LMFDB - Embedded newform 25.33.c.b.7.12

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			7.12
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(42029.2 + 42029.2i) q^{2} +(2.23370e7 - 2.23370e7i) q^{3} -7.62067e8i q^{4} +1.87761e12 q^{6} +(2.39791e13 + 2.39791e13i) q^{7} +(2.12543e14 - 2.12543e14i) q^{8} +8.55140e14i q^{9} +O(q^{10})$	\(q+(42029.2 + 42029.2i) q^{2} +(2.23370e7 - 2.23370e7i) q^{3} -7.62067e8i q^{4} +1.87761e12 q^{6} +(2.39791e13 + 2.39791e13i) q^{7} +(2.12543e14 - 2.12543e14i) q^{8} +8.55140e14i q^{9} -3.17226e16 q^{11} +(-1.70223e16 - 1.70223e16i) q^{12} +(5.32549e17 - 5.32549e17i) q^{13} +2.01564e18i q^{14} +1.45929e19 q^{16} +(-4.10053e19 - 4.10053e19i) q^{17} +(-3.59408e19 + 3.59408e19i) q^{18} +2.22048e20i q^{19} +1.07124e21 q^{21} +(-1.33328e21 - 1.33328e21i) q^{22} +(6.22444e21 - 6.22444e21i) q^{23} -9.49513e21i q^{24} +4.47652e22 q^{26} +(6.04921e22 + 6.04921e22i) q^{27} +(1.82737e22 - 1.82737e22i) q^{28} -3.25507e23i q^{29} +1.21168e22 q^{31} +(-2.99536e23 - 2.99536e23i) q^{32} +(-7.08587e23 + 7.08587e23i) q^{33} -3.44684e24i q^{34} +6.51674e23 q^{36} +(1.53437e25 + 1.53437e25i) q^{37} +(-9.33250e24 + 9.33250e24i) q^{38} -2.37911e25i q^{39} -2.70283e25 q^{41} +(4.50234e25 + 4.50234e25i) q^{42} +(-9.54673e25 + 9.54673e25i) q^{43} +2.41748e25i q^{44} +5.23216e26 q^{46} +(-2.53838e26 - 2.53838e26i) q^{47} +(3.25962e26 - 3.25962e26i) q^{48} +4.55683e25i q^{49} -1.83187e27 q^{51} +(-4.05838e26 - 4.05838e26i) q^{52} +(1.49223e27 - 1.49223e27i) q^{53} +5.08486e27i q^{54} +1.01932e28 q^{56} +(4.95988e27 + 4.95988e27i) q^{57} +(1.36808e28 - 1.36808e28i) q^{58} +2.48663e28i q^{59} +3.17251e28 q^{61} +(5.09261e26 + 5.09261e26i) q^{62} +(-2.05055e28 + 2.05055e28i) q^{63} -8.78547e28i q^{64} -5.95627e28 q^{66} +(3.16482e27 + 3.16482e27i) q^{67} +(-3.12488e28 + 3.12488e28i) q^{68} -2.78070e29i q^{69} +4.69621e29 q^{71} +(1.81754e29 + 1.81754e29i) q^{72} +(3.04177e29 - 3.04177e29i) q^{73} +1.28976e30i q^{74} +1.69216e29 q^{76} +(-7.60681e29 - 7.60681e29i) q^{77} +(9.99918e29 - 9.99918e29i) q^{78} -1.79248e30i q^{79} +1.11783e30 q^{81} +(-1.13598e30 - 1.13598e30i) q^{82} +(4.68812e29 - 4.68812e29i) q^{83} -8.16358e29i q^{84} -8.02482e30 q^{86} +(-7.27084e30 - 7.27084e30i) q^{87} +(-6.74242e30 + 6.74242e30i) q^{88} -2.97738e31i q^{89} +2.55401e31 q^{91} +(-4.74344e30 - 4.74344e30i) q^{92} +(2.70654e29 - 2.70654e29i) q^{93} -2.13372e31i q^{94} -1.33814e31 q^{96} +(1.89647e31 + 1.89647e31i) q^{97} +(-1.91520e30 + 1.91520e30i) q^{98} -2.71273e31i 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 $

$2$	42029.2	+	42029.2i	0.641314	+	0.641314i	0.950878	−	0.309564i	$-0.100183\pi$
$2$	42029.2	+	42029.2i	0.641314	+	0.641314i	−0.309564	+	0.950878i	$0.600183\pi$
$3$	2.23370e7	−	2.23370e7i	0.518900	−	0.518900i	−0.398338	−	0.917239i	$-0.630413\pi$
$3$	2.23370e7	−	2.23370e7i	0.518900	−	0.518900i	0.917239	+	0.398338i	$0.130413\pi$
$4$		−	7.62067e8i		−	0.177433i
$5$		0			0
$5$		0			0
$6$	1.87761e12			0.665556
$7$	2.39791e13	+	2.39791e13i	0.721547	+	0.721547i	0.968920	−	0.247373i	$-0.0795674\pi$
$7$	2.39791e13	+	2.39791e13i	0.721547	+	0.721547i	−0.247373	+	0.968920i	$0.579567\pi$
$8$	2.12543e14	−	2.12543e14i	0.755104	−	0.755104i
$9$			8.55140e14i			0.461485i
$10$		0			0
$11$	−3.17226e16			−0.690377			−0.345188	−	0.938533i	$-0.612185\pi$
$11$	−3.17226e16			−0.690377			−0.345188	+	0.938533i	$0.612185\pi$
$12$	−1.70223e16	−	1.70223e16i	−0.0920698	−	0.0920698i
$13$	5.32549e17	−	5.32549e17i	0.800324	−	0.800324i	−0.182822	−	0.983146i	$-0.558523\pi$
$13$	5.32549e17	−	5.32549e17i	0.800324	−	0.800324i	0.983146	+	0.182822i	$0.0585231\pi$
$14$			2.01564e18i			0.925476i
$15$		0			0
$16$	1.45929e19			0.791085
$17$	−4.10053e19	−	4.10053e19i	−0.842669	−	0.842669i	0.146536	−	0.989205i	$-0.453188\pi$
$17$	−4.10053e19	−	4.10053e19i	−0.842669	−	0.842669i	−0.989205	+	0.146536i	$0.953188\pi$
$18$	−3.59408e19	+	3.59408e19i	−0.295957	+	0.295957i
$19$			2.22048e20i			0.769821i	0.922954	+	0.384911i	$0.125768\pi$
$19$			2.22048e20i			0.769821i	−0.922954	+	0.384911i	$0.874232\pi$
$20$		0			0
$21$	1.07124e21			0.748822
$22$	−1.33328e21	−	1.33328e21i	−0.442748	−	0.442748i
$23$	6.22444e21	−	6.22444e21i	1.01497	−	1.01497i	0.0150872	−	0.999886i	$-0.495197\pi$
$23$	6.22444e21	−	6.22444e21i	1.01497	−	1.01497i	0.999886	−	0.0150872i	$-0.00480259\pi$
$24$		−	9.49513e21i		−	0.783648i
$25$		0			0
$26$	4.47652e22			1.02652
$27$	6.04921e22	+	6.04921e22i	0.758365	+	0.758365i
$28$	1.82737e22	−	1.82737e22i	0.128026	−	0.128026i
$29$		−	3.25507e23i		−	1.30075i	−0.759615	−	0.650373i	$-0.774613\pi$
$29$		−	3.25507e23i		−	1.30075i	0.759615	−	0.650373i	$-0.225387\pi$
$30$		0			0
$31$	1.21168e22			0.0166572			0.00832861	−	0.999965i	$-0.497349\pi$
$31$	1.21168e22			0.0166572			0.00832861	+	0.999965i	$0.497349\pi$
$32$	−2.99536e23	−	2.99536e23i	−0.247770	−	0.247770i
$33$	−7.08587e23	+	7.08587e23i	−0.358237	+	0.358237i
$34$		−	3.44684e24i		−	1.08083i
$35$		0			0
$36$	6.51674e23			0.0818824
$37$	1.53437e25	+	1.53437e25i	1.24366	+	1.24366i	0.958472	+	0.285187i	$0.0920557\pi$
$37$	1.53437e25	+	1.53437e25i	1.24366	+	1.24366i	0.285187	+	0.958472i	$0.407944\pi$
$38$	−9.33250e24	+	9.33250e24i	−0.493697	+	0.493697i
$39$		−	2.37911e25i		−	0.830577i
$40$		0			0
$41$	−2.70283e25			−0.423913			−0.211957	−	0.977279i	$-0.567984\pi$
$41$	−2.70283e25			−0.423913			−0.211957	+	0.977279i	$0.567984\pi$
$42$	4.50234e25	+	4.50234e25i	0.480230	+	0.480230i
$43$	−9.54673e25	+	9.54673e25i	−0.698811	+	0.698811i	−0.964154	−	0.265343i	$-0.914515\pi$
$43$	−9.54673e25	+	9.54673e25i	−0.698811	+	0.698811i	0.265343	+	0.964154i	$0.414515\pi$
$44$			2.41748e25i			0.122495i
$45$		0			0
$46$	5.23216e26			1.30183
$47$	−2.53838e26	−	2.53838e26i	−0.447704	−	0.447704i	0.446887	−	0.894591i	$-0.352533\pi$
$47$	−2.53838e26	−	2.53838e26i	−0.447704	−	0.447704i	−0.894591	+	0.446887i	$0.852533\pi$
$48$	3.25962e26	−	3.25962e26i	0.410494	−	0.410494i
$49$			4.55683e25i			0.0412597i
$50$		0			0
$51$	−1.83187e27			−0.874523
$52$	−4.05838e26	−	4.05838e26i	−0.142004	−	0.142004i
$53$	1.49223e27	−	1.49223e27i	0.384966	−	0.384966i	−0.487921	−	0.872888i	$-0.662245\pi$
$53$	1.49223e27	−	1.49223e27i	0.384966	−	0.384966i	0.872888	+	0.487921i	$0.162245\pi$
$54$			5.08486e27i			0.972700i
$55$		0			0
$56$	1.01932e28			1.08969
$57$	4.95988e27	+	4.95988e27i	0.399460	+	0.399460i
$58$	1.36808e28	−	1.36808e28i	0.834186	−	0.834186i
$59$			2.48663e28i			1.15340i	0.816958	+	0.576698i	$0.195659\pi$
$59$			2.48663e28i			1.15340i	−0.816958	+	0.576698i	$0.804341\pi$
$60$		0			0
$61$	3.17251e28			0.863229			0.431615	−	0.902058i	$-0.357944\pi$
$61$	3.17251e28			0.863229			0.431615	+	0.902058i	$0.357944\pi$
$62$	5.09261e26	+	5.09261e26i	0.0106825	+	0.0106825i
$63$	−2.05055e28	+	2.05055e28i	−0.332983	+	0.332983i
$64$		−	8.78547e28i		−	1.10888i
$65$		0			0
$66$	−5.95627e28			−0.459485
$67$	3.16482e27	+	3.16482e27i	0.0191934	+	0.0191934i	0.716638	−	0.697445i	$-0.245680\pi$
$67$	3.16482e27	+	3.16482e27i	0.0191934	+	0.0191934i	−0.697445	+	0.716638i	$0.745680\pi$
$68$	−3.12488e28	+	3.12488e28i	−0.149517	+	0.149517i
$69$		−	2.78070e29i		−	1.05334i
$70$		0			0
$71$	4.69621e29			1.12620			0.563098	−	0.826390i	$-0.309609\pi$
$71$	4.69621e29			1.12620			0.563098	+	0.826390i	$0.309609\pi$
$72$	1.81754e29	+	1.81754e29i	0.348469	+	0.348469i
$73$	3.04177e29	−	3.04177e29i	0.467692	−	0.467692i	−0.433474	−	0.901166i	$-0.642712\pi$
$73$	3.04177e29	−	3.04177e29i	0.467692	−	0.467692i	0.901166	+	0.433474i	$0.142712\pi$
$74$			1.28976e30i			1.59515i
$75$		0			0
$76$	1.69216e29			0.136591
$77$	−7.60681e29	−	7.60681e29i	−0.498139	−	0.498139i
$78$	9.99918e29	−	9.99918e29i	0.532661	−	0.532661i
