LMFDB - Embedded newform 637.2.g.l.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-1.02197 + 1.77010i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.l.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777343 - 1.34640i) q^{2} +0.489252 q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 - 0.658727i) q^{6} -2.46099 q^{8} -2.76063 q^{9} +O(q^{10})$	\(q+(-0.777343 - 1.34640i) q^{2} +0.489252 q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 - 0.658727i) q^{6} -2.46099 q^{8} -2.76063 q^{9} +1.85243 q^{10} +2.11614 q^{11} +(-0.102021 + 0.176706i) q^{12} +(-2.86133 - 2.19381i) q^{13} +(-0.291474 + 0.504848i) q^{15} +(2.33009 + 4.03583i) q^{16} +(-0.453151 + 0.784881i) q^{17} +(2.14596 + 3.71691i) q^{18} -6.69028 q^{19} +(-0.248461 - 0.430346i) q^{20} +(-1.64497 - 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} -1.20404 q^{24} +(1.79015 + 3.10063i) q^{25} +(-0.729501 + 5.55783i) q^{26} -2.81840 q^{27} +(-4.25772 + 7.37459i) q^{29} +0.906303 q^{30} +(-2.64390 - 4.57937i) q^{31} +(1.16156 - 2.01189i) q^{32} +1.03532 q^{33} +1.40902 q^{34} +(0.575663 - 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} +(5.20065 + 9.00778i) q^{38} +(-1.39991 - 1.07332i) q^{39} +(1.46615 - 2.53944i) q^{40} +(0.768181 - 1.33053i) q^{41} +(-2.71636 - 4.70488i) q^{43} +(-0.441269 + 0.764301i) q^{44} +(1.64466 - 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} +(-1.59337 + 2.75979i) q^{47} +(1.14000 + 1.97453i) q^{48} +(2.78312 - 4.82051i) q^{50} +(-0.221705 + 0.384004i) q^{51} +(1.38901 - 0.575982i) q^{52} +(1.41239 + 2.44632i) q^{53} +(2.19086 + 3.79469i) q^{54} +(-1.26070 + 2.18360i) q^{55} -3.27323 q^{57} +13.2389 q^{58} +(-5.12298 + 8.87327i) q^{59} +(-0.121560 - 0.210548i) q^{60} +8.26845 q^{61} +(-4.11044 + 7.11949i) q^{62} +5.70861 q^{64} +(3.96840 - 1.64557i) q^{65} +(-0.804802 - 1.39396i) q^{66} -3.74363 q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.880000 - 1.52420i) q^{69} +(1.26510 + 2.19122i) q^{71} +6.79389 q^{72} +(-2.86522 - 4.96271i) q^{73} +(-3.88018 + 6.72066i) q^{74} +(0.875834 + 1.51699i) q^{75} +(1.39510 - 2.41638i) q^{76} +(-0.356910 + 2.71918i) q^{78} +(-3.03620 + 5.25885i) q^{79} -5.55265 q^{80} +6.90299 q^{81} -2.38856 q^{82} +11.6309 q^{83} +(-0.539935 - 0.935195i) q^{85} +(-4.22310 + 7.31462i) q^{86} +(-2.08310 + 3.60803i) q^{87} -5.20780 q^{88} +(-8.87557 - 15.3729i) q^{89} -5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +4.95437 q^{94} +(3.98577 - 6.90356i) q^{95} +(0.568297 - 0.984319i) q^{96} +(3.10217 + 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.777343	−	1.34640i	−0.549665	−	0.952047i	−0.998297	−	0.0583310i	$-0.981422\pi$
$2$	−0.777343	−	1.34640i	−0.549665	−	0.952047i	0.448632	−	0.893716i	$-0.351911\pi$
$3$	0.489252			0.282470			0.141235	−	0.989976i	$-0.454893\pi$
$3$	0.489252			0.282470			0.141235	+	0.989976i	$0.454893\pi$
$4$	−0.208526	+	0.361177i	−0.104263	+	0.180588i
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	−0.967937	−	0.251192i	$-0.919177\pi$
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	0.701507	+	0.712662i	$0.252511\pi$
$6$	−0.380316	−	0.658727i	−0.155264	−	0.268924i
$7$		0			0
$7$		0			0
$8$	−2.46099			−0.870091
$9$	−2.76063			−0.920211
$10$	1.85243			0.585789
$11$	2.11614			0.638040			0.319020	−	0.947748i	$-0.396646\pi$
$11$	2.11614			0.638040			0.319020	+	0.947748i	$0.396646\pi$
$12$	−0.102021	+	0.176706i	−0.0294511	+	0.0510107i
$13$	−2.86133	−	2.19381i	−0.793590	−	0.608453i
$13$	−2.86133	−	2.19381i	−0.793590	−	0.608453i
$14$		0			0
$15$	−0.291474	+	0.504848i	−0.0752584	+	0.130351i
$16$	2.33009	+	4.03583i	0.582521	+	1.00896i
$17$	−0.453151	+	0.784881i	−0.109905	+	0.190362i	−0.915732	−	0.401790i	$-0.868388\pi$
$17$	−0.453151	+	0.784881i	−0.109905	+	0.190362i	0.805826	+	0.592152i	$0.201721\pi$
$18$	2.14596	+	3.71691i	0.505808	+	0.876084i
$19$	−6.69028			−1.53486			−0.767428	−	0.641135i	$-0.778464\pi$
$19$	−6.69028			−1.53486			−0.767428	+	0.641135i	$0.778464\pi$
$20$	−0.248461	−	0.430346i	−0.0555575	−	0.0962284i
$21$		0			0
$22$	−1.64497	−	2.84917i	−0.350708	−	0.607444i
$23$	−1.79866	−	3.11538i	−0.375048	−	0.649601i	0.615287	−	0.788303i	$-0.289040\pi$
$23$	−1.79866	−	3.11538i	−0.375048	−	0.649601i	−0.990334	+	0.138702i	$0.955707\pi$
$24$	−1.20404			−0.245774
$25$	1.79015	+	3.10063i	0.358030	+	0.620126i
$26$	−0.729501	+	5.55783i	−0.143067	+	1.08998i
$27$	−2.81840			−0.542401
$28$		0			0
$29$	−4.25772	+	7.37459i	−0.790639	+	1.36943i	0.134932	+	0.990855i	$0.456918\pi$
$29$	−4.25772	+	7.37459i	−0.790639	+	1.36943i	−0.925572	+	0.378573i	$0.876415\pi$
$30$	0.906303			0.165467
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	0.524727	−	0.851271i	$-0.324168\pi$
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	−0.999585	+	0.0287913i	$0.990834\pi$
$32$	1.16156	−	2.01189i	0.205337	−	0.355655i
$33$	1.03532			0.180227
$34$	1.40902			0.241644
$35$		0			0
$36$	0.575663	−	0.997077i	0.0959438	−	0.166180i
$37$	−2.49579	−	4.32284i	−0.410306	−	0.710670i	0.584617	−	0.811309i	$-0.301245\pi$
$37$	−2.49579	−	4.32284i	−0.410306	−	0.710670i	−0.994923	+	0.100639i	$0.967911\pi$
$38$	5.20065	+	9.00778i	0.843656	+	1.46126i
$39$	−1.39991	−	1.07332i	−0.224165	−	0.171869i
$40$	1.46615	−	2.53944i	0.231818	−	0.401521i
$41$	0.768181	−	1.33053i	0.119970	−	0.207794i	−0.799786	−	0.600286i	$-0.795054\pi$
$41$	0.768181	−	1.33053i	0.119970	−	0.207794i	0.919755	+	0.392492i	$0.128387\pi$
$42$		0			0
$43$	−2.71636	−	4.70488i	−0.414242	−	0.717488i	0.581107	−	0.813827i	$-0.302620\pi$
$43$	−2.71636	−	4.70488i	−0.414242	−	0.717488i	−0.995349	+	0.0963397i	$0.969286\pi$
$44$	−0.441269	+	0.764301i	−0.0665238	+	0.115223i
$45$	1.64466	−	2.84864i	0.245172	−	0.424650i
$46$	−2.79636	+	4.84344i	−0.412301	+	0.714126i
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	−0.958519	−	0.285030i	$-0.907997\pi$
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	0.726102	+	0.687587i	$0.241330\pi$
$48$	1.14000	+	1.97453i	0.164545	+	0.284999i
$49$		0			0
$50$	2.78312	−	4.82051i	0.393593	−	0.681723i
$51$	−0.221705	+	0.384004i	−0.0310449	+	0.0537714i
$52$	1.38901	−	0.575982i	0.192621	−	0.0798743i
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	0.946574	−	0.322486i	$-0.104518\pi$
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	−0.752568	+	0.658514i	$0.771185\pi$
$54$	2.19086	+	3.79469i	0.298139	+	0.516391i
$55$	−1.26070	+	2.18360i	−0.169993	+	0.294436i
$56$		0			0
$57$	−3.27323			−0.433550
$58$	13.2389			1.73835
$59$	−5.12298	+	8.87327i	−0.666956	+	1.15520i	0.311795	+	0.950149i	$0.399070\pi$
$59$	−5.12298	+	8.87327i	−0.666956	+	1.15520i	−0.978751	+	0.205052i	$0.934264\pi$
$60$	−0.121560	−	0.210548i	−0.0156933	−	0.0271816i
$61$	8.26845			1.05867			0.529333	−	0.848414i	$-0.322442\pi$
$61$	8.26845			1.05867			0.529333	+	0.848414i	$0.322442\pi$
$62$	−4.11044	+	7.11949i	−0.522026	+	0.904176i
$63$		0			0
$64$	5.70861			0.713576
$65$	3.96840	−	1.64557i	0.492219	−	0.204108i
$66$	−0.804802	−	1.39396i	−0.0990643	−	0.171584i
$67$	−3.74363			−0.457358			−0.228679	−	0.973502i	$-0.573441\pi$
$67$	−3.74363			−0.457358			−0.228679	+	0.973502i	$0.573441\pi$
$68$	−0.188987	−	0.327336i	−0.0229181	−	0.0396953i
$69$	−0.880000	−	1.52420i	−0.105939	−	0.183493i
$70$		0			0
$71$	1.26510	+	2.19122i	0.150140	+	0.260050i	0.931279	−	0.364307i	$-0.118694\pi$
$71$	1.26510	+	2.19122i	0.150140	+	0.260050i	−0.781139	+	0.624357i	$0.785361\pi$
$72$	6.79389			0.800668
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	0.648203	−	0.761468i	$-0.275521\pi$
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	−0.983552	+	0.180627i	$0.942187\pi$
$74$	−3.88018	+	6.72066i	−0.451061	+	0.781261i
$75$	0.875834	+	1.51699i	0.101133	+	0.175167i
$76$	1.39510	−	2.41638i	0.160028	−	0.277177i
$77$		0			0
$78$	−0.356910	+	2.71918i	−0.0404121	+	0.307886i
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	−0.984730	−	0.174089i	$-0.944302\pi$
