LMFDB - Embedded newform 25.32.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,32,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	25.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:	$152.192832048$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4573872 $ x^2 - x - 4573872
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2139.16$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-71307.9 q^{2} -3.08552e7 q^{3} +2.93733e9 q^{4} +2.20022e12 q^{6} -1.14368e13 q^{7} -5.63222e13 q^{8} +3.34371e14 q^{9} +O(q^{10})$	\(q-71307.9 q^{2} -3.08552e7 q^{3} +2.93733e9 q^{4} +2.20022e12 q^{6} -1.14368e13 q^{7} -5.63222e13 q^{8} +3.34371e14 q^{9} -2.40262e15 q^{11} -9.06319e16 q^{12} +2.01886e17 q^{13} +8.15534e17 q^{14} -2.29165e18 q^{16} -1.09264e19 q^{17} -2.38433e19 q^{18} -1.42851e19 q^{19} +3.52885e20 q^{21} +1.71326e20 q^{22} +3.85062e18 q^{23} +1.73783e21 q^{24} -1.43960e22 q^{26} +8.74135e21 q^{27} -3.35937e22 q^{28} +7.63087e22 q^{29} +1.86701e23 q^{31} +2.84364e23 q^{32} +7.41334e22 q^{33} +7.79141e23 q^{34} +9.82158e23 q^{36} -1.23709e24 q^{37} +1.01864e24 q^{38} -6.22922e24 q^{39} +1.38199e25 q^{41} -2.51635e25 q^{42} +2.67871e25 q^{43} -7.05729e24 q^{44} -2.74580e23 q^{46} -7.40922e25 q^{47} +7.07094e25 q^{48} -2.69748e25 q^{49} +3.37138e26 q^{51} +5.93004e26 q^{52} -3.56092e25 q^{53} -6.23327e26 q^{54} +6.44146e26 q^{56} +4.40770e26 q^{57} -5.44141e27 q^{58} -2.36122e27 q^{59} -5.44842e27 q^{61} -1.33133e28 q^{62} -3.82414e27 q^{63} -1.53561e28 q^{64} -5.28630e27 q^{66} +9.41082e27 q^{67} -3.20945e28 q^{68} -1.18812e26 q^{69} -2.10678e28 q^{71} -1.88325e28 q^{72} -3.92731e28 q^{73} +8.82146e28 q^{74} -4.19601e28 q^{76} +2.74783e28 q^{77} +4.44193e29 q^{78} +1.79850e29 q^{79} -4.76249e29 q^{81} -9.85468e29 q^{82} +4.54329e29 q^{83} +1.03654e30 q^{84} -1.91013e30 q^{86} -2.35452e30 q^{87} +1.35321e29 q^{88} +2.60812e29 q^{89} -2.30893e30 q^{91} +1.13106e28 q^{92} -5.76072e30 q^{93} +5.28336e30 q^{94} -8.77410e30 q^{96} +5.38067e30 q^{97} +1.92352e30 q^{98} -8.03368e29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) $ 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9	$ 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9} - 77\!\cdots\!76 q^{11}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9 - 7782353745118776 * q^11 - 106347410955313920 * q^12 - 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 37499616229575978360 * q^18 - 12370563328022164040 * q^19 + 98954957416071161664 * q^21 + 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 - 23066680666744323279216 * q^26 - 5469986602319662295280 * q^27 - 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 1489586748818199413504832 * q^36 + 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 8724924335662925840671284 * q^41 - 33123669600002676603713280 * q^42 + 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 252162404739970320085380144 * q^51 + 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 + 2598355397749815172431728640 * q^56 + 466601717043760934967596640 * q^57 - 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 + 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 - 7561640583442461364265814912 * q^66 + 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 + 55784576625034657512878287344 * q^71 + 26400994734811244163462812160 * q^72 - 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 + 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 - 398906922646891269649062634158 * q^81 - 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 2173142482222838422832927019936 * q^86 - 1649324800814841914442821796240 * q^87 + 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 - 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 - 6084370432669606716368714858496 * q^96 + 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * 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 $

$2$	−71307.9	−1.53877	−0.769383	−	0.638788i	$-0.779436\pi$
$2$	−71307.9	−1.53877	−0.769383	+	0.638788i	$0.779436\pi$
$3$	−3.08552e7	−1.24151	−0.620754	−	0.784006i	$-0.713173\pi$
$3$	−3.08552e7	−1.24151	−0.620754	+	0.784006i	$0.713173\pi$
$4$	2.93733e9	1.36780
$5$	0	0
$5$	0	0
$6$	2.20022e12	1.91039
$7$	−1.14368e13	−0.910511	−0.455256	−	0.890361i	$-0.650452\pi$
$7$	−1.14368e13	−0.910511	−0.455256	+	0.890361i	$0.650452\pi$
$8$	−5.63222e13	−0.565959
$9$	3.34371e14	0.541340
$10$	0	0
$11$	−2.40262e15	−0.173420	−0.0867099	−	0.996234i	$-0.527635\pi$
$11$	−2.40262e15	−0.173420	−0.0867099	+	0.996234i	$0.527635\pi$
$12$	−9.06319e16	−1.69813
$13$	2.01886e17	1.09391	0.546957	−	0.837161i	$-0.315786\pi$
$13$	2.01886e17	1.09391	0.546957	+	0.837161i	$0.315786\pi$
$14$	8.15534e17	1.40106
$15$	0	0
$16$	−2.29165e18	−0.496923
$17$	−1.09264e19	−0.925807	−0.462903	−	0.886409i	$-0.653192\pi$
$17$	−1.09264e19	−0.925807	−0.462903	+	0.886409i	$0.653192\pi$
$18$	−2.38433e19	−0.832995
$19$	−1.42851e19	−0.215875	−0.107938	−	0.994158i	$-0.534425\pi$
$19$	−1.42851e19	−0.215875	−0.107938	+	0.994158i	$0.534425\pi$
$20$	0	0
$21$	3.52885e20	1.13041
$22$	1.71326e20	0.266853
$23$	3.85062e18	0.00301127	0.00150564	−	0.999999i	$-0.499521\pi$
$23$	3.85062e18	0.00301127	0.00150564	+	0.999999i	$0.499521\pi$
$24$	1.73783e21	0.702642
$25$	0	0
$26$	−1.43960e22	−1.68328
$27$	8.74135e21	0.569430
$28$	−3.35937e22	−1.24540
$29$	7.63087e22	1.64212	0.821060	−	0.570842i	$-0.193383\pi$
$29$	7.63087e22	1.64212	0.821060	+	0.570842i	$0.193383\pi$
$30$	0	0
$31$	1.86701e23	1.42903	0.714515	−	0.699620i	$-0.246647\pi$
$31$	1.86701e23	1.42903	0.714515	+	0.699620i	$0.246647\pi$
$32$	2.84364e23	1.33061
$33$	7.41334e22	0.215302
$34$	7.79141e23	1.42460
$35$	0	0
$36$	9.82158e23	0.740445
$37$	−1.23709e24	−0.609924	−0.304962	−	0.952364i	$-0.598644\pi$
$37$	−1.23709e24	−0.609924	−0.304962	+	0.952364i	$0.598644\pi$
$38$	1.01864e24	0.332182
$39$	−6.22922e24	−1.35810
$40$	0	0
$41$	1.38199e25	1.38789	0.693945	−	0.720028i	$-0.255871\pi$
$41$	1.38199e25	1.38789	0.693945	+	0.720028i	$0.255871\pi$
$42$	−2.51635e25	−1.73943
