LMFDB - Embedded newform 637.2.e.m.508.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.5
Root			$1.50426 + 2.60546i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.m.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00426 + 1.73943i) q^{2} +(0.879528 - 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(0.452861 + 0.784378i) q^{5} +3.53311 q^{6} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +O(q^{10})$	\(q+(1.00426 + 1.73943i) q^{2} +(0.879528 - 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(0.452861 + 0.784378i) q^{5} +3.53311 q^{6} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +(-0.909582 + 1.57544i) q^{10} +(-0.358181 + 0.620387i) q^{11} +(1.78911 + 3.09883i) q^{12} -1.00000 q^{13} +1.59322 q^{15} +(1.96525 + 3.40391i) q^{16} +(1.17614 - 2.03713i) q^{17} +(0.0946802 - 0.163991i) q^{18} +(3.31796 + 5.74687i) q^{19} -1.84239 q^{20} -1.43883 q^{22} +(-1.87953 - 3.25544i) q^{23} +(-0.0603641 + 0.104554i) q^{24} +(2.08983 - 3.61970i) q^{25} +(-1.00426 - 1.73943i) q^{26} +5.11133 q^{27} +3.25799 q^{29} +(1.60001 + 2.77129i) q^{30} +(0.785250 - 1.36009i) q^{31} +(-4.01588 + 6.95570i) q^{32} +(0.630060 + 1.09130i) q^{33} +4.72459 q^{34} +0.191778 q^{36} +(-2.60441 - 4.51098i) q^{37} +(-6.66419 + 11.5427i) q^{38} +(-0.879528 + 1.52339i) q^{39} +(-0.0310809 - 0.0538337i) q^{40} -4.92168 q^{41} -9.43766 q^{43} +(-0.728600 - 1.26197i) q^{44} +(0.0426950 - 0.0739499i) q^{45} +(3.77508 - 6.53863i) q^{46} +(-4.15993 - 7.20521i) q^{47} +6.91395 q^{48} +8.39497 q^{50} +(-2.06889 - 3.58342i) q^{51} +(1.01709 - 1.76164i) q^{52} +(-7.04163 + 12.1965i) q^{53} +(5.13311 + 8.89081i) q^{54} -0.648824 q^{55} +11.6729 q^{57} +(3.27188 + 5.66706i) q^{58} +(0.358181 - 0.620387i) q^{59} +(-1.62044 + 2.80668i) q^{60} +(-5.82633 - 10.0915i) q^{61} +3.15439 q^{62} -8.27099 q^{64} +(-0.452861 - 0.784378i) q^{65} +(-1.26549 + 2.19189i) q^{66} +(-4.69587 + 8.13349i) q^{67} +(2.39246 + 4.14386i) q^{68} -6.61239 q^{69} +10.9914 q^{71} +(0.00323527 + 0.00560366i) q^{72} +(-1.73650 + 3.00771i) q^{73} +(5.23103 - 9.06041i) q^{74} +(-3.67614 - 6.36725i) q^{75} -13.4986 q^{76} -3.53311 q^{78} +(-6.50408 - 11.2654i) q^{79} +(-1.77997 + 3.08299i) q^{80} +(4.63697 - 8.03147i) q^{81} +(-4.94265 - 8.56093i) q^{82} -3.54083 q^{83} +2.13050 q^{85} +(-9.47789 - 16.4162i) q^{86} +(2.86550 - 4.96318i) q^{87} +(0.0245828 - 0.0425786i) q^{88} +(6.02503 + 10.4357i) q^{89} +0.171508 q^{90} +7.64656 q^{92} +(-1.38130 - 2.39248i) q^{93} +(8.35532 - 14.4718i) q^{94} +(-3.00514 + 5.20506i) q^{95} +(7.06415 + 12.2355i) q^{96} -7.43766 q^{97} +0.0675374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00426	+	1.73943i	0.710121	+	1.22997i	0.964812	+	0.262942i	$0.0846930\pi$
$2$	1.00426	+	1.73943i	0.710121	+	1.22997i	−0.254691	+	0.967023i	$0.581974\pi$
$3$	0.879528	−	1.52339i	0.507796	−	0.879528i	−0.492164	−	0.870503i	$-0.663794\pi$
$3$	0.879528	−	1.52339i	0.507796	−	0.879528i	0.999959	−	0.00902528i	$-0.00287288\pi$
$4$	−1.01709	+	1.76164i	−0.508543	+	0.880822i
$5$	0.452861	+	0.784378i	0.202526	+	0.350784i	0.949342	−	0.314246i	$-0.101752\pi$
$5$	0.452861	+	0.784378i	0.202526	+	0.350784i	−0.746816	+	0.665031i	$0.768418\pi$
$6$	3.53311			1.44238
$7$		0			0
$7$		0			0
$8$	−0.0686323			−0.0242652
$9$	−0.0471392	−	0.0816475i	−0.0157131	−	0.0272158i
$10$	−0.909582	+	1.57544i	−0.287635	+	0.498199i
$11$	−0.358181	+	0.620387i	−0.107996	+	0.187054i	−0.914958	−	0.403549i	$-0.867777\pi$
$11$	−0.358181	+	0.620387i	−0.107996	+	0.187054i	0.806963	+	0.590603i	$0.201110\pi$
$12$	1.78911	+	3.09883i	0.516472	+	0.894555i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	1.59322			0.411366
$16$	1.96525	+	3.40391i	0.491311	+	0.850976i
$17$	1.17614	−	2.03713i	0.285255	−	0.494076i	−0.687416	−	0.726264i	$-0.741255\pi$
$17$	1.17614	−	2.03713i	0.285255	−	0.494076i	0.972671	+	0.232188i	$0.0745885\pi$
$18$	0.0946802	−	0.163991i	0.0223163	−	0.0386530i
$19$	3.31796	+	5.74687i	0.761191	+	1.31842i	0.942237	+	0.334947i	$0.108718\pi$
$19$	3.31796	+	5.74687i	0.761191	+	1.31842i	−0.181046	+	0.983475i	$0.557948\pi$
$20$	−1.84239			−0.411971
$21$		0			0
$22$	−1.43883			−0.306759
$23$	−1.87953	−	3.25544i	−0.391909	−	0.678806i	0.600793	−	0.799405i	$-0.294852\pi$
$23$	−1.87953	−	3.25544i	−0.391909	−	0.678806i	−0.992701	+	0.120599i	$0.961518\pi$
$24$	−0.0603641	+	0.104554i	−0.0123218	+	0.0213419i
$25$	2.08983	−	3.61970i	0.417967	−	0.723940i
$26$	−1.00426	−	1.73943i	−0.196952	−	0.341131i
$27$	5.11133			0.983675
$28$		0			0
$29$	3.25799			0.604994			0.302497	−	0.953150i	$-0.402180\pi$
$29$	3.25799			0.604994			0.302497	+	0.953150i	$0.402180\pi$
$30$	1.60001	+	2.77129i	0.292120	+	0.505966i
$31$	0.785250	−	1.36009i	0.141035	−	0.244280i	−0.786852	−	0.617142i	$-0.788290\pi$
$31$	0.785250	−	1.36009i	0.141035	−	0.244280i	0.927887	+	0.372862i	$0.121624\pi$
$32$	−4.01588	+	6.95570i	−0.709913	+	1.22961i
$33$	0.630060	+	1.09130i	0.109679	+	0.189970i
$34$	4.72459			0.810261
$35$		0			0
$36$	0.191778			0.0319631
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	0.568547	−	0.822651i	$-0.307506\pi$
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	−0.996710	+	0.0810508i	$0.974172\pi$
$38$	−6.66419	+	11.5427i	−1.08108	+	1.87248i
$39$	−0.879528	+	1.52339i	−0.140837	+	0.243937i
$40$	−0.0310809	−	0.0538337i	−0.00491432	−	0.00851185i
$41$	−4.92168			−0.768637			−0.384318	−	0.923201i	$-0.625563\pi$
$41$	−4.92168			−0.768637			−0.384318	+	0.923201i	$0.625563\pi$
$42$		0			0
$43$	−9.43766			−1.43923			−0.719615	−	0.694373i	$-0.755682\pi$
$43$	−9.43766			−1.43923			−0.719615	+	0.694373i	$0.755682\pi$
$44$	−0.728600	−	1.26197i	−0.109841	−	0.190250i
$45$	0.0426950	−	0.0739499i	0.00636459	−	0.0110238i
$46$	3.77508	−	6.53863i	0.556605	−	0.964068i
$47$	−4.15993	−	7.20521i	−0.606788	−	1.05099i	−0.991766	−	0.128062i	$-0.959124\pi$
$47$	−4.15993	−	7.20521i	−0.606788	−	1.05099i	0.384978	−	0.922926i	$-0.374209\pi$
$48$	6.91395			0.997943
$49$		0			0
$50$	8.39497			1.18723
$51$	−2.06889	−	3.58342i	−0.289702	−	0.501779i
$52$	1.01709	−	1.76164i	0.141044	−	0.244296i
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.263777	+	0.964584i	$0.584968\pi$
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.703465	+	0.710729i	$0.748365\pi$
$54$	5.13311	+	8.89081i	0.698528	+	1.20989i
$55$	−0.648824			−0.0874874
$56$		0			0
$57$	11.6729			1.54612
$58$	3.27188	+	5.66706i	0.429619	+	0.744122i
$59$	0.358181	−	0.620387i	0.0466311	−	0.0807675i	−0.841768	−	0.539840i	$-0.818485\pi$
$59$	0.358181	−	0.620387i	0.0466311	−	0.0807675i	0.888399	+	0.459072i	$0.151818\pi$
$60$	−1.62044	+	2.80668i	−0.209197	+	0.362340i
$61$	−5.82633	−	10.0915i	−0.745986	−	1.29208i	−0.949733	−	0.313061i	$-0.898645\pi$
$61$	−5.82633	−	10.0915i	−0.745986	−	1.29208i	0.203747	−	0.979024i	$-0.434688\pi$
$62$	3.15439			0.400607
$63$		0			0
$64$	−8.27099			−1.03387
$65$	−0.452861	−	0.784378i	−0.0561705	−	0.0972901i
$66$	−1.26549	+	2.19189i	−0.155771	+	0.269803i
$67$	−4.69587	+	8.13349i	−0.573692	+	0.993664i	0.422490	+	0.906367i	$0.361156\pi$
$67$	−4.69587	+	8.13349i	−0.573692	+	0.993664i	−0.996182	+	0.0872964i	$0.972177\pi$
$68$	2.39246	+	4.14386i	0.290128	+	0.502517i
$69$	−6.61239			−0.796038
$70$		0			0
$71$	10.9914			1.30444			0.652220	−	0.758030i	$-0.273838\pi$
$71$	10.9914			1.30444			0.652220	+	0.758030i	$0.273838\pi$
$72$	0.00323527	+	0.00560366i	0.000381281	+	0.000660397i
$73$	−1.73650	+	3.00771i	−0.203242	+	0.352025i	−0.949571	−	0.313552i	$-0.898481\pi$
$73$	−1.73650	+	3.00771i	−0.203242	+	0.352025i	0.746329	+	0.665577i	$0.231814\pi$
$74$	5.23103	−	9.06041i	0.608095	−	1.05325i
$75$	−3.67614	−	6.36725i	−0.424484	−	0.735227i
$76$	−13.4986			−1.54839
$77$		0			0
$78$	−3.53311			−0.400046
$79$	−6.50408	−	11.2654i	−0.731766	−	1.26746i	−0.956128	−	0.292950i	$-0.905363\pi$
