LMFDB - Embedded newform 637.2.g.l.263.3

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			263.3
Root			$-0.437442 - 0.757672i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.l.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.134063 - 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} +O(q^{10})$	\(q+(0.134063 - 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} -0.686871 q^{10} +3.94600 q^{11} +(1.10192 + 1.90859i) q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} +(-0.227039 + 0.393243i) q^{18} +7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(3.97759 - 6.88938i) q^{23} +1.20385 q^{24} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} -0.785100 q^{30} +(-1.27718 + 2.21215i) q^{31} +(1.53234 + 2.65409i) q^{32} +4.51032 q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(3.60475 + 1.99746i) q^{39} +(-1.34905 - 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(3.80416 + 6.58900i) q^{44} +(2.16920 + 3.75717i) q^{45} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} +(0.448688 + 0.777151i) q^{51} +(0.122340 + 6.95082i) q^{52} +(-4.63977 + 8.03632i) q^{53} +(-0.719212 + 1.24571i) q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +(2.82286 - 4.88933i) q^{60} -9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(-0.162546 - 9.23511i) q^{65} +(0.604665 - 1.04731i) q^{66} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} -1.78367 q^{72} +(0.384295 - 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(-0.893026 + 1.54677i) q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} -1.05136 q^{81} -0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(-0.301568 - 0.522332i) q^{86} +(-1.34402 - 2.32792i) q^{87} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 + 2.52850i) q^{93} +0.353001 q^{94} +(-9.60052 - 16.6286i) q^{95} +(1.75148 + 3.03365i) q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.134063	−	0.232203i	0.0947966	−	0.164193i	−0.814727	−	0.579845i	$-0.803113\pi$
$2$	0.134063	−	0.232203i	0.0947966	−	0.164193i	0.909524	+	0.415652i	$0.136447\pi$
$3$	1.14301			0.659917			0.329958	−	0.943996i	$-0.392965\pi$
$3$	1.14301			0.659917			0.329958	+	0.943996i	$0.392965\pi$
$4$	0.964054	+	1.66979i	0.482027	+	0.834896i
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	−0.996274	−	0.0862431i	$-0.972514\pi$
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	0.423448	−	0.905920i	$-0.360820\pi$
$6$	0.153235	−	0.265410i	0.0625578	−	0.108353i
$7$		0			0
$7$		0			0
$8$	1.05323			0.372371
$9$	−1.69353			−0.564510
$10$	−0.686871			−0.217208
$11$	3.94600			1.18976			0.594882	−	0.803813i	$-0.297199\pi$
$11$	3.94600			1.18976			0.594882	+	0.803813i	$0.297199\pi$
$12$	1.10192	+	1.90859i	0.318098	+	0.550961i
$13$	3.15374	+	1.74755i	0.874690	+	0.484682i
$13$	3.15374	+	1.74755i	0.874690	+	0.484682i
$14$		0			0
$15$	−1.46405	−	2.53582i	−0.378017	−	0.654745i
$16$	−1.78691	+	3.09502i	−0.446728	+	0.773755i
$17$	0.392550	+	0.679916i	0.0952073	+	0.164904i	0.909695	−	0.415277i	$-0.136315\pi$
$17$	0.392550	+	0.679916i	0.0952073	+	0.164904i	−0.814488	+	0.580181i	$0.802982\pi$
$18$	−0.227039	+	0.393243i	−0.0535136	+	0.0926883i
$19$	7.49527			1.71953			0.859767	−	0.510687i	$-0.170609\pi$
$19$	7.49527			1.71953			0.859767	+	0.510687i	$0.170609\pi$
$20$	2.46967	−	4.27760i	0.552235	−	0.956500i
$21$		0			0
$22$	0.529011	−	0.916274i	0.112786	−	0.195350i
$23$	3.97759	−	6.88938i	0.829384	−	1.43654i	−0.0691375	−	0.997607i	$-0.522025\pi$
$23$	3.97759	−	6.88938i	0.829384	−	1.43654i	0.898522	−	0.438929i	$-0.144642\pi$
$24$	1.20385			0.245734
$25$	−0.781294	+	1.35324i	−0.156259	+	0.270648i
$26$	0.828585	−	0.498028i	0.162499	−	0.0976714i
$27$	−5.36475			−1.03245
$28$		0			0
$29$	−1.17586	−	2.03666i	−0.218353	−	0.378198i	0.735952	−	0.677034i	$-0.236735\pi$
$29$	−1.17586	−	2.03666i	−0.218353	−	0.378198i	−0.954304	+	0.298836i	$0.903402\pi$
$30$	−0.785100			−0.143339
$31$	−1.27718	+	2.21215i	−0.229389	+	0.397313i	−0.957627	−	0.288011i	$-0.907006\pi$
$31$	−1.27718	+	2.21215i	−0.229389	+	0.397313i	0.728238	+	0.685324i	$0.240339\pi$
$32$	1.53234	+	2.65409i	0.270882	+	0.469182i
$33$	4.51032			0.785145
$34$	0.210505			0.0361013
$35$		0			0
$36$	−1.63266	−	2.82784i	−0.272109	−	0.471307i
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	0.442435	+	0.896801i	$0.354115\pi$
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	−0.997870	+	0.0652406i	$0.979219\pi$
$38$	1.00484	−	1.74043i	0.163006	−	0.282334i
$39$	3.60475	+	1.99746i	0.577223	+	0.319850i
$40$	−1.34905	−	2.33663i	−0.213304	−	0.369453i
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	0.755027	−	0.655694i	$-0.227624\pi$
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	−0.945361	+	0.326025i	$0.894291\pi$
$42$		0			0
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	−0.767432	−	0.641131i	$-0.778466\pi$
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	0.938951	+	0.344050i	$0.111799\pi$
$44$	3.80416	+	6.58900i	0.573499	+	0.993329i
$45$	2.16920	+	3.75717i	0.323366	+	0.560086i
$46$	−1.06649	−	1.84722i	−0.157246	−	0.272357i
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	0.910034	−	0.414534i	$-0.136056\pi$
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	−0.814014	+	0.580845i	$0.802722\pi$
$48$	−2.04246	+	3.53764i	−0.294803	+	0.510614i
$49$		0			0
$50$	0.209485	+	0.362838i	0.0296256	+	0.0513130i
$51$	0.448688	+	0.777151i	0.0628289	+	0.108823i
$52$	0.122340	+	6.95082i	0.0169655	+	0.963905i
$53$	−4.63977	+	8.03632i	−0.637321	+	1.10387i	0.348697	+	0.937236i	$0.386624\pi$
$53$	−4.63977	+	8.03632i	−0.637321	+	1.10387i	−0.986018	+	0.166637i	$0.946709\pi$
$54$	−0.719212	+	1.24571i	−0.0978724	+	0.169520i
$55$	−5.05434	−	8.75438i	−0.681528	−	1.18044i
$56$		0			0
$57$	8.56716			1.13475
$58$	−0.630558			−0.0827963
$59$	−4.48335	−	7.76540i	−0.583683	−	1.01097i	−0.995038	−	0.0994935i	$-0.968278\pi$
$59$	−4.48335	−	7.76540i	−0.583683	−	1.01097i	0.411355	−	0.911475i	$-0.365056\pi$
$60$	2.82286	−	4.88933i	0.364429	−	0.631210i
$61$	−9.44547			−1.20937			−0.604684	−	0.796465i	$-0.706701\pi$
$61$	−9.44547			−1.20937			−0.604684	+	0.796465i	$0.706701\pi$
$62$	0.342445	+	0.593132i	0.0434906	+	0.0753279i
$63$		0			0
$64$	−6.32592			−0.790741
$65$	−0.162546	−	9.23511i	−0.0201613	−	1.14547i
$66$	0.604665	−	1.04731i	0.0744291	−	0.128915i
$67$	−1.35256			−0.165242			−0.0826209	−	0.996581i	$-0.526329\pi$
$67$	−1.35256			−0.165242			−0.0826209	+	0.996581i	$0.526329\pi$
$68$	−0.756879	+	1.31095i	−0.0917851	+	0.158976i
$69$	4.54642	−	7.87463i	0.547324	−	0.947994i
$70$		0			0
$71$	−6.15808	+	10.6661i	−0.730829	+	1.26583i	0.225700	+	0.974197i	$0.427533\pi$
$71$	−6.15808	+	10.6661i	−0.730829	+	1.26583i	−0.956529	+	0.291637i	$0.905800\pi$
$72$	−1.78367			−0.210207
$73$	0.384295	−	0.665619i	0.0449783	−	0.0779048i	−0.842660	−	0.538446i	$-0.819011\pi$
$73$	0.384295	−	0.665619i	0.0449783	−	0.0779048i	0.887638	+	0.460542i	$0.152345\pi$
$74$	0.905882	+	1.56903i	0.105307	+	0.182396i
$75$	−0.893026	+	1.54677i	−0.103118	+	0.178605i
$76$	7.22585	+	12.5155i	0.828862	+	1.43563i
$77$		0			0
$78$	0.947080	−	0.569251i	0.107236	−	0.0644550i
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	0.637586	−	0.770379i	$-0.279933\pi$
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	−0.985961	+	0.166976i	$0.946600\pi$
$80$	9.15525			1.02359
$81$	−1.05136			−0.116818
$82$	−0.653548			−0.0721723
$83$	1.07292			0.117768			0.0588841	−	0.998265i	$-0.481246\pi$
$83$	1.07292			0.117768			0.0588841	+	0.998265i	$0.481246\pi$
$84$		0			0
$85$	1.00562	−	1.74178i	0.109074	−	0.188922i
$86$	−0.301568	−	0.522332i	−0.0325190	−	0.0563245i
$87$	−1.34402	−	2.32792i	−0.144094	−	0.249579i
$88$	4.15603			0.443034
$89$	3.83149	−	6.63634i	0.406138	−	0.703451i	−0.588316	−	0.808631i	$-0.700209\pi$