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	0.643131	+	0.765756i	$0.277635\pi$
$80$	−5.55265			−0.620805
$81$	6.90299			0.766999
$82$	−2.38856			−0.263773
$83$	11.6309			1.27665			0.638327	−	0.769766i	$-0.279627\pi$
$83$	11.6309			1.27665			0.638327	+	0.769766i	$0.279627\pi$
$84$		0			0
$85$	−0.539935	−	0.935195i	−0.0585642	−	0.101436i
$86$	−4.22310	+	7.31462i	−0.455388	+	0.788755i
$87$	−2.08310	+	3.60803i	−0.223331	+	0.386821i
$88$	−5.20780			−0.555153
$89$	−8.87557	−	15.3729i	−0.940808	−	1.62953i	−0.763934	−	0.645295i	$-0.776735\pi$
$89$	−8.87557	−	15.3729i	−0.940808	−	1.62953i	−0.176875	−	0.984233i	$-0.556599\pi$
$90$	−5.11387			−0.539049
$91$		0			0
$92$	1.50027			0.156414
$93$	−1.29353	−	2.24046i	−0.134133	−	0.232325i
$94$	4.95437			0.511004
$95$	3.98577	−	6.90356i	0.408932	−	0.708291i
$96$	0.568297	−	0.984319i	0.0580015	−	0.100462i
$97$	3.10217	+	5.37312i	0.314978	+	0.545557i	0.979433	−	0.201771i	$-0.0646696\pi$
$97$	3.10217	+	5.37312i	0.314978	+	0.545557i	−0.664455	+	0.747328i	$0.731336\pi$
$98$		0			0
$99$	−5.84188			−0.587131
$100$	−1.49317			−0.149317
$101$	7.22266			0.718682			0.359341	−	0.933206i	$-0.383001\pi$
$101$	7.22266			0.718682			0.359341	+	0.933206i	$0.383001\pi$
$102$	0.689364			0.0682572
$103$	4.96322	−	8.59656i	0.489041	−	0.847044i	−0.510879	−	0.859652i	$-0.670680\pi$
$103$	4.96322	−	8.59656i	0.489041	−	0.847044i	0.999921	+	0.0126084i	$0.00401349\pi$
$104$	7.04170	+	5.39894i	0.690496	+	0.529409i
$105$		0			0
$106$	2.19582	−	3.80327i	0.213277	−	0.369406i
$107$	1.10003	+	1.90531i	0.106344	+	0.184193i	0.914287	−	0.405068i	$-0.132752\pi$
$107$	1.10003	+	1.90531i	0.106344	+	0.184193i	−0.807942	+	0.589261i	$0.799419\pi$
$108$	0.587708	−	1.01794i	0.0565523	−	0.0979514i
$109$	−6.87291	−	11.9042i	−0.658305	−	1.14022i	−0.981054	−	0.193734i	$-0.937940\pi$
$109$	−6.87291	−	11.9042i	−0.658305	−	1.14022i	0.322749	−	0.946485i	$-0.395393\pi$
$110$	3.91999			0.373757
$111$	−1.22107	−	2.11496i	−0.115899	−	0.200743i
$112$		0			0
$113$	8.04736	+	13.9384i	0.757032	+	1.31122i	0.944358	+	0.328920i	$0.106685\pi$
$113$	8.04736	+	13.9384i	0.757032	+	1.31122i	−0.187326	+	0.982298i	$0.559982\pi$
$114$	2.54442	+	4.40707i	0.238307	+	0.412760i
$115$	4.28626			0.399696
$116$	−1.77569	−	3.07558i	−0.164869	−	0.285561i
$117$	7.89908	+	6.05630i	0.730270	+	0.559905i
$118$	15.9293			1.46641
$119$		0			0
$120$	0.717315	−	1.24243i	0.0654816	−	0.113418i
$121$	−6.52196			−0.592905
$122$	−6.42743	−	11.1326i	−0.581912	−	1.00790i
$123$	0.375834	−	0.650963i	0.0338878	−	0.0586954i
$124$	2.20528			0.198040
$125$	−10.2235			−0.914420
$126$		0			0
$127$	7.83921	−	13.5779i	0.695617	−	1.20484i	−0.274355	−	0.961628i	$-0.588464\pi$
$127$	7.83921	−	13.5779i	0.695617	−	1.20484i	0.969972	−	0.243216i	$-0.0782023\pi$
$128$	−6.76067	−	11.7098i	−0.597565	−	1.03501i
$129$	−1.32899	−	2.30187i	−0.117011	−	0.202668i
$130$	−5.30041	−	4.06387i	−0.464876	−	0.356425i
$131$	−4.76884	+	8.25988i	−0.416656	+	0.721669i	−0.995601	−	0.0936976i	$-0.970131\pi$
$131$	−4.76884	+	8.25988i	−0.416656	+	0.721669i	0.578945	+	0.815367i	$0.303465\pi$
$132$	−0.215892	+	0.373935i	−0.0187910	+	0.0325469i
$133$		0			0
$134$	2.91009	+	5.04042i	0.251393	+	0.435426i
$135$	1.67908	−	2.90825i	0.144512	−	0.250302i
$136$	1.11520	−	1.93158i	0.0956277	−	0.165632i
$137$	1.38231	−	2.39422i	0.118098	−	0.204552i	−0.800916	−	0.598777i	$-0.795654\pi$
$137$	1.38231	−	2.39422i	0.118098	−	0.204552i	0.919014	+	0.394225i	$0.128987\pi$
$138$	−1.36812	+	2.36966i	−0.116462	+	0.201719i
$139$	−11.3983	−	19.7425i	−0.966795	−	1.67454i	−0.704714	−	0.709492i	$-0.748925\pi$
$139$	−11.3983	−	19.7425i	−0.966795	−	1.67454i	−0.262081	−	0.965046i	$-0.584409\pi$
$140$		0			0
$141$	−0.779557	+	1.35023i	−0.0656505	+	0.113710i
$142$	1.96684	−	3.40666i	0.165053	−	0.285881i
$143$	−6.05497	−	4.64240i	−0.506342	−	0.388217i
$144$	−6.43251	−	11.1414i	−0.536043	−	0.928453i
$145$	−5.07312	−	8.78691i	−0.421300	−	0.729713i
$146$	−4.45452	+	7.71546i	−0.368659	+	0.638536i
$147$		0			0
$148$	2.08175			0.171119
$149$	−14.4116			−1.18065			−0.590323	−	0.807167i	$-0.701000\pi$
$149$	−14.4116			−1.18065			−0.590323	+	0.807167i	$0.701000\pi$
$150$	1.36165	−	2.35844i	0.111178	−	0.192566i
$151$	−7.62901	−	13.2138i	−0.620840	−	1.07533i	−0.989330	−	0.145695i	$-0.953458\pi$
$151$	−7.62901	−	13.2138i	−0.620840	−	1.07533i	0.368489	−	0.929632i	$-0.379875\pi$
$152$	16.4647			1.33546
$153$	1.25098	−	2.16677i	0.101136	−	0.175173i
$154$		0			0
$155$	6.30048			0.506067
$156$	0.679577	−	0.281800i	0.0544097	−	0.0225621i
$157$	−5.70745	−	9.88559i	−0.455504	−	0.788956i	0.543213	−	0.839595i	$-0.317208\pi$
$157$	−5.70745	−	9.88559i	−0.455504	−	0.788956i	−0.998717	+	0.0506387i	$0.983874\pi$
$158$	9.44068			0.751060
$159$	0.691012	+	1.19687i	0.0548008	+	0.0949178i
$160$	1.38402	+	2.39719i	0.109416	+	0.189514i
$161$		0			0
$162$	−5.36600	−	9.29418i	−0.421592	−	0.730220i
$163$	−14.4077			−1.12850			−0.564249	−	0.825605i	$-0.690834\pi$
$163$	−14.4077			−1.12850			−0.564249	+	0.825605i	$0.690834\pi$
$164$	0.320371	+	0.554899i	0.0250168	+	0.0433303i
$165$	−0.616800	+	1.06833i	−0.0480178	+	0.0831693i
$166$	−9.04118	−	15.6598i	−0.701731	−	1.21543i
$167$	3.88595	−	6.73066i	0.300704	−	0.520834i	−0.675592	−	0.737276i	$-0.736112\pi$
$167$	3.88595	−	6.73066i	0.300704	−	0.520834i	0.976296	+	0.216442i	$0.0694452\pi$
$168$		0			0
$169$	3.37442	+	12.5544i	0.259571	+	0.965724i
$170$	−0.839430	+	1.45394i	−0.0643813	+	0.111512i
$171$	18.4694			1.41239
$172$	2.26573			0.172760
$173$	−6.09461			−0.463365			−0.231682	−	0.972791i	$-0.574423\pi$
$173$	−6.09461			−0.463365			−0.231682	+	0.972791i	$0.574423\pi$
$174$	6.47713			0.491030
$175$		0			0
$176$	4.93078	+	8.54037i	0.371672	+	0.643754i
$177$	−2.50643	+	4.34126i	−0.188395	+	0.326309i
$178$	−13.7987	+	23.9001i	−1.03426	+	1.79139i
$179$	18.5298			1.38498			0.692490	−	0.721428i	$-0.256514\pi$
$179$	18.5298			1.38498			0.692490	+	0.721428i	$0.256514\pi$
$180$	0.685909	+	1.18803i	0.0511246	+	0.0885504i
$181$	5.60520			0.416631			0.208316	−	0.978062i	$-0.433202\pi$
$181$	5.60520			0.416631			0.208316	+	0.978062i	$0.433202\pi$
$182$		0			0
$183$	4.04535			0.299041
$184$	4.42650	+	7.66692i	0.326326	+	0.565212i
$185$	5.94753			0.437271
$186$	−2.01104	+	3.48322i	−0.147456	+	0.255402i
$187$	−0.958931	+	1.66092i	−0.0701240	+	0.121458i
$188$	−0.664516	−	1.15097i	−0.0484648	−	0.0839435i
$189$		0			0
$190$	−12.3933			−0.899102
$191$	0.503703			0.0364466			0.0182233	−	0.999834i	$-0.494199\pi$
$191$	0.503703			0.0364466			0.0182233	+	0.999834i	$0.494199\pi$
$192$	2.79294			0.201563
$193$	−3.71244			−0.267227			−0.133614	−	0.991033i	$-0.542658\pi$
$193$	−3.71244			−0.267227			−0.133614	+	0.991033i	$0.542658\pi$
$194$	4.82290	−	8.35351i	0.346264	−	0.599747i
$195$	1.94154	−	0.805100i	0.139037	−	0.0576544i
$196$		0			0
$197$	3.72225	−	6.44713i	0.265200	−	0.459339i	−0.702416	−	0.711766i	$-0.747895\pi$
$197$	3.72225	−	6.44713i	0.265200	−	0.459339i	0.967616	+	0.252427i	$0.0812288\pi$
$198$	4.54115	+	7.86550i	0.322725	+	0.558977i
$199$	3.75278	−	6.50001i	0.266028	−	0.460773i	−0.701805	−	0.712369i	$-0.747622\pi$
$199$	3.75278	−	6.50001i	0.266028	−	0.460773i	0.967832	+	0.251596i	$0.0809554\pi$
$200$	−4.40554	−	7.63062i	−0.311519	−	0.539566i
$201$	−1.83158			−0.129190
$202$	−5.61449	−	9.72458i	−0.395034	−	0.684219i
$203$		0			0
$204$	−0.0924624	−	0.160149i	−0.00647366	−	0.0112127i
$205$	0.915297	+	1.58534i	0.0639271	+	0.110725i
$206$	−15.4325			−1.07523
$207$	4.96545	+	8.60042i	0.345123	+	0.597770i
$208$	2.18668	−	16.6596i	0.151619	−	1.15513i
$209$	−14.1576			−0.979299
$210$		0			0
$211$	−1.89531	+	3.28278i	−0.130479	+	0.225996i	−0.923861	−	0.382728i	$-0.874985\pi$
$211$	−1.89531	+	3.28278i	−0.130479	+	0.225996i	0.793383	+	0.608723i	$0.208318\pi$
$212$	−1.17807			−0.0809105
$213$	0.618953	+	1.07206i	0.0424100	+	0.0734562i
$214$	1.71020	−	2.96216i	0.116907	−	0.202489i
$215$	6.47316			0.441466
$216$	6.93605			0.471938
$217$		0			0
