LMFDB - Embedded newform 242.2.c.e.27.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(3,242)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("242.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	242.27
Dual form			242.2.c.e.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(1.61803 + 1.17557i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.927051 + 2.85317i) q^{5} +(0.618034 - 1.90211i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +3.00000 q^{10} -2.00000 q^{12} +(1.54508 + 4.75528i) q^{13} +(1.61803 + 1.17557i) q^{14} +(-4.85410 + 3.52671i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.927051 - 2.85317i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.61803 - 1.17557i) q^{19} +(-0.927051 - 2.85317i) q^{20} -4.00000 q^{21} +6.00000 q^{23} +(0.618034 + 1.90211i) q^{24} +(-3.23607 - 2.35114i) q^{25} +(4.04508 - 2.93893i) q^{26} +(1.23607 - 3.80423i) q^{27} +(0.618034 - 1.90211i) q^{28} +(2.42705 - 1.76336i) q^{29} +(4.85410 + 3.52671i) q^{30} +(0.618034 + 1.90211i) q^{31} -1.00000 q^{32} -3.00000 q^{34} +(-1.85410 - 5.70634i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(5.66312 - 4.11450i) q^{37} +(-0.618034 + 1.90211i) q^{38} +(-3.09017 + 9.51057i) q^{39} +(-2.42705 + 1.76336i) q^{40} +(-2.42705 - 1.76336i) q^{41} +(1.23607 + 3.80423i) q^{42} +8.00000 q^{43} -3.00000 q^{45} +(-1.85410 - 5.70634i) q^{46} +(-4.85410 - 3.52671i) q^{47} +(1.61803 - 1.17557i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(-1.23607 + 3.80423i) q^{50} +(4.85410 - 3.52671i) q^{51} +(-4.04508 - 2.93893i) q^{52} +(-0.927051 - 2.85317i) q^{53} -4.00000 q^{54} -2.00000 q^{56} +(-1.23607 - 3.80423i) q^{57} +(-2.42705 - 1.76336i) q^{58} +(1.85410 - 5.70634i) q^{60} +(-3.09017 + 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{62} +(-1.61803 - 1.17557i) q^{63} +(0.309017 + 0.951057i) q^{64} -15.0000 q^{65} -10.0000 q^{67} +(0.927051 + 2.85317i) q^{68} +(9.70820 + 7.05342i) q^{69} +(-4.85410 + 3.52671i) q^{70} +(3.70820 - 11.4127i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(-5.66312 - 4.11450i) q^{74} +(-2.47214 - 7.60845i) q^{75} +2.00000 q^{76} +10.0000 q^{78} +(0.618034 + 1.90211i) q^{79} +(2.42705 + 1.76336i) q^{80} +(8.89919 - 6.46564i) q^{81} +(-0.927051 + 2.85317i) q^{82} +(5.56231 - 17.1190i) q^{83} +(3.23607 - 2.35114i) q^{84} +(7.28115 + 5.29007i) q^{85} +(-2.47214 - 7.60845i) q^{86} +6.00000 q^{87} -9.00000 q^{89} +(0.927051 + 2.85317i) q^{90} +(-8.09017 - 5.87785i) q^{91} +(-4.85410 + 3.52671i) q^{92} +(-1.23607 + 3.80423i) q^{93} +(-1.85410 + 5.70634i) q^{94} +(4.85410 - 3.52671i) q^{95} +(-1.61803 - 1.17557i) q^{96} +(3.39919 + 10.4616i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} + q^{8} - q^{9} + 12 q^{10} - 8 q^{12} - 5 q^{13} + 2 q^{14} - 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + 3 q^{20} - 16 q^{21} + 24 q^{23}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 + q^8 - q^9 + 12 * q^10 - 8 * q^12 - 5 * q^13 + 2 * q^14 - 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 + 3 * q^20 - 16 * q^21 + 24 * q^23 - 2 * q^24 - 4 * q^25 + 5 * q^26 - 4 * q^27 - 2 * q^28 + 3 * q^29 + 6 * q^30 - 2 * q^31 - 4 * q^32 - 12 * q^34 + 6 * q^35 - q^36 + 7 * q^37 + 2 * q^38 + 10 * q^39 - 3 * q^40 - 3 * q^41 - 4 * q^42 + 32 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 + 2 * q^48 + 3 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 3 * q^53 - 16 * q^54 - 8 * q^56 + 4 * q^57 - 3 * q^58 - 6 * q^60 + 10 * q^61 + 2 * q^62 - 2 * q^63 - q^64 - 60 * q^65 - 40 * q^67 - 3 * q^68 + 12 * q^69 - 6 * q^70 - 12 * q^71 + q^72 - 14 * q^73 - 7 * q^74 + 8 * q^75 + 8 * q^76 + 40 * q^78 - 2 * q^79 + 3 * q^80 + 11 * q^81 + 3 * q^82 - 18 * q^83 + 4 * q^84 + 9 * q^85 + 8 * q^86 + 24 * q^87 - 36 * q^89 - 3 * q^90 - 10 * q^91 - 6 * q^92 + 4 * q^93 + 6 * q^94 + 6 * q^95 - 2 * q^96 - 11 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	1.61803	+	1.17557i	0.934172	+	0.678716i	0.947011	−	0.321202i	$-0.104087\pi$
$3$	1.61803	+	1.17557i	0.934172	+	0.678716i	−0.0128385	+	0.999918i	$0.504087\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.927051	+	2.85317i	−0.414590	+	1.27598i	0.498027	+	0.867161i	$0.334058\pi$
$5$	−0.927051	+	2.85317i	−0.414590	+	1.27598i	−0.912617	+	0.408815i	$0.865942\pi$
$6$	0.618034	−	1.90211i	0.252311	−	0.776534i
$7$	−1.61803	+	1.17557i	−0.611559	+	0.444324i	−0.849963	−	0.526842i	$-0.823376\pi$
$7$	−1.61803	+	1.17557i	−0.611559	+	0.444324i	0.238404	+	0.971166i	$0.423376\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	3.00000			0.948683
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	1.54508	+	4.75528i	0.428529	+	1.31888i	0.899574	+	0.436769i	$0.143877\pi$
$13$	1.54508	+	4.75528i	0.428529	+	1.31888i	−0.471044	+	0.882109i	$0.656123\pi$
$14$	1.61803	+	1.17557i	0.432438	+	0.314184i
$15$	−4.85410	+	3.52671i	−1.25332	+	0.910593i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.927051	−	2.85317i	0.224843	−	0.691995i	−0.773465	−	0.633839i	$-0.781478\pi$
$17$	0.927051	−	2.85317i	0.224843	−	0.691995i	0.998308	−	0.0581558i	$-0.0185220\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−1.61803	−	1.17557i	−0.371202	−	0.269694i	0.386507	−	0.922287i	$-0.373682\pi$
$19$	−1.61803	−	1.17557i	−0.371202	−	0.269694i	−0.757709	+	0.652592i	$0.773682\pi$
$20$	−0.927051	−	2.85317i	−0.207295	−	0.637988i
$21$	−4.00000			−0.872872
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	0.618034	+	1.90211i	0.126156	+	0.388267i
$25$	−3.23607	−	2.35114i	−0.647214	−	0.470228i
$26$	4.04508	−	2.93893i	0.793306	−	0.576371i
$27$	1.23607	−	3.80423i	0.237881	−	0.732124i
$28$	0.618034	−	1.90211i	0.116797	−	0.359466i
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	−0.339177	−	0.940723i	$-0.610149\pi$
$29$	2.42705	−	1.76336i	0.450692	−	0.327447i	0.789869	+	0.613276i	$0.210149\pi$
$30$	4.85410	+	3.52671i	0.886234	+	0.643886i
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	0.991092	−	0.133177i	$-0.0425179\pi$
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	−0.880090	+	0.474807i	$0.842518\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.00000			−0.514496
$35$	−1.85410	−	5.70634i	−0.313400	−	0.964547i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	5.66312	−	4.11450i	0.931011	−	0.676419i	−0.0152291	−	0.999884i	$-0.504848\pi$
$37$	5.66312	−	4.11450i	0.931011	−	0.676419i	0.946240	+	0.323465i	$0.104848\pi$
$38$	−0.618034	+	1.90211i	−0.100258	+	0.308563i
$39$	−3.09017	+	9.51057i	−0.494823	+	1.52291i
$40$	−2.42705	+	1.76336i	−0.383750	+	0.278811i
$41$	−2.42705	−	1.76336i	−0.379042	−	0.275390i	0.381909	−	0.924200i	$-0.375267\pi$
$41$	−2.42705	−	1.76336i	−0.379042	−	0.275390i	−0.760950	+	0.648810i	$0.775267\pi$
$42$	1.23607	+	3.80423i	0.190729	+	0.587005i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	−1.85410	−	5.70634i	−0.273372	−	0.841354i
$47$	−4.85410	−	3.52671i	−0.708044	−	0.514424i	0.174498	−	0.984657i	$-0.444170\pi$
$47$	−4.85410	−	3.52671i	−0.708044	−	0.514424i	−0.882542	+	0.470234i	$0.844170\pi$
$48$	1.61803	−	1.17557i	0.233543	−	0.169679i
$49$	−0.927051	+	2.85317i	−0.132436	+	0.407596i
$50$	−1.23607	+	3.80423i	−0.174806	+	0.537999i
$51$	4.85410	−	3.52671i	0.679710	−	0.493838i
$52$	−4.04508	−	2.93893i	−0.560952	−	0.407556i
$53$	−0.927051	−	2.85317i	−0.127340	−	0.391913i	0.866980	−	0.498343i	$-0.166058\pi$
$53$	−0.927051	−	2.85317i	−0.127340	−	0.391913i	−0.994320	+	0.106430i	$0.966058\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−1.23607	−	3.80423i	−0.163721	−	0.503882i
$58$	−2.42705	−	1.76336i	−0.318687	−	0.231540i
$59$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$59$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$60$	1.85410	−	5.70634i	0.239364	−	0.736685i
$61$	−3.09017	+	9.51057i	−0.395656	+	1.21770i	0.532794	+	0.846245i	$0.321142\pi$
$61$	−3.09017	+	9.51057i	−0.395656	+	1.21770i	−0.928450	+	0.371458i	$0.878858\pi$
$62$	1.61803	−	1.17557i	0.205491	−	0.149298i
$63$	−1.61803	−	1.17557i	−0.203853	−	0.148108i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−15.0000			−1.86052
$66$		0			0
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$	0.927051	+	2.85317i	0.112421	+	0.345998i
$69$	9.70820	+	7.05342i	1.16873	+	0.849132i
