LMFDB - Embedded newform 50.26.a.d.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{95351}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 95351 $ x^2 - 95351
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\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			$-308.790$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} -618439. q^{3} +1.67772e7 q^{4} +2.53313e9 q^{6} -4.78762e10 q^{7} -6.87195e10 q^{8} -4.64821e11 q^{9} +3.58198e11 q^{11} -1.03757e13 q^{12} -7.76408e13 q^{13} +1.96101e14 q^{14} +2.81475e14 q^{16} -1.50624e15 q^{17} +1.90391e15 q^{18} +4.83611e15 q^{19} +2.96085e16 q^{21} -1.46718e15 q^{22} -2.59330e16 q^{23} +4.24988e16 q^{24} +3.18017e17 q^{26} +8.11461e17 q^{27} -8.03229e17 q^{28} +9.30223e17 q^{29} +3.10982e18 q^{31} -1.15292e18 q^{32} -2.21524e17 q^{33} +6.16957e18 q^{34} -7.79841e18 q^{36} +4.54619e19 q^{37} -1.98087e19 q^{38} +4.80162e19 q^{39} +1.02459e20 q^{41} -1.21276e20 q^{42} -4.58049e20 q^{43} +6.00957e18 q^{44} +1.06222e20 q^{46} -1.51063e21 q^{47} -1.74075e20 q^{48} +9.51058e20 q^{49} +9.31520e20 q^{51} -1.30260e21 q^{52} +2.00272e21 q^{53} -3.32374e21 q^{54} +3.29002e21 q^{56} -2.99084e21 q^{57} -3.81019e21 q^{58} +2.00362e22 q^{59} -2.40289e22 q^{61} -1.27378e22 q^{62} +2.22539e22 q^{63} +4.72237e21 q^{64} +9.07362e20 q^{66} +5.68406e22 q^{67} -2.52706e22 q^{68} +1.60380e22 q^{69} +2.06619e22 q^{71} +3.19423e22 q^{72} +3.20846e23 q^{73} -1.86212e23 q^{74} +8.11365e22 q^{76} -1.71492e22 q^{77} -1.96674e23 q^{78} -4.28561e23 q^{79} -1.08001e23 q^{81} -4.19671e23 q^{82} +1.11807e24 q^{83} +4.96748e23 q^{84} +1.87617e24 q^{86} -5.75287e23 q^{87} -2.46152e22 q^{88} +1.75157e24 q^{89} +3.71714e24 q^{91} -4.35084e23 q^{92} -1.92323e24 q^{93} +6.18754e24 q^{94} +7.13012e23 q^{96} +1.28690e25 q^{97} -3.89553e24 q^{98} -1.66498e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{2} + 97092 q^{3} + 33554432 q^{4} - 397688832 q^{6} + 16137160124 q^{7} - 137438953472 q^{8} - 800124539454 q^{9} + 14416600801344 q^{11} + 1628933455872 q^{12} - 93404548866628 q^{13} - 66097807867904 q^{14}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^2 + 97092 * q^3 + 33554432 * q^4 - 397688832 * q^6 + 16137160124 * q^7 - 137438953472 * q^8 - 800124539454 * q^9 + 14416600801344 * q^11 + 1628933455872 * q^12 - 93404548866628 * q^13 - 66097807867904 * q^14 + 562949953421312 * q^16 - 499266882181236 * q^17 + 3277310113603584 * q^18 - 3830204591906120 * q^19 + 75412053748282104 * q^21 - 59050396882305024 * q^22 - 169271186050723788 * q^23 - 6672111435251712 * q^24 + 382585032157708288 * q^26 - 34721228182863240 * q^27 + 270736621026934784 * q^28 + 569443622853716940 * q^29 + 3982769593868414584 * q^31 - 2305843009213693952 * q^32 + 9837705729224836224 * q^33 + 2044997149414342656 * q^34 - 13423862225320280064 * q^36 - 28241444663789328196 * q^37 + 15688518008447467520 * q^38 + 36736718047624459512 * q^39 + 36676428854020432524 * q^41 - 308887772152963497984 * q^42 - 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 693334778063764635648 * q^46 - 954929084389204818996 * q^47 + 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 1652042752773544110744 * q^51 - 1567068291717973147648 * q^52 - 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 1108937199726324875264 * q^56 - 9191867441696689119120 * q^57 - 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 - 26987853585082462424636 * q^61 - 16313424256485026136064 * q^62 + 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 40295242666904929173504 * q^66 + 14159647018044347838524 * q^67 - 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 - 173327708998984655450136 * q^71 + 54984139674911867142144 * q^72 + 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 64260169762600826961920 * q^76 + 882775887628764911584128 * q^77 - 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 429372483438817686010518 * q^81 - 150226652586067691618304 * q^82 - 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 + 3723334919365686278668288 * q^86 - 833435461987898381769960 * q^87 - 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 2708056932935479178393864 * q^91 - 2839899250949179947614208 * q^92 - 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 - 111939454725287986593792 * q^96 + 16314734149871901683914364 * q^97 - 15186717796562586217979904 * q^98 - 4880327126898398506596288 * 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
$3$	−618439.	−0.671864	−0.335932	−	0.941886i	$-0.609051\pi$
$3$	−618439.	−0.671864	−0.335932	+	0.941886i	$0.609051\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	2.53313e9	0.475080
$7$	−4.78762e10	−1.30736	−0.653678	−	0.756773i	$-0.726775\pi$
$7$	−4.78762e10	−1.30736	−0.653678	+	0.756773i	$0.726775\pi$
$8$	−6.87195e10	−0.353553
$9$	−4.64821e11	−0.548598
$10$	0	0
$11$	3.58198e11	0.0344124	0.0172062	−	0.999852i	$-0.494523\pi$
$11$	3.58198e11	0.0344124	0.0172062	+	0.999852i	$0.494523\pi$
$12$	−1.03757e13	−0.335932
$13$	−7.76408e13	−0.924269	−0.462134	−	0.886810i	$-0.652916\pi$
$13$	−7.76408e13	−0.924269	−0.462134	+	0.886810i	$0.652916\pi$
$14$	1.96101e14	0.924440
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−1.50624e15	−0.627023	−0.313511	−	0.949584i	$-0.601505\pi$
$17$	−1.50624e15	−0.627023	−0.313511	+	0.949584i	$0.601505\pi$
$18$	1.90391e15	0.387918
$19$	4.83611e15	0.501276	0.250638	−	0.968081i	$-0.419360\pi$
$19$	4.83611e15	0.501276	0.250638	+	0.968081i	$0.419360\pi$
$20$	0	0
$21$	2.96085e16	0.878366
$22$	−1.46718e15	−0.0243332
$23$	−2.59330e16	−0.246749	−0.123374	−	0.992360i	$-0.539372\pi$
$23$	−2.59330e16	−0.246749	−0.123374	+	0.992360i	$0.539372\pi$
$24$	4.24988e16	0.237540
$25$	0	0
$26$	3.18017e17	0.653557
$27$	8.11461e17	1.04045
$28$	−8.03229e17	−0.653678
$29$	9.30223e17	0.488216	0.244108	−	0.969748i	$-0.421505\pi$
$29$	9.30223e17	0.488216	0.244108	+	0.969748i	$0.421505\pi$
$30$	0	0
$31$	3.10982e18	0.709110	0.354555	−	0.935035i	$-0.384632\pi$
$31$	3.10982e18	0.709110	0.354555	+	0.935035i	$0.384632\pi$
$32$	−1.15292e18	−0.176777
$33$	−2.21524e17	−0.0231205
$34$	6.16957e18	0.443372
$35$	0	0
$36$	−7.79841e18	−0.274299
