LMFDB - Embedded newform 425.3.u.e.401.10

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 = [96,0,0,0,0,0,0,0,0,0,0,192] 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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.10
Character	$\chi$	$=$	425.401
Dual form			425.3.u.e.301.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866790 - 2.09262i) q^{2} +(-2.52684 - 1.68838i) q^{3} +(-0.799289 - 0.799289i) q^{4} +(-5.72336 + 3.82423i) q^{6} +(-8.48985 - 1.68874i) q^{7} +(6.00504 - 2.48737i) q^{8} +(0.0901317 + 0.217597i) q^{9} +(-6.93341 - 10.3766i) q^{11} +(0.670170 + 3.36917i) q^{12} +(6.75230 - 6.75230i) q^{13} +(-10.8928 + 16.3022i) q^{14} -19.2437i q^{16} +(5.68096 + 16.0227i) q^{17} +0.533473 q^{18} +(-12.4006 + 29.9377i) q^{19} +(18.6012 + 18.6012i) q^{21} +(-27.7240 + 5.51465i) q^{22} +(-35.0679 + 23.4316i) q^{23} +(-19.3734 - 3.85361i) q^{24} +(-8.27714 - 19.9828i) q^{26} +(-5.19628 + 26.1235i) q^{27} +(5.43605 + 8.13563i) q^{28} +(1.11614 + 5.61123i) q^{29} +(9.85122 - 14.7434i) q^{31} +(-16.2496 - 6.73079i) q^{32} +37.9261i q^{33} +(38.4535 + 2.00023i) q^{34} +(0.101882 - 0.245964i) q^{36} +(-19.4435 - 12.9917i) q^{37} +(51.8994 + 51.8994i) q^{38} +(-28.4624 + 5.66152i) q^{39} +(-7.16994 - 1.42619i) q^{41} +(55.0486 - 22.8019i) q^{42} +(-2.27340 - 5.48847i) q^{43} +(-2.75209 + 13.8357i) q^{44} +(18.6369 + 93.6940i) q^{46} +(12.4219 - 12.4219i) q^{47} +(-32.4907 + 48.6258i) q^{48} +(23.9555 + 9.92271i) q^{49} +(12.6975 - 50.0783i) q^{51} -10.7941 q^{52} +(27.3491 - 66.0266i) q^{53} +(50.1623 + 33.5174i) q^{54} +(-55.1824 + 10.9765i) q^{56} +(81.8804 - 54.7107i) q^{57} +(12.7096 + 2.52810i) q^{58} +(-80.2486 + 33.2400i) q^{59} +(2.22963 - 11.2091i) q^{61} +(-22.3133 - 33.3942i) q^{62} +(-0.397740 - 1.99958i) q^{63} +(26.2596 - 26.2596i) q^{64} +(79.3648 + 32.8740i) q^{66} +48.2950i q^{67} +(8.26603 - 17.3475i) q^{68} +128.172 q^{69} +(-75.6574 - 50.5527i) q^{71} +(1.08249 + 1.08249i) q^{72} +(-48.4052 + 9.62839i) q^{73} +(-44.0401 + 29.4266i) q^{74} +(33.8405 - 14.0172i) q^{76} +(41.3403 + 99.8042i) q^{77} +(-12.8235 + 64.4682i) q^{78} +(13.0615 + 19.5479i) q^{79} +(58.7353 - 58.7353i) q^{81} +(-9.19930 + 13.7677i) q^{82} +(-101.811 - 42.1714i) q^{83} -29.7355i q^{84} -13.4558 q^{86} +(6.65357 - 16.0631i) q^{87} +(-67.4458 - 45.0658i) q^{88} +(-20.1124 - 20.1124i) q^{89} +(-68.7288 + 45.9231i) q^{91} +(46.7580 + 9.30075i) q^{92} +(-49.7849 + 20.6216i) q^{93} +(-15.2270 - 36.7613i) q^{94} +(29.6959 + 44.4430i) q^{96} +(-17.7309 - 89.1393i) q^{97} +(41.5289 - 41.5289i) q^{98} +(1.63299 - 2.44395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * 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 $

$2$	0.866790	−	2.09262i	0.433395	−	1.04631i	−0.544790	−	0.838572i	$-0.683391\pi$
$2$	0.866790	−	2.09262i	0.433395	−	1.04631i	0.978185	−	0.207735i	$-0.0666093\pi$
$3$	−2.52684	−	1.68838i	−0.842279	−	0.562793i	0.0578954	−	0.998323i	$-0.481561\pi$
$3$	−2.52684	−	1.68838i	−0.842279	−	0.562793i	−0.900174	+	0.435530i	$0.856561\pi$
$4$	−0.799289	−	0.799289i	−0.199822	−	0.199822i
$5$		0			0
$5$		0			0
$6$	−5.72336	+	3.82423i	−0.953894	+	0.637372i
$7$	−8.48985	−	1.68874i	−1.21284	−	0.241248i	−0.453087	−	0.891466i	$-0.649677\pi$
$7$	−8.48985	−	1.68874i	−1.21284	−	0.241248i	−0.759748	+	0.650218i	$0.774677\pi$
$8$	6.00504	−	2.48737i	0.750630	−	0.310921i
$9$	0.0901317	+	0.217597i	0.0100146	+	0.0241775i
$10$		0			0
$11$	−6.93341	−	10.3766i	−0.630310	−	0.943325i	−0.999900	−	0.0141305i	$-0.995502\pi$
$11$	−6.93341	−	10.3766i	−0.630310	−	0.943325i	0.369590	−	0.929195i	$-0.379498\pi$
$12$	0.670170	+	3.36917i	0.0558475	+	0.280765i
$13$	6.75230	−	6.75230i	0.519408	−	0.519408i	−0.397984	−	0.917392i	$-0.630290\pi$
$13$	6.75230	−	6.75230i	0.519408	−	0.519408i	0.917392	+	0.397984i	$0.130290\pi$
$14$	−10.8928	+	16.3022i	−0.778056	+	1.16444i
$15$		0			0
$16$		−	19.2437i		−	1.20273i
$17$	5.68096	+	16.0227i	0.334174	+	0.942511i
$17$	5.68096	+	16.0227i	0.334174	+	0.942511i
$18$	0.533473			0.0296374
$19$	−12.4006	+	29.9377i	−0.652663	+	1.57567i	0.156236	+	0.987720i	$0.450064\pi$
$19$	−12.4006	+	29.9377i	−0.652663	+	1.57567i	−0.808899	+	0.587948i	$0.799936\pi$
$20$		0			0
$21$	18.6012	+	18.6012i	0.885773	+	0.885773i
$22$	−27.7240	+	5.51465i	−1.26018	+	0.250666i
$23$	−35.0679	+	23.4316i	−1.52469	+	1.01877i	−0.540565	+	0.841302i	$0.681789\pi$
$23$	−35.0679	+	23.4316i	−1.52469	+	1.01877i	−0.984127	+	0.177464i	$0.943211\pi$
$24$	−19.3734	−	3.85361i	−0.807224	−	0.160567i
$25$		0			0
$26$	−8.27714	−	19.9828i	−0.318352	−	0.768569i
$27$	−5.19628	+	26.1235i	−0.192455	+	0.967535i
$28$	5.43605	+	8.13563i	0.194145	+	0.290558i
$29$	1.11614	+	5.61123i	0.0384877	+	0.193491i	0.995246	−	0.0973936i	$-0.0310506\pi$
$29$	1.11614	+	5.61123i	0.0384877	+	0.193491i	−0.956758	+	0.290884i	$0.906051\pi$
$30$		0			0
$31$	9.85122	−	14.7434i	0.317781	−	0.475593i	−0.637849	−	0.770161i	$-0.720176\pi$
$31$	9.85122	−	14.7434i	0.317781	−	0.475593i	0.955631	+	0.294568i	$0.0951757\pi$
$32$	−16.2496	−	6.73079i	−0.507799	−	0.210337i
$33$			37.9261i			1.14928i
$34$	38.4535	+	2.00023i	1.13099	+	0.0588304i
$35$		0			0
$36$	0.101882	−	0.245964i	0.00283005	−	0.00683234i
$37$	−19.4435	−	12.9917i	−0.525499	−	0.351127i	0.264352	−	0.964426i	$-0.414842\pi$
$37$	−19.4435	−	12.9917i	−0.525499	−	0.351127i	−0.789851	+	0.613299i	$0.789842\pi$
$38$	51.8994	+	51.8994i	1.36577	+	1.36577i
$39$	−28.4624	+	5.66152i	−0.729805	+	0.145167i
$40$		0			0
$41$	−7.16994	−	1.42619i	−0.174877	−	0.0347851i	0.106875	−	0.994272i	$-0.465915\pi$
$41$	−7.16994	−	1.42619i	−0.174877	−	0.0347851i	−0.281752	+	0.959487i	$0.590915\pi$
$42$	55.0486	−	22.8019i	1.31068	−	0.542902i
$43$	−2.27340	−	5.48847i	−0.0528698	−	0.127639i	0.895238	−	0.445589i	$-0.147006\pi$
$43$	−2.27340	−	5.48847i	−0.0528698	−	0.127639i	−0.948108	+	0.317950i	$0.897006\pi$
$44$	−2.75209	+	13.8357i	−0.0625475	+	0.314447i
$45$		0			0
$46$	18.6369	+	93.6940i	0.405150	+	2.03683i
$47$	12.4219	−	12.4219i	0.264295	−	0.264295i	−0.562501	−	0.826796i	$-0.690161\pi$
$47$	12.4219	−	12.4219i	0.264295	−	0.264295i	0.826796	+	0.562501i	$0.190161\pi$
$48$	−32.4907	+	48.6258i	−0.676890	+	1.01304i
$49$	23.9555	+	9.92271i	0.488889	+	0.202504i
$50$		0			0
$51$	12.6975	−	50.0783i	0.248971	−	0.981928i
$52$	−10.7941			−0.207578
$53$	27.3491	−	66.0266i	0.516021	−	1.24579i	−0.424308	−	0.905518i	$-0.639482\pi$
$53$	27.3491	−	66.0266i	0.516021	−	1.24579i	0.940329	−	0.340267i	$-0.110518\pi$
$54$	50.1623	+	33.5174i	0.928931	+	0.620692i
$55$		0			0
$56$	−55.1824	+	10.9765i	−0.985400	+	0.196008i
$57$	81.8804	−	54.7107i	1.43650	−	0.959838i
$58$	12.7096	+	2.52810i	0.219131	+	0.0435879i
$59$	−80.2486	+	33.2400i	−1.36014	+	0.563391i	−0.939098	−	0.343648i	$-0.888337\pi$
$59$	−80.2486	+	33.2400i	−1.36014	+	0.563391i	−0.421047	+	0.907039i	$0.638337\pi$
$60$		0			0
$61$	2.22963	−	11.2091i	0.0365514	−	0.183756i	−0.958197	−	0.286110i	$-0.907638\pi$
$61$	2.22963	−	11.2091i	0.0365514	−	0.183756i	0.994748	+	0.102354i	$0.0326376\pi$
$62$	−22.3133	−	33.3942i	−0.359892	−	0.538617i
$63$	−0.397740	−	1.99958i	−0.00631334	−	0.0317393i
$64$	26.2596	−	26.2596i	0.410306	−	0.410306i
$65$		0			0
$66$	79.3648	+	32.8740i	1.20250	+	0.498091i
$67$			48.2950i			0.720821i	0.932794	+	0.360410i	$0.117363\pi$
$67$			48.2950i			0.720821i	−0.932794	+	0.360410i	$0.882637\pi$
$68$	8.26603	−	17.3475i	0.121559	−	0.255110i
$69$	128.172			1.85757
$70$		0			0
$71$	−75.6574	−	50.5527i	−1.06560	−	0.712009i	−0.106279	−	0.994336i	$-0.533894\pi$
$71$	−75.6574	−	50.5527i	−1.06560	−	0.712009i	−0.959318	+	0.282327i	$0.908894\pi$
$72$	1.08249	+	1.08249i	0.0150346	+	0.0150346i
$73$	−48.4052	+	9.62839i	−0.663084	+	0.131896i	−0.515148	−	0.857101i	$-0.672263\pi$
$73$	−48.4052	+	9.62839i	−0.663084	+	0.131896i	−0.147936	+	0.988997i	$0.547263\pi$
$74$	−44.0401	+	29.4266i	−0.595136	+	0.397657i
$75$		0			0
$76$	33.8405	−	14.0172i	0.445270	−	0.184437i
$77$	41.3403	+	99.8042i	0.536887	+	1.29616i
$78$	−12.8235	+	64.4682i	−0.164404	+	0.826516i
$79$	13.0615	+	19.5479i	0.165336	+	0.247442i	0.904881	−	0.425664i	$-0.139960\pi$
