LMFDB - Embedded newform 75.9.f.c.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:	8.0.151613669376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{4} + 256 $ x^8 - 7*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$1.88713 + 0.662382i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.c.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.8476 - 12.8476i) q^{2} +(33.0681 - 33.0681i) q^{3} +74.1200i q^{4} -849.690 q^{6} +(-333.082 - 333.082i) q^{7} +(-2336.72 + 2336.72i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-12.8476 - 12.8476i) q^{2} +(33.0681 - 33.0681i) q^{3} +74.1200i q^{4} -849.690 q^{6} +(-333.082 - 333.082i) q^{7} +(-2336.72 + 2336.72i) q^{8} -2187.00i q^{9} +9147.48 q^{11} +(2451.01 + 2451.01i) q^{12} +(-12379.8 + 12379.8i) q^{13} +8558.59i q^{14} +79017.0 q^{16} +(-7869.96 - 7869.96i) q^{17} +(-28097.6 + 28097.6i) q^{18} +178951. i q^{19} -22028.8 q^{21} +(-117523. - 117523. i) q^{22} +(-225841. + 225841. i) q^{23} +154542. i q^{24} +318101. q^{26} +(-72320.0 - 72320.0i) q^{27} +(24688.1 - 24688.1i) q^{28} +1.02501e6i q^{29} +392156. q^{31} +(-416977. - 416977. i) q^{32} +(302490. - 302490. i) q^{33} +202220. i q^{34} +162101. q^{36} +(-1.29445e6 - 1.29445e6i) q^{37} +(2.29909e6 - 2.29909e6i) q^{38} +818754. i q^{39} +3.20316e6 q^{41} +(283016. + 283016. i) q^{42} +(2.40065e6 - 2.40065e6i) q^{43} +678012. i q^{44} +5.80303e6 q^{46} +(4.45079e6 + 4.45079e6i) q^{47} +(2.61294e6 - 2.61294e6i) q^{48} -5.54291e6i q^{49} -520490. q^{51} +(-917592. - 917592. i) q^{52} +(4.09845e6 - 4.09845e6i) q^{53} +1.85827e6i q^{54} +1.55664e6 q^{56} +(5.91757e6 + 5.91757e6i) q^{57} +(1.31689e7 - 1.31689e7i) q^{58} +1.34059e7i q^{59} +2.38886e7 q^{61} +(-5.03825e6 - 5.03825e6i) q^{62} +(-728451. + 728451. i) q^{63} -9.51407e6i q^{64} -7.77252e6 q^{66} +(-1.67129e7 - 1.67129e7i) q^{67} +(583322. - 583322. i) q^{68} +1.49363e7i q^{69} +263343. q^{71} +(5.11040e6 + 5.11040e6i) q^{72} +(-3.04968e7 + 3.04968e7i) q^{73} +3.32611e7i q^{74} -1.32639e7 q^{76} +(-3.04686e6 - 3.04686e6i) q^{77} +(1.05190e7 - 1.05190e7i) q^{78} -3.35015e7i q^{79} -4.78297e6 q^{81} +(-4.11528e7 - 4.11528e7i) q^{82} +(-4.97990e7 + 4.97990e7i) q^{83} -1.63278e6i q^{84} -6.16850e7 q^{86} +(3.38951e7 + 3.38951e7i) q^{87} +(-2.13751e7 + 2.13751e7i) q^{88} +6.58761e7i q^{89} +8.24699e6 q^{91} +(-1.67394e7 - 1.67394e7i) q^{92} +(1.29678e7 - 1.29678e7i) q^{93} -1.14364e8i q^{94} -2.75773e7 q^{96} +(8.26311e7 + 8.26311e7i) q^{97} +(-7.12130e7 + 7.12130e7i) q^{98} -2.00055e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 1296 q^{6}+O(q^{10}) $ 8 * q + 1296 * q^6	$ 8 q + 1296 q^{6} + 107952 q^{11} + 401920 q^{16} - 953208 q^{21} + 4257936 q^{26} - 2908312 q^{31} + 3919104 q^{36} + 33914208 q^{41} + 50759328 q^{46} + 854064 q^{51} + 60954240 q^{56} + 29647000 q^{61} + 52666848 q^{66} - 28246944 q^{71} - 59323136 q^{76} - 38263752 q^{81} - 432922128 q^{86} - 517149432 q^{91} + 132129792 q^{96}+O(q^{100}) $ 8 * q + 1296 * q^6 + 107952 * q^11 + 401920 * q^16 - 953208 * q^21 + 4257936 * q^26 - 2908312 * q^31 + 3919104 * q^36 + 33914208 * q^41 + 50759328 * q^46 + 854064 * q^51 + 60954240 * q^56 + 29647000 * q^61 + 52666848 * q^66 - 28246944 * q^71 - 59323136 * q^76 - 38263752 * q^81 - 432922128 * q^86 - 517149432 * q^91 + 132129792 * 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 $

$2$	−12.8476	−	12.8476i	−0.802973	−	0.802973i	0.180586	−	0.983559i	$-0.442201\pi$
$2$	−12.8476	−	12.8476i	−0.802973	−	0.802973i	−0.983559	+	0.180586i	$0.942201\pi$
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$			74.1200i			0.289531i
$5$		0			0
$5$		0			0
$6$	−849.690			−0.655625
$7$	−333.082	−	333.082i	−0.138726	−	0.138726i	0.634333	−	0.773060i	$-0.281275\pi$
$7$	−333.082	−	333.082i	−0.138726	−	0.138726i	−0.773060	+	0.634333i	$0.781275\pi$
$8$	−2336.72	+	2336.72i	−0.570487	+	0.570487i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	9147.48			0.624785			0.312393	−	0.949953i	$-0.398870\pi$
$11$	9147.48			0.624785			0.312393	+	0.949953i	$0.398870\pi$
$12$	2451.01	+	2451.01i	0.118201	+	0.118201i
$13$	−12379.8	+	12379.8i	−0.433452	+	0.433452i	−0.889801	−	0.456349i	$-0.849157\pi$
$13$	−12379.8	+	12379.8i	−0.433452	+	0.433452i	0.456349	+	0.889801i	$0.349157\pi$
$14$			8558.59i			0.222787i
$15$		0			0
$16$	79017.0			1.20570
$17$	−7869.96	−	7869.96i	−0.0942274	−	0.0942274i	0.658422	−	0.752649i	$-0.271224\pi$
$17$	−7869.96	−	7869.96i	−0.0942274	−	0.0942274i	−0.752649	+	0.658422i	$0.771224\pi$
$18$	−28097.6	+	28097.6i	−0.267658	+	0.267658i
$19$			178951.i			1.37316i	0.727056	+	0.686578i	$0.240888\pi$
$19$			178951.i			1.37316i	−0.727056	+	0.686578i	$0.759112\pi$
$20$		0			0
$21$	−22028.8			−0.113270
$22$	−117523.	−	117523.i	−0.501686	−	0.501686i
$23$	−225841.	+	225841.i	−0.807035	+	0.807035i	−0.984184	−	0.177149i	$-0.943312\pi$
$23$	−225841.	+	225841.i	−0.807035	+	0.807035i	0.177149	+	0.984184i	$0.443312\pi$
$24$			154542.i			0.465801i
$25$		0			0
$26$	318101.			0.696100
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$	24688.1	−	24688.1i	0.0401657	−	0.0401657i
$29$			1.02501e6i			1.44923i	0.689156	+	0.724613i	$0.257981\pi$
$29$			1.02501e6i			1.44923i	−0.689156	+	0.724613i	$0.742019\pi$
$30$		0			0
$31$	392156.			0.424631			0.212316	−	0.977201i	$-0.431900\pi$
$31$	392156.			0.424631			0.212316	+	0.977201i	$0.431900\pi$
$32$	−416977.	−	416977.i	−0.397660	−	0.397660i
$33$	302490.	−	302490.i	0.255068	−	0.255068i
$34$			202220.i			0.151324i
$35$		0			0
$36$	162101.			0.0965105
$37$	−1.29445e6	−	1.29445e6i	−0.690684	−	0.690684i	0.271699	−	0.962382i	$-0.412415\pi$
$37$	−1.29445e6	−	1.29445e6i	−0.690684	−	0.690684i	−0.962382	+	0.271699i	$0.912415\pi$
$38$	2.29909e6	−	2.29909e6i	1.10261	−	1.10261i
$39$			818754.i			0.353912i
$40$		0			0
$41$	3.20316e6			1.13356			0.566778	−	0.823871i	$-0.308190\pi$
$41$	3.20316e6			1.13356			0.566778	+	0.823871i	$0.308190\pi$
$42$	283016.	+	283016.i	0.0909525	+	0.0909525i
$43$	2.40065e6	−	2.40065e6i	0.702190	−	0.702190i	−0.262690	−	0.964880i	$-0.584610\pi$
$43$	2.40065e6	−	2.40065e6i	0.702190	−	0.702190i	0.964880	+	0.262690i	$0.0846097\pi$
$44$			678012.i			0.180895i
$45$		0			0
$46$	5.80303e6			1.29605
$47$	4.45079e6	+	4.45079e6i	0.912106	+	0.912106i	0.996438	−	0.0843316i	$-0.0268755\pi$
$47$	4.45079e6	+	4.45079e6i	0.912106	+	0.912106i	−0.0843316	+	0.996438i	$0.526876\pi$
$48$	2.61294e6	−	2.61294e6i	0.492226	−	0.492226i
$49$		−	5.54291e6i		−	0.961510i
$50$		0			0
$51$	−520490.			−0.0769363
$52$	−917592.	−	917592.i	−0.125498	−	0.125498i
$53$	4.09845e6	−	4.09845e6i	0.519417	−	0.519417i	−0.397978	−	0.917395i	$-0.630288\pi$
$53$	4.09845e6	−	4.09845e6i	0.519417	−	0.519417i	0.917395	+	0.397978i	$0.130288\pi$
$54$			1.85827e6i			0.218542i
$55$		0			0
$56$	1.55664e6			0.158283
$57$	5.91757e6	+	5.91757e6i	0.560588	+	0.560588i
$58$	1.31689e7	−	1.31689e7i	1.16369	−	1.16369i
$59$			1.34059e7i			1.10634i	0.833068	+	0.553171i	$0.186582\pi$
$59$			1.34059e7i			1.10634i	−0.833068	+	0.553171i	$0.813418\pi$
$60$		0			0
$61$	2.38886e7			1.72532			0.862662	−	0.505781i	$-0.168796\pi$
$61$	2.38886e7			1.72532			0.862662	+	0.505781i	$0.168796\pi$
$62$	−5.03825e6	−	5.03825e6i	−0.340967	−	0.340967i
$63$	−728451.	+	728451.i	−0.0462421	+	0.0462421i
$64$		−	9.51407e6i		−	0.567083i
$65$		0			0
$66$	−7.77252e6			−0.409625
$67$	−1.67129e7	−	1.67129e7i	−0.829376	−	0.829376i	0.158054	−	0.987430i	$-0.449478\pi$
$67$	−1.67129e7	−	1.67129e7i	−0.829376	−	0.829376i	−0.987430	+	0.158054i	$0.949478\pi$
$68$	583322.	−	583322.i	0.0272818	−	0.0272818i
$69$			1.49363e7i			0.658941i
$70$		0			0
$71$	263343.			0.0103631			0.00518153	−	0.999987i	$-0.498351\pi$
$71$	263343.			0.0103631			0.00518153	+	0.999987i	$0.498351\pi$
$72$	5.11040e6	+	5.11040e6i	0.190162	+	0.190162i