$70$	−4.85410	+	3.52671i	−0.580176	+	0.421523i
$71$	3.70820	−	11.4127i	0.440083	−	1.35444i	−0.447704	−	0.894182i	$-0.647758\pi$
$71$	3.70820	−	11.4127i	0.440083	−	1.35444i	0.887787	−	0.460254i	$-0.152242\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.325792	+	0.945441i	$0.605631\pi$
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.999844	+	0.0176895i	$0.994369\pi$
$74$	−5.66312	−	4.11450i	−0.658324	−	0.478301i
$75$	−2.47214	−	7.60845i	−0.285458	−	0.878548i
$76$	2.00000			0.229416
$77$		0			0
$78$	10.0000			1.13228
$79$	0.618034	+	1.90211i	0.0695343	+	0.214004i	0.979785	−	0.200053i	$-0.0641114\pi$
$79$	0.618034	+	1.90211i	0.0695343	+	0.214004i	−0.910251	+	0.414057i	$0.864111\pi$
$80$	2.42705	+	1.76336i	0.271353	+	0.197149i
$81$	8.89919	−	6.46564i	0.988799	−	0.718404i
$82$	−0.927051	+	2.85317i	−0.102376	+	0.315080i
$83$	5.56231	−	17.1190i	0.610542	−	1.87906i	0.157639	−	0.987497i	$-0.449612\pi$
$83$	5.56231	−	17.1190i	0.610542	−	1.87906i	0.452904	−	0.891559i	$-0.350388\pi$
$84$	3.23607	−	2.35114i	0.353084	−	0.256531i
$85$	7.28115	+	5.29007i	0.789752	+	0.573788i
$86$	−2.47214	−	7.60845i	−0.266577	−	0.820440i
$87$	6.00000			0.643268
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	0.927051	+	2.85317i	0.0977198	+	0.300750i
$91$	−8.09017	−	5.87785i	−0.848080	−	0.616166i
$92$	−4.85410	+	3.52671i	−0.506075	+	0.367685i
$93$	−1.23607	+	3.80423i	−0.128174	+	0.394480i
$94$	−1.85410	+	5.70634i	−0.191236	+	0.588564i
$95$	4.85410	−	3.52671i	0.498020	−	0.361833i
$96$	−1.61803	−	1.17557i	−0.165140	−	0.119981i
$97$	3.39919	+	10.4616i	0.345135	+	1.06222i	0.961511	+	0.274765i	$0.0886000\pi$
$97$	3.39919	+	10.4616i	0.345135	+	1.06222i	−0.616376	+	0.787452i	$0.711400\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	4.00000			0.400000
$101$	1.85410	+	5.70634i	0.184490	+	0.567802i	0.999939	−	0.0110267i	$-0.00350999\pi$
$101$	1.85410	+	5.70634i	0.184490	+	0.567802i	−0.815449	+	0.578829i	$0.803510\pi$
$102$	−4.85410	−	3.52671i	−0.480628	−	0.349196i
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	−0.859066	−	0.511865i	$-0.828955\pi$
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	0.221347	+	0.975195i	$0.428955\pi$
$104$	−1.54508	+	4.75528i	−0.151508	+	0.466294i
$105$	3.70820	−	11.4127i	0.361884	−	1.11376i
$106$	−2.42705	+	1.76336i	−0.235736	+	0.171272i
$107$	4.85410	+	3.52671i	0.469264	+	0.340940i	0.797154	−	0.603776i	$-0.206338\pi$
$107$	4.85410	+	3.52671i	0.469264	+	0.340940i	−0.327891	+	0.944716i	$0.606338\pi$
$108$	1.23607	+	3.80423i	0.118941	+	0.366062i
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	14.0000			1.32882
$112$	0.618034	+	1.90211i	0.0583987	+	0.179733i
$113$	7.28115	+	5.29007i	0.684953	+	0.497648i	0.874997	−	0.484128i	$-0.160863\pi$
$113$	7.28115	+	5.29007i	0.684953	+	0.497648i	−0.190044	+	0.981776i	$0.560863\pi$
$114$	−3.23607	+	2.35114i	−0.303086	+	0.220205i
$115$	−5.56231	+	17.1190i	−0.518688	+	1.59636i
$116$	−0.927051	+	2.85317i	−0.0860745	+	0.264910i
$117$	−4.04508	+	2.93893i	−0.373968	+	0.271704i
$118$		0			0
$119$	1.85410	+	5.70634i	0.169965	+	0.523099i
$120$	−6.00000			−0.547723
$121$		0			0
$122$	10.0000			0.905357
$123$	−1.85410	−	5.70634i	−0.167179	−	0.514523i
$124$	−1.61803	−	1.17557i	−0.145304	−	0.105569i
$125$	−2.42705	+	1.76336i	−0.217082	+	0.157719i
$126$	−0.618034	+	1.90211i	−0.0550588	+	0.169454i
$127$	2.47214	−	7.60845i	0.219367	−	0.675141i	−0.779448	−	0.626467i	$-0.784500\pi$
$127$	2.47214	−	7.60845i	0.219367	−	0.675141i	0.998815	−	0.0486742i	$-0.0154996\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	12.9443	+	9.40456i	1.13968	+	0.828026i
$130$	4.63525	+	14.2658i	0.406539	+	1.25120i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	4.00000			0.346844
$134$	3.09017	+	9.51057i	0.266950	+	0.821588i
$135$	9.70820	+	7.05342i	0.835549	+	0.607062i
$136$	2.42705	−	1.76336i	0.208118	−	0.151207i
$137$	1.85410	−	5.70634i	0.158407	−	0.487525i	−0.840083	−	0.542457i	$-0.817494\pi$
$137$	1.85410	−	5.70634i	0.158407	−	0.487525i	0.998490	+	0.0549317i	$0.0174941\pi$
$138$	3.70820	−	11.4127i	0.315663	−	0.971512i
$139$	17.7984	−	12.9313i	1.50964	−	1.09682i	0.543301	−	0.839538i	$-0.317174\pi$
$139$	17.7984	−	12.9313i	1.50964	−	1.09682i	0.966337	−	0.257279i	$-0.0828258\pi$
$140$	4.85410	+	3.52671i	0.410246	+	0.298062i
$141$	−3.70820	−	11.4127i	−0.312287	−	0.961121i
$142$	−12.0000			−1.00702
$143$		0			0
$144$	1.00000			0.0833333
$145$	2.78115	+	8.55951i	0.230962	+	0.710829i
$146$	11.3262	+	8.22899i	0.937366	+	0.681036i
$147$	−4.85410	+	3.52671i	−0.400360	+	0.290878i
$148$	−2.16312	+	6.65740i	−0.177807	+	0.547235i
$149$	−0.927051	+	2.85317i	−0.0759470	+	0.233741i	−0.981822	−	0.189805i	$-0.939215\pi$
$149$	−0.927051	+	2.85317i	−0.0759470	+	0.233741i	0.905875	+	0.423545i	$0.139215\pi$
$150$	−6.47214	+	4.70228i	−0.528448	+	0.383940i
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	0.292425	−	0.956288i	$-0.405538\pi$
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	−0.819120	+	0.573622i	$0.805538\pi$
$152$	−0.618034	−	1.90211i	−0.0501292	−	0.154282i
$153$	3.00000			0.242536
$154$		0			0
$155$	−6.00000			−0.481932
$156$	−3.09017	−	9.51057i	−0.247412	−	0.761455i
$157$	−1.61803	−	1.17557i	−0.129133	−	0.0938207i	0.521344	−	0.853347i	$-0.325431\pi$
$157$	−1.61803	−	1.17557i	−0.129133	−	0.0938207i	−0.650477	+	0.759526i	$0.725431\pi$
$158$	1.61803	−	1.17557i	0.128724	−	0.0935234i
$159$	1.85410	−	5.70634i	0.147040	−	0.452542i
$160$	0.927051	−	2.85317i	0.0732898	−	0.225563i
$161$	−9.70820	+	7.05342i	−0.765114	+	0.555888i
$162$	−8.89919	−	6.46564i	−0.699186	−	0.507988i
$163$	−6.79837	−	20.9232i	−0.532490	−	1.63883i	−0.749011	−	0.662557i	$-0.769471\pi$
$163$	−6.79837	−	20.9232i	−0.532490	−	1.63883i	0.216522	−	0.976278i	$-0.430529\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	−18.0000			−1.39707
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	−0.985808	−	0.167879i	$-0.946308\pi$
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	0.698858	−	0.715260i	$-0.253692\pi$
$168$	−3.23607	−	2.35114i	−0.249668	−	0.181394i
$169$	−9.70820	+	7.05342i	−0.746785	+	0.542571i
$170$	2.78115	−	8.55951i	0.213305	−	0.656484i
$171$	0.618034	−	1.90211i	0.0472622	−	0.145458i
$172$	−6.47214	+	4.70228i	−0.493496	+	0.358546i
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	0.387767	−	0.921758i	$-0.373247\pi$
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	−0.756817	+	0.653627i	$0.773247\pi$
$174$	−1.85410	−	5.70634i	−0.140559	−	0.432596i
$175$	8.00000			0.604743
$176$		0			0
$177$		0			0
$178$	2.78115	+	8.55951i	0.208456	+	0.641562i
$179$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$179$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$180$	2.42705	−	1.76336i	0.180902	−	0.131433i
$181$	1.54508	−	4.75528i	0.114845	−	0.353457i	−0.877069	−	0.480364i	$-0.840505\pi$
$181$	1.54508	−	4.75528i	0.114845	−	0.353457i	0.991915	+	0.126906i	$0.0405047\pi$
$182$	−3.09017	+	9.51057i	−0.229059	+	0.704970i
$183$	−16.1803	+	11.7557i	−1.19609	+	0.869007i
$184$	4.85410	+	3.52671i	0.357849	+	0.259993i
$185$	6.48936	+	19.9722i	0.477107	+	1.46838i
$186$	4.00000			0.293294
$187$		0			0
$188$	6.00000			0.437595
$189$	2.47214	+	7.60845i	0.179821	+	0.553433i
$190$	−4.85410	−	3.52671i	−0.352154	−	0.255855i
$191$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$191$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$192$	−0.618034	+	1.90211i	−0.0446028	+	0.137273i
$193$	−4.01722	+	12.3637i	−0.289166	+	0.889961i	0.695953	+	0.718087i	$0.254982\pi$
$193$	−4.01722	+	12.3637i	−0.289166	+	0.889961i	−0.985119	+	0.171874i	$0.945018\pi$
$194$	8.89919	−	6.46564i	0.638924	−	0.464206i
$195$	−24.2705	−	17.6336i	−1.73805	−	1.26277i
$196$	−0.927051	−	2.85317i	−0.0662179	−	0.203798i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.23607	−	3.80423i	−0.0874032	−	0.268999i
$201$	−16.1803	−	11.7557i	−1.14127	−	0.829184i
$202$	4.85410	−	3.52671i	0.341533	−	0.248139i
$203$	−1.85410	+	5.70634i	−0.130132	+	0.400506i
$204$	−1.85410	+	5.70634i	−0.129813	+	0.399524i
$205$	7.28115	−	5.29007i	0.508538	−	0.369474i
$206$	6.47214	+	4.70228i	0.450935	+	0.327624i
$207$	1.85410	+	5.70634i	0.128869	+	0.396618i
$208$	5.00000			0.346688
$209$		0			0
$210$	−12.0000			−0.828079
