LMFDB - Embedded newform 1785.2.g.f.1429.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1785,2,Mod(1429,1785)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1785, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1785.1429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1785 = 3 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1785.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.2532967608$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1429.4
Character	$\chi$	$=$	1785.1429
Dual form			1785.2.g.f.1429.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12979i q^{2} -1.00000i q^{3} -2.53601 q^{4} +(1.73253 - 1.41363i) q^{5} -2.12979 q^{6} -1.00000i q^{7} +1.14159i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.12979i q^{2} -1.00000i q^{3} -2.53601 q^{4} +(1.73253 - 1.41363i) q^{5} -2.12979 q^{6} -1.00000i q^{7} +1.14159i q^{8} -1.00000 q^{9} +(-3.01073 - 3.68993i) q^{10} +6.08436 q^{11} +2.53601i q^{12} +3.34615i q^{13} -2.12979 q^{14} +(-1.41363 - 1.73253i) q^{15} -2.64067 q^{16} -1.00000i q^{17} +2.12979i q^{18} -5.68386 q^{19} +(-4.39372 + 3.58497i) q^{20} -1.00000 q^{21} -12.9584i q^{22} -3.19691i q^{23} +1.14159 q^{24} +(1.00332 - 4.89830i) q^{25} +7.12660 q^{26} +1.00000i q^{27} +2.53601i q^{28} -3.03853 q^{29} +(-3.68993 + 3.01073i) q^{30} -6.43165 q^{31} +7.90726i q^{32} -6.08436i q^{33} -2.12979 q^{34} +(-1.41363 - 1.73253i) q^{35} +2.53601 q^{36} -9.98097i q^{37} +12.1054i q^{38} +3.34615 q^{39} +(1.61378 + 1.97784i) q^{40} -7.91628 q^{41} +2.12979i q^{42} +3.05110i q^{43} -15.4300 q^{44} +(-1.73253 + 1.41363i) q^{45} -6.80876 q^{46} -11.0828i q^{47} +2.64067i q^{48} -1.00000 q^{49} +(-10.4324 - 2.13687i) q^{50} -1.00000 q^{51} -8.48587i q^{52} -8.70174i q^{53} +2.12979 q^{54} +(10.5413 - 8.60101i) q^{55} +1.14159 q^{56} +5.68386i q^{57} +6.47144i q^{58} +11.7218 q^{59} +(3.58497 + 4.39372i) q^{60} +3.88529 q^{61} +13.6981i q^{62} +1.00000i q^{63} +11.5595 q^{64} +(4.73020 + 5.79730i) q^{65} -12.9584 q^{66} -3.91084i q^{67} +2.53601i q^{68} -3.19691 q^{69} +(-3.68993 + 3.01073i) q^{70} +4.02687 q^{71} -1.14159i q^{72} +10.6661i q^{73} -21.2574 q^{74} +(-4.89830 - 1.00332i) q^{75} +14.4143 q^{76} -6.08436i q^{77} -7.12660i q^{78} -4.37814 q^{79} +(-4.57504 + 3.73292i) q^{80} +1.00000 q^{81} +16.8600i q^{82} +15.5785i q^{83} +2.53601 q^{84} +(-1.41363 - 1.73253i) q^{85} +6.49820 q^{86} +3.03853i q^{87} +6.94585i q^{88} +15.0190 q^{89} +(3.01073 + 3.68993i) q^{90} +3.34615 q^{91} +8.10741i q^{92} +6.43165i q^{93} -23.6040 q^{94} +(-9.84747 + 8.03486i) q^{95} +7.90726 q^{96} +2.14419i q^{97} +2.12979i q^{98} -6.08436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9}+O(q^{10}) $ 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9	$ 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} - 4 q^{15} + 38 q^{16} + 12 q^{19} - 4 q^{20} - 28 q^{21} + 30 q^{24} - 8 q^{25} - 36 q^{26} - 2 q^{30} + 14 q^{31} - 6 q^{34} - 4 q^{35} + 34 q^{36} + 18 q^{39} - 62 q^{40} - 50 q^{41} - 24 q^{44} + 52 q^{46} - 28 q^{49} + 6 q^{50} - 28 q^{51} + 6 q^{54} - 14 q^{55} + 30 q^{56} + 44 q^{59} + 10 q^{60} + 26 q^{61} - 6 q^{64} + 20 q^{65} - 48 q^{66} + 38 q^{69} - 2 q^{70} + 12 q^{71} + 24 q^{74} - 16 q^{75} - 20 q^{76} - 8 q^{79} - 32 q^{80} + 28 q^{81} + 34 q^{84} - 4 q^{85} + 8 q^{86} + 84 q^{89} - 4 q^{90} + 18 q^{91} - 8 q^{94} + 4 q^{95} - 66 q^{96} - 8 q^{99}+O(q^{100}) $ 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 - 4 * q^15 + 38 * q^16 + 12 * q^19 - 4 * q^20 - 28 * q^21 + 30 * q^24 - 8 * q^25 - 36 * q^26 - 2 * q^30 + 14 * q^31 - 6 * q^34 - 4 * q^35 + 34 * q^36 + 18 * q^39 - 62 * q^40 - 50 * q^41 - 24 * q^44 + 52 * q^46 - 28 * q^49 + 6 * q^50 - 28 * q^51 + 6 * q^54 - 14 * q^55 + 30 * q^56 + 44 * q^59 + 10 * q^60 + 26 * q^61 - 6 * q^64 + 20 * q^65 - 48 * q^66 + 38 * q^69 - 2 * q^70 + 12 * q^71 + 24 * q^74 - 16 * q^75 - 20 * q^76 - 8 * q^79 - 32 * q^80 + 28 * q^81 + 34 * q^84 - 4 * q^85 + 8 * q^86 + 84 * q^89 - 4 * q^90 + 18 * q^91 - 8 * q^94 + 4 * q^95 - 66 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1785\mathbb{Z}\right)^\times$.

$n$	$596$	$766$	$1072$	$1261$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$		−	2.12979i		−	1.50599i	−0.658026	−	0.752995i	$-0.728608\pi$
$2$		−	2.12979i		−	1.50599i	0.658026	−	0.752995i	$-0.271392\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−2.53601			−1.26801
$5$	1.73253	−	1.41363i	0.774811	−	0.632193i
$5$	1.73253	−	1.41363i	0.774811	−	0.632193i
$6$	−2.12979			−0.869484
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.14159i			0.403614i
$9$	−1.00000			−0.333333
$10$	−3.01073	−	3.68993i	−0.952076	−	1.16686i
$11$	6.08436			1.83450			0.917251	−	0.398309i	$-0.130403\pi$
$11$	6.08436			1.83450			0.917251	+	0.398309i	$0.130403\pi$
$12$			2.53601i			0.732083i
$13$			3.34615i			0.928055i	0.885821	+	0.464027i	$0.153596\pi$
$13$			3.34615i			0.928055i	−0.885821	+	0.464027i	$0.846404\pi$
$14$	−2.12979			−0.569211
$15$	−1.41363	−	1.73253i	−0.364997	−	0.447337i
$16$	−2.64067			−0.660167
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$			2.12979i			0.501997i
$19$	−5.68386			−1.30397			−0.651984	−	0.758233i	$-0.726063\pi$
$19$	−5.68386			−1.30397			−0.651984	+	0.758233i	$0.726063\pi$
$20$	−4.39372	+	3.58497i	−0.982465	+	0.801624i
$21$	−1.00000			−0.218218
$22$		−	12.9584i		−	2.76274i
$23$		−	3.19691i		−	0.666603i	−0.942820	−	0.333301i	$-0.891837\pi$
$23$		−	3.19691i		−	0.666603i	0.942820	−	0.333301i	$-0.108163\pi$
$24$	1.14159			0.233027
$25$	1.00332	−	4.89830i	0.200664	−	0.979660i
$26$	7.12660			1.39764
$27$			1.00000i			0.192450i
$28$			2.53601i			0.479261i
$29$	−3.03853			−0.564241			−0.282121	−	0.959379i	$-0.591038\pi$
$29$	−3.03853			−0.564241			−0.282121	+	0.959379i	$0.591038\pi$
$30$	−3.68993	+	3.01073i	−0.673686	+	0.549681i
$31$	−6.43165			−1.15516			−0.577580	−	0.816334i	$-0.696003\pi$
$31$	−6.43165			−1.15516			−0.577580	+	0.816334i	$0.696003\pi$
$32$			7.90726i			1.39782i
$33$		−	6.08436i		−	1.05915i
$34$	−2.12979			−0.365256
$35$	−1.41363	−	1.73253i	−0.238946	−	0.292851i
$36$	2.53601			0.422669
$37$		−	9.98097i		−	1.64086i	−0.571746	−	0.820431i	$-0.693734\pi$
$37$		−	9.98097i		−	1.64086i	0.571746	−	0.820431i	$-0.306266\pi$
$38$			12.1054i			1.96376i
$39$	3.34615			0.535813
$40$	1.61378	+	1.97784i	0.255162	+	0.312724i
$41$	−7.91628			−1.23632			−0.618158	−	0.786054i	$-0.712121\pi$
$41$	−7.91628			−1.23632			−0.618158	+	0.786054i	$0.712121\pi$
$42$			2.12979i			0.328634i
$43$			3.05110i			0.465288i	0.972562	+	0.232644i	$0.0747377\pi$
$43$			3.05110i			0.465288i	−0.972562	+	0.232644i	$0.925262\pi$
$44$	−15.4300			−2.32616
$45$	−1.73253	+	1.41363i	−0.258270	+	0.210731i
$46$	−6.80876			−1.00390
$47$		−	11.0828i		−	1.61659i	−0.588778	−	0.808294i	$-0.700391\pi$
$47$		−	11.0828i		−	1.61659i	0.588778	−	0.808294i	$-0.299609\pi$
$48$			2.64067i			0.381148i
$49$	−1.00000			−0.142857
$50$	−10.4324	−	2.13687i	−1.47536	−	0.302199i
$51$	−1.00000			−0.140028
$52$		−	8.48587i		−	1.17678i
$53$		−	8.70174i		−	1.19528i	−0.801766	−	0.597638i	$-0.796106\pi$
$53$		−	8.70174i		−	1.19528i	0.801766	−	0.597638i	$-0.203894\pi$
