LMFDB - Embedded newform 50.26.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(1,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
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} - 148387471 $ x^2 - 148387471
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-12181.4$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00 q^{2} -1.24712e6 q^{3} +1.67772e7 q^{4} -5.10821e9 q^{6} -3.92781e10 q^{7} +6.87195e10 q^{8} +7.08023e11 q^{9} -1.50696e13 q^{11} -2.09232e13 q^{12} +1.45379e14 q^{13} -1.60883e14 q^{14} +2.81475e14 q^{16} -1.30302e15 q^{17} +2.90006e15 q^{18} -9.75151e15 q^{19} +4.89845e16 q^{21} -6.17252e16 q^{22} -1.00704e17 q^{23} -8.57015e16 q^{24} +5.95471e17 q^{26} +1.73682e17 q^{27} -6.58976e17 q^{28} -1.41726e18 q^{29} -3.30375e18 q^{31} +1.15292e18 q^{32} +1.87937e19 q^{33} -5.33718e18 q^{34} +1.18786e19 q^{36} -6.55066e19 q^{37} -3.99422e19 q^{38} -1.81305e20 q^{39} -9.42027e19 q^{41} +2.00640e20 q^{42} -1.20866e20 q^{43} -2.52827e20 q^{44} -4.12482e20 q^{46} +8.86966e20 q^{47} -3.51033e20 q^{48} +2.01697e20 q^{49} +1.62503e21 q^{51} +2.43905e21 q^{52} +6.79454e21 q^{53} +7.11400e20 q^{54} -2.69917e21 q^{56} +1.21613e22 q^{57} -5.80511e21 q^{58} -1.11112e22 q^{59} -3.14899e22 q^{61} -1.35322e22 q^{62} -2.78098e22 q^{63} +4.72237e21 q^{64} +7.69788e22 q^{66} -4.52478e22 q^{67} -2.18611e22 q^{68} +1.25590e23 q^{69} -3.31126e22 q^{71} +4.86549e22 q^{72} -3.04253e23 q^{73} -2.68315e23 q^{74} -1.63603e23 q^{76} +5.91906e23 q^{77} -7.42625e23 q^{78} -1.45524e23 q^{79} -8.16501e23 q^{81} -3.85854e23 q^{82} -8.80567e23 q^{83} +8.21823e23 q^{84} -4.95068e23 q^{86} +1.76750e24 q^{87} -1.03558e24 q^{88} -1.79771e23 q^{89} -5.71019e24 q^{91} -1.68953e24 q^{92} +4.12018e24 q^{93} +3.63301e24 q^{94} -1.43783e24 q^{96} +7.02806e24 q^{97} +8.26151e23 q^{98} -1.06696e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8192 q^{2} - 545212 q^{3} + 33554432 q^{4} - 2233188352 q^{6} - 38567856964 q^{7} + 137438953472 q^{8} + 353410472386 q^{9} - 8379169876416 q^{11} - 9147139489792 q^{12} + 149443737196988 q^{13} - 157973942124544 q^{14}+ \cdots - 13\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 8192 * q^2 - 545212 * q^3 + 33554432 * q^4 - 2233188352 * q^6 - 38567856964 * q^7 + 137438953472 * q^8 + 353410472386 * q^9 - 8379169876416 * q^11 - 9147139489792 * q^12 + 149443737196988 * q^13 - 157973942124544 * q^14 + 562949953421312 * q^16 - 3359254299255924 * q^17 + 1447569294893056 * q^18 + 3489461415860920 * q^19 + 49482990719617784 * q^21 - 34321079813799936 * q^22 - 72370201928022732 * q^23 - 37466683350188032 * q^24 + 612121547558862848 * q^26 - 669943559840926600 * q^27 - 647061266942132224 * q^28 - 537443787959856180 * q^29 - 3624027784441312136 * q^31 + 2305843009213693952 * q^32 + 23489760709118906496 * q^33 - 13759505609752264704 * q^34 + 5929243831881957376 * q^36 - 19038572664443645764 * q^37 + 14292833959366328320 * q^38 - 178451546772299045128 * q^39 - 212589580623880771956 * q^41 + 202682329987554443264 * q^42 + 13668418927657846868 * q^43 - 140579142917324537856 * q^44 - 296428347097181110272 * q^46 + 1665681645557377854156 * q^47 - 153463535002370179072 * q^48 - 1138867157350741829766 * q^49 + 181740691723390600344 * q^51 + 2507249858801102225408 * q^52 + 9975823013097020329548 * q^53 - 2744088821108435353600 * q^54 - 2650362949394973589504 * q^56 + 21455279998725990048880 * q^57 - 2201369755483570913280 * q^58 - 13147506706206800097960 * q^59 + 114411778307375747524 * q^61 - 14844017805071614509056 * q^62 - 28061596756249158893252 * q^63 + 9444732965739290427392 * q^64 + 96214059864551041007616 * q^66 - 95143040936399031080644 * q^67 - 56358934977545276227584 * q^68 + 145477011313277750812392 * q^69 + 83749259495165337742824 * q^71 + 24286182735388497412096 * q^72 - 196631633422897936973572 * q^73 - 77981993633561173049344 * q^74 + 58543447897564480798720 * q^76 + 596657555842340580669312 * q^77 - 730937535579336888844288 * q^78 + 105871595026057220692240 * q^79 - 1108190878966022772827798 * q^81 - 870766922235415641931776 * q^82 + 599053017838528107773748 * q^83 + 830186823629022999609344 * q^84 + 55985843927686540771328 * q^86 + 2385054109175491523609880 * q^87 - 575812169389361307058176 * q^88 - 1877353952181279423739020 * q^89 - 5707305339748996500897016 * q^91 - 1214170509710053827674112 * q^92 + 3895374854369117044063216 * q^93 + 6822632020203019690622976 * q^94 - 628586639369708253478912 * q^96 + 11597588153054877446451836 * q^97 - 4664799876508638534721536 * q^98 - 13042162823998039381361088 * q^99

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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	−1.24712e6	−1.35486	−0.677428	−	0.735589i	$-0.736905\pi$
$3$	−1.24712e6	−1.35486	−0.677428	+	0.735589i	$0.736905\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−5.10821e9	−0.958027
$7$	−3.92781e10	−1.07257	−0.536284	−	0.844038i	$-0.680172\pi$
$7$	−3.92781e10	−1.07257	−0.536284	+	0.844038i	$0.680172\pi$
$8$	6.87195e10	0.353553
$9$	7.08023e11	0.835633
$10$	0	0
$11$	−1.50696e13	−1.44775	−0.723876	−	0.689930i	$-0.757641\pi$
$11$	−1.50696e13	−1.44775	−0.723876	+	0.689930i	$0.757641\pi$
$12$	−2.09232e13	−0.677428
$13$	1.45379e14	1.73065	0.865324	−	0.501213i	$-0.167113\pi$
$13$	1.45379e14	1.73065	0.865324	+	0.501213i	$0.167113\pi$
$14$	−1.60883e14	−0.758419
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−1.30302e15	−0.542426	−0.271213	−	0.962519i	$-0.587425\pi$
$17$	−1.30302e15	−0.542426	−0.271213	+	0.962519i	$0.587425\pi$
$18$	2.90006e15	0.590882
$19$	−9.75151e15	−1.01077	−0.505385	−	0.862894i	$-0.668649\pi$
$19$	−9.75151e15	−1.01077	−0.505385	+	0.862894i	$0.668649\pi$
$20$	0	0
$21$	4.89845e16	1.45317
$22$	−6.17252e16	−1.02372
$23$	−1.00704e17	−0.958180	−0.479090	−	0.877766i	$-0.659033\pi$
$23$	−1.00704e17	−0.958180	−0.479090	+	0.877766i	$0.659033\pi$
$24$	−8.57015e16	−0.479014
$25$	0	0
$26$	5.95471e17	1.22375
$27$	1.73682e17	0.222693
$28$	−6.58976e17	−0.536284
$29$	−1.41726e18	−0.743834	−0.371917	−	0.928266i	$-0.621299\pi$
$29$	−1.41726e18	−0.743834	−0.371917	+	0.928266i	$0.621299\pi$
$30$	0	0
$31$	−3.30375e18	−0.753332	−0.376666	−	0.926349i	$-0.622930\pi$
