LMFDB - Embedded newform 637.2.f.j.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$-1.02197 + 1.77010i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.j.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +O(q^{10})$	\(q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(-0.926214 - 1.60425i) q^{10} +(-1.05807 - 1.83263i) q^{11} +0.204043 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} -4.29192 q^{18} +(3.34514 - 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} +(0.602021 + 1.04273i) q^{24} -3.58030 q^{25} +(5.17797 + 2.14715i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 + 0.784881i) q^{30} +5.28780 q^{31} +(1.16156 - 2.01189i) q^{32} +(-0.517662 + 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} -10.4013 q^{38} +(1.62948 + 0.675696i) q^{39} -2.93230 q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +0.882538 q^{44} +(1.64466 - 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} +3.18673 q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +0.443410 q^{51} +(-0.195692 - 1.49091i) q^{52} -2.82477 q^{53} +(2.19086 + 3.79469i) q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 + 11.4652i) q^{58} +(-5.12298 + 8.87327i) q^{59} +0.243120 q^{60} +(-4.13423 + 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-3.40931 + 2.61395i) q^{65} +1.60960 q^{66} +(1.87182 + 3.24208i) q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 + 5.88368i) q^{72} +5.73044 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} +6.07240 q^{79} +(2.77632 + 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(1.19428 - 2.06856i) q^{82} +11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +8.44619 q^{86} +(-2.08310 + 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(-8.87557 - 15.3729i) q^{89} -5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +(-2.47719 - 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} -1.13659 q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23} + 11 q^{24} - 14 q^{25} - 11 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} + 32 q^{31} + 8 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} - 34 q^{38} + 43 q^{39} - 10 q^{40} + 8 q^{41} - 11 q^{43} - 42 q^{44} + 7 q^{45} + 16 q^{46} - 2 q^{47} - 21 q^{48} + 6 q^{50} + 40 q^{51} + 16 q^{52} + 4 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} - 13 q^{59} - 40 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 14 q^{65} + 36 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 60 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} - 14 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} + 14 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} - 45 q^{94} - 6 q^{95} + 38 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−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	$-0.351911\pi$
$3$	−0.244626	−	0.423704i	−0.141235	−	0.244626i	0.786727	−	0.617301i	$-0.211774\pi$
$3$	−0.244626	−	0.423704i	−0.141235	−	0.244626i	−0.927962	+	0.372675i	$0.878441\pi$
$4$	−0.208526	+	0.361177i	−0.104263	+	0.180588i
$5$	1.19151			0.532860			0.266430	−	0.963854i	$-0.414156\pi$
$5$	1.19151			0.532860			0.266430	+	0.963854i	$0.414156\pi$
$6$	−0.380316	+	0.658727i	−0.155264	+	0.268924i
$7$		0			0
$7$		0			0
$8$	−2.46099			−0.870091
$9$	1.38032	−	2.39078i	0.460105	−	0.796926i
$10$	−0.926214	−	1.60425i	−0.292894	−	0.507308i
$11$	−1.05807	−	1.83263i	−0.319020	−	0.552559i	0.661264	−	0.750153i	$-0.270020\pi$
$11$	−1.05807	−	1.83263i	−0.319020	−	0.552559i	−0.980284	+	0.197595i	$0.936687\pi$
$12$	0.204043			0.0589021
$13$	−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	$0.201721\pi$
$18$	−4.29192			−1.01162
$19$	3.34514	−	5.79395i	0.767428	−	1.32922i	−0.171525	−	0.985180i	$-0.554870\pi$
$19$	3.34514	−	5.79395i	0.767428	−	1.32922i	0.938953	−	0.344045i	$-0.111797\pi$
$20$	−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	$0.955707\pi$
$24$	0.602021	+	1.04273i	0.122887	+	0.212847i
$25$	−3.58030			−0.716060
$26$	5.17797	+	2.14715i	1.01548	+	0.421091i
$27$	−2.81840			−0.542401
$28$		0			0
$29$	−4.25772	−	7.37459i	−0.790639	−	1.36943i	−0.925572	−	0.378573i	$-0.876415\pi$
$29$	−4.25772	−	7.37459i	−0.790639	−	1.36943i	0.134932	−	0.990855i	$-0.456918\pi$
$30$	−0.453151	+	0.784881i	−0.0827337	+	0.143299i
$31$	5.28780			0.949717			0.474859	−	0.880062i	$-0.342499\pi$
$31$	5.28780			0.949717			0.474859	+	0.880062i	$0.342499\pi$
$32$	1.16156	−	2.01189i	0.205337	−	0.355655i
$33$	−0.517662	+	0.896617i	−0.0901134	+	0.156081i
$34$	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	$0.967911\pi$
$38$	−10.4013			−1.68731
$39$	1.62948	+	0.675696i	0.260926	+	0.108198i
$40$	−2.93230			−0.463637
$41$	0.768181	+	1.33053i	0.119970	+	0.207794i	0.919755	−	0.392492i	$-0.128387\pi$
$41$	0.768181	+	1.33053i	0.119970	+	0.207794i	−0.799786	+	0.600286i	$0.795054\pi$
$42$		0			0
$43$	−2.71636	+	4.70488i	−0.414242	+	0.717488i	−0.995349	−	0.0963397i	$-0.969286\pi$
$43$	−2.71636	+	4.70488i	−0.414242	+	0.717488i	0.581107	+	0.813827i	$0.302620\pi$
$44$	0.882538			0.133048
$45$	1.64466	−	2.84864i	0.245172	−	0.424650i
$46$	−2.79636	+	4.84344i	−0.412301	+	0.714126i
$47$	3.18673			0.464833			0.232416	−	0.972616i	$-0.425337\pi$
$47$	3.18673			0.464833			0.232416	+	0.972616i	$0.425337\pi$
$48$	1.14000	−	1.97453i	0.164545	−	0.284999i
$49$		0			0
$50$	2.78312	+	4.82051i	0.393593	+	0.681723i
$51$	0.443410			0.0620898
$52$	−0.195692	−	1.49091i	−0.0271376	−	0.206752i
$53$	−2.82477			−0.388012			−0.194006	−	0.981000i	$-0.562148\pi$
$53$	−2.82477			−0.388012			−0.194006	+	0.981000i	$0.562148\pi$
$54$	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
$58$	−6.61943	+	11.4652i	−0.869173	+	1.50545i
$59$	−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	$0.934264\pi$
$60$	0.243120			0.0313866
$61$	−4.13423	+	7.16069i	−0.529333	+	0.916832i	0.470081	+	0.882623i	$0.344225\pi$
$61$	−4.13423	+	7.16069i	−0.529333	+	0.916832i	−0.999415	+	0.0342093i	$0.989109\pi$
$62$	−4.11044	−	7.11949i	−0.522026	−	0.904176i
$63$		0			0
$64$	5.70861			0.713576
$65$	−3.40931	+	2.61395i	−0.422873	+	0.324220i
$66$	1.60960			0.198129
$67$	1.87182	+	3.24208i	0.228679	+	0.396083i	0.957417	−	0.288709i	$-0.0932261\pi$
$67$	1.87182	+	3.24208i	0.228679	+	0.396083i	−0.728738	+	0.684793i	$0.759893\pi$
$68$	−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	−0.781139	−	0.624357i	$-0.785361\pi$
$71$	1.26510	−	2.19122i	0.150140	−	0.260050i	0.931279	+	0.364307i	$0.118694\pi$