$79$	13.0615	+	19.5479i	0.165336	+	0.247442i	−0.739546	+	0.673107i	$0.764960\pi$
$80$		0			0
$81$	58.7353	−	58.7353i	0.725127	−	0.725127i
$82$	−9.19930	+	13.7677i	−0.112187	+	0.167899i
$83$	−101.811	−	42.1714i	−1.22663	−	0.508089i	−0.327121	−	0.944982i	$-0.606079\pi$
$83$	−101.811	−	42.1714i	−1.22663	−	0.508089i	−0.899513	+	0.436894i	$0.856079\pi$
$84$		−	29.7355i		−	0.353994i
$85$		0			0
$86$	−13.4558			−0.156463
$87$	6.65357	−	16.0631i	0.0764778	−	0.184634i
$88$	−67.4458	−	45.0658i	−0.766430	−	0.512112i
$89$	−20.1124	−	20.1124i	−0.225982	−	0.225982i	0.585030	−	0.811012i	$-0.301083\pi$
$89$	−20.1124	−	20.1124i	−0.225982	−	0.225982i	−0.811012	+	0.585030i	$0.801083\pi$
$90$		0			0
$91$	−68.7288	+	45.9231i	−0.755262	+	0.504650i
$92$	46.7580	+	9.30075i	0.508240	+	0.101095i
$93$	−49.7849	+	20.6216i	−0.535321	+	0.221737i
$94$	−15.2270	−	36.7613i	−0.161990	−	0.391078i
$95$		0			0
$96$	29.6959	+	44.4430i	0.309332	+	0.462948i
$97$	−17.7309	−	89.1393i	−0.182793	−	0.918962i	−0.957893	−	0.287124i	$-0.907301\pi$
$97$	−17.7309	−	89.1393i	−0.182793	−	0.918962i	0.775101	−	0.631838i	$-0.217699\pi$
$98$	41.5289	−	41.5289i	0.423764	−	0.423764i
$99$	1.63299	−	2.44395i	0.0164949	−	0.0246864i
$100$		0			0
$101$		−	93.8603i		−	0.929310i	−0.885492	−	0.464655i	$-0.846178\pi$
$101$		−	93.8603i		−	0.929310i	0.885492	−	0.464655i	$-0.153822\pi$
$102$	−93.7887	−	69.9784i	−0.919497	−	0.686063i
$103$	200.081			1.94254			0.971269	−	0.237984i	$-0.0764866\pi$
$103$	200.081			1.94254			0.971269	+	0.237984i	$0.0764866\pi$
$104$	23.7524	−	57.3433i	0.228388	−	0.551378i
$105$		0			0
$106$	−114.462	−	114.462i	−1.07983	−	1.07983i
$107$	120.129	−	23.8951i	1.12270	−	0.223318i	0.401372	−	0.915915i	$-0.368533\pi$
$107$	120.129	−	23.8951i	1.12270	−	0.223318i	0.721325	+	0.692597i	$0.243533\pi$
$108$	25.0335	−	16.7269i	0.231792	−	0.154878i
$109$	21.4988	+	4.27638i	0.197237	+	0.0392329i	0.292720	−	0.956198i	$-0.405440\pi$
$109$	21.4988	+	4.27638i	0.197237	+	0.0392329i	−0.0954832	+	0.995431i	$0.530440\pi$
$110$		0			0
$111$	27.1955	+	65.6559i	0.245005	+	0.591494i
$112$	−32.4976	+	163.376i	−0.290157	+	1.45872i
$113$	−86.8616	−	129.998i	−0.768687	−	1.15042i	−0.984739	−	0.174040i	$-0.944318\pi$
$113$	−86.8616	−	129.998i	−0.768687	−	1.15042i	0.216052	−	0.976382i	$-0.430682\pi$
$114$	−43.5155	−	218.767i	−0.381715	−	1.91901i
$115$		0			0
$116$	3.59287	−	5.37711i	0.0309730	−	0.0463544i
$117$	2.07788	+	0.860685i	0.0177596	+	0.00735628i
$118$			196.742i			1.66730i
$119$	−21.1724	−	145.624i	−0.177919	−	1.22373i
$120$		0			0
$121$	−13.2965	+	32.1007i	−0.109889	+	0.265295i
$122$	−21.5238	−	14.3817i	−0.176424	−	0.117883i
$123$	15.7093	+	15.7093i	0.127718	+	0.127718i
$124$	−19.6582	+	3.91026i	−0.158534	+	0.0315344i
$125$		0			0
$126$	−4.52910	−	0.900894i	−0.0359452	−	0.00714995i
$127$	4.34740	−	1.80075i	0.0342315	−	0.0141792i	−0.365502	−	0.930811i	$-0.619103\pi$
$127$	4.34740	−	1.80075i	0.0342315	−	0.0141792i	0.399734	+	0.916631i	$0.369103\pi$
$128$	−59.1128	−	142.711i	−0.461819	−	1.11493i
$129$	−3.52211	+	17.7068i	−0.0273032	+	0.137262i
$130$		0			0
$131$	31.8006	+	159.872i	0.242753	+	1.22040i	0.889228	+	0.457465i	$0.151242\pi$
$131$	31.8006	+	159.872i	0.242753	+	1.22040i	−0.646475	+	0.762935i	$0.723758\pi$
$132$	30.3139	−	30.3139i	0.229651	−	0.229651i
$133$	155.836	−	233.225i	1.17170	−	1.75357i
$134$	101.063	+	41.8616i	0.754200	+	0.312400i
$135$		0			0
$136$	73.9688	+	82.0863i	0.543888	+	0.603576i
$137$	−138.971			−1.01439			−0.507193	−	0.861832i	$-0.669317\pi$
$137$	−138.971			−1.01439			−0.507193	+	0.861832i	$0.669317\pi$
$138$	111.098	−	268.216i	0.805062	−	1.94359i
$139$	−188.264	−	125.794i	−1.35442	−	0.904992i	−0.354865	−	0.934918i	$-0.615473\pi$
$139$	−188.264	−	125.794i	−1.35442	−	0.904992i	−0.999552	+	0.0299254i	$0.990473\pi$
$140$		0			0
$141$	−52.3608	+	10.4152i	−0.371353	+	0.0738668i
$142$	−171.366	+	114.503i	−1.20681	+	0.806362i
$143$	−116.882	−	23.2493i	−0.817358	−	0.162583i
$144$	4.18738	−	1.73447i	0.0290790	−	0.0120449i
$145$		0			0
$146$	−21.8086	+	109.639i	−0.149374	+	0.750953i
$147$	−43.7785	−	65.5191i	−0.297813	−	0.445708i
$148$	5.15682	+	25.9251i	0.0348434	+	0.175169i
$149$	−105.654	+	105.654i	−0.709084	+	0.709084i	−0.966343	−	0.257259i	$-0.917181\pi$
$149$	−105.654	+	105.654i	−0.709084	+	0.709084i	0.257259	+	0.966343i	$0.417181\pi$
$150$		0			0
$151$	−23.7275	−	9.82824i	−0.157136	−	0.0650877i	0.302729	−	0.953077i	$-0.402102\pi$
$151$	−23.7275	−	9.82824i	−0.157136	−	0.0650877i	−0.459865	+	0.887989i	$0.652102\pi$
$152$			210.622i			1.38567i
$153$	−2.97446	+	2.68031i	−0.0194409	+	0.0175184i
$154$	244.685			1.58887
$155$		0			0
$156$	27.2749	+	18.2245i	0.174839	+	0.116824i
$157$	−140.205	−	140.205i	−0.893028	−	0.893028i	0.101779	−	0.994807i	$-0.467546\pi$
$157$	−140.205	−	140.205i	−0.893028	−	0.893028i	−0.994807	+	0.101779i	$0.967546\pi$
$158$	52.2279	−	10.3888i	0.330556	−	0.0657517i
$159$	−180.585	+	120.663i	−1.13575	+	0.758886i
$160$		0			0
$161$	337.291	−	139.711i	2.09498	−	0.867767i
$162$	−71.9993	−	173.822i	−0.444440	−	1.07297i
$163$	−34.1597	+	171.733i	−0.209569	+	1.05357i	0.722522	+	0.691348i	$0.242983\pi$
$163$	−34.1597	+	171.733i	−0.209569	+	1.05357i	−0.932091	+	0.362225i	$0.882017\pi$
$164$	4.59092	+	6.87079i	0.0279934	+	0.0418951i
$165$		0			0
$166$	−176.497	+	176.497i	−1.06323	+	1.06323i
$167$	77.6543	−	116.218i	0.464996	−	0.695916i	−0.522662	−	0.852540i	$-0.675061\pi$
$167$	77.6543	−	116.218i	0.464996	−	0.695916i	0.987658	+	0.156624i	$0.0500611\pi$
$168$	157.969	+	65.4330i	0.940294	+	0.389482i
$169$			77.8129i			0.460431i
$170$		0			0
$171$	−7.63204			−0.0446318
$172$	−2.56977	+	6.20398i	−0.0149405	+	0.0360697i
$173$	179.105	+	119.674i	1.03529	+	0.691757i	0.952416	−	0.304803i	$-0.0985905\pi$
$173$	179.105	+	119.674i	1.03529	+	0.691757i	0.0828726	+	0.996560i	$0.473591\pi$
$174$	−27.8467	−	27.8467i	−0.160039	−	0.160039i
$175$		0			0
$176$	−199.684	+	133.425i	−1.13457	+	0.758095i
$177$	258.897	+	51.4978i	1.46269	+	0.290948i
$178$	−59.5206	+	24.6542i	−0.334385	+	0.138507i
$179$	10.2028	+	24.6318i	0.0569990	+	0.137608i	0.949813	−	0.312817i	$-0.101273\pi$
$179$	10.2028	+	24.6318i	0.0569990	+	0.137608i	−0.892814	+	0.450425i	$0.851273\pi$
$180$		0			0
$181$	21.6217	+	32.3591i	0.119457	+	0.178780i	0.886379	−	0.462960i	$-0.153213\pi$
$181$	21.6217	+	32.3591i	0.119457	+	0.178780i	−0.766922	+	0.641740i	$0.778213\pi$
$182$	36.5260	+	183.629i	0.200692	+	1.00895i
$183$	−24.5592	+	24.5592i	−0.134203	+	0.134203i
$184$	−152.301	+	227.935i	−0.827724	+	1.23878i
$185$		0			0
$186$			122.055i			0.656210i
$187$	126.872	−	170.041i	0.678461	−	0.909309i
$188$	−19.8573			−0.105624
$189$	88.2312	−	213.009i	0.466832	−	1.12703i
$190$		0			0
$191$	−104.149	−	104.149i	−0.545285	−	0.545285i	0.379789	−	0.925073i	$-0.375997\pi$
$191$	−104.149	−	104.149i	−0.545285	−	0.545285i	−0.925073	+	0.379789i	$0.875997\pi$
$192$	−110.690	+	22.0176i	−0.576509	+	0.114675i
$193$	−191.054	+	127.658i	−0.989915	+	0.661440i	−0.941368	−	0.337381i	$-0.890459\pi$
$193$	−191.054	+	127.658i	−0.989915	+	0.661440i	−0.0485471	+	0.998821i	$0.515459\pi$
$194$	−201.903	−	40.1610i	−1.04074	−	0.207016i
$195$		0			0
$196$	−11.2163	−	27.0785i	−0.0572260	−	0.138156i
$197$	−4.33655	+	21.8013i	−0.0220130	+	0.110667i	−0.990230	−	0.139446i	$-0.955468\pi$
$197$	−4.33655	+	21.8013i	−0.0220130	+	0.110667i	0.968217	+	0.250113i	$0.0804677\pi$
$198$	−3.69878	−	5.53562i	−0.0186807	−	0.0279577i
$199$	−51.4884	−	258.849i	−0.258735	−	1.30075i	−0.863501	−	0.504347i	$-0.831733\pi$
$199$	−51.4884	−	258.849i	−0.258735	−	1.30075i	0.604765	−	0.796404i	$-0.293267\pi$
$200$		0			0
$201$	81.5402	−	122.034i	0.405673	−	0.607132i
$202$	−196.413	−	81.3571i	−0.972344	−	0.402758i
$203$		−	49.5233i		−	0.243957i
$204$	−50.1760	+	29.8781i	−0.245961	+	0.146461i
$205$		0			0
$206$	173.429	−	418.694i	0.841886	−	2.03249i
$207$	−8.25939	−	5.51875i	−0.0399004	−	0.0266606i
$208$	−129.939	−	129.939i	−0.624709	−	0.624709i
$209$	396.629	−	78.8944i	1.89775	−	0.377485i
$210$		0			0
$211$	−88.8409	−	17.6715i	−0.421047	−	0.0837514i	−0.0199803	−	0.999800i	$-0.506360\pi$
