LMFDB - Embedded newform 75.9.f.b.43.4

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			43.4
Root			$-1.08321 + 1.08321i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.7561 - 10.7561i) q^{2} +(33.0681 + 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(-986.622 + 986.622i) q^{7} +(3018.29 + 3018.29i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(10.7561 - 10.7561i) q^{2} +(33.0681 + 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(-986.622 + 986.622i) q^{7} +(3018.29 + 3018.29i) q^{8} +2187.00i q^{9} -7119.87 q^{11} +(-813.874 + 813.874i) q^{12} +(-21548.2 - 21548.2i) q^{13} +21224.4i q^{14} +58629.6 q^{16} +(-73737.3 + 73737.3i) q^{17} +(23523.6 + 23523.6i) q^{18} +118517. i q^{19} -65251.5 q^{21} +(-76582.1 + 76582.1i) q^{22} +(-115753. - 115753. i) q^{23} +199619. i q^{24} -463549. q^{26} +(-72320.0 + 72320.0i) q^{27} +(-24282.8 - 24282.8i) q^{28} +471964. i q^{29} -1.10387e6 q^{31} +(-142057. + 142057. i) q^{32} +(-235441. - 235441. i) q^{33} +1.58625e6i q^{34} -53826.5 q^{36} +(437375. - 437375. i) q^{37} +(1.27479e6 + 1.27479e6i) q^{38} -1.42511e6i q^{39} -2.59091e6 q^{41} +(-701852. + 701852. i) q^{42} +(4.52928e6 + 4.52928e6i) q^{43} -175235. i q^{44} -2.49011e6 q^{46} +(1.05817e6 - 1.05817e6i) q^{47} +(1.93877e6 + 1.93877e6i) q^{48} +3.81795e6i q^{49} -4.87671e6 q^{51} +(530344. - 530344. i) q^{52} +(1.00150e7 + 1.00150e7i) q^{53} +1.55576e6i q^{54} -5.95583e6 q^{56} +(-3.91915e6 + 3.91915e6i) q^{57} +(5.07649e6 + 5.07649e6i) q^{58} -6.33938e6i q^{59} +8.28532e6 q^{61} +(-1.18733e7 + 1.18733e7i) q^{62} +(-2.15774e6 - 2.15774e6i) q^{63} +1.80651e7i q^{64} -5.06485e6 q^{66} +(2.32318e7 - 2.32318e7i) q^{67} +(-1.81483e6 - 1.81483e6i) q^{68} -7.65549e6i q^{69} -3.22536e7 q^{71} +(-6.60101e6 + 6.60101e6i) q^{72} +(-1.49231e7 - 1.49231e7i) q^{73} -9.40892e6i q^{74} -2.91696e6 q^{76} +(7.02462e6 - 7.02462e6i) q^{77} +(-1.53287e7 - 1.53287e7i) q^{78} +7.17598e7i q^{79} -4.78297e6 q^{81} +(-2.78681e7 + 2.78681e7i) q^{82} +(-2.46934e7 - 2.46934e7i) q^{83} -1.60597e6i q^{84} +9.74350e7 q^{86} +(-1.56069e7 + 1.56069e7i) q^{87} +(-2.14899e7 - 2.14899e7i) q^{88} -8.60547e7i q^{89} +4.25198e7 q^{91} +(2.84892e6 - 2.84892e6i) q^{92} +(-3.65028e7 - 3.65028e7i) q^{93} -2.27636e7i q^{94} -9.39513e6 q^{96} +(7.27492e7 - 7.27492e7i) q^{97} +(4.10664e7 + 4.10664e7i) q^{98} -1.55712e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	10.7561	−	10.7561i	0.672257	−	0.672257i	−0.285979	−	0.958236i	$-0.592319\pi$
$2$	10.7561	−	10.7561i	0.672257	−	0.672257i	0.958236	+	0.285979i	$0.0923187\pi$
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$			24.6120i			0.0961408i
$5$		0			0
$5$		0			0
$6$	711.369			0.548896
$7$	−986.622	+	986.622i	−0.410921	+	0.410921i	−0.882059	−	0.471138i	$-0.843843\pi$
$7$	−986.622	+	986.622i	−0.410921	+	0.410921i	0.471138	+	0.882059i	$0.343843\pi$
$8$	3018.29	+	3018.29i	0.736888	+	0.736888i
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−7119.87			−0.486297			−0.243148	−	0.969989i	$-0.578180\pi$
$11$	−7119.87			−0.486297			−0.243148	+	0.969989i	$0.578180\pi$
$12$	−813.874	+	813.874i	−0.0392493	+	0.0392493i
$13$	−21548.2	−	21548.2i	−0.754461	−	0.754461i	0.220847	−	0.975308i	$-0.429118\pi$
$13$	−21548.2	−	21548.2i	−0.754461	−	0.754461i	−0.975308	+	0.220847i	$0.929118\pi$
$14$			21224.4i			0.552490i
$15$		0			0
$16$	58629.6			0.894616
$17$	−73737.3	+	73737.3i	−0.882860	+	0.882860i	−0.993824	−	0.110965i	$-0.964606\pi$
$17$	−73737.3	+	73737.3i	−0.882860	+	0.882860i	0.110965	+	0.993824i	$0.464606\pi$
$18$	23523.6	+	23523.6i	0.224086	+	0.224086i
$19$			118517.i			0.909427i	0.890638	+	0.454714i	$0.150258\pi$
$19$			118517.i			0.909427i	−0.890638	+	0.454714i	$0.849742\pi$
$20$		0			0
$21$	−65251.5			−0.335516
$22$	−76582.1	+	76582.1i	−0.326916	+	0.326916i
$23$	−115753.	−	115753.i	−0.413640	−	0.413640i	0.469365	−	0.883004i	$-0.344483\pi$
$23$	−115753.	−	115753.i	−0.413640	−	0.413640i	−0.883004	+	0.469365i	$0.844483\pi$
$24$			199619.i			0.601667i
$25$		0			0
$26$	−463549.			−1.01438
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	−24282.8	−	24282.8i	−0.0395063	−	0.0395063i
$29$			471964.i			0.667293i	0.942698	+	0.333646i	$0.108279\pi$
$29$			471964.i			0.667293i	−0.942698	+	0.333646i	$0.891721\pi$
$30$		0			0
$31$	−1.10387e6			−1.19528			−0.597641	−	0.801764i	$-0.703895\pi$
$31$	−1.10387e6			−1.19528			−0.597641	+	0.801764i	$0.703895\pi$
$32$	−142057.	+	142057.i	−0.135476	+	0.135476i
$33$	−235441.	−	235441.i	−0.198530	−	0.198530i
$34$			1.58625e6i			1.18702i
$35$		0			0
$36$	−53826.5			−0.0320469
$37$	437375.	−	437375.i	0.233371	−	0.233371i	−0.580727	−	0.814098i	$-0.697232\pi$
$37$	437375.	−	437375.i	0.233371	−	0.233371i	0.814098	+	0.580727i	$0.197232\pi$
$38$	1.27479e6	+	1.27479e6i	0.611369	+	0.611369i
$39$		−	1.42511e6i		−	0.616015i
$40$		0			0
$41$	−2.59091e6			−0.916888			−0.458444	−	0.888723i	$-0.651593\pi$
$41$	−2.59091e6			−0.916888			−0.458444	+	0.888723i	$0.651593\pi$
$42$	−701852.	+	701852.i	−0.225553	+	0.225553i
$43$	4.52928e6	+	4.52928e6i	1.32482	+	1.32482i	0.909826	+	0.414990i	$0.136215\pi$
$43$	4.52928e6	+	4.52928e6i	1.32482	+	1.32482i	0.414990	+	0.909826i	$0.363785\pi$
$44$		−	175235.i		−	0.0467530i
$45$		0			0
$46$	−2.49011e6			−0.556144
$47$	1.05817e6	−	1.05817e6i	0.216852	−	0.216852i	−0.590318	−	0.807170i	$-0.700998\pi$
$47$	1.05817e6	−	1.05817e6i	0.216852	−	0.216852i	0.807170	+	0.590318i	$0.200998\pi$
$48$	1.93877e6	+	1.93877e6i	0.365226	+	0.365226i
$49$			3.81795e6i			0.662287i
$50$		0			0
$51$	−4.87671e6			−0.720852
$52$	530344.	−	530344.i	0.0725345	−	0.0725345i
$53$	1.00150e7	+	1.00150e7i	1.26925	+	1.26925i	0.946478	+	0.322767i	$0.104613\pi$
$53$	1.00150e7	+	1.00150e7i	1.26925	+	1.26925i	0.322767	+	0.946478i	$0.395387\pi$
$54$			1.55576e6i			0.182965i
$55$		0			0
$56$	−5.95583e6			−0.605606
$57$	−3.91915e6	+	3.91915e6i	−0.371272	+	0.371272i
$58$	5.07649e6	+	5.07649e6i	0.448592	+	0.448592i
$59$		−	6.33938e6i		−	0.523165i	−0.965181	−	0.261583i	$-0.915756\pi$
$59$		−	6.33938e6i		−	0.523165i	0.965181	−	0.261583i	$-0.0842444\pi$
$60$		0			0
$61$	8.28532e6			0.598398			0.299199	−	0.954191i	$-0.403281\pi$
$61$	8.28532e6			0.598398			0.299199	+	0.954191i	$0.403281\pi$
$62$	−1.18733e7	+	1.18733e7i	−0.803537	+	0.803537i
$63$	−2.15774e6	−	2.15774e6i	−0.136974	−	0.136974i
$64$			1.80651e7i			1.07677i
$65$		0			0
$66$	−5.06485e6			−0.266926
$67$	2.32318e7	−	2.32318e7i	1.15288	−	1.15288i	0.166904	−	0.985973i	$-0.446623\pi$
$67$	2.32318e7	−	2.32318e7i	1.15288	−	1.15288i	0.985973	−	0.166904i	$-0.0533770\pi$
$68$	−1.81483e6	−	1.81483e6i	−0.0848788	−	0.0848788i
$69$		−	7.65549e6i		−	0.337735i
$70$		0			0
$71$	−3.22536e7			−1.26924			−0.634621	−	0.772823i	$-0.718844\pi$
$71$	−3.22536e7			−1.26924			−0.634621	+	0.772823i	$0.718844\pi$
$72$	−6.60101e6	+	6.60101e6i	−0.245629	+	0.245629i
$73$	−1.49231e7	−	1.49231e7i	−0.525493	−	0.525493i	0.393732	−	0.919225i	$-0.371184\pi$
$73$	−1.49231e7	−	1.49231e7i	−0.525493	−	0.525493i	−0.919225	+	0.393732i	$0.871184\pi$
$74$		−	9.40892e6i		−	0.313771i
$75$		0			0
$76$	−2.91696e6			−0.0874330
$77$	7.02462e6	−	7.02462e6i	0.199830	−	0.199830i
$78$	−1.53287e7	−	1.53287e7i	−0.414120	−	0.414120i
$79$			7.17598e7i			1.84235i	0.389146	+	0.921176i	$0.372770\pi$
$79$			7.17598e7i			1.84235i	−0.389146	+	0.921176i	$0.627230\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	−2.78681e7	+	2.78681e7i	−0.616385	+	0.616385i
$83$	−2.46934e7	−	2.46934e7i	−0.520318	−	0.520318i	0.397349	−	0.917667i	$-0.369930\pi$
