LMFDB - Embedded newform 735.2.b.d.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(146,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("735.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.b (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.1
Root			$2.33086i$ of defining polynomial
Character	$\chi$	$=$	735.146
Dual form			735.2.b.d.146.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33086i q^{2} +(-0.459555 + 1.66997i) q^{3} -3.43292 q^{4} -1.00000 q^{5} +(3.89248 + 1.07116i) q^{6} +3.33995i q^{8} +(-2.57762 - 1.53489i) q^{9} +O(q^{10})$	\(q-2.33086i q^{2} +(-0.459555 + 1.66997i) q^{3} -3.43292 q^{4} -1.00000 q^{5} +(3.89248 + 1.07116i) q^{6} +3.33995i q^{8} +(-2.57762 - 1.53489i) q^{9} +2.33086i q^{10} -2.79459i q^{11} +(1.57762 - 5.73289i) q^{12} +3.20486i q^{13} +(0.459555 - 1.66997i) q^{15} +0.919111 q^{16} +0.881938 q^{17} +(-3.57762 + 6.00807i) q^{18} +2.19578i q^{19} +3.43292 q^{20} -6.51381 q^{22} +7.54296i q^{23} +(-5.57762 - 1.53489i) q^{24} +1.00000 q^{25} +7.47010 q^{26} +(3.74778 - 3.59918i) q^{27} +8.15270i q^{29} +(-3.89248 - 1.07116i) q^{30} +8.80626i q^{31} +4.53757i q^{32} +(4.66689 + 1.28427i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +0.407453 q^{37} +5.11806 q^{38} +(-5.35203 - 1.47281i) q^{39} -3.33995i q^{40} -8.55098 q^{41} -0.118062 q^{43} +9.59362i q^{44} +(2.57762 + 1.53489i) q^{45} +17.5816 q^{46} +2.62972 q^{47} +(-0.422382 + 1.53489i) q^{48} -2.33086i q^{50} +(-0.405299 + 1.47281i) q^{51} -11.0020i q^{52} -7.46853i q^{53} +(-8.38921 - 8.73557i) q^{54} +2.79459i q^{55} +(-3.66689 - 1.00908i) q^{57} +19.0028 q^{58} -4.09982 q^{59} +(-1.57762 + 5.73289i) q^{60} +12.3557i q^{61} +20.5262 q^{62} +12.4147 q^{64} -3.20486i q^{65} +(2.99346 - 10.8779i) q^{66} -1.60425 q^{67} -3.02762 q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(5.12645 - 8.60910i) q^{72} -0.221728i q^{73} -0.949718i q^{74} +(-0.459555 + 1.66997i) q^{75} -7.53794i q^{76} +(-3.43292 + 12.4749i) q^{78} -3.13699 q^{79} -0.919111 q^{80} +(4.28823 + 7.91272i) q^{81} +19.9312i q^{82} -0.666893 q^{83} -0.881938 q^{85} +0.275187i q^{86} +(-13.6148 - 3.74662i) q^{87} +9.33379 q^{88} +0.874542 q^{89} +(3.57762 - 6.00807i) q^{90} -25.8944i q^{92} +(-14.7062 - 4.04697i) q^{93} -6.12952i q^{94} -2.19578i q^{95} +(-7.57762 - 2.08526i) q^{96} -6.37221i q^{97} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9}+O(q^{10}) $ 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9	$ 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9} - 9 q^{12} - q^{15} - 2 q^{16} + 24 q^{17} - 7 q^{18} + 6 q^{20} - 40 q^{22} - 23 q^{24} + 8 q^{25} + 12 q^{26} + 4 q^{27} - 5 q^{30} + 2 q^{33} + 9 q^{36} - 14 q^{37} + 24 q^{38} - 12 q^{39} - 30 q^{41} + 16 q^{43} - q^{45} + 14 q^{46} + 12 q^{47} - 25 q^{48} - 6 q^{51} - 10 q^{54} + 6 q^{57} + 26 q^{58} + 24 q^{59} + 9 q^{60} + 24 q^{62} + 38 q^{64} - 38 q^{66} - 8 q^{67} - 13 q^{69} + q^{72} + q^{75} - 6 q^{78} + 58 q^{79} + 2 q^{80} + 13 q^{81} + 30 q^{83} - 24 q^{85} - 61 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 36 q^{93} - 39 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9 - 9 * q^12 - q^15 - 2 * q^16 + 24 * q^17 - 7 * q^18 + 6 * q^20 - 40 * q^22 - 23 * q^24 + 8 * q^25 + 12 * q^26 + 4 * q^27 - 5 * q^30 + 2 * q^33 + 9 * q^36 - 14 * q^37 + 24 * q^38 - 12 * q^39 - 30 * q^41 + 16 * q^43 - q^45 + 14 * q^46 + 12 * q^47 - 25 * q^48 - 6 * q^51 - 10 * q^54 + 6 * q^57 + 26 * q^58 + 24 * q^59 + 9 * q^60 + 24 * q^62 + 38 * q^64 - 38 * q^66 - 8 * q^67 - 13 * q^69 + q^72 + q^75 - 6 * q^78 + 58 * q^79 + 2 * q^80 + 13 * q^81 + 30 * q^83 - 24 * q^85 - 61 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 36 * q^93 - 39 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	2.33086i		−	1.64817i	−0.566467	−	0.824085i	$-0.691690\pi$
$2$		−	2.33086i		−	1.64817i	0.566467	−	0.824085i	$-0.308310\pi$
$3$	−0.459555	+	1.66997i	−0.265324	+	0.964159i
$3$	−0.459555	+	1.66997i	−0.265324	+	0.964159i
$4$	−3.43292			−1.71646
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	3.89248	+	1.07116i	1.58910	+	0.437299i
$7$		0			0
$7$		0			0
$8$			3.33995i			1.18085i
$9$	−2.57762	−	1.53489i	−0.859206	−	0.511630i
$10$			2.33086i			0.737084i
$11$		−	2.79459i		−	0.842601i	−0.906921	−	0.421301i	$-0.861574\pi$
$11$		−	2.79459i		−	0.842601i	0.906921	−	0.421301i	$-0.138426\pi$
$12$	1.57762	−	5.73289i	0.455419	−	1.65494i
$13$			3.20486i			0.888869i	0.895811	+	0.444434i	$0.146595\pi$
$13$			3.20486i			0.888869i	−0.895811	+	0.444434i	$0.853405\pi$
$14$		0			0
$15$	0.459555	−	1.66997i	0.118657	−	0.431185i
$16$	0.919111			0.229778
$17$	0.881938			0.213901			0.106951	−	0.994264i	$-0.465891\pi$
$17$	0.881938			0.213901			0.106951	+	0.994264i	$0.465891\pi$
$18$	−3.57762	+	6.00807i	−0.843253	+	1.41612i
$19$			2.19578i			0.503746i	0.967760	+	0.251873i	$0.0810466\pi$
$19$			2.19578i			0.503746i	−0.967760	+	0.251873i	$0.918953\pi$
$20$	3.43292			0.767625
$21$		0			0
$22$	−6.51381			−1.38875
$23$			7.54296i			1.57282i	0.617707	+	0.786408i	$0.288062\pi$
$23$			7.54296i			1.57282i	−0.617707	+	0.786408i	$0.711938\pi$
$24$	−5.57762	−	1.53489i	−1.13853	−	0.313308i
$25$	1.00000			0.200000
$26$	7.47010			1.46501
$27$	3.74778	−	3.59918i	0.721261	−	0.692663i
$28$		0			0
$29$			8.15270i			1.51392i	0.653462	+	0.756959i	$0.273316\pi$
$29$			8.15270i			1.51392i	−0.653462	+	0.756959i	$0.726684\pi$
$30$	−3.89248	−	1.07116i	−0.710666	−	0.195566i
$31$			8.80626i			1.58165i	0.612041	+	0.790826i	$0.290349\pi$
$31$			8.80626i			1.58165i	−0.612041	+	0.790826i	$0.709651\pi$
$32$			4.53757i			0.802137i
$33$	4.66689	+	1.28427i	0.812402	+	0.223563i
$34$		−	2.05568i		−	0.352545i
$35$		0			0
$36$	8.84876	+	5.26916i	1.47479	+	0.878193i
$37$	0.407453			0.0669849			0.0334925	−	0.999439i	$-0.489337\pi$
$37$	0.407453			0.0669849			0.0334925	+	0.999439i	$0.489337\pi$
$38$	5.11806			0.830259
$39$	−5.35203	−	1.47281i	−0.857011	−	0.235839i
$40$		−	3.33995i		−	0.528092i
$41$	−8.55098			−1.33544			−0.667720	−	0.744413i	$-0.732730\pi$
$41$	−8.55098			−1.33544			−0.667720	+	0.744413i	$0.732730\pi$
$42$		0			0
$43$	−0.118062			−0.0180044			−0.00900218	−	0.999959i	$-0.502866\pi$
$43$	−0.118062			−0.0180044			−0.00900218	+	0.999959i	$0.502866\pi$
$44$			9.59362i			1.44629i
$45$	2.57762	+	1.53489i	0.384249	+	0.228808i
$46$	17.5816			2.59227
$47$	2.62972			0.383584			0.191792	−	0.981436i	$-0.438570\pi$
$47$	2.62972			0.383584			0.191792	+	0.981436i	$0.438570\pi$
$48$	−0.422382	+	1.53489i	−0.0609656	+	0.221542i
$49$		0			0
$50$		−	2.33086i		−	0.329634i
$51$	−0.405299	+	1.47281i	−0.0567532	+	0.206235i
$52$		−	11.0020i		−	1.52571i
$53$		−	7.46853i		−	1.02588i	−0.858424	−	0.512941i	$-0.828556\pi$
$53$		−	7.46853i		−	1.02588i	0.858424	−	0.512941i	$-0.171444\pi$
$54$	−8.38921	−	8.73557i	−1.14163	−	1.18876i
$55$			2.79459i			0.376823i
$56$		0			0
$57$	−3.66689	−	1.00908i	−0.485692	−	0.133656i
$58$	19.0028			2.49519
$59$	−4.09982			−0.533750			−0.266875	−	0.963731i	$-0.585991\pi$
$59$	−4.09982			−0.533750			−0.266875	+	0.963731i	$0.585991\pi$
$60$	−1.57762	+	5.73289i	−0.203670	+	0.740112i
$61$			12.3557i			1.58199i	0.611824	+	0.790994i	$0.290436\pi$
$61$			12.3557i			1.58199i	−0.611824	+	0.790994i	$0.709564\pi$
