LMFDB - Embedded newform 25.26.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,26,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, 26, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 26 $
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:	$98.9991949881$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 31823342x^{3} + 3040467992x^{2} + 155755658754016x - 41401144140044416 $ x^5 - x^4 - 31823342x^3 + 3040467992x^2 + 155755658754016*x - 41401144140044416
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5041.97$ 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)

$f(q)$	$=$	$q+11003.9 q^{2} +418448. q^{3} +8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10 q^{7} +5.93966e11 q^{8} -6.72190e11 q^{9} +O(q^{10})$	\(q+11003.9 q^{2} +418448. q^{3} +8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10 q^{7} +5.93966e11 q^{8} -6.72190e11 q^{9} -2.19858e12 q^{11} +3.66276e13 q^{12} -6.43659e13 q^{13} -7.77176e14 q^{14} +3.59887e15 q^{16} -5.70025e14 q^{17} -7.39673e15 q^{18} -8.57675e14 q^{19} -2.95538e16 q^{21} -2.41930e16 q^{22} +9.97218e15 q^{23} +2.48544e17 q^{24} -7.08278e17 q^{26} -6.35823e17 q^{27} -6.18214e18 q^{28} -1.82269e18 q^{29} -4.09356e18 q^{31} +1.96715e19 q^{32} -9.19990e17 q^{33} -6.27252e18 q^{34} -5.88382e19 q^{36} -4.56115e19 q^{37} -9.43780e18 q^{38} -2.69338e19 q^{39} +2.18308e20 q^{41} -3.25207e20 q^{42} +6.85002e19 q^{43} -1.92446e20 q^{44} +1.09733e20 q^{46} -1.23525e19 q^{47} +1.50594e21 q^{48} +3.64712e21 q^{49} -2.38526e20 q^{51} -5.63408e21 q^{52} -4.53955e21 q^{53} -6.99655e21 q^{54} -4.19501e22 q^{56} -3.58892e20 q^{57} -2.00568e22 q^{58} +8.45133e21 q^{59} -1.08894e22 q^{61} -4.50452e22 q^{62} +4.74748e22 q^{63} +9.57062e22 q^{64} -1.01235e22 q^{66} -3.89372e22 q^{67} -4.98955e22 q^{68} +4.17284e21 q^{69} -3.71162e22 q^{71} -3.99258e23 q^{72} +2.76367e23 q^{73} -5.01906e23 q^{74} -7.50741e22 q^{76} +1.55279e23 q^{77} -2.96378e23 q^{78} +8.72667e23 q^{79} +3.03480e23 q^{81} +2.40225e24 q^{82} -4.43419e23 q^{83} -2.58690e24 q^{84} +7.53772e23 q^{86} -7.62702e23 q^{87} -1.30588e24 q^{88} -5.97991e23 q^{89} +4.54598e24 q^{91} +8.72886e23 q^{92} -1.71294e24 q^{93} -1.35926e23 q^{94} +8.23151e24 q^{96} -9.83402e24 q^{97} +4.01327e25 q^{98} +1.47786e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4602 q^{2} - 626204 q^{3} + 91050260 q^{4} + 5696574760 q^{6} - 55481235808 q^{7} + 325515457080 q^{8} + 277996846465 q^{9}+O(q^{10}) $ 5 * q + 4602 * q^2 - 626204 * q^3 + 91050260 * q^4 + 5696574760 * q^6 - 55481235808 * q^7 + 325515457080 * q^8 + 277996846465 * q^9	$ 5 q + 4602 q^{2} - 626204 q^{3} + 91050260 q^{4} + 5696574760 q^{6} - 55481235808 q^{7} + 325515457080 q^{8} + 277996846465 q^{9} - 4144958451540 q^{11} + 26370992065712 q^{12} - 111211249076614 q^{13} - 445566653510880 q^{14} + 30\!\cdots\!80 q^{16}+ \cdots - 22\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q + 4602 * q^2 - 626204 * q^3 + 91050260 * q^4 + 5696574760 * q^6 - 55481235808 * q^7 + 325515457080 * q^8 + 277996846465 * q^9 - 4144958451540 * q^11 + 26370992065712 * q^12 - 111211249076614 * q^13 - 445566653510880 * q^14 + 3044988017630480 * q^16 - 3179191896192378 * q^17 - 9100952570763854 * q^18 + 13473188050195300 * q^19 + 76768095576060960 * q^21 - 222905601184950696 * q^22 - 409020396998250624 * q^23 + 738233252736381600 * q^24 + 331732385439154260 * q^26 - 1707963140919696920 * q^27 - 6745183853862681376 * q^28 + 1510518246057732150 * q^29 - 7800790900476562640 * q^31 + 26275496698670595552 * q^32 + 17083981126675017392 * q^33 - 30967164186095882580 * q^34 - 127816747210020977020 * q^36 + 45693640863683938082 * q^37 + 107313021439059142920 * q^38 - 28513155461010121720 * q^39 + 268182713424991346610 * q^41 - 472693454958668435136 * q^42 + 54212732396046197756 * q^43 + 1026843270980203159920 * q^44 + 1806261760861861731360 * q^46 - 1313959570250307870888 * q^47 - 393501331052082428224 * q^48 + 2928508402086077906685 * q^49 - 1679947779014963634440 * q^51 + 1533919945088032601192 * q^52 + 1722136215100242292146 * q^53 - 16134427338310747545200 * q^54 - 39415455111791618702400 * q^56 + 9510351594401743758160 * q^57 - 7814667131698315285620 * q^58 - 16547203533880040421300 * q^59 + 11587268554089248839510 * q^61 - 21314291783865447926496 * q^62 - 32595050340385317746784 * q^63 + 83981823170089659652160 * q^64 + 107686245599040557757920 * q^66 - 186273232047241909753228 * q^67 - 48790715540647305709416 * q^68 + 205103851249003209571680 * q^69 + 179635129178416728944760 * q^71 - 252302332499928005189160 * q^72 + 471333406608130631390126 * q^73 - 888672199125830235839580 * q^74 - 1191799860770260438242800 * q^76 + 286067188114809482097984 * q^77 + 1025178605609234961148112 * q^78 + 360282849255851991934000 * q^79 + 103584508446589901468605 * q^81 + 2050449668847875948936004 * q^82 - 1759227952818659145519084 * q^83 - 3837881595316615167665280 * q^84 - 565842386421331097744040 * q^86 - 8705381585373786685282760 * q^87 - 720634350501343968831840 * q^88 + 4092128669145981513024450 * q^89 + 11972573281108721260967360 * q^91 - 6613215336376724900082528 * q^92 - 7392084747484240267531008 * q^93 - 17112742333122902932304880 * q^94 - 10376386162767776801453440 * q^96 - 28613737566457196779163338 * q^97 + 56860534671603836155246314 * q^98 - 22864619024884333176273220 * 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 $

$2$	11003.9	1.89965	0.949823	−	0.312787i	$-0.101262\pi$
$2$	11003.9	1.89965	0.949823	+	0.312787i	$0.101262\pi$
$3$	418448.	0.454596	0.227298	−	0.973825i	$-0.427011\pi$
$3$	418448.	0.454596	0.227298	+	0.973825i	$0.427011\pi$
$4$	8.75320e7	2.60866
$5$	0	0
$5$	0	0
$6$	4.60457e9	0.863572
$7$	−7.06271e10	−1.92862	−0.964308	−	0.264782i	$-0.914700\pi$
$7$	−7.06271e10	−1.92862	−0.964308	+	0.264782i	$0.914700\pi$
$8$	5.93966e11	3.05588
$9$	−6.72190e11	−0.793342
$10$	0	0
$11$	−2.19858e12	−0.211219	−0.105610	−	0.994408i	$-0.533679\pi$
$11$	−2.19858e12	−0.211219	−0.105610	+	0.994408i	$0.533679\pi$
$12$	3.66276e13	1.18589
$13$	−6.43659e13	−0.766239	−0.383119	−	0.923699i	$-0.625150\pi$
$13$	−6.43659e13	−0.766239	−0.383119	+	0.923699i	$0.625150\pi$
$14$	−7.77176e14	−3.66369
$15$	0	0
$16$	3.59887e15	3.19644
$17$	−5.70025e14	−0.237292	−0.118646	−	0.992937i	$-0.537855\pi$
$17$	−5.70025e14	−0.237292	−0.118646	+	0.992937i	$0.537855\pi$
$18$	−7.39673e15	−1.50707
