LMFDB - Embedded newform 25.33.c.b.7.14

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			7.14
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(73528.8 + 73528.8i) q^{2} +(4.29377e6 - 4.29377e6i) q^{3} +6.51799e9i q^{4} +6.31431e11 q^{6} +(-1.36489e13 - 1.36489e13i) q^{7} +(-1.63456e14 + 1.63456e14i) q^{8} +1.81615e15i q^{9} +O(q^{10})$	\(q+(73528.8 + 73528.8i) q^{2} +(4.29377e6 - 4.29377e6i) q^{3} +6.51799e9i q^{4} +6.31431e11 q^{6} +(-1.36489e13 - 1.36489e13i) q^{7} +(-1.63456e14 + 1.63456e14i) q^{8} +1.81615e15i q^{9} -1.07665e16 q^{11} +(2.79867e16 + 2.79867e16i) q^{12} +(-5.33423e17 + 5.33423e17i) q^{13} -2.00717e18i q^{14} +3.95709e18 q^{16} +(-1.80495e19 - 1.80495e19i) q^{17} +(-1.33539e20 + 1.33539e20i) q^{18} -4.66461e20i q^{19} -1.17210e20 q^{21} +(-7.91647e20 - 7.91647e20i) q^{22} +(-7.85489e20 + 7.85489e20i) q^{23} +1.40369e21i q^{24} -7.84438e22 q^{26} +(1.57545e22 + 1.57545e22i) q^{27} +(8.89632e22 - 8.89632e22i) q^{28} +2.31649e23i q^{29} +3.24657e23 q^{31} +(9.92999e23 + 9.92999e23i) q^{32} +(-4.62288e22 + 4.62288e22i) q^{33} -2.65432e24i q^{34} -1.18376e25 q^{36} +(-4.94737e24 - 4.94737e24i) q^{37} +(3.42983e25 - 3.42983e25i) q^{38} +4.58078e24i q^{39} -1.24479e26 q^{41} +(-8.61831e24 - 8.61831e24i) q^{42} +(1.83776e25 - 1.83776e25i) q^{43} -7.01759e25i q^{44} -1.15512e26 q^{46} +(-3.45135e26 - 3.45135e26i) q^{47} +(1.69908e25 - 1.69908e25i) q^{48} -7.31845e26i q^{49} -1.55001e26 q^{51} +(-3.47684e27 - 3.47684e27i) q^{52} +(3.32895e27 - 3.32895e27i) q^{53} +2.31682e27i q^{54} +4.46198e27 q^{56} +(-2.00288e27 - 2.00288e27i) q^{57} +(-1.70329e28 + 1.70329e28i) q^{58} -3.29505e28i q^{59} +1.89259e28 q^{61} +(2.38717e28 + 2.38717e28i) q^{62} +(2.47884e28 - 2.47884e28i) q^{63} +1.29032e29i q^{64} -6.79830e27 q^{66} +(1.76361e29 + 1.76361e29i) q^{67} +(1.17647e29 - 1.17647e29i) q^{68} +6.74541e27i q^{69} -1.94403e29 q^{71} +(-2.96861e29 - 2.96861e29i) q^{72} +(-3.08897e29 + 3.08897e29i) q^{73} -7.27548e29i q^{74} +3.04039e30 q^{76} +(1.46951e29 + 1.46951e29i) q^{77} +(-3.36819e29 + 3.36819e29i) q^{78} -3.31447e30i q^{79} -3.23007e30 q^{81} +(-9.15279e30 - 9.15279e30i) q^{82} +(6.01743e30 - 6.01743e30i) q^{83} -7.63974e29i q^{84} +2.70257e30 q^{86} +(9.94648e29 + 9.94648e29i) q^{87} +(1.75985e30 - 1.75985e30i) q^{88} -2.42982e31i q^{89} +1.45612e31 q^{91} +(-5.11981e30 - 5.11981e30i) q^{92} +(1.39400e30 - 1.39400e30i) q^{93} -5.07547e31i q^{94} +8.52741e30 q^{96} +(-2.36400e31 - 2.36400e31i) q^{97} +(5.38116e31 - 5.38116e31i) q^{98} -1.95535e31i 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 $

$2$	73528.8	+	73528.8i	1.12196	+	1.12196i	0.991447	+	0.130513i	$0.0416626\pi$
$2$	73528.8	+	73528.8i	1.12196	+	1.12196i	0.130513	+	0.991447i	$0.458337\pi$
$3$	4.29377e6	−	4.29377e6i	0.0997466	−	0.0997466i	−0.655472	−	0.755219i	$-0.727530\pi$
$3$	4.29377e6	−	4.29377e6i	0.0997466	−	0.0997466i	0.755219	+	0.655472i	$0.227530\pi$
$4$			6.51799e9i			1.51759i
$5$		0			0
$5$		0			0
$6$	6.31431e11			0.223823
$7$	−1.36489e13	−	1.36489e13i	−0.410703	−	0.410703i	0.471280	−	0.881983i	$-0.343792\pi$
$7$	−1.36489e13	−	1.36489e13i	−0.410703	−	0.410703i	−0.881983	+	0.471280i	$0.843792\pi$
$8$	−1.63456e14	+	1.63456e14i	−0.580713	+	0.580713i
$9$			1.81615e15i			0.980101i
$10$		0			0
$11$	−1.07665e16			−0.234310			−0.117155	−	0.993114i	$-0.537377\pi$
$11$	−1.07665e16			−0.234310			−0.117155	+	0.993114i	$0.537377\pi$
$12$	2.79867e16	+	2.79867e16i	0.151374	+	0.151374i
$13$	−5.33423e17	+	5.33423e17i	−0.801637	+	0.801637i	−0.983351	−	0.181714i	$-0.941835\pi$
$13$	−5.33423e17	+	5.33423e17i	−0.801637	+	0.801637i	0.181714	+	0.983351i	$0.441835\pi$
$14$		−	2.00717e18i		−	0.921585i
$15$		0			0
$16$	3.95709e18			0.214514
$17$	−1.80495e19	−	1.80495e19i	−0.370922	−	0.370922i	0.496891	−	0.867813i	$-0.334475\pi$
$17$	−1.80495e19	−	1.80495e19i	−0.370922	−	0.370922i	−0.867813	+	0.496891i	$0.834475\pi$
$18$	−1.33539e20	+	1.33539e20i	−1.09963	+	1.09963i
$19$		−	4.66461e20i		−	1.61718i	−0.588373	−	0.808589i	$-0.700231\pi$
$19$		−	4.66461e20i		−	1.61718i	0.588373	−	0.808589i	$-0.299769\pi$
$20$		0			0
$21$	−1.17210e20			−0.0819325
$22$	−7.91647e20	−	7.91647e20i	−0.262887	−	0.262887i
$23$	−7.85489e20	+	7.85489e20i	−0.128084	+	0.128084i	−0.768243	−	0.640159i	$-0.778869\pi$
$23$	−7.85489e20	+	7.85489e20i	−0.128084	+	0.128084i	0.640159	+	0.768243i	$0.278869\pi$
$24$			1.40369e21i			0.115848i
$25$		0			0
$26$	−7.84438e22			−1.79881
$27$	1.57545e22	+	1.57545e22i	0.197508	+	0.197508i
$28$	8.89632e22	−	8.89632e22i	0.623278	−	0.623278i
$29$			2.31649e23i			0.925685i	0.886441	+	0.462842i	$0.153170\pi$
$29$			2.31649e23i			0.925685i	−0.886441	+	0.462842i	$0.846830\pi$
$30$		0			0
$31$	3.24657e23			0.446312			0.223156	−	0.974783i	$-0.428364\pi$
$31$	3.24657e23			0.446312			0.223156	+	0.974783i	$0.428364\pi$
$32$	9.92999e23	+	9.92999e23i	0.821390	+	0.821390i
$33$	−4.62288e22	+	4.62288e22i	−0.0233717	+	0.0233717i
$34$		−	2.65432e24i		−	0.832319i
$35$		0			0
$36$	−1.18376e25			−1.48739
$37$	−4.94737e24	−	4.94737e24i	−0.401002	−	0.401002i	0.477584	−	0.878586i	$-0.341513\pi$
$37$	−4.94737e24	−	4.94737e24i	−0.401002	−	0.401002i	−0.878586	+	0.477584i	$0.841513\pi$
$38$	3.42983e25	−	3.42983e25i	1.81441	−	1.81441i
$39$			4.58078e24i			0.159921i
$40$		0			0
$41$	−1.24479e26			−1.95234			−0.976168	−	0.217015i	$-0.930368\pi$
$41$	−1.24479e26			−1.95234			−0.976168	+	0.217015i	$0.930368\pi$
$42$	−8.61831e24	−	8.61831e24i	−0.0919250	−	0.0919250i
$43$	1.83776e25	−	1.83776e25i	0.134522	−	0.134522i	−0.636639	−	0.771162i	$-0.719676\pi$
$43$	1.83776e25	−	1.83776e25i	0.134522	−	0.134522i	0.771162	+	0.636639i	$0.219676\pi$
$44$		−	7.01759e25i		−	0.355587i
$45$		0			0
$46$	−1.15512e26			−0.287410
$47$	−3.45135e26	−	3.45135e26i	−0.608728	−	0.608728i	0.333886	−	0.942613i	$-0.391640\pi$
$47$	−3.45135e26	−	3.45135e26i	−0.608728	−	0.608728i	−0.942613	+	0.333886i	$0.891640\pi$
$48$	1.69908e25	−	1.69908e25i	0.0213971	−	0.0213971i
$49$		−	7.31845e26i		−	0.662646i
$50$		0			0
$51$	−1.55001e26			−0.0739965
$52$	−3.47684e27	−	3.47684e27i	−1.21655	−	1.21655i
$53$	3.32895e27	−	3.32895e27i	0.858804	−	0.858804i	−0.132393	−	0.991197i	$-0.542266\pi$
$53$	3.32895e27	−	3.32895e27i	0.858804	−	0.858804i	0.991197	+	0.132393i	$0.0422662\pi$
$54$			2.31682e27i			0.443193i
$55$		0			0
$56$	4.46198e27			0.477001
$57$	−2.00288e27	−	2.00288e27i	−0.161308	−	0.161308i
$58$	−1.70329e28	+	1.70329e28i	−1.03858	+	1.03858i
$59$		−	3.29505e28i		−	1.52837i	−0.644995	−	0.764187i	$-0.723141\pi$
$59$		−	3.29505e28i		−	1.52837i	0.644995	−	0.764187i	$-0.276859\pi$
$60$		0			0
$61$	1.89259e28			0.514967			0.257484	−	0.966283i	$-0.417107\pi$
$61$	1.89259e28			0.514967			0.257484	+	0.966283i	$0.417107\pi$
$62$	2.38717e28	+	2.38717e28i	0.500744	+	0.500744i
$63$	2.47884e28	−	2.47884e28i	0.402531	−	0.402531i
$64$			1.29032e29i			1.62862i
$65$		0			0
$66$	−6.79830e27			−0.0524442
$67$	1.76361e29	+	1.76361e29i	1.06956	+	1.06956i	0.997393	+	0.0721669i	$0.0229914\pi$
$67$	1.76361e29	+	1.76361e29i	1.06956	+	1.06956i	0.0721669	+	0.997393i	$0.477009\pi$
$68$	1.17647e29	−	1.17647e29i	0.562907	−	0.562907i
$69$			6.74541e27i			0.0255519i
$70$		0			0
$71$	−1.94403e29			−0.466197			−0.233098	−	0.972453i	$-0.574886\pi$
$71$	−1.94403e29			−0.466197			−0.233098	+	0.972453i	$0.574886\pi$
$72$	−2.96861e29	−	2.96861e29i	−0.569158	−	0.569158i
$73$	−3.08897e29	+	3.08897e29i	−0.474950	+	0.474950i	−0.903512	−	0.428562i	$-0.859020\pi$
$73$	−3.08897e29	+	3.08897e29i	−0.474950	+	0.474950i	0.428562	+	0.903512i	$0.359020\pi$
$74$		−	7.27548e29i		−	0.899817i
$75$		0			0
$76$	3.04039e30			2.45421
$77$	1.46951e29	+	1.46951e29i	0.0962320	+	0.0962320i
$78$	−3.36819e29	+	3.36819e29i	−0.179425	+	0.179425i
