LMFDB - Embedded newform 25.9.c.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{141})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 71x^{2} + 1225 $ x^4 + 71*x^2 + 1225
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$-5.43717i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.a.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.8743 + 11.8743i) q^{2} +(11.8743 - 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(2742.97 + 2742.97i) q^{7} +(2731.10 - 2731.10i) q^{8} +6279.00i q^{9} +O(q^{10})$	\(q+(11.8743 + 11.8743i) q^{2} +(11.8743 - 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(2742.97 + 2742.97i) q^{7} +(2731.10 - 2731.10i) q^{8} +6279.00i q^{9} +12132.0 q^{11} +(308.733 + 308.733i) q^{12} +(-2422.37 + 2422.37i) q^{13} +65142.0i q^{14} +71516.0 q^{16} +(-76993.2 - 76993.2i) q^{17} +(-74559.0 + 74559.0i) q^{18} +168380. i q^{19} +65142.0 q^{21} +(144060. + 144060. i) q^{22} +(221350. - 221350. i) q^{23} -64860.0i q^{24} -57528.0 q^{26} +(152467. + 152467. i) q^{27} +(-71317.3 + 71317.3i) q^{28} -666630. i q^{29} -1.04281e6 q^{31} +(150044. + 150044. i) q^{32} +(144060. - 144060. i) q^{33} -1.82849e6i q^{34} -163254. q^{36} +(-2.07639e6 - 2.07639e6i) q^{37} +(-1.99940e6 + 1.99940e6i) q^{38} +57528.0i q^{39} -1.32113e6 q^{41} +(773518. + 773518. i) q^{42} +(2.78134e6 - 2.78134e6i) q^{43} +315432. i q^{44} +5.25676e6 q^{46} +(3.63024e6 + 3.63024e6i) q^{47} +(849205. - 849205. i) q^{48} +9.28300e6i q^{49} -1.82849e6 q^{51} +(-62981.5 - 62981.5i) q^{52} +(-3.14105e6 + 3.14105e6i) q^{53} +3.62088e6i q^{54} +1.49827e7 q^{56} +(1.99940e6 + 1.99940e6i) q^{57} +(7.91579e6 - 7.91579e6i) q^{58} +6.49854e6i q^{59} -1.43940e7 q^{61} +(-1.23827e7 - 1.23827e7i) q^{62} +(-1.72231e7 + 1.72231e7i) q^{63} -1.47447e7i q^{64} +3.42122e6 q^{66} +(-1.14565e7 - 1.14565e7i) q^{67} +(2.00182e6 - 2.00182e6i) q^{68} -5.25676e6i q^{69} -2.30655e7 q^{71} +(1.71486e7 + 1.71486e7i) q^{72} +(1.74329e7 - 1.74329e7i) q^{73} -4.93116e7i q^{74} -4.37788e6 q^{76} +(3.32777e7 + 3.32777e7i) q^{77} +(-683107. + 683107. i) q^{78} -2.76068e6i q^{79} -3.75756e7 q^{81} +(-1.56875e7 - 1.56875e7i) q^{82} +(-1.15239e7 + 1.15239e7i) q^{83} +1.69369e6i q^{84} +6.60531e7 q^{86} +(-7.91579e6 - 7.91579e6i) q^{87} +(3.31337e7 - 3.31337e7i) q^{88} +2.61305e7i q^{89} -1.32890e7 q^{91} +(5.75509e6 + 5.75509e6i) q^{92} +(-1.23827e7 + 1.23827e7i) q^{93} +8.62133e7i q^{94} +3.56335e6 q^{96} +(-8.09308e7 - 8.09308e7i) q^{97} +(-1.10230e8 + 1.10230e8i) q^{98} +7.61768e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1128 q^{6}+O(q^{10}) $ 4 * q + 1128 * q^6	$ 4 q + 1128 q^{6} + 48528 q^{11} + 286064 q^{16} + 260568 q^{21} - 230112 q^{26} - 4171232 q^{31} - 653016 q^{36} - 5284512 q^{41} + 21027048 q^{46} - 7313952 q^{51} + 59930640 q^{56} - 57575872 q^{61} + 13684896 q^{66} - 92261952 q^{71} - 17511520 q^{76} - 150302556 q^{81} + 264212568 q^{86} - 53155872 q^{91} + 14253408 q^{96}+O(q^{100}) $ 4 * q + 1128 * q^6 + 48528 * q^11 + 286064 * q^16 + 260568 * q^21 - 230112 * q^26 - 4171232 * q^31 - 653016 * q^36 - 5284512 * q^41 + 21027048 * q^46 - 7313952 * q^51 + 59930640 * q^56 - 57575872 * q^61 + 13684896 * q^66 - 92261952 * q^71 - 17511520 * q^76 - 150302556 * q^81 + 264212568 * q^86 - 53155872 * q^91 + 14253408 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	11.8743	+	11.8743i	0.742146	+	0.742146i	0.972991	−	0.230844i	$-0.0741488\pi$
$2$	11.8743	+	11.8743i	0.742146	+	0.742146i	−0.230844	+	0.972991i	$0.574149\pi$
$3$	11.8743	−	11.8743i	0.146597	−	0.146597i	−0.629999	−	0.776596i	$-0.716945\pi$
$3$	11.8743	−	11.8743i	0.146597	−	0.146597i	0.776596	+	0.629999i	$0.216945\pi$
$4$			26.0000i			0.101562i
$5$		0			0
$5$		0			0
$6$	282.000			0.217593
$7$	2742.97	+	2742.97i	1.14243	+	1.14243i	0.988005	+	0.154425i	$0.0493525\pi$
$7$	2742.97	+	2742.97i	1.14243	+	1.14243i	0.154425	+	0.988005i	$0.450648\pi$
$8$	2731.10	−	2731.10i	0.666772	−	0.666772i
$9$			6279.00i			0.957019i
$10$		0			0
$11$	12132.0			0.828632			0.414316	−	0.910133i	$-0.364021\pi$
$11$	12132.0			0.828632			0.414316	+	0.910133i	$0.364021\pi$
$12$	308.733	+	308.733i	0.0148887	+	0.0148887i
$13$	−2422.37	+	2422.37i	−0.0848138	+	0.0848138i	−0.748241	−	0.663427i	$-0.769101\pi$
$13$	−2422.37	+	2422.37i	−0.0848138	+	0.0848138i	0.663427	+	0.748241i	$0.269101\pi$
$14$			65142.0i			1.69570i
$15$		0			0
$16$	71516.0			1.09125
$17$	−76993.2	−	76993.2i	−0.921843	−	0.921843i	0.0753168	−	0.997160i	$-0.476003\pi$
$17$	−76993.2	−	76993.2i	−0.921843	−	0.921843i	−0.997160	+	0.0753168i	$0.976003\pi$
$18$	−74559.0	+	74559.0i	−0.710248	+	0.710248i
$19$			168380.i			1.29204i	0.763320	+	0.646020i	$0.223568\pi$
$19$			168380.i			1.29204i	−0.763320	+	0.646020i	$0.776432\pi$
$20$		0			0
$21$	65142.0			0.334953
$22$	144060.	+	144060.i	0.614966	+	0.614966i
$23$	221350.	−	221350.i	0.790983	−	0.790983i	−0.190671	−	0.981654i	$-0.561066\pi$
$23$	221350.	−	221350.i	0.790983	−	0.790983i	0.981654	+	0.190671i	$0.0610662\pi$
$24$		−	64860.0i		−	0.195493i
$25$		0			0
$26$	−57528.0			−0.125888
$27$	152467.	+	152467.i	0.286893	+	0.286893i
$28$	−71317.3	+	71317.3i	−0.116028	+	0.116028i
$29$		−	666630.i		−	0.942525i	−0.881993	−	0.471262i	$-0.843798\pi$
$29$		−	666630.i		−	0.942525i	0.881993	−	0.471262i	$-0.156202\pi$
$30$		0			0
$31$	−1.04281e6			−1.12917			−0.564583	−	0.825376i	$-0.690963\pi$
$31$	−1.04281e6			−1.12917			−0.564583	+	0.825376i	$0.690963\pi$
$32$	150044.	+	150044.i	0.143093	+	0.143093i
$33$	144060.	−	144060.i	0.121475	−	0.121475i
$34$		−	1.82849e6i		−	1.36828i
$35$		0			0
$36$	−163254.			−0.0971972
$37$	−2.07639e6	−	2.07639e6i	−1.10791	−	1.10791i	−0.993425	−	0.114481i	$-0.963480\pi$
$37$	−2.07639e6	−	2.07639e6i	−1.10791	−	1.10791i	−0.114481	−	0.993425i	$-0.536520\pi$
$38$	−1.99940e6	+	1.99940e6i	−0.958883	+	0.958883i
$39$			57528.0i			0.0248669i
$40$		0			0
$41$	−1.32113e6			−0.467530			−0.233765	−	0.972293i	$-0.575105\pi$
$41$	−1.32113e6			−0.467530			−0.233765	+	0.972293i	$0.575105\pi$
$42$	773518.	+	773518.i	0.248584	+	0.248584i
$43$	2.78134e6	−	2.78134e6i	0.813542	−	0.813542i	−0.171621	−	0.985163i	$-0.554900\pi$
$43$	2.78134e6	−	2.78134e6i	0.813542	−	0.813542i	0.985163	+	0.171621i	$0.0549004\pi$
$44$			315432.i			0.0841579i
$45$		0			0
$46$	5.25676e6			1.17405
$47$	3.63024e6	+	3.63024e6i	0.743949	+	0.743949i	0.973336	−	0.229386i	$-0.0736718\pi$
$47$	3.63024e6	+	3.63024e6i	0.743949	+	0.743949i	−0.229386	+	0.973336i	$0.573672\pi$
$48$	849205.	−	849205.i	0.159973	−	0.159973i
$49$			9.28300e6i			1.61029i
$50$		0			0
$51$	−1.82849e6			−0.270278
$52$	−62981.5	−	62981.5i	−0.00861390	−	0.00861390i
$53$	−3.14105e6	+	3.14105e6i	−0.398081	+	0.398081i	−0.877556	−	0.479475i	$-0.840827\pi$
$53$	−3.14105e6	+	3.14105e6i	−0.398081	+	0.398081i	0.479475	+	0.877556i	$0.340827\pi$
$54$			3.62088e6i			0.425833i
$55$		0			0
$56$	1.49827e7			1.52348
$57$	1.99940e6	+	1.99940e6i	0.189409	+	0.189409i
$58$	7.91579e6	−	7.91579e6i	0.699491	−	0.699491i
$59$			6.49854e6i			0.536300i	0.963377	+	0.268150i	$0.0864123\pi$
$59$			6.49854e6i			0.536300i	−0.963377	+	0.268150i	$0.913588\pi$
$60$		0			0
$61$	−1.43940e7			−1.03959			−0.519794	−	0.854292i	$-0.673991\pi$
$61$	−1.43940e7			−1.03959			−0.519794	+	0.854292i	$0.673991\pi$
$62$	−1.23827e7	−	1.23827e7i	−0.838006	−	0.838006i
$63$	−1.72231e7	+	1.72231e7i	−1.09333	+	1.09333i
$64$		−	1.47447e7i		−	0.878855i
$65$		0			0
$66$	3.42122e6			0.180304
$67$	−1.14565e7	−	1.14565e7i	−0.568528	−	0.568528i	0.363188	−	0.931716i	$-0.381688\pi$
$67$	−1.14565e7	−	1.14565e7i	−0.568528	−	0.568528i	−0.931716	+	0.363188i	$0.881688\pi$
$68$	2.00182e6	−	2.00182e6i	0.0936247	−	0.0936247i
$69$		−	5.25676e6i		−	0.231911i
$70$		0			0
$71$	−2.30655e7			−0.907673			−0.453836	−	0.891085i	$-0.649945\pi$