$89$	3.83149	−	6.63634i	0.406138	−	0.703451i	0.994453	+	0.105180i	$0.0335420\pi$
$90$	1.16324			0.122616
$91$		0			0
$92$	15.3384			1.59914
$93$	−1.45983	+	2.52850i	−0.151378	+	0.262194i
$94$	0.353001			0.0364093
$95$	−9.60052	−	16.6286i	−0.984993	−	1.70606i
$96$	1.75148	+	3.03365i	0.178760	+	0.309621i
$97$	−1.18601	+	2.05423i	−0.120421	+	0.208575i	−0.919934	−	0.392074i	$-0.871758\pi$
$97$	−1.18601	+	2.05423i	−0.120421	+	0.208575i	0.799513	+	0.600649i	$0.205091\pi$
$98$		0			0
$99$	−6.68267			−0.671634
$100$	−3.01284			−0.301284
$101$	0.797330			0.0793373			0.0396686	−	0.999213i	$-0.487370\pi$
$101$	0.797330			0.0793373			0.0396686	+	0.999213i	$0.487370\pi$
$102$	0.240609			0.0238239
$103$	1.08309	+	1.87597i	0.106720	+	0.184844i	0.914440	−	0.404722i	$-0.132632\pi$
$103$	1.08309	+	1.87597i	0.106720	+	0.184844i	−0.807720	+	0.589567i	$0.799299\pi$
$104$	3.32160	+	1.84056i	0.325710	+	0.180482i
$105$		0			0
$106$	1.24404	+	2.15474i	0.120832	+	0.209287i
$107$	5.76311	−	9.98201i	0.557141	−	0.964997i	−0.440592	−	0.897707i	$-0.645232\pi$
$107$	5.76311	−	9.98201i	0.557141	−	0.964997i	0.997733	−	0.0672896i	$-0.0214351\pi$
$108$	−5.17191	−	8.95801i	−0.497667	−	0.861985i
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	−0.992028	−	0.126020i	$-0.959780\pi$
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	0.605151	+	0.796111i	$0.293113\pi$
$110$	−2.71039			−0.258426
$111$	−3.86174	+	6.68874i	−0.366541	+	0.634867i
$112$		0			0
$113$	−4.02067	+	6.96401i	−0.378233	+	0.655119i	−0.990805	−	0.135296i	$-0.956802\pi$
$113$	−4.02067	+	6.96401i	−0.378233	+	0.655119i	0.612572	+	0.790415i	$0.290135\pi$
$114$	1.14854	−	1.98932i	0.107570	−	0.186317i
$115$	−20.3792			−1.90037
$116$	2.26719	−	3.92690i	0.210504	−	0.364603i
$117$	−5.34096	−	2.95952i	−0.493772	−	0.273608i
$118$	−2.40420			−0.221325
$119$		0			0
$120$	−1.54198	−	2.67079i	−0.140763	−	0.243808i
$121$	4.57093			0.415539
$122$	−1.26628	+	2.19327i	−0.114644	+	0.198569i
$123$	−1.39303	−	2.41279i	−0.125605	−	0.217554i
$124$	−4.92510			−0.442287
$125$	−8.80581			−0.787615
$126$		0			0
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	0.823630	−	0.567127i	$-0.191945\pi$
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	−0.902962	+	0.429721i	$0.858612\pi$
$128$	−3.91275	+	6.77709i	−0.345842	+	0.599015i
$129$	1.28558	−	2.22668i	0.113189	−	0.196049i
$130$	−2.16621	−	1.20034i	−0.189989	−	0.105277i
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	0.691995	−	0.721902i	$-0.256732\pi$
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	−0.971183	+	0.238334i	$0.923399\pi$
$132$	4.34819	+	7.53129i	0.378461	+	0.655514i
$133$		0			0
$134$	−0.181328	+	0.314069i	−0.0156644	+	0.0271315i
$135$	6.87158	+	11.9019i	0.591412	+	1.02436i
$136$	0.413443	+	0.716105i	0.0354525	+	0.0614055i
$137$	−5.01827	−	8.69190i	−0.428740	−	0.742599i	0.568022	−	0.823014i	$-0.307709\pi$
$137$	−5.01827	−	8.69190i	−0.428740	−	0.742599i	−0.996762	+	0.0804144i	$0.974376\pi$
$138$	−1.21901	−	2.11139i	−0.103769	−	0.179733i
$139$	−2.77278	+	4.80260i	−0.235184	+	0.407351i	−0.959326	−	0.282300i	$-0.908903\pi$
$139$	−2.77278	+	4.80260i	−0.235184	+	0.407351i	0.724142	+	0.689651i	$0.242236\pi$
$140$		0			0
$141$	0.752416	+	1.30322i	0.0633648	+	0.109751i
$142$	1.65114	+	2.85985i	0.138560	+	0.239993i
$143$	12.4447	+	6.89582i	1.04068	+	0.576658i
$144$	3.02619	−	5.24151i	0.252182	−	0.436793i
$145$	−3.01228	+	5.21742i	−0.250156	+	0.433283i
$146$	−0.103039	−	0.178469i	−0.00852759	−	0.0147702i
$147$		0			0
$148$	−13.0285			−1.07094
$149$	18.4651			1.51272			0.756359	−	0.654157i	$-0.226976\pi$
$149$	18.4651			1.51272			0.756359	+	0.654157i	$0.226976\pi$
$150$	0.239443	+	0.414727i	0.0195504	+	0.0338623i
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	−0.896872	−	0.442289i	$-0.854166\pi$
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	0.831470	+	0.555570i	$0.187500\pi$
$152$	7.89421			0.640305
$153$	−0.664795	−	1.15146i	−0.0537455	−	0.0930900i
$154$		0			0
$155$	6.54366			0.525600
$156$	0.139836	+	7.94485i	0.0111958	+	0.636097i
$157$	−0.822967	+	1.42542i	−0.0656799	+	0.113761i	−0.896995	−	0.442040i	$-0.854255\pi$
$157$	−0.822967	+	1.42542i	−0.0656799	+	0.113761i	0.831315	+	0.555801i	$0.187588\pi$
$158$	−1.66046			−0.132099
$159$	−5.30330	+	9.18558i	−0.420579	+	0.728464i
$160$	3.92548	−	6.79913i	0.310337	−	0.537519i
$161$		0			0
$162$	−0.140949	+	0.244130i	−0.0110740	+	0.0191807i
$163$	−6.54819			−0.512894			−0.256447	−	0.966558i	$-0.582552\pi$
$163$	−6.54819			−0.512894			−0.256447	+	0.966558i	$0.582552\pi$
$164$	2.34986	−	4.07007i	0.183493	−	0.317819i
$165$	−5.77716	−	10.0063i	−0.449751	−	0.778992i
$166$	0.143838	−	0.249135i	0.0111640	−	0.0193367i
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	0.989480	−	0.144668i	$-0.0462114\pi$
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	−0.620026	+	0.784581i	$0.712878\pi$
$168$		0			0
$169$	6.89216	+	11.0226i	0.530166	+	0.847894i
$170$	−0.269631	−	0.467015i	−0.0206798	−	0.0358184i
$171$	−12.6935			−0.970694
$172$	4.33720			0.330709
$173$	−11.1316			−0.846322			−0.423161	−	0.906054i	$-0.639080\pi$
$173$	−11.1316			−0.846322			−0.423161	+	0.906054i	$0.639080\pi$
$174$	−0.720733			−0.0546386
$175$		0			0
$176$	−7.05115	+	12.2130i	−0.531501	+	0.920586i
$177$	−5.12451	−	8.87592i	−0.385182	−	0.667155i
$178$	−1.02732	−	1.77937i	−0.0770009	−	0.133369i
$179$	−12.6435			−0.945017			−0.472508	−	0.881326i	$-0.656651\pi$
$179$	−12.6435			−0.945017			−0.472508	+	0.881326i	$0.656651\pi$
$180$	−4.18246	+	7.24424i	−0.311742	+	0.539954i
$181$	−14.9158			−1.10868			−0.554341	−	0.832289i	$-0.687030\pi$
$181$	−14.9158			−1.10868			−0.554341	+	0.832289i	$0.687030\pi$
$182$		0			0
$183$	−10.7963			−0.798082
$184$	4.18930	−	7.25607i	0.308839	−	0.534925i
$185$	17.3102			1.27267
$186$	0.391418	+	0.677956i	0.0287001	+	0.0497101i
$187$	1.54900	+	2.68295i	0.113274	+	0.196197i
$188$	−1.26923	+	2.19837i	−0.0925680	+	0.160332i
$189$		0			0
$190$	−5.14829			−0.373496
$191$	−14.1306			−1.02245			−0.511226	−	0.859447i	$-0.670808\pi$
$191$	−14.1306			−1.02245			−0.511226	+	0.859447i	$0.670808\pi$
$192$	−7.23059			−0.521823
$193$	3.89454			0.280335			0.140167	−	0.990128i	$-0.455236\pi$
$193$	3.89454			0.280335			0.140167	+	0.990128i	$0.455236\pi$
$194$	0.317999	+	0.550790i	0.0228310	+	0.0395444i
$195$	−0.185791	−	10.5558i	−0.0133048	−	0.755917i
$196$		0			0
$197$	5.85445	+	10.1402i	0.417112	+	0.722459i	0.995648	−	0.0931979i	$-0.0297089\pi$
$197$	5.85445	+	10.1402i	0.417112	+	0.722459i	−0.578536	+	0.815657i	$0.696376\pi$
$198$	−0.895897	+	1.55174i	−0.0636686	+	0.110277i
$199$	1.74842	+	3.02835i	0.123942	+	0.214674i	0.921319	−	0.388808i	$-0.127113\pi$
$199$	1.74842	+	3.02835i	0.123942	+	0.214674i	−0.797377	+	0.603482i	$0.793780\pi$
$200$	−0.822878	+	1.42527i	−0.0581863	+	0.100782i
$201$	−1.54599			−0.109046
$202$	0.106892	−	0.185143i	0.00752090	−	0.0130266i
$203$		0			0
$204$	−0.865120	+	1.49843i	−0.0605705	+	0.104911i
$205$	−3.12210	+	5.40764i	−0.218057	+	0.377686i
$206$	0.580807			0.0404667
$207$	−6.73617	+	11.6674i	−0.468196	+	0.810939i
$208$	−11.0441	+	6.63818i	−0.765774	+	0.460275i
$209$	29.5764			2.04584
$210$		0			0
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	−0.982098	−	0.188373i	$-0.939679\pi$
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	0.327913	−	0.944708i	$-0.393655\pi$
$212$	−17.8920			−1.22882
$213$	−7.03874	+	12.1915i	−0.482286	+	0.835345i
$214$	−1.54524	−	2.67643i	−0.105630	−	0.182957i
$215$	−5.76256			−0.393004
$216$	−5.65029			−0.384453
$217$		0			0
$218$	1.08299	+	1.87579i	0.0733492	+	0.127045i
$219$	0.439253	−	0.760808i	0.0296820	−	0.0514106i
$220$	9.74533	−	16.8794i	0.657030	−	1.13801i
$221$	0.0498153	+	2.83028i	0.00335094	+	0.190385i
$222$	1.03543	+	1.79342i	0.0694936	+	0.120366i