$73$	−3.04968e7	+	3.04968e7i	−1.07390	+	1.07390i	−0.0768553	+	0.997042i	$0.524488\pi$
$73$	−3.04968e7	+	3.04968e7i	−1.07390	+	1.07390i	−0.997042	+	0.0768553i	$0.975512\pi$
$74$			3.32611e7i			1.10920i
$75$		0			0
$76$	−1.32639e7			−0.397572
$77$	−3.04686e6	−	3.04686e6i	−0.0866742	−	0.0866742i
$78$	1.05190e7	−	1.05190e7i	0.284182	−	0.284182i
$79$		−	3.35015e7i		−	0.860114i	−0.902802	−	0.430057i	$-0.858493\pi$
$79$		−	3.35015e7i		−	0.860114i	0.902802	−	0.430057i	$-0.141507\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	−4.11528e7	−	4.11528e7i	−0.910214	−	0.910214i
$83$	−4.97990e7	+	4.97990e7i	−1.04932	+	1.04932i	−0.0506010	+	0.998719i	$0.516114\pi$
$83$	−4.97990e7	+	4.97990e7i	−1.04932	+	1.04932i	−0.998719	+	0.0506010i	$0.983886\pi$
$84$		−	1.63278e6i		−	0.0327951i
$85$		0			0
$86$	−6.16850e7			−1.12768
$87$	3.38951e7	+	3.38951e7i	0.591644	+	0.591644i
$88$	−2.13751e7	+	2.13751e7i	−0.356432	+	0.356432i
$89$			6.58761e7i			1.04995i	0.851118	+	0.524974i	$0.175925\pi$
$89$			6.58761e7i			1.04995i	−0.851118	+	0.524974i	$0.824075\pi$
$90$		0			0
$91$	8.24699e6			0.120262
$92$	−1.67394e7	−	1.67394e7i	−0.233662	−	0.233662i
$93$	1.29678e7	−	1.29678e7i	0.173355	−	0.173355i
$94$		−	1.14364e8i		−	1.46479i
$95$		0			0
$96$	−2.75773e7			−0.324688
$97$	8.26311e7	+	8.26311e7i	0.933376	+	0.933376i	0.997915	−	0.0645396i	$-0.0205579\pi$
$97$	8.26311e7	+	8.26311e7i	0.933376	+	0.933376i	−0.0645396	+	0.997915i	$0.520558\pi$
$98$	−7.12130e7	+	7.12130e7i	−0.772067	+	0.772067i
$99$		−	2.00055e7i		−	0.208262i
$100$		0			0
$101$	−1.15531e6			−0.0111023			−0.00555115	−	0.999985i	$-0.501767\pi$
$101$	−1.15531e6			−0.0111023			−0.00555115	+	0.999985i	$0.501767\pi$
$102$	6.68703e6	+	6.68703e6i	0.0617778	+	0.0617778i
$103$	1.82085e7	−	1.82085e7i	0.161780	−	0.161780i	−0.621575	−	0.783355i	$-0.713507\pi$
$103$	1.82085e7	−	1.82085e7i	0.161780	−	0.161780i	0.783355	+	0.621575i	$0.213507\pi$
$104$		−	5.78562e7i		−	0.494557i
$105$		0			0
$106$	−1.05310e8			−0.834156
$107$	1.18148e8	+	1.18148e8i	0.901348	+	0.901348i	0.995553	−	0.0942049i	$-0.0300309\pi$
$107$	1.18148e8	+	1.18148e8i	0.901348	+	0.901348i	−0.0942049	+	0.995553i	$0.530031\pi$
$108$	5.36036e6	−	5.36036e6i	0.0394002	−	0.0394002i
$109$		−	1.53879e8i		−	1.09012i	−0.838398	−	0.545059i	$-0.816507\pi$
$109$		−	1.53879e8i		−	1.09012i	0.838398	−	0.545059i	$-0.183493\pi$
$110$		0			0
$111$	−8.56102e7			−0.563941
$112$	−2.63191e7	−	2.63191e7i	−0.167263	−	0.167263i
$113$	−6.96861e7	+	6.96861e7i	−0.427398	+	0.427398i	−0.887741	−	0.460343i	$-0.847726\pi$
$113$	−6.96861e7	+	6.96861e7i	−0.427398	+	0.427398i	0.460343	+	0.887741i	$0.347726\pi$
$114$		−	1.52053e8i		−	0.900275i
$115$		0			0
$116$	−7.59738e7			−0.419596
$117$	2.70747e7	+	2.70747e7i	0.144484	+	0.144484i
$118$	1.72234e8	−	1.72234e8i	0.888363	−	0.888363i
$119$			5.24269e6i			0.0261436i
$120$		0			0
$121$	−1.30682e8			−0.609643
$122$	−3.06910e8	−	3.06910e8i	−1.38539	−	1.38539i
$123$	1.05922e8	−	1.05922e8i	0.462772	−	0.462772i
$124$			2.90666e7i			0.122944i
$125$		0			0
$126$	1.87176e7			0.0742624
$127$	2.28028e8	+	2.28028e8i	0.876542	+	0.876542i	0.993175	−	0.116633i	$-0.0372103\pi$
$127$	2.28028e8	+	2.28028e8i	0.876542	+	0.876542i	−0.116633	+	0.993175i	$0.537210\pi$
$128$	−2.28979e8	+	2.28979e8i	−0.853012	+	0.853012i
$129$		−	1.58770e8i		−	0.573336i
$130$		0			0
$131$	2.11086e8			0.716760			0.358380	−	0.933576i	$-0.383329\pi$
$131$	2.11086e8			0.716760			0.358380	+	0.933576i	$0.383329\pi$
$132$	2.24206e7	+	2.24206e7i	0.0738501	+	0.0738501i
$133$	5.96054e7	−	5.96054e7i	0.190493	−	0.190493i
$134$			4.29439e8i			1.33193i
$135$		0			0
$136$	3.67797e7			0.107511
$137$	−1.65084e8	−	1.65084e8i	−0.468622	−	0.468622i	0.432846	−	0.901468i	$-0.357509\pi$
$137$	−1.65084e8	−	1.65084e8i	−0.468622	−	0.468622i	−0.901468	+	0.432846i	$0.857509\pi$
$138$	1.91895e8	−	1.91895e8i	0.529112	−	0.529112i
$139$			5.69012e8i			1.52427i	0.647418	+	0.762135i	$0.275849\pi$
$139$			5.69012e8i			1.52427i	−0.647418	+	0.762135i	$0.724151\pi$
$140$		0			0
$141$	2.94358e8			0.744732
$142$	−3.38332e6	−	3.38332e6i	−0.00832126	−	0.00832126i
$143$	−1.13244e8	+	1.13244e8i	−0.270814	+	0.270814i
$144$		−	1.72810e8i		−	0.401901i
$145$		0			0
$146$	7.83620e8			1.72462
$147$	−1.83294e8	−	1.83294e8i	−0.392535	−	0.392535i
$148$	9.59449e7	−	9.59449e7i	0.199975	−	0.199975i
$149$			7.28638e8i			1.47831i	0.673533	+	0.739157i	$0.264776\pi$
$149$			7.28638e8i			1.47831i	−0.673533	+	0.739157i	$0.735224\pi$
$150$		0			0
$151$	−3.27033e8			−0.629048			−0.314524	−	0.949250i	$-0.601845\pi$
$151$	−3.27033e8			−0.629048			−0.314524	+	0.949250i	$0.601845\pi$
$152$	−4.18158e8	−	4.18158e8i	−0.783368	−	0.783368i
$153$	−1.72116e7	+	1.72116e7i	−0.0314091	+	0.0314091i
$154$			7.82895e7i			0.139194i
$155$		0			0
$156$	−6.06861e7			−0.102469
$157$	5.90569e8	+	5.90569e8i	0.972013	+	0.972013i	0.999619	−	0.0276064i	$-0.00878849\pi$
$157$	5.90569e8	+	5.90569e8i	0.972013	+	0.972013i	−0.0276064	+	0.999619i	$0.508788\pi$
$158$	−4.30413e8	+	4.30413e8i	−0.690648	+	0.690648i
$159$		−	2.71056e8i		−	0.424102i
$160$		0			0
$161$	1.50447e8			0.223914
$162$	6.14495e7	+	6.14495e7i	0.0892192	+	0.0892192i
$163$	5.14036e8	−	5.14036e8i	0.728188	−	0.728188i	−0.242071	−	0.970259i	$-0.577827\pi$
$163$	5.14036e8	−	5.14036e8i	0.728188	−	0.728188i	0.970259	+	0.242071i	$0.0778267\pi$
$164$			2.37418e8i			0.328200i
$165$		0			0
$166$	1.27959e9			1.68515
$167$	−5.60597e8	−	5.60597e8i	−0.720750	−	0.720750i	0.248008	−	0.968758i	$-0.420224\pi$
$167$	−5.60597e8	−	5.60597e8i	−0.720750	−	0.720750i	−0.968758	+	0.248008i	$0.920224\pi$
$168$	5.14750e7	−	5.14750e7i	0.0646189	−	0.0646189i
$169$			5.09211e8i			0.624239i
$170$		0			0
$171$	3.91366e8			0.457719
$172$	1.77936e8	+	1.77936e8i	0.203306	+	0.203306i
$173$	1.11036e8	−	1.11036e8i	0.123959	−	0.123959i	−0.642406	−	0.766365i	$-0.722064\pi$
$173$	1.11036e8	−	1.11036e8i	0.123959	−	0.123959i	0.766365	+	0.642406i	$0.222064\pi$
$174$		−	8.70940e8i		−	0.950148i
$175$		0			0
$176$	7.22806e8			0.753305
$177$	4.43309e8	+	4.43309e8i	0.451662	+	0.451662i
$178$	8.46348e8	−	8.46348e8i	0.843080	−	0.843080i
$179$			9.39164e8i			0.914807i	0.889259	+	0.457403i	$0.151220\pi$
$179$			9.39164e8i			0.914807i	−0.889259	+	0.457403i	$0.848780\pi$
$180$		0			0
$181$	−1.19785e9			−1.11606			−0.558030	−	0.829821i	$-0.688443\pi$
$181$	−1.19785e9			−1.11606			−0.558030	+	0.829821i	$0.688443\pi$
$182$	−1.05954e8	−	1.05954e8i	−0.0965675	−	0.0965675i
$183$	7.89950e8	−	7.89950e8i	0.704361	−	0.704361i
$184$		−	1.05545e9i		−	0.920806i
$185$		0			0
$186$	−3.33211e8			−0.278399
$187$	−7.19903e7	−	7.19903e7i	−0.0588719	−	0.0588719i
$188$	−3.29893e8	+	3.29893e8i	−0.264083	+	0.264083i
$189$			4.81770e7i			0.0377565i
$190$		0			0
$191$	−1.70668e9			−1.28239			−0.641194	−	0.767378i	$-0.721561\pi$
$191$	−1.70668e9			−1.28239			−0.641194	+	0.767378i	$0.721561\pi$
$192$	−3.14612e8	−	3.14612e8i	−0.231511	−	0.231511i
$193$	3.08858e8	−	3.08858e8i	0.222602	−	0.222602i	−0.586991	−	0.809593i	$-0.699688\pi$
$193$	3.08858e8	−	3.08858e8i	0.222602	−	0.222602i	0.809593	+	0.586991i	$0.199688\pi$
$194$		−	2.12322e9i		−	1.49895i
$195$		0			0
$196$	4.10841e8			0.278387
$197$	6.41714e8	+	6.41714e8i	0.426065	+	0.426065i	0.887286	−	0.461220i	$-0.152588\pi$
$197$	6.41714e8	+	6.41714e8i	0.426065	+	0.426065i	−0.461220	+	0.887286i	$0.652588\pi$
$198$	−2.57023e8	+	2.57023e8i	−0.167229	+	0.167229i
$199$		−	5.59952e8i		−	0.357058i	−0.983935	−	0.178529i	$-0.942866\pi$
$199$		−	5.59952e8i		−	0.357058i	0.983935	−	0.178529i	$-0.0571338\pi$
$200$		0			0
$201$	−1.10533e9			−0.677183
$202$	1.48429e7	+	1.48429e7i	0.00891485	+	0.00891485i
$203$	3.41412e8	−	3.41412e8i	0.201046	−	0.201046i
$204$		−	3.85787e7i		−	0.0222755i
$205$		0			0
