LMFDB - Embedded newform 550.2.h.d.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(201,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.201"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,6,-1,0,-4,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.d.201.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.381966 - 1.17557i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.00000 + 0.726543i) q^{6} +(-0.190983 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.19098 + 0.865300i) q^{9} +(1.69098 + 2.85317i) q^{11} +1.23607 q^{12} +(1.92705 + 1.40008i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(5.23607 - 3.80423i) q^{17} +(-0.454915 - 1.40008i) q^{18} +(1.11803 - 3.44095i) q^{19} -0.763932 q^{21} +(0.309017 - 3.30220i) q^{22} -4.61803 q^{23} +(-1.00000 - 0.726543i) q^{24} +(-0.736068 - 2.26538i) q^{26} +(4.47214 - 3.24920i) q^{27} +(0.500000 - 0.363271i) q^{28} +(1.38197 + 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} +1.00000 q^{32} +(4.00000 - 0.898056i) q^{33} -6.47214 q^{34} +(-0.454915 + 1.40008i) q^{36} +(-1.73607 - 5.34307i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(2.38197 - 1.73060i) q^{39} +(0.190983 - 0.587785i) q^{41} +(0.618034 + 0.449028i) q^{42} +8.47214 q^{43} +(-2.19098 + 2.48990i) q^{44} +(3.73607 + 2.71441i) q^{46} +(-3.11803 + 9.59632i) q^{47} +(0.381966 + 1.17557i) q^{48} +(5.35410 - 3.88998i) q^{49} +(-2.47214 - 7.60845i) q^{51} +(-0.736068 + 2.26538i) q^{52} +(-5.73607 - 4.16750i) q^{53} -5.52786 q^{54} -0.618034 q^{56} +(-3.61803 - 2.62866i) q^{57} +(1.38197 - 4.25325i) q^{58} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(0.618034 + 1.90211i) q^{62} +(0.281153 - 0.865300i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.76393 - 1.62460i) q^{66} -9.23607 q^{67} +(5.23607 + 3.80423i) q^{68} +(-1.76393 + 5.42882i) q^{69} +(-1.61803 + 1.17557i) q^{71} +(1.19098 - 0.865300i) q^{72} +(-0.472136 - 1.45309i) q^{73} +(-1.73607 + 5.34307i) q^{74} +3.61803 q^{76} +(1.35410 - 1.53884i) q^{77} -2.94427 q^{78} +(5.00000 + 3.63271i) q^{79} +(-0.746711 - 2.29814i) q^{81} +(-0.500000 + 0.363271i) q^{82} +(-8.23607 + 5.98385i) q^{83} +(-0.236068 - 0.726543i) q^{84} +(-6.85410 - 4.97980i) q^{86} +5.52786 q^{87} +(3.23607 - 0.726543i) q^{88} +11.3820 q^{89} +(0.454915 - 1.40008i) q^{91} +(-1.42705 - 4.39201i) q^{92} +(-2.00000 + 1.45309i) q^{93} +(8.16312 - 5.93085i) q^{94} +(0.381966 - 1.17557i) q^{96} +(7.47214 + 5.42882i) q^{97} -6.61803 q^{98} +(-0.454915 + 4.86128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 6 q^{3} - q^{4} - 4 q^{6} - 3 q^{7} - q^{8} + 7 q^{9} + 9 q^{11} - 4 q^{12} + q^{13} - 3 q^{14} - q^{16} + 12 q^{17} - 13 q^{18} - 12 q^{21} - q^{22} - 14 q^{23} - 4 q^{24} + 6 q^{26}+ \cdots - 13 q^{99}+O(q^{100}) $ 4 * q - q^2 + 6 * q^3 - q^4 - 4 * q^6 - 3 * q^7 - q^8 + 7 * q^9 + 9 * q^11 - 4 * q^12 + q^13 - 3 * q^14 - q^16 + 12 * q^17 - 13 * q^18 - 12 * q^21 - q^22 - 14 * q^23 - 4 * q^24 + 6 * q^26 + 2 * q^28 + 10 * q^29 - 2 * q^31 + 4 * q^32 + 16 * q^33 - 8 * q^34 - 13 * q^36 + 2 * q^37 - 5 * q^38 + 14 * q^39 + 3 * q^41 - 2 * q^42 + 16 * q^43 - 11 * q^44 + 6 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 + 8 * q^51 + 6 * q^52 - 14 * q^53 - 40 * q^54 + 2 * q^56 - 10 * q^57 + 10 * q^58 + 18 * q^61 - 2 * q^62 - 19 * q^63 - q^64 - 24 * q^66 - 28 * q^67 + 12 * q^68 - 16 * q^69 - 2 * q^71 + 7 * q^72 + 16 * q^73 + 2 * q^74 + 10 * q^76 - 8 * q^77 + 24 * q^78 + 20 * q^79 - 41 * q^81 - 2 * q^82 - 24 * q^83 + 8 * q^84 - 14 * q^86 + 40 * q^87 + 4 * q^88 + 50 * q^89 + 13 * q^91 + q^92 - 8 * q^93 + 17 * q^94 + 6 * q^96 + 12 * q^97 - 22 * q^98 - 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.381966	−	1.17557i	0.220528	−	0.678716i	−0.778187	−	0.628033i	$-0.783860\pi$
$3$	0.381966	−	1.17557i	0.220528	−	0.678716i	0.998715	−	0.0506828i	$-0.0161398\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−1.00000	+	0.726543i	−0.408248	+	0.296610i
$7$	−0.190983	−	0.587785i	−0.0721848	−	0.222162i	0.908455	−	0.417983i	$-0.137263\pi$
$7$	−0.190983	−	0.587785i	−0.0721848	−	0.222162i	−0.980640	+	0.195821i	$0.937263\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	1.19098	+	0.865300i	0.396994	+	0.288433i
$10$		0			0
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$12$	1.23607			0.356822
$13$	1.92705	+	1.40008i	0.534468	+	0.388314i	0.822026	−	0.569449i	$-0.192844\pi$
$13$	1.92705	+	1.40008i	0.534468	+	0.388314i	−0.287559	+	0.957763i	$0.592844\pi$
$14$	−0.190983	+	0.587785i	−0.0510424	+	0.157092i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	5.23607	−	3.80423i	1.26993	−	0.922660i	0.270733	−	0.962654i	$-0.412734\pi$
$17$	5.23607	−	3.80423i	1.26993	−	0.922660i	0.999200	+	0.0399941i	$0.0127339\pi$
$18$	−0.454915	−	1.40008i	−0.107225	−	0.330003i
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	−0.737037	−	0.675852i	$-0.763776\pi$
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	0.993532	−	0.113557i	$-0.0362244\pi$
$20$		0			0
$21$	−0.763932			−0.166704
$22$	0.309017	−	3.30220i	0.0658826	−	0.704031i
$23$	−4.61803			−0.962927			−0.481463	−	0.876466i	$-0.659895\pi$
$23$	−4.61803			−0.962927			−0.481463	+	0.876466i	$0.659895\pi$
$24$	−1.00000	−	0.726543i	−0.204124	−	0.148305i
$25$		0			0
$26$	−0.736068	−	2.26538i	−0.144355	−	0.444278i
$27$	4.47214	−	3.24920i	0.860663	−	0.625308i
$28$	0.500000	−	0.363271i	0.0944911	−	0.0686518i
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	0.993505	+	0.113787i	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$		0			0
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$	1.00000			0.176777
$33$	4.00000	−	0.898056i	0.696311	−	0.156331i
$34$	−6.47214			−1.10996
$35$		0			0
$36$	−0.454915	+	1.40008i	−0.0758192	+	0.233347i
$37$	−1.73607	−	5.34307i	−0.285408	−	0.878395i	−0.986276	−	0.165104i	$-0.947204\pi$
$37$	−1.73607	−	5.34307i	−0.285408	−	0.878395i	0.700868	−	0.713291i	$-0.252796\pi$
$38$	−2.92705	+	2.12663i	−0.474830	+	0.344984i
$39$	2.38197	−	1.73060i	0.381420	−	0.277118i
$40$		0			0
$41$	0.190983	−	0.587785i	0.0298265	−	0.0917966i	−0.935035	−	0.354555i	$-0.884632\pi$
$41$	0.190983	−	0.587785i	0.0298265	−	0.0917966i	0.964862	+	0.262759i	$0.0846323\pi$
$42$	0.618034	+	0.449028i	0.0953647	+	0.0692865i
$43$	8.47214			1.29199			0.645994	−	0.763342i	$-0.276443\pi$
$43$	8.47214			1.29199			0.645994	+	0.763342i	$0.276443\pi$
$44$	−2.19098	+	2.48990i	−0.330303	+	0.375366i
$45$		0			0
$46$	3.73607	+	2.71441i	0.550853	+	0.400218i
$47$	−3.11803	+	9.59632i	−0.454812	+	1.39977i	0.416544	+	0.909116i	$0.363241\pi$
$47$	−3.11803	+	9.59632i	−0.454812	+	1.39977i	−0.871356	+	0.490652i	$0.836759\pi$
$48$	0.381966	+	1.17557i	0.0551320	+	0.169679i
$49$	5.35410	−	3.88998i	0.764872	−	0.555712i
$50$		0			0
$51$	−2.47214	−	7.60845i	−0.346168	−	1.06540i
$52$	−0.736068	+	2.26538i	−0.102074	+	0.314152i
$53$	−5.73607	−	4.16750i	−0.787910	−	0.572450i	0.119433	−	0.992842i	$-0.461892\pi$
$53$	−5.73607	−	4.16750i	−0.787910	−	0.572450i	−0.907342	+	0.420393i	$0.861892\pi$
$54$	−5.52786			−0.752247
$55$		0			0
$56$	−0.618034			−0.0825883
$57$	−3.61803	−	2.62866i	−0.479220	−	0.348174i
$58$	1.38197	−	4.25325i	0.181461	−	0.558480i
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	−0.891369	−	0.453279i	$-0.850254\pi$
$59$	−3.35410	−	10.3229i	−0.436667	−	1.34392i	0.454702	−	0.890644i	$-0.349746\pi$
$60$		0			0
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	−0.166850	−	0.985982i	$-0.553360\pi$
$61$	5.61803	−	4.08174i	0.719316	−	0.522613i	0.886165	+	0.463369i	$0.153360\pi$
$62$	0.618034	+	1.90211i	0.0784904	+	0.241569i
$63$	0.281153	−	0.865300i	0.0354219	−	0.109018i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−3.76393	−	1.62460i	−0.463308	−	0.199974i
$67$	−9.23607			−1.12837			−0.564183	−	0.825650i	$-0.690809\pi$
$67$	−9.23607			−1.12837			−0.564183	+	0.825650i	$0.690809\pi$
$68$	5.23607	+	3.80423i	0.634967	+	0.461330i
$69$	−1.76393	+	5.42882i	−0.212352	+	0.653554i
$70$		0			0
$71$	−1.61803	+	1.17557i	−0.192025	+	0.139515i	−0.679644	−	0.733542i	$-0.737866\pi$
$71$	−1.61803	+	1.17557i	−0.192025	+	0.139515i	0.487619	+	0.873057i	$0.337866\pi$
$72$	1.19098	−	0.865300i	0.140359	−	0.101977i
$73$	−0.472136	−	1.45309i	−0.0552593	−	0.170071i	0.919618	−	0.392815i	$-0.128499\pi$