$71$	−2.30655e7			−0.907673			−0.453836	+	0.891085i	$0.649945\pi$
$72$	1.71486e7	+	1.71486e7i	0.638113	+	0.638113i
$73$	1.74329e7	−	1.74329e7i	0.613873	−	0.613873i	−0.330080	−	0.943953i	$-0.607076\pi$
$73$	1.74329e7	−	1.74329e7i	0.613873	−	0.613873i	0.943953	+	0.330080i	$0.107076\pi$
$74$		−	4.93116e7i		−	1.64446i
$75$		0			0
$76$	−4.37788e6			−0.131223
$77$	3.32777e7	+	3.32777e7i	0.946653	+	0.946653i
$78$	−683107.	+	683107.i	−0.0184548	+	0.0184548i
$79$		−	2.76068e6i		−	0.0708774i	−0.999372	−	0.0354387i	$-0.988717\pi$
$79$		−	2.76068e6i		−	0.0708774i	0.999372	−	0.0354387i	$-0.0112828\pi$
$80$		0			0
$81$	−3.75756e7			−0.872904
$82$	−1.56875e7	−	1.56875e7i	−0.346976	−	0.346976i
$83$	−1.15239e7	+	1.15239e7i	−0.242822	+	0.242822i	−0.818017	−	0.575195i	$-0.804926\pi$
$83$	−1.15239e7	+	1.15239e7i	−0.242822	+	0.242822i	0.575195	+	0.818017i	$0.304926\pi$
$84$			1.69369e6i			0.0340187i
$85$		0			0
$86$	6.60531e7			1.20753
$87$	−7.91579e6	−	7.91579e6i	−0.138171	−	0.138171i
$88$	3.31337e7	−	3.31337e7i	0.552509	−	0.552509i
$89$			2.61305e7i			0.416474i	0.978078	+	0.208237i	$0.0667725\pi$
$89$			2.61305e7i			0.416474i	−0.978078	+	0.208237i	$0.933227\pi$
$90$		0			0
$91$	−1.32890e7			−0.193787
$92$	5.75509e6	+	5.75509e6i	0.0803343	+	0.0803343i
$93$	−1.23827e7	+	1.23827e7i	−0.165532	+	0.165532i
$94$			8.62133e7i			1.10424i
$95$		0			0
$96$	3.56335e6			0.0419540
$97$	−8.09308e7	−	8.09308e7i	−0.914170	−	0.914170i	0.0824271	−	0.996597i	$-0.473733\pi$
$97$	−8.09308e7	−	8.09308e7i	−0.914170	−	0.914170i	−0.996597	+	0.0824271i	$0.973733\pi$
$98$	−1.10230e8	+	1.10230e8i	−1.19507	+	1.19507i
$99$			7.61768e7i			0.793016i
$100$		0			0
$101$	1.80720e8			1.73668			0.868341	−	0.495968i	$-0.165187\pi$
$101$	1.80720e8			1.73668			0.868341	+	0.495968i	$0.165187\pi$
$102$	−2.17121e7	−	2.17121e7i	−0.200586	−	0.200586i
$103$	7.33591e7	−	7.33591e7i	0.651786	−	0.651786i	−0.301637	−	0.953423i	$-0.597533\pi$
$103$	7.33591e7	−	7.33591e7i	0.651786	−	0.651786i	0.953423	+	0.301637i	$0.0975330\pi$
$104$			1.32314e7i			0.113103i
$105$		0			0
$106$	−7.45958e7			−0.590868
$107$	5.06569e7	+	5.06569e7i	0.386459	+	0.386459i	0.873422	−	0.486963i	$-0.161895\pi$
$107$	5.06569e7	+	5.06569e7i	0.386459	+	0.386459i	−0.486963	+	0.873422i	$0.661895\pi$
$108$	−3.96413e6	+	3.96413e6i	−0.0291375	+	0.0291375i
$109$			3.65622e7i			0.259016i	0.991578	+	0.129508i	$0.0413398\pi$
$109$			3.65622e7i			0.259016i	−0.991578	+	0.129508i	$0.958660\pi$
$110$		0			0
$111$	−4.93116e7			−0.324831
$112$	1.96166e8	+	1.96166e8i	1.24667	+	1.24667i
$113$	1.29733e8	−	1.29733e8i	0.795677	−	0.795677i	−0.186733	−	0.982411i	$-0.559790\pi$
$113$	1.29733e8	−	1.29733e8i	0.795677	−	0.795677i	0.982411	+	0.186733i	$0.0597900\pi$
$114$			4.74832e7i			0.281138i
$115$		0			0
$116$	1.73324e7			0.0957252
$117$	−1.52100e7	−	1.52100e7i	−0.0811684	−	0.0811684i
$118$	−7.71659e7	+	7.71659e7i	−0.398013	+	0.398013i
$119$		−	4.22381e8i		−	2.10628i
$120$		0			0
$121$	−6.71735e7			−0.313369
$122$	−1.70919e8	−	1.70919e8i	−0.771526	−	0.771526i
$123$	−1.56875e7	+	1.56875e7i	−0.0685384	+	0.0685384i
$124$		−	2.71130e7i		−	0.114681i
$125$		0			0
$126$	−4.09027e8			−1.62282
$127$	5.09023e7	+	5.09023e7i	0.195669	+	0.195669i	0.798141	−	0.602471i	$-0.205817\pi$
$127$	5.09023e7	+	5.09023e7i	0.195669	+	0.195669i	−0.602471	+	0.798141i	$0.705817\pi$
$128$	2.13495e8	−	2.13495e8i	0.795333	−	0.795333i
$129$		−	6.60531e7i		−	0.238525i
$130$		0			0
$131$	3.84564e8			1.30582			0.652911	−	0.757435i	$-0.273548\pi$
$131$	3.84564e8			1.30582			0.652911	+	0.757435i	$0.273548\pi$
$132$	3.74555e6	+	3.74555e6i	0.0123373	+	0.0123373i
$133$	−4.61862e8	+	4.61862e8i	−1.47606	+	1.47606i
$134$		−	2.72076e8i		−	0.843862i
$135$		0			0
$136$	−4.20552e8			−1.22932
$137$	−1.62634e8	−	1.62634e8i	−0.461668	−	0.461668i	0.437534	−	0.899202i	$-0.355852\pi$
$137$	−1.62634e8	−	1.62634e8i	−0.461668	−	0.461668i	−0.899202	+	0.437534i	$0.855852\pi$
$138$	6.24206e7	−	6.24206e7i	0.172112	−	0.172112i
$139$		−	9.16665e7i		−	0.245557i	−0.992434	−	0.122778i	$-0.960820\pi$
$139$		−	9.16665e7i		−	0.245557i	0.992434	−	0.122778i	$-0.0391804\pi$
$140$		0			0
$141$	8.62133e7			0.218121
$142$	−2.73887e8	−	2.73887e8i	−0.673626	−	0.673626i
$143$	−2.93881e7	+	2.93881e7i	−0.0702794	+	0.0702794i
$144$			4.49049e8i			1.04434i
$145$		0			0
$146$	4.14009e8			0.911167
$147$	1.10230e8	+	1.10230e8i	0.236063	+	0.236063i
$148$	5.39863e7	−	5.39863e7i	0.112522	−	0.112522i
$149$			1.45300e8i			0.294794i	0.989077	+	0.147397i	$0.0470896\pi$
$149$			1.45300e8i			0.294794i	−0.989077	+	0.147397i	$0.952910\pi$
$150$		0			0
$151$	−2.35910e7			−0.0453774			−0.0226887	−	0.999743i	$-0.507223\pi$
$151$	−2.35910e7			−0.0453774			−0.0226887	+	0.999743i	$0.507223\pi$
$152$	4.59862e8	+	4.59862e8i	0.861497	+	0.861497i
$153$	4.83441e8	−	4.83441e8i	0.882221	−	0.882221i
$154$			7.90303e8i			1.40511i
$155$		0			0
$156$	−1.49573e6			−0.00252554
$157$	6.67495e8	+	6.67495e8i	1.09863	+	1.09863i	0.994572	+	0.104054i	$0.0331814\pi$
$157$	6.67495e8	+	6.67495e8i	1.09863	+	1.09863i	0.104054	+	0.994572i	$0.466819\pi$
$158$	3.27813e7	−	3.27813e7i	0.0526014	−	0.0526014i
$159$			7.45958e7i			0.116715i
$160$		0			0
$161$	1.21431e9			1.80729
$162$	−4.46186e8	−	4.46186e8i	−0.647822	−	0.647822i
$163$	−2.57869e8	+	2.57869e8i	−0.365300	+	0.365300i	−0.865760	−	0.500460i	$-0.833164\pi$
$163$	−2.57869e8	+	2.57869e8i	−0.365300	+	0.365300i	0.500460	+	0.865760i	$0.333164\pi$
$164$		−	3.43493e7i		−	0.0474835i
$165$		0			0
$166$	−2.73678e8			−0.360419
$167$	−4.92455e8	−	4.92455e8i	−0.633142	−	0.633142i	0.315713	−	0.948855i	$-0.397756\pi$
$167$	−4.92455e8	−	4.92455e8i	−0.633142	−	0.633142i	−0.948855	+	0.315713i	$0.897756\pi$
$168$	1.77909e8	−	1.77909e8i	0.223337	−	0.223337i
$169$			8.03995e8i			0.985613i
$170$		0			0
$171$	−1.05726e9			−1.23651
$172$	7.23148e7	+	7.23148e7i	0.0826254	+	0.0826254i
$173$	−3.51863e8	+	3.51863e8i	−0.392816	+	0.392816i	−0.875690	−	0.482874i	$-0.839593\pi$
$173$	−3.51863e8	+	3.51863e8i	−0.392816	+	0.392816i	0.482874	+	0.875690i	$0.339593\pi$
$174$		−	1.87990e8i		−	0.205086i
$175$		0			0
$176$	8.67632e8			0.904243
$177$	7.71659e7	+	7.71659e7i	0.0786199	+	0.0786199i
$178$	−3.10283e8	+	3.10283e8i	−0.309085	+	0.309085i
$179$		−	1.16205e9i		−	1.13191i	−0.824436	−	0.565955i	$-0.808508\pi$
$179$		−	1.16205e9i		−	1.13191i	0.824436	−	0.565955i	$-0.191492\pi$
$180$		0			0
$181$	−4.84017e8			−0.450968			−0.225484	−	0.974247i	$-0.572396\pi$
$181$	−4.84017e8			−0.450968			−0.225484	+	0.974247i	$0.572396\pi$
$182$	−1.57798e8	−	1.57798e8i	−0.143819	−	0.143819i
$183$	−1.70919e8	+	1.70919e8i	−0.152400	+	0.152400i
$184$		−	1.20906e9i		−	1.05481i
$185$		0			0
$186$	−2.94072e8			−0.245698
$187$	−9.34082e8	−	9.34082e8i	−0.763868	−	0.763868i
$188$	−9.43861e7	+	9.43861e7i	−0.0755574	+	0.0755574i
$189$			8.36423e8i			0.655509i
$190$		0			0
$191$	−1.49354e9			−1.12223			−0.561117	−	0.827736i	$-0.689628\pi$
$191$	−1.49354e9			−1.12223			−0.561117	+	0.827736i	$0.689628\pi$
$192$	−1.75084e8	−	1.75084e8i	−0.128837	−	0.128837i
$193$	8.77896e8	−	8.77896e8i	0.632723	−	0.632723i	−0.316027	−	0.948750i	$-0.602349\pi$
$193$	8.77896e8	−	8.77896e8i	0.632723	−	0.632723i	0.948750	+	0.316027i	$0.102349\pi$
$194$		−	1.92200e9i		−	1.35690i
$195$		0			0
$196$	−2.41358e8			−0.163545
$197$	2.10520e8	+	2.10520e8i	0.139775	+	0.139775i	0.773532	−	0.633757i	$-0.218488\pi$
$197$	2.10520e8	+	2.10520e8i	0.139775	+	0.139775i	−0.633757	+	0.773532i	$0.718488\pi$
$198$	−9.04550e8	+	9.04550e8i	−0.588534	+	0.588534i
$199$		−	1.44381e9i		−	0.920655i	−0.887749	−	0.460327i	$-0.847732\pi$
$199$		−	1.44381e9i		−	0.920655i	0.887749	−	0.460327i	$-0.152268\pi$
$200$		0			0
$201$	−2.72076e8			−0.166689
$202$	2.14593e9	+	2.14593e9i	1.28887	+	1.28887i
$203$	1.82855e9	−	1.82855e9i	1.07677	−	1.07677i
$204$		−	4.75407e7i		−	0.0274502i
