LMFDB - Embedded newform 425.3.u.f.401.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,16,0,-16,0,0,16,0,-96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.16
Character	$\chi$	$=$	425.401
Dual form			425.3.u.f.301.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42932 - 3.45068i) q^{2} +(-2.42313 - 1.61908i) q^{3} +(-7.03579 - 7.03579i) q^{4} +(-9.05036 + 6.04726i) q^{6} +(-8.53763 - 1.69824i) q^{7} +(-20.5319 + 8.50460i) q^{8} +(-0.194021 - 0.468407i) q^{9} +(1.94402 + 2.90944i) q^{11} +(5.65711 + 28.4402i) q^{12} +(11.5538 - 11.5538i) q^{13} +(-18.0631 + 27.0333i) q^{14} +43.2043i q^{16} +(10.9247 - 13.0250i) q^{17} -1.89364 q^{18} +(-6.12848 + 14.7955i) q^{19} +(17.9382 + 17.9382i) q^{21} +(12.8182 - 2.54969i) q^{22} +(15.7311 - 10.5112i) q^{23} +(63.5212 + 12.6352i) q^{24} +(-23.3545 - 56.3826i) q^{26} +(-5.40518 + 27.1737i) q^{27} +(48.1206 + 72.0175i) q^{28} +(-0.161105 - 0.809929i) q^{29} +(-27.1672 + 40.6586i) q^{31} +(66.9565 + 27.7343i) q^{32} -10.1975i q^{33} +(-29.3301 - 56.3145i) q^{34} +(-1.93053 + 4.66071i) q^{36} +(-12.7024 - 8.48749i) q^{37} +(42.2948 + 42.2948i) q^{38} +(-46.7031 + 9.28982i) q^{39} +(7.15520 + 1.42326i) q^{41} +(87.5383 - 36.2596i) q^{42} +(-29.6179 - 71.5040i) q^{43} +(6.79245 - 34.1480i) q^{44} +(-13.7859 - 69.3066i) q^{46} +(-6.97451 + 6.97451i) q^{47} +(69.9515 - 104.690i) q^{48} +(24.7371 + 10.2464i) q^{49} +(-47.5606 + 13.8732i) q^{51} -162.581 q^{52} +(-20.2772 + 48.9536i) q^{53} +(86.0418 + 57.4913i) q^{54} +(189.737 - 37.7410i) q^{56} +(38.8052 - 25.9288i) q^{57} +(-3.02507 - 0.601725i) q^{58} +(-18.5654 + 7.69002i) q^{59} +(6.09486 - 30.6409i) q^{61} +(101.469 + 151.859i) q^{62} +(0.861009 + 4.32858i) q^{63} +(69.2039 - 69.2039i) q^{64} +(-35.1883 - 14.5755i) q^{66} -32.7490i q^{67} +(-168.505 + 14.7769i) q^{68} -55.1369 q^{69} +(47.1234 + 31.4868i) q^{71} +(7.96724 + 7.96724i) q^{72} +(-132.555 + 26.3668i) q^{73} +(-47.4434 + 31.7007i) q^{74} +(147.217 - 60.9791i) q^{76} +(-11.6564 - 28.1411i) q^{77} +(-34.6974 + 174.435i) q^{78} +(33.2990 + 49.8354i) q^{79} +(53.8674 - 53.8674i) q^{81} +(15.1382 - 22.6560i) q^{82} +(90.0810 + 37.3128i) q^{83} -252.419i q^{84} -289.071 q^{86} +(-0.920966 + 2.22341i) q^{87} +(-64.6582 - 43.2032i) q^{88} +(-65.9279 - 65.9279i) q^{89} +(-118.264 + 79.0212i) q^{91} +(-184.635 - 36.7262i) q^{92} +(131.659 - 54.5351i) q^{93} +(14.0980 + 34.0355i) q^{94} +(-117.340 - 175.612i) q^{96} +(3.04857 + 15.3262i) q^{97} +(70.7142 - 70.7142i) q^{98} +(0.985622 - 1.47509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{4} - 16 q^{6} + 16 q^{9} - 96 q^{11} + 16 q^{14} + 16 q^{19} + 224 q^{21} + 160 q^{24} + 288 q^{26} + 176 q^{29} + 48 q^{31} - 48 q^{34} - 144 q^{36} - 336 q^{41} + 48 q^{44} - 224 q^{46}+ \cdots + 1664 q^{99}+O(q^{100}) $ 128 * q + 16 * q^4 - 16 * q^6 + 16 * q^9 - 96 * q^11 + 16 * q^14 + 16 * q^19 + 224 * q^21 + 160 * q^24 + 288 * q^26 + 176 * q^29 + 48 * q^31 - 48 * q^34 - 144 * q^36 - 336 * q^41 + 48 * q^44 - 224 * q^46 + 48 * q^49 - 16 * q^51 - 512 * q^54 - 16 * q^56 - 272 * q^59 - 16 * q^61 - 688 * q^64 - 80 * q^66 - 448 * q^69 + 192 * q^71 - 704 * q^74 + 496 * q^76 - 304 * q^79 + 128 * q^81 - 2496 * q^86 + 256 * q^89 - 1632 * q^91 + 1296 * q^94 - 1728 * q^96 + 1664 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.42932	−	3.45068i	0.714659	−	1.72534i	0.0266401	−	0.999645i	$-0.491519\pi$
$2$	1.42932	−	3.45068i	0.714659	−	1.72534i	0.688018	−	0.725693i	$-0.258481\pi$
$3$	−2.42313	−	1.61908i	−0.807710	−	0.539695i	0.0817791	−	0.996650i	$-0.473940\pi$
$3$	−2.42313	−	1.61908i	−0.807710	−	0.539695i	−0.889489	+	0.456956i	$0.848940\pi$
$4$	−7.03579	−	7.03579i	−1.75895	−	1.75895i
$5$		0			0
$5$		0			0
$6$	−9.05036	+	6.04726i	−1.50839	+	1.00788i
$7$	−8.53763	−	1.69824i	−1.21966	−	0.242606i	−0.457037	−	0.889447i	$-0.651089\pi$
$7$	−8.53763	−	1.69824i	−1.21966	−	0.242606i	−0.762624	+	0.646842i	$0.776089\pi$
$8$	−20.5319	+	8.50460i	−2.56649	+	1.06308i
$9$	−0.194021	−	0.468407i	−0.0215579	−	0.0520453i
$10$		0			0
$11$	1.94402	+	2.90944i	0.176730	+	0.264494i	0.909250	−	0.416251i	$-0.136656\pi$
$11$	1.94402	+	2.90944i	0.176730	+	0.264494i	−0.732520	+	0.680745i	$0.761656\pi$
$12$	5.65711	+	28.4402i	0.471426	+	2.37002i
$13$	11.5538	−	11.5538i	0.888756	−	0.888756i	−0.105647	−	0.994404i	$-0.533691\pi$
$13$	11.5538	−	11.5538i	0.888756	−	0.888756i	0.994404	+	0.105647i	$0.0336914\pi$
$14$	−18.0631	+	27.0333i	−1.29022	+	1.93095i
$15$		0			0
$16$			43.2043i			2.70027i
$17$	10.9247	−	13.0250i	0.642631	−	0.766176i
$17$	10.9247	−	13.0250i	0.642631	−	0.766176i
$18$	−1.89364			−0.105202
$19$	−6.12848	+	14.7955i	−0.322551	+	0.778708i	0.676553	+	0.736394i	$0.263473\pi$
$19$	−6.12848	+	14.7955i	−0.322551	+	0.778708i	−0.999104	+	0.0423141i	$0.986527\pi$
$20$		0			0
$21$	17.9382	+	17.9382i	0.854200	+	0.854200i
$22$	12.8182	−	2.54969i	0.582644	−	0.115895i
$23$	15.7311	−	10.5112i	0.683959	−	0.457007i	−0.164424	−	0.986390i	$-0.552576\pi$
$23$	15.7311	−	10.5112i	0.683959	−	0.457007i	0.848383	+	0.529383i	$0.177576\pi$
$24$	63.5212	+	12.6352i	2.64672	+	0.526465i
$25$		0			0
$26$	−23.3545	−	56.3826i	−0.898248	−	2.16856i
$27$	−5.40518	+	27.1737i	−0.200192	+	1.00643i
$28$	48.1206	+	72.0175i	1.71859	+	2.57205i
$29$	−0.161105	−	0.809929i	−0.00555534	−	0.0279286i	0.977908	−	0.209035i	$-0.0670322\pi$
$29$	−0.161105	−	0.809929i	−0.00555534	−	0.0279286i	−0.983464	+	0.181106i	$0.942032\pi$
$30$		0			0
$31$	−27.1672	+	40.6586i	−0.876361	+	1.31157i	0.0729847	+	0.997333i	$0.476748\pi$
$31$	−27.1672	+	40.6586i	−0.876361	+	1.31157i	−0.949346	+	0.314234i	$0.898252\pi$
$32$	66.9565	+	27.7343i	2.09239	+	0.866697i
$33$		−	10.1975i		−	0.309015i
$34$	−29.3301	−	56.3145i	−0.862650	−	1.65631i
$35$		0			0
$36$	−1.93053	+	4.66071i	−0.0536258	+	0.129464i
$37$	−12.7024	−	8.48749i	−0.343309	−	0.229392i	0.371948	−	0.928254i	$-0.378690\pi$
$37$	−12.7024	−	8.48749i	−0.343309	−	0.229392i	−0.715256	+	0.698862i	$0.753690\pi$
$38$	42.2948	+	42.2948i	1.11302	+	1.11302i
$39$	−46.7031	+	9.28982i	−1.19752	+	0.238201i
$40$		0			0
$41$	7.15520	+	1.42326i	0.174517	+	0.0347136i	0.281575	−	0.959539i	$-0.409143\pi$
$41$	7.15520	+	1.42326i	0.174517	+	0.0347136i	−0.107058	+	0.994253i	$0.534143\pi$
$42$	87.5383	−	36.2596i	2.08425	−	0.863323i
$43$	−29.6179	−	71.5040i	−0.688789	−	1.66288i	−0.747206	−	0.664593i	$-0.768605\pi$
$43$	−29.6179	−	71.5040i	−0.688789	−	1.66288i	0.0584166	−	0.998292i	$-0.481395\pi$
$44$	6.79245	−	34.1480i	0.154374	−	0.776090i
$45$		0			0
$46$	−13.7859	−	69.3066i	−0.299694	−	1.50667i
$47$	−6.97451	+	6.97451i	−0.148394	+	0.148394i	−0.777400	−	0.629006i	$-0.783462\pi$
$47$	−6.97451	+	6.97451i	−0.148394	+	0.148394i	0.629006	+	0.777400i	$0.283462\pi$
$48$	69.9515	−	104.690i	1.45732	−	2.18104i
$49$	24.7371	+	10.2464i	0.504838	+	0.209111i
$50$		0			0
$51$	−47.5606	+	13.8732i	−0.932561	+	0.272023i
$52$	−162.581			−3.12655
$53$	−20.2772	+	48.9536i	−0.382590	+	0.923653i	0.608874	+	0.793267i	$0.291622\pi$
$53$	−20.2772	+	48.9536i	−0.382590	+	0.923653i	−0.991463	+	0.130386i	$0.958378\pi$
$54$	86.0418	+	57.4913i	1.59337	+	1.06465i
$55$		0			0
$56$	189.737	−	37.7410i	3.38816	−	0.673947i
$57$	38.8052	−	25.9288i	0.680793	−	0.454891i
$58$	−3.02507	−	0.601725i	−0.0521565	−	0.0103746i
$59$	−18.5654	+	7.69002i	−0.314667	+	0.130339i	−0.534427	−	0.845215i	$-0.679473\pi$
$59$	−18.5654	+	7.69002i	−0.314667	+	0.130339i	0.219760	+	0.975554i	$0.429473\pi$
$60$		0			0
$61$	6.09486	−	30.6409i	0.0999157	−	0.502310i	−0.898125	−	0.439741i	$-0.855070\pi$
$61$	6.09486	−	30.6409i	0.0999157	−	0.502310i	0.998041	−	0.0625698i	$-0.0199296\pi$
$62$	101.469	+	151.859i	1.63660	+	2.44934i
$63$	0.861009	+	4.32858i	0.0136668	+	0.0687077i
$64$	69.2039	−	69.2039i	1.08131	−	1.08131i
$65$		0			0
$66$	−35.1883	−	14.5755i	−0.533155	−	0.220840i
$67$		−	32.7490i		−	0.488791i	−0.969676	−	0.244396i	$-0.921410\pi$
$67$		−	32.7490i		−	0.488791i	0.969676	−	0.244396i	$-0.0785896\pi$
$68$	−168.505	+	14.7769i	−2.47802	+	0.217308i
$69$	−55.1369			−0.799085
$70$		0			0
$71$	47.1234	+	31.4868i	0.663710	+	0.443477i	0.841257	−	0.540636i	$-0.181816\pi$
$71$	47.1234	+	31.4868i	0.663710	+	0.443477i	−0.177547	+	0.984112i	$0.556816\pi$
$72$	7.96724	+	7.96724i	0.110656	+	0.110656i
