LMFDB - Embedded newform 25.33.c.b.7.1

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			7.1
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-84542.4 - 84542.4i) q^{2} +(-5.85262e6 + 5.85262e6i) q^{3} +9.99987e9i q^{4} +9.89589e11 q^{6} +(4.06221e12 + 4.06221e12i) q^{7} +(4.82306e14 - 4.82306e14i) q^{8} +1.78451e15i q^{9} +O(q^{10})$	\(q+(-84542.4 - 84542.4i) q^{2} +(-5.85262e6 + 5.85262e6i) q^{3} +9.99987e9i q^{4} +9.89589e11 q^{6} +(4.06221e12 + 4.06221e12i) q^{7} +(4.82306e14 - 4.82306e14i) q^{8} +1.78451e15i q^{9} -1.93753e16 q^{11} +(-5.85254e16 - 5.85254e16i) q^{12} +(-6.35202e17 + 6.35202e17i) q^{13} -6.86859e17i q^{14} -3.86015e19 q^{16} +(4.90922e19 + 4.90922e19i) q^{17} +(1.50867e20 - 1.50867e20i) q^{18} +5.30302e17i q^{19} -4.75492e19 q^{21} +(1.63803e21 + 1.63803e21i) q^{22} +(7.61780e21 - 7.61780e21i) q^{23} +5.64550e21i q^{24} +1.07403e23 q^{26} +(-2.12891e22 - 2.12891e22i) q^{27} +(-4.06216e22 + 4.06216e22i) q^{28} -1.82808e21i q^{29} -1.01814e24 q^{31} +(1.19197e24 + 1.19197e24i) q^{32} +(1.13396e23 - 1.13396e23i) q^{33} -8.30074e24i q^{34} -1.78449e25 q^{36} +(-3.94346e24 - 3.94346e24i) q^{37} +(4.48330e22 - 4.48330e22i) q^{38} -7.43519e24i q^{39} +7.58500e25 q^{41} +(4.01992e24 + 4.01992e24i) q^{42} +(1.10287e26 - 1.10287e26i) q^{43} -1.93750e26i q^{44} -1.28805e27 q^{46} +(-6.32156e26 - 6.32156e26i) q^{47} +(2.25920e26 - 2.25920e26i) q^{48} -1.07142e27i q^{49} -5.74636e26 q^{51} +(-6.35194e27 - 6.35194e27i) q^{52} +(3.02021e27 - 3.02021e27i) q^{53} +3.59966e27i q^{54} +3.91846e27 q^{56} +(-3.10365e24 - 3.10365e24i) q^{57} +(-1.54550e26 + 1.54550e26i) q^{58} +1.06369e28i q^{59} -3.36099e27 q^{61} +(8.60759e28 + 8.60759e28i) q^{62} +(-7.24908e27 + 7.24908e27i) q^{63} -3.57525e28i q^{64} -1.91736e28 q^{66} +(-5.01232e28 - 5.01232e28i) q^{67} +(-4.90915e29 + 4.90915e29i) q^{68} +8.91681e28i q^{69} +6.84870e28 q^{71} +(8.60681e29 + 8.60681e29i) q^{72} +(8.59218e29 - 8.59218e29i) q^{73} +6.66779e29i q^{74} -5.30294e27 q^{76} +(-7.87065e28 - 7.87065e28i) q^{77} +(-6.28589e29 + 6.28589e29i) q^{78} +3.56643e30i q^{79} -3.05755e30 q^{81} +(-6.41254e30 - 6.41254e30i) q^{82} +(1.63821e30 - 1.63821e30i) q^{83} -4.75485e29i q^{84} -1.86478e31 q^{86} +(1.06990e28 + 1.06990e28i) q^{87} +(-9.34481e30 + 9.34481e30i) q^{88} +7.81891e30i q^{89} -5.16066e30 q^{91} +(7.61769e31 + 7.61769e31i) q^{92} +(5.95878e30 - 5.95878e30i) q^{93} +1.06888e32i q^{94} -1.39523e31 q^{96} +(3.43333e31 + 3.43333e31i) q^{97} +(-9.05808e31 + 9.05808e31i) q^{98} -3.45754e31i 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 $

$2$	−84542.4	−	84542.4i	−1.29001	−	1.29001i	−0.934775	−	0.355239i	$-0.884399\pi$
$2$	−84542.4	−	84542.4i	−1.29001	−	1.29001i	−0.355239	−	0.934775i	$-0.615601\pi$
$3$	−5.85262e6	+	5.85262e6i	−0.135960	+	0.135960i	−0.771811	−	0.635852i	$-0.780649\pi$
$3$	−5.85262e6	+	5.85262e6i	−0.135960	+	0.135960i	0.635852	+	0.771811i	$0.280649\pi$
$4$			9.99987e9i			2.32828i
$5$		0			0
$5$		0			0
$6$	9.89589e11			0.350780
$7$	4.06221e12	+	4.06221e12i	0.122235	+	0.122235i	0.765578	−	0.643343i	$-0.222453\pi$
$7$	4.06221e12	+	4.06221e12i	0.122235	+	0.122235i	−0.643343	+	0.765578i	$0.722453\pi$
$8$	4.82306e14	−	4.82306e14i	1.71349	−	1.71349i
$9$			1.78451e15i			0.963030i
$10$		0			0
$11$	−1.93753e16			−0.421662			−0.210831	−	0.977522i	$-0.567617\pi$
$11$	−1.93753e16			−0.421662			−0.210831	+	0.977522i	$0.567617\pi$
$12$	−5.85254e16	−	5.85254e16i	−0.316552	−	0.316552i
$13$	−6.35202e17	+	6.35202e17i	−0.954593	+	0.954593i	−0.999013	−	0.0444196i	$-0.985856\pi$
$13$	−6.35202e17	+	6.35202e17i	−0.954593	+	0.954593i	0.0444196	+	0.999013i	$0.485856\pi$
$14$		−	6.86859e17i		−	0.315369i
$15$		0			0
$16$	−3.86015e19			−2.09259
$17$	4.90922e19	+	4.90922e19i	1.00886	+	1.00886i	0.999960	+	0.00889669i	$0.00283194\pi$
$17$	4.90922e19	+	4.90922e19i	1.00886	+	1.00886i	0.00889669	+	0.999960i	$0.497168\pi$
$18$	1.50867e20	−	1.50867e20i	1.24232	−	1.24232i
$19$			5.30302e17i			0.00183851i	1.00000		0.000919254i	$0.000292608\pi$
$19$			5.30302e17i			0.00183851i	−1.00000		0.000919254i	$0.999707\pi$
$20$		0			0
$21$	−4.75492e19			−0.0332380
$22$	1.63803e21	+	1.63803e21i	0.543951	+	0.543951i
$23$	7.61780e21	−	7.61780e21i	1.24218	−	1.24218i	0.283083	−	0.959095i	$-0.408643\pi$
$23$	7.61780e21	−	7.61780e21i	1.24218	−	1.24218i	0.959095	−	0.283083i	$-0.0913571\pi$
$24$			5.64550e21i			0.465932i
$25$		0			0
$26$	1.07403e23			2.46288
$27$	−2.12891e22	−	2.12891e22i	−0.266893	−	0.266893i
$28$	−4.06216e22	+	4.06216e22i	−0.284596	+	0.284596i
$29$		−	1.82808e21i		−	0.00730511i	−0.999993	−	0.00365255i	$-0.998837\pi$
$29$		−	1.82808e21i		−	0.00730511i	0.999993	−	0.00365255i	$-0.00116265\pi$
$30$		0			0
$31$	−1.01814e24			−1.39965			−0.699826	−	0.714313i	$-0.746739\pi$
$31$	−1.01814e24			−1.39965			−0.699826	+	0.714313i	$0.746739\pi$
$32$	1.19197e24	+	1.19197e24i	0.985977	+	0.985977i
$33$	1.13396e23	−	1.13396e23i	0.0573291	−	0.0573291i
$34$		−	8.30074e24i		−	2.60288i
$35$		0			0
$36$	−1.78449e25			−2.24220
$37$	−3.94346e24	−	3.94346e24i	−0.319632	−	0.319632i	0.528994	−	0.848626i	$-0.322569\pi$
$37$	−3.94346e24	−	3.94346e24i	−0.319632	−	0.319632i	−0.848626	+	0.528994i	$0.822569\pi$
$38$	4.48330e22	−	4.48330e22i	0.00237170	−	0.00237170i
$39$		−	7.43519e24i		−	0.259572i
$40$		0			0
$41$	7.58500e25			1.18964			0.594818	−	0.803860i	$-0.297224\pi$
$41$	7.58500e25			1.18964			0.594818	+	0.803860i	$0.297224\pi$
$42$	4.01992e24	+	4.01992e24i	0.0428775	+	0.0428775i
$43$	1.10287e26	−	1.10287e26i	0.807286	−	0.807286i	−0.176937	−	0.984222i	$-0.556619\pi$
$43$	1.10287e26	−	1.10287e26i	0.807286	−	0.807286i	0.984222	+	0.176937i	$0.0566187\pi$
$44$		−	1.93750e26i		−	0.981746i
$45$		0			0
$46$	−1.28805e27			−3.20486
$47$	−6.32156e26	−	6.32156e26i	−1.11496	−	1.11496i	−0.992470	−	0.122488i	$-0.960913\pi$
$47$	−6.32156e26	−	6.32156e26i	−1.11496	−	1.11496i	−0.122488	−	0.992470i	$-0.539087\pi$
$48$	2.25920e26	−	2.25920e26i	0.284508	−	0.284508i
$49$		−	1.07142e27i		−	0.970117i
$50$		0			0
$51$	−5.74636e26			−0.274328
$52$	−6.35194e27	−	6.35194e27i	−2.22256	−	2.22256i
$53$	3.02021e27	−	3.02021e27i	0.779154	−	0.779154i	−0.200533	−	0.979687i	$-0.564267\pi$
$53$	3.02021e27	−	3.02021e27i	0.779154	−	0.779154i	0.979687	+	0.200533i	$0.0642673\pi$
$54$			3.59966e27i			0.688592i
$55$		0			0
$56$	3.91846e27			0.418897
$57$	−3.10365e24	−	3.10365e24i	−0.000249963	−	0.000249963i
$58$	−1.54550e26	+	1.54550e26i	−0.00942370	+	0.00942370i
$59$			1.06369e28i			0.493380i	0.969094	+	0.246690i	$0.0793430\pi$
$59$			1.06369e28i			0.493380i	−0.969094	+	0.246690i	$0.920657\pi$
$60$		0			0
$61$	−3.36099e27			−0.0914513			−0.0457256	−	0.998954i	$-0.514560\pi$
$61$	−3.36099e27			−0.0914513			−0.0457256	+	0.998954i	$0.514560\pi$
$62$	8.60759e28	+	8.60759e28i	1.80557	+	1.80557i
$63$	−7.24908e27	+	7.24908e27i	−0.117716	+	0.117716i
$64$		−	3.57525e28i		−	0.451260i
$65$		0			0
$66$	−1.91736e28			−0.147911
$67$	−5.01232e28	−	5.01232e28i	−0.303978	−	0.303978i	0.538590	−	0.842568i	$-0.318957\pi$
$67$	−5.01232e28	−	5.01232e28i	−0.303978	−	0.303978i	−0.842568	+	0.538590i	$0.818957\pi$
$68$	−4.90915e29	+	4.90915e29i	−2.34890	+	2.34890i
$69$			8.91681e28i			0.337772i
$70$		0			0
$71$	6.84870e28			0.164238			0.0821192	−	0.996623i	$-0.473831\pi$
$71$	6.84870e28			0.164238			0.0821192	+	0.996623i	$0.473831\pi$
$72$	8.60681e29	+	8.60681e29i	1.65015	+	1.65015i
$73$	8.59218e29	−	8.59218e29i	1.32111	−	1.32111i	0.408224	−	0.912882i	$-0.366148\pi$
$73$	8.59218e29	−	8.59218e29i	1.32111	−	1.32111i	0.912882	−	0.408224i	$-0.133852\pi$
$74$			6.66779e29i			0.824659i
$75$		0			0
$76$	−5.30294e27			−0.00428055
$77$	−7.87065e28	−	7.87065e28i	−0.0515417	−	0.0515417i