$205$		0			0
$206$	1.74218e9			0.967441
$207$	1.38985e9	+	1.38985e9i	0.756986	+	0.756986i
$208$	−1.73238e8	+	1.73238e8i	−0.0925528	+	0.0925528i
$209$			2.04279e9i			1.07063i
$210$		0			0
$211$	−1.57176e9			−0.792968			−0.396484	−	0.918042i	$-0.629770\pi$
$211$	−1.57176e9			−0.792968			−0.396484	+	0.918042i	$0.629770\pi$
$212$	−8.16673e7	−	8.16673e7i	−0.0404301	−	0.0404301i
$213$	−2.73887e8	+	2.73887e8i	−0.133062	+	0.133062i
$214$			1.20303e9i			0.573618i
$215$		0			0
$216$	8.32802e8			0.382584
$217$	−2.86039e9	−	2.86039e9i	−1.28999	−	1.28999i
$218$	−4.34153e8	+	4.34153e8i	−0.192228	+	0.192228i
$219$		−	4.14009e8i		−	0.179984i
$220$		0			0
$221$	3.73012e8			0.156370
$222$	−5.85543e8	−	5.85543e8i	−0.241072	−	0.241072i
$223$	−4.52258e8	+	4.52258e8i	−0.182880	+	0.182880i	−0.792610	−	0.609729i	$-0.791278\pi$
$223$	−4.52258e8	+	4.52258e8i	−0.182880	+	0.182880i	0.609729	+	0.792610i	$0.291278\pi$
$224$			8.23134e8i			0.326948i
$225$		0			0
$226$	3.08099e9			1.18102
$227$	1.41755e9	+	1.41755e9i	0.533871	+	0.533871i	0.921722	−	0.387851i	$-0.126783\pi$
$227$	1.41755e9	+	1.41755e9i	0.533871	+	0.533871i	−0.387851	+	0.921722i	$0.626783\pi$
$228$	−5.19844e7	+	5.19844e7i	−0.0192369	+	0.0192369i
$229$			5.09083e9i			1.85117i	0.378536	+	0.925586i	$0.376428\pi$
$229$			5.09083e9i			1.85117i	−0.378536	+	0.925586i	$0.623572\pi$
$230$		0			0
$231$	7.90303e8			0.277553
$232$	−1.82063e9	−	1.82063e9i	−0.628449	−	0.628449i
$233$	−3.23753e9	+	3.23753e9i	−1.09848	+	1.09848i	−0.103887	+	0.994589i	$0.533128\pi$
$233$	−3.23753e9	+	3.23753e9i	−1.09848	+	1.09848i	−0.994589	+	0.103887i	$0.966872\pi$
$234$		−	3.61218e8i		−	0.120478i
$235$		0			0
$236$	−1.68962e8			−0.0544680
$237$	−3.27813e7	−	3.27813e7i	−0.0103904	−	0.0103904i
$238$	5.01549e9	−	5.01549e9i	1.56317	−	1.56317i
$239$			6.45678e8i			0.197890i	0.995093	+	0.0989452i	$0.0315468\pi$
$239$			6.45678e8i			0.197890i	−0.995093	+	0.0989452i	$0.968453\pi$
$240$		0			0
$241$	1.04063e9			0.308482			0.154241	−	0.988033i	$-0.450707\pi$
$241$	1.04063e9			0.308482			0.154241	+	0.988033i	$0.450707\pi$
$242$	−7.97641e8	−	7.97641e8i	−0.232566	−	0.232566i
$243$	−1.44652e9	+	1.44652e9i	−0.414858	+	0.414858i
$244$		−	3.74243e8i		−	0.105583i
$245$		0			0
$246$	−3.72558e8			−0.101731
$247$	−4.07878e8	−	4.07878e8i	−0.109583	−	0.109583i
$248$	−2.84801e9	+	2.84801e9i	−0.752896	+	0.752896i
$249$			2.73678e8i			0.0711938i
$250$		0			0
$251$	−4.15092e9			−1.04580			−0.522901	−	0.852394i	$-0.675150\pi$
$251$	−4.15092e9			−1.04580			−0.522901	+	0.852394i	$0.675150\pi$
$252$	−4.47801e8	−	4.47801e8i	−0.111041	−	0.111041i
$253$	2.68541e9	−	2.68541e9i	0.655434	−	0.655434i
$254$			1.20886e9i			0.290431i
$255$		0			0
$256$	1.29558e9			0.301651
$257$	5.71495e9	+	5.71495e9i	1.31003	+	1.31003i	0.921392	+	0.388635i	$0.127053\pi$
$257$	5.71495e9	+	5.71495e9i	1.31003	+	1.31003i	0.388635	+	0.921392i	$0.372947\pi$
$258$	7.84338e8	−	7.84338e8i	0.177021	−	0.177021i
$259$		−	1.13910e10i		−	2.53141i
$260$		0			0
$261$	4.18577e9			0.902014
$262$	4.56645e9	+	4.56645e9i	0.969111	+	0.969111i
$263$	1.59379e9	−	1.59379e9i	0.333127	−	0.333127i	−0.520646	−	0.853773i	$-0.674309\pi$
$263$	1.59379e9	−	1.59379e9i	0.333127	−	0.333127i	0.853773	+	0.520646i	$0.174309\pi$
$264$		−	7.86882e8i		−	0.161992i
$265$		0			0
$266$	−1.09686e10			−2.19091
$267$	3.10283e8	+	3.10283e8i	0.0610538	+	0.0610538i
$268$	2.97868e8	−	2.97868e8i	0.0577411	−	0.0577411i
$269$			2.62849e9i			0.501992i	0.967988	+	0.250996i	$0.0807581\pi$
$269$			2.62849e9i			0.501992i	−0.967988	+	0.250996i	$0.919242\pi$
$270$		0			0
$271$	−2.04396e9			−0.378961			−0.189481	−	0.981884i	$-0.560680\pi$
$271$	−2.04396e9			−0.378961			−0.189481	+	0.981884i	$0.560680\pi$
$272$	−5.50625e9	−	5.50625e9i	−1.00596	−	1.00596i
$273$	−1.57798e8	+	1.57798e8i	−0.0284086	+	0.0284086i
$274$		−	3.86235e9i		−	0.685250i
$275$		0			0
$276$	1.36676e8			0.0235535
$277$	−4.31300e9	−	4.31300e9i	−0.732589	−	0.732589i	0.238543	−	0.971132i	$-0.423330\pi$
$277$	−4.31300e9	−	4.31300e9i	−0.732589	−	0.732589i	−0.971132	+	0.238543i	$0.923330\pi$
$278$	1.08848e9	−	1.08848e9i	0.182239	−	0.182239i
$279$		−	6.54779e9i		−	1.08063i
$280$		0			0
$281$	5.50789e9			0.883405			0.441703	−	0.897162i	$-0.354375\pi$
$281$	5.50789e9			0.883405			0.441703	+	0.897162i	$0.354375\pi$
$282$	1.02373e9	+	1.02373e9i	0.161878	+	0.161878i
$283$	−7.63368e9	+	7.63368e9i	−1.19011	+	1.19011i	−0.213078	+	0.977035i	$0.568349\pi$
$283$	−7.63368e9	+	7.63368e9i	−1.19011	+	1.19011i	−0.977035	+	0.213078i	$0.931651\pi$
$284$		−	5.99703e8i		−	0.0921855i
$285$		0			0
$286$	−6.97930e8			−0.104315
$287$	−3.62382e9	−	3.62382e9i	−0.534120	−	0.534120i
$288$	−9.42127e8	+	9.42127e8i	−0.136943	+	0.136943i
$289$			4.88016e9i			0.699588i
$290$		0			0
$291$	−1.92200e9			−0.268029
$292$	4.53256e8	+	4.53256e8i	0.0623465	+	0.0623465i
$293$	4.49841e9	−	4.49841e9i	0.610364	−	0.610364i	−0.332677	−	0.943041i	$-0.607952\pi$
$293$	4.49841e9	−	4.49841e9i	0.610364	−	0.610364i	0.943041	+	0.332677i	$0.107952\pi$
$294$			2.61781e9i			0.350387i
$295$		0			0
$296$	−1.13417e10			−1.47744
$297$	1.84972e9	+	1.84972e9i	0.237728	+	0.237728i
$298$	−1.72534e9	+	1.72534e9i	−0.218781	+	0.218781i
$299$			1.07238e9i			0.134173i
$300$		0			0
$301$	1.52583e10			1.85883
$302$	−2.80128e8	−	2.80128e8i	−0.0336767	−	0.0336767i
$303$	2.14593e9	−	2.14593e9i	0.254592	−	0.254592i
$304$			1.20419e10i			1.40994i
$305$		0			0
$306$	1.14811e10			1.30947
$307$	−1.53928e9	−	1.53928e9i	−0.173287	−	0.173287i	0.615135	−	0.788422i	$-0.289101\pi$
$307$	−1.53928e9	−	1.53928e9i	−0.173287	−	0.173287i	−0.788422	+	0.615135i	$0.789101\pi$
$308$	−8.65221e8	+	8.65221e8i	−0.0961445	+	0.0961445i
$309$		−	1.74218e9i		−	0.191100i
$310$		0			0
$311$	−5.22581e8			−0.0558614			−0.0279307	−	0.999610i	$-0.508892\pi$
$311$	−5.22581e8			−0.0558614			−0.0279307	+	0.999610i	$0.508892\pi$
$312$	1.57115e8	+	1.57115e8i	0.0165805	+	0.0165805i
$313$	−3.27149e9	+	3.27149e9i	−0.340854	+	0.340854i	−0.856688	−	0.515834i	$-0.827482\pi$
$313$	−3.27149e9	+	3.27149e9i	−0.340854	+	0.340854i	0.515834	+	0.856688i	$0.327482\pi$
$314$			1.58521e10i			1.63068i
$315$		0			0
$316$	7.17777e7			0.00719848
$317$	3.24669e9	+	3.24669e9i	0.321517	+	0.321517i	0.849349	−	0.527832i	$-0.176995\pi$
$317$	3.24669e9	+	3.24669e9i	0.321517	+	0.321517i	−0.527832	+	0.849349i	$0.676995\pi$
$318$	−8.85776e8	+	8.85776e8i	−0.0866194	+	0.0866194i
$319$		−	8.08756e9i		−	0.781006i
$320$		0			0
$321$	1.20303e9			0.113307
$322$	1.44192e10	+	1.44192e10i	1.34127	+	1.34127i
$323$	1.29641e10	−	1.29641e10i	1.19106	−	1.19106i
$324$		−	9.76967e8i		−	0.0886543i
$325$		0			0
$326$	−6.12406e9			−0.542212
$327$	4.34153e8	+	4.34153e8i	0.0379709	+	0.0379709i
$328$	−3.60813e9	+	3.60813e9i	−0.311736	+	0.311736i
$329$			1.99153e10i			1.69982i
$330$		0			0
$331$	8.55909e9			0.713043			0.356522	−	0.934287i	$-0.383963\pi$
$331$	8.55909e9			0.713043			0.356522	+	0.934287i	$0.383963\pi$
$332$	−2.99622e8	−	2.99622e8i	−0.0246616	−	0.0246616i
$333$	1.30377e10	−	1.30377e10i	1.06029	−	1.06029i
$334$		−	1.16952e10i		−	0.939767i
$335$		0			0
$336$	4.65870e9			0.365517
$337$	−7.19609e9	−	7.19609e9i	−0.557926	−	0.557926i	0.370790	−	0.928717i	$-0.379087\pi$
$337$	−7.19609e9	−	7.19609e9i	−0.557926	−	0.557926i	−0.928717	+	0.370790i	$0.879087\pi$
$338$	−9.54691e9	+	9.54691e9i	−0.731469	+	0.731469i
$339$		−	3.08099e9i		−	0.233288i
$340$		0			0
$341$	−1.26513e10			−0.935663
$342$	−1.25542e10	−	1.25542e10i	−0.917669	−	0.917669i
$343$	−9.65033e9	+	9.65033e9i	−0.697213	+	0.697213i
$344$		−	1.51922e10i		−	1.08489i
$345$		0			0
$346$	−8.35628e9			−0.583053
$347$	−2.76044e9	−	2.76044e9i	−0.190397	−	0.190397i	0.605471	−	0.795868i	$-0.292985\pi$
$347$	−2.76044e9	−	2.76044e9i	−0.190397	−	0.190397i	−0.795868	+	0.605471i	$0.792985\pi$
