LMFDB - Embedded newform 75.22.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	75.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:	$209.608008215$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} - 13701836 x^{6} + 201589162 x^{5} + 55078074399586 x^{4} + \cdots + 23\!\cdots\!25 $ x^8 - 2x^7 - 13701836x^6 + 201589162x^5 + 55078074399586x^4 - 1921148793416750x^3 - 63775892303255475300x^2 - 5448867057840511928250*x + 2374849659307636957978125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{10}\cdot 5^{14}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$155.916$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+238.916 q^{2} -59049.0 q^{3} -2.04007e6 q^{4} -1.41077e7 q^{6} +6.22955e8 q^{7} -9.88448e8 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q+238.916 q^{2} -59049.0 q^{3} -2.04007e6 q^{4} -1.41077e7 q^{6} +6.22955e8 q^{7} -9.88448e8 q^{8} +3.48678e9 q^{9} +1.17658e10 q^{11} +1.20464e11 q^{12} +6.64700e11 q^{13} +1.48834e11 q^{14} +4.04218e12 q^{16} +1.24087e13 q^{17} +8.33048e11 q^{18} +1.38702e13 q^{19} -3.67849e13 q^{21} +2.81105e12 q^{22} +2.44684e14 q^{23} +5.83669e13 q^{24} +1.58807e14 q^{26} -2.05891e14 q^{27} -1.27087e15 q^{28} -2.45457e15 q^{29} +6.56996e15 q^{31} +3.03867e15 q^{32} -6.94761e14 q^{33} +2.96464e15 q^{34} -7.11329e15 q^{36} +8.38999e15 q^{37} +3.31381e15 q^{38} -3.92499e16 q^{39} -1.59593e16 q^{41} -8.78849e15 q^{42} +1.03720e17 q^{43} -2.40032e16 q^{44} +5.84589e16 q^{46} +6.98293e17 q^{47} -2.38687e17 q^{48} -1.70473e17 q^{49} -7.32723e17 q^{51} -1.35603e18 q^{52} -1.25834e18 q^{53} -4.91906e16 q^{54} -6.15759e17 q^{56} -8.19022e17 q^{57} -5.86435e17 q^{58} +2.40302e18 q^{59} -6.88392e18 q^{61} +1.56967e18 q^{62} +2.17211e18 q^{63} -7.75109e18 q^{64} -1.65989e17 q^{66} +1.90793e19 q^{67} -2.53147e19 q^{68} -1.44483e19 q^{69} +6.30232e18 q^{71} -3.44650e18 q^{72} -3.72824e19 q^{73} +2.00450e18 q^{74} -2.82962e19 q^{76} +7.32959e18 q^{77} -9.37741e18 q^{78} -9.29902e19 q^{79} +1.21577e19 q^{81} -3.81292e18 q^{82} +5.72322e19 q^{83} +7.50438e19 q^{84} +2.47804e19 q^{86} +1.44940e20 q^{87} -1.16299e19 q^{88} -1.21048e20 q^{89} +4.14078e20 q^{91} -4.99173e20 q^{92} -3.87950e20 q^{93} +1.66833e20 q^{94} -1.79430e20 q^{96} -7.43455e20 q^{97} -4.07286e19 q^{98} +4.10250e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 666 q^{2} - 472392 q^{3} + 10681904 q^{4} - 39326634 q^{6} + 134034472 q^{7} + 3512168028 q^{8} + 27894275208 q^{9}+O(q^{10}) $ 8 * q + 666 * q^2 - 472392 * q^3 + 10681904 * q^4 - 39326634 * q^6 + 134034472 * q^7 + 3512168028 * q^8 + 27894275208 * q^9	$ 8 q + 666 q^{2} - 472392 q^{3} + 10681904 q^{4} - 39326634 q^{6} + 134034472 q^{7} + 3512168028 q^{8} + 27894275208 q^{9} - 14410165968 q^{11} - 630755749296 q^{12} - 328226481176 q^{13} + 4068036669186 q^{14} + 18553054308920 q^{16} - 5718214953936 q^{17} + 2322198411066 q^{18} + 75919698170296 q^{19} - 7914601537128 q^{21} - 426897542691372 q^{22} + 49712781537936 q^{23} - 207390009885372 q^{24} - 126056679642054 q^{26} - 16\!\cdots\!92 q^{27}+ \cdots - 50\!\cdots\!68 q^{99}+O(q^{100}) $ 8 * q + 666 * q^2 - 472392 * q^3 + 10681904 * q^4 - 39326634 * q^6 + 134034472 * q^7 + 3512168028 * q^8 + 27894275208 * q^9 - 14410165968 * q^11 - 630755749296 * q^12 - 328226481176 * q^13 + 4068036669186 * q^14 + 18553054308920 * q^16 - 5718214953936 * q^17 + 2322198411066 * q^18 + 75919698170296 * q^19 - 7914601537128 * q^21 - 426897542691372 * q^22 + 49712781537936 * q^23 - 207390009885372 * q^24 - 126056679642054 * q^26 - 1647129056757192 * q^27 + 4235167126399504 * q^28 + 2111332005818352 * q^29 + 5677451410844968 * q^31 + 17528957992420632 * q^32 + 850905890244432 * q^33 + 9944754702742068 * q^34 + 37245496240179504 * q^36 - 26538401323409648 * q^37 + 85729618982552526 * q^38 + 19381445486961624 * q^39 - 9719778050982432 * q^41 - 240213497278764114 * q^42 - 20888744714565080 * q^43 - 388904820117856128 * q^44 - 156886987299808452 * q^46 + 405141072730526160 * q^47 - 1095539303887417080 * q^48 + 1172899395436368720 * q^49 + 337654874814966864 * q^51 - 2264281219115894096 * q^52 + 1890950875516930176 * q^53 - 137123493975036234 * q^54 + 19720793170524660300 * q^56 - 4482982257257808504 * q^57 + 12636224332772065092 * q^58 - 3496737905134765776 * q^59 + 17508733151770015960 * q^61 - 30404101355896200606 * q^62 + 467349306165871272 * q^63 + 27809823573720908096 * q^64 + 25207872998382825228 * q^66 - 29911607071855004216 * q^67 - 29571773973515759808 * q^68 - 2935490037033582864 * q^69 + 52204030316256846816 * q^71 + 12246172693721331228 * q^72 - 39697032757192143344 * q^73 - 32301811215943606764 * q^74 + 383913379529874070384 * q^76 - 202348742072764877136 * q^77 + 7443520876183646646 * q^78 - 274125739348498990400 * q^79 + 97261323672455430408 * q^81 - 231746572148446490256 * q^82 - 276883976086286712912 * q^83 - 250082383646764311696 * q^84 + 486708932755841131242 * q^86 - 124672043611567867248 * q^87 - 2078122304879724561672 * q^88 - 319129684977517046784 * q^89 + 45068531423660000648 * q^91 + 147706203809955886272 * q^92 - 335247828358984515432 * q^93 - 1499781052151613424236 * q^94 - 1035067440494445898968 * q^96 + 451807368184588489864 * q^97 - 2604193962467412900204 * q^98 - 50245141913043465168 * q^99

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 $

$2$	238.916	0.164979	0.0824897	−	0.996592i	$-0.473713\pi$
$2$	238.916	0.164979	0.0824897	+	0.996592i	$0.473713\pi$
$3$	−59049.0	−0.577350
$3$	−59049.0	−0.577350
$4$	−2.04007e6	−0.972782
$5$	0	0
$5$	0	0
$6$	−1.41077e7	−0.0952509
$7$	6.22955e8	0.833542	0.416771	−	0.909012i	$-0.363162\pi$
$7$	6.22955e8	0.833542	0.416771	+	0.909012i	$0.363162\pi$
$8$	−9.88448e8	−0.325468
$9$	3.48678e9	0.333333
$10$	0	0
$11$	1.17658e10	0.136773	0.0683864	−	0.997659i	$-0.478215\pi$
$11$	1.17658e10	0.136773	0.0683864	+	0.997659i	$0.478215\pi$
$12$	1.20464e11	0.561636
$13$	6.64700e11	1.33727	0.668637	−	0.743589i	$-0.266878\pi$
$13$	6.64700e11	1.33727	0.668637	+	0.743589i	$0.266878\pi$
$14$	1.48834e11	0.137517
$15$	0	0
$16$	4.04218e12	0.919086
$17$	1.24087e13	1.49284	0.746421	−	0.665474i	$-0.231771\pi$
$17$	1.24087e13	1.49284	0.746421	+	0.665474i	$0.231771\pi$
$18$	8.33048e11	0.0549932
$19$	1.38702e13	0.519003	0.259502	−	0.965743i	$-0.416442\pi$
$19$	1.38702e13	0.519003	0.259502	+	0.965743i	$0.416442\pi$
$20$	0	0