$79$	−6.50408	−	11.2654i	−0.731766	−	1.26746i	0.224361	−	0.974506i	$-0.427970\pi$
$80$	−1.77997	+	3.08299i	−0.199006	+	0.344689i
$81$	4.63697	−	8.03147i	0.515219	−	0.892386i
$82$	−4.94265	−	8.56093i	−0.545825	−	0.945396i
$83$	−3.54083			−0.388656			−0.194328	−	0.980937i	$-0.562253\pi$
$83$	−3.54083			−0.388656			−0.194328	+	0.980937i	$0.562253\pi$
$84$		0			0
$85$	2.13050			0.231085
$86$	−9.47789	−	16.4162i	−1.02203	−	1.77020i
$87$	2.86550	−	4.96318i	0.307213	−	0.532109i
$88$	0.0245828	−	0.0425786i	0.00262053	−	0.00453889i
$89$	6.02503	+	10.4357i	0.638651	+	1.10618i	0.985729	+	0.168340i	$0.0538408\pi$
$89$	6.02503	+	10.4357i	0.638651	+	1.10618i	−0.347077	+	0.937836i	$0.612826\pi$
$90$	0.171508			0.0180785
$91$		0			0
$92$	7.64656			0.797209
$93$	−1.38130	−	2.39248i	−0.143234	−	0.248088i
$94$	8.35532	−	14.4718i	0.861786	−	1.49266i
$95$	−3.00514	+	5.20506i	−0.308321	+	0.534028i
$96$	7.06415	+	12.2355i	0.720982	+	1.24878i
$97$	−7.43766			−0.755180			−0.377590	−	0.925973i	$-0.623247\pi$
$97$	−7.43766			−0.755180			−0.377590	+	0.925973i	$0.623247\pi$
$98$		0			0
$99$	0.0675374			0.00678776
$100$	4.25108	+	7.36309i	0.425108	+	0.736309i
$101$	−0.599526	+	1.03841i	−0.0596551	+	0.103326i	−0.894311	−	0.447447i	$-0.852333\pi$
$101$	−0.599526	+	1.03841i	−0.0596551	+	0.103326i	0.834656	+	0.550772i	$0.185667\pi$
$102$	4.15541	−	7.19739i	0.411447	−	0.712647i
$103$	−7.20615	−	12.4814i	−0.710043	−	1.22983i	−0.964840	−	0.262837i	$-0.915342\pi$
$103$	−7.20615	−	12.4814i	−0.710043	−	1.22983i	0.254797	−	0.966995i	$-0.417991\pi$
$104$	0.0686323			0.00672995
$105$		0			0
$106$	−28.2866			−2.74744
$107$	−6.79661	−	11.7721i	−0.657053	−	1.13805i	−0.981375	−	0.192102i	$-0.938469\pi$
$107$	−6.79661	−	11.7721i	−0.657053	−	1.13805i	0.324322	−	0.945947i	$-0.394864\pi$
$108$	−5.19866	+	9.00434i	−0.500241	+	0.866443i
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	−0.324013	−	0.946053i	$-0.605032\pi$
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	0.981312	−	0.192423i	$-0.0616346\pi$
$110$	−0.651589	−	1.12859i	−0.0621266	−	0.107606i
$111$	−9.16262			−0.869677
$112$		0			0
$113$	−3.25799			−0.306486			−0.153243	−	0.988189i	$-0.548972\pi$
$113$	−3.25799			−0.306486			−0.153243	+	0.988189i	$0.548972\pi$
$114$	11.7227	+	20.3043i	1.09793	+	1.90167i
$115$	1.70233	−	2.94852i	0.158743	−	0.274951i
$116$	−3.31366	+	5.73942i	−0.307665	+	0.532892i
$117$	0.0471392	+	0.0816475i	0.00435802	+	0.00754831i
$118$	1.43883			0.132455
$119$		0			0
$120$	−0.109346			−0.00998189
$121$	5.24341	+	9.08186i	0.476674	+	0.825623i
$122$	11.7023	−	20.2690i	1.05948	−	1.83507i
$123$	−4.32875	+	7.49762i	−0.390310	+	0.676037i
$124$	1.59733	+	2.76666i	0.143445	+	0.248453i
$125$	8.31422			0.743647
$126$		0			0
$127$	−0.950834			−0.0843729			−0.0421865	−	0.999110i	$-0.513432\pi$
$127$	−0.950834			−0.0843729			−0.0421865	+	0.999110i	$0.513432\pi$
$128$	−0.274489	−	0.475429i	−0.0242617	−	0.0420224i
$129$	−8.30069	+	14.3772i	−0.730835	+	1.26584i
$130$	0.909582	−	1.57544i	0.0797756	−	0.138175i
$131$	−9.40980	−	16.2983i	−0.822138	−	1.42399i	−0.904087	−	0.427349i	$-0.859448\pi$
$131$	−9.40980	−	16.2983i	−0.822138	−	1.42399i	0.0819487	−	0.996637i	$-0.473886\pi$
$132$	−2.56330			−0.223106
$133$		0			0
$134$	−18.8635			−1.62956
$135$	2.31472	+	4.00921i	0.199219	+	0.345058i
$136$	−0.0807209	+	0.139813i	−0.00692176	+	0.0119888i
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	−0.967320	−	0.253557i	$-0.918399\pi$
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	0.703247	+	0.710945i	$0.251733\pi$
$138$	−6.64057	−	11.5018i	−0.565283	−	0.979099i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−14.6351			−1.23250
$142$	11.0383	+	19.1188i	0.926309	+	1.60441i
$143$	0.358181	−	0.620387i	0.0299526	−	0.0518794i
$144$	0.185280	−	0.320915i	0.0154400	−	0.0267429i
$145$	1.47542	+	2.55550i	0.122527	+	0.212223i
$146$	−6.97560			−0.577305
$147$		0			0
$148$	10.5956			0.870956
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	0.868675	+	0.495382i	$0.164972\pi$
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	−0.00532425	+	0.999986i	$0.501695\pi$
$150$	7.38361	−	12.7888i	0.602869	−	1.04420i
$151$	7.86171	−	13.6169i	0.639777	−	1.10813i	−0.345704	−	0.938344i	$-0.612360\pi$
$151$	7.86171	−	13.6169i	0.639777	−	1.10813i	0.985481	−	0.169783i	$-0.0543067\pi$
$152$	−0.227719	−	0.394421i	−0.0184705	−	0.0319918i
$153$	−0.221768			−0.0179289
$154$		0			0
$155$	1.42244			0.114253
$156$	−1.78911	−	3.09883i	−0.143243	−	0.248105i
$157$	−3.89250	+	6.74200i	−0.310655	+	0.538070i	−0.978504	−	0.206226i	$-0.933882\pi$
$157$	−3.89250	+	6.74200i	−0.310655	+	0.538070i	0.667849	+	0.744297i	$0.267215\pi$
$158$	13.0636	−	22.6268i	1.03928	−	1.80009i
$159$	12.3866	+	21.4543i	0.982323	+	1.70143i
$160$	−7.27453			−0.575102
$161$		0			0
$162$	18.6269			1.46347
$163$	−0.844956	−	1.46351i	−0.0661820	−	0.114631i	0.831036	−	0.556219i	$-0.187748\pi$
$163$	−0.844956	−	1.46351i	−0.0661820	−	0.114631i	−0.897218	+	0.441588i	$0.854415\pi$
$164$	5.00576	−	8.67024i	0.390884	−	0.677032i
$165$	−0.570659	+	0.988410i	−0.0444257	+	0.0769476i
$166$	−3.55592	−	6.15903i	−0.275993	−	0.478034i
$167$	21.8667			1.69210			0.846049	−	0.533105i	$-0.178975\pi$
$167$	21.8667			1.69210			0.846049	+	0.533105i	$0.178975\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	2.13958	+	3.70587i	0.164099	+	0.284227i
$171$	0.312812	−	0.541805i	0.0239213	−	0.0414329i
$172$	9.59891	−	16.6258i	0.731910	−	1.26770i
$173$	2.92061	+	5.05865i	0.222050	+	0.384602i	0.955430	−	0.295217i	$-0.0953918\pi$
$173$	2.92061	+	5.05865i	0.222050	+	0.384602i	−0.733380	+	0.679819i	$0.762058\pi$
$174$	11.5108			0.872634
$175$		0			0
$176$	−2.81565			−0.212238
$177$	−0.630060	−	1.09130i	−0.0473582	−	0.0820268i
$178$	−12.1014	+	20.9603i	−0.907039	+	1.57104i
$179$	−1.26714	+	2.19475i	−0.0947103	+	0.164043i	−0.909488	−	0.415731i	$-0.863526\pi$
$179$	−1.26714	+	2.19475i	−0.0947103	+	0.164043i	0.814777	+	0.579774i	$0.196859\pi$
$180$	0.0868489	+	0.150427i	0.00647333	+	0.0112121i
$181$	10.7248			0.797169			0.398585	−	0.917132i	$-0.369502\pi$
$181$	10.7248			0.797169			0.398585	+	0.917132i	$0.369502\pi$
$182$		0			0
$183$	−20.4977			−1.51523
$184$	0.128996	+	0.223428i	0.00950974	+	0.0164714i
$185$	2.35887	−	4.08569i	0.173428	−	0.300386i
$186$	2.77437	−	4.80535i	0.203427	−	0.352345i
$187$	0.842538	+	1.45932i	0.0616125	+	0.106716i
$188$	16.9240			1.23431
$189$		0			0
$190$	−12.0718			−0.875781
$191$	0.839303	+	1.45371i	0.0607298	+	0.105187i	0.894792	−	0.446484i	$-0.147324\pi$
$191$	0.839303	+	1.45371i	0.0607298	+	0.105187i	−0.834062	+	0.551671i	$0.813991\pi$
$192$	−7.27457	+	12.5999i	−0.524997	+	0.909321i
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	−0.726344	−	0.687331i	$-0.758782\pi$
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	0.958418	+	0.285367i	$0.0921154\pi$
$194$	−7.46936	−	12.9373i	−0.536269	−	0.928845i
$195$	−1.59322			−0.114093
$196$		0			0
$197$	1.87251			0.133411			0.0667054	−	0.997773i	$-0.478751\pi$
$197$	1.87251			0.133411			0.0667054	+	0.997773i	$0.478751\pi$
$198$	0.0678252	+	0.117477i	0.00482013	+	0.00834871i
$199$	−5.69833	+	9.86979i	−0.403944	+	0.699651i	−0.994198	−	0.107566i	$-0.965694\pi$
$199$	−5.69833	+	9.86979i	−0.403944	+	0.699651i	0.590254	+	0.807217i	$0.299028\pi$
$200$	−0.143430	+	0.248428i	−0.0101420	+	0.0175665i
$201$	8.26030	+	14.3073i	0.582637	+	1.00916i
$202$	−2.40833			−0.169449
$203$		0			0
$204$	8.41694			0.589304
$205$	−2.22883	−	3.86045i	−0.155669	−	0.269626i
$206$	14.4737	−	25.0692i	1.00843	−	1.74666i
$207$	−0.177199	+	0.306918i	−0.0123162	+	0.0213322i
$208$	−1.96525	−	3.40391i	−0.136265	−	0.236018i
$209$	−4.75371			−0.328821
$210$		0			0
$211$	7.53599			0.518799			0.259400	−	0.965770i	$-0.416475\pi$
$211$	7.53599			0.518799			0.259400	+	0.965770i	$0.416475\pi$
$212$	−14.3239	−	24.8097i	−0.983768	−	1.70394i