$348$	2.05811e8	−	2.05811e8i	0.0140330	−	0.0140330i
$349$		−	7.99627e9i		−	0.538996i	−0.963001	−	0.269498i	$-0.913142\pi$
$349$		−	7.99627e9i		−	0.538996i	0.963001	−	0.269498i	$-0.0868578\pi$
$350$		0			0
$351$	−7.38660e8			−0.0486649
$352$	1.82034e9	+	1.82034e9i	0.118572	+	0.118572i
$353$	−1.99730e10	+	1.99730e10i	−1.28630	+	1.28630i	−0.349290	+	0.937015i	$0.613577\pi$
$353$	−1.99730e10	+	1.99730e10i	−1.28630	+	1.28630i	−0.937015	+	0.349290i	$0.886423\pi$
$354$			1.83259e9i			0.116695i
$355$		0			0
$356$	−6.79393e8			−0.0422981
$357$	−5.01549e9	−	5.01549e9i	−0.308774	−	0.308774i
$358$	1.37986e10	−	1.37986e10i	0.840043	−	0.840043i
$359$		−	1.92076e10i		−	1.15637i	−0.815906	−	0.578184i	$-0.803762\pi$
$359$		−	1.92076e10i		−	1.15637i	0.815906	−	0.578184i	$-0.196238\pi$
$360$		0			0
$361$	−1.13683e10			−0.669368
$362$	−5.74738e9	−	5.74738e9i	−0.334685	−	0.334685i
$363$	−7.97641e8	+	7.97641e8i	−0.0459389	+	0.0459389i
$364$		−	3.45513e8i		−	0.0196815i
$365$		0			0
$366$	−4.05910e9			−0.226207
$367$	1.85651e10	+	1.85651e10i	1.02337	+	1.02337i	0.999720	+	0.0236511i	$0.00752907\pi$
$367$	1.85651e10	+	1.85651e10i	1.02337	+	1.02337i	0.0236511	+	0.999720i	$0.492471\pi$
$368$	1.58300e10	−	1.58300e10i	0.863159	−	0.863159i
$369$		−	8.29536e9i		−	0.447435i
$370$		0			0
$371$	−1.72316e10			−0.909558
$372$	−3.21949e8	−	3.21949e8i	−0.0168118	−	0.0168118i
$373$	−7.55571e9	+	7.55571e9i	−0.390337	+	0.390337i	−0.874808	−	0.484470i	$-0.839012\pi$
$373$	−7.55571e9	+	7.55571e9i	−0.390337	+	0.390337i	0.484470	+	0.874808i	$0.339012\pi$
$374$		−	2.21832e10i		−	1.13380i
$375$		0			0
$376$	1.98291e10			0.992089
$377$	1.61482e9	+	1.61482e9i	0.0799391	+	0.0799391i
$378$	−9.93198e9	+	9.93198e9i	−0.486484	+	0.486484i
$379$			1.95966e10i			0.949783i	0.880044	+	0.474892i	$0.157513\pi$
$379$			1.95966e10i			0.949783i	−0.880044	+	0.474892i	$0.842487\pi$
$380$		0			0
$381$	1.20886e9			0.0573690
$382$	−1.77348e10	−	1.77348e10i	−0.832862	−	0.832862i
$383$	1.07480e10	−	1.07480e10i	0.499497	−	0.499497i	−0.411784	−	0.911281i	$-0.635094\pi$
$383$	1.07480e10	−	1.07480e10i	0.499497	−	0.499497i	0.911281	+	0.411784i	$0.135094\pi$
$384$		−	5.07024e9i		−	0.233186i
$385$		0			0
$386$	2.08489e10			0.939146
$387$	1.74640e10	+	1.74640e10i	0.778575	+	0.778575i
$388$	2.10420e9	−	2.10420e9i	0.0928454	−	0.0928454i
$389$			3.58035e10i			1.56361i	0.623526	+	0.781803i	$0.285700\pi$
$389$			3.58035e10i			1.56361i	−0.623526	+	0.781803i	$0.714300\pi$
$390$		0			0
$391$	−3.40848e10			−1.45832
$392$	2.53528e10	+	2.53528e10i	1.07370	+	1.07370i
$393$	4.56645e9	−	4.56645e9i	0.191429	−	0.191429i
$394$			4.99958e9i			0.207467i
$395$		0			0
$396$	−1.98060e9			−0.0805407
$397$	3.85643e9	+	3.85643e9i	0.155247	+	0.155247i	0.780457	−	0.625210i	$-0.214987\pi$
$397$	3.85643e9	+	3.85643e9i	0.155247	+	0.155247i	−0.625210	+	0.780457i	$0.714987\pi$
$398$	1.71443e10	−	1.71443e10i	0.683261	−	0.683261i
$399$			1.09686e10i			0.432773i
$400$		0			0
$401$	3.39784e10			1.31409			0.657046	−	0.753851i	$-0.271806\pi$
$401$	3.39784e10			1.31409			0.657046	+	0.753851i	$0.271806\pi$
$402$	−3.23073e9	−	3.23073e9i	−0.123707	−	0.123707i
$403$	2.52606e9	−	2.52606e9i	0.0957688	−	0.0957688i
$404$			4.69871e9i			0.176382i
$405$		0			0
$406$	4.34256e10			1.59824
$407$	−2.51908e10	−	2.51908e10i	−0.918047	−	0.918047i
$408$	−4.99378e9	+	4.99378e9i	−0.180214	+	0.180214i
$409$		−	1.10826e10i		−	0.396048i	−0.980197	−	0.198024i	$-0.936548\pi$
$409$		−	1.10826e10i		−	0.396048i	0.980197	−	0.198024i	$-0.0634523\pi$
$410$		0			0
$411$	−3.86235e9			−0.135358
$412$	1.90734e9	+	1.90734e9i	0.0661970	+	0.0661970i
$413$	−1.78253e10	+	1.78253e10i	−0.612685	+	0.612685i
$414$			3.30072e10i			1.12359i
$415$		0			0
$416$	−7.26924e8			−0.0242726
$417$	−1.08848e9	−	1.08848e9i	−0.0359978	−	0.0359978i
$418$	−2.42567e10	+	2.42567e10i	−0.794561	+	0.794561i
$419$			3.54167e10i			1.14909i	0.818474	+	0.574543i	$0.194820\pi$
$419$			3.54167e10i			1.14909i	−0.818474	+	0.574543i	$0.805180\pi$
$420$		0			0
$421$	−2.98731e10			−0.950938			−0.475469	−	0.879733i	$-0.657722\pi$
$421$	−2.98731e10			−0.950938			−0.475469	+	0.879733i	$0.657722\pi$
$422$	−1.86636e10	−	1.86636e10i	−0.588498	−	0.588498i
$423$	−2.27943e10	+	2.27943e10i	−0.711974	+	0.711974i
$424$			1.71570e10i			0.530858i
$425$		0			0
$426$	−6.50447e9			−0.197503
$427$	−3.94823e10	−	3.94823e10i	−1.18766	−	1.18766i
$428$	−1.31708e9	+	1.31708e9i	−0.0392498	+	0.0392498i
$429$			6.97930e8i			0.0206055i
$430$		0			0
$431$	6.06834e10			1.75857			0.879287	−	0.476293i	$-0.158020\pi$
$431$	6.06834e10			1.75857			0.879287	+	0.476293i	$0.158020\pi$
$432$	1.09038e10	+	1.09038e10i	0.313071	+	0.313071i
$433$	4.29956e10	−	4.29956e10i	1.22313	−	1.22313i	0.256617	−	0.966513i	$-0.417392\pi$
$433$	4.29956e10	−	4.29956e10i	1.22313	−	1.22313i	0.966513	−	0.256617i	$-0.0826079\pi$
$434$		−	6.79306e10i		−	1.91473i
$435$		0			0
$436$	−9.50618e8			−0.0263063
$437$	3.72708e10	+	3.72708e10i	1.02198	+	1.02198i
$438$	4.91608e9	−	4.91608e9i	0.133574	−	0.133574i
$439$			8.86294e9i			0.238627i	0.992857	+	0.119314i	$0.0380694\pi$
$439$			8.86294e9i			0.238627i	−0.992857	+	0.119314i	$0.961931\pi$
$440$		0			0
$441$	−5.82880e10			−1.54108
$442$	4.42927e9	+	4.42927e9i	0.116049	+	0.116049i
$443$	−1.68455e10	+	1.68455e10i	−0.437390	+	0.437390i	−0.891133	−	0.453743i	$-0.850088\pi$
$443$	−1.68455e10	+	1.68455e10i	−0.437390	+	0.437390i	0.453743	+	0.891133i	$0.350088\pi$
$444$		−	1.28210e9i		−	0.0329907i
$445$		0			0
$446$	−1.07405e10			−0.271448
$447$	1.72534e9	+	1.72534e9i	0.0432159	+	0.0432159i
$448$	4.04444e10	−	4.04444e10i	1.00403	−	1.00403i
$449$		−	5.95055e10i		−	1.46410i	−0.681250	−	0.732051i	$-0.738563\pi$
$449$		−	5.95055e10i		−	1.46410i	0.681250	−	0.732051i	$-0.261437\pi$
$450$		0			0
$451$	−1.60279e10			−0.387410
$452$	3.37306e9	+	3.37306e9i	0.0808110	+	0.0808110i
$453$	−2.80128e8	+	2.80128e8i	−0.00665218	+	0.00665218i
$454$			3.36650e10i			0.792421i
$455$		0			0
$456$	1.09211e10			0.252585
$457$	−2.91131e9	−	2.91131e9i	−0.0667459	−	0.0667459i	0.672946	−	0.739692i	$-0.265029\pi$
$457$	−2.91131e9	−	2.91131e9i	−0.0667459	−	0.0667459i	−0.739692	+	0.672946i	$0.765029\pi$
$458$	−6.04503e10	+	6.04503e10i	−1.37384	+	1.37384i
$459$		−	2.34778e10i		−	0.528940i
$460$		0			0
$461$	4.79933e9			0.106262			0.0531309	−	0.998588i	$-0.483080\pi$
$461$	4.79933e9			0.106262			0.0531309	+	0.998588i	$0.483080\pi$
$462$	9.38433e9	+	9.38433e9i	0.205985	+	0.205985i
$463$	4.23409e10	−	4.23409e10i	0.921375	−	0.921375i	−0.0757516	−	0.997127i	$-0.524136\pi$
$463$	4.23409e10	−	4.23409e10i	0.921375	−	0.921375i	0.997127	+	0.0757516i	$0.0241356\pi$
$464$		−	4.76747e10i		−	1.02853i
$465$		0			0
$466$	−7.68872e10			−1.63046
$467$	2.55795e10	+	2.55795e10i	0.537805	+	0.537805i	0.922884	−	0.385079i	$-0.125826\pi$
$467$	2.55795e10	+	2.55795e10i	0.537805	+	0.537805i	−0.385079	+	0.922884i	$0.625826\pi$
$468$	3.95461e8	−	3.95461e8i	0.00824366	−	0.00824366i
$469$		−	6.28496e10i		−	1.29901i
$470$		0			0
$471$	1.58521e10			0.322110
$472$	1.77482e10	+	1.77482e10i	0.357590	+	0.357590i
$473$	3.37432e10	−	3.37432e10i	0.674127	−	0.674127i
$474$		−	7.78512e8i		−	0.0154224i
$475$		0			0
$476$	1.09819e10			0.213919
$477$	−1.97226e10	−	1.97226e10i	−0.380971	−	0.380971i
$478$	−7.66701e9	+	7.66701e9i	−0.146864	+	0.146864i
$479$			4.66044e10i			0.885288i	0.896697	+	0.442644i	$0.145959\pi$
$479$			4.66044e10i			0.885288i	−0.896697	+	0.442644i	$0.854041\pi$
$480$		0			0
$481$	1.00596e10			0.187931
$482$	1.23568e10	+	1.23568e10i	0.228938	+	0.228938i
$483$	1.44192e10	−	1.44192e10i	0.264942	−	0.264942i
$484$		−	1.74651e9i		−	0.0318266i
$485$		0			0
$486$	−3.43529e10			−0.615770
$487$	−1.63896e10	−	1.63896e10i	−0.291375	−	0.291375i	0.546248	−	0.837623i	$-0.316055\pi$
