LMFDB - Embedded newform 207.8.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,8,Mod(1,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, 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("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	207.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:	$64.6637002752$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 104x^{3} + 200x^{2} + 2037x - 3704 $ x^5 - 2x^4 - 104x^3 + 200x^2 + 2037x - 3704
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.20719$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.41439 q^{2} -86.8556 q^{4} -258.464 q^{5} -1375.00 q^{7} +1378.17 q^{8} +O(q^{10})$	\(q-6.41439 q^{2} -86.8556 q^{4} -258.464 q^{5} -1375.00 q^{7} +1378.17 q^{8} +1657.89 q^{10} +628.639 q^{11} -664.703 q^{13} +8819.81 q^{14} +2277.42 q^{16} +16506.6 q^{17} +40169.7 q^{19} +22449.1 q^{20} -4032.34 q^{22} -12167.0 q^{23} -11321.2 q^{25} +4263.66 q^{26} +119427. q^{28} +108018. q^{29} +228208. q^{31} -191014. q^{32} -105880. q^{34} +355390. q^{35} -575563. q^{37} -257664. q^{38} -356207. q^{40} +425720. q^{41} -433464. q^{43} -54600.8 q^{44} +78043.9 q^{46} -547322. q^{47} +1.06709e6 q^{49} +72618.6 q^{50} +57733.2 q^{52} +1.27499e6 q^{53} -162481. q^{55} -1.89499e6 q^{56} -692871. q^{58} +869996. q^{59} +1.45260e6 q^{61} -1.46382e6 q^{62} +933727. q^{64} +171802. q^{65} -2.47925e6 q^{67} -1.43369e6 q^{68} -2.27961e6 q^{70} +3.74614e6 q^{71} +2.20514e6 q^{73} +3.69189e6 q^{74} -3.48896e6 q^{76} -864381. q^{77} -2.99240e6 q^{79} -588631. q^{80} -2.73074e6 q^{82} -7.14685e6 q^{83} -4.26637e6 q^{85} +2.78041e6 q^{86} +866370. q^{88} -99929.8 q^{89} +913969. q^{91} +1.05677e6 q^{92} +3.51074e6 q^{94} -1.03824e7 q^{95} -1.23187e7 q^{97} -6.84475e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 16 q^{2} + 256 q^{4} + 56 q^{5} - 1156 q^{7} + 5952 q^{8}+O(q^{10}) $ 5 * q + 16 * q^2 + 256 * q^4 + 56 * q^5 - 1156 * q^7 + 5952 * q^8	\( 5 q + 16 q^{2} + 256 q^{4} + 56 q^{5} - 1156 q^{7} + 5952 q^{8} - 11260 q^{10} + 1318 q^{11} - 19662 q^{13} + 6848 q^{14} + 32448 q^{16} + 5002 q^{17} - 38314 q^{19} - 104440 q^{20} - 74872 q^{22} - 60835 q^{23} + 54959 q^{25} - 345430 q^{26} + 90800 q^{28} + 150634 q^{29} - 179940 q^{31} + 404032 q^{32} + 32116 q^{34} + 374032 q^{35} - 752672 q^{37} - 456808 q^{38} - 1082576 q^{40} + 1192910 q^{41} - 932646 q^{43} - 2467104 q^{44} - 194672 q^{46} + 1008460 q^{47} - 2005219 q^{49} - 1571224 q^{50} - 1740516 q^{52} - 897104 q^{53} + 1203168 q^{55} - 3050144 q^{56} + 5685090 q^{58} - 1020972 q^{59} - 2758364 q^{61} - 2661794 q^{62} + 5173248 q^{64} + 1350472 q^{65} - 1523138 q^{67} - 2501304 q^{68} - 2794240 q^{70} - 3044884 q^{71} - 8872022 q^{73} - 1408492 q^{74} - 17963952 q^{76} + 3501672 q^{77} - 4437540 q^{79} - 