$43$	2.67871e25	1.28578	0.642888	−	0.765960i	$-0.277736\pi$
$43$	2.67871e25	1.28578	0.642888	+	0.765960i	$0.277736\pi$
$44$	−7.05729e24	−0.237204
$45$	0	0
$46$	−2.74580e23	−0.00463364
$47$	−7.40922e25	−0.895892	−0.447946	−	0.894061i	$-0.647844\pi$
$47$	−7.40922e25	−0.895892	−0.447946	+	0.894061i	$0.647844\pi$
$48$	7.07094e25	0.616933
$49$	−2.69748e25	−0.170970
$50$	0	0
$51$	3.37138e26	1.14940
$52$	5.93004e26	1.49626
$53$	−3.56092e25	−0.0668784	−0.0334392	−	0.999441i	$-0.510646\pi$
$53$	−3.56092e25	−0.0668784	−0.0334392	+	0.999441i	$0.510646\pi$
$54$	−6.23327e26	−0.876219
$55$	0	0
$56$	6.44146e26	0.515312
$57$	4.40770e26	0.268011
$58$	−5.44141e27	−2.52684
$59$	−2.36122e27	−0.841260	−0.420630	−	0.907232i	$-0.638191\pi$
$59$	−2.36122e27	−0.841260	−0.420630	+	0.907232i	$0.638191\pi$
$60$	0	0
$61$	−5.44842e27	−1.15786	−0.578932	−	0.815376i	$-0.696530\pi$
$61$	−5.44842e27	−1.15786	−0.578932	+	0.815376i	$0.696530\pi$
$62$	−1.33133e28	−2.19894
$63$	−3.82414e27	−0.492896
$64$	−1.53561e28	−1.55057
$65$	0	0
$66$	−5.28630e27	−0.331299
$67$	9.41082e27	0.467163	0.233581	−	0.972337i	$-0.424956\pi$
$67$	9.41082e27	0.467163	0.233581	+	0.972337i	$0.424956\pi$
$68$	−3.20945e28	−1.26632
$69$	−1.18812e26	−0.00373851
$70$	0	0
$71$	−2.10678e28	−0.425712	−0.212856	−	0.977084i	$-0.568276\pi$
$71$	−2.10678e28	−0.425712	−0.212856	+	0.977084i	$0.568276\pi$
$72$	−1.88325e28	−0.306376
$73$	−3.92731e28	−0.515929	−0.257965	−	0.966154i	$-0.583052\pi$
$73$	−3.92731e28	−0.515929	−0.257965	+	0.966154i	$0.583052\pi$
$74$	8.82146e28	0.938531
$75$	0	0
$76$	−4.19601e28	−0.295274
$77$	2.74783e28	0.157901
$78$	4.44193e29	2.08980
$79$	1.79850e29	0.694529	0.347264	−	0.937767i	$-0.387111\pi$
$79$	1.79850e29	0.694529	0.347264	+	0.937767i	$0.387111\pi$
$80$	0	0
$81$	−4.76249e29	−1.24829
$82$	−9.85468e29	−2.13564
$83$	4.54329e29	0.815944	0.407972	−	0.912995i	$-0.366236\pi$
$83$	4.54329e29	0.815944	0.407972	+	0.912995i	$0.366236\pi$
$84$	1.03654e30	1.54617
$85$	0	0
$86$	−1.91013e30	−1.97851
$87$	−2.35452e30	−2.03870
$88$	1.35321e29	0.0981485
$89$	2.60812e29	0.158775	0.0793875	−	0.996844i	$-0.474704\pi$
$89$	2.60812e29	0.158775	0.0793875	+	0.996844i	$0.474704\pi$
$90$	0	0
$91$	−2.30893e30	−0.996021
$92$	1.13106e28	0.00411882
$93$	−5.76072e30	−1.77415
$94$	5.28336e30	1.37857
$95$	0	0
$96$	−8.77410e30	−1.65196
$97$	5.38067e30	0.862729	0.431365	−	0.902178i	$-0.358032\pi$
$97$	5.38067e30	0.862729	0.431365	+	0.902178i	$0.358032\pi$
$98$	1.92352e30	0.263082
$99$	−8.03368e29	−0.0938791
$100$	0	0
$101$	−1.28863e31	−1.10445	−0.552225	−	0.833695i	$-0.686221\pi$
$101$	−1.28863e31	−1.10445	−0.552225	+	0.833695i	$0.686221\pi$
$102$	−2.40406e31	−1.76865
$103$	−1.91208e31	−1.20928	−0.604642	−	0.796497i	$-0.706684\pi$
$103$	−1.91208e31	−1.20928	−0.604642	+	0.796497i	$0.706684\pi$
$104$	−1.13706e31	−0.619110
$105$	0	0
$106$	2.53922e30	0.102910
$107$	−3.15334e31	−1.10490	−0.552449	−	0.833547i	$-0.686307\pi$
$107$	−3.15334e31	−1.10490	−0.552449	+	0.833547i	$0.686307\pi$
$108$	2.56762e31	0.778866
$109$	−3.61029e31	−0.949360	−0.474680	−	0.880158i	$-0.657436\pi$
$109$	−3.61029e31	−0.949360	−0.474680	+	0.880158i	$0.657436\pi$
$110$	0	0
$111$	3.81708e31	0.757226
$112$	2.62092e31	0.452453
$113$	−1.52549e31	−0.229454	−0.114727	−	0.993397i	$-0.536599\pi$
$113$	−1.52549e31	−0.229454	−0.114727	+	0.993397i	$0.536599\pi$
$114$	−3.14304e31	−0.412406
$115$	0	0
$116$	2.24144e32	2.24609
$117$	6.75047e31	0.592179
$118$	1.68374e32	1.29450
$119$	1.24964e32	0.842957
$120$	0	0
$121$	−1.86171e32	−0.969926
$122$	3.88515e32	1.78168
$123$	−4.26416e32	−1.72308
$124$	5.48404e32	1.95463
$125$	0	0
$126$	2.72691e32	0.758451
$127$	5.69060e32	1.40023	0.700116	−	0.714029i	$-0.253131\pi$
$127$	5.69060e32	1.40023	0.700116	+	0.714029i	$0.253131\pi$
$128$	4.84344e32	1.05536
$129$	−8.26523e32	−1.59630
$130$	0	0
$131$	1.80373e31	0.0274452	0.0137226	−	0.999906i	$-0.495632\pi$
$131$	1.80373e31	0.0274452	0.0137226	+	0.999906i	$0.495632\pi$
$132$	2.17754e32	0.294490
$133$	1.63376e32	0.196557
$134$	−6.71065e32	−0.718854
$135$	0	0
$136$	6.15401e32	0.523968
$137$	1.53340e32	0.116543	0.0582716	−	0.998301i	$-0.481441\pi$
$137$	1.53340e32	0.116543	0.0582716	+	0.998301i	$0.481441\pi$
$138$	8.47222e30	0.00575270
$139$	1.88034e33	1.14158	0.570791	−	0.821095i	$-0.306636\pi$
$139$	1.88034e33	1.14158	0.570791	+	0.821095i	$0.306636\pi$
$140$	0	0
$141$	2.28613e33	1.11226
$142$	1.50230e33	0.655070
$143$	−4.85055e32	−0.189706
$144$	−7.66262e32	−0.269004
$145$	0	0
$146$	2.80048e33	0.793895
$147$	8.32313e32	0.212260
$148$	−3.63375e33	−0.834255
$149$	6.64703e33	1.37480	0.687401	−	0.726278i	$-0.258751\pi$
$149$	6.64703e33	1.37480	0.687401	+	0.726278i	$0.258751\pi$
$150$	0	0
$151$	−6.58887e33	−1.10833	−0.554164	−	0.832408i	$-0.686962\pi$
$151$	−6.58887e33	−1.10833	−0.554164	+	0.832408i	$0.686962\pi$
$152$	8.04569e32	0.122177
$153$	−3.65349e33	−0.501176
$154$	−1.95942e33	−0.242972
$155$	0	0
$156$	−1.82973e34	−1.85761
$157$	−1.60319e34	−1.47414	−0.737072	−	0.675814i	$-0.763792\pi$
$157$	−1.60319e34	−1.47414	−0.737072	+	0.675814i	$0.763792\pi$
$158$	−1.28247e34	−1.06872
$159$	1.09873e33	0.0830300
$160$	0	0
$161$	−4.40389e31	−0.00274179
$162$	3.39603e34	1.92083
$163$	1.63484e34	0.840555	0.420277	−	0.907396i	$-0.361933\pi$
$163$	1.63484e34	0.840555	0.420277	+	0.907396i	$0.361933\pi$
$164$	4.05936e34	1.89836
$165$	0	0
$166$	−3.23972e34	−1.25555
$167$	−1.68065e34	−0.593433	−0.296717	−	0.954966i	$-0.595892\pi$
$167$	−1.68065e34	−0.593433	−0.296717	+	0.954966i	$0.595892\pi$
$168$	−1.98753e34	−0.639763
$169$	6.69784e33	0.196649
$170$	0	0
$171$	−4.77653e33	−0.116862
$172$	7.86826e34	1.75868
$173$	−1.67734e34	−0.342695	−0.171347	−	0.985211i	$-0.554812\pi$
$173$	−1.67734e34	−0.342695	−0.171347	+	0.985211i	$0.554812\pi$
$174$	1.67896e35	3.13709
$175$	0	0
$176$	5.50597e33	0.0861762
$177$	7.28560e34	1.04443
$178$	−1.85979e34	−0.244318
$179$	5.67856e33	0.0683937	0.0341968	−	0.999415i	$-0.489113\pi$
$179$	5.67856e33	0.0683937	0.0341968	+	0.999415i	$0.489113\pi$
$180$	0	0