$31$	−3.30375e18	−0.753332	−0.376666	+	0.926349i	$0.622930\pi$
$32$	1.15292e18	0.176777
$33$	1.87937e19	1.96149
$34$	−5.33718e18	−0.383553
$35$	0	0
$36$	1.18786e19	0.417817
$37$	−6.55066e19	−1.63593	−0.817963	−	0.575271i	$-0.804897\pi$
$37$	−6.55066e19	−1.63593	−0.817963	+	0.575271i	$0.804897\pi$
$38$	−3.99422e19	−0.714722
$39$	−1.81305e20	−2.34478
$40$	0	0
$41$	−9.42027e19	−0.652026	−0.326013	−	0.945365i	$-0.605705\pi$
$41$	−9.42027e19	−0.652026	−0.326013	+	0.945365i	$0.605705\pi$
$42$	2.00640e20	1.02755
$43$	−1.20866e20	−0.461263	−0.230632	−	0.973041i	$-0.574079\pi$
$43$	−1.20866e20	−0.461263	−0.230632	+	0.973041i	$0.574079\pi$
$44$	−2.52827e20	−0.723876
$45$	0	0
$46$	−4.12482e20	−0.677535
$47$	8.86966e20	1.11348	0.556742	−	0.830686i	$-0.312051\pi$
$47$	8.86966e20	1.11348	0.556742	+	0.830686i	$0.312051\pi$
$48$	−3.51033e20	−0.338714
$49$	2.01697e20	0.150400
$50$	0	0
$51$	1.62503e21	0.734909
$52$	2.43905e21	0.865324
$53$	6.79454e21	1.89982	0.949908	−	0.312530i	$-0.101176\pi$
$53$	6.79454e21	1.89982	0.949908	+	0.312530i	$0.101176\pi$
$54$	7.11400e20	0.157468
$55$	0	0
$56$	−2.69917e21	−0.379210
$57$	1.21613e22	1.36945
$58$	−5.80511e21	−0.525970
$59$	−1.11112e22	−0.813039	−0.406520	−	0.913642i	$-0.633258\pi$
$59$	−1.11112e22	−0.813039	−0.406520	+	0.913642i	$0.633258\pi$
$60$	0	0
$61$	−3.14899e22	−1.51897	−0.759483	−	0.650527i	$-0.774548\pi$
$61$	−3.14899e22	−1.51897	−0.759483	+	0.650527i	$0.774548\pi$
$62$	−1.35322e22	−0.532686
$63$	−2.78098e22	−0.896273
$64$	4.72237e21	0.125000
$65$	0	0
$66$	7.69788e22	1.38699
$67$	−4.52478e22	−0.675558	−0.337779	−	0.941225i	$-0.609676\pi$
$67$	−4.52478e22	−0.675558	−0.337779	+	0.941225i	$0.609676\pi$
$68$	−2.18611e22	−0.271213
$69$	1.25590e23	1.29819
$70$	0	0
$71$	−3.31126e22	−0.239477	−0.119739	−	0.992805i	$-0.538206\pi$
$71$	−3.31126e22	−0.239477	−0.119739	+	0.992805i	$0.538206\pi$
$72$	4.86549e22	0.295441
$73$	−3.04253e23	−1.55489	−0.777445	−	0.628952i	$-0.783484\pi$
$73$	−3.04253e23	−1.55489	−0.777445	+	0.628952i	$0.783484\pi$
$74$	−2.68315e23	−1.15677
$75$	0	0
$76$	−1.63603e23	−0.505385
$77$	5.91906e23	1.55281
$78$	−7.42625e23	−1.65801
$79$	−1.45524e23	−0.277075	−0.138537	−	0.990357i	$-0.544240\pi$
$79$	−1.45524e23	−0.277075	−0.138537	+	0.990357i	$0.544240\pi$
$80$	0	0
$81$	−8.16501e23	−1.13735
$82$	−3.85854e23	−0.461052
$83$	−8.80567e23	−0.904245	−0.452122	−	0.891956i	$-0.649333\pi$
$83$	−8.80567e23	−0.904245	−0.452122	+	0.891956i	$0.649333\pi$
$84$	8.21823e23	0.726587
$85$	0	0
$86$	−4.95068e23	−0.326162
$87$	1.76750e24	1.00779
$88$	−1.03558e24	−0.511858
$89$	−1.79771e23	−0.0771514	−0.0385757	−	0.999256i	$-0.512282\pi$
$89$	−1.79771e23	−0.0771514	−0.0385757	+	0.999256i	$0.512282\pi$
$90$	0	0
$91$	−5.71019e24	−1.85624
$92$	−1.68953e24	−0.479090
$93$	4.12018e24	1.02066
$94$	3.63301e24	0.787352
$95$	0	0
$96$	−1.43783e24	−0.239507
$97$	7.02806e24	1.02846	0.514232	−	0.857651i	$-0.328077\pi$
$97$	7.02806e24	1.02846	0.514232	+	0.857651i	$0.328077\pi$
$98$	8.26151e23	0.106349
$99$	−1.06696e25	−1.20979
$100$	0	0
$101$	−6.59850e24	−0.582677	−0.291339	−	0.956620i	$-0.594101\pi$
$101$	−6.59850e24	−0.582677	−0.291339	+	0.956620i	$0.594101\pi$
$102$	6.65611e24	0.519659
$103$	−2.14556e25	−1.48278	−0.741389	−	0.671075i	$-0.765833\pi$
$103$	−2.14556e25	−1.48278	−0.741389	+	0.671075i	$0.765833\pi$
$104$	9.99035e24	0.611877
$105$	0	0
$106$	2.78304e25	1.34337
$107$	−2.29745e24	−0.0986164	−0.0493082	−	0.998784i	$-0.515702\pi$
$107$	−2.29745e24	−0.0986164	−0.0493082	+	0.998784i	$0.515702\pi$
$108$	2.91389e24	0.111347
$109$	2.46259e25	0.838611	0.419305	−	0.907845i	$-0.362274\pi$
$109$	2.46259e25	0.838611	0.419305	+	0.907845i	$0.362274\pi$
$110$	0	0
$111$	8.16947e25	2.21644
$112$	−1.10558e25	−0.268142
$113$	4.71863e25	1.02408	0.512042	−	0.858960i	$-0.328889\pi$
$113$	4.71863e25	1.02408	0.512042	+	0.858960i	$0.328889\pi$
$114$	4.98128e25	0.968345
$115$	0	0
$116$	−2.37777e25	−0.371917
$117$	1.02931e26	1.44619
$118$	−4.55116e25	−0.574906
$119$	5.11802e25	0.581789
$120$	0	0
$121$	1.18747e26	1.09599
$122$	−1.28982e26	−1.07407
$123$	1.17482e26	0.883401
$124$	−5.54278e25	−0.376666
$125$	0	0
$126$	−1.13909e26	−0.633761
$127$	1.28089e26	0.645605	0.322802	−	0.946466i	$-0.395375\pi$
$127$	1.28089e26	0.645605	0.322802	+	0.946466i	$0.395375\pi$
$128$	1.93428e25	0.0883883
$129$	1.50735e26	0.624945
$130$	0	0
$131$	1.65371e26	0.565675	0.282838	−	0.959168i	$-0.408724\pi$
$131$	1.65371e26	0.565675	0.282838	+	0.959168i	$0.408724\pi$
$132$	3.15305e26	0.980747
$133$	3.83020e26	1.08412
$134$	−1.85335e26	−0.477692
$135$	0	0
$136$	−8.95431e25	−0.191777
$137$	3.20644e26	0.626637	0.313319	−	0.949648i	$-0.398559\pi$
$137$	3.20644e26	0.626637	0.313319	+	0.949648i	$0.398559\pi$
$138$	5.14415e26	0.917962
$139$	5.33177e26	0.869333	0.434666	−	0.900592i	$-0.356866\pi$
$139$	5.33177e26	0.869333	0.434666	+	0.900592i	$0.356866\pi$
$140$	0	0
$141$	−1.10615e27	−1.50861
$142$	−1.35629e26	−0.169336
$143$	−2.19080e27	−2.50555
$144$	1.99291e26	0.208908
$145$	0	0
$146$	−1.24622e27	−1.09947
$147$	−2.51541e26	−0.203771
$148$	−1.09902e27	−0.817963
$149$	5.79851e26	0.396724	0.198362	−	0.980129i	$-0.436438\pi$
$149$	5.79851e26	0.396724	0.198362	+	0.980129i	$0.436438\pi$
$150$	0	0
$151$	2.88738e27	1.67222	0.836109	−	0.548564i	$-0.184825\pi$
$151$	2.88738e27	1.67222	0.836109	+	0.548564i	$0.184825\pi$
$152$	−6.70119e26	−0.357361
$153$	−9.22570e26	−0.453269
$154$	2.42445e27	1.09800
$155$	0	0
$156$	−3.04179e27	−1.17239
$157$	4.99584e27	1.77772	0.888859	−	0.458181i	$-0.151499\pi$
$157$	4.99584e27	1.77772	0.888859	+	0.458181i	$0.151499\pi$
$158$	−5.96067e26	−0.195921
$159$	−8.47361e27	−2.57398
$160$	0	0
$161$	3.95544e27	1.02771
$162$	−3.34439e27	−0.804228
$163$	−9.78636e25	−0.0217909	−0.0108955	−	0.999941i	$-0.503468\pi$
$163$	−9.78636e25	−0.0217909	−0.0108955	+	0.999941i	$0.503468\pi$
$164$	−1.58046e27	−0.326013
$165$	0	0
$166$	−3.60680e27	−0.639398
$167$	−8.79974e27	−1.44715	−0.723576	−	0.690245i	$-0.757503\pi$
$167$	−8.79974e27	−1.44715	−0.723576	+	0.690245i	$0.757503\pi$
$168$	3.36619e27	0.513774
$169$	1.40786e28	1.99514
$170$	0	0
$171$	−6.90429e27	−0.844632
$172$	−2.02780e27	−0.230632
$173$	1.48916e28	1.57530	0.787651	−	0.616122i	$-0.211297\pi$
