LMFDB - Embedded newform 75.9.f.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1485512441856.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 119x^{4} + 625 $ x^8 + 119*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$2.30795 + 2.30795i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.85713 - 5.85713i) q^{2} +(33.0681 - 33.0681i) q^{3} -187.388i q^{4} -387.369 q^{6} +(1106.65 + 1106.65i) q^{7} +(-2596.98 + 2596.98i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-5.85713 - 5.85713i) q^{2} +(33.0681 - 33.0681i) q^{3} -187.388i q^{4} -387.369 q^{6} +(1106.65 + 1106.65i) q^{7} +(-2596.98 + 2596.98i) q^{8} -2187.00i q^{9} +20307.9 q^{11} +(-6196.57 - 6196.57i) q^{12} +(38060.2 - 38060.2i) q^{13} -12963.6i q^{14} -17549.6 q^{16} +(35079.5 + 35079.5i) q^{17} +(-12809.6 + 12809.6i) q^{18} +33759.4i q^{19} +73189.5 q^{21} +(-118946. - 118946. i) q^{22} +(180062. - 180062. i) q^{23} +171755. i q^{24} -445847. q^{26} +(-72320.0 - 72320.0i) q^{27} +(207372. - 207372. i) q^{28} +126808. i q^{29} -606669. q^{31} +(767618. + 767618. i) q^{32} +(671543. - 671543. i) q^{33} -410930. i q^{34} -409817. q^{36} +(-32513.8 - 32513.8i) q^{37} +(197734. - 197734. i) q^{38} -2.51716e6i q^{39} -4.66638e6 q^{41} +(-428680. - 428680. i) q^{42} +(2.52144e6 - 2.52144e6i) q^{43} -3.80545e6i q^{44} -2.10930e6 q^{46} +(-2.01575e6 - 2.01575e6i) q^{47} +(-580331. + 580331. i) q^{48} -3.31547e6i q^{49} +2.32002e6 q^{51} +(-7.13202e6 - 7.13202e6i) q^{52} +(6.90838e6 - 6.90838e6i) q^{53} +847175. i q^{54} -5.74789e6 q^{56} +(1.11636e6 + 1.11636e6i) q^{57} +(742729. - 742729. i) q^{58} -3.09316e6i q^{59} -2.67808e7 q^{61} +(3.55334e6 + 3.55334e6i) q^{62} +(2.42024e6 - 2.42024e6i) q^{63} -4.49939e6i q^{64} -7.86663e6 q^{66} +(-5.43157e6 - 5.43157e6i) q^{67} +(6.57347e6 - 6.57347e6i) q^{68} -1.19086e7i q^{69} +4.05288e7 q^{71} +(5.67960e6 + 5.67960e6i) q^{72} +(-1.17468e6 + 1.17468e6i) q^{73} +380876. i q^{74} +6.32611e6 q^{76} +(2.24736e7 + 2.24736e7i) q^{77} +(-1.47433e7 + 1.47433e7i) q^{78} +5.57922e7i q^{79} -4.78297e6 q^{81} +(2.73316e7 + 2.73316e7i) q^{82} +(3.11112e7 - 3.11112e7i) q^{83} -1.37148e7i q^{84} -2.95368e7 q^{86} +(4.19329e6 + 4.19329e6i) q^{87} +(-5.27392e7 + 5.27392e7i) q^{88} +5.37783e7i q^{89} +8.42384e7 q^{91} +(-3.37415e7 - 3.37415e7i) q^{92} +(-2.00614e7 + 2.00614e7i) q^{93} +2.36130e7i q^{94} +5.07673e7 q^{96} +(-9.15785e7 - 9.15785e7i) q^{97} +(-1.94191e7 + 1.94191e7i) q^{98} -4.44133e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 1296 q^{6}+O(q^{10}) $ 8 * q + 1296 * q^6	$ 8 q + 1296 q^{6} + 52752 q^{11} + 164320 q^{16} + 31752 q^{21} - 3637584 q^{26} - 6842152 q^{31} - 1854576 q^{36} - 29029152 q^{41} - 18397632 q^{46} - 10226736 q^{51} - 46814880 q^{56} - 73982120 q^{61} - 51725952 q^{66} + 33100896 q^{71} + 13636624 q^{76} - 38263752 q^{81} + 271592592 q^{86} + 507032568 q^{91} + 165488832 q^{96}+O(q^{100}) $ 8 * q + 1296 * q^6 + 52752 * q^11 + 164320 * q^16 + 31752 * q^21 - 3637584 * q^26 - 6842152 * q^31 - 1854576 * q^36 - 29029152 * q^41 - 18397632 * q^46 - 10226736 * q^51 - 46814880 * q^56 - 73982120 * q^61 - 51725952 * q^66 + 33100896 * q^71 + 13636624 * q^76 - 38263752 * q^81 + 271592592 * q^86 + 507032568 * q^91 + 165488832 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−5.85713	−	5.85713i	−0.366071	−	0.366071i	0.499971	−	0.866042i	$-0.333344\pi$
$2$	−5.85713	−	5.85713i	−0.366071	−	0.366071i	−0.866042	+	0.499971i	$0.833344\pi$
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$		−	187.388i		−	0.731984i
$5$		0			0
$5$		0			0
$6$	−387.369			−0.298896
$7$	1106.65	+	1106.65i	0.460911	+	0.460911i	0.898954	−	0.438043i	$-0.144328\pi$
$7$	1106.65	+	1106.65i	0.460911	+	0.460911i	−0.438043	+	0.898954i	$0.644328\pi$
$8$	−2596.98	+	2596.98i	−0.634029	+	0.634029i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	20307.9			1.38705			0.693527	−	0.720430i	$-0.256056\pi$
$11$	20307.9			1.38705			0.693527	+	0.720430i	$0.256056\pi$
$12$	−6196.57	−	6196.57i	−0.298831	−	0.298831i
$13$	38060.2	−	38060.2i	1.33259	−	1.33259i	0.429549	−	0.903044i	$-0.358673\pi$
$13$	38060.2	−	38060.2i	1.33259	−	1.33259i	0.903044	−	0.429549i	$-0.141327\pi$
$14$		−	12963.6i		−	0.337452i
$15$		0			0
$16$	−17549.6			−0.267785
$17$	35079.5	+	35079.5i	0.420008	+	0.420008i	0.885206	−	0.465199i	$-0.154017\pi$
$17$	35079.5	+	35079.5i	0.420008	+	0.420008i	−0.465199	+	0.885206i	$0.654017\pi$
$18$	−12809.6	+	12809.6i	−0.122024	+	0.122024i
$19$			33759.4i			0.259048i	0.991576	+	0.129524i	$0.0413450\pi$
$19$			33759.4i			0.259048i	−0.991576	+	0.129524i	$0.958655\pi$
$20$		0			0
$21$	73189.5			0.376332
$22$	−118946.	−	118946.i	−0.507760	−	0.507760i
$23$	180062.	−	180062.i	0.643445	−	0.643445i	−0.307956	−	0.951401i	$-0.599645\pi$
$23$	180062.	−	180062.i	0.643445	−	0.643445i	0.951401	+	0.307956i	$0.0996449\pi$
$24$			171755.i			0.517683i
$25$		0			0
$26$	−445847.			−0.975647
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$	207372.	−	207372.i	0.337380	−	0.337380i
$29$			126808.i			0.179289i	0.995974	+	0.0896444i	$0.0285731\pi$
$29$			126808.i			0.179289i	−0.995974	+	0.0896444i	$0.971427\pi$
$30$		0			0
$31$	−606669.			−0.656909			−0.328455	−	0.944520i	$-0.606528\pi$
$31$	−606669.			−0.656909			−0.328455	+	0.944520i	$0.606528\pi$
$32$	767618.	+	767618.i	0.732057	+	0.732057i
$33$	671543.	−	671543.i	0.566263	−	0.566263i
$34$		−	410930.i		−	0.307505i
$35$		0			0
$36$	−409817.			−0.243995
$37$	−32513.8	−	32513.8i	−0.0173485	−	0.0173485i	0.698379	−	0.715728i	$-0.253905\pi$
$37$	−32513.8	−	32513.8i	−0.0173485	−	0.0173485i	−0.715728	+	0.698379i	$0.753905\pi$
$38$	197734.	−	197734.i	0.0948300	−	0.0948300i
$39$		−	2.51716e6i		−	1.08806i
$40$		0			0
$41$	−4.66638e6			−1.65137			−0.825686	−	0.564130i	$-0.809212\pi$
$41$	−4.66638e6			−1.65137			−0.825686	+	0.564130i	$0.809212\pi$
$42$	−428680.	−	428680.i	−0.137764	−	0.137764i
$43$	2.52144e6	−	2.52144e6i	0.737521	−	0.737521i	−0.234576	−	0.972098i	$-0.575370\pi$
$43$	2.52144e6	−	2.52144e6i	0.737521	−	0.737521i	0.972098	+	0.234576i	$0.0753703\pi$
$44$		−	3.80545e6i		−	1.01530i
$45$		0			0
$46$	−2.10930e6			−0.471093
$47$	−2.01575e6	−	2.01575e6i	−0.413090	−	0.413090i	0.469724	−	0.882814i	$-0.344354\pi$
$47$	−2.01575e6	−	2.01575e6i	−0.413090	−	0.413090i	−0.882814	+	0.469724i	$0.844354\pi$
$48$	−580331.	+	580331.i	−0.109323	+	0.109323i
$49$		−	3.31547e6i		−	0.575122i
$50$		0			0
$51$	2.32002e6			0.342935
$52$	−7.13202e6	−	7.13202e6i	−0.975437	−	0.975437i
$53$	6.90838e6	−	6.90838e6i	0.875533	−	0.875533i	−0.117535	−	0.993069i	$-0.537499\pi$
$53$	6.90838e6	−	6.90838e6i	0.875533	−	0.875533i	0.993069	+	0.117535i	$0.0374993\pi$
$54$			847175.i			0.0996319i
$55$		0			0
$56$	−5.74789e6			−0.584462
$57$	1.11636e6	+	1.11636e6i	0.105756	+	0.105756i
$58$	742729.	−	742729.i	0.0656324	−	0.0656324i
$59$		−	3.09316e6i		−	0.255266i	−0.991821	−	0.127633i	$-0.959262\pi$
$59$		−	3.09316e6i		−	0.255266i	0.991821	−	0.127633i	$-0.0407380\pi$
$60$		0			0
$61$	−2.67808e7			−1.93422			−0.967108	−	0.254366i	$-0.918133\pi$
$61$	−2.67808e7			−1.93422			−0.967108	+	0.254366i	$0.918133\pi$
$62$	3.55334e6	+	3.55334e6i	0.240475	+	0.240475i
$63$	2.42024e6	−	2.42024e6i	0.153637	−	0.153637i
$64$		−	4.49939e6i		−	0.268185i
$65$		0			0
$66$	−7.86663e6			−0.414585
$67$	−5.43157e6	−	5.43157e6i	−0.269542	−	0.269542i	0.559374	−	0.828915i	$-0.311042\pi$
$67$	−5.43157e6	−	5.43157e6i	−0.269542	−	0.269542i	−0.828915	+	0.559374i	$0.811042\pi$
$68$	6.57347e6	−	6.57347e6i	0.307439	−	0.307439i
$69$		−	1.19086e7i		−	0.525370i
$70$		0			0
$71$	4.05288e7			1.59489			0.797445	−	0.603392i	$-0.206185\pi$
$71$	4.05288e7			1.59489			0.797445	+	0.603392i	$0.206185\pi$
$72$	5.67960e6	+	5.67960e6i	0.211343	+	0.211343i