$181$	1.47595e35	1.49642	0.748210	−	0.663462i	$-0.230914\pi$
$181$	1.47595e35	1.49642	0.748210	+	0.663462i	$0.230914\pi$
$182$	1.64645e35	1.53264
$183$	1.68112e35	1.43750
$184$	−2.16876e32	−0.00170425
$185$	0	0
$186$	4.10784e35	2.73000
$187$	2.62521e34	0.160553
$188$	−2.17633e35	−1.22540
$189$	−9.99731e34	−0.518472
$190$	0	0
$191$	−4.38203e34	−0.193045	−0.0965224	−	0.995331i	$-0.530772\pi$
$191$	−4.38203e34	−0.193045	−0.0965224	+	0.995331i	$0.530772\pi$
$192$	4.73815e35	1.92504
$193$	−2.63656e35	−0.988323	−0.494161	−	0.869370i	$-0.664525\pi$
$193$	−2.63656e35	−0.988323	−0.494161	+	0.869370i	$0.664525\pi$
$194$	−3.83684e35	−1.32754
$195$	0	0
$196$	−7.92339e34	−0.233852
$197$	2.72680e35	0.743749	0.371875	−	0.928283i	$-0.378715\pi$
$197$	2.72680e35	0.743749	0.371875	+	0.928283i	$0.378715\pi$
$198$	5.72864e34	0.144458
$199$	3.17714e35	0.740991	0.370496	−	0.928834i	$-0.379188\pi$
$199$	3.17714e35	0.740991	0.370496	+	0.928834i	$0.379188\pi$
$200$	0	0
$201$	−2.90373e35	−0.579986
$202$	9.18893e35	1.69949
$203$	−8.72728e35	−1.49517
$204$	9.90284e35	1.57214
$205$	0	0
$206$	1.36346e36	1.86081
$207$	1.28754e33	0.00163012
$208$	−4.62651e35	−0.543591
$209$	3.43217e34	0.0374371
$210$	0	0
$211$	−2.10102e36	−1.97721	−0.988604	−	0.150541i	$-0.951898\pi$
$211$	−2.10102e36	−1.97721	−0.988604	+	0.150541i	$0.951898\pi$
$212$	−1.04596e35	−0.0914763
$213$	6.50053e35	0.528524
$214$	2.24858e36	1.70018
$215$	0	0
$216$	−4.92332e35	−0.322274
$217$	−2.13527e36	−1.30115
$218$	2.57442e36	1.46084
$219$	1.21178e36	0.640530
$220$	0	0
$221$	−2.20589e36	−1.01275
$222$	−2.72188e36	−1.16519
$223$	2.62490e36	1.04806	0.524032	−	0.851699i	$-0.324427\pi$
$223$	2.62490e36	1.04806	0.524032	+	0.851699i	$0.324427\pi$
$224$	−3.25221e36	−1.21153
$225$	0	0
$226$	1.08780e36	0.353075
$227$	−1.16088e35	−0.0351874	−0.0175937	−	0.999845i	$-0.505601\pi$
$227$	−1.16088e35	−0.0351874	−0.0175937	+	0.999845i	$0.505601\pi$
$228$	1.29469e36	0.366585
$229$	1.39980e36	0.370353	0.185177	−	0.982705i	$-0.440714\pi$
$229$	1.39980e36	0.370353	0.185177	+	0.982705i	$0.440714\pi$
$230$	0	0
$231$	−8.47850e35	−0.196035
$232$	−4.29787e36	−0.929372
$233$	−7.15120e36	−1.44665	−0.723323	−	0.690510i	$-0.757386\pi$
$233$	−7.15120e36	−1.44665	−0.723323	+	0.690510i	$0.757386\pi$
$234$	−4.81362e36	−0.911226
$235$	0	0
$236$	−6.93568e36	−1.15068
$237$	−5.54931e36	−0.862262
$238$	−8.91089e36	−1.29711
$239$	2.96558e36	0.404522	0.202261	−	0.979332i	$-0.435171\pi$
$239$	2.96558e36	0.404522	0.202261	+	0.979332i	$0.435171\pi$
$240$	0	0
$241$	−7.20536e36	−0.863757	−0.431879	−	0.901932i	$-0.642149\pi$
$241$	−7.20536e36	−0.863757	−0.431879	+	0.901932i	$0.642149\pi$
$242$	1.32754e37	1.49249
$243$	9.29545e36	0.980332
$244$	−1.60038e37	−1.58373
$245$	0	0
$246$	3.04068e37	2.65141
$247$	−2.88396e36	−0.236149
$248$	−1.05154e37	−0.808772
$249$	−1.40184e37	−1.01300
$250$	0	0
$251$	9.47842e36	0.605053	0.302526	−	0.953141i	$-0.402170\pi$
$251$	9.47842e36	0.605053	0.302526	+	0.953141i	$0.402170\pi$
$252$	−1.12328e37	−0.674183
$253$	−9.25159e33	−0.000522214 0
$254$	−4.05784e37	−2.15463
$255$	0	0
$256$	−1.56056e36	−0.0733772
$257$	−3.15504e37	−1.39650	−0.698252	−	0.715852i	$-0.746038\pi$
$257$	−3.15504e37	−1.39650	−0.698252	+	0.715852i	$0.746038\pi$
$258$	5.89376e37	2.45633
$259$	1.41484e37	0.555343
$260$	0	0
$261$	2.55154e37	0.888945
$262$	−1.28620e36	−0.0422318
$263$	1.25731e37	0.389159	0.194580	−	0.980887i	$-0.437666\pi$
$263$	1.25731e37	0.389159	0.194580	+	0.980887i	$0.437666\pi$
$264$	−4.17536e36	−0.121852
$265$	0	0
$266$	−1.16500e37	−0.302455
$267$	−8.04741e36	−0.197120
$268$	2.76427e37	0.638985
$269$	3.34018e37	0.728801	0.364401	−	0.931242i	$-0.381274\pi$
$269$	3.34018e37	0.728801	0.364401	+	0.931242i	$0.381274\pi$
$270$	0	0
$271$	−4.00526e36	−0.0779125	−0.0389562	−	0.999241i	$-0.512403\pi$
$271$	−4.00526e36	−0.0779125	−0.0389562	+	0.999241i	$0.512403\pi$
$272$	2.50396e37	0.460054
$273$	7.12424e37	1.23657
$274$	−1.09344e37	−0.179333
$275$	0	0
$276$	−3.48990e35	−0.00511354
$277$	7.94796e37	1.10108	0.550541	−	0.834808i	$-0.314422\pi$
$277$	7.94796e37	1.10108	0.550541	+	0.834808i	$0.314422\pi$
$278$	−1.34083e38	−1.75663
$279$	6.24276e37	0.773591
$280$	0	0
$281$	−1.69314e38	−1.87822	−0.939108	−	0.343621i	$-0.888346\pi$
$281$	−1.69314e38	−1.87822	−0.939108	+	0.343621i	$0.888346\pi$
$282$	−1.63019e38	−1.71150
$283$	−1.18735e38	−1.18002	−0.590008	−	0.807397i	$-0.700875\pi$
$283$	−1.18735e38	−1.18002	−0.590008	+	0.807397i	$0.700875\pi$
$284$	−6.18832e37	−0.582288
$285$	0	0
$286$	3.45882e37	0.291914
$287$	−1.58056e38	−1.26369
$288$	9.50830e37	0.720310
$289$	−1.99019e37	−0.142882
$290$	0	0
$291$	−1.66022e38	−1.07108
$292$	−1.15358e38	−0.705689
$293$	−9.32191e37	−0.540825	−0.270413	−	0.962745i	$-0.587160\pi$
$293$	−9.32191e37	−0.540825	−0.270413	+	0.962745i	$0.587160\pi$
$294$	−5.93505e37	−0.326618
$295$	0	0
$296$	6.96759e37	0.345192
$297$	−2.10022e37	−0.0987504
$298$	−4.73985e38	−2.11550
$299$	7.77386e35	0.00329407
$300$	0	0
$301$	−3.06359e38	−1.17071
$302$	4.69838e38	1.70546
$303$	3.97609e38	1.37118
$304$	3.27365e37	0.107273
$305$	0	0
$306$	2.60522e38	0.771193
$307$	2.10829e38	0.593314	0.296657	−	0.954984i	$-0.404128\pi$
$307$	2.10829e38	0.593314	0.296657	+	0.954984i	$0.404128\pi$
$308$	8.07129e37	0.215977
$309$	5.89976e38	1.50134
$310$	0	0
$311$	4.24765e38	0.978053	0.489027	−	0.872269i	$-0.337352\pi$
$311$	4.24765e38	0.978053	0.489027	+	0.872269i	$0.337352\pi$
$312$	3.50844e38	0.768630
$313$	3.07637e38	0.641360	0.320680	−	0.947188i	$-0.396089\pi$
$313$	3.07637e38	0.641360	0.320680	+	0.947188i	$0.396089\pi$
$314$	1.14320e39	2.26836
$315$	0	0
$316$	5.28278e38	0.949976
$317$	9.76522e38	1.67210	0.836052	−	0.548650i	$-0.184858\pi$
$317$	9.76522e38	1.67210	0.836052	+	0.548650i	$0.184858\pi$
$318$	−7.83480e37	−0.127764
$319$	−1.83341e38	−0.284776
$320$	0	0
$321$	9.72970e38	1.37174
$322$	3.14032e36	0.00421898
$323$	1.56085e38	0.199859
$324$	−1.39890e39	−1.70741
$325$	0	0
$326$	−1.16577e39	−1.29342
$327$	1.11396e39	1.17864
$328$	−7.78367e38	−0.785489
$329$	8.47379e38	0.815720