$211$	−88.8409	−	17.6715i	−0.421047	−	0.0837514i	−0.401066	+	0.916049i	$0.631360\pi$
$212$	−74.6342	+	30.9145i	−0.352048	+	0.145823i
$213$	105.822	+	255.477i	0.496817	+	1.19942i
$214$	54.1231	−	272.095i	0.252911	−	1.27147i
$215$		0			0
$216$	33.7748	+	169.798i	0.156365	+	0.786100i
$217$	−108.533	+	108.533i	−0.500152	+	0.500152i
$218$	27.5838	−	41.2820i	0.126531	−	0.189367i
$219$	138.568	+	57.3969i	0.632732	+	0.262086i
$220$		0			0
$221$	146.550	+	69.8305i	0.663120	+	0.315975i
$222$	160.965			0.725069
$223$	−14.3366	+	34.6116i	−0.0642897	+	0.155209i	−0.952759	−	0.303726i	$-0.901769\pi$
$223$	−14.3366	+	34.6116i	−0.0642897	+	0.155209i	0.888470	+	0.458936i	$0.151769\pi$
$224$	126.590	+	84.5846i	0.565133	+	0.377610i
$225$		0			0
$226$	−347.326	+	69.0874i	−1.53684	+	0.305697i
$227$	225.918	−	150.954i	0.995234	−	0.664994i	0.0525286	−	0.998619i	$-0.483272\pi$
$227$	225.918	−	150.954i	0.995234	−	0.664994i	0.942706	+	0.333625i	$0.108272\pi$
$228$	−109.176	−	21.7164i	−0.478841	−	0.0952474i
$229$	1.93040	−	0.799599i	0.00842971	−	0.00349170i	−0.378465	−	0.925616i	$-0.623548\pi$
$229$	1.93040	−	0.799599i	0.00842971	−	0.00349170i	0.386894	+	0.922124i	$0.373548\pi$
$230$		0			0
$231$	64.0472	−	321.987i	0.277261	−	1.39388i
$232$	20.6597	+	30.9194i	0.0890504	+	0.133273i
$233$	−48.1808	−	242.221i	−0.206785	−	1.03958i	−0.935113	−	0.354349i	$-0.884703\pi$
$233$	−48.1808	−	242.221i	−0.206785	−	1.03958i	0.728329	−	0.685228i	$-0.240297\pi$
$234$	3.60217	−	3.60217i	0.0153939	−	0.0153939i
$235$		0			0
$236$	90.7102	+	37.5734i	0.384365	+	0.159209i
$237$		−	71.4472i		−	0.301465i
$238$	−323.087	−	81.9195i	−1.35751	−	0.344200i
$239$	−73.3632			−0.306959			−0.153479	−	0.988152i	$-0.549048\pi$
$239$	−73.3632			−0.306959			−0.153479	+	0.988152i	$0.549048\pi$
$240$		0			0
$241$	181.747	+	121.439i	0.754137	+	0.503898i	0.872225	−	0.489105i	$-0.162676\pi$
$241$	181.747	+	121.439i	0.754137	+	0.503898i	−0.118088	+	0.993003i	$0.537676\pi$
$242$	55.6491	+	55.6491i	0.229955	+	0.229955i
$243$	−12.4708	+	2.48060i	−0.0513203	+	0.0102082i
$244$	−10.7414	+	7.17721i	−0.0440223	+	0.0294148i
$245$		0			0
$246$	46.4903	−	19.2569i	0.188985	−	0.0782801i
$247$	118.416	+	285.881i	0.479416	+	1.15741i
$248$	22.4847	−	113.038i	0.0906642	−	0.455800i
$249$	186.058	+	278.455i	0.747220	+	1.11829i
$250$		0			0
$251$	316.879	−	316.879i	1.26247	−	1.26247i	0.312573	−	0.949894i	$-0.398809\pi$
$251$	316.879	−	316.879i	1.26247	−	1.26247i	0.949894	−	0.312573i	$-0.101191\pi$
$252$	−1.28033	+	1.91615i	−0.00508067	+	0.00760376i
$253$	486.280	+	201.424i	1.92206	+	0.796142i
$254$		−	10.6583i		−	0.0419619i
$255$		0			0
$256$	−201.331			−0.786450
$257$	47.6536	−	115.046i	0.185422	−	0.447649i	−0.803646	−	0.595108i	$-0.797109\pi$
$257$	47.6536	−	115.046i	0.185422	−	0.447649i	0.989068	+	0.147459i	$0.0471093\pi$
$258$	34.0007	+	22.7185i	0.131786	+	0.0880563i
$259$	143.132	+	143.132i	0.552635	+	0.552635i
$260$		0			0
$261$	−1.12039	+	0.748619i	−0.00429267	+	0.00286827i
$262$	362.116	+	72.0293i	1.38212	+	0.274921i
$263$	−242.117	+	100.288i	−0.920598	+	0.381324i	−0.792104	−	0.610386i	$-0.791014\pi$
$263$	−242.117	+	100.288i	−0.920598	+	0.381324i	−0.128494	+	0.991710i	$0.541014\pi$
$264$	94.3363	+	227.748i	0.357335	+	0.862682i
$265$		0			0
$266$	−352.973	−	528.262i	−1.32697	−	1.98595i
$267$	16.8634	+	84.7779i	0.0631587	+	0.317520i
$268$	38.6016	−	38.6016i	0.144036	−	0.144036i
$269$	108.483	−	162.356i	0.403283	−	0.603556i	−0.573131	−	0.819464i	$-0.694271\pi$
$269$	108.483	−	162.356i	0.403283	−	0.603556i	0.976414	+	0.215908i	$0.0692712\pi$
$270$		0			0
$271$			434.612i			1.60373i	0.597503	+	0.801867i	$0.296160\pi$
$271$			434.612i			1.60373i	−0.597503	+	0.801867i	$0.703840\pi$
$272$	308.336	−	109.323i	1.13359	−	0.401923i
$273$	251.202			0.920154
$274$	−120.459	+	290.813i	−0.439630	+	1.06136i
$275$		0			0
$276$	−102.447	−	102.447i	−0.371184	−	0.371184i
$277$	−208.517	+	41.4767i	−0.752770	+	0.149735i	−0.556538	−	0.830822i	$-0.687871\pi$
$277$	−208.517	+	41.4767i	−0.752770	+	0.149735i	−0.196232	+	0.980557i	$0.562871\pi$
$278$	−426.424	+	284.927i	−1.53390	+	1.02492i
$279$	4.09603	+	0.814751i	0.0146811	+	0.00292025i
$280$		0			0
$281$	29.4340	+	71.0600i	0.104747	+	0.252883i	0.967560	−	0.252641i	$-0.0812993\pi$
$281$	29.4340	+	71.0600i	0.104747	+	0.252883i	−0.862813	+	0.505524i	$0.831299\pi$
$282$	−23.5908	+	118.599i	−0.0836553	+	0.420564i
$283$	−189.480	−	283.577i	−0.669540	−	1.00204i	−0.998338	−	0.0576369i	$-0.981643\pi$
$283$	−189.480	−	283.577i	−0.669540	−	1.00204i	0.328798	−	0.944400i	$-0.393357\pi$
$284$	20.0659	+	100.878i	0.0706547	+	0.355205i
$285$		0			0
$286$	−149.964	+	224.437i	−0.524350	+	0.784746i
$287$	58.4633	+	24.2163i	0.203705	+	0.0843773i
$288$		−	4.14252i		−	0.0143837i
$289$	−224.453	+	182.049i	−0.776655	+	0.629926i
$290$		0			0
$291$	−105.698	+	255.177i	−0.363222	+	0.876896i
$292$	46.3856	+	30.9938i	0.158855	+	0.106143i
$293$	−52.6621	−	52.6621i	−0.179734	−	0.179734i	0.611506	−	0.791240i	$-0.290564\pi$
$293$	−52.6621	−	52.6621i	−0.179734	−	0.179734i	−0.791240	+	0.611506i	$0.790564\pi$
$294$	−175.053	+	34.8202i	−0.595419	+	0.118436i
$295$		0			0
$296$	−149.074	−	29.6527i	−0.503628	−	0.100178i
$297$	307.100	−	127.205i	1.03401	−	0.428300i
$298$	129.513	+	312.672i	0.434607	+	1.04923i
$299$	−78.5717	+	395.007i	−0.262782	+	1.32109i
$300$		0			0
$301$	10.0322	+	50.4355i	0.0333297	+	0.167560i
$302$	−41.1335	+	41.1335i	−0.136204	+	0.136204i
$303$	−158.472	+	237.170i	−0.523009	+	0.782738i
$304$	576.113	+	238.634i	1.89511	+	0.784979i
$305$		0			0
$306$	3.03064	+	8.54767i	0.00990404	+	0.0279336i
$307$	−376.746			−1.22719			−0.613593	−	0.789623i	$-0.710276\pi$
$307$	−376.746			−1.22719			−0.613593	+	0.789623i	$0.710276\pi$
$308$	46.7296	−	112.815i	0.151719	−	0.366283i
$309$	−505.573	−	337.813i	−1.63616	−	1.09325i
$310$		0			0
$311$	449.551	−	89.4212i	1.44550	−	0.287528i	0.590871	−	0.806766i	$-0.298784\pi$
$311$	449.551	−	89.4212i	1.44550	−	0.287528i	0.854630	+	0.519238i	$0.173784\pi$
$312$	−156.836	+	104.794i	−0.502678	+	0.335879i
$313$	326.004	+	64.8462i	1.04155	+	0.207176i	0.686090	−	0.727516i	$-0.259325\pi$
$313$	326.004	+	64.8462i	1.04155	+	0.207176i	0.355456	+	0.934693i	$0.384325\pi$
$314$	−414.924	+	171.867i	−1.32142	+	0.547348i
$315$		0			0
$316$	5.18453	−	26.0644i	0.0164067	−	0.0824822i
$317$	−102.174	−	152.915i	−0.322317	−	0.482381i	0.634561	−	0.772873i	$-0.281181\pi$
$317$	−102.174	−	152.915i	−0.322317	−	0.482381i	−0.956877	+	0.290492i	$0.906181\pi$
$318$	95.9720	+	482.484i	0.301799	+	1.51724i
$319$	50.4867	−	50.4867i	0.158265	−	0.158265i
$320$		0			0
$321$	−343.889	−	142.444i	−1.07131	−	0.443750i
$322$		−	826.920i		−	2.56807i
$323$	−550.130	−	28.6160i	−1.70319	−	0.0885946i
$324$	−93.8929			−0.289793
$325$		0			0
$326$	329.761	+	220.339i	1.01154	+	0.675887i
$327$	−47.1039	−	47.1039i	−0.144048	−	0.144048i
$328$	−46.6033	+	9.26997i	−0.142083	+	0.0282621i
$329$	−126.437	+	84.4825i	−0.384307	+	0.256786i
$330$		0			0
$331$	254.365	−	105.362i	0.768475	−	0.318313i	0.0362206	−	0.999344i	$-0.488468\pi$
$331$	254.365	−	105.362i	0.768475	−	0.318313i	0.732255	+	0.681031i	$0.238468\pi$
$332$	47.6690	+	115.083i	0.143581	+	0.346636i
$333$	1.07449	−	5.40181i	0.00322669	−	0.0162216i
$334$	−175.889	−	263.237i	−0.526615	−	0.788135i
$335$		0			0
$336$	357.957	−	357.957i	1.06535	−	1.06535i
$337$	−120.370	+	180.146i	−0.357180	+	0.534558i	−0.965930	−	0.258805i	$-0.916671\pi$
$337$	−120.370	+	180.146i	−0.357180	+	0.534558i	0.608750	+	0.793362i	$0.291671\pi$
$338$	162.832	+	67.4474i	0.481753	+	0.199549i
$339$			475.138i			1.40159i
$340$		0			0
$341$	−221.289			−0.648940
$342$	−6.61538	+	15.9709i	−0.0193432	+	0.0466986i
$343$	166.048	+	110.950i	0.484104	+	0.323468i
$344$	−27.3037	−	27.3037i	−0.0793713	−	0.0793713i
$345$		0			0
$346$	405.678	−	271.065i	1.17248	−	0.783426i
$347$	−633.392	−	125.990i	−1.82534	−	0.363082i	−0.841233	−	0.540672i	$-0.818170\pi$
$347$	−633.392	−	125.990i	−1.82534	−	0.363082i	−0.984105	+	0.177590i	$0.943170\pi$
$348$	−18.1572	+	7.52096i	−0.0521759	+	0.0216119i
