LMFDB - Embedded newform 637.2.h.l.471.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Embedding invariants

Embedding label			471.5
Root			$-1.02197 - 1.77010i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.l.165.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +O(q^{10})$	\(q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) 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} +(-0.102021 + 0.176706i) q^{12} +(-2.86133 + 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} -4.66017 q^{16} +0.906303 q^{17} +(2.14596 + 3.71691i) q^{18} +(3.34514 + 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +3.59733 q^{23} +(0.602021 - 1.04273i) q^{24} +(1.79015 + 3.10063i) q^{25} +(-4.44847 + 3.41068i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 - 0.784881i) q^{30} +(-2.64390 - 4.57937i) q^{31} -2.32313 q^{32} +(-0.517662 - 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +4.99159 q^{37} +(5.20065 + 9.00778i) q^{38} +(-0.229570 - 1.74902i) q^{39} +(1.46615 - 2.53944i) q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +(-0.441269 + 0.764301i) q^{44} -3.28933 q^{45} +5.59272 q^{46} +(-1.59337 + 2.75979i) q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +(-0.221705 + 0.384004i) q^{51} +(-1.19332 + 0.914930i) q^{52} +(1.41239 + 2.44632i) q^{53} -4.38173 q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 - 11.4652i) q^{58} +10.2460 q^{59} +(-0.121560 - 0.210548i) q^{60} +(-4.13423 - 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-0.559090 - 4.25952i) q^{65} +(-0.804802 - 1.39396i) q^{66} +(1.87182 - 3.24208i) q^{67} +0.377975 q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 - 5.88368i) q^{72} +(-2.86522 - 4.96271i) q^{73} +7.76035 q^{74} -1.75167 q^{75} +(1.39510 + 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +(-3.03620 + 5.25885i) 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} +(-4.22310 + 7.31462i) q^{86} +4.16619 q^{87} +(2.60390 - 4.51008i) q^{88} +17.7511 q^{89} -5.11387 q^{90} +1.50027 q^{92} +2.58707 q^{93} +(-2.47719 + 4.29061i) q^{94} -7.97155 q^{95} +(0.568297 - 0.984319i) q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.55469			1.09933			0.549665	−	0.835385i	$-0.314755\pi$
$2$	1.55469			1.09933			0.549665	+	0.835385i	$0.314755\pi$
$3$	−0.244626	+	0.423704i	−0.141235	+	0.244626i	−0.927962	−	0.372675i	$-0.878441\pi$
$3$	−0.244626	+	0.423704i	−0.141235	+	0.244626i	0.786727	+	0.617301i	$0.211774\pi$
$4$	0.417051			0.208526
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	−0.967937	−	0.251192i	$-0.919177\pi$
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	0.701507	+	0.712662i	$0.252511\pi$
$6$	−0.380316	+	0.658727i	−0.155264	+	0.268924i
$7$		0			0
$7$		0			0
$8$	−2.46099			−0.870091
$9$	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	−0.980284	−	0.197595i	$-0.936687\pi$
$11$	−1.05807	+	1.83263i	−0.319020	+	0.552559i	0.661264	+	0.750153i	$0.270020\pi$
$12$	−0.102021	+	0.176706i	−0.0294511	+	0.0510107i
$13$	−2.86133	+	2.19381i	−0.793590	+	0.608453i
$13$	−2.86133	+	2.19381i	−0.793590	+	0.608453i
$14$		0			0
$15$	−0.291474	−	0.504848i	−0.0752584	−	0.130351i
$16$	−4.66017			−1.16504
$17$	0.906303			0.219811			0.109905	−	0.993942i	$-0.464945\pi$
$17$	0.906303			0.219811			0.109905	+	0.993942i	$0.464945\pi$
$18$	2.14596	+	3.71691i	0.505808	+	0.876084i
$19$	3.34514	+	5.79395i	0.767428	+	1.32922i	0.938953	+	0.344045i	$0.111797\pi$
$19$	3.34514	+	5.79395i	0.767428	+	1.32922i	−0.171525	+	0.985180i	$0.554870\pi$
$20$	−0.248461	+	0.430346i	−0.0555575	+	0.0962284i
$21$		0			0
$22$	−1.64497	+	2.84917i	−0.350708	+	0.607444i
$23$	3.59733			0.750095			0.375048	−	0.927006i	$-0.377626\pi$
$23$	3.59733			0.750095			0.375048	+	0.927006i	$0.377626\pi$
$24$	0.602021	−	1.04273i	0.122887	−	0.212847i
$25$	1.79015	+	3.10063i	0.358030	+	0.620126i
$26$	−4.44847	+	3.41068i	−0.872417	+	0.668890i
$27$	−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
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	0.524727	−	0.851271i	$-0.324168\pi$
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	−0.999585	+	0.0287913i	$0.990834\pi$
$32$	−2.32313			−0.410675
$33$	−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
$37$	4.99159			0.820612			0.410306	−	0.911948i	$-0.365422\pi$
$37$	4.99159			0.820612			0.410306	+	0.911948i	$0.365422\pi$
$38$	5.20065	+	9.00778i	0.843656	+	1.46126i
$39$	−0.229570	−	1.74902i	−0.0367606	−	0.280067i
$40$	1.46615	−	2.53944i	0.231818	−	0.401521i
$41$	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	$0.302620\pi$
$44$	−0.441269	+	0.764301i	−0.0665238	+	0.115223i
$45$	−3.28933			−0.490344
$46$	5.59272			0.824602
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	−0.958519	−	0.285030i	$-0.907997\pi$
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	0.726102	+	0.687587i	$0.241330\pi$