$79$		−	1.79248e30i		−	0.778791i	−0.921071	−	0.389395i	$-0.872684\pi$
$79$		−	1.79248e30i		−	0.778791i	0.921071	−	0.389395i	$-0.127316\pi$
$80$		0			0
$81$	1.11783e30			0.325547
$82$	−1.13598e30	−	1.13598e30i	−0.271861	−	0.271861i
$83$	4.68812e29	−	4.68812e29i	0.0924165	−	0.0924165i	−0.659387	−	0.751804i	$-0.729184\pi$
$83$	4.68812e29	−	4.68812e29i	0.0924165	−	0.0924165i	0.751804	+	0.659387i	$0.229184\pi$
$84$		−	8.16358e29i		−	0.132865i
$85$		0			0
$86$	−8.02482e30			−0.896314
$87$	−7.27084e30	−	7.27084e30i	−0.674957	−	0.674957i
$88$	−6.74242e30	+	6.74242e30i	−0.521306	+	0.521306i
$89$		−	2.97738e31i		−	1.92130i	−0.277765	−	0.960649i	$-0.589594\pi$
$89$		−	2.97738e31i		−	1.92130i	0.277765	−	0.960649i	$-0.410406\pi$
$90$		0			0
$91$	2.55401e31			1.15494
$92$	−4.74344e30	−	4.74344e30i	−0.180089	−	0.180089i
$93$	2.70654e29	−	2.70654e29i	0.00864344	−	0.00864344i
$94$		−	2.13372e31i		−	0.574237i
$95$		0			0
$96$	−1.33814e31			−0.257136
$97$	1.89647e31	+	1.89647e31i	0.308743	+	0.308743i	0.844422	−	0.535679i	$-0.179944\pi$
$97$	1.89647e31	+	1.89647e31i	0.308743	+	0.308743i	−0.535679	+	0.844422i	$0.679944\pi$
$98$	−1.91520e30	+	1.91520e30i	−0.0264604	+	0.0264604i
$99$		−	2.71273e31i		−	0.318598i
$100$		0			0
$101$	2.42812e31			0.207075			0.103538	−	0.994626i	$-0.466984\pi$
$101$	2.42812e31			0.207075			0.103538	+	0.994626i	$0.466984\pi$
$102$	−7.69919e31	−	7.69919e31i	−0.560844	−	0.560844i
$103$	1.53297e32	−	1.53297e32i	0.955297	−	0.955297i	−0.0437452	−	0.999043i	$-0.513929\pi$
$103$	1.53297e32	−	1.53297e32i	0.955297	−	0.955297i	0.999043	+	0.0437452i	$0.0139290\pi$
$104$		−	2.26379e32i		−	1.20866i
$105$		0			0
$106$	1.25434e32			0.493768
$107$	−3.13053e32	−	3.13053e32i	−1.06042	−	1.06042i	−0.998053	−	0.0623638i	$-0.980136\pi$
$107$	−3.13053e32	−	3.13053e32i	−1.06042	−	1.06042i	−0.0623638	−	0.998053i	$-0.519864\pi$
$108$	4.60990e31	−	4.60990e31i	0.134559	−	0.134559i
$109$			4.40291e32i			1.10896i	0.832197	+	0.554480i	$0.187083\pi$
$109$			4.40291e32i			1.10896i	−0.832197	+	0.554480i	$0.812917\pi$
$110$		0			0
$111$	6.85461e32			1.29067
$112$	3.49926e32	+	3.49926e32i	0.570805	+	0.570805i
$113$	3.62769e32	−	3.62769e32i	0.513304	−	0.513304i	−0.402233	−	0.915537i	$-0.631766\pi$
$113$	3.62769e32	−	3.62769e32i	0.513304	−	0.513304i	0.915537	+	0.402233i	$0.131766\pi$
$114$			4.16920e32i			0.512359i
$115$		0			0
$116$	−2.48058e32			−0.230795
$117$	4.55404e32	+	4.55404e32i	0.369337	+	0.369337i
$118$	−1.04511e33	+	1.04511e33i	−0.739689	+	0.739689i
$119$		−	1.96654e33i		−	1.21605i
$120$		0			0
$121$	−1.10505e33			−0.523380
$122$	1.33338e33	+	1.33338e33i	0.553601	+	0.553601i
$123$	−6.03730e32	+	6.03730e32i	−0.219969	+	0.219969i
$124$		−	9.23385e30i		−	0.00295553i
$125$		0			0
$126$	−1.72366e33			−0.427093
$127$	−1.06536e33	−	1.06536e33i	−0.232616	−	0.232616i	0.581168	−	0.813784i	$-0.302596\pi$
$127$	−1.06536e33	−	1.06536e33i	−0.232616	−	0.232616i	−0.813784	+	0.581168i	$0.802596\pi$
$128$	2.40596e33	−	2.40596e33i	0.463372	−	0.463372i
$129$			4.26490e33i			0.725226i
$130$		0			0
$131$	3.24991e33			0.432047			0.216023	−	0.976388i	$-0.430691\pi$
$131$	3.24991e33			0.432047			0.216023	+	0.976388i	$0.430691\pi$
$132$	5.39991e32	+	5.39991e32i	0.0635629	+	0.0635629i
$133$	−5.32452e33	+	5.32452e33i	−0.555462	+	0.555462i
$134$			2.66029e32i			0.0246180i
$135$		0			0
$136$	−1.74308e34			−1.27261
$137$	−2.72630e33	−	2.72630e33i	−0.177029	−	0.177029i	0.613030	−	0.790059i	$-0.289950\pi$
$137$	−2.72630e33	−	2.72630e33i	−0.177029	−	0.177029i	−0.790059	+	0.613030i	$0.789950\pi$
$138$	1.16870e34	−	1.16870e34i	0.675522	−	0.675522i
$139$			2.06077e34i			1.06119i	0.847626	+	0.530594i	$0.178031\pi$
$139$			2.06077e34i			1.06119i	−0.847626	+	0.530594i	$0.821969\pi$
$140$		0			0
$141$	−1.13399e34			−0.464627
$142$	1.97378e34	+	1.97378e34i	0.722245	+	0.722245i
$143$	−1.68939e34	+	1.68939e34i	−0.552525	+	0.552525i
$144$			1.24790e34i			0.365074i
$145$		0			0
$146$	2.55686e34			0.599875
$147$	1.01786e33	+	1.01786e33i	0.0214097	+	0.0214097i
$148$	1.16929e34	−	1.16929e34i	0.220666	−	0.220666i
$149$		−	8.61495e34i		−	1.45973i	−0.683591	−	0.729865i	$-0.739583\pi$
$149$		−	8.61495e34i		−	1.45973i	0.683591	−	0.729865i	$-0.260417\pi$
$150$		0			0
$151$	7.13058e34			0.976098			0.488049	−	0.872816i	$-0.337709\pi$
$151$	7.13058e34			0.976098			0.488049	+	0.872816i	$0.337709\pi$
$152$	4.71948e34	+	4.71948e34i	0.581295	+	0.581295i
$153$	3.50653e34	−	3.50653e34i	0.388879	−	0.388879i
$154$		−	6.39415e34i		−	0.638927i
$155$		0			0
$156$	−1.81304e34			−0.147371
$157$	1.43355e34	+	1.43355e34i	0.105201	+	0.105201i	0.757748	−	0.652547i	$-0.226300\pi$
$157$	1.43355e34	+	1.43355e34i	0.105201	+	0.105201i	−0.652547	+	0.757748i	$0.726300\pi$
$158$	7.53364e34	−	7.53364e34i	0.499449	−	0.499449i
$159$		−	6.66639e34i		−	0.399518i
$160$		0			0
$161$	2.98513e35			1.46470
$162$	4.69813e34	+	4.69813e34i	0.208778	+	0.208778i
$163$	2.71331e35	−	2.71331e35i	1.09269	−	1.09269i	0.0974522	−	0.995240i	$-0.468931\pi$
$163$	2.71331e35	−	2.71331e35i	1.09269	−	1.09269i	0.995240	−	0.0974522i	$-0.0310693\pi$
$164$			2.05974e34i			0.0752160i
$165$		0			0
$166$	3.94076e34			0.118536
$167$	−3.89137e35	−	3.89137e35i	−1.06326	−	1.06326i	−0.997859	−	0.0654007i	$-0.979167\pi$
$167$	−3.89137e35	−	3.89137e35i	−1.06326	−	1.06326i	−0.0654007	−	0.997859i	$-0.520833\pi$
$168$	2.27685e35	−	2.27685e35i	0.565438	−	0.565438i
$169$		−	1.24438e35i		−	0.281038i
$170$		0			0
$171$	−1.89882e35			−0.355261
$172$	7.27525e34	+	7.27525e34i	0.123992	+	0.123992i
$173$	−4.75765e35	+	4.75765e35i	−0.739018	+	0.739018i	−0.972388	−	0.233370i	$-0.925025\pi$
$173$	−4.75765e35	+	4.75765e35i	−0.739018	+	0.739018i	0.233370	+	0.972388i	$0.425025\pi$
$174$		−	6.11174e35i		−	0.865719i
$175$		0			0
$176$	−4.62927e35			−0.546147
$177$	5.55437e35	+	5.55437e35i	0.598497	+	0.598497i
$178$	1.25137e36	−	1.25137e36i	1.23216	−	1.23216i
$179$		−	1.99998e36i		−	1.80044i	−0.435440	−	0.900218i	$-0.643407\pi$
$179$		−	1.99998e36i		−	1.80044i	0.435440	−	0.900218i	$-0.356593\pi$
$180$		0			0
$181$	2.34543e36			1.76752			0.883762	−	0.467936i	$-0.155002\pi$
$181$	2.34543e36			1.76752			0.883762	+	0.467936i	$0.155002\pi$
$182$	1.07343e36	+	1.07343e36i	0.740681	+	0.740681i
$183$	7.08643e35	−	7.08643e35i	0.447930	−	0.447930i
$184$		−	2.64592e36i		−	1.53282i
$185$		0			0
$186$	2.27507e34			0.0110863
$187$	1.30080e36	+	1.30080e36i	0.581760	+	0.581760i
$188$	−1.93441e35	+	1.93441e35i	−0.0794372	+	0.0794372i
$189$			2.90109e36i			1.09439i
$190$		0			0
$191$	−9.51069e35			−0.303164			−0.151582	−	0.988445i	$-0.548437\pi$
$191$	−9.51069e35			−0.303164			−0.151582	+	0.988445i	$0.548437\pi$
$192$	−1.96241e36	−	1.96241e36i	−0.575399	−	0.575399i
$193$	2.25391e36	−	2.25391e36i	0.608163	−	0.608163i	−0.334303	−	0.942466i	$-0.608501\pi$
$193$	2.25391e36	−	2.25391e36i	0.608163	−	0.608163i	0.942466	+	0.334303i	$0.108501\pi$
$194$			1.59414e36i			0.396003i
$195$		0			0
$196$	3.47261e34			0.00732081
$197$	7.15338e36	+	7.15338e36i	1.39012	+	1.39012i	0.825034	+	0.565083i	$0.191156\pi$
$197$	7.15338e36	+	7.15338e36i	1.39012	+	1.39012i	0.565083	+	0.825034i	$0.308844\pi$
$198$	1.14014e36	−	1.14014e36i	0.204322	−	0.204322i
$199$			2.07919e36i			0.343753i	0.985119	+	0.171876i	$0.0549829\pi$
$199$			2.07919e36i			0.343753i	−0.985119	+	0.171876i	$0.945017\pi$
$200$		0			0
$201$	1.41385e35			0.0199189
$202$	1.02052e36	+	1.02052e36i	0.132800	+	0.132800i
$203$	7.80537e36	−	7.80537e36i	0.938549	−	0.938549i
$204$			1.39601e36i			0.155169i
$205$		0			0
$206$	1.28859e37			1.22529
$207$	5.32277e36	+	5.32277e36i	0.468395	+	0.468395i
$208$	7.77146e36	−	7.77146e36i	0.633125	−	0.633125i
$209$		−	7.04396e36i		−	0.531467i
$210$		0			0