$330$	0	0
$331$	8.30576e38	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$331$	8.30576e38	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$332$	1.33451e39	1.11605
$333$	−4.13649e38	−0.330176
$334$	1.19844e39	0.913155
$335$	0	0
$336$	−8.08690e38	−0.561724
$337$	−1.84495e39	−1.22383	−0.611916	−	0.790923i	$-0.709601\pi$
$337$	−1.84495e39	−1.22383	−0.611916	+	0.790923i	$0.709601\pi$
$338$	−4.77609e38	−0.302596
$339$	4.70695e38	0.284868
$340$	0	0
$341$	−4.48573e38	−0.247822
$342$	3.40604e38	0.179823
$343$	2.11295e39	1.06618
$344$	−1.50871e39	−0.727696
$345$	0	0
$346$	1.19608e39	0.527327
$347$	3.59852e39	1.51711	0.758555	−	0.651609i	$-0.225906\pi$
$347$	3.59852e39	1.51711	0.758555	+	0.651609i	$0.225906\pi$
$348$	−6.91600e39	−2.78854
$349$	4.09325e38	0.157861	0.0789303	−	0.996880i	$-0.474850\pi$
$349$	4.09325e38	0.157861	0.0789303	+	0.996880i	$0.474850\pi$
$350$	0	0
$351$	1.76475e39	0.622907
$352$	−6.83218e38	−0.230754
$353$	5.32510e39	1.72116	0.860578	−	0.509319i	$-0.170103\pi$
$353$	5.32510e39	1.72116	0.860578	+	0.509319i	$0.170103\pi$
$354$	−5.19520e39	−1.60713
$355$	0	0
$356$	7.66090e38	0.217173
$357$	−3.85578e39	−1.04654
$358$	−4.04926e38	−0.105242
$359$	4.10824e39	1.02257	0.511283	−	0.859412i	$-0.329170\pi$
$359$	4.10824e39	1.02257	0.511283	+	0.859412i	$0.329170\pi$
$360$	0	0
$361$	−4.17480e39	−0.953398
$362$	−1.05247e40	−2.30264
$363$	5.74434e39	1.20417
$364$	−6.78208e39	−1.36236
$365$	0	0
$366$	−1.19877e40	−2.21197
$367$	−9.50139e39	−1.68060	−0.840298	−	0.542125i	$-0.817620\pi$
$367$	−9.50139e39	−1.68060	−0.840298	+	0.542125i	$0.817620\pi$
$368$	−8.82429e36	−0.00149637
$369$	4.62098e39	0.751320
$370$	0	0
$371$	4.07255e38	0.0608935
$372$	−1.69211e40	−2.42669
$373$	−5.31105e39	−0.730624	−0.365312	−	0.930885i	$-0.619038\pi$
$373$	−5.31105e39	−0.730624	−0.365312	+	0.930885i	$0.619038\pi$
$374$	−1.87198e39	−0.247054
$375$	0	0
$376$	4.17304e39	0.507038
$377$	1.54056e40	1.79634
$378$	7.12887e39	0.797807
$379$	6.56433e39	0.705152	0.352576	−	0.935783i	$-0.385306\pi$
$379$	6.56433e39	0.705152	0.352576	+	0.935783i	$0.385306\pi$
$380$	0	0
$381$	−1.75585e40	−1.73840
$382$	3.12473e39	0.297051
$383$	−4.90622e39	−0.447884	−0.223942	−	0.974602i	$-0.571893\pi$
$383$	−4.90622e39	−0.447884	−0.223942	+	0.974602i	$0.571893\pi$
$384$	−1.49445e40	−1.31023
$385$	0	0
$386$	1.88007e40	1.52080
$387$	8.95685e39	0.696041
$388$	1.58048e40	1.18004
$389$	1.47786e40	1.06026	0.530132	−	0.847915i	$-0.322142\pi$
$389$	1.47786e40	1.06026	0.530132	+	0.847915i	$0.322142\pi$
$390$	0	0
$391$	−4.20736e37	−0.00278785
$392$	1.51928e39	0.0967617
$393$	−5.56545e38	−0.0340734
$394$	−1.94442e40	−1.14446
$395$	0	0
$396$	−2.35976e39	−0.128408
$397$	−9.79733e39	−0.512690	−0.256345	−	0.966585i	$-0.582518\pi$
$397$	−9.79733e39	−0.512690	−0.256345	+	0.966585i	$0.582518\pi$
$398$	−2.26555e40	−1.14021
$399$	−5.04101e39	−0.244027
$400$	0	0
$401$	1.11974e40	0.501624	0.250812	−	0.968036i	$-0.419302\pi$
$401$	1.11974e40	0.501624	0.250812	+	0.968036i	$0.419302\pi$
$402$	2.07059e40	0.892462
$403$	3.76923e40	1.56324
$404$	−3.78513e40	−1.51067
$405$	0	0
$406$	6.22323e40	2.30071
$407$	2.97227e39	0.105773
$408$	−1.89883e40	−0.650510
$409$	−2.34914e40	−0.774815	−0.387408	−	0.921909i	$-0.626629\pi$
$409$	−2.34914e40	−0.774815	−0.387408	+	0.921909i	$0.626629\pi$
$410$	0	0
$411$	−4.73134e39	−0.144689
$412$	−5.61640e40	−1.65406
$413$	2.70048e40	0.765977
$414$	−9.18116e37	−0.00250837
$415$	0	0
$416$	5.74089e40	1.45557
$417$	−5.80184e40	−1.41728
$418$	−2.44741e39	−0.0576069
$419$	4.42578e40	1.00386	0.501929	−	0.864909i	$-0.332624\pi$
$419$	4.42578e40	1.00386	0.501929	+	0.864909i	$0.332624\pi$
$420$	0	0
$421$	−4.58467e40	−0.965907	−0.482954	−	0.875646i	$-0.660436\pi$
$421$	−4.58467e40	−0.965907	−0.482954	+	0.875646i	$0.660436\pi$
$422$	1.49819e41	3.04246
$423$	−2.47743e40	−0.484982
$424$	2.00559e39	0.0378504
$425$	0	0
$426$	−4.63539e40	−0.813275
$427$	6.23125e40	1.05425
$428$	−9.26239e40	−1.51128
$429$	1.49665e40	0.235522
$430$	0	0
$431$	−1.63894e40	−0.239975	−0.119987	−	0.992775i	$-0.538285\pi$
$431$	−1.63894e40	−0.239975	−0.119987	+	0.992775i	$0.538285\pi$
$432$	−2.00321e40	−0.282962
$433$	−7.21840e39	−0.0983737	−0.0491868	−	0.998790i	$-0.515663\pi$
$433$	−7.21840e39	−0.0983737	−0.0491868	+	0.998790i	$0.515663\pi$
$434$	1.52261e41	2.00216
$435$	0	0
$436$	−1.06046e41	−1.29854
$437$	−5.50066e37	−0.000650059 0
$438$	−8.64094e40	−0.985626
$439$	1.72040e40	0.189422	0.0947109	−	0.995505i	$-0.469807\pi$
$439$	1.72040e40	0.189422	0.0947109	+	0.995505i	$0.469807\pi$
$440$	0	0
$441$	−9.01960e39	−0.0925527
$442$	1.57297e41	1.55839
$443$	9.22567e39	0.0882552	0.0441276	−	0.999026i	$-0.485949\pi$
$443$	9.22567e39	0.0882552	0.0441276	+	0.999026i	$0.485949\pi$
$444$	1.12120e41	1.03573
$445$	0	0
$446$	−1.87176e41	−1.61272
$447$	−2.05095e41	−1.70683
$448$	1.75625e41	1.41181
$449$	1.80147e41	1.39897	0.699484	−	0.714648i	$-0.253413\pi$
$449$	1.80147e41	1.39897	0.699484	+	0.714648i	$0.253413\pi$
$450$	0	0
$451$	−3.32040e40	−0.240688
$452$	−4.48088e40	−0.313847
$453$	2.03301e41	1.37600
$454$	8.27801e39	0.0541452
$455$	0	0
$456$	−2.48252e40	−0.151683
$457$	−7.03528e40	−0.415509	−0.207754	−	0.978181i	$-0.566615\pi$
$457$	−7.03528e40	−0.415509	−0.207754	+	0.978181i	$0.566615\pi$
$458$	−9.98168e40	−0.569887
$459$	−9.55118e40	−0.527182
$460$	0	0
$461$	−2.15013e40	−0.110943	−0.0554717	−	0.998460i	$-0.517666\pi$
$461$	−2.15013e40	−0.110943	−0.0554717	+	0.998460i	$0.517666\pi$
$462$	6.04584e40	0.301652
$463$	−3.68798e41	−1.77944	−0.889720	−	0.456506i	$-0.849101\pi$
$463$	−3.68798e41	−1.77944	−0.889720	+	0.456506i	$0.849101\pi$
$464$	−1.74873e41	−0.816006
$465$	0	0
$466$	5.09937e41	2.22605
$467$	3.35225e41	1.41555	0.707775	−	0.706438i	$-0.249699\pi$
$467$	3.35225e41	1.41555	0.707775	+	0.706438i	$0.249699\pi$
$468$	1.98284e41	0.809983
$469$	−1.07630e41	−0.425357
$470$	0	0
$471$	4.94668e41	1.83016
$472$	1.32989e41	0.476118
$473$	−6.43593e40	−0.222979
$474$	3.95709e41	1.32682
$475$	0	0
$476$	3.67059e41	1.15300
