LMFDB - Embedded newform 25.33.c.b.7.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,33,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 33, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$162.166637856$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(70960.9 + 70960.9i) q^{2} +(4.83700e7 - 4.83700e7i) q^{3} +5.77593e9i q^{4} +6.86476e12 q^{6} +(-2.09740e13 - 2.09740e13i) q^{7} +(-1.05090e14 + 1.05090e14i) q^{8} -2.82629e15i q^{9} +O(q^{10})$	\(q+(70960.9 + 70960.9i) q^{2} +(4.83700e7 - 4.83700e7i) q^{3} +5.77593e9i q^{4} +6.86476e12 q^{6} +(-2.09740e13 - 2.09740e13i) q^{7} +(-1.05090e14 + 1.05090e14i) q^{8} -2.82629e15i q^{9} +6.47623e16 q^{11} +(2.79382e17 + 2.79382e17i) q^{12} +(4.20416e17 - 4.20416e17i) q^{13} -2.97666e18i q^{14} +9.89284e18 q^{16} +(1.82331e19 + 1.82331e19i) q^{17} +(2.00556e20 - 2.00556e20i) q^{18} +1.23600e20i q^{19} -2.02902e21 q^{21} +(4.59559e21 + 4.59559e21i) q^{22} +(-6.48274e21 + 6.48274e21i) q^{23} +1.01664e22i q^{24} +5.96662e22 q^{26} +(-4.70772e22 - 4.70772e22i) q^{27} +(1.21144e23 - 1.21144e23i) q^{28} -4.68141e23i q^{29} +2.94207e22 q^{31} +(1.15336e24 + 1.15336e24i) q^{32} +(3.13255e24 - 3.13255e24i) q^{33} +2.58767e24i q^{34} +1.63245e25 q^{36} +(-1.50424e25 - 1.50424e25i) q^{37} +(-8.77074e24 + 8.77074e24i) q^{38} -4.06711e25i q^{39} +4.08942e25 q^{41} +(-1.43981e26 - 1.43981e26i) q^{42} +(-5.01997e25 + 5.01997e25i) q^{43} +3.74062e26i q^{44} -9.20042e26 q^{46} +(-4.23386e26 - 4.23386e26i) q^{47} +(4.78517e26 - 4.78517e26i) q^{48} -2.24614e26i q^{49} +1.76387e27 q^{51} +(2.42829e27 + 2.42829e27i) q^{52} +(2.94663e27 - 2.94663e27i) q^{53} -6.68128e27i q^{54} +4.40831e27 q^{56} +(5.97851e27 + 5.97851e27i) q^{57} +(3.32197e28 - 3.32197e28i) q^{58} +8.62486e27i q^{59} +1.77137e28 q^{61} +(2.08772e27 + 2.08772e27i) q^{62} +(-5.92786e28 + 5.92786e28i) q^{63} +1.21198e29i q^{64} +4.44577e29 q^{66} +(2.48410e28 + 2.48410e28i) q^{67} +(-1.05313e29 + 1.05313e29i) q^{68} +6.27141e29i q^{69} +3.63249e29 q^{71} +(2.97015e29 + 2.97015e29i) q^{72} +(5.94905e29 - 5.94905e29i) q^{73} -2.13484e30i q^{74} -7.13902e29 q^{76} +(-1.35832e30 - 1.35832e30i) q^{77} +(2.88605e30 - 2.88605e30i) q^{78} -1.45813e30i q^{79} +6.82928e29 q^{81} +(2.90189e30 + 2.90189e30i) q^{82} +(-3.27935e30 + 3.27935e30i) q^{83} -1.17195e31i q^{84} -7.12443e30 q^{86} +(-2.26440e31 - 2.26440e31i) q^{87} +(-6.80587e30 + 6.80587e30i) q^{88} +8.42590e29i q^{89} -1.76356e31 q^{91} +(-3.74438e31 - 3.74438e31i) q^{92} +(1.42308e30 - 1.42308e30i) q^{93} -6.00877e31i q^{94} +1.11576e32 q^{96} +(3.56654e30 + 3.56654e30i) q^{97} +(1.59388e31 - 1.59388e31i) q^{98} -1.83037e32i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8}+O(q^{10}) $ 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8	$ 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8} - 60\!\cdots\!40 q^{11}+ \cdots - 12\!\cdots\!02 q^{98}+O(q^{100}) $ 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8 - 60908362837533640 * q^11 - 444566273630869608 * q^12 - 649759187023107138 * q^13 - 46108906958970522120 * q^16 + 218107661739005884502 * q^17 - 240407468159884203858 * q^18 + 4549905652154594876760 * q^21 + 11386561172247365212944 * q^22 - 13896091629970965206008 * q^23 - 23129486500762683557740 * q^26 - 176388356775702789525960 * q^27 - 59665474478272755491112 * q^28 - 1285786827516670637255040 * q^31 - 3122517776856150857591368 * q^32 + 1644615516923295701112504 * q^33 + 31947551193266858523505980 * q^36 + 126275105375668809211002 * q^37 - 57601564734016178366855880 * q^38 - 155417315271390260892986440 * q^41 - 797836438482097707185724336 * q^42 + 545147034084978191886568152 * q^43 - 3454637097270705106900721640 * q^46 - 2735203198488492729395621848 * q^47 + 3192952350241941373327314192 * q^48 - 6129415060408014316542923040 * q^51 - 6000870590399837156109494028 * q^52 + 11282171275183571262774628682 * q^53 - 47918174764291639802549158800 * q^56 - 44765351794015370451647799120 * q^57 + 29637988346430122895588672480 * q^58 + 50784540875895586667393303160 * q^61 + 218235799024898727529128868024 * q^62 - 213794735887989269330759842008 * q^63 + 1348836243659025586642346421120 * q^66 + 736483403252315334072161239752 * q^67 - 1085395947449178489054935855012 * q^68 + 817740403780342392034746361760 * q^71 + 951267702824572414087545605820 * q^72 + 379868722209495311437504600242 * q^73 - 6689750080738358201358794259600 * q^76 - 6381539826853244422672988941256 * q^77 + 9179143477318522110451614982584 * q^78 - 14239669107938661073624705472070 * q^81 - 2725313872720345364461277817936 * q^82 - 4996401755555614465785455997328 * q^83 + 16049932109847278395442966171960 * q^86 - 36834415428157346041110451524480 * q^87 + 47132513308908068698430156048160 * q^88 - 104150500668224029090357708737840 * q^91 + 18747876848872687606754750486552 * q^92 - 112210213536624471769268225064216 * q^93 + 380819283905835347723966665116960 * q^96 + 155781506757725945270376012026802 * q^97 - 125692870459469366775669291878702 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	70960.9	+	70960.9i	1.08278	+	1.08278i	0.996249	+	0.0865276i	$0.0275771\pi$
$2$	70960.9	+	70960.9i	1.08278	+	1.08278i	0.0865276	+	0.996249i	$0.472423\pi$
$3$	4.83700e7	−	4.83700e7i	1.12366	−	1.12366i	0.132477	−	0.991186i	$-0.457707\pi$
$3$	4.83700e7	−	4.83700e7i	1.12366	−	1.12366i	0.991186	−	0.132477i	$-0.0422930\pi$
$4$			5.77593e9i			1.34481i
$5$		0			0
$5$		0			0
$6$	6.86476e12			2.43335
$7$	−2.09740e13	−	2.09740e13i	−0.631120	−	0.631120i	0.317229	−	0.948349i	$-0.397248\pi$
$7$	−2.09740e13	−	2.09740e13i	−0.631120	−	0.631120i	−0.948349	+	0.317229i	$0.897248\pi$
$8$	−1.05090e14	+	1.05090e14i	−0.373355	+	0.373355i
$9$		−	2.82629e15i		−	1.52524i
$10$		0			0
$11$	6.47623e16			1.40942			0.704708	−	0.709498i	$-0.251078\pi$
$11$	6.47623e16			1.40942			0.704708	+	0.709498i	$0.251078\pi$
$12$	2.79382e17	+	2.79382e17i	1.51112	+	1.51112i
$13$	4.20416e17	−	4.20416e17i	0.631809	−	0.631809i	−0.316713	−	0.948522i	$-0.602579\pi$
$13$	4.20416e17	−	4.20416e17i	0.631809	−	0.631809i	0.948522	+	0.316713i	$0.102579\pi$
$14$		−	2.97666e18i		−	1.36672i
$15$		0			0
$16$	9.89284e18			0.536292
$17$	1.82331e19	+	1.82331e19i	0.374695	+	0.374695i	0.869184	−	0.494489i	$-0.164645\pi$
$17$	1.82331e19	+	1.82331e19i	0.374695	+	0.374695i	−0.494489	+	0.869184i	$0.664645\pi$
$18$	2.00556e20	−	2.00556e20i	1.65149	−	1.65149i
$19$			1.23600e20i			0.428508i	0.976778	+	0.214254i	$0.0687321\pi$
$19$			1.23600e20i			0.428508i	−0.976778	+	0.214254i	$0.931268\pi$
$20$		0			0
$21$	−2.02902e21			−1.41833
$22$	4.59559e21	+	4.59559e21i	1.52608	+	1.52608i
$23$	−6.48274e21	+	6.48274e21i	−1.05709	+	1.05709i	−0.0588254	+	0.998268i	$0.518736\pi$
$23$	−6.48274e21	+	6.48274e21i	−1.05709	+	1.05709i	−0.998268	+	0.0588254i	$0.981264\pi$
$24$			1.01664e22i			0.839050i
$25$		0			0
$26$	5.96662e22			1.36822
$27$	−4.70772e22	−	4.70772e22i	−0.590188	−	0.590188i
$28$	1.21144e23	−	1.21144e23i	0.848738	−	0.848738i
$29$		−	4.68141e23i		−	1.87072i	−0.353699	−	0.935359i	$-0.615076\pi$
$29$		−	4.68141e23i		−	1.87072i	0.353699	−	0.935359i	$-0.384924\pi$
$30$		0			0
$31$	2.94207e22			0.0404451			0.0202226	−	0.999796i	$-0.493563\pi$
$31$	2.94207e22			0.0404451			0.0202226	+	0.999796i	$0.493563\pi$
$32$	1.15336e24	+	1.15336e24i	0.954040	+	0.954040i
$33$	3.13255e24	−	3.13255e24i	1.58371	−	1.58371i
$34$			2.58767e24i			0.811422i
$35$		0			0
$36$	1.63245e25			2.05116
$37$	−1.50424e25	−	1.50424e25i	−1.21924	−	1.21924i	−0.967899	−	0.251340i	$-0.919129\pi$
$37$	−1.50424e25	−	1.50424e25i	−1.21924	−	1.21924i	−0.251340	−	0.967899i	$-0.580871\pi$
$38$	−8.77074e24	+	8.77074e24i	−0.463979	+	0.463979i
$39$		−	4.06711e25i		−	1.41988i
$40$		0			0
$41$	4.08942e25			0.641387			0.320693	−	0.947183i	$-0.396084\pi$
$41$	4.08942e25			0.641387			0.320693	+	0.947183i	$0.396084\pi$
$42$	−1.43981e26	−	1.43981e26i	−1.53574	−	1.53574i
$43$	−5.01997e25	+	5.01997e25i	−0.367456	+	0.367456i	−0.866549	−	0.499093i	$-0.833667\pi$
$43$	−5.01997e25	+	5.01997e25i	−0.367456	+	0.367456i	0.499093	+	0.866549i	$0.333667\pi$
$44$			3.74062e26i			1.89540i
$45$		0			0
$46$	−9.20042e26			−2.28919
$47$	−4.23386e26	−	4.23386e26i	−0.746742	−	0.746742i	0.227124	−	0.973866i	$-0.427068\pi$