$37$	4.54619e19	1.13534	0.567670	−	0.823256i	$-0.307845\pi$
$37$	4.54619e19	1.13534	0.567670	+	0.823256i	$0.307845\pi$
$38$	−1.98087e19	−0.354455
$39$	4.80162e19	0.620983
$40$	0	0
$41$	1.02459e20	0.709172	0.354586	−	0.935023i	$-0.384622\pi$
$41$	1.02459e20	0.709172	0.354586	+	0.935023i	$0.384622\pi$
$42$	−1.21276e20	−0.621098
$43$	−4.58049e20	−1.74806	−0.874029	−	0.485874i	$-0.838502\pi$
$43$	−4.58049e20	−1.74806	−0.874029	+	0.485874i	$0.838502\pi$
$44$	6.00957e18	0.0172062
$45$	0	0
$46$	1.06222e20	0.174478
$47$	−1.51063e21	−1.89642	−0.948210	−	0.317644i	$-0.897108\pi$
$47$	−1.51063e21	−1.89642	−0.948210	+	0.317644i	$0.897108\pi$
$48$	−1.74075e20	−0.167966
$49$	9.51058e20	0.709179
$50$	0	0
$51$	9.31520e20	0.421274
$52$	−1.30260e21	−0.462134
$53$	2.00272e21	0.559980	0.279990	−	0.960003i	$-0.409669\pi$
$53$	2.00272e21	0.559980	0.279990	+	0.960003i	$0.409669\pi$
$54$	−3.32374e21	−0.735708
$55$	0	0
$56$	3.29002e21	0.462220
$57$	−2.99084e21	−0.336789
$58$	−3.81019e21	−0.345221
$59$	2.00362e22	1.46611	0.733053	−	0.680171i	$-0.238095\pi$
$59$	2.00362e22	1.46611	0.733053	+	0.680171i	$0.238095\pi$
$60$	0	0
$61$	−2.40289e22	−1.15908	−0.579538	−	0.814945i	$-0.696767\pi$
$61$	−2.40289e22	−1.15908	−0.579538	+	0.814945i	$0.696767\pi$
$62$	−1.27378e22	−0.501417
$63$	2.22539e22	0.717213
$64$	4.72237e21	0.125000
$65$	0	0
$66$	9.07362e20	0.0163486
$67$	5.68406e22	0.848640	0.424320	−	0.905512i	$-0.360513\pi$
$67$	5.68406e22	0.848640	0.424320	+	0.905512i	$0.360513\pi$
$68$	−2.52706e22	−0.313511
$69$	1.60380e22	0.165782
$70$	0	0
$71$	2.06619e22	0.149431	0.0747156	−	0.997205i	$-0.476195\pi$
$71$	2.06619e22	0.149431	0.0747156	+	0.997205i	$0.476195\pi$
$72$	3.19423e22	0.193959
$73$	3.20846e23	1.63969	0.819843	−	0.572588i	$-0.194061\pi$
$73$	3.20846e23	1.63969	0.819843	+	0.572588i	$0.194061\pi$
$74$	−1.86212e23	−0.802806
$75$	0	0
$76$	8.11365e22	0.250638
$77$	−1.71492e22	−0.0449892
$78$	−1.96674e23	−0.439101
$79$	−4.28561e23	−0.815969	−0.407985	−	0.912989i	$-0.633768\pi$
$79$	−4.28561e23	−0.815969	−0.407985	+	0.912989i	$0.633768\pi$
$80$	0	0
$81$	−1.08001e23	−0.150441
$82$	−4.19671e23	−0.501460
$83$	1.11807e24	1.14814	0.574069	−	0.818807i	$-0.305364\pi$
$83$	1.11807e24	1.14814	0.574069	+	0.818807i	$0.305364\pi$
$84$	4.96748e23	0.439183
$85$	0	0
$86$	1.87617e24	1.23606
$87$	−5.75287e23	−0.328015
$88$	−2.46152e22	−0.0121666
$89$	1.75157e24	0.751712	0.375856	−	0.926678i	$-0.377349\pi$
$89$	1.75157e24	0.751712	0.375856	+	0.926678i	$0.377349\pi$
$90$	0	0
$91$	3.71714e24	1.20835
$92$	−4.35084e23	−0.123374
$93$	−1.92323e24	−0.476426
$94$	6.18754e24	1.34097
$95$	0	0
$96$	7.13012e23	0.118770
$97$	1.28690e25	1.88320	0.941601	−	0.336729i	$-0.109321\pi$
$97$	1.28690e25	1.88320	0.941601	+	0.336729i	$0.109321\pi$
$98$	−3.89553e24	−0.501466
$99$	−1.66498e23	−0.0188786
$100$	0	0
$101$	−3.20176e24	−0.282730	−0.141365	−	0.989958i	$-0.545149\pi$
$101$	−3.20176e24	−0.282730	−0.141365	+	0.989958i	$0.545149\pi$
$102$	−3.81551e24	−0.297886
$103$	5.43797e23	0.0375813	0.0187906	−	0.999823i	$-0.494018\pi$
$103$	5.43797e23	0.0375813	0.0187906	+	0.999823i	$0.494018\pi$
$104$	5.33544e24	0.326778
$105$	0	0
$106$	−8.20316e24	−0.395966
$107$	1.45562e25	0.624816	0.312408	−	0.949948i	$-0.398864\pi$
$107$	1.45562e25	0.624816	0.312408	+	0.949948i	$0.398864\pi$
$108$	1.36140e25	0.520224
$109$	−3.33253e25	−1.13486	−0.567431	−	0.823421i	$-0.692063\pi$
$109$	−3.33253e25	−1.13486	−0.567431	+	0.823421i	$0.692063\pi$
$110$	0	0
$111$	−2.81154e25	−0.762794
$112$	−1.34759e25	−0.326839
$113$	−1.71253e25	−0.371670	−0.185835	−	0.982581i	$-0.559499\pi$
$113$	−1.71253e25	−0.371670	−0.185835	+	0.982581i	$0.559499\pi$
$114$	1.22505e25	0.238146
$115$	0	0
$116$	1.56066e25	0.244108
$117$	3.60891e25	0.507052
$118$	−8.20683e25	−1.03669
$119$	7.21131e25	0.819742
$120$	0	0
$121$	−1.08219e26	−0.998816
$122$	9.84225e25	0.819590
$123$	−6.33646e25	−0.476467
$124$	5.21741e25	0.354555
$125$	0	0
$126$	−9.11518e25	−0.507146
$127$	2.80916e26	1.41589	0.707947	−	0.706266i	$-0.249622\pi$
$127$	2.80916e26	1.41589	0.707947	+	0.706266i	$0.249622\pi$
$128$	−1.93428e25	−0.0883883
$129$	2.83275e26	1.17446
$130$	0	0
$131$	3.91683e26	1.33981	0.669906	−	0.742446i	$-0.266334\pi$
$131$	3.91683e26	1.33981	0.669906	+	0.742446i	$0.266334\pi$
$132$	−3.71655e24	−0.0115602
$133$	−2.31535e26	−0.655346
$134$	−2.32819e26	−0.600079
$135$	0	0
$136$	1.03508e26	0.221686
$137$	−7.30593e24	−0.0142780	−0.00713902	−	0.999975i	$-0.502272\pi$
$137$	−7.30593e24	−0.0142780	−0.00713902	+	0.999975i	$0.502272\pi$
$138$	−6.56916e25	−0.117225
$139$	9.32000e26	1.51961	0.759803	−	0.650154i	$-0.225295\pi$
$139$	9.32000e26	1.51961	0.759803	+	0.650154i	$0.225295\pi$
$140$	0	0
$141$	9.34233e26	1.27414
$142$	−8.46313e25	−0.105664
$143$	−2.78108e25	−0.0318063
$144$	−1.30836e26	−0.137150
$145$	0	0
$146$	−1.31419e27	−1.15943
$147$	−5.88172e26	−0.476472
$148$	7.62723e26	0.567670
$149$	−2.86893e27	−1.96287	−0.981434	−	0.191800i	$-0.938567\pi$
$149$	−2.86893e27	−1.96287	−0.981434	+	0.191800i	$0.938567\pi$
$150$	0	0
$151$	6.35122e26	0.367828	0.183914	−	0.982942i	$-0.441123\pi$
$151$	6.35122e26	0.367828	0.183914	+	0.982942i	$0.441123\pi$
$152$	−3.32335e26	−0.177228
$153$	7.00134e26	0.343984
$154$	7.02429e25	0.0318122
$155$	0	0
$156$	8.05577e26	0.310492
$157$	2.51786e27	0.895954	0.447977	−	0.894045i	$-0.352145\pi$
$157$	2.51786e27	0.895954	0.447977	+	0.894045i	$0.352145\pi$
$158$	1.75538e27	0.576977
$159$	−1.23856e27	−0.376231
$160$	0	0
$161$	1.24157e27	0.322588
$162$	4.42374e26	0.106378
$163$	4.89494e26	0.108994	0.0544970	−	0.998514i	$-0.482644\pi$
$163$	4.89494e26	0.108994	0.0544970	+	0.998514i	$0.482644\pi$
$164$	1.71897e27	0.354586
$165$	0	0
$166$	−4.57963e27	−0.811856
$167$	−2.73255e27	−0.449378	−0.224689	−	0.974430i	$-0.572137\pi$
$167$	−2.73255e27	−0.449378	−0.224689	+	0.974430i	$0.572137\pi$
$168$	−2.03468e27	−0.310549
$169$	−1.02831e27	−0.145727
$170$	0	0
$171$	−2.24793e27	−0.274999
$172$	−7.68478e27	−0.874029
$173$	−8.64082e27	−0.914069	−0.457034	−	0.889449i	$-0.651088\pi$
$173$	−8.64082e27	−0.914069	−0.457034	+	0.889449i	$0.651088\pi$
$174$	2.35637e27	0.231942
$175$	0	0
$176$	1.00824e26	0.00860310
$177$	−1.23912e28	−0.985025
