.184342i
$383$	169.205	−	520.759i	0.441788	−	1.35968i	−0.444181	−	0.895937i	$-0.646505\pi$
$383$	169.205	−	520.759i	0.441788	−	1.35968i	0.885968	−	0.463746i	$-0.153495\pi$
$384$		−	178.805i		−	0.465637i
$385$		0			0
$386$	−21.2322			−0.0550058
$387$	155.513	+	50.5293i	0.401843	+	0.130567i
$388$	−217.441	+	157.980i	−0.560415	+	0.407166i
$389$	−272.259	−	197.808i	−0.699895	−	0.508504i	0.180003	−	0.983666i	$-0.442389\pi$
$389$	−272.259	−	197.808i	−0.699895	−	0.508504i	−0.879898	+	0.475162i	$0.842389\pi$
$390$		0			0
$391$	−40.1722	+	13.0527i	−0.102742	+	0.0333830i
$392$	−160.167	+	220.450i	−0.408588	+	0.562373i
$393$	−115.291	−	158.685i	−0.293362	−	0.403778i
$394$	−63.3212	+	194.883i	−0.160714	+	0.494626i
$395$		0			0
$396$	−259.599	+	77.0713i	−0.655554	+	0.194624i
$397$	−115.374			−0.290614			−0.145307	−	0.989387i	$-0.546417\pi$
$397$	−115.374			−0.290614			−0.145307	+	0.989387i	$0.546417\pi$
$398$	122.628	+	39.8443i	0.308111	+	0.100111i
$399$	−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	$0.874653\pi$
$402$	36.7579	−	11.9434i	0.0914377	−	0.0297099i
$403$	−22.0163	+	30.3028i	−0.0546309	+	0.0751930i
$404$	229.952	+	316.502i	0.569189	+	0.783422i
$405$		0			0
$406$		−	205.690i		−	0.506626i
$407$	250.997	+	364.720i	0.616700	+	0.896118i
$408$	114.656			0.281019
$409$	−581.745	−	189.020i	−1.42236	−	0.462152i	−0.506008	−	0.862529i	$-0.668879\pi$
$409$	−581.745	−	189.020i	−1.42236	−	0.462152i	−0.916351	+	0.400377i	$0.868879\pi$
$410$		0			0
$411$	−18.1763	−	13.2058i	−0.0442245	−	0.0321310i
$412$	−99.3657	−	305.816i	−0.241179	−	0.742272i
$413$	−21.5066	+	6.98791i	−0.0520740	+	0.0169199i
$414$	−8.36881	+	11.5187i	−0.0202145	+	0.0278229i
$415$		0			0
$416$	−47.0163	+	144.701i	−0.113020	+	0.347839i
$417$			312.957i			0.750495i
$418$	0.423579	−	16.5669i	0.00101335	−	0.0396338i
$419$	146.156			0.348821			0.174410	−	0.984673i	$-0.444198\pi$
$419$	146.156			0.348821			0.174410	+	0.984673i	$0.444198\pi$
$420$		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	$0.548947\pi$
$422$	57.8081	+	42.0000i	0.136986	+	0.0995261i
$423$	59.6738	+	183.657i	0.141073	+	0.434177i
$424$	−59.1641	+	19.2236i	−0.139538	+	0.0453386i
$425$		0			0
$426$	45.0407	+	61.9931i	0.105729	+	0.145524i
$427$	−69.5967	+	214.197i	−0.162990	+	0.501632i
$428$		−	294.535i		−	0.688165i
$429$	−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	$0.535175\pi$
$432$	−178.891	+	129.972i	−0.414100	+	0.300861i
$433$	502.109	+	364.804i	1.15961	+	0.842503i	0.989728	−	0.142962i	$-0.0456627\pi$
$433$	502.109	+	364.804i	1.15961	+	0.842503i	0.169878	+	0.985465i	$0.445663\pi$
$434$	−15.9311	−	49.0309i	−0.0367076	−	0.112975i
$435$		0			0
$436$	191.998	−	264.263i	0.440363	−	0.606107i
$437$	3.36881	+	4.63677i	0.00770895	+	0.0106105i
$438$	−31.9176	+	98.2323i	−0.0728712	+	0.224275i
$439$			676.778i			1.54164i	0.637055	+	0.770818i	$0.280152\pi$
$439$			676.778i			1.54164i	−0.637055	+	0.770818i	$0.719848\pi$
$440$		0			0
$441$	355.880			0.806985
$442$	−55.5166	−	18.0384i	−0.125603	−	0.0408110i
$443$	−209.784	+	152.417i	−0.473552	+	0.344056i	−0.798824	−	0.601565i	$-0.794544\pi$
$443$	−209.784	+	152.417i	−0.473552	+	0.344056i	0.325272	+	0.945621i	$0.394544\pi$
$444$	156.246	+	113.519i	0.351906	+	0.255674i
$445$		0			0
$446$	183.820	−	59.7266i	0.412152	−	0.133916i
$447$	−54.5743	+	75.1150i	−0.122090	+	0.168043i
$448$	109.769	+	151.084i	0.245020	+	0.337241i
$449$	124.349	−	382.707i	0.276947	−	0.852354i	−0.711751	−	0.702432i	$-0.752098\pi$
$449$	124.349	−	382.707i	0.276947	−	0.852354i	0.988698	−	0.149923i	$-0.0479024\pi$
$450$		0			0
$451$	219.668	+	739.908i	0.487069	+	1.64059i
$452$	29.4903			0.0652441
$453$	132.123	+	42.9293i	0.291662	+	0.0947666i
$454$	−149.606	+	108.695i	−0.329528	+	0.239416i
$455$		0			0
$456$	−4.80746	−	14.7959i	−0.0105427	−	0.0324470i
$457$	−243.209	+	79.0234i	−0.532186	+	0.172918i	−0.562769	−	0.826614i	$-0.690264\pi$
$457$	−243.209	+	79.0234i	−0.532186	+	0.172918i	0.0305823	+	0.999532i	$0.490264\pi$
$458$	−17.1703	+	23.6329i	−0.0374897	+	0.0516002i
$459$	−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	$-0.160827\pi$
$462$	66.9098	−	87.3102i	0.144826	−	0.188983i
$463$	−73.1308			−0.157950			−0.0789750	−	0.996877i	$-0.525165\pi$
$463$	−73.1308			−0.157950			−0.0789750	+	0.996877i	$0.525165\pi$
$464$	−268.838	−	87.3507i	−0.579392	−	0.188256i
$465$		0			0
$466$	135.744	+	98.6239i	0.291297	+	0.211639i
$467$	−3.43459	−	10.5706i	−0.00735458	−	0.0226351i	0.947312	−	0.320313i	$-0.103788\pi$
$467$	−3.43459	−	10.5706i	−0.00735458	−	0.0226351i	−0.954666	+	0.297678i	$0.903788\pi$