$211$	−6.09709e36			−0.395006			−0.197503	−	0.980302i	$-0.563283\pi$
$211$	−6.09709e36			−0.395006			−0.197503	+	0.980302i	$0.563283\pi$
$212$	−1.13718e36	−	1.13718e36i	−0.0683055	−	0.0683055i
$213$	1.04899e37	−	1.04899e37i	0.584383	−	0.584383i
$214$		−	2.63147e37i		−	1.36012i
$215$		0			0
$216$	2.57143e37			1.14529
$217$	2.90551e35	+	2.90551e35i	0.0120190	+	0.0120190i
$218$	−1.85051e37	+	1.85051e37i	−0.711192	+	0.711192i
$219$		−	1.35888e37i		−	0.485371i
$220$		0			0
$221$	−4.36747e37			−1.34882
$222$	2.88094e37	+	2.88094e37i	0.827725	+	0.827725i
$223$	−1.87440e36	+	1.87440e36i	−0.0501170	+	0.0501170i	−0.731721	−	0.681604i	$-0.761283\pi$
$223$	−1.87440e36	+	1.87440e36i	−0.0501170	+	0.0501170i	0.681604	+	0.731721i	$0.261283\pi$
$224$		−	1.43652e37i		−	0.357555i
$225$		0			0
$226$	3.04937e37			0.658378
$227$	−1.09568e37	−	1.09568e37i	−0.220429	−	0.220429i	0.588250	−	0.808679i	$-0.299817\pi$
$227$	−1.09568e37	−	1.09568e37i	−0.220429	−	0.220429i	−0.808679	+	0.588250i	$0.799817\pi$
$228$	3.77976e36	−	3.77976e36i	0.0708773	−	0.0708773i
$229$		−	3.80575e37i		−	0.665384i	−0.943035	−	0.332692i	$-0.892043\pi$
$229$		−	3.80575e37i		−	0.665384i	0.943035	−	0.332692i	$-0.107957\pi$
$230$		0			0
$231$	−3.39826e37			−0.516969
$232$	−6.91842e37	−	6.91842e37i	−0.982198	−	0.982198i
$233$	2.53746e37	−	2.53746e37i	0.336283	−	0.336283i	−0.518684	−	0.854966i	$-0.673578\pi$
$233$	2.53746e37	−	2.53746e37i	0.336283	−	0.336283i	0.854966	+	0.518684i	$0.173578\pi$
$234$			3.82805e37i			0.473723i
$235$		0			0
$236$	1.89498e37			0.204650
$237$	−4.00385e37	−	4.00385e37i	−0.404115	−	0.404115i
$238$	8.26521e37	−	8.26521e37i	0.779871	−	0.779871i
$239$			5.62465e37i			0.496283i	0.968724	+	0.248141i	$0.0798197\pi$
$239$			5.62465e37i			0.496283i	−0.968724	+	0.248141i	$0.920180\pi$
$240$		0			0
$241$	2.06335e38			1.59331			0.796655	−	0.604434i	$-0.206601\pi$
$241$	2.06335e38			1.59331			0.796655	+	0.604434i	$0.206601\pi$
$242$	−4.64444e37	−	4.64444e37i	−0.335651	−	0.335651i
$243$	−8.71242e37	+	8.71242e37i	−0.589438	+	0.589438i
$244$		−	2.41767e37i		−	0.153165i
$245$		0			0
$246$	−5.07485e37			−0.282138
$247$	1.18252e38	+	1.18252e38i	0.616107	+	0.616107i
$248$	2.57535e36	−	2.57535e36i	0.0125779	−	0.0125779i
$249$		−	2.09437e37i		−	0.0959100i
$250$		0			0
$251$	−3.09148e38			−1.24563			−0.622813	−	0.782371i	$-0.714010\pi$
$251$	−3.09148e38			−1.24563			−0.622813	+	0.782371i	$0.714010\pi$
$252$	1.56266e37	+	1.56266e37i	0.0590820	+	0.0590820i
$253$	−1.97456e38	+	1.97456e38i	−0.700714	+	0.700714i
$254$		−	8.95528e37i		−	0.298359i
$255$		0			0
$256$	−1.75092e38			−0.514549
$257$	1.74296e37	+	1.74296e37i	0.0481235	+	0.0481235i	0.730759	−	0.682636i	$-0.239166\pi$
$257$	1.74296e37	+	1.74296e37i	0.0481235	+	0.0481235i	−0.682636	+	0.730759i	$0.739166\pi$
$258$	−1.79250e38	+	1.79250e38i	−0.465098	+	0.465098i
$259$			7.35855e38i			1.79472i
$260$		0			0
$261$	2.78354e38			0.600274
$262$	1.36591e38	+	1.36591e38i	0.277078	+	0.277078i
$263$	−6.54950e38	+	6.54950e38i	−1.25002	+	1.25002i	−0.294306	+	0.955711i	$0.595088\pi$
$263$	−6.54950e38	+	6.54950e38i	−1.25002	+	1.25002i	−0.955711	+	0.294306i	$0.904912\pi$
$264$			3.01210e38i			0.541012i
$265$		0			0
$266$	−4.47570e38			−0.712451
$267$	−6.65057e38	−	6.65057e38i	−0.996962	−	0.996962i
$268$	2.41180e36	−	2.41180e36i	0.00340553	−	0.00340553i
$269$			1.20052e39i			1.59710i	0.601929	+	0.798550i	$0.294399\pi$
$269$			1.20052e39i			1.59710i	−0.601929	+	0.798550i	$0.705601\pi$
$270$		0			0
$271$	−4.89496e38			−0.578416			−0.289208	−	0.957266i	$-0.593392\pi$
$271$	−4.89496e38			−0.578416			−0.289208	+	0.957266i	$0.593392\pi$
$272$	−5.98388e38	−	5.98388e38i	−0.666623	−	0.666623i
$273$	5.70489e38	−	5.70489e38i	0.599300	−	0.599300i
$274$		−	2.29168e38i		−	0.227062i
$275$		0			0
$276$	−2.11908e38			−0.186897
$277$	9.08699e38	+	9.08699e38i	0.756386	+	0.756386i	0.975663	−	0.219276i	$-0.0703696\pi$
$277$	9.08699e38	+	9.08699e38i	0.756386	+	0.756386i	−0.219276	+	0.975663i	$0.570370\pi$
$278$	−8.66124e38	+	8.66124e38i	−0.680555	+	0.680555i
$279$			1.03616e37i			0.00768705i
$280$		0			0
$281$	−1.02037e39			−0.675234			−0.337617	−	0.941284i	$-0.609621\pi$
$281$	−1.02037e39			−0.675234			−0.337617	+	0.941284i	$0.609621\pi$
$282$	−4.76608e38	−	4.76608e38i	−0.297972	−	0.297972i
$283$	−1.63961e39	+	1.63961e39i	−0.968627	+	0.968627i	−0.999523	−	0.0308960i	$-0.990164\pi$
$283$	−1.63961e39	+	1.63961e39i	−0.968627	+	0.968627i	0.0308960	+	0.999523i	$0.490164\pi$
$284$		−	3.57883e38i		−	0.199824i
$285$		0			0
$286$	−1.42007e39			−0.708685
$287$	−6.48115e38	−	6.48115e38i	−0.305873	−	0.305873i
$288$	2.56145e38	−	2.56145e38i	0.114342	−	0.114342i
$289$			9.94958e38i			0.420184i
$290$		0			0
$291$	8.47226e38			0.320414
$292$	−2.31803e38	−	2.31803e38i	−0.0829838	−	0.0829838i
$293$	−1.46044e39	+	1.46044e39i	−0.494997	+	0.494997i	−0.909876	−	0.414879i	$-0.863824\pi$
$293$	−1.46044e39	+	1.46044e39i	−0.494997	+	0.494997i	0.414879	+	0.909876i	$0.363824\pi$
$294$			8.55595e37i			0.0274606i
$295$		0			0
$296$	6.52237e39			1.87818
$297$	−1.91897e39	−	1.91897e39i	−0.523558	−	0.523558i
$298$	3.62079e39	−	3.62079e39i	0.936145	−	0.936145i
$299$		−	6.62964e39i		−	1.62462i
$300$		0			0
$301$	−4.57844e39			−1.00845
$302$	2.99692e39	+	2.99692e39i	0.625985	+	0.625985i
$303$	5.42369e38	−	5.42369e38i	0.107452	−	0.107452i
$304$			3.24034e39i			0.608994i
$305$		0			0
$306$	2.94753e39			0.498787
$307$	1.70789e39	+	1.70789e39i	0.274313	+	0.274313i	0.830834	−	0.556521i	$-0.187864\pi$
$307$	1.70789e39	+	1.70789e39i	0.274313	+	0.274313i	−0.556521	+	0.830834i	$0.687864\pi$
$308$	−5.79690e38	+	5.79690e38i	−0.0883861	+	0.0883861i
$309$		−	6.84839e39i		−	0.991409i
$310$		0			0
$311$	9.81154e39			1.28106			0.640532	−	0.767931i	$-0.278714\pi$
$311$	9.81154e39			1.28106			0.640532	+	0.767931i	$0.278714\pi$
$312$	−5.05662e39	−	5.05662e39i	−0.627172	−	0.627172i
$313$	8.21686e39	−	8.21686e39i	0.968270	−	0.968270i	−0.0312420	−	0.999512i	$-0.509946\pi$
$313$	8.21686e39	−	8.21686e39i	0.968270	−	0.968270i	0.999512	+	0.0312420i	$0.00994624\pi$
$314$			1.20502e39i			0.134934i
$315$		0			0
$316$	−1.36599e39			−0.138183
$317$	−4.52584e39	−	4.52584e39i	−0.435262	−	0.435262i	0.455152	−	0.890414i	$-0.349585\pi$
$317$	−4.52584e39	−	4.52584e39i	−0.435262	−	0.435262i	−0.890414	+	0.455152i	$0.849585\pi$
$318$	2.80183e39	−	2.80183e39i	0.256217	−	0.256217i
$319$			1.03259e40i			0.898005i
$320$		0			0
$321$	−1.39853e40			−1.10050
$322$	1.25462e40	+	1.25462e40i	0.939334	+	0.939334i
$323$	9.10516e39	−	9.10516e39i	0.648705	−	0.648705i
$324$		−	8.51858e38i		−	0.0577627i
$325$		0			0
$326$	2.28076e40			1.40152
$327$	9.83477e39	+	9.83477e39i	0.575440	+	0.575440i
$328$	−5.74467e39	+	5.74467e39i	−0.320099	+	0.320099i
$329$		−	1.21736e40i		−	0.646078i
$330$		0			0
$331$	−2.93203e40			−1.41228			−0.706139	−	0.708073i	$-0.749565\pi$
$331$	−2.93203e40			−1.41228			−0.706139	+	0.708073i	$0.749565\pi$
$332$	−3.57266e38	−	3.57266e38i	−0.0163977	−	0.0163977i
$333$	−1.31210e40	+	1.31210e40i	−0.573930	+	0.573930i
$334$		−	3.27102e40i		−	1.36377i
$335$		0			0
$336$	1.56326e40			0.592382
$337$	2.95040e40	+	2.95040e40i	1.06611	+	1.06611i	0.997654	+	0.0684559i	$0.0218072\pi$
$337$	2.95040e40	+	2.95040e40i	1.06611	+	1.06611i	0.0684559	+	0.997654i	$0.478193\pi$
$338$	5.23002e39	−	5.23002e39i	0.180234	−	0.180234i
$339$		−	1.62063e40i		−	0.532707i
$340$		0			0
$341$	−3.84378e38			−0.0114998
$342$	−7.98060e39	−	7.98060e39i	−0.227834	−	0.227834i
$343$	2.53905e40	−	2.53905e40i	0.691776	−	0.691776i
$344$			4.05818e40i			1.05535i
$345$		0			0
$346$	−3.99920e40			−0.947885
$347$	−5.13663e39	−	5.13663e39i	−0.116254	−	0.116254i	0.646587	−	0.762840i	$-0.276196\pi$
