LMFDB - Embedded newform 429.2.f.a.131.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.12
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88424 q^{2} +(1.68512 + 0.400473i) q^{3} +1.55036 q^{4} +4.10471i q^{5} +(-3.17517 - 0.754586i) q^{6} +3.01872i q^{7} +0.847231 q^{8} +(2.67924 + 1.34969i) q^{9} +O(q^{10})$	\(q-1.88424 q^{2} +(1.68512 + 0.400473i) q^{3} +1.55036 q^{4} +4.10471i q^{5} +(-3.17517 - 0.754586i) q^{6} +3.01872i q^{7} +0.847231 q^{8} +(2.67924 + 1.34969i) q^{9} -7.73425i q^{10} +(2.60016 - 2.05892i) q^{11} +(2.61254 + 0.620876i) q^{12} +1.00000i q^{13} -5.68800i q^{14} +(-1.64382 + 6.91692i) q^{15} -4.69710 q^{16} -6.56852 q^{17} +(-5.04834 - 2.54313i) q^{18} -1.38844i q^{19} +6.36377i q^{20} +(-1.20892 + 5.08690i) q^{21} +(-4.89933 + 3.87950i) q^{22} -5.41038i q^{23} +(1.42768 + 0.339293i) q^{24} -11.8486 q^{25} -1.88424i q^{26} +(3.97433 + 3.34735i) q^{27} +4.68011i q^{28} +6.07294 q^{29} +(3.09736 - 13.0331i) q^{30} +6.13736 q^{31} +7.15601 q^{32} +(5.20612 - 2.42823i) q^{33} +12.3767 q^{34} -12.3910 q^{35} +(4.15379 + 2.09250i) q^{36} -4.51416 q^{37} +2.61615i q^{38} +(-0.400473 + 1.68512i) q^{39} +3.47764i q^{40} +0.966521 q^{41} +(2.27789 - 9.58495i) q^{42} +3.07271i q^{43} +(4.03119 - 3.19206i) q^{44} +(-5.54007 + 10.9975i) q^{45} +10.1945i q^{46} +2.62300i q^{47} +(-7.91517 - 1.88106i) q^{48} -2.11269 q^{49} +22.3257 q^{50} +(-11.0687 - 2.63051i) q^{51} +1.55036i q^{52} -7.86994i q^{53} +(-7.48859 - 6.30720i) q^{54} +(8.45127 + 10.6729i) q^{55} +2.55756i q^{56} +(0.556032 - 2.33968i) q^{57} -11.4429 q^{58} +3.17057i q^{59} +(-2.54852 + 10.7237i) q^{60} +4.19576i q^{61} -11.5643 q^{62} +(-4.07433 + 8.08789i) q^{63} -4.08943 q^{64} -4.10471 q^{65} +(-9.80958 + 4.57536i) q^{66} -0.278169 q^{67} -10.1836 q^{68} +(2.16671 - 9.11713i) q^{69} +23.3476 q^{70} +1.72381i q^{71} +(2.26994 + 1.14350i) q^{72} -3.90626i q^{73} +8.50576 q^{74} +(-19.9663 - 4.74505i) q^{75} -2.15258i q^{76} +(6.21531 + 7.84917i) q^{77} +(0.754586 - 3.17517i) q^{78} -6.67487i q^{79} -19.2802i q^{80} +(5.35669 + 7.23228i) q^{81} -1.82116 q^{82} +6.62128 q^{83} +(-1.87425 + 7.88653i) q^{84} -26.9618i q^{85} -5.78972i q^{86} +(10.2336 + 2.43205i) q^{87} +(2.20294 - 1.74438i) q^{88} +17.4954i q^{89} +(10.4388 - 20.7219i) q^{90} -3.01872 q^{91} -8.38803i q^{92} +(10.3422 + 2.45784i) q^{93} -4.94237i q^{94} +5.69914 q^{95} +(12.0587 + 2.86579i) q^{96} -13.4604 q^{97} +3.98082 q^{98} +(9.74537 - 2.00694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.88424			−1.33236			−0.666179	−	0.745792i	$-0.732071\pi$
$2$	−1.88424			−1.33236			−0.666179	+	0.745792i	$0.732071\pi$
$3$	1.68512	+	0.400473i	0.972903	+	0.231213i
$3$	1.68512	+	0.400473i	0.972903	+	0.231213i
$4$	1.55036			0.775180
$5$			4.10471i			1.83568i	0.396949	+	0.917841i	$0.370069\pi$
$5$			4.10471i			1.83568i	−0.396949	+	0.917841i	$0.629931\pi$
$6$	−3.17517	−	0.754586i	−1.29626	−	0.308059i
$7$			3.01872i			1.14097i	0.821308	+	0.570485i	$0.193245\pi$
$7$			3.01872i			1.14097i	−0.821308	+	0.570485i	$0.806755\pi$
$8$	0.847231			0.299542
$9$	2.67924	+	1.34969i	0.893081	+	0.449896i
$10$		−	7.73425i		−	2.44579i
$11$	2.60016	−	2.05892i	0.783979	−	0.620788i
$11$	2.60016	−	2.05892i	0.783979	−	0.620788i
$12$	2.61254	+	0.620876i	0.754175	+	0.179232i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$		−	5.68800i		−	1.52018i
$15$	−1.64382	+	6.91692i	−0.424433	+	1.78594i
$16$	−4.69710			−1.17428
$17$	−6.56852			−1.59310			−0.796550	−	0.604573i	$-0.793344\pi$
$17$	−6.56852			−1.59310			−0.796550	+	0.604573i	$0.793344\pi$
$18$	−5.04834	−	2.54313i	−1.18990	−	0.599422i
$19$		−	1.38844i		−	0.318530i	−0.987236	−	0.159265i	$-0.949088\pi$
$19$		−	1.38844i		−	0.318530i	0.987236	−	0.159265i	$-0.0509124\pi$
$20$			6.36377i			1.42298i
$21$	−1.20892	+	5.08690i	−0.263807	+	1.11005i
$22$	−4.89933	+	3.87950i	−1.04454	+	0.827112i
$23$		−	5.41038i		−	1.12814i	−0.825726	−	0.564071i	$-0.809234\pi$
$23$		−	5.41038i		−	1.12814i	0.825726	−	0.564071i	$-0.190766\pi$
$24$	1.42768	+	0.339293i	0.291425	+	0.0692579i
$25$	−11.8486			−2.36973
$26$		−	1.88424i		−	0.369530i
$27$	3.97433	+	3.34735i	0.764860	+	0.644197i
$28$			4.68011i			0.884457i
$29$	6.07294			1.12772			0.563858	−	0.825872i	$-0.309317\pi$
$29$	6.07294			1.12772			0.563858	+	0.825872i	$0.309317\pi$
$30$	3.09736	−	13.0331i	0.565497	−	2.37951i
$31$	6.13736			1.10230			0.551151	−	0.834405i	$-0.314189\pi$
$31$	6.13736			1.10230			0.551151	+	0.834405i	$0.314189\pi$
$32$	7.15601			1.26502
$33$	5.20612	−	2.42823i	0.906270	−	0.422700i
$34$	12.3767			2.12258
$35$	−12.3910			−2.09446
$36$	4.15379	+	2.09250i	0.692298	+	0.348750i
$37$	−4.51416			−0.742123			−0.371062	−	0.928608i	$-0.621006\pi$
$37$	−4.51416			−0.742123			−0.371062	+	0.928608i	$0.621006\pi$
$38$			2.61615i			0.424396i
$39$	−0.400473	+	1.68512i	−0.0641269	+	0.269835i
$40$			3.47764i			0.549863i
$41$	0.966521			0.150945			0.0754726	−	0.997148i	$-0.475953\pi$
$41$	0.966521			0.150945			0.0754726	+	0.997148i	$0.475953\pi$
$42$	2.27789	−	9.58495i	0.351486	−	1.47899i
$43$			3.07271i			0.468583i	0.972166	+	0.234292i	$0.0752771\pi$
$43$			3.07271i			0.468583i	−0.972166	+	0.234292i	$0.924723\pi$
$44$	4.03119	−	3.19206i	0.607724	−	0.481222i
$45$	−5.54007	+	10.9975i	−0.825865	+	1.63941i
$46$			10.1945i			1.50309i
$47$			2.62300i			0.382604i	0.981531	+	0.191302i	$0.0612710\pi$
$47$			2.62300i			0.382604i	−0.981531	+	0.191302i	$0.938729\pi$
$48$	−7.91517	−	1.88106i	−1.14246	−	0.271508i
$49$	−2.11269			−0.301813
$50$	22.3257			3.15733
$51$	−11.0687	−	2.63051i	−1.54993	−	0.368345i
$52$			1.55036i			0.214996i
$53$		−	7.86994i		−	1.08102i	−0.841338	−	0.540510i	$-0.818231\pi$
$53$		−	7.86994i		−	1.08102i	0.841338	−	0.540510i	$-0.181769\pi$
$54$	−7.48859	−	6.30720i	−1.01907	−	0.858301i
$55$	8.45127	+	10.6729i	1.13957	+	1.43914i
$56$			2.55756i			0.341768i
$57$	0.556032	−	2.33968i	0.0736482	−	0.309898i
$58$	−11.4429			−1.50252
$59$			3.17057i			0.412772i	0.978471	+	0.206386i	$0.0661703\pi$
$59$			3.17057i			0.412772i	−0.978471	+	0.206386i	$0.933830\pi$
$60$	−2.54852	+	10.7237i	−0.329012	+	1.38442i
$61$			4.19576i			0.537213i	0.963250	+	0.268606i	$0.0865631\pi$
$61$			4.19576i			0.537213i	−0.963250	+	0.268606i	$0.913437\pi$
$62$	−11.5643			−1.46866
$63$	−4.07433	+	8.08789i	−0.513318	+	1.01898i
$64$	−4.08943			−0.511178
$65$	−4.10471			−0.509126
$66$	−9.80958	+	4.57536i	−1.20748	+	0.563188i
$67$	−0.278169			−0.0339838			−0.0169919	−	0.999856i	$-0.505409\pi$
$67$	−0.278169			−0.0339838			−0.0169919	+	0.999856i	$0.505409\pi$
$68$	−10.1836			−1.23494
$69$	2.16671	−	9.11713i	0.260841	−	1.09757i
$70$	23.3476			2.79057
$71$			1.72381i			0.204578i	0.994755	+	0.102289i	$0.0326167\pi$
$71$			1.72381i			0.204578i	−0.994755	+	0.102289i	$0.967383\pi$
$72$	2.26994	+	1.14350i	0.267515	+	0.134762i
$73$		−	3.90626i		−	0.457193i	−0.973521	−	0.228596i	$-0.926586\pi$
$73$		−	3.90626i		−	0.457193i	0.973521	−	0.228596i	$-0.0734136\pi$
$74$	8.50576			0.988775
$75$	−19.9663	−	4.74505i	−2.30551	−	0.547911i
$76$		−	2.15258i		−	0.246918i
$77$	6.21531	+	7.84917i	0.708300	+	0.894496i
$78$	0.754586	−	3.17517i	0.0854401	−	0.359517i
$79$		−	6.67487i		−	0.750981i	−0.926826	−	0.375490i	$-0.877474\pi$
$79$		−	6.67487i		−	0.750981i	0.926826	−	0.375490i	$-0.122526\pi$