$468$	123.090	−	39.9944i	0.263013	−	0.0854582i
$469$	−225.344	+	310.160i	−0.480479	+	0.661322i
$470$		0			0
$471$	−105.319	+	324.139i	−0.223608	+	0.688194i
$472$		−	12.3262i		−	0.0261148i
$473$	−84.5344	+	239.187i	−0.178720	+	0.505682i
$474$	−3.95122			−0.00833590
$475$		0			0
$476$	−427.551	+	310.634i	−0.898217	+	0.652593i
$477$	65.7295	+	47.7553i	0.137798	+	0.100116i
$478$	70.7589	+	217.774i	0.148031	+	0.455593i
$479$	−545.546	+	177.259i	−1.13893	+	0.370060i	−0.816962	−	0.576692i	$-0.804343\pi$
$479$	−545.546	+	177.259i	−1.13893	+	0.370060i	−0.321965	+	0.946752i	$0.604343\pi$
$480$		0			0
$481$	−124.377	−	171.190i	−0.258580	−	0.355905i
$482$	−60.8282	+	187.210i	−0.126199	+	0.388402i
$483$			38.0423i			0.0787624i
$484$	−109.239	−	405.678i	−0.225700	−	0.838178i
$485$		0			0
$486$	−169.873	−	55.1952i	−0.349533	−	0.113570i
$487$	−510.363	+	370.800i	−1.04797	+	0.761397i	−0.971826	−	0.235700i	$-0.924262\pi$
$487$	−510.363	+	370.800i	−1.04797	+	0.761397i	−0.0761466	+	0.997097i	$0.524262\pi$
$488$	−99.3181	−	72.1588i	−0.203521	−	0.147866i
$489$	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	$0.346452\pi$
$492$	197.898	+	272.383i	0.402231	+	0.553623i
$493$	134.241	−	413.152i	0.272294	−	0.838036i
$494$			7.92055i			0.0160335i
$495$		0			0
$496$	−70.8491			−0.142841
$497$	−722.895	−	234.883i	−1.45452	−	0.472602i
$498$	−67.6190	+	49.1281i	−0.135781	+	0.0986508i
$499$	376.446	+	273.504i	0.754401	+	0.548105i	0.897188	−	0.441649i	$-0.145606\pi$
$499$	376.446	+	273.504i	0.754401	+	0.548105i	−0.142787	+	0.989753i	$0.545606\pi$
$500$		0			0
$501$	−324.574	+	105.461i	−0.647853	+	0.210500i
$502$	4.75507	−	6.54479i	0.00947225	−	0.0130374i
$503$	−270.059	−	371.704i	−0.536896	−	0.738974i	0.451265	−	0.892390i	$-0.350973\pi$
$503$	−270.059	−	371.704i	−0.536896	−	0.738974i	−0.988162	+	0.153415i	$0.950973\pi$
$504$	−118.464	+	364.595i	−0.235048	+	0.723402i
$505$		0			0
$506$	−17.5329	−	13.4363i	−0.0346500	−	0.0265539i
$507$	−195.356			−0.385317
$508$	−621.649	−	201.986i	−1.22372	−	0.397610i
$509$	194.705	−	141.462i	0.382525	−	0.277920i	−0.379861	−	0.925044i	$-0.624028\pi$
$509$	194.705	−	141.462i	0.382525	−	0.277920i	0.762385	+	0.647123i	$0.224028\pi$
$510$		0			0
$511$	−316.602	−	974.400i	−0.619573	−	1.90685i
$512$	−479.078	+	155.662i	−0.935699	+	0.304027i
$513$	−27.1024	+	37.3032i	−0.0528311	+	0.0727158i
$514$	−172.221	−	237.042i	−0.335061	−	0.461172i
$515$		0			0
$516$			110.662i			0.214461i
$517$	−287.207	+	85.2675i	−0.555525	+	0.164928i
$518$	291.246			0.562251
$519$	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	$0.466448\pi$
$522$	−45.2492	−	139.263i	−0.0866843	−	0.266787i
$523$	353.526	−	114.868i	0.675959	−	0.219632i	0.0491334	−	0.998792i	$-0.484354\pi$
$523$	353.526	−	114.868i	0.675959	−	0.219632i	0.626825	+	0.779160i	$0.284354\pi$
$524$	−289.665	+	398.689i	−0.552795	+	0.760857i
$525$		0			0
$526$	9.57857	−	29.4798i	0.0182102	−	0.0560452i
$527$		−	108.881i		−	0.206606i
$528$	−85.7001	−	124.529i	−0.162311	−	0.235851i
$529$	−521.361			−0.985559
$530$		0			0
$531$	−13.0238	+	9.46234i	−0.0245269	+	0.0178199i
$532$	58.0132	+	42.1490i	0.109047	+	0.0792275i
$533$	−113.992	−	350.831i	−0.213868	−	0.658219i
$534$	117.738	−	38.2554i	0.220483	−	0.0716393i
$535$		0			0
$536$	−122.832	−	169.064i	−0.229164	−	0.315417i
$537$	−93.5025	+	287.771i	−0.174120	+	0.535887i
$538$		−	297.878i		−	0.553676i
$539$	−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	$0.619923\pi$
$542$	−136.400	+	99.1005i	−0.251661	+	0.182842i
$543$	43.4934	+	31.5998i	0.0800984	+	0.0581949i
$544$	−136.671	−	420.630i	−0.251233	−	0.773217i
$545$		0			0
$546$	−30.9017	+	42.5325i	−0.0565965	+	0.0778984i
$547$	436.380	+	600.625i	0.797769	+	1.09804i	0.993097	+	0.117297i	$0.0374230\pi$
$547$	436.380	+	600.625i	0.797769	+	1.09804i	−0.195328	+	0.980738i	$0.562577\pi$
$548$	−17.4433	+	53.6850i	−0.0318309	+	0.0979653i
$549$			160.333i			0.292045i
$550$		0			0
$551$	−58.9443			−0.106977
$552$	−19.7214	−	6.40786i	−0.0357271	−	0.0116084i
$553$	31.7082	−	23.0374i	0.0573385	−	0.0416589i
$554$	−180.036	−	130.804i	−0.324975	−	0.236108i
$555$		0			0
$556$	747.807	−	242.977i	1.34498	−	0.437010i
$557$	441.323	−	607.429i	0.792322	−	1.09054i	−0.201494	−	0.979490i	$-0.564579\pi$
$557$	441.323	−	607.429i	0.792322	−	1.09054i	0.993815	−	0.111047i	$-0.0354205\pi$
$558$	−21.5724	−	29.6918i	−0.0386601	−	0.0532111i
$559$	37.4671	−	115.312i	0.0670252	−	0.206282i
$560$		0			0
$561$	191.378	−	131.704i	0.341137	−	0.234767i
$562$	−94.0507			−0.167350
$563$	991.673	+	322.214i	1.76141	+	0.572316i	0.997345	−	0.0728240i	$-0.0232011\pi$