$211$	−1.23607	−	3.80423i	−0.0850944	−	0.261894i	0.899451	−	0.437021i	$-0.143966\pi$
$211$	−1.23607	−	3.80423i	−0.0850944	−	0.261894i	−0.984546	+	0.175127i	$0.943966\pi$
$212$	2.42705	+	1.76336i	0.166691	+	0.121108i
$213$	19.4164	−	14.1068i	1.33039	−	0.966585i
$214$	1.85410	−	5.70634i	0.126744	−	0.390077i
$215$	−7.41641	+	22.8254i	−0.505795	+	1.55668i
$216$	3.23607	−	2.35114i	0.220187	−	0.159975i
$217$	−3.23607	−	2.35114i	−0.219679	−	0.159606i
$218$	−5.25329	−	16.1680i	−0.355798	−	1.09503i
$219$	−28.0000			−1.89206
$220$		0			0
$221$	15.0000			1.00901
$222$	−4.32624	−	13.3148i	−0.290358	−	0.893630i
$223$	3.23607	+	2.35114i	0.216703	+	0.157444i	0.690841	−	0.723006i	$-0.257240\pi$
$223$	3.23607	+	2.35114i	0.216703	+	0.157444i	−0.474138	+	0.880450i	$0.657240\pi$
$224$	1.61803	−	1.17557i	0.108109	−	0.0785461i
$225$	1.23607	−	3.80423i	0.0824045	−	0.253615i
$226$	2.78115	−	8.55951i	0.185000	−	0.569370i
$227$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$227$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$228$	3.23607	+	2.35114i	0.214314	+	0.155708i
$229$	1.54508	+	4.75528i	0.102102	+	0.314238i	0.989039	−	0.147652i	$-0.0471715\pi$
$229$	1.54508	+	4.75528i	0.102102	+	0.314238i	−0.886937	+	0.461890i	$0.847172\pi$
$230$	18.0000			1.18688
$231$		0			0
$232$	3.00000			0.196960
$233$	−6.48936	−	19.9722i	−0.425132	−	1.30842i	−0.902868	−	0.429918i	$-0.858542\pi$
$233$	−6.48936	−	19.9722i	−0.425132	−	1.30842i	0.477736	−	0.878503i	$-0.341458\pi$
$234$	4.04508	+	2.93893i	0.264435	+	0.192124i
$235$	14.5623	−	10.5801i	0.949940	−	0.690172i
$236$		0			0
$237$	−1.23607	+	3.80423i	−0.0802912	+	0.247111i
$238$	4.85410	−	3.52671i	0.314645	−	0.228603i
$239$	24.2705	+	17.6336i	1.56993	+	1.14062i	0.927225	+	0.374505i	$0.122188\pi$
$239$	24.2705	+	17.6336i	1.56993	+	1.14062i	0.642704	+	0.766115i	$0.277812\pi$
$240$	1.85410	+	5.70634i	0.119682	+	0.368343i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	10.0000			0.641500
$244$	−3.09017	−	9.51057i	−0.197828	−	0.608852i
$245$	−7.28115	−	5.29007i	−0.465176	−	0.337970i
$246$	−4.85410	+	3.52671i	−0.309486	+	0.224855i
$247$	3.09017	−	9.51057i	0.196623	−	0.605143i
$248$	−0.618034	+	1.90211i	−0.0392452	+	0.120784i
$249$	29.1246	−	21.1603i	1.84570	−	1.34098i
$250$	2.42705	+	1.76336i	0.153500	+	0.111524i
$251$	5.56231	+	17.1190i	0.351090	+	1.08054i	0.958242	+	0.285958i	$0.0923116\pi$
$251$	5.56231	+	17.1190i	0.351090	+	1.08054i	−0.607153	+	0.794585i	$0.707688\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	−8.00000			−0.501965
$255$	5.56231	+	17.1190i	0.348325	+	1.07203i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.42705	+	1.76336i	−0.151395	+	0.109995i	−0.660904	−	0.750470i	$-0.729827\pi$
$257$	−2.42705	+	1.76336i	−0.151395	+	0.109995i	0.509509	+	0.860465i	$0.329827\pi$
$258$	4.94427	−	15.2169i	0.307817	−	0.947363i
$259$	−4.32624	+	13.3148i	−0.268819	+	0.827341i
$260$	12.1353	−	8.81678i	0.752597	−	0.546793i
$261$	2.42705	+	1.76336i	0.150231	+	0.109149i
$262$		0			0
$263$	6.00000			0.369976			0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000			0.369976			0.184988	+	0.982741i	$0.440775\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	−1.23607	−	3.80423i	−0.0757882	−	0.233252i
$267$	−14.5623	−	10.5801i	−0.891199	−	0.647494i
$268$	8.09017	−	5.87785i	0.494186	−	0.359047i
$269$	−0.927051	+	2.85317i	−0.0565233	+	0.173961i	−0.975332	−	0.220742i	$-0.929152\pi$
$269$	−0.927051	+	2.85317i	−0.0565233	+	0.173961i	0.918809	+	0.394702i	$0.129152\pi$
$270$	3.70820	−	11.4127i	0.225674	−	0.694553i
$271$	−16.1803	+	11.7557i	−0.982886	+	0.714108i	−0.958352	−	0.285591i	$-0.907810\pi$
$271$	−16.1803	+	11.7557i	−0.982886	+	0.714108i	−0.0245340	+	0.999699i	$0.507810\pi$
$272$	−2.42705	−	1.76336i	−0.147162	−	0.106919i
$273$	−6.18034	−	19.0211i	−0.374051	−	1.15121i
$274$	−6.00000			−0.362473
$275$		0			0
$276$	−12.0000			−0.722315
$277$	1.54508	+	4.75528i	0.0928352	+	0.285717i	0.986683	−	0.162652i	$-0.0520049\pi$
$277$	1.54508	+	4.75528i	0.0928352	+	0.285717i	−0.893848	+	0.448370i	$0.852005\pi$
$278$	−17.7984	−	12.9313i	−1.06748	−	0.775566i
$279$	−1.61803	+	1.17557i	−0.0968692	+	0.0703796i
$280$	1.85410	−	5.70634i	0.110804	−	0.341019i
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	−0.880399	−	0.474234i	$-0.842725\pi$
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	0.991005	+	0.133822i	$0.0427251\pi$
$282$	−9.70820	+	7.05342i	−0.578115	+	0.420025i
$283$	−16.1803	−	11.7557i	−0.961821	−	0.698804i	−0.00824833	−	0.999966i	$-0.502626\pi$
$283$	−16.1803	−	11.7557i	−0.961821	−	0.698804i	−0.953573	+	0.301162i	$0.902626\pi$
$284$	3.70820	+	11.4127i	0.220041	+	0.677218i
$285$	12.0000			0.710819
$286$		0			0
$287$	6.00000			0.354169
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	6.47214	+	4.70228i	0.380714	+	0.276605i
$290$	7.28115	−	5.29007i	0.427564	−	0.310643i
$291$	−6.79837	+	20.9232i	−0.398528	+	1.22654i
$292$	4.32624	−	13.3148i	0.253174	−	0.779189i
$293$	−16.9894	+	12.3435i	−0.992529	+	0.721114i	−0.960473	−	0.278372i	$-0.910205\pi$
$293$	−16.9894	+	12.3435i	−0.992529	+	0.721114i	−0.0320554	+	0.999486i	$0.510205\pi$
$294$	4.85410	+	3.52671i	0.283097	+	0.205682i
$295$		0			0
$296$	7.00000			0.406867
$297$		0			0
$298$	3.00000			0.173785
$299$	9.27051	+	28.5317i	0.536127	+	1.65003i
$300$	6.47214	+	4.70228i	0.373669	+	0.271486i
$301$	−12.9443	+	9.40456i	−0.746095	+	0.542070i
$302$	−2.47214	+	7.60845i	−0.142255	+	0.437817i
$303$	−3.70820	+	11.4127i	−0.213031	+	0.655641i
$304$	−1.61803	+	1.17557i	−0.0928006	+	0.0674236i
$305$	−24.2705	−	17.6336i	−1.38973	−	1.00969i
$306$	−0.927051	−	2.85317i	−0.0529960	−	0.163105i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$	1.85410	+	5.70634i	0.105306	+	0.324098i
$311$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$311$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$312$	−8.09017	+	5.87785i	−0.458016	+	0.332768i
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	−0.959410	−	0.282015i	$-0.908997\pi$
$313$	−0.309017	+	0.951057i	−0.0174667	+	0.0537569i	0.941943	+	0.335772i	$0.108997\pi$
$314$	−0.618034	+	1.90211i	−0.0348777	+	0.107342i
$315$	4.85410	−	3.52671i	0.273498	−	0.198708i
$316$	−1.61803	−	1.17557i	−0.0910215	−	0.0661310i
$317$	−5.56231	−	17.1190i	−0.312410	−	0.961500i	−0.976807	−	0.214120i	$-0.931312\pi$
$317$	−5.56231	−	17.1190i	−0.312410	−	0.961500i	0.664397	−	0.747380i	$-0.268688\pi$
$318$	−6.00000			−0.336463
$319$		0			0
$320$	−3.00000			−0.167705
$321$	3.70820	+	11.4127i	0.206972	+	0.636994i
$322$	9.70820	+	7.05342i	0.541017	+	0.393072i
$323$	−4.85410	+	3.52671i	−0.270089	+	0.196231i
$324$	−3.39919	+	10.4616i	−0.188844	+	0.581201i
$325$	6.18034	−	19.0211i	0.342824	−	1.05510i
$326$	−17.7984	+	12.9313i	−0.985761	+	0.716197i
$327$	27.5066	+	19.9847i	1.52112	+	1.10516i
$328$	−0.927051	−	2.85317i	−0.0511878	−	0.157540i
$329$	12.0000			0.661581
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	5.56231	+	17.1190i	0.305271	+	0.939528i
$333$	5.66312	+	4.11450i	0.310337	+	0.225473i
$334$	−9.70820	+	7.05342i	−0.531209	+	0.385946i
$335$	9.27051	−	28.5317i	0.506502	−	1.55885i
$336$	−1.23607	+	3.80423i	−0.0674330	+	0.207538i
$337$	10.5172	−	7.64121i	0.572910	−	0.416243i	−0.263251	−	0.964727i	$-0.584795\pi$
$337$	10.5172	−	7.64121i	0.572910	−	0.416243i	0.836161	+	0.548484i	$0.184795\pi$
$338$	9.70820	+	7.05342i	0.528057	+	0.383656i
$339$	5.56231	+	17.1190i	0.302103	+	0.929777i
$340$	−9.00000			−0.488094
$341$		0			0
$342$	−2.00000			−0.108148
$343$	−6.18034	−	19.0211i	−0.333707	−	1.02704i
$344$	6.47214	+	4.70228i	0.348954	+	0.253530i
$345$	−29.1246	+	21.1603i	−1.56802	+	1.13923i
$346$	−1.85410	+	5.70634i	−0.0996771	+	0.306775i
$347$	11.1246	−	34.2380i	0.597200	−	1.83799i	0.0537472	−	0.998555i	$-0.482883\pi$
$347$	11.1246	−	34.2380i	0.597200	−	1.83799i	0.543453	−	0.839439i	$-0.317117\pi$
$348$	−4.85410	+	3.52671i	−0.260207	+	0.189052i
$349$	−13.7533	−	9.99235i	−0.736197	−	0.534878i	0.155321	−	0.987864i	$-0.450359\pi$
$349$	−13.7533	−	9.99235i	−0.736197	−	0.534878i	−0.891518	+	0.452986i	$0.850359\pi$
$350$	−2.47214	−	7.60845i	−0.132141	−	0.406689i
$351$	20.0000			1.06752
$352$		0			0