$349$	197.003	+	475.608i	0.564480	+	1.36277i	0.906151	+	0.422955i	$0.139007\pi$
$349$	197.003	+	475.608i	0.564480	+	1.36277i	−0.341671	+	0.939820i	$0.610993\pi$
$350$		0			0
$351$	141.307	+	211.480i	0.402583	+	0.602508i
$352$	42.8223	+	215.282i	0.121654	+	0.611597i
$353$	338.137	−	338.137i	0.957896	−	0.957896i	−0.0412527	−	0.999149i	$-0.513135\pi$
$353$	338.137	−	338.137i	0.957896	−	0.957896i	0.999149	+	0.0412527i	$0.0131349\pi$
$354$	332.174	−	497.134i	0.938345	−	1.40433i
$355$		0			0
$356$			32.1512i			0.0903123i
$357$	−192.369	+	403.715i	−0.538848	+	1.13085i
$358$	60.3886			0.168683
$359$	186.181	−	449.482i	0.518611	−	1.25204i	−0.420145	−	0.907457i	$-0.638021\pi$
$359$	186.181	−	449.482i	0.518611	−	1.25204i	0.938756	−	0.344582i	$-0.111979\pi$
$360$		0			0
$361$	−487.225	−	487.225i	−1.34965	−	1.34965i
$362$	86.4567	−	17.1973i	0.238831	−	0.0475064i
$363$	87.7963	−	58.6636i	0.241863	−	0.161608i
$364$	91.6400	+	18.2283i	0.251758	+	0.0500779i
$365$		0			0
$366$	30.1053	+	72.6805i	0.0822548	+	0.198581i
$367$	1.25417	−	6.30513i	0.00341735	−	0.0171802i	−0.979039	−	0.203673i	$-0.934712\pi$
$367$	1.25417	−	6.30513i	0.00341735	−	0.0171802i	0.982456	+	0.186493i	$0.0597121\pi$
$368$	450.912	+	674.838i	1.22530	+	1.83380i
$369$	−0.335904	−	1.68870i	−0.000910310	−	0.00457644i
$370$		0			0
$371$	−343.691	+	514.370i	−0.926392	+	1.38644i
$372$	56.2751	+	23.3099i	0.151277	+	0.0626610i
$373$			622.933i			1.67006i	0.550202	+	0.835031i	$0.314551\pi$
$373$			622.933i			1.67006i	−0.550202	+	0.835031i	$0.685449\pi$
$374$	−245.858	−	412.885i	−0.657376	−	1.10397i
$375$		0			0
$376$	43.6961	−	105.492i	0.116213	−	0.280563i
$377$	45.4252	+	30.3522i	0.120491	+	0.0805097i
$378$	−369.268	−	369.268i	−0.976899	−	0.976899i
$379$	520.221	−	103.478i	1.37261	−	0.273030i	0.546937	−	0.837174i	$-0.315794\pi$
$379$	520.221	−	103.478i	1.37261	−	0.273030i	0.825676	+	0.564144i	$0.190794\pi$
$380$		0			0
$381$	−14.0255	−	2.78985i	−0.0368124	−	0.00732244i
$382$	−308.220	+	127.669i	−0.806859	+	0.334212i
$383$	208.008	+	502.177i	0.543103	+	1.31117i	0.922523	+	0.385942i	$0.126123\pi$
$383$	208.008	+	502.177i	0.543103	+	1.31117i	−0.379420	+	0.925224i	$0.623877\pi$
$384$	−91.5817	+	460.412i	−0.238494	+	1.19899i
$385$		0			0
$386$	101.536	+	510.455i	0.263046	+	1.32242i
$387$	0.989371	−	0.989371i	0.00255651	−	0.00255651i
$388$	−57.0759	+	85.4201i	−0.147103	+	0.220155i
$389$	−98.6183	−	40.8491i	−0.253518	−	0.105010i	0.252306	−	0.967648i	$-0.418811\pi$
$389$	−98.6183	−	40.8491i	−0.253518	−	0.105010i	−0.505823	+	0.862637i	$0.668811\pi$
$390$		0			0
$391$	−574.657	−	428.768i	−1.46971	−	1.09659i
$392$	168.536			0.429938
$393$	189.570	−	457.663i	0.482367	−	1.16454i
$394$	41.8629	+	27.9719i	0.106251	+	0.0709947i
$395$		0			0
$396$	−3.25866	+	0.648187i	−0.00822893	+	0.00163684i
$397$	−422.031	+	281.992i	−1.06305	+	0.710308i	−0.958754	−	0.284239i	$-0.908259\pi$
$397$	−422.031	+	281.992i	−1.06305	+	0.710308i	−0.104297	+	0.994546i	$0.533259\pi$
$398$	−586.302	−	116.623i	−1.47312	−	0.293022i
$399$	−787.544	+	326.211i	−1.97379	+	0.817572i
$400$		0			0
$401$	−31.1894	+	156.800i	−0.0777791	+	0.391022i	0.922211	+	0.386686i	$0.126380\pi$
$401$	−31.1894	+	156.800i	−0.0777791	+	0.391022i	−0.999991	+	0.00433613i	$0.998620\pi$
$402$	−184.691	−	276.410i	−0.459431	−	0.687586i
$403$	−33.0334	−	166.070i	−0.0819688	−	0.412085i
$404$	−75.0215	+	75.0215i	−0.185697	+	0.185697i
$405$		0			0
$406$	−103.633	−	42.9263i	−0.255254	−	0.105730i
$407$			291.833i			0.717036i
$408$	−48.3143	−	332.306i	−0.118418	−	0.814475i
$409$	−95.3354			−0.233094			−0.116547	−	0.993185i	$-0.537183\pi$
$409$	−95.3354			−0.233094			−0.116547	+	0.993185i	$0.537183\pi$
$410$		0			0
$411$	351.157	+	234.636i	0.854397	+	0.570890i
$412$	−159.923	−	159.923i	−0.388162	−	0.388162i
$413$	737.431	−	146.684i	1.78555	−	0.355168i
$414$	−18.7078	+	12.5001i	−0.0451879	+	0.0301936i
$415$		0			0
$416$	−155.170	+	64.2737i	−0.373006	+	0.154504i
$417$	263.324	+	635.721i	0.631474	+	1.52451i
$418$	178.698	−	898.377i	0.427508	−	2.14923i
$419$	−388.725	−	581.769i	−0.927745	−	1.38847i	−0.921453	−	0.388489i	$-0.872997\pi$
$419$	−388.725	−	581.769i	−0.927745	−	1.38847i	−0.00629204	−	0.999980i	$-0.502003\pi$
$420$		0			0
$421$	−312.222	+	312.222i	−0.741619	+	0.741619i	−0.972890	−	0.231270i	$-0.925712\pi$
$421$	−312.222	+	312.222i	−0.741619	+	0.741619i	0.231270	+	0.972890i	$0.425712\pi$
$422$	−113.986	+	170.592i	−0.270109	+	0.404247i
$423$	3.82257	+	1.58336i	0.00903680	+	0.00374317i
$424$		−	464.520i		−	1.09557i
$425$		0			0
$426$	626.340			1.47028
$427$	−37.8585	+	91.3985i	−0.0886616	+	0.214048i
$428$	−115.117	−	76.9184i	−0.268964	−	0.179716i
$429$	256.089	+	256.089i	0.596943	+	0.596943i
$430$		0			0
$431$	148.646	−	99.3222i	0.344887	−	0.230446i	−0.371047	−	0.928614i	$-0.621001\pi$
$431$	148.646	−	99.3222i	0.344887	−	0.230446i	0.715934	+	0.698168i	$0.246001\pi$
$432$	502.713	+	99.9958i	1.16369	+	0.231472i
$433$	−111.126	+	46.0297i	−0.256641	+	0.106304i	−0.507295	−	0.861773i	$-0.669354\pi$
$433$	−111.126	+	46.0297i	−0.256641	+	0.106304i	0.250654	+	0.968077i	$0.419354\pi$
$434$	133.043	+	321.193i	0.306550	+	0.740077i
$435$		0			0
$436$	−13.7657	−	20.6018i	−0.0315727	−	0.0472519i
$437$	−266.626	−	1340.42i	−0.610128	−	3.06732i
$438$	240.219	−	240.219i	0.548446	−	0.548446i
$439$	−38.0431	+	56.9356i	−0.0866586	+	0.129694i	−0.872266	−	0.489031i	$-0.837350\pi$
$439$	−38.0431	+	56.9356i	−0.0866586	+	0.129694i	0.785608	+	0.618725i	$0.212350\pi$
$440$		0			0
$441$			6.10701i			0.0138481i
$442$	273.156	−	246.144i	0.618000	−	0.556886i
$443$	50.2158			0.113354			0.0566770	−	0.998393i	$-0.481949\pi$
$443$	50.2158			0.113354			0.0566770	+	0.998393i	$0.481949\pi$
$444$	30.7409	−	74.2151i	0.0692363	−	0.167151i
$445$		0			0
$446$	60.0020	+	60.0020i	0.134534	+	0.134534i
$447$	445.352	−	88.5861i	0.996314	−	0.198179i
$448$	−267.285	+	178.594i	−0.596619	+	0.398648i
$449$	307.311	+	61.1279i	0.684434	+	0.136142i	0.525046	−	0.851074i	$-0.324048\pi$
$449$	307.311	+	61.1279i	0.684434	+	0.136142i	0.159388	+	0.987216i	$0.449048\pi$
$450$		0			0
$451$	34.9132	+	84.2879i	0.0774128	+	0.186891i
$452$	−34.4781	+	173.333i	−0.0762790	+	0.383481i
$453$	43.3617	+	64.8953i	0.0957211	+	0.143257i
$454$	−120.065	−	603.605i	−0.264459	−	1.32953i
$455$		0			0
$456$	355.610	−	532.207i	0.779845	−	1.16712i
$457$	454.099	+	188.094i	0.993652	+	0.411584i	0.819465	−	0.573129i	$-0.194270\pi$
$457$	454.099	+	188.094i	0.993652	+	0.411584i	0.174187	+	0.984713i	$0.444270\pi$
$458$		−	4.73268i		−	0.0103334i
$459$	−448.088	+	65.1480i	−0.976226	+	0.141935i
$460$		0			0
$461$	−48.7596	+	117.716i	−0.105769	+	0.255349i	−0.967900	−	0.251337i	$-0.919130\pi$
$461$	−48.7596	+	117.716i	−0.105769	+	0.255349i	0.862131	+	0.506686i	$0.169130\pi$
$462$	−618.280	−	413.121i	−1.33827	−	0.894202i
$463$	−586.946	−	586.946i	−1.26770	−	1.26770i	−0.947272	−	0.320430i	$-0.896173\pi$
$463$	−586.946	−	586.946i	−1.26770	−	1.26770i	−0.320430	−	0.947272i	$-0.603827\pi$
$464$	107.981	−	21.4788i	0.232718	−	0.0462904i
$465$		0			0
$466$	−548.639	−	109.131i	−1.17734	−	0.234187i
$467$	−38.2085	+	15.8265i	−0.0818168	+	0.0338896i	−0.423217	−	0.906029i	$-0.639099\pi$
$467$	−38.2085	+	15.8265i	−0.0818168	+	0.0338896i	0.341400	+	0.939918i	$0.389099\pi$
$468$	−0.972889	−	2.34876i	−0.00207882	−	0.00501872i
$469$	81.5574	−	410.017i	0.173896	−	0.874236i
$470$		0			0
$471$	117.556	+	590.996i	0.249589	+	1.25477i
$472$	−399.216	+	399.216i	−0.845796	+	0.845796i
$473$	−41.1892	+	61.6440i	−0.0870807	+	0.130325i
$474$	−149.512	−	61.9297i	−0.315425	−	0.130653i
$475$		0			0
$476$	−99.4726	+	133.318i	−0.208976	+	0.280081i
$477$	16.8322			0.0352877
$478$	−63.5904	+	153.521i	−0.133034	+	0.321173i
$479$	237.445	+	158.656i	0.495711	+	0.331223i	0.778168	−	0.628057i	$-0.216149\pi$
$479$	237.445	+	158.656i	0.495711	+	0.331223i	−0.282457	+	0.959280i	$0.591149\pi$
$480$		0			0
$481$	−219.012	+	43.5642i	−0.455326	+	0.0905701i
$482$	411.663	−	275.064i	0.854072	−	0.570673i
$483$	−1088.16	−	216.449i	−2.25293	−	0.448135i
$484$	36.2855	−	15.0299i	0.0749700	−	0.0310536i