$80$		−	19.2802i		−	2.15560i
$81$	5.35669	+	7.23228i	0.595188	+	0.803587i
$82$	−1.82116			−0.201113
$83$	6.62128			0.726780			0.363390	−	0.931637i	$-0.381619\pi$
$83$	6.62128			0.726780			0.363390	+	0.931637i	$0.381619\pi$
$84$	−1.87425	+	7.88653i	−0.204498	+	0.860491i
$85$		−	26.9618i		−	2.92442i
$86$		−	5.78972i		−	0.624321i
$87$	10.2336	+	2.43205i	1.09716	+	0.260743i
$88$	2.20294	−	1.74438i	0.234834	−	0.185952i
$89$			17.4954i			1.85450i	0.374438	+	0.927252i	$0.377836\pi$
$89$			17.4954i			1.85450i	−0.374438	+	0.927252i	$0.622164\pi$
$90$	10.4388	−	20.7219i	1.10035	−	2.18429i
$91$	−3.01872			−0.316448
$92$		−	8.38803i		−	0.874513i
$93$	10.3422	+	2.45784i	1.07243	+	0.254867i
$94$		−	4.94237i		−	0.509766i
$95$	5.69914			0.584719
$96$	12.0587	+	2.86579i	1.23074	+	0.292488i
$97$	−13.4604			−1.36670			−0.683349	−	0.730092i	$-0.739477\pi$
$97$	−13.4604			−1.36670			−0.683349	+	0.730092i	$0.739477\pi$
$98$	3.98082			0.402123
$99$	9.74537	−	2.00694i	0.979446	−	0.201705i
$100$	−18.3696			−1.83696
$101$	9.86160			0.981266			0.490633	−	0.871366i	$-0.336766\pi$
$101$	9.86160			0.981266			0.490633	+	0.871366i	$0.336766\pi$
$102$	20.8561	+	4.95651i	2.06506	+	0.490768i
$103$	3.19718			0.315028			0.157514	−	0.987517i	$-0.449652\pi$
$103$	3.19718			0.315028			0.157514	+	0.987517i	$0.449652\pi$
$104$			0.847231i			0.0830779i
$105$	−20.8803	−	4.96225i	−2.03770	−	0.484266i
$106$			14.8289i			1.44031i
$107$	−8.11768			−0.784766			−0.392383	−	0.919802i	$-0.628349\pi$
$107$	−8.11768			−0.784766			−0.392383	+	0.919802i	$0.628349\pi$
$108$	6.16163	+	5.18959i	0.592904	+	0.499368i
$109$		−	12.2631i		−	1.17460i	−0.809371	−	0.587298i	$-0.800192\pi$
$109$		−	12.2631i		−	1.17460i	0.809371	−	0.587298i	$-0.199808\pi$
$110$	−15.9242	−	20.1103i	−1.51831	−	1.91744i
$111$	−7.60689	−	1.80780i	−0.722014	−	0.171589i
$112$		−	14.1793i		−	1.33981i
$113$		−	1.91789i		−	0.180420i	−0.995923	−	0.0902100i	$-0.971246\pi$
$113$		−	1.91789i		−	0.180420i	0.995923	−	0.0902100i	$-0.0287538\pi$
$114$	−1.04770	+	4.40852i	−0.0981258	+	0.412896i
$115$	22.2080			2.07091
$116$	9.41523			0.874182
$117$	−1.34969	+	2.67924i	−0.124779	+	0.247696i
$118$		−	5.97410i		−	0.549961i
$119$		−	19.8285i		−	1.81768i
$120$	−1.39270	+	5.86023i	−0.127135	+	0.534963i
$121$	2.52170	−	10.7071i	0.229245	−	0.973369i
$122$		−	7.90583i		−	0.715760i
$123$	1.62870	+	0.387065i	0.146855	+	0.0349005i
$124$	9.51511			0.854482
$125$		−	28.1116i		−	2.51438i
$126$	7.67702	−	15.2395i	0.683923	−	1.35765i
$127$			4.23047i			0.375394i	0.982227	+	0.187697i	$0.0601023\pi$
$127$			4.23047i			0.375394i	−0.982227	+	0.187697i	$0.939898\pi$
$128$	−6.60656			−0.583943
$129$	−1.23053	+	5.17787i	−0.108343	+	0.455886i
$130$	7.73425			0.678339
$131$	2.88935			0.252444			0.126222	−	0.992002i	$-0.459715\pi$
$131$	2.88935			0.252444			0.126222	+	0.992002i	$0.459715\pi$
$132$	8.07136	−	3.76463i	0.702522	−	0.327669i
$133$	4.19131			0.363433
$134$	0.524137			0.0452786
$135$	−13.7399	+	16.3135i	−1.18254	+	1.40404i
$136$	−5.56505			−0.477199
$137$			3.32139i			0.283766i	0.989883	+	0.141883i	$0.0453156\pi$
$137$			3.32139i			0.283766i	−0.989883	+	0.141883i	$0.954684\pi$
$138$	−4.08260	+	17.1789i	−0.347534	+	1.46236i
$139$		−	21.7242i		−	1.84262i	−0.388823	−	0.921312i	$-0.627118\pi$
$139$		−	21.7242i		−	1.84262i	0.388823	−	0.921312i	$-0.372882\pi$
$140$	−19.2105			−1.62358
$141$	−1.05044	+	4.42007i	−0.0884631	+	0.372237i
$142$		−	3.24806i		−	0.272571i
$143$	2.05892	+	2.60016i	0.172176	+	0.217437i
$144$	−12.5847	−	6.33962i	−1.04872	−	0.528302i
$145$			24.9276i			2.07013i
$146$			7.36032i			0.609145i
$147$	−3.56013	−	0.846075i	−0.293635	−	0.0697831i
$148$	−6.99857			−0.575279
$149$	6.67256			0.546638			0.273319	−	0.961923i	$-0.411879\pi$
$149$	6.67256			0.546638			0.273319	+	0.961923i	$0.411879\pi$
$150$	37.6214	+	8.94082i	3.07177	+	0.730015i
$151$			17.1614i			1.39657i	0.715819	+	0.698286i	$0.246053\pi$
$151$			17.1614i			1.39657i	−0.715819	+	0.698286i	$0.753947\pi$
$152$		−	1.17633i		−	0.0954128i
$153$	−17.5987	−	8.86544i	−1.42277	−	0.716728i
$154$	−11.7111	−	14.7897i	−0.943710	−	1.19179i
$155$			25.1921i			2.02348i
$156$	−0.620876	+	2.61254i	−0.0497099	+	0.209170i
$157$	19.2326			1.53493			0.767463	−	0.641093i	$-0.221519\pi$
$157$	19.2326			1.53493			0.767463	+	0.641093i	$0.221519\pi$
$158$			12.5770i			1.00058i
$159$	3.15170	−	13.2618i	0.249946	−	1.05173i
$160$			29.3733i			2.32217i
$161$	16.3324			1.28718
$162$	−10.0933	−	13.6273i	−0.793004	−	1.07067i
$163$	10.6459			0.833853			0.416926	−	0.908940i	$-0.363107\pi$
$163$	10.6459			0.833853			0.416926	+	0.908940i	$0.363107\pi$
$164$	1.49846			0.117010
$165$	9.96717	+	21.3696i	0.775943	+	1.66362i
$166$	−12.4761			−0.968332
$167$	12.0223			0.930315			0.465157	−	0.885228i	$-0.345998\pi$
$167$	12.0223			0.930315			0.465157	+	0.885228i	$0.345998\pi$
$168$	−1.02423	+	4.30978i	−0.0790212	+	0.332507i
$169$	−1.00000			−0.0769231
$170$			50.8026i			3.89638i
$171$	1.87396	−	3.71996i	0.143305	−	0.284473i
$172$			4.76380i			0.363236i
$173$	−14.0553			−1.06861			−0.534304	−	0.845293i	$-0.679426\pi$
$173$	−14.0553			−1.06861			−0.534304	+	0.845293i	$0.679426\pi$
$174$	−19.2826	−	4.58256i	−1.46181	−	0.347403i
$175$		−	35.7677i		−	2.70379i
$176$	−12.2132	+	9.67096i	−0.920608	+	0.728976i
$177$	−1.26972	+	5.34278i	−0.0954383	+	0.401588i
$178$		−	32.9654i		−	2.47086i
$179$		−	5.93552i		−	0.443642i	−0.975087	−	0.221821i	$-0.928800\pi$
$179$		−	5.93552i		−	0.443642i	0.975087	−	0.221821i	$-0.0712000\pi$
$180$	−8.58910	+	17.0501i	−0.640194	+	1.27084i
$181$	−5.99449			−0.445567			−0.222784	−	0.974868i	$-0.571514\pi$
$181$	−5.99449			−0.445567			−0.222784	+	0.974868i	$0.571514\pi$
$182$	5.68800			0.421622
$183$	−1.68029	+	7.07036i	−0.124211	+	0.522656i
$184$		−	4.58384i		−	0.337926i
$185$		−	18.5293i		−	1.36230i
$186$	−19.4871	−	4.63117i	−1.42887	−	0.339574i
$187$	−17.0792	+	13.5240i	−1.24896	+	0.988976i
$188$			4.06660i			0.296587i
$189$	−10.1047	+	11.9974i	−0.735009	+	0.872682i
$190$	−10.7385			−0.779055
$191$		−	3.44442i		−	0.249230i	−0.992205	−	0.124615i	$-0.960230\pi$
$191$		−	3.44442i		−	0.249230i	0.992205	−	0.124615i	$-0.0397695\pi$
$192$	−6.89116	−	1.63770i	−0.497327	−	0.118191i
$193$			21.4172i			1.54164i	0.637052	+	0.770821i	$0.280154\pi$
$193$			21.4172i			1.54164i	−0.637052	+	0.770821i	$0.719846\pi$
$194$	25.3626			1.82093
$195$	−6.91692	−	1.64382i	−0.495331	−	0.117717i
$196$	−3.27543			−0.233959
$197$	20.3826			1.45220			0.726102	−	0.687587i	$-0.241330\pi$
$197$	20.3826			1.45220			0.726102	+	0.687587i	$0.241330\pi$
$198$	−18.3626	+	3.78156i	−1.30497	+	0.268744i
$199$	15.0750			1.06864			0.534320	−	0.845283i	$-0.320568\pi$
$199$	15.0750			1.06864			0.534320	+	0.845283i	$0.320568\pi$
$200$	−10.0385			−0.709831
$201$	−0.468748	−	0.111399i	−0.0330629	−	0.00785749i
$202$	−18.5816			−1.30740
$203$			18.3325i			1.28669i
$204$	−17.1605	−	4.07824i	−1.20147	−	0.285534i
$205$			3.96729i			0.277087i
$206$	−6.02426			−0.419730
$207$	7.30232	−	14.4957i	0.507546	−	1.00752i
$208$		−	4.69710i		−	0.325686i
$209$	−2.85868	−	3.61017i	−0.197739	−	0.249720i
$210$	39.3434	+	9.35007i	2.71495	+	0.645216i
$211$		−	8.64769i		−	0.595332i	−0.954670	−	0.297666i	$-0.903792\pi$
$211$		−	8.64769i		−	0.595332i	0.954670	−	0.297666i	$-0.0962081\pi$