$79$		−	3.31447e30i		−	1.44006i	−0.693944	−	0.720029i	$-0.744128\pi$
$79$		−	3.31447e30i		−	1.44006i	0.693944	−	0.720029i	$-0.255872\pi$
$80$		0			0
$81$	−3.23007e30			−0.940700
$82$	−9.15279e30	−	9.15279e30i	−2.19044	−	2.19044i
$83$	6.01743e30	−	6.01743e30i	1.18621	−	1.18621i	0.208104	−	0.978107i	$-0.433271\pi$
$83$	6.01743e30	−	6.01743e30i	1.18621	−	1.18621i	0.978107	−	0.208104i	$-0.0667293\pi$
$84$		−	7.63974e29i		−	0.124340i
$85$		0			0
$86$	2.70257e30			0.301858
$87$	9.94648e29	+	9.94648e29i	0.0923339	+	0.0923339i
$88$	1.75985e30	−	1.75985e30i	0.136067	−	0.136067i
$89$		−	2.42982e31i		−	1.56796i	−0.620787	−	0.783980i	$-0.713187\pi$
$89$		−	2.42982e31i		−	1.56796i	0.620787	−	0.783980i	$-0.286813\pi$
$90$		0			0
$91$	1.45612e31			0.658469
$92$	−5.11981e30	−	5.11981e30i	−0.194379	−	0.194379i
$93$	1.39400e30	−	1.39400e30i	0.0445181	−	0.0445181i
$94$		−	5.07547e31i		−	1.36594i
$95$		0			0
$96$	8.52741e30			0.163862
$97$	−2.36400e31	−	2.36400e31i	−0.384857	−	0.384857i	0.487992	−	0.872848i	$-0.337730\pi$
$97$	−2.36400e31	−	2.36400e31i	−0.384857	−	0.384857i	−0.872848	+	0.487992i	$0.837730\pi$
$98$	5.38116e31	−	5.38116e31i	0.743462	−	0.743462i
$99$		−	1.95535e31i		−	0.229648i
$100$		0			0
$101$	1.40781e32			1.20061			0.600306	−	0.799770i	$-0.295045\pi$
$101$	1.40781e32			1.20061			0.600306	+	0.799770i	$0.295045\pi$
$102$	−1.13970e31	−	1.13970e31i	−0.0830211	−	0.0830211i
$103$	−1.52613e30	+	1.52613e30i	−0.00951034	+	0.00951034i	−0.711846	−	0.702336i	$-0.752141\pi$
$103$	−1.52613e30	+	1.52613e30i	−0.00951034	+	0.00951034i	0.702336	+	0.711846i	$0.252141\pi$
$104$		−	1.74382e32i		−	0.931042i
$105$		0			0
$106$	4.89548e32			1.92709
$107$	−2.10167e32	−	2.10167e32i	−0.711909	−	0.711909i	0.255026	−	0.966934i	$-0.417916\pi$
$107$	−2.10167e32	−	2.10167e32i	−0.711909	−	0.711909i	−0.966934	+	0.255026i	$0.917916\pi$
$108$	−1.02688e32	+	1.02688e32i	−0.299736	+	0.299736i
$109$		−	3.24067e32i		−	0.816228i	−0.912931	−	0.408114i	$-0.866187\pi$
$109$		−	3.24067e32i		−	0.816228i	0.912931	−	0.408114i	$-0.133813\pi$
$110$		0			0
$111$	−4.24857e31			−0.0799973
$112$	−5.40098e31	−	5.40098e31i	−0.0881017	−	0.0881017i
$113$	−1.61141e32	+	1.61141e32i	−0.228009	+	0.228009i	−0.811861	−	0.583851i	$-0.801545\pi$
$113$	−1.61141e32	+	1.61141e32i	−0.228009	+	0.228009i	0.583851	+	0.811861i	$0.301545\pi$
$114$		−	2.94538e32i		−	0.361963i
$115$		0			0
$116$	−1.50989e33			−1.40481
$117$	−9.68774e32	−	9.68774e32i	−0.785685	−	0.785685i
$118$	2.42281e33	−	2.42281e33i	1.71477	−	1.71477i
$119$			4.92711e32i			0.304678i
$120$		0			0
$121$	−1.99546e33			−0.945099
$122$	1.39160e33	+	1.39160e33i	0.577773	+	0.577773i
$123$	−5.34484e32	+	5.34484e32i	−0.194739	+	0.194739i
$124$			2.11611e33i			0.677317i
$125$		0			0
$126$	3.64531e33			0.903246
$127$	5.66419e33	+	5.66419e33i	1.23674	+	1.23674i	0.961326	+	0.275413i	$0.0888148\pi$
$127$	5.66419e33	+	5.66419e33i	1.23674	+	1.23674i	0.275413	+	0.961326i	$0.411185\pi$
$128$	−5.22270e33	+	5.22270e33i	−1.00585	+	1.00585i
$129$		−	1.57819e32i		−	0.0268363i
$130$		0			0
$131$	−5.28215e33			−0.702215			−0.351107	−	0.936335i	$-0.614195\pi$
$131$	−5.28215e33			−0.702215			−0.351107	+	0.936335i	$0.614195\pi$
$132$	−3.01319e32	−	3.01319e32i	−0.0354686	−	0.0354686i
$133$	−6.36667e33	+	6.36667e33i	−0.664180	+	0.664180i
$134$			2.59352e34i			2.40001i
$135$		0			0
$136$	5.90061e33			0.430799
$137$	1.80703e34	+	1.80703e34i	1.17338	+	1.17338i	0.981400	+	0.191976i	$0.0614896\pi$
$137$	1.80703e34	+	1.80703e34i	1.17338	+	1.17338i	0.191976	+	0.981400i	$0.438510\pi$
$138$	−4.95982e32	+	4.95982e32i	−0.0286682	+	0.0286682i
$139$		−	7.18456e33i		−	0.369968i	−0.982742	−	0.184984i	$-0.940777\pi$
$139$		−	7.18456e33i		−	0.369968i	0.982742	−	0.184984i	$-0.0592233\pi$
$140$		0			0
$141$	−2.96386e33			−0.121437
$142$	−1.42942e34	−	1.42942e34i	−0.523054	−	0.523054i
$143$	5.74309e33	−	5.74309e33i	0.187832	−	0.187832i
$144$			7.18666e33i			0.210246i
$145$		0			0
$146$	−4.54257e34			−1.06575
$147$	−3.14237e33	−	3.14237e33i	−0.0660967	−	0.0660967i
$148$	3.22469e34	−	3.22469e34i	0.608556	−	0.608556i
$149$		−	6.89326e34i		−	1.16800i	−0.811752	−	0.584002i	$-0.801486\pi$
$149$		−	6.89326e34i		−	1.16800i	0.811752	−	0.584002i	$-0.198514\pi$
$150$		0			0
$151$	3.50808e34			0.480217			0.240109	−	0.970746i	$-0.422817\pi$
$151$	3.50808e34			0.480217			0.240109	+	0.970746i	$0.422817\pi$
$152$	7.62460e34	+	7.62460e34i	0.939117	+	0.939117i
$153$	3.27806e34	−	3.27806e34i	0.363541	−	0.363541i
$154$			2.16102e34i			0.215937i
$155$		0			0
$156$	−2.98575e34			−0.242695
$157$	−7.54668e34	−	7.54668e34i	−0.553811	−	0.553811i	0.373728	−	0.927538i	$-0.378079\pi$
$157$	−7.54668e34	−	7.54668e34i	−0.553811	−	0.553811i	−0.927538	+	0.373728i	$0.878079\pi$
$158$	2.43709e35	−	2.43709e35i	1.61569	−	1.61569i
$159$		−	2.85875e34i		−	0.171326i
$160$		0			0
$161$	2.14421e34			0.105209
$162$	−2.37503e35	−	2.37503e35i	−1.05543	−	1.05543i
$163$	−1.84124e35	+	1.84124e35i	−0.741498	+	0.741498i	−0.972866	−	0.231368i	$-0.925680\pi$
$163$	−1.84124e35	+	1.84124e35i	−0.741498	+	0.741498i	0.231368	+	0.972866i	$0.425680\pi$
$164$		−	8.11354e35i		−	2.96284i
$165$		0			0
$166$	8.84909e35			2.66176
$167$	3.43961e35	+	3.43961e35i	0.939821	+	0.939821i	0.998289	−	0.0584682i	$-0.0186216\pi$
$167$	3.43961e35	+	3.43961e35i	0.939821	+	0.939821i	−0.0584682	+	0.998289i	$0.518622\pi$
$168$	1.91587e34	−	1.91587e34i	0.0475793	−	0.0475793i
$169$		−	1.26300e35i		−	0.285244i
$170$		0			0
$171$	8.47162e35			1.58500
$172$	1.19785e35	+	1.19785e35i	0.204150	+	0.204150i
$173$	2.08878e35	−	2.08878e35i	0.324455	−	0.324455i	−0.526018	−	0.850473i	$-0.676316\pi$
$173$	2.08878e35	−	2.08878e35i	0.324455	−	0.324455i	0.850473	+	0.526018i	$0.176316\pi$
$174$			1.46270e35i			0.207190i
$175$		0			0
$176$	−4.26040e34			−0.0502629
$177$	−1.41482e35	−	1.41482e35i	−0.152450	−	0.152450i
$178$	1.78662e36	−	1.78662e36i	1.75919	−	1.75919i
$179$		−	1.53882e36i		−	1.38528i	−0.721282	−	0.692642i	$-0.756447\pi$
$179$		−	1.53882e36i		−	1.38528i	0.721282	−	0.692642i	$-0.243553\pi$
$180$		0			0
$181$	−2.37976e36			−1.79339			−0.896697	−	0.442644i	$-0.854040\pi$
$181$	−2.37976e36			−1.79339			−0.896697	+	0.442644i	$0.854040\pi$
$182$	1.07067e36	+	1.07067e36i	0.738776	+	0.738776i
$183$	8.12635e34	−	8.12635e34i	0.0513663	−	0.0513663i
$184$		−	2.56786e35i		−	0.148760i
$185$		0			0
$186$	2.04999e35			0.0998950
$187$	1.94330e35	+	1.94330e35i	0.0869109	+	0.0869109i
$188$	2.24959e36	−	2.24959e36i	0.923798	−	0.923798i
$189$		−	4.30063e35i		−	0.162235i
$190$		0			0
$191$	−2.98923e35			−0.0952852			−0.0476426	−	0.998864i	$-0.515171\pi$
$191$	−2.98923e35			−0.0952852			−0.0476426	+	0.998864i	$0.515171\pi$
$192$	5.54035e35	+	5.54035e35i	0.162449	+	0.162449i
$193$	−7.61484e35	+	7.61484e35i	−0.205468	+	0.205468i	−0.802338	−	0.596870i	$-0.796411\pi$
$193$	−7.61484e35	+	7.61484e35i	−0.205468	+	0.205468i	0.596870	+	0.802338i	$0.296411\pi$
$194$		−	3.47643e36i		−	0.863587i
$195$		0			0
$196$	4.77016e36			1.00562
$197$	2.38449e36	+	2.38449e36i	0.463378	+	0.463378i	0.899761	−	0.436383i	$-0.143741\pi$
$197$	2.38449e36	+	2.38449e36i	0.463378	+	0.463378i	−0.436383	+	0.899761i	$0.643741\pi$
$198$	1.43775e36	−	1.43775e36i	0.257656	−	0.257656i
$199$			9.96520e36i			1.64754i	0.566922	+	0.823772i	$0.308134\pi$
$199$			9.96520e36i			1.64754i	−0.566922	+	0.823772i	$0.691866\pi$
$200$		0			0
$201$	1.51450e36			0.213370
$202$	1.03515e37	+	1.03515e37i	1.34704	+	1.34704i
$203$	3.16175e36	−	3.16175e36i	0.380182	−	0.380182i
$204$		−	1.01029e36i		−	0.112296i
$205$		0			0
$206$	−2.24429e35			−0.0213404
$207$	−1.42656e36	−	1.42656e36i	−0.125535	−	0.125535i
$208$	−2.11080e36	+	2.11080e36i	−0.171963	+	0.171963i
$209$			5.02215e36i			0.378922i