$47$	−4.23386e26	−	4.23386e26i	−0.746742	−	0.746742i	−0.973866	+	0.227124i	$0.927068\pi$
$48$	4.78517e26	−	4.78517e26i	0.602611	−	0.602611i
$49$		−	2.24614e26i		−	0.203376i
$50$		0			0
$51$	1.76387e27			0.842062
$52$	2.42829e27	+	2.42829e27i	0.849665	+	0.849665i
$53$	2.94663e27	−	2.94663e27i	0.760171	−	0.760171i	−0.216182	−	0.976353i	$-0.569360\pi$
$53$	2.94663e27	−	2.94663e27i	0.760171	−	0.760171i	0.976353	+	0.216182i	$0.0693603\pi$
$54$		−	6.68128e27i		−	1.27809i
$55$		0			0
$56$	4.40831e27			0.471263
$57$	5.97851e27	+	5.97851e27i	0.481499	+	0.481499i
$58$	3.32197e28	−	3.32197e28i	2.02557	−	2.02557i
$59$			8.62486e27i			0.400055i	0.979790	+	0.200028i	$0.0641032\pi$
$59$			8.62486e27i			0.400055i	−0.979790	+	0.200028i	$0.935897\pi$
$60$		0			0
$61$	1.77137e28			0.481983			0.240992	−	0.970527i	$-0.422527\pi$
$61$	1.77137e28			0.481983			0.240992	+	0.970527i	$0.422527\pi$
$62$	2.08772e27	+	2.08772e27i	0.0437930	+	0.0437930i
$63$	−5.92786e28	+	5.92786e28i	−0.962607	+	0.962607i
$64$			1.21198e29i			1.52973i
$65$		0			0
$66$	4.44577e29			3.42960
$67$	2.48410e28	+	2.48410e28i	0.150651	+	0.150651i	0.778409	−	0.627758i	$-0.216027\pi$
$67$	2.48410e28	+	2.48410e28i	0.150651	+	0.150651i	−0.627758	+	0.778409i	$0.716027\pi$
$68$	−1.05313e29	+	1.05313e29i	−0.503894	+	0.503894i
$69$			6.27141e29i			2.37563i
$70$		0			0
$71$	3.63249e29			0.871106			0.435553	−	0.900163i	$-0.356553\pi$
$71$	3.63249e29			0.871106			0.435553	+	0.900163i	$0.356553\pi$
$72$	2.97015e29	+	2.97015e29i	0.569455	+	0.569455i
$73$	5.94905e29	−	5.94905e29i	0.914707	−	0.914707i	−0.0819307	−	0.996638i	$-0.526109\pi$
$73$	5.94905e29	−	5.94905e29i	0.914707	−	0.914707i	0.996638	+	0.0819307i	$0.0261086\pi$
$74$		−	2.13484e30i		−	2.64033i
$75$		0			0
$76$	−7.13902e29			−0.576263
$77$	−1.35832e30	−	1.35832e30i	−0.889510	−	0.889510i
$78$	2.88605e30	−	2.88605e30i	1.53741	−	1.53741i
$79$		−	1.45813e30i		−	0.633522i	−0.948505	−	0.316761i	$-0.897405\pi$
$79$		−	1.45813e30i		−	0.633522i	0.948505	−	0.316761i	$-0.102595\pi$
$80$		0			0
$81$	6.82928e29			0.198891
$82$	2.90189e30	+	2.90189e30i	0.694479	+	0.694479i
$83$	−3.27935e30	+	3.27935e30i	−0.646455	+	0.646455i	−0.952134	−	0.305680i	$-0.901116\pi$
$83$	−3.27935e30	+	3.27935e30i	−0.646455	+	0.646455i	0.305680	+	0.952134i	$0.401116\pi$
$84$		−	1.17195e31i		−	1.90739i
$85$		0			0
$86$	−7.12443e30			−0.795746
$87$	−2.26440e31	−	2.26440e31i	−2.10206	−	2.10206i
$88$	−6.80587e30	+	6.80587e30i	−0.526212	+	0.526212i
$89$			8.42590e29i			0.0543721i	0.999630	+	0.0271861i	$0.00865466\pi$
$89$			8.42590e29i			0.0543721i	−0.999630	+	0.0271861i	$0.991345\pi$
$90$		0			0
$91$	−1.76356e31			−0.797494
$92$	−3.74438e31	−	3.74438e31i	−1.42159	−	1.42159i
$93$	1.42308e30	−	1.42308e30i	0.0454467	−	0.0454467i
$94$		−	6.00877e31i		−	1.61711i
$95$		0			0
$96$	1.11576e32			2.14404
$97$	3.56654e30	+	3.56654e30i	0.0580630	+	0.0580630i	0.735542	−	0.677479i	$-0.236928\pi$
$97$	3.56654e30	+	3.56654e30i	0.0580630	+	0.0580630i	−0.677479	+	0.735542i	$0.736928\pi$
$98$	1.59388e31	−	1.59388e31i	0.220211	−	0.220211i
$99$		−	1.83037e32i		−	2.14969i
$100$		0			0
$101$	1.21714e32			1.03800			0.519001	−	0.854774i	$-0.326304\pi$
$101$	1.21714e32			1.03800			0.519001	+	0.854774i	$0.326304\pi$
$102$	1.25166e32	+	1.25166e32i	0.911765	+	0.911765i
$103$	1.10412e32	−	1.10412e32i	0.688049	−	0.688049i	−0.273752	−	0.961800i	$-0.588265\pi$
$103$	1.10412e32	−	1.10412e32i	0.688049	−	0.688049i	0.961800	+	0.273752i	$0.0882646\pi$
$104$			8.83631e31i			0.471778i
$105$		0			0
$106$	4.18191e32			1.64619
$107$	−8.71531e31	−	8.71531e31i	−0.295218	−	0.295218i	0.543920	−	0.839137i	$-0.316940\pi$
$107$	−8.71531e31	−	8.71531e31i	−0.295218	−	0.295218i	−0.839137	+	0.543920i	$0.816940\pi$
$108$	2.71915e32	−	2.71915e32i	0.793693	−	0.793693i
$109$		−	2.81745e32i		−	0.709631i	−0.934936	−	0.354816i	$-0.884544\pi$
$109$		−	2.81745e32i		−	0.709631i	0.934936	−	0.354816i	$-0.115456\pi$
$110$		0			0
$111$	−1.45520e33			−2.74003
$112$	−2.07492e32	−	2.07492e32i	−0.338464	−	0.338464i
$113$	9.12025e31	−	9.12025e31i	0.129048	−	0.129048i	−0.639633	−	0.768681i	$-0.720914\pi$
$113$	9.12025e31	−	9.12025e31i	0.129048	−	0.129048i	0.768681	+	0.639633i	$0.220914\pi$
$114$			8.48481e32i			1.04271i
$115$		0			0
$116$	2.70395e33			2.51577
$117$	−1.18822e33	−	1.18822e33i	−0.963658	−	0.963658i
$118$	−6.12028e32	+	6.12028e32i	−0.433171	+	0.433171i
$119$		−	7.64841e32i		−	0.472955i
$120$		0			0
$121$	2.08277e33			0.986451
$122$	1.25698e33	+	1.25698e33i	0.521880	+	0.521880i
$123$	1.97805e33	−	1.97805e33i	0.720702	−	0.720702i
$124$			1.69932e32i			0.0543911i
$125$		0			0
$126$	−8.41292e33			−2.08458
$127$	9.03506e32	+	9.03506e32i	0.197275	+	0.197275i	0.798831	−	0.601556i	$-0.205452\pi$
$127$	9.03506e32	+	9.03506e32i	0.197275	+	0.197275i	−0.601556	+	0.798831i	$0.705452\pi$
$128$	−3.64665e33	+	3.64665e33i	−0.702320	+	0.702320i
$129$			4.85632e33i			0.825794i
$130$		0			0
$131$	−8.72300e33			−1.15965			−0.579823	−	0.814743i	$-0.696878\pi$
$131$	−8.72300e33			−1.15965			−0.579823	+	0.814743i	$0.696878\pi$
$132$	1.80934e34	+	1.80934e34i	2.12979	+	2.12979i
$133$	2.59237e33	−	2.59237e33i	0.270440	−	0.270440i
$134$			3.52548e33i			0.326243i
$135$		0			0
$136$	−3.83224e33			−0.279788
$137$	−1.72380e34	−	1.72380e34i	−1.11933	−	1.11933i	−0.991840	−	0.127489i	$-0.959308\pi$
$137$	−1.72380e34	−	1.72380e34i	−1.11933	−	1.11933i	−0.127489	−	0.991840i	$-0.540692\pi$
$138$	−4.45024e34	+	4.45024e34i	−2.57228	+	2.57228i
$139$			1.44247e34i			0.742796i	0.928474	+	0.371398i	$0.121121\pi$
$139$			1.44247e34i			0.742796i	−0.928474	+	0.371398i	$0.878879\pi$
$140$		0			0
$141$	−4.09583e34			−1.67817
$142$	2.57765e34	+	2.57765e34i	0.943214	+	0.943214i
$143$	2.72271e34	−	2.72271e34i	0.890481	−	0.890481i
$144$		−	2.79601e34i		−	0.817972i
$145$		0			0
$146$	8.44300e34			1.98085
$147$	−1.08646e34	−	1.08646e34i	−0.228526	−	0.228526i
$148$	8.68836e34	−	8.68836e34i	1.63965	−	1.63965i
$149$			1.10494e35i			1.87223i	0.351691	+	0.936116i	$0.385607\pi$
$149$			1.10494e35i			1.87223i	−0.351691	+	0.936116i	$0.614393\pi$
$150$		0			0
$151$	−2.34941e34			−0.321609			−0.160804	−	0.986986i	$-0.551409\pi$
$151$	−2.34941e34			−0.321609			−0.160804	+	0.986986i	$0.551409\pi$
$152$	−1.29891e34	−	1.29891e34i	−0.159986	−	0.159986i
$153$	5.15321e34	−	5.15321e34i	0.571498	−	0.571498i
$154$		−	1.92775e35i		−	1.92628i
$155$		0			0
$156$	2.34913e35			1.90947
$157$	−1.07137e34	−	1.07137e34i	−0.0786218	−	0.0786218i	0.666702	−	0.745324i	$-0.267705\pi$
$157$	−1.07137e34	−	1.07137e34i	−0.0786218	−	0.0786218i	−0.745324	+	0.666702i	$0.767705\pi$
$158$	1.03470e35	−	1.03470e35i	0.685963	−	0.685963i
$159$		−	2.85057e35i		−	1.70835i
$160$		0			0
$161$	2.71938e35			1.33431
$162$	4.84611e34	+	4.84611e34i	0.215354	+	0.215354i
$163$	−6.59040e34	+	6.59040e34i	−0.265405	+	0.265405i	−0.827246	−	0.561840i	$-0.810094\pi$
$163$	−6.59040e34	+	6.59040e34i	−0.265405	+	0.265405i	0.561840	+	0.827246i	$0.310094\pi$
$164$			2.36202e35i			0.862545i
$165$		0			0
$166$	−4.65411e35			−1.39993
$167$	2.35707e35	+	2.35707e35i	0.644033	+	0.644033i	0.951545	−	0.307511i	$-0.0994961\pi$
$167$	2.35707e35	+	2.35707e35i	0.644033	+	0.644033i	−0.307511	+	0.951545i	$0.599496\pi$
$168$	2.13230e35	−	2.13230e35i	0.529541	−	0.529541i
$169$			8.92797e34i			0.201635i
$170$		0			0
$171$	3.49329e35			0.653577
$172$	−2.89950e35	−	2.89950e35i	−0.494160	−	0.494160i
$173$	4.05042e35	−	4.05042e35i	0.629162	−	0.629162i	−0.318695	−	0.947857i	$-0.603245\pi$
$173$	4.05042e35	−	4.05042e35i	0.629162	−	0.629162i	0.947857	+	0.318695i	$0.103245\pi$
$174$		−	3.21367e36i		−	4.55212i
$175$		0			0
$176$	6.40683e35			0.755858
$177$	4.17184e35	+	4.17184e35i	0.449527	+	0.449527i
$178$	−5.97909e34	+	5.97909e34i	−0.0588729	+	0.0588729i
$179$			8.24719e35i			0.742433i	0.928546	+	0.371217i	$0.121059\pi$
$179$			8.24719e35i			0.742433i	−0.928546	+	0.371217i	$0.878941\pi$
$180$		0			0
$181$	1.90528e35			0.143582			0.0717911	−	0.997420i	$-0.477128\pi$
$181$	1.90528e35			0.143582			0.0717911	+	0.997420i	$0.477128\pi$
$182$	−1.25144e36	−	1.25144e36i	−0.863508	−	0.863508i
$183$	8.56811e35	−	8.56811e35i	0.541586	−	0.541586i
$184$		−	1.36254e36i		−	0.789342i
$185$		0			0
$186$	2.01966e35			0.0984172
$187$	1.18082e36	+	1.18082e36i	0.528101	+	0.528101i