$173$	1.48916e28	1.57530	0.787651	+	0.616122i	$0.211297\pi$
$174$	7.23968e27	0.712613
$175$	0	0
$176$	−4.24173e27	−0.361938
$177$	1.38570e28	1.10155
$178$	−7.36341e26	−0.0545543
$179$	−1.83964e28	−1.27078	−0.635390	−	0.772191i	$-0.719161\pi$
$179$	−1.83964e28	−1.27078	−0.635390	+	0.772191i	$0.719161\pi$
$180$	0	0
$181$	1.98192e28	1.19153	0.595764	−	0.803160i	$-0.296849\pi$
$181$	1.98192e28	1.19153	0.595764	+	0.803160i	$0.296849\pi$
$182$	−2.33889e28	−1.31256
$183$	3.92717e28	2.05798
$184$	−6.92030e27	−0.338768
$185$	0	0
$186$	1.68763e28	0.721713
$187$	1.96361e28	0.785299
$188$	1.48808e28	0.556742
$189$	−6.82188e27	−0.238853
$190$	0	0
$191$	−3.54565e28	−1.08837	−0.544187	−	0.838964i	$-0.683162\pi$
$191$	−3.54565e28	−1.08837	−0.544187	+	0.838964i	$0.683162\pi$
$192$	−5.88936e27	−0.169357
$193$	1.29750e28	0.349657	0.174829	−	0.984599i	$-0.444063\pi$
$193$	1.29750e28	0.349657	0.174829	+	0.984599i	$0.444063\pi$
$194$	2.87869e28	0.727234
$195$	0	0
$196$	3.38392e27	0.0752001
$197$	−6.04380e28	−1.26032	−0.630162	−	0.776463i	$-0.717012\pi$
$197$	−6.04380e28	−1.26032	−0.630162	+	0.776463i	$0.717012\pi$
$198$	−4.37029e28	−0.855451
$199$	5.51931e28	1.01443	0.507215	−	0.861820i	$-0.330675\pi$
$199$	5.51931e28	1.01443	0.507215	+	0.861820i	$0.330675\pi$
$200$	0	0
$201$	5.64295e28	0.915283
$202$	−2.70275e28	−0.412015
$203$	5.56674e28	0.797812
$204$	2.72634e28	0.367455
$205$	0	0
$206$	−8.78823e28	−1.04848
$207$	−7.13004e28	−0.800687
$208$	4.09205e28	0.432662
$209$	1.46952e29	1.46334
$210$	0	0
$211$	−7.38048e28	−0.652460	−0.326230	−	0.945290i	$-0.605778\pi$
$211$	−7.38048e28	−0.652460	−0.326230	+	0.945290i	$0.605778\pi$
$212$	1.13993e29	0.949908
$213$	4.12955e28	0.324457
$214$	−9.41036e27	−0.0697323
$215$	0	0
$216$	1.19353e28	0.0787339
$217$	1.29765e29	0.807999
$218$	1.00868e29	0.592987
$219$	3.79441e29	2.10665
$220$	0	0
$221$	−1.89432e29	−0.938749
$222$	3.34621e29	1.56726
$223$	−3.22437e29	−1.42769	−0.713846	−	0.700303i	$-0.753048\pi$
$223$	−3.22437e29	−1.42769	−0.713846	+	0.700303i	$0.753048\pi$
$224$	−4.52845e28	−0.189605
$225$	0	0
$226$	1.93275e29	0.724137
$227$	4.50494e29	1.59722	0.798611	−	0.601847i	$-0.205568\pi$
$227$	4.50494e29	1.59722	0.798611	+	0.601847i	$0.205568\pi$
$228$	2.04033e29	0.684723
$229$	−3.03906e28	−0.0965596	−0.0482798	−	0.998834i	$-0.515374\pi$
$229$	−3.03906e28	−0.0965596	−0.0482798	+	0.998834i	$0.515374\pi$
$230$	0	0
$231$	−7.38178e29	−2.10383
$232$	−9.73937e28	−0.262985
$233$	1.03711e29	0.265386	0.132693	−	0.991157i	$-0.457638\pi$
$233$	1.03711e29	0.265386	0.132693	+	0.991157i	$0.457638\pi$
$234$	4.21607e29	1.02261
$235$	0	0
$236$	−1.86415e29	−0.406520
$237$	1.81486e29	0.375396
$238$	2.09634e29	0.411387
$239$	8.96475e29	1.66942	0.834708	−	0.550693i	$-0.185636\pi$
$239$	8.96475e29	1.66942	0.834708	+	0.550693i	$0.185636\pi$
$240$	0	0
$241$	1.66839e29	0.279952	0.139976	−	0.990155i	$-0.455297\pi$
$241$	1.66839e29	0.279952	0.139976	+	0.990155i	$0.455297\pi$
$242$	4.86387e29	0.774979
$243$	8.71118e29	1.31825
$244$	−5.28312e29	−0.759483
$245$	0	0
$246$	4.81207e29	0.624659
$247$	−1.41766e30	−1.74929
$248$	−2.27032e29	−0.266343
$249$	1.09817e30	1.22512
$250$	0	0
$251$	−1.77969e28	−0.0179648	−0.00898241	−	0.999960i	$-0.502859\pi$
$251$	−1.77969e28	−0.0179648	−0.00898241	+	0.999960i	$0.502859\pi$
$252$	−4.66570e29	−0.448136
$253$	1.51757e30	1.38721
$254$	5.24654e29	0.456512
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.02153e30	−0.767515	−0.383758	−	0.923434i	$-0.625370\pi$
$257$	−1.02153e30	−0.767515	−0.383758	+	0.923434i	$0.625370\pi$
$258$	6.17409e29	0.441903
$259$	2.57297e30	1.75464
$260$	0	0
$261$	−1.00346e30	−0.621572
$262$	6.77358e29	0.399993
$263$	2.39313e30	1.34747	0.673735	−	0.738973i	$-0.264689\pi$
$263$	2.39313e30	1.34747	0.673735	+	0.738973i	$0.264689\pi$
$264$	1.29149e30	0.693493
$265$	0	0
$266$	1.56885e30	0.766587
$267$	2.24196e29	0.104529
$268$	−7.59132e29	−0.337779
$269$	7.43966e29	0.315973	0.157986	−	0.987441i	$-0.449500\pi$
$269$	7.43966e29	0.315973	0.157986	+	0.987441i	$0.449500\pi$
$270$	0	0
$271$	−2.89456e30	−1.12064	−0.560319	−	0.828277i	$-0.689322\pi$
$271$	−2.89456e30	−1.12064	−0.560319	+	0.828277i	$0.689322\pi$
$272$	−3.66768e29	−0.135607
$273$	7.12130e30	2.51493
$274$	1.31336e30	0.443099
$275$	0	0
$276$	2.10704e30	0.649097
$277$	2.46028e30	0.724415	0.362208	−	0.932097i	$-0.382023\pi$
$277$	2.46028e30	0.724415	0.362208	+	0.932097i	$0.382023\pi$
$278$	2.18389e30	0.614711
$279$	−2.33913e30	−0.629509
$280$	0	0
$281$	5.42013e30	1.33408	0.667038	−	0.745024i	$-0.267562\pi$
$281$	5.42013e30	1.33408	0.667038	+	0.745024i	$0.267562\pi$
$282$	−4.53081e30	−1.06675
$283$	−6.30761e30	−1.42080	−0.710402	−	0.703796i	$-0.751487\pi$
$283$	−6.30761e30	−1.42080	−0.710402	+	0.703796i	$0.751487\pi$
$284$	−5.55538e29	−0.119739
$285$	0	0
$286$	−8.97353e30	−1.77169
$287$	3.70010e30	0.699342
$288$	8.16294e29	0.147720
$289$	−4.07276e30	−0.705774
$290$	0	0
$291$	−8.76484e30	−1.39342
$292$	−5.10452e30	−0.777445
$293$	−9.79285e30	−1.42910	−0.714552	−	0.699582i	$-0.753369\pi$
$293$	−9.79285e30	−1.42910	−0.714552	+	0.699582i	$0.753369\pi$
$294$	−1.03031e30	−0.144088
$295$	0	0
$296$	−4.50158e30	−0.578387
$297$	−2.61732e30	−0.322404
$298$	2.37507e30	0.280526
$299$	−1.46402e31	−1.65827
$300$	0	0
$301$	4.74739e30	0.494736
$302$	1.18267e31	1.18244
$303$	8.22913e30	0.789444
$304$	−2.74481e30	−0.252692
$305$	0	0
$306$	−3.77885e30	−0.320510
$307$	5.75594e30	0.468691	0.234345	−	0.972153i	$-0.424705\pi$
$307$	5.75594e30	0.468691	0.234345	+	0.972153i	$0.424705\pi$
$308$	9.93053e30	0.776406
$309$	2.67578e31	2.00895
$310$	0	0
$311$	1.84953e31	1.28102	0.640510	−	0.767950i	$-0.278723\pi$
$311$	1.84953e31	1.28102	0.640510	+	0.767950i	$0.278723\pi$
$312$	−1.24592e31	−0.829004
$313$	−2.39300e31	−1.52982	−0.764908	−	0.644140i	$-0.777216\pi$
$313$	−2.39300e31	−1.52982	−0.764908	+	0.644140i	$0.777216\pi$
$314$	2.04630e31	1.25704
$315$	0	0
$316$	−2.44149e30	−0.138537
$317$	2.04161e30	0.111360	0.0556802	−	0.998449i	$-0.482267\pi$
$317$	2.04161e30	0.111360	0.0556802	+	0.998449i	$0.482267\pi$
$318$	−3.47079e31	−1.82008
$319$	2.13577e31	1.07689
$320$	0	0
$321$	2.86520e30	0.133611
$322$	1.62015e31	0.726702