$78$	−6.28589e29	+	6.28589e29i	−0.334852	+	0.334852i
$79$			3.56643e30i			1.54953i	0.632249	+	0.774765i	$0.282132\pi$
$79$			3.56643e30i			1.54953i	−0.632249	+	0.774765i	$0.717868\pi$
$80$		0			0
$81$	−3.05755e30			−0.890457
$82$	−6.41254e30	−	6.41254e30i	−1.53465	−	1.53465i
$83$	1.63821e30	−	1.63821e30i	0.322938	−	0.322938i	−0.526955	−	0.849893i	$-0.676666\pi$
$83$	1.63821e30	−	1.63821e30i	0.322938	−	0.322938i	0.849893	+	0.526955i	$0.176666\pi$
$84$		−	4.75485e29i		−	0.0773871i
$85$		0			0
$86$	−1.86478e31			−2.08282
$87$	1.06990e28	+	1.06990e28i	0.000993200	+	0.000993200i
$88$	−9.34481e30	+	9.34481e30i	−0.722516	+	0.722516i
$89$			7.81891e30i			0.504552i	0.967655	+	0.252276i	$0.0811791\pi$
$89$			7.81891e30i			0.504552i	−0.967655	+	0.252276i	$0.918821\pi$
$90$		0			0
$91$	−5.16066e30			−0.233369
$92$	7.61769e31	+	7.61769e31i	2.89213	+	2.89213i
$93$	5.95878e30	−	5.95878e30i	0.190296	−	0.190296i
$94$			1.06888e32i			2.87662i
$95$		0			0
$96$	−1.39523e31			−0.268106
$97$	3.43333e31	+	3.43333e31i	0.558943	+	0.558943i	0.929007	−	0.370063i	$-0.120664\pi$
$97$	3.43333e31	+	3.43333e31i	0.558943	+	0.558943i	−0.370063	+	0.929007i	$0.620664\pi$
$98$	−9.05808e31	+	9.05808e31i	−1.25147	+	1.25147i
$99$		−	3.45754e31i		−	0.406074i
$100$		0			0
$101$	8.46617e31			0.722013			0.361007	−	0.932563i	$-0.382433\pi$
$101$	8.46617e31			0.722013			0.361007	+	0.932563i	$0.382433\pi$
$102$	4.85811e31	+	4.85811e31i	0.353887	+	0.353887i
$103$	−1.36234e32	+	1.36234e32i	−0.848966	+	0.848966i	−0.990004	−	0.141038i	$-0.954956\pi$
$103$	−1.36234e32	+	1.36234e32i	−0.848966	+	0.848966i	0.141038	+	0.990004i	$0.454956\pi$
$104$			6.12723e32i			3.27138i
$105$		0			0
$106$	−5.10672e32			−2.01024
$107$	1.53197e32	+	1.53197e32i	0.518930	+	0.518930i	0.917248	−	0.398317i	$-0.130406\pi$
$107$	1.53197e32	+	1.53197e32i	0.518930	+	0.518930i	−0.398317	+	0.917248i	$0.630406\pi$
$108$	2.12888e32	−	2.12888e32i	0.621400	−	0.621400i
$109$		−	2.33989e32i		−	0.589349i	−0.955598	−	0.294674i	$-0.904789\pi$
$109$		−	2.33989e32i		−	0.589349i	0.955598	−	0.294674i	$-0.0952112\pi$
$110$		0			0
$111$	4.61592e31			0.0869141
$112$	−1.56807e32	−	1.56807e32i	−0.255787	−	0.255787i
$113$	−1.27505e32	+	1.27505e32i	−0.180415	+	0.180415i	−0.791537	−	0.611122i	$-0.790719\pi$
$113$	−1.27505e32	+	1.27505e32i	−0.180415	+	0.180415i	0.611122	+	0.791537i	$0.290719\pi$
$114$			5.24781e29i			0.000644911i
$115$		0			0
$116$	1.82805e31			0.0170083
$117$	−1.13353e33	−	1.13353e33i	−0.919302	−	0.919302i
$118$	8.99267e32	−	8.99267e32i	0.636468	−	0.636468i
$119$			3.98846e32i			0.246635i
$120$		0			0
$121$	−1.73598e33			−0.822201
$122$	2.84146e32	+	2.84146e32i	0.117973	+	0.117973i
$123$	−4.43921e32	+	4.43921e32i	−0.161743	+	0.161743i
$124$		−	1.01813e34i		−	3.25877i
$125$		0			0
$126$	1.22571e33			0.303710
$127$	1.02268e33	+	1.02268e33i	0.223297	+	0.223297i	0.809885	−	0.586588i	$-0.199529\pi$
$127$	1.02268e33	+	1.02268e33i	0.223297	+	0.223297i	−0.586588	+	0.809885i	$0.699529\pi$
$128$	2.09689e33	−	2.09689e33i	0.403846	−	0.403846i
$129$			1.29093e33i			0.219517i
$130$		0			0
$131$	9.09503e33			1.20910			0.604551	−	0.796566i	$-0.293352\pi$
$131$	9.09503e33			1.20910			0.604551	+	0.796566i	$0.293352\pi$
$132$	1.13395e33	+	1.13395e33i	0.133478	+	0.133478i
$133$	−2.15420e30	+	2.15420e30i	−0.000224729	+	0.000224729i
$134$			8.47506e33i			0.784271i
$135$		0			0
$136$	4.73549e34			3.45734
$137$	−1.39497e34	−	1.39497e34i	−0.905805	−	0.905805i	0.0901254	−	0.995930i	$-0.471273\pi$
$137$	−1.39497e34	−	1.39497e34i	−0.905805	−	0.905805i	−0.995930	+	0.0901254i	$0.971273\pi$
$138$	7.53849e33	−	7.53849e33i	0.435731	−	0.435731i
$139$		−	9.38369e33i		−	0.483211i	−0.970375	−	0.241606i	$-0.922326\pi$
$139$		−	9.38369e33i		−	0.483211i	0.970375	−	0.241606i	$-0.0776740\pi$
$140$		0			0
$141$	7.39954e33			0.303179
$142$	−5.79006e33	−	5.79006e33i	−0.211870	−	0.211870i
$143$	1.23072e34	−	1.23072e34i	0.402516	−	0.402516i
$144$		−	6.88849e34i		−	2.01523i
$145$		0			0
$146$	−1.45281e35			−3.40849
$147$	6.27064e33	+	6.27064e33i	0.131897	+	0.131897i
$148$	3.94341e34	−	3.94341e34i	0.744191	−	0.744191i
$149$		−	5.90707e34i		−	1.00090i	−0.865765	−	0.500451i	$-0.833167\pi$
$149$		−	5.90707e34i		−	1.00090i	0.865765	−	0.500451i	$-0.166833\pi$
$150$		0			0
$151$	3.87072e34			0.529859			0.264929	−	0.964268i	$-0.414651\pi$
$151$	3.87072e34			0.529859			0.264929	+	0.964268i	$0.414651\pi$
$152$	2.55768e32	+	2.55768e32i	0.00315027	+	0.00315027i
$153$	−8.76057e34	+	8.76057e34i	−0.971560	+	0.971560i
$154$			1.33081e34i			0.132979i
$155$		0			0
$156$	7.43509e34			0.604356
$157$	1.06636e34	+	1.06636e34i	0.0782548	+	0.0782548i	0.745151	−	0.666896i	$-0.232377\pi$
$157$	1.06636e34	+	1.06636e34i	0.0782548	+	0.0782548i	−0.666896	+	0.745151i	$0.732377\pi$
$158$	3.01514e35	−	3.01514e35i	1.99892	−	1.99892i
$159$			3.53523e34i			0.211867i
$160$		0			0
$161$	6.18902e34			0.303674
$162$	2.58492e35	+	2.58492e35i	1.14870	+	1.14870i
$163$	−2.93398e35	+	2.93398e35i	−1.18156	+	1.18156i	−0.202217	+	0.979341i	$0.564815\pi$
$163$	−2.93398e35	+	2.93398e35i	−1.18156	+	1.18156i	−0.979341	+	0.202217i	$0.935185\pi$
$164$			7.58490e35i			2.76980i
$165$		0			0
$166$	−2.76996e35			−0.833191
$167$	6.86082e34	+	6.86082e34i	0.187462	+	0.187462i	0.794598	−	0.607136i	$-0.207682\pi$
$167$	6.86082e34	+	6.86082e34i	0.187462	+	0.187462i	−0.607136	+	0.794598i	$0.707682\pi$
$168$	−2.29332e34	+	2.29332e34i	−0.0569531	+	0.0569531i
$169$		−	3.64185e35i		−	0.822497i
$170$		0			0
$171$	−9.46331e32			−0.00177054
$172$	1.10285e36	+	1.10285e36i	1.87958	+	1.87958i
$173$	3.11746e34	−	3.11746e34i	0.0484243	−	0.0484243i	−0.682480	−	0.730904i	$-0.739099\pi$
$173$	3.11746e34	−	3.11746e34i	0.0484243	−	0.0484243i	0.730904	+	0.682480i	$0.239099\pi$
$174$		−	1.80905e33i		−	0.00256249i
$175$		0			0
$176$	7.47914e35			0.882366
$177$	−6.22535e34	−	6.22535e34i	−0.0670798	−	0.0670798i
$178$	6.61029e35	−	6.61029e35i	0.650880	−	0.650880i
$179$			1.80994e36i			1.62936i	0.579914	+	0.814678i	$0.303086\pi$
$179$			1.80994e36i			1.62936i	−0.579914	+	0.814678i	$0.696914\pi$
$180$		0			0
$181$	9.70489e35			0.731364			0.365682	−	0.930740i	$-0.380836\pi$
$181$	9.70489e35			0.731364			0.365682	+	0.930740i	$0.380836\pi$
$182$	4.36294e35	+	4.36294e35i	0.301049	+	0.301049i
$183$	1.96706e34	−	1.96706e34i	0.0124337	−	0.0124337i
$184$		−	7.34821e36i		−	4.25693i
$185$		0			0
$186$	−1.00754e36			−0.490970
$187$	−9.51175e35	−	9.51175e35i	−0.425397	−	0.425397i
$188$	6.32148e36	−	6.32148e36i	2.59593	−	2.59593i
$189$		−	1.72962e35i		−	0.0652471i
$190$		0			0
$191$	−3.26878e36			−1.04196			−0.520981	−	0.853568i	$-0.674434\pi$
$191$	−3.26878e36			−1.04196			−0.520981	+	0.853568i	$0.674434\pi$
$192$	2.09246e35	+	2.09246e35i	0.0613531	+	0.0613531i
$193$	1.78102e36	−	1.78102e36i	0.480566	−	0.480566i	−0.424747	−	0.905312i	$-0.639637\pi$
$193$	1.78102e36	−	1.78102e36i	0.480566	−	0.480566i	0.905312	+	0.424747i	$0.139637\pi$
$194$		−	5.80524e36i		−	1.44209i
$195$		0			0
$196$	1.07141e37			2.25870
$197$	−3.07795e36	−	3.07795e36i	−0.598139	−	0.598139i	0.341678	−	0.939817i	$-0.389005\pi$
$197$	−3.07795e36	−	3.07795e36i	−0.598139	−	0.598139i	−0.939817	+	0.341678i	$0.889005\pi$
$198$	−2.92309e36	+	2.92309e36i	−0.523841	+	0.523841i
$199$		−	3.66895e36i		−	0.606586i	−0.952897	−	0.303293i	$-0.901914\pi$
$199$		−	3.66895e36i		−	0.606586i	0.952897	−	0.303293i	$-0.0980861\pi$
$200$		0			0
$201$	5.86703e35			0.0826574
$202$	−7.15751e36	−	7.15751e36i	−0.931408	−	0.931408i
$203$	7.42605e33	−	7.42605e33i	0.000892937	−	0.000892937i
$204$		−	5.74628e36i		−	0.638711i
$205$		0			0
$206$	2.30351e37			2.19036
$207$	1.35941e37	+	1.35941e37i	1.19625	+	1.19625i
$208$	2.45197e37	−	2.45197e37i	1.99757	−	1.99757i
