LMFDB - Embedded newform 130.3.f.a.99.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,3,Mod(99,130)] 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("130.99"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	130.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54224343668$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 84x^{12} + 2668x^{10} + 40556x^{8} + 303080x^{6} + 1000960x^{4} + 1045476x^{2} + 193600 $ x^14 + 84x^12 + 2668x^10 + 40556x^8 + 303080x^6 + 1000960x^4 + 1045476x^2 + 193600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.6
Root			$3.84840i$ of defining polynomial
Character	$\chi$	$=$	130.99
Dual form			130.3.f.a.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +3.84840i q^{3} -2.00000i q^{4} +(0.429852 + 4.98149i) q^{5} +(-3.84840 - 3.84840i) q^{6} +(2.44952 + 2.44952i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.81016 q^{9} +(-5.41134 - 4.55164i) q^{10} +(-4.31164 + 4.31164i) q^{11} +7.69679 q^{12} +(-8.89425 - 9.48115i) q^{13} -4.89903 q^{14} +(-19.1707 + 1.65424i) q^{15} -4.00000 q^{16} +11.8592 q^{17} +(5.81016 - 5.81016i) q^{18} +(-9.71168 - 9.71168i) q^{19} +(9.96298 - 0.859704i) q^{20} +(-9.42671 + 9.42671i) q^{21} -8.62329i q^{22} -10.6797 q^{23} +(-7.69679 + 7.69679i) q^{24} +(-24.6305 + 4.28261i) q^{25} +(18.3754 + 0.586903i) q^{26} +12.2758i q^{27} +(4.89903 - 4.89903i) q^{28} +21.5195 q^{29} +(17.5165 - 20.8250i) q^{30} +(39.8823 + 39.8823i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-16.5929 - 16.5929i) q^{33} +(-11.8592 + 11.8592i) q^{34} +(-11.1493 + 13.2552i) q^{35} +11.6203i q^{36} +(-18.6605 - 18.6605i) q^{37} +19.4234 q^{38} +(36.4872 - 34.2286i) q^{39} +(-9.10327 + 10.8227i) q^{40} +(40.3015 + 40.3015i) q^{41} -18.8534i q^{42} +52.7965 q^{43} +(8.62329 + 8.62329i) q^{44} +(-2.49751 - 28.9432i) q^{45} +(10.6797 - 10.6797i) q^{46} +(40.6800 + 40.6800i) q^{47} -15.3936i q^{48} -36.9997i q^{49} +(20.3478 - 28.9131i) q^{50} +45.6388i q^{51} +(-18.9623 + 17.7885i) q^{52} -42.2147i q^{53} +(-12.2758 - 12.2758i) q^{54} +(-23.3318 - 19.6250i) q^{55} +9.79806i q^{56} +(37.3744 - 37.3744i) q^{57} +(-21.5195 + 21.5195i) q^{58} +(-5.34862 + 5.34862i) q^{59} +(3.30848 + 38.3415i) q^{60} -72.6777 q^{61} -79.7646 q^{62} +(-14.2321 - 14.2321i) q^{63} +8.00000i q^{64} +(43.4070 - 48.3821i) q^{65} +33.1858 q^{66} +(-48.5284 + 48.5284i) q^{67} -23.7183i q^{68} -41.0996i q^{69} +(-2.10586 - 24.4045i) q^{70} +(56.4982 + 56.4982i) q^{71} +(-11.6203 - 11.6203i) q^{72} +(54.1769 + 54.1769i) q^{73} +37.3210 q^{74} +(-16.4812 - 94.7878i) q^{75} +(-19.4234 + 19.4234i) q^{76} -21.1229 q^{77} +(-2.25863 + 70.7159i) q^{78} -38.8202 q^{79} +(-1.71941 - 19.9260i) q^{80} -99.5335 q^{81} -80.6030 q^{82} +(32.3864 - 32.3864i) q^{83} +(18.8534 + 18.8534i) q^{84} +(5.09769 + 59.0763i) q^{85} +(-52.7965 + 52.7965i) q^{86} +82.8156i q^{87} -17.2466 q^{88} +(-44.0147 + 44.0147i) q^{89} +(31.4407 + 26.4457i) q^{90} +(1.43763 - 45.0109i) q^{91} +21.3593i q^{92} +(-153.483 + 153.483i) q^{93} -81.3601 q^{94} +(44.2040 - 52.5532i) q^{95} +(15.3936 + 15.3936i) q^{96} +(49.9858 - 49.9858i) q^{97} +(36.9997 + 36.9997i) q^{98} +(25.0513 - 25.0513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 4 q^{5} + 28 q^{8} - 42 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{13} + 4 q^{15} - 56 q^{16} - 96 q^{17} + 42 q^{18} + 44 q^{19} + 4 q^{20} + 4 q^{21} - 8 q^{23} + 46 q^{25} + 10 q^{26} + 72 q^{29}+ \cdots + 292 q^{99}+O(q^{100}) $ 14 * q - 14 * q^2 - 4 * q^5 + 28 * q^8 - 42 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^13 + 4 * q^15 - 56 * q^16 - 96 * q^17 + 42 * q^18 + 44 * q^19 + 4 * q^20 + 4 * q^21 - 8 * q^23 + 46 * q^25 + 10 * q^26 + 72 * q^29 + 40 * q^30 - 64 * q^31 + 56 * q^32 - 56 * q^33 + 96 * q^34 + 124 * q^35 - 98 * q^37 - 88 * q^38 - 144 * q^39 - 12 * q^40 + 138 * q^41 + 120 * q^43 - 16 * q^44 - 80 * q^45 + 8 * q^46 + 40 * q^47 - 18 * q^50 - 4 * q^52 - 120 * q^54 - 76 * q^55 + 264 * q^57 - 72 * q^58 - 20 * q^59 - 88 * q^60 - 180 * q^61 + 128 * q^62 + 160 * q^63 - 2 * q^65 + 112 * q^66 - 8 * q^67 - 104 * q^70 - 100 * q^71 - 84 * q^72 + 54 * q^73 + 196 * q^74 - 520 * q^75 + 88 * q^76 + 336 * q^77 + 24 * q^78 + 344 * q^79 + 16 * q^80 + 38 * q^81 - 276 * q^82 - 296 * q^83 - 8 * q^84 + 284 * q^85 - 120 * q^86 + 32 * q^88 - 398 * q^89 - 6 * q^90 + 48 * q^91 - 120 * q^93 - 80 * q^94 + 476 * q^95 + 162 * q^97 - 130 * q^98 + 292 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$			3.84840i			1.28280i	0.767207	+	0.641399i	$0.221646\pi$
$3$			3.84840i			1.28280i	−0.767207	+	0.641399i	$0.778354\pi$
$4$		−	2.00000i		−	0.500000i
$5$	0.429852	+	4.98149i	0.0859704	+	0.996298i
$5$	0.429852	+	4.98149i	0.0859704	+	0.996298i
$6$	−3.84840	−	3.84840i	−0.641399	−	0.641399i
$7$	2.44952	+	2.44952i	0.349931	+	0.349931i	0.860084	−	0.510153i	$-0.170411\pi$
$7$	2.44952	+	2.44952i	0.349931	+	0.349931i	−0.510153	+	0.860084i	$0.670411\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−5.81016			−0.645573
$10$	−5.41134	−	4.55164i	−0.541134	−	0.455164i
$11$	−4.31164	+	4.31164i	−0.391968	+	0.391968i	−0.875388	−	0.483421i	$-0.839394\pi$
$11$	−4.31164	+	4.31164i	−0.391968	+	0.391968i	0.483421	+	0.875388i	$0.339394\pi$
$12$	7.69679			0.641399
$13$	−8.89425	−	9.48115i	−0.684173	−	0.729320i
$13$	−8.89425	−	9.48115i	−0.684173	−	0.729320i
$14$	−4.89903			−0.349931
$15$	−19.1707	+	1.65424i	−1.27805	+	0.110283i
$16$	−4.00000			−0.250000
$17$	11.8592			0.697598			0.348799	−	0.937198i	$-0.386590\pi$
$17$	11.8592			0.697598			0.348799	+	0.937198i	$0.386590\pi$
$18$	5.81016	−	5.81016i	0.322787	−	0.322787i
$19$	−9.71168	−	9.71168i	−0.511141	−	0.511141i	0.403735	−	0.914876i	$-0.367712\pi$
$19$	−9.71168	−	9.71168i	−0.511141	−	0.511141i	−0.914876	+	0.403735i	$0.867712\pi$
$20$	9.96298	−	0.859704i	0.498149	−	0.0429852i
$21$	−9.42671	+	9.42671i	−0.448891	+	0.448891i
$22$		−	8.62329i		−	0.391968i
$23$	−10.6797			−0.464333			−0.232167	−	0.972676i	$-0.574581\pi$
$23$	−10.6797			−0.464333			−0.232167	+	0.972676i	$0.574581\pi$
$24$	−7.69679	+	7.69679i	−0.320700	+	0.320700i
$25$	−24.6305	+	4.28261i	−0.985218	+	0.171304i
$26$	18.3754	+	0.586903i	0.706746	+	0.0225732i
$27$			12.2758i			0.454658i
$28$	4.89903	−	4.89903i	0.174965	−	0.174965i
$29$	21.5195			0.742052			0.371026	−	0.928622i	$-0.379006\pi$
$29$	21.5195			0.742052			0.371026	+	0.928622i	$0.379006\pi$
$30$	17.5165	−	20.8250i	0.583883	−	0.694166i
$31$	39.8823	+	39.8823i	1.28653	+	1.28653i	0.936883	+	0.349643i	$0.113697\pi$
$31$	39.8823	+	39.8823i	1.28653	+	1.28653i	0.349643	+	0.936883i	$0.386303\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−16.5929	−	16.5929i	−0.502816	−	0.502816i
$34$	−11.8592	+	11.8592i	−0.348799	+	0.348799i
$35$	−11.1493	+	13.2552i	−0.318552	+	0.378719i
$36$			11.6203i			0.322787i
$37$	−18.6605	−	18.6605i	−0.504338	−	0.504338i	0.408445	−	0.912783i	$-0.366071\pi$
$37$	−18.6605	−	18.6605i	−0.504338	−	0.504338i	−0.912783	+	0.408445i	$0.866071\pi$
$38$	19.4234			0.511141
$39$	36.4872	−	34.2286i	0.935570	−	0.877657i
$40$	−9.10327	+	10.8227i	−0.227582	+	0.270567i
$41$	40.3015	+	40.3015i	0.982963	+	0.982963i	0.999857	−	0.0168942i	$-0.00537784\pi$
$41$	40.3015	+	40.3015i	0.982963	+	0.982963i	−0.0168942	+	0.999857i	$0.505378\pi$
$42$		−	18.8534i		−	0.448891i
$43$	52.7965			1.22782			0.613912	−	0.789374i	$-0.289595\pi$
$43$	52.7965			1.22782			0.613912	+	0.789374i	$0.289595\pi$
$44$	8.62329	+	8.62329i	0.195984	+	0.195984i
$45$	−2.49751	−	28.9432i	−0.0555002	−	0.643183i
$46$	10.6797	−	10.6797i	0.232167	−	0.232167i
$47$	40.6800	+	40.6800i	0.865533	+	0.865533i	0.991974	−	0.126441i	$-0.0403555\pi$
$47$	40.6800	+	40.6800i	0.865533	+	0.865533i	−0.126441	+	0.991974i	$0.540356\pi$
$48$		−	15.3936i		−	0.320700i
$49$		−	36.9997i		−	0.755097i
$50$	20.3478	−	28.9131i	0.406957	−	0.578261i
$51$			45.6388i			0.894878i
$52$	−18.9623	+	17.7885i	−0.364660	+	0.342087i
$53$		−	42.2147i		−	0.796503i	−0.917276	−	0.398252i	$-0.869617\pi$
$53$		−	42.2147i		−	0.796503i	0.917276	−	0.398252i	$-0.130383\pi$
$54$	−12.2758	−	12.2758i	−0.227329	−	0.227329i
$55$	−23.3318	−	19.6250i	−0.424214	−	0.356819i
$56$			9.79806i			0.174965i
$57$	37.3744	−	37.3744i	0.655691	−	0.655691i
$58$	−21.5195	+	21.5195i	−0.371026	+	0.371026i
$59$	−5.34862	+	5.34862i	−0.0906546	+	0.0906546i	−0.750980	−	0.660325i	$-0.770418\pi$
$59$	−5.34862	+	5.34862i	−0.0906546	+	0.0906546i	0.660325	+	0.750980i	$0.270418\pi$
$60$	3.30848	+	38.3415i	0.0551414	+	0.639025i
$61$	−72.6777			−1.19144			−0.595719	−	0.803193i	$-0.703133\pi$