$218$	−10.6852	+	18.5073i	−0.723695	+	1.25348i
$219$	−1.40181	−	2.42801i	−0.0947258	−	0.164070i
$220$	−0.525777	−	0.910673i	−0.0354479	−	0.0613975i
$221$	3.01849	−	1.25168i	0.203046	−	0.0841970i
$222$	−1.89838	+	3.28809i	−0.127411	+	0.220682i
$223$	2.43440	−	4.21650i	0.163019	−	0.282358i	−0.772931	−	0.634490i	$-0.781210\pi$
$223$	2.43440	−	4.21650i	0.163019	−	0.282358i	0.935950	+	0.352133i	$0.114543\pi$
$224$		0			0
$225$	−4.94195	−	8.55971i	−0.329463	−	0.570647i
$226$	12.5111	−	21.6699i	0.832228	−	1.44146i
$227$	12.0884	−	20.9376i	0.802332	−	1.38968i	−0.115745	−	0.993279i	$-0.536925\pi$
$227$	12.0884	−	20.9376i	0.802332	−	1.38968i	0.918077	−	0.396402i	$-0.129741\pi$
$228$	0.682552	−	1.18222i	0.0452031	−	0.0782941i
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	0.244635	+	0.969615i	$0.421332\pi$
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	−0.962029	+	0.272947i	$0.912002\pi$
$230$	−3.33190	−	5.77101i	−0.219699	−	0.380529i
$231$		0			0
$232$	10.4782	−	18.1488i	0.687928	−	1.19153i
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	−0.921486	−	0.388411i	$-0.873024\pi$
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	0.797117	+	0.603825i	$0.206358\pi$
$234$	2.01389	−	15.3431i	0.131652	−	1.00301i
$235$	−1.89851	−	3.28832i	−0.123845	−	0.214507i
$236$	−2.13655	−	3.70061i	−0.139077	−	0.240889i
$237$	−1.48547	+	2.57290i	−0.0964914	+	0.167128i
$238$		0			0
$239$	21.9100			1.41724			0.708619	−	0.705592i	$-0.249319\pi$
$239$	21.9100			1.41724			0.708619	+	0.705592i	$0.249319\pi$
$240$	−2.71664			−0.175358
$241$	−10.3744	+	17.9690i	−0.668273	+	1.15748i	0.310114	+	0.950699i	$0.399633\pi$
$241$	−10.3744	+	17.9690i	−0.668273	+	1.15748i	−0.978387	+	0.206783i	$0.933701\pi$
$242$	5.06980	+	8.78115i	0.325899	+	0.564474i
$243$	11.8325			0.759055
$244$	−1.72418	+	2.98637i	−0.110380	+	0.191183i
$245$		0			0
$246$	−1.16861			−0.0745077
$247$	19.1431	+	14.6772i	1.21805	+	0.933887i
$248$	6.50661	+	11.2698i	0.413170	+	0.715632i
$249$	5.69042			0.360616
$250$	7.94719	+	13.7649i	0.502624	+	0.870571i
$251$	6.62891	+	11.4816i	0.418413	+	0.724713i	0.995780	−	0.0917718i	$-0.0292530\pi$
$251$	6.62891	+	11.4816i	0.418413	+	0.724713i	−0.577367	+	0.816485i	$0.695920\pi$
$252$		0			0
$253$	−3.80622	−	6.59257i	−0.239295	−	0.414472i
$254$	−24.3750			−1.52943
$255$	−0.264164	−	0.457546i	−0.0165426	−	0.0286526i
$256$	−4.80213	+	8.31753i	−0.300133	+	0.519845i
$257$	−6.58555	−	11.4065i	−0.410795	−	0.711518i	0.584182	−	0.811623i	$-0.301416\pi$
$257$	−6.58555	−	11.4065i	−0.410795	−	0.711518i	−0.994977	+	0.100105i	$0.968082\pi$
$258$	−2.06616	+	3.57869i	−0.128633	+	0.222799i
$259$		0			0
$260$	−0.233169	+	1.77644i	−0.0144605	+	0.110170i
$261$	11.7540	−	20.3585i	0.727555	−	1.26016i
$262$	14.8281			0.916084
$263$	−19.1406			−1.18026			−0.590129	−	0.807309i	$-0.700923\pi$
$263$	−19.1406			−1.18026			−0.590129	+	0.807309i	$0.700923\pi$
$264$	−2.54792			−0.156814
$265$	−3.36575			−0.206756
$266$		0			0
$267$	−4.34239	−	7.52123i	−0.265750	−	0.460292i
$268$	0.780643	−	1.35211i	0.0476854	−	0.0825935i
$269$	−14.2411	+	24.6663i	−0.868296	+	1.50393i	−0.00455867	+	0.999990i	$0.501451\pi$
$269$	−14.2411	+	24.6663i	−0.868296	+	1.50393i	−0.863737	+	0.503943i	$0.831882\pi$
$270$	−5.22088			−0.317732
$271$	8.97371	+	15.5429i	0.545114	+	0.944165i	0.998600	+	0.0529014i	$0.0168469\pi$
$271$	8.97371	+	15.5429i	0.545114	+	0.944165i	−0.453486	+	0.891263i	$0.649820\pi$
$272$	−4.22353			−0.256089
$273$		0			0
$274$	−4.29811			−0.259658
$275$	3.78821	+	6.56137i	0.228437	+	0.395665i
$276$	0.734010			0.0441822
$277$	−6.71943	+	11.6384i	−0.403732	+	0.699284i	−0.994173	−	0.107797i	$-0.965620\pi$
$277$	−6.71943	+	11.6384i	−0.403732	+	0.699284i	0.590441	+	0.807081i	$0.298954\pi$
$278$	−17.7209	+	30.6934i	−1.06283	+	1.84087i
$279$	7.29884	+	12.6420i	0.436970	+	0.756855i
$280$		0			0
$281$	−29.9530			−1.78685			−0.893424	−	0.449214i	$-0.851704\pi$
$281$	−29.9530			−1.78685			−0.893424	+	0.449214i	$0.851704\pi$
$282$	2.42393			0.144343
$283$	9.89122			0.587972			0.293986	−	0.955810i	$-0.405018\pi$
$283$	9.89122			0.587972			0.293986	+	0.955810i	$0.405018\pi$
$284$	−1.05523			−0.0626161
$285$	1.95005	−	3.37758i	0.115511	−	0.200070i
$286$	−1.54373	+	11.7611i	−0.0912824	+	0.695451i
$287$		0			0
$288$	−3.20665	+	5.55408i	−0.188954	+	0.327277i
$289$	8.08931	+	14.0111i	0.475842	+	0.824182i
$290$	−7.88712	+	13.6609i	−0.463148	+	0.802195i
$291$	1.51774	+	2.62881i	0.0889716	+	0.154103i
$292$	2.38989			0.139858
$293$	3.95529	+	6.85076i	0.231071	+	0.400226i	0.958123	−	0.286356i	$-0.0924438\pi$
$293$	3.95529	+	6.85076i	0.231071	+	0.400226i	−0.727053	+	0.686581i	$0.759111\pi$
$294$		0			0
$295$	−6.10409	−	10.5726i	−0.355394	−	0.615561i
$296$	6.14212	+	10.6385i	0.357003	+	0.618348i
$297$	−5.96412			−0.346073
$298$	11.2028	+	19.4038i	0.648959	+	1.12403i
$299$	−1.68797	+	12.8601i	−0.0976175	+	0.743716i
$300$	−0.730535			−0.0421775
$301$		0			0
$302$	−11.8607	+	20.5434i	−0.682508	+	1.18214i
$303$	3.53370			0.203006
$304$	−15.5889	−	27.0008i	−0.894086	−	1.54860i
$305$	−4.92598	+	8.53204i	−0.282061	+	0.488543i
$306$	−3.88978			−0.222364
$307$	−1.27238			−0.0726187			−0.0363094	−	0.999341i	$-0.511560\pi$
$307$	−1.27238			−0.0726187			−0.0363094	+	0.999341i	$0.511560\pi$
$308$		0			0
$309$	2.42827	−	4.20588i	0.138139	−	0.239264i
$310$	−4.89763	−	8.48295i	−0.278167	−	0.481799i
$311$	12.3817	+	21.4458i	0.702103	+	1.21608i	0.967727	+	0.252002i	$0.0810888\pi$
$311$	12.3817	+	21.4458i	0.702103	+	1.21608i	−0.265624	+	0.964077i	$0.585578\pi$
$312$	3.44516	+	2.64144i	0.195044	+	0.149542i
$313$	1.18826	−	2.05812i	0.0671642	−	0.116332i	−0.830488	−	0.557037i	$-0.811938\pi$
$313$	1.18826	−	2.05812i	0.0671642	−	0.116332i	0.897652	+	0.440705i	$0.145272\pi$
$314$	−8.87330	+	15.3690i	−0.500749	+	0.867323i
$315$		0			0
$316$	−1.26625	−	2.19321i	−0.0712322	−	0.123378i
$317$	9.88979	−	17.1296i	0.555466	−	0.962096i	−0.442401	−	0.896817i	$-0.645873\pi$
$317$	9.88979	−	17.1296i	0.555466	−	0.962096i	0.997867	−	0.0652782i	$-0.0207935\pi$
$318$	1.07431	−	1.86076i	0.0602442	−	0.104346i
$319$	−9.00993	+	15.6057i	−0.504459	+	0.873749i
$320$	−3.40093	+	5.89059i	−0.190118	+	0.329294i
$321$	0.538192	+	0.932176i	0.0300390	+	0.0520290i
$322$		0			0
$323$	3.03171	−	5.25108i	0.168689	−	0.292178i
$324$	−1.43945	+	2.49320i	−0.0799695	+	0.138511i
$325$	1.67997	−	12.7992i	0.0931882	−	0.709970i
$326$	11.1997	+	19.3985i	0.620295	+	1.07438i
$327$	−3.36258	−	5.82416i	−0.185951	−	0.322077i
$328$	−1.89049	+	3.27442i	−0.104385	+	0.180799i
$329$		0			0
$330$	1.91786			0.105575
$331$	3.92773			0.215888			0.107944	−	0.994157i	$-0.465573\pi$
$331$	3.92773			0.215888			0.107944	+	0.994157i	$0.465573\pi$
$332$	−2.42533	+	4.20080i	−0.133107	+	0.230549i
$333$	6.88997	+	11.9338i	0.377568	+	0.653967i
$334$	−12.0829			−0.661145
$335$	2.23029	−	3.86298i	0.121854	−	0.211057i
$336$		0			0
$337$	−7.14099			−0.388995			−0.194497	−	0.980903i	$-0.562308\pi$
$337$	−7.14099			−0.388995			−0.194497	+	0.980903i	$0.562308\pi$
$338$	14.2802	−	14.3024i	0.776738	−	0.777948i
$339$	3.93718	+	6.81940i	0.213838	+	0.370379i
$340$	0.450361			0.0244243
$341$	−5.59486	−	9.69059i	−0.302979	−	0.524775i
$342$	−14.3571	−	24.8672i	−0.776342	−	1.34466i
$343$		0			0
$344$	6.68494	+	11.5787i	0.360428	+	0.624280i
$345$	2.09706			0.112902
$346$	4.73761	+	8.20578i	0.254695	+	0.441145i
$347$	−5.03498	+	8.72085i	−0.270292	+	0.468160i	−0.968937	−	0.247309i	$-0.920454\pi$
$347$	−5.03498	+	8.72085i	−0.270292	+	0.468160i	0.698644	+	0.715469i	$0.253787\pi$
$348$	−0.868758	−	1.50473i	−0.0465703	−	0.0806622i
$349$	−3.14418	+	5.44588i	−0.168304	+	0.291512i	−0.937824	−	0.347112i	$-0.887162\pi$
$349$	−3.14418	+	5.44588i	−0.168304	+	0.291512i	0.769520	+	0.638623i	$0.220496\pi$
$350$		0			0
$351$	8.06437	+	6.18302i	0.430444	+	0.330025i
$352$	2.45803	−	4.25743i	0.131013	−	0.226922i
$353$	−34.1672			−1.81854			−0.909269	−	0.416210i	$-0.863358\pi$