$209$		−	1.02747e34i		−	0.000775229i
$210$		0			0
$211$	1.56199e37			1.01195			0.505976	−	0.862547i	$-0.331132\pi$
$211$	1.56199e37			1.01195			0.505976	+	0.862547i	$0.331132\pi$
$212$	3.02017e37	+	3.02017e37i	1.81409	+	1.81409i
$213$	−4.00828e35	+	4.00828e35i	−0.0223298	+	0.0223298i
$214$		−	2.59032e37i		−	1.33886i
$215$		0			0
$216$	−2.05357e37			−0.914639
$217$	−4.13590e36	−	4.13590e36i	−0.171086	−	0.171086i
$218$	−1.97820e37	+	1.97820e37i	−0.760268	+	0.760268i
$219$			1.00574e37i			0.359234i
$220$		0			0
$221$	−6.23669e37			−1.92610
$222$	−3.90241e36	−	3.90241e36i	−0.112120	−	0.112120i
$223$	1.38056e37	−	1.38056e37i	0.369129	−	0.369129i	−0.498030	−	0.867160i	$-0.665943\pi$
$223$	1.38056e37	−	1.38056e37i	0.369129	−	0.369129i	0.867160	+	0.498030i	$0.165943\pi$
$224$			9.68410e36i			0.241041i
$225$		0			0
$226$	2.15592e37			0.465476
$227$	−1.75494e37	−	1.75494e37i	−0.353060	−	0.353060i	0.508187	−	0.861247i	$-0.330316\pi$
$227$	−1.75494e37	−	1.75494e37i	−0.353060	−	0.353060i	−0.861247	+	0.508187i	$0.830316\pi$
$228$	3.10361e34	−	3.10361e34i	0.000581982	−	0.000581982i
$229$		−	1.71079e37i		−	0.299108i	−0.988754	−	0.149554i	$-0.952216\pi$
$229$		−	1.71079e37i		−	0.299108i	0.988754	−	0.149554i	$-0.0477838\pi$
$230$		0			0
$231$	9.21279e35			0.0140152
$232$	−8.81692e35	−	8.81692e35i	−0.0125173	−	0.0125173i
$233$	1.67794e36	−	1.67794e36i	0.0222373	−	0.0222373i	−0.695901	−	0.718138i	$-0.744995\pi$
$233$	1.67794e36	−	1.67794e36i	0.0222373	−	0.0222373i	0.718138	+	0.695901i	$0.244995\pi$
$234$			1.91662e38i			2.37183i
$235$		0			0
$236$	−1.06367e38			−1.14872
$237$	−2.08730e37	−	2.08730e37i	−0.210674	−	0.210674i
$238$	3.37194e37	−	3.37194e37i	0.318162	−	0.318162i
$239$			1.01699e38i			0.897330i	0.893700	+	0.448665i	$0.148100\pi$
$239$			1.01699e38i			0.897330i	−0.893700	+	0.448665i	$0.851900\pi$
$240$		0			0
$241$	−2.09334e37			−0.161647			−0.0808234	−	0.996728i	$-0.525755\pi$
$241$	−2.09334e37			−0.161647			−0.0808234	+	0.996728i	$0.525755\pi$
$242$	1.46764e38	+	1.46764e38i	1.06065	+	1.06065i
$243$	5.73438e37	−	5.73438e37i	0.387959	−	0.387959i
$244$		−	3.36094e37i		−	0.212924i
$245$		0			0
$246$	7.50603e37			0.417300
$247$	−3.36849e35	−	3.36849e35i	−0.00175503	−	0.00175503i
$248$	−4.91054e38	+	4.91054e38i	−2.39830	+	2.39830i
$249$			1.91756e37i			0.0878132i
$250$		0			0
$251$	3.44889e38			1.38963			0.694816	−	0.719187i	$-0.255486\pi$
$251$	3.44889e38			1.38963			0.694816	+	0.719187i	$0.255486\pi$
$252$	−7.24898e37	−	7.24898e37i	−0.274074	−	0.274074i
$253$	−1.47597e38	+	1.47597e38i	−0.523780	+	0.523780i
$254$		−	1.72920e38i		−	0.576112i
$255$		0			0
$256$	−5.08107e38			−1.49319
$257$	1.84454e38	+	1.84454e38i	0.509282	+	0.509282i	0.914306	−	0.405024i	$-0.132737\pi$
$257$	1.84454e38	+	1.84454e38i	0.509282	+	0.509282i	−0.405024	+	0.914306i	$0.632737\pi$
$258$	1.09138e38	−	1.09138e38i	0.283180	−	0.283180i
$259$		−	3.20384e37i		−	0.0781402i
$260$		0			0
$261$	3.26223e36			0.00703504
$262$	−7.68915e38	−	7.68915e38i	−1.55976	−	1.55976i
$263$	4.14571e37	−	4.14571e37i	0.0791237	−	0.0791237i	−0.666437	−	0.745561i	$-0.732182\pi$
$263$	4.14571e37	−	4.14571e37i	0.0791237	−	0.0791237i	0.745561	+	0.666437i	$0.232182\pi$
$264$		−	1.09383e38i		−	0.196466i
$265$		0			0
$266$	3.64242e35			0.000579808
$267$	−4.57611e37	−	4.57611e37i	−0.0685988	−	0.0685988i
$268$	5.01225e38	−	5.01225e38i	0.707743	−	0.707743i
$269$		−	1.03829e39i		−	1.38127i	−0.723201	−	0.690637i	$-0.757330\pi$
$269$		−	1.03829e39i		−	1.38127i	0.723201	−	0.690637i	$-0.242670\pi$
$270$		0			0
$271$	7.15719e38			0.845734			0.422867	−	0.906192i	$-0.361024\pi$
$271$	7.15719e38			0.845734			0.422867	+	0.906192i	$0.361024\pi$
$272$	−1.89503e39	−	1.89503e39i	−2.11112	−	2.11112i
$273$	3.02034e37	−	3.02034e37i	0.0317287	−	0.0317287i
$274$			2.35868e39i			2.33700i
$275$		0			0
$276$	−8.91669e38			−0.786427
$277$	−4.40275e38	−	4.40275e38i	−0.366478	−	0.366478i	0.499713	−	0.866191i	$-0.333439\pi$
$277$	−4.40275e38	−	4.40275e38i	−0.366478	−	0.366478i	−0.866191	+	0.499713i	$0.833439\pi$
$278$	−7.93320e38	+	7.93320e38i	−0.623349	+	0.623349i
$279$		−	1.81688e39i		−	1.34791i
$280$		0			0
$281$	1.10078e39			0.728452			0.364226	−	0.931311i	$-0.381333\pi$
$281$	1.10078e39			0.728452			0.364226	+	0.931311i	$0.381333\pi$
$282$	−6.25575e38	−	6.25575e38i	−0.391105	−	0.391105i
$283$	−6.35069e38	+	6.35069e38i	−0.375178	+	0.375178i	−0.869359	−	0.494181i	$-0.835468\pi$
$283$	−6.35069e38	+	6.35069e38i	−0.375178	+	0.375178i	0.494181	+	0.869359i	$0.335468\pi$
$284$			6.84861e38i			0.382392i
$285$		0			0
$286$	−2.08096e39			−1.03850
$287$	3.08119e38	+	3.08119e38i	0.145415	+	0.145415i
$288$	−2.12709e39	+	2.12709e39i	−0.949525	+	0.949525i
$289$			2.45217e39i			1.03559i
$290$		0			0
$291$	−4.01879e38			−0.151988
$292$	8.59206e39	+	8.59206e39i	3.07590	+	3.07590i
$293$	2.06948e39	−	2.06948e39i	0.701423	−	0.701423i	−0.263293	−	0.964716i	$-0.584809\pi$
$293$	2.06948e39	−	2.06948e39i	0.701423	−	0.701423i	0.964716	+	0.263293i	$0.0848086\pi$
$294$		−	1.06027e39i		−	0.340298i
$295$		0			0
$296$	−3.80391e39			−1.09537
$297$	4.12482e38	+	4.12482e38i	0.112539	+	0.112539i
$298$	−4.99398e39	+	4.99398e39i	−1.29118	+	1.29118i
$299$			9.67768e39i			2.37155i
$300$		0			0
$301$	8.96015e38			0.197357
$302$	−3.27240e39	−	3.27240e39i	−0.683526	−	0.683526i
$303$	−4.95493e38	+	4.95493e38i	−0.0981647	+	0.0981647i
$304$		−	2.04704e37i		−	0.00384724i
$305$		0			0
$306$	1.48128e40			2.50665
$307$	3.61620e39	+	3.61620e39i	0.580816	+	0.580816i	0.935128	−	0.354311i	$-0.115285\pi$
$307$	3.61620e39	+	3.61620e39i	0.580816	+	0.580816i	−0.354311	+	0.935128i	$0.615285\pi$
$308$	7.87055e38	−	7.87055e38i	0.120003	−	0.120003i
$309$		−	1.59465e39i		−	0.230850i
$310$		0			0
$311$	−6.85765e39			−0.895383			−0.447692	−	0.894188i	$-0.647754\pi$
$311$	−6.85765e39			−0.895383			−0.447692	+	0.894188i	$0.647754\pi$
$312$	−3.58604e39	−	3.58604e39i	−0.444776	−	0.444776i
$313$	7.78586e39	−	7.78586e39i	0.917481	−	0.917481i	−0.0793643	−	0.996846i	$-0.525289\pi$
$313$	7.78586e39	−	7.78586e39i	0.917481	−	0.917481i	0.996846	+	0.0793643i	$0.0252890\pi$
$314$		−	1.80306e39i		−	0.201900i
$315$		0			0
$316$	−3.56638e40			−3.60773
$317$	−4.58100e39	−	4.58100e39i	−0.440567	−	0.440567i	0.451635	−	0.892203i	$-0.350841\pi$
$317$	−4.58100e39	−	4.58100e39i	−0.440567	−	0.440567i	−0.892203	+	0.451635i	$0.850841\pi$
$318$	2.98877e39	−	2.98877e39i	0.273312	−	0.273312i
$319$			3.54195e37i			0.00308029i
$320$		0			0
$321$	−1.79320e39			−0.141107
$322$	−5.23235e39	−	5.23235e39i	−0.391744	−	0.391744i
$323$	−2.60337e37	+	2.60337e37i	−0.00185479	+	0.00185479i
$324$		−	3.05751e40i		−	2.07323i
$325$		0			0
$326$	4.96091e40			3.04845
$327$	1.36945e39	+	1.36945e39i	0.0801277	+	0.0801277i
$328$	3.65829e40	−	3.65829e40i	2.03843	−	2.03843i
$329$		−	5.13591e39i		−	0.272573i
$330$		0			0
$331$	3.21776e40			1.54991			0.774954	−	0.632017i	$-0.217773\pi$
$331$	3.21776e40			1.54991			0.774954	+	0.632017i	$0.217773\pi$
$332$	1.63819e40	+	1.63819e40i	0.751890	+	0.751890i
$333$	7.03716e39	−	7.03716e39i	0.307815	−	0.307815i
$334$		−	1.16006e40i		−	0.483657i
$335$		0			0
$336$	1.83547e39			0.0695534
$337$	1.12808e40	+	1.12808e40i	0.407624	+	0.407624i	0.880909	−	0.473285i	$-0.156932\pi$
$337$	1.12808e40	+	1.12808e40i	0.407624	+	0.407624i	−0.473285	+	0.880909i	$0.656932\pi$
$338$	−3.07890e40	+	3.07890e40i	−1.06103	+	1.06103i
$339$		−	1.49248e39i		−	0.0490583i
$340$		0			0
$341$	1.97267e40			0.590181
$342$	8.00051e37	+	8.00051e37i	0.00228402	+	0.00228402i
$343$	8.83878e39	−	8.83878e39i	0.240817	−	0.240817i
$344$		−	1.06384e41i		−	2.76656i
$345$		0			0
$346$	−5.27115e39			−0.124936
$347$	2.64560e40	+	2.64560e40i	0.598759	+	0.598759i	0.939982	−	0.341223i	$-0.110841\pi$