$487$	−1.63896e10	−	1.63896e10i	−0.291375	−	0.291375i	−0.837623	+	0.546248i	$0.816055\pi$
$488$	−3.93113e10	+	3.93113e10i	−0.693168	+	0.693168i
$489$			6.12406e9i			0.107104i
$490$		0			0
$491$	7.94765e10			1.36745			0.683727	−	0.729738i	$-0.260358\pi$
$491$	7.94765e10			1.36745			0.683727	+	0.729738i	$0.260358\pi$
$492$	−4.07876e8	−	4.07876e8i	−0.00696093	−	0.00696093i
$493$	−5.13260e10	+	5.13260e10i	−0.868860	+	0.868860i
$494$		−	9.68656e9i		−	0.162653i
$495$		0			0
$496$	−7.45775e10			−1.23220
$497$	−6.32680e10	−	6.32680e10i	−1.03695	−	1.03695i
$498$	−3.24974e9	+	3.24974e9i	−0.0528362	+	0.0528362i
$499$			1.83615e10i			0.296146i	0.988976	+	0.148073i	$0.0473070\pi$
$499$			1.83615e10i			0.296146i	−0.988976	+	0.148073i	$0.952693\pi$
$500$		0			0
$501$	−1.16952e10			−0.185633
$502$	−4.92894e10	−	4.92894e10i	−0.776138	−	0.776138i
$503$	−6.21239e9	+	6.21239e9i	−0.0970480	+	0.0970480i	−0.753964	−	0.656916i	$-0.771861\pi$
$503$	−6.21239e9	+	6.21239e9i	−0.0970480	+	0.0970480i	0.656916	+	0.753964i	$0.271861\pi$
$504$			9.40761e10i			1.45800i
$505$		0			0
$506$	6.37750e10			0.972856
$507$	9.54691e9	+	9.54691e9i	0.144488	+	0.144488i
$508$	−1.32346e9	+	1.32346e9i	−0.0198727	+	0.0198727i
$509$		−	4.31615e10i		−	0.643021i	−0.946906	−	0.321511i	$-0.895809\pi$
$509$		−	4.31615e10i		−	0.643021i	0.946906	−	0.321511i	$-0.104191\pi$
$510$		0			0
$511$	9.56360e10			1.40261
$512$	−3.92707e10	−	3.92707e10i	−0.571463	−	0.571463i
$513$	−2.56723e10	+	2.56723e10i	−0.370677	+	0.370677i
$514$			1.35723e11i			1.94446i
$515$		0			0
$516$	1.71738e9			0.0242252
$517$	4.40420e10	+	4.40420e10i	0.616460	+	0.616460i
$518$	1.35261e11	−	1.35261e11i	1.87868	−	1.87868i
$519$			8.35628e9i			0.115171i
$520$		0			0
$521$	2.90244e10			0.393923			0.196962	−	0.980411i	$-0.436893\pi$
$521$	2.90244e10			0.393923			0.196962	+	0.980411i	$0.436893\pi$
$522$	4.97033e10	+	4.97033e10i	0.669426	+	0.669426i
$523$	−4.27429e10	+	4.27429e10i	−0.571291	+	0.571291i	−0.932489	−	0.361198i	$-0.882368\pi$
$523$	−4.27429e10	+	4.27429e10i	−0.571291	+	0.571291i	0.361198	+	0.932489i	$0.382368\pi$
$524$			9.99868e9i			0.132623i
$525$		0			0
$526$	3.78505e10			0.494457
$527$	8.02892e10	+	8.02892e10i	1.04091	+	1.04091i
$528$	1.03026e10	−	1.03026e10i	0.132559	−	0.132559i
$529$		−	1.96803e10i		−	0.251310i
$530$		0			0
$531$	−4.08043e10			−0.513249
$532$	−1.20084e10	−	1.20084e10i	−0.149913	−	0.149913i
$533$	3.20026e9	−	3.20026e9i	0.0396530	−	0.0396530i
$534$			7.36880e9i			0.0906217i
$535$		0			0
$536$	−6.25775e10			−0.758157
$537$	−1.37986e10	−	1.37986e10i	−0.165934	−	0.165934i
$538$	−3.12116e10	+	3.12116e10i	−0.372552	+	0.372552i
$539$			1.12621e11i			1.33434i
$540$		0			0
$541$	−6.67715e9			−0.0779475			−0.0389738	−	0.999240i	$-0.512409\pi$
$541$	−6.67715e9			−0.0779475			−0.0389738	+	0.999240i	$0.512409\pi$
$542$	−2.42707e10	−	2.42707e10i	−0.281245	−	0.281245i
$543$	−5.74738e9	+	5.74738e9i	−0.0661105	+	0.0661105i
$544$		−	2.31048e10i		−	0.263819i
$545$		0			0
$546$	−3.74749e9			−0.0421667
$547$	7.25792e10	+	7.25792e10i	0.810705	+	0.810705i	0.984740	−	0.174035i	$-0.0556805\pi$
$547$	7.25792e10	+	7.25792e10i	0.810705	+	0.810705i	−0.174035	+	0.984740i	$0.555681\pi$
$548$	4.22849e9	−	4.22849e9i	0.0468881	−	0.0468881i
$549$		−	9.03797e10i		−	0.994905i
$550$		0			0
$551$	1.12247e11			1.21778
$552$	−1.43567e10	−	1.43567e10i	−0.154632	−	0.154632i
$553$	7.57247e9	−	7.57247e9i	0.0809724	−	0.0809724i
$554$		−	1.02428e11i		−	1.08738i
$555$		0			0
$556$	2.38333e9			0.0249393
$557$	−2.52569e10	−	2.52569e10i	−0.262397	−	0.262397i	0.563630	−	0.826027i	$-0.309404\pi$
$557$	−2.52569e10	−	2.52569e10i	−0.262397	−	0.262397i	−0.826027	+	0.563630i	$0.809404\pi$
$558$	7.77507e10	−	7.77507e10i	0.801987	−	0.801987i
$559$			1.34748e10i			0.137999i
$560$		0			0
$561$	−2.21832e10			−0.223961
$562$	6.54026e10	+	6.54026e10i	0.655616	+	0.655616i
$563$	1.77029e10	−	1.77029e10i	0.176202	−	0.176202i	−0.613496	−	0.789698i	$-0.710237\pi$
$563$	1.77029e10	−	1.77029e10i	0.176202	−	0.176202i	0.789698	+	0.613496i	$0.210237\pi$
$564$			2.24155e9i			0.0221529i
$565$		0			0
$566$	−1.81290e11			−1.76648
$567$	−1.03069e11	−	1.03069e11i	−0.997231	−	0.997231i
$568$	−6.29941e10	+	6.29941e10i	−0.605211	+	0.605211i
$569$		−	5.69768e10i		−	0.543562i	−0.962359	−	0.271781i	$-0.912387\pi$
$569$		−	5.69768e10i		−	0.543562i	0.962359	−	0.271781i	$-0.0876126\pi$
$570$		0			0
$571$	−1.40041e11			−1.31738			−0.658690	−	0.752415i	$-0.728889\pi$
$571$	−1.40041e11			−1.31738			−0.658690	+	0.752415i	$0.728889\pi$
$572$	−7.64092e8	−	7.64092e8i	−0.00713775	−	0.00713775i
$573$	−1.77348e10	+	1.77348e10i	−0.164516	+	0.164516i
$574$		−	8.60609e10i		−	0.792790i
$575$		0			0
$576$	9.25822e10			0.841081
$577$	4.33597e10	+	4.33597e10i	0.391186	+	0.391186i	0.875110	−	0.483924i	$-0.160789\pi$
$577$	4.33597e10	+	4.33597e10i	0.391186	+	0.391186i	−0.483924	+	0.875110i	$0.660789\pi$
$578$	−5.79487e10	+	5.79487e10i	−0.519197	+	0.519197i
$579$		−	2.08489e10i		−	0.185510i
$580$		0			0
$581$	−6.32196e10			−0.554814
$582$	−2.28225e10	−	2.28225e10i	−0.198917	−	0.198917i
$583$	−3.81072e10	+	3.81072e10i	−0.329862	+	0.329862i
$584$		−	9.52220e10i		−	0.818627i
$585$		0			0
$586$	1.06831e11			0.905959
$587$	−1.52268e11	−	1.52268e11i	−1.28250	−	1.28250i	−0.939241	−	0.343258i	$-0.888470\pi$
$587$	−1.52268e11	−	1.52268e11i	−1.28250	−	1.28250i	−0.343258	−	0.939241i	$-0.611530\pi$
$588$	−2.86597e9	+	2.86597e9i	−0.0239752	+	0.0239752i
$589$		−	1.75588e11i		−	1.45893i
$590$		0			0
$591$	4.99958e9			0.0409811
$592$	−1.48495e11	−	1.48495e11i	−1.20900	−	1.20900i
$593$	5.29744e8	−	5.29744e8i	0.00428397	−	0.00428397i	−0.704962	−	0.709246i	$-0.749036\pi$
$593$	5.29744e8	−	5.29744e8i	0.00428397	−	0.00428397i	0.709246	+	0.704962i	$0.249036\pi$
$594$			4.39285e10i			0.352859i
$595$		0			0
$596$	−3.77779e9			−0.0299401
$597$	−1.71443e10	−	1.71443e10i	−0.134965	−	0.134965i
$598$	−1.27338e10	+	1.27338e10i	−0.0995757	+	0.0995757i
$599$			1.98446e11i			1.54147i	0.637157	+	0.770734i	$0.280110\pi$
$599$			1.98446e11i			1.54147i	−0.637157	+	0.770734i	$0.719890\pi$
$600$		0			0
$601$	−2.01430e11			−1.54393			−0.771964	−	0.635666i	$-0.780726\pi$
$601$	−2.01430e11			−1.54393			−0.771964	+	0.635666i	$0.780726\pi$
$602$	1.81182e11	+	1.81182e11i	1.37952	+	1.37952i
$603$	7.19352e10	−	7.19352e10i	0.544092	−	0.544092i
$604$		−	6.13367e8i		−	0.00460864i
$605$		0			0
$606$	5.09630e10			0.377889
$607$	1.38674e11	+	1.38674e11i	1.02150	+	1.02150i	0.999764	+	0.0217387i	$0.00692018\pi$
$607$	1.38674e11	+	1.38674e11i	1.02150	+	1.02150i	0.0217387	+	0.999764i	$0.493080\pi$
$608$	−2.52644e10	+	2.52644e10i	−0.184882	+	0.184882i
$609$		−	4.34256e10i		−	0.315702i
$610$		0			0
$611$	−1.75875e10			−0.126194
$612$	1.25695e10	+	1.25695e10i	0.0896006	+	0.0896006i
$613$	1.07154e11	−	1.07154e11i	0.758871	−	0.758871i	−0.217246	−	0.976117i	$-0.569707\pi$
$613$	1.07154e11	−	1.07154e11i	0.758871	−	0.758871i	0.976117	+	0.217246i	$0.0697074\pi$
$614$		−	3.65559e10i		−	0.257208i
$615$		0			0
$616$	1.81770e11			1.26240
$617$	8.73671e10	+	8.73671e10i	0.602847	+	0.602847i	0.941067	−	0.338220i	$-0.109825\pi$
$617$	8.73671e10	+	8.73671e10i	0.602847	+	0.602847i	−0.338220	+	0.941067i	$0.609825\pi$
$618$	2.06873e10	−	2.06873e10i	0.141824	−	0.141824i
$619$			1.24104e11i			0.845325i	0.906287	+	0.422663i	$0.138904\pi$
$619$			1.24104e11i			0.845325i	−0.906287	+	0.422663i	$0.861096\pi$
$620$		0			0
$621$	6.74968e10			0.453855
$622$	−6.20531e9	−	6.20531e9i	−0.0414574	−	0.0414574i
$623$	−7.16753e10	+	7.16753e10i	−0.475792	+	0.475792i
$624$			4.11417e9i			0.0271359i
$625$		0			0
$626$	−7.76936e10			−0.505927
$627$	2.42567e10	+	2.42567e10i	0.156950	+	0.156950i
$628$	−1.73549e10	+	1.73549e10i	−0.111579	+	0.111579i
$629$			3.19737e11i			2.04263i
$630$		0			0
$631$	2.11881e11			1.33652			0.668258	−	0.743929i	$-0.267040\pi$