$48$	1.14000	−	1.97453i	0.164545	−	0.284999i
$49$		0			0
$50$	2.78312	+	4.82051i	0.393593	+	0.681723i
$51$	−0.221705	+	0.384004i	−0.0310449	+	0.0537714i
$52$	−1.19332	+	0.914930i	−0.165484	+	0.126878i
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	0.946574	−	0.322486i	$-0.104518\pi$
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	−0.752568	+	0.658514i	$0.771185\pi$
$54$	−4.38173			−0.596278
$55$	−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
$59$	10.2460			1.33391			0.666956	−	0.745097i	$-0.267597\pi$
$59$	10.2460			1.33391			0.666956	+	0.745097i	$0.267597\pi$
$60$	−0.121560	−	0.210548i	−0.0156933	−	0.0271816i
$61$	−4.13423	−	7.16069i	−0.529333	−	0.916832i	−0.999415	−	0.0342093i	$-0.989109\pi$
$61$	−4.13423	−	7.16069i	−0.529333	−	0.916832i	0.470081	−	0.882623i	$-0.344225\pi$
$62$	−4.11044	−	7.11949i	−0.522026	−	0.904176i
$63$		0			0
$64$	5.70861			0.713576
$65$	−0.559090	−	4.25952i	−0.0693465	−	0.528328i
$66$	−0.804802	−	1.39396i	−0.0990643	−	0.171584i
$67$	1.87182	−	3.24208i	0.228679	−	0.396083i	−0.728738	−	0.684793i	$-0.759893\pi$
$67$	1.87182	−	3.24208i	0.228679	−	0.396083i	0.957417	+	0.288709i	$0.0932261\pi$
$68$	0.377975			0.0458362
$69$	−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
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	0.648203	−	0.761468i	$-0.275521\pi$
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	−0.983552	+	0.180627i	$0.942187\pi$
$74$	7.76035			0.902123
$75$	−1.75167			−0.202265
$76$	1.39510	+	2.41638i	0.160028	+	0.277177i
$77$		0			0
$78$	−0.356910	−	2.71918i	−0.0404121	−	0.307886i
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	−0.984730	−	0.174089i	$-0.944302\pi$
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	0.643131	+	0.765756i	$0.277635\pi$
$80$	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
$86$	−4.22310	+	7.31462i	−0.455388	+	0.788755i
$87$	4.16619			0.446663
$88$	2.60390	−	4.51008i	0.277576	−	0.480776i
$89$	17.7511			1.88162			0.940808	−	0.338939i	$-0.110068\pi$
$89$	17.7511			1.88162			0.940808	+	0.338939i	$0.110068\pi$
$90$	−5.11387			−0.539049
$91$		0			0
$92$	1.50027			0.156414
$93$	2.58707			0.268266
$94$	−2.47719	+	4.29061i	−0.255502	+	0.442543i
$95$	−7.97155			−0.817863
$96$	0.568297	−	0.984319i	0.0580015	−	0.100462i
$97$	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	−0.987851	−	0.155405i	$-0.950332\pi$
$101$	−3.61133	+	6.25501i	−0.359341	+	0.622397i	0.628510	+	0.777802i	$0.283665\pi$
$102$	−0.344682	+	0.597007i	−0.0341286	+	0.0591125i
$103$	4.96322	−	8.59656i	0.489041	−	0.847044i	−0.510879	−	0.859652i	$-0.670680\pi$
$103$	4.96322	−	8.59656i	0.489041	−	0.847044i	0.999921	+	0.0126084i	$0.00401349\pi$
$104$	7.04170	−	5.39894i	0.690496	−	0.529409i
$105$		0			0
$106$	2.19582	+	3.80327i	0.213277	+	0.369406i
$107$	−2.20006			−0.212688			−0.106344	−	0.994329i	$-0.533915\pi$
$107$	−2.20006			−0.212688			−0.106344	+	0.994329i	$0.533915\pi$
$108$	−1.17542			−0.113105
$109$	−6.87291	−	11.9042i	−0.658305	−	1.14022i	−0.981054	−	0.193734i	$-0.937940\pi$
$109$	−6.87291	−	11.9042i	−0.658305	−	1.14022i	0.322749	−	0.946485i	$-0.395393\pi$
$110$	−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	$-0.106685\pi$
$114$	−5.08885			−0.476614
$115$	−2.14313	+	3.71201i	−0.199848	+	0.346147i
$116$	−1.77569	−	3.07558i	−0.164869	−	0.285561i
$117$	−9.19445	−	3.81266i	−0.850027	−	0.352480i
$118$	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
$122$	−6.42743	−	11.1326i	−0.581912	−	1.00790i
$123$	−0.751668			−0.0677756
$124$	−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	$0.588464\pi$
$128$	13.5213			1.19513
$129$	−1.32899	−	2.30187i	−0.117011	−	0.202668i
$130$	−0.869209	−	6.62222i	−0.0762347	−	0.580807i
$131$	−4.76884	+	8.25988i	−0.416656	+	0.721669i	−0.995601	−	0.0936976i	$-0.970131\pi$
$131$	−4.76884	+	8.25988i	−0.416656	+	0.721669i	0.578945	+	0.815367i	$0.303465\pi$
$132$	−0.215892	−	0.373935i	−0.0187910	−	0.0325469i
$133$		0			0
$134$	2.91009	−	5.04042i	0.251393	−	0.435426i
$135$	1.67908	−	2.90825i	0.144512	−	0.250302i
$136$	−2.23040			−0.191255
$137$	−2.76461			−0.236197			−0.118098	−	0.993002i	$-0.537680\pi$
$137$	−2.76461			−0.236197			−0.118098	+	0.993002i	$0.537680\pi$
$138$	−1.36812	+	2.36966i	−0.116462	+	0.201719i
$139$	−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
$142$	1.96684	−	3.40666i	0.165053	−	0.285881i
$143$	−0.992950	−	7.56496i	−0.0830346	−	0.632614i
$144$	−6.43251	−	11.1414i	−0.536043	−	0.928453i
$145$	10.1462			0.842600
$146$	−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	0.994189	+	0.107651i	$0.0343329\pi$
$149$	7.20581	+	12.4808i	0.590323	+	1.02247i	−0.403866	+	0.914818i	$0.632334\pi$
$150$	−2.72329			−0.222356
$151$	−7.62901	−	13.2138i	−0.620840	−	1.07533i	−0.989330	−	0.145695i	$-0.953458\pi$
$151$	−7.62901	−	13.2138i	−0.620840	−	1.07533i	0.368489	−	0.929632i	$-0.379875\pi$