$62$	20.5262			2.60683
$63$		0			0
$64$	12.4147			1.55183
$65$		−	3.20486i		−	0.397514i
$66$	2.99346	−	10.8779i	0.368469	−	1.33898i
$67$	−1.60425			−0.195990			−0.0979952	−	0.995187i	$-0.531243\pi$
$67$	−1.60425			−0.195990			−0.0979952	+	0.995187i	$0.531243\pi$
$68$	−3.02762			−0.367153
$69$	−12.5965	−	3.46641i	−1.51645	−	0.417307i
$70$		0			0
$71$		−	6.25869i		−	0.742770i	−0.928479	−	0.371385i	$-0.878883\pi$
$71$		−	6.25869i		−	0.742770i	0.928479	−	0.371385i	$-0.121117\pi$
$72$	5.12645	−	8.60910i	0.604158	−	1.01459i
$73$		−	0.221728i		−	0.0259513i	−0.999916	−	0.0129757i	$-0.995870\pi$
$73$		−	0.221728i		−	0.0259513i	0.999916	−	0.0129757i	$-0.00413040\pi$
$74$		−	0.949718i		−	0.110402i
$75$	−0.459555	+	1.66997i	−0.0530649	+	0.192832i
$76$		−	7.53794i		−	0.864661i
$77$		0			0
$78$	−3.43292	+	12.4749i	−0.388702	+	1.41250i
$79$	−3.13699			−0.352939			−0.176469	−	0.984306i	$-0.556468\pi$
$79$	−3.13699			−0.352939			−0.176469	+	0.984306i	$0.556468\pi$
$80$	−0.919111			−0.102760
$81$	4.28823	+	7.91272i	0.476470	+	0.879191i
$82$			19.9312i			2.20103i
$83$	−0.666893			−0.0732010			−0.0366005	−	0.999330i	$-0.511653\pi$
$83$	−0.666893			−0.0732010			−0.0366005	+	0.999330i	$0.511653\pi$
$84$		0			0
$85$	−0.881938			−0.0956596
$86$			0.275187i			0.0296742i
$87$	−13.6148	−	3.74662i	−1.45966	−	0.401680i
$88$	9.33379			0.994985
$89$	0.874542			0.0927013			0.0463506	−	0.998925i	$-0.485241\pi$
$89$	0.874542			0.0927013			0.0463506	+	0.998925i	$0.485241\pi$
$90$	3.57762	−	6.00807i	0.377114	−	0.633307i
$91$		0			0
$92$		−	25.8944i		−	2.69968i
$93$	−14.7062	−	4.04697i	−1.52496	−	0.419651i
$94$		−	6.12952i		−	0.632211i
$95$		−	2.19578i		−	0.225282i
$96$	−7.57762	−	2.08526i	−0.773387	−	0.212826i
$97$		−	6.37221i		−	0.647000i	−0.946228	−	0.323500i	$-0.895140\pi$
$97$		−	6.37221i		−	0.647000i	0.946228	−	0.323500i	$-0.104860\pi$
$98$		0			0
$99$	−4.28939	+	7.20339i	−0.431100	+	0.723968i
$100$	−3.43292			−0.343292
$101$	−10.6253			−1.05726			−0.528630	−	0.848852i	$-0.677294\pi$
$101$	−10.6253			−1.05726			−0.528630	+	0.848852i	$0.677294\pi$
$102$	3.43292	+	0.944697i	0.339910	+	0.0935389i
$103$		−	1.00318i		−	0.0988460i	−0.998778	−	0.0494230i	$-0.984262\pi$
$103$		−	1.00318i		−	0.0988460i	0.998778	−	0.0494230i	$-0.0157382\pi$
$104$	−10.7041			−1.04962
$105$		0			0
$106$	−17.4081			−1.69083
$107$		−	12.7769i		−	1.23519i	−0.786496	−	0.617596i	$-0.788107\pi$
$107$		−	12.7769i		−	1.23519i	0.786496	−	0.617596i	$-0.211893\pi$
$108$	−12.8658	+	12.3557i	−1.23802	+	1.18893i
$109$	0.0182474			0.00174778			0.000873892	−	1.00000i	$-0.499722\pi$
$109$	0.0182474			0.00174778			0.000873892		1.00000i	$0.499722\pi$
$110$	6.51381			0.621068
$111$	−0.187247	+	0.680436i	−0.0177727	+	0.0645841i
$112$		0			0
$113$		−	7.23027i		−	0.680166i	−0.940395	−	0.340083i	$-0.889545\pi$
$113$		−	7.23027i		−	0.680166i	0.940395	−	0.340083i	$-0.110455\pi$
$114$	−2.35203	+	8.54702i	−0.220288	+	0.800502i
$115$		−	7.54296i		−	0.703385i
$116$		−	27.9876i		−	2.59858i
$117$	4.91911	−	8.26091i	0.454772	−	0.763721i
$118$			9.55611i			0.879711i
$119$		0			0
$120$	5.57762	+	1.53489i	0.509165	+	0.140116i
$121$	3.19025			0.290023
$122$	28.7995			2.60738
$123$	3.92965	−	14.2799i	0.354325	−	1.28758i
$124$		−	30.2312i		−	2.71484i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.99561			0.620760			0.310380	−	0.950613i	$-0.399544\pi$
$127$	6.99561			0.620760			0.310380	+	0.950613i	$0.399544\pi$
$128$		−	19.8618i		−	1.75555i
$129$	0.0542562	−	0.197161i	0.00477699	−	0.0173591i
$130$	−7.47010			−0.655171
$131$	−9.89347			−0.864396			−0.432198	−	0.901779i	$-0.642262\pi$
$131$	−9.89347			−0.864396			−0.432198	+	0.901779i	$0.642262\pi$
$132$	−16.0211	−	4.40880i	−1.39446	−	0.383737i
$133$		0			0
$134$			3.73929i			0.323025i
$135$	−3.74778	+	3.59918i	−0.322558	+	0.309768i
$136$			2.94562i			0.252585i
$137$			12.5990i			1.07641i	0.842815	+	0.538203i	$0.180897\pi$
$137$			12.5990i			1.07641i	−0.842815	+	0.538203i	$0.819103\pi$
$138$	−8.07973	+	29.3608i	−0.687792	+	2.49936i
$139$			0.988113i			0.0838106i	0.999122	+	0.0419053i	$0.0133428\pi$
$139$			0.988113i			0.0838106i	−0.999122	+	0.0419053i	$0.986657\pi$
$140$		0			0
$141$	−1.20850	+	4.39156i	−0.101774	+	0.369836i
$142$	−14.5882			−1.22421
$143$	8.95628			0.748962
$144$	−2.36912	−	1.41073i	−0.197426	−	0.117561i
$145$		−	8.15270i		−	0.677045i
$146$	−0.516818			−0.0427722
$147$		0			0
$148$	−1.39876			−0.114977
$149$			17.7367i			1.45305i	0.687142	+	0.726523i	$0.258865\pi$
$149$			17.7367i			1.45305i	−0.687142	+	0.726523i	$0.741135\pi$
$150$	3.89248	+	1.07116i	0.317819	+	0.0874599i
$151$	−22.5007			−1.83108			−0.915542	−	0.402223i	$-0.868237\pi$
$151$	−22.5007			−1.83108			−0.915542	+	0.402223i	$0.868237\pi$
$152$	−7.33379			−0.594849
$153$	−2.27330	−	1.35368i	−0.183785	−	0.109438i
$154$		0			0
$155$		−	8.80626i		−	0.707336i
$156$	18.3731	+	5.05605i	1.47103	+	0.404808i
$157$			11.8920i			0.949084i	0.880233	+	0.474542i	$0.157386\pi$
$157$			11.8920i			0.949084i	−0.880233	+	0.474542i	$0.842614\pi$
$158$			7.31189i			0.581703i
$159$	12.4722	+	3.43221i	0.989114	+	0.272192i
$160$		−	4.53757i		−	0.358726i
$161$		0			0
$162$	18.4435	−	9.99527i	1.44906	−	0.785302i
$163$	8.52319			0.667588			0.333794	−	0.942646i	$-0.391671\pi$
$163$	8.52319			0.667588			0.333794	+	0.942646i	$0.391671\pi$
$164$	29.3549			2.29223
$165$	−4.66689	−	1.28427i	−0.363317	−	0.0999803i
$166$			1.55444i			0.120648i
$167$	3.56923			0.276195			0.138098	−	0.990419i	$-0.455901\pi$
$167$	3.56923			0.276195			0.138098	+	0.990419i	$0.455901\pi$
$168$		0			0
$169$	2.72886			0.209912
$170$			2.05568i			0.157663i
$171$	3.37028	−	5.65988i	0.257732	−	0.432822i
$172$	0.405299			0.0309038
$173$	8.54229			0.649458			0.324729	−	0.945807i	$-0.394727\pi$
$173$	8.54229			0.649458			0.324729	+	0.945807i	$0.394727\pi$
$174$	−8.73285	+	31.7342i	−0.662036	+	2.40576i
$175$		0			0
$176$		−	2.56854i		−	0.193611i
$177$	1.88409	−	6.84658i	0.141617	−	0.514620i
$178$		−	2.03844i		−	0.152787i
$179$		−	1.22952i		−	0.0918987i	−0.998944	−	0.0459493i	$-0.985369\pi$
$179$		−	1.22952i		−	0.0918987i	0.998944	−	0.0459493i	$-0.0146313\pi$
$180$	−8.84876	−	5.26916i	−0.659548	−	0.392740i
$181$			15.3995i			1.14464i	0.820032	+	0.572318i	$0.193956\pi$
$181$			15.3995i			1.14464i	−0.820032	+	0.572318i	$0.806044\pi$
$182$		0			0
$183$	−20.6337	−	5.67814i	−1.52529	−	0.419740i
$184$	−25.1931			−1.85726
$185$	−0.407453			−0.0299566
$186$	−9.43292	+	34.2782i	−0.691655	+	2.51340i
$187$		−	2.46466i		−	0.180233i
$188$	−9.02762			−0.658407
$189$		0			0
$190$	−5.11806			−0.371303
$191$		−	14.5255i		−	1.05103i	−0.850785	−	0.525514i	$-0.823873\pi$
$191$		−	14.5255i		−	1.05103i	0.850785	−	0.525514i	$-0.176127\pi$
$192$	−5.70523	+	20.7322i	−0.411740	+	1.49622i
$193$	−0.403145			−0.0290190			−0.0145095	−	0.999895i	$-0.504619\pi$
$193$	−0.403145			−0.0290190			−0.0145095	+	0.999895i	$0.504619\pi$
$194$	−14.8528			−1.06637
$195$	5.35203	+	1.47281i	0.383267	+	0.105470i
$196$		0			0
$197$			11.6716i			0.831564i	0.909464	+	0.415782i	$0.136492\pi$
$197$			11.6716i			0.831564i	−0.909464	+	0.415782i	$0.863508\pi$
$198$	16.7901	+	9.99798i	1.19322	+	0.710526i
$199$			18.5775i			1.31692i	0.752614	+	0.658462i	$0.228793\pi$