$347$	−5.13663e39	−	5.13663e39i	−0.116254	−	0.116254i	−0.762840	+	0.646587i	$0.776196\pi$
$348$	−5.54086e39	+	5.54086e39i	−0.119759	+	0.119759i
$349$		−	2.70211e40i		−	0.557823i	−0.960317	−	0.278911i	$-0.910026\pi$
$349$		−	2.70211e40i		−	0.557823i	0.960317	−	0.278911i	$-0.0899735\pi$
$350$		0			0
$351$	6.44300e40			1.21388
$352$	9.50206e39	+	9.50206e39i	0.171055	+	0.171055i
$353$	−1.34381e39	+	1.34381e39i	−0.0231176	+	0.0231176i	−0.718571	−	0.695454i	$-0.755204\pi$
$353$	−1.34381e39	+	1.34381e39i	−0.0231176	+	0.0231176i	0.695454	+	0.718571i	$0.255204\pi$
$354$			4.66891e40i			0.767650i
$355$		0			0
$356$	−2.26897e40			−0.340901
$357$	−4.39266e40	−	4.39266e40i	−0.631009	−	0.631009i
$358$	8.40575e40	−	8.40575e40i	1.15464	−	1.15464i
$359$			2.49711e40i			0.328040i	0.986457	+	0.164020i	$0.0524462\pi$
$359$			2.49711e40i			0.328040i	−0.986457	+	0.164020i	$0.947554\pi$
$360$		0			0
$361$	3.38930e40			0.407376
$362$	9.85765e40	+	9.85765e40i	1.13354	+	1.13354i
$363$	−2.46835e40	+	2.46835e40i	−0.271582	+	0.271582i
$364$		−	1.94633e40i		−	0.204924i
$365$		0			0
$366$	5.95673e40			0.574528
$367$	−3.75538e40	−	3.75538e40i	−0.346734	−	0.346734i	0.512157	−	0.858892i	$-0.328846\pi$
$367$	−3.75538e40	−	3.75538e40i	−0.346734	−	0.346734i	−0.858892	+	0.512157i	$0.828846\pi$
$368$	9.08329e40	−	9.08329e40i	0.802930	−	0.802930i
$369$		−	2.31130e40i		−	0.195629i
$370$		0			0
$371$	7.15648e40			0.555542
$372$	−2.06256e38	−	2.06256e38i	−0.00153363	−	0.00153363i
$373$	−1.13974e41	+	1.13974e41i	−0.811831	+	0.811831i	−0.984908	−	0.173077i	$-0.944629\pi$
$373$	−1.13974e41	+	1.13974e41i	−0.811831	+	0.811831i	0.173077	+	0.984908i	$0.444629\pi$
$374$			1.09343e41i			0.746181i
$375$		0			0
$376$	−1.07903e41			−0.676126
$377$	−1.73348e41	−	1.73348e41i	−1.04102	−	1.04102i
$378$	−1.21931e41	+	1.21931e41i	−0.701849	+	0.701849i
$379$		−	3.20505e41i		−	1.76851i	−0.467004	−	0.884255i	$-0.654667\pi$
$379$		−	3.20505e41i		−	1.76851i	0.467004	−	0.884255i	$-0.345333\pi$
$380$		0			0
$381$	−4.75940e40			−0.241409
$382$	−3.99726e40	−	3.99726e40i	−0.194424	−	0.194424i
$383$	−1.96001e41	+	1.96001e41i	−0.914279	+	0.914279i	−0.996605	−	0.0823267i	$-0.973765\pi$
$383$	−1.96001e41	+	1.96001e41i	−0.914279	+	0.914279i	0.0823267	+	0.996605i	$0.473765\pi$
$384$		−	1.07484e41i		−	0.480887i
$385$		0			0
$386$	1.89460e41			0.780047
$387$	−8.16380e40	−	8.16380e40i	−0.322490	−	0.322490i
$388$	1.44523e40	−	1.44523e40i	0.0547811	−	0.0547811i
$389$		−	6.41335e40i		−	0.233287i	−0.993174	−	0.116644i	$-0.962786\pi$
$389$		−	6.41335e40i		−	0.233287i	0.993174	−	0.116644i	$-0.0372136\pi$
$390$		0			0
$391$	−5.10470e41			−1.71057
$392$	9.68523e39	+	9.68523e39i	0.0311554	+	0.0311554i
$393$	7.25931e40	−	7.25931e40i	0.224189	−	0.224189i
$394$			6.01301e41i			1.78300i
$395$		0			0
$396$	−2.06728e40			−0.0565297
$397$	7.36589e40	+	7.36589e40i	0.193454	+	0.193454i	0.797187	−	0.603733i	$-0.206321\pi$
$397$	7.36589e40	+	7.36589e40i	0.193454	+	0.193454i	−0.603733	+	0.797187i	$0.706321\pi$
$398$	−8.73868e40	+	8.73868e40i	−0.220453	+	0.220453i
$399$			2.37867e41i			0.576459i
$400$		0			0
$401$	−4.94593e41			−1.10647			−0.553233	−	0.833027i	$-0.686606\pi$
$401$	−4.94593e41			−1.10647			−0.553233	+	0.833027i	$0.686606\pi$
$402$	5.94229e39	+	5.94229e39i	0.0127743	+	0.0127743i
$403$	6.45282e39	−	6.45282e39i	0.0133312	−	0.0133312i
$404$		−	1.85039e40i		−	0.0367419i
$405$		0			0
$406$	6.56106e41			1.20381
$407$	−4.86741e41	−	4.86741e41i	−0.858593	−	0.858593i
$408$	−3.89350e41	+	3.89350e41i	−0.660356	+	0.660356i
$409$			1.09263e42i			1.78197i	0.454030	+	0.890986i	$0.349986\pi$
$409$			1.09263e42i			1.78197i	−0.454030	+	0.890986i	$0.650014\pi$
$410$		0			0
$411$	−1.21794e41			−0.183721
$412$	−1.16823e41	−	1.16823e41i	−0.169501	−	0.169501i
$413$	−5.96271e41	+	5.96271e41i	−0.832229	+	0.832229i
$414$			4.47423e41i			0.600776i
$415$		0			0
$416$	−3.19035e41			−0.396593
$417$	4.60313e41	+	4.60313e41i	0.550651	+	0.550651i
$418$	2.96052e41	−	2.96052e41i	0.340837	−	0.340837i
$419$		−	6.94897e41i		−	0.770010i	−0.922915	−	0.385005i	$-0.874200\pi$
$419$		−	6.94897e41i		−	0.770010i	0.922915	−	0.385005i	$-0.125800\pi$
$420$		0			0
$421$	−1.06991e42			−1.09858			−0.549292	−	0.835631i	$-0.685103\pi$
$421$	−1.06991e42			−1.09858			−0.549292	+	0.835631i	$0.685103\pi$
$422$	−2.56256e41	−	2.56256e41i	−0.253323	−	0.253323i
$423$	2.17067e41	−	2.17067e41i	0.206608	−	0.206608i
$424$		−	6.34327e41i		−	0.581379i
$425$		0			0
$426$	8.81764e41			0.749547
$427$	7.60741e41	+	7.60741e41i	0.622860	+	0.622860i
$428$	−2.38567e41	+	2.38567e41i	−0.188153	+	0.188153i
$429$			7.54715e41i			0.573411i
$430$		0			0
$431$	8.14754e41			0.574632			0.287316	−	0.957836i	$-0.407237\pi$
$431$	8.14754e41			0.574632			0.287316	+	0.957836i	$0.407237\pi$
$432$	8.82758e41	+	8.82758e41i	0.599931	+	0.599931i
$433$	−7.61446e41	+	7.61446e41i	−0.498692	+	0.498692i	−0.911031	−	0.412338i	$-0.864712\pi$
$433$	−7.61446e41	+	7.61446e41i	−0.498692	+	0.498692i	0.412338	+	0.911031i	$0.364712\pi$
$434$			2.44233e40i			0.0154159i
$435$		0			0
$436$	3.35531e41			0.196766
$437$	1.38213e42	+	1.38213e42i	0.781348	+	0.781348i
$438$	5.71124e41	−	5.71124e41i	0.311276	−	0.311276i
$439$		−	4.16393e41i		−	0.218812i	−0.993997	−	0.109406i	$-0.965105\pi$
$439$		−	4.16393e41i		−	0.218812i	0.993997	−	0.109406i	$-0.0348949\pi$
$440$		0			0
$441$	−3.89673e40			−0.0190407
$442$	−1.83561e42	−	1.83561e42i	−0.865016	−	0.865016i
$443$	1.39387e42	−	1.39387e42i	0.633525	−	0.633525i	−0.315425	−	0.948950i	$-0.602147\pi$
$443$	1.39387e42	−	1.39387e42i	0.633525	−	0.633525i	0.948950	+	0.315425i	$0.102147\pi$
$444$		−	5.22367e41i		−	0.229007i
$445$		0			0
$446$	−1.57559e41			−0.0642814
$447$	−1.92432e42	−	1.92432e42i	−0.757455	−	0.757455i
$448$	2.10668e42	−	2.10668e42i	0.800110	−	0.800110i
$449$		−	1.23901e42i		−	0.454081i	−0.973885	−	0.227040i	$-0.927095\pi$
$449$		−	1.23901e42i		−	0.454081i	0.973885	−	0.227040i	$-0.0729049\pi$
$450$		0			0
$451$	8.57409e41			0.292660
$452$	−2.76454e41	−	2.76454e41i	−0.0910768	−	0.0910768i
$453$	1.59275e42	−	1.59275e42i	0.506498	−	0.506498i
$454$		−	9.21008e41i		−	0.282728i
$455$		0			0
$456$	2.10838e42			0.603268
$457$	5.74881e41	+	5.74881e41i	0.158825	+	0.158825i	0.782046	−	0.623221i	$-0.214176\pi$
$457$	5.74881e41	+	5.74881e41i	0.158825	+	0.158825i	−0.623221	+	0.782046i	$0.714176\pi$
$458$	1.59953e42	−	1.59953e42i	0.426720	−	0.426720i
$459$		−	4.96099e42i		−	1.27810i
$460$		0			0
$461$	−2.91709e42			−0.701028			−0.350514	−	0.936557i	$-0.613993\pi$
$461$	−2.91709e42			−0.701028			−0.350514	+	0.936557i	$0.613993\pi$
$462$	−1.42826e42	−	1.42826e42i	−0.331540	−	0.331540i
$463$	−2.70805e42	+	2.70805e42i	−0.607240	+	0.607240i	−0.942224	−	0.334984i	$-0.891269\pi$
$463$	−2.70805e42	+	2.70805e42i	−0.607240	+	0.607240i	0.334984	+	0.942224i	$0.391269\pi$
$464$		−	4.75011e42i		−	1.02900i
$465$		0			0
$466$	2.13295e42			0.431326
$467$	1.11563e42	+	1.11563e42i	0.217996	+	0.217996i	0.807653	−	0.589657i	$-0.200737\pi$
$467$	1.11563e42	+	1.11563e42i	0.217996	+	0.217996i	−0.589657	+	0.807653i	$0.700737\pi$
$468$	3.47049e41	−	3.47049e41i	0.0655325	−	0.0655325i
$469$			1.51779e41i			0.0276979i
$470$		0			0
$471$	6.40425e41			0.109178
$472$	5.28515e42	+	5.28515e42i	0.870934	+	0.870934i
$473$	3.02848e42	−	3.02848e42i	0.482443	−	0.482443i
$474$		−	3.36557e42i		−	0.518329i
$475$		0			0
$476$	−1.49864e42			−0.215767
$477$	1.27607e42	+	1.27607e42i	0.177656	+	0.177656i
$478$	−2.36399e42	+	2.36399e42i	−0.318273	+	0.318273i
$479$			8.04216e42i			1.04714i	0.851983	+	0.523569i	$0.175400\pi$
$479$			8.04216e42i			1.04714i	−0.851983	+	0.523569i	$0.824600\pi$
$480$		0			0
$481$	1.63425e43			1.99066
$482$	8.67209e42	+	8.67209e42i	1.02181	+	1.02181i
$483$	6.66787e42	−	6.66787e42i	0.760034	−	0.760034i