$72$	−3.39694	+	5.88368i	−0.400334	+	0.693398i
$73$	5.73044			0.670697			0.335349	−	0.942094i	$-0.391146\pi$
$73$	5.73044			0.670697			0.335349	+	0.942094i	$0.391146\pi$
$74$	−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
$79$	6.07240			0.683198			0.341599	−	0.939846i	$-0.389031\pi$
$79$	6.07240			0.683198			0.341599	+	0.939846i	$0.389031\pi$
$80$	2.77632	+	4.80873i	0.310402	+	0.537633i
$81$	−3.45150	−	5.97817i	−0.383500	−	0.664241i
$82$	1.19428	−	2.06856i	0.131886	−	0.228434i
$83$	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
$86$	8.44619			0.910776
$87$	−2.08310	+	3.60803i	−0.223331	+	0.386821i
$88$	2.60390	+	4.51008i	0.277576	+	0.480776i
$89$	−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
$94$	−2.47719	−	4.29061i	−0.255502	−	0.442543i
$95$	3.98577	−	6.90356i	0.408932	−	0.708291i
$96$	−1.13659			−0.116003
$97$	3.10217	−	5.37312i	0.314978	−	0.545557i	−0.664455	−	0.747328i	$-0.731336\pi$
$97$	3.10217	−	5.37312i	0.314978	−	0.545557i	0.979433	+	0.201771i	$0.0646696\pi$
$98$		0			0
$99$	−5.84188			−0.587131
$100$	0.746584	−	1.29312i	0.0746584	−	0.129312i
$101$	−3.61133	−	6.25501i	−0.359341	−	0.622397i	0.628510	−	0.777802i	$-0.283665\pi$
$101$	−3.61133	−	6.25501i	−0.359341	−	0.622397i	−0.987851	+	0.155405i	$0.950332\pi$
$102$	−0.344682	−	0.597007i	−0.0341286	−	0.0591125i
$103$	−9.92645			−0.978082			−0.489041	−	0.872261i	$-0.662653\pi$
$103$	−9.92645			−0.978082			−0.489041	+	0.872261i	$0.662653\pi$
$104$	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
$109$	13.7458			1.31661			0.658305	−	0.752751i	$-0.271274\pi$
$109$	13.7458			1.31661			0.658305	+	0.752751i	$0.271274\pi$
$110$	−1.96000	+	3.39481i	−0.186878	+	0.323683i
$111$	−1.22107	+	2.11496i	−0.115899	+	0.200743i
$112$		0			0
$113$	8.04736	−	13.9384i	0.757032	−	1.31122i	−0.187326	−	0.982298i	$-0.559982\pi$
$113$	8.04736	−	13.9384i	0.757032	−	1.31122i	0.944358	−	0.328920i	$-0.106685\pi$
$114$	2.54442	+	4.40707i	0.238307	+	0.412760i
$115$	−2.14313	−	3.71201i	−0.199848	−	0.346147i
$116$	3.55138			0.329737
$117$	1.29536	+	9.86895i	0.119756	+	0.912385i
$118$	15.9293			1.46641
$119$		0			0
$120$	0.717315	+	1.24243i	0.0654816	+	0.113418i
$121$	3.26098	−	5.64818i	0.296453	−	0.513471i
$122$	12.8549			1.16382
$123$	0.375834	−	0.650963i	0.0338878	−	0.0586954i
$124$	−1.10264	+	1.90983i	−0.0990202	+	0.171508i
$125$	−10.2235			−0.914420
$126$		0			0
$127$	7.83921	+	13.5779i	0.695617	+	1.20484i	0.969972	+	0.243216i	$0.0782023\pi$
$127$	7.83921	+	13.5779i	0.695617	+	1.20484i	−0.274355	+	0.961628i	$0.588464\pi$
$128$	−6.76067	−	11.7098i	−0.597565	−	1.03501i
$129$	2.65797			0.234021
$130$	6.16962	+	2.55835i	0.541111	+	0.224382i
$131$	9.53769			0.833312			0.416656	−	0.909064i	$-0.363202\pi$
$131$	9.53769			0.833312			0.416656	+	0.909064i	$0.363202\pi$
$132$	−0.215892	−	0.373935i	−0.0187910	−	0.0325469i
$133$		0			0
$134$	2.91009	−	5.04042i	0.251393	−	0.435426i
$135$	−3.35815			−0.289024
$136$	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	$0.128987\pi$
$138$	2.73625			0.232925
$139$	−11.3983	+	19.7425i	−0.966795	+	1.67454i	−0.262081	+	0.965046i	$0.584409\pi$
$139$	−11.3983	+	19.7425i	−0.966795	+	1.67454i	−0.704714	+	0.709492i	$0.748925\pi$
$140$		0			0
$141$	−0.779557	−	1.35023i	−0.0656505	−	0.113710i
$142$	−3.93368			−0.330107
$143$	7.04792	+	2.92256i	0.589377	+	0.244397i
$144$	12.8650			1.07209
$145$	−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
$149$	7.20581	−	12.4808i	0.590323	−	1.02247i	−0.403866	−	0.914818i	$-0.632334\pi$
$149$	7.20581	−	12.4808i	0.590323	−	1.02247i	0.994189	−	0.107651i	$-0.0343329\pi$
$150$	1.36165	−	2.35844i	0.111178	−	0.192566i
$151$	15.2580			1.24168			0.620840	−	0.783937i	$-0.286792\pi$
$151$	15.2580			1.24168			0.620840	+	0.783937i	$0.286792\pi$
$152$	−8.23236	+	14.2589i	−0.667732	+	1.15655i
$153$	1.25098	+	2.16677i	0.101136	+	0.175173i
$154$		0			0
$155$	6.30048			0.506067
$156$	−0.583834	+	0.447631i	−0.0467442	+	0.0358392i
$157$	11.4149			0.911008			0.455504	−	0.890234i	$-0.349459\pi$
$157$	11.4149			0.911008			0.455504	+	0.890234i	$0.349459\pi$
$158$	−4.72034	−	8.17587i	−0.375530	−	0.650437i
$159$	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
$163$	7.20385	−	12.4774i	0.564249	−	0.977308i	−0.432870	−	0.901456i	$-0.642499\pi$
$163$	7.20385	−	12.4774i	0.564249	−	0.977308i	0.997119	−	0.0758514i	$-0.0241675\pi$
$164$	−0.640742			−0.0500335
$165$	−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	0.976296	−	0.216442i	$-0.0694452\pi$
$167$	3.88595	+	6.73066i	0.300704	+	0.520834i	−0.675592	+	0.737276i	$0.736112\pi$
$168$		0			0
$169$	3.37442	−	12.5544i	0.259571	−	0.965724i
$170$	1.67886			0.128763
$171$	−9.23471	−	15.9950i	−0.706196	−	1.22317i
$172$	−1.13286	−	1.96218i	−0.0863800	−	0.149615i
$173$	3.04731	−	5.27809i	0.231682	−	0.401286i	−0.726621	−	0.687039i	$-0.758910\pi$
$173$	3.04731	−	5.27809i	0.231682	−	0.401286i	0.958303	+	0.285753i	$0.0922436\pi$
$174$	6.47713			0.491030
$175$		0			0
$176$	4.93078	−	8.54037i	0.371672	−	0.643754i
$177$	5.01286			0.376789
$178$	−13.7987	+	23.9001i	−1.03426	+	1.79139i
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	−0.971020	−	0.239000i	$-0.923181\pi$
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	0.278530	−	0.960428i	$-0.410153\pi$
$180$	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
$185$	−2.97377	−	5.15071i	−0.218636	−	0.378688i
$186$	−2.01104	+	3.48322i	−0.147456	+	0.255402i
$187$	1.91786			0.140248
$188$	−0.664516	+	1.15097i	−0.0484648	+	0.0839435i
$189$		0			0
$190$	−12.3933			−0.899102
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	−0.874993	−	0.484135i	$-0.839134\pi$
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	0.856770	+	0.515699i	$0.172468\pi$
$192$	−1.39647	−	2.41876i	−0.100782	−	0.174559i
$193$	1.85622	+	3.21507i	0.133614	+	0.231426i	0.925067	−	0.379804i	$-0.124009\pi$
$193$	1.85622	+	3.21507i	0.133614	+	0.231426i	−0.791453	+	0.611230i	$0.790675\pi$
$194$	−9.64581			−0.692529
$195$	1.94154	+	0.805100i	0.139037	+	0.0576544i
$196$		0			0
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	0.967616	−	0.252427i	$-0.0812288\pi$
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	−0.702416	+	0.711766i	$0.747895\pi$
$198$	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	$0.0809554\pi$
$200$	8.81108			0.623038
$201$	0.915789	−	1.58619i	0.0645948	−	0.111881i
$202$	−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