$61$	−72.6777			−1.19144			−0.595719	+	0.803193i	$0.703133\pi$
$62$	−79.7646			−1.28653
$63$	−14.2321	−	14.2321i	−0.225906	−	0.225906i
$64$			8.00000i			0.125000i
$65$	43.4070	−	48.3821i	0.667801	−	0.744340i
$66$	33.1858			0.502816
$67$	−48.5284	+	48.5284i	−0.724305	+	0.724305i	−0.969479	−	0.245174i	$-0.921155\pi$
$67$	−48.5284	+	48.5284i	−0.724305	+	0.724305i	0.245174	+	0.969479i	$0.421155\pi$
$68$		−	23.7183i		−	0.348799i
$69$		−	41.0996i		−	0.595646i
$70$	−2.10586	−	24.4045i	−0.0300837	−	0.348635i
$71$	56.4982	+	56.4982i	0.795749	+	0.795749i	0.982422	−	0.186673i	$-0.0597705\pi$
$71$	56.4982	+	56.4982i	0.795749	+	0.795749i	−0.186673	+	0.982422i	$0.559771\pi$
$72$	−11.6203	−	11.6203i	−0.161393	−	0.161393i
$73$	54.1769	+	54.1769i	0.742149	+	0.742149i	0.972991	−	0.230842i	$-0.0741482\pi$
$73$	54.1769	+	54.1769i	0.742149	+	0.742149i	−0.230842	+	0.972991i	$0.574148\pi$
$74$	37.3210			0.504338
$75$	−16.4812	−	94.7878i	−0.219749	−	1.26384i
$76$	−19.4234	+	19.4234i	−0.255570	+	0.255570i
$77$	−21.1229			−0.274323
$78$	−2.25863	+	70.7159i	−0.0289568	+	0.906613i
$79$	−38.8202			−0.491395			−0.245698	−	0.969347i	$-0.579017\pi$
$79$	−38.8202			−0.491395			−0.245698	+	0.969347i	$0.579017\pi$
$80$	−1.71941	−	19.9260i	−0.0214926	−	0.249074i
$81$	−99.5335			−1.22881
$82$	−80.6030			−0.982963
$83$	32.3864	−	32.3864i	0.390198	−	0.390198i	−0.484560	−	0.874758i	$-0.661020\pi$
$83$	32.3864	−	32.3864i	0.390198	−	0.390198i	0.874758	+	0.484560i	$0.161020\pi$
$84$	18.8534	+	18.8534i	0.224445	+	0.224445i
$85$	5.09769	+	59.0763i	0.0599728	+	0.695015i
$86$	−52.7965	+	52.7965i	−0.613912	+	0.613912i
$87$			82.8156i			0.951904i
$88$	−17.2466			−0.195984
$89$	−44.0147	+	44.0147i	−0.494547	+	0.494547i	−0.909735	−	0.415189i	$-0.863716\pi$
$89$	−44.0147	+	44.0147i	−0.494547	+	0.494547i	0.415189	+	0.909735i	$0.363716\pi$
$90$	31.4407	+	26.4457i	0.349342	+	0.293841i
$91$	1.43763	−	45.0109i	0.0157981	−	0.494625i
$92$			21.3593i			0.232167i
$93$	−153.483	+	153.483i	−1.65035	+	1.65035i
$94$	−81.3601			−0.865533
$95$	44.2040	−	52.5532i	0.465305	−	0.553191i
$96$	15.3936	+	15.3936i	0.160350	+	0.160350i
$97$	49.9858	−	49.9858i	0.515317	−	0.515317i	−0.400833	−	0.916151i	$-0.631279\pi$
$97$	49.9858	−	49.9858i	0.515317	−	0.515317i	0.916151	+	0.400833i	$0.131279\pi$
$98$	36.9997	+	36.9997i	0.377548	+	0.377548i
$99$	25.0513	−	25.0513i	0.253044	−	0.253044i
$100$	8.56522	+	49.2609i	0.0856522	+	0.492609i
$101$		−	85.1995i		−	0.843560i	−0.906698	−	0.421780i	$-0.861406\pi$
$101$		−	85.1995i		−	0.843560i	0.906698	−	0.421780i	$-0.138594\pi$
$102$	−45.6388	−	45.6388i	−0.447439	−	0.447439i
$103$	11.4074			0.110752			0.0553758	−	0.998466i	$-0.482364\pi$
$103$	11.4074			0.110752			0.0553758	+	0.998466i	$0.482364\pi$
$104$	1.17381	−	36.7508i	0.0112866	−	0.353373i
$105$	−51.0111	−	42.9070i	−0.485820	−	0.408638i
$106$	42.2147	+	42.2147i	0.398252	+	0.398252i
$107$		−	62.1056i		−	0.580426i	−0.956962	−	0.290213i	$-0.906274\pi$
$107$		−	62.1056i		−	0.580426i	0.956962	−	0.290213i	$-0.0937262\pi$
$108$	24.5516			0.227329
$109$	−133.664	−	133.664i	−1.22627	−	1.22627i	−0.965363	−	0.260909i	$-0.915978\pi$
$109$	−133.664	−	133.664i	−1.22627	−	1.22627i	−0.260909	−	0.965363i	$-0.584022\pi$
$110$	42.9568	−	3.70674i	0.390516	−	0.0336976i
$111$	71.8130	−	71.8130i	0.646964	−	0.646964i
$112$	−9.79806	−	9.79806i	−0.0874827	−	0.0874827i
$113$		−	148.138i		−	1.31096i	−0.755214	−	0.655478i	$-0.772467\pi$
$113$		−	148.138i		−	1.31096i	0.755214	−	0.655478i	$-0.227533\pi$
$114$			74.7488i			0.655691i
$115$	−4.59068	−	53.2006i	−0.0399189	−	0.462614i
$116$		−	43.0390i		−	0.371026i
$117$	51.6770	+	55.0870i	0.441684	+	0.470829i
$118$		−	10.6972i		−	0.0906546i
$119$	29.0492	+	29.0492i	0.244111	+	0.244111i
$120$	−41.6500	−	35.0330i	−0.347083	−	0.291942i
$121$			83.8195i			0.692723i
$122$	72.6777	−	72.6777i	0.595719	−	0.595719i
$123$	−155.096	+	155.096i	−1.26094	+	1.26094i
$124$	79.7646	−	79.7646i	0.643263	−	0.643263i
$125$	−31.9212	−	120.855i	−0.255370	−	0.966843i
$126$	28.4641			0.225906
$127$	230.518			1.81511			0.907553	−	0.419938i	$-0.137948\pi$
$127$	230.518			1.81511			0.907553	+	0.419938i	$0.137948\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			203.182i			1.57505i
$130$	4.97506	+	91.7892i	0.0382697	+	0.706070i
$131$	214.401			1.63665			0.818326	−	0.574755i	$-0.194903\pi$
$131$	214.401			1.63665			0.818326	+	0.574755i	$0.194903\pi$
$132$	−33.1858	+	33.1858i	−0.251408	+	0.251408i
$133$		−	47.5778i		−	0.357728i
$134$		−	97.0568i		−	0.724305i
$135$	−61.1517	+	5.27677i	−0.452975	+	0.0390872i
$136$	23.7183	+	23.7183i	0.174399	+	0.174399i
$137$	101.847	+	101.847i	0.743408	+	0.743408i	0.973232	−	0.229824i	$-0.0738152\pi$
$137$	101.847	+	101.847i	0.743408	+	0.743408i	−0.229824	+	0.973232i	$0.573815\pi$
$138$	41.0996	+	41.0996i	0.297823	+	0.297823i
$139$	−75.7601			−0.545037			−0.272519	−	0.962151i	$-0.587857\pi$
$139$	−75.7601			−0.545037			−0.272519	+	0.962151i	$0.587857\pi$
$140$	26.5103	+	22.2986i	0.189360	+	0.159276i
$141$	−156.553	+	156.553i	−1.11030	+	1.11030i
$142$	−112.996			−0.795749
$143$	79.2282	+	2.53052i	0.554043	+	0.0176959i
$144$	23.2406			0.161393
$145$	9.25021	+	107.199i	0.0637946	+	0.739305i
$146$	−108.354			−0.742149
$147$	142.390			0.968637
$148$	−37.3210	+	37.3210i	−0.252169	+	0.252169i
$149$	111.435	+	111.435i	0.747883	+	0.747883i	0.974081	−	0.226198i	$-0.0726296\pi$
$149$	111.435	+	111.435i	0.747883	+	0.747883i	−0.226198	+	0.974081i	$0.572630\pi$
$150$	111.269	+	78.3066i	0.741793	+	0.522044i
$151$	135.707	−	135.707i	0.898722	−	0.898722i	−0.0966013	−	0.995323i	$-0.530797\pi$
$151$	135.707	−	135.707i	0.898722	−	0.898722i	0.995323	+	0.0966013i	$0.0307972\pi$
$152$		−	38.8467i		−	0.255570i
$153$	−68.9036			−0.450350
$154$	21.1229	−	21.1229i	0.137162	−	0.137162i
$155$	−181.530	+	215.817i	−1.17116	+	1.39237i
$156$	−68.4572	−	72.9745i	−0.438828	−	0.467785i
$157$		−	172.878i		−	1.10114i	−0.834790	−	0.550568i	$-0.814411\pi$
$157$		−	172.878i		−	1.10114i	0.834790	−	0.550568i	$-0.185589\pi$
$158$	38.8202	−	38.8202i	0.245698	−	0.245698i
$159$	162.459			1.02175
$160$	21.6454	+	18.2065i	0.135284	+	0.113791i
$161$	−26.1600	−	26.1600i	−0.162485	−	0.162485i
$162$	99.5335	−	99.5335i	0.614404	−	0.614404i
$163$	−55.5819	−	55.5819i	−0.340993	−	0.340993i	0.515747	−	0.856741i	$-0.327514\pi$
$163$	−55.5819	−	55.5819i	−0.340993	−	0.340993i	−0.856741	+	0.515747i	$0.827514\pi$
$164$	80.6030	−	80.6030i	0.491482	−	0.491482i
$165$	75.5249	−	89.7899i	0.457727	−	0.544181i
$166$			64.7728i			0.390198i
$167$	−92.0373	−	92.0373i	−0.551121	−	0.551121i	0.375643	−	0.926764i	$-0.377422\pi$
$167$	−92.0373	−	92.0373i	−0.551121	−	0.551121i	−0.926764	+	0.375643i	$0.877422\pi$
$168$	−37.7068			−0.224445
$169$	−10.7846	+	168.656i	−0.0638140	+	0.997962i
$170$	−64.1740	−	53.9786i	−0.377494	−	0.317521i
$171$	56.4264	+	56.4264i	0.329979	+	0.329979i
$172$		−	105.593i		−	0.613912i
$173$	86.3308			0.499022			0.249511	−	0.968372i	$-0.419730\pi$
$173$	86.3308			0.499022			0.249511	+	0.968372i	$0.419730\pi$
$174$	−82.8156	−	82.8156i	−0.475952	−	0.475952i
$175$	−70.8230	−	49.8424i	−0.404703	−	0.284814i
$176$	17.2466	−	17.2466i	0.0979919	−	0.0979919i
$177$	−20.5836	−	20.5836i	−0.116292	−	0.116292i
$178$		−	88.0293i		−	0.494547i
$179$			223.879i			1.25072i	0.780336	+	0.625361i	$0.215048\pi$
$179$			223.879i			1.25072i	−0.780336	+	0.625361i	$0.784952\pi$
$180$	−57.8865	+	4.99502i	−0.321591	+	0.0277501i
$181$		−	305.729i		−	1.68911i	−0.535468	−	0.844555i	$-0.679865\pi$
$181$		−	305.729i		−	1.68911i	0.535468	−	0.844555i	$-0.320135\pi$
$182$	43.5732	+	46.4485i	0.239413	+	0.255211i
$183$		−	279.693i		−	1.52838i
$184$	−21.3593	−	21.3593i	−0.116083	−	0.116083i
$185$	84.9358	−	100.978i	0.459113	−	0.545829i
$186$		−	306.966i		−	1.65035i
$187$	−51.1325	+	51.1325i	−0.273436	+	0.273436i
$188$	81.3601	−	81.3601i	0.432766	−	0.432766i
$189$	−30.0697	+	30.0697i	−0.159099	+	0.159099i
$190$	8.34917	+	96.7572i	0.0439430	+	0.509248i
$191$	−288.933			−1.51274			−0.756368	−	0.654146i	$-0.773028\pi$
$191$	−288.933			−1.51274			−0.756368	+	0.654146i	$0.773028\pi$
$192$	−30.7872			−0.160350
$193$	116.591	+	116.591i	0.604098	+	0.604098i	0.941397	−	0.337299i	$-0.109513\pi$
$193$	116.591	+	116.591i	0.604098	+	0.604098i	−0.337299	+	0.941397i	$0.609513\pi$
$194$			99.9716i			0.515317i
$195$	186.194	+	167.048i	0.954839	+	0.856654i
$196$	−73.9995			−0.377548
$197$	−104.376	+	104.376i	−0.529827	+	0.529827i	−0.920521	−	0.390694i	$-0.872235\pi$