$223$	−5.98311	−	10.3630i	−0.400658	−	0.693961i	0.593147	−	0.805094i	$-0.297885\pi$
$223$	−5.98311	−	10.3630i	−0.400658	−	0.693961i	−0.993805	+	0.111133i	$0.964552\pi$
$224$		0			0
$225$	1.32315	−	2.29175i	0.0882097	−	0.152784i
$226$	1.07804	+	1.86723i	0.0717104	+	0.124206i
$227$	7.69209	+	13.3231i	0.510542	+	0.884284i	0.999925	+	0.0122157i	$0.00388847\pi$
$227$	7.69209	+	13.3231i	0.510542	+	0.884284i	−0.489384	+	0.872069i	$0.662778\pi$
$228$	8.25921	+	14.3054i	0.546980	+	0.947396i
$229$	4.33084	+	7.50123i	0.286190	+	0.495695i	0.972897	−	0.231239i	$-0.0742779\pi$
$229$	4.33084	+	7.50123i	0.286190	+	0.495695i	−0.686707	+	0.726934i	$0.740945\pi$
$230$	−2.73209	+	4.73212i	−0.180149	+	0.312027i
$231$		0			0
$232$	−1.23845	−	2.14506i	−0.0813082	−	0.140830i
$233$	−10.1253	−	17.5376i	−0.663333	−	1.14893i	−0.979734	−	0.200301i	$-0.935808\pi$
$233$	−10.1253	−	17.5376i	−0.663333	−	1.14893i	0.316402	−	0.948625i	$-0.397525\pi$
$234$	−1.40323	+	0.843426i	−0.0917322	+	0.0551365i
$235$	1.68634	−	2.92083i	0.110005	−	0.190534i
$236$	8.64440	−	14.9725i	0.562702	−	0.974629i
$237$	−3.53924	−	6.13014i	−0.229898	−	0.398195i
$238$		0			0
$239$	16.5526			1.07070			0.535350	−	0.844630i	$-0.320180\pi$
$239$	16.5526			1.07070			0.535350	+	0.844630i	$0.320180\pi$
$240$	10.4645			0.675483
$241$	−8.20038	−	14.2035i	−0.528233	−	0.914926i	−0.999458	−	0.0329132i	$-0.989522\pi$
$241$	−8.20038	−	14.2035i	−0.528233	−	0.914926i	0.471225	−	0.882013i	$-0.343812\pi$
$242$	0.612791	−	1.06138i	0.0393917	−	0.0682284i
$243$	14.8925			0.955356
$244$	−9.10595	−	15.7720i	−0.582949	−	1.00970i
$245$		0			0
$246$	−0.747011			−0.0476277
$247$	23.6381	+	13.0983i	1.50406	+	0.833427i
$248$	−1.34516	+	2.32989i	−0.0854178	+	0.147948i
$249$	1.22636			0.0777172
$250$	−1.18053	+	2.04474i	−0.0746632	+	0.129321i
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	0.339563	+	0.940583i	$0.389721\pi$
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	−0.984350	+	0.176222i	$0.943612\pi$
$252$		0			0
$253$	15.6956	−	27.1855i	0.986772	−	1.70914i
$254$	−0.479420			−0.0300815
$255$	1.14943	−	1.99087i	0.0719800	−	0.124673i
$256$	−5.27682	−	9.13972i	−0.329801	−	0.571232i
$257$	6.88895	−	11.9320i	0.429721	−	0.744299i	−0.567127	−	0.823630i	$-0.691945\pi$
$257$	6.88895	−	11.9320i	0.429721	−	0.744299i	0.996848	+	0.0793315i	$0.0252786\pi$
$258$	−0.344695	−	0.597030i	−0.0214598	−	0.0371695i
$259$		0			0
$260$	15.2640	−	9.17456i	0.946633	−	0.568982i
$261$	1.99136	+	3.44914i	0.123262	+	0.213496i
$262$	−1.71356			−0.105864
$263$	25.9173			1.59813			0.799065	−	0.601244i	$-0.205328\pi$
$263$	25.9173			1.59813			0.799065	+	0.601244i	$0.205328\pi$
$264$	4.75038			0.292366
$265$	23.7719			1.46030
$266$		0			0
$267$	4.37943	−	7.58540i	0.268017	−	0.464219i
$268$	−1.30394	−	2.25850i	−0.0796510	−	0.137960i
$269$	−15.0333	−	26.0384i	−0.916596	−	1.58759i	−0.804547	−	0.593889i	$-0.797592\pi$
$269$	−15.0333	−	26.0384i	−0.916596	−	1.58759i	−0.112050	−	0.993703i	$-0.535742\pi$
$270$	3.68489			0.224255
$271$	7.22527	−	12.5145i	0.438904	−	0.760204i	−0.558701	−	0.829369i	$-0.688700\pi$
$271$	7.22527	−	12.5145i	0.438904	−	0.760204i	0.997605	+	0.0691651i	$0.0220335\pi$
$272$	−2.80581			−0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	−3.08299	+	5.33989i	−0.185911	+	0.322008i
$276$	17.5320			1.05530
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	0.998981	−	0.0451272i	$-0.0143693\pi$
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	−0.538572	+	0.842580i	$0.681036\pi$
$278$	0.743453	+	1.28770i	0.0445894	+	0.0772310i
$279$	2.16295	−	3.74634i	0.129492	−	0.224287i
$280$		0			0
$281$	5.29279			0.315741			0.157871	−	0.987460i	$-0.449537\pi$
$281$	5.29279			0.315741			0.157871	+	0.987460i	$0.449537\pi$
$282$	0.403483			0.0240271
$283$	30.7845			1.82995			0.914975	−	0.403511i	$-0.132210\pi$
$283$	30.7845			1.82995			0.914975	+	0.403511i	$0.132210\pi$
$284$	−23.7469			−1.40912
$285$	−10.9735	−	19.0066i	−0.650013	−	1.12586i
$286$	3.26960	−	1.96522i	0.193335	−	0.116206i
$287$		0			0
$288$	−2.59507	−	4.49479i	−0.152916	−	0.264858i
$289$	8.19181	−	14.1886i	0.481871	−	0.834625i
$290$	0.807667	+	1.39892i	0.0474279	+	0.0821474i
$291$	−1.35562	+	2.34800i	−0.0794677	+	0.137642i
$292$	1.48193			0.0867231
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	0.488223	+	0.872719i	$0.337645\pi$
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	−0.999908	+	0.0135461i	$0.995688\pi$
$294$		0			0
$295$	−11.4853	+	19.8930i	−0.668697	+	1.15822i
$296$	−3.55840	+	6.16333i	−0.206828	+	0.358237i
$297$	−21.1693			−1.22837
$298$	2.47548	−	4.28765i	0.143400	−	0.248377i
$299$	24.5838	−	14.7763i	1.42172	−	0.854536i
$300$	−3.44370			−0.198822
$301$		0			0
$302$	0.215486	+	0.373233i	0.0123998	+	0.0214772i
$303$	0.911355			0.0523560
$304$	−13.3934	+	23.1980i	−0.768163	+	1.33050i
$305$	12.0985	+	20.9552i	0.692757	+	1.19989i
$306$	−0.356497			−0.0203796
$307$	8.63573			0.492867			0.246434	−	0.969160i	$-0.420741\pi$
$307$	8.63573			0.492867			0.246434	+	0.969160i	$0.420741\pi$
$308$		0			0
$309$	1.23798	+	2.14425i	0.0704262	+	0.121982i
$310$	0.877260	−	1.51946i	0.0498250	−	0.0862995i
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	−0.999229	−	0.0392535i	$-0.987502\pi$
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	0.533609	+	0.845731i	$0.320835\pi$
$312$	3.79662	+	2.10378i	0.214941	+	0.119103i
$313$	5.02308	+	8.70024i	0.283921	+	0.491766i	0.972347	−	0.233541i	$-0.0750312\pi$
$313$	5.02308	+	8.70024i	0.283921	+	0.491766i	−0.688426	+	0.725307i	$0.741698\pi$
$314$	0.220658	+	0.382191i	0.0124525	+	0.0215683i
$315$		0			0
$316$	5.97024	−	10.3408i	0.335852	−	0.581713i
$317$	−5.07249	−	8.78581i	−0.284899	−	0.493460i	0.687685	−	0.726009i	$-0.258627\pi$
$317$	−5.07249	−	8.78581i	−0.284899	−	0.493460i	−0.972585	+	0.232549i	$0.925294\pi$
$318$	1.42195	+	2.46289i	0.0797389	+	0.138112i
$319$	−4.63996	−	8.03665i	−0.259788	−	0.449966i
$320$	8.10273	+	14.0343i	0.452957	+	0.784544i
$321$	6.58729	−	11.4095i	0.367667	−	0.636817i
$322$		0			0
$323$	2.94227	+	5.09616i	0.163712	+	0.283558i
$324$	−1.01357	−	1.75556i	−0.0563095	−	0.0975310i
$325$	−4.82885	+	2.90242i	−0.267856	+	0.160998i
$326$	−0.877867	+	1.52051i	−0.0486206	+	0.0842133i
$327$	−4.61674	+	7.99644i	−0.255307	+	0.442204i
$328$	−1.28360	−	2.22327i	−0.0708751	−	0.122759i
$329$		0			0
$330$	−3.09801			−0.170540
$331$	2.31916			0.127473			0.0637363	−	0.997967i	$-0.479698\pi$
$331$	2.31916			0.127473			0.0637363	+	0.997967i	$0.479698\pi$
$332$	1.03435	+	1.79155i	0.0567675	+	0.0983242i
$333$	5.72172	−	9.91032i	0.313549	−	0.543082i
$334$	2.56027			0.140092
$335$	1.73247	+	3.00072i	0.0946547	+	0.163947i
$336$		0			0
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$	3.48347	−	0.122662i	0.189476	−	0.00667193i
$339$	−4.59567	+	7.95993i	−0.249602	+	0.432324i
$340$	3.87788			0.210307
$341$	−5.03977	+	8.72913i	−0.272919	+	0.472709i
$342$	−1.70172	+	2.94747i	−0.0920185	+	0.159381i
$343$		0			0
$344$	1.18459	−	2.05178i	0.0638690	−	0.110624i
$345$	−23.2936			−1.25409
$346$	−1.49234	+	2.58480i	−0.0802285	+	0.138960i
$347$	11.4104	+	19.7634i	0.612543	+	1.06096i	0.990810	+	0.135259i	$0.0431867\pi$
$347$	11.4104	+	19.7634i	0.612543	+	1.06096i	−0.378267	+	0.925696i	$0.623480\pi$
$348$	2.59142	−	4.48848i	0.138915	−	0.240608i
$349$	−11.3511	−	19.6607i	−0.607612	−	1.05241i	−0.991633	−	0.129090i	$-0.958794\pi$
$349$	−11.3511	−	19.6607i	−0.607612	−	1.05241i	0.384021	−	0.923324i	$-0.374539\pi$
$350$		0			0
$351$	−16.9190	−	9.37515i	−0.903071	−	0.500408i
$352$	6.04662	+	10.4731i	0.322286	+	0.558216i
$353$	27.2644			1.45114			0.725568	−	0.688150i	$-0.241577\pi$
$353$	27.2644			1.45114			0.725568	+	0.688150i	$0.241577\pi$
$354$	−2.74802			−0.146056
$355$	31.5510			1.67455
$356$	14.7751			0.783077