$477$	−1.19067e40	−0.0362040
$478$	−2.11469e41	−0.622464
$479$	−1.78256e41	−0.507976	−0.253988	−	0.967207i	$-0.581742\pi$
$479$	−1.78256e41	−0.507976	−0.253988	+	0.967207i	$0.581742\pi$
$480$	0	0
$481$	−2.49751e41	−0.667205
$482$	5.13799e41	1.32912
$483$	1.35883e39	0.00340396
$484$	−5.46845e41	−1.32666
$485$	0	0
$486$	−6.62839e41	−1.50850
$487$	2.96115e41	0.652772	0.326386	−	0.945237i	$-0.394169\pi$
$487$	2.96115e41	0.652772	0.326386	+	0.945237i	$0.394169\pi$
$488$	3.06867e41	0.655304
$489$	−5.04432e41	−1.04355
$490$	0	0
$491$	2.87172e41	0.557671	0.278836	−	0.960339i	$-0.410052\pi$
$491$	2.87172e41	0.557671	0.278836	+	0.960339i	$0.410052\pi$
$492$	−1.25252e42	−2.35682
$493$	−8.33782e41	−1.52029
$494$	2.05649e41	0.363378
$495$	0	0
$496$	−4.27855e41	−0.710117
$497$	2.40949e41	0.387615
$498$	9.99624e41	1.55877
$499$	−1.19160e42	−1.80125	−0.900623	−	0.434601i	$-0.856889\pi$
$499$	−1.19160e42	−1.80125	−0.900623	+	0.434601i	$0.856889\pi$
$500$	0	0
$501$	5.18568e41	0.736752
$502$	−6.75886e41	−0.931035
$503$	−1.92359e41	−0.256926	−0.128463	−	0.991714i	$-0.541004\pi$
$503$	−1.92359e41	−0.256926	−0.128463	+	0.991714i	$0.541004\pi$
$504$	2.15384e41	0.278959
$505$	0	0
$506$	6.59712e38	0.000803565 0
$507$	−2.06663e41	−0.244141
$508$	1.67152e42	1.91524
$509$	−4.08219e41	−0.453699	−0.226849	−	0.973930i	$-0.572843\pi$
$509$	−4.08219e41	−0.453699	−0.226849	+	0.973930i	$0.572843\pi$
$510$	0	0
$511$	4.49158e41	0.469759
$512$	−9.28840e41	−0.942446
$513$	−1.24871e41	−0.122926
$514$	2.24980e42	2.14889
$515$	0	0
$516$	−2.42777e42	−2.18342
$517$	1.78016e41	0.155366
$518$	−1.00889e42	−0.854543
$519$	5.17548e41	0.425458
$520$	0	0
$521$	8.76030e41	0.678476	0.339238	−	0.940701i	$-0.389831\pi$
$521$	8.76030e41	0.678476	0.339238	+	0.940701i	$0.389831\pi$
$522$	−1.81945e42	−1.36788
$523$	1.52051e42	1.10972	0.554859	−	0.831944i	$-0.312772\pi$
$523$	1.52051e42	1.10972	0.554859	+	0.831944i	$0.312772\pi$
$524$	5.29815e40	0.0375396
$525$	0	0
$526$	−8.96559e41	−0.598825
$527$	−2.03998e42	−1.32301
$528$	−1.69888e41	−0.106988
$529$	−1.63516e42	−0.999991
$530$	0	0
$531$	−7.89524e41	−0.455408
$532$	4.79889e41	0.268851
$533$	2.79004e42	1.51823
$534$	5.73844e41	0.303322
$535$	0	0
$536$	−5.30038e41	−0.264395
$537$	−1.75213e41	−0.0849113
$538$	−2.38181e42	−1.12145
$539$	6.48102e40	0.0296495
$540$	0	0
$541$	2.17683e42	0.940301	0.470150	−	0.882586i	$-0.344200\pi$
$541$	2.17683e42	0.940301	0.470150	+	0.882586i	$0.344200\pi$
$542$	2.85607e41	0.119889
$543$	−4.55407e42	−1.85782
$544$	−3.10708e42	−1.23188
$545$	0	0
$546$	−5.08015e42	−1.90279
$547$	−2.57006e42	−0.935707	−0.467854	−	0.883806i	$-0.654973\pi$
$547$	−2.57006e42	−0.935707	−0.467854	+	0.883806i	$0.654973\pi$
$548$	4.50410e41	0.159408
$549$	−1.82179e42	−0.626798
$550$	0	0
$551$	−1.09008e42	−0.354493
$552$	6.69174e39	0.00211584
$553$	−2.05691e42	−0.632376
$554$	−5.66752e42	−1.69431
$555$	0	0
$556$	5.52318e42	1.56146
$557$	2.88974e42	0.794517	0.397258	−	0.917707i	$-0.369962\pi$
$557$	2.88974e42	0.794517	0.397258	+	0.917707i	$0.369962\pi$
$558$	−4.45158e42	−1.19038
$559$	5.40793e42	1.40653
$560$	0	0
$561$	−8.10014e41	−0.199328
$562$	1.20734e43	2.89014
$563$	5.57652e42	1.29862	0.649312	−	0.760522i	$-0.275057\pi$
$563$	5.57652e42	1.29862	0.649312	+	0.760522i	$0.275057\pi$
$564$	6.71512e42	1.52135
$565$	0	0
$566$	8.46672e42	1.81577
$567$	5.44676e42	1.13658
$568$	1.18659e42	0.240935
$569$	−3.00301e42	−0.593357	−0.296679	−	0.954977i	$-0.595879\pi$
$569$	−3.00301e42	−0.593357	−0.296679	+	0.954977i	$0.595879\pi$
$570$	0	0
$571$	1.00812e43	1.88649	0.943245	−	0.332099i	$-0.107757\pi$
$571$	1.00812e43	1.88649	0.943245	+	0.332099i	$0.107757\pi$
$572$	−1.42477e42	−0.259481
$573$	1.35208e42	0.239666
$574$	1.12706e43	1.94452
$575$	0	0
$576$	−5.13463e42	−0.839385
$577$	7.02075e42	1.11727	0.558635	−	0.829413i	$-0.311325\pi$
$577$	7.02075e42	1.11727	0.558635	+	0.829413i	$0.311325\pi$
$578$	1.41916e42	0.219862
$579$	8.13515e42	1.22701
$580$	0	0
$581$	−5.19607e42	−0.742926
$582$	1.18387e43	1.64815
$583$	8.55554e40	0.0115980
$584$	2.21194e42	0.291995
$585$	0	0
$586$	6.64726e42	0.832203
$587$	−1.56627e43	−1.90974	−0.954872	−	0.297018i	$-0.904008\pi$
$587$	−1.56627e43	−1.90974	−0.954872	+	0.297018i	$0.904008\pi$
$588$	2.44478e42	0.290329
$589$	−2.66705e42	−0.308492
$590$	0	0
$591$	−8.41360e42	−0.923370
$592$	2.83499e42	0.303085
$593$	1.51645e42	0.157936	0.0789678	−	0.996877i	$-0.474838\pi$
$593$	1.51645e42	0.157936	0.0789678	+	0.996877i	$0.474838\pi$
$594$	1.49762e42	0.151954
$595$	0	0
$596$	1.95245e43	1.88046
$597$	−9.80312e42	−0.919946
$598$	−5.54337e40	−0.00506880
$599$	−8.56958e42	−0.763561	−0.381781	−	0.924253i	$-0.624689\pi$
$599$	−8.56958e42	−0.763561	−0.381781	+	0.924253i	$0.624689\pi$
$600$	0	0
$601$	−2.71633e42	−0.229841	−0.114921	−	0.993375i	$-0.536661\pi$
$601$	−2.71633e42	−0.229841	−0.114921	+	0.993375i	$0.536661\pi$
$602$	2.18458e43	1.80145
$603$	3.14671e42	0.252894
$604$	−1.93537e43	−1.51597
$605$	0	0
$606$	−2.83527e43	−2.10993
$607$	−5.39744e42	−0.391528	−0.195764	−	0.980651i	$-0.562719\pi$
$607$	−5.39744e42	−0.391528	−0.195764	+	0.980651i	$0.562719\pi$
$608$	−4.06217e42	−0.287245
$609$	2.69282e43	1.85626
$610$	0	0
$611$	−1.49582e43	−0.980030
$612$	−1.07315e43	−0.685509
$613$	−6.77481e42	−0.421949	−0.210975	−	0.977492i	$-0.567664\pi$
$613$	−6.77481e42	−0.421949	−0.210975	+	0.977492i	$0.567664\pi$
$614$	−1.50337e43	−0.912972
$615$	0	0
$616$	−1.54764e42	−0.0893653
$617$	8.39156e41	0.0472523	0.0236261	−	0.999721i	$-0.492479\pi$
$617$	8.39156e41	0.0472523	0.0236261	+	0.999721i	$0.492479\pi$
$618$	−4.20699e43	−2.31020
$619$	1.34876e43	0.722318	0.361159	−	0.932504i	$-0.382381\pi$
$619$	1.34876e43	0.722318	0.361159	+	0.932504i	$0.382381\pi$
$620$	0	0
$621$	3.36597e40	0.00171471
$622$	−3.02891e43	−1.50499
$623$	−2.98286e42	−0.144566
$624$	1.42752e43	0.674872
$625$	0	0
$626$	−2.19370e43	−0.986902
$627$	−1.05900e42	−0.0464784
$628$	−4.70909e43	−2.01634
$629$	1.35170e43	0.564672
$630$	0	0
$631$	−4.65263e42	−0.185031	−0.0925153	−	0.995711i	$-0.529491\pi$