$188$	2.44545e36	−	2.44545e36i	1.00423	−	1.00423i
$189$			1.97479e36i			0.744959i
$190$		0			0
$191$	−3.03843e36			−0.968534			−0.484267	−	0.874920i	$-0.660914\pi$
$191$	−3.03843e36			−0.968534			−0.484267	+	0.874920i	$0.660914\pi$
$192$	5.86234e36	+	5.86234e36i	1.71890	+	1.71890i
$193$	−2.73652e36	+	2.73652e36i	−0.738382	+	0.738382i	−0.972265	−	0.233883i	$-0.924857\pi$
$193$	−2.73652e36	+	2.73652e36i	−0.738382	+	0.738382i	0.233883	+	0.972265i	$0.424857\pi$
$194$			5.06170e35i			0.125739i
$195$		0			0
$196$	1.29735e36			0.273502
$197$	−4.35345e36	−	4.35345e36i	−0.846008	−	0.846008i	0.143625	−	0.989632i	$-0.454124\pi$
$197$	−4.35345e36	−	4.35345e36i	−0.846008	−	0.846008i	−0.989632	+	0.143625i	$0.954124\pi$
$198$	1.29885e37	−	1.29885e37i	2.32764	−	2.32764i
$199$		−	2.58518e36i		−	0.427406i	−0.976899	−	0.213703i	$-0.931447\pi$
$199$		−	2.58518e36i		−	0.427406i	0.976899	−	0.213703i	$-0.0685526\pi$
$200$		0			0
$201$	2.40312e36			0.338562
$202$	8.63693e36	+	8.63693e36i	1.12393	+	1.12393i
$203$	−9.81876e36	+	9.81876e36i	−1.18065	+	1.18065i
$204$			1.01880e37i			1.13241i
$205$		0			0
$206$	1.56698e37			1.49001
$207$	1.83221e37	+	1.83221e37i	1.61232	+	1.61232i
$208$	4.15911e36	−	4.15911e36i	0.338834	−	0.338834i
$209$			8.00459e36i			0.603946i
$210$		0			0
$211$	−7.07614e36			−0.458434			−0.229217	−	0.973375i	$-0.573617\pi$
$211$	−7.07614e36			−0.458434			−0.229217	+	0.973375i	$0.573617\pi$
$212$	1.70195e37	+	1.70195e37i	1.02229	+	1.02229i
$213$	1.75704e37	−	1.75704e37i	0.978830	−	0.978830i
$214$		−	1.23689e37i		−	0.639310i
$215$		0			0
$216$	9.89470e36			0.440700
$217$	−6.17069e35	−	6.17069e35i	−0.0255257	−	0.0255257i
$218$	1.99929e37	−	1.99929e37i	0.768372	−	0.768372i
$219$		−	5.75511e37i		−	2.05565i
$220$		0			0
$221$	1.53310e37			0.473471
$222$	−1.03262e38	−	1.03262e38i	−2.96684	−	2.96684i
$223$	−2.34997e37	+	2.34997e37i	−0.628324	+	0.628324i	−0.947646	−	0.319322i	$-0.896545\pi$
$223$	−2.34997e37	+	2.34997e37i	−0.628324	+	0.628324i	0.319322	+	0.947646i	$0.396545\pi$
$224$		−	4.83812e37i		−	1.20423i
$225$		0			0
$226$	1.29436e37			0.279461
$227$	−1.03786e37	−	1.03786e37i	−0.208797	−	0.208797i	0.594959	−	0.803756i	$-0.297168\pi$
$227$	−1.03786e37	−	1.03786e37i	−0.208797	−	0.208797i	−0.803756	+	0.594959i	$0.797168\pi$
$228$	−3.45314e37	+	3.45314e37i	−0.647526	+	0.647526i
$229$			7.21842e37i			1.26204i	0.775765	+	0.631022i	$0.217364\pi$
$229$			7.21842e37i			1.26204i	−0.775765	+	0.631022i	$0.782636\pi$
$230$		0			0
$231$	−1.31404e38			−1.99902
$232$	4.91970e37	+	4.91970e37i	0.698442	+	0.698442i
$233$	2.13484e37	−	2.13484e37i	0.282925	−	0.282925i	−0.551349	−	0.834274i	$-0.685887\pi$
$233$	2.13484e37	−	2.13484e37i	0.282925	−	0.282925i	0.834274	+	0.551349i	$0.185887\pi$
$234$		−	1.68634e38i		−	2.08685i
$235$		0			0
$236$	−4.98165e37			−0.537999
$237$	−7.05295e37	−	7.05295e37i	−0.711865	−	0.711865i
$238$	5.42738e37	−	5.42738e37i	0.512105	−	0.512105i
$239$		−	6.82182e37i		−	0.601913i	−0.953638	−	0.300957i	$-0.902694\pi$
$239$		−	6.82182e37i		−	0.601913i	0.953638	−	0.300957i	$-0.0973059\pi$
$240$		0			0
$241$	1.27871e38			0.987411			0.493705	−	0.869629i	$-0.335642\pi$
$241$	1.27871e38			0.987411			0.493705	+	0.869629i	$0.335642\pi$
$242$	1.47795e38	+	1.47795e38i	1.06811	+	1.06811i
$243$	1.20268e38	−	1.20268e38i	0.813674	−	0.813674i
$244$			1.02313e38i			0.648177i
$245$		0			0
$246$	2.80729e38			1.56072
$247$	5.19633e37	+	5.19633e37i	0.270736	+	0.270736i
$248$	−3.09182e36	+	3.09182e36i	−0.0151004	+	0.0151004i
$249$			3.17244e38i			1.45279i
$250$		0			0
$251$	3.15945e38			1.27301			0.636505	−	0.771272i	$-0.280379\pi$
$251$	3.15945e38			1.27301			0.636505	+	0.771272i	$0.280379\pi$
$252$	−3.42389e38	−	3.42389e38i	−1.29453	−	1.29453i
$253$	−4.19837e38	+	4.19837e38i	−1.48988	+	1.48988i
$254$			1.28227e38i			0.427209i
$255$		0			0
$256$	3.00172e36			0.00882125
$257$	4.52206e38	+	4.52206e38i	1.24855	+	1.24855i	0.956360	+	0.292190i	$0.0943839\pi$
$257$	4.52206e38	+	4.52206e38i	1.24855	+	1.24855i	0.292190	+	0.956360i	$0.405616\pi$
$258$	−3.44608e38	+	3.44608e38i	−0.894151	+	0.894151i
$259$			6.30996e38i			1.53897i
$260$		0			0
$261$	−1.32310e39			−2.85329
$262$	−6.18992e38	−	6.18992e38i	−1.25564	−	1.25564i
$263$	−4.78155e35	+	4.78155e35i	−0.000912592	+	0.000912592i	−0.707563	−	0.706650i	$-0.750205\pi$
$263$	−4.78155e35	+	4.78155e35i	−0.000912592	+	0.000912592i	0.706650	+	0.707563i	$0.250205\pi$
$264$			6.58400e38i			1.18257i
$265$		0			0
$266$	3.67914e38			0.585653
$267$	4.07561e37	+	4.07561e37i	0.0610959	+	0.0610959i
$268$	−1.43480e38	+	1.43480e38i	−0.202598	+	0.202598i
$269$			1.31262e39i			1.74623i	0.487516	+	0.873114i	$0.337903\pi$
$269$			1.31262e39i			1.74623i	−0.487516	+	0.873114i	$0.662097\pi$
$270$		0			0
$271$	−1.14469e39			−1.35263			−0.676313	−	0.736615i	$-0.736423\pi$
$271$	−1.14469e39			−1.35263			−0.676313	+	0.736615i	$0.736423\pi$
$272$	1.80377e38	+	1.80377e38i	0.200946	+	0.200946i
$273$	−8.53033e38	+	8.53033e38i	−0.896115	+	0.896115i
$274$		−	2.44645e39i		−	2.42397i
$275$		0			0
$276$	−3.62232e39			−3.19478
$277$	1.10625e39	+	1.10625e39i	0.920821	+	0.920821i	0.997087	−	0.0762666i	$-0.0243000\pi$
$277$	1.10625e39	+	1.10625e39i	0.920821	+	0.920821i	−0.0762666	+	0.997087i	$0.524300\pi$
$278$	−1.02359e39	+	1.02359e39i	−0.804282	+	0.804282i
$279$		−	8.31516e37i		−	0.0616884i
$280$		0			0
$281$	5.81623e38			0.384894			0.192447	−	0.981307i	$-0.438358\pi$
$281$	5.81623e38			0.384894			0.192447	+	0.981307i	$0.438358\pi$
$282$	−2.90644e39	−	2.90644e39i	−1.81709	−	1.81709i
$283$	7.96460e37	−	7.96460e37i	0.0470523	−	0.0470523i	−0.683189	−	0.730241i	$-0.739408\pi$
$283$	7.96460e37	−	7.96460e37i	0.0470523	−	0.0470523i	0.730241	+	0.683189i	$0.239408\pi$
$284$			2.09810e39i			1.17147i
$285$		0			0
$286$	3.86412e39			1.92839
$287$	−8.57713e38	−	8.57713e38i	−0.404792	−	0.404792i
$288$	3.25974e39	−	3.25974e39i	1.45514	−	1.45514i
$289$		−	1.70302e39i		−	0.719207i
$290$		0			0
$291$	3.45027e38			0.130487
$292$	3.43613e39	+	3.43613e39i	1.23011	+	1.23011i
$293$	−2.19598e39	+	2.19598e39i	−0.744297	+	0.744297i	−0.973402	−	0.229105i	$-0.926420\pi$
$293$	−2.19598e39	+	2.19598e39i	−0.744297	+	0.744297i	0.229105	+	0.973402i	$0.426420\pi$
$294$		−	1.54192e39i		−	0.494885i
$295$		0			0
$296$	3.16161e39			0.910418
$297$	−3.04883e39	−	3.04883e39i	−0.831821	−	0.831821i
$298$	−7.84078e39	+	7.84078e39i	−2.02721	+	2.02721i
$299$			5.45090e39i			1.33576i
$300$		0			0
$301$	2.10577e39			0.463818
$302$	−1.66716e39	−	1.66716e39i	−0.348231	−	0.348231i
$303$	5.88730e39	−	5.88730e39i	1.16636	−	1.16636i
$304$			1.22275e39i			0.229806i
$305$		0			0
$306$	7.31353e39			1.23761
$307$	−2.17654e39	−	2.17654e39i	−0.349585	−	0.349585i	0.510370	−	0.859955i	$-0.329508\pi$
$307$	−2.17654e39	−	2.17654e39i	−0.349585	−	0.349585i	−0.859955	+	0.510370i	$0.829508\pi$
$308$	7.84556e39	−	7.84556e39i	1.19622	−	1.19622i
$309$		−	1.06812e40i		−	1.54627i
$310$		0			0
$311$	−6.97928e39			−0.911264			−0.455632	−	0.890168i	$-0.650587\pi$
$311$	−6.97928e39			−0.911264			−0.455632	+	0.890168i	$0.650587\pi$
$312$	4.27413e39	+	4.27413e39i	0.530119	+	0.530119i
$313$	4.49442e39	−	4.49442e39i	0.529620	−	0.529620i	−0.390839	−	0.920459i	$-0.627815\pi$
$313$	4.49442e39	−	4.49442e39i	0.529620	−	0.529620i	0.920459	+	0.390839i	$0.127815\pi$
$314$		−	1.52050e39i		−	0.170260i
$315$		0			0
$316$	8.42202e39			0.851968
$317$	4.08831e39	+	4.08831e39i	0.393184	+	0.393184i	0.875821	−	0.482637i	$-0.160321\pi$
$317$	4.08831e39	+	4.08831e39i	0.393184	+	0.393184i	−0.482637	+	0.875821i	$0.660321\pi$
$318$	2.02279e40	−	2.02279e40i	1.84977	−	1.84977i
$319$		−	3.03179e40i		−	2.63662i
$320$		0			0
$321$	−8.43119e39			−0.663450
$322$	1.92969e40	+	1.92969e40i	1.44476	+	1.44476i
$323$	−2.25360e39	+	2.25360e39i	−0.160560	+	0.160560i
$324$			3.94454e39i			0.267471i
$325$		0			0
$326$	−9.35321e39			−0.574750
$327$	−1.36280e40	−	1.36280e40i	−0.797386	−	0.797386i
$328$	−4.29757e39	+	4.29757e39i	−0.239465	+	0.239465i
$329$			1.77602e40i			0.942567i
$330$		0			0
$331$	−1.94098e39			−0.0934915			−0.0467458	−	0.998907i	$-0.514885\pi$
$331$	−1.94098e39			−0.0934915			−0.0467458	+	0.998907i	$0.514885\pi$
$332$	−1.89413e40	−	1.89413e40i	−0.869360	−	0.869360i
$333$	−4.25142e40	+	4.25142e40i	−1.85963	+	1.85963i