$83$	−2.46934e7	−	2.46934e7i	−0.520318	−	0.520318i	−0.917667	+	0.397349i	$0.869930\pi$
$84$		−	1.60597e6i		−	0.0322568i
$85$		0			0
$86$	9.74350e7			1.78123
$87$	−1.56069e7	+	1.56069e7i	−0.272421	+	0.272421i
$88$	−2.14899e7	−	2.14899e7i	−0.358346	−	0.358346i
$89$		−	8.60547e7i		−	1.37156i	−0.727810	−	0.685779i	$-0.759462\pi$
$89$		−	8.60547e7i		−	1.37156i	0.727810	−	0.685779i	$-0.240538\pi$
$90$		0			0
$91$	4.25198e7			0.620048
$92$	2.84892e6	−	2.84892e6i	0.0397676	−	0.0397676i
$93$	−3.65028e7	−	3.65028e7i	−0.487972	−	0.487972i
$94$		−	2.27636e7i		−	0.291561i
$95$		0			0
$96$	−9.39513e6			−0.110616
$97$	7.27492e7	−	7.27492e7i	0.821753	−	0.821753i	−0.164607	−	0.986359i	$-0.552636\pi$
$97$	7.27492e7	−	7.27492e7i	0.821753	−	0.821753i	0.986359	+	0.164607i	$0.0526355\pi$
$98$	4.10664e7	+	4.10664e7i	0.445227	+	0.445227i
$99$		−	1.55712e7i		−	0.162099i
$100$		0			0
$101$	4.96287e7			0.476922			0.238461	−	0.971152i	$-0.423357\pi$
$101$	4.96287e7			0.476922			0.238461	+	0.971152i	$0.423357\pi$
$102$	−5.24544e7	+	5.24544e7i	−0.484598	+	0.484598i
$103$	−6.23246e7	−	6.23246e7i	−0.553746	−	0.553746i	0.373774	−	0.927520i	$-0.378064\pi$
$103$	−6.23246e7	−	6.23246e7i	−0.553746	−	0.553746i	−0.927520	+	0.373774i	$0.878064\pi$
$104$		−	1.30077e8i		−	1.11191i
$105$		0			0
$106$	2.15444e8			1.70652
$107$	9.91772e7	−	9.91772e7i	0.756618	−	0.756618i	−0.219087	−	0.975705i	$-0.570308\pi$
$107$	9.91772e7	−	9.91772e7i	0.756618	−	0.756618i	0.975705	+	0.219087i	$0.0703079\pi$
$108$	−1.77994e6	−	1.77994e6i	−0.0130831	−	0.0130831i
$109$		−	9.28159e7i		−	0.657531i	−0.944412	−	0.328766i	$-0.893367\pi$
$109$		−	9.28159e7i		−	0.657531i	0.944412	−	0.328766i	$-0.106633\pi$
$110$		0			0
$111$	2.89263e7			0.190547
$112$	−5.78452e7	+	5.78452e7i	−0.367617	+	0.367617i
$113$	1.25548e8	+	1.25548e8i	0.770009	+	0.770009i	0.978108	−	0.208099i	$-0.0667275\pi$
$113$	1.25548e8	+	1.25548e8i	0.770009	+	0.770009i	−0.208099	+	0.978108i	$0.566728\pi$
$114$			8.43096e7i			0.499181i
$115$		0			0
$116$	−1.16160e7			−0.0641541
$117$	4.71258e7	−	4.71258e7i	0.251487	−	0.251487i
$118$	−6.81871e7	−	6.81871e7i	−0.351702	−	0.351702i
$119$		−	1.45502e8i		−	0.725572i
$120$		0			0
$121$	−1.63666e8			−0.763515
$122$	8.91178e7	−	8.91178e7i	0.402277	−	0.402277i
$123$	−8.56764e7	−	8.56764e7i	−0.374318	−	0.374318i
$124$		−	2.71685e7i		−	0.114915i
$125$		0			0
$126$	−4.64178e7			−0.184163
$127$	−7.80666e7	+	7.80666e7i	−0.300089	+	0.300089i	−0.841049	−	0.540959i	$-0.818061\pi$
$127$	−7.80666e7	+	7.80666e7i	−0.300089	+	0.300089i	0.540959	+	0.841049i	$0.318061\pi$
$128$	1.57944e8	+	1.57944e8i	0.588387	+	0.588387i
$129$			2.99550e8i			1.08171i
$130$		0			0
$131$	1.86914e8			0.634682			0.317341	−	0.948311i	$-0.397210\pi$
$131$	1.86914e8			0.634682			0.317341	+	0.948311i	$0.397210\pi$
$132$	5.79468e6	−	5.79468e6i	0.0190868	−	0.0190868i
$133$	−1.16932e8	−	1.16932e8i	−0.373703	−	0.373703i
$134$		−	4.99767e8i		−	1.55006i
$135$		0			0
$136$	−4.45122e8			−1.30114
$137$	3.19732e8	−	3.19732e8i	0.907619	−	0.907619i	−0.0884605	−	0.996080i	$-0.528195\pi$
$137$	3.19732e8	−	3.19732e8i	0.907619	−	0.907619i	0.996080	+	0.0884605i	$0.0281947\pi$
$138$	−8.23433e7	−	8.23433e7i	−0.227045	−	0.227045i
$139$			5.44849e8i			1.45954i	0.683691	+	0.729772i	$0.260374\pi$
$139$			5.44849e8i			1.45954i	−0.683691	+	0.729772i	$0.739626\pi$
$140$		0			0
$141$	6.99833e7			0.177059
$142$	−3.46923e8	+	3.46923e8i	−0.853257	+	0.853257i
$143$	1.53420e8	+	1.53420e8i	0.366892	+	0.366892i
$144$			1.28223e8i			0.298205i
$145$		0			0
$146$	−3.21028e8			−0.706532
$147$	−1.26253e8	+	1.26253e8i	−0.270378	+	0.270378i
$148$	1.07647e7	+	1.07647e7i	0.0224365	+	0.0224365i
$149$			8.49730e8i			1.72400i	0.506912	+	0.861998i	$0.330787\pi$
$149$			8.49730e8i			1.72400i	−0.506912	+	0.861998i	$0.669213\pi$
$150$		0			0
$151$	−5.53942e8			−1.06551			−0.532754	−	0.846270i	$-0.678843\pi$
$151$	−5.53942e8			−1.06551			−0.532754	+	0.846270i	$0.678843\pi$
$152$	−3.57721e8	+	3.57721e8i	−0.670146	+	0.670146i
$153$	−1.61263e8	−	1.61263e8i	−0.294287	−	0.294287i
$154$		−	1.51115e8i		−	0.268674i
$155$		0			0
$156$	3.50750e7			0.0592241
$157$	−6.53141e8	+	6.53141e8i	−1.07500	+	1.07500i	−0.0780506	+	0.996949i	$0.524870\pi$
$157$	−6.53141e8	+	6.53141e8i	−1.07500	+	1.07500i	−0.996949	+	0.0780506i	$0.975130\pi$
$158$	7.71856e8	+	7.71856e8i	1.23853	+	1.23853i
$159$			6.62352e8i			1.03633i
$160$		0			0
$161$	2.28410e8			0.339947
$162$	−5.14462e7	+	5.14462e7i	−0.0746952	+	0.0746952i
$163$	1.36520e8	+	1.36520e8i	0.193395	+	0.193395i	0.797161	−	0.603766i	$-0.206334\pi$
$163$	1.36520e8	+	1.36520e8i	0.193395	+	0.193395i	−0.603766	+	0.797161i	$0.706334\pi$
$164$		−	6.37675e7i		−	0.0881503i
$165$		0			0
$166$	−5.31211e8			−0.699575
$167$	8.46479e8	−	8.46479e8i	1.08830	−	1.08830i	0.0926003	−	0.995703i	$-0.470482\pi$
$167$	8.46479e8	−	8.46479e8i	1.08830	−	1.08830i	0.995703	−	0.0926003i	$-0.0295179\pi$
$168$	−1.96948e8	−	1.96948e8i	−0.247238	−	0.247238i
$169$			1.12916e8i			0.138423i
$170$		0			0
$171$	−2.59198e8			−0.303142
$172$	−1.11475e8	+	1.11475e8i	−0.127369	+	0.127369i
$173$	9.98204e8	+	9.98204e8i	1.11438	+	1.11438i	0.992551	+	0.121833i	$0.0388772\pi$
$173$	9.98204e8	+	9.98204e8i	1.11438	+	1.11438i	0.121833	+	0.992551i	$0.461123\pi$
$174$			3.35740e8i			0.366274i
$175$		0			0
$176$	−4.17435e8			−0.435049
$177$	2.09631e8	−	2.09631e8i	0.213581	−	0.213581i
$178$	−9.25614e8	−	9.25614e8i	−0.922040	−	0.922040i
$179$		−	1.26965e9i		−	1.23672i	−0.785896	−	0.618359i	$-0.787798\pi$
$179$		−	1.26965e9i		−	1.23672i	0.785896	−	0.618359i	$-0.212202\pi$
$180$		0			0
$181$	6.81618e8			0.635077			0.317539	−	0.948245i	$-0.397144\pi$
$181$	6.81618e8			0.635077			0.317539	+	0.948245i	$0.397144\pi$
$182$	4.57348e8	−	4.57348e8i	0.416832	−	0.416832i
$183$	2.73980e8	+	2.73980e8i	0.244295	+	0.244295i
$184$		−	6.98755e8i		−	0.609612i
$185$		0			0
$186$	−7.85258e8			−0.656085
$187$	5.25000e8	−	5.25000e8i	0.429332	−	0.429332i
$188$	2.60437e7	+	2.60437e7i	0.0208483	+	0.0208483i
$189$		−	1.42705e8i		−	0.111839i
$190$		0			0
$191$	1.18866e9			0.893150			0.446575	−	0.894746i	$-0.352644\pi$
$191$	1.18866e9			0.893150			0.446575	+	0.894746i	$0.352644\pi$
$192$	−5.97380e8	+	5.97380e8i	−0.439588	+	0.439588i
$193$	1.09555e9	+	1.09555e9i	0.789594	+	0.789594i	0.981428	−	0.191833i	$-0.0614432\pi$
$193$	1.09555e9	+	1.09555e9i	0.789594	+	0.789594i	−0.191833	+	0.981428i	$0.561443\pi$
$194$		−	1.56500e9i		−	1.10486i
$195$		0			0
$196$	−9.39677e7			−0.0636728
$197$	−9.26327e7	+	9.26327e7i	−0.0615034	+	0.0615034i	−0.737189	−	0.675686i	$-0.763848\pi$
$197$	−9.26327e7	+	9.26327e7i	−0.0615034	+	0.0615034i	0.675686	+	0.737189i	$0.263848\pi$
$198$	−1.67485e8	−	1.67485e8i	−0.108972	−	0.108972i
$199$			1.76224e9i			1.12371i	0.827237	+	0.561854i	$0.189912\pi$
$199$			1.76224e9i			1.12371i	−0.827237	+	0.561854i	$0.810088\pi$
$200$		0			0
$201$	1.53646e9			0.941320
$202$	5.33812e8	−	5.33812e8i	0.320614	−	0.320614i
$203$	−4.65650e8	−	4.65650e8i	−0.274205	−	0.274205i
$204$		−	1.20026e8i		−	0.0693033i
$205$		0			0
$206$	−1.34074e9			−0.744520
$207$	2.53152e8	−	2.53152e8i	0.137880	−	0.137880i
$208$	−1.26336e9	−	1.26336e9i	−0.674953	−	0.674953i
$209$		−	8.43829e8i		−	0.442251i
$210$		0			0
$211$	1.02674e9			0.518001			0.259000	−	0.965877i	$-0.416607\pi$
$211$	1.02674e9			0.518001			0.259000	+	0.965877i	$0.416607\pi$
$212$	−2.46489e8	+	2.46489e8i	−0.122026	+	0.122026i
$213$	−1.06657e9	−	1.06657e9i	−0.518166	−	0.518166i
$214$		−	2.13352e9i		−	1.01728i
$215$		0			0
$216$	−4.36566e8			−0.200556
$217$	1.08910e9	−	1.08910e9i	0.491167	−	0.491167i