$212$		−	12.2012i		−	0.837984i
$213$	−0.690337	+	2.90482i	−0.0473011	+	0.199035i
$214$	15.2957			1.04559
$215$	−12.6126			−0.860170
$216$	3.36717	+	2.83598i	0.229107	+	0.192964i
$217$			18.5270i			1.25769i
$218$			23.1067i			1.56498i
$219$	1.56435	−	6.58250i	0.105709	−	0.444804i
$220$	13.1025	+	16.5468i	0.883370	+	1.11559i
$221$		−	6.56852i		−	0.441846i
$222$	14.3332	+	3.40632i	0.961982	+	0.228618i
$223$	3.58802			0.240272			0.120136	−	0.992757i	$-0.461667\pi$
$223$	3.58802			0.240272			0.120136	+	0.992757i	$0.461667\pi$
$224$			21.6020i			1.44335i
$225$	−31.7454	−	15.9919i	−2.11636	−	1.06613i
$226$			3.61376i			0.240384i
$227$	−26.0832			−1.73120			−0.865602	−	0.500733i	$-0.833064\pi$
$227$	−26.0832			−1.73120			−0.865602	+	0.500733i	$0.833064\pi$
$228$	0.862049	−	3.62735i	0.0570906	−	0.240227i
$229$	13.9303			0.920540			0.460270	−	0.887779i	$-0.347753\pi$
$229$	13.9303			0.920540			0.460270	+	0.887779i	$0.347753\pi$
$230$	−41.8453			−2.75920
$231$	7.33015	+	15.7158i	0.482288	+	1.03403i
$232$	5.14518			0.337798
$233$	−2.97575			−0.194948			−0.0974738	−	0.995238i	$-0.531076\pi$
$233$	−2.97575			−0.194948			−0.0974738	+	0.995238i	$0.531076\pi$
$234$	2.54313	−	5.04834i	0.166250	−	0.330020i
$235$	−10.7667			−0.702340
$236$			4.91551i			0.319973i
$237$	2.67310	−	11.2479i	0.173637	−	0.730632i
$238$			37.3617i			2.42180i
$239$	−10.0117			−0.647601			−0.323801	−	0.946125i	$-0.604961\pi$
$239$	−10.0117			−0.647601			−0.323801	+	0.946125i	$0.604961\pi$
$240$	7.72121	−	32.4895i	0.498402	−	2.09719i
$241$		−	26.0674i		−	1.67915i	−0.543246	−	0.839574i	$-0.682805\pi$
$241$		−	26.0674i		−	1.67915i	0.543246	−	0.839574i	$-0.317195\pi$
$242$	−4.75148	+	20.1747i	−0.305437	+	1.29688i
$243$	6.13032	+	14.3325i	0.393260	+	0.919427i
$244$			6.50494i			0.416436i
$245$		−	8.67198i		−	0.554033i
$246$	−3.06887	−	0.729324i	−0.195664	−	0.0465000i
$247$	1.38844			0.0883442
$248$	5.19976			0.330185
$249$	11.1576	+	2.65164i	0.707087	+	0.168041i
$250$			52.9691i			3.35006i
$251$			17.0365i			1.07534i	0.843156	+	0.537668i	$0.180695\pi$
$251$			17.0365i			1.07534i	−0.843156	+	0.537668i	$0.819305\pi$
$252$	−6.31668	+	12.5391i	−0.397913	+	0.789892i
$253$	−11.1395	−	14.0679i	−0.700337	−	0.884440i
$254$		−	7.97122i		−	0.500159i
$255$	10.7975	−	45.4339i	0.676164	−	2.84518i
$256$	20.6272			1.28920
$257$		−	19.4879i		−	1.21562i	−0.794081	−	0.607812i	$-0.792047\pi$
$257$		−	19.4879i		−	1.21562i	0.794081	−	0.607812i	$-0.207953\pi$
$258$	2.31862	−	9.75635i	0.144351	−	0.607404i
$259$		−	13.6270i		−	0.846741i
$260$	−6.36377			−0.394664
$261$	16.2709	+	8.19656i	1.00714	+	0.507355i
$262$	−5.44424			−0.336346
$263$	−2.77148			−0.170897			−0.0854484	−	0.996343i	$-0.527232\pi$
$263$	−2.77148			−0.170897			−0.0854484	+	0.996343i	$0.527232\pi$
$264$	4.41079	−	2.05727i	0.271465	−	0.126616i
$265$	32.3038			1.98441
$266$	−7.89744			−0.484223
$267$	−7.00641	+	29.4817i	−0.428785	+	1.80425i
$268$	−0.431262			−0.0263435
$269$			0.270441i			0.0164891i	0.999966	+	0.00824453i	$0.00262434\pi$
$269$			0.270441i			0.0164891i	−0.999966	+	0.00824453i	$0.997376\pi$
$270$	25.8892	−	30.7385i	1.57557	−	1.87068i
$271$			24.5102i			1.48889i	0.667685	+	0.744444i	$0.267285\pi$
$271$			24.5102i			1.48889i	−0.667685	+	0.744444i	$0.732715\pi$
$272$	30.8530			1.87074
$273$	−5.08690	−	1.20892i	−0.307873	−	0.0731669i
$274$		−	6.25830i		−	0.378078i
$275$	−30.8084	+	24.3954i	−1.85782	+	1.47110i
$276$	3.35918	−	14.1348i	0.202199	−	0.850816i
$277$			9.37034i			0.563009i	0.959560	+	0.281505i	$0.0908335\pi$
$277$			9.37034i			0.563009i	−0.959560	+	0.281505i	$0.909166\pi$
$278$			40.9336i			2.45504i
$279$	16.4435	+	8.28352i	0.984445	+	0.495921i
$280$	−10.4980			−0.627377
$281$	−3.05878			−0.182472			−0.0912359	−	0.995829i	$-0.529082\pi$
$281$	−3.05878			−0.182472			−0.0912359	+	0.995829i	$0.529082\pi$
$282$	1.97928	−	8.32847i	0.117865	−	0.495953i
$283$			19.5440i			1.16177i	0.813986	+	0.580884i	$0.197293\pi$
$283$			19.5440i			1.16177i	−0.813986	+	0.580884i	$0.802707\pi$
$284$			2.67252i			0.158585i
$285$	9.60371	+	2.28235i	0.568875	+	0.135195i
$286$	−3.87950	−	4.89933i	−0.229400	−	0.289704i
$287$			2.91766i			0.172224i
$288$	19.1727	+	9.65837i	1.12976	+	0.569125i
$289$	26.1454			1.53797
$290$		−	46.9696i		−	2.75815i
$291$	−22.6824	−	5.39053i	−1.32966	−	0.315998i
$292$		−	6.05610i		−	0.354406i
$293$	25.9783			1.51767			0.758834	−	0.651284i	$-0.225769\pi$
$293$	25.9783			1.51767			0.758834	+	0.651284i	$0.225769\pi$
$294$	6.70815	+	1.59421i	0.391227	+	0.0929761i
$295$	−13.0142			−0.757719
$296$	−3.82454			−0.222297
$297$	17.2258	+	0.520823i	0.999543	+	0.0302212i
$298$	−12.5727			−0.728318
$299$	5.41038			0.312890
$300$	−30.9550	−	7.35654i	−1.78719	−	0.424730i
$301$	−9.27565			−0.534640
$302$		−	32.3361i		−	1.86073i
$303$	16.6180	+	3.94930i	0.954677	+	0.226882i
$304$			6.52164i			0.374042i
$305$	−17.2224			−0.986151
$306$	33.1601	+	16.7046i	1.89564	+	0.954939i
$307$			3.51905i			0.200843i	0.994945	+	0.100422i	$0.0320191\pi$
$307$			3.51905i			0.200843i	−0.994945	+	0.100422i	$0.967981\pi$
$308$	9.63596	+	12.1690i	0.549060	+	0.693395i
$309$	5.38763	+	1.28038i	0.306492	+	0.0728385i
$310$		−	47.4679i		−	2.69600i
$311$		−	29.9257i		−	1.69693i	−0.529253	−	0.848464i	$-0.677528\pi$
$311$		−	29.9257i		−	1.69693i	0.529253	−	0.848464i	$-0.322472\pi$
$312$	−0.339293	+	1.42768i	−0.0192087	+	0.0808267i
$313$	−5.54855			−0.313623			−0.156811	−	0.987629i	$-0.550121\pi$
$313$	−5.54855			−0.313623			−0.156811	+	0.987629i	$0.550121\pi$
$314$	−36.2388			−2.04507
$315$	−33.1984	−	16.7239i	−1.87052	−	0.942288i
$316$		−	10.3484i		−	0.582145i
$317$		−	6.77109i		−	0.380302i	−0.981755	−	0.190151i	$-0.939102\pi$
$317$		−	6.77109i		−	0.380302i	0.981755	−	0.190151i	$-0.0608978\pi$
$318$	−5.93855	+	24.9884i	−0.333017	+	1.40128i
$319$	15.7906	−	12.5037i	0.884105	−	0.700072i
$320$		−	16.7859i		−	0.938360i
$321$	−13.6792	−	3.25091i	−0.763501	−	0.181448i
$322$	−30.7742			−1.71498
$323$			9.11998i			0.507449i
$324$	8.30479	+	11.2126i	0.461377	+	0.622924i
$325$		−	11.8486i		−	0.657244i
$326$	−20.0595			−1.11099
$327$	4.91105	−	20.6648i	0.271582	−	1.14277i
$328$	0.818867			0.0452144
$329$	−7.91812			−0.436540
$330$	−18.7805	−	40.2655i	−1.03383	−	2.21654i
$331$	−32.1221			−1.76559			−0.882795	−	0.469758i	$-0.844341\pi$
$331$	−32.1221			−1.76559			−0.882795	+	0.469758i	$0.844341\pi$
$332$	10.2654			0.563385
$333$	−12.0945	−	6.09270i	−0.662776	−	0.333878i
$334$	−22.6529			−1.23951
$335$		−	1.14180i		−	0.0623834i
$336$	5.67841	−	23.8937i	0.309782	−	1.30351i
$337$		−	23.3970i		−	1.27452i	−0.770650	−	0.637258i	$-0.780069\pi$
$337$		−	23.3970i		−	1.27452i	0.770650	−	0.637258i	$-0.219931\pi$
$338$	1.88424			0.102489
$339$	0.768063	−	3.23187i	0.0417154	−	0.175531i
$340$		−	41.8005i		−	2.26695i
$341$	15.9581	−	12.6363i	0.864182	−	0.684296i
$342$	−3.53098	+	7.00930i	−0.190934	+	0.379020i
$343$			14.7534i			0.796610i
$344$			2.60329i			0.140360i
$345$	37.4232	+	8.89371i	2.01480	+	0.478821i
$346$	26.4836			1.42377
$347$	−3.75656			−0.201663			−0.100831	−	0.994904i	$-0.532150\pi$
$347$	−3.75656			−0.201663			−0.100831	+	0.994904i	$0.532150\pi$
$348$	15.8658	+	3.77054i	0.850495	+	0.202122i
$349$		−	34.1776i		−	1.82948i	−0.404039	−	0.914742i	$-0.632394\pi$
