LMFDB - Embedded newform 9.18.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,18,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	9.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:	$16.4899878610$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14569}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3642 $ x^2 - x - 3642
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$60.8511$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-659.106 q^{2} +303349. q^{4} +1.08318e6 q^{5} +1.59855e6 q^{7} -1.13549e8 q^{8} +O(q^{10})$	\(q-659.106 q^{2} +303349. q^{4} +1.08318e6 q^{5} +1.59855e6 q^{7} -1.13549e8 q^{8} -7.13934e8 q^{10} +4.47381e8 q^{11} -2.48486e9 q^{13} -1.05361e9 q^{14} +3.50803e10 q^{16} +2.48745e10 q^{17} +8.23042e10 q^{19} +3.28583e11 q^{20} -2.94872e11 q^{22} -6.43083e11 q^{23} +4.10349e11 q^{25} +1.63779e12 q^{26} +4.84918e11 q^{28} +9.82213e11 q^{29} +3.28632e12 q^{31} -8.23853e12 q^{32} -1.63949e13 q^{34} +1.73152e12 q^{35} +2.63492e13 q^{37} -5.42472e13 q^{38} -1.22994e14 q^{40} +3.33007e13 q^{41} +9.83107e13 q^{43} +1.35713e14 q^{44} +4.23860e14 q^{46} +1.62068e14 q^{47} -2.30075e14 q^{49} -2.70463e14 q^{50} -7.53780e14 q^{52} +1.40921e14 q^{53} +4.84596e14 q^{55} -1.81514e14 q^{56} -6.47383e14 q^{58} +9.80930e13 q^{59} +1.37376e15 q^{61} -2.16603e15 q^{62} +8.32030e14 q^{64} -2.69156e15 q^{65} -1.85816e15 q^{67} +7.54565e15 q^{68} -1.14126e15 q^{70} +6.17500e15 q^{71} -1.30214e16 q^{73} -1.73670e16 q^{74} +2.49669e16 q^{76} +7.15160e14 q^{77} +1.27538e16 q^{79} +3.79984e16 q^{80} -2.19487e16 q^{82} +1.42886e16 q^{83} +2.69436e16 q^{85} -6.47972e16 q^{86} -5.07996e16 q^{88} +3.77818e16 q^{89} -3.97217e15 q^{91} -1.95079e17 q^{92} -1.06820e17 q^{94} +8.91506e16 q^{95} +1.09404e17 q^{97} +1.51644e17 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 594 q^{2} + 176516 q^{4} - 382860 q^{5} + 24471568 q^{7} - 130340232 q^{8}+O(q^{10}) $ 2 * q - 594 * q^2 + 176516 * q^4 - 382860 * q^5 + 24471568 * q^7 - 130340232 * q^8	$ 2 q - 594 q^{2} + 176516 q^{4} - 382860 q^{5} + 24471568 q^{7} - 130340232 q^{8} - 809382420 q^{10} + 987553512 q^{11} - 2519398244 q^{13} + 435565296 q^{14} + 50611323920 q^{16} + 34313126364 q^{17} + 80053542184 q^{19} + 514526095080 q^{20} - 259702850088 q^{22} - 297228742704 q^{23} + 1796695260350 q^{25} + 1635537155076 q^{26} - 2416139220704 q^{28} + 470374069572 q^{29} + 3400754454592 q^{31} - 5026499631648 q^{32} - 15780403538748 q^{34} - 31801338154080 q^{35} + 10652012180428 q^{37} - 54393717084264 q^{38} - 98377731579600 q^{40} + 113376799448748 q^{41} + 61637031489880 q^{43} + 67200775334352 q^{44} + 446377123388592 q^{46} + 279645641926560 q^{47} + 60469362475890 q^{49} - 180203550461550 q^{50} - 749398920924104 q^{52} + 530964038611476 q^{53} - 307321280077680 q^{55} - 565580346246720 q^{56} - 680706445363812 q^{58} - 17\!\cdots\!56 q^{59}+ \cdots + 17\!\cdots\!26 q^{98}+O(q^{100}) $ 2 * q - 594 * q^2 + 176516 * q^4 - 382860 * q^5 + 24471568 * q^7 - 130340232 * q^8 - 809382420 * q^10 + 987553512 * q^11 - 2519398244 * q^13 + 435565296 * q^14 + 50611323920 * q^16 + 34313126364 * q^17 + 80053542184 * q^19 + 514526095080 * q^20 - 259702850088 * q^22 - 297228742704 * q^23 + 1796695260350 * q^25 + 1635537155076 * q^26 - 2416139220704 * q^28 + 470374069572 * q^29 + 3400754454592 * q^31 - 5026499631648 * q^32 - 15780403538748 * q^34 - 31801338154080 * q^35 + 10652012180428 * q^37 - 54393717084264 * q^38 - 98377731579600 * q^40 + 113376799448748 * q^41 + 61637031489880 * q^43 + 67200775334352 * q^44 + 446377123388592 * q^46 + 279645641926560 * q^47 + 60469362475890 * q^49 - 180203550461550 * q^50 - 749398920924104 * q^52 + 530964038611476 * q^53 - 307321280077680 * q^55 - 565580346246720 * q^56 - 680706445363812 * q^58 - 1727524231086456 * q^59 + 2784287656027900 * q^61 - 2158582756499136 * q^62 - 994533569423296 * q^64 - 2640922679811240 * q^65 - 3329301676696184 * q^67 + 6348514481766072 * q^68 - 3324459101139360 * q^70 + 13489402206504816 * q^71 + 436589918136724 * q^73 - 18388942762073004 * q^74 + 25252347669111376 * q^76 + 13070541011736384 * q^77 + 4376041565214880 * q^79 + 15229171694708640 * q^80 - 16735234653750924 * q^82 + 39886442265612888 * q^83 + 13106143850552280 * q^85 - 67184884152159768 * q^86 - 59869809989481888 * q^88 - 6972184096107444 * q^89 - 4762196572326688 * q^91 - 238944325336039008 * q^92 - 99165314702307744 * q^94 + 92450059415485200 * q^95 + 183569555712460996 * q^97 + 170560284296616126 * 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 $

$2$	−659.106	−1.82054	−0.910271	−	0.414014i	$-0.864127\pi$
$2$	−659.106	−1.82054	−0.910271	+	0.414014i	$0.864127\pi$
$3$	0	0
$3$	0	0
$4$	303349.	2.31437
$5$	1.08318e6	1.24010	0.620051	−	0.784562i	$-0.287112\pi$
$5$	1.08318e6	1.24010	0.620051	+	0.784562i	$0.287112\pi$
$6$	0	0
$7$	1.59855e6	0.104808	0.0524038	−	0.998626i	$-0.483312\pi$
$7$	1.59855e6	0.104808	0.0524038	+	0.998626i	$0.483312\pi$
$8$	−1.13549e8	−2.39287
$9$	0	0
$10$	−7.13934e8	−2.25766
$11$	4.47381e8	0.629274	0.314637	−	0.949212i	$-0.398117\pi$
$11$	4.47381e8	0.629274	0.314637	+	0.949212i	$0.398117\pi$
$12$	0	0
$13$	−2.48486e9	−0.844857	−0.422428	−	0.906396i	$-0.638822\pi$
$13$	−2.48486e9	−0.844857	−0.422428	+	0.906396i	$0.638822\pi$
$14$	−1.05361e9	−0.190806
$15$	0	0
$16$	3.50803e10	2.04194
$17$	2.48745e10	0.864844	0.432422	−	0.901671i	$-0.357659\pi$
$17$	2.48745e10	0.864844	0.432422	+	0.901671i	$0.357659\pi$
$18$	0	0
$19$	8.23042e10	1.11177	0.555887	−	0.831258i	$-0.312379\pi$
$19$	8.23042e10	1.11177	0.555887	+	0.831258i	$0.312379\pi$
$20$	3.28583e11	2.87005
$21$	0	0
$22$	−2.94872e11	−1.14562
$23$	−6.43083e11	−1.71230	−0.856151	−	0.516726i	$-0.827150\pi$
$23$	−6.43083e11	−1.71230	−0.856151	+	0.516726i	$0.827150\pi$
$24$	0	0
$25$	4.10349e11	0.537852
$26$	1.63779e12	1.53810
$27$	0	0
$28$	4.84918e11	0.242563