$206$	7.71626	+	13.3650i	0.537617	+	0.931181i
$207$	−9.93091			−0.690246
$208$	−15.5210	−	6.43608i	−1.07619	−	0.446262i
$209$	−14.1576			−0.979299
$210$		0			0
$211$	−1.89531	−	3.28278i	−0.130479	−	0.225996i	0.793383	−	0.608723i	$-0.208318\pi$
$211$	−1.89531	−	3.28278i	−0.130479	−	0.225996i	−0.923861	+	0.382728i	$0.874985\pi$
$212$	0.589037	−	1.02024i	0.0404553	−	0.0700706i
$213$	−1.23791			−0.0848200
$214$	1.71020	−	2.96216i	0.116907	−	0.202489i
$215$	−3.23658	+	5.60592i	−0.220733	+	0.382320i
$216$	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
$220$	1.05155			0.0708958
$221$	−0.425262	−	3.23993i	−0.0286062	−	0.217941i
$222$	3.79676			0.254822
$223$	2.43440	+	4.21650i	0.163019	+	0.282358i	0.935950	−	0.352133i	$-0.114543\pi$
$223$	2.43440	+	4.21650i	0.163019	+	0.282358i	−0.772931	+	0.634490i	$0.781210\pi$
$224$		0			0
$225$	−4.94195	+	8.55971i	−0.329463	+	0.570647i
$226$	−25.0223			−1.66446
$227$	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
$229$	21.7123			1.43479			0.717394	−	0.696668i	$-0.245335\pi$
$229$	21.7123			1.43479			0.717394	+	0.696668i	$0.245335\pi$
$230$	−3.33190	+	5.77101i	−0.219699	+	0.380529i
$231$		0			0
$232$	10.4782	+	18.1488i	0.687928	+	1.19153i
$233$	3.79684			0.248739			0.124370	−	0.992236i	$-0.460309\pi$
$233$	3.79684			0.248739			0.124370	+	0.992236i	$0.460309\pi$
$234$	12.2806	−	9.41564i	0.802808	−	0.615520i
$235$	3.79703			0.247691
$236$	−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	$0.249319\pi$
$240$	1.35832	−	2.35268i	0.0876792	−	0.151865i
$241$	−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	$0.933701\pi$
$242$	−10.1396			−0.651798
$243$	−5.91625	+	10.2472i	−0.379527	+	0.657361i
$244$	−1.72418	−	2.98637i	−0.110380	−	0.191183i
$245$		0			0
$246$	−1.16861			−0.0745077
$247$	3.13926	+	23.9170i	0.199747	+	1.52180i
$248$	−13.0132			−0.826341
$249$	−2.84521	−	4.92805i	−0.180308	−	0.312302i
$250$	7.94719	+	13.7649i	0.502624	+	0.870571i
$251$	6.62891	−	11.4816i	0.418413	−	0.724713i	−0.577367	−	0.816485i	$-0.695920\pi$
$251$	6.62891	−	11.4816i	0.418413	−	0.724713i	0.995780	+	0.0917718i	$0.0292530\pi$
$252$		0			0
$253$	−3.80622	+	6.59257i	−0.239295	+	0.414472i
$254$	12.1875	−	21.1094i	0.764713	−	1.32452i
$255$	0.528328			0.0330852
$256$	−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
$261$	−23.5080			−1.45511
$262$	−7.41406	−	12.8415i	−0.458042	−	0.793352i
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	0.994215	+	0.107412i	$0.0342564\pi$
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	−0.404086	+	0.914721i	$0.632410\pi$
$264$	1.27396	−	2.20657i	0.0784069	−	0.135805i
$265$	−3.36575			−0.206756
$266$		0			0
$267$	−4.34239	+	7.52123i	−0.265750	+	0.460292i
$268$	−1.56129			−0.0953708
$269$	−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	$0.831882\pi$
$270$	2.61044	+	4.52141i	0.158866	+	0.275164i
$271$	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
$276$	−0.367005	−	0.635671i	−0.0220911	−	0.0382629i
$277$	−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	$0.298954\pi$
$278$	35.4417			2.12565
$279$	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	$0.851704\pi$
$282$	−1.21197	+	2.09919i	−0.0721716	+	0.125005i
$283$	−4.94561	−	8.56604i	−0.293986	−	0.509199i	0.680763	−	0.732504i	$-0.261649\pi$
$283$	−4.94561	−	8.56604i	−0.293986	−	0.509199i	−0.974748	+	0.223306i	$0.928315\pi$
$284$	0.527613	+	0.913852i	0.0313080	+	0.0542271i
$285$	−3.90009			−0.231021
$286$	−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
$291$	−3.03548			−0.177943
$292$	−1.19494	+	2.06970i	−0.0699288	+	0.121120i
$293$	3.95529	−	6.85076i	0.231071	−	0.400226i	−0.727053	−	0.686581i	$-0.759111\pi$
$293$	3.95529	−	6.85076i	0.231071	−	0.400226i	0.958123	+	0.286356i	$0.0924438\pi$
$294$		0			0
$295$	−6.10409	+	10.5726i	−0.355394	+	0.615561i
$296$	6.14212	+	10.6385i	0.357003	+	0.618348i
$297$	2.98206	+	5.16508i	0.173037	+	0.299708i
$298$	−22.4056			−1.29792
$299$	11.9811	+	4.96821i	0.692886	+	0.287319i
$300$	−0.730535			−0.0421775
$301$		0			0
$302$	−11.8607	−	20.5434i	−0.682508	−	1.18214i
$303$	−1.76685	+	3.06027i	−0.101503	+	0.175808i
$304$	31.1779			1.78817
$305$	−4.92598	+	8.53204i	−0.282061	+	0.488543i
$306$	1.94489	−	3.36865i	0.111182	−	0.192573i
$307$	−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
$311$	−24.7635			−1.40421			−0.702103	−	0.712075i	$-0.747756\pi$
$311$	−24.7635			−1.40421			−0.702103	+	0.712075i	$0.747756\pi$
$312$	−4.01013	−	1.66288i	−0.227029	−	0.0941421i
$313$	−2.37651			−0.134328			−0.0671642	−	0.997742i	$-0.521395\pi$
$313$	−2.37651			−0.134328			−0.0671642	+	0.997742i	$0.521395\pi$
$314$	−8.87330	−	15.3690i	−0.500749	−	0.867323i
$315$		0			0
$316$	−1.26625	+	2.19321i	−0.0712322	+	0.123378i
$317$	−19.7796			−1.11093			−0.555466	−	0.831539i	$-0.687460\pi$
$317$	−19.7796			−1.11093			−0.555466	+	0.831539i	$0.687460\pi$
$318$	1.07431	−	1.86076i	0.0602442	−	0.104346i
$319$	−9.00993	+	15.6057i	−0.504459	+	0.873749i
$320$	6.80187			0.380236
$321$	0.538192	−	0.932176i	0.0300390	−	0.0520290i
$322$		0			0
$323$	3.03171	+	5.25108i	0.168689	+	0.292178i
$324$	2.87890			0.159939
$325$	10.2444	−	7.85449i	0.568258	−	0.435689i
$326$	−22.3995			−1.24059
$327$	−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
$331$	−1.96386	+	3.40151i	−0.107944	+	0.186964i	−0.914937	−	0.403596i	$-0.867760\pi$
$331$	−1.96386	+	3.40151i	−0.107944	+	0.186964i	0.806993	+	0.590561i	$0.201093\pi$
$332$	−2.42533	+	4.20080i	−0.133107	+	0.230549i
$333$	−13.7799			−0.755136
$334$	6.04143	−	10.4641i	0.330572	−	0.572568i
$335$	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	$0.562308\pi$
$338$	−19.5263	+	5.21577i	−1.06209	+	0.283701i
$339$	−7.87437			−0.427677
$340$	−0.225181	−	0.390024i	−0.0122121	−	0.0211520i
$341$	−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
$345$	−1.04853	+	1.81611i	−0.0564509	+	0.0977759i
$346$	−9.47522			−0.509391
$347$	−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	0.769520	−	0.638623i	$-0.220496\pi$
$349$	−3.14418	−	5.44588i	−0.168304	−	0.291512i	−0.937824	+	0.347112i	$0.887162\pi$
$350$		0			0
$351$	8.06437	−	6.18302i	0.430444	−	0.330025i
$352$	−4.91606			−0.262027
$353$	17.0836	+	29.5897i	0.909269	+	1.57490i	0.815083	+	0.579345i	$0.196692\pi$
$353$	17.0836	+	29.5897i	0.909269	+	1.57490i	0.0941861	+	0.995555i	$0.469975\pi$
$354$	−3.89671	−	6.74930i	−0.207108	−	0.358721i
$355$	1.50738	−	2.61087i	0.0800036	−	0.138570i
