LMFDB - Embedded newform 550.2.h.d.201.1

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			201.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	550.201
Dual form			550.2.h.d.301.1

$q$-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 $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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	0.998715	+	0.0506828i	$0.0161398\pi$
$3$	0.381966	+	1.17557i	0.220528	+	0.678716i	−0.778187	+	0.628033i	$0.783860\pi$
$4$	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	−0.980640	−	0.195821i	$-0.937263\pi$
$7$	−0.190983	+	0.587785i	−0.0721848	+	0.222162i	0.908455	+	0.417983i	$0.137263\pi$
$8$	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	−0.287559	−	0.957763i	$-0.592844\pi$
$13$	1.92705	−	1.40008i	0.534468	−	0.388314i	0.822026	+	0.569449i	$0.192844\pi$
$14$	−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	0.999200	−	0.0399941i	$-0.0127339\pi$
$17$	5.23607	+	3.80423i	1.26993	+	0.922660i	0.270733	+	0.962654i	$0.412734\pi$
$18$	−0.454915	+	1.40008i	−0.107225	+	0.330003i
$19$	1.11803	+	3.44095i	0.256495	+	0.789409i	0.993532	+	0.113557i	$0.0362244\pi$
$19$	1.11803	+	3.44095i	0.256495	+	0.789409i	−0.737037	+	0.675852i	$0.763776\pi$
$20$		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	−0.736881	−	0.676023i	$-0.763702\pi$
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	0.993505	−	0.113787i	$-0.0362980\pi$
$30$		0			0
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	−0.723531	−	0.690292i	$-0.757482\pi$
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	0.432923	+	0.901431i	$0.357482\pi$
$32$	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	0.700868	+	0.713291i	$0.252796\pi$
$37$	−1.73607	+	5.34307i	−0.285408	+	0.878395i	−0.986276	+	0.165104i	$0.947204\pi$
$38$	−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	0.964862	−	0.262759i	$-0.0846323\pi$
$41$	0.190983	+	0.587785i	0.0298265	+	0.0917966i	−0.935035	+	0.354555i	$0.884632\pi$
$42$	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	−0.871356	−	0.490652i	$-0.836759\pi$
$47$	−3.11803	−	9.59632i	−0.454812	−	1.39977i	0.416544	−	0.909116i	$-0.363241\pi$
$48$	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	−0.907342	−	0.420393i	$-0.861892\pi$
$53$	−5.73607	+	4.16750i	−0.787910	+	0.572450i	0.119433	+	0.992842i	$0.461892\pi$
$54$	−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	0.454702	+	0.890644i	$0.349746\pi$
$59$	−3.35410	+	10.3229i	−0.436667	+	1.34392i	−0.891369	+	0.453279i	$0.850254\pi$
$60$		0			0
$61$	5.61803	+	4.08174i	0.719316	+	0.522613i	0.886165	−	0.463369i	$-0.153360\pi$
$61$	5.61803	+	4.08174i	0.719316	+	0.522613i	−0.166850	+	0.985982i	$0.553360\pi$
$62$	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	0.487619	−	0.873057i	$-0.337866\pi$
$71$	−1.61803	−	1.17557i	−0.192025	−	0.139515i	−0.679644	+	0.733542i	$0.737866\pi$
$72$	1.19098	+	0.865300i	0.140359	+	0.101977i
$73$	−0.472136	+	1.45309i	−0.0552593	+	0.170071i	−0.974877	−	0.222744i	$-0.928499\pi$
$73$	−0.472136	+	1.45309i	−0.0552593	+	0.170071i	0.919618	+	0.392815i	$0.128499\pi$
$74$	−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	−0.269845	−	0.962904i	$-0.586973\pi$
$79$	5.00000	−	3.63271i	0.562544	−	0.408712i	0.832389	+	0.554192i	$0.186973\pi$
$80$		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	0.0354710	−	0.999371i	$-0.488707\pi$