$213$	9.66725	−	16.7442i	0.662389	−	1.14729i
$214$	13.6512	−	23.6445i	0.933174	−	1.61630i
$215$	−4.27395	−	7.40269i	−0.291481	−	0.504859i
$216$	−0.350802			−0.0238691
$217$		0			0
$218$	27.5666			1.86705
$219$	3.05460	+	5.29072i	0.206411	+	0.357514i
$220$	0.659909	−	1.14300i	0.0444911	−	0.0770608i
$221$	−1.17614	+	2.03713i	−0.0791154	+	0.137032i
$222$	−9.20167	−	15.9378i	−0.617576	−	1.06967i
$223$	−17.6349			−1.18092			−0.590459	−	0.807067i	$-0.701053\pi$
$223$	−17.6349			−1.18092			−0.590459	+	0.807067i	$0.701053\pi$
$224$		0			0
$225$	−0.394052			−0.0262702
$226$	−3.27188	−	5.66706i	−0.217642	−	0.376967i
$227$	−2.66452	+	4.61509i	−0.176851	+	0.306314i	−0.940800	−	0.338962i	$-0.889924\pi$
$227$	−2.66452	+	4.61509i	−0.176851	+	0.306314i	0.763950	+	0.645276i	$0.223258\pi$
$228$	−11.8724	+	20.5636i	−0.786267	+	1.36185i
$229$	−4.25950	−	7.37767i	−0.281476	−	0.487530i	0.690273	−	0.723549i	$-0.257491\pi$
$229$	−4.25950	−	7.37767i	−0.281476	−	0.487530i	−0.971748	+	0.236019i	$0.924157\pi$
$230$	6.83834			0.450907
$231$		0			0
$232$	−0.223604			−0.0146803
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	0.777605	−	0.628752i	$-0.216434\pi$
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	−0.933318	+	0.359050i	$0.883101\pi$
$234$	−0.0946802	+	0.163991i	−0.00618944	+	0.0107204i
$235$	3.76774	−	6.52592i	0.245780	−	0.425704i
$236$	0.728600	+	1.26197i	0.0474278	+	0.0821474i
$237$	−22.8821			−1.48635
$238$		0			0
$239$	14.8314			0.959365			0.479682	−	0.877442i	$-0.340752\pi$
$239$	14.8314			0.959365			0.479682	+	0.877442i	$0.340752\pi$
$240$	3.13106	+	5.42315i	0.202109	+	0.350063i
$241$	−3.06066	+	5.30121i	−0.197154	+	0.341481i	−0.947605	−	0.319446i	$-0.896503\pi$
$241$	−3.06066	+	5.30121i	−0.197154	+	0.341481i	0.750450	+	0.660927i	$0.229837\pi$
$242$	−10.5315	+	18.2411i	−0.676992	+	1.17258i
$243$	−0.489705	−	0.848195i	−0.0314146	−	0.0544117i
$244$	23.7035			1.51746
$245$		0			0
$246$	−17.3888			−1.10867
$247$	−3.31796	−	5.74687i	−0.211116	−	0.365664i
$248$	−0.0538935	+	0.0933463i	−0.00342224	+	0.00592750i
$249$	−3.11426	+	5.39405i	−0.197358	+	0.341834i
$250$	8.34966	+	14.4620i	0.528079	+	0.914660i
$251$	13.9708			0.881832			0.440916	−	0.897548i	$-0.354654\pi$
$251$	13.9708			0.881832			0.440916	+	0.897548i	$0.354654\pi$
$252$		0			0
$253$	2.69284			0.169298
$254$	−0.954887	−	1.65391i	−0.0599149	−	0.103776i
$255$	1.87384	−	3.24558i	0.117344	−	0.203246i
$256$	−7.71967	+	13.3709i	−0.482479	+	0.835679i
$257$	8.63253	+	14.9520i	0.538482	+	0.932679i	0.998986	+	0.0450210i	$0.0143355\pi$
$257$	8.63253	+	14.9520i	0.538482	+	0.932679i	−0.460504	+	0.887658i	$0.652331\pi$
$258$	−33.3443			−2.07592
$259$		0			0
$260$	1.84239			0.114260
$261$	−0.153579	−	0.266007i	−0.00950631	−	0.0164654i
$262$	18.8998	−	32.7354i	1.16763	−	2.02240i
$263$	1.30336	−	2.25749i	0.0803687	−	0.139203i	−0.823040	−	0.567984i	$-0.807724\pi$
$263$	1.30336	−	2.25749i	0.0803687	−	0.139203i	0.903408	+	0.428781i	$0.141057\pi$
$264$	−0.0432425	−	0.0748982i	−0.00266139	−	0.00460966i
$265$	−12.7555			−0.783565
$266$		0			0
$267$	21.1967			1.29722
$268$	−9.55221	−	16.5449i	−0.583494	−	1.01064i
$269$	−7.24477	+	12.5483i	−0.441721	+	0.765084i	−0.997817	−	0.0660343i	$-0.978965\pi$
$269$	−7.24477	+	12.5483i	−0.441721	+	0.765084i	0.556096	+	0.831118i	$0.312299\pi$
$270$	−4.64917	+	8.05260i	−0.282940	+	0.490066i
$271$	−4.31796	−	7.47892i	−0.262297	−	0.454312i	0.704555	−	0.709650i	$-0.251147\pi$
$271$	−4.31796	−	7.47892i	−0.262297	−	0.454312i	−0.966852	+	0.255338i	$0.917813\pi$
$272$	9.24558			0.560596
$273$		0			0
$274$	−12.4163			−0.750095
$275$	1.49708	+	2.59301i	0.0902771	+	0.156364i
$276$	6.72537	−	11.6487i	0.404819	−	0.701168i
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	−0.989146	−	0.146935i	$-0.953059\pi$
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	0.621822	+	0.783158i	$0.286393\pi$
$278$	4.01705	+	6.95773i	0.240927	+	0.417297i
$279$	−0.148064			−0.00886437
$280$		0			0
$281$	−24.1822			−1.44259			−0.721293	−	0.692630i	$-0.756452\pi$
$281$	−24.1822			−1.44259			−0.721293	+	0.692630i	$0.756452\pi$
$282$	−14.6975	−	25.4568i	−0.875222	−	1.51593i
$283$	−15.3842	+	26.6461i	−0.914493	+	1.58395i	−0.106851	+	0.994275i	$0.534077\pi$
$283$	−15.3842	+	26.6461i	−0.914493	+	1.58395i	−0.807642	+	0.589674i	$0.799256\pi$
$284$	−11.1792	+	19.3629i	−0.663363	+	1.14898i
$285$	5.28622	+	9.15599i	0.313128	+	0.542354i
$286$	1.43883			0.0850797
$287$		0			0
$288$	0.757221			0.0446197
$289$	5.73341	+	9.93056i	0.337259	+	0.584150i
$290$	−2.96341	+	5.13278i	−0.174018	+	0.301407i
$291$	−6.54163	+	11.3304i	−0.383477	+	0.664202i
$292$	−3.53234	−	6.11819i	−0.206714	−	0.358040i
$293$	31.8295			1.85950			0.929749	−	0.368193i	$-0.120024\pi$
$293$	31.8295			1.85950			0.929749	+	0.368193i	$0.120024\pi$
$294$		0			0
$295$	0.648824			0.0377760
$296$	0.178747	+	0.309599i	0.0103895	+	0.0179951i
$297$	−1.83078	+	3.17100i	−0.106233	+	0.184000i
$298$	−21.1669	+	36.6622i	−1.22617	+	2.12378i
$299$	1.87953	+	3.25544i	0.108696	+	0.188267i
$300$	14.9558			0.863472
$301$		0			0
$302$	31.5809			1.81728
$303$	1.05460	+	1.82662i	0.0605852	+	0.104937i
$304$	−13.0412	+	22.5880i	−0.747964	+	1.29551i
$305$	5.27704	−	9.14010i	0.302162	−	0.523360i
$306$	−0.222714	−	0.385751i	−0.0127317	−	0.0220519i
$307$	−28.7884			−1.64304			−0.821520	−	0.570179i	$-0.806874\pi$
$307$	−28.7884			−1.64304			−0.821520	+	0.570179i	$0.806874\pi$
$308$		0			0
$309$	−25.3521			−1.44223
$310$	1.42850	+	2.47423i	0.0811332	+	0.140527i
$311$	2.75931	−	4.77927i	0.156466	−	0.271007i	−0.777126	−	0.629345i	$-0.783323\pi$
$311$	2.75931	−	4.77927i	0.156466	−	0.271007i	0.933592	+	0.358338i	$0.116656\pi$
$312$	0.0603641	−	0.104554i	0.00341744	−	0.00591918i
$313$	−2.42399	−	4.19848i	−0.137012	−	0.237312i	0.789352	−	0.613941i	$-0.210417\pi$
$313$	−2.42399	−	4.19848i	−0.137012	−	0.237312i	−0.926364	+	0.376629i	$0.877083\pi$
$314$	−15.6363			−0.882410
$315$		0			0
$316$	26.4608			1.48854
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	0.953265	−	0.302134i	$-0.0976990\pi$
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	−0.738288	+	0.674485i	$0.764366\pi$
$318$	−24.8788	+	43.0914i	−1.39514	+	2.41645i
$319$	−1.16695	+	2.02122i	−0.0653366	+	0.113166i
$320$	−3.74561	−	6.48758i	−0.209386	−	0.362667i
$321$	−23.9112			−1.33459
$322$		0			0
$323$	15.6095			0.868534
$324$	9.43239	+	16.3374i	0.524022	+	0.907633i
$325$	−2.08983	+	3.61970i	−0.115923	+	0.200785i
$326$	1.69711	−	2.93949i	0.0939945	−	0.162803i
$327$	−12.0714	−	20.9082i	−0.667548	−	1.15623i
$328$	0.337786			0.0186511
$329$		0			0
$330$	−2.29236			−0.126190
$331$	−5.67159	−	9.82348i	−0.311739	−	0.539947i	0.667000	−	0.745058i	$-0.267578\pi$
$331$	−5.67159	−	9.82348i	−0.311739	−	0.539947i	−0.978739	+	0.205110i	$0.934245\pi$
$332$	3.60132	−	6.23768i	0.197648	−	0.342337i
$333$	−0.245540	+	0.425288i	−0.0134555	+	0.0233056i
$334$	21.9599	+	38.0357i	1.20159	+	2.08122i
$335$	−8.50631			−0.464749
$336$		0			0
$337$	1.74149			0.0948649			0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149			0.0948649			0.0474324	+	0.998874i	$0.484896\pi$
$338$	1.00426	+	1.73943i	0.0546247	+	0.0946127i
$339$	−2.86550	+	4.96318i	−0.155632	+	0.269563i
$340$	−2.16690	+	3.75319i	−0.117517	+	0.203545i
$341$	0.562522	+	0.974317i	0.0304623	+	0.0527622i
$342$	1.25658			0.0679480
$343$		0			0
$344$	0.647729			0.0349232
$345$	−2.99449	−	5.18661i	−0.161218	−	0.279238i
$346$	−5.86612	+	10.1604i	−0.315365	+	0.546228i
$347$	−10.5251	+	18.2301i	−0.565019	+	0.978641i	0.432029	+	0.901860i	$0.357798\pi$
$347$	−10.5251	+	18.2301i	−0.565019	+	0.978641i	−0.997048	+	0.0767814i	$0.975536\pi$
$348$	5.82891	+	10.0960i	0.312462	+	0.541200i
$349$	8.35601			0.447287			0.223643	−	0.974671i	$-0.428205\pi$
$349$	8.35601			0.447287			0.223643	+	0.974671i	$0.428205\pi$
$350$		0			0
$351$	−5.11133			−0.272822