$73$	−132.555	+	26.3668i	−1.81582	+	0.361189i	−0.981706	−	0.190403i	$-0.939020\pi$
$73$	−132.555	+	26.3668i	−1.81582	+	0.361189i	−0.834114	+	0.551592i	$0.814020\pi$
$74$	−47.4434	+	31.7007i	−0.641127	+	0.428387i
$75$		0			0
$76$	147.217	−	60.9791i	1.93706	−	0.802356i
$77$	−11.6564	−	28.1411i	−0.151382	−	0.365469i
$78$	−34.6974	+	174.435i	−0.444838	+	2.23635i
$79$	33.2990	+	49.8354i	0.421506	+	0.630828i	0.980075	−	0.198630i	$-0.0636493\pi$
$79$	33.2990	+	49.8354i	0.421506	+	0.630828i	−0.558569	+	0.829458i	$0.688649\pi$
$80$		0			0
$81$	53.8674	−	53.8674i	0.665029	−	0.665029i
$82$	15.1382	−	22.6560i	0.184613	−	0.276292i
$83$	90.0810	+	37.3128i	1.08531	+	0.449552i	0.852370	−	0.522939i	$-0.175164\pi$
$83$	90.0810	+	37.3128i	1.08531	+	0.449552i	0.232943	+	0.972490i	$0.425164\pi$
$84$		−	252.419i		−	3.00499i
$85$		0			0
$86$	−289.071			−3.36129
$87$	−0.920966	+	2.22341i	−0.0105858	+	0.0255564i
$88$	−64.6582	−	43.2032i	−0.734752	−	0.490946i
$89$	−65.9279	−	65.9279i	−0.740763	−	0.740763i	0.231962	−	0.972725i	$-0.425485\pi$
$89$	−65.9279	−	65.9279i	−0.740763	−	0.740763i	−0.972725	+	0.231962i	$0.925485\pi$
$90$		0			0
$91$	−118.264	+	79.0212i	−1.29960	+	0.868365i
$92$	−184.635	−	36.7262i	−2.00690	−	0.399197i
$93$	131.659	−	54.5351i	1.41569	−	0.586399i
$94$	14.0980	+	34.0355i	0.149979	+	0.362080i
$95$		0			0
$96$	−117.340	−	175.612i	−1.22229	−	1.82929i
$97$	3.04857	+	15.3262i	0.0314285	+	0.158002i	0.993313	−	0.115455i	$-0.0368328\pi$
$97$	3.04857	+	15.3262i	0.0314285	+	0.158002i	−0.961884	+	0.273457i	$0.911833\pi$
$98$	70.7142	−	70.7142i	0.721573	−	0.721573i
$99$	0.985622	−	1.47509i	0.00995578	−	0.0148999i
$100$		0			0
$101$		−	144.225i		−	1.42797i	−0.700161	−	0.713985i	$-0.746889\pi$
$101$		−	144.225i		−	1.42797i	0.700161	−	0.713985i	$-0.253111\pi$
$102$	−20.1073	+	183.945i	−0.197131	+	1.80339i
$103$	−92.8389			−0.901349			−0.450675	−	0.892688i	$-0.648816\pi$
$103$	−92.8389			−0.901349			−0.450675	+	0.892688i	$0.648816\pi$
$104$	−138.962	+	335.483i	−1.33617	+	3.22580i
$105$		0			0
$106$	139.940	+	139.940i	1.32019	+	1.32019i
$107$	−22.6903	+	4.51338i	−0.212059	+	0.0421811i	−0.299976	−	0.953947i	$-0.596979\pi$
$107$	−22.6903	+	4.51338i	−0.212059	+	0.0421811i	0.0879176	+	0.996128i	$0.471979\pi$
$108$	229.218	−	153.159i	2.12239	−	1.41813i
$109$	−88.5096	−	17.6056i	−0.812014	−	0.161520i	−0.228418	−	0.973563i	$-0.573355\pi$
$109$	−88.5096	−	17.6056i	−0.812014	−	0.161520i	−0.583597	+	0.812044i	$0.698355\pi$
$110$		0			0
$111$	17.0377	+	41.1326i	0.153493	+	0.370564i
$112$	73.3714	−	368.863i	0.655102	−	3.29342i
$113$	−23.4547	−	35.1025i	−0.207564	−	0.310642i	0.713052	−	0.701112i	$-0.247313\pi$
$113$	−23.4547	−	35.1025i	−0.207564	−	0.310642i	−0.920616	+	0.390470i	$0.872313\pi$
$114$	−34.0070	−	170.965i	−0.298307	−	1.49969i
$115$		0			0
$116$	−4.56500	+	6.83200i	−0.0393534	+	0.0588965i
$117$	−7.65359	−	3.17022i	−0.0654153	−	0.0270959i
$118$			75.0545i			0.636055i
$119$	−115.391	+	92.6497i	−0.969671	+	0.778569i
$120$		0			0
$121$	41.6191	−	100.477i	0.343959	−	0.830392i
$122$	−97.0204	−	64.8270i	−0.795250	−	0.531369i
$123$	−15.0336	−	15.0336i	−0.122224	−	0.122224i
$124$	477.208	−	94.9226i	3.84845	−	0.765505i
$125$		0			0
$126$	16.1672	+	3.21586i	0.128311	+	0.0255227i
$127$	−54.7476	+	22.6772i	−0.431084	+	0.178561i	−0.587665	−	0.809104i	$-0.699953\pi$
$127$	−54.7476	+	22.6772i	−0.431084	+	0.178561i	0.156581	+	0.987665i	$0.449953\pi$
$128$	−28.9487	−	69.8883i	−0.226162	−	0.546002i
$129$	−44.0029	+	221.218i	−0.341108	+	1.71487i
$130$		0			0
$131$	20.7486	+	104.310i	0.158386	+	0.796263i	0.975536	+	0.219838i	$0.0705527\pi$
$131$	20.7486	+	104.310i	0.158386	+	0.796263i	−0.817150	+	0.576425i	$0.804447\pi$
$132$	−71.7475	+	71.7475i	−0.543541	+	0.543541i
$133$	77.4489	−	115.911i	0.582323	−	0.871508i
$134$	−113.006	−	46.8087i	−0.843331	−	0.349319i
$135$		0			0
$136$	−113.533	+	360.339i	−0.834805	+	2.64955i
$137$	20.0630			0.146445			0.0732225	−	0.997316i	$-0.476672\pi$
$137$	20.0630			0.146445			0.0732225	+	0.997316i	$0.476672\pi$
$138$	−78.8081	+	190.260i	−0.571073	+	1.37869i
$139$	168.627	+	112.673i	1.21314	+	0.810596i	0.986561	−	0.163396i	$-0.0522448\pi$
$139$	168.627	+	112.673i	1.21314	+	0.810596i	0.226582	+	0.973992i	$0.427245\pi$
$140$		0			0
$141$	28.1925	−	5.60783i	0.199946	−	0.0397718i
$142$	176.005	−	117.603i	1.23947	−	0.828190i
$143$	56.0761	+	11.1542i	0.392141	+	0.0780016i
$144$	20.2372	−	8.38254i	0.140536	−	0.0582121i
$145$		0			0
$146$	−98.4796	+	495.090i	−0.674518	+	3.39103i
$147$	−43.3513	−	64.8798i	−0.294907	−	0.441359i
$148$	29.6554	+	149.088i	0.200375	+	1.00735i
$149$	−67.3690	+	67.3690i	−0.452141	+	0.452141i	−0.896065	−	0.443924i	$-0.853586\pi$
$149$	−67.3690	+	67.3690i	−0.452141	+	0.452141i	0.443924	+	0.896065i	$0.353586\pi$
$150$		0			0
$151$	−118.654	−	49.1479i	−0.785786	−	0.325483i	−0.0465378	−	0.998917i	$-0.514819\pi$
$151$	−118.654	−	49.1479i	−0.785786	−	0.325483i	−0.739248	+	0.673433i	$0.764819\pi$
$152$		−	355.899i		−	2.34144i
$153$	−8.22062	−	2.59011i	−0.0537296	−	0.0169288i
$154$	−113.767			−0.738745
$155$		0			0
$156$	393.955	+	263.232i	2.52535	+	1.68739i
$157$	34.9319	+	34.9319i	0.222496	+	0.222496i	0.809549	−	0.587053i	$-0.199712\pi$
$157$	34.9319	+	34.9319i	0.222496	+	0.222496i	−0.587053	+	0.809549i	$0.699712\pi$
$158$	219.561	−	43.6733i	1.38962	−	0.276414i
$159$	128.394	−	85.7904i	0.807512	−	0.539562i
$160$		0			0
$161$	−152.157	+	63.0253i	−0.945072	+	0.391461i
$162$	−108.885	−	262.872i	−0.672131	−	1.62267i
$163$	28.5906	−	143.735i	0.175403	−	0.881808i	−0.788394	−	0.615170i	$-0.789087\pi$
$163$	28.5906	−	143.735i	0.175403	−	0.881808i	0.963797	−	0.266638i	$-0.0859128\pi$
$164$	−40.3287	−	60.3562i	−0.245907	−	0.368026i
$165$		0			0
$166$	257.509	−	257.509i	1.55126	−	1.55126i
$167$	−31.0169	+	46.4201i	−0.185730	+	0.277965i	−0.912637	−	0.408772i	$-0.865957\pi$
$167$	−31.0169	+	46.4201i	−0.185730	+	0.277965i	0.726907	+	0.686736i	$0.240957\pi$
$168$	−520.863	−	215.749i	−3.10038	−	1.28422i
$169$		−	97.9822i		−	0.579776i
$170$		0			0
$171$	8.11935			0.0474816
$172$	−294.702	+	711.474i	−1.71338	+	4.13647i
$173$	−128.670	−	85.9747i	−0.743759	−	0.496964i	0.125026	−	0.992153i	$-0.460099\pi$
$173$	−128.670	−	85.9747i	−0.743759	−	0.496964i	−0.868785	+	0.495190i	$0.835099\pi$
$174$	6.35591	+	6.35591i	0.0365282	+	0.0365282i
$175$		0			0
$176$	−125.700	+	83.9903i	−0.714207	+	0.477218i
$177$	57.4371	+	11.4249i	0.324503	+	0.0645477i
$178$	−321.728	+	133.264i	−1.80746	+	0.748674i
$179$	−75.8446	−	183.105i	−0.423713	−	1.02293i	−0.981243	−	0.192776i	$-0.938251\pi$
$179$	−75.8446	−	183.105i	−0.423713	−	1.02293i	0.557530	−	0.830157i	$-0.311749\pi$
$180$		0			0
$181$	14.6367	+	21.9053i	0.0808655	+	0.121024i	0.869697	−	0.493585i	$-0.164314\pi$
$181$	14.6367	+	21.9053i	0.0808655	+	0.121024i	−0.788832	+	0.614609i	$0.789314\pi$
$182$	103.640	+	521.036i	0.569453	+	2.86283i
$183$	−64.3789	+	64.3789i	−0.351797	+	0.351797i
$184$	−233.596	+	349.601i	−1.26954	+	1.90000i
$185$		0			0
$186$		−	532.262i		−	2.86162i
$187$	59.1333	+	6.46394i	0.316221	+	0.0345665i
$188$	98.1424			0.522034
$189$	92.2948	−	222.819i	0.488332	−	1.17894i
$190$		0			0
$191$	−8.07395	−	8.07395i	−0.0422720	−	0.0422720i	0.685655	−	0.727927i	$-0.259516\pi$
$191$	−8.07395	−	8.07395i	−0.0422720	−	0.0422720i	−0.727927	+	0.685655i	$0.759516\pi$
$192$	−279.737	+	55.6431i	−1.45696	+	0.289808i
$193$	−44.4550	+	29.7039i	−0.230337	+	0.153906i	−0.665383	−	0.746502i	$-0.731732\pi$
$193$	−44.4550	+	29.7039i	−0.230337	+	0.153906i	0.435047	+	0.900408i	$0.356732\pi$
$194$	57.2431	+	11.3864i	0.295067	+	0.0586926i
$195$		0			0
$196$	−101.953	−	246.137i	−0.520169	−	1.25580i
$197$	41.8171	−	210.229i	0.212270	−	1.06715i	−0.716809	−	0.697269i	$-0.754398\pi$
$197$	41.8171	−	210.229i	0.212270	−	1.06715i	0.929079	−	0.369882i	$-0.120602\pi$
$198$	−3.68128	−	5.50943i	−0.0185923	−	0.0278254i
$199$	−13.6665	−	68.7059i	−0.0686757	−	0.345256i	0.931136	−	0.364673i	$-0.118819\pi$
$199$	−13.6665	−	68.7059i	−0.0686757	−	0.345256i	−0.999811	+	0.0194167i	$0.993819\pi$
$200$		0			0
$201$	−53.0234	+	79.3552i	−0.263798	+	0.394802i
$202$	−497.673	−	206.143i	−2.46373	−	1.02051i
$203$			7.18848i			0.0354112i
$204$	432.236	+	237.018i	2.11880	+	1.16185i