$323$	1.27064e31	0.548268
$324$	−1.36986e31	−0.568675
$325$	0	0
$326$	−4.00849e29	−0.0154085
$327$	−3.07114e31	−1.13620
$328$	−6.47356e30	−0.230526
$329$	−3.48383e31	−1.19429
$330$	0	0
$331$	−1.75414e31	−0.557459	−0.278730	−	0.960370i	$-0.589913\pi$
$331$	−1.75414e31	−0.557459	−0.278730	+	0.960370i	$0.589913\pi$
$332$	−1.47735e31	−0.452122
$333$	−4.63802e31	−1.36703
$334$	−3.60437e31	−1.02329
$335$	0	0
$336$	1.37879e31	0.363293
$337$	7.33154e31	1.86132	0.930661	−	0.365882i	$-0.119232\pi$
$337$	7.33154e31	1.86132	0.930661	+	0.365882i	$0.119232\pi$
$338$	5.76658e31	1.41078
$339$	−5.88471e31	−1.38749
$340$	0	0
$341$	4.97863e31	1.09064
$342$	−2.82800e31	−0.597245
$343$	4.47523e31	0.911253
$344$	−8.30586e30	−0.163081
$345$	0	0
$346$	6.09958e31	1.11391
$347$	1.54701e31	0.272505	0.136253	−	0.990674i	$-0.456494\pi$
$347$	1.54701e31	0.272505	0.136253	+	0.990674i	$0.456494\pi$
$348$	2.96537e31	0.503894
$349$	−1.14544e31	−0.187782	−0.0938910	−	0.995582i	$-0.529931\pi$
$349$	−1.14544e31	−0.187782	−0.0938910	+	0.995582i	$0.529931\pi$
$350$	0	0
$351$	2.52496e31	0.385403
$352$	−1.73741e31	−0.255929
$353$	−3.77306e31	−0.536427	−0.268213	−	0.963360i	$-0.586433\pi$
$353$	−3.77306e31	−0.536427	−0.268213	+	0.963360i	$0.586433\pi$
$354$	5.67584e31	0.778914
$355$	0	0
$356$	−3.01605e30	−0.0385757
$357$	−6.38279e31	−0.788239
$358$	−7.53518e31	−0.898578
$359$	−1.13693e32	−1.30934	−0.654671	−	0.755914i	$-0.727193\pi$
$359$	−1.13693e32	−1.30934	−0.654671	+	0.755914i	$0.727193\pi$
$360$	0	0
$361$	2.01551e30	0.0216544
$362$	8.11795e31	0.842537
$363$	−1.48092e32	−1.48490
$364$	−9.58011e31	−0.928118
$365$	0	0
$366$	1.60857e32	1.45521
$367$	7.28071e31	0.636572	0.318286	−	0.947995i	$-0.396893\pi$
$367$	7.28071e31	0.636572	0.318286	+	0.947995i	$0.396893\pi$
$368$	−2.83455e31	−0.239545
$369$	−6.66976e31	−0.544855
$370$	0	0
$371$	−2.66876e32	−2.03768
$372$	6.91251e31	0.510328
$373$	−1.71061e32	−1.22121	−0.610604	−	0.791936i	$-0.709073\pi$
$373$	−1.71061e32	−1.22121	−0.610604	+	0.791936i	$0.709073\pi$
$374$	8.04294e31	0.555290
$375$	0	0
$376$	6.09518e31	0.393676
$377$	−2.06040e32	−1.28731
$378$	−2.79424e31	−0.168895
$379$	2.81613e31	0.164688	0.0823441	−	0.996604i	$-0.473759\pi$
$379$	2.81613e31	0.164688	0.0823441	+	0.996604i	$0.473759\pi$
$380$	0	0
$381$	−1.59743e32	−0.874701
$382$	−1.45230e32	−0.769597
$383$	−9.78501e31	−0.501853	−0.250926	−	0.968006i	$-0.580735\pi$
$383$	−9.78501e31	−0.501853	−0.250926	+	0.968006i	$0.580735\pi$
$384$	−2.41228e31	−0.119753
$385$	0	0
$386$	5.31458e31	0.247245
$387$	−8.55760e31	−0.385447
$388$	1.17911e32	0.514232
$389$	−1.33194e32	−0.562489	−0.281244	−	0.959636i	$-0.590747\pi$
$389$	−1.33194e32	−0.562489	−0.281244	+	0.959636i	$0.590747\pi$
$390$	0	0
$391$	1.31219e32	0.519742
$392$	1.38605e31	0.0531745
$393$	−2.06237e32	−0.766408
$394$	−2.47554e32	−0.891184
$395$	0	0
$396$	−1.79007e32	−0.604895
$397$	−5.53789e32	−1.81327	−0.906637	−	0.421912i	$-0.861359\pi$
$397$	−5.53789e32	−1.81327	−0.906637	+	0.421912i	$0.861359\pi$
$398$	2.26071e32	0.717310
$399$	−4.77673e32	−1.46882
$400$	0	0
$401$	−1.52543e32	−0.440643	−0.220321	−	0.975427i	$-0.570711\pi$
$401$	−1.52543e32	−0.440643	−0.220321	+	0.975427i	$0.570711\pi$
$402$	2.31135e32	0.647203
$403$	−4.80295e32	−1.30375
$404$	−1.10704e32	−0.291339
$405$	0	0
$406$	2.28014e32	0.564138
$407$	9.87161e32	2.36841
$408$	1.11671e32	0.259830
$409$	6.35123e32	1.43323	0.716616	−	0.697468i	$-0.245690\pi$
$409$	6.35123e32	1.43323	0.716616	+	0.697468i	$0.245690\pi$
$410$	0	0
$411$	−3.99882e32	−0.849003
$412$	−3.59966e32	−0.741389
$413$	4.36427e32	0.872039
$414$	−2.92046e32	−0.566171
$415$	0	0
$416$	1.67610e32	0.305938
$417$	−6.64936e32	−1.17782
$418$	6.01914e32	1.03474
$419$	−7.80832e32	−1.30281	−0.651406	−	0.758729i	$-0.725821\pi$
$419$	−7.80832e32	−1.30281	−0.651406	+	0.758729i	$0.725821\pi$
$420$	0	0
$421$	3.57315e32	0.561726	0.280863	−	0.959748i	$-0.409379\pi$
$421$	3.57315e32	0.561726	0.280863	+	0.959748i	$0.409379\pi$
$422$	−3.02305e32	−0.461359
$423$	6.27992e32	0.930464
$424$	4.66917e32	0.671686
$425$	0	0
$426$	1.69146e32	0.229426
$427$	1.23686e33	1.62919
$428$	−3.85448e31	−0.0493082
$429$	2.73220e33	3.39466
$430$	0	0
$431$	9.85346e31	0.115511	0.0577554	−	0.998331i	$-0.481606\pi$
$431$	9.85346e31	0.115511	0.0577554	+	0.998331i	$0.481606\pi$
$432$	4.88870e31	0.0556733
$433$	5.52126e32	0.610857	0.305429	−	0.952215i	$-0.401200\pi$
$433$	5.52126e32	0.610857	0.305429	+	0.952215i	$0.401200\pi$
$434$	5.31517e32	0.571342
$435$	0	0
$436$	4.13153e32	0.419305
$437$	9.82012e32	0.968498
$438$	1.55419e33	1.48963
$439$	1.02785e33	0.957470	0.478735	−	0.877959i	$-0.341095\pi$
$439$	1.02785e33	0.957470	0.478735	+	0.877959i	$0.341095\pi$
$440$	0	0
$441$	1.42806e32	0.125679
$442$	−7.75913e32	−0.663796
$443$	8.34580e32	0.694099	0.347050	−	0.937847i	$-0.387184\pi$
$443$	8.34580e32	0.694099	0.347050	+	0.937847i	$0.387184\pi$
$444$	1.37061e33	1.10822
$445$	0	0
$446$	−1.32070e33	−1.00953
$447$	−7.23145e32	−0.537503
$448$	−1.85485e32	−0.134071
$449$	−2.21599e33	−1.55772	−0.778859	−	0.627199i	$-0.784201\pi$
$449$	−2.21599e33	−1.55772	−0.778859	+	0.627199i	$0.784201\pi$
$450$	0	0
$451$	1.41960e33	0.943972
$452$	7.91655e32	0.512042
$453$	−3.60092e33	−2.26561
$454$	1.84522e33	1.12941
$455$	0	0
$456$	8.35719e32	0.484172
$457$	1.41006e33	0.794847	0.397424	−	0.917635i	$-0.369904\pi$
$457$	1.41006e33	0.794847	0.397424	+	0.917635i	$0.369904\pi$
$458$	−1.24480e32	−0.0682780
$459$	−2.26311e32	−0.120795
$460$	0	0
$461$	−1.02806e33	−0.519704	−0.259852	−	0.965648i	$-0.583674\pi$
$461$	−1.02806e33	−0.519704	−0.259852	+	0.965648i	$0.583674\pi$
$462$	−3.02358e33	−1.48764
$463$	5.11786e31	0.0245090	0.0122545	−	0.999925i	$-0.496099\pi$
$463$	5.11786e31	0.0245090	0.0122545	+	0.999925i	$0.496099\pi$
$464$	−3.98924e32	−0.185958
$465$	0	0
$466$	4.24802e32	0.187656
$467$	1.60375e33	0.689723	0.344861	−	0.938654i	$-0.387926\pi$
$467$	1.60375e33	0.689723	0.344861	+	0.938654i	$0.387926\pi$
$468$	1.72690e33	0.723094
$469$	1.77725e33	0.724581
$470$	0	0
$471$	−6.23042e33	−2.40855
$472$	−7.63557e32	−0.287453
$473$	1.82141e33	0.667795
$474$	7.43368e32	0.265445
$475$	0	0
$476$	8.58662e32	0.290894
$477$	4.81069e33	1.58755
$478$	3.67196e33	1.18046