$218$	−9.98338e8	−	9.98338e8i	−0.442030	−	0.442030i
$219$		−	9.86955e8i		−	0.429063i
$220$		0			0
$221$	3.17781e9			1.33217
$222$	3.11135e8	−	3.11135e8i	0.128096	−	0.128096i
$223$	1.83455e8	+	1.83455e8i	0.0741841	+	0.0741841i	0.743225	−	0.669041i	$-0.233295\pi$
$223$	1.83455e8	+	1.83455e8i	0.0741841	+	0.0741841i	−0.669041	+	0.743225i	$0.733295\pi$
$224$		−	2.80314e8i		−	0.111340i
$225$		0			0
$226$	2.70082e9			1.03529
$227$	−7.64853e8	+	7.64853e8i	−0.288055	+	0.288055i	−0.836311	−	0.548256i	$-0.815292\pi$
$227$	−7.64853e8	+	7.64853e8i	−0.288055	+	0.288055i	0.548256	+	0.836311i	$0.315292\pi$
$228$	−9.64582e7	−	9.64582e7i	−0.0356944	−	0.0356944i
$229$			4.06794e9i			1.47922i	0.673037	+	0.739609i	$0.264989\pi$
$229$			4.06794e9i			1.47922i	−0.673037	+	0.739609i	$0.735011\pi$
$230$		0			0
$231$	4.64582e8			0.163160
$232$	−1.42453e9	+	1.42453e9i	−0.491720	+	0.491720i
$233$	−1.88027e9	−	1.88027e9i	−0.637964	−	0.637964i	0.312089	−	0.950053i	$-0.398971\pi$
$233$	−1.88027e9	−	1.88027e9i	−0.637964	−	0.637964i	−0.950053	+	0.312089i	$0.898971\pi$
$234$		−	1.01378e9i		−	0.338128i
$235$		0			0
$236$	1.56025e8			0.0502975
$237$	−2.37296e9	+	2.37296e9i	−0.752137	+	0.752137i
$238$	−1.56503e9	−	1.56503e9i	−0.487771	−	0.487771i
$239$			1.27628e9i			0.391160i	0.980688	+	0.195580i	$0.0626589\pi$
$239$			1.27628e9i			0.391160i	−0.980688	+	0.195580i	$0.937341\pi$
$240$		0			0
$241$	3.56750e9			1.05754			0.528768	−	0.848766i	$-0.322654\pi$
$241$	3.56750e9			1.05754			0.528768	+	0.848766i	$0.322654\pi$
$242$	−1.76041e9	+	1.76041e9i	−0.513279	+	0.513279i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$			2.03919e8i			0.0575304i
$245$		0			0
$246$	−1.84309e9			−0.503276
$247$	2.55383e9	−	2.55383e9i	0.686127	−	0.686127i
$248$	−3.33180e9	−	3.33180e9i	−0.880790	−	0.880790i
$249$		−	1.63313e9i		−	0.424838i
$250$		0			0
$251$	−1.90299e9			−0.479447			−0.239724	−	0.970841i	$-0.577057\pi$
$251$	−1.90299e9			−0.479447			−0.239724	+	0.970841i	$0.577057\pi$
$252$	5.31064e7	−	5.31064e7i	0.0131688	−	0.0131688i
$253$	8.24149e8	+	8.24149e8i	0.201152	+	0.201152i
$254$			1.67939e9i			0.403474i
$255$		0			0
$256$	−1.22695e9			−0.285671
$257$	7.71199e8	−	7.71199e8i	0.176780	−	0.176780i	−0.613170	−	0.789951i	$-0.710106\pi$
$257$	7.71199e8	−	7.71199e8i	0.176780	−	0.176780i	0.789951	+	0.613170i	$0.210106\pi$
$258$	3.22199e9	+	3.22199e9i	0.727186	+	0.727186i
$259$			8.63048e8i			0.191794i
$260$		0			0
$261$	−1.03218e9			−0.222431
$262$	2.01047e9	−	2.01047e9i	0.426669	−	0.426669i
$263$	−7.60308e8	−	7.60308e8i	−0.158916	−	0.158916i	0.623170	−	0.782086i	$-0.285844\pi$
$263$	−7.60308e8	−	7.60308e8i	−0.158916	−	0.158916i	−0.782086	+	0.623170i	$0.785844\pi$
$264$		−	1.42126e9i		−	0.292589i
$265$		0			0
$266$	−2.51547e9			−0.502449
$267$	2.84566e9	−	2.84566e9i	0.559936	−	0.559936i
$268$	5.71781e8	+	5.71781e8i	0.110839	+	0.110839i
$269$			6.05851e9i			1.15706i	0.815660	+	0.578531i	$0.196374\pi$
$269$			6.05851e9i			1.15706i	−0.815660	+	0.578531i	$0.803626\pi$
$270$		0			0
$271$	−4.99620e9			−0.926324			−0.463162	−	0.886274i	$-0.653285\pi$
$271$	−4.99620e9			−0.926324			−0.463162	+	0.886274i	$0.653285\pi$
$272$	−4.32319e9	+	4.32319e9i	−0.789820	+	0.789820i
$273$	1.40605e9	+	1.40605e9i	0.253134	+	0.253134i
$274$		−	6.87814e9i		−	1.22031i
$275$		0			0
$276$	1.88417e8			0.0324701
$277$	1.30830e9	−	1.30830e9i	0.222222	−	0.222222i	−0.587211	−	0.809434i	$-0.699774\pi$
$277$	1.30830e9	−	1.30830e9i	0.222222	−	0.222222i	0.809434	+	0.587211i	$0.199774\pi$
$278$	5.86046e9	+	5.86046e9i	0.981189	+	0.981189i
$279$		−	2.41416e9i		−	0.398428i
$280$		0			0
$281$	−6.91480e9			−1.10906			−0.554529	−	0.832164i	$-0.687102\pi$
$281$	−6.91480e9			−1.10906			−0.554529	+	0.832164i	$0.687102\pi$
$282$	7.52748e8	−	7.52748e8i	0.119029	−	0.119029i
$283$	5.90916e9	+	5.90916e9i	0.921255	+	0.921255i	0.997118	−	0.0758636i	$-0.0241714\pi$
$283$	5.90916e9	+	5.90916e9i	0.921255	+	0.921255i	−0.0758636	+	0.997118i	$0.524171\pi$
$284$		−	7.93827e8i		−	0.122026i
$285$		0			0
$286$	3.30041e9			0.493291
$287$	2.55625e9	−	2.55625e9i	0.376769	−	0.376769i
$288$	−3.10679e8	−	3.10679e8i	−0.0451588	−	0.0451588i
$289$		−	3.89862e9i		−	0.558882i
$290$		0			0
$291$	4.81135e9			0.670958
$292$	3.67287e8	−	3.67287e8i	0.0505213	−	0.0505213i
$293$	−4.72997e9	−	4.72997e9i	−0.641783	−	0.641783i	0.309211	−	0.950994i	$-0.399935\pi$
$293$	−4.72997e9	−	4.72997e9i	−0.641783	−	0.641783i	−0.950994	+	0.309211i	$0.899935\pi$
$294$			2.71597e9i			0.363527i
$295$		0			0
$296$	2.64026e9			0.343937
$297$	5.14909e8	−	5.14909e8i	0.0661766	−	0.0661766i
$298$	9.13980e9	+	9.13980e9i	1.15897	+	1.15897i
$299$			4.98854e9i			0.624150i
$300$		0			0
$301$	−8.93738e9			−1.08879
$302$	−5.95826e9	+	5.95826e9i	−0.716295	+	0.716295i
$303$	1.64113e9	+	1.64113e9i	0.194703	+	0.194703i
$304$			6.94863e9i			0.813588i
$305$		0			0
$306$	−3.46914e9			−0.395672
$307$	−5.52832e9	+	5.52832e9i	−0.622357	+	0.622357i	−0.946133	−	0.323777i	$-0.895047\pi$
$307$	−5.52832e9	+	5.52832e9i	−0.622357	+	0.622357i	0.323777	+	0.946133i	$0.395047\pi$
$308$	1.72890e8	+	1.72890e8i	0.0192118	+	0.0192118i
$309$		−	4.12192e9i		−	0.452132i
$310$		0			0
$311$	−5.99042e9			−0.640347			−0.320174	−	0.947359i	$-0.603741\pi$
$311$	−5.99042e9			−0.640347			−0.320174	+	0.947359i	$0.603741\pi$
$312$	4.30141e9	−	4.30141e9i	0.453934	−	0.453934i
$313$	6.95852e9	+	6.95852e9i	0.725003	+	0.725003i	0.969620	−	0.244617i	$-0.0786622\pi$
$313$	6.95852e9	+	6.95852e9i	0.725003	+	0.725003i	−0.244617	+	0.969620i	$0.578662\pi$
$314$			1.40505e10i			1.44535i
$315$		0			0
$316$	−1.76615e9			−0.177125
$317$	−1.67452e9	+	1.67452e9i	−0.165826	+	0.165826i	−0.785142	−	0.619316i	$-0.787410\pi$
$317$	−1.67452e9	+	1.67452e9i	−0.165826	+	0.165826i	0.619316	+	0.785142i	$0.287410\pi$
$318$	7.12433e9	+	7.12433e9i	0.696683	+	0.696683i
$319$		−	3.36032e9i		−	0.324502i
$320$		0			0
$321$	6.55921e9			0.617776
$322$	2.45680e9	−	2.45680e9i	0.228532	−	0.228532i
$323$	−8.73916e9	−	8.73916e9i	−0.802896	−	0.802896i
$324$		−	1.17719e8i		−	0.0106823i
$325$		0			0
$326$	2.93685e9			0.260023
$327$	3.06925e9	−	3.06925e9i	0.268436	−	0.268436i
$328$	−7.82012e9	−	7.82012e9i	−0.675644	−	0.675644i
$329$			2.08802e9i			0.178218i
$330$		0			0
$331$	−1.77038e10			−1.47487			−0.737436	−	0.675417i	$-0.763964\pi$
$331$	−1.77038e10			−1.47487			−0.737436	+	0.675417i	$0.763964\pi$
$332$	6.07756e8	−	6.07756e8i	0.0500238	−	0.0500238i
$333$	9.56540e8	+	9.56540e8i	0.0777904	+	0.0777904i
$334$		−	1.82096e10i		−	1.46324i
$335$		0			0
$336$	−3.82566e9			−0.300158
$337$	−1.30214e10	+	1.30214e10i	−1.00957	+	1.00957i	−0.00961969	+	0.999954i	$0.503062\pi$
$337$	−1.30214e10	+	1.30214e10i	−1.00957	+	1.00957i	−0.999954	+	0.00961969i	$0.996938\pi$
$338$	1.21454e9	+	1.21454e9i	0.0930558	+	0.0930558i
$339$			8.30327e9i			0.628710i
$340$		0			0
$341$	7.85940e9			0.581262
$342$	−2.78796e9	+	2.78796e9i	−0.203790	+	0.203790i
$343$	−9.45456e9	−	9.45456e9i	−0.683069	−	0.683069i
$344$			2.73414e10i			1.95248i
$345$		0			0
$346$	2.14736e10			1.49830
$347$	−1.29834e9	+	1.29834e9i	−0.0895509	+	0.0895509i	−0.750463	−	0.660912i	$-0.770170\pi$
$347$	−1.29834e9	+	1.29834e9i	−0.0895509	+	0.0895509i	0.660912	+	0.750463i	$0.270170\pi$
$348$	−3.84119e8	−	3.84119e8i	−0.0261908	−	0.0261908i
$349$		−	8.25437e9i		−	0.556394i	−0.960524	−	0.278197i	$-0.910263\pi$
$349$		−	8.25437e9i		−	0.556394i	0.960524	−	0.278197i	$-0.0897368\pi$
$350$		0			0
$351$	3.11672e9			0.205338
$352$	1.01143e9	−	1.01143e9i	0.0658817	−	0.0658817i
$353$	−9.06303e9	−	9.06303e9i	−0.583679	−	0.583679i	0.352233	−	0.935912i	$-0.385422\pi$