$152$	−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
$156$	−0.0957425	−	0.729431i	−0.00766554	−	0.0584012i
$157$	−5.70745	−	9.88559i	−0.455504	−	0.788956i	0.543213	−	0.839595i	$-0.317208\pi$
$157$	−5.70745	−	9.88559i	−0.455504	−	0.788956i	−0.998717	+	0.0506387i	$0.983874\pi$
$158$	−4.72034	+	8.17587i	−0.375530	+	0.650437i
$159$	−1.38202			−0.109602
$160$	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	0.997119	+	0.0758514i	$0.0241675\pi$
$163$	7.20385	+	12.4774i	0.564249	+	0.977308i	−0.432870	+	0.901456i	$0.642499\pi$
$164$	0.320371	+	0.554899i	0.0250168	+	0.0433303i
$165$	1.23360			0.0960357
$166$	18.0824			1.40346
$167$	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
$170$	−0.839430	+	1.45394i	−0.0643813	+	0.111512i
$171$	−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	0.958303	−	0.285753i	$-0.0922436\pi$
$173$	3.04731	+	5.27809i	0.231682	+	0.401286i	−0.726621	+	0.687039i	$0.758910\pi$
$174$	6.47713			0.491030
$175$		0			0
$176$	4.93078	−	8.54037i	0.371672	−	0.643754i
$177$	−2.50643	+	4.34126i	−0.188395	+	0.326309i
$178$	27.5975			2.06852
$179$	−9.26488	+	16.0472i	−0.692490	+	1.19943i	0.278530	+	0.960428i	$0.410153\pi$
$179$	−9.26488	+	16.0472i	−0.692490	+	1.19943i	−0.971020	+	0.239000i	$0.923181\pi$
$180$	−1.37182			−0.102249
$181$	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
$184$	−8.85299			−0.652651
$185$	−2.97377	+	5.15071i	−0.218636	+	0.378688i
$186$	4.02208			0.294913
$187$	−0.958931	+	1.66092i	−0.0701240	+	0.121458i
$188$	−0.664516	+	1.15097i	−0.0484648	+	0.0839435i
$189$		0			0
$190$	−12.3933			−0.899102
$191$	−0.251851	−	0.436219i	−0.0182233	−	0.0315637i	0.856770	−	0.515699i	$-0.172468\pi$
$191$	−0.251851	−	0.436219i	−0.0182233	−	0.0315637i	−0.874993	+	0.484135i	$0.839134\pi$
$192$	−1.39647	+	2.41876i	−0.100782	+	0.174559i
$193$	1.85622	−	3.21507i	0.133614	−	0.231426i	−0.791453	−	0.611230i	$-0.790675\pi$
$193$	1.85622	−	3.21507i	0.133614	−	0.231426i	0.925067	+	0.379804i	$0.124009\pi$
$194$	4.82290	−	8.35351i	0.346264	−	0.599747i
$195$	1.94154	+	0.805100i	0.139037	+	0.0576544i
$196$		0			0
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	0.967616	−	0.252427i	$-0.0812288\pi$
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	−0.702416	+	0.711766i	$0.747895\pi$
$198$	−9.08230			−0.645451
$199$	−7.50556			−0.532055			−0.266028	−	0.963965i	$-0.585711\pi$
$199$	−7.50556			−0.532055			−0.266028	+	0.963965i	$0.585711\pi$
$200$	−4.40554	−	7.63062i	−0.311519	−	0.539566i
$201$	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
$205$	−1.83059			−0.127854
$206$	7.71626	−	13.3650i	0.537617	−	0.931181i
$207$	4.96545	+	8.60042i	0.345123	+	0.597770i
$208$	13.3343	−	10.2235i	0.924567	−	0.708873i
$209$	−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
$213$	0.618953	+	1.07206i	0.0424100	+	0.0734562i
$214$	−3.42041			−0.233814
$215$	−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
$219$	2.80363			0.189452
$220$	−0.525777	−	0.910673i	−0.0354479	−	0.0613975i
$221$	−2.59323	+	1.98825i	−0.174440	+	0.133744i
$222$	−1.89838	+	3.28809i	−0.127411	+	0.220682i
$223$	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
$226$	12.5111	−	21.6699i	0.832228	−	1.44146i
$227$	−24.1767			−1.60466			−0.802332	−	0.596877i	$-0.796408\pi$
$227$	−24.1767			−1.60466			−0.802332	+	0.596877i	$0.796408\pi$
$228$	−1.36510			−0.0904063
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	0.244635	+	0.969615i	$0.421332\pi$
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	−0.962029	+	0.272947i	$0.912002\pi$
$230$	−3.33190	+	5.77101i	−0.219699	+	0.380529i
$231$		0			0
$232$	10.4782	+	18.1488i	0.687928	+	1.19153i
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	−0.921486	−	0.388411i	$-0.873024\pi$
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	0.797117	+	0.603825i	$0.206358\pi$
$234$	−14.2945	−	5.92749i	−0.934460	−	0.387492i
$235$	−1.89851	−	3.28832i	−0.123845	−	0.214507i
$236$	4.27309			0.278155
$237$	−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
$241$	20.7488			1.33655			0.668273	−	0.743916i	$-0.267034\pi$
$241$	20.7488			1.33655			0.668273	+	0.743916i	$0.267034\pi$
$242$	5.06980	+	8.78115i	0.325899	+	0.564474i
$243$	−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
$247$	−22.2824	−	9.23982i	−1.41779	−	0.587916i
$248$	6.50661	+	11.2698i	0.413170	+	0.715632i
$249$	−2.84521	+	4.92805i	−0.180308	+	0.312302i
$250$	−15.8944			−1.00525
$251$	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
$255$	−0.264164	−	0.457546i	−0.0165426	−	0.0286526i
$256$	9.60425			0.600266
$257$	13.1711			0.821590			0.410795	−	0.911728i	$-0.365251\pi$
$257$	13.1711			0.821590			0.410795	+	0.911728i	$0.365251\pi$
$258$	−2.06616	−	3.57869i	−0.128633	−	0.222799i
$259$		0			0
$260$	−0.233169	−	1.77644i	−0.0144605	−	0.110170i
$261$	11.7540	−	20.3585i	0.727555	−	1.26016i