$199$			18.5775i			1.31692i	−0.752614	+	0.658462i	$0.771207\pi$
$200$			3.33995i			0.236170i
$201$	0.737242	−	2.67906i	0.0520010	−	0.188966i
$202$			24.7662i			1.74254i
$203$		0			0
$204$	1.39136	−	5.05605i	0.0974147	−	0.353994i
$205$	8.55098			0.597227
$206$	−2.33827			−0.162915
$207$	11.5776	−	19.4429i	0.804700	−	1.35137i
$208$			2.94562i			0.204242i
$209$	6.13631			0.424457
$210$		0			0
$211$	6.98175			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$211$	6.98175			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$212$			25.6389i			1.76089i
$213$	10.4518	+	2.87622i	0.716149	+	0.197075i
$214$	−29.7812			−2.03580
$215$	0.118062			0.00805179
$216$	12.0211	+	12.5174i	0.817931	+	0.851700i
$217$		0			0
$218$		−	0.0425322i		−	0.00288064i
$219$	0.370280	+	0.101896i	0.0250212	+	0.00688552i
$220$		−	9.59362i		−	0.646802i
$221$			2.82649i			0.190130i
$222$	1.58600	+	0.436448i	0.106446	+	0.0292925i
$223$		−	1.44594i		−	0.0968271i	−0.998827	−	0.0484135i	$-0.984583\pi$
$223$		−	1.44594i		−	0.0968271i	0.998827	−	0.0484135i	$-0.0154165\pi$
$224$		0			0
$225$	−2.57762	−	1.53489i	−0.171841	−	0.102326i
$226$	−16.8528			−1.12103
$227$	1.06712			0.0708276			0.0354138	−	0.999373i	$-0.488725\pi$
$227$	1.06712			0.0708276			0.0354138	+	0.999373i	$0.488725\pi$
$228$	12.5882	+	3.46410i	0.833671	+	0.229416i
$229$		−	7.59860i		−	0.502129i	−0.967970	−	0.251065i	$-0.919219\pi$
$229$		−	7.59860i		−	0.502129i	0.967970	−	0.251065i	$-0.0807807\pi$
$230$	−17.5816			−1.15930
$231$		0			0
$232$	−27.2296			−1.78771
$233$			17.9997i			1.17920i	0.807697	+	0.589598i	$0.200714\pi$
$233$			17.9997i			1.17920i	−0.807697	+	0.589598i	$0.799286\pi$
$234$	−19.2551	−	11.4658i	−1.25874	−	0.749541i
$235$	−2.62972			−0.171544
$236$	14.0743			0.916162
$237$	1.44162	−	5.23868i	0.0936433	−	0.340289i
$238$		0			0
$239$		−	29.8816i		−	1.93288i	−0.256892	−	0.966440i	$-0.582698\pi$
$239$		−	29.8816i		−	1.93288i	0.256892	−	0.966440i	$-0.417302\pi$
$240$	0.422382	−	1.53489i	0.0272647	−	0.0990767i
$241$		−	5.23957i		−	0.337510i	−0.985658	−	0.168755i	$-0.946025\pi$
$241$		−	5.23957i		−	0.337510i	0.985658	−	0.168755i	$-0.0539747\pi$
$242$		−	7.43605i		−	0.478007i
$243$	−15.1847	+	3.52489i	−0.974099	+	0.226122i
$244$		−	42.4162i		−	2.71542i
$245$		0			0
$246$	−33.2845	−	9.15948i	−2.12214	−	0.583987i
$247$	−7.03717			−0.447765
$248$	−29.4124			−1.86769
$249$	0.306474	−	1.11369i	0.0194220	−	0.0705774i
$250$			2.33086i			0.147417i
$251$	−15.0765			−0.951620			−0.475810	−	0.879548i	$-0.657845\pi$
$251$	−15.0765			−0.951620			−0.475810	+	0.879548i	$0.657845\pi$
$252$		0			0
$253$	21.0795			1.32526
$254$		−	16.3058i		−	1.02312i
$255$	0.405299	−	1.47281i	0.0253808	−	0.0922310i
$256$	−21.4657			−1.34161
$257$	−15.9096			−0.992411			−0.496206	−	0.868205i	$-0.665274\pi$
$257$	−15.9096			−0.992411			−0.496206	+	0.868205i	$0.665274\pi$
$258$	−0.459555	−	0.126464i	−0.0286107	−	0.00787329i
$259$		0			0
$260$			11.0020i			0.682318i
$261$	12.5135	−	21.0146i	0.774566	−	1.30077i
$262$			23.0603i			1.42467i
$263$		−	8.30373i		−	0.512030i	−0.966673	−	0.256015i	$-0.917590\pi$
$263$		−	8.30373i		−	0.512030i	0.966673	−	0.256015i	$-0.0824097\pi$
$264$	−4.28939	+	15.5872i	−0.263994	+	0.959324i
$265$			7.46853i			0.458788i
$266$		0			0
$267$	−0.401900	+	1.46046i	−0.0245959	+	0.0893788i
$268$	5.50727			0.336410
$269$	−17.3871			−1.06011			−0.530054	−	0.847964i	$-0.677828\pi$
$269$	−17.3871			−1.06011			−0.530054	+	0.847964i	$0.677828\pi$
$270$	8.38921	+	8.73557i	0.510551	+	0.531630i
$271$		−	10.1915i		−	0.619092i	−0.950884	−	0.309546i	$-0.899823\pi$
$271$		−	10.1915i		−	0.619092i	0.950884	−	0.309546i	$-0.100177\pi$
$272$	0.810598			0.0491497
$273$		0			0
$274$	29.3666			1.77410
$275$		−	2.79459i		−	0.168520i
$276$	43.2430	+	11.8999i	2.60292	+	0.716291i
$277$	9.56036			0.574426			0.287213	−	0.957867i	$-0.407271\pi$
$277$	9.56036			0.574426			0.287213	+	0.957867i	$0.407271\pi$
$278$	2.30316			0.138134
$279$	13.5166	−	22.6992i	0.809220	−	1.35896i
$280$		0			0
$281$			11.9239i			0.711320i	0.934616	+	0.355660i	$0.115744\pi$
$281$			11.9239i			0.711320i	−0.934616	+	0.355660i	$0.884256\pi$
$282$	10.2361	+	2.81685i	0.609552	+	0.167741i
$283$		−	19.9694i		−	1.18706i	−0.804813	−	0.593528i	$-0.797735\pi$
$283$		−	19.9694i		−	1.18706i	0.804813	−	0.593528i	$-0.202265\pi$
$284$			21.4856i			1.27494i
$285$	3.66689	+	1.00908i	0.217208	+	0.0597729i
$286$		−	20.8759i		−	1.23442i
$287$		0			0
$288$	6.96467	−	11.6961i	0.410397	−	0.689201i
$289$	−16.2222			−0.954246
$290$	−19.0028			−1.11588
$291$	10.6414	+	2.92839i	0.623811	+	0.171665i
$292$			0.761176i			0.0445445i
$293$	3.01023			0.175859			0.0879297	−	0.996127i	$-0.471975\pi$
$293$	3.01023			0.175859			0.0879297	+	0.996127i	$0.471975\pi$
$294$		0			0
$295$	4.09982			0.238700
$296$			1.36087i			0.0790991i
$297$	−10.0583	−	10.4735i	−0.583639	−	0.607735i
$298$	41.3418			2.39486
$299$	−24.1742			−1.39803
$300$	1.57762	−	5.73289i	0.0910838	−	0.330988i
$301$		0			0
$302$			52.4461i			3.01793i
$303$	4.88293	−	17.7440i	0.280517	−	1.01937i
$304$			2.01816i			0.115750i
$305$		−	12.3557i		−	0.707487i
$306$	−3.15524	+	5.29875i	−0.180373	+	0.302909i
$307$			20.3794i			1.16311i	0.813507	+	0.581556i	$0.197556\pi$
$307$			20.3794i			1.16311i	−0.813507	+	0.581556i	$0.802444\pi$
$308$		0			0
$309$	1.67528	+	0.461015i	0.0953033	+	0.0262263i
$310$	−20.5262			−1.16581
$311$	−27.2718			−1.54644			−0.773222	−	0.634136i	$-0.781356\pi$
$311$	−27.2718			−1.54644			−0.773222	+	0.634136i	$0.781356\pi$
$312$	4.91911	−	17.8755i	0.278490	−	1.01200i
$313$			0.630709i			0.0356498i	0.999841	+	0.0178249i	$0.00567414\pi$
$313$			0.630709i			0.0356498i	−0.999841	+	0.0178249i	$0.994326\pi$
$314$	27.7186			1.56425
$315$		0			0
$316$	10.7690			0.605806
$317$			25.4303i			1.42831i	0.699989	+	0.714153i	$0.253188\pi$
$317$			25.4303i			1.42831i	−0.699989	+	0.714153i	$0.746812\pi$
$318$	8.00000	−	29.0711i	0.448618	−	1.63023i
$319$	22.7835			1.27563
$320$	−12.4147			−0.694001
$321$	21.3371	+	5.87170i	1.19092	+	0.327726i
$322$		0			0
$323$			1.93654i			0.107752i
$324$	−14.7211	−	27.1637i	−0.817842	−	1.50910i
$325$			3.20486i			0.177774i
$326$		−	19.8664i		−	1.10030i
$327$	−0.00838569	+	0.0304727i	−0.000463730	+	0.00168514i
$328$		−	28.5598i		−	1.57695i
$329$		0			0
$330$	−2.99346	+	10.8779i	−0.164784	+	0.598808i
$331$	11.4933			0.631731			0.315865	−	0.948804i	$-0.397705\pi$
$331$	11.4933			0.631731			0.315865	+	0.948804i	$0.397705\pi$
$332$	2.28939			0.125647
$333$	−1.05026	−	0.625396i	−0.0575539	−	0.0342715i
$334$		−	8.31939i		−	0.455217i
$335$	1.60425			0.0876496
$336$		0			0
$337$	−16.2041			−0.882694			−0.441347	−	0.897336i	$-0.645499\pi$
$337$	−16.2041			−0.882694			−0.441347	+	0.897336i	$0.645499\pi$
$338$		−	6.36059i		−	0.345971i
$339$	12.0743	+	3.32271i	0.655788	+	0.180465i
$340$	3.02762			0.164196
$341$	24.6099			1.33270
$342$	−13.1924	−	7.85566i	−0.713364	−	0.424786i
$343$		0			0
$344$		−	0.394322i		−	0.0212604i
$345$	12.5965	+	3.46641i	0.678175	+	0.186625i
$346$		−	19.9109i		−	1.07042i
$347$			17.9824i			0.965347i	0.875800	+	0.482673i	$0.160334\pi$
$347$			17.9824i			0.965347i	−0.875800	+	0.482673i	$0.839666\pi$