$353$	−9.00000			−0.479022			−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000			−0.479022			−0.239511	+	0.970894i	$0.576987\pi$
$354$		0			0
$355$	29.1246	+	21.1603i	1.54577	+	1.12307i
$356$	7.28115	−	5.29007i	0.385900	−	0.280373i
$357$	−3.70820	+	11.4127i	−0.196259	+	0.604023i
$358$		0			0
$359$	−14.5623	+	10.5801i	−0.768569	+	0.558398i	−0.901527	−	0.432724i	$-0.857553\pi$
$359$	−14.5623	+	10.5801i	−0.768569	+	0.558398i	0.132958	+	0.991122i	$0.457553\pi$
$360$	−2.42705	−	1.76336i	−0.127917	−	0.0929370i
$361$	−4.63525	−	14.2658i	−0.243961	−	0.750834i
$362$	−5.00000			−0.262794
$363$		0			0
$364$	10.0000			0.524142
$365$	−12.9787	−	39.9444i	−0.679337	−	2.09078i
$366$	16.1803	+	11.7557i	0.845760	+	0.614481i
$367$	8.09017	−	5.87785i	0.422303	−	0.306821i	−0.356261	−	0.934387i	$-0.615948\pi$
$367$	8.09017	−	5.87785i	0.422303	−	0.306821i	0.778564	+	0.627565i	$0.215948\pi$
$368$	1.85410	−	5.70634i	0.0966517	−	0.297463i
$369$	0.927051	−	2.85317i	0.0482603	−	0.148530i
$370$	16.9894	−	12.3435i	0.883235	−	0.641708i
$371$	4.85410	+	3.52671i	0.252012	+	0.183098i
$372$	−1.23607	−	3.80423i	−0.0640871	−	0.197240i
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$	−6.00000			−0.309839
$376$	−1.85410	−	5.70634i	−0.0956180	−	0.294282i
$377$	12.1353	+	8.81678i	0.624997	+	0.454087i
$378$	6.47214	−	4.70228i	0.332891	−	0.241859i
$379$	−4.94427	+	15.2169i	−0.253970	+	0.781640i	0.740061	+	0.672540i	$0.234797\pi$
$379$	−4.94427	+	15.2169i	−0.253970	+	0.781640i	−0.994031	+	0.109100i	$0.965203\pi$
$380$	−1.85410	+	5.70634i	−0.0951134	+	0.292729i
$381$	12.9443	−	9.40456i	0.663155	−	0.481810i
$382$		0			0
$383$	3.70820	+	11.4127i	0.189480	+	0.583161i	0.999997	−	0.00255538i	$-0.000813402\pi$
$383$	3.70820	+	11.4127i	0.189480	+	0.583161i	−0.810516	+	0.585716i	$0.800813\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	13.0000			0.661683
$387$	2.47214	+	7.60845i	0.125666	+	0.386759i
$388$	−8.89919	−	6.46564i	−0.451788	−	0.328243i
$389$	−26.6976	+	19.3969i	−1.35362	+	0.983463i	−0.354798	+	0.934943i	$0.615450\pi$
$389$	−26.6976	+	19.3969i	−1.35362	+	0.983463i	−0.998822	+	0.0485195i	$0.984550\pi$
$390$	−9.27051	+	28.5317i	−0.469431	+	1.44476i
$391$	5.56231	−	17.1190i	0.281298	−	0.865746i
$392$	−2.42705	+	1.76336i	−0.122585	+	0.0890629i
$393$		0			0
$394$	4.63525	+	14.2658i	0.233521	+	0.718703i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	17.0000			0.853206			0.426603	−	0.904439i	$-0.359710\pi$
$397$	17.0000			0.853206			0.426603	+	0.904439i	$0.359710\pi$
$398$	4.94427	+	15.2169i	0.247834	+	0.762754i
$399$	6.47214	+	4.70228i	0.324012	+	0.235409i
$400$	−3.23607	+	2.35114i	−0.161803	+	0.117557i
$401$	−10.1976	+	31.3849i	−0.509242	+	1.56729i	0.284279	+	0.958742i	$0.408246\pi$
$401$	−10.1976	+	31.3849i	−0.509242	+	1.56729i	−0.793520	+	0.608544i	$0.791754\pi$
$402$	−6.18034	+	19.0211i	−0.308247	+	0.948688i
$403$	−8.09017	+	5.87785i	−0.403000	+	0.292797i
$404$	−4.85410	−	3.52671i	−0.241501	−	0.175460i
$405$	10.1976	+	31.3849i	0.506721	+	1.55953i
$406$	6.00000			0.297775
$407$		0			0
$408$	6.00000			0.297044
$409$	−4.01722	−	12.3637i	−0.198639	−	0.611347i	−0.999915	−	0.0130525i	$-0.995845\pi$
$409$	−4.01722	−	12.3637i	−0.198639	−	0.611347i	0.801276	−	0.598295i	$-0.204155\pi$
$410$	−7.28115	−	5.29007i	−0.359591	−	0.261258i
$411$	9.70820	−	7.05342i	0.478870	−	0.347920i
$412$	2.47214	−	7.60845i	0.121793	−	0.374842i
$413$		0			0
$414$	4.85410	−	3.52671i	0.238566	−	0.173328i
$415$	43.6869	+	31.7404i	2.14451	+	1.55808i
$416$	−1.54508	−	4.75528i	−0.0757540	−	0.233147i
$417$	44.0000			2.15469
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$	3.70820	+	11.4127i	0.180942	+	0.556882i
$421$	−13.7533	−	9.99235i	−0.670294	−	0.486997i	0.199829	−	0.979831i	$-0.435961\pi$
$421$	−13.7533	−	9.99235i	−0.670294	−	0.486997i	−0.870124	+	0.492833i	$0.835961\pi$
$422$	−3.23607	+	2.35114i	−0.157529	+	0.114452i
$423$	1.85410	−	5.70634i	0.0901495	−	0.277452i
$424$	0.927051	−	2.85317i	0.0450216	−	0.138562i
$425$	−9.70820	+	7.05342i	−0.470917	+	0.342141i
$426$	−19.4164	−	14.1068i	−0.940728	−	0.683479i
$427$	−6.18034	−	19.0211i	−0.299088	−	0.920497i
$428$	−6.00000			−0.290021
$429$		0			0
$430$	24.0000			1.15738
$431$	11.1246	+	34.2380i	0.535854	+	1.64919i	0.741797	+	0.670624i	$0.233974\pi$
$431$	11.1246	+	34.2380i	0.535854	+	1.64919i	−0.205944	+	0.978564i	$0.566026\pi$
$432$	−3.23607	−	2.35114i	−0.155695	−	0.113119i
$433$	29.9336	−	21.7481i	1.43852	−	1.04514i	0.450169	−	0.892943i	$-0.351364\pi$
$433$	29.9336	−	21.7481i	1.43852	−	1.04514i	0.988350	−	0.152201i	$-0.0486362\pi$
$434$	−1.23607	+	3.80423i	−0.0593332	+	0.182609i
$435$	−5.56231	+	17.1190i	−0.266692	+	0.820794i
$436$	−13.7533	+	9.99235i	−0.658663	+	0.478547i
$437$	−9.70820	−	7.05342i	−0.464406	−	0.337411i
$438$	8.65248	+	26.6296i	0.413431	+	1.27241i
$439$	−22.0000			−1.05000			−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000			−1.05000			−0.525001	+	0.851101i	$0.675935\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−4.63525	−	14.2658i	−0.220477	−	0.678557i
$443$	−29.1246	−	21.1603i	−1.38375	−	1.00535i	−0.996518	−	0.0833731i	$-0.973431\pi$
$443$	−29.1246	−	21.1603i	−1.38375	−	1.00535i	−0.387234	−	0.921982i	$-0.626569\pi$
$444$	−11.3262	+	8.22899i	−0.537519	+	0.390531i
$445$	8.34346	−	25.6785i	0.395518	−	1.21728i
$446$	1.23607	−	3.80423i	0.0585295	−	0.180135i
$447$	−4.85410	+	3.52671i	−0.229591	+	0.166808i
$448$	−1.61803	−	1.17557i	−0.0764449	−	0.0555405i
$449$	−6.48936	−	19.9722i	−0.306252	−	0.942546i	−0.979207	−	0.202863i	$-0.934975\pi$
$449$	−6.48936	−	19.9722i	−0.306252	−	0.942546i	0.672955	−	0.739683i	$-0.265025\pi$
$450$	−4.00000			−0.188562
$451$		0			0
$452$	−9.00000			−0.423324
$453$	−4.94427	−	15.2169i	−0.232302	−	0.714953i
$454$		0			0
$455$	24.2705	−	17.6336i	1.13782	−	0.826674i
$456$	1.23607	−	3.80423i	0.0578842	−	0.178149i
$457$	−0.309017	+	0.951057i	−0.0144552	+	0.0444885i	−0.958024	−	0.286688i	$-0.907446\pi$
$457$	−0.309017	+	0.951057i	−0.0144552	+	0.0444885i	0.943569	+	0.331177i	$0.107446\pi$
$458$	4.04508	−	2.93893i	0.189014	−	0.137327i
$459$	−9.70820	−	7.05342i	−0.453140	−	0.329226i
$460$	−5.56231	−	17.1190i	−0.259344	−	0.798178i
$461$	21.0000			0.978068			0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000			0.978068			0.489034	+	0.872265i	$0.337349\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−0.927051	−	2.85317i	−0.0430373	−	0.132455i
$465$	−9.70820	−	7.05342i	−0.450207	−	0.327095i
$466$	−16.9894	+	12.3435i	−0.787017	+	0.571801i
$467$	−3.70820	+	11.4127i	−0.171595	+	0.528116i	−0.999462	−	0.0328096i	$-0.989555\pi$
$467$	−3.70820	+	11.4127i	−0.171595	+	0.528116i	0.827866	+	0.560925i	$0.189555\pi$
$468$	1.54508	−	4.75528i	0.0714216	−	0.219813i
$469$	16.1803	−	11.7557i	0.747139	−	0.542828i
$470$	−14.5623	−	10.5801i	−0.671709	−	0.488025i
$471$	−1.23607	−	3.80423i	−0.0569550	−	0.175289i
$472$		0			0
$473$		0			0
$474$	4.00000			0.183726
$475$	2.47214	+	7.60845i	0.113429	+	0.349100i
$476$	−4.85410	−	3.52671i	−0.222487	−	0.161647i
$477$	2.42705	−	1.76336i	0.111127	−	0.0807385i
$478$	9.27051	−	28.5317i	0.424023	−	1.30501i
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$	4.85410	−	3.52671i	0.221558	−	0.160972i
$481$	28.3156	+	20.5725i	1.29108	+	0.938025i
$482$	3.09017	+	9.51057i	0.140753	+	0.433194i
$483$	−24.0000			−1.09204
$484$		0			0
$485$	−33.0000			−1.49845
$486$	−3.09017	−	9.51057i	−0.140173	−	0.431408i
$487$	27.5066	+	19.9847i	1.24644	+	0.905593i	0.998010	−	0.0630562i	$-0.0200847\pi$
$487$	27.5066	+	19.9847i	1.24644	+	0.905593i	0.248432	+	0.968649i	$0.420085\pi$
$488$	−8.09017	+	5.87785i	−0.366225	+	0.266078i
$489$	13.5967	−	41.8465i	0.614866	−	1.89236i
$490$	−2.78115	+	8.55951i	−0.125640	+	0.386679i
$491$	24.2705	−	17.6336i	1.09531	−	0.795791i	0.115024	−	0.993363i	$-0.463305\pi$
$491$	24.2705	−	17.6336i	1.09531	−	0.795791i	0.980289	+	0.197571i	$0.0633054\pi$
$492$	4.85410	+	3.52671i	0.218840	+	0.158996i
$493$	−2.78115	−	8.55951i	−0.125257	−	0.385501i
$494$	−10.0000			−0.449921
$495$		0			0
$496$	2.00000			0.0898027
$497$	7.41641	+	22.8254i	0.332671	+	1.02386i
$498$	−29.1246	−	21.1603i	−1.30511	−	0.948214i
$499$	12.9443	−	9.40456i	0.579465	−	0.421006i	−0.259066	−	0.965860i	$-0.583415\pi$