$631$	−4.65263e42	−0.185031	−0.0925153	+	0.995711i	$0.529491\pi$
$632$	−1.01295e43	−0.393074
$633$	6.48274e43	2.45472
$634$	−6.96337e43	−2.57298
$635$	0	0
$636$	3.22733e42	0.113569
$637$	−5.44582e42	−0.187026
$638$	1.30736e43	0.438204
$639$	−7.04448e42	−0.230455
$640$	0	0
$641$	4.24972e43	1.32453	0.662263	−	0.749271i	$-0.269596\pi$
$641$	4.24972e43	1.32453	0.662263	+	0.749271i	$0.269596\pi$
$642$	−6.93804e43	−2.11078
$643$	5.33186e43	1.58347	0.791733	−	0.610868i	$-0.209179\pi$
$643$	5.33186e43	1.58347	0.791733	+	0.610868i	$0.209179\pi$
$644$	−1.29357e41	−0.00375023
$645$	0	0
$646$	−1.11301e43	−0.307536
$647$	1.00492e43	0.271092	0.135546	−	0.990771i	$-0.456721\pi$
$647$	1.00492e43	0.271092	0.135546	+	0.990771i	$0.456721\pi$
$648$	2.68234e43	0.706481
$649$	5.67312e42	0.145891
$650$	0	0
$651$	6.58842e43	1.61538
$652$	4.80205e43	1.14971
$653$	7.98263e43	1.86634	0.933172	−	0.359430i	$-0.117029\pi$
$653$	7.98263e43	1.86634	0.933172	+	0.359430i	$0.117029\pi$
$654$	−7.94343e43	−1.81365
$655$	0	0
$656$	−3.16704e43	−0.689674
$657$	−1.31318e43	−0.279293
$658$	−6.04248e43	−1.25520
$659$	7.54017e43	1.52988	0.764940	−	0.644102i	$-0.222769\pi$
$659$	7.54017e43	1.52988	0.764940	+	0.644102i	$0.222769\pi$
$660$	0	0
$661$	−3.00409e42	−0.0581555	−0.0290777	−	0.999577i	$-0.509257\pi$
$661$	−3.00409e42	−0.0581555	−0.0290777	+	0.999577i	$0.509257\pi$
$662$	−5.92266e43	−1.12000
$663$	6.80632e43	1.25734
$664$	−2.55888e43	−0.461790
$665$	0	0
$666$	2.94964e43	0.508064
$667$	2.93836e41	0.00494487
$668$	−4.93662e43	−0.811698
$669$	−8.09919e43	−1.30118
$670$	0	0
$671$	1.30905e43	0.200797
$672$	1.00348e44	1.50412
$673$	−2.05730e43	−0.301346	−0.150673	−	0.988584i	$-0.548144\pi$
$673$	−2.05730e43	−0.301346	−0.150673	+	0.988584i	$0.548144\pi$
$674$	1.31560e44	1.88319
$675$	0	0
$676$	1.96738e43	0.268976
$677$	1.03692e44	1.38554	0.692772	−	0.721157i	$-0.256389\pi$
$677$	1.03692e44	1.38554	0.692772	+	0.721157i	$0.256389\pi$
$678$	−3.35642e43	−0.438345
$679$	−6.15377e43	−0.785524
$680$	0	0
$681$	3.58193e42	0.0436855
$682$	3.19868e43	0.381340
$683$	−1.01818e44	−1.18660	−0.593302	−	0.804980i	$-0.702176\pi$
$683$	−1.01818e44	−1.18660	−0.593302	+	0.804980i	$0.702176\pi$
$684$	−1.40302e43	−0.159844
$685$	0	0
$686$	−1.50670e44	−1.64060
$687$	−4.31911e43	−0.459796
$688$	−6.13867e43	−0.638931
$689$	−7.18898e42	−0.0731593
$690$	0	0
$691$	1.12626e44	1.09579	0.547895	−	0.836547i	$-0.315429\pi$
$691$	1.12626e44	1.09579	0.547895	+	0.836547i	$0.315429\pi$
$692$	−4.92691e43	−0.468738
$693$	9.18796e42	0.0854779
$694$	−2.56603e44	−2.33448
$695$	0	0
$696$	1.32612e44	1.15382
$697$	−1.51002e44	−1.28492
$698$	−2.91881e43	−0.242911
$699$	2.20652e44	1.79602
$700$	0	0
$701$	3.06210e43	0.238446	0.119223	−	0.992867i	$-0.461960\pi$
$701$	3.06210e43	0.238446	0.119223	+	0.992867i	$0.461960\pi$
$702$	−1.25841e44	−0.958509
$703$	1.76720e43	0.131668
$704$	3.68949e43	0.268899
$705$	0	0
$706$	−3.79722e44	−2.64846
$707$	1.47378e44	1.00561
$708$	2.14002e44	1.42857
$709$	−9.24433e43	−0.603752	−0.301876	−	0.953347i	$-0.597613\pi$
$709$	−9.24433e43	−0.603752	−0.301876	+	0.953347i	$0.597613\pi$
$710$	0	0
$711$	6.01366e43	0.375976
$712$	−1.46895e43	−0.0898601
$713$	7.18917e41	0.00430320
$714$	2.74947e44	1.61038
$715$	0	0
$716$	1.66798e43	0.0935489
$717$	−9.15036e43	−0.502217
$718$	−2.92950e44	−1.57349
$719$	−9.29670e43	−0.488687	−0.244344	−	0.969689i	$-0.578572\pi$
$719$	−9.29670e43	−0.488687	−0.244344	+	0.969689i	$0.578572\pi$
$720$	0	0
$721$	2.18681e44	1.10107
$722$	2.97696e44	1.46706
$723$	2.22323e44	1.07236
$724$	4.33535e44	2.04680
$725$	0	0
$726$	−4.09617e44	−1.85293
$727$	−1.34756e44	−0.596710	−0.298355	−	0.954455i	$-0.596438\pi$
$727$	−1.34756e44	−0.596710	−0.298355	+	0.954455i	$0.596438\pi$
$728$	1.30044e44	0.563707
$729$	7.35277e42	0.0312014
$730$	0	0
$731$	−2.92688e44	−1.19038
$732$	4.93800e44	1.96621
$733$	−1.96770e44	−0.767093	−0.383546	−	0.923522i	$-0.625297\pi$
$733$	−1.96770e44	−0.767093	−0.383546	+	0.923522i	$0.625297\pi$
$734$	6.77524e44	2.58604
$735$	0	0
$736$	1.09498e42	0.00400681
$737$	−2.26106e43	−0.0810153
$738$	−3.29512e44	−1.15611
$739$	−3.41064e44	−1.17178	−0.585891	−	0.810390i	$-0.699255\pi$
$739$	−3.41064e44	−1.17178	−0.585891	+	0.810390i	$0.699255\pi$
$740$	0	0
$741$	8.89852e43	0.293181
$742$	−2.90405e43	−0.0937009
$743$	2.64820e44	0.836805	0.418403	−	0.908262i	$-0.362590\pi$
$743$	2.64820e44	0.836805	0.418403	+	0.908262i	$0.362590\pi$
$744$	3.24456e44	1.00410
$745$	0	0
$746$	3.78720e44	1.12426
$747$	1.51915e44	0.441703
$748$	7.71111e43	0.219605
$749$	3.60641e44	1.00602
$750$	0	0
$751$	3.88190e44	1.03902	0.519511	−	0.854464i	$-0.326114\pi$
$751$	3.88190e44	1.03902	0.519511	+	0.854464i	$0.326114\pi$
$752$	1.69794e44	0.445189
$753$	−2.92459e44	−0.751177
$754$	−1.09854e45	−2.76414
$755$	0	0
$756$	−2.93654e44	−0.709166
$757$	−2.10907e44	−0.499004	−0.249502	−	0.968374i	$-0.580267\pi$
$757$	−2.10907e44	−0.499004	−0.249502	+	0.968374i	$0.580267\pi$
$758$	−4.68088e44	−1.08506
$759$	2.85460e41	0.000648332 0
$760$	0	0
$761$	3.24151e43	0.0706782	0.0353391	−	0.999375i	$-0.488749\pi$
$761$	3.24151e43	0.0706782	0.0353391	+	0.999375i	$0.488749\pi$
$762$	1.25206e45	2.67499
$763$	4.12902e44	0.864403
$764$	−1.28715e44	−0.264047
$765$	0	0
$766$	3.49852e44	0.689189
$767$	−4.76696e44	−0.920266
$768$	4.81514e43	0.0910983
$769$	−6.38736e44	−1.18430	−0.592152	−	0.805827i	$-0.701721\pi$
$769$	−6.38736e44	−1.18430	−0.592152	+	0.805827i	$0.701721\pi$
$770$	0	0
$771$	9.73496e44	1.73377
$772$	−7.74443e44	−1.35183
$773$	8.28645e44	1.41771	0.708853	−	0.705356i	$-0.249213\pi$
$773$	8.28645e44	1.41771	0.708853	+	0.705356i	$0.249213\pi$
$774$	−6.38694e44	−1.07104
$775$	0	0
$776$	−3.03051e44	−0.488269
$777$	−4.36552e44	−0.689462
$778$	−1.05383e45	−1.63150
$779$	−1.97419e44	−0.299611
$780$	0	0
$781$	5.06180e43	0.0738268
$782$	3.00018e42	0.00428985
$783$	6.67041e44	0.935072
$784$	6.18168e43	0.0849587
$785$	0	0
$786$	3.96860e43	0.0524310
$787$	8.07362e44	1.04583	0.522913	−	0.852386i	$-0.324845\pi$
$787$	8.07362e44	1.04583	0.522913	+	0.852386i	$0.324845\pi$
