LMFDB - Embedded newform 63.18.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,18,Mod(1,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("63.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	63.a (trivial)

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:	yes
Analytic conductor:	$115.429915027$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 542084x^{3} + 28429210x^{2} + 53238758035x - 7826067153800 $ x^5 - 2x^4 - 542084x^3 + 28429210x^2 + 53238758035x - 7826067153800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$220.674$ of defining polynomial
Character	$\chi$	$=$	63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-169.674 q^{2} -102283. q^{4} -291836. q^{5} -5.76480e6 q^{7} +3.95942e7 q^{8} +O(q^{10})$	\(q-169.674 q^{2} -102283. q^{4} -291836. q^{5} -5.76480e6 q^{7} +3.95942e7 q^{8} +4.95168e7 q^{10} -9.20155e8 q^{11} -3.54811e9 q^{13} +9.78135e8 q^{14} +6.68833e9 q^{16} -1.33551e10 q^{17} +1.01556e11 q^{19} +2.98498e10 q^{20} +1.56126e11 q^{22} -5.71257e11 q^{23} -6.77771e11 q^{25} +6.02022e11 q^{26} +5.89640e11 q^{28} -2.09059e12 q^{29} -7.36060e12 q^{31} -6.32452e12 q^{32} +2.26601e12 q^{34} +1.68237e12 q^{35} +4.05978e13 q^{37} -1.72313e13 q^{38} -1.15550e13 q^{40} -6.41353e13 q^{41} -6.38323e13 q^{43} +9.41161e13 q^{44} +9.69273e13 q^{46} -2.90148e14 q^{47} +3.32329e13 q^{49} +1.15000e14 q^{50} +3.62911e14 q^{52} -5.20904e14 q^{53} +2.68534e14 q^{55} -2.28253e14 q^{56} +3.54718e14 q^{58} -8.11878e14 q^{59} +7.20690e14 q^{61} +1.24890e15 q^{62} +1.96452e14 q^{64} +1.03547e15 q^{65} -4.00961e15 q^{67} +1.36600e15 q^{68} -2.85455e14 q^{70} +1.62921e15 q^{71} -1.98765e15 q^{73} -6.88838e15 q^{74} -1.03874e16 q^{76} +5.30451e15 q^{77} -1.79646e16 q^{79} -1.95189e15 q^{80} +1.08821e16 q^{82} +1.19809e16 q^{83} +3.89749e15 q^{85} +1.08307e16 q^{86} -3.64328e16 q^{88} -3.90684e16 q^{89} +2.04542e16 q^{91} +5.84298e16 q^{92} +4.92304e16 q^{94} -2.96376e16 q^{95} -1.12062e17 q^{97} -5.63875e15 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 253 q^{2} + 441613 q^{4} + 906662 q^{5} - 28824005 q^{7} + 182238651 q^{8}+O(q^{10}) $ 5 * q + 253 * q^2 + 441613 * q^4 + 906662 * q^5 - 28824005 * q^7 + 182238651 * q^8	$ 5 q + 253 q^{2} + 441613 q^{4} + 906662 q^{5} - 28824005 q^{7} + 182238651 q^{8} + 1194057802 q^{10} - 1111338736 q^{11} + 5215478294 q^{13} - 1458494653 q^{14} + 62775861505 q^{16} - 25747891566 q^{17} + 142208068556 q^{19} + 129890562778 q^{20} - 448421189252 q^{22} + 700488736068 q^{23} + 1178351016379 q^{25} - 2889360071546 q^{26} - 2545811064013 q^{28} + 3529421241410 q^{29} + 1688850702072 q^{31} + 17321396050955 q^{32} + 40556147819358 q^{34} - 5226726004262 q^{35} + 16886745594894 q^{37} + 20515887907732 q^{38} + 320653834434294 q^{40} - 58103631330302 q^{41} + 49458422903068 q^{43} - 401313211061300 q^{44} + 325662527133360 q^{46} - 321151801515192 q^{47} + 166164652848005 q^{49} + 130885367368259 q^{50} - 447415499102234 q^{52} - 16\!\cdots\!54 q^{53}+ \cdots + 84\!\cdots\!53 q^{98}+O(q^{100}) $ 5 * q + 253 * q^2 + 441613 * q^4 + 906662 * q^5 - 28824005 * q^7 + 182238651 * q^8 + 1194057802 * q^10 - 1111338736 * q^11 + 5215478294 * q^13 - 1458494653 * q^14 + 62775861505 * q^16 - 25747891566 * q^17 + 142208068556 * q^19 + 129890562778 * q^20 - 448421189252 * q^22 + 700488736068 * q^23 + 1178351016379 * q^25 - 2889360071546 * q^26 - 2545811064013 * q^28 + 3529421241410 * q^29 + 1688850702072 * q^31 + 17321396050955 * q^32 + 40556147819358 * q^34 - 5226726004262 * q^35 + 16886745594894 * q^37 + 20515887907732 * q^38 + 320653834434294 * q^40 - 58103631330302 * q^41 + 49458422903068 * q^43 - 401313211061300 * q^44 + 325662527133360 * q^46 - 321151801515192 * q^47 + 166164652848005 * q^49 + 130885367368259 * q^50 - 447415499102234 * q^52 - 1624886228519454 * q^53 + 1551981825532832 * q^55 - 1050569557523451 * q^56 + 3599479065043546 * q^58 - 4642231410191796 * q^59 + 383521828948430 * q^61 - 3303800808324960 * q^62 + 7678662933303305 * q^64 - 1668701347292044 * q^65 - 4060475251851460 * q^67 + 16890755118576270 * q^68 - 6883505611027402 * q^70 - 6398015136563460 * q^71 - 15734132975098902 * q^73 + 25189581013328238 * q^74 - 14323380376996940 * q^76 + 6406646656631536 * q^77 + 2199683795891080 * q^79 + 115762642448214658 * q^80 - 6015570522729706 * q^82 - 23947511376405780 * q^83 + 21310596918487932 * q^85 + 3933835697843468 * q^86 - 87148613365646124 * q^88 + 12131366869070066 * q^89 - 30066194484729494 * q^91 + 198814114679296704 * q^92 + 14990206001176800 * q^94 + 239731994312770088 * q^95 + 4112564616338706 * q^97 + 8407931434109053 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−169.674	−0.468662	−0.234331	−	0.972157i	$-0.575290\pi$
$2$	−169.674	−0.468662	−0.234331	+	0.972157i	$0.575290\pi$
$3$	0	0
$3$	0	0
$4$	−102283.	−0.780356
$5$	−291836.	−0.334113	−0.167056	−	0.985947i	$-0.553426\pi$
$5$	−291836.	−0.334113	−0.167056	+	0.985947i	$0.553426\pi$
$6$	0	0
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	3.95942e7	0.834385
$9$	0	0
$10$	4.95168e7	0.156586
$11$	−9.20155e8	−1.29427	−0.647133	−	0.762378i	$-0.724032\pi$
$11$	−9.20155e8	−1.29427	−0.647133	+	0.762378i	$0.724032\pi$
$12$	0	0
$13$	−3.54811e9	−1.20637	−0.603183	−	0.797603i	$-0.706101\pi$
$13$	−3.54811e9	−1.20637	−0.603183	+	0.797603i	$0.706101\pi$
$14$	9.78135e8	0.177137
$15$	0	0
$16$	6.68833e9	0.389312
$17$	−1.33551e10	−0.464335	−0.232167	−	0.972676i	$-0.574582\pi$
$17$	−1.33551e10	−0.464335	−0.232167	+	0.972676i	$0.574582\pi$
$18$	0	0
$19$	1.01556e11	1.37183	0.685913	−	0.727683i	$-0.259403\pi$
$19$	1.01556e11	1.37183	0.685913	+	0.727683i	$0.259403\pi$
$20$	2.98498e10	0.260727
$21$	0	0
$22$	1.56126e11	0.606572
$23$	−5.71257e11	−1.52106	−0.760528	−	0.649305i	$-0.775060\pi$
$23$	−5.71257e11	−1.52106	−0.760528	+	0.649305i	$0.775060\pi$
$24$	0	0
$25$	−6.77771e11	−0.888369
$26$	6.02022e11	0.565378