$73$	−0.472136	−	1.45309i	−0.0552593	−	0.170071i	−0.974877	+	0.222744i	$0.928499\pi$
$74$	−1.73607	+	5.34307i	−0.201814	+	0.621119i
$75$		0			0
$76$	3.61803			0.415017
$77$	1.35410	−	1.53884i	0.154314	−	0.175367i
$78$	−2.94427			−0.333373
$79$	5.00000	+	3.63271i	0.562544	+	0.408712i	0.832389	−	0.554192i	$-0.186973\pi$
$79$	5.00000	+	3.63271i	0.562544	+	0.408712i	−0.269845	+	0.962904i	$0.586973\pi$
$80$		0			0
$81$	−0.746711	−	2.29814i	−0.0829679	−	0.255349i
$82$	−0.500000	+	0.363271i	−0.0552158	+	0.0401166i
$83$	−8.23607	+	5.98385i	−0.904026	+	0.656813i	−0.939497	−	0.342557i	$-0.888707\pi$
$83$	−8.23607	+	5.98385i	−0.904026	+	0.656813i	0.0354710	+	0.999371i	$0.488707\pi$
$84$	−0.236068	−	0.726543i	−0.0257571	−	0.0792723i
$85$		0			0
$86$	−6.85410	−	4.97980i	−0.739097	−	0.536985i
$87$	5.52786			0.592649
$88$	3.23607	−	0.726543i	0.344966	−	0.0774497i
$89$	11.3820			1.20649			0.603243	−	0.797557i	$-0.293875\pi$
$89$	11.3820			1.20649			0.603243	+	0.797557i	$0.293875\pi$
$90$		0			0
$91$	0.454915	−	1.40008i	0.0476881	−	0.146769i
$92$	−1.42705	−	4.39201i	−0.148780	−	0.457899i
$93$	−2.00000	+	1.45309i	−0.207390	+	0.150678i
$94$	8.16312	−	5.93085i	0.841961	−	0.611721i
$95$		0			0
$96$	0.381966	−	1.17557i	0.0389842	−	0.119981i
$97$	7.47214	+	5.42882i	0.758680	+	0.551214i	0.898505	−	0.438963i	$-0.144654\pi$
$97$	7.47214	+	5.42882i	0.758680	+	0.551214i	−0.139825	+	0.990176i	$0.544654\pi$
$98$	−6.61803			−0.668522
$99$	−0.454915	+	4.86128i	−0.0457207	+	0.488577i
$100$		0			0
$101$	15.9443	+	11.5842i	1.58651	+	1.15267i	0.908710	+	0.417428i	$0.137068\pi$
$101$	15.9443	+	11.5842i	1.58651	+	1.15267i	0.677804	+	0.735242i	$0.262932\pi$
$102$	−2.47214	+	7.60845i	−0.244778	+	0.753349i
$103$	−2.11803	−	6.51864i	−0.208696	−	0.642301i	−0.999541	−	0.0302843i	$-0.990359\pi$
$103$	−2.11803	−	6.51864i	−0.208696	−	0.642301i	0.790845	−	0.612016i	$-0.209641\pi$
$104$	1.92705	−	1.40008i	0.188963	−	0.137290i
$105$		0			0
$106$	2.19098	+	6.74315i	0.212807	+	0.654953i
$107$	−4.76393	+	14.6619i	−0.460547	+	1.41742i	0.403951	+	0.914781i	$0.367637\pi$
$107$	−4.76393	+	14.6619i	−0.460547	+	1.41742i	−0.864498	+	0.502636i	$0.832363\pi$
$108$	4.47214	+	3.24920i	0.430331	+	0.312654i
$109$	−5.52786			−0.529473			−0.264737	−	0.964321i	$-0.585285\pi$
$109$	−5.52786			−0.529473			−0.264737	+	0.964321i	$0.585285\pi$
$110$		0			0
$111$	−6.94427			−0.659121
$112$	0.500000	+	0.363271i	0.0472456	+	0.0343259i
$113$	−2.90983	+	8.95554i	−0.273734	+	0.842466i	0.715818	+	0.698287i	$0.246054\pi$
$113$	−2.90983	+	8.95554i	−0.273734	+	0.842466i	−0.989552	+	0.144179i	$0.953946\pi$
$114$	1.38197	+	4.25325i	0.129433	+	0.398354i
$115$		0			0
$116$	−3.61803	+	2.62866i	−0.335926	+	0.244065i
$117$	1.08359	+	3.33495i	0.100178	+	0.308317i
$118$	−3.35410	+	10.3229i	−0.308770	+	0.950297i
$119$	−3.23607	−	2.35114i	−0.296650	−	0.215529i
$120$		0			0
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	−6.94427			−0.628705
$123$	−0.618034	−	0.449028i	−0.0557262	−	0.0404875i
$124$	0.618034	−	1.90211i	0.0555011	−	0.170815i
$125$		0			0
$126$	−0.736068	+	0.534785i	−0.0655741	+	0.0476424i
$127$	2.30902	−	1.67760i	0.204892	−	0.148863i	−0.480608	−	0.876936i	$-0.659584\pi$
$127$	2.30902	−	1.67760i	0.204892	−	0.148863i	0.685500	+	0.728073i	$0.259584\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	3.23607	−	9.95959i	0.284920	−	0.876893i
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	2.09017	+	3.52671i	0.181926	+	0.306961i
$133$	−2.23607			−0.193892
$134$	7.47214	+	5.42882i	0.645494	+	0.468979i
$135$		0			0
$136$	−2.00000	−	6.15537i	−0.171499	−	0.527818i
$137$	−17.3262	+	12.5882i	−1.48028	+	1.07549i	−0.502814	+	0.864394i	$0.667702\pi$
$137$	−17.3262	+	12.5882i	−1.48028	+	1.07549i	−0.977466	+	0.211092i	$0.932298\pi$
$138$	4.61803	−	3.35520i	0.393113	−	0.285613i
$139$	0.100813	+	0.310271i	0.00855085	+	0.0263168i	0.955241	−	0.295829i	$-0.0955959\pi$
$139$	0.100813	+	0.310271i	0.00855085	+	0.0263168i	−0.946690	+	0.322146i	$0.895596\pi$
$140$		0			0
$141$	10.0902	+	7.33094i	0.849746	+	0.617376i
$142$	2.00000			0.167836
$143$	−0.736068	+	7.86572i	−0.0615531	+	0.657765i
$144$	−1.47214			−0.122678
$145$		0			0
$146$	−0.472136	+	1.45309i	−0.0390742	+	0.120258i
$147$	−2.52786	−	7.77997i	−0.208495	−	0.641681i
$148$	4.54508	−	3.30220i	0.373604	−	0.271439i
$149$	−17.5623	+	12.7598i	−1.43876	+	1.04532i	−0.450460	+	0.892796i	$0.648740\pi$
$149$	−17.5623	+	12.7598i	−1.43876	+	1.04532i	−0.988300	+	0.152524i	$0.951260\pi$
$150$		0			0
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	−0.617004	−	0.786960i	$-0.711654\pi$
$151$	4.23607	−	13.0373i	0.344726	−	1.06096i	0.961730	−	0.273998i	$-0.0883463\pi$
$152$	−2.92705	−	2.12663i	−0.237415	−	0.172492i
$153$	9.52786			0.770282
$154$	−2.00000	+	0.449028i	−0.161165	+	0.0361837i
$155$		0			0
$156$	2.38197	+	1.73060i	0.190710	+	0.138559i
$157$	−1.89919	+	5.84510i	−0.151572	+	0.466489i	−0.997797	−	0.0663350i	$-0.978869\pi$
$157$	−1.89919	+	5.84510i	−0.151572	+	0.466489i	0.846226	+	0.532824i	$0.178869\pi$
$158$	−1.90983	−	5.87785i	−0.151938	−	0.467617i
$159$	−7.09017	+	5.15131i	−0.562287	+	0.408525i
$160$		0			0
$161$	0.881966	+	2.71441i	0.0695087	+	0.213926i
$162$	−0.746711	+	2.29814i	−0.0586672	+	0.180559i
$163$	7.61803	+	5.53483i	0.596690	+	0.433521i	0.844703	−	0.535236i	$-0.179777\pi$
$163$	7.61803	+	5.53483i	0.596690	+	0.433521i	−0.248012	+	0.968757i	$0.579777\pi$
$164$	0.618034			0.0482603
$165$		0			0
$166$	10.1803			0.790148
$167$	−10.7812	−	7.83297i	−0.834271	−	0.606133i	0.0864937	−	0.996252i	$-0.472434\pi$
$167$	−10.7812	−	7.83297i	−0.834271	−	0.606133i	−0.920764	+	0.390119i	$0.872434\pi$
$168$	−0.236068	+	0.726543i	−0.0182130	+	0.0560540i
$169$	−2.26393	−	6.96767i	−0.174149	−	0.535974i
$170$		0			0
$171$	4.30902	−	3.13068i	0.329519	−	0.239409i
$172$	2.61803	+	8.05748i	0.199623	+	0.614377i
$173$	−0.572949	+	1.76336i	−0.0435605	+	0.134065i	−0.970472	−	0.241216i	$-0.922454\pi$
$173$	−0.572949	+	1.76336i	−0.0435605	+	0.134065i	0.926911	+	0.375281i	$0.122454\pi$
$174$	−4.47214	−	3.24920i	−0.339032	−	0.246321i
$175$		0			0
$176$	−3.04508	−	1.31433i	−0.229532	−	0.0990712i
$177$	−13.4164			−1.00844
$178$	−9.20820	−	6.69015i	−0.690184	−	0.501448i
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	0.785094	+	0.619377i	$0.212615\pi$
$179$	−2.86475	+	8.81678i	−0.214121	+	0.658997i	−0.999215	+	0.0396200i	$0.987385\pi$
$180$		0			0
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.993883	−	0.110442i	$-0.964773\pi$
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.202090	+	0.979367i	$0.564773\pi$
$182$	−1.19098	+	0.865300i	−0.0882815	+	0.0641403i
$183$	−2.65248	−	8.16348i	−0.196077	−	0.603462i
$184$	−1.42705	+	4.39201i	−0.105204	+	0.323783i
$185$		0			0
$186$	2.47214			0.181266
$187$	19.7082	+	8.50651i	1.44121	+	0.622057i
$188$	−10.0902			−0.735901
$189$	−2.76393	−	2.00811i	−0.201046	−	0.146069i
$190$		0			0
$191$	−2.79837	−	8.61251i	−0.202483	−	0.623179i	−0.999807	−	0.0196279i	$-0.993752\pi$
$191$	−2.79837	−	8.61251i	−0.202483	−	0.623179i	0.797324	−	0.603551i	$-0.206248\pi$
$192$	−1.00000	+	0.726543i	−0.0721688	+	0.0524337i
$193$	10.7082	−	7.77997i	0.770793	−	0.560014i	−0.131408	−	0.991328i	$-0.541950\pi$
$193$	10.7082	−	7.77997i	0.770793	−	0.560014i	0.902202	+	0.431314i	$0.141950\pi$
$194$	−2.85410	−	8.78402i	−0.204913	−	0.630656i
$195$		0			0
$196$	5.35410	+	3.88998i	0.382436	+	0.277856i
$197$	26.2148			1.86773			0.933863	−	0.357631i	$-0.116415\pi$
$197$	26.2148			1.86773			0.933863	+	0.357631i	$0.116415\pi$
$198$	3.22542	−	3.66547i	0.229221	−	0.260494i
$199$	−5.52786			−0.391860			−0.195930	−	0.980618i	$-0.562773\pi$
$199$	−5.52786			−0.391860			−0.195930	+	0.980618i	$0.562773\pi$
$200$		0			0
$201$	−3.52786	+	10.8576i	−0.248836	+	0.765840i
$202$	−6.09017	−	18.7436i	−0.428503	−	1.31880i
$203$	2.23607	−	1.62460i	0.156941	−	0.114024i
$204$	6.47214	−	4.70228i	0.453140	−	0.329226i
$205$		0			0
$206$	−2.11803	+	6.51864i	−0.147570	+	0.454175i
$207$	−5.50000	−	3.99598i	−0.382276	−	0.277740i
$208$	−2.38197			−0.165160
$209$	11.7082	−	2.62866i	0.809873	−	0.181828i
$210$		0			0
$211$	−21.4164	−	15.5599i	−1.47437	−	1.07119i	−0.979319	−	0.202324i	$-0.935151\pi$
$211$	−21.4164	−	15.5599i	−1.47437	−	1.07119i	−0.495048	−	0.868866i	$-0.664849\pi$