$262$	−7.41406	+	12.8415i	−0.458042	+	0.793352i
$263$	9.57028	−	16.5762i	0.590129	−	1.02213i	−0.404086	−	0.914721i	$-0.632410\pi$
$263$	9.57028	−	16.5762i	0.590129	−	1.02213i	0.994215	−	0.107412i	$-0.0342564\pi$
$264$	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
$268$	0.780643	−	1.35211i	0.0476854	−	0.0825935i
$269$	28.4822			1.73659			0.868296	−	0.496047i	$-0.165216\pi$
$269$	28.4822			1.73659			0.868296	+	0.496047i	$0.165216\pi$
$270$	2.61044	−	4.52141i	0.158866	−	0.275164i
$271$	−17.9474			−1.09023			−0.545114	−	0.838362i	$-0.683514\pi$
$271$	−17.9474			−1.09023			−0.545114	+	0.838362i	$0.683514\pi$
$272$	−4.22353			−0.256089
$273$		0			0
$274$	−4.29811			−0.259658
$275$	−7.57641			−0.456875
$276$	−0.367005	+	0.635671i	−0.0220911	+	0.0382629i
$277$	13.4389			0.807463			0.403732	−	0.914877i	$-0.367713\pi$
$277$	13.4389			0.807463			0.403732	+	0.914877i	$0.367713\pi$
$278$	−17.7209	+	30.6934i	−1.06283	+	1.84087i
$279$	7.29884	−	12.6420i	0.436970	−	0.756855i
$280$		0			0
$281$	−29.9530			−1.78685			−0.893424	−	0.449214i	$-0.851704\pi$
$281$	−29.9530			−1.78685			−0.893424	+	0.449214i	$0.851704\pi$
$282$	−1.21197	−	2.09919i	−0.0721716	−	0.125005i
$283$	−4.94561	+	8.56604i	−0.293986	+	0.509199i	−0.974748	−	0.223306i	$-0.928315\pi$
$283$	−4.94561	+	8.56604i	−0.293986	+	0.509199i	0.680763	+	0.732504i	$0.261649\pi$
$284$	0.527613	−	0.913852i	0.0313080	−	0.0542271i
$285$	1.95005	−	3.37758i	0.115511	−	0.200070i
$286$	−1.54373	−	11.7611i	−0.0912824	−	0.695451i
$287$		0			0
$288$	−3.20665	−	5.55408i	−0.188954	−	0.327277i
$289$	−16.1786			−0.951683
$290$	15.7742			0.926295
$291$	1.51774	+	2.62881i	0.0889716	+	0.154103i
$292$	−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
$296$	−12.2842			−0.714007
$297$	2.98206	−	5.16508i	0.173037	−	0.299708i
$298$	11.2028	+	19.4038i	0.648959	+	1.12403i
$299$	−10.2931	+	7.89185i	−0.595268	+	0.456397i
$300$	−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
$304$	−15.5889	−	27.0008i	−0.894086	−	1.54860i
$305$	9.85196			0.564121
$306$	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
$310$	9.79527			0.556334
$311$	12.3817	+	21.4458i	0.702103	+	1.21608i	0.967727	+	0.252002i	$0.0810888\pi$
$311$	12.3817	+	21.4458i	0.702103	+	1.21608i	−0.265624	+	0.964077i	$0.585578\pi$
$312$	0.564970	+	4.30432i	0.0319851	+	0.243684i
$313$	1.18826	−	2.05812i	0.0671642	−	0.116332i	−0.830488	−	0.557037i	$-0.811938\pi$
$313$	1.18826	−	2.05812i	0.0671642	−	0.116332i	0.897652	+	0.440705i	$0.145272\pi$
$314$	−8.87330	−	15.3690i	−0.500749	−	0.867323i
$315$		0			0
$316$	−1.26625	+	2.19321i	−0.0712322	+	0.123378i
$317$	9.88979	−	17.1296i	0.555466	−	0.962096i	−0.442401	−	0.896817i	$-0.645873\pi$
$317$	9.88979	−	17.1296i	0.555466	−	0.962096i	0.997867	−	0.0652782i	$-0.0207935\pi$
$318$	−2.14862			−0.120488
$319$	18.0199			1.00892
$320$	−3.40093	+	5.89059i	−0.190118	+	0.329294i
$321$	0.538192	−	0.932176i	0.0300390	−	0.0520290i
$322$		0			0
$323$	3.03171	+	5.25108i	0.168689	+	0.292178i
$324$	−1.43945	+	2.49320i	−0.0799695	+	0.138511i
$325$	−11.9244	−	4.94469i	−0.661447	−	0.274282i
$326$	11.1997	+	19.3985i	0.620295	+	1.07438i
$327$	6.72516			0.371902
$328$	−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	0.806993	−	0.590561i	$-0.201093\pi$
$331$	−1.96386	−	3.40151i	−0.107944	−	0.186964i	−0.914937	+	0.403596i	$0.867760\pi$
$332$	4.85067			0.266215
$333$	6.88997	+	11.9338i	0.377568	+	0.653967i
$334$	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	$0.562308\pi$
$338$	5.24617	−	19.5182i	0.285354	−	1.06165i
$339$	3.93718	+	6.81940i	0.213838	+	0.370379i
$340$	−0.225181	+	0.390024i	−0.0122121	+	0.0211520i
$341$	11.1897			0.605958
$342$	−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
$346$	4.73761	+	8.20578i	0.254695	+	0.441145i
$347$	10.0700			0.540584			0.270292	−	0.962778i	$-0.412880\pi$
$347$	10.0700			0.540584			0.270292	+	0.962778i	$0.412880\pi$
$348$	1.73752			0.0931407
$349$	−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
$352$	2.45803	−	4.25743i	0.131013	−	0.226922i
$353$	17.0836	−	29.5897i	0.909269	−	1.57490i	0.0941861	−	0.995555i	$-0.469975\pi$
$353$	17.0836	−	29.5897i	0.909269	−	1.57490i	0.815083	−	0.579345i	$-0.196692\pi$
$354$	−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
$359$	−9.34327	+	16.1830i	−0.493119	+	0.854107i	−0.999969	−	0.00792750i	$-0.997477\pi$
$359$	−9.34327	+	16.1830i	−0.493119	+	0.854107i	0.506850	+	0.862034i	$0.330810\pi$
$360$	8.09500			0.426644
$361$	−12.8799	+	22.3087i	−0.677891	+	1.17414i
$362$	8.71433			0.458015
$363$	−3.19088			−0.167478
$364$		0			0
$365$	6.82788			0.357388
$366$	6.28926			0.328745
$367$	−15.5305	+	26.8997i	−0.810687	+	1.40415i	0.101696	+	0.994816i	$0.467573\pi$
$367$	−15.5305	+	26.8997i	−0.810687	+	1.40415i	−0.912384	+	0.409336i	$0.865760\pi$
$368$	−16.7642			−0.873893
$369$	−2.12067	+	3.67310i	−0.110397	+	0.191214i