$563$	991.673	+	322.214i	1.76141	+	0.572316i	0.764064	+	0.645140i	$0.223201\pi$
$564$	−105.729	+	76.8170i	−0.187464	+	0.136200i
$565$		0			0
$566$	94.7214	+	291.522i	0.167352	+	0.515057i
$567$	313.358	−	101.816i	0.552659	−	0.179570i
$568$	243.530	−	335.190i	0.428750	−	0.590123i
$569$	−136.967	−	188.518i	−0.240714	−	0.331315i	0.671518	−	0.740988i	$-0.265643\pi$
$569$	−136.967	−	188.518i	−0.240714	−	0.331315i	−0.912232	+	0.409673i	$0.865643\pi$
$570$		0			0
$571$		−	196.324i		−	0.343825i	−0.985112	−	0.171912i	$-0.945005\pi$
$571$		−	196.324i		−	0.343825i	0.985112	−	0.171912i	$-0.0549946\pi$
$572$	57.1478	+	192.491i	0.0999088	+	0.336523i
$573$	−165.564			−0.288943
$574$	482.877	+	156.896i	0.841250	+	0.273339i
$575$		0			0
$576$	107.556	+	78.1438i	0.186729	+	0.135666i
$577$	−43.9884	−	135.382i	−0.0762364	−	0.234631i	0.905675	−	0.423973i	$-0.139365\pi$
$577$	−43.9884	−	135.382i	−0.0762364	−	0.234631i	−0.981911	+	0.189341i	$0.939365\pi$
$578$	−38.3134	+	12.4488i	−0.0662862	+	0.0215377i
$579$	−23.7384	+	32.6730i	−0.0409989	+	0.0564301i
$580$		0			0
$581$	256.199	−	788.498i	0.440961	−	1.35714i
$582$		−	77.7223i		−	0.133544i
$583$	−76.6718	+	100.049i	−0.131513	+	0.171610i
$584$	558.464			0.956274
$585$		0			0
$586$	37.8998	−	27.5358i	0.0646754	−	0.0469894i
$587$	−193.847	−	140.838i	−0.330233	−	0.239929i	0.410296	−	0.911952i	$-0.365425\pi$
$587$	−193.847	−	140.838i	−0.330233	−	0.239929i	−0.740530	+	0.672024i	$0.765425\pi$
$588$	74.4259	+	229.059i	0.126575	+	0.389557i
$589$	−14.0507	+	4.56535i	−0.0238552	+	0.00775102i
$590$		0			0
$591$	229.098	+	315.327i	0.387645	+	0.533548i
$592$	123.684	−	380.660i	0.208925	−	0.643006i
$593$			598.782i			1.00975i	0.863192	+	0.504875i	$0.168462\pi$
$593$			598.782i			1.00975i	−0.863192	+	0.504875i	$0.831538\pi$
$594$	59.2173	−	167.553i	0.0996924	−	0.282076i
$595$		0			0
$596$	221.858	+	72.0860i	0.372245	+	0.120950i
$597$	198.416	−	144.158i	0.332356	−	0.241471i
$598$	8.54102	+	6.20541i	0.0142826	+	0.0103769i
$599$	93.8359	+	288.797i	0.156654	+	0.482132i	0.998325	−	0.0578592i	$-0.0184274\pi$
$599$	93.8359	+	288.797i	0.156654	+	0.482132i	−0.841670	+	0.539992i	$0.818427\pi$
$600$		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	$0.248583\pi$
$602$	98.0902	+	135.010i	0.162940	+	0.224268i
$603$	−84.3384	+	259.567i	−0.139865	+	0.430459i
$604$		−	349.036i		−	0.577874i
$605$		0			0
$606$	−113.131			−0.186685
$607$	769.237	+	249.940i	1.26728	+	0.411763i	0.864082	−	0.503351i	$-0.167900\pi$
$607$	769.237	+	249.940i	1.26728	+	0.411763i	0.403195	+	0.915114i	$0.367900\pi$
$608$	−48.5501	+	35.2737i	−0.0798522	+	0.0580160i
$609$	−316.525	−	229.969i	−0.519745	−	0.377617i
$610$		0			0
$611$	136.180	−	44.2477i	0.222881	−	0.0724185i
$612$	−221.138	+	304.371i	−0.361337	+	0.497338i
$613$	−701.597	−	965.666i	−1.14453	−	1.57531i	−0.756946	−	0.653478i	$-0.773309\pi$
$613$	−701.597	−	965.666i	−1.14453	−	1.57531i	−0.387585	−	0.921834i	$-0.626691\pi$
$614$	−80.0420	+	246.344i	−0.130362	+	0.401212i
$615$		0			0
$616$	−560.766	−	198.188i	−0.910334	−	0.321733i
$617$	−107.900			−0.174878			−0.0874390	−	0.996170i	$-0.527868\pi$
$617$	−107.900			−0.174878			−0.0874390	+	0.996170i	$0.527868\pi$
$618$	88.4346	+	28.7341i	0.143098	+	0.0464954i
$619$	457.719	−	332.552i	0.739449	−	0.537241i	−0.153089	−	0.988212i	$-0.548922\pi$
$619$	457.719	−	332.552i	0.739449	−	0.537241i	0.892539	+	0.450971i	$0.148922\pi$
$620$		0			0
$621$	18.9919	+	58.4510i	0.0305827	+	0.0941239i
$622$	383.643	−	124.653i	0.616790	−	0.200407i
$623$	−721.792	+	993.462i	−1.15857	+	1.59464i
$624$	42.4671	+	58.4510i	0.0680563	+	0.0936714i
$625$		0			0
$626$			240.768i			0.384614i
$627$	−25.0203	−	19.1742i	−0.0399048	−	0.0305809i
$628$	856.298			1.36353
$629$	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	$0.884378\pi$
$632$	6.60177	+	20.3182i	0.0104458	+	0.0321490i
$633$	129.263	−	42.0000i	0.204207	−	0.0663507i
$634$	220.755	−	303.843i	0.348193	−	0.479247i
$635$		0			0
$636$	−16.9911	+	52.2933i	−0.0267156	+	0.0822222i
$637$		−	263.883i		−	0.414259i
$638$	217.782	−	64.6564i	0.341351	−	0.101342i
$639$	−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	$0.505778\pi$
$642$	68.9058	+	50.0630i	0.107330	+	0.0779797i
$643$	−291.864	−	898.264i	−0.453909	−	1.39699i	−0.872411	−	0.488773i	$-0.837445\pi$
$643$	−291.864	−	898.264i	−0.453909	−	1.39699i	0.418502	−	0.908216i	$-0.362555\pi$
$644$	90.9017	−	29.5358i	0.141152	−	0.0458630i
$645$		0			0
$646$	−13.5333	−	18.6269i	−0.0209493	−	0.0288343i
$647$	301.400	−	927.614i	0.465843	−	1.43372i	−0.392077	−	0.919932i	$-0.628243\pi$