$348$	46.7385	+	12.8618i	2.50545	+	0.689467i
$349$			6.15422i			0.329428i	0.986341	+	0.164714i	$0.0526701\pi$
$349$			6.15422i			0.329428i	−0.986341	+	0.164714i	$0.947330\pi$
$350$		0			0
$351$	11.5349	+	12.0111i	0.615687	+	0.641106i
$352$	12.6807			0.675881
$353$	29.4664			1.56834			0.784169	−	0.620548i	$-0.213090\pi$
$353$	29.4664			1.56834			0.784169	+	0.620548i	$0.213090\pi$
$354$	−15.9584	−	4.39156i	−0.848181	−	0.233409i
$355$			6.25869i			0.332177i
$356$	−3.00223			−0.159118
$357$		0			0
$358$	−2.86584			−0.151465
$359$		−	35.2447i		−	1.86015i	−0.367375	−	0.930073i	$-0.619743\pi$
$359$		−	35.2447i		−	1.86015i	0.367375	−	0.930073i	$-0.380257\pi$
$360$	−5.12645	+	8.60910i	−0.270188	+	0.453740i
$361$	14.1786			0.746239
$362$	35.8941			1.88655
$363$	−1.46610	+	5.32764i	−0.0769502	+	0.279628i
$364$		0			0
$365$			0.221728i			0.0116058i
$366$	−13.2350	+	48.0944i	−0.691802	+	2.51393i
$367$		−	34.8273i		−	1.81797i	−0.416830	−	0.908984i	$-0.636859\pi$
$367$		−	34.8273i		−	1.81797i	0.416830	−	0.908984i	$-0.363141\pi$
$368$			6.93282i			0.361398i
$369$	22.0412	+	13.1248i	1.14742	+	0.683251i
$370$			0.949718i			0.0493735i
$371$		0			0
$372$	50.4853	+	13.8929i	2.61754	+	0.720314i
$373$	20.2742			1.04976			0.524878	−	0.851178i	$-0.324111\pi$
$373$	20.2742			1.04976			0.524878	+	0.851178i	$0.324111\pi$
$374$	−5.74478			−0.297055
$375$	0.459555	−	1.66997i	0.0237313	−	0.0862370i
$376$			8.78312i			0.452955i
$377$	−26.1283			−1.34568
$378$		0			0
$379$	−9.07202			−0.465998			−0.232999	−	0.972477i	$-0.574854\pi$
$379$	−9.07202			−0.465998			−0.232999	+	0.972477i	$0.574854\pi$
$380$			7.53794i			0.386688i
$381$	−3.21487	+	11.6825i	−0.164703	+	0.598512i
$382$	−33.8570			−1.73227
$383$	27.7762			1.41930			0.709648	−	0.704556i	$-0.248854\pi$
$383$	27.7762			1.41930			0.709648	+	0.704556i	$0.248854\pi$
$384$	33.1686	+	9.12758i	1.69263	+	0.465790i
$385$		0			0
$386$			0.939675i			0.0478282i
$387$	0.304320	+	0.181213i	0.0154694	+	0.00921156i
$388$			21.8753i			1.11055i
$389$			15.5821i			0.790046i	0.918671	+	0.395023i	$0.129263\pi$
$389$			15.5821i			0.790046i	−0.918671	+	0.395023i	$0.870737\pi$
$390$	3.43292	−	12.4749i	0.173833	−	0.631689i
$391$			6.65242i			0.336427i
$392$		0			0
$393$	4.54660	−	16.5218i	0.229345	−	0.833416i
$394$	27.2048			1.37056
$395$	3.13699			0.157839
$396$	14.7251	−	24.7287i	0.739966	−	1.24266i
$397$		−	18.8905i		−	0.948086i	−0.880502	−	0.474043i	$-0.842794\pi$
$397$		−	18.8905i		−	0.948086i	0.880502	−	0.474043i	$-0.157206\pi$
$398$	43.3016			2.17051
$399$		0			0
$400$	0.919111			0.0459555
$401$			20.7993i			1.03867i	0.854572	+	0.519333i	$0.173820\pi$
$401$			20.7993i			1.03867i	−0.854572	+	0.519333i	$0.826180\pi$
$402$	−6.24451	−	1.71841i	−0.311448	−	0.0857065i
$403$	−28.2229			−1.40588
$404$	36.4759			1.81475
$405$	−4.28823	−	7.91272i	−0.213084	−	0.393186i
$406$		0			0
$407$		−	1.13867i		−	0.0564416i
$408$	−4.91911	−	1.35368i	−0.243532	−	0.0670170i
$409$		−	28.8287i		−	1.42549i	−0.701425	−	0.712744i	$-0.747452\pi$
$409$		−	28.8287i		−	1.42549i	0.701425	−	0.712744i	$-0.252548\pi$
$410$		−	19.9312i		−	0.984331i
$411$	−21.0400	−	5.78994i	−1.03783	−	0.285597i
$412$			3.44383i			0.169665i
$413$		0			0
$414$	−45.3187	−	26.9858i	−2.22729	−	1.32628i
$415$	0.666893			0.0327365
$416$	−14.5423			−0.712994
$417$	−1.65012	−	0.454093i	−0.0808068	−	0.0222370i
$418$		−	14.3029i		−	0.699578i
$419$	−3.24500			−0.158528			−0.0792642	−	0.996854i	$-0.525257\pi$
$419$	−3.24500			−0.158528			−0.0792642	+	0.996854i	$0.525257\pi$
$420$		0			0
$421$	27.9322			1.36133			0.680665	−	0.732594i	$-0.261691\pi$
$421$	27.9322			1.36133			0.680665	+	0.732594i	$0.261691\pi$
$422$		−	16.2735i		−	0.792182i
$423$	−6.77841	−	4.03633i	−0.329578	−	0.196253i
$424$	24.9445			1.21141
$425$	0.881938			0.0427803
$426$	6.70407	−	24.3618i	0.324813	−	1.18033i
$427$		0			0
$428$			43.8622i			2.12016i
$429$	−4.11591	+	14.9567i	−0.198718	+	0.722119i
$430$		−	0.275187i		−	0.0132707i
$431$			38.3121i			1.84543i	0.385486	+	0.922714i	$0.374034\pi$
$431$			38.3121i			1.84543i	−0.385486	+	0.922714i	$0.625966\pi$
$432$	3.44463	−	3.30805i	0.165730	−	0.159159i
$433$		−	28.9533i		−	1.39140i	−0.718330	−	0.695702i	$-0.755093\pi$
$433$		−	28.9533i		−	1.39140i	0.718330	−	0.695702i	$-0.244907\pi$
$434$		0			0
$435$	13.6148	+	3.74662i	0.652779	+	0.179637i
$436$	−0.0626419			−0.00300000
$437$	−16.5627			−0.792301
$438$	0.237507	−	0.863073i	0.0113485	−	0.0412392i
$439$		−	15.2648i		−	0.728551i	−0.931291	−	0.364275i	$-0.881317\pi$
$439$		−	15.2648i		−	0.728551i	0.931291	−	0.364275i	$-0.118683\pi$
$440$	−9.33379			−0.444971
$441$		0			0
$442$	6.58816			0.313367
$443$		−	2.28372i		−	0.108503i	−0.998527	−	0.0542513i	$-0.982723\pi$
$443$		−	2.28372i		−	0.108503i	0.998527	−	0.0542513i	$-0.0172772\pi$
$444$	0.642806	−	2.33588i	0.0305062	−	0.110856i
$445$	−0.874542			−0.0414573
$446$	−3.37028			−0.159587
$447$	−29.6198	−	8.15099i	−1.40097	−	0.385528i
$448$		0			0
$449$			10.3113i			0.486619i	0.969949	+	0.243310i	$0.0782331\pi$
$449$			10.3113i			0.486619i	−0.969949	+	0.243310i	$0.921767\pi$
$450$	−3.57762	+	6.00807i	−0.168651	+	0.283223i
$451$			23.8965i			1.12524i
$452$			24.8209i			1.16748i
$453$	10.3403	−	37.5756i	0.485831	−	1.76546i
$454$		−	2.48732i		−	0.116736i
$455$		0			0
$456$	3.37028	−	12.2472i	0.157828	−	0.573529i
$457$	32.7973			1.53419			0.767097	−	0.641531i	$-0.221700\pi$
$457$	32.7973			1.53419			0.767097	+	0.641531i	$0.221700\pi$
$458$	−17.7113			−0.827594
$459$	3.30531	−	3.17426i	0.154279	−	0.148162i
$460$			25.8944i			1.20733i
$461$	16.5678			0.771637			0.385819	−	0.922575i	$-0.373919\pi$
$461$	16.5678			0.771637			0.385819	+	0.922575i	$0.373919\pi$
$462$		0			0
$463$	−36.5866			−1.70032			−0.850162	−	0.526522i	$-0.823496\pi$
$463$	−36.5866			−1.70032			−0.850162	+	0.526522i	$0.823496\pi$
$464$			7.49324i			0.347865i
$465$	14.7062	+	4.04697i	0.681985	+	0.187674i
$466$	41.9547			1.94352
$467$	−41.1100			−1.90234			−0.951171	−	0.308664i	$-0.900118\pi$
$467$	−41.1100			−1.90234			−0.951171	+	0.308664i	$0.900118\pi$
$468$	−16.8869	+	28.3591i	−0.780598	+	1.31090i
$469$		0			0
$470$			6.12952i			0.282733i
$471$	−19.8593	−	5.46503i	−0.915068	−	0.251815i
$472$		−	13.6932i		−	0.630279i
$473$			0.329936i			0.0151705i
$474$	−12.2107	−	3.36022i	−0.560854	−	0.154340i
$475$			2.19578i			0.100749i
$476$		0			0
$477$	−11.4634	+	19.2510i	−0.524872	+	0.881444i
$478$	−69.6499			−3.18571
$479$	16.5189			0.754767			0.377383	−	0.926057i	$-0.376824\pi$
$479$	16.5189			0.754767			0.377383	+	0.926057i	$0.376824\pi$
$480$	7.57762	+	2.08526i	0.345869	+	0.0951789i
$481$			1.30583i			0.0595408i
$482$	−12.2127			−0.556274
$483$		0			0
$484$	−10.9519			−0.497813
$485$			6.37221i			0.289347i
$486$	8.21603	+	35.3935i	0.372687	+	1.60548i
$487$	−2.03201			−0.0920792			−0.0460396	−	0.998940i	$-0.514660\pi$
$487$	−2.03201			−0.0920792			−0.0460396	+	0.998940i	$0.514660\pi$
$488$	−41.2674			−1.86809
$489$	−3.91688	+	14.2335i	−0.177127	+	0.643661i
$490$		0			0
$491$			5.97889i			0.269824i	0.990858	+	0.134912i	$0.0430751\pi$
$491$			5.97889i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$492$	−13.4902	+	49.0218i	−0.608185	+	2.21007i
$493$			7.19017i			0.323829i
