LMFDB - Embedded newform 99.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, 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("99.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.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:	$30.9261175229$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24 $ x^2 - x - 24
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.42443$ of defining polynomial
Character	$\chi$	$=$	99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.2733 q^{2} +105.273 q^{4} +303.826 q^{5} -829.478 q^{7} +347.112 q^{8} +O(q^{10})$	\(q-15.2733 q^{2} +105.273 q^{4} +303.826 q^{5} -829.478 q^{7} +347.112 q^{8} -4640.42 q^{10} -1331.00 q^{11} -6061.62 q^{13} +12668.9 q^{14} -18776.5 q^{16} +2468.81 q^{17} +42140.2 q^{19} +31984.8 q^{20} +20328.7 q^{22} +37118.2 q^{23} +14185.2 q^{25} +92580.8 q^{26} -87321.9 q^{28} +59769.3 q^{29} -21301.7 q^{31} +242349. q^{32} -37706.8 q^{34} -252017. q^{35} +330635. q^{37} -643620. q^{38} +105462. q^{40} -816862. q^{41} -958652. q^{43} -140119. q^{44} -566917. q^{46} -38915.5 q^{47} -135509. q^{49} -216655. q^{50} -638126. q^{52} +1.47350e6 q^{53} -404392. q^{55} -287921. q^{56} -912873. q^{58} -1.59205e6 q^{59} -3.08178e6 q^{61} +325347. q^{62} -1.29807e6 q^{64} -1.84168e6 q^{65} -1.59464e6 q^{67} +259900. q^{68} +3.84913e6 q^{70} +2.69496e6 q^{71} -4.48213e6 q^{73} -5.04989e6 q^{74} +4.43624e6 q^{76} +1.10404e6 q^{77} -1.41084e6 q^{79} -5.70479e6 q^{80} +1.24762e7 q^{82} -653174. q^{83} +750088. q^{85} +1.46418e7 q^{86} -462006. q^{88} -2.32673e6 q^{89} +5.02798e6 q^{91} +3.90756e6 q^{92} +594367. q^{94} +1.28033e7 q^{95} -2.16642e6 q^{97} +2.06967e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 181 q^{4} + 194 q^{5} - 418 q^{7} - 399 q^{8}+O(q^{10}) $ 2 * q - q^2 + 181 * q^4 + 194 * q^5 - 418 * q^7 - 399 * q^8	\( 2 q - q^{2} + 181 q^{4} + 194 q^{5} - 418 q^{7} - 399 q^{8} - 6208 q^{10} - 2662 q^{11} - 13246 q^{13} + 18542 q^{14} - 39119 q^{16} + 10256 q^{17} + 14196 q^{19} + 23668 q^{20} + 1331 q^{22} + 13666 q^{23} - 51878 q^{25} - 9964 q^{26} - 56162 q^{28} - 15312 q^{29} - 48040 q^{31} + 47497 q^{32} + 73442 q^{34} - 297208 q^{35} + 274092 q^{37} - 1042476 q^{38} + 187404 q^{40} - 755836 q^{41} - 1704096 q^{43} - 240911 q^{44} - 901658 q^{46} + 1182094 q^{47} - 789738 q^{49} - 1159595 q^{50} - 1182176 q^{52} + 2156394 q^{53} - 258214 q^{55} - 594930 q^{56} - 1984530 q^{58} - 927332 q^{59} - 1061994 q^{61} - 56296 q^{62} - 1475407 q^{64} - 1052644 q^{65} - 3259952 q^{67} + 849598 q^{68} + 3204104 q^{70} + 5495514 q^{71} - 5450812 q^{73} - 5856942 q^{74} + 2320116 q^{76} + 556358 q^{77} - 1536590 q^{79} - 3470660 q^{80} + 13347206 q^{82} - 8850888 q^{83} - 105148 q^{85} + 4001832 q^{86} + 531069 q^{88} - 6810132 q^{89} + 2071760 q^{91} + 2131598 q^{92} + 18022186 q^{94} + 15872304 q^{95} + 9897376 q^{97} - 7268325 q^{98}+O(q^{100}) \) 2 * q - q^2 + 181 * q^4 + 194 * q^5 - 418 * q^7 - 399 * q^8 - 6208 * q^10 - 2662 * q^11 - 13246 * q^13 + 18542 * q^14 - 39119 * q^16 + 10256 * q^17 + 14196 * q^19 + 23668 * q^20 + 1331 * q^22 + 13666 * q^23 - 51878 * q^25 - 9964 * q^26 - 56162 * q^28 - 15312 * q^29 - 48040 * q^31 + 47497 * q^32 + 73442 * q^34 - 297208 * q^35 + 274092 * q^37 - 1042476 * q^38 + 187404 * q^40 - 755836 * q^41 - 1704096 * q^43 - 240911 * q^44 - 901658 * q^46 + 1182094 * q^47 - 789738 * q^49 - 1159595 * q^50 - 1182176 * q^52 + 2156394 * q^53 - 258214 * q^55 - 594930 * q^56 - 1984530 * q^58 - 927332 * q^59 - 1061994 * q^61 - 56296 * q^62 - 1475407 * q^64 - 1052644 * q^65 - 3259952 * q^67 + 849598 * q^68 + 3204104 * q^70 + 5495514 * q^71 - 5450812 * q^73 - 5856942 * q^74 + 2320116 * q^76 + 556358 * q^77 - 1536590 * q^79 - 3470660 * q^80 + 13347206 * q^82 - 8850888 * q^83 - 105148 * q^85 + 4001832 * q^86 + 531069 * q^88 - 6810132 * q^89 + 2071760 * q^91 + 2131598 * q^92 + 18022186 * q^94 + 15872304 * q^95 + 9897376 * q^97 - 7268325 * 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 $

$2$	−15.2733	−1.34998	−0.674990	−	0.737827i	$-0.735852\pi$
$2$	−15.2733	−1.34998	−0.674990	+	0.737827i	$0.735852\pi$
$3$	0	0
$3$	0	0
$4$	105.273	0.822448
$5$	303.826	1.08700	0.543500	−	0.839409i	$-0.317099\pi$
$5$	303.826	1.08700	0.543500	+	0.839409i	$0.317099\pi$
$6$	0	0
$7$	−829.478	−0.914033	−0.457016	−	0.889458i	$-0.651082\pi$
$7$	−829.478	−0.914033	−0.457016	+	0.889458i	$0.651082\pi$
$8$	347.112	0.239692
$9$	0	0
$10$	−4640.42	−1.46743
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	0	0
$13$	−6061.62	−0.765221	−0.382610	−	0.923910i	$-0.624975\pi$
$13$	−6061.62	−0.765221	−0.382610	+	0.923910i	$0.624975\pi$
$14$	12668.9	1.23393
$15$	0	0
$16$	−18776.5	−1.14603
$17$	2468.81	0.121875	0.0609377	−	0.998142i	$-0.480591\pi$
$17$	2468.81	0.121875	0.0609377	+	0.998142i	$0.480591\pi$
$18$	0	0
$19$	42140.2	1.40948	0.704741	−	0.709465i	$-0.251063\pi$
$19$	42140.2	1.40948	0.704741	+	0.709465i	$0.251063\pi$
$20$	31984.8	0.894001
$21$	0	0
$22$	20328.7	0.407034
$23$	37118.2	0.636121	0.318061	−	0.948070i	$-0.396968\pi$
$23$	37118.2	0.636121	0.318061	+	0.948070i	$0.396968\pi$
$24$	0	0
$25$	14185.2	0.181571
$26$	92580.8	1.03303
$27$	0	0
$28$	−87321.9	−0.751744
$29$	59769.3	0.455077	0.227539	−	0.973769i	$-0.426932\pi$
$29$	59769.3	0.455077	0.227539	+	0.973769i	$0.426932\pi$
$30$	0	0
$31$	−21301.7	−0.128425	−0.0642124	−	0.997936i	$-0.520454\pi$
$31$	−21301.7	−0.128425	−0.0642124	+	0.997936i	$0.520454\pi$
$32$	242349.	1.30742
$33$	0	0
$34$	−37706.8	−0.164529
$35$	−252017.	−0.993554
$36$	0	0
$37$	330635.	1.07311	0.536553	−	0.843866i	$-0.319726\pi$
$37$	330635.	1.07311	0.536553	+	0.843866i	$0.319726\pi$