$647$	301.400	−	927.614i	0.465843	−	1.43372i	0.857920	−	0.513784i	$-0.171757\pi$
$648$			179.597i			0.277155i
$649$	−14.1591	−	20.5743i	−0.0218167	−	0.0317016i
$650$		0			0
$651$	−93.2624	−	30.3028i	−0.143260	−	0.0465481i
$652$	489.796	−	355.858i	0.751221	−	0.545794i
$653$	194.615	+	141.396i	0.298032	+	0.216533i	0.726744	−	0.686908i	$-0.241033\pi$
$653$	194.615	+	141.396i	0.298032	+	0.216533i	−0.428712	+	0.903441i	$0.641033\pi$
$654$	29.1892	+	89.8351i	0.0446318	+	0.137363i
$655$		0			0
$656$	410.128	−	564.493i	0.625195	−	0.860507i
$657$	−428.711	−	590.070i	−0.652528	−	0.898128i
$658$	−60.9017	+	187.436i	−0.0925558	+	0.284857i
$659$		−	937.713i		−	1.42293i	−0.702720	−	0.711467i	$-0.748031\pi$
$659$		−	937.713i		−	1.42293i	0.702720	−	0.711467i	$-0.251969\pi$
$660$		0			0
$661$	133.305			0.201672			0.100836	−	0.994903i	$-0.467848\pi$
$661$	133.305			0.201672			0.100836	+	0.994903i	$0.467848\pi$
$662$	144.335	+	46.8973i	0.218029	+	0.0708418i
$663$	−89.8278	+	65.2637i	−0.135487	+	0.0984370i
$664$	365.608	+	265.630i	0.550615	+	0.400045i
$665$		0			0
$666$	197.188	−	64.0704i	0.296079	−	0.0962018i
$667$	−46.1803	+	63.5618i	−0.0692359	+	0.0952950i
$668$	503.995	+	693.689i	0.754483	+	1.03846i
$669$	113.607	−	349.646i	0.169816	−	0.522639i
$670$		0			0
$671$	−248.666	−	6.35781i	−0.370590	−	0.00947513i
$672$	−398.328			−0.592750
$673$	−860.230	−	279.506i	−1.27820	−	0.415313i	−0.410256	−	0.911971i	$-0.634561\pi$
$673$	−860.230	−	279.506i	−1.27820	−	0.415313i	−0.867947	+	0.496657i	$0.834561\pi$
$674$	79.3090	−	57.6214i	0.117669	−	0.0854917i
$675$		0			0
$676$	151.673	+	466.801i	0.224368	+	0.690534i
$677$	−574.798	+	186.763i	−0.849037	+	0.275869i	−0.701043	−	0.713119i	$-0.747282\pi$
$677$	−574.798	+	186.763i	−0.849037	+	0.275869i	−0.147995	+	0.988988i	$0.547282\pi$
$678$	−5.01256	+	6.89920i	−0.00739316	+	0.0101758i
$679$	453.156	+	623.716i	0.667387	+	0.918580i
$680$		0			0
$681$			351.744i			0.516512i
$682$	46.9055	−	32.2800i	0.0687764	−	0.0473313i
$683$	−1261.32			−1.84673			−0.923367	−	0.383919i	$-0.874574\pi$
$683$	−1261.32			−1.84673			−0.923367	+	0.383919i	$0.874574\pi$
$684$	48.5501	+	15.7749i	0.0709797	+	0.0230627i
$685$		0			0
$686$	6.98684	+	5.07624i	0.0101849	+	0.00739977i
$687$	17.1703	+	52.8447i	0.0249931	+	0.0769210i
$688$	218.114	−	70.8695i	0.317026	−	0.103008i
$689$	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	$0.999258\pi$
$692$		−	172.732i		−	0.249612i
$693$	221.074	+	744.643i	0.319010	+	1.07452i
$694$	68.8603			0.0992224
$695$		0			0
$696$	172.533	−	125.352i	0.247892	−	0.180104i
$697$	867.516	+	630.287i	1.24464	+	0.904286i
$698$	−38.5774	−	118.729i	−0.0552685	−	0.170099i
$699$	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	$0.918231\pi$
$702$	−26.2461	+	80.7772i	−0.0373876	+	0.115067i
$703$		−	83.4619i		−	0.118722i
$704$	−125.461	+	163.713i	−0.178212	+	0.232548i
$705$		0			0
$706$	82.6722	+	26.8618i	0.117099	+	0.0380479i
$707$	907.866	−	659.603i	1.28411	−	0.932961i
$708$	−8.81404	−	6.40378i	−0.0124492	−	0.00904488i
$709$	−227.956	−	701.577i	−0.321518	−	0.989531i	−0.972988	−	0.230856i	$-0.925847\pi$
$709$	−227.956	−	701.577i	−0.321518	−	0.989531i	0.651470	−	0.758674i	$-0.274153\pi$
$710$		0			0
$711$	16.4001	−	22.5729i	0.0230663	−	0.0317481i
$712$	−393.438	−	541.521i	−0.552582	−	0.760563i
$713$	−6.08514	+	18.7282i	−0.00853457	+	0.0262667i
$714$		−	152.824i		−	0.214039i
$715$		0			0
$716$	760.222			1.06176
$717$	414.230	+	134.591i	0.577726	+	0.187715i
$718$	274.681	−	199.567i	0.382564	−	0.277949i
$719$	425.782	+	309.349i	0.592187	+	0.430249i	0.843097	−	0.537762i	$-0.180730\pi$
$719$	425.782	+	309.349i	0.592187	+	0.430249i	−0.250910	+	0.968010i	$0.580730\pi$
$720$		0			0
$721$	−877.214	+	285.024i	−1.21666	+	0.395318i
$722$	152.329	−	209.663i	0.210982	−	0.290392i
$723$	220.078	+	302.912i	0.304396	+	0.418965i
$724$	41.7395	−	128.461i	0.0576513	−	0.177432i
$725$		0			0
$726$	113.475	+	43.3983i	0.156302	+	0.0597772i
$727$	756.122			1.04006			0.520029	−	0.854149i	$-0.325921\pi$
$727$	756.122			1.04006			0.520029	+	0.854149i	$0.325921\pi$
$728$	270.344	+	87.8402i	0.371352	+	0.120660i
$729$	−33.9853	+	24.6918i	−0.0466191	+	0.0338707i
$730$		0			0
$731$	108.913	+	335.199i	0.148991	+	0.458548i
$732$	−103.197	+	33.5306i	−0.140979	+	0.0458068i
$733$	−250.381	+	344.620i	−0.341584	+	0.470149i	−0.944903	−	0.327350i	$-0.893844\pi$
$733$	−250.381	+	344.620i	−0.341584	+	0.470149i	0.603320	+	0.797500i	$0.293844\pi$
$734$	−140.426	−	193.279i	−0.191316	−	0.263323i
$735$		0			0
$736$			79.9888i			0.108680i