$484$			8.42124e41i			0.0928646i
$485$		0			0
$486$	−7.32351e42			−0.756030
$487$	−7.74349e42	−	7.74349e42i	−0.773523	−	0.773523i	0.205197	−	0.978721i	$-0.434216\pi$
$487$	−7.74349e42	−	7.74349e42i	−0.773523	−	0.773523i	−0.978721	+	0.205197i	$0.934216\pi$
$488$	6.74295e42	−	6.74295e42i	0.651828	−	0.651828i
$489$		−	1.21214e43i		−	1.13400i
$490$		0			0
$491$	2.72662e41			0.0238957			0.0119479	−	0.999929i	$-0.496197\pi$
$491$	2.72662e41			0.0238957			0.0119479	+	0.999929i	$0.496197\pi$
$492$	4.60083e41	+	4.60083e41i	0.0390296	+	0.0390296i
$493$	−1.33475e43	+	1.33475e43i	−1.09610	+	1.09610i
$494$			9.94003e42i			0.790236i
$495$		0			0
$496$	1.76821e41			0.0131773
$497$	1.12611e43	+	1.12611e43i	0.812603	+	0.812603i
$498$	8.80246e41	−	8.80246e41i	0.0615084	−	0.0615084i
$499$			1.35812e43i			0.919031i	0.888170	+	0.459515i	$0.151977\pi$
$499$			1.35812e43i			0.919031i	−0.888170	+	0.459515i	$0.848023\pi$
$500$		0			0
$501$	−1.73843e43			−1.10345
$502$	−1.29932e43	−	1.29932e43i	−0.798837	−	0.798837i
$503$	8.85029e42	−	8.85029e42i	0.527072	−	0.527072i	−0.392626	−	0.919698i	$-0.628433\pi$
$503$	8.85029e42	−	8.85029e42i	0.527072	−	0.527072i	0.919698	+	0.392626i	$0.128433\pi$
$504$			8.71660e42i			0.502873i
$505$		0			0
$506$	−1.65978e43			−0.898756
$507$	−2.77956e42	−	2.77956e42i	−0.145831	−	0.145831i
$508$	−8.11879e41	+	8.11879e41i	−0.0412736	+	0.0412736i
$509$			1.49840e43i			0.738146i	0.929400	+	0.369073i	$0.120325\pi$
$509$			1.49840e43i			0.738146i	−0.929400	+	0.369073i	$0.879675\pi$
$510$		0			0
$511$	1.45878e43			0.674924
$512$	−1.76925e43	−	1.76925e43i	−0.793359	−	0.793359i
$513$	−1.34322e43	+	1.34322e43i	−0.583805	+	0.583805i
$514$			1.46510e42i			0.0617246i
$515$		0			0
$516$	3.25014e42			0.128679
$517$	8.05241e42	+	8.05241e42i	0.309084	+	0.309084i
$518$	−3.09274e43	+	3.09274e43i	−1.15098	+	1.15098i
$519$			2.12543e43i			0.766953i
$520$		0			0
$521$	2.06750e43			0.701523			0.350761	−	0.936465i	$-0.385923\pi$
$521$	2.06750e43			0.701523			0.350761	+	0.936465i	$0.385923\pi$
$522$	1.16990e43	+	1.16990e43i	0.384964	+	0.384964i
$523$	3.34965e42	−	3.34965e42i	0.106899	−	0.106899i	−0.651634	−	0.758533i	$-0.725916\pi$
$523$	3.34965e42	−	3.34965e42i	0.106899	−	0.106899i	0.758533	+	0.651634i	$0.225916\pi$
$524$		−	2.47665e42i		−	0.0766591i
$525$		0			0
$526$	−5.50540e43			−1.60331
$527$	−4.96855e41	−	4.96855e41i	−0.0140365	−	0.0140365i
$528$	−1.03404e43	+	1.03404e43i	−0.283396	+	0.283396i
$529$		−	3.98783e43i		−	1.06034i
$530$		0			0
$531$	−2.12641e43			−0.532274
$532$	4.05764e42	+	4.05764e42i	0.0985570	+	0.0985570i
$533$	−1.43939e43	+	1.43939e43i	−0.339268	+	0.339268i
$534$		−	5.59036e43i		−	1.27873i
$535$		0			0
$536$	1.34532e42			0.0289860
$537$	−4.46735e43	−	4.46735e43i	−0.934247	−	0.934247i
$538$	−5.04567e43	+	5.04567e43i	−1.02424	+	1.02424i
$539$		−	1.44555e42i		−	0.0284847i
$540$		0			0
$541$	−1.12660e43			−0.209224			−0.104612	−	0.994513i	$-0.533360\pi$
$541$	−1.12660e43			−0.209224			−0.104612	+	0.994513i	$0.533360\pi$
$542$	−2.05731e43	−	2.05731e43i	−0.370946	−	0.370946i
$543$	5.23898e43	−	5.23898e43i	0.917169	−	0.917169i
$544$			2.45651e43i			0.417576i
$545$		0			0
$546$	4.79543e43			0.768680
$547$	−1.80975e43	−	1.80975e43i	−0.281723	−	0.281723i	0.552073	−	0.833796i	$-0.313837\pi$
$547$	−1.80975e43	−	1.80975e43i	−0.281723	−	0.281723i	−0.833796	+	0.552073i	$0.813837\pi$
$548$	−2.07762e42	+	2.07762e42i	−0.0314107	+	0.0314107i
$549$			2.71294e43i			0.398367i
$550$		0			0
$551$	7.22783e43			1.00134
$552$	−5.91018e43	−	5.91018e43i	−0.795382	−	0.795382i
$553$	4.29821e43	−	4.29821e43i	0.561934	−	0.561934i
$554$			7.63837e43i			0.970162i
$555$		0			0
$556$	1.57044e43			0.188289
$557$	7.51595e43	+	7.51595e43i	0.875590	+	0.875590i	0.993075	−	0.117485i	$-0.0374831\pi$
$557$	7.51595e43	+	7.51595e43i	0.875590	+	0.875590i	−0.117485	+	0.993075i	$0.537483\pi$
$558$	−4.35490e41	+	4.35490e41i	−0.00492981	+	0.00492981i
$559$			1.01682e44i			1.11855i
$560$		0			0
$561$	5.81117e43			0.603751
$562$	−4.28851e43	−	4.28851e43i	−0.433037	−	0.433037i
$563$	−5.95350e43	+	5.95350e43i	−0.584303	+	0.584303i	−0.936083	−	0.351780i	$-0.885577\pi$
$563$	−5.95350e43	+	5.95350e43i	−0.584303	+	0.584303i	0.351780	+	0.936083i	$0.385577\pi$
$564$			8.64179e42i			0.0824400i
$565$		0			0
$566$	−1.37822e44			−1.24239
$567$	2.68045e43	+	2.68045e43i	0.234898	+	0.234898i
$568$	9.98146e43	−	9.98146e43i	0.850395	−	0.850395i
$569$		−	7.38465e43i		−	0.611693i	−0.952081	−	0.305847i	$-0.901061\pi$
$569$		−	7.38465e43i		−	0.611693i	0.952081	−	0.305847i	$-0.0989395\pi$
$570$		0			0
$571$	−1.06965e44			−0.837654			−0.418827	−	0.908066i	$-0.637559\pi$
$571$	−1.06965e44			−0.837654			−0.418827	+	0.908066i	$0.637559\pi$
$572$	1.28743e43	+	1.28743e43i	0.0980360	+	0.0980360i
$573$	−2.12440e43	+	2.12440e43i	−0.157312	+	0.157312i
$574$		−	5.44794e43i		−	0.392322i
$575$		0			0
$576$	7.51281e43			0.511732
$577$	1.21439e44	+	1.21439e44i	0.804535	+	0.804535i	0.983801	−	0.179266i	$-0.0573721\pi$
$577$	1.21439e44	+	1.21439e44i	0.804535	+	0.804535i	−0.179266	+	0.983801i	$0.557372\pi$
$578$	−4.18172e43	+	4.18172e43i	−0.269470	+	0.269470i
$579$		−	1.00691e44i		−	0.631152i
$580$		0			0
$581$	2.24834e43			0.133366
$582$	3.56082e43	+	3.56082e43i	0.205486	+	0.205486i
$583$	−4.73375e43	+	4.73375e43i	−0.265772	+	0.265772i
$584$		−	1.29301e44i		−	0.706313i
$585$		0			0
$586$	−1.22762e44			−0.634897
$587$	−3.83162e43	−	3.83162e43i	−0.192829	−	0.192829i	0.604088	−	0.796917i	$-0.293537\pi$
$587$	−3.83162e43	−	3.83162e43i	−0.192829	−	0.192829i	−0.796917	+	0.604088i	$0.793537\pi$
$588$	7.75676e41	−	7.75676e41i	0.00379877	−	0.00379877i
$589$			2.69053e42i			0.0128231i
$590$		0			0
$591$	3.19569e44			1.44266
$592$	2.23909e44	+	2.23909e44i	0.983840	+	0.983840i
$593$	4.71832e43	−	4.71832e43i	0.201796	−	0.201796i	−0.598973	−	0.800769i	$-0.704424\pi$
$593$	4.71832e43	−	4.71832e43i	0.201796	−	0.201796i	0.800769	+	0.598973i	$0.204424\pi$
$594$		−	1.61305e44i		−	0.671530i
$595$		0			0
$596$	−6.56517e43			−0.259004
$597$	4.64429e43	+	4.64429e43i	0.178373	+	0.178373i
$598$	2.78638e44	−	2.78638e44i	1.04189	−	1.04189i
$599$			4.37547e44i			1.59293i	0.604686	+	0.796464i	$0.293298\pi$
$599$			4.37547e44i			1.59293i	−0.604686	+	0.796464i	$0.706702\pi$
$600$		0			0
$601$	−1.15484e44			−0.398594			−0.199297	−	0.979939i	$-0.563866\pi$
$601$	−1.15484e44			−0.398594			−0.199297	+	0.979939i	$0.563866\pi$
$602$	−1.92428e44	−	1.92428e44i	−0.646733	−	0.646733i
$603$	−2.70636e42	+	2.70636e42i	−0.00885746	+	0.00885746i
$604$		−	5.43398e43i		−	0.173192i
$605$		0			0
$606$	4.55906e43			0.137820
$607$	7.80195e43	+	7.80195e43i	0.229712	+	0.229712i	0.812572	−	0.582860i	$-0.198066\pi$
$607$	7.80195e43	+	7.80195e43i	0.229712	+	0.229712i	−0.582860	+	0.812572i	$0.698066\pi$
$608$	6.65114e43	−	6.65114e43i	0.190739	−	0.190739i
$609$		−	3.48696e44i		−	0.974027i
$610$		0			0
$611$	−2.70362e44			−0.716616
$612$	−2.67221e43	−	2.67221e43i	−0.0689998	−	0.0689998i
$613$	−3.31005e44	+	3.31005e44i	−0.832659	+	0.832659i	−0.987880	−	0.155221i	$-0.950391\pi$
$613$	−3.31005e44	+	3.31005e44i	−0.832659	+	0.832659i	0.155221	+	0.987880i	$0.450391\pi$
$614$			1.43562e44i			0.351841i
$615$		0			0
$616$	−3.23355e44			−0.752294
$617$	−5.34985e43	−	5.34985e43i	−0.121277	−	0.121277i	0.643863	−	0.765141i	$-0.277331\pi$
$617$	−5.34985e43	−	5.34985e43i	−0.121277	−	0.121277i	−0.765141	+	0.643863i	$0.777331\pi$
$618$	2.87832e44	−	2.87832e44i	0.635804	−	0.635804i
$619$			5.67847e44i			1.22231i	0.791511	+	0.611155i	$0.209295\pi$
$619$			5.67847e44i			1.22231i	−0.791511	+	0.611155i	$0.790705\pi$
$620$		0			0
$621$	7.53058e44			1.53944
$622$	4.12371e44	+	4.12371e44i	0.821564	+	0.821564i