$352$	−2.87682	−	4.98279i	−0.153335	−	0.265584i
$353$	−4.26677	+	7.39027i	−0.227097	+	0.393344i	−0.956947	−	0.290264i	$-0.906257\pi$
$353$	−4.26677	+	7.39027i	−0.227097	+	0.393344i	0.729849	+	0.683608i	$0.239590\pi$
$354$	1.26549	−	2.19189i	0.0672601	−	0.116498i
$355$	4.97758	+	8.62141i	0.264182	+	0.457577i
$356$	−24.5119			−1.29913
$357$		0			0
$358$	−5.09015			−0.269023
$359$	8.08565	+	14.0047i	0.426744	+	0.739142i	0.996582	−	0.0826150i	$-0.0263272\pi$
$359$	8.08565	+	14.0047i	0.426744	+	0.739142i	−0.569837	+	0.821757i	$0.692994\pi$
$360$	−0.00293026	+	0.00507535i	−0.000154438	+	0.000267495i
$361$	−12.5177	+	21.6812i	−0.658824	+	1.14112i
$362$	10.7705	+	18.6551i	0.566086	+	0.980490i
$363$	18.4469			0.968212
$364$		0			0
$365$	−3.14557			−0.164647
$366$	−20.5851	−	35.6544i	−1.07600	−	1.86368i
$367$	14.0770	−	24.3821i	0.734813	−	1.27273i	−0.219992	−	0.975502i	$-0.570603\pi$
$367$	14.0770	−	24.3821i	0.734813	−	1.27273i	0.954805	−	0.297232i	$-0.0960636\pi$
$368$	7.38747	−	12.7955i	0.385098	−	0.667010i
$369$	0.232004	+	0.401842i	0.0120776	+	0.0209191i
$370$	9.47571			0.492619
$371$		0			0
$372$	5.61959			0.291362
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	0.953425	+	0.301630i	$0.0975308\pi$
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	−0.215493	+	0.976505i	$0.569136\pi$
$374$	−1.69226	+	2.93108i	−0.0875046	+	0.151562i
$375$	7.31259	−	12.6658i	0.377621	−	0.654058i
$376$	0.285506	+	0.494511i	0.0147238	+	0.0255024i
$377$	−3.25799			−0.167795
$378$		0			0
$379$	−7.26263			−0.373056			−0.186528	−	0.982450i	$-0.559724\pi$
$379$	−7.26263			−0.373056			−0.186528	+	0.982450i	$0.559724\pi$
$380$	−6.11297	−	10.5880i	−0.313589	−	0.543152i
$381$	−0.836286	+	1.44849i	−0.0428442	+	0.0742083i
$382$	−1.68576	+	2.91982i	−0.0862510	+	0.149391i
$383$	6.46627	+	11.1999i	0.330411	+	0.572289i	0.982592	−	0.185774i	$-0.0594793\pi$
$383$	6.46627	+	11.1999i	0.330411	+	0.572289i	−0.652181	+	0.758063i	$0.726146\pi$
$384$	−0.965684			−0.0492799
$385$		0			0
$386$	12.9513			0.659203
$387$	0.444884	+	0.770561i	0.0226147	+	0.0391698i
$388$	7.56474	−	13.1025i	0.384041	−	0.665179i
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	−0.463312	−	0.886195i	$-0.653339\pi$
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	0.999124	−	0.0418574i	$-0.0133275\pi$
$390$	−1.60001	−	2.77129i	−0.0810194	−	0.140330i
$391$	−8.84232			−0.447175
$392$		0			0
$393$	−33.1047			−1.66991
$394$	1.88049	+	3.25711i	0.0947378	+	0.164091i
$395$	5.89089	−	10.2033i	0.296403	−	0.513384i
$396$	−0.0686913	+	0.118977i	−0.00345187	+	0.00597881i
$397$	9.60366	+	16.6340i	0.481994	+	0.834838i	0.999786	−	0.0206683i	$-0.00657938\pi$
$397$	9.60366	+	16.6340i	0.481994	+	0.834838i	−0.517792	+	0.855506i	$0.673246\pi$
$398$	−22.8905			−1.14740
$399$		0			0
$400$	16.4282			0.821408
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	0.579344	−	0.815083i	$-0.303309\pi$
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	−0.995555	+	0.0941856i	$0.969975\pi$
$402$	−16.5910	+	28.7365i	−0.827485	+	1.43325i
$403$	−0.785250	+	1.36009i	−0.0391161	+	0.0677510i
$404$	−1.21954	−	2.11230i	−0.0606743	−	0.105091i
$405$	8.39961			0.417380
$406$		0			0
$407$	3.73140			0.184959
$408$	0.141993	+	0.245939i	0.00702968	+	0.0121758i
$409$	6.17416	−	10.6940i	0.305293	−	0.528782i	−0.672034	−	0.740520i	$-0.734579\pi$
$409$	6.17416	−	10.6940i	0.305293	−	0.528782i	0.977326	+	0.211738i	$0.0679124\pi$
$410$	4.47667	−	7.75382i	0.221087	−	0.382934i
$411$	5.43706	+	9.41727i	0.268190	+	0.464520i
$412$	29.3171			1.44435
$413$		0			0
$414$	−0.711817			−0.0349839
$415$	−1.60350	−	2.77735i	−0.0787128	−	0.136335i
$416$	4.01588	−	6.95570i	0.196895	−	0.341031i
$417$	3.51811	−	6.09355i	0.172283	−	0.298402i
$418$	−4.77397	−	8.26876i	−0.233502	−	0.404438i
$419$	−4.35934			−0.212968			−0.106484	−	0.994314i	$-0.533959\pi$
$419$	−4.35934			−0.212968			−0.106484	+	0.994314i	$0.533959\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	7.56811	+	13.1084i	0.368410	+	0.638105i
$423$	−0.392192	+	0.679296i	−0.0190690	+	0.0330285i
$424$	0.483284	−	0.837072i	0.0234703	−	0.0406518i
$425$	−4.91586	−	8.51451i	−0.238454	−	0.413015i
$426$	38.8338			1.88150
$427$		0			0
$428$	27.6509			1.33656
$429$	−0.630060	−	1.09130i	−0.0304196	−	0.0526882i
$430$	8.58433	−	14.8685i	0.413973	−	0.717022i
$431$	11.6813	−	20.2326i	0.562667	−	0.974569i	−0.434595	−	0.900626i	$-0.643109\pi$
$431$	11.6813	−	20.2326i	0.562667	−	0.974569i	0.997262	−	0.0739426i	$-0.0235582\pi$
$432$	10.0450	+	17.3985i	0.483291	+	0.837084i
$433$	2.71285			0.130371			0.0651856	−	0.997873i	$-0.479236\pi$
$433$	2.71285			0.130371			0.0651856	+	0.997873i	$0.479236\pi$
$434$		0			0
$435$	5.19068			0.248874
$436$	13.9593	+	24.1782i	0.668529	+	1.15793i
$437$	12.4724	−	21.6028i	0.596635	−	1.03340i
$438$	−6.13524	+	10.6265i	−0.293153	+	0.507756i
$439$	−4.41760	−	7.65150i	−0.210840	−	0.365186i	0.741137	−	0.671353i	$-0.234287\pi$
$439$	−4.41760	−	7.65150i	−0.210840	−	0.365186i	−0.951978	+	0.306167i	$0.900953\pi$
$440$	0.0445303			0.00212290
$441$		0			0
$442$	−4.72459			−0.224726
$443$	1.45279	+	2.51630i	0.0690240	+	0.119553i	0.898472	−	0.439031i	$-0.144678\pi$
$443$	1.45279	+	2.51630i	0.0690240	+	0.119553i	−0.829448	+	0.558584i	$0.811345\pi$
$444$	9.31917	−	16.1413i	0.442268	−	0.766031i
$445$	−5.45700	+	9.45179i	−0.258686	+	0.448058i
$446$	−17.7100	−	30.6747i	−0.838595	−	1.45249i
$447$	37.0758			1.75362
$448$		0			0
$449$	−15.2777			−0.720998			−0.360499	−	0.932760i	$-0.617394\pi$
$449$	−15.2777			−0.720998			−0.360499	+	0.932760i	$0.617394\pi$
$450$	−0.395732	−	0.685428i	−0.0186550	−	0.0323114i
$451$	1.76285	−	3.05334i	0.0830093	−	0.143776i
$452$	3.31366	−	5.73942i	0.155861	−	0.269960i
$453$	−13.8292	−	23.9529i	−0.649752	−	1.12540i
$454$	−10.7035			−0.502341
$455$		0			0
$456$	−0.801141			−0.0375169
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	−0.998027	−	0.0627815i	$-0.980003\pi$
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	0.444643	−	0.895708i	$-0.353330\pi$
$458$	8.55531	−	14.8182i	0.399763	−	0.692410i
$459$	6.01161	−	10.4124i	0.280598	−	0.486010i
$460$	3.46283	+	5.99779i	0.161455	+	0.279649i
$461$	26.6170			1.23968			0.619839	−	0.784729i	$-0.287198\pi$
$461$	26.6170			1.23968			0.619839	+	0.784729i	$0.287198\pi$
$462$		0			0
$463$	−1.44250			−0.0670385			−0.0335193	−	0.999438i	$-0.510672\pi$
$463$	−1.44250			−0.0670385			−0.0335193	+	0.999438i	$0.510672\pi$
$464$	6.40276	+	11.0899i	0.297240	+	0.514836i
$465$	1.25107	−	2.16692i	0.0580171	−	0.100488i
$466$	4.77397	−	8.26876i	0.221150	−	0.383043i
$467$	−4.19480	−	7.26560i	−0.194112	−	0.336212i	0.752497	−	0.658596i	$-0.228849\pi$
$467$	−4.19480	−	7.26560i	−0.194112	−	0.336212i	−0.946609	+	0.322384i	$0.895516\pi$
$468$	−0.191778			−0.00886496
$469$		0			0
$470$	15.1352			0.698135
$471$	6.84712	+	11.8596i	0.315499	+	0.546460i
$472$	−0.0245828	+	0.0425786i	−0.00113151	+	0.00195984i
$473$	3.38039	−	5.85500i	0.155430	−	0.269213i
$474$	−22.9796	−	39.8019i	−1.05549	−	1.82816i
$475$	27.7359			1.27261
$476$		0			0
$477$	1.32775			0.0607934
$478$	14.8946	+	25.7983i	0.681265	+	1.17999i
$479$	6.30608	−	10.9225i	0.288132	−	0.499060i	−0.685232	−	0.728325i	$-0.740299\pi$
$479$	6.30608	−	10.9225i	0.288132	−	0.499060i	0.973364	+	0.229265i	$0.0736324\pi$
$480$	−6.39815	+	11.0819i	−0.292034	+	0.505819i
$481$	2.60441	+	4.51098i	0.118751	+	0.205683i
$482$	−12.2948			−0.560013
$483$		0			0
$484$	−21.3320			−0.969636
$485$	−3.36823	−	5.83394i	−0.152943	−	0.264905i
$486$	0.983585	−	1.70362i	0.0446163	−	0.0772778i
$487$	−10.7840	+	18.6785i	−0.488671	+	0.846403i	−0.999915	−	0.0130329i	$-0.995851\pi$
$487$	−10.7840	+	18.6785i	−0.488671	+	0.846403i	0.511244	+	0.859435i	$0.329185\pi$
$488$	0.399875	+	0.692604i	0.0181015	+	0.0313527i
$489$	−2.97265			−0.134428
$490$		0			0