$347$	2.64560e40	+	2.64560e40i	0.598759	+	0.598759i	−0.341223	+	0.939982i	$0.610841\pi$
$348$	−1.06989e38	+	1.06989e38i	−0.00231244	+	0.00231244i
$349$			2.73612e40i			0.564845i	0.959290	+	0.282422i	$0.0911379\pi$
$349$			2.73612e40i			0.564845i	−0.959290	+	0.282422i	$0.908862\pi$
$350$		0			0
$351$	2.70458e40			0.509548
$352$	−2.30948e40	−	2.30948e40i	−0.415749	−	0.415749i
$353$	−3.76900e39	+	3.76900e39i	−0.0648382	+	0.0648382i	−0.738782	−	0.673944i	$-0.764599\pi$
$353$	−3.76900e39	+	3.76900e39i	−0.0648382	+	0.0648382i	0.673944	+	0.738782i	$0.264599\pi$
$354$			1.05261e40i			0.173068i
$355$		0			0
$356$	−7.81881e40			−1.17474
$357$	−2.33429e39	−	2.33429e39i	−0.0335324	−	0.0335324i
$358$	1.53017e41	−	1.53017e41i	2.10189	−	2.10189i
$359$			8.73548e40i			1.14756i	0.819009	+	0.573780i	$0.194524\pi$
$359$			8.73548e40i			1.14756i	−0.819009	+	0.573780i	$0.805476\pi$
$360$		0			0
$361$	8.31982e40			0.999997
$362$	−8.20475e40	−	8.20475e40i	−0.943470	−	0.943470i
$363$	1.01600e40	−	1.01600e40i	0.111786	−	0.111786i
$364$		−	5.16059e40i		−	0.543347i
$365$		0			0
$366$	−3.32600e39			−0.0320793
$367$	−2.42775e40	−	2.42775e40i	−0.224154	−	0.224154i	0.586091	−	0.810245i	$-0.300666\pi$
$367$	−2.42775e40	−	2.42775e40i	−0.224154	−	0.224154i	−0.810245	+	0.586091i	$0.800666\pi$
$368$	−2.94058e41	+	2.94058e41i	−2.59937	+	2.59937i
$369$			1.35355e41i			1.14566i
$370$		0			0
$371$	2.45375e40			0.190479
$372$	5.95870e40	+	5.95870e40i	0.443062	+	0.443062i
$373$	1.24174e41	−	1.24174e41i	0.884484	−	0.884484i	−0.109502	−	0.993987i	$-0.534926\pi$
$373$	1.24174e41	−	1.24174e41i	0.884484	−	0.884484i	0.993987	+	0.109502i	$0.0349257\pi$
$374$			1.60829e41i			1.09754i
$375$		0			0
$376$	−6.09785e41			−3.82095
$377$	1.16120e39	+	1.16120e39i	0.00697341	+	0.00697341i
$378$	−1.46226e40	+	1.46226e40i	−0.0841697	+	0.0841697i
$379$		−	1.33324e41i		−	0.735667i	−0.929892	−	0.367833i	$-0.880100\pi$
$379$		−	1.33324e41i		−	0.735667i	0.929892	−	0.367833i	$-0.119900\pi$
$380$		0			0
$381$	−1.19708e40			−0.0607187
$382$	2.76351e41	+	2.76351e41i	1.34415	+	1.34415i
$383$	−1.21302e41	+	1.21302e41i	−0.565833	+	0.565833i	−0.930958	−	0.365125i	$-0.881026\pi$
$383$	−1.21302e41	+	1.21302e41i	−0.565833	+	0.565833i	0.365125	+	0.930958i	$0.381026\pi$
$384$			2.45445e40i			0.109813i
$385$		0			0
$386$	−3.01144e41			−1.23987
$387$	1.96808e41	+	1.96808e41i	0.777440	+	0.777440i
$388$	−3.43328e41	+	3.43328e41i	−1.30137	+	1.30137i
$389$			2.36463e41i			0.860139i	0.902796	+	0.430070i	$0.141511\pi$
$389$			2.36463e41i			0.860139i	−0.902796	+	0.430070i	$0.858489\pi$
$390$		0			0
$391$	7.47949e41			2.50636
$392$	−5.16754e41	−	5.16754e41i	−1.66229	−	1.66229i
$393$	−5.32297e40	+	5.32297e40i	−0.164389	+	0.164389i
$394$			5.20435e41i			1.54322i
$395$		0			0
$396$	3.45750e41			0.945451
$397$	1.07880e41	+	1.07880e41i	0.283329	+	0.283329i	0.834435	−	0.551106i	$-0.185794\pi$
$397$	1.07880e41	+	1.07880e41i	0.283329	+	0.283329i	−0.551106	+	0.834435i	$0.685794\pi$
$398$	−3.10182e41	+	3.10182e41i	−0.782505	+	0.782505i
$399$		−	2.52154e37i		−	6.11082e-5i
$400$		0			0
$401$	1.19971e41			0.268391			0.134196	−	0.990955i	$-0.457155\pi$
$401$	1.19971e41			0.268391			0.134196	+	0.990955i	$0.457155\pi$
$402$	−4.96013e40	−	4.96013e40i	−0.106629	−	0.106629i
$403$	6.46724e41	−	6.46724e41i	1.33610	−	1.33610i
$404$			8.46606e41i			1.68105i
$405$		0			0
$406$	−1.25563e39			−0.00230380
$407$	7.64057e40	+	7.64057e40i	0.134777	+	0.134777i
$408$	−2.77150e41	+	2.77150e41i	−0.470059	+	0.470059i
$409$		−	7.26242e41i		−	1.18443i	−0.805781	−	0.592214i	$-0.798254\pi$
$409$		−	7.26242e41i		−	1.18443i	0.805781	−	0.592214i	$-0.201746\pi$
$410$		0			0
$411$	1.63284e41			0.246306
$412$	−1.36232e42	−	1.36232e42i	−1.97663	−	1.97663i
$413$	−4.32093e40	+	4.32093e40i	−0.0603081	+	0.0603081i
$414$		−	2.29855e42i		−	3.08637i
$415$		0			0
$416$	−1.51429e42			−1.88241
$417$	5.49192e40	+	5.49192e40i	0.0656972	+	0.0656972i
$418$	−8.68651e38	+	8.68651e38i	−0.00100006	+	0.00100006i
$419$			1.35103e42i			1.49706i	0.663099	+	0.748532i	$0.269241\pi$
$419$			1.35103e42i			1.49706i	−0.663099	+	0.748532i	$0.730759\pi$
$420$		0			0
$421$	−5.85490e41			−0.601182			−0.300591	−	0.953753i	$-0.597184\pi$
$421$	−5.85490e41			−0.601182			−0.300591	+	0.953753i	$0.597184\pi$
$422$	−1.32055e42	−	1.32055e42i	−1.30543	−	1.30543i
$423$	1.12809e42	−	1.12809e42i	1.07374	−	1.07374i
$424$		−	2.91333e42i		−	2.67015i
$425$		0			0
$426$	6.77740e40			0.0576115
$427$	−1.36531e40	−	1.36531e40i	−0.0111785	−	0.0111785i
$428$	−1.53195e42	+	1.53195e42i	−1.20821	+	1.20821i
$429$			1.44059e41i			0.109452i
$430$		0			0
$431$	7.83392e41			0.552513			0.276257	−	0.961084i	$-0.410906\pi$
$431$	7.83392e41			0.552513			0.276257	+	0.961084i	$0.410906\pi$
$432$	8.21790e41	+	8.21790e41i	0.558497	+	0.558497i
$433$	5.60168e41	−	5.60168e41i	0.366870	−	0.366870i	−0.499465	−	0.866334i	$-0.666470\pi$
$433$	5.60168e41	−	5.60168e41i	0.366870	−	0.366870i	0.866334	+	0.499465i	$0.166470\pi$
$434$			6.99318e41i			0.441407i
$435$		0			0
$436$	2.33986e42			1.37217
$437$	4.03973e39	+	4.03973e39i	0.00228375	+	0.00228375i
$438$	8.50273e41	−	8.50273e41i	0.463417	−	0.463417i
$439$			2.47115e42i			1.29857i	0.760543	+	0.649287i	$0.224933\pi$
$439$			2.47115e42i			1.29857i	−0.760543	+	0.649287i	$0.775067\pi$
$440$		0			0
$441$	1.91197e42			0.934252
$442$	5.27265e42	+	5.27265e42i	2.48469	+	2.48469i
$443$	−1.12421e40	+	1.12421e40i	−0.00510960	+	0.00510960i	−0.709657	−	0.704547i	$-0.751150\pi$
$443$	−1.12421e40	+	1.12421e40i	−0.00510960	+	0.00510960i	0.704547	+	0.709657i	$0.251150\pi$
$444$			4.61585e41i			0.202360i
$445$		0			0
$446$	−2.33432e42			−0.952365
$447$	3.45718e41	+	3.45718e41i	0.136082	+	0.136082i
$448$	1.45234e41	−	1.45234e41i	0.0551595	−	0.0551595i
$449$			1.14064e42i			0.418028i	0.977913	+	0.209014i	$0.0670255\pi$
$449$			1.14064e42i			0.418028i	−0.977913	+	0.209014i	$0.932975\pi$
$450$		0			0
$451$	−1.46962e42			−0.501625
$452$	−1.27503e42	−	1.27503e42i	−0.420056	−	0.420056i
$453$	−2.26538e41	+	2.26538e41i	−0.0720395	+	0.0720395i
$454$			2.96734e42i			0.910905i
$455$		0			0
$456$	−2.99382e39			−0.000856620
$457$	2.06814e42	+	2.06814e42i	0.571375	+	0.571375i	0.932513	−	0.361138i	$-0.117612\pi$
$457$	2.06814e42	+	2.06814e42i	0.571375	+	0.571375i	−0.361138	+	0.932513i	$0.617612\pi$
$458$	−1.44634e42	+	1.44634e42i	−0.385854	+	0.385854i
$459$		−	2.09026e42i		−	0.538514i
$460$		0			0
$461$	7.62382e41			0.183214			0.0916068	−	0.995795i	$-0.470800\pi$
$461$	7.62382e41			0.183214			0.0916068	+	0.995795i	$0.470800\pi$
$462$	−7.78871e40	−	7.78871e40i	−0.0180798	−	0.0180798i
$463$	−3.25834e42	+	3.25834e42i	−0.730634	+	0.730634i	−0.970745	−	0.240111i	$-0.922816\pi$
$463$	−3.25834e42	+	3.25834e42i	−0.730634	+	0.730634i	0.240111	+	0.970745i	$0.422816\pi$
$464$			7.05665e40i			0.0152866i
$465$		0			0
$466$	−2.83715e41			−0.0573729
$467$	−3.85475e42	−	3.85475e42i	−0.753228	−	0.753228i	0.221852	−	0.975080i	$-0.428790\pi$
$467$	−3.85475e42	−	3.85475e42i	−0.753228	−	0.753228i	−0.975080	+	0.221852i	$0.928790\pi$
$468$	1.13351e43	−	1.13351e43i	2.14039	−	2.14039i
$469$		−	4.07222e41i		−	0.0743132i
$470$		0			0
$471$	−1.24820e41			−0.0212790
$472$	5.13022e42	+	5.13022e42i	0.845404	+	0.845404i
$473$	−2.13683e42	+	2.13683e42i	−0.340402	+	0.340402i
$474$			3.52930e42i			0.543544i
$475$		0			0
$476$	−3.98841e42			−0.574233
$477$	5.38961e42	+	5.38961e42i	0.750349	+	0.750349i
$478$	8.59792e42	−	8.59792e42i	1.15757	−	1.15757i
$479$		−	1.17477e43i		−	1.52963i	−0.644252	−	0.764813i	$-0.722831\pi$
$479$		−	1.17477e43i		−	1.52963i	0.644252	−	0.764813i	$-0.277169\pi$
$480$		0			0
$481$	5.00979e42			0.610237
$482$	1.76976e42	+	1.76976e42i	0.208527	+	0.208527i