$54$	2.12979			0.289828
$55$	10.5413	−	8.60101i	1.42139	−	1.15976i
$56$	1.14159			0.152552
$57$			5.68386i			0.752846i
$58$			6.47144i			0.849742i
$59$	11.7218			1.52605			0.763024	−	0.646371i	$-0.223714\pi$
$59$	11.7218			1.52605			0.763024	+	0.646371i	$0.223714\pi$
$60$	3.58497	+	4.39372i	0.462818	+	0.567226i
$61$	3.88529			0.497461			0.248731	−	0.968573i	$-0.419987\pi$
$61$	3.88529			0.497461			0.248731	+	0.968573i	$0.419987\pi$
$62$			13.6981i			1.73966i
$63$			1.00000i			0.125988i
$64$	11.5595			1.44493
$65$	4.73020	+	5.79730i	0.586709	+	0.719067i
$66$	−12.9584			−1.59507
$67$		−	3.91084i		−	0.477785i	−0.971046	−	0.238893i	$-0.923216\pi$
$67$		−	3.91084i		−	0.477785i	0.971046	−	0.238893i	$-0.0767844\pi$
$68$			2.53601i			0.307537i
$69$	−3.19691			−0.384863
$70$	−3.68993	+	3.01073i	−0.441031	+	0.359851i
$71$	4.02687			0.477902			0.238951	−	0.971032i	$-0.423196\pi$
$71$	4.02687			0.477902			0.238951	+	0.971032i	$0.423196\pi$
$72$		−	1.14159i		−	0.134538i
$73$			10.6661i			1.24838i	0.781274	+	0.624188i	$0.214570\pi$
$73$			10.6661i			1.24838i	−0.781274	+	0.624188i	$0.785430\pi$
$74$	−21.2574			−2.47112
$75$	−4.89830	−	1.00332i	−0.565607	−	0.115854i
$76$	14.4143			1.65344
$77$		−	6.08436i		−	0.693377i
$78$		−	7.12660i		−	0.806928i
$79$	−4.37814			−0.492579			−0.246290	−	0.969196i	$-0.579211\pi$
$79$	−4.37814			−0.492579			−0.246290	+	0.969196i	$0.579211\pi$
$80$	−4.57504	+	3.73292i	−0.511505	+	0.417353i
$81$	1.00000			0.111111
$82$			16.8600i			1.86188i
$83$			15.5785i			1.70996i	0.518661	+	0.854980i	$0.326431\pi$
$83$			15.5785i			1.70996i	−0.518661	+	0.854980i	$0.673569\pi$
$84$	2.53601			0.276702
$85$	−1.41363	−	1.73253i	−0.153329	−	0.187919i
$86$	6.49820			0.700719
$87$			3.03853i			0.325765i
$88$			6.94585i			0.740431i
$89$	15.0190			1.59201			0.796007	−	0.605287i	$-0.206942\pi$
$89$	15.0190			1.59201			0.796007	+	0.605287i	$0.206942\pi$
$90$	3.01073	+	3.68993i	0.317359	+	0.388953i
$91$	3.34615			0.350772
$92$			8.10741i			0.845256i
$93$			6.43165i			0.666931i
$94$	−23.6040			−2.43457
$95$	−9.84747	+	8.03486i	−1.01033	+	0.824359i
$96$	7.90726			0.807031
$97$			2.14419i			0.217709i	0.994058	+	0.108855i	$0.0347183\pi$
$97$			2.14419i			0.217709i	−0.994058	+	0.108855i	$0.965282\pi$
$98$			2.12979i			0.215141i
$99$	−6.08436			−0.611501
$100$	−2.54444	+	12.4221i	−0.254444	+	1.24221i
$101$	−13.5668			−1.34994			−0.674971	−	0.737844i	$-0.735844\pi$
$101$	−13.5668			−1.34994			−0.674971	+	0.737844i	$0.735844\pi$
$102$			2.12979i			0.210881i
$103$		−	13.3291i		−	1.31335i	−0.754172	−	0.656677i	$-0.771962\pi$
$103$		−	13.3291i		−	1.31335i	0.754172	−	0.656677i	$-0.228038\pi$
$104$	−3.81994			−0.374576
$105$	−1.73253	+	1.41363i	−0.169078	+	0.137956i
$106$	−18.5329			−1.80007
$107$			3.68280i			0.356029i	0.984028	+	0.178015i	$0.0569675\pi$
$107$			3.68280i			0.356029i	−0.984028	+	0.178015i	$0.943033\pi$
$108$		−	2.53601i		−	0.244028i
$109$	4.46747			0.427906			0.213953	−	0.976844i	$-0.431366\pi$
$109$	4.46747			0.427906			0.213953	+	0.976844i	$0.431366\pi$
$110$	−18.3183	−	22.4508i	−1.74659	−	2.14060i
$111$	−9.98097			−0.947352
$112$			2.64067i			0.249520i
$113$			9.26682i			0.871749i	0.900008	+	0.435874i	$0.143561\pi$
$113$			9.26682i			0.871749i	−0.900008	+	0.435874i	$0.856439\pi$
$114$	12.1054			1.13378
$115$	−4.51924	−	5.53875i	−0.421422	−	0.516491i
$116$	7.70575			0.715461
$117$		−	3.34615i		−	0.309352i
$118$		−	24.9650i		−	2.29821i
$119$	−1.00000			−0.0916698
$120$	1.97784	−	1.61378i	0.180552	−	0.147318i
$121$	26.0194			2.36540
$122$		−	8.27487i		−	0.749171i
$123$			7.91628i			0.713787i
$124$	16.3107			1.46475
$125$	−5.18608	−	9.90478i	−0.463857	−	0.885910i
$126$	2.12979			0.189737
$127$			15.4132i			1.36770i	0.729623	+	0.683849i	$0.239695\pi$
$127$			15.4132i			1.36770i	−0.729623	+	0.683849i	$0.760305\pi$
$128$		−	8.80475i		−	0.778237i
$129$	3.05110			0.268634
$130$	12.3470	−	10.0743i	1.08291	−	0.883578i
$131$	−7.60394			−0.664359			−0.332180	−	0.943216i	$-0.607784\pi$
$131$	−7.60394			−0.664359			−0.332180	+	0.943216i	$0.607784\pi$
$132$			15.4300i			1.34301i
$133$			5.68386i			0.492853i
$134$	−8.32927			−0.719540
$135$	1.41363	+	1.73253i	0.121666	+	0.149112i
$136$	1.14159			0.0978907
$137$		−	12.8704i		−	1.09960i	−0.835298	−	0.549798i	$-0.814705\pi$
$137$		−	12.8704i		−	1.09960i	0.835298	−	0.549798i	$-0.185295\pi$
$138$			6.80876i			0.579600i
$139$	12.9312			1.09681			0.548404	−	0.836213i	$-0.315236\pi$
$139$	12.9312			1.09681			0.548404	+	0.836213i	$0.315236\pi$
$140$	3.58497	+	4.39372i	0.302985	+	0.371337i
$141$	−11.0828			−0.933338
$142$		−	8.57640i		−	0.719715i
$143$			20.3592i			1.70252i
$144$	2.64067			0.220056
$145$	−5.26435	+	4.29535i	−0.437181	+	0.356709i
$146$	22.7166			1.88004
$147$			1.00000i			0.0824786i
$148$			25.3119i			2.08062i
$149$	2.76357			0.226400			0.113200	−	0.993572i	$-0.463890\pi$
$149$	2.76357			0.226400			0.113200	+	0.993572i	$0.463890\pi$
$150$	−2.13687	+	10.4324i	−0.174474	+	0.851798i
$151$	15.2251			1.23900			0.619502	−	0.784995i	$-0.287335\pi$
$151$	15.2251			1.23900			0.619502	+	0.784995i	$0.287335\pi$
$152$		−	6.48865i		−	0.526299i
$153$			1.00000i			0.0808452i
$154$	−12.9584			−1.04422
$155$	−11.1430	+	9.09195i	−0.895030	+	0.730283i
$156$	−8.48587			−0.679413
$157$		−	12.1039i		−	0.965998i	−0.875621	−	0.482999i	$-0.839547\pi$
$157$		−	12.1039i		−	0.965998i	0.875621	−	0.482999i	$-0.160453\pi$
$158$			9.32452i			0.741819i
$159$	−8.70174			−0.690093
$160$	11.1779	+	13.6996i	0.883691	+	1.08305i
$161$	−3.19691			−0.251952
$162$		−	2.12979i		−	0.167332i
$163$		−	2.11865i		−	0.165946i	−0.996552	−	0.0829728i	$-0.973559\pi$
$163$		−	2.11865i		−	0.165946i	0.996552	−	0.0829728i	$-0.0264415\pi$
$164$	20.0758			1.56766
$165$	−8.60101	−	10.5413i	−0.669587	−	0.820642i
$166$	33.1789			2.57518
$167$			3.29364i			0.254869i	0.991847	+	0.127435i	$0.0406743\pi$
$167$			3.29364i			0.254869i	−0.991847	+	0.127435i	$0.959326\pi$
$168$		−	1.14159i		−	0.0880757i
$169$	1.80329			0.138715
$170$	−3.68993	+	3.01073i	−0.283005	+	0.230912i
$171$	5.68386			0.434656
$172$		−	7.73762i		−	0.589988i
$173$		−	7.87285i		−	0.598562i	−0.954165	−	0.299281i	$-0.903253\pi$
$173$		−	7.87285i		−	0.598562i	0.954165	−	0.299281i	$-0.0967468\pi$
$174$	6.47144			0.490599
$175$	−4.89830	−	1.00332i	−0.370277	−	0.0758440i
$176$	−16.0668			−1.21108
$177$		−	11.7218i		−	0.881064i
$178$		−	31.9874i		−	2.39756i
$179$	2.77830			0.207660			0.103830	−	0.994595i	$-0.466890\pi$
$179$	2.77830			0.207660			0.103830	+	0.994595i	$0.466890\pi$
$180$	4.39372	−	3.58497i	0.327488	−	0.267208i
$181$	24.3990			1.81356			0.906781	−	0.421603i	$-0.138532\pi$
$181$	24.3990			1.81356			0.906781	+	0.421603i	$0.138532\pi$
$182$		−	7.12660i		−	0.528259i
$183$		−	3.88529i		−	0.287209i
$184$	3.64957			0.269050
$185$	−14.1094	−	17.2923i	−1.03734	−	1.27136i
$186$	13.6981			1.00439
$187$		−	6.08436i		−	0.444932i
$188$			28.1060i			2.04984i
$189$	1.00000			0.0727393
$190$	17.1126	+	20.9730i	1.24148	+	1.52154i
$191$	18.5629			1.34317			0.671583	−	0.740929i	$-0.265615\pi$
$191$	18.5629			1.34317			0.671583	+	0.740929i	$0.265615\pi$
$192$		−	11.5595i		−	0.834233i
