LMFDB - Embedded newform 380.3.b.a.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (of order $2$, degree $1$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.2
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 0.00104961i) q^{2} -3.00750i q^{3} +(4.00000 - 0.00419842i) q^{4} +2.23607 q^{5} +(0.00315669 + 6.01499i) q^{6} +0.387511i q^{7} +(-7.99999 + 0.0125953i) q^{8} -0.0450421 q^{9} +O(q^{10})$	\(q+(-2.00000 + 0.00104961i) q^{2} -3.00750i q^{3} +(4.00000 - 0.00419842i) q^{4} +2.23607 q^{5} +(0.00315669 + 6.01499i) q^{6} +0.387511i q^{7} +(-7.99999 + 0.0125953i) q^{8} -0.0450421 q^{9} +(-4.47214 + 0.00234699i) q^{10} -7.54388i q^{11} +(-0.0126268 - 12.0300i) q^{12} +11.3246 q^{13} +(-0.000406734 - 0.775022i) q^{14} -6.72497i q^{15} +(16.0000 - 0.0335874i) q^{16} +7.39859 q^{17} +(0.0900841 - 4.72765e-5i) q^{18} +4.35890i q^{19} +(8.94427 - 0.00938796i) q^{20} +1.16544 q^{21} +(0.00791811 + 15.0878i) q^{22} -17.7270i q^{23} +(0.0378802 + 24.0600i) q^{24} +5.00000 q^{25} +(-22.6492 + 0.0118864i) q^{26} -26.9320i q^{27} +(0.00162694 + 1.55004i) q^{28} +51.3037 q^{29} +(0.00705857 + 13.4499i) q^{30} +54.2734i q^{31} +(-31.9999 + 0.0839684i) q^{32} -22.6882 q^{33} +(-14.7972 + 0.00776561i) q^{34} +0.866501i q^{35} +(-0.180168 + 0.000189106i) q^{36} -54.2963 q^{37} +(-0.00457513 - 8.71780i) q^{38} -34.0587i q^{39} +(-17.8885 + 0.0281639i) q^{40} -46.4109 q^{41} +(-2.33088 + 0.00122325i) q^{42} -81.4441i q^{43} +(-0.0316724 - 30.1755i) q^{44} -0.100717 q^{45} +(0.0186064 + 35.4541i) q^{46} -85.4706i q^{47} +(-0.101014 - 48.1199i) q^{48} +48.8498 q^{49} +(-10.0000 + 0.00524803i) q^{50} -22.2513i q^{51} +(45.2983 - 0.0475454i) q^{52} +6.57686 q^{53} +(0.0282680 + 53.8640i) q^{54} -16.8686i q^{55} +(-0.00488081 - 3.10009i) q^{56} +13.1094 q^{57} +(-102.607 + 0.0538487i) q^{58} -48.9050i q^{59} +(-0.0282343 - 26.8999i) q^{60} -6.74207 q^{61} +(-0.0569657 - 108.547i) q^{62} -0.0174543i q^{63} +(63.9997 - 0.201524i) q^{64} +25.3226 q^{65} +(45.3764 - 0.0238137i) q^{66} +19.9113i q^{67} +(29.5944 - 0.0310624i) q^{68} -53.3140 q^{69} +(-0.000909485 - 1.73300i) q^{70} -19.7374i q^{71} +(0.360336 - 0.000567317i) q^{72} -27.2088 q^{73} +(108.593 - 0.0569898i) q^{74} -15.0375i q^{75} +(0.0183005 + 17.4356i) q^{76} +2.92334 q^{77} +(0.0357482 + 68.1173i) q^{78} -60.7089i q^{79} +(35.7770 - 0.0751037i) q^{80} -81.4033 q^{81} +(92.8217 - 0.0487131i) q^{82} +93.1252i q^{83} +(4.66175 - 0.00489301i) q^{84} +16.5438 q^{85} +(0.0854843 + 162.888i) q^{86} -154.296i q^{87} +(0.0950172 + 60.3510i) q^{88} -85.7242 q^{89} +(0.201434 - 0.000105713i) q^{90} +4.38841i q^{91} +(-0.0744256 - 70.9081i) q^{92} +163.227 q^{93} +(0.0897105 + 170.941i) q^{94} +9.74679i q^{95} +(0.252535 + 96.2396i) q^{96} -29.5085 q^{97} +(-97.6997 + 0.0512731i) q^{98} +0.339792i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.00000	+	0.00104961i	−1.00000	+	0.000524803i
$2$	−2.00000	+	0.00104961i	−1.00000	+	0.000524803i
$3$		−	3.00750i		−	1.00250i	−0.865303	−	0.501250i	$-0.832874\pi$
$3$		−	3.00750i		−	1.00250i	0.865303	−	0.501250i	$-0.167126\pi$
$4$	4.00000	−	0.00419842i	0.999999	−	0.00104961i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	0.00315669	+	6.01499i	0.000526115	+	1.00250i
$7$			0.387511i			0.0553587i	0.999617	+	0.0276794i	$0.00881174\pi$
$7$			0.387511i			0.0553587i	−0.999617	+	0.0276794i	$0.991188\pi$
$8$	−7.99999	+	0.0125953i	−0.999999	+	0.00157441i
$9$	−0.0450421			−0.00500468
$10$	−4.47214	+	0.00234699i	−0.447214	+	0.000234699i
$11$		−	7.54388i		−	0.685807i	−0.939371	−	0.342904i	$-0.888590\pi$
$11$		−	7.54388i		−	0.685807i	0.939371	−	0.342904i	$-0.111410\pi$
$12$	−0.0126268	−	12.0300i	−0.00105223	−	1.00250i
$13$	11.3246			0.871122			0.435561	−	0.900159i	$-0.356550\pi$
$13$	11.3246			0.871122			0.435561	+	0.900159i	$0.356550\pi$
$14$	−0.000406734	−	0.775022i	−2.90524e−5	−	0.0553587i
$15$		−	6.72497i		−	0.448331i
$16$	16.0000	−	0.0335874i	0.999998	−	0.00209921i
$17$	7.39859			0.435211			0.217606	−	0.976037i	$-0.430175\pi$
$17$	7.39859			0.435211			0.217606	+	0.976037i	$0.430175\pi$
$18$	0.0900841		4.72765e-5i	0.00500467		2.62647e-6i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	8.94427	−	0.00938796i	0.447213	−	0.000469398i
$21$	1.16544			0.0554971
$22$	0.00791811	+	15.0878i	0.000359914	+	0.685807i
$23$		−	17.7270i		−	0.770741i	−0.922762	−	0.385370i	$-0.874074\pi$
$23$		−	17.7270i		−	0.770741i	0.922762	−	0.385370i	$-0.125926\pi$
$24$	0.0378802	+	24.0600i	0.00157834	+	1.00250i
$25$	5.00000			0.200000
$26$	−22.6492	+	0.0118864i	−0.871122	+	0.000457168i
$27$		−	26.9320i		−	0.997482i
$28$	0.00162694	+	1.55004i	5.81049e−5	+	0.0553587i
$29$	51.3037			1.76909			0.884547	−	0.466451i	$-0.154468\pi$
$29$	51.3037			1.76909			0.884547	+	0.466451i	$0.154468\pi$
$30$	0.00705857	+	13.4499i	0.000235286	+	0.448331i
$31$			54.2734i			1.75075i	0.483440	+	0.875377i	$0.339387\pi$
$31$			54.2734i			1.75075i	−0.483440	+	0.875377i	$0.660613\pi$
$32$	−31.9999	+	0.0839684i	−0.999997	+	0.00262401i
$33$	−22.6882			−0.687521
$34$	−14.7972	+	0.00776561i	−0.435211	+	0.000228400i
$35$			0.866501i			0.0247572i
$36$	−0.180168		0.000189106i	−0.00500467		5.25294e-6i
$37$	−54.2963			−1.46747			−0.733734	−	0.679437i	$-0.762224\pi$
$37$	−54.2963			−1.46747			−0.733734	+	0.679437i	$0.762224\pi$
$38$	−0.00457513	−	8.71780i	−0.000120398	−	0.229416i
$39$		−	34.0587i		−	0.873299i
$40$	−17.8885	+	0.0281639i	−0.447213	+	0.000704097i
$41$	−46.4109			−1.13197			−0.565986	−	0.824415i	$-0.691504\pi$
$41$	−46.4109			−1.13197			−0.565986	+	0.824415i	$0.691504\pi$
$42$	−2.33088	+	0.00122325i	−0.0554971	+	2.91251e-5i
$43$		−	81.4441i		−	1.89405i	−0.321161	−	0.947025i	$-0.604073\pi$
$43$		−	81.4441i		−	1.89405i	0.321161	−	0.947025i	$-0.395927\pi$
$44$	−0.0316724	−	30.1755i	−0.000719828	−	0.685807i
$45$	−0.100717			−0.00223816
$46$	0.0186064	+	35.4541i	0.000404487	+	0.770740i
$47$		−	85.4706i		−	1.81852i	−0.416224	−	0.909262i	$-0.636647\pi$
$47$		−	85.4706i		−	1.81852i	0.416224	−	0.909262i	$-0.363353\pi$
$48$	−0.101014	−	48.1199i	−0.00210446	−	1.00250i
$49$	48.8498			0.996935
$50$	−10.0000	+	0.00524803i	−0.200000	+	0.000104961i
$51$		−	22.2513i		−	0.436299i
$52$	45.2983	−	0.0475454i	0.871122	−	0.000914335i
$53$	6.57686			0.124092			0.0620459	−	0.998073i	$-0.480237\pi$
$53$	6.57686			0.124092			0.0620459	+	0.998073i	$0.480237\pi$
$54$	0.0282680	+	53.8640i	0.000523482	+	0.997482i
$55$		−	16.8686i		−	0.306702i
$56$	−0.00488081	−	3.10009i	−8.71573e−5	−	0.0553587i
$57$	13.1094			0.229989
$58$	−102.607	+	0.0538487i	−1.76909	+	0.000928426i
$59$		−	48.9050i		−	0.828899i	−0.910072	−	0.414449i	$-0.863974\pi$
$59$		−	48.9050i		−	0.828899i	0.910072	−	0.414449i	$-0.136026\pi$
$60$	−0.0282343	−	26.8999i	−0.000470571	−	0.448331i
$61$	−6.74207			−0.110526			−0.0552629	−	0.998472i	$-0.517600\pi$
$61$	−6.74207			−0.110526			−0.0552629	+	0.998472i	$0.517600\pi$
$62$	−0.0569657	−	108.547i	−0.000918802	−	1.75075i
$63$		−	0.0174543i		−	0.000277053i
$64$	63.9997	−	0.201524i	0.999995	−	0.00314881i
$65$	25.3226			0.389578
$66$	45.3764	−	0.0238137i	0.687521	−	0.000360813i
$67$			19.9113i			0.297183i	0.988899	+	0.148592i	$0.0474740\pi$
$67$			19.9113i			0.297183i	−0.988899	+	0.148592i	$0.952526\pi$
$68$	29.5944	−	0.0310624i	0.435211	−	0.000456801i
$69$	−53.3140			−0.772667
$70$	−0.000909485	−	1.73300i	−1.29926e−5	−	0.0247572i
$71$		−	19.7374i		−	0.277992i	−0.990293	−	0.138996i	$-0.955612\pi$
$71$		−	19.7374i		−	0.277992i	0.990293	−	0.138996i	$-0.0443875\pi$
$72$	0.360336		0.000567317i	0.00500467		7.87941e-6i
$73$	−27.2088			−0.372724			−0.186362	−	0.982481i	$-0.559670\pi$
$73$	−27.2088			−0.372724			−0.186362	+	0.982481i	$0.559670\pi$
$74$	108.593	−	0.0569898i	1.46747	−	0.000770132i
$75$		−	15.0375i		−	0.200500i
$76$	0.0183005	+	17.4356i	0.000240796	+	0.229416i
$77$	2.92334			0.0379654
$78$	0.0357482	+	68.1173i	0.000458310	+	0.873299i