$205$		0			0
$206$	−132.696	+	320.357i	−0.644157	+	1.55513i
$207$	−7.97566	−	5.32916i	−0.0385298	−	0.0257448i
$208$	499.176	+	499.176i	2.39988	+	2.39988i
$209$	−54.9604	+	10.9323i	−0.262968	+	0.0523077i
$210$		0			0
$211$	91.8067	+	18.2615i	0.435103	+	0.0865473i	0.407782	−	0.913079i	$-0.366302\pi$
$211$	91.8067	+	18.2615i	0.435103	+	0.0865473i	0.0273209	+	0.999627i	$0.491302\pi$
$212$	487.094	−	201.761i	2.29761	−	0.951703i
$213$	−63.2063	−	152.594i	−0.296743	−	0.716402i
$214$	−16.8574	+	84.7479i	−0.0787729	+	0.396018i
$215$		0			0
$216$	−120.122	−	603.896i	−0.556122	−	2.79582i
$217$	300.992	−	300.992i	1.38706	−	1.38706i
$218$	−187.260	+	280.254i	−0.858989	+	1.28557i
$219$	363.888	+	150.727i	1.66159	+	0.688252i
$220$		0			0
$221$	−24.2660	−	276.711i	−0.109801	−	1.25209i
$222$	166.288			0.749043
$223$	125.735	−	303.552i	0.563836	−	1.36122i	−0.342841	−	0.939393i	$-0.611389\pi$
$223$	125.735	−	303.552i	0.563836	−	1.36122i	0.906677	−	0.421826i	$-0.138611\pi$
$224$	−524.551	−	350.494i	−2.34174	−	1.56470i
$225$		0			0
$226$	−154.652	+	30.7621i	−0.684299	+	0.136116i
$227$	−162.059	+	108.285i	−0.713918	+	0.477025i	−0.858726	−	0.512435i	$-0.828743\pi$
$227$	−162.059	+	108.285i	−0.713918	+	0.477025i	0.144808	+	0.989460i	$0.453743\pi$
$228$	−455.455	−	90.5957i	−1.99761	−	0.397349i
$229$	286.132	−	118.520i	1.24948	−	0.517553i	0.342817	−	0.939402i	$-0.388619\pi$
$229$	286.132	−	118.520i	1.24948	−	0.517553i	0.906666	+	0.421849i	$0.138619\pi$
$230$		0			0
$231$	−17.3178	+	87.0624i	−0.0749688	+	0.376894i
$232$	10.1959	+	15.2593i	0.0439480	+	0.0657728i
$233$	−13.7868	−	69.3111i	−0.0591709	−	0.297472i	0.939856	−	0.341570i	$-0.110959\pi$
$233$	−13.7868	−	69.3111i	−0.0591709	−	0.297472i	−0.999027	+	0.0440978i	$0.985959\pi$
$234$	−21.8788	+	21.8788i	−0.0934991	+	0.0934991i
$235$		0			0
$236$	184.727	+	76.5166i	0.782743	+	0.324223i
$237$		−	174.672i		−	0.737011i
$238$	154.774	+	530.603i	0.650311	+	2.22942i
$239$	−152.671			−0.638791			−0.319396	−	0.947621i	$-0.603480\pi$
$239$	−152.671			−0.638791			−0.319396	+	0.947621i	$0.603480\pi$
$240$		0			0
$241$	246.844	+	164.936i	1.02425	+	0.684381i	0.949804	−	0.312845i	$-0.101282\pi$
$241$	246.844	+	164.936i	1.02425	+	0.684381i	0.0744436	+	0.997225i	$0.476282\pi$
$242$	−287.228	−	287.228i	−1.18689	−	1.18689i
$243$	26.8194	−	5.33471i	0.110368	−	0.0219535i
$244$	−258.465	+	172.701i	−1.05928	+	0.707791i
$245$		0			0
$246$	−73.3639	+	30.3883i	−0.298227	+	0.123530i
$247$	100.137	+	241.752i	0.405412	+	0.978752i
$248$	212.010	−	1065.85i	0.854878	−	4.29776i
$249$	−157.866	−	236.263i	−0.633998	−	0.948846i
$250$		0			0
$251$	79.1736	−	79.1736i	0.315433	−	0.315433i	−0.531577	−	0.847010i	$-0.678400\pi$
$251$	79.1736	−	79.1736i	0.315433	−	0.315433i	0.847010	+	0.531577i	$0.178400\pi$
$252$	24.3972	−	36.5129i	0.0968141	−	0.144893i
$253$	61.1632	+	25.3346i	0.241752	+	0.100137i
$254$			221.329i			0.871375i
$255$		0			0
$256$	108.937			0.425537
$257$	50.1084	−	120.972i	0.194974	−	0.470710i	−0.795912	−	0.605413i	$-0.793008\pi$
$257$	50.1084	−	120.972i	0.194974	−	0.470710i	0.990886	+	0.134703i	$0.0430080\pi$
$258$	700.456	+	468.030i	2.71495	+	1.81407i
$259$	94.0349	+	94.0349i	0.363069	+	0.363069i
$260$		0			0
$261$	−0.348119	+	0.232606i	−0.00133379	+	0.000891210i
$262$	389.598	+	77.4958i	1.48701	+	0.295786i
$263$	−140.222	+	58.0817i	−0.533162	+	0.220843i	−0.632987	−	0.774162i	$-0.718172\pi$
$263$	−140.222	+	58.0817i	−0.533162	+	0.220843i	0.0998256	+	0.995005i	$0.468172\pi$
$264$	86.7256	+	209.374i	0.328506	+	0.793084i
$265$		0			0
$266$	−289.271	−	432.924i	−1.08748	−	1.62753i
$267$	53.0091	+	266.495i	0.198536	+	0.998107i
$268$	−230.415	+	230.415i	−0.859759	+	0.859759i
$269$	125.901	−	188.425i	0.468035	−	0.700464i	−0.520091	−	0.854111i	$-0.674102\pi$
$269$	125.901	−	188.425i	0.468035	−	0.700464i	0.988126	+	0.153647i	$0.0491020\pi$
$270$		0			0
$271$		−	410.506i		−	1.51478i	−0.652960	−	0.757392i	$-0.726473\pi$
$271$		−	410.506i		−	1.51478i	0.652960	−	0.757392i	$-0.273527\pi$
$272$	562.736	+	471.996i	2.06888	+	1.73528i
$273$	414.510			1.51835
$274$	28.6763	−	69.2308i	0.104658	−	0.252667i
$275$		0			0
$276$	387.932	+	387.932i	1.40555	+	1.40555i
$277$	−452.347	+	89.9775i	−1.63302	+	0.324828i	−0.924594	−	0.380954i	$-0.875596\pi$
$277$	−452.347	+	89.9775i	−1.63302	+	0.324828i	−0.708429	+	0.705782i	$0.750596\pi$
$278$	629.819	−	420.831i	2.26554	−	1.51378i
$279$	24.3158	+	4.83671i	0.0871533	+	0.0173359i
$280$		0			0
$281$	−162.874	−	393.212i	−0.579622	−	1.39933i	−0.893153	−	0.449754i	$-0.851512\pi$
$281$	−162.874	−	393.212i	−0.579622	−	1.39933i	0.313530	−	0.949578i	$-0.398488\pi$
$282$	20.9452	−	105.298i	0.0742736	−	0.373399i
$283$	−123.528	−	184.873i	−0.436494	−	0.653260i	0.546380	−	0.837537i	$-0.316005\pi$
$283$	−123.528	−	184.873i	−0.436494	−	0.653260i	−0.982874	+	0.184278i	$0.941005\pi$
$284$	−110.016	−	553.086i	−0.387379	−	1.94748i
$285$		0			0
$286$	118.640	−	177.558i	0.414826	−	0.620831i
$287$	−58.6714	−	24.3025i	−0.204430	−	0.0846777i
$288$		−	36.7440i		−	0.127583i
$289$	−50.3005	−	284.589i	−0.174050	−	0.984737i
$290$		0			0
$291$	17.4273	−	42.0732i	0.0598877	−	0.144582i
$292$	1118.14	+	747.117i	3.82925	+	2.55862i
$293$	−177.357	−	177.357i	−0.605315	−	0.605315i	0.336403	−	0.941718i	$-0.390789\pi$
$293$	−177.357	−	177.357i	−0.605315	−	0.605315i	−0.941718	+	0.336403i	$0.890789\pi$
$294$	−285.842	+	56.8575i	−0.972252	+	0.193393i
$295$		0			0
$296$	332.988	+	66.2354i	1.12496	+	0.223768i
$297$	−89.5679	+	37.1002i	−0.301575	+	0.124917i
$298$	136.177	+	328.760i	0.456970	+	1.10322i
$299$	60.3099	−	303.198i	0.201705	−	1.01404i
$300$		0			0
$301$	131.436	+	660.774i	0.436665	+	2.19526i
$302$	−339.187	+	339.187i	−1.12314	+	1.12314i
$303$	−233.512	+	349.476i	−0.770668	+	1.15339i
$304$	−639.228	−	264.777i	−2.10272	−	0.870977i
$305$		0			0
$306$	−20.6875	+	24.6646i	−0.0676062	+	0.0806034i
$307$	−405.125			−1.31963			−0.659813	−	0.751430i	$-0.729365\pi$
$307$	−405.125			−1.31963			−0.659813	+	0.751430i	$0.729365\pi$
$308$	−115.983	+	280.008i	−0.376568	+	0.909116i
$309$	224.961	+	150.314i	0.728029	+	0.486453i
$310$		0			0
$311$	324.561	−	64.5592i	1.04360	−	0.207586i	0.356614	−	0.934252i	$-0.383931\pi$
$311$	324.561	−	64.5592i	1.04360	−	0.207586i	0.686991	+	0.726666i	$0.258931\pi$
$312$	879.898	−	587.929i	2.82019	−	1.88439i
$313$	289.595	+	57.6040i	0.925223	+	0.184038i	0.634637	−	0.772811i	$-0.281150\pi$
$313$	289.595	+	57.6040i	0.925223	+	0.184038i	0.290586	+	0.956849i	$0.406150\pi$
$314$	170.467	−	70.6099i	0.542889	−	0.224872i
$315$		0			0
$316$	116.347	−	584.916i	0.368187	−	1.85100i
$317$	36.3595	+	54.4158i	0.114699	+	0.171659i	0.884377	−	0.466773i	$-0.154583\pi$
$317$	36.3595	+	54.4158i	0.114699	+	0.171659i	−0.769678	+	0.638432i	$0.779583\pi$
$318$	−112.519	−	565.669i	−0.353832	−	1.77883i
$319$	2.04325	−	2.04325i	0.00640517	−	0.00640517i
$320$		0			0
$321$	62.2891	+	25.8010i	0.194047	+	0.0803769i
$322$			615.126i			1.91033i
$323$	125.759	+	241.460i	0.389346	+	0.747553i
$324$	−757.999			−2.33950
$325$		0			0
$326$	−455.117	−	304.100i	−1.39606	−	0.932821i
$327$	185.965	+	185.965i	0.568701	+	0.568701i
$328$	−159.014	+	31.6299i	−0.484799	+	0.0964326i
$329$	71.3902	−	47.7014i	0.216991	−	0.144989i
$330$		0			0
$331$	−382.193	+	158.310i	−1.15466	+	0.478277i	−0.876095	−	0.482139i	$-0.839860\pi$
$331$	−382.193	+	158.310i	−1.15466	+	0.478277i	−0.278568	+	0.960416i	$0.589860\pi$
$332$	−371.267	−	896.317i	−1.11827	−	2.69975i
$333$	−1.51107	+	7.59666i	−0.00453775	+	0.0228128i
$334$	115.848	+	173.378i	0.346849	+	0.519097i
$335$		0			0
$336$	−775.009	+	775.009i	−2.30657	+	2.30657i
$337$	−222.500	+	332.995i	−0.660239	+	0.988117i	0.338647	+	0.940914i	$0.390031\pi$
$337$	−222.500	+	332.995i	−0.660239	+	0.988117i	−0.998885	+	0.0472035i	$0.984969\pi$
$338$	−338.105	−	140.048i	−1.00031	−	0.414342i
$339$			123.033i			0.362930i
$340$		0			0
$341$	−171.107			−0.501781
$342$	11.6051	−	28.0173i	0.0339331	−	0.0819218i
$343$	160.860	+	107.483i	0.468979	+	0.313362i
$344$	1216.23	+	1216.23i	3.53554	+	3.53554i
$345$		0			0
$346$	−480.581	+	321.114i	−1.38896	+	0.928076i
$347$	−300.399	−	59.7530i	−0.865702	−	0.172199i	−0.257788	−	0.966202i	$-0.582994\pi$