$193$			6.87338i			0.494757i	0.968919	+	0.247378i	$0.0795691\pi$
$193$			6.87338i			0.494757i	−0.968919	+	0.247378i	$0.920431\pi$
$194$	4.56668			0.327868
$195$	5.79730	−	4.73020i	0.415154	−	0.338737i
$196$	2.53601			0.181144
$197$			4.55879i			0.324800i	0.986725	+	0.162400i	$0.0519235\pi$
$197$			4.55879i			0.324800i	−0.986725	+	0.162400i	$0.948076\pi$
$198$			12.9584i			0.920914i
$199$	15.1682			1.07525			0.537624	−	0.843185i	$-0.319322\pi$
$199$	15.1682			1.07525			0.537624	+	0.843185i	$0.319322\pi$
$200$	5.59186	+	1.14538i	0.395404	+	0.0809909i
$201$	−3.91084			−0.275849
$202$			28.8944i			2.03300i
$203$			3.03853i			0.213263i
$204$	2.53601			0.177556
$205$	−13.7152	+	11.1907i	−0.957911	+	0.781590i
$206$	−28.3882			−1.97790
$207$			3.19691i			0.222201i
$208$		−	8.83607i		−	0.612671i
$209$	−34.5827			−2.39213
$210$	3.01073	+	3.68993i	0.207760	+	0.254629i
$211$	5.50247			0.378805			0.189403	−	0.981899i	$-0.439345\pi$
$211$	5.50247			0.378805			0.189403	+	0.981899i	$0.439345\pi$
$212$			22.0677i			1.51562i
$213$		−	4.02687i		−	0.275917i
$214$	7.84359			0.536177
$215$	4.31311	+	5.28612i	0.294152	+	0.360511i
$216$	−1.14159			−0.0776755
$217$			6.43165i			0.436609i
$218$		−	9.51477i		−	0.644422i
$219$	10.6661			0.720750
$220$	−26.7329	+	21.8122i	−1.80233	+	1.47058i
$221$	3.34615			0.225086
$222$			21.2574i			1.42670i
$223$			17.0957i			1.14481i	0.819971	+	0.572405i	$0.193989\pi$
$223$			17.0957i			1.14481i	−0.819971	+	0.572405i	$0.806011\pi$
$224$	7.90726			0.528326
$225$	−1.00332	+	4.89830i	−0.0668882	+	0.326553i
$226$	19.7364			1.31284
$227$		−	12.5890i		−	0.835562i	−0.908548	−	0.417781i	$-0.862808\pi$
$227$		−	12.5890i		−	0.835562i	0.908548	−	0.417781i	$-0.137192\pi$
$228$		−	14.4143i		−	0.954613i
$229$	1.85956			0.122883			0.0614417	−	0.998111i	$-0.480430\pi$
$229$	1.85956			0.122883			0.0614417	+	0.998111i	$0.480430\pi$
$230$	−11.7964	+	9.62504i	−0.777831	+	0.634657i
$231$	−6.08436			−0.400321
$232$		−	3.46877i		−	0.227736i
$233$			5.36375i			0.351391i	0.984445	+	0.175696i	$0.0562174\pi$
$233$			5.36375i			0.351391i	−0.984445	+	0.175696i	$0.943783\pi$
$234$	−7.12660			−0.465880
$235$	−15.6669	−	19.2012i	−1.02200	−	1.25255i
$236$	−29.7266			−1.93504
$237$			4.37814i			0.284391i
$238$			2.12979i			0.138054i
$239$	−10.0753			−0.651716			−0.325858	−	0.945419i	$-0.605653\pi$
$239$	−10.0753			−0.651716			−0.325858	+	0.945419i	$0.605653\pi$
$240$	3.73292	+	4.57504i	0.240959	+	0.295318i
$241$	−8.68299			−0.559321			−0.279660	−	0.960099i	$-0.590222\pi$
$241$	−8.68299			−0.559321			−0.279660	+	0.960099i	$0.590222\pi$
$242$		−	55.4159i		−	3.56227i
$243$		−	1.00000i		−	0.0641500i
$244$	−9.85315			−0.630783
$245$	−1.73253	+	1.41363i	−0.110687	+	0.0903133i
$246$	16.8600			1.07496
$247$		−	19.0191i		−	1.21015i
$248$		−	7.34233i		−	0.466238i
$249$	15.5785			0.987246
$250$	−21.0951	+	11.0453i	−1.33417	+	0.698564i
$251$	14.5842			0.920547			0.460273	−	0.887777i	$-0.347751\pi$
$251$	14.5842			0.920547			0.460273	+	0.887777i	$0.347751\pi$
$252$		−	2.53601i		−	0.159754i
$253$		−	19.4512i		−	1.22288i
$254$	32.8269			2.05974
$255$	−1.73253	+	1.41363i	−0.108495	+	0.0885247i
$256$	4.36667			0.272917
$257$			9.05937i			0.565108i	0.959251	+	0.282554i	$0.0911816\pi$
$257$			9.05937i			0.565108i	−0.959251	+	0.282554i	$0.908818\pi$
$258$		−	6.49820i		−	0.404561i
$259$	−9.98097			−0.620187
$260$	−11.9958	−	14.7020i	−0.743951	−	0.911781i
$261$	3.03853			0.188080
$262$			16.1948i			1.00052i
$263$			11.6758i			0.719958i	0.932960	+	0.359979i	$0.117216\pi$
$263$			11.6758i			0.719958i	−0.932960	+	0.359979i	$0.882784\pi$
$264$	6.94585			0.427488
$265$	−12.3010	−	15.0760i	−0.755645	−	0.926113i
$266$	12.1054			0.742232
$267$		−	15.0190i		−	0.919150i
$268$			9.91793i			0.605834i
$269$	−0.0956370			−0.00583109			−0.00291555	−	0.999996i	$-0.500928\pi$
$269$	−0.0956370			−0.00583109			−0.00291555	+	0.999996i	$0.500928\pi$
$270$	3.68993	−	3.01073i	0.224562	−	0.183227i
$271$	−3.82150			−0.232140			−0.116070	−	0.993241i	$-0.537030\pi$
$271$	−3.82150			−0.232140			−0.116070	+	0.993241i	$0.537030\pi$
$272$			2.64067i			0.160114i
$273$		−	3.34615i		−	0.202518i
$274$	−27.4113			−1.65598
$275$	6.10457	−	29.8030i	0.368120	−	1.79719i
$276$	8.10741			0.488009
$277$		−	25.5049i		−	1.53244i	−0.642579	−	0.766219i	$-0.722136\pi$
$277$		−	25.5049i		−	1.53244i	0.642579	−	0.766219i	$-0.277864\pi$
$278$		−	27.5407i		−	1.65178i
$279$	6.43165			0.385053
$280$	1.97784	−	1.61378i	0.118199	−	0.0964421i
$281$	27.6246			1.64795			0.823974	−	0.566628i	$-0.191752\pi$
$281$	27.6246			1.64795			0.823974	+	0.566628i	$0.191752\pi$
$282$			23.6040i			1.40560i
$283$		−	12.0694i		−	0.717449i	−0.933444	−	0.358724i	$-0.883212\pi$
$283$		−	12.0694i		−	0.717449i	0.933444	−	0.358724i	$-0.116788\pi$
$284$	−10.2122			−0.605982
$285$	8.03486	+	9.84747i	0.475944	+	0.583314i
$286$	43.3608			2.56398
$287$			7.91628i			0.467283i
$288$		−	7.90726i		−	0.465940i
$289$	−1.00000			−0.0588235
$290$	9.14820	+	11.2120i	0.537201	+	0.658389i
$291$	2.14419			0.125695
$292$		−	27.0494i		−	1.58295i
$293$			18.1684i			1.06141i	0.847558	+	0.530703i	$0.178072\pi$
$293$			18.1684i			1.06141i	−0.847558	+	0.530703i	$0.821928\pi$
$294$	2.12979			0.124212
$295$	20.3084	−	16.5702i	1.18240	−	0.964756i
$296$	11.3942			0.662274
$297$			6.08436i			0.353050i
$298$		−	5.88583i		−	0.340957i
$299$	10.6974			0.618644
$300$	12.4221	+	2.54444i	0.717193	+	0.146903i
$301$	3.05110			0.175862
$302$		−	32.4263i		−	1.86593i
$303$			13.5668i			0.779390i
$304$	15.0092			0.860837
$305$	6.73139	−	5.49235i	0.385438	−	0.314491i
$306$	2.12979			0.121752
$307$			7.50048i			0.428075i	0.976825	+	0.214038i	$0.0686615\pi$
$307$			7.50048i			0.428075i	−0.976825	+	0.214038i	$0.931339\pi$
$308$			15.4300i			0.879206i
$309$	−13.3291			−0.758265
$310$	19.3640	+	23.7323i	1.09980	+	1.34791i
$311$	9.20361			0.521889			0.260944	−	0.965354i	$-0.415966\pi$
$311$	9.20361			0.521889			0.260944	+	0.965354i	$0.415966\pi$
$312$			3.81994i			0.216261i
$313$			26.8664i			1.51858i	0.650754	+	0.759288i	$0.274453\pi$
$313$			26.8664i			1.51858i	−0.650754	+	0.759288i	$0.725547\pi$
$314$	−25.7788			−1.45478
$315$	1.41363	+	1.73253i	0.0796488	+	0.0976170i
$316$	11.1030			0.624593
$317$		−	33.5370i		−	1.88362i	−0.336139	−	0.941812i	$-0.609121\pi$
$317$		−	33.5370i		−	1.88362i	0.336139	−	0.941812i	$-0.390879\pi$
$318$			18.5329i			1.03927i
$319$	−18.4875			−1.03510
$320$	20.0271	−	16.3408i	1.11955	−	0.913477i
$321$	3.68280			0.205554
$322$			6.80876i			0.379437i
$323$			5.68386i			0.316259i
$324$	−2.53601			−0.140890
$325$	16.3904	+	3.35727i	0.909178	+	0.186228i
$326$	−4.51229			−0.249912
$327$		−	4.46747i		−	0.247052i
$328$		−	9.03717i		−	0.498994i
$329$	−11.0828			−0.611013
$330$	−22.4508	+	18.3183i	−1.23588	+	1.00839i
$331$	−20.2428			−1.11265			−0.556323	−	0.830966i	$-0.687788\pi$
$331$	−20.2428			−1.11265			−0.556323	+	0.830966i	$0.687788\pi$
$332$		−	39.5072i		−	2.16824i
$333$			9.98097i			0.546954i
$334$	7.01476			0.383830
$335$	−5.52847	−	6.77565i	−0.302052	−	0.370193i
$336$	2.64067			0.144060
$337$		−	32.6592i		−	1.77906i	−0.456876	−	0.889530i	$-0.651032\pi$