$353$	−34.1672			−1.81854			−0.909269	+	0.416210i	$0.863358\pi$
$354$	7.79342			0.414216
$355$	−3.01477			−0.160007
$356$	7.40313			0.392365
$357$		0			0
$358$	−14.4040	−	24.9484i	−0.761274	−	1.31857i
$359$	−9.34327	+	16.1830i	−0.493119	+	0.854107i	−0.999969	−	0.00792750i	$-0.997477\pi$
$359$	−9.34327	+	16.1830i	−0.493119	+	0.854107i	0.506850	+	0.862034i	$0.330810\pi$
$360$	−4.04750	+	7.01047i	−0.213322	+	0.369484i
$361$	25.7599			1.35578
$362$	−4.35716	−	7.54683i	−0.229007	−	0.396653i
$363$	−3.19088			−0.167478
$364$		0			0
$365$	6.82788			0.357388
$366$	−3.14463	−	5.44666i	−0.164372	−	0.284701i
$367$	31.0611			1.62137			0.810687	−	0.585479i	$-0.199094\pi$
$367$	31.0611			1.62137			0.810687	+	0.585479i	$0.199094\pi$
$368$	8.38209	−	14.5182i	0.436946	−	0.756813i
$369$	−2.12067	+	3.67310i	−0.110397	+	0.191214i
$370$	−4.62327	−	8.00775i	−0.240353	−	0.416303i
$371$		0			0
$372$	1.07894			0.0559404
$373$	−2.93704			−0.152074			−0.0760371	−	0.997105i	$-0.524227\pi$
$373$	−2.93704			−0.152074			−0.0760371	+	0.997105i	$0.524227\pi$
$374$	2.98168			0.154179
$375$	−5.00188			−0.258296
$376$	3.92126	−	6.79182i	0.202223	−	0.350261i
$377$	28.3612	−	11.7605i	1.46068	−	0.605698i
$378$		0			0
$379$	−5.04254	+	8.73394i	−0.259018	+	0.448632i	−0.965979	−	0.258620i	$-0.916732\pi$
$379$	−5.04254	+	8.73394i	−0.259018	+	0.448632i	0.706961	+	0.707252i	$0.250066\pi$
$380$	1.66227	+	2.87914i	0.0852727	+	0.147697i
$381$	3.83534	−	6.64301i	0.196491	−	0.340332i
$382$	−0.391550	−	0.678184i	−0.0200334	−	0.0346989i
$383$	−3.68931			−0.188515			−0.0942576	−	0.995548i	$-0.530048\pi$
$383$	−3.68931			−0.188515			−0.0942576	+	0.995548i	$0.530048\pi$
$384$	−3.30767	−	5.72905i	−0.168794	−	0.292360i
$385$		0			0
$386$	2.88584	+	4.99842i	0.146885	+	0.254413i
$387$	7.49888	+	12.9884i	0.381190	+	0.660240i
$388$	−2.58753			−0.131362
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	−0.996082	−	0.0884295i	$-0.971815\pi$
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	0.421459	−	0.906847i	$-0.361518\pi$
$390$	−2.59323	−	1.98825i	−0.131313	−	0.100679i
$391$	3.26027			0.164879
$392$		0			0
$393$	−2.33316	+	4.04116i	−0.117693	+	0.203849i
$394$	−11.5739			−0.583084
$395$	−3.61767	−	6.26598i	−0.182025	−	0.315276i
$396$	1.21818	−	2.10995i	0.0612160	−	0.106029i
$397$	29.1360			1.46229			0.731146	−	0.682221i	$-0.238986\pi$
$397$	29.1360			1.46229			0.731146	+	0.682221i	$0.238986\pi$
$398$	−11.6688			−0.584904
$399$		0			0
$400$	−8.34241	+	14.4495i	−0.417120	+	0.722474i
$401$	−4.06026	−	7.03258i	−0.202760	−	0.351190i	0.746657	−	0.665209i	$-0.231658\pi$
$401$	−4.06026	−	7.03258i	−0.202760	−	0.351190i	−0.949417	+	0.314019i	$0.898324\pi$
$402$	1.42377	+	2.46603i	0.0710110	+	0.122995i
$403$	−2.48118	+	18.9033i	−0.123596	+	0.941641i
$404$	−1.50611	+	2.60866i	−0.0749318	+	0.129786i
$405$	−4.11250	+	7.12305i	−0.204352	+	0.353947i
$406$		0			0
$407$	−5.28144	−	9.14773i	−0.261791	−	0.453436i
$408$	0.545614	−	0.945031i	0.0270119	−	0.0467860i
$409$	−4.16131	+	7.20759i	−0.205763	+	0.356393i	−0.950376	−	0.311105i	$-0.899301\pi$
$409$	−4.16131	+	7.20759i	−0.205763	+	0.356393i	0.744612	+	0.667497i	$0.232634\pi$
$410$	1.42300	−	2.46471i	0.0702769	−	0.121723i
$411$	0.676295	−	1.17138i	0.0333592	−	0.0577798i
$412$	2.06992	+	3.58520i	0.101978	+	0.176630i
$413$		0			0
$414$	7.71973	−	13.3710i	0.379404	−	0.657147i
$415$	−6.92915	+	12.0016i	−0.340139	+	0.589138i
$416$	−7.73731	+	3.20843i	−0.379353	+	0.157306i
$417$	−5.57666	−	9.65905i	−0.273090	−	0.473006i
$418$	11.0053	+	19.0617i	0.538286	+	0.932339i
$419$	−6.50832	+	11.2727i	−0.317952	+	0.550710i	−0.980061	−	0.198699i	$-0.936329\pi$
$419$	−6.50832	+	11.2727i	−0.317952	+	0.550710i	0.662108	+	0.749408i	$0.269662\pi$
$420$		0			0
$421$	−8.89681			−0.433604			−0.216802	−	0.976216i	$-0.569563\pi$
$421$	−8.89681			−0.433604			−0.216802	+	0.976216i	$0.569563\pi$
$422$	5.89323			0.286878
$423$	4.39870	−	7.61877i	0.213872	−	0.370437i
$424$	−3.47587	−	6.02038i	−0.168803	−	0.292376i
$425$	−3.24484			−0.157398
$426$	0.962279	−	1.66672i	0.0466225	−	0.0807526i
$427$		0			0
$428$	−0.917539			−0.0443509
$429$	−2.96240	−	2.27130i	−0.143026	−	0.109659i
$430$	−5.03187	−	8.71545i	−0.242658	−	0.420296i
$431$	−8.95743			−0.431464			−0.215732	−	0.976453i	$-0.569214\pi$
$431$	−8.95743			−0.431464			−0.215732	+	0.976453i	$0.569214\pi$
$432$	−6.56711	−	11.3746i	−0.315960	−	0.547259i
$433$	−0.0864547	−	0.149744i	−0.00415475	−	0.00719624i	0.863941	−	0.503594i	$-0.167989\pi$
$433$	−0.0864547	−	0.149744i	−0.00415475	−	0.00719624i	−0.868095	+	0.496398i	$0.834656\pi$
$434$		0			0
$435$	−2.48203	−	4.29901i	−0.119004	−	0.206122i
$436$	5.73271			0.274547
$437$	12.0336	+	20.8428i	0.575644	+	0.997045i
$438$	−2.17938	+	3.77480i	−0.104135	+	0.180367i
$439$	4.77080	+	8.26327i	0.227698	+	0.394384i	0.957125	−	0.289674i	$-0.0935468\pi$
$439$	4.77080	+	8.26327i	0.227698	+	0.394384i	−0.729428	+	0.684058i	$0.760213\pi$
$440$	3.10257	−	5.37382i	0.147909	−	0.256187i
$441$		0			0
$442$	−4.03166	−	3.09111i	−0.191767	−	0.147029i
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	−0.652852	−	0.757485i	$-0.726428\pi$
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	0.982428	+	0.186644i	$0.0597610\pi$
$444$	1.01850			0.0483358
$445$	21.1507			1.00264
$446$	−7.56945			−0.358424
$447$	−7.05091			−0.333496
$448$		0			0
$449$	10.6456	+	18.4388i	0.502398	+	0.870180i	0.999996	+	0.00277167i	$0.000882252\pi$
$449$	10.6456	+	18.4388i	0.502398	+	0.870180i	−0.497598	+	0.867408i	$0.665784\pi$
$450$	−7.68318	+	13.3077i	−0.362189	+	0.627329i
$451$	1.62558	−	2.81558i	0.0765455	−	0.132581i
$452$	−6.71232			−0.315721
$453$	−3.73251	−	6.46489i	−0.175368	−	0.303747i
$454$	−37.5872			−1.76406
$455$		0			0
$456$	8.05539			0.377228
$457$	−4.84282	−	8.38801i	−0.226538	−	0.392375i	0.730242	−	0.683189i	$-0.239407\pi$
$457$	−4.84282	−	8.38801i	−0.226538	−	0.392375i	−0.956780	+	0.290814i	$0.906074\pi$
$458$	33.7558			1.57730
$459$	1.27716	−	2.21211i	0.0596128	−	0.103252i
$460$	−0.893795	+	1.54810i	−0.0416734	+	0.0721804i
$461$	−0.687178	−	1.19023i	−0.0320051	−	0.0554344i	0.849579	−	0.527461i	$-0.176856\pi$
$461$	−0.687178	−	1.19023i	−0.0320051	−	0.0554344i	−0.881584	+	0.472027i	$0.843523\pi$
$462$		0			0
$463$	31.7710			1.47653			0.738263	−	0.674513i	$-0.235646\pi$
$463$	31.7710			1.47653			0.738263	+	0.674513i	$0.235646\pi$
$464$	−39.6834			−1.84226
$465$	3.08252			0.142948
$466$	5.90290			0.273446
$467$	−14.5605	+	25.2195i	−0.673778	+	1.16702i	0.303046	+	0.952976i	$0.401996\pi$
$467$	−14.5605	+	25.2195i	−0.673778	+	1.16702i	−0.976824	+	0.214042i	$0.931337\pi$
$468$	−3.83456	+	1.59007i	−0.177252	+	0.0735012i
$469$		0			0
$470$	−2.95160	+	5.11231i	−0.136147	+	0.235813i
$471$	−2.79238	−	4.83654i	−0.128666	−	0.222856i
$472$	12.6076	−	21.8370i	0.580312	−	1.00513i
$473$	−5.74820	−	9.95618i	−0.264303	−	0.457786i
$474$	4.61887			0.212152
$475$	−11.9766	−	20.7441i	−0.549525	−	0.951804i
$476$		0			0
$477$	−3.89908	−	6.75341i	−0.178527	−	0.309217i
$478$	−17.0316	−	29.4995i	−0.779005	−	1.34928i
$479$	−9.72184			−0.444202			−0.222101	−	0.975024i	$-0.571292\pi$
$479$	−9.72184			−0.444202			−0.222101	+	0.975024i	$0.571292\pi$
$480$	0.677132	+	1.17283i	0.0309067	+	0.0535320i
$481$	−2.34219	+	17.8444i	−0.106795	+	0.813633i
$482$	32.2578			1.46930
$483$		0			0
$484$	1.36000	−	2.35558i	0.0618180	−	0.107072i
$485$	−7.39254			−0.335678
$486$	−9.19791	−	15.9313i	−0.417226	−	0.722656i
$487$	8.55666	−	14.8206i	0.387739	−	0.671584i	−0.604406	−	0.796676i	$-0.706589\pi$
$487$	8.55666	−	14.8206i	0.387739	−	0.671584i	0.992145	+	0.125093i	$0.0399228\pi$
$488$	−20.3486			−0.921137
$489$	−7.04899			−0.318766
$490$		0			0
$491$	12.8607	−	22.2753i	0.580394	−	1.00527i	−0.415038	−	0.909804i	$-0.636232\pi$
$491$	12.8607	−	22.2753i	0.580394	−	1.00527i	0.995432	−	0.0954681i	$-0.0304348\pi$
$492$	0.156742	+	0.271485i	0.00706647	+	0.0122395i
$493$	−3.85879	−	6.68361i	−0.173791	−	0.301015i