$356$	7.40313			0.392365
$357$		0			0
$358$	−14.4040	+	24.9484i	−0.761274	+	1.31857i
$359$	18.6865			0.986238			0.493119	−	0.869962i	$-0.335857\pi$
$359$	18.6865			0.986238			0.493119	+	0.869962i	$0.335857\pi$
$360$	−4.04750	+	7.01047i	−0.213322	+	0.369484i
$361$	−12.8799	−	22.3087i	−0.677891	−	1.17414i
$362$	−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
$367$	−15.5305	−	26.8997i	−0.810687	−	1.40415i	−0.912384	−	0.409336i	$-0.865760\pi$
$367$	−15.5305	−	26.8997i	−0.810687	−	1.40415i	0.101696	−	0.994816i	$-0.467573\pi$
$368$	8.38209	−	14.5182i	0.436946	−	0.756813i
$369$	4.24133			0.220795
$370$	−4.62327	+	8.00775i	−0.240353	+	0.416303i
$371$		0			0
$372$	1.07894			0.0559404
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	−0.825500	−	0.564403i	$-0.809107\pi$
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	0.901537	+	0.432702i	$0.142440\pi$
$374$	−1.49084	−	2.58221i	−0.0770894	−	0.133523i
$375$	2.50094	+	4.33175i	0.129148	+	0.223691i
$376$	−7.84252			−0.404447
$377$	28.3612	+	11.7605i	1.46068	+	0.605698i
$378$		0			0
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	0.706961	−	0.707252i	$-0.250066\pi$
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	−0.965979	+	0.258620i	$0.916732\pi$
$380$	1.66227	+	2.87914i	0.0852727	+	0.147697i
$381$	3.83534	−	6.64301i	0.196491	−	0.340332i
$382$	0.783100			0.0400669
$383$	1.84466	−	3.19504i	0.0942576	−	0.163259i	−0.815041	−	0.579403i	$-0.803286\pi$
$383$	1.84466	−	3.19504i	0.0942576	−	0.163259i	0.909299	+	0.416144i	$0.136619\pi$
$384$	−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
$388$	1.29376	+	2.24086i	0.0656809	+	0.113763i
$389$	22.6667			1.14925			0.574623	−	0.818418i	$-0.305149\pi$
$389$	22.6667			1.14925			0.574623	+	0.818418i	$0.305149\pi$
$390$	−0.425262	−	3.23993i	−0.0215340	−	0.164060i
$391$	3.26027			0.164879
$392$		0			0
$393$	−2.33316	−	4.04116i	−0.117693	−	0.203849i
$394$	5.78694	−	10.0233i	0.291542	−	0.504965i
$395$	7.23533			0.364049
$396$	1.21818	−	2.10995i	0.0612160	−	0.106029i
$397$	−14.5680	+	25.2325i	−0.731146	+	1.26638i	0.225248	+	0.974302i	$0.427681\pi$
$397$	−14.5680	+	25.2325i	−0.731146	+	1.26638i	−0.956394	+	0.292080i	$0.905652\pi$
$398$	−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	$0.898324\pi$
$402$	−2.84753			−0.142022
$403$	−15.1302	+	11.6004i	−0.753687	+	0.577858i
$404$	3.01222			0.149864
$405$	−4.11250	−	7.12305i	−0.204352	−	0.353947i
$406$		0			0
$407$	−5.28144	+	9.14773i	−0.261791	+	0.453436i
$408$	−1.09123			−0.0540238
$409$	−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
$411$	−1.35259			−0.0667184
$412$	2.06992	−	3.58520i	0.101978	−	0.176630i
$413$		0			0
$414$	7.71973	+	13.3710i	0.379404	+	0.657147i
$415$	13.8583			0.680278
$416$	1.09007	+	8.30492i	0.0534453	+	0.407182i
$417$	11.1533			0.546180
$418$	11.0053	+	19.0617i	0.538286	+	0.932339i
$419$	−6.50832	−	11.2727i	−0.317952	−	0.550710i	0.662108	−	0.749408i	$-0.269662\pi$
$419$	−6.50832	−	11.2727i	−0.317952	−	0.550710i	−0.980061	+	0.198699i	$0.936329\pi$
$420$		0			0
$421$	−8.89681			−0.433604			−0.216802	−	0.976216i	$-0.569563\pi$
$421$	−8.89681			−0.433604			−0.216802	+	0.976216i	$0.569563\pi$
$422$	−2.94662	+	5.10369i	−0.143439	+	0.248444i
$423$	4.39870	−	7.61877i	0.213872	−	0.370437i
$424$	6.95174			0.337606
$425$	1.62242	−	2.81011i	0.0786988	−	0.136310i
$426$	0.962279	+	1.66672i	0.0466225	+	0.0807526i
$427$		0			0
$428$	−0.917539			−0.0443509
$429$	−0.485802	−	3.70117i	−0.0234548	−	0.178694i
$430$	10.0637			0.485316
$431$	4.47872	+	7.75736i	0.215732	+	0.373659i	0.953499	−	0.301397i	$-0.0974529\pi$
$431$	4.47872	+	7.75736i	0.215732	+	0.373659i	−0.737767	+	0.675056i	$0.764120\pi$
$432$	−6.56711	−	11.3746i	−0.315960	−	0.547259i
$433$	−0.0864547	+	0.149744i	−0.00415475	+	0.00719624i	−0.868095	−	0.496398i	$-0.834656\pi$
$433$	−0.0864547	+	0.149744i	−0.00415475	+	0.00719624i	0.863941	+	0.503594i	$0.167989\pi$
$434$		0			0
$435$	−2.48203	+	4.29901i	−0.119004	+	0.206122i
$436$	−2.86636	+	4.96467i	−0.137274	+	0.237765i
$437$	−24.0671			−1.15129
$438$	−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
$443$	−13.8735			−0.659151			−0.329576	−	0.944129i	$-0.606906\pi$
$443$	−13.8735			−0.659151			−0.329576	+	0.944129i	$0.606906\pi$
$444$	−0.509249	−	0.882045i	−0.0241679	−	0.0418600i
$445$	−10.5753	−	18.3170i	−0.501319	−	0.868310i
$446$	3.78473	−	6.55534i	0.179212	−	0.310404i
$447$	−7.05091			−0.333496
$448$		0			0
$449$	10.6456	−	18.4388i	0.502398	−	0.870180i	−0.497598	−	0.867408i	$-0.665784\pi$
$449$	10.6456	−	18.4388i	0.502398	−	0.870180i	0.999996	−	0.00277167i	$-0.000882252\pi$
$450$	15.3664			0.724377
$451$	1.62558	−	2.81558i	0.0765455	−	0.132581i
$452$	3.35616	+	5.81304i	0.157861	+	0.273423i
$453$	−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	$0.906074\pi$
$458$	−16.8779	−	29.2334i	−0.788652	−	1.36599i
$459$	1.27716	−	2.21211i	0.0596128	−	0.103252i
$460$	1.78759			0.0833468
$461$	−0.687178	+	1.19023i	−0.0320051	+	0.0554344i	−0.881584	−	0.472027i	$-0.843523\pi$
$461$	−0.687178	+	1.19023i	−0.0320051	+	0.0554344i	0.849579	+	0.527461i	$0.176856\pi$
$462$		0			0
$463$	31.7710			1.47653			0.738263	−	0.674513i	$-0.235646\pi$
$463$	31.7710			1.47653			0.738263	+	0.674513i	$0.235646\pi$
$464$	19.8417	−	34.3669i	0.921128	−	1.59544i
$465$	−1.54126	−	2.66954i	−0.0714742	−	0.123797i
$466$	−2.95145	−	5.11206i	−0.136723	−	0.236812i
$467$	29.1209			1.34756			0.673778	−	0.738934i	$-0.264670\pi$
$467$	29.1209			1.34756			0.673778	+	0.738934i	$0.264670\pi$
$468$	−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
$473$	11.4964			0.528605
$474$	−2.30943	+	4.00006i	−0.106076	+	0.183729i
$475$	−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
$479$	4.86092	+	8.41936i	0.222101	+	0.384690i	0.955446	−	0.295167i	$-0.0953752\pi$
$479$	4.86092	+	8.41936i	0.222101	+	0.384690i	−0.733345	+	0.679857i	$0.762042\pi$
$480$	−1.35426			−0.0618134
$481$	16.6248	+	6.89379i	0.758024	+	0.314330i
$482$	32.2578			1.46930
$483$		0			0
$484$	1.36000	+	2.35558i	0.0618180	+	0.107072i
$485$	3.69627	−	6.40213i	0.167839	−	0.290706i
$486$	18.3958			0.834452
$487$	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	$0.0399228\pi$
$488$	10.1743	−	17.6224i	0.460568	−	0.797728i
$489$	−7.04899			−0.318766
$490$		0			0
$491$	12.8607	+	22.2753i	0.580394	+	1.00527i	0.995432	+	0.0954681i	$0.0304348\pi$
$491$	12.8607	+	22.2753i	0.580394	+	1.00527i	−0.415038	+	0.909804i	$0.636232\pi$
