LMFDB - Embedded newform 279.8.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,8,Mod(1,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("279.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	279.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:	$87.1554221101$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 538x^{5} + 2328x^{4} + 78000x^{3} - 344224x^{2} - 3123712x + 13256192 $ x^7 - 3x^6 - 538x^5 + 2328x^4 + 78000x^3 - 344224x^2 - 3123712x + 13256192
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$15.7787$ of defining polynomial
Character	$\chi$	$=$	279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17.7787 q^{2} +188.081 q^{4} -66.6445 q^{5} +686.409 q^{7} +1068.16 q^{8} +O(q^{10})$	\(q+17.7787 q^{2} +188.081 q^{4} -66.6445 q^{5} +686.409 q^{7} +1068.16 q^{8} -1184.85 q^{10} +2883.59 q^{11} +6467.92 q^{13} +12203.4 q^{14} -5083.85 q^{16} +15053.0 q^{17} +16361.2 q^{19} -12534.6 q^{20} +51266.4 q^{22} -82813.3 q^{23} -73683.5 q^{25} +114991. q^{26} +129101. q^{28} +204845. q^{29} +29791.0 q^{31} -227109. q^{32} +267623. q^{34} -45745.4 q^{35} +252609. q^{37} +290880. q^{38} -71187.3 q^{40} +779327. q^{41} -228505. q^{43} +542349. q^{44} -1.47231e6 q^{46} +1.26908e6 q^{47} -352386. q^{49} -1.31000e6 q^{50} +1.21650e6 q^{52} +987964. q^{53} -192175. q^{55} +733197. q^{56} +3.64187e6 q^{58} +952323. q^{59} +1.71628e6 q^{61} +529644. q^{62} -3.38697e6 q^{64} -431051. q^{65} +1.33563e6 q^{67} +2.83119e6 q^{68} -813292. q^{70} -4.03243e6 q^{71} +3.85064e6 q^{73} +4.49106e6 q^{74} +3.07723e6 q^{76} +1.97932e6 q^{77} -4.47981e6 q^{79} +338810. q^{80} +1.38554e7 q^{82} +2.23749e6 q^{83} -1.00320e6 q^{85} -4.06252e6 q^{86} +3.08015e6 q^{88} +142190. q^{89} +4.43964e6 q^{91} -1.55756e7 q^{92} +2.25625e7 q^{94} -1.09038e6 q^{95} -1.41852e7 q^{97} -6.26496e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 17 q^{2} + 229 q^{4} + 430 q^{5} - 832 q^{7} + 135 q^{8}+O(q^{10}) $ 7 * q + 17 * q^2 + 229 * q^4 + 430 * q^5 - 832 * q^7 + 135 * q^8	\( 7 q + 17 q^{2} + 229 q^{4} + 430 q^{5} - 832 q^{7} + 135 q^{8} - 5232 q^{10} + 7886 q^{11} - 21844 q^{13} + 37902 q^{14} - 49583 q^{16} + 54822 q^{17} - 45352 q^{19} + 50110 q^{20} + 30696 q^{22} + 18464 q^{23} - 37691 q^{25} - 3906 q^{26} + 323084 q^{28} + 81488 q^{29} + 208537 q^{31} - 276513 q^{32} + 1152342 q^{34} - 154340 q^{35} + 431648 q^{37} - 798430 q^{38} + 600366 q^{40} + 1465990 q^{41} - 598714 q^{43} + 660872 q^{44} - 356652 q^{46} + 2003572 q^{47} - 331317 q^{49} - 91595 q^{50} - 28582 q^{52} + 1496844 q^{53} - 1414452 q^{55} + 2199880 q^{56} + 1517430 q^{58} + 2853828 q^{59} - 1486900 q^{61} + 506447 q^{62} - 1940543 q^{64} + 2252240 q^{65} - 5647492 q^{67} - 829234 q^{68} + 8307114 q^{70} + 5168828 q^{71} + 4710926 q^{73} - 4058410 q^{74} + 15097160 q^{76} + 2020724 q^{77} + 4582796 q^{79} - 6495030 q^{80} + 8295096 q^{82} + 626514 q^{83} + 8323116 q^{85} + 3575108 q^{86} + 2100840 q^{88} + 13906634 q^{89} + 10966300 q^{91} + 2803952 q^{92} + 21167040 q^{94} + 11547396 q^{95} + 2962898 q^{97} + 25061151 q^{98}+O(q^{100}) \) 7 * q + 17 * q^2 + 229 * q^4 + 430 * q^5 - 832 * q^7 + 135 * q^8 - 5232 * q^10 + 7886 * q^11 - 21844 * q^13 + 37902 * q^14 - 49583 * q^16 + 54822 * q^17 - 45352 * q^19 + 50110 * q^20 + 30696 * q^22 + 18464 * q^23 - 37691 * q^25 - 3906 * q^26 + 323084 * q^28 + 81488 * q^29 + 208537 * q^31 - 276513 * q^32 + 1152342 * q^34 - 154340 * q^35 + 431648 * q^37 - 798430 * q^38 + 600366 * q^40 + 1465990 * q^41 - 598714 * q^43 + 660872 * q^44 - 356652 * q^46 + 2003572 * q^47 - 331317 * q^49 - 91595 * q^50 - 28582 * q^52 + 1496844 * q^53 - 1414452 * q^55 + 2199880 * q^56 + 1517430 * q^58 + 2853828 * q^59 - 1486900 * q^61 + 506447 * q^62 - 1940543 * q^64 + 2252240 * q^65 - 5647492 * q^67 - 829234 * q^68 + 8307114 * q^70 + 5168828 * q^71 + 4710926 * q^73 - 4058410 * q^74 + 15097160 * q^76 + 2020724 * q^77 + 4582796 * q^79 - 6495030 * q^80 + 8295096 * q^82 + 626514 * q^83 + 8323116 * q^85 + 3575108 * q^86 + 2100840 * q^88 + 13906634 * q^89 + 10966300 * q^91 + 2803952 * q^92 + 21167040 * q^94 + 11547396 * q^95 + 2962898 * q^97 + 25061151 * q^98

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 $

$2$	17.7787	1.57143	0.785714	−	0.618590i	$-0.212296\pi$
$2$	17.7787	1.57143	0.785714	+	0.618590i	$0.212296\pi$
$3$	0	0
$3$	0	0
$4$	188.081	1.46938
$5$	−66.6445	−0.238435	−0.119217	−	0.992868i	$-0.538039\pi$
$5$	−66.6445	−0.238435	−0.119217	+	0.992868i	$0.538039\pi$
$6$	0	0
$7$	686.409	0.756379	0.378190	−	0.925728i	$-0.376547\pi$
$7$	686.409	0.756379	0.378190	+	0.925728i	$0.376547\pi$
$8$	1068.16	0.737604
$9$	0	0
$10$	−1184.85	−0.374683
$11$	2883.59	0.653219	0.326610	−	0.945159i	$-0.394094\pi$
$11$	2883.59	0.653219	0.326610	+	0.945159i	$0.394094\pi$
$12$	0	0
$13$	6467.92	0.816513	0.408257	−	0.912867i	$-0.366137\pi$
$13$	6467.92	0.816513	0.408257	+	0.912867i	$0.366137\pi$
$14$	12203.4	1.18860
$15$	0	0
$16$	−5083.85	−0.310294
$17$	15053.0	0.743109	0.371555	−	0.928411i	$-0.378825\pi$
$17$	15053.0	0.743109	0.371555	+	0.928411i	$0.378825\pi$
$18$	0	0
$19$	16361.2	0.547238	0.273619	−	0.961838i	$-0.411779\pi$
$19$	16361.2	0.547238	0.273619	+	0.961838i	$0.411779\pi$
$20$	−12534.6	−0.350352
$21$	0	0
$22$	51266.4	1.02649
$23$	−82813.3	−1.41923	−0.709615	−	0.704590i	$-0.751131\pi$
$23$	−82813.3	−1.41923	−0.709615	+	0.704590i	$0.751131\pi$
$24$	0	0
$25$	−73683.5	−0.943149
$26$	114991.	1.28309
$27$	0	0
$28$	129101.	1.11141
$29$	204845.	1.55967	0.779834	−	0.625986i	$-0.215303\pi$
$29$	204845.	1.55967	0.779834	+	0.625986i	$0.215303\pi$
$30$	0	0
$31$	29791.0	0.179605
$31$	29791.0	0.179605
$32$	−227109.	−1.22521
$33$	0	0