$494$	4.88057	−	37.1835i	0.219587	−	1.67296i
$495$	3.48033	−	6.02812i	0.156429	−	0.270944i
$496$	12.3210	−	21.3407i	0.553231	−	0.958224i
$497$		0			0
$498$	−4.42341	−	7.66157i	−0.198218	−	0.343323i
$499$	−2.70198	+	4.67996i	−0.120957	+	0.209504i	−0.920145	−	0.391577i	$-0.871930\pi$
$499$	−2.70198	+	4.67996i	−0.120957	+	0.209504i	0.799188	+	0.601081i	$0.205263\pi$
$500$	2.13187	−	3.69250i	0.0953400	−	0.165134i
$501$	1.90121	−	3.29299i	0.0849396	−	0.147120i
$502$	10.3059	−	17.8503i	0.459974	−	0.796699i
$503$	−6.30847	−	10.9266i	−0.281281	−	0.487193i	0.690420	−	0.723409i	$-0.257426\pi$
$503$	−6.30847	−	10.9266i	−0.281281	−	0.487193i	−0.971700	+	0.236216i	$0.924093\pi$
$504$		0			0
$505$	−4.30294	+	7.45292i	−0.191478	+	0.331650i
$506$	−5.91749	+	10.2494i	−0.263064	+	0.455641i
$507$	1.65094	+	6.14227i	0.0733209	+	0.272788i
$508$	3.26935	+	5.66268i	0.145054	+	0.251241i
$509$	−0.979379	−	1.69633i	−0.0434102	−	0.0751887i	0.843504	−	0.537123i	$-0.180489\pi$
$509$	−0.979379	−	1.69633i	−0.0434102	−	0.0751887i	−0.886914	+	0.461934i	$0.847156\pi$
$510$	−0.410692	+	0.711340i	−0.0181858	+	0.0314987i
$511$		0			0
$512$	−12.1111			−0.535240
$513$	18.8559			0.832507
$514$	−10.2385	+	17.7335i	−0.451599	+	0.782193i
$515$	5.91374	+	10.2429i	0.260590	+	0.451356i
$516$	1.10851			0.0487994
$517$	−3.37178	+	5.84010i	−0.148291	+	0.256847i
$518$		0			0
$519$	−2.98180			−0.130886
$520$	−9.76618	+	4.04974i	−0.428276	+	0.177593i
$521$	−19.5477	−	33.8576i	−0.856401	−	1.48333i	−0.875339	−	0.483509i	$-0.839362\pi$
$521$	−19.5477	−	33.8576i	−0.856401	−	1.48333i	0.0189387	−	0.999821i	$-0.493971\pi$
$522$	−36.5476			−1.59965
$523$	−4.35634	−	7.54540i	−0.190489	−	0.329937i	0.754923	−	0.655813i	$-0.227674\pi$
$523$	−4.35634	−	7.54540i	−0.190489	−	0.329937i	−0.945413	+	0.325876i	$0.894341\pi$
$524$	−1.98885	−	3.44479i	−0.0868834	−	0.150486i
$525$		0			0
$526$	14.8788	+	25.7708i	0.648746	+	1.12366i
$527$	4.79235			0.208758
$528$	2.41239	+	4.17839i	0.104986	+	0.181841i
$529$	5.02961	−	8.71154i	0.218679	−	0.378763i
$530$	2.61634	+	4.53164i	0.113647	+	0.196842i
$531$	14.1427	−	24.4958i	0.613740	−	1.06303i
$532$		0			0
$533$	−5.11694	+	2.12184i	−0.221639	+	0.0919072i
$534$	−6.75105	+	11.6932i	−0.292147	+	0.506013i
$535$	−2.62140			−0.113333
$536$	9.21304			0.397943
$537$	9.06571			0.391214
$538$	44.2809			1.90909
$539$		0			0
$540$	0.700261	+	1.21289i	0.0301344	+	0.0521944i
$541$	10.7497	−	18.6190i	0.462165	−	0.800493i	−0.536904	−	0.843644i	$-0.680406\pi$
$541$	10.7497	−	18.6190i	0.462165	−	0.800493i	0.999069	+	0.0431505i	$0.0137395\pi$
$542$	13.9513	−	24.1644i	0.599260	−	1.03795i
$543$	2.74235			0.117686
$544$	1.05273	+	1.82338i	0.0451353	+	0.0781767i
$545$	16.3783			0.701569
$546$		0			0
$547$	−30.2968			−1.29540			−0.647699	−	0.761896i	$-0.724269\pi$
$547$	−30.2968			−1.29540			−0.647699	+	0.761896i	$0.724269\pi$
$548$	0.576493	+	0.998514i	0.0246265	+	0.0426544i
$549$	−22.8262			−0.974197
$550$	5.88947	−	10.2009i	0.251128	−	0.434967i
$551$	28.4854	−	49.3381i	1.21352	−	2.10187i
$552$	2.16567	+	3.75105i	0.0921770	+	0.159655i
$553$		0			0
$554$	20.8932			0.887668
$555$	2.90984			0.123516
$556$	9.50738			0.403203
$557$	−17.6840			−0.749296			−0.374648	−	0.927167i	$-0.622236\pi$
$557$	−17.6840			−0.749296			−0.374648	+	0.927167i	$0.622236\pi$
$558$	11.3474	−	19.6543i	0.480374	−	0.832033i
$559$	−2.54918	+	19.4214i	−0.107819	+	0.821437i
$560$		0			0
$561$	−0.469159	+	0.812606i	−0.0198079	+	0.0343083i
$562$	23.2838	+	40.3287i	0.982167	+	1.70116i
$563$	−20.8695	+	36.1471i	−0.879545	+	1.52342i	−0.0277042	+	0.999616i	$0.508820\pi$
$563$	−20.8695	+	36.1471i	−0.879545	+	1.52342i	−0.851841	+	0.523801i	$0.824514\pi$
$564$	−0.325115	−	0.563116i	−0.0136898	−	0.0237115i
$565$	−19.1770			−0.806784
$566$	−7.68887	−	13.3175i	−0.323187	−	0.559777i
$567$		0			0
$568$	−3.11340	−	5.39257i	−0.130636	−	0.226267i
$569$	−2.73388	−	4.73521i	−0.114610	−	0.198510i	0.803014	−	0.595960i	$-0.203229\pi$
$569$	−2.73388	−	4.73521i	−0.114610	−	0.198510i	−0.917624	+	0.397450i	$0.869895\pi$
$570$	−6.06342			−0.253969
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	0.751434	−	0.659808i	$-0.229362\pi$
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	−0.947128	+	0.320857i	$0.896029\pi$
$572$	2.93934	−	1.21886i	0.122900	−	0.0509630i
$573$	0.246437			0.0102951
$574$		0			0
$575$	6.43976	−	11.1540i	0.268557	−	0.465154i
$576$	−15.7594			−0.656640
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	0.828827	−	0.559505i	$-0.189009\pi$
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	−0.898959	+	0.438033i	$0.855675\pi$
$578$	12.5763	−	21.7829i	0.523107	−	0.906048i
$579$	−1.81632			−0.0754836
$580$	4.23151			0.175704
$581$		0			0
$582$	2.35961	−	4.08697i	0.0978091	−	0.169410i
$583$	2.98881	+	5.17676i	0.123784	+	0.214400i
$584$	7.05128	+	12.2132i	0.291784	+	0.505385i
$585$	−10.9553	+	4.54283i	−0.452945	+	0.187823i
$586$	6.14924	−	10.6508i	0.254023	−	0.439980i
$587$	−6.57639	+	11.3906i	−0.271437	+	0.470142i	−0.969230	−	0.246157i	$-0.920832\pi$
$587$	−6.57639	+	11.3906i	−0.271437	+	0.470142i	0.697793	+	0.716299i	$0.254165\pi$
$588$		0			0
$589$	17.6884	+	30.6373i	0.728840	+	1.26239i
$590$	−9.48995	+	16.4371i	−0.390695	+	0.676704i
$591$	1.82112	−	3.15427i	0.0749108	−	0.129749i
$592$	11.6308	−	20.1452i	0.478024	−	0.827961i
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	−0.132102	−	0.991236i	$-0.542173\pi$
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	0.924487	−	0.381214i	$-0.124494\pi$
$594$	4.63617	+	8.03008i	0.190224	+	0.329478i
$595$		0			0
$596$	3.00519	−	5.20515i	0.123097	−	0.213211i
$597$	1.83605	−	3.18014i	0.0751447	−	0.130154i
$598$	18.6269	−	7.72400i	0.761710	−	0.315858i
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	0.614295	−	0.789077i	$-0.289441\pi$
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	−0.990508	+	0.137457i	$0.956107\pi$
$600$	−2.15542	−	3.73329i	−0.0879946	−	0.152411i
$601$	−20.7018	+	35.8566i	−0.844445	+	1.46262i	0.0416571	+	0.999132i	$0.486736\pi$
$601$	−20.7018	+	35.8566i	−0.844445	+	1.46262i	−0.886102	+	0.463490i	$0.846597\pi$
$602$		0			0
$603$	10.3348			0.420865
$604$	6.36338			0.258922
$605$	3.88549	−	6.72987i	0.157968	−	0.273608i
$606$	−2.74690	−	4.75777i	−0.111585	−	0.193271i
$607$	−12.3051			−0.499449			−0.249724	−	0.968317i	$-0.580340\pi$
$607$	−12.3051			−0.499449			−0.249724	+	0.968317i	$0.580340\pi$
$608$	−7.77119	+	13.4601i	−0.315163	+	0.545879i
$609$		0			0
$610$	15.3167			0.620155
$611$	10.6136	−	4.40114i	0.429380	−	0.178051i
$612$	0.521725	+	0.903654i	0.0210895	+	0.0365280i
$613$	26.2224			1.05911			0.529556	−	0.848275i	$-0.322358\pi$
$613$	26.2224			1.05911			0.529556	+	0.848275i	$0.322358\pi$
$614$	0.989078	+	1.71313i	0.0399160	+	0.0691365i
$615$	0.447810	+	0.775630i	0.0180575	+	0.0312764i
$616$		0			0
$617$	9.41259	+	16.3031i	0.378936	+	0.656337i	0.990908	−	0.134543i	$-0.0429565\pi$
$617$	9.41259	+	16.3031i	0.378936	+	0.656337i	−0.611971	+	0.790880i	$0.709623\pi$
$618$	−7.55038			−0.303721
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	0.662312	−	0.749228i	$-0.269575\pi$
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	−0.980007	+	0.198965i	$0.936242\pi$
$620$	−1.31381	+	2.27559i	−0.0527639	+	0.0913898i
$621$	5.06935	+	8.78038i	0.203426	+	0.352344i
$622$	19.2497	−	33.3415i	0.771843	−	1.33687i
$623$		0			0
$624$	1.06984	−	8.15073i	0.0428277	−	0.326290i
$625$	−2.86003	+	4.95371i	−0.114401	+	0.198149i
$626$	−3.69473			−0.147671
$627$	−6.92661			−0.276622
$628$	4.76060			0.189969
$629$	4.52389			0.180379
$630$		0			0
$631$	8.33817	+	14.4421i	0.331937	+	0.574933i	0.982892	−	0.184184i	$-0.0589644\pi$
$631$	8.33817	+	14.4421i	0.331937	+	0.574933i	−0.650954	+	0.759117i	$0.725631\pi$
$632$	7.47206	−	12.9420i	0.297222	−	0.514804i
$633$	−0.927285	+	1.60610i	−0.0368563	+	0.0638369i
$634$	−30.7511			−1.22128
$635$	9.34050	+	16.1782i	0.370667	+	0.642013i
$636$	−0.576375			−0.0228548