$29$	9.82213e11	0.364605	0.182302	−	0.983243i	$-0.441645\pi$
$29$	9.82213e11	0.364605	0.182302	+	0.983243i	$0.441645\pi$
$30$	0	0
$31$	3.28632e12	0.692046	0.346023	−	0.938226i	$-0.387532\pi$
$31$	3.28632e12	0.692046	0.346023	+	0.938226i	$0.387532\pi$
$32$	−8.23853e12	−1.32457
$33$	0	0
$34$	−1.63949e13	−1.57448
$35$	1.73152e12	0.129972
$36$	0	0
$37$	2.63492e13	1.23326	0.616628	−	0.787254i	$-0.288498\pi$
$37$	2.63492e13	1.23326	0.616628	+	0.787254i	$0.288498\pi$
$38$	−5.42472e13	−2.02403
$39$	0	0
$40$	−1.22994e14	−2.96740
$41$	3.33007e13	0.651314	0.325657	−	0.945488i	$-0.394415\pi$
$41$	3.33007e13	0.651314	0.325657	+	0.945488i	$0.394415\pi$
$42$	0	0
$43$	9.83107e13	1.28268	0.641341	−	0.767256i	$-0.278378\pi$
$43$	9.83107e13	1.28268	0.641341	+	0.767256i	$0.278378\pi$
$44$	1.35713e14	1.45637
$45$	0	0
$46$	4.23860e14	3.11732
$47$	1.62068e14	0.992811	0.496406	−	0.868091i	$-0.334653\pi$
$47$	1.62068e14	0.992811	0.496406	+	0.868091i	$0.334653\pi$
$48$	0	0
$49$	−2.30075e14	−0.989015
$50$	−2.70463e14	−0.979182
$51$	0	0
$52$	−7.53780e14	−1.95531
$53$	1.40921e14	0.310907	0.155453	−	0.987843i	$-0.450316\pi$
$53$	1.40921e14	0.310907	0.155453	+	0.987843i	$0.450316\pi$
$54$	0	0
$55$	4.84596e14	0.780363
$56$	−1.81514e14	−0.250790
$57$	0	0
$58$	−6.47383e14	−0.663778
$59$	9.80930e13	0.0869753	0.0434876	−	0.999054i	$-0.486153\pi$
$59$	9.80930e13	0.0869753	0.0434876	+	0.999054i	$0.486153\pi$
$60$	0	0
$61$	1.37376e15	0.917503	0.458751	−	0.888565i	$-0.348297\pi$
$61$	1.37376e15	0.917503	0.458751	+	0.888565i	$0.348297\pi$
$62$	−2.16603e15	−1.25990
$63$	0	0
$64$	8.32030e14	0.369495
$65$	−2.69156e15	−1.04771
$66$	0	0
$67$	−1.85816e15	−0.559046	−0.279523	−	0.960139i	$-0.590176\pi$
$67$	−1.85816e15	−0.559046	−0.279523	+	0.960139i	$0.590176\pi$
$68$	7.54565e15	2.00157
$69$	0	0
$70$	−1.14126e15	−0.236619
$71$	6.17500e15	1.13486	0.567428	−	0.823423i	$-0.307939\pi$
$71$	6.17500e15	1.13486	0.567428	+	0.823423i	$0.307939\pi$
$72$	0	0
$73$	−1.30214e16	−1.88979	−0.944896	−	0.327371i	$-0.893837\pi$
$73$	−1.30214e16	−1.88979	−0.944896	+	0.327371i	$0.893837\pi$
$74$	−1.73670e16	−2.24519
$75$	0	0
$76$	2.49669e16	2.57305
$77$	7.15160e14	0.0659526
$78$	0	0
$79$	1.27538e16	0.945824	0.472912	−	0.881110i	$-0.343203\pi$
$79$	1.27538e16	0.945824	0.472912	+	0.881110i	$0.343203\pi$
$80$	3.79984e16	2.53221
$81$	0	0
$82$	−2.19487e16	−1.18574
$83$	1.42886e16	0.696348	0.348174	−	0.937430i	$-0.386802\pi$
$83$	1.42886e16	0.696348	0.348174	+	0.937430i	$0.386802\pi$
$84$	0	0
$85$	2.69436e16	1.07250
$86$	−6.47972e16	−2.33517
$87$	0	0
$88$	−5.07996e16	−1.50577
$89$	3.77818e16	1.01734	0.508672	−	0.860961i	$-0.330137\pi$
$89$	3.77818e16	1.01734	0.508672	+	0.860961i	$0.330137\pi$
$90$	0	0
$91$	−3.97217e15	−0.0885473
$92$	−1.95079e17	−3.96290
$93$	0	0
$94$	−1.06820e17	−1.80745
$95$	8.91506e16	1.37871
$96$	0	0
$97$	1.09404e17	1.41733	0.708667	−	0.705543i	$-0.249297\pi$
$97$	1.09404e17	1.41733	0.708667	+	0.705543i	$0.249297\pi$
$98$	1.51644e17	1.80054
$99$	0	0
$100$	1.24479e17	1.24479
$101$	−1.19047e17	−1.09392	−0.546962	−	0.837157i	$-0.684216\pi$
$101$	−1.19047e17	−1.09392	−0.546962	+	0.837157i	$0.684216\pi$
$102$	0	0
$103$	−3.78871e16	−0.294697	−0.147348	−	0.989085i	$-0.547074\pi$
$103$	−3.78871e16	−0.294697	−0.147348	+	0.989085i	$0.547074\pi$
$104$	2.82153e17	2.02163
$105$	0	0
$106$	−9.28817e16	−0.566018
$107$	5.58893e16	0.314461	0.157230	−	0.987562i	$-0.449743\pi$
$107$	5.58893e16	0.314461	0.157230	+	0.987562i	$0.449743\pi$
$108$	0	0
$109$	3.40417e17	1.63639	0.818193	−	0.574944i	$-0.194976\pi$
$109$	3.40417e17	1.63639	0.818193	+	0.574944i	$0.194976\pi$
$110$	−3.19400e17	−1.42068
$111$	0	0
$112$	5.60775e16	0.214011
$113$	1.05411e16	0.0373009	0.0186505	−	0.999826i	$-0.494063\pi$
$113$	1.05411e16	0.0373009	0.0186505	+	0.999826i	$0.494063\pi$
$114$	0	0
$115$	−6.96577e17	−2.12343
$116$	2.97953e17	0.843831
$117$	0	0
$118$	−6.46537e16	−0.158342
$119$	3.97630e16	0.0906422
$120$	0	0
$121$	−3.05297e17	−0.604015
$122$	−9.05454e17	−1.67035
$123$	0	0
$124$	9.96902e17	1.60165
$125$	−3.81921e17	−0.573110
$126$	0	0
$127$	−7.32464e17	−0.960406	−0.480203	−	0.877157i	$-0.659437\pi$
$127$	−7.32464e17	−0.960406	−0.480203	+	0.877157i	$0.659437\pi$
$128$	5.31445e17	0.651889
$129$	0	0
$130$	1.77402e18	1.90740
$131$	2.70892e17	0.272891	0.136446	−	0.990648i	$-0.456432\pi$
$131$	2.70892e17	0.272891	0.136446	+	0.990648i	$0.456432\pi$
$132$	0	0
$133$	1.31567e17	0.116522
$134$	1.22473e18	1.01777
$135$	0	0
$136$	−2.82447e18	−2.06946
$137$	−2.60762e18	−1.79523	−0.897614	−	0.440782i	$-0.854701\pi$
$137$	−2.60762e18	−1.79523	−0.897614	+	0.440782i	$0.854701\pi$
$138$	0	0
$139$	1.06238e18	0.646628	0.323314	−	0.946292i	$-0.395203\pi$
$139$	1.06238e18	0.646628	0.323314	+	0.946292i	$0.395203\pi$
$140$	5.25256e17	0.300803
$141$	0	0
$142$	−4.06998e18	−2.06605
$143$	−1.11168e18	−0.531646
$144$	0	0
$145$	1.06392e18	0.452147
$146$	8.58250e18	3.44044
$147$	0	0
$148$	7.99302e18	2.85421
$149$	1.93103e18	0.651186	0.325593	−	0.945510i	$-0.394436\pi$
$149$	1.93103e18	0.651186	0.325593	+	0.945510i	$0.394436\pi$
$150$	0	0
$151$	2.89305e18	0.871067	0.435533	−	0.900173i	$-0.356560\pi$
$151$	2.89305e18	0.871067	0.435533	+	0.900173i	$0.356560\pi$
$152$	−9.34555e18	−2.66032
$153$	0	0
$154$	−4.71366e17	−0.120069
$155$	3.55969e18	0.858208
$156$	0	0
$157$	−3.49613e18	−0.755858	−0.377929	−	0.925835i	$-0.623364\pi$
$157$	−3.49613e18	−0.755858	−0.377929	+	0.925835i	$0.623364\pi$
$158$	−8.40613e18	−1.72191
$159$	0	0
$160$	−8.92385e18	−1.64260
$161$	−1.02800e18	−0.179462
$162$	0	0
$163$	−1.15214e18	−0.181096	−0.0905481	−	0.995892i	$-0.528862\pi$
$163$	−1.15214e18	−0.181096	−0.0905481	+	0.995892i	$0.528862\pi$
$164$	1.01017e19	1.50738
$165$	0	0
$166$	−9.41771e18	−1.26773
$167$	−3.89891e18	−0.498715	−0.249358	−	0.968411i	$-0.580219\pi$
$167$	−3.89891e18	−0.498715	−0.249358	+	0.968411i	$0.580219\pi$
$168$	0	0
$169$	−2.47589e18	−0.286217