$19$	−8.57675e14	−0.0889002	−0.0444501	−	0.999012i	$-0.514154\pi$
$19$	−8.57675e14	−0.0889002	−0.0444501	+	0.999012i	$0.514154\pi$
$20$	0	0
$21$	−2.95538e16	−0.876741
$22$	−2.41930e16	−0.401242
$23$	9.97218e15	0.0948838	0.0474419	−	0.998874i	$-0.484893\pi$
$23$	9.97218e15	0.0948838	0.0474419	+	0.998874i	$0.484893\pi$
$24$	2.48544e17	1.38919
$25$	0	0
$26$	−7.08278e17	−1.45558
$27$	−6.35823e17	−0.815246
$28$	−6.18214e18	−5.03110
$29$	−1.82269e18	−0.956618	−0.478309	−	0.878192i	$-0.658750\pi$
$29$	−1.82269e18	−0.956618	−0.478309	+	0.878192i	$0.658750\pi$
$30$	0	0
$31$	−4.09356e18	−0.933425	−0.466713	−	0.884409i	$-0.654562\pi$
$31$	−4.09356e18	−0.933425	−0.466713	+	0.884409i	$0.654562\pi$
$32$	1.96715e19	3.01622
$33$	−9.19990e17	−0.0960194
$34$	−6.27252e18	−0.450770
$35$	0	0
$36$	−5.88382e19	−2.06956
$37$	−4.56115e19	−1.13908	−0.569538	−	0.821965i	$-0.692878\pi$
$37$	−4.56115e19	−1.13908	−0.569538	+	0.821965i	$0.692878\pi$
$38$	−9.43780e18	−0.168879
$39$	−2.69338e19	−0.348329
$40$	0	0
$41$	2.18308e20	1.51102	0.755512	−	0.655134i	$-0.227388\pi$
$41$	2.18308e20	1.51102	0.755512	+	0.655134i	$0.227388\pi$
$42$	−3.25207e20	−1.66550
$43$	6.85002e19	0.261419	0.130709	−	0.991421i	$-0.458275\pi$
$43$	6.85002e19	0.261419	0.130709	+	0.991421i	$0.458275\pi$
$44$	−1.92446e20	−0.550999
$45$	0	0
$46$	1.09733e20	0.180246
$47$	−1.23525e19	−0.0155071	−0.00775356	−	0.999970i	$-0.502468\pi$
$47$	−1.23525e19	−0.0155071	−0.00775356	+	0.999970i	$0.502468\pi$
$48$	1.50594e21	1.45309
$49$	3.64712e21	2.71956
$50$	0	0
$51$	−2.38526e20	−0.107872
$52$	−5.63408e21	−1.99886
$53$	−4.53955e21	−1.26930	−0.634650	−	0.772800i	$-0.718856\pi$
$53$	−4.53955e21	−1.26930	−0.634650	+	0.772800i	$0.718856\pi$
$54$	−6.99655e21	−1.54868
$55$	0	0
$56$	−4.19501e22	−5.89363
$57$	−3.58892e20	−0.0404137
$58$	−2.00568e22	−1.81724
$59$	8.45133e21	0.618407	0.309204	−	0.950996i	$-0.399938\pi$
$59$	8.45133e21	0.618407	0.309204	+	0.950996i	$0.399938\pi$
$60$	0	0
$61$	−1.08894e22	−0.525266	−0.262633	−	0.964896i	$-0.584591\pi$
$61$	−1.08894e22	−0.525266	−0.262633	+	0.964896i	$0.584591\pi$
$62$	−4.50452e22	−1.77318
$63$	4.74748e22	1.53005
$64$	9.57062e22	2.53332
$65$	0	0
$66$	−1.01235e22	−0.182403
$67$	−3.89372e22	−0.581339	−0.290669	−	0.956824i	$-0.593878\pi$
$67$	−3.89372e22	−0.581339	−0.290669	+	0.956824i	$0.593878\pi$
$68$	−4.98955e22	−0.619013
$69$	4.17284e21	0.0431338
$70$	0	0
$71$	−3.71162e22	−0.268432	−0.134216	−	0.990952i	$-0.542852\pi$
$71$	−3.71162e22	−0.268432	−0.134216	+	0.990952i	$0.542852\pi$
$72$	−3.99258e23	−2.42436
$73$	2.76367e23	1.41238	0.706188	−	0.708024i	$-0.250413\pi$
$73$	2.76367e23	1.41238	0.706188	+	0.708024i	$0.250413\pi$
$74$	−5.01906e23	−2.16384
$75$	0	0
$76$	−7.50741e22	−0.231910
$77$	1.55279e23	0.407361
$78$	−2.96378e23	−0.661702
$79$	8.72667e23	1.66154	0.830768	−	0.556619i	$-0.187902\pi$
$79$	8.72667e23	1.66154	0.830768	+	0.556619i	$0.187902\pi$
$80$	0	0
$81$	3.03480e23	0.422735
$82$	2.40225e24	2.87041
$83$	−4.43419e23	−0.455342	−0.227671	−	0.973738i	$-0.573111\pi$
$83$	−4.43419e23	−0.455342	−0.227671	+	0.973738i	$0.573111\pi$
$84$	−2.58690e24	−2.28712
$85$	0	0
$86$	7.53772e23	0.496603
$87$	−7.62702e23	−0.434875
$88$	−1.30588e24	−0.645461
$89$	−5.97991e23	−0.256637	−0.128319	−	0.991733i	$-0.540958\pi$
$89$	−5.97991e23	−0.256637	−0.128319	+	0.991733i	$0.540958\pi$
$90$	0	0
$91$	4.54598e24	1.47778
$92$	8.72886e23	0.247520
$93$	−1.71294e24	−0.424331
$94$	−1.35926e23	−0.0294581
$95$	0	0
$96$	8.23151e24	1.37116
$97$	−9.83402e24	−1.43908	−0.719539	−	0.694452i	$-0.755647\pi$
$97$	−9.83402e24	−1.43908	−0.719539	+	0.694452i	$0.755647\pi$
$98$	4.01327e25	5.16621
$99$	1.47786e24	0.167569
$100$	0	0
$101$	6.56554e24	0.579766	0.289883	−	0.957062i	$-0.406384\pi$
$101$	6.56554e24	0.579766	0.289883	+	0.957062i	$0.406384\pi$
$102$	−2.62472e24	−0.204918
$103$	−1.60371e25	−1.10831	−0.554156	−	0.832413i	$-0.686959\pi$
$103$	−1.60371e25	−1.10831	−0.554156	+	0.832413i	$0.686959\pi$
$104$	−3.82312e25	−2.34154
$105$	0	0
$106$	−4.99528e25	−2.41122
$107$	3.10689e25	1.33361	0.666804	−	0.745233i	$-0.267662\pi$
$107$	3.10689e25	1.33361	0.666804	+	0.745233i	$0.267662\pi$
$108$	−5.56548e25	−2.12670
$109$	5.99855e24	0.204275	0.102138	−	0.994770i	$-0.467432\pi$
$109$	5.99855e24	0.204275	0.102138	+	0.994770i	$0.467432\pi$
$110$	0	0
$111$	−1.90860e25	−0.517820
$112$	−2.54178e26	−6.16471
$113$	−3.19736e25	−0.693923	−0.346962	−	0.937879i	$-0.612787\pi$
$113$	−3.19736e25	−0.693923	−0.346962	+	0.937879i	$0.612787\pi$
$114$	−3.94923e24	−0.0767718
$115$	0	0
$116$	−1.59544e26	−2.49549
$117$	4.32661e25	0.607890
$118$	9.29978e25	1.17476
$119$	4.02592e25	0.457645
$120$	0	0
$121$	−1.03513e26	−0.955386
$122$	−1.19826e26	−0.997820
$123$	9.13505e25	0.686906
$124$	−3.58317e26	−2.43499
$125$	0	0
$126$	5.22410e26	2.90656
$127$	−3.11422e26	−1.56965	−0.784825	−	0.619718i	$-0.787247\pi$
$127$	−3.11422e26	−1.56965	−0.784825	+	0.619718i	$0.787247\pi$
$128$	3.93077e26	1.79619
$129$	2.86638e25	0.118840
$130$	0	0
$131$	7.42883e25	0.254114	0.127057	−	0.991895i	$-0.459447\pi$
$131$	7.42883e25	0.254114	0.127057	+	0.991895i	$0.459447\pi$
$132$	−8.05286e25	−0.250482
$133$	6.05751e25	0.171454
$134$	−4.28462e26	−1.10434
$135$	0	0
$136$	−3.38576e26	−0.725136
$137$	5.97553e26	1.16780	0.583901	−	0.811825i	$-0.301526\pi$
$137$	5.97553e26	1.16780	0.583901	+	0.811825i	$0.301526\pi$
$138$	4.59176e25	0.0819390
$139$	6.66965e26	1.08747	0.543736	−	0.839256i	$-0.317009\pi$
$139$	6.66965e26	1.08747	0.543736	+	0.839256i	$0.317009\pi$
$140$	0	0
$141$	−5.16887e24	−0.00704948
$142$	−4.08424e26	−0.509926
$143$	1.41514e26	0.161844
$144$	−2.41913e27	−2.53587
$145$	0	0
$146$	3.04112e27	2.68302
$147$	1.52613e27	1.23630
$148$	−3.99247e27	−2.97146
$149$	−6.79823e26	−0.465123	−0.232561	−	0.972582i	$-0.574711\pi$
$149$	−6.79823e26	−0.465123	−0.232561	+	0.972582i	$0.574711\pi$
$150$	0	0
$151$	−1.38341e27	−0.801195	−0.400597	−	0.916254i	$-0.631197\pi$
$151$	−1.38341e27	−0.801195	−0.400597	+	0.916254i	$0.631197\pi$
$152$	−5.09430e26	−0.271669
$153$	3.83165e26	0.188254
$154$	1.70868e27	0.773842
$155$	0	0
$156$	−2.35757e27	−0.908672
$157$	−2.26682e27	−0.806625	−0.403312	−	0.915062i	$-0.632141\pi$
$157$	−2.26682e27	−0.806625	−0.403312	+	0.915062i	$0.632141\pi$
$158$	9.60276e27	3.15633
$159$	−1.89956e27	−0.577018
$160$	0	0
$161$	−7.04306e26	−0.182995
$162$	3.33948e27	0.803047