$631$	2.11881e11			1.33652			0.668258	+	0.743929i	$0.267040\pi$
$632$	−7.53969e9	−	7.53969e9i	−0.0472591	−	0.0472591i
$633$	−1.86636e10	+	1.86636e10i	−0.116247	+	0.116247i
$634$			7.71045e10i			0.477225i
$635$		0			0
$636$	−1.93949e9			−0.0118538
$637$	−2.24868e10	−	2.24868e10i	−0.136575	−	0.136575i
$638$	9.60344e10	−	9.60344e10i	0.579621	−	0.579621i
$639$		−	1.44828e11i		−	0.868660i
$640$		0			0
$641$	−1.20192e11			−0.711940			−0.355970	−	0.934497i	$-0.615849\pi$
$641$	−1.20192e11			−0.711940			−0.355970	+	0.934497i	$0.615849\pi$
$642$	1.42852e10	+	1.42852e10i	0.0840906	+	0.0840906i
$643$	8.34104e10	−	8.34104e10i	0.487951	−	0.487951i	−0.419708	−	0.907659i	$-0.637868\pi$
$643$	8.34104e10	−	8.34104e10i	0.487951	−	0.487951i	0.907659	+	0.419708i	$0.137868\pi$
$644$			3.15721e10i			0.183552i
$645$		0			0
$646$	3.07881e11			1.76788
$647$	−1.74293e11	−	1.74293e11i	−0.994635	−	0.994635i	0.00535087	−	0.999986i	$-0.498297\pi$
$647$	−1.74293e11	−	1.74293e11i	−0.994635	−	0.994635i	−0.999986	+	0.00535087i	$0.998297\pi$
$648$	−1.02623e11	+	1.02623e11i	−0.582028	+	0.582028i
$649$			7.88403e10i			0.444395i
$650$		0			0
$651$	−6.79306e10			−0.378217
$652$	−6.70461e9	−	6.70461e9i	−0.0371008	−	0.0371008i
$653$	1.69727e11	−	1.69727e11i	0.933465	−	0.933465i	−0.0644553	−	0.997921i	$-0.520531\pi$
$653$	1.69727e11	−	1.69727e11i	0.933465	−	0.933465i	0.997921	+	0.0644553i	$0.0205310\pi$
$654$			1.03106e10i			0.0563600i
$655$		0			0
$656$	−9.44818e10			−0.510191
$657$	1.09461e11	+	1.09461e11i	0.587488	+	0.587488i
$658$	−2.36481e11	+	2.36481e11i	−1.26151	+	1.26151i
$659$			2.61429e11i			1.38616i	0.720862	+	0.693078i	$0.243746\pi$
$659$			2.61429e11i			1.38616i	−0.720862	+	0.693078i	$0.756254\pi$
$660$		0			0
$661$	−9.90557e10			−0.518888			−0.259444	−	0.965758i	$-0.583539\pi$
$661$	−9.90557e10			−0.518888			−0.259444	+	0.965758i	$0.583539\pi$
$662$	1.01634e11	+	1.01634e11i	0.529182	+	0.529182i
$663$	4.42927e9	−	4.42927e9i	0.0229233	−	0.0229233i
$664$			6.29459e10i			0.323814i
$665$		0			0
$666$	3.09628e11			1.57378
$667$	−1.47558e11	−	1.47558e11i	−0.745522	−	0.745522i
$668$	1.28038e10	−	1.28038e10i	0.0643034	−	0.0643034i
$669$			1.07405e10i			0.0536193i
$670$		0			0
$671$	−1.74628e11			−0.861436
$672$	9.77418e9	+	9.77418e9i	0.0479295	+	0.0479295i
$673$	−1.05855e11	+	1.05855e11i	−0.516003	+	0.516003i	−0.916359	−	0.400357i	$-0.868886\pi$
$673$	−1.05855e11	+	1.05855e11i	−0.516003	+	0.516003i	0.400357	+	0.916359i	$0.368886\pi$
$674$		−	1.70898e11i		−	0.828126i
$675$		0			0
$676$	−2.09039e10			−0.100101
$677$	−2.34302e11	−	2.34302e11i	−1.11538	−	1.11538i	−0.992411	−	0.122965i	$-0.960760\pi$
$677$	−2.34302e11	−	2.34302e11i	−1.11538	−	1.11538i	−0.122965	−	0.992411i	$-0.539240\pi$
$678$	3.65847e10	−	3.65847e10i	0.173133	−	0.173133i
$679$		−	4.43982e11i		−	2.08875i
$680$		0			0
$681$	3.36650e10			0.156528
$682$	−1.50226e11	−	1.50226e11i	−0.694399	−	0.694399i
$683$	−2.10586e11	+	2.10586e11i	−0.967715	+	0.967715i	−0.999495	−	0.0317802i	$-0.989882\pi$
$683$	−2.10586e11	+	2.10586e11i	−0.967715	+	0.967715i	0.0317802	+	0.999495i	$0.489882\pi$
$684$		−	2.74887e10i		−	0.125583i
$685$		0			0
$686$	−2.29183e11			−1.03487
$687$	6.04503e10	+	6.04503e10i	0.271376	+	0.271376i
$688$	1.98910e11	−	1.98910e11i	0.887776	−	0.887776i
$689$		−	1.52175e10i		−	0.0675254i
$690$		0			0
$691$	−4.57396e10			−0.200623			−0.100311	−	0.994956i	$-0.531984\pi$
$691$	−4.57396e10			−0.200623			−0.100311	+	0.994956i	$0.531984\pi$
$692$	−9.14843e9	−	9.14843e9i	−0.0398953	−	0.0398953i
$693$	−2.08951e11	+	2.08951e11i	−0.905965	+	0.905965i
$694$		−	6.55567e10i		−	0.282605i
$695$		0			0
$696$	−4.32376e10			−0.184257
$697$	1.01718e11	+	1.01718e11i	0.430989	+	0.430989i
$698$	9.49504e10	−	9.49504e10i	0.400014	−	0.400014i
$699$			7.68872e10i			0.322066i
$700$		0			0
$701$	9.83586e10			0.407324			0.203662	−	0.979041i	$-0.434716\pi$
$701$	9.83586e10			0.407324			0.203662	+	0.979041i	$0.434716\pi$
$702$	−8.77110e9	−	8.77110e9i	−0.0361165	−	0.0361165i
$703$	3.49623e11	−	3.49623e11i	1.43146	−	1.43146i
$704$		−	1.78883e11i		−	0.728247i
$705$		0			0
$706$	−4.74332e11			−1.90925
$707$	4.95710e11	+	4.95710e11i	1.98404	+	1.98404i
$708$	−2.00631e9	+	2.00631e9i	−0.00798483	+	0.00798483i
$709$		−	1.32351e11i		−	0.523771i	−0.965099	−	0.261885i	$-0.915656\pi$
$709$		−	1.32351e11i		−	0.523771i	0.965099	−	0.261885i	$-0.0843443\pi$
$710$		0			0
$711$	1.73343e10			0.0678310
$712$	7.13650e10	+	7.13650e10i	0.277693	+	0.277693i
$713$	−2.30825e11	+	2.30825e11i	−0.893151	+	0.893151i
$714$		−	1.19111e11i		−	0.458311i
$715$		0			0
$716$	3.02132e10			0.114960
$717$	7.66701e9	+	7.66701e9i	0.0290101	+	0.0290101i
$718$	2.28078e11	−	2.28078e11i	0.858194	−	0.858194i
$719$		−	2.14771e11i		−	0.803636i	−0.915720	−	0.401818i	$-0.868378\pi$
$719$		−	2.14771e11i		−	0.803636i	0.915720	−	0.401818i	$-0.131622\pi$
$720$		0			0
$721$	4.02444e11			1.48924
$722$	−1.34991e11	−	1.34991e11i	−0.496769	−	0.496769i
$723$	1.23568e10	−	1.23568e10i	0.0452224	−	0.0452224i
$724$		−	1.25844e10i		−	0.0458015i
$725$		0			0
$726$	−1.89429e10			−0.0681868
$727$	3.41170e10	+	3.41170e10i	0.122133	+	0.122133i	0.765531	−	0.643398i	$-0.222476\pi$
$727$	3.41170e10	+	3.41170e10i	0.122133	+	0.122133i	−0.643398	+	0.765531i	$0.722476\pi$
$728$	−3.62935e10	+	3.62935e10i	−0.129212	+	0.129212i
$729$		−	2.12181e11i		−	0.751270i
$730$		0			0
$731$	−4.28289e11			−1.49992
$732$	−4.44389e9	−	4.44389e9i	−0.0154782	−	0.0154782i
$733$	6.69873e10	−	6.69873e10i	0.232047	−	0.232047i	−0.581499	−	0.813547i	$-0.697534\pi$
$733$	6.69873e10	−	6.69873e10i	0.232047	−	0.232047i	0.813547	+	0.581499i	$0.197534\pi$
$734$			4.40897e11i			1.51898i
$735$		0			0
$736$	6.64244e10			0.226369
$737$	−1.38990e11	−	1.38990e11i	−0.471100	−	0.471100i
$738$	9.85020e10	−	9.85020e10i	0.332062	−	0.332062i
$739$			6.08310e10i			0.203961i	0.994786	+	0.101981i	$0.0325180\pi$
$739$			6.08310e10i			0.203961i	−0.994786	+	0.101981i	$0.967482\pi$
$740$		0			0
$741$	−9.68656e9			−0.0321290
$742$	−2.04614e11	−	2.04614e11i	−0.675025	−	0.675025i
$743$	−1.90364e11	+	1.90364e11i	−0.624639	+	0.624639i	−0.946714	−	0.322075i	$-0.895620\pi$
$743$	−1.90364e11	+	1.90364e11i	−0.624639	+	0.624639i	0.322075	+	0.946714i	$0.395620\pi$
$744$			6.76365e10i			0.220744i
$745$		0			0
$746$	−1.79438e11			−0.579375
$747$	−7.23587e10	−	7.23587e10i	−0.232385	−	0.232385i
$748$	2.42861e10	−	2.42861e10i	0.0775804	−	0.0775804i
$749$			2.77901e11i			0.883004i
$750$		0			0
$751$	3.43050e11			1.07844			0.539222	−	0.842164i	$-0.318718\pi$
$751$	3.43050e11			1.07844			0.539222	+	0.842164i	$0.318718\pi$
$752$	2.59620e11	+	2.59620e11i	0.811833	+	0.811833i
$753$	−4.92894e10	+	4.92894e10i	−0.153311	+	0.153311i
$754$			3.83499e10i			0.118653i
$755$		0			0
$756$	−2.17470e10			−0.0665752
$757$	−7.34063e10	−	7.34063e10i	−0.223537	−	0.223537i	0.586449	−	0.809986i	$-0.300525\pi$
$757$	−7.34063e10	−	7.34063e10i	−0.223537	−	0.223537i	−0.809986	+	0.586449i	$0.800525\pi$
$758$	−2.32697e11	+	2.32697e11i	−0.704878	+	0.704878i
$759$		−	6.37750e10i		−	0.192169i
$760$		0			0
$761$	5.88790e11			1.75558			0.877792	−	0.479042i	$-0.159016\pi$
$761$	5.88790e11			1.75558			0.877792	+	0.479042i	$0.159016\pi$
$762$	1.43545e10	+	1.43545e10i	0.0425762	+	0.0425762i
$763$	−1.00289e11	+	1.00289e11i	−0.295908	+	0.295908i
$764$		−	3.88321e10i		−	0.113977i
$765$		0			0
$766$	2.55251e11			0.741400
$767$	−1.57418e10	−	1.57418e10i	−0.0454856	−	0.0454856i
$768$	1.53842e10	−	1.53842e10i	0.0442211	−	0.0442211i
$769$			3.95721e11i			1.13158i	0.824550	+	0.565789i	$0.191428\pi$
$769$			3.95721e11i			1.13158i	−0.824550	+	0.565789i	$0.808572\pi$
$770$		0			0
$771$	1.35723e11			0.384091
$772$	2.28253e10	+	2.28253e10i	0.0642609	+	0.0642609i
$773$	3.23931e11	−	3.23931e11i	0.907265	−	0.907265i	−0.0887861	−	0.996051i	$-0.528299\pi$