$38$	−643620.	−1.90277
$39$	0	0
$40$	105462.	0.260546
$41$	−816862.	−1.85099	−0.925497	−	0.378754i	$-0.876353\pi$
$41$	−816862.	−1.85099	−0.925497	+	0.378754i	$0.876353\pi$
$42$	0	0
$43$	−958652.	−1.83874	−0.919372	−	0.393389i	$-0.871303\pi$
$43$	−958652.	−1.83874	−0.919372	+	0.393389i	$0.871303\pi$
$44$	−140119.	−0.247977
$45$	0	0
$46$	−566917.	−0.858751
$47$	−38915.5	−0.0546739	−0.0273369	−	0.999626i	$-0.508703\pi$
$47$	−38915.5	−0.0546739	−0.0273369	+	0.999626i	$0.508703\pi$
$48$	0	0
$49$	−135509.	−0.164544
$50$	−216655.	−0.245118
$51$	0	0
$52$	−638126.	−0.629354
$53$	1.47350e6	1.35952	0.679759	−	0.733436i	$-0.262084\pi$
$53$	1.47350e6	1.35952	0.679759	+	0.733436i	$0.262084\pi$
$54$	0	0
$55$	−404392.	−0.327743
$56$	−287921.	−0.219087
$57$	0	0
$58$	−912873.	−0.614345
$59$	−1.59205e6	−1.00919	−0.504597	−	0.863355i	$-0.668359\pi$
$59$	−1.59205e6	−1.00919	−0.504597	+	0.863355i	$0.668359\pi$
$60$	0	0
$61$	−3.08178e6	−1.73839	−0.869196	−	0.494468i	$-0.835363\pi$
$61$	−3.08178e6	−1.73839	−0.869196	+	0.494468i	$0.835363\pi$
$62$	325347.	0.173371
$63$	0	0
$64$	−1.29807e6	−0.618968
$65$	−1.84168e6	−0.831795
$66$	0	0
$67$	−1.59464e6	−0.647739	−0.323870	−	0.946102i	$-0.604984\pi$
$67$	−1.59464e6	−0.647739	−0.323870	+	0.946102i	$0.604984\pi$
$68$	259900.	0.100236
$69$	0	0
$70$	3.84913e6	1.34128
$71$	2.69496e6	0.893609	0.446805	−	0.894632i	$-0.352562\pi$
$71$	2.69496e6	0.893609	0.446805	+	0.894632i	$0.352562\pi$
$72$	0	0
$73$	−4.48213e6	−1.34851	−0.674255	−	0.738499i	$-0.735535\pi$
$73$	−4.48213e6	−1.34851	−0.674255	+	0.738499i	$0.735535\pi$
$74$	−5.04989e6	−1.44867
$75$	0	0
$76$	4.43624e6	1.15922
$77$	1.10404e6	0.275591
$78$	0	0
$79$	−1.41084e6	−0.321947	−0.160973	−	0.986959i	$-0.551463\pi$
$79$	−1.41084e6	−0.321947	−0.160973	+	0.986959i	$0.551463\pi$
$80$	−5.70479e6	−1.24573
$81$	0	0
$82$	1.24762e7	2.49881
$83$	−653174.	−0.125388	−0.0626939	−	0.998033i	$-0.519969\pi$
$83$	−653174.	−0.125388	−0.0626939	+	0.998033i	$0.519969\pi$
$84$	0	0
$85$	750088.	0.132479
$86$	1.46418e7	2.48227
$87$	0	0
$88$	−462006.	−0.0722700
$89$	−2.32673e6	−0.349850	−0.174925	−	0.984582i	$-0.555968\pi$
$89$	−2.32673e6	−0.349850	−0.174925	+	0.984582i	$0.555968\pi$
$90$	0	0
$91$	5.02798e6	0.699437
$92$	3.90756e6	0.523176
$93$	0	0
$94$	594367.	0.0738087
$95$	1.28033e7	1.53211
$96$	0	0
$97$	−2.16642e6	−0.241014	−0.120507	−	0.992712i	$-0.538452\pi$
$97$	−2.16642e6	−0.241014	−0.120507	+	0.992712i	$0.538452\pi$
$98$	2.06967e6	0.222131
$99$	0	0
$100$	1.49333e6	0.149333
$101$	−6.34311e6	−0.612600	−0.306300	−	0.951935i	$-0.599091\pi$
$101$	−6.34311e6	−0.612600	−0.306300	+	0.951935i	$0.599091\pi$
$102$	0	0
$103$	5.53067e6	0.498709	0.249355	−	0.968412i	$-0.419782\pi$
$103$	5.53067e6	0.498709	0.249355	+	0.968412i	$0.419782\pi$
$104$	−2.10406e6	−0.183418
$105$	0	0
$106$	−2.25052e7	−1.83532
$107$	1.24836e7	0.985141	0.492570	−	0.870273i	$-0.336057\pi$
$107$	1.24836e7	0.985141	0.492570	+	0.870273i	$0.336057\pi$
$108$	0	0
$109$	1.15577e7	0.854831	0.427416	−	0.904055i	$-0.359424\pi$
$109$	1.15577e7	0.854831	0.427416	+	0.904055i	$0.359424\pi$
$110$	6.17640e6	0.442447
$111$	0	0
$112$	1.55747e7	1.04751
$113$	−2.91312e7	−1.89926	−0.949629	−	0.313378i	$-0.898539\pi$
$113$	−2.91312e7	−1.89926	−0.949629	+	0.313378i	$0.898539\pi$
$114$	0	0
$115$	1.12775e7	0.691464
$116$	6.29211e6	0.374277
$117$	0	0
$118$	2.43158e7	1.36239
$119$	−2.04782e6	−0.111398
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	4.70689e7	2.34679
$123$	0	0
$124$	−2.24250e6	−0.105623
$125$	−1.94266e7	−0.889633
$126$	0	0
$127$	−4.29589e7	−1.86097	−0.930487	−	0.366326i	$-0.880616\pi$
$127$	−4.29589e7	−1.86097	−0.930487	+	0.366326i	$0.880616\pi$
$128$	−1.11949e7	−0.471828
$129$	0	0
$130$	2.81285e7	1.12291
$131$	−3.87619e7	−1.50645	−0.753226	−	0.657761i	$-0.771504\pi$
$131$	−3.87619e7	−1.50645	−0.753226	+	0.657761i	$0.771504\pi$
$132$	0	0
$133$	−3.49544e7	−1.28831
$134$	2.43554e7	0.874436
$135$	0	0
$136$	856952.	0.0292126
$137$	−2.16108e7	−0.718040	−0.359020	−	0.933330i	$-0.616889\pi$
$137$	−2.16108e7	−0.718040	−0.359020	+	0.933330i	$0.616889\pi$
$138$	0	0
$139$	−1.06241e7	−0.335537	−0.167769	−	0.985826i	$-0.553656\pi$
$139$	−1.06241e7	−0.335537	−0.167769	+	0.985826i	$0.553656\pi$
$140$	−2.65307e7	−0.817146
$141$	0	0
$142$	−4.11609e7	−1.20636
$143$	8.06801e6	0.230723
$144$	0	0
$145$	1.81595e7	0.494669
$146$	6.84568e7	1.82046
$147$	0	0
$148$	3.48070e7	0.882574
$149$	−6.36303e7	−1.57584	−0.787920	−	0.615777i	$-0.788842\pi$
$149$	−6.36303e7	−1.57584	−0.787920	+	0.615777i	$0.788842\pi$
$150$	0	0
$151$	−1.42528e7	−0.336885	−0.168443	−	0.985711i	$-0.553874\pi$
$151$	−1.42528e7	−0.336885	−0.168443	+	0.985711i	$0.553874\pi$
$152$	1.46274e7	0.337842
$153$	0	0
$154$	−1.68622e7	−0.372043
$155$	−6.47202e6	−0.139598
$156$	0	0
$157$	−1.42133e7	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$157$	−1.42133e7	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$158$	2.15482e7	0.434622
$159$	0	0
$160$	7.36319e7	1.42117
$161$	−3.07888e7	−0.581436
$162$	0	0
$163$	8.04737e7	1.45545	0.727725	−	0.685869i	$-0.240578\pi$
$163$	8.04737e7	1.45545	0.727725	+	0.685869i	$0.240578\pi$
$164$	−8.59937e7	−1.52235
$165$	0	0
$166$	9.97611e6	0.169271
$167$	−7.01073e6	−0.116481	−0.0582406	−	0.998303i	$-0.518549\pi$
$167$	−7.01073e6	−0.116481	−0.0582406	+	0.998303i	$0.518549\pi$
$168$	0	0
$169$	−2.60053e7	−0.414438
$170$	−1.14563e7	−0.178844
$171$	0	0
$172$	−1.00920e8	−1.51227
$173$	1.81447e7	0.266433	0.133216	−	0.991087i	$-0.457469\pi$
$173$	1.81447e7	0.266433	0.133216	+	0.991087i	$0.457469\pi$
$174$	0	0
$175$	−1.17664e7	−0.165962
$176$	2.49915e7	0.345540
$177$	0	0
$178$	3.55369e7	0.472291