$349$		−	34.1776i		−	1.82948i	0.404039	−	0.914742i	$-0.367606\pi$
$350$			67.3950i			3.60241i
$351$	−3.34735	+	3.97433i	−0.178668	+	0.212134i
$352$	18.6068	−	14.7336i	0.991745	−	0.785306i
$353$		−	0.794704i		−	0.0422978i	−0.999776	−	0.0211489i	$-0.993268\pi$
$353$		−	0.794704i		−	0.0422978i	0.999776	−	0.0211489i	$-0.00673241\pi$
$354$	2.39247	−	10.0671i	0.127158	−	0.535059i
$355$	−7.07572			−0.375540
$356$			27.1241i			1.43757i
$357$	7.94079	−	33.4134i	0.420271	−	1.76843i
$358$			11.1839i			0.591090i
$359$	−23.5126			−1.24095			−0.620474	−	0.784227i	$-0.713060\pi$
$359$	−23.5126			−1.24095			−0.620474	+	0.784227i	$0.713060\pi$
$360$	−4.69372	+	9.31744i	−0.247381	+	0.491072i
$361$	17.0722			0.898539
$362$	11.2951			0.593655
$363$	8.53724	−	17.0328i	0.448089	−	0.893989i
$364$	−4.68011			−0.245304
$365$	16.0340			0.839260
$366$	3.16607	−	13.3222i	0.165493	−	0.696365i
$367$	−10.0390			−0.524032			−0.262016	−	0.965064i	$-0.584387\pi$
$367$	−10.0390			−0.524032			−0.262016	+	0.965064i	$0.584387\pi$
$368$			25.4131i			1.32475i
$369$	2.58955	+	1.30450i	0.134806	+	0.0679096i
$370$			34.9137i			1.81508i
$371$	23.7572			1.23341
$372$	16.0341	+	3.81054i	0.831328	+	0.197567i
$373$			16.1039i			0.833828i	0.908946	+	0.416914i	$0.136888\pi$
$373$			16.1039i			0.833828i	−0.908946	+	0.416914i	$0.863112\pi$
$374$	32.1813	−	25.4825i	1.66406	−	1.31767i
$375$	11.2579	−	47.3714i	0.581358	−	2.44625i
$376$			2.22229i			0.114606i
$377$			6.07294i			0.312772i
$378$	19.0397	−	22.6060i	0.979296	−	1.16273i
$379$	7.87690			0.404609			0.202305	−	0.979323i	$-0.435157\pi$
$379$	7.87690			0.404609			0.202305	+	0.979323i	$0.435157\pi$
$380$	8.83571			0.453262
$381$	−1.69419	+	7.12884i	−0.0867959	+	0.365222i
$382$			6.49011i			0.332063i
$383$			4.04223i			0.206548i	0.994653	+	0.103274i	$0.0329319\pi$
$383$			4.04223i			0.206548i	−0.994653	+	0.103274i	$0.967068\pi$
$384$	−11.1328	−	2.64575i	−0.568120	−	0.135015i
$385$	−32.2186	+	25.5120i	−1.64201	+	1.30021i
$386$		−	40.3551i		−	2.05402i
$387$	−4.14719	+	8.23253i	−0.210814	+	0.418483i
$388$	−20.8685			−1.05944
$389$		−	7.85014i		−	0.398018i	−0.979998	−	0.199009i	$-0.936228\pi$
$389$		−	7.85014i		−	0.398018i	0.979998	−	0.199009i	$-0.0637723\pi$
$390$	13.0331	+	3.09736i	0.659958	+	0.156841i
$391$			35.5382i			1.79724i
$392$	−1.78994			−0.0904055
$393$	4.86890	+	1.15711i	0.245604	+	0.0583684i
$394$	−38.4058			−1.93486
$395$	27.3984			1.37856
$396$	15.1088	−	3.11148i	0.759247	−	0.156358i
$397$	−33.7724			−1.69499			−0.847494	−	0.530805i	$-0.821890\pi$
$397$	−33.7724			−1.69499			−0.847494	+	0.530805i	$0.821890\pi$
$398$	−28.4049			−1.42381
$399$	7.06285	+	1.67851i	0.353585	+	0.0840304i
$400$	55.6543			2.78271
$401$		−	5.89329i		−	0.294297i	−0.989114	−	0.147148i	$-0.952991\pi$
$401$		−	5.89329i		−	0.294297i	0.989114	−	0.147148i	$-0.0470095\pi$
$402$	0.883233	+	0.209903i	0.0440517	+	0.0104690i
$403$			6.13736i			0.305724i
$404$	15.2890			0.760658
$405$	−29.6864	+	21.9876i	−1.47513	+	1.09258i
$406$		−	34.5429i		−	1.71433i
$407$	−11.7376	+	9.29429i	−0.581809	+	0.460701i
$408$	−9.37777	−	2.22865i	−0.464269	−	0.110335i
$409$			18.3193i			0.905831i	0.891553	+	0.452916i	$0.149616\pi$
$409$			18.3193i			0.905831i	−0.891553	+	0.452916i	$0.850384\pi$
$410$		−	7.47532i		−	0.369180i
$411$	−1.33013	+	5.59694i	−0.0656103	+	0.276077i
$412$	4.95678			0.244203
$413$	−9.57106			−0.470961
$414$	−13.7593	+	27.3134i	−0.676234	+	1.34238i
$415$			27.1784i			1.33414i
$416$			7.15601i			0.350852i
$417$	8.69996	−	36.6079i	0.426039	−	1.79270i
$418$	5.38644	+	6.80242i	0.263460	+	0.332717i
$419$			10.7764i			0.526462i	0.964733	+	0.263231i	$0.0847882\pi$
$419$			10.7764i			0.526462i	−0.964733	+	0.263231i	$0.915212\pi$
$420$	−32.3719	−	7.69327i	−1.57959	−	0.375393i
$421$	−4.42065			−0.215449			−0.107725	−	0.994181i	$-0.534356\pi$
$421$	−4.42065			−0.215449			−0.107725	+	0.994181i	$0.534356\pi$
$422$			16.2943i			0.793195i
$423$	−3.54023	+	7.02766i	−0.172132	+	0.341697i
$424$		−	6.66766i		−	0.323810i
$425$	77.8279			3.77521
$426$	1.30076	−	5.47337i	0.0630221	−	0.265186i
$427$	−12.6659			−0.612944
$428$	−12.5853			−0.608334
$429$	2.42823	+	5.20612i	0.117236	+	0.251354i
$430$	23.7651			1.14605
$431$	20.0553			0.966028			0.483014	−	0.875612i	$-0.339542\pi$
$431$	20.0553			0.966028			0.483014	+	0.875612i	$0.339542\pi$
$432$	−18.6678	−	15.7228i	−0.898157	−	0.756465i
$433$	5.85835			0.281534			0.140767	−	0.990043i	$-0.455043\pi$
$433$	5.85835			0.281534			0.140767	+	0.990043i	$0.455043\pi$
$434$		−	34.9093i		−	1.67570i
$435$	−9.98284	+	42.0060i	−0.478640	+	2.01403i
$436$		−	19.0123i		−	0.910522i
$437$	−7.51198			−0.359347
$438$	−2.94761	+	12.4030i	−0.140842	+	0.592639i
$439$			12.6153i			0.602096i	0.953609	+	0.301048i	$0.0973364\pi$
$439$			12.6153i			0.602096i	−0.953609	+	0.301048i	$0.902664\pi$
$440$	7.16018	+	9.04243i	0.341348	+	0.431081i
$441$	−5.66041	−	2.85147i	−0.269544	−	0.135784i
$442$			12.3767i			0.588698i
$443$		−	11.8664i		−	0.563791i	−0.959445	−	0.281895i	$-0.909037\pi$
$443$		−	11.8664i		−	0.563791i	0.959445	−	0.281895i	$-0.0909631\pi$
$444$	−11.7934	−	2.80274i	−0.559691	−	0.133012i
$445$	−71.8133			−3.40428
$446$	−6.76070			−0.320128
$447$	11.2441	+	2.67218i	0.531826	+	0.126390i
$448$		−	12.3448i		−	0.583239i
$449$		−	31.1647i		−	1.47075i	−0.677659	−	0.735377i	$-0.737005\pi$
$449$		−	31.1647i		−	1.47075i	0.677659	−	0.735377i	$-0.262995\pi$
$450$	59.8159	+	30.1327i	2.81975	+	1.42047i
$451$	2.51311	−	1.98999i	0.118338	−	0.0937050i
$452$		−	2.97342i		−	0.139858i
$453$	−6.87265	+	28.9189i	−0.322905	+	1.35873i
$454$	49.1470			2.30658
$455$		−	12.3910i		−	0.580898i
$456$	0.471087	−	1.98225i	0.0220607	−	0.0928275i
$457$		−	11.8411i		−	0.553902i	−0.960884	−	0.276951i	$-0.910676\pi$
$457$		−	11.8411i		−	0.553902i	0.960884	−	0.276951i	$-0.0893239\pi$
$458$	−26.2480			−1.22649
$459$	−26.1054	−	21.9871i	−1.21850	−	1.02627i
$460$	34.4304			1.60533
$461$	2.21741			0.103275			0.0516376	−	0.998666i	$-0.483556\pi$
$461$	2.21741			0.103275			0.0516376	+	0.998666i	$0.483556\pi$
$462$	−13.8118	−	29.6124i	−0.642581	−	1.37769i
$463$	−30.7871			−1.43080			−0.715399	−	0.698716i	$-0.753755\pi$
$463$	−30.7871			−1.43080			−0.715399	+	0.698716i	$0.753755\pi$
$464$	−28.5252			−1.32425
$465$	−10.0887	+	42.4516i	−0.467854	+	1.96865i
$466$	5.60702			0.259740
$467$			9.81644i			0.454251i	0.973866	+	0.227125i	$0.0729327\pi$
$467$			9.81644i			0.454251i	−0.973866	+	0.227125i	$0.927067\pi$
$468$	−2.09250	+	4.15379i	−0.0967258	+	0.192009i
$469$		−	0.839716i		−	0.0387745i
$470$	20.2870			0.935768
$471$	32.4092	+	7.70212i	1.49333	+	0.354895i
$472$			2.68620i			0.123642i
$473$	6.32646	+	7.98954i	0.290891	+	0.367359i
$474$	−5.03676	+	21.1938i	−0.231346	+	0.973464i
$475$			16.4511i			0.754828i
$476$		−	30.7413i		−	1.40903i
$477$	10.6220	−	21.0855i	0.486346	−	0.965438i
$478$	18.8644			0.862837
$479$	−7.99109			−0.365122			−0.182561	−	0.983195i	$-0.558439\pi$
$479$	−7.99109			−0.365122			−0.182561	+	0.983195i	$0.558439\pi$
$480$	−11.7632	+	49.4975i	−0.536915	+	2.25924i
$481$		−	4.51416i		−	0.205828i
$482$			49.1172i			2.23723i
$483$	27.5221	+	6.54070i	1.25230	+	0.297612i
$484$	3.90954	−	16.5998i	0.177706	−	0.754535i
$485$		−	55.2511i		−	2.50882i
$486$	−11.5510	−	27.0058i	−0.523964	−	1.22501i