$27$	0	0
$28$	5.89640e11	0.294947
$29$	−2.09059e12	−0.776044	−0.388022	−	0.921650i	$-0.626842\pi$
$29$	−2.09059e12	−0.776044	−0.388022	+	0.921650i	$0.626842\pi$
$30$	0	0
$31$	−7.36060e12	−1.55002	−0.775012	−	0.631946i	$-0.782256\pi$
$31$	−7.36060e12	−1.55002	−0.775012	+	0.631946i	$0.782256\pi$
$32$	−6.32452e12	−1.01684
$33$	0	0
$34$	2.26601e12	0.217616
$35$	1.68237e12	0.126283
$36$	0	0
$37$	4.05978e13	1.90015	0.950075	−	0.312021i	$-0.101006\pi$
$37$	4.05978e13	1.90015	0.950075	+	0.312021i	$0.101006\pi$
$38$	−1.72313e13	−0.642922
$39$	0	0
$40$	−1.15550e13	−0.278779
$41$	−6.41353e13	−1.25440	−0.627198	−	0.778860i	$-0.715798\pi$
$41$	−6.41353e13	−1.25440	−0.627198	+	0.778860i	$0.715798\pi$
$42$	0	0
$43$	−6.38323e13	−0.832835	−0.416417	−	0.909174i	$-0.636714\pi$
$43$	−6.38323e13	−0.832835	−0.416417	+	0.909174i	$0.636714\pi$
$44$	9.41161e13	1.00999
$45$	0	0
$46$	9.69273e13	0.712861
$47$	−2.90148e14	−1.77741	−0.888705	−	0.458480i	$-0.848394\pi$
$47$	−2.90148e14	−1.77741	−0.888705	+	0.458480i	$0.848394\pi$
$48$	0	0
$49$	3.32329e13	0.142857
$50$	1.15000e14	0.416344
$51$	0	0
$52$	3.62911e14	0.941395
$53$	−5.20904e14	−1.14925	−0.574623	−	0.818418i	$-0.694851\pi$
$53$	−5.20904e14	−1.14925	−0.574623	+	0.818418i	$0.694851\pi$
$54$	0	0
$55$	2.68534e14	0.432431
$56$	−2.28253e14	−0.315368
$57$	0	0
$58$	3.54718e14	0.363702
$59$	−8.11878e14	−0.719861	−0.359931	−	0.932979i	$-0.617200\pi$
$59$	−8.11878e14	−0.719861	−0.359931	+	0.932979i	$0.617200\pi$
$60$	0	0
$61$	7.20690e14	0.481332	0.240666	−	0.970608i	$-0.422634\pi$
$61$	7.20690e14	0.481332	0.240666	+	0.970608i	$0.422634\pi$
$62$	1.24890e15	0.726437
$63$	0	0
$64$	1.96452e14	0.0872422
$65$	1.03547e15	0.403063
$66$	0	0
$67$	−4.00961e15	−1.20633	−0.603166	−	0.797616i	$-0.706094\pi$
$67$	−4.00961e15	−1.20633	−0.603166	+	0.797616i	$0.706094\pi$
$68$	1.36600e15	0.362346
$69$	0	0
$70$	−2.85455e14	−0.0591839
$71$	1.62921e15	0.299420	0.149710	−	0.988730i	$-0.452166\pi$
$71$	1.62921e15	0.299420	0.149710	+	0.988730i	$0.452166\pi$
$72$	0	0
$73$	−1.98765e15	−0.288467	−0.144234	−	0.989544i	$-0.546072\pi$
$73$	−1.98765e15	−0.288467	−0.144234	+	0.989544i	$0.546072\pi$
$74$	−6.88838e15	−0.890528
$75$	0	0
$76$	−1.03874e16	−1.07051
$77$	5.30451e15	0.489186
$78$	0	0
$79$	−1.79646e16	−1.33225	−0.666126	−	0.745840i	$-0.732049\pi$
$79$	−1.79646e16	−1.33225	−0.666126	+	0.745840i	$0.732049\pi$
$80$	−1.95189e15	−0.130074
$81$	0	0
$82$	1.08821e16	0.587887
$83$	1.19809e16	0.583881	0.291941	−	0.956436i	$-0.405699\pi$
$83$	1.19809e16	0.583881	0.291941	+	0.956436i	$0.405699\pi$
$84$	0	0
$85$	3.89749e15	0.155140
$86$	1.08307e16	0.390318
$87$	0	0
$88$	−3.64328e16	−1.07992
$89$	−3.90684e16	−1.05199	−0.525994	−	0.850488i	$-0.676307\pi$
$89$	−3.90684e16	−1.05199	−0.525994	+	0.850488i	$0.676307\pi$
$90$	0	0
$91$	2.04542e16	0.455964
$92$	5.84298e16	1.18697
$93$	0	0
$94$	4.92304e16	0.833004
$95$	−2.96376e16	−0.458345
$96$	0	0
$97$	−1.12062e17	−1.45177	−0.725887	−	0.687814i	$-0.758570\pi$
$97$	−1.12062e17	−1.45177	−0.725887	+	0.687814i	$0.758570\pi$
$98$	−5.63875e15	−0.0669517
$99$	0	0
$100$	6.93244e16	0.693244
$101$	1.58365e17	1.45521	0.727607	−	0.685994i	$-0.240632\pi$
$101$	1.58365e17	1.45521	0.727607	+	0.685994i	$0.240632\pi$
$102$	0	0
$103$	1.10715e17	0.861170	0.430585	−	0.902550i	$-0.358307\pi$
$103$	1.10715e17	0.861170	0.430585	+	0.902550i	$0.358307\pi$
$104$	−1.40485e17	−1.00657
$105$	0	0
$106$	8.83837e16	0.538607
$107$	2.03902e17	1.14725	0.573626	−	0.819117i	$-0.305536\pi$
$107$	2.03902e17	1.14725	0.573626	+	0.819117i	$0.305536\pi$
$108$	0	0
$109$	8.56307e16	0.411628	0.205814	−	0.978591i	$-0.434016\pi$
$109$	8.56307e16	0.411628	0.205814	+	0.978591i	$0.434016\pi$
$110$	−4.55632e16	−0.202664
$111$	0	0
$112$	−3.85569e16	−0.147146
$113$	−2.39017e17	−0.845790	−0.422895	−	0.906179i	$-0.638986\pi$
$113$	−2.39017e17	−0.845790	−0.422895	+	0.906179i	$0.638986\pi$
$114$	0	0
$115$	1.66713e17	0.508205
$116$	2.13832e17	0.605591
$117$	0	0
$118$	1.37754e17	0.337371
$119$	7.69894e16	0.175502
$120$	0	0
$121$	3.41238e17	0.675122
$122$	−1.22282e17	−0.225582
$123$	0	0
$124$	7.52863e17	1.20957
$125$	4.20451e17	0.630928
$126$	0	0
$127$	4.42726e17	0.580501	0.290251	−	0.956951i	$-0.406261\pi$
$127$	4.42726e17	0.580501	0.290251	+	0.956951i	$0.406261\pi$
$128$	7.95635e17	0.975953
$129$	0	0
$130$	−1.75691e17	−0.188900
$131$	5.09779e17	0.513542	0.256771	−	0.966472i	$-0.417341\pi$
$131$	5.09779e17	0.513542	0.256771	+	0.966472i	$0.417341\pi$
$132$	0	0
$133$	−5.85449e17	−0.518502
$134$	6.80326e17	0.565361
$135$	0	0
$136$	−5.28784e17	−0.387434
$137$	8.48788e17	0.584352	0.292176	−	0.956365i	$-0.405621\pi$
$137$	8.48788e17	0.584352	0.292176	+	0.956365i	$0.405621\pi$
$138$	0	0
$139$	1.56163e17	0.0950502	0.0475251	−	0.998870i	$-0.484867\pi$
$139$	1.56163e17	0.0950502	0.0475251	+	0.998870i	$0.484867\pi$
$140$	−1.72078e17	−0.0985456
$141$	0	0
$142$	−2.76434e17	−0.140327
$143$	3.26482e18	1.56136
$144$	0	0
$145$	6.10109e17	0.259286
$146$	3.37253e17	0.135194
$147$	0	0
$148$	−4.15246e18	−1.48279
$149$	−1.55747e18	−0.525214	−0.262607	−	0.964903i	$-0.584582\pi$
$149$	−1.55747e18	−0.525214	−0.262607	+	0.964903i	$0.584582\pi$
$150$	0	0
$151$	1.47356e18	0.443673	0.221837	−	0.975084i	$-0.428795\pi$
$151$	1.47356e18	0.443673	0.221837	+	0.975084i	$0.428795\pi$
$152$	4.02102e18	1.14463
$153$	0	0
$154$	−9.00036e17	−0.229263
$155$	2.14808e18	0.517883
$156$	0	0
$157$	5.10804e18	1.10435	0.552176	−	0.833728i	$-0.313798\pi$
$157$	5.10804e18	1.10435	0.552176	+	0.833728i	$0.313798\pi$
$158$	3.04811e18	0.624375
$159$	0	0
$160$	1.84572e18	0.339740
$161$	3.29319e18	0.574905
$162$	0	0
$163$	6.07675e18	0.955161	0.477580	−	0.878588i	$-0.341514\pi$
$163$	6.07675e18	0.955161	0.477580	+	0.878588i	$0.341514\pi$
$164$	6.55994e18	0.978875
$165$	0	0
$166$	−2.03284e18	−0.273643
$167$	4.14077e18	0.529653	0.264827	−	0.964296i	$-0.414685\pi$