$179$	1.16784e8	1.52195	0.760973	−	0.648784i	$-0.224722\pi$
$179$	1.16784e8	1.52195	0.760973	+	0.648784i	$0.224722\pi$
$180$	0	0
$181$	−9.11199e7	−1.14219	−0.571095	−	0.820884i	$-0.693481\pi$
$181$	−9.11199e7	−1.14219	−0.571095	+	0.820884i	$0.693481\pi$
$182$	−7.67937e7	−0.944226
$183$	0	0
$184$	1.28842e7	0.152473
$185$	1.00456e8	1.16647
$186$	0	0
$187$	−3.28598e6	−0.0367468
$188$	−4.09676e6	−0.0449664
$189$	0	0
$190$	−1.95548e8	−2.06832
$191$	1.82885e8	1.89916	0.949581	−	0.313522i	$-0.101509\pi$
$191$	1.82885e8	1.89916	0.949581	+	0.313522i	$0.101509\pi$
$192$	0	0
$193$	1.32994e8	1.33163	0.665814	−	0.746118i	$-0.268084\pi$
$193$	1.32994e8	1.33163	0.665814	+	0.746118i	$0.268084\pi$
$194$	3.30884e7	0.325364
$195$	0	0
$196$	−1.42655e7	−0.135329
$197$	2.82339e7	0.263111	0.131555	−	0.991309i	$-0.458003\pi$
$197$	2.82339e7	0.263111	0.131555	+	0.991309i	$0.458003\pi$
$198$	0	0
$199$	−1.99071e8	−1.79070	−0.895350	−	0.445362i	$-0.853075\pi$
$199$	−1.99071e8	−1.79070	−0.895350	+	0.445362i	$0.853075\pi$
$200$	4.92386e6	0.0435212
$201$	0	0
$202$	9.68801e7	0.826999
$203$	−4.95773e7	−0.415955
$204$	0	0
$205$	−2.48184e8	−2.01203
$206$	−8.44715e7	−0.673248
$207$	0	0
$208$	1.13816e8	0.876964
$209$	−5.60887e7	−0.424975
$210$	0	0
$211$	3.80016e7	0.278493	0.139246	−	0.990258i	$-0.455532\pi$
$211$	3.80016e7	0.278493	0.139246	+	0.990258i	$0.455532\pi$
$212$	1.55120e8	1.11813
$213$	0	0
$214$	−1.90666e8	−1.32992
$215$	−2.91263e8	−1.99872
$216$	0	0
$217$	1.76693e7	0.117384
$218$	−1.76525e8	−1.15401
$219$	0	0
$220$	−4.25717e7	−0.269552
$221$	−1.49650e7	−0.0932616
$222$	0	0
$223$	1.14601e8	0.692022	0.346011	−	0.938230i	$-0.387536\pi$
$223$	1.14601e8	0.692022	0.346011	+	0.938230i	$0.387536\pi$
$224$	−2.01023e8	−1.19503
$225$	0	0
$226$	4.44929e8	2.56396
$227$	9.29427e7	0.527381	0.263691	−	0.964607i	$-0.415060\pi$
$227$	9.29427e7	0.527381	0.263691	+	0.964607i	$0.415060\pi$
$228$	0	0
$229$	3.51772e8	1.93569	0.967847	−	0.251541i	$-0.0809374\pi$
$229$	3.51772e8	1.93569	0.967847	+	0.251541i	$0.0809374\pi$
$230$	−1.72244e8	−0.933464
$231$	0	0
$232$	2.07466e7	0.109079
$233$	−1.90315e8	−0.985661	−0.492831	−	0.870125i	$-0.664038\pi$
$233$	−1.90315e8	−0.985661	−0.492831	+	0.870125i	$0.664038\pi$
$234$	0	0
$235$	−1.18235e7	−0.0594306
$236$	−1.67600e8	−0.830009
$237$	0	0
$238$	3.12770e7	0.150385
$239$	2.00720e8	0.951038	0.475519	−	0.879705i	$-0.342260\pi$
$239$	2.00720e8	0.951038	0.475519	+	0.879705i	$0.342260\pi$
$240$	0	0
$241$	−2.08229e8	−0.958258	−0.479129	−	0.877745i	$-0.659047\pi$
$241$	−2.08229e8	−0.958258	−0.479129	+	0.877745i	$0.659047\pi$
$242$	−2.70576e7	−0.122726
$243$	0	0
$244$	−3.24429e8	−1.42974
$245$	−4.11712e7	−0.178860
$246$	0	0
$247$	−2.55438e8	−1.07856
$248$	−7.39407e6	−0.0307824
$249$	0	0
$250$	2.96707e8	1.20099
$251$	4.78103e7	0.190837	0.0954186	−	0.995437i	$-0.469581\pi$
$251$	4.78103e7	0.190837	0.0954186	+	0.995437i	$0.469581\pi$
$252$	0	0
$253$	−4.94044e7	−0.191798
$254$	6.56124e8	2.51228
$255$	0	0
$256$	3.37135e8	1.25593
$257$	2.02303e8	0.743425	0.371712	−	0.928348i	$-0.378771\pi$
$257$	2.02303e8	0.743425	0.371712	+	0.928348i	$0.378771\pi$
$258$	0	0
$259$	−2.74255e8	−0.980855
$260$	−1.93879e8	−0.684108
$261$	0	0
$262$	5.92022e8	2.03368
$263$	4.06426e8	1.37764	0.688822	−	0.724931i	$-0.258128\pi$
$263$	4.06426e8	1.37764	0.688822	+	0.724931i	$0.258128\pi$
$264$	0	0
$265$	4.47688e8	1.47780
$266$	5.33869e8	1.73920
$267$	0	0
$268$	−1.67873e8	−0.532732
$269$	−5.29696e8	−1.65918	−0.829590	−	0.558373i	$-0.811426\pi$
$269$	−5.29696e8	−1.65918	−0.829590	+	0.558373i	$0.811426\pi$
$270$	0	0
$271$	−4.79694e8	−1.46410	−0.732051	−	0.681249i	$-0.761437\pi$
$271$	−4.79694e8	−1.46410	−0.732051	+	0.681249i	$0.761437\pi$
$272$	−4.63556e7	−0.139673
$273$	0	0
$274$	3.30068e8	0.969340
$275$	−1.88806e7	−0.0547458
$276$	0	0
$277$	5.74020e8	1.62274	0.811369	−	0.584535i	$-0.198723\pi$
$277$	5.74020e8	1.62274	0.811369	+	0.584535i	$0.198723\pi$
$278$	1.62265e8	0.452969
$279$	0	0
$280$	−8.74780e7	−0.238147
$281$	5.08869e8	1.36815	0.684075	−	0.729412i	$-0.260206\pi$
$281$	5.08869e8	1.36815	0.684075	+	0.729412i	$0.260206\pi$
$282$	0	0
$283$	1.55996e8	0.409130	0.204565	−	0.978853i	$-0.434422\pi$
$283$	1.55996e8	0.409130	0.204565	+	0.978853i	$0.434422\pi$
$284$	2.83707e8	0.734947
$285$	0	0
$286$	−1.23225e8	−0.311471
$287$	6.77569e8	1.69187
$288$	0	0
$289$	−4.04244e8	−0.985146
$290$	−2.77355e8	−0.667794
$291$	0	0
$292$	−4.71848e8	−1.10908
$293$	−3.31026e8	−0.768821	−0.384411	−	0.923162i	$-0.625595\pi$
$293$	−3.31026e8	−0.768821	−0.384411	+	0.923162i	$0.625595\pi$
$294$	0	0
$295$	−4.83706e8	−1.09699
$296$	1.14767e8	0.257216
$297$	0	0
$298$	9.71845e8	2.12735
$299$	−2.24996e8	−0.486773
$300$	0	0
$301$	7.95181e8	1.68067
$302$	2.17688e8	0.454788
$303$	0	0
$304$	−7.91247e8	−1.61530
$305$	−9.36326e8	−1.88963
$306$	0	0
$307$	−1.59688e8	−0.314983	−0.157491	−	0.987520i	$-0.550341\pi$
$307$	−1.59688e8	−0.314983	−0.157491	+	0.987520i	$0.550341\pi$
$308$	1.16225e8	0.226659
$309$	0	0
$310$	9.88489e7	0.188454
$311$	−3.51157e8	−0.661973	−0.330986	−	0.943636i	$-0.607381\pi$
$311$	−3.51157e8	−0.661973	−0.330986	+	0.943636i	$0.607381\pi$
$312$	0	0
$313$	−5.46772e8	−1.00786	−0.503931	−	0.863744i	$-0.668114\pi$
$313$	−5.46772e8	−1.00786	−0.503931	+	0.863744i	$0.668114\pi$
$314$	2.17083e8	0.395706
$315$	0	0
$316$	−1.48524e8	−0.264784
$317$	6.18068e8	1.08975	0.544877	−	0.838516i	$-0.316576\pi$
$317$	6.18068e8	1.08975	0.544877	+	0.838516i	$0.316576\pi$
$318$	0	0
$319$	−7.95529e7	−0.137211
$320$	−3.94387e8	−0.672818
$321$	0	0
$322$	4.70246e8	0.784927
$323$	1.04036e8	0.171781
$324$	0	0
$325$	−8.59855e7	−0.138942