$370$	−4.62327	+	8.00775i	−0.240353	+	0.416303i
$371$		0			0
$372$	1.07894			0.0559404
$373$	1.46852	+	2.54355i	0.0760371	+	0.131700i	0.901537	−	0.432702i	$-0.142440\pi$
$373$	1.46852	+	2.54355i	0.0760371	+	0.131700i	−0.825500	+	0.564403i	$0.809107\pi$
$374$	−1.49084	+	2.58221i	−0.0770894	+	0.133523i
$375$	2.50094	−	4.33175i	0.129148	−	0.223691i
$376$	3.92126	−	6.79182i	0.202223	−	0.350261i
$377$	28.3612	+	11.7605i	1.46068	+	0.605698i
$378$		0			0
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	0.706961	−	0.707252i	$-0.250066\pi$
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	−0.965979	+	0.258620i	$0.916732\pi$
$380$	−3.32454			−0.170545
$381$	−7.67069			−0.392981
$382$	−0.391550	−	0.678184i	−0.0200334	−	0.0346989i
$383$	1.84466	+	3.19504i	0.0942576	+	0.163259i	0.909299	−	0.416144i	$-0.136619\pi$
$383$	1.84466	+	3.19504i	0.0942576	+	0.163259i	−0.815041	+	0.579403i	$0.803286\pi$
$384$	−3.30767	+	5.72905i	−0.168794	+	0.292360i
$385$		0			0
$386$	2.88584	−	4.99842i	0.146885	−	0.254413i
$387$	−14.9978			−0.762379
$388$	1.29376	−	2.24086i	0.0656809	−	0.113763i
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	−0.996082	−	0.0884295i	$-0.971815\pi$
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	0.421459	−	0.906847i	$-0.361518\pi$
$390$	3.01849	+	1.25168i	0.152847	+	0.0633812i
$391$	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
$395$	−3.61767	−	6.26598i	−0.182025	−	0.315276i
$396$	−2.43636			−0.122432
$397$	−14.5680	−	25.2325i	−0.731146	−	1.26638i	−0.956394	−	0.292080i	$-0.905652\pi$
$397$	−14.5680	−	25.2325i	−0.731146	−	1.26638i	0.225248	−	0.974302i	$-0.427681\pi$
$398$	−11.6688			−0.584904
$399$		0			0
$400$	−8.34241	−	14.4495i	−0.417120	−	0.722474i
$401$	8.12052			0.405519			0.202760	−	0.979229i	$-0.435009\pi$
$401$	8.12052			0.405519			0.202760	+	0.979229i	$0.435009\pi$
$402$	1.42377	+	2.46603i	0.0710110	+	0.122995i
$403$	17.6113	+	7.30289i	0.877283	+	0.363783i
$404$	−1.50611	+	2.60866i	−0.0749318	+	0.129786i
$405$	−4.11250	−	7.12305i	−0.204352	−	0.353947i
$406$		0			0
$407$	−5.28144	+	9.14773i	−0.261791	+	0.453436i
$408$	0.545614	−	0.945031i	0.0270119	−	0.0467860i
$409$	8.32261			0.411527			0.205763	−	0.978602i	$-0.434032\pi$
$409$	8.32261			0.411527			0.205763	+	0.978602i	$0.434032\pi$
$410$	−2.84600			−0.140554
$411$	0.676295	−	1.17138i	0.0333592	−	0.0577798i
$412$	2.06992	−	3.58520i	0.101978	−	0.176630i
$413$		0			0
$414$	7.71973	+	13.3710i	0.379404	+	0.657147i
$415$	−6.92915	+	12.0016i	−0.340139	+	0.589138i
$416$	6.64723	−	5.09649i	0.325907	−	0.249876i
$417$	−5.57666	−	9.65905i	−0.273090	−	0.473006i
$418$	−22.0106			−1.07657
$419$	−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
$423$	−8.79740			−0.427744
$424$	−3.47587	−	6.02038i	−0.168803	−	0.292376i
$425$	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
$429$	3.44821	+	1.42987i	0.166481	+	0.0690346i
$430$	−5.03187	−	8.71545i	−0.242658	−	0.420296i
$431$	4.47872	−	7.75736i	0.215732	−	0.373659i	−0.737767	−	0.675056i	$-0.764120\pi$
$431$	4.47872	−	7.75736i	0.215732	−	0.373659i	0.953499	+	0.301397i	$0.0974529\pi$
$432$	13.1342			0.631920
$433$	−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
$437$	12.0336	+	20.8428i	0.575644	+	0.997045i
$438$	4.35876			0.208270
$439$	−9.54160			−0.455396			−0.227698	−	0.973732i	$-0.573120\pi$
$439$	−9.54160			−0.455396			−0.227698	+	0.973732i	$0.573120\pi$
$440$	3.10257	+	5.37382i	0.147909	+	0.256187i
$441$		0			0
$442$	−4.03166	+	3.09111i	−0.191767	+	0.147029i
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	−0.652852	−	0.757485i	$-0.726428\pi$
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	0.982428	+	0.186644i	$0.0597610\pi$
$444$	−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	$-0.000882252\pi$
$450$	−7.68318	+	13.3077i	−0.362189	+	0.627329i
$451$	−3.25116			−0.153091
$452$	3.35616	−	5.81304i	0.157861	−	0.273423i
$453$	7.46501			0.350737
$454$	−37.5872			−1.76406
$455$		0			0
$456$	8.05539			0.377228
$457$	9.68564			0.453075			0.226538	−	0.974002i	$-0.427259\pi$
$457$	9.68564			0.453075			0.226538	+	0.974002i	$0.427259\pi$
$458$	−16.8779	+	29.2334i	−0.788652	+	1.36599i
$459$	−2.55432			−0.119226
$460$	−0.893795	+	1.54810i	−0.0416734	+	0.0721804i
$461$	−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
$467$	−14.5605	+	25.2195i	−0.673778	+	1.16702i	0.303046	+	0.952976i	$0.401996\pi$
$467$	−14.5605	+	25.2195i	−0.673778	+	1.16702i	−0.976824	+	0.214042i	$0.931337\pi$
$468$	−3.83456	−	1.59007i	−0.177252	−	0.0735012i
$469$		0			0
$470$	−2.95160	−	5.11231i	−0.136147	−	0.235813i
$471$	5.58476			0.257332
$472$	−25.2152			−1.16062
$473$	−5.74820	−	9.95618i	−0.264303	−	0.457786i
$474$	−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
$478$	34.0631			1.55801
$479$	4.86092	−	8.41936i	0.222101	−	0.384690i	−0.733345	−	0.679857i	$-0.762042\pi$