$167$	4.14077e18	0.529653	0.264827	+	0.964296i	$0.414685\pi$
$168$	0	0
$169$	3.93870e18	0.455319
$170$	−6.61302e17	−0.0727083
$171$	0	0
$172$	6.52895e18	0.649908
$173$	−7.62197e18	−0.722229	−0.361115	−	0.932521i	$-0.617604\pi$
$173$	−7.62197e18	−0.722229	−0.361115	+	0.932521i	$0.617604\pi$
$174$	0	0
$175$	3.90722e18	0.335772
$176$	−6.15430e18	−0.503873
$177$	0	0
$178$	6.62889e18	0.493027
$179$	−2.43355e19	−1.72580	−0.862898	−	0.505377i	$-0.831353\pi$
$179$	−2.43355e19	−1.72580	−0.862898	+	0.505377i	$0.831353\pi$
$180$	0	0
$181$	−1.00605e19	−0.649158	−0.324579	−	0.945859i	$-0.605223\pi$
$181$	−1.00605e19	−0.649158	−0.324579	+	0.945859i	$0.605223\pi$
$182$	−3.47053e18	−0.213693
$183$	0	0
$184$	−2.26185e19	−1.26915
$185$	−1.18479e19	−0.634865
$186$	0	0
$187$	1.22888e19	0.600972
$188$	2.96771e19	1.38701
$189$	0	0
$190$	5.02872e18	0.214809
$191$	1.39085e19	0.568196	0.284098	−	0.958795i	$-0.408306\pi$
$191$	1.39085e19	0.568196	0.284098	+	0.958795i	$0.408306\pi$
$192$	0	0
$193$	2.93143e19	1.09608	0.548040	−	0.836452i	$-0.315374\pi$
$193$	2.93143e19	1.09608	0.548040	+	0.836452i	$0.315374\pi$
$194$	1.90140e19	0.680391
$195$	0	0
$196$	−3.39916e18	−0.111479
$197$	5.50386e19	1.72864	0.864320	−	0.502943i	$-0.167749\pi$
$197$	5.50386e19	1.72864	0.864320	+	0.502943i	$0.167749\pi$
$198$	0	0
$199$	−3.27987e19	−0.945377	−0.472688	−	0.881230i	$-0.656716\pi$
$199$	−3.27987e19	−0.945377	−0.472688	+	0.881230i	$0.656716\pi$
$200$	−2.68358e19	−0.741241
$201$	0	0
$202$	−2.68703e19	−0.682003
$203$	1.20518e19	0.293317
$204$	0	0
$205$	1.87170e19	0.419110
$206$	−1.87854e19	−0.403597
$207$	0	0
$208$	−2.37310e19	−0.469653
$209$	−9.34471e19	−1.77551
$210$	0	0
$211$	4.61906e19	0.809380	0.404690	−	0.914454i	$-0.367379\pi$
$211$	4.61906e19	0.809380	0.404690	+	0.914454i	$0.367379\pi$
$212$	5.32795e19	0.896821
$213$	0	0
$214$	−3.45968e19	−0.537674
$215$	1.86285e19	0.278261
$216$	0	0
$217$	4.24324e19	0.585854
$218$	−1.45293e19	−0.192914
$219$	0	0
$220$	−2.74664e19	−0.337450
$221$	4.73854e19	0.560157
$222$	0	0
$223$	−1.09000e20	−1.19354	−0.596768	−	0.802414i	$-0.703549\pi$
$223$	−1.09000e20	−1.19354	−0.596768	+	0.802414i	$0.703549\pi$
$224$	3.64596e19	0.384330
$225$	0	0
$226$	4.05549e19	0.396389
$227$	−7.95341e18	−0.0748745	−0.0374372	−	0.999299i	$-0.511919\pi$
$227$	−7.95341e18	−0.0748745	−0.0374372	+	0.999299i	$0.511919\pi$
$228$	0	0
$229$	5.82844e19	0.509273	0.254636	−	0.967037i	$-0.418044\pi$
$229$	5.82844e19	0.509273	0.254636	+	0.967037i	$0.418044\pi$
$230$	−2.82869e19	−0.238176
$231$	0	0
$232$	−8.27752e19	−0.647519
$233$	−1.50170e20	−1.13255	−0.566276	−	0.824216i	$-0.691616\pi$
$233$	−1.50170e20	−1.13255	−0.566276	+	0.824216i	$0.691616\pi$
$234$	0	0
$235$	8.46755e19	0.593856
$236$	8.30412e19	0.561748
$237$	0	0
$238$	−1.30631e19	−0.0822511
$239$	−2.45916e20	−1.49419	−0.747093	−	0.664720i	$-0.768551\pi$
$239$	−2.45916e20	−1.49419	−0.747093	+	0.664720i	$0.768551\pi$
$240$	0	0
$241$	6.21102e19	0.351575	0.175787	−	0.984428i	$-0.443753\pi$
$241$	6.21102e19	0.351575	0.175787	+	0.984428i	$0.443753\pi$
$242$	−5.78992e19	−0.316404
$243$	0	0
$244$	−7.37142e19	−0.375611
$245$	−9.69855e18	−0.0477304
$246$	0	0
$247$	−3.60332e20	−1.65492
$248$	−2.91437e20	−1.29332
$249$	0	0
$250$	−7.13394e19	−0.295692
$251$	−3.51341e20	−1.40768	−0.703838	−	0.710361i	$-0.748532\pi$
$251$	−3.51341e20	−1.40768	−0.703838	+	0.710361i	$0.748532\pi$
$252$	0	0
$253$	5.25645e20	1.96865
$254$	−7.51189e19	−0.272059
$255$	0	0
$256$	−1.60748e20	−0.544634
$257$	−1.70495e20	−0.558829	−0.279415	−	0.960171i	$-0.590140\pi$
$257$	−1.70495e20	−0.558829	−0.279415	+	0.960171i	$0.590140\pi$
$258$	0	0
$259$	−2.34038e20	−0.718189
$260$	−1.05910e20	−0.314532
$261$	0	0
$262$	−8.64961e19	−0.240678
$263$	−2.05201e20	−0.552784	−0.276392	−	0.961045i	$-0.589139\pi$
$263$	−2.05201e20	−0.552784	−0.276392	+	0.961045i	$0.589139\pi$
$264$	0	0
$265$	1.52018e20	0.383978
$266$	9.93353e19	0.243002
$267$	0	0
$268$	4.10115e20	0.941368
$269$	4.30812e19	0.0958062	0.0479031	−	0.998852i	$-0.484746\pi$
$269$	4.30812e19	0.0958062	0.0479031	+	0.998852i	$0.484746\pi$
$270$	0	0
$271$	−5.41493e20	−1.13072	−0.565358	−	0.824845i	$-0.691262\pi$
$271$	−5.41493e20	−1.13072	−0.565358	+	0.824845i	$0.691262\pi$
$272$	−8.93232e19	−0.180771
$273$	0	0
$274$	−1.44017e20	−0.273863
$275$	6.23655e20	1.14978
$276$	0	0
$277$	−7.21087e20	−1.25000	−0.625000	−	0.780625i	$-0.714901\pi$
$277$	−7.21087e20	−1.25000	−0.625000	+	0.780625i	$0.714901\pi$
$278$	−2.64968e19	−0.0445464
$279$	0	0
$280$	6.66122e19	0.105368
$281$	−3.40535e20	−0.522586	−0.261293	−	0.965260i	$-0.584149\pi$
$281$	−3.40535e20	−0.522586	−0.261293	+	0.965260i	$0.584149\pi$
$282$	0	0
$283$	7.89527e20	1.14073	0.570364	−	0.821392i	$-0.306802\pi$
$283$	7.89527e20	1.14073	0.570364	+	0.821392i	$0.306802\pi$
$284$	−1.66640e20	−0.233654
$285$	0	0
$286$	−5.53953e20	−0.731748
$287$	3.69727e20	0.474117
$288$	0	0
$289$	−6.48882e20	−0.784393
$290$	−1.03519e20	−0.121518
$291$	0	0
$292$	2.03303e20	0.225107
$293$	9.20811e20	0.990366	0.495183	−	0.868789i	$-0.335101\pi$
$293$	9.20811e20	0.990366	0.495183	+	0.868789i	$0.335101\pi$
$294$	0	0
$295$	2.36935e20	0.240515
$296$	1.60744e21	1.58546
$297$	0	0
$298$	2.64262e20	0.246148
$299$	2.02689e21	1.83495
$300$	0	0
$301$	3.67981e20	0.314782
$302$	−2.50024e20	−0.207933
$303$	0	0
$304$	6.79238e20	0.534068
$305$	−2.10323e20	−0.160819
$306$	0	0
$307$	−1.04338e20	−0.0754684	−0.0377342	−	0.999288i	$-0.512014\pi$
$307$	−1.04338e20	−0.0754684	−0.0377342	+	0.999288i	$0.512014\pi$
$308$	−5.42560e20	−0.381739
$309$	0	0
$310$	−3.64473e20	−0.242712
$311$	−5.25503e20	−0.340496	−0.170248	−	0.985401i	$-0.554457\pi$
$311$	−5.25503e20	−0.340496	−0.170248	+	0.985401i	$0.554457\pi$
$312$	0	0
$313$	−1.35655e21	−0.832354	−0.416177	−	0.909284i	$-0.636630\pi$
$313$	−1.35655e21	−0.832354	−0.416177	+	0.909284i	$0.636630\pi$
$314$	−8.66700e20	−0.517567
$315$	0	0
$316$	1.83747e21	1.03963