$483$	−3.62220e41	+	3.62220e41i	−0.0412875	+	0.0412875i
$484$		−	1.73595e43i		−	1.91431i
$485$		0			0
$486$	−9.69596e42			−1.00095
$487$	−9.46302e42	−	9.46302e42i	−0.945293	−	0.945293i	0.0532860	−	0.998579i	$-0.483030\pi$
$487$	−9.46302e42	−	9.46302e42i	−0.945293	−	0.945293i	−0.998579	+	0.0532860i	$0.983030\pi$
$488$	−1.62102e42	+	1.62102e42i	−0.156701	+	0.156701i
$489$		−	3.43429e42i		−	0.321288i
$490$		0			0
$491$	−8.07646e42			−0.707811			−0.353905	−	0.935281i	$-0.615147\pi$
$491$	−8.07646e42			−0.707811			−0.353905	+	0.935281i	$0.615147\pi$
$492$	−4.43915e42	−	4.43915e42i	−0.376581	−	0.376581i
$493$	8.97443e40	−	8.97443e40i	0.00736981	−	0.00736981i
$494$			5.69560e40i			0.00452802i
$495$		0			0
$496$	3.93017e43			2.92890
$497$	2.78209e41	+	2.78209e41i	0.0200756	+	0.0200756i
$498$	1.62115e42	−	1.62115e42i	0.113280	−	0.113280i
$499$			5.86916e42i			0.397162i	0.980085	+	0.198581i	$0.0636332\pi$
$499$			5.86916e42i			0.397162i	−0.980085	+	0.198581i	$0.936367\pi$
$500$		0			0
$501$	−8.03076e41			−0.0509745
$502$	−2.91578e43	−	2.91578e43i	−1.79265	−	1.79265i
$503$	−9.39744e42	+	9.39744e42i	−0.559657	+	0.559657i	−0.929210	−	0.369553i	$-0.879511\pi$
$503$	−9.39744e42	+	9.39744e42i	−0.559657	+	0.559657i	0.369553	+	0.929210i	$0.379511\pi$
$504$			6.99254e42i			0.403410i
$505$		0			0
$506$	2.49564e43			1.35137
$507$	2.13143e42	+	2.13143e42i	0.111826	+	0.111826i
$508$	−1.02267e43	+	1.02267e43i	−0.519896	+	0.519896i
$509$			1.85122e43i			0.911957i	0.889991	+	0.455978i	$0.150711\pi$
$509$			1.85122e43i			0.911957i	−0.889991	+	0.455978i	$0.849289\pi$
$510$		0			0
$511$	6.98066e42			0.322970
$512$	3.39505e43	+	3.39505e43i	1.52239	+	1.52239i
$513$	1.12896e40	−	1.12896e40i	0.000490685	−	0.000490685i
$514$		−	3.11884e43i		−	1.31396i
$515$		0			0
$516$	−1.29091e43			−0.511095
$517$	1.22482e43	+	1.22482e43i	0.470136	+	0.470136i
$518$	−2.70860e42	+	2.70860e42i	−0.100802	+	0.100802i
$519$			3.64906e41i			0.0131675i
$520$		0			0
$521$	−4.40184e43			−1.49359			−0.746793	−	0.665056i	$-0.768408\pi$
$521$	−4.40184e43			−1.49359			−0.746793	+	0.665056i	$0.768408\pi$
$522$	−2.75797e41	−	2.75797e41i	−0.00907530	−	0.00907530i
$523$	2.58361e43	−	2.58361e43i	0.824516	−	0.824516i	−0.162236	−	0.986752i	$-0.551871\pi$
$523$	2.58361e43	−	2.58361e43i	0.824516	−	0.824516i	0.986752	+	0.162236i	$0.0518705\pi$
$524$			9.09490e43i			2.81512i
$525$		0			0
$526$	−7.00976e42			−0.204141
$527$	−4.99827e43	−	4.99827e43i	−1.41205	−	1.41205i
$528$	−4.37726e42	+	4.37726e42i	−0.119966	+	0.119966i
$529$		−	7.84527e43i		−	2.08601i
$530$		0			0
$531$	−1.89816e43			−0.475140
$532$	−2.15417e40	−	2.15417e40i	−0.000523231	−	0.000523231i
$533$	−4.81801e43	+	4.81801e43i	−1.13562	+	1.13562i
$534$			7.73751e42i			0.176987i
$535$		0			0
$536$	−4.83494e43			−1.04173
$537$	−1.05929e43	−	1.05929e43i	−0.221527	−	0.221527i
$538$	−8.77791e43	+	8.77791e43i	−1.78186	+	1.78186i
$539$			2.07591e43i			0.409062i
$540$		0			0
$541$	−8.17307e43			−1.51785			−0.758926	−	0.651177i	$-0.774275\pi$
$541$	−8.17307e43			−1.51785			−0.758926	+	0.651177i	$0.774275\pi$
$542$	−6.05086e43	−	6.05086e43i	−1.09101	−	1.09101i
$543$	−5.67990e42	+	5.67990e42i	−0.0994360	+	0.0994360i
$544$			1.17033e44i			1.98942i
$545$		0			0
$546$	−5.10693e42			−0.0818611
$547$	6.54115e43	+	6.54115e43i	1.01826	+	1.01826i	0.999830	+	0.0184255i	$0.00586536\pi$
$547$	6.54115e43	+	6.54115e43i	1.01826	+	1.01826i	0.0184255	+	0.999830i	$0.494135\pi$
$548$	1.39495e44	−	1.39495e44i	2.10896	−	2.10896i
$549$		−	5.99773e42i		−	0.0880703i
$550$		0			0
$551$	9.69433e38			1.34305e−5
$552$	4.30063e43	+	4.30063e43i	0.578771	+	0.578771i
$553$	−1.44876e43	+	1.44876e43i	−0.189406	+	0.189406i
$554$			7.44438e43i			0.945524i
$555$		0			0
$556$	9.38357e43			1.12505
$557$	1.01533e44	+	1.01533e44i	1.18283	+	1.18283i	0.979007	+	0.203824i	$0.0653372\pi$
$557$	1.01533e44	+	1.01533e44i	1.18283	+	1.18283i	0.203824	+	0.979007i	$0.434663\pi$
$558$	−1.53604e44	+	1.53604e44i	−1.73882	+	1.73882i
$559$			1.40109e44i			1.54126i
$560$		0			0
$561$	1.11337e43			0.115674
$562$	−9.30630e43	−	9.30630e43i	−0.939714	−	0.939714i
$563$	−4.41398e43	+	4.41398e43i	−0.433208	+	0.433208i	−0.889718	−	0.456510i	$-0.849099\pi$
$563$	−4.41398e43	+	4.41398e43i	−0.433208	+	0.433208i	0.456510	+	0.889718i	$0.349099\pi$
$564$			7.39944e43i			0.705884i
$565$		0			0
$566$	1.07380e44			0.967971
$567$	−1.24204e43	−	1.24204e43i	−0.108845	−	0.108845i
$568$	3.30317e43	−	3.30317e43i	0.281422	−	0.281422i
$569$		−	2.23566e44i		−	1.85187i	−0.377689	−	0.925933i	$-0.623281\pi$
$569$		−	2.23566e44i		−	1.85187i	0.377689	−	0.925933i	$-0.376719\pi$
$570$		0			0
$571$	1.88532e43			0.147641			0.0738205	−	0.997272i	$-0.476481\pi$
$571$	1.88532e43			0.147641			0.0738205	+	0.997272i	$0.476481\pi$
$572$	1.23071e44	+	1.23071e44i	0.937168	+	0.937168i
$573$	1.91309e43	−	1.91309e43i	0.141665	−	0.141665i
$574$		−	5.20983e43i		−	0.375174i
$575$		0			0
$576$	6.38008e43			0.434576
$577$	−1.36243e44	−	1.36243e44i	−0.902611	−	0.902611i	0.0930502	−	0.995661i	$-0.470338\pi$
$577$	−1.36243e44	−	1.36243e44i	−0.902611	−	0.902611i	−0.995661	+	0.0930502i	$0.970338\pi$
$578$	2.07313e44	−	2.07313e44i	1.33592	−	1.33592i
$579$			2.08473e43i			0.130675i
$580$		0			0
$581$	1.33095e43			0.0789485
$582$	3.39759e43	+	3.39759e43i	0.196066	+	0.196066i
$583$	−5.85174e43	+	5.85174e43i	−0.328540	+	0.328540i
$584$		−	8.28812e44i		−	4.52741i
$585$		0			0
$586$	−3.49918e44			−1.80969
$587$	−1.94584e44	−	1.94584e44i	−0.979259	−	0.979259i	0.0205303	−	0.999789i	$-0.493465\pi$
$587$	−1.94584e44	−	1.94584e44i	−0.979259	−	0.979259i	−0.999789	+	0.0205303i	$0.993465\pi$
$588$	−6.27055e43	+	6.27055e43i	−0.307092	+	0.307092i
$589$		−	5.39921e41i		−	0.00257327i
$590$		0			0
$591$	3.60282e43			0.162646
$592$	1.52223e44	+	1.52223e44i	0.668858	+	0.668858i
$593$	8.07127e43	−	8.07127e43i	0.345197	−	0.345197i	−0.513120	−	0.858317i	$-0.671510\pi$
$593$	8.07127e43	−	8.07127e43i	0.345197	−	0.345197i	0.858317	+	0.513120i	$0.171510\pi$
$594$		−	6.97445e43i		−	0.290353i
$595$		0			0
$596$	5.90699e44			2.33038
$597$	2.14730e43	+	2.14730e43i	0.0824713	+	0.0824713i
$598$	8.18174e44	−	8.18174e44i	3.05933	−	3.05933i
$599$		−	6.48099e43i		−	0.235946i	−0.993017	−	0.117973i	$-0.962360\pi$
$599$		−	6.48099e43i		−	0.235946i	0.993017	−	0.117973i	$-0.0376396\pi$
$600$		0			0
$601$	−2.21893e44			−0.765865			−0.382933	−	0.923776i	$-0.625086\pi$
$601$	−2.21893e44			−0.765865			−0.382933	+	0.923776i	$0.625086\pi$
$602$	−7.57513e43	−	7.57513e43i	−0.254593	−	0.254593i
$603$	8.94455e43	−	8.94455e43i	0.292740	−	0.292740i
$604$			3.87067e44i			1.23366i
$605$		0			0
$606$	8.37803e43			0.253268
$607$	1.45859e44	+	1.45859e44i	0.429451	+	0.429451i	0.888441	−	0.458990i	$-0.151789\pi$
$607$	1.45859e44	+	1.45859e44i	0.429451	+	0.429451i	−0.458990	+	0.888441i	$0.651789\pi$
$608$	−6.32105e41	+	6.32105e41i	−0.00181273	+	0.00181273i
$609$			8.69236e40i			0.000242807i
$610$		0			0
$611$	8.03094e44			2.12866
$612$	−8.76045e44	−	8.76045e44i	−2.26206	−	2.26206i
$613$	−5.13025e44	+	5.13025e44i	−1.29054	+	1.29054i	−0.356084	+	0.934454i	$0.615888\pi$
$613$	−5.13025e44	+	5.13025e44i	−1.29054	+	1.29054i	−0.934454	+	0.356084i	$0.884112\pi$
$614$		−	6.11445e44i		−	1.49852i
$615$		0			0
$616$	−7.59212e43			−0.176633
$617$	3.30744e44	+	3.30744e44i	0.749772	+	0.749772i	0.974436	−	0.224664i	$-0.0721284\pi$
$617$	3.30744e44	+	3.30744e44i	0.749772	+	0.749772i	−0.224664	+	0.974436i	$0.572128\pi$
$618$	−1.34816e44	+	1.34816e44i	−0.297800	+	0.297800i
$619$			7.05795e44i			1.51925i	0.650364	+	0.759623i	$0.274616\pi$
$619$			7.05795e44i			1.51925i	−0.650364	+	0.759623i	$0.725384\pi$
$620$		0			0
$621$	−3.24352e44			−0.663057