$737$	−399.228	−	141.096i	−0.541693	−	0.191447i
$738$	361.448			0.489767
$739$	184.618	+	59.9862i	0.249822	+	0.0811721i	0.431251	−	0.902232i	$-0.358072\pi$
$739$	184.618	+	59.9862i	0.249822	+	0.0811721i	−0.181429	+	0.983404i	$0.558072\pi$
$740$		0			0
$741$	12.1885	+	8.85544i	0.0164487	+	0.0119507i
$742$	25.6231	+	78.8597i	0.0345324	+	0.106280i
$743$	−211.584	+	68.7477i	−0.284769	+	0.0925272i	−0.447919	−	0.894074i	$-0.647835\pi$
$743$	−211.584	+	68.7477i	−0.284769	+	0.0925272i	0.163150	+	0.986601i	$0.447835\pi$
$744$	31.4183	−	43.2436i	0.0422289	−	0.0581231i
$745$		0			0
$746$	48.0763	−	147.964i	0.0644454	−	0.198343i
$747$		−	590.214i		−	0.790112i
$748$	−463.291	−	355.041i	−0.619373	−	0.474654i
$749$	−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	$-0.130733\pi$
$752$	219.116	+	159.197i	0.291378	+	0.211699i
$753$	−4.75507	−	14.6346i	−0.00631483	−	0.0194351i
$754$	−103.262	+	33.5520i	−0.136953	+	0.0444986i
$755$		0			0
$756$	451.976	+	622.091i	0.597851	+	0.822872i
$757$	−410.832	+	1264.41i	−0.542710	+	1.67029i	0.183663	+	0.982989i	$0.441205\pi$
$757$	−410.832	+	1264.41i	−0.542710	+	1.67029i	−0.726373	+	0.687301i	$0.758795\pi$
$758$			232.676i			0.306961i
$759$	−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	$0.450599\pi$
$762$	152.918	−	111.101i	0.200680	−	0.145802i
$763$	−758.020	−	550.734i	−0.993473	−	0.721801i
$764$	128.543	+	395.614i	0.168250	+	0.517820i
$765$		0			0
$766$	233.835	−	321.847i	0.305268	−	0.420165i
$767$	7.01626	+	9.65706i	0.00914767	+	0.0125907i
$768$	8.11397	−	24.9722i	0.0105651	−	0.0325159i
$769$		−	695.838i		−	0.904860i	−0.891800	−	0.452430i	$-0.850557\pi$
$769$		−	695.838i		−	0.904860i	0.891800	−	0.452430i	$-0.149443\pi$
$770$		0			0
$771$	−557.320			−0.722853
$772$	96.5023	+	31.3555i	0.125003	+	0.0406159i
$773$	67.1591	−	48.7939i	0.0868811	−	0.0631228i	−0.543497	−	0.839411i	$-0.682900\pi$
$773$	67.1591	−	48.7939i	0.0868811	−	0.0631228i	0.630378	+	0.776288i	$0.282900\pi$
$774$	96.1124	+	69.8298i	0.124176	+	0.0902193i
$775$		0			0
$776$	−399.668	+	129.860i	−0.515036	+	0.167345i
$777$	325.623	−	448.182i	0.419077	−	0.576810i
$778$	−143.716	−	197.808i	−0.184725	−	0.254252i
$779$	44.9615	−	138.377i	0.0577169	−	0.177634i
$780$		0			0
$781$	21.4571	−	839.225i	0.0274738	−	1.07455i
$782$	−30.6888			−0.0392440
$783$	−601.140	−	195.322i	−0.767739	−	0.249454i
$784$	403.811	−	293.386i	0.515065	−	0.374217i
$785$		0			0
$786$	−44.0373	−	135.533i	−0.0560271	−	0.172434i
$787$	−103.159	+	33.5185i	−0.131079	+	0.0425903i	−0.373822	−	0.927500i	$-0.621953\pi$
$787$	−103.159	+	33.5185i	−0.131079	+	0.0425903i	0.242743	+	0.970091i	$0.421953\pi$
$788$	575.601	−	792.246i	0.730458	−	1.00539i
$789$	−34.6556	−	47.6993i	−0.0439234	−	0.0604554i
$790$		0			0
$791$		−	84.5910i		−	0.106942i
$792$	−423.266	−	10.8219i	−0.534427	−	0.0136641i
$793$	118.885			0.149919
$794$	−79.7214	−	25.9030i	−0.100405	−	0.0326235i
$795$		0			0
$796$	−498.514	−	362.191i	−0.626273	−	0.455014i
$797$	308.596	+	949.759i	0.387196	+	1.19167i	0.934874	+	0.354979i	$0.115512\pi$
$797$	308.596	+	949.759i	0.387196	+	1.19167i	−0.547678	+	0.836689i	$0.684488\pi$
$798$	−19.7214	+	6.40786i	−0.0247135	+	0.00802990i
$799$	−244.656	+	336.740i	−0.306202	+	0.421451i
$800$		0			0
$801$	−270.141	+	831.409i	−0.337255	+	1.03796i
$802$			46.3500i			0.0577930i
$803$	932.162	−	641.505i	1.16085	−	0.798886i
$804$	−184.706			−0.229734
$805$		0			0
$806$	−22.0163	+	15.9958i	−0.0273155	+	0.0198458i
$807$	−458.387	−	333.038i	−0.568014	−	0.412686i
$808$	189.021	+	581.748i	0.233937	+	0.719985i
$809$	71.6823	−	23.2910i	0.0886060	−	0.0287898i	−0.264379	−	0.964419i	$-0.585167\pi$
$809$	71.6823	−	23.2910i	0.0886060	−	0.0287898i	0.352985	+	0.935629i	$0.385167\pi$
$810$		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	$-0.409605\pi$
$812$	−303.761	+	934.880i	−0.374090	+	1.15133i
$813$			320.696i			0.394460i
$814$	91.5499	+	308.368i	0.112469	+	0.378830i
$815$		0			0
$816$	−199.742	−	64.9000i	−0.244781	−	0.0795343i
$817$	38.6894	−	28.1095i	0.0473555	−	0.0344058i
$818$	−359.538	−	261.220i	−0.439533	−	0.319339i
$819$	−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	$0.925417\pi$
$822$	−9.59460	−	13.2058i	−0.0116723	−	0.0160655i
$823$	165.319	−	508.800i	0.200874	−	0.618227i	−0.798984	−	0.601353i	$-0.794629\pi$
$823$	165.319	−	508.800i	0.200874	−	0.618227i	0.999858	−	0.0168738i	$-0.00537135\pi$
$824$		−	502.763i		−	0.610149i
$825$		0			0
$826$	−16.4296			−0.0198905
$827$	−53.4969	−	17.3822i	−0.0646879	−	0.0210184i	0.276494	−	0.961016i	$-0.410827\pi$
$827$	−53.4969	−	17.3822i	−0.0646879	−	0.0210184i	−0.341182	+	0.939997i	$0.610827\pi$