$479$	2.94257e33	0.921580	0.460790	−	0.887509i	$-0.347566\pi$
$479$	2.94257e33	0.921580	0.460790	+	0.887509i	$0.347566\pi$
$480$	0	0
$481$	−9.52326e33	−2.83121
$482$	6.83371e32	0.197956
$483$	−4.93291e33	−1.39240
$484$	1.99224e33	0.547993
$485$	0	0
$486$	3.56810e33	0.932145
$487$	7.02175e32	0.178786	0.0893929	−	0.995996i	$-0.471507\pi$
$487$	7.02175e32	0.178786	0.0893929	+	0.995996i	$0.471507\pi$
$488$	−2.16397e33	−0.537035
$489$	1.22048e32	0.0295236
$490$	0	0
$491$	−5.67432e33	−1.30435	−0.652176	−	0.758067i	$-0.726144\pi$
$491$	−5.67432e33	−1.30435	−0.652176	+	0.758067i	$0.726144\pi$
$492$	1.97102e33	0.441701
$493$	1.84673e33	0.403475
$494$	−5.80674e33	−1.23693
$495$	0	0
$496$	−9.29924e32	−0.188333
$497$	1.30060e33	0.256856
$498$	4.49812e33	0.866291
$499$	2.29378e33	0.430818	0.215409	−	0.976524i	$-0.430891\pi$
$499$	2.29378e33	0.430818	0.215409	+	0.976524i	$0.430891\pi$
$500$	0	0
$501$	1.09743e34	1.96068
$502$	−7.28961e31	−0.0127031
$503$	−5.06724e32	−0.0861334	−0.0430667	−	0.999072i	$-0.513713\pi$
$503$	−5.06724e32	−0.0861334	−0.0430667	+	0.999072i	$0.513713\pi$
$504$	−1.91107e33	−0.316880
$505$	0	0
$506$	6.21595e33	0.980903
$507$	−1.75577e34	−2.70313
$508$	2.14898e33	0.322802
$509$	5.67895e33	0.832330	0.416165	−	0.909289i	$-0.363374\pi$
$509$	5.67895e33	0.832330	0.416165	+	0.909289i	$0.363374\pi$
$510$	0	0
$511$	1.19505e34	1.66772
$512$	3.24519e32	0.0441942
$513$	−1.69366e33	−0.225091
$514$	−4.18419e33	−0.542715
$515$	0	0
$516$	2.52891e33	0.312473
$517$	−1.33663e34	−1.61205
$518$	1.05389e34	1.24072
$519$	−1.85716e34	−2.13431
$520$	0	0
$521$	−9.13970e33	−1.00106	−0.500530	−	0.865719i	$-0.666862\pi$
$521$	−9.13970e33	−1.00106	−0.500530	+	0.865719i	$0.666862\pi$
$522$	−4.11015e33	−0.439518
$523$	−3.76955e33	−0.393566	−0.196783	−	0.980447i	$-0.563050\pi$
$523$	−3.76955e33	−0.393566	−0.196783	+	0.980447i	$0.563050\pi$
$524$	2.77446e33	0.282838
$525$	0	0
$526$	9.80226e33	0.952806
$527$	4.30487e33	0.408627
$528$	5.28995e33	0.490374
$529$	−9.04558e32	−0.0818918
$530$	0	0
$531$	−7.86699e33	−0.679403
$532$	6.42602e33	0.542059
$533$	−1.36951e34	−1.12843
$534$	9.18306e32	0.0739132
$535$	0	0
$536$	−3.10941e33	−0.238846
$537$	2.29426e34	1.72172
$538$	3.04729e33	0.223427
$539$	−3.03950e33	−0.217742
$540$	0	0
$541$	−1.11229e34	−0.760770	−0.380385	−	0.924828i	$-0.624209\pi$
$541$	−1.11229e34	−0.760770	−0.380385	+	0.924828i	$0.624209\pi$
$542$	−1.18561e34	−0.792411
$543$	−2.47170e34	−1.61435
$544$	−1.50228e33	−0.0958883
$545$	0	0
$546$	2.91689e34	1.77833
$547$	−1.75655e34	−1.04669	−0.523346	−	0.852120i	$-0.675317\pi$
$547$	−1.75655e34	−1.04669	−0.523346	+	0.852120i	$0.675317\pi$
$548$	5.37952e33	0.313319
$549$	−2.22955e34	−1.26930
$550$	0	0
$551$	1.38205e34	0.751844
$552$	8.63045e33	0.458981
$553$	5.71591e33	0.297181
$554$	1.00773e34	0.512239
$555$	0	0
$556$	8.94522e33	0.434666
$557$	−3.64954e33	−0.173400	−0.0866999	−	0.996234i	$-0.527632\pi$
$557$	−3.64954e33	−0.173400	−0.0866999	+	0.996234i	$0.527632\pi$
$558$	−9.58108e33	−0.445130
$559$	−1.75714e34	−0.798285
$560$	0	0
$561$	−2.44886e34	−1.06397
$562$	2.22008e34	0.943334
$563$	−4.06393e34	−1.68885	−0.844426	−	0.535672i	$-0.820058\pi$
$563$	−4.06393e34	−1.68885	−0.844426	+	0.535672i	$0.820058\pi$
$564$	−1.85582e34	−0.754305
$565$	0	0
$566$	−2.58360e34	−1.00466
$567$	3.20706e34	1.21988
$568$	−2.27548e33	−0.0846680
$569$	1.05009e34	0.382228	0.191114	−	0.981568i	$-0.438790\pi$
$569$	1.05009e34	0.382228	0.191114	+	0.981568i	$0.438790\pi$
$570$	0	0
$571$	−3.85212e34	−1.34199	−0.670994	−	0.741463i	$-0.734132\pi$
$571$	−3.85212e34	−1.34199	−0.670994	+	0.741463i	$0.734132\pi$
$572$	−3.67556e34	−1.25277
$573$	4.42185e34	1.47459
$574$	1.51556e34	0.494509
$575$	0	0
$576$	3.34354e33	0.104454
$577$	5.52922e34	1.69031	0.845154	−	0.534522i	$-0.179508\pi$
$577$	5.52922e34	1.69031	0.845154	+	0.534522i	$0.179508\pi$
$578$	−1.66820e34	−0.499057
$579$	−1.61814e34	−0.473735
$580$	0	0
$581$	3.45869e34	0.969863
$582$	−3.59008e34	−0.985296
$583$	−1.02391e35	−2.75046
$584$	−2.09081e34	−0.549736
$585$	0	0
$586$	−4.01115e34	−1.01053
$587$	3.59799e34	0.887326	0.443663	−	0.896194i	$-0.353679\pi$
$587$	3.59799e34	0.887326	0.443663	+	0.896194i	$0.353679\pi$
$588$	−4.22015e33	−0.101885
$589$	3.22166e34	0.761445
$590$	0	0
$591$	7.53735e34	1.70756
$592$	−1.84385e34	−0.408981
$593$	−6.31486e33	−0.137145	−0.0685725	−	0.997646i	$-0.521844\pi$
$593$	−6.31486e33	−0.137145	−0.0685725	+	0.997646i	$0.521844\pi$
$594$	−1.07205e34	−0.227974
$595$	0	0
$596$	9.72829e33	0.198362
$597$	−6.88325e34	−1.37440
$598$	−5.99661e34	−1.17258
$599$	−5.02848e34	−0.962945	−0.481472	−	0.876461i	$-0.659898\pi$
$599$	−5.02848e34	−0.962945	−0.481472	+	0.876461i	$0.659898\pi$
$600$	0	0
$601$	−4.57441e34	−0.840241	−0.420120	−	0.907468i	$-0.638012\pi$
$601$	−4.57441e34	−0.840241	−0.420120	+	0.907468i	$0.638012\pi$
$602$	1.94453e34	0.349831
$603$	−3.20365e34	−0.564519
$604$	4.84423e34	0.836109
$605$	0	0
$606$	3.37065e34	0.558221
$607$	2.94626e34	0.477983	0.238991	−	0.971022i	$-0.423183\pi$
$607$	2.94626e34	0.477983	0.238991	+	0.971022i	$0.423183\pi$
$608$	−1.12427e34	−0.178680
$609$	−6.94240e34	−1.08092
$610$	0	0
$611$	1.28946e35	1.92705
$612$	−1.54782e34	−0.226635
$613$	1.15985e35	1.66398	0.831989	−	0.554792i	$-0.187202\pi$
$613$	1.15985e35	1.66398	0.831989	+	0.554792i	$0.187202\pi$
$614$	2.35763e34	0.331414
$615$	0	0
$616$	4.06755e34	0.549002
$617$	5.88912e34	0.778907	0.389454	−	0.921046i	$-0.372664\pi$
$617$	5.88912e34	0.778907	0.389454	+	0.921046i	$0.372664\pi$
$618$	1.09600e35	1.42054
$619$	6.29583e34	0.799687	0.399844	−	0.916583i	$-0.369064\pi$
$619$	6.29583e34	0.799687	0.399844	+	0.916583i	$0.369064\pi$
$620$	0	0
$621$	−1.74904e34	−0.213380
$622$	7.57566e34	0.905817
$623$	7.06104e33	0.0827501
$624$	−5.10328e34	−0.586195
$625$	0	0
$626$	−9.80174e34	−1.08174
$627$	−1.83267e35	−1.98262
$628$	8.38163e34	0.888859
$629$	8.53566e34	0.887369
$630$	0	0
$631$	−5.00486e33	−0.0500063	−0.0250032	−	0.999687i	$-0.507960\pi$
$631$	−5.00486e33	−0.0500063	−0.0250032	+	0.999687i	$0.507960\pi$
$632$	−1.00003e34	−0.0979607
$633$	9.20436e34	0.883989
$634$	8.36242e33	0.0787438
$635$	0	0
$636$	−1.42164e35	−1.28699
$637$	2.93225e34	0.260290