$326$	−1.22910e9	−1.96483
$327$	0	0
$328$	−2.83542e8	−0.443669
$329$	3.22795e7	0.0499737
$330$	0	0
$331$	−6.84846e8	−1.03799	−0.518997	−	0.854776i	$-0.673694\pi$
$331$	−6.84846e8	−1.03799	−0.518997	+	0.854776i	$0.673694\pi$
$332$	−6.87618e7	−0.103125
$333$	0	0
$334$	1.07077e8	0.157247
$335$	−4.84493e8	−0.704093
$336$	0	0
$337$	1.19934e6	0.00170701	0.000853507	−	1.00000i	$-0.499728\pi$
$337$	1.19934e6	0.00170701	0.000853507		1.00000i	$0.499728\pi$
$338$	3.97187e8	0.559483
$339$	0	0
$340$	7.89643e7	0.108957
$341$	2.83526e7	0.0387215
$342$	0	0
$343$	7.95513e8	1.06443
$344$	−3.32759e8	−0.440733
$345$	0	0
$346$	−2.77129e8	−0.359679
$347$	2.08559e8	0.267964	0.133982	−	0.990984i	$-0.457224\pi$
$347$	2.08559e8	0.267964	0.133982	+	0.990984i	$0.457224\pi$
$348$	0	0
$349$	1.13428e7	0.0142834	0.00714172	−	0.999974i	$-0.497727\pi$
$349$	1.13428e7	0.0142834	0.00714172	+	0.999974i	$0.497727\pi$
$350$	1.79711e8	0.224045
$351$	0	0
$352$	−3.22566e8	−0.394203
$353$	−5.47130e8	−0.662032	−0.331016	−	0.943625i	$-0.607391\pi$
$353$	−5.47130e8	−0.662032	−0.331016	+	0.943625i	$0.607391\pi$
$354$	0	0
$355$	8.18798e8	0.971354
$356$	−2.44943e8	−0.287733
$357$	0	0
$358$	−1.78368e9	−2.05460
$359$	−1.04623e9	−1.19343	−0.596715	−	0.802453i	$-0.703528\pi$
$359$	−1.04623e9	−1.19343	−0.596715	+	0.802453i	$0.703528\pi$
$360$	0	0
$361$	8.81928e8	0.986638
$362$	1.39170e9	1.54193
$363$	0	0
$364$	5.29312e8	0.575250
$365$	−1.36179e9	−1.46583
$366$	0	0
$367$	4.80538e8	0.507453	0.253727	−	0.967276i	$-0.418344\pi$
$367$	4.80538e8	0.507453	0.253727	+	0.967276i	$0.418344\pi$
$368$	−6.96951e8	−0.729013
$369$	0	0
$370$	−1.53429e9	−1.57471
$371$	−1.22224e9	−1.24264
$372$	0	0
$373$	−1.45793e9	−1.45464	−0.727320	−	0.686298i	$-0.759235\pi$
$373$	−1.45793e9	−1.45464	−0.727320	+	0.686298i	$0.759235\pi$
$374$	5.01878e7	0.0496075
$375$	0	0
$376$	−1.35080e7	−0.0131049
$377$	−3.62298e8	−0.348234
$378$	0	0
$379$	−1.16963e8	−0.110359	−0.0551797	−	0.998476i	$-0.517573\pi$
$379$	−1.16963e8	−0.110359	−0.0551797	+	0.998476i	$0.517573\pi$
$380$	1.34785e9	1.26008
$381$	0	0
$382$	−2.79326e9	−2.56383
$383$	1.54022e9	1.40084	0.700418	−	0.713732i	$-0.252997\pi$
$383$	1.54022e9	1.40084	0.700418	+	0.713732i	$0.252997\pi$
$384$	0	0
$385$	3.35435e8	0.299568
$386$	−2.03126e9	−1.79767
$387$	0	0
$388$	−2.28066e8	−0.198221
$389$	−6.82704e8	−0.588043	−0.294022	−	0.955799i	$-0.594994\pi$
$389$	−6.82704e8	−0.588043	−0.294022	+	0.955799i	$0.594994\pi$
$390$	0	0
$391$	9.16378e7	0.0775276
$392$	−4.70368e7	−0.0394400
$393$	0	0
$394$	−4.31224e8	−0.355195
$395$	−4.28651e8	−0.349957
$396$	0	0
$397$	−4.39437e8	−0.352476	−0.176238	−	0.984348i	$-0.556393\pi$
$397$	−4.39437e8	−0.352476	−0.176238	+	0.984348i	$0.556393\pi$
$398$	3.04047e9	2.41741
$399$	0	0
$400$	−2.66350e8	−0.208086
$401$	1.92220e9	1.48865	0.744326	−	0.667816i	$-0.232771\pi$
$401$	1.92220e9	1.48865	0.744326	+	0.667816i	$0.232771\pi$
$402$	0	0
$403$	1.29123e8	0.0982732
$404$	−6.67760e8	−0.503832
$405$	0	0
$406$	7.57208e8	0.561532
$407$	−4.40075e8	−0.323554
$408$	0	0
$409$	−5.70106e8	−0.412026	−0.206013	−	0.978549i	$-0.566049\pi$
$409$	−5.70106e8	−0.412026	−0.206013	+	0.978549i	$0.566049\pi$
$410$	3.79058e9	2.71621
$411$	0	0
$412$	5.82232e8	0.410162
$413$	1.32057e9	0.922436
$414$	0	0
$415$	−1.98451e8	−0.136297
$416$	−1.46903e9	−1.00047
$417$	0	0
$418$	8.56658e8	0.573708
$419$	1.12807e9	0.749179	0.374589	−	0.927191i	$-0.377784\pi$
$419$	1.12807e9	0.749179	0.374589	+	0.927191i	$0.377784\pi$
$420$	0	0
$421$	2.91413e9	1.90336	0.951681	−	0.307089i	$-0.0993549\pi$
$421$	2.91413e9	1.90336	0.951681	+	0.307089i	$0.0993549\pi$
$422$	−5.80410e8	−0.375960
$423$	0	0
$424$	5.11469e8	0.325866
$425$	3.50207e7	0.0221291
$426$	0	0
$427$	2.55627e9	1.58895
$428$	1.31419e9	0.810226
$429$	0	0
$430$	4.44855e9	2.69823
$431$	−8.77990e8	−0.528225	−0.264113	−	0.964492i	$-0.585079\pi$
$431$	−8.77990e8	−0.528225	−0.264113	+	0.964492i	$0.585079\pi$
$432$	0	0
$433$	−7.45894e8	−0.441539	−0.220770	−	0.975326i	$-0.570857\pi$
$433$	−7.45894e8	−0.441539	−0.220770	+	0.975326i	$0.570857\pi$
$434$	−2.69868e8	−0.158467
$435$	0	0
$436$	1.21672e9	0.703054
$437$	1.56417e9	0.896601
$438$	0	0
$439$	3.31044e8	0.186749	0.0933747	−	0.995631i	$-0.470235\pi$
$439$	3.31044e8	0.186749	0.0933747	+	0.995631i	$0.470235\pi$
$440$	−1.40369e8	−0.0785575
$441$	0	0
$442$	2.28564e8	0.125901
$443$	1.92657e9	1.05286	0.526432	−	0.850217i	$-0.323530\pi$
$443$	1.92657e9	1.05286	0.526432	+	0.850217i	$0.323530\pi$
$444$	0	0
$445$	−7.06922e8	−0.380287
$446$	−1.75033e9	−0.934217
$447$	0	0
$448$	1.07672e9	0.565757
$449$	−3.35149e8	−0.174733	−0.0873667	−	0.996176i	$-0.527845\pi$
$449$	−3.35149e8	−0.174733	−0.0873667	+	0.996176i	$0.527845\pi$
$450$	0	0
$451$	1.08724e9	0.558096
$452$	−3.06674e9	−1.56204
$453$	0	0
$454$	−1.41954e9	−0.711955
$455$	1.52763e9	0.760288
$456$	0	0
$457$	−9.81385e8	−0.480986	−0.240493	−	0.970651i	$-0.577309\pi$
$457$	−9.81385e8	−0.480986	−0.240493	+	0.970651i	$0.577309\pi$
$458$	−5.37271e9	−2.61315
$459$	0	0
$460$	1.18722e9	0.568693
$461$	7.99148e8	0.379904	0.189952	−	0.981793i	$-0.439167\pi$
$461$	7.99148e8	0.379904	0.189952	+	0.981793i	$0.439167\pi$
$462$	0	0
$463$	−1.01685e9	−0.476128	−0.238064	−	0.971249i	$-0.576513\pi$
$463$	−1.01685e9	−0.476128	−0.238064	+	0.971249i	$0.576513\pi$
$464$	−1.12226e9	−0.521531
$465$	0	0
$466$	2.90674e9	1.33062
$467$	2.83923e9	1.29000	0.645002	−	0.764181i	$-0.276857\pi$
$467$	2.83923e9	1.29000	0.645002	+	0.764181i	$0.276857\pi$
$468$	0	0
$469$	1.32272e9	0.592055
$470$	1.80584e8	0.0802301
$471$	0	0
$472$	−5.52619e8	−0.241896
$473$	1.27597e9	0.554402
$474$	0	0
$475$	5.97770e8	0.255921
$476$	−2.15581e8	−0.0916191