$828$	55.0476	−	39.9944i	0.0664826	−	0.0483024i
$829$	660.320	+	479.751i	0.796526	+	0.578710i	0.909893	−	0.414843i	$-0.136164\pi$
$829$	660.320	+	479.751i	0.796526	+	0.578710i	−0.113367	+	0.993553i	$0.536164\pi$
$830$		0			0
$831$	−402.574	+	130.804i	−0.484445	+	0.157406i
$832$	57.9431	−	79.7518i	0.0696431	−	0.0958555i
$833$	450.877	+	620.579i	0.541269	+	0.744993i
$834$	−70.2631	+	216.248i	−0.0842483	+	0.259290i
$835$		0			0
$836$	−26.3911	+	74.6726i	−0.0315682	+	0.0893213i
$837$	−158.423			−0.189275
$838$	100.991	+	32.8141i	0.120515	+	0.0391576i
$839$	−49.8216	+	36.1975i	−0.0593821	+	0.0431436i	−0.617080	−	0.786900i	$-0.711685\pi$
$839$	−49.8216	+	36.1975i	−0.0593821	+	0.0431436i	0.557698	+	0.830044i	$0.311685\pi$
$840$		0			0
$841$	10.1913	+	31.3657i	0.0121181	+	0.0372958i
$842$	−410.036	+	133.229i	−0.486979	+	0.158229i
$843$	−105.152	+	144.729i	−0.124735	+	0.171683i
$844$	−200.717	−	276.264i	−0.237817	−	0.327327i
$845$		0			0
$846$			140.301i			0.165841i
$847$	−1163.66	+	313.344i	−1.37386	+	0.369945i
$848$	113.951			0.134376
$849$	554.508	+	180.171i	0.653131	+	0.212215i
$850$		0			0
$851$	−90.0000	−	65.3888i	−0.105758	−	0.0768376i
$852$	−113.163	−	348.280i	−0.132820	−	0.408779i
$853$	−1347.24	+	437.746i	−1.57942	+	0.513184i	−0.961907	−	0.273379i	$-0.911859\pi$
$853$	−1347.24	+	437.746i	−1.57942	+	0.513184i	−0.617511	+	0.786562i	$0.711859\pi$
$854$	−96.1803	+	132.381i	−0.112623	+	0.155013i
$855$		0			0
$856$	142.307	−	437.977i	0.166247	−	0.511656i
$857$		−	1249.64i		−	1.45815i	−0.684432	−	0.729077i	$-0.739950\pi$
$857$		−	1249.64i		−	1.45815i	0.684432	−	0.729077i	$-0.260050\pi$
$858$	−54.7465	−	19.3487i	−0.0638071	−	0.0225509i
$859$	−345.229			−0.401896			−0.200948	−	0.979602i	$-0.564402\pi$
$859$	−345.229			−0.401896			−0.200948	+	0.979602i	$0.564402\pi$
$860$		0			0
$861$	781.312	−	567.656i	0.907447	−	0.659299i
$862$	102.474	+	74.4518i	0.118879	+	0.0863710i
$863$	125.242	+	385.456i	0.145124	+	0.446647i	0.997027	−	0.0770535i	$-0.0245512\pi$
$863$	125.242	+	385.456i	0.145124	+	0.446647i	−0.851903	+	0.523700i	$0.824551\pi$
$864$	−612.021	+	198.858i	−0.708358	+	0.230159i
$865$		0			0
$866$	265.045	+	364.804i	0.306057	+	0.421251i
$867$	−23.6790	+	72.8765i	−0.0273114	+	0.0840560i
$868$			246.377i			0.283844i
$869$	34.3588	+	26.3307i	0.0395383	+	0.0303000i
$870$		0			0
$871$	192.467	+	62.5364i	0.220973	+	0.0717983i
$872$	413.185	−	300.197i	0.473836	−	0.344262i
$873$	444.019	+	322.599i	0.508613	+	0.369529i
$874$	1.28677	+	3.96027i	0.00147228	+	0.00453121i
$875$		0			0
$876$	290.136	−	399.338i	0.331206	−	0.455866i
$877$	−209.069	−	287.759i	−0.238391	−	0.328117i	0.673012	−	0.739631i	$-0.265000\pi$
$877$	−209.069	−	287.759i	−0.238391	−	0.328117i	−0.911403	+	0.411514i	$0.865000\pi$
$878$	−151.946	+	467.642i	−0.173059	+	0.532622i
$879$		−	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	$0.667161\pi$
$882$	245.907	+	79.9001i	0.278806	+	0.0905897i
$883$	674.512	−	490.062i	0.763887	−	0.554996i	−0.136213	−	0.990680i	$-0.543493\pi$
$883$	674.512	−	490.062i	0.763887	−	0.554996i	0.900100	+	0.435683i	$0.143493\pi$
$884$	225.689	+	163.973i	0.255304	+	0.185489i
$885$		0			0
$886$	−179.177	+	58.2180i	−0.202231	+	0.0657088i
$887$	−54.3406	+	74.7934i	−0.0612633	+	0.0843217i	−0.838549	−	0.544826i	$-0.816596\pi$
$887$	−54.3406	+	74.7934i	−0.0612633	+	0.0843217i	0.777286	+	0.629147i	$0.216596\pi$
$888$	177.492	+	244.297i	0.199879	+	0.275109i
$889$	−579.384	+	1783.16i	−0.651725	+	2.00580i
$890$		0			0
$891$	206.302	+	299.774i	0.231540	+	0.336447i
$892$	−923.680			−1.03552
$893$	53.7132	+	17.4525i	0.0601492	+	0.0195437i
$894$	−54.5743	+	39.6505i	−0.0610451	+	0.0443518i
$895$		0			0
$896$	398.204	+	1225.54i	0.444424	+	1.36780i
$897$	19.0983	−	6.20541i	0.0212913	−	0.00691796i
$898$	171.846	−	236.526i	0.191365	−	0.263392i
$899$	−119.039	−	163.844i	−0.132413	−	0.182251i
$900$		0			0
$901$			175.121i			0.194363i
$902$	−14.3328	+	560.583i	−0.0158900	+	0.621489i
$903$	317.426			0.351524
$904$	43.8525	+	14.2486i	0.0485095	+	0.0157617i
$905$		0			0
$906$	81.6563	+	59.3268i	0.0901284	+	0.0654821i
$907$	454.784	+	1399.68i	0.501415	+	1.54320i	0.806715	+	0.590941i	$0.201243\pi$
$907$	454.784	+	1399.68i	0.501415	+	1.54320i	−0.305299	+	0.952256i	$0.598757\pi$
$908$	840.491	−	273.092i	0.925651	−	0.300762i
$909$	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	$0.0692237\pi$
$912$			28.4971i			0.0312468i
$913$	915.384	+	23.4043i	1.00261	+	0.0256345i
$914$	−185.795			−0.203277
$915$		0			0
$916$	112.941	−	82.0566i	0.123298	−	0.0895814i