$637$		0			0
$638$	28.0152			1.10913
$639$	−3.49248	−	6.04916i	−0.138161	−	0.239301i
$640$	16.1108			0.636837
$641$	−24.6232	+	42.6487i	−0.972559	+	1.68452i	−0.284792	+	0.958589i	$0.591925\pi$
$641$	−24.6232	+	42.6487i	−0.972559	+	1.68452i	−0.687767	+	0.725932i	$0.741409\pi$
$642$	0.836720	−	1.44924i	0.0330227	−	0.0571970i
$643$	21.4355	+	37.1275i	0.845335	+	1.46416i	0.885330	+	0.464964i	$0.153933\pi$
$643$	21.4355	+	37.1275i	0.845335	+	1.46416i	−0.0399940	+	0.999200i	$0.512734\pi$
$644$		0			0
$645$	3.16700			0.124701
$646$	−9.42672			−0.370889
$647$	−4.25859			−0.167422			−0.0837112	−	0.996490i	$-0.526677\pi$
$647$	−4.25859			−0.167422			−0.0837112	+	0.996490i	$0.526677\pi$
$648$	−16.9882			−0.667359
$649$	−10.8409	+	18.7771i	−0.425544	+	0.737064i
$650$	−18.5387	+	7.68744i	−0.727148	+	0.301526i
$651$		0			0
$652$	3.00437	−	5.20373i	0.117660	−	0.203794i
$653$	1.04776	+	1.81477i	0.0410020	+	0.0710176i	0.885798	−	0.464071i	$-0.153612\pi$
$653$	1.04776	+	1.81477i	0.0410020	+	0.0710176i	−0.844796	+	0.535088i	$0.820278\pi$
$654$	−5.22776	+	9.05475i	−0.204422	+	0.354069i
$655$	−5.68213	−	9.84174i	−0.222019	−	0.384549i
$656$	7.15971			0.279540
$657$	7.90982	+	13.7002i	0.308592	+	0.534496i
$658$		0			0
$659$	−12.7259	−	22.0419i	−0.495732	−	0.858632i	0.504256	−	0.863554i	$-0.331767\pi$
$659$	−12.7259	−	22.0419i	−0.495732	−	0.858632i	−0.999988	+	0.00492170i	$0.998433\pi$
$660$	−0.257237	−	0.445548i	−0.0100129	−	0.0173429i
$661$	−27.8108			−1.08171			−0.540857	−	0.841115i	$-0.681900\pi$
$661$	−27.8108			−1.08171			−0.540857	+	0.841115i	$0.681900\pi$
$662$	−3.05319	−	5.28829i	−0.118666	−	0.205535i
$663$	1.47680	−	0.612385i	0.0573543	−	0.0237831i
$664$	−28.6234			−1.11080
$665$		0			0
$666$	10.7117	−	18.5533i	0.415072	−	0.718925i
$667$	30.6329			1.18611
$668$	1.62064	+	2.80703i	0.0627044	+	0.108607i
$669$	1.19103	−	2.06293i	0.0460480	−	0.0797574i
$670$	−6.93481			−0.267915
$671$	17.4972			0.675472
$672$		0			0
$673$	−7.76033	+	13.4413i	−0.299139	+	0.518124i	−0.975939	−	0.218043i	$-0.930033\pi$
$673$	−7.76033	+	13.4413i	−0.299139	+	0.518124i	0.676800	+	0.736167i	$0.263366\pi$
$674$	5.55100	+	9.61462i	0.213817	+	0.370341i
$675$	−5.04536	−	8.73881i	−0.194196	−	0.336357i
$676$	−5.23802	−	1.39915i	−0.201462	−	0.0538136i
$677$	17.2813	−	29.9321i	0.664175	−	1.15038i	−0.315334	−	0.948981i	$-0.602116\pi$
$677$	17.2813	−	29.9321i	0.664175	−	1.15038i	0.979508	−	0.201403i	$-0.0645502\pi$
$678$	6.12109	−	10.6020i	0.235079	−	0.407169i
$679$		0			0
$680$	1.32877	+	2.30150i	0.0509562	+	0.0882587i
$681$	5.91425	−	10.2438i	0.226634	−	0.392542i
$682$	−8.69826	+	15.0658i	−0.333074	+	0.576900i
$683$	−23.5032	+	40.7087i	−0.899325	+	1.55768i	−0.0709661	+	0.997479i	$0.522608\pi$
$683$	−23.5032	+	40.7087i	−0.899325	+	1.55768i	−0.828359	+	0.560198i	$0.810725\pi$
$684$	−3.85135	+	6.67073i	−0.147260	+	0.255062i
$685$	1.64703	+	2.85275i	0.0629299	+	0.108998i
$686$		0			0
$687$	−5.31138	+	9.19958i	−0.202642	+	0.350986i
$688$	12.6587	−	21.9255i	0.482609	−	0.835904i
$689$	1.32546	−	10.0982i	0.0504960	−	0.384713i
$690$	−1.63013	−	2.82348i	−0.0620582	−	0.107488i
$691$	9.50301	+	16.4597i	0.361512	+	0.626156i	0.988210	−	0.153106i	$-0.0489275\pi$
$691$	9.50301	+	16.4597i	0.361512	+	0.626156i	−0.626698	+	0.779262i	$0.715594\pi$
$692$	1.27088	−	2.20123i	0.0483117	−	0.0836784i
$693$		0			0
$694$	15.6556			0.594280
$695$	27.1625			1.03033
$696$	5.12648	−	8.87933i	0.194319	−	0.336570i
$697$	0.696205	+	1.20586i	0.0263706	+	0.0456753i
$698$	9.77644			0.370044
$699$	−0.928805	+	1.60874i	−0.0351306	+	0.0608480i
$700$		0			0
$701$	−45.4648			−1.71718			−0.858591	−	0.512662i	$-0.828659\pi$
$701$	−45.4648			−1.71718			−0.858591	+	0.512662i	$0.828659\pi$
$702$	2.05603	−	15.6642i	0.0775997	−	0.591207i
$703$	16.6976	+	28.9210i	0.629760	+	1.09078i
$704$	12.0802			0.455290
$705$	−0.928851	−	1.60882i	−0.0349826	−	0.0605916i
$706$	26.5597	+	46.0027i	0.999586	+	1.73133i
$707$		0			0
$708$	−1.04531	−	1.81053i	−0.0392851	−	0.0680438i
$709$	−9.78779			−0.367588			−0.183794	−	0.982965i	$-0.558838\pi$
$709$	−9.78779			−0.367588			−0.183794	+	0.982965i	$0.558838\pi$
$710$	2.34351	+	4.05908i	0.0879504	+	0.152334i
$711$	8.38183	−	14.5178i	0.314343	−	0.544459i
$712$	21.8427	+	37.8326i	0.818589	+	1.41784i
$713$	−9.51099	+	16.4735i	−0.356189	+	0.616938i
$714$		0			0
$715$	8.39768	−	3.48226i	0.314055	−	0.130229i
$716$	−3.86393	+	6.69252i	−0.144402	+	0.250111i
$717$	10.7195			0.400326
$718$	29.0517			1.08420
$719$	27.8403			1.03827			0.519133	−	0.854693i	$-0.326255\pi$
$719$	27.8403			1.03827			0.519133	+	0.854693i	$0.326255\pi$
$720$	15.3288			0.571271
$721$		0			0
$722$	−20.0243	−	34.6830i	−0.745226	−	1.29077i
$723$	−5.07568	+	8.79134i	−0.188767	+	0.326953i
$724$	−1.16883	+	2.02447i	−0.0434391	+	0.0752388i
$725$	−30.4879			−1.13229
$726$	2.48041	+	4.29619i	0.0920566	+	0.159447i
$727$	14.5650			0.540186			0.270093	−	0.962834i	$-0.412945\pi$
$727$	14.5650			0.540186			0.270093	+	0.962834i	$0.412945\pi$
$728$		0			0
$729$	−14.9199			−0.552589
$730$	−5.30761	−	9.19305i	−0.196444	−	0.340250i
$731$	4.92370			0.182109
$732$	−0.843560	+	1.46109i	−0.0311789	+	0.0540034i
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	−0.655591	−	0.755116i	$-0.727580\pi$
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	0.981745	+	0.190200i	$0.0609136\pi$
$734$	−24.1451	−	41.8206i	−0.891213	−	1.54363i
$735$		0			0
$736$	−8.35705			−0.308045
$737$	−7.92205			−0.291812
$738$	6.59394			0.242726
$739$	8.96559			0.329804			0.164902	−	0.986310i	$-0.447269\pi$
$739$	8.96559			0.329804			0.164902	+	0.986310i	$0.447269\pi$
$740$	−1.24021	+	2.14811i	−0.0455911	+	0.0789661i
$741$	9.36579	+	7.18084i	0.344061	+	0.263795i
$742$		0			0
$743$	13.1839	−	22.8352i	0.483671	−	0.837743i	−0.516153	−	0.856497i	$-0.672636\pi$
$743$	13.1839	−	22.8352i	0.483671	−	0.837743i	0.999824	+	0.0187532i	$0.00596968\pi$
$744$	3.18337	+	5.51376i	0.116708	+	0.202144i
$745$	8.58580	−	14.8710i	0.314560	−	0.544833i
$746$	2.28309	+	3.95442i	0.0835898	+	0.144782i
$747$	−32.1086			−1.17479
$748$	−0.399923	−	0.692688i	−0.0146226	−	0.0253272i
$749$		0			0
$750$	3.88818	+	6.73452i	0.141976	+	0.245910i
$751$	10.1438	+	17.5696i	0.370152	+	0.641123i	0.989589	−	0.143924i	$-0.0459721\pi$
$751$	10.1438	+	17.5696i	0.370152	+	0.641123i	−0.619436	+	0.785047i	$0.712639\pi$
$752$	−14.8507			−0.541550
$753$	3.24321	+	5.61740i	0.118189	+	0.204709i
$754$	−37.8807	−	29.0435i	−1.37953	−	1.05770i
$755$	18.1801			0.661642
$756$		0			0
$757$	−12.4992	+	21.6493i	−0.454292	+	0.786857i	−0.998647	−	0.0519981i	$-0.983441\pi$
$757$	−12.4992	+	21.6493i	−0.454292	+	0.786857i	0.544355	+	0.838855i	$0.316774\pi$
$758$	15.6791			0.569492
$759$	−1.86220	−	3.22543i	−0.0675936	−	0.117076i
$760$	−9.80895	+	16.9896i	−0.355808	+	0.616277i
$761$	−20.1422			−0.730154			−0.365077	−	0.930977i	$-0.618957\pi$
$761$	−20.1422			−0.730154			−0.365077	+	0.930977i	$0.618957\pi$
$762$	−11.9255			−0.432016
$763$		0			0
$764$	−0.105035	+	0.181926i	−0.00380003	+	0.00658184i
$765$	1.49056	+	2.58173i	0.0538914	+	0.0933426i
$766$	2.86786	+	4.96729i	0.103620	+	0.179475i
$767$	34.1248	−	14.1505i	1.23217	−	0.510945i
$768$	−2.34945	+	4.06936i	−0.0847784	+	0.146840i
$769$	4.33610	−	7.51034i	0.156364	−	0.270830i	−0.777191	−	0.629265i	$-0.783356\pi$
$769$	4.33610	−	7.51034i	0.156364	−	0.270830i	0.933555	+	0.358435i	$0.116689\pi$
$770$		0			0
$771$	−3.22199	−	5.58065i	−0.116037	−	0.200982i
$772$	0.774139	−	1.34085i	0.0278619	−	0.0482582i
$773$	1.17283	−	2.03141i	0.0421839	−	0.0730647i	−0.844163	−	0.536087i	$-0.819902\pi$
$773$	1.17283	−	2.03141i	0.0421839	−	0.0730647i	0.886346	+	0.463023i	$0.153235\pi$
$774$	11.6584	−	20.1930i	0.419053	−	0.725821i
$775$	9.46596	−	16.3955i	0.340027	−	0.588945i
$776$	−7.63441	−	13.2232i	−0.274059	−	0.474685i
$777$		0			0
$778$	−17.6198	+	30.5184i	−0.631701	+	1.09414i
$779$	−5.13935	+	8.90161i	−0.184136	+	0.318933i
$780$	−0.114078	+	0.869125i	−0.00408466	+	0.0311197i