$170$	−1.77587e19	−1.95252
$171$	0	0
$172$	2.98225e19	2.96860
$173$	6.89759e17	0.0653590	0.0326795	−	0.999466i	$-0.489596\pi$
$173$	6.89759e17	0.0653590	0.0326795	+	0.999466i	$0.489596\pi$
$174$	0	0
$175$	6.55962e17	0.0563710
$176$	1.56942e19	1.28494
$177$	0	0
$178$	−2.49022e19	−1.85212
$179$	1.57675e18	0.111818	0.0559092	−	0.998436i	$-0.482194\pi$
$179$	1.57675e18	0.111818	0.0559092	+	0.998436i	$0.482194\pi$
$180$	0	0
$181$	−8.66463e18	−0.559091	−0.279545	−	0.960133i	$-0.590184\pi$
$181$	−8.66463e18	−0.559091	−0.279545	+	0.960133i	$0.590184\pi$
$182$	2.61808e18	0.161204
$183$	0	0
$184$	7.30214e19	4.09731
$185$	2.85411e19	1.52936
$186$	0	0
$187$	1.11284e19	0.544224
$188$	4.91633e19	2.29773
$189$	0	0
$190$	−5.87597e19	−2.51000
$191$	−3.05782e19	−1.24919	−0.624595	−	0.780949i	$-0.714736\pi$
$191$	−3.05782e19	−1.24919	−0.624595	+	0.780949i	$0.714736\pi$
$192$	0	0
$193$	−8.47673e18	−0.316950	−0.158475	−	0.987363i	$-0.550658\pi$
$193$	−8.47673e18	−0.316950	−0.158475	+	0.987363i	$0.550658\pi$
$194$	−7.21087e19	−2.58032
$195$	0	0
$196$	−6.97931e19	−2.28895
$197$	1.02174e18	0.0320906	0.0160453	−	0.999871i	$-0.494892\pi$
$197$	1.02174e18	0.0320906	0.0160453	+	0.999871i	$0.494892\pi$
$198$	0	0
$199$	1.36420e19	0.393213	0.196606	−	0.980482i	$-0.437008\pi$
$199$	1.36420e19	0.393213	0.196606	+	0.980482i	$0.437008\pi$
$200$	−4.65947e19	−1.28701
$201$	0	0
$202$	7.84647e19	1.99153
$203$	1.57011e18	0.0382133
$204$	0	0
$205$	3.60708e19	0.807696
$206$	2.49716e19	0.536507
$207$	0	0
$208$	−8.71695e19	−1.72515
$209$	3.68213e19	0.699609
$210$	0	0
$211$	3.54105e19	0.620485	0.310242	−	0.950657i	$-0.399590\pi$
$211$	3.54105e19	0.620485	0.310242	+	0.950657i	$0.399590\pi$
$212$	4.27482e19	0.719553
$213$	0	0
$214$	−3.68370e19	−0.572489
$215$	1.06489e20	1.59066
$216$	0	0
$217$	5.25334e18	0.0725317
$218$	−2.24371e20	−2.97911
$219$	0	0
$220$	1.47002e20	1.80605
$221$	−6.18095e19	−0.730670
$222$	0	0
$223$	−1.07563e20	−1.17780	−0.588900	−	0.808206i	$-0.700439\pi$
$223$	−1.07563e20	−1.17780	−0.588900	+	0.808206i	$0.700439\pi$
$224$	−1.31697e19	−0.138825
$225$	0	0
$226$	−6.94771e18	−0.0679078
$227$	3.19163e19	0.300464	0.150232	−	0.988651i	$-0.451998\pi$
$227$	3.19163e19	0.300464	0.150232	+	0.988651i	$0.451998\pi$
$228$	0	0
$229$	−3.62295e19	−0.316564	−0.158282	−	0.987394i	$-0.550595\pi$
$229$	−3.62295e19	−0.316564	−0.158282	+	0.987394i	$0.550595\pi$
$230$	4.59118e20	3.86579
$231$	0	0
$232$	−1.11529e20	−0.872451
$233$	−1.40197e20	−1.05734	−0.528669	−	0.848828i	$-0.677309\pi$
$233$	−1.40197e20	−1.05734	−0.528669	+	0.848828i	$0.677309\pi$
$234$	0	0
$235$	1.75550e20	1.23119
$236$	2.97564e19	0.201293
$237$	0	0
$238$	−2.62081e19	−0.165018
$239$	−1.59138e20	−0.966921	−0.483461	−	0.875366i	$-0.660620\pi$
$239$	−1.59138e20	−0.966921	−0.483461	+	0.875366i	$0.660620\pi$
$240$	0	0
$241$	−7.13132e19	−0.403669	−0.201834	−	0.979420i	$-0.564690\pi$
$241$	−7.13132e19	−0.403669	−0.201834	+	0.979420i	$0.564690\pi$
$242$	2.01223e20	1.09963
$243$	0	0
$244$	4.16729e20	2.12344
$245$	−2.49214e20	−1.22648
$246$	0	0
$247$	−2.04514e20	−0.939289
$248$	−3.73158e20	−1.65597
$249$	0	0
$250$	2.51726e20	1.04337
$251$	1.69237e20	0.678063	0.339031	−	0.940775i	$-0.389901\pi$
$251$	1.69237e20	0.678063	0.339031	+	0.940775i	$0.389901\pi$
$252$	0	0
$253$	−2.87703e20	−1.07751
$254$	4.82772e20	1.74846
$255$	0	0
$256$	−4.59335e20	−1.55629
$257$	−4.63024e20	−1.51765	−0.758826	−	0.651293i	$-0.774227\pi$
$257$	−4.63024e20	−1.51765	−0.758826	+	0.651293i	$0.774227\pi$
$258$	0	0
$259$	4.21205e19	0.129255
$260$	−8.16482e20	−2.42479
$261$	0	0
$262$	−1.78546e20	−0.496810
$263$	5.31839e20	1.43270	0.716351	−	0.697740i	$-0.245811\pi$
$263$	5.31839e20	1.43270	0.716351	+	0.697740i	$0.245811\pi$
$264$	0	0
$265$	1.52643e20	0.385556
$266$	−8.67167e19	−0.212133
$267$	0	0
$268$	−5.63672e20	−1.29384
$269$	2.28606e20	0.508386	0.254193	−	0.967154i	$-0.418190\pi$
$269$	2.28606e20	0.508386	0.254193	+	0.967154i	$0.418190\pi$
$270$	0	0
$271$	−3.88488e20	−0.811220	−0.405610	−	0.914046i	$-0.632941\pi$
$271$	−3.88488e20	−0.811220	−0.405610	+	0.914046i	$0.632941\pi$
$272$	8.72603e20	1.76596
$273$	0	0
$274$	1.71870e21	3.26829
$275$	1.83582e20	0.338456
$276$	0	0
$277$	8.66031e20	1.50126	0.750629	−	0.660724i	$-0.229751\pi$
$277$	8.66031e20	1.50126	0.750629	+	0.660724i	$0.229751\pi$
$278$	−7.00222e20	−1.17721
$279$	0	0
$280$	−1.96613e20	−0.311005
$281$	−1.08570e20	−0.166612	−0.0833059	−	0.996524i	$-0.526548\pi$
$281$	−1.08570e20	−0.166612	−0.0833059	+	0.996524i	$0.526548\pi$
$282$	0	0
$283$	4.17569e20	0.603314	0.301657	−	0.953416i	$-0.402460\pi$
$283$	4.17569e20	0.603314	0.301657	+	0.953416i	$0.402460\pi$
$284$	1.87318e21	2.62648
$285$	0	0
$286$	7.32714e20	0.967884
$287$	5.32328e19	0.0682626
$288$	0	0
$289$	−2.08501e20	−0.252044
$290$	−7.01235e20	−0.823153
$291$	0	0
$292$	−3.95004e21	−4.37368
$293$	−2.71816e20	−0.292348	−0.146174	−	0.989259i	$-0.546696\pi$
$293$	−2.71816e20	−0.292348	−0.146174	+	0.989259i	$0.546696\pi$
$294$	0	0
$295$	1.06253e20	0.107858
$296$	−2.99193e21	−2.95102
$297$	0	0
$298$	−1.27275e21	−1.18551
$299$	1.59797e21	1.44665
$300$	0	0
$301$	1.57154e20	0.134435
$302$	−1.90683e21	−1.58581
$303$	0	0
$304$	2.88725e21	2.27017
$305$	1.48804e21	1.13780
$306$	0	0
$307$	2.41849e21	1.74932	0.874659	−	0.484739i	$-0.161085\pi$
$307$	2.41849e21	1.74932	0.874659	+	0.484739i	$0.161085\pi$
$308$	2.16943e20	0.152639
$309$	0	0
$310$	−2.34621e21	−1.56240
$311$	−9.44749e20	−0.612144	−0.306072	−	0.952008i	$-0.599015\pi$
$311$	−9.44749e20	−0.612144	−0.306072	+	0.952008i	$0.599015\pi$
$312$	0	0
$313$	−2.44821e21	−1.50218	−0.751089	−	0.660201i	$-0.770471\pi$
$313$	−2.44821e21	−1.50218	−0.751089	+	0.660201i	$0.770471\pi$
$314$	2.30432e21	1.37607
$315$	0	0
$316$	3.86886e21	2.18899
$317$	−3.49751e21	−1.92644	−0.963219	−	0.268718i	$-0.913400\pi$
$317$	−3.49751e21	−1.92644	−0.963219	+	0.268718i	$0.913400\pi$
$318$	0	0