$353$	−9.06303e9	−	9.06303e9i	−0.583679	−	0.583679i	−0.935912	+	0.352233i	$0.885422\pi$
$354$		−	4.50964e9i		−	0.287163i
$355$		0			0
$356$	2.11798e9			0.131863
$357$	4.81147e9	−	4.81147e9i	0.296213	−	0.296213i
$358$	−1.36565e10	−	1.36565e10i	−0.831393	−	0.831393i
$359$		−	7.06291e9i		−	0.425212i	−0.977138	−	0.212606i	$-0.931805\pi$
$359$		−	7.06291e9i		−	0.425212i	0.977138	−	0.212606i	$-0.0681951\pi$
$360$		0			0
$361$	2.93718e9			0.172943
$362$	7.33156e9	−	7.33156e9i	0.426935	−	0.426935i
$363$	−5.41214e9	−	5.41214e9i	−0.311704	−	0.311704i
$364$			1.04650e9i			0.0596119i
$365$		0			0
$366$	5.89392e9			0.328458
$367$	1.17036e9	−	1.17036e9i	0.0645144	−	0.0645144i	−0.674113	−	0.738628i	$-0.735474\pi$
$367$	1.17036e9	−	1.17036e9i	0.0645144	−	0.0645144i	0.738628	+	0.674113i	$0.235474\pi$
$368$	−6.78657e9	−	6.78657e9i	−0.370049	−	0.370049i
$369$		−	5.66631e9i		−	0.305629i
$370$		0			0
$371$	−1.97620e10			−1.04312
$372$	8.98410e8	−	8.98410e8i	0.0469140	−	0.0469140i
$373$	8.36934e8	+	8.36934e8i	0.0432370	+	0.0432370i	0.728395	−	0.685158i	$-0.240267\pi$
$373$	8.36934e8	+	8.36934e8i	0.0432370	+	0.0432370i	−0.685158	+	0.728395i	$0.740267\pi$
$374$		−	1.12939e10i		−	0.577243i
$375$		0			0
$376$	6.38773e9			0.319591
$377$	1.01699e10	−	1.01699e10i	0.503447	−	0.503447i
$378$	−1.53495e9	−	1.53495e9i	−0.0751843	−	0.0751843i
$379$		−	7.43822e9i		−	0.360506i	−0.983620	−	0.180253i	$-0.942308\pi$
$379$		−	7.43822e9i		−	0.360506i	0.983620	−	0.180253i	$-0.0576916\pi$
$380$		0			0
$381$	−5.16303e9			−0.245022
$382$	1.27854e10	−	1.27854e10i	0.600426	−	0.600426i
$383$	−8.80678e9	−	8.80678e9i	−0.409281	−	0.409281i	0.472207	−	0.881488i	$-0.343458\pi$
$383$	−8.80678e9	−	8.80678e9i	−0.409281	−	0.409281i	−0.881488	+	0.472207i	$0.843458\pi$
$384$			1.04458e10i			0.480416i
$385$		0			0
$386$	2.35678e10			1.06162
$387$	−9.90554e9	+	9.90554e9i	−0.441605	+	0.441605i
$388$	1.79051e9	+	1.79051e9i	0.0790039	+	0.0790039i
$389$		−	3.67525e10i		−	1.60505i	−0.596620	−	0.802524i	$-0.703490\pi$
$389$		−	3.67525e10i		−	1.60505i	0.596620	−	0.802524i	$-0.296510\pi$
$390$		0			0
$391$	1.70707e10			0.730371
$392$	−1.15237e10	+	1.15237e10i	−0.488032	+	0.488032i
$393$	6.18089e9	+	6.18089e9i	0.259108	+	0.259108i
$394$			1.99274e9i			0.0826922i
$395$		0			0
$396$	3.83238e8			0.0155843
$397$	8.61053e8	−	8.61053e8i	0.0346631	−	0.0346631i	−0.689563	−	0.724226i	$-0.742197\pi$
$397$	8.61053e8	−	8.61053e8i	0.0346631	−	0.0346631i	0.724226	+	0.689563i	$0.242197\pi$
$398$	1.89549e10	+	1.89549e10i	0.755420	+	0.755420i
$399$		−	7.73344e9i		−	0.305127i
$400$		0			0
$401$	4.86650e10			1.88208			0.941042	−	0.338290i	$-0.109849\pi$
$401$	4.86650e10			1.88208			0.941042	+	0.338290i	$0.109849\pi$
$402$	1.65264e10	−	1.65264e10i	0.632809	−	0.632809i
$403$	2.37863e10	+	2.37863e10i	0.901794	+	0.901794i
$404$			1.22146e9i			0.0458517i
$405$		0			0
$406$	−1.00172e10			−0.368672
$407$	−3.11406e9	+	3.11406e9i	−0.113488	+	0.113488i
$408$	−1.47193e10	−	1.47193e10i	−0.531187	−	0.531187i
$409$		−	1.40974e10i		−	0.503785i	−0.967755	−	0.251892i	$-0.918947\pi$
$409$		−	1.40974e10i		−	0.503785i	0.967755	−	0.251892i	$-0.0810529\pi$
$410$		0			0
$411$	2.11459e10			0.741068
$412$	1.53394e9	−	1.53394e9i	0.0532376	−	0.0532376i
$413$	6.25458e9	+	6.25458e9i	0.214980	+	0.214980i
$414$		−	5.44587e9i		−	0.185381i
$415$		0			0
$416$	6.12215e9			0.204423
$417$	−1.80171e10	+	1.80171e10i	−0.595856	+	0.595856i
$418$	−9.07632e9	−	9.07632e9i	−0.297307	−	0.297307i
$419$		−	4.51696e10i		−	1.46551i	−0.680491	−	0.732757i	$-0.738233\pi$
$419$		−	4.51696e10i		−	1.46551i	0.680491	−	0.732757i	$-0.261767\pi$
$420$		0			0
$421$	5.87369e9			0.186975			0.0934873	−	0.995620i	$-0.470199\pi$
$421$	5.87369e9			0.186975			0.0934873	+	0.995620i	$0.470199\pi$
$422$	1.10437e10	−	1.10437e10i	0.348230	−	0.348230i
$423$	2.31421e9	+	2.31421e9i	0.0722840	+	0.0722840i
$424$			6.04562e10i			1.87058i
$425$		0			0
$426$	−2.29442e10			−0.696682
$427$	−8.17448e9	+	8.17448e9i	−0.245894	+	0.245894i
$428$	2.44095e9	+	2.44095e9i	0.0727419	+	0.0727419i
$429$			1.01466e10i			0.299566i
$430$		0			0
$431$	−6.34592e10			−1.83902			−0.919508	−	0.393072i	$-0.871412\pi$
$431$	−6.34592e10			−1.83902			−0.919508	+	0.393072i	$0.871412\pi$
$432$	−4.24009e9	+	4.24009e9i	−0.121742	+	0.121742i
$433$	−1.88003e10	−	1.88003e10i	−0.534828	−	0.534828i	0.387177	−	0.922005i	$-0.373450\pi$
$433$	−1.88003e10	−	1.88003e10i	−0.534828	−	0.534828i	−0.922005	+	0.387177i	$0.873450\pi$
$434$		−	2.34290e10i		−	0.660381i
$435$		0			0
$436$	2.28439e9			0.0632156
$437$	1.37188e10	−	1.37188e10i	0.376175	−	0.376175i
$438$	−1.06158e10	−	1.06158e10i	−0.288441	−	0.288441i
$439$			3.57969e10i			0.963800i	0.876226	+	0.481900i	$0.160053\pi$
$439$			3.57969e10i			0.963800i	−0.876226	+	0.481900i	$0.839947\pi$
$440$		0			0
$441$	−8.34987e9			−0.220762
$442$	3.41809e10	−	3.41809e10i	0.895558	−	0.895558i
$443$	4.37162e10	+	4.37162e10i	1.13508	+	1.13508i	0.989319	+	0.145764i	$0.0465639\pi$
$443$	4.37162e10	+	4.37162e10i	1.13508	+	1.13508i	0.145764	+	0.989319i	$0.453436\pi$
$444$			7.11936e8i			0.0183193i
$445$		0			0
$446$	3.94653e9			0.0997416
$447$	−2.80990e10	+	2.80990e10i	−0.703818	+	0.703818i
$448$	−1.78235e10	−	1.78235e10i	−0.442466	−	0.442466i
$449$			1.65888e9i			0.0408159i	0.999792	+	0.0204079i	$0.00649650\pi$
$449$			1.65888e9i			0.0408159i	−0.999792	+	0.0204079i	$0.993504\pi$
$450$		0			0
$451$	1.84469e10			0.445880
$452$	−3.08999e9	+	3.08999e9i	−0.0740293	+	0.0740293i
$453$	−1.83178e10	−	1.83178e10i	−0.434992	−	0.434992i
$454$			1.64537e10i			0.387293i
$455$		0			0
$456$	−2.36583e10			−0.547172
$457$	−2.84520e10	+	2.84520e10i	−0.652302	+	0.652302i	−0.953547	−	0.301245i	$-0.902598\pi$
$457$	−2.84520e10	+	2.84520e10i	−0.652302	+	0.652302i	0.301245	+	0.953547i	$0.402598\pi$
$458$	4.37552e10	+	4.37552e10i	0.994415	+	0.994415i
$459$		−	1.06654e10i		−	0.240284i
$460$		0			0
$461$	−6.07445e10			−1.34494			−0.672471	−	0.740124i	$-0.734767\pi$
$461$	−6.07445e10			−1.34494			−0.672471	+	0.740124i	$0.734767\pi$
$462$	4.99710e9	−	4.99710e9i	0.109686	−	0.109686i
$463$	1.71916e10	+	1.71916e10i	0.374104	+	0.374104i	0.868970	−	0.494865i	$-0.164783\pi$
$463$	1.71916e10	+	1.71916e10i	0.374104	+	0.374104i	−0.494865	+	0.868970i	$0.664783\pi$
$464$			2.76710e10i			0.596971i
$465$		0			0
$466$	−4.04488e10			−0.857752
$467$	−3.12336e10	+	3.12336e10i	−0.656680	+	0.656680i	−0.954593	−	0.297913i	$-0.903710\pi$
$467$	−3.12336e10	+	3.12336e10i	−0.656680	+	0.656680i	0.297913	+	0.954593i	$0.403710\pi$
$468$	1.15986e9	+	1.15986e9i	0.0241782	+	0.0241782i
$469$			4.58420e10i			0.947484i
$470$		0			0
$471$	−4.31963e10			−0.877734
$472$	1.91341e10	−	1.91341e10i	0.385514	−	0.385514i
$473$	−3.22479e10	−	3.22479e10i	−0.644254	−	0.644254i
$474$			5.10477e10i			1.01126i
$475$		0			0
$476$	3.58109e9			0.0697570
$477$	−2.19027e10	+	2.19027e10i	−0.423082	+	0.423082i
$478$	1.37278e10	+	1.37278e10i	0.262960	+	0.262960i
$479$			4.02757e10i			0.765069i	0.923941	+	0.382535i	$0.124949\pi$
$479$			4.02757e10i			0.765069i	−0.923941	+	0.382535i	$0.875051\pi$
$480$		0			0
$481$	−1.88493e10			−0.352139
$482$	3.83724e10	−	3.83724e10i	0.710937	−	0.710937i
$483$	7.55307e9	+	7.55307e9i	0.138783	+	0.138783i
$484$		−	4.02816e9i		−	0.0734050i
$485$		0			0
$486$	−3.40245e9			−0.0609884
$487$	−2.78327e10	+	2.78327e10i	−0.494811	+	0.494811i	−0.909818	−	0.415007i	$-0.863779\pi$
$487$	−2.78327e10	+	2.78327e10i	−0.494811	+	0.494811i	0.415007	+	0.909818i	$0.363779\pi$
$488$	2.50075e10	+	2.50075e10i	0.440952	+	0.440952i
$489$			9.02891e9i			0.157907i
