LMFDB - Embedded newform 25.33.c.b.7.8

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			7.8
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5100.58 + 5100.58i) q^{2} +(7.18185e6 - 7.18185e6i) q^{3} -4.24294e9i q^{4} +7.32632e10 q^{6} +(-2.17171e13 - 2.17171e13i) q^{7} +(4.35482e13 - 4.35482e13i) q^{8} +1.74986e15i q^{9} +O(q^{10})$	\(q+(5100.58 + 5100.58i) q^{2} +(7.18185e6 - 7.18185e6i) q^{3} -4.24294e9i q^{4} +7.32632e10 q^{6} +(-2.17171e13 - 2.17171e13i) q^{7} +(4.35482e13 - 4.35482e13i) q^{8} +1.74986e15i q^{9} -5.19447e16 q^{11} +(-3.04721e16 - 3.04721e16i) q^{12} +(-6.04100e17 + 6.04100e17i) q^{13} -2.21539e17i q^{14} -1.77790e19 q^{16} +(-2.55450e19 - 2.55450e19i) q^{17} +(-8.92531e18 + 8.92531e18i) q^{18} +1.62776e20i q^{19} -3.11938e20 q^{21} +(-2.64948e20 - 2.64948e20i) q^{22} +(2.79781e21 - 2.79781e21i) q^{23} -6.25514e20i q^{24} -6.16252e21 q^{26} +(2.58754e22 + 2.58754e22i) q^{27} +(-9.21442e22 + 9.21442e22i) q^{28} +3.52661e23i q^{29} +4.98494e23 q^{31} +(-2.77722e23 - 2.77722e23i) q^{32} +(-3.73059e23 + 3.73059e23i) q^{33} -2.60589e23i q^{34} +7.42455e24 q^{36} +(-1.32176e25 - 1.32176e25i) q^{37} +(-8.30252e23 + 8.30252e23i) q^{38} +8.67711e24i q^{39} +1.17803e26 q^{41} +(-1.59106e24 - 1.59106e24i) q^{42} +(-9.57807e25 + 9.57807e25i) q^{43} +2.20398e26i q^{44} +2.85409e25 q^{46} +(4.63469e26 + 4.63469e26i) q^{47} +(-1.27686e26 + 1.27686e26i) q^{48} -1.61163e26i q^{49} -3.66921e26 q^{51} +(2.56316e27 + 2.56316e27i) q^{52} +(7.08726e26 - 7.08726e26i) q^{53} +2.63959e26i q^{54} -1.89148e27 q^{56} +(1.16903e27 + 1.16903e27i) q^{57} +(-1.79878e27 + 1.79878e27i) q^{58} -1.33400e28i q^{59} +2.13789e28 q^{61} +(2.54261e27 + 2.54261e27i) q^{62} +(3.80019e28 - 3.80019e28i) q^{63} +7.35273e28i q^{64} -3.80564e27 q^{66} +(-2.29693e29 - 2.29693e29i) q^{67} +(-1.08386e29 + 1.08386e29i) q^{68} -4.01869e28i q^{69} -3.37234e28 q^{71} +(7.62034e28 + 7.62034e28i) q^{72} +(4.11610e29 - 4.11610e29i) q^{73} -1.34835e29i q^{74} +6.90648e29 q^{76} +(1.12809e30 + 1.12809e30i) q^{77} +(-4.42583e28 + 4.42583e28i) q^{78} -9.94314e29i q^{79} -2.87086e30 q^{81} +(6.00861e29 + 6.00861e29i) q^{82} +(-1.82705e30 + 1.82705e30i) q^{83} +1.32353e30i q^{84} -9.77075e29 q^{86} +(2.53276e30 + 2.53276e30i) q^{87} +(-2.26210e30 + 2.26210e30i) q^{88} +3.30204e30i q^{89} +2.62386e31 q^{91} +(-1.18709e31 - 1.18709e31i) q^{92} +(3.58011e30 - 3.58011e30i) q^{93} +4.72792e30i q^{94} -3.98911e30 q^{96} +(-5.20836e31 - 5.20836e31i) q^{97} +(8.22027e29 - 8.22027e29i) q^{98} -9.08961e31i 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 $

$2$	5100.58	+	5100.58i	0.0778287	+	0.0778287i	0.744950	−	0.667121i	$-0.232474\pi$
$2$	5100.58	+	5100.58i	0.0778287	+	0.0778287i	−0.667121	+	0.744950i	$0.732474\pi$
$3$	7.18185e6	−	7.18185e6i	0.166838	−	0.166838i	−0.618750	−	0.785588i	$-0.712360\pi$
$3$	7.18185e6	−	7.18185e6i	0.166838	−	0.166838i	0.785588	+	0.618750i	$0.212360\pi$
$4$		−	4.24294e9i		−	0.987885i
$5$		0			0
$5$		0			0
$6$	7.32632e10			0.0259696
$7$	−2.17171e13	−	2.17171e13i	−0.653481	−	0.653481i	0.300348	−	0.953830i	$-0.402897\pi$
$7$	−2.17171e13	−	2.17171e13i	−0.653481	−	0.653481i	−0.953830	+	0.300348i	$0.902897\pi$
$8$	4.35482e13	−	4.35482e13i	0.154714	−	0.154714i
$9$			1.74986e15i			0.944330i
$10$		0			0
$11$	−5.19447e16			−1.13047			−0.565234	−	0.824930i	$-0.691214\pi$
$11$	−5.19447e16			−1.13047			−0.565234	+	0.824930i	$0.691214\pi$
$12$	−3.04721e16	−	3.04721e16i	−0.164817	−	0.164817i
$13$	−6.04100e17	+	6.04100e17i	−0.907852	+	0.907852i	−0.996099	−	0.0882469i	$-0.971874\pi$
$13$	−6.04100e17	+	6.04100e17i	−0.907852	+	0.907852i	0.0882469	+	0.996099i	$0.471874\pi$
$14$		−	2.21539e17i		−	0.101719i
$15$		0			0
$16$	−1.77790e19			−0.963803
$17$	−2.55450e19	−	2.55450e19i	−0.524957	−	0.524957i	0.394107	−	0.919064i	$-0.371054\pi$
$17$	−2.55450e19	−	2.55450e19i	−0.524957	−	0.524957i	−0.919064	+	0.394107i	$0.871054\pi$
$18$	−8.92531e18	+	8.92531e18i	−0.0734959	+	0.0734959i
$19$			1.62776e20i			0.564329i	0.959366	+	0.282165i	$0.0910524\pi$
$19$			1.62776e20i			0.564329i	−0.959366	+	0.282165i	$0.908948\pi$
$20$		0			0
$21$	−3.11938e20			−0.218052
$22$	−2.64948e20	−	2.64948e20i	−0.0879829	−	0.0879829i
$23$	2.79781e21	−	2.79781e21i	0.456218	−	0.456218i	−0.441194	−	0.897412i	$-0.645445\pi$
$23$	2.79781e21	−	2.79781e21i	0.456218	−	0.456218i	0.897412	+	0.441194i	$0.145445\pi$
$24$		−	6.25514e20i		−	0.0516247i
$25$		0			0
$26$	−6.16252e21			−0.141314
$27$	2.58754e22	+	2.58754e22i	0.324389	+	0.324389i
$28$	−9.21442e22	+	9.21442e22i	−0.645564	+	0.645564i
$29$			3.52661e23i			1.40926i	0.709577	+	0.704628i	$0.248886\pi$
$29$			3.52661e23i			1.40926i	−0.709577	+	0.704628i	$0.751114\pi$
$30$		0			0
$31$	4.98494e23			0.685287			0.342643	−	0.939466i	$-0.388678\pi$
$31$	4.98494e23			0.685287			0.342643	+	0.939466i	$0.388678\pi$
$32$	−2.77722e23	−	2.77722e23i	−0.229726	−	0.229726i
$33$	−3.73059e23	+	3.73059e23i	−0.188606	+	0.188606i
$34$		−	2.60589e23i		−	0.0817134i
$35$		0			0
$36$	7.42455e24			0.932890
$37$	−1.32176e25	−	1.32176e25i	−1.07134	−	1.07134i	−0.997252	−	0.0740830i	$-0.976397\pi$
$37$	−1.32176e25	−	1.32176e25i	−1.07134	−	1.07134i	−0.0740830	−	0.997252i	$-0.523603\pi$
$38$	−8.30252e23	+	8.30252e23i	−0.0439210	+	0.0439210i
$39$			8.67711e24i			0.302929i
$40$		0			0
$41$	1.17803e26			1.84762			0.923811	−	0.382849i	$-0.125057\pi$
$41$	1.17803e26			1.84762			0.923811	+	0.382849i	$0.125057\pi$
$42$	−1.59106e24	−	1.59106e24i	−0.0169707	−	0.0169707i
$43$	−9.57807e25	+	9.57807e25i	−0.701105	+	0.701105i	−0.964648	−	0.263543i	$-0.915109\pi$
$43$	−9.57807e25	+	9.57807e25i	−0.701105	+	0.701105i	0.263543	+	0.964648i	$0.415109\pi$
$44$			2.20398e26i			1.11677i
$45$		0			0
$46$	2.85409e25			0.0710137
$47$	4.63469e26	+	4.63469e26i	0.817439	+	0.817439i	0.985736	−	0.168297i	$-0.0538269\pi$
$47$	4.63469e26	+	4.63469e26i	0.817439	+	0.817439i	−0.168297	+	0.985736i	$0.553827\pi$
$48$	−1.27686e26	+	1.27686e26i	−0.160799	+	0.160799i
$49$		−	1.61163e26i		−	0.145925i
$50$		0			0
$51$	−3.66921e26			−0.175166
$52$	2.56316e27	+	2.56316e27i	0.896853	+	0.896853i
$53$	7.08726e26	−	7.08726e26i	0.182837	−	0.182837i	−0.609754	−	0.792591i	$-0.708732\pi$
$53$	7.08726e26	−	7.08726e26i	0.182837	−	0.182837i	0.792591	+	0.609754i	$0.208732\pi$
$54$			2.63959e26i			0.0504935i
$55$		0			0
$56$	−1.89148e27			−0.202206
$57$	1.16903e27	+	1.16903e27i	0.0941519	+	0.0941519i
$58$	−1.79878e27	+	1.79878e27i	−0.109680	+	0.109680i
$59$		−	1.33400e28i		−	0.618764i	−0.950938	−	0.309382i	$-0.899878\pi$
$59$		−	1.33400e28i		−	0.618764i	0.950938	−	0.309382i	$-0.100122\pi$
$60$		0			0
$61$	2.13789e28			0.581712			0.290856	−	0.956767i	$-0.406060\pi$
$61$	2.13789e28			0.581712			0.290856	+	0.956767i	$0.406060\pi$
$62$	2.54261e27	+	2.54261e27i	0.0533350	+	0.0533350i
$63$	3.80019e28	−	3.80019e28i	0.617102	−	0.617102i
$64$			7.35273e28i			0.928044i
$65$		0			0
$66$	−3.80564e27			−0.0293579
$67$	−2.29693e29	−	2.29693e29i	−1.39300	−	1.39300i	−0.818514	−	0.574487i	$-0.805202\pi$
$67$	−2.29693e29	−	2.29693e29i	−1.39300	−	1.39300i	−0.574487	−	0.818514i	$-0.694798\pi$
$68$	−1.08386e29	+	1.08386e29i	−0.518598	+	0.518598i
$69$		−	4.01869e28i		−	0.152230i
$70$		0			0
$71$	−3.37234e28			−0.0808719			−0.0404360	−	0.999182i	$-0.512875\pi$
$71$	−3.37234e28			−0.0808719			−0.0404360	+	0.999182i	$0.512875\pi$
$72$	7.62034e28	+	7.62034e28i	0.146101	+	0.146101i
$73$	4.11610e29	−	4.11610e29i	0.632878	−	0.632878i	−0.315911	−	0.948789i	$-0.602310\pi$
$73$	4.11610e29	−	4.11610e29i	0.632878	−	0.632878i	0.948789	+	0.315911i	$0.102310\pi$
$74$		−	1.34835e29i		−	0.166761i
$75$		0			0
$76$	6.90648e29			0.557493
$77$	1.12809e30	+	1.12809e30i	0.738740	+	0.738740i
$78$	−4.42583e28	+	4.42583e28i	−0.0235766	+	0.0235766i