$319$	4.39423e20	0.229436
$320$	9.01241e20	0.458212
$321$	0	0
$322$	6.77560e20	0.326718
$323$	2.04727e21	0.961511
$324$	0	0
$325$	−1.01966e21	−0.454408
$326$	7.59381e20	0.329693
$327$	0	0
$328$	−3.78126e21	−1.55851
$329$	2.59074e20	0.104054
$330$	0	0
$331$	−1.98378e20	−0.0756754	−0.0378377	−	0.999284i	$-0.512047\pi$
$331$	−1.98378e20	−0.0756754	−0.0378377	+	0.999284i	$0.512047\pi$
$332$	4.33444e21	1.61161
$333$	0	0
$334$	2.56979e21	0.907932
$335$	−2.01273e21	−0.693274
$336$	0	0
$337$	−4.38592e21	−1.43617	−0.718087	−	0.695954i	$-0.754982\pi$
$337$	−4.38592e21	−1.43617	−0.718087	+	0.695954i	$0.754982\pi$
$338$	1.63188e21	0.521070
$339$	0	0
$340$	8.17333e21	2.48215
$341$	1.47024e21	0.435487
$342$	0	0
$343$	−7.39657e20	−0.208464
$344$	−1.11631e22	−3.06928
$345$	0	0
$346$	−4.54625e20	−0.118989
$347$	1.91053e20	0.0487926	0.0243963	−	0.999702i	$-0.492234\pi$
$347$	1.91053e20	0.0487926	0.0243963	+	0.999702i	$0.492234\pi$
$348$	0	0
$349$	−3.63772e21	−0.884735	−0.442368	−	0.896834i	$-0.645861\pi$
$349$	−3.63772e21	−0.884735	−0.442368	+	0.896834i	$0.645861\pi$
$350$	−4.32349e20	−0.102626
$351$	0	0
$352$	−3.68576e21	−0.833517
$353$	−3.41663e21	−0.754245	−0.377123	−	0.926163i	$-0.623087\pi$
$353$	−3.41663e21	−0.754245	−0.377123	+	0.926163i	$0.623087\pi$
$354$	0	0
$355$	6.68866e21	1.40734
$356$	1.14611e22	2.35451
$357$	0	0
$358$	−1.03925e21	−0.203570
$359$	1.00013e22	1.91317	0.956587	−	0.291447i	$-0.0941366\pi$
$359$	1.00013e22	1.91317	0.956587	+	0.291447i	$0.0941366\pi$
$360$	0	0
$361$	1.29359e21	0.236039
$362$	5.71091e21	1.01785
$363$	0	0
$364$	−1.20495e21	−0.204931
$365$	−1.41046e22	−2.34353
$366$	0	0
$367$	1.19598e22	1.89698	0.948490	−	0.316807i	$-0.102611\pi$
$367$	1.19598e22	1.89698	0.948490	+	0.316807i	$0.102611\pi$
$368$	−2.25595e22	−3.49642
$369$	0	0
$370$	−1.88116e22	−2.78427
$371$	2.25269e20	0.0325853
$372$	0	0
$373$	6.67362e21	0.922224	0.461112	−	0.887342i	$-0.347451\pi$
$373$	6.67362e21	0.922224	0.461112	+	0.887342i	$0.347451\pi$
$374$	−7.33477e21	−0.990782
$375$	0	0
$376$	−1.84027e22	−2.37566
$377$	−2.44066e21	−0.308039
$378$	0	0
$379$	−1.30692e22	−1.57694	−0.788470	−	0.615073i	$-0.789127\pi$
$379$	−1.30692e22	−1.57694	−0.788470	+	0.615073i	$0.789127\pi$
$380$	2.70437e22	3.19085
$381$	0	0
$382$	2.01543e22	2.27420
$383$	−7.55282e19	−0.00833527	−0.00416763	−	0.999991i	$-0.501327\pi$
$383$	−7.55282e19	−0.00833527	−0.00416763	+	0.999991i	$0.501327\pi$
$384$	0	0
$385$	7.74650e20	0.0817879
$386$	5.58706e21	0.577021
$387$	0	0
$388$	3.31875e22	3.28024
$389$	−3.90337e21	−0.377457	−0.188729	−	0.982029i	$-0.560437\pi$
$389$	−3.90337e21	−0.377457	−0.188729	+	0.982029i	$0.560437\pi$
$390$	0	0
$391$	−1.59963e22	−1.48087
$392$	2.61248e22	2.36658
$393$	0	0
$394$	−6.73437e20	−0.0584224
$395$	1.38147e22	1.17292
$396$	0	0
$397$	6.50366e21	0.528979	0.264489	−	0.964389i	$-0.414797\pi$
$397$	6.50366e21	0.528979	0.264489	+	0.964389i	$0.414797\pi$
$398$	−8.99155e21	−0.715860
$399$	0	0
$400$	1.43951e22	1.09826
$401$	−2.12436e21	−0.158672	−0.0793361	−	0.996848i	$-0.525280\pi$
$401$	−2.12436e21	−0.158672	−0.0793361	+	0.996848i	$0.525280\pi$
$402$	0	0
$403$	−8.16604e21	−0.584680
$404$	−3.61128e22	−2.53175
$405$	0	0
$406$	−1.03487e21	−0.0695689
$407$	1.17881e22	0.776056
$408$	0	0
$409$	−1.66641e22	−1.05229	−0.526143	−	0.850396i	$-0.676362\pi$
$409$	−1.66641e22	−1.05229	−0.526143	+	0.850396i	$0.676362\pi$
$410$	−2.37745e22	−1.47044
$411$	0	0
$412$	−1.14930e22	−0.682037
$413$	1.56806e20	0.00911566
$414$	0	0
$415$	1.54772e22	0.863542
$416$	2.04716e22	1.11907
$417$	0	0
$418$	−2.42692e22	−1.27367
$419$	−2.00258e22	−1.02984	−0.514920	−	0.857238i	$-0.672178\pi$
$419$	−2.00258e22	−1.02984	−0.514920	+	0.857238i	$0.672178\pi$
$420$	0	0
$421$	1.39887e22	0.690846	0.345423	−	0.938447i	$-0.387736\pi$
$421$	1.39887e22	0.690846	0.345423	+	0.938447i	$0.387736\pi$
$422$	−2.33393e22	−1.12962
$423$	0	0
$424$	−1.60014e22	−0.743958
$425$	1.02072e22	0.465159
$426$	0	0
$427$	2.19602e21	0.0961612
$428$	1.69540e22	0.727779
$429$	0	0
$430$	−7.01873e22	−2.89585
$431$	3.18029e22	1.28650	0.643250	−	0.765656i	$-0.277586\pi$
$431$	3.18029e22	1.28650	0.643250	+	0.765656i	$0.277586\pi$
$432$	0	0
$433$	−1.40201e22	−0.545259	−0.272630	−	0.962119i	$-0.587893\pi$
$433$	−1.40201e22	−0.545259	−0.272630	+	0.962119i	$0.587893\pi$
$434$	−3.46251e21	−0.132047
$435$	0	0
$436$	1.03265e23	3.78720
$437$	−5.29284e22	−1.90369
$438$	0	0
$439$	6.28127e21	0.217320	0.108660	−	0.994079i	$-0.465344\pi$
$439$	6.28127e21	0.217320	0.108660	+	0.994079i	$0.465344\pi$
$440$	−5.50254e22	−1.86730
$441$	0	0
$442$	4.07391e22	1.33021
$443$	2.96942e22	0.951131	0.475566	−	0.879680i	$-0.342243\pi$
$443$	2.96942e22	0.951131	0.475566	+	0.879680i	$0.342243\pi$
$444$	0	0
$445$	4.09246e22	1.26161
$446$	7.08955e22	2.14423
$447$	0	0
$448$	1.33004e21	0.0387259
$449$	6.58706e22	1.88190	0.940952	−	0.338540i	$-0.109933\pi$
$449$	6.58706e22	1.88190	0.940952	+	0.338540i	$0.109933\pi$
$450$	0	0
$451$	1.48981e22	0.409855
$452$	3.19764e21	0.0863281
$453$	0	0
$454$	−2.10362e22	−0.547007
$455$	−4.30259e21	−0.109808
$456$	0	0
$457$	−4.15015e22	−1.02041	−0.510207	−	0.860052i	$-0.670431\pi$
$457$	−4.15015e22	−1.02041	−0.510207	+	0.860052i	$0.670431\pi$
$458$	2.38791e22	0.576317
$459$	0	0
$460$	−2.11306e23	−4.91440
$461$	−5.89682e22	−1.34636	−0.673178	−	0.739480i	$-0.735071\pi$
$461$	−5.89682e22	−1.34636	−0.673178	+	0.739480i	$0.735071\pi$
$462$	0	0
$463$	5.09403e22	1.12104	0.560522	−	0.828139i	$-0.310600\pi$
$463$	5.09403e22	1.12104	0.560522	+	0.828139i	$0.310600\pi$
$464$	3.44563e22	0.744501
$465$	0	0
$466$	9.24049e22	1.92493
$467$	−3.80032e22	−0.777369	−0.388684	−	0.921371i	$-0.627070\pi$
$467$	−3.80032e22	−0.777369	−0.388684	+	0.921371i	$0.627070\pi$
$468$	0	0
$469$	−2.97036e21	−0.0585922
$470$	−1.15706e23	−2.24143
$471$	0	0
$472$	−1.11384e22	−0.208120
$473$	4.39823e22	0.807158
$474$	0	0
$475$	3.37734e22	0.597970
$476$	1.20621e22	0.209780