$317$	8.62613e20	0.475130	0.237565	−	0.971372i	$-0.423651\pi$
$317$	8.62613e20	0.475130	0.237565	+	0.971372i	$0.423651\pi$
$318$	0	0
$319$	1.92367e21	1.00441
$320$	−5.73317e19	−0.0291488
$321$	0	0
$322$	−5.58767e20	−0.269436
$323$	−1.35629e21	−0.636986
$324$	0	0
$325$	2.40481e21	1.07170
$326$	−1.03106e21	−0.447647
$327$	0	0
$328$	−2.53939e21	−1.04665
$329$	1.67264e21	0.671798
$330$	0	0
$331$	2.23356e21	0.852038	0.426019	−	0.904714i	$-0.359916\pi$
$331$	2.23356e21	0.852038	0.426019	+	0.904714i	$0.359916\pi$
$332$	−1.22544e21	−0.455635
$333$	0	0
$334$	−7.02580e20	−0.248228
$335$	1.17015e21	0.403051
$336$	0	0
$337$	5.42566e21	1.77664	0.888318	−	0.459229i	$-0.151874\pi$
$337$	5.42566e21	1.77664	0.888318	+	0.459229i	$0.151874\pi$
$338$	−6.68294e20	−0.213391
$339$	0	0
$340$	−3.98647e20	−0.121065
$341$	6.77289e21	2.00614
$342$	0	0
$343$	−1.91581e20	−0.0539949
$344$	−2.52739e21	−0.694905
$345$	0	0
$346$	1.29325e21	0.338481
$347$	3.37032e21	0.860737	0.430368	−	0.902653i	$-0.358384\pi$
$347$	3.37032e21	0.860737	0.430368	+	0.902653i	$0.358384\pi$
$348$	0	0
$349$	−4.53090e21	−1.10197	−0.550983	−	0.834517i	$-0.685747\pi$
$349$	−4.53090e21	−1.10197	−0.550983	+	0.834517i	$0.685747\pi$
$350$	−6.62952e20	−0.157363
$351$	0	0
$352$	5.81954e21	1.31606
$353$	−3.02965e21	−0.668818	−0.334409	−	0.942428i	$-0.608537\pi$
$353$	−3.02965e21	−0.668818	−0.334409	+	0.942428i	$0.608537\pi$
$354$	0	0
$355$	−4.75461e20	−0.100040
$356$	3.99603e21	0.820926
$357$	0	0
$358$	4.12909e21	0.808815
$359$	5.05829e21	0.967612	0.483806	−	0.875175i	$-0.339254\pi$
$359$	5.05829e21	0.967612	0.483806	+	0.875175i	$0.339254\pi$
$360$	0	0
$361$	4.83319e21	0.881907
$362$	1.70700e21	0.304235
$363$	0	0
$364$	−2.09211e21	−0.355814
$365$	5.80068e20	0.0963806
$366$	0	0
$367$	−1.19647e22	−1.89775	−0.948876	−	0.315648i	$-0.897778\pi$
$367$	−1.19647e22	−1.89775	−0.948876	+	0.315648i	$0.897778\pi$
$368$	−3.82076e21	−0.592165
$369$	0	0
$370$	2.01027e21	0.297537
$371$	3.00291e21	0.434374
$372$	0	0
$373$	−1.01919e22	−1.40842	−0.704209	−	0.709992i	$-0.748698\pi$
$373$	−1.01919e22	−1.40842	−0.704209	+	0.709992i	$0.748698\pi$
$374$	−2.08508e21	−0.281653
$375$	0	0
$376$	−1.14882e22	−1.48304
$377$	7.41766e21	0.936193
$378$	0	0
$379$	1.18402e21	0.142865	0.0714324	−	0.997445i	$-0.477243\pi$
$379$	1.18402e21	0.142865	0.0714324	+	0.997445i	$0.477243\pi$
$380$	3.03142e21	0.357672
$381$	0	0
$382$	−2.35991e21	−0.266292
$383$	−9.05732e21	−0.999563	−0.499781	−	0.866152i	$-0.666586\pi$
$383$	−9.05732e21	−0.999563	−0.499781	+	0.866152i	$0.666586\pi$
$384$	0	0
$385$	−1.54805e21	−0.163443
$386$	−4.97387e21	−0.513691
$387$	0	0
$388$	1.14620e22	1.13290
$389$	2.27494e20	0.0219988	0.0109994	−	0.999940i	$-0.496499\pi$
$389$	2.27494e20	0.0219988	0.0109994	+	0.999940i	$0.496499\pi$
$390$	0	0
$391$	7.62920e21	0.706279
$392$	1.31583e21	0.119198
$393$	0	0
$394$	−9.33860e21	−0.810147
$395$	5.24270e21	0.445122
$396$	0	0
$397$	−2.31568e22	−1.88347	−0.941736	−	0.336354i	$-0.890806\pi$
$397$	−2.31568e22	−1.88347	−0.941736	+	0.336354i	$0.890806\pi$
$398$	5.56507e21	0.443062
$399$	0	0
$400$	−4.53316e21	−0.345852
$401$	−1.82783e22	−1.36524	−0.682619	−	0.730774i	$-0.739159\pi$
$401$	−1.82783e22	−1.36524	−0.682619	+	0.730774i	$0.739159\pi$
$402$	0	0
$403$	2.61162e22	1.86990
$404$	−1.61980e22	−1.13559
$405$	0	0
$406$	−2.04488e21	−0.137466
$407$	−3.73563e22	−2.45930
$408$	0	0
$409$	7.68503e21	0.485286	0.242643	−	0.970116i	$-0.421986\pi$
$409$	7.68503e21	0.485286	0.242643	+	0.970116i	$0.421986\pi$
$410$	−3.17578e21	−0.196421
$411$	0	0
$412$	−1.13242e22	−0.672019
$413$	4.68032e21	0.272082
$414$	0	0
$415$	−3.49644e21	−0.195082
$416$	2.24401e22	1.22668
$417$	0	0
$418$	1.58555e22	0.832112
$419$	1.60766e22	0.826753	0.413377	−	0.910560i	$-0.364349\pi$
$419$	1.60766e22	0.826753	0.413377	+	0.910560i	$0.364349\pi$
$420$	0	0
$421$	1.66192e22	0.820751	0.410375	−	0.911917i	$-0.365398\pi$
$421$	1.66192e22	0.820751	0.410375	+	0.911917i	$0.365398\pi$
$422$	−7.83732e21	−0.379325
$423$	0	0
$424$	−2.06248e22	−0.958913
$425$	9.05170e21	0.412500
$426$	0	0
$427$	−4.15463e21	−0.181926
$428$	−2.08557e22	−0.895266
$429$	0	0
$430$	−3.16077e21	−0.130410
$431$	−2.73146e22	−1.10494	−0.552468	−	0.833534i	$-0.686314\pi$
$431$	−2.73146e22	−1.10494	−0.552468	+	0.833534i	$0.686314\pi$
$432$	0	0
$433$	−1.90830e21	−0.0742164	−0.0371082	−	0.999311i	$-0.511815\pi$
$433$	−1.90830e21	−0.0742164	−0.0371082	+	0.999311i	$0.511815\pi$
$434$	−7.19966e21	−0.274567
$435$	0	0
$436$	−8.75856e21	−0.321216
$437$	−5.80145e22	−2.08662
$438$	0	0
$439$	2.45247e22	0.848506	0.424253	−	0.905544i	$-0.360537\pi$
$439$	2.45247e22	0.848506	0.424253	+	0.905544i	$0.360537\pi$
$440$	1.06324e22	0.360814
$441$	0	0
$442$	−8.04005e21	−0.262524
$443$	3.10174e22	0.993514	0.496757	−	0.867890i	$-0.334524\pi$
$443$	3.10174e22	0.993514	0.496757	+	0.867890i	$0.334524\pi$
$444$	0	0
$445$	1.14016e22	0.351483
$446$	1.84945e22	0.559365
$447$	0	0
$448$	−1.13251e21	−0.0329745
$449$	1.10133e22	0.314646	0.157323	−	0.987547i	$-0.449714\pi$
$449$	1.10133e22	0.314646	0.157323	+	0.987547i	$0.449714\pi$
$450$	0	0
$451$	5.90145e22	1.62352
$452$	2.44474e22	0.660017
$453$	0	0
$454$	1.34949e21	0.0350908
$455$	−5.96926e21	−0.152343
$456$	0	0
$457$	−9.29048e21	−0.228429	−0.114214	−	0.993456i	$-0.536435\pi$
$457$	−9.29048e21	−0.228429	−0.114214	+	0.993456i	$0.536435\pi$
$458$	−9.88932e21	−0.238677
$459$	0	0
$460$	−1.70519e22	−0.396581
$461$	−3.76152e22	−0.858826	−0.429413	−	0.903108i	$-0.641279\pi$
$461$	−3.76152e22	−0.858826	−0.429413	+	0.903108i	$0.641279\pi$
$462$	0	0
$463$	−3.54538e22	−0.780232	−0.390116	−	0.920766i	$-0.627565\pi$
$463$	−3.54538e22	−0.780232	−0.390116	+	0.920766i	$0.627565\pi$
$464$	−1.39826e22	−0.302123
$465$	0	0
$466$	2.54799e22	0.530784
$467$	−6.19686e22	−1.26759	−0.633794	−	0.773502i	$-0.718503\pi$
$467$	−6.19686e22	−1.26759	−0.633794	+	0.773502i	$0.718503\pi$
$468$	0	0