$79$		−	9.94314e29i		−	0.432006i	−0.976393	−	0.216003i	$-0.930698\pi$
$79$		−	9.94314e29i		−	0.432006i	0.976393	−	0.216003i	$-0.0693022\pi$
$80$		0			0
$81$	−2.87086e30			−0.836089
$82$	6.00861e29	+	6.00861e29i	0.143798	+	0.143798i
$83$	−1.82705e30	+	1.82705e30i	−0.360164	+	0.360164i	−0.863873	−	0.503709i	$-0.831968\pi$
$83$	−1.82705e30	+	1.82705e30i	−0.360164	+	0.360164i	0.503709	+	0.863873i	$0.331968\pi$
$84$			1.32353e30i			0.215410i
$85$		0			0
$86$	−9.77075e29			−0.109132
$87$	2.53276e30	+	2.53276e30i	0.235118	+	0.235118i
$88$	−2.26210e30	+	2.26210e30i	−0.174900	+	0.174900i
$89$			3.30204e30i			0.213079i	0.994308	+	0.106540i	$0.0339771\pi$
$89$			3.30204e30i			0.213079i	−0.994308	+	0.106540i	$0.966023\pi$
$90$		0			0
$91$	2.62386e31			1.18653
$92$	−1.18709e31	−	1.18709e31i	−0.450692	−	0.450692i
$93$	3.58011e30	−	3.58011e30i	0.114332	−	0.114332i
$94$			4.72792e30i			0.127240i
$95$		0			0
$96$	−3.98911e30			−0.0766543
$97$	−5.20836e31	−	5.20836e31i	−0.847916	−	0.847916i	0.141956	−	0.989873i	$-0.454661\pi$
$97$	−5.20836e31	−	5.20836e31i	−0.847916	−	0.847916i	−0.989873	+	0.141956i	$0.954661\pi$
$98$	8.22027e29	−	8.22027e29i	0.0113571	−	0.0113571i
$99$		−	9.08961e31i		−	1.06754i
$100$		0			0
$101$	−1.05656e32			−0.901053			−0.450527	−	0.892763i	$-0.648764\pi$
$101$	−1.05656e32			−0.901053			−0.450527	+	0.892763i	$0.648764\pi$
$102$	−1.87151e30	−	1.87151e30i	−0.0136329	−	0.0136329i
$103$	6.05176e31	−	6.05176e31i	0.377126	−	0.377126i	−0.492939	−	0.870064i	$-0.664077\pi$
$103$	6.05176e31	−	6.05176e31i	0.377126	−	0.377126i	0.870064	+	0.492939i	$0.164077\pi$
$104$			5.26150e31i			0.280916i
$105$		0			0
$106$	7.22983e30			0.0284600
$107$	2.28247e32	+	2.28247e32i	0.773152	+	0.773152i	0.978656	−	0.205504i	$-0.0658833\pi$
$107$	2.28247e32	+	2.28247e32i	0.773152	+	0.773152i	−0.205504	+	0.978656i	$0.565883\pi$
$108$	1.09787e32	−	1.09787e32i	0.320459	−	0.320459i
$109$		−	1.01353e31i		−	0.0255278i	−0.999919	−	0.0127639i	$-0.995937\pi$
$109$		−	1.01353e31i		−	0.0255278i	0.999919	−	0.0127639i	$-0.00406299\pi$
$110$		0			0
$111$	−1.89854e32			−0.357480
$112$	3.86109e32	+	3.86109e32i	0.629827	+	0.629827i
$113$	−4.25348e32	+	4.25348e32i	−0.601852	+	0.601852i	−0.940804	−	0.338952i	$-0.889928\pi$
$113$	−4.25348e32	+	4.25348e32i	−0.601852	+	0.601852i	0.338952	+	0.940804i	$0.389928\pi$
$114$			1.19255e31i			0.0146554i
$115$		0			0
$116$	1.49632e33			1.39218
$117$	−1.05709e33	−	1.05709e33i	−0.857311	−	0.857311i
$118$	6.80420e31	−	6.80420e31i	0.0481576	−	0.0481576i
$119$			1.10953e33i			0.686099i
$120$		0			0
$121$	5.86878e32			0.277960
$122$	1.09045e32	+	1.09045e32i	0.0452739	+	0.0452739i
$123$	8.46040e32	−	8.46040e32i	0.308254	−	0.308254i
$124$		−	2.11508e33i		−	0.676985i
$125$		0			0
$126$	3.87664e32			0.0960564
$127$	2.19370e32	+	2.19370e32i	0.0478981	+	0.0478981i	0.730650	−	0.682752i	$-0.239217\pi$
$127$	2.19370e32	+	2.19370e32i	0.0478981	+	0.0478981i	−0.682752	+	0.730650i	$0.739217\pi$
$128$	−1.56784e33	+	1.56784e33i	−0.301954	+	0.301954i
$129$			1.37577e33i			0.233943i
$130$		0			0
$131$	−1.06780e34			−1.41954			−0.709771	−	0.704433i	$-0.751201\pi$
$131$	−1.06780e34			−1.41954			−0.709771	+	0.704433i	$0.751201\pi$
$132$	1.58287e33	+	1.58287e33i	0.186321	+	0.186321i
$133$	3.53502e33	−	3.53502e33i	0.368779	−	0.368779i
$134$		−	2.34314e33i		−	0.216831i
$135$		0			0
$136$	−2.22488e33			−0.162437
$137$	3.30014e33	+	3.30014e33i	0.214290	+	0.214290i	0.806087	−	0.591797i	$-0.201581\pi$
$137$	3.30014e33	+	3.30014e33i	0.214290	+	0.214290i	−0.591797	+	0.806087i	$0.701581\pi$
$138$	2.04976e32	−	2.04976e32i	0.0118478	−	0.0118478i
$139$		−	7.98496e33i		−	0.411184i	−0.978638	−	0.205592i	$-0.934088\pi$
$139$		−	7.98496e33i		−	0.411184i	0.978638	−	0.205592i	$-0.0659119\pi$
$140$		0			0
$141$	6.65713e33			0.272761
$142$	−1.72009e32	−	1.72009e32i	−0.00629415	−	0.00629415i
$143$	3.13798e34	−	3.13798e34i	1.02630	−	1.02630i
$144$		−	3.11108e34i		−	0.910148i
$145$		0			0
$146$	4.19889e33			0.0985120
$147$	−1.15745e33	−	1.15745e33i	−0.0243459	−	0.0243459i
$148$	−5.60815e34	+	5.60815e34i	−1.05836	+	1.05836i
$149$			6.45391e34i			1.09356i	0.837276	+	0.546780i	$0.184147\pi$
$149$			6.45391e34i			1.09356i	−0.837276	+	0.546780i	$0.815853\pi$
$150$		0			0
$151$	1.15864e35			1.58605			0.793027	−	0.609187i	$-0.208504\pi$
$151$	1.15864e35			1.58605			0.793027	+	0.609187i	$0.208504\pi$
$152$	7.08861e33	+	7.08861e33i	0.0873099	+	0.0873099i
$153$	4.47003e34	−	4.47003e34i	0.495733	−	0.495733i
$154$			1.15078e34i			0.114990i
$155$		0			0
$156$	3.68164e34			0.299259
$157$	1.13553e35	+	1.13553e35i	0.833303	+	0.833303i	0.987967	−	0.154664i	$-0.0494294\pi$
$157$	1.13553e35	+	1.13553e35i	0.833303	+	0.833303i	−0.154664	+	0.987967i	$0.549429\pi$
$158$	5.07158e33	−	5.07158e33i	0.0336225	−	0.0336225i
$159$		−	1.01799e34i		−	0.0610086i
$160$		0			0
$161$	−1.21521e35			−0.596260
$162$	−1.46431e34	−	1.46431e34i	−0.0650717	−	0.0650717i
$163$	3.28695e35	−	3.28695e35i	1.32371	−	1.32371i	0.412957	−	0.910751i	$-0.364496\pi$
$163$	3.28695e35	−	3.28695e35i	1.32371	−	1.32371i	0.910751	−	0.412957i	$-0.135504\pi$
$164$		−	4.99829e35i		−	1.82524i
$165$		0			0
$166$	−1.86380e34			−0.0560621
$167$	−7.18851e34	−	7.18851e34i	−0.196415	−	0.196415i	0.602046	−	0.798461i	$-0.294352\pi$
$167$	−7.18851e34	−	7.18851e34i	−0.196415	−	0.196415i	−0.798461	+	0.602046i	$0.794352\pi$
$168$	−1.35843e34	+	1.35843e34i	−0.0337357	+	0.0337357i
$169$		−	2.87093e35i		−	0.648389i
$170$		0			0
$171$	−2.84835e35			−0.532913
$172$	4.06392e35	+	4.06392e35i	0.692611	+	0.692611i
$173$	5.80898e35	−	5.80898e35i	0.902323	−	0.902323i	−0.0933134	−	0.995637i	$-0.529746\pi$
$173$	5.80898e35	−	5.80898e35i	0.902323	−	0.902323i	0.995637	+	0.0933134i	$0.0297458\pi$
$174$			2.58371e34i			0.0365979i
$175$		0			0
$176$	9.23527e35			1.08955
$177$	−9.58062e34	−	9.58062e34i	−0.103234	−	0.103234i
$178$	−1.68423e34	+	1.68423e34i	−0.0165837	+	0.0165837i
$179$		−	4.88973e35i		−	0.440186i	−0.975479	−	0.220093i	$-0.929364\pi$
$179$		−	4.88973e35i		−	0.440186i	0.975479	−	0.220093i	$-0.0706361\pi$
$180$		0			0
$181$	7.74061e35			0.583335			0.291667	−	0.956520i	$-0.405790\pi$
$181$	7.74061e35			0.583335			0.291667	+	0.956520i	$0.405790\pi$
$182$	1.33832e35	+	1.33832e35i	0.0923459	+	0.0923459i
$183$	1.53540e35	−	1.53540e35i	0.0970519	−	0.0970519i
$184$		−	2.43679e35i		−	0.141167i
$185$		0			0
$186$	3.65212e34			0.0177966
$187$	1.32693e36	+	1.32693e36i	0.593448	+	0.593448i
$188$	1.96647e36	−	1.96647e36i	0.807536	−	0.807536i
$189$		−	1.12388e36i		−	0.423964i
$190$		0			0
$191$	3.98723e36			1.27098			0.635489	−	0.772110i	$-0.280799\pi$
$191$	3.98723e36			1.27098			0.635489	+	0.772110i	$0.280799\pi$
$192$	5.28062e35	+	5.28062e35i	0.154834	+	0.154834i
$193$	1.92242e36	−	1.92242e36i	0.518717	−	0.518717i	−0.398466	−	0.917183i	$-0.630457\pi$
$193$	1.92242e36	−	1.92242e36i	0.518717	−	0.518717i	0.917183	+	0.398466i	$0.130457\pi$
$194$		−	5.31313e35i		−	0.131984i
$195$		0			0
$196$	−6.83806e35			−0.144157
$197$	5.92024e36	+	5.92024e36i	1.15048	+	1.15048i	0.986456	+	0.164025i	$0.0524478\pi$
$197$	5.92024e36	+	5.92024e36i	1.15048	+	1.15048i	0.164025	+	0.986456i	$0.447552\pi$
$198$	4.63623e35	−	4.63623e35i	0.0830849	−	0.0830849i
$199$		−	9.63563e36i		−	1.59305i	−0.604602	−	0.796527i	$-0.706668\pi$
$199$		−	9.63563e36i		−	1.59305i	0.604602	−	0.796527i	$-0.293332\pi$
$200$		0			0
$201$	−3.29924e36			−0.464812
$202$	−5.38905e35	−	5.38905e35i	−0.0701278	−	0.0701278i
$203$	7.65878e36	−	7.65878e36i	0.920922	−	0.920922i
$204$			1.55682e36i			0.173044i
$205$		0			0
$206$	6.17350e35			0.0587024
$207$	4.89578e36	+	4.89578e36i	0.430821	+	0.430821i
$208$	1.07403e37	−	1.07403e37i	0.874990	−	0.874990i
$209$		−	8.45535e36i		−	0.637957i