$337$		−	32.6592i		−	1.77906i	0.456876	−	0.889530i	$-0.348968\pi$
$338$		−	3.84063i		−	0.208903i
$339$	9.26682			0.503304
$340$	3.58497	+	4.39372i	0.194422	+	0.238283i
$341$	−39.1325			−2.11914
$342$		−	12.1054i		−	0.654587i
$343$			1.00000i			0.0539949i
$344$	−3.48311			−0.187797
$345$	−5.53875	+	4.51924i	−0.298196	+	0.243308i
$346$	−16.7675			−0.901428
$347$			13.1509i			0.705980i	0.935627	+	0.352990i	$0.114835\pi$
$347$			13.1509i			0.705980i	−0.935627	+	0.352990i	$0.885165\pi$
$348$		−	7.70575i		−	0.413072i
$349$	22.9925			1.23076			0.615379	−	0.788231i	$-0.289003\pi$
$349$	22.9925			1.23076			0.615379	+	0.788231i	$0.289003\pi$
$350$	−2.13687	+	10.4324i	−0.114220	+	0.557633i
$351$	−3.34615			−0.178604
$352$			48.1106i			2.56430i
$353$		−	15.3000i		−	0.814339i	−0.913353	−	0.407169i	$-0.866516\pi$
$353$		−	15.3000i		−	0.814339i	0.913353	−	0.407169i	$-0.133484\pi$
$354$	−24.9650			−1.32687
$355$	6.97668	−	5.69249i	0.370284	−	0.302126i
$356$	−38.0884			−2.01868
$357$			1.00000i			0.0529256i
$358$		−	5.91720i		−	0.312734i
$359$	−2.07549			−0.109540			−0.0547700	−	0.998499i	$-0.517443\pi$
$359$	−2.07549			−0.109540			−0.0547700	+	0.998499i	$0.517443\pi$
$360$	−1.61378	−	1.97784i	−0.0850539	−	0.104241i
$361$	13.3063			0.700332
$362$		−	51.9647i		−	2.73121i
$363$		−	26.0194i		−	1.36566i
$364$	−8.48587			−0.444780
$365$	15.0779	+	18.4794i	0.789215	+	0.967256i
$366$	−8.27487			−0.432534
$367$			35.0999i			1.83220i	0.400948	+	0.916101i	$0.368681\pi$
$367$			35.0999i			1.83220i	−0.400948	+	0.916101i	$0.631319\pi$
$368$			8.44200i			0.440069i
$369$	7.91628			0.412105
$370$	−36.8291	+	30.0500i	−1.91465	+	1.56223i
$371$	−8.70174			−0.451772
$372$		−	16.3107i		−	0.845673i
$373$		−	32.1632i		−	1.66535i	−0.553765	−	0.832673i	$-0.686809\pi$
$373$		−	32.1632i		−	1.66535i	0.553765	−	0.832673i	$-0.313191\pi$
$374$	−12.9584			−0.670064
$375$	−9.90478	+	5.18608i	−0.511480	+	0.267808i
$376$	12.6520			0.652478
$377$		−	10.1674i		−	0.523647i
$378$		−	2.12979i		−	0.109545i
$379$	−33.6964			−1.73087			−0.865435	−	0.501022i	$-0.832958\pi$
$379$	−33.6964			−1.73087			−0.865435	+	0.501022i	$0.832958\pi$
$380$	24.9733	−	20.3765i	1.28110	−	1.04529i
$381$	15.4132			0.789641
$382$		−	39.5352i		−	2.02279i
$383$			6.64402i			0.339494i	0.985488	+	0.169747i	$0.0542950\pi$
$383$			6.64402i			0.339494i	−0.985488	+	0.169747i	$0.945705\pi$
$384$	−8.80475			−0.449315
$385$	−8.60101	−	10.5413i	−0.438348	−	0.537236i
$386$	14.6389			0.745099
$387$		−	3.05110i		−	0.155096i
$388$		−	5.43769i		−	0.276057i
$389$	13.8462			0.702032			0.351016	−	0.936369i	$-0.385836\pi$
$389$	13.8462			0.702032			0.351016	+	0.936369i	$0.385836\pi$
$390$	−10.0743	−	12.3470i	−0.510134	−	0.625217i
$391$	−3.19691			−0.161675
$392$		−	1.14159i		−	0.0576591i
$393$			7.60394i			0.383568i
$394$	9.70927			0.489146
$395$	−7.58526	+	6.18905i	−0.381656	+	0.311405i
$396$	15.4300			0.775387
$397$			19.6455i			0.985979i	0.870035	+	0.492990i	$0.164096\pi$
$397$			19.6455i			0.985979i	−0.870035	+	0.492990i	$0.835904\pi$
$398$		−	32.3052i		−	1.61931i
$399$	5.68386			0.284549
$400$	−2.64944	+	12.9348i	−0.132472	+	0.646740i
$401$	−23.1366			−1.15539			−0.577693	−	0.816254i	$-0.696047\pi$
$401$	−23.1366			−1.15539			−0.577693	+	0.816254i	$0.696047\pi$
$402$			8.32927i			0.415426i
$403$		−	21.5213i		−	1.07205i
$404$	34.4054			1.71174
$405$	1.73253	−	1.41363i	0.0860901	−	0.0702436i
$406$	6.47144			0.321172
$407$		−	60.7278i		−	3.01017i
$408$		−	1.14159i		−	0.0565172i
$409$	−11.7237			−0.579701			−0.289851	−	0.957072i	$-0.593606\pi$
$409$	−11.7237			−0.579701			−0.289851	+	0.957072i	$0.593606\pi$
$410$	23.8338	+	29.2105i	1.17707	+	1.44260i
$411$	−12.8704			−0.634852
$412$			33.8027i			1.66534i
$413$		−	11.7218i		−	0.576792i
$414$	6.80876			0.334632
$415$	22.0221	+	26.9902i	1.08102	+	1.32490i
$416$	−26.4589			−1.29725
$417$		−	12.9312i		−	0.633243i
$418$			73.6538i			3.60253i
$419$	−7.06198			−0.345000			−0.172500	−	0.985009i	$-0.555185\pi$
$419$	−7.06198			−0.345000			−0.172500	+	0.985009i	$0.555185\pi$
$420$	4.39372	−	3.58497i	0.214391	−	0.174929i
$421$	−16.5251			−0.805385			−0.402693	−	0.915335i	$-0.631926\pi$
$421$	−16.5251			−0.805385			−0.402693	+	0.915335i	$0.631926\pi$
$422$		−	11.7191i		−	0.570477i
$423$			11.0828i			0.538863i
$424$	9.93384			0.482430
$425$	−4.89830	−	1.00332i	−0.237602	−	0.0486683i
$426$	−8.57640			−0.415528
$427$		−	3.88529i		−	0.188023i
$428$		−	9.33961i		−	0.451447i
$429$	20.3592			0.982950
$430$	11.2583	−	9.18603i	0.542925	−	0.442990i
$431$	−2.70660			−0.130372			−0.0651861	−	0.997873i	$-0.520764\pi$
$431$	−2.70660			−0.130372			−0.0651861	+	0.997873i	$0.520764\pi$
$432$		−	2.64067i		−	0.127049i
$433$		−	22.4228i		−	1.07757i	−0.842444	−	0.538784i	$-0.818884\pi$
$433$		−	22.4228i		−	1.07757i	0.842444	−	0.538784i	$-0.181116\pi$
$434$	13.6981			0.657529
$435$	4.29535	+	5.26435i	0.205946	+	0.252406i
$436$	−11.3295			−0.542587
$437$			18.1708i			0.869229i
$438$		−	22.7166i		−	1.08544i
$439$	−10.2170			−0.487632			−0.243816	−	0.969822i	$-0.578399\pi$
$439$	−10.2170			−0.487632			−0.243816	+	0.969822i	$0.578399\pi$
$440$	9.81884	+	12.0339i	0.468095	+	0.573694i
$441$	1.00000			0.0476190
$442$		−	7.12660i		−	0.338978i
$443$		−	18.6654i		−	0.886822i	−0.896318	−	0.443411i	$-0.853768\pi$
$443$		−	18.6654i		−	0.886822i	0.896318	−	0.443411i	$-0.146232\pi$
$444$	25.3119			1.20125
$445$	26.0209	−	21.2313i	1.23351	−	1.00646i
$446$	36.4102			1.72407
$447$		−	2.76357i		−	0.130712i
$448$		−	11.5595i		−	0.546134i
$449$	27.3755			1.29193			0.645966	−	0.763366i	$-0.276455\pi$
$449$	27.3755			1.29193			0.645966	+	0.763366i	$0.276455\pi$
$450$	10.4324	+	2.13687i	0.491786	+	0.100733i
$451$	−48.1655			−2.26802
$452$		−	23.5008i		−	1.10538i
$453$		−	15.2251i		−	0.715339i
$454$	−26.8120			−1.25835
$455$	5.79730	−	4.73020i	0.271782	−	0.221755i
$456$	−6.48865			−0.303859
$457$		−	5.05328i		−	0.236382i	−0.992991	−	0.118191i	$-0.962290\pi$
$457$		−	5.05328i		−	0.236382i	0.992991	−	0.118191i	$-0.0377096\pi$
$458$		−	3.96048i		−	0.185061i
$459$	1.00000			0.0466760
$460$	11.4608	+	14.0463i	0.534365	+	0.654914i
$461$	−25.5242			−1.18878			−0.594391	−	0.804176i	$-0.702607\pi$
$461$	−25.5242			−1.18878			−0.594391	+	0.804176i	$0.702607\pi$
$462$			12.9584i			0.602880i
$463$		−	8.18340i		−	0.380315i	−0.981754	−	0.190157i	$-0.939100\pi$
$463$		−	8.18340i		−	0.380315i	0.981754	−	0.190157i	$-0.0608998\pi$
$464$	8.02376			0.372494
$465$	9.09195	+	11.1430i	0.421629	+	0.516746i
$466$	11.4237			0.529192
$467$			13.0047i			0.601787i	0.953658	+	0.300893i	$0.0972848\pi$
$467$			13.0047i			0.601787i	−0.953658	+	0.300893i	$0.902715\pi$
$468$			8.48587i			0.392259i
$469$	−3.91084			−0.180586
$470$	−40.8946	+	33.3672i	−1.88633	+	1.53912i
$471$	−12.1039			−0.557719
$472$			13.3815i			0.615934i
$473$			18.5640i			0.853573i
$474$	9.32452			0.428290
$475$	−5.70275	+	27.8413i	−0.261660	+	1.27745i
$476$	2.53601			0.116238
$477$			8.70174i			0.398425i
$478$			21.4583i			0.981478i
$479$	−8.18194			−0.373842			−0.186921	−	0.982375i	$-0.559851\pi$
$479$	−8.18194			−0.373842			−0.186921	+	0.982375i	$0.559851\pi$