$21$	−3.67849e13	−0.481246
$22$	2.81105e12	0.0225647
$23$	2.44684e14	1.23158	0.615791	−	0.787910i	$-0.288837\pi$
$23$	2.44684e14	1.23158	0.615791	+	0.787910i	$0.288837\pi$
$24$	5.83669e13	0.187909
$25$	0	0
$26$	1.58807e14	0.220623
$27$	−2.05891e14	−0.192450
$28$	−1.27087e15	−0.810854
$29$	−2.45457e15	−1.08342	−0.541709	−	0.840566i	$-0.682223\pi$
$29$	−2.45457e15	−1.08342	−0.541709	+	0.840566i	$0.682223\pi$
$30$	0	0
$31$	6.56996e15	1.43968	0.719838	−	0.694142i	$-0.244216\pi$
$31$	6.56996e15	1.43968	0.719838	+	0.694142i	$0.244216\pi$
$32$	3.03867e15	0.477099
$33$	−6.94761e14	−0.0789658
$34$	2.96464e15	0.246288
$35$	0	0
$36$	−7.11329e15	−0.324261
$37$	8.38999e15	0.286842	0.143421	−	0.989662i	$-0.454190\pi$
$37$	8.38999e15	0.286842	0.143421	+	0.989662i	$0.454190\pi$
$38$	3.31381e15	0.0856249
$39$	−3.92499e16	−0.772075
$40$	0	0
$41$	−1.59593e16	−0.185687	−0.0928437	−	0.995681i	$-0.529596\pi$
$41$	−1.59593e16	−0.185687	−0.0928437	+	0.995681i	$0.529596\pi$
$42$	−8.78849e15	−0.0793956
$43$	1.03720e17	0.731890	0.365945	−	0.930637i	$-0.380746\pi$
$43$	1.03720e17	0.731890	0.365945	+	0.930637i	$0.380746\pi$
$44$	−2.40032e16	−0.133050
$45$	0	0
$46$	5.84589e16	0.203186
$47$	6.98293e17	1.93647	0.968234	−	0.250047i	$-0.0804460\pi$
$47$	6.98293e17	1.93647	0.968234	+	0.250047i	$0.0804460\pi$
$48$	−2.38687e17	−0.530635
$49$	−1.70473e17	−0.305208
$50$	0	0
$51$	−7.32723e17	−0.861892
$52$	−1.35603e18	−1.30088
$53$	−1.25834e18	−0.988331	−0.494165	−	0.869368i	$-0.664526\pi$
$53$	−1.25834e18	−0.988331	−0.494165	+	0.869368i	$0.664526\pi$
$54$	−4.91906e16	−0.0317503
$55$	0	0
$56$	−6.15759e17	−0.271292
$57$	−8.19022e17	−0.299647
$58$	−5.86435e17	−0.178742
$59$	2.40302e18	0.612084	0.306042	−	0.952018i	$-0.400995\pi$
$59$	2.40302e18	0.612084	0.306042	+	0.952018i	$0.400995\pi$
$60$	0	0
$61$	−6.88392e18	−1.23558	−0.617792	−	0.786342i	$-0.711973\pi$
$61$	−6.88392e18	−1.23558	−0.617792	+	0.786342i	$0.711973\pi$
$62$	1.56967e18	0.237517
$63$	2.17211e18	0.277847
$64$	−7.75109e18	−0.840375
$65$	0	0
$66$	−1.65989e17	−0.0130277
$67$	1.90793e19	1.27872	0.639361	−	0.768907i	$-0.279199\pi$
$67$	1.90793e19	1.27872	0.639361	+	0.768907i	$0.279199\pi$
$68$	−2.53147e19	−1.45221
$69$	−1.44483e19	−0.711054
$70$	0	0
$71$	6.30232e18	0.229767	0.114884	−	0.993379i	$-0.463351\pi$
$71$	6.30232e18	0.229767	0.114884	+	0.993379i	$0.463351\pi$
$72$	−3.44650e18	−0.108489
$73$	−3.72824e19	−1.01534	−0.507672	−	0.861550i	$-0.669494\pi$
$73$	−3.72824e19	−1.01534	−0.507672	+	0.861550i	$0.669494\pi$
$74$	2.00450e18	0.0473231
$75$	0	0
$76$	−2.82962e19	−0.504877
$77$	7.32959e18	0.114006
$78$	−9.37741e18	−0.127377
$79$	−9.29902e19	−1.10498	−0.552488	−	0.833521i	$-0.686321\pi$
$79$	−9.29902e19	−1.10498	−0.552488	+	0.833521i	$0.686321\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	−3.81292e18	−0.0306346
$83$	5.72322e19	0.404875	0.202437	−	0.979295i	$-0.435114\pi$
$83$	5.72322e19	0.404875	0.202437	+	0.979295i	$0.435114\pi$
$84$	7.50438e19	0.468147
$85$	0	0
$86$	2.47804e19	0.120747
$87$	1.44940e20	0.625512
$88$	−1.16299e19	−0.0445152
$89$	−1.21048e20	−0.411492	−0.205746	−	0.978605i	$-0.565962\pi$
$89$	−1.21048e20	−0.411492	−0.205746	+	0.978605i	$0.565962\pi$
$90$	0	0
$91$	4.14078e20	1.11467
$92$	−4.99173e20	−1.19806
$93$	−3.87950e20	−0.831198
$94$	1.66833e20	0.319477
$95$	0	0
$96$	−1.79430e20	−0.275453
$97$	−7.43455e20	−1.02365	−0.511825	−	0.859090i	$-0.671030\pi$
$97$	−7.43455e20	−1.02365	−0.511825	+	0.859090i	$0.671030\pi$
$98$	−4.07286e19	−0.0503530
$99$	4.10250e19	0.0455909
$100$	0	0
$101$	1.78527e21	1.60816	0.804079	−	0.594523i	$-0.202659\pi$
$101$	1.78527e21	1.60816	0.804079	+	0.594523i	$0.202659\pi$
$102$	−1.75059e20	−0.142195
$103$	−2.03656e20	−0.149316	−0.0746578	−	0.997209i	$-0.523786\pi$
$103$	−2.03656e20	−0.149316	−0.0746578	+	0.997209i	$0.523786\pi$
$104$	−6.57021e20	−0.435240
$105$	0	0
$106$	−3.00638e20	−0.163054
$107$	1.84578e20	0.0907090	0.0453545	−	0.998971i	$-0.485558\pi$
$107$	1.84578e20	0.0907090	0.0453545	+	0.998971i	$0.485558\pi$
$108$	4.20033e20	0.187212
$109$	−1.88509e19	−0.00762701	−0.00381351	−	0.999993i	$-0.501214\pi$
$109$	−1.88509e19	−0.00762701	−0.00381351	+	0.999993i	$0.501214\pi$
$110$	0	0
$111$	−4.95420e20	−0.165609
$112$	2.51810e21	0.766097
$113$	2.80252e21	0.776651	0.388325	−	0.921522i	$-0.373054\pi$
$113$	2.80252e21	0.776651	0.388325	+	0.921522i	$0.373054\pi$
$114$	−1.95677e20	−0.0494356
$115$	0	0
$116$	5.00750e21	1.05393
$117$	2.31766e21	0.445758
$118$	5.74119e20	0.100981
$119$	7.73008e21	1.24435
$120$	0	0
$121$	−7.26181e21	−0.981293
$122$	−1.64468e21	−0.203846
$123$	9.42379e20	0.107207
$124$	−1.34032e22	−1.40049
$125$	0	0
$126$	5.18952e20	0.0458391
$127$	7.11473e21	0.578388	0.289194	−	0.957271i	$-0.406613\pi$
$127$	7.11473e21	0.578388	0.289194	+	0.957271i	$0.406613\pi$
$128$	−8.22440e21	−0.615743
$129$	−6.12459e21	−0.422557
$130$	0	0
$131$	−8.82556e21	−0.518076	−0.259038	−	0.965867i	$-0.583406\pi$
$131$	−8.82556e21	−0.518076	−0.259038	+	0.965867i	$0.583406\pi$
$132$	1.41736e21	0.0768165
$133$	8.64052e21	0.432611
$134$	4.55833e21	0.210963
$135$	0	0
$136$	−1.22654e22	−0.485873
$137$	1.39205e22	0.510611	0.255305	−	0.966860i	$-0.417824\pi$
$137$	1.39205e22	0.510611	0.255305	+	0.966860i	$0.417824\pi$
$138$	−3.45194e21	−0.117309
$139$	4.93436e22	1.55445	0.777223	−	0.629225i	$-0.216628\pi$
$139$	4.93436e22	1.55445	0.777223	+	0.629225i	$0.216628\pi$
$140$	0	0
$141$	−4.12335e22	−1.11802
$142$	1.50572e21	0.0379068
$143$	7.82075e21	0.182903
$144$	1.40942e22	0.306362
$145$	0	0
$146$	−8.90735e21	−0.167511
$147$	1.00662e22	0.176212
$148$	−1.71162e22	−0.279035
$149$	−1.06667e23	−1.62022	−0.810108	−	0.586280i	$-0.800592\pi$
$149$	−1.06667e23	−1.62022	−0.810108	+	0.586280i	$0.800592\pi$
$150$	0	0
$151$	6.44371e22	0.850899	0.425449	−	0.904982i	$-0.360116\pi$
$151$	6.44371e22	0.850899	0.425449	+	0.904982i	$0.360116\pi$
$152$	−1.37100e22	−0.168919
$153$	4.32666e22	0.497614
$154$	1.75116e21	0.0188086
$155$	0	0
$156$	8.00725e22	0.751061
$157$	9.89402e22	0.867814	0.433907	−	0.900958i	$-0.357135\pi$
$157$	9.89402e22	0.867814	0.433907	+	0.900958i	$0.357135\pi$
$158$	−2.22168e22	−0.182298
$159$	7.43039e22	0.570613
$160$	0	0
$161$	1.52427e23	1.02657
$162$	2.90466e21	0.0183311
$163$	1.08411e23	0.641360	0.320680	−	0.947188i	$-0.396089\pi$
$163$	1.08411e23	0.641360	0.320680	+	0.947188i	$0.396089\pi$