$479$	4.86092	−	8.41936i	0.222101	−	0.384690i	0.955446	+	0.295167i	$0.0953752\pi$
$480$	0.677132	+	1.17283i	0.0309067	+	0.0535320i
$481$	−14.2826	+	10.9506i	−0.651229	+	0.499303i
$482$	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
$486$	−9.19791	−	15.9313i	−0.417226	−	0.722656i
$487$	−17.1133			−0.775478			−0.387739	−	0.921769i	$-0.626744\pi$
$487$	−17.1133			−0.775478			−0.387739	+	0.921769i	$0.626744\pi$
$488$	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	$0.636232\pi$
$492$	−0.313484			−0.0141329
$493$	−3.85879	−	6.68361i	−0.173791	−	0.301015i
$494$	−34.6421	−	14.3650i	−1.55862	−	0.646313i
$495$	3.48033	−	6.02812i	0.156429	−	0.270944i
$496$	12.3210	+	21.3407i	0.553231	+	0.958224i
$497$		0			0
$498$	−4.42341	+	7.66157i	−0.198218	+	0.343323i
$499$	−2.70198	+	4.67996i	−0.120957	+	0.209504i	−0.920145	−	0.391577i	$-0.871930\pi$
$499$	−2.70198	+	4.67996i	−0.120957	+	0.209504i	0.799188	+	0.601081i	$0.205263\pi$
$500$	−4.26373			−0.190680
$501$	−3.80241			−0.169879
$502$	10.3059	−	17.8503i	0.459974	−	0.796699i
$503$	−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
$506$	−5.91749	+	10.2494i	−0.263064	+	0.455641i
$507$	4.49389	+	4.50089i	0.199581	+	0.199892i
$508$	3.26935	+	5.66268i	0.145054	+	0.251241i
$509$	1.95876			0.0868204			0.0434102	−	0.999057i	$-0.486178\pi$
$509$	1.95876			0.0868204			0.0434102	+	0.999057i	$0.486178\pi$
$510$	−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
$514$	20.4769			0.903198
$515$	5.91374	+	10.2429i	0.260590	+	0.451356i
$516$	−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
$520$	1.37591	+	10.4826i	0.0603378	+	0.459694i
$521$	−19.5477	−	33.8576i	−0.856401	−	1.48333i	−0.875339	−	0.483509i	$-0.839362\pi$
$521$	−19.5477	−	33.8576i	−0.856401	−	1.48333i	0.0189387	−	0.999821i	$-0.493971\pi$
$522$	18.2738	−	31.6512i	0.799823	−	1.38533i
$523$	8.71268			0.380979			0.190489	−	0.981689i	$-0.438993\pi$
$523$	8.71268			0.380979			0.190489	+	0.981689i	$0.438993\pi$
$524$	−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
$528$	2.41239	+	4.17839i	0.104986	+	0.181841i
$529$	−10.0592			−0.437357
$530$	−5.23269			−0.227293
$531$	14.1427	+	24.4958i	0.613740	+	1.06303i
$532$		0			0
$533$	−5.11694	−	2.12184i	−0.221639	−	0.0919072i
$534$	−6.75105	+	11.6932i	−0.292147	+	0.506013i
$535$	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
$541$	10.7497	−	18.6190i	0.462165	−	0.800493i	−0.536904	−	0.843644i	$-0.680406\pi$
$541$	10.7497	−	18.6190i	0.462165	−	0.800493i	0.999069	+	0.0431505i	$0.0137395\pi$
$542$	−27.9026			−1.19852
$543$	−1.37118	+	2.37495i	−0.0588428	+	0.101919i
$544$	−2.10546			−0.0902707
$545$	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	$0.724269\pi$
$548$	−1.15299			−0.0492531
$549$	11.4131	−	19.7680i	0.487098	−	0.843679i
$550$	−11.7789			−0.502256
$551$	28.4854	−	49.3381i	1.21352	−	2.10187i
$552$	2.16567	−	3.75105i	0.0921770	−	0.159655i
$553$		0			0
$554$	20.8932			0.887668
$555$	−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	−0.615626	−	0.788038i	$-0.711097\pi$
$557$	8.84201	−	15.3148i	0.374648	−	0.648909i	0.990274	+	0.139129i	$0.0444302\pi$
$558$	11.3474	−	19.6543i	0.480374	−	0.832033i
$559$	−2.54918	−	19.4214i	−0.107819	−	0.821437i
$560$		0			0
$561$	−0.469159	−	0.812606i	−0.0198079	−	0.0343083i
$562$	−46.5676			−1.96433
$563$	41.7390			1.75909			0.879545	−	0.475816i	$-0.157847\pi$
$563$	41.7390			1.75909			0.879545	+	0.475816i	$0.157847\pi$
$564$	−0.325115	−	0.563116i	−0.0136898	−	0.0237115i
$565$	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
$569$	5.46775			0.229220			0.114610	−	0.993411i	$-0.463438\pi$
$569$	5.46775			0.229220			0.114610	+	0.993411i	$0.463438\pi$
$570$	3.03171	−	5.25108i	0.126984	−	0.219943i
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	0.751434	−	0.659808i	$-0.229362\pi$
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	−0.947128	+	0.320857i	$0.896029\pi$
$572$	−0.414111	−	3.15498i	−0.0173149	−	0.131916i
$573$	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
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	0.828827	−	0.559505i	$-0.189009\pi$
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	−0.898959	+	0.438033i	$0.855675\pi$
$578$	−25.1527			−1.04621
$579$	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
$583$	−5.97761			−0.247567
$584$	7.05128	+	12.2132i	0.291784	+	0.505385i
$585$	9.41185	−	7.21614i	0.389132	−	0.298351i
$586$	6.14924	−	10.6508i	0.254023	−	0.439980i
$587$	−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
$590$	−9.48995	+	16.4371i	−0.390695	+	0.676704i
$591$	−3.64224			−0.149822
$592$	−23.2616			−0.956048
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	−0.132102	−	0.991236i	$-0.542173\pi$
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	0.924487	−	0.381214i	$-0.124494\pi$
$594$	4.63617	−	8.03008i	0.190224	−	0.329478i