$206$	−4.67870e8			−0.259810
$207$	4.93915e8	+	4.93915e8i	0.269012	+	0.269012i
$208$	−9.78215e8	+	9.78215e8i	−0.522614	+	0.522614i
$209$			1.63695e9i			0.857927i
$210$		0			0
$211$	−2.69992e9			−1.36214			−0.681068	−	0.732220i	$-0.738484\pi$
$211$	−2.69992e9			−1.36214			−0.681068	+	0.732220i	$0.738484\pi$
$212$	3.03777e8	+	3.03777e8i	0.150388	+	0.150388i
$213$	8.70826e6	−	8.70826e6i	0.00423070	−	0.00423070i
$214$		−	3.03584e9i		−	1.44752i
$215$		0			0
$216$	3.37982e8			0.155267
$217$	−1.30620e8	−	1.30620e8i	−0.0589075	−	0.0589075i
$218$	−1.97697e9	+	1.97697e9i	−0.875335	+	0.875335i
$219$			2.01694e9i			0.876834i
$220$		0			0
$221$	1.94857e8			0.0816860
$222$	1.09988e9	+	1.09988e9i	0.452829	+	0.452829i
$223$	−3.27835e9	+	3.27835e9i	−1.32567	+	1.32567i	−0.416564	+	0.909107i	$0.636766\pi$
$223$	−3.27835e9	+	3.27835e9i	−1.32567	+	1.32567i	−0.909107	+	0.416564i	$0.863234\pi$
$224$			2.77775e8i			0.110332i
$225$		0			0
$226$	1.79059e9			0.686378
$227$	2.34941e8	+	2.34941e8i	0.0884820	+	0.0884820i	0.749962	−	0.661480i	$-0.230072\pi$
$227$	2.34941e8	+	2.34941e8i	0.0884820	+	0.0884820i	−0.661480	+	0.749962i	$0.730072\pi$
$228$	−4.38611e8	+	4.38611e8i	−0.162308	+	0.162308i
$229$		−	1.85932e9i		−	0.676101i	−0.941128	−	0.338051i	$-0.890232\pi$
$229$		−	1.85932e9i		−	0.676101i	0.941128	−	0.338051i	$-0.109768\pi$
$230$		0			0
$231$	−2.01508e8			−0.0707692
$232$	−2.39516e9	−	2.39516e9i	−0.826764	−	0.826764i
$233$	−9.60879e8	+	9.60879e8i	−0.326021	+	0.326021i	−0.851071	−	0.525050i	$-0.824046\pi$
$233$	−9.60879e8	+	9.60879e8i	−0.326021	+	0.326021i	0.525050	+	0.851071i	$0.324046\pi$
$234$		−	6.95687e8i		−	0.232033i
$235$		0			0
$236$	−9.93649e8			−0.320321
$237$	−1.10783e9	−	1.10783e9i	−0.351140	−	0.351140i
$238$	6.73558e7	−	6.73558e7i	0.0209926	−	0.0209926i
$239$			2.40669e9i			0.737613i	0.929506	+	0.368807i	$0.120234\pi$
$239$			2.40669e9i			0.737613i	−0.929506	+	0.368807i	$0.879766\pi$
$240$		0			0
$241$	7.47993e8			0.221733			0.110866	−	0.993835i	$-0.464637\pi$
$241$	7.47993e8			0.221733			0.110866	+	0.993835i	$0.464637\pi$
$242$	1.67895e9	+	1.67895e9i	0.489527	+	0.489527i
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$			1.77062e9i			0.499535i
$245$		0			0
$246$	−2.72169e9			−0.743187
$247$	−2.21538e9	−	2.21538e9i	−0.595197	−	0.595197i
$248$	−9.16356e8	+	9.16356e8i	−0.242247	+	0.242247i
$249$			3.29352e9i			0.856766i
$250$		0			0
$251$	−3.38810e9			−0.853615			−0.426807	−	0.904343i	$-0.640362\pi$
$251$	−3.38810e9			−0.853615			−0.426807	+	0.904343i	$0.640362\pi$
$252$	−5.39928e7	−	5.39928e7i	−0.0133886	−	0.0133886i
$253$	−2.06588e9	+	2.06588e9i	−0.504223	+	0.504223i
$254$		−	5.85920e9i		−	1.40768i
$255$		0			0
$256$	3.44804e9			0.802809
$257$	2.56381e9	+	2.56381e9i	0.587697	+	0.587697i	0.937007	−	0.349310i	$-0.113584\pi$
$257$	2.56381e9	+	2.56381e9i	0.587697	+	0.587697i	−0.349310	+	0.937007i	$0.613584\pi$
$258$	−2.03981e9	+	2.03981e9i	−0.460373	+	0.460373i
$259$			8.62318e8i			0.191632i
$260$		0			0
$261$	2.24170e9			0.483075
$262$	−2.71194e9	−	2.71194e9i	−0.575539	−	0.575539i
$263$	6.04705e9	−	6.04705e9i	1.26392	−	1.26392i	0.314746	−	0.949176i	$-0.398081\pi$
$263$	6.04705e9	−	6.04705e9i	1.26392	−	1.26392i	0.949176	−	0.314746i	$-0.101919\pi$
$264$			1.41367e9i			0.291025i
$265$		0			0
$266$	−1.53157e9			−0.305921
$267$	2.17840e9	+	2.17840e9i	0.428640	+	0.428640i
$268$	1.23876e9	−	1.23876e9i	0.240130	−	0.240130i
$269$		−	1.61487e9i		−	0.308410i	−0.988039	−	0.154205i	$-0.950718\pi$
$269$		−	1.61487e9i		−	0.308410i	0.988039	−	0.154205i	$-0.0492817\pi$
$270$		0			0
$271$	1.86096e8			0.0345032			0.0172516	−	0.999851i	$-0.494508\pi$
$271$	1.86096e8			0.0345032			0.0172516	+	0.999851i	$0.494508\pi$
$272$	−6.21860e8	−	6.21860e8i	−0.113610	−	0.113610i
$273$	2.72712e8	−	2.72712e8i	0.0490969	−	0.0490969i
$274$			4.24185e9i			0.752581i
$275$		0			0
$276$	−1.10708e9			−0.190784
$277$	4.05703e9	+	4.05703e9i	0.689111	+	0.689111i	0.962036	−	0.272924i	$-0.0879908\pi$
$277$	4.05703e9	+	4.05703e9i	0.689111	+	0.689111i	−0.272924	+	0.962036i	$0.587991\pi$
$278$	7.31042e9	−	7.31042e9i	1.22395	−	1.22395i
$279$		−	8.57645e8i		−	0.141544i
$280$		0			0
$281$	2.02195e9			0.324298			0.162149	−	0.986766i	$-0.448157\pi$
$281$	2.02195e9			0.324298			0.162149	+	0.986766i	$0.448157\pi$
$282$	−3.78179e9	−	3.78179e9i	−0.597999	−	0.597999i
$283$	1.77537e9	−	1.77537e9i	0.276786	−	0.276786i	−0.555039	−	0.831825i	$-0.687297\pi$
$283$	1.77537e9	−	1.77537e9i	0.276786	−	0.276786i	0.831825	+	0.555039i	$0.187297\pi$
$284$			1.95190e7i			0.00300043i
$285$		0			0
$286$	2.90982e9			0.434913
$287$	−1.06691e9	−	1.06691e9i	−0.157254	−	0.157254i
$288$	−9.11928e8	+	9.11928e8i	−0.132553	+	0.132553i
$289$		−	6.85188e9i		−	0.982242i
$290$		0			0
$291$	5.46491e9			0.762098
$292$	−2.26042e9	−	2.26042e9i	−0.310927	−	0.310927i
$293$	8.41639e9	−	8.41639e9i	1.14197	−	1.14197i	0.153882	−	0.988089i	$-0.450822\pi$
$293$	8.41639e9	−	8.41639e9i	1.14197	−	1.14197i	0.988089	−	0.153882i	$-0.0491776\pi$
$294$			4.70976e9i			0.630390i
$295$		0			0
$296$	6.04954e9			0.788053
$297$	−6.61545e8	−	6.61545e8i	−0.0850225	−	0.0850225i
$298$	9.36122e9	−	9.36122e9i	1.18705	−	1.18705i
$299$		−	5.59175e9i		−	0.699621i
$300$		0			0
$301$	−1.59923e9			−0.194825
$302$	4.20158e9	+	4.20158e9i	0.505108	+	0.505108i
$303$	−3.82039e7	+	3.82039e7i	−0.00453250	+	0.00453250i
$304$			1.41402e10i			1.65562i
$305$		0			0
$306$	4.42255e8			0.0504413
$307$	6.86322e9	+	6.86322e9i	0.772635	+	0.772635i	0.978566	−	0.205932i	$-0.0660224\pi$
$307$	6.86322e9	+	6.86322e9i	0.772635	+	0.772635i	−0.205932	+	0.978566i	$0.566022\pi$
$308$	2.25834e8	−	2.25834e8i	0.0250949	−	0.0250949i
$309$		−	1.20424e9i		−	0.132093i
$310$		0			0
$311$	1.22090e10			1.30508			0.652540	−	0.757754i	$-0.273703\pi$
$311$	1.22090e10			1.30508			0.652540	+	0.757754i	$0.273703\pi$
$312$	−1.91320e9	−	1.91320e9i	−0.201902	−	0.201902i
$313$	−8.97892e9	+	8.97892e9i	−0.935507	+	0.935507i	−0.998043	−	0.0625360i	$-0.980081\pi$
$313$	−8.97892e9	+	8.97892e9i	−0.935507	+	0.935507i	0.0625360	+	0.998043i	$0.480081\pi$
$314$		−	1.51747e10i		−	1.56100i
$315$		0			0
$316$	2.48313e9			0.249030
$317$	2.41244e9	+	2.41244e9i	0.238901	+	0.238901i	0.816395	−	0.577494i	$-0.195969\pi$
$317$	2.41244e9	+	2.41244e9i	0.238901	+	0.238901i	−0.577494	+	0.816395i	$0.695969\pi$
$318$	−3.48241e9	+	3.48241e9i	−0.340543	+	0.340543i
$319$			9.37626e9i			0.905455i
$320$		0			0
$321$	7.81388e9			0.735948
$322$	−1.93288e9	−	1.93288e9i	−0.179797	−	0.179797i
$323$	1.40834e9	−	1.40834e9i	0.129389	−	0.129389i
$324$		−	3.54514e8i		−	0.0321702i
$325$		0			0
$326$	−1.32082e10			−1.16943
$327$	−5.08849e9	−	5.08849e9i	−0.445039	−	0.445039i
$328$	−7.48486e9	+	7.48486e9i	−0.646679	+	0.646679i
$329$		−	2.96495e9i		−	0.253066i
$330$		0			0
$331$	−1.31501e9			−0.109552			−0.0547758	−	0.998499i	$-0.517444\pi$
$331$	−1.31501e9			−0.109552			−0.0547758	+	0.998499i	$0.517444\pi$
$332$	−3.69110e9	−	3.69110e9i	−0.303811	−	0.303811i
$333$	−2.83097e9	+	2.83097e9i	−0.230228	+	0.230228i
$334$			1.44046e10i			1.15749i
$335$		0			0
$336$	−1.74065e9			−0.136570
$337$	2.89442e9	+	2.89442e9i	0.224410	+	0.224410i	0.810352	−	0.585943i	$-0.199276\pi$
$337$	2.89442e9	+	2.89442e9i	0.224410	+	0.224410i	−0.585943	+	0.810352i	$0.699276\pi$
$338$	6.54213e9	−	6.54213e9i	0.501247	−	0.501247i
$339$			4.60878e9i			0.348969i
$340$		0			0
$341$	3.58724e9			0.265303
$342$	−5.02810e9	−	5.02810e9i	−0.367536	−	0.367536i
$343$	−3.76640e9	+	3.76640e9i	−0.272113	+	0.272113i
$344$			1.12193e10i			0.801181i
$345$		0			0
$346$	−2.85308e9			−0.199072
$347$	−8.24434e9	−	8.24434e9i	−0.568641	−	0.568641i	0.363107	−	0.931748i	$-0.381716\pi$
$347$	−8.24434e9	−	8.24434e9i	−0.568641	−	0.568641i	−0.931748	+	0.363107i	$0.881716\pi$