$917$	1143.61	+	830.884i	1.24713	+	0.906089i
$918$	−76.2945	−	234.810i	−0.0831095	−	0.255785i
$919$	−1636.12	+	531.609i	−1.78033	+	0.578465i	−0.998960	−	0.0456019i	$-0.985479\pi$
$919$	−1636.12	+	531.609i	−1.78033	+	0.578465i	−0.781371	+	0.624066i	$0.785479\pi$
$920$		0			0
$921$	289.595	+	398.593i	0.314435	+	0.432783i
$922$	100.195	−	308.368i	0.108671	−	0.334455i
$923$			401.228i			0.434700i
$924$	−433.050	+	298.021i	−0.468668	+	0.322533i
$925$		0			0
$926$	−50.5322	−	16.4189i	−0.0545704	−	0.0177310i
$927$	−531.217	+	385.952i	−0.573049	+	0.416345i
$928$	−665.535	−	483.539i	−0.717171	−	0.521055i
$929$	288.957	+	889.317i	0.311040	+	0.957284i	0.977354	+	0.211612i	$0.0678714\pi$
$929$	288.957	+	889.317i	0.311040	+	0.957284i	−0.666313	+	0.745672i	$0.732129\pi$
$930$		0			0
$931$	61.1782	−	84.2046i	0.0657123	−	0.0904453i
$932$	−471.322	−	648.720i	−0.505711	−	0.696051i
$933$	237.105	−	729.733i	0.254131	−	0.782136i
$934$		−	8.07520i		−	0.00864583i
$935$		0			0
$936$	202.361			0.216197
$937$	853.544	+	277.333i	0.910933	+	0.295980i	0.726742	−	0.686910i	$-0.241033\pi$
$937$	853.544	+	277.333i	0.910933	+	0.295980i	0.184191	+	0.982890i	$0.441033\pi$
$938$	−225.344	+	163.722i	−0.240239	+	0.174544i
$939$	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	$0.321345\pi$
$942$	−145.548	+	200.329i	−0.154509	+	0.212664i
$943$	−113.992	−	156.896i	−0.120882	−	0.166380i
$944$	−6.97716	+	21.4735i	−0.00739106	+	0.0227473i
$945$		0			0
$946$	−112.113	+	146.295i	−0.118512	+	0.154646i
$947$	−1781.44			−1.88114			−0.940570	−	0.339600i	$-0.889708\pi$
$947$	−1781.44			−1.88114			−0.940570	+	0.339600i	$0.889708\pi$
$948$	17.9586	+	5.83511i	0.0189437	+	0.00615518i
$949$	−437.533	+	317.886i	−0.461046	+	0.334970i
$950$		0			0
$951$	−220.755	−	679.413i	−0.232129	−	0.714419i
$952$	−785.861	+	255.342i	−0.825484	+	0.268216i
$953$	−472.394	+	650.194i	−0.495691	+	0.682260i	−0.981425	−	0.191847i	$-0.938552\pi$
$953$	−472.394	+	650.194i	−0.495691	+	0.682260i	0.485734	+	0.874107i	$0.338552\pi$
$954$	34.6962	+	47.7553i	0.0363692	+	0.0500579i
$955$		0			0
$956$		−	1094.30i		−	1.14466i
$957$	143.992	−	407.420i	0.150462	−	0.425726i
$958$	−416.760			−0.435031
$959$	153.992	+	50.0350i	0.160575	+	0.0521741i
$960$		0			0
$961$	736.400	+	535.026i	0.766285	+	0.556738i
$962$	−47.5078	−	146.214i	−0.0493844	−	0.151989i
$963$	−572.008	+	185.857i	−0.593986	+	0.192998i
$964$	552.938	−	761.054i	0.573587	−	0.789475i
$965$		0			0
$966$	−8.54102	+	26.2866i	−0.00884164	+	0.0272118i
$967$		−	915.454i		−	0.946695i	−0.880876	−	0.473347i	$-0.843046\pi$
$967$		−	915.454i		−	0.946695i	0.880876	−	0.473347i	$-0.156954\pi$
$968$	33.5683	−	656.030i	0.0346780	−	0.677716i
$969$	−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	$0.423932\pi$
$972$	690.577	+	501.733i	0.710470	+	0.516187i
$973$	−696.964	−	2145.04i	−0.716305	−	2.20456i
$974$	−435.902	+	141.633i	−0.447538	+	0.145414i
$975$		0			0
$976$	132.177	+	181.926i	0.135427	+	0.186400i
$977$	−59.1165	+	181.942i	−0.0605082	+	0.186225i	−0.976742	−	0.214420i	$-0.931214\pi$
$977$	−59.1165	+	181.942i	−0.0605082	+	0.186225i	0.916233	+	0.400645i	$0.131214\pi$
$978$			175.073i			0.179011i
$979$	−1278.75	−	451.941i	−1.30618	−	0.461635i
$980$		0			0
$981$	−634.373	−	206.120i	−0.646659	−	0.210112i
$982$	−256.297	+	186.211i	−0.260995	+	0.189624i
$983$	772.503	+	561.257i	0.785863	+	0.570963i	0.906733	−	0.421705i	$-0.138568\pi$
$983$	772.503	+	561.257i	0.785863	+	0.570963i	−0.120870	+	0.992668i	$0.538568\pi$
$984$	162.672	+	500.654i	0.165317	+	0.508794i
$985$		0			0
$986$	185.517	−	255.342i	0.188151	−	0.258967i
$987$	220.344	+	303.278i	0.223247	+	0.307273i
$988$	11.6970	−	35.9996i	0.0118390	−	0.0364368i
$989$		−	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	$0.682673\pi$
$992$	−196.096	−	63.7156i	−0.197678	−	0.0642294i
$993$	233.539	−	169.676i	0.235185	−	0.170872i
$994$	−446.774	−	324.600i	−0.449471	−	0.326560i
$995$		0			0
$996$	379.886	−	123.432i	0.381411	−	0.123928i
$997$	−283.439	+	390.120i	−0.284292	+	0.391294i	−0.927150	−	0.374692i	$-0.877749\pi$
$997$	−283.439	+	390.120i	−0.284292	+	0.391294i	0.642858	+	0.765986i	$0.277749\pi$
$998$	198.712	+	273.504i	0.199111	+	0.274052i
$999$	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.x.e.101.1		4
5.2	odd	4		275.3.q.d.24.1		8
5.3	odd	4		275.3.q.d.24.2		8
5.4	even	2		11.3.d.a.2.1	✓	4
11.6	odd	10	inner	275.3.x.e.226.1		4
15.14	odd	2		99.3.k.a.46.1		4
20.19	odd	2		176.3.n.a.145.1		4
55.4	even	10		121.3.b.b.120.2		4
55.9	even	10		121.3.d.a.118.1		4
55.14	even	10		121.3.d.c.40.1		4
55.17	even	20		275.3.q.d.149.2		8