$163$	4.82353e27	1.07404	0.537019	−	0.843570i	$-0.319550\pi$
$163$	4.82353e27	1.07404	0.537019	+	0.843570i	$0.319550\pi$
$164$	1.91090e28	3.94175
$165$	0	0
$166$	−4.87935e27	−0.864989
$167$	−1.02034e28	−1.67798	−0.838992	−	0.544144i	$-0.816855\pi$
$167$	−1.02034e28	−1.67798	−0.838992	+	0.544144i	$0.816855\pi$
$168$	−1.75539e28	−2.67922
$169$	−2.91344e27	−0.412878
$170$	0	0
$171$	5.76521e26	0.0705283
$172$	5.99597e27	0.681952
$173$	−9.52715e27	−1.00783	−0.503914	−	0.863754i	$-0.668107\pi$
$173$	−9.52715e27	−1.00783	−0.503914	+	0.863754i	$0.668107\pi$
$174$	−8.39272e27	−0.826108
$175$	0	0
$176$	−7.91240e27	−0.675149
$177$	3.53644e27	0.281126
$178$	−6.58026e27	−0.487520
$179$	2.29857e28	1.58779	0.793897	−	0.608052i	$-0.208049\pi$
$179$	2.29857e28	1.58779	0.793897	+	0.608052i	$0.208049\pi$
$180$	0	0
$181$	−2.20864e27	−0.132783	−0.0663916	−	0.997794i	$-0.521149\pi$
$181$	−2.20864e27	−0.132783	−0.0663916	+	0.997794i	$0.521149\pi$
$182$	5.00237e28	2.80726
$183$	−4.55663e27	−0.238784
$184$	5.92314e27	0.289954
$185$	0	0
$186$	−1.88491e28	−0.806080
$187$	1.25325e27	0.0501206
$188$	−1.08124e27	−0.0404528
$189$	4.49063e28	1.57230
$190$	0	0
$191$	−1.67599e28	−0.514464	−0.257232	−	0.966350i	$-0.582810\pi$
$191$	−1.67599e28	−0.514464	−0.257232	+	0.966350i	$0.582810\pi$
$192$	4.00480e28	1.15164
$193$	2.90398e28	0.782578	0.391289	−	0.920268i	$-0.372029\pi$
$193$	2.90398e28	0.782578	0.391289	+	0.920268i	$0.372029\pi$
$194$	−1.08213e29	−2.73374
$195$	0	0
$196$	3.19240e29	7.09441
$197$	−8.94384e27	−0.186507	−0.0932537	−	0.995642i	$-0.529727\pi$
$197$	−8.94384e27	−0.186507	−0.0932537	+	0.995642i	$0.529727\pi$
$198$	1.62623e28	0.318322
$199$	−1.94449e27	−0.0357390	−0.0178695	−	0.999840i	$-0.505688\pi$
$199$	−1.94449e27	−0.0357390	−0.0178695	+	0.999840i	$0.505688\pi$
$200$	0	0
$201$	−1.62932e28	−0.264274
$202$	7.22467e28	1.10135
$203$	1.28732e29	1.84495
$204$	−2.08786e28	−0.281401
$205$	0	0
$206$	−1.76472e29	−2.10540
$207$	−6.70320e27	−0.0752754
$208$	−2.31645e29	−2.44924
$209$	1.88567e27	0.0187774
$210$	0	0
$211$	−6.30554e28	−0.557431	−0.278716	−	0.960374i	$-0.589909\pi$
$211$	−6.30554e28	−0.557431	−0.278716	+	0.960374i	$0.589909\pi$
$212$	−3.97356e29	−3.31117
$213$	−1.55312e28	−0.122028
$214$	3.41880e29	2.53338
$215$	0	0
$216$	−3.77657e29	−2.49130
$217$	2.89116e29	1.80022
$218$	6.60077e28	0.388050
$219$	1.15645e29	0.642061
$220$	0	0
$221$	3.66902e28	0.181822
$222$	−2.10021e29	−0.983675
$223$	−3.91233e28	−0.173231	−0.0866154	−	0.996242i	$-0.527605\pi$
$223$	−3.91233e28	−0.173231	−0.0866154	+	0.996242i	$0.527605\pi$
$224$	−1.38934e30	−5.81714
$225$	0	0
$226$	−3.51836e29	−1.31821
$227$	−3.10822e29	−1.10202	−0.551008	−	0.834500i	$-0.685757\pi$
$227$	−3.10822e29	−1.10202	−0.551008	+	0.834500i	$0.685757\pi$
$228$	−3.14146e28	−0.105426
$229$	3.39409e29	1.07840	0.539200	−	0.842178i	$-0.318727\pi$
$229$	3.39409e29	1.07840	0.539200	+	0.842178i	$0.318727\pi$
$230$	0	0
$231$	6.49763e28	0.185185
$232$	−1.08262e30	−2.92331
$233$	6.18615e29	1.58296	0.791482	−	0.611192i	$-0.209310\pi$
$233$	6.18615e29	1.58296	0.791482	+	0.611192i	$0.209310\pi$
$234$	4.76098e29	1.15478
$235$	0	0
$236$	7.39762e29	1.61321
$237$	3.65165e29	0.755328
$238$	4.43010e29	0.869363
$239$	6.21272e29	1.15693	0.578467	−	0.815706i	$-0.303651\pi$
$239$	6.21272e29	1.15693	0.578467	+	0.815706i	$0.303651\pi$
$240$	0	0
$241$	−2.86821e29	−0.481280	−0.240640	−	0.970614i	$-0.577357\pi$
$241$	−2.86821e29	−0.481280	−0.240640	+	0.970614i	$0.577357\pi$
$242$	−1.13905e30	−1.81490
$243$	6.65716e29	1.00742
$244$	−9.53168e29	−1.37024
$245$	0	0
$246$	1.00521e30	1.30488
$247$	5.52051e28	0.0681188
$248$	−2.43143e30	−2.85244
$249$	−1.85548e29	−0.206997
$250$	0	0
$251$	−9.43362e29	−0.952263	−0.476132	−	0.879374i	$-0.657961\pi$
$251$	−9.43362e29	−0.952263	−0.476132	+	0.879374i	$0.657961\pi$
$252$	4.15557e30	3.99139
$253$	−2.19246e28	−0.0200413
$254$	−3.42687e30	−2.98178
$255$	0	0
$256$	1.11402e30	0.878808
$257$	9.76952e29	0.734022	0.367011	−	0.930217i	$-0.380381\pi$
$257$	9.76952e29	0.734022	0.367011	+	0.930217i	$0.380381\pi$
$258$	3.15414e29	0.225754
$259$	3.22141e30	2.19684
$260$	0	0
$261$	1.22520e30	0.758926
$262$	8.17464e29	0.482728
$263$	1.56365e30	0.880423	0.440212	−	0.897894i	$-0.354903\pi$
$263$	1.56365e30	0.880423	0.440212	+	0.897894i	$0.354903\pi$
$264$	−5.46443e29	−0.293424
$265$	0	0
$266$	6.66565e29	0.325703
$267$	−2.50228e29	−0.116666
$268$	−3.40825e30	−1.51651
$269$	1.22545e30	0.520465	0.260233	−	0.965546i	$-0.416201\pi$
$269$	1.22545e30	0.520465	0.260233	+	0.965546i	$0.416201\pi$
$270$	0	0
$271$	−4.30067e30	−1.66502	−0.832511	−	0.554008i	$-0.813098\pi$
$271$	−4.30067e30	−1.66502	−0.832511	+	0.554008i	$0.813098\pi$
$272$	−2.05145e30	−0.758489
$273$	1.90226e30	0.671793
$274$	6.57543e30	2.21841
$275$	0	0
$276$	3.65257e29	0.112521
$277$	2.53485e30	0.746372	0.373186	−	0.927757i	$-0.378265\pi$
$277$	2.53485e30	0.746372	0.373186	+	0.927757i	$0.378265\pi$
$278$	7.33924e30	2.06581
$279$	2.75165e30	0.740526
$280$	0	0
$281$	6.20850e30	1.52812	0.764060	−	0.645145i	$-0.223203\pi$
$281$	6.20850e30	1.52812	0.764060	+	0.645145i	$0.223203\pi$
$282$	−5.68779e28	−0.0133915
$283$	−5.38721e30	−1.21348	−0.606741	−	0.794900i	$-0.707523\pi$
$283$	−5.38721e30	−1.21348	−0.606741	+	0.794900i	$0.707523\pi$
$284$	−3.24886e30	−0.700247
$285$	0	0
$286$	1.55721e30	0.307447
$287$	−1.54185e31	−2.91419
$288$	−1.32230e31	−2.39290
$289$	−5.44570e30	−0.943693
$290$	0	0
$291$	−4.11502e30	−0.654199
$292$	2.41910e31	3.68441
$293$	5.63029e30	0.821647	0.410823	−	0.911715i	$-0.365241\pi$
$293$	5.63029e30	0.821647	0.410823	+	0.911715i	$0.365241\pi$
$294$	1.67934e31	2.34854
$295$	0	0
$296$	−2.70917e31	−3.48089
$297$	1.39791e30	0.172196
$298$	−7.48073e30	−0.883569
$299$	−6.41869e29	−0.0727037
$300$	0	0
$301$	−4.83797e30	−0.504176
$302$	−1.52229e31	−1.52199
$303$	2.74733e30	0.263559
$304$	−3.08666e30	−0.284164
$305$	0	0
$306$	4.21632e30	0.357615
$307$	1.10992e31	0.903782	0.451891	−	0.892073i	$-0.350750\pi$
$307$	1.10992e31	0.903782	0.451891	+	0.892073i	$0.350750\pi$
$308$	1.35919e31	1.06267
$309$	−6.71071e30	−0.503834
$310$	0	0
$311$	−8.27207e30	−0.572940	−0.286470	−	0.958089i	$-0.592482\pi$
$311$	−8.27207e30	−0.572940	−0.286470	+	0.958089i	$0.592482\pi$
$312$	−1.59978e31	−1.06445
$313$	−7.97044e30	−0.509540	−0.254770	−	0.967002i	$-0.582000\pi$
$313$	−7.97044e30	−0.509540	−0.254770	+	0.967002i	$0.582000\pi$