$83$	−8.23607	−	5.98385i	−0.904026	−	0.656813i	−0.939497	+	0.342557i	$0.888707\pi$
$84$	−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	−0.139825	−	0.990176i	$-0.544654\pi$
$97$	7.47214	−	5.42882i	0.758680	−	0.551214i	0.898505	+	0.438963i	$0.144654\pi$
$98$	−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	0.677804	−	0.735242i	$-0.262932\pi$
$101$	15.9443	−	11.5842i	1.58651	−	1.15267i	0.908710	−	0.417428i	$-0.137068\pi$
$102$	−2.47214	−	7.60845i	−0.244778	−	0.753349i
$103$	−2.11803	+	6.51864i	−0.208696	+	0.642301i	0.790845	+	0.612016i	$0.209641\pi$
$103$	−2.11803	+	6.51864i	−0.208696	+	0.642301i	−0.999541	+	0.0302843i	$0.990359\pi$
$104$	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	−0.864498	−	0.502636i	$-0.832363\pi$
$107$	−4.76393	−	14.6619i	−0.460547	−	1.41742i	0.403951	−	0.914781i	$-0.367637\pi$
$108$	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	−0.989552	−	0.144179i	$-0.953946\pi$
$113$	−2.90983	−	8.95554i	−0.273734	−	0.842466i	0.715818	−	0.698287i	$-0.246054\pi$
$114$	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	0.685500	−	0.728073i	$-0.259584\pi$
$127$	2.30902	+	1.67760i	0.204892	+	0.148863i	−0.480608	+	0.876936i	$0.659584\pi$
$128$	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	−0.977466	−	0.211092i	$-0.932298\pi$
$137$	−17.3262	−	12.5882i	−1.48028	−	1.07549i	−0.502814	−	0.864394i	$-0.667702\pi$
$138$	4.61803	+	3.35520i	0.393113	+	0.285613i
$139$	0.100813	−	0.310271i	0.00855085	−	0.0263168i	−0.946690	−	0.322146i	$-0.895596\pi$
$139$	0.100813	−	0.310271i	0.00855085	−	0.0263168i	0.955241	+	0.295829i	$0.0955959\pi$
$140$		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	−0.988300	−	0.152524i	$-0.951260\pi$
$149$	−17.5623	−	12.7598i	−1.43876	−	1.04532i	−0.450460	−	0.892796i	$-0.648740\pi$
$150$		0			0
$151$	4.23607	+	13.0373i	0.344726	+	1.06096i	0.961730	+	0.273998i	$0.0883463\pi$
$151$	4.23607	+	13.0373i	0.344726	+	1.06096i	−0.617004	+	0.786960i	$0.711654\pi$
$152$	−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	0.846226	−	0.532824i	$-0.178869\pi$
$157$	−1.89919	−	5.84510i	−0.151572	−	0.466489i	−0.997797	+	0.0663350i	$0.978869\pi$
$158$	−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	−0.248012	−	0.968757i	$-0.579777\pi$
$163$	7.61803	−	5.53483i	0.596690	−	0.433521i	0.844703	+	0.535236i	$0.179777\pi$
$164$	0.618034			0.0482603
$165$		0			0
$166$	10.1803			0.790148
$167$	−10.7812	+	7.83297i	−0.834271	+	0.606133i	−0.920764	−	0.390119i	$-0.872434\pi$
$167$	−10.7812	+	7.83297i	−0.834271	+	0.606133i	0.0864937	+	0.996252i	$0.472434\pi$
$168$	−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	0.926911	−	0.375281i	$-0.122454\pi$
$173$	−0.572949	−	1.76336i	−0.0435605	−	0.134065i	−0.970472	+	0.241216i	$0.922454\pi$
$174$	−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	−0.999215	−	0.0396200i	$-0.987385\pi$
$179$	−2.86475	−	8.81678i	−0.214121	−	0.658997i	0.785094	−	0.619377i	$-0.212615\pi$
$180$		0			0
$181$	−16.0902	−	11.6902i	−1.19597	−	0.868925i	−0.202090	−	0.979367i	$-0.564773\pi$
$181$	−16.0902	−	11.6902i	−1.19597	−	0.868925i	−0.993883	+	0.110442i	$0.964773\pi$
$182$	−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	0.797324	+	0.603551i	$0.206248\pi$
$191$	−2.79837	+	8.61251i	−0.202483	+	0.623179i	−0.999807	+	0.0196279i	$0.993752\pi$