$494$			16.4027i			0.737992i
$495$	4.28939	−	7.20339i	0.192794	−	0.323768i
$496$			8.09393i			0.363428i
$497$		0			0
$498$	−2.59587	−	0.714349i	−0.116323	−	0.0320108i
$499$	8.48310			0.379756			0.189878	−	0.981808i	$-0.439191\pi$
$499$	8.48310			0.379756			0.189878	+	0.981808i	$0.439191\pi$
$500$	3.43292			0.153525
$501$	−1.64026	+	5.96052i	−0.0732814	+	0.266296i
$502$			35.1413i			1.56843i
$503$	17.0296			0.759312			0.379656	−	0.925128i	$-0.376042\pi$
$503$	17.0296			0.759312			0.379656	+	0.925128i	$0.376042\pi$
$504$		0			0
$505$	10.6253			0.472821
$506$		−	49.1334i		−	2.18425i
$507$	−1.25406	+	4.55712i	−0.0556948	+	0.202389i
$508$	−24.0154			−1.06551
$509$	−12.8682			−0.570372			−0.285186	−	0.958472i	$-0.592055\pi$
$509$	−12.8682			−0.570372			−0.285186	+	0.958472i	$0.592055\pi$
$510$	−3.43292	−	0.944697i	−0.152012	−	0.0418319i
$511$		0			0
$512$			10.3101i			0.455646i
$513$	7.90302	+	8.22931i	0.348927	+	0.363333i
$514$			37.0830i			1.63566i
$515$			1.00318i			0.0442053i
$516$	−0.186257	+	0.676838i	−0.00819952	+	0.0297962i
$517$		−	7.34899i		−	0.323208i
$518$		0			0
$519$	−3.92565	+	14.2654i	−0.172317	+	0.626181i
$520$	10.7041			0.469404
$521$	16.6545			0.729646			0.364823	−	0.931077i	$-0.381129\pi$
$521$	16.6545			0.729646			0.364823	+	0.931077i	$0.381129\pi$
$522$	−48.9820	−	29.1673i	−2.14389	−	1.27662i
$523$			36.3655i			1.59015i	0.606511	+	0.795075i	$0.292569\pi$
$523$			36.3655i			1.59015i	−0.606511	+	0.795075i	$0.707431\pi$
$524$	33.9635			1.48370
$525$		0			0
$526$	−19.3549			−0.843912
$527$			7.76657i			0.338317i
$528$	4.28939	+	1.18039i	0.186672	+	0.0513697i
$529$	−33.8963			−1.47375
$530$	17.4081			0.756161
$531$	10.5678	+	6.29276i	0.458602	+	0.273083i
$532$		0			0
$533$		−	27.4047i		−	1.18703i
$534$	3.40413	+	0.936775i	0.147311	+	0.0405382i
$535$			12.7769i			0.552394i
$536$		−	5.35811i		−	0.231435i
$537$	2.05327	+	0.565033i	0.0886050	+	0.0243830i
$538$			40.5268i			1.74724i
$539$		0			0
$540$	12.8658	−	12.3557i	0.553658	−	0.531706i
$541$	3.79150			0.163009			0.0815046	−	0.996673i	$-0.474027\pi$
$541$	3.79150			0.163009			0.0815046	+	0.996673i	$0.474027\pi$
$542$	−23.7551			−1.02037
$543$	−25.7168	−	7.07693i	−1.10361	−	0.303700i
$544$			4.00185i			0.171578i
$545$	−0.0182474			−0.000781633
$546$		0			0
$547$	−10.9382			−0.467684			−0.233842	−	0.972275i	$-0.575130\pi$
$547$	−10.9382			−0.467684			−0.233842	+	0.972275i	$0.575130\pi$
$548$		−	43.2514i		−	1.84761i
$549$	18.9647	−	31.8483i	0.809392	−	1.35925i
$550$	−6.51381			−0.277750
$551$	−17.9015			−0.762631
$552$	11.5776	−	42.0718i	0.492776	−	1.79069i
$553$		0			0
$554$		−	22.2839i		−	0.946752i
$555$	0.187247	−	0.680436i	0.00794821	−	0.0288829i
$556$		−	3.39211i		−	0.143858i
$557$		−	9.73243i		−	0.412376i	−0.978512	−	0.206188i	$-0.933894\pi$
$557$		−	9.73243i		−	0.412376i	0.978512	−	0.206188i	$-0.0661059\pi$
$558$	−52.9087	−	31.5054i	−2.23980	−	1.33373i
$559$		−	0.378374i		−	0.0160035i
$560$		0			0
$561$	4.11591	+	1.13265i	0.173774	+	0.0478203i
$562$	27.7929			1.17237
$563$	−0.470270			−0.0198195			−0.00990975	−	0.999951i	$-0.503154\pi$
$563$	−0.470270			−0.0198195			−0.00990975	+	0.999951i	$0.503154\pi$
$564$	4.14869	−	15.0759i	0.174691	−	0.634809i
$565$			7.23027i			0.304180i
$566$	−46.5459			−1.95647
$567$		0			0
$568$	20.9037			0.877100
$569$		−	6.21675i		−	0.260620i	−0.991473	−	0.130310i	$-0.958403\pi$
$569$		−	6.21675i		−	0.260620i	0.991473	−	0.130310i	$-0.0415972\pi$
$570$	2.35203	−	8.54702i	0.0985158	−	0.357995i
$571$	10.6224			0.444534			0.222267	−	0.974986i	$-0.428654\pi$
$571$	10.6224			0.444534			0.222267	+	0.974986i	$0.428654\pi$
$572$	−30.7462			−1.28556
$573$	24.2572	+	6.67528i	1.01336	+	0.278864i
$574$		0			0
$575$			7.54296i			0.314563i
$576$	−32.0003	−	19.0552i	−1.33335	−	0.793965i
$577$			2.96659i			0.123501i	0.998092	+	0.0617504i	$0.0196683\pi$
$577$			2.96659i			0.123501i	−0.998092	+	0.0617504i	$0.980332\pi$
$578$			37.8117i			1.57276i
$579$	0.185267	−	0.673241i	0.00769945	−	0.0279789i
$580$			27.9876i			1.16212i
$581$		0			0
$582$	6.82566	−	24.8037i	0.282933	−	1.02815i
$583$	−20.8715			−0.864410
$584$	0.740561			0.0306446
$585$	−4.91911	+	8.26091i	−0.203380	+	0.341547i
$586$		−	7.01643i		−	0.289846i
$587$	18.8819			0.779341			0.389670	−	0.920954i	$-0.372589\pi$
$587$	18.8819			0.779341			0.389670	+	0.920954i	$0.372589\pi$
$588$		0			0
$589$	−19.3366			−0.796751
$590$		−	9.55611i		−	0.393419i
$591$	−19.4912	−	5.36372i	−0.801760	−	0.220634i
$592$	0.374495			0.0153916
$593$	−30.2944			−1.24404			−0.622020	−	0.783001i	$-0.713688\pi$
$593$	−30.2944			−1.24404			−0.622020	+	0.783001i	$0.713688\pi$
$594$	−24.4123	+	23.4444i	−1.00165	+	0.961936i
$595$		0			0
$596$		−	60.8887i		−	2.49410i
$597$	−31.0239	−	8.53739i	−1.26972	−	0.349412i
$598$			56.3467i			2.30419i
$599$		−	7.26335i		−	0.296772i	−0.988929	−	0.148386i	$-0.952592\pi$
$599$		−	7.26335i		−	0.296772i	0.988929	−	0.148386i	$-0.0474079\pi$
$600$	−5.57762	−	1.53489i	−0.227705	−	0.0626616i
$601$			45.3302i			1.84906i	0.381110	+	0.924530i	$0.375542\pi$
$601$			45.3302i			1.84906i	−0.381110	+	0.924530i	$0.624458\pi$
$602$		0			0
$603$	4.13515	+	2.46235i	0.168396	+	0.100275i
$604$	77.2432			3.14298
$605$	−3.19025			−0.129702
$606$	−41.3589	−	11.3814i	−1.68009	−	0.462339i
$607$			26.0235i			1.05626i	0.849163	+	0.528130i	$0.177107\pi$
$607$			26.0235i			1.05626i	−0.849163	+	0.528130i	$0.822893\pi$
$608$	−9.96351			−0.404073
$609$		0			0
$610$	−28.7995			−1.16606
$611$			8.42789i			0.340956i
$612$	7.80406	+	4.64707i	0.315460	+	0.187847i
$613$	25.7049			1.03821			0.519106	−	0.854710i	$-0.326265\pi$
$613$	25.7049			1.03821			0.519106	+	0.854710i	$0.326265\pi$
$614$	47.5015			1.91700
$615$	−3.92965	+	14.2799i	−0.158459	+	0.575822i
$616$		0			0
$617$			8.88258i			0.357599i	0.983886	+	0.178800i	$0.0572213\pi$
$617$			8.88258i			0.357599i	−0.983886	+	0.178800i	$0.942779\pi$
$618$	1.07456	−	3.90484i	0.0432253	−	0.157076i
$619$			30.4971i			1.22578i	0.790168	+	0.612890i	$0.209993\pi$
$619$			30.4971i			1.22578i	−0.790168	+	0.612890i	$0.790007\pi$
$620$			30.2312i			1.21411i
$621$	27.1485	+	28.2694i	1.08943	+	1.13441i
$622$			63.5669i			2.54880i
$623$		0			0
$624$	−4.91911	−	1.35368i	−0.196922	−	0.0541904i
$625$	1.00000			0.0400000
$626$	1.47010			0.0587568
$627$	−2.81997	+	10.2475i	−0.112619	+	0.409245i
$628$		−	40.8243i		−	1.62907i
$629$	0.359349			0.0143282
$630$		0			0
$631$	44.3335			1.76489			0.882445	−	0.470416i	$-0.155896\pi$
$631$	44.3335			1.76489			0.882445	+	0.470416i	$0.155896\pi$
$632$		−	10.4774i		−	0.416767i
$633$	−3.20850	+	11.6593i	−0.127526	+	0.463417i
$634$	59.2745			2.35409
$635$	−6.99561			−0.277612
$636$	−42.8163	−	11.7825i	−1.69778	−	0.467206i
$637$		0			0
$638$		−	53.1052i		−	2.10245i
$639$	−9.60641	+	16.1325i	−0.380024	+	0.638193i
$640$			19.8618i			0.785105i
$641$		−	6.96512i		−	0.275106i	−0.990494	−	0.137553i	$-0.956076\pi$
$641$		−	6.96512i		−	0.275106i	0.990494	−	0.137553i	$-0.0439237\pi$
$642$	13.6861	−	49.7339i	0.540148	−	1.96284i
$643$		−	25.8907i		−	1.02103i	−0.859869	−	0.510514i	$-0.829455\pi$
$643$		−	25.8907i		−	1.02103i	0.859869	−	0.510514i	$-0.170545\pi$
$644$		0			0
$645$	−0.0542562	+	0.197161i	−0.00213634	+	0.00776321i