$469$	2.31146e22	0.455950
$470$	−1.43672e22	−0.278317
$471$	0	0
$472$	−3.21456e22	−0.600641
$473$	5.87356e22	1.07791
$474$	0	0
$475$	−6.88316e22	−1.21869
$476$	−7.87470e21	−0.136954
$477$	0	0
$478$	4.17255e22	0.700267
$479$	9.73266e22	1.60465	0.802324	−	0.596889i	$-0.203597\pi$
$479$	9.73266e22	1.60465	0.802324	+	0.596889i	$0.203597\pi$
$480$	0	0
$481$	−1.44046e23	−2.29228
$482$	−1.05385e22	−0.164770
$483$	0	0
$484$	−3.49028e22	−0.526836
$485$	3.27037e22	0.485056
$486$	0	0
$487$	−4.54443e22	−0.650854	−0.325427	−	0.945567i	$-0.605508\pi$
$487$	−4.54443e22	−0.650854	−0.325427	+	0.945567i	$0.605508\pi$
$488$	2.85351e22	0.401616
$489$	0	0
$490$	1.64559e21	0.0223694
$491$	6.81622e22	0.910649	0.455324	−	0.890326i	$-0.349523\pi$
$491$	6.81622e22	0.910649	0.455324	+	0.890326i	$0.349523\pi$
$492$	0	0
$493$	2.79200e22	0.360344
$494$	6.11388e22	0.775600
$495$	0	0
$496$	−4.92301e22	−0.603443
$497$	−9.39206e21	−0.113170
$498$	0	0
$499$	1.17826e23	1.37211	0.686054	−	0.727551i	$-0.259342\pi$
$499$	1.17826e23	1.37211	0.686054	+	0.727551i	$0.259342\pi$
$500$	−4.30049e22	−0.492349
$501$	0	0
$502$	5.96134e22	0.659724
$503$	−2.37499e22	−0.258425	−0.129212	−	0.991617i	$-0.541245\pi$
$503$	−2.37499e22	−0.258425	−0.129212	+	0.991617i	$0.541245\pi$
$504$	0	0
$505$	−4.62165e22	−0.486206
$506$	−8.91882e22	−0.922631
$507$	0	0
$508$	−4.52832e22	−0.452998
$509$	9.62819e22	0.947204	0.473602	−	0.880739i	$-0.342954\pi$
$509$	9.62819e22	0.947204	0.473602	+	0.880739i	$0.342954\pi$
$510$	0	0
$511$	1.14584e22	0.109030
$512$	−7.70108e22	−0.720704
$513$	0	0
$514$	2.89284e22	0.261902
$515$	−3.23105e22	−0.287728
$516$	0	0
$517$	2.66981e23	2.30044
$518$	3.97101e22	0.336588
$519$	0	0
$520$	4.09984e22	0.336309
$521$	1.28582e23	1.03767	0.518834	−	0.854875i	$-0.326366\pi$
$521$	1.28582e23	1.03767	0.518834	+	0.854875i	$0.326366\pi$
$522$	0	0
$523$	4.24893e21	0.0331906	0.0165953	−	0.999862i	$-0.494717\pi$
$523$	4.24893e21	0.0331906	0.0165953	+	0.999862i	$0.494717\pi$
$524$	−5.21417e22	−0.400746
$525$	0	0
$526$	3.48172e22	0.259069
$527$	9.83014e22	0.719730
$528$	0	0
$529$	1.85285e23	1.31361
$530$	−2.57935e22	−0.179956
$531$	0	0
$532$	5.98814e22	0.404616
$533$	2.27559e23	1.51326
$534$	0	0
$535$	−5.95058e22	−0.383312
$536$	−1.58757e23	−1.00654
$537$	0	0
$538$	−7.30975e21	−0.0449007
$539$	−3.05795e22	−0.184895
$540$	0	0
$541$	−1.38337e23	−0.810516	−0.405258	−	0.914202i	$-0.632818\pi$
$541$	−1.38337e23	−0.810516	−0.405258	+	0.914202i	$0.632818\pi$
$542$	9.18771e22	0.529924
$543$	0	0
$544$	8.44645e22	0.472154
$545$	−2.49901e22	−0.137530
$546$	0	0
$547$	−1.61112e23	−0.859480	−0.429740	−	0.902953i	$-0.641395\pi$
$547$	−1.61112e23	−0.859480	−0.429740	+	0.902953i	$0.641395\pi$
$548$	−8.68165e22	−0.456003
$549$	0	0
$550$	−1.05818e23	−0.538860
$551$	−2.12312e23	−1.06460
$552$	0	0
$553$	1.03562e23	0.503544
$554$	1.22349e23	0.585827
$555$	0	0
$556$	−1.59728e22	−0.0741730
$557$	3.83446e23	1.75362	0.876808	−	0.480840i	$-0.159668\pi$
$557$	3.83446e23	1.75362	0.876808	+	0.480840i	$0.159668\pi$
$558$	0	0
$559$	2.26484e23	1.00470
$560$	1.12523e22	0.0491634
$561$	0	0
$562$	5.77798e22	0.244916
$563$	1.12860e23	0.471217	0.235608	−	0.971848i	$-0.424292\pi$
$563$	1.12860e23	0.471217	0.235608	+	0.971848i	$0.424292\pi$
$564$	0	0
$565$	6.97537e22	0.282589
$566$	−1.33962e23	−0.534615
$567$	0	0
$568$	6.45072e22	0.249831
$569$	1.50174e23	0.572981	0.286490	−	0.958083i	$-0.407511\pi$
$569$	1.50174e23	0.572981	0.286490	+	0.958083i	$0.407511\pi$
$570$	0	0
$571$	−1.01524e21	−0.00375976	−0.00187988	−	0.999998i	$-0.500598\pi$
$571$	−1.01524e21	−0.00375976	−0.00187988	+	0.999998i	$0.500598\pi$
$572$	−3.33935e23	−1.21841
$573$	0	0
$574$	−6.27330e22	−0.222201
$575$	3.87182e23	1.35126
$576$	0	0
$577$	−2.29872e23	−0.778917	−0.389458	−	0.921044i	$-0.627338\pi$
$577$	−2.29872e23	−0.778917	−0.389458	+	0.921044i	$0.627338\pi$
$578$	1.10098e23	0.367615
$579$	0	0
$580$	−6.24037e22	−0.202336
$581$	−6.90673e22	−0.220686
$582$	0	0
$583$	4.79312e23	1.48743
$584$	−7.86995e22	−0.240693
$585$	0	0
$586$	−1.56237e23	−0.464147
$587$	8.88716e22	0.260219	0.130110	−	0.991500i	$-0.458467\pi$
$587$	8.88716e22	0.260219	0.130110	+	0.991500i	$0.458467\pi$
$588$	0	0
$589$	−7.47511e23	−2.12636
$590$	−4.02016e22	−0.112720
$591$	0	0
$592$	2.71532e23	0.739751
$593$	−1.75217e23	−0.470557	−0.235278	−	0.971928i	$-0.575600\pi$
$593$	−1.75217e23	−0.470557	−0.235278	+	0.971928i	$0.575600\pi$
$594$	0	0
$595$	−2.24683e22	−0.0586375
$596$	1.59302e23	0.409854
$597$	0	0
$598$	−3.43909e23	−0.859971
$599$	−5.34079e23	−1.31667	−0.658336	−	0.752724i	$-0.728739\pi$
$599$	−5.34079e23	−1.31667	−0.658336	+	0.752724i	$0.728739\pi$
$600$	0	0
$601$	−5.23655e23	−1.25491	−0.627454	−	0.778653i	$-0.715903\pi$
$601$	−5.23655e23	−1.25491	−0.627454	+	0.778653i	$0.715903\pi$
$602$	−6.24366e22	−0.147526
$603$	0	0
$604$	−1.50720e23	−0.346223
$605$	−9.95855e22	−0.225567
$606$	0	0
$607$	4.32161e23	0.951791	0.475895	−	0.879502i	$-0.342124\pi$
$607$	4.32161e23	0.951791	0.475895	+	0.879502i	$0.342124\pi$
$608$	−6.42292e23	−1.39493
$609$	0	0
$610$	3.56863e22	0.0753699
$611$	1.02948e24	2.14421
$612$	0	0
$613$	−3.42612e23	−0.694046	−0.347023	−	0.937857i	$-0.612807\pi$
$613$	−3.42612e23	−0.694046	−0.347023	+	0.937857i	$0.612807\pi$
$614$	1.77034e22	0.0353691
$615$	0	0
$616$	2.10028e23	0.408170
$617$	−4.02144e23	−0.770828	−0.385414	−	0.922744i	$-0.625941\pi$
$617$	−4.02144e23	−0.770828	−0.385414	+	0.922744i	$0.625941\pi$
$618$	0	0
$619$	5.86756e23	1.09418	0.547088	−	0.837075i	$-0.315736\pi$
$619$	5.86756e23	1.09418	0.547088	+	0.837075i	$0.315736\pi$
$620$	−2.19712e23	−0.404133
$621$	0	0
$622$	8.91640e22	0.159577
$623$	2.25222e23	0.397614
$624$	0	0
$625$	3.94396e23	0.677567
$626$	2.30170e23	0.390093
$627$	0	0
$628$	−5.22465e23	−0.861787
$629$	−5.42188e23	−0.882306
$630$	0	0
$631$	−1.71101e23	−0.271021	−0.135511	−	0.990776i	$-0.543267\pi$