$477$	0	0
$478$	−3.06565e9	−1.28388
$479$	−3.24833e9	−1.35047	−0.675236	−	0.737602i	$-0.735958\pi$
$479$	−3.24833e9	−1.35047	−0.675236	+	0.737602i	$0.735958\pi$
$480$	0	0
$481$	−2.00418e9	−0.821163
$482$	3.18035e9	1.29363
$483$	0	0
$484$	1.86498e8	0.0747680
$485$	−6.58215e8	−0.261982
$486$	0	0
$487$	−6.55732e8	−0.257262	−0.128631	−	0.991693i	$-0.541058\pi$
$487$	−6.55732e8	−0.257262	−0.128631	+	0.991693i	$0.541058\pi$
$488$	−1.06972e9	−0.416679
$489$	0	0
$490$	6.28820e8	0.241457
$491$	−9.37028e8	−0.357246	−0.178623	−	0.983918i	$-0.557164\pi$
$491$	−9.37028e8	−0.357246	−0.178623	+	0.983918i	$0.557164\pi$
$492$	0	0
$493$	1.47559e8	0.0554627
$494$	3.90138e9	1.45604
$495$	0	0
$496$	3.99972e8	0.147178
$497$	−2.23541e9	−0.816788
$498$	0	0
$499$	−5.07602e9	−1.82882	−0.914411	−	0.404786i	$-0.867346\pi$
$499$	−5.07602e9	−1.82882	−0.914411	+	0.404786i	$0.867346\pi$
$500$	−2.04510e9	−0.731676
$501$	0	0
$502$	−7.30220e8	−0.257627
$503$	3.30955e9	1.15953	0.579763	−	0.814785i	$-0.303145\pi$
$503$	3.30955e9	1.15953	0.579763	+	0.814785i	$0.303145\pi$
$504$	0	0
$505$	−1.92720e9	−0.665897
$506$	7.54567e8	0.258923
$507$	0	0
$508$	−4.52242e9	−1.53055
$509$	5.09686e8	0.171313	0.0856566	−	0.996325i	$-0.472701\pi$
$509$	5.09686e8	0.171313	0.0856566	+	0.996325i	$0.472701\pi$
$510$	0	0
$511$	3.71783e9	1.23258
$512$	−3.71622e9	−1.22365
$513$	0	0
$514$	−3.08984e9	−1.00361
$515$	1.68036e9	0.542097
$516$	0	0
$517$	5.17965e7	0.0164848
$518$	4.18877e9	1.32413
$519$	0	0
$520$	−6.39267e8	−0.199375
$521$	−4.24284e9	−1.31439	−0.657196	−	0.753720i	$-0.728258\pi$
$521$	−4.24284e9	−1.31439	−0.657196	+	0.753720i	$0.728258\pi$
$522$	0	0
$523$	4.77407e9	1.45926	0.729630	−	0.683843i	$-0.239692\pi$
$523$	4.77407e9	1.45926	0.729630	+	0.683843i	$0.239692\pi$
$524$	−4.08059e9	−1.23898
$525$	0	0
$526$	−6.20747e9	−1.85979
$527$	−5.25899e7	−0.0156518
$528$	0	0
$529$	−2.02706e9	−0.595350
$530$	−6.83766e9	−1.99500
$531$	0	0
$532$	−3.67976e9	−1.05957
$533$	4.95150e9	1.41642
$534$	0	0
$535$	3.79286e9	1.07085
$536$	−5.53517e8	−0.155258
$537$	0	0
$538$	8.09019e9	2.23986
$539$	1.80363e8	0.0496119
$540$	0	0
$541$	3.10457e9	0.842967	0.421483	−	0.906836i	$-0.361510\pi$
$541$	3.10457e9	0.842967	0.421483	+	0.906836i	$0.361510\pi$
$542$	7.32650e9	1.97651
$543$	0	0
$544$	5.98313e8	0.159343
$545$	3.51154e9	0.929202
$546$	0	0
$547$	5.81117e9	1.51813	0.759063	−	0.651017i	$-0.225658\pi$
$547$	5.81117e9	1.51813	0.759063	+	0.651017i	$0.225658\pi$
$548$	−2.27504e9	−0.590550
$549$	0	0
$550$	2.88368e8	0.0739057
$551$	2.51869e9	0.641423
$552$	0	0
$553$	1.17026e9	0.294270
$554$	−8.76718e9	−2.19066
$555$	0	0
$556$	−1.11844e9	−0.275962
$557$	4.69891e8	0.115214	0.0576068	−	0.998339i	$-0.481653\pi$
$557$	4.69891e8	0.115214	0.0576068	+	0.998339i	$0.481653\pi$
$558$	0	0
$559$	5.81098e9	1.40705
$560$	4.73200e9	1.13864
$561$	0	0
$562$	−7.77209e9	−1.84697
$563$	−4.00223e9	−0.945199	−0.472599	−	0.881277i	$-0.656684\pi$
$563$	−4.00223e9	−0.945199	−0.472599	+	0.881277i	$0.656684\pi$
$564$	0	0
$565$	−8.85082e9	−2.06449
$566$	−2.38258e9	−0.552318
$567$	0	0
$568$	9.35451e8	0.214191
$569$	−1.36018e9	−0.309530	−0.154765	−	0.987951i	$-0.549462\pi$
$569$	−1.36018e9	−0.309530	−0.154765	+	0.987951i	$0.549462\pi$
$570$	0	0
$571$	5.92967e9	1.33292	0.666461	−	0.745540i	$-0.267808\pi$
$571$	5.92967e9	1.33292	0.666461	+	0.745540i	$0.267808\pi$
$572$	8.49346e8	0.189757
$573$	0	0
$574$	−1.03487e10	−2.28399
$575$	5.26531e8	0.115501
$576$	0	0
$577$	−5.08690e9	−1.10240	−0.551199	−	0.834374i	$-0.685829\pi$
$577$	−5.08690e9	−1.10240	−0.551199	+	0.834374i	$0.685829\pi$
$578$	6.17413e9	1.32993
$579$	0	0
$580$	1.91171e9	0.406840
$581$	5.41793e8	0.114609
$582$	0	0
$583$	−1.96123e9	−0.409910
$584$	−1.55580e9	−0.323228
$585$	0	0
$586$	5.05585e9	1.03789
$587$	3.07480e9	0.627456	0.313728	−	0.949513i	$-0.398422\pi$
$587$	3.07480e9	0.627456	0.313728	+	0.949513i	$0.398422\pi$
$588$	0	0
$589$	−8.97659e8	−0.181012
$590$	7.38778e9	1.48092
$591$	0	0
$592$	−6.20818e9	−1.22981
$593$	−4.96104e9	−0.976970	−0.488485	−	0.872572i	$-0.662450\pi$
$593$	−4.96104e9	−0.976970	−0.488485	+	0.872572i	$0.662450\pi$
$594$	0	0
$595$	−6.22182e8	−0.121090
$596$	−6.69858e9	−1.29605
$597$	0	0
$598$	3.43644e9	0.657134
$599$	−4.34257e9	−0.825568	−0.412784	−	0.910829i	$-0.635443\pi$
$599$	−4.34257e9	−0.825568	−0.412784	+	0.910829i	$0.635443\pi$
$600$	0	0
$601$	1.77668e9	0.333848	0.166924	−	0.985970i	$-0.446617\pi$
$601$	1.77668e9	0.333848	0.166924	+	0.985970i	$0.446617\pi$
$602$	−1.21450e10	−2.26888
$603$	0	0
$604$	−1.50044e9	−0.277070
$605$	5.38246e8	0.0988183
$606$	0	0
$607$	−8.76418e9	−1.59056	−0.795282	−	0.606240i	$-0.792677\pi$
$607$	−8.76418e9	−1.59056	−0.795282	+	0.606240i	$0.792677\pi$
$608$	1.02126e10	1.84279
$609$	0	0
$610$	1.43008e10	2.55097
$611$	2.35891e8	0.0418376
$612$	0	0
$613$	−1.13075e9	−0.198269	−0.0991346	−	0.995074i	$-0.531607\pi$
$613$	−1.13075e9	−0.198269	−0.0991346	+	0.995074i	$0.531607\pi$
$614$	2.43895e9	0.425221
$615$	0	0
$616$	3.83223e8	0.0660571
$617$	−2.36299e7	−0.00405008	−0.00202504	−	0.999998i	$-0.500645\pi$
$617$	−2.36299e7	−0.00405008	−0.00202504	+	0.999998i	$0.500645\pi$
$618$	0	0
$619$	5.90610e9	1.00088	0.500442	−	0.865770i	$-0.333171\pi$
$619$	5.90610e9	1.00088	0.500442	+	0.865770i	$0.333171\pi$
$620$	−6.81330e8	−0.114812
$621$	0	0
$622$	5.36332e9	0.893650
$623$	1.92997e9	0.319774
$624$	0	0
$625$	−7.01052e9	−1.14860
$626$	8.35101e9	1.36059
$627$	0	0
$628$	−1.49628e9	−0.241075
$629$	8.16275e8	0.130785
$630$	0	0
$631$	−3.87609e9	−0.614173	−0.307087	−	0.951682i	$-0.599354\pi$
$631$	−3.87609e9	−0.614173	−0.307087	+	0.951682i	$0.599354\pi$
$632$	−4.89720e8	−0.0771682