$491$	39.2347			1.77064			0.885318	−	0.464987i	$-0.153941\pi$
$491$	39.2347			1.77064			0.885318	+	0.464987i	$0.153941\pi$
$492$	−8.80542	−	15.2514i	−0.396979	−	0.687588i
$493$	3.83184	−	6.63694i	0.172577	−	0.298913i
$494$	6.66419	−	11.5427i	0.299836	−	0.519332i
$495$	0.0305850	+	0.0529748i	0.00137469	+	0.00238104i
$496$	6.17283			0.277168
$497$		0			0
$498$	−12.5101			−0.560592
$499$	−4.58407	−	7.93984i	−0.205211	−	0.355436i	0.744989	−	0.667077i	$-0.232455\pi$
$499$	−4.58407	−	7.93984i	−0.205211	−	0.355436i	−0.950200	+	0.311641i	$0.899121\pi$
$500$	−8.45627	+	14.6467i	−0.378176	+	0.655020i
$501$	19.2324	−	33.3115i	0.859240	−	1.48825i
$502$	14.0304	+	24.3013i	0.626207	+	1.08462i
$503$	−24.9370			−1.11188			−0.555942	−	0.831221i	$-0.687642\pi$
$503$	−24.9370			−1.11188			−0.555942	+	0.831221i	$0.687642\pi$
$504$		0			0
$505$	−1.08601			−0.0483267
$506$	2.70432	+	4.68402i	0.120222	+	0.208230i
$507$	0.879528	−	1.52339i	0.0390612	−	0.0676560i
$508$	0.967080	−	1.67503i	0.0429072	−	0.0743175i
$509$	2.94904	+	5.10788i	0.130714	+	0.226403i	0.923952	−	0.382509i	$-0.124940\pi$
$509$	2.94904	+	5.10788i	0.130714	+	0.226403i	−0.793238	+	0.608912i	$0.791606\pi$
$510$	7.52730			0.333314
$511$		0			0
$512$	−32.1083			−1.41900
$513$	16.9592	+	29.3741i	0.748765	+	1.29690i
$514$	−17.3386	+	30.0314i	−0.764775	+	1.32463i
$515$	6.52677	−	11.3047i	0.287604	−	0.498144i
$516$	−16.8850	−	29.2457i	−0.743321	−	1.28747i
$517$	5.96003			0.262122
$518$		0			0
$519$	10.2750			0.451024
$520$	0.0310809	+	0.0538337i	0.00136299	+	0.00236076i
$521$	−18.5948	+	32.2071i	−0.814652	+	1.41102i	0.0949259	+	0.995484i	$0.469739\pi$
$521$	−18.5948	+	32.2071i	−0.814652	+	1.41102i	−0.909578	+	0.415534i	$0.863595\pi$
$522$	0.308468	−	0.534281i	0.0135013	−	0.0233849i
$523$	−2.54540	−	4.40876i	−0.111303	−	0.192782i	0.804993	−	0.593284i	$-0.202169\pi$
$523$	−2.54540	−	4.40876i	−0.111303	−	0.192782i	−0.916296	+	0.400502i	$0.868836\pi$
$524$	38.2823			1.67237
$525$		0			0
$526$	5.23567			0.228286
$527$	−1.84712	−	3.19931i	−0.0804618	−	0.139364i
$528$	−2.47644	+	4.28933i	−0.107773	+	0.186669i
$529$	4.43475	−	7.68121i	0.192815	−	0.333966i
$530$	−12.8099	−	22.1874i	−0.556426	−	0.963758i
$531$	−0.0675374			−0.00293087
$532$		0			0
$533$	4.92168			0.213181
$534$	21.2871	+	36.8703i	0.921181	+	1.59553i
$535$	6.15583	−	10.6622i	0.266140	−	0.460968i
$536$	0.322289	−	0.558220i	0.0139208	−	0.0241114i
$537$	2.22897	+	3.86068i	0.0961870	+	0.166601i
$538$	−29.1026			−1.25470
$539$		0			0
$540$	−9.41707			−0.405246
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	0.874150	−	0.485656i	$-0.161419\pi$
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	−0.857665	+	0.514208i	$0.828086\pi$
$542$	8.67272	−	15.0216i	0.372525	−	0.645232i
$543$	9.43277	−	16.3380i	0.404799	−	0.701133i
$544$	9.44643	+	16.3617i	0.405012	+	0.701502i
$545$	12.4309			0.532480
$546$		0			0
$547$	14.1428			0.604702			0.302351	−	0.953197i	$-0.402229\pi$
$547$	14.1428			0.604702			0.302351	+	0.953197i	$0.402229\pi$
$548$	−6.28741	−	10.8901i	−0.268585	−	0.465203i
$549$	−0.549297	+	0.951411i	−0.0234434	+	0.0406052i
$550$	−3.00691	+	5.20813i	−0.128215	+	0.222075i
$551$	10.8099	+	18.7233i	0.460516	+	0.797637i
$552$	0.453824			0.0193160
$553$		0			0
$554$	−24.5582			−1.04338
$555$	−4.14939	−	7.18696i	−0.176132	−	0.305069i
$556$	−4.06834	+	7.04657i	−0.172536	+	0.298841i
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	−0.472782	−	0.881180i	$-0.656750\pi$
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	0.999515	−	0.0311490i	$-0.00991664\pi$
$558$	−0.148695	−	0.257548i	−0.00629477	−	0.0109029i
$559$	9.43766			0.399171
$560$		0			0
$561$	2.96414			0.125146
$562$	−24.2852	−	42.0633i	−1.02441	−	1.77433i
$563$	22.0047	−	38.1133i	0.927388	−	1.60628i	0.139713	−	0.990192i	$-0.455382\pi$
$563$	22.0047	−	38.1133i	0.927388	−	1.60628i	0.787675	−	0.616091i	$-0.211285\pi$
$564$	14.8852	−	25.7818i	0.626778	−	1.08561i
$565$	−1.47542	−	2.55550i	−0.0620713	−	0.107511i
$566$	−61.7989			−2.59760
$567$		0			0
$568$	−0.754366			−0.0316525
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	0.969434	+	0.245353i	$0.0789040\pi$
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	−0.272235	+	0.962231i	$0.587763\pi$
$570$	−10.6175	+	18.3900i	−0.444718	+	0.770274i
$571$	6.17699	−	10.6989i	0.258499	−	0.447734i	−0.707341	−	0.706873i	$-0.750105\pi$
$571$	6.17699	−	10.6989i	0.258499	−	0.447734i	0.965840	+	0.259139i	$0.0834387\pi$
$572$	0.728600	+	1.26197i	0.0304643	+	0.0527657i
$573$	2.95276			0.123353
$574$		0			0
$575$	−15.7116			−0.655219
$576$	0.389888	+	0.675306i	0.0162453	+	0.0281377i
$577$	−12.9829	+	22.4871i	−0.540486	+	0.936150i	0.458390	+	0.888751i	$0.348426\pi$
$577$	−12.9829	+	22.4871i	−0.540486	+	0.936150i	−0.998876	+	0.0473984i	$0.984907\pi$
$578$	−11.5157	+	19.9458i	−0.478990	+	0.829635i
$579$	−5.67133	−	9.82304i	−0.235693	−	0.408232i
$580$	−6.00250			−0.249240
$581$		0			0
$582$	−26.2781			−1.08926
$583$	−5.04435	−	8.73707i	−0.208916	−	0.361853i
$584$	0.119180	−	0.206426i	0.00493171	−	0.00854196i
$585$	−0.0426950	+	0.0739499i	−0.00176522	+	0.00305745i
$586$	31.9652	+	55.3653i	1.32047	+	2.28712i
$587$	23.9747			0.989543			0.494771	−	0.869023i	$-0.335252\pi$
$587$	23.9747			0.989543			0.494771	+	0.869023i	$0.335252\pi$
$588$		0			0
$589$	10.4217			0.429418
$590$	0.651589	+	1.12859i	0.0268255	+	0.0464631i
$591$	1.64693	−	2.85256i	0.0677454	−	0.117339i
$592$	10.2366	−	17.7304i	0.420723	−	0.728713i
$593$	23.5240	+	40.7448i	0.966015	+	1.67319i	0.706862	+	0.707352i	$0.250110\pi$
$593$	23.5240	+	40.7448i	0.966015	+	1.67319i	0.259154	+	0.965836i	$0.416556\pi$
$594$	−7.35433			−0.301752
$595$		0			0
$596$	−42.8744			−1.75620
$597$	10.0237	+	17.3615i	0.410242	+	0.710560i
$598$	−3.77508	+	6.53863i	−0.154374	+	0.267384i
$599$	−10.0868	+	17.4708i	−0.412135	+	0.713840i	−0.995123	−	0.0986415i	$-0.968550\pi$
$599$	−10.0868	+	17.4708i	−0.412135	+	0.713840i	0.582988	+	0.812481i	$0.301884\pi$
$600$	0.252302	+	0.437000i	0.0103002	+	0.0178404i
$601$	−29.5773			−1.20648			−0.603242	−	0.797558i	$-0.706125\pi$
$601$	−29.5773			−1.20648			−0.603242	+	0.797558i	$0.706125\pi$
$602$		0			0
$603$	0.885439			0.0360579
$604$	15.9921	+	27.6991i	0.650708	+	1.12706i
$605$	−4.74907	+	8.22564i	−0.193077	+	0.334420i
$606$	−2.11819	+	3.66881i	−0.0860456	+	0.149035i
$607$	−7.72099	−	13.3732i	−0.313385	−	0.542799i	0.665708	−	0.746213i	$-0.268130\pi$
$607$	−7.72099	−	13.3732i	−0.313385	−	0.542799i	−0.979093	+	0.203413i	$0.934796\pi$
$608$	−53.2980			−2.16152
$609$		0			0
$610$	21.1981			0.858287
$611$	4.15993	+	7.20521i	0.168293	+	0.291492i
$612$	0.225557	−	0.390677i	0.00911762	−	0.0157922i
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	−0.885465	−	0.464706i	$-0.846160\pi$
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	0.845180	+	0.534482i	$0.179493\pi$
$614$	−28.9111	−	50.0755i	−1.16676	−	2.02088i
$615$	−7.84129			−0.316191
$616$		0			0
$617$	−2.85584			−0.114972			−0.0574858	−	0.998346i	$-0.518308\pi$
$617$	−2.85584			−0.114972			−0.0574858	+	0.998346i	$0.518308\pi$
$618$	−25.4601	−	44.0982i	−1.02416	−	1.77389i
$619$	15.9911	−	27.6975i	0.642738	−	1.11326i	−0.342080	−	0.939671i	$-0.611132\pi$
$619$	15.9911	−	27.6975i	0.642738	−	1.11326i	0.984819	−	0.173585i	$-0.0555351\pi$
$620$	−1.44674	+	2.50582i	−0.0581024	+	0.100636i
$621$	−9.60688	−	16.6396i	−0.385511	−	0.667725i
$622$	11.0843			0.444440
$623$		0			0
$624$	−6.91395			−0.276780
$625$	−6.68398	−	11.5770i	−0.267359	−	0.463080i
$626$	4.86865	−	8.43275i	0.194590	−	0.337040i
$627$	−4.18102	+	7.24174i	−0.166974	+	0.289207i
$628$	−7.91800	−	13.7144i	−0.315963	−	0.547263i
$629$	−12.2526			−0.488542
$630$		0			0
$631$	32.1115			1.27834			0.639169	−	0.769066i	$-0.279278\pi$
$631$	32.1115			1.27834			0.639169	+	0.769066i	$0.279278\pi$
$632$	0.446390	+	0.773171i	0.0177565	+	0.0307551i