12197536 q^{80} - 7738154 q^{82} + 4637362 q^{83} - 8625728 q^{85} + 3025868 q^{86} - 41815040 q^{88} - 6381402 q^{89} + 3240808 q^{91} - 3114752 q^{92} - 13893974 q^{94} - 15762704 q^{95} - 6432034 q^{97} - 22652640 q^{98}+O(q^{100}) \) 5 * q + 16 * q^2 + 256 * q^4 + 56 * q^5 - 1156 * q^7 + 5952 * q^8 - 11260 * q^10 + 1318 * q^11 - 19662 * q^13 + 6848 * q^14 + 32448 * q^16 + 5002 * q^17 - 38314 * q^19 - 104440 * q^20 - 74872 * q^22 - 60835 * q^23 + 54959 * q^25 - 345430 * q^26 + 90800 * q^28 + 150634 * q^29 - 179940 * q^31 + 404032 * q^32 + 32116 * q^34 + 374032 * q^35 - 752672 * q^37 - 456808 * q^38 - 1082576 * q^40 + 1192910 * q^41 - 932646 * q^43 - 2467104 * q^44 - 194672 * q^46 + 1008460 * q^47 - 2005219 * q^49 - 1571224 * q^50 - 1740516 * q^52 - 897104 * q^53 + 1203168 * q^55 - 3050144 * q^56 + 5685090 * q^58 - 1020972 * q^59 - 2758364 * q^61 - 2661794 * q^62 + 5173248 * q^64 + 1350472 * q^65 - 1523138 * q^67 - 2501304 * q^68 - 2794240 * q^70 - 3044884 * q^71 - 8872022 * q^73 - 1408492 * q^74 - 17963952 * q^76 + 3501672 * q^77 - 4437540 * q^79 - 12197536 * q^80 - 7738154 * q^82 + 4637362 * q^83 - 8625728 * q^85 + 3025868 * q^86 - 41815040 * q^88 - 6381402 * q^89 + 3240808 * q^91 - 3114752 * q^92 - 13893974 * q^94 - 15762704 * q^95 - 6432034 * q^97 - 22652640 * 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 $

$2$	−6.41439	−0.566957	−0.283479	−	0.958979i	$-0.591488\pi$
$2$	−6.41439	−0.566957	−0.283479	+	0.958979i	$0.591488\pi$
$3$	0	0
$3$	0	0
$4$	−86.8556	−0.678559
$5$	−258.464	−0.924710	−0.462355	−	0.886695i	$-0.652995\pi$
$5$	−258.464	−0.924710	−0.462355	+	0.886695i	$0.652995\pi$
$6$	0	0
$7$	−1375.00	−1.51517	−0.757584	−	0.652737i	$-0.773620\pi$
$7$	−1375.00	−1.51517	−0.757584	+	0.652737i	$0.773620\pi$
$8$	1378.17	0.951671
$9$	0	0
$10$	1657.89	0.524271
$11$	628.639	0.142406	0.0712028	−	0.997462i	$-0.477316\pi$
$11$	628.639	0.142406	0.0712028	+	0.997462i	$0.477316\pi$
$12$	0	0
$13$	−664.703	−0.0839124	−0.0419562	−	0.999119i	$-0.513359\pi$
$13$	−664.703	−0.0839124	−0.0419562	+	0.999119i	$0.513359\pi$
$14$	8819.81	0.859036
$15$	0	0
$16$	2277.42	0.139002
$17$	16506.6	0.814867	0.407433	−	0.913235i	$-0.366424\pi$
$17$	16506.6	0.814867	0.407433	+	0.913235i	$0.366424\pi$
$18$	0	0
$19$	40169.7	1.34357	0.671785	−	0.740746i	$-0.265528\pi$
$19$	40169.7	1.34357	0.671785	+	0.740746i	$0.265528\pi$
$20$	22449.1	0.627471
$21$	0	0
$22$	−4032.34	−0.0807379
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−11321.2	−0.144911
$26$	4263.66	0.0475747
$27$	0	0
$28$	119427.	1.02813
$29$	108018.	0.822439	0.411220	−	0.911536i	$-0.365103\pi$
$29$	108018.	0.822439	0.411220	+	0.911536i	$0.365103\pi$
$30$	0	0
$31$	228208.	1.37583	0.687917	−	0.725790i	$-0.258525\pi$
$31$	228208.	1.37583	0.687917	+	0.725790i	$0.258525\pi$