$622$	5.79762e44	+	5.79762e44i	1.15506	+	1.15506i
$623$	−3.17621e43	+	3.17621e43i	−0.0616738	+	0.0616738i
$624$			2.87009e44i			0.543179i
$625$		0			0
$626$	−1.31647e45			−2.36713
$627$	6.01341e40	+	6.01341e40i	0.000105400	+	0.000105400i
$628$	−1.06635e44	+	1.06635e44i	−0.182199	+	0.182199i
$629$		−	3.87186e44i		−	0.644926i
$630$		0			0
$631$	2.94853e44			0.466805			0.233402	−	0.972380i	$-0.425014\pi$
$631$	2.94853e44			0.466805			0.233402	+	0.972380i	$0.425014\pi$
$632$	1.72011e45	+	1.72011e45i	2.65511	+	2.65511i
$633$	−9.14176e43	+	9.14176e43i	−0.137585	+	0.137585i
$634$			7.74577e44i			1.13668i
$635$		0			0
$636$	−3.53518e44			−0.493285
$637$	6.80571e44	+	6.80571e44i	0.926068	+	0.926068i
$638$	2.99445e42	−	2.99445e42i	0.00397362	−	0.00397362i
$639$			1.22216e44i			0.158166i
$640$		0			0
$641$	1.31960e45			1.62447			0.812236	−	0.583329i	$-0.198250\pi$
$641$	1.31960e45			1.62447			0.812236	+	0.583329i	$0.198250\pi$
$642$	1.51602e44	+	1.51602e44i	0.182030	+	0.182030i
$643$	2.95984e44	−	2.95984e44i	0.346651	−	0.346651i	−0.512210	−	0.858860i	$-0.671173\pi$
$643$	2.95984e44	−	2.95984e44i	0.346651	−	0.346651i	0.858860	+	0.512210i	$0.171173\pi$
$644$			6.18894e44i			0.707038i
$645$		0			0
$646$	4.40190e42			0.00478541
$647$	−6.41039e44	−	6.41039e44i	−0.679855	−	0.679855i	0.280113	−	0.959967i	$-0.409628\pi$
$647$	−6.41039e44	−	6.41039e44i	−0.679855	−	0.679855i	−0.959967	+	0.280113i	$0.909628\pi$
$648$	−1.47467e45	+	1.47467e45i	−1.52579	+	1.52579i
$649$		−	2.06092e44i		−	0.208040i
$650$		0			0
$651$	4.84117e43			0.0465216
$652$	−2.93394e45	−	2.93394e45i	−2.75099	−	2.75099i
$653$	8.98199e44	−	8.98199e44i	0.821792	−	0.821792i	−0.164573	−	0.986365i	$-0.552625\pi$
$653$	8.98199e44	−	8.98199e44i	0.821792	−	0.821792i	0.986365	+	0.164573i	$0.0526247\pi$
$654$		−	2.31553e44i		−	0.206732i
$655$		0			0
$656$	−2.92792e45			−2.48942
$657$	1.53329e45	+	1.53329e45i	1.27226	+	1.27226i
$658$	−4.34202e44	+	4.34202e44i	−0.351623	+	0.351623i
$659$			2.09807e45i			1.65827i	0.559052	+	0.829133i	$0.311165\pi$
$659$			2.09807e45i			1.65827i	−0.559052	+	0.829133i	$0.688835\pi$
$660$		0			0
$661$	−3.92624e43			−0.0295634			−0.0147817	−	0.999891i	$-0.504705\pi$
$661$	−3.92624e43			−0.0295634			−0.0147817	+	0.999891i	$0.504705\pi$
$662$	−2.72037e45	−	2.72037e45i	−1.99940	−	1.99940i
$663$	3.65010e44	−	3.65010e44i	0.261871	−	0.261871i
$664$		−	1.58023e45i		−	1.10671i
$665$		0			0
$666$	−1.18988e45			−0.794172
$667$	−1.39259e43	−	1.39259e43i	−0.00907425	−	0.00907425i
$668$	−6.86073e44	+	6.86073e44i	−0.436463	+	0.436463i
$669$			1.61598e44i			0.100373i
$670$		0			0
$671$	6.51201e43			0.0385616
$672$	−5.66773e43	−	5.66773e43i	−0.0327719	−	0.0327719i
$673$	1.35579e45	−	1.35579e45i	0.765511	−	0.765511i	−0.211802	−	0.977313i	$-0.567933\pi$
$673$	1.35579e45	−	1.35579e45i	0.765511	−	0.765511i	0.977313	+	0.211802i	$0.0679331\pi$
$674$		−	1.90741e45i		−	1.05168i
$675$		0			0
$676$	3.64180e45			1.91500
$677$	8.28262e43	+	8.28262e43i	0.0425353	+	0.0425353i	0.728055	−	0.685519i	$-0.240425\pi$
$677$	8.28262e43	+	8.28262e43i	0.0425353	+	0.0425353i	−0.685519	+	0.728055i	$0.740425\pi$
$678$	−1.26178e44	+	1.26178e44i	−0.0632859	+	0.0632859i
$679$			2.78939e44i			0.136644i
$680$		0			0
$681$	2.05420e44			0.0960039
$682$	−1.66774e45	−	1.66774e45i	−0.761341	−	0.761341i
$683$	−2.90358e44	+	2.90358e44i	−0.129480	+	0.129480i	−0.768877	−	0.639397i	$-0.779184\pi$
$683$	−2.90358e44	+	2.90358e44i	−0.129480	+	0.129480i	0.639397	+	0.768877i	$0.279184\pi$
$684$		−	9.46318e42i		−	0.00412230i
$685$		0			0
$686$	−1.49450e45			−0.621314
$687$	1.00126e44	+	1.00126e44i	0.0406666	+	0.0406666i
$688$	−4.25722e45	+	4.25722e45i	−1.68932	+	1.68932i
$689$			3.83689e45i			1.48755i
$690$		0			0
$691$	4.36777e45			1.61663			0.808317	−	0.588748i	$-0.200379\pi$
$691$	4.36777e45			1.61663			0.808317	+	0.588748i	$0.200379\pi$
$692$	3.11742e44	+	3.11742e44i	0.112745	+	0.112745i
$693$	1.40453e44	−	1.40453e44i	0.0496362	−	0.0496362i
$694$		−	4.47330e45i		−	1.54481i
$695$		0			0
$696$	1.03204e43			0.00340369
$697$	3.72364e45	+	3.72364e45i	1.20017	+	1.20017i
$698$	2.31319e45	−	2.31319e45i	0.728658	−	0.728658i
$699$			1.96407e43i			0.00604676i
$700$		0			0
$701$	6.04918e45			1.77913			0.889567	−	0.456806i	$-0.151006\pi$
$701$	6.04918e45			1.77913			0.889567	+	0.456806i	$0.151006\pi$
$702$	−2.28651e45	−	2.28651e45i	−0.657325	−	0.657325i
$703$	2.09122e42	−	2.09122e42i	0.000587645	−	0.000587645i
$704$			6.92714e44i			0.190279i
$705$		0			0
$706$	6.37281e44			0.167284
$707$	3.43914e44	+	3.43914e44i	0.0882550	+	0.0882550i
$708$	6.22527e44	−	6.22527e44i	0.156180	−	0.156180i
$709$		−	3.60443e45i		−	0.884091i	−0.896993	−	0.442045i	$-0.854253\pi$
$709$		−	3.60443e45i		−	0.884091i	0.896993	−	0.442045i	$-0.145747\pi$
$710$		0			0
$711$	−6.36434e45			−1.49224
$712$	3.77111e45	+	3.77111e45i	0.864547	+	0.864547i
$713$	−7.75598e45	+	7.75598e45i	−1.73862	+	1.73862i
$714$			3.94694e44i			0.0865145i
$715$		0			0
$716$	−1.80992e46			−3.79359
$717$	−5.95208e44	−	5.95208e44i	−0.122001	−	0.122001i
$718$	7.38518e45	−	7.38518e45i	1.48037	−	1.48037i
$719$			1.14528e45i			0.224517i	0.993679	+	0.112258i	$0.0358084\pi$
$719$			1.14528e45i			0.224517i	−0.993679	+	0.112258i	$0.964192\pi$
$720$		0			0
$721$	−1.10683e45			−0.207546
$722$	−7.03377e45	−	7.03377e45i	−1.29001	−	1.29001i
$723$	1.22515e44	−	1.22515e44i	0.0219775	−	0.0219775i
$724$			9.70476e45i			1.70282i
$725$		0			0
$726$	−1.71790e45			−0.288412
$727$	1.34397e45	+	1.34397e45i	0.220719	+	0.220719i	0.808801	−	0.588082i	$-0.200117\pi$
$727$	1.34397e45	+	1.34397e45i	0.220719	+	0.220719i	−0.588082	+	0.808801i	$0.700117\pi$
$728$	−2.48901e45	+	2.48901e45i	−0.399876	+	0.399876i
$729$		−	4.99447e45i		−	0.784963i
$730$		0			0
$731$	1.08284e46			1.62887
$732$	1.96703e44	+	1.96703e44i	0.0289490	+	0.0289490i
$733$	1.38366e45	−	1.38366e45i	0.199235	−	0.199235i	−0.600437	−	0.799672i	$-0.705007\pi$
$733$	1.38366e45	−	1.38366e45i	0.199235	−	0.199235i	0.799672	+	0.600437i	$0.205007\pi$
$734$			4.10496e45i			0.578325i
$735$		0			0
$736$	1.81604e46			2.44952
$737$	9.71150e44	+	9.71150e44i	0.128176	+	0.128176i
$738$	1.14433e46	−	1.14433e46i	1.47791	−	1.47791i
$739$			8.35853e45i			1.05638i	0.849127	+	0.528188i	$0.177128\pi$
$739$			8.35853e45i			1.05638i	−0.849127	+	0.528188i	$0.822872\pi$
$740$		0			0
$741$	3.94290e42			0.000477226
$742$	−2.07446e45	−	2.07446e45i	−0.245721	−	0.245721i
$743$	−3.30450e45	+	3.30450e45i	−0.383075	+	0.383075i	−0.872209	−	0.489134i	$-0.837313\pi$
$743$	−3.30450e45	+	3.30450e45i	−0.383075	+	0.383075i	0.489134	+	0.872209i	$0.337313\pi$
$744$		−	5.74791e45i		−	0.652143i
$745$		0			0
$746$	−2.09960e46			−2.28200
$747$	2.92341e45	+	2.92341e45i	0.310999	+	0.310999i
$748$	9.51162e45	−	9.51162e45i	0.990442	−	0.990442i
$749$			1.24464e45i			0.126862i
$750$		0			0
$751$	3.17733e45			0.310330			0.155165	−	0.987889i	$-0.450409\pi$
$751$	3.17733e45			0.310330			0.155165	+	0.987889i	$0.450409\pi$
$752$	2.44022e46	+	2.44022e46i	2.33315	+	2.33315i
$753$	−2.01850e45	+	2.01850e45i	−0.188934	+	0.188934i
$754$		−	1.96341e44i		−	0.0179916i
$755$		0			0
$756$	1.72959e45			0.151913
$757$	6.57529e45	+	6.57529e45i	0.565432	+	0.565432i	0.930845	−	0.365413i	$-0.119072\pi$
$757$	6.57529e45	+	6.57529e45i	0.565432	+	0.565432i	−0.365413	+	0.930845i	$0.619072\pi$
$758$	−1.12715e46	+	1.12715e46i	−0.949021	+	0.949021i
$759$		−	1.72766e45i		−	0.142426i
$760$		0			0
$761$	−1.10400e46			−0.872601			−0.436301	−	0.899801i	$-0.643712\pi$
$761$	−1.10400e46			−0.872601			−0.436301	+	0.899801i	$0.643712\pi$
$762$	1.01204e45	+	1.01204e45i	0.0783280	+	0.0783280i
$763$	9.50516e44	−	9.50516e44i	0.0720388	−	0.0720388i
$764$		−	3.26874e46i		−	2.42598i
$765$		0			0