$633$	6.62812	−	11.4802i	0.263444	−	0.456298i
$634$	−7.68774	+	13.3156i	−0.305319	+	0.528828i
$635$	−0.430596	−	0.745814i	−0.0170877	−	0.0295967i
$636$	−50.3930			−1.99821
$637$		0			0
$638$	−4.68769			−0.185588
$639$	−0.518126	−	0.897420i	−0.0204967	−	0.0355014i
$640$	0.248611	−	0.430607i	0.00982721	−	0.0170212i
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	0.330387	+	0.943845i	$0.392821\pi$
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	−0.982588	+	0.185799i	$0.940513\pi$
$642$	−24.0131	−	41.5920i	−0.947723	−	1.64150i
$643$	−15.7942			−0.622863			−0.311432	−	0.950269i	$-0.600808\pi$
$643$	−15.7942			−0.622863			−0.311432	+	0.950269i	$0.600808\pi$
$644$		0			0
$645$	−15.0362			−0.592051
$646$	15.6760	+	27.1516i	0.616764	+	1.06827i
$647$	−2.32036	+	4.01898i	−0.0912227	+	0.158002i	−0.908026	−	0.418914i	$-0.862411\pi$
$647$	−2.32036	+	4.01898i	−0.0912227	+	0.158002i	0.816803	+	0.576916i	$0.195744\pi$
$648$	−0.318246	+	0.551219i	−0.0125019	+	0.0216539i
$649$	0.256587	+	0.444421i	0.0100719	+	0.0174451i
$650$	−8.39497			−0.329278
$651$		0			0
$652$	3.43757			0.134626
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	−0.999578	−	0.0290430i	$-0.990754\pi$
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	0.474637	−	0.880182i	$-0.342579\pi$
$654$	24.2456	−	41.9946i	0.948079	−	1.64212i
$655$	8.52266	−	14.7617i	0.333008	−	0.576787i
$656$	−9.67230	−	16.7529i	−0.377640	−	0.654092i
$657$	0.327429			0.0127742
$658$		0			0
$659$	−42.9889			−1.67461			−0.837306	−	0.546735i	$-0.815871\pi$
$659$	−42.9889			−1.67461			−0.837306	+	0.546735i	$0.815871\pi$
$660$	−1.16082	−	2.01059i	−0.0451847	−	0.0782623i
$661$	−14.7349	+	25.5216i	−0.573122	+	0.992676i	0.423121	+	0.906073i	$0.360934\pi$
$661$	−14.7349	+	25.5216i	−0.573122	+	0.992676i	−0.996243	+	0.0866030i	$0.972399\pi$
$662$	11.3915	−	19.7307i	0.442744	−	0.766855i
$663$	2.06889	+	3.58342i	0.0803490	+	0.139169i
$664$	0.243015			0.00943082
$665$		0			0
$666$	−0.986346			−0.0382201
$667$	−6.12349	−	10.6062i	−0.237102	−	0.410673i
$668$	−22.2403	+	38.5214i	−0.860504	+	1.49044i
$669$	−15.5104	+	26.8647i	−0.599666	+	1.03865i
$670$	−8.54256	−	14.7962i	−0.330028	−	0.571625i
$671$	8.34752			0.322252
$672$		0			0
$673$	−20.1702			−0.777504			−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702			−0.777504			−0.388752	+	0.921342i	$0.627094\pi$
$674$	1.74891	+	3.02920i	0.0673655	+	0.116680i
$675$	10.6818	−	18.5015i	0.411144	−	0.712122i
$676$	−1.01709	+	1.76164i	−0.0391187	+	0.0677555i
$677$	−3.10241	−	5.37353i	−0.119235	−	0.206521i	0.800230	−	0.599694i	$-0.204711\pi$
$677$	−3.10241	−	5.37353i	−0.119235	−	0.206521i	−0.919465	+	0.393172i	$0.871378\pi$
$678$	−11.5108			−0.442071
$679$		0			0
$680$	−0.146221			−0.00560733
$681$	4.68704	+	8.11820i	0.179608	+	0.311090i
$682$	−1.12984	+	1.95694i	−0.0432638	+	0.0749351i
$683$	0.884758	−	1.53245i	0.0338543	−	0.0586374i	−0.848602	−	0.529032i	$-0.822555\pi$
$683$	0.884758	−	1.53245i	0.0338543	−	0.0586374i	0.882456	+	0.470395i	$0.155888\pi$
$684$	0.636312	+	1.10212i	0.0243300	+	0.0421408i
$685$	−5.59899			−0.213926
$686$		0			0
$687$	−14.9854			−0.571729
$688$	−18.5473	−	32.1249i	−0.707110	−	1.22475i
$689$	7.04163	−	12.1965i	0.268265	−	0.464648i
$690$	6.01451	−	10.4174i	0.228969	−	0.396585i
$691$	22.4658	+	38.9120i	0.854641	+	1.48028i	0.876977	+	0.480531i	$0.159556\pi$
$691$	22.4658	+	38.9120i	0.854641	+	1.48028i	−0.0223363	+	0.999751i	$0.507110\pi$
$692$	−11.8820			−0.451688
$693$		0			0
$694$	−42.2800			−1.60493
$695$	1.81144	+	3.13751i	0.0687120	+	0.119013i
$696$	−0.196666	+	0.340635i	−0.00745459	+	0.0129117i
$697$	−5.78856	+	10.0261i	−0.219257	+	0.379765i
$698$	8.39162	+	14.5347i	0.317628	+	0.550147i
$699$	−8.36204			−0.316281
$700$		0			0
$701$	38.5707			1.45679			0.728397	−	0.685156i	$-0.240266\pi$
$701$	38.5707			1.45679			0.728397	+	0.685156i	$0.240266\pi$
$702$	−5.13311	−	8.89081i	−0.193737	−	0.335562i
$703$	17.2827	−	29.9344i	0.651828	−	1.12900i
$704$	2.96251	−	5.13121i	0.111654	−	0.193390i
$705$	−6.62767	−	11.4795i	−0.249612	−	0.432341i
$706$	−17.1398			−0.645066
$707$		0			0
$708$	2.56330			0.0963346
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	0.771772	−	0.635900i	$-0.219371\pi$
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	−0.936591	+	0.350424i	$0.886037\pi$
$710$	−9.99758	+	17.3163i	−0.375203	+	0.649870i
$711$	−0.613194	+	1.06208i	−0.0229966	+	0.0398312i
$712$	−0.413512	−	0.716223i	−0.0154970	−	0.0268416i
$713$	−5.90360			−0.221091
$714$		0			0
$715$	0.648824			0.0242646
$716$	−2.57757	−	4.46449i	−0.0963284	−	0.166846i
$717$	13.0447	−	22.5940i	0.487161	−	0.843788i
$718$	−16.2402	+	28.1289i	−0.606080	+	1.04976i
$719$	2.10218	+	3.64109i	0.0783982	+	0.135790i	0.902559	−	0.430566i	$-0.141686\pi$
$719$	2.10218	+	3.64109i	0.0783982	+	0.135790i	−0.824161	+	0.566356i	$0.808353\pi$
$720$	0.335625			0.0125080
$721$		0			0
$722$	−50.2840			−1.87138
$723$	5.38386	+	9.32513i	0.200228	+	0.346805i
$724$	−10.9080	+	18.8933i	−0.405394	+	0.702164i
$725$	6.80866	−	11.7930i	0.252867	−	0.437979i
$726$	18.5255	+	32.0872i	0.687547	+	1.19087i
$727$	28.9856			1.07502			0.537509	−	0.843258i	$-0.319366\pi$
$727$	28.9856			1.07502			0.537509	+	0.843258i	$0.319366\pi$
$728$		0			0
$729$	26.0990			0.966630
$730$	−3.15898	−	5.47151i	−0.116919	−	0.202510i
$731$	−11.1000	+	19.2257i	−0.410547	+	0.711089i
$732$	20.8479	−	36.1096i	0.770561	−	1.33465i
$733$	−12.0172	−	20.8145i	−0.443867	−	0.768800i	0.554106	−	0.832446i	$-0.313060\pi$
$733$	−12.0172	−	20.8145i	−0.443867	−	0.768800i	−0.997972	+	0.0636467i	$0.979727\pi$
$734$	56.5480			2.08722
$735$		0			0
$736$	30.1918			1.11288
$737$	−3.36394	−	5.82652i	−0.123912	−	0.214622i
$738$	−0.465985	+	0.807110i	−0.0171532	+	0.0297101i
$739$	−5.90276	+	10.2239i	−0.217136	+	0.376091i	−0.953931	−	0.300025i	$-0.903005\pi$
$739$	−5.90276	+	10.2239i	−0.217136	+	0.376091i	0.736795	+	0.676116i	$0.236338\pi$
$740$	4.79835	+	8.31099i	0.176391	+	0.305518i
$741$	−11.6729			−0.428816
$742$		0			0
$743$	47.2786			1.73448			0.867241	−	0.497888i	$-0.165891\pi$
$743$	47.2786			1.73448			0.867241	+	0.497888i	$0.165891\pi$
$744$	0.0948017	+	0.164201i	0.00347560	+	0.00601992i
$745$	−9.54499	+	16.5324i	−0.349701	+	0.605700i
$746$	−28.6252	+	49.5802i	−1.04804	+	1.81526i
$747$	0.166912	+	0.289100i	0.00610698	+	0.0105776i
$748$	−3.42773			−0.125330
$749$		0			0
$750$	29.3750			1.07262
$751$	−2.73850	−	4.74322i	−0.0999294	−	0.173083i	0.811726	−	0.584039i	$-0.198528\pi$
$751$	−2.73850	−	4.74322i	−0.0999294	−	0.173083i	−0.911655	+	0.410956i	$0.865195\pi$
$752$	16.3506	−	28.3200i	0.596244	−	1.03273i
$753$	12.2877	−	21.2830i	0.447790	−	0.775596i
$754$	−3.27188	−	5.66706i	−0.119155	−	0.206382i
$755$	14.2410			0.518285
$756$		0			0
$757$	10.7453			0.390546			0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453			0.390546			0.195273	+	0.980749i	$0.437441\pi$
$758$	−7.29358	−	12.6329i	−0.264915	−	0.458846i
$759$	2.36843	−	4.10224i	0.0859686	−	0.148902i
$760$	0.206250	−	0.357236i	0.00748148	−	0.0129583i
$761$	−16.5200	−	28.6134i	−0.598848	−	1.03724i	−0.992991	−	0.118186i	$-0.962292\pi$
$761$	−16.5200	−	28.6134i	−0.598848	−	1.03724i	0.394143	−	0.919049i	$-0.371041\pi$
$762$	−3.35940			−0.121698
$763$		0			0
$764$	−3.41457			−0.123535
$765$	−0.100430	−	0.173950i	−0.00363106	−	0.00628918i
$766$	−12.9877	+	22.4953i	−0.469263	+	0.812788i
$767$	−0.358181	+	0.620387i	−0.0129332	+	0.0224009i
$768$	13.5793	+	23.5201i	0.490002	+	0.848708i
$769$	−2.98332			−0.107581			−0.0537907	−	0.998552i	$-0.517130\pi$
$769$	−2.98332			−0.107581			−0.0537907	+	0.998552i	$0.517130\pi$
$770$		0			0
$771$	30.3702			1.09376
$772$	6.55833	+	11.3594i	0.236039	+	0.408832i
$773$	−10.9543	+	18.9733i	−0.393998	+	0.682424i	−0.992973	−	0.118344i	$-0.962242\pi$
$773$	−10.9543	+	18.9733i	−0.393998	+	0.682424i	0.598975	+	0.800768i	$0.295575\pi$