$73$	−1.17468e6	+	1.17468e6i	−0.0413644	+	0.0413644i	−0.727486	−	0.686122i	$-0.759312\pi$
$73$	−1.17468e6	+	1.17468e6i	−0.0413644	+	0.0413644i	0.686122	+	0.727486i	$0.259312\pi$
$74$			380876.i			0.0127015i
$75$		0			0
$76$	6.32611e6			0.189619
$77$	2.24736e7	+	2.24736e7i	0.639309	+	0.639309i
$78$	−1.47433e7	+	1.47433e7i	−0.398306	+	0.398306i
$79$			5.57922e7i			1.43240i	0.697893	+	0.716202i	$0.254121\pi$
$79$			5.57922e7i			1.43240i	−0.697893	+	0.716202i	$0.745879\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	2.73316e7	+	2.73316e7i	0.604519	+	0.604519i
$83$	3.11112e7	−	3.11112e7i	0.655548	−	0.655548i	−0.298776	−	0.954323i	$-0.596578\pi$
$83$	3.11112e7	−	3.11112e7i	0.655548	−	0.655548i	0.954323	+	0.298776i	$0.0965782\pi$
$84$		−	1.37148e7i		−	0.275469i
$85$		0			0
$86$	−2.95368e7			−0.539970
$87$	4.19329e6	+	4.19329e6i	0.0731944	+	0.0731944i
$88$	−5.27392e7	+	5.27392e7i	−0.879433	+	0.879433i
$89$			5.37783e7i			0.857131i	0.903511	+	0.428565i	$0.140981\pi$
$89$			5.37783e7i			0.857131i	−0.903511	+	0.428565i	$0.859019\pi$
$90$		0			0
$91$	8.42384e7			1.22841
$92$	−3.37415e7	−	3.37415e7i	−0.470991	−	0.470991i
$93$	−2.00614e7	+	2.00614e7i	−0.268182	+	0.268182i
$94$			2.36130e7i			0.302440i
$95$		0			0
$96$	5.07673e7			0.597722
$97$	−9.15785e7	−	9.15785e7i	−1.03444	−	1.03444i	−0.999385	−	0.0350572i	$-0.988839\pi$
$97$	−9.15785e7	−	9.15785e7i	−1.03444	−	1.03444i	−0.0350572	−	0.999385i	$-0.511161\pi$
$98$	−1.94191e7	+	1.94191e7i	−0.210536	+	0.210536i
$99$		−	4.44133e7i		−	0.462352i
$100$		0			0
$101$	1.86102e8			1.78841			0.894203	−	0.447662i	$-0.147743\pi$
$101$	1.86102e8			1.78841			0.894203	+	0.447662i	$0.147743\pi$
$102$	−1.35887e7	−	1.35887e7i	−0.125538	−	0.125538i
$103$	−8.62396e7	+	8.62396e7i	−0.766227	+	0.766227i	−0.977440	−	0.211213i	$-0.932259\pi$
$103$	−8.62396e7	+	8.62396e7i	−0.766227	+	0.766227i	0.211213	+	0.977440i	$0.432259\pi$
$104$			1.97683e8i			1.68980i
$105$		0			0
$106$	−8.09266e7			−0.641015
$107$	1.42221e8	+	1.42221e8i	1.08500	+	1.08500i	0.996035	+	0.0889663i	$0.0283563\pi$
$107$	1.42221e8	+	1.42221e8i	1.08500	+	1.08500i	0.0889663	+	0.996035i	$0.471644\pi$
$108$	−1.35519e7	+	1.35519e7i	−0.0996104	+	0.0996104i
$109$		−	2.30661e8i		−	1.63406i	−0.576595	−	0.817030i	$-0.695619\pi$
$109$		−	2.30661e8i		−	1.63406i	0.576595	−	0.817030i	$-0.304381\pi$
$110$		0			0
$111$	−2.15034e6			−0.0141650
$112$	−1.94212e7	−	1.94212e7i	−0.123425	−	0.123425i
$113$	−3.83447e7	+	3.83447e7i	−0.235175	+	0.235175i	−0.814849	−	0.579674i	$-0.803180\pi$
$113$	−3.83447e7	+	3.83447e7i	−0.235175	+	0.235175i	0.579674	+	0.814849i	$0.303180\pi$
$114$		−	1.30773e7i		−	0.0774284i
$115$		0			0
$116$	2.37622e7			0.131237
$117$	−8.32376e7	−	8.32376e7i	−0.444197	−	0.444197i
$118$	−1.81170e7	+	1.81170e7i	−0.0934456	+	0.0934456i
$119$			7.76412e7i			0.387172i
$120$		0			0
$121$	1.98051e8			0.923921
$122$	1.56859e8	+	1.56859e8i	0.708060	+	0.708060i
$123$	−1.54308e8	+	1.54308e8i	−0.674170	+	0.674170i
$124$			1.13683e8i			0.480847i
$125$		0			0
$126$	−2.83513e7			−0.112484
$127$	1.07039e8	+	1.07039e8i	0.411460	+	0.411460i	0.882247	−	0.470787i	$-0.156030\pi$
$127$	1.07039e8	+	1.07039e8i	0.411460	+	0.411460i	−0.470787	+	0.882247i	$0.656030\pi$
$128$	1.70157e8	−	1.70157e8i	0.633883	−	0.633883i
$129$		−	1.66758e8i		−	0.602184i
$130$		0			0
$131$	−3.75517e8			−1.27510			−0.637551	−	0.770408i	$-0.720052\pi$
$131$	−3.75517e8			−1.27510			−0.637551	+	0.770408i	$0.720052\pi$
$132$	−1.25839e8	−	1.25839e8i	−0.414495	−	0.414495i
$133$	−3.73598e7	+	3.73598e7i	−0.119398	+	0.119398i
$134$			6.36268e7i			0.197343i
$135$		0			0
$136$	−1.82202e8			−0.532594
$137$	4.18355e7	+	4.18355e7i	0.118758	+	0.118758i	0.763988	−	0.645230i	$-0.223239\pi$
$137$	4.18355e7	+	4.18355e7i	0.118758	+	0.118758i	−0.645230	+	0.763988i	$0.723239\pi$
$138$	−6.97505e7	+	6.97505e7i	−0.192323	+	0.192323i
$139$		−	3.73312e8i		−	1.00003i	−0.866017	−	0.500015i	$-0.833328\pi$
$139$		−	3.73312e8i		−	1.00003i	0.866017	−	0.500015i	$-0.166672\pi$
$140$		0			0
$141$	−1.33314e8			−0.337287
$142$	−2.37383e8	−	2.37383e8i	−0.583842	−	0.583842i
$143$	7.72921e8	−	7.72921e8i	1.84838	−	1.84838i
$144$			3.83809e7i			0.0892617i
$145$		0			0
$146$	1.37605e7			0.0302846
$147$	−1.09636e8	−	1.09636e8i	−0.234793	−	0.234793i
$148$	−6.09270e6	+	6.09270e6i	−0.0126988	+	0.0126988i
$149$			7.24478e8i			1.46987i	0.678136	+	0.734937i	$0.262788\pi$
$149$			7.24478e8i			1.46987i	−0.678136	+	0.734937i	$0.737212\pi$
$150$		0			0
$151$	−2.28197e8			−0.438937			−0.219468	−	0.975620i	$-0.570432\pi$
$151$	−2.28197e8			−0.438937			−0.219468	+	0.975620i	$0.570432\pi$
$152$	−8.76727e7	−	8.76727e7i	−0.164244	−	0.164244i
$153$	7.67188e7	−	7.67188e7i	0.140003	−	0.140003i
$154$		−	2.63262e8i		−	0.468065i
$155$		0			0
$156$	−4.71685e8			−0.796441
$157$	3.20804e8	+	3.20804e8i	0.528008	+	0.528008i	0.919978	−	0.391970i	$-0.128206\pi$
$157$	3.20804e8	+	3.20804e8i	0.528008	+	0.528008i	−0.391970	+	0.919978i	$0.628206\pi$
$158$	3.26783e8	−	3.26783e8i	0.524361	−	0.524361i
$159$		−	4.56894e8i		−	0.714870i
$160$		0			0
$161$	3.98531e8			0.593141
$162$	2.80145e7	+	2.80145e7i	0.0406745	+	0.0406745i
$163$	1.31891e8	−	1.31891e8i	0.186838	−	0.186838i	−0.607489	−	0.794328i	$-0.707823\pi$
$163$	1.31891e8	−	1.31891e8i	0.186838	−	0.186838i	0.794328	+	0.607489i	$0.207823\pi$
$164$			8.74424e8i			1.20878i
$165$		0			0
$166$	−3.64445e8			−0.479954
$167$	8.72543e7	+	8.72543e7i	0.112181	+	0.112181i	0.760969	−	0.648788i	$-0.224724\pi$
$167$	8.72543e7	+	8.72543e7i	0.112181	+	0.112181i	−0.648788	+	0.760969i	$0.724724\pi$
$168$	−1.90072e8	+	1.90072e8i	−0.238606	+	0.238606i
$169$		−	2.08142e9i		−	2.55161i
$170$		0			0
$171$	7.38319e7			0.0863494
$172$	−4.72487e8	−	4.72487e8i	−0.539854	−	0.539854i
$173$	8.30340e8	−	8.30340e8i	0.926983	−	0.926983i	−0.0705268	−	0.997510i	$-0.522468\pi$
$173$	8.30340e8	−	8.30340e8i	0.926983	−	0.926983i	0.997510	+	0.0705268i	$0.0224680\pi$
$174$		−	4.91213e7i		−	0.0535887i
$175$		0			0
$176$	−3.56394e8			−0.371433
$177$	−1.02285e8	−	1.02285e8i	−0.104212	−	0.104212i
$178$	3.14987e8	−	3.14987e8i	0.313771	−	0.313771i
$179$		−	1.18482e9i		−	1.15409i	−0.816711	−	0.577047i	$-0.804205\pi$
$179$		−	1.18482e9i		−	1.15409i	0.816711	−	0.577047i	$-0.195795\pi$
$180$		0			0
$181$	−2.64466e8			−0.246408			−0.123204	−	0.992381i	$-0.539317\pi$
$181$	−2.64466e8			−0.246408			−0.123204	+	0.992381i	$0.539317\pi$
$182$	−4.93395e8	−	4.93395e8i	−0.449686	−	0.449686i
$183$	−8.85592e8	+	8.85592e8i	−0.789640	+	0.789640i
$184$			9.35237e8i			0.815925i
$185$		0			0
$186$	2.35005e8			0.196347
$187$	7.12389e8	+	7.12389e8i	0.582574	+	0.582574i
$188$	−3.77727e8	+	3.77727e8i	−0.302375	+	0.302375i
$189$		−	1.60065e8i		−	0.125444i
$190$		0			0
$191$	−2.35604e8			−0.177031			−0.0885154	−	0.996075i	$-0.528212\pi$
$191$	−2.35604e8			−0.177031			−0.0885154	+	0.996075i	$0.528212\pi$
$192$	−1.48786e8	−	1.48786e8i	−0.109486	−	0.109486i
$193$	−1.36934e9	+	1.36934e9i	−0.986920	+	0.986920i	−0.999916	−	0.0129952i	$-0.995863\pi$
$193$	−1.36934e9	+	1.36934e9i	−0.986920	+	0.986920i	0.0129952	+	0.999916i	$0.495863\pi$
$194$			1.07277e9i			0.757359i
$195$		0			0
$196$	−6.21278e8			−0.420980
$197$	2.01542e9	+	2.01542e9i	1.33814	+	1.33814i	0.897864	+	0.440274i	$0.145119\pi$
$197$	2.01542e9	+	2.01542e9i	1.33814	+	1.33814i	0.440274	+	0.897864i	$0.354881\pi$
$198$	−2.60135e8	+	2.60135e8i	−0.169253	+	0.169253i
$199$			2.07907e9i			1.32573i	0.748737	+	0.662867i	$0.230661\pi$
$199$			2.07907e9i			1.32573i	−0.748737	+	0.662867i	$0.769339\pi$
$200$		0			0
$201$	−3.59223e8			−0.220080
$202$	−1.09003e9	−	1.09003e9i	−0.654683	−	0.654683i
$203$	−1.40331e8	+	1.40331e8i	−0.0826362	+	0.0826362i
$204$		−	4.34744e8i		−	0.251023i
$205$		0			0
$206$	1.01023e9			0.560987
$207$	−3.93796e8	−	3.93796e8i	−0.214482	−	0.214482i