$178$	−7.17441e27	−0.531540
$179$	−2.03598e28	−1.40640	−0.703201	−	0.710991i	$-0.748247\pi$
$179$	−2.03598e28	−1.40640	−0.703201	+	0.710991i	$0.748247\pi$
$180$	0	0
$181$	1.34351e28	0.807718	0.403859	−	0.914821i	$-0.367669\pi$
$181$	1.34351e28	0.807718	0.403859	+	0.914821i	$0.367669\pi$
$182$	−1.52254e28	−0.854431
$183$	1.48604e28	0.778741
$184$	1.78210e27	0.0872388
$185$	0	0
$186$	7.87757e27	0.336884
$187$	−5.39533e26	−0.0215774
$188$	−2.53441e28	−0.948210
$189$	−3.88496e28	−1.36024
$190$	0	0
$191$	−1.46283e28	−0.449030	−0.224515	−	0.974471i	$-0.572080\pi$
$191$	−1.46283e28	−0.449030	−0.224515	+	0.974471i	$0.572080\pi$
$192$	−2.92050e27	−0.0839830
$193$	−3.37927e28	−0.910659	−0.455330	−	0.890323i	$-0.650479\pi$
$193$	−3.37927e28	−0.910659	−0.455330	+	0.890323i	$0.650479\pi$
$194$	−5.27113e28	−1.33163
$195$	0	0
$196$	1.59561e28	0.354590
$197$	5.93119e28	1.23684	0.618420	−	0.785847i	$-0.287773\pi$
$197$	5.93119e28	1.23684	0.618420	+	0.785847i	$0.287773\pi$
$198$	6.81976e26	0.0133492
$199$	−1.85919e28	−0.341712	−0.170856	−	0.985296i	$-0.554653\pi$
$199$	−1.85919e28	−0.341712	−0.170856	+	0.985296i	$0.554653\pi$
$200$	0	0
$201$	−3.51525e28	−0.570171
$202$	1.31144e28	0.199920
$203$	−4.45355e28	−0.638272
$204$	1.56283e28	0.210637
$205$	0	0
$206$	−2.22739e27	−0.0265740
$207$	1.20542e28	0.135366
$208$	−2.18540e28	−0.231067
$209$	1.73229e27	0.0172501
$210$	0	0
$211$	1.59544e29	1.41042	0.705212	−	0.708996i	$-0.250852\pi$
$211$	1.59544e29	1.41042	0.705212	+	0.708996i	$0.250852\pi$
$212$	3.36001e28	0.279990
$213$	−1.27782e28	−0.100398
$214$	−5.96224e28	−0.441812
$215$	0	0
$216$	−5.57631e28	−0.367854
$217$	−1.48886e29	−0.927060
$218$	1.36501e29	0.802469
$219$	−1.98424e29	−1.10165
$220$	0	0
$221$	1.16946e29	0.579538
$222$	1.15161e29	0.539377
$223$	−2.93272e29	−1.29855	−0.649277	−	0.760552i	$-0.724928\pi$
$223$	−2.93272e29	−1.29855	−0.649277	+	0.760552i	$0.724928\pi$
$224$	5.51975e28	0.231110
$225$	0	0
$226$	7.01452e28	0.262810
$227$	−2.86033e29	−1.01413	−0.507065	−	0.861908i	$-0.669270\pi$
$227$	−2.86033e29	−1.01413	−0.507065	+	0.861908i	$0.669270\pi$
$228$	−5.01780e28	−0.168395
$229$	−2.27815e29	−0.723833	−0.361916	−	0.932211i	$-0.617877\pi$
$229$	−2.27815e29	−0.723833	−0.361916	+	0.932211i	$0.617877\pi$
$230$	0	0
$231$	1.06057e28	0.0302267
$232$	−6.39244e28	−0.172610
$233$	−6.95835e29	−1.78056	−0.890281	−	0.455411i	$-0.849492\pi$
$233$	−6.95835e29	−1.78056	−0.890281	+	0.455411i	$0.849492\pi$
$234$	−1.47821e29	−0.358540
$235$	0	0
$236$	3.36152e29	0.733053
$237$	2.65039e29	0.548220
$238$	−2.95375e29	−0.579645
$239$	1.46812e29	0.273393	0.136696	−	0.990613i	$-0.456352\pi$
$239$	1.46812e29	0.273393	0.136696	+	0.990613i	$0.456352\pi$
$240$	0	0
$241$	7.86832e29	1.32029	0.660144	−	0.751139i	$-0.270495\pi$
$241$	7.86832e29	1.32029	0.660144	+	0.751139i	$0.270495\pi$
$242$	4.43264e29	0.706269
$243$	−6.20749e29	−0.939372
$244$	−4.03139e29	−0.579538
$245$	0	0
$246$	2.59541e29	0.336913
$247$	−3.75480e29	−0.463313
$248$	−2.13705e29	−0.250708
$249$	−6.91461e29	−0.771393
$250$	0	0
$251$	−1.30352e30	−1.31582	−0.657910	−	0.753097i	$-0.728559\pi$
$251$	−1.30352e30	−1.31582	−0.657910	+	0.753097i	$0.728559\pi$
$252$	3.73358e29	0.358607
$253$	−9.28916e27	−0.00849121
$254$	−1.15063e30	−1.00119
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	2.21600e30	1.66496	0.832482	−	0.554052i	$-0.186919\pi$
$257$	2.21600e30	1.66496	0.832482	+	0.554052i	$0.186919\pi$
$258$	−1.16030e30	−0.830467
$259$	−2.17654e30	−1.48429
$260$	0	0
$261$	−4.32387e29	−0.267835
$262$	−1.60433e30	−0.947390
$263$	−3.37258e29	−0.189896	−0.0949479	−	0.995482i	$-0.530268\pi$
$263$	−3.37258e29	−0.189896	−0.0949479	+	0.995482i	$0.530268\pi$
$264$	1.52230e28	0.00817431
$265$	0	0
$266$	9.48366e29	0.463399
$267$	−1.08324e30	−0.505048
$268$	9.53627e29	0.424320
$269$	−4.13865e30	−1.75774	−0.878871	−	0.477059i	$-0.841703\pi$
$269$	−4.13865e30	−1.75774	−0.878871	+	0.477059i	$0.841703\pi$
$270$	0	0
$271$	2.28080e29	0.0883021	0.0441511	−	0.999025i	$-0.485942\pi$
$271$	2.28080e29	0.0883021	0.0441511	+	0.999025i	$0.485942\pi$
$272$	−4.23970e29	−0.156756
$273$	−2.29883e30	−0.811846
$274$	2.99251e28	0.0100961
$275$	0	0
$276$	2.69073e29	0.0828908
$277$	−3.78637e30	−1.11487	−0.557437	−	0.830219i	$-0.688215\pi$
$277$	−3.78637e30	−1.11487	−0.557437	+	0.830219i	$0.688215\pi$
$278$	−3.81747e30	−1.07452
$279$	−1.44551e30	−0.389017
$280$	0	0
$281$	4.87412e30	1.19969	0.599843	−	0.800118i	$-0.295230\pi$
$281$	4.87412e30	1.19969	0.599843	+	0.800118i	$0.295230\pi$
$282$	−3.82662e30	−0.900951
$283$	7.79414e29	0.175565	0.0877825	−	0.996140i	$-0.472022\pi$
$283$	7.79414e29	0.175565	0.0877825	+	0.996140i	$0.472022\pi$
$284$	3.46650e29	0.0747156
$285$	0	0
$286$	1.13913e29	0.0224904
$287$	−4.90534e30	−0.927140
$288$	5.35902e29	0.0969794
$289$	−3.50186e30	−0.606842
$290$	0	0
$291$	−7.95868e30	−1.26526
$292$	5.38290e30	0.819843
$293$	−8.97738e30	−1.31010	−0.655050	−	0.755586i	$-0.727352\pi$
$293$	−8.97738e30	−1.31010	−0.655050	+	0.755586i	$0.727352\pi$
$294$	2.40915e30	0.336917
$295$	0	0
$296$	−3.12412e30	−0.401403
$297$	2.90664e29	0.0358043
$298$	1.17511e31	1.38796
$299$	2.01346e30	0.228062
$300$	0	0
$301$	2.19296e31	2.28533
$302$	−2.60146e30	−0.260094
$303$	1.98009e30	0.189956
$304$	1.36125e30	0.125319
$305$	0	0
$306$	−2.86775e30	−0.243233
$307$	1.03718e31	0.844547	0.422274	−	0.906468i	$-0.361232\pi$
$307$	1.03718e31	0.844547	0.422274	+	0.906468i	$0.361232\pi$
$308$	−2.87715e29	−0.0224946
$309$	−3.36306e29	−0.0252495
$310$	0	0
$311$	−3.85228e30	−0.266817	−0.133408	−	0.991061i	$-0.542592\pi$
$311$	−3.85228e30	−0.266817	−0.133408	+	0.991061i	$0.542592\pi$
$312$	−3.29965e30	−0.219551
$313$	2.63756e31	1.68616	0.843079	−	0.537789i	$-0.180740\pi$
$313$	2.63756e31	1.68616	0.843079	+	0.537789i	$0.180740\pi$
$314$	−1.03132e31	−0.633535
$315$	0	0
$316$	−7.19006e30	−0.407985
$317$	3.65330e30	0.199271	0.0996355	−	0.995024i	$-0.468232\pi$
$317$	3.65330e30	0.199271	0.0996355	+	0.995024i	$0.468232\pi$
$318$	5.07316e30	0.266035
$319$	3.33204e29	0.0168007
$320$	0	0
$321$	−9.00216e30	−0.419792
$322$	−5.08548e30	−0.228104
$323$	−7.28436e30	−0.314311
$324$	−1.81196e30	−0.0752206
$325$	0	0