$348$	−2.51231e9	+	2.51231e9i	−0.171299	+	0.171299i
$349$			1.52787e10i			1.02987i	0.857228	+	0.514937i	$0.172185\pi$
$349$			1.52787e10i			1.02987i	−0.857228	+	0.514937i	$0.827815\pi$
$350$		0			0
$351$	1.79062e9			0.117971
$352$	−3.81429e9	−	3.81429e9i	−0.248452	−	0.248452i
$353$	−1.34106e10	+	1.34106e10i	−0.863675	+	0.863675i	−0.991763	−	0.128088i	$-0.959116\pi$
$353$	−1.34106e10	+	1.34106e10i	−0.863675	+	0.863675i	0.128088	+	0.991763i	$0.459116\pi$
$354$		−	1.13909e10i		−	0.725345i
$355$		0			0
$356$	−4.88274e9			−0.303993
$357$	1.73366e8	+	1.73366e8i	0.0106731	+	0.0106731i
$358$	1.20660e10	−	1.20660e10i	0.734565	−	0.734565i
$359$		−	1.41350e10i		−	0.850976i	−0.904964	−	0.425488i	$-0.860102\pi$
$359$		−	1.41350e10i		−	0.850976i	0.904964	−	0.425488i	$-0.139898\pi$
$360$		0			0
$361$	−1.50399e10			−0.885556
$362$	1.53894e10	+	1.53894e10i	0.896166	+	0.896166i
$363$	−4.32142e9	+	4.32142e9i	−0.248886	+	0.248886i
$364$			6.11267e8i			0.0348197i
$365$		0			0
$366$	−2.02979e10			−1.13117
$367$	−5.17117e9	−	5.17117e9i	−0.285052	−	0.285052i	0.550068	−	0.835120i	$-0.314602\pi$
$367$	−5.17117e9	−	5.17117e9i	−0.285052	−	0.285052i	−0.835120	+	0.550068i	$0.814602\pi$
$368$	−1.78453e10	+	1.78453e10i	−0.973044	+	0.973044i
$369$		−	7.00530e9i		−	0.377852i
$370$		0			0
$371$	−2.73024e9			−0.144114
$372$	9.61178e8	+	9.61178e8i	0.0501917	+	0.0501917i
$373$	−1.24174e10	+	1.24174e10i	−0.641496	+	0.641496i	−0.950923	−	0.309427i	$-0.899863\pi$
$373$	−1.24174e10	+	1.24174e10i	−0.641496	+	0.641496i	0.309427	+	0.950923i	$0.399863\pi$
$374$			1.84980e9i			0.0945450i
$375$		0			0
$376$	−2.08004e10			−1.04069
$377$	−1.26894e10	−	1.26894e10i	−0.628169	−	0.628169i
$378$	6.18957e8	−	6.18957e8i	0.0303175	−	0.0303175i
$379$		−	2.85775e10i		−	1.38506i	−0.721390	−	0.692529i	$-0.756496\pi$
$379$		−	2.85775e10i		−	1.38506i	0.721390	−	0.692529i	$-0.243504\pi$
$380$		0			0
$381$	1.50809e10			0.715693
$382$	2.19267e10	+	2.19267e10i	1.02972	+	1.02972i
$383$	1.26480e10	−	1.26480e10i	0.587795	−	0.587795i	−0.349238	−	0.937034i	$-0.613560\pi$
$383$	1.26480e10	−	1.26480e10i	0.587795	−	0.587795i	0.937034	+	0.349238i	$0.113560\pi$
$384$			1.51438e10i			0.696481i
$385$		0			0
$386$	−7.93614e9			−0.357487
$387$	−5.25022e9	−	5.25022e9i	−0.234063	−	0.234063i
$388$	−6.12462e9	+	6.12462e9i	−0.270242	+	0.270242i
$389$		−	2.90672e10i		−	1.26942i	−0.772751	−	0.634709i	$-0.781120\pi$
$389$		−	2.90672e10i		−	1.26942i	0.772751	−	0.634709i	$-0.218880\pi$
$390$		0			0
$391$	3.55473e9			0.152089
$392$	1.29522e10	+	1.29522e10i	0.548529	+	0.548529i
$393$	6.98021e9	−	6.98021e9i	0.292616	−	0.292616i
$394$		−	1.64889e10i		−	0.684238i
$395$		0			0
$396$	1.48281e9			0.0602983
$397$	−4.58091e9	−	4.58091e9i	−0.184412	−	0.184412i	0.608863	−	0.793275i	$-0.291626\pi$
$397$	−4.58091e9	−	4.58091e9i	−0.184412	−	0.184412i	−0.793275	+	0.608863i	$0.791626\pi$
$398$	−7.19403e9	+	7.19403e9i	−0.286708	+	0.286708i
$399$		−	3.94207e9i		−	0.155537i
$400$		0			0
$401$	−2.56775e10			−0.993060			−0.496530	−	0.868020i	$-0.665393\pi$
$401$	−2.56775e10			−0.993060			−0.496530	+	0.868020i	$0.665393\pi$
$402$	1.42007e10	+	1.42007e10i	0.543760	+	0.543760i
$403$	−4.85481e9	+	4.85481e9i	−0.184057	+	0.184057i
$404$		−	8.56316e7i		−	0.00321447i
$405$		0			0
$406$	−8.77264e9			−0.322869
$407$	−1.18410e10	−	1.18410e10i	−0.431529	−	0.431529i
$408$	1.21624e9	−	1.21624e9i	0.0438912	−	0.0438912i
$409$		−	5.15362e10i		−	1.84170i	−0.389916	−	0.920850i	$-0.627496\pi$
$409$		−	5.15362e10i		−	1.84170i	0.389916	−	0.920850i	$-0.372504\pi$
$410$		0			0
$411$	−1.09180e10			−0.382628
$412$	1.34961e9	+	1.34961e9i	0.0468404	+	0.0468404i
$413$	4.46528e9	−	4.46528e9i	0.153479	−	0.153479i
$414$		−	1.26912e10i		−	0.432018i
$415$		0			0
$416$	1.03242e10			0.344733
$417$	1.88162e10	+	1.88162e10i	0.622281	+	0.622281i
$418$	2.10308e10	−	2.10308e10i	0.688893	−	0.688893i
$419$			5.16799e10i			1.67674i	0.545102	+	0.838370i	$0.316491\pi$
$419$			5.16799e10i			1.67674i	−0.545102	+	0.838370i	$0.683509\pi$
$420$		0			0
$421$	2.90468e10			0.924633			0.462316	−	0.886715i	$-0.347018\pi$
$421$	2.90468e10			0.924633			0.462316	+	0.886715i	$0.347018\pi$
$422$	3.46874e10	+	3.46874e10i	1.09376	+	1.09376i
$423$	9.73387e9	−	9.73387e9i	0.304035	−	0.304035i
$424$			1.91538e10i			0.592641i
$425$		0			0
$426$	−2.23760e8			−0.00679428
$427$	−7.95685e9	−	7.95685e9i	−0.239348	−	0.239348i
$428$	−8.75716e9	+	8.75716e9i	−0.260969	+	0.260969i
$429$			7.48954e9i			0.221119i
$430$		0			0
$431$	−3.38176e9			−0.0980018			−0.0490009	−	0.998799i	$-0.515604\pi$
$431$	−3.38176e9			−0.0980018			−0.0490009	+	0.998799i	$0.515604\pi$
$432$	−5.71450e9	−	5.71450e9i	−0.164075	−	0.164075i
$433$	4.76643e9	−	4.76643e9i	0.135594	−	0.135594i	−0.636052	−	0.771646i	$-0.719434\pi$
$433$	4.76643e9	−	4.76643e9i	0.135594	−	0.135594i	0.771646	+	0.636052i	$0.219434\pi$
$434$			3.35630e9i			0.0946023i
$435$		0			0
$436$	1.14055e10			0.315623
$437$	−4.04145e10	−	4.04145e10i	−1.10818	−	1.10818i
$438$	2.59128e10	−	2.59128e10i	0.704074	−	0.704074i
$439$		−	3.12405e10i		−	0.841125i	−0.907264	−	0.420562i	$-0.861833\pi$
$439$		−	3.12405e10i		−	0.841125i	0.907264	−	0.420562i	$-0.138167\pi$
$440$		0			0
$441$	−1.21224e10			−0.320503
$442$	−2.50344e9	−	2.50344e9i	−0.0655917	−	0.0655917i
$443$	−1.38928e10	+	1.38928e10i	−0.360725	+	0.360725i	−0.864080	−	0.503355i	$-0.832099\pi$
$443$	−1.38928e10	+	1.38928e10i	−0.360725	+	0.360725i	0.503355	+	0.864080i	$0.332099\pi$
$444$		−	6.34543e9i		−	0.163279i
$445$		0			0
$446$	8.42376e10			2.12895
$447$	2.40947e10	+	2.40947e10i	0.603519	+	0.603519i
$448$	−3.16897e9	+	3.16897e9i	−0.0786693	+	0.0786693i
$449$			7.46158e10i			1.83588i	0.396715	+	0.917942i	$0.370150\pi$
$449$			7.46158e10i			1.83588i	−0.396715	+	0.917942i	$0.629850\pi$
$450$		0			0
$451$	2.93008e10			0.708229
$452$	−5.16514e9	−	5.16514e9i	−0.123745	−	0.123745i
$453$	−1.08144e10	+	1.08144e10i	−0.256808	+	0.256808i
$454$		−	6.03684e9i		−	0.142097i
$455$		0			0
$456$	−2.76554e10			−0.639617
$457$	−3.35344e10	−	3.35344e10i	−0.768822	−	0.768822i	0.209077	−	0.977899i	$-0.432954\pi$
$457$	−3.35344e10	−	3.35344e10i	−0.768822	−	0.768822i	−0.977899	+	0.209077i	$0.932954\pi$
$458$	−2.38877e10	+	2.38877e10i	−0.542891	+	0.542891i
$459$			1.13831e9i			0.0256454i
$460$		0			0
$461$	−8.49468e10			−1.88080			−0.940401	−	0.340067i	$-0.889550\pi$
$461$	−8.49468e10			−1.88080			−0.940401	+	0.340067i	$0.889550\pi$
$462$	2.58889e9	+	2.58889e9i	0.0568258	+	0.0568258i
$463$	2.48427e10	−	2.48427e10i	0.540598	−	0.540598i	−0.383106	−	0.923704i	$-0.625146\pi$
$463$	2.48427e10	−	2.48427e10i	0.540598	−	0.540598i	0.923704	+	0.383106i	$0.125146\pi$
$464$			8.09931e10i			1.74734i
$465$		0			0
$466$	2.46899e10			0.523572
$467$	−3.37883e10	−	3.37883e10i	−0.710393	−	0.710393i	0.256224	−	0.966617i	$-0.417521\pi$
$467$	−3.37883e10	−	3.37883e10i	−0.710393	−	0.710393i	−0.966617	+	0.256224i	$0.917521\pi$
$468$	−2.00677e9	+	2.00677e9i	−0.0418326	+	0.0418326i
$469$			1.11335e10i			0.230113i
$470$		0			0
$471$	3.90580e10			0.793645
$472$	−3.13259e10	−	3.13259e10i	−0.631154	−	0.631154i
$473$	2.19599e10	−	2.19599e10i	0.438718	−	0.438718i
$474$			2.84659e10i			0.563912i
$475$		0			0
$476$	−3.88588e8			−0.00756941
$477$	−8.96331e9	−	8.96331e9i	−0.173139	−	0.173139i
$478$	3.09201e10	−	3.09201e10i	0.592283	−	0.592283i
$479$			9.81566e9i			0.186456i	0.995645	+	0.0932282i	$0.0297186\pi$
$479$			9.81566e9i			0.186456i	−0.995645	+	0.0932282i	$0.970281\pi$
$480$		0			0
$481$	3.20502e10			0.598756
$482$	−9.60989e9	−	9.60989e9i	−0.178045	−	0.178045i
$483$	4.97501e9	−	4.97501e9i	0.0914125	−	0.0914125i
$484$		−	9.68619e9i		−	0.176511i
$485$		0			0
$486$	4.06404e9			0.0728472
$487$	−3.83213e9	−	3.83213e9i	−0.0681279	−	0.0681279i	0.672222	−	0.740350i	$-0.265340\pi$