$208$	−6.67939e8	+	6.67939e8i	−0.356848	+	0.356848i
$209$			6.85582e8i			0.359314i
$210$		0			0
$211$	2.81393e9			1.41966			0.709829	−	0.704374i	$-0.248772\pi$
$211$	2.81393e9			1.41966			0.709829	+	0.704374i	$0.248772\pi$
$212$	−1.29455e9	−	1.29455e9i	−0.640877	−	0.640877i
$213$	1.34021e9	−	1.34021e9i	0.651111	−	0.651111i
$214$		−	1.66602e9i		−	0.794374i
$215$		0			0
$216$	3.75627e8			0.172561
$217$	−6.71369e8	−	6.71369e8i	−0.302777	−	0.302777i
$218$	−1.35101e9	+	1.35101e9i	−0.598182	+	0.598182i
$219$			7.76886e7i			0.0337739i
$220$		0			0
$221$	2.67026e9			1.11940
$222$	1.25948e7	+	1.25948e7i	0.00518538	+	0.00518538i
$223$	−8.44395e8	+	8.44395e8i	−0.341449	+	0.341449i	−0.856912	−	0.515463i	$-0.827620\pi$
$223$	−8.44395e8	+	8.44395e8i	−0.341449	+	0.341449i	0.515463	+	0.856912i	$0.327620\pi$
$224$			1.69896e9i			0.674826i
$225$		0			0
$226$	4.49180e8			0.172181
$227$	3.17731e9	+	3.17731e9i	1.19662	+	1.19662i	0.975173	+	0.221445i	$0.0710774\pi$
$227$	3.17731e9	+	3.17731e9i	1.19662	+	1.19662i	0.221445	+	0.975173i	$0.428923\pi$
$228$	2.09193e8	−	2.09193e8i	0.0774117	−	0.0774117i
$229$			1.98891e9i			0.723225i	0.932329	+	0.361612i	$0.117774\pi$
$229$			1.98891e9i			0.723225i	−0.932329	+	0.361612i	$0.882226\pi$
$230$		0			0
$231$	1.48632e9			0.521993
$232$	−3.29317e8	−	3.29317e8i	−0.113674	−	0.113674i
$233$	−1.15947e9	+	1.15947e9i	−0.393402	+	0.393402i	−0.875898	−	0.482496i	$-0.839730\pi$
$233$	−1.15947e9	+	1.15947e9i	−0.393402	+	0.393402i	0.482496	+	0.875898i	$0.339730\pi$
$234$			9.75068e8i			0.325216i
$235$		0			0
$236$	−5.79620e8			−0.186851
$237$	1.84494e9	+	1.84494e9i	0.584776	+	0.584776i
$238$	4.54755e8	−	4.54755e8i	0.141732	−	0.141732i
$239$		−	2.87212e9i		−	0.880261i	−0.897934	−	0.440131i	$-0.854932\pi$
$239$		−	2.87212e9i		−	0.880261i	0.897934	−	0.440131i	$-0.145068\pi$
$240$		0			0
$241$	2.92807e9			0.867988			0.433994	−	0.900916i	$-0.357104\pi$
$241$	2.92807e9			0.867988			0.433994	+	0.900916i	$0.357104\pi$
$242$	−1.16001e9	−	1.16001e9i	−0.338221	−	0.338221i
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$			5.01841e9i			1.41582i
$245$		0			0
$246$	1.80761e9			0.493588
$247$	1.28489e9	+	1.28489e9i	0.345206	+	0.345206i
$248$	1.57551e9	−	1.57551e9i	0.416500	−	0.416500i
$249$		−	2.05758e9i		−	0.535253i
$250$		0			0
$251$	−2.42046e9			−0.609822			−0.304911	−	0.952381i	$-0.598627\pi$
$251$	−2.42046e9			−0.609822			−0.304911	+	0.952381i	$0.598627\pi$
$252$	−4.53523e8	−	4.53523e8i	−0.112460	−	0.112460i
$253$	3.65668e9	−	3.65668e9i	0.892493	−	0.892493i
$254$		−	1.25389e9i		−	0.301247i
$255$		0			0
$256$	−3.14510e9			−0.732277
$257$	−3.61426e9	−	3.61426e9i	−0.828490	−	0.828490i	0.158818	−	0.987308i	$-0.449232\pi$
$257$	−3.61426e9	−	3.61426e9i	−0.828490	−	0.828490i	−0.987308	+	0.158818i	$0.949232\pi$
$258$	−9.76727e8	+	9.76727e8i	−0.220442	+	0.220442i
$259$		−	7.19626e7i		−	0.0159922i
$260$		0			0
$261$	2.77328e8			0.0597630
$262$	2.19946e9	+	2.19946e9i	0.466778	+	0.466778i
$263$	−4.87560e9	+	4.87560e9i	−1.01907	+	1.01907i	−0.0192588	+	0.999815i	$0.506131\pi$
$263$	−4.87560e9	+	4.87560e9i	−1.01907	+	1.01907i	−0.999815	+	0.0192588i	$0.993869\pi$
$264$			3.48797e9i			0.718054i
$265$		0			0
$266$	4.37643e8			0.0874164
$267$	1.77835e9	+	1.77835e9i	0.349922	+	0.349922i
$268$	−1.01781e9	+	1.01781e9i	−0.197300	+	0.197300i
$269$		−	2.34422e9i		−	0.447703i	−0.974623	−	0.223851i	$-0.928137\pi$
$269$		−	2.34422e9i		−	0.447703i	0.974623	−	0.223851i	$-0.0718630\pi$
$270$		0			0
$271$	−4.34686e9			−0.805931			−0.402966	−	0.915215i	$-0.632021\pi$
$271$	−4.34686e9			−0.805931			−0.402966	+	0.915215i	$0.632021\pi$
$272$	−6.15629e8	−	6.15629e8i	−0.112472	−	0.112472i
$273$	2.78560e9	−	2.78560e9i	0.501497	−	0.501497i
$274$		−	4.90072e8i		−	0.0869477i
$275$		0			0
$276$	−2.23153e9			−0.384563
$277$	−2.78931e9	−	2.78931e9i	−0.473781	−	0.473781i	0.429355	−	0.903136i	$-0.358741\pi$
$277$	−2.78931e9	−	2.78931e9i	−0.473781	−	0.473781i	−0.903136	+	0.429355i	$0.858741\pi$
$278$	−2.18654e9	+	2.18654e9i	−0.366082	+	0.366082i
$279$			1.32679e9i			0.218970i
$280$		0			0
$281$	−2.37876e9			−0.381526			−0.190763	−	0.981636i	$-0.561096\pi$
$281$	−2.37876e9			−0.381526			−0.190763	+	0.981636i	$0.561096\pi$
$282$	7.80838e8	+	7.80838e8i	0.123471	+	0.123471i
$283$	2.50114e9	−	2.50114e9i	0.389935	−	0.389935i	−0.484729	−	0.874664i	$-0.661082\pi$
$283$	2.50114e9	−	2.50114e9i	0.389935	−	0.389935i	0.874664	+	0.484729i	$0.161082\pi$
$284$		−	7.59461e9i		−	1.16743i
$285$		0			0
$286$	−9.05420e9			−1.35328
$287$	−5.16404e9	−	5.16404e9i	−0.761135	−	0.761135i
$288$	1.67878e9	−	1.67878e9i	0.244019	−	0.244019i
$289$		−	4.51462e9i		−	0.647187i
$290$		0			0
$291$	−6.05665e9			−0.844619
$292$	2.20120e8	+	2.20120e8i	0.0302781	+	0.0302781i
$293$	9.38037e8	−	9.38037e8i	0.127277	−	0.127277i	−0.640599	−	0.767876i	$-0.721314\pi$
$293$	9.38037e8	−	9.38037e8i	0.127277	−	0.127277i	0.767876	+	0.640599i	$0.221314\pi$
$294$			1.28431e9i			0.171902i
$295$		0			0
$296$	1.68876e8			0.0219989
$297$	−1.46866e9	−	1.46866e9i	−0.188754	−	0.188754i
$298$	4.24336e9	−	4.24336e9i	0.538078	−	0.538078i
$299$		−	1.37064e10i		−	1.71490i
$300$		0			0
$301$	5.58069e9			0.679863
$302$	1.33658e9	+	1.33658e9i	0.160682	+	0.160682i
$303$	6.15405e9	−	6.15405e9i	0.730114	−	0.730114i
$304$		−	5.92463e8i		−	0.0693693i
$305$		0			0
$306$	−8.98704e8			−0.102502
$307$	5.86175e9	+	5.86175e9i	0.659893	+	0.659893i	0.955355	−	0.295462i	$-0.0954734\pi$
$307$	5.86175e9	+	5.86175e9i	0.659893	+	0.659893i	−0.295462	+	0.955355i	$0.595473\pi$
$308$	4.21129e9	−	4.21129e9i	0.467964	−	0.467964i
$309$			5.70356e9i			0.625622i
$310$		0			0
$311$	−9.11229e9			−0.974061			−0.487030	−	0.873385i	$-0.661920\pi$
$311$	−9.11229e9			−0.974061			−0.487030	+	0.873385i	$0.661920\pi$
$312$	6.53701e9	+	6.53701e9i	0.689860	+	0.689860i
$313$	−4.02063e9	+	4.02063e9i	−0.418906	+	0.418906i	−0.884827	−	0.465920i	$-0.845723\pi$
$313$	−4.02063e9	+	4.02063e9i	−0.418906	+	0.418906i	0.465920	+	0.884827i	$0.345723\pi$
$314$		−	3.75798e9i		−	0.386577i
$315$		0			0
$316$	1.04548e10			1.04850
$317$	−9.03622e9	−	9.03622e9i	−0.894849	−	0.894849i	0.100126	−	0.994975i	$-0.468076\pi$
$317$	−9.03622e9	−	9.03622e9i	−0.894849	−	0.894849i	−0.994975	+	0.100126i	$0.968076\pi$
$318$	−2.67609e9	+	2.67609e9i	−0.261693	+	0.261693i
$319$			2.57519e9i			0.248684i
$320$		0			0
$321$	9.40599e9			0.885900
$322$	−2.33425e9	−	2.33425e9i	−0.217132	−	0.217132i
$323$	−1.18426e9	+	1.18426e9i	−0.108802	+	0.108802i
$324$			8.96271e8i			0.0813316i
$325$		0			0
$326$	−1.54501e9			−0.136792
$327$	−7.62752e9	−	7.62752e9i	−0.667102	−	0.667102i
$328$	1.21185e10	−	1.21185e10i	1.04702	−	1.04702i
$329$		−	4.46144e9i		−	0.380795i
$330$		0			0
$331$	−1.22140e8			−0.0101753			−0.00508765	−	0.999987i	$-0.501619\pi$
$331$	−1.22140e8			−0.0101753			−0.00508765	+	0.999987i	$0.501619\pi$
$332$	−5.82986e9	−	5.82986e9i	−0.479851	−	0.479851i
$333$	−7.11077e7	+	7.11077e7i	−0.00578282	+	0.00578282i
$334$		−	1.02212e9i		−	0.0821327i
$335$		0			0
$336$	−1.28444e9			−0.100776
$337$	5.75655e9	+	5.75655e9i	0.446316	+	0.446316i	0.894128	−	0.447812i	$-0.147797\pi$
$337$	5.75655e9	+	5.75655e9i	0.446316	+	0.446316i	−0.447812	+	0.894128i	$0.647797\pi$
$338$	−1.21912e10	+	1.21912e10i	−0.934068	+	0.934068i
$339$			2.53597e9i			0.192020i
$340$		0			0
$341$	−1.23202e10			−0.911169
$342$	−4.32443e8	−	4.32443e8i	−0.0316100	−	0.0316100i
$343$	1.00487e10	−	1.00487e10i	0.725991	−	0.725991i
$344$			1.30963e10i			0.935220i
$345$		0			0
$346$	−9.72683e9			−0.678683
$347$	1.02276e10	+	1.02276e10i	0.705431	+	0.705431i	0.965571	−	0.260140i	$-0.0837688\pi$
$347$	1.02276e10	+	1.02276e10i	0.705431	+	0.705431i	−0.260140	+	0.965571i	$0.583769\pi$
$348$	7.85772e8	−	7.85772e8i	0.0535771	−	0.0535771i