$788$	8.00950e44	1.01730
$789$	−3.87945e44	−0.483144
$790$	0	0
$791$	1.74468e44	0.208920
$792$	4.52474e43	0.0531317
$793$	−1.09996e45	−1.26660
$794$	6.98627e44	0.788910
$795$	0	0
$796$	9.33229e44	1.01353
$797$	−8.20375e44	−0.873792	−0.436896	−	0.899512i	$-0.643922\pi$
$797$	−8.20375e44	−0.873792	−0.436896	+	0.899512i	$0.643922\pi$
$798$	3.59463e44	0.375500
$799$	8.09564e44	0.829423
$800$	0	0
$801$	8.72080e43	0.0859513
$802$	−7.98461e44	−0.771882
$803$	9.43583e43	0.0894724
$804$	−8.52921e44	−0.793304
$805$	0	0
$806$	−2.68776e45	−2.40546
$807$	−1.03062e45	−0.904812
$808$	7.25784e44	0.625073
$809$	−2.25872e44	−0.190836	−0.0954182	−	0.995437i	$-0.530419\pi$
$809$	−2.25872e44	−0.190836	−0.0954182	+	0.995437i	$0.530419\pi$
$810$	0	0
$811$	−1.42546e45	−1.15913	−0.579565	−	0.814926i	$-0.696778\pi$
$811$	−1.42546e45	−1.15913	−0.579565	+	0.814926i	$0.696778\pi$
$812$	−2.56349e45	−2.04509
$813$	1.23583e44	0.0967289
$814$	−2.11946e44	−0.162760
$815$	0	0
$816$	−7.72602e44	−0.571161
$817$	−3.82657e44	−0.277567
$818$	1.67512e45	1.19226
$819$	−7.72039e44	−0.539186
$820$	0	0
$821$	−2.34861e44	−0.157940	−0.0789699	−	0.996877i	$-0.525163\pi$
$821$	−2.34861e44	−0.157940	−0.0789699	+	0.996877i	$0.525163\pi$
$822$	3.37382e44	0.222643
$823$	−2.26372e45	−1.46597	−0.732984	−	0.680246i	$-0.761873\pi$
$823$	−2.26372e45	−1.46597	−0.732984	+	0.680246i	$0.761873\pi$
$824$	1.07692e45	0.684405
$825$	0	0
$826$	−1.92566e45	−1.17866
$827$	−1.11856e45	−0.671929	−0.335965	−	0.941875i	$-0.609062\pi$
$827$	−1.11856e45	−0.671929	−0.335965	+	0.941875i	$0.609062\pi$
$828$	3.78192e42	0.00222968
$829$	−2.19670e45	−1.27109	−0.635544	−	0.772064i	$-0.719224\pi$
$829$	−2.19670e45	−1.27109	−0.635544	+	0.772064i	$0.719224\pi$
$830$	0	0
$831$	−2.45236e45	−1.36700
$832$	−3.10017e45	−1.69619
$833$	2.94738e44	0.158285
$834$	4.13717e45	2.18087
$835$	0	0
$836$	1.00814e44	0.0512064
$837$	1.63202e45	0.813733
$838$	−3.15593e45	−1.54470
$839$	3.71878e45	1.78686	0.893429	−	0.449204i	$-0.148293\pi$
$839$	3.71878e45	1.78686	0.893429	+	0.449204i	$0.148293\pi$
$840$	0	0
$841$	3.66359e45	1.69656
$842$	3.26923e45	1.48631
$843$	5.22423e45	2.33182
$844$	−6.17139e45	−2.70442
$845$	0	0
$846$	1.76660e45	0.746274
$847$	2.12920e45	0.883128
$848$	8.16038e43	0.0332334
$849$	3.66359e45	1.46500
$850$	0	0
$851$	−4.76359e42	−0.00183665
$852$	1.90942e45	0.722915
$853$	−2.48938e45	−0.925509	−0.462754	−	0.886487i	$-0.653139\pi$
$853$	−2.48938e45	−0.925509	−0.462754	+	0.886487i	$0.653139\pi$
$854$	−4.44337e45	−1.62224
$855$	0	0
$856$	1.77603e45	0.625326
$857$	8.68133e44	0.300181	0.150091	−	0.988672i	$-0.452043\pi$
$857$	8.68133e44	0.300181	0.150091	+	0.988672i	$0.452043\pi$
$858$	−1.06723e45	−0.362413
$859$	−1.43587e45	−0.478875	−0.239437	−	0.970912i	$-0.576963\pi$
$859$	−1.43587e45	−0.478875	−0.239437	+	0.970912i	$0.576963\pi$
$860$	0	0
$861$	4.87684e45	1.56888
$862$	1.16869e45	0.369265
$863$	3.91776e45	1.21582	0.607911	−	0.794005i	$-0.292008\pi$
$863$	3.91776e45	1.21582	0.607911	+	0.794005i	$0.292008\pi$
$864$	2.48572e45	0.757687
$865$	0	0
$866$	5.14729e44	0.151374
$867$	6.14076e44	0.177389
$868$	−6.27199e45	−1.77971
$869$	−4.32111e44	−0.120445
$870$	0	0
$871$	1.89991e45	0.511036
$872$	2.03339e45	0.537299
$873$	1.79914e45	0.467030
$874$	3.92241e42	0.00100029
$875$	0	0
$876$	3.55939e45	0.876117
$877$	2.59910e45	0.628535	0.314267	−	0.949335i	$-0.398241\pi$
$877$	2.59910e45	0.628535	0.314267	+	0.949335i	$0.398241\pi$
$878$	−1.22678e45	−0.291476
$879$	2.87630e45	0.671438
$880$	0	0
$881$	1.04135e45	0.234676	0.117338	−	0.993092i	$-0.462564\pi$
$881$	1.04135e45	0.234676	0.117338	+	0.993092i	$0.462564\pi$
$882$	6.43168e44	0.142417
$883$	9.31982e44	0.202776	0.101388	−	0.994847i	$-0.467672\pi$
$883$	9.31982e44	0.202776	0.101388	+	0.994847i	$0.467672\pi$
$884$	−6.47943e45	−1.38524
$885$	0	0
$886$	−6.57863e44	−0.135804
$887$	−1.93996e45	−0.393529	−0.196764	−	0.980451i	$-0.563043\pi$
$887$	−1.93996e45	−0.393529	−0.196764	+	0.980451i	$0.563043\pi$
$888$	−2.14986e45	−0.428558
$889$	−6.50823e45	−1.27493
$890$	0	0
$891$	1.14425e45	0.216478
$892$	7.71020e45	1.43354
$893$	1.05842e45	0.193401
$894$	1.46249e46	2.62641
$895$	0	0
$896$	−5.53934e45	−0.960913
$897$	−2.39864e43	−0.00408961
$898$	−1.28459e46	−2.15269
$899$	1.42469e46	2.34664
$900$	0	0
$901$	3.89082e44	0.0619165
$902$	2.36771e45	0.370362
$903$	9.45278e45	1.45345
$904$	8.59192e44	0.129861
$905$	0	0
$906$	−1.44970e46	−2.11734
$907$	8.10222e45	1.16330	0.581649	−	0.813440i	$-0.302408\pi$
$907$	8.10222e45	1.16330	0.581649	+	0.813440i	$0.302408\pi$
$908$	−3.40990e44	−0.0481294
$909$	−4.30880e45	−0.597883
$910$	0	0
$911$	−1.13425e46	−1.52115	−0.760575	−	0.649250i	$-0.775083\pi$
$911$	−1.13425e46	−1.52115	−0.760575	+	0.649250i	$0.775083\pi$
$912$	−1.01009e45	−0.133181
$913$	−1.09158e45	−0.141501
$914$	5.01671e45	0.639370
$915$	0	0
$916$	4.11167e45	0.506569
$917$	−2.06289e44	−0.0249892
$918$	6.81075e45	0.811210
$919$	1.39631e46	1.63527	0.817637	−	0.575734i	$-0.195283\pi$
$919$	1.39631e46	1.63527	0.817637	+	0.575734i	$0.195283\pi$
$920$	0	0
$921$	−6.50516e45	−0.736604
$922$	1.53322e45	0.170716
$923$	−4.25329e45	−0.465692
$924$	−2.49041e45	−0.268137
$925$	0	0
$926$	2.62982e46	2.73814
$927$	−6.39344e45	−0.654634
$928$	2.16994e46	2.18501
$929$	−3.21761e45	−0.318632	−0.159316	−	0.987228i	$-0.550929\pi$
$929$	−3.21761e45	−0.318632	−0.159316	+	0.987228i	$0.550929\pi$
$930$	0	0
$931$	3.85338e44	0.0369081
$932$	−2.10054e46	−1.97872
$933$	−1.31062e46	−1.21426
$934$	−2.39042e46	−2.17820
$935$	0	0
$936$	−3.80201e45	−0.335149
$937$	−1.44001e46	−1.24853	−0.624267	−	0.781211i	$-0.714602\pi$
$937$	−1.44001e46	−1.24853	−0.624267	+	0.781211i	$0.714602\pi$
$938$	7.67485e45	0.654524
$939$	−9.49221e45	−0.796252
$940$	0	0
$941$	−1.38781e46	−1.12640	−0.563198	−	0.826322i	$-0.690429\pi$
$941$	−1.38781e46	−1.12640	−0.563198	+	0.826322i	$0.690429\pi$
$942$	−3.52737e46	−2.81619
$943$	5.32153e43	0.00417931
$944$	5.41109e45	0.418041
$945$	0	0
$946$	4.58933e45	0.343112