$197$	−104.376	+	104.376i	−0.529827	+	0.529827i	0.390694	+	0.920521i	$0.372235\pi$
$198$			50.1027i			0.253044i
$199$		−	194.443i		−	0.977101i	−0.872536	−	0.488551i	$-0.837526\pi$
$199$		−	194.443i		−	0.977101i	0.872536	−	0.488551i	$-0.162474\pi$
$200$	−57.8261	−	40.6957i	−0.289131	−	0.203478i
$201$	−186.757	−	186.757i	−0.929137	−	0.929137i
$202$	85.1995	+	85.1995i	0.421780	+	0.421780i
$203$	52.7124	+	52.7124i	0.259667	+	0.259667i
$204$	91.2775			0.447439
$205$	−183.438	+	218.085i	−0.894818	+	1.06383i
$206$	−11.4074	+	11.4074i	−0.0553758	+	0.0553758i
$207$	62.0506			0.299761
$208$	35.5770	+	37.9246i	0.171043	+	0.182330i
$209$	83.7466			0.400701
$210$	93.9181	−	8.10418i	0.447229	−	0.0385914i
$211$	−103.472			−0.490389			−0.245195	−	0.969474i	$-0.578852\pi$
$211$	−103.472			−0.490389			−0.245195	+	0.969474i	$0.578852\pi$
$212$	−84.4293			−0.398252
$213$	−217.427	+	217.427i	−1.02079	+	1.02079i
$214$	62.1056	+	62.1056i	0.290213	+	0.290213i
$215$	22.6947	+	263.005i	0.105557	+	1.22328i
$216$	−24.5516	+	24.5516i	−0.113665	+	0.113665i
$217$			195.385i			0.900390i
$218$	267.327			1.22627
$219$	−208.494	+	208.494i	−0.952028	+	0.952028i
$220$	−39.2501	+	46.6635i	−0.178409	+	0.212107i
$221$	−105.478	−	112.439i	−0.477278	−	0.508772i
$222$			143.626i			0.646964i
$223$	14.2146	−	14.2146i	0.0637428	−	0.0637428i	−0.674517	−	0.738260i	$-0.735648\pi$
$223$	14.2146	−	14.2146i	0.0637428	−	0.0637428i	0.738260	+	0.674517i	$0.235648\pi$
$224$	19.5961			0.0874827
$225$	143.107	−	24.8826i	0.636030	−	0.110589i
$226$	148.138	+	148.138i	0.655478	+	0.655478i
$227$	−283.524	+	283.524i	−1.24900	+	1.24900i	−0.292842	+	0.956161i	$0.594601\pi$
$227$	−283.524	+	283.524i	−1.24900	+	1.24900i	−0.956161	+	0.292842i	$0.905399\pi$
$228$	−74.7488	−	74.7488i	−0.327845	−	0.327845i
$229$	303.668	−	303.668i	1.32606	−	1.32606i	0.417288	−	0.908774i	$-0.362981\pi$
$229$	303.668	−	303.668i	1.32606	−	1.32606i	0.908774	−	0.417288i	$-0.137019\pi$
$230$	57.7913	+	48.6100i	0.251267	+	0.211348i
$231$		−	81.2892i		−	0.351901i
$232$	43.0390	+	43.0390i	0.185513	+	0.185513i
$233$	−134.811			−0.578588			−0.289294	−	0.957240i	$-0.593420\pi$
$233$	−134.811			−0.578588			−0.289294	+	0.957240i	$0.593420\pi$
$234$	−106.764	−	3.41000i	−0.456256	−	0.0145726i
$235$	−185.161	+	220.134i	−0.787918	+	0.936739i
$236$	10.6972	+	10.6972i	0.0453273	+	0.0453273i
$237$		−	149.396i		−	0.630361i
$238$	−58.0984			−0.244111
$239$	−204.968	−	204.968i	−0.857606	−	0.857606i	0.133449	−	0.991056i	$-0.457395\pi$
$239$	−204.968	−	204.968i	−0.857606	−	0.857606i	−0.991056	+	0.133449i	$0.957395\pi$
$240$	76.6830	−	6.61697i	0.319512	−	0.0275707i
$241$	264.576	−	264.576i	1.09782	−	1.09782i	0.103160	−	0.994665i	$-0.467105\pi$
$241$	264.576	−	264.576i	1.09782	−	1.09782i	0.994665	−	0.103160i	$-0.0328953\pi$
$242$	−83.8195	−	83.8195i	−0.346361	−	0.346361i
$243$		−	272.562i		−	1.12166i
$244$			145.355i			0.595719i
$245$	184.314	−	15.9044i	0.752301	−	0.0649160i
$246$		−	310.192i		−	1.26094i
$247$	−5.69981	+	178.456i	−0.0230761	+	0.722494i
$248$			159.529i			0.643263i
$249$	124.636	+	124.636i	0.500545	+	0.500545i
$250$	152.777	+	88.9342i	0.611107	+	0.355737i
$251$			89.6680i			0.357243i	0.983918	+	0.178621i	$0.0571638\pi$
$251$			89.6680i			0.357243i	−0.983918	+	0.178621i	$0.942836\pi$
$252$	−28.4641	+	28.4641i	−0.112953	+	0.112953i
$253$	46.0469	−	46.0469i	0.182004	−	0.182004i
$254$	−230.518	+	230.518i	−0.907553	+	0.907553i
$255$	−227.349	+	19.6179i	−0.891565	+	0.0769330i
$256$	16.0000			0.0625000
$257$	−209.326			−0.814497			−0.407248	−	0.913317i	$-0.633512\pi$
$257$	−209.326			−0.814497			−0.407248	+	0.913317i	$0.633512\pi$
$258$	−203.182	−	203.182i	−0.787526	−	0.787526i
$259$		−	91.4184i		−	0.352967i
$260$	−96.7642	−	86.8141i	−0.372170	−	0.333900i
$261$	−125.032			−0.479049
$262$	−214.401	+	214.401i	−0.818326	+	0.818326i
$263$		−	135.381i		−	0.514756i	−0.966311	−	0.257378i	$-0.917141\pi$
$263$		−	135.381i		−	0.514756i	0.966311	−	0.257378i	$-0.0828585\pi$
$264$		−	66.3717i		−	0.251408i
$265$	210.292	−	18.1461i	0.793554	−	0.0684757i
$266$	47.5778	+	47.5778i	0.178864	+	0.178864i
$267$	−169.386	−	169.386i	−0.634404	−	0.634404i
$268$	97.0568	+	97.0568i	0.362152	+	0.362152i
$269$	65.9632			0.245217			0.122608	−	0.992455i	$-0.460874\pi$
$269$	65.9632			0.245217			0.122608	+	0.992455i	$0.460874\pi$
$270$	55.8749	−	66.4284i	0.206944	−	0.246031i
$271$	−290.080	+	290.080i	−1.07040	+	1.07040i	−0.0730788	+	0.997326i	$0.523282\pi$
$271$	−290.080	+	290.080i	−1.07040	+	1.07040i	−0.997326	+	0.0730788i	$0.976718\pi$
$272$	−47.4367			−0.174399
$273$	173.220	+	5.53256i	0.634504	+	0.0202658i
$274$	−203.694			−0.743408
$275$	87.7327	−	124.663i	0.319028	−	0.453319i
$276$	−82.1992			−0.297823
$277$	191.294			0.690593			0.345296	−	0.938494i	$-0.387778\pi$
$277$	191.294			0.690593			0.345296	+	0.938494i	$0.387778\pi$
$278$	75.7601	−	75.7601i	0.272519	−	0.272519i
$279$	−231.722	−	231.722i	−0.830546	−	0.830546i
$280$	−48.8089	+	4.21172i	−0.174318	+	0.0150419i
$281$	131.638	−	131.638i	0.468464	−	0.468464i	−0.432953	−	0.901417i	$-0.642528\pi$
$281$	131.638	−	131.638i	0.468464	−	0.468464i	0.901417	+	0.432953i	$0.142528\pi$
$282$		−	313.106i		−	1.11030i
$283$	380.847			1.34575			0.672875	−	0.739756i	$-0.265059\pi$
$283$	380.847			1.34575			0.672875	+	0.739756i	$0.265059\pi$
$284$	112.996	−	112.996i	0.397874	−	0.397874i
$285$	202.246	+	170.115i	0.709633	+	0.596893i
$286$	−81.7587	+	76.6977i	−0.285870	+	0.268174i
$287$			197.438i			0.687938i
$288$	−23.2406	+	23.2406i	−0.0806966	+	0.0806966i
$289$	−148.360			−0.513357
$290$	−116.449	−	97.9490i	−0.401550	−	0.337755i
$291$	192.365	+	192.365i	0.661049	+	0.661049i
$292$	108.354	−	108.354i	0.371074	−	0.371074i
$293$	−33.0661	−	33.0661i	−0.112854	−	0.112854i	0.648425	−	0.761279i	$-0.275428\pi$
$293$	−33.0661	−	33.0661i	−0.112854	−	0.112854i	−0.761279	+	0.648425i	$0.775428\pi$
$294$	−142.390	+	142.390i	−0.484319	+	0.484319i
$295$	−28.9432	−	24.3450i	−0.0981126	−	0.0825254i
$296$		−	74.6420i		−	0.252169i
$297$	−52.9288	−	52.9288i	−0.178211	−	0.178211i
$298$	−222.869			−0.747883
$299$	94.9877	+	101.256i	0.317684	+	0.338647i
$300$	−189.576	+	32.9623i	−0.631918	+	0.109874i
$301$	129.326	+	129.326i	0.429654	+	0.429654i
$302$			271.414i			0.898722i
$303$	327.882			1.08212
$304$	38.8467	+	38.8467i	0.127785	+	0.127785i
$305$	−31.2407	−	362.043i	−0.102428	−	1.18703i
$306$	68.9036	−	68.9036i	0.225175	−	0.225175i
$307$	−365.876	−	365.876i	−1.19178	−	1.19178i	−0.976568	−	0.215210i	$-0.930956\pi$
$307$	−365.876	−	365.876i	−1.19178	−	1.19178i	−0.215210	−	0.976568i	$-0.569044\pi$
$308$			42.2458i			0.137162i
$309$			43.9002i			0.142072i
$310$	−34.2870	−	397.346i	−0.110603	−	1.28176i
$311$		−	315.994i		−	1.01606i	−0.861340	−	0.508028i	$-0.830374\pi$
$311$		−	315.994i		−	1.01606i	0.861340	−	0.508028i	$-0.169626\pi$
$312$	141.432	+	4.51727i	0.453307	+	0.0144784i
$313$			65.8042i			0.210237i	0.994460	+	0.105118i	$0.0335222\pi$
$313$			65.8042i			0.210237i	−0.994460	+	0.105118i	$0.966478\pi$
$314$	172.878	+	172.878i	0.550568	+	0.550568i
$315$	64.7792	−	77.0146i	0.205648	−	0.244491i
$316$			77.6405i			0.245698i
$317$	169.512	−	169.512i	0.534739	−	0.534739i	−0.387240	−	0.921979i	$-0.626571\pi$
$317$	169.512	−	169.512i	0.534739	−	0.534739i	0.921979	+	0.387240i	$0.126571\pi$
$318$	−162.459	+	162.459i	−0.510877	+	0.510877i
$319$	−92.7845	+	92.7845i	−0.290861	+	0.290861i
$320$	−39.8519	+	3.43882i	−0.124537	+	0.0107463i
$321$	239.007			0.744570
$322$	52.3200			0.162485
$323$	−115.172	−	115.172i	−0.356571	−	0.356571i
$324$			199.067i			0.614404i
$325$	259.674	+	195.435i	0.798995	+	0.601337i
$326$	111.164			0.340993
$327$	514.391	−	514.391i	1.57306	−	1.57306i
$328$			161.206i			0.491482i
$329$			199.293i			0.605753i
$330$	14.2650	+	165.315i	0.0432273	+	0.500954i
$331$	140.641	+	140.641i	0.424896	+	0.424896i	0.886886	−	0.461989i	$-0.152864\pi$
$331$	140.641	+	140.641i	0.424896	+	0.424896i	−0.461989	+	0.886886i	$0.652864\pi$
$332$	−64.7728	−	64.7728i	−0.195099	−	0.195099i
$333$	108.420	+	108.420i	0.325587	+	0.325587i
$334$	184.075			0.551121
$335$	−262.604	−	220.884i	−0.783892	−	0.659354i
$336$	37.7068	−	37.7068i	0.112223	−	0.112223i
$337$	275.256			0.816784			0.408392	−	0.912807i	$-0.366090\pi$
$337$	275.256			0.816784			0.408392	+	0.912807i	$0.366090\pi$
$338$	−157.871	−	179.440i	−0.467074	−	0.530888i
$339$	570.094			1.68169
$340$	118.153	−	10.1954i	0.347508	−	0.0299864i
$341$	−343.917			−1.00855
$342$	−112.853			−0.329979