$79$		−	60.7089i		−	0.768466i	−0.923236	−	0.384233i	$-0.874466\pi$
$79$		−	60.7089i		−	0.768466i	0.923236	−	0.384233i	$-0.125534\pi$
$80$	35.7770	−	0.0751037i	0.447213	−	0.000938796i
$81$	−81.4033			−1.00498
$82$	92.8217	−	0.0487131i	1.13197	−	0.000594063i
$83$			93.1252i			1.12199i	0.827819	+	0.560995i	$0.189581\pi$
$83$			93.1252i			1.12199i	−0.827819	+	0.560995i	$0.810419\pi$
$84$	4.66175	−	0.00489301i	0.0554971	−	5.82501e-5i
$85$	16.5438			0.194632
$86$	0.0854843	+	162.888i	0.000994003	+	1.89405i
$87$		−	154.296i		−	1.77352i
$88$	0.0950172	+	60.3510i	0.00107974	+	0.685807i
$89$	−85.7242			−0.963194			−0.481597	−	0.876393i	$-0.659943\pi$
$89$	−85.7242			−0.963194			−0.481597	+	0.876393i	$0.659943\pi$
$90$	0.201434		0.000105713i	0.00223816		1.17459e-6i
$91$			4.38841i			0.0482242i
$92$	−0.0744256	−	70.9081i	−0.000808974	−	0.770740i
$93$	163.227			1.75513
$94$	0.0897105	+	170.941i	0.000954367	+	1.81852i
$95$			9.74679i			0.102598i
$96$	0.252535	+	96.2396i	0.00263057	+	1.00250i
$97$	−29.5085			−0.304212			−0.152106	−	0.988364i	$-0.548605\pi$
$97$	−29.5085			−0.304212			−0.152106	+	0.988364i	$0.548605\pi$
$98$	−97.6997	+	0.0512731i	−0.996935	+	0.000523195i
$99$			0.339792i			0.00343224i
$100$	20.0000	−	0.0209921i	0.200000	−	0.000209921i
$101$	22.4780			0.222554			0.111277	−	0.993789i	$-0.464506\pi$
$101$	22.4780			0.222554			0.111277	+	0.993789i	$0.464506\pi$
$102$	0.0233551	+	44.5025i	0.000228971	+	0.436299i
$103$			150.487i			1.46103i	0.682894	+	0.730517i	$0.260721\pi$
$103$			150.487i			1.46103i	−0.682894	+	0.730517i	$0.739279\pi$
$104$	−90.5966	+	0.142636i	−0.871121	+	0.00137150i
$105$	2.60600			0.0248191
$106$	−13.1537	+	0.00690312i	−0.124092	+	6.51237e-5i
$107$		−	100.016i		−	0.934730i	−0.884065	−	0.467365i	$-0.845203\pi$
$107$		−	100.016i		−	0.934730i	0.884065	−	0.467365i	$-0.154797\pi$
$108$	−0.113072	−	107.728i	−0.00104696	−	0.997481i
$109$	24.2110			0.222119			0.111059	−	0.993814i	$-0.464576\pi$
$109$	24.2110			0.222119			0.111059	+	0.993814i	$0.464576\pi$
$110$	0.0177054	+	33.7373i	0.000160958	+	0.306702i
$111$			163.296i			1.47114i
$112$	0.0130155	+	6.20017i	0.000116210	+	0.0553586i
$113$	−22.3783			−0.198038			−0.0990191	−	0.995086i	$-0.531571\pi$
$113$	−22.3783			−0.198038			−0.0990191	+	0.995086i	$0.531571\pi$
$114$	−26.2188	+	0.0137597i	−0.229989	+	0.000120699i
$115$		−	39.6388i		−	0.344686i
$116$	205.215	−	0.215395i	1.76909	−	0.00185685i
$117$	−0.510083			−0.00435968
$118$	0.0513310	+	97.8100i	0.000435009	+	0.828899i
$119$			2.86704i			0.0240928i
$120$	0.0847028	+	53.7997i	0.000705857	+	0.448331i
$121$	64.0898			0.529668
$122$	13.4841	−	0.00707652i	0.110526	−	5.80043e-5i
$123$			139.581i			1.13480i
$124$	0.227863	+	217.093i	0.00183760	+	1.75075i
$125$	11.1803			0.0894427
$126$	1.83202e−5		0.0349086i	1.45398e−7		0.000277053i
$127$			129.705i			1.02130i	0.859789	+	0.510650i	$0.170595\pi$
$127$			129.705i			1.02130i	−0.859789	+	0.510650i	$0.829405\pi$
$128$	−127.999	+	0.470223i	−0.999993	+	0.00367361i
$129$	−244.943			−1.89878
$130$	−50.6451	+	0.0265787i	−0.389578	+	0.000204452i
$131$		−	27.1847i		−	0.207517i	−0.994603	−	0.103759i	$-0.966913\pi$
$131$		−	27.1847i		−	0.207517i	0.994603	−	0.103759i	$-0.0330869\pi$
$132$	−90.7528	+	0.0952547i	−0.687521	+	0.000721627i
$133$	−1.68912			−0.0127002
$134$	−0.0208990	−	39.8225i	−0.000155963	−	0.297183i
$135$		−	60.2218i		−	0.446088i
$136$	−59.1887	+	0.0931873i	−0.435211	+	0.000685201i
$137$	43.0769			0.314430			0.157215	−	0.987564i	$-0.449748\pi$
$137$	43.0769			0.314430			0.157215	+	0.987564i	$0.449748\pi$
$138$	106.628	−	0.0559587i	0.772667	−	0.000405498i
$139$			134.233i			0.965703i	0.875702	+	0.482852i	$0.160399\pi$
$139$			134.233i			0.965703i	−0.875702	+	0.482852i	$0.839601\pi$
$140$	0.00363794	+	3.46600i	2.59853e−5	+	0.0247572i
$141$	−257.053			−1.82307
$142$	0.0207165	+	39.4749i	0.000145891	+	0.277992i
$143$		−	85.4314i		−	0.597422i
$144$	−0.720672	+	0.00151285i	−0.00500466	+	1.05059e-5i
$145$	114.719			0.791163
$146$	54.4176	−	0.0285586i	0.372724	−	0.000195607i
$147$		−	146.916i		−	0.999427i
$148$	−217.185	+	0.227959i	−1.46747	+	0.00154026i
$149$	265.784			1.78379			0.891894	−	0.452245i	$-0.149377\pi$
$149$	265.784			1.78379			0.891894	+	0.452245i	$0.149377\pi$
$150$	0.0157834	+	30.0750i	0.000105223	+	0.200500i
$151$			173.310i			1.14775i	0.818944	+	0.573873i	$0.194560\pi$
$151$			173.310i			1.14775i	−0.818944	+	0.573873i	$0.805440\pi$
$152$	−0.0549015	−	34.8711i	−0.000361194	−	0.229415i
$153$	−0.333248			−0.00217809
$154$	−5.84668	+	0.00306836i	−0.0379654	+	1.99244e-5i
$155$			121.359i			0.782961i
$156$	−0.142993	−	136.235i	−0.000916620	−	0.873299i
$157$	99.6901			0.634969			0.317484	−	0.948264i	$-0.397162\pi$
$157$	99.6901			0.634969			0.317484	+	0.948264i	$0.397162\pi$
$158$	0.0637204	+	121.418i	0.000403294	+	0.768466i
$159$		−	19.7799i		−	0.124402i
$160$	−71.5539	+	0.187759i	−0.447212	+	0.00117349i
$161$	6.86942			0.0426672
$162$	162.807	−	0.0854415i	1.00498	−	0.000527417i
$163$			284.384i			1.74469i	0.488892	+	0.872344i	$0.337401\pi$
$163$			284.384i			1.74469i	−0.488892	+	0.872344i	$0.662599\pi$
$164$	−185.643	+	0.194853i	−1.13197	+	0.00118813i
$165$	−50.7324			−0.307469
$166$	−0.0977448	−	186.250i	−0.000588824	−	1.12199i
$167$		−	104.208i		−	0.624000i	−0.950082	−	0.312000i	$-0.899001\pi$
$167$		−	104.208i		−	0.624000i	0.950082	−	0.312000i	$-0.100999\pi$
$168$	−9.32350	+	0.0146790i	−0.0554970	+	8.73751e-5i
$169$	−40.7537			−0.241146
$170$	−33.0875	+	0.0173644i	−0.194632	+	0.000102144i
$171$		−	0.196334i		−	0.00114815i
$172$	−0.341937	−	325.776i	−0.00198801	−	1.89405i
$173$	272.012			1.57232			0.786161	−	0.618022i	$-0.212066\pi$
$173$	272.012			1.57232			0.786161	+	0.618022i	$0.212066\pi$
$174$	0.161950	+	308.592i	0.000930747	+	1.77352i
$175$			1.93756i			0.0110717i
$176$	−0.253379	−	120.702i	−0.00143965	−	0.685806i
$177$	−147.082			−0.830970
$178$	171.448	−	0.0899767i	0.963193	−	0.000505487i
$179$			123.115i			0.687791i	0.939008	+	0.343896i	$0.111747\pi$
$179$			123.115i			0.687791i	−0.939008	+	0.343896i	$0.888253\pi$
$180$	−0.402868		0.000422853i	−0.00223816		2.34919e-6i
$181$	112.988			0.624241			0.312120	−	0.950043i	$-0.398961\pi$
$181$	112.988			0.624241			0.312120	+	0.950043i	$0.398961\pi$
$182$	−0.00460610	−	8.77681i	−2.53082e−5	−	0.0482242i
$183$			20.2768i			0.110802i
$184$	0.223277	+	141.816i	0.00121346	+	0.770740i
$185$	−121.410			−0.656272
$186$	−326.454	+	0.171324i	−1.75513	+	0.000921098i
$187$		−	55.8141i		−	0.298471i
$188$	−0.358842	−	341.882i	−0.00190873	−	1.81852i
$189$	10.4365			0.0552194
$190$	−0.0102303	−	19.4936i	−5.38437e−5	−	0.102598i
$191$		−	131.556i		−	0.688776i	−0.938827	−	0.344388i	$-0.888086\pi$
$191$		−	131.556i		−	0.688776i	0.938827	−	0.344388i	$-0.111914\pi$
$192$	−0.606083	−	192.479i	−0.00315668	−	1.00249i
$193$	186.947			0.968637			0.484319	−	0.874892i	$-0.339068\pi$
$193$	186.947			0.968637			0.484319	+	0.874892i	$0.339068\pi$
$194$	59.0171	−	0.0309724i	0.304212	−	0.000159651i
$195$		−	76.1575i		−	0.390551i
$196$	195.399	−	0.205092i	0.996935	−	0.00104639i
$197$	−54.7774			−0.278058			−0.139029	−	0.990288i	$-0.544398\pi$
$197$	−54.7774			−0.278058			−0.139029	+	0.990288i	$0.544398\pi$
$198$	−0.000356648	−	0.679584i	−1.80125e−6	−	0.00343224i
$199$		−	55.1416i		−	0.277094i	−0.990356	−	0.138547i	$-0.955757\pi$
$199$		−	55.1416i		−	0.277094i	0.990356	−	0.138547i	$-0.0442432\pi$
$200$	−40.0000	+	0.0629764i	−0.200000	+	0.000314882i
$201$	59.8831			0.297926
$202$	−44.9559	+	0.0235930i	−0.222554	+	0.000116797i
$203$			19.8808i			0.0979348i
$204$	−0.0934202	−	89.0050i	−0.000457942	−	0.436299i
$205$	−103.778			−0.506233
$206$	−0.157952	−	300.973i	−0.000766756	−	1.46103i
$207$			0.798462i			0.00385731i
$208$	181.193	−	0.380363i	0.871120	−	0.00182867i
$209$	32.8830			0.157335
$210$	−5.21200	+	0.00273528i	−0.0248191	+	1.30251e-5i