$326$	−2.00497e30	−0.0770703
$327$	2.06097e31	0.762474
$328$	−7.04092e30	−0.250730
$329$	7.23231e31	2.47930
$330$	0	0
$331$	−2.52293e31	−0.801781	−0.400890	−	0.916126i	$-0.631299\pi$
$331$	−2.52293e31	−0.801781	−0.400890	+	0.916126i	$0.631299\pi$
$332$	1.87582e31	0.574069
$333$	−2.11316e31	−0.622845
$334$	1.11925e31	0.317759
$335$	0	0
$336$	8.33405e30	0.219591
$337$	2.57479e31	0.653684	0.326842	−	0.945079i	$-0.394015\pi$
$337$	2.57479e31	0.653684	0.326842	+	0.945079i	$0.394015\pi$
$338$	4.21196e30	0.103045
$339$	1.05910e31	0.249712
$340$	0	0
$341$	1.11393e30	0.0244022
$342$	9.20751e30	0.194454
$343$	1.86722e31	0.380206
$344$	3.14769e31	0.618032
$345$	0	0
$346$	3.53928e31	0.646344
$347$	1.71059e31	0.301319	0.150660	−	0.988586i	$-0.451860\pi$
$347$	1.71059e31	0.301319	0.150660	+	0.988586i	$0.451860\pi$
$348$	−9.65171e30	−0.164007
$349$	6.93560e31	1.13702	0.568508	−	0.822678i	$-0.307521\pi$
$349$	6.93560e31	1.13702	0.568508	+	0.822678i	$0.307521\pi$
$350$	0	0
$351$	−6.30025e31	−0.961653
$352$	−4.12974e29	−0.00608331
$353$	−1.22234e31	−0.173783	−0.0868914	−	0.996218i	$-0.527693\pi$
$353$	−1.22234e31	−0.173783	−0.0868914	+	0.996218i	$0.527693\pi$
$354$	5.07543e31	0.696518
$355$	0	0
$356$	2.93864e31	0.375856
$357$	−4.45976e31	−0.550755
$358$	8.33936e31	0.994477
$359$	5.26279e31	0.606087	0.303044	−	0.952977i	$-0.401997\pi$
$359$	5.26279e31	0.606087	0.303044	+	0.952977i	$0.401997\pi$
$360$	0	0
$361$	−6.96885e31	−0.748723
$362$	−5.50303e31	−0.571143
$363$	6.69267e31	0.671069
$364$	6.23633e31	0.604174
$365$	0	0
$366$	−6.08684e31	−0.550653
$367$	1.04735e31	0.0915729	0.0457864	−	0.998951i	$-0.485421\pi$
$367$	1.04735e31	0.0915729	0.0457864	+	0.998951i	$0.485421\pi$
$368$	−7.29949e30	−0.0616872
$369$	−4.76250e31	−0.389050
$370$	0	0
$371$	−9.58828e31	−0.732094
$372$	−3.22665e31	−0.238213
$373$	1.24978e32	0.892221	0.446111	−	0.894978i	$-0.352809\pi$
$373$	1.24978e32	0.892221	0.446111	+	0.894978i	$0.352809\pi$
$374$	2.20993e30	0.0152575
$375$	0	0
$376$	1.03810e32	0.670486
$377$	−7.22233e31	−0.451243
$378$	1.59128e32	0.961832
$379$	−1.71176e32	−1.00104	−0.500522	−	0.865724i	$-0.666859\pi$
$379$	−1.71176e32	−1.00104	−0.500522	+	0.865724i	$0.666859\pi$
$380$	0	0
$381$	−1.73730e32	−0.951288
$382$	5.99173e31	0.317512
$383$	2.63626e32	1.35209	0.676043	−	0.736862i	$-0.263693\pi$
$383$	2.63626e32	1.35209	0.676043	+	0.736862i	$0.263693\pi$
$384$	1.19624e31	0.0593850
$385$	0	0
$386$	1.38415e32	0.643933
$387$	2.12911e32	0.958982
$388$	2.15905e32	0.941601
$389$	3.01567e32	1.27354	0.636772	−	0.771052i	$-0.280269\pi$
$389$	3.01567e32	1.27354	0.636772	+	0.771052i	$0.280269\pi$
$390$	0	0
$391$	3.90614e31	0.154717
$392$	−6.53562e31	−0.250733
$393$	−2.42232e32	−0.900172
$394$	−2.42941e32	−0.874578
$395$	0	0
$396$	−2.79337e30	−0.00943929
$397$	−3.60886e32	−1.18165	−0.590824	−	0.806800i	$-0.701197\pi$
$397$	−3.60886e32	−1.18165	−0.590824	+	0.806800i	$0.701197\pi$
$398$	7.61523e31	0.241627
$399$	1.43190e32	0.440303
$400$	0	0
$401$	3.40848e32	0.984591	0.492295	−	0.870428i	$-0.336158\pi$
$401$	3.40848e32	0.984591	0.492295	+	0.870428i	$0.336158\pi$
$402$	1.43985e32	0.403172
$403$	−2.41449e32	−0.655409
$404$	−5.37166e31	−0.141365
$405$	0	0
$406$	1.82417e32	0.451327
$407$	1.62844e31	0.0390697
$408$	−6.40136e31	−0.148943
$409$	1.88820e32	0.426095	0.213048	−	0.977042i	$-0.431661\pi$
$409$	1.88820e32	0.426095	0.213048	+	0.977042i	$0.431661\pi$
$410$	0	0
$411$	4.51827e30	0.00959290
$412$	9.12340e30	0.0187906
$413$	−9.59257e32	−1.91672
$414$	−4.93741e31	−0.0957182
$415$	0	0
$416$	8.95138e31	0.163389
$417$	−5.76386e32	−1.02097
$418$	−7.09545e30	−0.0121977
$419$	−6.53498e32	−1.09036	−0.545179	−	0.838320i	$-0.683538\pi$
$419$	−6.53498e32	−1.09036	−0.545179	+	0.838320i	$0.683538\pi$
$420$	0	0
$421$	−8.06557e32	−1.26797	−0.633985	−	0.773345i	$-0.718582\pi$
$421$	−8.06557e32	−1.26797	−0.633985	+	0.773345i	$0.718582\pi$
$422$	−6.53492e32	−0.997321
$423$	7.02172e32	1.04037
$424$	−1.37626e32	−0.197983
$425$	0	0
$426$	5.23393e31	0.0709918
$427$	1.15041e33	1.51532
$428$	2.44213e32	0.312408
$429$	1.71993e31	0.0213695
$430$	0	0
$431$	−1.89617e32	−0.222285	−0.111143	−	0.993804i	$-0.535451\pi$
$431$	−1.89617e32	−0.222285	−0.111143	+	0.993804i	$0.535451\pi$
$432$	2.28406e32	0.260112
$433$	−1.55976e33	−1.72567	−0.862835	−	0.505485i	$-0.831313\pi$
$433$	−1.55976e33	−1.72567	−0.862835	+	0.505485i	$0.831313\pi$
$434$	6.09838e32	0.655530
$435$	0	0
$436$	−5.59106e32	−0.567431
$437$	−1.25415e32	−0.123689
$438$	8.12744e32	0.778982
$439$	−1.73749e33	−1.61851	−0.809254	−	0.587460i	$-0.800128\pi$
$439$	−1.73749e33	−1.61851	−0.809254	+	0.587460i	$0.800128\pi$
$440$	0	0
$441$	−4.42072e32	−0.389055
$442$	−4.79011e32	−0.409795
$443$	−2.09110e33	−1.73912	−0.869559	−	0.493830i	$-0.835597\pi$
$443$	−2.09110e33	−1.73912	−0.869559	+	0.493830i	$0.835597\pi$
$444$	−4.71698e32	−0.381397
$445$	0	0
$446$	1.20124e33	0.918216
$447$	1.77426e33	1.31878
$448$	−2.26089e32	−0.163419
$449$	−2.57391e32	−0.180932	−0.0904659	−	0.995900i	$-0.528836\pi$
$449$	−2.57391e32	−0.180932	−0.0904659	+	0.995900i	$0.528836\pi$
$450$	0	0
$451$	3.67006e31	0.0244043
$452$	−2.87315e32	−0.185835
$453$	−3.92785e32	−0.247131
$454$	1.17159e33	0.717098
$455$	0	0
$456$	2.05529e32	0.119073
$457$	3.29162e33	1.85548	0.927742	−	0.373222i	$-0.121747\pi$
$457$	3.29162e33	1.85548	0.927742	+	0.373222i	$0.121747\pi$
$458$	9.33129e32	0.511827
$459$	−1.22226e33	−0.652385
$460$	0	0
$461$	2.82594e33	1.42857	0.714286	−	0.699854i	$-0.246752\pi$
$461$	2.82594e33	1.42857	0.714286	+	0.699854i	$0.246752\pi$
$462$	−4.34410e31	−0.0213735
$463$	−3.15530e33	−1.51105	−0.755523	−	0.655122i	$-0.772617\pi$
$463$	−3.15530e33	−1.51105	−0.755523	+	0.655122i	$0.772617\pi$
$464$	2.61834e32	0.122054
$465$	0	0
$466$	2.85014e33	1.25905
$467$	−1.46352e33	−0.629417	−0.314709	−	0.949188i	$-0.601907\pi$
$467$	−1.46352e33	−0.629417	−0.314709	+	0.949188i	$0.601907\pi$
$468$	6.05475e32	0.253526
$469$	−2.72131e33	−1.10947
$470$	0	0
$471$	−1.55714e33	−0.601960
$472$	−1.37688e33	−0.518347
$473$	−1.64072e32	−0.0601549
$474$	−1.08560e33	−0.387650
$475$	0	0
$476$	1.20986e33	0.409871
$477$	−9.30909e32	−0.307204
$478$	−6.01341e32	−0.193318