$487$	−3.83213e9	−	3.83213e9i	−0.0681279	−	0.0681279i	−0.740350	+	0.672222i	$0.765340\pi$
$488$	−5.58208e10	+	5.58208e10i	−0.984275	+	0.984275i
$489$		−	3.39964e10i		−	0.594563i
$490$		0			0
$491$	1.03138e11			1.77457			0.887287	−	0.461218i	$-0.152587\pi$
$491$	1.03138e11			1.77457			0.887287	+	0.461218i	$0.152587\pi$
$492$	7.85097e9	+	7.85097e9i	0.133987	+	0.133987i
$493$	8.06679e9	−	8.06679e9i	0.136557	−	0.136557i
$494$			5.69245e10i			0.955854i
$495$		0			0
$496$	3.09869e10			0.511979
$497$	−8.77148e7	−	8.77148e7i	−0.00143763	−	0.00143763i
$498$	4.23137e10	−	4.23137e10i	0.687960	−	0.687960i
$499$			4.57149e10i			0.737320i	0.929564	+	0.368660i	$0.120183\pi$
$499$			4.57149e10i			0.737320i	−0.929564	+	0.368660i	$0.879817\pi$
$500$		0			0
$501$	−3.70758e10			−0.588490
$502$	4.35289e10	+	4.35289e10i	0.685430	+	0.685430i
$503$	4.38110e9	−	4.38110e9i	0.0684402	−	0.0684402i	−0.672058	−	0.740498i	$-0.734590\pi$
$503$	4.38110e9	−	4.38110e9i	0.0684402	−	0.0684402i	0.740498	+	0.672058i	$0.234590\pi$
$504$		−	3.40436e9i		−	0.0527611i
$505$		0			0
$506$	5.30831e10			0.809756
$507$	1.68387e10	+	1.68387e10i	0.254845	+	0.254845i
$508$	−1.69014e10	+	1.69014e10i	−0.253786	+	0.253786i
$509$		−	4.42948e10i		−	0.659906i	−0.943997	−	0.329953i	$-0.892967\pi$
$509$		−	4.42948e10i		−	0.659906i	0.943997	−	0.329953i	$-0.107033\pi$
$510$		0			0
$511$	2.03159e10			0.297956
$512$	1.43196e10	+	1.43196e10i	0.208378	+	0.208378i
$513$	1.29417e10	−	1.29417e10i	0.186863	−	0.186863i
$514$		−	6.58775e10i		−	0.943809i
$515$		0			0
$516$	1.17680e10			0.165999
$517$	4.07135e10	+	4.07135e10i	0.569870	+	0.569870i
$518$	1.10787e10	−	1.10787e10i	0.153875	−	0.153875i
$519$		−	7.34349e9i		−	0.101212i
$520$		0			0
$521$	−3.25192e10			−0.441356			−0.220678	−	0.975347i	$-0.570827\pi$
$521$	−3.25192e10			−0.441356			−0.220678	+	0.975347i	$0.570827\pi$
$522$	−2.88003e10	−	2.88003e10i	−0.387896	−	0.387896i
$523$	4.21601e10	−	4.21601e10i	0.563502	−	0.563502i	−0.366799	−	0.930300i	$-0.619546\pi$
$523$	4.21601e10	−	4.21601e10i	0.563502	−	0.563502i	0.930300	+	0.366799i	$0.119546\pi$
$524$			1.56457e10i			0.207524i
$525$		0			0
$526$	−1.55380e11			−2.02979
$527$	−3.08625e9	−	3.08625e9i	−0.0400119	−	0.0400119i
$528$	2.39018e10	−	2.39018e10i	0.307536	−	0.307536i
$529$		−	2.36977e10i		−	0.302610i
$530$		0			0
$531$	2.93188e10			0.368781
$532$	4.41795e9	+	4.41795e9i	0.0551537	+	0.0551537i
$533$	−3.96545e10	+	3.96545e10i	−0.491341	+	0.491341i
$534$		−	5.59743e10i		−	0.688372i
$535$		0			0
$536$	7.81064e10			0.946297
$537$	3.10564e10	+	3.10564e10i	0.373468	+	0.373468i
$538$	−2.07472e10	+	2.07472e10i	−0.247645	+	0.247645i
$539$		−	5.07037e10i		−	0.600737i
$540$		0			0
$541$	−1.13586e11			−1.32598			−0.662991	−	0.748628i	$-0.730713\pi$
$541$	−1.13586e11			−1.32598			−0.662991	+	0.748628i	$0.730713\pi$
$542$	−2.39088e9	−	2.39088e9i	−0.0277051	−	0.0277051i
$543$	−3.96106e10	+	3.96106e10i	−0.455629	+	0.455629i
$544$			6.56318e9i			0.0749409i
$545$		0			0
$546$	−7.00738e9			−0.0788470
$547$	9.36616e10	+	9.36616e10i	1.04619	+	1.04619i	0.998880	+	0.0473143i	$0.0150662\pi$
$547$	9.36616e10	+	9.36616e10i	1.04619	+	1.04619i	0.0473143	+	0.998880i	$0.484934\pi$
$548$	1.22360e10	−	1.22360e10i	0.135681	−	0.135681i
$549$		−	5.22443e10i		−	0.575108i
$550$		0			0
$551$	−1.83427e11			−1.99001
$552$	−3.49019e10	−	3.49019e10i	−0.375917	−	0.375917i
$553$	−1.11588e10	+	1.11588e10i	−0.119321	+	0.119321i
$554$		−	1.04246e11i		−	1.10668i
$555$		0			0
$556$	−4.21752e10			−0.441324
$557$	3.10922e9	+	3.10922e9i	0.0323021	+	0.0323021i	0.723073	−	0.690771i	$-0.242729\pi$
$557$	3.10922e9	+	3.10922e9i	0.0323021	+	0.0323021i	−0.690771	+	0.723073i	$0.742729\pi$
$558$	−1.10186e10	+	1.10186e10i	−0.113656	+	0.113656i
$559$			5.94392e10i			0.608731i
$560$		0			0
$561$	−4.76117e9			−0.0480687
$562$	−2.59771e10	−	2.59771e10i	−0.260402	−	0.260402i
$563$	7.58588e10	−	7.58588e10i	0.755044	−	0.755044i	−0.220372	−	0.975416i	$-0.570727\pi$
$563$	7.58588e10	−	7.58588e10i	0.755044	−	0.755044i	0.975416	+	0.220372i	$0.0707271\pi$
$564$			2.18178e10i			0.215623i
$565$		0			0
$566$	−4.56184e10			−0.444503
$567$	1.59312e9	+	1.59312e9i	0.0154140	+	0.0154140i
$568$	−6.15358e8	+	6.15358e8i	−0.00591200	+	0.00591200i
$569$		−	9.33092e10i		−	0.890175i	−0.895487	−	0.445087i	$-0.853173\pi$
$569$		−	9.33092e10i		−	0.890175i	0.895487	−	0.445087i	$-0.146827\pi$
$570$		0			0
$571$	1.94129e11			1.82619			0.913096	−	0.407744i	$-0.133684\pi$
$571$	1.94129e11			1.82619			0.913096	+	0.407744i	$0.133684\pi$
$572$	−8.39366e9	−	8.39366e9i	−0.0784092	−	0.0784092i
$573$	−5.64368e10	+	5.64368e10i	−0.523533	+	0.523533i
$574$			2.74145e10i			0.252541i
$575$		0			0
$576$	−2.08073e10			−0.189028
$577$	7.27282e10	+	7.27282e10i	0.656145	+	0.656145i	0.954466	−	0.298321i	$-0.0964266\pi$
$577$	7.27282e10	+	7.27282e10i	0.656145	+	0.656145i	−0.298321	+	0.954466i	$0.596427\pi$
$578$	−8.80301e10	+	8.80301e10i	−0.788714	+	0.788714i
$579$		−	2.04267e10i		−	0.181754i
$580$		0			0
$581$	3.31743e10			0.291137
$582$	−7.02108e10	−	7.02108e10i	−0.611944	−	0.611944i
$583$	3.74905e10	−	3.74905e10i	0.324524	−	0.324524i
$584$		−	1.42525e11i		−	1.22529i
$585$		0			0
$586$	−2.16260e11			−1.83394
$587$	−4.26547e10	−	4.26547e10i	−0.359265	−	0.359265i	0.504277	−	0.863542i	$-0.331759\pi$
$587$	−4.26547e10	−	4.26547e10i	−0.359265	−	0.359265i	−0.863542	+	0.504277i	$0.831759\pi$
$588$	1.35857e10	−	1.35857e10i	0.113651	−	0.113651i
$589$			7.01767e10i			0.583085i
$590$		0			0
$591$	4.24405e10			0.347881
$592$	−1.02284e11	−	1.02284e11i	−0.832760	−	0.832760i
$593$	−1.30080e11	+	1.30080e11i	−1.05194	+	1.05194i	−0.0533661	+	0.998575i	$0.516995\pi$
$593$	−1.30080e11	+	1.30080e11i	−1.05194	+	1.05194i	−0.998575	+	0.0533661i	$0.983005\pi$
$594$			1.69985e10i			0.136542i
$595$		0			0
$596$	−5.40067e10			−0.428018
$597$	−1.85166e10	−	1.85166e10i	−0.145768	−	0.145768i
$598$	−7.18404e10	+	7.18404e10i	−0.561777	+	0.561777i
$599$			2.34286e11i			1.81986i	0.414758	+	0.909932i	$0.363866\pi$
$599$			2.34286e11i			1.81986i	−0.414758	+	0.909932i	$0.636134\pi$
$600$		0			0
$601$	−1.22178e11			−0.936475			−0.468237	−	0.883603i	$-0.655111\pi$
$601$	−1.22178e11			−0.936475			−0.468237	+	0.883603i	$0.655111\pi$
$602$	2.05462e10	+	2.05462e10i	0.156439	+	0.156439i
$603$	−3.65510e10	+	3.65510e10i	−0.276459	+	0.276459i
$604$		−	2.42397e10i		−	0.182129i
$605$		0			0
$606$	9.81655e8			0.00727894
$607$	1.18161e11	+	1.18161e11i	0.870404	+	0.870404i	0.992516	−	0.122112i	$-0.0389667\pi$
$607$	1.18161e11	+	1.18161e11i	0.870404	+	0.870404i	−0.122112	+	0.992516i	$0.538967\pi$
$608$	7.46184e10	−	7.46184e10i	0.546049	−	0.546049i
$609$		−	2.25797e10i		−	0.164153i
$610$		0			0
$611$	−1.10200e11			−0.790708
$612$	−1.27573e9	−	1.27573e9i	−0.00909393	−	0.00909393i
$613$	−1.40772e11	+	1.40772e11i	−0.996955	+	0.996955i	−0.999995	−	0.00304005i	$-0.999032\pi$
$613$	−1.40772e11	+	1.40772e11i	−0.996955	+	0.996955i	0.00304005	+	0.999995i	$0.499032\pi$
$614$		−	1.76351e11i		−	1.24081i
$615$		0			0
$616$	1.42393e10			0.0988930
$617$	−5.57976e10	−	5.57976e10i	−0.385013	−	0.385013i	0.487892	−	0.872904i	$-0.337766\pi$
$617$	−5.57976e10	−	5.57976e10i	−0.385013	−	0.385013i	−0.872904	+	0.487892i	$0.837766\pi$
$618$	−1.54716e10	+	1.54716e10i	−0.106067	+	0.106067i
$619$			2.74494e11i			1.86969i	0.355053	+	0.934846i	$0.384463\pi$
$619$			2.74494e11i			1.86969i	−0.355053	+	0.934846i	$0.615537\pi$
$620$		0			0
$621$	3.26657e10			0.219647
$622$	−1.56856e11	−	1.56856e11i	−1.04794	−	1.04794i
$623$	2.19422e10	−	2.19422e10i	0.145656	−	0.145656i
$624$			6.46955e10i			0.426713i
$625$		0			0
$626$	2.30715e11			1.50237
$627$	5.41309e10	+	5.41309e10i	0.350247	+	0.350247i
$628$	−4.37730e10	+	4.37730e10i	−0.281428	+	0.281428i
$629$			2.03746e10i			0.130163i