$490$		0			0
$491$	3.48952e10			0.600399			0.300199	−	0.953876i	$-0.402947\pi$
$491$	3.48952e10			0.600399			0.300199	+	0.953876i	$0.402947\pi$
$492$	2.10867e9	−	2.10867e9i	0.0359872	−	0.0359872i
$493$	−3.48013e10	−	3.48013e10i	−0.589126	−	0.589126i
$494$		−	5.49386e10i		−	0.922508i
$495$		0			0
$496$	−6.47193e10			−1.06932
$497$	3.18221e10	−	3.18221e10i	0.521559	−	0.521559i
$498$	−1.75661e10	−	1.75661e10i	−0.285600	−	0.285600i
$499$			8.29525e10i			1.33791i	0.743302	+	0.668956i	$0.233258\pi$
$499$			8.29525e10i			1.33791i	−0.743302	+	0.668956i	$0.766742\pi$
$500$		0			0
$501$	5.59829e10			0.888596
$502$	−2.04687e10	+	2.04687e10i	−0.322312	+	0.322312i
$503$	3.75026e10	+	3.75026e10i	0.585855	+	0.585855i	0.936506	−	0.350651i	$-0.114040\pi$
$503$	3.75026e10	+	3.75026e10i	0.585855	+	0.585855i	−0.350651	+	0.936506i	$0.614040\pi$
$504$		−	1.30254e10i		−	0.201869i
$505$		0			0
$506$	1.77293e10			0.270451
$507$	−3.73391e9	+	3.73391e9i	−0.0565109	+	0.0565109i
$508$	−1.92138e9	−	1.92138e9i	−0.0288508	−	0.0288508i
$509$		−	1.07216e11i		−	1.59730i	−0.601795	−	0.798651i	$-0.705548\pi$
$509$		−	1.07216e11i		−	1.59730i	0.601795	−	0.798651i	$-0.294452\pi$
$510$		0			0
$511$	2.94469e10			0.431872
$512$	−5.36309e10	+	5.36309e10i	−0.780432	+	0.780432i
$513$	−8.57118e9	−	8.57118e9i	−0.123757	−	0.123757i
$514$		−	1.65902e10i		−	0.237684i
$515$		0			0
$516$	−7.37253e9			−0.103996
$517$	−7.53402e9	+	7.53402e9i	−0.105454	+	0.105454i
$518$	9.28304e9	+	9.28304e9i	0.128935	+	0.128935i
$519$			6.60174e10i			0.909890i
$520$		0			0
$521$	−7.65990e10			−1.03961			−0.519807	−	0.854284i	$-0.673996\pi$
$521$	−7.65990e10			−1.03961			−0.519807	+	0.854284i	$0.673996\pi$
$522$	−1.11023e10	+	1.11023e10i	−0.149531	+	0.149531i
$523$	3.31472e10	+	3.31472e10i	0.443038	+	0.443038i	0.893032	−	0.449994i	$-0.148574\pi$
$523$	3.31472e10	+	3.31472e10i	0.443038	+	0.443038i	−0.449994	+	0.893032i	$0.648574\pi$
$524$			4.60033e9i			0.0610188i
$525$		0			0
$526$	−1.63559e10			−0.213664
$527$	8.13963e10	−	8.13963e10i	1.05527	−	1.05527i
$528$	−1.38038e10	−	1.38038e10i	−0.177608	−	0.177608i
$529$		−	5.15133e10i		−	0.657805i
$530$		0			0
$531$	1.38642e10			0.174388
$532$	2.87793e9	−	2.87793e9i	0.0359281	−	0.0359281i
$533$	5.58293e10	+	5.58293e10i	0.691756	+	0.691756i
$534$		−	6.12166e10i		−	0.752842i
$535$		0			0
$536$	1.40241e11			1.69908
$537$	4.19848e10	−	4.19848e10i	0.504888	−	0.504888i
$538$	6.51660e10	+	6.51660e10i	0.777843	+	0.777843i
$539$		−	2.71833e10i		−	0.322068i
$540$		0			0
$541$	1.00235e11			1.17012			0.585061	−	0.810989i	$-0.301071\pi$
$541$	1.00235e11			1.17012			0.585061	+	0.810989i	$0.301071\pi$
$542$	−5.37397e10	+	5.37397e10i	−0.622728	+	0.622728i
$543$	2.25398e10	+	2.25398e10i	0.259269	+	0.259269i
$544$		−	2.09498e10i		−	0.239213i
$545$		0			0
$546$	3.02472e10			0.340342
$547$	5.03272e9	−	5.03272e9i	0.0562151	−	0.0562151i	−0.678440	−	0.734655i	$-0.737344\pi$
$547$	5.03272e9	−	5.03272e9i	0.0562151	−	0.0562151i	0.734655	+	0.678440i	$0.237344\pi$
$548$	7.86925e9	+	7.86925e9i	0.0872592	+	0.0872592i
$549$			1.81200e10i			0.199466i
$550$		0			0
$551$	−5.59359e10			−0.606854
$552$	2.31065e10	−	2.31065e10i	0.248873	−	0.248873i
$553$	−7.07998e10	−	7.07998e10i	−0.757062	−	0.757062i
$554$		−	2.81444e10i		−	0.298781i
$555$		0			0
$556$	−1.34099e10			−0.140322
$557$	8.75954e10	−	8.75954e10i	0.910040	−	0.910040i	−0.0862350	−	0.996275i	$-0.527484\pi$
$557$	8.75954e10	−	8.75954e10i	0.910040	−	0.910040i	0.996275	+	0.0862350i	$0.0274836\pi$
$558$	−2.59670e10	−	2.59670e10i	−0.267846	−	0.267846i
$559$		−	1.95195e11i		−	1.99904i
$560$		0			0
$561$	3.47215e10			0.350548
$562$	−7.43764e10	+	7.43764e10i	−0.745572	+	0.745572i
$563$	−9.70300e10	−	9.70300e10i	−0.965767	−	0.965767i	0.0336664	−	0.999433i	$-0.489282\pi$
$563$	−9.70300e10	−	9.70300e10i	−0.965767	−	0.965767i	−0.999433	+	0.0336664i	$0.989282\pi$
$564$			1.72243e9i			0.0170226i
$565$		0			0
$566$	1.27119e11			1.23864
$567$	4.71898e9	−	4.71898e9i	0.0456579	−	0.0456579i
$568$	−9.73508e10	−	9.73508e10i	−0.935290	−	0.935290i
$569$			1.41438e11i			1.34932i	0.738127	+	0.674662i	$0.235711\pi$
$569$			1.41438e11i			1.34932i	−0.738127	+	0.674662i	$0.764289\pi$
$570$		0			0
$571$	−3.01297e10			−0.283433			−0.141716	−	0.989907i	$-0.545262\pi$
$571$	−3.01297e10			−0.283433			−0.141716	+	0.989907i	$0.545262\pi$
$572$	−3.77598e9	+	3.77598e9i	−0.0352733	+	0.0352733i
$573$	3.93068e10	+	3.93068e10i	0.364627	+	0.364627i
$574$		−	5.49905e10i		−	0.506571i
$575$		0			0
$576$	−3.95085e10			−0.358922
$577$	6.35231e10	−	6.35231e10i	0.573097	−	0.573097i	−0.359896	−	0.932993i	$-0.617188\pi$
$577$	6.35231e10	−	6.35231e10i	0.573097	−	0.573097i	0.932993	+	0.359896i	$0.117188\pi$
$578$	−4.19340e10	−	4.19340e10i	−0.375712	−	0.375712i
$579$			7.24557e10i			0.644701i
$580$		0			0
$581$	4.87262e10			0.427620
$582$	5.17515e10	−	5.17515e10i	0.451056	−	0.451056i
$583$	−7.13052e10	−	7.13052e10i	−0.617230	−	0.617230i
$584$		−	9.00844e10i		−	0.774459i
$585$		0			0
$586$	−1.01752e11			−0.862886
$587$	6.15149e10	−	6.15149e10i	0.518117	−	0.518117i	−0.398884	−	0.917001i	$-0.630602\pi$
$587$	6.15149e10	−	6.15149e10i	0.518117	−	0.518117i	0.917001	+	0.398884i	$0.130602\pi$
$588$	−3.10733e9	−	3.10733e9i	−0.0259943	−	0.0259943i
$589$		−	1.30828e11i		−	1.08702i
$590$		0			0
$591$	−6.12638e9			−0.0502173
$592$	2.56431e10	−	2.56431e10i	0.208778	−	0.208778i
$593$	−1.54470e11	−	1.54470e11i	−1.24918	−	1.24918i	−0.956082	−	0.293098i	$-0.905314\pi$
$593$	−1.54470e11	−	1.54470e11i	−1.24918	−	1.24918i	−0.293098	−	0.956082i	$-0.594686\pi$
$594$		−	1.10768e10i		−	0.0889754i
$595$		0			0
$596$	−2.09136e10			−0.165746
$597$	−5.82740e10	+	5.82740e10i	−0.458752	+	0.458752i
$598$	5.36573e10	+	5.36573e10i	0.419589	+	0.419589i
$599$			1.71649e11i			1.33332i	0.745363	+	0.666658i	$0.232276\pi$
$599$			1.71649e11i			1.33332i	−0.745363	+	0.666658i	$0.767724\pi$
$600$		0			0
$601$	2.52528e11			1.93558			0.967790	−	0.251759i	$-0.0810090\pi$
$601$	2.52528e11			1.93558			0.967790	+	0.251759i	$0.0810090\pi$
$602$	−9.61315e10	+	9.61315e10i	−0.731947	+	0.731947i
$603$	5.08079e10	+	5.08079e10i	0.384292	+	0.384292i
$604$		−	1.36336e10i		−	0.102439i
$605$		0			0
$606$	3.53043e10			0.261780
$607$	−8.26378e10	+	8.26378e10i	−0.608729	+	0.608729i	−0.942614	−	0.333885i	$-0.891640\pi$
$607$	−8.26378e10	+	8.26378e10i	−0.608729	+	0.608729i	0.333885	+	0.942614i	$0.391640\pi$
$608$	−1.68363e10	−	1.68363e10i	−0.123206	−	0.123206i
$609$		−	3.07963e10i		−	0.223887i
$610$		0			0
$611$	−4.56032e10			−0.327213
$612$	3.96902e9	−	3.96902e9i	0.0282929	−	0.0282929i
$613$	−5.27356e10	−	5.27356e10i	−0.373476	−	0.373476i	0.495266	−	0.868741i	$-0.335071\pi$
$613$	−5.27356e10	−	5.27356e10i	−0.373476	−	0.373476i	−0.868741	+	0.495266i	$0.835071\pi$
$614$			1.18926e11i			0.836767i
$615$		0			0
$616$	4.24048e10			0.294504
$617$	2.53400e10	−	2.53400e10i	0.174850	−	0.174850i	−0.614256	−	0.789107i	$-0.710544\pi$
$617$	2.53400e10	−	2.53400e10i	0.174850	−	0.174850i	0.789107	+	0.614256i	$0.210544\pi$
$618$	−4.43358e10	−	4.43358e10i	−0.303949	−	0.303949i
$619$			1.55331e11i			1.05802i	0.848614	+	0.529012i	$0.177437\pi$
$619$			1.55331e11i			1.05802i	−0.848614	+	0.529012i	$0.822563\pi$
$620$		0			0
$621$	1.67425e10			0.112578
$622$	−6.44336e10	+	6.44336e10i	−0.430478	+	0.430478i
$623$	8.49034e10	+	8.49034e10i	0.563603	+	0.563603i
$624$		−	8.35538e10i		−	0.551097i
$625$		0			0
$626$	1.49693e11			0.974777
$627$	2.79038e10	−	2.79038e10i	0.180548	−	0.180548i
$628$	−1.60751e10	−	1.60751e10i	−0.103351	−	0.103351i
$629$			6.45018e10i			0.412068i