$485$		0			0
$486$	−5.61864	+	28.2468i	−0.0115610	+	0.0581210i
$487$	275.022	+	411.599i	0.564727	+	0.845173i	0.998438	−	0.0558790i	$-0.0177961\pi$
$487$	275.022	+	411.599i	0.564727	+	0.845173i	−0.433711	+	0.901052i	$0.642796\pi$
$488$	−14.4922	−	72.8572i	−0.0296971	−	0.149298i
$489$	376.265	−	376.265i	0.769459	−	0.769459i
$490$		0			0
$491$	−449.400	−	186.147i	−0.915274	−	0.379119i	−0.125201	−	0.992131i	$-0.539958\pi$
$491$	−449.400	−	186.147i	−0.915274	−	0.379119i	−0.790073	+	0.613013i	$0.789958\pi$
$492$		−	25.1126i		−	0.0510418i
$493$	−83.5662	+	49.7608i	−0.169505	+	0.100935i
$494$	700.880			1.41879
$495$		0			0
$496$	−283.718	−	189.574i	−0.572012	−	0.382206i
$497$	556.950	+	556.950i	1.12062	+	1.12062i
$498$	743.972	−	147.985i	1.49392	−	0.297159i
$499$	−257.371	+	171.970i	−0.515773	+	0.344628i	−0.786059	−	0.618152i	$-0.787882\pi$
$499$	−257.371	+	171.970i	−0.515773	+	0.344628i	0.270286	+	0.962780i	$0.412882\pi$
$500$		0			0
$501$	−392.440	+	162.554i	−0.783313	+	0.324459i
$502$	−388.439	−	937.774i	−0.773782	−	1.86808i
$503$	−6.22881	+	31.3143i	−0.0123833	+	0.0622552i	−0.986483	−	0.163864i	$-0.947604\pi$
$503$	−6.22881	+	31.3143i	−0.0123833	+	0.0622552i	0.974100	+	0.226120i	$0.0726040\pi$
$504$	−7.36213	−	11.0182i	−0.0146074	−	0.0218615i
$505$		0			0
$506$	843.006	−	843.006i	1.66602	−	1.66602i
$507$	131.378	−	196.620i	0.259127	−	0.387812i
$508$	−4.91415	−	2.03551i	−0.00967352	−	0.00400690i
$509$			518.506i			1.01868i	0.860567	+	0.509338i	$0.170110\pi$
$509$			518.506i			1.01868i	−0.860567	+	0.509338i	$0.829890\pi$
$510$		0			0
$511$	427.212			0.836032
$512$	61.9396	−	149.535i	0.120976	−	0.292061i
$513$	−717.639	−	479.511i	−1.39891	−	0.934719i
$514$	−199.441	−	199.441i	−0.388018	−	0.388018i
$515$		0			0
$516$	16.9681	−	11.3377i	0.0328838	−	0.0219723i
$517$	−215.022	−	42.7706i	−0.415904	−	0.0827284i
$518$	423.587	−	175.455i	0.817735	−	0.338717i
$519$	−250.514	−	604.793i	−0.482685	−	1.16531i
$520$		0			0
$521$	102.308	+	153.115i	0.196369	+	0.293887i	0.916567	−	0.399882i	$-0.130949\pi$
$521$	102.308	+	153.115i	0.196369	+	0.293887i	−0.720198	+	0.693769i	$0.755949\pi$
$522$	0.595431	+	2.99344i	0.00114067	+	0.00573455i
$523$	362.318	−	362.318i	0.692769	−	0.692769i	−0.270071	−	0.962840i	$-0.587047\pi$
$523$	362.318	−	362.318i	0.692769	−	0.692769i	0.962840	+	0.270071i	$0.0870472\pi$
$524$	102.366	−	153.202i	0.195356	−	0.292370i
$525$		0			0
$526$			593.587i			1.12849i
$527$	292.193	+	74.0864i	0.554447	+	0.140581i
$528$	729.841			1.38227
$529$	478.278	−	1154.66i	0.904117	−	2.18273i
$530$		0			0
$531$	−14.4659	−	14.4659i	−0.0272427	−	0.0272427i
$532$	−310.972	+	61.8562i	−0.584534	+	0.116271i
$533$	−58.0437	+	38.7835i	−0.108900	+	0.0727646i
$534$	192.025	+	38.1961i	0.359597	+	0.0715282i
$535$		0			0
$536$	120.127	+	290.013i	0.224118	+	0.541070i
$537$	15.8069	−	79.4667i	0.0294356	−	0.147983i
$538$	−245.718	−	367.742i	−0.456724	−	0.683536i
$539$	−63.1298	−	317.375i	−0.117124	−	0.588822i
$540$		0			0
$541$	225.117	−	336.911i	0.416113	−	0.622757i	−0.562907	−	0.826520i	$-0.690317\pi$
$541$	225.117	−	336.911i	0.416113	−	0.622757i	0.979020	+	0.203763i	$0.0653173\pi$
$542$	909.476	+	376.717i	1.67800	+	0.695050i
$543$		−	118.272i		−	0.217812i
$544$	15.5322	−	298.599i	0.0285519	−	0.548896i
$545$		0			0
$546$	217.739	−	525.670i	0.398790	−	0.962765i
$547$	−208.273	−	139.163i	−0.380755	−	0.254412i	0.350434	−	0.936587i	$-0.386034\pi$
$547$	−208.273	−	139.163i	−0.380755	−	0.254412i	−0.731189	+	0.682175i	$0.761034\pi$
$548$	111.078	+	111.078i	0.202697	+	0.202697i
$549$	2.64003	−	0.525136i	0.00480881	−	0.000956531i
$550$		0			0
$551$	−181.828	−	36.1678i	−0.329996	−	0.0656404i
$552$	769.681	−	318.812i	1.39435	−	0.577558i
$553$	−77.8789	−	188.016i	−0.140830	−	0.339993i
$554$	−93.9460	+	472.298i	−0.169578	+	0.852524i
$555$		0			0
$556$	49.9316	+	251.023i	0.0898050	+	0.451480i
$557$	308.383	−	308.383i	0.553650	−	0.553650i	−0.373843	−	0.927492i	$-0.621960\pi$
$557$	308.383	−	308.383i	0.553650	−	0.553650i	0.927492	+	0.373843i	$0.121960\pi$
$558$	5.25536	−	7.86520i	0.00941820	−	0.0140953i
$559$	−52.4105	−	21.7091i	−0.0937576	−	0.0388357i
$560$		0			0
$561$	−607.679	+	215.457i	−1.08321	+	0.384059i
$562$	174.214			0.309990
$563$	102.073	−	246.425i	0.181301	−	0.437700i	−0.806934	−	0.590642i	$-0.798875\pi$
$563$	102.073	−	246.425i	0.181301	−	0.437700i	0.988235	+	0.152942i	$0.0488747\pi$
$564$	50.1762	+	33.5267i	0.0889649	+	0.0594444i
$565$		0			0
$566$	−757.656	+	150.707i	−1.33861	+	0.266267i
$567$	−597.842	+	399.465i	−1.05440	+	0.704524i
$568$	−580.069	−	115.383i	−1.02125	−	0.203139i
$569$	847.496	−	351.044i	1.48945	−	0.616949i	0.518251	−	0.855229i	$-0.326583\pi$
$569$	847.496	−	351.044i	1.48945	−	0.616949i	0.971197	+	0.238280i	$0.0765834\pi$
$570$		0			0
$571$	87.7452	−	441.125i	0.153669	−	0.772548i	−0.824682	−	0.565597i	$-0.808646\pi$
$571$	87.7452	−	441.125i	0.153669	−	0.772548i	0.978351	−	0.206951i	$-0.0663541\pi$
$572$	74.8397	+	112.006i	0.130839	+	0.195814i
$573$	87.3249	+	439.012i	0.152399	+	0.766164i
$574$	101.351	−	101.351i	0.176569	−	0.176569i
$575$		0			0
$576$	8.08083	+	3.34719i	0.0140292	+	0.00581109i
$577$			181.502i			0.314561i	0.987554	+	0.157281i	$0.0502727\pi$
$577$			181.502i			0.314561i	−0.987554	+	0.157281i	$0.949727\pi$
$578$	186.404	+	627.492i	0.322498	+	1.08563i
$579$	698.296			1.20604
$580$		0			0
$581$	793.141	+	529.960i	1.36513	+	0.912151i
$582$	442.369	+	442.369i	0.760085	+	0.760085i
$583$	−874.753	+	173.999i	−1.50043	+	0.298455i
$584$	−266.726	+	178.220i	−0.456722	+	0.305172i
$585$		0			0
$586$	−155.848	+	64.5546i	−0.265953	+	0.110161i
$587$	−379.719	−	916.723i	−0.646881	−	1.56171i	−0.817222	−	0.576324i	$-0.804487\pi$
$587$	−379.719	−	916.723i	−0.646881	−	1.56171i	0.170341	−	0.985385i	$-0.445513\pi$
$588$	−17.3771	+	87.3603i	−0.0295528	+	0.148572i
$589$	319.222	+	477.750i	0.541973	+	0.811120i
$590$		0			0
$591$	47.7666	−	47.7666i	0.0808234	−	0.0808234i
$592$	−250.009	+	374.165i	−0.422312	+	0.632035i
$593$	419.577	+	173.795i	0.707550	+	0.293077i	0.707290	−	0.706923i	$-0.249917\pi$
$593$	419.577	+	173.795i	0.707550	+	0.293077i	0.000259609		1.00000i	$0.499917\pi$
$594$		−	752.902i		−	1.26751i
$595$		0			0
$596$	168.895			0.283382
$597$	−306.933	+	741.002i	−0.514126	+	1.24121i
$598$	758.492	+	506.808i	1.26838	+	0.847505i
$599$	−550.958	−	550.958i	−0.919797	−	0.919797i	0.0772177	−	0.997014i	$-0.475396\pi$
$599$	−550.958	−	550.958i	−0.919797	−	0.919797i	−0.997014	+	0.0772177i	$0.975396\pi$
$600$		0			0
$601$	−645.794	+	431.506i	−1.07453	+	0.717980i	−0.961276	−	0.275586i	$-0.911128\pi$
$601$	−645.794	+	431.506i	−1.07453	+	0.717980i	−0.113257	+	0.993566i	$0.536128\pi$
$602$	114.238	+	22.7233i	0.189764	+	0.0377464i
$603$	−10.5089	+	4.35291i	−0.0174276	+	0.00721875i
$604$	11.1095	+	26.8207i	0.0183932	+	0.0444052i
$605$		0			0
$606$	358.943	+	537.196i	0.592315	+	0.886463i
$607$	103.953	+	522.608i	0.171257	+	0.860969i	0.966891	+	0.255190i	$0.0821382\pi$
$607$	103.953	+	522.608i	0.171257	+	0.860969i	−0.795633	+	0.605778i	$0.792862\pi$
$608$	403.009	−	403.009i	0.662843	−	0.662843i
$609$	−83.6141	+	125.137i	−0.137297	+	0.205480i
$610$		0			0
$611$		−	167.752i		−	0.274554i
$612$	4.51980	+	0.235106i	0.00738529	+	0.000384160i
$613$	223.657			0.364857			0.182429	−	0.983219i	$-0.441604\pi$
$613$	223.657			0.364857			0.182429	+	0.983219i	$0.441604\pi$
$614$	−326.560	+	788.384i	−0.531856	+	1.28401i
$615$		0			0
$616$	496.500	+	496.500i	0.806007	+	0.806007i
$617$	310.061	−	61.6750i	0.502530	−	0.0999595i	0.0626855	−	0.998033i	$-0.480033\pi$
$617$	310.061	−	61.6750i	0.502530	−	0.0999595i	0.439845	+	0.898074i	$0.355033\pi$
$618$	−1145.14	+	765.157i	−1.85298	+	1.23812i
$619$	148.503	+	29.5391i	0.239908	+	0.0477208i	0.313580	−	0.949562i	$-0.398472\pi$
$619$	148.503	+	29.5391i	0.239908	+	0.0477208i	−0.0736715	+	0.997283i	$0.523472\pi$
$620$		0			0
$621$	−429.893	−	1037.85i	−0.692259	−	1.67126i
$622$	202.542	−	1018.25i	0.325630	−	1.63705i
$623$	136.786	+	204.715i	0.219561	+	0.328596i
$624$	108.949	+	547.723i	0.174598	+	0.877761i