$357$		0			0
$358$	−1.69502	+	2.93585i	−0.0895844	+	0.155165i
$359$	7.21309	+	12.4934i	0.380692	+	0.659378i	0.991161	−	0.132662i	$-0.0423524\pi$
$359$	7.21309	+	12.4934i	0.380692	+	0.659378i	−0.610469	+	0.792040i	$0.709019\pi$
$360$	2.28466	+	3.95715i	0.120412	+	0.208560i
$361$	37.1791			1.95679
$362$	−1.99965	+	3.46350i	−0.105099	+	0.182037i
$363$	5.22461			0.274221
$364$		0			0
$365$	−1.96894			−0.103059
$366$	−1.44737	+	2.50693i	−0.0756555	+	0.131039i
$367$	11.3917			0.594643			0.297322	−	0.954777i	$-0.403907\pi$
$367$	11.3917			0.594643			0.297322	+	0.954777i	$0.403907\pi$
$368$	14.2152	+	24.6214i	0.741018	+	1.28348i
$369$	2.06397	+	3.57489i	0.107446	+	0.186102i
$370$	2.32065	−	4.01948i	0.120645	−	0.208963i
$371$		0			0
$372$	−5.62943			−0.291872
$373$	−30.9629			−1.60320			−0.801599	−	0.597862i	$-0.796017\pi$
$373$	−30.9629			−1.60320			−0.801599	+	0.597862i	$0.796017\pi$
$374$	0.830653			0.0429521
$375$	−10.0651			−0.519760
$376$	0.693313	+	1.20085i	0.0357549	+	0.0619293i
$377$	−0.149219	−	8.47796i	−0.00768518	−	0.436637i
$378$		0			0
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	0.697450	−	0.716634i	$-0.254318\pi$
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	−0.969348	+	0.245692i	$0.920985\pi$
$380$	18.5109	−	32.0617i	0.949587	−	1.64473i
$381$	−1.02188	−	1.76994i	−0.0523523	−	0.0906768i
$382$	−1.89438	+	3.28116i	−0.0969249	+	0.167879i
$383$	−30.7517			−1.57134			−0.785668	−	0.618648i	$-0.787681\pi$
$383$	−30.7517			−1.57134			−0.785668	+	0.618648i	$0.787681\pi$
$384$	−4.47231	+	7.74627i	−0.228227	+	0.395300i
$385$		0			0
$386$	0.522112	−	0.904324i	0.0265748	−	0.0460289i
$387$	−1.90476	+	3.29915i	−0.0968246	+	0.167705i
$388$	−4.57351			−0.232185
$389$	8.18978	−	14.1851i	0.415239	−	0.719214i	−0.580215	−	0.814463i	$-0.697031\pi$
$389$	8.18978	−	14.1851i	0.415239	−	0.719214i	0.995453	+	0.0952492i	$0.0303648\pi$
$390$	−2.47600	−	1.37200i	−0.125377	−	0.0694738i
$391$	6.24561			0.315854
$392$		0			0
$393$	−3.65243	−	6.32620i	−0.184241	−	0.319114i
$394$	3.13945			0.158163
$395$	−7.93227	+	13.7391i	−0.399116	+	0.691289i
$396$	−6.44246	−	11.1587i	−0.323746	−	0.560744i
$397$	15.8827			0.797127			0.398564	−	0.917141i	$-0.369509\pi$
$397$	15.8827			0.797127			0.398564	+	0.917141i	$0.369509\pi$
$398$	0.937591			0.0469972
$399$		0			0
$400$	−2.79221	−	4.83624i	−0.139610	−	0.241812i
$401$	−3.31787	+	5.74671i	−0.165686	+	0.286977i	−0.936899	−	0.349601i	$-0.886317\pi$
$401$	−3.31787	+	5.74671i	−0.165686	+	0.286977i	0.771212	+	0.636578i	$0.219651\pi$
$402$	−0.207259	+	0.358984i	−0.0103372	+	0.0179045i
$403$	−7.89373	+	4.74460i	−0.393215	+	0.236345i
$404$	0.768670	+	1.33137i	0.0382427	+	0.0662384i
$405$	1.34667	+	2.33250i	0.0669164	+	0.115903i
$406$		0			0
$407$	−13.3319	+	23.0915i	−0.660836	+	1.14460i
$408$	0.472570	+	0.818515i	0.0233957	+	0.0405225i
$409$	2.93617	+	5.08560i	0.145184	+	0.251467i	0.929442	−	0.368969i	$-0.120289\pi$
$409$	2.93617	+	5.08560i	0.145184	+	0.251467i	−0.784257	+	0.620436i	$0.786956\pi$
$410$	0.837115	+	1.44992i	0.0413421	+	0.0716067i
$411$	−5.73593	−	9.93492i	−0.282933	−	0.490053i
$412$	−2.08831	+	3.61707i	−0.102884	+	0.178200i
$413$		0			0
$414$	1.80614	+	3.12832i	0.0887667	+	0.153749i
$415$	−1.37428	−	2.38032i	−0.0674607	−	0.116845i
$416$	0.194457	+	11.0482i	0.00953403	+	0.541680i
$417$	−3.16932	+	5.48942i	−0.155202	+	0.268818i
$418$	3.96508	−	6.86773i	0.193939	−	0.335911i
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	−0.954162	−	0.299290i	$-0.903250\pi$
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	0.217888	−	0.975974i	$-0.430083\pi$
$420$		0			0
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	−5.09576			−0.248058
$423$	−1.11481	−	1.93091i	−0.0542040	−	0.0938840i
$424$	−4.88672	+	8.46405i	−0.237320	+	0.411051i
$425$	−1.22679			−0.0595079
$426$	1.88726	+	3.26884i	0.0914382	+	0.158376i
$427$		0			0
$428$	22.2238			1.07423
$429$	14.2244	+	7.88199i	0.686759	+	0.380546i
$430$	−0.772544	+	1.33809i	−0.0372554	+	0.0645282i
$431$	−3.91587			−0.188621			−0.0943104	−	0.995543i	$-0.530065\pi$
$431$	−3.91587			−0.188621			−0.0943104	+	0.995543i	$0.530065\pi$
$432$	9.58632	−	16.6040i	0.461222	−	0.798860i
$433$	−20.3963	+	35.3274i	−0.980182	+	1.69772i	−0.318532	+	0.947912i	$0.603190\pi$
$433$	−20.3963	+	35.3274i	−0.980182	+	1.69772i	−0.661650	+	0.749813i	$0.730144\pi$
$434$		0			0
$435$	−3.44306	+	5.96355i	−0.165082	+	0.285930i
$436$	−15.5757			−0.745941
$437$	29.8131	−	51.6378i	1.42615	−	2.47017i
$438$	−0.117775	−	0.203992i	−0.00562750	−	0.00974711i
$439$	−12.7811	+	22.1376i	−0.610010	+	1.05657i	0.381228	+	0.924481i	$0.375501\pi$
$439$	−12.7811	+	22.1376i	−0.610010	+	1.05657i	−0.991238	+	0.132087i	$0.957832\pi$
$440$	−5.32336	−	9.22033i	−0.253781	−	0.439562i
$441$		0			0
$442$	0.663878	+	0.367867i	0.0315775	+	0.0174977i
$443$	13.7282	+	23.7779i	0.652247	+	1.12972i	0.982576	+	0.185859i	$0.0595067\pi$
$443$	13.7282	+	23.7779i	0.652247	+	1.12972i	−0.330330	+	0.943866i	$0.607160\pi$
$444$	−14.8917			−0.706730
$445$	−19.6307			−0.930584
$446$	−3.20844			−0.151924
$447$	21.1057			0.998267
$448$		0			0
$449$	7.40181	−	12.8203i	0.349313	−	0.605028i	−0.636815	−	0.771017i	$-0.719748\pi$
$449$	7.40181	−	12.8203i	0.349313	−	0.605028i	0.986128	+	0.165989i	$0.0530816\pi$
$450$	−0.354769	−	0.614477i	−0.0167240	−	0.0289667i
$451$	−4.80913	−	8.32966i	−0.226453	−	0.392229i
$452$	−15.5046			−0.729275
$453$	−0.918611	+	1.59108i	−0.0431601	+	0.0747555i
$454$	4.12489			0.193590
$455$		0			0
$456$	9.02315			0.422548
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	−0.858300	−	0.513147i	$-0.828479\pi$
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	0.873549	+	0.486736i	$0.161813\pi$
$458$	2.32241			0.108519
$459$	−2.10593	−	3.64758i	−0.0982965	−	0.170254i
$460$	−19.6467	−	34.0290i	−0.916031	−	1.58661i
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	−0.683057	−	0.730365i	$-0.739350\pi$
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	0.974043	+	0.226362i	$0.0726833\pi$
$462$		0			0
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	8.40466			0.390176
$465$	7.47946			0.346852
$466$	−5.42972			−0.251527
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	0.996924	+	0.0783762i	$0.0249735\pi$
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	−0.430586	+	0.902549i	$0.641693\pi$
$468$	−0.207187	−	11.7714i	−0.00957722	−	0.544134i
$469$		0			0
$470$	−0.452151	−	0.783149i	−0.0208562	−	0.0361240i
$471$	−0.940659	+	1.62927i	−0.0433433	+	0.0750727i
$472$	−4.72198	−	8.17871i	−0.217347	−	0.376456i
$473$	4.43818	−	7.68716i	0.204068	−	0.353456i
$474$	−1.89792			−0.0871742
$475$	−5.85601	+	10.1429i	−0.268692	+	0.465389i
$476$		0			0
$477$	7.85759	−	13.6097i	0.359774	−	0.623147i
$478$	2.21909	−	3.84357i	0.101499	−	0.175801i
$479$	−8.13850			−0.371858			−0.185929	−	0.982563i	$-0.559529\pi$
$479$	−8.13850			−0.371858			−0.185929	+	0.982563i	$0.559529\pi$
$480$	4.48686	−	7.77147i	0.204796	−	0.354718i
$481$	−20.8816	+	12.5511i	−0.952118	+	0.572279i
$482$	−4.39746			−0.200299
$483$		0			0
$484$	4.40662	+	7.63250i	0.200301	+	0.346932i
$485$	6.07653			0.275921
$486$	1.99653	−	3.45809i	0.0905645	−	0.156862i
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	0.809069	−	0.587714i	$-0.199972\pi$
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	−0.913509	+	0.406817i	$0.866638\pi$
$488$	−9.94821			−0.450334
$489$	−7.48464			−0.338467
$490$		0			0
$491$	−6.50947	−	11.2747i	−0.293768	−	0.508822i	0.680929	−	0.732349i	$-0.261576\pi$
$491$	−6.50947	−	11.2747i	−0.293768	−	0.508822i	−0.974698	+	0.223527i	$0.928243\pi$
$492$	2.68591	−	4.65213i	0.121090	−	0.209734i
$493$	0.923171	−	1.59898i	0.0415775	−	0.0720144i
$494$	6.21047	−	3.73286i	0.279422	−	0.167949i
$495$	8.55969	+	14.8258i	0.384729	+	0.666371i