$595$		0			0
$596$	3.00519	+	5.20515i	0.123097	+	0.213211i
$597$	1.83605	−	3.18014i	0.0751447	−	0.130154i
$598$	−16.0026	+	12.2694i	−0.654396	+	0.501731i
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	0.614295	−	0.789077i	$-0.289441\pi$
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	−0.990508	+	0.137457i	$0.956107\pi$
$600$	4.31084			0.175989
$601$	−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
$605$	−7.77099			−0.315936
$606$	−2.74690	−	4.75777i	−0.111585	−	0.193271i
$607$	6.15255	+	10.6565i	0.249724	+	0.432535i	0.963449	−	0.267891i	$-0.0863266\pi$
$607$	6.15255	+	10.6565i	0.249724	+	0.432535i	−0.713725	+	0.700426i	$0.752993\pi$
$608$	−7.77119	−	13.4601i	−0.315163	−	0.545879i
$609$		0			0
$610$	15.3167			0.620155
$611$	−1.49530	−	11.3922i	−0.0604934	−	0.460880i
$612$	0.521725	+	0.903654i	0.0210895	+	0.0365280i
$613$	−13.1112	+	22.7093i	−0.529556	+	0.917219i	0.469849	+	0.882747i	$0.344308\pi$
$613$	−13.1112	+	22.7093i	−0.529556	+	0.917219i	−0.999406	+	0.0344720i	$0.989025\pi$
$614$	−1.97816			−0.0798319
$615$	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
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	0.662312	−	0.749228i	$-0.269575\pi$
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	−0.980007	+	0.198965i	$0.936242\pi$
$620$	2.62762			0.105528
$621$	−10.1387			−0.406852
$622$	19.2497	+	33.3415i	0.771843	+	1.33687i
$623$		0			0
$624$	1.06984	+	8.15073i	0.0428277	+	0.326290i
$625$	−2.86003	+	4.95371i	−0.114401	+	0.198149i
$626$	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	$0.0589644\pi$
$632$	7.47206	−	12.9420i	0.297222	−	0.514804i
$633$	1.85457			0.0737125
$634$	15.3755	−	26.6312i	0.610640	−	1.05766i
$635$	−18.6810			−0.741333
$636$	−0.576375			−0.0228548
$637$		0			0
$638$	28.0152			1.10913
$639$	6.98497			0.276321
$640$	−8.05542	+	13.9524i	−0.318418	+	0.551517i
$641$	49.2464			1.94512			0.972559	−	0.232658i	$-0.0747422\pi$
$641$	49.2464			1.94512			0.972559	+	0.232658i	$0.0747422\pi$
$642$	0.836720	−	1.44924i	0.0330227	−	0.0571970i
$643$	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	−0.821130	−	0.570741i	$-0.806656\pi$
$647$	2.12929	−	3.68804i	0.0837112	−	0.144992i	0.904841	+	0.425749i	$0.139989\pi$
$648$	8.49410	−	14.7122i	0.333680	−	0.577950i
$649$	−10.8409	+	18.7771i	−0.425544	+	0.737064i
$650$	−18.5387	−	7.68744i	−0.727148	−	0.301526i
$651$		0			0
$652$	3.00437	+	5.20373i	0.117660	+	0.203794i
$653$	−2.09552			−0.0820040			−0.0410020	−	0.999159i	$-0.513055\pi$
$653$	−2.09552			−0.0820040			−0.0410020	+	0.999159i	$0.513055\pi$
$654$	10.4555			0.408843
$655$	−5.68213	−	9.84174i	−0.222019	−	0.384549i
$656$	−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	$0.331767\pi$
$660$	0.514475			0.0200259
$661$	13.9054	−	24.0848i	0.540857	−	0.936792i	−0.457998	−	0.888953i	$-0.651433\pi$
$661$	13.9054	−	24.0848i	0.540857	−	0.936792i	0.998855	−	0.0478387i	$-0.0152333\pi$
$662$	−3.05319	−	5.28829i	−0.118666	−	0.205535i
$663$	−0.208060	−	1.58514i	−0.00808038	−	0.0615618i
$664$	−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
$668$	1.62064	+	2.80703i	0.0627044	+	0.108607i
$669$	−2.38207			−0.0920960
$670$	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	$0.930033\pi$
$674$	−11.1020			−0.427633
$675$	−5.04536	−	8.73881i	−0.194196	−	0.336357i
$676$	1.40731	−	5.23583i	0.0541272	−	0.201378i
$677$	17.2813	−	29.9321i	0.664175	−	1.15038i	−0.315334	−	0.948981i	$-0.602116\pi$
$677$	17.2813	−	29.9321i	0.664175	−	1.15038i	0.979508	−	0.201403i	$-0.0645502\pi$
$678$	6.12109	+	10.6020i	0.235079	+	0.407169i
$679$		0			0
$680$	1.32877	−	2.30150i	0.0509562	−	0.0882587i
$681$	5.91425	−	10.2438i	0.226634	−	0.392542i
$682$	17.3965			0.666147
$683$	47.0064			1.79865			0.899325	−	0.437281i	$-0.144058\pi$
$683$	47.0064			1.79865			0.899325	+	0.437281i	$0.144058\pi$
$684$	−3.85135	+	6.67073i	−0.147260	+	0.255062i
$685$	1.64703	−	2.85275i	0.0629299	−	0.108998i
$686$		0			0
$687$	−5.31138	−	9.19958i	−0.202642	−	0.350986i
$688$	12.6587	−	21.9255i	0.482609	−	0.835904i
$689$	−9.40807	−	3.90124i	−0.358419	−	0.148625i
$690$	−1.63013	−	2.82348i	−0.0620582	−	0.107488i
$691$	−19.0060			−0.723023			−0.361512	−	0.932368i	$-0.617739\pi$
$691$	−19.0060			−0.723023			−0.361512	+	0.932368i	$0.617739\pi$
$692$	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
$696$	−10.2530			−0.388638
$697$	0.696205	+	1.20586i	0.0263706	+	0.0456753i
$698$	−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	$0.828659\pi$
$702$	12.5376	−	9.61266i	0.473200	−	0.362807i
$703$	16.6976	+	28.9210i	0.629760	+	1.09078i
$704$	−6.04010	+	10.4618i	−0.227645	+	0.394293i
$705$	1.85770			0.0699651
$706$	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	0.943170	−	0.332312i	$-0.107829\pi$
$709$	4.89390	+	8.47648i	0.183794	+	0.318341i	−0.759375	+	0.650653i	$0.774495\pi$