$192$	−1.00000	−	0.726543i	−0.0721688	−	0.0524337i
$193$	10.7082	+	7.77997i	0.770793	+	0.560014i	0.902202	−	0.431314i	$-0.141950\pi$
$193$	10.7082	+	7.77997i	0.770793	+	0.560014i	−0.131408	+	0.991328i	$0.541950\pi$
$194$	−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	−0.495048	+	0.868866i	$0.664849\pi$
$211$	−21.4164	+	15.5599i	−1.47437	+	1.07119i	−0.979319	+	0.202324i	$0.935151\pi$
$212$	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	−0.928931	−	0.370252i	$-0.879271\pi$
$223$	−5.89919	−	18.1558i	−0.395039	−	1.21580i	0.533893	−	0.845552i	$-0.320729\pi$
$224$	−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	0.749328	+	0.662199i	$0.230377\pi$
$227$	−3.70820	+	11.4127i	−0.246122	+	0.757486i	−0.995450	+	0.0952867i	$0.969623\pi$
$228$	1.38197	+	4.25325i	0.0915229	+	0.281679i
$229$	5.85410	−	4.25325i	0.386850	−	0.281063i	−0.377314	−	0.926086i	$-0.623152\pi$
$229$	5.85410	−	4.25325i	0.386850	−	0.281063i	0.764163	+	0.645023i	$0.223152\pi$
$230$		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	−0.964964	−	0.262383i	$-0.915492\pi$
$233$	−15.4721	+	11.2412i	−1.01361	+	0.736433i	−0.0486494	+	0.998816i	$0.515492\pi$
$234$	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	0.996964	−	0.0778584i	$-0.0248082\pi$
$239$	2.23607	+	6.88191i	0.144639	+	0.445154i	−0.852325	+	0.523012i	$0.824808\pi$
$240$		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	−0.747675	−	0.664064i	$-0.768830\pi$
$251$	−5.50000	+	3.99598i	−0.347157	+	0.252224i	0.400518	+	0.916289i	$0.368830\pi$
$252$	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	0.518238	+	0.855236i	$0.326588\pi$
$257$	−6.47214	+	19.9192i	−0.403721	+	1.24252i	−0.921959	+	0.387288i	$0.873412\pi$
$258$	−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	−0.121434	−	0.992600i	$-0.538749\pi$
$269$	−18.0902	−	13.1433i	−1.10298	−	0.801360i	−0.981543	+	0.191240i	$0.938749\pi$
$270$		0			0
$271$	−0.437694	+	1.34708i	−0.0265880	+	0.0818295i	−0.963470	−	0.267816i	$-0.913698\pi$
$271$	−0.437694	+	1.34708i	−0.0265880	+	0.0818295i	0.936882	+	0.349646i	$0.113698\pi$
$272$	−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	−0.588622	−	0.808408i	$-0.700329\pi$
$277$	−0.0278640	+	0.0202444i	−0.00167419	+	0.00121637i	0.586948	+	0.809625i	$0.300329\pi$
$278$	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	0.784460	−	0.620179i	$-0.212940\pi$
$281$	7.32624	+	5.32282i	0.437047	+	0.317533i	−0.347414	+	0.937712i	$0.612940\pi$
$282$	−3.85410	+	11.8617i	−0.229508	+	0.706354i
$283$	0.0557281	+	0.171513i	0.00331269	+	0.0101954i	0.952699	−	0.303915i	$-0.0982938\pi$
$283$	0.0557281	+	0.171513i	0.00331269	+	0.0101954i	−0.949387	+	0.314110i	$0.898294\pi$
$284$	−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	−0.195990	−	0.980606i	$-0.562792\pi$
$293$	9.22542	−	28.3929i	0.538955	−	1.65873i	0.734945	−	0.678127i	$-0.237208\pi$
$294$	−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	0.907727	−	0.419561i	$-0.137816\pi$
$311$	−1.29180	−	3.97574i	−0.0732510	−	0.225444i	−0.980978	+	0.194117i	$0.937816\pi$
$312$	−0.909830	+	2.80017i	−0.0515090	+	0.158528i
$313$	9.32624	+	6.77591i	0.527150	+	0.382997i	0.819291	−	0.573378i	$-0.194368\pi$
$313$	9.32624	+	6.77591i	0.527150	+	0.382997i	−0.292141	+	0.956375i	$0.594368\pi$
$314$	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	−0.864462	−	0.502698i	$-0.832341\pi$