$334$			3.34519e40i			1.39469i
$335$		0			0
$336$	−2.00728e40			−0.760640
$337$	9.81357e39	+	9.81357e39i	0.354608	+	0.354608i	0.861821	−	0.507213i	$-0.169324\pi$
$337$	9.81357e39	+	9.81357e39i	0.354608	+	0.354608i	−0.507213	+	0.861821i	$0.669324\pi$
$338$	−6.33536e39	+	6.33536e39i	−0.218325	+	0.218325i
$339$		−	8.82293e39i		−	0.290013i
$340$		0			0
$341$	1.90535e39			0.0570040
$342$	2.47887e40	+	2.47887e40i	0.707678	+	0.707678i
$343$	−2.78753e40	+	2.78753e40i	−0.759474	+	0.759474i
$344$		−	1.05510e40i		−	0.274383i
$345$		0			0
$346$	5.74843e40			1.36249
$347$	4.20820e40	+	4.20820e40i	0.952412	+	0.952412i	0.998918	−	0.0465061i	$-0.0148087\pi$
$347$	4.20820e40	+	4.20820e40i	0.952412	+	0.952412i	−0.0465061	+	0.998918i	$0.514809\pi$
$348$	1.30790e41	−	1.30790e41i	2.82687	−	2.82687i
$349$		−	1.27846e40i		−	0.263924i	−0.991255	−	0.131962i	$-0.957872\pi$
$349$		−	1.27846e40i		−	0.263924i	0.991255	−	0.131962i	$-0.0421277\pi$
$350$		0			0
$351$	−3.95841e40			−0.745773
$352$	7.46944e40	+	7.46944e40i	1.34464	+	1.34464i
$353$	2.01050e40	−	2.01050e40i	0.345867	−	0.345867i	−0.512701	−	0.858568i	$-0.671355\pi$
$353$	2.01050e40	−	2.01050e40i	0.345867	−	0.345867i	0.858568	+	0.512701i	$0.171355\pi$
$354$			5.92076e40i			0.973475i
$355$		0			0
$356$	−4.86674e39			−0.0731203
$357$	−3.69953e40	−	3.69953e40i	−0.531442	−	0.531442i
$358$	−5.85228e40	+	5.85228e40i	−0.803890	+	0.803890i
$359$		−	5.41303e40i		−	0.711097i	−0.934658	−	0.355549i	$-0.884294\pi$
$359$		−	5.41303e40i		−	0.711097i	0.934658	−	0.355549i	$-0.115706\pi$
$360$		0			0
$361$	6.79216e40			0.816381
$362$	1.35200e40	+	1.35200e40i	0.155468	+	0.155468i
$363$	1.00744e41	−	1.00744e41i	1.10844	−	1.10844i
$364$		−	1.01862e41i		−	1.07248i
$365$		0			0
$366$	1.21600e41			1.17283
$367$	−1.48355e41	−	1.48355e41i	−1.36976	−	1.36976i	−0.860778	−	0.508980i	$-0.830023\pi$
$367$	−1.48355e41	−	1.48355e41i	−1.36976	−	1.36976i	−0.508980	−	0.860778i	$-0.669977\pi$
$368$	−6.41328e40	+	6.41328e40i	−0.566911	+	0.566911i
$369$		−	1.15579e41i		−	0.978266i
$370$		0			0
$371$	−1.23605e41			−0.959518
$372$	8.21960e39	+	8.21960e39i	0.0611172	+	0.0611172i
$373$	1.53770e41	−	1.53770e41i	1.09529	−	1.09529i	0.100342	−	0.994953i	$-0.468006\pi$
$373$	1.53770e41	−	1.53770e41i	1.09529	−	1.09529i	0.994953	−	0.100342i	$-0.0319936\pi$
$374$			1.67584e41i			1.14363i
$375$		0			0
$376$	8.89873e40			0.557600
$377$	−1.96814e41	−	1.96814e41i	−1.18194	−	1.18194i
$378$	−1.40133e41	+	1.40133e41i	−0.806625	+	0.806625i
$379$		−	5.24978e40i		−	0.289677i	−0.989455	−	0.144839i	$-0.953734\pi$
$379$		−	5.24978e40i		−	0.289677i	0.989455	−	0.144839i	$-0.0462663\pi$
$380$		0			0
$381$	8.74052e40			0.443341
$382$	−2.15609e41	−	2.15609e41i	−1.04871	−	1.04871i
$383$	−2.58968e41	+	2.58968e41i	−1.20800	+	1.20800i	−0.236321	+	0.971675i	$0.575942\pi$
$383$	−2.58968e41	+	2.58968e41i	−1.20800	+	1.20800i	−0.971675	+	0.236321i	$0.924058\pi$
$384$			3.52777e41i			1.57834i
$385$		0			0
$386$	−3.88371e41			−1.59901
$387$	1.41879e41	+	1.41879e41i	0.560458	+	0.560458i
$388$	−2.06001e40	+	2.06001e40i	−0.0780839	+	0.0780839i
$389$		−	9.10279e39i		−	0.0331117i	−0.999863	−	0.0165558i	$-0.994730\pi$
$389$		−	9.10279e39i		−	0.0331117i	0.999863	−	0.0165558i	$-0.00527013\pi$
$390$		0			0
$391$	−2.36401e41			−0.792175
$392$	2.36047e40	+	2.36047e40i	0.0759314	+	0.0759314i
$393$	−4.21932e41	+	4.21932e41i	−1.30305	+	1.30305i
$394$		−	6.17850e41i		−	1.83208i
$395$		0			0
$396$	1.05721e42			2.89093
$397$	2.71551e41	+	2.71551e41i	0.713186	+	0.713186i	0.967201	−	0.254014i	$-0.0817509\pi$
$397$	2.71551e41	+	2.71551e41i	0.713186	+	0.713186i	−0.254014	+	0.967201i	$0.581751\pi$
$398$	1.83446e41	−	1.83446e41i	0.462786	−	0.462786i
$399$		−	2.50786e41i		−	0.607767i
$400$		0			0
$401$	−3.41277e41			−0.763479			−0.381739	−	0.924270i	$-0.624675\pi$
$401$	−3.41277e41			−0.763479			−0.381739	+	0.924270i	$0.624675\pi$
$402$	1.70528e41	+	1.70528e41i	0.366588	+	0.366588i
$403$	1.23689e40	−	1.23689e40i	0.0255536	−	0.0255536i
$404$			7.03011e41i			1.39592i
$405$		0			0
$406$	−1.39350e42			−2.55676
$407$	−9.74178e41	−	9.74178e41i	−1.71841	−	1.71841i
$408$	−1.85365e41	+	1.85365e41i	−0.314388	+	0.314388i
$409$		−	4.34442e41i		−	0.708532i	−0.935145	−	0.354266i	$-0.884731\pi$
$409$		−	4.34442e41i		−	0.708532i	0.935145	−	0.354266i	$-0.115269\pi$
$410$		0			0
$411$	−1.66760e42			−2.51550
$412$	6.37729e41	+	6.37729e41i	0.925297	+	0.925297i
$413$	1.80897e41	−	1.80897e41i	0.252483	−	0.252483i
$414$			2.60031e42i			3.49156i
$415$		0			0
$416$	9.69785e41			1.20554
$417$	6.97722e41	+	6.97722e41i	0.834652	+	0.834652i
$418$	−5.68013e41	+	5.68013e41i	−0.653939	+	0.653939i
$419$			1.57134e42i			1.74118i	0.492006	+	0.870592i	$0.336264\pi$
$419$			1.57134e42i			1.74118i	−0.492006	+	0.870592i	$0.663736\pi$
$420$		0			0
$421$	1.69437e41			0.173978			0.0869890	−	0.996209i	$-0.472275\pi$
$421$	1.69437e41			0.173978			0.0869890	+	0.996209i	$0.472275\pi$
$422$	−5.02129e41	−	5.02129e41i	−0.496382	−	0.496382i
$423$	−1.19661e42	+	1.19661e42i	−1.13896	+	1.13896i
$424$			6.19323e41i			0.567628i
$425$		0			0
$426$	2.49362e42			2.11971
$427$	−3.71526e41	−	3.71526e41i	−0.304189	−	0.304189i
$428$	5.03390e41	−	5.03390e41i	0.397012	−	0.397012i
$429$		−	2.63395e42i		−	2.00120i
$430$		0			0
$431$	−2.44401e41			−0.172372			−0.0861860	−	0.996279i	$-0.527468\pi$
$431$	−2.44401e41			−0.172372			−0.0861860	+	0.996279i	$0.527468\pi$
$432$	−4.65728e41	−	4.65728e41i	−0.316513	−	0.316513i
$433$	3.70453e41	−	3.70453e41i	0.242620	−	0.242620i	−0.575313	−	0.817933i	$-0.695120\pi$
$433$	3.70453e41	−	3.70453e41i	0.242620	−	0.242620i	0.817933	+	0.575313i	$0.195120\pi$
$434$		−	8.75755e40i		−	0.0552773i
$435$		0			0
$436$	1.62734e42			0.954321
$437$	−8.01264e41	−	8.01264e41i	−0.452974	−	0.452974i
$438$	4.08388e42	−	4.08388e42i	2.22581	−	2.22581i
$439$			1.71000e42i			0.898596i	0.893382	+	0.449298i	$0.148326\pi$
$439$			1.71000e42i			0.898596i	−0.893382	+	0.449298i	$0.851674\pi$
$440$		0			0
$441$	−6.34825e41			−0.310196
$442$	1.08790e42	+	1.08790e42i	0.512664	+	0.512664i
$443$	−1.78408e42	+	1.78408e42i	−0.810876	+	0.810876i	−0.984765	−	0.173889i	$-0.944366\pi$
$443$	−1.78408e42	+	1.78408e42i	−0.810876	+	0.810876i	0.173889	+	0.984765i	$0.444366\pi$
$444$		−	8.40512e42i		−	3.68482i
$445$		0			0
$446$	−3.33511e42			−1.36067
$447$	5.34461e42	+	5.34461e42i	2.10376	+	2.10376i
$448$	2.54200e42	−	2.54200e42i	0.965444	−	0.965444i
$449$			2.22686e42i			0.816116i	0.912956	+	0.408058i	$0.133794\pi$
$449$			2.22686e42i			0.816116i	−0.912956	+	0.408058i	$0.866206\pi$
$450$		0			0
$451$	2.64840e42			0.903980
$452$	5.26779e41	+	5.26779e41i	0.173545	+	0.173545i
$453$	−1.13641e42	+	1.13641e42i	−0.361380	+	0.361380i
$454$		−	1.47295e42i		−	0.452161i
$455$		0			0
$456$	−1.25656e42			−0.359540
$457$	−2.70839e42	−	2.70839e42i	−0.748258	−	0.748258i	0.225894	−	0.974152i	$-0.427470\pi$
$457$	−2.70839e42	−	2.70839e42i	−0.748258	−	0.748258i	−0.974152	+	0.225894i	$0.927470\pi$
$458$	−5.12225e42	+	5.12225e42i	−1.36651	+	1.36651i
$459$		−	1.71673e42i		−	0.442281i
$460$		0			0
$461$	1.78848e42			0.429803			0.214902	−	0.976636i	$-0.431057\pi$
$461$	1.78848e42			0.429803			0.214902	+	0.976636i	$0.431057\pi$
$462$	−9.32454e42	−	9.32454e42i	−2.16449	−	2.16449i
$463$	2.40450e42	−	2.40450e42i	0.539173	−	0.539173i	−0.384113	−	0.923286i	$-0.625493\pi$
$463$	2.40450e42	−	2.40450e42i	0.539173	−	0.539173i	0.923286	+	0.384113i	$0.125493\pi$
$464$		−	4.63124e42i		−	1.00325i
$465$		0			0
$466$	3.02981e42			0.612690
$467$	5.73323e42	+	5.73323e42i	1.12029	+	1.12029i	0.991698	+	0.128589i	$0.0410446\pi$
$467$	5.73323e42	+	5.73323e42i	1.12029	+	1.12029i	0.128589	+	0.991698i	$0.458955\pi$
$468$	6.86307e42	−	6.86307e42i	1.29594	−	1.29594i
$469$		−	1.04203e42i		−	0.190158i
$470$		0			0
$471$	−1.03644e42			−0.176689
$472$	−9.06387e41	−	9.06387e41i	−0.149363	−	0.149363i
$473$	−3.25104e42	+	3.25104e42i	−0.517898	+	0.517898i
$474$		−	1.00097e43i		−	1.54158i
$475$		0			0
$476$	4.41766e42			0.636035
$477$	−8.32804e42	−	8.32804e42i	−1.15944	−	1.15944i
$478$	4.84082e42	−	4.84082e42i	0.651738	−	0.651738i
$479$			1.59387e42i			0.207532i	0.994602	+	0.103766i	$0.0330893\pi$
$479$			1.59387e42i			0.207532i	−0.994602	+	0.103766i	$0.966911\pi$
$480$		0			0