$479$	−9.44658e31	−0.0295856	−0.0147928	−	0.999891i	$-0.504709\pi$
$479$	−9.44658e31	−0.0295856	−0.0147928	+	0.999891i	$0.504709\pi$
$480$	0	0
$481$	−3.52970e33	−1.04936
$482$	−3.22286e33	−0.933585
$483$	−7.67838e32	−0.216736
$484$	−1.81561e33	−0.499408
$485$	0	0
$486$	2.54259e33	0.664236
$487$	−2.95578e33	−0.752593	−0.376296	−	0.926499i	$-0.622803\pi$
$487$	−2.95578e33	−0.752593	−0.376296	+	0.926499i	$0.622803\pi$
$488$	1.65126e33	0.409795
$489$	−3.02722e32	−0.0732291
$490$	0	0
$491$	3.19357e33	0.734103	0.367052	−	0.930201i	$-0.380367\pi$
$491$	3.19357e33	0.734103	0.367052	+	0.930201i	$0.380367\pi$
$492$	−1.06308e33	−0.238233
$493$	−1.40114e33	−0.306123
$494$	1.53797e33	0.327612
$495$	0	0
$496$	8.75336e32	0.177278
$497$	−9.89214e32	−0.195360
$498$	2.83222e33	0.545457
$499$	−3.38640e33	−0.636036	−0.318018	−	0.948085i	$-0.603017\pi$
$499$	−3.38640e33	−0.636036	−0.318018	+	0.948085i	$0.603017\pi$
$500$	0	0
$501$	1.68992e33	0.301921
$502$	5.33922e33	0.930425
$503$	−6.76442e33	−1.14982	−0.574911	−	0.818216i	$-0.694963\pi$
$503$	−6.76442e33	−1.14982	−0.574911	+	0.818216i	$0.694963\pi$
$504$	−1.52927e33	−0.253573
$505$	0	0
$506$	3.80484e31	0.00600419
$507$	6.35948e32	0.0979089
$508$	4.71299e33	0.707947
$509$	6.69189e33	0.980791	0.490395	−	0.871500i	$-0.336852\pi$
$509$	6.69189e33	0.980791	0.490395	+	0.871500i	$0.336852\pi$
$510$	0	0
$511$	−1.53609e34	−2.14365
$512$	−3.24519e32	−0.0441942
$513$	3.92432e33	0.521551
$514$	−9.07672e33	−1.17731
$515$	0	0
$516$	4.75257e33	0.587229
$517$	−5.41105e32	−0.0652603
$518$	8.91511e33	1.04955
$519$	5.34383e33	0.614130
$520$	0	0
$521$	−1.12229e34	−1.22923	−0.614616	−	0.788826i	$-0.710689\pi$
$521$	−1.12229e34	−1.22923	−0.614616	+	0.788826i	$0.710689\pi$
$522$	1.77106e33	0.189388
$523$	−7.35349e33	−0.767754	−0.383877	−	0.923384i	$-0.625411\pi$
$523$	−7.35349e33	−0.767754	−0.383877	+	0.923384i	$0.625411\pi$
$524$	6.57136e33	0.669906
$525$	0	0
$526$	1.38141e33	0.134277
$527$	−4.68414e33	−0.444628
$528$	−6.23534e31	−0.00578011
$529$	−1.03732e34	−0.939115
$530$	0	0
$531$	−9.31326e33	−0.804304
$532$	−3.88451e33	−0.327673
$533$	−7.95499e33	−0.655465
$534$	4.43694e33	0.357123
$535$	0	0
$536$	−3.90606e33	−0.300040
$537$	1.25913e34	0.944912
$538$	1.69519e34	1.24291
$539$	3.40667e32	0.0244046
$540$	0	0
$541$	6.91384e32	0.0472883	0.0236441	−	0.999720i	$-0.492473\pi$
$541$	6.91384e32	0.0472883	0.0236441	+	0.999720i	$0.492473\pi$
$542$	−9.34216e32	−0.0624390
$543$	−8.30881e33	−0.542677
$544$	1.73658e33	0.110843
$545$	0	0
$546$	9.41600e33	0.574062
$547$	−1.40577e34	−0.837672	−0.418836	−	0.908062i	$-0.637562\pi$
$547$	−1.40577e34	−0.837672	−0.418836	+	0.908062i	$0.637562\pi$
$548$	−1.22573e32	−0.00713902
$549$	1.11692e34	0.635867
$550$	0	0
$551$	4.49866e33	0.244731
$552$	−1.10212e33	−0.0586127
$553$	2.05178e34	1.06676
$554$	1.55090e34	0.788335
$555$	0	0
$556$	1.56364e34	0.759803
$557$	2.49292e34	1.18445	0.592227	−	0.805771i	$-0.298249\pi$
$557$	2.49292e34	1.18445	0.592227	+	0.805771i	$0.298249\pi$
$558$	5.92081e33	0.275076
$559$	3.55633e34	1.61568
$560$	0	0
$561$	3.33669e32	0.0144971
$562$	−1.99644e34	−0.848306
$563$	1.70240e34	0.707466	0.353733	−	0.935346i	$-0.384912\pi$
$563$	1.70240e34	0.707466	0.353733	+	0.935346i	$0.384912\pi$
$564$	1.56738e34	0.637068
$565$	0	0
$566$	−3.19248e33	−0.124143
$567$	5.17070e33	0.196680
$568$	−1.41988e33	−0.0528319
$569$	1.90307e34	0.692709	0.346355	−	0.938104i	$-0.387419\pi$
$569$	1.90307e34	0.692709	0.346355	+	0.938104i	$0.387419\pi$
$570$	0	0
$571$	2.13655e34	0.744323	0.372162	−	0.928168i	$-0.378617\pi$
$571$	2.13655e34	0.744323	0.372162	+	0.928168i	$0.378617\pi$
$572$	−4.66588e32	−0.0159031
$573$	9.04669e33	0.301687
$574$	2.00923e34	0.655587
$575$	0	0
$576$	−2.19506e33	−0.0685748
$577$	2.06745e34	0.632030	0.316015	−	0.948754i	$-0.397655\pi$
$577$	2.06745e34	0.632030	0.316015	+	0.948754i	$0.397655\pi$
$578$	1.43436e34	0.429102
$579$	2.08987e34	0.611839
$580$	0	0
$581$	−5.35291e34	−1.50103
$582$	3.25988e34	0.894672
$583$	7.17372e32	0.0192703
$584$	−2.20484e34	−0.579717
$585$	0	0
$586$	3.67713e34	0.926380
$587$	5.55725e34	1.37052	0.685258	−	0.728301i	$-0.259690\pi$
$587$	5.55725e34	1.37052	0.685258	+	0.728301i	$0.259690\pi$
$588$	−9.86789e33	−0.238236
$589$	1.50394e34	0.355460
$590$	0	0
$591$	−3.66808e34	−0.830989
$592$	1.27964e34	0.283835
$593$	6.93628e34	1.50641	0.753204	−	0.657787i	$-0.228507\pi$
$593$	6.93628e34	1.50641	0.753204	+	0.657787i	$0.228507\pi$
$594$	−1.19056e33	−0.0253175
$595$	0	0
$596$	−4.81326e34	−0.981434
$597$	1.14979e34	0.229584
$598$	−8.24713e33	−0.161264
$599$	−3.28492e34	−0.629056	−0.314528	−	0.949248i	$-0.601846\pi$
$599$	−3.28492e34	−0.629056	−0.314528	+	0.949248i	$0.601846\pi$
$600$	0	0
$601$	−2.89648e34	−0.532034	−0.266017	−	0.963968i	$-0.585708\pi$
$601$	−2.89648e34	−0.532034	−0.266017	+	0.963968i	$0.585708\pi$
$602$	−8.98237e34	−1.61598
$603$	−2.64207e34	−0.465563
$604$	1.06556e34	0.183914
$605$	0	0
$606$	−8.11046e33	−0.134319
$607$	−8.42327e34	−1.36654	−0.683270	−	0.730166i	$-0.739443\pi$
$607$	−8.42327e34	−1.36654	−0.683270	+	0.730166i	$0.739443\pi$
$608$	−5.57566e33	−0.0886138
$609$	2.75425e34	0.428832
$610$	0	0
$611$	1.17286e35	1.75280
$612$	1.17463e34	0.171992
$613$	−1.08389e34	−0.155499	−0.0777496	−	0.996973i	$-0.524773\pi$
$613$	−1.08389e34	−0.155499	−0.0777496	+	0.996973i	$0.524773\pi$
$614$	−4.24829e34	−0.597185
$615$	0	0
$616$	1.17848e33	0.0159061
$617$	−7.99721e33	−0.105773	−0.0528864	−	0.998601i	$-0.516842\pi$
$617$	−7.99721e33	−0.105773	−0.0528864	+	0.998601i	$0.516842\pi$
$618$	1.37751e33	0.0178541
$619$	−6.34272e34	−0.805643	−0.402822	−	0.915279i	$-0.631970\pi$
$619$	−6.34272e34	−0.805643	−0.402822	+	0.915279i	$0.631970\pi$
$620$	0	0
$621$	−2.10436e34	−0.256729
$622$	1.57789e34	0.188668
$623$	−8.38582e34	−0.982755
$624$	1.35153e34	0.155246
$625$	0	0
$626$	−1.08035e35	−1.19229
$627$	−1.07131e33	−0.0115897
$628$	4.22427e34	0.447977
$629$	−6.84766e34	−0.711884
$630$	0	0
$631$	1.41569e35	1.41449	0.707245	−	0.706968i	$-0.249938\pi$
$631$	1.41569e35	1.41449	0.707245	+	0.706968i	$0.249938\pi$
$632$	2.94505e34	0.288489
$633$	−9.86683e34	−0.947614
$634$	−1.49639e34	−0.140906
$635$	0	0