$317$	−11.6353	+	8.45351i	−0.653501	+	0.474796i	0.210961	+	0.977494i	$0.432341\pi$
$318$	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	−0.934572	−	0.355773i	$-0.884218\pi$
$337$	0.562306	−	1.73060i	0.0306308	−	0.0942718i	0.965203	+	0.261501i	$0.0842176\pi$
$338$	−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	0.643893	−	0.765116i	$-0.277318\pi$
$347$	2.14590	+	1.55909i	0.115198	+	0.0836961i	−0.528695	+	0.848812i	$0.677318\pi$
$348$	1.70820	−	5.25731i	0.0915693	−	0.281821i
$349$	−2.23607	−	6.88191i	−0.119694	−	0.368380i	0.873203	−	0.487356i	$-0.162039\pi$
$349$	−2.23607	−	6.88191i	−0.119694	−	0.368380i	−0.992897	+	0.118976i	$0.962039\pi$
$350$		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	0.230973	+	0.972960i	$0.425809\pi$
$359$	−10.0000	+	30.7768i	−0.527780	+	1.62434i	−0.758753	+	0.651379i	$0.774191\pi$
$360$		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	0.353992	+	0.935248i	$0.384824\pi$
$367$	−9.23607	+	28.4257i	−0.482119	+	1.48381i	−0.836111	+	0.548561i	$0.815176\pi$
$368$	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	−0.999718	−	0.0237512i	$-0.992439\pi$
$379$	−25.9164	−	18.8294i	−1.33124	−	0.967200i	−0.331519	−	0.943449i	$-0.607561\pi$
$380$		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	−0.943109	−	0.332485i	$-0.892113\pi$
$383$	−17.9721	+	13.0575i	−0.918333	+	0.667208i	0.0247753	+	0.999693i	$0.492113\pi$
$384$	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	−0.536363	−	0.843987i	$-0.680202\pi$
$389$	7.76393	−	23.8949i	0.393647	−	1.21152i	0.930010	−	0.367534i	$-0.119798\pi$
$390$		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	0.585962	−	0.810338i	$-0.300717\pi$
$401$	−0.0729490	−	0.0530006i	−0.00364290	−	0.00264672i	−0.589605	+	0.807692i	$0.700717\pi$
$402$	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	−0.970136	−	0.242562i	$-0.922012\pi$
$409$	−21.0172	+	15.2699i	−1.03923	+	0.755048i	−0.0690987	+	0.997610i	$0.522012\pi$
$410$		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	0.964987	−	0.262298i	$-0.0844804\pi$
$421$	0.618034	+	1.90211i	0.0301211	+	0.0927033i	−0.934866	+	0.355001i	$0.884480\pi$
$422$	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	−0.980758	−	0.195225i	$-0.937456\pi$
$431$	−22.7984	+	16.5640i	−1.09816	+	0.797859i	−0.117401	+	0.993085i	$0.537456\pi$
$432$	−1.70820	−	5.25731i	−0.0821860	−	0.252942i
$433$	2.29180	−	7.05342i	0.110137	−	0.338966i	−0.880765	−	0.473554i	$-0.842971\pi$
$433$	2.29180	−	7.05342i	0.110137	−	0.338966i	0.990902	+	0.134588i	$0.0429710\pi$
$434$	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	0.952372	−	0.304940i	$-0.0986363\pi$
$443$	0.0557281	+	0.171513i	0.00264772	+	0.00814885i	−0.949724	+	0.313089i	$0.898636\pi$
$444$	−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	−0.113592	−	0.993527i	$-0.536236\pi$
$449$	16.8713	−	12.2577i	0.796207	−	0.578478i	0.909799	+	0.415049i	$0.136236\pi$
$450$		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	0.731716	−	0.681610i	$-0.238720\pi$
$457$	6.61803	+	4.80828i	0.309579	+	0.224922i	−0.422137	+	0.906532i	$0.638720\pi$
$458$	−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	0.181085	−	0.983467i	$-0.442039\pi$
$467$	−15.0902	−	10.9637i	−0.698290	−	0.507337i	−0.879375	+	0.476130i	$0.842039\pi$
$468$	−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	0.963531	−	0.267596i	$-0.0862294\pi$