$314$	−2.49439e31	−1.53230
$315$	0	0
$316$	7.63863e31	4.33438
$317$	2.64724e31	1.44395	0.721975	−	0.691919i	$-0.243234\pi$
$317$	2.64724e31	1.44395	0.721975	+	0.691919i	$0.243234\pi$
$318$	−2.09027e31	−1.09613
$319$	4.00733e30	0.202056
$320$	0	0
$321$	1.30007e31	0.606253
$322$	−7.75014e30	−0.347625
$323$	4.88897e29	0.0210953
$324$	2.65643e31	1.10277
$325$	0	0
$326$	5.30778e31	2.04029
$327$	2.51008e30	0.0928626
$328$	1.29668e32	4.61751
$329$	8.72421e29	0.0299073
$330$	0	0
$331$	−1.55467e31	−0.494071	−0.247035	−	0.969006i	$-0.579456\pi$
$331$	−1.55467e31	−0.494071	−0.247035	+	0.969006i	$0.579456\pi$
$332$	−3.88133e31	−1.18783
$333$	3.06596e31	0.903678
$334$	−1.12277e32	−3.18758
$335$	0	0
$336$	−1.06360e32	−2.80245
$337$	−5.02293e30	−0.127522	−0.0637608	−	0.997965i	$-0.520309\pi$
$337$	−5.02293e30	−0.127522	−0.0637608	+	0.997965i	$0.520309\pi$
$338$	−3.20592e31	−0.784322
$339$	−1.33793e31	−0.315455
$340$	0	0
$341$	9.00000e30	0.197157
$342$	6.34400e30	0.133979
$343$	−1.62870e32	−3.31638
$344$	4.06868e31	0.798864
$345$	0	0
$346$	−1.04836e32	−1.91452
$347$	−1.03151e32	−1.81701	−0.908503	−	0.417879i	$-0.862774\pi$
$347$	−1.03151e32	−1.81701	−0.908503	+	0.417879i	$0.862774\pi$
$348$	−6.67609e31	−1.13444
$349$	−8.10691e31	−1.32904	−0.664519	−	0.747271i	$-0.731364\pi$
$349$	−8.10691e31	−1.32904	−0.664519	+	0.747271i	$0.731364\pi$
$350$	0	0
$351$	4.09253e31	0.624673
$352$	−4.32494e31	−0.637084
$353$	−5.76769e31	−0.820008	−0.410004	−	0.912084i	$-0.634473\pi$
$353$	−5.76769e31	−0.820008	−0.410004	+	0.912084i	$0.634473\pi$
$354$	3.89147e31	0.534039
$355$	0	0
$356$	−5.23434e31	−0.669479
$357$	1.68464e31	0.208043
$358$	2.52933e32	3.01625
$359$	1.44570e31	0.166493	0.0832467	−	0.996529i	$-0.473471\pi$
$359$	1.44570e31	0.166493	0.0832467	+	0.996529i	$0.473471\pi$
$360$	0	0
$361$	−9.23409e31	−0.992097
$362$	−2.43037e31	−0.252241
$363$	−4.33149e31	−0.434315
$364$	3.97919e32	3.85503
$365$	0	0
$366$	−5.01408e31	−0.453605
$367$	9.78544e31	0.855568	0.427784	−	0.903881i	$-0.359294\pi$
$367$	9.78544e31	0.855568	0.427784	+	0.903881i	$0.359294\pi$
$368$	3.58886e31	0.303290
$369$	−1.46745e32	−1.19876
$370$	0	0
$371$	3.20615e32	2.44799
$372$	−1.49937e32	−1.10694
$373$	−5.60597e31	−0.400212	−0.200106	−	0.979774i	$-0.564129\pi$
$373$	−5.60597e31	−0.400212	−0.200106	+	0.979774i	$0.564129\pi$
$374$	1.37906e31	0.0952114
$375$	0	0
$376$	−7.33696e30	−0.0473880
$377$	1.17319e32	0.732998
$378$	4.94146e32	2.98681
$379$	−2.05156e32	−1.19976	−0.599879	−	0.800091i	$-0.704785\pi$
$379$	−2.05156e32	−1.19976	−0.599879	+	0.800091i	$0.704785\pi$
$380$	0	0
$381$	−1.30314e32	−0.713557
$382$	−1.84425e32	−0.977299
$383$	−1.17765e32	−0.603993	−0.301997	−	0.953309i	$-0.597653\pi$
$383$	−1.17765e32	−0.603993	−0.301997	+	0.953309i	$0.597653\pi$
$384$	1.64482e32	0.816541
$385$	0	0
$386$	3.19552e32	1.48662
$387$	−4.60452e31	−0.207394
$388$	−8.60792e32	−3.75406
$389$	−1.81043e31	−0.0764560	−0.0382280	−	0.999269i	$-0.512171\pi$
$389$	−1.81043e31	−0.0764560	−0.0382280	+	0.999269i	$0.512171\pi$
$390$	0	0
$391$	−5.68439e30	−0.0225151
$392$	2.16626e33	8.31066
$393$	3.10858e31	0.115519
$394$	−9.84174e31	−0.354298
$395$	0	0
$396$	1.29360e32	0.437131
$397$	−2.64215e32	−0.865118	−0.432559	−	0.901606i	$-0.642389\pi$
$397$	−2.64215e32	−0.865118	−0.432559	+	0.901606i	$0.642389\pi$
$398$	−2.13970e31	−0.0678914
$399$	2.53475e31	0.0779425
$400$	0	0
$401$	−5.85566e32	−1.69150	−0.845749	−	0.533581i	$-0.820846\pi$
$401$	−5.85566e32	−1.69150	−0.845749	+	0.533581i	$0.820846\pi$
$402$	−1.79289e32	−0.502028
$403$	2.63486e32	0.715227
$404$	5.74695e32	1.51241
$405$	0	0
$406$	1.41655e33	3.50475
$407$	1.00281e32	0.240595
$408$	−1.41676e32	−0.329644
$409$	−1.45035e32	−0.327288	−0.163644	−	0.986519i	$-0.552325\pi$
$409$	−1.45035e32	−0.327288	−0.163644	+	0.986519i	$0.552325\pi$
$410$	0	0
$411$	2.50045e32	0.530878
$412$	−1.40376e33	−2.89121
$413$	−5.96893e32	−1.19267
$414$	−7.37616e31	−0.142997
$415$	0	0
$416$	−1.26618e33	−2.31115
$417$	2.79090e32	0.494361
$418$	2.07497e31	0.0356705
$419$	9.57851e32	1.59817	0.799085	−	0.601219i	$-0.205318\pi$
$419$	9.57851e32	1.59817	0.799085	+	0.601219i	$0.205318\pi$
$420$	0	0
$421$	−6.05056e32	−0.951194	−0.475597	−	0.879663i	$-0.657768\pi$
$421$	−6.05056e32	−0.951194	−0.475597	+	0.879663i	$0.657768\pi$
$422$	−6.93857e32	−1.05892
$423$	8.30322e30	0.0123025
$424$	−2.69634e33	−3.87883
$425$	0	0
$426$	−1.70904e32	−0.231810
$427$	7.69084e32	1.01304
$428$	2.71952e33	3.47893
$429$	5.92160e31	0.0735738
$430$	0	0
$431$	1.39054e32	0.163011	0.0815057	−	0.996673i	$-0.474027\pi$
$431$	1.39054e32	0.163011	0.0815057	+	0.996673i	$0.474027\pi$
$432$	−2.28824e33	−2.60589
$433$	8.29892e32	0.918169	0.459085	−	0.888392i	$-0.348177\pi$
$433$	8.29892e32	0.918169	0.459085	+	0.888392i	$0.348177\pi$
$434$	3.18141e33	3.41978
$435$	0	0
$436$	5.25066e32	0.532884
$437$	−8.55290e30	−0.00843520
$438$	1.27255e33	1.21969
$439$	2.32179e32	0.216280	0.108140	−	0.994136i	$-0.465511\pi$
$439$	2.32179e32	0.216280	0.108140	+	0.994136i	$0.465511\pi$
$440$	0	0
$441$	−2.45156e33	−2.15754
$442$	4.03736e32	0.345398
$443$	−1.86142e33	−1.54810	−0.774048	−	0.633127i	$-0.781771\pi$
$443$	−1.86142e33	−1.54810	−0.774048	+	0.633127i	$0.781771\pi$
$444$	−1.67064e33	−1.35081
$445$	0	0
$446$	−4.30510e32	−0.329077
$447$	−2.84471e32	−0.211443
$448$	−6.75945e33	−4.88580
$449$	1.07392e32	0.0754902	0.0377451	−	0.999287i	$-0.487983\pi$
$449$	1.07392e32	0.0754902	0.0377451	+	0.999287i	$0.487983\pi$
$450$	0	0
$451$	−4.79967e32	−0.319157
$452$	−2.79872e33	−1.81021
$453$	−5.78884e32	−0.364220
$454$	−3.42026e33	−2.09344
$455$	0	0
$456$	−2.13170e32	−0.123500
$457$	−3.21506e31	−0.0181233	−0.00906163	−	0.999959i	$-0.502884\pi$
$457$	−3.21506e31	−0.0181233	−0.00906163	+	0.999959i	$0.502884\pi$
$458$	3.73483e33	2.04858
$459$	3.62435e32	0.193451
$460$	0	0
$461$	−2.80044e31	−0.0141568	−0.00707840	−	0.999975i	$-0.502253\pi$
$461$	−2.80044e31	−0.0141568	−0.00707840	+	0.999975i	$0.502253\pi$
$462$	7.14994e32	0.351785
$463$	5.73654e32	0.274718	0.137359	−	0.990521i	$-0.456139\pi$
$463$	5.73654e32	0.274718	0.137359	+	0.990521i	$0.456139\pi$
$464$	−6.55964e33	−3.05777
$465$	0	0
$466$	6.80719e33	3.00707
$467$	−3.10395e32	−0.133492	−0.0667458	−	0.997770i	$-0.521262\pi$
$467$	−3.10395e32	−0.133492	−0.0667458	+	0.997770i	$0.521262\pi$
$468$	3.78717e33	1.58578
$469$	2.75002e33	1.12118
$470$	0	0
$471$	−9.48546e32	−0.366688