$210$		0			0
$211$	7.42910e36			0.481301			0.240651	−	0.970612i	$-0.422639\pi$
$211$	7.42910e36			0.481301			0.240651	+	0.970612i	$0.422639\pi$
$212$	−3.00708e36	−	3.00708e36i	−0.180622	−	0.180622i
$213$	−2.42196e35	+	2.42196e35i	−0.0134925	+	0.0134925i
$214$			2.32839e36i			0.120347i
$215$		0			0
$216$	2.25365e36			0.100375
$217$	−1.08258e37	−	1.08258e37i	−0.447822	−	0.447822i
$218$	5.16960e34	−	5.16960e34i	0.00198680	−	0.00198680i
$219$		−	5.91224e36i		−	0.211177i
$220$		0			0
$221$	3.08635e37			0.953167
$222$	−9.68364e35	−	9.68364e35i	−0.0278222	−	0.0278222i
$223$	−2.97856e36	+	2.97856e36i	−0.0796394	+	0.0796394i	−0.745804	−	0.666165i	$-0.767935\pi$
$223$	−2.97856e36	+	2.97856e36i	−0.0796394	+	0.0796394i	0.666165	+	0.745804i	$0.267935\pi$
$224$			1.20626e37i			0.300243i
$225$		0			0
$226$	−4.33904e36			−0.0936826
$227$	4.34126e37	+	4.34126e37i	0.873379	+	0.873379i	0.992839	−	0.119460i	$-0.0381165\pi$
$227$	4.34126e37	+	4.34126e37i	0.873379	+	0.873379i	−0.119460	+	0.992839i	$0.538116\pi$
$228$	4.96013e36	−	4.96013e36i	0.0930112	−	0.0930112i
$229$		−	7.21605e37i		−	1.26163i	−0.775934	−	0.630815i	$-0.782721\pi$
$229$		−	7.21605e37i		−	1.26163i	0.775934	−	0.630815i	$-0.217279\pi$
$230$		0			0
$231$	1.62035e37			0.246501
$232$	1.53578e37	+	1.53578e37i	0.218032	+	0.218032i
$233$	1.48428e37	−	1.48428e37i	0.196708	−	0.196708i	−0.601879	−	0.798587i	$-0.705581\pi$
$233$	1.48428e37	−	1.48428e37i	0.196708	−	0.196708i	0.798587	+	0.601879i	$0.205581\pi$
$234$		−	1.07836e37i		−	0.133447i
$235$		0			0
$236$	−5.66010e37			−0.611268
$237$	−7.14101e36	−	7.14101e36i	−0.0720753	−	0.0720753i
$238$	−5.65924e36	+	5.65924e36i	−0.0533982	+	0.0533982i
$239$			1.79423e38i			1.58311i	0.611096	+	0.791556i	$0.290729\pi$
$239$			1.79423e38i			1.58311i	−0.611096	+	0.791556i	$0.709271\pi$
$240$		0			0
$241$	−1.30342e38			−1.00650			−0.503249	−	0.864141i	$-0.667862\pi$
$241$	−1.30342e38			−1.00650			−0.503249	+	0.864141i	$0.667862\pi$
$242$	2.99342e36	+	2.99342e36i	0.0216332	+	0.0216332i
$243$	−6.85657e37	+	6.85657e37i	−0.463881	+	0.463881i
$244$		−	9.07093e37i		−	0.574665i
$245$		0			0
$246$	8.63059e36			0.0479821
$247$	−9.83329e37	−	9.83329e37i	−0.512327	−	0.512327i
$248$	2.17085e37	−	2.17085e37i	0.106024	−	0.106024i
$249$			2.62431e37i			0.120178i
$250$		0			0
$251$	1.38891e38			0.559623			0.279812	−	0.960055i	$-0.409728\pi$
$251$	1.38891e38			0.559623			0.279812	+	0.960055i	$0.409728\pi$
$252$	−1.61240e38	−	1.61240e38i	−0.609626	−	0.609626i
$253$	−1.45332e38	+	1.45332e38i	−0.515741	+	0.515741i
$254$			2.23783e36i			0.00745570i
$255$		0			0
$256$	2.99803e38			0.881043
$257$	−2.30472e38	−	2.30472e38i	−0.636339	−	0.636339i	0.313312	−	0.949650i	$-0.398562\pi$
$257$	−2.30472e38	−	2.30472e38i	−0.636339	−	0.636339i	−0.949650	+	0.313312i	$0.898562\pi$
$258$	−7.01720e36	+	7.01720e36i	−0.0182074	+	0.0182074i
$259$			5.74096e38i			1.40019i
$260$		0			0
$261$	−6.17109e38			−1.33080
$262$	−5.44638e37	−	5.44638e37i	−0.110481	−	0.110481i
$263$	−1.71630e38	+	1.71630e38i	−0.327568	+	0.327568i	−0.851661	−	0.524093i	$-0.824404\pi$
$263$	−1.71630e38	+	1.71630e38i	−0.327568	+	0.327568i	0.524093	+	0.851661i	$0.324404\pi$
$264$			3.24922e37i			0.0583601i
$265$		0			0
$266$	3.60613e37			0.0574031
$267$	2.37147e37	+	2.37147e37i	0.0355499	+	0.0355499i
$268$	−9.74574e38	+	9.74574e38i	−1.37613	+	1.37613i
$269$			3.57871e38i			0.476091i	0.971254	+	0.238045i	$0.0765067\pi$
$269$			3.57871e38i			0.476091i	−0.971254	+	0.238045i	$0.923493\pi$
$270$		0			0
$271$	−8.92028e38			−1.05407			−0.527036	−	0.849843i	$-0.676697\pi$
$271$	−8.92028e38			−1.05407			−0.527036	+	0.849843i	$0.676697\pi$
$272$	4.54166e38	+	4.54166e38i	0.505955	+	0.505955i
$273$	1.88442e38	−	1.88442e38i	0.197959	−	0.197959i
$274$			3.36652e37i			0.0333559i
$275$		0			0
$276$	−1.70510e38			−0.150385
$277$	4.08137e38	+	4.08137e38i	0.339726	+	0.339726i	0.856264	−	0.516538i	$-0.172779\pi$
$277$	4.08137e38	+	4.08137e38i	0.339726	+	0.339726i	−0.516538	+	0.856264i	$0.672779\pi$
$278$	4.07279e37	−	4.07279e37i	0.0320019	−	0.0320019i
$279$			8.72295e38i			0.647137i
$280$		0			0
$281$	1.97166e38			0.130476			0.0652379	−	0.997870i	$-0.479219\pi$
$281$	1.97166e38			0.130476			0.0652379	+	0.997870i	$0.479219\pi$
$282$	3.39552e37	+	3.39552e37i	0.0212286	+	0.0212286i
$283$	−1.67880e39	+	1.67880e39i	−0.991779	+	0.991779i	−0.999966	−	0.00818785i	$-0.997394\pi$
$283$	−1.67880e39	+	1.67880e39i	−0.991779	+	0.991779i	0.00818785	+	0.999966i	$0.497394\pi$
$284$			1.43086e38i			0.0798922i
$285$		0			0
$286$	3.20110e38			0.159751
$287$	−2.55833e39	−	2.55833e39i	−1.20739	−	1.20739i
$288$	4.85975e38	−	4.85975e38i	0.216937	−	0.216937i
$289$		−	1.06281e39i		−	0.448840i
$290$		0			0
$291$	−7.48113e38			−0.282930
$292$	−1.74643e39	−	1.74643e39i	−0.625210	−	0.625210i
$293$	8.92137e38	−	8.92137e38i	0.302378	−	0.302378i	−0.539566	−	0.841943i	$-0.681412\pi$
$293$	8.92137e38	−	8.92137e38i	0.302378	−	0.302378i	0.841943	+	0.539566i	$0.181412\pi$
$294$		−	1.18074e37i		−	0.00378962i
$295$		0			0
$296$	−1.15121e39			−0.331502
$297$	−1.34409e39	−	1.34409e39i	−0.366712	−	0.366712i
$298$	−3.29187e38	+	3.29187e38i	−0.0851103	+	0.0851103i
$299$			3.38031e39i			0.828357i
$300$		0			0
$301$	4.16016e39			0.916317
$302$	5.90974e38	+	5.90974e38i	0.123440	+	0.123440i
$303$	−7.58803e38	+	7.58803e38i	−0.150330	+	0.150330i
$304$		−	2.89400e39i		−	0.543902i
$305$		0			0
$306$	4.55995e38			0.0771644
$307$	7.96399e39	+	7.96399e39i	1.27914	+	1.27914i	0.941152	+	0.337983i	$0.109745\pi$
$307$	7.96399e39	+	7.96399e39i	1.27914	+	1.27914i	0.337983	+	0.941152i	$0.390255\pi$
$308$	4.78641e39	−	4.78641e39i	0.729791	−	0.729791i
$309$		−	8.69257e38i		−	0.125838i
$310$		0			0
$311$	−7.82326e38			−0.102146			−0.0510730	−	0.998695i	$-0.516264\pi$
$311$	−7.82326e38			−0.102146			−0.0510730	+	0.998695i	$0.516264\pi$
$312$	3.77873e38	+	3.77873e38i	0.0468675	+	0.0468675i
$313$	−6.87661e36	+	6.87661e36i	−0.000810336	+	0.000810336i	−0.707512	−	0.706701i	$-0.750182\pi$
$313$	−6.87661e36	+	6.87661e36i	−0.000810336	+	0.000810336i	0.706701	+	0.707512i	$0.250182\pi$
$314$			1.15837e39i			0.129710i
$315$		0			0
$316$	−4.21881e39			−0.426773
$317$	6.11072e39	+	6.11072e39i	0.587684	+	0.587684i	0.937004	−	0.349319i	$-0.113587\pi$
$317$	6.11072e39	+	6.11072e39i	0.587684	+	0.587684i	−0.349319	+	0.937004i	$0.613587\pi$
$318$	5.19235e37	−	5.19235e37i	0.00474822	−	0.00474822i
$319$		−	1.83189e40i		−	1.59312i
$320$		0			0
$321$	3.27848e39			0.257983
$322$	−6.19825e38	−	6.19825e38i	−0.0464061	−	0.0464061i
$323$	4.15812e39	−	4.15812e39i	0.296249	−	0.296249i
$324$			1.21809e40i			0.825960i
$325$		0			0
$326$	3.35307e39			0.206045
$327$	−7.27904e37	−	7.27904e37i	−0.00425902	−	0.00425902i
$328$	5.13010e39	−	5.13010e39i	0.285854	−	0.285854i
$329$		−	2.01304e40i		−	1.06836i
$330$		0			0
$331$	2.73484e40			1.31730			0.658650	−	0.752449i	$-0.271128\pi$
$331$	2.73484e40			1.31730			0.658650	+	0.752449i	$0.271128\pi$
$332$	7.75204e39	+	7.75204e39i	0.355801	+	0.355801i
$333$	2.31290e40	−	2.31290e40i	1.01169	−	1.01169i
$334$		−	7.33311e38i		−	0.0305735i
$335$		0			0
$336$	5.54595e39			0.210159
$337$	−1.27351e40	−	1.27351e40i	−0.460176	−	0.460176i	0.438537	−	0.898713i	$-0.355497\pi$
$337$	−1.27351e40	−	1.27351e40i	−0.460176	−	0.460176i	−0.898713	+	0.438537i	$0.855497\pi$
$338$	1.46434e39	−	1.46434e39i	0.0504633	−	0.0504633i
$339$			6.10957e39i			0.200824i
$340$		0			0
$341$	−2.58941e40			−0.774695
$342$	−1.45283e39	−	1.45283e39i	−0.0414759	−	0.0414759i
$343$	−2.74850e40	+	2.74850e40i	−0.748840	+	0.748840i
$344$			8.34217e39i			0.216942i
$345$		0			0
$346$	5.92583e39			0.140453
$347$	1.27904e40	+	1.27904e40i	0.289475	+	0.289475i	0.836873	−	0.547398i	$-0.184381\pi$