$630$		0			0
$631$	−2.06463e11			−1.30234			−0.651171	−	0.758931i	$-0.725722\pi$
$631$	−2.06463e11			−1.30234			−0.651171	+	0.758931i	$0.725722\pi$
$632$	−2.16592e11	+	2.16592e11i	−1.35761	+	1.35761i
$633$	3.39523e10	+	3.39523e10i	0.211473	+	0.211473i
$634$			3.60227e10i			0.222956i
$635$		0			0
$636$	−1.63018e10			−0.0996340
$637$	8.22699e10	−	8.22699e10i	0.499670	−	0.499670i
$638$	−3.61440e10	−	3.61440e10i	−0.218149	−	0.218149i
$639$		−	7.05386e10i		−	0.423081i
$640$		0			0
$641$	−1.81421e11			−1.07462			−0.537311	−	0.843384i	$-0.680560\pi$
$641$	−1.81421e11			−1.07462			−0.537311	+	0.843384i	$0.680560\pi$
$642$	7.05516e10	−	7.05516e10i	0.415304	−	0.415304i
$643$	2.13170e11	+	2.13170e11i	1.24704	+	1.24704i	0.957019	+	0.290025i	$0.0936635\pi$
$643$	2.13170e11	+	2.13170e11i	1.24704	+	1.24704i	0.290025	+	0.957019i	$0.406337\pi$
$644$			5.62162e9i			0.0326827i
$645$		0			0
$646$	−1.87999e11			−1.07951
$647$	5.73225e10	−	5.73225e10i	0.327120	−	0.327120i	−0.524370	−	0.851491i	$-0.675699\pi$
$647$	5.73225e10	−	5.73225e10i	0.327120	−	0.327120i	0.851491	+	0.524370i	$0.175699\pi$
$648$	−1.44364e10	−	1.44364e10i	−0.0818765	−	0.0818765i
$649$			4.51356e10i			0.254414i
$650$		0			0
$651$	7.20290e10			0.401036
$652$	−3.36003e9	+	3.36003e9i	−0.0185932	+	0.0185932i
$653$	−2.36175e11	−	2.36175e11i	−1.29892	−	1.29892i	−0.929109	−	0.369807i	$-0.879424\pi$
$653$	−2.36175e11	−	2.36175e11i	−1.29892	−	1.29892i	−0.369807	−	0.929109i	$-0.620576\pi$
$654$		−	6.60263e10i		−	0.360916i
$655$		0			0
$656$	−1.51904e11			−0.820263
$657$	3.26367e10	−	3.26367e10i	0.175164	−	0.175164i
$658$	2.24590e10	+	2.24590e10i	0.119808	+	0.119808i
$659$			1.35776e11i			0.719918i	0.932968	+	0.359959i	$0.117209\pi$
$659$			1.35776e11i			0.719918i	−0.932968	+	0.359959i	$0.882791\pi$
$660$		0			0
$661$	2.20549e11			1.15531			0.577655	−	0.816281i	$-0.303968\pi$
$661$	2.20549e11			1.15531			0.577655	+	0.816281i	$0.303968\pi$
$662$	−1.90424e11	+	1.90424e11i	−0.991494	+	0.991494i
$663$	1.05084e11	+	1.05084e11i	0.543855	+	0.543855i
$664$		−	1.49064e11i		−	0.766833i
$665$		0			0
$666$	2.05773e10			0.104590
$667$	5.46313e10	−	5.46313e10i	0.276019	−	0.276019i
$668$	2.08336e10	+	2.08336e10i	0.104630	+	0.104630i
$669$			1.21330e10i			0.0605711i
$670$		0			0
$671$	−5.89904e10			−0.290999
$672$	9.26944e9	−	9.26944e9i	0.0454545	−	0.0454545i
$673$	1.71937e11	+	1.71937e11i	0.838124	+	0.838124i	0.988612	−	0.150488i	$-0.0480844\pi$
$673$	1.71937e11	+	1.71937e11i	0.838124	+	0.838124i	−0.150488	+	0.988612i	$0.548084\pi$
$674$			2.80119e11i			1.35739i
$675$		0			0
$676$	−2.77909e9			−0.0133081
$677$	5.77761e10	−	5.77761e10i	0.275038	−	0.275038i	−0.556086	−	0.831125i	$-0.687698\pi$
$677$	5.77761e10	−	5.77761e10i	0.275038	−	0.275038i	0.831125	+	0.556086i	$0.187698\pi$
$678$	8.93109e10	+	8.93109e10i	0.422655	+	0.422655i
$679$			1.43552e11i			0.675351i
$680$		0			0
$681$	−5.05845e10			−0.235196
$682$	8.45366e10	−	8.45366e10i	0.390758	−	0.390758i
$683$	1.41107e11	+	1.41107e11i	0.648432	+	0.648432i	0.952614	−	0.304182i	$-0.0983831\pi$
$683$	1.41107e11	+	1.41107e11i	0.648432	+	0.648432i	−0.304182	+	0.952614i	$0.598383\pi$
$684$		−	6.37938e9i		−	0.0291443i
$685$		0			0
$686$	−2.03389e11			−0.918396
$687$	−1.34519e11	+	1.34519e11i	−0.603888	+	0.603888i
$688$	2.65550e11	+	2.65550e11i	1.18520	+	1.18520i
$689$		−	4.31608e11i		−	1.91519i
$690$		0			0
$691$	1.42595e10			0.0625450			0.0312725	−	0.999511i	$-0.490044\pi$
$691$	1.42595e10			0.0625450			0.0312725	+	0.999511i	$0.490044\pi$
$692$	−2.45678e10	+	2.45678e10i	−0.107138	+	0.107138i
$693$	1.53628e10	+	1.53628e10i	0.0666099	+	0.0666099i
$694$			2.79302e10i			0.120402i
$695$		0			0
$696$	−9.42127e10			−0.401488
$697$	1.91046e11	−	1.91046e11i	0.809483	−	0.809483i
$698$	−8.87850e10	−	8.87850e10i	−0.374040	−	0.374040i
$699$		−	1.24354e11i		−	0.520896i
$700$		0			0
$701$	6.57751e10			0.272389			0.136195	−	0.990682i	$-0.456513\pi$
$701$	6.57751e10			0.272389			0.136195	+	0.990682i	$0.456513\pi$
$702$	3.35238e10	−	3.35238e10i	0.138040	−	0.138040i
$703$	5.18366e10	+	5.18366e10i	0.212234	+	0.212234i
$704$		−	1.28621e11i		−	0.523628i
$705$		0			0
$706$	−1.94966e11			−0.784765
$707$	−4.89648e10	+	4.89648e10i	−0.195977	+	0.195977i
$708$	5.15946e9	+	5.15946e9i	0.0205339	+	0.0205339i
$709$			5.22271e10i			0.206686i	0.994646	+	0.103343i	$0.0329539\pi$
$709$			5.22271e10i			0.206686i	−0.994646	+	0.103343i	$0.967046\pi$
$710$		0			0
$711$	−1.56939e11			−0.614118
$712$	2.59738e11	−	2.59738e11i	1.01069	−	1.01069i
$713$	1.27776e11	+	1.27776e11i	0.494416	+	0.494416i
$714$		−	1.03505e11i		−	0.398263i
$715$		0			0
$716$	3.12486e10			0.118899
$717$	−4.22042e10	+	4.22042e10i	−0.159690	+	0.159690i
$718$	−7.59694e10	−	7.59694e10i	−0.285852	−	0.285852i
$719$			4.96442e11i			1.85760i	0.370579	+	0.928801i	$0.379159\pi$
$719$			4.96442e11i			1.85760i	−0.370579	+	0.928801i	$0.620841\pi$
$720$		0			0
$721$	1.22982e11			0.455092
$722$	3.15926e10	−	3.15926e10i	0.116262	−	0.116262i
$723$	1.17970e11	+	1.17970e11i	0.431738	+	0.431738i
$724$			1.67760e10i			0.0610568i
$725$		0			0
$726$	−1.16427e11			−0.419090
$727$	−1.06405e10	+	1.06405e10i	−0.0380911	+	0.0380911i	−0.725896	−	0.687805i	$-0.758575\pi$
$727$	−1.06405e10	+	1.06405e10i	−0.0380911	+	0.0380911i	0.687805	+	0.725896i	$0.258575\pi$
$728$	1.28337e11	+	1.28337e11i	0.456906	+	0.456906i
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−6.67954e11			−2.33925
$732$	−6.74320e9	+	6.74320e9i	−0.0234867	+	0.0234867i
$733$	−1.39079e11	−	1.39079e11i	−0.481778	−	0.481778i	0.423921	−	0.905699i	$-0.360653\pi$
$733$	−1.39079e11	−	1.39079e11i	−0.481778	−	0.481778i	−0.905699	+	0.423921i	$0.860653\pi$
$734$		−	2.51771e10i		−	0.0867405i
$735$		0			0
$736$	3.28872e10			0.112077
$737$	−1.65407e11	+	1.65407e11i	−0.560641	+	0.560641i
$738$	−6.09475e10	−	6.09475e10i	−0.205462	−	0.205462i
$739$			1.49124e11i			0.500001i	0.968246	+	0.250000i	$0.0804308\pi$
$739$			1.49124e11i			0.500001i	−0.968246	+	0.250000i	$0.919569\pi$
$740$		0			0
$741$	1.68901e11			0.560221
$742$	−2.12562e11	+	2.12562e11i	−0.701245	+	0.701245i
$743$	−3.03305e11	−	3.03305e11i	−0.995231	−	0.995231i	0.00475782	−	0.999989i	$-0.498486\pi$
$743$	−3.03305e11	−	3.03305e11i	−0.995231	−	0.995231i	−0.999989	+	0.00475782i	$0.998486\pi$
$744$		−	2.20353e11i		−	0.719162i
$745$		0			0
$746$	1.80043e10			0.0581328
$747$	5.40045e10	−	5.40045e10i	0.173439	−	0.173439i
$748$	1.29213e10	+	1.29213e10i	0.0412763	+	0.0412763i
$749$			1.95701e11i			0.621821i
$750$		0			0
$751$	4.43851e11			1.39533			0.697666	−	0.716424i	$-0.254222\pi$
$751$	4.43851e11			1.39533			0.697666	+	0.716424i	$0.254222\pi$
$752$	6.20400e10	−	6.20400e10i	0.193999	−	0.193999i
$753$	−6.29282e10	−	6.29282e10i	−0.195733	−	0.195733i
$754$		−	2.18778e11i		−	0.676891i
$755$		0			0
$756$	3.51226e9			0.0107523
$757$	−5.37427e10	+	5.37427e10i	−0.163658	+	0.163658i	−0.784185	−	0.620527i	$-0.786919\pi$
$757$	−5.37427e10	+	5.37427e10i	−0.163658	+	0.163658i	0.620527	+	0.784185i	$0.286919\pi$
$758$	−8.00063e10	−	8.00063e10i	−0.242353	−	0.242353i
$759$			5.45061e10i			0.164240i
$760$		0			0
$761$	5.87151e11			1.75070			0.875349	−	0.483492i	$-0.160632\pi$
$761$	5.87151e11			1.75070			0.875349	+	0.483492i	$0.160632\pi$
$762$	−5.55341e10	+	5.55341e10i	−0.164718	+	0.164718i
$763$	9.15742e10	+	9.15742e10i	0.270194	+	0.270194i
$764$			2.92554e10i			0.0858681i
$765$		0			0
$766$	−1.89453e11			−0.550285
$767$	−1.36602e11	+	1.36602e11i	−0.394708	+	0.394708i
$768$	−4.05728e10	−	4.05728e10i	−0.116625	−	0.116625i