$625$		0			0
$626$	418.275	−	625.993i	0.668171	−	0.999989i
$627$	−1135.42	−	470.307i	−1.81088	−	0.750090i
$628$			224.129i			0.356893i
$629$	97.7045	−	385.342i	0.155333	−	0.612626i
$630$		0			0
$631$	96.3665	−	232.649i	0.152720	−	0.368699i	−0.828940	−	0.559337i	$-0.811056\pi$
$631$	96.3665	−	232.649i	0.152720	−	0.368699i	0.981660	+	0.190638i	$0.0610556\pi$
$632$	127.058	+	84.8974i	0.201041	+	0.134331i
$633$	194.650	+	194.650i	0.307504	+	0.307504i
$634$	−408.556	+	81.2668i	−0.644410	+	0.128181i
$635$		0			0
$636$	240.784	+	47.8949i	0.378591	+	0.0753064i
$637$	228.756	−	94.7539i	0.359115	−	0.148750i
$638$	−61.8879	−	149.411i	−0.0970029	−	0.234186i
$639$	4.18099	−	21.0192i	0.00654302	−	0.0328940i
$640$		0			0
$641$	12.1076	+	60.8689i	0.0188886	+	0.0949592i	0.989080	−	0.147382i	$-0.0470847\pi$
$641$	12.1076	+	60.8689i	0.0188886	+	0.0949592i	−0.970191	+	0.242341i	$0.922085\pi$
$642$	−596.159	+	596.159i	−0.928597	+	0.928597i
$643$	−30.5959	+	45.7900i	−0.0475831	+	0.0712131i	−0.854498	−	0.519454i	$-0.826135\pi$
$643$	−30.5959	+	45.7900i	−0.0475831	+	0.0712131i	0.806915	+	0.590667i	$0.201135\pi$
$644$	−381.262	−	157.924i	−0.592022	−	0.245223i
$645$		0			0
$646$	−536.729	+	1126.41i	−0.830850	+	1.74366i
$647$	−689.341			−1.06544			−0.532721	−	0.846291i	$-0.678830\pi$
$647$	−689.341			−1.06544			−0.532721	+	0.846291i	$0.678830\pi$
$648$	206.612	−	498.804i	0.318845	−	0.769760i
$649$	901.314	+	602.239i	1.38877	+	0.927949i
$650$		0			0
$651$	457.490	−	91.0004i	0.702750	−	0.139786i
$652$	164.567	−	109.960i	0.252404	−	0.168651i
$653$	−857.031	−	170.474i	−1.31245	−	0.261063i	−0.511237	−	0.859440i	$-0.670813\pi$
$653$	−857.031	−	170.474i	−1.31245	−	0.261063i	−0.801215	+	0.598377i	$0.795813\pi$
$654$	−139.399	+	57.7411i	−0.213149	+	0.0882892i
$655$		0			0
$656$	−27.4452	+	137.977i	−0.0418372	+	0.210330i
$657$	−6.45795	−	9.66500i	−0.00982945	−	0.0147108i
$658$	67.1951	+	337.813i	0.102120	+	0.513393i
$659$	−347.128	+	347.128i	−0.526750	+	0.526750i	−0.919602	−	0.392852i	$-0.871488\pi$
$659$	−347.128	+	347.128i	−0.526750	+	0.526750i	0.392852	+	0.919602i	$0.371488\pi$
$660$		0			0
$661$	299.168	+	123.919i	0.452599	+	0.187473i	0.597325	−	0.801999i	$-0.296230\pi$
$661$	299.168	+	123.919i	0.452599	+	0.187473i	−0.144726	+	0.989472i	$0.546230\pi$
$662$		−	623.615i		−	0.942017i
$663$	−252.407	−	423.881i	−0.380704	−	0.639338i
$664$	−716.273			−1.07872
$665$		0			0
$666$	−10.3726	−	6.93072i	−0.0155744	−	0.0104065i
$667$	−170.621	−	170.621i	−0.255804	−	0.255804i
$668$	−154.960	+	30.8234i	−0.231976	+	0.0461429i
$669$	94.6638	−	63.2523i	0.141500	−	0.0945475i
$670$		0			0
$671$	−131.771	+	54.5815i	−0.196381	+	0.0813435i
$672$	−177.061	−	427.463i	−0.263484	−	0.636106i
$673$	−122.596	+	616.330i	−0.182163	+	0.915796i	0.776253	+	0.630421i	$0.217118\pi$
$673$	−122.596	+	616.330i	−0.182163	+	0.915796i	−0.958416	+	0.285374i	$0.907882\pi$
$674$	272.641	+	408.036i	0.404512	+	0.605395i
$675$		0			0
$676$	62.1950	−	62.1950i	0.0920044	−	0.0920044i
$677$	184.949	−	276.796i	0.273189	−	0.408856i	−0.669353	−	0.742945i	$-0.733428\pi$
$677$	184.949	−	276.796i	0.273189	−	0.408856i	0.942542	+	0.334089i	$0.108428\pi$
$678$	994.281	+	411.845i	1.46649	+	0.607441i
$679$			786.721i			1.15865i
$680$		0			0
$681$	−825.725			−1.21252
$682$	−191.811	+	463.072i	−0.281247	+	0.678991i
$683$	939.366	+	627.664i	1.37535	+	0.918981i	0.999969	−	0.00788807i	$-0.00251088\pi$
$683$	939.366	+	627.664i	1.37535	+	0.918981i	0.375384	+	0.926869i	$0.377511\pi$
$684$	6.10021	+	6.10021i	0.00891843	+	0.00891843i
$685$		0			0
$686$	376.103	−	251.304i	0.548256	−	0.366333i
$687$	−6.22784	−	1.23879i	−0.00906527	−	0.00180319i
$688$	−105.619	+	43.7487i	−0.153516	+	0.0635883i
$689$	−261.162	−	630.501i	−0.379045	−	0.915096i
$690$		0			0
$691$	302.850	+	453.247i	0.438278	+	0.655929i	0.983194	−	0.182561i	$-0.0584388\pi$
$691$	302.850	+	453.247i	0.438278	+	0.655929i	−0.544917	+	0.838490i	$0.683439\pi$
$692$	−47.5024	−	238.811i	−0.0686451	−	0.345102i
$693$	−17.9911	+	17.9911i	−0.0259611	+	0.0259611i
$694$	−812.666	+	1216.24i	−1.17099	+	1.75251i
$695$		0			0
$696$		−	113.010i		−	0.162370i
$697$	−17.8808	−	122.984i	−0.0256539	−	0.176448i
$698$	1166.03			1.67052
$699$	−287.216	+	693.401i	−0.410896	+	0.991990i
$700$		0			0
$701$	322.860	+	322.860i	0.460571	+	0.460571i	0.898843	−	0.438271i	$-0.144409\pi$
$701$	322.860	+	322.860i	0.460571	+	0.460571i	−0.438271	+	0.898843i	$0.644409\pi$
$702$	565.030	−	112.391i	0.804886	−	0.160102i
$703$	630.052	−	420.987i	0.896234	−	0.598844i
$704$	−454.553	−	90.4162i	−0.645672	−	0.128432i
$705$		0			0
$706$	−414.497	−	1000.69i	−0.587107	−	1.41740i
$707$	−158.505	+	796.859i	−0.224194	+	1.12710i
$708$	−165.772	−	248.095i	−0.234141	−	0.350417i
$709$	14.4960	+	72.8762i	0.0204457	+	0.102787i	0.989661	−	0.143429i	$-0.0458128\pi$
$709$	14.4960	+	72.8762i	0.0204457	+	0.102787i	−0.969215	+	0.246216i	$0.920813\pi$
$710$		0			0
$711$	−3.07632	+	4.60404i	−0.00432675	+	0.00647544i
$712$	−170.802	−	70.7487i	−0.239891	−	0.0993661i
$713$			747.850i			1.04888i
$714$	678.076	+	752.490i	0.949687	+	1.05391i
$715$		0			0
$716$	11.5329	−	27.8429i	0.0161074	−	0.0388868i
$717$	185.377	+	123.865i	0.258545	+	0.172754i
$718$	−779.213	−	779.213i	−1.08525	−	1.08525i
$719$	−623.839	+	124.089i	−0.867649	+	0.172586i	−0.608792	−	0.793330i	$-0.708346\pi$
$719$	−623.839	+	124.089i	−0.867649	+	0.172586i	−0.258856	+	0.965916i	$0.583346\pi$
$720$		0			0
$721$	−1698.66	−	337.885i	−2.35598	−	0.468633i
$722$	−1441.90	+	597.253i	−1.99708	+	0.827220i
$723$	−254.209	−	613.715i	−0.351603	−	0.848846i
$724$	8.58233	−	43.1463i	0.0118540	−	0.0595943i
$725$		0			0
$726$	−46.6595	−	234.573i	−0.0642692	−	0.323103i
$727$	321.409	−	321.409i	0.442103	−	0.442103i	−0.450615	−	0.892718i	$-0.648795\pi$
$727$	321.409	−	321.409i	0.442103	−	0.442103i	0.892718	+	0.450615i	$0.148795\pi$
$728$	−298.492	+	446.724i	−0.410016	+	0.613633i
$729$	−654.972	−	271.298i	−0.898453	−	0.372152i
$730$		0			0
$731$	75.0250	−	67.6058i	0.102633	−	0.0924840i
$732$	39.2597			0.0536335
$733$	283.876	−	685.338i	0.387280	−	0.934977i	−0.603234	−	0.797564i	$-0.706121\pi$
$733$	283.876	−	685.338i	0.387280	−	0.934977i	0.990514	−	0.137413i	$-0.0438786\pi$
$734$	−12.1071	−	8.08972i	−0.0164947	−	0.0110214i
$735$		0			0
$736$	727.552	−	144.719i	0.988522	−	0.196629i
$737$	501.137	−	334.849i	0.679968	−	0.454340i
$738$	−3.82497	−	0.760834i	−0.00518288	−	0.00103094i
$739$	−95.2857	+	39.4686i	−0.128939	+	0.0534081i	−0.446220	−	0.894923i	$-0.647230\pi$
$739$	−95.2857	+	39.4686i	−0.128939	+	0.0534081i	0.317281	+	0.948331i	$0.397230\pi$
$740$		0			0
$741$	183.458	−	922.305i	0.247581	−	1.24468i
$742$	778.471	+	1165.06i	1.04915	+	1.57017i
$743$	159.447	+	801.593i	0.214599	+	1.07886i	0.926418	+	0.376497i	$0.122872\pi$
$743$	159.447	+	801.593i	0.214599	+	1.07886i	−0.711819	+	0.702363i	$0.752128\pi$
$744$	−247.667	+	247.667i	−0.332885	+	0.332885i
$745$		0			0
$746$	1303.56	+	539.952i	1.74740	+	0.723797i
$747$		−	25.9547i		−	0.0347452i
$748$	−237.319	+	34.5041i	−0.317272	+	0.0461285i
$749$	−1060.23			−1.41552
$750$		0			0
$751$	−882.764	−	589.844i	−1.17545	−	0.785411i	−0.194737	−	0.980856i	$-0.562385\pi$
$751$	−882.764	−	589.844i	−1.17545	−	0.785411i	−0.980715	+	0.195444i	$0.937385\pi$
$752$	−239.043	−	239.043i	−0.317876	−	0.317876i
$753$	−1335.71	+	265.690i	−1.77386	+	0.352842i
$754$	102.890	−	68.7486i	0.136458	−	0.0911785i
$755$		0			0
$756$	−240.778	+	99.7335i	−0.318489	+	0.131923i
$757$	222.848	+	538.002i	0.294383	+	0.710702i	0.999998	+	0.00210719i	$0.000670740\pi$
$757$	222.848	+	538.002i	0.294383	+	0.710702i	−0.705615	+	0.708595i	$0.749329\pi$
$758$	234.382	−	1178.32i	0.309210	−	1.55451i
$759$	−888.671	−	1329.99i	−1.17084	−	1.75229i
$760$		0			0
$761$	2.47478	−	2.47478i	0.00325201	−	0.00325201i	−0.705479	−	0.708731i	$-0.749268\pi$
$761$	2.47478	−	2.47478i	0.00325201	−	0.00325201i	0.708731	+	0.705479i	$0.249268\pi$
$762$	−17.9953	+	26.9318i	−0.0236158	+	0.0353436i
$763$	−175.300	−	72.6116i	−0.229751	−	0.0951660i
$764$			166.491i			0.217920i
$765$		0			0