$212$	2.19098	−	6.74315i	0.150477	−	0.463122i
$213$	0.763932	+	2.35114i	0.0523438	+	0.161098i
$214$	12.4721	−	9.06154i	0.852578	−	0.619434i
$215$		0			0
$216$	−1.70820	−	5.25731i	−0.116229	−	0.357715i
$217$	−0.381966	+	1.17557i	−0.0259295	+	0.0798029i
$218$	4.47214	+	3.24920i	0.302891	+	0.220063i
$219$	−1.88854			−0.127616
$220$		0			0
$221$	15.4164			1.03702
$222$	5.61803	+	4.08174i	0.377058	+	0.273948i
$223$	−5.89919	+	18.1558i	−0.395039	+	1.21580i	0.533893	+	0.845552i	$0.320729\pi$
$223$	−5.89919	+	18.1558i	−0.395039	+	1.21580i	−0.928931	+	0.370252i	$0.879271\pi$
$224$	−0.190983	−	0.587785i	−0.0127606	−	0.0392731i
$225$		0			0
$226$	7.61803	−	5.53483i	0.506744	−	0.368171i
$227$	−3.70820	−	11.4127i	−0.246122	−	0.757486i	−0.995450	−	0.0952867i	$-0.969623\pi$
$227$	−3.70820	−	11.4127i	−0.246122	−	0.757486i	0.749328	−	0.662199i	$-0.230377\pi$
$228$	1.38197	−	4.25325i	0.0915229	−	0.281679i
$229$	5.85410	+	4.25325i	0.386850	+	0.281063i	0.764163	−	0.645023i	$-0.223152\pi$
$229$	5.85410	+	4.25325i	0.386850	+	0.281063i	−0.377314	+	0.926086i	$0.623152\pi$
$230$		0			0
$231$	−1.29180	−	2.17963i	−0.0849939	−	0.143409i
$232$	4.47214			0.293610
$233$	−15.4721	−	11.2412i	−1.01361	−	0.736433i	−0.0486494	−	0.998816i	$-0.515492\pi$
$233$	−15.4721	−	11.2412i	−1.01361	−	0.736433i	−0.964964	+	0.262383i	$0.915492\pi$
$234$	1.08359	−	3.33495i	0.0708366	−	0.218013i
$235$		0			0
$236$	8.78115	−	6.37988i	0.571604	−	0.415295i
$237$	6.18034	−	4.49028i	0.401456	−	0.291675i
$238$	1.23607	+	3.80423i	0.0801224	+	0.246591i
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	−0.852325	−	0.523012i	$-0.824808\pi$
$239$	2.23607	−	6.88191i	0.144639	−	0.445154i	0.996964	+	0.0778584i	$0.0248082\pi$
$240$		0			0
$241$	−4.90983			−0.316270			−0.158135	−	0.987418i	$-0.550548\pi$
$241$	−4.90983			−0.316270			−0.158135	+	0.987418i	$0.550548\pi$
$242$	9.94427	−	4.70228i	0.639242	−	0.302274i
$243$	13.5967			0.872232
$244$	5.61803	+	4.08174i	0.359658	+	0.261307i
$245$		0			0
$246$	0.236068	+	0.726543i	0.0150511	+	0.0463227i
$247$	6.97214	−	5.06555i	0.443626	−	0.322313i
$248$	−1.61803	+	1.17557i	−0.102745	+	0.0746488i
$249$	3.88854	+	11.9677i	0.246426	+	0.758423i
$250$		0			0
$251$	−5.50000	−	3.99598i	−0.347157	−	0.252224i	0.400518	−	0.916289i	$-0.368830\pi$
$251$	−5.50000	−	3.99598i	−0.347157	−	0.252224i	−0.747675	+	0.664064i	$0.768830\pi$
$252$	0.909830			0.0573139
$253$	−7.80902	−	13.1760i	−0.490949	−	0.828370i
$254$	−2.85410			−0.179082
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.47214	−	19.9192i	−0.403721	−	1.24252i	−0.921959	−	0.387288i	$-0.873412\pi$
$257$	−6.47214	−	19.9192i	−0.403721	−	1.24252i	0.518238	−	0.855236i	$-0.326588\pi$
$258$	−8.47214	+	6.15537i	−0.527452	+	0.383216i
$259$	−2.80902	+	2.04087i	−0.174544	+	0.126814i
$260$		0			0
$261$	−2.03444	+	6.26137i	−0.125929	+	0.387569i
$262$	6.47214	+	4.70228i	0.399850	+	0.290508i
$263$	−5.14590			−0.317310			−0.158655	−	0.987334i	$-0.550716\pi$
$263$	−5.14590			−0.317310			−0.158655	+	0.987334i	$0.550716\pi$
$264$	0.381966	−	4.08174i	0.0235084	−	0.251214i
$265$		0			0
$266$	1.80902	+	1.31433i	0.110918	+	0.0805866i
$267$	4.34752	−	13.3803i	0.266064	−	0.818861i
$268$	−2.85410	−	8.78402i	−0.174342	−	0.536570i
$269$	−18.0902	+	13.1433i	−1.10298	+	0.801360i	−0.981543	−	0.191240i	$-0.938749\pi$
$269$	−18.0902	+	13.1433i	−1.10298	+	0.801360i	−0.121434	+	0.992600i	$0.538749\pi$
$270$		0			0
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	0.936882	−	0.349646i	$-0.113698\pi$
$271$	−0.437694	−	1.34708i	−0.0265880	−	0.0818295i	−0.963470	+	0.267816i	$0.913698\pi$
$272$	−2.00000	+	6.15537i	−0.121268	+	0.373224i
$273$	−1.47214	−	1.06957i	−0.0890977	−	0.0647333i
$274$	21.4164			1.29381
$275$		0			0
$276$	−5.70820			−0.343594
$277$	−0.0278640	−	0.0202444i	−0.00167419	−	0.00121637i	0.586948	−	0.809625i	$-0.300329\pi$
$277$	−0.0278640	−	0.0202444i	−0.00167419	−	0.00121637i	−0.588622	+	0.808408i	$0.700329\pi$
$278$	0.100813	−	0.310271i	0.00604637	−	0.0186088i
$279$	−0.909830	−	2.80017i	−0.0544701	−	0.167642i
$280$		0			0
$281$	7.32624	−	5.32282i	0.437047	−	0.317533i	−0.347414	−	0.937712i	$-0.612940\pi$
$281$	7.32624	−	5.32282i	0.437047	−	0.317533i	0.784460	+	0.620179i	$0.212940\pi$
$282$	−3.85410	−	11.8617i	−0.229508	−	0.706354i
$283$	0.0557281	−	0.171513i	0.00331269	−	0.0101954i	−0.949387	−	0.314110i	$-0.898294\pi$
$283$	0.0557281	−	0.171513i	0.00331269	−	0.0101954i	0.952699	+	0.303915i	$0.0982938\pi$
$284$	−1.61803	−	1.17557i	−0.0960127	−	0.0697573i
$285$		0			0
$286$	5.21885	−	5.93085i	0.308597	−	0.350699i
$287$	−0.381966			−0.0225467
$288$	1.19098	+	0.865300i	0.0701793	+	0.0509883i
$289$	7.69098	−	23.6704i	0.452411	−	1.39238i
$290$		0			0
$291$	9.23607	−	6.71040i	0.541428	−	0.393370i
$292$	1.23607	−	0.898056i	0.0723354	−	0.0525547i
$293$	9.22542	+	28.3929i	0.538955	+	1.65873i	0.734945	+	0.678127i	$0.237208\pi$
$293$	9.22542	+	28.3929i	0.538955	+	1.65873i	−0.195990	+	0.980606i	$0.562792\pi$
$294$	−2.52786	+	7.77997i	−0.147428	+	0.453737i
$295$		0			0
$296$	−5.61803			−0.326542
$297$	16.8328	+	7.26543i	0.976739	+	0.421583i
$298$	21.7082			1.25752
$299$	−8.89919	−	6.46564i	−0.514653	−	0.373917i
$300$		0			0
$301$	−1.61803	−	4.97980i	−0.0932619	−	0.287031i
$302$	−11.0902	+	8.05748i	−0.638168	+	0.463656i
$303$	19.7082	−	14.3188i	1.13221	−	0.822596i
$304$	1.11803	+	3.44095i	0.0641236	+	0.197352i
$305$		0			0
$306$	−7.70820	−	5.60034i	−0.440649	−	0.320150i
$307$	15.2361			0.869568			0.434784	−	0.900535i	$-0.356825\pi$
$307$	15.2361			0.869568			0.434784	+	0.900535i	$0.356825\pi$
$308$	1.88197	+	0.812299i	0.107235	+	0.0462850i
$309$	−8.47214			−0.481963
$310$		0			0
$311$	−1.29180	+	3.97574i	−0.0732510	+	0.225444i	−0.980978	−	0.194117i	$-0.937816\pi$
$311$	−1.29180	+	3.97574i	−0.0732510	+	0.225444i	0.907727	+	0.419561i	$0.137816\pi$
$312$	−0.909830	−	2.80017i	−0.0515090	−	0.158528i
$313$	9.32624	−	6.77591i	0.527150	−	0.382997i	−0.292141	−	0.956375i	$-0.594368\pi$
$313$	9.32624	−	6.77591i	0.527150	−	0.382997i	0.819291	+	0.573378i	$0.194368\pi$
$314$	4.97214	−	3.61247i	0.280594	−	0.203863i
$315$		0			0
$316$	−1.90983	+	5.87785i	−0.107436	+	0.330655i
$317$	−11.6353	−	8.45351i	−0.653501	−	0.474796i	0.210961	−	0.977494i	$-0.432341\pi$
$317$	−11.6353	−	8.45351i	−0.653501	−	0.474796i	−0.864462	+	0.502698i	$0.832341\pi$
$318$	8.76393			0.491457
$319$	−9.79837	+	11.1352i	−0.548604	+	0.623449i
$320$		0			0
$321$	15.4164	+	11.2007i	0.860460	+	0.625161i
$322$	0.881966	−	2.71441i	0.0491500	−	0.151268i
$323$	−7.23607	−	22.2703i	−0.402626	−	1.23915i
$324$	1.95492	−	1.42033i	0.108606	−	0.0789072i
$325$		0			0
$326$	−2.90983	−	8.95554i	−0.161161	−	0.496001i
$327$	−2.11146	+	6.49839i	−0.116764	+	0.359362i
$328$	−0.500000	−	0.363271i	−0.0276079	−	0.0200583i
$329$	6.23607			0.343806
$330$		0			0
$331$	−6.09017			−0.334746			−0.167373	−	0.985894i	$-0.553528\pi$
$331$	−6.09017			−0.334746			−0.167373	+	0.985894i	$0.553528\pi$
$332$	−8.23607	−	5.98385i	−0.452013	−	0.328407i
$333$	2.55573	−	7.86572i	0.140053	−	0.431039i
$334$	4.11803	+	12.6740i	0.225329	+	0.693491i
$335$		0			0
$336$	0.618034	−	0.449028i	0.0337165	−	0.0244965i
$337$	0.562306	+	1.73060i	0.0306308	+	0.0942718i	0.965203	−	0.261501i	$-0.0842176\pi$
$337$	0.562306	+	1.73060i	0.0306308	+	0.0942718i	−0.934572	+	0.355773i	$0.884218\pi$
$338$	−2.26393	+	6.96767i	−0.123142	+	0.378991i
$339$	9.41641	+	6.84142i	0.511429	+	0.371575i
$340$		0			0
$341$	0.618034	−	6.60440i	0.0334684	−	0.357648i
$342$	−5.32624			−0.288010
$343$	−6.80902	−	4.94704i	−0.367652	−	0.267115i
$344$	2.61803	−	8.05748i	0.141155	−	0.434430i
$345$		0			0
$346$	1.50000	−	1.08981i	0.0806405	−	0.0585888i
$347$	2.14590	−	1.55909i	0.115198	−	0.0836961i	−0.528695	−	0.848812i	$-0.677318\pi$
$347$	2.14590	−	1.55909i	0.115198	−	0.0836961i	0.643893	+	0.765116i	$0.277318\pi$
$348$	1.70820	+	5.25731i	0.0915693	+	0.281821i
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	−0.992897	−	0.118976i	$-0.962039\pi$
$349$	−2.23607	+	6.88191i	−0.119694	+	0.368380i	0.873203	+	0.487356i	$0.162039\pi$
$350$		0			0
$351$	13.1672			0.702812
$352$	1.69098	+	2.85317i	0.0901297	+	0.152074i
$353$	−16.0000			−0.851594			−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−16.0000			−0.851594			−0.425797	+	0.904819i	$0.640006\pi$