$164$	3.25580e22	0.180633
$165$	0	0
$166$	1.36737e22	0.0667960
$167$	−7.76750e22	−0.356253	−0.178127	−	0.984008i	$-0.557004\pi$
$167$	−7.76750e22	−0.356253	−0.178127	+	0.984008i	$0.557004\pi$
$168$	3.63599e22	0.156630
$169$	1.94761e23	0.788301
$170$	0	0
$171$	4.83624e22	0.173001
$172$	−2.11597e23	−0.711969
$173$	−4.65341e23	−1.47329	−0.736643	−	0.676282i	$-0.763590\pi$
$173$	−4.65341e23	−1.47329	−0.736643	+	0.676282i	$0.763590\pi$
$174$	3.46284e22	0.103197
$175$	0	0
$176$	4.75597e22	0.125706
$177$	−1.41896e23	−0.353387
$178$	−2.89202e22	−0.0678877
$179$	8.42823e22	0.186543	0.0932717	−	0.995641i	$-0.470267\pi$
$179$	8.42823e22	0.186543	0.0932717	+	0.995641i	$0.470267\pi$
$180$	0	0
$181$	8.95022e21	0.0176282	0.00881412	−	0.999961i	$-0.497194\pi$
$181$	8.95022e21	0.0176282	0.00881412	+	0.999961i	$0.497194\pi$
$182$	9.89298e22	0.183898
$183$	4.06488e23	0.713365
$184$	−2.41857e23	−0.400841
$185$	0	0
$186$	−9.26873e22	−0.137131
$187$	1.45999e23	0.204180
$188$	−1.42457e24	−1.88376
$189$	−1.28261e23	−0.160415
$190$	0	0
$191$	2.42464e23	0.271517	0.135759	−	0.990742i	$-0.456653\pi$
$191$	2.42464e23	0.271517	0.135759	+	0.990742i	$0.456653\pi$
$192$	4.57694e23	0.485191
$193$	−4.05656e23	−0.407199	−0.203599	−	0.979054i	$-0.565264\pi$
$193$	−4.05656e23	−0.407199	−0.203599	+	0.979054i	$0.565264\pi$
$194$	−1.77623e23	−0.168881
$195$	0	0
$196$	3.47776e23	0.296901
$197$	1.30868e23	0.105910	0.0529550	−	0.998597i	$-0.483136\pi$
$197$	1.30868e23	0.105910	0.0529550	+	0.998597i	$0.483136\pi$
$198$	9.80151e21	0.00752157
$199$	2.06881e24	1.50579	0.752893	−	0.658143i	$-0.228658\pi$
$199$	2.06881e24	1.50579	0.752893	+	0.658143i	$0.228658\pi$
$200$	0	0
$201$	−1.12661e24	−0.738270
$202$	4.26528e23	0.265313
$203$	−1.52909e24	−0.903075
$204$	1.49481e24	0.838433
$205$	0	0
$206$	−4.86565e22	−0.0246340
$207$	8.53160e23	0.410527
$208$	2.68684e24	1.22907
$209$	1.63195e23	0.0709856
$210$	0	0
$211$	−3.07171e24	−1.20897	−0.604483	−	0.796618i	$-0.706620\pi$
$211$	−3.07171e24	−1.20897	−0.604483	+	0.796618i	$0.706620\pi$
$212$	2.56711e24	0.961430
$213$	−3.72146e23	−0.132656
$214$	4.40986e22	0.0149651
$215$	0	0
$216$	2.03513e23	0.0626364
$217$	4.09279e24	1.20003
$218$	−4.50378e21	−0.00125830
$219$	2.20149e24	0.586210
$220$	0	0
$221$	8.24808e24	1.99634
$222$	−1.18364e23	−0.0273220
$223$	−7.14085e24	−1.57235	−0.786174	−	0.618005i	$-0.787941\pi$
$223$	−7.14085e24	−1.57235	−0.786174	+	0.618005i	$0.787941\pi$
$224$	1.89295e24	0.397682
$225$	0	0
$226$	6.69567e23	0.128131
$227$	−7.23862e24	−1.32246	−0.661232	−	0.750181i	$-0.729966\pi$
$227$	−7.23862e24	−1.32246	−0.661232	+	0.750181i	$0.729966\pi$
$228$	1.67086e24	0.291491
$229$	9.22621e24	1.53727	0.768636	−	0.639686i	$-0.220936\pi$
$229$	9.22621e24	1.53727	0.768636	+	0.639686i	$0.220936\pi$
$230$	0	0
$231$	−4.32805e23	−0.0658213
$232$	2.42621e24	0.352619
$233$	−1.65552e24	−0.229983	−0.114992	−	0.993366i	$-0.536684\pi$
$233$	−1.65552e24	−0.229983	−0.114992	+	0.993366i	$0.536684\pi$
$234$	5.53727e23	0.0735409
$235$	0	0
$236$	−4.90233e24	−0.595424
$237$	5.49098e24	0.637958
$238$	1.84684e24	0.205292
$239$	1.58345e25	1.68433	0.842165	−	0.539220i	$-0.181281\pi$
$239$	1.58345e25	1.68433	0.842165	+	0.539220i	$0.181281\pi$
$240$	0	0
$241$	8.20116e24	0.799275	0.399637	−	0.916673i	$-0.369136\pi$
$241$	8.20116e24	0.799275	0.399637	+	0.916673i	$0.369136\pi$
$242$	−1.73496e24	−0.161893
$243$	−7.17898e23	−0.0641500
$244$	1.40437e25	1.20195
$245$	0	0
$246$	2.25149e23	0.0176869
$247$	9.21952e24	0.694049
$248$	−6.49406e24	−0.468569
$249$	−3.37950e24	−0.233754
$250$	0	0
$251$	2.56271e25	1.62976	0.814882	−	0.579627i	$-0.196802\pi$
$251$	2.56271e25	1.62976	0.814882	+	0.579627i	$0.196802\pi$
$252$	−4.43126e24	−0.270285
$253$	2.87891e24	0.168447
$254$	1.69982e24	0.0954221
$255$	0	0
$256$	1.42903e25	0.738790
$257$	3.92069e25	1.94565	0.972826	−	0.231537i	$-0.0743753\pi$
$257$	3.92069e25	1.94565	0.972826	+	0.231537i	$0.0743753\pi$
$258$	−1.46326e24	−0.0697132
$259$	5.22659e24	0.239095
$260$	0	0
$261$	−8.55855e24	−0.361140
$262$	−2.10857e24	−0.0854719
$263$	−4.53674e25	−1.76689	−0.883444	−	0.468538i	$-0.844781\pi$
$263$	−4.53674e25	−1.76689	−0.883444	+	0.468538i	$0.844781\pi$
$264$	6.86735e23	0.0257009
$265$	0	0
$266$	2.06436e24	0.0713719
$267$	7.14774e24	0.237575
$268$	−3.89230e25	−1.24392
$269$	4.05174e25	1.24521	0.622605	−	0.782537i	$-0.286075\pi$
$269$	4.05174e25	1.24521	0.622605	+	0.782537i	$0.286075\pi$
$270$	0	0
$271$	1.27979e25	0.363883	0.181941	−	0.983309i	$-0.441762\pi$
$271$	1.27979e25	0.363883	0.181941	+	0.983309i	$0.441762\pi$
$272$	5.01584e25	1.37205
$273$	−2.44509e25	−0.643557
$274$	3.32584e24	0.0842403
$275$	0	0
$276$	2.94756e25	0.691700
$277$	2.24981e25	0.508286	0.254143	−	0.967167i	$-0.418207\pi$
$277$	2.24981e25	0.508286	0.254143	+	0.967167i	$0.418207\pi$
$278$	1.17890e25	0.256452
$279$	2.29080e25	0.479892
$280$	0	0
$281$	−7.16732e25	−1.39296	−0.696482	−	0.717574i	$-0.745253\pi$
$281$	−7.16732e25	−1.39296	−0.696482	+	0.717574i	$0.745253\pi$
$282$	−9.85134e24	−0.184450
$283$	−8.64233e25	−1.55910	−0.779548	−	0.626342i	$-0.784551\pi$
$283$	−8.64233e25	−1.55910	−0.779548	+	0.626342i	$0.784551\pi$
$284$	−1.28572e25	−0.223513
$285$	0	0
$286$	1.86850e24	0.0301752
$287$	−9.94191e24	−0.154778
$288$	1.05952e25	0.159033
$289$	8.48847e25	1.22858
$290$	0	0
$291$	4.39003e25	0.591005
$292$	7.60587e25	0.987709
$293$	3.51471e25	0.440331	0.220166	−	0.975463i	$-0.429340\pi$
$293$	3.51471e25	0.440331	0.220166	+	0.975463i	$0.429340\pi$
$294$	2.40498e24	0.0290713
$295$	0	0
$296$	−8.29307e24	−0.0933582
$297$	−2.42248e24	−0.0263219
$298$	−2.54844e25	−0.267302
$299$	1.62641e26	1.64696
$300$	0	0
$301$	6.46132e25	0.610061
$302$	1.53950e25	0.140381
$303$	−1.05418e26	−0.928470
$304$	5.60659e25	0.477009
$305$	0	0
$306$	1.03371e25	0.0820961
$307$	−8.57923e25	−0.658408	−0.329204	−	0.944259i	$-0.606780\pi$
$307$	−8.57923e25	−0.658408	−0.329204	+	0.944259i	$0.606780\pi$
$308$	−1.49529e25	−0.110903
$309$	1.20257e25	0.0862074
$310$	0	0
$311$	1.84449e24	0.0123564	0.00617822	−	0.999981i	$-0.498033\pi$
$311$	1.84449e24	0.0123564	0.00617822	+	0.999981i	$0.498033\pi$
$312$	3.87964e25	0.251286
$313$	1.74224e26	1.09117	0.545586	−	0.838055i	$-0.316307\pi$
$313$	1.74224e26	1.09117	0.545586	+	0.838055i	$0.316307\pi$
$314$	2.36384e25	0.143171
$315$	0	0
$316$	1.89707e26	1.07490
$317$	2.20674e26	1.20957	0.604783	−	0.796390i	$-0.293260\pi$