$774$	−0.893560	+	1.54769i	−0.0321184	+	0.0556306i
$775$	−3.28208	−	5.68473i	−0.117896	−	0.204202i
$776$	0.510464			0.0183246
$777$		0			0
$778$	42.4516			1.52196
$779$	−16.3299	−	28.2842i	−0.585079	−	1.01339i
$780$	1.62044	−	2.80668i	0.0580209	−	0.100495i
$781$	−3.93691	+	6.81892i	−0.140874	+	0.244000i
$782$	−8.88001	−	15.3806i	−0.317548	−	0.550010i
$783$	16.6527			0.595118
$784$		0			0
$785$	−7.05104			−0.251662
$786$	−33.2458	−	57.5835i	−1.18584	−	2.05393i
$787$	−6.68161	+	11.5729i	−0.238174	+	0.412529i	−0.960190	−	0.279347i	$-0.909882\pi$
$787$	−6.68161	+	11.5729i	−0.238174	+	0.412529i	0.722017	+	0.691876i	$0.243215\pi$
$788$	−1.90450	+	3.29869i	−0.0678451	+	0.117511i
$789$	−2.29269	−	3.97105i	−0.0816218	−	0.141373i
$790$	23.6640			0.841927
$791$		0			0
$792$	−0.00463525			−0.000164706
$793$	5.82633	+	10.0915i	0.206899	+	0.358360i
$794$	−19.2892	+	33.4099i	−0.684548	+	1.18567i
$795$	−11.2188	+	19.4316i	−0.397891	+	0.689167i
$796$	−11.5914	−	20.0768i	−0.410845	−	0.711605i
$797$	−32.5388			−1.15258			−0.576292	−	0.817244i	$-0.695501\pi$
$797$	−32.5388			−1.15258			−0.576292	+	0.817244i	$0.695501\pi$
$798$		0			0
$799$	−19.5706			−0.692357
$800$	16.7850	+	29.0725i	0.593440	+	1.02787i
$801$	0.568030	−	0.983857i	0.0200703	−	0.0347629i
$802$	16.7403	−	28.9950i	0.591119	−	1.02385i
$803$	−1.24396	−	2.15460i	−0.0438984	−	0.0760343i
$804$	−33.6057			−1.18518
$805$		0			0
$806$	−3.15439			−0.111109
$807$	12.7440	+	22.0732i	0.448608	+	0.777013i
$808$	0.0411469	−	0.0712685i	0.00144754	−	0.00250722i
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	−0.925656	−	0.378367i	$-0.876486\pi$
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	0.790503	+	0.612458i	$0.209819\pi$
$810$	8.43542	+	14.6106i	0.296390	+	0.513363i
$811$	48.3178			1.69667			0.848334	−	0.529461i	$-0.177606\pi$
$811$	48.3178			1.69667			0.848334	+	0.529461i	$0.177606\pi$
$812$		0			0
$813$	−15.1911			−0.532773
$814$	3.74731	+	6.49052i	0.131343	+	0.227493i
$815$	0.765295	−	1.32553i	0.0268071	−	0.0464313i
$816$	8.13175	−	14.0846i	0.284668	−	0.493060i
$817$	−31.3137	−	54.2370i	−1.09553	−	1.89751i
$818$	24.8019			0.867178
$819$		0			0
$820$	9.06766			0.316656
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	0.896768	−	0.442502i	$-0.145909\pi$
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	−0.831602	+	0.555373i	$0.812576\pi$
$822$	−10.9205	+	18.9148i	−0.380895	+	0.659730i
$823$	−7.11590	+	12.3251i	−0.248045	+	0.429626i	−0.962983	−	0.269561i	$-0.913121\pi$
$823$	−7.11590	+	12.3251i	−0.248045	+	0.429626i	0.714939	+	0.699187i	$0.246455\pi$
$824$	0.494575	+	0.856629i	0.0172293	+	0.0298421i
$825$	5.26688			0.183369
$826$		0			0
$827$	48.3016			1.67961			0.839805	−	0.542888i	$-0.182669\pi$
$827$	48.3016			1.67961			0.839805	+	0.542888i	$0.182669\pi$
$828$	−0.360453	−	0.624323i	−0.0125266	−	0.0216967i
$829$	5.75506	−	9.96806i	0.199882	−	0.346205i	−0.748608	−	0.663013i	$-0.769278\pi$
$829$	5.75506	−	9.96806i	0.199882	−	0.346205i	0.948490	+	0.316808i	$0.102611\pi$
$830$	3.22067	−	5.57837i	0.111791	−	0.193628i
$831$	10.7540	+	18.6264i	0.373051	+	0.646143i
$832$	8.27099			0.286745
$833$		0			0
$834$	14.1324			0.489366
$835$	9.90258	+	17.1518i	0.342693	+	0.593562i
$836$	4.83493	−	8.37434i	0.167219	−	0.289633i
$837$	4.01367	−	6.95188i	0.138733	−	0.240292i
$838$	−4.37792	−	7.58278i	−0.151233	−	0.261943i
$839$	−13.1103			−0.452616			−0.226308	−	0.974056i	$-0.572666\pi$
$839$	−13.1103			−0.452616			−0.226308	+	0.974056i	$0.572666\pi$
$840$		0			0
$841$	−18.3855			−0.633982
$842$	−10.0426	−	17.3943i	−0.346092	−	0.599448i
$843$	−21.2689	+	36.8388i	−0.732539	+	1.26880i
$844$	−7.66475	+	13.2757i	−0.263831	+	0.456969i
$845$	0.452861	+	0.784378i	0.0155789	+	0.0269834i
$846$	−1.57545			−0.0541652
$847$		0			0
$848$	−55.3541			−1.90087
$849$	27.0616	+	46.8721i	0.928751	+	1.60864i
$850$	9.87362	−	17.1016i	0.338662	−	0.586580i
$851$	−9.79014	+	16.9570i	−0.335602	+	0.581279i
$852$	19.6648	+	34.0605i	0.673706	+	1.16689i
$853$	−8.80346			−0.301425			−0.150712	−	0.988578i	$-0.548157\pi$
$853$	−8.80346			−0.301425			−0.150712	+	0.988578i	$0.548157\pi$
$854$		0			0
$855$	0.566640			0.0193787
$856$	0.466467	+	0.807945i	0.0159435	+	0.0276150i
$857$	8.48254	−	14.6922i	0.289758	−	0.501876i	−0.683994	−	0.729488i	$-0.739758\pi$
$857$	8.48254	−	14.6922i	0.289758	−	0.501876i	0.973752	+	0.227612i	$0.0730918\pi$
$858$	1.26549	−	2.19189i	0.0432031	−	0.0748300i
$859$	7.27049	+	12.5929i	0.248066	+	0.429663i	0.962989	−	0.269540i	$-0.0868717\pi$
$859$	7.27049	+	12.5929i	0.248066	+	0.429663i	−0.714923	+	0.699203i	$0.753538\pi$
$860$	17.3879			0.592922
$861$		0			0
$862$	46.9243			1.59825
$863$	−19.5222	−	33.8135i	−0.664544	−	1.15102i	−0.979409	−	0.201887i	$-0.935293\pi$
$863$	−19.5222	−	33.8135i	−0.664544	−	1.15102i	0.314865	−	0.949136i	$-0.398041\pi$
$864$	−20.5265	+	35.5529i	−0.698324	+	1.20953i
$865$	−2.64526	+	4.58173i	−0.0899416	+	0.155783i
$866$	2.72441	+	4.71882i	0.0925793	+	0.160352i
$867$	20.1708			0.685036
$868$		0			0
$869$	9.31854			0.316110
$870$	5.21281	+	9.02885i	0.176731	+	0.306107i
$871$	4.69587	−	8.13349i	0.159114	−	0.275593i
$872$	−0.470983	+	0.815767i	−0.0159495	+	0.0276253i
$873$	0.350605	+	0.607266i	0.0118662	+	0.0205529i
$874$	50.1022			1.69473
$875$		0			0
$876$	−12.4272			−0.419875
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	−0.998252	−	0.0591051i	$-0.981175\pi$
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	0.447939	−	0.894064i	$-0.352158\pi$
$878$	8.87285	−	15.3682i	0.299444	−	0.518652i
$879$	27.9949	−	48.4886i	0.944245	−	1.63548i
$880$	−1.27510	−	2.20853i	−0.0429835	−	0.0744497i
$881$	43.4141			1.46266			0.731330	−	0.682024i	$-0.238900\pi$
$881$	43.4141			1.46266			0.731330	+	0.682024i	$0.238900\pi$
$882$		0			0
$883$	28.2902			0.952040			0.476020	−	0.879434i	$-0.342079\pi$
$883$	28.2902			0.952040			0.476020	+	0.879434i	$0.342079\pi$
$884$	−2.39246	−	4.14386i	−0.0804672	−	0.139373i
$885$	0.570659	−	0.988410i	0.0191825	−	0.0332250i
$886$	−2.91796	+	5.05406i	−0.0980308	+	0.169794i
$887$	−25.1325	−	43.5307i	−0.843866	−	1.46162i	−0.886602	−	0.462532i	$-0.846941\pi$
$887$	−25.1325	−	43.5307i	−0.843866	−	1.46162i	0.0427364	−	0.999086i	$-0.486392\pi$
$888$	0.628852			0.0211029
$889$		0			0
$890$	−21.9210			−0.734794
$891$	3.32175	+	5.75344i	0.111283	+	0.192747i
$892$	17.9362	−	31.0664i	0.600548	−	1.04018i
$893$	27.6049	−	47.8131i	0.923764	−	1.60001i
$894$	37.2338	+	64.4908i	1.24528	+	2.15690i
$895$	−2.29535			−0.0767250
$896$		0			0
$897$	6.61239			0.220781
$898$	−15.3428	−	26.5745i	−0.511996	−	0.886803i
$899$	2.55834	−	4.43117i	0.0853253	−	0.147788i
$900$	0.400785	−	0.694180i	0.0133595	−	0.0231393i
$901$	16.5638	+	28.6894i	0.551821	+	0.955782i
$902$	7.08145			0.235786
$903$		0			0
$904$	0.223604			0.00743695
$905$	4.85685	+	8.41231i	0.161447	+	0.279635i
$906$	27.7763	−	48.1099i	0.922805	−	1.59835i
$907$	−13.4138	+	23.2334i	−0.445399	+	0.771453i	−0.998080	−	0.0619394i	$-0.980271\pi$
$907$	−13.4138	+	23.2334i	−0.445399	+	0.771453i	0.552681	+	0.833393i	$0.313605\pi$
$908$	−5.42009	−	9.38787i	−0.179872	−	0.311548i
$909$	0.113045			0.00374946
$910$		0			0
$911$	−22.3560			−0.740687			−0.370344	−	0.928895i	$-0.620760\pi$
$911$	−22.3560			−0.740687			−0.370344	+	0.928895i	$0.620760\pi$
$912$	22.9402	+	39.7336i	0.759626	+	1.31571i
$913$	1.26826	−	2.19668i	0.0419731	−	0.0726996i
$914$	23.7608	−	41.1550i	0.785939	−	1.36129i
$915$	−9.28260	−	16.0779i	−0.306873	−	0.531520i
$916$	17.3291			0.572569
$917$		0			0
$918$	24.1489			0.797034
$919$	4.31122	+	7.46725i	0.142214	+	0.246322i	0.928330	−	0.371757i	$-0.121245\pi$
$919$	4.31122	+	7.46725i	0.142214	+	0.246322i	−0.786116	+	0.618079i	$0.787911\pi$
$920$	−0.116835	+	0.202364i	−0.00385193	+	0.00667174i
$921$	−25.3202	+	43.8559i	−0.834329	+	1.44510i