$349$			1.35109e10i			0.910712i	0.890309	+	0.455356i	$0.150488\pi$
$349$			1.35109e10i			0.910712i	−0.890309	+	0.455356i	$0.849512\pi$
$350$		0			0
$351$	−5.50502e9			−0.362686
$352$	1.55887e10	+	1.55887e10i	1.01540	+	1.01540i
$353$	−1.50393e10	+	1.50393e10i	−0.968564	+	0.968564i	−0.999521	−	0.0309571i	$-0.990144\pi$
$353$	−1.50393e10	+	1.50393e10i	−0.968564	+	0.968564i	0.0309571	+	0.999521i	$0.490144\pi$
$354$			1.19819e9i			0.0762980i
$355$		0			0
$356$	1.00774e10			0.627406
$357$	2.56745e9	+	2.56745e9i	0.158062	+	0.158062i
$358$	−6.93966e9	+	6.93966e9i	−0.422480	+	0.422480i
$359$			2.41219e10i			1.45222i	0.687577	+	0.726111i	$0.258674\pi$
$359$			2.41219e10i			1.45222i	−0.687577	+	0.726111i	$0.741326\pi$
$360$		0			0
$361$	1.58439e10			0.932894
$362$	1.54901e9	+	1.54901e9i	0.0902029	+	0.0902029i
$363$	6.54916e9	−	6.54916e9i	0.377189	−	0.377189i
$364$		−	1.57853e10i		−	0.899179i
$365$		0			0
$366$	1.03741e10			0.578129
$367$	−1.77795e10	−	1.77795e10i	−0.980068	−	0.980068i	0.0197370	−	0.999805i	$-0.493717\pi$
$367$	−1.77795e10	−	1.77795e10i	−0.980068	−	0.980068i	−0.999805	+	0.0197370i	$0.993717\pi$
$368$	−3.16001e9	+	3.16001e9i	−0.172305	+	0.172305i
$369$			1.02054e10i			0.550457i
$370$		0			0
$371$	1.52903e10			0.807086
$372$	3.75927e9	+	3.75927e9i	0.196305	+	0.196305i
$373$	−9.55861e9	+	9.55861e9i	−0.493810	+	0.493810i	−0.909504	−	0.415695i	$-0.863539\pi$
$373$	−9.55861e9	+	9.55861e9i	−0.493810	+	0.493810i	0.415695	+	0.909504i	$0.363539\pi$
$374$		−	8.34512e9i		−	0.426527i
$375$		0			0
$376$	1.04697e10			0.523822
$377$	4.82632e9	+	4.82632e9i	0.238919	+	0.238919i
$378$	−9.37524e8	+	9.37524e8i	−0.0459214	+	0.0459214i
$379$			1.39162e10i			0.674474i	0.941420	+	0.337237i	$0.109492\pi$
$379$			1.39162e10i			0.674474i	−0.941420	+	0.337237i	$0.890508\pi$
$380$		0			0
$381$	7.07917e9			0.335956
$382$	1.37996e9	+	1.37996e9i	0.0648058	+	0.0648058i
$383$	3.87421e8	−	3.87421e8i	0.0180048	−	0.0180048i	−0.698047	−	0.716052i	$-0.745947\pi$
$383$	3.87421e8	−	3.87421e8i	0.0180048	−	0.0180048i	0.716052	+	0.698047i	$0.245947\pi$
$384$		−	1.12535e10i		−	0.517563i
$385$		0			0
$386$	1.60408e10			0.722566
$387$	−5.51439e9	−	5.51439e9i	−0.245840	−	0.245840i
$388$	−1.71607e10	+	1.71607e10i	−0.757196	+	0.757196i
$389$			6.64677e9i			0.290277i	0.989411	+	0.145138i	$0.0463627\pi$
$389$			6.64677e9i			0.290277i	−0.989411	+	0.145138i	$0.953637\pi$
$390$		0			0
$391$	1.26330e10			0.540503
$392$	8.61021e9	+	8.61021e9i	0.364644	+	0.364644i
$393$	−1.24177e10	+	1.24177e10i	−0.520558	+	0.520558i
$394$		−	2.36092e10i		−	0.979706i
$395$		0			0
$396$	−8.32252e9			−0.338434
$397$	−5.86473e9	−	5.86473e9i	−0.236095	−	0.236095i	0.579136	−	0.815231i	$-0.303390\pi$
$397$	−5.86473e9	−	5.86473e9i	−0.236095	−	0.236095i	−0.815231	+	0.579136i	$0.803390\pi$
$398$	1.21774e10	−	1.21774e10i	0.485313	−	0.485313i
$399$			2.47083e9i			0.0974882i
$400$		0			0
$401$	−3.20472e10			−1.23940			−0.619701	−	0.784838i	$-0.712746\pi$
$401$	−3.20472e10			−1.23940			−0.619701	+	0.784838i	$0.712746\pi$
$402$	2.10402e9	+	2.10402e9i	0.0805648	+	0.0805648i
$403$	−2.30899e10	+	2.30899e10i	−0.875392	+	0.875392i
$404$		−	3.48733e10i		−	1.30908i
$405$		0			0
$406$	1.64388e9			0.0605014
$407$	−6.60286e8	−	6.60286e8i	−0.0240633	−	0.0240633i
$408$	−6.02506e9	+	6.02506e9i	−0.217431	+	0.217431i
$409$			2.75999e10i			0.986313i	0.869941	+	0.493157i	$0.164157\pi$
$409$			2.75999e10i			0.986313i	−0.869941	+	0.493157i	$0.835843\pi$
$410$		0			0
$411$	2.76684e9			0.0969655
$412$	1.61603e10	+	1.61603e10i	0.560866	+	0.560866i
$413$	3.42303e9	−	3.42303e9i	0.117655	−	0.117655i
$414$			4.61303e9i			0.157031i
$415$		0			0
$416$	5.84313e10			1.95107
$417$	−1.23447e10	−	1.23447e10i	−0.408261	−	0.408261i
$418$	4.01555e9	−	4.01555e9i	0.131534	−	0.131534i
$419$			2.09715e10i			0.680414i	0.940351	+	0.340207i	$0.110497\pi$
$419$			2.09715e10i			0.680414i	−0.940351	+	0.340207i	$0.889503\pi$
$420$		0			0
$421$	1.19854e10			0.381526			0.190763	−	0.981636i	$-0.438904\pi$
$421$	1.19854e10			0.381526			0.190763	+	0.981636i	$0.438904\pi$
$422$	−1.64816e10	−	1.64816e10i	−0.519695	−	0.519695i
$423$	−4.40844e9	+	4.40844e9i	−0.137697	+	0.137697i
$424$			3.58819e10i			1.11023i
$425$		0			0
$426$	−1.56996e10			−0.476705
$427$	−2.96369e10	−	2.96369e10i	−0.891501	−	0.891501i
$428$	2.66506e10	−	2.66506e10i	0.794204	−	0.794204i
$429$		−	5.11181e10i		−	1.50920i
$430$		0			0
$431$	−9.29044e9			−0.269232			−0.134616	−	0.990898i	$-0.542980\pi$
$431$	−9.29044e9			−0.269232			−0.134616	+	0.990898i	$0.542980\pi$
$432$	1.26918e9	+	1.26918e9i	0.0364409	+	0.0364409i
$433$	1.48436e10	−	1.48436e10i	0.422267	−	0.422267i	−0.463717	−	0.885984i	$-0.653484\pi$
$433$	1.48436e10	−	1.48436e10i	0.422267	−	0.422267i	0.885984	+	0.463717i	$0.153484\pi$
$434$			7.86460e9i			0.221675i
$435$		0			0
$436$	−4.32231e10			−1.19611
$437$	6.07880e9	+	6.07880e9i	0.166683	+	0.166683i
$438$	4.55032e8	−	4.55032e8i	0.0123636	−	0.0123636i
$439$		−	3.74565e10i		−	1.00848i	−0.863562	−	0.504242i	$-0.831772\pi$
$439$		−	3.74565e10i		−	1.00848i	0.863562	−	0.504242i	$-0.168228\pi$
$440$		0			0
$441$	−7.25092e9			−0.191707
$442$	−1.56401e10	−	1.56401e10i	−0.409779	−	0.409779i
$443$	1.12412e10	−	1.12412e10i	0.291877	−	0.291877i	−0.545945	−	0.837821i	$-0.683829\pi$
$443$	1.12412e10	−	1.12412e10i	0.291877	−	0.291877i	0.837821	+	0.545945i	$0.183829\pi$
$444$			4.02948e8i			0.0103685i
$445$		0			0
$446$	9.89147e9			0.249989
$447$	2.39571e10	+	2.39571e10i	0.600073	+	0.600073i
$448$	4.97924e9	−	4.97924e9i	0.123609	−	0.123609i
$449$			6.71064e10i			1.65112i	0.564315	+	0.825560i	$0.309140\pi$
$449$			6.71064e10i			1.65112i	−0.564315	+	0.825560i	$0.690860\pi$
$450$		0			0
$451$	−9.47643e10			−2.29054
$452$	7.18533e9	+	7.18533e9i	0.172144	+	0.172144i
$453$	−7.54604e9	+	7.54604e9i	−0.179195	+	0.179195i
$454$		−	3.72198e10i		−	0.876094i
$455$		0			0
$456$	−5.79834e9			−0.134105
$457$	5.45475e9	+	5.45475e9i	0.125058	+	0.125058i	0.766865	−	0.641808i	$-0.221815\pi$
$457$	5.45475e9	+	5.45475e9i	0.125058	+	0.125058i	−0.641808	+	0.766865i	$0.721815\pi$
$458$	1.16493e10	−	1.16493e10i	0.264751	−	0.264751i
$459$		−	5.07389e9i		−	0.114312i
$460$		0			0
$461$	−2.99346e10			−0.662780			−0.331390	−	0.943494i	$-0.607518\pi$
$461$	−2.99346e10			−0.662780			−0.331390	+	0.943494i	$0.607518\pi$
$462$	−8.70559e9	−	8.70559e9i	−0.191087	−	0.191087i
$463$	7.39909e9	−	7.39909e9i	0.161011	−	0.161011i	−0.622004	−	0.783014i	$-0.713681\pi$
$463$	7.39909e9	−	7.39909e9i	0.161011	−	0.161011i	0.783014	+	0.622004i	$0.213681\pi$
$464$		−	2.22542e9i		−	0.0480109i
$465$		0			0
$466$	1.35824e10			0.288026
$467$	5.76602e10	+	5.76602e10i	1.21230	+	1.21230i	0.970270	+	0.242025i	$0.0778117\pi$
$467$	5.76602e10	+	5.76602e10i	1.21230	+	1.21230i	0.242025	+	0.970270i	$0.422188\pi$
$468$	−1.55977e10	+	1.55977e10i	−0.325146	+	0.325146i
$469$		−	1.20217e10i		−	0.248469i
$470$		0			0
$471$	2.12167e10			0.431117
$472$	8.03287e9	+	8.03287e9i	0.161846	+	0.161846i
$473$	5.12051e10	−	5.12051e10i	1.02298	−	1.02298i
$474$		−	2.16122e10i		−	0.428139i
$475$		0			0
$476$	1.45490e10			0.283404
$477$	−1.51086e10	−	1.51086e10i	−0.291844	−	0.291844i
$478$	−1.68224e10	+	1.68224e10i	−0.322238	+	0.322238i
$479$			8.46861e9i			0.160868i	0.996760	+	0.0804341i	$0.0256307\pi$
$479$			8.46861e9i			0.160868i	−0.996760	+	0.0804341i	$0.974369\pi$
$480$		0			0
$481$	−2.47496e9			−0.0462369
$482$	−1.71501e10	−	1.71501e10i	−0.317745	−	0.317745i
$483$	1.31787e10	−	1.31787e10i	0.242149	−	0.242149i
$484$		−	3.71123e10i		−	0.676296i
$485$		0			0
$486$	1.85277e9			0.0332106
$487$	−3.40281e10	−	3.40281e10i	−0.604954	−	0.604954i	0.336669	−	0.941623i	$-0.390700\pi$
$487$	−3.40281e10	−	3.40281e10i	−0.604954	−	0.604954i	−0.941623	+	0.336669i	$0.890700\pi$