$347$	1.27904e40	+	1.27904e40i	0.289475	+	0.289475i	−0.547398	+	0.836873i	$0.684381\pi$
$348$	1.07463e40	−	1.07463e40i	0.232270	−	0.232270i
$349$		−	5.37615e40i		−	1.10985i	−0.831900	−	0.554925i	$-0.812747\pi$
$349$		−	5.37615e40i		−	1.10985i	0.831900	−	0.554925i	$-0.187253\pi$
$350$		0			0
$351$	−3.12626e40			−0.588994
$352$	1.44262e40	+	1.44262e40i	0.259698	+	0.259698i
$353$	7.74551e40	−	7.74551e40i	1.33246	−	1.33246i	0.429300	−	0.903162i	$-0.358760\pi$
$353$	7.74551e40	−	7.74551e40i	1.33246	−	1.33246i	0.903162	−	0.429300i	$-0.141240\pi$
$354$		−	9.77334e38i		−	0.0160691i
$355$		0			0
$356$	1.40103e40			0.210498
$357$	7.96847e39	+	7.96847e39i	0.114468	+	0.114468i
$358$	2.49404e39	−	2.49404e39i	0.0342591	−	0.0342591i
$359$		−	4.46431e39i		−	0.0586467i	−0.999570	−	0.0293234i	$-0.990665\pi$
$359$		−	4.46431e39i		−	0.0586467i	0.999570	−	0.0293234i	$-0.00933525\pi$
$360$		0			0
$361$	5.67024e40			0.681532
$362$	3.94816e39	+	3.94816e39i	0.0454002	+	0.0454002i
$363$	4.21487e39	−	4.21487e39i	0.0463744	−	0.0463744i
$364$		−	1.11329e41i		−	1.17215i
$365$		0			0
$366$	1.56629e39			0.0151068
$367$	9.91282e40	+	9.91282e40i	0.915251	+	0.915251i	0.996679	−	0.0814285i	$-0.0259482\pi$
$367$	9.91282e40	+	9.91282e40i	0.915251	+	0.915251i	−0.0814285	+	0.996679i	$0.525948\pi$
$368$	−4.97423e40	+	4.97423e40i	−0.439705	+	0.439705i
$369$			2.06138e41i			1.74476i
$370$		0			0
$371$	−3.07829e40			−0.238961
$372$	−1.51902e40	−	1.51902e40i	−0.112947	−	0.112947i
$373$	−1.85950e41	+	1.85950e41i	−1.32451	+	1.32451i	−0.414423	+	0.910084i	$0.636017\pi$
$373$	−1.85950e41	+	1.85950e41i	−1.32451	+	1.32451i	−0.910084	+	0.414423i	$0.863983\pi$
$374$			1.35362e40i			0.0923745i
$375$		0			0
$376$	4.03666e40			0.252939
$377$	−2.13043e41	−	2.13043e41i	−1.27940	−	1.27940i
$378$	5.73241e39	−	5.73241e39i	0.0329966	−	0.0329966i
$379$			1.93679e41i			1.06870i	0.845264	+	0.534349i	$0.179443\pi$
$379$			1.93679e41i			1.06870i	−0.845264	+	0.534349i	$0.820557\pi$
$380$		0			0
$381$	3.15097e39			0.0159825
$382$	2.03372e40	+	2.03372e40i	0.0989185	+	0.0989185i
$383$	1.64205e41	−	1.64205e41i	0.765961	−	0.765961i	−0.211432	−	0.977393i	$-0.567813\pi$
$383$	1.64205e41	−	1.64205e41i	0.765961	−	0.765961i	0.977393	+	0.211432i	$0.0678126\pi$
$384$			2.25199e40i			0.100755i
$385$		0			0
$386$	1.96109e40			0.0807421
$387$	−1.67603e41	−	1.67603e41i	−0.662074	−	0.662074i
$388$	−2.20987e41	+	2.20987e41i	−0.837644	+	0.837644i
$389$		−	2.37002e41i		−	0.862103i	−0.902327	−	0.431052i	$-0.858143\pi$
$389$		−	2.37002e41i		−	0.862103i	0.902327	−	0.431052i	$-0.141857\pi$
$390$		0			0
$391$	−1.42940e41			−0.478990
$392$	−7.01839e39	−	7.01839e39i	−0.0225767	−	0.0225767i
$393$	−7.66876e40	+	7.66876e40i	−0.236834	+	0.236834i
$394$			6.03933e40i			0.179081i
$395$		0			0
$396$	−3.85666e41			−1.05460
$397$	−2.85614e41	−	2.85614e41i	−0.750121	−	0.750121i	0.224381	−	0.974502i	$-0.427964\pi$
$397$	−2.85614e41	−	2.85614e41i	−0.750121	−	0.750121i	−0.974502	+	0.224381i	$0.927964\pi$
$398$	4.91473e40	−	4.91473e40i	0.123985	−	0.123985i
$399$		−	5.07760e40i		−	0.123053i
$400$		0			0
$401$	−3.29029e41			−0.736078			−0.368039	−	0.929810i	$-0.619971\pi$
$401$	−3.29029e41			−0.736078			−0.368039	+	0.929810i	$0.619971\pi$
$402$	−1.68281e40	−	1.68281e40i	−0.0361757	−	0.0361757i
$403$	−3.01140e41	+	3.01140e41i	−0.622139	+	0.622139i
$404$			4.48290e41i			0.890138i
$405$		0			0
$406$	7.81284e40			0.143348
$407$	6.86585e41	+	6.86585e41i	1.21111	+	1.21111i
$408$	−1.59788e40	+	1.59788e40i	−0.0271007	+	0.0271007i
$409$			7.42695e40i			0.121126i	0.998164	+	0.0605630i	$0.0192896\pi$
$409$			7.42695e40i			0.121126i	−0.998164	+	0.0605630i	$0.980710\pi$
$410$		0			0
$411$	4.74022e40			0.0715038
$412$	−2.56772e41	−	2.56772e41i	−0.372557	−	0.372557i
$413$	−2.89707e41	+	2.89707e41i	−0.404351	+	0.404351i
$414$			4.99426e40i			0.0670604i
$415$		0			0
$416$	3.35543e41			0.417114
$417$	−5.73468e40	−	5.73468e40i	−0.0686013	−	0.0686013i
$418$	4.31272e40	−	4.31272e40i	0.0496513	−	0.0496513i
$419$			1.03667e42i			1.14873i	0.818600	+	0.574364i	$0.194751\pi$
$419$			1.03667e42i			1.14873i	−0.818600	+	0.574364i	$0.805249\pi$
$420$		0			0
$421$	−2.97711e41			−0.305691			−0.152845	−	0.988250i	$-0.548844\pi$
$421$	−2.97711e41			−0.305691			−0.152845	+	0.988250i	$0.548844\pi$
$422$	3.78927e40	+	3.78927e40i	0.0374591	+	0.0374591i
$423$	−8.11007e41	+	8.11007e41i	−0.771932	+	0.771932i
$424$		−	6.17276e40i		−	0.0565751i
$425$		0			0
$426$	−2.47068e39			−0.00210021
$427$	−4.64287e41	−	4.64287e41i	−0.380138	−	0.380138i
$428$	9.68438e41	−	9.68438e41i	0.763786	−	0.763786i
$429$		−	4.50730e41i		−	0.342452i
$430$		0			0
$431$	1.89770e42			1.33842			0.669209	−	0.743075i	$-0.266633\pi$
$431$	1.89770e42			1.33842			0.669209	+	0.743075i	$0.266633\pi$
$432$	−4.60039e41	−	4.60039e41i	−0.312647	−	0.312647i
$433$	−3.55115e41	+	3.55115e41i	−0.232575	+	0.232575i	−0.813766	−	0.581192i	$-0.802587\pi$
$433$	−3.55115e41	+	3.55115e41i	−0.232575	+	0.232575i	0.581192	+	0.813766i	$0.302587\pi$
$434$		−	1.10436e41i		−	0.0697068i
$435$		0			0
$436$	−4.30035e40			−0.0252186
$437$	4.55416e41	+	4.55416e41i	0.257457	+	0.257457i
$438$	3.01558e40	−	3.01558e40i	0.0164356	−	0.0164356i
$439$		−	5.29926e41i		−	0.278473i	−0.990259	−	0.139236i	$-0.955535\pi$
$439$		−	5.29926e41i		−	0.278473i	0.990259	−	0.139236i	$-0.0444648\pi$
$440$		0			0
$441$	2.82014e41			0.137801
$442$	1.57422e41	+	1.57422e41i	0.0741837	+	0.0741837i
$443$	1.34884e42	−	1.34884e42i	0.613058	−	0.613058i	−0.330684	−	0.943742i	$-0.607279\pi$
$443$	1.34884e42	−	1.34884e42i	0.613058	−	0.613058i	0.943742	+	0.330684i	$0.107279\pi$
$444$			8.05537e41i			0.353149i
$445$		0			0
$446$	−3.03847e40			−0.0123965
$447$	4.63510e41	+	4.63510e41i	0.182448	+	0.182448i
$448$	1.59680e42	−	1.59680e42i	0.606460	−	0.606460i
$449$		−	5.15854e42i		−	1.89054i	−0.326293	−	0.945269i	$-0.605800\pi$
$449$		−	5.15854e42i		−	1.89054i	0.326293	−	0.945269i	$-0.394200\pi$
$450$		0			0
$451$	−6.11922e42			−2.08868
$452$	1.80472e42	+	1.80472e42i	0.594561	+	0.594561i
$453$	8.32119e41	−	8.32119e41i	0.264615	−	0.264615i
$454$			4.42859e41i			0.135948i
$455$		0			0
$456$	1.01819e41			0.0291333
$457$	1.83049e41	+	1.83049e41i	0.0505718	+	0.0505718i	0.731940	−	0.681369i	$-0.238615\pi$
$457$	1.83049e41	+	1.83049e41i	0.0505718	+	0.0505718i	−0.681369	+	0.731940i	$0.738615\pi$
$458$	3.68060e41	−	3.68060e41i	0.0981909	−	0.0981909i
$459$		−	1.32197e42i		−	0.340581i
$460$		0			0
$461$	5.64635e42			1.35692			0.678458	−	0.734639i	$-0.262649\pi$
$461$	5.64635e42			1.35692			0.678458	+	0.734639i	$0.262649\pi$
$462$	8.26474e40	+	8.26474e40i	0.0191848	+	0.0191848i
$463$	3.17014e42	−	3.17014e42i	0.710858	−	0.710858i	−0.255857	−	0.966715i	$-0.582358\pi$
$463$	3.17014e42	−	3.17014e42i	0.710858	−	0.710858i	0.966715	+	0.255857i	$0.0823575\pi$
$464$		−	6.26997e42i		−	1.35824i
$465$		0			0
$466$	1.51414e41			0.0306190
$467$	1.45092e42	+	1.45092e42i	0.283514	+	0.283514i	0.834509	−	0.550995i	$-0.185752\pi$
$467$	1.45092e42	+	1.45092e42i	0.283514	+	0.283514i	−0.550995	+	0.834509i	$0.685752\pi$
$468$	−4.48517e42	+	4.48517e42i	−0.846925	+	0.846925i
$469$			9.97654e42i			1.82060i
$470$		0			0
$471$	1.63104e42			0.278054
$472$	−5.80936e41	−	5.80936e41i	−0.0957318	−	0.0957318i
$473$	4.97531e42	−	4.97531e42i	0.792577	−	0.792577i
$474$		−	7.28466e40i		−	0.0112190i
$475$		0			0
$476$	4.70766e42			0.677787
$477$	1.24017e42	+	1.24017e42i	0.172659	+	0.172659i
$478$	−9.15162e41	+	9.15162e41i	−0.123212	+	0.123212i
$479$		−	4.93083e42i		−	0.642025i	−0.947075	−	0.321013i	$-0.895977\pi$
$479$		−	4.93083e42i		−	0.642025i	0.947075	−	0.321013i	$-0.104023\pi$
$480$		0			0
$481$	1.59695e43			1.94523
$482$	−6.64822e41	−	6.64822e41i	−0.0783344	−	0.0783344i
$483$	−8.72743e41	+	8.72743e41i	−0.0994792	+	0.0994792i