$638$	8.74810e34	0.761474
$639$	−2.34445e34	−0.200115
$640$	0	0
$641$	2.47946e34	0.203532	0.101766	−	0.994808i	$-0.467551\pi$
$641$	2.47946e34	0.203532	0.101766	+	0.994808i	$0.467551\pi$
$642$	1.17359e34	0.0944772
$643$	1.87298e35	1.47875	0.739376	−	0.673293i	$-0.235121\pi$
$643$	1.87298e35	1.47875	0.739376	+	0.673293i	$0.235121\pi$
$644$	6.63613e34	0.513856
$645$	0	0
$646$	5.20456e34	0.387684
$647$	−1.37605e35	−1.00538	−0.502692	−	0.864465i	$-0.667657\pi$
$647$	−1.37605e35	−1.00538	−0.502692	+	0.864465i	$0.667657\pi$
$648$	−5.61096e34	−0.402114
$649$	1.67442e35	1.17708
$650$	0	0
$651$	−1.61833e35	−1.09472
$652$	−1.64188e33	−0.0108955
$653$	1.43663e35	0.935256	0.467628	−	0.883925i	$-0.345109\pi$
$653$	1.43663e35	0.935256	0.467628	+	0.883925i	$0.345109\pi$
$654$	−1.25794e35	−0.803412
$655$	0	0
$656$	−2.65157e34	−0.163007
$657$	−2.15418e35	−1.29932
$658$	−1.42698e35	−0.844488
$659$	−1.67433e35	−0.972238	−0.486119	−	0.873893i	$-0.661588\pi$
$659$	−1.67433e35	−0.972238	−0.486119	+	0.873893i	$0.661588\pi$
$660$	0	0
$661$	−8.14435e34	−0.455342	−0.227671	−	0.973738i	$-0.573111\pi$
$661$	−8.14435e34	−0.455342	−0.227671	+	0.973738i	$0.573111\pi$
$662$	−7.18494e34	−0.394183
$663$	2.36244e35	1.27187
$664$	−6.05121e34	−0.319699
$665$	0	0
$666$	−1.89973e35	−0.966639
$667$	1.42724e35	0.712726
$668$	−1.47635e35	−0.723576
$669$	4.02118e35	1.93432
$670$	0	0
$671$	4.74541e35	2.19909
$672$	5.64753e34	0.256887
$673$	−2.14831e35	−0.959198	−0.479599	−	0.877488i	$-0.659218\pi$
$673$	−2.14831e35	−0.959198	−0.479599	+	0.877488i	$0.659218\pi$
$674$	3.00300e35	1.31615
$675$	0	0
$676$	2.36199e35	0.997572
$677$	1.65762e35	0.687268	0.343634	−	0.939104i	$-0.388342\pi$
$677$	1.65762e35	0.687268	0.343634	+	0.939104i	$0.388342\pi$
$678$	−2.41038e35	−0.981100
$679$	−2.76049e35	−1.10310
$680$	0	0
$681$	−5.61820e35	−2.16401
$682$	2.03925e35	0.771197
$683$	−4.25978e35	−1.58172	−0.790858	−	0.612000i	$-0.790365\pi$
$683$	−4.25978e35	−1.58172	−0.790858	+	0.612000i	$0.790365\pi$
$684$	−1.15835e35	−0.422316
$685$	0	0
$686$	1.83305e35	0.644353
$687$	3.79007e34	0.130824
$688$	−3.40208e34	−0.115316
$689$	9.87781e35	3.28791
$690$	0	0
$691$	−3.56127e35	−1.14322	−0.571609	−	0.820526i	$-0.693681\pi$
$691$	−3.56127e35	−1.14322	−0.571609	+	0.820526i	$0.693681\pi$
$692$	2.49839e35	0.787651
$693$	4.19083e35	1.29758
$694$	6.33656e34	0.192690
$695$	0	0
$696$	1.21462e35	0.356307
$697$	1.22748e35	0.353676
$698$	−4.69172e34	−0.132782
$699$	−1.29341e35	−0.359559
$700$	0	0
$701$	−6.93164e34	−0.185935	−0.0929674	−	0.995669i	$-0.529635\pi$
$701$	−6.93164e34	−0.185935	−0.0929674	+	0.995669i	$0.529635\pi$
$702$	1.03422e35	0.272521
$703$	6.38788e35	1.65354
$704$	−7.11643e34	−0.180969
$705$	0	0
$706$	−1.54545e35	−0.379311
$707$	2.59176e35	0.624961
$708$	2.32482e35	0.550775
$709$	−1.75968e34	−0.0409596	−0.0204798	−	0.999790i	$-0.506519\pi$
$709$	−1.75968e34	−0.0409596	−0.0204798	+	0.999790i	$0.506519\pi$
$710$	0	0
$711$	−1.03034e35	−0.231533
$712$	−1.23538e34	−0.0272771
$713$	3.32700e35	0.721827
$714$	−2.61439e35	−0.557369
$715$	0	0
$716$	−3.08641e35	−0.635390
$717$	−1.11801e36	−2.26182
$718$	−4.65687e35	−0.925845
$719$	−3.47246e35	−0.678462	−0.339231	−	0.940703i	$-0.610167\pi$
$719$	−3.47246e35	−0.678462	−0.339231	+	0.940703i	$0.610167\pi$
$720$	0	0
$721$	8.42736e35	1.59038
$722$	8.25554e33	0.0153120
$723$	−2.08068e35	−0.379294
$724$	3.32511e35	0.595764
$725$	0	0
$726$	−6.06584e35	−1.04998
$727$	4.86443e35	0.827660	0.413830	−	0.910354i	$-0.364191\pi$
$727$	4.86443e35	0.827660	0.413830	+	0.910354i	$0.364191\pi$
$728$	−3.92401e35	−0.656279
$729$	−3.94577e35	−0.648691
$730$	0	0
$731$	1.57491e35	0.250201
$732$	6.58869e35	1.02899
$733$	1.02677e36	1.57643	0.788216	−	0.615398i	$-0.211005\pi$
$733$	1.02677e36	1.57643	0.788216	+	0.615398i	$0.211005\pi$
$734$	2.98218e35	0.450125
$735$	0	0
$736$	−1.16103e35	−0.169384
$737$	6.81868e35	0.978040
$738$	−2.73194e35	−0.385271
$739$	5.26186e35	0.729599	0.364799	−	0.931086i	$-0.381138\pi$
$739$	5.26186e35	0.729599	0.364799	+	0.931086i	$0.381138\pi$
$740$	0	0
$741$	1.76800e36	2.37003
$742$	−1.09313e36	−1.44086
$743$	−6.09530e35	−0.790014	−0.395007	−	0.918678i	$-0.629258\pi$
$743$	−6.09530e35	−0.790014	−0.395007	+	0.918678i	$0.629258\pi$
$744$	2.83137e35	0.360856
$745$	0	0
$746$	−7.00664e35	−0.863525
$747$	−6.23461e35	−0.755617
$748$	3.29439e35	0.392649
$749$	9.02394e34	0.105773
$750$	0	0
$751$	1.00495e36	1.13932	0.569660	−	0.821881i	$-0.307075\pi$
$751$	1.00495e36	1.13932	0.569660	+	0.821881i	$0.307075\pi$
$752$	2.49659e35	0.278371
$753$	2.21949e34	0.0243397
$754$	−8.43940e35	−0.910269
$755$	0	0
$756$	−1.14452e35	−0.119427
$757$	8.28193e35	0.850028	0.425014	−	0.905187i	$-0.360269\pi$
$757$	8.28193e35	0.850028	0.425014	+	0.905187i	$0.360269\pi$
$758$	1.15349e35	0.116452
$759$	−1.89259e36	−1.87946
$760$	0	0
$761$	−1.30553e35	−0.125452	−0.0627261	−	0.998031i	$-0.519979\pi$
$761$	−1.30553e35	−0.125452	−0.0627261	+	0.998031i	$0.519979\pi$
$762$	−6.54308e35	−0.618507
$763$	−9.67256e35	−0.899466
$764$	−5.94861e35	−0.544187
$765$	0	0
$766$	−4.00794e35	−0.354864
$767$	−1.61533e36	−1.40709
$768$	−9.88071e34	−0.0846785
$769$	−7.86348e34	−0.0663033	−0.0331517	−	0.999450i	$-0.510554\pi$
$769$	−7.86348e34	−0.0663033	−0.0331517	+	0.999450i	$0.510554\pi$
$770$	0	0
$771$	1.27397e36	1.03987
$772$	2.17685e35	0.174829
$773$	−3.60085e35	−0.284552	−0.142276	−	0.989827i	$-0.545442\pi$
$773$	−3.60085e35	−0.284552	−0.142276	+	0.989827i	$0.545442\pi$
$774$	−3.50519e35	−0.272552
$775$	0	0
$776$	4.82965e35	0.363617
$777$	−3.20881e36	−2.37728
$778$	−5.45562e35	−0.397740
$779$	9.18619e35	0.659048
$780$	0	0
$781$	4.98996e35	0.346704
$782$	5.37473e35	0.367513
$783$	−2.46153e35	−0.165647
$784$	5.67727e34	0.0376001
$785$	0	0
$786$	−8.44747e35	−0.541932
$787$	1.70122e36	1.07418	0.537089	−	0.843526i	$-0.319524\pi$
$787$	1.70122e36	1.07418	0.537089	+	0.843526i	$0.319524\pi$
$788$	−1.01398e36	−0.630162
$789$	−2.98452e36	−1.82563
$790$	0	0
$791$	−1.85339e36	−1.09840
$792$	−7.33212e35	−0.427725
$793$	−4.57796e36	−2.62880
$794$	−2.26832e36	−1.28218
$795$	0	0
$796$	9.25987e35	0.507215
$797$	3.28276e36	1.77015	0.885075	−	0.465449i	$-0.154107\pi$
$797$	3.28276e36	1.77015	0.885075	+	0.465449i	$0.154107\pi$