$317$	2.20674e26	1.20957	0.604783	+	0.796390i	$0.293260\pi$
$318$	1.77524e25	0.0941394
$319$	−2.88801e25	−0.148182
$320$	0	0
$321$	−1.08991e25	−0.0523708
$322$	3.64172e25	0.169364
$323$	1.72112e26	0.774790
$324$	−2.48025e25	−0.108087
$325$	0	0
$326$	2.59010e25	0.105811
$327$	1.11313e24	0.00440346
$328$	1.57749e25	0.0604354
$329$	4.35005e26	1.61413
$330$	0	0
$331$	−1.10750e26	−0.385613	−0.192806	−	0.981237i	$-0.561759\pi$
$331$	−1.10750e26	−0.385613	−0.192806	+	0.981237i	$0.561759\pi$
$332$	−1.16758e26	−0.393855
$333$	2.92541e25	0.0956141
$334$	−1.85578e25	−0.0587744
$335$	0	0
$336$	−1.48691e26	−0.442306
$337$	−2.24462e26	−0.647187	−0.323593	−	0.946196i	$-0.604891\pi$
$337$	−2.24462e26	−0.647187	−0.323593	+	0.946196i	$0.604891\pi$
$338$	4.65315e25	0.130053
$339$	−1.65486e26	−0.448399
$340$	0	0
$341$	7.73011e25	0.196909
$342$	1.15545e25	0.0285416
$343$	−4.54146e26	−1.08795
$344$	−1.02522e26	−0.238207
$345$	0	0
$346$	−1.11177e26	−0.243062
$347$	−1.21672e26	−0.258067	−0.129033	−	0.991640i	$-0.541187\pi$
$347$	−1.21672e26	−0.258067	−0.129033	+	0.991640i	$0.541187\pi$
$348$	−2.95688e26	−0.608487
$349$	3.00266e26	0.599570	0.299785	−	0.954007i	$-0.403085\pi$
$349$	3.00266e26	0.599570	0.299785	+	0.954007i	$0.403085\pi$
$350$	0	0
$351$	−1.36856e26	−0.257358
$352$	3.57525e25	0.0652542
$353$	−2.67970e26	−0.474736	−0.237368	−	0.971420i	$-0.576285\pi$
$353$	−2.67970e26	−0.474736	−0.237368	+	0.971420i	$0.576285\pi$
$354$	−3.39012e25	−0.0583016
$355$	0	0
$356$	2.46946e26	0.400291
$357$	−4.56454e26	−0.718424
$358$	2.01364e25	0.0307758
$359$	−1.26376e27	−1.87574	−0.937871	−	0.346983i	$-0.887206\pi$
$359$	−1.26376e27	−1.87574	−0.937871	+	0.346983i	$0.887206\pi$
$360$	0	0
$361$	−5.21827e26	−0.730636
$362$	2.13835e24	0.00290830
$363$	4.28803e26	0.566550
$364$	−8.44749e26	−1.08433
$365$	0	0
$366$	9.71165e25	0.117691
$367$	2.61225e26	0.307625	0.153813	−	0.988100i	$-0.450845\pi$
$367$	2.61225e26	0.307625	0.153813	+	0.988100i	$0.450845\pi$
$368$	9.89057e26	1.13193
$369$	−5.56465e25	−0.0618958
$370$	0	0
$371$	−7.83891e26	−0.823815
$372$	7.91445e26	0.808574
$373$	2.44037e26	0.242389	0.121194	−	0.992629i	$-0.461328\pi$
$373$	2.44037e26	0.242389	0.121194	+	0.992629i	$0.461328\pi$
$374$	3.48815e25	0.0336855
$375$	0	0
$376$	−6.90226e26	−0.630259
$377$	−1.63155e27	−1.44883
$378$	−3.06436e25	−0.0264652
$379$	−8.36662e26	−0.702811	−0.351405	−	0.936223i	$-0.614296\pi$
$379$	−8.36662e26	−0.702811	−0.351405	+	0.936223i	$0.614296\pi$
$380$	0	0
$381$	−4.20117e26	−0.333932
$382$	5.79286e25	0.0447948
$383$	−2.27339e27	−1.71036	−0.855180	−	0.518331i	$-0.826553\pi$
$383$	−2.27339e27	−1.71036	−0.855180	+	0.518331i	$0.826553\pi$
$384$	4.85643e26	0.355500
$385$	0	0
$386$	−9.69177e25	−0.0671794
$387$	3.61651e26	0.243963
$388$	1.51670e27	0.995788
$389$	−2.73112e27	−1.74530	−0.872650	−	0.488346i	$-0.837600\pi$
$389$	−2.73112e27	−1.74530	−0.872650	+	0.488346i	$0.837600\pi$
$390$	0	0
$391$	3.03622e27	1.83856
$392$	1.68503e26	0.0993356
$393$	5.21140e26	0.299111
$394$	3.12663e25	0.0174730
$395$	0	0
$396$	−8.36938e25	−0.0443500
$397$	−3.32220e27	−1.71445	−0.857225	−	0.514942i	$-0.827814\pi$
$397$	−3.32220e27	−1.71445	−0.857225	+	0.514942i	$0.827814\pi$
$398$	4.94271e26	0.248424
$399$	−5.10214e26	−0.249768
$400$	0	0
$401$	2.00698e25	0.00932238	0.00466119	−	0.999989i	$-0.498516\pi$
$401$	2.00698e25	0.00932238	0.00466119	+	0.999989i	$0.498516\pi$
$402$	−2.69165e26	−0.121799
$403$	4.36705e27	1.92524
$404$	−3.64207e27	−1.56439
$405$	0	0
$406$	−3.65323e26	−0.148989
$407$	9.87153e25	0.0392322
$408$	7.24259e26	0.280519
$409$	−7.78690e26	−0.293948	−0.146974	−	0.989140i	$-0.546953\pi$
$409$	−7.78690e26	−0.293948	−0.146974	+	0.989140i	$0.546953\pi$
$410$	0	0
$411$	−8.21994e26	−0.294801
$412$	4.15472e26	0.145252
$413$	1.49697e27	0.510198
$414$	2.03833e26	0.0677286
$415$	0	0
$416$	2.01980e27	0.638012
$417$	−2.91369e27	−0.897460
$418$	3.89898e25	0.0117112
$419$	2.65635e27	0.778105	0.389053	−	0.921216i	$-0.372802\pi$
$419$	2.65635e27	0.778105	0.389053	+	0.921216i	$0.372802\pi$
$420$	0	0
$421$	−5.30672e27	−1.47865	−0.739323	−	0.673351i	$-0.764854\pi$
$421$	−5.30672e27	−1.47865	−0.739323	+	0.673351i	$0.764854\pi$
$422$	−7.33880e26	−0.199455
$423$	2.43480e27	0.645489
$424$	1.24381e27	0.321670
$425$	0	0
$426$	−8.89115e25	−0.0218855
$427$	−4.28837e27	−1.02991
$428$	−3.76552e26	−0.0882400
$429$	−4.61808e26	−0.105599
$430$	0	0
$431$	−4.05593e27	−0.883240	−0.441620	−	0.897202i	$-0.645596\pi$
$431$	−4.05593e27	−0.883240	−0.441620	+	0.897202i	$0.645596\pi$
$432$	−8.32250e26	−0.176878
$433$	4.54389e27	0.942551	0.471276	−	0.881986i	$-0.343794\pi$
$433$	4.54389e27	0.942551	0.471276	+	0.881986i	$0.343794\pi$
$434$	9.77832e26	0.197980
$435$	0	0
$436$	3.84572e25	0.00741942
$437$	3.39382e27	0.639195
$438$	5.25970e26	0.0967126
$439$	−8.75725e27	−1.57214	−0.786068	−	0.618139i	$-0.787887\pi$
$439$	−8.75725e27	−1.57214	−0.786068	+	0.618139i	$0.787887\pi$
$440$	0	0
$441$	−5.94401e26	−0.101736
$442$	1.97060e27	0.329355
$443$	1.26129e27	0.205861	0.102931	−	0.994689i	$-0.467178\pi$
$443$	1.26129e27	0.205861	0.102931	+	0.994689i	$0.467178\pi$
$444$	1.01069e27	0.161101
$445$	0	0
$446$	−1.70606e27	−0.259405
$447$	6.29856e27	0.935432
$448$	−4.82858e27	−0.700487
$449$	−7.95388e27	−1.12718	−0.563589	−	0.826056i	$-0.690580\pi$
$449$	−7.95388e27	−1.12718	−0.563589	+	0.826056i	$0.690580\pi$
$450$	0	0
$451$	−1.87774e26	−0.0253970
$452$	−5.71735e27	−0.755511
$453$	−3.80495e27	−0.491267
$454$	−1.72942e27	−0.218180
$455$	0	0
$456$	8.09560e26	0.0975256
$457$	4.40411e27	0.518487	0.259244	−	0.965812i	$-0.416527\pi$
$457$	4.40411e27	0.518487	0.259244	+	0.965812i	$0.416527\pi$
$458$	2.20429e27	0.253618
$459$	−2.55485e27	−0.287297
$460$	0	0
$461$	5.56648e27	0.598027	0.299014	−	0.954249i	$-0.403342\pi$
$461$	5.56648e27	0.598027	0.299014	+	0.954249i	$0.403342\pi$
$462$	−1.03404e26	−0.0108592
$463$	−5.57113e27	−0.571930	−0.285965	−	0.958240i	$-0.592314\pi$
$463$	−5.57113e27	−0.571930	−0.285965	+	0.958240i	$0.592314\pi$
$464$	−9.92182e27	−0.995755
$465$	0	0
$466$	−3.95529e26	−0.0379425
$467$	9.37044e26	0.0878886	0.0439443	−	0.999034i	$-0.486008\pi$
$467$	9.37044e26	0.0878886	0.0439443	+	0.999034i	$0.486008\pi$
$468$	−4.72820e27	−0.433625
$469$	1.18855e28	1.06587
$470$	0	0
$471$	−5.84232e27	−0.501033
$472$	−2.37526e27	−0.199214
$473$	1.22036e27	0.100103