$211$			99.8400i			0.473175i	0.971610	+	0.236588i	$0.0760291\pi$
$211$			99.8400i			0.473175i	−0.971610	+	0.236588i	$0.923971\pi$
$212$	26.3074	−	0.0276125i	0.124092	−	0.000130247i
$213$	−59.3603			−0.278687
$214$	0.104978	+	200.032i	0.000490549	+	0.934730i
$215$		−	182.115i		−	0.847045i
$216$	0.339216	+	215.456i	0.00157044	+	0.997481i
$217$	−21.0316			−0.0969196
$218$	−48.4219	+	0.0254120i	−0.222119	+	0.000116569i
$219$			81.8305i			0.373655i
$220$	−0.0708217	−	67.4745i	−0.000321917	−	0.306702i
$221$	83.7860			0.379122
$222$	−0.171397	−	326.592i	−0.000772057	−	1.47114i
$223$			167.748i			0.752231i	0.926573	+	0.376116i	$0.122740\pi$
$223$			167.748i			0.752231i	−0.926573	+	0.376116i	$0.877260\pi$
$224$	−0.0325387	−	12.4003i	−0.000145262	−	0.0553586i
$225$	−0.225210			−0.00100094
$226$	44.7566	−	0.0234884i	0.198038	−	0.000103931i
$227$			148.472i			0.654060i	0.945014	+	0.327030i	$0.106048\pi$
$227$			148.472i			0.654060i	−0.945014	+	0.327030i	$0.893952\pi$
$228$	52.4375	−	0.0550387i	0.229989	−	0.000241398i
$229$	−106.434			−0.464778			−0.232389	−	0.972623i	$-0.574654\pi$
$229$	−106.434			−0.464778			−0.232389	+	0.972623i	$0.574654\pi$
$230$	0.0416052	+	79.2777i	0.000180892	+	0.344686i
$231$		−	8.79194i		−	0.0380603i
$232$	−410.429	+	0.646184i	−1.76909	+	0.00278528i
$233$	−7.37205			−0.0316397			−0.0158198	−	0.999875i	$-0.505036\pi$
$233$	−7.37205			−0.0316397			−0.0158198	+	0.999875i	$0.505036\pi$
$234$	1.02017		0.000535386i	0.00435968		2.28798e-6i
$235$		−	191.118i		−	0.813269i
$236$	−0.205324	−	195.620i	−0.000870017	−	0.828898i
$237$	−182.582			−0.770387
$238$	−0.00300926	−	5.73408i	−1.26440e−5	−	0.0240928i
$239$		−	353.681i		−	1.47984i	−0.672697	−	0.739918i	$-0.734864\pi$
$239$		−	353.681i		−	1.47984i	0.672697	−	0.739918i	$-0.265136\pi$
$240$	−0.225874	−	107.599i	−0.000941142	−	0.448330i
$241$	241.361			1.00150			0.500749	−	0.865593i	$-0.333058\pi$
$241$	241.361			1.00150			0.500749	+	0.865593i	$0.333058\pi$
$242$	−128.180	+	0.0672691i	−0.529668	+	0.000277972i
$243$			2.43225i			0.0100093i
$244$	−26.9683	+	0.0283061i	−0.110526	+	0.000116009i
$245$	109.232			0.445843
$246$	−0.146505	−	279.161i	−0.000595547	−	1.13480i
$247$			49.3627i			0.199849i
$248$	−0.683588	−	434.187i	−0.00275640	−	1.75075i
$249$	280.074			1.12479
$250$	−22.3607	+	0.0117350i	−0.0894427	+	4.69398e-5i
$251$			241.567i			0.962419i	0.876606	+	0.481209i	$0.159802\pi$
$251$			241.567i			0.962419i	−0.876606	+	0.481209i	$0.840198\pi$
$252$	−7.32806e−5	−	0.0698172i	−2.90796e−7	−	0.000277052i
$253$	−133.731			−0.528580
$254$	−0.136139	−	259.410i	−0.000535981	−	1.02130i
$255$		−	49.7553i		−	0.195119i
$256$	255.998	−	1.07479i	0.999991	−	0.00419841i
$257$	195.989			0.762604			0.381302	−	0.924451i	$-0.375476\pi$
$257$	195.989			0.762604			0.381302	+	0.924451i	$0.375476\pi$
$258$	489.886	−	0.257094i	1.89878	−	0.000996487i
$259$		−	21.0404i		−	0.0812372i
$260$	101.290	−	0.106315i	0.389577	−	0.000408903i
$261$	−2.31083			−0.00885374
$262$	0.0285333	+	54.3695i	0.000108906	+	0.207517i
$263$			390.355i			1.48424i	0.670267	+	0.742120i	$0.266180\pi$
$263$			390.355i			1.48424i	−0.670267	+	0.742120i	$0.733820\pi$
$264$	181.505	−	0.285764i	0.687521	−	0.00108244i
$265$	14.7063			0.0554955
$266$	3.37824	−	0.00177291i	0.0127002	−	6.66509e-6i
$267$			257.815i			0.965601i
$268$	0.0835960	+	79.6450i	0.000311925	+	0.297183i
$269$	−453.097			−1.68437			−0.842187	−	0.539185i	$-0.818732\pi$
$269$	−453.097			−1.68437			−0.842187	+	0.539185i	$0.818732\pi$
$270$	0.0632092	+	120.444i	0.000234108	+	0.446087i
$271$		−	495.422i		−	1.82812i	−0.405575	−	0.914062i	$-0.632929\pi$
$271$		−	495.422i		−	1.82812i	0.405575	−	0.914062i	$-0.367071\pi$
$272$	118.377	−	0.248499i	0.435210	−	0.000913601i
$273$	13.1981			0.0483448
$274$	−86.1539	+	0.0452138i	−0.314430	+	0.000165014i
$275$		−	37.7194i		−	0.137161i
$276$	−213.256	+	0.223835i	−0.772666	+	0.000810996i
$277$	454.982			1.64253			0.821267	−	0.570544i	$-0.193267\pi$
$277$	454.982			1.64253			0.821267	+	0.570544i	$0.193267\pi$
$278$	−0.140892	−	268.465i	−0.000506804	−	0.965703i
$279$		−	2.44459i		−	0.00876196i
$280$	−0.0109138	−	6.93200i	−3.89779e−5	−	0.0247572i
$281$	−420.948			−1.49804			−0.749018	−	0.662550i	$-0.769474\pi$
$281$	−420.948			−1.49804			−0.749018	+	0.662550i	$0.769474\pi$
$282$	514.105	−	0.269804i	1.82307	−	0.000956752i
$283$			173.151i			0.611840i	0.952057	+	0.305920i	$0.0989640\pi$
$283$			173.151i			0.611840i	−0.952057	+	0.305920i	$0.901036\pi$
$284$	−0.0828662	−	78.9497i	−0.000291782	−	0.277992i
$285$	29.3135			0.102854
$286$	0.0896693	+	170.863i	0.000313529	+	0.597422i
$287$		−	17.9847i		−	0.0626646i
$288$	1.44134	−	0.00378211i	0.00500466	−	1.31323e-5i
$289$	−234.261			−0.810591
$290$	−229.437	+	0.120409i	−0.791163	+	0.000415205i
$291$			88.7469i			0.304972i
$292$	−108.835	+	0.114234i	−0.372723	+	0.000391213i
$293$	−206.250			−0.703925			−0.351962	−	0.936014i	$-0.614486\pi$
$293$	−206.250			−0.703925			−0.351962	+	0.936014i	$0.614486\pi$
$294$	0.154204	+	293.831i	0.000524502	+	0.999427i
$295$		−	109.355i		−	0.370695i
$296$	434.370	−	0.683877i	1.46747	−	0.00231039i
$297$	−203.172			−0.684081
$298$	−531.569	+	0.278969i	−1.78379	+	0.000936137i
$299$		−	200.751i		−	0.671409i
$300$	−0.0631338	−	60.1499i	−0.000210446	−	0.200500i
$301$	31.5605			0.104852
$302$	−0.181907	−	346.620i	−0.000602341	−	1.14775i
$303$		−	67.6024i		−	0.223110i
$304$	0.146404	+	69.7422i	0.000481592	+	0.229415i
$305$	−15.0757			−0.0494286
$306$	0.666496		0.000349779i	0.00217809		1.14307e-6i
$307$		−	121.331i		−	0.395213i	−0.980281	−	0.197607i	$-0.936683\pi$
$307$		−	121.331i		−	0.395213i	0.980281	−	0.197607i	$-0.0633169\pi$
$308$	11.6933	−	0.0122734i	0.0379654	−	3.98488e-5i
$309$	452.588			1.46469
$310$	−0.127379	−	242.718i	−0.000410901	−	0.782961i
$311$			343.405i			1.10419i	0.833780	+	0.552097i	$0.186172\pi$
$311$			343.405i			1.10419i	−0.833780	+	0.552097i	$0.813828\pi$
$312$	0.428978	+	272.469i	0.00137493	+	0.873298i
$313$	−338.899			−1.08275			−0.541373	−	0.840783i	$-0.682095\pi$
$313$	−338.899			−1.08275			−0.541373	+	0.840783i	$0.682095\pi$
$314$	−199.380	+	0.104635i	−0.634969	+	0.000333234i
$315$		−	0.0390290i		−	0.000123902i
$316$	−0.254882	−	242.835i	−0.000806587	−	0.768466i
$317$	−316.984			−0.999949			−0.499975	−	0.866040i	$-0.666657\pi$
$317$	−316.984			−0.999949			−0.499975	+	0.866040i	$0.666657\pi$
$318$	0.0207611	+	39.5598i	6.52865e−5	+	0.124402i
$319$		−	387.029i		−	1.21326i
$320$	143.108	−	0.450622i	0.447211	−	0.00140819i
$321$	−300.798			−0.937066
$322$	−13.7388	+	0.00721019i	−0.0426672	+	2.23919e-5i
$323$			32.2497i			0.0998443i
$324$	−325.613	+	0.341766i	−1.00498	+	0.00105483i
$325$	56.6229			0.174224
$326$	−0.298491	−	568.768i	−0.000915618	−	1.74469i
$327$		−	72.8144i		−	0.222674i
$328$	371.286	−	0.584557i	1.13197	−	0.00178219i
$329$	33.1208			0.100671
$330$	101.465	−	0.0532490i	0.307469	−	0.000161361i
$331$			507.463i			1.53312i	0.642172	+	0.766561i	$0.278034\pi$
$331$			507.463i			1.53312i	−0.642172	+	0.766561i	$0.721966\pi$
$332$	0.390979	+	372.501i	0.00117765	+	1.12199i
$333$	2.44562			0.00734420
$334$	0.109377	+	208.416i	0.000327477	+	0.624000i
$335$			44.5230i			0.132904i
$336$	18.6470	−	0.0391440i	0.0554970	−	0.000116500i
$337$	−473.525			−1.40512			−0.702560	−	0.711625i	$-0.747960\pi$
$337$	−473.525			−1.40512			−0.702560	+	0.711625i	$0.747960\pi$
$338$	81.5074	−	0.0427753i	0.241146	−	0.000126554i
$339$			67.3028i			0.198533i
$340$	66.1750	−	0.0694577i	0.194632	−	0.000204287i
$341$	409.432			1.20068
$342$	0.000206073		0.392668i	6.02553e−7		0.00114815i
$343$			37.9179i			0.110548i
$344$	1.02581	+	651.552i	0.00298201	+	1.89405i
$345$	−119.214			−0.345547
$346$	−544.023	+	0.285505i	−1.57232	+	0.000825159i
$347$			262.939i			0.757750i	0.925448	+	0.378875i	$0.123689\pi$
$347$			262.939i			0.757750i	−0.925448	+	0.378875i	$0.876311\pi$