$480$	13.6996	−	11.1779i	0.625297	−	0.510199i
$481$	33.3978			1.52281
$482$			18.4930i			0.842331i
$483$			3.19691i			0.145465i
$484$	−65.9855			−2.99934
$485$	3.03108	+	3.71487i	0.137634	+	0.168684i
$486$	−2.12979			−0.0966093
$487$			4.88443i			0.221335i	0.993858	+	0.110667i	$0.0352988\pi$
$487$			4.88443i			0.221335i	−0.993858	+	0.110667i	$0.964701\pi$
$488$			4.43542i			0.200782i
$489$	−2.11865			−0.0958088
$490$	3.01073	+	3.68993i	0.136011	+	0.166694i
$491$	−12.2582			−0.553206			−0.276603	−	0.960984i	$-0.589209\pi$
$491$	−12.2582			−0.553206			−0.276603	+	0.960984i	$0.589209\pi$
$492$		−	20.0758i		−	0.905086i
$493$			3.03853i			0.136849i
$494$	−40.5066			−1.82248
$495$	−10.5413	+	8.60101i	−0.473798	+	0.386586i
$496$	16.9839			0.762598
$497$		−	4.02687i		−	0.180630i
$498$		−	33.1789i		−	1.48678i
$499$	−26.8067			−1.20003			−0.600017	−	0.799987i	$-0.704840\pi$
$499$	−26.8067			−1.20003			−0.600017	+	0.799987i	$0.704840\pi$
$500$	13.1520	+	25.1186i	0.588173	+	1.12334i
$501$	3.29364			0.147149
$502$		−	31.0613i		−	1.38633i
$503$			9.64081i			0.429863i	0.976629	+	0.214931i	$0.0689528\pi$
$503$			9.64081i			0.429863i	−0.976629	+	0.214931i	$0.931047\pi$
$504$	−1.14159			−0.0508506
$505$	−23.5048	+	19.1783i	−1.04595	+	0.853424i
$506$	−41.4269			−1.84165
$507$		−	1.80329i		−	0.0800870i
$508$		−	39.0880i		−	1.73425i
$509$	39.5043			1.75100			0.875498	−	0.483222i	$-0.160533\pi$
$509$	39.5043			1.75100			0.875498	+	0.483222i	$0.160533\pi$
$510$	3.01073	+	3.68993i	0.133317	+	0.163393i
$511$	10.6661			0.471842
$512$		−	26.9096i		−	1.18925i
$513$		−	5.68386i		−	0.250949i
$514$	19.2946			0.851047
$515$	−18.8423	−	23.0930i	−0.830292	−	1.01760i
$516$	−7.73762			−0.340630
$517$		−	67.4316i		−	2.96564i
$518$			21.2574i			0.933996i
$519$	−7.87285			−0.345580
$520$	−6.61816	+	5.39996i	−0.290225	+	0.236804i
$521$	−33.3440			−1.46083			−0.730413	−	0.683006i	$-0.760672\pi$
$521$	−33.3440			−1.46083			−0.730413	+	0.683006i	$0.760672\pi$
$522$		−	6.47144i		−	0.283247i
$523$			25.4059i			1.11092i	0.831543	+	0.555461i	$0.187458\pi$
$523$			25.4059i			1.11092i	−0.831543	+	0.555461i	$0.812542\pi$
$524$	19.2837			0.842412
$525$	−1.00332	+	4.89830i	−0.0437886	+	0.213779i
$526$	24.8669			1.08425
$527$			6.43165i			0.280167i
$528$			16.0668i			0.699217i
$529$	12.7797			0.555641
$530$	−32.1088	+	26.1986i	−1.39472	+	1.13799i
$531$	−11.7218			−0.508682
$532$		−	14.4143i		−	0.624941i
$533$		−	26.4891i		−	1.14737i
$534$	−31.9874			−1.38423
$535$	5.20610	+	6.38056i	0.225079	+	0.275856i
$536$	4.46458			0.192841
$537$		−	2.77830i		−	0.119893i
$538$			0.203687i			0.00878156i
$539$	−6.08436			−0.262072
$540$	−3.58497	−	4.39372i	−0.154273	−	0.189075i
$541$	33.3675			1.43458			0.717291	−	0.696774i	$-0.245382\pi$
$541$	33.3675			1.43458			0.717291	+	0.696774i	$0.245382\pi$
$542$			8.13900i			0.349600i
$543$		−	24.3990i		−	1.04706i
$544$	7.90726			0.339021
$545$	7.74002	−	6.31533i	0.331546	−	0.270519i
$546$	−7.12660			−0.304990
$547$			10.6343i			0.454688i	0.973814	+	0.227344i	$0.0730042\pi$
$547$			10.6343i			0.454688i	−0.973814	+	0.227344i	$0.926996\pi$
$548$			32.6396i			1.39429i
$549$	−3.88529			−0.165820
$550$	−63.4742	−	13.0015i	−2.70655	−	0.554384i
$551$	17.2706			0.735753
$552$		−	3.64957i		−	0.155336i
$553$			4.37814i			0.186177i
$554$	−54.3200			−2.30784
$555$	−17.2923	+	14.1094i	−0.734019	+	0.598909i
$556$	−32.7936			−1.39076
$557$			34.3788i			1.45668i	0.685218	+	0.728338i	$0.259707\pi$
$557$			34.3788i			1.45668i	−0.685218	+	0.728338i	$0.740293\pi$
$558$		−	13.6981i		−	0.579886i
$559$	−10.2094			−0.431813
$560$	3.73292	+	4.57504i	0.157745	+	0.193331i
$561$	−6.08436			−0.256882
$562$		−	58.8347i		−	2.48179i
$563$			12.3525i			0.520595i	0.965528	+	0.260298i	$0.0838207\pi$
$563$			12.3525i			0.520595i	−0.965528	+	0.260298i	$0.916179\pi$
$564$	28.1060			1.18348
$565$	13.0998	+	16.0550i	0.551113	+	0.675441i
$566$	−25.7052			−1.08047
$567$		−	1.00000i		−	0.0419961i
$568$			4.59705i			0.192888i
$569$	12.2532			0.513681			0.256841	−	0.966454i	$-0.417318\pi$
$569$	12.2532			0.513681			0.256841	+	0.966454i	$0.417318\pi$
$570$	20.9730	−	17.1126i	0.878464	−	0.716767i
$571$	−9.29410			−0.388946			−0.194473	−	0.980908i	$-0.562300\pi$
$571$	−9.29410			−0.388946			−0.194473	+	0.980908i	$0.562300\pi$
$572$		−	51.6311i		−	2.15880i
$573$		−	18.5629i		−	0.775477i
$574$	16.8600			0.703724
$575$	−15.6594	−	3.20754i	−0.653044	−	0.133764i
$576$	−11.5595			−0.481645
$577$		−	16.8503i		−	0.701486i	−0.936472	−	0.350743i	$-0.885929\pi$
$577$		−	16.8503i		−	0.701486i	0.936472	−	0.350743i	$-0.114071\pi$
$578$			2.12979i			0.0885876i
$579$	6.87338			0.285648
$580$	13.3505	−	10.8931i	0.554347	−	0.452309i
$581$	15.5785			0.646304
$582$		−	4.56668i		−	0.189295i
$583$		−	52.9445i		−	2.19274i
$584$	−12.1764			−0.503862
$585$	−4.73020	−	5.79730i	−0.195570	−	0.239689i
$586$	38.6948			1.59847
$587$			40.9350i			1.68957i	0.535107	+	0.844784i	$0.320271\pi$
$587$			40.9350i			1.68957i	−0.535107	+	0.844784i	$0.679729\pi$
$588$		−	2.53601i		−	0.104583i
$589$	36.5566			1.50629
$590$	−35.2911	−	43.2526i	−1.45291	−	1.78068i
$591$	4.55879			0.187524
$592$			26.3565i			1.08324i
$593$			39.9760i			1.64162i	0.571204	+	0.820808i	$0.306477\pi$
$593$			39.9760i			1.64162i	−0.571204	+	0.820808i	$0.693523\pi$
$594$	12.9584			0.531690
$595$	−1.73253	+	1.41363i	−0.0710268	+	0.0579530i
$596$	−7.00844			−0.287077
$597$		−	15.1682i		−	0.620794i
$598$		−	22.7831i		−	0.931671i
$599$	−29.5649			−1.20799			−0.603995	−	0.796988i	$-0.706425\pi$
$599$	−29.5649			−1.20799			−0.603995	+	0.796988i	$0.706425\pi$
$600$	1.14538	−	5.59186i	0.0467601	−	0.228287i
$601$	3.78171			0.154259			0.0771296	−	0.997021i	$-0.475424\pi$
$601$	3.78171			0.154259			0.0771296	+	0.997021i	$0.475424\pi$
$602$		−	6.49820i		−	0.264847i
$603$			3.91084i			0.159262i
$604$	−38.6111			−1.57106
$605$	45.0794	−	36.7817i	1.83274	−	1.49539i
$606$	28.8944			1.17375
$607$			0.389196i			0.0157970i	0.999969	+	0.00789849i	$0.00251419\pi$
$607$			0.389196i			0.0157970i	−0.999969	+	0.00789849i	$0.997486\pi$
$608$		−	44.9438i		−	1.82271i
$609$	3.03853			0.123128
$610$	−11.6976	−	14.3365i	−0.473621	−	0.580466i
$611$	37.0846			1.50028
$612$		−	2.53601i		−	0.102512i
$613$			8.22482i			0.332197i	0.986109	+	0.166099i	$0.0531170\pi$
$613$			8.22482i			0.332197i	−0.986109	+	0.166099i	$0.946883\pi$
$614$	15.9745			0.644677
$615$	11.1907	+	13.7152i	0.451251	+	0.553050i
$616$	6.94585			0.279856
$617$			14.7725i			0.594717i	0.954766	+	0.297359i	$0.0961057\pi$
$617$			14.7725i			0.594717i	−0.954766	+	0.297359i	$0.903894\pi$
$618$			28.3882i			1.14194i
$619$	−20.7740			−0.834978			−0.417489	−	0.908682i	$-0.637090\pi$
$619$	−20.7740			−0.834978			−0.417489	+	0.908682i	$0.637090\pi$
$620$	28.2589	−	23.0573i	1.13490	−	0.926003i
$621$	3.19691			0.128288
$622$		−	19.6018i		−	0.785959i
$623$		−	15.0190i		−	0.601725i
$624$	−8.83607			−0.353726
$625$	−22.9867	−	9.82915i	−0.919468	−	0.393166i
$626$	57.2197			2.28696
$627$			34.5827i			1.38110i
$628$			30.6957i			1.22489i
$629$	−9.98097			−0.397967
$630$	3.68993	−	3.01073i	0.147010	−	0.119950i
$631$	22.9044			0.911808			0.455904	−	0.890029i	$-0.349316\pi$