$472$	5.01980e33	1.88978
$473$	−1.50603e32	−0.0552166
$474$	4.01826e33	1.43486
$475$	0	0
$476$	3.52397e33	1.19384
$477$	3.05144e33	1.00699
$478$	6.83644e33	2.19776
$479$	4.51990e33	1.41558	0.707790	−	0.706423i	$-0.249692\pi$
$479$	4.51990e33	1.41558	0.707790	+	0.706423i	$0.249692\pi$
$480$	0	0
$481$	2.93583e33	0.872805
$482$	−3.15616e33	−0.914262
$483$	−2.94715e32	−0.0831886
$484$	−9.06073e33	−2.49228
$485$	0	0
$486$	7.32549e33	1.91374
$487$	−9.92789e32	−0.252781	−0.126391	−	0.991981i	$-0.540339\pi$
$487$	−9.92789e32	−0.252781	−0.126391	+	0.991981i	$0.540339\pi$
$488$	−6.46791e33	−1.60515
$489$	2.01839e33	0.488254
$490$	0	0
$491$	−2.94756e33	−0.677554	−0.338777	−	0.940867i	$-0.610013\pi$
$491$	−2.94756e33	−0.677554	−0.338777	+	0.940867i	$0.610013\pi$
$492$	7.99610e33	1.79190
$493$	1.03898e33	0.226998
$494$	6.07473e32	0.129402
$495$	0	0
$496$	−1.47322e34	−2.98364
$497$	2.62141e33	0.517702
$498$	−2.04175e33	−0.393221
$499$	−2.99602e33	−0.562714	−0.281357	−	0.959603i	$-0.590785\pi$
$499$	−2.99602e33	−0.562714	−0.281357	+	0.959603i	$0.590785\pi$
$500$	0	0
$501$	−4.26958e33	−0.762805
$502$	−1.03807e34	−1.80896
$503$	−3.33386e33	−0.566693	−0.283347	−	0.959018i	$-0.591445\pi$
$503$	−3.33386e33	−0.566693	−0.283347	+	0.959018i	$0.591445\pi$
$504$	2.81984e34	4.67566
$505$	0	0
$506$	−2.41257e32	−0.0380714
$507$	−1.21912e33	−0.187693
$508$	−2.72594e34	−4.09468
$509$	−9.93252e33	−1.45575	−0.727876	−	0.685709i	$-0.759492\pi$
$509$	−9.93252e33	−1.45575	−0.727876	+	0.685709i	$0.759492\pi$
$510$	0	0
$511$	−1.95190e34	−2.72393
$512$	−9.30849e32	−0.126767
$513$	5.45329e32	0.0724756
$514$	1.07503e34	1.39438
$515$	0	0
$516$	2.50900e33	0.310012
$517$	2.71579e31	0.00327540
$518$	3.54482e34	4.17323
$519$	−3.98661e33	−0.458155
$520$	0	0
$521$	9.94456e33	1.08922	0.544608	−	0.838691i	$-0.316678\pi$
$521$	9.94456e33	1.08922	0.544608	+	0.838691i	$0.316678\pi$
$522$	1.34820e34	1.44169
$523$	−7.17197e33	−0.748803	−0.374401	−	0.927267i	$-0.622152\pi$
$523$	−7.17197e33	−0.748803	−0.374401	+	0.927267i	$0.622152\pi$
$524$	6.50261e33	0.662898
$525$	0	0
$526$	1.72062e34	1.67249
$527$	2.33343e33	0.221494
$528$	−3.31093e33	−0.306920
$529$	−1.09463e34	−0.990997
$530$	0	0
$531$	−5.68090e33	−0.490609
$532$	5.30227e33	0.447266
$533$	−1.40516e34	−1.15781
$534$	−2.75349e33	−0.221625
$535$	0	0
$536$	−2.31273e34	−1.77650
$537$	9.61830e33	0.721805
$538$	1.34848e34	0.988700
$539$	−8.01848e33	−0.574424
$540$	0	0
$541$	1.93584e34	1.32405	0.662023	−	0.749483i	$-0.269698\pi$
$541$	1.93584e34	1.32405	0.662023	+	0.749483i	$0.269698\pi$
$542$	−4.73243e34	−3.16295
$543$	−9.24201e32	−0.0603627
$544$	−1.12133e34	−0.715725
$545$	0	0
$546$	2.09323e34	1.27617
$547$	1.61834e34	0.964337	0.482169	−	0.876078i	$-0.339849\pi$
$547$	1.61834e34	0.964337	0.482169	+	0.876078i	$0.339849\pi$
$548$	5.23050e34	3.04640
$549$	7.31972e33	0.416716
$550$	0	0
$551$	1.56328e33	0.0850436
$552$	2.47852e33	0.131812
$553$	−6.16339e34	−3.20447
$554$	2.78933e34	1.41784
$555$	0	0
$556$	5.83808e34	2.83684
$557$	−1.09645e34	−0.520953	−0.260476	−	0.965480i	$-0.583880\pi$
$557$	−1.09645e34	−0.520953	−0.260476	+	0.965480i	$0.583880\pi$
$558$	3.02789e34	1.40674
$559$	−4.40908e33	−0.200309
$560$	0	0
$561$	5.24418e32	0.0227846
$562$	6.83179e34	2.90289
$563$	1.82665e33	0.0759102	0.0379551	−	0.999279i	$-0.487916\pi$
$563$	1.82665e33	0.0759102	0.0379551	+	0.999279i	$0.487916\pi$
$564$	−4.52442e32	−0.0183897
$565$	0	0
$566$	−5.92804e34	−2.30519
$567$	−2.14339e34	−0.815293
$568$	−2.20458e34	−0.820296
$569$	−3.22829e34	−1.17508	−0.587542	−	0.809193i	$-0.699904\pi$
$569$	−3.22829e34	−1.17508	−0.587542	+	0.809193i	$0.699904\pi$
$570$	0	0
$571$	−9.23601e33	−0.321761	−0.160880	−	0.986974i	$-0.551433\pi$
$571$	−9.23601e33	−0.321761	−0.160880	+	0.986974i	$0.551433\pi$
$572$	1.23870e34	0.422197
$573$	−7.01315e33	−0.233873
$574$	−1.69664e35	−5.53593
$575$	0	0
$576$	−6.43327e34	−2.00979
$577$	−3.72256e34	−1.13801	−0.569003	−	0.822335i	$-0.692671\pi$
$577$	−3.72256e34	−1.13801	−0.569003	+	0.822335i	$0.692671\pi$
$578$	−5.99241e34	−1.79268
$579$	1.21517e34	0.355757
$580$	0	0
$581$	3.13174e34	0.878181
$582$	−4.52814e34	−1.24275
$583$	9.98055e33	0.268100
$584$	1.64153e35	4.31606
$585$	0	0
$586$	6.19553e34	1.56084
$587$	3.62671e34	0.894411	0.447205	−	0.894431i	$-0.352419\pi$
$587$	3.62671e34	0.894411	0.447205	+	0.894431i	$0.352419\pi$
$588$	1.33585e35	3.22509
$589$	3.51094e33	0.0829817
$590$	0	0
$591$	−3.74253e33	−0.0847855
$592$	−1.64150e35	−3.64099
$593$	4.50782e34	0.979000	0.489500	−	0.872003i	$-0.337179\pi$
$593$	4.50782e34	0.979000	0.489500	+	0.872003i	$0.337179\pi$
$594$	1.53825e34	0.327111
$595$	0	0
$596$	−5.95063e34	−1.21335
$597$	−8.13667e32	−0.0162468
$598$	−7.06308e33	−0.138111
$599$	−2.41289e33	−0.0462064	−0.0231032	−	0.999733i	$-0.507355\pi$
$599$	−2.41289e33	−0.0462064	−0.0231032	+	0.999733i	$0.507355\pi$
$600$	0	0
$601$	−9.16411e34	−1.68329	−0.841646	−	0.540030i	$-0.818413\pi$
$601$	−9.16411e34	−1.68329	−0.841646	+	0.540030i	$0.818413\pi$
$602$	−5.32367e34	−0.957757
$603$	2.61732e34	0.461201
$604$	−1.21092e35	−2.09004
$605$	0	0
$606$	3.02315e34	0.500670
$607$	1.55450e33	0.0252192	0.0126096	−	0.999920i	$-0.495986\pi$
$607$	1.55450e33	0.0252192	0.0126096	+	0.999920i	$0.495986\pi$
$608$	−1.68718e34	−0.268143
$609$	5.38674e34	0.838707
$610$	0	0
$611$	7.95080e32	0.0118822
$612$	3.35392e34	0.491089
$613$	−1.25803e35	−1.80482	−0.902412	−	0.430875i	$-0.858205\pi$
$613$	−1.25803e35	−1.80482	−0.902412	+	0.430875i	$0.858205\pi$
$614$	1.22135e35	1.71687
$615$	0	0
$616$	9.22306e34	1.24485
$617$	1.01184e35	1.33828	0.669141	−	0.743136i	$-0.266662\pi$
$617$	1.01184e35	1.33828	0.669141	+	0.743136i	$0.266662\pi$
$618$	−7.38442e34	−0.957107
$619$	−7.24722e34	−0.920531	−0.460265	−	0.887781i	$-0.652246\pi$
$619$	−7.24722e34	−0.920531	−0.460265	+	0.887781i	$0.652246\pi$
$620$	0	0
$621$	−6.34054e33	−0.0773537
$622$	−9.10252e34	−1.08838
$623$	4.22344e34	0.494955
$624$	−9.69312e34	−1.11341
$625$	0	0
$626$	−8.77062e34	−0.967946
$627$	7.89053e32	0.00853615
$628$	−1.98419e35	−2.10421
$629$	2.59997e34	0.270293
$630$	0	0
$631$	3.67312e34	0.367002	0.183501	−	0.983020i	$-0.441257\pi$
$631$	3.67312e34	0.367002	0.183501	+	0.983020i	$0.441257\pi$
$632$	5.18334e35	5.07746
$633$	−2.63854e34	−0.253406
$634$	2.91300e35	2.74300
$635$	0	0
$636$	−1.66273e35	−1.50524
$637$	−2.34750e35	−2.08383
$638$	4.40964e34	0.383835