$343$	210.658	−	210.658i	0.614163	−	0.614163i
$344$	105.593	+	105.593i	0.306956	+	0.306956i
$345$	204.737	−	17.6668i	0.593441	−	0.0512080i
$346$	−86.3308	+	86.3308i	−0.249511	+	0.249511i
$347$			539.829i			1.55570i	0.628448	+	0.777851i	$0.283690\pi$
$347$			539.829i			1.55570i	−0.628448	+	0.777851i	$0.716310\pi$
$348$	165.631			0.475952
$349$	387.267	−	387.267i	1.10965	−	1.10965i	0.116452	−	0.993196i	$-0.462848\pi$
$349$	387.267	−	387.267i	1.10965	−	1.10965i	0.993196	−	0.116452i	$-0.0371522\pi$
$350$	120.665	−	20.9806i	0.344758	−	0.0599447i
$351$	116.389	−	109.184i	0.331591	−	0.311065i
$352$			34.4932i			0.0979919i
$353$	−440.861	+	440.861i	−1.24890	+	1.24890i	−0.292693	+	0.956207i	$0.594551\pi$
$353$	−440.861	+	440.861i	−1.24890	+	1.24890i	−0.956207	+	0.292693i	$0.905449\pi$
$354$	41.1673			0.116292
$355$	−257.159	+	305.731i	−0.724392	+	0.861214i
$356$	88.0293	+	88.0293i	0.247273	+	0.247273i
$357$	−111.793	+	111.793i	−0.313145	+	0.313145i
$358$	−223.879	−	223.879i	−0.625361	−	0.625361i
$359$	−122.211	+	122.211i	−0.340421	+	0.340421i	−0.856525	−	0.516105i	$-0.827382\pi$
$359$	−122.211	+	122.211i	−0.340421	+	0.340421i	0.516105	+	0.856525i	$0.327382\pi$
$360$	52.8914	−	62.8815i	0.146921	−	0.174671i
$361$		−	172.367i		−	0.477470i
$362$	305.729	+	305.729i	0.844555	+	0.844555i
$363$	−322.571			−0.888624
$364$	−90.0217	−	2.87525i	−0.247312	−	0.00789905i
$365$	−246.593	+	293.169i	−0.675598	+	0.803204i
$366$	279.693	+	279.693i	0.764188	+	0.764188i
$367$		−	460.229i		−	1.25403i	−0.779007	−	0.627015i	$-0.784277\pi$
$367$		−	460.229i		−	1.25403i	0.779007	−	0.627015i	$-0.215723\pi$
$368$	42.7187			0.116083
$369$	−234.158	−	234.158i	−0.634575	−	0.634575i
$370$	16.0425	+	185.914i	0.0433582	+	0.502471i
$371$	103.406	−	103.406i	0.278721	−	0.278721i
$372$	306.966	+	306.966i	0.825177	+	0.825177i
$373$			550.843i			1.47679i	0.674369	+	0.738395i	$0.264416\pi$
$373$			550.843i			1.47679i	−0.674369	+	0.738395i	$0.735584\pi$
$374$		−	102.265i		−	0.273436i
$375$	465.100	−	122.846i	1.24027	−	0.327588i
$376$			162.720i			0.432766i
$377$	−191.400	−	204.030i	−0.507692	−	0.541193i
$378$		−	60.1394i		−	0.159099i
$379$	−318.854	−	318.854i	−0.841303	−	0.841303i	0.147726	−	0.989028i	$-0.452805\pi$
$379$	−318.854	−	318.854i	−0.841303	−	0.841303i	−0.989028	+	0.147726i	$0.952805\pi$
$380$	−105.106	−	88.4080i	−0.276596	−	0.232653i
$381$			887.126i			2.32842i
$382$	288.933	−	288.933i	0.756368	−	0.756368i
$383$	87.4053	−	87.4053i	0.228212	−	0.228212i	−0.583733	−	0.811946i	$-0.698409\pi$
$383$	87.4053	−	87.4053i	0.228212	−	0.228212i	0.811946	+	0.583733i	$0.198409\pi$
$384$	30.7872	−	30.7872i	0.0801749	−	0.0801749i
$385$	−9.07972	−	105.223i	−0.0235837	−	0.273308i
$386$	−233.182			−0.604098
$387$	−306.756			−0.792651
$388$	−99.9716	−	99.9716i	−0.257659	−	0.257659i
$389$		−	221.342i		−	0.569004i	−0.958675	−	0.284502i	$-0.908172\pi$
$389$		−	221.342i		−	0.569004i	0.958675	−	0.284502i	$-0.0918282\pi$
$390$	−353.241	+	19.1460i	−0.905746	+	0.0490923i
$391$	−126.652			−0.323918
$392$	73.9995	−	73.9995i	0.188774	−	0.188774i
$393$			825.101i			2.09949i
$394$		−	208.752i		−	0.529827i
$395$	−16.6870	−	193.383i	−0.0422455	−	0.489576i
$396$	−50.1027	−	50.1027i	−0.126522	−	0.126522i
$397$	2.99158	+	2.99158i	0.00753545	+	0.00753545i	0.710864	−	0.703329i	$-0.248304\pi$
$397$	2.99158	+	2.99158i	0.00753545	+	0.00753545i	−0.703329	+	0.710864i	$0.748304\pi$
$398$	194.443	+	194.443i	0.488551	+	0.488551i
$399$	183.098			0.458893
$400$	98.5218	−	17.1304i	0.246305	−	0.0428261i
$401$	27.4281	−	27.4281i	0.0683993	−	0.0683993i	−0.672080	−	0.740479i	$-0.734599\pi$
$401$	27.4281	−	27.4281i	0.0683993	−	0.0683993i	0.740479	+	0.672080i	$0.234599\pi$
$402$	373.513			0.929137
$403$	23.4070	−	732.853i	0.0580820	−	1.81850i
$404$	−170.399			−0.421780
$405$	−42.7847	−	495.825i	−0.105641	−	1.22426i
$406$	−105.425			−0.259667
$407$	160.915			0.395368
$408$	−91.2775	+	91.2775i	−0.223719	+	0.223719i
$409$	−226.925	−	226.925i	−0.554828	−	0.554828i	0.373002	−	0.927830i	$-0.378328\pi$
$409$	−226.925	−	226.925i	−0.554828	−	0.554828i	−0.927830	+	0.373002i	$0.878328\pi$
$410$	−34.6474	−	401.523i	−0.0845058	−	0.979324i
$411$	−391.947	+	391.947i	−0.953643	+	0.953643i
$412$		−	22.8148i		−	0.0553758i
$413$	−26.2031			−0.0634457
$414$	−62.0506	+	62.0506i	−0.149881	+	0.149881i
$415$	175.254	+	147.411i	0.422298	+	0.355207i
$416$	−73.5016	−	2.34761i	−0.176687	−	0.00564329i
$417$		−	291.555i		−	0.699173i
$418$	−83.7466	+	83.7466i	−0.200351	+	0.200351i
$419$	146.384			0.349364			0.174682	−	0.984625i	$-0.444110\pi$
$419$	146.384			0.349364			0.174682	+	0.984625i	$0.444110\pi$
$420$	−85.8139	+	102.022i	−0.204319	+	0.242910i
$421$	465.756	+	465.756i	1.10631	+	1.10631i	0.993632	+	0.112676i	$0.0359423\pi$
$421$	465.756	+	465.756i	1.10631	+	1.10631i	0.112676	+	0.993632i	$0.464058\pi$
$422$	103.472	−	103.472i	0.245195	−	0.245195i
$423$	−236.357	−	236.357i	−0.558765	−	0.558765i
$424$	84.4293	−	84.4293i	0.199126	−	0.199126i
$425$	−292.097	+	50.7881i	−0.687286	+	0.119502i
$426$		−	434.855i		−	1.02079i
$427$	−178.025	−	178.025i	−0.416921	−	0.416921i
$428$	−124.211			−0.290213
$429$	−9.73843	+	304.902i	−0.0227003	+	0.710726i
$430$	−285.700	−	240.310i	−0.664418	−	0.558861i
$431$	−412.642	−	412.642i	−0.957406	−	0.957406i	0.0417231	−	0.999129i	$-0.486715\pi$
$431$	−412.642	−	412.642i	−0.957406	−	0.957406i	−0.999129	+	0.0417231i	$0.986715\pi$
$432$		−	49.1031i		−	0.113665i
$433$	−490.129			−1.13194			−0.565968	−	0.824427i	$-0.691498\pi$
$433$	−490.129			−1.13194			−0.565968	+	0.824427i	$0.691498\pi$
$434$	−195.385	−	195.385i	−0.450195	−	0.450195i
$435$	−412.545	+	35.5985i	−0.948380	+	0.0818356i
$436$	−267.327	+	267.327i	−0.613136	+	0.613136i
$437$	103.717	+	103.717i	0.237340	+	0.237340i
$438$		−	416.988i		−	0.952028i
$439$			32.6479i			0.0743687i	0.999308	+	0.0371844i	$0.0118389\pi$
$439$			32.6479i			0.0743687i	−0.999308	+	0.0371844i	$0.988161\pi$
$440$	−7.41348	−	85.9136i	−0.0168488	−	0.195258i
$441$			214.974i			0.487470i
$442$	217.917	+	6.96017i	0.493025	+	0.0157470i
$443$			458.868i			1.03582i	0.855436	+	0.517909i	$0.173289\pi$
$443$			458.868i			1.03582i	−0.855436	+	0.517909i	$0.826711\pi$
$444$	−143.626	−	143.626i	−0.323482	−	0.323482i
$445$	−238.178	−	200.339i	−0.535232	−	0.450199i
$446$			28.4293i			0.0637428i
$447$	−428.845	+	428.845i	−0.959384	+	0.959384i
$448$	−19.5961	+	19.5961i	−0.0437414	+	0.0437414i
$449$	−290.072	+	290.072i	−0.646041	+	0.646041i	−0.952034	−	0.305993i	$-0.901012\pi$
$449$	−290.072	+	290.072i	−0.646041	+	0.646041i	0.305993	+	0.952034i	$0.401012\pi$
$450$	−118.224	+	167.989i	−0.262720	+	0.373310i
$451$	−347.531			−0.770579
$452$	−296.276			−0.655478
$453$	522.254	+	522.254i	1.15288	+	1.15288i
$454$		−	567.047i		−	1.24900i
$455$	224.839	−	12.1865i	0.494152	−	0.0267835i
$456$	149.498			0.327845
$457$	338.468	−	338.468i	0.740631	−	0.740631i	−0.232068	−	0.972699i	$-0.574549\pi$
$457$	338.468	−	338.468i	0.740631	−	0.740631i	0.972699	+	0.232068i	$0.0745493\pi$
$458$			607.337i			1.32606i
$459$			145.580i			0.317169i
$460$	−106.401	+	9.18136i	−0.231307	+	0.0199595i
$461$	351.781	+	351.781i	0.763082	+	0.763082i	0.976878	−	0.213796i	$-0.0685828\pi$
$461$	351.781	+	351.781i	0.763082	+	0.763082i	−0.213796	+	0.976878i	$0.568583\pi$
$462$	81.2892	+	81.2892i	0.175951	+	0.175951i
$463$	−283.858	−	283.858i	−0.613085	−	0.613085i	0.330664	−	0.943749i	$-0.392727\pi$
$463$	−283.858	−	283.858i	−0.613085	−	0.613085i	−0.943749	+	0.330664i	$0.892727\pi$
$464$	−86.0781			−0.185513
$465$	−830.548	−	698.598i	−1.78613	−	1.50236i
$466$	134.811	−	134.811i	0.289294	−	0.289294i
$467$	−267.631			−0.573085			−0.286543	−	0.958067i	$-0.592506\pi$
$467$	−267.631			−0.573085			−0.286543	+	0.958067i	$0.592506\pi$
$468$	110.174	−	103.354i	0.235415	−	0.220842i
$469$	−237.742			−0.506913
$470$	−34.9728	−	405.294i	−0.0744102	−	0.862328i
$471$	665.304			1.41254
$472$	−21.3945			−0.0453273
$473$	−227.640	+	227.640i	−0.481268	+	0.481268i
$474$	149.396	+	149.396i	0.315181	+	0.315181i
$475$	280.794	+	197.612i	0.591146	+	0.416025i
$476$	58.0984	−	58.0984i	0.122056	−	0.122056i
$477$			245.274i			0.514201i
$478$	409.936			0.857606
$479$	−226.465	+	226.465i	−0.472788	+	0.472788i	−0.902816	−	0.430028i	$-0.858504\pi$
$479$	−226.465	+	226.465i	−0.472788	+	0.472788i	0.430028	+	0.902816i	$0.358504\pi$
$480$	−70.0660	+	83.2999i	−0.145971	+	0.173542i
$481$	−10.9519	+	342.894i	−0.0227690	+	0.712878i
$482$			529.151i			1.09782i
$483$	100.674	−	100.674i	0.208435	−	0.208435i