$354$	10.8541	+	7.88597i	0.576889	+	0.419134i
$355$		0			0
$356$	3.51722	+	10.8249i	0.186412	+	0.573718i
$357$	−4.00000	+	2.90617i	−0.211702	+	0.153811i
$358$	7.50000	−	5.44907i	0.396387	−	0.287992i
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	−0.758753	−	0.651379i	$-0.774191\pi$
$359$	−10.0000	−	30.7768i	−0.527780	−	1.62434i	0.230973	−	0.972960i	$-0.425809\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$	19.8885			1.04532
$363$	9.32624	+	9.89408i	0.489501	+	0.519305i
$364$	1.47214			0.0771609
$365$		0			0
$366$	−2.65248	+	8.16348i	−0.138647	+	0.426712i
$367$	−9.23607	−	28.4257i	−0.482119	−	1.48381i	−0.836111	−	0.548561i	$-0.815176\pi$
$367$	−9.23607	−	28.4257i	−0.482119	−	1.48381i	0.353992	−	0.935248i	$-0.384824\pi$
$368$	3.73607	−	2.71441i	0.194756	−	0.141499i
$369$	0.736068	−	0.534785i	0.0383182	−	0.0278398i
$370$		0			0
$371$	−1.35410	+	4.16750i	−0.0703015	+	0.216366i
$372$	−2.00000	−	1.45309i	−0.103695	−	0.0753390i
$373$	6.56231			0.339783			0.169892	−	0.985463i	$-0.445658\pi$
$373$	6.56231			0.339783			0.169892	+	0.985463i	$0.445658\pi$
$374$	−10.9443	−	18.4661i	−0.565915	−	0.954859i
$375$		0			0
$376$	8.16312	+	5.93085i	0.420981	+	0.305860i
$377$	−3.29180	+	10.1311i	−0.169536	+	0.521779i
$378$	1.05573	+	3.24920i	0.0543008	+	0.167121i
$379$	−25.9164	+	18.8294i	−1.33124	+	0.967200i	−0.331519	+	0.943449i	$0.607561\pi$
$379$	−25.9164	+	18.8294i	−1.33124	+	0.967200i	−0.999718	+	0.0237512i	$0.992439\pi$
$380$		0			0
$381$	−1.09017	−	3.35520i	−0.0558511	−	0.171892i
$382$	−2.79837	+	8.61251i	−0.143177	+	0.440654i
$383$	−17.9721	−	13.0575i	−0.918333	−	0.667208i	0.0247753	−	0.999693i	$-0.492113\pi$
$383$	−17.9721	−	13.0575i	−0.918333	−	0.667208i	−0.943109	+	0.332485i	$0.892113\pi$
$384$	1.23607			0.0630778
$385$		0			0
$386$	−13.2361			−0.673698
$387$	10.0902	+	7.33094i	0.512912	+	0.372652i
$388$	−2.85410	+	8.78402i	−0.144895	+	0.445941i
$389$	7.76393	+	23.8949i	0.393647	+	1.21152i	0.930010	+	0.367534i	$0.119798\pi$
$389$	7.76393	+	23.8949i	0.393647	+	1.21152i	−0.536363	+	0.843987i	$0.680202\pi$
$390$		0			0
$391$	−24.1803	+	17.5680i	−1.22285	+	0.888454i
$392$	−2.04508	−	6.29412i	−0.103292	−	0.317901i
$393$	−3.05573	+	9.40456i	−0.154141	+	0.474398i
$394$	−21.2082	−	15.4087i	−1.06845	−	0.776277i
$395$		0			0
$396$	−4.76393	+	1.06957i	−0.239397	+	0.0537479i
$397$	−12.3262			−0.618636			−0.309318	−	0.950959i	$-0.600101\pi$
$397$	−12.3262			−0.618636			−0.309318	+	0.950959i	$0.600101\pi$
$398$	4.47214	+	3.24920i	0.224168	+	0.162868i
$399$	−0.854102	+	2.62866i	−0.0427586	+	0.131597i
$400$		0			0
$401$	−0.0729490	+	0.0530006i	−0.00364290	+	0.00264672i	−0.589605	−	0.807692i	$-0.700717\pi$
$401$	−0.0729490	+	0.0530006i	−0.00364290	+	0.00264672i	0.585962	+	0.810338i	$0.300717\pi$
$402$	9.23607	−	6.71040i	0.460653	−	0.334684i
$403$	−1.47214	−	4.53077i	−0.0733323	−	0.225694i
$404$	−6.09017	+	18.7436i	−0.302997	+	0.932530i
$405$		0			0
$406$	−2.76393			−0.137172
$407$	12.3090	−	13.9883i	0.610135	−	0.693376i
$408$	−8.00000			−0.396059
$409$	−21.0172	−	15.2699i	−1.03923	−	0.755048i	−0.0690987	−	0.997610i	$-0.522012\pi$
$409$	−21.0172	−	15.2699i	−1.03923	−	0.755048i	−0.970136	+	0.242562i	$0.922012\pi$
$410$		0			0
$411$	8.18034	+	25.1765i	0.403506	+	1.24187i
$412$	5.54508	−	4.02874i	0.273187	−	0.198482i
$413$	−5.42705	+	3.94298i	−0.267048	+	0.194022i
$414$	2.10081	+	6.46564i	0.103249	+	0.317769i
$415$		0			0
$416$	1.92705	+	1.40008i	0.0944814	+	0.0686448i
$417$	0.403252			0.0197473
$418$	−11.0172	−	4.75528i	−0.538870	−	0.232588i
$419$	35.9787			1.75768			0.878838	−	0.477121i	$-0.158320\pi$
$419$	35.9787			1.75768			0.878838	+	0.477121i	$0.158320\pi$
$420$		0			0
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	−0.934866	−	0.355001i	$-0.884480\pi$
$421$	0.618034	−	1.90211i	0.0301211	−	0.0927033i	0.964987	+	0.262298i	$0.0844804\pi$
$422$	8.18034	+	25.1765i	0.398213	+	1.22557i
$423$	−12.0172	+	8.73102i	−0.584297	+	0.424517i
$424$	−5.73607	+	4.16750i	−0.278568	+	0.202392i
$425$		0			0
$426$	0.763932	−	2.35114i	0.0370126	−	0.113913i
$427$	−3.47214	−	2.52265i	−0.168028	−	0.122080i
$428$	−15.4164			−0.745180
$429$	8.96556	+	3.86974i	0.432861	+	0.186833i
$430$		0			0
$431$	−22.7984	−	16.5640i	−1.09816	−	0.797859i	−0.117401	−	0.993085i	$-0.537456\pi$
$431$	−22.7984	−	16.5640i	−1.09816	−	0.797859i	−0.980758	+	0.195225i	$0.937456\pi$
$432$	−1.70820	+	5.25731i	−0.0821860	+	0.252942i
$433$	2.29180	+	7.05342i	0.110137	+	0.338966i	0.990902	−	0.134588i	$-0.0429710\pi$
$433$	2.29180	+	7.05342i	0.110137	+	0.338966i	−0.880765	+	0.473554i	$0.842971\pi$
$434$	1.00000	−	0.726543i	0.0480015	−	0.0348752i
$435$		0			0
$436$	−1.70820	−	5.25731i	−0.0818081	−	0.251780i
$437$	−5.16312	+	15.8904i	−0.246985	+	0.760143i
$438$	1.52786	+	1.11006i	0.0730042	+	0.0530406i
$439$	−6.18034			−0.294972			−0.147486	−	0.989064i	$-0.547118\pi$
$439$	−6.18034			−0.294972			−0.147486	+	0.989064i	$0.547118\pi$
$440$		0			0
$441$	9.74265			0.463936
$442$	−12.4721	−	9.06154i	−0.593239	−	0.431013i
$443$	0.0557281	−	0.171513i	0.00264772	−	0.00814885i	−0.949724	−	0.313089i	$-0.898636\pi$
$443$	0.0557281	−	0.171513i	0.00264772	−	0.00814885i	0.952372	+	0.304940i	$0.0986363\pi$
$444$	−2.14590	−	6.60440i	−0.101840	−	0.313431i
$445$		0			0
$446$	15.4443	−	11.2209i	0.731307	−	0.531326i
$447$	8.29180	+	25.5195i	0.392188	+	1.20703i
$448$	−0.190983	+	0.587785i	−0.00902310	+	0.0277702i
$449$	16.8713	+	12.2577i	0.796207	+	0.578478i	0.909799	−	0.415049i	$-0.136236\pi$
$449$	16.8713	+	12.2577i	0.796207	+	0.578478i	−0.113592	+	0.993527i	$0.536236\pi$
$450$		0			0
$451$	2.00000	−	0.449028i	0.0941763	−	0.0211439i
$452$	−9.41641			−0.442911
$453$	−13.7082	−	9.95959i	−0.644068	−	0.467943i
$454$	−3.70820	+	11.4127i	−0.174035	+	0.535624i
$455$		0			0
$456$	−3.61803	+	2.62866i	−0.169430	+	0.123098i
$457$	6.61803	−	4.80828i	0.309579	−	0.224922i	−0.422137	−	0.906532i	$-0.638720\pi$
$457$	6.61803	−	4.80828i	0.309579	−	0.224922i	0.731716	+	0.681610i	$0.238720\pi$
$458$	−2.23607	−	6.88191i	−0.104485	−	0.321571i
$459$	11.0557	−	34.0260i	0.516037	−	1.58820i
$460$		0			0
$461$	−9.70820			−0.452156			−0.226078	−	0.974109i	$-0.572590\pi$
$461$	−9.70820			−0.452156			−0.226078	+	0.974109i	$0.572590\pi$
$462$	−0.236068	+	2.52265i	−0.0109829	+	0.117365i
$463$	−1.32624			−0.0616355			−0.0308178	−	0.999525i	$-0.509811\pi$
$463$	−1.32624			−0.0616355			−0.0308178	+	0.999525i	$0.509811\pi$
$464$	−3.61803	−	2.62866i	−0.167963	−	0.122032i
$465$		0			0
$466$	5.90983	+	18.1886i	0.273768	+	0.842570i
$467$	−15.0902	+	10.9637i	−0.698290	+	0.507337i	−0.879375	−	0.476130i	$-0.842039\pi$
$467$	−15.0902	+	10.9637i	−0.698290	+	0.507337i	0.181085	+	0.983467i	$0.442039\pi$
$468$	−2.83688	+	2.06111i	−0.131135	+	0.0952751i
$469$	1.76393	+	5.42882i	0.0814508	+	0.250680i
$470$		0			0
$471$	6.14590	+	4.46526i	0.283188	+	0.205748i
$472$	−10.8541			−0.499601
$473$	14.3262	+	24.1724i	0.658721	+	1.11145i
$474$	−7.63932			−0.350886
$475$		0			0
$476$	1.23607	−	3.80423i	0.0566551	−	0.174366i
$477$	−3.22542	−	9.92684i	−0.147682	−	0.454519i
$478$	−5.85410	+	4.25325i	−0.267760	+	0.194539i
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.0432482	−	0.999064i	$-0.486229\pi$
$479$	22.0344	−	16.0090i	1.00678	−	0.731468i	0.963531	+	0.267596i	$0.0862294\pi$
$480$		0			0
$481$	4.13525	−	12.7270i	0.188551	−	0.580302i
$482$	3.97214	+	2.88593i	0.180926	+	0.131450i
$483$	3.52786			0.160523
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$		0			0
$486$	−11.0000	−	7.99197i	−0.498970	−	0.362523i
$487$	−12.6525	+	38.9403i	−0.573338	+	1.76455i	0.0684303	+	0.997656i	$0.478201\pi$
$487$	−12.6525	+	38.9403i	−0.573338	+	1.76455i	−0.641769	+	0.766898i	$0.721799\pi$
$488$	−2.14590	−	6.60440i	−0.0971402	−	0.298967i
$489$	9.41641	−	6.84142i	0.425825	−	0.309380i
$490$		0			0
$491$	8.11803	+	24.9847i	0.366362	+	1.12755i	0.949124	+	0.314903i	$0.101972\pi$
$491$	8.11803	+	24.9847i	0.366362	+	1.12755i	−0.582762	+	0.812643i	$0.698028\pi$
$492$	0.236068	−	0.726543i	0.0106428	−	0.0327551i
$493$	23.4164	+	17.0130i	1.05462	+	0.766228i
$494$	−8.61803			−0.387744
$495$		0			0
$496$	2.00000			0.0898027
$497$	1.00000	+	0.726543i	0.0448561	+	0.0325899i