$499$	12.9443	−	9.40456i	0.579465	−	0.421006i	0.838531	+	0.544853i	$0.183415\pi$
$500$	0.927051	−	2.85317i	0.0414590	−	0.127598i
$501$	7.41641	−	22.8254i	0.331341	−	1.01976i
$502$	14.5623	−	10.5801i	0.649948	−	0.472215i
$503$	−24.2705	−	17.6336i	−1.08217	−	0.786241i	−0.104109	−	0.994566i	$-0.533199\pi$
$503$	−24.2705	−	17.6336i	−1.08217	−	0.786241i	−0.978060	+	0.208324i	$0.933199\pi$
$504$	−0.618034	−	1.90211i	−0.0275294	−	0.0847268i
$505$	−18.0000			−0.800989
$506$		0			0
$507$	−24.0000			−1.06588
$508$	2.47214	+	7.60845i	0.109683	+	0.337570i
$509$	−4.85410	−	3.52671i	−0.215154	−	0.156319i	0.474988	−	0.879992i	$-0.342452\pi$
$509$	−4.85410	−	3.52671i	−0.215154	−	0.156319i	−0.690143	+	0.723673i	$0.742452\pi$
$510$	14.5623	−	10.5801i	0.644830	−	0.468496i
$511$	8.65248	−	26.6296i	0.382763	−	1.17802i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−6.47214	+	4.70228i	−0.285752	+	0.207611i
$514$	2.42705	+	1.76336i	0.107053	+	0.0777783i
$515$	−7.41641	−	22.8254i	−0.326806	−	1.00581i
$516$	−16.0000			−0.704361
$517$		0			0
$518$	14.0000			0.615125
$519$	−3.70820	−	11.4127i	−0.162772	−	0.500961i
$520$	−12.1353	−	8.81678i	−0.532166	−	0.386641i
$521$	14.5623	−	10.5801i	0.637986	−	0.463524i	−0.221172	−	0.975235i	$-0.570988\pi$
$521$	14.5623	−	10.5801i	0.637986	−	0.463524i	0.859158	+	0.511711i	$0.170988\pi$
$522$	0.927051	−	2.85317i	0.0405759	−	0.124880i
$523$	−4.94427	+	15.2169i	−0.216198	+	0.665389i	0.782868	+	0.622187i	$0.213756\pi$
$523$	−4.94427	+	15.2169i	−0.216198	+	0.665389i	−0.999066	+	0.0432015i	$0.986244\pi$
$524$		0			0
$525$	12.9443	+	9.40456i	0.564934	+	0.410449i
$526$	−1.85410	−	5.70634i	−0.0808427	−	0.248808i
$527$	6.00000			0.261364
$528$		0			0
$529$	13.0000			0.565217
$530$	−2.78115	−	8.55951i	−0.120806	−	0.371801i
$531$		0			0
$532$	−3.23607	+	2.35114i	−0.140301	+	0.101935i
$533$	4.63525	−	14.2658i	0.200775	−	0.617922i
$534$	−5.56231	+	17.1190i	−0.240705	+	0.740812i
$535$	−14.5623	+	10.5801i	−0.629583	+	0.457419i
$536$	−8.09017	−	5.87785i	−0.349442	−	0.253885i
$537$		0			0
$538$	3.00000			0.129339
$539$		0			0
$540$	−12.0000			−0.516398
$541$	0.618034	+	1.90211i	0.0265714	+	0.0817782i	0.963463	−	0.267842i	$-0.0863106\pi$
$541$	0.618034	+	1.90211i	0.0265714	+	0.0817782i	−0.936891	+	0.349620i	$0.886311\pi$
$542$	16.1803	+	11.7557i	0.695005	+	0.504951i
$543$	8.09017	−	5.87785i	0.347182	−	0.252243i
$544$	−0.927051	+	2.85317i	−0.0397470	+	0.122329i
$545$	−15.7599	+	48.5039i	−0.675079	+	2.07768i
$546$	−16.1803	+	11.7557i	−0.692455	+	0.503098i
$547$	−6.47214	−	4.70228i	−0.276729	−	0.201055i	0.440761	−	0.897625i	$-0.354709\pi$
$547$	−6.47214	−	4.70228i	−0.276729	−	0.201055i	−0.717489	+	0.696570i	$0.754709\pi$
$548$	1.85410	+	5.70634i	0.0792033	+	0.243763i
$549$	−10.0000			−0.426790
$550$		0			0
$551$	−6.00000			−0.255609
$552$	3.70820	+	11.4127i	0.157832	+	0.485756i
$553$	−3.23607	−	2.35114i	−0.137612	−	0.0999807i
$554$	4.04508	−	2.93893i	0.171859	−	0.124863i
$555$	−12.9787	+	39.9444i	−0.550916	+	1.69554i
$556$	−6.79837	+	20.9232i	−0.288315	+	0.887343i
$557$	14.5623	−	10.5801i	0.617025	−	0.448295i	−0.234856	−	0.972030i	$-0.575462\pi$
$557$	14.5623	−	10.5801i	0.617025	−	0.448295i	0.851881	+	0.523735i	$0.175462\pi$
$558$	1.61803	+	1.17557i	0.0684968	+	0.0497659i
$559$	12.3607	+	38.0423i	0.522801	+	1.60902i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	−6.00000			−0.253095
$563$	−12.9787	−	39.9444i	−0.546988	−	1.68345i	−0.716217	−	0.697878i	$-0.754128\pi$
$563$	−12.9787	−	39.9444i	−0.546988	−	1.68345i	0.169229	−	0.985577i	$-0.445872\pi$
$564$	9.70820	+	7.05342i	0.408789	+	0.297003i
$565$	−21.8435	+	15.8702i	−0.918961	+	0.667664i
$566$	−6.18034	+	19.0211i	−0.259779	+	0.799518i
$567$	−6.79837	+	20.9232i	−0.285505	+	0.878694i
$568$	9.70820	−	7.05342i	0.407347	−	0.295955i
$569$	−4.85410	−	3.52671i	−0.203495	−	0.147847i	0.481371	−	0.876517i	$-0.340139\pi$
$569$	−4.85410	−	3.52671i	−0.203495	−	0.147847i	−0.684865	+	0.728670i	$0.740139\pi$
$570$	−3.70820	−	11.4127i	−0.155320	−	0.478024i
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$		0			0
$573$		0			0
$574$	−1.85410	−	5.70634i	−0.0773887	−	0.238178i
$575$	−19.4164	−	14.1068i	−0.809720	−	0.588296i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	3.39919	−	10.4616i	0.141510	−	0.435523i	−0.855036	−	0.518569i	$-0.826465\pi$
$577$	3.39919	−	10.4616i	0.141510	−	0.435523i	0.996546	+	0.0830461i	$0.0264649\pi$
$578$	2.47214	−	7.60845i	0.102827	−	0.316470i
$579$	−21.0344	+	15.2824i	−0.874162	+	0.635116i
$580$	−7.28115	−	5.29007i	−0.302333	−	0.219658i
$581$	11.1246	+	34.2380i	0.461527	+	1.42043i
$582$	22.0000			0.911929
$583$		0			0
$584$	−14.0000			−0.579324
$585$	−4.63525	−	14.2658i	−0.191644	−	0.589820i
$586$	16.9894	+	12.3435i	0.701824	+	0.509905i
$587$	14.5623	−	10.5801i	0.601051	−	0.436689i	−0.245201	−	0.969472i	$-0.578854\pi$
$587$	14.5623	−	10.5801i	0.601051	−	0.436689i	0.846252	+	0.532783i	$0.178854\pi$
$588$	1.85410	−	5.70634i	0.0764619	−	0.235325i
$589$	1.23607	−	3.80423i	0.0509313	−	0.156750i
$590$		0			0
$591$	−24.2705	−	17.6336i	−0.998355	−	0.725348i
$592$	−2.16312	−	6.65740i	−0.0889036	−	0.273617i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	−0.927051	−	2.85317i	−0.0379735	−	0.116870i
$597$	−25.8885	−	18.8091i	−1.05955	−	0.769806i
$598$	24.2705	−	17.6336i	0.992495	−	0.721090i
$599$	−12.9787	+	39.9444i	−0.530296	+	1.63208i	0.223304	+	0.974749i	$0.428316\pi$
$599$	−12.9787	+	39.9444i	−0.530296	+	1.63208i	−0.753599	+	0.657334i	$0.771684\pi$
$600$	2.47214	−	7.60845i	0.100925	−	0.310614i
$601$	10.5172	−	7.64121i	0.429006	−	0.311691i	−0.352245	−	0.935908i	$-0.614582\pi$
$601$	10.5172	−	7.64121i	0.429006	−	0.311691i	0.781251	+	0.624216i	$0.214582\pi$
$602$	12.9443	+	9.40456i	0.527569	+	0.383301i
$603$	−3.09017	−	9.51057i	−0.125841	−	0.387300i
$604$	8.00000			0.325515
$605$		0			0
$606$	12.0000			0.487467
$607$	−6.79837	−	20.9232i	−0.275937	−	0.849248i	−0.988970	−	0.148117i	$-0.952679\pi$
$607$	−6.79837	−	20.9232i	−0.275937	−	0.849248i	0.713032	−	0.701131i	$-0.247321\pi$
$608$	1.61803	+	1.17557i	0.0656199	+	0.0476757i
$609$	−9.70820	+	7.05342i	−0.393396	+	0.285819i
$610$	−9.27051	+	28.5317i	−0.375352	+	1.15521i
$611$	9.27051	−	28.5317i	0.375045	−	1.15427i
$612$	−2.42705	+	1.76336i	−0.0981077	+	0.0712794i
$613$	−4.04508	−	2.93893i	−0.163379	−	0.118702i	0.503091	−	0.864233i	$-0.332196\pi$
$613$	−4.04508	−	2.93893i	−0.163379	−	0.118702i	−0.666471	+	0.745531i	$0.732196\pi$
$614$	3.09017	+	9.51057i	0.124709	+	0.383815i
$615$	18.0000			0.725830
$616$		0			0
$617$	39.0000			1.57008			0.785040	−	0.619445i	$-0.212642\pi$
$617$	39.0000			1.57008			0.785040	+	0.619445i	$0.212642\pi$
$618$	4.94427	+	15.2169i	0.198888	+	0.612114i
$619$	8.09017	+	5.87785i	0.325171	+	0.236251i	0.738379	−	0.674386i	$-0.235592\pi$
$619$	8.09017	+	5.87785i	0.325171	+	0.236251i	−0.413208	+	0.910637i	$0.635592\pi$
$620$	4.85410	−	3.52671i	0.194945	−	0.141636i
$621$	7.41641	−	22.8254i	0.297610	−	0.915950i
$622$		0			0
$623$	14.5623	−	10.5801i	0.583426	−	0.423884i
$624$	8.09017	+	5.87785i	0.323866	+	0.235302i
$625$	−8.96149	−	27.5806i	−0.358460	−	1.10323i
$626$	1.00000			0.0399680
$627$		0			0
$628$	2.00000			0.0798087
$629$	−6.48936	−	19.9722i	−0.258748	−	0.796343i
$630$	−4.85410	−	3.52671i	−0.193392	−	0.140508i
$631$	−30.7426	+	22.3358i	−1.22385	+	0.889176i	−0.996413	−	0.0846182i	$-0.973033\pi$
$631$	−30.7426	+	22.3358i	−1.22385	+	0.889176i	−0.227432	+	0.973794i	$0.573033\pi$
$632$	−0.618034	+	1.90211i	−0.0245841	+	0.0756620i
$633$	2.47214	−	7.60845i	0.0982586	−	0.302409i
$634$	−14.5623	+	10.5801i	−0.578343	+	0.420191i
$635$	19.4164	+	14.1068i	0.770517	+	0.559813i
$636$	1.85410	+	5.70634i	0.0735199	+	0.226271i
$637$	−15.0000			−0.594322
$638$		0			0
$639$	12.0000			0.474713
$640$	0.927051	+	2.85317i	0.0366449	+	0.112781i
$641$	26.6976	+	19.3969i	1.05449	+	0.766132i	0.973061	−	0.230547i	$-0.0740516\pi$
$641$	26.6976	+	19.3969i	1.05449	+	0.766132i	0.0814291	+	0.996679i	$0.474052\pi$
$642$	9.70820	−	7.05342i	0.383152	−	0.278376i
$643$	0.618034	−	1.90211i	0.0243729	−	0.0750120i	−0.938130	−	0.346283i	$-0.887444\pi$
$643$	0.618034	−	1.90211i	0.0243729	−	0.0750120i	0.962503	+	0.271271i	$0.0874438\pi$
$644$	3.70820	−	11.4127i	0.146124	−	0.449723i