$210$		0			0
$211$	3.70758e36			0.240199			0.120100	−	0.992762i	$-0.461679\pi$
$211$	3.70758e36			0.240199			0.120100	+	0.992762i	$0.461679\pi$
$212$	2.16981e37	+	2.16981e37i	1.30331	+	1.30331i
$213$	−8.34721e35	+	8.34721e35i	−0.0465016	+	0.0465016i
$214$		−	3.09067e37i		−	1.59747i
$215$		0			0
$216$	−5.15036e36			−0.229392
$217$	−4.43121e36	−	4.43121e36i	−0.183302	−	0.183302i
$218$	2.38283e37	−	2.38283e37i	0.915775	−	0.915775i
$219$			2.65267e36i			0.0947494i
$220$		0			0
$221$	1.92560e37			0.594690
$222$	−3.12392e36	−	3.12392e36i	−0.0897537	−	0.0897537i
$223$	3.90648e37	−	3.90648e37i	1.04450	−	1.04450i	0.0455366	−	0.998963i	$-0.485500\pi$
$223$	3.90648e37	−	3.90648e37i	1.04450	−	1.04450i	0.998963	−	0.0455366i	$-0.0144998\pi$
$224$		−	2.71066e37i		−	0.674694i
$225$		0			0
$226$	−2.36971e37			−0.511634
$227$	−5.36850e37	−	5.36850e37i	−1.08004	−	1.08004i	−0.996505	−	0.0835337i	$-0.973379\pi$
$227$	−5.36850e37	−	5.36850e37i	−1.08004	−	1.08004i	−0.0835337	−	0.996505i	$-0.526621\pi$
$228$	1.30547e37	−	1.30547e37i	0.244799	−	0.244799i
$229$		−	2.92992e37i		−	0.512258i	−0.966643	−	0.256129i	$-0.917553\pi$
$229$		−	2.92992e37i		−	0.512258i	0.966643	−	0.256129i	$-0.0824472\pi$
$230$		0			0
$231$	1.26194e36			0.0191976
$232$	−3.78645e37	−	3.78645e37i	−0.537557	−	0.537557i
$233$	−2.68145e37	+	2.68145e37i	−0.355365	+	0.355365i	−0.862101	−	0.506736i	$-0.830852\pi$
$233$	−2.68145e37	+	2.68145e37i	−0.355365	+	0.355365i	0.506736	+	0.862101i	$0.330852\pi$
$234$		−	1.42465e38i		−	1.76301i
$235$		0			0
$236$	2.14771e38			2.31944
$237$	−1.42315e37	−	1.42315e37i	−0.143641	−	0.143641i
$238$	−3.62284e37	+	3.62284e37i	−0.341836	+	0.341836i
$239$			3.78326e36i			0.0333810i	0.999861	+	0.0166905i	$0.00531300\pi$
$239$			3.78326e36i			0.0333810i	−0.999861	+	0.0166905i	$0.994687\pi$
$240$		0			0
$241$	−1.14277e38			−0.882444			−0.441222	−	0.897398i	$-0.645455\pi$
$241$	−1.14277e38			−0.882444			−0.441222	+	0.897398i	$0.645455\pi$
$242$	−1.46724e38	−	1.46724e38i	−1.06036	−	1.06036i
$243$	−4.30626e37	+	4.30626e37i	−0.291340	+	0.291340i
$244$			1.23359e38i			0.781509i
$245$		0			0
$246$	−7.85999e37			−0.436979
$247$	2.48821e38	+	2.48821e38i	1.29639	+	1.29639i
$248$	−5.30673e37	+	5.30673e37i	−0.259179	+	0.259179i
$249$		−	5.16749e37i		−	0.236641i
$250$		0			0
$251$	1.24950e38			0.503451			0.251726	−	0.967799i	$-0.419002\pi$
$251$	1.24950e38			0.503451			0.251726	+	0.967799i	$0.419002\pi$
$252$	1.61570e38	+	1.61570e38i	0.610876	+	0.610876i
$253$	8.45696e36	−	8.45696e36i	0.0300114	−	0.0300114i
$254$			8.32962e38i			2.77514i
$255$		0			0
$256$	−2.13847e38			−0.628439
$257$	3.14722e37	+	3.14722e37i	0.0868955	+	0.0868955i	0.749218	−	0.662323i	$-0.230429\pi$
$257$	3.14722e37	+	3.14722e37i	0.0868955	+	0.0868955i	−0.662323	+	0.749218i	$0.730429\pi$
$258$	1.16042e37	−	1.16042e37i	0.0301093	−	0.0301093i
$259$			1.35052e38i			0.329386i
$260$		0			0
$261$	−4.20709e38			−0.907265
$262$	−3.88390e38	−	3.88390e38i	−0.787857	−	0.787857i
$263$	−5.13620e38	+	5.13620e38i	−0.980280	+	0.980280i	−0.999809	−	0.0195293i	$-0.993783\pi$
$263$	−5.13620e38	+	5.13620e38i	−0.980280	+	0.980280i	0.0195293	+	0.999809i	$0.493783\pi$
$264$		−	1.51128e37i		−	0.0271445i
$265$		0			0
$266$	−9.36266e38			−1.49037
$267$	−1.04331e38	−	1.04331e38i	−0.156399	−	0.156399i
$268$	−1.14952e39	+	1.14952e39i	−1.62315	+	1.62315i
$269$		−	3.09601e38i		−	0.411876i	−0.978565	−	0.205938i	$-0.933976\pi$
$269$		−	3.09601e38i		−	0.411876i	0.978565	−	0.205938i	$-0.0660245\pi$
$270$		0			0
$271$	−1.07090e37			−0.0126543			−0.00632717	−	0.999980i	$-0.502014\pi$
$271$	−1.07090e37			−0.0126543			−0.00632717	+	0.999980i	$0.502014\pi$
$272$	−7.14235e37	−	7.14235e37i	−0.0795681	−	0.0795681i
$273$	6.25225e37	−	6.25225e37i	0.0656801	−	0.0656801i
$274$			2.65738e39i			2.63296i
$275$		0			0
$276$	−4.39665e37			−0.0387772
$277$	−8.09685e38	−	8.09685e38i	−0.673969	−	0.673969i	0.284660	−	0.958629i	$-0.408119\pi$
$277$	−8.09685e38	−	8.09685e38i	−0.673969	−	0.673969i	−0.958629	+	0.284660i	$0.908119\pi$
$278$	5.28272e38	−	5.28272e38i	0.415089	−	0.415089i
$279$			5.89626e38i			0.437431i
$280$		0			0
$281$	−3.83768e38			−0.253962			−0.126981	−	0.991905i	$-0.540529\pi$
$281$	−3.83768e38			−0.253962			−0.126981	+	0.991905i	$0.540529\pi$
$282$	−2.17929e38	−	2.17929e38i	−0.136248	−	0.136248i
$283$	−5.87085e37	+	5.87085e37i	−0.0346831	+	0.0346831i	−0.724236	−	0.689553i	$-0.757807\pi$
$283$	−5.87085e37	+	5.87085e37i	−0.0346831	+	0.0346831i	0.689553	+	0.724236i	$0.257807\pi$
$284$		−	1.26712e39i		−	0.707495i
$285$		0			0
$286$	8.44565e38			0.421480
$287$	1.69900e39	+	1.69900e39i	0.801831	+	0.801831i
$288$	−1.80343e39	+	1.80343e39i	−0.805045	+	0.805045i
$289$		−	1.71634e39i		−	0.724834i
$290$		0			0
$291$	−2.03009e38			−0.0767763
$292$	−2.01339e39	−	2.01339e39i	−0.720779	−	0.720779i
$293$	−1.48123e39	+	1.48123e39i	−0.502043	+	0.502043i	−0.912072	−	0.410029i	$-0.865519\pi$
$293$	−1.48123e39	+	1.48123e39i	−0.502043	+	0.502043i	0.410029	+	0.912072i	$0.365519\pi$
$294$		−	4.62109e38i		−	0.148316i
$295$		0			0
$296$	1.61736e39			0.465735
$297$	−1.69621e38	−	1.69621e38i	−0.0462783	−	0.0462783i
$298$	5.06853e39	−	5.06853e39i	1.31045	−	1.31045i
$299$		−	8.37995e38i		−	0.205354i
$300$		0			0
$301$	−5.01668e38			−0.110498
$302$	2.57945e39	+	2.57945e39i	0.538785	+	0.538785i
$303$	6.04482e38	−	6.04482e38i	0.119757	−	0.119757i
$304$		−	1.84583e39i		−	0.346908i
$305$		0			0
$306$	4.82063e39			0.815757
$307$	−4.05852e39	−	4.05852e39i	−0.651859	−	0.651859i	0.301581	−	0.953440i	$-0.402486\pi$
$307$	−4.05852e39	−	4.05852e39i	−0.651859	−	0.651859i	−0.953440	+	0.301581i	$0.902486\pi$
$308$	−9.57822e38	+	9.57822e38i	−0.146041	+	0.146041i
$309$			1.31057e37i			0.00189725i
$310$		0			0
$311$	−3.39327e39			−0.443050			−0.221525	−	0.975155i	$-0.571103\pi$
$311$	−3.39327e39			−0.443050			−0.221525	+	0.975155i	$0.571103\pi$
$312$	−7.48758e38	−	7.48758e38i	−0.0928683	−	0.0928683i
$313$	6.32312e39	−	6.32312e39i	0.745112	−	0.745112i	−0.228445	−	0.973557i	$-0.573364\pi$
$313$	6.32312e39	−	6.32312e39i	0.745112	−	0.745112i	0.973557	+	0.228445i	$0.0733640\pi$
$314$		−	1.10980e40i		−	1.24271i
$315$		0			0
$316$	2.16037e40			2.18542
$317$	−4.79685e39	−	4.79685e39i	−0.461326	−	0.461326i	0.437764	−	0.899090i	$-0.355770\pi$
$317$	−4.79685e39	−	4.79685e39i	−0.461326	−	0.461326i	−0.899090	+	0.437764i	$0.855770\pi$
$318$	2.10200e39	−	2.10200e39i	0.192220	−	0.192220i
$319$		−	2.49405e39i		−	0.216898i
$320$		0			0
$321$	−1.80482e39			−0.142021
$322$	1.57661e39	+	1.57661e39i	0.118040	+	0.118040i
$323$	−8.41940e39	+	8.41940e39i	−0.599847	+	0.599847i
$324$		−	2.10535e40i		−	1.42759i
$325$		0			0
$326$	−2.70769e40			−1.66386
$327$	−1.39147e39	−	1.39147e39i	−0.0814160	−	0.0814160i
$328$	2.03469e40	−	2.03469e40i	1.13375	−	1.13375i
$329$			9.42140e39i			0.500013i
$330$		0			0
$331$	−9.51082e39			−0.458111			−0.229055	−	0.973413i	$-0.573564\pi$
$331$	−9.51082e39			−0.458111			−0.229055	+	0.973413i	$0.573564\pi$
$332$	3.92216e40	+	3.92216e40i	1.80018	+	1.80018i
$333$	8.98515e39	−	8.98515e39i	0.393023	−	0.393023i
$334$			5.05820e40i			2.10888i
$335$		0			0
$336$	−4.63811e38			−0.0175757
$337$	−2.44947e39	−	2.44947e39i	−0.0885102	−	0.0885102i	0.661465	−	0.749976i	$-0.269935\pi$
$337$	−2.44947e39	−	2.44947e39i	−0.0885102	−	0.0885102i	−0.749976	+	0.661465i	$0.769935\pi$
$338$	9.28668e39	−	9.28668e39i	0.320032	−	0.320032i
$339$			1.38381e39i			0.0454863i
$340$		0			0
$341$	−3.49542e39			−0.104575
$342$	6.22908e40	+	6.22908e40i	1.77831	+	1.77831i
$343$	−2.50630e40	+	2.50630e40i	−0.682854	+	0.682854i
$344$			6.00788e39i			0.156238i
$345$		0			0
$346$	3.07171e40			0.728052
$347$	7.00506e38	+	7.00506e38i	0.0158540	+	0.0158540i	0.714989	−	0.699135i	$-0.246432\pi$