$348$	−0.647800	−	617.183i	−0.00186149	−	1.77351i
$349$	−241.561			−0.692151			−0.346076	−	0.938207i	$-0.612486\pi$
$349$	−241.561			−0.692151			−0.346076	+	0.938207i	$0.612486\pi$
$350$	−0.00203367	−	3.87511i	−5.81049e−6	−	0.0110717i
$351$		−	304.994i		−	0.868929i
$352$	0.633448	+	241.403i	0.00179957	+	0.685805i
$353$	−137.505			−0.389534			−0.194767	−	0.980850i	$-0.562395\pi$
$353$	−137.505			−0.389534			−0.194767	+	0.980850i	$0.562395\pi$
$354$	294.163	−	0.154378i	0.830970	−	0.000436096i
$355$		−	44.1343i		−	0.124322i
$356$	−342.897	+	0.359907i	−0.963193	+	0.00101097i
$357$	8.62261			0.0241530
$358$	−0.129222	−	246.229i	−0.000360955	−	0.687791i
$359$			157.804i			0.439565i	0.975549	+	0.219782i	$0.0705347\pi$
$359$			157.804i			0.439565i	−0.975549	+	0.219782i	$0.929465\pi$
$360$	0.805736	−	0.00126856i	0.00223816	−	3.52378e-6i
$361$	−19.0000			−0.0526316
$362$	−225.975	+	0.118593i	−0.624241	+	0.000327604i
$363$		−	192.750i		−	0.530992i
$364$	0.0184244	+	17.5536i	5.06165e−5	+	0.0482242i
$365$	−60.8408			−0.166687
$366$	−0.0212826	−	40.5535i	−5.81492e−5	−	0.110802i
$367$			502.556i			1.36936i	0.728843	+	0.684681i	$0.240058\pi$
$367$			502.556i			1.36936i	−0.728843	+	0.684681i	$0.759942\pi$
$368$	−0.595405	−	283.632i	−0.00161795	−	0.770739i
$369$	2.09044			0.00566515
$370$	242.820	−	0.127433i	0.656272	−	0.000344413i
$371$			2.54861i			0.00686956i
$372$	652.908	−	0.685297i	1.75513	−	0.00184220i
$373$	−133.294			−0.357355			−0.178678	−	0.983908i	$-0.557182\pi$
$373$	−133.294			−0.357355			−0.178678	+	0.983908i	$0.557182\pi$
$374$	0.0585829	+	111.628i	0.000156639	+	0.298471i
$375$		−	33.6248i		−	0.0896663i
$376$	1.07653	+	683.764i	0.00286310	+	1.81852i
$377$	580.994			1.54110
$378$	−20.8729	+	0.0109542i	−0.0552193	+	2.89793e-5i
$379$			40.4818i			0.106812i	0.998573	+	0.0534061i	$0.0170078\pi$
$379$			40.4818i			0.106812i	−0.998573	+	0.0534061i	$0.982992\pi$
$380$	0.0409212	+	38.9872i	0.000107687	+	0.102598i
$381$	390.088			1.02385
$382$	0.138082	+	263.113i	0.000361472	+	0.688776i
$383$			410.887i			1.07281i	0.843960	+	0.536406i	$0.180218\pi$
$383$			410.887i			1.07281i	−0.843960	+	0.536406i	$0.819782\pi$
$384$	1.41419	+	384.957i	0.00368280	+	1.00249i
$385$	6.53678			0.0169787
$386$	−373.894	+	0.196221i	−0.968637	+	0.000508344i
$387$			3.66841i			0.00947910i
$388$	−118.034	+	0.123889i	−0.304212	+	0.000319303i
$389$	−61.4593			−0.157993			−0.0789965	−	0.996875i	$-0.525172\pi$
$389$	−61.4593			−0.157993			−0.0789965	+	0.996875i	$0.525172\pi$
$390$	0.0799354	+	152.315i	0.000204963	+	0.390551i
$391$		−	131.155i		−	0.335435i
$392$	−390.798	+	0.615277i	−0.996934	+	0.00156958i
$393$	−81.7580			−0.208036
$394$	109.555	−	0.0574947i	0.278058	−	0.000145926i
$395$		−	135.749i		−	0.343669i
$396$	0.00142659	+	1.35917i	3.60250e−6	+	0.00343224i
$397$	602.032			1.51645			0.758227	−	0.651991i	$-0.226066\pi$
$397$	602.032			1.51645			0.758227	+	0.651991i	$0.226066\pi$
$398$	0.0578770	+	110.283i	0.000145420	+	0.277094i
$399$			5.08003i			0.0127319i
$400$	79.9998	−	0.167937i	0.200000	−	0.000419842i
$401$	336.035			0.837993			0.418997	−	0.907988i	$-0.362382\pi$
$401$	336.035			0.837993			0.418997	+	0.907988i	$0.362382\pi$
$402$	−119.766	+	0.0628537i	−0.297926	+	0.000156352i
$403$			614.624i			1.52512i
$404$	89.9118	−	0.0943720i	0.222554	−	0.000233594i
$405$	−182.023			−0.449441
$406$	−0.0208670	−	39.7615i	−5.13965e−5	−	0.0979348i
$407$			409.605i			1.00640i
$408$	0.280261	+	178.010i	0.000686913	+	0.436299i
$409$	571.085			1.39630			0.698148	−	0.715953i	$-0.254008\pi$
$409$	571.085			1.39630			0.698148	+	0.715953i	$0.254008\pi$
$410$	207.556	−	0.108926i	0.506233	−	0.000265673i
$411$		−	129.554i		−	0.315216i
$412$	0.631806	+	601.946i	0.00153351	+	1.46103i
$413$	18.9512			0.0458868
$414$	−0.000838071	−	1.59692i	−2.02433e−6	−	0.00385731i
$415$			208.234i			0.501770i
$416$	−362.386	+	0.950908i	−0.871119	+	0.00228584i
$417$	403.705			0.968117
$418$	−65.7660	+	0.0345142i	−0.157335	+	8.25699e-5i
$419$			265.623i			0.633945i	0.948435	+	0.316972i	$0.102666\pi$
$419$			265.623i			0.633945i	−0.948435	+	0.316972i	$0.897334\pi$
$420$	10.4240	−	0.0109411i	0.0248190	−	2.60502e-5i
$421$	8.21063			0.0195027			0.00975134	−	0.999952i	$-0.496896\pi$
$421$	8.21063			0.0195027			0.00975134	+	0.999952i	$0.496896\pi$
$422$	−0.104793	−	199.680i	−0.000248324	−	0.473175i
$423$			3.84977i			0.00910112i
$424$	−52.6148	+	0.0828374i	−0.124092	+	0.000195371i
$425$	36.9930			0.0870423
$426$	118.721	−	0.0623050i	0.278687	−	0.000146256i
$427$		−	2.61263i		−	0.00611857i
$428$	−0.419910	−	400.064i	−0.000981098	−	0.934729i
$429$	−256.935			−0.598915
$430$	0.191149	+	364.229i	0.000444532	+	0.847045i
$431$		−	182.357i		−	0.423103i	−0.977367	−	0.211551i	$-0.932148\pi$
$431$		−	182.357i		−	0.423103i	0.977367	−	0.211551i	$-0.0678516\pi$
$432$	−0.904576	−	430.911i	−0.00209393	−	0.997480i
$433$	−511.669			−1.18168			−0.590842	−	0.806787i	$-0.701204\pi$
$433$	−511.669			−1.18168			−0.590842	+	0.806787i	$0.701204\pi$
$434$	42.0631	−	0.0220749i	0.0969196	−	5.08637e-5i
$435$		−	345.016i		−	0.793140i
$436$	96.8438	−	0.101648i	0.222119	−	0.000233137i
$437$	77.2703			0.176820
$438$	−0.0858898	−	163.661i	−0.000196095	−	0.373655i
$439$		−	746.448i		−	1.70034i	−0.526510	−	0.850169i	$-0.676500\pi$
$439$		−	746.448i		−	1.70034i	0.526510	−	0.850169i	$-0.323500\pi$
$440$	0.212465	+	134.949i	0.000482875	+	0.306702i
$441$	−2.20030			−0.00498934
$442$	−167.572	+	0.0879424i	−0.379122	+	0.000198965i
$443$			194.603i			0.439284i	0.975580	+	0.219642i	$0.0704890\pi$
$443$			194.603i			0.439284i	−0.975580	+	0.219642i	$0.929511\pi$
$444$	0.685586	+	653.184i	0.00154411	+	1.47113i
$445$	−191.685			−0.430753
$446$	−0.176069	−	335.495i	−0.000394773	−	0.752231i
$447$		−	799.346i		−	1.78825i
$448$	0.0780929	+	24.8006i	0.000174314	+	0.0553585i
$449$	238.510			0.531202			0.265601	−	0.964083i	$-0.414430\pi$
$449$	238.510			0.531202			0.265601	+	0.964083i	$0.414430\pi$
$450$	0.450421		0.000236382i	0.00100093		5.25294e-7i
$451$			350.118i			0.776315i
$452$	−89.5132	+	0.0939537i	−0.198038	+	0.000207862i
$453$	521.229			1.15062
$454$	−0.155837	−	296.943i	−0.000343253	−	0.654060i
$455$			9.81277i			0.0215665i
$456$	−104.875	+	0.165116i	−0.229989	+	0.000362097i
$457$	−109.140			−0.238818			−0.119409	−	0.992845i	$-0.538100\pi$
$457$	−109.140			−0.238818			−0.119409	+	0.992845i	$0.538100\pi$
$458$	212.868	−	0.111714i	0.464778	−	0.000243917i
$459$		−	199.259i		−	0.434116i
$460$	−0.166421	−	158.555i	−0.000361784	−	0.344685i
$461$	357.920			0.776400			0.388200	−	0.921575i	$-0.373097\pi$
$461$	357.920			0.776400			0.388200	+	0.921575i	$0.373097\pi$
$462$	0.00922807	+	17.5839i	1.99742e−5	+	0.0380603i
$463$		−	723.225i		−	1.56204i	−0.624505	−	0.781021i	$-0.714699\pi$
$463$		−	723.225i		−	1.56204i	0.624505	−	0.781021i	$-0.285301\pi$
$464$	820.858	−	1.72316i	1.76909	−	0.00371370i
$465$	364.987			0.784918
$466$	14.7441	−	0.00773775i	0.0316397	−	1.66046e-5i
$467$			621.847i			1.33158i	0.746140	+	0.665789i	$0.231905\pi$
$467$			621.847i			1.33158i	−0.746140	+	0.665789i	$0.768095\pi$
$468$	−2.04033	+	0.00214155i	−0.00435968	+	4.57595e-6i
$469$	−7.71584			−0.0164517
$470$	0.200599	+	382.236i	0.000426806	+	0.813268i
$471$		−	299.818i		−	0.636556i
$472$	0.615972	+	391.240i	0.00130503	+	0.828898i
$473$	−614.405			−1.29895
$474$	365.163	−	0.191639i	0.770387	−	0.000404302i
$475$			21.7945i			0.0458831i
$476$	0.0120370	+	11.4681i	2.52879e−5	+	0.0240927i
$477$	−0.296236			−0.000621039
$478$	0.371225	+	707.361i	0.000776622	+	1.47984i
$479$		−	95.2003i		−	0.198748i	−0.995050	−	0.0993740i	$-0.968316\pi$
$479$		−	95.2003i		−	0.198748i	0.995050	−	0.0993740i	$-0.0316840\pi$
$480$	0.564685	+	215.198i	0.00117643	+	0.448330i
$481$	−614.884			−1.27834
$482$	−482.722	+	0.253334i	−1.00150	+	0.000525589i
$483$		−	20.6598i		−	0.0427739i
$484$	256.359	−	0.269076i	0.529668	−	0.000555943i