$631$	−1.71101e23	−0.271021	−0.135511	+	0.990776i	$0.543267\pi$
$632$	−7.11292e23	−1.11161
$633$	0	0
$634$	−1.46363e23	−0.222675
$635$	−1.29203e23	−0.193953
$636$	0	0
$637$	−1.17914e23	−0.172338
$638$	−3.26396e23	−0.470727
$639$	0	0
$640$	−2.32195e23	−0.326079
$641$	1.93358e21	0.00267959	0.00133980	−	0.999999i	$-0.499574\pi$
$641$	1.93358e21	0.00267959	0.00133980	+	0.999999i	$0.499574\pi$
$642$	0	0
$643$	−7.75825e23	−1.04706	−0.523529	−	0.852008i	$-0.675385\pi$
$643$	−7.75825e23	−1.04706	−0.523529	+	0.852008i	$0.675385\pi$
$644$	−3.36836e23	−0.448631
$645$	0	0
$646$	2.30126e23	0.298531
$647$	4.87052e23	0.623576	0.311788	−	0.950152i	$-0.399072\pi$
$647$	4.87052e23	0.623576	0.311788	+	0.950152i	$0.399072\pi$
$648$	0	0
$649$	7.47054e23	0.931691
$650$	−4.08033e23	−0.502264
$651$	0	0
$652$	−6.21547e23	−0.745366
$653$	−7.39792e23	−0.875684	−0.437842	−	0.899052i	$-0.644257\pi$
$653$	−7.39792e23	−0.875684	−0.437842	+	0.899052i	$0.644257\pi$
$654$	0	0
$655$	−1.48772e23	−0.171581
$656$	−4.28958e23	−0.488351
$657$	0	0
$658$	−2.83804e23	−0.314846
$659$	4.70939e22	0.0515749	0.0257875	−	0.999667i	$-0.491791\pi$
$659$	4.70939e22	0.0515749	0.0257875	+	0.999667i	$0.491791\pi$
$660$	0	0
$661$	−6.85000e21	−0.00731103	−0.00365551	−	0.999993i	$-0.501164\pi$
$661$	−6.85000e21	−0.00731103	−0.00365551	+	0.999993i	$0.501164\pi$
$662$	−3.78976e23	−0.399318
$663$	0	0
$664$	4.74372e23	0.487181
$665$	1.70855e23	0.173238
$666$	0	0
$667$	1.19427e24	1.18041
$668$	−4.23530e23	−0.413318
$669$	0	0
$670$	−1.98543e23	−0.188895
$671$	−6.63147e23	−0.622971
$672$	0	0
$673$	7.05203e23	0.645931	0.322966	−	0.946411i	$-0.395320\pi$
$673$	7.05203e23	0.645931	0.322966	+	0.946411i	$0.395320\pi$
$674$	−9.20592e23	−0.832641
$675$	0	0
$676$	−4.02861e23	−0.355311
$677$	1.31444e24	1.14482	0.572409	−	0.819968i	$-0.306009\pi$
$677$	1.31444e24	1.14482	0.572409	+	0.819968i	$0.306009\pi$
$678$	0	0
$679$	6.46016e23	0.548719
$680$	1.54318e23	0.129447
$681$	0	0
$682$	−1.14918e24	−0.940202
$683$	−8.44133e23	−0.682080	−0.341040	−	0.940049i	$-0.610779\pi$
$683$	−8.44133e23	−0.682080	−0.341040	+	0.940049i	$0.610779\pi$
$684$	0	0
$685$	−2.47707e23	−0.195240
$686$	3.25063e22	0.0253054
$687$	0	0
$688$	−4.26932e23	−0.324232
$689$	1.84823e24	1.38641
$690$	0	0
$691$	−1.54835e24	−1.13320	−0.566600	−	0.823993i	$-0.691741\pi$
$691$	−1.54835e24	−1.13320	−0.566600	+	0.823993i	$0.691741\pi$
$692$	7.79597e23	0.563596
$693$	0	0
$694$	−5.71854e23	−0.403394
$695$	−4.55740e22	−0.0317575
$696$	0	0
$697$	8.56533e23	0.582459
$698$	7.68774e23	0.516449
$699$	0	0
$700$	−3.99641e23	−0.262022
$701$	−1.05664e24	−0.684419	−0.342209	−	0.939624i	$-0.611175\pi$
$701$	−1.05664e24	−0.684419	−0.342209	+	0.939624i	$0.611175\pi$
$702$	0	0
$703$	4.12294e24	2.60668
$704$	−1.80766e23	−0.112915
$705$	0	0
$706$	5.14053e23	0.313449
$707$	−9.12942e23	−0.550019
$708$	0	0
$709$	−2.37391e24	−1.39628	−0.698138	−	0.715964i	$-0.745988\pi$
$709$	−2.37391e24	−1.39628	−0.698138	+	0.715964i	$0.745988\pi$
$710$	8.06732e22	0.0468849
$711$	0	0
$712$	−1.54688e24	−0.877763
$713$	4.20480e24	2.35767
$714$	0	0
$715$	−9.52790e23	−0.521670
$716$	2.48910e24	1.34674
$717$	0	0
$718$	−8.58259e23	−0.453483
$719$	−1.29765e24	−0.677581	−0.338790	−	0.940862i	$-0.610018\pi$
$719$	−1.29765e24	−0.677581	−0.338790	+	0.940862i	$0.610018\pi$
$720$	0	0
$721$	−6.38248e23	−0.325492
$722$	−8.20066e23	−0.413316
$723$	0	0
$724$	1.02901e24	0.506574
$725$	1.41694e24	0.689413
$726$	0	0
$727$	1.48171e24	0.704240	0.352120	−	0.935955i	$-0.385461\pi$
$727$	1.48171e24	0.704240	0.352120	+	0.935955i	$0.385461\pi$
$728$	8.09866e23	0.380449
$729$	0	0
$730$	−9.84223e22	−0.0451699
$731$	8.52486e23	0.386714
$732$	0	0
$733$	1.47050e24	0.651750	0.325875	−	0.945413i	$-0.394341\pi$
$733$	1.47050e24	0.651750	0.325875	+	0.945413i	$0.394341\pi$
$734$	2.03009e24	0.889404
$735$	0	0
$736$	3.61293e24	1.54667
$737$	3.68947e24	1.56131
$738$	0	0
$739$	2.95680e24	1.22277	0.611384	−	0.791334i	$-0.290613\pi$
$739$	2.95680e24	1.22277	0.611384	+	0.791334i	$0.290613\pi$
$740$	1.21184e24	0.495421
$741$	0	0
$742$	−5.09514e23	−0.203574
$743$	−3.52761e24	−1.39340	−0.696699	−	0.717364i	$-0.745349\pi$
$743$	−3.52761e24	−1.39340	−0.696699	+	0.717364i	$0.745349\pi$
$744$	0	0
$745$	4.54525e23	0.175481
$746$	1.72930e24	0.660072
$747$	0	0
$748$	−1.25693e24	−0.468972
$749$	−1.17545e24	−0.433621
$750$	0	0
$751$	−1.71735e24	−0.619328	−0.309664	−	0.950846i	$-0.600217\pi$
$751$	−1.71735e24	−0.619328	−0.309664	+	0.950846i	$0.600217\pi$
$752$	−1.94060e24	−0.691967
$753$	0	0
$754$	−1.25858e24	−0.438758
$755$	−4.30037e23	−0.148237
$756$	0	0
$757$	3.29628e24	1.11099	0.555494	−	0.831521i	$-0.312529\pi$
$757$	3.29628e24	1.11099	0.555494	+	0.831521i	$0.312529\pi$
$758$	−2.00897e23	−0.0669552
$759$	0	0
$760$	−1.17348e24	−0.382436
$761$	5.06982e24	1.63389	0.816945	−	0.576715i	$-0.195666\pi$
$761$	5.06982e24	1.63389	0.816945	+	0.576715i	$0.195666\pi$
$762$	0	0
$763$	−4.93644e23	−0.155581
$764$	−1.42261e24	−0.443395
$765$	0	0
$766$	1.53679e24	0.468457
$767$	2.88064e24	0.868416
$768$	0	0
$769$	1.74162e24	0.513548	0.256774	−	0.966472i	$-0.417340\pi$
$769$	1.74162e24	0.513548	0.256774	+	0.966472i	$0.417340\pi$
$770$	2.62663e23	0.0765997
$771$	0	0
$772$	−2.99835e24	−0.855333
$773$	−2.01656e23	−0.0568965	−0.0284482	−	0.999595i	$-0.509057\pi$
$773$	−2.01656e23	−0.0568965	−0.0284482	+	0.999595i	$0.509057\pi$
$774$	0	0
$775$	4.98880e24	1.37699
$776$	−4.43701e24	−1.21134
$777$	0	0
$778$	−3.85998e22	−0.0103100
$779$	−6.51331e24	−1.72081
$780$	0	0
$781$	−1.49912e24	−0.387529
$782$	−1.29447e24	−0.331006
$783$	0	0
$784$	2.22273e23	0.0556160
$785$	−1.49071e24	−0.368978
$786$	0	0
$787$	−2.23637e24	−0.541699	−0.270850	−	0.962622i	$-0.587305\pi$
$787$	−2.23637e24	−0.541699	−0.270850	+	0.962622i	$0.587305\pi$
$788$	−5.62950e24	−1.34895
$789$	0	0
$790$	−8.89548e23	−0.208612
$791$	1.37789e24	0.319678
$792$	0	0
$793$	−2.55709e24	−0.580663
$794$	3.92910e24	0.882711