55.19	odd	10		121.3.d.a.40.1		4
55.24	odd	10		121.3.d.c.118.1		4
55.28	even	20		275.3.q.d.149.1		8
55.29	odd	10		121.3.b.b.120.3		4
55.39	odd	10		11.3.d.a.6.1	yes	4
55.49	even	10		121.3.d.d.94.1		4
55.54	odd	2		121.3.d.d.112.1		4
165.29	even	10		1089.3.c.e.604.2		4
165.59	odd	10		1089.3.c.e.604.3		4
165.149	even	10		99.3.k.a.28.1		4
220.39	even	10		176.3.n.a.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	5.4	even	2
11.3.d.a.6.1	yes	4	55.39	odd	10
99.3.k.a.28.1		4	165.149	even	10
99.3.k.a.46.1		4	15.14	odd	2
121.3.b.b.120.2		4	55.4	even	10
121.3.b.b.120.3		4	55.29	odd	10
121.3.d.a.40.1		4	55.19	odd	10
121.3.d.a.118.1		4	55.9	even	10
121.3.d.c.40.1		4	55.14	even	10
121.3.d.c.118.1		4	55.24	odd	10
121.3.d.d.94.1		4	55.49	even	10
121.3.d.d.112.1		4	55.54	odd	2
176.3.n.a.17.1		4	220.39	even	10
176.3.n.a.145.1		4	20.19	odd	2
275.3.q.d.24.1		8	5.2	odd	4
275.3.q.d.24.2		8	5.3	odd	4
275.3.q.d.149.1		8	55.28	even	20
275.3.q.d.149.2		8	55.17	even	20
275.3.x.e.101.1		4	1.1	even	1	trivial
275.3.x.e.226.1		4	11.6	odd	10	inner
1089.3.c.e.604.2		4	165.29	even	10
1089.3.c.e.604.3		4	165.59	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 + 0.224514i) q^{2} +(1.11803 - 0.812299i) q^{3} +(-2.80902 - 2.04087i) q^{4} +(0.954915 - 0.310271i) q^{6} +(-5.85410 + 8.05748i) q^{7} +(-3.19098 - 4.39201i) q^{8} +(-2.19098 + 6.74315i) q^{9} +(-10.3713 - 3.66547i) q^{11} -4.79837 q^{12} +(5.00000 + 1.62460i) q^{13} +(-5.85410 + 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-14.5344 + 4.72253i) q^{17} +(-3.02786 + 4.16750i) q^{18} +(1.21885 + 1.67760i) q^{19} +13.7638i q^{21} +(-6.34346 - 4.86128i) q^{22} +2.76393 q^{23} +(-7.13525 - 2.31838i) q^{24} +(3.09017 + 2.24514i) q^{26} +(6.87132 + 21.1478i) q^{27} +(32.8885 - 10.6861i) q^{28} +(-16.7082 + 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} +28.9402i q^{32} +(-14.5729 + 4.32650i) q^{33} -11.1033 q^{34} +(19.9164 - 14.4701i) q^{36} +(-32.5623 - 23.6579i) q^{37} +(0.465558 + 1.43284i) q^{38} +(6.90983 - 2.24514i) q^{39} +(-41.2426 - 56.7656i) q^{41} +(-3.09017 + 9.51057i) q^{42} -23.0624i q^{43} +(21.6525 + 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(22.0344 - 16.0090i) q^{47} +(11.1180 + 8.07772i) q^{48} +(-15.5106 - 47.7369i) q^{49} +(-12.4139 + 17.0863i) q^{51} +(-10.7295 - 14.7679i) q^{52} +(3.54102 - 10.8981i) q^{53} +16.1554i q^{54} +54.0689 q^{56} +(2.72542 + 0.885544i) q^{57} +(-16.7082 + 12.1392i) q^{58} +(1.83688 + 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-3.04257 + 4.18774i) q^{62} +(-41.5066 - 57.1289i) q^{63} +(5.79431 - 17.8330i) q^{64} +(-11.0410 - 0.282294i) q^{66} +38.4934 q^{67} +(50.4656 + 16.3973i) q^{68} +(3.09017 - 2.24514i) q^{69} +(23.5836 + 72.5828i) q^{71} +(36.6074 - 11.8945i) q^{72} +(-60.4656 + 83.2237i) q^{73} +(-17.1885 - 23.6579i) q^{74} -7.19991i q^{76} +(90.2492 - 62.1087i) q^{77} +5.27864 q^{78} +(-3.74265 - 1.21606i) q^{79} +(-26.7639 - 19.4451i) q^{81} +(-15.7533 - 48.4836i) q^{82} +(-79.1697 + 25.7238i) q^{83} +(28.0902 - 38.6628i) q^{84} +(5.17783 - 15.9357i) q^{86} +39.2833i q^{87} +(16.9959 + 57.2474i) q^{88} +123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(-7.76393 - 5.64083i) q^{92} +(3.04257 + 9.36408i) q^{93} +(18.8197 - 6.11488i) q^{94} +(23.5081 + 32.3562i) q^{96} +(23.9205 - 73.6196i) q^{97} -36.4677i q^{98} +(47.4402 - 61.9044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 9 q^{4} + 15 q^{6} - 10 q^{7} - 15 q^{8} - 11 q^{9} + q^{11} + 30 q^{12} + 20 q^{13} - 10 q^{14} + 19 q^{16} - 30 q^{18} + 25 q^{19} + 35 q^{22} + 20 q^{23} + 5 q^{24} - 10 q^{26} - 15 q^{27}+ \cdots + 31 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - 9 * q^4 + 15 * q^6 - 10 * q^7 - 15 * q^8 - 11 * q^9 + q^11 + 30 * q^12 + 20 * q^13 - 10 * q^14 + 19 * q^16 - 30 * q^18 + 25 * q^19 + 35 * q^22 + 20 * q^23 + 5 * q^24 - 10 * q^26 - 15 * q^27 + 60 * q^28 - 40 * q^29 - 58 * q^31 - 65 * q^33 + 130 * q^34 + 26 * q^36 - 90 * q^37 + 60 * q^38 + 50 * q^39 - 80 * q^41 + 10 * q^42 + 24 * q^44 + 30 * q^46 + 30 * q^47 + 40 * q^48 - 109 * q^49 - 195 * q^51 - 110 * q^52 - 120 * q^53 + 100 * q^56 - 45 * q^57 - 40 * q^58 + 23 * q^59 + 10 * q^61 - 200 * q^62 - 90 * q^63 - 149 * q^64 + 90 * q^66 + 230 * q^67 + 260 * q^68 - 10 * q^69 + 148 * q^71 + 95 * q^72 - 300 * q^73 - 270 * q^74 + 200 * q^77 + 200 * q^78 + 70 * q^79 - 116 * q^81 - 25 * q^82 - 225 * q^83 + 90 * q^84 + 175 * q^86 - 55 * q^88 + 122 * q^89 - 80 * q^91 - 40 * q^92 + 200 * q^93 + 120 * q^94 + 340 * q^96 + 165 * q^97 + 31 * q^99

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