$347$	7.00506e38	+	7.00506e38i	0.0158540	+	0.0158540i	−0.699135	+	0.714989i	$0.746432\pi$
$348$	−6.48311e39	+	6.48311e39i	−0.140125	+	0.140125i
$349$		−	1.99842e40i		−	0.412554i	−0.978494	−	0.206277i	$-0.933865\pi$
$349$		−	1.99842e40i		−	0.412554i	0.978494	−	0.206277i	$-0.0661348\pi$
$350$		0			0
$351$	−1.68077e40			−0.316660
$352$	−1.06911e40	−	1.06911e40i	−0.192460	−	0.192460i
$353$	−3.68038e40	+	3.68038e40i	−0.633137	+	0.633137i	−0.948854	−	0.315716i	$-0.897755\pi$
$353$	−3.68038e40	+	3.68038e40i	−0.633137	+	0.633137i	0.315716	+	0.948854i	$0.397755\pi$
$354$		−	2.08059e40i		−	0.342086i
$355$		0			0
$356$	1.58376e41			2.37952
$357$	2.11558e39	+	2.11558e39i	0.0303906	+	0.0303906i
$358$	1.13147e41	−	1.13147e41i	1.55423	−	1.55423i
$359$		−	6.42322e40i		−	0.843804i	−0.906641	−	0.421902i	$-0.861363\pi$
$359$		−	6.42322e40i		−	0.843804i	0.906641	−	0.421902i	$-0.138637\pi$
$360$		0			0
$361$	−1.34388e41			−1.61527
$362$	−1.74981e41	−	1.74981e41i	−2.01212	−	2.01212i
$363$	−8.56804e39	+	8.56804e39i	−0.0942704	+	0.0942704i
$364$			9.49099e40i			0.999286i
$365$		0			0
$366$	1.19504e40			0.115262
$367$	4.85289e40	+	4.85289e40i	0.448068	+	0.448068i	0.894712	−	0.446644i	$-0.147381\pi$
$367$	4.85289e40	+	4.85289e40i	0.448068	+	0.448068i	−0.446644	+	0.894712i	$0.647381\pi$
$368$	−3.10825e39	+	3.10825e39i	−0.0274758	+	0.0274758i
$369$		−	2.26072e41i		−	1.91349i
$370$		0			0
$371$	−9.08729e40			−0.705427
$372$	9.08610e39	+	9.08610e39i	0.0675601	+	0.0675601i
$373$	−2.48905e39	+	2.48905e39i	−0.0177293	+	0.0177293i	−0.715916	−	0.698187i	$-0.753991\pi$
$373$	−2.48905e39	+	2.48905e39i	−0.0177293	+	0.0177293i	0.698187	+	0.715916i	$0.253991\pi$
$374$			2.85777e40i			0.195021i
$375$		0			0
$376$	1.12829e41			0.706992
$377$	−1.23567e41	−	1.23567e41i	−0.742063	−	0.742063i
$378$	3.16220e40	−	3.16220e40i	0.182021	−	0.182021i
$379$			1.82862e40i			0.100901i	0.998727	+	0.0504506i	$0.0160657\pi$
$379$			1.82862e40i			0.100901i	−0.998727	+	0.0504506i	$0.983934\pi$
$380$		0			0
$381$	4.86414e40			0.246721
$382$	−2.19794e40	−	2.19794e40i	−0.106906	−	0.106906i
$383$	−1.70157e41	+	1.70157e41i	−0.793725	+	0.793725i	−0.982098	−	0.188373i	$-0.939679\pi$
$383$	−1.70157e41	+	1.70157e41i	−0.793725	+	0.793725i	0.188373	+	0.982098i	$0.439679\pi$
$384$			4.48501e40i			0.200661i
$385$		0			0
$386$	−1.11982e41			−0.461053
$387$	3.33765e40	+	3.33765e40i	0.131846	+	0.131846i
$388$	1.54085e41	−	1.54085e41i	0.584054	−	0.584054i
$389$		−	1.31225e41i		−	0.477336i	−0.971101	−	0.238668i	$-0.923289\pi$
$389$		−	1.31225e41i		−	0.477336i	0.971101	−	0.238668i	$-0.0767108\pi$
$390$		0			0
$391$	2.83554e40			0.0950183
$392$	1.19625e41	+	1.19625e41i	0.384807	+	0.384807i
$393$	−2.26803e40	+	2.26803e40i	−0.0700436	+	0.0700436i
$394$			3.50657e41i			1.03978i
$395$		0			0
$396$	1.27450e41			0.348511
$397$	−3.66960e41	−	3.66960e41i	−0.963764	−	0.963764i	0.0356022	−	0.999366i	$-0.488665\pi$
$397$	−3.66960e41	−	3.66960e41i	−0.963764	−	0.963764i	−0.999366	+	0.0356022i	$0.988665\pi$
$398$	−7.32729e41	+	7.32729e41i	−1.84848	+	1.84848i
$399$			5.46740e40i			0.132499i
$400$		0			0
$401$	−5.15463e41			−1.15315			−0.576577	−	0.817043i	$-0.695612\pi$
$401$	−5.15463e41			−1.15315			−0.576577	+	0.817043i	$0.695612\pi$
$402$	1.11360e41	+	1.11360e41i	0.239393	+	0.239393i
$403$	−1.73180e41	+	1.73180e41i	−0.357780	+	0.357780i
$404$			9.17611e41i			1.82204i
$405$		0			0
$406$	4.64959e41			0.853097
$407$	5.32659e40	+	5.32659e40i	0.0939590	+	0.0939590i
$408$	2.53358e40	−	2.53358e40i	0.0429707	−	0.0429707i
$409$		−	1.67695e41i		−	0.273493i	−0.990606	−	0.136747i	$-0.956335\pi$
$409$		−	1.67695e41i		−	0.273493i	0.990606	−	0.136747i	$-0.0436646\pi$
$410$		0			0
$411$	1.55180e41			0.234081
$412$	−9.94731e39	−	9.94731e39i	−0.0144328	−	0.0144328i
$413$	−4.49737e41	+	4.49737e41i	−0.627708	+	0.627708i
$414$		−	2.09787e41i		−	0.281691i
$415$		0			0
$416$	−1.05938e42			−1.31691
$417$	−3.08488e40	−	3.08488e40i	−0.0369030	−	0.0369030i
$418$	−3.69273e41	+	3.69273e41i	−0.425135	+	0.425135i
$419$			1.15069e42i			1.27507i	0.770422	+	0.637534i	$0.220046\pi$
$419$			1.15069e42i			1.27507i	−0.770422	+	0.637534i	$0.779954\pi$
$420$		0			0
$421$	−1.36468e42			−1.40125			−0.700627	−	0.713528i	$-0.747096\pi$
$421$	−1.36468e42			−1.40125			−0.700627	+	0.713528i	$0.747096\pi$
$422$	2.72614e41	+	2.72614e41i	0.269494	+	0.269494i
$423$	6.26816e41	−	6.26816e41i	0.596615	−	0.596615i
$424$			1.08828e42i			0.997438i
$425$		0			0
$426$	−1.22752e41			−0.104346
$427$	−2.58317e41	−	2.58317e41i	−0.211499	−	0.211499i
$428$	1.36987e42	−	1.36987e42i	1.08038	−	1.08038i
$429$		−	4.93190e40i		−	0.0374712i
$430$		0			0
$431$	−2.07089e42			−1.46056			−0.730281	−	0.683147i	$-0.760611\pi$
$431$	−2.07089e42			−1.46056			−0.730281	+	0.683147i	$0.760611\pi$
$432$	6.23421e40	+	6.23421e40i	0.0423684	+	0.0423684i
$433$	3.50169e41	−	3.50169e41i	0.229336	−	0.229336i	−0.583079	−	0.812415i	$-0.698152\pi$
$433$	3.50169e41	−	3.50169e41i	0.229336	−	0.229336i	0.812415	+	0.583079i	$0.198152\pi$
$434$		−	6.51642e41i		−	0.411314i
$435$		0			0
$436$	2.11227e42			1.23870
$437$	3.66400e41	+	3.66400e41i	0.207135	+	0.207135i
$438$	−1.95047e41	+	1.95047e41i	−0.106305	+	0.106305i
$439$		−	2.70111e42i		−	1.41942i	−0.704495	−	0.709709i	$-0.748826\pi$
$439$		−	2.70111e42i		−	1.41942i	0.704495	−	0.709709i	$-0.251174\pi$
$440$		0			0
$441$	1.32914e42			0.649460
$442$	1.41587e42	+	1.41587e42i	0.667218	+	0.667218i
$443$	−2.77357e42	+	2.77357e42i	−1.26061	+	1.26061i	−0.309805	+	0.950800i	$0.600264\pi$
$443$	−2.77357e42	+	2.77357e42i	−1.26061	+	1.26061i	−0.950800	+	0.309805i	$0.899736\pi$
$444$		−	2.76921e41i		−	0.121403i
$445$		0			0
$446$	5.74478e42			2.34377
$447$	−2.95980e41	−	2.95980e41i	−0.116504	−	0.116504i
$448$	1.76115e42	−	1.76115e42i	0.668879	−	0.668879i
$449$			1.44734e42i			0.530432i	0.964189	+	0.265216i	$0.0854433\pi$
$449$			1.44734e42i			0.530432i	−0.964189	+	0.265216i	$0.914557\pi$
$450$		0			0
$451$	1.34020e42			0.457453
$452$	−1.05032e42	−	1.05032e42i	−0.346024	−	0.346024i
$453$	1.50629e41	−	1.50629e41i	0.0479001	−	0.0479001i
$454$		−	7.89478e42i		−	2.42352i
$455$		0			0
$456$	6.54765e41			0.187348
$457$	5.31800e41	+	5.31800e41i	0.146923	+	0.146923i	0.776742	−	0.629819i	$-0.216871\pi$
$457$	5.31800e41	+	5.31800e41i	0.146923	+	0.146923i	−0.629819	+	0.776742i	$0.716871\pi$
$458$	2.15434e42	−	2.15434e42i	0.574733	−	0.574733i
$459$		−	5.68724e41i		−	0.146520i
$460$		0			0
$461$	1.57789e42			0.379194			0.189597	−	0.981862i	$-0.439282\pi$
$461$	1.57789e42			0.379194			0.189597	+	0.981862i	$0.439282\pi$
$462$	9.27890e40	+	9.27890e40i	0.0215390	+	0.0215390i
$463$	3.55955e42	−	3.55955e42i	0.798178	−	0.798178i	−0.184630	−	0.982808i	$-0.559109\pi$
$463$	3.55955e42	−	3.55955e42i	0.798178	−	0.798178i	0.982808	+	0.184630i	$0.0591087\pi$
$464$			9.16657e41i			0.198573i
$465$		0			0
$466$	−3.94327e42			−0.797411
$467$	−6.77978e42	−	6.77978e42i	−1.32479	−	1.32479i	−0.909852	−	0.414934i	$-0.863805\pi$
$467$	−6.77978e42	−	6.77978e42i	−1.32479	−	1.32479i	−0.414934	−	0.909852i	$-0.636195\pi$
$468$	6.31446e42	−	6.31446e42i	1.19235	−	1.19235i
$469$		−	4.81425e42i		−	0.878543i
$470$		0			0
$471$	−6.48073e41			−0.110482
$472$	5.38596e42	+	5.38596e42i	0.887547	+	0.887547i
$473$	−1.97863e41	+	1.97863e41i	−0.0315200	+	0.0315200i
$474$		−	2.09286e42i		−	0.322319i
$475$		0			0
$476$	−3.21148e42			−0.462375
$477$	6.04587e42	+	6.04587e42i	0.841715	+	0.841715i
$478$	−2.78178e41	+	2.78178e41i	−0.0374521	+	0.0374521i
$479$			8.92375e41i			0.116193i	0.998311	+	0.0580964i	$0.0185031\pi$
$479$			8.92375e41i			0.116193i	−0.998311	+	0.0580964i	$0.981497\pi$
$480$		0			0
$481$	5.27808e42			0.642916
$482$	−8.40266e42	−	8.40266e42i	−0.990066	−	0.990066i