$798$	−1.95655e36	−1.03861
$799$	−1.15574e36	−0.603983
$800$	0	0
$801$	−1.27282e35	−0.0644703
$802$	−6.24815e35	−0.311581
$803$	4.58498e36	2.25109
$804$	9.46730e35	0.457642
$805$	0	0
$806$	−1.96729e36	−0.921892
$807$	−9.27816e35	−0.428098
$808$	−4.53446e35	−0.206008
$809$	−1.22121e36	−0.546303	−0.273152	−	0.961971i	$-0.588066\pi$
$809$	−1.22121e36	−0.546303	−0.273152	+	0.961971i	$0.588066\pi$
$810$	0	0
$811$	−2.29432e36	−0.995160	−0.497580	−	0.867418i	$-0.665778\pi$
$811$	−2.29432e36	−0.995160	−0.497580	+	0.867418i	$0.665778\pi$
$812$	9.33944e35	0.398906
$813$	3.60986e36	1.51830
$814$	4.04341e36	1.67472
$815$	0	0
$816$	4.57405e35	0.183727
$817$	1.17863e36	0.466231
$818$	2.60147e36	1.01345
$819$	−4.04295e36	−1.55113
$820$	0	0
$821$	1.68233e36	0.626067	0.313033	−	0.949742i	$-0.398655\pi$
$821$	1.68233e36	0.626067	0.313033	+	0.949742i	$0.398655\pi$
$822$	−1.63792e36	−0.600336
$823$	−3.28620e36	−1.18630	−0.593152	−	0.805091i	$-0.702117\pi$
$823$	−3.28620e36	−1.18630	−0.593152	+	0.805091i	$0.702117\pi$
$824$	−1.47442e36	−0.524241
$825$	0	0
$826$	1.78761e36	0.616625
$827$	1.84899e36	0.628225	0.314112	−	0.949386i	$-0.398293\pi$
$827$	1.84899e36	0.628225	0.314112	+	0.949386i	$0.398293\pi$
$828$	−1.19622e36	−0.400343
$829$	6.47231e35	0.213367	0.106684	−	0.994293i	$-0.465977\pi$
$829$	6.47231e35	0.213367	0.106684	+	0.994293i	$0.465977\pi$
$830$	0	0
$831$	−3.06827e36	−0.981478
$832$	6.86531e35	0.216331
$833$	−2.62816e35	−0.0815811
$834$	−2.72358e36	−0.832845
$835$	0	0
$836$	2.46544e36	0.731672
$837$	−5.73801e35	−0.167762
$838$	−3.19829e36	−0.921228
$839$	3.82378e36	1.08510	0.542549	−	0.840024i	$-0.317459\pi$
$839$	3.82378e36	1.08510	0.542549	+	0.840024i	$0.317459\pi$
$840$	0	0
$841$	−1.62172e36	−0.446711
$842$	1.46356e36	0.397200
$843$	−6.75956e36	−1.80748
$844$	−1.23824e36	−0.326230
$845$	0	0
$846$	2.57226e36	0.657937
$847$	−4.66415e36	−1.17552
$848$	1.91249e36	0.474954
$849$	7.86635e36	1.92499
$850$	0	0
$851$	6.59675e36	1.56751
$852$	6.92823e35	0.162229
$853$	−2.67006e36	−0.616110	−0.308055	−	0.951369i	$-0.599678\pi$
$853$	−2.67006e36	−0.616110	−0.308055	+	0.951369i	$0.599678\pi$
$854$	5.06618e36	1.15201
$855$	0	0
$856$	−1.57880e35	−0.0348661
$857$	−5.29681e36	−1.15280	−0.576400	−	0.817167i	$-0.695543\pi$
$857$	−5.29681e36	−1.15280	−0.576400	+	0.817167i	$0.695543\pi$
$858$	1.11911e37	2.40039
$859$	9.48590e35	0.200523	0.100261	−	0.994961i	$-0.468032\pi$
$859$	9.48590e35	0.200523	0.100261	+	0.994961i	$0.468032\pi$
$860$	0	0
$861$	−4.61447e36	−0.947507
$862$	4.03598e35	0.0816785
$863$	6.15179e36	1.22706	0.613532	−	0.789670i	$-0.289748\pi$
$863$	6.15179e36	1.22706	0.613532	+	0.789670i	$0.289748\pi$
$864$	2.00241e35	0.0393669
$865$	0	0
$866$	2.26151e36	0.431941
$867$	5.07922e36	0.956221
$868$	2.17709e36	0.403999
$869$	2.19300e36	0.401135
$870$	0	0
$871$	−6.57807e36	−1.16915
$872$	1.69228e36	0.296494
$873$	4.97603e36	0.859418
$874$	4.02232e36	0.684832
$875$	0	0
$876$	6.36596e36	1.05332
$877$	−7.20268e35	−0.117490	−0.0587448	−	0.998273i	$-0.518710\pi$
$877$	−7.20268e35	−0.117490	−0.0587448	+	0.998273i	$0.518710\pi$
$878$	4.21009e36	0.677034
$879$	1.22129e37	1.93623
$880$	0	0
$881$	−6.22632e36	−0.959472	−0.479736	−	0.877413i	$-0.659268\pi$
$881$	−6.22632e36	−0.959472	−0.479736	+	0.877413i	$0.659268\pi$
$882$	5.84934e35	0.0888688
$883$	7.42861e36	1.11275	0.556376	−	0.830930i	$-0.312191\pi$
$883$	7.42861e36	1.11275	0.556376	+	0.830930i	$0.312191\pi$
$884$	−3.17814e36	−0.469375
$885$	0	0
$886$	3.41844e36	0.490802
$887$	−2.96498e36	−0.419736	−0.209868	−	0.977730i	$-0.567303\pi$
$887$	−2.96498e36	−0.419736	−0.209868	+	0.977730i	$0.567303\pi$
$888$	5.61401e36	0.783631
$889$	−5.03110e36	−0.692455
$890$	0	0
$891$	1.23044e37	1.64660
$892$	−5.40960e36	−0.713846
$893$	−8.64926e36	−1.12547
$894$	−2.96200e36	−0.380072
$895$	0	0
$896$	−7.59748e35	−0.0948024
$897$	1.82580e37	2.24672
$898$	−9.07670e36	−1.10147
$899$	4.68229e36	0.560354
$900$	0	0
$901$	−8.85344e36	−1.03051
$902$	5.81468e36	0.667489
$903$	−5.92057e36	−0.670296
$904$	3.24262e36	0.362068
$905$	0	0
$906$	−1.47494e37	−1.60203
$907$	7.50976e36	0.804516	0.402258	−	0.915526i	$-0.368225\pi$
$907$	7.50976e36	0.804516	0.402258	+	0.915526i	$0.368225\pi$
$908$	7.55803e36	0.798611
$909$	−4.67189e36	−0.486905
$910$	0	0
$911$	−9.29828e36	−0.942807	−0.471404	−	0.881918i	$-0.656252\pi$
$911$	−9.29828e36	−0.942807	−0.471404	+	0.881918i	$0.656252\pi$
$912$	3.42311e36	0.342362
$913$	1.32698e37	1.30912
$914$	5.77559e36	0.562042
$915$	0	0
$916$	−5.09869e35	−0.0482798
$917$	−6.49544e36	−0.606725
$918$	−9.26971e35	−0.0854147
$919$	7.54098e36	0.685463	0.342731	−	0.939433i	$-0.388648\pi$
$919$	7.54098e36	0.685463	0.342731	+	0.939433i	$0.388648\pi$
$920$	0	0
$921$	−7.17835e36	−0.635008
$922$	−4.21093e36	−0.367486
$923$	−4.81387e36	−0.414451
$924$	−1.23846e37	−1.05192
$925$	0	0
$926$	2.09627e35	0.0173305
$927$	−1.51911e37	−1.23906
$928$	−1.63399e36	−0.131492
$929$	−7.02005e36	−0.557370	−0.278685	−	0.960383i	$-0.589899\pi$
$929$	−7.02005e36	−0.557370	−0.278685	+	0.960383i	$0.589899\pi$
$930$	0	0
$931$	−1.96685e36	−0.152020
$932$	1.73999e36	0.132693
$933$	−2.30658e37	−1.73560
$934$	6.56894e36	0.487708
$935$	0	0
$936$	7.07339e36	0.511304
$937$	1.69888e37	1.21176	0.605881	−	0.795555i	$-0.292821\pi$
$937$	1.69888e37	1.21176	0.605881	+	0.795555i	$0.292821\pi$
$938$	7.27960e36	0.512356
$939$	2.98437e37	2.07268
$940$	0	0
$941$	−1.18390e36	−0.0800651	−0.0400325	−	0.999198i	$-0.512746\pi$
$941$	−1.18390e36	−0.0800651	−0.0400325	+	0.999198i	$0.512746\pi$
$942$	−2.55198e37	−1.70310
$943$	9.48655e36	0.624758
$944$	−3.12753e36	−0.203260
$945$	0	0
$946$	7.46049e36	0.472202
$947$	3.22631e36	0.201526	0.100763	−	0.994910i	$-0.467872\pi$
$947$	3.22631e36	0.201526	0.100763	+	0.994910i	$0.467872\pi$
$948$	3.04484e36	0.187698
$949$	−4.42319e37	−2.69097
$950$	0	0
$951$	−2.54613e36	−0.150877
$952$	3.51708e36	0.205693
$953$	−1.29808e37	−0.749271	−0.374635	−	0.927172i	$-0.622232\pi$
$953$	−1.29808e37	−0.749271	−0.374635	+	0.927172i	$0.622232\pi$
$954$	1.97046e37	1.12257
$955$	0	0
$956$	1.50404e37	0.834708
$957$	−2.66356e37	−1.45903
$958$	1.20528e37	0.651656
$959$	−1.25943e37	−0.672110
$960$	0	0