$474$	1.31188e27	0.105250
$475$	0	0
$476$	−1.57699e28	−1.21048
$477$	−4.38757e27	−0.329444
$478$	3.78312e27	0.277880
$479$	2.09902e28	1.50832	0.754160	−	0.656690i	$-0.228044\pi$
$479$	2.09902e28	1.50832	0.754160	+	0.656690i	$0.228044\pi$
$480$	0	0
$481$	5.57682e27	0.383587
$482$	1.95939e27	0.131864
$483$	−9.00067e27	−0.592693
$484$	1.48146e28	0.954584
$485$	0	0
$486$	−1.71517e26	−0.0105834
$487$	−1.01659e28	−0.613890	−0.306945	−	0.951727i	$-0.599307\pi$
$487$	−1.01659e28	−0.613890	−0.306945	+	0.951727i	$0.599307\pi$
$488$	6.80439e27	0.402144
$489$	−6.40153e27	−0.370289
$490$	0	0
$491$	2.39966e28	1.32982	0.664912	−	0.746922i	$-0.268469\pi$
$491$	2.39966e28	1.32982	0.664912	+	0.746922i	$0.268469\pi$
$492$	−1.92252e27	−0.104289
$493$	−3.04581e28	−1.61737
$494$	2.20269e27	0.114504
$495$	0	0
$496$	2.65570e28	1.32319
$497$	3.92606e27	0.191520
$498$	−8.07417e26	−0.0385647
$499$	−1.36280e28	−0.637347	−0.318674	−	0.947865i	$-0.603237\pi$
$499$	−1.36280e28	−0.637347	−0.318674	+	0.947865i	$0.603237\pi$
$500$	0	0
$501$	4.58663e27	0.205683
$502$	6.12271e27	0.268878
$503$	8.66833e27	0.372796	0.186398	−	0.982474i	$-0.440319\pi$
$503$	8.66833e27	0.372796	0.186398	+	0.982474i	$0.440319\pi$
$504$	−2.14702e27	−0.0904305
$505$	0	0
$506$	6.87818e26	0.0277903
$507$	−1.15005e28	−0.455126
$508$	−1.45145e28	−0.562645
$509$	4.28603e28	1.62749	0.813746	−	0.581221i	$-0.197425\pi$
$509$	4.28603e28	1.62749	0.813746	+	0.581221i	$0.197425\pi$
$510$	0	0
$511$	−2.32253e28	−0.846333
$512$	2.06620e28	0.737628
$513$	−2.85575e27	−0.0998822
$514$	9.36716e27	0.320993
$515$	0	0
$516$	1.24946e28	0.411055
$517$	8.21601e27	0.264856
$518$	1.24871e27	0.0394458
$519$	2.74779e28	0.850602
$520$	0	0
$521$	3.43988e28	1.02270	0.511348	−	0.859374i	$-0.329146\pi$
$521$	3.43988e28	1.02270	0.511348	+	0.859374i	$0.329146\pi$
$522$	−2.04477e27	−0.0595806
$523$	1.93221e28	0.551805	0.275902	−	0.961186i	$-0.411023\pi$
$523$	1.93221e28	0.551805	0.275902	+	0.961186i	$0.411023\pi$
$524$	1.80048e28	0.503975
$525$	0	0
$526$	−1.08390e28	−0.291500
$527$	8.15249e28	2.14921
$528$	−2.80835e27	−0.0725764
$529$	2.03986e28	0.516793
$530$	0	0
$531$	8.37881e27	0.204028
$532$	−1.76273e28	−0.420836
$533$	−1.06081e28	−0.248315
$534$	1.70771e27	0.0391950
$535$	0	0
$536$	−1.88588e28	−0.416183
$537$	−4.97679e27	−0.107701
$538$	9.68024e27	0.205434
$539$	−2.00575e27	−0.0417442
$540$	0	0
$541$	7.87852e28	1.57715	0.788576	−	0.614937i	$-0.210819\pi$
$541$	7.87852e28	1.57715	0.788576	+	0.614937i	$0.210819\pi$
$542$	3.05762e27	0.0600332
$543$	−5.28502e26	−0.0101777
$544$	3.77060e28	0.712233
$545$	0	0
$546$	−5.84171e27	−0.106174
$547$	7.58840e28	1.35295	0.676477	−	0.736463i	$-0.263506\pi$
$547$	7.58840e28	1.35295	0.676477	+	0.736463i	$0.263506\pi$
$548$	−2.83989e28	−0.496713
$549$	−2.40027e28	−0.411861
$550$	0	0
$551$	−3.40454e28	−0.562298
$552$	1.42814e28	0.231426
$553$	−5.79287e28	−0.921043
$554$	5.37514e27	0.0838567
$555$	0	0
$556$	−1.00665e29	−1.51214
$557$	2.99634e28	0.441684	0.220842	−	0.975310i	$-0.429120\pi$
$557$	2.99634e28	0.441684	0.220842	+	0.975310i	$0.429120\pi$
$558$	5.47309e27	0.0791724
$559$	6.89429e28	0.978737
$560$	0	0
$561$	−8.62111e27	−0.117883
$562$	−1.71238e28	−0.229811
$563$	−5.00310e28	−0.659024	−0.329512	−	0.944151i	$-0.606884\pi$
$563$	−5.00310e28	−0.659024	−0.329512	+	0.944151i	$0.606884\pi$
$564$	8.41193e28	1.08759
$565$	0	0
$566$	−2.06479e28	−0.257219
$567$	7.57368e27	0.0926158
$568$	−6.22951e27	−0.0747819
$569$	−7.22336e28	−0.851257	−0.425628	−	0.904898i	$-0.639947\pi$
$569$	−7.22336e28	−0.851257	−0.425628	+	0.904898i	$0.639947\pi$
$570$	0	0
$571$	4.75601e28	0.540211	0.270105	−	0.962831i	$-0.412941\pi$
$571$	4.75601e28	0.540211	0.270105	+	0.962831i	$0.412941\pi$
$572$	−1.59549e28	−0.177924
$573$	−1.43173e28	−0.156761
$574$	−2.37528e27	−0.0255352
$575$	0	0
$576$	−2.70264e28	−0.280125
$577$	−1.81982e28	−0.185218	−0.0926089	−	0.995703i	$-0.529521\pi$
$577$	−1.81982e28	−0.185218	−0.0926089	+	0.995703i	$0.529521\pi$
$578$	2.02803e28	0.202690
$579$	2.39536e28	0.235096
$580$	0	0
$581$	3.56531e28	0.337480
$582$	1.04885e28	0.0975037
$583$	−1.48055e28	−0.135177
$584$	3.68517e28	0.330463
$585$	0	0
$586$	8.39719e27	0.0726456
$587$	1.43285e29	1.21759	0.608793	−	0.793329i	$-0.291654\pi$
$587$	1.43285e29	1.21759	0.608793	+	0.793329i	$0.291654\pi$
$588$	−2.05358e28	−0.171416
$589$	9.11267e28	0.747197
$590$	0	0
$591$	−7.72760e27	−0.0611471
$592$	3.39139e28	0.263633
$593$	8.65845e27	0.0661250	0.0330625	−	0.999453i	$-0.489474\pi$
$593$	8.65845e27	0.0661250	0.0330625	+	0.999453i	$0.489474\pi$
$594$	−5.78769e26	−0.00434258
$595$	0	0
$596$	2.17608e29	1.57612
$597$	−1.22161e29	−0.869366
$598$	3.88576e28	0.271715
$599$	−2.52821e29	−1.73712	−0.868562	−	0.495580i	$-0.834956\pi$
$599$	−2.52821e29	−1.73712	−0.868562	+	0.495580i	$0.834956\pi$
$600$	0	0
$601$	−2.34861e29	−1.55822	−0.779111	−	0.626886i	$-0.784329\pi$
$601$	−2.34861e29	−1.55822	−0.779111	+	0.626886i	$0.784329\pi$
$602$	1.54371e28	0.100647
$603$	6.65252e28	0.426240
$604$	−1.31456e29	−0.827739
$605$	0	0
$606$	−2.51861e28	−0.153178
$607$	−1.40619e29	−0.840551	−0.420275	−	0.907397i	$-0.638067\pi$
$607$	−1.40619e29	−0.840551	−0.420275	+	0.907397i	$0.638067\pi$
$608$	4.21469e28	0.247616
$609$	9.02911e28	0.521391
$610$	0	0
$611$	4.64155e29	2.58959
$612$	−8.82669e28	−0.484070
$613$	−2.49046e27	−0.0134259	−0.00671297	−	0.999977i	$-0.502137\pi$
$613$	−2.49046e27	−0.0134259	−0.00671297	+	0.999977i	$0.502137\pi$
$614$	−2.04971e28	−0.108624
$615$	0	0
$616$	−7.24492e27	−0.0371053
$617$	−3.02386e29	−1.52253	−0.761267	−	0.648439i	$-0.775422\pi$
$617$	−3.02386e29	−1.52253	−0.761267	+	0.648439i	$0.775422\pi$
$618$	2.87312e27	0.0142225
$619$	−1.15264e29	−0.560972	−0.280486	−	0.959858i	$-0.590496\pi$
$619$	−1.15264e29	−0.560972	−0.280486	+	0.959858i	$0.590496\pi$
$620$	0	0
$621$	−5.03782e28	−0.237018
$622$	4.40679e26	0.00203856
$623$	−7.54072e28	−0.342995
$624$	−1.58655e29	−0.709604
$625$	0	0
$626$	4.16249e28	0.180021
$627$	−9.63648e27	−0.0409835
$628$	−2.01845e29	−0.844193
$629$	1.04109e29	0.428210
$630$	0	0
$631$	3.78376e28	0.150527	0.0752636	−	0.997164i	$-0.476020\pi$
$631$	3.78376e28	0.150527	0.0752636	+	0.997164i	$0.476020\pi$
$632$	9.19160e28	0.359635
$633$	1.81381e29	0.697997
$634$	5.27226e28	0.199554
$635$	0	0
$636$	−1.51585e29	−0.555082
$637$	−1.13313e29	−0.408146
$638$	−6.89991e27	−0.0244470