$347$	−300.399	−	59.7530i	−0.865702	−	0.172199i	−0.607914	+	0.794003i	$0.707994\pi$
$348$	22.1232	−	9.16372i	0.0635723	−	0.0263325i
$349$	57.6579	+	139.199i	0.165209	+	0.398850i	0.984704	−	0.174237i	$-0.0557458\pi$
$349$	57.6579	+	139.199i	0.165209	+	0.398850i	−0.819495	+	0.573087i	$0.805746\pi$
$350$		0			0
$351$	251.509	+	376.410i	0.716551	+	1.07239i
$352$	49.4739	+	248.722i	0.140551	+	0.706597i
$353$	−449.779	+	449.779i	−1.27416	+	1.27416i	−0.330276	+	0.943884i	$0.607142\pi$
$353$	−449.779	+	449.779i	−1.27416	+	1.27416i	−0.943884	+	0.330276i	$0.892858\pi$
$354$	121.520	−	181.867i	0.343276	−	0.513748i
$355$		0			0
$356$			927.710i			2.60593i
$357$	429.615	−	37.6748i	1.20340	−	0.105532i
$358$	−740.242			−2.06772
$359$	−118.700	+	286.568i	−0.330641	+	0.798239i	0.667900	+	0.744251i	$0.267193\pi$
$359$	−118.700	+	286.568i	−0.330641	+	0.798239i	−0.998542	+	0.0539879i	$0.982807\pi$
$360$		0			0
$361$	73.9183	+	73.9183i	0.204760	+	0.204760i
$362$	96.5085	−	19.1967i	0.266598	−	0.0530297i
$363$	−263.530	+	176.085i	−0.725978	+	0.485083i
$364$	1388.06	+	276.101i	3.81334	+	0.758520i
$365$		0			0
$366$	130.133	+	314.169i	0.355554	+	0.858384i
$367$	72.4876	−	364.420i	0.197514	−	0.992970i	−0.747081	−	0.664733i	$-0.768545\pi$
$367$	72.4876	−	364.420i	0.197514	−	0.992970i	0.944595	−	0.328237i	$-0.106455\pi$
$368$	454.128	+	679.650i	1.23404	+	1.84688i
$369$	−0.721592	−	3.62769i	−0.00195553	−	0.00983113i
$370$		0			0
$371$	256.255	−	383.512i	0.690713	−	1.03373i
$372$	−1310.03	−	542.630i	−3.52157	−	1.45868i
$373$			180.910i			0.485014i	0.970150	+	0.242507i	$0.0779698\pi$
$373$			180.910i			0.485014i	−0.970150	+	0.242507i	$0.922030\pi$
$374$	106.825	−	194.811i	0.285629	−	0.520885i
$375$		0			0
$376$	83.8846	−	202.515i	0.223097	−	0.538605i
$377$	−11.2192	−	7.49641i	−0.0297591	−	0.0198844i
$378$	−636.959	−	636.959i	−1.68508	−	1.68508i
$379$	−433.860	+	86.3002i	−1.14475	+	0.227705i	−0.730798	−	0.682594i	$-0.760852\pi$
$379$	−433.860	+	86.3002i	−1.14475	+	0.227705i	−0.413952	+	0.910299i	$0.635852\pi$
$380$		0			0
$381$	169.377	+	33.6912i	0.444559	+	0.0884283i
$382$	−39.4008	+	16.3204i	−0.103143	+	0.0427234i
$383$	−217.522	−	525.146i	−0.567944	−	1.37114i	−0.903285	−	0.429041i	$-0.858852\pi$
$383$	−217.522	−	525.146i	−0.567944	−	1.37114i	0.335341	−	0.942097i	$-0.391148\pi$
$384$	−43.0086	+	216.219i	−0.112002	+	0.563070i
$385$		0			0
$386$	38.9582	+	195.856i	0.100928	+	0.507399i
$387$	−27.7465	+	27.7465i	−0.0716965	+	0.0716965i
$388$	86.3828	−	129.281i	0.222636	−	0.333198i
$389$	548.703	+	227.280i	1.41055	+	0.584268i	0.952467	−	0.304642i	$-0.0985370\pi$
$389$	548.703	+	227.280i	1.41055	+	0.584268i	0.458081	+	0.888910i	$0.348537\pi$
$390$		0			0
$391$	34.9499	−	319.728i	0.0893860	−	0.817720i
$392$	−595.041			−1.51796
$393$	118.611	−	286.352i	0.301808	−	0.728630i
$394$	−665.662	−	444.781i	−1.68950	−	1.12889i
$395$		0			0
$396$	−17.3130	+	3.44378i	−0.0437198	+	0.00869641i
$397$	651.083	−	435.040i	1.64001	−	1.09582i	0.728059	−	0.685515i	$-0.240423\pi$
$397$	651.083	−	435.040i	1.64001	−	1.09582i	0.911949	−	0.410303i	$-0.134577\pi$
$398$	−256.616	−	51.0440i	−0.644763	−	0.128251i
$399$	−375.338	+	155.470i	−0.940696	+	0.389649i
$400$		0			0
$401$	0.0949249	−	0.477219i	0.000236720	−	0.00119007i	−0.980667	−	0.195685i	$-0.937307\pi$
$401$	0.0949249	−	0.477219i	0.000236720	−	0.00119007i	0.980903	+	0.194495i	$0.0623069\pi$
$402$	198.042	+	296.390i	0.492641	+	0.737290i
$403$	155.877	+	783.648i	0.386792	+	1.94454i
$404$	−1014.74	+	1014.74i	−2.51172	+	2.51172i
$405$		0			0
$406$	24.8051	+	10.2746i	0.0610963	+	0.0253069i
$407$		−	53.4568i		−	0.131344i
$408$	858.525	−	689.327i	2.10423	−	1.68953i
$409$	586.259			1.43340			0.716698	−	0.697383i	$-0.245652\pi$
$409$	586.259			1.43340			0.716698	+	0.697383i	$0.245652\pi$
$410$		0			0
$411$	−48.6152	−	32.4836i	−0.118285	−	0.0790356i
$412$	653.196	+	653.196i	1.58543	+	1.58543i
$413$	171.564	−	34.1261i	0.415408	−	0.0826299i
$414$	−29.7890	+	19.9044i	−0.0719540	+	0.0480781i
$415$		0			0
$416$	1094.04	−	453.167i	2.62991	−	1.08934i
$417$	−226.178	−	546.042i	−0.542393	−	1.30945i
$418$	−40.8320	+	205.276i	−0.0976842	+	0.491092i
$419$	81.6559	+	122.207i	0.194883	+	0.291663i	0.916022	−	0.401127i	$-0.131381\pi$
$419$	81.6559	+	122.207i	0.194883	+	0.291663i	−0.721140	+	0.692790i	$0.756381\pi$
$420$		0			0
$421$	−176.167	+	176.167i	−0.418450	+	0.418450i	−0.884669	−	0.466219i	$-0.845616\pi$
$421$	−176.167	+	176.167i	−0.418450	+	0.418450i	0.466219	+	0.884669i	$0.345616\pi$
$422$	194.235	−	290.694i	0.460273	−	0.688848i
$423$	4.62011	+	1.91371i	0.0109222	+	0.00452414i
$424$		−	1177.56i		−	2.77727i
$425$		0			0
$426$	−616.893			−1.44811
$427$	−104.071	+	251.250i	−0.243727	+	0.588409i
$428$	191.399	+	127.889i	0.447195	+	0.298806i
$429$	−117.820	−	117.820i	−0.274639	−	0.274639i
$430$		0			0
$431$	−1.20310	+	0.803884i	−0.00279141	+	0.00186516i	−0.556965	−	0.830536i	$-0.688034\pi$
$431$	−1.20310	+	0.803884i	−0.00279141	+	0.00186516i	0.554174	+	0.832401i	$0.313034\pi$
$432$	−1174.02	−	233.527i	−2.71764	−	0.540572i
$433$	120.467	−	49.8989i	0.278214	−	0.115240i	−0.239214	−	0.970967i	$-0.576890\pi$
$433$	120.467	−	49.8989i	0.278214	−	0.115240i	0.517428	+	0.855727i	$0.326890\pi$
$434$	−608.412	−	1468.84i	−1.40187	−	3.38442i
$435$		0			0
$436$	498.865	+	746.605i	1.14419	+	1.71240i
$437$	59.1099	+	297.166i	0.135263	+	0.680013i
$438$	1040.22	−	1040.22i	2.37494	−	2.37494i
$439$	100.179	−	149.928i	0.228197	−	0.341521i	−0.699647	−	0.714488i	$-0.746660\pi$
$439$	100.179	−	149.928i	0.228197	−	0.341521i	0.927845	+	0.372967i	$0.121660\pi$
$440$		0			0
$441$		−	13.5750i		−	0.0307824i
$442$	−989.524	−	311.774i	−2.23874	−	0.705371i
$443$	−444.888			−1.00426			−0.502131	−	0.864792i	$-0.667450\pi$
$443$	−444.888			−1.00426			−0.502131	+	0.864792i	$0.667450\pi$
$444$	169.527	−	409.274i	0.381817	−	0.921789i
$445$		0			0
$446$	−867.744	−	867.744i	−1.94561	−	1.94561i
$447$	272.320	−	54.1678i	0.609217	−	0.121181i
$448$	−708.362	+	473.312i	−1.58117	+	1.05650i
$449$	−371.143	−	73.8248i	−0.826598	−	0.164421i	−0.236376	−	0.971662i	$-0.575960\pi$
$449$	−371.143	−	73.8248i	−0.826598	−	0.164421i	−0.590222	+	0.807241i	$0.700960\pi$
$450$		0			0
$451$	9.76900	+	23.5845i	0.0216608	+	0.0522937i
$452$	−81.9513	+	411.997i	−0.181308	+	0.911497i
$453$	207.939	+	311.202i	0.459026	+	0.686980i
$454$	142.021	+	713.987i	0.312821	+	1.57266i
$455$		0			0
$456$	−576.231	+	862.391i	−1.26367	+	1.89121i
$457$	631.401	+	261.535i	1.38162	+	0.572287i	0.944915	−	0.327317i	$-0.106144\pi$
$457$	631.401	+	261.535i	1.38162	+	0.572287i	0.436708	+	0.899603i	$0.356144\pi$
$458$		−	1156.75i		−	2.52565i
$459$	294.886	+	367.267i	0.642454	+	0.800146i
$460$		0			0
$461$	−322.539	+	778.678i	−0.699651	+	1.68911i	0.0247194	+	0.999694i	$0.492131\pi$
$461$	−322.539	+	778.678i	−0.699651	+	1.68911i	−0.724370	+	0.689411i	$0.757869\pi$
$462$	275.672	+	184.198i	0.596692	+	0.398697i
$463$	201.457	+	201.457i	0.435113	+	0.435113i	0.890363	−	0.455251i	$-0.150450\pi$
$463$	201.457	+	201.457i	0.435113	+	0.435113i	−0.455251	+	0.890363i	$0.650450\pi$
$464$	34.9925	−	6.96044i	0.0754148	−	0.0150009i
$465$		0			0
$466$	−258.876	−	51.4936i	−0.555528	−	0.110501i
$467$	86.2764	−	35.7368i	0.184746	−	0.0765243i	−0.288393	−	0.957512i	$-0.593121\pi$
$467$	86.2764	−	35.7368i	0.184746	−	0.0765243i	0.473139	+	0.880988i	$0.343121\pi$
$468$	31.5440	+	76.1541i	0.0674018	+	0.162722i
$469$	−55.6157	+	279.599i	−0.118584	+	0.596160i
$470$		0			0
$471$	−28.0868	−	141.202i	−0.0596324	−	0.299792i
$472$	315.782	−	315.782i	0.669029	−	0.669029i
$473$	150.459	−	225.177i	0.318094	−	0.476062i
$474$	−602.735	−	249.661i	−1.27159	−	0.526711i
$475$		0			0
$476$	1463.73	+	160.002i	3.07507	+	0.336139i
$477$	26.8644			0.0563196
$478$	−218.215	+	526.819i	−0.456518	+	1.10213i
$479$	−141.414	−	94.4898i	−0.295228	−	0.197265i	0.399131	−	0.916894i	$-0.369312\pi$
$479$	−141.414	−	94.4898i	−0.295228	−	0.197265i	−0.694359	+	0.719629i	$0.744312\pi$
$480$		0			0
$481$	−244.825	+	48.6987i	−0.508991	+	0.101245i
$482$	921.958	−	616.033i	1.91278	−	1.27808i
$483$	470.739	+	93.6357i	0.974614	+	0.193863i
$484$	−999.762	+	414.115i	−2.06562	+	0.855609i
$485$		0			0
$486$	19.9251	−	100.170i	0.0409981	−	0.206111i