$496$	−4.56443	−	7.90582i	−0.204949	−	0.354982i
$497$		0			0
$498$	0.164409	−	0.284764i	0.00736733	−	0.0127606i
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	0.959614	+	0.281319i	$0.0907717\pi$
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	−0.236178	+	0.971710i	$0.575895\pi$
$500$	−8.48928	−	14.7039i	−0.379652	−	0.657577i
$501$	5.45718	+	9.45211i	0.243809	+	0.422289i
$502$	2.73900	+	4.74408i	0.122247	+	0.211739i
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	0.255531	+	0.966801i	$0.417750\pi$
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	−0.965039	+	0.262105i	$0.915583\pi$
$504$		0			0
$505$	−1.02128	−	1.76891i	−0.0454465	−	0.0787156i
$506$	−4.20838	−	7.28912i	−0.187085	−	0.324041i
$507$	7.87780	+	12.5990i	0.349866	+	0.559539i
$508$	1.72377	−	2.98566i	0.0764801	−	0.132467i
$509$	1.12788	−	1.95354i	0.0499922	−	0.0865891i	−0.839946	−	0.542669i	$-0.817414\pi$
$509$	1.12788	−	1.95354i	0.0499922	−	0.0865891i	0.889939	+	0.456080i	$0.150747\pi$
$510$	−0.308191	−	0.533802i	−0.0136469	−	0.0236372i
$511$		0			0
$512$	−18.4807			−0.816739
$513$	−40.2102			−1.77533
$514$	−1.84710	−	3.19927i	−0.0814722	−	0.141114i
$515$	2.77461	−	4.80576i	0.122264	−	0.211767i
$516$	4.95746			0.218240
$517$	2.59756	+	4.49911i	0.114241	+	0.197870i
$518$		0			0
$519$	−12.7236			−0.558502
$520$	−0.171197	−	9.72665i	−0.00750749	−	0.426542i
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	−0.723600	−	0.690220i	$-0.757514\pi$
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	0.959548	+	0.281546i	$0.0908471\pi$
$522$	1.06787			0.0467393
$523$	3.70397	−	6.41546i	0.161963	−	0.280528i	−0.773610	−	0.633663i	$-0.781551\pi$
$523$	3.70397	−	6.41546i	0.161963	−	0.280528i	0.935573	+	0.353134i	$0.114884\pi$
$524$	6.16118	−	10.6715i	0.269152	−	0.466186i
$525$		0			0
$526$	3.47454	−	6.01809i	0.151497	−	0.262401i
$527$	−2.00543			−0.0873580
$528$	−8.05953	+	13.9595i	−0.350746	+	0.607510i
$529$	−20.1424	−	34.8877i	−0.875757	−	1.51686i
$530$	3.18692	−	5.51991i	0.138431	−	0.239770i
$531$	7.59270	+	13.1509i	0.329495	+	0.570702i
$532$		0			0
$533$	−0.154660	−	8.78707i	−0.00669906	−	0.380610i
$534$	−1.17424	−	2.03384i	−0.0508142	−	0.0880127i
$535$	−29.5274			−1.27658
$536$	−1.42455			−0.0615313
$537$	−14.4516			−0.623632
$538$	−8.06161			−0.347561
$539$		0			0
$540$	−13.2492	+	22.9482i	−0.570153	+	0.987534i
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	−0.968579	−	0.248708i	$-0.919994\pi$
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	0.268902	−	0.963168i	$-0.413339\pi$
$542$	−1.93728	−	3.35546i	−0.0832132	−	0.144129i
$543$	−17.0489			−0.731638
$544$	−1.20304	+	2.08373i	−0.0515799	+	0.0893391i
$545$	20.6944			0.886453
$546$		0			0
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	9.67577	−	16.7589i	0.413329	−	0.715906i
$549$	15.9962			0.682701
$550$	0.826627	+	1.43176i	0.0352475	+	0.0610504i
$551$	−8.81342	−	15.2653i	−0.375464	−	0.650323i
$552$	4.78840	−	8.29376i	0.203808	−	0.353006i
$553$		0			0
$554$	4.10915			0.174581
$555$	19.7857			0.839856
$556$	−10.6925			−0.453461
$557$	−29.7703			−1.26141			−0.630703	−	0.776024i	$-0.717233\pi$
$557$	−29.7703			−1.26141			−0.630703	+	0.776024i	$0.717233\pi$
$558$	−0.579941	−	1.00449i	−0.0245509	−	0.0425233i
$559$	6.95148	−	4.17825i	0.294016	−	0.176721i
$560$		0			0
$561$	1.77052	+	3.06664i	0.0747516	+	0.129474i
$562$	0.709566	−	1.22900i	0.0299312	−	0.0518424i
$563$	7.06629	+	12.2392i	0.297809	+	0.515819i	0.975634	−	0.219403i	$-0.0704110\pi$
$563$	7.06629	+	12.2392i	0.297809	+	0.515819i	−0.677826	+	0.735223i	$0.737078\pi$
$564$	−1.45074	+	2.51275i	−0.0610872	+	0.105806i
$565$	20.6000			0.866647
$566$	4.12705	−	7.14826i	0.173473	−	0.300464i
$567$		0			0
$568$	−6.48584	+	11.2338i	−0.272140	+	0.471360i
$569$	12.1270	−	21.0046i	0.508391	−	0.880558i	−0.491562	−	0.870842i	$-0.663574\pi$
$569$	12.1270	−	21.0046i	0.508391	−	0.880558i	0.999953	−	0.00971585i	$-0.00309270\pi$
$570$	−5.88454			−0.246476
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	−0.878390	−	0.477944i	$-0.841382\pi$
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	0.853107	+	0.521736i	$0.174715\pi$
$572$	0.482755	+	27.4279i	0.0201850	+	1.14682i
$573$	−16.1514			−0.674732
$574$		0			0
$575$	6.21533	+	10.7653i	0.259197	+	0.448943i
$576$	10.7131			0.446381
$577$	−7.30518	+	12.6529i	−0.304119	+	0.526749i	−0.977065	−	0.212943i	$-0.931695\pi$
$577$	−7.30518	+	12.6529i	−0.304119	+	0.526749i	0.672946	+	0.739692i	$0.265029\pi$
$578$	−2.19643	−	3.80433i	−0.0913595	−	0.158239i
$579$	4.45149			0.184998
$580$	−11.6160			−0.482328
$581$		0			0
$582$	0.363475	+	0.629558i	0.0150665	+	0.0260960i
$583$	−18.3085	+	31.7113i	−0.758262	+	1.31335i
$584$	0.404749	−	0.701046i	0.0167486	−	0.0290095i
$585$	0.275276	+	15.6399i	0.0113813	+	0.646632i
$586$	2.34841	+	4.06757i	0.0970120	+	0.168030i
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	0.997975	−	0.0636132i	$-0.0202624\pi$
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	−0.554078	+	0.832465i	$0.686929\pi$
$588$		0			0
$589$	−9.57284	+	16.5806i	−0.394442	+	0.683193i
$590$	3.07949	+	5.33383i	0.126780	+	0.219590i
$591$	6.69168	+	11.5903i	0.275259	+	0.476763i
$592$	−12.0744	−	20.9135i	−0.496256	−	0.859541i
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	0.837553	−	0.546356i	$-0.183986\pi$
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	−0.891935	+	0.452164i	$0.850652\pi$
$594$	−2.83801	+	4.91558i	−0.116445	+	0.201689i
$595$		0			0
$596$	17.8013	+	30.8328i	0.729171	+	1.26296i
$597$	1.99846	+	3.46143i	0.0817915	+	0.141667i
$598$	−0.135340	−	7.68939i	−0.00553445	−	0.314443i
$599$	20.1250	−	34.8576i	0.822287	−	1.42424i	−0.0816889	−	0.996658i	$-0.526031\pi$
$599$	20.1250	−	34.8576i	0.822287	−	1.42424i	0.903975	−	0.427584i	$-0.140635\pi$
$600$	−0.940558	+	1.62909i	−0.0383981	+	0.0665075i
$601$	19.1725	+	33.2077i	0.782061	+	1.35457i	0.930739	+	0.365683i	$0.119165\pi$
$601$	19.1725	+	33.2077i	0.782061	+	1.35457i	−0.148679	+	0.988886i	$0.547502\pi$
$602$		0			0
$603$	2.29060			0.0932806
$604$	−3.09916			−0.126103
$605$	−5.85480	−	10.1408i	−0.238031	−	0.412283i
$606$	0.122179	−	0.211620i	0.00496317	−	0.00859646i
$607$	−42.5547			−1.72724			−0.863620	−	0.504143i	$-0.831808\pi$
$607$	−42.5547			−1.72724			−0.863620	+	0.504143i	$0.831808\pi$
$608$	11.4853	+	19.8931i	0.465791	+	0.806773i
$609$		0			0
$610$	6.48782			0.262684
$611$	0.0835364	+	4.74616i	0.00337952	+	0.192009i
$612$	1.28180	−	2.22014i	0.0518136	−	0.0897438i
$613$	15.2652			0.616556			0.308278	−	0.951296i	$-0.400247\pi$
$613$	15.2652			0.616556			0.308278	+	0.951296i	$0.400247\pi$
$614$	1.15773	−	2.00524i	0.0467221	−	0.0809251i
$615$	−3.56859	+	6.18098i	−0.143899	+	0.249241i
$616$		0			0
$617$	−6.99061	+	12.1081i	−0.281431	+	0.487453i	−0.971737	−	0.236064i	$-0.924142\pi$
$617$	−6.99061	+	12.1081i	−0.281431	+	0.487453i	0.690306	+	0.723517i	$0.257476\pi$
$618$	0.663868			0.0267047
$619$	−4.25792	+	7.37494i	−0.171140	+	0.296424i	−0.938819	−	0.344411i	$-0.888079\pi$
$619$	−4.25792	+	7.37494i	−0.171140	+	0.296424i	0.767678	+	0.640835i	$0.221412\pi$
$620$	6.30845	+	10.9265i	0.253353	+	0.438821i
$621$	−21.3388	+	36.9598i	−0.856295	+	1.48315i
$622$	2.20166	+	3.81338i	0.0882784	+	0.152903i
$623$		0			0
$624$	−12.6236	+	7.58750i	−0.505347	+	0.303743i
$625$	15.1856	+	26.3023i	0.607425	+	1.05209i
$626$	2.69363			0.107659
$627$	33.8060			1.35008
$628$	−3.17354			−0.126638
$629$	−5.30504			−0.211526
$630$		0			0
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	0.222490	+	0.974935i	$0.428582\pi$
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	−0.955563	+	0.294786i	$0.904752\pi$
$632$	−3.26123	−	5.64861i	−0.129725	−	0.224690i
$633$	−10.8615	−	18.8127i	−0.431707	−	0.747739i
$634$	−2.72013			−0.108030