$34$	267623.	1.16774
$35$	−45745.4	−0.180347
$36$	0	0
$37$	252609.	0.819866	0.409933	−	0.912116i	$-0.365552\pi$
$37$	252609.	0.819866	0.409933	+	0.912116i	$0.365552\pi$
$38$	290880.	0.859945
$39$	0	0
$40$	−71187.3	−0.175870
$41$	779327.	1.76594	0.882971	−	0.469428i	$-0.155540\pi$
$41$	779327.	1.76594	0.882971	+	0.469428i	$0.155540\pi$
$42$	0	0
$43$	−228505.	−0.438285	−0.219143	−	0.975693i	$-0.570326\pi$
$43$	−228505.	−0.438285	−0.219143	+	0.975693i	$0.570326\pi$
$44$	542349.	0.959830
$45$	0	0
$46$	−1.47231e6	−2.23022
$47$	1.26908e6	1.78298	0.891488	−	0.453043i	$-0.149662\pi$
$47$	1.26908e6	1.78298	0.891488	+	0.453043i	$0.149662\pi$
$48$	0	0
$49$	−352386.	−0.427890
$50$	−1.31000e6	−1.48209
$51$	0	0
$52$	1.21650e6	1.19977
$53$	987964.	0.911540	0.455770	−	0.890098i	$-0.349364\pi$
$53$	987964.	0.911540	0.455770	+	0.890098i	$0.349364\pi$
$54$	0	0
$55$	−192175.	−0.155750
$56$	733197.	0.557908
$57$	0	0
$58$	3.64187e6	2.45091
$59$	952323.	0.603674	0.301837	−	0.953360i	$-0.402400\pi$
$59$	952323.	0.603674	0.301837	+	0.953360i	$0.402400\pi$
$60$	0	0
$61$	1.71628e6	0.968131	0.484066	−	0.875032i	$-0.339160\pi$
$61$	1.71628e6	0.968131	0.484066	+	0.875032i	$0.339160\pi$
$62$	529644.	0.282237
$63$	0	0
$64$	−3.38697e6	−1.61503
$65$	−431051.	−0.194685
$66$	0	0
$67$	1.33563e6	0.542530	0.271265	−	0.962505i	$-0.412558\pi$
$67$	1.33563e6	0.542530	0.271265	+	0.962505i	$0.412558\pi$
$68$	2.83119e6	1.09191
$69$	0	0
$70$	−813292.	−0.283402
$71$	−4.03243e6	−1.33710	−0.668548	−	0.743669i	$-0.733084\pi$
$71$	−4.03243e6	−1.33710	−0.668548	+	0.743669i	$0.733084\pi$
$72$	0	0
$73$	3.85064e6	1.15852	0.579260	−	0.815143i	$-0.303342\pi$
$73$	3.85064e6	1.15852	0.579260	+	0.815143i	$0.303342\pi$
$74$	4.49106e6	1.28836
$75$	0	0
$76$	3.07723e6	0.804103
$77$	1.97932e6	0.494082
$78$	0	0
$79$	−4.47981e6	−1.02227	−0.511134	−	0.859501i	$-0.670774\pi$
$79$	−4.47981e6	−1.02227	−0.511134	+	0.859501i	$0.670774\pi$
$80$	338810.	0.0739847
$81$	0	0
$82$	1.38554e7	2.77505
$83$	2.23749e6	0.429524	0.214762	−	0.976666i	$-0.431102\pi$
$83$	2.23749e6	0.429524	0.214762	+	0.976666i	$0.431102\pi$
$84$	0	0
$85$	−1.00320e6	−0.177183
$86$	−4.06252e6	−0.688733
$87$	0	0
$88$	3.08015e6	0.481817
$89$	142190.	0.0213799	0.0106899	−	0.999943i	$-0.496597\pi$
$89$	142190.	0.0213799	0.0106899	+	0.999943i	$0.496597\pi$
$90$	0	0
$91$	4.43964e6	0.617594
$92$	−1.55756e7	−2.08539
$93$	0	0
$94$	2.25625e7	2.80182
$95$	−1.09038e6	−0.130480
$96$	0	0
$97$	−1.41852e7	−1.57810	−0.789048	−	0.614331i	$-0.789426\pi$
$97$	−1.41852e7	−1.57810	−0.789048	+	0.614331i	$0.789426\pi$
$98$	−6.26496e6	−0.672399
$99$	0	0
$100$	−1.38585e7	−1.38585
$101$	1.27518e7	1.23154	0.615768	−	0.787927i	$-0.288846\pi$
$101$	1.27518e7	1.23154	0.615768	+	0.787927i	$0.288846\pi$
$102$	0	0
$103$	−1.18137e7	−1.06526	−0.532632	−	0.846347i	$-0.678797\pi$
$103$	−1.18137e7	−1.06526	−0.532632	+	0.846347i	$0.678797\pi$
$104$	6.90881e6	0.602263
$105$	0	0
$106$	1.75647e7	1.43242
$107$	−7.93394e6	−0.626103	−0.313052	−	0.949736i	$-0.601351\pi$
$107$	−7.93394e6	−0.626103	−0.313052	+	0.949736i	$0.601351\pi$
$108$	0	0
$109$	5.32299e6	0.393698	0.196849	−	0.980434i	$-0.436929\pi$
$109$	5.32299e6	0.393698	0.196849	+	0.980434i	$0.436929\pi$
$110$	−3.41662e6	−0.244750
$111$	0	0
$112$	−3.48960e6	−0.234700
$113$	1.96185e7	1.27906	0.639531	−	0.768765i	$-0.279129\pi$
$113$	1.96185e7	1.27906	0.639531	+	0.768765i	$0.279129\pi$
$114$	0	0
$115$	5.51905e6	0.338393
$116$	3.85275e7	2.29175
$117$	0	0
$118$	1.69310e7	0.948629
$119$	1.03325e7	0.562072
$120$	0	0
$121$	−1.11721e7	−0.573304
$122$	3.05132e7	1.52135
$123$	0	0
$124$	5.60313e6	0.263909
$125$	1.01172e7	0.463314
$126$	0	0
$127$	1.18043e7	0.511360	0.255680	−	0.966761i	$-0.417701\pi$
$127$	1.18043e7	0.511360	0.255680	+	0.966761i	$0.417701\pi$
$128$	−3.11458e7	−1.31270
$129$	0	0
$130$	−7.66352e6	−0.305933
$131$	1.04384e7	0.405679	0.202840	−	0.979212i	$-0.434983\pi$
$131$	1.04384e7	0.405679	0.202840	+	0.979212i	$0.434983\pi$
$132$	0	0
$133$	1.12304e7	0.413920
$134$	2.37457e7	0.852546
$135$	0	0
$136$	1.60791e7	0.548120
$137$	−1.59701e7	−0.530622	−0.265311	−	0.964163i	$-0.585475\pi$
$137$	−1.59701e7	−0.530622	−0.265311	+	0.964163i	$0.585475\pi$
$138$	0	0
$139$	2.45850e6	0.0776458	0.0388229	−	0.999246i	$-0.487639\pi$
$139$	2.45850e6	0.0776458	0.0388229	+	0.999246i	$0.487639\pi$
$140$	−8.60384e6	−0.264999
$141$	0	0
$142$	−7.16912e7	−2.10115
$143$	1.86508e7	0.533362
$144$	0	0
$145$	−1.36518e7	−0.371879
$146$	6.84593e7	1.82053
$147$	0	0
$148$	4.75110e7	1.20470
$149$	967011.	0.0239486	0.0119743	−	0.999928i	$-0.496188\pi$
$149$	967011.	0.0239486	0.0119743	+	0.999928i	$0.496188\pi$
$150$	0	0
$151$	−4.72383e7	−1.11654	−0.558271	−	0.829658i	$-0.688535\pi$
$151$	−4.72383e7	−1.11654	−0.558271	+	0.829658i	$0.688535\pi$
$152$	1.74764e7	0.403645
$153$	0	0
$154$	3.51897e7	0.776413
$155$	−1.98541e6	−0.0428241
$156$	0	0
$157$	−6.10249e7	−1.25851	−0.629257	−	0.777197i	$-0.716641\pi$
$157$	−6.10249e7	−1.25851	−0.629257	+	0.777197i	$0.716641\pi$
$158$	−7.96450e7	−1.60642
$159$	0	0
$160$	1.51356e7	0.292132
$161$	−5.68438e7	−1.07348
$162$	0	0
$163$	397126.	0.00718243	0.00359122	−	0.999994i	$-0.498857\pi$
$163$	397126.	0.00718243	0.00359122	+	0.999994i	$0.498857\pi$
$164$	1.46577e8	2.59485
$165$	0	0
$166$	3.97796e7	0.674967
$167$	−7.47782e7	−1.24242	−0.621209	−	0.783645i	$-0.713358\pi$
$167$	−7.47782e7	−1.24242	−0.621209	+	0.783645i	$0.713358\pi$
$168$	0	0
$169$	−2.09145e7	−0.333306
$170$	−1.78356e7	−0.278430
$171$	0	0
$172$	−4.29776e7	−0.644009
$173$	−8.75293e7	−1.28526	−0.642632	−	0.766175i	$-0.722158\pi$
$173$	−8.75293e7	−1.28526	−0.642632	+	0.766175i	$0.722158\pi$
$174$	0	0
$175$	−5.05770e7	−0.713378