$646$	4.51381			0.177594
$647$	−10.0372			−0.394602			−0.197301	−	0.980343i	$-0.563218\pi$
$647$	−10.0372			−0.394602			−0.197301	+	0.980343i	$0.563218\pi$
$648$	−26.4280	+	14.3224i	−1.03819	+	0.562639i
$649$			11.4573i			0.449739i
$650$	7.47010			0.293001
$651$		0			0
$652$	−29.2594			−1.14589
$653$			39.6000i			1.54967i	0.632166	+	0.774833i	$0.282166\pi$
$653$			39.6000i			1.54967i	−0.632166	+	0.774833i	$0.717834\pi$
$654$	0.0710276	+	0.0195459i	0.00277740	+	0.000764305i
$655$	9.89347			0.386570
$656$	−7.85930			−0.306854
$657$	−0.340329	+	0.571531i	−0.0132775	+	0.0222975i
$658$		0			0
$659$			17.9364i			0.698705i	0.936991	+	0.349352i	$0.113598\pi$
$659$			17.9364i			0.698705i	−0.936991	+	0.349352i	$0.886402\pi$
$660$	16.0211	+	4.40880i	0.623620	+	0.171612i
$661$			3.82220i			0.148666i	0.997233	+	0.0743332i	$0.0236828\pi$
$661$			3.82220i			0.148666i	−0.997233	+	0.0743332i	$0.976317\pi$
$662$		−	26.7894i		−	1.04120i
$663$	−4.72016	−	1.29893i	−0.183316	−	0.0504462i
$664$		−	2.22739i		−	0.0864393i
$665$		0			0
$666$	−1.45771	+	2.44801i	−0.0564852	+	0.0948585i
$667$	−61.4955			−2.38112
$668$	−12.2529			−0.474079
$669$	2.41467	+	0.664488i	0.0933567	+	0.0256906i
$670$		−	3.73929i		−	0.144461i
$671$	34.5292			1.33299
$672$		0			0
$673$	1.08304			0.0417483			0.0208741	−	0.999782i	$-0.493355\pi$
$673$	1.08304			0.0417483			0.0208741	+	0.999782i	$0.493355\pi$
$674$			37.7696i			1.45483i
$675$	3.74778	−	3.59918i	0.144252	−	0.138533i
$676$	−9.36795			−0.360306
$677$	31.0028			1.19153			0.595766	−	0.803158i	$-0.296848\pi$
$677$	31.0028			1.19153			0.595766	+	0.803158i	$0.296848\pi$
$678$	7.74478	−	28.1436i	0.297436	−	1.08085i
$679$		0			0
$680$		−	2.94562i		−	0.112960i
$681$	−0.490403	+	1.78207i	−0.0187923	+	0.0682890i
$682$		−	57.3623i		−	2.19652i
$683$			19.1010i			0.730879i	0.930835	+	0.365440i	$0.119081\pi$
$683$			19.1010i			0.730879i	−0.930835	+	0.365440i	$0.880919\pi$
$684$	−11.5699	+	19.4299i	−0.442387	+	0.742922i
$685$		−	12.5990i		−	0.481383i
$686$		0			0
$687$	12.6894	+	3.49198i	0.484133	+	0.133227i
$688$	−0.108512			−0.00413700
$689$	23.9356			0.911875
$690$	8.07973	−	29.3608i	0.307590	−	1.11775i
$691$		−	16.8326i		−	0.640344i	−0.947359	−	0.320172i	$-0.896259\pi$
$691$		−	16.8326i		−	0.640344i	0.947359	−	0.320172i	$-0.103741\pi$
$692$	−29.3250			−1.11477
$693$		0			0
$694$	41.9145			1.59105
$695$		−	0.988113i		−	0.0374813i
$696$	12.5135	−	45.4727i	0.474323	−	1.72364i
$697$	−7.54143			−0.285652
$698$	14.3446			0.542953
$699$	−30.0589	−	8.27184i	−1.13693	−	0.312870i
$700$		0			0
$701$			21.8878i			0.826691i	0.910574	+	0.413345i	$0.135640\pi$
$701$			21.8878i			0.826691i	−0.910574	+	0.413345i	$0.864360\pi$
$702$	27.9963	−	26.8863i	1.05665	−	1.01476i
$703$			0.894678i			0.0337434i
$704$		−	34.6940i		−	1.30758i
$705$	1.20850	−	4.39156i	0.0455148	−	0.165396i
$706$		−	68.6821i		−	2.58489i
$707$		0			0
$708$	−6.46794	+	23.5038i	−0.243080	+	0.883326i
$709$	−10.8206			−0.406376			−0.203188	−	0.979140i	$-0.565130\pi$
$709$	−10.8206			−0.406376			−0.203188	+	0.979140i	$0.565130\pi$
$710$	14.5882			0.547484
$711$	8.08596	+	4.81493i	0.303247	+	0.180574i
$712$			2.92092i			0.109466i
$713$	−66.4253			−2.48765
$714$		0			0
$715$	−8.95628			−0.334946
$716$			4.22085i			0.157741i
$717$	49.9015	+	13.7323i	1.86360	+	0.512840i
$718$	−82.1506			−3.06583
$719$	−22.2592			−0.830128			−0.415064	−	0.909792i	$-0.636241\pi$
$719$	−22.2592			−0.830128			−0.415064	+	0.909792i	$0.636241\pi$
$720$	2.36912	+	1.41073i	0.0882917	+	0.0525749i
$721$		0			0
$722$		−	33.0483i		−	1.22993i
$723$	8.74994	+	2.40787i	0.325414	+	0.0895497i
$724$		−	52.8653i		−	1.96472i
$725$			8.15270i			0.302784i
$726$	12.4180	+	3.41727i	0.460875	+	0.126827i
$727$		−	43.7899i		−	1.62408i	−0.583604	−	0.812038i	$-0.698358\pi$
$727$		−	43.7899i		−	1.62408i	0.583604	−	0.812038i	$-0.301642\pi$
$728$		0			0
$729$	1.09174	−	26.9779i	0.0404349	−	0.999182i
$730$	0.516818			0.0191283
$731$	−0.104124			−0.00385115
$732$	70.8339	+	19.4926i	2.61810	+	0.720467i
$733$			26.1709i			0.966644i	0.875443	+	0.483322i	$0.160570\pi$
$733$			26.1709i			0.966644i	−0.875443	+	0.483322i	$0.839430\pi$
$734$	−81.1776			−2.99632
$735$		0			0
$736$	−34.2267			−1.26161
$737$			4.48323i			0.165142i
$738$	30.5922	−	51.3749i	1.12611	−	1.89114i
$739$	40.3555			1.48450			0.742250	−	0.670123i	$-0.233759\pi$
$739$	40.3555			1.48450			0.742250	+	0.670123i	$0.233759\pi$
$740$	1.39876			0.0514193
$741$	3.23397	−	11.7519i	0.118803	−	0.431716i
$742$		0			0
$743$			8.82565i			0.323782i	0.986809	+	0.161891i	$0.0517593\pi$
$743$			8.82565i			0.323782i	−0.986809	+	0.161891i	$0.948241\pi$
$744$	13.5166	−	49.1180i	0.495544	−	1.80075i
$745$		−	17.7367i		−	0.649822i
$746$		−	47.2563i		−	1.73017i
$747$	1.71899	+	1.02361i	0.0628947	+	0.0374518i
$748$			8.46097i			0.309364i
$749$		0			0
$750$	−3.89248	−	1.07116i	−0.142133	−	0.0391133i
$751$	37.8330			1.38055			0.690274	−	0.723549i	$-0.257490\pi$
$751$	37.8330			1.38055			0.690274	+	0.723549i	$0.257490\pi$
$752$	2.41700			0.0881390
$753$	6.92849	−	25.1773i	0.252488	−	0.917513i
$754$			60.9015i			2.21790i
$755$	22.5007			0.818885
$756$		0			0
$757$	−34.7636			−1.26351			−0.631753	−	0.775170i	$-0.717664\pi$
$757$	−34.7636			−1.26351			−0.631753	+	0.775170i	$0.717664\pi$
$758$			21.1456i			0.768044i
$759$	−9.68720	+	35.2022i	−0.351623	+	1.27776i
$760$	7.33379			0.266024
$761$	1.83015			0.0663428			0.0331714	−	0.999450i	$-0.489439\pi$
$761$	1.83015			0.0663428			0.0331714	+	0.999450i	$0.489439\pi$
$762$	27.2303	+	7.49342i	0.986448	+	0.271458i
$763$		0			0
$764$			49.8649i			1.80405i
$765$	2.27330	+	1.35368i	0.0821913	+	0.0489423i
$766$		−	64.7425i		−	2.33924i
$767$		−	13.1393i		−	0.474434i
$768$	9.86468	−	35.8471i	0.355961	−	1.29352i
$769$		−	23.5601i		−	0.849598i	−0.905288	−	0.424799i	$-0.860345\pi$
$769$		−	23.5601i		−	0.849598i	0.905288	−	0.424799i	$-0.139655\pi$
$770$		0			0
$771$	7.31132	−	26.5685i	0.263311	−	0.956842i
$772$	1.38396			0.0498100
$773$	48.0873			1.72958			0.864790	−	0.502133i	$-0.167451\pi$
$773$	48.0873			1.72958			0.864790	+	0.502133i	$0.167451\pi$
$774$	0.422382	−	0.709328i	0.0151822	−	0.0254963i
$775$			8.80626i			0.316330i
$776$	21.2828			0.764010
$777$		0			0
$778$	36.3198			1.30213
$779$		−	18.7761i		−	0.672723i
$780$	−18.3731	−	5.05605i	−0.657863	−	0.181036i
$781$	−17.4905			−0.625859
$782$	15.5059			0.554489
$783$	29.3431	+	30.5546i	1.04864	+	1.09193i
$784$		0			0
$785$		−	11.8920i		−	0.424443i
$786$	−38.5101	−	10.5975i	−1.37361	−	0.378000i
$787$			30.1647i			1.07525i	0.843183	+	0.537627i	$0.180679\pi$
$787$			30.1647i			1.07525i	−0.843183	+	0.537627i	$0.819321\pi$
$788$		−	40.0675i		−	1.42735i
$789$	13.8670	+	3.81603i	0.493679	+	0.135854i
$790$		−	7.31189i		−	0.260145i
$791$		0			0
$792$	−24.0589	−	14.3263i	−0.854897	−	0.509064i
$793$	−39.5984			−1.40618
$794$	−44.0311			−1.56261
$795$	−12.4722	−	3.43221i	−0.442345	−	0.121728i
$796$		−	63.7751i		−	2.26045i
$797$	3.60475			0.127687			0.0638435	−	0.997960i	$-0.479664\pi$
$797$	3.60475			0.127687			0.0638435	+	0.997960i	$0.479664\pi$
$798$		0			0
$799$	2.31925			0.0820491
$800$			4.53757i			0.160427i
$801$	−2.25423	−	1.34233i	−0.0796495	−	0.0474287i