$766$	2.05104e46			1.45987
$767$	−6.75656e45	−	6.75656e45i	−0.470977	−	0.470977i
$768$	2.97376e45	−	2.97376e45i	0.203014	−	0.203014i
$769$			1.21763e46i			0.814127i	0.913400	+	0.407064i	$0.133447\pi$
$769$			1.21763e46i			0.814127i	−0.913400	+	0.407064i	$0.866553\pi$
$770$		0			0
$771$	−2.15908e45			−0.138484
$772$	1.78100e46	+	1.78100e46i	1.11889	+	1.11889i
$773$	−1.53073e46	+	1.53073e46i	−0.941945	+	0.941945i	−0.998405	−	0.0564602i	$-0.982019\pi$
$773$	−1.53073e46	+	1.53073e46i	−0.941945	+	0.941945i	0.0564602	+	0.998405i	$0.482019\pi$
$774$		−	3.32772e46i		−	2.00582i
$775$		0			0
$776$	3.31183e46			1.91549
$777$	1.87508e44	+	1.87508e44i	0.0106239	+	0.0106239i
$778$	1.99911e46	−	1.99911e46i	1.10959	−	1.10959i
$779$			4.02234e43i			0.00218715i
$780$		0			0
$781$	−1.32695e45			−0.0692532
$782$	−6.32334e46	−	6.32334e46i	−3.23324	−	3.23324i
$783$	−3.89181e43	+	3.89181e43i	−0.00194968	+	0.00194968i
$784$			4.13586e46i			2.03006i
$785$		0			0
$786$	9.00034e45			0.424129
$787$	1.93360e46	+	1.93360e46i	0.892832	+	0.892832i	0.994789	−	0.101957i	$-0.0325103\pi$
$787$	1.93360e46	+	1.93360e46i	0.892832	+	0.892832i	−0.101957	+	0.994789i	$0.532510\pi$
$788$	3.07791e46	−	3.07791e46i	1.39263	−	1.39263i
$789$			4.85265e44i			0.0215153i
$790$		0			0
$791$	−1.03591e45			−0.0441059
$792$	−1.66759e46	−	1.66759e46i	−0.695805	−	0.695805i
$793$	2.13491e45	−	2.13491e45i	0.0872988	−	0.0872988i
$794$		−	1.82408e46i		−	0.730997i
$795$		0			0
$796$	3.66890e46			1.41230
$797$	−2.24556e46	−	2.24556e46i	−0.847209	−	0.847209i	0.142575	−	0.989784i	$-0.454462\pi$
$797$	−2.24556e46	−	2.24556e46i	−0.847209	−	0.847209i	−0.989784	+	0.142575i	$0.954462\pi$
$798$	−2.13177e42	+	2.13177e42i	−7.88305e−5	+	7.88305e-5i
$799$		−	6.20679e46i		−	2.24967i
$800$		0			0
$801$	−1.39530e46			−0.485899
$802$	−1.01427e46	−	1.01427e46i	−0.346228	−	0.346228i
$803$	−1.66476e46	+	1.66476e46i	−0.557061	+	0.557061i
$804$			5.86696e45i			0.192449i
$805$		0			0
$806$	−1.09351e47			−3.44717
$807$	6.07669e45	+	6.07669e45i	0.187798	+	0.187798i
$808$	4.08328e46	−	4.08328e46i	1.23717	−	1.23717i
$809$			1.62226e46i			0.481886i	0.970539	+	0.240943i	$0.0774567\pi$
$809$			1.62226e46i			0.481886i	−0.970539	+	0.240943i	$0.922543\pi$
$810$		0			0
$811$	−4.01951e46			−1.14773			−0.573864	−	0.818950i	$-0.694556\pi$
$811$	−4.01951e46			−1.14773			−0.573864	+	0.818950i	$0.694556\pi$
$812$	7.42595e43	+	7.42595e43i	0.00207900	+	0.00207900i
$813$	−4.18883e45	+	4.18883e45i	−0.114986	+	0.114986i
$814$		−	1.29190e46i		−	0.347728i
$815$		0			0
$816$	2.21818e46			0.574055
$817$	5.84851e43	+	5.84851e43i	0.00148420	+	0.00148420i
$818$	−6.13982e46	+	6.13982e46i	−1.52793	+	1.52793i
$819$		−	9.20926e45i		−	0.224741i
$820$		0			0
$821$	4.45189e46			1.04485			0.522425	−	0.852685i	$-0.325027\pi$
$821$	4.45189e46			1.04485			0.522425	+	0.852685i	$0.325027\pi$
$822$	−1.38044e46	−	1.38044e46i	−0.317738	−	0.317738i
$823$	−5.55851e46	+	5.55851e46i	−1.25476	+	1.25476i	−0.301200	+	0.953561i	$0.597387\pi$
$823$	−5.55851e46	+	5.55851e46i	−1.25476	+	1.25476i	−0.953561	+	0.301200i	$0.902613\pi$
$824$			1.31413e47i			2.90940i
$825$		0			0
$826$	7.30603e45			0.155597
$827$	6.54928e46	+	6.54928e46i	1.36806	+	1.36806i	0.863201	+	0.504861i	$0.168456\pi$
$827$	6.54928e46	+	6.54928e46i	1.36806	+	1.36806i	0.504861	+	0.863201i	$0.331544\pi$
$828$	−1.35939e47	+	1.35939e47i	−2.78521	+	2.78521i
$829$			7.35096e46i			1.47731i	0.674084	+	0.738655i	$0.264539\pi$
$829$			7.35096e46i			1.47731i	−0.674084	+	0.738655i	$0.735461\pi$
$830$		0			0
$831$	5.15352e45			0.0996525
$832$	2.27100e46	+	2.27100e46i	0.430769	+	0.430769i
$833$	5.25986e46	−	5.25986e46i	0.978710	−	0.978710i
$834$		−	9.28600e45i		−	0.169501i
$835$		0			0
$836$	1.02746e44			0.00180495
$837$	2.16753e46	+	2.16753e46i	0.373557	+	0.373557i
$838$	1.14219e47	−	1.14219e47i	1.93123	−	1.93123i
$839$		−	2.82921e46i		−	0.469326i	−0.972077	−	0.234663i	$-0.924601\pi$
$839$		−	2.82921e46i		−	0.469326i	0.972077	−	0.234663i	$-0.0753986\pi$
$840$		0			0
$841$	6.26200e46			0.999947
$842$	4.94987e46	+	4.94987e46i	0.775533	+	0.775533i
$843$	−6.44247e45	+	6.44247e45i	−0.0990402	+	0.0990402i
$844$			1.56197e47i			2.35610i
$845$		0			0
$846$	−1.90743e47			−2.77028
$847$	−7.05191e45	−	7.05191e45i	−0.100501	−	0.100501i
$848$	−1.16585e47	+	1.16585e47i	−1.63045	+	1.63045i
$849$		−	7.43363e45i		−	0.102018i
$850$		0			0
$851$	−6.00810e46			−0.794079
$852$	−4.00823e45	−	4.00823e45i	−0.0519899	−	0.0519899i
$853$	1.04164e46	−	1.04164e46i	0.132597	−	0.132597i	−0.637693	−	0.770290i	$-0.720111\pi$
$853$	1.04164e46	−	1.04164e46i	0.132597	−	0.132597i	0.770290	+	0.637693i	$0.220111\pi$
$854$			2.30853e45i			0.0288409i
$855$		0			0
$856$	1.47775e47			1.77837
$857$	−5.70463e46	−	5.70463e46i	−0.673805	−	0.673805i	0.284786	−	0.958591i	$-0.408077\pi$
$857$	−5.70463e46	−	5.70463e46i	−0.673805	−	0.673805i	−0.958591	+	0.284786i	$0.908077\pi$
$858$	1.21791e46	−	1.21791e46i	0.141195	−	0.141195i
$859$			8.45121e46i			0.961675i	0.876810	+	0.480837i	$0.159667\pi$
$859$			8.45121e46i			0.961675i	−0.876810	+	0.480837i	$0.840333\pi$
$860$		0			0
$861$	−3.60661e45			−0.0395411
$862$	−6.62298e46	−	6.62298e46i	−0.712750	−	0.712750i
$863$	−3.59185e46	+	3.59185e46i	−0.379442	+	0.379442i	−0.870901	−	0.491459i	$-0.836464\pi$
$863$	−3.59185e46	+	3.59185e46i	−0.379442	+	0.379442i	0.491459	+	0.870901i	$0.336464\pi$
$864$		−	5.07521e46i		−	0.526301i
$865$		0			0
$866$	−9.47159e46			−0.946534
$867$	−1.43516e46	−	1.43516e46i	−0.140798	−	0.140798i
$868$	4.13584e46	−	4.13584e46i	0.398335	−	0.398335i
$869$		−	6.91005e46i		−	0.653379i
$870$		0			0
$871$	6.36767e46			0.580350
$872$	−1.12854e47	−	1.12854e47i	−1.00985	−	1.00985i
$873$	−6.12683e46	+	6.12683e46i	−0.538279	+	0.538279i
$874$		−	6.83057e44i		−	0.00589215i
$875$		0			0
$876$	−1.00572e47			−0.836396
$877$	2.58708e44	+	2.58708e44i	0.00211260	+	0.00211260i	0.708162	−	0.706050i	$-0.249524\pi$
$877$	2.58708e44	+	2.58708e44i	0.00211260	+	0.00211260i	−0.706050	+	0.708162i	$0.749524\pi$
$878$	2.08917e47	−	2.08917e47i	1.67518	−	1.67518i
$879$			2.42238e46i			0.190730i
$880$		0			0
$881$	5.70576e46			0.433211			0.216605	−	0.976259i	$-0.430502\pi$
$881$	5.70576e46			0.433211			0.216605	+	0.976259i	$0.430502\pi$
$882$	−1.61643e47	−	1.61643e47i	−1.20520	−	1.20520i
$883$	3.54385e46	−	3.54385e46i	0.259480	−	0.259480i	−0.565363	−	0.824842i	$-0.691264\pi$
$883$	3.54385e46	−	3.54385e46i	0.259480	−	0.259480i	0.824842	+	0.565363i	$0.191264\pi$
$884$		−	6.23661e47i		−	4.48448i
$885$		0			0
$886$	1.90086e45			0.0131829
$887$	1.55571e47	+	1.55571e47i	1.05962	+	1.05962i	0.998106	+	0.0615166i	$0.0195937\pi$
$887$	1.55571e47	+	1.55571e47i	1.05962	+	1.05962i	0.0615166	+	0.998106i	$0.480406\pi$
$888$	2.22628e46	−	2.22628e46i	0.148927	−	0.148927i
$889$			8.30873e45i			0.0545892i
$890$		0			0
$891$	5.92408e46			0.375472
$892$	1.38054e47	+	1.38054e47i	0.859435	+	0.859435i
$893$	3.35233e44	−	3.35233e44i	0.00204986	−	0.00204986i
$894$		−	5.84557e46i		−	0.351097i
$895$		0			0
$896$	1.70360e46			0.0987278
$897$	−5.66398e46	−	5.66398e46i	−0.322435	−	0.322435i
$898$	9.64321e46	−	9.64321e46i	0.539263	−	0.539263i
$899$			1.86124e45i			0.0102246i
$900$		0			0
$901$	2.96538e47			1.57211
$902$	1.24245e47	+	1.24245e47i	0.647103	+	0.647103i
$903$	−5.24404e45	+	5.24404e45i	−0.0268325	+	0.0268325i
$904$			1.22993e47i			0.618280i
$905$		0			0
$906$	3.83042e46			0.185864
$907$	1.54419e47	+	1.54419e47i	0.736180	+	0.736180i	0.971836	−	0.235656i	$-0.0757240\pi$
$907$	1.54419e47	+	1.54419e47i	0.736180	+	0.736180i	−0.235656	+	0.971836i	$0.575724\pi$
$908$	1.75492e47	−	1.75492e47i	0.822021	−	0.822021i
$909$			1.51080e47i			0.695320i
$910$		0			0