$636$	−2.07797e34	−0.188115
$637$	−7.38409e34	−0.655472
$638$	−1.36480e33	−0.0118799
$639$	−9.60410e33	−0.0819778
$640$	0	0
$641$	−4.50631e34	−0.369910	−0.184955	−	0.982747i	$-0.559214\pi$
$641$	−4.50631e34	−0.369910	−0.184955	+	0.982747i	$0.559214\pi$
$642$	3.68728e34	0.296837
$643$	−1.18877e35	−0.938561	−0.469280	−	0.883049i	$-0.655487\pi$
$643$	−1.18877e35	−0.938561	−0.469280	+	0.883049i	$0.655487\pi$
$644$	2.08301e34	0.161294
$645$	0	0
$646$	2.98367e34	0.222252
$647$	−1.85298e34	−0.135384	−0.0676921	−	0.997706i	$-0.521564\pi$
$647$	−1.85298e34	−0.135384	−0.0676921	+	0.997706i	$0.521564\pi$
$648$	7.42181e33	0.0531890
$649$	7.17694e33	0.0504522
$650$	0	0
$651$	9.20771e34	0.622858
$652$	8.21234e33	0.0544970
$653$	1.84607e35	1.20180	0.600902	−	0.799323i	$-0.294808\pi$
$653$	1.84607e35	1.20180	0.600902	+	0.799323i	$0.294808\pi$
$654$	−8.44173e34	−0.539150
$655$	0	0
$656$	2.88396e34	0.177293
$657$	−1.49136e35	−0.899530
$658$	−2.96235e35	−1.75313
$659$	−3.04390e35	−1.76752	−0.883758	−	0.467944i	$-0.844995\pi$
$659$	−3.04390e35	−1.76752	−0.883758	+	0.467944i	$0.844995\pi$
$660$	0	0
$661$	2.88465e34	0.161278	0.0806389	−	0.996743i	$-0.474304\pi$
$661$	2.88465e34	0.161278	0.0806389	+	0.996743i	$0.474304\pi$
$662$	1.03339e35	0.566945
$663$	−7.23240e34	−0.389371
$664$	−7.68334e34	−0.405928
$665$	0	0
$666$	8.65552e34	0.440418
$667$	−2.41235e34	−0.120467
$668$	−4.58446e34	−0.224689
$669$	1.81371e35	0.872452
$670$	0	0
$671$	−8.60712e33	−0.0398865
$672$	−3.41363e34	−0.155275
$673$	6.39436e34	0.285502	0.142751	−	0.989759i	$-0.454405\pi$
$673$	6.39436e34	0.285502	0.142751	+	0.989759i	$0.454405\pi$
$674$	−1.05463e35	−0.462225
$675$	0	0
$676$	−1.72522e34	−0.0728636
$677$	−6.00220e34	−0.248858	−0.124429	−	0.992229i	$-0.539710\pi$
$677$	−6.00220e34	−0.248858	−0.124429	+	0.992229i	$0.539710\pi$
$678$	−4.33806e34	−0.176573
$679$	−6.16117e35	−2.46202
$680$	0	0
$681$	1.76894e35	0.681358
$682$	−4.56266e33	−0.0172549
$683$	3.76829e35	1.39922	0.699610	−	0.714525i	$-0.253357\pi$
$683$	3.76829e35	1.39922	0.699610	+	0.714525i	$0.253357\pi$
$684$	−3.77140e34	−0.137499
$685$	0	0
$686$	−7.64813e34	−0.268846
$687$	1.40890e35	0.486317
$688$	−1.28929e35	−0.437015
$689$	−1.55493e35	−0.517572
$690$	0	0
$691$	−3.26709e35	−1.04878	−0.524392	−	0.851477i	$-0.675707\pi$
$691$	−3.26709e35	−1.04878	−0.524392	+	0.851477i	$0.675707\pi$
$692$	−1.44969e35	−0.457034
$693$	7.97129e33	0.0246810
$694$	−7.00657e34	−0.213065
$695$	0	0
$696$	3.95334e34	0.115971
$697$	−1.54328e35	−0.444667
$698$	−2.84082e35	−0.803991
$699$	4.30332e35	1.19630
$700$	0	0
$701$	3.88741e35	1.04276	0.521381	−	0.853324i	$-0.325417\pi$
$701$	3.88741e35	1.04276	0.521381	+	0.853324i	$0.325417\pi$
$702$	2.58058e35	0.679992
$703$	2.19859e35	0.569118
$704$	1.69154e33	0.00430155
$705$	0	0
$706$	5.00669e34	0.122883
$707$	1.53288e35	0.369628
$708$	−2.07890e35	−0.492512
$709$	4.23533e35	0.985848	0.492924	−	0.870072i	$-0.335928\pi$
$709$	4.23533e35	0.985848	0.492924	+	0.870072i	$0.335928\pi$
$710$	0	0
$711$	1.99204e35	0.447639
$712$	−1.20367e35	−0.265770
$713$	−8.06469e34	−0.174972
$714$	1.82672e35	0.389443
$715$	0	0
$716$	−3.41580e35	−0.703201
$717$	−9.07941e34	−0.183683
$718$	−2.15564e35	−0.428568
$719$	6.21554e35	1.21442	0.607208	−	0.794543i	$-0.292289\pi$
$719$	6.21554e35	1.21442	0.607208	+	0.794543i	$0.292289\pi$
$720$	0	0
$721$	−2.60349e34	−0.0491321
$722$	2.85444e35	0.529427
$723$	−4.86608e35	−0.887055
$724$	2.25404e35	0.403859
$725$	0	0
$726$	−2.74132e35	−0.474517
$727$	4.24475e35	0.722225	0.361112	−	0.932522i	$-0.382397\pi$
$727$	4.24475e35	0.722225	0.361112	+	0.932522i	$0.382397\pi$
$728$	−2.55440e35	−0.427216
$729$	4.75404e35	0.781572
$730$	0	0
$731$	6.89932e35	1.09607
$732$	2.49317e35	0.389371
$733$	−7.04925e34	−0.108229	−0.0541145	−	0.998535i	$-0.517234\pi$
$733$	−7.04925e34	−0.108229	−0.0541145	+	0.998535i	$0.517234\pi$
$734$	−4.28995e34	−0.0647518
$735$	0	0
$736$	2.98987e34	0.0436194
$737$	2.03602e34	0.0292037
$738$	1.95072e35	0.275100
$739$	−9.55082e35	−1.32430	−0.662148	−	0.749373i	$-0.730355\pi$
$739$	−9.55082e35	−1.32430	−0.662148	+	0.749373i	$0.730355\pi$
$740$	0	0
$741$	2.32212e35	0.311284
$742$	3.92736e35	0.517668
$743$	1.29129e35	0.167364	0.0836820	−	0.996493i	$-0.473332\pi$
$743$	1.29129e35	0.167364	0.0836820	+	0.996493i	$0.473332\pi$
$744$	1.32164e35	0.168442
$745$	0	0
$746$	−5.11909e35	−0.630896
$747$	−5.19704e35	−0.629867
$748$	−9.05187e33	−0.0107887
$749$	−6.96897e35	−0.816857
$750$	0	0
$751$	−1.00002e36	−1.13373	−0.566864	−	0.823812i	$-0.691843\pi$
$751$	−1.00002e36	−1.13373	−0.566864	+	0.823812i	$0.691843\pi$
$752$	−4.25204e35	−0.474105
$753$	8.06149e35	0.884052
$754$	2.95827e35	0.319077
$755$	0	0
$756$	−6.51788e35	−0.680118
$757$	4.62323e35	0.474511	0.237256	−	0.971447i	$-0.423752\pi$
$757$	4.62323e35	0.474511	0.237256	+	0.971447i	$0.423752\pi$
$758$	7.01138e35	0.707846
$759$	5.74478e33	0.00570494
$760$	0	0
$761$	1.71968e36	1.65249	0.826247	−	0.563308i	$-0.190471\pi$
$761$	1.71968e36	1.65249	0.826247	+	0.563308i	$0.190471\pi$
$762$	7.11597e35	0.672662
$763$	1.59549e36	1.48367
$764$	−2.45421e35	−0.224515
$765$	0	0
$766$	−1.07981e36	−0.956069
$767$	−1.55563e36	−1.35508
$768$	−4.89978e34	−0.0419915
$769$	1.91462e36	1.61437	0.807184	−	0.590299i	$-0.200990\pi$
$769$	1.91462e36	1.61437	0.807184	+	0.590299i	$0.200990\pi$
$770$	0	0
$771$	−1.37046e36	−1.11863
$772$	−5.66947e35	−0.455330
$773$	9.08398e35	0.717848	0.358924	−	0.933367i	$-0.383144\pi$
$773$	9.08398e35	0.717848	0.358924	+	0.933367i	$0.383144\pi$
$774$	−8.72082e35	−0.678103
$775$	0	0
$776$	−8.84349e35	−0.665813
$777$	1.34606e36	0.997243
$778$	−1.23522e36	−0.900532
$779$	4.95503e35	0.355490
$780$	0	0
$781$	7.40106e33	0.00514229
$782$	−1.59995e35	−0.109402
$783$	7.54839e35	0.507963
$784$	2.67699e35	0.177295
$785$	0	0
$786$	9.92184e35	0.636518
$787$	−5.77613e35	−0.364714	−0.182357	−	0.983232i	$-0.558373\pi$
$787$	−5.77613e35	−0.364714	−0.182357	+	0.983232i	$0.558373\pi$
$788$	9.95088e35	0.618420
$789$	2.08574e35	0.127584
$790$	0	0
$791$	8.19893e35	0.485905
$792$	1.14417e34	0.00667459
$793$	1.86563e36	1.07130
$794$	1.47819e36	0.835552
$795$	0	0
$796$	−3.11920e35	−0.170856