$802$	48.4802			1.71190
$803$	−0.619640			−0.0218666
$804$	−2.53089	+	9.19699i	−0.0892578	+	0.324353i
$805$		0			0
$806$			65.7836i			2.31713i
$807$	7.99031	−	29.0359i	0.281272	−	1.02211i
$808$		−	35.4880i		−	1.24846i
$809$			21.6635i			0.761649i	0.924647	+	0.380824i	$0.124360\pi$
$809$			21.6635i			0.761649i	−0.924647	+	0.380824i	$0.875640\pi$
$810$	−18.4435	+	9.99527i	−0.648037	+	0.351198i
$811$		−	27.6526i		−	0.971015i	−0.874232	−	0.485508i	$-0.838635\pi$
$811$		−	27.6526i		−	0.971015i	0.874232	−	0.485508i	$-0.161365\pi$
$812$		0			0
$813$	17.0196	+	4.68358i	0.596904	+	0.164260i
$814$	−2.65408			−0.0930253
$815$	−8.52319			−0.298554
$816$	−0.372515	+	1.35368i	−0.0130406	+	0.0473882i
$817$		−	0.259239i		−	0.00906963i
$818$	−67.1957			−2.34944
$819$		0			0
$820$	−29.3549			−1.02512
$821$			14.1707i			0.494560i	0.968944	+	0.247280i	$0.0795368\pi$
$821$			14.1707i			0.494560i	−0.968944	+	0.247280i	$0.920463\pi$
$822$	−13.4956	+	49.0414i	−0.470712	+	1.71051i
$823$	23.3076			0.812453			0.406227	−	0.913772i	$-0.366844\pi$
$823$	23.3076			0.812453			0.406227	+	0.913772i	$0.366844\pi$
$824$	3.35056			0.116722
$825$	4.66689	+	1.28427i	0.162480	+	0.0447125i
$826$		0			0
$827$		−	32.0877i		−	1.11580i	−0.829908	−	0.557900i	$-0.811607\pi$
$827$		−	32.0877i		−	1.11580i	0.829908	−	0.557900i	$-0.188393\pi$
$828$	−39.7451	+	66.7459i	−1.38124	+	2.31958i
$829$		−	30.0161i		−	1.04250i	−0.853403	−	0.521251i	$-0.825466\pi$
$829$		−	30.0161i		−	1.04250i	0.853403	−	0.521251i	$-0.174534\pi$
$830$		−	1.55444i		−	0.0539552i
$831$	−4.39351	+	15.9655i	−0.152409	+	0.553838i
$832$			39.7873i			1.37938i
$833$		0			0
$834$	−1.05843	+	3.84621i	−0.0366503	+	0.133183i
$835$	−3.56923			−0.123518
$836$	−21.0655			−0.728565
$837$	31.6954	+	33.0040i	1.09555	+	1.14078i
$838$			7.56364i			0.261282i
$839$	28.6277			0.988337			0.494168	−	0.869366i	$-0.335473\pi$
$839$	28.6277			0.988337			0.494168	+	0.869366i	$0.335473\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$		−	65.1061i		−	2.24370i
$843$	−19.9126	−	5.47969i	−0.685825	−	0.188730i
$844$	−23.9678			−0.825006
$845$	−2.72886			−0.0938755
$846$	−9.40813	+	15.7995i	−0.323458	+	0.543200i
$847$		0			0
$848$		−	6.86441i		−	0.235725i
$849$	33.3483	+	9.17704i	1.14451	+	0.314955i
$850$		−	2.05568i		−	0.0705091i
$851$			3.07341i			0.105355i
$852$	−35.8804	−	9.87383i	−1.22924	−	0.338272i
$853$		−	17.3563i		−	0.594269i	−0.954836	−	0.297135i	$-0.903969\pi$
$853$		−	17.3563i		−	0.594269i	0.954836	−	0.297135i	$-0.0960310\pi$
$854$		0			0
$855$	−3.37028	+	5.65988i	−0.115261	+	0.193564i
$856$	42.6742			1.45857
$857$	46.5684			1.59074			0.795372	−	0.606121i	$-0.207275\pi$
$857$	46.5684			1.59074			0.795372	+	0.606121i	$0.207275\pi$
$858$	34.8621	+	9.59362i	1.19017	+	0.327521i
$859$			36.4145i			1.24245i	0.783634	+	0.621223i	$0.213364\pi$
$859$			36.4145i			1.24245i	−0.783634	+	0.621223i	$0.786636\pi$
$860$	−0.405299			−0.0138206
$861$		0			0
$862$	89.3002			3.04158
$863$		−	2.37801i		−	0.0809484i	−0.999181	−	0.0404742i	$-0.987113\pi$
$863$		−	2.37801i		−	0.0809484i	0.999181	−	0.0404742i	$-0.0128869\pi$
$864$	16.3316	+	17.0058i	0.555611	+	0.578550i
$865$	−8.54229			−0.290446
$866$	−67.4861			−2.29327
$867$	7.45499	−	27.0906i	0.253185	−	0.920045i
$868$		0			0
$869$			8.76660i			0.297387i
$870$	8.73285	−	31.7342i	0.296071	−	1.07589i
$871$		−	5.14140i		−	0.174210i
$872$			0.0609453i			0.00206387i
$873$	−9.78065	+	16.4251i	−0.331025	+	0.555907i
$874$			38.6054i			1.30585i
$875$		0			0
$876$	−1.27114	−	0.349803i	−0.0429480	−	0.0118187i
$877$	−22.0931			−0.746031			−0.373015	−	0.927825i	$-0.621676\pi$
$877$	−22.0931			−0.746031			−0.373015	+	0.927825i	$0.621676\pi$
$878$	−35.5802			−1.20077
$879$	−1.38337	+	5.02700i	−0.0466598	+	0.169556i
$880$			2.56854i			0.0865855i
$881$	−33.5633			−1.13078			−0.565388	−	0.824825i	$-0.691273\pi$
$881$	−33.5633			−1.13078			−0.565388	+	0.824825i	$0.691273\pi$
$882$		0			0
$883$	−3.74124			−0.125903			−0.0629514	−	0.998017i	$-0.520051\pi$
$883$	−3.74124			−0.125903			−0.0629514	+	0.998017i	$0.520051\pi$
$884$		−	9.70312i		−	0.326351i
$885$	−1.88409	+	6.84658i	−0.0633331	+	0.230145i
$886$	−5.32303			−0.178831
$887$	27.5370			0.924604			0.462302	−	0.886723i	$-0.347024\pi$
$887$	27.5370			0.924604			0.462302	+	0.886723i	$0.347024\pi$
$888$	−2.27262	−	0.625396i	−0.0762641	−	0.0209869i
$889$		0			0
$890$			2.03844i			0.0683286i
$891$	22.1128	−	11.9838i	0.740807	−	0.401474i
$892$			4.96379i			0.166200i
$893$			5.77429i			0.193229i
$894$	−18.9988	+	69.0396i	−0.635416	+	2.30903i
$895$			1.22952i			0.0410983i
$896$		0			0
$897$	11.1094	−	40.3702i	0.370931	−	1.34792i
$898$	24.0342			0.802031
$899$	−71.7948			−2.39449
$900$	8.84876	+	5.26916i	0.294959	+	0.175639i
$901$		−	6.58678i		−	0.219438i
$902$	55.6995			1.85459
$903$		0			0
$904$	24.1487			0.803174
$905$		−	15.3995i		−	0.511897i
$906$	−87.5836	−	24.1019i	−2.90977	−	0.800732i
$907$	38.7300			1.28601			0.643005	−	0.765862i	$-0.277687\pi$
$907$	38.7300			1.28601			0.643005	+	0.765862i	$0.277687\pi$
$908$	−3.66336			−0.121573
$909$	27.3880	+	16.3087i	0.908404	+	0.540926i
$910$		0			0
$911$		−	23.3967i		−	0.775167i	−0.921835	−	0.387583i	$-0.873310\pi$
$911$		−	23.3967i		−	0.775167i	0.921835	−	0.387583i	$-0.126690\pi$
$912$	−3.37028	−	0.927458i	−0.111601	−	0.0307112i
$913$			1.86369i			0.0616792i
$914$		−	76.4461i		−	2.52861i
$915$	20.6337	+	5.67814i	0.682130	+	0.187713i
$916$			26.0854i			0.861886i
$917$		0			0
$918$	−7.39876	−	7.70422i	−0.244195	−	0.254277i
$919$	−8.64659			−0.285225			−0.142612	−	0.989779i	$-0.545550\pi$
$919$	−8.64659			−0.285225			−0.142612	+	0.989779i	$0.545550\pi$
$920$	25.1931			0.830591
$921$	−34.0330	−	9.36544i	−1.12142	−	0.308602i
$922$		−	38.6172i		−	1.27179i
$923$	20.0583			0.660225
$924$		0			0
$925$	0.407453			0.0133970
$926$			85.2784i			2.80242i
$927$	−1.53977	+	2.58581i	−0.0505726	+	0.0849291i
$928$	−36.9935			−1.21437
$929$	−12.5596			−0.412067			−0.206034	−	0.978545i	$-0.566056\pi$
$929$	−12.5596			−0.412067			−0.206034	+	0.978545i	$0.566056\pi$
$930$	9.43292	−	34.2782i	0.309318	−	1.12403i
$931$		0			0
$932$		−	61.7914i		−	2.02405i
$933$	12.5329	−	45.5432i	0.410309	−	1.49102i
$934$			95.8217i			3.13538i
$935$			2.46466i			0.0806029i
$936$	27.5910	+	16.4296i	0.901840	+	0.537017i
$937$		−	11.3901i		−	0.372097i	−0.982541	−	0.186048i	$-0.940432\pi$
$937$		−	11.3901i		−	0.372097i	0.982541	−	0.186048i	$-0.0595681\pi$
$938$		0			0
$939$	−1.05327	−	0.289846i	−0.0343720	−	0.00945875i
$940$	9.02762			0.294449
$941$	42.0867			1.37199			0.685994	−	0.727607i	$-0.259368\pi$
$941$	42.0867			1.37199			0.685994	+	0.727607i	$0.259368\pi$
$942$	−12.7382	+	46.2893i	−0.415034	+	1.50819i
$943$		−	64.4998i		−	2.10040i
$944$	−3.76818			−0.122644
$945$		0			0
$946$	0.769036			0.0250035
$947$			14.6074i			0.474677i	0.971427	+	0.237338i	$0.0762750\pi$
$947$			14.6074i			0.474677i	−0.971427	+	0.237338i	$0.923725\pi$
$948$	−4.94897	+	17.9840i	−0.160735	+	0.584093i
$949$	0.710609			0.0230673
$950$	5.11806			0.166052
$951$	−42.4679	−	11.6866i	−1.37711	−	0.378965i
$952$		0			0
$953$			28.8817i			0.935570i	0.883842	+	0.467785i	$0.154948\pi$
$953$			28.8817i			0.935570i	−0.883842	+	0.467785i	$0.845052\pi$