$639$	2.19748e28	0.0765890
$640$	0	0
$641$	−3.77565e29	−1.27345	−0.636726	−	0.771090i	$-0.719712\pi$
$641$	−3.77565e29	−1.27345	−0.636726	+	0.771090i	$0.719712\pi$
$642$	−2.60398e27	−0.00864011
$643$	4.92823e29	1.60870	0.804351	−	0.594154i	$-0.202513\pi$
$643$	4.92823e29	1.60870	0.804351	+	0.594154i	$0.202513\pi$
$644$	−3.10962e29	−0.998633
$645$	0	0
$646$	4.11202e28	0.127824
$647$	1.91254e29	0.584946	0.292473	−	0.956274i	$-0.405522\pi$
$647$	1.91254e29	0.584946	0.292473	+	0.956274i	$0.405522\pi$
$648$	−1.20172e28	−0.0361632
$649$	2.82735e28	0.0837165
$650$	0	0
$651$	−2.41675e29	−0.692838
$652$	−2.21165e29	−0.623903
$653$	5.64626e29	1.56737	0.783686	−	0.621157i	$-0.213337\pi$
$653$	5.64626e29	1.56737	0.783686	+	0.621157i	$0.213337\pi$
$654$	2.65944e26	0.000726480 0
$655$	0	0
$656$	−6.45103e28	−0.170663
$657$	−1.29996e29	−0.338448
$658$	1.03930e29	0.266298
$659$	−7.36315e29	−1.85681	−0.928404	−	0.371573i	$-0.878819\pi$
$659$	−7.36315e29	−1.85681	−0.928404	+	0.371573i	$0.878819\pi$
$660$	0	0
$661$	−7.28744e29	−1.78016	−0.890081	−	0.455802i	$-0.849353\pi$
$661$	−7.28744e29	−1.78016	−0.890081	+	0.455802i	$0.849353\pi$
$662$	−2.64600e28	−0.0636182
$663$	−4.87041e29	−1.15259
$664$	−5.65711e28	−0.131774
$665$	0	0
$666$	6.98926e27	0.0157744
$667$	−6.00594e29	−1.33432
$668$	1.58463e29	0.346556
$669$	4.21660e29	0.907795
$670$	0	0
$671$	−8.09951e28	−0.168994
$672$	−1.11777e29	−0.229602
$673$	−5.49339e29	−1.11092	−0.555460	−	0.831543i	$-0.687458\pi$
$673$	−5.49339e29	−1.11092	−0.555460	+	0.831543i	$0.687458\pi$
$674$	−5.36276e28	−0.106773
$675$	0	0
$676$	−3.97327e29	−0.766845
$677$	4.21550e29	0.801065	0.400533	−	0.916282i	$-0.368825\pi$
$677$	4.21550e29	0.801065	0.400533	+	0.916282i	$0.368825\pi$
$678$	−3.95373e28	−0.0739767
$679$	−4.63139e29	−0.853256
$680$	0	0
$681$	4.27433e29	0.763525
$682$	1.84685e28	0.0324859
$683$	6.15920e29	1.06686	0.533430	−	0.845844i	$-0.320903\pi$
$683$	6.15920e29	1.06686	0.533430	+	0.845844i	$0.320903\pi$
$684$	−9.86628e28	−0.168292
$685$	0	0
$686$	−1.08503e29	−0.179489
$687$	−5.44799e29	−0.887545
$688$	4.19257e29	0.672670
$689$	−8.36420e29	−1.32167
$690$	0	0
$691$	3.19456e29	0.489657	0.244829	−	0.969566i	$-0.421268\pi$
$691$	3.19456e29	0.489657	0.244829	+	0.969566i	$0.421268\pi$
$692$	9.49328e29	1.43319
$693$	2.55567e28	0.0380020
$694$	−2.90694e28	−0.0425757
$695$	0	0
$696$	−1.43266e29	−0.203584
$697$	−1.98034e29	−0.277202
$698$	7.17383e28	0.0989167
$699$	9.77565e28	0.132781
$700$	0	0
$701$	3.68402e29	0.485605	0.242802	−	0.970076i	$-0.421933\pi$
$701$	3.68402e29	0.485605	0.242802	+	0.970076i	$0.421933\pi$
$702$	−3.26970e28	−0.0424589
$703$	1.16371e29	0.148872
$704$	−9.11981e28	−0.114940
$705$	0	0
$706$	−6.40224e28	−0.0783218
$707$	1.11214e30	1.34047
$708$	2.89478e29	0.343768
$709$	−2.65319e29	−0.310444	−0.155222	−	0.987880i	$-0.549609\pi$
$709$	−2.65319e29	−0.310444	−0.155222	+	0.987880i	$0.549609\pi$
$710$	0	0
$711$	−3.24237e29	−0.368325
$712$	1.19649e29	0.133928
$713$	1.60756e30	1.77308
$714$	−1.09054e29	−0.118525
$715$	0	0
$716$	−1.71942e29	−0.181466
$717$	−9.35013e29	−0.972448
$718$	−3.01932e29	−0.309459
$719$	−3.34469e28	−0.0337833	−0.0168916	−	0.999857i	$-0.505377\pi$
$719$	−3.34469e28	−0.0337833	−0.0168916	+	0.999857i	$0.505377\pi$
$720$	0	0
$721$	−1.26868e29	−0.124461
$722$	−1.24673e29	−0.120540
$723$	−4.84270e29	−0.461462
$724$	−1.82591e28	−0.0171484
$725$	0	0
$726$	1.02448e29	0.0934691
$727$	−2.10941e30	−1.89692	−0.948461	−	0.316893i	$-0.897360\pi$
$727$	−2.10941e30	−1.89692	−0.948461	+	0.316893i	$0.897360\pi$
$728$	−4.09295e29	−0.362791
$729$	4.23912e28	0.0370370
$730$	0	0
$731$	1.28704e30	1.09260
$732$	−8.29265e29	−0.693948
$733$	−7.89829e29	−0.651540	−0.325770	−	0.945449i	$-0.605624\pi$
$733$	−7.89829e29	−0.651540	−0.325770	+	0.945449i	$0.605624\pi$
$734$	6.24109e28	0.0507518
$735$	0	0
$736$	7.43513e29	0.587586
$737$	2.24483e29	0.174894
$738$	−1.32948e28	−0.0102115
$739$	1.77434e30	1.34360	0.671801	−	0.740732i	$-0.265521\pi$
$739$	1.77434e30	1.34360	0.671801	+	0.740732i	$0.265521\pi$
$740$	0	0
$741$	−5.44404e29	−0.400710
$742$	−1.87284e29	−0.135913
$743$	−4.10542e29	−0.293748	−0.146874	−	0.989155i	$-0.546921\pi$
$743$	−4.10542e29	−0.293748	−0.146874	+	0.989155i	$0.546921\pi$
$744$	3.83468e29	0.270529
$745$	0	0
$746$	5.83043e28	0.0399892
$747$	1.99556e29	0.134958
$748$	−2.97849e29	−0.198623
$749$	1.14984e29	0.0756097
$750$	0	0
$751$	9.69088e29	0.619647	0.309823	−	0.950794i	$-0.399730\pi$
$751$	9.69088e29	0.619647	0.309823	+	0.950794i	$0.399730\pi$
$752$	2.82263e30	1.77978
$753$	−1.51325e30	−0.940945
$754$	−3.89803e29	−0.239027
$755$	0	0
$756$	2.61662e29	0.156049
$757$	−7.60535e29	−0.447314	−0.223657	−	0.974668i	$-0.571800\pi$
$757$	−7.60535e29	−0.447314	−0.223657	+	0.974668i	$0.571800\pi$
$758$	−1.99892e29	−0.115949
$759$	−1.69997e29	−0.0972529
$760$	0	0
$761$	2.38436e30	1.32688	0.663442	−	0.748228i	$-0.269095\pi$
$761$	2.38436e30	1.32688	0.663442	+	0.748228i	$0.269095\pi$
$762$	−1.00373e29	−0.0550920
$763$	−1.17433e28	−0.00635743
$764$	−4.94645e29	−0.264127
$765$	0	0
$766$	−5.43150e29	−0.282174
$767$	1.59729e30	0.818524
$768$	−8.43826e29	−0.426540
$769$	1.52146e30	0.758636	0.379318	−	0.925266i	$-0.376159\pi$
$769$	1.52146e30	0.758636	0.379318	+	0.925266i	$0.376159\pi$
$770$	0	0
$771$	−2.31513e30	−1.12332
$772$	8.27568e29	0.396116
$773$	1.63448e30	0.771783	0.385891	−	0.922544i	$-0.373894\pi$
$773$	1.63448e30	0.771783	0.385891	+	0.922544i	$0.373894\pi$
$774$	8.64041e28	0.0402489
$775$	0	0
$776$	7.34867e29	0.333166
$777$	−3.08625e29	−0.138042
$778$	−6.52508e29	−0.287939
$779$	−2.21358e29	−0.0963724
$780$	0	0
$781$	7.41521e28	0.0314259
$782$	7.25400e29	0.303324
$783$	5.05374e29	0.208504
$784$	−6.89082e29	−0.280512
$785$	0	0
$786$	1.24509e29	0.0493472
$787$	1.59330e30	0.623109	0.311554	−	0.950228i	$-0.399150\pi$
$787$	1.59330e30	0.623109	0.311554	+	0.950228i	$0.399150\pi$
$788$	−2.66979e29	−0.103027
$789$	2.67890e30	1.02011
$790$	0	0
$791$	1.74585e30	0.647371
$792$	−4.05510e28	−0.0148384
$793$	−4.57574e30	−1.65231
$794$	−7.93725e29	−0.282849
$795$	0	0
$796$	−4.22052e30	−1.46480
$797$	3.98384e30	1.36455	0.682276	−	0.731095i	$-0.260990\pi$
$797$	3.98384e30	1.36455	0.682276	+	0.731095i	$0.260990\pi$
$798$	−1.21898e29	−0.0412066
$799$	8.66493e30	2.89084
$800$	0	0
$801$	−4.22067e29	−0.137164
$802$	4.79499e27	0.00153800