$487$	149.487	+	223.723i	0.306955	+	0.459390i	0.952591	−	0.304255i	$-0.0984076\pi$
$487$	149.487	+	223.723i	0.306955	+	0.459390i	−0.645636	+	0.763645i	$0.723408\pi$
$488$	135.450	+	680.952i	0.277561	+	1.39539i
$489$	−301.998	+	301.998i	−0.617582	+	0.617582i
$490$		0			0
$491$	−264.603	−	109.602i	−0.538906	−	0.223222i	0.0965929	−	0.995324i	$-0.469206\pi$
$491$	−264.603	−	109.602i	−0.538906	−	0.223222i	−0.635499	+	0.772102i	$0.719206\pi$
$492$			211.547i			0.429973i
$493$	−12.3093	−	6.74987i	−0.0249683	−	0.0136914i
$494$	977.334			1.97841
$495$		0			0
$496$	−1756.63	−	1173.74i	−3.54159	−	2.36641i
$497$	−348.850	−	348.850i	−0.701911	−	0.701911i
$498$	−1040.91	+	207.049i	−2.09017	+	0.415761i
$499$	21.7691	−	14.5457i	0.0436255	−	0.0291497i	−0.533566	−	0.845758i	$-0.679149\pi$
$499$	21.7691	−	14.5457i	0.0436255	−	0.0291497i	0.577192	+	0.816609i	$0.304149\pi$
$500$		0			0
$501$	150.316	−	62.2630i	0.300032	−	0.124277i
$502$	−160.038	−	386.367i	−0.318801	−	0.769655i
$503$	−17.8608	+	89.7923i	−0.0355085	+	0.178513i	−0.994470	−	0.105024i	$-0.966508\pi$
$503$	−17.8608	+	89.7923i	−0.0355085	+	0.178513i	0.958961	+	0.283538i	$0.0915080\pi$
$504$	−54.4911	−	81.5516i	−0.108117	−	0.161809i
$505$		0			0
$506$	174.843	−	174.843i	0.345540	−	0.345540i
$507$	−158.641	+	237.424i	−0.312902	+	0.468291i
$508$	544.745	+	225.641i	1.07233	+	0.444175i
$509$		−	268.089i		−	0.526698i	−0.964701	−	0.263349i	$-0.915173\pi$
$509$		−	268.089i		−	0.526698i	0.964701	−	0.263349i	$-0.0848270\pi$
$510$		0			0
$511$	1176.48			2.30231
$512$	271.501	−	655.461i	0.530275	−	1.28020i
$513$	−368.921	−	246.505i	−0.719144	−	0.480517i
$514$	−345.816	−	345.816i	−0.672793	−	0.672793i
$515$		0			0
$516$	1866.04	−	1246.85i	3.61635	−	2.41637i
$517$	−33.8505	−	6.73329i	−0.0654749	−	0.0130238i
$518$	458.890	−	190.078i	0.885887	−	0.366946i
$519$	172.585	+	416.656i	0.332533	+	0.802805i
$520$		0			0
$521$	−421.790	−	631.254i	−0.809578	−	1.21162i	−0.974294	−	0.225278i	$-0.927671\pi$
$521$	−421.790	−	631.254i	−0.809578	−	1.21162i	0.164716	−	0.986341i	$-0.447329\pi$
$522$	0.305075	+	1.53371i	0.000584435	+	0.00293815i
$523$	51.8647	−	51.8647i	0.0991676	−	0.0991676i	−0.655782	−	0.754950i	$-0.727661\pi$
$523$	51.8647	−	51.8647i	0.0991676	−	0.0991676i	0.754950	+	0.655782i	$0.227661\pi$
$524$	587.924	−	879.890i	1.12199	−	1.67918i
$525$		0			0
$526$			566.876i			1.07771i
$527$	232.783	+	798.036i	0.441714	+	1.51430i
$528$	440.576			0.834424
$529$	−65.4577	+	158.029i	−0.123738	+	0.298731i
$530$		0			0
$531$	7.20413	+	7.20413i	0.0135671	+	0.0135671i
$532$	−1360.44	+	270.608i	−2.55721	+	0.508661i
$533$	99.1140	−	66.2259i	0.185955	−	0.124251i
$534$	995.354	+	197.988i	1.86396	+	0.370764i
$535$		0			0
$536$	278.517	+	672.401i	0.519622	+	1.25448i
$537$	−112.681	+	566.486i	−0.209834	+	1.05491i
$538$	−470.240	−	703.764i	−0.874052	−	1.30811i
$539$	18.2781	+	91.8902i	0.0339111	+	0.170483i
$540$		0			0
$541$	−159.386	+	238.538i	−0.294614	+	0.440921i	−0.949017	−	0.315225i	$-0.897920\pi$
$541$	−159.386	+	238.538i	−0.294614	+	0.440921i	0.654403	+	0.756146i	$0.272920\pi$
$542$	−1416.53	−	586.744i	−2.61352	−	1.08255i
$543$		−	76.7774i		−	0.141395i
$544$	1092.72	−	569.118i	2.00868	−	1.04617i
$545$		0			0
$546$	592.466	−	1430.34i	1.08510	−	2.61967i
$547$	−784.088	−	523.911i	−1.43343	−	0.957789i	−0.998351	−	0.0573983i	$-0.981719\pi$
$547$	−784.088	−	523.911i	−1.43343	−	0.957789i	−0.435082	−	0.900391i	$-0.643281\pi$
$548$	−141.159	−	141.159i	−0.257589	−	0.257589i
$549$	−15.5350	+	3.09010i	−0.0282968	+	0.00562859i
$550$		0			0
$551$	12.9706	+	2.58001i	0.0235401	+	0.00468242i
$552$	1132.07	−	468.917i	2.05085	−	0.849488i
$553$	−199.662	−	482.026i	−0.361052	−	0.871657i
$554$	−336.065	+	1689.51i	−0.606615	+	3.04966i
$555$		0			0
$556$	−393.681	−	1979.17i	−0.708059	−	3.55965i
$557$	−144.163	+	144.163i	−0.258820	+	0.258820i	−0.824574	−	0.565754i	$-0.808585\pi$
$557$	−144.163	+	144.163i	−0.258820	+	0.258820i	0.565754	+	0.824574i	$0.308585\pi$
$558$	51.4449	−	76.9927i	0.0921951	−	0.137980i
$559$	−1168.35	−	483.945i	−2.09007	−	0.865734i
$560$		0			0
$561$	−132.822	−	111.405i	−0.236760	−	0.198583i
$562$	−1589.65			−2.82855
$563$	−93.9226	+	226.749i	−0.166825	+	0.402752i	−0.985078	−	0.172106i	$-0.944943\pi$
$563$	−93.9226	+	226.749i	−0.166825	+	0.402752i	0.818253	+	0.574858i	$0.194943\pi$
$564$	−237.812	−	158.901i	−0.421652	−	0.281739i
$565$		0			0
$566$	−814.496	+	162.013i	−1.43904	+	0.286243i
$567$	−551.379	+	368.420i	−0.972451	+	0.649771i
$568$	−1235.32	−	245.720i	−2.17485	−	0.432605i
$569$	−629.952	+	260.935i	−1.10712	+	0.458585i	−0.859945	−	0.510386i	$-0.829502\pi$
$569$	−629.952	+	260.935i	−1.10712	+	0.458585i	−0.247176	+	0.968971i	$0.579502\pi$
$570$		0			0
$571$	−10.2807	+	51.6844i	−0.0180047	+	0.0905157i	−0.988743	−	0.149625i	$-0.952193\pi$
$571$	−10.2807	+	51.6844i	−0.0180047	+	0.0905157i	0.970738	+	0.240140i	$0.0771935\pi$
$572$	−316.061	−	473.019i	−0.552554	−	0.826956i
$573$	6.49183	+	32.6366i	0.0113295	+	0.0569575i
$574$	−167.720	+	167.720i	−0.292195	+	0.292195i
$575$		0			0
$576$	−45.8426	−	18.9886i	−0.0795878	−	0.0329664i
$577$		−	906.394i		−	1.57087i	−0.618942	−	0.785437i	$-0.712438\pi$
$577$		−	906.394i		−	1.57087i	0.618942	−	0.785437i	$-0.287562\pi$
$578$	−1053.92	−	233.197i	−1.82339	−	0.403455i
$579$	155.813			0.269108
$580$		0			0
$581$	−705.713	−	471.542i	−1.21465	−	0.811604i
$582$	−120.272	−	120.272i	−0.206653	−	0.206653i
$583$	−181.847	+	36.1716i	−0.311916	+	0.0620439i
$584$	2497.37	−	1668.69i	4.27631	−	2.85734i
$585$		0			0
$586$	−865.502	+	358.503i	−1.47697	+	0.611779i
$587$	240.227	+	579.960i	0.409246	+	0.988006i	0.985337	+	0.170621i	$0.0545773\pi$
$587$	240.227	+	579.960i	0.409246	+	0.988006i	−0.576091	+	0.817385i	$0.695423\pi$
$588$	−151.470	+	761.492i	−0.257602	+	1.29505i
$589$	−435.069	−	651.126i	−0.738656	−	1.10548i
$590$		0			0
$591$	−441.707	+	441.707i	−0.747389	+	0.747389i
$592$	366.697	−	548.800i	0.619420	−	0.927027i
$593$	747.965	+	309.817i	1.26132	+	0.522457i	0.910315	−	0.413915i	$-0.135839\pi$
$593$	747.965	+	309.817i	1.26132	+	0.522457i	0.351008	+	0.936373i	$0.385839\pi$
$594$			362.098i			0.609592i
$595$		0			0
$596$	947.989			1.59059
$597$	−78.1251	+	188.611i	−0.130863	+	0.315931i
$598$	−960.037	−	641.476i	−1.60541	−	1.07270i
$599$	−556.749	−	556.749i	−0.929465	−	0.929465i	0.0682066	−	0.997671i	$-0.478272\pi$
$599$	−556.749	−	556.749i	−0.929465	−	0.929465i	−0.997671	+	0.0682066i	$0.978272\pi$
$600$		0			0
$601$	598.829	−	400.125i	0.996388	−	0.665765i	0.0533932	−	0.998574i	$-0.482996\pi$
$601$	598.829	−	400.125i	0.996388	−	0.665765i	0.942994	+	0.332809i	$0.107996\pi$
$602$	2467.98	+	490.912i	4.09963	+	0.815468i
$603$	−15.3399	+	6.35399i	−0.0254393	+	0.0105373i
$604$	489.028	+	1180.62i	0.809649	+	1.95466i
$605$		0			0
$606$	872.165	+	1305.29i	1.43922	+	2.15394i
$607$	−20.2887	−	101.998i	−0.0334246	−	0.168037i	0.960468	−	0.278392i	$-0.0898013\pi$
$607$	−20.2887	−	101.998i	−0.0334246	−	0.168037i	−0.993892	+	0.110355i	$0.964801\pi$
$608$	−820.683	+	820.683i	−1.34981	+	1.34981i
$609$	11.6387	−	17.4186i	0.0191112	−	0.0286020i
$610$		0			0
$611$			161.165i			0.263772i
$612$	39.6152	+	76.0621i	0.0647306	+	0.124284i
$613$	392.106			0.639650			0.319825	−	0.947477i	$-0.396376\pi$
$613$	392.106			0.639650			0.319825	+	0.947477i	$0.396376\pi$
$614$	−579.052	+	1397.96i	−0.943082	+	2.27680i
$615$		0			0
$616$	478.658	+	478.658i	0.777043	+	0.777043i
$617$	−90.5076	+	18.0031i	−0.146690	+	0.0291784i	−0.267889	−	0.963450i	$-0.586326\pi$
$617$	−90.5076	+	18.0031i	−0.146690	+	0.0291784i	0.121199	+	0.992628i	$0.461326\pi$
$618$	840.226	−	561.421i	1.35959	−	0.908448i
$619$	116.029	+	23.0797i	0.187446	+	0.0372854i	0.287921	−	0.957654i	$-0.407036\pi$
$619$	116.029	+	23.0797i	0.187446	+	0.0372854i	−0.100474	+	0.994940i	$0.532036\pi$
$620$		0			0
$621$	200.597	+	484.285i	0.323023	+	0.779847i
$622$	241.128	−	1212.23i	0.387665	−	1.94892i
$623$	450.907	+	674.829i	0.723767	+	1.08319i
$624$	−401.361	−	2017.78i	−0.643206	−	3.23362i
$625$		0			0
$626$	612.696	−	916.964i	0.978747	−	1.46480i
$627$	150.877	+	62.4951i	0.240632	+	0.0996732i
$628$		−	491.547i		−	0.782718i
$629$	−249.320	+	72.7254i	−0.396375	+	0.115621i
$630$		0			0