$484$		−	2.49009e42i		−	0.274592i
$485$		0			0
$486$	−6.99449e41			−0.0722065
$487$	4.98113e42	+	4.98113e42i	0.497582	+	0.497582i	0.910684	−	0.413103i	$-0.135555\pi$
$487$	4.98113e42	+	4.98113e42i	0.497582	+	0.497582i	−0.413103	+	0.910684i	$0.635555\pi$
$488$	9.31013e41	−	9.31013e41i	0.0899992	−	0.0899992i
$489$		−	4.72128e42i		−	0.441691i
$490$		0			0
$491$	−1.98459e43			−1.73927			−0.869636	−	0.493693i	$-0.835647\pi$
$491$	−1.98459e43			−1.73927			−0.869636	+	0.493693i	$0.835647\pi$
$492$	−3.58969e42	−	3.58969e42i	−0.304520	−	0.304520i
$493$	9.00875e42	−	9.00875e42i	0.739799	−	0.739799i
$494$		−	1.00311e42i		−	0.0797475i
$495$		0			0
$496$	−8.86273e42			−0.660482
$497$	7.32374e41	+	7.32374e41i	0.0528483	+	0.0528483i
$498$	−1.33855e41	+	1.33855e41i	−0.00935332	+	0.00935332i
$499$			2.02767e43i			1.37211i	0.727551	+	0.686054i	$0.240659\pi$
$499$			2.02767e43i			1.37211i	−0.727551	+	0.686054i	$0.759341\pi$
$500$		0			0
$501$	−1.03254e42			−0.0655393
$502$	7.08427e41	+	7.08427e41i	0.0435547	+	0.0435547i
$503$	−1.19644e43	+	1.19644e43i	−0.712529	+	0.712529i	−0.967064	−	0.254535i	$-0.918078\pi$
$503$	−1.19644e43	+	1.19644e43i	−0.712529	+	0.712529i	0.254535	+	0.967064i	$0.418078\pi$
$504$		−	3.30983e42i		−	0.190949i
$505$		0			0
$506$	−1.48255e42			−0.0802788
$507$	−2.06186e42	−	2.06186e42i	−0.108176	−	0.108176i
$508$	9.30775e41	−	9.30775e41i	0.0473179	−	0.0473179i
$509$		−	8.65032e42i		−	0.426136i	−0.977037	−	0.213068i	$-0.931654\pi$
$509$		−	8.65032e42i		−	0.426136i	0.977037	−	0.213068i	$-0.0683455\pi$
$510$		0			0
$511$	−1.78779e43			−0.827147
$512$	8.26298e42	+	8.26298e42i	0.370525	+	0.370525i
$513$	−4.21189e42	+	4.21189e42i	−0.183062	+	0.183062i
$514$		−	2.35108e42i		−	0.0990508i
$515$		0			0
$516$	5.83729e42			0.231108
$517$	−2.40748e43	−	2.40748e43i	−0.924089	−	0.924089i
$518$	−2.92822e42	+	2.92822e42i	−0.108975	+	0.108975i
$519$		−	8.34384e42i		−	0.301085i
$520$		0			0
$521$	1.77245e43			0.601411			0.300706	−	0.953717i	$-0.402778\pi$
$521$	1.77245e43			0.601411			0.300706	+	0.953717i	$0.402778\pi$
$522$	−3.14761e42	−	3.14761e42i	−0.103575	−	0.103575i
$523$	−1.29808e43	+	1.29808e43i	−0.414260	+	0.414260i	−0.883220	−	0.468960i	$-0.844629\pi$
$523$	−1.29808e43	+	1.29808e43i	−0.414260	+	0.414260i	0.468960	+	0.883220i	$0.344629\pi$
$524$			4.53059e43i			1.40234i
$525$		0			0
$526$	−1.75083e42			−0.0509884
$527$	−1.27340e43	−	1.27340e43i	−0.359746	−	0.359746i
$528$	6.63263e42	−	6.63263e42i	0.181779	−	0.181779i
$529$			2.19534e43i			0.583730i
$530$		0			0
$531$	2.33432e43			0.584317
$532$	−1.49989e43	−	1.49989e43i	−0.364311	−	0.364311i
$533$	−7.11645e43	+	7.11645e43i	−1.67737	+	1.67737i
$534$			2.41918e41i			0.00553360i
$535$		0			0
$536$	−2.00055e43			−0.431035
$537$	−3.51173e42	−	3.51173e42i	−0.0734400	−	0.0734400i
$538$	−1.82535e42	+	1.82535e42i	−0.0370535	+	0.0370535i
$539$			8.37159e42i			0.164964i
$540$		0			0
$541$	−1.63100e43			−0.302899			−0.151449	−	0.988465i	$-0.548394\pi$
$541$	−1.63100e43			−0.302899			−0.151449	+	0.988465i	$0.548394\pi$
$542$	−4.54986e42	−	4.54986e42i	−0.0820370	−	0.0820370i
$543$	5.55919e42	−	5.55919e42i	0.0973227	−	0.0973227i
$544$			1.41888e43i			0.241193i
$545$		0			0
$546$	1.92232e42			0.0308137
$547$	4.27534e43	+	4.27534e43i	0.665539	+	0.665539i	0.956680	−	0.291141i	$-0.0940348\pi$
$547$	4.27534e43	+	4.27534e43i	0.665539	+	0.665539i	−0.291141	+	0.956680i	$0.594035\pi$
$548$	1.40023e43	−	1.40023e43i	0.211694	−	0.211694i
$549$			3.74101e43i			0.549328i
$550$		0			0
$551$	−5.74048e43			−0.795284
$552$	−1.75007e42	−	1.75007e42i	−0.0235521	−	0.0235521i
$553$	−2.15936e43	+	2.15936e43i	−0.282308	+	0.282308i
$554$			4.16347e42i			0.0528809i
$555$		0			0
$556$	−3.38797e43			−0.406202
$557$	−1.27671e43	−	1.27671e43i	−0.148734	−	0.148734i	0.628818	−	0.777552i	$-0.283539\pi$
$557$	−1.27671e43	−	1.27671e43i	−0.148734	−	0.148734i	−0.777552	+	0.628818i	$0.783539\pi$
$558$	−4.44921e42	+	4.44921e42i	−0.0503658	+	0.0503658i
$559$		−	1.15722e44i		−	1.27300i
$560$		0			0
$561$	1.90596e43			0.198020
$562$	1.00566e42	+	1.00566e42i	0.0101548	+	0.0101548i
$563$	8.17225e43	−	8.17225e43i	0.802061	−	0.802061i	−0.181356	−	0.983417i	$-0.558049\pi$
$563$	8.17225e43	−	8.17225e43i	0.802061	−	0.802061i	0.983417	+	0.181356i	$0.0580488\pi$
$564$		−	2.82458e43i		−	0.269456i
$565$		0			0
$566$	−1.71257e43			−0.154378
$567$	6.23468e43	+	6.23468e43i	0.546368	+	0.546368i
$568$	−1.46859e42	+	1.46859e42i	−0.0125121	+	0.0125121i
$569$			7.56311e43i			0.626476i	0.949675	+	0.313238i	$0.101414\pi$
$569$			7.56311e43i			0.626476i	−0.949675	+	0.313238i	$0.898586\pi$
$570$		0			0
$571$	1.54228e44			1.20777			0.603887	−	0.797070i	$-0.293618\pi$
$571$	1.54228e44			1.20777			0.603887	+	0.797070i	$0.293618\pi$
$572$	−1.33142e44	−	1.33142e44i	−1.01386	−	1.01386i
$573$	2.86357e43	−	2.86357e43i	0.212048	−	0.212048i
$574$		−	2.60979e43i		−	0.187938i
$575$		0			0
$576$	−1.28663e44			−0.876380
$577$	−1.09219e44	−	1.09219e44i	−0.723575	−	0.723575i	0.245757	−	0.969332i	$-0.420964\pi$
$577$	−1.09219e44	−	1.09219e44i	−0.723575	−	0.723575i	−0.969332	+	0.245757i	$0.920964\pi$
$578$	5.42096e42	−	5.42096e42i	0.0349326	−	0.0349326i
$579$		−	2.76130e43i		−	0.173084i
$580$		0			0
$581$	7.93563e43			0.470720
$582$	−3.81581e42	−	3.81581e42i	−0.0220201	−	0.0220201i
$583$	−3.68146e43	+	3.68146e43i	−0.206692	+	0.206692i
$584$		−	3.58497e43i		−	0.195831i
$585$		0			0
$586$	9.10083e42			0.0470673
$587$	2.14797e44	+	2.14797e44i	1.08098	+	1.08098i	0.996418	+	0.0845635i	$0.0269496\pi$
$587$	2.14797e44	+	2.14797e44i	1.08098	+	1.08098i	0.0845635	+	0.996418i	$0.473050\pi$
$588$	−4.91099e42	+	4.91099e42i	−0.0240509	+	0.0240509i
$589$			8.11428e43i			0.386727i
$590$		0			0
$591$	8.50365e43			0.383889
$592$	2.34996e44	+	2.34996e44i	1.03256	+	1.03256i
$593$	1.74021e43	−	1.74021e43i	0.0744263	−	0.0744263i	−0.668914	−	0.743340i	$-0.733240\pi$
$593$	1.74021e43	−	1.74021e43i	0.0744263	−	0.0744263i	0.743340	+	0.668914i	$0.233240\pi$
$594$		−	1.37113e43i		−	0.0570814i
$595$		0			0
$596$	2.73835e44			1.08031
$597$	−6.92016e43	−	6.92016e43i	−0.265783	−	0.265783i
$598$	−1.72415e43	+	1.72415e43i	−0.0644699	+	0.0644699i
$599$			1.15737e44i			0.421350i	0.977556	+	0.210675i	$0.0675662\pi$
$599$			1.15737e44i			0.421350i	−0.977556	+	0.210675i	$0.932434\pi$
$600$		0			0
$601$	1.20468e43			0.0415796			0.0207898	−	0.999784i	$-0.493382\pi$
$601$	1.20468e43			0.0415796			0.0207898	+	0.999784i	$0.493382\pi$
$602$	2.12192e43	+	2.12192e43i	0.0713158	+	0.0713158i
$603$	4.01932e44	−	4.01932e44i	1.31545	−	1.31545i
$604$		−	4.91604e44i		−	1.56684i
$605$		0			0
$606$	−7.74067e42			−0.0234000
$607$	4.01564e44	+	4.01564e44i	1.18232	+	1.18232i	0.979141	+	0.203182i	$0.0651283\pi$
$607$	4.01564e44	+	4.01564e44i	1.18232	+	1.18232i	0.203182	+	0.979141i	$0.434872\pi$
$608$	4.52064e43	−	4.52064e43i	0.129641	−	0.129641i
$609$		−	1.10008e44i		−	0.307291i
$610$		0			0
$611$	−5.59963e44			−1.48423
$612$	−1.89661e44	−	1.89661e44i	−0.489727	−	0.489727i
$613$	−6.00864e43	+	6.00864e43i	−0.151150	+	0.151150i	−0.778632	−	0.627481i	$-0.784086\pi$
$613$	−6.00864e43	+	6.00864e43i	−0.151150	+	0.151150i	0.627481	+	0.778632i	$0.284086\pi$
$614$			8.12419e43i			0.199107i
$615$		0			0
$616$	9.82526e43			0.228588
$617$	−1.50007e44	−	1.50007e44i	−0.340055	−	0.340055i	0.516333	−	0.856388i	$-0.327297\pi$
$617$	−1.50007e44	−	1.50007e44i	−0.340055	−	0.340055i	−0.856388	+	0.516333i	$0.827297\pi$
$618$	4.43371e42	−	4.43371e42i	0.00979381	−	0.00979381i
$619$		−	6.43848e44i		−	1.38590i	−0.720984	−	0.692951i	$-0.756310\pi$
$619$		−	6.43848e44i		−	1.38590i	0.720984	−	0.692951i	$-0.243690\pi$
$620$		0			0
$621$	1.44789e44			0.295985
$622$	−3.99032e42	−	3.99032e42i	−0.00794989	−	0.00794989i