$803$	−4.38659e29	−0.138872
$804$	2.29837e30	0.718176
$805$	0	0
$806$	1.04336e30	0.317625
$807$	−2.39251e30	−0.718922
$808$	−1.76464e30	−0.523405
$809$	−5.29166e30	−1.54929	−0.774645	−	0.632396i	$-0.782071\pi$
$809$	−5.29166e30	−1.54929	−0.774645	+	0.632396i	$0.782071\pi$
$810$	0	0
$811$	−2.38103e30	−0.679276	−0.339638	−	0.940556i	$-0.610305\pi$
$811$	−2.38103e30	−0.679276	−0.339638	+	0.940556i	$0.610305\pi$
$812$	3.11945e30	0.878495
$813$	−7.55704e29	−0.210088
$814$	2.35846e28	0.00647252
$815$	0	0
$816$	−2.96180e30	−0.792153
$817$	1.43862e30	0.379853
$818$	−1.86041e29	−0.0484953
$819$	1.44380e30	0.371558
$820$	0	0
$821$	6.82391e30	1.71171	0.855855	−	0.517216i	$-0.173031\pi$
$821$	6.82391e30	1.71171	0.855855	+	0.517216i	$0.173031\pi$
$822$	−1.96387e29	−0.0486362
$823$	3.46830e30	0.848044	0.424022	−	0.905652i	$-0.360618\pi$
$823$	3.46830e30	0.848044	0.424022	+	0.905652i	$0.360618\pi$
$824$	2.01303e29	0.0485975
$825$	0	0
$826$	3.57650e29	0.0841721
$827$	3.88117e30	0.901893	0.450946	−	0.892551i	$-0.351087\pi$
$827$	3.88117e30	0.901893	0.450946	+	0.892551i	$0.351087\pi$
$828$	−1.74051e30	−0.399353
$829$	2.71415e30	0.614909	0.307454	−	0.951563i	$-0.400523\pi$
$829$	2.71415e30	0.614909	0.307454	+	0.951563i	$0.400523\pi$
$830$	0	0
$831$	−1.32849e30	−0.293459
$832$	−5.15215e30	−1.12381
$833$	−2.11535e30	−0.455627
$834$	−6.96127e29	−0.148062
$835$	0	0
$836$	−3.32929e29	−0.0690535
$837$	−1.35270e30	−0.277066
$838$	6.34644e29	0.128371
$839$	7.41628e30	1.48144	0.740722	−	0.671811i	$-0.234483\pi$
$839$	7.41628e30	1.48144	0.740722	+	0.671811i	$0.234483\pi$
$840$	0	0
$841$	8.92068e29	0.173796
$842$	−1.26786e30	−0.243946
$843$	4.23223e30	0.804229
$844$	6.26651e30	1.17606
$845$	0	0
$846$	5.81712e29	0.106492
$847$	−4.52379e30	−0.817949
$848$	−5.08645e30	−0.908361
$849$	5.10321e30	0.900145
$850$	0	0
$851$	2.05290e30	0.353270
$852$	7.59203e29	0.129045
$853$	1.13715e31	1.90920	0.954602	−	0.297885i	$-0.0962811\pi$
$853$	1.13715e31	1.90920	0.954602	+	0.297885i	$0.0962811\pi$
$854$	−1.02456e30	−0.169914
$855$	0	0
$856$	−1.82446e29	−0.0295229
$857$	1.05299e31	1.68315	0.841577	−	0.540137i	$-0.181628\pi$
$857$	1.05299e31	1.68315	0.841577	+	0.540137i	$0.181628\pi$
$858$	−1.10333e29	−0.0174217
$859$	−7.09784e30	−1.10713	−0.553564	−	0.832806i	$-0.686733\pi$
$859$	−7.09784e30	−1.10713	−0.553564	+	0.832806i	$0.686733\pi$
$860$	0	0
$861$	5.87060e29	0.0893613
$862$	−9.69025e29	−0.145716
$863$	−3.54700e27	−0.000526923 0	−0.000263462	−	1.00000i	$-0.500084\pi$
$863$	−3.54700e27	−0.000526923 0	−0.000263462		1.00000i	$0.500084\pi$
$864$	−6.25635e29	−0.0918177
$865$	0	0
$866$	1.08561e30	0.155502
$867$	−5.01236e30	−0.709319
$868$	−8.34959e30	−1.16737
$869$	−1.09411e30	−0.151131
$870$	0	0
$871$	1.26820e31	1.71000
$872$	1.86332e28	0.00248235
$873$	−2.59227e30	−0.341217
$874$	8.10836e29	0.105454
$875$	0	0
$876$	−4.49119e30	−0.570254
$877$	−1.15261e31	−1.44607	−0.723033	−	0.690814i	$-0.757252\pi$
$877$	−1.15261e31	−1.44607	−0.723033	+	0.690814i	$0.757252\pi$
$878$	−2.09225e30	−0.259370
$879$	−2.07540e30	−0.254225
$880$	0	0
$881$	9.58779e30	1.14676	0.573379	−	0.819291i	$-0.305632\pi$
$881$	9.58779e30	1.14676	0.573379	+	0.819291i	$0.305632\pi$
$882$	−1.42012e29	−0.0167843
$883$	−5.46477e30	−0.638241	−0.319120	−	0.947714i	$-0.603387\pi$
$883$	−5.46477e30	−0.638241	−0.319120	+	0.947714i	$0.603387\pi$
$884$	−1.68267e31	−1.94200
$885$	0	0
$886$	3.01341e29	0.0339629
$887$	1.25659e31	1.39957	0.699787	−	0.714352i	$-0.253278\pi$
$887$	1.25659e31	1.39957	0.699787	+	0.714352i	$0.253278\pi$
$888$	4.89697e29	0.0539004
$889$	4.43216e30	0.482110
$890$	0	0
$891$	1.43045e29	0.0151970
$892$	1.45678e31	1.52955
$893$	9.68547e30	1.00503
$894$	1.50483e30	0.154327
$895$	0	0
$896$	−5.12344e30	−0.513248
$897$	−9.60381e30	−0.950874
$898$	−1.90031e30	−0.185961
$899$	−1.61264e31	−1.55977
$900$	0	0
$901$	−1.56144e31	−1.47542
$902$	−4.48622e28	−0.00418998
$903$	−3.81534e30	−0.352219
$904$	−2.77015e30	−0.252775
$905$	0	0
$906$	−9.09061e29	−0.0810489
$907$	−1.10098e31	−0.970292	−0.485146	−	0.874433i	$-0.661234\pi$
$907$	−1.10098e31	−0.970292	−0.485146	+	0.874433i	$0.661234\pi$
$908$	1.47673e31	1.28647
$909$	6.22484e30	0.536052
$910$	0	0
$911$	1.42131e30	0.119604	0.0598021	−	0.998210i	$-0.480953\pi$
$911$	1.42131e30	0.119604	0.0598021	+	0.998210i	$0.480953\pi$
$912$	−3.31064e30	−0.275401
$913$	6.73385e29	0.0553758
$914$	1.05221e30	0.0855398
$915$	0	0
$916$	−1.88221e31	−1.49543
$917$	−5.49793e30	−0.431838
$918$	−6.10393e29	−0.0473982
$919$	−3.78618e30	−0.290662	−0.145331	−	0.989383i	$-0.546425\pi$
$919$	−3.78618e30	−0.290662	−0.145331	+	0.989383i	$0.546425\pi$
$920$	0	0
$921$	5.06595e30	0.380132
$922$	1.32992e30	0.0986622
$923$	4.18915e30	0.307261
$924$	8.82953e29	0.0640298
$925$	0	0
$926$	−1.33103e30	−0.0943567
$927$	−7.10103e29	−0.0497719
$928$	−7.45862e30	−0.516898
$929$	−2.18847e31	−1.49960	−0.749801	−	0.661664i	$-0.769851\pi$
$929$	−2.18847e31	−1.49960	−0.749801	+	0.661664i	$0.769851\pi$
$930$	0	0
$931$	−2.36449e30	−0.158404
$932$	3.37737e30	0.223723
$933$	−1.08916e29	−0.00713399
$934$	2.23875e29	0.0144998
$935$	0	0
$936$	−2.29089e30	−0.145080
$937$	−4.82022e30	−0.301857	−0.150928	−	0.988545i	$-0.548226\pi$
$937$	−4.82022e30	−0.301857	−0.150928	+	0.988545i	$0.548226\pi$
$938$	2.83964e30	0.175846
$939$	−1.02878e31	−0.629988
$940$	0	0
$941$	4.95284e30	0.296594	0.148297	−	0.988943i	$-0.452621\pi$
$941$	4.95284e30	0.296594	0.148297	+	0.988943i	$0.452621\pi$
$942$	−1.39582e30	−0.0826601
$943$	−3.90498e30	−0.228689
$944$	9.71344e30	0.562558
$945$	0	0
$946$	2.91563e29	0.0165149
$947$	1.93524e30	0.108408	0.0542038	−	0.998530i	$-0.482738\pi$
$947$	1.93524e30	0.108408	0.0542038	+	0.998530i	$0.482738\pi$
$948$	−1.12020e31	−0.620594
$949$	−2.47816e31	−1.35779
$950$	0	0
$951$	−1.30306e31	−0.698343
$952$	−7.64079e30	−0.404995
$953$	2.80007e31	1.46789	0.733946	−	0.679208i	$-0.237677\pi$
$953$	2.80007e31	1.46789	0.733946	+	0.679208i	$0.237677\pi$
$954$	−1.04826e30	−0.0543514
$955$	0	0
$956$	−3.23036e31	−1.63849
$957$	1.70534e30	0.0855531
$958$	5.01489e30	0.248842
$959$	8.67187e30	0.425615
$960$	0	0
$961$	2.23389e31	1.07267
$962$	1.33239e30	0.0632839
$963$	6.43584e29	0.0302363
$964$	−1.67309e31	−0.777520
$965$	0	0
$966$	−2.15040e30	−0.0977822
$967$	−3.92899e31	−1.76727	−0.883634	−	0.468177i	$-0.844911\pi$
$967$	−3.92899e31	−1.76727	−0.883634	+	0.468177i	$0.844911\pi$