$635$	−2.29027	+	3.96686i	−0.0908865	+	0.157420i
$636$	−20.4507			−0.810922
$637$		0			0
$638$	−2.48818			−0.0985081
$639$	10.4289	−	18.0634i	0.412561	−	0.714576i
$640$	20.0470			0.792428
$641$	−12.9374	−	22.4082i	−0.510996	−	0.885070i	−0.999919	−	0.0127435i	$-0.995944\pi$
$641$	−12.9374	−	22.4082i	−0.510996	−	0.885070i	0.488923	−	0.872327i	$-0.337390\pi$
$642$	−1.76622	−	3.05918i	−0.0697071	−	0.120736i
$643$	20.2626	−	35.0958i	0.799078	−	1.38404i	−0.121139	−	0.992636i	$-0.538655\pi$
$643$	20.2626	−	35.0958i	0.799078	−	1.38404i	0.920217	−	0.391408i	$-0.128012\pi$
$644$		0			0
$645$	−6.58666			−0.259350
$646$	1.57779			0.0620774
$647$	−1.78400			−0.0701364			−0.0350682	−	0.999385i	$-0.511165\pi$
$647$	−1.78400			−0.0701364			−0.0350682	+	0.999385i	$0.511165\pi$
$648$	−1.10732			−0.0434997
$649$	−17.6913	−	30.6423i	−0.694445	−	1.20281i
$650$	0.0265840	+	1.51038i	0.00104271	+	0.0592420i
$651$		0			0
$652$	−6.31281	−	10.9341i	−0.247229	−	0.428213i
$653$	−6.20210	+	10.7424i	−0.242707	+	0.420381i	−0.961484	−	0.274860i	$-0.911369\pi$
$653$	−6.20210	+	10.7424i	−0.242707	+	0.420381i	0.718778	+	0.695240i	$0.244702\pi$
$654$	1.23787	+	2.14405i	0.0484044	+	0.0838389i
$655$	−8.18597	+	14.1785i	−0.319852	+	0.554000i
$656$	8.71109			0.340111
$657$	−0.650815	+	1.12725i	−0.0253907	+	0.0439780i
$658$		0			0
$659$	0.564336	−	0.977458i	0.0219834	−	0.0380764i	−0.854824	−	0.518917i	$-0.826335\pi$
$659$	0.564336	−	0.977458i	0.0219834	−	0.0380764i	0.876808	+	0.480841i	$0.159669\pi$
$660$	11.1390	−	19.2933i	0.433585	−	0.750991i
$661$	28.9254			1.12507			0.562534	−	0.826774i	$-0.309826\pi$
$661$	28.9254			1.12507			0.562534	+	0.826774i	$0.309826\pi$
$662$	0.310913	−	0.538517i	0.0120840	−	0.0209301i
$663$	0.0569393	+	3.23503i	0.00221134	+	0.125638i
$664$	1.13003			0.0438535
$665$		0			0
$666$	−1.53414	−	2.65721i	−0.0594467	−	0.102965i
$667$	−18.7084			−0.724393
$668$	−9.20556	+	15.9445i	−0.356174	+	0.616911i
$669$	−6.83874	−	11.8451i	−0.264401	−	0.457956i
$670$	0.929036			0.0358918
$671$	−37.2718			−1.43886
$672$		0			0
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	0.926297	−	0.376795i	$-0.122974\pi$
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	−0.789462	+	0.613799i	$0.789640\pi$
$674$	−2.14498	+	3.71521i	−0.0826214	+	0.143104i
$675$	4.19145	−	7.25980i	0.161329	−	0.279430i
$676$	−11.7610	+	22.1349i	−0.452348	+	0.851341i
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.699752	−	0.714386i	$-0.746706\pi$
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.268800	−	0.963196i	$-0.586627\pi$
$678$	1.23221	+	2.13426i	0.0473229	+	0.0819657i
$679$		0			0
$680$	1.05914	−	1.83449i	0.0406162	−	0.0703493i
$681$	8.79213	+	15.2284i	0.336915	+	0.583554i
$682$	1.35129	+	2.34050i	0.0517435	+	0.0896224i
$683$	−13.7641	−	23.8401i	−0.526669	−	0.912217i	−0.999517	−	0.0310735i	$-0.990107\pi$
$683$	−13.7641	−	23.8401i	−0.526669	−	0.912217i	0.472848	−	0.881144i	$-0.343226\pi$
$684$	−12.2372	−	21.1954i	−0.467901	−	0.810428i
$685$	−12.8556	+	22.2665i	−0.491186	+	0.850760i
$686$		0			0
$687$	4.95019	+	8.57398i	0.188861	+	0.327118i
$688$	4.01958	+	6.96212i	0.153245	+	0.265428i
$689$	−28.6765	+	17.2362i	−1.09249	+	0.656649i
$690$	−3.12280	+	5.40885i	−0.118883	+	0.205912i
$691$	−12.1669	+	21.0737i	−0.462851	+	0.801682i	−0.999102	−	0.0423772i	$-0.986507\pi$
$691$	−12.1669	+	21.0737i	−0.462851	+	0.801682i	0.536251	+	0.844059i	$0.319840\pi$
$692$	−10.7315	−	18.5875i	−0.407950	−	0.706591i
$693$		0			0
$694$	6.11884			0.232268
$695$	14.2064			0.538879
$696$	−1.41556	−	2.45182i	−0.0536566	−	0.0929360i
$697$	0.956829	−	1.65728i	0.0362425	−	0.0627738i
$698$	−6.08704			−0.230398
$699$	−11.5733	−	20.0456i	−0.437744	−	0.758195i
$700$		0			0
$701$	−20.5588			−0.776495			−0.388248	−	0.921555i	$-0.626919\pi$
$701$	−20.5588			−0.776495			−0.388248	+	0.921555i	$0.626919\pi$
$702$	−4.44515	+	2.67180i	−0.167771	+	0.100840i
$703$	−25.3234	+	43.8613i	−0.955088	+	1.65426i
$704$	−24.9621			−0.940795
$705$	1.92751	−	3.33854i	0.0725940	−	0.125737i
$706$	3.65513	−	6.33088i	0.137563	−	0.238266i
$707$		0			0
$708$	9.88062	−	17.1137i	0.371336	−	0.643174i
$709$	40.9089			1.53637			0.768183	−	0.640230i	$-0.221161\pi$
$709$	40.9089			1.53637			0.768183	+	0.640230i	$0.221161\pi$
$710$	4.22981	−	7.32624i	0.158742	−	0.274949i
$711$	5.24388	+	9.08267i	0.196661	+	0.340627i
$712$	4.03543	−	6.98956i	0.151234	−	0.261945i
$713$	10.1602	+	17.5980i	0.380503	+	0.659051i
$714$		0			0
$715$	−0.641405	−	36.4418i	−0.0239872	−	1.36284i
$716$	−12.1890	−	21.1119i	−0.455524	−	0.788990i
$717$	18.9198			0.706572
$718$	3.86802			0.144353
$719$	1.19947			0.0447326			0.0223663	−	0.999750i	$-0.492880\pi$
$719$	1.19947			0.0447326			0.0223663	+	0.999750i	$0.492880\pi$
$720$	−15.5047			−0.577826
$721$		0			0
$722$	4.98433	−	8.63311i	0.185497	−	0.321291i
$723$	−9.37311	−	16.2347i	−0.348590	−	0.603775i
$724$	−14.3796	−	24.9063i	−0.534415	−	0.925634i
$725$	3.67478			0.136478
$726$	0.700425	−	1.21317i	0.0259952	−	0.0450250i
$727$	2.06230			0.0764865			0.0382433	−	0.999268i	$-0.487824\pi$
$727$	2.06230			0.0764865			0.0382433	+	0.999268i	$0.487824\pi$
$728$		0			0
$729$	20.1764			0.747273
$730$	−0.263961	+	0.457194i	−0.00976964	+	0.0169215i
$731$	1.76605			0.0653197
$732$	−10.4082	−	18.0275i	−0.384697	−	0.666315i
$733$	15.0310	+	26.0345i	0.555184	+	0.961606i	0.997889	+	0.0649392i	$0.0206853\pi$
$733$	15.0310	+	26.0345i	0.555184	+	0.961606i	−0.442706	+	0.896667i	$0.645981\pi$
$734$	1.52720	−	2.64520i	0.0563702	−	0.0976360i
$735$		0			0
$736$	24.3801			0.898662
$737$	−5.33721			−0.196599
$738$	1.10680			0.0407420
$739$	44.2548			1.62794			0.813969	−	0.580908i	$-0.197303\pi$
$739$	44.2548			1.62794			0.813969	+	0.580908i	$0.197303\pi$
$740$	16.6880	+	28.9044i	0.613461	+	1.06255i
$741$	27.0186	+	14.9715i	0.992553	+	0.549992i
$742$		0			0
$743$	4.31326	+	7.47078i	0.158238	+	0.274076i	0.934233	−	0.356662i	$-0.116085\pi$
$743$	4.31326	+	7.47078i	0.158238	+	0.274076i	−0.775995	+	0.630739i	$0.782752\pi$
$744$	−1.53753	+	2.66308i	−0.0563686	+	0.0976334i
$745$	−23.6515	−	40.9656i	−0.866524	−	1.50086i
$746$	−4.15097	+	7.18969i	−0.151978	+	0.263233i
$747$	−1.81702			−0.0664814
$748$	−2.98665	+	5.17302i	−0.109203	+	0.189144i
$749$		0			0
$750$	−1.34936	+	2.33715i	−0.0492715	+	0.0853408i
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	−0.913493	−	0.406853i	$-0.866626\pi$
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	0.809092	+	0.587682i	$0.199959\pi$
$752$	−4.70512			−0.171578
$753$	−11.6763	+	20.2239i	−0.425506	+	0.736998i
$754$	−1.98862	−	1.10193i	−0.0724211	−	0.0401299i
$755$	4.11765			0.149857
$756$		0			0
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	0.987348	+	0.158571i	$0.0506887\pi$
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	−0.356347	+	0.934354i	$0.615978\pi$
$758$	−2.83853			−0.103100
$759$	17.9402	−	31.0733i	0.651187	−	1.12789i
$760$	−10.1115	−	17.5137i	−0.366783	−	0.635287i
$761$	53.1735			1.92754			0.963768	−	0.266741i	$-0.0859467\pi$
$761$	53.1735			1.92754			0.963768	+	0.266741i	$0.0859467\pi$
$762$	−0.547981			−0.0198513
$763$		0			0
$764$	−13.6226	−	23.5951i	−0.492849	−	0.853640i
$765$	−1.70304	+	2.94976i	−0.0615736	+	0.106649i
$766$	−4.12265	+	7.14063i	−0.148957	+	0.258002i
$767$	−0.568946	−	32.3249i	−0.0205434	−	1.16719i
$768$	−6.03145	−	10.4468i	−0.217641	−	0.376966i
$769$	2.45578	+	4.25354i	0.0885578	+	0.153387i	0.906902	−	0.421342i	$-0.138441\pi$
$769$	2.45578	+	4.25354i	0.0885578	+	0.153387i	−0.818344	+	0.574729i	$0.805108\pi$
$770$		0			0
$771$	7.87414	−	13.6384i	0.283580	−	0.491175i
$772$	3.75455	+	6.50306i	0.135129	+	0.234050i
$773$	−11.4903	−	19.9018i	−0.413279	−	0.715819i	0.581967	−	0.813212i	$-0.302283\pi$
$773$	−11.4903	−	19.9018i	−0.413279	−	0.715819i	−0.995246	+	0.0973926i	$0.968950\pi$