$623$	7.13950e44	−	7.13950e44i	1.38631	−	1.38631i
$624$		−	3.47182e44i		−	0.657057i
$625$		0			0
$626$	6.90695e44			1.24193
$627$	−1.57341e44	−	1.57341e44i	−0.275778	−	0.275778i
$628$	1.09246e43	−	1.09246e43i	0.0186661	−	0.0186661i
$629$		−	1.25834e45i		−	2.09599i
$630$		0			0
$631$	−1.58265e44			−0.250562			−0.125281	−	0.992121i	$-0.539983\pi$
$631$	−1.58265e44			−0.250562			−0.125281	+	0.992121i	$0.539983\pi$
$632$	−3.80979e44	−	3.80979e44i	−0.588068	−	0.588068i
$633$	−1.36190e44	+	1.36190e44i	−0.204969	+	0.204969i
$634$		−	3.80435e44i		−	0.558280i
$635$		0			0
$636$	−5.08023e43			−0.0708875
$637$	2.42674e43	+	2.42674e43i	0.0330211	+	0.0330211i
$638$	−4.33990e44	+	4.33990e44i	−0.575903	+	0.575903i
$639$			4.01592e44i			0.519722i
$640$		0			0
$641$	2.56042e44			0.315198			0.157599	−	0.987503i	$-0.449625\pi$
$641$	2.56042e44			0.315198			0.157599	+	0.987503i	$0.449625\pi$
$642$	−5.87790e44	−	5.87790e44i	−0.705767	−	0.705767i
$643$	3.22789e44	−	3.22789e44i	0.378045	−	0.378045i	−0.492352	−	0.870396i	$-0.663863\pi$
$643$	3.22789e44	−	3.22789e44i	0.378045	−	0.378045i	0.870396	+	0.492352i	$0.163863\pi$
$644$		−	2.27487e44i		−	0.259886i
$645$		0			0
$646$	7.65364e44			0.832047
$647$	1.31997e45	+	1.31997e45i	1.39990	+	1.39990i	0.800304	+	0.599595i	$0.204672\pi$
$647$	1.31997e45	+	1.31997e45i	1.39990	+	1.39990i	0.599595	+	0.800304i	$0.295328\pi$
$648$	2.37586e44	−	2.37586e44i	0.245822	−	0.245822i
$649$		−	7.88823e44i		−	0.796278i
$650$		0			0
$651$	1.29801e43			0.0124733
$652$	−2.06772e44	−	2.06772e44i	−0.193879	−	0.193879i
$653$	−1.19634e45	+	1.19634e45i	−1.09457	+	1.09457i	−0.0995407	+	0.995033i	$0.531737\pi$
$653$	−1.19634e45	+	1.19634e45i	−1.09457	+	1.09457i	−0.995033	+	0.0995407i	$0.968263\pi$
$654$			8.26694e44i			0.738076i
$655$		0			0
$656$	−3.94422e44			−0.335351
$657$	2.60114e44	+	2.60114e44i	0.215833	+	0.215833i
$658$	5.11647e44	−	5.11647e44i	0.414339	−	0.414339i
$659$			2.44141e45i			1.92963i	0.262933	+	0.964814i	$0.415310\pi$
$659$			2.44141e45i			1.92963i	−0.262933	+	0.964814i	$0.584690\pi$
$660$		0			0
$661$	−1.93434e45			−1.45649			−0.728247	−	0.685314i	$-0.759665\pi$
$661$	−1.93434e45			−1.45649			−0.728247	+	0.685314i	$0.759665\pi$
$662$	−1.23231e45	−	1.23231e45i	−0.905714	−	0.905714i
$663$	−9.75560e44	+	9.75560e44i	−0.699902	+	0.699902i
$664$		−	1.99286e44i		−	0.139568i
$665$		0			0
$666$	−1.10293e45			−0.736138
$667$	−2.02610e45	−	2.02610e45i	−1.32022	−	1.32022i
$668$	−2.96549e44	+	2.96549e44i	−0.188657	+	0.188657i
$669$			8.37368e43i			0.0520114i
$670$		0			0
$671$	−1.00640e45			−0.595953
$672$	−3.20875e44	−	3.20875e44i	−0.185536	−	0.185536i
$673$	−1.60472e45	+	1.60472e45i	−0.906065	+	0.906065i	−0.995952	−	0.0898869i	$-0.971349\pi$
$673$	−1.60472e45	+	1.60472e45i	−0.906065	+	0.906065i	0.0898869	+	0.995952i	$0.471349\pi$
$674$			2.48005e45i			1.36742i
$675$		0			0
$676$	−9.48300e43			−0.0498653
$677$	1.82987e45	+	1.82987e45i	0.939727	+	0.939727i	0.998284	−	0.0585573i	$-0.0186500\pi$
$677$	1.82987e45	+	1.82987e45i	0.939727	+	0.939727i	−0.0585573	+	0.998284i	$0.518650\pi$
$678$	6.81137e44	−	6.81137e44i	0.341633	−	0.341633i
$679$			9.09512e44i			0.445545i
$680$		0			0
$681$	−4.89482e44			−0.228761
$682$	−1.61551e43	−	1.61551e43i	−0.00737496	−	0.00737496i
$683$	−6.03515e44	+	6.03515e44i	−0.269127	+	0.269127i	−0.828748	−	0.559622i	$-0.810946\pi$
$683$	−6.03515e44	+	6.03515e44i	−0.269127	+	0.269127i	0.559622	+	0.828748i	$0.310946\pi$
$684$			1.44703e44i			0.0630348i
$685$		0			0
$686$	2.13428e45			0.887291
$687$	−8.50089e44	−	8.50089e44i	−0.345268	−	0.345268i
$688$	−1.39315e45	+	1.39315e45i	−0.552819	+	0.552819i
$689$		−	1.58937e45i		−	0.616195i
$690$		0			0
$691$	8.47415e43			0.0313652			0.0156826	−	0.999877i	$-0.495008\pi$
$691$	8.47415e43			0.0313652			0.0156826	+	0.999877i	$0.495008\pi$
$692$	3.62565e44	+	3.62565e44i	0.131126	+	0.131126i
$693$	6.50489e44	−	6.50489e44i	0.229884	−	0.229884i
$694$		−	4.31777e44i		−	0.149110i
$695$		0			0
$696$	−3.09073e45			−1.01933
$697$	1.10830e45	+	1.10830e45i	0.357219	+	0.357219i
$698$	1.13567e45	−	1.13567e45i	0.357739	−	0.357739i
$699$		−	1.13358e45i		−	0.348994i
$700$		0			0
$701$	−4.47213e43			−0.0131530			−0.00657652	−	0.999978i	$-0.502093\pi$
$701$	−4.47213e43			−0.0131530			−0.00657652	+	0.999978i	$0.502093\pi$
$702$	2.70794e45	+	2.70794e45i	0.778476	+	0.778476i
$703$	−3.40703e45	+	3.40703e45i	−0.957395	+	0.957395i
$704$			2.78698e45i			0.765547i
$705$		0			0
$706$	−1.12958e44			−0.0296513
$707$	5.82242e44	+	5.82242e44i	0.149415	+	0.149415i
$708$	4.23280e44	−	4.23280e44i	0.106193	−	0.106193i
$709$			3.36170e45i			0.824555i	0.911058	+	0.412278i	$0.135267\pi$
$709$			3.36170e45i			0.824555i	−0.911058	+	0.412278i	$0.864733\pi$
$710$		0			0
$711$	1.53282e45			0.359400
$712$	−6.32822e45	−	6.32822e45i	−1.45078	−	1.45078i
$713$	7.54206e43	−	7.54206e43i	0.0169066	−	0.0169066i
$714$		−	3.69239e45i		−	0.809350i
$715$		0			0
$716$	−1.52412e45			−0.319456
$717$	1.25638e45	+	1.25638e45i	0.257521	+	0.257521i
$718$	−1.04951e45	+	1.04951e45i	−0.210377	+	0.210377i
$719$			9.15494e43i			0.0179471i	0.999960	+	0.00897353i	$0.00285640\pi$
$719$			9.15494e43i			0.0179471i	−0.999960	+	0.00897353i	$0.997144\pi$
$720$		0			0
$721$	7.35186e45			1.37858
$722$	1.42449e45	+	1.42449e45i	0.261256	+	0.261256i
$723$	4.60890e45	−	4.60890e45i	0.826770	−	0.826770i
$724$		−	1.78738e45i		−	0.313616i
$725$		0			0
$726$	−2.07485e45			−0.348339
$727$	−1.12691e45	−	1.12691e45i	−0.185071	−	0.185071i	0.608490	−	0.793561i	$-0.291775\pi$
$727$	−1.12691e45	−	1.12691e45i	−0.185071	−	0.185071i	−0.793561	+	0.608490i	$0.791775\pi$
$728$	5.42837e45	−	5.42837e45i	0.872102	−	0.872102i
$729$			5.96353e45i			0.937267i
$730$		0			0
$731$	7.82933e45			1.17773
$732$	−5.40033e44	−	5.40033e44i	−0.0794773	−	0.0794773i
$733$	1.66007e45	−	1.66007e45i	0.239036	−	0.239036i	−0.577415	−	0.816451i	$-0.695938\pi$
$733$	1.66007e45	−	1.66007e45i	0.239036	−	0.239036i	0.816451	+	0.577415i	$0.195938\pi$
$734$		−	3.15671e45i		−	0.444731i
$735$		0			0
$736$	−3.72888e45			−0.502960
$737$	−1.00396e44	−	1.00396e44i	−0.0132507	−	0.0132507i
$738$	9.71419e44	−	9.71419e44i	0.125460	−	0.125460i
$739$		−	1.30139e46i		−	1.64474i	−0.568954	−	0.822370i	$-0.692652\pi$
$739$		−	1.30139e46i		−	1.64474i	0.568954	−	0.822370i	$-0.307348\pi$
$740$		0			0
$741$	5.28276e45			0.639396
$742$	3.00781e45	+	3.00781e45i	0.356277	+	0.356277i
$743$	6.13827e45	−	6.13827e45i	0.711583	−	0.711583i	−0.255284	−	0.966866i	$-0.582169\pi$
$743$	6.13827e45	−	6.13827e45i	0.711583	−	0.711583i	0.966866	+	0.255284i	$0.0821688\pi$
$744$		−	1.15051e44i		−	0.0130534i
$745$		0			0
$746$	−9.58049e45			−1.04128
$747$	4.00900e44	+	4.00900e44i	0.0426488	+	0.0426488i
$748$	9.91294e44	−	9.91294e44i	0.103223	−	0.103223i
$749$		−	1.50134e46i		−	1.53028i
$750$		0			0
$751$	1.18592e46			1.15829			0.579146	−	0.815224i	$-0.303386\pi$
$751$	1.18592e46			1.15829			0.579146	+	0.815224i	$0.303386\pi$
$752$	−3.70424e45	−	3.70424e45i	−0.354172	−	0.354172i
$753$	−6.90544e45	+	6.90544e45i	−0.646355	+	0.646355i
$754$		−	1.45714e46i		−	1.33524i
$755$		0			0
$756$	2.21083e45			0.194181
$757$	5.54304e45	+	5.54304e45i	0.476666	+	0.476666i	0.904064	−	0.427398i	$-0.140570\pi$
$757$	5.54304e45	+	5.54304e45i	0.476666	+	0.476666i	−0.427398	+	0.904064i	$0.640570\pi$
$758$	1.34706e46	−	1.34706e46i	1.13417	−	1.13417i
$759$			8.82111e45i			0.727202i
$760$		0			0
$761$	−2.78615e45			−0.220217			−0.110108	−	0.993920i	$-0.535120\pi$
$761$	−2.78615e45			−0.220217			−0.110108	+	0.993920i	$0.535120\pi$
$762$	−2.00034e45	−	2.00034e45i	−0.154819	−	0.154819i
$763$	−1.05578e46	+	1.05578e46i	−0.800167	+	0.800167i
$764$			7.24778e44i			0.0537912i
$765$		0			0