$488$	6.95494e10	−	6.95494e10i	1.22635	−	1.22635i
$489$		−	8.72280e9i		−	0.152553i
$490$		0			0
$491$	−8.86536e10			−1.52535			−0.762677	−	0.646780i	$-0.776115\pi$
$491$	−8.86536e10			−1.52535			−0.762677	+	0.646780i	$0.776115\pi$
$492$	2.89155e10	+	2.89155e10i	0.493482	+	0.493482i
$493$	−4.44834e9	+	4.44834e9i	−0.0753027	+	0.0753027i
$494$		−	1.50515e10i		−	0.252740i
$495$		0			0
$496$	1.06468e10			0.175911
$497$	4.48511e10	+	4.48511e10i	0.735102	+	0.735102i
$498$	−1.20515e10	+	1.20515e10i	−0.195940	+	0.195940i
$499$		−	2.44875e10i		−	0.394949i	−0.980308	−	0.197475i	$-0.936726\pi$
$499$		−	2.44875e10i		−	0.394949i	0.980308	−	0.197475i	$-0.0632740\pi$
$500$		0			0
$501$	5.77067e9			0.0915957
$502$	1.41770e10	+	1.41770e10i	0.223238	+	0.223238i
$503$	2.95139e10	−	2.95139e10i	0.461057	−	0.461057i	−0.437945	−	0.899002i	$-0.644293\pi$
$503$	2.95139e10	−	2.95139e10i	0.461057	−	0.461057i	0.899002	+	0.437945i	$0.144293\pi$
$504$			1.25706e10i			0.194821i
$505$		0			0
$506$	−4.28353e10			−0.653431
$507$	−6.88287e10	−	6.88287e10i	−1.04169	−	1.04169i
$508$	2.00579e10	−	2.00579e10i	0.301183	−	0.301183i
$509$			9.36366e9i			0.139500i	0.997565	+	0.0697500i	$0.0222202\pi$
$509$			9.36366e9i			0.139500i	−0.997565	+	0.0697500i	$0.977780\pi$
$510$		0			0
$511$	−2.59990e9			−0.0381306
$512$	−2.51388e10	−	2.51388e10i	−0.365818	−	0.365818i
$513$	2.44148e9	−	2.44148e9i	0.0352520	−	0.0352520i
$514$			4.23385e10i			0.606572i
$515$		0			0
$516$	−3.12485e10			−0.440789
$517$	−4.09355e10	−	4.09355e10i	−0.572979	−	0.572979i
$518$	−4.21495e8	+	4.21495e8i	−0.00585428	+	0.00585428i
$519$		−	5.49156e10i		−	0.756879i
$520$		0			0
$521$	1.05168e11			1.42735			0.713675	−	0.700477i	$-0.247029\pi$
$521$	1.05168e11			1.42735			0.713675	+	0.700477i	$0.247029\pi$
$522$	−1.62435e9	−	1.62435e9i	−0.0218775	−	0.0218775i
$523$	3.38658e9	−	3.38658e9i	0.0452642	−	0.0452642i	−0.684112	−	0.729377i	$-0.739810\pi$
$523$	3.38658e9	−	3.38658e9i	0.0452642	−	0.0452642i	0.729377	+	0.684112i	$0.239810\pi$
$524$			7.03674e10i			0.933355i
$525$		0			0
$526$	5.71141e10			0.746106
$527$	−2.12816e10	−	2.12816e10i	−0.275907	−	0.275907i
$528$	−1.17853e10	+	1.17853e10i	−0.151637	+	0.151637i
$529$			1.34662e10i			0.171958i
$530$		0			0
$531$	−6.76473e9			−0.0850888
$532$	7.00077e9	+	7.00077e9i	0.0873976	+	0.0873976i
$533$	−1.77603e11	+	1.77603e11i	−2.20061	+	2.20061i
$534$		−	2.08320e10i		−	0.256193i
$535$		0			0
$536$	2.82114e10			0.341794
$537$	−3.91798e10	−	3.91798e10i	−0.471157	−	0.471157i
$538$	−1.37304e10	+	1.37304e10i	−0.163891	+	0.163891i
$539$		−	6.73300e10i		−	0.797726i
$540$		0			0
$541$	3.94182e10			0.460159			0.230080	−	0.973172i	$-0.426101\pi$
$541$	3.94182e10			0.460159			0.230080	+	0.973172i	$0.426101\pi$
$542$	2.54601e10	+	2.54601e10i	0.295028	+	0.295028i
$543$	−8.74539e9	+	8.74539e9i	−0.100596	+	0.100596i
$544$			5.38552e10i			0.614939i
$545$		0			0
$546$	−3.26313e10			−0.367167
$547$	−1.18155e10	−	1.18155e10i	−0.131978	−	0.131978i	0.638032	−	0.770010i	$-0.279749\pi$
$547$	−1.18155e10	−	1.18155e10i	−0.131978	−	0.131978i	−0.770010	+	0.638032i	$0.779749\pi$
$548$	7.83947e9	−	7.83947e9i	0.0869289	−	0.0869289i
$549$			5.85697e10i			0.644739i
$550$		0			0
$551$	−4.28095e9			−0.0464445
$552$	3.09265e10	+	3.09265e10i	0.333100	+	0.333100i
$553$	−6.17423e10	+	6.17423e10i	−0.660211	+	0.660211i
$554$			3.26747e10i			0.346875i
$555$		0			0
$556$	−6.99542e10			−0.732006
$557$	1.10650e11	+	1.10650e11i	1.14956	+	1.14956i	0.986640	+	0.162917i	$0.0520903\pi$
$557$	1.10650e11	+	1.10650e11i	1.14956	+	1.14956i	0.162917	+	0.986640i	$0.447910\pi$
$558$	7.77116e9	−	7.77116e9i	0.0801584	−	0.0801584i
$559$		−	1.91933e11i		−	1.96563i
$560$		0			0
$561$	4.71147e10			0.475669
$562$	1.39327e10	+	1.39327e10i	0.139666	+	0.139666i
$563$	7.40471e10	−	7.40471e10i	0.737012	−	0.737012i	−0.234987	−	0.971999i	$-0.575505\pi$
$563$	7.40471e10	−	7.40471e10i	0.737012	−	0.737012i	0.971999	+	0.234987i	$0.0755046\pi$
$564$			2.49814e10i			0.246888i
$565$		0			0
$566$	−2.92990e10			−0.285488
$567$	−5.29306e9	−	5.29306e9i	−0.0512123	−	0.0512123i
$568$	−1.05253e11	+	1.05253e11i	−1.01121	+	1.01121i
$569$			1.23910e11i			1.18211i	0.806631	+	0.591056i	$0.201289\pi$
$569$			1.23910e11i			1.18211i	−0.806631	+	0.591056i	$0.798711\pi$
$570$		0			0
$571$	1.83145e11			1.72286			0.861429	−	0.507877i	$-0.169570\pi$
$571$	1.83145e11			1.72286			0.861429	+	0.507877i	$0.169570\pi$
$572$	−1.44836e11	−	1.44836e11i	−1.35298	−	1.35298i
$573$	−7.79098e9	+	7.79098e9i	−0.0722725	+	0.0722725i
$574$			6.04929e10i			0.557259i
$575$		0			0
$576$	−9.84017e9			−0.0893949
$577$	1.40883e11	+	1.40883e11i	1.27103	+	1.27103i	0.945549	+	0.325481i	$0.105526\pi$
$577$	1.40883e11	+	1.40883e11i	1.27103	+	1.27103i	0.325481	+	0.945549i	$0.394474\pi$
$578$	−2.64427e10	+	2.64427e10i	−0.236916	+	0.236916i
$579$			9.05630e10i			0.805817i
$580$		0			0
$581$	6.88582e10			0.604298
$582$	3.54746e10	+	3.54746e10i	0.309190	+	0.309190i
$583$	1.40294e11	−	1.40294e11i	1.21441	−	1.21441i
$584$		−	6.10122e9i		−	0.0524524i
$585$		0			0
$586$	−1.09884e10			−0.0931847
$587$	−2.56405e10	−	2.56405e10i	−0.215960	−	0.215960i	0.590833	−	0.806794i	$-0.298799\pi$
$587$	−2.56405e10	−	2.56405e10i	−0.215960	−	0.215960i	−0.806794	+	0.590833i	$0.798799\pi$
$588$	−2.05445e10	+	2.05445e10i	−0.171865	+	0.171865i
$589$		−	2.04808e10i		−	0.170171i
$590$		0			0
$591$	1.33292e11			1.09258
$592$	5.70603e8	+	5.70603e8i	0.00464566	+	0.00464566i
$593$	−9.86176e10	+	9.86176e10i	−0.797509	+	0.797509i	−0.982702	−	0.185193i	$-0.940709\pi$
$593$	−9.86176e10	+	9.86176e10i	−0.797509	+	0.797509i	0.185193	+	0.982702i	$0.440709\pi$
$594$			1.72043e10i			0.138195i
$595$		0			0
$596$	1.35758e11			1.07592
$597$	6.87509e10	+	6.87509e10i	0.541229	+	0.541229i
$598$	−8.02802e10	+	8.02802e10i	−0.627775	+	0.627775i
$599$		−	5.83980e10i		−	0.453619i	−0.973939	−	0.226809i	$-0.927171\pi$
$599$		−	5.83980e10i		−	0.453619i	0.973939	−	0.226809i	$-0.0728294\pi$
$600$		0			0
$601$	2.35703e10			0.180662			0.0903309	−	0.995912i	$-0.471208\pi$
$601$	2.35703e10			0.180662			0.0903309	+	0.995912i	$0.471208\pi$
$602$	−3.26868e10	−	3.26868e10i	−0.248878	−	0.248878i
$603$	−1.18788e10	+	1.18788e10i	−0.0898472	+	0.0898472i
$604$			4.27613e10i			0.321295i
$605$		0			0
$606$	−7.20902e10			−0.534547
$607$	6.46123e10	+	6.46123e10i	0.475949	+	0.475949i	0.903833	−	0.427884i	$-0.140741\pi$
$607$	6.46123e10	+	6.46123e10i	0.475949	+	0.475949i	−0.427884	+	0.903833i	$0.640741\pi$
$608$	−2.59143e10	+	2.59143e10i	−0.189638	+	0.189638i
$609$			9.28098e9i			0.0674722i
$610$		0			0
$611$	−1.53439e11			−1.10096
$612$	−1.43762e10	−	1.43762e10i	−0.102480	−	0.102480i
$613$	3.03819e10	−	3.03819e10i	0.215165	−	0.215165i	−0.591292	−	0.806457i	$-0.701382\pi$
$613$	3.03819e10	−	3.03819e10i	0.215165	−	0.215165i	0.806457	+	0.591292i	$0.201382\pi$
$614$		−	6.86661e10i		−	0.483135i
$615$		0			0
$616$	−1.16727e11			−0.810681
$617$	2.55523e10	+	2.55523e10i	0.176315	+	0.176315i	0.789747	−	0.613432i	$-0.210212\pi$
$617$	2.55523e10	+	2.55523e10i	0.176315	+	0.176315i	−0.613432	+	0.789747i	$0.710212\pi$
$618$	3.34065e10	−	3.34065e10i	0.229022	−	0.229022i
$619$			1.91818e11i			1.30655i	0.757121	+	0.653275i	$0.226605\pi$
$619$			1.91818e11i			1.30655i	−0.757121	+	0.653275i	$0.773395\pi$
$620$		0			0
$621$	−2.60442e10			−0.175123
$622$	5.33719e10	+	5.33719e10i	0.356575	+	0.356575i
$623$	−5.95136e10	+	5.95136e10i	−0.395061	+	0.395061i
$624$			4.41750e10i			0.291366i
$625$		0			0
$626$	4.70987e10			0.306699
$627$	2.26709e10	+	2.26709e10i	0.146689	+	0.146689i
$628$	6.01147e10	−	6.01147e10i	0.386494	−	0.386494i
$629$		−	2.28113e9i		−	0.0145730i
$630$		0			0
$631$	9.85374e10			0.621561			0.310781	−	0.950482i	$-0.399410\pi$
$631$	9.85374e10			0.621561			0.310781	+	0.950482i	$0.399410\pi$