$176$	−1.46597e7	−0.202690
$177$	0	0
$178$	2.52796e6	0.0335970
$179$	−1.14337e8	−1.49005	−0.745027	−	0.667034i	$-0.767564\pi$
$179$	−1.14337e8	−1.49005	−0.745027	+	0.667034i	$0.767564\pi$
$180$	0	0
$181$	−6.25246e7	−0.783747	−0.391873	−	0.920019i	$-0.628173\pi$
$181$	−6.25246e7	−0.783747	−0.391873	+	0.920019i	$0.628173\pi$
$182$	7.89309e7	0.970504
$183$	0	0
$184$	−8.84582e7	−1.04683
$185$	−1.68350e7	−0.195484
$186$	0	0
$187$	4.34068e7	0.485413
$188$	2.38690e8	2.61988
$189$	0	0
$190$	−1.93855e7	−0.205041
$191$	1.46859e8	1.52505	0.762526	−	0.646957i	$-0.223959\pi$
$191$	1.46859e8	1.52505	0.762526	+	0.646957i	$0.223959\pi$
$192$	0	0
$193$	−3.29314e7	−0.329731	−0.164865	−	0.986316i	$-0.552719\pi$
$193$	−3.29314e7	−0.329731	−0.164865	+	0.986316i	$0.552719\pi$
$194$	−2.52194e8	−2.47986
$195$	0	0
$196$	−6.62772e7	−0.628735
$197$	1.29534e8	1.20713	0.603564	−	0.797315i	$-0.293747\pi$
$197$	1.29534e8	1.20713	0.603564	+	0.797315i	$0.293747\pi$
$198$	0	0
$199$	4.53412e7	0.407856	0.203928	−	0.978986i	$-0.434629\pi$
$199$	4.53412e7	0.407856	0.203928	+	0.978986i	$0.434629\pi$
$200$	−7.87061e7	−0.695670
$201$	0	0
$202$	2.26710e8	1.93527
$203$	1.40607e8	1.17970
$204$	0	0
$205$	−5.19379e7	−0.421062
$206$	−2.10033e8	−1.67398
$207$	0	0
$208$	−3.28820e7	−0.253359
$209$	4.71789e7	0.357467
$210$	0	0
$211$	−2.40362e7	−0.176148	−0.0880739	−	0.996114i	$-0.528071\pi$
$211$	−2.40362e7	−0.176148	−0.0880739	+	0.996114i	$0.528071\pi$
$212$	1.85817e8	1.33940
$213$	0	0
$214$	−1.41055e8	−0.983876
$215$	1.52286e7	0.104502
$216$	0	0
$217$	2.04488e7	0.135850
$218$	9.46358e7	0.618668
$219$	0	0
$220$	−3.61446e7	−0.228857
$221$	9.73619e7	0.606759
$222$	0	0
$223$	−1.10811e8	−0.669137	−0.334569	−	0.942371i	$-0.608591\pi$
$223$	−1.10811e8	−0.669137	−0.334569	+	0.942371i	$0.608591\pi$
$224$	−1.55890e8	−0.926722
$225$	0	0
$226$	3.48791e8	2.00995
$227$	−2.99831e8	−1.70132	−0.850661	−	0.525715i	$-0.823798\pi$
$227$	−2.99831e8	−1.70132	−0.850661	+	0.525715i	$0.823798\pi$
$228$	0	0
$229$	3.37036e8	1.85461	0.927305	−	0.374306i	$-0.122119\pi$
$229$	3.37036e8	1.85461	0.927305	+	0.374306i	$0.122119\pi$
$230$	9.81214e7	0.531761
$231$	0	0
$232$	2.18808e8	1.15042
$233$	1.18388e8	0.613145	0.306572	−	0.951847i	$-0.400818\pi$
$233$	1.18388e8	0.613145	0.306572	+	0.951847i	$0.400818\pi$
$234$	0	0
$235$	−8.45770e7	−0.425123
$236$	1.79114e8	0.887029
$237$	0	0
$238$	1.83699e8	0.883256
$239$	1.66861e8	0.790610	0.395305	−	0.918550i	$-0.370639\pi$
$239$	1.66861e8	0.790610	0.395305	+	0.918550i	$0.370639\pi$
$240$	0	0
$241$	6.70826e7	0.308710	0.154355	−	0.988015i	$-0.450670\pi$
$241$	6.70826e7	0.308710	0.154355	+	0.988015i	$0.450670\pi$
$242$	−1.98625e8	−0.900906
$243$	0	0
$244$	3.22800e8	1.42256
$245$	2.34846e7	0.102024
$246$	0	0
$247$	1.05823e8	0.446827
$248$	3.18217e7	0.132478
$249$	0	0
$250$	1.79870e8	0.728064
$251$	−1.32817e7	−0.0530145	−0.0265072	−	0.999649i	$-0.508439\pi$
$251$	−1.32817e7	−0.0530145	−0.0265072	+	0.999649i	$0.508439\pi$
$252$	0	0
$253$	−2.38800e8	−0.927068
$254$	2.09865e8	0.803566
$255$	0	0
$256$	−1.20199e8	−0.447777
$257$	−4.76683e8	−1.75172	−0.875858	−	0.482569i	$-0.839704\pi$
$257$	−4.76683e8	−1.75172	−0.875858	+	0.482569i	$0.839704\pi$
$258$	0	0
$259$	1.73393e8	0.620130
$260$	−8.10727e7	−0.286067
$261$	0	0
$262$	1.85580e8	0.637495
$263$	2.82902e8	0.958938	0.479469	−	0.877559i	$-0.340829\pi$
$263$	2.82902e8	0.958938	0.479469	+	0.877559i	$0.340829\pi$
$264$	0	0
$265$	−6.58423e7	−0.217343
$266$	1.99662e8	0.650445
$267$	0	0
$268$	2.51206e8	0.797185
$269$	2.01149e8	0.630064	0.315032	−	0.949081i	$-0.397985\pi$
$269$	2.01149e8	0.630064	0.315032	+	0.949081i	$0.397985\pi$
$270$	0	0
$271$	−1.44594e8	−0.441324	−0.220662	−	0.975350i	$-0.570822\pi$
$271$	−1.44594e8	−0.441324	−0.220662	+	0.975350i	$0.570822\pi$
$272$	−7.65273e7	−0.230582
$273$	0	0
$274$	−2.83927e8	−0.833833
$275$	−2.12473e8	−0.616083
$276$	0	0
$277$	−6.63088e8	−1.87453	−0.937264	−	0.348620i	$-0.886650\pi$
$277$	−6.63088e8	−1.87453	−0.937264	+	0.348620i	$0.886650\pi$
$278$	4.37088e7	0.122015
$279$	0	0
$280$	−4.88636e7	−0.133025
$281$	−6.17451e8	−1.66009	−0.830043	−	0.557700i	$-0.811684\pi$
$281$	−6.17451e8	−1.66009	−0.830043	+	0.557700i	$0.811684\pi$
$282$	0	0
$283$	6.05253e7	0.158739	0.0793697	−	0.996845i	$-0.474709\pi$
$283$	6.05253e7	0.158739	0.0793697	+	0.996845i	$0.474709\pi$
$284$	−7.58424e8	−1.96471
$285$	0	0
$286$	3.31587e8	0.838140
$287$	5.34937e8	1.33572
$288$	0	0
$289$	−1.83745e8	−0.447789
$290$	−2.42711e8	−0.584381
$291$	0	0
$292$	7.24234e8	1.70231
$293$	7.06523e8	1.64093	0.820464	−	0.571698i	$-0.193715\pi$
$293$	7.06523e8	1.64093	0.820464	+	0.571698i	$0.193715\pi$
$294$	0	0
$295$	−6.34671e7	−0.143937
$296$	2.69828e8	0.604737
$297$	0	0
$298$	1.71922e7	0.0376334
$299$	−5.35630e8	−1.15882
$300$	0	0
$301$	−1.56848e8	−0.331510
$302$	−8.39835e8	−1.75457
$303$	0	0
$304$	−8.31776e7	−0.169804
$305$	−1.14381e8	−0.230836
$306$	0	0
$307$	8.65076e8	1.70636	0.853179	−	0.521619i	$-0.174672\pi$
$307$	8.65076e8	1.70636	0.853179	+	0.521619i	$0.174672\pi$
$308$	3.72273e8	0.725996
$309$	0	0
$310$	−3.52979e7	−0.0672950
$311$	−6.64291e8	−1.25227	−0.626134	−	0.779715i	$-0.715364\pi$
$311$	−6.64291e8	−1.25227	−0.626134	+	0.779715i	$0.715364\pi$
$312$	0	0
$313$	−7.87347e8	−1.45131	−0.725657	−	0.688057i	$-0.758464\pi$
$313$	−7.87347e8	−1.45131	−0.725657	+	0.688057i	$0.758464\pi$
$314$	−1.08494e9	−1.97766
$315$	0	0
$316$	−8.42567e8	−1.50210
$317$	−3.50228e8	−0.617510	−0.308755	−	0.951142i	$-0.599912\pi$
$317$	−3.50228e8	−0.617510	−0.308755	+	0.951142i	$0.599912\pi$
$318$	0	0
$319$	5.90689e8	1.01881
$320$	2.25723e8	0.385079
$321$	0	0
$322$	−1.01061e9	−1.68689
$323$	2.46285e8	0.406658