$645$	−38.8328	+	28.2137i	−1.52904	+	1.11091i
$646$	4.85410	+	3.52671i	0.190982	+	0.138757i
$647$	−3.70820	−	11.4127i	−0.145785	−	0.448679i	0.851327	−	0.524636i	$-0.175799\pi$
$647$	−3.70820	−	11.4127i	−0.145785	−	0.448679i	−0.997111	+	0.0759575i	$0.975799\pi$
$648$	11.0000			0.432121
$649$		0			0
$650$	−20.0000			−0.784465
$651$	−2.47214	−	7.60845i	−0.0968906	−	0.298199i
$652$	17.7984	+	12.9313i	0.697038	+	0.506428i
$653$	−14.5623	+	10.5801i	−0.569867	+	0.414033i	−0.835057	−	0.550164i	$-0.814565\pi$
$653$	−14.5623	+	10.5801i	−0.569867	+	0.414033i	0.265190	+	0.964196i	$0.414565\pi$
$654$	10.5066	−	32.3359i	0.410840	−	1.26443i
$655$		0			0
$656$	−2.42705	+	1.76336i	−0.0947604	+	0.0688475i
$657$	−11.3262	−	8.22899i	−0.441879	−	0.321044i
$658$	−3.70820	−	11.4127i	−0.144561	−	0.444913i
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	17.0000			0.661223			0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000			0.661223			0.330612	+	0.943767i	$0.392745\pi$
$662$	−6.18034	−	19.0211i	−0.240206	−	0.739277i
$663$	24.2705	+	17.6336i	0.942588	+	0.684831i
$664$	14.5623	−	10.5801i	0.565127	−	0.410589i
$665$	−3.70820	+	11.4127i	−0.143798	+	0.442565i
$666$	2.16312	−	6.65740i	0.0838192	−	0.257969i
$667$	14.5623	−	10.5801i	0.563855	−	0.409664i
$668$	9.70820	+	7.05342i	0.375622	+	0.272905i
$669$	2.47214	+	7.60845i	0.0955783	+	0.294160i
$670$	−30.0000			−1.15900
$671$		0			0
$672$	4.00000			0.154303
$673$	11.7426	+	36.1401i	0.452646	+	1.39310i	0.873877	+	0.486147i	$0.161598\pi$
$673$	11.7426	+	36.1401i	0.452646	+	1.39310i	−0.421231	+	0.906953i	$0.638402\pi$
$674$	−10.5172	−	7.64121i	−0.405108	−	0.294328i
$675$	−12.9443	+	9.40456i	−0.498225	+	0.361982i
$676$	3.70820	−	11.4127i	0.142623	−	0.438949i
$677$	−4.63525	+	14.2658i	−0.178147	+	0.548281i	−0.999763	−	0.0217604i	$-0.993073\pi$
$677$	−4.63525	+	14.2658i	−0.178147	+	0.548281i	0.821616	+	0.570042i	$0.193073\pi$
$678$	14.5623	−	10.5801i	0.559262	−	0.406328i
$679$	−17.7984	−	12.9313i	−0.683039	−	0.496257i
$680$	2.78115	+	8.55951i	0.106652	+	0.328242i
$681$		0			0
$682$		0			0
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$	0.618034	+	1.90211i	0.0236311	+	0.0727291i
$685$	14.5623	+	10.5801i	0.556397	+	0.404246i
$686$	−16.1803	+	11.7557i	−0.617768	+	0.448835i
$687$	−3.09017	+	9.51057i	−0.117897	+	0.362851i
$688$	2.47214	−	7.60845i	0.0942493	−	0.290070i
$689$	12.1353	−	8.81678i	0.462316	−	0.335893i
$690$	29.1246	+	21.1603i	1.10876	+	0.805558i
$691$	−1.23607	−	3.80423i	−0.0470222	−	0.144720i	0.924789	−	0.380481i	$-0.124242\pi$
$691$	−1.23607	−	3.80423i	−0.0470222	−	0.144720i	−0.971811	+	0.235762i	$0.924242\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−36.0000			−1.36654
$695$	20.3951	+	62.7697i	0.773631	+	2.38099i
$696$	4.85410	+	3.52671i	0.183994	+	0.133680i
$697$	−7.28115	+	5.29007i	−0.275793	+	0.200376i
$698$	−5.25329	+	16.1680i	−0.198840	+	0.611966i
$699$	12.9787	−	39.9444i	0.490900	−	1.51083i
$700$	−6.47214	+	4.70228i	−0.244624	+	0.177730i
$701$	21.8435	+	15.8702i	0.825016	+	0.599409i	0.918145	−	0.396245i	$-0.129687\pi$
$701$	21.8435	+	15.8702i	0.825016	+	0.599409i	−0.0931288	+	0.995654i	$0.529687\pi$
$702$	−6.18034	−	19.0211i	−0.233262	−	0.717906i
$703$	−14.0000			−0.528020
$704$		0			0
$705$	36.0000			1.35584
$706$	2.78115	+	8.55951i	0.104670	+	0.322141i
$707$	−9.70820	−	7.05342i	−0.365115	−	0.265271i
$708$		0			0
$709$	−3.09017	+	9.51057i	−0.116054	+	0.357177i	−0.992165	−	0.124932i	$-0.960129\pi$
$709$	−3.09017	+	9.51057i	−0.116054	+	0.357177i	0.876112	+	0.482108i	$0.160129\pi$
$710$	11.1246	−	34.2380i	0.417499	−	1.28493i
$711$	−1.61803	+	1.17557i	−0.0606810	+	0.0440873i
$712$	−7.28115	−	5.29007i	−0.272873	−	0.198254i
$713$	3.70820	+	11.4127i	0.138873	+	0.427408i
$714$	12.0000			0.449089
$715$		0			0
$716$		0			0
$717$	18.5410	+	57.0634i	0.692427	+	2.13107i
$718$	14.5623	+	10.5801i	0.543460	+	0.394847i
$719$	−14.5623	+	10.5801i	−0.543082	+	0.394572i	−0.825229	−	0.564799i	$-0.808954\pi$
$719$	−14.5623	+	10.5801i	−0.543082	+	0.394572i	0.282146	+	0.959371i	$0.408954\pi$
$720$	−0.927051	+	2.85317i	−0.0345492	+	0.106331i
$721$	4.94427	−	15.2169i	0.184134	−	0.566707i
$722$	−12.1353	+	8.81678i	−0.451627	+	0.328127i
$723$	−16.1803	−	11.7557i	−0.601753	−	0.437199i
$724$	1.54508	+	4.75528i	0.0574226	+	0.176729i
$725$	−12.0000			−0.445669
$726$		0			0
$727$	26.0000			0.964287			0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000			0.964287			0.482143	+	0.876092i	$0.339858\pi$
$728$	−3.09017	−	9.51057i	−0.114529	−	0.352485i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	−33.9787	+	24.6870i	−1.25761	+	0.913706i
$731$	7.41641	−	22.8254i	0.274306	−	0.844226i
$732$	6.18034	−	19.0211i	0.228432	−	0.703041i
$733$	−4.04508	+	2.93893i	−0.149409	+	0.108552i	−0.659978	−	0.751285i	$-0.729435\pi$
$733$	−4.04508	+	2.93893i	−0.149409	+	0.108552i	0.510570	+	0.859836i	$0.329435\pi$
$734$	−8.09017	−	5.87785i	−0.298614	−	0.216955i
$735$	−5.56231	−	17.1190i	−0.205169	−	0.631444i
$736$	−6.00000			−0.221163
$737$		0			0
$738$	−3.00000			−0.110432
$739$	8.03444	+	24.7275i	0.295552	+	0.909615i	0.983036	+	0.183415i	$0.0587152\pi$
$739$	8.03444	+	24.7275i	0.295552	+	0.909615i	−0.687484	+	0.726200i	$0.741285\pi$
$740$	−16.9894	−	12.3435i	−0.624541	−	0.453756i
$741$	16.1803	−	11.7557i	0.594400	−	0.431857i
$742$	1.85410	−	5.70634i	0.0680662	−	0.209486i
$743$	−5.56231	+	17.1190i	−0.204061	+	0.628036i	0.795689	+	0.605705i	$0.207109\pi$
$743$	−5.56231	+	17.1190i	−0.204061	+	0.628036i	−0.999751	+	0.0223310i	$0.992891\pi$
$744$	−3.23607	+	2.35114i	−0.118640	+	0.0861970i
$745$	−7.28115	−	5.29007i	−0.266761	−	0.193813i
$746$	3.09017	+	9.51057i	0.113139	+	0.348207i
$747$	18.0000			0.658586
$748$		0			0
$749$	−12.0000			−0.438470
$750$	1.85410	+	5.70634i	0.0677022	+	0.208366i
$751$	−35.5967	−	25.8626i	−1.29894	−	0.943738i	−0.298999	−	0.954253i	$-0.596653\pi$
$751$	−35.5967	−	25.8626i	−1.29894	−	0.943738i	−0.999945	+	0.0105155i	$0.996653\pi$
$752$	−4.85410	+	3.52671i	−0.177011	+	0.128606i
$753$	−11.1246	+	34.2380i	−0.405403	+	1.24770i
$754$	4.63525	−	14.2658i	0.168806	−	0.519532i
$755$	19.4164	−	14.1068i	0.706635	−	0.513401i
$756$	−6.47214	−	4.70228i	−0.235389	−	0.171020i
$757$	12.6697	+	38.9933i	0.460488	+	1.41724i	0.864570	+	0.502513i	$0.167591\pi$
$757$	12.6697	+	38.9933i	0.460488	+	1.41724i	−0.404082	+	0.914723i	$0.632409\pi$
$758$	16.0000			0.581146
$759$		0			0
$760$	6.00000			0.217643
$761$	0.927051	+	2.85317i	0.0336056	+	0.103427i	0.966452	−	0.256846i	$-0.0826834\pi$
$761$	0.927051	+	2.85317i	0.0336056	+	0.103427i	−0.932847	+	0.360273i	$0.882683\pi$
$762$	−12.9443	−	9.40456i	−0.468921	−	0.340691i
$763$	−27.5066	+	19.9847i	−0.995805	+	0.723495i
$764$		0			0
$765$	−2.78115	+	8.55951i	−0.100553	+	0.309470i
$766$	9.70820	−	7.05342i	0.350772	−	0.254851i
$767$		0			0
$768$	−0.618034	−	1.90211i	−0.0223014	−	0.0686366i
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	−4.01722	−	12.3637i	−0.144583	−	0.444981i
$773$	33.9787	+	24.6870i	1.22213	+	0.887929i	0.996275	−	0.0862321i	$-0.0274827\pi$
$773$	33.9787	+	24.6870i	1.22213	+	0.887929i	0.225854	+	0.974161i	$0.427483\pi$
$774$	6.47214	−	4.70228i	0.232636	−	0.169020i
$775$	2.47214	−	7.60845i	0.0888017	−	0.273304i
$776$	−3.39919	+	10.4616i	−0.122024	+	0.375550i
$777$	−22.6525	+	16.4580i	−0.812653	+	0.590427i
$778$	26.6976	+	19.3969i	0.957154	+	0.695413i
$779$	1.85410	+	5.70634i	0.0664301	+	0.204451i
$780$	30.0000			1.07417
$781$		0			0
$782$	−18.0000			−0.643679
$783$	−3.70820	−	11.4127i	−0.132520	−	0.407856i
$784$	2.42705	+	1.76336i	0.0866804	+	0.0629770i
$785$	4.85410	−	3.52671i	0.173250	−	0.125874i
$786$		0			0
$787$	−1.23607	+	3.80423i	−0.0440611	+	0.135606i	−0.970667	−	0.240428i	$-0.922712\pi$
$787$	−1.23607	+	3.80423i	−0.0440611	+	0.135606i	0.926606	+	0.376034i	$0.122712\pi$
$788$	12.1353	−	8.81678i	0.432301	−	0.314085i
$789$	9.70820	+	7.05342i	0.345621	+	0.251109i
$790$	1.85410	+	5.70634i	0.0659660	+	0.203022i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	−50.0000			−1.77555
$794$	−5.25329	−	16.1680i	−0.186432	−	0.573779i
$795$	14.5623	+	10.5801i	0.516472	+	0.375239i
$796$	12.9443	−	9.40456i	0.458798	−	0.333336i