$633$	0	0
$634$	−9.43992e9	−1.47115
$635$	−1.30520e10	−2.02288
$636$	0	0
$637$	8.21404e8	0.125913
$638$	1.21503e9	0.185232
$639$	0	0
$640$	−3.40129e9	−0.512878
$641$	−4.60264e9	−0.690246	−0.345123	−	0.938558i	$-0.612163\pi$
$641$	−4.60264e9	−0.690246	−0.345123	+	0.938558i	$0.612163\pi$
$642$	0	0
$643$	1.10814e10	1.64383	0.821917	−	0.569607i	$-0.192905\pi$
$643$	1.10814e10	1.64383	0.821917	+	0.569607i	$0.192905\pi$
$644$	−3.24123e9	−0.478200
$645$	0	0
$646$	−1.58897e9	−0.231901
$647$	−3.95562e9	−0.574183	−0.287091	−	0.957903i	$-0.592688\pi$
$647$	−3.95562e9	−0.574183	−0.287091	+	0.957903i	$0.592688\pi$
$648$	0	0
$649$	2.11902e9	0.304283
$650$	1.31328e9	0.187569
$651$	0	0
$652$	8.47173e9	1.19703
$653$	3.72327e9	0.523274	0.261637	−	0.965166i	$-0.415738\pi$
$653$	3.72327e9	0.523274	0.261637	+	0.965166i	$0.415738\pi$
$654$	0	0
$655$	−1.17769e10	−1.63752
$656$	1.53378e10	2.12129
$657$	0	0
$658$	−4.93015e8	−0.0674636
$659$	2.45031e9	0.333520	0.166760	−	0.985998i	$-0.446670\pi$
$659$	2.45031e9	0.333520	0.166760	+	0.985998i	$0.446670\pi$
$660$	0	0
$661$	−4.82392e9	−0.649673	−0.324836	−	0.945770i	$-0.605309\pi$
$661$	−4.82392e9	−0.649673	−0.324836	+	0.945770i	$0.605309\pi$
$662$	1.04599e10	1.40127
$663$	0	0
$664$	−2.26724e8	−0.0300545
$665$	−1.06201e10	−1.40040
$666$	0	0
$667$	2.21853e9	0.289484
$668$	−7.38043e8	−0.0957996
$669$	0	0
$670$	7.39979e9	0.950513
$671$	4.10185e9	0.524145
$672$	0	0
$673$	−2.17377e9	−0.274891	−0.137446	−	0.990509i	$-0.543889\pi$
$673$	−2.17377e9	−0.274891	−0.137446	+	0.990509i	$0.543889\pi$
$674$	−1.83178e7	−0.00230444
$675$	0	0
$676$	−2.73767e9	−0.340853
$677$	4.71648e9	0.584194	0.292097	−	0.956389i	$-0.405647\pi$
$677$	4.71648e9	0.584194	0.292097	+	0.956389i	$0.405647\pi$
$678$	0	0
$679$	1.79700e9	0.220295
$680$	2.60364e8	0.0317541
$681$	0	0
$682$	−4.33037e8	−0.0522733
$683$	6.72757e9	0.807953	0.403976	−	0.914769i	$-0.367628\pi$
$683$	6.72757e9	0.807953	0.403976	+	0.914769i	$0.367628\pi$
$684$	0	0
$685$	−6.56592e9	−0.780510
$686$	−1.21501e10	−1.43696
$687$	0	0
$688$	1.80001e10	2.10725
$689$	−8.93179e9	−1.04033
$690$	0	0
$691$	−4.98106e9	−0.574313	−0.287157	−	0.957884i	$-0.592710\pi$
$691$	−4.98106e9	−0.574313	−0.287157	+	0.957884i	$0.592710\pi$
$692$	1.91015e9	0.219127
$693$	0	0
$694$	−3.18538e9	−0.361746
$695$	−3.22788e9	−0.364729
$696$	0	0
$697$	−2.01668e9	−0.225591
$698$	−1.73242e8	−0.0192824
$699$	0	0
$700$	−1.23868e9	−0.136495
$701$	−4.43468e9	−0.486238	−0.243119	−	0.969996i	$-0.578171\pi$
$701$	−4.43468e9	−0.486238	−0.243119	+	0.969996i	$0.578171\pi$
$702$	0	0
$703$	1.39330e10	1.51252
$704$	1.72773e9	0.186626
$705$	0	0
$706$	8.35647e9	0.893730
$707$	5.26147e9	0.559937
$708$	0	0
$709$	−4.96472e9	−0.523158	−0.261579	−	0.965182i	$-0.584243\pi$
$709$	−4.96472e9	−0.523158	−0.261579	+	0.965182i	$0.584243\pi$
$710$	−1.25057e10	−1.31131
$711$	0	0
$712$	−8.07636e8	−0.0838563
$713$	−7.90682e8	−0.0816937
$714$	0	0
$715$	2.45127e9	0.250796
$716$	1.22943e10	1.25172
$717$	0	0
$718$	1.59794e10	1.61111
$719$	−7.62145e9	−0.764692	−0.382346	−	0.924019i	$-0.624884\pi$
$719$	−7.62145e9	−0.764692	−0.382346	+	0.924019i	$0.624884\pi$
$720$	0	0
$721$	−4.58757e9	−0.455837
$722$	−1.34699e10	−1.33194
$723$	0	0
$724$	−9.59249e9	−0.939391
$725$	8.47842e8	0.0826289
$726$	0	0
$727$	−9.67350e9	−0.933712	−0.466856	−	0.884333i	$-0.654613\pi$
$727$	−9.67350e9	−0.933712	−0.466856	+	0.884333i	$0.654613\pi$
$728$	1.74527e9	0.167650
$729$	0	0
$730$	2.07990e10	1.97884
$731$	−2.36673e9	−0.224098
$732$	0	0
$733$	6.37101e9	0.597509	0.298755	−	0.954330i	$-0.403429\pi$
$733$	6.37101e9	0.597509	0.298755	+	0.954330i	$0.403429\pi$
$734$	−7.33939e9	−0.685052
$735$	0	0
$736$	8.99556e9	0.831679
$737$	2.12246e9	0.195301
$738$	0	0
$739$	1.16634e10	1.06309	0.531544	−	0.847031i	$-0.321612\pi$
$739$	1.16634e10	1.06309	0.531544	+	0.847031i	$0.321612\pi$
$740$	1.05753e10	0.959359
$741$	0	0
$742$	1.86676e10	1.67754
$743$	1.87781e9	0.167955	0.0839773	−	0.996468i	$-0.473238\pi$
$743$	1.87781e9	0.167955	0.0839773	+	0.996468i	$0.473238\pi$
$744$	0	0
$745$	−1.93326e10	−1.71294
$746$	2.22674e10	1.96374
$747$	0	0
$748$	−3.45926e8	−0.0302223
$749$	−1.03549e10	−0.900451
$750$	0	0
$751$	−1.89594e10	−1.63337	−0.816684	−	0.577085i	$-0.804190\pi$
$751$	−1.89594e10	−1.63337	−0.816684	+	0.577085i	$0.804190\pi$
$752$	7.30697e8	0.0626578
$753$	0	0
$754$	5.53349e9	0.470110
$755$	−4.33038e9	−0.366194
$756$	0	0
$757$	2.13638e9	0.178996	0.0894980	−	0.995987i	$-0.471474\pi$
$757$	2.13638e9	0.178996	0.0894980	+	0.995987i	$0.471474\pi$
$758$	1.78640e9	0.148983
$759$	0	0
$760$	4.44417e9	0.367235
$761$	8.14245e9	0.669744	0.334872	−	0.942264i	$-0.391307\pi$
$761$	8.14245e9	0.669744	0.334872	+	0.942264i	$0.391307\pi$
$762$	0	0
$763$	−9.58690e9	−0.781344
$764$	1.92529e10	1.56196
$765$	0	0
$766$	−2.35242e10	−1.89110
$767$	9.65039e9	0.772256
$768$	0	0
$769$	3.93260e9	0.311844	0.155922	−	0.987769i	$-0.450165\pi$
$769$	3.93260e9	0.311844	0.155922	+	0.987769i	$0.450165\pi$
$770$	−5.12319e9	−0.404411
$771$	0	0
$772$	1.40008e10	1.09519
$773$	2.04769e10	1.59455	0.797273	−	0.603619i	$-0.206275\pi$
$773$	2.04769e10	1.59455	0.797273	+	0.603619i	$0.206275\pi$
$774$	0	0
$775$	−3.02170e8	−0.0233182
$776$	−7.51990e8	−0.0577692
$777$	0	0
$778$	1.04271e10	0.793847
$779$	−3.44228e10	−2.60894
$780$	0	0
$781$	−3.58699e9	−0.269433
$782$	−1.39961e9	−0.104661
$783$	0	0
$784$	2.54439e9	0.188572
$785$	−4.31836e9	−0.318621
$786$	0	0
$787$	2.33821e10	1.70991	0.854954	−	0.518704i	$-0.173585\pi$
$787$	2.33821e10	1.70991	0.854954	+	0.518704i	$0.173585\pi$
$788$	2.97227e9	0.216395
$789$	0	0
$790$	6.54691e9	0.472435
$791$	2.41637e10	1.73598
$792$	0	0