$773$	3.23931e11	−	3.23931e11i	0.907265	−	0.907265i	0.996051	+	0.0887861i	$0.0282988\pi$
$774$			4.14748e11i			1.15563i
$775$		0			0
$776$	−4.42060e11			−1.21909
$777$	−1.35261e11	−	1.35261e11i	−0.371097	−	0.371097i
$778$	−4.25143e11	+	4.25143e11i	−1.16042	+	1.16042i
$779$		−	2.22452e11i		−	0.604068i
$780$		0			0
$781$	−2.79831e11			−0.752127
$782$	−4.04735e11	−	4.04735e11i	−1.08229	−	1.08229i
$783$	1.01639e11	−	1.01639e11i	0.270404	−	0.270404i
$784$			6.63883e11i			1.75722i
$785$		0			0
$786$	1.08447e11			0.284137
$787$	−4.07165e11	−	4.07165e11i	−1.06138	−	1.06138i	−0.997989	−	0.0633933i	$-0.979808\pi$
$787$	−4.07165e11	−	4.07165e11i	−1.06138	−	1.06138i	−0.0633933	−	0.997989i	$-0.520192\pi$
$788$	−5.47352e9	+	5.47352e9i	−0.0141959	+	0.0141959i
$789$		−	3.78505e10i		−	0.0976706i
$790$		0			0
$791$	7.11709e11			1.81801
$792$	2.08046e11	+	2.08046e11i	0.528761	+	0.528761i
$793$	3.48675e10	−	3.48675e10i	0.0881714	−	0.0881714i
$794$			9.15852e10i			0.230432i
$795$		0			0
$796$	3.75390e10			0.0935040
$797$	4.23268e11	+	4.23268e11i	1.04902	+	1.04902i	0.998735	+	0.0502807i	$0.0160116\pi$
$797$	4.23268e11	+	4.23268e11i	1.04902	+	1.04902i	0.0502807	+	0.998735i	$0.483988\pi$
$798$	−1.30245e11	+	1.30245e11i	−0.321181	+	0.321181i
$799$		−	5.59007e11i		−	1.37161i
$800$		0			0
$801$	−1.64073e11			−0.398573
$802$	4.03471e11	+	4.03471e11i	0.975248	+	0.975248i
$803$	2.11496e11	−	2.11496e11i	0.508675	−	0.508675i
$804$		−	7.07398e9i		−	0.0169293i
$805$		0			0
$806$	5.99907e10			0.142149
$807$	3.12116e10	+	3.12116e10i	0.0735905	+	0.0735905i
$808$	4.93564e11	−	4.93564e11i	1.15797	−	1.15797i
$809$			4.26454e11i			0.995584i	0.867296	+	0.497792i	$0.165856\pi$
$809$			4.26454e11i			0.995584i	−0.867296	+	0.497792i	$0.834144\pi$
$810$		0			0
$811$	−8.23140e11			−1.90279			−0.951394	−	0.307976i	$-0.900348\pi$
$811$	−8.23140e11			−1.90279			−0.951394	+	0.307976i	$0.900348\pi$
$812$	4.75423e10	+	4.75423e10i	0.109359	+	0.109359i
$813$	−2.42707e10	+	2.42707e10i	−0.0555545	+	0.0555545i
$814$		−	5.98249e11i		−	1.36265i
$815$		0			0
$816$	−1.30766e11			−0.294941
$817$	4.68322e11	+	4.68322e11i	1.05113	+	1.05113i
$818$	1.31598e11	−	1.31598e11i	0.293925	−	0.293925i
$819$		−	8.34414e10i		−	0.185458i
$820$		0			0
$821$	8.07431e11			1.77719			0.888593	−	0.458696i	$-0.151683\pi$
$821$	8.07431e11			1.77719			0.888593	+	0.458696i	$0.151683\pi$
$822$	−4.58628e10	−	4.58628e10i	−0.100455	−	0.100455i
$823$	−3.98475e11	+	3.98475e11i	−0.868564	+	0.868564i	−0.992313	−	0.123750i	$-0.960508\pi$
$823$	−3.98475e11	+	3.98475e11i	−0.868564	+	0.868564i	0.123750	+	0.992313i	$0.460508\pi$
$824$		−	4.00702e11i		−	0.869186i
$825$		0			0
$826$	−4.23328e11			−0.909404
$827$	−1.00453e11	−	1.00453e11i	−0.214755	−	0.214755i	0.591529	−	0.806284i	$-0.298525\pi$
$827$	−1.00453e11	−	1.00453e11i	−0.214755	−	0.214755i	−0.806284	+	0.591529i	$0.798525\pi$
$828$	−3.61362e10	+	3.61362e10i	−0.0768814	+	0.0768814i
$829$			3.20562e11i			0.678725i	0.940656	+	0.339363i	$0.110211\pi$
$829$			3.20562e11i			0.678725i	−0.940656	+	0.339363i	$0.889789\pi$
$830$		0			0
$831$	−1.02428e11			−0.214790
$832$	3.57172e10	+	3.57172e10i	0.0745390	+	0.0745390i
$833$	7.14728e11	−	7.14728e11i	1.48443	−	1.48443i
$834$		−	2.58500e10i		−	0.0534313i
$835$		0			0
$836$	−5.31124e10			−0.108735
$837$	−1.58993e11	−	1.58993e11i	−0.323949	−	0.323949i
$838$	−4.20551e11	+	4.20551e11i	−0.852790	+	0.852790i
$839$		−	8.34529e11i		−	1.68420i	−0.539322	−	0.842100i	$-0.681319\pi$
$839$		−	8.34529e11i		−	1.68420i	0.539322	−	0.842100i	$-0.318681\pi$
$840$		0			0
$841$	5.58509e10			0.111647
$842$	−3.54723e11	−	3.54723e11i	−0.705735	−	0.705735i
$843$	6.54026e10	−	6.54026e10i	0.129504	−	0.129504i
$844$		−	4.08657e10i		−	0.0805358i
$845$		0			0
$846$	−5.41333e11			−1.05678
$847$	−1.84255e11	−	1.84255e11i	−0.358002	−	0.358002i
$848$	−2.24635e11	+	2.24635e11i	−0.434405	+	0.434405i
$849$			1.81290e11i			0.348934i
$850$		0			0
$851$	−9.19218e11			−1.75267
$852$	−7.12107e9	−	7.12107e9i	−0.0135141	−	0.0135141i
$853$	−6.47254e11	+	6.47254e11i	−1.22258	+	1.22258i	−0.255873	+	0.966710i	$0.582363\pi$
$853$	−6.47254e11	+	6.47254e11i	−1.22258	+	1.22258i	−0.966710	+	0.255873i	$0.917637\pi$
$854$		−	9.37652e11i		−	1.76283i
$855$		0			0
$856$	2.76698e11			0.515360
$857$	−4.74533e11	−	4.74533e11i	−0.879717	−	0.879717i	0.113788	−	0.993505i	$-0.463702\pi$
$857$	−4.74533e11	−	4.74533e11i	−0.879717	−	0.879717i	−0.993505	+	0.113788i	$0.963702\pi$
$858$	−8.28746e9	+	8.28746e9i	−0.0152923	+	0.0152923i
$859$		−	3.29698e11i		−	0.605542i	−0.953063	−	0.302771i	$-0.902088\pi$
$859$		−	3.29698e11i		−	0.605542i	0.953063	−	0.302771i	$-0.0979117\pi$
$860$		0			0
$861$	−8.60609e10			−0.156601
$862$	7.20575e11	+	7.20575e11i	1.30512	+	1.30512i
$863$	−1.01436e10	+	1.01436e10i	−0.0182872	+	0.0182872i	−0.716191	−	0.697904i	$-0.754116\pi$
$863$	−1.01436e10	+	1.01436e10i	−0.0182872	+	0.0182872i	0.697904	+	0.716191i	$0.254116\pi$
$864$			4.57534e10i			0.0821048i
$865$		0			0
$866$	1.02109e12			1.81548
$867$	5.79487e10	+	5.79487e10i	0.102557	+	0.102557i
$868$	7.43702e10	−	7.43702e10i	0.131015	−	0.131015i
$869$		−	3.34926e10i		−	0.0587313i
$870$		0			0
$871$	5.55035e10			0.0964380
$872$	9.98551e10	+	9.98551e10i	0.172705	+	0.172705i
$873$	5.08165e11	−	5.08165e11i	0.874878	−	0.874878i
$874$			8.85134e11i			1.51692i
$875$		0			0
$876$	1.07642e10			0.0182796
$877$	−4.42556e11	−	4.42556e11i	−0.748118	−	0.748118i	0.226007	−	0.974126i	$-0.427433\pi$
$877$	−4.42556e11	−	4.42556e11i	−0.748118	−	0.748118i	−0.974126	+	0.226007i	$0.927433\pi$
$878$	−1.05242e11	+	1.05242e11i	−0.177096	+	0.177096i
$879$		−	1.06831e11i		−	0.178955i
$880$		0			0
$881$	−6.60238e11			−1.09597			−0.547983	−	0.836489i	$-0.684604\pi$
$881$	−6.60238e11			−1.09597			−0.547983	+	0.836489i	$0.684604\pi$
$882$	−6.92131e11	−	6.92131e11i	−1.14371	−	1.14371i
$883$	−4.41285e10	+	4.41285e10i	−0.0725899	+	0.0725899i	−0.742470	−	0.669880i	$-0.766346\pi$
$883$	−4.41285e10	+	4.41285e10i	−0.0725899	+	0.0725899i	0.669880	+	0.742470i	$0.266346\pi$
$884$			9.69830e9i			0.0158813i
$885$		0			0
$886$	−4.00058e11			−0.649215
$887$	1.59209e11	+	1.59209e11i	0.257202	+	0.257202i	0.823915	−	0.566713i	$-0.191785\pi$
$887$	1.59209e11	+	1.59209e11i	0.257202	+	0.257202i	−0.566713	+	0.823915i	$0.691785\pi$
$888$	−1.34675e11	+	1.34675e11i	−0.216588	+	0.216588i
$889$			2.79248e11i			0.447077i
$890$		0			0
$891$	−4.55868e11			−0.723316
$892$	−1.17587e10	−	1.17587e10i	−0.0185738	−	0.0185738i
$893$	−6.11259e11	+	6.11259e11i	−0.961213	+	0.961213i
$894$			4.09745e10i			0.0641451i
$895$		0			0
$896$	1.17122e12			1.81722
$897$	1.27338e10	+	1.27338e10i	0.0196693	+	0.0196693i
$898$	7.06588e11	−	7.06588e11i	1.08658	−	1.08658i
$899$			6.95167e11i			1.06427i
$900$		0			0
$901$	4.83679e11			0.733936
$902$	−1.90321e11	−	1.90321e11i	−0.287515	−	0.287515i
$903$	1.81182e11	−	1.81182e11i	0.272498	−	0.272498i
$904$		−	7.08628e11i		−	1.06107i
$905$		0			0
$906$	−6.65268e9			−0.00987378
$907$	5.09834e11	+	5.09834e11i	0.753355	+	0.753355i	0.975104	−	0.221749i	$-0.0711765\pi$
$907$	5.09834e11	+	5.09834e11i	0.753355	+	0.753355i	−0.221749	+	0.975104i	$0.571176\pi$
$908$	−3.68564e10	+	3.68564e10i	−0.0542213	+	0.0542213i
$909$			1.13474e12i			1.66204i
$910$		0			0
$911$	1.03435e12			1.50173			0.750867	−	0.660454i	$-0.229636\pi$
$911$	1.03435e12			1.50173			0.750867	+	0.660454i	$0.229636\pi$
$912$	1.42989e11	+	1.42989e11i	0.206692	+	0.206692i
$913$	−1.39808e11	+	1.39808e11i	−0.201210	+	0.201210i
$914$		−	6.91399e10i		−	0.0990704i
$915$		0			0
$916$	−1.32362e11			−0.188010
$917$	1.05485e12	+	1.05485e12i	1.49181	+	1.49181i
$918$	2.78783e11	−	2.78783e11i	0.392551	−	0.392551i
$919$			7.04400e11i			0.987545i	0.869591	+	0.493773i	$0.164383\pi$