$324$	0	0
$325$	−4.76579e8	−0.770094
$326$	7.06037e6	0.0112867
$327$	0	0
$328$	8.32450e8	1.30257
$329$	8.71106e8	1.34861
$330$	0	0
$331$	−3.82449e8	−0.579663	−0.289831	−	0.957078i	$-0.593599\pi$
$331$	−3.82449e8	−0.579663	−0.289831	+	0.957078i	$0.593599\pi$
$332$	4.20830e8	0.631137
$333$	0	0
$334$	−1.32946e9	−1.95237
$335$	−8.90122e7	−0.129358
$336$	0	0
$337$	−2.10576e8	−0.299713	−0.149856	−	0.988708i	$-0.547881\pi$
$337$	−2.10576e8	−0.299713	−0.149856	+	0.988708i	$0.547881\pi$
$338$	−3.71832e8	−0.523767
$339$	0	0
$340$	−1.88683e8	−0.260350
$341$	8.59050e7	0.117322
$342$	0	0
$343$	−8.07168e8	−1.08003
$344$	−2.44081e8	−0.323281
$345$	0	0
$346$	−1.55616e9	−2.01970
$347$	1.33619e8	0.171678	0.0858388	−	0.996309i	$-0.472643\pi$
$347$	1.33619e8	0.171678	0.0858388	+	0.996309i	$0.472643\pi$
$348$	0	0
$349$	−8.50804e7	−0.107137	−0.0535686	−	0.998564i	$-0.517060\pi$
$349$	−8.50804e7	−0.107137	−0.0535686	+	0.998564i	$0.517060\pi$
$350$	−8.99192e8	−1.12102
$351$	0	0
$352$	−6.54890e8	−0.800329
$353$	−1.00864e9	−1.22046	−0.610231	−	0.792224i	$-0.708923\pi$
$353$	−1.00864e9	−1.22046	−0.610231	+	0.792224i	$0.708923\pi$
$354$	0	0
$355$	2.68739e8	0.318810
$356$	2.67434e7	0.0314153
$357$	0	0
$358$	−2.03276e9	−2.34151
$359$	6.28832e8	0.717306	0.358653	−	0.933471i	$-0.383236\pi$
$359$	6.28832e8	0.717306	0.358653	+	0.933471i	$0.383236\pi$
$360$	0	0
$361$	−6.26184e8	−0.700530
$362$	−1.11160e9	−1.23160
$363$	0	0
$364$	8.35013e8	0.907483
$365$	−2.56624e8	−0.276231
$366$	0	0
$367$	−1.22300e9	−1.29150	−0.645752	−	0.763547i	$-0.723456\pi$
$367$	−1.22300e9	−1.29150	−0.645752	+	0.763547i	$0.723456\pi$
$368$	4.21010e8	0.440378
$369$	0	0
$370$	−2.99304e8	−0.307190
$371$	6.78147e8	0.689470
$372$	0	0
$373$	9.45435e8	0.943302	0.471651	−	0.881785i	$-0.343658\pi$
$373$	9.45435e8	0.943302	0.471651	+	0.881785i	$0.343658\pi$
$374$	7.71715e8	0.762792
$375$	0	0
$376$	1.35558e9	1.31513
$377$	1.32492e9	1.27349
$378$	0	0
$379$	7.06115e8	0.666251	0.333126	−	0.942882i	$-0.391897\pi$
$379$	7.06115e8	0.666251	0.333126	+	0.942882i	$0.391897\pi$
$380$	−2.05080e8	−0.191726
$381$	0	0
$382$	2.61096e9	2.39651
$383$	−1.45767e9	−1.32576	−0.662878	−	0.748727i	$-0.730665\pi$
$383$	−1.45767e9	−1.32576	−0.662878	+	0.748727i	$0.730665\pi$
$384$	0	0
$385$	−1.31911e8	−0.117806
$386$	−5.85476e8	−0.518148
$387$	0	0
$388$	−2.66796e9	−2.31883
$389$	−1.20483e9	−1.03777	−0.518885	−	0.854844i	$-0.673653\pi$
$389$	−1.20483e9	−1.03777	−0.518885	+	0.854844i	$0.673653\pi$
$390$	0	0
$391$	−1.24659e9	−1.05464
$392$	−3.76406e8	−0.315614
$393$	0	0
$394$	2.30295e9	1.89691
$395$	2.98554e8	0.243744
$396$	0	0
$397$	1.18292e9	0.948827	0.474413	−	0.880302i	$-0.342660\pi$
$397$	1.18292e9	0.948827	0.474413	+	0.880302i	$0.342660\pi$
$398$	8.06106e8	0.640916
$399$	0	0
$400$	3.74596e8	0.292653
$401$	−2.40152e9	−1.85986	−0.929931	−	0.367734i	$-0.880134\pi$
$401$	−2.40152e9	−1.85986	−0.929931	+	0.367734i	$0.880134\pi$
$402$	0	0
$403$	1.92686e8	0.146650
$404$	2.39838e9	1.80960
$405$	0	0
$406$	2.49981e9	1.85382
$407$	7.28421e8	0.535553
$408$	0	0
$409$	1.83827e9	1.32855	0.664275	−	0.747488i	$-0.268740\pi$
$409$	1.83827e9	1.32855	0.664275	+	0.747488i	$0.268740\pi$
$410$	−9.23386e8	−0.661668
$411$	0	0
$412$	−2.22194e9	−1.56528
$413$	6.53683e8	0.456606
$414$	0	0
$415$	−1.49116e8	−0.102413
$416$	−1.46892e9	−1.00040
$417$	0	0
$418$	8.38778e8	0.561733
$419$	2.30007e9	1.52754	0.763768	−	0.645491i	$-0.223347\pi$
$419$	2.30007e9	1.52754	0.763768	+	0.645491i	$0.223347\pi$
$420$	0	0
$421$	−6.25449e8	−0.408512	−0.204256	−	0.978918i	$-0.565477\pi$
$421$	−6.25449e8	−0.408512	−0.204256	+	0.978918i	$0.565477\pi$
$422$	−4.27332e8	−0.276804
$423$	0	0
$424$	1.05531e9	0.672355
$425$	−1.10916e9	−0.700863
$426$	0	0
$427$	1.17807e9	0.732274
$428$	−1.49223e9	−0.919986
$429$	0	0
$430$	2.70745e8	0.164218
$431$	7.79146e6	0.00468758	0.00234379	−	0.999997i	$-0.499254\pi$
$431$	7.79146e6	0.00468758	0.00234379	+	0.999997i	$0.499254\pi$
$432$	0	0
$433$	−2.49979e9	−1.47978	−0.739889	−	0.672729i	$-0.765122\pi$
$433$	−2.49979e9	−1.47978	−0.739889	+	0.672729i	$0.765122\pi$
$434$	3.63553e8	0.213478
$435$	0	0
$436$	1.00116e9	0.578494
$437$	−1.35492e9	−0.776657
$438$	0	0
$439$	−5.26141e8	−0.296809	−0.148404	−	0.988927i	$-0.547414\pi$
$439$	−5.26141e8	−0.296809	−0.148404	+	0.988927i	$0.547414\pi$
$440$	−2.05275e8	−0.114882
$441$	0	0
$442$	1.73096e9	0.953477
$443$	1.79026e9	0.978370	0.489185	−	0.872180i	$-0.337294\pi$
$443$	1.79026e9	0.978370	0.489185	+	0.872180i	$0.337294\pi$
$444$	0	0
$445$	−9.47621e6	−0.00509771
$446$	−1.97007e9	−1.05150
$447$	0	0
$448$	−2.32484e9	−1.22158
$449$	2.22533e9	1.16020	0.580099	−	0.814546i	$-0.303014\pi$
$449$	2.22533e9	1.16020	0.580099	+	0.814546i	$0.303014\pi$
$450$	0	0
$451$	2.24726e9	1.15355
$452$	3.68988e9	1.87943
$453$	0	0
$454$	−5.33060e9	−2.67350
$455$	−2.95877e8	−0.147256
$456$	0	0
$457$	3.27707e9	1.60612	0.803061	−	0.595897i	$-0.203203\pi$
$457$	3.27707e9	1.60612	0.803061	+	0.595897i	$0.203203\pi$
$458$	5.99206e9	2.91439
$459$	0	0
$460$	1.03803e9	0.497230
$461$	1.26834e9	0.602952	0.301476	−	0.953474i	$-0.402521\pi$
$461$	1.26834e9	0.602952	0.301476	+	0.953474i	$0.402521\pi$
$462$	0	0
$463$	−2.11328e9	−0.989520	−0.494760	−	0.869030i	$-0.664744\pi$
$463$	−2.11328e9	−0.989520	−0.494760	+	0.869030i	$0.664744\pi$
$464$	−1.04140e9	−0.483955
$465$	0	0
$466$	2.10479e9	0.963513
$467$	−1.74008e9	−0.790608	−0.395304	−	0.918550i	$-0.629361\pi$
$467$	−1.74008e9	−0.790608	−0.395304	+	0.918550i	$0.629361\pi$
$468$	0	0
$469$	9.16786e8	0.410358
$470$	−1.50367e9	−0.668050
$471$	0	0
$472$	1.01724e9	0.445272
$473$	−6.58916e8	−0.286296
$474$	0	0
$475$	−1.20555e9	−0.516127
$476$	1.94335e9	0.825901