$479$	22.0344	+	16.0090i	1.00678	+	0.731468i	0.0432482	+	0.999064i	$0.486229\pi$
$480$		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	−0.641769	−	0.766898i	$-0.721799\pi$
$487$	−12.6525	−	38.9403i	−0.573338	−	1.76455i	0.0684303	−	0.997656i	$-0.478201\pi$
$488$	−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	−0.582762	−	0.812643i	$-0.698028\pi$
$491$	8.11803	−	24.9847i	0.366362	−	1.12755i	0.949124	−	0.314903i	$-0.101972\pi$
$492$	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	−0.953288	−	0.302064i	$-0.902324\pi$
$499$	−0.100813	+	0.310271i	−0.00451301	+	0.0138896i	0.948775	+	0.315954i	$0.102324\pi$
$500$		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	0.828802	−	0.559542i	$-0.189023\pi$
$503$	−3.82624	−	11.7759i	−0.170604	−	0.525064i	−0.999405	+	0.0344785i	$0.989023\pi$
$504$	−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	0.838298	−	0.545212i	$-0.183551\pi$
$509$	−3.61803	−	11.1352i	−0.160367	−	0.493557i	−0.998665	+	0.0516541i	$0.983551\pi$
$510$		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	0.485952	+	0.873986i	$0.338473\pi$
$521$	−9.60739	+	29.5685i	−0.420907	+	1.29542i	−0.906859	+	0.421434i	$0.861527\pi$
$522$	5.32624	+	3.86974i	0.233123	+	0.169374i
$523$	0.909830	+	0.661030i	0.0397841	+	0.0289048i	0.607500	−	0.794320i	$-0.292173\pi$
$523$	0.909830	+	0.661030i	0.0397841	+	0.0289048i	−0.567716	+	0.823225i	$0.692173\pi$
$524$	−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	−0.827876	−	0.560911i	$-0.810451\pi$
$541$	−12.7984	+	9.29856i	−0.550245	+	0.399776i	0.277631	+	0.960688i	$0.410451\pi$
$542$	−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	−0.992197	−	0.124683i	$-0.960209\pi$
$547$	−6.14590	−	18.9151i	−0.262780	−	0.808753i	0.729417	−	0.684069i	$-0.239791\pi$
$548$	−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	−0.857791	−	0.513999i	$-0.828164\pi$
$557$	3.26393	−	10.0453i	0.138297	−	0.425635i	0.996088	+	0.0883634i	$0.0281637\pi$
$558$	−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	0.614450	−	0.788956i	$-0.289378\pi$
$563$	36.8885	−	26.8011i	1.55467	−	1.12953i	0.940217	−	0.340575i	$-0.110622\pi$
$564$	−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	0.981788	−	0.189979i	$-0.0608420\pi$
$569$	1.80902	+	5.56758i	0.0758379	+	0.233405i	−0.905950	+	0.423384i	$0.860842\pi$
$570$		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	0.842435	−	0.538797i	$-0.181121\pi$
$577$	14.1803	+	10.3026i	0.590335	+	0.428904i	−0.252100	+	0.967701i	$0.581121\pi$
$578$	−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	−0.669975	−	0.742383i	$-0.733695\pi$
$587$	7.47214	−	22.9969i	0.308408	−	0.949182i	0.978383	−	0.206799i	$-0.0663046\pi$
$588$	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	0.685228	−	0.728328i	$-0.259702\pi$
$599$	5.00000	+	3.63271i	0.204294	+	0.148429i	−0.480934	+	0.876757i	$0.659702\pi$
$600$		0			0
$601$	0.0278640	−	0.0857567i	0.00113660	−	0.00349809i	−0.950487	−	0.310766i	$-0.899415\pi$
$601$	0.0278640	−	0.0857567i	0.00113660	−	0.00349809i	0.951623	+	0.307267i	$0.0994146\pi$
$602$	−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	−0.981215	−	0.192916i	$-0.938206\pi$
$607$	−27.1246	+	19.7072i	−1.10095	+	0.799890i	−0.119739	+	0.992805i	$0.538206\pi$
$608$	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	0.906606	−	0.421979i	$-0.138664\pi$