$766$	−1.64755e46			−1.17268
$767$	1.32425e46	+	1.32425e46i	0.923091	+	0.923091i
$768$	−3.91102e45	+	3.91102e45i	−0.266999	+	0.266999i
$769$			1.81007e46i			1.21025i	0.796132	+	0.605123i	$0.206876\pi$
$769$			1.81007e46i			1.21025i	−0.796132	+	0.605123i	$0.793124\pi$
$770$		0			0
$771$	7.78649e44			0.0499426
$772$	−1.71763e45	−	1.71763e45i	−0.107908	−	0.107908i
$773$	−1.12025e46	+	1.12025e46i	−0.689353	+	0.689353i	−0.962089	−	0.272736i	$-0.912071\pi$
$773$	−1.12025e46	+	1.12025e46i	−0.689353	+	0.689353i	0.272736	+	0.962089i	$0.412071\pi$
$774$		−	6.86235e45i		−	0.413635i
$775$		0			0
$776$	8.06161e45			0.466266
$777$	1.64368e46	+	1.64368e46i	0.931279	+	0.931279i
$778$	2.69548e45	−	2.69548e45i	0.149611	−	0.149611i
$779$		−	6.00159e45i		−	0.326337i
$780$		0			0
$781$	−1.48976e46			−0.777500
$782$	−2.14546e46	−	2.14546e46i	−1.09702	−	1.09702i
$783$	1.96906e46	−	1.96906e46i	0.986440	−	0.986440i
$784$			6.64976e44i			0.0326399i
$785$		0			0
$786$	6.10206e45			0.287551
$787$	1.27012e46	+	1.27012e46i	0.586476	+	0.586476i	0.936675	−	0.350200i	$-0.113886\pi$
$787$	1.27012e46	+	1.27012e46i	0.586476	+	0.586476i	−0.350200	+	0.936675i	$0.613886\pi$
$788$	5.45135e45	−	5.45135e45i	0.246652	−	0.246652i
$789$			2.92592e46i			1.29727i
$790$		0			0
$791$	1.73977e46			0.740746
$792$	−5.76572e45	−	5.76572e45i	−0.240575	−	0.240575i
$793$	1.68952e46	−	1.68952e46i	0.690863	−	0.690863i
$794$			6.19164e45i			0.248129i
$795$		0			0
$796$	1.58449e45			0.0609929
$797$	1.87034e45	+	1.87034e45i	0.0705648	+	0.0705648i	0.741508	−	0.670944i	$-0.234111\pi$
$797$	1.87034e45	+	1.87034e45i	0.0705648	+	0.0705648i	−0.670944	+	0.741508i	$0.734111\pi$
$798$	−9.99736e45	+	9.99736e45i	−0.369691	+	0.369691i
$799$			2.08174e46i			0.754532i
$800$		0			0
$801$	2.54608e46			0.886650
$802$	−2.07873e46	−	2.07873e46i	−0.709592	−	0.709592i
$803$	−9.64929e45	+	9.64929e45i	−0.322884	+	0.322884i
$804$		−	1.07745e44i		−	0.00353427i
$805$		0			0
$806$	5.42413e44			0.0170989
$807$	2.68159e46	+	2.68159e46i	0.828736	+	0.828736i
$808$	5.16080e45	−	5.16080e45i	0.156363	−	0.156363i
$809$			4.89689e46i			1.45460i	0.686320	+	0.727300i	$0.259225\pi$
$809$			4.89689e46i			1.45460i	−0.686320	+	0.727300i	$0.740775\pi$
$810$		0			0
$811$	−4.61301e46			−1.31720			−0.658599	−	0.752494i	$-0.728850\pi$
$811$	−4.61301e46			−1.31720			−0.658599	+	0.752494i	$0.728850\pi$
$812$	−5.94821e45	−	5.94821e45i	−0.166529	−	0.166529i
$813$	−1.09338e46	+	1.09338e46i	−0.300140	+	0.300140i
$814$		−	4.09146e46i		−	1.10126i
$815$		0			0
$816$	−2.67323e46			−0.691822
$817$	−2.11984e46	−	2.11984e46i	−0.537959	−	0.537959i
$818$	−4.59224e46	+	4.59224e46i	−1.14280	+	1.14280i
$819$			2.18404e46i			0.532988i
$820$		0			0
$821$	8.84798e45			0.207660			0.103830	−	0.994595i	$-0.466890\pi$
$821$	8.84798e45			0.207660			0.103830	+	0.994595i	$0.466890\pi$
$822$	−5.11892e45	−	5.11892e45i	−0.117823	−	0.117823i
$823$	−5.47403e46	+	5.47403e46i	−1.23569	+	1.23569i	−0.273945	+	0.961745i	$0.588329\pi$
$823$	−5.47403e46	+	5.47403e46i	−1.23569	+	1.23569i	−0.961745	+	0.273945i	$0.911671\pi$
$824$		−	6.51645e46i		−	1.44270i
$825$		0			0
$826$	−5.01215e46			−1.06744
$827$	2.97638e46	+	2.97638e46i	0.621728	+	0.621728i	0.945973	−	0.324245i	$-0.105110\pi$
$827$	2.97638e46	+	2.97638e46i	0.621728	+	0.621728i	−0.324245	+	0.945973i	$0.605110\pi$
$828$	4.05630e45	−	4.05630e45i	0.0831085	−	0.0831085i
$829$		−	6.73611e46i		−	1.35374i	−0.736100	−	0.676872i	$-0.763335\pi$
$829$		−	6.73611e46i		−	1.35374i	0.736100	−	0.676872i	$-0.236665\pi$
$830$		0			0
$831$	4.05951e46			0.784978
$832$	−4.67869e46	−	4.67869e46i	−0.887465	−	0.887465i
$833$	1.86854e45	−	1.86854e45i	0.0347683	−	0.0347683i
$834$			3.86932e46i			0.706281i
$835$		0			0
$836$	−5.36797e45			−0.0942995
$837$	7.32973e44	+	7.32973e44i	0.0126323	+	0.0126323i
$838$	2.92059e46	−	2.92059e46i	0.493818	−	0.493818i
$839$			1.61722e46i			0.268274i	0.990963	+	0.134137i	$0.0428263\pi$
$839$			1.61722e46i			0.268274i	−0.990963	+	0.134137i	$0.957174\pi$
$840$		0			0
$841$	−4.33315e46			−0.691939
$842$	−4.49674e46	−	4.49674e46i	−0.704537	−	0.704537i
$843$	−2.27919e46	+	2.27919e46i	−0.350379	+	0.350379i
$844$			4.64639e45i			0.0700868i
$845$		0			0
$846$	1.82463e46			0.265002
$847$	−2.64982e46	−	2.64982e46i	−0.377643	−	0.377643i
$848$	2.17761e46	−	2.17761e46i	0.304541	−	0.304541i
$849$			7.32476e46i			1.00524i
$850$		0			0
$851$	1.91011e47			2.52456
$852$	−7.99401e45	−	7.99401e45i	−0.103689	−	0.103689i
$853$	3.90613e45	−	3.90613e45i	0.0497236	−	0.0497236i	−0.681808	−	0.731531i	$-0.738806\pi$
$853$	3.90613e45	−	3.90613e45i	0.0497236	−	0.0497236i	0.731531	+	0.681808i	$0.238806\pi$
$854$			6.39466e46i			0.798898i
$855$		0			0
$856$	−1.33074e47			−1.60145
$857$	−9.29511e46	−	9.29511e46i	−1.09790	−	1.09790i	−0.994656	−	0.103240i	$-0.967079\pi$
$857$	−9.29511e46	−	9.29511e46i	−1.09790	−	1.09790i	−0.103240	−	0.994656i	$-0.532921\pi$
$858$	−3.17200e46	+	3.17200e46i	−0.367737	+	0.367737i
$859$		−	1.39216e47i		−	1.58416i	−0.610419	−	0.792079i	$-0.708999\pi$
$859$		−	1.39216e47i		−	1.58416i	0.610419	−	0.792079i	$-0.291001\pi$
$860$		0			0
$861$	−2.89538e46			−0.317436
$862$	3.42434e46	+	3.42434e46i	0.368520	+	0.368520i
$863$	4.99342e46	−	4.99342e46i	0.527504	−	0.527504i	−0.392324	−	0.919827i	$-0.628329\pi$
$863$	4.99342e46	−	4.99342e46i	0.527504	−	0.527504i	0.919827	+	0.392324i	$0.128329\pi$
$864$		−	3.62391e46i		−	0.375800i
$865$		0			0
$866$	−6.40059e46			−0.639637
$867$	2.22243e46	+	2.22243e46i	0.218033	+	0.218033i
$868$	2.21420e44	−	2.21420e44i	0.00213256	−	0.00213256i
$869$			5.68622e46i			0.537659i
$870$		0			0
$871$	3.37084e45			0.0307219
$872$	9.35808e46	+	9.35808e46i	0.837381	+	0.837381i
$873$	−1.62174e46	+	1.62174e46i	−0.142480	+	0.142480i
$874$			1.16179e47i			1.00218i
$875$		0			0
$876$	−1.03555e46			−0.0861207
$877$	1.03630e47	+	1.03630e47i	0.846233	+	0.846233i	0.989661	−	0.143428i	$-0.0458124\pi$
$877$	1.03630e47	+	1.03630e47i	0.846233	+	0.846233i	−0.143428	+	0.989661i	$0.545812\pi$
$878$	1.75007e46	−	1.75007e46i	0.140327	−	0.140327i
$879$			6.52437e46i			0.513708i
$880$		0			0
$881$	7.53777e46			0.572306			0.286153	−	0.958184i	$-0.407623\pi$
$881$	7.53777e46			0.572306			0.286153	+	0.958184i	$0.407623\pi$
$882$	−1.63776e45	−	1.63776e45i	−0.0122111	−	0.0122111i
$883$	−1.25662e47	+	1.25662e47i	−0.920094	+	0.920094i	−0.997036	−	0.0769415i	$-0.975485\pi$
$883$	−1.25662e47	+	1.25662e47i	−0.920094	+	0.920094i	0.0769415	+	0.997036i	$0.475485\pi$
$884$			3.32830e46i			0.239324i
$885$		0			0
$886$	1.17167e47			0.812577
$887$	1.10198e47	+	1.10198e47i	0.750578	+	0.750578i	0.974587	−	0.224009i	$-0.0719146\pi$
$887$	1.10198e47	+	1.10198e47i	0.750578	+	0.750578i	−0.224009	+	0.974587i	$0.571915\pi$
$888$	1.45690e47	−	1.45690e47i	0.974590	−	0.974590i
$889$		−	5.10930e46i		−	0.335686i
$890$		0			0
$891$	−3.54604e46			−0.224750
$892$	1.42842e45	+	1.42842e45i	0.00889238	+	0.00889238i
$893$	5.63643e46	−	5.63643e46i	0.344652	−	0.344652i
$894$		−	1.61755e47i		−	0.971533i
$895$		0			0
$896$	1.15386e47			0.668689
$897$	−1.48086e47	−	1.48086e47i	−0.843014	−	0.843014i
$898$	5.20745e46	−	5.20745e46i	0.291208	−	0.291208i
$899$		−	3.94412e45i		−	0.0216668i
$900$		0			0
$901$	−1.22379e47			−0.648798
$902$	3.60362e46	+	3.60362e46i	0.187687	+	0.187687i
$903$	−1.02269e47	+	1.02269e47i	−0.523285	+	0.523285i
$904$		−	1.54208e47i		−	0.775196i
$905$		0			0
$906$	1.33884e47			0.649648
$907$	9.33158e46	+	9.33158e46i	0.444876	+	0.444876i	0.893647	−	0.448771i	$-0.148138\pi$
$907$	9.33158e46	+	9.33158e46i	0.444876	+	0.444876i	−0.448771	+	0.893647i	$0.648138\pi$
$908$	−8.34979e45	+	8.34979e45i	−0.0391113	+	0.0391113i
$909$			2.07639e46i			0.0955621i
$910$		0			0