$481$	−1.26481e43			−1.54065
$482$	9.07381e42	+	9.07381e42i	1.06915	+	1.06915i
$483$	1.31536e43	−	1.31536e43i	1.49931	−	1.49931i
$484$			1.20299e43i			1.32659i
$485$		0			0
$486$	1.70687e43			1.76206
$487$	6.72903e42	+	6.72903e42i	0.672186	+	0.672186i	0.958220	−	0.286034i	$-0.0923370\pi$
$487$	6.72903e42	+	6.72903e42i	0.672186	+	0.672186i	−0.286034	+	0.958220i	$0.592337\pi$
$488$	−1.86153e42	+	1.86153e42i	−0.179951	+	0.179951i
$489$			6.37555e42i			0.596452i
$490$		0			0
$491$	6.77920e42			0.594120			0.297060	−	0.954859i	$-0.403994\pi$
$491$	6.77920e42			0.594120			0.297060	+	0.954859i	$0.403994\pi$
$492$	1.14251e43	+	1.14251e43i	0.969209	+	0.969209i
$493$	8.53566e42	−	8.53566e42i	0.700949	−	0.700949i
$494$			7.37472e42i			0.586292i
$495$		0			0
$496$	2.91054e41			0.0216904
$497$	−7.61877e42	−	7.61877e42i	−0.549772	−	0.549772i
$498$	−2.25119e43	+	2.25119e43i	−1.57305	+	1.57305i
$499$			9.54221e42i			0.645714i	0.946448	+	0.322857i	$0.104643\pi$
$499$			9.54221e42i			0.645714i	−0.946448	+	0.322857i	$0.895357\pi$
$500$		0			0
$501$	2.28023e43			1.44735
$502$	2.24197e43	+	2.24197e43i	1.37839	+	1.37839i
$503$	−1.48419e43	+	1.48419e43i	−0.883898	+	0.883898i	−0.993928	−	0.110030i	$-0.964905\pi$
$503$	−1.48419e43	+	1.48419e43i	−0.883898	+	0.883898i	0.110030	+	0.993928i	$0.464905\pi$
$504$		−	1.24592e43i		−	0.718788i
$505$		0			0
$506$	−5.95840e43			−3.22642
$507$	4.31846e42	+	4.31846e42i	0.226569	+	0.226569i
$508$	−5.21858e42	+	5.21858e42i	−0.265298	+	0.265298i
$509$			3.08574e43i			1.52011i	0.649860	+	0.760054i	$0.274827\pi$
$509$			3.08574e43i			1.52011i	−0.649860	+	0.760054i	$0.725173\pi$
$510$		0			0
$511$	−2.49550e43			−1.15458
$512$	1.58753e43	+	1.58753e43i	0.711871	+	0.711871i
$513$	5.81873e42	−	5.81873e42i	0.252901	−	0.252901i
$514$			6.41778e43i			2.70380i
$515$		0			0
$516$	−2.80497e43			−1.11054
$517$	−2.74194e43	−	2.74194e43i	−1.05247	−	1.05247i
$518$	−4.47760e43	+	4.47760e43i	−1.66636	+	1.66636i
$519$		−	3.91838e43i		−	1.41393i
$520$		0			0
$521$	3.26653e43			1.10837			0.554183	−	0.832395i	$-0.313031\pi$
$521$	3.26653e43			1.10837			0.554183	+	0.832395i	$0.313031\pi$
$522$	−9.38886e43	−	9.38886e43i	−3.08947	−	3.08947i
$523$	6.61183e42	−	6.61183e42i	0.211006	−	0.211006i	−0.593689	−	0.804695i	$-0.702329\pi$
$523$	6.61183e42	−	6.61183e42i	0.211006	−	0.211006i	0.804695	+	0.593689i	$0.202329\pi$
$524$		−	5.03834e43i		−	1.55951i
$525$		0			0
$526$	−6.78606e40			−0.00197627
$527$	5.36431e41	+	5.36431e41i	0.0151546	+	0.0151546i
$528$	3.09898e43	−	3.09898e43i	0.849330	−	0.849330i
$529$		−	4.64430e43i		−	1.23489i
$530$		0			0
$531$	2.43764e43			0.610179
$532$	1.49733e43	+	1.49733e43i	0.363691	+	0.363691i
$533$	1.71926e43	−	1.71926e43i	0.405234	−	0.405234i
$534$			5.78418e42i			0.132307i
$535$		0			0
$536$	−5.22109e42			−0.112493
$537$	3.98916e43	+	3.98916e43i	0.834244	+	0.834244i
$538$	−9.31444e43	+	9.31444e43i	−1.89078	+	1.89078i
$539$		−	1.45465e43i		−	0.286641i
$540$		0			0
$541$	6.87486e43			1.27676			0.638378	−	0.769723i	$-0.279606\pi$
$541$	6.87486e43			1.27676			0.638378	+	0.769723i	$0.279606\pi$
$542$	−8.12279e43	−	8.12279e43i	−1.46459	−	1.46459i
$543$	9.21582e42	−	9.21582e42i	0.161338	−	0.161338i
$544$			4.20588e43i			0.714948i
$545$		0			0
$546$	−1.21064e44			−1.94058
$547$	3.23477e43	+	3.23477e43i	0.503554	+	0.503554i	0.912541	−	0.408986i	$-0.134118\pi$
$547$	3.23477e43	+	3.23477e43i	0.503554	+	0.503554i	−0.408986	+	0.912541i	$0.634118\pi$
$548$	9.95654e43	−	9.95654e43i	1.50529	−	1.50529i
$549$		−	5.00641e43i		−	0.735138i
$550$		0			0
$551$	5.78620e43			0.801619
$552$	−6.59063e43	−	6.59063e43i	−0.886955	−	0.886955i
$553$	−3.05827e43	+	3.05827e43i	−0.399828	+	0.399828i
$554$			1.57000e44i			1.99409i
$555$		0			0
$556$	−8.33159e43			−0.998921
$557$	3.13296e43	+	3.13296e43i	0.364983	+	0.364983i	0.865644	−	0.500661i	$-0.166910\pi$
$557$	3.13296e43	+	3.13296e43i	0.364983	+	0.364983i	−0.500661	+	0.865644i	$0.666910\pi$
$558$	5.90051e42	−	5.90051e42i	0.0667947	−	0.0667947i
$559$			4.22095e43i			0.464324i
$560$		0			0
$561$	1.14232e44			1.18681
$562$	4.12725e43	+	4.12725e43i	0.416754	+	0.416754i
$563$	−6.92248e42	+	6.92248e42i	−0.0679403	+	0.0679403i	−0.740260	−	0.672320i	$-0.765298\pi$
$563$	−6.92248e42	+	6.92248e42i	−0.0679403	+	0.0679403i	0.672320	+	0.740260i	$0.265298\pi$
$564$		−	2.36572e44i		−	2.25683i
$565$		0			0
$566$	1.13035e43			0.101894
$567$	−1.43237e43	−	1.43237e43i	−0.125524	−	0.125524i
$568$	−3.81739e43	+	3.81739e43i	−0.325232	+	0.325232i
$569$			1.60795e44i			1.33192i	0.745989	+	0.665959i	$0.231977\pi$
$569$			1.60795e44i			1.33192i	−0.745989	+	0.665959i	$0.768023\pi$
$570$		0			0
$571$	1.07925e43			0.0845171			0.0422585	−	0.999107i	$-0.486545\pi$
$571$	1.07925e43			0.0845171			0.0422585	+	0.999107i	$0.486545\pi$
$572$	1.57262e44	+	1.57262e44i	1.19753	+	1.19753i
$573$	−1.46969e44	+	1.46969e44i	−1.08831	+	1.08831i
$574$		−	1.21728e44i		−	0.876598i
$575$		0			0
$576$	3.42541e44			2.33320
$577$	4.97328e43	+	4.97328e43i	0.329480	+	0.329480i	0.852389	−	0.522908i	$-0.175153\pi$
$577$	4.97328e43	+	4.97328e43i	0.329480	+	0.329480i	−0.522908	+	0.852389i	$0.675153\pi$
$578$	1.20848e44	−	1.20848e44i	0.778741	−	0.778741i
$579$			2.64731e44i			1.65939i
$580$		0			0
$581$	1.37562e44			0.815981
$582$	2.44835e43	+	2.44835e43i	0.141288	+	0.141288i
$583$	1.90830e44	−	1.90830e44i	1.07140	−	1.07140i
$584$			1.25037e44i			0.683021i
$585$		0			0
$586$	−3.11657e44			−1.61181
$587$	2.76561e43	+	2.76561e43i	0.139182	+	0.139182i	0.773265	−	0.634083i	$-0.218622\pi$
$587$	2.76561e43	+	2.76561e43i	0.139182	+	0.139182i	−0.634083	+	0.773265i	$0.718622\pi$
$588$	6.27530e43	−	6.27530e43i	0.307325	−	0.307325i
$589$			3.63639e42i			0.0173311i
$590$		0			0
$591$	−4.21153e44			−1.90125
$592$	−1.48812e44	−	1.48812e44i	−0.653868	−	0.653868i
$593$	1.50406e44	−	1.50406e44i	0.643264	−	0.643264i	−0.308092	−	0.951356i	$-0.599691\pi$
$593$	1.50406e44	−	1.50406e44i	0.643264	−	0.643264i	0.951356	+	0.308092i	$0.0996906\pi$
$594$		−	4.32695e44i		−	1.80135i
$595$		0			0
$596$	−6.38207e44			−2.51780
$597$	−1.25045e44	−	1.25045e44i	−0.480261	−	0.480261i
$598$	−3.86801e44	+	3.86801e44i	−1.44633	+	1.44633i
$599$		−	3.84482e44i		−	1.39974i	−0.714270	−	0.699870i	$-0.753241\pi$
$599$		−	3.84482e44i		−	1.39974i	0.714270	−	0.699870i	$-0.246759\pi$
$600$		0			0
$601$	−1.63936e44			−0.565825			−0.282912	−	0.959146i	$-0.591301\pi$
$601$	−1.63936e44			−0.565825			−0.282912	+	0.959146i	$0.591301\pi$
$602$	1.49427e44	+	1.49427e44i	0.502211	+	0.502211i
$603$	7.02080e43	−	7.02080e43i	0.229779	−	0.229779i
$604$		−	1.35700e44i		−	0.432503i
$605$		0			0
$606$	8.35536e44			2.52583
$607$	−1.04371e43	−	1.04371e43i	−0.0307298	−	0.0307298i	0.691575	−	0.722305i	$-0.256917\pi$
$607$	−1.04371e43	−	1.04371e43i	−0.0307298	−	0.0307298i	−0.722305	+	0.691575i	$0.756917\pi$
$608$	−1.42555e44	+	1.42555e44i	−0.408814	+	0.408814i
$609$			9.49867e44i			2.65330i
$610$		0			0
$611$	−3.55997e44			−0.943597
$612$	2.97646e44	+	2.97646e44i	0.768558	+	0.768558i
$613$	−5.96306e43	+	5.96306e43i	−0.150003	+	0.150003i	−0.778120	−	0.628116i	$-0.783826\pi$
$613$	−5.96306e43	+	5.96306e43i	−0.150003	+	0.150003i	0.628116	+	0.778120i	$0.283826\pi$
$614$		−	3.08898e44i		−	0.757044i
$615$		0			0
$616$	2.85492e44			0.664206
$617$	3.56284e44	+	3.56284e44i	0.807670	+	0.807670i	0.984281	−	0.176611i	$-0.0565134\pi$
$617$	3.56284e44	+	3.56284e44i	0.807670	+	0.807670i	−0.176611	+	0.984281i	$0.556513\pi$
$618$	7.57949e44	−	7.57949e44i	1.67427	−	1.67427i
$619$		−	3.36795e44i		−	0.724963i	−0.931991	−	0.362481i	$-0.881930\pi$
$619$		−	3.36795e44i		−	0.724963i	0.931991	−	0.362481i	$-0.118070\pi$
$620$		0			0
$621$	6.10379e44			1.24777
$622$	−4.95256e44	−	4.95256e44i	−0.986696	−	0.986696i
$623$	1.76725e43	−	1.76725e43i	0.0343153	−	0.0343153i
$624$		−	4.02352e44i		−	0.761471i
$625$		0			0
$626$	6.37857e44			1.14692
$627$	3.87182e44	+	3.87182e44i	0.678632	+	0.678632i
$628$	6.18813e43	−	6.18813e43i	0.105732	−	0.105732i
$629$		−	5.48538e44i		−	0.913685i
$630$		0			0
$631$	−6.04416e44			−0.956899			−0.478450	−	0.878115i	$-0.658801\pi$
$631$	−6.04416e44			−0.956899			−0.478450	+	0.878115i	$0.658801\pi$
$632$	1.53235e44	+	1.53235e44i	0.236528	+	0.236528i
$633$	−3.42273e44	+	3.42273e44i	−0.515126	+	0.515126i