$613$	−1.85410	−	5.70634i	−0.0748865	−	0.230477i	−0.981492	+	0.191502i	$0.938664\pi$
$614$	−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	0.894182	−	0.447703i	$-0.147758\pi$
$619$	−2.29837	−	7.07367i	−0.0923794	−	0.284315i	−0.986562	+	0.163388i	$0.947758\pi$
$620$		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	−0.633687	−	0.773589i	$-0.718459\pi$
$631$	8.38197	−	25.7970i	0.333681	−	1.02696i	0.967368	−	0.253375i	$-0.0815406\pi$
$632$	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	0.943325	+	0.331870i	$0.107680\pi$
$641$	9.50000	+	29.2380i	0.375227	+	1.15483i	−0.568098	+	0.822961i	$0.692320\pi$
$642$	−5.88854	+	18.1231i	−0.232402	+	0.715261i
$643$	−16.8541	−	12.2452i	−0.664661	−	0.482904i	0.203573	−	0.979060i	$-0.434745\pi$
$643$	−16.8541	−	12.2452i	−0.664661	−	0.482904i	−0.868234	+	0.496155i	$0.834745\pi$
$644$	−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	−0.0506966	−	0.998714i	$-0.516144\pi$
$647$	22.4721	−	16.3270i	0.883471	−	0.641879i	0.934167	+	0.356835i	$0.116144\pi$
$648$	−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	0.603708	+	0.797205i	$0.293689\pi$
$653$	−9.02786	+	27.7849i	−0.353288	+	1.08731i	−0.956996	+	0.290102i	$0.906311\pi$
$654$	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	−0.553269	−	0.833003i	$-0.686620\pi$
$673$	1.76393	−	1.28157i	0.0679946	−	0.0494010i	0.621263	+	0.783602i	$0.286620\pi$
$674$	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	0.813646	−	0.581361i	$-0.197480\pi$
$677$	13.3262	+	9.68208i	0.512169	+	0.372113i	−0.301477	+	0.953474i	$0.597480\pi$
$678$	−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	−0.994784	−	0.102005i	$-0.967474\pi$
$691$	−31.6803	+	23.0171i	−1.20518	+	0.875612i	−0.210393	+	0.977617i	$0.567474\pi$
$692$	−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	−0.977854	−	0.209290i	$-0.932885\pi$
$701$	−8.20163	−	25.2420i	−0.309771	−	0.953378i	0.668082	−	0.744087i	$-0.267115\pi$
$702$	−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	0.653648	−	0.756799i	$-0.273238\pi$
$709$	3.61803	+	2.62866i	0.135878	+	0.0987212i	−0.517770	+	0.855520i	$0.673238\pi$
$710$		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	−0.772365	−	0.635179i	$-0.780926\pi$
$719$	6.05573	−	18.6376i	0.225841	−	0.695066i	0.998205	−	0.0598864i	$-0.0190738\pi$
$720$		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	−0.990304	−	0.138918i	$-0.955637\pi$
$733$	−2.90983	+	8.95554i	−0.107477	+	0.330780i	0.882827	+	0.469699i	$0.155637\pi$
$734$	−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	−0.708591	−	0.705619i	$-0.750669\pi$
$739$	−6.97214	+	5.06555i	−0.256474	+	0.186339i	0.452117	+	0.891959i	$0.350669\pi$
$740$		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	0.795566	−	0.605867i	$-0.207173\pi$
$743$	12.6803	+	9.21281i	0.465197	+	0.337985i	−0.330370	+	0.943852i	$0.607173\pi$
$744$	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	−0.992640	−	0.121099i	$-0.961358\pi$
$751$	−7.14590	−	21.9928i	−0.260758	−	0.802529i	0.731883	−	0.681430i	$-0.238642\pi$
$752$	−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	−0.468318	−	0.883560i	$-0.655140\pi$
$757$	6.25329	−	4.54328i	0.227280	−	0.165128i	0.695597	+	0.718432i	$0.255140\pi$
$758$	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	−0.425405	−	0.905003i	$-0.639868\pi$