$484$	167.639			0.346361
$485$	270.490	+	227.517i	0.557712	+	0.469108i
$486$	272.562	+	272.562i	0.560828	+	0.560828i
$487$	−127.792	+	127.792i	−0.262406	+	0.262406i	−0.826031	−	0.563625i	$-0.809406\pi$
$487$	−127.792	+	127.792i	−0.262406	+	0.262406i	0.563625	+	0.826031i	$0.309406\pi$
$488$	−145.355	−	145.355i	−0.297860	−	0.297860i
$489$	213.901	−	213.901i	0.437426	−	0.437426i
$490$	−168.409	+	200.218i	−0.343693	+	0.408609i
$491$			430.146i			0.876060i	0.898960	+	0.438030i	$0.144324\pi$
$491$			430.146i			0.876060i	−0.898960	+	0.438030i	$0.855676\pi$
$492$	310.192	+	310.192i	0.630472	+	0.630472i
$493$	255.204			0.517654
$494$	−172.756	−	184.156i	−0.349709	−	0.372785i
$495$	135.561	+	114.025i	0.273861	+	0.230353i
$496$	−159.529	−	159.529i	−0.321631	−	0.321631i
$497$			276.786i			0.556914i
$498$	−249.271			−0.500545
$499$	270.521	+	270.521i	0.542127	+	0.542127i	0.924152	−	0.382025i	$-0.124773\pi$
$499$	270.521	+	270.521i	0.542127	+	0.542127i	−0.382025	+	0.924152i	$0.624773\pi$
$500$	−241.711	+	63.8424i	−0.483422	+	0.127685i
$501$	354.196	−	354.196i	0.706978	−	0.706978i
$502$	−89.6680	−	89.6680i	−0.178621	−	0.178621i
$503$		−	455.762i		−	0.906088i	−0.891488	−	0.453044i	$-0.850338\pi$
$503$		−	455.762i		−	0.906088i	0.891488	−	0.453044i	$-0.149662\pi$
$504$		−	56.9283i		−	0.112953i
$505$	424.420	−	36.6232i	0.840436	−	0.0725212i
$506$			92.0939i			0.182004i
$507$	−649.053	−	41.5033i	−1.28018	−	0.0818606i
$508$		−	461.037i		−	0.907553i
$509$	−169.114	−	169.114i	−0.332248	−	0.332248i	0.521192	−	0.853440i	$-0.325488\pi$
$509$	−169.114	−	169.114i	−0.332248	−	0.332248i	−0.853440	+	0.521192i	$0.825488\pi$
$510$	207.731	−	246.967i	0.407316	−	0.484249i
$511$			265.414i			0.519402i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	119.218	−	119.218i	0.232395	−	0.232395i
$514$	209.326	−	209.326i	0.407248	−	0.407248i
$515$	4.90350	+	56.8259i	0.00952136	+	0.110342i
$516$	406.363			0.787526
$517$	−350.796			−0.678522
$518$	91.4184	+	91.4184i	0.176483	+	0.176483i
$519$			332.235i			0.640145i
$520$	183.578	−	9.95012i	0.353035	−	0.0191348i
$521$	388.553			0.745782			0.372891	−	0.927875i	$-0.378366\pi$
$521$	388.553			0.745782			0.372891	+	0.927875i	$0.378366\pi$
$522$	125.032	−	125.032i	0.239525	−	0.239525i
$523$			508.158i			0.971622i	0.874064	+	0.485811i	$0.161476\pi$
$523$			508.158i			0.971622i	−0.874064	+	0.485811i	$0.838524\pi$
$524$		−	428.803i		−	0.818326i
$525$	191.813	−	272.555i	0.365359	−	0.519152i
$526$	135.381	+	135.381i	0.257378	+	0.257378i
$527$	472.971	+	472.971i	0.897478	+	0.897478i
$528$	66.3717	+	66.3717i	0.125704	+	0.125704i
$529$	−414.945			−0.784395
$530$	−192.146	+	228.438i	−0.362539	+	0.431015i
$531$	31.0763	−	31.0763i	0.0585242	−	0.0585242i
$532$	−95.1556			−0.178864
$533$	23.6530	−	740.556i	0.0443772	−	1.38941i
$534$	338.772			0.634404
$535$	309.378	−	26.6962i	0.578278	−	0.0498995i
$536$	−194.114			−0.362152
$537$	−861.576			−1.60442
$538$	−65.9632	+	65.9632i	−0.122608	+	0.122608i
$539$	159.530	+	159.530i	0.295973	+	0.295973i
$540$	10.5535	+	122.303i	0.0195436	+	0.226488i
$541$	−154.103	+	154.103i	−0.284849	+	0.284849i	−0.835039	−	0.550190i	$-0.814555\pi$
$541$	−154.103	+	154.103i	−0.284849	+	0.284849i	0.550190	+	0.835039i	$0.314555\pi$
$542$		−	580.159i		−	1.07040i
$543$	1176.57			2.16679
$544$	47.4367	−	47.4367i	0.0871997	−	0.0871997i
$545$	608.388	−	723.300i	1.11631	−	1.32716i
$546$	−178.752	+	167.687i	−0.327385	+	0.307119i
$547$		−	164.591i		−	0.300898i	−0.988618	−	0.150449i	$-0.951928\pi$
$547$		−	164.591i		−	0.300898i	0.988618	−	0.150449i	$-0.0480720\pi$
$548$	203.694	−	203.694i	0.371704	−	0.371704i
$549$	422.269			0.769160
$550$	36.9302	+	212.395i	0.0671457	+	0.386174i
$551$	−208.991	−	208.991i	−0.379293	−	0.379293i
$552$	82.1992	−	82.1992i	0.148912	−	0.148912i
$553$	−95.0908	−	95.0908i	−0.171954	−	0.171954i
$554$	−191.294	+	191.294i	−0.345296	+	0.345296i
$555$	388.605	+	326.867i	0.700189	+	0.588949i
$556$			151.520i			0.272519i
$557$	−551.903	−	551.903i	−0.990850	−	0.990850i	0.00910881	−	0.999959i	$-0.497101\pi$
$557$	−551.903	−	551.903i	−0.990850	−	0.990850i	−0.999959	+	0.00910881i	$0.997101\pi$
$558$	463.445			0.830546
$559$	−469.585	−	500.571i	−0.840045	−	0.895477i
$560$	44.5972	−	53.0207i	0.0796379	−	0.0946798i
$561$	−196.778	−	196.778i	−0.350763	−	0.350763i
$562$			263.277i			0.468464i
$563$	128.247			0.227792			0.113896	−	0.993493i	$-0.463667\pi$
$563$	128.247			0.227792			0.113896	+	0.993493i	$0.463667\pi$
$564$	313.106	+	313.106i	0.555152	+	0.555152i
$565$	737.948	−	63.6775i	1.30610	−	0.112704i
$566$	−380.847	+	380.847i	−0.672875	+	0.672875i
$567$	−243.809	−	243.809i	−0.429998	−	0.429998i
$568$			225.993i			0.397874i
$569$			758.893i			1.33373i	0.745178	+	0.666865i	$0.232364\pi$
$569$			758.893i			1.33373i	−0.745178	+	0.666865i	$0.767636\pi$
$570$	−372.360	+	32.1309i	−0.653263	+	0.0563700i
$571$			87.8635i			0.153877i	0.997036	+	0.0769383i	$0.0245144\pi$
$571$			87.8635i			0.153877i	−0.997036	+	0.0769383i	$0.975486\pi$
$572$	5.06103	−	158.456i	0.00884796	−	0.277022i
$573$		−	1111.93i		−	1.94054i
$574$	−197.438	−	197.438i	−0.343969	−	0.343969i
$575$	263.045	−	45.7368i	0.457470	−	0.0795423i
$576$		−	46.4813i		−	0.0806966i
$577$	−297.465	+	297.465i	−0.515537	+	0.515537i	−0.916218	−	0.400681i	$-0.868774\pi$
$577$	−297.465	+	297.465i	−0.515537	+	0.515537i	0.400681	+	0.916218i	$0.368774\pi$
$578$	148.360	−	148.360i	0.256679	−	0.256679i
$579$	−448.688	+	448.688i	−0.774936	+	0.774936i
$580$	214.398	−	18.5004i	0.369653	−	0.0318973i
$581$	158.662			0.273084
$582$	−384.730			−0.661049
$583$	182.015	+	182.015i	0.312203	+	0.312203i
$584$			216.707i			0.371074i
$585$	−252.202	+	281.108i	−0.431114	+	0.480526i
$586$	66.1323			0.112854
$587$	132.481	−	132.481i	0.225692	−	0.225692i	−0.585198	−	0.810890i	$-0.698983\pi$
$587$	132.481	−	132.481i	0.225692	−	0.225692i	0.810890	+	0.585198i	$0.198983\pi$
$588$		−	284.779i		−	0.484319i
$589$		−	774.648i		−	1.31519i
$590$	53.2882	−	4.59824i	0.0903190	−	0.00779362i
$591$	−401.680	−	401.680i	−0.679662	−	0.679662i
$592$	74.6420	+	74.6420i	0.126085	+	0.126085i
$593$	−94.7444	−	94.7444i	−0.159771	−	0.159771i	0.622694	−	0.782465i	$-0.286038\pi$
$593$	−94.7444	−	94.7444i	−0.159771	−	0.159771i	−0.782465	+	0.622694i	$0.786038\pi$
$594$	105.858			0.178211
$595$	−132.221	+	157.195i	−0.222221	+	0.264194i
$596$	222.869	−	222.869i	0.373942	−	0.373942i
$597$	748.294			1.25342
$598$	−196.243	−	6.26793i	−0.328166	−	0.0104815i
$599$	1004.01			1.67615			0.838076	−	0.545554i	$-0.183681\pi$
$599$	1004.01			1.67615			0.838076	+	0.545554i	$0.183681\pi$
$600$	156.613	−	222.538i	0.261022	−	0.370896i
$601$	1002.31			1.66773			0.833867	−	0.551965i	$-0.186122\pi$
$601$	1002.31			1.66773			0.833867	+	0.551965i	$0.186122\pi$
$602$	−258.652			−0.429654
$603$	281.958	−	281.958i	0.467592	−	0.467592i
$604$	−271.414	−	271.414i	−0.449361	−	0.449361i
$605$	−417.546	+	36.0300i	−0.690158	+	0.0595537i
$606$	−327.882	+	327.882i	−0.541059	+	0.541059i
$607$			238.427i			0.392796i	0.980524	+	0.196398i	$0.0629245\pi$
$607$			238.427i			0.392796i	−0.980524	+	0.196398i	$0.937076\pi$
$608$	−77.6934			−0.127785
$609$	−202.858	+	202.858i	−0.333101	+	0.333101i
$610$	393.284	+	330.803i	0.644728	+	0.542299i
$611$	23.8752	−	747.512i	0.0390757	−	1.22342i
$612$			137.807i			0.225175i
$613$	−580.531	+	580.531i	−0.947033	+	0.947033i	−0.998666	−	0.0516332i	$-0.983557\pi$
$613$	−580.531	+	580.531i	−0.947033	+	0.947033i	0.0516332	+	0.998666i	$0.483557\pi$
$614$	731.752			1.19178
$615$	−839.278	−	705.941i	−1.36468	−	1.14787i
$616$	−42.2458	−	42.2458i	−0.0685808	−	0.0685808i
$617$	567.878	−	567.878i	0.920385	−	0.920385i	−0.0766713	−	0.997056i	$-0.524429\pi$
$617$	567.878	−	567.878i	0.920385	−	0.920385i	0.997056	+	0.0766713i	$0.0244292\pi$
$618$	−43.9002	−	43.9002i	−0.0710360	−	0.0710360i
$619$	−26.0583	+	26.0583i	−0.0420973	+	0.0420973i	−0.727842	−	0.685745i	$-0.759477\pi$
$619$	−26.0583	+	26.0583i	−0.0420973	+	0.0420973i	0.685745	+	0.727842i	$0.259477\pi$
$620$	431.633	+	363.059i	0.696183	+	0.585580i
$621$		−	131.101i		−	0.211113i
$622$	315.994	+	315.994i	0.508028	+	0.508028i
$623$	−215.629			−0.346114
$624$	−145.949	+	136.914i	−0.233893	+	0.219414i
$625$	588.319	−	210.965i	0.941310	−	0.337544i
$626$	−65.8042	−	65.8042i	−0.105118	−	0.105118i
$627$			322.290i			0.514019i
$628$	−345.757			−0.550568
$629$	−221.298	−	221.298i	−0.351825	−	0.351825i
$630$	12.2354	+	141.794i	0.0194212	+	0.225070i
$631$	−407.417	+	407.417i	−0.645668	+	0.645668i	−0.951943	−	0.306275i	$-0.900917\pi$