$954$	44.8715	+	26.7196i	1.45277	+	0.865078i
$955$			14.5255i			0.470034i
$956$			102.581i			3.31771i
$957$	−10.4703	+	38.0478i	−0.338456	+	1.22991i
$958$		−	38.5032i		−	1.24398i
$959$		0			0
$960$	5.70523	−	20.7322i	0.184136	−	0.669128i
$961$	−46.5503			−1.50162
$962$	3.04372			0.0981333
$963$	−19.6112	+	32.9340i	−0.631961	+	1.06128i
$964$			17.9870i			0.579323i
$965$	0.403145			0.0129777
$966$		0			0
$967$	0.409782			0.0131777			0.00658885	−	0.999978i	$-0.497903\pi$
$967$	0.409782			0.0131777			0.00658885	+	0.999978i	$0.497903\pi$
$968$			10.6553i			0.342474i
$969$	−3.23397	−	0.889948i	−0.103890	−	0.0285892i
$970$	14.8528			0.476893
$971$	5.29729			0.169998			0.0849991	−	0.996381i	$-0.472911\pi$
$971$	5.29729			0.169998			0.0849991	+	0.996381i	$0.472911\pi$
$972$	52.1279	−	12.1007i	1.67200	−	0.388129i
$973$		0			0
$974$			4.73634i			0.151762i
$975$	−5.35203	−	1.47281i	−0.171402	−	0.0471677i
$976$			11.3563i			0.363506i
$977$		−	27.8568i		−	0.891219i	−0.895227	−	0.445610i	$-0.852987\pi$
$977$		−	27.8568i		−	0.891219i	0.895227	−	0.445610i	$-0.147013\pi$
$978$	33.1763	+	9.12970i	1.06086	+	0.291936i
$979$		−	2.44399i		−	0.0781102i
$980$		0			0
$981$	−0.0470348	−	0.0280077i	−0.00150171	−	0.000894219i
$982$	13.9360			0.444715
$983$	0.661227			0.0210899			0.0105449	−	0.999944i	$-0.496643\pi$
$983$	0.661227			0.0210899			0.0105449	+	0.999944i	$0.496643\pi$
$984$	47.6941	+	13.1248i	1.52043	+	0.418404i
$985$		−	11.6716i		−	0.371887i
$986$	16.7593			0.533725
$987$		0			0
$988$	24.1581			0.768571
$989$		−	0.890541i		−	0.0283175i
$990$	−16.7901	−	9.99798i	−0.533625	−	0.317757i
$991$	−50.6747			−1.60974			−0.804868	−	0.593454i	$-0.797764\pi$
$991$	−50.6747			−1.60974			−0.804868	+	0.593454i	$0.797764\pi$
$992$	−39.9590			−1.26870
$993$	−5.28182	+	19.1935i	−0.167614	+	0.609089i
$994$		0			0
$995$		−	18.5775i		−	0.588946i
$996$	−1.05210	+	3.82322i	−0.0333371	+	0.121143i
$997$		−	6.02614i		−	0.190850i	−0.995437	−	0.0954249i	$-0.969579\pi$
$997$		−	6.02614i		−	0.190850i	0.995437	−	0.0954249i	$-0.0304210\pi$
$998$		−	19.7729i		−	0.625902i
$999$	1.52705	−	1.46650i	0.0483136	−	0.0463980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.b.d.146.1		8
3.2	odd	2		735.2.b.c.146.8		8
7.2	even	3		105.2.s.c.101.1	yes	8
7.3	odd	6		105.2.s.d.26.4	yes	8
7.4	even	3		735.2.s.l.656.4		8
7.5	odd	6		735.2.s.k.521.1		8
7.6	odd	2		735.2.b.c.146.1		8
21.2	odd	6		105.2.s.d.101.4	yes	8
21.5	even	6		735.2.s.l.521.4		8
21.11	odd	6		735.2.s.k.656.1		8
21.17	even	6		105.2.s.c.26.1	✓	8
21.20	even	2	inner	735.2.b.d.146.8		8
35.2	odd	12		525.2.q.f.374.1		16
35.3	even	12		525.2.q.e.299.8		16
35.9	even	6		525.2.t.g.101.4		8
35.17	even	12		525.2.q.e.299.1		16
35.23	odd	12		525.2.q.f.374.8		16
35.24	odd	6		525.2.t.f.26.1		8
105.2	even	12		525.2.q.e.374.8		16
105.17	odd	12		525.2.q.f.299.8		16
105.23	even	12		525.2.q.e.374.1		16
105.38	odd	12		525.2.q.f.299.1		16
105.44	odd	6		525.2.t.f.101.1		8
105.59	even	6		525.2.t.g.26.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	21.17	even	6
105.2.s.c.101.1	yes	8	7.2	even	3
105.2.s.d.26.4	yes	8	7.3	odd	6
105.2.s.d.101.4	yes	8	21.2	odd	6
525.2.q.e.299.1		16	35.17	even	12
525.2.q.e.299.8		16	35.3	even	12
525.2.q.e.374.1		16	105.23	even	12
525.2.q.e.374.8		16	105.2	even	12
525.2.q.f.299.1		16	105.38	odd	12
525.2.q.f.299.8		16	105.17	odd	12
525.2.q.f.374.1		16	35.2	odd	12
525.2.q.f.374.8		16	35.23	odd	12
525.2.t.f.26.1		8	35.24	odd	6
525.2.t.f.101.1		8	105.44	odd	6
525.2.t.g.26.4		8	105.59	even	6
525.2.t.g.101.4		8	35.9	even	6
735.2.b.c.146.1		8	7.6	odd	2
735.2.b.c.146.8		8	3.2	odd	2
735.2.b.d.146.1		8	1.1	even	1	trivial
735.2.b.d.146.8		8	21.20	even	2	inner
735.2.s.k.521.1		8	7.5	odd	6
735.2.s.k.656.1		8	21.11	odd	6
735.2.s.l.521.4		8	21.5	even	6
735.2.s.l.656.4		8	7.4	even	3

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.33086i q^{2} +(-0.459555 + 1.66997i) q^{3} -3.43292 q^{4} -1.00000 q^{5} +(3.89248 + 1.07116i) q^{6} +3.33995i q^{8} +(-2.57762 - 1.53489i) q^{9} +O(q^{10})\)	\(q-2.33086i q^{2} +(-0.459555 + 1.66997i) q^{3} -3.43292 q^{4} -1.00000 q^{5} +(3.89248 + 1.07116i) q^{6} +3.33995i q^{8} +(-2.57762 - 1.53489i) q^{9} +2.33086i q^{10} -2.79459i q^{11} +(1.57762 - 5.73289i) q^{12} +3.20486i q^{13} +(0.459555 - 1.66997i) q^{15} +0.919111 q^{16} +0.881938 q^{17} +(-3.57762 + 6.00807i) q^{18} +2.19578i q^{19} +3.43292 q^{20} -6.51381 q^{22} +7.54296i q^{23} +(-5.57762 - 1.53489i) q^{24} +1.00000 q^{25} +7.47010 q^{26} +(3.74778 - 3.59918i) q^{27} +8.15270i q^{29} +(-3.89248 - 1.07116i) q^{30} +8.80626i q^{31} +4.53757i q^{32} +(4.66689 + 1.28427i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +0.407453 q^{37} +5.11806 q^{38} +(-5.35203 - 1.47281i) q^{39} -3.33995i q^{40} -8.55098 q^{41} -0.118062 q^{43} +9.59362i q^{44} +(2.57762 + 1.53489i) q^{45} +17.5816 q^{46} +2.62972 q^{47} +(-0.422382 + 1.53489i) q^{48} -2.33086i q^{50} +(-0.405299 + 1.47281i) q^{51} -11.0020i q^{52} -7.46853i q^{53} +(-8.38921 - 8.73557i) q^{54} +2.79459i q^{55} +(-3.66689 - 1.00908i) q^{57} +19.0028 q^{58} -4.09982 q^{59} +(-1.57762 + 5.73289i) q^{60} +12.3557i q^{61} +20.5262 q^{62} +12.4147 q^{64} -3.20486i q^{65} +(2.99346 - 10.8779i) q^{66} -1.60425 q^{67} -3.02762 q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(5.12645 - 8.60910i) q^{72} -0.221728i q^{73} -0.949718i q^{74} +(-0.459555 + 1.66997i) q^{75} -7.53794i q^{76} +(-3.43292 + 12.4749i) q^{78} -3.13699 q^{79} -0.919111 q^{80} +(4.28823 + 7.91272i) q^{81} +19.9312i q^{82} -0.666893 q^{83} -0.881938 q^{85} +0.275187i q^{86} +(-13.6148 - 3.74662i) q^{87} +9.33379 q^{88} +0.874542 q^{89} +(3.57762 - 6.00807i) q^{90} -25.8944i q^{92} +(-14.7062 - 4.04697i) q^{93} -6.12952i q^{94} -2.19578i q^{95} +(-7.57762 - 2.08526i) q^{96} -6.37221i q^{97} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9}+O(q^{10}) \) 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9	\( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9} - 9 q^{12} - q^{15} - 2 q^{16} + 24 q^{17} - 7 q^{18} + 6 q^{20} - 40 q^{22} - 23 q^{24} + 8 q^{25} + 12 q^{26} + 4 q^{27} - 5 q^{30} + 2 q^{33} + 9 q^{36} - 14 q^{37} + 24 q^{38} - 12 q^{39} - 30 q^{41} + 16 q^{43} - q^{45} + 14 q^{46} + 12 q^{47} - 25 q^{48} - 6 q^{51} - 10 q^{54} + 6 q^{57} + 26 q^{58} + 24 q^{59} + 9 q^{60} + 24 q^{62} + 38 q^{64} - 38 q^{66} - 8 q^{67} - 13 q^{69} + q^{72} + q^{75} - 6 q^{78} + 58 q^{79} + 2 q^{80} + 13 q^{81} + 30 q^{83} - 24 q^{85} - 61 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 36 q^{93} - 39 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9 - 9 * q^12 - q^15 - 2 * q^16 + 24 * q^17 - 7 * q^18 + 6 * q^20 - 40 * q^22 - 23 * q^24 + 8 * q^25 + 12 * q^26 + 4 * q^27 - 5 * q^30 + 2 * q^33 + 9 * q^36 - 14 * q^37 + 24 * q^38 - 12 * q^39 - 30 * q^41 + 16 * q^43 - q^45 + 14 * q^46 + 12 * q^47 - 25 * q^48 - 6 * q^51 - 10 * q^54 + 6 * q^57 + 26 * q^58 + 24 * q^59 + 9 * q^60 + 24 * q^62 + 38 * q^64 - 38 * q^66 - 8 * q^67 - 13 * q^69 + q^72 + q^75 - 6 * q^78 + 58 * q^79 + 2 * q^80 + 13 * q^81 + 30 * q^83 - 24 * q^85 - 61 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 36 * q^93 - 39 * q^96 - 34 * q^99

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