$781$	2.67713	+	4.63693i	0.0957953	+	0.165922i
$782$	−2.53435	−	4.38962i	−0.0906281	−	0.156973i
$783$	12.0000	−	20.7845i	0.428844	−	0.742779i
$784$		0			0
$785$	13.6010			0.485440
$786$	7.25468			0.258766
$787$	−17.0583	+	29.5459i	−0.608063	+	1.05320i	0.383496	+	0.923543i	$0.374720\pi$
$787$	−17.0583	+	29.5459i	−0.608063	+	1.05320i	−0.991559	+	0.129654i	$0.958613\pi$
$788$	1.55237	+	2.68878i	0.0553009	+	0.0957840i
$789$	−9.36455			−0.333387
$790$	−5.62434	+	9.74164i	−0.200105	+	0.346592i
$791$		0			0
$792$	14.3768			0.510858
$793$	−23.6588	−	18.1394i	−0.840148	−	0.644149i
$794$	−22.6486	−	39.2286i	−0.803770	−	1.39217i
$795$	−1.64670			−0.0584024
$796$	1.56510	+	2.71084i	0.0554736	+	0.0960830i
$797$	−17.0422	−	29.5180i	−0.603666	−	1.04558i	−0.992261	−	0.124172i	$-0.960373\pi$
$797$	−17.0422	−	29.5180i	−0.603666	−	1.04558i	0.388594	−	0.921409i	$-0.372961\pi$
$798$		0			0
$799$	−1.44407	−	2.50121i	−0.0510876	−	0.0884863i
$800$	8.31749			0.294068
$801$	24.5022	+	42.4390i	0.865742	+	1.49951i
$802$	−6.31243	+	10.9335i	−0.222900	+	0.386074i
$803$	−6.06320	−	10.5018i	−0.213966	−	0.370600i
$804$	0.381931	−	0.661524i	0.0134697	−	0.0233302i
$805$		0			0
$806$	27.3801	−	11.3537i	0.964423	−	0.399917i
$807$	−6.96748	+	12.0680i	−0.245267	+	0.424815i
$808$	−17.7749			−0.625319
$809$	−26.5205			−0.932413			−0.466206	−	0.884676i	$-0.654380\pi$
$809$	−26.5205			−0.932413			−0.466206	+	0.884676i	$0.654380\pi$
$810$	12.7873			0.449300
$811$	−52.5463			−1.84515			−0.922575	−	0.385818i	$-0.873919\pi$
$811$	−52.5463			−1.84515			−0.922575	+	0.385818i	$0.873919\pi$
$812$		0			0
$813$	4.39040	+	7.60439i	0.153978	+	0.266698i
$814$	−8.21099	+	14.2219i	−0.287795	+	0.498476i
$815$	8.58347	−	14.8670i	0.300666	−	0.520768i
$816$	−2.06637			−0.0723373
$817$	18.1732	+	31.4770i	0.635801	+	1.10124i
$818$	12.9391			0.452403
$819$		0			0
$820$	−0.763451			−0.0266609
$821$	15.3773	+	26.6343i	0.536671	+	0.929542i	0.999080	+	0.0428753i	$0.0136518\pi$
$821$	15.3773	+	26.6343i	0.536671	+	0.929542i	−0.462409	+	0.886667i	$0.653015\pi$
$822$	−2.10286			−0.0733455
$823$	14.8519	−	25.7243i	0.517705	−	0.896691i	−0.482084	−	0.876125i	$-0.660120\pi$
$823$	14.8519	−	25.7243i	0.517705	−	0.896691i	0.999789	−	0.0205659i	$-0.00654678\pi$
$824$	−12.2144	+	21.1560i	−0.425510	+	0.737006i
$825$	1.85339	+	3.21016i	0.0645266	+	0.111763i
$826$		0			0
$827$	14.8351			0.515866			0.257933	−	0.966163i	$-0.416959\pi$
$827$	14.8351			0.515866			0.257933	+	0.966163i	$0.416959\pi$
$828$	−4.14170			−0.143934
$829$	−14.5849			−0.506554			−0.253277	−	0.967394i	$-0.581508\pi$
$829$	−14.5849			−0.506554			−0.253277	+	0.967394i	$0.581508\pi$
$830$	21.5453			0.747849
$831$	−3.28749	+	5.69411i	−0.114042	+	0.197526i
$832$	−16.3342	−	12.5236i	−0.566287	−	0.434177i
$833$		0			0
$834$	−8.66995	+	15.0168i	−0.300216	+	0.519989i
$835$	4.63015	+	8.01966i	0.160233	+	0.277532i
$836$	2.95221	−	5.11339i	0.102104	−	0.176850i
$837$	7.45157	+	12.9065i	0.257564	+	0.446114i
$838$	20.2368			0.699069
$839$	18.4043	+	31.8772i	0.635386	+	1.10052i	0.986433	+	0.164164i	$0.0524925\pi$
$839$	18.4043	+	31.8772i	0.635386	+	1.10052i	−0.351047	+	0.936358i	$0.614174\pi$
$840$		0			0
$841$	−21.7564	−	37.6832i	−0.750221	−	1.29942i
$842$	6.91588	+	11.9787i	0.238337	+	0.412812i
$843$	−14.6546			−0.504730
$844$	−0.790442	−	1.36909i	−0.0272082	−	0.0471259i
$845$	−14.9650	−	3.99737i	−0.514811	−	0.137514i
$846$	−13.6772			−0.470232
$847$		0			0
$848$	−6.58196	+	11.4003i	−0.226025	+	0.391488i
$849$	4.83929			0.166084
$850$	2.52235	+	4.36884i	0.0865160	+	0.149850i
$851$	−8.97819	+	15.5507i	−0.307768	+	0.533070i
$852$	−0.516270			−0.0176871
$853$	4.10728			0.140630			0.0703152	−	0.997525i	$-0.477599\pi$
$853$	4.10728			0.140630			0.0703152	+	0.997525i	$0.477599\pi$
$854$		0			0
$855$	−11.0033	+	19.0582i	−0.376303	+	0.651777i
$856$	−2.70717	−	4.68895i	−0.0925291	−	0.160265i
$857$	−19.1656	−	33.1958i	−0.654684	−	1.13395i	−0.981973	−	0.189022i	$-0.939468\pi$
$857$	−19.1656	−	33.1958i	−0.654684	−	1.13395i	0.327288	−	0.944925i	$-0.393865\pi$
$858$	−0.755270	+	5.75416i	−0.0257845	+	0.196444i
$859$	−19.7185	+	34.1534i	−0.672785	+	1.16530i	0.304326	+	0.952568i	$0.401569\pi$
$859$	−19.7185	+	34.1534i	−0.672785	+	1.16530i	−0.977111	+	0.212730i	$0.931764\pi$
$860$	−1.34982	+	2.33796i	−0.0460284	+	0.0797236i
$861$		0			0
$862$	6.96300	+	12.0603i	0.237161	+	0.410775i
$863$	19.3220	−	33.4667i	0.657728	−	1.13922i	−0.323474	−	0.946237i	$-0.604851\pi$
$863$	19.3220	−	33.4667i	0.657728	−	1.13922i	0.981202	−	0.192982i	$-0.0618159\pi$
$864$	−3.27375	+	5.67030i	−0.111375	+	0.192907i
$865$	3.63090	−	6.28891i	0.123454	−	0.213829i
$866$	−0.134410	+	0.232805i	−0.00456744	+	0.00791104i
$867$	3.95771	+	6.85495i	0.134411	+	0.232806i
$868$		0			0
$869$	−6.42502	+	11.1285i	−0.217954	+	0.377507i
$870$	−3.85879	+	6.68361i	−0.130825	+	0.226596i
$871$	10.7118	+	8.21281i	0.362955	+	0.278280i
$872$	16.9142	+	29.2962i	0.572786	+	0.992094i
$873$	−8.56395	−	14.8332i	−0.289846	−	0.502028i
$874$	18.7084	−	32.4040i	0.632822	−	1.09608i
$875$		0			0
$876$	1.16926			0.0395055
$877$	−58.0741			−1.96102			−0.980512	−	0.196458i	$-0.937056\pi$
$877$	−58.0741			−1.96102			−0.980512	+	0.196458i	$0.937056\pi$
$878$	7.41710	−	12.8468i	0.250315	−	0.433558i
$879$	1.93513	+	3.35175i	0.0652704	+	0.113052i
$880$	−11.7502			−0.396098
$881$	10.8118	−	18.7266i	0.364259	−	0.630916i	−0.624398	−	0.781107i	$-0.714655\pi$
$881$	10.8118	−	18.7266i	0.364259	−	0.630916i	0.988657	+	0.150191i	$0.0479888\pi$
$882$		0			0
$883$	−22.7329			−0.765022			−0.382511	−	0.923951i	$-0.624941\pi$
$883$	−22.7329			−0.765022			−0.382511	+	0.923951i	$0.624941\pi$
$884$	−0.177356	+	1.35122i	−0.00596513	+	0.0454464i
$885$	−2.98644	−	5.17266i	−0.100388	−	0.173877i
$886$	−21.5690			−0.724624
$887$	−8.16585	−	14.1437i	−0.274182	−	0.474898i	0.695746	−	0.718288i	$-0.255074\pi$
$887$	−8.16585	−	14.1437i	−0.274182	−	0.474898i	−0.969929	+	0.243390i	$0.921741\pi$
$888$	3.00504	+	5.20488i	0.100843	+	0.174664i
$889$		0			0
$890$	−16.4413	−	28.4772i	−0.551115	−	0.954559i
$891$	14.6077			0.489376
$892$	1.01527	+	1.75850i	0.0339937	+	0.0588788i
$893$	10.6601	−	18.4638i	0.356726	−	0.617867i
$894$	5.48098	+	9.49333i	0.183311	+	0.317504i
$895$	−11.0392	+	19.1205i	−0.369000	+	0.639127i
$896$		0			0
$897$	−0.825840	+	6.29180i	−0.0275740	+	0.210077i
$898$	16.5506	−	28.6665i	0.552301	−	0.956614i
$899$	45.0280			1.50177
$900$	4.12209			0.137403
$901$	−2.56010			−0.0852893
$902$	−5.05453			−0.168297
$903$		0			0
$904$	−19.8045	−	34.3023i	−0.658687	−	1.14088i
$905$	−3.33933	+	5.78389i	−0.111003	+	0.192263i
$906$	−5.80288	+	10.0509i	−0.192788	+	0.333918i
$907$	14.4096			0.478463			0.239232	−	0.970963i	$-0.423105\pi$
$907$	14.4096			0.478463			0.239232	+	0.970963i	$0.423105\pi$
$908$	5.04146	+	8.73207i	0.167307	+	0.289784i
$909$	−19.9391			−0.661339
$910$		0			0
$911$	−1.32236			−0.0438118			−0.0219059	−	0.999760i	$-0.506973\pi$
$911$	−1.32236			−0.0438118			−0.0219059	+	0.999760i	$0.506973\pi$
$912$	−7.62691	−	13.2102i	−0.252552	−	0.437433i
$913$	24.6125			0.814556
$914$	−7.52907	+	13.0407i	−0.249039	+	0.431349i
$915$	−2.41004	+	4.17432i	−0.0796735	+	0.137999i
$916$	−4.52757	−	7.84197i	−0.149595	−	0.259106i
$917$		0			0
$918$	−3.97117			−0.131068
$919$	−27.4458			−0.905354			−0.452677	−	0.891675i	$-0.649531\pi$
$919$	−27.4458			−0.905354			−0.452677	+	0.891675i	$0.649531\pi$
$920$	−10.5484			−0.347772
$921$	−0.622515			−0.0205126
$922$	−1.06835	+	1.85043i	−0.0351841	+	0.0609407i
$923$	1.18724	−	9.04520i	0.0390785	−	0.297726i
$924$		0			0
$925$	8.93569	−	15.4771i	0.293804	−	0.508883i
$926$	−24.6970	−	42.7765i	−0.811594	−	1.40572i
$927$	−13.7016	+	23.7319i	−0.450021	+	0.779459i
$928$	9.89123	+	17.1321i	0.324696	+	0.562389i
$929$	28.6389			0.939611			0.469805	−	0.882770i	$-0.344324\pi$
$929$	28.6389			0.939611			0.469805	+	0.882770i	$0.344324\pi$
$930$	−2.39618	−	4.15030i	−0.0785737	−	0.136094i