$498$	3.88854	−	11.9677i	0.174250	−	0.536286i
$499$	−0.100813	−	0.310271i	−0.00451301	−	0.0138896i	0.948775	−	0.315954i	$-0.102324\pi$
$499$	−0.100813	−	0.310271i	−0.00451301	−	0.0138896i	−0.953288	+	0.302064i	$0.902324\pi$
$500$		0			0
$501$	−13.3262	+	9.68208i	−0.595372	+	0.432563i
$502$	2.10081	+	6.46564i	0.0937639	+	0.288576i
$503$	−3.82624	+	11.7759i	−0.170604	+	0.525064i	−0.999405	−	0.0344785i	$-0.989023\pi$
$503$	−3.82624	+	11.7759i	−0.170604	+	0.525064i	0.828802	+	0.559542i	$0.189023\pi$
$504$	−0.736068	−	0.534785i	−0.0327871	−	0.0238212i
$505$		0			0
$506$	−1.42705	+	15.2497i	−0.0634402	+	0.677930i
$507$	−9.05573			−0.402179
$508$	2.30902	+	1.67760i	0.102446	+	0.0744314i
$509$	−3.61803	+	11.1352i	−0.160367	+	0.493557i	−0.998665	−	0.0516541i	$-0.983551\pi$
$509$	−3.61803	+	11.1352i	−0.160367	+	0.493557i	0.838298	+	0.545212i	$0.183551\pi$
$510$		0			0
$511$	−0.763932	+	0.555029i	−0.0337944	+	0.0245530i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.18034	−	19.0211i	−0.272869	−	0.839803i
$514$	−6.47214	+	19.9192i	−0.285474	+	0.878598i
$515$		0			0
$516$	10.4721			0.461010
$517$	−32.6525	+	7.33094i	−1.43605	+	0.322414i
$518$	3.47214			0.152557
$519$	1.85410	+	1.34708i	0.0813860	+	0.0591304i
$520$		0			0
$521$	−9.60739	−	29.5685i	−0.420907	−	1.29542i	−0.906859	−	0.421434i	$-0.861527\pi$
$521$	−9.60739	−	29.5685i	−0.420907	−	1.29542i	0.485952	−	0.873986i	$-0.338473\pi$
$522$	5.32624	−	3.86974i	0.233123	−	0.169374i
$523$	0.909830	−	0.661030i	0.0397841	−	0.0289048i	−0.567716	−	0.823225i	$-0.692173\pi$
$523$	0.909830	−	0.661030i	0.0397841	−	0.0289048i	0.607500	+	0.794320i	$0.292173\pi$
$524$	−2.47214	−	7.60845i	−0.107996	−	0.332377i
$525$		0			0
$526$	4.16312	+	3.02468i	0.181521	+	0.131882i
$527$	−12.9443			−0.563861
$528$	−2.70820	+	3.07768i	−0.117859	+	0.133939i
$529$	−1.67376			−0.0727723
$530$		0			0
$531$	4.93769	−	15.1967i	0.214278	−	0.659479i
$532$	−0.690983	−	2.12663i	−0.0299579	−	0.0922010i
$533$	1.19098	−	0.865300i	0.0515872	−	0.0374803i
$534$	−11.3820	+	8.26948i	−0.492546	+	0.357856i
$535$		0			0
$536$	−2.85410	+	8.78402i	−0.123278	+	0.379412i
$537$	9.27051	+	6.73542i	0.400052	+	0.290655i
$538$	22.3607			0.964037
$539$	20.1525	+	8.69827i	0.868029	+	0.374661i
$540$		0			0
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	0.277631	−	0.960688i	$-0.410451\pi$
$541$	−12.7984	−	9.29856i	−0.550245	−	0.399776i	−0.827876	+	0.560911i	$0.810451\pi$
$542$	−0.437694	+	1.34708i	−0.0188006	+	0.0578622i
$543$	7.59675	+	23.3804i	0.326008	+	1.00335i
$544$	5.23607	−	3.80423i	0.224495	−	0.163105i
$545$		0			0
$546$	0.562306	+	1.73060i	0.0240645	+	0.0740628i
$547$	−6.14590	+	18.9151i	−0.262780	+	0.808753i	0.729417	+	0.684069i	$0.239791\pi$
$547$	−6.14590	+	18.9151i	−0.262780	+	0.808753i	−0.992197	+	0.124683i	$0.960209\pi$
$548$	−17.3262	−	12.5882i	−0.740140	−	0.537743i
$549$	10.2229			0.436303
$550$		0			0
$551$	16.1803			0.689306
$552$	4.61803	+	3.35520i	0.196557	+	0.142807i
$553$	1.18034	−	3.63271i	0.0501932	−	0.154479i
$554$	0.0106431	+	0.0327561i	0.000452183	+	0.00139168i
$555$		0			0
$556$	−0.263932	+	0.191758i	−0.0111932	+	0.00813234i
$557$	3.26393	+	10.0453i	0.138297	+	0.425635i	0.996088	−	0.0883634i	$-0.0281637\pi$
$557$	3.26393	+	10.0453i	0.138297	+	0.425635i	−0.857791	+	0.513999i	$0.828164\pi$
$558$	−0.909830	+	2.80017i	−0.0385162	+	0.118541i
$559$	16.3262	+	11.8617i	0.690526	+	0.501697i
$560$		0			0
$561$	17.5279	−	19.9192i	0.740027	−	0.840989i
$562$	−9.05573			−0.381993
$563$	36.8885	+	26.8011i	1.55467	+	1.12953i	0.940217	+	0.340575i	$0.110622\pi$
$563$	36.8885	+	26.8011i	1.55467	+	1.12953i	0.614450	+	0.788956i	$0.289378\pi$
$564$	−3.85410	+	11.8617i	−0.162287	+	0.499468i
$565$		0			0
$566$	−0.145898	+	0.106001i	−0.00613255	+	0.00445556i
$567$	−1.20820	+	0.877812i	−0.0507398	+	0.0368646i
$568$	0.618034	+	1.90211i	0.0259321	+	0.0798109i
$569$	1.80902	−	5.56758i	0.0758379	−	0.233405i	−0.905950	−	0.423384i	$-0.860842\pi$
$569$	1.80902	−	5.56758i	0.0758379	−	0.233405i	0.981788	+	0.189979i	$0.0608420\pi$
$570$		0			0
$571$	44.6869			1.87009			0.935045	−	0.354530i	$-0.115359\pi$
$571$	44.6869			1.87009			0.935045	+	0.354530i	$0.115359\pi$
$572$	−7.70820	+	1.73060i	−0.322296	+	0.0723600i
$573$	−11.1935			−0.467615
$574$	0.309017	+	0.224514i	0.0128981	+	0.00937103i
$575$		0			0
$576$	−0.454915	−	1.40008i	−0.0189548	−	0.0583369i
$577$	14.1803	−	10.3026i	0.590335	−	0.428904i	−0.252100	−	0.967701i	$-0.581121\pi$
$577$	14.1803	−	10.3026i	0.590335	−	0.428904i	0.842435	+	0.538797i	$0.181121\pi$
$578$	−20.1353	+	14.6291i	−0.837516	+	0.608491i
$579$	−5.05573	−	15.5599i	−0.210109	−	0.646649i
$580$		0			0
$581$	5.09017	+	3.69822i	0.211176	+	0.153428i
$582$	−11.4164			−0.473225
$583$	2.19098	−	23.4131i	0.0907412	−	0.969673i
$584$	−1.52786			−0.0632235
$585$		0			0
$586$	9.22542	−	28.3929i	0.381099	−	1.17290i
$587$	7.47214	+	22.9969i	0.308408	+	0.949182i	0.978383	+	0.206799i	$0.0663046\pi$
$587$	7.47214	+	22.9969i	0.308408	+	0.949182i	−0.669975	+	0.742383i	$0.733695\pi$
$588$	6.61803	−	4.80828i	0.272923	−	0.198290i
$589$	−5.85410	+	4.25325i	−0.241214	+	0.175252i
$590$		0			0
$591$	10.0132	−	30.8173i	0.411886	−	1.26766i
$592$	4.54508	+	3.30220i	0.186802	+	0.135719i
$593$	6.11146			0.250967			0.125484	−	0.992096i	$-0.459952\pi$
$593$	6.11146			0.250967			0.125484	+	0.992096i	$0.459952\pi$
$594$	−9.34752	−	15.7719i	−0.383534	−	0.647130i
$595$		0			0
$596$	−17.5623	−	12.7598i	−0.719380	−	0.522660i
$597$	−2.11146	+	6.49839i	−0.0864161	+	0.265962i
$598$	3.39919	+	10.4616i	0.139003	+	0.427808i
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	−0.480934	−	0.876757i	$-0.659702\pi$
$599$	5.00000	−	3.63271i	0.204294	−	0.148429i	0.685228	+	0.728328i	$0.259702\pi$
$600$		0			0
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	0.951623	−	0.307267i	$-0.0994146\pi$
$601$	0.0278640	+	0.0857567i	0.00113660	+	0.00349809i	−0.950487	+	0.310766i	$0.899415\pi$
$602$	−1.61803	+	4.97980i	−0.0659461	+	0.202961i
$603$	−11.0000	−	7.99197i	−0.447955	−	0.325458i
$604$	13.7082			0.557779
$605$		0			0
$606$	−24.3607			−0.989585
$607$	−27.1246	−	19.7072i	−1.10095	−	0.799890i	−0.119739	−	0.992805i	$-0.538206\pi$
$607$	−27.1246	−	19.7072i	−1.10095	−	0.799890i	−0.981215	+	0.192916i	$0.938206\pi$
$608$	1.11803	−	3.44095i	0.0453423	−	0.139549i
$609$	−1.05573	−	3.24920i	−0.0427803	−	0.131664i
$610$		0			0
$611$	−19.4443	+	14.1271i	−0.786631	+	0.571521i
$612$	2.94427	+	9.06154i	0.119015	+	0.366291i
$613$	−1.85410	+	5.70634i	−0.0748865	+	0.230477i	−0.981492	−	0.191502i	$-0.938664\pi$
$613$	−1.85410	+	5.70634i	−0.0748865	+	0.230477i	0.906606	+	0.421979i	$0.138664\pi$
$614$	−12.3262	−	8.95554i	−0.497446	−	0.361416i
$615$		0			0
$616$	−1.04508	−	1.76336i	−0.0421077	−	0.0710476i
$617$	9.05573			0.364570			0.182285	−	0.983246i	$-0.441651\pi$
$617$	9.05573			0.364570			0.182285	+	0.983246i	$0.441651\pi$
$618$	6.85410	+	4.97980i	0.275712	+	0.200317i
$619$	−2.29837	+	7.07367i	−0.0923794	+	0.284315i	−0.986562	−	0.163388i	$-0.947758\pi$
$619$	−2.29837	+	7.07367i	−0.0923794	+	0.284315i	0.894182	+	0.447703i	$0.147758\pi$
$620$		0			0
$621$	−20.6525	+	15.0049i	−0.828755	+	0.602126i
$622$	3.38197	−	2.45714i	0.135604	−	0.0985224i
$623$	−2.17376	−	6.69015i	−0.0870899	−	0.268035i
$624$	−0.909830	+	2.80017i	−0.0364224	+	0.112096i
$625$		0			0
$626$	−11.5279			−0.460746
$627$	1.38197	−	14.7679i	0.0551904	−	0.589772i
$628$	−6.14590			−0.245248
$629$	−29.4164	−	21.3723i	−1.17291	−	0.852168i
$630$		0			0
$631$	8.38197	+	25.7970i	0.333681	+	1.02696i	0.967368	+	0.253375i	$0.0815406\pi$
$631$	8.38197	+	25.7970i	0.333681	+	1.02696i	−0.633687	+	0.773589i	$0.718459\pi$
$632$	5.00000	−	3.63271i	0.198889	−	0.144502i
$633$	−26.4721	+	19.2331i	−1.05217	+	0.764448i
$634$	4.44427	+	13.6781i	0.176505	+	0.543225i
$635$		0			0
$636$	−7.09017	−	5.15131i	−0.281144	−	0.204263i
$637$	15.7639			0.624590
$638$	14.4721	−	3.24920i	0.572957	−	0.128637i
$639$	−2.94427			−0.116474
$640$		0			0
$641$	9.50000	−	29.2380i	0.375227	−	1.15483i	−0.568098	−	0.822961i	$-0.692320\pi$
$641$	9.50000	−	29.2380i	0.375227	−	1.15483i	0.943325	−	0.331870i	$-0.107680\pi$
$642$	−5.88854	−	18.1231i	−0.232402	−	0.715261i
$643$	−16.8541	+	12.2452i	−0.664661	+	0.482904i	−0.868234	−	0.496155i	$-0.834745\pi$