$630$		0			0
$631$	2.79192e11			1.76111			0.880554	−	0.473946i	$-0.157171\pi$
$631$	2.79192e11			1.76111			0.880554	+	0.473946i	$0.157171\pi$
$632$	7.82835e10	+	7.82835e10i	0.490684	+	0.490684i
$633$	−8.92812e10	+	8.92812e10i	−0.556090	+	0.556090i
$634$		−	6.19879e10i		−	0.383663i
$635$		0			0
$636$	2.00907e10			0.122791
$637$	6.86202e10	+	6.86202e10i	0.416768	+	0.416768i
$638$	1.20462e11	−	1.20462e11i	0.727056	−	0.727056i
$639$		−	5.75931e8i		−	0.00345436i
$640$		0			0
$641$	−2.94406e11			−1.74387			−0.871935	−	0.489622i	$-0.837135\pi$
$641$	−2.94406e11			−1.74387			−0.871935	+	0.489622i	$0.837135\pi$
$642$	−1.00389e11	−	1.00389e11i	−0.590946	−	0.590946i
$643$	−7.60521e10	+	7.60521e10i	−0.444905	+	0.444905i	−0.893657	−	0.448751i	$-0.851869\pi$
$643$	−7.60521e10	+	7.60521e10i	−0.444905	+	0.444905i	0.448751	+	0.893657i	$0.351869\pi$
$644$			1.11512e10i			0.0648301i
$645$		0			0
$646$	−3.61874e10			−0.207791
$647$	1.14831e11	+	1.14831e11i	0.655302	+	0.655302i	0.954265	−	0.298963i	$-0.0966407\pi$
$647$	1.14831e11	+	1.14831e11i	0.655302	+	0.655302i	−0.298963	+	0.954265i	$0.596641\pi$
$648$	1.11764e10	−	1.11764e10i	0.0633875	−	0.0633875i
$649$			1.22631e11i			0.691226i
$650$		0			0
$651$	−8.63872e9			−0.0480978
$652$	3.81004e10	+	3.81004e10i	0.210833	+	0.210833i
$653$	2.21539e11	−	2.21539e11i	1.21842	−	1.21842i	0.250240	−	0.968184i	$-0.419490\pi$
$653$	2.21539e11	−	2.21539e11i	1.21842	−	1.21842i	0.968184	−	0.250240i	$-0.0805095\pi$
$654$			1.30749e11i			0.714708i
$655$		0			0
$656$	2.53104e11			1.36673
$657$	6.66965e10	+	6.66965e10i	0.357966	+	0.357966i
$658$	−3.80925e10	+	3.80925e10i	−0.203205	+	0.203205i
$659$		−	2.01867e11i		−	1.07034i	−0.844744	−	0.535171i	$-0.820247\pi$
$659$		−	2.01867e11i		−	1.07034i	0.844744	−	0.535171i	$-0.179753\pi$
$660$		0			0
$661$	1.01557e11			0.531993			0.265996	−	0.963974i	$-0.414299\pi$
$661$	1.01557e11			0.531993			0.265996	+	0.963974i	$0.414299\pi$
$662$	1.68947e10	+	1.68947e10i	0.0879669	+	0.0879669i
$663$	6.44356e9	−	6.44356e9i	0.0333482	−	0.0333482i
$664$		−	2.32732e11i		−	1.19725i
$665$		0			0
$666$	7.27421e10			0.369734
$667$	−2.31490e11	−	2.31490e11i	−1.16958	−	1.16958i
$668$	4.15515e10	−	4.15515e10i	0.208680	−	0.208680i
$669$			2.16817e11i			1.08241i
$670$		0			0
$671$	2.18520e11			1.07796
$672$	9.18549e9	+	9.18549e9i	0.0450428	+	0.0450428i
$673$	1.52057e11	−	1.52057e11i	0.741220	−	0.741220i	−0.231593	−	0.972813i	$-0.574394\pi$
$673$	1.52057e11	−	1.52057e11i	0.741220	−	0.741220i	0.972813	+	0.231593i	$0.0743937\pi$
$674$		−	7.43724e10i		−	0.360390i
$675$		0			0
$676$	−3.77428e10			−0.180737
$677$	1.50332e11	+	1.50332e11i	0.715643	+	0.715643i	0.967710	−	0.252067i	$-0.0811103\pi$
$677$	1.50332e11	+	1.50332e11i	0.715643	+	0.715643i	−0.252067	+	0.967710i	$0.581110\pi$
$678$	5.92116e10	−	5.92116e10i	0.280213	−	0.280213i
$679$		−	5.50459e10i		−	0.258968i
$680$		0			0
$681$	1.55381e10			0.0722453
$682$	−4.60873e10	−	4.60873e10i	−0.213031	−	0.213031i
$683$	1.99757e11	−	1.99757e11i	0.917952	−	0.917952i	−0.0789283	−	0.996880i	$-0.525150\pi$
$683$	1.99757e11	−	1.99757e11i	0.917952	−	0.917952i	0.996880	+	0.0789283i	$0.0251498\pi$
$684$			2.90081e10i			0.132524i
$685$		0			0
$686$	9.67781e10			0.436999
$687$	−6.14841e10	−	6.14841e10i	−0.276017	−	0.276017i
$688$	1.89692e11	−	1.89692e11i	0.846633	−	0.846633i
$689$			1.01476e11i			0.450284i
$690$		0			0
$691$	1.62540e11			0.712933			0.356467	−	0.934308i	$-0.383981\pi$
$691$	1.62540e11			0.712933			0.356467	+	0.934308i	$0.383981\pi$
$692$	8.22998e9	+	8.22998e9i	0.0358901	+	0.0358901i
$693$	−6.66349e9	+	6.66349e9i	−0.0288914	+	0.0288914i
$694$			2.11840e11i			0.913207i
$695$		0			0
$696$	−1.58407e11			−0.675050
$697$	−2.52087e10	−	2.52087e10i	−0.106812	−	0.106812i
$698$	1.96294e11	−	1.96294e11i	0.826961	−	0.826961i
$699$			6.35489e10i			0.266195i
$700$		0			0
$701$	−4.42435e11			−1.83222			−0.916109	−	0.400929i	$-0.868687\pi$
$701$	−4.42435e11			−1.83222			−0.916109	+	0.400929i	$0.868687\pi$
$702$	−2.30051e10	−	2.30051e10i	−0.0947272	−	0.0947272i
$703$	2.31644e11	−	2.31644e11i	0.948416	−	0.948416i
$704$		−	8.70298e10i		−	0.354305i
$705$		0			0
$706$	3.44588e11			1.38702
$707$	3.84813e8	+	3.84813e8i	0.00154018	+	0.00154018i
$708$	−3.28581e10	+	3.28581e10i	−0.130770	+	0.130770i
$709$		−	4.15887e11i		−	1.64585i	−0.568149	−	0.822926i	$-0.692340\pi$
$709$		−	4.15887e11i		−	1.64585i	0.568149	−	0.822926i	$-0.307660\pi$
$710$		0			0
$711$	−7.32678e10			−0.286705
$712$	−1.53934e11	−	1.53934e11i	−0.598982	−	0.598982i
$713$	−8.85650e10	+	8.85650e10i	−0.342692	+	0.342692i
$714$		−	4.45466e9i		−	0.0171404i
$715$		0			0
$716$	−6.96109e10			−0.264865
$717$	7.95847e10	+	7.95847e10i	0.301129	+	0.301129i
$718$	−1.81600e11	+	1.81600e11i	−0.683311	+	0.683311i
$719$		−	7.73071e9i		−	0.0289270i	−0.999895	−	0.0144635i	$-0.995396\pi$
$719$		−	7.73071e9i		−	0.0289270i	0.999895	−	0.0144635i	$-0.00460404\pi$
$720$		0			0
$721$	−1.21298e10			−0.0448863
$722$	1.93226e11	+	1.93226e11i	0.711078	+	0.711078i
$723$	2.47347e10	−	2.47347e10i	0.0905219	−	0.0905219i
$724$		−	8.87845e10i		−	0.323134i
$725$		0			0
$726$	1.11040e11			0.399697
$727$	−1.02377e11	−	1.02377e11i	−0.366492	−	0.366492i	0.499704	−	0.866196i	$-0.333442\pi$
$727$	−1.02377e11	−	1.02377e11i	−0.366492	−	0.366492i	−0.866196	+	0.499704i	$0.833442\pi$
$728$	−1.92709e10	+	1.92709e10i	−0.0686081	+	0.0686081i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−3.77860e10			−0.132331
$732$	5.85511e10	+	5.85511e10i	0.203935	+	0.203935i
$733$	−1.73130e11	+	1.73130e11i	−0.599730	+	0.599730i	−0.940241	−	0.340510i	$-0.889400\pi$
$733$	−1.73130e11	+	1.73130e11i	−0.599730	+	0.599730i	0.340510	+	0.940241i	$0.389400\pi$
$734$			1.32874e11i			0.457778i
$735$		0			0
$736$	1.88341e11			0.641851
$737$	−1.52881e11	−	1.52881e11i	−0.518182	−	0.518182i
$738$	−9.00011e10	+	9.00011e10i	−0.303405	+	0.303405i
$739$			1.63608e11i			0.548563i	0.961649	+	0.274281i	$0.0884400\pi$
$739$			1.63608e11i			0.548563i	−0.961649	+	0.274281i	$0.911560\pi$
$740$		0			0
$741$	−1.46517e11			−0.485976
$742$	3.50769e10	+	3.50769e10i	0.115719	+	0.115719i
$743$	3.99366e11	−	3.99366e11i	1.31044	−	1.31044i	0.389345	−	0.921092i	$-0.372701\pi$
$743$	3.99366e11	−	3.99366e11i	1.31044	−	1.31044i	0.921092	−	0.389345i	$-0.127299\pi$
$744$			6.06043e10i			0.197793i
$745$		0			0
$746$	3.19066e11			1.03021
$747$	1.08910e11	+	1.08910e11i	0.349773	+	0.349773i
$748$	5.33593e9	−	5.33593e9i	0.0170453	−	0.0170453i
$749$		−	7.87062e10i		−	0.250082i
$750$		0			0
$751$	−8.42899e10			−0.264982			−0.132491	−	0.991184i	$-0.542297\pi$
$751$	−8.42899e10			−0.264982			−0.132491	+	0.991184i	$0.542297\pi$
$752$	3.51688e11	+	3.51688e11i	1.09973	+	1.09973i
$753$	−1.12038e11	+	1.12038e11i	−0.348487	+	0.348487i
$754$			3.26057e11i			1.00881i
$755$		0			0
$756$	−3.57088e9			−0.0109317
$757$	−1.30447e11	−	1.30447e11i	−0.397237	−	0.397237i	0.480020	−	0.877257i	$-0.340629\pi$
$757$	−1.30447e11	−	1.30447e11i	−0.397237	−	0.397237i	−0.877257	+	0.480020i	$0.840629\pi$
$758$	−3.67152e11	+	3.67152e11i	−1.11216	+	1.11216i
$759$			1.36629e11i			0.411697i
$760$		0			0
$761$	6.33668e10			0.188940			0.0944698	−	0.995528i	$-0.469884\pi$
$761$	6.33668e10			0.188940			0.0944698	+	0.995528i	$0.469884\pi$
$762$	−1.93753e11	−	1.93753e11i	−0.574682	−	0.574682i
$763$	−5.12543e10	+	5.12543e10i	−0.151228	+	0.151228i
$764$		−	1.26500e11i		−	0.371292i
$765$		0			0
$766$	−3.24992e11			−0.943968
$767$	−1.65963e11	−	1.65963e11i	−0.479546	−	0.479546i
$768$	1.14020e11	−	1.14020e11i	0.327745	−	0.327745i
$769$		−	3.55053e10i		−	0.101528i	−0.998711	−	0.0507642i	$-0.983834\pi$
$769$		−	3.55053e10i		−	0.101528i	0.998711	−	0.0507642i	$-0.0161657\pi$
$770$		0			0
$771$	1.69561e11			0.479852
$772$	2.28926e10	+	2.28926e10i	0.0644503	+	0.0644503i