$477$	0	0
$478$	2.96657e9	1.24239
$479$	9.96854e8	0.414436	0.207218	−	0.978295i	$-0.433559\pi$
$479$	9.96854e8	0.414436	0.207218	+	0.978295i	$0.433559\pi$
$480$	0	0
$481$	1.63386e9	0.669432
$482$	1.19264e9	0.485115
$483$	0	0
$484$	−2.10126e9	−0.842405
$485$	9.45363e8	0.376273
$486$	0	0
$487$	−3.93984e9	−1.54571	−0.772853	−	0.634585i	$-0.781171\pi$
$487$	−3.93984e9	−1.54571	−0.772853	+	0.634585i	$0.781171\pi$
$488$	1.83327e9	0.714097
$489$	0	0
$490$	4.17525e8	0.160323
$491$	3.93792e8	0.150135	0.0750674	−	0.997178i	$-0.476083\pi$
$491$	3.93792e8	0.150135	0.0750674	+	0.997178i	$0.476083\pi$
$492$	0	0
$493$	3.08354e9	1.15900
$494$	1.88139e9	0.702157
$495$	0	0
$496$	−1.51453e8	−0.0557304
$497$	−2.76789e9	−1.01135
$498$	0	0
$499$	1.38870e9	0.500329	0.250164	−	0.968203i	$-0.419515\pi$
$499$	1.38870e9	0.500329	0.250164	+	0.968203i	$0.419515\pi$
$500$	1.90286e9	0.680786
$501$	0	0
$502$	−2.36130e8	−0.0833084
$503$	6.25515e8	0.219154	0.109577	−	0.993978i	$-0.465050\pi$
$503$	6.25515e8	0.219154	0.109577	+	0.993978i	$0.465050\pi$
$504$	0	0
$505$	−8.49838e8	−0.293641
$506$	−4.24554e9	−1.45682
$507$	0	0
$508$	2.22017e9	0.751385
$509$	−2.21089e9	−0.743114	−0.371557	−	0.928410i	$-0.621176\pi$
$509$	−2.21089e9	−0.743114	−0.371557	+	0.928410i	$0.621176\pi$
$510$	0	0
$511$	2.64312e9	0.876280
$512$	1.84968e9	0.609048
$513$	0	0
$514$	−8.47479e9	−2.75269
$515$	7.87320e8	0.253996
$516$	0	0
$517$	3.65950e9	1.16468
$518$	3.08270e9	0.974489
$519$	0	0
$520$	−4.60434e8	−0.143600
$521$	1.15858e9	0.358916	0.179458	−	0.983766i	$-0.442566\pi$
$521$	1.15858e9	0.358916	0.179458	+	0.983766i	$0.442566\pi$
$522$	0	0
$523$	4.79427e9	1.46544	0.732718	−	0.680533i	$-0.238252\pi$
$523$	4.79427e9	1.46544	0.732718	+	0.680533i	$0.238252\pi$
$524$	1.96326e9	0.596099
$525$	0	0
$526$	5.02962e9	1.50690
$527$	4.48445e8	0.133466
$528$	0	0
$529$	3.45322e9	1.01421
$530$	−1.17059e9	−0.341538
$531$	0	0
$532$	2.11223e9	0.608207
$533$	5.04063e9	1.44191
$534$	0	0
$535$	5.28754e8	0.149285
$536$	1.42667e9	0.400172
$537$	0	0
$538$	3.57616e9	0.990100
$539$	−1.01614e9	−0.279506
$540$	0	0
$541$	−3.40517e8	−0.0924587	−0.0462294	−	0.998931i	$-0.514721\pi$
$541$	−3.40517e8	−0.0924587	−0.0462294	+	0.998931i	$0.514721\pi$
$542$	−2.57069e9	−0.693509
$543$	0	0
$544$	−3.41868e9	−0.910463
$545$	−3.54748e8	−0.0938712
$546$	0	0
$547$	5.56092e9	1.45275	0.726376	−	0.687298i	$-0.241203\pi$
$547$	5.56092e9	1.45275	0.726376	+	0.687298i	$0.241203\pi$
$548$	−3.00367e9	−0.779687
$549$	0	0
$550$	−3.77749e9	−0.968130
$551$	3.35150e9	0.853510
$552$	0	0
$553$	−3.07498e9	−0.773222
$554$	−1.17888e10	−2.94569
$555$	0	0
$556$	4.62397e8	0.114091
$557$	2.55758e8	0.0627098	0.0313549	−	0.999508i	$-0.490018\pi$
$557$	2.55758e8	0.0627098	0.0313549	+	0.999508i	$0.490018\pi$
$558$	0	0
$559$	−1.47796e9	−0.357866
$560$	2.32562e8	0.0559605
$561$	0	0
$562$	−1.09775e10	−2.60870
$563$	5.94963e9	1.40511	0.702555	−	0.711629i	$-0.252042\pi$
$563$	5.94963e9	1.40511	0.702555	+	0.711629i	$0.252042\pi$
$564$	0	0
$565$	−1.30747e9	−0.304973
$566$	1.07606e9	0.249447
$567$	0	0
$568$	−4.30730e9	−0.986247
$569$	7.95486e8	0.181025	0.0905127	−	0.995895i	$-0.471149\pi$
$569$	7.95486e8	0.181025	0.0905127	+	0.995895i	$0.471149\pi$
$570$	0	0
$571$	−4.03947e9	−0.908026	−0.454013	−	0.890995i	$-0.650008\pi$
$571$	−4.03947e9	−0.908026	−0.454013	+	0.890995i	$0.650008\pi$
$572$	3.50787e9	0.783714
$573$	0	0
$574$	9.51047e9	2.09899
$575$	6.10197e9	1.33854
$576$	0	0
$577$	6.93338e9	1.50255	0.751276	−	0.659988i	$-0.229439\pi$
$577$	6.93338e9	1.50255	0.751276	+	0.659988i	$0.229439\pi$
$578$	−3.26674e9	−0.703667
$579$	0	0
$580$	−2.56765e9	−0.546433
$581$	1.53583e9	0.324883
$582$	0	0
$583$	2.84888e9	0.595435
$584$	4.11312e9	0.854528
$585$	0	0
$586$	1.25610e10	2.57860
$587$	−7.58879e8	−0.154860	−0.0774300	−	0.996998i	$-0.524671\pi$
$587$	−7.58879e8	−0.154860	−0.0774300	+	0.996998i	$0.524671\pi$
$588$	0	0
$589$	4.87415e8	0.0982869
$590$	−1.12836e9	−0.226186
$591$	0	0
$592$	−1.28423e9	−0.254399
$593$	1.34569e9	0.265005	0.132502	−	0.991183i	$-0.457699\pi$
$593$	1.34569e9	0.265005	0.132502	+	0.991183i	$0.457699\pi$
$594$	0	0
$595$	−6.88606e8	−0.134017
$596$	1.81877e8	0.0351896
$597$	0	0
$598$	−9.52279e9	−1.82100
$599$	−1.17622e9	−0.223612	−0.111806	−	0.993730i	$-0.535664\pi$
$599$	−1.17622e9	−0.223612	−0.111806	+	0.993730i	$0.535664\pi$
$600$	0	0
$601$	−8.53093e8	−0.160301	−0.0801504	−	0.996783i	$-0.525540\pi$
$601$	−8.53093e8	−0.160301	−0.0801504	+	0.996783i	$0.525540\pi$
$602$	−2.78855e9	−0.520944
$603$	0	0
$604$	−8.88465e9	−1.64063
$605$	7.44558e8	0.136696
$606$	0	0
$607$	3.51705e9	0.638289	0.319145	−	0.947706i	$-0.396604\pi$
$607$	3.51705e9	0.638289	0.319145	+	0.947706i	$0.396604\pi$
$608$	−3.71577e9	−0.670480
$609$	0	0
$610$	−2.03354e9	−0.362742
$611$	8.20830e9	1.45582
$612$	0	0
$613$	6.20528e9	1.08805	0.544026	−	0.839069i	$-0.316899\pi$
$613$	6.20528e9	1.08805	0.544026	+	0.839069i	$0.316899\pi$
$614$	1.53799e10	2.68142
$615$	0	0
$616$	2.11424e9	0.364437
$617$	3.32482e9	0.569862	0.284931	−	0.958548i	$-0.408029\pi$
$617$	3.32482e9	0.569862	0.284931	+	0.958548i	$0.408029\pi$
$618$	0	0
$619$	−6.34229e9	−1.07480	−0.537401	−	0.843327i	$-0.680594\pi$
$619$	−6.34229e9	−1.07480	−0.537401	+	0.843327i	$0.680594\pi$
$620$	−3.73418e8	−0.0629251
$621$	0	0
$622$	−1.18102e10	−1.96785
$623$	9.76008e7	0.0161713
$624$	0	0
$625$	5.08227e9	0.832679
$626$	−1.39980e10	−2.28063
$627$	0	0
$628$	−1.14776e10	−1.84924
$629$	3.80253e9	0.609250
$630$	0	0
$631$	−4.57212e8	−0.0724461	−0.0362230	−	0.999344i	$-0.511533\pi$
$631$	−4.57212e8	−0.0724461	−0.0362230	+	0.999344i	$0.511533\pi$
$632$	−4.78517e9	−0.754028
$633$	0	0
$634$	−6.22660e9	−0.970372