$797$	−12.9787	+	39.9444i	−0.459730	+	1.41490i	0.405762	+	0.913979i	$0.367006\pi$
$797$	−12.9787	+	39.9444i	−0.459730	+	1.41490i	−0.865492	+	0.500924i	$0.832994\pi$
$798$	2.47214	−	7.60845i	0.0875127	−	0.269336i
$799$	−14.5623	+	10.5801i	−0.515177	+	0.374298i
$800$	3.23607	+	2.35114i	0.114412	+	0.0831254i
$801$	−2.78115	−	8.55951i	−0.0982672	−	0.302435i
$802$	33.0000			1.16527
$803$		0			0
$804$	20.0000			0.705346
$805$	−11.1246	−	34.2380i	−0.392091	−	1.20673i
$806$	8.09017	+	5.87785i	0.284964	+	0.207039i
$807$	−4.85410	+	3.52671i	−0.170872	+	0.124146i
$808$	−1.85410	+	5.70634i	−0.0652271	+	0.200748i
$809$	1.85410	−	5.70634i	0.0651868	−	0.200624i	−0.913158	−	0.407605i	$-0.866364\pi$
$809$	1.85410	−	5.70634i	0.0651868	−	0.200624i	0.978345	+	0.206981i	$0.0663639\pi$
$810$	26.6976	−	19.3969i	0.938057	−	0.681538i
$811$	22.6525	+	16.4580i	0.795436	+	0.577918i	0.909572	−	0.415547i	$-0.136410\pi$
$811$	22.6525	+	16.4580i	0.795436	+	0.577918i	−0.114136	+	0.993465i	$0.536410\pi$
$812$	−1.85410	−	5.70634i	−0.0650662	−	0.200253i
$813$	−40.0000			−1.40286
$814$		0			0
$815$	66.0000			2.31188
$816$	−1.85410	−	5.70634i	−0.0649066	−	0.199762i
$817$	−12.9443	−	9.40456i	−0.452863	−	0.329024i
$818$	−10.5172	+	7.64121i	−0.367726	+	0.267169i
$819$	3.09017	−	9.51057i	0.107979	−	0.332326i
$820$	−2.78115	+	8.55951i	−0.0971221	+	0.298911i
$821$	−24.2705	+	17.6336i	−0.847047	+	0.615415i	−0.924330	−	0.381594i	$-0.875375\pi$
$821$	−24.2705	+	17.6336i	−0.847047	+	0.615415i	0.0772835	+	0.997009i	$0.475375\pi$
$822$	−9.70820	−	7.05342i	−0.338612	−	0.246016i
$823$	9.88854	+	30.4338i	0.344693	+	1.06086i	0.961748	+	0.273936i	$0.0883256\pi$
$823$	9.88854	+	30.4338i	0.344693	+	1.06086i	−0.617055	+	0.786920i	$0.711674\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$		0			0
$827$	5.56231	+	17.1190i	0.193420	+	0.595287i	0.999991	+	0.00414942i	$0.00132080\pi$
$827$	5.56231	+	17.1190i	0.193420	+	0.595287i	−0.806571	+	0.591137i	$0.798679\pi$
$828$	−4.85410	−	3.52671i	−0.168692	−	0.122562i
$829$	34.7877	−	25.2748i	1.20823	−	0.877829i	0.213159	−	0.977017i	$-0.431625\pi$
$829$	34.7877	−	25.2748i	1.20823	−	0.877829i	0.995069	+	0.0991886i	$0.0316247\pi$
$830$	16.6869	−	51.3571i	0.579211	−	1.78263i
$831$	−3.09017	+	9.51057i	−0.107197	+	0.329918i
$832$	−4.04508	+	2.93893i	−0.140238	+	0.101889i
$833$	7.28115	+	5.29007i	0.252277	+	0.183290i
$834$	−13.5967	−	41.8465i	−0.470817	−	1.44903i
$835$	36.0000			1.24583
$836$		0			0
$837$	8.00000			0.276520
$838$	5.56231	+	17.1190i	0.192147	+	0.591367i
$839$	−14.5623	−	10.5801i	−0.502747	−	0.365267i	0.307318	−	0.951607i	$-0.400568\pi$
$839$	−14.5623	−	10.5801i	−0.502747	−	0.365267i	−0.810065	+	0.586340i	$0.800568\pi$
$840$	9.70820	−	7.05342i	0.334965	−	0.243366i
$841$	−6.18034	+	19.0211i	−0.213115	+	0.655901i
$842$	−5.25329	+	16.1680i	−0.181040	+	0.557185i
$843$	9.70820	−	7.05342i	0.334368	−	0.242933i
$844$	3.23607	+	2.35114i	0.111390	+	0.0809296i
$845$	−11.1246	−	34.2380i	−0.382698	−	1.17782i
$846$	−6.00000			−0.206284
$847$		0			0
$848$	−3.00000			−0.103020
$849$	−12.3607	−	38.0423i	−0.424217	−	1.30561i
$850$	9.70820	+	7.05342i	0.332989	+	0.241930i
$851$	33.9787	−	24.6870i	1.16478	−	0.846259i
$852$	−7.41641	+	22.8254i	−0.254082	+	0.781984i
$853$	8.96149	−	27.5806i	0.306836	−	0.944343i	−0.672150	−	0.740415i	$-0.734629\pi$
$853$	8.96149	−	27.5806i	0.306836	−	0.944343i	0.978986	−	0.203928i	$-0.0653709\pi$
$854$	−16.1803	+	11.7557i	−0.553680	+	0.402272i
$855$	4.85410	+	3.52671i	0.166007	+	0.120611i
$856$	1.85410	+	5.70634i	0.0633719	+	0.195039i
$857$	−54.0000			−1.84460			−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000			−1.84460			−0.922302	+	0.386469i	$0.873695\pi$
$858$		0			0
$859$	32.0000			1.09183			0.545913	−	0.837842i	$-0.316183\pi$
$859$	32.0000			1.09183			0.545913	+	0.837842i	$0.316183\pi$
$860$	−7.41641	−	22.8254i	−0.252897	−	0.778338i
$861$	9.70820	+	7.05342i	0.330855	+	0.240380i
$862$	29.1246	−	21.1603i	0.991988	−	0.720722i
$863$	1.85410	−	5.70634i	0.0631144	−	0.194246i	−0.914527	−	0.404524i	$-0.867437\pi$
$863$	1.85410	−	5.70634i	0.0631144	−	0.194246i	0.977642	+	0.210278i	$0.0674370\pi$
$864$	−1.23607	+	3.80423i	−0.0420519	+	0.129422i
$865$	14.5623	−	10.5801i	0.495133	−	0.359735i
$866$	−29.9336	−	21.7481i	−1.01719	−	0.739029i
$867$	4.94427	+	15.2169i	0.167916	+	0.516793i
$868$	4.00000			0.135769
$869$		0			0
$870$	18.0000			0.610257
$871$	−15.4508	−	47.5528i	−0.523532	−	1.61127i
$872$	13.7533	+	9.99235i	0.465745	+	0.338384i
$873$	−8.89919	+	6.46564i	−0.301192	+	0.218829i
$874$	−3.70820	+	11.4127i	−0.125432	+	0.386040i
$875$	1.85410	−	5.70634i	0.0626801	−	0.192909i
$876$	22.6525	−	16.4580i	0.765356	−	0.556064i
$877$	−33.1697	−	24.0992i	−1.12006	−	0.813772i	−0.135843	−	0.990730i	$-0.543374\pi$
$877$	−33.1697	−	24.0992i	−1.12006	−	0.813772i	−0.984218	+	0.176958i	$0.943374\pi$
$878$	6.79837	+	20.9232i	0.229434	+	0.706125i
$879$	−42.0000			−1.41662
$880$		0			0
$881$	−45.0000			−1.51609			−0.758044	−	0.652203i	$-0.773845\pi$
$881$	−45.0000			−1.51609			−0.758044	+	0.652203i	$0.773845\pi$
$882$	0.927051	+	2.85317i	0.0312154	+	0.0960712i
$883$	3.23607	+	2.35114i	0.108902	+	0.0791222i	0.640904	−	0.767621i	$-0.278560\pi$
$883$	3.23607	+	2.35114i	0.108902	+	0.0791222i	−0.532001	+	0.846744i	$0.678560\pi$
$884$	−12.1353	+	8.81678i	−0.408153	+	0.296540i
$885$		0			0
$886$	−11.1246	+	34.2380i	−0.373739	+	1.15025i
$887$	14.5623	−	10.5801i	0.488954	−	0.355246i	−0.315828	−	0.948817i	$-0.602282\pi$
$887$	14.5623	−	10.5801i	0.488954	−	0.355246i	0.804782	+	0.593570i	$0.202282\pi$
$888$	11.3262	+	8.22899i	0.380084	+	0.276147i
$889$	4.94427	+	15.2169i	0.165826	+	0.510359i
$890$	−27.0000			−0.905042
$891$		0			0
$892$	−4.00000			−0.133930
$893$	3.70820	+	11.4127i	0.124090	+	0.381911i
$894$	4.85410	+	3.52671i	0.162345	+	0.117951i
$895$		0			0
$896$	−0.618034	+	1.90211i	−0.0206471	+	0.0635451i
$897$	−18.5410	+	57.0634i	−0.619067	+	1.90529i
$898$	−16.9894	+	12.3435i	−0.566942	+	0.411908i
$899$	4.85410	+	3.52671i	0.161893	+	0.117622i
$900$	1.23607	+	3.80423i	0.0412023	+	0.126808i
$901$	−9.00000			−0.299833
$902$		0			0
$903$	−32.0000			−1.06489
$904$	2.78115	+	8.55951i	0.0924998	+	0.284685i
$905$	12.1353	+	8.81678i	0.403390	+	0.293080i
$906$	−12.9443	+	9.40456i	−0.430045	+	0.312446i
$907$	13.5967	−	41.8465i	0.451473	−	1.38949i	−0.423754	−	0.905777i	$-0.639288\pi$
$907$	13.5967	−	41.8465i	0.451473	−	1.38949i	0.875227	−	0.483713i	$-0.160712\pi$
$908$		0			0
$909$	−4.85410	+	3.52671i	−0.161000	+	0.116974i
$910$	−24.2705	−	17.6336i	−0.804560	−	0.584547i
$911$	−7.41641	−	22.8254i	−0.245717	−	0.756238i	−0.995518	−	0.0945746i	$-0.969851\pi$
$911$	−7.41641	−	22.8254i	−0.245717	−	0.756238i	0.749801	−	0.661663i	$-0.230149\pi$
$912$	−4.00000			−0.132453
$913$		0			0
$914$	1.00000			0.0330771
$915$	−18.5410	−	57.0634i	−0.612947	−	1.88646i
$916$	−4.04508	−	2.93893i	−0.133653	−	0.0971049i
$917$		0			0
$918$	−3.70820	+	11.4127i	−0.122389	+	0.376675i
$919$	−8.65248	+	26.6296i	−0.285419	+	0.878429i	0.700854	+	0.713305i	$0.252802\pi$
$919$	−8.65248	+	26.6296i	−0.285419	+	0.878429i	−0.986273	+	0.165124i	$0.947198\pi$
$920$	−14.5623	+	10.5801i	−0.480105	+	0.348817i
$921$	−16.1803	−	11.7557i	−0.533160	−	0.387364i
$922$	−6.48936	−	19.9722i	−0.213716	−	0.657749i
$923$	60.0000			1.97492
$924$		0			0
$925$	−28.0000			−0.920634
$926$	1.23607	+	3.80423i	0.0406197	+	0.125015i
$927$	−6.47214	−	4.70228i	−0.212573	−	0.154443i
$928$	−2.42705	+	1.76336i	−0.0796719	+	0.0578850i
$929$	15.7599	−	48.5039i	0.517064	−	1.59136i	−0.262430	−	0.964951i	$-0.584524\pi$
$929$	15.7599	−	48.5039i	0.517064	−	1.59136i	0.779494	−	0.626410i	$-0.215476\pi$
$930$	−3.70820	+	11.4127i	−0.121597	+	0.374236i
$931$	4.85410	−	3.52671i	0.159087	−	0.115583i
$932$	16.9894	+	12.3435i	0.556505	+	0.404324i
$933$		0			0
$934$	12.0000			0.392652
$935$		0			0
$936$	−5.00000			−0.163430
$937$	7.10739	+	21.8743i	0.232188	+	0.714602i	0.997482	+	0.0709209i	$0.0225938\pi$
$937$	7.10739	+	21.8743i	0.232188	+	0.714602i	−0.765294	+	0.643681i	$0.777406\pi$
$938$	−16.1803	−	11.7557i	−0.528307	−	0.383837i
$939$	−1.61803	+	1.17557i	−0.0528025	+	0.0383633i
$940$	−5.56231	+	17.1190i	−0.181422	+	0.558361i
$941$	−12.0517	+	37.0912i	−0.392873	+	1.20914i	0.537733	+	0.843115i	$0.319281\pi$