$483$	9.20672e40	−	9.20672e40i	0.0104942	−	0.0104942i
$484$		−	1.30064e43i		−	1.43427i
$485$		0			0
$486$	−6.33269e42			−0.653744
$487$	1.22579e43	+	1.22579e43i	1.22449	+	1.22449i	0.966020	+	0.258466i	$0.0832171\pi$
$487$	1.22579e43	+	1.22579e43i	1.22449	+	1.22449i	0.258466	+	0.966020i	$0.416783\pi$
$488$	−3.09356e42	+	3.09356e42i	−0.299048	+	0.299048i
$489$			1.58117e42i			0.147924i
$490$		0			0
$491$	−2.63692e42			−0.231097			−0.115548	−	0.993302i	$-0.536863\pi$
$491$	−2.63692e42			−0.231097			−0.115548	+	0.993302i	$0.536863\pi$
$492$	−3.48376e42	−	3.48376e42i	−0.295534	−	0.295534i
$493$	4.18116e42	−	4.18116e42i	0.343357	−	0.343357i
$494$			3.65910e43i			2.90900i
$495$		0			0
$496$	1.28470e42			0.0957402
$497$	2.65338e42	+	2.65338e42i	0.191468	+	0.191468i
$498$	3.79959e42	−	3.79959e42i	0.265502	−	0.265502i
$499$			1.31661e43i			0.890940i	0.895297	+	0.445470i	$0.146963\pi$
$499$			1.31661e43i			0.890940i	−0.895297	+	0.445470i	$0.853037\pi$
$500$		0			0
$501$	2.95377e42			0.187488
$502$	9.18744e42	+	9.18744e42i	0.564852	+	0.564852i
$503$	−1.47887e43	+	1.47887e43i	−0.880731	+	0.880731i	−0.993609	−	0.112878i	$-0.963993\pi$
$503$	−1.47887e43	+	1.47887e43i	−0.880731	+	0.880731i	0.112878	+	0.993609i	$0.463993\pi$
$504$			8.10362e42i			0.467510i
$505$		0			0
$506$	1.24366e42			0.0673432
$507$	−5.42302e41	−	5.42302e41i	−0.0284521	−	0.0284521i
$508$	−3.69191e43	+	3.69191e43i	−1.87686	+	1.87686i
$509$		−	1.64319e42i		−	0.0809474i	−0.999181	−	0.0404737i	$-0.987113\pi$
$509$		−	1.64319e42i		−	0.0809474i	0.999181	−	0.0404737i	$-0.0128867\pi$
$510$		0			0
$511$	8.43220e42			0.390127
$512$	6.70742e42	+	6.70742e42i	0.300771	+	0.300771i
$513$	7.34889e42	−	7.34889e42i	0.319406	−	0.319406i
$514$			4.62823e42i			0.194987i
$515$		0			0
$516$	1.02866e42			0.0407265
$517$	3.71589e42	+	3.71589e42i	0.142631	+	0.142631i
$518$	−9.93021e42	+	9.93021e42i	−0.369558	+	0.369558i
$519$		−	1.79375e42i		−	0.0647267i
$520$		0			0
$521$	−2.19345e43			−0.744259			−0.372129	−	0.928181i	$-0.621372\pi$
$521$	−2.19345e43			−0.744259			−0.372129	+	0.928181i	$0.621372\pi$
$522$	−3.09342e43	−	3.09342e43i	−1.01791	−	1.01791i
$523$	−3.73189e42	+	3.73189e42i	−0.119097	+	0.119097i	−0.764143	−	0.645046i	$-0.776838\pi$
$523$	−3.73189e42	+	3.73189e42i	−0.119097	+	0.119097i	0.645046	+	0.764143i	$0.276838\pi$
$524$		−	3.44290e43i		−	1.06567i
$525$		0			0
$526$	−7.55317e43			−2.19967
$527$	−5.85991e42	−	5.85991e42i	−0.165547	−	0.165547i
$528$	−1.82932e41	+	1.82932e41i	−0.00501356	+	0.00501356i
$529$			3.63749e43i			0.967189i
$530$		0			0
$531$	5.98429e43			1.49796
$532$	−4.14979e43	−	4.14979e43i	−1.00795	−	1.00795i
$533$	6.64000e43	−	6.64000e43i	1.56507	−	1.56507i
$534$		−	1.53427e43i		−	0.350946i
$535$		0			0
$536$	−5.76545e43			−1.24221
$537$	−6.60733e42	−	6.60733e42i	−0.138177	−	0.138177i
$538$	2.27646e43	−	2.27646e43i	0.462108	−	0.462108i
$539$			7.87940e42i			0.155265i
$540$		0			0
$541$	1.87852e43			0.348867			0.174434	−	0.984669i	$-0.444191\pi$
$541$	1.87852e43			0.348867			0.174434	+	0.984669i	$0.444191\pi$
$542$	−7.87419e41	−	7.87419e41i	−0.0141977	−	0.0141977i
$543$	−1.02181e43	+	1.02181e43i	−0.178885	+	0.178885i
$544$		−	3.58463e43i		−	0.609343i
$545$		0			0
$546$	9.19440e42			0.147381
$547$	−6.77331e43	−	6.77331e43i	−1.05440	−	1.05440i	−0.998433	−	0.0559635i	$-0.982177\pi$
$547$	−6.77331e43	−	6.77331e43i	−1.05440	−	1.05440i	−0.0559635	−	0.998433i	$-0.517823\pi$
$548$	−1.17782e44	+	1.17782e44i	−1.78070	+	1.78070i
$549$			3.43723e43i			0.504720i
$550$		0			0
$551$	1.08055e44			1.49700
$552$	−1.10258e42	−	1.10258e42i	−0.0148383	−	0.0148383i
$553$	−4.52387e43	+	4.52387e43i	−0.591436	+	0.591436i
$554$		−	1.19070e44i		−	1.51233i
$555$		0			0
$556$	4.68289e43			0.561458
$557$	4.56808e43	+	4.56808e43i	0.532171	+	0.532171i	0.921218	−	0.389047i	$-0.127196\pi$
$557$	4.56808e43	+	4.56808e43i	0.532171	+	0.532171i	−0.389047	+	0.921218i	$0.627196\pi$
$558$	−4.33544e43	+	4.33544e43i	−0.490780	+	0.490780i
$559$			1.96061e43i			0.215676i
$560$		0			0
$561$	1.66882e42			0.0173381
$562$	−2.82180e43	−	2.82180e43i	−0.284935	−	0.284935i
$563$	8.18099e43	−	8.18099e43i	0.802919	−	0.802919i	−0.180632	−	0.983551i	$-0.557814\pi$
$563$	8.18099e43	−	8.18099e43i	0.802919	−	0.802919i	0.983551	+	0.180632i	$0.0578144\pi$
$564$		−	1.93184e43i		−	0.184291i
$565$		0			0
$566$	−8.63353e42			−0.0778262
$567$	4.40867e43	+	4.40867e43i	0.386348	+	0.386348i
$568$	3.17764e43	−	3.17764e43i	0.270727	−	0.270727i
$569$			8.47985e43i			0.702412i	0.936298	+	0.351206i	$0.114228\pi$
$569$			8.47985e43i			0.702412i	−0.936298	+	0.351206i	$0.885772\pi$
$570$		0			0
$571$	1.51113e44			1.18338			0.591691	−	0.806165i	$-0.298461\pi$
$571$	1.51113e44			1.18338			0.591691	+	0.806165i	$0.298461\pi$
$572$	3.74334e43	+	3.74334e43i	0.285051	+	0.285051i
$573$	−1.28351e42	+	1.28351e42i	−0.00950438	+	0.00950438i
$574$			2.49851e44i			1.79924i
$575$		0			0
$576$	−2.34342e44			−1.59621
$577$	1.08765e44	+	1.08765e44i	0.720568	+	0.720568i	0.968721	−	0.248153i	$-0.0798234\pi$
$577$	1.08765e44	+	1.08765e44i	0.720568	+	0.720568i	−0.248153	+	0.968721i	$0.579823\pi$
$578$	1.26201e44	−	1.26201e44i	0.813234	−	0.813234i
$579$			6.53927e42i			0.0409894i
$580$		0			0
$581$	−1.64262e44			−0.974361
$582$	−1.49270e43	−	1.49270e43i	−0.0861399	−	0.0861399i
$583$	−3.58412e43	+	3.58412e43i	−0.201227	+	0.201227i
$584$		−	1.00982e44i		−	0.551620i
$585$		0			0
$586$	−2.17826e44			−1.12655
$587$	2.06363e44	+	2.06363e44i	1.03854	+	1.03854i	0.999227	+	0.0393087i	$0.0125156\pi$
$587$	2.06363e44	+	2.06363e44i	1.03854	+	1.03854i	0.0393087	+	0.999227i	$0.487484\pi$
$588$	2.04819e43	−	2.04819e43i	0.100308	−	0.100308i
$589$		−	1.51440e44i		−	0.721766i
$590$		0			0
$591$	2.04769e43			0.0924409
$592$	−1.95772e43	−	1.95772e43i	−0.0860207	−	0.0860207i
$593$	7.69129e43	−	7.69129e43i	0.328945	−	0.328945i	−0.523240	−	0.852185i	$-0.675277\pi$
$593$	7.69129e43	−	7.69129e43i	0.328945	−	0.328945i	0.852185	+	0.523240i	$0.175277\pi$
$594$		−	2.49441e43i		−	0.103845i
$595$		0			0
$596$	4.49302e44			1.77255
$597$	4.27882e43	+	4.27882e43i	0.164337	+	0.164337i
$598$	6.16167e43	−	6.16167e43i	0.230399	−	0.230399i
$599$			6.34714e42i			0.0231073i	0.999933	+	0.0115536i	$0.00367772\pi$
$599$			6.34714e42i			0.0231073i	−0.999933	+	0.0115536i	$0.996322\pi$
$600$		0			0
$601$	−4.35566e44			−1.50336			−0.751679	−	0.659530i	$-0.770756\pi$
$601$	−4.35566e44			−1.50336			−0.751679	+	0.659530i	$0.770756\pi$
$602$	−3.68870e43	−	3.68870e43i	−0.123974	−	0.123974i
$603$	−3.20297e44	+	3.20297e44i	−1.04828	+	1.04828i
$604$			2.28656e44i			0.728772i
$605$		0			0
$606$	8.88936e43			0.268725
$607$	−2.45046e44	−	2.45046e44i	−0.721486	−	0.721486i	0.247422	−	0.968908i	$-0.420417\pi$
$607$	−2.45046e44	−	2.45046e44i	−0.721486	−	0.721486i	−0.968908	+	0.247422i	$0.920417\pi$
$608$	4.63196e44	−	4.63196e44i	1.32833	−	1.32833i
$609$		−	2.71516e43i		−	0.0758437i
$610$		0			0
$611$	3.68205e44			0.975957
$612$	2.13663e44	+	2.13663e44i	0.551706	+	0.551706i
$613$	1.49701e44	−	1.49701e44i	0.376579	−	0.376579i	−0.493288	−	0.869866i	$-0.664205\pi$
$613$	1.49701e44	−	1.49701e44i	0.376579	−	0.376579i	0.869866	+	0.493288i	$0.164205\pi$
$614$		−	5.96836e44i		−	1.46272i
$615$		0			0
$616$	−4.80400e43			−0.111766
$617$	5.94730e43	+	5.94730e43i	0.134821	+	0.134821i	0.771297	−	0.636476i	$-0.219609\pi$
$617$	5.94730e43	+	5.94730e43i	0.134821	+	0.134821i	−0.636476	+	0.771297i	$0.719609\pi$
$618$	−9.63646e41	+	9.63646e41i	−0.00212864	+	0.00212864i
$619$		−	2.09980e44i		−	0.451989i	−0.974129	−	0.225994i	$-0.927437\pi$
$619$		−	2.09980e44i		−	0.451989i	0.974129	−	0.225994i	$-0.0725631\pi$
$620$		0			0
$621$	−2.47500e43			−0.0505953
$622$	−2.49503e44	−	2.49503e44i	−0.497084	−	0.497084i