$769$			4.98735e10i			0.142615i	0.997454	+	0.0713074i	$0.0227171\pi$
$769$			4.98735e10i			0.142615i	−0.997454	+	0.0713074i	$0.977283\pi$
$770$		0			0
$771$	5.10042e10			0.144341
$772$	−2.69638e10	+	2.69638e10i	−0.0759122	+	0.0759122i
$773$	−1.45752e11	−	1.45752e11i	−0.408223	−	0.408223i	0.472895	−	0.881119i	$-0.343209\pi$
$773$	−1.45752e11	−	1.45752e11i	−0.408223	−	0.408223i	−0.881119	+	0.472895i	$0.843209\pi$
$774$			2.13090e11i			0.593745i
$775$		0			0
$776$	4.39157e11			1.21108
$777$	−2.85394e10	+	2.85394e10i	−0.0782998	+	0.0782998i
$778$	−3.95314e11	−	3.95314e11i	−1.07900	−	1.07900i
$779$		−	3.07068e11i		−	0.833843i
$780$		0			0
$781$	2.29641e11			0.617229
$782$	1.83614e11	−	1.83614e11i	0.490997	−	0.490997i
$783$	−3.41324e10	−	3.41324e10i	−0.0908071	−	0.0908071i
$784$			2.23845e11i			0.592493i
$785$		0			0
$786$	1.32965e11			0.348374
$787$	−3.40029e11	+	3.40029e11i	−0.886374	+	0.886374i	−0.994173	−	0.107798i	$-0.965620\pi$
$787$	−3.40029e11	+	3.40029e11i	−0.886374	+	0.886374i	0.107798	+	0.994173i	$0.465620\pi$
$788$	−2.27988e9	−	2.27988e9i	−0.00591299	−	0.00591299i
$789$		−	5.02839e10i		−	0.129754i
$790$		0			0
$791$	−2.47737e11			−0.632826
$792$	4.69983e10	−	4.69983e10i	0.119449	−	0.119449i
$793$	−1.78533e11	−	1.78533e11i	−0.451468	−	0.451468i
$794$		−	1.85232e10i		−	0.0466051i
$795$		0			0
$796$	−4.33724e10			−0.108034
$797$	−5.24767e10	+	5.24767e10i	−0.130057	+	0.130057i	−0.769139	−	0.639082i	$-0.779315\pi$
$797$	−5.24767e10	+	5.24767e10i	−0.130057	+	0.130057i	0.639082	+	0.769139i	$0.279315\pi$
$798$	−8.31817e10	−	8.31817e10i	−0.205124	−	0.205124i
$799$			1.56053e11i			0.382900i
$800$		0			0
$801$	1.88202e11			0.457186
$802$	5.23446e11	−	5.23446e11i	1.26524	−	1.26524i
$803$	1.06250e11	+	1.06250e11i	0.255545	+	0.255545i
$804$			3.78155e10i			0.0904993i
$805$		0			0
$806$	5.11697e11			1.21247
$807$	−2.00343e11	+	2.00343e11i	−0.472369	+	0.472369i
$808$	1.49794e11	+	1.49794e11i	0.351438	+	0.351438i
$809$		−	5.20379e11i		−	1.21486i	−0.794374	−	0.607429i	$-0.792201\pi$
$809$		−	5.20379e11i		−	1.21486i	0.794374	−	0.607429i	$-0.207799\pi$
$810$		0			0
$811$	−5.64818e11			−1.30565			−0.652823	−	0.757511i	$-0.726415\pi$
$811$	−5.64818e11			−1.30565			−0.652823	+	0.757511i	$0.726415\pi$
$812$	1.14606e10	−	1.14606e10i	0.0263623	−	0.0263623i
$813$	−1.65215e11	−	1.65215e11i	−0.378170	−	0.378170i
$814$			6.69903e10i			0.152586i
$815$		0			0
$816$	−2.85919e11			−0.644886
$817$	−5.36799e11	+	5.36799e11i	−1.20482	+	1.20482i
$818$	−1.51633e11	−	1.51633e11i	−0.338673	−	0.338673i
$819$			9.29908e10i			0.206683i
$820$		0			0
$821$	2.29433e11			0.504990			0.252495	−	0.967598i	$-0.418749\pi$
$821$	2.29433e11			0.504990			0.252495	+	0.967598i	$0.418749\pi$
$822$	2.27447e11	−	2.27447e11i	0.498188	−	0.498188i
$823$	6.02259e10	+	6.02259e10i	0.131276	+	0.131276i	0.769692	−	0.638416i	$-0.220410\pi$
$823$	6.02259e10	+	6.02259e10i	0.131276	+	0.131276i	−0.638416	+	0.769692i	$0.720410\pi$
$824$		−	3.76228e11i		−	0.816099i
$825$		0			0
$826$	1.34550e11			0.289043
$827$	3.29701e11	−	3.29701e11i	0.704853	−	0.704853i	−0.260595	−	0.965448i	$-0.583919\pi$
$827$	3.29701e11	−	3.29701e11i	0.704853	−	0.704853i	0.965448	+	0.260595i	$0.0839188\pi$
$828$	6.23060e9	+	6.23060e9i	0.0132559	+	0.0132559i
$829$		−	7.15909e11i		−	1.51579i	−0.652375	−	0.757897i	$-0.726227\pi$
$829$		−	7.15909e11i		−	1.51579i	0.652375	−	0.757897i	$-0.273773\pi$
$830$		0			0
$831$	8.65260e10			0.181444
$832$	3.89270e11	−	3.89270e11i	0.812378	−	0.812378i
$833$	−2.81526e11	−	2.81526e11i	−0.584707	−	0.584707i
$834$			3.87589e11i			0.801137i
$835$		0			0
$836$	2.07684e10			0.0425184
$837$	7.98317e10	−	7.98317e10i	0.162657	−	0.162657i
$838$	−4.85849e11	−	4.85849e11i	−0.985202	−	0.985202i
$839$		−	6.38354e10i		−	0.128829i	−0.997923	−	0.0644145i	$-0.979482\pi$
$839$		−	6.38354e10i		−	0.128829i	0.997923	−	0.0644145i	$-0.0205180\pi$
$840$		0			0
$841$	2.77497e11			0.554720
$842$	6.31781e10	−	6.31781e10i	0.125695	−	0.125695i
$843$	−2.28659e11	−	2.28659e11i	−0.452771	−	0.452771i
$844$			2.52701e10i			0.0498010i
$845$		0			0
$846$	4.97839e10			0.0971869
$847$	1.61477e11	−	1.61477e11i	0.313745	−	0.313745i
$848$	5.87173e11	+	5.87173e11i	1.13549	+	1.13549i
$849$			3.90809e11i			0.752201i
$850$		0			0
$851$	−1.01255e11			−0.193063
$852$	2.62503e10	−	2.62503e10i	0.0498169	−	0.0498169i
$853$	−2.89736e11	−	2.89736e11i	−0.547276	−	0.547276i	0.378376	−	0.925652i	$-0.376483\pi$
$853$	−2.89736e11	−	2.89736e11i	−0.547276	−	0.547276i	−0.925652	+	0.378376i	$0.876483\pi$
$854$			1.75851e11i			0.330608i
$855$		0			0
$856$	5.98692e11			1.11509
$857$	3.42707e11	−	3.42707e11i	0.635330	−	0.635330i	−0.314070	−	0.949400i	$-0.601693\pi$
$857$	3.42707e11	−	3.42707e11i	0.635330	−	0.635330i	0.949400	+	0.314070i	$0.101693\pi$
$858$	1.09138e11	+	1.09138e11i	0.201385	+	0.201385i
$859$		−	7.22659e11i		−	1.32727i	−0.748054	−	0.663637i	$-0.769012\pi$
$859$		−	7.22659e11i		−	1.32727i	0.748054	−	0.663637i	$-0.230988\pi$
$860$		0			0
$861$	1.69060e11			0.307631
$862$	−6.82574e11	+	6.82574e11i	−1.23629	+	1.23629i
$863$	7.53219e11	+	7.53219e11i	1.35793	+	1.35793i	0.876463	+	0.481469i	$0.159897\pi$
$863$	7.53219e11	+	7.53219e11i	1.35793	+	1.35793i	0.481469	+	0.876463i	$0.340103\pi$
$864$		−	2.05471e10i		−	0.0368720i
$865$		0			0
$866$	−4.04437e11			−0.719084
$867$	1.28920e11	−	1.28920e11i	0.228163	−	0.228163i
$868$	2.68050e10	+	2.68050e10i	0.0472212	+	0.0472212i
$869$		−	5.10920e11i		−	0.895930i
$870$		0			0
$871$	−1.00120e12			−1.73960
$872$	2.80146e11	−	2.80146e11i	0.484527	−	0.484527i
$873$	1.59102e11	+	1.59102e11i	0.273918	+	0.273918i
$874$		−	2.95122e11i		−	0.505773i
$875$		0			0
$876$	2.42910e10			0.0412505
$877$	−4.95750e11	+	4.95750e11i	−0.838039	+	0.838039i	−0.988601	−	0.150562i	$-0.951892\pi$
$877$	−4.95750e11	+	4.95750e11i	−0.838039	+	0.838039i	0.150562	+	0.988601i	$0.451892\pi$
$878$	3.85035e11	+	3.85035e11i	0.647921	+	0.647921i
$879$		−	3.12823e11i		−	0.524014i
$880$		0			0
$881$	6.59305e11			1.09442			0.547208	−	0.836997i	$-0.315691\pi$
$881$	6.59305e11			1.09442			0.547208	+	0.836997i	$0.315691\pi$
$882$	−8.98121e10	+	8.98121e10i	−0.148409	+	0.148409i
$883$	9.31998e10	+	9.31998e10i	0.153311	+	0.153311i	0.779595	−	0.626284i	$-0.215425\pi$
$883$	9.31998e10	+	9.31998e10i	0.153311	+	0.153311i	−0.626284	+	0.779595i	$0.715425\pi$
$884$			7.82123e10i			0.128075i
$885$		0			0
$886$	9.40433e11			1.52614
$887$	3.56333e11	−	3.56333e11i	0.575654	−	0.575654i	−0.358049	−	0.933703i	$-0.616558\pi$
$887$	3.56333e11	−	3.56333e11i	0.575654	−	0.575654i	0.933703	+	0.358049i	$0.116558\pi$
$888$	8.73083e10	+	8.73083e10i	0.140412	+	0.140412i
$889$		−	1.54044e11i		−	0.246626i
$890$		0			0
$891$	3.40541e10			0.0540330
$892$	−4.51521e9	+	4.51521e9i	−0.00713212	+	0.00713212i
$893$	1.25411e11	+	1.25411e11i	0.197211	+	0.197211i
$894$			6.04472e11i			0.946294i
$895$		0			0
$896$	−3.11662e11			−0.483562
$897$	−1.64962e11	+	1.64962e11i	−0.254808	+	0.254808i
$898$	1.78431e10	+	1.78431e10i	0.0274388	+	0.0274388i
$899$		−	5.20986e11i		−	0.797604i
$900$		0			0
$901$	−1.47695e12			−2.24113
$902$	1.98417e11	−	1.98417e11i	0.299746	−	0.299746i
$903$	−2.95542e11	−	2.95542e11i	−0.444497	−	0.444497i
$904$			7.57881e11i			1.13482i
$905$		0			0
$906$	−3.94057e11			−0.584852
$907$	4.99028e11	−	4.99028e11i	0.737388	−	0.737388i	−0.234684	−	0.972072i	$-0.575405\pi$
$907$	4.99028e11	−	4.99028e11i	0.737388	−	0.737388i	0.972072	+	0.234684i	$0.0754054\pi$
$908$	−1.88246e10	−	1.88246e10i	−0.0276938	−	0.0276938i
$909$			1.08538e11i			0.158974i
$910$		0			0
$911$	−2.35231e11			−0.341523			−0.170762	−	0.985312i	$-0.554623\pi$