$631$	−102.872	+	248.356i	−0.163030	+	0.393590i	−0.984192	−	0.177106i	$-0.943327\pi$
$631$	−102.872	+	248.356i	−0.163030	+	0.393590i	0.821161	+	0.570696i	$0.193327\pi$
$632$	−1107.52	−	740.023i	−1.75241	−	1.17092i
$633$	−192.893	−	192.893i	−0.304728	−	0.304728i
$634$	239.741	−	47.6874i	0.378140	−	0.0752167i
$635$		0			0
$636$	−1506.96	−	299.753i	−2.36944	−	0.471310i
$637$	404.193	−	167.422i	0.634526	−	0.262829i
$638$	−4.13014	−	9.97104i	−0.00647357	−	0.0156286i
$639$	5.60576	−	28.1821i	0.00877271	−	0.0441034i
$640$		0			0
$641$	109.020	+	548.080i	0.170078	+	0.855039i	0.967743	+	0.251939i	$0.0810681\pi$
$641$	109.020	+	548.080i	0.170078	+	0.855039i	−0.797665	+	0.603100i	$0.793932\pi$
$642$	178.062	−	178.062i	0.277355	−	0.277355i
$643$	−565.616	+	846.504i	−0.879651	+	1.31649i	0.0681649	+	0.997674i	$0.478286\pi$
$643$	−565.616	+	846.504i	−0.879651	+	1.31649i	−0.947816	+	0.318817i	$0.896714\pi$
$644$	1513.98	+	627.109i	2.35089	+	0.973772i
$645$		0			0
$646$	1012.95	−	88.8298i	1.56803	−	0.137507i
$647$	640.405			0.989807			0.494903	−	0.868948i	$-0.335203\pi$
$647$	640.405			0.989807			0.494903	+	0.868948i	$0.335203\pi$
$648$	−647.880	+	1564.12i	−0.999815	+	2.41377i
$649$	−58.4651	−	39.0652i	−0.0900850	−	0.0601929i
$650$		0			0
$651$	−1216.67	+	242.011i	−1.86893	+	0.371753i
$652$	−1212.45	+	810.131i	−1.85958	+	1.24253i
$653$	800.836	+	159.296i	1.22640	+	0.243945i	0.765457	−	0.643487i	$-0.222513\pi$
$653$	800.836	+	159.296i	1.22640	+	0.243945i	0.460938	+	0.887432i	$0.347513\pi$
$654$	907.509	−	375.903i	1.38763	−	0.574775i
$655$		0			0
$656$	−61.4909	+	309.136i	−0.0937361	+	0.471243i
$657$	38.0688	+	56.9740i	0.0579434	+	0.0867184i
$658$	−62.5629	−	314.525i	−0.0950803	−	0.478001i
$659$	800.307	−	800.307i	1.21443	−	1.21443i	0.244870	−	0.969556i	$-0.421255\pi$
$659$	800.307	−	800.307i	1.21443	−	1.21443i	0.969556	−	0.244870i	$-0.0787452\pi$
$660$		0			0
$661$	−173.492	−	71.8629i	−0.262470	−	0.108718i	0.247568	−	0.968870i	$-0.420369\pi$
$661$	−173.492	−	71.8629i	−0.262470	−	0.108718i	−0.510038	+	0.860152i	$0.670369\pi$
$662$			1545.10i			2.33399i
$663$	−389.219	+	709.796i	−0.587057	+	1.07058i
$664$	−2166.87			−3.26335
$665$		0			0
$666$	24.0538	+	16.0722i	0.0361168	+	0.0241325i
$667$	−11.0477	−	11.0477i	−0.0165632	−	0.0165632i
$668$	544.831	−	108.374i	0.815615	−	0.162236i
$669$	−796.149	+	531.970i	−1.19006	+	0.795172i
$670$		0			0
$671$	100.996	−	41.8341i	0.150516	−	0.0623459i
$672$	703.576	+	1698.58i	1.04699	+	2.52765i
$673$	126.681	−	636.869i	0.188233	−	0.946313i	−0.764989	−	0.644043i	$-0.777256\pi$
$673$	126.681	−	636.869i	0.188233	−	0.946313i	0.953222	−	0.302270i	$-0.0977443\pi$
$674$	831.036	+	1243.73i	1.23299	+	1.84530i
$675$		0			0
$676$	−689.382	+	689.382i	−1.01980	+	1.01980i
$677$	400.638	−	599.596i	0.591784	−	0.885667i	−0.407841	−	0.913053i	$-0.633718\pi$
$677$	400.638	−	599.596i	0.591784	−	0.885667i	0.999625	+	0.0273861i	$0.00871834\pi$
$678$	424.548	+	175.853i	0.626177	+	0.259371i
$679$		−	136.027i		−	0.200334i
$680$		0			0
$681$	568.013			0.834086
$682$	−244.567	+	590.436i	−0.358602	+	0.865742i
$683$	−777.517	−	519.520i	−1.13839	−	0.760645i	−0.164207	−	0.986426i	$-0.552507\pi$
$683$	−777.517	−	519.520i	−1.13839	−	0.760645i	−0.974178	+	0.225781i	$0.927507\pi$
$684$	−57.1261	−	57.1261i	−0.0835177	−	0.0835177i
$685$		0			0
$686$	600.810	−	401.448i	0.875816	−	0.585201i
$687$	−885.228	−	176.083i	−1.28854	−	0.256307i
$688$	3089.29	−	1279.62i	4.49024	−	1.85992i
$689$	331.322	+	799.882i	0.480874	+	1.16093i
$690$		0			0
$691$	0.367324	+	0.549739i	0.000531583	+	0.000795571i	0.831735	−	0.555172i	$-0.187348\pi$
$691$	0.367324	+	0.549739i	0.000531583	+	0.000795571i	−0.831204	+	0.555968i	$0.812348\pi$
$692$	300.397	+	1510.20i	0.434100	+	2.18237i
$693$	−10.9199	+	10.9199i	−0.0157575	+	0.0157575i
$694$	−635.553	+	951.173i	−0.915783	+	1.37057i
$695$		0			0
$696$		−	53.4833i		−	0.0768438i
$697$	96.7065	−	77.6476i	0.138747	−	0.111403i
$698$	562.741			0.806219
$699$	−78.8132	+	190.272i	−0.112751	+	0.272206i
$700$		0			0
$701$	−584.250	−	584.250i	−0.833453	−	0.833453i	0.154535	−	0.987987i	$-0.450612\pi$
$701$	−584.250	−	584.250i	−0.833453	−	0.833453i	−0.987987	+	0.154535i	$0.950612\pi$
$702$	1658.36	−	329.868i	2.36233	−	0.469897i
$703$	203.423	−	135.923i	0.289364	−	0.193347i
$704$	335.878	+	66.8104i	0.477100	+	0.0949011i
$705$		0			0
$706$	909.164	+	2194.92i	1.28777	+	3.10895i
$707$	−244.929	+	1231.34i	−0.346434	+	1.74164i
$708$	−323.732	−	484.499i	−0.457248	−	0.684321i
$709$	112.540	+	565.777i	0.158731	+	0.797993i	0.975324	+	0.220779i	$0.0708601\pi$
$709$	112.540	+	565.777i	0.158731	+	0.797993i	−0.816593	+	0.577214i	$0.804140\pi$
$710$		0			0
$711$	16.8826	−	25.2666i	0.0237449	−	0.0355367i
$712$	1914.32	+	792.936i	2.68865	+	1.11367i
$713$			925.161i			1.29756i
$714$	484.053	−	1536.31i	0.677945	−	2.15170i
$715$		0			0
$716$	−754.662	+	1821.92i	−1.05400	+	2.54458i
$717$	369.942	+	247.188i	0.515959	+	0.344752i
$718$	819.192	+	819.192i	1.14094	+	1.14094i
$719$	−163.392	+	32.5008i	−0.227249	+	0.0452027i	−0.307401	−	0.951580i	$-0.599459\pi$
$719$	−163.392	+	32.5008i	−0.227249	+	0.0452027i	0.0801520	+	0.996783i	$0.474459\pi$
$720$		0			0
$721$	792.625	+	157.663i	1.09934	+	0.218673i
$722$	360.721	−	149.415i	0.499613	−	0.206947i
$723$	−331.090	−	799.322i	−0.457939	−	1.10556i
$724$	51.1407	−	257.102i	0.0706363	−	0.355113i
$725$		0			0
$726$	230.945	+	1161.04i	0.318106	+	1.59923i
$727$	430.278	−	430.278i	0.591854	−	0.591854i	−0.346278	−	0.938132i	$-0.612555\pi$
$727$	430.278	−	430.278i	0.591854	−	0.591854i	0.938132	+	0.346278i	$0.112555\pi$
$728$	1756.14	−	2628.24i	2.41227	−	3.61022i
$729$	−707.054	−	292.871i	−0.969896	−	0.401744i
$730$		0			0
$731$	−1254.91	−	395.389i	−1.71670	−	0.540888i
$732$	905.913			1.23759
$733$	−132.180	+	319.111i	−0.180327	+	0.435349i	−0.988034	−	0.154236i	$-0.950709\pi$
$733$	−132.180	+	319.111i	−0.180327	+	0.435349i	0.807707	+	0.589585i	$0.200709\pi$
$734$	−1153.89	−	771.003i	−1.57205	−	1.05041i
$735$		0			0
$736$	1344.82	−	267.501i	1.82720	−	0.363452i
$737$	95.2813	−	63.6649i	0.129283	−	0.0863839i
$738$	−13.5494	−	2.69514i	−0.0183596	−	0.00365195i
$739$	221.305	−	91.6677i	0.299466	−	0.124043i	−0.227891	−	0.973687i	$-0.573183\pi$
$739$	221.305	−	91.6677i	0.299466	−	0.124043i	0.527357	+	0.849644i	$0.323183\pi$
$740$		0			0
$741$	148.772	−	747.926i	0.200772	−	1.00935i
$742$	−957.108	−	1432.41i	−1.28990	−	1.93048i
$743$	49.7495	+	250.108i	0.0669576	+	0.336619i	0.999715	−	0.0238869i	$-0.00760417\pi$
$743$	49.7495	+	250.108i	0.0669576	+	0.336619i	−0.932757	+	0.360506i	$0.882604\pi$
$744$	−2239.42	+	2239.42i	−3.00997	+	3.00997i
$745$		0			0
$746$	624.263	+	258.578i	0.836813	+	0.346619i
$747$		−	49.4341i		−	0.0661768i
$748$	−370.571	−	461.529i	−0.495416	−	0.617018i
$749$	201.386			0.268873
$750$		0			0
$751$	207.078	+	138.365i	0.275736	+	0.184241i	0.685748	−	0.727839i	$-0.259475\pi$
$751$	207.078	+	138.365i	0.275736	+	0.184241i	−0.410011	+	0.912080i	$0.634475\pi$
$752$	−301.329	−	301.329i	−0.400703	−	0.400703i
$753$	−320.037	+	63.6593i	−0.425016	+	0.0845409i
$754$	−41.9034	+	27.9990i	−0.0555749	+	0.0371339i
$755$		0			0
$756$	−2217.08	+	918.344i	−2.93264	+	1.21474i
$757$	−92.0780	−	222.296i	−0.121635	−	0.293654i	0.851320	−	0.524647i	$-0.175803\pi$
$757$	−92.0780	−	222.296i	−0.121635	−	0.293654i	−0.972955	+	0.230993i	$0.925803\pi$
$758$	−322.330	+	1620.46i	−0.425237	+	2.13781i
$759$	−107.187	−	160.417i	−0.141222	−	0.211354i
$760$		0			0
$761$	126.760	−	126.760i	0.166570	−	0.166570i	−0.618900	−	0.785470i	$-0.712421\pi$
$761$	126.760	−	126.760i	0.166570	−	0.166570i	0.785470	+	0.618900i	$0.212421\pi$
$762$	358.351	−	536.310i	0.470277	−	0.703819i
$763$	725.764	+	300.621i	0.951197	+	0.393999i
$764$			113.613i			0.148708i
$765$		0			0
$766$	−2123.02			−2.77156
$767$	−125.652	+	303.350i	−0.163822	+	0.395502i
$768$	−263.970	−	176.379i	−0.343710	−	0.229660i
$769$	861.829	+	861.829i	1.12071	+	1.12071i	0.991634	+	0.129080i	$0.0412023\pi$
$769$	861.829	+	861.829i	1.12071	+	1.12071i	0.129080	+	0.991634i	$0.458798\pi$
$770$		0			0
$771$	−317.284	+	212.002i	−0.411522	+	0.274971i
$772$	521.767	+	103.786i	0.675864	+	0.134438i
$773$	−1077.46	+	446.300i	−1.39387	+	0.577361i	−0.948154	−	0.317812i	$-0.897052\pi$