$766$	1231.16			1.60726
$767$	−317.416	+	766.309i	−0.413840	+	0.999099i
$768$	508.731	+	339.923i	0.662410	+	0.442608i
$769$	832.190	+	832.190i	1.08217	+	1.08217i	0.996307	+	0.0858646i	$0.0273652\pi$
$769$	832.190	+	832.190i	1.08217	+	1.08217i	0.0858646	+	0.996307i	$0.472635\pi$
$770$		0			0
$771$	−314.654	+	210.245i	−0.408111	+	0.272691i
$772$	254.743	+	50.6715i	0.329978	+	0.0656366i
$773$	−781.877	+	323.864i	−1.01148	+	0.418970i	−0.825996	−	0.563676i	$-0.809386\pi$
$773$	−781.877	+	323.864i	−1.01148	+	0.418970i	−0.185488	+	0.982647i	$0.559386\pi$
$774$	−1.21280	−	2.92795i	−0.00156692	−	0.00378288i
$775$		0			0
$776$	−328.197	−	491.182i	−0.422935	−	0.632966i
$777$	−120.011	−	603.334i	−0.154454	−	0.776492i
$778$	−170.963	+	170.963i	−0.219746	+	0.219746i
$779$	131.608	−	196.966i	0.168945	−	0.252845i
$780$		0			0
$781$			1135.57i			1.45399i
$782$	−1395.35	+	830.885i	−1.78434	+	1.06251i
$783$	−152.384			−0.194616
$784$	190.950	−	460.994i	0.243559	−	0.588003i
$785$		0			0
$786$	−793.395	−	793.395i	−1.00941	−	1.00941i
$787$	−420.371	+	83.6170i	−0.534144	+	0.106248i	−0.454790	−	0.890599i	$-0.650286\pi$
$787$	−420.371	+	83.6170i	−0.534144	+	0.106248i	−0.0793537	+	0.996847i	$0.525286\pi$
$788$	20.8917	−	13.9594i	0.0265123	−	0.0177150i
$789$	781.115	+	155.373i	0.990006	+	0.196925i
$790$		0			0
$791$	517.910	+	1250.35i	0.654754	+	1.58072i
$792$	3.72720	−	18.7379i	0.00470606	−	0.0236589i
$793$	−60.6322	−	90.7425i	−0.0764593	−	0.114429i
$794$	224.289	+	1127.58i	0.282480	+	1.42012i
$795$		0			0
$796$	−165.741	+	248.050i	−0.208218	+	0.311620i
$797$	−787.879	−	326.350i	−0.988555	−	0.409473i	−0.170967	−	0.985277i	$-0.554689\pi$
$797$	−787.879	−	326.350i	−0.988555	−	0.409473i	−0.817588	+	0.575804i	$0.804689\pi$
$798$			1930.78i			2.41953i
$799$	269.600	+	128.464i	0.337422	+	0.160780i
$800$		0			0
$801$	2.56363	−	6.18915i	0.00320054	−	0.00772678i
$802$	301.087	+	201.180i	0.375420	+	0.250848i
$803$	435.522	+	435.522i	0.542369	+	0.542369i
$804$	−162.714	+	32.3659i	−0.202381	+	0.0402561i
$805$		0			0
$806$	−376.154	−	74.8217i	−0.466693	−	0.0928309i
$807$	−548.238	+	227.088i	−0.679354	+	0.281397i
$808$	−233.465	−	563.635i	−0.288942	−	0.697568i
$809$	−179.783	+	903.832i	−0.222229	+	1.11722i	0.695045	+	0.718966i	$0.255384\pi$
$809$	−179.783	+	903.832i	−0.222229	+	1.11722i	−0.917275	+	0.398255i	$0.869616\pi$
$810$		0			0
$811$	−201.219	−	1011.60i	−0.248112	−	1.24734i	−0.881006	−	0.473105i	$-0.843133\pi$
$811$	−201.219	−	1011.60i	−0.248112	−	1.24734i	0.632894	−	0.774239i	$-0.281867\pi$
$812$	−39.5834	+	39.5834i	−0.0487481	+	0.0487481i
$813$	733.789	−	1098.19i	0.902570	−	1.35079i
$814$	610.695	+	252.958i	0.750240	+	0.310760i
$815$		0			0
$816$	−963.694	−	244.347i	−1.18100	−	0.299445i
$817$	192.504			0.235623
$818$	−82.6358	+	199.500i	−0.101022	+	0.243888i
$819$	−16.1874	−	10.8161i	−0.0197648	−	0.0132064i
$820$		0			0
$821$	−1386.48	+	275.788i	−1.68877	+	0.335918i	−0.943633	−	0.330992i	$-0.892617\pi$
$821$	−1386.48	+	275.788i	−1.68877	+	0.335918i	−0.745138	+	0.666910i	$0.767617\pi$
$822$	795.381	−	531.457i	0.967617	−	0.646541i
$823$	955.396	+	190.040i	1.16087	+	0.230911i	0.737694	−	0.675136i	$-0.235915\pi$
$823$	955.396	+	190.040i	1.16087	+	0.230911i	0.423177	+	0.906047i	$0.360915\pi$
$824$	1201.50	−	497.677i	1.45813	−	0.603976i
$825$		0			0
$826$	332.244	−	1670.31i	0.402233	−	2.02216i
$827$	321.110	+	480.574i	0.388282	+	0.581106i	0.973192	−	0.229992i	$-0.0738702\pi$
$827$	321.110	+	480.574i	0.388282	+	0.581106i	−0.584910	+	0.811098i	$0.698870\pi$
$828$	2.19056	+	11.0127i	0.00264561	+	0.0133004i
$829$	129.943	−	129.943i	0.156747	−	0.156747i	−0.624377	−	0.781123i	$-0.714647\pi$
$829$	129.943	−	129.943i	0.156747	−	0.156747i	0.781123	+	0.624377i	$0.214647\pi$
$830$		0			0
$831$	596.918	+	247.251i	0.718313	+	0.297535i
$832$		−	354.625i		−	0.426232i
$833$	−22.8980	+	440.203i	−0.0274886	+	0.528455i
$834$	1558.57			1.86879
$835$		0			0
$836$	−380.081	−	253.962i	−0.454642	−	0.303782i
$837$	333.959	+	333.959i	0.398995	+	0.398995i
$838$	−1554.36	+	309.182i	−1.85485	+	0.368952i
$839$	125.718	−	84.0020i	0.149843	−	0.100122i	−0.478389	−	0.878148i	$-0.658779\pi$
$839$	125.718	−	84.0020i	0.149843	−	0.100122i	0.628232	+	0.778026i	$0.283779\pi$
$840$		0			0
$841$	746.743	−	309.311i	0.887922	−	0.367789i
$842$	382.730	+	923.991i	0.454548	+	1.09738i
$843$	45.6012	−	229.253i	0.0540940	−	0.271949i
$844$	56.8848	+	85.1342i	0.0673991	+	0.100870i
$845$		0			0
$846$	6.62673	−	6.62673i	0.00783301	−	0.00783301i
$847$	167.095	−	250.076i	0.197279	−	0.295249i
$848$	−1270.60	−	526.299i	−1.49835	−	0.620636i
$849$			1036.47i			1.22081i
$850$		0			0
$851$	986.259			1.15894
$852$	119.617	−	288.782i	0.140396	−	0.338946i
$853$	533.335	+	356.363i	0.625246	+	0.417776i	0.827428	−	0.561572i	$-0.189803\pi$
$853$	533.335	+	356.363i	0.625246	+	0.417776i	−0.202182	+	0.979348i	$0.564803\pi$
$854$	158.447	+	158.447i	0.185535	+	0.185535i
$855$		0			0
$856$	661.942	−	442.295i	0.773296	−	0.516700i
$857$	−388.859	−	77.3489i	−0.453745	−	0.0902554i	−0.0370731	−	0.999313i	$-0.511803\pi$
$857$	−388.859	−	77.3489i	−0.453745	−	0.0902554i	−0.416671	+	0.909057i	$0.636803\pi$
$858$	757.870	−	313.920i	0.883299	−	0.365874i
$859$	−220.120	−	531.415i	−0.256251	−	0.618644i	0.742434	−	0.669920i	$-0.233671\pi$
$859$	−220.120	−	531.415i	−0.256251	−	0.618644i	−0.998685	+	0.0512752i	$0.983671\pi$
$860$		0			0
$861$	−106.841	−	159.899i	−0.124089	−	0.185713i
$862$	−78.9982	−	397.151i	−0.0916453	−	0.460732i
$863$	−53.5935	+	53.5935i	−0.0621014	+	0.0621014i	−0.737475	−	0.675374i	$-0.763982\pi$
$863$	−53.5935	+	53.5935i	−0.0621014	+	0.0621014i	0.675374	+	0.737475i	$0.263982\pi$
$864$	260.269	−	389.520i	0.301237	−	0.450833i
$865$		0			0
$866$			272.441i			0.314597i
$867$	874.524	−	81.0451i	1.00868	−	0.0934776i
$868$	173.499			0.199883
$869$	112.280	−	271.068i	0.129206	−	0.311931i
$870$		0			0
$871$	326.102	+	326.102i	0.374400	+	0.374400i
$872$	139.738	−	27.7957i	0.160250	−	0.0318758i
$873$	17.7983	−	11.8925i	0.0203876	−	0.0136225i
$874$	−3036.09	−	603.916i	−3.47379	−	0.690979i
$875$		0			0
$876$	−64.8794	−	156.633i	−0.0740633	−	0.178805i
$877$	−133.064	+	668.960i	−0.151727	+	0.762782i	0.827730	+	0.561127i	$0.189632\pi$
$877$	−133.064	+	668.960i	−0.151727	+	0.762782i	−0.979457	+	0.201655i	$0.935368\pi$
$878$	86.1689	+	128.961i	0.0981422	+	0.146880i
$879$	44.1550	+	221.982i	0.0502332	+	0.252539i
$880$		0			0
$881$	553.002	−	827.626i	0.627698	−	0.939416i	−0.372239	−	0.928137i	$-0.621410\pi$
$881$	553.002	−	827.626i	0.627698	−	0.939416i	0.999936	−	0.0112790i	$-0.00359030\pi$
$882$	12.7796	+	5.29350i	0.0144894	+	0.00600170i
$883$		−	374.875i		−	0.424547i	−0.977210	−	0.212274i	$-0.931913\pi$
$883$		−	374.875i		−	0.424547i	0.977210	−	0.212274i	$-0.0680868\pi$
$884$	−61.3208	−	172.950i	−0.0693674	−	0.195645i
$885$		0			0
$886$	43.5266	−	105.082i	0.0491271	−	0.118603i
$887$	233.253	+	155.854i	0.262968	+	0.175710i	0.680064	−	0.733153i	$-0.261952\pi$
$887$	233.253	+	155.854i	0.262968	+	0.175710i	−0.417096	+	0.908863i	$0.636952\pi$
$888$	326.621	+	326.621i	0.367816	+	0.367816i
$889$	−39.9498	+	7.94650i	−0.0449379	+	0.00893869i
$890$		0			0
$891$	−1016.71	−	202.236i	−1.14109	−	0.226976i
$892$	39.1238	−	16.2056i	0.0438607	−	0.0181677i
$893$	217.843	+	525.920i	0.243946	+	0.588937i
$894$	200.650	−	1008.74i	0.224441	−	1.12834i
$895$		0			0
$896$	260.858	+	1311.42i	0.291136	+	1.46364i
$897$	865.458	−	865.458i	0.964836	−	0.964836i
$898$	394.291	−	590.098i	0.439077	−	0.657125i
$899$	93.7239	+	38.8217i	0.104254	+	0.0431832i
$900$		0			0
$901$	1213.29	+	63.1118i	1.34661	+	0.0700464i
$902$	206.644			0.229096
$903$	59.8043	−	144.380i	0.0662285	−	0.159890i
$904$	−844.960	−	564.584i	−0.934690	−	0.624540i
$905$		0			0
$906$	173.386	−	34.4887i	0.191376	−	0.0380670i
$907$	1164.09	−	777.821i	1.28345	−	0.857575i	0.288456	−	0.957493i	$-0.406858\pi$
$907$	1164.09	−	777.821i	1.28345	−	0.857575i	0.994996	+	0.0999181i	$0.0318581\pi$
$908$	−301.230	−	59.9183i	−0.331751	−	0.0659893i
$909$	20.4237	−	8.45979i	0.0224683	−	0.00930669i
$910$		0			0