$631$	22.9044			0.911808			0.455904	+	0.890029i	$0.349316\pi$
$632$		−	4.99805i		−	0.198812i
$633$		−	5.50247i		−	0.218703i
$634$	−71.4268			−2.83672
$635$	21.7885	+	26.7038i	0.864649	+	1.05971i
$636$	22.0677			0.875042
$637$		−	3.34615i		−	0.132579i
$638$			39.3746i			1.55885i
$639$	−4.02687			−0.159301
$640$	−12.4466	−	15.2545i	−0.491996	−	0.602987i
$641$	19.4913			0.769861			0.384930	−	0.922946i	$-0.374225\pi$
$641$	19.4913			0.769861			0.384930	+	0.922946i	$0.374225\pi$
$642$		−	7.84359i		−	0.309562i
$643$		−	4.00863i		−	0.158085i	−0.996871	−	0.0790424i	$-0.974814\pi$
$643$		−	4.00863i		−	0.158085i	0.996871	−	0.0790424i	$-0.0251863\pi$
$644$	8.10741			0.319477
$645$	5.28612	−	4.31311i	0.208141	−	0.169829i
$646$	12.1054			0.476282
$647$			29.3350i			1.15328i	0.817000	+	0.576638i	$0.195636\pi$
$647$			29.3350i			1.15328i	−0.817000	+	0.576638i	$0.804364\pi$
$648$			1.14159i			0.0448460i
$649$	71.3196			2.79954
$650$	7.15028	−	34.9082i	0.280457	−	1.36921i
$651$	6.43165			0.252076
$652$			5.37293i			0.210420i
$653$			23.5839i			0.922908i	0.887164	+	0.461454i	$0.152672\pi$
$653$			23.5839i			0.922908i	−0.887164	+	0.461454i	$0.847328\pi$
$654$	−9.51477			−0.372057
$655$	−13.1741	+	10.7491i	−0.514753	+	0.420003i
$656$	20.9043			0.816175
$657$		−	10.6661i		−	0.416125i
$658$			23.6040i			0.920180i
$659$	32.9035			1.28174			0.640869	−	0.767650i	$-0.278574\pi$
$659$	32.9035			1.28174			0.640869	+	0.767650i	$0.278574\pi$
$660$	21.8122	+	26.7329i	0.849041	+	1.04058i
$661$	−43.5386			−1.69345			−0.846727	−	0.532027i	$-0.821431\pi$
$661$	−43.5386			−1.69345			−0.846727	+	0.532027i	$0.821431\pi$
$662$			43.1130i			1.67563i
$663$		−	3.34615i		−	0.129954i
$664$	−17.7843			−0.690163
$665$	8.03486	+	9.84747i	0.311578	+	0.381868i
$666$	21.2574			0.823707
$667$			9.71393i			0.376125i
$668$		−	8.35270i		−	0.323176i
$669$	17.0957			0.660956
$670$	−14.4307	+	11.7745i	−0.557507	+	0.454888i
$671$	23.6395			0.912594
$672$		−	7.90726i		−	0.305029i
$673$		−	32.2938i		−	1.24483i	−0.782686	−	0.622417i	$-0.786151\pi$
$673$		−	32.2938i		−	1.24483i	0.782686	−	0.622417i	$-0.213849\pi$
$674$	−69.5573			−2.67925
$675$	4.89830	+	1.00332i	0.188536	+	0.0386179i
$676$	−4.57317			−0.175891
$677$			30.7834i			1.18310i	0.806268	+	0.591551i	$0.201484\pi$
$677$			30.7834i			1.18310i	−0.806268	+	0.591551i	$0.798516\pi$
$678$		−	19.7364i		−	0.757971i
$679$	2.14419			0.0822864
$680$	1.97784	−	1.61378i	0.0758468	−	0.0618858i
$681$	−12.5890			−0.482412
$682$			83.3440i			3.19141i
$683$		−	13.0232i		−	0.498318i	−0.968463	−	0.249159i	$-0.919846\pi$
$683$		−	13.0232i		−	0.498318i	0.968463	−	0.249159i	$-0.0801542\pi$
$684$	−14.4143			−0.551146
$685$	−18.1940	−	22.2984i	−0.695156	−	0.851979i
$686$	2.12979			0.0813158
$687$		−	1.85956i		−	0.0709468i
$688$		−	8.05694i		−	0.307168i
$689$	29.1173			1.10928
$690$	9.62504	+	11.7964i	0.366419	+	0.449081i
$691$	42.4075			1.61326			0.806629	−	0.591059i	$-0.201290\pi$
$691$	42.4075			1.61326			0.806629	+	0.591059i	$0.201290\pi$
$692$			19.9656i			0.758980i
$693$			6.08436i			0.231126i
$694$	28.0088			1.06320
$695$	22.4037	−	18.2799i	0.849819	−	0.693394i
$696$	−3.46877			−0.131483
$697$			7.91628i			0.299851i
$698$		−	48.9692i		−	1.85351i
$699$	5.36375			0.202876
$700$	12.4221	+	2.54444i	0.469513	+	0.0961707i
$701$	14.0724			0.531509			0.265754	−	0.964041i	$-0.414379\pi$
$701$	14.0724			0.531509			0.265754	+	0.964041i	$0.414379\pi$
$702$			7.12660i			0.268976i
$703$			56.7305i			2.13963i
$704$	70.3320			2.65074
$705$	−19.2012	+	15.6669i	−0.723161	+	0.590050i
$706$	−32.5859			−1.22639
$707$			13.5668i			0.510230i
$708$			29.7266i			1.11719i
$709$	14.0388			0.527238			0.263619	−	0.964627i	$-0.415084\pi$
$709$	14.0388			0.527238			0.263619	+	0.964627i	$0.415084\pi$
$710$	−12.1238	−	14.8589i	−0.454999	−	0.557644i
$711$	4.37814			0.164193
$712$			17.1456i			0.642559i
$713$			20.5615i			0.770032i
$714$	2.12979			0.0797054
$715$	28.7802	+	35.2729i	1.07632	+	1.31913i
$716$	−7.04580			−0.263314
$717$			10.0753i			0.376269i
$718$			4.42035i			0.164966i
$719$	34.9414			1.30309			0.651547	−	0.758608i	$-0.274120\pi$
$719$	34.9414			1.30309			0.651547	+	0.758608i	$0.274120\pi$
$720$	4.57504	−	3.73292i	0.170502	−	0.139118i
$721$	−13.3291			−0.496401
$722$		−	28.3397i		−	1.05469i
$723$			8.68299i			0.322924i
$724$	−61.8761			−2.29961
$725$	−3.04863	+	14.8836i	−0.113223	+	0.552765i
$726$	−55.4159			−2.05668
$727$			39.4810i			1.46427i	0.681161	+	0.732134i	$0.261476\pi$
$727$			39.4810i			1.46427i	−0.681161	+	0.732134i	$0.738524\pi$
$728$			3.81994i			0.141576i
$729$	−1.00000			−0.0370370
$730$	39.3573	−	32.1128i	1.45668	−	1.18855i
$731$	3.05110			0.112849
$732$			9.85315i			0.364183i
$733$		−	32.3767i		−	1.19586i	−0.801548	−	0.597930i	$-0.795990\pi$
$733$		−	32.3767i		−	1.19586i	0.801548	−	0.597930i	$-0.204010\pi$
$734$	74.7555			2.75928
$735$	1.41363	+	1.73253i	0.0521424	+	0.0639053i
$736$	25.2788			0.931790
$737$		−	23.7949i		−	0.876498i
$738$		−	16.8600i		−	0.620626i
$739$	−11.4901			−0.422671			−0.211335	−	0.977414i	$-0.567781\pi$
$739$	−11.4901			−0.422671			−0.211335	+	0.977414i	$0.567781\pi$
$740$	35.7815	+	43.8536i	1.31535	+	1.61209i
$741$	−19.0191			−0.698682
$742$			18.5329i			0.680364i
$743$		−	35.4594i		−	1.30088i	−0.759558	−	0.650439i	$-0.774585\pi$
$743$		−	35.4594i		−	1.30088i	0.759558	−	0.650439i	$-0.225415\pi$
$744$	−7.34233			−0.269183
$745$	4.78797	−	3.90665i	0.175418	−	0.143129i
$746$	−68.5009			−2.50799
$747$		−	15.5785i		−	0.569987i
$748$			15.4300i			0.564177i
$749$	3.68280			0.134566
$750$	11.0453	+	21.0951i	0.403316	+	0.770284i
$751$	−39.2058			−1.43064			−0.715320	−	0.698797i	$-0.753719\pi$
$751$	−39.2058			−1.43064			−0.715320	+	0.698797i	$0.753719\pi$
$752$			29.2659i			1.06722i
$753$		−	14.5842i		−	0.531478i
$754$	−21.6544			−0.788607
$755$	26.3780	−	21.5226i	0.959993	−	0.783289i
$756$	−2.53601			−0.0922338
$757$			4.59281i			0.166929i	0.996511	+	0.0834643i	$0.0265984\pi$
$757$			4.59281i			0.166929i	−0.996511	+	0.0834643i	$0.973402\pi$
$758$			71.7664i			2.60667i
$759$	−19.4512			−0.706033
$760$	−9.17253	−	11.2418i	−0.332723	−	0.407783i
$761$	−50.6303			−1.83535			−0.917674	−	0.397335i	$-0.869935\pi$
$761$	−50.6303			−1.83535			−0.917674	+	0.397335i	$0.869935\pi$
$762$		−	32.8269i		−	1.18919i
$763$		−	4.46747i		−	0.161733i
$764$	−47.0758			−1.70314
$765$	1.41363	+	1.73253i	0.0511098	+	0.0626398i
$766$	14.1504			0.511274
$767$			39.2228i			1.41626i
$768$		−	4.36667i		−	0.157569i
$769$	2.97711			0.107357			0.0536787	−	0.998558i	$-0.482905\pi$
$769$	2.97711			0.107357			0.0536787	+	0.998558i	$0.482905\pi$
$770$	−22.4508	+	18.3183i	−0.809072	+	0.660147i
$771$	9.05937			0.326265
$772$		−	17.4310i		−	0.627354i
$773$		−	43.6865i		−	1.57130i	−0.618674	−	0.785648i	$-0.712330\pi$
$773$		−	43.6865i		−	1.57130i	0.618674	−	0.785648i	$-0.287670\pi$
$774$	−6.49820			−0.233573
$775$	−6.45302	+	31.5042i	−0.231799	+	1.13166i
$776$	−2.44779			−0.0878705
$777$			9.98097i			0.358065i
$778$		−	29.4896i		−	1.05725i
$779$	44.9951			1.61212
$780$	−14.7020	+	11.9958i	−0.526417	+	0.429520i
$781$	24.5009			0.876712