$623$	−3.31643e44	+	3.31643e44i	−0.643966	+	0.643966i
$624$			1.81266e43i			0.0343054i
$625$		0			0
$626$	9.29862e44			1.67197
$627$	2.15640e43	+	2.15640e43i	0.0377962	+	0.0377962i
$628$	4.91892e44	−	4.91892e44i	0.840457	−	0.840457i
$629$			1.78595e44i			0.297481i
$630$		0			0
$631$	8.53003e44			1.35046			0.675229	−	0.737608i	$-0.264045\pi$
$631$	8.53003e44			1.35046			0.675229	+	0.737608i	$0.264045\pi$
$632$	5.41770e44	+	5.41770e44i	0.836261	+	0.836261i
$633$	1.59195e43	−	1.59195e43i	0.0239590	−	0.0239590i
$634$		−	7.05412e44i		−	1.03518i
$635$		0			0
$636$	1.86333e44			0.260002
$637$	3.90382e44	+	3.90382e44i	0.531201	+	0.531201i
$638$	1.83385e44	−	1.83385e44i	0.243350	−	0.243350i
$639$		−	3.53064e44i		−	0.456920i
$640$		0			0
$641$	−9.50370e44			−1.16994			−0.584971	−	0.811054i	$-0.698894\pi$
$641$	−9.50370e44			−1.16994			−0.584971	+	0.811054i	$0.698894\pi$
$642$	−1.32706e44	−	1.32706e44i	−0.159342	−	0.159342i
$643$	−9.01509e44	+	9.01509e44i	−1.05583	+	1.05583i	−0.0574844	+	0.998346i	$0.518308\pi$
$643$	−9.01509e44	+	9.01509e44i	−1.05583	+	1.05583i	−0.998346	+	0.0574844i	$0.981692\pi$
$644$			1.39759e44i			0.159664i
$645$		0			0
$646$	−1.23814e45			−1.34601
$647$	−5.98377e44	−	5.98377e44i	−0.634609	−	0.634609i	0.314612	−	0.949220i	$-0.398126\pi$
$647$	−5.98377e44	−	5.98377e44i	−0.634609	−	0.634609i	−0.949220	+	0.314612i	$0.898126\pi$
$648$	5.27974e44	−	5.27974e44i	0.546277	−	0.546277i
$649$			3.54761e44i			0.358114i
$650$		0			0
$651$	−3.80531e43			−0.0365674
$652$	−1.20012e45	−	1.20012e45i	−1.12529	−	1.12529i
$653$	1.35964e45	−	1.35964e45i	1.24398	−	1.24398i	0.285647	−	0.958335i	$-0.407792\pi$
$653$	1.35964e45	−	1.35964e45i	1.24398	−	1.24398i	0.958335	−	0.285647i	$-0.0922084\pi$
$654$		−	2.04626e44i		−	0.182691i
$655$		0			0
$656$	−4.92575e44			−0.418804
$657$	−5.61003e44	−	5.61003e44i	−0.465500	−	0.465500i
$658$	−6.92744e44	+	6.92744e44i	−0.560994	+	0.560994i
$659$		−	3.61938e44i		−	0.286067i	−0.989718	−	0.143033i	$-0.954314\pi$
$659$		−	3.61938e44i		−	0.286067i	0.989718	−	0.143033i	$-0.0456857\pi$
$660$		0			0
$661$	−3.80764e44			−0.286704			−0.143352	−	0.989672i	$-0.545788\pi$
$661$	−3.80764e44			−0.286704			−0.143352	+	0.989672i	$0.545788\pi$
$662$	−6.99319e44	−	6.99319e44i	−0.513982	−	0.513982i
$663$	8.26809e43	−	8.26809e43i	0.0593183	−	0.0593183i
$664$			1.96717e45i			1.37770i
$665$		0			0
$666$	1.32133e45			0.881912
$667$	−1.81958e44	−	1.81958e44i	−0.118565	−	0.118565i
$668$	−2.24193e45	+	2.24193e45i	−1.42626	+	1.42626i
$669$		−	3.35470e44i		−	0.208371i
$670$		0			0
$671$	−2.03766e44			−0.120662
$672$	−1.16390e44	−	1.16390e44i	−0.0672985	−	0.0672985i
$673$	−2.30699e45	+	2.30699e45i	−1.30258	+	1.30258i	−0.375938	+	0.926645i	$0.622679\pi$
$673$	−2.30699e45	+	2.30699e45i	−1.30258	+	1.30258i	−0.926645	+	0.375938i	$0.877321\pi$
$674$		−	3.60213e44i		−	0.198610i
$675$		0			0
$676$	8.23222e44			0.432882
$677$	2.41143e45	+	2.41143e45i	1.23839	+	1.23839i	0.960660	+	0.277728i	$0.0895816\pi$
$677$	2.41143e45	+	2.41143e45i	1.23839	+	1.23839i	0.277728	+	0.960660i	$0.410418\pi$
$678$	−1.01750e44	+	1.01750e44i	−0.0510338	+	0.0510338i
$679$			6.45317e44i			0.316124i
$680$		0			0
$681$	−4.61022e44			−0.215460
$682$	−2.57014e44	−	2.57014e44i	−0.117329	−	0.117329i
$683$	−7.65334e44	+	7.65334e44i	−0.341287	+	0.341287i	−0.856851	−	0.515564i	$-0.827582\pi$
$683$	−7.65334e44	+	7.65334e44i	−0.341287	+	0.341287i	0.515564	+	0.856851i	$0.327582\pi$
$684$			5.52180e45i			2.40538i
$685$		0			0
$686$	−3.68571e45			−1.53227
$687$	−1.25804e44	−	1.25804e44i	−0.0510960	−	0.0510960i
$688$	7.27220e43	−	7.27220e43i	0.0288570	−	0.0288570i
$689$			3.55148e45i			1.37690i
$690$		0			0
$691$	−2.84955e45			−1.05470			−0.527349	−	0.849649i	$-0.676814\pi$
$691$	−2.84955e45			−1.05470			−0.527349	+	0.849649i	$0.676814\pi$
$692$	1.36146e45	+	1.36146e45i	0.492390	+	0.492390i
$693$	−2.66884e44	+	2.66884e44i	−0.0943171	+	0.0943171i
$694$			1.03015e44i			0.0355752i
$695$		0			0
$696$	−3.25163e44			−0.107239
$697$	2.24679e45	+	2.24679e45i	0.724165	+	0.724165i
$698$	1.46942e45	−	1.46942e45i	0.462869	−	0.462869i
$699$			2.30270e44i			0.0708930i
$700$		0			0
$701$	8.83073e44			0.259722			0.129861	−	0.991532i	$-0.458547\pi$
$701$	8.83073e44			0.259722			0.129861	+	0.991532i	$0.458547\pi$
$702$	−1.23585e45	−	1.23585e45i	−0.355280	−	0.355280i
$703$	−2.30776e45	+	2.30776e45i	−0.648492	+	0.648492i
$704$		−	1.38923e45i		−	0.381602i
$705$		0			0
$706$	−5.41228e45			−1.42071
$707$	−1.92150e45	−	1.92150e45i	−0.493095	−	0.493095i
$708$	9.22176e44	−	9.22176e44i	0.231357	−	0.231357i
$709$		−	2.85476e45i		−	0.700213i	−0.936710	−	0.350106i	$-0.886145\pi$
$709$		−	2.85476e45i		−	0.700213i	0.936710	−	0.350106i	$-0.113855\pi$
$710$		0			0
$711$	6.01956e45			1.41140
$712$	3.97170e45	+	3.97170e45i	0.910535	+	0.910535i
$713$	−2.55015e44	+	2.55015e44i	−0.0571653	+	0.0571653i
$714$			3.11113e44i			0.0681940i
$715$		0			0
$716$	1.00300e46			2.10229
$717$	1.62444e43	+	1.62444e43i	0.00332964	+	0.00332964i
$718$	4.72292e45	−	4.72292e45i	0.946715	−	0.946715i
$719$			3.50390e45i			0.686894i	0.939172	+	0.343447i	$0.111595\pi$
$719$			3.50390e45i			0.686894i	−0.939172	+	0.343447i	$0.888405\pi$
$720$		0			0
$721$	4.16599e43			0.00781185
$722$	−9.88136e45	−	9.88136e45i	−1.81226	−	1.81226i
$723$	−4.90680e44	+	4.90680e44i	−0.0880208	+	0.0880208i
$724$		−	1.55113e46i		−	2.72163i
$725$		0			0
$726$	−1.25999e45			−0.211535
$727$	−6.22114e44	−	6.22114e44i	−0.102169	−	0.102169i	0.654175	−	0.756344i	$-0.273016\pi$
$727$	−6.22114e44	−	6.22114e44i	−0.102169	−	0.102169i	−0.756344	+	0.654175i	$0.773016\pi$
$728$	−2.38012e45	+	2.38012e45i	−0.382382	+	0.382382i
$729$		−	5.61557e45i		−	0.882579i
$730$		0			0
$731$	−6.63415e44			−0.0997947
$732$	5.29675e44	+	5.29675e44i	0.0779529	+	0.0779529i
$733$	−3.05780e45	+	3.05780e45i	−0.440296	+	0.440296i	−0.892111	−	0.451815i	$-0.850777\pi$
$733$	−3.05780e45	+	3.05780e45i	−0.440296	+	0.440296i	0.451815	+	0.892111i	$0.350777\pi$
$734$			7.13654e45i			1.00543i
$735$		0			0
$736$	−1.55998e45			−0.210414
$737$	−1.89879e45	−	1.89879e45i	−0.250609	−	0.250609i
$738$	1.66228e46	−	1.66228e46i	2.14686	−	2.14686i
$739$		−	1.32401e46i		−	1.67333i	−0.547716	−	0.836664i	$-0.684503\pi$
$739$		−	1.32401e46i		−	1.67333i	0.547716	−	0.836664i	$-0.315497\pi$
$740$		0			0
$741$	2.13676e45			0.258621
$742$	−6.68177e45	−	6.68177e45i	−0.791461	−	0.791461i
$743$	5.48359e45	−	5.48359e45i	0.635688	−	0.635688i	−0.313801	−	0.949489i	$-0.601602\pi$
$743$	5.48359e45	−	5.48359e45i	0.635688	−	0.635688i	0.949489	+	0.313801i	$0.101602\pi$
$744$			4.55717e44i			0.0517045i
$745$		0			0
$746$	−3.66034e44			−0.0397832
$747$	1.09285e46	+	1.09285e46i	1.16261	+	1.16261i
$748$	−1.26664e45	+	1.26664e45i	−0.131895	+	0.131895i
$749$			5.73709e45i			0.584766i
$750$		0			0
$751$	1.34012e46			1.30889			0.654447	−	0.756108i	$-0.272902\pi$
$751$	1.34012e46			1.30889			0.654447	+	0.756108i	$0.272902\pi$
$752$	−1.36573e45	−	1.36573e45i	−0.130581	−	0.130581i
$753$	5.36507e44	−	5.36507e44i	0.0502176	−	0.0502176i
$754$		−	1.81715e46i		−	1.66513i
$755$		0			0
$756$	2.80315e45			0.246205
$757$	1.05837e46	+	1.05837e46i	0.910129	+	0.910129i	0.996282	−	0.0861534i	$-0.0274575\pi$
$757$	1.05837e46	+	1.05837e46i	0.910129	+	0.910129i	−0.0861534	+	0.996282i	$0.527458\pi$
$758$	−1.34456e45	+	1.34456e45i	−0.113207	+	0.113207i
$759$		−	7.26245e43i		−	0.00598707i
$760$		0			0
$761$	7.81481e45			0.617681			0.308840	−	0.951114i	$-0.400059\pi$
$761$	7.81481e45			0.617681			0.308840	+	0.951114i	$0.400059\pi$
$762$	3.57654e45	+	3.57654e45i	0.276811	+	0.276811i
$763$	−4.42315e45	+	4.42315e45i	−0.335227	+	0.335227i
$764$		−	1.94838e45i		−	0.144604i
$765$		0			0
$766$	−2.50229e46			−1.78106