$32$	−191014.	−1.03048
$33$	0	0
$34$	−105880.	−0.461995
$35$	355390.	1.40109
$36$	0	0
$37$	−575563.	−1.86804	−0.934021	−	0.357217i	$-0.883726\pi$
$37$	−575563.	−1.86804	−0.934021	+	0.357217i	$0.883726\pi$
$38$	−257664.	−0.761747
$39$	0	0
$40$	−356207.	−0.880020
$41$	425720.	0.964675	0.482337	−	0.875986i	$-0.339788\pi$
$41$	425720.	0.964675	0.482337	+	0.875986i	$0.339788\pi$
$42$	0	0
$43$	−433464.	−0.831407	−0.415703	−	0.909500i	$-0.636465\pi$
$43$	−433464.	−0.831407	−0.415703	+	0.909500i	$0.636465\pi$
$44$	−54600.8	−0.0966306
$45$	0	0
$46$	78043.9	0.118219
$47$	−547322.	−0.768955	−0.384477	−	0.923134i	$-0.625618\pi$
$47$	−547322.	−0.768955	−0.384477	+	0.923134i	$0.625618\pi$
$48$	0	0
$49$	1.06709e6	1.29574
$50$	72618.6	0.0821585
$51$	0	0
$52$	57733.2	0.0569395
$53$	1.27499e6	1.17637	0.588183	−	0.808728i	$-0.299844\pi$
$53$	1.27499e6	1.17637	0.588183	+	0.808728i	$0.299844\pi$
$54$	0	0
$55$	−162481.	−0.131684
$56$	−1.89499e6	−1.44194
$57$	0	0
$58$	−692871.	−0.466288
$59$	869996.	0.551487	0.275743	−	0.961231i	$-0.411076\pi$
$59$	869996.	0.551487	0.275743	+	0.961231i	$0.411076\pi$
$60$	0	0
$61$	1.45260e6	0.819392	0.409696	−	0.912222i	$-0.365635\pi$
$61$	1.45260e6	0.819392	0.409696	+	0.912222i	$0.365635\pi$
$62$	−1.46382e6	−0.780039
$63$	0	0
$64$	933727.	0.445236
$65$	171802.	0.0775946
$66$	0	0
$67$	−2.47925e6	−1.00707	−0.503534	−	0.863975i	$-0.667967\pi$
$67$	−2.47925e6	−1.00707	−0.503534	+	0.863975i	$0.667967\pi$
$68$	−1.43369e6	−0.552936
$69$	0	0
$70$	−2.27961e6	−0.794359
$71$	3.74614e6	1.24217	0.621083	−	0.783745i	$-0.286693\pi$
$71$	3.74614e6	1.24217	0.621083	+	0.783745i	$0.286693\pi$
$72$	0	0
$73$	2.20514e6	0.663448	0.331724	−	0.943376i	$-0.392370\pi$
$73$	2.20514e6	0.663448	0.331724	+	0.943376i	$0.392370\pi$
$74$	3.69189e6	1.05910
$75$	0	0
$76$	−3.48896e6	−0.911693
$77$	−864381.	−0.215768
$78$	0	0
$79$	−2.99240e6	−0.682849	−0.341425	−	0.939909i	$-0.610909\pi$
$79$	−2.99240e6	−0.682849	−0.341425	+	0.939909i	$0.610909\pi$
$80$	−588631.	−0.128537
$81$	0	0
$82$	−2.73074e6	−0.546929
$83$	−7.14685e6	−1.37196	−0.685980	−	0.727621i	$-0.740626\pi$
$83$	−7.14685e6	−1.37196	−0.685980	+	0.727621i	$0.740626\pi$
$84$	0	0
$85$	−4.26637e6	−0.753516
$86$	2.78041e6	0.471372
$87$	0	0
$88$	866370.	0.135523
$89$	−99929.8	−0.0150255	−0.00751277	−	0.999972i	$-0.502391\pi$
$89$	−99929.8	−0.0150255	−0.00751277	+	0.999972i	$0.502391\pi$
$90$	0	0
$91$	913969.	0.127141
$92$	1.05677e6	0.141489
$93$	0	0
$94$	3.51074e6	0.435964
$95$	−1.03824e7	−1.24241
$96$	0	0
$97$	−1.23187e7	−1.37045	−0.685227	−	0.728330i	$-0.740297\pi$
$97$	−1.23187e7	−1.37045	−0.685227	+	0.728330i	$0.740297\pi$
$98$	−6.84475e6	−0.734627
$99$	0	0
$100$	983310.	0.0983310
$101$	−2.58580e6	−0.249729	−0.124865	−	0.992174i	$-0.539850\pi$