$911$	−2.09272e47			−0.929860			−0.464930	−	0.885347i	$-0.653921\pi$
$911$	−2.09272e47			−0.929860			−0.464930	+	0.885347i	$0.653921\pi$
$912$	7.23793e46	+	7.23793e46i	0.316007	+	0.316007i
$913$	−1.48720e46	+	1.48720e46i	−0.0638022	+	0.0638022i
$914$			4.83235e46i			0.203713i
$915$		0			0
$916$	−2.90024e46			−0.118061
$917$	7.79300e46	+	7.79300e46i	0.311742	+	0.311742i
$918$	2.08506e47	−	2.08506e47i	0.819665	−	0.819665i
$919$		−	1.72180e46i		−	0.0665175i	−0.999447	−	0.0332587i	$-0.989411\pi$
$919$		−	1.72180e46i		−	0.0665175i	0.999447	−	0.0332587i	$-0.0105885\pi$
$920$		0			0
$921$	7.62982e46			0.284682
$922$	−1.22603e47	−	1.22603e47i	−0.449579	−	0.449579i
$923$	2.50096e47	−	2.50096e47i	0.901322	−	0.901322i
$924$			2.58970e46i			0.0917272i
$925$		0			0
$926$	−2.27634e47			−0.778863
$927$	1.31091e47	+	1.31091e47i	0.440855	+	0.440855i
$928$	−9.75009e46	+	9.75009e46i	−0.322286	+	0.322286i
$929$		−	2.64416e47i		−	0.859084i	−0.903047	−	0.429542i	$-0.858675\pi$
$929$		−	2.64416e47i		−	0.859084i	0.903047	−	0.429542i	$-0.141325\pi$
$930$		0			0
$931$	−1.01184e46			−0.0317626
$932$	−1.93371e46	−	1.93371e46i	−0.0596675	−	0.0596675i
$933$	2.19160e47	−	2.19160e47i	0.664745	−	0.664745i
$934$			9.37776e46i			0.279608i
$935$		0			0
$936$	1.93586e47			0.557776
$937$	−1.43168e47	−	1.43168e47i	−0.405522	−	0.405522i	0.474652	−	0.880174i	$-0.342574\pi$
$937$	−1.43168e47	−	1.43168e47i	−0.405522	−	0.405522i	−0.880174	+	0.474652i	$0.842574\pi$
$938$	−6.37915e45	+	6.37915e45i	−0.0177630	+	0.0177630i
$939$		−	3.67079e47i		−	1.00487i
$940$		0			0
$941$	3.89222e47			1.02983			0.514913	−	0.857242i	$-0.327824\pi$
$941$	3.89222e47			1.02983			0.514913	+	0.857242i	$0.327824\pi$
$942$	2.69165e46	+	2.69165e46i	0.0700171	+	0.0700171i
$943$	−1.68236e47	+	1.68236e47i	−0.430261	+	0.430261i
$944$			3.62872e47i			0.912434i
$945$		0			0
$946$	2.54569e47			0.618795
$947$	−2.43935e47	−	2.43935e47i	−0.583009	−	0.583009i	0.352720	−	0.935729i	$-0.385257\pi$
$947$	−2.43935e47	−	2.43935e47i	−0.583009	−	0.583009i	−0.935729	+	0.352720i	$0.885257\pi$
$948$	−3.05121e46	+	3.05121e46i	−0.0717031	+	0.0717031i
$949$		−	3.23978e47i		−	0.748611i
$950$		0			0
$951$	−2.02187e47			−0.451716
$952$	−4.17974e47	−	4.17974e47i	−0.918245	−	0.918245i
$953$	1.43165e47	−	1.43165e47i	0.309280	−	0.309280i	−0.535350	−	0.844630i	$-0.679820\pi$
$953$	1.43165e47	−	1.43165e47i	0.309280	−	0.309280i	0.844630	+	0.535350i	$0.179820\pi$
$954$			1.07264e47i			0.227866i
$955$		0			0
$956$	4.28636e46			0.0880567
$957$	2.30650e47	+	2.30650e47i	0.465975	+	0.465975i
$958$	−3.38005e47	+	3.38005e47i	−0.671545	+	0.671545i
$959$		−	1.30748e47i		−	0.255469i
$960$		0			0
$961$	−5.28998e47			−0.999723
$962$	6.86862e47	+	6.86862e47i	1.27664	+	1.27664i
$963$	2.67704e47	−	2.67704e47i	0.489366	−	0.489366i
$964$		−	1.57241e47i		−	0.282705i
$965$		0			0
$966$	5.60490e47			0.974841
$967$	3.42384e45	+	3.42384e45i	0.00585721	+	0.00585721i	0.710029	−	0.704172i	$-0.248682\pi$
$967$	3.42384e45	+	3.42384e45i	0.00585721	+	0.00585721i	−0.704172	+	0.710029i	$0.748682\pi$
$968$	−2.34871e47	+	2.34871e47i	−0.395206	+	0.395206i
$969$		−	4.06763e47i		−	0.673226i
$970$		0			0
$971$	4.09981e47			0.656532			0.328266	−	0.944585i	$-0.393536\pi$
$971$	4.09981e47			0.656532			0.328266	+	0.944585i	$0.393536\pi$
$972$	6.63945e46	+	6.63945e46i	0.104586	+	0.104586i
$973$	−4.94154e47	+	4.94154e47i	−0.765697	+	0.765697i
$974$		−	6.50905e47i		−	0.992143i
$975$		0			0
$976$	4.62963e47			0.682888
$977$	−6.06829e47	−	6.06829e47i	−0.880549	−	0.880549i	0.113042	−	0.993590i	$-0.463941\pi$
$977$	−6.06829e47	−	6.06829e47i	−0.880549	−	0.880549i	−0.993590	+	0.113042i	$0.963941\pi$
$978$	5.09453e47	−	5.09453e47i	0.727248	−	0.727248i
$979$			9.44505e47i			1.32642i
$980$		0			0
$981$	−3.76511e47			−0.511768
$982$	1.14597e46	+	1.14597e46i	0.0153247	+	0.0153247i
$983$	−1.63313e47	+	1.63313e47i	−0.214864	+	0.214864i	−0.806330	−	0.591466i	$-0.798549\pi$
$983$	−1.63313e47	+	1.63313e47i	−0.214864	+	0.214864i	0.591466	+	0.806330i	$0.298549\pi$
$984$			2.56637e47i			0.332199i
$985$		0			0
$986$	−1.12197e48			−1.40589
$987$	−2.71922e47	−	2.71922e47i	−0.335250	−	0.335250i
$988$	9.01156e46	−	9.01156e46i	0.109317	−	0.109317i
$989$			1.18846e48i			1.41855i
$990$		0			0
$991$	−7.49308e47			−0.865928			−0.432964	−	0.901411i	$-0.642532\pi$
$991$	−7.49308e47			−0.865928			−0.432964	+	0.901411i	$0.642532\pi$
$992$	−3.62943e45	−	3.62943e45i	−0.00412716	−	0.00412716i
$993$	−6.54926e47	+	6.54926e47i	−0.732832	+	0.732832i
$994$			9.46589e47i			1.04227i
$995$		0			0
$996$	−1.59605e46			−0.0170175
$997$	−1.54277e47	−	1.54277e47i	−0.161875	−	0.161875i	0.621522	−	0.783397i	$-0.286515\pi$
$997$	−1.54277e47	−	1.54277e47i	−0.161875	−	0.161875i	−0.783397	+	0.621522i	$0.786515\pi$
$998$	−5.70807e47	+	5.70807e47i	−0.589387	+	0.589387i
$999$			1.85634e48i			1.88629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.12		30
5.2	odd	4		5.33.c.a.3.4	yes	30
5.3	odd	4	inner	25.33.c.b.18.12		30
5.4	even	2		5.33.c.a.2.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.4	✓	30	5.4	even	2
5.33.c.a.3.4	yes	30	5.2	odd	4
25.33.c.b.7.12		30	1.1	even	1	trivial
25.33.c.b.18.12		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)

\(f(q)\)	\(=\)	\(q+(42029.2 + 42029.2i) q^{2} +(2.23370e7 - 2.23370e7i) q^{3} -7.62067e8i q^{4} +1.87761e12 q^{6} +(2.39791e13 + 2.39791e13i) q^{7} +(2.12543e14 - 2.12543e14i) q^{8} +8.55140e14i q^{9} +O(q^{10})\)	\(q+(42029.2 + 42029.2i) q^{2} +(2.23370e7 - 2.23370e7i) q^{3} -7.62067e8i q^{4} +1.87761e12 q^{6} +(2.39791e13 + 2.39791e13i) q^{7} +(2.12543e14 - 2.12543e14i) q^{8} +8.55140e14i q^{9} -3.17226e16 q^{11} +(-1.70223e16 - 1.70223e16i) q^{12} +(5.32549e17 - 5.32549e17i) q^{13} +2.01564e18i q^{14} +1.45929e19 q^{16} +(-4.10053e19 - 4.10053e19i) q^{17} +(-3.59408e19 + 3.59408e19i) q^{18} +2.22048e20i q^{19} +1.07124e21 q^{21} +(-1.33328e21 - 1.33328e21i) q^{22} +(6.22444e21 - 6.22444e21i) q^{23} -9.49513e21i q^{24} +4.47652e22 q^{26} +(6.04921e22 + 6.04921e22i) q^{27} +(1.82737e22 - 1.82737e22i) q^{28} -3.25507e23i q^{29} +1.21168e22 q^{31} +(-2.99536e23 - 2.99536e23i) q^{32} +(-7.08587e23 + 7.08587e23i) q^{33} -3.44684e24i q^{34} +6.51674e23 q^{36} +(1.53437e25 + 1.53437e25i) q^{37} +(-9.33250e24 + 9.33250e24i) q^{38} -2.37911e25i q^{39} -2.70283e25 q^{41} +(4.50234e25 + 4.50234e25i) q^{42} +(-9.54673e25 + 9.54673e25i) q^{43} +2.41748e25i q^{44} +5.23216e26 q^{46} +(-2.53838e26 - 2.53838e26i) q^{47} +(3.25962e26 - 3.25962e26i) q^{48} +4.55683e25i q^{49} -1.83187e27 q^{51} +(-4.05838e26 - 4.05838e26i) q^{52} +(1.49223e27 - 1.49223e27i) q^{53} +5.08486e27i q^{54} +1.01932e28 q^{56} +(4.95988e27 + 4.95988e27i) q^{57} +(1.36808e28 - 1.36808e28i) q^{58} +2.48663e28i q^{59} +3.17251e28 q^{61} +(5.09261e26 + 5.09261e26i) q^{62} +(-2.05055e28 + 2.05055e28i) q^{63} -8.78547e28i q^{64} -5.95627e28 q^{66} +(3.16482e27 + 3.16482e27i) q^{67} +(-3.12488e28 + 3.12488e28i) q^{68} -2.78070e29i q^{69} +4.69621e29 q^{71} +(1.81754e29 + 1.81754e29i) q^{72} +(3.04177e29 - 3.04177e29i) q^{73} +1.28976e30i q^{74} +1.69216e29 q^{76} +(-7.60681e29 - 7.60681e29i) q^{77} +(9.99918e29 - 9.99918e29i) q^{78} -1.79248e30i q^{79} +1.11783e30 q^{81} +(-1.13598e30 - 1.13598e30i) q^{82} +(4.68812e29 - 4.68812e29i) q^{83} -8.16358e29i q^{84} -8.02482e30 q^{86} +(-7.27084e30 - 7.27084e30i) q^{87} +(-6.74242e30 + 6.74242e30i) q^{88} -2.97738e31i q^{89} +2.55401e31 q^{91} +(-4.74344e30 - 4.74344e30i) q^{92} +(2.70654e29 - 2.70654e29i) q^{93} -2.13372e31i q^{94} -1.33814e31 q^{96} +(1.89647e31 + 1.89647e31i) q^{97} +(-1.91520e30 + 1.91520e30i) q^{98} -2.71273e31i 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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