$492$	0.156742	+	0.271485i	0.00706647	+	0.0122395i
$493$	7.71757			0.347582
$494$	29.7615	−	22.8184i	1.33903	−	1.02665i
$495$	−6.96067			−0.312859
$496$	12.3210	+	21.3407i	0.553231	+	0.958224i
$497$		0			0
$498$	−4.42341	+	7.66157i	−0.198218	+	0.343323i
$499$	5.40396			0.241914			0.120957	−	0.992658i	$-0.461404\pi$
$499$	5.40396			0.241914			0.120957	+	0.992658i	$0.461404\pi$
$500$	2.13187	−	3.69250i	0.0953400	−	0.165134i
$501$	1.90121	−	3.29299i	0.0849396	−	0.147120i
$502$	−20.6118			−0.919948
$503$	−6.30847	+	10.9266i	−0.281281	+	0.487193i	−0.971700	−	0.236216i	$-0.924093\pi$
$503$	−6.30847	+	10.9266i	−0.281281	+	0.487193i	0.690420	+	0.723409i	$0.257426\pi$
$504$		0			0
$505$	−4.30294	−	7.45292i	−0.191478	−	0.331650i
$506$	11.8350			0.526129
$507$	−6.14483	+	1.64138i	−0.272901	+	0.0728960i
$508$	−6.53870			−0.290108
$509$	−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
$513$	−9.42794	+	16.3297i	−0.416254	+	0.720973i
$514$	−10.2385	+	17.7335i	−0.451599	+	0.782193i
$515$	−11.8275			−0.521181
$516$	−0.554255	+	0.959998i	−0.0243997	+	0.0422615i
$517$	−3.37178	−	5.84010i	−0.148291	−	0.256847i
$518$		0			0
$519$	−2.98180			−0.130886
$520$	8.39027	−	6.43289i	0.367938	−	0.282101i
$521$	39.0954			1.71280			0.856401	−	0.516312i	$-0.172695\pi$
$521$	39.0954			1.71280			0.856401	+	0.516312i	$0.172695\pi$
$522$	18.2738	+	31.6512i	0.799823	+	1.38533i
$523$	−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
$527$	−2.39618	+	4.15030i	−0.104379	+	0.180790i
$528$	−4.82479			−0.209972
$529$	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
$534$	13.5021			0.584293
$535$	1.31070	+	2.27020i	0.0566665	+	0.0981493i
$536$	−4.60652	−	7.97873i	−0.198971	−	0.344629i
$537$	−4.53286	+	7.85114i	−0.195607	+	0.338802i
$538$	44.2809			1.90909
$539$		0			0
$540$	0.700261	−	1.21289i	0.0301344	−	0.0521944i
$541$	−21.4994			−0.924330			−0.462165	−	0.886794i	$-0.652927\pi$
$541$	−21.4994			−0.924330			−0.462165	+	0.886794i	$0.652927\pi$
$542$	13.9513	−	24.1644i	0.599260	−	1.03795i
$543$	−1.37118	−	2.37495i	−0.0588428	−	0.101919i
$544$	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
$549$	11.4131	+	19.7680i	0.487098	+	0.843679i
$550$	5.88947	−	10.2009i	0.251128	−	0.434967i
$551$	−56.9707			−2.42703
$552$	2.16567	−	3.75105i	0.0921770	−	0.159655i
$553$		0			0
$554$	20.8932			0.887668
$555$	−1.45492	+	2.51999i	−0.0617579	+	0.106968i
$556$	−4.75369	−	8.23364i	−0.201601	−	0.349184i
$557$	8.84201	+	15.3148i	0.374648	+	0.648909i	0.990274	−	0.139129i	$-0.0444302\pi$
$557$	8.84201	+	15.3148i	0.374648	+	0.648909i	−0.615626	+	0.788038i	$0.711097\pi$
$558$	−22.6948			−0.960749
$559$	−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	$0.824514\pi$
$564$	0.650230			0.0273796
$565$	9.58852	−	16.6078i	0.403392	−	0.698696i
$566$	−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	$0.869895\pi$
$570$	3.03171	+	5.25108i	0.126984	+	0.219943i
$571$	9.35242			0.391387			0.195693	−	0.980665i	$-0.437304\pi$
$571$	9.35242			0.391387			0.195693	+	0.980665i	$0.437304\pi$
$572$	−2.52523	+	1.93612i	−0.105585	+	0.0809532i
$573$	0.246437			0.0102951
$574$		0			0
$575$	6.43976	+	11.1540i	0.268557	+	0.465154i
$576$	7.87968	−	13.6480i	0.328320	−	0.568667i
$577$	3.36925			0.140264			0.0701318	−	0.997538i	$-0.477658\pi$
$577$	3.36925			0.140264			0.0701318	+	0.997538i	$0.477658\pi$
$578$	12.5763	−	21.7829i	0.523107	−	0.906048i
$579$	0.908159	−	1.57298i	0.0377418	−	0.0653707i
$580$	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
$584$	−14.1026			−0.583568
$585$	1.54344	+	11.7590i	0.0638134	+	0.486174i
$586$	−12.2985			−0.508045
$587$	−6.57639	−	11.3906i	−0.271437	−	0.470142i	0.697793	−	0.716299i	$-0.254165\pi$
$587$	−6.57639	−	11.3906i	−0.271437	−	0.470142i	−0.969230	+	0.246157i	$0.920832\pi$
$588$		0			0
$589$	17.6884	−	30.6373i	0.728840	−	1.26239i
$590$	18.9799			0.781390
$591$	1.82112	−	3.15427i	0.0749108	−	0.129749i
$592$	11.6308	−	20.1452i	0.478024	−	0.827961i
$593$	−38.5916			−1.58477			−0.792384	−	0.610022i	$-0.791161\pi$
$593$	−38.5916			−1.58477			−0.792384	+	0.610022i	$0.791161\pi$
$594$	4.63617	−	8.03008i	0.190224	−	0.329478i
$595$		0			0
$596$	3.00519	+	5.20515i	0.123097	+	0.213211i
$597$	−3.67211			−0.150289
$598$	−2.62426	−	19.9934i	−0.107314	−	0.817589i
$599$	18.4152			0.752426			0.376213	−	0.926533i	$-0.377226\pi$
$599$	18.4152			0.752426			0.376213	+	0.926533i	$0.377226\pi$
$600$	−2.15542	−	3.73329i	−0.0879946	−	0.152411i
$601$	−20.7018	−	35.8566i	−0.844445	−	1.46262i	−0.886102	−	0.463490i	$-0.846597\pi$
$601$	−20.7018	−	35.8566i	−0.844445	−	1.46262i	0.0416571	−	0.999132i	$-0.486736\pi$
$602$		0			0
$603$	10.3348			0.420865
$604$	−3.18169	+	5.51085i	−0.129461	+	0.224233i
$605$	3.88549	−	6.72987i	0.157968	−	0.273608i
$606$	5.49380			0.223170
$607$	6.15255	−	10.6565i	0.249724	−	0.432535i	−0.713725	−	0.700426i	$-0.752993\pi$
$607$	6.15255	−	10.6565i	0.249724	−	0.432535i	0.963449	+	0.267891i	$0.0863266\pi$
$608$	−7.77119	−	13.4601i	−0.315163	−	0.545879i
$609$		0			0
$610$	15.3167			0.620155
$611$	−9.11830	+	6.99108i	−0.368887	+	0.282829i
$612$	−1.04345			−0.0421789
$613$	−13.1112	−	22.7093i	−0.529556	−	0.917219i	−0.999406	−	0.0344720i	$-0.989025\pi$
$613$	−13.1112	−	22.7093i	−0.529556	−	0.917219i	0.469849	−	0.882747i	$-0.344308\pi$
$614$	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	−0.611971	−	0.790880i	$-0.709623\pi$
$617$	9.41259	−	16.3031i	0.378936	−	0.656337i	0.990908	+	0.134543i	$0.0429565\pi$
$618$	3.77519	−	6.53882i	0.151860	−	0.263030i
$619$	15.8083			0.635389			0.317695	−	0.948193i	$-0.397091\pi$
$619$	15.8083			0.635389			0.317695	+	0.948193i	$0.397091\pi$
$620$	−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
$625$	5.72006			0.228802
$626$	1.84737	+	3.19973i	0.0738356	+	0.127887i
$627$	3.46331	+	5.99862i	0.138311	+	0.239562i
$628$	−2.38030	+	4.12280i	−0.0949843	+	0.164518i
$629$	4.52389			0.180379
$630$		0			0
$631$	8.33817	−	14.4421i	0.331937	−	0.574933i	−0.650954	−	0.759117i	$-0.725631\pi$
$631$	8.33817	−	14.4421i	0.331937	−	0.574933i	0.982892	+	0.184184i	$0.0589644\pi$
$632$	−14.9441			−0.594445
$633$	−0.927285	+	1.60610i	−0.0368563	+	0.0638369i
$634$	15.3755	+	26.6312i	0.610640	+	1.05766i
$635$	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
$640$	−8.05542	−	13.9524i	−0.318418	−	0.551517i
$641$	−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	$0.741409\pi$
$642$	−1.67344			−0.0660454