$631$	−407.417	+	407.417i	−0.645668	+	0.645668i	0.306275	+	0.951943i	$0.400917\pi$
$632$	−77.6405	−	77.6405i	−0.122849	−	0.122849i
$633$		−	398.202i		−	0.629071i
$634$			339.025i			0.534739i
$635$	99.0888	+	1148.32i	0.156045	+	1.80839i
$636$		−	324.918i		−	0.510877i
$637$	−350.800	+	329.085i	−0.550707	+	0.516617i
$638$		−	185.569i		−	0.290861i
$639$	−328.263	−	328.263i	−0.513714	−	0.513714i
$640$	36.4131	−	43.2907i	0.0568955	−	0.0676418i
$641$			144.048i			0.224724i	0.993667	+	0.112362i	$0.0358416\pi$
$641$			144.048i			0.224724i	−0.993667	+	0.112362i	$0.964158\pi$
$642$	−239.007	+	239.007i	−0.372285	+	0.372285i
$643$	−82.2042	+	82.2042i	−0.127845	+	0.127845i	−0.768134	−	0.640289i	$-0.778815\pi$
$643$	−82.2042	+	82.2042i	−0.127845	+	0.127845i	0.640289	+	0.768134i	$0.278815\pi$
$644$	−52.3200	+	52.3200i	−0.0812423	+	0.0812423i
$645$	−1012.15	+	87.3381i	−1.56922	+	0.135408i
$646$	230.345			0.356571
$647$	657.369			1.01603			0.508013	−	0.861349i	$-0.330380\pi$
$647$	657.369			1.01603			0.508013	+	0.861349i	$0.330380\pi$
$648$	−199.067	−	199.067i	−0.307202	−	0.307202i
$649$		−	46.1227i		−	0.0710674i
$650$	−455.108	+	64.2390i	−0.700166	+	0.0988292i
$651$	−751.918			−1.15502
$652$	−111.164	+	111.164i	−0.170497	+	0.170497i
$653$			792.552i			1.21371i	0.794813	+	0.606854i	$0.207569\pi$
$653$			792.552i			1.21371i	−0.794813	+	0.606854i	$0.792431\pi$
$654$			1028.78i			1.57306i
$655$	92.1609	+	1068.04i	0.140704	+	1.63059i
$656$	−161.206	−	161.206i	−0.245741	−	0.245741i
$657$	−314.776	−	314.776i	−0.479111	−	0.479111i
$658$	−199.293	−	199.293i	−0.302877	−	0.302877i
$659$	617.958			0.937722			0.468861	−	0.883272i	$-0.344665\pi$
$659$	617.958			0.937722			0.468861	+	0.883272i	$0.344665\pi$
$660$	−179.580	−	151.050i	−0.272091	−	0.228863i
$661$	206.874	−	206.874i	0.312971	−	0.312971i	−0.533089	−	0.846059i	$-0.678969\pi$
$661$	206.874	−	206.874i	0.312971	−	0.312971i	0.846059	+	0.533089i	$0.178969\pi$
$662$	−281.281			−0.424896
$663$	432.708	−	405.923i	0.652652	−	0.612251i
$664$	129.546			0.195099
$665$	237.008	−	20.4514i	0.356404	−	0.0307540i
$666$	−216.841			−0.325587
$667$	−229.821			−0.344560
$668$	−184.075	+	184.075i	−0.275561	+	0.275561i
$669$	54.7036	+	54.7036i	0.0817691	+	0.0817691i
$670$	483.487	−	41.7201i	0.721623	−	0.0622688i
$671$	313.361	−	313.361i	0.467005	−	0.467005i
$672$			75.4137i			0.112223i
$673$	1124.43			1.67077			0.835386	−	0.549663i	$-0.185244\pi$
$673$	1124.43			1.67077			0.835386	+	0.549663i	$0.185244\pi$
$674$	−275.256	+	275.256i	−0.408392	+	0.408392i
$675$	−52.5723	−	302.358i	−0.0778850	−	0.447938i
$676$	337.311	+	21.5691i	0.498981	+	0.0319070i
$677$		−	446.105i		−	0.658943i	−0.944165	−	0.329472i	$-0.893129\pi$
$677$		−	446.105i		−	0.658943i	0.944165	−	0.329472i	$-0.106871\pi$
$678$	−570.094	+	570.094i	−0.840847	+	0.840847i
$679$	244.882			0.360651
$680$	−107.957	+	128.348i	−0.158761	+	0.188747i
$681$	−1091.11	−	1091.11i	−1.60222	−	1.60222i
$682$	343.917	−	343.917i	0.504276	−	0.504276i
$683$	−897.278	−	897.278i	−1.31373	−	1.31373i	−0.918644	−	0.395086i	$-0.870715\pi$
$683$	−897.278	−	897.278i	−1.31373	−	1.31373i	−0.395086	−	0.918644i	$-0.629285\pi$
$684$	112.853	−	112.853i	0.164989	−	0.164989i
$685$	−463.570	+	551.128i	−0.676744	+	0.804567i
$686$			421.315i			0.614163i
$687$	1168.64	+	1168.64i	1.70107	+	1.70107i
$688$	−211.186			−0.306956
$689$	−400.244	+	375.468i	−0.580905	+	0.544946i
$690$	−187.070	+	222.404i	−0.271117	+	0.322325i
$691$	−447.025	−	447.025i	−0.646924	−	0.646924i	0.305324	−	0.952249i	$-0.401235\pi$
$691$	−447.025	−	447.025i	−0.646924	−	0.646924i	−0.952249	+	0.305324i	$0.901235\pi$
$692$		−	172.662i		−	0.249511i
$693$	122.727			0.177096
$694$	−539.829	−	539.829i	−0.777851	−	0.777851i
$695$	−32.5657	−	377.398i	−0.0468571	−	0.543019i
$696$	−165.631	+	165.631i	−0.237976	+	0.237976i
$697$	477.942	+	477.942i	0.685713	+	0.685713i
$698$			774.535i			1.10965i
$699$		−	518.806i		−	0.742212i
$700$	−99.6848	+	141.646i	−0.142407	+	0.202351i
$701$			182.818i			0.260795i	0.991462	+	0.130398i	$0.0416254\pi$
$701$			182.818i			0.260795i	−0.991462	+	0.130398i	$0.958375\pi$
$702$	−7.20469	+	225.572i	−0.0102631	+	0.321328i
$703$			362.450i			0.515576i
$704$	−34.4932	−	34.4932i	−0.0489960	−	0.0489960i
$705$	−847.161	−	712.572i	−1.20165	−	1.01074i
$706$		−	881.723i		−	1.24890i
$707$	208.698	−	208.698i	0.295188	−	0.295188i
$708$	−41.1673	+	41.1673i	−0.0581458	+	0.0581458i
$709$	16.2875	−	16.2875i	0.0229726	−	0.0229726i	−0.695527	−	0.718500i	$-0.744829\pi$
$709$	16.2875	−	16.2875i	0.0229726	−	0.0229726i	0.718500	+	0.695527i	$0.244829\pi$
$710$	−48.5717	−	562.890i	−0.0684109	−	0.792803i
$711$	225.552			0.317232
$712$	−176.059			−0.247273
$713$	−425.930	−	425.930i	−0.597377	−	0.597377i
$714$		−	223.586i		−	0.313145i
$715$	21.4507	+	395.762i	0.0300010	+	0.553513i
$716$	447.758			0.625361
$717$	788.798	−	788.798i	1.10014	−	1.10014i
$718$		−	244.422i		−	0.340421i
$719$		−	60.4508i		−	0.0840762i	−0.999116	−	0.0420381i	$-0.986615\pi$
$719$		−	60.4508i		−	0.0840762i	0.999116	−	0.0420381i	$-0.0133851\pi$
$720$	9.99004	+	115.773i	0.0138751	+	0.160796i
$721$	27.9426	+	27.9426i	0.0387554	+	0.0387554i
$722$	172.367	+	172.367i	0.238735	+	0.238735i
$723$	1018.19	+	1018.19i	1.40829	+	1.40829i
$724$	−611.458			−0.844555
$725$	−530.036	+	92.1597i	−0.731084	+	0.127117i
$726$	322.571	−	322.571i	0.444312	−	0.444312i
$727$	149.229			0.205266			0.102633	−	0.994719i	$-0.467273\pi$
$727$	149.229			0.205266			0.102633	+	0.994719i	$0.467273\pi$
$728$	92.8970	−	87.1464i	0.127606	−	0.119707i
$729$	153.127			0.210050
$730$	−46.5761	−	539.763i	−0.0638029	−	0.739401i
$731$	626.122			0.856528
$732$	−559.386			−0.764188
$733$	−894.559	+	894.559i	−1.22041	+	1.22041i	−0.252921	+	0.967487i	$0.581391\pi$
$733$	−894.559	+	894.559i	−1.22041	+	1.22041i	−0.967487	+	0.252921i	$0.918609\pi$
$734$	460.229	+	460.229i	0.627015	+	0.627015i
$735$	61.2065	+	709.313i	0.0832742	+	0.965051i
$736$	−42.7187	+	42.7187i	−0.0580417	+	0.0580417i
$737$		−	418.474i		−	0.567808i
$738$	468.316			0.634575
$739$	113.697	−	113.697i	0.153852	−	0.153852i	−0.625984	−	0.779836i	$-0.715302\pi$
$739$	113.697	−	113.697i	0.153852	−	0.153852i	0.779836	+	0.625984i	$0.215302\pi$
$740$	−201.957	−	169.872i	−0.272914	−	0.229556i
$741$	−686.770	−	21.9351i	−0.926814	−	0.0296021i
$742$			206.811i			0.278721i
$743$	−387.099	+	387.099i	−0.520994	+	0.520994i	−0.917872	−	0.396877i	$-0.870094\pi$
$743$	−387.099	+	387.099i	−0.520994	+	0.520994i	0.396877	+	0.917872i	$0.370094\pi$
$744$	−613.932			−0.825177
$745$	−507.210	+	603.011i	−0.680819	+	0.809410i
$746$	−550.843	−	550.843i	−0.738395	−	0.738395i
$747$	−188.170	+	188.170i	−0.251901	+	0.251901i
$748$	102.265	+	102.265i	0.136718	+	0.136718i
$749$	152.129	−	152.129i	0.203109	−	0.203109i
$750$	−342.254	+	587.945i	−0.456339	+	0.783927i
$751$		−	342.334i		−	0.455837i	−0.973680	−	0.227919i	$-0.926808\pi$
$751$		−	342.334i		−	0.455837i	0.973680	−	0.227919i	$-0.0731920\pi$
$752$	−162.720	−	162.720i	−0.216383	−	0.216383i
$753$	−345.078			−0.458271
$754$	395.430	+	12.6299i	0.524443	+	0.0167505i
$755$	734.357	+	617.689i	0.972658	+	0.818131i
$756$	60.1394	+	60.1394i	0.0795495	+	0.0795495i
$757$			243.161i			0.321217i	0.987018	+	0.160608i	$0.0513456\pi$
$757$			243.161i			0.321217i	−0.987018	+	0.160608i	$0.948654\pi$
$758$	637.707			0.841303
$759$	177.207	+	177.207i	0.233474	+	0.233474i
$760$	193.514	−	16.6983i	0.254624	−	0.0219715i
$761$	−419.621	+	419.621i	−0.551407	+	0.551407i	−0.926847	−	0.375440i	$-0.877492\pi$
$761$	−419.621	+	419.621i	−0.551407	+	0.551407i	0.375440	+	0.926847i	$0.377492\pi$
$762$	−887.126	−	887.126i	−1.16421	−	1.16421i
$763$		−	654.823i		−	0.858221i
$764$			577.866i			0.756368i
$765$	−29.6184	−	343.243i	−0.0387168	−	0.448683i
$766$			174.811i			0.228212i
$767$	98.2831	+	3.13912i	0.128140	+	0.00409273i
$768$			61.5743i			0.0801749i
$769$	80.4079	+	80.4079i	0.104562	+	0.104562i	0.757452	−	0.652891i	$-0.226444\pi$
$769$	80.4079	+	80.4079i	0.104562	+	0.104562i	−0.652891	+	0.757452i	$0.726444\pi$
$770$	114.303	+	96.1437i	0.148446	+	0.124862i
$771$		−	805.568i		−	1.04484i
$772$	233.182	−	233.182i	0.302049	−	0.302049i
$773$	−714.523	+	714.523i	−0.924351	+	0.924351i	−0.997333	−	0.0729822i	$-0.976748\pi$
$773$	−714.523	+	714.523i	−0.924351	+	0.924351i	0.0729822	+	0.997333i	$0.476748\pi$
$774$	306.756	−	306.756i	0.396325	−	0.396325i
$775$	−1153.12	−	811.519i	−1.48790	−	1.04712i
$776$	199.943			0.257659