$487$	25.4562			1.15353			0.576765	−	0.816910i	$-0.304315\pi$
$487$	25.4562			1.15353			0.576765	+	0.816910i	$0.304315\pi$
$488$			3.55478i			0.160917i
$489$	17.9396	+	4.26340i	0.811258	+	0.192798i
$490$			16.3401i			0.738170i
$491$	12.4232			0.560650			0.280325	−	0.959905i	$-0.409558\pi$
$491$	12.4232			0.560650			0.280325	+	0.959905i	$0.409558\pi$
$492$	2.52507	+	0.600090i	0.113839	+	0.0270542i
$493$	−39.8902			−1.79656
$494$	−2.61615			−0.117706
$495$	8.23790	+	40.0019i	0.370266	+	1.79795i
$496$	−28.8278			−1.29441
$497$	−5.20369			−0.233418
$498$	−21.0237	−	4.99633i	−0.942093	−	0.223891i
$499$	−4.71887			−0.211246			−0.105623	−	0.994406i	$-0.533684\pi$
$499$	−4.71887			−0.211246			−0.105623	+	0.994406i	$0.533684\pi$
$500$		−	43.5831i		−	1.94910i
$501$	20.2590	+	4.81461i	0.905106	+	0.215101i
$502$		−	32.1009i		−	1.43273i
$503$	31.6505			1.41123			0.705614	−	0.708596i	$-0.250671\pi$
$503$	31.6505			1.41123			0.705614	+	0.708596i	$0.250671\pi$
$504$	−3.45190	+	6.85232i	−0.153760	+	0.305227i
$505$			40.4790i			1.80129i
$506$	20.9896	+	26.5072i	0.933100	+	1.17839i
$507$	−1.68512	−	0.400473i	−0.0748387	−	0.0177856i
$508$			6.55875i			0.290998i
$509$			26.8283i			1.18914i	0.804042	+	0.594572i	$0.202678\pi$
$509$			26.8283i			1.18914i	−0.804042	+	0.594572i	$0.797322\pi$
$510$	−20.3450	+	85.6083i	−0.900894	+	3.79080i
$511$	11.7919			0.521643
$512$	−25.6535			−1.13373
$513$	4.64758	−	5.51811i	0.205196	−	0.243630i
$514$			36.7200i			1.61965i
$515$			13.1235i			0.578291i
$516$	−1.90777	+	8.02756i	−0.0839849	+	0.353394i
$517$	5.40055	+	6.82024i	0.237516	+	0.299954i
$518$			25.6765i			1.12816i
$519$	−23.6849	−	5.62878i	−1.03965	−	0.247076i
$520$	−3.47764			−0.152505
$521$		−	44.6789i		−	1.95742i	−0.205255	−	0.978709i	$-0.565802\pi$
$521$		−	44.6789i		−	1.95742i	0.205255	−	0.978709i	$-0.434198\pi$
$522$	−30.6582	−	15.4443i	−1.34187	−	0.675978i
$523$		−	22.1046i		−	0.966565i	−0.875464	−	0.483283i	$-0.839444\pi$
$523$		−	22.1046i		−	0.966565i	0.875464	−	0.483283i	$-0.160556\pi$
$524$	4.47954			0.195689
$525$	14.3240	−	60.2729i	0.625151	−	2.63052i
$526$	5.22213			0.227696
$527$	−40.3133			−1.75608
$528$	−24.4537	+	11.4056i	−1.06421	+	0.496367i
$529$	−6.27223			−0.272706
$530$	−60.8681			−2.64394
$531$	−4.27927	+	8.49472i	−0.185705	+	0.368639i
$532$	6.49804			0.281726
$533$			0.966521i			0.0418647i
$534$	13.2018	−	55.5506i	0.571296	−	2.40391i
$535$		−	33.3207i		−	1.44058i
$536$	−0.235674			−0.0101795
$537$	2.37701	−	10.0020i	0.102576	−	0.431620i
$538$		−	0.509575i		−	0.0219693i
$539$	−5.49334	+	4.34986i	−0.236615	+	0.187362i
$540$	−21.3017	+	25.2917i	−0.916681	+	1.08838i
$541$		−	14.9134i		−	0.641178i	−0.947218	−	0.320589i	$-0.896119\pi$
$541$		−	14.9134i		−	0.641178i	0.947218	−	0.320589i	$-0.103881\pi$
$542$		−	46.1831i		−	1.98373i
$543$	−10.1014	−	2.40063i	−0.433494	−	0.103021i
$544$	−47.0044			−2.01530
$545$	50.3366			2.15618
$546$	9.58495	+	2.27789i	0.410198	+	0.0974846i
$547$			18.1085i			0.774264i	0.922024	+	0.387132i	$0.126534\pi$
$547$			18.1085i			0.774264i	−0.922024	+	0.387132i	$0.873466\pi$
$548$			5.14935i			0.219969i
$549$	−5.66297	+	11.2415i	−0.241690	+	0.479774i
$550$	58.0504	−	45.9667i	2.47528	−	1.96003i
$551$		−	8.43190i		−	0.359211i
$552$	1.83570	−	7.72432i	0.0781328	−	0.328769i
$553$	20.1496			0.856847
$554$		−	17.6560i		−	0.750130i
$555$	7.42048	−	31.2241i	0.314982	−	1.32539i
$556$		−	33.6803i		−	1.42836i
$557$	−28.3590			−1.20161			−0.600805	−	0.799396i	$-0.705153\pi$
$557$	−28.3590			−1.20161			−0.600805	+	0.799396i	$0.705153\pi$
$558$	−30.9835	−	15.6081i	−1.31163	−	0.660745i
$559$	−3.07271			−0.129962
$560$	58.2017			2.45947
$561$	−34.1965	+	15.9499i	−1.44378	+	0.673403i
$562$	5.76348			0.243118
$563$	−16.9211			−0.713139			−0.356569	−	0.934269i	$-0.616054\pi$
$563$	−16.9211			−0.713139			−0.356569	+	0.934269i	$0.616054\pi$
$564$	−1.62856	+	6.85269i	−0.0685748	+	0.288550i
$565$	7.87238			0.331194
$566$		−	36.8255i		−	1.54789i
$567$	−21.8323	+	16.1704i	−0.916868	+	0.679091i
$568$			1.46046i			0.0612796i
$569$	−3.67328			−0.153992			−0.0769960	−	0.997031i	$-0.524533\pi$
$569$	−3.67328			−0.153992			−0.0769960	+	0.997031i	$0.524533\pi$
$570$	−18.0957	−	4.30049i	−0.757945	−	0.180128i
$571$		−	33.2610i		−	1.39193i	−0.718075	−	0.695965i	$-0.754977\pi$
$571$		−	33.2610i		−	1.39193i	0.718075	−	0.695965i	$-0.245023\pi$
$572$	3.19206	+	4.03119i	0.133467	+	0.168552i
$573$	1.37940	−	5.80425i	0.0576251	−	0.242476i
$574$		−	5.49757i		−	0.229464i
$575$			64.1056i			2.67339i
$576$	−10.9566	−	5.51944i	−0.456524	−	0.229977i
$577$	25.8888			1.07777			0.538883	−	0.842381i	$-0.318846\pi$
$577$	25.8888			1.07777			0.538883	+	0.842381i	$0.318846\pi$
$578$	−49.2642			−2.04912
$579$	−8.57699	+	36.0905i	−0.356448	+	1.49987i
$580$			38.6468i			1.60472i
$581$			19.9878i			0.829234i
$582$	42.7390	+	10.1570i	1.77159	+	0.421023i
$583$	−16.2036	−	20.4631i	−0.671084	−	0.847497i
$584$		−	3.30950i		−	0.136948i
$585$	−10.9975	−	5.54007i	−0.454691	−	0.229054i
$586$	−48.9493			−2.02208
$587$		−	20.1376i		−	0.831167i	−0.909555	−	0.415584i	$-0.863577\pi$
$587$		−	20.1376i		−	0.831167i	0.909555	−	0.415584i	$-0.136423\pi$
$588$	−5.51949	−	1.31172i	−0.227620	−	0.0540944i
$589$		−	8.52135i		−	0.351116i
$590$	24.5220			1.00955
$591$	34.3472	+	8.16269i	1.41285	+	0.335768i
$592$	21.2035			0.871458
$593$	−35.7447			−1.46786			−0.733929	−	0.679226i	$-0.762315\pi$
$593$	−35.7447			−1.46786			−0.733929	+	0.679226i	$0.762315\pi$
$594$	−32.4576	−	0.981354i	−1.33175	−	0.0402655i
$595$	81.3904			3.33668
$596$	10.3449			0.423742
$597$	25.4032	+	6.03713i	1.03968	+	0.247083i
$598$	−10.1945			−0.416882
$599$		−	9.11274i		−	0.372336i	−0.982518	−	0.186168i	$-0.940393\pi$
$599$		−	9.11274i		−	0.372336i	0.982518	−	0.186168i	$-0.0596069\pi$
$600$	−16.9161	−	4.02016i	−0.690597	−	0.164122i
$601$			12.6824i			0.517327i	0.965967	+	0.258664i	$0.0832821\pi$
$601$			12.6824i			0.517327i	−0.965967	+	0.258664i	$0.916718\pi$
$602$	17.4775			0.712332
$603$	−0.745283	−	0.375441i	−0.0303503	−	0.0152892i
$604$			26.6063i			1.08259i
$605$	43.9493	+	10.3508i	1.78679	+	0.420821i
$606$	−31.3122	−	7.44143i	−1.27197	−	0.302288i
$607$			5.58764i			0.226795i	0.993550	+	0.113398i	$0.0361734\pi$
$607$			5.58764i			0.226795i	−0.993550	+	0.113398i	$0.963827\pi$
$608$		−	9.93568i		−	0.402945i
$609$	−7.34167	+	30.8924i	−0.297500	+	1.25183i
$610$	32.4511			1.31391
$611$	−2.62300			−0.106115
$612$	−27.2842	−	13.7446i	−1.10290	−	0.555593i
$613$		−	26.6064i		−	1.07462i	−0.843384	−	0.537311i	$-0.819440\pi$
$613$		−	26.6064i		−	1.07462i	0.843384	−	0.537311i	$-0.180560\pi$
$614$		−	6.63074i		−	0.267595i
$615$	−1.58879	+	6.68535i	−0.0640662	+	0.269579i
$616$	5.26581	+	6.65007i	0.212165	+	0.267939i
$617$		−	22.5906i		−	0.909465i	−0.890628	−	0.454732i	$-0.849735\pi$
$617$		−	22.5906i		−	0.909465i	0.890628	−	0.454732i	$-0.150265\pi$
$618$	−10.1516	−	2.41255i	−0.408357	−	0.0970470i
$619$	−0.844039			−0.0339248			−0.0169624	−	0.999856i	$-0.505400\pi$
$619$	−0.844039			−0.0339248			−0.0169624	+	0.999856i	$0.505400\pi$
$620$			39.0568i			1.56856i
$621$	18.1104	−	21.5026i	0.726746	−	0.862871i
$622$			56.3871i			2.26092i
$623$	−52.8136			−2.11593
$624$	1.88106	−	7.91517i	0.0753027	−	0.316861i
$625$	56.1469			2.24588
$626$	10.4548			0.417858