$485$	−65.9831			−0.136048
$486$	−0.00255290	−	4.86450i	−5.25289e−6	−	0.0100093i
$487$		−	492.206i		−	1.01069i	−0.862917	−	0.505345i	$-0.831365\pi$
$487$		−	492.206i		−	1.01069i	0.862917	−	0.505345i	$-0.168635\pi$
$488$	53.9365	−	0.0849182i	0.110526	−	0.000174013i
$489$	855.285			1.74905
$490$	−218.463	+	0.114650i	−0.445843	+	0.000233980i
$491$		−	204.539i		−	0.416577i	−0.978067	−	0.208289i	$-0.933211\pi$
$491$		−	204.539i		−	0.416577i	0.978067	−	0.208289i	$-0.0667893\pi$
$492$	0.586018	+	558.322i	0.00119109	+	1.13480i
$493$	379.575			0.769930
$494$	−0.0518114	−	98.7255i	−0.000104881	−	0.199849i
$495$			0.759798i			0.00153495i
$496$	1.82290	+	868.372i	0.00367520	+	1.75075i
$497$	7.64848			0.0153893
$498$	−560.148	+	0.293967i	−1.12479	+	0.000590296i
$499$		−	370.398i		−	0.742281i	−0.928577	−	0.371141i	$-0.878967\pi$
$499$		−	370.398i		−	0.742281i	0.928577	−	0.371141i	$-0.121033\pi$
$500$	44.7213	−	0.0469398i	0.0894427	−	9.38796e-5i
$501$	−313.405			−0.625559
$502$	−0.253550	−	483.134i	−0.000505080	−	0.962418i
$503$		−	78.7848i		−	0.156630i	−0.996929	−	0.0783149i	$-0.975046\pi$
$503$		−	78.7848i		−	0.156630i	0.996929	−	0.0783149i	$-0.0249540\pi$
$504$	0.000219842		0.139634i	4.36194e−7		0.000277052i
$505$	50.2622			0.0995292
$506$	267.461	−	0.140365i	0.528580	−	0.000277400i
$507$			122.567i			0.241749i
$508$	0.544557	+	518.820i	0.00107196	+	1.02130i
$509$	−660.274			−1.29720			−0.648599	−	0.761130i	$-0.724645\pi$
$509$	−660.274			−1.29720			−0.648599	+	0.761130i	$0.724645\pi$
$510$	0.0522235	+	99.5106i	0.000102399	+	0.195119i
$511$		−	10.5437i		−	0.0206335i
$512$	−511.994	+	2.41828i	−0.999989	+	0.00472321i
$513$	117.394			0.228838
$514$	−391.978	+	0.205712i	−0.762604	+	0.000400217i
$515$			336.498i			0.653394i
$516$	−979.772	+	1.02837i	−1.89878	+	0.00199297i
$517$	−644.780			−1.24716
$518$	0.0220842	+	42.0809i	4.26335e−5	+	0.0812372i
$519$		−	818.074i		−	1.57625i
$520$	−202.580	+	0.318944i	−0.389577	+	0.000613355i
$521$	528.295			1.01400			0.507000	−	0.861946i	$-0.330754\pi$
$521$	528.295			1.01400			0.507000	+	0.861946i	$0.330754\pi$
$522$	4.62165	−	0.00242546i	0.00885374	−	4.64647e-6i
$523$		−	461.734i		−	0.882856i	−0.897297	−	0.441428i	$-0.854472\pi$
$523$		−	461.734i		−	0.882856i	0.897297	−	0.441428i	$-0.145528\pi$
$524$	−0.114133	−	108.739i	−0.000217811	−	0.207517i
$525$	5.82720			0.0110994
$526$	−0.409719	−	780.711i	−0.000778934	−	1.48424i
$527$			401.547i			0.761948i
$528$	−363.011	+	0.762037i	−0.687520	+	0.00144325i
$529$	214.752			0.405959
$530$	−29.4126	+	0.0154358i	−0.0554955	+	2.91242e-5i
$531$			2.20278i			0.00414837i
$532$	−6.75649	+	0.00709165i	−0.0127002	+	1.33302e-5i
$533$	−525.584			−0.986086
$534$	−0.270605	−	515.631i	−0.000506750	−	0.965601i
$535$		−	223.643i		−	0.418024i
$536$	−0.250788	−	159.290i	−0.000467888	−	0.297183i
$537$	370.267			0.689510
$538$	906.193	−	0.475573i	1.68437	−	0.000883965i
$539$		−	368.517i		−	0.683706i
$540$	−0.252837	−	240.887i	−0.000468216	−	0.446087i
$541$	453.696			0.838625			0.419313	−	0.907842i	$-0.362271\pi$
$541$	453.696			0.838625			0.419313	+	0.907842i	$0.362271\pi$
$542$	0.519998	+	990.843i	0.000959405	+	1.82812i
$543$		−	339.810i		−	0.625801i
$544$	−236.754	+	0.621248i	−0.435210	+	0.00114200i
$545$	54.1374			0.0993346
$546$	−26.3962	+	0.0138528i	−0.0483448	+	2.53715e-5i
$547$		−	162.454i		−	0.296990i	−0.988913	−	0.148495i	$-0.952557\pi$
$547$		−	162.454i		−	0.296990i	0.988913	−	0.148495i	$-0.0474429\pi$
$548$	172.308	−	0.180855i	0.314430	−	0.000330028i
$549$	0.303677			0.000553145
$550$	0.0395905	+	75.4388i	7.19828e−5	+	0.137161i
$551$			223.628i			0.405858i
$552$	426.512	−	0.671504i	0.772666	−	0.00121649i
$553$	23.5254			0.0425413
$554$	−909.964	+	0.477552i	−1.64253	+	0.000862007i
$555$			365.141i			0.657912i
$556$	0.563566	+	536.931i	0.00101361	+	0.965702i
$557$	−1010.33			−1.81389			−0.906943	−	0.421254i	$-0.861590\pi$
$557$	−1010.33			−1.81389			−0.906943	+	0.421254i	$0.861590\pi$
$558$	0.00256585	+	4.88917i	4.59830e−6	+	0.00876196i
$559$		−	922.321i		−	1.64995i
$560$	0.0291035	+	13.8640i	5.19706e−5	+	0.0247571i
$561$	−167.861			−0.299217
$562$	841.896	−	0.441830i	1.49804	−	0.000786174i
$563$			603.448i			1.07184i	0.844268	+	0.535922i	$0.180036\pi$
$563$			603.448i			1.07184i	−0.844268	+	0.535922i	$0.819964\pi$
$564$	−1028.21	+	1.07922i	−1.82307	+	0.00191350i
$565$	−50.0395			−0.0885654
$566$	−0.181740	−	346.301i	−0.000321096	−	0.611840i
$567$		−	31.5447i		−	0.0556344i
$568$	0.248598	+	157.899i	0.000437673	+	0.277992i
$569$	472.683			0.830726			0.415363	−	0.909656i	$-0.363655\pi$
$569$	472.683			0.830726			0.415363	+	0.909656i	$0.363655\pi$
$570$	−58.6269	+	0.0307676i	−0.102854	+	5.39782e-5i
$571$			1082.79i			1.89630i	0.317818	+	0.948152i	$0.397050\pi$
$571$			1082.79i			1.89630i	−0.317818	+	0.948152i	$0.602950\pi$
$572$	−0.358677	−	341.725i	−0.000627058	−	0.597422i
$573$	−395.655			−0.690498
$574$	0.0188769	+	35.9695i	3.28866e−5	+	0.0626646i
$575$		−	88.6352i		−	0.154148i
$576$	−2.88268	+	0.00907706i	−0.00500465	+	1.57588e-5i
$577$	−669.986			−1.16115			−0.580577	−	0.814205i	$-0.697173\pi$
$577$	−669.986			−1.16115			−0.580577	+	0.814205i	$0.697173\pi$
$578$	468.522	−	0.245882i	0.810591	−	0.000425401i
$579$		−	562.243i		−	0.971058i
$580$	458.874	−	0.481638i	0.791163	−	0.000830410i
$581$	−36.0871			−0.0621120
$582$	−0.0931493	−	177.494i	−0.000160050	−	0.304972i
$583$		−	49.6151i		−	0.0851031i
$584$	217.670	−	0.342703i	0.372723	−	0.000586819i
$585$	−1.14058			−0.00194971
$586$	412.500	−	0.216481i	0.703925	−	0.000369422i
$587$			667.108i			1.13647i	0.822866	+	0.568235i	$0.192374\pi$
$587$			667.108i			1.13647i	−0.822866	+	0.568235i	$0.807626\pi$
$588$	−0.616815	−	587.663i	−0.00104900	−	0.999426i
$589$	−236.572			−0.401651
$590$	0.114780	+	218.710i	0.000194542	+	0.370695i
$591$			164.743i			0.278753i
$592$	−868.739	+	1.82367i	−1.46746	+	0.00308053i
$593$	−626.541			−1.05656			−0.528280	−	0.849070i	$-0.677163\pi$
$593$	−626.541			−1.05656			−0.528280	+	0.849070i	$0.677163\pi$
$594$	406.344	−	0.213251i	0.684081	−	0.000359008i
$595$			6.41089i			0.0107746i
$596$	1063.14	−	1.11588i	1.78379	−	0.00187227i
$597$	−165.838			−0.277786
$598$	0.210710	+	401.503i	0.000352358	+	0.671409i
$599$		−	463.799i		−	0.774290i	−0.922019	−	0.387145i	$-0.873461\pi$
$599$		−	463.799i		−	0.774290i	0.922019	−	0.387145i	$-0.126539\pi$
$600$	0.189401	+	120.300i	0.000315669	+	0.200500i
$601$	521.233			0.867277			0.433638	−	0.901087i	$-0.357230\pi$
$601$	521.233			0.867277			0.433638	+	0.901087i	$0.357230\pi$
$602$	−63.1210	+	0.0331261i	−0.104852	+	5.50268e-5i
$603$		−	0.896845i		−	0.00148731i
$604$	0.727628	+	693.239i	0.00120468	+	1.14775i
$605$	143.309			0.236875
$606$	0.0709559	+	135.205i	0.000117089	+	0.223110i
$607$		−	711.337i		−	1.17189i	−0.810351	−	0.585945i	$-0.800724\pi$
$607$		−	711.337i		−	1.17189i	0.810351	−	0.585945i	$-0.199276\pi$
$608$	−0.366010	−	139.484i	−0.000601990	−	0.229415i
$609$	59.7914			0.0981796
$610$	30.1514	−	0.0158236i	0.0494286	−	2.59403e-5i
$611$		−	967.920i		−	1.58416i
$612$	−1.33299	+	0.00139912i	−0.00217809	+	2.28614e-6i
$613$	976.843			1.59355			0.796773	−	0.604279i	$-0.206539\pi$
$613$	976.843			1.59355			0.796773	+	0.604279i	$0.206539\pi$
$614$	0.127349	+	242.661i	0.000207409	+	0.395213i
$615$			312.112i			0.507499i
$616$	−23.3867	+	0.0368202i	−0.0379654	+	5.97731e-5i
$617$	772.584			1.25216			0.626081	−	0.779758i	$-0.284658\pi$
$617$	772.584			1.25216			0.626081	+	0.779758i	$0.284658\pi$
$618$	−905.176	+	0.475039i	−1.46469	+	0.000768672i
$619$		−	166.554i		−	0.269069i	−0.990909	−	0.134535i	$-0.957046\pi$
$619$		−	166.554i		−	0.269069i	0.990909	−	0.134535i	$-0.0429539\pi$
$620$	0.509517	+	485.436i	0.000821801	+	0.782961i
$621$	−477.425			−0.768800
$622$	−0.360440	−	686.809i	−0.000579485	−	1.10419i
$623$		−	33.2191i		−	0.0533212i