$623$	7.17106e43	−	7.17106e43i	0.139243	−	0.139243i
$624$		−	1.54270e44i		−	0.291964i
$625$		0			0
$626$	−7.01494e40			−0.000126135
$627$	−6.07251e43	−	6.07251e43i	−0.106436	−	0.106436i
$628$	4.81797e44	−	4.81797e44i	0.823208	−	0.823208i
$629$			6.75289e44i			1.12481i
$630$		0			0
$631$	1.29342e44			0.204772			0.102386	−	0.994745i	$-0.467352\pi$
$631$	1.29342e44			0.204772			0.102386	+	0.994745i	$0.467352\pi$
$632$	−4.33006e43	−	4.33006e43i	−0.0668376	−	0.0668376i
$633$	5.33547e43	−	5.33547e43i	0.0802996	−	0.0802996i
$634$			6.23364e43i			0.0914774i
$635$		0			0
$636$	−4.31928e43			−0.0602695
$637$	9.73588e43	+	9.73588e43i	0.132478	+	0.132478i
$638$	9.34370e43	−	9.34370e43i	0.123990	−	0.123990i
$639$		−	5.90113e43i		−	0.0763698i
$640$		0			0
$641$	1.04469e45			1.28606			0.643028	−	0.765843i	$-0.277678\pi$
$641$	1.04469e45			1.28606			0.643028	+	0.765843i	$0.277678\pi$
$642$	1.67221e43	+	1.67221e43i	0.0200785	+	0.0200785i
$643$	−9.53779e44	+	9.53779e44i	−1.11705	+	1.11705i	−0.124877	+	0.992172i	$0.539854\pi$
$643$	−9.53779e44	+	9.53779e44i	−1.11705	+	1.11705i	−0.992172	+	0.124877i	$0.960146\pi$
$644$			5.15604e44i			0.589037i
$645$		0			0
$646$	4.24176e43			0.0461133
$647$	−1.17210e44	−	1.17210e44i	−0.124308	−	0.124308i	0.642216	−	0.766524i	$-0.278015\pi$
$647$	−1.17210e44	−	1.17210e44i	−0.124308	−	0.124308i	−0.766524	+	0.642216i	$0.778015\pi$
$648$	−1.25021e44	+	1.25021e44i	−0.129355	+	0.129355i
$649$			6.92945e44i			0.699494i
$650$		0			0
$651$	−1.55499e44			−0.149428
$652$	−1.39463e45	−	1.39463e45i	−1.30767	−	1.30767i
$653$	−5.84265e44	+	5.84265e44i	−0.534563	+	0.534563i	−0.921927	−	0.387364i	$-0.873386\pi$
$653$	−5.84265e44	+	5.84265e44i	−0.534563	+	0.534563i	0.387364	+	0.921927i	$0.373386\pi$
$654$		−	7.42546e41i		−	0.000662948i
$655$		0			0
$656$	−2.09442e45			−1.78074
$657$	7.20260e44	+	7.20260e44i	0.597645	+	0.597645i
$658$	1.02677e44	−	1.02677e44i	0.0831492	−	0.0831492i
$659$		−	8.79148e44i		−	0.694857i	−0.937707	−	0.347428i	$-0.887055\pi$
$659$		−	8.79148e44i		−	0.694857i	0.937707	−	0.347428i	$-0.112945\pi$
$660$		0			0
$661$	9.80458e44			0.738254			0.369127	−	0.929379i	$-0.379657\pi$
$661$	9.80458e44			0.738254			0.369127	+	0.929379i	$0.379657\pi$
$662$	1.39493e44	+	1.39493e44i	0.102524	+	0.102524i
$663$	2.21657e44	−	2.21657e44i	0.159025	−	0.159025i
$664$			1.59129e44i			0.111445i
$665$		0			0
$666$	2.35943e44			0.157478
$667$	9.86679e44	+	9.86679e44i	0.642928	+	0.642928i
$668$	−3.05004e44	+	3.05004e44i	−0.194036	+	0.194036i
$669$			4.27831e43i			0.0265738i
$670$		0			0
$671$	−1.11052e45			−0.657607
$672$	8.66319e43	+	8.66319e43i	0.0500921	+	0.0500921i
$673$	−6.46753e44	+	6.46753e44i	−0.365172	+	0.365172i	−0.865713	−	0.500541i	$-0.833134\pi$
$673$	−6.46753e44	+	6.46753e44i	−0.365172	+	0.365172i	0.500541	+	0.865713i	$0.333134\pi$
$674$		−	1.29913e44i		−	0.0716298i
$675$		0			0
$676$	−1.21812e45			−0.640534
$677$	−3.66386e44	−	3.66386e44i	−0.188157	−	0.188157i	0.606742	−	0.794899i	$-0.292476\pi$
$677$	−3.66386e44	−	3.66386e44i	−0.188157	−	0.188157i	−0.794899	+	0.606742i	$0.792476\pi$
$678$	−3.11624e43	+	3.11624e43i	−0.0156299	+	0.0156299i
$679$			2.26221e45i			1.10819i
$680$		0			0
$681$	6.23566e44			0.291426
$682$	−1.32075e44	−	1.32075e44i	−0.0602935	−	0.0602935i
$683$	−2.94810e45	+	2.94810e45i	−1.31465	+	1.31465i	−0.396708	+	0.917945i	$0.629848\pi$
$683$	−2.94810e45	+	2.94810e45i	−1.31465	+	1.31465i	−0.917945	+	0.396708i	$0.870152\pi$
$684$			1.20854e45i			0.526457i
$685$		0			0
$686$	−2.80378e44			−0.116562
$687$	−5.18246e44	−	5.18246e44i	−0.210488	−	0.210488i
$688$	1.70289e45	−	1.70289e45i	0.675727	−	0.675727i
$689$			8.56282e44i			0.331978i
$690$		0			0
$691$	−3.82490e45			−1.41570			−0.707850	−	0.706363i	$-0.750335\pi$
$691$	−3.82490e45			−1.41570			−0.707850	+	0.706363i	$0.750335\pi$
$692$	−2.46471e45	−	2.46471e45i	−0.891392	−	0.891392i
$693$	−1.97400e45	+	1.97400e45i	−0.697614	+	0.697614i
$694$			1.30477e44i			0.0450589i
$695$		0			0
$696$	2.20595e44			0.0727523
$697$	−3.00927e45	−	3.00927e45i	−0.969922	−	0.969922i
$698$	2.74215e44	−	2.74215e44i	0.0863782	−	0.0863782i
$699$		−	2.13198e44i		−	0.0656369i
$700$		0			0
$701$	5.21709e45			1.53441			0.767203	−	0.641404i	$-0.221648\pi$
$701$	5.21709e45			1.53441			0.767203	+	0.641404i	$0.221648\pi$
$702$	−1.59457e44	−	1.59457e44i	−0.0458406	−	0.0458406i
$703$	2.15151e45	−	2.15151e45i	0.604586	−	0.604586i
$704$		−	3.81935e45i		−	1.04913i
$705$		0			0
$706$	7.90132e44			0.207407
$707$	2.29453e45	+	2.29453e45i	0.588821	+	0.588821i
$708$	−4.06500e44	+	4.06500e44i	−0.101983	+	0.101983i
$709$			4.59255e45i			1.12645i	0.826302	+	0.563227i	$0.190440\pi$
$709$			4.59255e45i			1.12645i	−0.826302	+	0.563227i	$0.809560\pi$
$710$		0			0
$711$	1.73991e45			0.407956
$712$	1.43798e44	+	1.43798e44i	0.0329665	+	0.0329665i
$713$	1.39469e45	−	1.39469e45i	0.312640	−	0.312640i
$714$			8.12876e43i			0.0178177i
$715$		0			0
$716$	−2.07468e45			−0.434853
$717$	1.28859e45	+	1.28859e45i	0.264124	+	0.264124i
$718$	2.27706e43	−	2.27706e43i	0.00456439	−	0.00456439i
$719$		−	1.38193e45i		−	0.270909i	−0.990784	−	0.135454i	$-0.956751\pi$
$719$		−	1.38193e45i		−	0.270909i	0.990784	−	0.135454i	$-0.0432494\pi$
$720$		0			0
$721$	−2.62853e45			−0.492889
$722$	2.89215e44	+	2.89215e44i	0.0530428	+	0.0530428i
$723$	−9.36100e44	+	9.36100e44i	−0.167923	+	0.167923i
$724$		−	3.28429e45i		−	0.576268i
$725$		0			0
$726$	4.29966e43			0.00721852
$727$	4.22465e45	+	4.22465e45i	0.693809	+	0.693809i	0.963068	−	0.269259i	$-0.0867787\pi$
$727$	4.22465e45	+	4.22465e45i	0.693809	+	0.693809i	−0.269259	+	0.963068i	$0.586779\pi$
$728$	1.14264e45	−	1.14264e45i	0.183573	−	0.183573i
$729$		−	4.33491e45i		−	0.681302i
$730$		0			0
$731$	4.89345e45			0.736100
$732$	−6.51460e44	−	6.51460e44i	−0.0958762	−	0.0958762i
$733$	−1.90729e45	+	1.90729e45i	−0.274634	+	0.274634i	−0.830962	−	0.556329i	$-0.812210\pi$
$733$	−1.90729e45	+	1.90729e45i	−0.274634	+	0.274634i	0.556329	+	0.830962i	$0.312210\pi$
$734$			1.01122e45i			0.142465i
$735$		0			0
$736$	−1.55402e45			−0.209610
$737$	1.19314e46	+	1.19314e46i	1.57474	+	1.57474i
$738$	−1.05142e45	+	1.05142e45i	−0.135793	+	0.135793i
$739$			3.71447e45i			0.469446i	0.972062	+	0.234723i	$0.0754183\pi$
$739$			3.71447e45i			0.469446i	−0.972062	+	0.234723i	$0.924582\pi$
$740$		0			0
$741$	−1.41242e45			−0.170952
$742$	−1.57011e44	−	1.57011e44i	−0.0185980	−	0.0185980i
$743$	1.06173e46	−	1.06173e46i	1.23082	−	1.23082i	0.267166	−	0.963650i	$-0.413913\pi$
$743$	1.06173e46	−	1.06173e46i	1.23082	−	1.23082i	0.963650	−	0.267166i	$-0.0860872\pi$
$744$		−	3.11815e44i		−	0.0353777i
$745$		0			0
$746$	−1.89690e45			−0.206169
$747$	−3.19708e45	−	3.19708e45i	−0.340113	−	0.340113i
$748$	5.63008e45	−	5.63008e45i	0.586258	−	0.586258i
$749$		−	9.91373e45i		−	1.01048i
$750$		0			0
$751$	1.11575e46			1.08975			0.544876	−	0.838517i	$-0.316577\pi$
$751$	1.11575e46			1.08975			0.544876	+	0.838517i	$0.316577\pi$
$752$	−8.24003e45	−	8.24003e45i	−0.787850	−	0.787850i
$753$	9.97497e44	−	9.97497e44i	0.0933667	−	0.0933667i
$754$		−	2.17328e45i		−	0.199147i
$755$		0			0
$756$	−4.76853e45			−0.418828
$757$	−6.40797e45	−	6.40797e45i	−0.551044	−	0.551044i	0.375698	−	0.926742i	$-0.377403\pi$
$757$	−6.40797e45	−	6.40797e45i	−0.551044	−	0.551044i	−0.926742	+	0.375698i	$0.877403\pi$
$758$	−9.87875e44	+	9.87875e44i	−0.0831754	+	0.0831754i
$759$			2.08750e45i			0.172091i
$760$		0			0
$761$	9.90396e45			0.782806			0.391403	−	0.920219i	$-0.371990\pi$
$761$	9.90396e45			0.782806			0.391403	+	0.920219i	$0.371990\pi$
$762$	1.60718e43	+	1.60718e43i	0.00124390	+	0.00124390i
$763$	−2.20110e44	+	2.20110e44i	−0.0166819	+	0.0166819i
$764$		−	1.69176e46i		−	1.25558i
$765$		0			0
$766$	1.67508e45			0.119227