$795$	0	0
$796$	3.35474e24	0.737731
$797$	1.69195e24	0.368122	0.184061	−	0.982915i	$-0.441076\pi$
$797$	1.69195e24	0.368122	0.184061	+	0.982915i	$0.441076\pi$
$798$	0	0
$799$	3.87495e24	0.825313
$800$	4.28658e24	0.903329
$801$	0	0
$802$	3.10134e24	0.639835
$803$	1.82895e24	0.373353
$804$	0	0
$805$	−9.61069e23	−0.192083
$806$	−4.43124e24	−0.876349
$807$	0	0
$808$	6.27032e24	1.21421
$809$	−4.88049e23	−0.0935192	−0.0467596	−	0.998906i	$-0.514889\pi$
$809$	−4.88049e23	−0.0935192	−0.0467596	+	0.998906i	$0.514889\pi$
$810$	0	0
$811$	−7.28775e24	−1.36747	−0.683733	−	0.729733i	$-0.739644\pi$
$811$	−7.28775e24	−1.36747	−0.683733	+	0.729733i	$0.739644\pi$
$812$	−1.23270e24	−0.228892
$813$	0	0
$814$	6.33838e24	1.15258
$815$	−1.77341e24	−0.319132
$816$	0	0
$817$	−6.48254e24	−1.14250
$818$	−1.30395e24	−0.227435
$819$	0	0
$820$	−1.91443e24	−0.327055
$821$	8.68268e24	1.46804	0.734018	−	0.679130i	$-0.237643\pi$
$821$	8.68268e24	1.46804	0.734018	+	0.679130i	$0.237643\pi$
$822$	0	0
$823$	−8.01837e24	−1.32797	−0.663984	−	0.747747i	$-0.731136\pi$
$823$	−8.01837e24	−1.32797	−0.663984	+	0.747747i	$0.731136\pi$
$824$	4.38366e24	0.718547
$825$	0	0
$826$	−7.94126e23	−0.127514
$827$	−1.04025e25	−1.65325	−0.826627	−	0.562751i	$-0.809743\pi$
$827$	−1.04025e25	−1.65325	−0.826627	+	0.562751i	$0.809743\pi$
$828$	0	0
$829$	−8.40608e24	−1.30882	−0.654410	−	0.756140i	$-0.727083\pi$
$829$	−8.40608e24	−1.30882	−0.654410	+	0.756140i	$0.727083\pi$
$830$	5.93254e23	0.0914276
$831$	0	0
$832$	−6.97034e23	−0.105246
$833$	−4.43829e23	−0.0663335
$834$	0	0
$835$	−1.20843e24	−0.176964
$836$	9.55803e24	1.38553
$837$	0	0
$838$	−2.72778e24	−0.387468
$839$	8.68249e24	1.22086	0.610432	−	0.792068i	$-0.290996\pi$
$839$	8.68249e24	1.22086	0.610432	+	0.792068i	$0.290996\pi$
$840$	0	0
$841$	−2.88657e24	−0.397756
$842$	−2.81983e24	−0.384654
$843$	0	0
$844$	−4.72450e24	−0.631605
$845$	−1.14945e24	−0.152128
$846$	0	0
$847$	−1.96717e24	−0.255172
$848$	−3.48398e24	−0.447415
$849$	0	0
$850$	−1.53583e24	−0.193323
$851$	−2.31918e25	−2.89024
$852$	0	0
$853$	−1.10718e25	−1.35255	−0.676274	−	0.736650i	$-0.736406\pi$
$853$	−1.10718e25	−1.35255	−0.676274	+	0.736650i	$0.736406\pi$
$854$	7.04932e23	0.0852620
$855$	0	0
$856$	8.07333e24	0.957250
$857$	4.56561e24	0.535997	0.267998	−	0.963419i	$-0.413638\pi$
$857$	4.56561e24	0.535997	0.267998	+	0.963419i	$0.413638\pi$
$858$	0	0
$859$	2.37515e24	0.273369	0.136685	−	0.990615i	$-0.456355\pi$
$859$	2.37515e24	0.273369	0.136685	+	0.990615i	$0.456355\pi$
$860$	−1.90538e24	−0.217143
$861$	0	0
$862$	4.63456e24	0.517842
$863$	1.17701e24	0.130224	0.0651119	−	0.997878i	$-0.479260\pi$
$863$	1.17701e24	0.130224	0.0651119	+	0.997878i	$0.479260\pi$
$864$	0	0
$865$	2.22436e24	0.241306
$866$	3.23788e23	0.0347824
$867$	0	0
$868$	−4.34010e24	−0.457175
$869$	1.65302e25	1.72429
$870$	0	0
$871$	1.42266e25	1.45528
$872$	3.39048e24	0.343456
$873$	0	0
$874$	9.84353e24	0.977921
$875$	−2.42382e24	−0.238469
$876$	0	0
$877$	2.33893e24	0.225695	0.112847	−	0.993612i	$-0.464003\pi$
$877$	2.33893e24	0.225695	0.112847	+	0.993612i	$0.464003\pi$
$878$	−4.16119e24	−0.397662
$879$	0	0
$880$	1.79604e24	0.168350
$881$	−1.77952e25	−1.65199	−0.825994	−	0.563679i	$-0.809386\pi$
$881$	−1.77952e25	−1.65199	−0.825994	+	0.563679i	$0.809386\pi$
$882$	0	0
$883$	3.71235e24	0.338051	0.169026	−	0.985612i	$-0.445938\pi$
$883$	3.71235e24	0.338051	0.169026	+	0.985612i	$0.445938\pi$
$884$	−4.84671e24	−0.437122
$885$	0	0
$886$	−5.26284e24	−0.465622
$887$	9.79998e24	0.858765	0.429383	−	0.903123i	$-0.358731\pi$
$887$	9.79998e24	0.858765	0.429383	+	0.903123i	$0.358731\pi$
$888$	0	0
$889$	−2.55223e24	−0.219409
$890$	−1.93455e24	−0.164727
$891$	0	0
$892$	1.11488e25	0.931384
$893$	−2.94662e25	−2.43830
$894$	0	0
$895$	7.10197e24	0.576611
$896$	−4.58668e24	−0.368876
$897$	0	0
$898$	−1.86866e24	−0.147463
$899$	1.53880e25	1.20289
$900$	0	0
$901$	6.95672e24	0.533634
$902$	−1.00132e25	−0.760882
$903$	0	0
$904$	−9.46369e24	−0.705714
$905$	2.93600e24	0.216892
$906$	0	0
$907$	−1.35840e25	−0.984842	−0.492421	−	0.870357i	$-0.663888\pi$
$907$	−1.35840e25	−0.984842	−0.492421	+	0.870357i	$0.663888\pi$
$908$	8.13498e23	0.0584288
$909$	0	0
$910$	1.01283e24	0.0713975
$911$	−1.80678e25	−1.26183	−0.630913	−	0.775853i	$-0.717320\pi$
$911$	−1.80678e25	−1.26183	−0.630913	+	0.775853i	$0.717320\pi$
$912$	0	0
$913$	−1.10243e25	−0.755697
$914$	1.57635e24	0.107056
$915$	0	0
$916$	−5.96149e24	−0.397414
$917$	−2.93878e24	−0.194101
$918$	0	0
$919$	−1.39175e24	−0.0902362	−0.0451181	−	0.998982i	$-0.514366\pi$
$919$	−1.39175e24	−0.0902362	−0.0451181	+	0.998982i	$0.514366\pi$
$920$	6.60087e24	0.424038
$921$	0	0
$922$	6.38230e24	0.402499
$923$	−5.78062e24	−0.361210
$924$	0	0
$925$	−2.75160e25	−1.68803
$926$	6.01557e24	0.365665
$927$	0	0
$928$	1.32220e25	0.789113
$929$	−1.74710e25	−1.03320	−0.516601	−	0.856226i	$-0.672803\pi$
$929$	−1.74710e25	−1.03320	−0.516601	+	0.856226i	$0.672803\pi$
$930$	0	0
$931$	3.37500e24	0.195975
$932$	1.53598e25	0.883794
$933$	0	0
$934$	1.05144e25	0.594070
$935$	−3.58630e24	−0.200793
$936$	0	0
$937$	−4.17552e24	−0.229575	−0.114787	−	0.993390i	$-0.536619\pi$
$937$	−4.17552e24	−0.229575	−0.114787	+	0.993390i	$0.536619\pi$
$938$	−3.92194e24	−0.213687
$939$	0	0
$940$	−8.66085e24	−0.463419
$941$	−9.89797e23	−0.0524849	−0.0262425	−	0.999656i	$-0.508354\pi$
$941$	−9.89797e23	−0.0524849	−0.0262425	+	0.999656i	$0.508354\pi$
$942$	0	0
$943$	3.66378e25	1.90801
$944$	−5.43011e24	−0.280251
$945$	0	0
$946$	−9.96589e24	−0.505175
$947$	9.70314e24	0.487459	0.243729	−	0.969843i	$-0.421629\pi$
$947$	9.70314e24	0.487459	0.243729	+	0.969843i	$0.421629\pi$
$948$	0	0
$949$	7.05242e24	0.347997
$950$	1.16789e25	0.571152
$951$	0	0
$952$	3.04833e24	0.146436
$953$	−7.79627e24	−0.371191	−0.185595	−	0.982626i	$-0.559421\pi$
$953$	−7.79627e24	−0.371191	−0.185595	+	0.982626i	$0.559421\pi$
$954$	0	0