$624$	−1.14394	−	544.938i	−0.00183324	−	0.873297i
$625$	25.0000			0.0400000
$626$	677.798	−	0.355711i	1.08275	−	0.000568228i
$627$		−	98.8956i		−	0.157728i
$628$	398.760	−	0.418541i	0.634968	−	0.000666467i
$629$	−401.716			−0.638659
$630$	4.09651e−5		0.0780580i	6.50240e−8		0.000123902i
$631$		−	395.145i		−	0.626221i	−0.949717	−	0.313110i	$-0.898629\pi$
$631$		−	395.145i		−	0.626221i	0.949717	−	0.313110i	$-0.101371\pi$
$632$	0.764644	+	485.670i	0.00120988	+	0.768466i
$633$	300.269			0.474358
$634$	633.968	−	0.332708i	0.999949	−	0.000524777i
$635$			290.029i			0.456739i
$636$	−0.0830444	−	79.1196i	−0.000130573	−	0.124402i
$637$	553.204			0.868453
$638$	0.406228	+	774.058i	0.000636722	+	1.21326i
$639$			0.889015i			0.00139126i
$640$	−286.215	+	1.05145i	−0.447211	+	0.00164289i
$641$	−757.579			−1.18187			−0.590935	−	0.806719i	$-0.701241\pi$
$641$	−757.579			−1.18187			−0.590935	+	0.806719i	$0.701241\pi$
$642$	601.596	−	0.315720i	0.937066	−	0.000491775i
$643$			519.503i			0.807936i	0.914773	+	0.403968i	$0.132369\pi$
$643$			519.503i			0.807936i	−0.914773	+	0.403968i	$0.867631\pi$
$644$	27.4777	−	0.0288408i	0.0426672	−	4.47838e-5i
$645$	−547.709			−0.849162
$646$	−0.0338495	−	64.4994i	−5.23986e−5	−	0.0998443i
$647$			201.590i			0.311576i	0.987791	+	0.155788i	$0.0497917\pi$
$647$			201.590i			0.311576i	−0.987791	+	0.155788i	$0.950208\pi$
$648$	651.226	−	1.02530i	1.00498	−	0.00158225i
$649$	−368.934			−0.568465
$650$	−113.246	+	0.0594318i	−0.174224	+	9.14335e-5i
$651$			63.2523i			0.0971618i
$652$	1.19397	+	1137.54i	0.00183124	+	1.74469i
$653$	−279.933			−0.428688			−0.214344	−	0.976758i	$-0.568761\pi$
$653$	−279.933			−0.428688			−0.214344	+	0.976758i	$0.568761\pi$
$654$	0.0764265	+	145.629i	0.000116860	+	0.222674i
$655$		−	60.7869i		−	0.0928045i
$656$	−742.572	+	1.55882i	−1.13197	+	0.00237625i
$657$	1.22554			0.00186536
$658$	−66.2416	+	0.0347638i	−0.100671	+	5.28326e-5i
$659$			471.426i			0.715365i	0.933843	+	0.357683i	$0.116433\pi$
$659$			471.426i			0.715365i	−0.933843	+	0.357683i	$0.883567\pi$
$660$	−202.929	+	0.212996i	−0.307469	+	0.000322721i
$661$	−517.233			−0.782501			−0.391250	−	0.920284i	$-0.627957\pi$
$661$	−517.233			−0.782501			−0.391250	+	0.920284i	$0.627957\pi$
$662$	−0.532637	−	1014.93i	−0.000804587	−	1.53312i
$663$		−	251.986i		−	0.380070i
$664$	−1.17294	−	745.001i	−0.00176647	−	1.12199i
$665$	−3.77699			−0.00567969
$666$	−4.89124	+	0.00256694i	−0.00734420	+	3.85426e-6i
$667$		−	909.463i		−	1.36351i
$668$	−0.437509	−	416.832i	−0.000654954	−	0.624000i
$669$	504.500			0.754111
$670$	−0.0467316	−	89.0459i	−6.97486e−5	−	0.132904i
$671$			50.8614i			0.0757994i
$672$	−37.2939	+	0.0978601i	−0.0554969	+	0.000145625i
$673$	−310.165			−0.460869			−0.230435	−	0.973088i	$-0.574015\pi$
$673$	−310.165			−0.460869			−0.230435	+	0.973088i	$0.574015\pi$
$674$	947.050	−	0.497015i	1.40512	−	0.000737411i
$675$		−	134.660i		−	0.199496i
$676$	−163.015	+	0.171101i	−0.241146	+	0.000253108i
$677$	859.721			1.26990			0.634949	−	0.772554i	$-0.281021\pi$
$677$	859.721			1.26990			0.634949	+	0.772554i	$0.281021\pi$
$678$	−0.0706414	−	134.605i	−0.000104191	−	0.198533i
$679$		−	11.4349i		−	0.0168408i
$680$	−132.350	+	0.208373i	−0.194632	+	0.000306431i
$681$	446.528			0.655695
$682$	−818.864	+	0.429743i	−1.20068	+	0.000630121i
$683$			883.439i			1.29347i	0.762716	+	0.646734i	$0.223866\pi$
$683$			883.439i			1.29347i	−0.762716	+	0.646734i	$0.776134\pi$
$684$	−0.000824293	−	0.785335i	−1.20511e−6	−	0.00114815i
$685$	96.3230			0.140617
$686$	−0.0397989	−	75.8358i	−5.80159e−5	−	0.110548i
$687$			320.100i			0.465939i
$688$	−2.73549	−	1303.10i	−0.00397601	−	1.89405i
$689$	74.4803			0.108099
$690$	238.427	−	0.125127i	0.345547	−	0.000181344i
$691$			302.631i			0.437961i	0.975729	+	0.218980i	$0.0702731\pi$
$691$			302.631i			0.437961i	−0.975729	+	0.218980i	$0.929727\pi$
$692$	1088.05	−	1.14202i	1.57232	−	0.00165032i
$693$	−0.131673			−0.000190005
$694$	−0.275983	−	525.878i	−0.000397669	−	0.757749i
$695$			300.153i			0.431876i
$696$	1.94340	+	1234.37i	0.00279224	+	1.77351i
$697$	−343.375			−0.492647
$698$	483.122	−	0.253544i	0.692151	−	0.000363243i
$699$			22.1714i			0.0317188i
$700$	0.00813468	+	7.75022i	1.16210e−5	+	0.0110717i
$701$	−597.800			−0.852782			−0.426391	−	0.904539i	$-0.640215\pi$
$701$	−597.800			−0.852782			−0.426391	+	0.904539i	$0.640215\pi$
$702$	0.320124	+	609.988i	0.000456017	+	0.868929i
$703$		−	236.672i		−	0.336660i
$704$	−1.52027	−	482.806i	−0.00215948	−	0.685804i
$705$	−574.787			−0.815301
$706$	275.011	−	0.144326i	0.389534	−	0.000204428i
$707$			8.71046i			0.0123203i
$708$	−588.327	+	0.617512i	−0.830970	+	0.000872192i
$709$	−998.564			−1.40841			−0.704206	−	0.709996i	$-0.748697\pi$
$709$	−998.564			−1.40841			−0.704206	+	0.709996i	$0.748697\pi$
$710$	0.0463236	+	88.2685i	6.52445e−5	+	0.124322i
$711$			2.73445i			0.00384593i
$712$	685.793	−	1.07972i	0.963192	−	0.00151646i
$713$	962.106			1.34938
$714$	−17.2452	+	0.00905035i	−0.0241530	+	1.26756e-5i
$715$		−	191.030i		−	0.267175i
$716$	0.516888	+	492.458i	0.000721910	+	0.687791i
$717$	−1063.69			−1.48353
$718$	−0.165632	−	315.607i	−0.000230685	−	0.439565i
$719$			68.8759i			0.0957940i	0.998852	+	0.0478970i	$0.0152519\pi$
$719$			68.8759i			0.0957940i	−0.998852	+	0.0478970i	$0.984748\pi$
$720$	−1.61147	+	0.00338283i	−0.00223815	+	4.69837e-6i
$721$	−58.3152			−0.0808810
$722$	38.0000	−	0.0199425i	0.0526316	−	2.76212e-5i
$723$		−	725.893i		−	1.00400i
$724$	451.950	−	0.474370i	0.624241	−	0.000655207i
$725$	256.519			0.353819
$726$	0.202312	+	385.500i	0.000278666	+	0.530992i
$727$			998.148i			1.37297i	0.727145	+	0.686484i	$0.240847\pi$
$727$			998.148i			1.37297i	−0.727145	+	0.686484i	$0.759153\pi$
$728$	−0.0552732	−	35.1072i	−7.59247e−5	−	0.0482242i
$729$	−725.315			−0.994945
$730$	121.682	−	0.0638589i	0.166687	−	8.74779e-5i
$731$		−	602.572i		−	0.824312i
$732$	0.0851305	+	81.1070i	0.000116298	+	0.110802i
$733$	584.823			0.797849			0.398924	−	0.916984i	$-0.369384\pi$
$733$	584.823			0.797849			0.398924	+	0.916984i	$0.369384\pi$
$734$	−0.527486	−	1005.11i	−0.000718645	−	1.36936i
$735$		−	328.514i		−	0.446957i
$736$	1.48851	+	567.263i	0.00202243	+	0.770738i
$737$	150.208			0.203810
$738$	−4.18088	+	0.00219414i	−0.00566515	+	2.97309e-6i
$739$			454.008i			0.614355i	0.951652	+	0.307177i	$0.0993845\pi$
$739$			454.008i			0.614355i	−0.951652	+	0.307177i	$0.900615\pi$
$740$	−485.641	+	0.509732i	−0.656271	+	0.000688827i
$741$	148.458			0.200349
$742$	−0.00267504	−	5.09722i	−3.60517e−6	−	0.00686956i
$743$		−	791.498i		−	1.06527i	−0.846344	−	0.532636i	$-0.821201\pi$
$743$		−	791.498i		−	1.06527i	0.846344	−	0.532636i	$-0.178799\pi$
$744$	−1305.82	+	2.05589i	−1.75513	+	0.00276329i
$745$	594.312			0.797734
$746$	266.587	−	0.139906i	0.357355	−	0.000187541i
$747$		−	4.19455i		−	0.00561520i
$748$	−0.234331	−	223.256i	−0.000313277	−	0.298471i
$749$	38.7574			0.0517455
$750$	0.0352929	+	67.2497i	4.70571e−5	+	0.0896662i
$751$			1497.38i			1.99385i	0.0783357	+	0.996927i	$0.475039\pi$
$751$			1497.38i			1.99385i	−0.0783357	+	0.996927i	$0.524961\pi$
$752$	−2.87073	−	1367.53i	−0.00381747	−	1.81852i
$753$	726.512			0.964824
$754$	−1161.99	+	0.609815i	−1.54110	+	0.000808773i
$755$			387.532i			0.513288i
$756$	41.7458	−	0.0438167i	0.0552193	−	5.79586e-5i
$757$	−5.68429			−0.00750897			−0.00375449	−	0.999993i	$-0.501195\pi$
$757$	−5.68429			−0.00750897			−0.00375449	+	0.999993i	$0.501195\pi$
$758$	−0.0424900	−	80.9636i	−5.60554e−5	−	0.106812i
$759$			402.195i			0.529901i
$760$	−0.122764	−	77.9743i	−0.000161531	−	0.102598i
$761$	674.465			0.886287			0.443144	−	0.896451i	$-0.353863\pi$
$761$	674.465			0.886287			0.443144	+	0.896451i	$0.353863\pi$
$762$	−780.175	+	0.409438i	−1.02385	+	0.000537321i
$763$			9.38202i			0.0122962i
$764$	−0.552329	−	526.225i	−0.000722944	−	0.688776i
$765$	−0.745165			−0.000974072