$947$	3.58686e45	0.263809	0.131905	−	0.991262i	$-0.457891\pi$
$947$	3.58686e45	0.263809	0.131905	+	0.991262i	$0.457891\pi$
$948$	−1.63001e46	−1.17940
$949$	−7.92866e45	−0.564383
$950$	0	0
$951$	−3.01308e46	−2.07593
$952$	−7.03822e45	−0.477079
$953$	−8.63539e45	−0.575893	−0.287947	−	0.957646i	$-0.592973\pi$
$953$	−8.63539e45	−0.575893	−0.287947	+	0.957646i	$0.592973\pi$
$954$	8.49040e44	0.0557094
$955$	0	0
$956$	8.71088e45	0.553305
$957$	5.65702e45	0.353552
$958$	1.27110e46	0.781656
$959$	−1.75372e45	−0.106114
$960$	0	0
$961$	1.77883e46	1.04213
$962$	1.78092e46	1.02667
$963$	−1.05439e46	−0.598125
$964$	−2.11645e46	−1.18145
$965$	0	0
$966$	−9.68952e43	−0.00523789
$967$	1.07239e46	0.570481	0.285241	−	0.958456i	$-0.407927\pi$
$967$	1.07239e46	0.570481	0.285241	+	0.958456i	$0.407927\pi$
$968$	1.04855e46	0.548938
$969$	−4.81605e45	−0.248126
$970$	0	0
$971$	1.69197e46	0.844295	0.422148	−	0.906527i	$-0.361276\pi$
$971$	1.69197e46	0.844295	0.422148	+	0.906527i	$0.361276\pi$
$972$	2.73038e46	1.34090
$973$	−2.15051e46	−1.03942
$974$	−2.11153e46	−1.00446
$975$	0	0
$976$	1.24859e46	0.575369
$977$	1.63831e46	0.743069	0.371534	−	0.928419i	$-0.378832\pi$
$977$	1.63831e46	0.743069	0.371534	+	0.928419i	$0.378832\pi$
$978$	3.59700e46	1.60579
$979$	−6.26632e44	−0.0275347
$980$	0	0
$981$	−1.20718e46	−0.513927
$982$	−2.04776e46	−0.858126
$983$	−1.26750e46	−0.522839	−0.261419	−	0.965225i	$-0.584191\pi$
$983$	−1.26750e46	−0.522839	−0.261419	+	0.965225i	$0.584191\pi$
$984$	2.40167e46	0.975190
$985$	0	0
$986$	5.94552e46	2.33936
$987$	−2.61461e46	−1.01272
$988$	−8.47114e45	−0.323005
$989$	1.03147e44	0.00387182
$990$	0	0
$991$	−3.41939e46	−1.24396	−0.621980	−	0.783033i	$-0.713672\pi$
$991$	−3.41939e46	−1.24396	−0.621980	+	0.783033i	$0.713672\pi$
$992$	5.30911e46	1.90148
$993$	−2.56276e46	−0.903638
$994$	−1.71815e46	−0.596449
$995$	0	0
$996$	−4.11767e46	−1.38558
$997$	−3.16608e46	−1.04893	−0.524466	−	0.851432i	$-0.675735\pi$
$997$	−3.16608e46	−1.04893	−0.524466	+	0.851432i	$0.675735\pi$
$998$	8.49707e46	2.77170
$999$	−1.08139e46	−0.347309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.a.a.1.1		2
5.2	odd	4		25.32.b.a.24.1		4
5.3	odd	4		25.32.b.a.24.4		4
5.4	even	2		1.32.a.a.1.2	✓	2
15.14	odd	2		9.32.a.a.1.1		2
20.19	odd	2		16.32.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.2	✓	2	5.4	even	2
9.32.a.a.1.1		2	15.14	odd	2
16.32.a.b.1.1		2	20.19	odd	2
25.32.a.a.1.1		2	1.1	even	1	trivial
25.32.b.a.24.1		4	5.2	odd	4
25.32.b.a.24.4		4	5.3	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-71307.9 q^{2} -3.08552e7 q^{3} +2.93733e9 q^{4} +2.20022e12 q^{6} -1.14368e13 q^{7} -5.63222e13 q^{8} +3.34371e14 q^{9} +O(q^{10})\)	\(q-71307.9 q^{2} -3.08552e7 q^{3} +2.93733e9 q^{4} +2.20022e12 q^{6} -1.14368e13 q^{7} -5.63222e13 q^{8} +3.34371e14 q^{9} -2.40262e15 q^{11} -9.06319e16 q^{12} +2.01886e17 q^{13} +8.15534e17 q^{14} -2.29165e18 q^{16} -1.09264e19 q^{17} -2.38433e19 q^{18} -1.42851e19 q^{19} +3.52885e20 q^{21} +1.71326e20 q^{22} +3.85062e18 q^{23} +1.73783e21 q^{24} -1.43960e22 q^{26} +8.74135e21 q^{27} -3.35937e22 q^{28} +7.63087e22 q^{29} +1.86701e23 q^{31} +2.84364e23 q^{32} +7.41334e22 q^{33} +7.79141e23 q^{34} +9.82158e23 q^{36} -1.23709e24 q^{37} +1.01864e24 q^{38} -6.22922e24 q^{39} +1.38199e25 q^{41} -2.51635e25 q^{42} +2.67871e25 q^{43} -7.05729e24 q^{44} -2.74580e23 q^{46} -7.40922e25 q^{47} +7.07094e25 q^{48} -2.69748e25 q^{49} +3.37138e26 q^{51} +5.93004e26 q^{52} -3.56092e25 q^{53} -6.23327e26 q^{54} +6.44146e26 q^{56} +4.40770e26 q^{57} -5.44141e27 q^{58} -2.36122e27 q^{59} -5.44842e27 q^{61} -1.33133e28 q^{62} -3.82414e27 q^{63} -1.53561e28 q^{64} -5.28630e27 q^{66} +9.41082e27 q^{67} -3.20945e28 q^{68} -1.18812e26 q^{69} -2.10678e28 q^{71} -1.88325e28 q^{72} -3.92731e28 q^{73} +8.82146e28 q^{74} -4.19601e28 q^{76} +2.74783e28 q^{77} +4.44193e29 q^{78} +1.79850e29 q^{79} -4.76249e29 q^{81} -9.85468e29 q^{82} +4.54329e29 q^{83} +1.03654e30 q^{84} -1.91013e30 q^{86} -2.35452e30 q^{87} +1.35321e29 q^{88} +2.60812e29 q^{89} -2.30893e30 q^{91} +1.13106e28 q^{92} -5.76072e30 q^{93} +5.28336e30 q^{94} -8.77410e30 q^{96} +5.38067e30 q^{97} +1.92352e30 q^{98} -8.03368e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) \) 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9	\( 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9} - 77\!\cdots\!76 q^{11}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9 - 7782353745118776 * q^11 - 106347410955313920 * q^12 - 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 37499616229575978360 * q^18 - 12370563328022164040 * q^19 + 98954957416071161664 * q^21 + 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 - 23066680666744323279216 * q^26 - 5469986602319662295280 * q^27 - 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 1489586748818199413504832 * q^36 + 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 8724924335662925840671284 * q^41 - 33123669600002676603713280 * q^42 + 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 252162404739970320085380144 * q^51 + 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 + 2598355397749815172431728640 * q^56 + 466601717043760934967596640 * q^57 - 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 + 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 - 7561640583442461364265814912 * q^66 + 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 + 55784576625034657512878287344 * q^71 + 26400994734811244163462812160 * q^72 - 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 + 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 - 398906922646891269649062634158 * q^81 - 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 2173142482222838422832927019936 * q^86 - 1649324800814841914442821796240 * q^87 + 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 - 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 - 6084370432669606716368714858496 * q^96 + 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * q^99

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