$777$	351.814			0.452786
$778$	221.342	+	221.342i	0.284502	+	0.284502i
$779$		−	782.790i		−	1.00487i
$780$	334.095	−	372.387i	0.428327	−	0.477419i
$781$	−487.200			−0.623816
$782$	126.652	−	126.652i	0.161959	−	0.161959i
$783$			264.169i			0.337380i
$784$			147.999i			0.188774i
$785$	861.191	−	74.3121i	1.09706	−	0.0946651i
$786$	−825.101	−	825.101i	−1.04975	−	1.04975i
$787$	−72.2015	−	72.2015i	−0.0917428	−	0.0917428i	0.659746	−	0.751489i	$-0.270664\pi$
$787$	−72.2015	−	72.2015i	−0.0917428	−	0.0917428i	−0.751489	+	0.659746i	$0.770664\pi$
$788$	208.752	+	208.752i	0.264914	+	0.264914i
$789$	520.999			0.660328
$790$	210.070	+	176.696i	0.265911	+	0.223665i
$791$	362.867	−	362.867i	0.458744	−	0.458744i
$792$	100.205			0.126522
$793$	646.414	+	689.069i	0.815150	+	0.868939i
$794$	−5.98315			−0.00753545
$795$	69.8333	+	809.287i	0.0878406	+	1.01797i
$796$	−388.886			−0.488551
$797$	1012.42			1.27029			0.635146	−	0.772392i	$-0.280940\pi$
$797$	1012.42			1.27029			0.635146	+	0.772392i	$0.280940\pi$
$798$	−183.098	+	183.098i	−0.229447	+	0.229447i
$799$	482.431	+	482.431i	0.603794	+	0.603794i
$800$	−81.3914	+	115.652i	−0.101739	+	0.144565i
$801$	255.732	−	255.732i	0.319266	−	0.319266i
$802$			54.8562i			0.0683993i
$803$	−467.183			−0.581797
$804$	−373.513	+	373.513i	−0.464569	+	0.464569i
$805$	119.071	−	141.561i	0.147914	−	0.175852i
$806$	709.446	+	756.261i	0.880207	+	0.938288i
$807$			253.853i			0.314563i
$808$	170.399	−	170.399i	0.210890	−	0.210890i
$809$	−1107.04			−1.36840			−0.684202	−	0.729293i	$-0.739849\pi$
$809$	−1107.04			−1.36840			−0.684202	+	0.729293i	$0.739849\pi$
$810$	538.610	+	453.040i	0.664950	+	0.559309i
$811$	3.44353	+	3.44353i	0.00424603	+	0.00424603i	0.709227	−	0.704981i	$-0.249044\pi$
$811$	3.44353	+	3.44353i	0.00424603	+	0.00424603i	−0.704981	+	0.709227i	$0.749044\pi$
$812$	105.425	−	105.425i	0.129834	−	0.129834i
$813$	−1116.34	−	1116.34i	−1.37311	−	1.37311i
$814$	−160.915	+	160.915i	−0.197684	+	0.197684i
$815$	252.989	−	300.773i	0.310416	−	0.369046i
$816$		−	182.555i		−	0.223719i
$817$	−512.742	−	512.742i	−0.627591	−	0.627591i
$818$	453.849			0.554828
$819$	−8.35284	+	261.520i	−0.0101988	+	0.319316i
$820$	436.170	+	366.875i	0.531915	+	0.447409i
$821$	67.6867	+	67.6867i	0.0824442	+	0.0824442i	0.747126	−	0.664682i	$-0.231433\pi$
$821$	67.6867	+	67.6867i	0.0824442	+	0.0824442i	−0.664682	+	0.747126i	$0.731433\pi$
$822$		−	783.894i		−	0.953643i
$823$	−975.932			−1.18582			−0.592911	−	0.805268i	$-0.702022\pi$
$823$	−975.932			−1.18582			−0.592911	+	0.805268i	$0.702022\pi$
$824$	22.8148	+	22.8148i	0.0276879	+	0.0276879i
$825$	479.752	+	337.630i	0.581518	+	0.409249i
$826$	26.2031	−	26.2031i	0.0317229	−	0.0317229i
$827$	629.158	+	629.158i	0.760772	+	0.760772i	0.976462	−	0.215690i	$-0.0692001\pi$
$827$	629.158	+	629.158i	0.760772	+	0.760772i	−0.215690	+	0.976462i	$0.569200\pi$
$828$		−	124.101i		−	0.149881i
$829$		−	989.174i		−	1.19321i	−0.802534	−	0.596607i	$-0.796515\pi$
$829$		−	989.174i		−	1.19321i	0.802534	−	0.596607i	$-0.203485\pi$
$830$	−322.665	+	27.8427i	−0.388753	+	0.0335455i
$831$			736.176i			0.885892i
$832$	75.8492	−	71.1540i	0.0911649	−	0.0855217i
$833$		−	438.786i		−	0.526754i
$834$	291.555	+	291.555i	0.349586	+	0.349586i
$835$	418.920	−	498.045i	0.501701	−	0.596461i
$836$		−	167.493i		−	0.200351i
$837$	−489.586	+	489.586i	−0.584930	+	0.584930i
$838$	−146.384	+	146.384i	−0.174682	+	0.174682i
$839$	309.990	−	309.990i	0.369476	−	0.369476i	−0.497810	−	0.867286i	$-0.665862\pi$
$839$	309.990	−	309.990i	0.369476	−	0.369476i	0.867286	+	0.497810i	$0.165862\pi$
$840$	−16.2084	−	187.836i	−0.0192957	−	0.223614i
$841$	−377.910			−0.449358
$842$	−931.511			−1.10631
$843$	506.597	+	506.597i	0.600945	+	0.600945i
$844$			206.944i			0.245195i
$845$	−844.791	+	18.7737i	−0.999753	+	0.0222174i
$846$	472.715			0.558765
$847$	−205.317	+	205.317i	−0.242405	+	0.242405i
$848$			168.859i			0.199126i
$849$			1465.65i			1.72633i
$850$	241.308	−	342.885i	0.283892	−	0.403394i
$851$	199.288	+	199.288i	0.234181	+	0.234181i
$852$	434.855	+	434.855i	0.510393	+	0.510393i
$853$	16.3492	+	16.3492i	0.0191667	+	0.0191667i	0.716625	−	0.697459i	$-0.245686\pi$
$853$	16.3492	+	16.3492i	0.0191667	+	0.0191667i	−0.697459	+	0.716625i	$0.745686\pi$
$854$	356.051			0.416921
$855$	−256.832	+	305.342i	−0.300389	+	0.357126i
$856$	124.211	−	124.211i	0.145107	−	0.145107i
$857$	173.877			0.202890			0.101445	−	0.994841i	$-0.467653\pi$
$857$	173.877			0.202890			0.101445	+	0.994841i	$0.467653\pi$
$858$	−295.163	−	314.640i	−0.344013	−	0.366713i
$859$	−516.287			−0.601033			−0.300516	−	0.953777i	$-0.597159\pi$
$859$	−516.287			−0.601033			−0.300516	+	0.953777i	$0.597159\pi$
$860$	526.010	−	45.3894i	0.611639	−	0.0527783i
$861$	−759.821			−0.882486
$862$	825.284			0.957406
$863$	490.757	−	490.757i	0.568664	−	0.568664i	−0.363090	−	0.931754i	$-0.618278\pi$
$863$	490.757	−	490.757i	0.568664	−	0.568664i	0.931754	+	0.363090i	$0.118278\pi$
$864$	49.1031	+	49.1031i	0.0568323	+	0.0568323i
$865$	37.1095	+	430.056i	0.0429011	+	0.497174i
$866$	490.129	−	490.129i	0.565968	−	0.565968i
$867$		−	570.949i		−	0.658534i
$868$	390.769			0.450195
$869$	167.379	−	167.379i	0.192611	−	0.192611i
$870$	376.947	−	448.144i	0.433272	−	0.515108i
$871$	891.729	+	28.4815i	1.02380	+	0.0326997i
$872$		−	534.655i		−	0.613136i
$873$	−290.425	+	290.425i	−0.332675	+	0.332675i
$874$	−207.435			−0.237340
$875$	217.846	−	374.229i	0.248967	−	0.427690i
$876$	416.988	+	416.988i	0.476014	+	0.476014i
$877$	−36.7229	+	36.7229i	−0.0418733	+	0.0418733i	−0.727733	−	0.685860i	$-0.759426\pi$
$877$	−36.7229	+	36.7229i	−0.0418733	+	0.0418733i	0.685860	+	0.727733i	$0.259426\pi$
$878$	−32.6479	−	32.6479i	−0.0371844	−	0.0371844i
$879$	127.252	−	127.252i	0.144769	−	0.144769i
$880$	93.3271	+	78.5001i	0.106054	+	0.0892047i
$881$			144.572i			0.164100i	0.996628	+	0.0820501i	$0.0261468\pi$
$881$			144.572i			0.164100i	−0.996628	+	0.0820501i	$0.973853\pi$
$882$	−214.974	−	214.974i	−0.243735	−	0.243735i
$883$	−221.400			−0.250736			−0.125368	−	0.992110i	$-0.540011\pi$
$883$	−221.400			−0.250736			−0.125368	+	0.992110i	$0.540011\pi$
$884$	−224.877	+	210.957i	−0.254386	+	0.238639i
$885$	93.6892	−	111.385i	0.105863	−	0.125859i
$886$	−458.868	−	458.868i	−0.517909	−	0.517909i
$887$		−	867.086i		−	0.977549i	−0.872410	−	0.488774i	$-0.837444\pi$
$887$		−	867.086i		−	0.977549i	0.872410	−	0.488774i	$-0.162556\pi$
$888$	287.252			0.323482
$889$	564.659	+	564.659i	0.635161	+	0.635161i
$890$	438.517	−	37.8396i	0.492716	−	0.0425164i
$891$	429.153	−	429.153i	0.481653	−	0.481653i
$892$	−28.4293	−	28.4293i	−0.0318714	−	0.0318714i
$893$		−	790.143i		−	0.884818i
$894$		−	857.689i		−	0.959384i
$895$	−1115.25	+	96.2349i	−1.24609	+	0.107525i
$896$		−	39.1923i		−	0.0437414i
$897$	−389.672	+	365.550i	−0.434417	+	0.407525i
$898$		−	580.145i		−	0.646041i
$899$	858.248	+	858.248i	0.954670	+	0.954670i
$900$	−49.7653	−	286.214i	−0.0552947	−	0.318015i
$901$		−	500.631i		−	0.555639i
$902$	347.531	−	347.531i	0.385290	−	0.385290i
$903$	−497.697	+	497.697i	−0.551159	+	0.551159i
$904$	296.276	−	296.276i	0.327739	−	0.327739i
$905$	1522.99	−	131.418i	1.68286	−	0.145214i
$906$	−1044.51			−1.15288
$907$	−214.025			−0.235970			−0.117985	−	0.993015i	$-0.537644\pi$
$907$	−214.025			−0.235970			−0.117985	+	0.993015i	$0.537644\pi$
$908$	567.047	+	567.047i	0.624501	+	0.624501i
$909$			495.023i			0.544579i
$910$	−212.653	+	237.025i	−0.233684	+	0.260468i
$911$	−1755.52			−1.92702			−0.963511	−	0.267669i	$-0.913747\pi$
$911$	−1755.52			−1.92702			−0.963511	+	0.267669i	$0.913747\pi$
$912$	−149.498	+	149.498i	−0.163923	+	0.163923i
$913$			279.277i			0.305890i
$914$			676.937i			0.740631i
$915$	1393.29	−	120.227i	1.52272	−	0.131395i
$916$	−607.337	−	607.337i	−0.663031	−	0.663031i
$917$	525.179	+	525.179i	0.572715	+	0.572715i
$918$	−145.580	−	145.580i	−0.158584	−	0.158584i
$919$	−917.734			−0.998623			−0.499311	−	0.866423i	$-0.666414\pi$
$919$	−917.734			−0.998623			−0.499311	+	0.866423i	$0.666414\pi$
$920$	97.2199	−	115.583i	0.105674	−	0.125633i
$921$	1408.04	−	1408.04i	1.52881	−	1.52881i
$922$	−703.562			−0.763082
$923$	33.1589	−	1038.18i	0.0359252	−	1.12479i
$924$	−162.578			−0.175951
$925$	539.532	+	379.701i	0.583278	+	0.410488i
$926$	567.716			0.613085
$927$	−66.2789			−0.0714982
$928$	86.0781	−	86.0781i	0.0927566	−	0.0927566i
$929$	471.906	+	471.906i	0.507972	+	0.507972i	0.913903	−	0.405932i	$-0.133053\pi$
$929$	471.906	+	471.906i	0.507972	+	0.507972i	−0.405932	+	0.913903i	$0.633053\pi$