$766$	−0.431269	−	821.773i	−0.000563015	−	1.07281i
$767$		−	553.829i		−	0.722072i
$768$	−3.23244	−	769.913i	−0.00420891	−	1.00249i
$769$	143.205			0.186223			0.0931113	−	0.995656i	$-0.470319\pi$
$769$	143.205			0.186223			0.0931113	+	0.995656i	$0.470319\pi$
$770$	−13.0736	+	0.00686105i	−0.0169787	+	8.91046e-6i
$771$		−	589.437i		−	0.764510i
$772$	747.788	−	0.784883i	0.968637	−	0.00101669i
$773$	1429.97			1.84990			0.924948	−	0.380093i	$-0.124108\pi$
$773$	1429.97			1.84990			0.924948	+	0.380093i	$0.124108\pi$
$774$	−0.00385039	−	7.33682i	−4.97466e−6	−	0.00947910i
$775$			271.367i			0.350151i
$776$	236.068	−	0.371668i	0.304211	−	0.000478954i
$777$	−63.2791			−0.0814402
$778$	122.919	−	0.0645080i	0.157993	−	8.29152e-5i
$779$		−	202.300i		−	0.259692i
$780$	−0.319742	−	304.630i	−0.000409925	−	0.390551i
$781$	−148.897			−0.190649
$782$	0.137661	+	262.310i	0.000176037	+	0.335435i
$783$		−	1381.71i		−	1.76464i
$784$	781.596	−	1.64074i	0.996933	−	0.00209278i
$785$	222.914			0.283967
$786$	163.516	−	0.0858138i	0.208036	−	0.000109178i
$787$		−	650.387i		−	0.826413i	−0.910637	−	0.413207i	$-0.864409\pi$
$787$		−	650.387i		−	0.826413i	0.910637	−	0.413207i	$-0.135591\pi$
$788$	−219.110	+	0.229979i	−0.278058	+	0.000291851i
$789$	1173.99			1.48795
$790$	0.142483	+	271.498i	0.000180358	+	0.343669i
$791$		−	8.67185i		−	0.0109631i
$792$	−0.00427977	−	2.71833i	−5.40376e−6	−	0.00343224i
$793$	−76.3512			−0.0962814
$794$	−1204.06	+	0.631896i	−1.51645	+	0.000795839i
$795$		−	44.2292i		−	0.0556342i
$796$	−0.231508	−	220.566i	−0.000290839	−	0.277094i
$797$	397.368			0.498580			0.249290	−	0.968429i	$-0.419803\pi$
$797$	397.368			0.498580			0.249290	+	0.968429i	$0.419803\pi$
$798$	−0.00533203	−	10.1601i	−6.68175e−6	−	0.0127319i
$799$		−	632.362i		−	0.791442i
$800$	−159.999	+	0.419842i	−0.199999	+	0.000524803i
$801$	3.86120			0.00482047
$802$	−672.071	+	0.352705i	−0.837993	+	0.000439782i
$803$			205.260i			0.255617i
$804$	239.532	−	0.251415i	0.297926	−	0.000312705i
$805$	15.3605			0.0190814
$806$	−0.645113	−	1229.25i	−0.000800389	−	1.52512i
$807$			1362.69i			1.68858i
$808$	−179.823	+	0.283116i	−0.222554	+	0.000350391i
$809$	−1323.31			−1.63574			−0.817870	−	0.575403i	$-0.804845\pi$
$809$	−1323.31			−1.63574			−0.817870	+	0.575403i	$0.804845\pi$
$810$	364.047	−	0.191053i	0.449440	−	0.000235868i
$811$			421.967i			0.520305i	0.965568	+	0.260152i	$0.0837728\pi$
$811$			421.967i			0.520305i	−0.965568	+	0.260152i	$0.916227\pi$
$812$	0.0834679	+	79.5230i	0.000102793	+	0.0979348i
$813$	−1489.98			−1.83269
$814$	−0.429924	−	819.210i	−0.000528162	−	1.00640i
$815$			635.902i			0.780248i
$816$	−0.747361	−	356.019i	−0.000915884	−	0.436298i
$817$	355.007			0.434525
$818$	−1142.17	+	0.599415i	−1.39630	+	0.000732781i
$819$		−	0.197663i		−	0.000241347i
$820$	−415.111	+	0.435703i	−0.506233	+	0.000531346i
$821$	−909.735			−1.10808			−0.554041	−	0.832490i	$-0.686915\pi$
$821$	−909.735			−1.10808			−0.554041	+	0.832490i	$0.686915\pi$
$822$	0.135980	+	259.108i	0.000165426	+	0.315216i
$823$		−	192.585i		−	0.234004i	−0.993132	−	0.117002i	$-0.962672\pi$
$823$		−	192.585i		−	0.234004i	0.993132	−	0.117002i	$-0.0373283\pi$
$824$	−1.89542	−	1203.89i	−0.00230027	−	1.46103i
$825$	−113.441			−0.137504
$826$	−37.9025	+	0.0198914i	−0.0458868	+	2.40815e-5i
$827$		−	535.109i		−	0.647049i	−0.946220	−	0.323524i	$-0.895132\pi$
$827$		−	535.109i		−	0.647049i	0.946220	−	0.323524i	$-0.104868\pi$
$828$	0.00335228	+	3.19385i	4.04865e−6	+	0.00385730i
$829$	−826.603			−0.997109			−0.498554	−	0.866858i	$-0.666136\pi$
$829$	−826.603			−0.997109			−0.498554	+	0.866858i	$0.666136\pi$
$830$	−0.218564	−	416.469i	−0.000263330	−	0.501769i
$831$		−	1368.36i		−	1.64664i
$832$	724.770	−	2.28218i	0.871118	−	0.00274300i
$833$	361.420			0.433878
$834$	−807.409	+	0.423731i	−0.968116	+	0.000508071i
$835$		−	233.016i		−	0.279061i
$836$	131.532	−	0.138057i	0.157335	−	0.000165140i
$837$	1461.69			1.74635
$838$	−0.278799	−	531.245i	−0.000332696	−	0.633945i
$839$			386.874i			0.461113i	0.973059	+	0.230557i	$0.0740547\pi$
$839$			386.874i			0.461113i	−0.973059	+	0.230557i	$0.925945\pi$
$840$	−20.8480	+	0.0328233i	−0.0248190	+	3.90753e-5i
$841$	1791.07			2.12969
$842$	−16.4212	+	0.00861792i	−0.0195027	+	1.02351e-5i
$843$			1266.00i			1.50178i
$844$	0.419171	+	399.360i	0.000496648	+	0.473175i
$845$	−91.1280			−0.107844
$846$	−0.00404075	−	7.69955i	−4.77630e−6	−	0.00910112i
$847$			24.8355i			0.0293218i
$848$	105.230	−	0.220900i	0.124091	−	0.000260495i
$849$	520.750			0.613369
$850$	−73.9859	+	0.0388281i	−0.0870423	+	4.56801e-5i
$851$			962.513i			1.13104i
$852$	−237.441	+	0.249220i	−0.278687	+	0.000292512i
$853$	−669.891			−0.785335			−0.392667	−	0.919681i	$-0.628448\pi$
$853$	−669.891			−0.785335			−0.392667	+	0.919681i	$0.628448\pi$
$854$	0.00274223	+	5.22526i	3.21104e−6	+	0.00611857i
$855$		−	0.439016i		−	0.000513469i
$856$	1.25973	+	800.128i	0.00147165	+	0.934729i
$857$	−1599.89			−1.86684			−0.933422	−	0.358779i	$-0.883193\pi$
$857$	−1599.89			−1.86684			−0.933422	+	0.358779i	$0.883193\pi$
$858$	513.869	−	0.269680i	0.598915	−	0.000314313i
$859$		−	1660.42i		−	1.93297i	−0.256731	−	0.966483i	$-0.582645\pi$
$859$		−	1660.42i		−	1.93297i	0.256731	−	0.966483i	$-0.417355\pi$
$860$	−0.764594	−	728.458i	−0.000889063	−	0.847044i
$861$	−54.0890			−0.0628212
$862$	0.191403	+	364.715i	0.000222046	+	0.423103i
$863$		−	717.448i		−	0.831342i	−0.909515	−	0.415671i	$-0.863547\pi$
$863$		−	717.448i		−	0.831342i	0.909515	−	0.415671i	$-0.136453\pi$
$864$	2.26144	+	861.822i	0.00261741	+	0.997479i
$865$	608.236			0.703164
$866$	1023.34	−	0.537051i	1.18168	−	0.000620152i
$867$			704.539i			0.812617i
$868$	−84.1262	+	0.0882994i	−0.0969195	+	0.000101727i
$869$	−457.980			−0.527020
$870$	0.362131	+	690.032i	0.000416243	+	0.793140i
$871$			225.487i			0.258883i
$872$	−193.687	+	0.304944i	−0.222119	+	0.000349706i
$873$	1.32913			0.00152248
$874$	−154.541	+	0.0811034i	−0.176820	+	9.27957e-5i
$875$			4.33251i			0.00495144i
$876$	0.343559	+	327.322i	0.000392191	+	0.373655i
$877$	148.725			0.169584			0.0847919	−	0.996399i	$-0.472977\pi$
$877$	148.725			0.169584			0.0847919	+	0.996399i	$0.472977\pi$
$878$	0.783477	+	1492.90i	0.000892343	+	1.70034i
$879$			620.296i			0.705684i
$880$	−0.566573	−	269.898i	−0.000643833	−	0.306702i
$881$	−965.425			−1.09583			−0.547914	−	0.836534i	$-0.684578\pi$
$881$	−965.425			−1.09583			−0.547914	+	0.836534i	$0.684578\pi$
$882$	4.40060	−	0.00230945i	0.00498934	−	2.61842e-6i
$883$		−	801.062i		−	0.907205i	−0.891204	−	0.453602i	$-0.850139\pi$
$883$		−	801.062i		−	0.907205i	0.891204	−	0.453602i	$-0.149861\pi$
$884$	335.144	−	0.351769i	0.379122	−	0.000397929i
$885$	−328.885			−0.371621
$886$	−0.204257	−	389.206i	−0.000230538	−	0.439284i
$887$			1115.61i			1.25774i	0.777512	+	0.628868i	$0.216481\pi$
$887$			1115.61i			1.25774i	−0.777512	+	0.628868i	$0.783519\pi$
$888$	−2.05676	−	1306.37i	−0.00231617	−	1.47113i
$889$	−50.2622			−0.0565379
$890$	383.370	−	0.201194i	0.430753	−	0.000226061i
$891$			614.097i			0.689223i
$892$	0.704275	+	670.990i	0.000789546	+	0.752231i
$893$	372.558			0.417198
$894$	0.838998	+	1598.69i	0.000938477	+	1.78825i
$895$			275.293i			0.307590i
$896$	−0.182217	−	49.6011i	−0.000203367	−	0.0553584i
$897$	−603.759			−0.673087
$898$	−477.020	+	0.250342i	−0.531202	+	0.000278777i
$899$			2784.43i			3.09725i
$900$	−0.900841		0.000945529i	−0.00100093		1.05059e-6i
$901$	48.6595			0.0540062
$902$	−0.367486	−	700.236i	−0.000407413	−	0.776315i
$903$		−	94.9182i		−	0.105114i
$904$	179.026	−	0.281861i	0.198038	−	0.000311793i
$905$	252.648			0.279169
$906$	−1042.46	+	0.547085i	−1.15062	+	0.000603847i
$907$			42.5582i			0.0469220i	0.999725	+	0.0234610i	$0.00746855\pi$
$907$			42.5582i			0.0469220i	−0.999725	+	0.0234610i	$0.992531\pi$
$908$	0.623347	+	593.886i	0.000686505	+	0.654060i
$909$	−1.01245			−0.00111381