$627$	−3.37145	−	7.22838i	−0.134643	−	0.288674i
$628$	29.8174			1.18984
$629$	29.6513			1.18228
$630$	62.5538	+	31.5119i	2.49220	+	1.25546i
$631$	−40.5727			−1.61517			−0.807586	−	0.589750i	$-0.799226\pi$
$631$	−40.5727			−1.61517			−0.807586	+	0.589750i	$0.799226\pi$
$632$		−	5.65516i		−	0.224950i
$633$	3.46316	−	14.5724i	0.137648	−	0.579200i
$634$			12.7584i			0.506699i
$635$	−17.3649			−0.689103
$636$	4.88626	−	20.5605i	0.193753	−	0.815278i
$637$		−	2.11269i		−	0.0837079i
$638$	−29.7533	+	23.5599i	−1.17795	+	0.932747i
$639$	−2.32660	+	4.61850i	−0.0920388	+	0.182705i
$640$		−	27.1180i		−	1.07193i
$641$			4.39298i			0.173512i	0.996230	+	0.0867562i	$0.0276501\pi$
$641$			4.39298i			0.173512i	−0.996230	+	0.0867562i	$0.972350\pi$
$642$	25.7750	+	6.12549i	1.01726	+	0.241754i
$643$	16.0125			0.631470			0.315735	−	0.948847i	$-0.397749\pi$
$643$	16.0125			0.631470			0.315735	+	0.948847i	$0.397749\pi$
$644$	25.3212			0.997793
$645$	−21.2537	−	5.05099i	−0.836862	−	0.198882i
$646$		−	17.1842i		−	0.676104i
$647$			7.46337i			0.293416i	0.989180	+	0.146708i	$0.0468677\pi$
$647$			7.46337i			0.293416i	−0.989180	+	0.146708i	$0.953132\pi$
$648$	4.53836	+	6.12741i	0.178283	+	0.240708i
$649$	6.52794	+	8.24399i	0.256244	+	0.323605i
$650$			22.3257i			0.875684i
$651$	−7.41955	+	31.2202i	−0.290795	+	1.22361i
$652$	16.5050			0.646386
$653$		−	33.8304i		−	1.32388i	−0.749555	−	0.661942i	$-0.769732\pi$
$653$		−	33.8304i		−	1.32388i	0.749555	−	0.661942i	$-0.230268\pi$
$654$	−9.25360	+	38.9375i	−0.361844	+	1.52258i
$655$			11.8600i			0.463407i
$656$	−4.53985			−0.177251
$657$	5.27222	−	10.4658i	0.205689	−	0.408310i
$658$	14.9196			0.581628
$659$	−15.4775			−0.602920			−0.301460	−	0.953479i	$-0.597474\pi$
$659$	−15.4775			−0.602920			−0.301460	+	0.953479i	$0.597474\pi$
$660$	15.4527	+	33.1306i	0.601495	+	1.28961i
$661$	13.3508			0.519286			0.259643	−	0.965705i	$-0.416395\pi$
$661$	13.3508			0.519286			0.259643	+	0.965705i	$0.416395\pi$
$662$	60.5258			2.35240
$663$	2.63051	−	11.0687i	0.102161	−	0.429874i
$664$	5.60976			0.217701
$665$			17.2041i			0.667147i
$666$	22.7890	+	11.4801i	0.883056	+	0.444845i
$667$		−	32.8569i		−	1.27222i
$668$	18.6389			0.721161
$669$	6.04624	+	1.43691i	0.233761	+	0.0555540i
$670$			2.15143i			0.0831170i
$671$	8.63874	+	10.9097i	0.333495	+	0.421163i
$672$	−8.65101	+	36.4019i	−0.333720	+	1.40424i
$673$		−	11.0842i		−	0.427265i	−0.976914	−	0.213632i	$-0.931471\pi$
$673$		−	11.0842i		−	0.427265i	0.976914	−	0.213632i	$-0.0685295\pi$
$674$			44.0856i			1.69811i
$675$	−47.0903	−	39.6615i	−1.81251	−	1.52657i
$676$	−1.55036			−0.0596292
$677$	8.24754			0.316979			0.158489	−	0.987361i	$-0.449338\pi$
$677$	8.24754			0.316979			0.158489	+	0.987361i	$0.449338\pi$
$678$	−1.44721	+	6.08962i	−0.0555799	+	0.233870i
$679$		−	40.6333i		−	1.55936i
$680$		−	22.8429i		−	0.875986i
$681$	−43.9533	−	10.4456i	−1.68429	−	0.400277i
$682$	−30.0690	+	23.8099i	−1.15140	+	0.911727i
$683$			36.1967i			1.38503i	0.721404	+	0.692515i	$0.243497\pi$
$683$			36.1967i			1.38503i	−0.721404	+	0.692515i	$0.756503\pi$
$684$	2.90531	−	5.76728i	0.111087	−	0.220517i
$685$	−13.6334			−0.520904
$686$		−	27.7990i		−	1.06137i
$687$	23.4742	+	5.57870i	0.895596	+	0.212841i
$688$		−	14.4328i		−	0.550246i
$689$	7.86994			0.299821
$690$	−70.5142	−	16.7579i	−2.68443	−	0.637962i
$691$	−10.3945			−0.395424			−0.197712	−	0.980260i	$-0.563351\pi$
$691$	−10.3945			−0.395424			−0.197712	+	0.980260i	$0.563351\pi$
$692$	−21.7908			−0.828362
$693$	6.05840	+	29.4186i	0.230140	+	1.11752i
$694$	7.07827			0.268687
$695$	89.1716			3.38247
$696$	8.67024	+	2.06050i	0.328645	+	0.0781032i
$697$	−6.34861			−0.240471
$698$			64.3987i			2.43753i
$699$	−5.01448	−	1.19171i	−0.189665	−	0.0450744i
$700$		−	55.4528i		−	2.09592i
$701$	−22.5832			−0.852957			−0.426479	−	0.904498i	$-0.640246\pi$
$701$	−22.5832			−0.852957			−0.426479	+	0.904498i	$0.640246\pi$
$702$	6.30720	−	7.48859i	0.238050	−	0.282638i
$703$			6.26763i			0.236388i
$704$	−10.6332	+	8.41980i	−0.400753	+	0.317333i
$705$	−18.1431	−	4.31175i	−0.683309	−	0.162390i
$706$			1.49741i			0.0563559i
$707$			29.7695i			1.11960i
$708$	−1.96853	+	8.28322i	−0.0739818	+	0.311302i
$709$	−5.89842			−0.221520			−0.110760	−	0.993847i	$-0.535328\pi$
$709$	−5.89842			−0.221520			−0.110760	+	0.993847i	$0.535328\pi$
$710$	13.3324			0.500354
$711$	9.00898	−	17.8836i	0.337863	−	0.670687i
$712$			14.8226i			0.555501i
$713$		−	33.2055i		−	1.24355i
$714$	−14.9623	+	62.9589i	−0.559952	+	2.35618i
$715$	−10.6729	+	8.45127i	−0.399144	+	0.316059i
$716$		−	9.20219i		−	0.343902i
$717$	−16.8709	−	4.00940i	−0.630053	−	0.149734i
$718$	44.3034			1.65339
$719$			22.6125i			0.843305i	0.906758	+	0.421652i	$0.138550\pi$
$719$			22.6125i			0.843305i	−0.906758	+	0.421652i	$0.861450\pi$
$720$	26.0223	−	51.6565i	0.969794	−	1.92512i
$721$			9.65141i			0.359437i
$722$	−32.1682			−1.19718
$723$	10.4393	−	43.9266i	0.388241	−	1.63365i
$724$	−9.29361			−0.345394
$725$	−71.9560			−2.67238
$726$	−16.0862	+	32.0938i	−0.597015	+	1.19111i
$727$	8.76925			0.325234			0.162617	−	0.986689i	$-0.448007\pi$
$727$	8.76925			0.325234			0.162617	+	0.986689i	$0.448007\pi$
$728$	−2.55756			−0.0947894
$729$	4.59056	+	26.6069i	0.170021	+	0.985440i
$730$	−30.2120			−1.11820
$731$		−	20.1831i		−	0.746500i
$732$	−2.60505	+	10.9616i	−0.0962855	+	0.405152i
$733$		−	29.8758i		−	1.10349i	−0.834013	−	0.551745i	$-0.813962\pi$
$733$		−	29.8758i		−	1.10349i	0.834013	−	0.551745i	$-0.186038\pi$
$734$	18.9159			0.698199
$735$	3.47289	−	14.6133i	0.128100	−	0.539020i
$736$		−	38.7167i		−	1.42712i
$737$	−0.723285	+	0.572728i	−0.0266426	+	0.0210967i
$738$	−4.87932	−	2.45799i	−0.179610	−	0.0904800i
$739$		−	24.6772i		−	0.907766i	−0.891061	−	0.453883i	$-0.850038\pi$
$739$		−	24.6772i		−	0.907766i	0.891061	−	0.453883i	$-0.149962\pi$
$740$		−	28.7271i		−	1.05603i
$741$	2.33968	+	0.556032i	0.0859504	+	0.0204263i
$742$	−44.7642			−1.64335
$743$	−37.6760			−1.38220			−0.691099	−	0.722760i	$-0.742873\pi$
$743$	−37.6760			−1.38220			−0.691099	+	0.722760i	$0.742873\pi$
$744$	8.76221	+	2.08236i	0.321238	+	0.0763431i
$745$			27.3889i			1.00345i
$746$		−	30.3436i		−	1.11096i
$747$	17.7400	+	8.93666i	0.649074	+	0.326975i
$748$	−26.4789	+	20.9671i	−0.968165	+	0.766634i
$749$		−	24.5050i		−	0.895394i
$750$	−21.2127	+	89.2591i	−0.774577	+	3.25928i
$751$	−10.5031			−0.383264			−0.191632	−	0.981467i	$-0.561378\pi$
$751$	−10.5031			−0.383264			−0.191632	+	0.981467i	$0.561378\pi$
$752$		−	12.3205i		−	0.449283i
$753$	−6.82267	+	28.7086i	−0.248632	+	1.04620i
$754$		−	11.4429i		−	0.416725i
$755$	−70.4424			−2.56366
$756$	−15.6659	+	18.6003i	−0.569764	+	0.676485i
$757$	−36.4664			−1.32539			−0.662696	−	0.748888i	$-0.730588\pi$
$757$	−36.4664			−1.32539			−0.662696	+	0.748888i	$0.730588\pi$
$758$	−14.8420			−0.539085
$759$	−13.1376	−	28.1671i	−0.476866	−	1.02240i
$760$	4.82849			0.175148
$761$	−20.2902			−0.735519			−0.367759	−	0.929921i	$-0.619875\pi$
$761$	−20.2902			−0.735519			−0.367759	+	0.929921i	$0.619875\pi$
$762$	3.19226	−	13.4325i	0.115643	−	0.486606i
$763$	37.0190			1.34018
$764$		−	5.34009i		−	0.193198i
$765$	36.3901	−	72.2373i	1.31569	−	2.61175i
$766$		−	7.61652i		−	0.275196i
$767$	−3.17057			−0.114482
$768$	34.7592	+	8.26063i	1.25427	+	0.298080i