$643$	−16.8541	+	12.2452i	−0.664661	+	0.482904i	0.203573	+	0.979060i	$0.434745\pi$
$644$	−2.30902	+	1.67760i	−0.0909880	+	0.0661067i
$645$		0			0
$646$	−7.23607	+	22.2703i	−0.284699	+	0.876214i
$647$	22.4721	+	16.3270i	0.883471	+	0.641879i	0.934167	−	0.356835i	$-0.116144\pi$
$647$	22.4721	+	16.3270i	0.883471	+	0.641879i	−0.0506966	+	0.998714i	$0.516144\pi$
$648$	−2.41641			−0.0949255
$649$	23.7812	−	27.0256i	0.933492	−	1.06085i
$650$		0			0
$651$	1.23607	+	0.898056i	0.0484453	+	0.0351976i
$652$	−2.90983	+	8.95554i	−0.113958	+	0.350726i
$653$	−9.02786	−	27.7849i	−0.353288	−	1.08731i	−0.956996	−	0.290102i	$-0.906311\pi$
$653$	−9.02786	−	27.7849i	−0.353288	−	1.08731i	0.603708	−	0.797205i	$-0.293689\pi$
$654$	5.52786	−	4.01623i	0.216157	−	0.157047i
$655$		0			0
$656$	0.190983	+	0.587785i	0.00745663	+	0.0229492i
$657$	0.695048	−	2.13914i	0.0271164	−	0.0834558i
$658$	−5.04508	−	3.66547i	−0.196678	−	0.142895i
$659$	−11.3820			−0.443378			−0.221689	−	0.975117i	$-0.571157\pi$
$659$	−11.3820			−0.443378			−0.221689	+	0.975117i	$0.571157\pi$
$660$		0			0
$661$	−5.88854			−0.229038			−0.114519	−	0.993421i	$-0.536533\pi$
$661$	−5.88854			−0.229038			−0.114519	+	0.993421i	$0.536533\pi$
$662$	4.92705	+	3.57971i	0.191495	+	0.139129i
$663$	5.88854	−	18.1231i	0.228692	−	0.703842i
$664$	3.14590	+	9.68208i	0.122085	+	0.375738i
$665$		0			0
$666$	−6.69098	+	4.86128i	−0.259270	+	0.188371i
$667$	−6.38197	−	19.6417i	−0.247111	−	0.760529i
$668$	4.11803	−	12.6740i	0.159332	−	0.490372i
$669$	19.0902	+	13.8698i	0.738069	+	0.536238i
$670$		0			0
$671$	21.1459	+	9.12705i	0.816328	+	0.352346i
$672$	−0.763932			−0.0294693
$673$	1.76393	+	1.28157i	0.0679946	+	0.0494010i	0.621263	−	0.783602i	$-0.286620\pi$
$673$	1.76393	+	1.28157i	0.0679946	+	0.0494010i	−0.553269	+	0.833003i	$0.686620\pi$
$674$	0.562306	−	1.73060i	0.0216592	−	0.0666602i
$675$		0			0
$676$	5.92705	−	4.30625i	0.227963	−	0.165625i
$677$	13.3262	−	9.68208i	0.512169	−	0.372113i	−0.301477	−	0.953474i	$-0.597480\pi$
$677$	13.3262	−	9.68208i	0.512169	−	0.372113i	0.813646	+	0.581361i	$0.197480\pi$
$678$	−3.59675	−	11.0697i	−0.138132	−	0.425127i
$679$	1.76393	−	5.42882i	0.0676935	−	0.208339i
$680$		0			0
$681$	−14.8328			−0.568395
$682$	−4.38197	+	4.97980i	−0.167794	+	0.190686i
$683$	−15.5967			−0.596793			−0.298396	−	0.954442i	$-0.596452\pi$
$683$	−15.5967			−0.596793			−0.298396	+	0.954442i	$0.596452\pi$
$684$	4.30902	+	3.13068i	0.164759	+	0.119705i
$685$		0			0
$686$	2.60081	+	8.00448i	0.0992995	+	0.305612i
$687$	7.23607	−	5.25731i	0.276073	−	0.200579i
$688$	−6.85410	+	4.97980i	−0.261310	+	0.189853i
$689$	−5.21885	−	16.0620i	−0.198822	−	0.611912i
$690$		0			0
$691$	−31.6803	−	23.0171i	−1.20518	−	0.875612i	−0.210393	−	0.977617i	$-0.567474\pi$
$691$	−31.6803	−	23.0171i	−1.20518	−	0.875612i	−0.994784	+	0.102005i	$0.967474\pi$
$692$	−1.85410			−0.0704824
$693$	2.94427	−	0.661030i	0.111844	−	0.0251105i
$694$	−2.65248			−0.100687
$695$		0			0
$696$	1.70820	−	5.25731i	0.0647493	−	0.199278i
$697$	−1.23607	−	3.80423i	−0.0468194	−	0.144095i
$698$	5.85410	−	4.25325i	0.221581	−	0.160988i
$699$	−19.1246	+	13.8948i	−0.723359	+	0.525551i
$700$		0			0
$701$	−8.20163	+	25.2420i	−0.309771	+	0.953378i	0.668082	+	0.744087i	$0.267115\pi$
$701$	−8.20163	+	25.2420i	−0.309771	+	0.953378i	−0.977854	+	0.209290i	$0.932885\pi$
$702$	−10.6525	−	7.73948i	−0.402052	−	0.292108i
$703$	−20.3262			−0.766619
$704$	0.309017	−	3.30220i	0.0116465	−	0.124456i
$705$		0			0
$706$	12.9443	+	9.40456i	0.487164	+	0.353945i
$707$	3.76393	−	11.5842i	0.141557	−	0.435668i
$708$	−4.14590	−	12.7598i	−0.155812	−	0.479541i
$709$	3.61803	−	2.62866i	0.135878	−	0.0987212i	−0.517770	−	0.855520i	$-0.673238\pi$
$709$	3.61803	−	2.62866i	0.135878	−	0.0987212i	0.653648	+	0.756799i	$0.273238\pi$
$710$		0			0
$711$	2.81153	+	8.65300i	0.105441	+	0.324513i
$712$	3.51722	−	10.8249i	0.131813	−	0.405680i
$713$	7.47214	+	5.42882i	0.279834	+	0.203311i
$714$	4.94427			0.185035
$715$		0			0
$716$	−9.27051			−0.346455
$717$	−7.23607	−	5.25731i	−0.270236	−	0.196338i
$718$	−10.0000	+	30.7768i	−0.373197	+	1.14858i
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	0.998205	+	0.0598864i	$0.0190738\pi$
$719$	6.05573	+	18.6376i	0.225841	+	0.695066i	−0.772365	+	0.635179i	$0.780926\pi$
$720$		0			0
$721$	−3.42705	+	2.48990i	−0.127630	+	0.0927287i
$722$	−1.82624	−	5.62058i	−0.0679655	−	0.209176i
$723$	−1.87539	+	5.77185i	−0.0697464	+	0.214657i
$724$	−16.0902	−	11.6902i	−0.597986	−	0.434463i
$725$		0			0
$726$	−1.72949	−	13.4863i	−0.0641874	−	0.500524i
$727$	31.7426			1.17727			0.588635	−	0.808399i	$-0.299666\pi$
$727$	31.7426			1.17727			0.588635	+	0.808399i	$0.299666\pi$
$728$	−1.19098	−	0.865300i	−0.0441408	−	0.0320701i
$729$	7.43363	−	22.8784i	0.275320	−	0.847347i
$730$		0			0
$731$	44.3607	−	32.2299i	1.64074	−	1.19207i
$732$	6.94427	−	5.04531i	0.256668	−	0.186480i
$733$	−2.90983	−	8.95554i	−0.107477	−	0.330780i	0.882827	−	0.469699i	$-0.155637\pi$
$733$	−2.90983	−	8.95554i	−0.107477	−	0.330780i	−0.990304	+	0.138918i	$0.955637\pi$
$734$	−9.23607	+	28.4257i	−0.340909	+	1.04921i
$735$		0			0
$736$	−4.61803			−0.170223
$737$	−15.6180	−	26.3521i	−0.575298	−	0.970691i
$738$	−0.909830			−0.0334913
$739$	−6.97214	−	5.06555i	−0.256474	−	0.186339i	0.452117	−	0.891959i	$-0.350669\pi$
$739$	−6.97214	−	5.06555i	−0.256474	−	0.186339i	−0.708591	+	0.705619i	$0.750669\pi$
$740$		0			0
$741$	−3.29180	−	10.1311i	−0.120927	−	0.372175i
$742$	3.54508	−	2.57565i	0.130144	−	0.0945553i
$743$	12.6803	−	9.21281i	0.465197	−	0.337985i	−0.330370	−	0.943852i	$-0.607173\pi$
$743$	12.6803	−	9.21281i	0.465197	−	0.337985i	0.795566	+	0.605867i	$0.207173\pi$
$744$	0.763932	+	2.35114i	0.0280071	+	0.0861970i
$745$		0			0
$746$	−5.30902	−	3.85723i	−0.194377	−	0.141223i
$747$	−14.9868			−0.548340
$748$	−2.00000	+	21.3723i	−0.0731272	+	0.781448i
$749$	9.52786			0.348141
$750$		0			0
$751$	−7.14590	+	21.9928i	−0.260758	+	0.802529i	0.731883	+	0.681430i	$0.238642\pi$
$751$	−7.14590	+	21.9928i	−0.260758	+	0.802529i	−0.992640	+	0.121099i	$0.961358\pi$
$752$	−3.11803	−	9.59632i	−0.113703	−	0.349942i
$753$	−6.79837	+	4.93931i	−0.247747	+	0.179998i
$754$	8.61803	−	6.26137i	0.313850	−	0.228026i
$755$		0			0
$756$	1.05573	−	3.24920i	0.0383965	−	0.118172i
$757$	6.25329	+	4.54328i	0.227280	+	0.165128i	0.695597	−	0.718432i	$-0.255140\pi$
$757$	6.25329	+	4.54328i	0.227280	+	0.165128i	−0.468318	+	0.883560i	$0.655140\pi$
$758$	32.0344			1.16354
$759$	−18.4721	+	4.14725i	−0.670496	+	0.150536i
$760$		0			0
$761$	8.38197	+	6.08985i	0.303846	+	0.220757i	0.729251	−	0.684246i	$-0.239868\pi$
$761$	8.38197	+	6.08985i	0.303846	+	0.220757i	−0.425405	+	0.905003i	$0.639868\pi$
$762$	−1.09017	+	3.35520i	−0.0394927	+	0.121546i
$763$	1.05573	+	3.24920i	0.0382199	+	0.117629i
$764$	7.32624	−	5.32282i	0.265054	−	0.192573i
$765$		0			0
$766$	6.86475	+	21.1275i	0.248033	+	0.763368i
$767$	7.98936	−	24.5887i	0.288479	−	0.887847i
$768$	−1.00000	−	0.726543i	−0.0360844	−	0.0262168i
$769$	−37.0344			−1.33550			−0.667748	−	0.744387i	$-0.732742\pi$
$769$	−37.0344			−1.33550			−0.667748	+	0.744387i	$0.732742\pi$
$770$		0			0
$771$	−25.8885			−0.932353
$772$	10.7082	+	7.77997i	0.385397	+	0.280007i
$773$	12.1910	−	37.5200i	0.438479	−	1.34950i	−0.451000	−	0.892524i	$-0.648932\pi$
$773$	12.1910	−	37.5200i	0.438479	−	1.34950i	0.889479	−	0.456976i	$-0.151068\pi$
$774$	−3.85410	−	11.8617i	−0.138533	−	0.426360i
$775$		0			0
$776$	7.47214	−	5.42882i	0.268234	−	0.194883i
$777$	1.32624	+	4.08174i	0.0475785	+	0.146432i
$778$	7.76393	−	23.8949i	0.278350	−	0.856675i
$779$	−1.80902	−	1.31433i	−0.0648148	−	0.0470907i
$780$		0			0
$781$	−6.09017	−	2.62866i	−0.217923	−	0.0940607i
$782$	29.8885			1.06881
$783$	20.0000	+	14.5309i	0.714742	+	0.519290i
$784$	−2.04508	+	6.29412i	−0.0730387	+	0.224790i
$785$		0			0
$786$	8.00000	−	5.81234i	0.285351	−	0.207319i
$787$	−15.0902	+	10.9637i	−0.537906	+	0.390812i	−0.823307	−	0.567596i	$-0.807873\pi$
$787$	−15.0902	+	10.9637i	−0.537906	+	0.390812i	0.285400	+	0.958408i	$0.407873\pi$
$788$	8.10081	+	24.9317i	0.288580	+	0.888156i
$789$	−1.96556	+	6.04937i	−0.0699757	+	0.215363i
$790$		0			0
$791$	5.81966			0.206923
$792$	4.48278	+	1.93487i	0.159289	+	0.0687526i