$632$	−1.44891e11	−	1.44891e11i	−0.908186	−	0.908186i
$633$	9.30514e10	−	9.30514e10i	0.579573	−	0.579573i
$634$			1.05853e11i			0.655156i
$635$		0			0
$636$	−8.56165e10			−0.523274
$637$	−1.26187e11	−	1.26187e11i	−0.766404	−	0.766404i
$638$	1.50832e10	−	1.50832e10i	0.0910358	−	0.0910358i
$639$		−	8.86365e10i		−	0.531630i
$640$		0			0
$641$	9.97357e10			0.590770			0.295385	−	0.955378i	$-0.404552\pi$
$641$	9.97357e10			0.590770			0.295385	+	0.955378i	$0.404552\pi$
$642$	−5.50922e10	−	5.50922e10i	−0.324302	−	0.324302i
$643$	2.05223e11	−	2.05223e11i	1.20056	−	1.20056i	0.226559	−	0.973997i	$-0.427252\pi$
$643$	2.05223e11	−	2.05223e11i	1.20056	−	1.20056i	0.973997	−	0.226559i	$-0.0727478\pi$
$644$		−	7.46798e10i		−	0.434170i
$645$		0			0
$646$	1.38728e10			0.0796587
$647$	−9.08930e10	−	9.08930e10i	−0.518696	−	0.518696i	0.398480	−	0.917177i	$-0.369538\pi$
$647$	−9.08930e10	−	9.08930e10i	−0.518696	−	0.518696i	−0.917177	+	0.398480i	$0.869538\pi$
$648$	1.24213e10	−	1.24213e10i	0.0704477	−	0.0704477i
$649$		−	6.28154e10i		−	0.354069i
$650$		0			0
$651$	−4.44018e10			−0.247216
$652$	−2.47148e10	−	2.47148e10i	−0.136763	−	0.136763i
$653$	−6.42783e10	+	6.42783e10i	−0.353518	+	0.353518i	−0.861417	−	0.507899i	$-0.830422\pi$
$653$	−6.42783e10	+	6.42783e10i	−0.353518	+	0.353518i	0.507899	+	0.861417i	$0.330422\pi$
$654$			8.93508e10i			0.488413i
$655$		0			0
$656$	8.18930e10			0.442213
$657$	2.56901e9	+	2.56901e9i	0.0137881	+	0.0137881i
$658$	−2.61313e10	+	2.61313e10i	−0.139398	+	0.139398i
$659$		−	2.78073e11i		−	1.47441i	−0.675670	−	0.737204i	$-0.736146\pi$
$659$		−	2.78073e11i		−	1.47441i	0.675670	−	0.737204i	$-0.263854\pi$
$660$		0			0
$661$	1.68908e11			0.884799			0.442400	−	0.896818i	$-0.354127\pi$
$661$	1.68908e11			0.884799			0.442400	+	0.896818i	$0.354127\pi$
$662$	7.15393e8	+	7.15393e8i	0.00372488	+	0.00372488i
$663$	8.83005e10	−	8.83005e10i	0.456992	−	0.456992i
$664$			1.61590e11i			0.831273i
$665$		0			0
$666$	8.32975e8			0.00423385
$667$	2.28333e10	+	2.28333e10i	0.115362	+	0.115362i
$668$	1.63504e10	−	1.63504e10i	0.0821150	−	0.0821150i
$669$			5.58451e10i			0.278792i
$670$		0			0
$671$	−5.43862e11			−2.68286
$672$	5.61815e10	+	5.61815e10i	0.275497	+	0.275497i
$673$	2.63803e10	−	2.63803e10i	0.128593	−	0.128593i	−0.639881	−	0.768474i	$-0.721016\pi$
$673$	2.63803e10	−	2.63803e10i	0.128593	−	0.128593i	0.768474	+	0.639881i	$0.221016\pi$
$674$		−	6.74337e10i		−	0.326766i
$675$		0			0
$676$	−3.90034e11			−1.86773
$677$	1.77432e11	+	1.77432e11i	0.844652	+	0.844652i	0.989460	−	0.144808i	$-0.0462565\pi$
$677$	1.77432e11	+	1.77432e11i	0.844652	+	0.844652i	−0.144808	+	0.989460i	$0.546256\pi$
$678$	1.48535e10	−	1.48535e10i	0.0702928	−	0.0702928i
$679$		−	2.02690e11i		−	0.953572i
$680$		0			0
$681$	2.10135e11			0.977034
$682$	7.21609e10	+	7.21609e10i	0.333553	+	0.333553i
$683$	−2.40451e10	+	2.40451e10i	−0.110495	+	0.110495i	−0.760193	−	0.649697i	$-0.774896\pi$
$683$	−2.40451e10	+	2.40451e10i	−0.110495	+	0.110495i	0.649697	+	0.760193i	$0.274896\pi$
$684$		−	1.38352e10i		−	0.0632064i
$685$		0			0
$686$	−1.17713e11			−0.531528
$687$	6.57695e10	+	6.57695e10i	0.295255	+	0.295255i
$688$	−4.42502e10	+	4.42502e10i	−0.197497	+	0.197497i
$689$		−	5.25868e11i		−	2.33346i
$690$		0			0
$691$	−2.97853e11			−1.30644			−0.653221	−	0.757168i	$-0.726583\pi$
$691$	−2.97853e11			−1.30644			−0.653221	+	0.757168i	$0.726583\pi$
$692$	−1.55596e11	−	1.55596e11i	−0.678537	−	0.678537i
$693$	4.91499e10	−	4.91499e10i	0.213103	−	0.213103i
$694$		−	1.19808e11i		−	0.516475i
$695$		0			0
$696$	−2.17798e10			−0.0928147
$697$	−1.63694e11	−	1.63694e11i	−0.693589	−	0.693589i
$698$	7.91349e10	−	7.91349e10i	0.333385	−	0.333385i
$699$			7.66831e10i			0.321211i
$700$		0			0
$701$	−2.00659e10			−0.0830973			−0.0415487	−	0.999136i	$-0.513229\pi$
$701$	−2.00659e10			−0.0830973			−0.0415487	+	0.999136i	$0.513229\pi$
$702$	3.22436e10	+	3.22436e10i	0.132769	+	0.132769i
$703$	1.09765e9	−	1.09765e9i	0.00449409	−	0.00449409i
$704$		−	9.13731e10i		−	0.371987i
$705$		0			0
$706$	1.76174e11			0.709126
$707$	2.05949e11	+	2.05949e11i	0.824296	+	0.824296i
$708$	−1.91669e10	+	1.91669e10i	−0.0762816	+	0.0762816i
$709$			3.15404e10i			0.124820i	0.998051	+	0.0624098i	$0.0198786\pi$
$709$			3.15404e10i			0.124820i	−0.998051	+	0.0624098i	$0.980121\pi$
$710$		0			0
$711$	1.22018e11			0.477468
$712$	−1.39661e11	−	1.39661e11i	−0.543446	−	0.543446i
$713$	−1.09238e11	+	1.09238e11i	−0.422685	+	0.422685i
$714$		−	3.00758e10i		−	0.115724i
$715$		0			0
$716$	−2.22021e11			−0.844778
$717$	−9.49757e10	−	9.49757e10i	−0.359365	−	0.359365i
$718$	1.41285e11	−	1.41285e11i	0.531616	−	0.531616i
$719$			3.58390e10i			0.134104i	0.997749	+	0.0670518i	$0.0213593\pi$
$719$			3.58390e10i			0.134104i	−0.997749	+	0.0670518i	$0.978641\pi$
$720$		0			0
$721$	−1.90873e11			−0.706325
$722$	−9.27996e10	−	9.27996e10i	−0.341505	−	0.341505i
$723$	9.68259e10	−	9.68259e10i	0.354355	−	0.354355i
$724$			4.95577e10i			0.180367i
$725$		0			0
$726$	−7.67187e10			−0.276156
$727$	1.18145e11	+	1.18145e11i	0.422940	+	0.422940i	0.886215	−	0.463274i	$-0.153326\pi$
$727$	1.18145e11	+	1.18145e11i	0.422940	+	0.422940i	−0.463274	+	0.886215i	$0.653326\pi$
$728$	−2.18766e11	+	2.18766e11i	−0.778849	+	0.778849i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	1.76901e11			0.619529
$732$	1.65949e11	+	1.65949e11i	0.578004	+	0.578004i
$733$	4.46957e10	−	4.46957e10i	0.154828	−	0.154828i	−0.625442	−	0.780270i	$-0.715081\pi$
$733$	4.46957e10	−	4.46957e10i	0.154828	−	0.154828i	0.780270	+	0.625442i	$0.215081\pi$
$734$			2.08274e11i			0.717549i
$735$		0			0
$736$	2.76438e11			0.942077
$737$	−1.10304e11	−	1.10304e11i	−0.373869	−	0.373869i
$738$	5.97743e10	−	5.97743e10i	0.201506	−	0.201506i
$739$			3.09256e11i			1.03691i	0.855105	+	0.518454i	$0.173492\pi$
$739$			3.09256e11i			1.03691i	−0.855105	+	0.518454i	$0.826508\pi$
$740$		0			0
$741$	8.49778e10			0.281859
$742$	−8.95572e10	−	8.95572e10i	−0.295451	−	0.295451i
$743$	−1.52845e11	+	1.52845e11i	−0.501529	+	0.501529i	−0.911913	−	0.410384i	$-0.865395\pi$
$743$	−1.52845e11	+	1.52845e11i	−0.501529	+	0.501529i	0.410384	+	0.911913i	$0.365395\pi$
$744$		−	1.04198e11i		−	0.340070i
$745$		0			0
$746$	1.11972e11			0.361539
$747$	−6.80402e10	−	6.80402e10i	−0.218516	−	0.218516i
$748$	1.33493e11	−	1.33493e11i	0.426435	−	0.426435i
$749$			3.14778e11i			1.00018i
$750$		0			0
$751$	−3.96392e11			−1.24613			−0.623067	−	0.782168i	$-0.714114\pi$
$751$	−3.96392e11			−1.24613			−0.623067	+	0.782168i	$0.714114\pi$
$752$	3.53755e10	+	3.53755e10i	0.110619	+	0.110619i
$753$	−8.00401e10	+	8.00401e10i	−0.248959	+	0.248959i
$754$		−	5.65368e10i		−	0.174923i
$755$		0			0
$756$	−2.99943e10			−0.0918231
$757$	4.74476e10	+	4.74476e10i	0.144488	+	0.144488i	0.775650	−	0.631163i	$-0.217422\pi$
$757$	4.74476e10	+	4.74476e10i	0.144488	+	0.144488i	−0.631163	+	0.775650i	$0.717422\pi$
$758$	8.15093e10	−	8.15093e10i	0.246905	−	0.246905i
$759$		−	2.41839e11i		−	0.728718i
$760$		0			0
$761$	−2.88001e10			−0.0858727			−0.0429363	−	0.999078i	$-0.513671\pi$
$761$	−2.88001e10			−0.0858727			−0.0429363	+	0.999078i	$0.513671\pi$
$762$	−4.14636e10	−	4.14636e10i	−0.122984	−	0.122984i
$763$	2.55260e11	−	2.55260e11i	0.753156	−	0.753156i
$764$			4.41493e10i			0.129584i
$765$		0			0
$766$	−4.53835e9			−0.0131820
$767$	−1.17726e11	−	1.17726e11i	−0.340166	−	0.340166i
$768$	−1.04003e11	+	1.04003e11i	−0.298951	+	0.298951i
$769$			2.37524e11i			0.679207i	0.940569	+	0.339604i	$0.110293\pi$
$769$			2.37524e11i			0.679207i	−0.940569	+	0.339604i	$0.889707\pi$
$770$		0			0
$771$	−2.39034e11			−0.676459
$772$	2.56598e11	+	2.56598e11i	0.722410	+	0.722410i
$773$	2.30602e10	−	2.30602e10i	0.0645869	−	0.0645869i	−0.674076	−	0.738662i	$-0.735458\pi$