$769$		−	5.02613i		−	0.181247i	−0.995885	−	0.0906234i	$-0.971114\pi$
$769$		−	5.02613i		−	0.181247i	0.995885	−	0.0906234i	$-0.0288860\pi$
$770$	60.7075	−	48.0708i	2.18775	−	1.73235i
$771$	7.80439	−	32.8395i	0.281068	−	1.18268i
$772$			33.2043i			1.19505i
$773$		−	3.19371i		−	0.114870i	−0.998349	−	0.0574350i	$-0.981708\pi$
$773$		−	3.19371i		−	0.114870i	0.998349	−	0.0574350i	$-0.0182922\pi$
$774$	7.81430	−	15.5121i	0.280879	−	0.557569i
$775$	−72.7193			−2.61216
$776$	−11.4041			−0.409383
$777$	5.45724	−	22.9631i	0.195777	−	0.823797i
$778$			14.7916i			0.530303i
$779$		−	1.34196i		−	0.0480805i
$780$	−10.7237	−	2.54852i	−0.383970	−	0.0912515i
$781$	3.54918	+	4.48218i	0.127000	+	0.160385i
$782$		−	66.9624i		−	2.39457i
$783$	24.1358	+	20.3282i	0.862545	+	0.726471i
$784$	9.92353			0.354412
$785$			78.9441i			2.81764i
$786$	−9.17418	−	2.18027i	−0.327232	−	0.0777676i
$787$			10.1572i			0.362064i	0.983477	+	0.181032i	$0.0579437\pi$
$787$			10.1572i			0.362064i	−0.983477	+	0.181032i	$0.942056\pi$
$788$	31.6004			1.12572
$789$	−4.67027	−	1.10990i	−0.166266	−	0.0395135i
$790$	−51.6251			−1.83674
$791$	5.78958			0.205854
$792$	8.25658	−	1.70034i	0.293385	−	0.0604190i
$793$	−4.19576			−0.148996
$794$	63.6353			2.25833
$795$	54.4357	+	12.9368i	1.93064	+	0.458821i
$796$	23.3717			0.828387
$797$			52.6097i			1.86353i	0.363059	+	0.931766i	$0.381732\pi$
$797$			52.6097i			1.86353i	−0.363059	+	0.931766i	$0.618268\pi$
$798$	−13.3081	−	3.16271i	−0.471102	−	0.111959i
$799$		−	17.2292i		−	0.609527i
$800$	−84.7889			−2.99774
$801$	−23.6133	+	46.8743i	−0.834333	+	1.65622i
$802$			11.1044i			0.392109i
$803$	−8.04267	−	10.1569i	−0.283820	−	0.358429i
$804$	−0.726727	−	0.172709i	−0.0256297	−	0.00609096i
$805$			67.0399i			2.36285i
$806$		−	11.5643i		−	0.407334i
$807$	−0.108304	+	0.455724i	−0.00381248	+	0.0160423i
$808$	8.35506			0.293930
$809$	−4.05951			−0.142725			−0.0713624	−	0.997450i	$-0.522735\pi$
$809$	−4.05951			−0.142725			−0.0713624	+	0.997450i	$0.522735\pi$
$810$	55.9363	−	41.4300i	1.96540	−	1.45570i
$811$			10.2935i			0.361455i	0.983533	+	0.180727i	$0.0578452\pi$
$811$			10.2935i			0.361455i	−0.983533	+	0.180727i	$0.942155\pi$
$812$			28.4220i			0.997416i
$813$	−9.81566	+	41.3026i	−0.344250	+	1.44854i
$814$	22.1164	−	17.5127i	0.775178	−	0.613819i
$815$			43.6984i			1.53069i
$816$	51.9910	+	12.3558i	1.82005	+	0.432539i
$817$	4.26626			0.149258
$818$		−	34.5180i		−	1.20689i
$819$	−8.08789	−	4.07433i	−0.282614	−	0.142369i
$820$			6.15072i			0.214792i
$821$	−4.20608			−0.146793			−0.0733966	−	0.997303i	$-0.523384\pi$
$821$	−4.20608			−0.146793			−0.0733966	+	0.997303i	$0.523384\pi$
$822$	2.50628	−	10.5460i	0.0874165	−	0.367833i
$823$	44.0949			1.53705			0.768526	−	0.639818i	$-0.220990\pi$
$823$	44.0949			1.53705			0.768526	+	0.639818i	$0.220990\pi$
$824$	2.70875			0.0943639
$825$	−61.6854	+	28.7712i	−2.14761	+	1.00168i
$826$	18.0342			0.627489
$827$	7.48662			0.260335			0.130168	−	0.991492i	$-0.458448\pi$
$827$	7.48662			0.260335			0.130168	+	0.991492i	$0.458448\pi$
$828$	11.3212	−	22.4736i	0.393440	−	0.781011i
$829$	−30.8821			−1.07258			−0.536290	−	0.844034i	$-0.680175\pi$
$829$	−30.8821			−1.07258			−0.536290	+	0.844034i	$0.680175\pi$
$830$		−	51.2107i		−	1.77755i
$831$	−3.75257	+	15.7901i	−0.130175	+	0.547754i
$832$		−	4.08943i		−	0.141775i
$833$	13.8772			0.480818
$834$	−16.3928	+	68.9780i	−0.567636	+	2.38851i
$835$			49.3481i			1.70776i
$836$	−4.43199	−	5.59705i	−0.153283	−	0.193578i
$837$	24.3919	+	20.5439i	0.843107	+	0.710100i
$838$		−	20.3054i		−	0.701437i
$839$		−	44.4859i		−	1.53582i	−0.640555	−	0.767912i	$-0.721296\pi$
$839$		−	44.4859i		−	1.53582i	0.640555	−	0.767912i	$-0.278704\pi$
$840$	−17.6904	−	4.20417i	−0.610377	−	0.145058i
$841$	7.88056			0.271744
$842$	8.32956			0.287056
$843$	−5.15441	−	1.22496i	−0.177527	−	0.0421898i
$844$		−	13.4070i		−	0.461489i
$845$		−	4.10471i		−	0.141206i
$846$	6.67065	−	13.2418i	0.229342	−	0.455263i
$847$	32.3216	+	7.61231i	1.11058	+	0.261562i
$848$			36.9659i			1.26942i
$849$	−7.82683	+	32.9339i	−0.268616	+	1.13029i
$850$	−146.646			−5.02993
$851$			24.4233i			0.837221i
$852$	−1.07027	+	4.50351i	−0.0366669	+	0.154288i
$853$		−	30.6209i		−	1.04844i	−0.851583	−	0.524220i	$-0.824357\pi$
$853$		−	30.6209i		−	1.04844i	0.851583	−	0.524220i	$-0.175643\pi$
$854$	23.8655			0.816661
$855$	15.2694	+	7.69205i	0.522201	+	0.263063i
$856$	−6.87755			−0.235070
$857$	26.5244			0.906056			0.453028	−	0.891496i	$-0.350344\pi$
$857$	26.5244			0.906056			0.453028	+	0.891496i	$0.350344\pi$
$858$	−4.57536	−	9.80958i	−0.156200	−	0.334894i
$859$	−50.2655			−1.71504			−0.857519	−	0.514453i	$-0.827995\pi$
$859$	−50.2655			−1.71504			−0.857519	+	0.514453i	$0.827995\pi$
$860$	−19.5540			−0.666786
$861$	−1.16844	+	4.91660i	−0.0398204	+	0.167557i
$862$	−37.7889			−1.28710
$863$			19.3415i			0.658393i	0.944261	+	0.329196i	$0.106778\pi$
$863$			19.3415i			0.658393i	−0.944261	+	0.329196i	$0.893222\pi$
$864$	28.4403	+	23.9536i	0.967559	+	0.814919i
$865$		−	57.6930i		−	1.96162i
$866$	−11.0385			−0.375105
$867$	44.0581	+	10.4705i	1.49629	+	0.355597i
$868$			28.7235i			0.974939i
$869$	−13.7430	−	17.3557i	−0.466200	−	0.588753i
$870$	18.8101	−	79.1494i	0.637721	−	2.68341i
$871$		−	0.278169i		−	0.00942540i
$872$		−	10.3897i		−	0.351840i
$873$	−36.0637	−	18.1673i	−1.22057	−	0.614871i
$874$	14.1544			0.478779
$875$	84.8613			2.86883
$876$	2.42530	−	10.2052i	0.0819434	−	0.344803i
$877$			56.2745i			1.90026i	0.311860	+	0.950128i	$0.399048\pi$
$877$			56.2745i			1.90026i	−0.311860	+	0.950128i	$0.600952\pi$
$878$		−	23.7703i		−	0.802207i
$879$	43.7765	+	10.4036i	1.47654	+	0.350904i
$880$	−39.6965	−	50.1318i	−1.33817	−	1.68994i
$881$			15.9154i			0.536204i	0.963391	+	0.268102i	$0.0863965\pi$
$881$			15.9154i			0.536204i	−0.963391	+	0.268102i	$0.913604\pi$
$882$	10.6656	+	5.37286i	0.359129	+	0.180914i
$883$	6.01473			0.202412			0.101206	−	0.994866i	$-0.467730\pi$
$883$	6.01473			0.202412			0.101206	+	0.994866i	$0.467730\pi$
$884$		−	10.1836i		−	0.342510i
$885$	−21.9305	−	5.21185i	−0.737187	−	0.175194i
$886$			22.3592i			0.751172i
$887$	31.0266			1.04177			0.520886	−	0.853627i	$-0.325602\pi$
$887$	31.0266			1.04177			0.520886	+	0.853627i	$0.325602\pi$
$888$	−6.44480	−	1.53162i	−0.216273	−	0.0513979i
$889$	−12.7706			−0.428313
$890$	135.314			4.53572
$891$	28.8190	+	7.77612i	0.965471	+	0.260510i
$892$	5.56273			0.186254
$893$	3.64188			0.121871
$894$	−21.1865	−	5.03503i	−0.708582	−	0.168396i
$895$	24.3636			0.814385
$896$		−	19.9434i		−	0.666262i
$897$	9.11713	+	2.16671i	0.304412	+	0.0723443i
$898$			58.7218i			1.95957i
$899$	37.2718			1.24308
$900$	−49.2167	−	24.7933i	−1.64056	−	0.826442i
$901$			51.6938i			1.72217i
$902$	−4.73531	+	3.74962i	−0.157668	+	0.124849i
$903$	−15.6306	−	3.71464i	−0.520153	−	0.123616i
$904$		−	1.62490i		−	0.0540433i
$905$		−	24.6056i		−	0.817919i
$906$	12.9497	−	54.4901i	0.430226	−	1.81031i
$907$	24.0776			0.799484			0.399742	−	0.916628i	$-0.369100\pi$
$907$	24.0776			0.799484			0.399742	+	0.916628i	$0.369100\pi$
$908$	−40.4383			−1.34199
$909$	26.4216	+	13.3101i	0.876350	+	0.441467i
$910$			23.3476i			0.773965i
$911$		−	28.6556i		−	0.949404i	−0.880147	−	0.474702i	$-0.842556\pi$
$911$		−	28.6556i		−	0.949404i	0.880147	−	0.474702i	$-0.157444\pi$