$634$			5.80221e44i			0.851462i
$635$		0			0
$636$	1.64647e45			2.29741
$637$	−9.44314e43	−	9.44314e43i	−0.128495	−	0.128495i
$638$	2.15138e45	−	2.15138e45i	2.85487	−	2.85487i
$639$		−	1.02665e45i		−	1.32864i
$640$		0			0
$641$	6.60694e44			0.813340			0.406670	−	0.913575i	$-0.366690\pi$
$641$	6.60694e44			0.813340			0.406670	+	0.913575i	$0.366690\pi$
$642$	−5.98285e44	−	5.98285e44i	−0.718369	−	0.718369i
$643$	−8.71333e44	+	8.71333e44i	−1.02049	+	1.02049i	−0.0207038	+	0.999786i	$0.506591\pi$
$643$	−8.71333e44	+	8.71333e44i	−1.02049	+	1.02049i	−0.999786	+	0.0207038i	$0.993409\pi$
$644$			1.57069e45i			1.79439i
$645$		0			0
$646$	−3.19835e44			−0.347701
$647$	−2.03401e44	−	2.03401e44i	−0.215718	−	0.215718i	0.590973	−	0.806691i	$-0.298744\pi$
$647$	−2.03401e44	−	2.03401e44i	−0.215718	−	0.215718i	−0.806691	+	0.590973i	$0.798744\pi$
$648$	−7.17689e43	+	7.17689e43i	−0.0742568	+	0.0742568i
$649$			5.58565e44i			0.563844i
$650$		0			0
$651$	−5.96952e43			−0.0573646
$652$	−3.80656e44	−	3.80656e44i	−0.356921	−	0.356921i
$653$	−1.51723e45	+	1.51723e45i	−1.38816	+	1.38816i	−0.558984	+	0.829178i	$0.688809\pi$
$653$	−1.51723e45	+	1.51723e45i	−1.38816	+	1.38816i	−0.829178	+	0.558984i	$0.811191\pi$
$654$		−	1.93411e45i		−	1.72678i
$655$		0			0
$656$	4.04560e44			0.343971
$657$	−1.68138e45	−	1.68138e45i	−1.39514	−	1.39514i
$658$	−1.26028e45	+	1.26028e45i	−1.02059	+	1.02059i
$659$			4.47404e44i			0.353617i	0.984245	+	0.176809i	$0.0565773\pi$
$659$			4.47404e44i			0.353617i	−0.984245	+	0.176809i	$0.943423\pi$
$660$		0			0
$661$	−1.76365e45			−1.32797			−0.663986	−	0.747745i	$-0.731137\pi$
$661$	−1.76365e45			−1.32797			−0.663986	+	0.747745i	$0.731137\pi$
$662$	−1.37733e44	−	1.37733e44i	−0.101230	−	0.101230i
$663$	7.41560e44	−	7.41560e44i	0.532022	−	0.532022i
$664$		−	6.89254e44i		−	0.482714i
$665$		0			0
$666$	−6.03368e45			−4.02712
$667$	3.03484e45	+	3.03484e45i	1.97752	+	1.97752i
$668$	−1.36142e45	+	1.36142e45i	−0.866104	+	0.866104i
$669$			2.27336e45i			1.41205i
$670$		0			0
$671$	1.14718e45			0.679314
$672$	−2.34020e45	−	2.34020e45i	−1.35314	−	1.35314i
$673$	2.15879e44	−	2.15879e44i	0.121891	−	0.121891i	−0.643530	−	0.765421i	$-0.722531\pi$
$673$	2.15879e44	−	2.15879e44i	0.121891	−	0.121891i	0.765421	+	0.643530i	$0.222531\pi$
$674$			1.39276e45i			0.767923i
$675$		0			0
$676$	−5.15673e44			−0.271161
$677$	−1.11069e45	−	1.11069e45i	−0.570391	−	0.570391i	0.361846	−	0.932238i	$-0.382146\pi$
$677$	−1.11069e45	−	1.11069e45i	−0.570391	−	0.570391i	−0.932238	+	0.361846i	$0.882146\pi$
$678$	6.26083e44	−	6.26083e44i	0.314019	−	0.314019i
$679$		−	1.49609e44i		−	0.0732895i
$680$		0			0
$681$	−1.00402e45			−0.469235
$682$	1.35205e44	+	1.35205e44i	0.0617226	+	0.0617226i
$683$	−1.58313e45	+	1.58313e45i	−0.705968	+	0.705968i	−0.965685	−	0.259717i	$-0.916371\pi$
$683$	−1.58313e45	+	1.58313e45i	−0.705968	+	0.705968i	0.259717	+	0.965685i	$0.416371\pi$
$684$			2.01770e45i			0.878938i
$685$		0			0
$686$	−3.95611e45			−1.64468
$687$	3.49155e45	+	3.49155e45i	1.41811	+	1.41811i
$688$	−4.96617e44	+	4.96617e44i	−0.197064	+	0.197064i
$689$		−	2.47762e45i		−	0.960566i
$690$		0			0
$691$	2.87038e45			1.06241			0.531203	−	0.847244i	$-0.321740\pi$
$691$	2.87038e45			1.06241			0.531203	+	0.847244i	$0.321740\pi$
$692$	2.33949e45	+	2.33949e45i	0.846106	+	0.846106i
$693$	−3.83901e45	+	3.83901e45i	−1.35671	+	1.35671i
$694$			5.97235e45i			2.06250i
$695$		0			0
$696$	4.75931e45			1.56963
$697$	7.45628e44	+	7.45628e44i	0.240324	+	0.240324i
$698$	9.07204e44	−	9.07204e44i	0.285771	−	0.285771i
$699$		−	2.06525e45i		−	0.635825i
$700$		0			0
$701$	5.70234e45			1.67712			0.838561	−	0.544808i	$-0.183398\pi$
$701$	5.70234e45			1.67712			0.838561	+	0.544808i	$0.183398\pi$
$702$	−2.80892e45	−	2.80892e45i	−0.807506	−	0.807506i
$703$	1.85923e45	−	1.85923e45i	0.522454	−	0.522454i
$704$			7.84905e45i			2.15603i
$705$		0			0
$706$	2.85334e45			0.748994
$707$	−2.55282e45	−	2.55282e45i	−0.655104	−	0.655104i
$708$	−2.40963e45	+	2.40963e45i	−0.604530	+	0.604530i
$709$		−	2.03881e45i		−	0.500078i	−0.968236	−	0.250039i	$-0.919557\pi$
$709$		−	2.03881e45i		−	0.500078i	0.968236	−	0.250039i	$-0.0804435\pi$
$710$		0			0
$711$	−4.12109e45			−0.966270
$712$	−8.85479e43	−	8.85479e43i	−0.0203001	−	0.0203001i
$713$	−1.90727e44	+	1.90727e44i	−0.0427543	+	0.0427543i
$714$		−	5.25044e45i		−	1.15087i
$715$		0			0
$716$	−4.76351e45			−0.998433
$717$	−3.29971e45	−	3.29971e45i	−0.676347	−	0.676347i
$718$	3.84113e45	−	3.84113e45i	0.769960	−	0.769960i
$719$			5.56388e45i			1.09073i	0.838200	+	0.545363i	$0.183608\pi$
$719$			5.56388e45i			1.09073i	−0.838200	+	0.545363i	$0.816392\pi$
$720$		0			0
$721$	−4.63154e45			−0.868482
$722$	4.81978e45	+	4.81978e45i	0.883958	+	0.883958i
$723$	6.18510e45	−	6.18510e45i	1.10952	−	1.10952i
$724$			1.10047e45i			0.193091i
$725$		0			0
$726$	1.42977e46			2.40038
$727$	−4.74908e45	−	4.74908e45i	−0.779936	−	0.779936i	0.199884	−	0.979820i	$-0.435943\pi$
$727$	−4.74908e45	−	4.74908e45i	−0.779936	−	0.779936i	−0.979820	+	0.199884i	$0.935943\pi$
$728$	1.85332e45	−	1.85332e45i	0.297748	−	0.297748i
$729$		−	1.03693e46i		−	1.62970i
$730$		0			0
$731$	−1.83059e45			−0.275368
$732$	4.94888e45	+	4.94888e45i	0.728332	+	0.728332i
$733$	4.38889e45	−	4.38889e45i	0.631962	−	0.631962i	−0.316598	−	0.948560i	$-0.602541\pi$
$733$	4.38889e45	−	4.38889e45i	0.631962	−	0.631962i	0.948560	+	0.316598i	$0.102541\pi$
$734$		−	2.10547e46i		−	2.96629i
$735$		0			0
$736$	−1.49539e46			−2.01702
$737$	1.60876e45	+	1.60876e45i	0.212330	+	0.212330i
$738$	8.20159e45	−	8.20159e45i	1.05924	−	1.05924i
$739$		−	7.10193e45i		−	0.897564i	−0.893641	−	0.448782i	$-0.851858\pi$
$739$		−	7.10193e45i		−	0.897564i	0.893641	−	0.448782i	$-0.148142\pi$
$740$		0			0
$741$	5.02693e45			0.608431
$742$	−8.77112e45	−	8.77112e45i	−1.03894	−	1.03894i
$743$	−1.09906e46	+	1.09906e46i	−1.27409	+	1.27409i	−0.330166	+	0.943923i	$0.607105\pi$
$743$	−1.09906e46	+	1.09906e46i	−1.27409	+	1.27409i	−0.943923	+	0.330166i	$0.892895\pi$
$744$			2.99103e44i			0.0339355i
$745$		0			0
$746$	2.18233e46			2.37192
$747$	9.26840e45	+	9.26840e45i	0.985996	+	0.985996i
$748$	−6.82031e45	+	6.82031e45i	−0.710197	+	0.710197i
$749$			3.65589e45i			0.372635i
$750$		0			0
$751$	4.28111e45			0.418136			0.209068	−	0.977901i	$-0.432957\pi$
$751$	4.28111e45			0.418136			0.209068	+	0.977901i	$0.432957\pi$
$752$	−4.18849e45	−	4.18849e45i	−0.400472	−	0.400472i
$753$	1.52823e46	−	1.52823e46i	1.43043	−	1.43043i
$754$		−	2.79322e46i		−	2.55955i
$755$		0			0
$756$	−1.14062e46			−1.00183
$757$	−5.65953e44	−	5.65953e44i	−0.0486684	−	0.0486684i	0.682354	−	0.731022i	$-0.260956\pi$
$757$	−5.65953e44	−	5.65953e44i	−0.0486684	−	0.0486684i	−0.731022	+	0.682354i	$0.760956\pi$
$758$	3.72529e45	−	3.72529e45i	0.313656	−	0.313656i
$759$			4.06150e46i			3.34825i
$760$		0			0
$761$	2.10848e45			0.166654			0.0833270	−	0.996522i	$-0.473445\pi$
$761$	2.10848e45			0.166654			0.0833270	+	0.996522i	$0.473445\pi$
$762$	6.20235e45	+	6.20235e45i	0.480039	+	0.480039i
$763$	−5.90931e45	+	5.90931e45i	−0.447862	+	0.447862i
$764$		−	1.75497e46i		−	1.30250i
$765$		0			0
$766$	−3.67532e46			−2.61598
$767$	3.62603e45	+	3.62603e45i	0.252758	+	0.252758i
$768$	1.45193e44	−	1.45193e44i	0.00991211	−	0.00991211i
$769$			4.87762e45i			0.326127i	0.986616	+	0.163063i	$0.0521375\pi$
$769$			4.87762e45i			0.326127i	−0.986616	+	0.163063i	$0.947862\pi$
$770$		0			0
$771$	4.37464e46			2.80590
$772$	−1.58059e46	−	1.58059e46i	−0.992986	−	0.992986i
$773$	−1.41692e46	+	1.41692e46i	−0.871913	+	0.871913i	−0.992681	−	0.120768i	$-0.961464\pi$
$773$	−1.41692e46	+	1.41692e46i	−0.871913	+	0.871913i	0.120768	+	0.992681i	$0.461464\pi$
$774$			2.01357e46i			1.21370i
$775$		0			0
$776$	−7.49617e44			−0.0433563
$777$	3.05213e46	+	3.05213e46i	1.72928	+	1.72928i
$778$	6.45942e44	−	6.45942e44i	0.0358526	−	0.0358526i
$779$			5.05451e45i			0.274840i
$780$		0			0
$781$	2.35248e46			1.22775
$782$	−1.67752e46	−	1.67752e46i	−0.857749	−	0.857749i
$783$	−2.20388e46	+	2.20388e46i	−1.10408	+	1.10408i
$784$		−	2.22207e45i		−	0.109069i
$785$		0			0
$786$	−5.98813e46			−2.82183
$787$	5.78063e45	+	5.78063e45i	0.266919	+	0.266919i	0.827858	−	0.560938i	$-0.189560\pi$
$787$	5.78063e45	+	5.78063e45i	0.266919	+	0.266919i	−0.560938	+	0.827858i	$0.689560\pi$