$635$	−7.86691e8	−0.121926
$636$	0	0
$637$	−2.27921e9	−0.349378
$638$	1.05017e10	1.60098
$639$	0	0
$640$	2.07570e9	0.312992
$641$	3.40660e9	0.510880	0.255440	−	0.966825i	$-0.417780\pi$
$641$	3.40660e9	0.510880	0.255440	+	0.966825i	$0.417780\pi$
$642$	0	0
$643$	3.28085e9	0.486685	0.243343	−	0.969940i	$-0.421756\pi$
$643$	3.28085e9	0.486685	0.243343	+	0.969940i	$0.421756\pi$
$644$	−1.06912e10	−1.57735
$645$	0	0
$646$	4.37862e9	0.639033
$647$	−1.24280e10	−1.80400	−0.902001	−	0.431733i	$-0.857902\pi$
$647$	−1.24280e10	−1.80400	−0.902001	+	0.431733i	$0.857902\pi$
$648$	0	0
$649$	2.74611e9	0.394331
$650$	−8.47295e9	−1.21015
$651$	0	0
$652$	7.46919e7	0.0105538
$653$	−3.24629e9	−0.456238	−0.228119	−	0.973633i	$-0.573258\pi$
$653$	−3.24629e9	−0.456238	−0.228119	+	0.973633i	$0.573258\pi$
$654$	0	0
$655$	−6.95659e8	−0.0967279
$656$	−3.96198e9	−0.547960
$657$	0	0
$658$	1.54871e10	2.11924
$659$	−1.01236e10	−1.37795	−0.688976	−	0.724784i	$-0.741940\pi$
$659$	−1.01236e10	−1.37795	−0.688976	+	0.724784i	$0.741940\pi$
$660$	0	0
$661$	−5.80319e9	−0.781559	−0.390780	−	0.920484i	$-0.627795\pi$
$661$	−5.80319e9	−0.781559	−0.390780	+	0.920484i	$0.627795\pi$
$662$	−6.79943e9	−0.910898
$663$	0	0
$664$	2.39001e9	0.316819
$665$	−7.48447e8	−0.0986927
$666$	0	0
$667$	−1.69639e10	−2.21353
$668$	−1.40644e10	−1.82559
$669$	0	0
$670$	−1.58252e9	−0.203276
$671$	4.94905e9	0.632402
$672$	0	0
$673$	−9.58718e9	−1.21238	−0.606189	−	0.795321i	$-0.707302\pi$
$673$	−9.58718e9	−1.21238	−0.606189	+	0.795321i	$0.707302\pi$
$674$	−3.74377e9	−0.470977
$675$	0	0
$676$	−3.93362e9	−0.489755
$677$	1.59330e9	0.197350	0.0986751	−	0.995120i	$-0.468540\pi$
$677$	1.59330e9	0.197350	0.0986751	+	0.995120i	$0.468540\pi$
$678$	0	0
$679$	−9.73683e9	−1.19364
$680$	−1.07158e9	−0.130691
$681$	0	0
$682$	1.52728e9	0.184362
$683$	1.11674e10	1.34116	0.670579	−	0.741838i	$-0.266046\pi$
$683$	1.11674e10	1.34116	0.670579	+	0.741838i	$0.266046\pi$
$684$	0	0
$685$	1.06432e9	0.126519
$686$	−1.43504e10	−1.69718
$687$	0	0
$688$	1.16169e9	0.135997
$689$	6.39008e9	0.744284
$690$	0	0
$691$	−2.43715e9	−0.281001	−0.140501	−	0.990081i	$-0.544871\pi$
$691$	−2.43715e9	−0.281001	−0.140501	+	0.990081i	$0.544871\pi$
$692$	−1.64626e10	−1.88855
$693$	0	0
$694$	2.37556e9	0.269779
$695$	−1.63845e8	−0.0185134
$696$	0	0
$697$	1.17312e10	1.31229
$698$	−1.51262e9	−0.168358
$699$	0	0
$700$	−9.51258e9	−1.04823
$701$	1.29449e10	1.41934	0.709668	−	0.704536i	$-0.248845\pi$
$701$	1.29449e10	1.41934	0.709668	+	0.704536i	$0.248845\pi$
$702$	0	0
$703$	4.13298e9	0.448662
$704$	−9.76662e9	−1.05497
$705$	0	0
$706$	−1.79323e10	−1.91787
$707$	8.75296e9	0.931509
$708$	0	0
$709$	1.86974e10	1.97024	0.985118	−	0.171877i	$-0.0549831\pi$
$709$	1.86974e10	1.97024	0.985118	+	0.171877i	$0.0549831\pi$
$710$	4.77782e9	0.500986
$711$	0	0
$712$	1.51883e8	0.0157699
$713$	−2.46709e9	−0.254901
$714$	0	0
$715$	−1.24298e9	−0.127172
$716$	−2.15047e10	−2.18946
$717$	0	0
$718$	1.11798e10	1.12719
$719$	−1.45164e9	−0.145649	−0.0728246	−	0.997345i	$-0.523201\pi$
$719$	−1.45164e9	−0.145649	−0.0728246	+	0.997345i	$0.523201\pi$
$720$	0	0
$721$	−8.10905e9	−0.805743
$722$	−1.11327e10	−1.10083
$723$	0	0
$724$	−1.17597e10	−1.15163
$725$	−1.50937e10	−1.47100
$726$	0	0
$727$	1.47412e10	1.42286	0.711432	−	0.702755i	$-0.248047\pi$
$727$	1.47412e10	1.42286	0.711432	+	0.702755i	$0.248047\pi$
$728$	4.74227e9	0.455539
$729$	0	0
$730$	−4.56244e9	−0.434077
$731$	−3.43970e9	−0.325694
$732$	0	0
$733$	−1.96720e10	−1.84495	−0.922475	−	0.386058i	$-0.873837\pi$
$733$	−1.96720e10	−1.84495	−0.922475	+	0.386058i	$0.873837\pi$
$734$	−2.17434e10	−2.02951
$735$	0	0
$736$	1.88077e10	1.73885
$737$	3.85140e9	0.354391
$738$	0	0
$739$	−1.48159e10	−1.35043	−0.675215	−	0.737621i	$-0.735949\pi$
$739$	−1.48159e10	−1.35043	−0.675215	+	0.737621i	$0.735949\pi$
$740$	−3.16635e9	−0.287242
$741$	0	0
$742$	1.20566e10	1.08345
$743$	2.66103e9	0.238007	0.119003	−	0.992894i	$-0.462030\pi$
$743$	2.66103e9	0.238007	0.119003	+	0.992894i	$0.462030\pi$
$744$	0	0
$745$	−6.44459e7	−0.00571016
$746$	1.68086e10	1.48233
$747$	0	0
$748$	8.16400e9	0.713259
$749$	−5.44593e9	−0.473572
$750$	0	0
$751$	4.01550e9	0.345940	0.172970	−	0.984927i	$-0.444664\pi$
$751$	4.01550e9	0.345940	0.172970	+	0.984927i	$0.444664\pi$
$752$	−6.45180e9	−0.553246
$753$	0	0
$754$	2.35554e10	2.00120
$755$	3.14818e9	0.266222
$756$	0	0
$757$	2.04832e10	1.71618	0.858090	−	0.513500i	$-0.171651\pi$
$757$	2.04832e10	1.71618	0.858090	+	0.513500i	$0.171651\pi$
$758$	1.25538e10	1.04697
$759$	0	0
$760$	−1.16471e9	−0.0962429
$761$	7.81181e9	0.642548	0.321274	−	0.946986i	$-0.395889\pi$
$761$	7.81181e9	0.642548	0.321274	+	0.946986i	$0.395889\pi$
$762$	0	0
$763$	3.65375e9	0.297785
$764$	2.76215e10	2.24089
$765$	0	0
$766$	−2.59155e10	−2.08333
$767$	6.15955e9	0.492907
$768$	0	0
$769$	−8.36138e9	−0.663034	−0.331517	−	0.943449i	$-0.607560\pi$
$769$	−8.36138e9	−0.663034	−0.331517	+	0.943449i	$0.607560\pi$
$770$	−2.34520e9	−0.185124
$771$	0	0
$772$	−6.19377e9	−0.484501
$773$	−1.15155e10	−0.896714	−0.448357	−	0.893854i	$-0.647991\pi$
$773$	−1.15155e10	−0.896714	−0.448357	+	0.893854i	$0.647991\pi$
$774$	0	0
$775$	−2.19511e9	−0.169395
$776$	−1.51521e10	−1.16401
$777$	0	0
$778$	−2.14202e10	−1.63078
$779$	1.27507e10	0.966391
$780$	0	0
$781$	−1.16279e10	−0.873417
$782$	−2.21627e10	−1.65729
$783$	0	0
$784$	1.79148e9	0.132772
$785$	4.06697e9	0.300073
$786$	0	0
$787$	−6.25272e9	−0.457254	−0.228627	−	0.973514i	$-0.573424\pi$
$787$	−6.25272e9	−0.457254	−0.228627	+	0.973514i	$0.573424\pi$
$788$	2.43630e10	1.77373
$789$	0	0
$790$	5.30790e9	0.383026
$791$	1.34663e10	0.967456
$792$	0	0
$793$	1.11008e10	0.790492
$794$	2.10307e10	1.49101