$912$	−2.61174	+	10.9897i	−0.0864833	+	0.363906i
$913$	17.2164	−	13.6327i	0.569780	−	0.451176i
$914$			22.3114i			0.737995i
$915$	−29.0218	−	6.89710i	−0.959430	−	0.228011i
$916$	21.5970			0.713584
$917$			8.72216i			0.288031i
$918$	49.1889	+	41.4289i	1.62348	+	1.36736i
$919$			37.2014i			1.22716i	0.789633	+	0.613580i	$0.210271\pi$
$919$			37.2014i			1.22716i	−0.789633	+	0.613580i	$0.789729\pi$
$920$	18.8153			0.620324
$921$	−1.40929	+	5.93002i	−0.0464375	+	0.195401i
$922$	−4.17814			−0.137600
$923$	−1.72381			−0.0567398
$924$	11.3644	+	24.3652i	0.373860	+	0.801556i
$925$	53.4866			1.75863
$926$	58.0103			1.90634
$927$	8.56603	+	4.31520i	0.281345	+	0.141730i
$928$	43.4580			1.42658
$929$		−	48.2321i		−	1.58245i	−0.611528	−	0.791223i	$-0.709445\pi$
$929$		−	48.2321i		−	1.58245i	0.611528	−	0.791223i	$-0.290555\pi$
$930$	19.0096	−	79.9890i	0.623349	−	2.62294i
$931$			2.93334i			0.0961364i
$932$	−4.61348			−0.151119
$933$	11.9844	−	50.4283i	0.392352	−	1.65095i
$934$		−	18.4965i		−	0.605225i
$935$	−55.5123	−	70.1052i	−1.81545	−	2.29269i
$936$	−1.14350	+	2.26994i	−0.0373764	+	0.0741953i
$937$		−	30.9187i		−	1.01007i	−0.863099	−	0.505035i	$-0.831479\pi$
$937$		−	30.9187i		−	1.01007i	0.863099	−	0.505035i	$-0.168521\pi$
$938$			1.58223i			0.0516615i
$939$	−9.34996	−	2.22204i	−0.305124	−	0.0725136i
$940$	−16.6922			−0.544439
$941$	−31.1608			−1.01581			−0.507907	−	0.861412i	$-0.669581\pi$
$941$	−31.1608			−1.01581			−0.507907	+	0.861412i	$0.669581\pi$
$942$	−61.0666	−	14.5126i	−1.98966	−	0.472847i
$943$		−	5.22925i		−	0.170288i
$944$		−	14.8925i		−	0.484709i
$945$	−49.2458	−	41.4769i	−1.60197	−	1.34924i
$946$	−11.9206	−	15.0542i	−0.387571	−	0.489454i
$947$			11.3628i			0.369241i	0.982810	+	0.184620i	$0.0591055\pi$
$947$			11.3628i			0.369241i	−0.982810	+	0.184620i	$0.940894\pi$
$948$	4.14427	−	17.4383i	0.134600	−	0.566371i
$949$	3.90626			0.126802
$950$		−	30.9978i		−	1.00570i
$951$	2.71164	−	11.4101i	0.0879308	−	0.369997i
$952$		−	16.7994i		−	0.544470i
$953$	−6.43186			−0.208348			−0.104174	−	0.994559i	$-0.533220\pi$
$953$	−6.43186			−0.208348			−0.104174	+	0.994559i	$0.533220\pi$
$954$	−20.0143	+	39.7301i	−0.647987	+	1.28631i
$955$	14.1383			0.457506
$956$	−15.5217			−0.502007
$957$	31.6165	−	14.7465i	1.02201	−	0.476686i
$958$	15.0571			0.486474
$959$	−10.0264			−0.323768
$960$	6.72229	−	28.2862i	0.216961	−	0.912934i
$961$	6.66719			0.215071
$962$			8.50576i			0.274237i
$963$	−21.7492	−	10.9563i	−0.700860	−	0.353063i
$964$		−	40.4138i		−	1.30164i
$965$	−87.9112			−2.82996
$966$	−51.8582	−	12.3242i	−1.66851	−	0.396526i
$967$			5.55432i			0.178615i	0.996004	+	0.0893074i	$0.0284654\pi$
$967$			5.55432i			0.178615i	−0.996004	+	0.0893074i	$0.971535\pi$
$968$	2.13646	−	9.07135i	0.0686685	−	0.291564i
$969$	−3.65230	+	15.3682i	−0.117329	+	0.493699i
$970$			104.106i			3.34265i
$971$			40.1432i			1.28826i	0.764918	+	0.644128i	$0.222780\pi$
$971$			40.1432i			1.28826i	−0.764918	+	0.644128i	$0.777220\pi$
$972$	9.50420	+	22.2204i	0.304847	+	0.712721i
$973$	65.5794			2.10238
$974$	−47.9656			−1.53692
$975$	4.74505	−	19.9663i	0.151963	−	0.639435i
$976$		−	19.7079i		−	0.630836i
$977$		−	15.4311i		−	0.493683i	−0.969056	−	0.246842i	$-0.920607\pi$
$977$		−	15.4311i		−	0.493683i	0.969056	−	0.246842i	$-0.0793928\pi$
$978$	−33.8026	−	8.03327i	−1.08089	−	0.256876i
$979$	36.0215	+	45.4908i	1.15125	+	1.45389i
$980$		−	13.4447i		−	0.429475i
$981$	16.5514	−	32.8559i	0.528445	−	1.04901i
$982$	−23.4083			−0.746987
$983$		−	22.2438i		−	0.709468i	−0.934967	−	0.354734i	$-0.884571\pi$
$983$		−	22.2438i		−	0.709468i	0.934967	−	0.354734i	$-0.115429\pi$
$984$	1.37989	+	0.327934i	0.0439892	+	0.0104542i
$985$			83.6648i			2.66578i
$986$	75.1627			2.39367
$987$	−13.3430	−	3.17099i	−0.424711	−	0.100934i
$988$	2.15258			0.0684826
$989$	16.6245			0.528629
$990$	−15.5222	−	75.3732i	−0.493327	−	2.39552i
$991$	−47.8944			−1.52142			−0.760708	−	0.649094i	$-0.775148\pi$
$991$	−47.8944			−1.52142			−0.760708	+	0.649094i	$0.775148\pi$
$992$	43.9190			1.39443
$993$	−54.1295	−	12.8640i	−1.71775	−	0.408228i
$994$	9.80501			0.310996
$995$			61.8785i			1.96168i
$996$	17.2983	+	4.11100i	0.548119	+	0.130262i
$997$		−	14.9641i		−	0.473919i	−0.971520	−	0.236959i	$-0.923849\pi$
$997$		−	14.9641i		−	0.473919i	0.971520	−	0.236959i	$-0.0761508\pi$
$998$	8.89148			0.281455
$999$	−17.9408	−	15.1105i	−0.567620	−	0.478074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.12	yes	48
3.2	odd	2	inner	429.2.f.a.131.37	yes	48
11.10	odd	2	inner	429.2.f.a.131.38	yes	48
33.32	even	2	inner	429.2.f.a.131.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.11	✓	48	33.32	even	2	inner
429.2.f.a.131.12	yes	48	1.1	even	1	trivial
429.2.f.a.131.37	yes	48	3.2	odd	2	inner
429.2.f.a.131.38	yes	48	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.88424 q^{2} +(1.68512 + 0.400473i) q^{3} +1.55036 q^{4} +4.10471i q^{5} +(-3.17517 - 0.754586i) q^{6} +3.01872i q^{7} +0.847231 q^{8} +(2.67924 + 1.34969i) q^{9} +O(q^{10})\)	\(q-1.88424 q^{2} +(1.68512 + 0.400473i) q^{3} +1.55036 q^{4} +4.10471i q^{5} +(-3.17517 - 0.754586i) q^{6} +3.01872i q^{7} +0.847231 q^{8} +(2.67924 + 1.34969i) q^{9} -7.73425i q^{10} +(2.60016 - 2.05892i) q^{11} +(2.61254 + 0.620876i) q^{12} +1.00000i q^{13} -5.68800i q^{14} +(-1.64382 + 6.91692i) q^{15} -4.69710 q^{16} -6.56852 q^{17} +(-5.04834 - 2.54313i) q^{18} -1.38844i q^{19} +6.36377i q^{20} +(-1.20892 + 5.08690i) q^{21} +(-4.89933 + 3.87950i) q^{22} -5.41038i q^{23} +(1.42768 + 0.339293i) q^{24} -11.8486 q^{25} -1.88424i q^{26} +(3.97433 + 3.34735i) q^{27} +4.68011i q^{28} +6.07294 q^{29} +(3.09736 - 13.0331i) q^{30} +6.13736 q^{31} +7.15601 q^{32} +(5.20612 - 2.42823i) q^{33} +12.3767 q^{34} -12.3910 q^{35} +(4.15379 + 2.09250i) q^{36} -4.51416 q^{37} +2.61615i q^{38} +(-0.400473 + 1.68512i) q^{39} +3.47764i q^{40} +0.966521 q^{41} +(2.27789 - 9.58495i) q^{42} +3.07271i q^{43} +(4.03119 - 3.19206i) q^{44} +(-5.54007 + 10.9975i) q^{45} +10.1945i q^{46} +2.62300i q^{47} +(-7.91517 - 1.88106i) q^{48} -2.11269 q^{49} +22.3257 q^{50} +(-11.0687 - 2.63051i) q^{51} +1.55036i q^{52} -7.86994i q^{53} +(-7.48859 - 6.30720i) q^{54} +(8.45127 + 10.6729i) q^{55} +2.55756i q^{56} +(0.556032 - 2.33968i) q^{57} -11.4429 q^{58} +3.17057i q^{59} +(-2.54852 + 10.7237i) q^{60} +4.19576i q^{61} -11.5643 q^{62} +(-4.07433 + 8.08789i) q^{63} -4.08943 q^{64} -4.10471 q^{65} +(-9.80958 + 4.57536i) q^{66} -0.278169 q^{67} -10.1836 q^{68} +(2.16671 - 9.11713i) q^{69} +23.3476 q^{70} +1.72381i q^{71} +(2.26994 + 1.14350i) q^{72} -3.90626i q^{73} +8.50576 q^{74} +(-19.9663 - 4.74505i) q^{75} -2.15258i q^{76} +(6.21531 + 7.84917i) q^{77} +(0.754586 - 3.17517i) q^{78} -6.67487i q^{79} -19.2802i q^{80} +(5.35669 + 7.23228i) q^{81} -1.82116 q^{82} +6.62128 q^{83} +(-1.87425 + 7.88653i) q^{84} -26.9618i q^{85} -5.78972i q^{86} +(10.2336 + 2.43205i) q^{87} +(2.20294 - 1.74438i) q^{88} +17.4954i q^{89} +(10.4388 - 20.7219i) q^{90} -3.01872 q^{91} -8.38803i q^{92} +(10.3422 + 2.45784i) q^{93} -4.94237i q^{94} +5.69914 q^{95} +(12.0587 + 2.86579i) q^{96} -13.4604 q^{97} +3.98082 q^{98} +(9.74537 - 2.00694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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