$910$	−0.0102995	−	19.6255i	−1.13182e−5	−	0.0215665i
$911$		−	424.617i		−	0.466100i	−0.972465	−	0.233050i	$-0.925129\pi$
$911$		−	424.617i		−	0.466100i	0.972465	−	0.233050i	$-0.0748706\pi$
$912$	209.750	−	0.440310i	0.229989	−	0.000482796i
$913$	702.526			0.769470
$914$	218.280	−	0.114554i	0.238818	−	0.000125333i
$915$			45.3402i			0.0495521i
$916$	−425.736	+	0.446856i	−0.464777	+	0.000487834i
$917$	10.5344			0.0114879
$918$	0.209144	+	398.518i	0.000227825	+	0.434116i
$919$			1046.09i			1.13829i	0.822236	+	0.569146i	$0.192726\pi$
$919$			1046.09i			1.13829i	−0.822236	+	0.569146i	$0.807274\pi$
$920$	0.499262	+	317.110i	0.000542676	+	0.344685i
$921$	−364.901			−0.396201
$922$	−715.840	+	0.375675i	−0.776400	+	0.000407457i
$923$		−	223.518i		−	0.242165i
$924$	−0.0369123	−	35.1677i	−3.99484e−5	−	0.0380603i
$925$	−271.482			−0.293494
$926$	0.759102	+	1446.45i	0.000819764	+	1.56204i
$927$		−	6.77823i		−	0.00731200i
$928$	−1641.71	+	4.30789i	−1.76909	+	0.00464213i
$929$	908.067			0.977468			0.488734	−	0.872433i	$-0.337459\pi$
$929$	908.067			0.977468			0.488734	+	0.872433i	$0.337459\pi$
$930$	−729.974	+	0.383093i	−0.784918	+	0.000411928i
$931$			212.931i			0.228713i
$932$	−29.4882	+	0.0309510i	−0.0316397	+	3.32092e-5i
$933$	1032.79			1.10695
$934$	−0.652694	−	1243.69i	−0.000698816	−	1.33158i
$935$		−	124.804i		−	0.133480i
$936$	4.08066	−	0.00642463i	0.00435968	−	6.86393e-6i
$937$	842.757			0.899420			0.449710	−	0.893175i	$-0.351527\pi$
$937$	842.757			0.899420			0.449710	+	0.893175i	$0.351527\pi$
$938$	15.4317	−	0.00809860i	0.0164517	−	8.63390e-6i
$939$			1019.24i			1.08545i
$940$	−0.802395	−	764.472i	−0.000853612	−	0.813268i
$941$	535.908			0.569509			0.284754	−	0.958601i	$-0.408088\pi$
$941$	535.908			0.569509			0.284754	+	0.958601i	$0.408088\pi$
$942$	0.314691	+	599.635i	0.000334066	+	0.636555i
$943$			822.727i			0.872457i
$944$	−1.64259	−	782.479i	−0.00174003	−	0.828897i
$945$	23.3366			0.0246948
$946$	1228.81	−	0.644883i	1.29895	−	0.000681695i
$947$			464.361i			0.490350i	0.969479	+	0.245175i	$0.0788453\pi$
$947$			464.361i			0.490350i	−0.969479	+	0.245175i	$0.921155\pi$
$948$	−730.327	+	0.766556i	−0.770387	+	0.000808603i
$949$	−308.129			−0.324688
$950$	−0.0228756	−	43.5890i	−2.40796e−5	−	0.0458831i
$951$			953.328i			1.00245i
$952$	−0.0361111	−	22.9363i	−3.79319e−5	−	0.0240927i
$953$	674.748			0.708025			0.354013	−	0.935241i	$-0.384817\pi$
$953$	674.748			0.708025			0.354013	+	0.935241i	$0.384817\pi$
$954$	0.592471		0.000310931i	0.000621039		3.25923e-7i
$955$		−	294.169i		−	0.308030i
$956$	−1.48490	−	1414.72i	−0.00155324	−	1.47983i
$957$	−1163.99			−1.21629
$958$	0.0999229	+	190.401i	0.000104304	+	0.198748i
$959$			16.6928i			0.0174065i
$960$	−1.35524	−	430.396i	−0.00141171	−	0.448329i
$961$	−1984.60			−2.06514
$962$	1229.77	−	0.645386i	1.27834	−	0.000670879i
$963$			4.50493i			0.00467802i
$964$	965.443	−	1.01334i	1.00150	−	0.00105118i
$965$	418.026			0.433188
$966$	0.0216846	+	41.3195i	2.24479e−5	+	0.0427739i
$967$		−	78.6057i		−	0.0812882i	−0.999174	−	0.0406441i	$-0.987059\pi$
$967$		−	78.6057i		−	0.0812882i	0.999174	−	0.0406441i	$-0.0129410\pi$
$968$	−512.718	+	0.807229i	−0.529667	+	0.000833914i
$969$	96.9910			0.100094
$970$	131.966	−	0.0692563i	0.136048	−	7.13982e-5i
$971$			1367.74i			1.40859i	0.709907	+	0.704296i	$0.248737\pi$
$971$			1367.74i			1.40859i	−0.709907	+	0.704296i	$0.751263\pi$
$972$	0.0102116	+	9.72899i	1.05058e−5	+	0.0100093i
$973$	−52.0167			−0.0534601
$974$	0.516623	+	984.412i	0.000530413	+	1.01069i
$975$		−	170.293i		−	0.174660i
$976$	−107.873	+	0.226448i	−0.110525	+	0.000232017i
$977$	−684.857			−0.700979			−0.350490	−	0.936567i	$-0.613985\pi$
$977$	−684.857			−0.700979			−0.350490	+	0.936567i	$0.613985\pi$
$978$	−1710.57	+	0.897712i	−1.74905	+	0.000917906i
$979$			646.693i			0.660565i
$980$	436.926	−	0.458600i	0.445843	−	0.000467960i
$981$	−1.09051			−0.00111163
$982$	0.214686	+	409.079i	0.000218621	+	0.416577i
$983$			1755.16i			1.78551i	0.450543	+	0.892755i	$0.351231\pi$
$983$			1755.16i			1.78551i	−0.450543	+	0.892755i	$0.648769\pi$
$984$	−1.75806	−	1116.64i	−0.00178664	−	1.13480i
$985$	−122.486			−0.124351
$986$	−759.151	+	0.398405i	−0.769930	+	0.000404062i
$987$		−	99.6108i		−	0.100923i
$988$	0.207246	+	197.451i	0.000209763	+	0.199849i
$989$	−1443.76			−1.45982
$990$	−0.000797489	−	1.51960i	−8.05545e−7	−	0.00153495i
$991$		−	278.107i		−	0.280632i	−0.990107	−	0.140316i	$-0.955188\pi$
$991$		−	278.107i		−	0.280632i	0.990107	−	0.140316i	$-0.0448119\pi$
$992$	−4.55725	−	1736.74i	−0.00459400	−	1.75075i
$993$	1526.19			1.53695
$994$	−15.2970	+	0.00802789i	−0.0153893	+	8.07635e-6i
$995$		−	123.300i		−	0.123920i
$996$	1120.30	−	1.17587i	1.12479	−	0.00118059i
$997$	716.164			0.718319			0.359160	−	0.933276i	$-0.383063\pi$
$997$	716.164			0.718319			0.359160	+	0.933276i	$0.383063\pi$
$998$	0.388772	+	740.796i	0.000389551	+	0.742281i
$999$			1462.31i			1.46377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.2	yes	72
4.3	odd	2	inner	380.3.b.a.191.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.1	✓	72	4.3	odd	2	inner
380.3.b.a.191.2	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 0.00104961i) q^{2} -3.00750i q^{3} +(4.00000 - 0.00419842i) q^{4} +2.23607 q^{5} +(0.00315669 + 6.01499i) q^{6} +0.387511i q^{7} +(-7.99999 + 0.0125953i) q^{8} -0.0450421 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 0.00104961i) q^{2} -3.00750i q^{3} +(4.00000 - 0.00419842i) q^{4} +2.23607 q^{5} +(0.00315669 + 6.01499i) q^{6} +0.387511i q^{7} +(-7.99999 + 0.0125953i) q^{8} -0.0450421 q^{9} +(-4.47214 + 0.00234699i) q^{10} -7.54388i q^{11} +(-0.0126268 - 12.0300i) q^{12} +11.3246 q^{13} +(-0.000406734 - 0.775022i) q^{14} -6.72497i q^{15} +(16.0000 - 0.0335874i) q^{16} +7.39859 q^{17} +(0.0900841 - 4.72765e-5i) q^{18} +4.35890i q^{19} +(8.94427 - 0.00938796i) q^{20} +1.16544 q^{21} +(0.00791811 + 15.0878i) q^{22} -17.7270i q^{23} +(0.0378802 + 24.0600i) q^{24} +5.00000 q^{25} +(-22.6492 + 0.0118864i) q^{26} -26.9320i q^{27} +(0.00162694 + 1.55004i) q^{28} +51.3037 q^{29} +(0.00705857 + 13.4499i) q^{30} +54.2734i q^{31} +(-31.9999 + 0.0839684i) q^{32} -22.6882 q^{33} +(-14.7972 + 0.00776561i) q^{34} +0.866501i q^{35} +(-0.180168 + 0.000189106i) q^{36} -54.2963 q^{37} +(-0.00457513 - 8.71780i) q^{38} -34.0587i q^{39} +(-17.8885 + 0.0281639i) q^{40} -46.4109 q^{41} +(-2.33088 + 0.00122325i) q^{42} -81.4441i q^{43} +(-0.0316724 - 30.1755i) q^{44} -0.100717 q^{45} +(0.0186064 + 35.4541i) q^{46} -85.4706i q^{47} +(-0.101014 - 48.1199i) q^{48} +48.8498 q^{49} +(-10.0000 + 0.00524803i) q^{50} -22.2513i q^{51} +(45.2983 - 0.0475454i) q^{52} +6.57686 q^{53} +(0.0282680 + 53.8640i) q^{54} -16.8686i q^{55} +(-0.00488081 - 3.10009i) q^{56} +13.1094 q^{57} +(-102.607 + 0.0538487i) q^{58} -48.9050i q^{59} +(-0.0282343 - 26.8999i) q^{60} -6.74207 q^{61} +(-0.0569657 - 108.547i) q^{62} -0.0174543i q^{63} +(63.9997 - 0.201524i) q^{64} +25.3226 q^{65} +(45.3764 - 0.0238137i) q^{66} +19.9113i q^{67} +(29.5944 - 0.0310624i) q^{68} -53.3140 q^{69} +(-0.000909485 - 1.73300i) q^{70} -19.7374i q^{71} +(0.360336 - 0.000567317i) q^{72} -27.2088 q^{73} +(108.593 - 0.0569898i) q^{74} -15.0375i q^{75} +(0.0183005 + 17.4356i) q^{76} +2.92334 q^{77} +(0.0357482 + 68.1173i) q^{78} -60.7089i q^{79} +(35.7770 - 0.0751037i) q^{80} -81.4033 q^{81} +(92.8217 - 0.0487131i) q^{82} +93.1252i q^{83} +(4.66175 - 0.00489301i) q^{84} +16.5438 q^{85} +(0.0854843 + 162.888i) q^{86} -154.296i q^{87} +(0.0950172 + 60.3510i) q^{88} -85.7242 q^{89} +(0.201434 - 0.000105713i) q^{90} +4.38841i q^{91} +(-0.0744256 - 70.9081i) q^{92} +163.227 q^{93} +(0.0897105 + 170.941i) q^{94} +9.74679i q^{95} +(0.252535 + 96.2396i) q^{96} -29.5085 q^{97} +(-97.6997 + 0.0512731i) q^{98} +0.339792i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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