$782$			6.80876i			0.243481i
$783$		−	3.03853i		−	0.108588i
$784$	2.64067			0.0943096
$785$	−17.1104	−	20.9704i	−0.610697	−	0.748466i
$786$	16.1948			0.577650
$787$		−	7.76874i		−	0.276926i	−0.990368	−	0.138463i	$-0.955784\pi$
$787$		−	7.76874i		−	0.276926i	0.990368	−	0.138463i	$-0.0442161\pi$
$788$		−	11.5611i		−	0.411849i
$789$	11.6758			0.415668
$790$	13.1814	+	16.1550i	0.468973	+	0.574770i
$791$	9.26682			0.329490
$792$		−	6.94585i		−	0.246810i
$793$			13.0008i			0.461671i
$794$	41.8408			1.48487
$795$	−15.0760	+	12.3010i	−0.534692	+	0.436272i
$796$	−38.4668			−1.36342
$797$			11.4325i			0.404959i	0.979286	+	0.202480i	$0.0649000\pi$
$797$			11.4325i			0.404959i	−0.979286	+	0.202480i	$0.935100\pi$
$798$		−	12.1054i		−	0.428528i
$799$	−11.0828			−0.392080
$800$	38.7321	+	7.93353i	1.36939	+	0.280493i
$801$	−15.0190			−0.530671
$802$			49.2761i			1.74000i
$803$			64.8966i			2.29015i
$804$	9.91793			0.349779
$805$	−5.53875	+	4.51924i	−0.195215	+	0.159282i
$806$	−45.8358			−1.61450
$807$			0.0956370i			0.00336658i
$808$		−	15.4877i		−	0.544855i
$809$	52.9093			1.86019			0.930096	−	0.367316i	$-0.119723\pi$
$809$	52.9093			1.86019			0.930096	+	0.367316i	$0.119723\pi$
$810$	−3.01073	−	3.68993i	−0.105786	−	0.129651i
$811$	−28.4663			−0.999587			−0.499794	−	0.866145i	$-0.666591\pi$
$811$	−28.4663			−0.999587			−0.499794	+	0.866145i	$0.666591\pi$
$812$		−	7.70575i		−	0.270419i
$813$			3.82150i			0.134026i
$814$	−129.338			−4.53328
$815$	−2.99498	−	3.67063i	−0.104910	−	0.128577i
$816$	2.64067			0.0924419
$817$		−	17.3420i		−	0.606721i
$818$			24.9691i			0.873024i
$819$	−3.34615			−0.116924
$820$	34.7819	−	28.3797i	1.21464	−	0.991061i
$821$	53.4777			1.86638			0.933192	−	0.359377i	$-0.117011\pi$
$821$	53.4777			1.86638			0.933192	+	0.359377i	$0.117011\pi$
$822$			27.4113i			0.956080i
$823$			27.6936i			0.965337i	0.875803	+	0.482669i	$0.160332\pi$
$823$			27.6936i			0.965337i	−0.875803	+	0.482669i	$0.839668\pi$
$824$	15.2164			0.530087
$825$	−29.8030	−	6.10457i	−1.03761	−	0.212534i
$826$	−24.9650			−0.868642
$827$			7.36209i			0.256005i	0.991774	+	0.128002i	$0.0408565\pi$
$827$			7.36209i			0.256005i	−0.991774	+	0.128002i	$0.959143\pi$
$828$		−	8.10741i		−	0.281752i
$829$	12.8531			0.446406			0.223203	−	0.974772i	$-0.428349\pi$
$829$	12.8531			0.446406			0.223203	+	0.974772i	$0.428349\pi$
$830$	57.4835	−	46.9026i	1.99528	−	1.62801i
$831$	−25.5049			−0.884754
$832$			38.6797i			1.34098i
$833$			1.00000i			0.0346479i
$834$	−27.5407			−0.953657
$835$	4.65597	+	5.70632i	0.161126	+	0.197475i
$836$	87.7020			3.03324
$837$		−	6.43165i		−	0.222310i
$838$			15.0405i			0.519567i
$839$	−0.507889			−0.0175343			−0.00876714	−	0.999962i	$-0.502791\pi$
$839$	−0.507889			−0.0175343			−0.00876714	+	0.999962i	$0.502791\pi$
$840$	−1.61378	−	1.97784i	−0.0556809	−	0.0682421i
$841$	−19.7673			−0.681632
$842$			35.1951i			1.21290i
$843$		−	27.6246i		−	0.951443i
$844$	−13.9543			−0.480327
$845$	3.12426	−	2.54918i	0.107478	−	0.0876944i
$846$	23.6040			0.811522
$847$		−	26.0194i		−	0.894037i
$848$			22.9784i			0.789082i
$849$	−12.0694			−0.414219
$850$	−2.13687	+	10.4324i	−0.0732939	+	0.357827i
$851$	−31.9083			−1.09380
$852$			10.2122i			0.349864i
$853$		−	27.6786i		−	0.947696i	−0.880607	−	0.473848i	$-0.842865\pi$
$853$		−	27.6786i		−	0.947696i	0.880607	−	0.473848i	$-0.157135\pi$
$854$	−8.27487			−0.283160
$855$	9.84747	−	8.03486i	0.336776	−	0.274786i
$856$	−4.20425			−0.143698
$857$		−	54.8479i		−	1.87357i	−0.349908	−	0.936784i	$-0.613787\pi$
$857$		−	54.8479i		−	1.87357i	0.349908	−	0.936784i	$-0.386213\pi$
$858$		−	43.3608i		−	1.48031i
$859$	29.9224			1.02094			0.510470	−	0.859896i	$-0.329472\pi$
$859$	29.9224			1.02094			0.510470	+	0.859896i	$0.329472\pi$
$860$	−10.9381	−	13.4057i	−0.372986	−	0.457129i
$861$	7.91628			0.269786
$862$			5.76448i			0.196339i
$863$			25.3937i			0.864411i	0.901775	+	0.432206i	$0.142265\pi$
$863$			25.3937i			0.864411i	−0.901775	+	0.432206i	$0.857735\pi$
$864$	−7.90726			−0.269010
$865$	−11.1293	−	13.6400i	−0.378406	−	0.463772i
$866$	−47.7558			−1.62281
$867$			1.00000i			0.0339618i
$868$		−	16.3107i		−	0.553623i
$869$	−26.6382			−0.903638
$870$	11.2120	−	9.14820i	0.380121	−	0.310153i
$871$	13.0863			0.443411
$872$			5.10003i			0.172709i
$873$		−	2.14419i		−	0.0725698i
$874$	38.7001			1.30905
$875$	−9.90478	+	5.18608i	−0.334843	+	0.175321i
$876$	−27.0494			−0.913916
$877$		−	47.1727i		−	1.59291i	−0.604699	−	0.796454i	$-0.706707\pi$
$877$		−	47.1727i		−	1.59291i	0.604699	−	0.796454i	$-0.293293\pi$
$878$			21.7601i			0.734368i
$879$	18.1684			0.612803
$880$	−27.8362	+	22.7124i	−0.938357	+	0.765635i
$881$	−12.9987			−0.437938			−0.218969	−	0.975732i	$-0.570269\pi$
$881$	−12.9987			−0.437938			−0.218969	+	0.975732i	$0.570269\pi$
$882$		−	2.12979i		−	0.0717138i
$883$			8.36834i			0.281617i	0.990037	+	0.140808i	$0.0449702\pi$
$883$			8.36834i			0.281617i	−0.990037	+	0.140808i	$0.955030\pi$
$884$	−8.48587			−0.285411
$885$	−16.5702	−	20.3084i	−0.557002	−	0.682658i
$886$	−39.7535			−1.33555
$887$		−	26.4628i		−	0.888534i	−0.895894	−	0.444267i	$-0.853464\pi$
$887$		−	26.4628i		−	0.888534i	0.895894	−	0.444267i	$-0.146536\pi$
$888$		−	11.3942i		−	0.382364i
$889$	15.4132			0.516941
$890$	−45.2182	−	55.4191i	−1.51572	−	1.85765i
$891$	6.08436			0.203834
$892$		−	43.3548i		−	1.45163i
$893$			62.9930i			2.10798i
$894$	−5.88583			−0.196851
$895$	4.81349	−	3.92748i	0.160897	−	0.131281i
$896$	−8.80475			−0.294146
$897$		−	10.6974i		−	0.357174i
$898$		−	58.3042i		−	1.94564i
$899$	19.5428			0.651789
$900$	2.54444	−	12.4221i	0.0848146	−	0.414071i
$901$	−8.70174			−0.289897
$902$			102.582i			3.41562i
$903$		−	3.05110i		−	0.101534i
$904$	−10.5789			−0.351850
$905$	42.2720	−	34.4910i	1.40517	−	1.14652i
$906$	−32.4263			−1.07729
$907$		−	30.3041i		−	1.00623i	−0.864219	−	0.503116i	$-0.832187\pi$
$907$		−	30.3041i		−	1.00623i	0.864219	−	0.503116i	$-0.167813\pi$
$908$			31.9259i			1.05950i
$909$	13.5668			0.449981
$910$	−10.0743	−	12.3470i	−0.333961	−	0.409301i
$911$	−50.8332			−1.68418			−0.842089	−	0.539338i	$-0.818674\pi$
$911$	−50.8332			−1.68418			−0.842089	+	0.539338i	$0.818674\pi$
$912$		−	15.0092i		−	0.497004i
$913$			94.7850i			3.13693i
$914$	−10.7624			−0.355989
$915$	−5.49235	−	6.73139i	−0.181572	−	0.222533i
$916$	−4.71587			−0.155817
$917$			7.60394i			0.251104i
$918$		−	2.12979i		−	0.0702936i
$919$	18.2329			0.601446			0.300723	−	0.953711i	$-0.402772\pi$
$919$	18.2329			0.601446			0.300723	+	0.953711i	$0.402772\pi$
$920$	6.32300	−	5.15913i	0.208463	−	0.170092i
$921$	7.50048			0.247149
$922$			54.3613i			1.79029i
$923$			13.4745i			0.443519i
$924$	15.4300			0.507610
$925$	−48.8898	−	10.0141i	−1.60749	−	0.329263i
$926$	−17.4289			−0.572750
$927$			13.3291i			0.437784i
$928$		−	24.0265i		−	0.788707i
$929$	−8.61416			−0.282621			−0.141311	−	0.989965i	$-0.545132\pi$
$929$	−8.61416			−0.282621			−0.141311	+	0.989965i	$0.545132\pi$
$930$	23.7323	−	19.3640i	0.778214	−	0.634969i
$931$	5.68386			0.186281
$932$		−	13.6025i		−	0.445566i
$933$		−	9.20361i		−	0.301313i
$934$	27.6973			0.906284
$935$	−8.60101	−	10.5413i	−0.281283	−	0.344738i