$793$	1.86806e10	1.33025
$794$	6.71165e9	0.475836
$795$	0	0
$796$	−2.09569e10	−1.47276
$797$	−5.55295e9	−0.388526	−0.194263	−	0.980950i	$-0.562231\pi$
$797$	−5.55295e9	−0.388526	−0.194263	+	0.980950i	$0.562231\pi$
$798$	0	0
$799$	−9.60749e7	−0.00666340
$800$	3.43778e9	0.237390
$801$	0	0
$802$	−2.93583e10	−2.00965
$803$	5.96571e9	0.406591
$804$	0	0
$805$	−9.35443e9	−0.632021
$806$	−1.97213e9	−0.132667
$807$	0	0
$808$	−2.20177e9	−0.146836
$809$	1.91933e10	1.27447	0.637237	−	0.770668i	$-0.280077\pi$
$809$	1.91933e10	1.27447	0.637237	+	0.770668i	$0.280077\pi$
$810$	0	0
$811$	−1.30956e9	−0.0862091	−0.0431045	−	0.999071i	$-0.513725\pi$
$811$	−1.30956e9	−0.0862091	−0.0431045	+	0.999071i	$0.513725\pi$
$812$	−5.21917e9	−0.342102
$813$	0	0
$814$	6.72140e9	0.436791
$815$	2.44500e10	1.58208
$816$	0	0
$817$	−4.03978e10	−2.59168
$818$	8.70740e9	0.556227
$819$	0	0
$820$	−2.61271e10	−1.65479
$821$	−1.43007e10	−0.901896	−0.450948	−	0.892550i	$-0.648914\pi$
$821$	−1.43007e10	−0.901896	−0.450948	+	0.892550i	$0.648914\pi$
$822$	0	0
$823$	2.08892e10	1.30624	0.653120	−	0.757254i	$-0.273460\pi$
$823$	2.08892e10	1.30624	0.653120	+	0.757254i	$0.273460\pi$
$824$	1.91976e9	0.119537
$825$	0	0
$826$	−2.01694e10	−1.24527
$827$	−1.31770e10	−0.810116	−0.405058	−	0.914291i	$-0.632749\pi$
$827$	−1.31770e10	−0.810116	−0.405058	+	0.914291i	$0.632749\pi$
$828$	0	0
$829$	−1.77646e10	−1.08296	−0.541481	−	0.840713i	$-0.682136\pi$
$829$	−1.77646e10	−1.08296	−0.541481	+	0.840713i	$0.682136\pi$
$830$	3.03100e9	0.183998
$831$	0	0
$832$	7.86839e9	0.473647
$833$	−3.34546e8	−0.0200539
$834$	0	0
$835$	−2.13004e9	−0.126615
$836$	−5.90464e9	−0.349519
$837$	0	0
$838$	−1.72293e10	−1.01138
$839$	−1.05490e10	−0.616659	−0.308329	−	0.951280i	$-0.599770\pi$
$839$	−1.05490e10	−0.616659	−0.308329	+	0.951280i	$0.599770\pi$
$840$	0	0
$841$	−1.36775e10	−0.792905
$842$	−4.45083e10	−2.56950
$843$	0	0
$844$	4.00056e9	0.229046
$845$	−7.90110e9	−0.450494
$846$	0	0
$847$	−1.46947e9	−0.0830939
$848$	−2.76672e10	−1.55804
$849$	0	0
$850$	−5.34881e8	−0.0298738
$851$	1.22726e10	0.682626
$852$	0	0
$853$	6.93413e8	0.0382534	0.0191267	−	0.999817i	$-0.493911\pi$
$853$	6.93413e8	0.0382534	0.0191267	+	0.999817i	$0.493911\pi$
$854$	−3.90427e10	−2.14505
$855$	0	0
$856$	4.33322e9	0.236131
$857$	−2.42332e10	−1.31516	−0.657578	−	0.753387i	$-0.728419\pi$
$857$	−2.42332e10	−1.31516	−0.657578	+	0.753387i	$0.728419\pi$
$858$	0	0
$859$	1.50069e10	0.807823	0.403911	−	0.914798i	$-0.367650\pi$
$859$	1.50069e10	0.807823	0.403911	+	0.914798i	$0.367650\pi$
$860$	−3.06623e10	−1.64384
$861$	0	0
$862$	1.34098e10	0.713094
$863$	−4.48430e9	−0.237496	−0.118748	−	0.992924i	$-0.537888\pi$
$863$	−4.48430e9	−0.237496	−0.118748	+	0.992924i	$0.537888\pi$
$864$	0	0
$865$	5.51282e9	0.289613
$866$	1.13922e10	0.596069
$867$	0	0
$868$	1.86011e9	0.0965425
$869$	1.87783e9	0.0970706
$870$	0	0
$871$	9.66608e9	0.495664
$872$	4.01183e9	0.204897
$873$	0	0
$874$	−2.38900e10	−1.21039
$875$	1.61139e10	0.813154
$876$	0	0
$877$	−2.15250e10	−1.07757	−0.538784	−	0.842444i	$-0.681116\pi$
$877$	−2.15250e10	−1.07757	−0.538784	+	0.842444i	$0.681116\pi$
$878$	−5.05612e9	−0.252108
$879$	0	0
$880$	7.59308e9	0.375603
$881$	−1.89298e10	−0.932676	−0.466338	−	0.884607i	$-0.654427\pi$
$881$	−1.89298e10	−0.932676	−0.466338	+	0.884607i	$0.654427\pi$
$882$	0	0
$883$	7.30415e9	0.357032	0.178516	−	0.983937i	$-0.442870\pi$
$883$	7.30415e9	0.357032	0.178516	+	0.983937i	$0.442870\pi$
$884$	−1.57541e9	−0.0767028
$885$	0	0
$886$	−2.94251e10	−1.42134
$887$	2.12379e10	1.02183	0.510915	−	0.859631i	$-0.329307\pi$
$887$	2.12379e10	1.02183	0.510915	+	0.859631i	$0.329307\pi$
$888$	0	0
$889$	3.56335e10	1.70099
$890$	1.07970e10	0.513380
$891$	0	0
$892$	1.20644e10	0.569152
$893$	−1.63991e9	−0.0770618
$894$	0	0
$895$	3.54821e10	1.65436
$896$	9.28590e9	0.431267
$897$	0	0
$898$	5.11883e9	0.235887
$899$	−1.27319e9	−0.0584432
$900$	0	0
$901$	3.63779e9	0.165692
$902$	−1.66058e10	−0.753419
$903$	0	0
$904$	−1.01118e10	−0.455237
$905$	−2.76846e10	−1.24156
$906$	0	0
$907$	−3.80530e10	−1.69341	−0.846707	−	0.532059i	$-0.821419\pi$
$907$	−3.80530e10	−1.69341	−0.846707	+	0.532059i	$0.821419\pi$
$908$	9.78439e9	0.433744
$909$	0	0
$910$	−2.33319e10	−1.02637
$911$	3.43756e10	1.50638	0.753192	−	0.657800i	$-0.228513\pi$
$911$	3.43756e10	1.50638	0.753192	+	0.657800i	$0.228513\pi$
$912$	0	0
$913$	8.69374e8	0.0378059
$914$	1.49890e10	0.649322
$915$	0	0
$916$	3.70321e10	1.59201
$917$	3.21521e10	1.37695
$918$	0	0
$919$	−9.00499e9	−0.382718	−0.191359	−	0.981520i	$-0.561289\pi$
$919$	−9.00499e9	−0.382718	−0.191359	+	0.981520i	$0.561289\pi$
$920$	3.91455e9	0.165739
$921$	0	0
$922$	−1.22056e10	−0.512863
$923$	−1.63358e10	−0.683808
$924$	0	0
$925$	4.69014e9	0.194845
$926$	1.55307e10	0.642764
$927$	0	0
$928$	1.44850e10	0.594978
$929$	1.39486e10	0.570788	0.285394	−	0.958410i	$-0.407875\pi$
$929$	1.39486e10	0.570788	0.285394	+	0.958410i	$0.407875\pi$
$930$	0	0
$931$	−5.71039e9	−0.231922
$932$	−2.00351e10	−0.810655
$933$	0	0
$934$	−4.33643e10	−1.74148
$935$	−9.98367e8	−0.0399438
$936$	0	0
$937$	3.54170e10	1.40645	0.703223	−	0.710970i	$-0.251744\pi$
$937$	3.54170e10	1.40645	0.703223	+	0.710970i	$0.251744\pi$
$938$	−2.02022e10	−0.799263
$939$	0	0
$940$	−1.24470e9	−0.0488785
$941$	−2.25006e10	−0.880299	−0.440150	−	0.897924i	$-0.645075\pi$
$941$	−2.25006e10	−0.880299	−0.440150	+	0.897924i	$0.645075\pi$
$942$	0	0
$943$	−3.03205e10	−1.17746
$944$	2.98931e10	1.15656
$945$	0	0
$946$	−1.94882e10	−0.748432
$947$	−1.92828e10	−0.737810	−0.368905	−	0.929467i	$-0.620267\pi$
$947$	−1.92828e10	−0.737810	−0.368905	+	0.929467i	$0.620267\pi$
$948$	0	0
$949$	2.71689e10	1.03191