$788$	2.51452e46	−	2.51452e46i	1.13772	−	1.13772i
$789$			4.62567e43i			0.00205089i
$790$		0			0
$791$	−3.82575e45			−0.162890
$792$	1.92354e46	+	1.92354e46i	0.802598	+	0.802598i
$793$	7.44712e45	−	7.44712e45i	0.304521	−	0.304521i
$794$			3.85390e46i			1.54444i
$795$		0			0
$796$	1.49318e46			0.574782
$797$	2.66123e46	+	2.66123e46i	1.00404	+	1.00404i	0.999992	+	0.00404579i	$0.00128782\pi$
$797$	2.66123e46	+	2.66123e46i	1.00404	+	1.00404i	0.00404579	+	0.999992i	$0.498712\pi$
$798$	1.77960e46	−	1.77960e46i	0.658076	−	0.658076i
$799$		−	1.54393e46i		−	0.559601i
$800$		0			0
$801$	2.38141e45			0.0829303
$802$	−2.42173e46	−	2.42173e46i	−0.826677	−	0.826677i
$803$	3.85274e46	−	3.85274e46i	1.28920	−	1.28920i
$804$			1.38802e46i			0.455303i
$805$		0			0
$806$	1.75542e45			0.0553377
$807$	6.34912e46	+	6.34912e46i	1.96217	+	1.96217i
$808$	−1.27909e46	+	1.27909e46i	−0.387543	+	0.387543i
$809$			6.15738e46i			1.82902i	0.404559	+	0.914512i	$0.367425\pi$
$809$			6.15738e46i			1.82902i	−0.404559	+	0.914512i	$0.632575\pi$
$810$		0			0
$811$	−5.45389e46			−1.55730			−0.778651	−	0.627457i	$-0.784096\pi$
$811$	−5.45389e46			−1.55730			−0.778651	+	0.627457i	$0.784096\pi$
$812$	−5.67124e46	−	5.67124e46i	−1.58775	−	1.58775i
$813$	−5.53684e46	+	5.53684e46i	−1.51989	+	1.51989i
$814$		−	1.38257e47i		−	3.72132i
$815$		0			0
$816$	1.74497e46			0.451591
$817$	−6.20466e45	−	6.20466e45i	−0.157458	−	0.157458i
$818$	3.08284e46	−	3.08284e46i	0.767182	−	0.767182i
$819$			4.98433e46i			1.21637i
$820$		0			0
$821$	3.41486e46			0.801460			0.400730	−	0.916196i	$-0.368757\pi$
$821$	3.41486e46			0.801460			0.400730	+	0.916196i	$0.368757\pi$
$822$	−1.18335e47	−	1.18335e47i	−2.72372	−	2.72372i
$823$	−1.31774e46	+	1.31774e46i	−0.297462	+	0.297462i	−0.840019	−	0.542557i	$-0.817456\pi$
$823$	−1.31774e46	+	1.31774e46i	−0.297462	+	0.297462i	0.542557	+	0.840019i	$0.317456\pi$
$824$			2.32063e46i			0.513773i
$825$		0			0
$826$	2.56733e46			0.546765
$827$	−5.56010e46	−	5.56010e46i	−1.16143	−	1.16143i	−0.984162	−	0.177272i	$-0.943273\pi$
$827$	−5.56010e46	−	5.56010e46i	−1.16143	−	1.16143i	−0.177272	−	0.984162i	$-0.556727\pi$
$828$	−1.05827e47	+	1.05827e47i	−2.16826	+	2.16826i
$829$		−	3.68580e46i		−	0.740730i	−0.928886	−	0.370365i	$-0.879233\pi$
$829$		−	3.68580e46i		−	0.740730i	0.928886	−	0.370365i	$-0.120767\pi$
$830$		0			0
$831$	1.07018e47			2.06938
$832$	5.09536e46	+	5.09536e46i	0.966499	+	0.966499i
$833$	4.09541e45	−	4.09541e45i	0.0762039	−	0.0762039i
$834$			9.90219e46i			1.80748i
$835$		0			0
$836$	−4.62339e46			−0.812195
$837$	−1.38505e45	−	1.38505e45i	−0.0238702	−	0.0238702i
$838$	−1.11503e47	+	1.11503e47i	−1.88531	+	1.88531i
$839$		−	6.10188e46i		−	1.01221i	−0.862471	−	0.506107i	$-0.831084\pi$
$839$		−	6.10188e46i		−	1.01221i	0.862471	−	0.506107i	$-0.168916\pi$
$840$		0			0
$841$	−1.56532e47			−2.49959
$842$	1.20234e46	+	1.20234e46i	0.188379	+	0.188379i
$843$	2.81331e46	−	2.81331e46i	0.432491	−	0.432491i
$844$		−	4.08713e46i		−	0.616508i
$845$		0			0
$846$	−1.69825e47			−2.46648
$847$	−4.36840e46	−	4.36840e46i	−0.622569	−	0.622569i
$848$	2.91505e46	−	2.91505e46i	0.407674	−	0.407674i
$849$		−	7.70496e45i		−	0.105742i
$850$		0			0
$851$	1.95032e47			2.57770
$852$	1.01485e47	+	1.01485e47i	1.31634	+	1.31634i
$853$	−3.40920e46	+	3.40920e46i	−0.433978	+	0.433978i	−0.889979	−	0.456001i	$-0.849281\pi$
$853$	−3.40920e46	+	3.40920e46i	−0.433978	+	0.433978i	0.456001	+	0.889979i	$0.349281\pi$
$854$		−	5.27277e46i		−	0.658738i
$855$		0			0
$856$	1.83178e46			0.220442
$857$	2.48840e46	+	2.48840e46i	0.293919	+	0.293919i	0.838626	−	0.544707i	$-0.183359\pi$
$857$	2.48840e46	+	2.48840e46i	0.293919	+	0.293919i	−0.544707	+	0.838626i	$0.683359\pi$
$858$	1.86907e47	−	1.86907e47i	2.16685	−	2.16685i
$859$			1.16097e47i			1.32108i	0.750790	+	0.660541i	$0.229673\pi$
$859$			1.16097e47i			1.32108i	−0.750790	+	0.660541i	$0.770327\pi$
$860$		0			0
$861$	−8.29752e46			−0.909699
$862$	−1.73429e46	−	1.73429e46i	−0.186640	−	0.186640i
$863$	7.90109e46	−	7.90109e46i	0.834669	−	0.834669i	−0.153482	−	0.988151i	$-0.549049\pi$
$863$	7.90109e46	−	7.90109e46i	0.834669	−	0.834669i	0.988151	+	0.153482i	$0.0490488\pi$
$864$		−	1.08594e47i		−	1.12613i
$865$		0			0
$866$	5.25753e46			0.525406
$867$	−8.23750e46	−	8.23750e46i	−0.808147	−	0.808147i
$868$	3.56414e45	−	3.56414e45i	0.0343273	−	0.0343273i
$869$		−	9.44315e46i		−	0.892895i
$870$		0			0
$871$	2.08871e46			0.190366
$872$	2.96086e46	+	2.96086e46i	0.264944	+	0.264944i
$873$	1.00801e46	−	1.00801e46i	0.0885599	−	0.0885599i
$874$		−	1.13717e47i		−	0.980939i
$875$		0			0
$876$	3.32411e47			2.76446
$877$	−5.21393e46	−	5.21393e46i	−0.425767	−	0.425767i	0.461417	−	0.887184i	$-0.347341\pi$
$877$	−5.21393e46	−	5.21393e46i	−0.425767	−	0.425767i	−0.887184	+	0.461417i	$0.847341\pi$
$878$	−1.21343e47	+	1.21343e47i	−0.972980	+	0.972980i
$879$			2.12439e47i			1.67268i
$880$		0			0
$881$	−1.91463e47			−1.45368			−0.726842	−	0.686804i	$-0.759013\pi$
$881$	−1.91463e47			−1.45368			−0.726842	+	0.686804i	$0.759013\pi$
$882$	−4.50477e46	−	4.50477e46i	−0.335873	−	0.335873i
$883$	−1.20699e47	+	1.20699e47i	−0.883758	+	0.883758i	−0.993914	−	0.110156i	$-0.964865\pi$
$883$	−1.20699e47	+	1.20699e47i	−0.883758	+	0.883758i	0.110156	+	0.993914i	$0.464865\pi$
$884$			8.85506e46i			0.636730i
$885$		0			0
$886$	−2.53200e47			−1.75600
$887$	1.82028e47	+	1.82028e47i	1.23983	+	1.23983i	0.960072	+	0.279754i	$0.0902528\pi$
$887$	1.82028e47	+	1.82028e47i	1.23983	+	1.23983i	0.279754	+	0.960072i	$0.409747\pi$
$888$	1.52927e47	−	1.52927e47i	1.02300	−	1.02300i
$889$		−	3.79002e46i		−	0.249008i
$890$		0			0
$891$	4.42279e46			0.280319
$892$	−1.35732e47	−	1.35732e47i	−0.844978	−	0.844978i
$893$	5.23303e46	−	5.23303e46i	0.319985	−	0.319985i
$894$			7.58517e47i			4.55580i
$895$		0			0
$896$	1.52969e47			0.886496
$897$	2.63660e47	+	2.63660e47i	1.50095	+	1.50095i
$898$	−1.58020e47	+	1.58020e47i	−0.883672	+	0.883672i
$899$		−	1.37730e46i		−	0.0756614i
$900$		0			0
$901$	1.07452e47			0.569665
$902$	1.87933e47	+	1.87933e47i	0.978809	+	0.978809i
$903$	1.01856e47	−	1.01856e47i	0.521175	−	0.521175i
$904$			1.91689e46i			0.0963615i
$905$		0			0
$906$	−1.61281e47			−0.782587
$907$	−1.34862e47	−	1.34862e47i	−0.642943	−	0.642943i	0.308335	−	0.951278i	$-0.400228\pi$
$907$	−1.34862e47	−	1.34862e47i	−0.642943	−	0.642943i	−0.951278	+	0.308335i	$0.900228\pi$
$908$	5.99459e46	−	5.99459e46i	0.280793	−	0.280793i
$909$		−	3.43999e47i		−	1.58320i
$910$		0			0
$911$	3.40639e47			1.51356			0.756782	−	0.653667i	$-0.226770\pi$
$911$	3.40639e47			1.51356			0.756782	+	0.653667i	$0.226770\pi$
$912$	5.91445e46	+	5.91445e46i	0.258224	+	0.258224i
$913$	−2.12378e47	+	2.12378e47i	−0.911123	+	0.911123i
$914$		−	3.84379e47i		−	1.62039i
$915$		0			0
$916$	−4.16930e47			−1.69721
$917$	1.82956e47	+	1.82956e47i	0.731875	+	0.731875i
$918$	1.21821e47	−	1.21821e47i	0.478892	−	0.478892i
$919$		−	4.16579e47i		−	1.60934i	−0.593720	−	0.804672i	$-0.702341\pi$
$919$		−	4.16579e47i		−	1.60934i	0.593720	−	0.804672i	$-0.297659\pi$
$920$		0			0
$921$	−2.10558e47			−0.785630
$922$	1.26912e47	+	1.26912e47i	0.465381	+	0.465381i
$923$	1.52716e47	−	1.52716e47i	0.550373	−	0.550373i
$924$		−	7.58979e47i		−	2.68830i
$925$		0			0
$926$	3.41250e47			1.16761
$927$	−3.12056e47	−	3.12056e47i	−1.04944	−	1.04944i
$928$	5.39936e47	−	5.39936e47i	1.78474	−	1.78474i
$929$			2.53877e47i			0.824843i	0.910993	+	0.412422i	$0.135317\pi$
$929$			2.53877e47i			0.824843i	−0.910993	+	0.412422i	$0.864683\pi$
$930$		0			0
$931$	2.77622e46			0.0871483
$932$	1.23307e47	+	1.23307e47i	0.380481	+	0.380481i
$933$	−3.37588e47	+	3.37588e47i	−1.02395	+	1.02395i
$934$			8.13670e47i			2.42604i
$935$		0			0
$936$	2.49740e47			0.719573
$937$	−1.08549e47	−	1.08549e47i	−0.307462	−	0.307462i	0.536463	−	0.843924i	$-0.319760\pi$
$937$	−1.08549e47	−	1.08549e47i	−0.307462	−	0.307462i	−0.843924	+	0.536463i	$0.819760\pi$
$938$	7.39433e46	−	7.39433e46i	0.205899	−	0.205899i
$939$		−	4.34791e47i		−	1.19023i
$940$		0			0
$941$	−4.38458e47			−1.16010			−0.580049	−	0.814582i	$-0.696966\pi$
$941$	−4.38458e47			−1.16010			−0.580049	+	0.814582i	$0.696966\pi$
$942$	−7.35466e46	−	7.35466e46i	−0.191315	−	0.191315i
$943$	−2.65107e47	+	2.65107e47i	−0.678006	+	0.678006i