$767$	8.05872e45	+	8.05872e45i	0.561746	+	0.561746i
$768$	2.15314e45	−	2.15314e45i	0.146992	−	0.146992i
$769$		−	5.88387e44i		−	0.0393407i	−0.999807	−	0.0196703i	$-0.993738\pi$
$769$		−	5.88387e44i		−	0.0393407i	0.999807	−	0.0196703i	$-0.00626166\pi$
$770$		0			0
$771$	−3.31043e45			−0.212332
$772$	−8.15669e45	−	8.15669e45i	−0.512433	−	0.512433i
$773$	2.55868e45	−	2.55868e45i	0.157450	−	0.157450i	−0.623985	−	0.781436i	$-0.714488\pi$
$773$	2.55868e45	−	2.55868e45i	0.157450	−	0.157450i	0.781436	+	0.623985i	$0.214488\pi$
$774$		−	1.70975e45i		−	0.103057i
$775$		0			0
$776$	−4.53630e45			−0.262370
$777$	4.12307e45	+	4.12307e45i	0.233606	+	0.233606i
$778$	1.20885e45	−	1.20885e45i	0.0670963	−	0.0670963i
$779$			1.91754e46i			1.04267i
$780$		0			0
$781$	1.75175e45			0.0914232
$782$	−7.29079e44	−	7.29079e44i	−0.0372792	−	0.0372792i
$783$	−9.12524e45	+	9.12524e45i	−0.457147	+	0.457147i
$784$			2.86533e45i			0.140643i
$785$		0			0
$786$	−7.82302e44			−0.0368650
$787$	2.65272e46	+	2.65272e46i	1.22489	+	1.22489i	0.965873	+	0.259014i	$0.0833977\pi$
$787$	2.65272e46	+	2.65272e46i	1.22489	+	1.22489i	0.259014	+	0.965873i	$0.416602\pi$
$788$	2.51192e46	−	2.51192e46i	1.13654	−	1.13654i
$789$			2.46524e45i			0.109302i
$790$		0			0
$791$	1.84747e46			0.786597
$792$	−3.95837e45	−	3.95837e45i	−0.165163	−	0.165163i
$793$	−1.29150e46	+	1.29150e46i	−0.528108	+	0.528108i
$794$		−	2.91359e45i		−	0.116762i
$795$		0			0
$796$	−4.08833e46			−1.57376
$797$	1.46500e46	+	1.46500e46i	0.552718	+	0.552718i	0.927224	−	0.374506i	$-0.122188\pi$
$797$	1.46500e46	+	1.46500e46i	0.552718	+	0.552718i	−0.374506	+	0.927224i	$0.622188\pi$
$798$	2.58987e44	−	2.58987e44i	0.00957704	−	0.00957704i
$799$		−	2.36787e46i		−	0.858241i
$800$		0			0
$801$	−5.77811e45			−0.201217
$802$	−1.67824e45	−	1.67824e45i	−0.0572880	−	0.0572880i
$803$	−2.13809e46	+	2.13809e46i	−0.715448	+	0.715448i
$804$			1.39985e46i			0.459181i
$805$		0			0
$806$	−3.07197e45			−0.0968405
$807$	2.57017e45	+	2.57017e45i	0.0794303	+	0.0794303i
$808$	−4.60112e45	+	4.60112e45i	−0.139406	+	0.139406i
$809$			2.49211e46i			0.740271i	0.928978	+	0.370136i	$0.120689\pi$
$809$			2.49211e46i			0.740271i	−0.928978	+	0.370136i	$0.879311\pi$
$810$		0			0
$811$	2.55847e46			0.730545			0.365273	−	0.930901i	$-0.380976\pi$
$811$	2.55847e46			0.730545			0.365273	+	0.930901i	$0.380976\pi$
$812$	−3.24957e46	−	3.24957e46i	−0.909765	−	0.909765i
$813$	−6.40641e45	+	6.40641e45i	−0.175860	+	0.175860i
$814$			7.00396e45i			0.188518i
$815$		0			0
$816$	6.52350e45			0.168826
$817$	−1.55908e46	−	1.55908e46i	−0.395654	−	0.395654i
$818$	−3.78817e44	+	3.78817e44i	−0.00942708	+	0.00942708i
$819$			4.59139e46i			1.12047i
$820$		0			0
$821$	1.58755e46			0.372595			0.186298	−	0.982493i	$-0.440351\pi$
$821$	1.58755e46			0.372595			0.186298	+	0.982493i	$0.440351\pi$
$822$	2.41779e44	+	2.41779e44i	0.00556504	+	0.00556504i
$823$	−5.24557e46	+	5.24557e46i	−1.18412	+	1.18412i	−0.205453	+	0.978667i	$0.565867\pi$
$823$	−5.24557e46	+	5.24557e46i	−1.18412	+	1.18412i	−0.978667	+	0.205453i	$0.934133\pi$
$824$		−	5.27087e45i		−	0.116694i
$825$		0			0
$826$	−2.95535e45			−0.0629401
$827$	−3.35852e46	−	3.35852e46i	−0.701553	−	0.701553i	0.263191	−	0.964744i	$-0.415225\pi$
$827$	−3.35852e46	−	3.35852e46i	−0.701553	−	0.701553i	−0.964744	+	0.263191i	$0.915225\pi$
$828$	2.07725e46	−	2.07725e46i	0.425601	−	0.425601i
$829$		−	3.69874e46i		−	0.743330i	−0.928367	−	0.371665i	$-0.878787\pi$
$829$		−	3.69874e46i		−	0.743330i	0.928367	−	0.371665i	$-0.121213\pi$
$830$		0			0
$831$	5.86235e45			0.113359
$832$	−4.44178e46	−	4.44178e46i	−0.842527	−	0.842527i
$833$	−4.11693e45	+	4.11693e45i	−0.0766043	+	0.0766043i
$834$		−	5.85004e44i		−	0.0106783i
$835$		0			0
$836$	−3.58755e46			−0.630228
$837$	1.28987e46	+	1.28987e46i	0.222300	+	0.222300i
$838$	−5.28763e45	+	5.28763e45i	−0.0894040	+	0.0894040i
$839$			6.06375e46i			1.00589i	0.864319	+	0.502945i	$0.167750\pi$
$839$			6.06375e46i			1.00589i	−0.864319	+	0.502945i	$0.832250\pi$
$840$		0			0
$841$	−6.17467e46			−0.986002
$842$	−1.51850e45	−	1.51850e45i	−0.0237915	−	0.0237915i
$843$	1.41601e45	−	1.41601e45i	0.0217684	−	0.0217684i
$844$		−	3.15212e46i		−	0.475471i
$845$		0			0
$846$	−8.27322e45			−0.120157
$847$	−1.27453e46	−	1.27453e46i	−0.181642	−	0.181642i
$848$	−1.26005e46	+	1.26005e46i	−0.176219	+	0.176219i
$849$			2.41137e46i			0.330934i
$850$		0			0
$851$	−7.39607e46			−0.977526
$852$	1.02762e45	+	1.02762e45i	0.0133291	+	0.0133291i
$853$	−2.40976e45	+	2.40976e45i	−0.0306754	+	0.0306754i	−0.722278	−	0.691603i	$-0.756905\pi$
$853$	−2.40976e45	+	2.40976e45i	−0.0306754	+	0.0306754i	0.691603	+	0.722278i	$0.256905\pi$
$854$		−	4.73627e45i		−	0.0591712i
$855$		0			0
$856$	1.98795e46			0.239236
$857$	6.32209e46	+	6.32209e46i	0.746737	+	0.746737i	0.973865	−	0.227128i	$-0.0729337\pi$
$857$	6.32209e46	+	6.32209e46i	0.746737	+	0.746737i	−0.227128	+	0.973865i	$0.572934\pi$
$858$	2.29898e45	−	2.29898e45i	0.0266526	−	0.0266526i
$859$		−	3.36701e45i		−	0.0383137i	−0.999816	−	0.0191569i	$-0.993902\pi$
$859$		−	3.36701e45i		−	0.0383137i	0.999816	−	0.0191569i	$-0.00609819\pi$
$860$		0			0
$861$	−3.67471e46			−0.402877
$862$	9.67937e45	+	9.67937e45i	0.104167	+	0.104167i
$863$	−5.35645e46	+	5.35645e46i	−0.565853	+	0.565853i	−0.930964	−	0.365111i	$-0.881031\pi$
$863$	−5.35645e46	+	5.35645e46i	−0.565853	+	0.565853i	0.365111	+	0.930964i	$0.381031\pi$
$864$		−	1.43723e46i		−	0.149041i
$865$		0			0
$866$	−3.62258e45			−0.0362019
$867$	−7.63296e45	−	7.63296e45i	−0.0748838	−	0.0748838i
$868$	−4.59333e46	+	4.59333e46i	−0.442397	+	0.442397i
$869$			5.16494e46i			0.488370i
$870$		0			0
$871$	2.77515e47			2.52928
$872$	−4.41376e44	−	4.41376e44i	−0.00394952	−	0.00394952i
$873$	9.11391e46	−	9.11391e46i	0.800713	−	0.800713i
$874$			4.64577e45i			0.0400751i
$875$		0			0
$876$	−2.50852e46			−0.208618
$877$	1.41132e47	+	1.41132e47i	1.15248	+	1.15248i	0.986054	+	0.166426i	$0.0532226\pi$
$877$	1.41132e47	+	1.41132e47i	1.15248	+	1.15248i	0.166426	+	0.986054i	$0.446777\pi$
$878$	2.70293e45	−	2.70293e45i	0.0216732	−	0.0216732i
$879$		−	1.28144e46i		−	0.100896i
$880$		0			0
$881$	−1.09203e47			−0.829129			−0.414564	−	0.910020i	$-0.636066\pi$
$881$	−1.09203e47			−0.829129			−0.414564	+	0.910020i	$0.636066\pi$
$882$	1.43843e45	+	1.43843e45i	0.0107249	+	0.0107249i
$883$	1.00767e47	−	1.00767e47i	0.737816	−	0.737816i	−0.234339	−	0.972155i	$-0.575293\pi$
$883$	1.00767e47	−	1.00767e47i	0.737816	−	0.737816i	0.972155	+	0.234339i	$0.0752927\pi$
$884$		−	1.30952e47i		−	0.941619i
$885$		0			0
$886$	1.37597e46			0.0954269
$887$	−1.91354e47	−	1.91354e47i	−1.30334	−	1.30334i	−0.926124	−	0.377220i	$-0.876880\pi$
$887$	−1.91354e47	−	1.91354e47i	−1.30334	−	1.30334i	−0.377220	−	0.926124i	$-0.623120\pi$
$888$	−8.26780e45	+	8.26780e45i	−0.0553073	+	0.0553073i
$889$		−	9.52818e45i		−	0.0626011i
$890$		0			0
$891$	1.49126e47			0.945172
$892$	1.26378e46	+	1.26378e46i	0.0786746	+	0.0786746i
$893$	−7.54417e46	+	7.54417e46i	−0.461305	+	0.461305i
$894$			4.72834e45i			0.0283993i
$895$		0			0
$896$	6.80977e46			0.394643
$897$	2.42769e46	+	2.42769e46i	0.138202	+	0.138202i
$898$	2.63115e46	−	2.63115e46i	0.147138	−	0.147138i
$899$			1.75799e47i			0.965744i
$900$		0			0
$901$	−3.62089e46			−0.191963
$902$	−3.12116e46	−	3.12116e46i	−0.162559	−	0.162559i
$903$	2.98776e46	−	2.98776e46i	0.152877	−	0.152877i
$904$			3.70463e46i			0.186230i
$905$		0			0
$906$	8.48857e45			0.0411892
$907$	7.36912e46	+	7.36912e46i	0.351317	+	0.351317i	0.860599	−	0.509283i	$-0.170089\pi$
$907$	7.36912e46	+	7.36912e46i	0.351317	+	0.351317i	−0.509283	+	0.860599i	$0.670089\pi$
$908$	1.84197e47	−	1.84197e47i	0.862798	−	0.862798i
$909$		−	1.84883e47i		−	0.850892i
$910$		0			0