$941$	−12.0517	+	37.0912i	−0.392873	+	1.20914i	−0.930606	+	0.366023i	$0.880719\pi$
$942$	−3.23607	+	2.35114i	−0.105437	+	0.0766043i
$943$	−14.5623	−	10.5801i	−0.474214	−	0.344537i
$944$		0			0
$945$	−24.0000			−0.780720
$946$		0			0
$947$	−30.0000			−0.974869			−0.487435	−	0.873160i	$-0.662067\pi$
$947$	−30.0000			−0.974869			−0.487435	+	0.873160i	$0.662067\pi$
$948$	−1.23607	−	3.80423i	−0.0401456	−	0.123556i
$949$	−56.6312	−	41.1450i	−1.83833	−	1.33562i
$950$	6.47214	−	4.70228i	0.209984	−	0.152562i
$951$	11.1246	−	34.2380i	0.360740	−	1.11024i
$952$	−1.85410	+	5.70634i	−0.0600918	+	0.184944i
$953$	−31.5517	+	22.9236i	−1.02206	+	0.742569i	−0.966704	−	0.255898i	$-0.917629\pi$
$953$	−31.5517	+	22.9236i	−1.02206	+	0.742569i	−0.0553547	+	0.998467i	$0.517629\pi$
$954$	−2.42705	−	1.76336i	−0.0785787	−	0.0570908i
$955$		0			0
$956$	−30.0000			−0.970269
$957$		0			0
$958$		0			0
$959$	3.70820	+	11.4127i	0.119744	+	0.368535i
$960$	−4.85410	−	3.52671i	−0.156665	−	0.113824i
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	10.8156	−	33.2870i	0.348709	−	1.07322i
$963$	−1.85410	+	5.70634i	−0.0597476	+	0.183884i
$964$	8.09017	−	5.87785i	0.260567	−	0.189313i
$965$	−31.5517	−	22.9236i	−1.01568	−	0.737938i
$966$	7.41641	+	22.8254i	0.238619	+	0.734394i
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$	10.1976	+	31.3849i	0.327424	+	1.00771i
$971$	−4.85410	−	3.52671i	−0.155776	−	0.113178i	0.507167	−	0.861848i	$-0.330693\pi$
$971$	−4.85410	−	3.52671i	−0.155776	−	0.113178i	−0.662943	+	0.748670i	$0.730693\pi$
$972$	−8.09017	+	5.87785i	−0.259492	+	0.188532i
$973$	−13.5967	+	41.8465i	−0.435892	+	1.34154i
$974$	10.5066	−	32.3359i	0.336652	−	1.03611i
$975$	32.3607	−	23.5114i	1.03637	−	0.752968i
$976$	8.09017	+	5.87785i	0.258960	+	0.188145i
$977$	−10.1976	−	31.3849i	−0.326249	−	1.00409i	−0.970874	−	0.239592i	$-0.922986\pi$
$977$	−10.1976	−	31.3849i	−0.326249	−	1.00409i	0.644625	−	0.764499i	$-0.277014\pi$
$978$	−44.0000			−1.40696
$979$		0			0
$980$	9.00000			0.287494
$981$	5.25329	+	16.1680i	0.167725	+	0.516203i
$982$	−24.2705	−	17.6336i	−0.774503	−	0.562709i
$983$	−48.5410	+	35.2671i	−1.54822	+	1.12485i	−0.603312	+	0.797505i	$0.706153\pi$
$983$	−48.5410	+	35.2671i	−1.54822	+	1.12485i	−0.944906	+	0.327341i	$0.893847\pi$
$984$	1.85410	−	5.70634i	0.0591066	−	0.181911i
$985$	13.9058	−	42.7975i	0.443075	−	1.36364i
$986$	−7.28115	+	5.29007i	−0.231879	+	0.168470i
$987$	19.4164	+	14.1068i	0.618031	+	0.449026i
$988$	3.09017	+	9.51057i	0.0983114	+	0.302571i
$989$	48.0000			1.52631
$990$		0			0
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$	−0.618034	−	1.90211i	−0.0196226	−	0.0603921i
$993$	32.3607	+	23.5114i	1.02694	+	0.746112i
$994$	19.4164	−	14.1068i	0.615851	−	0.447442i
$995$	14.8328	−	45.6507i	0.470232	−	1.44722i
$996$	−11.1246	+	34.2380i	−0.352497	+	1.08487i
$997$	25.0795	−	18.2213i	0.794277	−	0.577076i	−0.114953	−	0.993371i	$-0.536672\pi$
$997$	25.0795	−	18.2213i	0.794277	−	0.577076i	0.909230	+	0.416295i	$0.136672\pi$
$998$	−12.9443	−	9.40456i	−0.409744	−	0.297696i
$999$	−8.65248	−	26.6296i	−0.273752	−	0.842523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.c.e.27.1		4
11.2	odd	10		242.2.c.b.9.1		4
11.3	even	5		242.2.a.a.1.1	✓	1
11.4	even	5	inner	242.2.c.e.3.1		4
11.5	even	5	inner	242.2.c.e.81.1		4
11.6	odd	10		242.2.c.b.81.1		4
11.7	odd	10		242.2.c.b.3.1		4
11.8	odd	10		242.2.a.b.1.1	yes	1
11.9	even	5	inner	242.2.c.e.9.1		4
11.10	odd	2		242.2.c.b.27.1		4
33.8	even	10		2178.2.a.f.1.1		1
33.14	odd	10		2178.2.a.l.1.1		1
44.3	odd	10		1936.2.a.j.1.1		1
44.19	even	10		1936.2.a.k.1.1		1
55.14	even	10		6050.2.a.bl.1.1		1
55.19	odd	10		6050.2.a.s.1.1		1
88.3	odd	10		7744.2.a.g.1.1		1
88.19	even	10		7744.2.a.h.1.1		1
88.69	even	10		7744.2.a.bi.1.1		1
88.85	odd	10		7744.2.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.a.a.1.1	✓	1	11.3	even	5
242.2.a.b.1.1	yes	1	11.8	odd	10
242.2.c.b.3.1		4	11.7	odd	10
242.2.c.b.9.1		4	11.2	odd	10
242.2.c.b.27.1		4	11.10	odd	2
242.2.c.b.81.1		4	11.6	odd	10
242.2.c.e.3.1		4	11.4	even	5	inner
242.2.c.e.9.1		4	11.9	even	5	inner
242.2.c.e.27.1		4	1.1	even	1	trivial
242.2.c.e.81.1		4	11.5	even	5	inner
1936.2.a.j.1.1		1	44.3	odd	10
1936.2.a.k.1.1		1	44.19	even	10
2178.2.a.f.1.1		1	33.8	even	10
2178.2.a.l.1.1		1	33.14	odd	10
6050.2.a.s.1.1		1	55.19	odd	10
6050.2.a.bl.1.1		1	55.14	even	10
7744.2.a.g.1.1		1	88.3	odd	10
7744.2.a.h.1.1		1	88.19	even	10
7744.2.a.bh.1.1		1	88.85	odd	10
7744.2.a.bi.1.1		1	88.69	even	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.61803 + 1.17557i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.927051 + 2.85317i) q^{5} +(0.618034 - 1.90211i) q^{6} +(-1.61803 + 1.17557i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +3.00000 q^{10} -2.00000 q^{12} +(1.54508 + 4.75528i) q^{13} +(1.61803 + 1.17557i) q^{14} +(-4.85410 + 3.52671i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.927051 - 2.85317i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.61803 - 1.17557i) q^{19} +(-0.927051 - 2.85317i) q^{20} -4.00000 q^{21} +6.00000 q^{23} +(0.618034 + 1.90211i) q^{24} +(-3.23607 - 2.35114i) q^{25} +(4.04508 - 2.93893i) q^{26} +(1.23607 - 3.80423i) q^{27} +(0.618034 - 1.90211i) q^{28} +(2.42705 - 1.76336i) q^{29} +(4.85410 + 3.52671i) q^{30} +(0.618034 + 1.90211i) q^{31} -1.00000 q^{32} -3.00000 q^{34} +(-1.85410 - 5.70634i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(5.66312 - 4.11450i) q^{37} +(-0.618034 + 1.90211i) q^{38} +(-3.09017 + 9.51057i) q^{39} +(-2.42705 + 1.76336i) q^{40} +(-2.42705 - 1.76336i) q^{41} +(1.23607 + 3.80423i) q^{42} +8.00000 q^{43} -3.00000 q^{45} +(-1.85410 - 5.70634i) q^{46} +(-4.85410 - 3.52671i) q^{47} +(1.61803 - 1.17557i) q^{48} +(-0.927051 + 2.85317i) q^{49} +(-1.23607 + 3.80423i) q^{50} +(4.85410 - 3.52671i) q^{51} +(-4.04508 - 2.93893i) q^{52} +(-0.927051 - 2.85317i) q^{53} -4.00000 q^{54} -2.00000 q^{56} +(-1.23607 - 3.80423i) q^{57} +(-2.42705 - 1.76336i) q^{58} +(1.85410 - 5.70634i) q^{60} +(-3.09017 + 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{62} +(-1.61803 - 1.17557i) q^{63} +(0.309017 + 0.951057i) q^{64} -15.0000 q^{65} -10.0000 q^{67} +(0.927051 + 2.85317i) q^{68} +(9.70820 + 7.05342i) q^{69} +(-4.85410 + 3.52671i) q^{70} +(3.70820 - 11.4127i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(-5.66312 - 4.11450i) q^{74} +(-2.47214 - 7.60845i) q^{75} +2.00000 q^{76} +10.0000 q^{78} +(0.618034 + 1.90211i) q^{79} +(2.42705 + 1.76336i) q^{80} +(8.89919 - 6.46564i) q^{81} +(-0.927051 + 2.85317i) q^{82} +(5.56231 - 17.1190i) q^{83} +(3.23607 - 2.35114i) q^{84} +(7.28115 + 5.29007i) q^{85} +(-2.47214 - 7.60845i) q^{86} +6.00000 q^{87} -9.00000 q^{89} +(0.927051 + 2.85317i) q^{90} +(-8.09017 - 5.87785i) q^{91} +(-4.85410 + 3.52671i) q^{92} +(-1.23607 + 3.80423i) q^{93} +(-1.85410 + 5.70634i) q^{94} +(4.85410 - 3.52671i) q^{95} +(-1.61803 - 1.17557i) q^{96} +(3.39919 + 10.4616i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} + q^{8} - q^{9} + 12 q^{10} - 8 q^{12} - 5 q^{13} + 2 q^{14} - 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + 3 q^{20} - 16 q^{21} + 24 q^{23}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 + q^8 - q^9 + 12 * q^10 - 8 * q^12 - 5 * q^13 + 2 * q^14 - 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 + 3 * q^20 - 16 * q^21 + 24 * q^23 - 2 * q^24 - 4 * q^25 + 5 * q^26 - 4 * q^27 - 2 * q^28 + 3 * q^29 + 6 * q^30 - 2 * q^31 - 4 * q^32 - 12 * q^34 + 6 * q^35 - q^36 + 7 * q^37 + 2 * q^38 + 10 * q^39 - 3 * q^40 - 3 * q^41 - 4 * q^42 + 32 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 + 2 * q^48 + 3 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 3 * q^53 - 16 * q^54 - 8 * q^56 + 4 * q^57 - 3 * q^58 - 6 * q^60 + 10 * q^61 + 2 * q^62 - 2 * q^63 - q^64 - 60 * q^65 - 40 * q^67 - 3 * q^68 + 12 * q^69 - 6 * q^70 - 12 * q^71 + q^72 - 14 * q^73 - 7 * q^74 + 8 * q^75 + 8 * q^76 + 40 * q^78 - 2 * q^79 + 3 * q^80 + 11 * q^81 + 3 * q^82 - 18 * q^83 + 4 * q^84 + 9 * q^85 + 8 * q^86 + 24 * q^87 - 36 * q^89 - 3 * q^90 - 10 * q^91 - 6 * q^92 + 4 * q^93 + 6 * q^94 + 6 * q^95 - 2 * q^96 - 11 * q^97 + 12 * q^98

Introduction

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