$944$			8.53244e46i			0.214546i
$945$		0			0
$946$	−4.61394e47			−1.12154
$947$	3.04987e47	+	3.04987e47i	0.728923	+	0.728923i	0.970405	−	0.241482i	$-0.0776336\pi$
$947$	3.04987e47	+	3.04987e47i	0.728923	+	0.728923i	−0.241482	+	0.970405i	$0.577634\pi$
$948$	4.07373e47	−	4.07373e47i	0.957325	−	0.957325i
$949$		−	5.00216e47i		−	1.15584i
$950$		0			0
$951$	3.95504e47			0.883613
$952$	8.03772e46	+	8.03772e46i	0.176580	+	0.176580i
$953$	8.22360e46	−	8.22360e46i	0.177654	−	0.177654i	−0.612678	−	0.790332i	$-0.709908\pi$
$953$	8.22360e46	−	8.22360e46i	0.177654	−	0.177654i	0.790332	+	0.612678i	$0.209908\pi$
$954$		−	1.18193e48i		−	2.51083i
$955$		0			0
$956$	3.94023e47			0.809460
$957$	−1.46647e48	−	1.46647e48i	−2.96267	−	2.96267i
$958$	−1.13102e47	+	1.13102e47i	−0.224711	+	0.224711i
$959$			7.23098e47i			1.41286i
$960$		0			0
$961$	−5.28279e47			−0.998364
$962$	−8.97521e47	−	8.97521e47i	−1.66818	−	1.66818i
$963$	−2.46320e47	+	2.46320e47i	−0.450277	+	0.450277i
$964$			7.38571e47i			1.32788i
$965$		0			0
$966$	1.86678e48			3.24684
$967$	3.61146e47	+	3.61146e47i	0.617816	+	0.617816i	0.944971	−	0.327155i	$-0.106090\pi$
$967$	3.61146e47	+	3.61146e47i	0.617816	+	0.617816i	−0.327155	+	0.944971i	$0.606090\pi$
$968$	−2.18879e47	+	2.18879e47i	−0.368297	+	0.368297i
$969$			2.18014e47i			0.360831i
$970$		0			0
$971$	−9.50192e46			−0.152161			−0.0760805	−	0.997102i	$-0.524241\pi$
$971$	−9.50192e46			−0.152161			−0.0760805	+	0.997102i	$0.524241\pi$
$972$	6.94661e47	+	6.94661e47i	1.09424	+	1.09424i
$973$	3.02543e47	−	3.02543e47i	0.468793	−	0.468793i
$974$			9.54996e47i			1.45565i
$975$		0			0
$976$	1.75239e47			0.258484
$977$	1.13097e47	+	1.13097e47i	0.164110	+	0.164110i	0.784385	−	0.620274i	$-0.212979\pi$
$977$	1.13097e47	+	1.13097e47i	0.164110	+	0.164110i	−0.620274	+	0.784385i	$0.712979\pi$
$978$	−4.52415e47	+	4.52415e47i	−0.645825	+	0.645825i
$979$			5.45680e46i			0.0766329i
$980$		0			0
$981$	−7.96295e47			−1.08236
$982$	4.81058e47	+	4.81058e47i	0.643300	+	0.643300i
$983$	8.34409e47	−	8.34409e47i	1.09780	−	1.09780i	0.103131	−	0.994668i	$-0.467114\pi$
$983$	8.34409e47	−	8.34409e47i	1.09780	−	1.09780i	0.994668	−	0.103131i	$-0.0328862\pi$
$984$			4.15747e47i			0.538156i
$985$		0			0
$986$	1.21140e48			1.51794
$987$	8.59059e47	+	8.59059e47i	1.05913	+	1.05913i
$988$	−3.00136e47	+	3.00136e47i	−0.364088	+	0.364088i
$989$		−	6.50863e47i		−	0.776871i
$990$		0			0
$991$	−2.00119e47			−0.231265			−0.115632	−	0.993292i	$-0.536889\pi$
$991$	−2.00119e47			−0.231265			−0.115632	+	0.993292i	$0.536889\pi$
$992$	3.39328e46	+	3.39328e46i	0.0385862	+	0.0385862i
$993$	−9.38850e46	+	9.38850e46i	−0.105053	+	0.105053i
$994$		−	1.08127e48i		−	1.19056i
$995$		0			0
$996$	−1.83238e48			−1.95374
$997$	−3.68986e47	−	3.68986e47i	−0.387157	−	0.387157i	0.486515	−	0.873672i	$-0.338268\pi$
$997$	−3.68986e47	−	3.68986e47i	−0.387157	−	0.387157i	−0.873672	+	0.486515i	$0.838268\pi$
$998$	−6.77123e47	+	6.77123e47i	−0.699164	+	0.699164i
$999$			1.41631e48i			1.43916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.13		30
5.2	odd	4		5.33.c.a.3.3	yes	30
5.3	odd	4	inner	25.33.c.b.18.13		30
5.4	even	2		5.33.c.a.2.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.3	✓	30	5.4	even	2
5.33.c.a.3.3	yes	30	5.2	odd	4
25.33.c.b.7.13		30	1.1	even	1	trivial
25.33.c.b.18.13		30	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(70960.9 + 70960.9i) q^{2} +(4.83700e7 - 4.83700e7i) q^{3} +5.77593e9i q^{4} +6.86476e12 q^{6} +(-2.09740e13 - 2.09740e13i) q^{7} +(-1.05090e14 + 1.05090e14i) q^{8} -2.82629e15i q^{9} +O(q^{10})\)	\(q+(70960.9 + 70960.9i) q^{2} +(4.83700e7 - 4.83700e7i) q^{3} +5.77593e9i q^{4} +6.86476e12 q^{6} +(-2.09740e13 - 2.09740e13i) q^{7} +(-1.05090e14 + 1.05090e14i) q^{8} -2.82629e15i q^{9} +6.47623e16 q^{11} +(2.79382e17 + 2.79382e17i) q^{12} +(4.20416e17 - 4.20416e17i) q^{13} -2.97666e18i q^{14} +9.89284e18 q^{16} +(1.82331e19 + 1.82331e19i) q^{17} +(2.00556e20 - 2.00556e20i) q^{18} +1.23600e20i q^{19} -2.02902e21 q^{21} +(4.59559e21 + 4.59559e21i) q^{22} +(-6.48274e21 + 6.48274e21i) q^{23} +1.01664e22i q^{24} +5.96662e22 q^{26} +(-4.70772e22 - 4.70772e22i) q^{27} +(1.21144e23 - 1.21144e23i) q^{28} -4.68141e23i q^{29} +2.94207e22 q^{31} +(1.15336e24 + 1.15336e24i) q^{32} +(3.13255e24 - 3.13255e24i) q^{33} +2.58767e24i q^{34} +1.63245e25 q^{36} +(-1.50424e25 - 1.50424e25i) q^{37} +(-8.77074e24 + 8.77074e24i) q^{38} -4.06711e25i q^{39} +4.08942e25 q^{41} +(-1.43981e26 - 1.43981e26i) q^{42} +(-5.01997e25 + 5.01997e25i) q^{43} +3.74062e26i q^{44} -9.20042e26 q^{46} +(-4.23386e26 - 4.23386e26i) q^{47} +(4.78517e26 - 4.78517e26i) q^{48} -2.24614e26i q^{49} +1.76387e27 q^{51} +(2.42829e27 + 2.42829e27i) q^{52} +(2.94663e27 - 2.94663e27i) q^{53} -6.68128e27i q^{54} +4.40831e27 q^{56} +(5.97851e27 + 5.97851e27i) q^{57} +(3.32197e28 - 3.32197e28i) q^{58} +8.62486e27i q^{59} +1.77137e28 q^{61} +(2.08772e27 + 2.08772e27i) q^{62} +(-5.92786e28 + 5.92786e28i) q^{63} +1.21198e29i q^{64} +4.44577e29 q^{66} +(2.48410e28 + 2.48410e28i) q^{67} +(-1.05313e29 + 1.05313e29i) q^{68} +6.27141e29i q^{69} +3.63249e29 q^{71} +(2.97015e29 + 2.97015e29i) q^{72} +(5.94905e29 - 5.94905e29i) q^{73} -2.13484e30i q^{74} -7.13902e29 q^{76} +(-1.35832e30 - 1.35832e30i) q^{77} +(2.88605e30 - 2.88605e30i) q^{78} -1.45813e30i q^{79} +6.82928e29 q^{81} +(2.90189e30 + 2.90189e30i) q^{82} +(-3.27935e30 + 3.27935e30i) q^{83} -1.17195e31i q^{84} -7.12443e30 q^{86} +(-2.26440e31 - 2.26440e31i) q^{87} +(-6.80587e30 + 6.80587e30i) q^{88} +8.42590e29i q^{89} -1.76356e31 q^{91} +(-3.74438e31 - 3.74438e31i) q^{92} +(1.42308e30 - 1.42308e30i) q^{93} -6.00877e31i q^{94} +1.11576e32 q^{96} +(3.56654e30 + 3.56654e30i) q^{97} +(1.59388e31 - 1.59388e31i) q^{98} -1.83037e32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8}+O(q^{10}) \) 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8	\( 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8} - 60\!\cdots\!40 q^{11}+ \cdots - 12\!\cdots\!02 q^{98}+O(q^{100}) \) 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8 - 60908362837533640 * q^11 - 444566273630869608 * q^12 - 649759187023107138 * q^13 - 46108906958970522120 * q^16 + 218107661739005884502 * q^17 - 240407468159884203858 * q^18 + 4549905652154594876760 * q^21 + 11386561172247365212944 * q^22 - 13896091629970965206008 * q^23 - 23129486500762683557740 * q^26 - 176388356775702789525960 * q^27 - 59665474478272755491112 * q^28 - 1285786827516670637255040 * q^31 - 3122517776856150857591368 * q^32 + 1644615516923295701112504 * q^33 + 31947551193266858523505980 * q^36 + 126275105375668809211002 * q^37 - 57601564734016178366855880 * q^38 - 155417315271390260892986440 * q^41 - 797836438482097707185724336 * q^42 + 545147034084978191886568152 * q^43 - 3454637097270705106900721640 * q^46 - 2735203198488492729395621848 * q^47 + 3192952350241941373327314192 * q^48 - 6129415060408014316542923040 * q^51 - 6000870590399837156109494028 * q^52 + 11282171275183571262774628682 * q^53 - 47918174764291639802549158800 * q^56 - 44765351794015370451647799120 * q^57 + 29637988346430122895588672480 * q^58 + 50784540875895586667393303160 * q^61 + 218235799024898727529128868024 * q^62 - 213794735887989269330759842008 * q^63 + 1348836243659025586642346421120 * q^66 + 736483403252315334072161239752 * q^67 - 1085395947449178489054935855012 * q^68 + 817740403780342392034746361760 * q^71 + 951267702824572414087545605820 * q^72 + 379868722209495311437504600242 * q^73 - 6689750080738358201358794259600 * q^76 - 6381539826853244422672988941256 * q^77 + 9179143477318522110451614982584 * q^78 - 14239669107938661073624705472070 * q^81 - 2725313872720345364461277817936 * q^82 - 4996401755555614465785455997328 * q^83 + 16049932109847278395442966171960 * q^86 - 36834415428157346041110451524480 * q^87 + 47132513308908068698430156048160 * q^88 - 104150500668224029090357708737840 * q^91 + 18747876848872687606754750486552 * q^92 - 112210213536624471769268225064216 * q^93 + 380819283905835347723966665116960 * q^96 + 155781506757725945270376012026802 * q^97 - 125692870459469366775669291878702 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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