$773$	−2.87747e11	+	2.87747e11i	−0.805921	+	0.805921i	−0.984014	−	0.178093i	$-0.943007\pi$
$773$	−2.87747e11	+	2.87747e11i	−0.805921	+	0.805921i	0.178093	+	0.984014i	$0.443007\pi$
$774$			1.34905e11i			0.375893i
$775$		0			0
$776$	−3.86171e11			−1.06496
$777$	2.85152e10	+	2.85152e10i	0.0782335	+	0.0782335i
$778$	−3.73443e11	+	3.73443e11i	−1.01931	+	1.01931i
$779$			5.73208e11i			1.55655i
$780$		0			0
$781$	2.40893e9			0.00647469
$782$	−4.56696e10	−	4.56696e10i	−0.122124	−	0.122124i
$783$	7.41287e10	−	7.41287e10i	0.197215	−	0.197215i
$784$		−	4.37984e11i		−	1.15930i
$785$		0			0
$786$	−1.79357e11			−0.469925
$787$	−6.58669e10	−	6.58669e10i	−0.171699	−	0.171699i	0.616026	−	0.787726i	$-0.288741\pi$
$787$	−6.58669e10	−	6.58669e10i	−0.171699	−	0.171699i	−0.787726	+	0.616026i	$0.788741\pi$
$788$	−4.75638e10	+	4.75638e10i	−0.123359	+	0.123359i
$789$		−	3.99929e11i		−	1.03199i
$790$		0			0
$791$	4.64224e10			0.118583
$792$	4.67473e10	+	4.67473e10i	0.118811	+	0.118811i
$793$	−2.95736e11	+	2.95736e11i	−0.747845	+	0.747845i
$794$			1.17707e11i			0.296156i
$795$		0			0
$796$	4.15037e10			0.103380
$797$	−3.21177e11	−	3.21177e11i	−0.795996	−	0.795996i	0.186465	−	0.982462i	$-0.440297\pi$
$797$	−3.21177e11	−	3.21177e11i	−0.795996	−	0.795996i	−0.982462	+	0.186465i	$0.940297\pi$
$798$	−5.06461e10	+	5.06461e10i	−0.124892	+	0.124892i
$799$		−	7.00551e10i		−	0.171891i
$800$		0			0
$801$	1.44071e11			0.349983
$802$	3.29893e11	+	3.29893e11i	0.797400	+	0.797400i
$803$	−2.78969e11	+	2.78969e11i	−0.670955	+	0.670955i
$804$		−	8.19268e10i		−	0.196066i
$805$		0			0
$806$	1.24745e11			0.295586
$807$	−5.34008e10	−	5.34008e10i	−0.125908	−	0.125908i
$808$	2.69963e9	−	2.69963e9i	0.00633372	−	0.00633372i
$809$		−	5.25661e11i		−	1.22719i	−0.789621	−	0.613595i	$-0.789723\pi$
$809$		−	5.25661e11i		−	1.22719i	0.789621	−	0.613595i	$-0.210277\pi$
$810$		0			0
$811$	−5.31498e11			−1.22862			−0.614311	−	0.789064i	$-0.710566\pi$
$811$	−5.31498e11			−1.22862			−0.614311	+	0.789064i	$0.710566\pi$
$812$	2.53055e10	+	2.53055e10i	0.0582091	+	0.0582091i
$813$	6.15383e9	−	6.15383e9i	0.0140859	−	0.0140859i
$814$			3.04256e11i			0.693013i
$815$		0			0
$816$	−4.11275e10			−0.0927623
$817$	4.29598e11	+	4.29598e11i	0.964216	+	0.964216i
$818$	−6.62115e11	+	6.62115e11i	−1.47884	+	1.47884i
$819$		−	1.80362e10i		−	0.0400875i
$820$		0			0
$821$	−6.70252e11			−1.47525			−0.737625	−	0.675211i	$-0.764053\pi$
$821$	−6.70252e11			−1.47525			−0.737625	+	0.675211i	$0.764053\pi$
$822$	1.40270e11	+	1.40270e11i	0.307240	+	0.307240i
$823$	2.18846e11	−	2.18846e11i	0.477022	−	0.477022i	−0.427156	−	0.904178i	$-0.640484\pi$
$823$	2.18846e11	−	2.18846e11i	0.477022	−	0.477022i	0.904178	+	0.427156i	$0.140484\pi$
$824$			8.50961e10i			0.184587i
$825$		0			0
$826$	−1.14736e11			−0.246479
$827$	−3.35456e11	−	3.35456e11i	−0.717155	−	0.717155i	0.250867	−	0.968022i	$-0.419284\pi$
$827$	−3.35456e11	−	3.35456e11i	−0.717155	−	0.717155i	−0.968022	+	0.250867i	$0.919284\pi$
$828$	−3.66090e10	+	3.66090e10i	−0.0778873	+	0.0778873i
$829$		−	3.31479e11i		−	0.701839i	−0.936406	−	0.350920i	$-0.885869\pi$
$829$		−	3.31479e11i		−	0.701839i	0.936406	−	0.350920i	$-0.114131\pi$
$830$		0			0
$831$	2.68317e11			0.562657
$832$	1.17782e11	+	1.17782e11i	0.245803	+	0.245803i
$833$	−4.36225e10	+	4.36225e10i	−0.0906005	+	0.0906005i
$834$		−	4.83484e11i		−	0.999350i
$835$		0			0
$836$	−1.21331e11			−0.248397
$837$	−2.83607e10	−	2.83607e10i	−0.0577850	−	0.0577850i
$838$	6.63961e11	−	6.63961e11i	1.34638	−	1.34638i
$839$		−	1.20093e11i		−	0.242365i	−0.992630	−	0.121183i	$-0.961331\pi$
$839$		−	1.20093e11i		−	0.242365i	0.992630	−	0.121183i	$-0.0386687\pi$
$840$		0			0
$841$	−5.50398e11			−1.10025
$842$	−3.73180e11	−	3.73180e11i	−0.742455	−	0.742455i
$843$	6.68619e10	−	6.68619e10i	0.132394	−	0.132394i
$844$		−	2.00118e11i		−	0.394381i
$845$		0			0
$846$	−2.50113e11			−0.488264
$847$	4.35280e10	+	4.35280e10i	0.0845736	+	0.0845736i
$848$	3.23847e11	−	3.23847e11i	0.626263	−	0.626263i
$849$		−	1.17416e11i		−	0.225995i
$850$		0			0
$851$	5.84682e11			1.11481
$852$	6.45456e8	+	6.45456e8i	0.00122492	+	0.00122492i
$853$	−1.17094e11	+	1.17094e11i	−0.221176	+	0.221176i	−0.808993	−	0.587818i	$-0.799987\pi$
$853$	−1.17094e11	+	1.17094e11i	−0.221176	+	0.221176i	0.587818	+	0.808993i	$0.299987\pi$
$854$			2.04452e11i			0.384380i
$855$		0			0
$856$	−5.52158e11			−1.02841
$857$	1.60077e11	+	1.60077e11i	0.296759	+	0.296759i	0.839743	−	0.542984i	$-0.182705\pi$
$857$	1.60077e11	+	1.60077e11i	0.296759	+	0.296759i	−0.542984	+	0.839743i	$0.682705\pi$
$858$	9.62224e10	−	9.62224e10i	0.177553	−	0.177553i
$859$			1.81742e10i			0.0333797i	0.999861	+	0.0166898i	$0.00531278\pi$
$859$			1.81742e10i			0.0333797i	−0.999861	+	0.0166898i	$0.994687\pi$
$860$		0			0
$861$	−7.05617e10			−0.128397
$862$	4.34474e10	+	4.34474e10i	0.0786928	+	0.0786928i
$863$	5.99083e11	−	5.99083e11i	1.08005	−	1.08005i	0.0835450	−	0.996504i	$-0.473376\pi$
$863$	5.99083e11	−	5.99083e11i	1.08005	−	1.08005i	0.996504	−	0.0835450i	$-0.0266242\pi$
$864$			6.03115e10i			0.108229i
$865$		0			0
$866$	−1.22474e11			−0.217757
$867$	−2.26579e11	−	2.26579e11i	−0.400999	−	0.400999i
$868$	9.68156e9	−	9.68156e9i	0.0170556	−	0.0170556i
$869$		−	3.06454e11i		−	0.537387i
$870$		0			0
$871$	4.13804e11			0.718989
$872$	3.59571e11	+	3.59571e11i	0.621898	+	0.621898i
$873$	1.80714e11	−	1.80714e11i	0.311125	−	0.311125i
$874$			1.03846e12i			1.77968i
$875$		0			0
$876$	−1.49496e11			−0.253871
$877$	5.84260e11	+	5.84260e11i	0.987661	+	0.987661i	0.999925	−	0.0122638i	$-0.00390378\pi$
$877$	5.84260e11	+	5.84260e11i	0.987661	+	0.987661i	−0.0122638	+	0.999925i	$0.503904\pi$
$878$	−4.01365e11	+	4.01365e11i	−0.675401	+	0.675401i
$879$		−	5.56628e11i		−	0.932416i
$880$		0			0
$881$	3.18962e11			0.529463			0.264732	−	0.964322i	$-0.414717\pi$
$881$	3.18962e11			0.529463			0.264732	+	0.964322i	$0.414717\pi$
$882$	1.55743e11	+	1.55743e11i	0.257356	+	0.257356i
$883$	3.93523e11	−	3.93523e11i	0.647333	−	0.647333i	−0.305015	−	0.952348i	$-0.598661\pi$
$883$	3.93523e11	−	3.93523e11i	0.647333	−	0.647333i	0.952348	+	0.305015i	$0.0986614\pi$
$884$			1.44428e10i			0.0236507i
$885$		0			0
$886$	3.56979e11			0.579305
$887$	−1.97346e11	−	1.97346e11i	−0.318812	−	0.318812i	0.529499	−	0.848311i	$-0.322380\pi$
$887$	−1.97346e11	−	1.97346e11i	−0.318812	−	0.318812i	−0.848311	+	0.529499i	$0.822380\pi$
$888$	2.00047e11	−	2.00047e11i	0.321721	−	0.321721i
$889$		−	1.51904e11i		−	0.243199i
$890$		0			0
$891$	−4.37521e10			−0.0694206
$892$	−2.42991e11	−	2.42991e11i	−0.383823	−	0.383823i
$893$	−7.96473e11	+	7.96473e11i	−1.25246	+	1.25246i
$894$		−	6.19116e11i		−	0.969219i
$895$		0			0
$896$	1.52537e11			0.236671
$897$	−1.84909e11	−	1.84909e11i	−0.285619	−	0.285619i
$898$	9.58631e11	−	9.58631e11i	1.47417	−	1.47417i
$899$			4.01963e11i			0.615386i
$900$		0			0
$901$	−6.45093e10			−0.0978866
$902$	−3.76444e11	−	3.76444e11i	−0.568688	−	0.568688i
$903$	−5.28834e10	+	5.28834e10i	−0.0795368	+	0.0795368i
$904$		−	3.25673e11i		−	0.487650i
$905$		0			0
$906$	2.77876e11			0.412419
$907$	−1.55260e10	−	1.55260e10i	−0.0229419	−	0.0229419i	0.695543	−	0.718485i	$-0.255164\pi$
$907$	−1.55260e10	−	1.55260e10i	−0.0229419	−	0.0229419i	−0.718485	+	0.695543i	$0.755164\pi$
$908$	−1.74138e10	+	1.74138e10i	−0.0256183	+	0.0256183i
$909$			2.52666e9i			0.00370077i
$910$		0			0
$911$	9.70829e11			1.40951			0.704757	−	0.709449i	$-0.251056\pi$
$911$	9.70829e11			1.40951			0.704757	+	0.709449i	$0.251056\pi$
$912$	4.67588e11	+	4.67588e11i	0.675903	+	0.675903i
$913$	−4.55535e11	+	4.55535e11i	−0.655600	+	0.655600i
$914$			8.61671e11i			1.23469i
$915$		0			0
$916$	1.37813e11			0.195753
$917$	−7.03089e10	−	7.03089e10i	−0.0994335	−	0.0994335i