$477$	0	0
$478$	1.04889e23	1.76032
$479$	−2.68315e22	−0.442378	−0.221189	−	0.975231i	$-0.570994\pi$
$479$	−2.68315e22	−0.442378	−0.221189	+	0.975231i	$0.570994\pi$
$480$	0	0
$481$	−6.54741e22	−1.04193
$482$	4.70030e22	0.734895
$483$	0	0
$484$	−9.26117e22	−1.39791
$485$	1.18504e23	1.75764
$486$	0	0
$487$	−1.42499e22	−0.204088	−0.102044	−	0.994780i	$-0.532538\pi$
$487$	−1.42499e22	−0.204088	−0.102044	+	0.994780i	$0.532538\pi$
$488$	−1.55989e23	−2.19546
$489$	0	0
$490$	1.64258e23	2.23286
$491$	−8.22531e22	−1.09890	−0.549452	−	0.835525i	$-0.685163\pi$
$491$	−8.22531e22	−1.09890	−0.549452	+	0.835525i	$0.685163\pi$
$492$	0	0
$493$	2.44320e22	0.315327
$494$	1.34797e23	1.71001
$495$	0	0
$496$	1.15285e23	1.41312
$497$	9.87103e21	0.118941
$498$	0	0
$499$	−1.57611e23	−1.83541	−0.917703	−	0.397267i	$-0.869959\pi$
$499$	−1.57611e23	−1.83541	−0.917703	+	0.397267i	$0.869959\pi$
$500$	−1.15855e23	−1.32639
$501$	0	0
$502$	−1.11545e23	−1.23444
$503$	−1.64035e23	−1.78488	−0.892439	−	0.451169i	$-0.851007\pi$
$503$	−1.64035e23	−1.78488	−0.892439	+	0.451169i	$0.851007\pi$
$504$	0	0
$505$	−1.28950e23	−1.35658
$506$	1.89627e23	1.96164
$507$	0	0
$508$	−2.22192e23	−2.22274
$509$	−6.26797e22	−0.616632	−0.308316	−	0.951284i	$-0.599765\pi$
$509$	−6.26797e22	−0.616632	−0.308316	+	0.951284i	$0.599765\pi$
$510$	0	0
$511$	−2.08154e22	−0.198064
$512$	2.33093e23	2.18139
$513$	0	0
$514$	3.05182e23	2.76295
$515$	−4.10387e22	−0.365454
$516$	0	0
$517$	7.25063e22	0.624750
$518$	−2.77619e22	−0.235313
$519$	0	0
$520$	3.05624e23	2.50703
$521$	−2.67297e21	−0.0215712	−0.0107856	−	0.999942i	$-0.503433\pi$
$521$	−2.67297e21	−0.0215712	−0.0107856	+	0.999942i	$0.503433\pi$
$522$	0	0
$523$	−1.11499e22	−0.0870975	−0.0435487	−	0.999051i	$-0.513866\pi$
$523$	−1.11499e22	−0.0870975	−0.0435487	+	0.999051i	$0.513866\pi$
$524$	8.21748e22	0.631572
$525$	0	0
$526$	−3.50538e23	−2.60829
$527$	8.17454e22	0.598512
$528$	0	0
$529$	2.72505e23	1.93198
$530$	−1.00608e23	−0.701920
$531$	0	0
$532$	3.99108e22	0.269675
$533$	−8.27475e22	−0.550267
$534$	0	0
$535$	6.05384e22	0.389963
$536$	2.10992e23	1.33772
$537$	0	0
$538$	−1.50676e23	−0.925537
$539$	−1.02931e23	−0.622361
$540$	0	0
$541$	1.32087e23	0.773895	0.386948	−	0.922102i	$-0.373529\pi$
$541$	1.32087e23	0.773895	0.386948	+	0.922102i	$0.373529\pi$
$542$	2.56055e23	1.47686
$543$	0	0
$544$	−2.04929e23	−1.14555
$545$	3.68734e23	2.02929
$546$	0	0
$547$	−1.49221e23	−0.796044	−0.398022	−	0.917376i	$-0.630303\pi$
$547$	−1.49221e23	−0.796044	−0.398022	+	0.917376i	$0.630303\pi$
$548$	−7.91020e23	−4.15482
$549$	0	0
$550$	−1.21000e23	−0.616174
$551$	8.08402e22	0.405358
$552$	0	0
$553$	2.03876e22	0.0991295
$554$	−5.70806e23	−2.73310
$555$	0	0
$556$	3.22272e23	1.49654
$557$	1.16177e23	0.531314	0.265657	−	0.964068i	$-0.414411\pi$
$557$	1.16177e23	0.531314	0.265657	+	0.964068i	$0.414411\pi$
$558$	0	0
$559$	−2.44288e23	−1.08368
$560$	6.07423e22	0.265395
$561$	0	0
$562$	7.15591e22	0.303324
$563$	1.98226e23	0.827635	0.413818	−	0.910360i	$-0.364195\pi$
$563$	1.98226e23	0.827635	0.413818	+	0.910360i	$0.364195\pi$
$564$	0	0
$565$	1.14180e22	0.0462569
$566$	−2.75222e23	−1.09836
$567$	0	0
$568$	−7.01164e23	−2.71556
$569$	1.75181e23	0.668393	0.334196	−	0.942504i	$-0.391535\pi$
$569$	1.75181e23	0.668393	0.334196	+	0.942504i	$0.391535\pi$
$570$	0	0
$571$	2.24895e23	0.832862	0.416431	−	0.909167i	$-0.363281\pi$
$571$	2.24895e23	0.832862	0.416431	+	0.909167i	$0.363281\pi$
$572$	−3.37227e23	−1.23043
$573$	0	0
$574$	−3.50861e22	−0.124275
$575$	−2.63888e23	−0.920965
$576$	0	0
$577$	1.19606e23	0.405282	0.202641	−	0.979253i	$-0.435048\pi$
$577$	1.19606e23	0.405282	0.202641	+	0.979253i	$0.435048\pi$
$578$	1.37424e23	0.458857
$579$	0	0
$580$	3.22738e23	1.04644
$581$	2.28410e22	0.0729825
$582$	0	0
$583$	6.30452e22	0.195645
$584$	1.47857e24	4.52202
$585$	0	0
$586$	1.79155e23	0.532231
$587$	3.75879e23	1.10059	0.550294	−	0.834971i	$-0.314516\pi$
$587$	3.75879e23	1.10059	0.550294	+	0.834971i	$0.314516\pi$
$588$	0	0
$589$	2.70478e23	0.769399
$590$	−7.00319e22	−0.196360
$591$	0	0
$592$	9.24338e23	2.51824
$593$	−5.09614e23	−1.36860	−0.684299	−	0.729201i	$-0.739892\pi$
$593$	−5.09614e23	−1.36860	−0.684299	+	0.729201i	$0.739892\pi$
$594$	0	0
$595$	4.30707e22	0.112406
$596$	5.85775e23	1.50709
$597$	0	0
$598$	−1.05323e24	−2.63369
$599$	−1.79949e23	−0.443631	−0.221816	−	0.975089i	$-0.571198\pi$
$599$	−1.79949e23	−0.443631	−0.221816	+	0.975089i	$0.571198\pi$
$600$	0	0
$601$	−2.48454e23	−0.595406	−0.297703	−	0.954659i	$-0.596220\pi$
$601$	−2.48454e23	−0.595406	−0.297703	+	0.954659i	$0.596220\pi$
$602$	−1.03581e23	−0.244744
$603$	0	0
$604$	8.77603e23	2.01597
$605$	−3.30693e23	−0.749040
$606$	0	0
$607$	−6.42239e23	−1.41447	−0.707233	−	0.706980i	$-0.750057\pi$
$607$	−6.42239e23	−1.41447	−0.707233	+	0.706980i	$0.750057\pi$
$608$	−6.78066e23	−1.47262
$609$	0	0
$610$	−9.80774e23	−2.07141
$611$	−4.02717e23	−0.838783
$612$	0	0
$613$	−1.05608e23	−0.213936	−0.106968	−	0.994262i	$-0.534114\pi$
$613$	−1.05608e23	−0.213936	−0.106968	+	0.994262i	$0.534114\pi$
$614$	−1.59404e24	−3.18470
$615$	0	0
$616$	−8.12057e22	−0.157816
$617$	7.88025e23	1.51048	0.755242	−	0.655446i	$-0.227519\pi$
$617$	7.88025e23	1.51048	0.755242	+	0.655446i	$0.227519\pi$
$618$	0	0
$619$	5.08064e23	0.947432	0.473716	−	0.880678i	$-0.342912\pi$
$619$	5.08064e23	0.947432	0.473716	+	0.880678i	$0.342912\pi$
$620$	1.07983e24	1.98621
$621$	0	0
$622$	6.22690e23	1.11443
$623$	6.03960e22	0.106625
$624$	0	0
$625$	−7.26762e23	−1.24857
$626$	1.61363e24	2.73478
$627$	0	0
$628$	−1.06055e24	−1.74934
$629$	6.55423e23	1.06658
$630$	0	0
$631$	−6.58521e23	−1.04309	−0.521543	−	0.853225i	$-0.674643\pi$
$631$	−6.58521e23	−1.04309	−0.521543	+	0.853225i	$0.674643\pi$
$632$	−1.44818e24	−2.26323
$633$	0	0
$634$	2.30523e24	3.50716
$635$	−7.93394e23	−1.19100
$636$	0	0
$637$	5.71704e23	0.835576
$638$	−2.89627e23	−0.417698
$639$	0	0