$643$	21.4355	−	37.1275i	0.845335	−	1.46416i	−0.0399940	−	0.999200i	$-0.512734\pi$
$643$	21.4355	−	37.1275i	0.845335	−	1.46416i	0.885330	−	0.464964i	$-0.153933\pi$
$644$		0			0
$645$	3.16700			0.124701
$646$	4.71336	−	8.16378i	0.185445	−	0.321200i
$647$	2.12929	+	3.68804i	0.0837112	+	0.144992i	0.904841	−	0.425749i	$-0.139989\pi$
$647$	2.12929	+	3.68804i	0.0837112	+	0.144992i	−0.821130	+	0.570741i	$0.806656\pi$
$648$	8.49410	+	14.7122i	0.333680	+	0.577950i
$649$	21.6819			0.851089
$650$	−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
$655$	11.3643			0.444038
$656$	−3.57986	+	6.20049i	−0.139770	+	0.242089i
$657$	7.90982	−	13.7002i	0.308592	−	0.534496i
$658$		0			0
$659$	−12.7259	+	22.0419i	−0.495732	+	0.858632i	−0.999988	−	0.00492170i	$-0.998433\pi$
$659$	−12.7259	+	22.0419i	−0.495732	+	0.858632i	0.504256	+	0.863554i	$0.331767\pi$
$660$	−0.257237	−	0.445548i	−0.0100129	−	0.0173429i
$661$	13.9054	+	24.0848i	0.540857	+	0.936792i	0.998855	+	0.0478387i	$0.0152333\pi$
$661$	13.9054	+	24.0848i	0.540857	+	0.936792i	−0.457998	+	0.888953i	$0.651433\pi$
$662$	6.10639			0.237332
$663$	−1.26874	+	0.972756i	−0.0492739	+	0.0377787i
$664$	−28.6234			−1.11080
$665$		0			0
$666$	10.7117	+	18.5533i	0.415072	+	0.718925i
$667$	−15.3164	+	26.5288i	−0.593055	+	1.02720i
$668$	−3.24128			−0.125409
$669$	1.19103	−	2.06293i	0.0460480	−	0.0797574i
$670$	3.46740	−	6.00572i	0.133957	−	0.232021i
$671$	17.4972			0.675472
$672$		0			0
$673$	−7.76033	−	13.4413i	−0.299139	−	0.518124i	0.676800	−	0.736167i	$-0.263366\pi$
$673$	−7.76033	−	13.4413i	−0.299139	−	0.518124i	−0.975939	+	0.218043i	$0.930033\pi$
$674$	5.55100	+	9.61462i	0.213817	+	0.370341i
$675$	10.0907			0.388392
$676$	3.83071	+	3.83668i	0.147335	+	0.147565i
$677$	−34.5626			−1.32835			−0.664175	−	0.747577i	$-0.731217\pi$
$677$	−34.5626			−1.32835			−0.664175	+	0.747577i	$0.731217\pi$
$678$	6.12109	+	10.6020i	0.235079	+	0.407169i
$679$		0			0
$680$	1.32877	−	2.30150i	0.0509562	−	0.0882587i
$681$	−11.8285			−0.453269
$682$	−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	$0.810725\pi$
$684$	7.70269			0.294520
$685$	1.64703	−	2.85275i	0.0629299	−	0.108998i
$686$		0			0
$687$	−5.31138	−	9.19958i	−0.202642	−	0.350986i
$688$	−25.3174			−0.965218
$689$	8.08261	−	6.19701i	0.307923	−	0.236087i
$690$	3.26027			0.124116
$691$	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
$695$	−13.5813	+	23.5234i	−0.515166	+	0.892294i
$696$	5.12648	−	8.87933i	0.194319	−	0.336570i
$697$	−1.39241			−0.0527413
$698$	−4.88822	+	8.46665i	−0.185022	+	0.320467i
$699$	−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	$0.828659\pi$
$702$	−14.5936	−	6.05152i	−0.550800	−	0.228400i
$703$	−33.3951			−1.25952
$704$	−6.04010	−	10.4618i	−0.227645	−	0.394293i
$705$	−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
$709$	4.89390	−	8.47648i	0.183794	−	0.318341i	−0.759375	−	0.650653i	$-0.774495\pi$
$709$	4.89390	−	8.47648i	0.183794	−	0.318341i	0.943170	+	0.332312i	$0.107829\pi$
$710$	−4.68702			−0.175901
$711$	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
$716$	7.72786			0.288804
$717$	−5.35974	−	9.28334i	−0.200163	−	0.346693i
$718$	−14.5259	−	25.1595i	−0.542100	−	0.938945i
$719$	−13.9201	+	24.1104i	−0.519133	+	0.899165i	0.480620	+	0.876929i	$0.340412\pi$
$719$	−13.9201	+	24.1104i	−0.519133	+	0.899165i	−0.999753	+	0.0222358i	$0.992922\pi$
$720$	15.3288			0.571271
$721$		0			0
$722$	−20.0243	+	34.6830i	−0.745226	+	1.29077i
$723$	10.1514			0.377533
$724$	−1.16883	+	2.02447i	−0.0434391	+	0.0752388i
$725$	15.2439	+	26.4033i	0.566145	+	0.980592i
$726$	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
$731$	−2.46185	−	4.26405i	−0.0910547	−	0.157711i
$732$	−0.843560	+	1.46109i	−0.0311789	+	0.0540034i
$733$	−17.6606			−0.652309			−0.326155	−	0.945316i	$-0.605753\pi$
$733$	−17.6606			−0.652309			−0.326155	+	0.945316i	$0.605753\pi$
$734$	−24.1451	+	41.8206i	−0.891213	+	1.54363i
$735$		0			0
$736$	−8.35705			−0.308045
$737$	3.96102	−	6.86069i	0.145906	−	0.252717i
$738$	−3.29697	−	5.71052i	−0.121363	−	0.210207i
$739$	−4.48279	−	7.76443i	−0.164902	−	0.285619i	0.771718	−	0.635964i	$-0.219398\pi$
$739$	−4.48279	−	7.76443i	−0.164902	−	0.285619i	−0.936621	+	0.350345i	$0.886064\pi$
$740$	2.48042			0.0911822
$741$	9.36579	−	7.18084i	0.344061	−	0.263795i
$742$		0			0
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	0.999824	−	0.0187532i	$-0.00596968\pi$
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	−0.516153	+	0.856497i	$0.672636\pi$
$744$	3.18337	+	5.51376i	0.116708	+	0.202144i
$745$	8.58580	−	14.8710i	0.314560	−	0.544833i
$746$	−4.56618			−0.167180
$747$	16.0543	−	27.8068i	0.587395	−	1.01740i
$748$	−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	$0.712639\pi$
$752$	7.42536	+	12.8611i	0.270775	+	0.468996i
$753$	−6.48641			−0.236378
$754$	−6.21203	−	47.3274i	−0.226229	−	1.72356i
$755$	18.1801			0.661642
$756$		0			0
$757$	−12.4992	−	21.6493i	−0.454292	−	0.786857i	0.544355	−	0.838855i	$-0.316774\pi$
$757$	−12.4992	−	21.6493i	−0.454292	−	0.786857i	−0.998647	+	0.0519981i	$0.983441\pi$
$758$	−7.83957	+	13.5785i	−0.284746	+	0.493195i
$759$	3.72440			0.135187
$760$	−9.80895	+	16.9896i	−0.355808	+	0.616277i
$761$	10.0711	−	17.4436i	0.365077	−	0.632332i	−0.623712	−	0.781655i	$-0.714376\pi$
$761$	10.0711	−	17.4436i	0.365077	−	0.632332i	0.988789	+	0.149323i	$0.0477094\pi$
$762$	−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
$766$	−5.73573			−0.207240
$767$	−4.80769	−	36.6282i	−0.173596	−	1.32257i
$768$	4.69889			0.169557
$769$	4.33610	+	7.51034i	0.156364	+	0.270830i	0.933555	−	0.358435i	$-0.116689\pi$
$769$	4.33610	+	7.51034i	0.156364	+	0.270830i	−0.777191	+	0.629265i	$0.783356\pi$
$770$		0			0
$771$	−3.22199	+	5.58065i	−0.116037	+	0.200982i
$772$	−1.54828			−0.0557237
$773$	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
$775$	−18.9319			−0.680055
$776$	−7.63441	+	13.2232i	−0.274059	+	0.474685i
$777$		0			0
$778$	−17.6198	−	30.5184i	−0.631701	−	1.09414i
$779$	10.2787			0.368273
$780$	−0.695645	+	0.533357i	−0.0249081	+	0.0190973i
$781$	−5.35426			−0.191591
$782$	−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
$786$	−3.62734	+	6.28274i	−0.129383	+	0.224098i
$787$	−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	$0.958613\pi$
$788$	−3.10474			−0.110602
$789$	4.68228	−	8.10994i	0.166693	−	0.288721i
$790$	−5.62434	−	9.74164i	−0.200105	−	0.346592i
$791$		0			0
$792$	14.3768			0.510858