$767$	1.75765e46	+	1.75765e46i	1.22520	+	1.22520i
$768$	−9.18208e44	+	9.18208e44i	−0.0626847	+	0.0626847i
$769$			3.85853e45i			0.257988i	0.991645	+	0.128994i	$0.0411749\pi$
$769$			3.85853e45i			0.257988i	−0.991645	+	0.128994i	$0.958825\pi$
$770$		0			0
$771$	2.70269e44			0.0173351
$772$	−4.96334e45	−	4.96334e45i	−0.311815	−	0.311815i
$773$	7.60993e45	−	7.60993e45i	0.468283	−	0.468283i	−0.433075	−	0.901358i	$-0.642571\pi$
$773$	7.60993e45	−	7.60993e45i	0.468283	−	0.468283i	0.901358	+	0.433075i	$0.142571\pi$
$774$			4.90827e45i			0.295851i
$775$		0			0
$776$	7.72820e45			0.446983
$777$	5.79882e44	+	5.79882e44i	0.0328551	+	0.0328551i
$778$	9.64885e45	−	9.64885e45i	0.535552	−	0.535552i
$779$			5.80647e46i			3.15728i
$780$		0			0
$781$	2.09304e45			0.109235
$782$	2.08494e45	+	2.08494e45i	0.106607	+	0.106607i
$783$	−3.64953e45	+	3.64953e45i	−0.182831	+	0.182831i
$784$		−	2.89597e45i		−	0.142147i
$785$		0			0
$786$	−3.33531e45			−0.157172
$787$	4.07849e45	+	4.07849e45i	0.188323	+	0.188323i	0.794971	−	0.606648i	$-0.207486\pi$
$787$	4.07849e45	+	4.07849e45i	0.188323	+	0.188323i	−0.606648	+	0.794971i	$0.707486\pi$
$788$	−1.55421e46	+	1.55421e46i	−0.703217	+	0.703217i
$789$			4.41073e45i			0.195559i
$790$		0			0
$791$	4.39880e45			0.187288
$792$	3.19615e45	+	3.19615e45i	0.133360	+	0.133360i
$793$	−1.00955e46	+	1.00955e46i	−0.412817	+	0.412817i
$794$		−	5.39642e46i		−	2.16261i
$795$		0			0
$796$	−6.49531e46			−2.50029
$797$	−1.39427e46	−	1.39427e46i	−0.526035	−	0.526035i	0.393353	−	0.919388i	$-0.371315\pi$
$797$	−1.39427e46	−	1.39427e46i	−0.526035	−	0.526035i	−0.919388	+	0.393353i	$0.871315\pi$
$798$	−4.02011e45	+	4.02011e45i	−0.148659	+	0.148659i
$799$			1.24590e46i			0.451581i
$800$		0			0
$801$	4.41292e46			1.53676
$802$	−3.79013e46	−	3.79013e46i	−1.29379	−	1.29379i
$803$	3.32574e45	−	3.32574e45i	0.111286	−	0.111286i
$804$			9.87152e45i			0.323808i
$805$		0			0
$806$	−2.54674e46			−0.802829
$807$	−1.32936e45	−	1.32936e45i	−0.0410832	−	0.0410832i
$808$	−2.30116e46	+	2.30116e46i	−0.697211	+	0.697211i
$809$			1.50110e46i			0.445895i	0.974830	+	0.222948i	$0.0715679\pi$
$809$			1.50110e46i			0.445895i	−0.974830	+	0.222948i	$0.928432\pi$
$810$		0			0
$811$	5.97396e45			0.170580			0.0852901	−	0.996356i	$-0.472818\pi$
$811$	5.97396e45			0.170580			0.0852901	+	0.996356i	$0.472818\pi$
$812$	2.06083e46	+	2.06083e46i	0.576959	+	0.576959i
$813$	−4.59819e43	+	4.59819e43i	−0.00126223	+	0.00126223i
$814$			7.83314e45i			0.210836i
$815$		0			0
$816$	−6.13352e44			−0.0158733
$817$	−8.57246e45	−	8.57246e45i	−0.217547	−	0.217547i
$818$	1.23304e46	−	1.23304e46i	0.306848	−	0.306848i
$819$			2.64453e46i			0.645367i
$820$		0			0
$821$	5.85416e46			1.37396			0.686980	−	0.726676i	$-0.258936\pi$
$821$	5.85416e46			1.37396			0.686980	+	0.726676i	$0.258936\pi$
$822$	1.14102e46	+	1.14102e46i	0.262629	+	0.262629i
$823$	2.58223e46	−	2.58223e46i	0.582904	−	0.582904i	−0.352796	−	0.935700i	$-0.614769\pi$
$823$	2.58223e46	−	2.58223e46i	0.582904	−	0.582904i	0.935700	+	0.352796i	$0.114769\pi$
$824$		−	4.98911e44i		−	0.0110456i
$825$		0			0
$826$	−6.61372e46			−1.40853
$827$	4.19023e46	+	4.19023e46i	0.875285	+	0.875285i	0.993042	−	0.117758i	$-0.0375706\pi$
$827$	4.19023e46	+	4.19023e46i	0.875285	+	0.875285i	−0.117758	+	0.993042i	$0.537571\pi$
$828$	9.29833e45	−	9.29833e45i	0.190511	−	0.190511i
$829$			3.58810e45i			0.0721095i	0.999350	+	0.0360548i	$0.0114791\pi$
$829$			3.58810e45i			0.0721095i	−0.999350	+	0.0360548i	$0.988521\pi$
$830$		0			0
$831$	−6.95320e45			−0.134452
$832$	−6.88288e46	−	6.88288e46i	−1.30556	−	1.30556i
$833$	−1.32094e46	+	1.32094e46i	−0.245790	+	0.245790i
$834$		−	4.53655e45i		−	0.0828074i
$835$		0			0
$836$	−3.27344e46			−0.575047
$837$	5.11483e45	+	5.11483e45i	0.0881503	+	0.0881503i
$838$	−8.46087e46	+	8.46087e46i	−1.43058	+	1.43058i
$839$		−	7.86412e46i		−	1.30454i	−0.757985	−	0.652272i	$-0.773816\pi$
$839$		−	7.86412e46i		−	1.30454i	0.757985	−	0.652272i	$-0.226184\pi$
$840$		0			0
$841$	8.96189e45			0.143108
$842$	−1.00343e47	−	1.00343e47i	−1.57215	−	1.57215i
$843$	−1.64781e45	+	1.64781e45i	−0.0253318	+	0.0253318i
$844$			2.41660e46i			0.364523i
$845$		0			0
$846$	9.21779e46			1.33876
$847$	2.72358e46	+	2.72358e46i	0.388155	+	0.388155i
$848$	1.31730e46	−	1.31730e46i	0.184226	−	0.184226i
$849$			5.04161e44i			0.00691905i
$850$		0			0
$851$	7.77221e45			0.102724
$852$	−5.44070e45	−	5.44070e45i	−0.0705702	−	0.0705702i
$853$	−7.08826e46	+	7.08826e46i	−0.902309	+	0.902309i	−0.995636	−	0.0933266i	$-0.970250\pi$
$853$	−7.08826e46	+	7.08826e46i	−0.902309	+	0.902309i	0.0933266	+	0.995636i	$0.470250\pi$
$854$		−	3.79875e46i		−	0.474586i
$855$		0			0
$856$	6.87062e46			0.826830
$857$	1.06787e47	+	1.06787e47i	1.26132	+	1.26132i	0.950454	+	0.310866i	$0.100619\pi$
$857$	1.06787e47	+	1.06787e47i	1.26132	+	1.26132i	0.310866	+	0.950454i	$0.399381\pi$
$858$	3.62636e45	−	3.62636e45i	0.0420412	−	0.0420412i
$859$		−	2.92725e46i		−	0.333096i	−0.986033	−	0.166548i	$-0.946738\pi$
$859$		−	2.92725e46i		−	0.333096i	0.986033	−	0.166548i	$-0.0532620\pi$
$860$		0			0
$861$	1.45902e46			0.159960
$862$	−1.52270e47	−	1.52270e47i	−1.63869	−	1.63869i
$863$	5.37632e45	−	5.37632e45i	0.0567953	−	0.0567953i	−0.678139	−	0.734934i	$-0.737213\pi$
$863$	5.37632e45	−	5.37632e45i	0.0567953	−	0.0567953i	0.734934	+	0.678139i	$0.237213\pi$
$864$			3.12885e46i			0.324463i
$865$		0			0
$866$	5.14950e46			0.514611
$867$	−7.36957e45	−	7.36957e45i	−0.0722997	−	0.0722997i
$868$	2.88826e46	−	2.88826e46i	0.278176	−	0.278176i
$869$			3.56852e46i			0.337421i
$870$		0			0
$871$	−1.88150e47			−1.71480
$872$	5.29708e46	+	5.29708e46i	0.473994	+	0.473994i
$873$	4.29336e46	−	4.29336e46i	0.377198	−	0.377198i
$874$			5.38819e46i			0.464793i
$875$		0			0
$876$	−1.72901e46			−0.143791
$877$	−1.13109e47	−	1.13109e47i	−0.923644	−	0.923644i	0.0736410	−	0.997285i	$-0.476538\pi$
$877$	−1.13109e47	−	1.13109e47i	−0.923644	−	0.923644i	−0.997285	+	0.0736410i	$0.976538\pi$
$878$	1.98610e47	−	1.98610e47i	1.59253	−	1.59253i
$879$			1.27201e46i			0.100154i
$880$		0			0
$881$	9.60849e46			0.729526			0.364763	−	0.931100i	$-0.381150\pi$
$881$	9.60849e46			0.729526			0.364763	+	0.931100i	$0.381150\pi$
$882$	9.77298e46	+	9.77298e46i	0.728668	+	0.728668i
$883$	−3.73264e46	+	3.73264e46i	−0.273303	+	0.273303i	−0.830429	−	0.557125i	$-0.811904\pi$
$883$	−3.73264e46	+	3.73264e46i	−0.273303	+	0.273303i	0.557125	+	0.830429i	$0.311904\pi$
$884$			1.25511e47i			0.902494i
$885$		0			0
$886$	−4.07874e47			−2.82870
$887$	1.17917e46	+	1.17917e46i	0.0803156	+	0.0803156i	0.746123	−	0.665808i	$-0.231913\pi$
$887$	1.17917e46	+	1.17917e46i	0.0803156	+	0.0803156i	−0.665808	+	0.746123i	$0.731913\pi$
$888$	6.94455e45	−	6.94455e45i	0.0464555	−	0.0464555i
$889$		−	1.54620e47i		−	1.01587i
$890$		0			0
$891$	3.47765e46			0.220416
$892$	2.54624e47	+	2.54624e47i	1.58512	+	1.58512i
$893$	−1.60992e47	+	1.60992e47i	−0.984421	+	0.984421i
$894$		−	4.35261e46i		−	0.261427i
$895$		0			0
$896$	1.42568e47			0.826215
$897$	−3.59815e45	−	3.59815e45i	−0.0204833	−	0.0204833i
$898$	−1.06421e47	+	1.06421e47i	−0.595124	+	0.595124i
$899$			7.52067e46i			0.413144i
$900$		0			0
$901$	−1.20172e47			−0.637099
$902$	9.85435e46	+	9.85435e46i	0.513244	+	0.513244i
$903$	−2.15405e45	+	2.15405e45i	−0.0110218	+	0.0110218i
$904$		−	5.26792e46i		−	0.264816i
$905$		0			0
$906$	2.21511e46			0.107484
$907$	1.24431e47	+	1.24431e47i	0.593214	+	0.593214i	0.938498	−	0.345284i	$-0.112217\pi$
$907$	1.24431e47	+	1.24431e47i	0.593214	+	0.593214i	−0.345284	+	0.938498i	$0.612217\pi$
$908$	3.49918e47	−	3.49918e47i	1.63905	−	1.63905i
$909$			2.55679e47i			1.17672i
$910$		0			0
$911$	2.35092e47			1.04458			0.522292	−	0.852767i	$-0.325077\pi$