$968$	7.17793e30	0.319380
$969$	−1.01630e31	−0.447325
$970$	0	0
$971$	3.41965e31	1.47292	0.736462	−	0.676479i	$-0.236495\pi$
$971$	3.41965e31	1.47292	0.736462	+	0.676479i	$0.236495\pi$
$972$	1.46456e30	0.0624040
$973$	3.07389e31	1.29570
$974$	−2.42879e30	−0.101279
$975$	0	0
$976$	−2.78261e31	−1.13561
$977$	−4.27738e30	−0.172697	−0.0863486	−	0.996265i	$-0.527520\pi$
$977$	−4.27738e30	−0.172697	−0.0863486	+	0.996265i	$0.527520\pi$
$978$	−1.52943e30	−0.0610901
$979$	−1.42423e30	−0.0562809
$980$	0	0
$981$	−6.57291e28	−0.00254234
$982$	5.73317e30	0.219394
$983$	3.07553e31	1.16441	0.582207	−	0.813041i	$-0.302189\pi$
$983$	3.07553e31	1.16441	0.582207	+	0.813041i	$0.302189\pi$
$984$	−9.31492e29	−0.0348924
$985$	0	0
$986$	−7.27692e30	−0.266833
$987$	−2.56866e31	−0.931917
$988$	−1.88085e31	−0.675159
$989$	2.53787e31	0.901382
$990$	0	0
$991$	1.50222e30	0.0522348	0.0261174	−	0.999659i	$-0.491686\pi$
$991$	1.50222e30	0.0522348	0.0261174	+	0.999659i	$0.491686\pi$
$992$	1.99639e31	0.686868
$993$	6.53970e30	0.222634
$994$	9.37998e29	0.0315969
$995$	0	0
$996$	6.89443e30	0.227392
$997$	4.25981e31	1.39024	0.695122	−	0.718891i	$-0.255350\pi$
$997$	4.25981e31	1.39024	0.695122	+	0.718891i	$0.255350\pi$
$998$	−3.25594e30	−0.105149
$999$	−1.72742e30	−0.0552028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.a.l.1.5	yes	8
5.2	odd	4		75.22.b.j.49.10		16
5.3	odd	4		75.22.b.j.49.7		16
5.4	even	2		75.22.a.k.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.22.a.k.1.4	✓	8	5.4	even	2
75.22.a.l.1.5	yes	8	1.1	even	1	trivial
75.22.b.j.49.7		16	5.3	odd	4
75.22.b.j.49.10		16	5.2	odd	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+238.916 q^{2} -59049.0 q^{3} -2.04007e6 q^{4} -1.41077e7 q^{6} +6.22955e8 q^{7} -9.88448e8 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q+238.916 q^{2} -59049.0 q^{3} -2.04007e6 q^{4} -1.41077e7 q^{6} +6.22955e8 q^{7} -9.88448e8 q^{8} +3.48678e9 q^{9} +1.17658e10 q^{11} +1.20464e11 q^{12} +6.64700e11 q^{13} +1.48834e11 q^{14} +4.04218e12 q^{16} +1.24087e13 q^{17} +8.33048e11 q^{18} +1.38702e13 q^{19} -3.67849e13 q^{21} +2.81105e12 q^{22} +2.44684e14 q^{23} +5.83669e13 q^{24} +1.58807e14 q^{26} -2.05891e14 q^{27} -1.27087e15 q^{28} -2.45457e15 q^{29} +6.56996e15 q^{31} +3.03867e15 q^{32} -6.94761e14 q^{33} +2.96464e15 q^{34} -7.11329e15 q^{36} +8.38999e15 q^{37} +3.31381e15 q^{38} -3.92499e16 q^{39} -1.59593e16 q^{41} -8.78849e15 q^{42} +1.03720e17 q^{43} -2.40032e16 q^{44} +5.84589e16 q^{46} +6.98293e17 q^{47} -2.38687e17 q^{48} -1.70473e17 q^{49} -7.32723e17 q^{51} -1.35603e18 q^{52} -1.25834e18 q^{53} -4.91906e16 q^{54} -6.15759e17 q^{56} -8.19022e17 q^{57} -5.86435e17 q^{58} +2.40302e18 q^{59} -6.88392e18 q^{61} +1.56967e18 q^{62} +2.17211e18 q^{63} -7.75109e18 q^{64} -1.65989e17 q^{66} +1.90793e19 q^{67} -2.53147e19 q^{68} -1.44483e19 q^{69} +6.30232e18 q^{71} -3.44650e18 q^{72} -3.72824e19 q^{73} +2.00450e18 q^{74} -2.82962e19 q^{76} +7.32959e18 q^{77} -9.37741e18 q^{78} -9.29902e19 q^{79} +1.21577e19 q^{81} -3.81292e18 q^{82} +5.72322e19 q^{83} +7.50438e19 q^{84} +2.47804e19 q^{86} +1.44940e20 q^{87} -1.16299e19 q^{88} -1.21048e20 q^{89} +4.14078e20 q^{91} -4.99173e20 q^{92} -3.87950e20 q^{93} +1.66833e20 q^{94} -1.79430e20 q^{96} -7.43455e20 q^{97} -4.07286e19 q^{98} +4.10250e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 666 q^{2} - 472392 q^{3} + 10681904 q^{4} - 39326634 q^{6} + 134034472 q^{7} + 3512168028 q^{8} + 27894275208 q^{9}+O(q^{10}) \) 8 * q + 666 * q^2 - 472392 * q^3 + 10681904 * q^4 - 39326634 * q^6 + 134034472 * q^7 + 3512168028 * q^8 + 27894275208 * q^9	\( 8 q + 666 q^{2} - 472392 q^{3} + 10681904 q^{4} - 39326634 q^{6} + 134034472 q^{7} + 3512168028 q^{8} + 27894275208 q^{9} - 14410165968 q^{11} - 630755749296 q^{12} - 328226481176 q^{13} + 4068036669186 q^{14} + 18553054308920 q^{16} - 5718214953936 q^{17} + 2322198411066 q^{18} + 75919698170296 q^{19} - 7914601537128 q^{21} - 426897542691372 q^{22} + 49712781537936 q^{23} - 207390009885372 q^{24} - 126056679642054 q^{26} - 16\!\cdots\!92 q^{27}+ \cdots - 50\!\cdots\!68 q^{99}+O(q^{100}) \) 8 * q + 666 * q^2 - 472392 * q^3 + 10681904 * q^4 - 39326634 * q^6 + 134034472 * q^7 + 3512168028 * q^8 + 27894275208 * q^9 - 14410165968 * q^11 - 630755749296 * q^12 - 328226481176 * q^13 + 4068036669186 * q^14 + 18553054308920 * q^16 - 5718214953936 * q^17 + 2322198411066 * q^18 + 75919698170296 * q^19 - 7914601537128 * q^21 - 426897542691372 * q^22 + 49712781537936 * q^23 - 207390009885372 * q^24 - 126056679642054 * q^26 - 1647129056757192 * q^27 + 4235167126399504 * q^28 + 2111332005818352 * q^29 + 5677451410844968 * q^31 + 17528957992420632 * q^32 + 850905890244432 * q^33 + 9944754702742068 * q^34 + 37245496240179504 * q^36 - 26538401323409648 * q^37 + 85729618982552526 * q^38 + 19381445486961624 * q^39 - 9719778050982432 * q^41 - 240213497278764114 * q^42 - 20888744714565080 * q^43 - 388904820117856128 * q^44 - 156886987299808452 * q^46 + 405141072730526160 * q^47 - 1095539303887417080 * q^48 + 1172899395436368720 * q^49 + 337654874814966864 * q^51 - 2264281219115894096 * q^52 + 1890950875516930176 * q^53 - 137123493975036234 * q^54 + 19720793170524660300 * q^56 - 4482982257257808504 * q^57 + 12636224332772065092 * q^58 - 3496737905134765776 * q^59 + 17508733151770015960 * q^61 - 30404101355896200606 * q^62 + 467349306165871272 * q^63 + 27809823573720908096 * q^64 + 25207872998382825228 * q^66 - 29911607071855004216 * q^67 - 29571773973515759808 * q^68 - 2935490037033582864 * q^69 + 52204030316256846816 * q^71 + 12246172693721331228 * q^72 - 39697032757192143344 * q^73 - 32301811215943606764 * q^74 + 383913379529874070384 * q^76 - 202348742072764877136 * q^77 + 7443520876183646646 * q^78 - 274125739348498990400 * q^79 + 97261323672455430408 * q^81 - 231746572148446490256 * q^82 - 276883976086286712912 * q^83 - 250082383646764311696 * q^84 + 486708932755841131242 * q^86 - 124672043611567867248 * q^87 - 2078122304879724561672 * q^88 - 319129684977517046784 * q^89 + 45068531423660000648 * q^91 + 147706203809955886272 * q^92 - 335247828358984515432 * q^93 - 1499781052151613424236 * q^94 - 1035067440494445898968 * q^96 + 451807368184588489864 * q^97 - 2604193962467412900204 * q^98 - 50245141913043465168 * q^99

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