$773$	−1077.46	+	446.300i	−1.39387	+	0.577361i	−0.445719	+	0.895173i	$0.647052\pi$
$774$	56.0857	+	135.403i	0.0724622	+	0.174939i
$775$		0			0
$776$	−192.936	−	288.749i	−0.248629	−	0.372100i
$777$	−75.6084	−	380.109i	−0.0973081	−	0.489201i
$778$	1568.54	−	1568.54i	2.01612	−	2.01612i
$779$	−64.9082	+	97.1420i	−0.0833225	+	0.124701i
$780$		0			0
$781$			198.314i			0.253923i
$782$	−1053.33	−	577.594i	−1.34696	−	0.738612i
$783$	22.8795			0.0292204
$784$	−442.690	+	1068.75i	−0.564656	+	1.36320i
$785$		0			0
$786$	−818.574	−	818.574i	−1.04144	−	1.04144i
$787$	−378.371	+	75.2626i	−0.480776	+	0.0956323i	−0.429528	−	0.903054i	$-0.641320\pi$
$787$	−378.371	+	75.2626i	−0.480776	+	0.0956323i	−0.0512482	+	0.998686i	$0.516320\pi$
$788$	−1773.34	+	1184.91i	−2.25044	+	1.50369i
$789$	433.814	+	86.2910i	0.549828	+	0.109368i
$790$		0			0
$791$	140.635	+	339.524i	0.177795	+	0.429234i
$792$	−7.69168	+	38.6687i	−0.00971172	+	0.0488241i
$793$	−283.601	−	424.439i	−0.357631	−	0.535232i
$794$	−570.578	−	2868.49i	−0.718612	−	3.61270i
$795$		0			0
$796$	−387.246	+	579.555i	−0.486491	+	0.728085i
$797$	457.343	+	189.438i	0.573831	+	0.237688i	0.650677	−	0.759355i	$-0.274485\pi$
$797$	457.343	+	189.438i	0.573831	+	0.237688i	−0.0768465	+	0.997043i	$0.524485\pi$
$798$			1517.39i			1.90149i
$799$	14.6482	+	167.037i	0.0183332	+	0.209058i
$800$		0			0
$801$	−18.0897	+	43.6725i	−0.0225839	+	0.0545224i
$802$	−1.51105	−	1.00965i	−0.00188411	−	0.00125892i
$803$	−334.402	−	334.402i	−0.416441	−	0.416441i
$804$	931.389	−	185.265i	1.15844	−	0.230429i
$805$		0			0
$806$	2926.91	+	582.199i	3.63141	+	0.722331i
$807$	−610.151	+	252.733i	−0.756073	+	0.313176i
$808$	1226.58	+	2961.21i	1.51804	+	3.66487i
$809$	239.101	−	1202.04i	0.295552	−	1.48584i	−0.492545	−	0.870287i	$-0.663933\pi$
$809$	239.101	−	1202.04i	0.295552	−	1.48584i	0.788097	−	0.615551i	$-0.211067\pi$
$810$		0			0
$811$	−192.807	−	969.306i	−0.237740	−	1.19520i	−0.896568	−	0.442906i	$-0.853948\pi$
$811$	−192.807	−	969.306i	−0.237740	−	1.19520i	0.658828	−	0.752293i	$-0.271052\pi$
$812$	50.5766	−	50.5766i	0.0622865	−	0.0622865i
$813$	−664.645	+	994.711i	−0.817521	+	1.22351i
$814$	−184.462	−	76.4068i	−0.226612	−	0.0938658i
$815$		0			0
$816$	−599.382	−	2054.83i	−0.734537	−	2.51817i
$817$	1239.45			1.51707
$818$	837.950	−	2022.99i	1.02439	−	2.47309i
$819$	59.9597	+	40.0638i	0.0732109	+	0.0489179i
$820$		0			0
$821$	−703.792	+	139.993i	−0.857238	+	0.170515i	−0.604094	−	0.796913i	$-0.706465\pi$
$821$	−703.792	+	139.993i	−0.857238	+	0.170515i	−0.253144	+	0.967429i	$0.581465\pi$
$822$	−181.577	+	121.326i	−0.220897	+	0.147598i
$823$	147.140	+	29.2679i	0.178784	+	0.0355624i	0.283671	−	0.958922i	$-0.408448\pi$
$823$	147.140	+	29.2679i	0.178784	+	0.0355624i	−0.104886	+	0.994484i	$0.533448\pi$
$824$	1906.16	−	789.558i	2.31330	−	0.958202i
$825$		0			0
$826$	127.461	−	640.788i	0.154311	−	0.775772i
$827$	−194.581	−	291.211i	−0.235285	−	0.352129i	0.694972	−	0.719036i	$-0.255417\pi$
$827$	−194.581	−	291.211i	−0.235285	−	0.352129i	−0.930257	+	0.366907i	$0.880417\pi$
$828$	18.6202	+	93.6100i	0.0224881	+	0.113056i
$829$	494.252	−	494.252i	0.596203	−	0.596203i	−0.343097	−	0.939300i	$-0.611476\pi$
$829$	494.252	−	494.252i	0.596203	−	0.596203i	0.939300	+	0.343097i	$0.111476\pi$
$830$		0			0
$831$	1241.78	+	514.361i	1.49432	+	0.618967i
$832$		−	1599.14i		−	1.92204i
$833$	403.705	−	210.260i	0.484640	−	0.252413i
$834$	−2207.50			−2.64688
$835$		0			0
$836$	463.607	+	309.773i	0.554554	+	0.370541i
$837$	−957.998	−	957.998i	−1.14456	−	1.14456i
$838$	538.408	−	107.096i	0.642492	−	0.127800i
$839$	216.460	−	144.634i	0.257998	−	0.172389i	−0.419844	−	0.907596i	$-0.637915\pi$
$839$	216.460	−	144.634i	0.257998	−	0.172389i	0.677842	+	0.735208i	$0.262915\pi$
$840$		0			0
$841$	776.353	−	321.576i	0.923130	−	0.382373i
$842$	356.098	+	859.695i	0.422919	+	1.02102i
$843$	−241.979	+	1216.51i	−0.287045	+	1.44307i
$844$	−517.449	−	774.417i	−0.613091	−	0.917556i
$845$		0			0
$846$	13.2072	−	13.2072i	0.0156113	−	0.0156113i
$847$	−525.963	+	787.160i	−0.620972	+	0.929350i
$848$	−2115.01	−	876.065i	−2.49411	−	1.03310i
$849$			647.972i			0.763218i
$850$		0			0
$851$	−289.036			−0.339643
$852$	−628.910	+	1518.32i	−0.738157	+	1.78207i
$853$	108.122	+	72.2449i	0.126755	+	0.0846951i	0.617332	−	0.786703i	$-0.288214\pi$
$853$	108.122	+	72.2449i	0.126755	+	0.0846951i	−0.490576	+	0.871398i	$0.663214\pi$
$854$	718.233	+	718.233i	0.841022	+	0.841022i
$855$		0			0
$856$	427.491	−	285.640i	0.499405	−	0.333692i
$857$	378.726	+	75.3332i	0.441920	+	0.0879034i	0.411035	−	0.911620i	$-0.365167\pi$
$857$	378.726	+	75.3332i	0.441920	+	0.0879034i	0.0308851	+	0.999523i	$0.490167\pi$
$858$	−574.962	+	238.157i	−0.670118	+	0.277572i
$859$	−97.4301	−	235.217i	−0.113423	−	0.273827i	0.856967	−	0.515371i	$-0.172346\pi$
$859$	−97.4301	−	235.217i	−0.113423	−	0.273827i	−0.970390	+	0.241545i	$0.922346\pi$
$860$		0			0
$861$	102.821	+	153.882i	0.119420	+	0.178725i
$862$	1.05434	+	5.30051i	0.00122313	+	0.00614908i
$863$	588.512	−	588.512i	0.681938	−	0.681938i	−0.278499	−	0.960437i	$-0.589837\pi$
$863$	588.512	−	588.512i	0.681938	−	0.681938i	0.960437	+	0.278499i	$0.0898369\pi$
$864$	−1115.55	+	1669.54i	−1.29115	+	1.93234i
$865$		0			0
$866$		−	487.013i		−	0.562370i
$867$	−338.889	+	771.037i	−0.390875	+	0.889316i
$868$	−4235.43			−4.87953
$869$	−80.2591	+	193.763i	−0.0923580	+	0.222972i
$870$		0			0
$871$	−378.377	−	378.377i	−0.434417	−	0.434417i
$872$	1967.00	−	391.261i	2.25574	−	0.448694i
$873$	6.58741	−	4.40157i	0.00754572	−	0.00504189i
$874$	1109.91	+	220.775i	1.26992	+	0.252603i
$875$		0			0
$876$	−1499.75	−	3620.73i	−1.71205	−	4.13325i
$877$	184.887	−	929.491i	0.210818	−	1.05985i	−0.719890	−	0.694088i	$-0.755808\pi$
$877$	184.887	−	929.491i	0.210818	−	1.05985i	0.930708	−	0.365764i	$-0.119192\pi$
$878$	−374.165	−	559.978i	−0.426156	−	0.637788i
$879$	142.603	+	716.916i	0.162234	+	0.815604i
$880$		0			0
$881$	488.879	−	731.659i	0.554914	−	0.830487i	−0.442900	−	0.896571i	$-0.646050\pi$
$881$	488.879	−	731.659i	0.554914	−	0.830487i	0.997814	+	0.0660837i	$0.0210504\pi$
$882$	−46.8431	−	19.4030i	−0.0531101	−	0.0219989i
$883$		−	1172.98i		−	1.32840i	−0.747554	−	0.664201i	$-0.768772\pi$
$883$		−	1172.98i		−	1.32840i	0.747554	−	0.664201i	$-0.231228\pi$
$884$	−1776.15	+	2117.61i	−2.00922	+	2.39549i
$885$		0			0
$886$	−635.886	+	1535.16i	−0.717704	+	1.73269i
$887$	−120.341	−	80.4091i	−0.135672	−	0.0906528i	0.485882	−	0.874024i	$-0.338498\pi$
$887$	−120.341	−	80.4091i	−0.135672	−	0.0906528i	−0.621554	+	0.783371i	$0.713498\pi$
$888$	−699.633	−	699.633i	−0.787875	−	0.787875i
$889$	505.927	−	100.635i	0.569096	−	0.113200i
$890$		0			0
$891$	261.443	+	52.0043i	0.293427	+	0.0583662i
$892$	−3020.38	+	1251.08i	−3.38607	+	1.40256i
$893$	−60.4479	−	145.934i	−0.0676908	−	0.163420i
$894$	202.316	−	1017.11i	0.226304	−	1.13771i
$895$		0			0
$896$	128.466	+	645.842i	0.143377	+	0.720806i
$897$	−637.042	+	637.042i	−0.710192	+	0.710192i
$898$	−785.226	+	1175.17i	−0.874417	+	1.30866i
$899$	37.3073	+	15.4532i	0.0414987	+	0.0171893i
$900$		0			0
$901$	416.096	+	798.916i	0.461816	+	0.886699i
$902$	95.3453			0.105704
$903$	751.362	−	1813.95i	0.832073	−	2.00880i
$904$	780.104	+	521.249i	0.862947	+	0.576603i
$905$		0			0
$906$	1371.07	−	272.722i	1.51332	−	0.301018i
$907$	−451.807	+	301.888i	−0.498133	+	0.332842i	−0.779125	−	0.626868i	$-0.784337\pi$
$907$	−451.807	+	301.888i	−0.498133	+	0.332842i	0.280992	+	0.959710i	$0.409337\pi$
$908$	1902.08	+	378.348i	2.09481	+	0.416683i
$909$	−67.5560	+	27.9826i	−0.0743190	+	0.0307840i
$910$		0			0
$911$	−88.1446	+	443.133i	−0.0967559	+	0.486425i	0.901773	+	0.432209i	$0.142266\pi$
$911$	−88.1446	+	443.133i	−0.0967559	+	0.486425i	−0.998529	+	0.0542155i	$0.982734\pi$
$912$	1120.24	+	1676.55i	1.22833	+	1.83833i
$913$	66.5605	+	334.622i	0.0729031	+	0.366508i
$914$	1804.95	−	1804.95i	1.97478	−	1.97478i
$915$		0			0
$916$	−2847.04	−	1179.28i	−3.10813	−	1.28743i
$917$		−	925.800i		−	1.00960i
$918$	1688.81	−	492.616i	1.83966	−	0.536619i
$919$	1007.28			1.09606			0.548028	−	0.836460i	$-0.315379\pi$
$919$	1007.28			1.09606			0.548028	+	0.836460i	$0.315379\pi$
$920$		0			0