$911$	−1.25829e46			−0.0559098			−0.0279549	−	0.999609i	$-0.508899\pi$
$911$	−1.25829e46			−0.0559098			−0.0279549	+	0.999609i	$0.508899\pi$
$912$	−2.07843e46	−	2.07843e46i	−0.0907438	−	0.0907438i
$913$	9.49054e46	−	9.49054e46i	0.407154	−	0.407154i
$914$			1.86731e45i			0.00787187i
$915$		0			0
$916$	−3.06172e47			−1.24635
$917$	2.31895e47	+	2.31895e47i	0.927643	+	0.927643i
$918$	6.74284e45	−	6.74284e45i	0.0265069	−	0.0265069i
$919$		−	3.11454e47i		−	1.20322i	−0.798789	−	0.601611i	$-0.794526\pi$
$919$		−	3.11454e47i		−	1.20322i	0.798789	−	0.601611i	$-0.205474\pi$
$920$		0			0
$921$	1.14392e47			0.426818
$922$	2.87996e46	+	2.87996e46i	0.105607	+	0.105607i
$923$	2.03723e46	−	2.03723e46i	0.0734197	−	0.0734197i
$924$		−	6.87505e46i		−	0.243514i
$925$		0			0
$926$	3.23391e46			0.110650
$927$	1.05897e47	+	1.05897e47i	0.356131	+	0.356131i
$928$	9.79417e46	−	9.79417e46i	0.323743	−	0.323743i
$929$		−	4.55049e47i		−	1.47845i	−0.673458	−	0.739226i	$-0.735192\pi$
$929$		−	4.55049e47i		−	1.47845i	0.673458	−	0.739226i	$-0.264808\pi$
$930$		0			0
$931$	2.62335e46			0.0823497
$932$	−6.29772e46	−	6.29772e46i	−0.194325	−	0.194325i
$933$	−5.61855e45	+	5.61855e45i	−0.0170419	+	0.0170419i
$934$			1.48011e46i			0.0441310i
$935$		0			0
$936$	−9.20689e46			−0.265277
$937$	−1.47931e47	−	1.47931e47i	−0.419012	−	0.419012i	0.465851	−	0.884863i	$-0.345748\pi$
$937$	−1.47931e47	−	1.47931e47i	−0.419012	−	0.419012i	−0.884863	+	0.465851i	$0.845748\pi$
$938$	−5.08861e46	+	5.08861e46i	−0.141695	+	0.141695i
$939$			9.87736e43i			0.000270390i
$940$		0			0
$941$	8.20417e46			0.217071			0.108535	−	0.994093i	$-0.465384\pi$
$941$	8.20417e46			0.217071			0.108535	+	0.994093i	$0.465384\pi$
$942$	8.31924e45	+	8.31924e45i	0.0216406	+	0.0216406i
$943$	3.29589e47	−	3.29589e47i	0.842919	−	0.842919i
$944$			2.37173e47i			0.596367i
$945$		0			0
$946$	5.07539e46			0.123370
$947$	2.19757e47	+	2.19757e47i	0.525221	+	0.525221i	0.919144	−	0.393923i	$-0.128882\pi$
$947$	2.19757e47	+	2.19757e47i	0.525221	+	0.525221i	−0.393923	+	0.919144i	$0.628882\pi$
$948$	−3.02989e46	+	3.02989e46i	−0.0712021	+	0.0712021i
$949$			4.97306e47i			1.14912i
$950$		0			0
$951$	8.77725e46			0.196097
$952$	4.83180e46	+	4.83180e46i	0.106149	+	0.106149i
$953$	−4.43968e47	+	4.43968e47i	−0.959102	+	0.959102i	−0.999196	−	0.0400935i	$-0.987234\pi$
$953$	−4.43968e47	+	4.43968e47i	−0.959102	+	0.959102i	0.0400935	+	0.999196i	$0.487234\pi$
$954$			1.26512e46i			0.0268756i
$955$		0			0
$956$	7.61281e47			1.56393
$957$	−1.31564e47	−	1.31564e47i	−0.265794	−	0.265794i
$958$	2.51501e46	−	2.51501e46i	0.0499680	−	0.0499680i
$959$		−	1.43339e47i		−	0.280070i
$960$		0			0
$961$	−2.80649e47			−0.530382
$962$	8.14537e46	+	8.14537e46i	0.151394	+	0.151394i
$963$	−3.99401e47	+	3.99401e47i	−0.730111	+	0.730111i
$964$			5.53035e47i			0.994305i
$965$		0			0
$966$	−8.90299e45			−0.0154847
$967$	−5.37817e47	−	5.37817e47i	−0.920049	−	0.920049i	0.0769837	−	0.997032i	$-0.475471\pi$
$967$	−5.37817e47	−	5.37817e47i	−0.920049	−	0.920049i	−0.997032	+	0.0769837i	$0.975471\pi$
$968$	2.55575e46	−	2.55575e46i	0.0430044	−	0.0430044i
$969$		−	5.97260e46i		−	0.0988514i
$970$		0			0
$971$	2.57376e46			0.0412155			0.0206077	−	0.999788i	$-0.493440\pi$
$971$	2.57376e46			0.0412155			0.0206077	+	0.999788i	$0.493440\pi$
$972$	2.90920e47	+	2.90920e47i	0.458261	+	0.458261i
$973$	−1.73410e47	+	1.73410e47i	−0.268701	+	0.268701i
$974$			5.08133e46i			0.0774523i
$975$		0			0
$976$	−3.80096e47			−0.560656
$977$	−2.38154e47	−	2.38154e47i	−0.345578	−	0.345578i	0.512882	−	0.858459i	$-0.328578\pi$
$977$	−2.38154e47	−	2.38154e47i	−0.345578	−	0.345578i	−0.858459	+	0.512882i	$0.828578\pi$
$978$	2.40813e46	−	2.40813e46i	0.0343762	−	0.0343762i
$979$		−	1.71523e47i		−	0.240880i
$980$		0			0
$981$	1.77354e46			0.0241067
$982$	−1.01226e47	−	1.01226e47i	−0.135365	−	0.135365i
$983$	4.61511e47	−	4.61511e47i	0.607191	−	0.607191i	−0.335020	−	0.942211i	$-0.608743\pi$
$983$	4.61511e47	−	4.61511e47i	0.607191	−	0.607191i	0.942211	+	0.335020i	$0.108743\pi$
$984$		−	7.36872e46i		−	0.0953828i
$985$		0			0
$986$	9.18997e46			0.115155
$987$	−1.44574e47	−	1.44574e47i	−0.178244	−	0.178244i
$988$	−4.17220e47	+	4.17220e47i	−0.506121	+	0.506121i
$989$			5.35953e47i			0.639714i
$990$		0			0
$991$	−1.12287e48			−1.29762			−0.648812	−	0.760948i	$-0.724734\pi$
$991$	−1.12287e48			−1.29762			−0.648812	+	0.760948i	$0.724734\pi$
$992$	−1.38442e47	−	1.38442e47i	−0.157428	−	0.157428i
$993$	1.96412e47	−	1.96412e47i	0.219776	−	0.219776i
$994$			7.47106e45i			0.00822622i
$995$		0			0
$996$	1.11348e47			0.118722
$997$	−3.81475e47	−	3.81475e47i	−0.400261	−	0.400261i	0.478064	−	0.878325i	$-0.341339\pi$
$997$	−3.81475e47	−	3.81475e47i	−0.400261	−	0.400261i	−0.878325	+	0.478064i	$0.841339\pi$
$998$	−1.03423e47	+	1.03423e47i	−0.106789	+	0.106789i
$999$		−	6.84021e47i		−	0.695059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.8		30
5.2	odd	4		5.33.c.a.3.8	yes	30
5.3	odd	4	inner	25.33.c.b.18.8		30
5.4	even	2		5.33.c.a.2.8	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.8	✓	30	5.4	even	2
5.33.c.a.3.8	yes	30	5.2	odd	4
25.33.c.b.7.8		30	1.1	even	1	trivial
25.33.c.b.18.8		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)

\(f(q)\)	\(=\)	\(q+(5100.58 + 5100.58i) q^{2} +(7.18185e6 - 7.18185e6i) q^{3} -4.24294e9i q^{4} +7.32632e10 q^{6} +(-2.17171e13 - 2.17171e13i) q^{7} +(4.35482e13 - 4.35482e13i) q^{8} +1.74986e15i q^{9} +O(q^{10})\)	\(q+(5100.58 + 5100.58i) q^{2} +(7.18185e6 - 7.18185e6i) q^{3} -4.24294e9i q^{4} +7.32632e10 q^{6} +(-2.17171e13 - 2.17171e13i) q^{7} +(4.35482e13 - 4.35482e13i) q^{8} +1.74986e15i q^{9} -5.19447e16 q^{11} +(-3.04721e16 - 3.04721e16i) q^{12} +(-6.04100e17 + 6.04100e17i) q^{13} -2.21539e17i q^{14} -1.77790e19 q^{16} +(-2.55450e19 - 2.55450e19i) q^{17} +(-8.92531e18 + 8.92531e18i) q^{18} +1.62776e20i q^{19} -3.11938e20 q^{21} +(-2.64948e20 - 2.64948e20i) q^{22} +(2.79781e21 - 2.79781e21i) q^{23} -6.25514e20i q^{24} -6.16252e21 q^{26} +(2.58754e22 + 2.58754e22i) q^{27} +(-9.21442e22 + 9.21442e22i) q^{28} +3.52661e23i q^{29} +4.98494e23 q^{31} +(-2.77722e23 - 2.77722e23i) q^{32} +(-3.73059e23 + 3.73059e23i) q^{33} -2.60589e23i q^{34} +7.42455e24 q^{36} +(-1.32176e25 - 1.32176e25i) q^{37} +(-8.30252e23 + 8.30252e23i) q^{38} +8.67711e24i q^{39} +1.17803e26 q^{41} +(-1.59106e24 - 1.59106e24i) q^{42} +(-9.57807e25 + 9.57807e25i) q^{43} +2.20398e26i q^{44} +2.85409e25 q^{46} +(4.63469e26 + 4.63469e26i) q^{47} +(-1.27686e26 + 1.27686e26i) q^{48} -1.61163e26i q^{49} -3.66921e26 q^{51} +(2.56316e27 + 2.56316e27i) q^{52} +(7.08726e26 - 7.08726e26i) q^{53} +2.63959e26i q^{54} -1.89148e27 q^{56} +(1.16903e27 + 1.16903e27i) q^{57} +(-1.79878e27 + 1.79878e27i) q^{58} -1.33400e28i q^{59} +2.13789e28 q^{61} +(2.54261e27 + 2.54261e27i) q^{62} +(3.80019e28 - 3.80019e28i) q^{63} +7.35273e28i q^{64} -3.80564e27 q^{66} +(-2.29693e29 - 2.29693e29i) q^{67} +(-1.08386e29 + 1.08386e29i) q^{68} -4.01869e28i q^{69} -3.37234e28 q^{71} +(7.62034e28 + 7.62034e28i) q^{72} +(4.11610e29 - 4.11610e29i) q^{73} -1.34835e29i q^{74} +6.90648e29 q^{76} +(1.12809e30 + 1.12809e30i) q^{77} +(-4.42583e28 + 4.42583e28i) q^{78} -9.94314e29i q^{79} -2.87086e30 q^{81} +(6.00861e29 + 6.00861e29i) q^{82} +(-1.82705e30 + 1.82705e30i) q^{83} +1.32353e30i q^{84} -9.77075e29 q^{86} +(2.53276e30 + 2.53276e30i) q^{87} +(-2.26210e30 + 2.26210e30i) q^{88} +3.30204e30i q^{89} +2.62386e31 q^{91} +(-1.18709e31 - 1.18709e31i) q^{92} +(3.58011e30 - 3.58011e30i) q^{93} +4.72792e30i q^{94} -3.98911e30 q^{96} +(-5.20836e31 - 5.20836e31i) q^{97} +(8.22027e29 - 8.22027e29i) q^{98} -9.08961e31i 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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