$795$	0	0
$796$	8.52782e9	0.599297
$797$	−2.43108e10	−1.70096	−0.850482	−	0.526004i	$-0.823690\pi$
$797$	−2.43108e10	−1.70096	−0.850482	+	0.526004i	$0.823690\pi$
$798$	0	0
$799$	1.91035e10	1.32495
$800$	1.67342e10	1.15555
$801$	0	0
$802$	−4.26958e10	−2.92264
$803$	1.11037e10	0.756767
$804$	0	0
$805$	3.78832e9	0.255954
$806$	3.42570e9	0.230450
$807$	0	0
$808$	1.36210e10	0.908386
$809$	2.27903e10	1.51332	0.756658	−	0.653811i	$-0.226831\pi$
$809$	2.27903e10	1.51332	0.756658	+	0.653811i	$0.226831\pi$
$810$	0	0
$811$	1.74087e10	1.14602	0.573011	−	0.819548i	$-0.305775\pi$
$811$	1.74087e10	1.14602	0.573011	+	0.819548i	$0.305775\pi$
$812$	2.64456e10	1.73343
$813$	0	0
$814$	1.29504e10	0.841582
$815$	−2.64663e7	−0.00171254
$816$	0	0
$817$	−3.73861e9	−0.239846
$818$	3.26820e10	2.08772
$819$	0	0
$820$	−9.76854e9	−0.618701
$821$	8.16671e8	0.0515046	0.0257523	−	0.999668i	$-0.491802\pi$
$821$	8.16671e8	0.0515046	0.0257523	+	0.999668i	$0.491802\pi$
$822$	0	0
$823$	4.40653e9	0.275548	0.137774	−	0.990464i	$-0.456005\pi$
$823$	4.40653e9	0.275548	0.137774	+	0.990464i	$0.456005\pi$
$824$	−1.26190e10	−0.785742
$825$	0	0
$826$	1.16216e10	0.717524
$827$	−2.64306e10	−1.62494	−0.812471	−	0.583002i	$-0.801878\pi$
$827$	−2.64306e10	−1.62494	−0.812471	+	0.583002i	$0.801878\pi$
$828$	0	0
$829$	1.29309e10	0.788290	0.394145	−	0.919048i	$-0.371041\pi$
$829$	1.29309e10	0.788290	0.394145	+	0.919048i	$0.371041\pi$
$830$	−2.65109e9	−0.160935
$831$	0	0
$832$	−2.19066e10	−1.31869
$833$	−5.30448e9	−0.317969
$834$	0	0
$835$	4.98356e9	0.296235
$836$	8.87346e9	0.525256
$837$	0	0
$838$	4.08922e10	2.40041
$839$	−4.19322e9	−0.245121	−0.122561	−	0.992461i	$-0.539111\pi$
$839$	−4.19322e9	−0.245121	−0.122561	+	0.992461i	$0.539111\pi$
$840$	0	0
$841$	2.47116e10	1.43257
$842$	−1.11197e10	−0.641946
$843$	0	0
$844$	−4.52076e9	−0.258829
$845$	1.39383e9	0.0794717
$846$	0	0
$847$	−7.66861e9	−0.433636
$848$	−5.02266e9	−0.282845
$849$	0	0
$850$	−1.97194e10	−1.10136
$851$	−2.09194e10	−1.16358
$852$	0	0
$853$	−4.30506e9	−0.237497	−0.118748	−	0.992924i	$-0.537888\pi$
$853$	−4.30506e9	−0.237497	−0.118748	+	0.992924i	$0.537888\pi$
$854$	2.09445e10	1.15072
$855$	0	0
$856$	−8.47476e9	−0.461816
$857$	5.75854e9	0.312521	0.156261	−	0.987716i	$-0.450056\pi$
$857$	5.75854e9	0.312521	0.156261	+	0.987716i	$0.450056\pi$
$858$	0	0
$859$	1.98600e9	0.106906	0.0534532	−	0.998570i	$-0.482977\pi$
$859$	1.98600e9	0.106906	0.0534532	+	0.998570i	$0.482977\pi$
$860$	2.86422e9	0.153554
$861$	0	0
$862$	1.38522e8	0.00736619
$863$	2.32324e10	1.23043	0.615214	−	0.788360i	$-0.289069\pi$
$863$	2.32324e10	1.23043	0.615214	+	0.788360i	$0.289069\pi$
$864$	0	0
$865$	5.83335e9	0.306451
$866$	−4.44430e10	−2.32536
$867$	0	0
$868$	3.84604e9	0.199616
$869$	−1.29179e10	−0.667765
$870$	0	0
$871$	8.63874e9	0.442983
$872$	5.68583e9	0.290393
$873$	0	0
$874$	−2.40887e10	−1.22046
$875$	6.94453e9	0.350441
$876$	0	0
$877$	−3.43141e10	−1.71781	−0.858904	−	0.512137i	$-0.828854\pi$
$877$	−3.43141e10	−1.71781	−0.858904	+	0.512137i	$0.828854\pi$
$878$	−9.35410e9	−0.466413
$879$	0	0
$880$	9.76990e8	0.0483282
$881$	−1.07877e10	−0.531512	−0.265756	−	0.964040i	$-0.585622\pi$
$881$	−1.07877e10	−0.531512	−0.265756	+	0.964040i	$0.585622\pi$
$882$	0	0
$883$	7.23350e9	0.353578	0.176789	−	0.984249i	$-0.443429\pi$
$883$	7.23350e9	0.353578	0.176789	+	0.984249i	$0.443429\pi$
$884$	1.83119e10	0.891562
$885$	0	0
$886$	3.18285e10	1.53744
$887$	−8.47997e9	−0.408002	−0.204001	−	0.978971i	$-0.565395\pi$
$887$	−8.47997e9	−0.408002	−0.204001	+	0.978971i	$0.565395\pi$
$888$	0	0
$889$	8.10257e9	0.386782
$890$	−1.68474e8	−0.00801067
$891$	0	0
$892$	−2.08414e10	−0.983220
$893$	2.07636e10	0.975713
$894$	0	0
$895$	7.61995e9	0.355280
$896$	−2.13788e10	−0.992897
$897$	0	0
$898$	3.95634e10	1.82317
$899$	6.10254e9	0.280125
$900$	0	0
$901$	1.48719e10	0.677374
$902$	3.99533e10	1.81272
$903$	0	0
$904$	2.09558e10	0.943441
$905$	4.16692e9	0.186872
$906$	0	0
$907$	−2.75004e10	−1.22381	−0.611904	−	0.790932i	$-0.709596\pi$
$907$	−2.75004e10	−1.22381	−0.611904	+	0.790932i	$0.709596\pi$
$908$	−5.63926e10	−2.49990
$909$	0	0
$910$	−5.26031e9	−0.231402
$911$	−3.95002e10	−1.73095	−0.865475	−	0.500952i	$-0.832983\pi$
$911$	−3.95002e10	−1.73095	−0.865475	+	0.500952i	$0.832983\pi$
$912$	0	0
$913$	6.45201e9	0.280574
$914$	5.82619e10	2.52390
$915$	0	0
$916$	6.33902e10	2.72514
$917$	7.16498e9	0.306847
$918$	0	0
$919$	−3.20963e8	−0.0136411	−0.00682057	−	0.999977i	$-0.502171\pi$
$919$	−3.20963e8	−0.0136411	−0.00682057	+	0.999977i	$0.502171\pi$
$920$	5.89525e9	0.249600
$921$	0	0
$922$	2.25494e10	0.947495
$923$	−2.60814e10	−1.09176
$924$	0	0
$925$	−1.86131e10	−0.773256
$926$	−3.75714e10	−1.55496
$927$	0	0
$928$	−4.65222e10	−1.91092
$929$	−1.64291e10	−0.672294	−0.336147	−	0.941810i	$-0.609124\pi$
$929$	−1.64291e10	−0.672294	−0.336147	+	0.941810i	$0.609124\pi$
$930$	0	0
$931$	−5.76544e9	−0.234158
$932$	2.22666e10	0.900946
$933$	0	0
$934$	−3.09364e10	−1.24238
$935$	−2.89282e9	−0.115739
$936$	0	0
$937$	−6.45937e9	−0.256508	−0.128254	−	0.991741i	$-0.540937\pi$
$937$	−6.45937e9	−0.256508	−0.128254	+	0.991741i	$0.540937\pi$
$938$	1.62992e10	0.644848
$939$	0	0
$940$	−1.59074e10	−0.624670
$941$	−1.53005e10	−0.598609	−0.299304	−	0.954158i	$-0.596755\pi$
$941$	−1.53005e10	−0.598609	−0.299304	+	0.954158i	$0.596755\pi$
$942$	0	0
$943$	−6.45387e10	−2.50628
$944$	−4.84147e9	−0.187316
$945$	0	0
$946$	−1.17146e10	−0.449894
$947$	−1.36187e10	−0.521087	−0.260543	−	0.965462i	$-0.583902\pi$
$947$	−1.36187e10	−0.521087	−0.260543	+	0.965462i	$0.583902\pi$
$948$	0	0
$949$	2.49057e10	0.945946
$950$	−2.14330e10	−0.811056
$951$	0	0
$952$	1.10368e10	0.414587