$936$	3.81994			0.124859
$937$			23.1892i			0.757559i	0.925487	+	0.378779i	$0.123656\pi$
$937$			23.1892i			0.757559i	−0.925487	+	0.378779i	$0.876344\pi$
$938$			8.32927i			0.271960i
$939$	26.8664			0.876751
$940$	39.7314	+	48.6946i	1.29590	+	1.58824i
$941$	−8.51852			−0.277696			−0.138848	−	0.990314i	$-0.544340\pi$
$941$	−8.51852			−0.277696			−0.138848	+	0.990314i	$0.544340\pi$
$942$			25.7788i			0.839920i
$943$			25.3077i			0.824132i
$944$	−30.9534			−1.00745
$945$	1.73253	−	1.41363i	0.0563592	−	0.0459853i
$946$	39.5374			1.28547
$947$			8.54242i			0.277591i	0.990321	+	0.138796i	$0.0443231\pi$
$947$			8.54242i			0.277591i	−0.990321	+	0.138796i	$0.955677\pi$
$948$		−	11.1030i		−	0.360609i
$949$	−35.6905			−1.15856
$950$	59.2961	+	12.1457i	1.92382	+	0.394057i
$951$	−33.5370			−1.08751
$952$		−	1.14159i		−	0.0369992i
$953$			4.02491i			0.130380i	0.997873	+	0.0651898i	$0.0207653\pi$
$953$			4.02491i			0.130380i	−0.997873	+	0.0651898i	$0.979235\pi$
$954$	18.5329			0.600025
$955$	32.1608	−	26.2410i	1.04070	−	0.849140i
$956$	25.5510			0.826380
$957$			18.4875i			0.597617i
$958$			17.4258i			0.563003i
$959$	−12.8704			−0.415608
$960$	−16.3408	−	20.0271i	−0.527396	−	0.646373i
$961$	10.3662			0.334393
$962$		−	71.1304i		−	2.29334i
$963$		−	3.68280i		−	0.118676i
$964$	22.0202			0.709222
$965$	9.71639	+	11.9083i	0.312782	+	0.383343i
$966$	6.80876			0.219068
$967$			2.23083i			0.0717388i	0.999356	+	0.0358694i	$0.0114200\pi$
$967$			2.23083i			0.0717388i	−0.999356	+	0.0358694i	$0.988580\pi$
$968$			29.7035i			0.954708i
$969$	5.68386			0.182592
$970$	7.91190	−	6.45557i	0.254036	−	0.207276i
$971$	−50.8051			−1.63041			−0.815207	−	0.579170i	$-0.803377\pi$
$971$	−50.8051			−1.63041			−0.815207	+	0.579170i	$0.803377\pi$
$972$			2.53601i			0.0813426i
$973$		−	12.9312i		−	0.414555i
$974$	10.4028			0.333328
$975$	3.35727	−	16.3904i	0.107519	−	0.524914i
$976$	−10.2598			−0.328408
$977$			15.6347i			0.500197i	0.968220	+	0.250099i	$0.0804631\pi$
$977$			15.6347i			0.500197i	−0.968220	+	0.250099i	$0.919537\pi$
$978$			4.51229i			0.144287i
$979$	91.3811			2.92055
$980$	4.39372	−	3.58497i	0.140352	−	0.114518i
$981$	−4.46747			−0.142635
$982$			26.1075i			0.833123i
$983$			5.96705i			0.190319i	0.995462	+	0.0951597i	$0.0303362\pi$
$983$			5.96705i			0.190319i	−0.995462	+	0.0951597i	$0.969664\pi$
$984$	−9.03717			−0.288094
$985$	6.44442	+	7.89824i	0.205336	+	0.251659i
$986$	6.47144			0.206093
$987$			11.0828i			0.352769i
$988$			48.2325i			1.53448i
$989$	9.75410			0.310162
$990$	18.3183	+	22.4508i	0.582195	+	0.713535i
$991$	−6.08005			−0.193139			−0.0965696	−	0.995326i	$-0.530787\pi$
$991$	−6.08005			−0.193139			−0.0965696	+	0.995326i	$0.530787\pi$
$992$		−	50.8568i		−	1.61470i
$993$			20.2428i			0.642387i
$994$	−8.57640			−0.272027
$995$	26.2794	−	21.4422i	0.833113	−	0.679764i
$996$	−39.5072			−1.25183
$997$			12.1266i			0.384052i	0.981390	+	0.192026i	$0.0615058\pi$
$997$			12.1266i			0.384052i	−0.981390	+	0.192026i	$0.938494\pi$
$998$			57.0927i			1.80724i
$999$	9.98097			0.315784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1785.2.g.f.1429.4	✓	28
5.2	odd	4		8925.2.a.cw.1.12		14
5.3	odd	4		8925.2.a.cv.1.3		14
5.4	even	2	inner	1785.2.g.f.1429.25	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1785.2.g.f.1429.4	✓	28	1.1	even	1	trivial
1785.2.g.f.1429.25	yes	28	5.4	even	2	inner
8925.2.a.cv.1.3		14	5.3	odd	4
8925.2.a.cw.1.12		14	5.2	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1785 = 3 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1785.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.12979i q^{2} -1.00000i q^{3} -2.53601 q^{4} +(1.73253 - 1.41363i) q^{5} -2.12979 q^{6} -1.00000i q^{7} +1.14159i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.12979i q^{2} -1.00000i q^{3} -2.53601 q^{4} +(1.73253 - 1.41363i) q^{5} -2.12979 q^{6} -1.00000i q^{7} +1.14159i q^{8} -1.00000 q^{9} +(-3.01073 - 3.68993i) q^{10} +6.08436 q^{11} +2.53601i q^{12} +3.34615i q^{13} -2.12979 q^{14} +(-1.41363 - 1.73253i) q^{15} -2.64067 q^{16} -1.00000i q^{17} +2.12979i q^{18} -5.68386 q^{19} +(-4.39372 + 3.58497i) q^{20} -1.00000 q^{21} -12.9584i q^{22} -3.19691i q^{23} +1.14159 q^{24} +(1.00332 - 4.89830i) q^{25} +7.12660 q^{26} +1.00000i q^{27} +2.53601i q^{28} -3.03853 q^{29} +(-3.68993 + 3.01073i) q^{30} -6.43165 q^{31} +7.90726i q^{32} -6.08436i q^{33} -2.12979 q^{34} +(-1.41363 - 1.73253i) q^{35} +2.53601 q^{36} -9.98097i q^{37} +12.1054i q^{38} +3.34615 q^{39} +(1.61378 + 1.97784i) q^{40} -7.91628 q^{41} +2.12979i q^{42} +3.05110i q^{43} -15.4300 q^{44} +(-1.73253 + 1.41363i) q^{45} -6.80876 q^{46} -11.0828i q^{47} +2.64067i q^{48} -1.00000 q^{49} +(-10.4324 - 2.13687i) q^{50} -1.00000 q^{51} -8.48587i q^{52} -8.70174i q^{53} +2.12979 q^{54} +(10.5413 - 8.60101i) q^{55} +1.14159 q^{56} +5.68386i q^{57} +6.47144i q^{58} +11.7218 q^{59} +(3.58497 + 4.39372i) q^{60} +3.88529 q^{61} +13.6981i q^{62} +1.00000i q^{63} +11.5595 q^{64} +(4.73020 + 5.79730i) q^{65} -12.9584 q^{66} -3.91084i q^{67} +2.53601i q^{68} -3.19691 q^{69} +(-3.68993 + 3.01073i) q^{70} +4.02687 q^{71} -1.14159i q^{72} +10.6661i q^{73} -21.2574 q^{74} +(-4.89830 - 1.00332i) q^{75} +14.4143 q^{76} -6.08436i q^{77} -7.12660i q^{78} -4.37814 q^{79} +(-4.57504 + 3.73292i) q^{80} +1.00000 q^{81} +16.8600i q^{82} +15.5785i q^{83} +2.53601 q^{84} +(-1.41363 - 1.73253i) q^{85} +6.49820 q^{86} +3.03853i q^{87} +6.94585i q^{88} +15.0190 q^{89} +(3.01073 + 3.68993i) q^{90} +3.34615 q^{91} +8.10741i q^{92} +6.43165i q^{93} -23.6040 q^{94} +(-9.84747 + 8.03486i) q^{95} +7.90726 q^{96} +2.14419i q^{97} +2.12979i q^{98} -6.08436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9}+O(q^{10}) \) 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9	\( 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} - 4 q^{15} + 38 q^{16} + 12 q^{19} - 4 q^{20} - 28 q^{21} + 30 q^{24} - 8 q^{25} - 36 q^{26} - 2 q^{30} + 14 q^{31} - 6 q^{34} - 4 q^{35} + 34 q^{36} + 18 q^{39} - 62 q^{40} - 50 q^{41} - 24 q^{44} + 52 q^{46} - 28 q^{49} + 6 q^{50} - 28 q^{51} + 6 q^{54} - 14 q^{55} + 30 q^{56} + 44 q^{59} + 10 q^{60} + 26 q^{61} - 6 q^{64} + 20 q^{65} - 48 q^{66} + 38 q^{69} - 2 q^{70} + 12 q^{71} + 24 q^{74} - 16 q^{75} - 20 q^{76} - 8 q^{79} - 32 q^{80} + 28 q^{81} + 34 q^{84} - 4 q^{85} + 8 q^{86} + 84 q^{89} - 4 q^{90} + 18 q^{91} - 8 q^{94} + 4 q^{95} - 66 q^{96} - 8 q^{99}+O(q^{100}) \) 28 * q - 34 * q^4 - 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 - 4 * q^15 + 38 * q^16 + 12 * q^19 - 4 * q^20 - 28 * q^21 + 30 * q^24 - 8 * q^25 - 36 * q^26 - 2 * q^30 + 14 * q^31 - 6 * q^34 - 4 * q^35 + 34 * q^36 + 18 * q^39 - 62 * q^40 - 50 * q^41 - 24 * q^44 + 52 * q^46 - 28 * q^49 + 6 * q^50 - 28 * q^51 + 6 * q^54 - 14 * q^55 + 30 * q^56 + 44 * q^59 + 10 * q^60 + 26 * q^61 - 6 * q^64 + 20 * q^65 - 48 * q^66 + 38 * q^69 - 2 * q^70 + 12 * q^71 + 24 * q^74 - 16 * q^75 - 20 * q^76 - 8 * q^79 - 32 * q^80 + 28 * q^81 + 34 * q^84 - 4 * q^85 + 8 * q^86 + 84 * q^89 - 4 * q^90 + 18 * q^91 - 8 * q^94 + 4 * q^95 - 66 * q^96 - 8 * q^99

Introduction

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