$640$	5.75653e23	0.808409
$641$	−8.38263e23	−1.16168	−0.580841	−	0.814017i	$-0.697276\pi$
$641$	−8.38263e23	−1.16168	−0.580841	+	0.814017i	$0.697276\pi$
$642$	0	0
$643$	4.04743e23	0.546243	0.273122	−	0.961980i	$-0.411944\pi$
$643$	4.04743e23	0.546243	0.273122	+	0.961980i	$0.411944\pi$
$644$	−3.11843e23	−0.415342
$645$	0	0
$646$	−1.34937e24	−1.75047
$647$	−1.11703e24	−1.43014	−0.715068	−	0.699055i	$-0.753604\pi$
$647$	−1.11703e24	−1.43014	−0.715068	+	0.699055i	$0.753604\pi$
$648$	0	0
$649$	4.38849e22	0.0547313
$650$	6.72063e23	0.827269
$651$	0	0
$652$	−3.49500e23	−0.419124
$653$	7.44989e23	0.881836	0.440918	−	0.897547i	$-0.354653\pi$
$653$	7.44989e23	0.881836	0.440918	+	0.897547i	$0.354653\pi$
$654$	0	0
$655$	2.93426e23	0.338413
$656$	1.16820e24	1.32994
$657$	0	0
$658$	−1.70757e23	−0.189435
$659$	1.19920e24	1.31331	0.656653	−	0.754192i	$-0.271971\pi$
$659$	1.19920e24	1.31331	0.656653	+	0.754192i	$0.271971\pi$
$660$	0	0
$661$	−8.62286e22	−0.0920320	−0.0460160	−	0.998941i	$-0.514653\pi$
$661$	−8.62286e22	−0.0920320	−0.0460160	+	0.998941i	$0.514653\pi$
$662$	1.30752e23	0.137770
$663$	0	0
$664$	−1.62246e24	−1.66627
$665$	1.42511e23	0.144499
$666$	0	0
$667$	−6.31644e23	−0.624313
$668$	−1.18273e24	−1.15421
$669$	0	0
$670$	1.32660e24	1.26213
$671$	6.14594e23	0.577360
$672$	0	0
$673$	1.93031e24	1.76807	0.884033	−	0.467425i	$-0.154818\pi$
$673$	1.93031e24	1.76807	0.884033	+	0.467425i	$0.154818\pi$
$674$	2.89079e24	2.61461
$675$	0	0
$676$	−7.51061e23	−0.662412
$677$	9.44660e22	0.0822757	0.0411379	−	0.999153i	$-0.486902\pi$
$677$	9.44660e22	0.0822757	0.0411379	+	0.999153i	$0.486902\pi$
$678$	0	0
$679$	1.74887e23	0.148547
$680$	−3.05942e24	−2.56634
$681$	0	0
$682$	−9.69042e23	−0.792821
$683$	−1.90689e24	−1.54081	−0.770404	−	0.637556i	$-0.779945\pi$
$683$	−1.90689e24	−1.54081	−0.770404	+	0.637556i	$0.779945\pi$
$684$	0	0
$685$	−2.82453e24	−2.22627
$686$	4.87513e23	0.379517
$687$	0	0
$688$	3.44876e24	2.61916
$689$	−3.50168e23	−0.262672
$690$	0	0
$691$	1.44684e24	1.05890	0.529451	−	0.848341i	$-0.322398\pi$
$691$	1.44684e24	1.05890	0.529451	+	0.848341i	$0.322398\pi$
$692$	2.09238e23	0.151265
$693$	0	0
$694$	−1.25924e23	−0.0888289
$695$	1.15075e24	0.801884
$696$	0	0
$697$	8.28337e23	0.563285
$698$	2.39765e24	1.61070
$699$	0	0
$700$	1.98986e23	0.130463
$701$	−3.28966e23	−0.213083	−0.106541	−	0.994308i	$-0.533978\pi$
$701$	−3.28966e23	−0.213083	−0.106541	+	0.994308i	$0.533978\pi$
$702$	0	0
$703$	2.16865e24	1.37110
$704$	3.72234e23	0.232514
$705$	0	0
$706$	2.25192e24	1.37313
$707$	−1.90303e23	−0.114651
$708$	0	0
$709$	−3.08015e24	−1.81167	−0.905833	−	0.423634i	$-0.860754\pi$
$709$	−3.08015e24	−1.81167	−0.905833	+	0.423634i	$0.860754\pi$
$710$	−4.40854e24	−2.56211
$711$	0	0
$712$	−4.29008e24	−2.43437
$713$	−2.11337e24	−1.18499
$714$	0	0
$715$	−1.20415e24	−0.659295
$716$	4.78307e23	0.258789
$717$	0	0
$718$	−6.59193e24	−3.48301
$719$	1.08990e24	0.569103	0.284551	−	0.958661i	$-0.408155\pi$
$719$	1.08990e24	0.569103	0.284551	+	0.958661i	$0.408155\pi$
$720$	0	0
$721$	−6.05644e22	−0.0308864
$722$	−8.52611e23	−0.429719
$723$	0	0
$724$	−2.62841e24	−1.29394
$725$	4.03050e23	0.196104
$726$	0	0
$727$	1.49760e24	0.711795	0.355897	−	0.934525i	$-0.384175\pi$
$727$	1.49760e24	0.711795	0.355897	+	0.934525i	$0.384175\pi$
$728$	4.51035e23	0.211882
$729$	0	0
$730$	9.29643e24	4.26650
$731$	2.44543e24	1.10932
$732$	0	0
$733$	−9.64969e23	−0.427691	−0.213845	−	0.976868i	$-0.568599\pi$
$733$	−9.64969e23	−0.427691	−0.213845	+	0.976868i	$0.568599\pi$
$734$	−7.88279e24	−3.45353
$735$	0	0
$736$	5.29806e24	2.26806
$737$	−8.31306e23	−0.351793
$738$	0	0
$739$	−3.37306e24	−1.39491	−0.697456	−	0.716627i	$-0.745685\pi$
$739$	−3.37306e24	−1.39491	−0.697456	+	0.716627i	$0.745685\pi$
$740$	8.65791e24	3.53951
$741$	0	0
$742$	−1.48476e23	−0.0593230
$743$	4.24164e24	1.67544	0.837719	−	0.546101i	$-0.183889\pi$
$743$	4.24164e24	1.67544	0.837719	+	0.546101i	$0.183889\pi$
$744$	0	0
$745$	2.09166e24	0.807537
$746$	−4.39862e24	−1.67895
$747$	0	0
$748$	3.37578e24	1.25954
$749$	8.93417e22	0.0329578
$750$	0	0
$751$	−8.44312e23	−0.304483	−0.152242	−	0.988343i	$-0.548649\pi$
$751$	−8.44312e23	−0.304483	−0.152242	+	0.988343i	$0.548649\pi$
$752$	5.68540e24	2.02726
$753$	0	0
$754$	1.60865e24	0.560798
$755$	3.13370e24	1.08021
$756$	0	0
$757$	3.10995e24	1.04819	0.524093	−	0.851661i	$-0.324404\pi$
$757$	3.10995e24	1.04819	0.524093	+	0.851661i	$0.324404\pi$
$758$	8.61398e24	2.87089
$759$	0	0
$760$	−1.01230e25	−3.29907
$761$	−5.22689e24	−1.68451	−0.842256	−	0.539078i	$-0.818773\pi$
$761$	−5.22689e24	−1.68451	−0.842256	+	0.539078i	$0.818773\pi$
$762$	0	0
$763$	5.44173e23	0.171506
$764$	−9.27588e24	−2.89109
$765$	0	0
$766$	4.97811e22	0.0151747
$767$	−2.43747e23	−0.0734817
$768$	0	0
$769$	−5.37000e23	−0.158343	−0.0791717	−	0.996861i	$-0.525228\pi$
$769$	−5.37000e23	−0.158343	−0.0791717	+	0.996861i	$0.525228\pi$
$770$	−5.10577e23	−0.148898
$771$	0	0
$772$	−2.57141e24	−0.733540
$773$	1.13193e23	0.0319370	0.0159685	−	0.999872i	$-0.494917\pi$
$773$	1.13193e23	0.0319370	0.0159685	+	0.999872i	$0.494917\pi$
$774$	0	0
$775$	1.34854e24	0.372219
$776$	−1.24227e25	−3.39149
$777$	0	0
$778$	2.57274e24	0.687177
$779$	2.74079e24	0.724113
$780$	0	0
$781$	2.76257e24	0.714135
$782$	1.05433e25	2.69599
$783$	0	0
$784$	−8.07110e24	−2.01951
$785$	−3.78695e24	−0.937341
$786$	0	0
$787$	4.40987e24	1.06817	0.534085	−	0.845431i	$-0.320656\pi$
$787$	4.40987e24	1.06817	0.534085	+	0.845431i	$0.320656\pi$
$788$	3.09945e23	0.0742696
$789$	0	0
$790$	−9.10539e24	−2.13535
$791$	1.68505e22	0.00390942
$792$	0	0
$793$	−3.41360e24	−0.775158
$794$	−4.28660e24	−0.963028
$795$	0	0
$796$	4.13830e24	0.910040
$797$	−1.93825e24	−0.421710	−0.210855	−	0.977517i	$-0.567625\pi$
$797$	−1.93825e24	−0.421710	−0.210855	+	0.977517i	$0.567625\pi$
$798$	0	0
$799$	4.03137e24	0.858627
$800$	−3.38067e24	−0.712423
$801$	0	0
$802$	1.40018e24	0.288869