$639$	2.49491e34	0.212958
$640$	0	0
$641$	4.16518e34	0.341907	0.170954	−	0.985279i	$-0.445315\pi$
$641$	4.16518e34	0.341907	0.170954	+	0.985279i	$0.445315\pi$
$642$	1.43059e35	1.15167
$643$	1.03651e35	0.818343	0.409171	−	0.912458i	$-0.365818\pi$
$643$	1.03651e35	0.818343	0.409171	+	0.912458i	$0.365818\pi$
$644$	−6.16494e34	−0.477370
$645$	0	0
$646$	5.37978e33	0.0400736
$647$	1.50099e35	1.09667	0.548333	−	0.836260i	$-0.315263\pi$
$647$	1.50099e35	1.09667	0.548333	+	0.836260i	$0.315263\pi$
$648$	1.80257e35	1.29183
$649$	−1.85809e34	−0.130620
$650$	0	0
$651$	1.20980e35	0.818373
$652$	4.22213e35	2.80180
$653$	2.54834e35	1.65898	0.829492	−	0.558519i	$-0.188630\pi$
$653$	2.54834e35	1.65898	0.829492	+	0.558519i	$0.188630\pi$
$654$	2.76208e34	0.176406
$655$	0	0
$656$	7.85663e35	4.82990
$657$	−1.85771e35	−1.12050
$658$	9.60006e33	0.0568133
$659$	−2.97012e34	−0.172467	−0.0862337	−	0.996275i	$-0.527483\pi$
$659$	−2.97012e34	−0.172467	−0.0862337	+	0.996275i	$0.527483\pi$
$660$	0	0
$661$	−1.44950e35	−0.810399	−0.405200	−	0.914228i	$-0.632798\pi$
$661$	−1.44950e35	−0.810399	−0.405200	+	0.914228i	$0.632798\pi$
$662$	−1.71075e35	−0.938560
$663$	1.53529e34	0.0826556
$664$	−2.63376e35	−1.39147
$665$	0	0
$666$	3.37376e35	1.71667
$667$	−1.81762e34	−0.0907676
$668$	−8.93122e35	−4.37729
$669$	−1.63711e34	−0.0787500
$670$	0	0
$671$	2.39411e34	0.110946
$672$	−5.81368e35	−2.64445
$673$	3.33613e35	1.48955	0.744774	−	0.667317i	$-0.232557\pi$
$673$	3.33613e35	1.48955	0.744774	+	0.667317i	$0.232557\pi$
$674$	−5.52720e34	−0.242246
$675$	0	0
$676$	−2.55019e35	−1.07706
$677$	2.77900e35	1.15221	0.576103	−	0.817377i	$-0.304573\pi$
$677$	2.77900e35	1.15221	0.576103	+	0.817377i	$0.304573\pi$
$678$	−1.47225e35	−0.599253
$679$	6.94549e35	2.77543
$680$	0	0
$681$	−1.30063e35	−0.500972
$682$	9.90354e34	0.374529
$683$	4.15368e35	1.54232	0.771159	−	0.636643i	$-0.219677\pi$
$683$	4.15368e35	1.54232	0.771159	+	0.636643i	$0.219677\pi$
$684$	5.04641e34	0.183984
$685$	0	0
$686$	−1.79221e36	−6.29994
$687$	1.42025e35	0.490236
$688$	2.46523e35	0.835608
$689$	2.92192e35	0.972586
$690$	0	0
$691$	4.18833e35	1.34451	0.672256	−	0.740318i	$-0.265325\pi$
$691$	4.18833e35	1.34451	0.672256	+	0.740318i	$0.265325\pi$
$692$	−8.33931e35	−2.62908
$693$	−1.04377e35	−0.323177
$694$	−1.13507e36	−3.45167
$695$	0	0
$696$	−4.53019e35	−1.32893
$697$	−1.24441e35	−0.358554
$698$	−8.92079e35	−2.52470
$699$	2.58858e35	0.719609
$700$	0	0
$701$	3.15026e35	0.845029	0.422515	−	0.906356i	$-0.361147\pi$
$701$	3.15026e35	0.845029	0.422515	+	0.906356i	$0.361147\pi$
$702$	4.50339e35	1.18666
$703$	3.91199e34	0.101264
$704$	−2.10417e35	−0.535086
$705$	0	0
$706$	−6.34673e35	−1.55773
$707$	−4.63705e35	−1.11815
$708$	3.09552e35	0.733360
$709$	−2.19302e35	−0.510464	−0.255232	−	0.966880i	$-0.582152\pi$
$709$	−2.19302e35	−0.510464	−0.255232	+	0.966880i	$0.582152\pi$
$710$	0	0
$711$	−5.86598e35	−1.31817
$712$	−3.55186e35	−0.784254
$713$	−4.08217e34	−0.0885670
$714$	1.85376e35	0.395209
$715$	0	0
$716$	2.01198e36	4.14201
$717$	2.59970e35	0.525937
$718$	1.59084e35	0.316279
$719$	−5.84662e35	−1.14234	−0.571168	−	0.820833i	$-0.693510\pi$
$719$	−5.84662e35	−1.14234	−0.571168	+	0.820833i	$0.693510\pi$
$720$	0	0
$721$	1.13266e36	2.13751
$722$	−1.01611e36	−1.88463
$723$	−1.20020e35	−0.218788
$724$	−1.93327e35	−0.346386
$725$	0	0
$726$	−4.76634e35	−0.825045
$727$	−6.80932e35	−1.15857	−0.579287	−	0.815124i	$-0.696669\pi$
$727$	−6.80932e35	−1.15857	−0.579287	+	0.815124i	$0.696669\pi$
$728$	2.70016e36	4.51593
$729$	2.14318e34	0.0352343
$730$	0	0
$731$	−3.90469e34	−0.0620324
$732$	−3.98851e35	−0.622906
$733$	7.38126e35	1.13326	0.566632	−	0.823971i	$-0.308246\pi$
$733$	7.38126e35	1.13326	0.566632	+	0.823971i	$0.308246\pi$
$734$	1.07678e36	1.62528
$735$	0	0
$736$	1.96168e35	0.286191
$737$	8.56064e34	0.122790
$738$	−1.61477e36	−2.27722
$739$	8.56912e35	1.18818	0.594088	−	0.804400i	$-0.297513\pi$
$739$	8.56912e35	1.18818	0.594088	+	0.804400i	$0.297513\pi$
$740$	0	0
$741$	2.31004e34	0.0309665
$742$	3.52802e36	4.65032
$743$	−5.38846e35	−0.698401	−0.349201	−	0.937048i	$-0.613547\pi$
$743$	−5.38846e35	−0.698401	−0.349201	+	0.937048i	$0.613547\pi$
$744$	−1.01743e36	−1.29671
$745$	0	0
$746$	−6.16877e35	−0.760262
$747$	2.98062e35	0.361242
$748$	1.09699e35	0.130747
$749$	−2.19430e36	−2.57202
$750$	0	0
$751$	1.45167e35	0.164577	0.0822883	−	0.996609i	$-0.473777\pi$
$751$	1.45167e35	0.164577	0.0822883	+	0.996609i	$0.473777\pi$
$752$	−4.44550e34	−0.0495676
$753$	−3.94748e35	−0.432895
$754$	1.29097e36	1.39244
$755$	0	0
$756$	3.93074e36	4.10159
$757$	8.93687e35	0.917248	0.458624	−	0.888630i	$-0.348342\pi$
$757$	8.93687e35	0.917248	0.458624	+	0.888630i	$0.348342\pi$
$758$	−2.25752e36	−2.27912
$759$	−9.17431e33	−0.00911069
$760$	0	0
$761$	−1.00712e36	−0.967776	−0.483888	−	0.875130i	$-0.660776\pi$
$761$	−1.00712e36	−0.967776	−0.483888	+	0.875130i	$0.660776\pi$
$762$	−1.43396e36	−1.35551
$763$	−4.23660e35	−0.393968
$764$	−1.46703e36	−1.34206
$765$	0	0
$766$	−1.29588e36	−1.14737
$767$	−5.43978e35	−0.473848
$768$	4.66160e35	0.399502
$769$	−1.58710e36	−1.33822	−0.669108	−	0.743165i	$-0.733324\pi$
$769$	−1.58710e36	−1.33822	−0.669108	+	0.743165i	$0.733324\pi$
$770$	0	0
$771$	4.08803e35	0.333684
$772$	2.54192e36	2.04148
$773$	2.56502e35	0.202697	0.101349	−	0.994851i	$-0.467684\pi$
$773$	2.56502e35	0.202697	0.101349	+	0.994851i	$0.467684\pi$
$774$	−5.06678e35	−0.393976
$775$	0	0
$776$	−5.84107e36	−4.39766
$777$	1.34799e36	0.998676
$778$	−1.99218e35	−0.145239
$779$	−1.87237e35	−0.134330
$780$	0	0
$781$	8.16029e34	0.0566980
$782$	−6.25507e34	−0.0427708
$783$	1.15891e36	0.779879
$784$	1.31255e37	8.69292
$785$	0	0
$786$	3.42066e35	0.219446
$787$	−3.06819e36	−1.93731	−0.968653	−	0.248418i	$-0.920089\pi$
$787$	−3.06819e36	−1.93731	−0.968653	+	0.248418i	$0.920089\pi$
$788$	−7.82872e35	−0.486534
$789$	6.54304e35	0.400237
$790$	0	0
$791$	2.25821e36	1.33831
$792$	8.77800e35	0.512072
$793$	7.00904e35	0.402479
$794$	−2.90740e36	−1.64342
$795$	0	0
$796$	−1.70205e35	−0.0932307
$797$	−2.63790e36	−1.42243	−0.711214	−	0.702976i	$-0.751854\pi$
$797$	−2.63790e36	−1.42243	−0.711214	+	0.702976i	$0.751854\pi$
$798$	2.78922e35	0.148063
$799$	7.04123e33	0.00367971
$800$	0	0
$801$	4.01964e35	0.203601
$802$	−6.44353e36	−3.21325
$803$	−6.07614e35	−0.298321
$804$	−1.42617e36	−0.689401
$805$	0	0
$806$	2.89938e36	1.35868
$807$	5.12786e35	0.236601