$922$	26.7305	+	46.2985i	0.880321	+	1.52476i
$923$	−10.9914			−0.361786
$924$		0			0
$925$	−21.7712			−0.715832
$926$	−1.44865	−	2.50913i	−0.0476054	−	0.0824550i
$927$	−0.679385	+	1.17673i	−0.0223139	+	0.0386488i
$928$	−13.0837	+	22.6616i	−0.429493	+	0.743904i
$929$	20.6930	+	35.8414i	0.678916	+	1.17592i	0.975308	+	0.220851i	$0.0708834\pi$
$929$	20.6930	+	35.8414i	0.678916	+	1.17592i	−0.296391	+	0.955067i	$0.595783\pi$
$930$	5.02562			0.164796
$931$		0			0
$932$	9.66985			0.316747
$933$	−4.85379	−	8.40700i	−0.158906	−	0.275233i
$934$	8.42535	−	14.5931i	0.275686	−	0.477502i
$935$	−0.763105	+	1.32174i	−0.0249562	+	0.0432254i
$936$	−0.00323527	−	0.00560366i	−0.000105748	−	0.000183161i
$937$	−21.3818			−0.698514			−0.349257	−	0.937027i	$-0.613566\pi$
$937$	−21.3818			−0.698514			−0.349257	+	0.937027i	$0.613566\pi$
$938$		0			0
$939$	−8.52788			−0.278297
$940$	7.66423	+	13.2748i	0.249979	+	0.432977i
$941$	−26.5740	+	46.0275i	−0.866288	+	1.50046i	−0.000525658		1.00000i	$0.500167\pi$
$941$	−26.5740	+	46.0275i	−0.866288	+	1.50046i	−0.865762	+	0.500455i	$0.833166\pi$
$942$	−13.7526	+	23.8202i	−0.448084	+	0.776105i
$943$	9.25043	+	16.0222i	0.301235	+	0.521755i
$944$	2.81565			0.0916416
$945$		0			0
$946$	13.5792			0.441497
$947$	4.43468	+	7.68109i	0.144108	+	0.249602i	0.929040	−	0.369980i	$-0.120635\pi$
$947$	4.43468	+	7.68109i	0.144108	+	0.249602i	−0.784932	+	0.619582i	$0.787302\pi$
$948$	23.2730	−	40.3101i	0.755873	−	1.30921i
$949$	1.73650	−	3.00771i	0.0563692	−	0.0976343i
$950$	27.8541	+	48.2448i	0.903707	+	1.56527i
$951$	13.4658			0.436658
$952$		0			0
$953$	−39.8167			−1.28979			−0.644894	−	0.764272i	$-0.723099\pi$
$953$	−39.8167			−1.28979			−0.644894	+	0.764272i	$0.723099\pi$
$954$	1.33341	+	2.30953i	0.0431706	+	0.0747737i
$955$	−0.760174	+	1.31666i	−0.0245987	+	0.0426061i
$956$	−15.0848	+	26.1277i	−0.487878	+	0.845029i
$957$	2.05273	+	3.55543i	0.0663553	+	0.114931i
$958$	25.3319			0.818435
$959$		0			0
$960$	−13.1775			−0.425301
$961$	14.2668	+	24.7108i	0.460218	+	0.797121i
$962$	−5.23103	+	9.06041i	−0.168655	+	0.292119i
$963$	−0.640773	+	1.10985i	−0.0206486	+	0.0357645i
$964$	−6.22589	−	10.7836i	−0.200523	−	0.347315i
$965$	5.84024			0.188004
$966$		0			0
$967$	−22.1611			−0.712652			−0.356326	−	0.934362i	$-0.615971\pi$
$967$	−22.1611			−0.712652			−0.356326	+	0.934362i	$0.615971\pi$
$968$	−0.359868	−	0.623309i	−0.0115666	−	0.0200339i
$969$	13.7290	−	23.7793i	0.441038	−	0.763900i
$970$	6.76516	−	11.7176i	0.217216	−	0.376230i
$971$	18.0212	+	31.2136i	0.578327	+	1.00169i	0.995671	+	0.0929428i	$0.0296274\pi$
$971$	18.0212	+	31.2136i	0.578327	+	1.00169i	−0.417345	+	0.908748i	$0.637039\pi$
$972$	1.99229			0.0639027
$973$		0			0
$974$	−43.3199			−1.38806
$975$	3.67614	+	6.36725i	0.117731	+	0.203915i
$976$	22.9004	−	39.6646i	0.733022	−	1.26963i
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	0.472559	+	0.881299i	$0.343330\pi$
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	−0.999507	+	0.0314009i	$0.990003\pi$
$978$	−2.98532	−	5.17072i	−0.0954600	−	0.165342i
$979$	−8.63219			−0.275886
$980$		0			0
$981$	−1.29395			−0.0413128
$982$	39.4019	+	68.2461i	1.25736	+	2.17782i
$983$	−2.09973	+	3.63683i	−0.0669709	+	0.115997i	−0.897567	−	0.440879i	$-0.854667\pi$
$983$	−2.09973	+	3.63683i	−0.0669709	+	0.115997i	0.830596	+	0.556876i	$0.188000\pi$
$984$	0.297092	−	0.514579i	0.00947096	−	0.0164042i
$985$	0.847986	+	1.46876i	0.0270191	+	0.0467984i
$986$	15.3927			0.490203
$987$		0			0
$988$	13.4986			0.429447
$989$	17.7383	+	30.7237i	0.564047	+	0.976958i
$990$	−0.0614308	+	0.106401i	−0.00195240	+	0.00338165i
$991$	6.70693	−	11.6167i	0.213053	−	0.369018i	−0.739616	−	0.673029i	$-0.764993\pi$
$991$	6.70693	−	11.6167i	0.213053	−	0.369018i	0.952668	+	0.304011i	$0.0983261\pi$
$992$	6.30693	+	10.9239i	0.200245	+	0.346835i
$993$	−19.9533			−0.633198
$994$		0			0
$995$	−10.3222			−0.327236
$996$	−6.33493	−	10.9724i	−0.200730	−	0.347675i
$997$	−23.9434	+	41.4712i	−0.758295	+	1.31341i	0.185424	+	0.982659i	$0.440634\pi$
$997$	−23.9434	+	41.4712i	−0.758295	+	1.31341i	−0.943719	+	0.330747i	$0.892699\pi$
$998$	9.20722	−	15.9474i	0.291449	−	0.504805i
$999$	−13.3120	−	23.0571i	−0.421173	−	0.729494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.m.508.5		10
7.2	even	3	inner	637.2.e.m.79.5		10
7.3	odd	6		637.2.a.l.1.1		5
7.4	even	3		637.2.a.k.1.1		5
7.5	odd	6		91.2.e.c.79.5	yes	10
7.6	odd	2		91.2.e.c.53.5	✓	10
21.5	even	6		819.2.j.h.352.1		10
21.11	odd	6		5733.2.a.bm.1.5		5
21.17	even	6		5733.2.a.bl.1.5		5
21.20	even	2		819.2.j.h.235.1		10
28.19	even	6		1456.2.r.p.625.4		10
28.27	even	2		1456.2.r.p.417.4		10
91.12	odd	6		1183.2.e.f.170.1		10
91.25	even	6		8281.2.a.bx.1.5		5
91.38	odd	6		8281.2.a.bw.1.5		5
91.90	odd	2		1183.2.e.f.508.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	7.6	odd	2
91.2.e.c.79.5	yes	10	7.5	odd	6
637.2.a.k.1.1		5	7.4	even	3
637.2.a.l.1.1		5	7.3	odd	6
637.2.e.m.79.5		10	7.2	even	3	inner
637.2.e.m.508.5		10	1.1	even	1	trivial
819.2.j.h.235.1		10	21.20	even	2
819.2.j.h.352.1		10	21.5	even	6
1183.2.e.f.170.1		10	91.12	odd	6
1183.2.e.f.508.1		10	91.90	odd	2
1456.2.r.p.417.4		10	28.27	even	2
1456.2.r.p.625.4		10	28.19	even	6
5733.2.a.bl.1.5		5	21.17	even	6
5733.2.a.bm.1.5		5	21.11	odd	6
8281.2.a.bw.1.5		5	91.38	odd	6
8281.2.a.bx.1.5		5	91.25	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00426 + 1.73943i) q^{2} +(0.879528 - 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(0.452861 + 0.784378i) q^{5} +3.53311 q^{6} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +O(q^{10})\)	\(q+(1.00426 + 1.73943i) q^{2} +(0.879528 - 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(0.452861 + 0.784378i) q^{5} +3.53311 q^{6} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +(-0.909582 + 1.57544i) q^{10} +(-0.358181 + 0.620387i) q^{11} +(1.78911 + 3.09883i) q^{12} -1.00000 q^{13} +1.59322 q^{15} +(1.96525 + 3.40391i) q^{16} +(1.17614 - 2.03713i) q^{17} +(0.0946802 - 0.163991i) q^{18} +(3.31796 + 5.74687i) q^{19} -1.84239 q^{20} -1.43883 q^{22} +(-1.87953 - 3.25544i) q^{23} +(-0.0603641 + 0.104554i) q^{24} +(2.08983 - 3.61970i) q^{25} +(-1.00426 - 1.73943i) q^{26} +5.11133 q^{27} +3.25799 q^{29} +(1.60001 + 2.77129i) q^{30} +(0.785250 - 1.36009i) q^{31} +(-4.01588 + 6.95570i) q^{32} +(0.630060 + 1.09130i) q^{33} +4.72459 q^{34} +0.191778 q^{36} +(-2.60441 - 4.51098i) q^{37} +(-6.66419 + 11.5427i) q^{38} +(-0.879528 + 1.52339i) q^{39} +(-0.0310809 - 0.0538337i) q^{40} -4.92168 q^{41} -9.43766 q^{43} +(-0.728600 - 1.26197i) q^{44} +(0.0426950 - 0.0739499i) q^{45} +(3.77508 - 6.53863i) q^{46} +(-4.15993 - 7.20521i) q^{47} +6.91395 q^{48} +8.39497 q^{50} +(-2.06889 - 3.58342i) q^{51} +(1.01709 - 1.76164i) q^{52} +(-7.04163 + 12.1965i) q^{53} +(5.13311 + 8.89081i) q^{54} -0.648824 q^{55} +11.6729 q^{57} +(3.27188 + 5.66706i) q^{58} +(0.358181 - 0.620387i) q^{59} +(-1.62044 + 2.80668i) q^{60} +(-5.82633 - 10.0915i) q^{61} +3.15439 q^{62} -8.27099 q^{64} +(-0.452861 - 0.784378i) q^{65} +(-1.26549 + 2.19189i) q^{66} +(-4.69587 + 8.13349i) q^{67} +(2.39246 + 4.14386i) q^{68} -6.61239 q^{69} +10.9914 q^{71} +(0.00323527 + 0.00560366i) q^{72} +(-1.73650 + 3.00771i) q^{73} +(5.23103 - 9.06041i) q^{74} +(-3.67614 - 6.36725i) q^{75} -13.4986 q^{76} -3.53311 q^{78} +(-6.50408 - 11.2654i) q^{79} +(-1.77997 + 3.08299i) q^{80} +(4.63697 - 8.03147i) q^{81} +(-4.94265 - 8.56093i) q^{82} -3.54083 q^{83} +2.13050 q^{85} +(-9.47789 - 16.4162i) q^{86} +(2.86550 - 4.96318i) q^{87} +(0.0245828 - 0.0425786i) q^{88} +(6.02503 + 10.4357i) q^{89} +0.171508 q^{90} +7.64656 q^{92} +(-1.38130 - 2.39248i) q^{93} +(8.35532 - 14.4718i) q^{94} +(-3.00514 + 5.20506i) q^{95} +(7.06415 + 12.2355i) q^{96} -7.43766 q^{97} +0.0675374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

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