$803$	−5.82553e24	−1.18920
$804$	0	0
$805$	−1.11351e24	−0.222551
$806$	5.38229e24	1.06443
$807$	0	0
$808$	1.35177e25	2.61761
$809$	5.28909e24	1.01349	0.506744	−	0.862096i	$-0.330849\pi$
$809$	5.28909e24	1.01349	0.506744	+	0.862096i	$0.330849\pi$
$810$	0	0
$811$	−9.67847e24	−1.81606	−0.908028	−	0.418909i	$-0.862413\pi$
$811$	−9.67847e24	−1.81606	−0.908028	+	0.418909i	$0.862413\pi$
$812$	4.76293e23	0.0884398
$813$	0	0
$814$	−7.76964e24	−1.41284
$815$	−1.24798e24	−0.224578
$816$	0	0
$817$	8.09138e24	1.42605
$818$	1.09834e25	1.91573
$819$	0	0
$820$	1.09420e25	1.86931
$821$	1.86577e24	0.315458	0.157729	−	0.987482i	$-0.449583\pi$
$821$	1.86577e24	0.315458	0.157729	+	0.987482i	$0.449583\pi$
$822$	0	0
$823$	−5.64893e23	−0.0935552	−0.0467776	−	0.998905i	$-0.514895\pi$
$823$	−5.64893e23	−0.0935552	−0.0467776	+	0.998905i	$0.514895\pi$
$824$	4.30204e24	0.705169
$825$	0	0
$826$	−1.03352e23	−0.0165954
$827$	3.63429e24	0.577595	0.288797	−	0.957390i	$-0.406745\pi$
$827$	3.63429e24	0.577595	0.288797	+	0.957390i	$0.406745\pi$
$828$	0	0
$829$	−1.24734e25	−1.94210	−0.971052	−	0.238870i	$-0.923223\pi$
$829$	−1.24734e25	−1.94210	−0.971052	+	0.238870i	$0.923223\pi$
$830$	−1.02011e25	−1.57211
$831$	0	0
$832$	−2.06748e24	−0.312171
$833$	−5.72300e24	−0.855344
$834$	0	0
$835$	−4.22323e24	−0.618458
$836$	1.11697e25	1.61916
$837$	0	0
$838$	1.31991e25	1.87487
$839$	1.32854e24	0.186809	0.0934045	−	0.995628i	$-0.470225\pi$
$839$	1.32854e24	0.186809	0.0934045	+	0.995628i	$0.470225\pi$
$840$	0	0
$841$	−6.29241e24	−0.867063
$842$	−9.22007e24	−1.25771
$843$	0	0
$844$	1.07417e25	1.43603
$845$	−2.68185e24	−0.354938
$846$	0	0
$847$	−4.88033e23	−0.0633053
$848$	4.94353e24	0.634853
$849$	0	0
$850$	−6.72764e24	−0.846840
$851$	−1.69447e25	−2.11171
$852$	0	0
$853$	−5.83602e23	−0.0712935	−0.0356468	−	0.999364i	$-0.511349\pi$
$853$	−5.83602e23	−0.0712935	−0.0356468	+	0.999364i	$0.511349\pi$
$854$	−1.44741e24	−0.175065
$855$	0	0
$856$	−6.34617e24	−0.752462
$857$	−5.11451e24	−0.600437	−0.300218	−	0.953871i	$-0.597060\pi$
$857$	−5.11451e24	−0.600437	−0.300218	+	0.953871i	$0.597060\pi$
$858$	0	0
$859$	2.96778e24	0.341578	0.170789	−	0.985308i	$-0.445368\pi$
$859$	2.96778e24	0.341578	0.170789	+	0.985308i	$0.445368\pi$
$860$	3.23032e25	3.68137
$861$	0	0
$862$	−2.09615e25	−2.34213
$863$	8.25654e24	0.913495	0.456748	−	0.889596i	$-0.349014\pi$
$863$	8.25654e24	0.913495	0.456748	+	0.889596i	$0.349014\pi$
$864$	0	0
$865$	7.47136e23	0.0810519
$866$	9.24071e24	0.992667
$867$	0	0
$868$	1.59360e24	0.167865
$869$	5.70582e24	0.595182
$870$	0	0
$871$	4.61727e24	0.472314
$872$	−3.86540e25	−3.91565
$873$	0	0
$874$	3.48854e25	3.46575
$875$	−6.10519e23	−0.0600662
$876$	0	0
$877$	−2.48925e24	−0.240199	−0.120100	−	0.992762i	$-0.538321\pi$
$877$	−2.48925e24	−0.240199	−0.120100	+	0.992762i	$0.538321\pi$
$878$	−4.14002e24	−0.395639
$879$	0	0
$880$	1.69998e25	1.59346
$881$	1.53069e25	1.42099	0.710495	−	0.703702i	$-0.248471\pi$
$881$	1.53069e25	1.42099	0.710495	+	0.703702i	$0.248471\pi$
$882$	0	0
$883$	1.37054e25	1.24803	0.624014	−	0.781413i	$-0.285501\pi$
$883$	1.37054e25	1.24803	0.624014	+	0.781413i	$0.285501\pi$
$884$	−1.87499e25	−1.69104
$885$	0	0
$886$	−1.95717e25	−1.73157
$887$	1.43271e24	0.125548	0.0627739	−	0.998028i	$-0.480005\pi$
$887$	1.43271e24	0.125548	0.0627739	+	0.998028i	$0.480005\pi$
$888$	0	0
$889$	−1.17088e24	−0.100658
$890$	−2.69737e25	−2.29681
$891$	0	0
$892$	−3.26292e25	−2.72587
$893$	1.33389e25	1.10378
$894$	0	0
$895$	1.70792e24	0.138666
$896$	8.49541e23	0.0683229
$897$	0	0
$898$	−4.34157e25	−3.42608
$899$	3.22786e24	0.252324
$900$	0	0
$901$	3.50533e24	0.268886
$902$	−9.81943e24	−0.746157
$903$	0	0
$904$	−1.19693e24	−0.0892561
$905$	−9.38539e24	−0.693329
$906$	0	0
$907$	2.00624e25	1.45453	0.727263	−	0.686359i	$-0.240792\pi$
$907$	2.00624e25	1.45453	0.727263	+	0.686359i	$0.240792\pi$
$908$	9.68177e24	0.695385
$909$	0	0
$910$	2.83586e24	0.199909
$911$	−7.29637e24	−0.509566	−0.254783	−	0.966998i	$-0.582004\pi$
$911$	−7.29637e24	−0.509566	−0.254783	+	0.966998i	$0.582004\pi$
$912$	0	0
$913$	6.39245e24	0.438193
$914$	2.73539e25	1.85771
$915$	0	0
$916$	−1.09902e25	−0.732645
$917$	4.33034e23	0.0286011
$918$	0	0
$919$	4.06033e24	0.263257	0.131628	−	0.991299i	$-0.457979\pi$
$919$	4.06033e24	0.263257	0.131628	+	0.991299i	$0.457979\pi$
$920$	7.90956e25	5.08108
$921$	0	0
$922$	3.88663e25	2.45110
$923$	−1.53440e25	−0.958791
$924$	0	0
$925$	1.08124e25	0.663310
$926$	−3.35751e25	−2.04091
$927$	0	0
$928$	−8.09199e24	−0.482945
$929$	2.87442e25	1.69987	0.849936	−	0.526886i	$-0.176641\pi$
$929$	2.87442e25	1.69987	0.849936	+	0.526886i	$0.176641\pi$
$930$	0	0
$931$	−1.89361e25	−1.09956
$932$	−4.25287e25	−2.44707
$933$	0	0
$934$	2.50482e25	1.41523
$935$	1.20541e25	0.674893
$936$	0	0
$937$	−9.52788e24	−0.523853	−0.261927	−	0.965088i	$-0.584358\pi$
$937$	−9.52788e24	−0.523853	−0.261927	+	0.965088i	$0.584358\pi$
$938$	1.95778e24	0.106670
$939$	0	0
$940$	5.32529e25	2.84942
$941$	−4.74128e24	−0.251411	−0.125705	−	0.992068i	$-0.540119\pi$
$941$	−4.74128e24	−0.251411	−0.125705	+	0.992068i	$0.540119\pi$
$942$	0	0
$943$	−2.14151e25	−1.11525
$944$	3.44113e24	0.177598
$945$	0	0
$946$	−2.89890e25	−1.46946
$947$	1.05058e25	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$947$	1.05058e25	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$948$	0	0
$949$	3.23564e25	1.59660
$950$	−2.22603e25	−1.08863
$951$	0	0
$952$	−4.51505e24	−0.216895
$953$	2.86764e24	0.136532	0.0682660	−	0.997667i	$-0.478253\pi$
$953$	2.86764e24	0.136532	0.0682660	+	0.997667i	$0.478253\pi$
$954$	0	0
$955$	−3.31218e25	−1.54912
$956$	−4.82743e25	−2.23781
$957$	0	0
$958$	1.76848e25	0.805367
$959$	−4.16841e24	−0.188153
$960$	0	0
$961$	−1.17502e25	−0.521072
$962$	4.31544e25	1.89687
$963$	0	0
$964$	−2.16328e25	−0.934239
$965$	−9.18186e24	−0.393050
$966$	0	0
$967$	−3.11121e25	−1.30859	−0.654297	−	0.756238i	$-0.727035\pi$