$761$	8.38197	−	6.08985i	0.303846	−	0.220757i	0.729251	+	0.684246i	$0.239868\pi$
$762$	−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	0.889479	+	0.456976i	$0.151068\pi$
$773$	12.1910	+	37.5200i	0.438479	+	1.34950i	−0.451000	+	0.892524i	$0.648932\pi$
$774$	−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	0.285400	−	0.958408i	$-0.407873\pi$
$787$	−15.0902	−	10.9637i	−0.537906	−	0.390812i	−0.823307	+	0.567596i	$0.807873\pi$
$788$	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	0.665366	−	0.746517i	$-0.268276\pi$
$797$	4.54508	+	3.30220i	0.160995	+	0.116970i	−0.504371	+	0.863487i	$0.668276\pi$
$798$	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	0.623629	−	0.781720i	$-0.285658\pi$
$809$	2.07295	+	1.50609i	0.0728810	+	0.0529512i	−0.550748	+	0.834671i	$0.685658\pi$
$810$		0			0
$811$	−13.0238	−	40.0831i	−0.457327	−	1.40751i	−0.868381	−	0.495898i	$-0.834839\pi$
$811$	−13.0238	−	40.0831i	−0.457327	−	1.40751i	0.411053	−	0.911611i	$-0.365161\pi$
$812$	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	−0.935734	−	0.352706i	$-0.885261\pi$
$821$	0.819660	−	2.52265i	0.0286063	−	0.0880412i	0.964340	+	0.264665i	$0.0852614\pi$
$822$	8.18034	+	25.1765i	0.285322	+	0.878131i
$823$	5.21885	−	3.79171i	0.181918	−	0.132171i	−0.493100	−	0.869973i	$-0.664136\pi$
$823$	5.21885	−	3.79171i	0.181918	−	0.132171i	0.675017	+	0.737802i	$0.264136\pi$
$824$	−6.85410			−0.238774
$825$		0			0
$826$	6.70820			0.233408
$827$	7.14590	−	5.19180i	0.248487	−	0.180537i	−0.456569	−	0.889688i	$-0.650922\pi$
$827$	7.14590	−	5.19180i	0.248487	−	0.180537i	0.705056	+	0.709152i	$0.250922\pi$
$828$	2.10081	+	6.46564i	0.0730083	+	0.224696i
$829$	−7.88854	+	24.2784i	−0.273980	+	0.843225i	0.715507	+	0.698606i	$0.246196\pi$
$829$	−7.88854	+	24.2784i	−0.273980	+	0.843225i	−0.989487	+	0.144619i	$0.953804\pi$
$830$		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	0.905009	−	0.425392i	$-0.139864\pi$
$839$	−2.23607	−	6.88191i	−0.0771976	−	0.237590i	−0.982207	+	0.187802i	$0.939864\pi$
$840$		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	0.658385	−	0.752682i	$-0.271240\pi$
$853$	4.26393	+	3.09793i	0.145994	+	0.106071i	−0.512391	+	0.858753i	$0.671240\pi$
$854$	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	0.857905	−	0.513808i	$-0.171766\pi$
$863$	18.6353	+	13.5393i	0.634351	+	0.460883i	−0.223554	+	0.974692i	$0.571766\pi$
$864$	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	0.729806	+	0.683654i	$0.239610\pi$
$877$	16.0279	+	49.3287i	0.541223	+	1.66571i	−0.188583	+	0.982057i	$0.560390\pi$
$878$	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	0.848835	−	0.528657i	$-0.177304\pi$
$883$	−4.41641	−	13.5923i	−0.148624	−	0.457418i	−0.997459	+	0.0712400i	$0.977304\pi$
$884$	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	0.513495	+	0.858093i	$0.328351\pi$
$887$	−12.1008	+	37.2425i	−0.406306	+	1.25048i	−0.919800	+	0.392387i	$0.871649\pi$
$888$	−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	0.908575	−	0.417722i	$-0.137171\pi$
$907$	23.8541	+	17.3310i	0.792062	+	0.575467i	−0.116512	+	0.993189i	$0.537171\pi$
$908$	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	−0.214505	−	0.976723i	$-0.568814\pi$
$911$	19.5623	−	14.2128i	0.648128	−	0.470893i	0.862633	+	0.505830i	$0.168814\pi$
$912$	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	0.446300	−	0.894883i	$-0.352741\pi$