$931$		0			0
$932$	−0.791738	−	1.37133i	−0.0259343	−	0.0449194i
$933$	6.05778	+	10.4924i	0.198323	+	0.343505i
$934$	45.2739			1.48141
$935$	−1.14258	−	1.97900i	−0.0373663	−	0.0647203i
$936$	−19.4396	−	14.9045i	−0.635402	−	0.487168i
$937$	−27.9990			−0.914688			−0.457344	−	0.889290i	$-0.651199\pi$
$937$	−27.9990			−0.914688			−0.457344	+	0.889290i	$0.651199\pi$
$938$		0			0
$939$	0.581356	−	1.00694i	0.0189718	−	0.0328602i
$940$	1.58356			0.0516499
$941$	14.4502	+	25.0284i	0.471062	+	0.815903i	0.999452	−	0.0330983i	$-0.0105375\pi$
$941$	14.4502	+	25.0284i	0.471062	+	0.815903i	−0.528390	+	0.849002i	$0.677204\pi$
$942$	−4.34127	+	7.51931i	−0.141446	+	0.244992i
$943$	−5.52680			−0.179977
$944$	−47.7480			−1.55406
$945$		0			0
$946$	−8.93666	+	15.4787i	−0.290556	+	0.503257i
$947$	−15.0617	−	26.0877i	−0.489441	−	0.847736i	0.510486	−	0.859886i	$-0.329466\pi$
$947$	−15.0617	−	26.0877i	−0.489441	−	0.847736i	−0.999926	+	0.0121504i	$0.996132\pi$
$948$	−0.619515	−	1.07303i	−0.0201209	−	0.0348505i
$949$	−2.68888	+	20.4857i	−0.0872847	+	0.664993i
$950$	−18.6199	+	32.2506i	−0.604109	+	1.04635i
$951$	4.83860	−	8.38070i	0.156902	−	0.271763i
$952$		0			0
$953$	−2.46511	−	4.26969i	−0.0798527	−	0.138309i	0.823334	−	0.567558i	$-0.192112\pi$
$953$	−2.46511	−	4.26969i	−0.0798527	−	0.138309i	−0.903186	+	0.429249i	$0.858778\pi$
$954$	−6.06185	+	10.4994i	−0.196260	+	0.339932i
$955$	−0.300084	+	0.519760i	−0.00971048	+	0.0168190i
$956$	−4.56879	+	7.91337i	−0.147765	+	0.255937i
$957$	−4.40812	+	7.63509i	−0.142494	+	0.246808i
$958$	7.55721	+	13.0895i	0.244162	+	0.422902i
$959$		0			0
$960$	−1.66391	+	2.88198i	−0.0537025	+	0.0930155i
$961$	1.51957	−	2.63197i	0.0490184	−	0.0849024i
$962$	25.8463	−	10.7177i	0.833318	−	0.345552i
$963$	−3.03678	−	5.25986i	−0.0978590	−	0.169497i
$964$	−4.32665	−	7.49398i	−0.139352	−	0.241365i
$965$	2.21171	−	3.83079i	0.0711974	−	0.123317i
$966$		0			0
$967$	29.1431			0.937180			0.468590	−	0.883416i	$-0.344762\pi$
$967$	29.1431			0.937180			0.468590	+	0.883416i	$0.344762\pi$
$968$	16.0505			0.515882
$969$	1.48327	−	2.56910i	0.0476495	−	0.0825313i
$970$	5.74654	+	9.95331i	0.184510	+	0.319581i
$971$	−14.5769			−0.467794			−0.233897	−	0.972261i	$-0.575148\pi$
$971$	−14.5769			−0.467794			−0.233897	+	0.972261i	$0.575148\pi$
$972$	−2.46738	+	4.27362i	−0.0791412	+	0.137077i
$973$		0			0
$974$	−26.6058			−0.852506
$975$	0.821930	−	6.26202i	0.0263228	−	0.200545i
$976$	19.2662	+	33.3700i	0.616696	+	1.06815i
$977$	52.5218			1.68032			0.840161	−	0.542337i	$-0.182460\pi$
$977$	52.5218			1.68032			0.840161	+	0.542337i	$0.182460\pi$
$978$	5.47948	+	9.49074i	0.175215	+	0.303481i
$979$	−18.7819	−	32.5313i	−0.600273	−	1.03970i
$980$		0			0
$981$	18.9736	+	32.8632i	0.605780	+	1.04924i
$982$	−39.9886			−1.27609
$983$	−3.01884	−	5.22879i	−0.0962862	−	0.166773i	0.813858	−	0.581063i	$-0.197363\pi$
$983$	−3.01884	−	5.22879i	−0.0962862	−	0.166773i	−0.910145	+	0.414291i	$0.864030\pi$
$984$	−0.924923	+	1.60201i	−0.0294855	+	0.0510703i
$985$	4.43511	+	7.68183i	0.141314	+	0.244764i
$986$	−5.99920	+	10.3909i	−0.191054	+	0.330914i
$987$		0			0
$988$	−9.29289	+	3.85348i	−0.295646	+	0.122596i
$989$	−9.77166	+	16.9250i	−0.310721	+	0.538184i
$990$	−10.8217			−0.343935
$991$	31.3484			0.995813			0.497907	−	0.867231i	$-0.334102\pi$
$991$	31.3484			0.995813			0.497907	+	0.867231i	$0.334102\pi$
$992$	−12.2842			−0.390025
$993$	1.92165			0.0609816
$994$		0			0
$995$	4.47148	+	7.74483i	0.141755	+	0.245528i
$996$	−1.18660	+	2.05525i	−0.0375988	+	0.0651230i
$997$	2.74017	−	4.74611i	0.0867819	−	0.150311i	−0.819367	−	0.573269i	$-0.805675\pi$
$997$	2.74017	−	4.74611i	0.0867819	−	0.150311i	0.906149	+	0.422958i	$0.139008\pi$
$998$	8.40146			0.265944
$999$	7.03414	+	12.1835i	0.222550	+	0.385468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.l.373.2		12
7.2	even	3		637.2.f.j.295.2		12
7.3	odd	6		91.2.h.b.74.5	yes	12
7.4	even	3		637.2.h.l.165.5		12
7.5	odd	6		637.2.f.k.295.2		12
7.6	odd	2		91.2.g.b.9.2	✓	12
13.3	even	3		637.2.h.l.471.5		12
21.17	even	6		819.2.s.d.802.2		12
21.20	even	2		819.2.n.d.100.5		12
91.3	odd	6		91.2.g.b.81.2	yes	12
91.9	even	3		8281.2.a.ca.1.5		6
91.16	even	3		637.2.f.j.393.2		12
91.17	odd	6		1183.2.e.g.508.5		12
91.30	even	6		8281.2.a.cf.1.2		6
91.48	odd	6		1183.2.e.h.170.2		12
91.55	odd	6		91.2.h.b.16.5	yes	12
91.61	odd	6		8281.2.a.bz.1.5		6
91.68	odd	6		637.2.f.k.393.2		12
91.69	odd	6		1183.2.e.g.170.5		12
91.81	even	3	inner	637.2.g.l.263.2		12
91.82	odd	6		8281.2.a.ce.1.2		6
91.87	odd	6		1183.2.e.h.508.2		12
273.146	even	6		819.2.s.d.289.2		12
273.185	even	6		819.2.n.d.172.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.2	✓	12	7.6	odd	2
91.2.g.b.81.2	yes	12	91.3	odd	6
91.2.h.b.16.5	yes	12	91.55	odd	6
91.2.h.b.74.5	yes	12	7.3	odd	6
637.2.f.j.295.2		12	7.2	even	3
637.2.f.j.393.2		12	91.16	even	3
637.2.f.k.295.2		12	7.5	odd	6
637.2.f.k.393.2		12	91.68	odd	6
637.2.g.l.263.2		12	91.81	even	3	inner
637.2.g.l.373.2		12	1.1	even	1	trivial
637.2.h.l.165.5		12	7.4	even	3
637.2.h.l.471.5		12	13.3	even	3
819.2.n.d.100.5		12	21.20	even	2
819.2.n.d.172.5		12	273.185	even	6
819.2.s.d.289.2		12	273.146	even	6
819.2.s.d.802.2		12	21.17	even	6
1183.2.e.g.170.5		12	91.69	odd	6
1183.2.e.g.508.5		12	91.17	odd	6
1183.2.e.h.170.2		12	91.48	odd	6
1183.2.e.h.508.2		12	91.87	odd	6
8281.2.a.bz.1.5		6	91.61	odd	6
8281.2.a.ca.1.5		6	91.9	even	3
8281.2.a.ce.1.2		6	91.82	odd	6
8281.2.a.cf.1.2		6	91.30	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.777343 - 1.34640i) q^{2} +0.489252 q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 - 0.658727i) q^{6} -2.46099 q^{8} -2.76063 q^{9} +O(q^{10})\)	\(q+(-0.777343 - 1.34640i) q^{2} +0.489252 q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 - 0.658727i) q^{6} -2.46099 q^{8} -2.76063 q^{9} +1.85243 q^{10} +2.11614 q^{11} +(-0.102021 + 0.176706i) q^{12} +(-2.86133 - 2.19381i) q^{13} +(-0.291474 + 0.504848i) q^{15} +(2.33009 + 4.03583i) q^{16} +(-0.453151 + 0.784881i) q^{17} +(2.14596 + 3.71691i) q^{18} -6.69028 q^{19} +(-0.248461 - 0.430346i) q^{20} +(-1.64497 - 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} -1.20404 q^{24} +(1.79015 + 3.10063i) q^{25} +(-0.729501 + 5.55783i) q^{26} -2.81840 q^{27} +(-4.25772 + 7.37459i) q^{29} +0.906303 q^{30} +(-2.64390 - 4.57937i) q^{31} +(1.16156 - 2.01189i) q^{32} +1.03532 q^{33} +1.40902 q^{34} +(0.575663 - 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} +(5.20065 + 9.00778i) q^{38} +(-1.39991 - 1.07332i) q^{39} +(1.46615 - 2.53944i) q^{40} +(0.768181 - 1.33053i) q^{41} +(-2.71636 - 4.70488i) q^{43} +(-0.441269 + 0.764301i) q^{44} +(1.64466 - 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} +(-1.59337 + 2.75979i) q^{47} +(1.14000 + 1.97453i) q^{48} +(2.78312 - 4.82051i) q^{50} +(-0.221705 + 0.384004i) q^{51} +(1.38901 - 0.575982i) q^{52} +(1.41239 + 2.44632i) q^{53} +(2.19086 + 3.79469i) q^{54} +(-1.26070 + 2.18360i) q^{55} -3.27323 q^{57} +13.2389 q^{58} +(-5.12298 + 8.87327i) q^{59} +(-0.121560 - 0.210548i) q^{60} +8.26845 q^{61} +(-4.11044 + 7.11949i) q^{62} +5.70861 q^{64} +(3.96840 - 1.64557i) q^{65} +(-0.804802 - 1.39396i) q^{66} -3.74363 q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.880000 - 1.52420i) q^{69} +(1.26510 + 2.19122i) q^{71} +6.79389 q^{72} +(-2.86522 - 4.96271i) q^{73} +(-3.88018 + 6.72066i) q^{74} +(0.875834 + 1.51699i) q^{75} +(1.39510 - 2.41638i) q^{76} +(-0.356910 + 2.71918i) q^{78} +(-3.03620 + 5.25885i) q^{79} -5.55265 q^{80} +6.90299 q^{81} -2.38856 q^{82} +11.6309 q^{83} +(-0.539935 - 0.935195i) q^{85} +(-4.22310 + 7.31462i) q^{86} +(-2.08310 + 3.60803i) q^{87} -5.20780 q^{88} +(-8.87557 - 15.3729i) q^{89} -5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +4.95437 q^{94} +(3.98577 - 6.90356i) q^{95} +(0.568297 - 0.984319i) q^{96} +(3.10217 + 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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