$774$	0.510715	+	0.884585i	0.0183573	+	0.0317957i
$775$	−1.99571	−	3.45667i	−0.0716881	−	0.124167i
$776$	−1.24913	+	2.16356i	−0.0448413	+	0.0776674i
$777$		0			0
$778$	−2.19589	−	3.80339i	−0.0787264	−	0.136358i
$779$	−9.13476	−	15.8219i	−0.327287	−	0.566877i
$780$	17.4469	−	10.4866i	0.624699	−	0.375481i
$781$	−24.2998	+	42.0885i	−0.869515	+	1.50604i
$782$	0.837302	−	1.45025i	0.0299419	−	0.0518608i
$783$	6.30821	+	10.9261i	0.225437	+	0.390469i
$784$		0			0
$785$	4.21648			0.150493
$786$	−1.95862			−0.0698616
$787$	−1.59387	−	2.76067i	−0.0568154	−	0.0984071i	0.836219	−	0.548396i	$-0.184761\pi$
$787$	−1.59387	−	2.76067i	−0.0568154	−	0.0984071i	−0.893034	+	0.449989i	$0.851428\pi$
$788$	−11.2880	+	19.5514i	−0.402119	+	0.696490i
$789$	29.6237			1.05463
$790$	2.12684	+	3.68380i	0.0756696	+	0.131064i
$791$		0			0
$792$	−7.03836			−0.250097
$793$	−29.7886	−	16.5064i	−1.05782	−	0.586159i
$794$	2.12927	−	3.68800i	0.0755650	−	0.130882i
$795$	27.1715			0.963674
$796$	−3.37114	+	5.83899i	−0.119487	+	0.206958i
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.266355	−	0.963875i	$-0.414180\pi$
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.701562	−	0.712608i	$-0.252486\pi$
$798$		0			0
$799$	−0.516813	+	0.895146i	−0.0182835	+	0.0316680i
$800$	−4.78884			−0.169311
$801$	−6.48875	+	11.2388i	−0.229269	+	0.397105i
$802$	0.889604	+	1.54084i	0.0314130	+	0.0544089i
$803$	1.51643	−	2.62653i	0.0535136	−	0.0926883i
$804$	−1.49042	−	2.58148i	−0.0525630	−	0.0910418i
$805$		0			0
$806$	0.0434569	+	2.46902i	0.00153070	+	0.0869677i
$807$	−17.1832	−	29.7622i	−0.604877	−	1.04768i
$808$	0.839768			0.0295429
$809$	−20.2995			−0.713694			−0.356847	−	0.934163i	$-0.616148\pi$
$809$	−20.2995			−0.713694			−0.356847	+	0.934163i	$0.616148\pi$
$810$	0.722151			0.0253738
$811$	−2.43587			−0.0855350			−0.0427675	−	0.999085i	$-0.513617\pi$
$811$	−2.43587			−0.0855350			−0.0427675	+	0.999085i	$0.513617\pi$
$812$		0			0
$813$	8.25855	−	14.3042i	0.289640	−	0.501671i
$814$	3.57461	+	6.19141i	0.125290	+	0.217009i
$815$	8.38742	+	14.5274i	0.293799	+	0.508874i
$816$	−3.20706			−0.112270
$817$	8.43015	−	14.6015i	0.294934	−	0.510840i
$818$	1.57452			0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	−22.6762	+	39.2763i	−0.791405	+	1.37075i	0.133692	+	0.991023i	$0.457317\pi$
$821$	−22.6762	+	39.2763i	−0.791405	+	1.37075i	−0.925097	+	0.379731i	$0.876017\pi$
$822$	−3.07589			−0.107284
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	0.889054	−	0.457802i	$-0.151363\pi$
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	−0.840995	+	0.541042i	$0.818030\pi$
$824$	1.14074	+	1.97581i	0.0397394	+	0.0688307i
$825$	−3.52388	+	6.10354i	−0.122686	+	0.212498i
$826$		0			0
$827$	−8.64504			−0.300618			−0.150309	−	0.988639i	$-0.548027\pi$
$827$	−8.64504			−0.300618			−0.150309	+	0.988639i	$0.548027\pi$
$828$	−25.9761			−0.902733
$829$	29.5741			1.02715			0.513576	−	0.858044i	$-0.328320\pi$
$829$	29.5741			1.02715			0.513576	+	0.858044i	$0.328320\pi$
$830$	−0.736958			−0.0255802
$831$	8.75858	+	15.1703i	0.303832	+	0.526252i
$832$	−19.9503	−	11.0548i	−0.691653	−	0.383258i
$833$		0			0
$834$	0.849774	+	1.47185i	0.0294253	+	0.0509660i
$835$	12.2308	−	21.1844i	0.423266	−	0.733117i
$836$	28.5132	+	49.3863i	0.986150	+	1.70806i
$837$	6.85177	−	11.8676i	0.236832	−	0.410204i
$838$	−8.08191			−0.279185
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	−0.561545	−	0.827446i	$-0.689793\pi$
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	0.997362	+	0.0725895i	$0.0231263\pi$
$840$		0			0
$841$	11.7347	−	20.3251i	0.404644	−	0.700865i
$842$	5.37028	−	9.30159i	0.185072	−	0.320554i
$843$	6.04971			0.208363
$844$	18.3220	−	31.7346i	0.630669	−	1.09235i
$845$	15.6262	−	29.4092i	0.537556	−	1.01171i
$846$	−0.597818			−0.0205534
$847$		0			0
$848$	−16.5817	−	28.7204i	−0.569418	−	0.986261i
$849$	35.1870			1.20761
$850$	−0.164466	+	0.284864i	−0.00564115	+	0.00977076i
$851$	26.8772	+	46.5526i	0.921338	+	1.59580i
$852$	−27.1429			−0.929901
$853$	35.1368			1.20306			0.601531	−	0.798850i	$-0.294558\pi$
$853$	35.1368			1.20306			0.601531	+	0.798850i	$0.294558\pi$
$854$		0			0
$855$	16.2588	+	28.1610i	0.556039	+	0.963087i
$856$	6.06986	−	10.5133i	0.207463	−	0.359337i
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	−0.877264	−	0.480008i	$-0.840634\pi$
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	0.854331	+	0.519729i	$0.173967\pi$
$858$	3.73718	−	2.24626i	0.127585	−	0.0766862i
$859$	2.38386	+	4.12897i	0.0813363	+	0.140879i	0.903824	−	0.427904i	$-0.140748\pi$
$859$	2.38386	+	4.12897i	0.0813363	+	0.140879i	−0.822488	+	0.568783i	$0.807415\pi$
$860$	−5.55542	−	9.62228i	−0.189438	−	0.328117i
$861$		0			0
$862$	−0.524972	+	0.909278i	−0.0178806	+	0.0309701i
$863$	13.3052	+	23.0453i	0.452915	+	0.784472i	0.998566	−	0.0535407i	$-0.0170507\pi$
$863$	13.3052	+	23.0453i	0.452915	+	0.784472i	−0.545650	+	0.838013i	$0.683717\pi$
$864$	−8.22062	−	14.2385i	−0.279671	−	0.484405i
$865$	14.2583	+	24.6960i	0.484795	+	0.839690i
$866$	5.46875	+	9.47216i	0.185836	+	0.321877i
$867$	9.36331	−	16.2177i	0.317995	−	0.550783i
$868$		0			0
$869$	−12.2185	−	21.1630i	−0.414484	−	0.717907i
$870$	0.923171	+	1.59898i	0.0312984	+	0.0542105i
$871$	−4.26563	−	2.36366i	−0.144535	−	0.0800897i
$872$	−4.25410	+	7.36831i	−0.144062	+	0.249523i
$873$	2.00854	−	3.47890i	0.0679788	−	0.117743i
$874$	−7.99364	−	13.8454i	−0.270389	−	0.468328i
$875$		0			0
$876$	1.69385			0.0572300
$877$	8.03696			0.271389			0.135695	−	0.990751i	$-0.456673\pi$
$877$	8.03696			0.271389			0.135695	+	0.990751i	$0.456673\pi$
$878$	3.42694	+	5.93564i	0.115654	+	0.200318i
$879$	−10.0112	+	17.3399i	−0.337670	+	0.584861i
$880$	36.1266			1.21783
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.797971	−	0.602695i	$-0.794093\pi$
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.122964	−	0.992411i	$-0.539240\pi$
$882$		0			0
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	−4.67795	+	2.81172i	−0.157337	+	0.0945685i
$885$	−13.1277	+	22.7379i	−0.441284	+	0.764327i
$886$	7.36176			0.247323
$887$	−5.17784	+	8.96829i	−0.173855	+	0.301126i	−0.939764	−	0.341823i	$-0.888956\pi$
$887$	−5.17784	+	8.96829i	−0.173855	+	0.301126i	0.765909	+	0.642948i	$0.222289\pi$
$888$	−4.06729	+	7.04475i	−0.136489	+	0.236406i
$889$		0			0
$890$	−2.63174	+	4.55831i	−0.0882162	+	0.152795i
$891$	−4.14868			−0.138986
$892$	11.5361	−	19.9811i	0.386256	−	0.669016i
$893$	4.93396	+	8.54587i	0.165109	+	0.285977i
$894$	2.82949	−	4.90082i	0.0946323	−	0.163908i
$895$	16.1947	+	28.0501i	0.541330	+	0.937611i
$896$		0			0
$897$	28.0995	−	16.8895i	0.938215	−	0.563923i
$898$	−1.98461	−	3.43745i	−0.0662274	−	0.114709i
$899$	6.00718			0.200351
$900$	5.10234			0.170078
$901$	−7.28536			−0.242711
$902$	−2.57890			−0.0858680
$903$		0			0
$904$	−4.23468	+	7.33467i	−0.140843	+	0.243948i
$905$	19.1053	+	33.0914i	0.635082	+	1.09999i
$906$	0.246303	+	0.426609i	0.00818287	+	0.0141731i
$907$	18.4804			0.613631			0.306815	−	0.951769i	$-0.400737\pi$
$907$	18.4804			0.613631			0.306815	+	0.951769i	$0.400737\pi$
$908$	−14.8312	+	25.6884i	−0.492190	+	0.852498i
$909$	−1.35030			−0.0447867
$910$		0			0
$911$	−26.6282			−0.882230			−0.441115	−	0.897451i	$-0.645417\pi$
$911$	−26.6282			−0.882230			−0.441115	+	0.897451i	$0.645417\pi$
$912$	−15.3088	+	26.5155i	−0.506924	+	0.878017i
$913$	4.23374			0.140116
$914$	−0.0874022	−	0.151385i	−0.00289101	−	0.00500737i
$915$	13.8287	+	23.9520i	0.457162	+	0.791828i
$916$	−8.35033	+	14.4632i	−0.275903	+	0.477877i
$917$		0			0
$918$	−1.12931			−0.0372727
$919$	−11.1493			−0.367783			−0.183891	−	0.982947i	$-0.558869\pi$
$919$	−11.1493			−0.367783			−0.183891	+	0.982947i	$0.558869\pi$
$920$	−21.4639			−0.707644
$921$	9.87072			0.325251
$922$	−1.67518	−	2.90149i	−0.0551690	−	0.0955555i