$919$			7.04400e11i			0.987545i	−0.869591	+	0.493773i	$0.835617\pi$
$920$		0			0
$921$	−3.65559e10			−0.0508065
$922$	5.69889e10	+	5.69889e10i	0.0788618	+	0.0788618i
$923$	5.58730e10	−	5.58730e10i	0.0769831	−	0.0769831i
$924$			2.05479e10i			0.0281890i
$925$		0			0
$926$	1.00554e12			1.36759
$927$	4.60622e11	+	4.60622e11i	0.623772	+	0.623772i
$928$	1.00024e11	−	1.00024e11i	0.134869	−	0.134869i
$929$		−	1.87137e10i		−	0.0251244i	−0.999921	−	0.0125622i	$-0.996001\pi$
$929$		−	1.87137e10i		−	0.0251244i	0.999921	−	0.0125622i	$-0.00399878\pi$
$930$		0			0
$931$	−1.56307e12			−2.08056
$932$	−8.41759e10	−	8.41759e10i	−0.111564	−	0.111564i
$933$	−6.20531e9	+	6.20531e9i	−0.00818911	+	0.00818911i
$934$			6.07480e11i			0.798260i
$935$		0			0
$936$	−8.30802e10			−0.108242
$937$	−3.35310e11	−	3.35310e11i	−0.434999	−	0.434999i	0.455326	−	0.890325i	$-0.349523\pi$
$937$	−3.35310e11	−	3.35310e11i	−0.434999	−	0.434999i	−0.890325	+	0.455326i	$0.849523\pi$
$938$	7.46298e11	−	7.46298e11i	0.964052	−	0.964052i
$939$			7.76936e10i			0.0999362i
$940$		0			0
$941$	8.90806e10			0.113612			0.0568060	−	0.998385i	$-0.481908\pi$
$941$	8.90806e10			0.113612			0.0568060	+	0.998385i	$0.481908\pi$
$942$	1.88234e11	+	1.88234e11i	0.239053	+	0.239053i
$943$	−2.92431e11	+	2.92431e11i	−0.369808	+	0.369808i
$944$			4.64750e11i			0.585236i
$945$		0			0
$946$	8.01357e11			1.00060
$947$	−2.19250e11	−	2.19250e11i	−0.272609	−	0.272609i	0.557541	−	0.830149i	$-0.311745\pi$
$947$	−2.19250e11	−	2.19250e11i	−0.272609	−	0.272609i	−0.830149	+	0.557541i	$0.811745\pi$
$948$	8.52313e8	−	8.52313e8i	0.00105527	−	0.00105527i
$949$			8.44578e10i			0.104130i
$950$		0			0
$951$	7.71045e10			0.0942666
$952$	−1.15356e12	−	1.15356e12i	−1.40441	−	1.40441i
$953$	−6.14838e11	+	6.14838e11i	−0.745399	+	0.745399i	−0.973611	−	0.228212i	$-0.926712\pi$
$953$	−6.14838e11	+	6.14838e11i	−0.745399	+	0.745399i	0.228212	+	0.973611i	$0.426712\pi$
$954$		−	4.68387e11i		−	0.565472i
$955$		0			0
$956$	−1.67876e10			−0.0200982
$957$	−9.60344e10	−	9.60344e10i	−0.114493	−	0.114493i
$958$	−5.53396e11	+	5.53396e11i	−0.657013	+	0.657013i
$959$		−	8.92202e11i		−	1.05485i
$960$		0			0
$961$	2.34557e11			0.275015
$962$	1.19451e11	+	1.19451e11i	0.139473	+	0.139473i
$963$	−3.18075e11	+	3.18075e11i	−0.369849	+	0.369849i
$964$			2.70564e10i			0.0313302i
$965$		0			0
$966$	3.42436e11			0.393252
$967$	−1.52674e11	−	1.52674e11i	−0.174606	−	0.174606i	0.614394	−	0.789000i	$-0.289401\pi$
$967$	−1.52674e11	−	1.52674e11i	−0.174606	−	0.174606i	−0.789000	+	0.614394i	$0.789401\pi$
$968$	−1.83457e11	+	1.83457e11i	−0.208946	+	0.208946i
$969$		−	3.07881e11i		−	0.349211i
$970$		0			0
$971$	−9.19748e11			−1.03465			−0.517323	−	0.855790i	$-0.673072\pi$
$971$	−9.19748e11			−1.03465			−0.517323	+	0.855790i	$0.673072\pi$
$972$	−3.76095e10	−	3.76095e10i	−0.0421340	−	0.0421340i
$973$	2.51439e11	−	2.51439e11i	0.280531	−	0.280531i
$974$		−	3.89231e11i		−	0.432486i
$975$		0			0
$976$	−1.02940e12			−1.13445
$977$	−8.77267e11	−	8.77267e11i	−0.962839	−	0.962839i	0.0364953	−	0.999334i	$-0.488381\pi$
$977$	−8.77267e11	−	8.77267e11i	−0.962839	−	0.962839i	−0.999334	+	0.0364953i	$0.988381\pi$
$978$	−7.27192e10	+	7.27192e10i	−0.0794866	+	0.0794866i
$979$			3.17015e11i			0.345104i
$980$		0			0
$981$	−2.29574e11			−0.247883
$982$	9.43732e11	+	9.43732e11i	1.01485	+	1.01485i
$983$	7.35056e11	−	7.35056e11i	0.787238	−	0.787238i	−0.193803	−	0.981041i	$-0.562082\pi$
$983$	7.35056e11	−	7.35056e11i	0.787238	−	0.787238i	0.981041	+	0.193803i	$0.0620821\pi$
$984$			8.56884e10i			0.0913990i
$985$		0			0
$986$	−1.21892e12			−1.28964
$987$	2.36481e11	+	2.36481e11i	0.249188	+	0.249188i
$988$	1.06048e10	−	1.06048e10i	0.0111295	−	0.0111295i
$989$		−	1.23130e12i		−	1.28700i
$990$		0			0
$991$	9.59785e11			0.995128			0.497564	−	0.867427i	$-0.334228\pi$
$991$	9.59785e11			0.995128			0.497564	+	0.867427i	$0.334228\pi$
$992$	−1.56467e11	−	1.56467e11i	−0.161576	−	0.161576i
$993$	1.01634e11	−	1.01634e11i	0.104530	−	0.104530i
$994$		−	1.50253e12i		−	1.53914i
$995$		0			0
$996$	−7.11563e9			−0.00723062
$997$	−4.56146e11	−	4.56146e11i	−0.461661	−	0.461661i	0.437538	−	0.899200i	$-0.355850\pi$
$997$	−4.56146e11	−	4.56146e11i	−0.461661	−	0.461661i	−0.899200	+	0.437538i	$0.855850\pi$
$998$	−2.18030e11	+	2.18030e11i	−0.219783	+	0.219783i
$999$		−	6.33162e11i		−	0.635701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.a.7.2	yes	4
5.2	odd	4	inner	25.9.c.a.18.1	yes	4
5.3	odd	4	inner	25.9.c.a.18.2	yes	4
5.4	even	2	inner	25.9.c.a.7.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.c.a.7.1	✓	4	5.4	even	2	inner
25.9.c.a.7.2	yes	4	1.1	even	1	trivial
25.9.c.a.18.1	yes	4	5.2	odd	4	inner
25.9.c.a.18.2	yes	4	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.8743 + 11.8743i) q^{2} +(11.8743 - 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(2742.97 + 2742.97i) q^{7} +(2731.10 - 2731.10i) q^{8} +6279.00i q^{9} +O(q^{10})\)	\(q+(11.8743 + 11.8743i) q^{2} +(11.8743 - 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(2742.97 + 2742.97i) q^{7} +(2731.10 - 2731.10i) q^{8} +6279.00i q^{9} +12132.0 q^{11} +(308.733 + 308.733i) q^{12} +(-2422.37 + 2422.37i) q^{13} +65142.0i q^{14} +71516.0 q^{16} +(-76993.2 - 76993.2i) q^{17} +(-74559.0 + 74559.0i) q^{18} +168380. i q^{19} +65142.0 q^{21} +(144060. + 144060. i) q^{22} +(221350. - 221350. i) q^{23} -64860.0i q^{24} -57528.0 q^{26} +(152467. + 152467. i) q^{27} +(-71317.3 + 71317.3i) q^{28} -666630. i q^{29} -1.04281e6 q^{31} +(150044. + 150044. i) q^{32} +(144060. - 144060. i) q^{33} -1.82849e6i q^{34} -163254. q^{36} +(-2.07639e6 - 2.07639e6i) q^{37} +(-1.99940e6 + 1.99940e6i) q^{38} +57528.0i q^{39} -1.32113e6 q^{41} +(773518. + 773518. i) q^{42} +(2.78134e6 - 2.78134e6i) q^{43} +315432. i q^{44} +5.25676e6 q^{46} +(3.63024e6 + 3.63024e6i) q^{47} +(849205. - 849205. i) q^{48} +9.28300e6i q^{49} -1.82849e6 q^{51} +(-62981.5 - 62981.5i) q^{52} +(-3.14105e6 + 3.14105e6i) q^{53} +3.62088e6i q^{54} +1.49827e7 q^{56} +(1.99940e6 + 1.99940e6i) q^{57} +(7.91579e6 - 7.91579e6i) q^{58} +6.49854e6i q^{59} -1.43940e7 q^{61} +(-1.23827e7 - 1.23827e7i) q^{62} +(-1.72231e7 + 1.72231e7i) q^{63} -1.47447e7i q^{64} +3.42122e6 q^{66} +(-1.14565e7 - 1.14565e7i) q^{67} +(2.00182e6 - 2.00182e6i) q^{68} -5.25676e6i q^{69} -2.30655e7 q^{71} +(1.71486e7 + 1.71486e7i) q^{72} +(1.74329e7 - 1.74329e7i) q^{73} -4.93116e7i q^{74} -4.37788e6 q^{76} +(3.32777e7 + 3.32777e7i) q^{77} +(-683107. + 683107. i) q^{78} -2.76068e6i q^{79} -3.75756e7 q^{81} +(-1.56875e7 - 1.56875e7i) q^{82} +(-1.15239e7 + 1.15239e7i) q^{83} +1.69369e6i q^{84} +6.60531e7 q^{86} +(-7.91579e6 - 7.91579e6i) q^{87} +(3.31337e7 - 3.31337e7i) q^{88} +2.61305e7i q^{89} -1.32890e7 q^{91} +(5.75509e6 + 5.75509e6i) q^{92} +(-1.23827e7 + 1.23827e7i) q^{93} +8.62133e7i q^{94} +3.56335e6 q^{96} +(-8.09308e7 - 8.09308e7i) q^{97} +(-1.10230e8 + 1.10230e8i) q^{98} +7.61768e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1128 q^{6}+O(q^{10}) \) 4 * q + 1128 * q^6	\( 4 q + 1128 q^{6} + 48528 q^{11} + 286064 q^{16} + 260568 q^{21} - 230112 q^{26} - 4171232 q^{31} - 653016 q^{36} - 5284512 q^{41} + 21027048 q^{46} - 7313952 q^{51} + 59930640 q^{56} - 57575872 q^{61} + 13684896 q^{66} - 92261952 q^{71} - 17511520 q^{76} - 150302556 q^{81} + 264212568 q^{86} - 53155872 q^{91} + 14253408 q^{96}+O(q^{100}) \) 4 * q + 1128 * q^6 + 48528 * q^11 + 286064 * q^16 + 260568 * q^21 - 230112 * q^26 - 4171232 * q^31 - 653016 * q^36 - 5284512 * q^41 + 21027048 * q^46 - 7313952 * q^51 + 59930640 * q^56 - 57575872 * q^61 + 13684896 * q^66 - 92261952 * q^71 - 17511520 * q^76 - 150302556 * q^81 + 264212568 * q^86 - 53155872 * q^91 + 14253408 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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