$967$	−3.11121e25	−1.30859	−0.654297	+	0.756238i	$0.727035\pi$
$968$	3.46662e25	1.44533
$969$	0	0
$970$	−7.81070e25	−3.19985
$971$	−1.46309e25	−0.594165	−0.297083	−	0.954852i	$-0.596014\pi$
$971$	−1.46309e25	−0.594165	−0.297083	+	0.954852i	$0.596014\pi$
$972$	0	0
$973$	1.69827e24	0.0677715
$974$	9.39223e24	0.371550
$975$	0	0
$976$	4.81919e25	1.87349
$977$	3.44513e25	1.32771	0.663853	−	0.747863i	$-0.268920\pi$
$977$	3.44513e25	1.32771	0.663853	+	0.747863i	$0.268920\pi$
$978$	0	0
$979$	1.69028e25	0.640187
$980$	−7.55988e25	−2.83853
$981$	0	0
$982$	5.42135e25	2.00060
$983$	−4.21774e25	−1.54303	−0.771515	−	0.636211i	$-0.780501\pi$
$983$	−4.21774e25	−1.54303	−0.771515	+	0.636211i	$0.780501\pi$
$984$	0	0
$985$	1.10674e24	0.0397957
$986$	−1.61033e25	−0.574065
$987$	0	0
$988$	−6.20392e25	−2.17386
$989$	−6.32219e25	−2.19634
$990$	0	0
$991$	−2.46032e25	−0.840169	−0.420084	−	0.907485i	$-0.637999\pi$
$991$	−2.46032e25	−0.840169	−0.420084	+	0.907485i	$0.637999\pi$
$992$	−2.70744e25	−0.916664
$993$	0	0
$994$	−6.50606e24	−0.216538
$995$	1.47768e25	0.487624
$996$	0	0
$997$	5.58760e25	1.81266	0.906330	−	0.422571i	$-0.138872\pi$
$997$	5.58760e25	1.81266	0.906330	+	0.422571i	$0.138872\pi$
$998$	1.03883e26	3.34143
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.18.a.c.1.1		2
3.2	odd	2		3.18.a.b.1.2	✓	2
12.11	even	2		48.18.a.h.1.1		2
15.2	even	4		75.18.b.c.49.4		4
15.8	even	4		75.18.b.c.49.1		4
15.14	odd	2		75.18.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.18.a.b.1.2	✓	2	3.2	odd	2
9.18.a.c.1.1		2	1.1	even	1	trivial
48.18.a.h.1.1		2	12.11	even	2
75.18.a.b.1.1		2	15.14	odd	2
75.18.b.c.49.1		4	15.8	even	4
75.18.b.c.49.4		4	15.2	even	4

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-659.106 q^{2} +303349. q^{4} +1.08318e6 q^{5} +1.59855e6 q^{7} -1.13549e8 q^{8} +O(q^{10})\)	\(q-659.106 q^{2} +303349. q^{4} +1.08318e6 q^{5} +1.59855e6 q^{7} -1.13549e8 q^{8} -7.13934e8 q^{10} +4.47381e8 q^{11} -2.48486e9 q^{13} -1.05361e9 q^{14} +3.50803e10 q^{16} +2.48745e10 q^{17} +8.23042e10 q^{19} +3.28583e11 q^{20} -2.94872e11 q^{22} -6.43083e11 q^{23} +4.10349e11 q^{25} +1.63779e12 q^{26} +4.84918e11 q^{28} +9.82213e11 q^{29} +3.28632e12 q^{31} -8.23853e12 q^{32} -1.63949e13 q^{34} +1.73152e12 q^{35} +2.63492e13 q^{37} -5.42472e13 q^{38} -1.22994e14 q^{40} +3.33007e13 q^{41} +9.83107e13 q^{43} +1.35713e14 q^{44} +4.23860e14 q^{46} +1.62068e14 q^{47} -2.30075e14 q^{49} -2.70463e14 q^{50} -7.53780e14 q^{52} +1.40921e14 q^{53} +4.84596e14 q^{55} -1.81514e14 q^{56} -6.47383e14 q^{58} +9.80930e13 q^{59} +1.37376e15 q^{61} -2.16603e15 q^{62} +8.32030e14 q^{64} -2.69156e15 q^{65} -1.85816e15 q^{67} +7.54565e15 q^{68} -1.14126e15 q^{70} +6.17500e15 q^{71} -1.30214e16 q^{73} -1.73670e16 q^{74} +2.49669e16 q^{76} +7.15160e14 q^{77} +1.27538e16 q^{79} +3.79984e16 q^{80} -2.19487e16 q^{82} +1.42886e16 q^{83} +2.69436e16 q^{85} -6.47972e16 q^{86} -5.07996e16 q^{88} +3.77818e16 q^{89} -3.97217e15 q^{91} -1.95079e17 q^{92} -1.06820e17 q^{94} +8.91506e16 q^{95} +1.09404e17 q^{97} +1.51644e17 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 594 q^{2} + 176516 q^{4} - 382860 q^{5} + 24471568 q^{7} - 130340232 q^{8}+O(q^{10}) \) 2 * q - 594 * q^2 + 176516 * q^4 - 382860 * q^5 + 24471568 * q^7 - 130340232 * q^8	\( 2 q - 594 q^{2} + 176516 q^{4} - 382860 q^{5} + 24471568 q^{7} - 130340232 q^{8} - 809382420 q^{10} + 987553512 q^{11} - 2519398244 q^{13} + 435565296 q^{14} + 50611323920 q^{16} + 34313126364 q^{17} + 80053542184 q^{19} + 514526095080 q^{20} - 259702850088 q^{22} - 297228742704 q^{23} + 1796695260350 q^{25} + 1635537155076 q^{26} - 2416139220704 q^{28} + 470374069572 q^{29} + 3400754454592 q^{31} - 5026499631648 q^{32} - 15780403538748 q^{34} - 31801338154080 q^{35} + 10652012180428 q^{37} - 54393717084264 q^{38} - 98377731579600 q^{40} + 113376799448748 q^{41} + 61637031489880 q^{43} + 67200775334352 q^{44} + 446377123388592 q^{46} + 279645641926560 q^{47} + 60469362475890 q^{49} - 180203550461550 q^{50} - 749398920924104 q^{52} + 530964038611476 q^{53} - 307321280077680 q^{55} - 565580346246720 q^{56} - 680706445363812 q^{58} - 17\!\cdots\!56 q^{59}+ \cdots + 17\!\cdots\!26 q^{98}+O(q^{100}) \) 2 * q - 594 * q^2 + 176516 * q^4 - 382860 * q^5 + 24471568 * q^7 - 130340232 * q^8 - 809382420 * q^10 + 987553512 * q^11 - 2519398244 * q^13 + 435565296 * q^14 + 50611323920 * q^16 + 34313126364 * q^17 + 80053542184 * q^19 + 514526095080 * q^20 - 259702850088 * q^22 - 297228742704 * q^23 + 1796695260350 * q^25 + 1635537155076 * q^26 - 2416139220704 * q^28 + 470374069572 * q^29 + 3400754454592 * q^31 - 5026499631648 * q^32 - 15780403538748 * q^34 - 31801338154080 * q^35 + 10652012180428 * q^37 - 54393717084264 * q^38 - 98377731579600 * q^40 + 113376799448748 * q^41 + 61637031489880 * q^43 + 67200775334352 * q^44 + 446377123388592 * q^46 + 279645641926560 * q^47 + 60469362475890 * q^49 - 180203550461550 * q^50 - 749398920924104 * q^52 + 530964038611476 * q^53 - 307321280077680 * q^55 - 565580346246720 * q^56 - 680706445363812 * q^58 - 1727524231086456 * q^59 + 2784287656027900 * q^61 - 2158582756499136 * q^62 - 994533569423296 * q^64 - 2640922679811240 * q^65 - 3329301676696184 * q^67 + 6348514481766072 * q^68 - 3324459101139360 * q^70 + 13489402206504816 * q^71 + 436589918136724 * q^73 - 18388942762073004 * q^74 + 25252347669111376 * q^76 + 13070541011736384 * q^77 + 4376041565214880 * q^79 + 15229171694708640 * q^80 - 16735234653750924 * q^82 + 39886442265612888 * q^83 + 13106143850552280 * q^85 - 67184884152159768 * q^86 - 59869809989481888 * q^88 - 6972184096107444 * q^89 - 4762196572326688 * q^91 - 238944325336039008 * q^92 - 99165314702307744 * q^94 + 92450059415485200 * q^95 + 183569555712460996 * q^97 + 170560284296616126 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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