$911$	2.35092e47			1.04458			0.522292	+	0.852767i	$0.325077\pi$
$912$	−7.92556e45	−	7.92556e45i	−0.0346029	−	0.0346029i
$913$	−6.47867e46	+	6.47867e46i	−0.277942	+	0.277942i
$914$			7.82052e46i			0.329683i
$915$		0			0
$916$	1.90972e47			0.777397
$917$	7.20953e46	+	7.20953e46i	0.288402	+	0.288402i
$918$	4.18175e46	−	4.18175e46i	0.164390	−	0.164390i
$919$			2.77508e46i			0.107208i	0.998562	+	0.0536040i	$0.0170709\pi$
$919$			2.77508e46i			0.107208i	−0.998562	+	0.0536040i	$0.982929\pi$
$920$		0			0
$921$	−3.48527e46			−0.130042
$922$	1.16020e47	+	1.16020e47i	0.425440	+	0.425440i
$923$	1.03699e47	−	1.03699e47i	0.373721	−	0.373721i
$924$			8.22533e45i			0.0291341i
$925$		0			0
$926$	5.23459e47			1.79105
$927$	−2.77168e45	−	2.77168e45i	−0.00932110	−	0.00932110i
$928$	−2.30028e47	+	2.30028e47i	−0.760348	+	0.760348i
$929$		−	2.57398e47i		−	0.836283i	−0.908382	−	0.418142i	$-0.862682\pi$
$929$		−	2.57398e47i		−	0.836283i	0.908382	−	0.418142i	$-0.137318\pi$
$930$		0			0
$931$	−3.41377e47			−1.07162
$932$	−1.74777e47	−	1.74777e47i	−0.539298	−	0.539298i
$933$	−1.45699e46	+	1.45699e46i	−0.0441927	+	0.0441927i
$934$		−	9.97018e47i		−	2.97271i
$935$		0			0
$936$	3.16704e47			0.912516
$937$	−4.07621e47	−	4.07621e47i	−1.15458	−	1.15458i	−0.985624	−	0.168953i	$-0.945961\pi$
$937$	−4.07621e47	−	4.07621e47i	−1.15458	−	1.15458i	−0.168953	−	0.985624i	$-0.554039\pi$
$938$	3.53986e47	−	3.53986e47i	0.985690	−	0.985690i
$939$		−	5.43000e46i		−	0.148645i
$940$		0			0
$941$	−1.11967e47			−0.296248			−0.148124	−	0.988969i	$-0.547323\pi$
$941$	−1.11967e47			−0.296248			−0.148124	+	0.988969i	$0.547323\pi$
$942$	−4.76520e46	−	4.76520e46i	−0.123956	−	0.123956i
$943$	9.77769e46	−	9.77769e46i	0.250063	−	0.250063i
$944$		−	1.30388e47i		−	0.327858i
$945$		0			0
$946$	−2.90972e46			−0.0707284
$947$	−2.18739e47	−	2.18739e47i	−0.522790	−	0.522790i	0.395623	−	0.918413i	$-0.370529\pi$
$947$	−2.18739e47	−	2.18739e47i	−0.522790	−	0.522790i	−0.918413	+	0.395623i	$0.870529\pi$
$948$	9.27611e46	−	9.27611e46i	0.217988	−	0.217988i
$949$		−	3.29546e47i		−	0.761476i
$950$		0			0
$951$	−4.11931e46			−0.0920314
$952$	−8.05366e46	−	8.05366e46i	−0.176930	−	0.176930i
$953$	−1.10802e47	+	1.10802e47i	−0.239366	+	0.239366i	−0.816588	−	0.577222i	$-0.804137\pi$
$953$	−1.10802e47	+	1.10802e47i	−0.239366	+	0.239366i	0.577222	+	0.816588i	$0.304137\pi$
$954$			8.89091e47i			1.88874i
$955$		0			0
$956$	−2.46592e46			−0.0506586
$957$	−1.07089e46	−	1.07089e46i	−0.0216348	−	0.0216348i
$958$	−6.56152e46	+	6.56152e46i	−0.130364	+	0.130364i
$959$		−	4.93279e47i		−	0.963818i
$960$		0			0
$961$	−4.23742e47			−0.800806
$962$	3.88091e47	+	3.88091e47i	0.721326	+	0.721326i
$963$	3.81694e47	−	3.81694e47i	0.697743	−	0.697743i
$964$		−	7.44858e47i		−	1.33919i
$965$		0			0
$966$	1.35392e46			0.0235482
$967$	−3.38691e47	−	3.38691e47i	−0.579402	−	0.579402i	0.355337	−	0.934738i	$-0.384366\pi$
$967$	−3.38691e47	−	3.38691e47i	−0.579402	−	0.579402i	−0.934738	+	0.355337i	$0.884366\pi$
$968$	3.26170e47	−	3.26170e47i	0.548831	−	0.548831i
$969$			7.23018e46i			0.119665i
$970$		0			0
$971$	−6.64648e47			−1.06435			−0.532174	−	0.846635i	$-0.678625\pi$
$971$	−6.64648e47			−1.06435			−0.532174	+	0.846635i	$0.678625\pi$
$972$	−2.80682e47	−	2.80682e47i	−0.442134	−	0.442134i
$973$	−9.80612e46	+	9.80612e46i	−0.151947	+	0.151947i
$974$			1.80262e48i			2.74765i
$975$		0			0
$976$	7.48916e46			0.110468
$977$	5.06966e47	+	5.06966e47i	0.735641	+	0.735641i	0.971731	−	0.236090i	$-0.0758660\pi$
$977$	5.06966e47	+	5.06966e47i	0.735641	+	0.735641i	−0.236090	+	0.971731i	$0.575866\pi$
$978$	−1.16262e47	+	1.16262e47i	−0.165965	+	0.165965i
$979$			2.61607e47i			0.367389i
$980$		0			0
$981$	5.88554e47			0.799986
$982$	−1.93890e47	−	1.93890e47i	−0.259281	−	0.259281i
$983$	−3.06025e47	+	3.06025e47i	−0.402625	+	0.402625i	−0.879157	−	0.476532i	$-0.841894\pi$
$983$	−3.06025e47	+	3.06025e47i	−0.402625	+	0.402625i	0.476532	+	0.879157i	$0.341894\pi$
$984$		−	1.74730e47i		−	0.226175i
$985$		0			0
$986$	6.14871e47			0.770465
$987$	4.04533e46	+	4.04533e46i	0.0498746	+	0.0498746i
$988$	−1.62181e48	+	1.62181e48i	−1.96739	+	1.96739i
$989$			2.88709e46i			0.0344603i
$990$		0			0
$991$	5.91864e47			0.683980			0.341990	−	0.939704i	$-0.388899\pi$
$991$	5.91864e47			0.683980			0.341990	+	0.939704i	$0.388899\pi$
$992$	3.22384e47	+	3.22384e47i	0.366596	+	0.366596i
$993$	−4.08373e46	+	4.08373e46i	−0.0456950	+	0.0456950i
$994$			3.90199e47i			0.429640i
$995$		0			0
$996$	3.36817e47			0.359124
$997$	3.79469e47	+	3.79469e47i	0.398156	+	0.398156i	0.877582	−	0.479426i	$-0.159155\pi$
$997$	3.79469e47	+	3.79469e47i	0.398156	+	0.398156i	−0.479426	+	0.877582i	$0.659155\pi$
$998$	−9.68088e47	+	9.68088e47i	−0.999599	+	0.999599i
$999$		−	1.55887e47i		−	0.158403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.14		30
5.2	odd	4		5.33.c.a.3.2	yes	30
5.3	odd	4	inner	25.33.c.b.18.14		30
5.4	even	2		5.33.c.a.2.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.2	✓	30	5.4	even	2
5.33.c.a.3.2	yes	30	5.2	odd	4
25.33.c.b.7.14		30	1.1	even	1	trivial
25.33.c.b.18.14		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)

\(f(q)\)	\(=\)	\(q+(73528.8 + 73528.8i) q^{2} +(4.29377e6 - 4.29377e6i) q^{3} +6.51799e9i q^{4} +6.31431e11 q^{6} +(-1.36489e13 - 1.36489e13i) q^{7} +(-1.63456e14 + 1.63456e14i) q^{8} +1.81615e15i q^{9} +O(q^{10})\)	\(q+(73528.8 + 73528.8i) q^{2} +(4.29377e6 - 4.29377e6i) q^{3} +6.51799e9i q^{4} +6.31431e11 q^{6} +(-1.36489e13 - 1.36489e13i) q^{7} +(-1.63456e14 + 1.63456e14i) q^{8} +1.81615e15i q^{9} -1.07665e16 q^{11} +(2.79867e16 + 2.79867e16i) q^{12} +(-5.33423e17 + 5.33423e17i) q^{13} -2.00717e18i q^{14} +3.95709e18 q^{16} +(-1.80495e19 - 1.80495e19i) q^{17} +(-1.33539e20 + 1.33539e20i) q^{18} -4.66461e20i q^{19} -1.17210e20 q^{21} +(-7.91647e20 - 7.91647e20i) q^{22} +(-7.85489e20 + 7.85489e20i) q^{23} +1.40369e21i q^{24} -7.84438e22 q^{26} +(1.57545e22 + 1.57545e22i) q^{27} +(8.89632e22 - 8.89632e22i) q^{28} +2.31649e23i q^{29} +3.24657e23 q^{31} +(9.92999e23 + 9.92999e23i) q^{32} +(-4.62288e22 + 4.62288e22i) q^{33} -2.65432e24i q^{34} -1.18376e25 q^{36} +(-4.94737e24 - 4.94737e24i) q^{37} +(3.42983e25 - 3.42983e25i) q^{38} +4.58078e24i q^{39} -1.24479e26 q^{41} +(-8.61831e24 - 8.61831e24i) q^{42} +(1.83776e25 - 1.83776e25i) q^{43} -7.01759e25i q^{44} -1.15512e26 q^{46} +(-3.45135e26 - 3.45135e26i) q^{47} +(1.69908e25 - 1.69908e25i) q^{48} -7.31845e26i q^{49} -1.55001e26 q^{51} +(-3.47684e27 - 3.47684e27i) q^{52} +(3.32895e27 - 3.32895e27i) q^{53} +2.31682e27i q^{54} +4.46198e27 q^{56} +(-2.00288e27 - 2.00288e27i) q^{57} +(-1.70329e28 + 1.70329e28i) q^{58} -3.29505e28i q^{59} +1.89259e28 q^{61} +(2.38717e28 + 2.38717e28i) q^{62} +(2.47884e28 - 2.47884e28i) q^{63} +1.29032e29i q^{64} -6.79830e27 q^{66} +(1.76361e29 + 1.76361e29i) q^{67} +(1.17647e29 - 1.17647e29i) q^{68} +6.74541e27i q^{69} -1.94403e29 q^{71} +(-2.96861e29 - 2.96861e29i) q^{72} +(-3.08897e29 + 3.08897e29i) q^{73} -7.27548e29i q^{74} +3.04039e30 q^{76} +(1.46951e29 + 1.46951e29i) q^{77} +(-3.36819e29 + 3.36819e29i) q^{78} -3.31447e30i q^{79} -3.23007e30 q^{81} +(-9.15279e30 - 9.15279e30i) q^{82} +(6.01743e30 - 6.01743e30i) q^{83} -7.63974e29i q^{84} +2.70257e30 q^{86} +(9.94648e29 + 9.94648e29i) q^{87} +(1.75985e30 - 1.75985e30i) q^{88} -2.42982e31i q^{89} +1.45612e31 q^{91} +(-5.11981e30 - 5.11981e30i) q^{92} +(1.39400e30 - 1.39400e30i) q^{93} -5.07547e31i q^{94} +8.52741e30 q^{96} +(-2.36400e31 - 2.36400e31i) q^{97} +(5.38116e31 - 5.38116e31i) q^{98} -1.95535e31i 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

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Database

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