$911$	1.17212e47			0.520807			0.260403	−	0.965500i	$-0.416144\pi$
$911$	1.17212e47			0.520807			0.260403	+	0.965500i	$0.416144\pi$
$912$	1.19806e44	+	1.19806e44i	0.000523070	+	0.000523070i
$913$	−3.17407e46	+	3.17407e46i	−0.136171	+	0.136171i
$914$		−	3.49691e47i		−	1.47416i
$915$		0			0
$916$	1.71076e47			0.696406
$917$	3.69460e46	+	3.69460e46i	0.147794	+	0.147794i
$918$	−1.76715e47	+	1.76715e47i	−0.694690	+	0.694690i
$919$		−	1.69436e47i		−	0.654573i	−0.944925	−	0.327287i	$-0.893866\pi$
$919$		−	1.69436e47i		−	0.654573i	0.944925	−	0.327287i	$-0.106134\pi$
$920$		0			0
$921$	−4.23285e46			−0.157935
$922$	−6.44536e46	−	6.44536e46i	−0.236348	−	0.236348i
$923$	−4.35031e46	+	4.35031e46i	−0.156781	+	0.156781i
$924$			9.21266e45i			0.0326312i
$925$		0			0
$926$	5.50935e47			1.88506
$927$	−2.43112e47	−	2.43112e47i	−0.817580	−	0.817580i
$928$	2.17902e45	−	2.17902e45i	0.00720267	−	0.00720267i
$929$			1.45277e47i			0.472005i	0.971752	+	0.236003i	$0.0758374\pi$
$929$			1.45277e47i			0.472005i	−0.971752	+	0.236003i	$0.924163\pi$
$930$		0			0
$931$	5.68178e44			0.00178357
$932$	1.67792e46	+	1.67792e46i	0.0517746	+	0.0517746i
$933$	4.01352e46	−	4.01352e46i	0.121736	−	0.121736i
$934$			6.51780e47i			1.94335i
$935$		0			0
$936$	−1.09341e48			−3.15044
$937$	2.91188e47	+	2.91188e47i	0.824783	+	0.824783i	0.986790	−	0.162007i	$-0.0517966\pi$
$937$	2.91188e47	+	2.91188e47i	0.824783	+	0.824783i	−0.162007	+	0.986790i	$0.551797\pi$
$938$	−3.44275e46	+	3.44275e46i	−0.0958651	+	0.0958651i
$939$			9.11354e46i			0.249481i
$940$		0			0
$941$	−3.92460e47			−1.03839			−0.519196	−	0.854655i	$-0.673768\pi$
$941$	−3.92460e47			−1.03839			−0.519196	+	0.854655i	$0.673768\pi$
$942$	1.05526e46	+	1.05526e46i	0.0274502	+	0.0274502i
$943$	5.77810e47	−	5.77810e47i	1.47774	−	1.47774i
$944$		−	4.10599e47i		−	1.03244i
$945$		0			0
$946$	3.61306e47			0.878247
$947$	2.40052e47	+	2.40052e47i	0.573728	+	0.573728i	0.933168	−	0.359440i	$-0.117032\pi$
$947$	2.40052e47	+	2.40052e47i	0.573728	+	0.573728i	−0.359440	+	0.933168i	$0.617032\pi$
$948$	2.08727e47	−	2.08727e47i	0.490506	−	0.490506i
$949$			1.09155e48i			2.52224i
$950$		0			0
$951$	5.36217e46			0.119799
$952$	1.92366e47	+	1.92366e47i	0.422607	+	0.422607i
$953$	4.68847e47	−	4.68847e47i	1.01285	−	1.01285i	0.0129331	−	0.999916i	$-0.495883\pi$
$953$	4.68847e47	−	4.68847e47i	1.01285	−	1.01285i	0.999916	−	0.0129331i	$-0.00411684\pi$
$954$		−	9.11301e47i		−	1.93592i
$955$		0			0
$956$	−1.01698e48			−2.08923
$957$	−2.07297e44	−	2.07297e44i	−0.000418795	−	0.000418795i
$958$	−9.93181e47	+	9.93181e47i	−1.97324	+	1.97324i
$959$		−	1.13333e47i		−	0.221441i
$960$		0			0
$961$	5.07463e47			0.959025
$962$	−4.23540e47	−	4.23540e47i	−0.787214	−	0.787214i
$963$	−2.73382e47	+	2.73382e47i	−0.499745	+	0.499745i
$964$		−	2.09331e47i		−	0.376358i
$965$		0			0
$966$	6.12459e46			0.106523
$967$	−4.83138e47	−	4.83138e47i	−0.826510	−	0.826510i	0.160522	−	0.987032i	$-0.448682\pi$
$967$	−4.83138e47	−	4.83138e47i	−0.826510	−	0.826510i	−0.987032	+	0.160522i	$0.948682\pi$
$968$	−8.37271e47	+	8.37271e47i	−1.40884	+	1.40884i
$969$		−	3.04730e44i		−	0.000504354i
$970$		0			0
$971$	−1.04183e48			−1.66835			−0.834176	−	0.551498i	$-0.814056\pi$
$971$	−1.04183e48			−1.66835			−0.834176	+	0.551498i	$0.814056\pi$
$972$	5.73430e47	+	5.73430e47i	0.903276	+	0.903276i
$973$	3.81186e46	−	3.81186e46i	0.0590651	−	0.0590651i
$974$			1.60005e48i			2.43888i
$975$		0			0
$976$	1.29739e47			0.191370
$977$	−2.78721e47	−	2.78721e47i	−0.404443	−	0.404443i	0.475352	−	0.879795i	$-0.342321\pi$
$977$	−2.78721e47	−	2.78721e47i	−0.404443	−	0.404443i	−0.879795	+	0.475352i	$0.842321\pi$
$978$	−2.90343e47	+	2.90343e47i	−0.414467	+	0.414467i
$979$		−	1.51494e47i		−	0.212751i
$980$		0			0
$981$	4.17557e47			0.567561
$982$	6.82803e47	+	6.82803e47i	0.913086	+	0.913086i
$983$	3.09325e47	−	3.09325e47i	0.406967	−	0.406967i	−0.473713	−	0.880680i	$-0.657086\pi$
$983$	3.09325e47	−	3.09325e47i	0.406967	−	0.406967i	0.880680	+	0.473713i	$0.157086\pi$
$984$			4.28212e47i			0.554290i
$985$		0			0
$986$	−1.51744e46			−0.0190143
$987$	3.00585e46	+	3.00585e46i	0.0370589	+	0.0370589i
$988$	3.36844e45	−	3.36844e45i	0.00408619	−	0.00408619i
$989$		−	1.68028e48i		−	2.00559i
$990$		0			0
$991$	1.34300e48			1.55202			0.776010	−	0.630720i	$-0.217240\pi$
$991$	1.34300e48			1.55202			0.776010	+	0.630720i	$0.217240\pi$
$992$	−1.21359e48	−	1.21359e48i	−1.38002	−	1.38002i
$993$	−1.88323e47	+	1.88323e47i	−0.210725	+	0.210725i
$994$		−	4.70409e46i		−	0.0517957i
$995$		0			0
$996$	−1.91754e47			−0.204453
$997$	2.55318e47	+	2.55318e47i	0.267891	+	0.267891i	0.828250	−	0.560359i	$-0.189337\pi$
$997$	2.55318e47	+	2.55318e47i	0.267891	+	0.267891i	−0.560359	+	0.828250i	$0.689337\pi$
$998$	4.96193e47	−	4.96193e47i	0.512344	−	0.512344i
$999$			1.67905e47i			0.170615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.1		30
5.2	odd	4		5.33.c.a.3.15	yes	30
5.3	odd	4	inner	25.33.c.b.18.1		30
5.4	even	2		5.33.c.a.2.15	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.15	✓	30	5.4	even	2
5.33.c.a.3.15	yes	30	5.2	odd	4
25.33.c.b.7.1		30	1.1	even	1	trivial
25.33.c.b.18.1		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)

\(f(q)\)	\(=\)	\(q+(-84542.4 - 84542.4i) q^{2} +(-5.85262e6 + 5.85262e6i) q^{3} +9.99987e9i q^{4} +9.89589e11 q^{6} +(4.06221e12 + 4.06221e12i) q^{7} +(4.82306e14 - 4.82306e14i) q^{8} +1.78451e15i q^{9} +O(q^{10})\)	\(q+(-84542.4 - 84542.4i) q^{2} +(-5.85262e6 + 5.85262e6i) q^{3} +9.99987e9i q^{4} +9.89589e11 q^{6} +(4.06221e12 + 4.06221e12i) q^{7} +(4.82306e14 - 4.82306e14i) q^{8} +1.78451e15i q^{9} -1.93753e16 q^{11} +(-5.85254e16 - 5.85254e16i) q^{12} +(-6.35202e17 + 6.35202e17i) q^{13} -6.86859e17i q^{14} -3.86015e19 q^{16} +(4.90922e19 + 4.90922e19i) q^{17} +(1.50867e20 - 1.50867e20i) q^{18} +5.30302e17i q^{19} -4.75492e19 q^{21} +(1.63803e21 + 1.63803e21i) q^{22} +(7.61780e21 - 7.61780e21i) q^{23} +5.64550e21i q^{24} +1.07403e23 q^{26} +(-2.12891e22 - 2.12891e22i) q^{27} +(-4.06216e22 + 4.06216e22i) q^{28} -1.82808e21i q^{29} -1.01814e24 q^{31} +(1.19197e24 + 1.19197e24i) q^{32} +(1.13396e23 - 1.13396e23i) q^{33} -8.30074e24i q^{34} -1.78449e25 q^{36} +(-3.94346e24 - 3.94346e24i) q^{37} +(4.48330e22 - 4.48330e22i) q^{38} -7.43519e24i q^{39} +7.58500e25 q^{41} +(4.01992e24 + 4.01992e24i) q^{42} +(1.10287e26 - 1.10287e26i) q^{43} -1.93750e26i q^{44} -1.28805e27 q^{46} +(-6.32156e26 - 6.32156e26i) q^{47} +(2.25920e26 - 2.25920e26i) q^{48} -1.07142e27i q^{49} -5.74636e26 q^{51} +(-6.35194e27 - 6.35194e27i) q^{52} +(3.02021e27 - 3.02021e27i) q^{53} +3.59966e27i q^{54} +3.91846e27 q^{56} +(-3.10365e24 - 3.10365e24i) q^{57} +(-1.54550e26 + 1.54550e26i) q^{58} +1.06369e28i q^{59} -3.36099e27 q^{61} +(8.60759e28 + 8.60759e28i) q^{62} +(-7.24908e27 + 7.24908e27i) q^{63} -3.57525e28i q^{64} -1.91736e28 q^{66} +(-5.01232e28 - 5.01232e28i) q^{67} +(-4.90915e29 + 4.90915e29i) q^{68} +8.91681e28i q^{69} +6.84870e28 q^{71} +(8.60681e29 + 8.60681e29i) q^{72} +(8.59218e29 - 8.59218e29i) q^{73} +6.66779e29i q^{74} -5.30294e27 q^{76} +(-7.87065e28 - 7.87065e28i) q^{77} +(-6.28589e29 + 6.28589e29i) q^{78} +3.56643e30i q^{79} -3.05755e30 q^{81} +(-6.41254e30 - 6.41254e30i) q^{82} +(1.63821e30 - 1.63821e30i) q^{83} -4.75485e29i q^{84} -1.86478e31 q^{86} +(1.06990e28 + 1.06990e28i) q^{87} +(-9.34481e30 + 9.34481e30i) q^{88} +7.81891e30i q^{89} -5.16066e30 q^{91} +(7.61769e31 + 7.61769e31i) q^{92} +(5.95878e30 - 5.95878e30i) q^{93} +1.06888e32i q^{94} -1.39523e31 q^{96} +(3.43333e31 + 3.43333e31i) q^{97} +(-9.05808e31 + 9.05808e31i) q^{98} -3.45754e31i 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

Properties

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