$793$	−3.87978	−	29.5588i	−0.137775	−	1.04966i
$794$	45.2973			1.60754
$795$	0.823349	+	1.42608i	0.0292012	+	0.0505779i
$796$	1.56510	+	2.71084i	0.0554736	+	0.0960830i
$797$	−17.0422	+	29.5180i	−0.603666	+	1.04558i	0.388594	+	0.921409i	$0.372961\pi$
$797$	−17.0422	+	29.5180i	−0.603666	+	1.04558i	−0.992261	+	0.124172i	$0.960373\pi$
$798$		0			0
$799$	−1.44407	+	2.50121i	−0.0510876	+	0.0884863i
$800$	−4.15875	+	7.20316i	−0.147034	+	0.254670i
$801$	−49.0044			−1.73148
$802$	−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
$807$	13.9350			0.490534
$808$	8.88745	+	15.3935i	0.312659	+	0.541542i
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	0.999255	−	0.0385914i	$-0.0122871\pi$
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	−0.533049	+	0.846085i	$0.678954\pi$
$810$	−6.39365	+	11.0741i	−0.224650	+	0.389105i
$811$	−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
$814$	16.4220			0.575590
$815$	8.58347	−	14.8670i	0.300666	−	0.520768i
$816$	1.03318	+	1.78953i	0.0361686	+	0.0626459i
$817$	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	$0.653015\pi$
$822$	1.05143	+	1.82113i	0.0366728	+	0.0635191i
$823$	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	$-0.00654678\pi$
$824$	24.4289			0.851021
$825$	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	$0.416959\pi$
$828$	2.07085	−	3.58681i	0.0719670	−	0.124650i
$829$	7.29244	+	12.6309i	0.253277	+	0.438688i	0.964426	−	0.264353i	$-0.0851583\pi$
$829$	7.29244	+	12.6309i	0.253277	+	0.438688i	−0.711149	+	0.703041i	$0.751825\pi$
$830$	−10.7727	−	18.6588i	−0.373925	−	0.647657i
$831$	6.57499			0.228084
$832$	−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
$837$	−14.9031			−0.515128
$838$	−10.1184	+	17.5256i	−0.349534	+	0.605411i
$839$	18.4043	−	31.8772i	0.635386	−	1.10052i	−0.351047	−	0.936358i	$-0.614174\pi$
$839$	18.4043	−	31.8772i	0.635386	−	1.10052i	0.986433	−	0.164164i	$-0.0524925\pi$
$840$		0			0
$841$	−21.7564	+	37.6832i	−0.750221	+	1.29942i
$842$	6.91588	+	11.9787i	0.238337	+	0.412812i
$843$	7.32728	+	12.6912i	0.252365	+	0.437109i
$844$	1.58088			0.0544163
$845$	4.02066	−	14.9587i	0.138315	−	0.514596i
$846$	−13.6772			−0.470232
$847$		0			0
$848$	−6.58196	−	11.4003i	−0.226025	−	0.391488i
$849$	−2.41965	+	4.19095i	−0.0830421	+	0.143833i
$850$	−5.04470			−0.173032
$851$	−8.97819	+	15.5507i	−0.307768	+	0.533070i
$852$	0.258135	−	0.447103i	0.00884357	−	0.0153175i
$853$	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
$857$	38.3312			1.30937			0.654684	−	0.755902i	$-0.272801\pi$
$857$	38.3312			1.30937			0.654684	+	0.755902i	$0.272801\pi$
$858$	−4.60561	+	3.53116i	−0.157233	+	0.120552i
$859$	39.4369			1.34557			0.672785	−	0.739838i	$-0.265098\pi$
$859$	39.4369			1.34557			0.672785	+	0.739838i	$0.265098\pi$
$860$	−1.34982	−	2.33796i	−0.0460284	−	0.0797236i
$861$		0			0
$862$	6.96300	−	12.0603i	0.237161	−	0.410775i
$863$	−38.6440			−1.31546			−0.657728	−	0.753255i	$-0.728483\pi$
$863$	−38.6440			−1.31546			−0.657728	+	0.753255i	$0.728483\pi$
$864$	−3.27375	+	5.67030i	−0.111375	+	0.192907i
$865$	3.63090	−	6.28891i	0.123454	−	0.213829i
$866$	0.268820			0.00913488
$867$	3.95771	−	6.85495i	0.134411	−	0.232806i
$868$		0			0
$869$	−6.42502	−	11.1285i	−0.217954	−	0.377507i
$870$	7.71757			0.261650
$871$	−12.4684	−	5.17026i	−0.422475	−	0.175188i
$872$	−33.8283			−1.14557
$873$	−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
$877$	29.0371	−	50.2937i	0.980512	−	1.69830i	0.320118	−	0.947378i	$-0.396277\pi$
$877$	29.0371	−	50.2937i	0.980512	−	1.69830i	0.660394	−	0.750919i	$-0.270389\pi$
$878$	7.41710	−	12.8468i	0.250315	−	0.433558i
$879$	−3.87026			−0.130541
$880$	5.87508	−	10.1759i	0.198049	−	0.343031i
$881$	10.8118	+	18.7266i	0.364259	+	0.630916i	0.988657	−	0.150191i	$-0.0479888\pi$
$881$	10.8118	+	18.7266i	0.364259	+	0.630916i	−0.624398	+	0.781107i	$0.714655\pi$
$882$		0			0
$883$	−22.7329			−0.765022			−0.382511	−	0.923951i	$-0.624941\pi$
$883$	−22.7329			−0.765022			−0.382511	+	0.923951i	$0.624941\pi$
$884$	1.25887	+	0.522014i	0.0423403	+	0.0175572i
$885$	5.97287			0.200776
$886$	10.7845	+	18.6793i	0.362312	+	0.627543i
$887$	−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
$891$	−7.30385	+	12.6506i	−0.244688	+	0.423812i
$892$	−2.03054			−0.0679874
$893$	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
$898$	−33.1012			−1.10460
$899$	−22.5140	−	38.9954i	−0.750884	−	1.30057i
$900$	−2.06105	−	3.56984i	−0.0687015	−	0.118995i
$901$	1.28005	−	2.21711i	0.0426446	−	0.0738627i
$902$	−5.05453			−0.168297
$903$		0			0
$904$	−19.8045	+	34.3023i	−0.658687	+	1.14088i
$905$	6.67866			0.222006
$906$	−5.80288	+	10.0509i	−0.192788	+	0.333918i
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	0.721262	−	0.692662i	$-0.243562\pi$
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	−0.960494	+	0.278301i	$0.910229\pi$
$908$	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
$913$	−12.3063	−	21.3151i	−0.407278	−	0.705426i
$914$	−7.52907	+	13.0407i	−0.249039	+	0.431349i
$915$	4.82008			0.159347
$916$	−4.52757	+	7.84197i	−0.149595	+	0.259106i
$917$		0			0
$918$	−3.97117			−0.131068
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	−0.545875	−	0.837867i	$-0.683802\pi$
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	0.998551	+	0.0538078i	$0.0171358\pi$
$920$	5.27422	+	9.13522i	0.173886	+	0.301179i
$921$	0.311258	+	0.539114i	0.0102563	+	0.0177644i
$922$	2.13669			0.0703682
$923$	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
$928$	−19.7825			−0.649391
$929$	−14.3194	+	24.8020i	−0.469805	+	0.813727i	−0.999404	−	0.0345217i	$-0.989009\pi$
$929$	−14.3194	+	24.8020i	−0.469805	+	0.813727i	0.529599	+	0.848248i	$0.322343\pi$
$930$	−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
$934$	−22.6370	−	39.2084i	−0.740704	−	1.28294i
$935$	2.28515			0.0747326
$936$	−3.18788	−	24.2874i	−0.104199	−	0.793858i
$937$	−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
$940$	−0.791778	+	1.37140i	−0.0258249	+	0.0447301i
$941$	−28.9003			−0.942124			−0.471062	−	0.882100i	$-0.656129\pi$
$941$	−28.9003			−0.942124			−0.471062	+	0.882100i	$0.656129\pi$
$942$	−4.34127	+	7.51931i	−0.141446	+	0.244992i
$943$	2.76340	−	4.78635i	0.0899887	−	0.155865i
$944$	−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	$0.996132\pi$
$948$	1.23903			0.0402418
$949$	−16.3967	+	12.5715i	−0.532259	+	0.408087i
$950$	37.2398			1.20822
$951$	4.83860	+	8.38070i	0.156902	+	0.271763i