$918$	1.46245e10	−	1.46245e10i	0.0205926	−	0.0205926i
$919$		−	2.16464e11i		−	0.303475i	−0.988421	−	0.151738i	$-0.951513\pi$
$919$		−	2.16464e11i		−	0.303475i	0.988421	−	0.151738i	$-0.0484868\pi$
$920$		0			0
$921$	4.53907e11			0.630854
$922$	1.09136e12	+	1.09136e12i	1.51023	+	1.51023i
$923$	−3.26014e9	+	3.26014e9i	−0.00449189	+	0.00449189i
$924$		−	1.49358e10i		−	0.0204899i
$925$		0			0
$926$	−6.38336e11			−0.868172
$927$	−3.98220e10	−	3.98220e10i	−0.0539267	−	0.0539267i
$928$	4.27405e11	−	4.27405e11i	0.576299	−	0.576299i
$929$			2.35669e11i			0.316402i	0.987407	+	0.158201i	$0.0505694\pi$
$929$			2.35669e11i			0.316402i	−0.987407	+	0.158201i	$0.949431\pi$
$930$		0			0
$931$	9.91910e11			1.32030
$932$	−7.12204e10	−	7.12204e10i	−0.0943932	−	0.0943932i
$933$	4.03727e11	−	4.03727e11i	0.532797	−	0.532797i
$934$			8.68195e11i			1.14085i
$935$		0			0
$936$	−1.26532e11			−0.164852
$937$	−9.84325e11	−	9.84325e11i	−1.27697	−	1.27697i	−0.942356	−	0.334613i	$-0.891394\pi$
$937$	−9.84325e11	−	9.84325e11i	−1.27697	−	1.27697i	−0.334613	−	0.942356i	$-0.608606\pi$
$938$	1.43039e11	−	1.43039e11i	0.184774	−	0.184774i
$939$			5.93832e11i			0.763838i
$940$		0			0
$941$	1.48728e12			1.89686			0.948430	−	0.316986i	$-0.102671\pi$
$941$	1.48728e12			1.89686			0.948430	+	0.316986i	$0.102671\pi$
$942$	−5.01800e11	−	5.01800e11i	−0.637275	−	0.637275i
$943$	−7.23405e11	+	7.23405e11i	−0.914818	+	0.914818i
$944$			1.05930e12i			1.33392i
$945$		0			0
$946$	−5.64262e11			−0.704558
$947$	−5.61976e11	−	5.61976e11i	−0.698743	−	0.698743i	0.265396	−	0.964139i	$-0.414497\pi$
$947$	−5.61976e11	−	5.61976e11i	−0.698743	−	0.698743i	−0.964139	+	0.265396i	$0.914497\pi$
$948$	8.21125e10	−	8.21125e10i	0.101666	−	0.101666i
$949$		−	7.55089e11i		−	0.930965i
$950$		0			0
$951$	1.59549e11			0.195062
$952$	−1.22507e10	−	1.22507e10i	−0.0149146	−	0.0149146i
$953$	−5.83237e11	+	5.83237e11i	−0.707088	+	0.707088i	−0.965922	−	0.258834i	$-0.916662\pi$
$953$	−5.83237e11	+	5.83237e11i	−0.707088	+	0.707088i	0.258834	+	0.965922i	$0.416662\pi$
$954$			2.30313e11i			0.278052i
$955$		0			0
$956$	−1.78384e11			−0.213562
$957$	3.10055e11	+	3.10055e11i	0.369650	+	0.369650i
$958$	1.26107e11	−	1.26107e11i	0.149719	−	0.149719i
$959$			1.09973e11i			0.130020i
$960$		0			0
$961$	−6.99105e11			−0.819688
$962$	−4.11767e11	−	4.11767e11i	−0.480785	−	0.480785i
$963$	2.58390e11	−	2.58390e11i	0.300449	−	0.300449i
$964$			5.54413e10i			0.0641985i
$965$		0			0
$966$	−1.27834e11			−0.146804
$967$	1.37758e10	+	1.37758e10i	0.0157547	+	0.0157547i	0.714940	−	0.699186i	$-0.246454\pi$
$967$	1.37758e10	+	1.37758e10i	0.0157547	+	0.0157547i	−0.699186	+	0.714940i	$0.746454\pi$
$968$	3.05368e11	−	3.05368e11i	0.347794	−	0.347794i
$969$		−	9.31421e10i		−	0.105646i
$970$		0			0
$971$	5.31026e11			0.597364			0.298682	−	0.954353i	$-0.403453\pi$
$971$	5.31026e11			0.597364			0.298682	+	0.954353i	$0.403453\pi$
$972$	−1.17231e10	−	1.17231e10i	−0.0131334	−	0.0131334i
$973$	1.89528e11	−	1.89528e11i	0.211457	−	0.211457i
$974$			9.84672e10i			0.109410i
$975$		0			0
$976$	1.88760e12			2.08023
$977$	7.35034e11	+	7.35034e11i	0.806731	+	0.806731i	0.984138	−	0.177406i	$-0.0567706\pi$
$977$	7.35034e11	+	7.35034e11i	0.806731	+	0.806731i	−0.177406	+	0.984138i	$0.556771\pi$
$978$	−4.36771e11	+	4.36771e11i	−0.477418	+	0.477418i
$979$			6.02601e11i			0.655992i
$980$		0			0
$981$	−3.36533e11			−0.363373
$982$	−1.32508e12	−	1.32508e12i	−1.42494	−	1.42494i
$983$	−1.73787e10	+	1.73787e10i	−0.0186124	+	0.0186124i	−0.716352	−	0.697739i	$-0.754189\pi$
$983$	−1.73787e10	+	1.73787e10i	−0.0186124	+	0.0186124i	0.697739	+	0.716352i	$0.254189\pi$
$984$			4.95021e11i			0.528011i
$985$		0			0
$986$	−2.07277e11			−0.219303
$987$	−9.80455e10	−	9.80455e10i	−0.103314	−	0.103314i
$988$	1.64204e11	−	1.64204e11i	0.172328	−	0.172328i
$989$			1.08433e12i			1.13338i
$990$		0			0
$991$	−1.57804e11			−0.163615			−0.0818077	−	0.996648i	$-0.526069\pi$
$991$	−1.57804e11			−0.163615			−0.0818077	+	0.996648i	$0.526069\pi$
$992$	−1.63520e11	−	1.63520e11i	−0.168859	−	0.168859i
$993$	−4.34850e10	+	4.34850e10i	−0.0447242	+	0.0447242i
$994$			2.25384e9i			0.00230876i
$995$		0			0
$996$	−2.44116e11			−0.248061
$997$	−1.62852e11	−	1.62852e11i	−0.164821	−	0.164821i	0.619877	−	0.784699i	$-0.287182\pi$
$997$	−1.62852e11	−	1.62852e11i	−0.164821	−	0.164821i	−0.784699	+	0.619877i	$0.787182\pi$
$998$	5.87326e11	−	5.87326e11i	0.592048	−	0.592048i
$999$			1.87230e11i			0.187980i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.c.7.2	✓	8	1.1	even	1	trivial
75.9.f.c.7.3	yes	8	5.4	even	2	inner
75.9.f.c.43.2	yes	8	5.3	odd	4	inner
75.9.f.c.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)

\(f(q)\)	\(=\)	\(q+(-12.8476 - 12.8476i) q^{2} +(33.0681 - 33.0681i) q^{3} +74.1200i q^{4} -849.690 q^{6} +(-333.082 - 333.082i) q^{7} +(-2336.72 + 2336.72i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-12.8476 - 12.8476i) q^{2} +(33.0681 - 33.0681i) q^{3} +74.1200i q^{4} -849.690 q^{6} +(-333.082 - 333.082i) q^{7} +(-2336.72 + 2336.72i) q^{8} -2187.00i q^{9} +9147.48 q^{11} +(2451.01 + 2451.01i) q^{12} +(-12379.8 + 12379.8i) q^{13} +8558.59i q^{14} +79017.0 q^{16} +(-7869.96 - 7869.96i) q^{17} +(-28097.6 + 28097.6i) q^{18} +178951. i q^{19} -22028.8 q^{21} +(-117523. - 117523. i) q^{22} +(-225841. + 225841. i) q^{23} +154542. i q^{24} +318101. q^{26} +(-72320.0 - 72320.0i) q^{27} +(24688.1 - 24688.1i) q^{28} +1.02501e6i q^{29} +392156. q^{31} +(-416977. - 416977. i) q^{32} +(302490. - 302490. i) q^{33} +202220. i q^{34} +162101. q^{36} +(-1.29445e6 - 1.29445e6i) q^{37} +(2.29909e6 - 2.29909e6i) q^{38} +818754. i q^{39} +3.20316e6 q^{41} +(283016. + 283016. i) q^{42} +(2.40065e6 - 2.40065e6i) q^{43} +678012. i q^{44} +5.80303e6 q^{46} +(4.45079e6 + 4.45079e6i) q^{47} +(2.61294e6 - 2.61294e6i) q^{48} -5.54291e6i q^{49} -520490. q^{51} +(-917592. - 917592. i) q^{52} +(4.09845e6 - 4.09845e6i) q^{53} +1.85827e6i q^{54} +1.55664e6 q^{56} +(5.91757e6 + 5.91757e6i) q^{57} +(1.31689e7 - 1.31689e7i) q^{58} +1.34059e7i q^{59} +2.38886e7 q^{61} +(-5.03825e6 - 5.03825e6i) q^{62} +(-728451. + 728451. i) q^{63} -9.51407e6i q^{64} -7.77252e6 q^{66} +(-1.67129e7 - 1.67129e7i) q^{67} +(583322. - 583322. i) q^{68} +1.49363e7i q^{69} +263343. q^{71} +(5.11040e6 + 5.11040e6i) q^{72} +(-3.04968e7 + 3.04968e7i) q^{73} +3.32611e7i q^{74} -1.32639e7 q^{76} +(-3.04686e6 - 3.04686e6i) q^{77} +(1.05190e7 - 1.05190e7i) q^{78} -3.35015e7i q^{79} -4.78297e6 q^{81} +(-4.11528e7 - 4.11528e7i) q^{82} +(-4.97990e7 + 4.97990e7i) q^{83} -1.63278e6i q^{84} -6.16850e7 q^{86} +(3.38951e7 + 3.38951e7i) q^{87} +(-2.13751e7 + 2.13751e7i) q^{88} +6.58761e7i q^{89} +8.24699e6 q^{91} +(-1.67394e7 - 1.67394e7i) q^{92} +(1.29678e7 - 1.29678e7i) q^{93} -1.14364e8i q^{94} -2.75773e7 q^{96} +(8.26311e7 + 8.26311e7i) q^{97} +(-7.12130e7 + 7.12130e7i) q^{98} -2.00055e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1296 q^{6}+O(q^{10}) \) 8 * q + 1296 * q^6	\( 8 q + 1296 q^{6} + 107952 q^{11} + 401920 q^{16} - 953208 q^{21} + 4257936 q^{26} - 2908312 q^{31} + 3919104 q^{36} + 33914208 q^{41} + 50759328 q^{46} + 854064 q^{51} + 60954240 q^{56} + 29647000 q^{61} + 52666848 q^{66} - 28246944 q^{71} - 59323136 q^{76} - 38263752 q^{81} - 432922128 q^{86} - 517149432 q^{91} + 132129792 q^{96}+O(q^{100}) \) 8 * q + 1296 * q^6 + 107952 * q^11 + 401920 * q^16 - 953208 * q^21 + 4257936 * q^26 - 2908312 * q^31 + 3919104 * q^36 + 33914208 * q^41 + 50759328 * q^46 + 854064 * q^51 + 60954240 * q^56 + 29647000 * q^61 + 52666848 * q^66 - 28246944 * q^71 - 59323136 * q^76 - 38263752 * q^81 - 432922128 * q^86 - 517149432 * q^91 + 132129792 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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