$797$	−1.37116e36	−0.739364	−0.369682	−	0.929158i	$-0.620533\pi$
$797$	−1.37116e36	−0.739364	−0.369682	+	0.929158i	$0.620533\pi$
$798$	−5.86507e35	−0.311341
$799$	2.27537e36	1.18910
$800$	0	0
$801$	−8.14165e35	−0.412388
$802$	−1.39611e36	−0.696211
$803$	1.14926e35	0.0564255
$804$	−5.89761e35	−0.285085
$805$	0	0
$806$	9.88975e35	0.463444
$807$	2.55951e36	1.18096
$808$	2.20023e35	0.0999600
$809$	3.58962e36	1.60580	0.802902	−	0.596111i	$-0.203288\pi$
$809$	3.58962e36	1.60580	0.802902	+	0.596111i	$0.203288\pi$
$810$	0	0
$811$	1.03429e35	0.0448624	0.0224312	−	0.999748i	$-0.492859\pi$
$811$	1.03429e35	0.0448624	0.0224312	+	0.999748i	$0.492859\pi$
$812$	−7.47182e35	−0.319136
$813$	−1.41054e35	−0.0593270
$814$	−6.67007e34	−0.0276265
$815$	0	0
$816$	2.62200e35	0.105319
$817$	−2.21518e36	−0.876259
$818$	−7.73407e35	−0.301295
$819$	−1.72781e36	−0.662898
$820$	0	0
$821$	−2.70025e36	−1.00488	−0.502439	−	0.864612i	$-0.667564\pi$
$821$	−2.70025e36	−1.00488	−0.502439	+	0.864612i	$0.667564\pi$
$822$	−1.85069e34	−0.00678320
$823$	2.53917e36	0.916630	0.458315	−	0.888790i	$-0.348453\pi$
$823$	2.53917e36	0.916630	0.458315	+	0.888790i	$0.348453\pi$
$824$	−3.73695e34	−0.0132870
$825$	0	0
$826$	3.92912e36	1.35533
$827$	−2.67322e36	−0.908270	−0.454135	−	0.890933i	$-0.650052\pi$
$827$	−2.67322e36	−0.908270	−0.454135	+	0.890933i	$0.650052\pi$
$828$	2.02236e35	0.0676830
$829$	−5.79155e36	−1.90925	−0.954626	−	0.297806i	$-0.903745\pi$
$829$	−5.79155e36	−1.90925	−0.954626	+	0.297806i	$0.903745\pi$
$830$	0	0
$831$	2.34164e36	0.749044
$832$	−3.66648e35	−0.115534
$833$	−1.43252e36	−0.444672
$834$	2.36088e36	0.721934
$835$	0	0
$836$	2.90630e34	0.00862504
$837$	2.52349e36	0.737792
$838$	2.67673e36	0.770999
$839$	−2.27845e36	−0.646568	−0.323284	−	0.946302i	$-0.604787\pi$
$839$	−2.27845e36	−0.646568	−0.323284	+	0.946302i	$0.604787\pi$
$840$	0	0
$841$	−2.76505e36	−0.761645
$842$	3.30366e36	0.896590
$843$	−3.01435e36	−0.806026
$844$	2.67671e36	0.705212
$845$	0	0
$846$	−2.87610e36	−0.735655
$847$	5.18110e36	1.30581
$848$	5.63717e35	0.139995
$849$	−4.82020e35	−0.117956
$850$	0	0
$851$	−1.17896e36	−0.280144
$852$	−2.14382e35	−0.0501988
$853$	−3.72321e36	−0.859122	−0.429561	−	0.903038i	$-0.641332\pi$
$853$	−3.72321e36	−0.859122	−0.429561	+	0.903038i	$0.641332\pi$
$854$	−4.71209e36	−1.07150
$855$	0	0
$856$	−1.00030e36	−0.220906
$857$	−1.02353e36	−0.222761	−0.111381	−	0.993778i	$-0.535527\pi$
$857$	−1.02353e36	−0.222761	−0.111381	+	0.993778i	$0.535527\pi$
$858$	−7.04483e34	−0.0151105
$859$	1.85947e36	0.393074	0.196537	−	0.980496i	$-0.437030\pi$
$859$	1.85947e36	0.393074	0.196537	+	0.980496i	$0.437030\pi$
$860$	0	0
$861$	3.03365e36	0.622912
$862$	7.76670e35	0.157180
$863$	−8.67106e36	−1.72957	−0.864783	−	0.502146i	$-0.832544\pi$
$863$	−8.67106e36	−1.72957	−0.864783	+	0.502146i	$0.832544\pi$
$864$	−9.35550e35	−0.183927
$865$	0	0
$866$	6.38876e36	1.22023
$867$	2.16569e36	0.407716
$868$	−2.49790e36	−0.463530
$869$	−1.53510e35	−0.0280794
$870$	0	0
$871$	−4.41315e36	−0.784372
$872$	2.29010e36	0.401235
$873$	−5.98177e36	−1.03312
$874$	5.13700e35	0.0874614
$875$	0	0
$876$	−3.32900e36	−0.550823
$877$	7.14177e36	1.16496	0.582480	−	0.812845i	$-0.302082\pi$
$877$	7.14177e36	1.16496	0.582480	+	0.812845i	$0.302082\pi$
$878$	7.11674e36	1.14446
$879$	5.55196e36	0.880209
$880$	0	0
$881$	−3.00182e36	−0.462579	−0.231290	−	0.972885i	$-0.574294\pi$
$881$	−3.00182e36	−0.462579	−0.231290	+	0.972885i	$0.574294\pi$
$882$	1.81073e36	0.275103
$883$	2.65767e36	0.398100	0.199050	−	0.979989i	$-0.436214\pi$
$883$	2.65767e36	0.398100	0.199050	+	0.979989i	$0.436214\pi$
$884$	1.96203e36	0.289769
$885$	0	0
$886$	8.56516e36	1.22974
$887$	−2.39194e36	−0.338613	−0.169307	−	0.985563i	$-0.554153\pi$
$887$	−2.39194e36	−0.338613	−0.169307	+	0.985563i	$0.554153\pi$
$888$	1.93208e36	0.269688
$889$	−1.34492e37	−1.85108
$890$	0	0
$891$	−3.86859e34	−0.00517704
$892$	−4.92029e36	−0.649277
$893$	−7.30557e36	−0.950629
$894$	−7.26736e36	−0.932519
$895$	0	0
$896$	9.26060e35	0.115555
$897$	−1.24520e36	−0.153227
$898$	1.05428e36	0.127938
$899$	2.89282e36	0.346199
$900$	0	0
$901$	−3.01659e36	−0.351121
$902$	−1.50326e35	−0.0172564
$903$	−1.35621e37	−1.53543
$904$	1.17684e36	0.131405
$905$	0	0
$906$	1.60885e36	0.174748
$907$	−1.27834e37	−1.36948	−0.684741	−	0.728787i	$-0.740085\pi$
$907$	−1.27834e37	−1.36948	−0.684741	+	0.728787i	$0.740085\pi$
$908$	−4.79885e36	−0.507065
$909$	1.48824e36	0.155105
$910$	0	0
$911$	1.51675e37	1.53792	0.768961	−	0.639296i	$-0.220774\pi$
$911$	1.51675e37	1.53792	0.768961	+	0.639296i	$0.220774\pi$
$912$	−8.41848e35	−0.0841973
$913$	4.00492e35	0.0395102
$914$	−1.34825e37	−1.31203
$915$	0	0
$916$	−3.82210e36	−0.361916
$917$	−1.87523e37	−1.75161
$918$	5.00636e36	0.461306
$919$	−1.63543e36	−0.148658	−0.0743292	−	0.997234i	$-0.523682\pi$
$919$	−1.63543e36	−0.148658	−0.0743292	+	0.997234i	$0.523682\pi$
$920$	0	0
$921$	−6.41432e36	−0.567421
$922$	−1.15751e37	−1.01015
$923$	−1.60421e36	−0.138115
$924$	1.77934e35	0.0151133
$925$	0	0
$926$	1.29241e37	1.06847
$927$	−2.52769e35	−0.0206170
$928$	−1.07247e36	−0.0863052
$929$	−7.47115e36	−0.593186	−0.296593	−	0.955004i	$-0.595850\pi$
$929$	−7.47115e36	−0.593186	−0.296593	+	0.955004i	$0.595850\pi$
$930$	0	0
$931$	4.59943e36	0.355494
$932$	−1.16742e37	−0.890281
$933$	2.38240e36	0.179265
$934$	5.99459e36	0.445065
$935$	0	0
$936$	−2.48002e36	−0.179270
$937$	2.45447e37	1.75070	0.875351	−	0.483488i	$-0.160630\pi$
$937$	2.45447e37	1.75070	0.875351	+	0.483488i	$0.160630\pi$
$938$	1.11465e37	0.784517
$939$	−1.63117e37	−1.13287
$940$	0	0
$941$	−1.35589e36	−0.0916968	−0.0458484	−	0.998948i	$-0.514599\pi$
$941$	−1.35589e36	−0.0916968	−0.0458484	+	0.998948i	$0.514599\pi$
$942$	6.37806e36	0.425650
$943$	−2.65707e36	−0.174987
$944$	5.63969e36	0.366527
$945$	0	0
$946$	6.72040e35	0.0425359
$947$	2.07354e37	1.29520	0.647601	−	0.761980i	$-0.275773\pi$
$947$	2.07354e37	1.29520	0.647601	+	0.761980i	$0.275773\pi$
$948$	4.44661e36	0.274110
$949$	−2.49107e37	−1.51551
$950$	0	0
$951$	−2.25934e36	−0.133883
$952$	−4.95558e36	−0.289823
$953$	2.04124e37	1.17823	0.589117	−	0.808048i	$-0.299476\pi$
$953$	2.04124e37	1.17823	0.589117	+	0.808048i	$0.299476\pi$