$952$		0			0
$953$	−2.46511	+	4.26969i	−0.0798527	+	0.138309i	−0.903186	−	0.429249i	$-0.858778\pi$
$953$	−2.46511	+	4.26969i	−0.0798527	+	0.138309i	0.823334	+	0.567558i	$0.192112\pi$
$954$	12.1237			0.392519
$955$	−0.300084	+	0.519760i	−0.00971048	+	0.0168190i
$956$	−4.56879	+	7.91337i	−0.147765	+	0.255937i
$957$	8.81625			0.284989
$958$	7.55721	−	13.0895i	0.244162	−	0.422902i
$959$		0			0
$960$	−1.66391	−	2.88198i	−0.0537025	−	0.0930155i
$961$	−3.03914			−0.0980368
$962$	−3.64137	−	27.7424i	−0.117402	−	0.894451i
$963$	6.07357			0.195718
$964$	−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	$0.344762\pi$
$968$	−8.02523	+	13.9001i	−0.257941	+	0.446767i
$969$	1.48327	−	2.56910i	0.0476495	−	0.0825313i
$970$	−11.4931			−0.369021
$971$	7.28843	−	12.6239i	0.233897	−	0.405121i	−0.725055	−	0.688691i	$-0.758186\pi$
$971$	7.28843	−	12.6239i	0.233897	−	0.405121i	0.958952	+	0.283570i	$0.0915188\pi$
$972$	−2.46738	−	4.27362i	−0.0791412	−	0.137077i
$973$		0			0
$974$	−26.6058			−0.852506
$975$	−5.83403	−	2.41920i	−0.186838	−	0.0774763i
$976$	−38.5324			−1.23339
$977$	−26.2609	−	45.4852i	−0.840161	−	1.45520i	−0.889758	−	0.456432i	$-0.849127\pi$
$977$	−26.2609	−	45.4852i	−0.840161	−	1.45520i	0.0495974	−	0.998769i	$-0.484206\pi$
$978$	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
$982$	19.9943	−	34.6312i	0.638044	−	1.10513i
$983$	6.03769			0.192572			0.0962862	−	0.995354i	$-0.469304\pi$
$983$	6.03769			0.192572			0.0962862	+	0.995354i	$0.469304\pi$
$984$	−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
$989$	19.5433			0.621441
$990$	5.41083	+	9.37183i	0.171967	+	0.297856i
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	0.502090	−	0.864815i	$-0.332564\pi$
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	−0.999997	+	0.00241558i	$0.999231\pi$
$992$	6.14212	−	10.6385i	0.195012	−	0.337771i
$993$	1.92165			0.0609816
$994$		0			0
$995$	4.47148	−	7.74483i	0.141755	−	0.245528i
$996$	2.37320			0.0751976
$997$	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	$0.139008\pi$
$998$	−4.20073	−	7.27588i	−0.132972	−	0.230314i
$999$	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.f.j.393.2		12
7.2	even	3		637.2.g.l.263.2		12
7.3	odd	6		91.2.h.b.16.5	yes	12
7.4	even	3		637.2.h.l.471.5		12
7.5	odd	6		91.2.g.b.81.2	yes	12
7.6	odd	2		637.2.f.k.393.2		12
13.3	even	3		8281.2.a.ca.1.5		6
13.9	even	3	inner	637.2.f.j.295.2		12
13.10	even	6		8281.2.a.cf.1.2		6
21.5	even	6		819.2.n.d.172.5		12
21.17	even	6		819.2.s.d.289.2		12
91.3	odd	6		1183.2.e.h.170.2		12
91.9	even	3		637.2.h.l.165.5		12
91.10	odd	6		1183.2.e.g.170.5		12
91.48	odd	6		637.2.f.k.295.2		12
91.55	odd	6		8281.2.a.bz.1.5		6
91.61	odd	6		91.2.h.b.74.5	yes	12
91.62	odd	6		8281.2.a.ce.1.2		6
91.68	odd	6		1183.2.e.h.508.2		12
91.74	even	3		637.2.g.l.373.2		12
91.75	odd	6		1183.2.e.g.508.5		12
91.87	odd	6		91.2.g.b.9.2	✓	12
273.152	even	6		819.2.s.d.802.2		12
273.269	even	6		819.2.n.d.100.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.2	✓	12	91.87	odd	6
91.2.g.b.81.2	yes	12	7.5	odd	6
91.2.h.b.16.5	yes	12	7.3	odd	6
91.2.h.b.74.5	yes	12	91.61	odd	6
637.2.f.j.295.2		12	13.9	even	3	inner
637.2.f.j.393.2		12	1.1	even	1	trivial
637.2.f.k.295.2		12	91.48	odd	6
637.2.f.k.393.2		12	7.6	odd	2
637.2.g.l.263.2		12	7.2	even	3
637.2.g.l.373.2		12	91.74	even	3
637.2.h.l.165.5		12	91.9	even	3
637.2.h.l.471.5		12	7.4	even	3
819.2.n.d.100.5		12	273.269	even	6
819.2.n.d.172.5		12	21.5	even	6
819.2.s.d.289.2		12	21.17	even	6
819.2.s.d.802.2		12	273.152	even	6
1183.2.e.g.170.5		12	91.10	odd	6
1183.2.e.g.508.5		12	91.75	odd	6
1183.2.e.h.170.2		12	91.3	odd	6
1183.2.e.h.508.2		12	91.68	odd	6
8281.2.a.bz.1.5		6	91.55	odd	6
8281.2.a.ca.1.5		6	13.3	even	3
8281.2.a.ce.1.2		6	91.62	odd	6
8281.2.a.cf.1.2		6	13.10	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +O(q^{10})\)	\(q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(-0.926214 - 1.60425i) q^{10} +(-1.05807 - 1.83263i) q^{11} +0.204043 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} -4.29192 q^{18} +(3.34514 - 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} +(0.602021 + 1.04273i) q^{24} -3.58030 q^{25} +(5.17797 + 2.14715i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 + 0.784881i) q^{30} +5.28780 q^{31} +(1.16156 - 2.01189i) q^{32} +(-0.517662 + 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} -10.4013 q^{38} +(1.62948 + 0.675696i) q^{39} -2.93230 q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +0.882538 q^{44} +(1.64466 - 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} +3.18673 q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +0.443410 q^{51} +(-0.195692 - 1.49091i) q^{52} -2.82477 q^{53} +(2.19086 + 3.79469i) q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 + 11.4652i) q^{58} +(-5.12298 + 8.87327i) q^{59} +0.243120 q^{60} +(-4.13423 + 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-3.40931 + 2.61395i) q^{65} +1.60960 q^{66} +(1.87182 + 3.24208i) q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 + 5.88368i) q^{72} +5.73044 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} +6.07240 q^{79} +(2.77632 + 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(1.19428 - 2.06856i) q^{82} +11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +8.44619 q^{86} +(-2.08310 + 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(-8.87557 - 15.3729i) q^{89} -5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +(-2.47719 - 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} -1.13659 q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23} + 11 q^{24} - 14 q^{25} - 11 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} + 32 q^{31} + 8 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} - 34 q^{38} + 43 q^{39} - 10 q^{40} + 8 q^{41} - 11 q^{43} - 42 q^{44} + 7 q^{45} + 16 q^{46} - 2 q^{47} - 21 q^{48} + 6 q^{50} + 40 q^{51} + 16 q^{52} + 4 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} - 13 q^{59} - 40 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 14 q^{65} + 36 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 60 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} - 14 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} + 14 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} - 45 q^{94} - 6 q^{95} + 38 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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