$955$	−4.05901e24	−0.189842
$956$	2.51530e25	1.16600
$957$	0	0
$958$	−1.65138e25	−0.752037
$959$	−4.89309e24	−0.220864
$960$	0	0
$961$	3.16283e25	1.40258
$962$	2.44408e25	1.07430
$963$	0	0
$964$	−6.35280e24	−0.274354
$965$	−8.55496e24	−0.366215
$966$	0	0
$967$	−3.46373e25	−1.45686	−0.728432	−	0.685118i	$-0.759751\pi$
$967$	−3.46373e25	−1.45686	−0.728432	+	0.685118i	$0.759751\pi$
$968$	1.35111e25	0.563312
$969$	0	0
$970$	−5.54896e24	−0.227327
$971$	−1.73405e25	−0.704203	−0.352102	−	0.935962i	$-0.614533\pi$
$971$	−1.73405e25	−0.704203	−0.352102	+	0.935962i	$0.614533\pi$
$972$	0	0
$973$	−9.00250e23	−0.0359256
$974$	7.71070e24	0.305030
$975$	0	0
$976$	4.82021e24	0.187388
$977$	2.75581e25	1.06205	0.531025	−	0.847356i	$-0.321807\pi$
$977$	2.75581e25	1.06205	0.531025	+	0.847356i	$0.321807\pi$
$978$	0	0
$979$	3.59490e25	1.36155
$980$	9.91996e23	0.0372467
$981$	0	0
$982$	−1.15653e25	−0.426786
$983$	4.00417e25	1.46490	0.732450	−	0.680821i	$-0.238377\pi$
$983$	4.00417e25	1.46490	0.732450	+	0.680821i	$0.238377\pi$
$984$	0	0
$985$	−1.60622e25	−0.577561
$986$	−4.73730e24	−0.168879
$987$	0	0
$988$	3.68557e25	1.29143
$989$	3.64647e25	1.26679
$990$	0	0
$991$	−3.64139e25	−1.24349	−0.621744	−	0.783221i	$-0.713576\pi$
$991$	−3.64139e25	−1.24349	−0.621744	+	0.783221i	$0.713576\pi$
$992$	4.65522e25	1.57613
$993$	0	0
$994$	1.59359e24	0.0530385
$995$	9.57182e24	0.315863
$996$	0	0
$997$	−3.05694e25	−0.991695	−0.495847	−	0.868410i	$-0.665142\pi$
$997$	−3.05694e25	−0.991695	−0.495847	+	0.868410i	$0.665142\pi$
$998$	−1.99920e25	−0.643054
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.18.a.f.1.2		5
3.2	odd	2		21.18.a.d.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.a.d.1.4	✓	5	3.2	odd	2
63.18.a.f.1.2		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	63.a (trivial)

\(f(q)\)	\(=\)	\(q-169.674 q^{2} -102283. q^{4} -291836. q^{5} -5.76480e6 q^{7} +3.95942e7 q^{8} +O(q^{10})\)	\(q-169.674 q^{2} -102283. q^{4} -291836. q^{5} -5.76480e6 q^{7} +3.95942e7 q^{8} +4.95168e7 q^{10} -9.20155e8 q^{11} -3.54811e9 q^{13} +9.78135e8 q^{14} +6.68833e9 q^{16} -1.33551e10 q^{17} +1.01556e11 q^{19} +2.98498e10 q^{20} +1.56126e11 q^{22} -5.71257e11 q^{23} -6.77771e11 q^{25} +6.02022e11 q^{26} +5.89640e11 q^{28} -2.09059e12 q^{29} -7.36060e12 q^{31} -6.32452e12 q^{32} +2.26601e12 q^{34} +1.68237e12 q^{35} +4.05978e13 q^{37} -1.72313e13 q^{38} -1.15550e13 q^{40} -6.41353e13 q^{41} -6.38323e13 q^{43} +9.41161e13 q^{44} +9.69273e13 q^{46} -2.90148e14 q^{47} +3.32329e13 q^{49} +1.15000e14 q^{50} +3.62911e14 q^{52} -5.20904e14 q^{53} +2.68534e14 q^{55} -2.28253e14 q^{56} +3.54718e14 q^{58} -8.11878e14 q^{59} +7.20690e14 q^{61} +1.24890e15 q^{62} +1.96452e14 q^{64} +1.03547e15 q^{65} -4.00961e15 q^{67} +1.36600e15 q^{68} -2.85455e14 q^{70} +1.62921e15 q^{71} -1.98765e15 q^{73} -6.88838e15 q^{74} -1.03874e16 q^{76} +5.30451e15 q^{77} -1.79646e16 q^{79} -1.95189e15 q^{80} +1.08821e16 q^{82} +1.19809e16 q^{83} +3.89749e15 q^{85} +1.08307e16 q^{86} -3.64328e16 q^{88} -3.90684e16 q^{89} +2.04542e16 q^{91} +5.84298e16 q^{92} +4.92304e16 q^{94} -2.96376e16 q^{95} -1.12062e17 q^{97} -5.63875e15 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 253 q^{2} + 441613 q^{4} + 906662 q^{5} - 28824005 q^{7} + 182238651 q^{8}+O(q^{10}) \) 5 * q + 253 * q^2 + 441613 * q^4 + 906662 * q^5 - 28824005 * q^7 + 182238651 * q^8	\( 5 q + 253 q^{2} + 441613 q^{4} + 906662 q^{5} - 28824005 q^{7} + 182238651 q^{8} + 1194057802 q^{10} - 1111338736 q^{11} + 5215478294 q^{13} - 1458494653 q^{14} + 62775861505 q^{16} - 25747891566 q^{17} + 142208068556 q^{19} + 129890562778 q^{20} - 448421189252 q^{22} + 700488736068 q^{23} + 1178351016379 q^{25} - 2889360071546 q^{26} - 2545811064013 q^{28} + 3529421241410 q^{29} + 1688850702072 q^{31} + 17321396050955 q^{32} + 40556147819358 q^{34} - 5226726004262 q^{35} + 16886745594894 q^{37} + 20515887907732 q^{38} + 320653834434294 q^{40} - 58103631330302 q^{41} + 49458422903068 q^{43} - 401313211061300 q^{44} + 325662527133360 q^{46} - 321151801515192 q^{47} + 166164652848005 q^{49} + 130885367368259 q^{50} - 447415499102234 q^{52} - 16\!\cdots\!54 q^{53}+ \cdots + 84\!\cdots\!53 q^{98}+O(q^{100}) \) 5 * q + 253 * q^2 + 441613 * q^4 + 906662 * q^5 - 28824005 * q^7 + 182238651 * q^8 + 1194057802 * q^10 - 1111338736 * q^11 + 5215478294 * q^13 - 1458494653 * q^14 + 62775861505 * q^16 - 25747891566 * q^17 + 142208068556 * q^19 + 129890562778 * q^20 - 448421189252 * q^22 + 700488736068 * q^23 + 1178351016379 * q^25 - 2889360071546 * q^26 - 2545811064013 * q^28 + 3529421241410 * q^29 + 1688850702072 * q^31 + 17321396050955 * q^32 + 40556147819358 * q^34 - 5226726004262 * q^35 + 16886745594894 * q^37 + 20515887907732 * q^38 + 320653834434294 * q^40 - 58103631330302 * q^41 + 49458422903068 * q^43 - 401313211061300 * q^44 + 325662527133360 * q^46 - 321151801515192 * q^47 + 166164652848005 * q^49 + 130885367368259 * q^50 - 447415499102234 * q^52 - 1624886228519454 * q^53 + 1551981825532832 * q^55 - 1050569557523451 * q^56 + 3599479065043546 * q^58 - 4642231410191796 * q^59 + 383521828948430 * q^61 - 3303800808324960 * q^62 + 7678662933303305 * q^64 - 1668701347292044 * q^65 - 4060475251851460 * q^67 + 16890755118576270 * q^68 - 6883505611027402 * q^70 - 6398015136563460 * q^71 - 15734132975098902 * q^73 + 25189581013328238 * q^74 - 14323380376996940 * q^76 + 6406646656631536 * q^77 + 2199683795891080 * q^79 + 115762642448214658 * q^80 - 6015570522729706 * q^82 - 23947511376405780 * q^83 + 21310596918487932 * q^85 + 3933835697843468 * q^86 - 87148613365646124 * q^88 + 12131366869070066 * q^89 - 30066194484729494 * q^91 + 198814114679296704 * q^92 + 14990206001176800 * q^94 + 239731994312770088 * q^95 + 4112564616338706 * q^97 + 8407931434109053 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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