$950$	−9.12991e9	−0.345489
$951$	0	0
$952$	−7.10823e8	−0.0267013
$953$	−1.08950e10	−0.407759	−0.203879	−	0.978996i	$-0.565355\pi$
$953$	−1.08950e10	−0.407759	−0.203879	+	0.978996i	$0.565355\pi$
$954$	0	0
$955$	5.55653e10	2.06439
$956$	2.11304e10	0.782179
$957$	0	0
$958$	4.96126e10	1.82311
$959$	1.79257e10	0.656312
$960$	0	0
$961$	−2.70589e10	−0.983507
$962$	3.06105e10	1.10855
$963$	0	0
$964$	−2.19210e10	−0.788117
$965$	4.04072e10	1.44748
$966$	0	0
$967$	−1.35695e10	−0.482584	−0.241292	−	0.970453i	$-0.577571\pi$
$967$	−1.35695e10	−0.482584	−0.241292	+	0.970453i	$0.577571\pi$
$968$	6.14929e8	0.0217902
$969$	0	0
$970$	1.00531e10	0.353671
$971$	4.33843e9	0.152078	0.0760388	−	0.997105i	$-0.475773\pi$
$971$	4.33843e9	0.152078	0.0760388	+	0.997105i	$0.475773\pi$
$972$	0	0
$973$	8.81247e9	0.306692
$974$	1.00152e10	0.347298
$975$	0	0
$976$	5.78651e10	1.99224
$977$	3.90981e10	1.34130	0.670648	−	0.741776i	$-0.266016\pi$
$977$	3.90981e10	1.34130	0.670648	+	0.741776i	$0.266016\pi$
$978$	0	0
$979$	3.09688e9	0.105484
$980$	−4.33423e9	−0.147103
$981$	0	0
$982$	1.43115e10	0.482275
$983$	3.05704e10	1.02651	0.513257	−	0.858235i	$-0.328439\pi$
$983$	3.05704e10	1.02651	0.513257	+	0.858235i	$0.328439\pi$
$984$	0	0
$985$	8.57819e9	0.286002
$986$	−2.25371e9	−0.0748736
$987$	0	0
$988$	−2.68908e10	−0.887062
$989$	−3.55835e10	−1.16966
$990$	0	0
$991$	3.59751e10	1.17421	0.587103	−	0.809512i	$-0.300268\pi$
$991$	3.59751e10	1.17421	0.587103	+	0.809512i	$0.300268\pi$
$992$	−5.16245e9	−0.167905
$993$	0	0
$994$	3.41420e10	1.10265
$995$	−6.04831e10	−1.94649
$996$	0	0
$997$	2.97463e10	0.950604	0.475302	−	0.879823i	$-0.342339\pi$
$997$	2.97463e10	0.950604	0.475302	+	0.879823i	$0.342339\pi$
$998$	7.75275e10	2.46888
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.a.b.1.1		2
3.2	odd	2		33.8.a.c.1.2	✓	2
12.11	even	2		528.8.a.h.1.1		2
33.32	even	2		363.8.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.c.1.2	✓	2	3.2	odd	2
99.8.a.b.1.1		2	1.1	even	1	trivial
363.8.a.c.1.1		2	33.32	even	2
528.8.a.h.1.1		2	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

\(f(q)\)	\(=\)	\(q-15.2733 q^{2} +105.273 q^{4} +303.826 q^{5} -829.478 q^{7} +347.112 q^{8} +O(q^{10})\)	\(q-15.2733 q^{2} +105.273 q^{4} +303.826 q^{5} -829.478 q^{7} +347.112 q^{8} -4640.42 q^{10} -1331.00 q^{11} -6061.62 q^{13} +12668.9 q^{14} -18776.5 q^{16} +2468.81 q^{17} +42140.2 q^{19} +31984.8 q^{20} +20328.7 q^{22} +37118.2 q^{23} +14185.2 q^{25} +92580.8 q^{26} -87321.9 q^{28} +59769.3 q^{29} -21301.7 q^{31} +242349. q^{32} -37706.8 q^{34} -252017. q^{35} +330635. q^{37} -643620. q^{38} +105462. q^{40} -816862. q^{41} -958652. q^{43} -140119. q^{44} -566917. q^{46} -38915.5 q^{47} -135509. q^{49} -216655. q^{50} -638126. q^{52} +1.47350e6 q^{53} -404392. q^{55} -287921. q^{56} -912873. q^{58} -1.59205e6 q^{59} -3.08178e6 q^{61} +325347. q^{62} -1.29807e6 q^{64} -1.84168e6 q^{65} -1.59464e6 q^{67} +259900. q^{68} +3.84913e6 q^{70} +2.69496e6 q^{71} -4.48213e6 q^{73} -5.04989e6 q^{74} +4.43624e6 q^{76} +1.10404e6 q^{77} -1.41084e6 q^{79} -5.70479e6 q^{80} +1.24762e7 q^{82} -653174. q^{83} +750088. q^{85} +1.46418e7 q^{86} -462006. q^{88} -2.32673e6 q^{89} +5.02798e6 q^{91} +3.90756e6 q^{92} +594367. q^{94} +1.28033e7 q^{95} -2.16642e6 q^{97} +2.06967e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 181 q^{4} + 194 q^{5} - 418 q^{7} - 399 q^{8}+O(q^{10}) \) 2 * q - q^2 + 181 * q^4 + 194 * q^5 - 418 * q^7 - 399 * q^8	\( 2 q - q^{2} + 181 q^{4} + 194 q^{5} - 418 q^{7} - 399 q^{8} - 6208 q^{10} - 2662 q^{11} - 13246 q^{13} + 18542 q^{14} - 39119 q^{16} + 10256 q^{17} + 14196 q^{19} + 23668 q^{20} + 1331 q^{22} + 13666 q^{23} - 51878 q^{25} - 9964 q^{26} - 56162 q^{28} - 15312 q^{29} - 48040 q^{31} + 47497 q^{32} + 73442 q^{34} - 297208 q^{35} + 274092 q^{37} - 1042476 q^{38} + 187404 q^{40} - 755836 q^{41} - 1704096 q^{43} - 240911 q^{44} - 901658 q^{46} + 1182094 q^{47} - 789738 q^{49} - 1159595 q^{50} - 1182176 q^{52} + 2156394 q^{53} - 258214 q^{55} - 594930 q^{56} - 1984530 q^{58} - 927332 q^{59} - 1061994 q^{61} - 56296 q^{62} - 1475407 q^{64} - 1052644 q^{65} - 3259952 q^{67} + 849598 q^{68} + 3204104 q^{70} + 5495514 q^{71} - 5450812 q^{73} - 5856942 q^{74} + 2320116 q^{76} + 556358 q^{77} - 1536590 q^{79} - 3470660 q^{80} + 13347206 q^{82} - 8850888 q^{83} - 105148 q^{85} + 4001832 q^{86} + 531069 q^{88} - 6810132 q^{89} + 2071760 q^{91} + 2131598 q^{92} + 18022186 q^{94} + 15872304 q^{95} + 9897376 q^{97} - 7268325 q^{98}+O(q^{100}) \) 2 * q - q^2 + 181 * q^4 + 194 * q^5 - 418 * q^7 - 399 * q^8 - 6208 * q^10 - 2662 * q^11 - 13246 * q^13 + 18542 * q^14 - 39119 * q^16 + 10256 * q^17 + 14196 * q^19 + 23668 * q^20 + 1331 * q^22 + 13666 * q^23 - 51878 * q^25 - 9964 * q^26 - 56162 * q^28 - 15312 * q^29 - 48040 * q^31 + 47497 * q^32 + 73442 * q^34 - 297208 * q^35 + 274092 * q^37 - 1042476 * q^38 + 187404 * q^40 - 755836 * q^41 - 1704096 * q^43 - 240911 * q^44 - 901658 * q^46 + 1182094 * q^47 - 789738 * q^49 - 1159595 * q^50 - 1182176 * q^52 + 2156394 * q^53 - 258214 * q^55 - 594930 * q^56 - 1984530 * q^58 - 927332 * q^59 - 1061994 * q^61 - 56296 * q^62 - 1475407 * q^64 - 1052644 * q^65 - 3259952 * q^67 + 849598 * q^68 + 3204104 * q^70 + 5495514 * q^71 - 5450812 * q^73 - 5856942 * q^74 + 2320116 * q^76 + 556358 * q^77 - 1536590 * q^79 - 3470660 * q^80 + 13347206 * q^82 - 8850888 * q^83 - 105148 * q^85 + 4001832 * q^86 + 531069 * q^88 - 6810132 * q^89 + 2071760 * q^91 + 2131598 * q^92 + 18022186 * q^94 + 15872304 * q^95 + 9897376 * q^97 - 7268325 * q^98

Introduction

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