$919$	−8.09017	−	5.87785i	−0.266870	−	0.193892i	−0.713170	+	0.700991i	$0.752741\pi$
$920$		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	0.670779	−	0.741657i	$-0.265960\pi$
$929$	5.26393	+	3.82447i	0.172704	+	0.125477i	−0.498075	+	0.867134i	$0.665960\pi$
$930$		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	0.415327	−	0.909672i	$-0.363667\pi$
$937$	43.1246	−	31.3319i	1.40882	−	1.02357i	0.993493	−	0.113895i	$-0.0363328\pi$
$938$	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	0.293781	−	0.955873i	$-0.405086\pi$
$941$	−16.0902	−	11.6902i	−0.524525	−	0.381089i	−0.818306	+	0.574783i	$0.805086\pi$
$942$	−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	−0.911478	−	0.411348i	$-0.865058\pi$
$953$	2.09017	−	6.43288i	0.0677072	−	0.208381i	0.979186	+	0.202966i	$0.0650582\pi$
$954$	−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	−0.959592	−	0.281396i	$-0.909202\pi$
$971$	−10.8647	−	33.4382i	−0.348666	−	1.07308i	0.610925	−	0.791688i	$-0.290798\pi$
$972$	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	−0.467580	−	0.883951i	$-0.654874\pi$
$977$	7.14590	−	5.19180i	0.228618	−	0.166100i	0.696197	+	0.717851i	$0.254874\pi$
$978$	−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	−0.779898	−	0.625907i	$-0.784729\pi$
$983$	6.86475	−	21.1275i	0.218951	−	0.673863i	0.998849	−	0.0479565i	$-0.0152709\pi$
$984$	−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	−0.728297	−	0.685262i	$-0.759688\pi$
$997$	8.32624	−	25.6255i	0.263695	−	0.811569i	0.991991	−	0.126307i	$-0.0403123\pi$
$998$	−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.201.1		4
5.2	odd	4		110.2.j.a.69.1	yes	8
5.3	odd	4		110.2.j.a.69.2	yes	8
5.4	even	2		550.2.h.e.201.1		4
11.2	odd	10		6050.2.a.bv.1.2		2
11.4	even	5	inner	550.2.h.d.301.1		4
11.9	even	5		6050.2.a.cl.1.2		2
15.2	even	4		990.2.ba.b.289.2		8
15.8	even	4		990.2.ba.b.289.1		8
20.3	even	4		880.2.cd.a.289.2		8
20.7	even	4		880.2.cd.a.289.1		8
55.2	even	20		1210.2.b.g.969.1		4
55.4	even	10		550.2.h.e.301.1		4
55.9	even	10		6050.2.a.ce.1.1		2
55.13	even	20		1210.2.b.g.969.4		4
55.24	odd	10		6050.2.a.ct.1.1		2
55.37	odd	20		110.2.j.a.59.2	yes	8
55.42	odd	20		1210.2.b.f.969.3		4
55.48	odd	20		110.2.j.a.59.1	✓	8
55.53	odd	20		1210.2.b.f.969.2		4
165.92	even	20		990.2.ba.b.829.1		8
165.158	even	20		990.2.ba.b.829.2		8
220.103	even	20		880.2.cd.a.609.1		8
220.147	even	20		880.2.cd.a.609.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.a.59.1	✓	8	55.48	odd	20
110.2.j.a.59.2	yes	8	55.37	odd	20
110.2.j.a.69.1	yes	8	5.2	odd	4
110.2.j.a.69.2	yes	8	5.3	odd	4
550.2.h.d.201.1		4	1.1	even	1	trivial
550.2.h.d.301.1		4	11.4	even	5	inner
550.2.h.e.201.1		4	5.4	even	2
550.2.h.e.301.1		4	55.4	even	10
880.2.cd.a.289.1		8	20.7	even	4
880.2.cd.a.289.2		8	20.3	even	4
880.2.cd.a.609.1		8	220.103	even	20
880.2.cd.a.609.2		8	220.147	even	20
990.2.ba.b.289.1		8	15.8	even	4
990.2.ba.b.289.2		8	15.2	even	4
990.2.ba.b.829.1		8	165.92	even	20
990.2.ba.b.829.2		8	165.158	even	20
1210.2.b.f.969.2		4	55.53	odd	20
1210.2.b.f.969.3		4	55.42	odd	20
1210.2.b.g.969.1		4	55.2	even	20
1210.2.b.g.969.4		4	55.13	even	20
6050.2.a.bv.1.2		2	11.2	odd	10
6050.2.a.ce.1.1		2	55.9	even	10
6050.2.a.cl.1.2		2	11.9	even	5
6050.2.a.ct.1.1		2	55.24	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more