$921$	981.672	+	655.932i	1.06588	+	0.712195i
$922$	2225.95	+	2225.95i	2.41427	+	2.41427i
$923$	908.250	−	180.662i	0.984019	−	0.195734i
$924$	734.398	−	490.709i	0.794803	−	0.531070i
$925$		0			0
$926$	983.110	−	407.217i	1.06167	−	0.439760i
$927$	18.0127	+	43.4865i	0.0194312	+	0.0469110i
$928$	11.6758	−	58.6982i	0.0125817	−	0.0632524i
$929$	700.044	+	1047.69i	0.753546	+	1.12776i	0.987822	+	0.155591i	$0.0497281\pi$
$929$	700.044	+	1047.69i	0.753546	+	1.12776i	−0.234276	+	0.972170i	$0.575272\pi$
$930$		0			0
$931$	−303.201	+	303.201i	−0.325672	+	0.325672i
$932$	−390.657	+	584.660i	−0.419160	+	0.627317i
$933$	−890.981	−	369.056i	−0.954963	−	0.395559i
$934$		−	348.791i		−	0.373438i
$935$		0			0
$936$	184.104			0.196693
$937$	608.558	−	1469.19i	0.649475	−	1.56797i	−0.164056	−	0.986451i	$-0.552458\pi$
$937$	608.558	−	1469.19i	0.649475	−	1.56797i	0.813531	−	0.581521i	$-0.197542\pi$
$938$	885.314	+	591.548i	0.943831	+	0.630648i
$939$	−608.460	−	608.460i	−0.647988	−	0.647988i
$940$		0			0
$941$	−507.987	+	339.426i	−0.539837	+	0.360708i	−0.795400	−	0.606085i	$-0.792739\pi$
$941$	−507.987	+	339.426i	−0.539837	+	0.360708i	0.255563	+	0.966792i	$0.417739\pi$
$942$	−527.388	−	104.904i	−0.559860	−	0.111363i
$943$	127.519	−	52.8201i	0.135227	−	0.0560128i
$944$	−332.242	−	802.104i	−0.351952	−	0.849686i
$945$		0			0
$946$	−561.961	−	841.034i	−0.594039	−	0.889042i
$947$	−291.781	−	1466.88i	−0.308110	−	1.54898i	−0.755810	−	0.654791i	$-0.772756\pi$
$947$	−291.781	−	1466.88i	−0.308110	−	1.54898i	0.447699	−	0.894184i	$-0.352244\pi$
$948$	−1228.95	+	1228.95i	−1.29636	+	1.29636i
$949$	−1226.88	+	1836.15i	−1.29281	+	1.93483i
$950$		0			0
$951$		−	190.726i		−	0.200553i
$952$	1581.25	−	2883.63i	1.66098	−	3.02902i
$953$	1573.72			1.65133			0.825664	−	0.564162i	$-0.190801\pi$
$953$	1573.72			1.65133			0.825664	+	0.564162i	$0.190801\pi$
$954$	38.3978	−	92.7005i	0.0402493	−	0.0971703i
$955$		0			0
$956$	1074.16	+	1074.16i	1.12360	+	1.12360i
$957$	−8.25925	+	1.64287i	−0.00863036	+	0.00171668i
$958$	−528.179	+	352.918i	−0.551335	+	0.368391i
$959$	−171.290	−	34.0718i	−0.178613	−	0.0355284i
$960$		0			0
$961$	−547.305	−	1321.31i	−0.569516	−	1.37493i
$962$	−181.889	+	914.417i	−0.189074	+	0.950537i
$963$	6.51649	+	9.75261i	0.00676686	+	0.0101273i
$964$	−576.288	−	2897.20i	−0.597809	−	3.00539i
$965$		0			0
$966$	995.941	−	1490.53i	1.03099	−	1.54299i
$967$	1634.44	+	677.006i	1.69021	+	0.700110i	0.999730	−	0.0232380i	$-0.00739755\pi$
$967$	1634.44	+	677.006i	1.69021	+	0.700110i	0.690484	+	0.723348i	$0.257398\pi$
$968$			2416.95i			2.49685i
$969$	86.2141	−	788.702i	0.0889722	−	0.813934i
$970$		0			0
$971$	642.545	−	1551.24i	0.661735	−	1.59757i	−0.133348	−	0.991069i	$-0.542573\pi$
$971$	642.545	−	1551.24i	0.661735	−	1.59757i	0.795083	−	0.606500i	$-0.207427\pi$
$972$	−226.230	−	151.162i	−0.232747	−	0.155516i
$973$	−1248.33	−	1248.33i	−1.28297	−	1.28297i
$974$	985.660	−	196.060i	1.01197	−	0.201294i
$975$		0			0
$976$	1323.82	+	263.324i	1.35637	+	0.269800i
$977$	−1086.81	+	450.173i	−1.11240	+	0.460771i	−0.861764	−	0.507310i	$-0.830640\pi$
$977$	−1086.81	+	450.173i	−1.11240	+	0.460771i	−0.250636	+	0.968081i	$0.580640\pi$
$978$	610.446	+	1473.75i	0.624178	+	1.50690i
$979$	63.6477	−	319.979i	0.0650130	−	0.326842i
$980$		0			0
$981$	8.92607	+	44.8744i	0.00909895	+	0.0457435i
$982$	−756.403	+	756.403i	−0.770268	+	0.770268i
$983$	−769.353	+	1151.42i	−0.782658	+	1.17133i	0.198873	+	0.980025i	$0.436272\pi$
$983$	−769.353	+	1151.42i	−0.782658	+	1.17133i	−0.981531	+	0.191305i	$0.938728\pi$
$984$	436.524	+	180.814i	0.443622	+	0.183754i
$985$		0			0
$986$	−40.8856	+	32.8279i	−0.0414661	+	0.0332940i
$987$	−250.220			−0.253516
$988$	996.373	−	2405.46i	1.00847	−	2.43467i
$989$	−1217.51	−	813.516i	−1.23105	−	0.822564i
$990$		0			0
$991$	901.874	−	179.394i	0.910064	−	0.181023i	0.282209	−	0.959353i	$-0.408933\pi$
$991$	901.874	−	179.394i	0.910064	−	0.181023i	0.627855	+	0.778330i	$0.283933\pi$
$992$	−2946.66	+	1968.89i	−2.97042	+	1.98477i
$993$	1182.42	+	235.198i	1.19076	+	0.236856i
$994$	−1702.39	+	705.151i	−1.71266	+	0.709408i
$995$		0			0
$996$	−551.585	+	2773.00i	−0.553800	+	2.78414i
$997$	474.437	+	710.045i	0.475865	+	0.712182i	0.989292	−	0.145951i	$-0.0466243\pi$
$997$	474.437	+	710.045i	0.475865	+	0.712182i	−0.513427	+	0.858133i	$0.671624\pi$
$998$	−19.0774	−	95.9087i	−0.0191156	−	0.0961009i
$999$	299.295	−	299.295i	0.299595	−	0.299595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.f.401.16		128
5.2	odd	4		85.3.p.a.44.16	yes	128
5.3	odd	4		85.3.p.a.44.1	yes	128
5.4	even	2	inner	425.3.u.f.401.1		128
17.12	odd	16	inner	425.3.u.f.301.16		128
85.12	even	16		85.3.p.a.29.1	✓	128
85.29	odd	16	inner	425.3.u.f.301.1		128
85.63	even	16		85.3.p.a.29.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.p.a.29.1	✓	128	85.12	even	16
85.3.p.a.29.16	yes	128	85.63	even	16
85.3.p.a.44.1	yes	128	5.3	odd	4
85.3.p.a.44.16	yes	128	5.2	odd	4
425.3.u.f.301.1		128	85.29	odd	16	inner
425.3.u.f.301.16		128	17.12	odd	16	inner
425.3.u.f.401.1		128	5.4	even	2	inner
425.3.u.f.401.16		128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42932 - 3.45068i) q^{2} +(-2.42313 - 1.61908i) q^{3} +(-7.03579 - 7.03579i) q^{4} +(-9.05036 + 6.04726i) q^{6} +(-8.53763 - 1.69824i) q^{7} +(-20.5319 + 8.50460i) q^{8} +(-0.194021 - 0.468407i) q^{9} +(1.94402 + 2.90944i) q^{11} +(5.65711 + 28.4402i) q^{12} +(11.5538 - 11.5538i) q^{13} +(-18.0631 + 27.0333i) q^{14} +43.2043i q^{16} +(10.9247 - 13.0250i) q^{17} -1.89364 q^{18} +(-6.12848 + 14.7955i) q^{19} +(17.9382 + 17.9382i) q^{21} +(12.8182 - 2.54969i) q^{22} +(15.7311 - 10.5112i) q^{23} +(63.5212 + 12.6352i) q^{24} +(-23.3545 - 56.3826i) q^{26} +(-5.40518 + 27.1737i) q^{27} +(48.1206 + 72.0175i) q^{28} +(-0.161105 - 0.809929i) q^{29} +(-27.1672 + 40.6586i) q^{31} +(66.9565 + 27.7343i) q^{32} -10.1975i q^{33} +(-29.3301 - 56.3145i) q^{34} +(-1.93053 + 4.66071i) q^{36} +(-12.7024 - 8.48749i) q^{37} +(42.2948 + 42.2948i) q^{38} +(-46.7031 + 9.28982i) q^{39} +(7.15520 + 1.42326i) q^{41} +(87.5383 - 36.2596i) q^{42} +(-29.6179 - 71.5040i) q^{43} +(6.79245 - 34.1480i) q^{44} +(-13.7859 - 69.3066i) q^{46} +(-6.97451 + 6.97451i) q^{47} +(69.9515 - 104.690i) q^{48} +(24.7371 + 10.2464i) q^{49} +(-47.5606 + 13.8732i) q^{51} -162.581 q^{52} +(-20.2772 + 48.9536i) q^{53} +(86.0418 + 57.4913i) q^{54} +(189.737 - 37.7410i) q^{56} +(38.8052 - 25.9288i) q^{57} +(-3.02507 - 0.601725i) q^{58} +(-18.5654 + 7.69002i) q^{59} +(6.09486 - 30.6409i) q^{61} +(101.469 + 151.859i) q^{62} +(0.861009 + 4.32858i) q^{63} +(69.2039 - 69.2039i) q^{64} +(-35.1883 - 14.5755i) q^{66} -32.7490i q^{67} +(-168.505 + 14.7769i) q^{68} -55.1369 q^{69} +(47.1234 + 31.4868i) q^{71} +(7.96724 + 7.96724i) q^{72} +(-132.555 + 26.3668i) q^{73} +(-47.4434 + 31.7007i) q^{74} +(147.217 - 60.9791i) q^{76} +(-11.6564 - 28.1411i) q^{77} +(-34.6974 + 174.435i) q^{78} +(33.2990 + 49.8354i) q^{79} +(53.8674 - 53.8674i) q^{81} +(15.1382 - 22.6560i) q^{82} +(90.0810 + 37.3128i) q^{83} -252.419i q^{84} -289.071 q^{86} +(-0.920966 + 2.22341i) q^{87} +(-64.6582 - 43.2032i) q^{88} +(-65.9279 - 65.9279i) q^{89} +(-118.264 + 79.0212i) q^{91} +(-184.635 - 36.7262i) q^{92} +(131.659 - 54.5351i) q^{93} +(14.0980 + 34.0355i) q^{94} +(-117.340 - 175.612i) q^{96} +(3.04857 + 15.3262i) q^{97} +(70.7142 - 70.7142i) q^{98} +(0.985622 - 1.47509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{4} - 16 q^{6} + 16 q^{9} - 96 q^{11} + 16 q^{14} + 16 q^{19} + 224 q^{21} + 160 q^{24} + 288 q^{26} + 176 q^{29} + 48 q^{31} - 48 q^{34} - 144 q^{36} - 336 q^{41} + 48 q^{44} - 224 q^{46}+ \cdots + 1664 q^{99}+O(q^{100}) \) 128 * q + 16 * q^4 - 16 * q^6 + 16 * q^9 - 96 * q^11 + 16 * q^14 + 16 * q^19 + 224 * q^21 + 160 * q^24 + 288 * q^26 + 176 * q^29 + 48 * q^31 - 48 * q^34 - 144 * q^36 - 336 * q^41 + 48 * q^44 - 224 * q^46 + 48 * q^49 - 16 * q^51 - 512 * q^54 - 16 * q^56 - 272 * q^59 - 16 * q^61 - 688 * q^64 - 80 * q^66 - 448 * q^69 + 192 * q^71 - 704 * q^74 + 496 * q^76 - 304 * q^79 + 128 * q^81 - 2496 * q^86 + 256 * q^89 - 1632 * q^91 + 1296 * q^94 - 1728 * q^96 + 1664 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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