$911$	160.305	−	805.907i	0.175966	−	0.884640i	−0.787399	−	0.616444i	$-0.788573\pi$
$911$	160.305	−	805.907i	0.175966	−	0.884640i	0.963364	−	0.268196i	$-0.0864274\pi$
$912$	−1052.84	−	1575.69i	−1.15443	−	1.72772i
$913$	268.300	+	1348.84i	0.293867	+	1.47737i
$914$	787.217	−	787.217i	0.861287	−	0.861287i
$915$		0			0
$916$	−2.18206	−	0.903839i	−0.00238216	−	0.000986724i
$917$		−	1410.99i		−	1.53871i
$918$	−252.068	+	994.146i	−0.274584	+	1.08295i
$919$	−1120.50			−1.21926			−0.609629	−	0.792687i	$-0.708681\pi$
$919$	−1120.50			−1.21926			−0.609629	+	0.792687i	$0.708681\pi$
$920$		0			0
$921$	951.976	+	636.090i	1.03363	+	0.690651i
$922$	204.070	+	204.070i	0.221334	+	0.221334i
$923$	−852.208	+	169.515i	−0.923303	+	0.183656i
$924$	−308.553	+	206.168i	−0.333932	+	0.223126i
$925$		0			0
$926$	−1737.01	+	719.494i	−1.87582	+	0.776991i
$927$	18.0337	+	43.5372i	0.0194538	+	0.0469656i
$928$	19.6312	−	98.6926i	0.0211543	−	0.106350i
$929$	436.195	+	652.812i	0.469532	+	0.702704i	0.988353	−	0.152179i	$-0.0486290\pi$
$929$	436.195	+	652.812i	0.469532	+	0.702704i	−0.518821	+	0.854883i	$0.673629\pi$
$930$		0			0
$931$	−594.126	+	594.126i	−0.638159	+	0.638159i
$932$	−155.094	+	232.115i	−0.166410	+	0.249051i
$933$	−1286.92	−	533.059i	−1.37933	−	0.571339i
$934$			93.6738i			0.100293i
$935$		0			0
$936$	14.6186			0.0156182
$937$	59.2177	−	142.964i	0.0631993	−	0.152577i	−0.889125	−	0.457665i	$-0.848686\pi$
$937$	59.2177	−	142.964i	0.0631993	−	0.152577i	0.952324	+	0.305088i	$0.0986860\pi$
$938$	−787.315	−	526.067i	−0.839355	−	0.560839i
$939$	−714.274	−	714.274i	−0.760675	−	0.760675i
$940$		0			0
$941$	−592.097	+	395.627i	−0.629221	+	0.420432i	−0.828875	−	0.559434i	$-0.811018\pi$
$941$	−592.097	+	395.627i	−0.629221	+	0.420432i	0.199653	+	0.979867i	$0.436018\pi$
$942$	1338.62	+	266.269i	1.42104	+	0.282663i
$943$	284.853	−	117.990i	0.302071	−	0.125122i
$944$	639.663	+	1544.28i	0.677609	+	1.63589i
$945$		0			0
$946$	93.2947	+	139.625i	0.0986202	+	0.147596i
$947$	−255.927	−	1286.63i	−0.270250	−	1.35864i	−0.842561	−	0.538601i	$-0.818953\pi$
$947$	−255.927	−	1286.63i	−0.270250	−	1.35864i	0.572311	−	0.820037i	$-0.306047\pi$
$948$	−57.1070	+	57.1070i	−0.0602394	+	0.0602394i
$949$	−261.832	+	391.860i	−0.275904	+	0.412919i
$950$		0			0
$951$			558.900i			0.587697i
$952$	−489.362	−	821.814i	−0.514035	−	0.863250i
$953$	780.393			0.818880			0.409440	−	0.912337i	$-0.365724\pi$
$953$	780.393			0.818880			0.409440	+	0.912337i	$0.365724\pi$
$954$	14.5900	−	35.2234i	0.0152935	−	0.0369218i
$955$		0			0
$956$	58.6384	+	58.6384i	0.0613372	+	0.0613372i
$957$	−212.812	+	42.3310i	−0.222374	+	0.0442330i
$958$	537.821	−	359.361i	0.561400	−	0.375115i
$959$	1179.84	+	234.685i	1.23028	+	0.244719i
$960$		0			0
$961$	247.438	+	597.367i	0.257479	+	0.621610i
$962$	−98.6743	+	496.069i	−0.102572	+	0.515664i
$963$	16.0269	+	23.9859i	0.0166427	+	0.0249075i
$964$	−48.2031	−	242.334i	−0.0500033	−	0.251383i
$965$		0			0
$966$	−1396.15	+	2089.49i	−1.44529	+	2.16304i
$967$	471.272	+	195.207i	0.487355	+	0.201869i	0.612810	−	0.790230i	$-0.290039\pi$
$967$	471.272	+	195.207i	0.487355	+	0.201869i	−0.125455	+	0.992099i	$0.540039\pi$
$968$			225.839i			0.233305i
$969$	1341.77	+	1001.14i	1.38470	+	1.03316i
$970$		0			0
$971$	184.941	−	446.487i	0.190464	−	0.459822i	−0.799583	−	0.600555i	$-0.794946\pi$
$971$	184.941	−	446.487i	0.190464	−	0.459822i	0.990047	+	0.140734i	$0.0449462\pi$
$972$	11.9505	+	7.98507i	0.0122948	+	0.00821509i
$973$	1385.90	+	1385.90i	1.42436	+	1.42436i
$974$	1099.71	−	218.745i	1.12906	−	0.224584i
$975$		0			0
$976$	−215.705	−	42.9065i	−0.221010	−	0.0439616i
$977$	−1057.21	+	437.911i	−1.08210	+	0.448220i	−0.851245	−	0.524768i	$-0.824152\pi$
$977$	−1057.21	+	437.911i	−1.08210	+	0.448220i	−0.230854	+	0.972988i	$0.574152\pi$
$978$	−461.236	−	1113.52i	−0.471611	−	1.13857i
$979$	−69.2503	+	348.145i	−0.0707357	+	0.355612i
$980$		0			0
$981$	1.00720	+	5.06352i	0.00102670	+	0.00516159i
$982$	−779.070	+	779.070i	−0.793350	+	0.793350i
$983$	282.402	−	422.644i	0.287286	−	0.429953i	−0.659555	−	0.751656i	$-0.729255\pi$
$983$	282.402	−	422.644i	0.287286	−	0.429953i	0.946841	+	0.321703i	$0.104255\pi$
$984$	133.410	+	55.2603i	0.135579	+	0.0561588i
$985$		0			0
$986$	31.6959	+	218.004i	0.0321459	+	0.221099i
$987$	462.124			0.468211
$988$	133.853	−	323.150i	0.135479	−	0.327075i
$989$	208.327	+	139.200i	0.210644	+	0.140748i
$990$		0			0
$991$	1123.35	−	223.448i	1.13355	−	0.225477i	0.407558	−	0.913179i	$-0.366381\pi$
$991$	1123.35	−	223.448i	1.13355	−	0.225477i	0.725993	+	0.687702i	$0.241381\pi$
$992$	−259.313	+	173.267i	−0.261404	+	0.174665i
$993$	−820.630	−	163.233i	−0.826415	−	0.164384i
$994$	1648.24	−	682.723i	1.65819	−	0.686844i
$995$		0			0
$996$	73.8522	−	371.280i	0.0741488	−	0.372771i
$997$	−40.7309	−	60.9581i	−0.0408534	−	0.0611415i	0.810481	−	0.585765i	$-0.199206\pi$
$997$	−40.7309	−	60.9581i	−0.0408534	−	0.0611415i	−0.851334	+	0.524624i	$0.824206\pi$
$998$	136.780	+	687.639i	0.137054	+	0.689017i
$999$	440.422	−	440.422i	0.440863	−	0.440863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.e.401.10		96
5.2	odd	4		425.3.t.e.299.10		96
5.3	odd	4		425.3.t.h.299.3		96
5.4	even	2		85.3.q.a.61.3	yes	96
17.12	odd	16	inner	425.3.u.e.301.10		96
85.12	even	16		425.3.t.h.199.3		96
85.29	odd	16		85.3.q.a.46.3	✓	96
85.63	even	16		425.3.t.e.199.10		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.3	✓	96	85.29	odd	16
85.3.q.a.61.3	yes	96	5.4	even	2
425.3.t.e.199.10		96	85.63	even	16
425.3.t.e.299.10		96	5.2	odd	4
425.3.t.h.199.3		96	85.12	even	16
425.3.t.h.299.3		96	5.3	odd	4
425.3.u.e.301.10		96	17.12	odd	16	inner
425.3.u.e.401.10		96	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+(0.866790 - 2.09262i) q^{2} +(-2.52684 - 1.68838i) q^{3} +(-0.799289 - 0.799289i) q^{4} +(-5.72336 + 3.82423i) q^{6} +(-8.48985 - 1.68874i) q^{7} +(6.00504 - 2.48737i) q^{8} +(0.0901317 + 0.217597i) q^{9} +(-6.93341 - 10.3766i) q^{11} +(0.670170 + 3.36917i) q^{12} +(6.75230 - 6.75230i) q^{13} +(-10.8928 + 16.3022i) q^{14} -19.2437i q^{16} +(5.68096 + 16.0227i) q^{17} +0.533473 q^{18} +(-12.4006 + 29.9377i) q^{19} +(18.6012 + 18.6012i) q^{21} +(-27.7240 + 5.51465i) q^{22} +(-35.0679 + 23.4316i) q^{23} +(-19.3734 - 3.85361i) q^{24} +(-8.27714 - 19.9828i) q^{26} +(-5.19628 + 26.1235i) q^{27} +(5.43605 + 8.13563i) q^{28} +(1.11614 + 5.61123i) q^{29} +(9.85122 - 14.7434i) q^{31} +(-16.2496 - 6.73079i) q^{32} +37.9261i q^{33} +(38.4535 + 2.00023i) q^{34} +(0.101882 - 0.245964i) q^{36} +(-19.4435 - 12.9917i) q^{37} +(51.8994 + 51.8994i) q^{38} +(-28.4624 + 5.66152i) q^{39} +(-7.16994 - 1.42619i) q^{41} +(55.0486 - 22.8019i) q^{42} +(-2.27340 - 5.48847i) q^{43} +(-2.75209 + 13.8357i) q^{44} +(18.6369 + 93.6940i) q^{46} +(12.4219 - 12.4219i) q^{47} +(-32.4907 + 48.6258i) q^{48} +(23.9555 + 9.92271i) q^{49} +(12.6975 - 50.0783i) q^{51} -10.7941 q^{52} +(27.3491 - 66.0266i) q^{53} +(50.1623 + 33.5174i) q^{54} +(-55.1824 + 10.9765i) q^{56} +(81.8804 - 54.7107i) q^{57} +(12.7096 + 2.52810i) q^{58} +(-80.2486 + 33.2400i) q^{59} +(2.22963 - 11.2091i) q^{61} +(-22.3133 - 33.3942i) q^{62} +(-0.397740 - 1.99958i) q^{63} +(26.2596 - 26.2596i) q^{64} +(79.3648 + 32.8740i) q^{66} +48.2950i q^{67} +(8.26603 - 17.3475i) q^{68} +128.172 q^{69} +(-75.6574 - 50.5527i) q^{71} +(1.08249 + 1.08249i) q^{72} +(-48.4052 + 9.62839i) q^{73} +(-44.0401 + 29.4266i) q^{74} +(33.8405 - 14.0172i) q^{76} +(41.3403 + 99.8042i) q^{77} +(-12.8235 + 64.4682i) q^{78} +(13.0615 + 19.5479i) q^{79} +(58.7353 - 58.7353i) q^{81} +(-9.19930 + 13.7677i) q^{82} +(-101.811 - 42.1714i) q^{83} -29.7355i q^{84} -13.4558 q^{86} +(6.65357 - 16.0631i) q^{87} +(-67.4458 - 45.0658i) q^{88} +(-20.1124 - 20.1124i) q^{89} +(-68.7288 + 45.9231i) q^{91} +(46.7580 + 9.30075i) q^{92} +(-49.7849 + 20.6216i) q^{93} +(-15.2270 - 36.7613i) q^{94} +(29.6959 + 44.4430i) q^{96} +(-17.7309 - 89.1393i) q^{97} +(41.5289 - 41.5289i) q^{98} +(1.63299 - 2.44395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Introduction

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