$773$	2.30602e10	−	2.30602e10i	0.0645869	−	0.0645869i	0.738662	+	0.674076i	$0.235458\pi$
$774$			6.45970e10i			0.179990i
$775$		0			0
$776$	4.75655e11			1.31173
$777$	−2.37967e9	−	2.37967e9i	−0.00652879	−	0.00652879i
$778$	3.89310e10	−	3.89310e10i	0.106262	−	0.106262i
$779$		−	1.57534e11i		−	0.427785i
$780$		0			0
$781$	8.23054e11			2.21220
$782$	−7.39930e10	−	7.39930e10i	−0.197863	−	0.197863i
$783$	9.17072e9	−	9.17072e9i	0.0243981	−	0.0243981i
$784$			5.81850e10i			0.154009i
$785$		0			0
$786$	1.45464e11			0.381122
$787$	−2.21187e11	−	2.21187e11i	−0.576582	−	0.576582i	0.357378	−	0.933960i	$-0.383671\pi$
$787$	−2.21187e11	−	2.21187e11i	−0.576582	−	0.576582i	−0.933960	+	0.357378i	$0.883671\pi$
$788$	3.77665e11	−	3.77665e11i	0.979495	−	0.979495i
$789$			3.22454e11i			0.832070i
$790$		0			0
$791$	−8.48680e10			−0.216789
$792$	1.15341e11	+	1.15341e11i	0.293144	+	0.293144i
$793$	−1.01928e12	+	1.01928e12i	−2.57752	+	2.57752i
$794$			6.87010e10i			0.172855i
$795$		0			0
$796$	3.89592e11			0.970417
$797$	2.59953e11	+	2.59953e11i	0.644260	+	0.644260i	0.951600	−	0.307340i	$-0.0994387\pi$
$797$	2.59953e11	+	2.59953e11i	0.644260	+	0.644260i	−0.307340	+	0.951600i	$0.599439\pi$
$798$	1.44720e10	−	1.44720e10i	0.0356876	−	0.0356876i
$799$		−	1.41423e11i		−	0.347002i
$800$		0			0
$801$	1.17613e11			0.285710
$802$	1.87704e11	+	1.87704e11i	0.453709	+	0.453709i
$803$	−2.38551e10	+	2.38551e10i	−0.0573746	+	0.0573746i
$804$			6.73141e10i			0.161095i
$805$		0			0
$806$	2.70482e11			0.640911
$807$	−7.75190e10	−	7.75190e10i	−0.182774	−	0.182774i
$808$	−4.83304e11	+	4.83304e11i	−1.13390	+	1.13390i
$809$			4.01818e11i			0.938071i	0.883179	+	0.469036i	$0.155398\pi$
$809$			4.01818e11i			0.938071i	−0.883179	+	0.469036i	$0.844602\pi$
$810$		0			0
$811$	−2.61109e11			−0.603584			−0.301792	−	0.953374i	$-0.597585\pi$
$811$	−2.61109e11			−0.603584			−0.301792	+	0.953374i	$0.597585\pi$
$812$	2.62964e10	+	2.62964e10i	0.0604884	+	0.0604884i
$813$	−1.43742e11	+	1.43742e11i	−0.329020	+	0.329020i
$814$			7.73477e9i			0.0176177i
$815$		0			0
$816$	−4.07154e10			−0.0918328
$817$	8.51224e10	+	8.51224e10i	0.191054	+	0.191054i
$818$	1.61657e11	−	1.61657e11i	0.361061	−	0.361061i
$819$		−	1.84229e11i		−	0.409471i
$820$		0			0
$821$	4.19668e11			0.923704			0.461852	−	0.886957i	$-0.347185\pi$
$821$	4.19668e11			0.923704			0.461852	+	0.886957i	$0.347185\pi$
$822$	−1.62058e10	−	1.62058e10i	−0.0354962	−	0.0354962i
$823$	2.76519e11	−	2.76519e11i	0.602734	−	0.602734i	−0.338303	−	0.941037i	$-0.609853\pi$
$823$	2.76519e11	−	2.76519e11i	0.602734	−	0.602734i	0.941037	+	0.338303i	$0.109853\pi$
$824$		−	4.47925e11i		−	0.971621i
$825$		0			0
$826$	−4.00983e10			−0.0861402
$827$	2.50038e11	+	2.50038e11i	0.534545	+	0.534545i	0.921922	−	0.387377i	$-0.126619\pi$
$827$	2.50038e11	+	2.50038e11i	0.534545	+	0.534545i	−0.387377	+	0.921922i	$0.626619\pi$
$828$	−7.37926e10	+	7.37926e10i	−0.156997	+	0.156997i
$829$			3.03680e11i			0.642981i	0.946913	+	0.321491i	$0.104184\pi$
$829$			3.03680e11i			0.642981i	−0.946913	+	0.321491i	$0.895816\pi$
$830$		0			0
$831$	−1.84475e11			−0.386841
$832$	−1.71248e11	−	1.71248e11i	−0.357381	−	0.357381i
$833$	1.16305e11	−	1.16305e11i	0.241556	−	0.241556i
$834$			1.44610e11i			0.298905i
$835$		0			0
$836$	1.28470e11			0.263012
$837$	4.38743e10	+	4.38743e10i	0.0893940	+	0.0893940i
$838$	1.22833e11	−	1.22833e11i	0.249080	−	0.249080i
$839$			7.68316e11i			1.55057i	0.631610	+	0.775286i	$0.282394\pi$
$839$			7.68316e11i			1.55057i	−0.631610	+	0.775286i	$0.717606\pi$
$840$		0			0
$841$	4.84166e11			0.967856
$842$	−7.02002e10	−	7.02002e10i	−0.139666	−	0.139666i
$843$	−7.86610e10	+	7.86610e10i	−0.155757	+	0.155757i
$844$		−	5.27297e11i		−	1.03917i
$845$		0			0
$846$	5.16416e10			0.100813
$847$	2.19172e11	+	2.19172e11i	0.425845	+	0.425845i
$848$	−1.21239e11	+	1.21239e11i	−0.234455	+	0.234455i
$849$		−	1.65416e11i		−	0.318381i
$850$		0			0
$851$	−1.17090e10			−0.0223256
$852$	−2.51139e11	−	2.51139e11i	−0.476603	−	0.476603i
$853$	−1.03763e11	+	1.03763e11i	−0.195995	+	0.195995i	−0.798281	−	0.602286i	$-0.794257\pi$
$853$	−1.03763e11	+	1.03763e11i	−0.195995	+	0.195995i	0.602286	+	0.798281i	$0.294257\pi$
$854$			3.47175e11i			0.652705i
$855$		0			0
$856$	−7.38694e11			−1.37584
$857$	−6.22521e10	−	6.22521e10i	−0.115407	−	0.115407i	0.647045	−	0.762452i	$-0.276005\pi$
$857$	−6.22521e10	−	6.22521e10i	−0.115407	−	0.115407i	−0.762452	+	0.647045i	$0.776005\pi$
$858$	−2.99405e11	+	2.99405e11i	−0.552472	+	0.552472i
$859$		−	1.01381e12i		−	1.86203i	−0.364986	−	0.931013i	$-0.618926\pi$
$859$		−	1.01381e12i		−	1.86203i	0.364986	−	0.931013i	$-0.381074\pi$
$860$		0			0
$861$	−3.41530e11			−0.621464
$862$	5.44154e10	+	5.44154e10i	0.0985581	+	0.0985581i
$863$	−1.41738e11	+	1.41738e11i	−0.255531	+	0.255531i	−0.823234	−	0.567703i	$-0.807832\pi$
$863$	−1.41738e11	+	1.41738e11i	−0.255531	+	0.255531i	0.567703	+	0.823234i	$0.307832\pi$
$864$		−	1.11028e11i		−	0.199241i
$865$		0			0
$866$	−1.73882e11			−0.309159
$867$	−1.49290e11	−	1.49290e11i	−0.264213	−	0.264213i
$868$	−1.25806e11	+	1.25806e11i	−0.221628	+	0.221628i
$869$			1.13302e12i			1.98682i
$870$		0			0
$871$	−4.13453e11			−0.718378
$872$	5.99022e11	+	5.99022e11i	1.03604	+	1.03604i
$873$	−2.00282e11	+	2.00282e11i	−0.344814	+	0.344814i
$874$		−	7.12087e10i		−	0.122036i
$875$		0			0
$876$	1.45579e10			0.0247219
$877$	−2.65966e11	−	2.65966e11i	−0.449601	−	0.449601i	0.445621	−	0.895222i	$-0.352983\pi$
$877$	−2.65966e11	−	2.65966e11i	−0.449601	−	0.449601i	−0.895222	+	0.445621i	$0.852983\pi$
$878$	−2.19388e11	+	2.19388e11i	−0.369177	+	0.369177i
$879$		−	6.20382e10i		−	0.103921i
$880$		0			0
$881$	−1.64084e11			−0.272372			−0.136186	−	0.990683i	$-0.543484\pi$
$881$	−1.64084e11			−0.272372			−0.136186	+	0.990683i	$0.543484\pi$
$882$	4.24696e10	+	4.24696e10i	0.0701785	+	0.0701785i
$883$	−1.00861e11	+	1.00861e11i	−0.165912	+	0.165912i	−0.785180	−	0.619268i	$-0.787430\pi$
$883$	−1.00861e11	+	1.00861e11i	−0.165912	+	0.165912i	0.619268	+	0.785180i	$0.287430\pi$
$884$		−	5.00375e11i		−	0.819382i
$885$		0			0
$886$	−1.31683e11			−0.213695
$887$	−7.92983e11	−	7.92983e11i	−1.28106	−	1.28106i	−0.940066	−	0.340993i	$-0.889237\pi$
$887$	−7.92983e11	−	7.92983e11i	−1.28106	−	1.28106i	−0.340993	−	0.940066i	$-0.610763\pi$
$888$	5.58440e9	−	5.58440e9i	0.00898100	−	0.00898100i
$889$			2.36909e11i			0.379293i
$890$		0			0
$891$	−9.71319e10			−0.154117
$892$	1.58230e11	+	1.58230e11i	0.249936	+	0.249936i
$893$	6.80505e10	−	6.80505e10i	0.107010	−	0.107010i
$894$		−	2.80640e11i		−	0.439339i
$895$		0			0
$896$	3.76607e11			0.584327
$897$	−4.53245e11	−	4.53245e11i	−0.700105	−	0.700105i
$898$	3.93051e11	−	3.93051e11i	0.604427	−	0.604427i
$899$		−	7.69303e10i		−	0.117777i
$900$		0			0
$901$	4.84685e11			0.735462
$902$	5.55047e11	+	5.55047e11i	0.838501	+	0.838501i
$903$	1.84543e11	−	1.84543e11i	0.277553	−	0.277553i
$904$		−	1.99161e11i		−	0.298216i
$905$		0			0
$906$	8.83963e10			0.131196
$907$	−8.20854e11	−	8.20854e11i	−1.21293	−	1.21293i	−0.970058	−	0.242875i	$-0.921910\pi$
$907$	−8.20854e11	−	8.20854e11i	−1.21293	−	1.21293i	−0.242875	−	0.970058i	$-0.578090\pi$
$908$	5.95389e11	−	5.95389e11i	0.875905	−	0.875905i
$909$		−	4.07006e11i		−	0.596135i
$910$		0			0
$911$	−1.34207e12			−1.94851			−0.974254	−	0.225454i	$-0.927613\pi$
$911$	−1.34207e12			−1.94851			−0.974254	+	0.225454i	$0.927613\pi$
$912$	−1.95916e10	−	1.95916e10i	−0.0283199	−	0.0283199i
$913$	6.31802e11	−	6.31802e11i	0.909281	−	0.909281i
$914$		−	6.38984e10i		−	0.0915598i
$915$		0			0
$916$	3.72698e11			0.529389
$917$	−4.15565e11	−	4.15565e11i	−0.587708	−	0.587708i
$918$	−2.97185e10	+	2.97185e10i	−0.0418462	+	0.0418462i
$919$		−	4.14286e11i		−	0.580815i	−0.956903	−	0.290408i	$-0.906209\pi$