$923$	−38.0605	+	22.8766i	−1.25278	+	0.752993i
$924$		0			0
$925$	−5.27933	−	9.14406i	−0.173583	−	0.300655i
$926$	−0.0414927	+	0.0718675i	−0.00136354	+	0.00236171i
$927$	−1.83424	−	3.17700i	−0.0602445	−	0.104347i
$928$	3.60365	−	6.24170i	0.118296	−	0.204894i
$929$	−7.74510			−0.254108			−0.127054	−	0.991896i	$-0.540552\pi$
$929$	−7.74510			−0.254108			−0.127054	+	0.991896i	$0.540552\pi$
$930$	1.00272	−	1.73676i	0.0328804	−	0.0569505i
$931$		0			0
$932$	19.5227	−	33.8144i	0.639489	−	1.10763i
$933$	−9.38559	+	16.2563i	−0.307270	+	0.532208i
$934$	6.56299			0.214748
$935$	3.96817	−	6.87306i	0.129773	−	0.224773i
$936$	−5.62523	−	3.11704i	−0.183866	−	0.101884i
$937$	−36.4239			−1.18992			−0.594959	−	0.803756i	$-0.702832\pi$
$937$	−36.4239			−1.18992			−0.594959	+	0.803756i	$0.702832\pi$
$938$		0			0
$939$	5.74143	+	9.94445i	0.187364	+	0.324525i
$940$	6.50291			0.212101
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	−0.981015	−	0.193933i	$-0.937876\pi$
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	0.658458	+	0.752617i	$0.271209\pi$
$942$	0.252214	+	0.436848i	0.00821759	+	0.0142333i
$943$	−19.3905			−0.631442
$944$	32.0454			1.04299
$945$		0			0
$946$	−1.18999	−	2.06112i	−0.0386899	−	0.0670129i
$947$	−4.97398	+	8.61519i	−0.161633	+	0.279956i	−0.935454	−	0.353448i	$-0.885009\pi$
$947$	−4.97398	+	8.61519i	−0.161633	+	0.279956i	0.773822	+	0.633403i	$0.218343\pi$
$948$	6.82403	−	11.8196i	0.221634	−	0.383882i
$949$	2.37517	−	1.42762i	0.0771012	−	0.0463424i
$950$	1.57014	+	2.71957i	0.0509422	+	0.0882345i
$951$	−5.79790	−	10.0423i	−0.188010	−	0.325643i
$952$		0			0
$953$	−0.0105567	+	0.0182847i	−0.000341965	+	0.000592300i	−0.866196	−	0.499704i	$-0.833442\pi$
$953$	−0.0105567	+	0.0182847i	−0.000341965	+	0.000592300i	0.865854	+	0.500296i	$0.166776\pi$
$954$	−2.10682	−	3.64912i	−0.0682108	−	0.118144i
$955$	18.0995	+	31.3493i	0.585686	+	1.01444i
$956$	15.9576	+	27.6394i	0.516106	+	0.893922i
$957$	−5.30352	−	9.18596i	−0.171438	−	0.296940i
$958$	−1.09107	+	1.88979i	−0.0352508	+	0.0610562i
$959$		0			0
$960$	9.26150	+	16.0414i	0.298914	+	0.517733i
$961$	12.2376	+	21.1962i	0.394761	+	0.683747i
$962$	0.114958	+	6.53140i	0.00370640	+	0.210581i
$963$	−9.76001	+	16.9048i	−0.314512	+	0.544751i
$964$	15.8112	−	27.3858i	0.509245	−	0.882039i
$965$	−4.98842	−	8.64020i	−0.160583	−	0.278138i
$966$		0			0
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	4.81422			0.154735
$969$	3.36304	+	5.82495i	0.108036	+	0.187124i
$970$	0.814635	−	1.41099i	0.0261563	−	0.0453041i
$971$	3.61774			0.116099			0.0580493	−	0.998314i	$-0.481512\pi$
$971$	3.61774			0.116099			0.0580493	+	0.998314i	$0.481512\pi$
$972$	14.3572	+	24.8674i	0.460508	+	0.797622i
$973$		0			0
$974$	−1.23595			−0.0396024
$975$	−5.51942	+	3.31750i	−0.176763	+	0.106245i
$976$	16.8782	−	29.2339i	0.540258	−	0.935755i
$977$	2.16169			0.0691586			0.0345793	−	0.999402i	$-0.488991\pi$
$977$	2.16169			0.0691586			0.0345793	+	0.999402i	$0.488991\pi$
$978$	−1.00341	+	1.73796i	−0.0320855	+	0.0555737i
$979$	15.1191	−	26.1870i	0.483208	−	0.836941i
$980$		0			0
$981$	6.84036	−	11.8479i	0.218396	−	0.378273i
$982$	−3.49071			−0.111393
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	−0.999741	−	0.0227535i	$-0.992757\pi$
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	0.519576	+	0.854424i	$0.326090\pi$
$984$	−1.46717	−	2.54121i	−0.0467717	−	0.0810109i
$985$	14.9977	−	25.9767i	0.477865	−	0.827687i
$986$	−0.247525	−	0.428727i	−0.00788281	−	0.0136534i
$987$		0			0
$988$	0.916973	+	52.0983i	0.0291728	+	1.65747i
$989$	−8.94742	−	15.4974i	−0.284511	−	0.492788i
$990$	4.59014			0.145884
$991$	−27.1460			−0.862323			−0.431161	−	0.902275i	$-0.641896\pi$
$991$	−27.1460			−0.862323			−0.431161	+	0.902275i	$0.641896\pi$
$992$	−7.82832			−0.248549
$993$	2.65082			0.0841213
$994$		0			0
$995$	4.47902	−	7.75790i	0.141995	−	0.245942i
$996$	1.18227	+	2.04776i	0.0374618	+	0.0648858i
$997$	25.4005	+	43.9949i	0.804441	+	1.39333i	0.916668	+	0.399650i	$0.130868\pi$
$997$	25.4005	+	43.9949i	0.804441	+	1.39333i	−0.112227	+	0.993683i	$0.535798\pi$
$998$	8.66599			0.274317
$999$	18.1252	−	31.3938i	0.573456	−	0.993256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.l.263.3		12
7.2	even	3		637.2.h.l.471.4		12
7.3	odd	6		637.2.f.k.393.3		12
7.4	even	3		637.2.f.j.393.3		12
7.5	odd	6		91.2.h.b.16.4	yes	12
7.6	odd	2		91.2.g.b.81.3	yes	12
13.9	even	3		637.2.h.l.165.4		12
21.5	even	6		819.2.s.d.289.3		12
21.20	even	2		819.2.n.d.172.4		12
91.3	odd	6		8281.2.a.bz.1.4		6
91.9	even	3	inner	637.2.g.l.373.3		12
91.10	odd	6		8281.2.a.ce.1.3		6
91.48	odd	6		91.2.h.b.74.4	yes	12
91.55	odd	6		1183.2.e.h.508.3		12
91.61	odd	6		91.2.g.b.9.3	✓	12
91.62	odd	6		1183.2.e.g.508.4		12
91.68	odd	6		1183.2.e.h.170.3		12
91.74	even	3		637.2.f.j.295.3		12
91.75	odd	6		1183.2.e.g.170.4		12
91.81	even	3		8281.2.a.ca.1.4		6
91.87	odd	6		637.2.f.k.295.3		12
91.88	even	6		8281.2.a.cf.1.3		6
273.152	even	6		819.2.n.d.100.4		12
273.230	even	6		819.2.s.d.802.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	91.61	odd	6
91.2.g.b.81.3	yes	12	7.6	odd	2
91.2.h.b.16.4	yes	12	7.5	odd	6
91.2.h.b.74.4	yes	12	91.48	odd	6
637.2.f.j.295.3		12	91.74	even	3
637.2.f.j.393.3		12	7.4	even	3
637.2.f.k.295.3		12	91.87	odd	6
637.2.f.k.393.3		12	7.3	odd	6
637.2.g.l.263.3		12	1.1	even	1	trivial
637.2.g.l.373.3		12	91.9	even	3	inner
637.2.h.l.165.4		12	13.9	even	3
637.2.h.l.471.4		12	7.2	even	3
819.2.n.d.100.4		12	273.152	even	6
819.2.n.d.172.4		12	21.20	even	2
819.2.s.d.289.3		12	21.5	even	6
819.2.s.d.802.3		12	273.230	even	6
1183.2.e.g.170.4		12	91.75	odd	6
1183.2.e.g.508.4		12	91.62	odd	6
1183.2.e.h.170.3		12	91.68	odd	6
1183.2.e.h.508.3		12	91.55	odd	6
8281.2.a.bz.1.4		6	91.3	odd	6
8281.2.a.ca.1.4		6	91.81	even	3
8281.2.a.ce.1.3		6	91.10	odd	6
8281.2.a.cf.1.3		6	91.88	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)

\(f(q)\)	\(=\)	\(q+(0.134063 - 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} +O(q^{10})\)	\(q+(0.134063 - 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} -0.686871 q^{10} +3.94600 q^{11} +(1.10192 + 1.90859i) q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} +(-0.227039 + 0.393243i) q^{18} +7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(3.97759 - 6.88938i) q^{23} +1.20385 q^{24} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} -0.785100 q^{30} +(-1.27718 + 2.21215i) q^{31} +(1.53234 + 2.65409i) q^{32} +4.51032 q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(3.60475 + 1.99746i) q^{39} +(-1.34905 - 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(3.80416 + 6.58900i) q^{44} +(2.16920 + 3.75717i) q^{45} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} +(0.448688 + 0.777151i) q^{51} +(0.122340 + 6.95082i) q^{52} +(-4.63977 + 8.03632i) q^{53} +(-0.719212 + 1.24571i) q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +(2.82286 - 4.88933i) q^{60} -9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(-0.162546 - 9.23511i) q^{65} +(0.604665 - 1.04731i) q^{66} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} -1.78367 q^{72} +(0.384295 - 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(-0.893026 + 1.54677i) q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} -1.05136 q^{81} -0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(-0.301568 - 0.522332i) q^{86} +(-1.34402 - 2.32792i) q^{87} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 + 2.52850i) q^{93} +0.353001 q^{94} +(-9.60052 - 16.6286i) q^{95} +(1.75148 + 3.03365i) q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 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

Varieties

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Database

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