$793$	16.5410			0.587389
$794$	9.97214	+	7.24518i	0.353898	+	0.257122i
$795$		0			0
$796$	−1.70820	−	5.25731i	−0.0605457	−	0.186340i
$797$	4.54508	−	3.30220i	0.160995	−	0.116970i	−0.504371	−	0.863487i	$-0.668276\pi$
$797$	4.54508	−	3.30220i	0.160995	−	0.116970i	0.665366	+	0.746517i	$0.268276\pi$
$798$	2.23607	−	1.62460i	0.0791559	−	0.0575102i
$799$	20.1803	+	62.1087i	0.713929	+	2.19725i
$800$		0			0
$801$	13.5557	+	9.84881i	0.478968	+	0.347991i
$802$	0.0901699			0.00318401
$803$	3.34752	−	3.80423i	0.118132	−	0.134248i
$804$	−11.4164			−0.402626
$805$		0			0
$806$	−1.47214	+	4.53077i	−0.0518538	+	0.159590i
$807$	8.54102	+	26.2866i	0.300658	+	0.925331i
$808$	15.9443	−	11.5842i	0.560918	−	0.407530i
$809$	2.07295	−	1.50609i	0.0728810	−	0.0529512i	−0.550748	−	0.834671i	$-0.685658\pi$
$809$	2.07295	−	1.50609i	0.0728810	−	0.0529512i	0.623629	+	0.781720i	$0.285658\pi$
$810$		0			0
$811$	−13.0238	+	40.0831i	−0.457327	+	1.40751i	0.411053	+	0.911611i	$0.365161\pi$
$811$	−13.0238	+	40.0831i	−0.457327	+	1.40751i	−0.868381	+	0.495898i	$0.834839\pi$
$812$	2.23607	+	1.62460i	0.0784706	+	0.0570122i
$813$	−1.75078			−0.0614024
$814$	−18.1803	+	4.08174i	−0.637221	+	0.143065i
$815$		0			0
$816$	6.47214	+	4.70228i	0.226570	+	0.164613i
$817$	9.47214	−	29.1522i	0.331388	−	1.01991i
$818$	8.02786	+	24.7072i	0.280688	+	0.863868i
$819$	1.75329	−	1.27384i	0.0612649	−	0.0445115i
$820$		0			0
$821$	0.819660	+	2.52265i	0.0286063	+	0.0880412i	0.964340	−	0.264665i	$-0.0852614\pi$
$821$	0.819660	+	2.52265i	0.0286063	+	0.0880412i	−0.935734	+	0.352706i	$0.885261\pi$
$822$	8.18034	−	25.1765i	0.285322	−	0.878131i
$823$	5.21885	+	3.79171i	0.181918	+	0.132171i	0.675017	−	0.737802i	$-0.264136\pi$
$823$	5.21885	+	3.79171i	0.181918	+	0.132171i	−0.493100	+	0.869973i	$0.664136\pi$
$824$	−6.85410			−0.238774
$825$		0			0
$826$	6.70820			0.233408
$827$	7.14590	+	5.19180i	0.248487	+	0.180537i	0.705056	−	0.709152i	$-0.250922\pi$
$827$	7.14590	+	5.19180i	0.248487	+	0.180537i	−0.456569	+	0.889688i	$0.650922\pi$
$828$	2.10081	−	6.46564i	0.0730083	−	0.224696i
$829$	−7.88854	−	24.2784i	−0.273980	−	0.843225i	−0.989487	−	0.144619i	$-0.953804\pi$
$829$	−7.88854	−	24.2784i	−0.273980	−	0.843225i	0.715507	−	0.698606i	$-0.246196\pi$
$830$		0			0
$831$	−0.0344419	+	0.0250235i	−0.00119477	+	0.000868055i
$832$	−0.736068	−	2.26538i	−0.0255186	−	0.0785381i
$833$	13.2361	−	40.7364i	0.458603	−	1.41143i
$834$	−0.326238	−	0.237026i	−0.0112967	−	0.00820753i
$835$		0			0
$836$	6.11803	+	10.3229i	0.211597	+	0.357024i
$837$	−11.0557			−0.382142
$838$	−29.1074	−	21.1478i	−1.00550	−	0.730537i
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	−0.982207	−	0.187802i	$-0.939864\pi$
$839$	−2.23607	+	6.88191i	−0.0771976	+	0.237590i	0.905009	+	0.425392i	$0.139864\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	−1.61803	+	1.17557i	−0.0557611	+	0.0405128i
$843$	−3.45898	−	10.6456i	−0.119134	−	0.366656i
$844$	8.18034	−	25.1765i	0.281579	−	0.866611i
$845$		0			0
$846$	14.8541			0.510695
$847$	6.68034	+	1.26133i	0.229539	+	0.0433397i
$848$	7.09017			0.243477
$849$	−0.180340	−	0.131025i	−0.00618925	−	0.00449675i
$850$		0			0
$851$	8.01722	+	24.6745i	0.274827	+	0.845830i
$852$	−2.00000	+	1.45309i	−0.0685189	+	0.0497819i
$853$	4.26393	−	3.09793i	0.145994	−	0.106071i	−0.512391	−	0.858753i	$-0.671240\pi$
$853$	4.26393	−	3.09793i	0.145994	−	0.106071i	0.658385	+	0.752682i	$0.271240\pi$
$854$	1.32624	+	4.08174i	0.0453829	+	0.139674i
$855$		0			0
$856$	12.4721	+	9.06154i	0.426289	+	0.309717i
$857$	−8.18034			−0.279435			−0.139718	−	0.990191i	$-0.544619\pi$
$857$	−8.18034			−0.279435			−0.139718	+	0.990191i	$0.544619\pi$
$858$	−4.97871	−	8.40051i	−0.169970	−	0.286789i
$859$	8.61803			0.294044			0.147022	−	0.989133i	$-0.453031\pi$
$859$	8.61803			0.294044			0.147022	+	0.989133i	$0.453031\pi$
$860$		0			0
$861$	−0.145898	+	0.449028i	−0.00497219	+	0.0153028i
$862$	8.70820	+	26.8011i	0.296603	+	0.912849i
$863$	18.6353	−	13.5393i	0.634351	−	0.460883i	−0.223554	−	0.974692i	$-0.571766\pi$
$863$	18.6353	−	13.5393i	0.634351	−	0.460883i	0.857905	+	0.513808i	$0.171766\pi$
$864$	4.47214	−	3.24920i	0.152145	−	0.110540i
$865$		0			0
$866$	2.29180	−	7.05342i	0.0778784	−	0.239685i
$867$	−24.8885	−	18.0826i	−0.845259	−	0.614117i
$868$	−1.23607			−0.0419549
$869$	−1.90983	+	20.4087i	−0.0647865	+	0.692318i
$870$		0			0
$871$	−17.7984	−	12.9313i	−0.603075	−	0.438160i
$872$	−1.70820	+	5.25731i	−0.0578471	+	0.178035i
$873$	4.20163	+	12.9313i	0.142203	+	0.437657i
$874$	13.5172	−	9.82084i	0.457227	−	0.332195i
$875$		0			0
$876$	−0.583592	−	1.79611i	−0.0197178	−	0.0606850i
$877$	16.0279	−	49.3287i	0.541223	−	1.66571i	−0.188583	−	0.982057i	$-0.560390\pi$
$877$	16.0279	−	49.3287i	0.541223	−	1.66571i	0.729806	−	0.683654i	$-0.239610\pi$
$878$	5.00000	+	3.63271i	0.168742	+	0.122598i
$879$	36.9017			1.24466
$880$		0			0
$881$	6.79837			0.229043			0.114522	−	0.993421i	$-0.463467\pi$
$881$	6.79837			0.229043			0.114522	+	0.993421i	$0.463467\pi$
$882$	−7.88197	−	5.72658i	−0.265400	−	0.192824i
$883$	−4.41641	+	13.5923i	−0.148624	+	0.457418i	−0.997459	−	0.0712400i	$-0.977304\pi$
$883$	−4.41641	+	13.5923i	−0.148624	+	0.457418i	0.848835	+	0.528657i	$0.177304\pi$
$884$	4.76393	+	14.6619i	0.160228	+	0.493132i
$885$		0			0
$886$	−0.145898	+	0.106001i	−0.00490154	+	0.00356118i
$887$	−12.1008	−	37.2425i	−0.406306	−	1.25048i	−0.919800	−	0.392387i	$-0.871649\pi$
$887$	−12.1008	−	37.2425i	−0.406306	−	1.25048i	0.513495	−	0.858093i	$-0.328351\pi$
$888$	−2.14590	+	6.60440i	−0.0720116	+	0.221629i
$889$	−1.42705	−	1.03681i	−0.0478618	−	0.0347736i
$890$		0			0
$891$	5.29431	−	6.01661i	0.177366	−	0.201564i
$892$	−19.0902			−0.639186
$893$	29.5344	+	21.4580i	0.988332	+	0.718066i
$894$	8.29180	−	25.5195i	0.277319	−	0.853501i
$895$		0			0
$896$	0.500000	−	0.363271i	0.0167038	−	0.0121360i
$897$	−11.0000	+	7.99197i	−0.367279	+	0.266844i
$898$	−6.44427	−	19.8334i	−0.215048	−	0.661850i
$899$	2.76393	−	8.50651i	0.0921823	−	0.283708i
$900$		0			0
$901$	−45.8885			−1.52877
$902$	−1.88197	−	0.812299i	−0.0626626	−	0.0270466i
$903$	−6.47214			−0.215379
$904$	7.61803	+	5.53483i	0.253372	+	0.184086i
$905$		0			0
$906$	5.23607	+	16.1150i	0.173957	+	0.535384i
$907$	23.8541	−	17.3310i	0.792062	−	0.575467i	−0.116512	−	0.993189i	$-0.537171\pi$
$907$	23.8541	−	17.3310i	0.792062	−	0.575467i	0.908575	+	0.417722i	$0.137171\pi$
$908$	9.70820	−	7.05342i	0.322178	−	0.234076i
$909$	8.96556	+	27.5932i	0.297369	+	0.915207i
$910$		0			0
$911$	19.5623	+	14.2128i	0.648128	+	0.470893i	0.862633	−	0.505830i	$-0.168814\pi$
$911$	19.5623	+	14.2128i	0.648128	+	0.470893i	−0.214505	+	0.976723i	$0.568814\pi$
$912$	4.47214			0.148087
$913$	−31.0000	−	13.3803i	−1.02595	−	0.442823i
$914$	−8.18034			−0.270582
$915$		0			0
$916$	−2.23607	+	6.88191i	−0.0738818	+	0.227385i
$917$	1.52786	+	4.70228i	0.0504545	+	0.155283i
$918$	−28.9443	+	21.0292i	−0.955303	+	0.694068i
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	−0.713170	−	0.700991i	$-0.752741\pi$
$919$	−8.09017	+	5.87785i	−0.266870	+	0.193892i	0.446300	+	0.894883i	$0.352741\pi$
$920$		0			0
$921$	5.81966	−	17.9111i	0.191764	−	0.590190i
$922$	7.85410	+	5.70634i	0.258661	+	0.187928i
$923$	−4.76393			−0.156807
$924$	1.67376	−	1.90211i	0.0550627	−	0.0625749i
$925$		0			0
$926$	1.07295	+	0.779543i	0.0352593	+	0.0256174i
$927$	3.11803	−	9.59632i	0.102410	−	0.315185i
$928$	1.38197	+	4.25325i	0.0453653	+	0.139620i
$929$	5.26393	−	3.82447i	0.172704	−	0.125477i	−0.498075	−	0.867134i	$-0.665960\pi$
$929$	5.26393	−	3.82447i	0.172704	−	0.125477i	0.670779	+	0.741657i	$0.265960\pi$
$930$		0			0
$931$	−7.39919	−	22.7724i	−0.242499	−	0.746334i
$932$	5.90983	−	18.1886i	0.193583	−	0.595787i
$933$	4.18034	+	3.03719i	0.136858	+	0.0994333i
$934$	18.6525			0.610328
$935$		0			0
$936$	3.50658			0.114616
$937$	43.1246	+	31.3319i	1.40882	+	1.02357i	0.993493	+	0.113895i	$0.0363328\pi$
$937$	43.1246	+	31.3319i	1.40882	+	1.02357i	0.415327	+	0.909672i	$0.363667\pi$
$938$	1.76393	−	5.42882i	0.0575944	−	0.177257i
$939$	−4.40325	−	13.5518i	−0.143695	−	0.442247i
$940$		0			0
$941$	−16.0902	+	11.6902i	−0.524525	+	0.381089i	−0.818306	−	0.574783i	$-0.805086\pi$
$941$	−16.0902	+	11.6902i	−0.524525	+	0.381089i	0.293781	+	0.955873i	$0.405086\pi$