$808$	3.89970e36	1.77170
$809$	1.49529e36	0.668914	0.334457	−	0.942411i	$-0.391447\pi$
$809$	1.49529e36	0.668914	0.334457	+	0.942411i	$0.391447\pi$
$810$	0	0
$811$	−3.69909e36	−1.60448	−0.802240	−	0.597001i	$-0.796359\pi$
$811$	−3.69909e36	−1.60448	−0.802240	+	0.597001i	$0.796359\pi$
$812$	1.12681e37	4.81284
$813$	−1.79961e36	−0.756912
$814$	1.10348e36	0.457045
$815$	0	0
$816$	−8.58424e35	−0.344806
$817$	−5.87510e34	−0.0232402
$818$	−1.59595e36	−0.621732
$819$	−3.05576e36	−1.17239
$820$	0	0
$821$	4.34580e36	1.61726	0.808630	−	0.588318i	$-0.200210\pi$
$821$	4.34580e36	1.61726	0.808630	+	0.588318i	$0.200210\pi$
$822$	2.75147e36	1.00848
$823$	−2.75082e36	−0.993034	−0.496517	−	0.868027i	$-0.665388\pi$
$823$	−2.75082e36	−0.993034	−0.496517	+	0.868027i	$0.665388\pi$
$824$	−9.52552e36	−3.38687
$825$	0	0
$826$	−6.56817e36	−2.26565
$827$	2.52838e35	0.0859062	0.0429531	−	0.999077i	$-0.486323\pi$
$827$	2.52838e35	0.0859062	0.0429531	+	0.999077i	$0.486323\pi$
$828$	−5.86745e35	−0.196368
$829$	2.36903e36	0.780978	0.390489	−	0.920608i	$-0.372306\pi$
$829$	2.36903e36	0.780978	0.390489	+	0.920608i	$0.372306\pi$
$830$	0	0
$831$	1.06070e36	0.339298
$832$	−6.16022e36	−1.94113
$833$	−2.07895e36	−0.645330
$834$	3.07109e36	0.939111
$835$	0	0
$836$	1.65056e35	0.0489839
$837$	2.60278e36	0.760972
$838$	1.05401e37	3.03596
$839$	3.84035e36	1.08980	0.544900	−	0.838501i	$-0.316568\pi$
$839$	3.84035e36	1.08980	0.544900	+	0.838501i	$0.316568\pi$
$840$	0	0
$841$	−3.08152e35	−0.0848818
$842$	−6.65799e36	−1.80693
$843$	2.59793e36	0.694678
$844$	−5.51936e36	−1.45415
$845$	0	0
$846$	9.13681e34	0.0233703
$847$	7.31085e36	1.84257
$848$	−1.63372e37	−4.05724
$849$	−2.25426e36	−0.551644
$850$	0	0
$851$	−4.54846e35	−0.108080
$852$	−1.35948e36	−0.318330
$853$	−5.50445e36	−1.27014	−0.635070	−	0.772455i	$-0.719029\pi$
$853$	−5.50445e36	−1.27014	−0.635070	+	0.772455i	$0.719029\pi$
$854$	8.46295e36	1.92441
$855$	0	0
$856$	1.84538e37	4.07535
$857$	−1.64592e36	−0.358219	−0.179109	−	0.983829i	$-0.557322\pi$
$857$	−1.64592e36	−0.358219	−0.179109	+	0.983829i	$0.557322\pi$
$858$	6.51609e35	0.139764
$859$	−9.07912e36	−1.91924	−0.959619	−	0.281301i	$-0.909234\pi$
$859$	−9.07912e36	−1.91924	−0.959619	+	0.281301i	$0.909234\pi$
$860$	0	0
$861$	−6.45182e36	−1.32478
$862$	1.53014e36	0.309664
$863$	3.86548e36	0.771025	0.385512	−	0.922703i	$-0.374025\pi$
$863$	3.86548e36	0.771025	0.385512	+	0.922703i	$0.374025\pi$
$864$	−1.25076e37	−2.45897
$865$	0	0
$866$	9.13207e36	1.74420
$867$	−2.27874e36	−0.428999
$868$	2.53069e37	4.69616
$869$	−1.91863e36	−0.350948
$870$	0	0
$871$	2.50623e36	0.445444
$872$	3.56294e36	0.624241
$873$	6.61033e36	1.14168
$874$	−9.41155e34	−0.0160239
$875$	0	0
$876$	1.01227e37	1.67492
$877$	−3.82388e36	−0.623748	−0.311874	−	0.950123i	$-0.600957\pi$
$877$	−3.82388e36	−0.623748	−0.311874	+	0.950123i	$0.600957\pi$
$878$	2.55488e36	0.410855
$879$	2.35598e36	0.373517
$880$	0	0
$881$	−1.18948e37	−1.83298	−0.916488	−	0.400061i	$-0.868989\pi$
$881$	−1.18948e37	−1.83298	−0.916488	+	0.400061i	$0.868989\pi$
$882$	−2.69768e37	−4.09857
$883$	−2.26008e36	−0.338544	−0.169272	−	0.985569i	$-0.554142\pi$
$883$	−2.26008e36	−0.338544	−0.169272	+	0.985569i	$0.554142\pi$
$884$	3.21157e36	0.474312
$885$	0	0
$886$	−2.04829e37	−2.94083
$887$	9.18825e36	1.30073	0.650365	−	0.759622i	$-0.274616\pi$
$887$	9.18825e36	1.30073	0.650365	+	0.759622i	$0.274616\pi$
$888$	−1.13365e37	−1.58240
$889$	2.19948e37	3.02725
$890$	0	0
$891$	−6.67226e35	−0.0892897
$892$	−3.42455e36	−0.451900
$893$	1.05944e34	0.00137859
$894$	−3.13029e36	−0.401667
$895$	0	0
$896$	−2.77619e37	−3.46416
$897$	−2.68589e35	−0.0330508
$898$	1.18173e36	0.143405
$899$	7.46130e36	0.892932
$900$	0	0
$901$	2.58766e36	0.301194
$902$	−5.28153e36	−0.606286
$903$	−2.02444e36	−0.229196
$904$	−1.89913e37	−2.12055
$905$	0	0
$906$	−6.36999e36	−0.691889
$907$	9.71863e36	1.04115	0.520576	−	0.853815i	$-0.325717\pi$
$907$	9.71863e36	1.04115	0.520576	+	0.853815i	$0.325717\pi$
$908$	−2.72069e37	−2.87478
$909$	−4.41329e36	−0.459953
$910$	0	0
$911$	−1.55044e37	−1.57208	−0.786042	−	0.618173i	$-0.787873\pi$
$911$	−1.55044e37	−1.57208	−0.786042	+	0.618173i	$0.787873\pi$
$912$	−1.29161e36	−0.129180
$913$	9.74891e35	0.0961770
$914$	−3.53783e35	−0.0344278
$915$	0	0
$916$	2.97092e37	2.81318
$917$	−5.24677e36	−0.490089
$918$	3.98821e36	0.367489
$919$	1.12812e36	0.102545	0.0512724	−	0.998685i	$-0.483672\pi$
$919$	1.12812e36	0.102545	0.0512724	+	0.998685i	$0.483672\pi$
$920$	0	0
$921$	4.64445e36	0.410856
$922$	−3.08159e35	−0.0268929
$923$	2.38902e36	0.205683
$924$	5.68750e36	0.483083
$925$	0	0
$926$	6.31245e36	0.521868
$927$	1.07800e37	0.879271
$928$	−3.58552e37	−2.88537
$929$	2.05674e37	1.63299	0.816496	−	0.577351i	$-0.195914\pi$
$929$	2.05674e37	1.63299	0.816496	+	0.577351i	$0.195914\pi$
$930$	0	0
$931$	−3.12805e36	−0.241770
$932$	5.41486e37	4.12941
$933$	−3.46143e36	−0.260456
$934$	−3.41557e36	−0.253587
$935$	0	0
$936$	2.56986e37	1.85764
$937$	−1.39662e37	−0.996173	−0.498086	−	0.867127i	$-0.665964\pi$
$937$	−1.39662e37	−0.996173	−0.498086	+	0.867127i	$0.665964\pi$
$938$	3.02610e37	2.12985
$939$	−3.33522e36	−0.231635
$940$	0	0
$941$	−8.01115e36	−0.541782	−0.270891	−	0.962610i	$-0.587318\pi$
$941$	−8.01115e36	−0.541782	−0.270891	+	0.962610i	$0.587318\pi$
$942$	−1.04377e37	−0.696578
$943$	2.17701e36	0.143372
$944$	3.04152e37	1.97670
$945$	0	0
$946$	−1.65723e36	−0.104892
$947$	−1.93560e37	−1.20904	−0.604522	−	0.796589i	$-0.706636\pi$
$947$	−1.93560e37	−1.20904	−0.604522	+	0.796589i	$0.706636\pi$
$948$	3.19637e37	1.97039
$949$	−1.77886e37	−1.08222
$950$	0	0
$951$	1.10773e37	0.656414
$952$	2.39126e37	1.39851
$953$	2.25154e37	1.29963	0.649813	−	0.760094i	$-0.274847\pi$
$953$	2.25154e37	1.29963	0.649813	+	0.760094i	$0.274847\pi$
$954$	3.35778e37	1.91292
$955$	0	0
$956$	5.43812e37	3.01804
$957$	1.67686e36	0.0918539
$958$	4.97366e37	2.68910
$959$	−4.22034e37	−2.25224
$960$	0	0
$961$	−2.47559e36	−0.128717
$962$	3.23057e37	1.65802
$963$	−2.08842e37	−1.05801
$964$	−2.51060e37	−1.25549
$965$	0	0
$966$	−3.24303e36	−0.158029
$967$	−1.09124e37	−0.524915	−0.262458	−	0.964944i	$-0.584533\pi$
$967$	−1.09124e37	−0.524915	−0.262458	+	0.964944i	$0.584533\pi$
$968$	−6.14834e37	−2.91955
$969$	2.04578e35	0.00958983
$970$	0	0
$971$	−9.90246e36	−0.452379	−0.226190	−	0.974083i	$-0.572627\pi$
$971$	−9.90246e36	−0.452379	−0.226190	+	0.974083i	$0.572627\pi$