$961$	−8.31801e36	−0.432491
$962$	−3.90073e37	−2.00197
$963$	−1.62665e36	−0.0824071
$964$	2.79909e36	0.139976
$965$	0	0
$966$	−2.02052e37	−0.984576
$967$	2.88610e37	1.38829	0.694146	−	0.719834i	$-0.255782\pi$
$967$	2.88610e37	1.38829	0.694146	+	0.719834i	$0.255782\pi$
$968$	8.16022e36	0.387490
$969$	−1.58465e37	−0.742824
$970$	0	0
$971$	1.13134e36	0.0516836	0.0258418	−	0.999666i	$-0.491773\pi$
$971$	1.13134e36	0.0516836	0.0258418	+	0.999666i	$0.491773\pi$
$972$	1.46149e37	0.659126
$973$	−2.09421e37	−0.932418
$974$	2.87611e36	0.126421
$975$	0	0
$976$	−8.86361e36	−0.379741
$977$	−1.01024e37	−0.427311	−0.213655	−	0.976909i	$-0.568537\pi$
$977$	−1.01024e37	−0.427311	−0.213655	+	0.976909i	$0.568537\pi$
$978$	4.99908e35	0.0208763
$979$	2.70908e36	0.111696
$980$	0	0
$981$	1.74357e37	0.700771
$982$	−2.32420e37	−0.922316
$983$	3.32494e37	1.30276	0.651380	−	0.758752i	$-0.274190\pi$
$983$	3.32494e37	1.30276	0.651380	+	0.758752i	$0.274190\pi$
$984$	8.07331e36	0.312330
$985$	0	0
$986$	7.56420e36	0.285300
$987$	4.34476e37	1.61808
$988$	−2.37844e37	−0.874643
$989$	1.21717e37	0.441973
$990$	0	0
$991$	2.31893e37	0.821044	0.410522	−	0.911851i	$-0.365347\pi$
$991$	2.31893e37	0.821044	0.410522	+	0.911851i	$0.365347\pi$
$992$	−3.80897e36	−0.133172
$993$	2.18762e37	0.755277
$994$	5.32726e36	0.181624
$995$	0	0
$996$	1.84243e37	0.612561
$997$	−6.52365e36	−0.214191	−0.107096	−	0.994249i	$-0.534155\pi$
$997$	−6.52365e36	−0.214191	−0.107096	+	0.994249i	$0.534155\pi$
$998$	9.39530e36	0.304634
$999$	−1.13773e37	−0.364309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.e.1.1		2
5.2	odd	4		50.26.b.c.49.4		4
5.3	odd	4		50.26.b.c.49.1		4
5.4	even	2		10.26.a.c.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.c.1.2	✓	2	5.4	even	2
50.26.a.e.1.1		2	1.1	even	1	trivial
50.26.b.c.49.1		4	5.3	odd	4
50.26.b.c.49.4		4	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q+4096.00 q^{2} -1.24712e6 q^{3} +1.67772e7 q^{4} -5.10821e9 q^{6} -3.92781e10 q^{7} +6.87195e10 q^{8} +7.08023e11 q^{9} -1.50696e13 q^{11} -2.09232e13 q^{12} +1.45379e14 q^{13} -1.60883e14 q^{14} +2.81475e14 q^{16} -1.30302e15 q^{17} +2.90006e15 q^{18} -9.75151e15 q^{19} +4.89845e16 q^{21} -6.17252e16 q^{22} -1.00704e17 q^{23} -8.57015e16 q^{24} +5.95471e17 q^{26} +1.73682e17 q^{27} -6.58976e17 q^{28} -1.41726e18 q^{29} -3.30375e18 q^{31} +1.15292e18 q^{32} +1.87937e19 q^{33} -5.33718e18 q^{34} +1.18786e19 q^{36} -6.55066e19 q^{37} -3.99422e19 q^{38} -1.81305e20 q^{39} -9.42027e19 q^{41} +2.00640e20 q^{42} -1.20866e20 q^{43} -2.52827e20 q^{44} -4.12482e20 q^{46} +8.86966e20 q^{47} -3.51033e20 q^{48} +2.01697e20 q^{49} +1.62503e21 q^{51} +2.43905e21 q^{52} +6.79454e21 q^{53} +7.11400e20 q^{54} -2.69917e21 q^{56} +1.21613e22 q^{57} -5.80511e21 q^{58} -1.11112e22 q^{59} -3.14899e22 q^{61} -1.35322e22 q^{62} -2.78098e22 q^{63} +4.72237e21 q^{64} +7.69788e22 q^{66} -4.52478e22 q^{67} -2.18611e22 q^{68} +1.25590e23 q^{69} -3.31126e22 q^{71} +4.86549e22 q^{72} -3.04253e23 q^{73} -2.68315e23 q^{74} -1.63603e23 q^{76} +5.91906e23 q^{77} -7.42625e23 q^{78} -1.45524e23 q^{79} -8.16501e23 q^{81} -3.85854e23 q^{82} -8.80567e23 q^{83} +8.21823e23 q^{84} -4.95068e23 q^{86} +1.76750e24 q^{87} -1.03558e24 q^{88} -1.79771e23 q^{89} -5.71019e24 q^{91} -1.68953e24 q^{92} +4.12018e24 q^{93} +3.63301e24 q^{94} -1.43783e24 q^{96} +7.02806e24 q^{97} +8.26151e23 q^{98} -1.06696e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8192 q^{2} - 545212 q^{3} + 33554432 q^{4} - 2233188352 q^{6} - 38567856964 q^{7} + 137438953472 q^{8} + 353410472386 q^{9} - 8379169876416 q^{11} - 9147139489792 q^{12} + 149443737196988 q^{13} - 157973942124544 q^{14}+ \cdots - 13\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 8192 * q^2 - 545212 * q^3 + 33554432 * q^4 - 2233188352 * q^6 - 38567856964 * q^7 + 137438953472 * q^8 + 353410472386 * q^9 - 8379169876416 * q^11 - 9147139489792 * q^12 + 149443737196988 * q^13 - 157973942124544 * q^14 + 562949953421312 * q^16 - 3359254299255924 * q^17 + 1447569294893056 * q^18 + 3489461415860920 * q^19 + 49482990719617784 * q^21 - 34321079813799936 * q^22 - 72370201928022732 * q^23 - 37466683350188032 * q^24 + 612121547558862848 * q^26 - 669943559840926600 * q^27 - 647061266942132224 * q^28 - 537443787959856180 * q^29 - 3624027784441312136 * q^31 + 2305843009213693952 * q^32 + 23489760709118906496 * q^33 - 13759505609752264704 * q^34 + 5929243831881957376 * q^36 - 19038572664443645764 * q^37 + 14292833959366328320 * q^38 - 178451546772299045128 * q^39 - 212589580623880771956 * q^41 + 202682329987554443264 * q^42 + 13668418927657846868 * q^43 - 140579142917324537856 * q^44 - 296428347097181110272 * q^46 + 1665681645557377854156 * q^47 - 153463535002370179072 * q^48 - 1138867157350741829766 * q^49 + 181740691723390600344 * q^51 + 2507249858801102225408 * q^52 + 9975823013097020329548 * q^53 - 2744088821108435353600 * q^54 - 2650362949394973589504 * q^56 + 21455279998725990048880 * q^57 - 2201369755483570913280 * q^58 - 13147506706206800097960 * q^59 + 114411778307375747524 * q^61 - 14844017805071614509056 * q^62 - 28061596756249158893252 * q^63 + 9444732965739290427392 * q^64 + 96214059864551041007616 * q^66 - 95143040936399031080644 * q^67 - 56358934977545276227584 * q^68 + 145477011313277750812392 * q^69 + 83749259495165337742824 * q^71 + 24286182735388497412096 * q^72 - 196631633422897936973572 * q^73 - 77981993633561173049344 * q^74 + 58543447897564480798720 * q^76 + 596657555842340580669312 * q^77 - 730937535579336888844288 * q^78 + 105871595026057220692240 * q^79 - 1108190878966022772827798 * q^81 - 870766922235415641931776 * q^82 + 599053017838528107773748 * q^83 + 830186823629022999609344 * q^84 + 55985843927686540771328 * q^86 + 2385054109175491523609880 * q^87 - 575812169389361307058176 * q^88 - 1877353952181279423739020 * q^89 - 5707305339748996500897016 * q^91 - 1214170509710053827674112 * q^92 + 3895374854369117044063216 * q^93 + 6822632020203019690622976 * q^94 - 628586639369708253478912 * q^96 + 11597588153054877446451836 * q^97 - 4664799876508638534721536 * q^98 - 13042162823998039381361088 * q^99

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