$930$	1529.15	−	131.950i	1.64424	−	0.141882i
$931$	−359.330	+	359.330i	−0.385961	+	0.385961i
$932$			269.622i			0.289294i
$933$	1216.07			1.30340
$934$	267.631	−	267.631i	0.286543	−	0.286543i
$935$	−276.695	−	232.737i	−0.295931	−	0.248916i
$936$	−6.81999	+	213.528i	−0.00728632	+	0.228128i
$937$			1133.03i			1.20921i	0.796524	+	0.604607i	$0.206670\pi$
$937$			1133.03i			1.20921i	−0.796524	+	0.604607i	$0.793330\pi$
$938$	237.742	−	237.742i	0.253457	−	0.253457i
$939$	−253.241			−0.269692
$940$	440.267	+	370.322i	0.468369	+	0.393959i
$941$	−965.320	−	965.320i	−1.02584	−	1.02584i	−0.999657	−	0.0261879i	$-0.991663\pi$
$941$	−965.320	−	965.320i	−1.02584	−	1.02584i	−0.0261879	−	0.999657i	$-0.508337\pi$
$942$	−665.304	+	665.304i	−0.706268	+	0.706268i
$943$	−430.406	−	430.406i	−0.456423	−	0.456423i
$944$	21.3945	−	21.3945i	0.0226637	−	0.0226637i
$945$	−162.717	−	136.866i	−0.172188	−	0.144832i
$946$		−	455.279i		−	0.481268i
$947$	−766.185	−	766.185i	−0.809065	−	0.809065i	0.175427	−	0.984492i	$-0.443869\pi$
$947$	−766.185	−	766.185i	−0.809065	−	0.809065i	−0.984492	+	0.175427i	$0.943869\pi$
$948$	−298.791			−0.315181
$949$	31.7965	−	995.522i	0.0335053	−	1.04902i
$950$	−478.406	+	83.1826i	−0.503585	+	0.0875606i
$951$	652.351	+	652.351i	0.685963	+	0.685963i
$952$			116.197i			0.122056i
$953$	743.766			0.780447			0.390223	−	0.920720i	$-0.372398\pi$
$953$	743.766			0.780447			0.390223	+	0.920720i	$0.372398\pi$
$954$	−245.274	−	245.274i	−0.257100	−	0.257100i
$955$	−124.198	−	1439.32i	−0.130051	−	1.50714i
$956$	−409.936	+	409.936i	−0.428803	+	0.428803i
$957$	−357.072	−	357.072i	−0.373116	−	0.373116i
$958$		−	452.931i		−	0.472788i
$959$			498.951i			0.520283i
$960$	−13.2339	−	153.366i	−0.0137853	−	0.159756i
$961$			2220.20i			2.31030i
$962$	−331.942	−	353.846i	−0.345055	−	0.367824i
$963$			360.844i			0.374708i
$964$	−529.151	−	529.151i	−0.548912	−	0.548912i
$965$	−530.679	+	630.913i	−0.549927	+	0.653796i
$966$			201.348i			0.208435i
$967$	228.660	−	228.660i	0.236463	−	0.236463i	−0.578921	−	0.815384i	$-0.696526\pi$
$967$	228.660	−	228.660i	0.236463	−	0.236463i	0.815384	+	0.578921i	$0.196526\pi$
$968$	−167.639	+	167.639i	−0.173181	+	0.173181i
$969$	443.229	−	443.229i	0.457409	−	0.457409i
$970$	−498.007	+	42.9730i	−0.513410	+	0.0443021i
$971$	1063.56			1.09532			0.547662	−	0.836699i	$-0.315518\pi$
$971$	1063.56			1.09532			0.547662	+	0.836699i	$0.315518\pi$
$972$	−545.125			−0.560828
$973$	−185.576	−	185.576i	−0.190725	−	0.190725i
$974$		−	255.583i		−	0.262406i
$975$	−752.110	+	999.327i	−0.771395	+	1.02495i
$976$	290.711			0.297860
$977$	347.768	−	347.768i	0.355955	−	0.355955i	−0.506364	−	0.862320i	$-0.669011\pi$
$977$	347.768	−	347.768i	0.355955	−	0.355955i	0.862320	+	0.506364i	$0.169011\pi$
$978$			427.803i			0.437426i
$979$		−	379.551i		−	0.387693i
$980$	−31.8088	−	368.628i	−0.0324580	−	0.376151i
$981$	776.607	+	776.607i	0.791648	+	0.791648i
$982$	−430.146	−	430.146i	−0.438030	−	0.438030i
$983$	1187.00	+	1187.00i	1.20753	+	1.20753i	0.971825	+	0.235705i	$0.0757400\pi$
$983$	1187.00	+	1187.00i	1.20753	+	1.20753i	0.235705	+	0.971825i	$0.424260\pi$
$984$	−620.384			−0.630472
$985$	−564.814	−	475.081i	−0.573415	−	0.482316i
$986$	−255.204	+	255.204i	−0.258827	+	0.258827i
$987$	−766.958			−0.777060
$988$	356.912	+	11.3996i	0.361247	+	0.0115381i
$989$	−563.849			−0.570120
$990$	−249.586	+	21.5367i	−0.252107	+	0.0217543i
$991$	566.323			0.571466			0.285733	−	0.958309i	$-0.407763\pi$
$991$	566.323			0.571466			0.285733	+	0.958309i	$0.407763\pi$
$992$	319.058			0.321631
$993$	−541.241	+	541.241i	−0.545057	+	0.545057i
$994$	−276.786	−	276.786i	−0.278457	−	0.278457i
$995$	968.616	−	83.5818i	0.973484	−	0.0840018i
$996$	249.271	−	249.271i	0.250273	−	0.250273i
$997$			1051.32i			1.05448i	0.849715	+	0.527242i	$0.176774\pi$
$997$			1051.32i			1.05448i	−0.849715	+	0.527242i	$0.823226\pi$
$998$	−541.043			−0.542127
$999$	229.072	−	229.072i	0.229302	−	0.229302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.3.f.a.99.6	✓	14
5.2	odd	4		650.3.k.l.151.6		14
5.3	odd	4		650.3.k.m.151.2		14
5.4	even	2		130.3.f.b.99.2	yes	14
13.5	odd	4		130.3.f.b.109.6	yes	14
65.18	even	4		650.3.k.m.551.2		14
65.44	odd	4	inner	130.3.f.a.109.2	yes	14
65.57	even	4		650.3.k.l.551.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.f.a.99.6	✓	14	1.1	even	1	trivial
130.3.f.a.109.2	yes	14	65.44	odd	4	inner
130.3.f.b.99.2	yes	14	5.4	even	2
130.3.f.b.109.6	yes	14	13.5	odd	4
650.3.k.l.151.6		14	5.2	odd	4
650.3.k.l.551.6		14	65.57	even	4
650.3.k.m.151.2		14	5.3	odd	4
650.3.k.m.551.2		14	65.18	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	130.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +3.84840i q^{3} -2.00000i q^{4} +(0.429852 + 4.98149i) q^{5} +(-3.84840 - 3.84840i) q^{6} +(2.44952 + 2.44952i) q^{7} +(2.00000 + 2.00000i) q^{8} -5.81016 q^{9} +(-5.41134 - 4.55164i) q^{10} +(-4.31164 + 4.31164i) q^{11} +7.69679 q^{12} +(-8.89425 - 9.48115i) q^{13} -4.89903 q^{14} +(-19.1707 + 1.65424i) q^{15} -4.00000 q^{16} +11.8592 q^{17} +(5.81016 - 5.81016i) q^{18} +(-9.71168 - 9.71168i) q^{19} +(9.96298 - 0.859704i) q^{20} +(-9.42671 + 9.42671i) q^{21} -8.62329i q^{22} -10.6797 q^{23} +(-7.69679 + 7.69679i) q^{24} +(-24.6305 + 4.28261i) q^{25} +(18.3754 + 0.586903i) q^{26} +12.2758i q^{27} +(4.89903 - 4.89903i) q^{28} +21.5195 q^{29} +(17.5165 - 20.8250i) q^{30} +(39.8823 + 39.8823i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-16.5929 - 16.5929i) q^{33} +(-11.8592 + 11.8592i) q^{34} +(-11.1493 + 13.2552i) q^{35} +11.6203i q^{36} +(-18.6605 - 18.6605i) q^{37} +19.4234 q^{38} +(36.4872 - 34.2286i) q^{39} +(-9.10327 + 10.8227i) q^{40} +(40.3015 + 40.3015i) q^{41} -18.8534i q^{42} +52.7965 q^{43} +(8.62329 + 8.62329i) q^{44} +(-2.49751 - 28.9432i) q^{45} +(10.6797 - 10.6797i) q^{46} +(40.6800 + 40.6800i) q^{47} -15.3936i q^{48} -36.9997i q^{49} +(20.3478 - 28.9131i) q^{50} +45.6388i q^{51} +(-18.9623 + 17.7885i) q^{52} -42.2147i q^{53} +(-12.2758 - 12.2758i) q^{54} +(-23.3318 - 19.6250i) q^{55} +9.79806i q^{56} +(37.3744 - 37.3744i) q^{57} +(-21.5195 + 21.5195i) q^{58} +(-5.34862 + 5.34862i) q^{59} +(3.30848 + 38.3415i) q^{60} -72.6777 q^{61} -79.7646 q^{62} +(-14.2321 - 14.2321i) q^{63} +8.00000i q^{64} +(43.4070 - 48.3821i) q^{65} +33.1858 q^{66} +(-48.5284 + 48.5284i) q^{67} -23.7183i q^{68} -41.0996i q^{69} +(-2.10586 - 24.4045i) q^{70} +(56.4982 + 56.4982i) q^{71} +(-11.6203 - 11.6203i) q^{72} +(54.1769 + 54.1769i) q^{73} +37.3210 q^{74} +(-16.4812 - 94.7878i) q^{75} +(-19.4234 + 19.4234i) q^{76} -21.1229 q^{77} +(-2.25863 + 70.7159i) q^{78} -38.8202 q^{79} +(-1.71941 - 19.9260i) q^{80} -99.5335 q^{81} -80.6030 q^{82} +(32.3864 - 32.3864i) q^{83} +(18.8534 + 18.8534i) q^{84} +(5.09769 + 59.0763i) q^{85} +(-52.7965 + 52.7965i) q^{86} +82.8156i q^{87} -17.2466 q^{88} +(-44.0147 + 44.0147i) q^{89} +(31.4407 + 26.4457i) q^{90} +(1.43763 - 45.0109i) q^{91} +21.3593i q^{92} +(-153.483 + 153.483i) q^{93} -81.3601 q^{94} +(44.2040 - 52.5532i) q^{95} +(15.3936 + 15.3936i) q^{96} +(49.9858 - 49.9858i) q^{97} +(36.9997 + 36.9997i) q^{98} +(25.0513 - 25.0513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 4 q^{5} + 28 q^{8} - 42 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{13} + 4 q^{15} - 56 q^{16} - 96 q^{17} + 42 q^{18} + 44 q^{19} + 4 q^{20} + 4 q^{21} - 8 q^{23} + 46 q^{25} + 10 q^{26} + 72 q^{29}+ \cdots + 292 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 4 * q^5 + 28 * q^8 - 42 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^13 + 4 * q^15 - 56 * q^16 - 96 * q^17 + 42 * q^18 + 44 * q^19 + 4 * q^20 + 4 * q^21 - 8 * q^23 + 46 * q^25 + 10 * q^26 + 72 * q^29 + 40 * q^30 - 64 * q^31 + 56 * q^32 - 56 * q^33 + 96 * q^34 + 124 * q^35 - 98 * q^37 - 88 * q^38 - 144 * q^39 - 12 * q^40 + 138 * q^41 + 120 * q^43 - 16 * q^44 - 80 * q^45 + 8 * q^46 + 40 * q^47 - 18 * q^50 - 4 * q^52 - 120 * q^54 - 76 * q^55 + 264 * q^57 - 72 * q^58 - 20 * q^59 - 88 * q^60 - 180 * q^61 + 128 * q^62 + 160 * q^63 - 2 * q^65 + 112 * q^66 - 8 * q^67 - 104 * q^70 - 100 * q^71 - 84 * q^72 + 54 * q^73 + 196 * q^74 - 520 * q^75 + 88 * q^76 + 336 * q^77 + 24 * q^78 + 344 * q^79 + 16 * q^80 + 38 * q^81 - 276 * q^82 - 296 * q^83 - 8 * q^84 + 284 * q^85 - 120 * q^86 + 32 * q^88 - 398 * q^89 - 6 * q^90 + 48 * q^91 - 120 * q^93 - 80 * q^94 + 476 * q^95 + 162 * q^97 - 130 * q^98 + 292 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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