$919$		−	4.14286e11i		−	0.580815i	0.956903	−	0.290408i	$-0.0937909\pi$
$920$		0			0
$921$	3.87674e11			0.538800
$922$	1.75331e11	+	1.75331e11i	0.242625	+	0.242625i
$923$	1.54253e12	−	1.54253e12i	2.12534	−	2.12534i
$924$		−	2.78519e11i		−	0.382091i
$925$		0			0
$926$	−8.66750e10			−0.117883
$927$	1.88606e11	+	1.88606e11i	0.255409	+	0.255409i
$928$	−9.73398e10	+	9.73398e10i	−0.131250	+	0.131250i
$929$			3.44057e11i			0.461920i	0.972963	+	0.230960i	$0.0741867\pi$
$929$			3.44057e11i			0.461920i	−0.972963	+	0.230960i	$0.925813\pi$
$930$		0			0
$931$	1.11928e11			0.148984
$932$	2.17271e11	+	2.17271e11i	0.287964	+	0.287964i
$933$	−3.01326e11	+	3.01326e11i	−0.397659	+	0.397659i
$934$		−	6.75447e11i		−	0.887572i
$935$		0			0
$936$	4.32333e11			0.563268
$937$	6.64709e11	+	6.64709e11i	0.862329	+	0.862329i	0.991608	−	0.129279i	$-0.0412664\pi$
$937$	6.64709e11	+	6.64709e11i	0.862329	+	0.862329i	−0.129279	+	0.991608i	$0.541266\pi$
$938$	−7.04124e10	+	7.04124e10i	−0.0909574	+	0.0909574i
$939$			2.65909e11i			0.342035i
$940$		0			0
$941$	−3.87481e11			−0.494187			−0.247094	−	0.968992i	$-0.579476\pi$
$941$	−3.87481e11			−0.494187			−0.247094	+	0.968992i	$0.579476\pi$
$942$	−1.24269e11	−	1.24269e11i	−0.157819	−	0.157819i
$943$	−8.40239e11	+	8.40239e11i	−1.06257	+	1.06257i
$944$			5.42835e10i			0.0683566i
$945$		0			0
$946$	−5.99830e11			−0.748968
$947$	9.94316e11	+	9.94316e11i	1.23630	+	1.23630i	0.961501	+	0.274800i	$0.0886118\pi$
$947$	9.94316e11	+	9.94316e11i	1.23630	+	1.23630i	0.274800	+	0.961501i	$0.411388\pi$
$948$	3.45720e11	−	3.45720e11i	0.428047	−	0.428047i
$949$			8.94167e10i			0.110244i
$950$		0			0
$951$	−5.97622e11			−0.730641
$952$	−2.01633e11	−	2.01633e11i	−0.245478	−	0.245478i
$953$	5.07969e11	−	5.07969e11i	0.615836	−	0.615836i	−0.328624	−	0.944461i	$-0.606585\pi$
$953$	5.07969e11	−	5.07969e11i	0.615836	−	0.615836i	0.944461	+	0.328624i	$0.106585\pi$
$954$			1.76987e11i			0.213672i
$955$		0			0
$956$	−5.38201e11			−0.644337
$957$	8.51568e10	+	8.51568e10i	0.101525	+	0.101525i
$958$	4.96018e10	−	4.96018e10i	0.0588892	−	0.0588892i
$959$			9.25943e10i			0.109474i
$960$		0			0
$961$	−4.84843e11			−0.568470
$962$	1.44962e10	+	1.44962e10i	0.0169260	+	0.0169260i
$963$	3.11038e11	−	3.11038e11i	0.361667	−	0.361667i
$964$		−	5.48686e11i		−	0.635354i
$965$		0			0
$966$	−1.54378e11			−0.177287
$967$	−8.82088e11	−	8.82088e11i	−1.00880	−	1.00880i	−0.999961	−	0.00884150i	$-0.997186\pi$
$967$	−8.82088e11	−	8.82088e11i	−1.00880	−	1.00880i	−0.00884150	−	0.999961i	$-0.502814\pi$
$968$	−5.14334e11	+	5.14334e11i	−0.585793	+	0.585793i
$969$			7.83227e10i			0.0888367i
$970$		0			0
$971$	3.47801e11			0.391249			0.195625	−	0.980679i	$-0.437327\pi$
$971$	3.47801e11			0.391249			0.195625	+	0.980679i	$0.437327\pi$
$972$	2.96380e10	+	2.96380e10i	0.0332035	+	0.0332035i
$973$	4.13125e11	−	4.13125e11i	0.460925	−	0.460925i
$974$			3.98615e11i			0.442912i
$975$		0			0
$976$	4.69992e11			0.517954
$977$	1.23243e11	+	1.23243e11i	0.135265	+	0.135265i	0.771497	−	0.636232i	$-0.219508\pi$
$977$	1.23243e11	+	1.23243e11i	0.135265	+	0.135265i	−0.636232	+	0.771497i	$0.719508\pi$
$978$	−5.10906e10	+	5.10906e10i	−0.0558451	+	0.0558451i
$979$			1.09212e12i			1.18889i
$980$		0			0
$981$	−5.04455e11			−0.544687
$982$	5.19256e11	+	5.19256e11i	0.558387	+	0.558387i
$983$	5.87218e11	−	5.87218e11i	0.628905	−	0.628905i	−0.318887	−	0.947793i	$-0.603309\pi$
$983$	5.87218e11	−	5.87218e11i	0.628905	−	0.628905i	0.947793	+	0.318887i	$0.103309\pi$
$984$		−	8.01473e11i		−	0.854886i
$985$		0			0
$986$	5.21091e10			0.0551323
$987$	−1.47531e11	−	1.47531e11i	−0.155459	−	0.155459i
$988$	2.40773e11	−	2.40773e11i	0.252685	−	0.252685i
$989$		−	9.08032e11i		−	0.949108i
$990$		0			0
$991$	−1.33829e12			−1.38757			−0.693786	−	0.720181i	$-0.744059\pi$
$991$	−1.33829e12			−1.38757			−0.693786	+	0.720181i	$0.744059\pi$
$992$	−4.65690e11	−	4.65690e11i	−0.480895	−	0.480895i
$993$	−4.03895e9	+	4.03895e9i	−0.00415405	+	0.00415405i
$994$		−	5.25398e11i		−	0.538199i
$995$		0			0
$996$	−3.85565e11			−0.391796
$997$	−6.49580e11	−	6.49580e11i	−0.657433	−	0.657433i	0.297339	−	0.954772i	$-0.403901\pi$
$997$	−6.49580e11	−	6.49580e11i	−0.657433	−	0.657433i	−0.954772	+	0.297339i	$0.903901\pi$
$998$	−1.43426e11	+	1.43426e11i	−0.144579	+	0.144579i
$999$			4.70280e9i			0.00472165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.b.7.2	✓	8
5.2	odd	4	inner	75.9.f.b.43.3	yes	8
5.3	odd	4	inner	75.9.f.b.43.2	yes	8
5.4	even	2	inner	75.9.f.b.7.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.b.7.2	✓	8	1.1	even	1	trivial
75.9.f.b.7.3	yes	8	5.4	even	2	inner
75.9.f.b.43.2	yes	8	5.3	odd	4	inner
75.9.f.b.43.3	yes	8	5.2	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.85713 - 5.85713i) q^{2} +(33.0681 - 33.0681i) q^{3} -187.388i q^{4} -387.369 q^{6} +(1106.65 + 1106.65i) q^{7} +(-2596.98 + 2596.98i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-5.85713 - 5.85713i) q^{2} +(33.0681 - 33.0681i) q^{3} -187.388i q^{4} -387.369 q^{6} +(1106.65 + 1106.65i) q^{7} +(-2596.98 + 2596.98i) q^{8} -2187.00i q^{9} +20307.9 q^{11} +(-6196.57 - 6196.57i) q^{12} +(38060.2 - 38060.2i) q^{13} -12963.6i q^{14} -17549.6 q^{16} +(35079.5 + 35079.5i) q^{17} +(-12809.6 + 12809.6i) q^{18} +33759.4i q^{19} +73189.5 q^{21} +(-118946. - 118946. i) q^{22} +(180062. - 180062. i) q^{23} +171755. i q^{24} -445847. q^{26} +(-72320.0 - 72320.0i) q^{27} +(207372. - 207372. i) q^{28} +126808. i q^{29} -606669. q^{31} +(767618. + 767618. i) q^{32} +(671543. - 671543. i) q^{33} -410930. i q^{34} -409817. q^{36} +(-32513.8 - 32513.8i) q^{37} +(197734. - 197734. i) q^{38} -2.51716e6i q^{39} -4.66638e6 q^{41} +(-428680. - 428680. i) q^{42} +(2.52144e6 - 2.52144e6i) q^{43} -3.80545e6i q^{44} -2.10930e6 q^{46} +(-2.01575e6 - 2.01575e6i) q^{47} +(-580331. + 580331. i) q^{48} -3.31547e6i q^{49} +2.32002e6 q^{51} +(-7.13202e6 - 7.13202e6i) q^{52} +(6.90838e6 - 6.90838e6i) q^{53} +847175. i q^{54} -5.74789e6 q^{56} +(1.11636e6 + 1.11636e6i) q^{57} +(742729. - 742729. i) q^{58} -3.09316e6i q^{59} -2.67808e7 q^{61} +(3.55334e6 + 3.55334e6i) q^{62} +(2.42024e6 - 2.42024e6i) q^{63} -4.49939e6i q^{64} -7.86663e6 q^{66} +(-5.43157e6 - 5.43157e6i) q^{67} +(6.57347e6 - 6.57347e6i) q^{68} -1.19086e7i q^{69} +4.05288e7 q^{71} +(5.67960e6 + 5.67960e6i) q^{72} +(-1.17468e6 + 1.17468e6i) q^{73} +380876. i q^{74} +6.32611e6 q^{76} +(2.24736e7 + 2.24736e7i) q^{77} +(-1.47433e7 + 1.47433e7i) q^{78} +5.57922e7i q^{79} -4.78297e6 q^{81} +(2.73316e7 + 2.73316e7i) q^{82} +(3.11112e7 - 3.11112e7i) q^{83} -1.37148e7i q^{84} -2.95368e7 q^{86} +(4.19329e6 + 4.19329e6i) q^{87} +(-5.27392e7 + 5.27392e7i) q^{88} +5.37783e7i q^{89} +8.42384e7 q^{91} +(-3.37415e7 - 3.37415e7i) q^{92} +(-2.00614e7 + 2.00614e7i) q^{93} +2.36130e7i q^{94} +5.07673e7 q^{96} +(-9.15785e7 - 9.15785e7i) q^{97} +(-1.94191e7 + 1.94191e7i) q^{98} -4.44133e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1296 q^{6}+O(q^{10}) \) 8 * q + 1296 * q^6	\( 8 q + 1296 q^{6} + 52752 q^{11} + 164320 q^{16} + 31752 q^{21} - 3637584 q^{26} - 6842152 q^{31} - 1854576 q^{36} - 29029152 q^{41} - 18397632 q^{46} - 10226736 q^{51} - 46814880 q^{56} - 73982120 q^{61} - 51725952 q^{66} + 33100896 q^{71} + 13636624 q^{76} - 38263752 q^{81} + 271592592 q^{86} + 507032568 q^{91} + 165488832 q^{96}+O(q^{100}) \) 8 * q + 1296 * q^6 + 52752 * q^11 + 164320 * q^16 + 31752 * q^21 - 3637584 * q^26 - 6842152 * q^31 - 1854576 * q^36 - 29029152 * q^41 - 18397632 * q^46 - 10226736 * q^51 - 46814880 * q^56 - 73982120 * q^61 - 51725952 * q^66 + 33100896 * q^71 + 13636624 * q^76 - 38263752 * q^81 + 271592592 * q^86 + 507032568 * q^91 + 165488832 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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