$911$	−2.35231e11			−0.341523			−0.170762	+	0.985312i	$0.554623\pi$
$912$	−2.29778e11	+	2.29778e11i	−0.332146	+	0.332146i
$913$	1.75814e11	+	1.75814e11i	0.253029	+	0.253029i
$914$			6.12067e11i			0.877029i
$915$		0			0
$916$	−1.00120e11			−0.142213
$917$	−1.84413e11	+	1.84413e11i	−0.260804	+	0.260804i
$918$	−1.14718e11	−	1.14718e11i	−0.161533	−	0.161533i
$919$			6.55314e11i			0.918729i	0.888248	+	0.459364i	$0.151923\pi$
$919$			6.55314e11i			0.918729i	−0.888248	+	0.459364i	$0.848077\pi$
$920$		0			0
$921$	−3.65622e11			−0.508152
$922$	−6.53375e11	+	6.53375e11i	−0.904147	+	0.904147i
$923$	6.95006e11	+	6.95006e11i	0.957594	+	0.957594i
$924$			1.14343e10i			0.0156864i
$925$		0			0
$926$	3.69830e11			0.502988
$927$	1.36304e11	−	1.36304e11i	0.184582	−	0.184582i
$928$	−6.70459e10	−	6.70459e10i	−0.0904024	−	0.0904024i
$929$		−	6.37954e10i		−	0.0856498i	−0.999083	−	0.0428249i	$-0.986364\pi$
$929$		−	6.37954e10i		−	0.0856498i	0.999083	−	0.0428249i	$-0.0136358\pi$
$930$		0			0
$931$	−4.52494e11			−0.602302
$932$	4.62773e10	−	4.62773e10i	0.0613344	−	0.0613344i
$933$	−1.98092e11	−	1.98092e11i	−0.261421	−	0.261421i
$934$			6.71903e11i			0.882916i
$935$		0			0
$936$	2.84479e11			0.370636
$937$	−2.92340e11	+	2.92340e11i	−0.379253	+	0.379253i	−0.870833	−	0.491580i	$-0.836420\pi$
$937$	−2.92340e11	+	2.92340e11i	−0.379253	+	0.379253i	0.491580	+	0.870833i	$0.336420\pi$
$938$	4.93081e11	+	4.93081e11i	0.636953	+	0.636953i
$939$			4.60210e11i			0.591962i
$940$		0			0
$941$	8.59770e10			0.109654			0.0548269	−	0.998496i	$-0.482539\pi$
$941$	8.59770e10			0.109654			0.0548269	+	0.998496i	$0.482539\pi$
$942$	−4.64624e11	+	4.64624e11i	−0.590063	+	0.590063i
$943$	2.99906e11	+	2.99906e11i	0.379261	+	0.379261i
$944$		−	3.71675e11i		−	0.468032i
$945$		0			0
$946$	−6.93724e11			−0.866208
$947$	−7.18344e11	+	7.18344e11i	−0.893167	+	0.893167i	−0.994820	−	0.101653i	$-0.967587\pi$
$947$	−7.18344e11	+	7.18344e11i	−0.893167	+	0.893167i	0.101653	+	0.994820i	$0.467587\pi$
$948$	−5.84034e10	−	5.84034e10i	−0.0723111	−	0.0723111i
$949$			6.43129e11i			0.792927i
$950$		0			0
$951$	−1.10747e11			−0.135397
$952$	4.39167e11	−	4.39167e11i	0.534665	−	0.534665i
$953$	−3.85444e11	−	3.85444e11i	−0.467294	−	0.467294i	0.433743	−	0.901037i	$-0.357193\pi$
$953$	−3.85444e11	−	3.85444e11i	−0.467294	−	0.467294i	−0.901037	+	0.433743i	$0.857193\pi$
$954$			4.71176e11i			0.568840i
$955$		0			0
$956$	−3.14118e10			−0.0376064
$957$	1.11119e11	−	1.11119e11i	0.132478	−	0.132478i
$958$	4.33210e11	+	4.33210e11i	0.514323	+	0.514323i
$959$			6.30909e11i			0.745920i
$960$		0			0
$961$	3.65635e11			0.428700
$962$	−2.02745e11	+	2.02745e11i	−0.236728	+	0.236728i
$963$	2.16901e11	+	2.16901e11i	0.252206	+	0.252206i
$964$			8.78034e10i			0.101672i
$965$		0			0
$966$	1.62483e11			0.186595
$967$	−1.01381e12	+	1.01381e12i	−1.15944	+	1.15944i	−0.174849	+	0.984595i	$0.555944\pi$
$967$	−1.01381e12	+	1.01381e12i	−1.15944	+	1.15944i	−0.984595	+	0.174849i	$0.944056\pi$
$968$	−4.93993e11	−	4.93993e11i	−0.562626	−	0.562626i
$969$		−	5.77975e11i		−	0.655562i
$970$		0			0
$971$	−1.08935e12			−1.22543			−0.612716	−	0.790303i	$-0.709923\pi$
$971$	−1.08935e12			−1.22543			−0.612716	+	0.790303i	$0.709923\pi$
$972$	3.89273e9	−	3.89273e9i	0.00436103	−	0.00436103i
$973$	−5.37560e11	−	5.37560e11i	−0.599758	−	0.599758i
$974$			5.98744e11i			0.665281i
$975$		0			0
$976$	4.85765e11			0.535336
$977$	8.57679e11	−	8.57679e11i	0.941340	−	0.941340i	−0.0570321	−	0.998372i	$-0.518164\pi$
$977$	8.57679e11	−	8.57679e11i	0.941340	−	0.941340i	0.998372	+	0.0570321i	$0.0181638\pi$
$978$	9.71160e10	+	9.71160e10i	0.106154	+	0.106154i
$979$			6.12698e11i			0.666984i
$980$		0			0
$981$	2.02988e11			0.219177
$982$	3.75337e11	−	3.75337e11i	0.403622	−	0.403622i
$983$	−7.84557e11	−	7.84557e11i	−0.840253	−	0.840253i	0.148638	−	0.988892i	$-0.452511\pi$
$983$	−7.84557e11	−	7.84557e11i	−0.840253	−	0.840253i	−0.988892	+	0.148638i	$0.952511\pi$
$984$		−	5.17193e11i		−	0.551661i
$985$		0			0
$986$	−7.48654e11			−0.792088
$987$	−6.90470e10	+	6.90470e10i	−0.0727573	+	0.0727573i
$988$	6.28550e10	+	6.28550e10i	0.0659648	+	0.0659648i
$989$		−	1.04856e12i		−	1.09599i
$990$		0			0
$991$	−1.18172e12			−1.22523			−0.612617	−	0.790380i	$-0.709883\pi$
$991$	−1.18172e12			−1.22523			−0.612617	+	0.790380i	$0.709883\pi$
$992$	1.56813e11	−	1.56813e11i	0.161933	−	0.161933i
$993$	−5.85431e11	−	5.85431e11i	−0.602114	−	0.602114i
$994$		−	6.84564e11i		−	0.701243i
$995$		0			0
$996$	4.01947e10			0.0408443
$997$	1.19697e12	−	1.19697e12i	1.21145	−	1.21145i	0.240894	−	0.970552i	$-0.422560\pi$
$997$	1.19697e12	−	1.19697e12i	1.21145	−	1.21145i	0.970552	−	0.240894i	$-0.0774405\pi$
$998$	8.92246e11	+	8.92246e11i	0.899420	+	0.899420i
$999$			6.32619e10i			0.0635156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.b.43.4	yes	8
5.2	odd	4	inner	75.9.f.b.7.4	yes	8
5.3	odd	4	inner	75.9.f.b.7.1	✓	8
5.4	even	2	inner	75.9.f.b.43.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.b.7.1	✓	8	5.3	odd	4	inner
75.9.f.b.7.4	yes	8	5.2	odd	4	inner
75.9.f.b.43.1	yes	8	5.4	even	2	inner
75.9.f.b.43.4	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(10.7561 - 10.7561i) q^{2} +(33.0681 + 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(-986.622 + 986.622i) q^{7} +(3018.29 + 3018.29i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(10.7561 - 10.7561i) q^{2} +(33.0681 + 33.0681i) q^{3} +24.6120i q^{4} +711.369 q^{6} +(-986.622 + 986.622i) q^{7} +(3018.29 + 3018.29i) q^{8} +2187.00i q^{9} -7119.87 q^{11} +(-813.874 + 813.874i) q^{12} +(-21548.2 - 21548.2i) q^{13} +21224.4i q^{14} +58629.6 q^{16} +(-73737.3 + 73737.3i) q^{17} +(23523.6 + 23523.6i) q^{18} +118517. i q^{19} -65251.5 q^{21} +(-76582.1 + 76582.1i) q^{22} +(-115753. - 115753. i) q^{23} +199619. i q^{24} -463549. q^{26} +(-72320.0 + 72320.0i) q^{27} +(-24282.8 - 24282.8i) q^{28} +471964. i q^{29} -1.10387e6 q^{31} +(-142057. + 142057. i) q^{32} +(-235441. - 235441. i) q^{33} +1.58625e6i q^{34} -53826.5 q^{36} +(437375. - 437375. i) q^{37} +(1.27479e6 + 1.27479e6i) q^{38} -1.42511e6i q^{39} -2.59091e6 q^{41} +(-701852. + 701852. i) q^{42} +(4.52928e6 + 4.52928e6i) q^{43} -175235. i q^{44} -2.49011e6 q^{46} +(1.05817e6 - 1.05817e6i) q^{47} +(1.93877e6 + 1.93877e6i) q^{48} +3.81795e6i q^{49} -4.87671e6 q^{51} +(530344. - 530344. i) q^{52} +(1.00150e7 + 1.00150e7i) q^{53} +1.55576e6i q^{54} -5.95583e6 q^{56} +(-3.91915e6 + 3.91915e6i) q^{57} +(5.07649e6 + 5.07649e6i) q^{58} -6.33938e6i q^{59} +8.28532e6 q^{61} +(-1.18733e7 + 1.18733e7i) q^{62} +(-2.15774e6 - 2.15774e6i) q^{63} +1.80651e7i q^{64} -5.06485e6 q^{66} +(2.32318e7 - 2.32318e7i) q^{67} +(-1.81483e6 - 1.81483e6i) q^{68} -7.65549e6i q^{69} -3.22536e7 q^{71} +(-6.60101e6 + 6.60101e6i) q^{72} +(-1.49231e7 - 1.49231e7i) q^{73} -9.40892e6i q^{74} -2.91696e6 q^{76} +(7.02462e6 - 7.02462e6i) q^{77} +(-1.53287e7 - 1.53287e7i) q^{78} +7.17598e7i q^{79} -4.78297e6 q^{81} +(-2.78681e7 + 2.78681e7i) q^{82} +(-2.46934e7 - 2.46934e7i) q^{83} -1.60597e6i q^{84} +9.74350e7 q^{86} +(-1.56069e7 + 1.56069e7i) q^{87} +(-2.14899e7 - 2.14899e7i) q^{88} -8.60547e7i q^{89} +4.25198e7 q^{91} +(2.84892e6 - 2.84892e6i) q^{92} +(-3.65028e7 - 3.65028e7i) q^{93} -2.27636e7i q^{94} -9.39513e6 q^{96} +(7.27492e7 - 7.27492e7i) q^{97} +(4.10664e7 + 4.10664e7i) q^{98} -1.55712e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1296 q^{6}+O(q^{10}) \) 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

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