$953$	−1.43126e9	−0.0535666	−0.0267833	−	0.999641i	$-0.508526\pi$
$953$	−1.43126e9	−0.0535666	−0.0267833	+	0.999641i	$0.508526\pi$
$954$	0	0
$955$	−9.78737e9	−0.363625
$956$	3.13834e10	1.16171
$957$	0	0
$958$	1.77227e10	0.651256
$959$	−1.09620e10	−0.401351
$960$	0	0
$961$	8.87504e8	0.0322581
$962$	2.90478e10	1.05196
$963$	0	0
$964$	1.26170e10	0.453613
$965$	2.19469e9	0.0786192
$966$	0	0
$967$	−9.10409e9	−0.323775	−0.161888	−	0.986809i	$-0.551758\pi$
$967$	−9.10409e9	−0.323775	−0.161888	+	0.986809i	$0.551758\pi$
$968$	−1.19336e10	−0.422872
$969$	0	0
$970$	1.68073e10	0.591285
$971$	2.51666e9	0.0882180	0.0441090	−	0.999027i	$-0.485955\pi$
$971$	2.51666e9	0.0882180	0.0441090	+	0.999027i	$0.485955\pi$
$972$	0	0
$973$	1.68753e9	0.0587296
$974$	−7.00451e10	−2.42897
$975$	0	0
$976$	−8.72532e9	−0.300405
$977$	−1.45618e10	−0.499554	−0.249777	−	0.968303i	$-0.580357\pi$
$977$	−1.45618e10	−0.499554	−0.249777	+	0.968303i	$0.580357\pi$
$978$	0	0
$979$	4.10019e8	0.0139658
$980$	4.41701e9	0.149912
$981$	0	0
$982$	7.00110e9	0.235926
$983$	1.09489e10	0.367648	0.183824	−	0.982959i	$-0.441152\pi$
$983$	1.09489e10	0.367648	0.183824	+	0.982959i	$0.441152\pi$
$984$	0	0
$985$	−8.63275e9	−0.287821
$986$	5.48212e10	1.82129
$987$	0	0
$988$	1.99033e10	0.656561
$989$	1.89233e10	0.622027
$990$	0	0
$991$	−4.82115e9	−0.157360	−0.0786798	−	0.996900i	$-0.525070\pi$
$991$	−4.82115e9	−0.157360	−0.0786798	+	0.996900i	$0.525070\pi$
$992$	−6.76581e9	−0.220054
$993$	0	0
$994$	−4.92095e10	−1.58927
$995$	−3.02174e9	−0.0972469
$996$	0	0
$997$	−1.91710e10	−0.612649	−0.306325	−	0.951927i	$-0.599099\pi$
$997$	−1.91710e10	−0.612649	−0.306325	+	0.951927i	$0.599099\pi$
$998$	2.46892e10	0.786231
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.8.a.b.1.7		7
3.2	odd	2		31.8.a.a.1.1	✓	7
12.11	even	2		496.8.a.e.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.8.a.a.1.1	✓	7	3.2	odd	2
279.8.a.b.1.7		7	1.1	even	1	trivial
496.8.a.e.1.7		7	12.11	even	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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	279.a (trivial)

\(f(q)\)	\(=\)	\(q+17.7787 q^{2} +188.081 q^{4} -66.6445 q^{5} +686.409 q^{7} +1068.16 q^{8} +O(q^{10})\)	\(q+17.7787 q^{2} +188.081 q^{4} -66.6445 q^{5} +686.409 q^{7} +1068.16 q^{8} -1184.85 q^{10} +2883.59 q^{11} +6467.92 q^{13} +12203.4 q^{14} -5083.85 q^{16} +15053.0 q^{17} +16361.2 q^{19} -12534.6 q^{20} +51266.4 q^{22} -82813.3 q^{23} -73683.5 q^{25} +114991. q^{26} +129101. q^{28} +204845. q^{29} +29791.0 q^{31} -227109. q^{32} +267623. q^{34} -45745.4 q^{35} +252609. q^{37} +290880. q^{38} -71187.3 q^{40} +779327. q^{41} -228505. q^{43} +542349. q^{44} -1.47231e6 q^{46} +1.26908e6 q^{47} -352386. q^{49} -1.31000e6 q^{50} +1.21650e6 q^{52} +987964. q^{53} -192175. q^{55} +733197. q^{56} +3.64187e6 q^{58} +952323. q^{59} +1.71628e6 q^{61} +529644. q^{62} -3.38697e6 q^{64} -431051. q^{65} +1.33563e6 q^{67} +2.83119e6 q^{68} -813292. q^{70} -4.03243e6 q^{71} +3.85064e6 q^{73} +4.49106e6 q^{74} +3.07723e6 q^{76} +1.97932e6 q^{77} -4.47981e6 q^{79} +338810. q^{80} +1.38554e7 q^{82} +2.23749e6 q^{83} -1.00320e6 q^{85} -4.06252e6 q^{86} +3.08015e6 q^{88} +142190. q^{89} +4.43964e6 q^{91} -1.55756e7 q^{92} +2.25625e7 q^{94} -1.09038e6 q^{95} -1.41852e7 q^{97} -6.26496e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 17 q^{2} + 229 q^{4} + 430 q^{5} - 832 q^{7} + 135 q^{8}+O(q^{10}) \) 7 * q + 17 * q^2 + 229 * q^4 + 430 * q^5 - 832 * q^7 + 135 * q^8	\( 7 q + 17 q^{2} + 229 q^{4} + 430 q^{5} - 832 q^{7} + 135 q^{8} - 5232 q^{10} + 7886 q^{11} - 21844 q^{13} + 37902 q^{14} - 49583 q^{16} + 54822 q^{17} - 45352 q^{19} + 50110 q^{20} + 30696 q^{22} + 18464 q^{23} - 37691 q^{25} - 3906 q^{26} + 323084 q^{28} + 81488 q^{29} + 208537 q^{31} - 276513 q^{32} + 1152342 q^{34} - 154340 q^{35} + 431648 q^{37} - 798430 q^{38} + 600366 q^{40} + 1465990 q^{41} - 598714 q^{43} + 660872 q^{44} - 356652 q^{46} + 2003572 q^{47} - 331317 q^{49} - 91595 q^{50} - 28582 q^{52} + 1496844 q^{53} - 1414452 q^{55} + 2199880 q^{56} + 1517430 q^{58} + 2853828 q^{59} - 1486900 q^{61} + 506447 q^{62} - 1940543 q^{64} + 2252240 q^{65} - 5647492 q^{67} - 829234 q^{68} + 8307114 q^{70} + 5168828 q^{71} + 4710926 q^{73} - 4058410 q^{74} + 15097160 q^{76} + 2020724 q^{77} + 4582796 q^{79} - 6495030 q^{80} + 8295096 q^{82} + 626514 q^{83} + 8323116 q^{85} + 3575108 q^{86} + 2100840 q^{88} + 13906634 q^{89} + 10966300 q^{91} + 2803952 q^{92} + 21167040 q^{94} + 11547396 q^{95} + 2962898 q^{97} + 25061151 q^{98}+O(q^{100}) \) 7 * q + 17 * q^2 + 229 * q^4 + 430 * q^5 - 832 * q^7 + 135 * q^8 - 5232 * q^10 + 7886 * q^11 - 21844 * q^13 + 37902 * q^14 - 49583 * q^16 + 54822 * q^17 - 45352 * q^19 + 50110 * q^20 + 30696 * q^22 + 18464 * q^23 - 37691 * q^25 - 3906 * q^26 + 323084 * q^28 + 81488 * q^29 + 208537 * q^31 - 276513 * q^32 + 1152342 * q^34 - 154340 * q^35 + 431648 * q^37 - 798430 * q^38 + 600366 * q^40 + 1465990 * q^41 - 598714 * q^43 + 660872 * q^44 - 356652 * q^46 + 2003572 * q^47 - 331317 * q^49 - 91595 * q^50 - 28582 * q^52 + 1496844 * q^53 - 1414452 * q^55 + 2199880 * q^56 + 1517430 * q^58 + 2853828 * q^59 - 1486900 * q^61 + 506447 * q^62 - 1940543 * q^64 + 2252240 * q^65 - 5647492 * q^67 - 829234 * q^68 + 8307114 * q^70 + 5168828 * q^71 + 4710926 * q^73 - 4058410 * q^74 + 15097160 * q^76 + 2020724 * q^77 + 4582796 * q^79 - 6495030 * q^80 + 8295096 * q^82 + 626514 * q^83 + 8323116 * q^85 + 3575108 * q^86 + 2100840 * q^88 + 13906634 * q^89 + 10966300 * q^91 + 2803952 * q^92 + 21167040 * q^94 + 11547396 * q^95 + 2962898 * q^97 + 25061151 * q^98

Introduction

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