$954$	3.81300e36	0.217226
$955$	0	0
$956$	2.46309e36	0.136696
$957$	−2.06067e35	−0.0112878
$958$	3.86932e35	0.0209202
$959$	3.49780e35	0.0186665
$960$	0	0
$961$	−9.56182e36	−0.497163
$962$	1.44576e37	0.742009
$963$	−6.76605e36	−0.342773
$964$	1.32008e37	0.660144
$965$	0	0
$966$	3.14506e36	0.153255
$967$	1.88209e37	0.905333	0.452666	−	0.891680i	$-0.350473\pi$
$967$	1.88209e37	0.905333	0.452666	+	0.891680i	$0.350473\pi$
$968$	7.43674e36	0.353135
$969$	4.50494e36	0.211174
$970$	0	0
$971$	−2.62810e37	−1.20061	−0.600305	−	0.799771i	$-0.704954\pi$
$971$	−2.62810e37	−1.20061	−0.600305	+	0.799771i	$0.704954\pi$
$972$	−1.04144e37	−0.469686
$973$	−4.46206e37	−1.98667
$974$	1.21069e37	0.532163
$975$	0	0
$976$	−6.76354e36	−0.289769
$977$	−6.14194e36	−0.259791	−0.129895	−	0.991528i	$-0.541464\pi$
$977$	−6.14194e36	−0.259791	−0.129895	+	0.991528i	$0.541464\pi$
$978$	1.23995e36	0.0517808
$979$	6.27407e35	0.0258682
$980$	0	0
$981$	1.54903e37	0.622584
$982$	−1.30808e37	−0.519089
$983$	5.02851e37	1.97025	0.985123	−	0.171849i	$-0.0549743\pi$
$983$	5.02851e37	1.97025	0.985123	+	0.171849i	$0.0549743\pi$
$984$	4.35438e36	0.168457
$985$	0	0
$986$	5.73908e36	0.216461
$987$	−4.47275e37	−1.66575
$988$	−6.29951e36	−0.231657
$989$	1.18786e37	0.431331
$990$	0	0
$991$	−2.22624e37	−0.788226	−0.394113	−	0.919062i	$-0.628948\pi$
$991$	−2.22624e37	−0.788226	−0.394113	+	0.919062i	$0.628948\pi$
$992$	−3.58538e36	−0.125354
$993$	1.56028e37	0.538688
$994$	4.05182e36	0.138140
$995$	0	0
$996$	−1.16008e37	−0.385697
$997$	7.44693e36	0.244505	0.122253	−	0.992499i	$-0.460988\pi$
$997$	7.44693e36	0.244505	0.122253	+	0.992499i	$0.460988\pi$
$998$	1.38707e37	0.449745
$999$	3.68905e37	1.18126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.d.1.1		2
5.2	odd	4		50.26.b.d.49.2		4
5.3	odd	4		50.26.b.d.49.3		4
5.4	even	2		10.26.a.d.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.d.1.2	✓	2	5.4	even	2
50.26.a.d.1.1		2	1.1	even	1	trivial
50.26.b.d.49.2		4	5.2	odd	4
50.26.b.d.49.3		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} -618439. q^{3} +1.67772e7 q^{4} +2.53313e9 q^{6} -4.78762e10 q^{7} -6.87195e10 q^{8} -4.64821e11 q^{9} +3.58198e11 q^{11} -1.03757e13 q^{12} -7.76408e13 q^{13} +1.96101e14 q^{14} +2.81475e14 q^{16} -1.50624e15 q^{17} +1.90391e15 q^{18} +4.83611e15 q^{19} +2.96085e16 q^{21} -1.46718e15 q^{22} -2.59330e16 q^{23} +4.24988e16 q^{24} +3.18017e17 q^{26} +8.11461e17 q^{27} -8.03229e17 q^{28} +9.30223e17 q^{29} +3.10982e18 q^{31} -1.15292e18 q^{32} -2.21524e17 q^{33} +6.16957e18 q^{34} -7.79841e18 q^{36} +4.54619e19 q^{37} -1.98087e19 q^{38} +4.80162e19 q^{39} +1.02459e20 q^{41} -1.21276e20 q^{42} -4.58049e20 q^{43} +6.00957e18 q^{44} +1.06222e20 q^{46} -1.51063e21 q^{47} -1.74075e20 q^{48} +9.51058e20 q^{49} +9.31520e20 q^{51} -1.30260e21 q^{52} +2.00272e21 q^{53} -3.32374e21 q^{54} +3.29002e21 q^{56} -2.99084e21 q^{57} -3.81019e21 q^{58} +2.00362e22 q^{59} -2.40289e22 q^{61} -1.27378e22 q^{62} +2.22539e22 q^{63} +4.72237e21 q^{64} +9.07362e20 q^{66} +5.68406e22 q^{67} -2.52706e22 q^{68} +1.60380e22 q^{69} +2.06619e22 q^{71} +3.19423e22 q^{72} +3.20846e23 q^{73} -1.86212e23 q^{74} +8.11365e22 q^{76} -1.71492e22 q^{77} -1.96674e23 q^{78} -4.28561e23 q^{79} -1.08001e23 q^{81} -4.19671e23 q^{82} +1.11807e24 q^{83} +4.96748e23 q^{84} +1.87617e24 q^{86} -5.75287e23 q^{87} -2.46152e22 q^{88} +1.75157e24 q^{89} +3.71714e24 q^{91} -4.35084e23 q^{92} -1.92323e24 q^{93} +6.18754e24 q^{94} +7.13012e23 q^{96} +1.28690e25 q^{97} -3.89553e24 q^{98} -1.66498e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} + 97092 q^{3} + 33554432 q^{4} - 397688832 q^{6} + 16137160124 q^{7} - 137438953472 q^{8} - 800124539454 q^{9} + 14416600801344 q^{11} + 1628933455872 q^{12} - 93404548866628 q^{13} - 66097807867904 q^{14}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^2 + 97092 * q^3 + 33554432 * q^4 - 397688832 * q^6 + 16137160124 * q^7 - 137438953472 * q^8 - 800124539454 * q^9 + 14416600801344 * q^11 + 1628933455872 * q^12 - 93404548866628 * q^13 - 66097807867904 * q^14 + 562949953421312 * q^16 - 499266882181236 * q^17 + 3277310113603584 * q^18 - 3830204591906120 * q^19 + 75412053748282104 * q^21 - 59050396882305024 * q^22 - 169271186050723788 * q^23 - 6672111435251712 * q^24 + 382585032157708288 * q^26 - 34721228182863240 * q^27 + 270736621026934784 * q^28 + 569443622853716940 * q^29 + 3982769593868414584 * q^31 - 2305843009213693952 * q^32 + 9837705729224836224 * q^33 + 2044997149414342656 * q^34 - 13423862225320280064 * q^36 - 28241444663789328196 * q^37 + 15688518008447467520 * q^38 + 36736718047624459512 * q^39 + 36676428854020432524 * q^41 - 308887772152963497984 * q^42 - 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 693334778063764635648 * q^46 - 954929084389204818996 * q^47 + 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 1652042752773544110744 * q^51 - 1567068291717973147648 * q^52 - 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 1108937199726324875264 * q^56 - 9191867441696689119120 * q^57 - 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 - 26987853585082462424636 * q^61 - 16313424256485026136064 * q^62 + 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 40295242666904929173504 * q^66 + 14159647018044347838524 * q^67 - 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 - 173327708998984655450136 * q^71 + 54984139674911867142144 * q^72 + 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 64260169762600826961920 * q^76 + 882775887628764911584128 * q^77 - 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 429372483438817686010518 * q^81 - 150226652586067691618304 * q^82 - 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 + 3723334919365686278668288 * q^86 - 833435461987898381769960 * q^87 - 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 2708056932935479178393864 * q^91 - 2839899250949179947614208 * q^92 - 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 - 111939454725287986593792 * q^96 + 16314734149871901683914364 * q^97 - 15186717796562586217979904 * q^98 - 4880327126898398506596288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more