$942$	−2.34752	−	7.22494i	−0.0764865	−	0.235401i
$943$	−0.881966	+	2.71441i	−0.0287208	+	0.0883934i
$944$	8.78115	+	6.37988i	0.285802	+	0.207647i
$945$		0			0
$946$	2.61803	−	27.9767i	0.0851196	−	0.909600i
$947$	28.0000			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$948$	6.18034	+	4.49028i	0.200728	+	0.145838i
$949$	1.12461	−	3.46120i	0.0365064	−	0.112355i
$950$		0			0
$951$	−14.3820	+	10.4491i	−0.466367	+	0.338836i
$952$	−3.23607	+	2.35114i	−0.104882	+	0.0762009i
$953$	2.09017	+	6.43288i	0.0677072	+	0.208381i	0.979186	−	0.202966i	$-0.0650582\pi$
$953$	2.09017	+	6.43288i	0.0677072	+	0.208381i	−0.911478	+	0.411348i	$0.865058\pi$
$954$	−3.22542	+	9.92684i	−0.104427	+	0.321393i
$955$		0			0
$956$	7.23607			0.234031
$957$	9.34752	+	15.7719i	0.302163	+	0.509834i
$958$	−27.2361			−0.879957
$959$	10.7082	+	7.77997i	0.345786	+	0.251228i
$960$		0			0
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	−10.8262	+	7.86572i	−0.349052	+	0.253601i
$963$	−18.3607	+	13.3398i	−0.591665	+	0.429870i
$964$	−1.51722	−	4.66953i	−0.0488664	−	0.150395i
$965$		0			0
$966$	−2.85410	−	2.07363i	−0.0918292	−	0.0667178i
$967$	−44.5623			−1.43303			−0.716514	−	0.697573i	$-0.754263\pi$
$967$	−44.5623			−1.43303			−0.716514	+	0.697573i	$0.754263\pi$
$968$	7.54508	+	8.00448i	0.242508	+	0.257274i
$969$	−28.9443			−0.929824
$970$		0			0
$971$	−10.8647	+	33.4382i	−0.348666	+	1.07308i	0.610925	+	0.791688i	$0.290798\pi$
$971$	−10.8647	+	33.4382i	−0.348666	+	1.07308i	−0.959592	+	0.281396i	$0.909202\pi$
$972$	4.20163	+	12.9313i	0.134767	+	0.414771i
$973$	0.163119	−	0.118513i	0.00522935	−	0.00379935i
$974$	33.1246	−	24.0664i	1.06138	−	0.771138i
$975$		0			0
$976$	−2.14590	+	6.60440i	−0.0686885	+	0.211402i
$977$	7.14590	+	5.19180i	0.228618	+	0.166100i	0.696197	−	0.717851i	$-0.254874\pi$
$977$	7.14590	+	5.19180i	0.228618	+	0.166100i	−0.467580	+	0.883951i	$0.654874\pi$
$978$	−11.6393			−0.372184
$979$	19.2467	+	32.4747i	0.615128	+	1.03790i
$980$		0			0
$981$	−6.58359	−	4.78326i	−0.210198	−	0.152718i
$982$	8.11803	−	24.9847i	0.259057	−	0.797295i
$983$	6.86475	+	21.1275i	0.218951	+	0.673863i	0.998849	+	0.0479565i	$0.0152709\pi$
$983$	6.86475	+	21.1275i	0.218951	+	0.673863i	−0.779898	+	0.625907i	$0.784729\pi$
$984$	−0.618034	+	0.449028i	−0.0197022	+	0.0143145i
$985$		0			0
$986$	−8.94427	−	27.5276i	−0.284844	−	0.876659i
$987$	2.38197	−	7.33094i	0.0758188	−	0.233346i
$988$	6.97214	+	5.06555i	0.221813	+	0.161157i
$989$	−39.1246			−1.24409
$990$		0			0
$991$	35.8197			1.13785			0.568925	−	0.822390i	$-0.307360\pi$
$991$	35.8197			1.13785			0.568925	+	0.822390i	$0.307360\pi$
$992$	−1.61803	−	1.17557i	−0.0513726	−	0.0373244i
$993$	−2.32624	+	7.15942i	−0.0738209	+	0.227197i
$994$	−0.381966	−	1.17557i	−0.0121152	−	0.0372868i
$995$		0			0
$996$	−10.1803	+	7.39645i	−0.322576	+	0.234365i
$997$	8.32624	+	25.6255i	0.263695	+	0.811569i	0.991991	+	0.126307i	$0.0403123\pi$
$997$	8.32624	+	25.6255i	0.263695	+	0.811569i	−0.728297	+	0.685262i	$0.759688\pi$
$998$	−0.100813	+	0.310271i	−0.00319118	+	0.00982145i
$999$	−25.1246	−	18.2541i	−0.794908	−	0.577534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.d.301.1		4
5.2	odd	4		110.2.j.a.59.2	yes	8
5.3	odd	4		110.2.j.a.59.1	✓	8
5.4	even	2		550.2.h.e.301.1		4
11.3	even	5	inner	550.2.h.d.201.1		4
11.5	even	5		6050.2.a.cl.1.2		2
11.6	odd	10		6050.2.a.bv.1.2		2
15.2	even	4		990.2.ba.b.829.1		8
15.8	even	4		990.2.ba.b.829.2		8
20.3	even	4		880.2.cd.a.609.1		8
20.7	even	4		880.2.cd.a.609.2		8
55.3	odd	20		110.2.j.a.69.2	yes	8
55.14	even	10		550.2.h.e.201.1		4
55.17	even	20		1210.2.b.g.969.1		4
55.27	odd	20		1210.2.b.f.969.3		4
55.28	even	20		1210.2.b.g.969.4		4
55.38	odd	20		1210.2.b.f.969.2		4
55.39	odd	10		6050.2.a.ct.1.1		2
55.47	odd	20		110.2.j.a.69.1	yes	8
55.49	even	10		6050.2.a.ce.1.1		2
165.47	even	20		990.2.ba.b.289.2		8
165.113	even	20		990.2.ba.b.289.1		8
220.3	even	20		880.2.cd.a.289.2		8
220.47	even	20		880.2.cd.a.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.a.59.1	✓	8	5.3	odd	4
110.2.j.a.59.2	yes	8	5.2	odd	4
110.2.j.a.69.1	yes	8	55.47	odd	20
110.2.j.a.69.2	yes	8	55.3	odd	20
550.2.h.d.201.1		4	11.3	even	5	inner
550.2.h.d.301.1		4	1.1	even	1	trivial
550.2.h.e.201.1		4	55.14	even	10
550.2.h.e.301.1		4	5.4	even	2
880.2.cd.a.289.1		8	220.47	even	20
880.2.cd.a.289.2		8	220.3	even	20
880.2.cd.a.609.1		8	20.3	even	4
880.2.cd.a.609.2		8	20.7	even	4
990.2.ba.b.289.1		8	165.113	even	20
990.2.ba.b.289.2		8	165.47	even	20
990.2.ba.b.829.1		8	15.2	even	4
990.2.ba.b.829.2		8	15.8	even	4
1210.2.b.f.969.2		4	55.38	odd	20
1210.2.b.f.969.3		4	55.27	odd	20
1210.2.b.g.969.1		4	55.17	even	20
1210.2.b.g.969.4		4	55.28	even	20
6050.2.a.bv.1.2		2	11.6	odd	10
6050.2.a.ce.1.1		2	55.49	even	10
6050.2.a.cl.1.2		2	11.5	even	5
6050.2.a.ct.1.1		2	55.39	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.381966 - 1.17557i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.00000 + 0.726543i) q^{6} +(-0.190983 - 0.587785i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.19098 + 0.865300i) q^{9} +(1.69098 + 2.85317i) q^{11} +1.23607 q^{12} +(1.92705 + 1.40008i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(5.23607 - 3.80423i) q^{17} +(-0.454915 - 1.40008i) q^{18} +(1.11803 - 3.44095i) q^{19} -0.763932 q^{21} +(0.309017 - 3.30220i) q^{22} -4.61803 q^{23} +(-1.00000 - 0.726543i) q^{24} +(-0.736068 - 2.26538i) q^{26} +(4.47214 - 3.24920i) q^{27} +(0.500000 - 0.363271i) q^{28} +(1.38197 + 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} +1.00000 q^{32} +(4.00000 - 0.898056i) q^{33} -6.47214 q^{34} +(-0.454915 + 1.40008i) q^{36} +(-1.73607 - 5.34307i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(2.38197 - 1.73060i) q^{39} +(0.190983 - 0.587785i) q^{41} +(0.618034 + 0.449028i) q^{42} +8.47214 q^{43} +(-2.19098 + 2.48990i) q^{44} +(3.73607 + 2.71441i) q^{46} +(-3.11803 + 9.59632i) q^{47} +(0.381966 + 1.17557i) q^{48} +(5.35410 - 3.88998i) q^{49} +(-2.47214 - 7.60845i) q^{51} +(-0.736068 + 2.26538i) q^{52} +(-5.73607 - 4.16750i) q^{53} -5.52786 q^{54} -0.618034 q^{56} +(-3.61803 - 2.62866i) q^{57} +(1.38197 - 4.25325i) q^{58} +(-3.35410 - 10.3229i) q^{59} +(5.61803 - 4.08174i) q^{61} +(0.618034 + 1.90211i) q^{62} +(0.281153 - 0.865300i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.76393 - 1.62460i) q^{66} -9.23607 q^{67} +(5.23607 + 3.80423i) q^{68} +(-1.76393 + 5.42882i) q^{69} +(-1.61803 + 1.17557i) q^{71} +(1.19098 - 0.865300i) q^{72} +(-0.472136 - 1.45309i) q^{73} +(-1.73607 + 5.34307i) q^{74} +3.61803 q^{76} +(1.35410 - 1.53884i) q^{77} -2.94427 q^{78} +(5.00000 + 3.63271i) q^{79} +(-0.746711 - 2.29814i) q^{81} +(-0.500000 + 0.363271i) q^{82} +(-8.23607 + 5.98385i) q^{83} +(-0.236068 - 0.726543i) q^{84} +(-6.85410 - 4.97980i) q^{86} +5.52786 q^{87} +(3.23607 - 0.726543i) q^{88} +11.3820 q^{89} +(0.454915 - 1.40008i) q^{91} +(-1.42705 - 4.39201i) q^{92} +(-2.00000 + 1.45309i) q^{93} +(8.16312 - 5.93085i) q^{94} +(0.381966 - 1.17557i) q^{96} +(7.47214 + 5.42882i) q^{97} -6.61803 q^{98} +(-0.454915 + 4.86128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 6 q^{3} - q^{4} - 4 q^{6} - 3 q^{7} - q^{8} + 7 q^{9} + 9 q^{11} - 4 q^{12} + q^{13} - 3 q^{14} - q^{16} + 12 q^{17} - 13 q^{18} - 12 q^{21} - q^{22} - 14 q^{23} - 4 q^{24} + 6 q^{26}+ \cdots - 13 q^{99}+O(q^{100}) \) 4 * q - q^2 + 6 * q^3 - q^4 - 4 * q^6 - 3 * q^7 - q^8 + 7 * q^9 + 9 * q^11 - 4 * q^12 + q^13 - 3 * q^14 - q^16 + 12 * q^17 - 13 * q^18 - 12 * q^21 - q^22 - 14 * q^23 - 4 * q^24 + 6 * q^26 + 2 * q^28 + 10 * q^29 - 2 * q^31 + 4 * q^32 + 16 * q^33 - 8 * q^34 - 13 * q^36 + 2 * q^37 - 5 * q^38 + 14 * q^39 + 3 * q^41 - 2 * q^42 + 16 * q^43 - 11 * q^44 + 6 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 + 8 * q^51 + 6 * q^52 - 14 * q^53 - 40 * q^54 + 2 * q^56 - 10 * q^57 + 10 * q^58 + 18 * q^61 - 2 * q^62 - 19 * q^63 - q^64 - 24 * q^66 - 28 * q^67 + 12 * q^68 - 16 * q^69 - 2 * q^71 + 7 * q^72 + 16 * q^73 + 2 * q^74 + 10 * q^76 - 8 * q^77 + 24 * q^78 + 20 * q^79 - 41 * q^81 - 2 * q^82 - 24 * q^83 + 8 * q^84 - 14 * q^86 + 40 * q^87 + 4 * q^88 + 50 * q^89 + 13 * q^91 + q^92 - 8 * q^93 + 17 * q^94 + 6 * q^96 + 12 * q^97 - 22 * q^98 - 13 * q^99

Introduction

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