$710$	2.34351	+	4.05908i	0.0879504	+	0.152334i
$711$	−16.7637			−0.628687
$712$	−43.6854			−1.63718
$713$	−9.51099	−	16.4735i	−0.356189	−	0.616938i
$714$		0			0
$715$	8.39768	+	3.48226i	0.314055	+	0.130229i
$716$	−3.86393	+	6.69252i	−0.144402	+	0.250111i
$717$	−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	−0.999753	−	0.0222358i	$-0.992922\pi$
$719$	−13.9201	−	24.1104i	−0.519133	−	0.899165i	0.480620	−	0.876929i	$-0.340412\pi$
$720$	15.3288			0.571271
$721$		0			0
$722$	−20.0243	+	34.6830i	−0.745226	+	1.29077i
$723$	−5.07568	+	8.79134i	−0.188767	+	0.326953i
$724$	2.33766			0.0868783
$725$	15.2439	−	26.4033i	0.566145	−	0.980592i
$726$	−4.96082			−0.184113
$727$	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
$730$	10.6152			0.392887
$731$	−2.46185	+	4.26405i	−0.0910547	+	0.157711i
$732$	1.68712			0.0623577
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	−0.655591	−	0.755116i	$-0.727580\pi$
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	0.981745	+	0.190200i	$0.0609136\pi$
$734$	−24.1451	+	41.8206i	−0.891213	+	1.54363i
$735$		0			0
$736$	−8.35705			−0.308045
$737$	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	−0.936621	−	0.350345i	$-0.886064\pi$
$739$	−4.48279	+	7.76443i	−0.164902	+	0.285619i	0.771718	+	0.635964i	$0.219398\pi$
$740$	−1.24021	+	2.14811i	−0.0455911	+	0.0789661i
$741$	9.36579	−	7.18084i	0.344061	−	0.263795i
$742$		0			0
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	0.999824	−	0.0187532i	$-0.00596968\pi$
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	−0.516153	+	0.856497i	$0.672636\pi$
$744$	−6.36674			−0.233416
$745$	−17.1716			−0.629119
$746$	2.28309	+	3.95442i	0.0835898	+	0.144782i
$747$	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
$751$	−20.2876			−0.740305			−0.370152	−	0.928971i	$-0.620695\pi$
$751$	−20.2876			−0.740305			−0.370152	+	0.928971i	$0.620695\pi$
$752$	7.42536	−	12.8611i	0.270775	−	0.468996i
$753$	3.24321	+	5.61740i	0.118189	+	0.204709i
$754$	44.0928	+	18.2839i	1.60576	+	0.665861i
$755$	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
$759$	−1.86220	−	3.22543i	−0.0675936	−	0.117076i
$760$	19.6179			0.711616
$761$	10.0711	+	17.4436i	0.365077	+	0.632332i	0.988789	−	0.149323i	$-0.0477094\pi$
$761$	10.0711	+	17.4436i	0.365077	+	0.632332i	−0.623712	+	0.781655i	$0.714376\pi$
$762$	−11.9255			−0.432016
$763$		0			0
$764$	−0.105035	−	0.181926i	−0.00380003	−	0.00658184i
$765$	−2.98112			−0.107783
$766$	2.86786	+	4.96729i	0.103620	+	0.179475i
$767$	−29.3171	+	22.4777i	−1.05858	+	0.811622i
$768$	−2.34945	+	4.06936i	−0.0847784	+	0.146840i
$769$	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
$772$	0.774139	−	1.34085i	0.0278619	−	0.0482582i
$773$	−2.34567			−0.0843679			−0.0421839	−	0.999110i	$-0.513432\pi$
$773$	−2.34567			−0.0843679			−0.0421839	+	0.999110i	$0.513432\pi$
$774$	−23.3168			−0.838106

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +O(q^{10})\)	\(q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) 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} +(-0.102021 + 0.176706i) q^{12} +(-2.86133 + 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} -4.66017 q^{16} +0.906303 q^{17} +(2.14596 + 3.71691i) q^{18} +(3.34514 + 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +3.59733 q^{23} +(0.602021 - 1.04273i) q^{24} +(1.79015 + 3.10063i) q^{25} +(-4.44847 + 3.41068i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 - 0.784881i) q^{30} +(-2.64390 - 4.57937i) q^{31} -2.32313 q^{32} +(-0.517662 - 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +4.99159 q^{37} +(5.20065 + 9.00778i) q^{38} +(-0.229570 - 1.74902i) q^{39} +(1.46615 - 2.53944i) q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +(-0.441269 + 0.764301i) q^{44} -3.28933 q^{45} +5.59272 q^{46} +(-1.59337 + 2.75979i) q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +(-0.221705 + 0.384004i) q^{51} +(-1.19332 + 0.914930i) q^{52} +(1.41239 + 2.44632i) q^{53} -4.38173 q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 - 11.4652i) q^{58} +10.2460 q^{59} +(-0.121560 - 0.210548i) q^{60} +(-4.13423 - 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-0.559090 - 4.25952i) q^{65} +(-0.804802 - 1.39396i) q^{66} +(1.87182 - 3.24208i) q^{67} +0.377975 q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 - 5.88368i) q^{72} +(-2.86522 - 4.96271i) q^{73} +7.76035 q^{74} -1.75167 q^{75} +(1.39510 + 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +(-3.03620 + 5.25885i) 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} +(-4.22310 + 7.31462i) q^{86} +4.16619 q^{87} +(2.60390 - 4.51008i) q^{88} +17.7511 q^{89} -5.11387 q^{90} +1.50027 q^{92} +2.58707 q^{93} +(-2.47719 + 4.29061i) q^{94} -7.97155 q^{95} +(0.568297 - 0.984319i) q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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