$972$	5.82715e37	2.62801
$973$	−4.71058e37	−2.09732
$974$	−1.09246e37	−0.480195
$975$	0	0
$976$	−3.91894e37	−1.67898
$977$	2.53501e37	1.07225	0.536127	−	0.844137i	$-0.319887\pi$
$977$	2.53501e37	1.07225	0.536127	+	0.844137i	$0.319887\pi$
$978$	2.22103e37	0.927509
$979$	1.31473e36	0.0542067
$980$	0	0
$981$	−4.03217e36	−0.162060
$982$	−3.24347e37	−1.28711
$983$	−3.23058e37	−1.26579	−0.632894	−	0.774238i	$-0.718133\pi$
$983$	−3.23058e37	−1.26579	−0.632894	+	0.774238i	$0.718133\pi$
$984$	5.42591e37	2.09910
$985$	0	0
$986$	1.14329e37	0.431215
$987$	3.65063e35	0.0135957
$988$	4.83221e36	0.177699
$989$	6.83097e35	0.0248044
$990$	0	0
$991$	1.28289e37	0.454223	0.227111	−	0.973869i	$-0.427072\pi$
$991$	1.28289e37	0.454223	0.227111	+	0.973869i	$0.427072\pi$
$992$	−8.05266e37	−2.81542
$993$	−6.50550e36	−0.224603
$994$	2.88458e37	0.983451
$995$	0	0
$996$	−1.62414e37	−0.539984
$997$	1.23049e37	0.404006	0.202003	−	0.979385i	$-0.435255\pi$
$997$	1.23049e37	0.404006	0.202003	+	0.979385i	$0.435255\pi$
$998$	−3.29680e37	−1.06896
$999$	2.90008e37	0.928628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.26.a.c.1.5		5
5.2	odd	4		25.26.b.c.24.10		10
5.3	odd	4		25.26.b.c.24.1		10
5.4	even	2		5.26.a.b.1.1	✓	5
15.14	odd	2		45.26.a.f.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.b.1.1	✓	5	5.4	even	2
25.26.a.c.1.5		5	1.1	even	1	trivial
25.26.b.c.24.1		10	5.3	odd	4
25.26.b.c.24.10		10	5.2	odd	4
45.26.a.f.1.5		5	15.14	odd	2

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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+11003.9 q^{2} +418448. q^{3} +8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10 q^{7} +5.93966e11 q^{8} -6.72190e11 q^{9} +O(q^{10})\)	\(q+11003.9 q^{2} +418448. q^{3} +8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10 q^{7} +5.93966e11 q^{8} -6.72190e11 q^{9} -2.19858e12 q^{11} +3.66276e13 q^{12} -6.43659e13 q^{13} -7.77176e14 q^{14} +3.59887e15 q^{16} -5.70025e14 q^{17} -7.39673e15 q^{18} -8.57675e14 q^{19} -2.95538e16 q^{21} -2.41930e16 q^{22} +9.97218e15 q^{23} +2.48544e17 q^{24} -7.08278e17 q^{26} -6.35823e17 q^{27} -6.18214e18 q^{28} -1.82269e18 q^{29} -4.09356e18 q^{31} +1.96715e19 q^{32} -9.19990e17 q^{33} -6.27252e18 q^{34} -5.88382e19 q^{36} -4.56115e19 q^{37} -9.43780e18 q^{38} -2.69338e19 q^{39} +2.18308e20 q^{41} -3.25207e20 q^{42} +6.85002e19 q^{43} -1.92446e20 q^{44} +1.09733e20 q^{46} -1.23525e19 q^{47} +1.50594e21 q^{48} +3.64712e21 q^{49} -2.38526e20 q^{51} -5.63408e21 q^{52} -4.53955e21 q^{53} -6.99655e21 q^{54} -4.19501e22 q^{56} -3.58892e20 q^{57} -2.00568e22 q^{58} +8.45133e21 q^{59} -1.08894e22 q^{61} -4.50452e22 q^{62} +4.74748e22 q^{63} +9.57062e22 q^{64} -1.01235e22 q^{66} -3.89372e22 q^{67} -4.98955e22 q^{68} +4.17284e21 q^{69} -3.71162e22 q^{71} -3.99258e23 q^{72} +2.76367e23 q^{73} -5.01906e23 q^{74} -7.50741e22 q^{76} +1.55279e23 q^{77} -2.96378e23 q^{78} +8.72667e23 q^{79} +3.03480e23 q^{81} +2.40225e24 q^{82} -4.43419e23 q^{83} -2.58690e24 q^{84} +7.53772e23 q^{86} -7.62702e23 q^{87} -1.30588e24 q^{88} -5.97991e23 q^{89} +4.54598e24 q^{91} +8.72886e23 q^{92} -1.71294e24 q^{93} -1.35926e23 q^{94} +8.23151e24 q^{96} -9.83402e24 q^{97} +4.01327e25 q^{98} +1.47786e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4602 q^{2} - 626204 q^{3} + 91050260 q^{4} + 5696574760 q^{6} - 55481235808 q^{7} + 325515457080 q^{8} + 277996846465 q^{9}+O(q^{10}) \) 5 * q + 4602 * q^2 - 626204 * q^3 + 91050260 * q^4 + 5696574760 * q^6 - 55481235808 * q^7 + 325515457080 * q^8 + 277996846465 * q^9	\( 5 q + 4602 q^{2} - 626204 q^{3} + 91050260 q^{4} + 5696574760 q^{6} - 55481235808 q^{7} + 325515457080 q^{8} + 277996846465 q^{9} - 4144958451540 q^{11} + 26370992065712 q^{12} - 111211249076614 q^{13} - 445566653510880 q^{14} + 30\!\cdots\!80 q^{16}+ \cdots - 22\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q + 4602 * q^2 - 626204 * q^3 + 91050260 * q^4 + 5696574760 * q^6 - 55481235808 * q^7 + 325515457080 * q^8 + 277996846465 * q^9 - 4144958451540 * q^11 + 26370992065712 * q^12 - 111211249076614 * q^13 - 445566653510880 * q^14 + 3044988017630480 * q^16 - 3179191896192378 * q^17 - 9100952570763854 * q^18 + 13473188050195300 * q^19 + 76768095576060960 * q^21 - 222905601184950696 * q^22 - 409020396998250624 * q^23 + 738233252736381600 * q^24 + 331732385439154260 * q^26 - 1707963140919696920 * q^27 - 6745183853862681376 * q^28 + 1510518246057732150 * q^29 - 7800790900476562640 * q^31 + 26275496698670595552 * q^32 + 17083981126675017392 * q^33 - 30967164186095882580 * q^34 - 127816747210020977020 * q^36 + 45693640863683938082 * q^37 + 107313021439059142920 * q^38 - 28513155461010121720 * q^39 + 268182713424991346610 * q^41 - 472693454958668435136 * q^42 + 54212732396046197756 * q^43 + 1026843270980203159920 * q^44 + 1806261760861861731360 * q^46 - 1313959570250307870888 * q^47 - 393501331052082428224 * q^48 + 2928508402086077906685 * q^49 - 1679947779014963634440 * q^51 + 1533919945088032601192 * q^52 + 1722136215100242292146 * q^53 - 16134427338310747545200 * q^54 - 39415455111791618702400 * q^56 + 9510351594401743758160 * q^57 - 7814667131698315285620 * q^58 - 16547203533880040421300 * q^59 + 11587268554089248839510 * q^61 - 21314291783865447926496 * q^62 - 32595050340385317746784 * q^63 + 83981823170089659652160 * q^64 + 107686245599040557757920 * q^66 - 186273232047241909753228 * q^67 - 48790715540647305709416 * q^68 + 205103851249003209571680 * q^69 + 179635129178416728944760 * q^71 - 252302332499928005189160 * q^72 + 471333406608130631390126 * q^73 - 888672199125830235839580 * q^74 - 1191799860770260438242800 * q^76 + 286067188114809482097984 * q^77 + 1025178605609234961148112 * q^78 + 360282849255851991934000 * q^79 + 103584508446589901468605 * q^81 + 2050449668847875948936004 * q^82 - 1759227952818659145519084 * q^83 - 3837881595316615167665280 * q^84 - 565842386421331097744040 * q^86 - 8705381585373786685282760 * q^87 - 720634350501343968831840 * q^88 + 4092128669145981513024450 * q^89 + 11972573281108721260967360 * q^91 - 6613215336376724900082528 * q^92 - 7392084747484240267531008 * q^93 - 17112742333122902932304880 * q^94 - 10376386162767776801453440 * q^96 - 28613737566457196779163338 * q^97 + 56860534671603836155246314 * q^98 - 22864619024884333176273220 * q^99

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