$101$	−2.58580e6	−0.249729	−0.124865	+	0.992174i	$0.539850\pi$
$102$	0	0
$103$	1.46020e7	1.31668	0.658342	−	0.752719i	$-0.271258\pi$
$103$	1.46020e7	1.31668	0.658342	+	0.752719i	$0.271258\pi$
$104$	−916072.	−0.0798570
$105$	0	0
$106$	−8.17830e6	−0.666949
$107$	1.13292e7	0.894038	0.447019	−	0.894525i	$-0.352486\pi$
$107$	1.13292e7	0.894038	0.447019	+	0.894525i	$0.352486\pi$
$108$	0	0
$109$	1.69590e6	0.125432	0.0627160	−	0.998031i	$-0.480024\pi$
$109$	1.69590e6	0.125432	0.0627160	+	0.998031i	$0.480024\pi$
$110$	1.04221e6	0.0746591
$111$	0	0
$112$	−3.13146e6	−0.210612
$113$	−2.66929e7	−1.74029	−0.870144	−	0.492798i	$-0.835974\pi$
$113$	−2.66929e7	−1.74029	−0.870144	+	0.492798i	$0.835974\pi$
$114$	0	0
$115$	3.14474e6	0.192815
$116$	−9.38199e6	−0.558074
$117$	0	0
$118$	−5.58049e6	−0.312669
$119$	−2.26967e7	−1.23466
$120$	0	0
$121$	−1.90920e7	−0.979721
$122$	−9.31754e6	−0.464560
$123$	0	0
$124$	−1.98212e7	−0.933585
$125$	2.31187e7	1.05871
$126$	0	0
$127$	−4.26950e7	−1.84954	−0.924771	−	0.380523i	$-0.875744\pi$
$127$	−4.26950e7	−1.84954	−0.924771	+	0.380523i	$0.875744\pi$
$128$	1.84605e7	0.778050
$129$	0	0
$130$	−1.10200e6	−0.0439928
$131$	2.14906e7	0.835218	0.417609	−	0.908627i	$-0.362868\pi$
$131$	2.14906e7	0.835218	0.417609	+	0.908627i	$0.362868\pi$
$132$	0	0
$133$	−5.52334e7	−2.03574
$134$	1.59029e7	0.570965
$135$	0	0
$136$	2.27489e7	0.775486
$137$	−2.39201e7	−0.794770	−0.397385	−	0.917652i	$-0.630082\pi$
$137$	−2.39201e7	−0.794770	−0.397385	+	0.917652i	$0.630082\pi$
$138$	0	0
$139$	−1.39476e7	−0.440502	−0.220251	−	0.975443i	$-0.570688\pi$
$139$	−1.39476e7	−0.440502	−0.220251	+	0.975443i	$0.570688\pi$
$140$	−3.08676e7	−0.950724
$141$	0	0
$142$	−2.40292e7	−0.704255
$143$	−417858.	−0.0119496
$144$	0	0
$145$	−2.79188e7	−0.760518
$146$	−1.41447e7	−0.376147
$147$	0	0
$148$	4.99909e7	1.26758
$149$	−1.70225e7	−0.421571	−0.210786	−	0.977532i	$-0.567602\pi$
$149$	−1.70225e7	−0.421571	−0.210786	+	0.977532i	$0.567602\pi$
$150$	0	0
$151$	2.36566e7	0.559155	0.279578	−	0.960123i	$-0.409806\pi$
$151$	2.36566e7	0.559155	0.279578	+	0.960123i	$0.409806\pi$
$152$	5.53605e7	1.27864
$153$	0	0
$154$	5.54448e6	0.122331
$155$	−5.89837e7	−1.27225
$156$	0	0
$157$	1.98190e7	0.408727	0.204363	−	0.978895i	$-0.434488\pi$
$157$	1.98190e7	0.408727	0.204363	+	0.978895i	$0.434488\pi$
$158$	1.91944e7	0.387146
$159$	0	0
$160$	4.93702e7	0.952895
$161$	1.67297e7	0.315934
$162$	0	0
$163$	1.07392e7	0.194230	0.0971148	−	0.995273i	$-0.469039\pi$
$163$	1.07392e7	0.194230	0.0971148	+	0.995273i	$0.469039\pi$
$164$	−3.69762e7	−0.654589
$165$	0	0
$166$	4.58427e7	0.777842
$167$	−2.60151e6	−0.0432234	−0.0216117	−	0.999766i	$-0.506880\pi$
$167$	−2.60151e6	−0.0432234	−0.0216117	+	0.999766i	$0.506880\pi$
$168$	0	0
$169$	−6.23067e7	−0.992959
$170$	2.73662e7	0.427211
$171$	0	0
$172$	3.76488e7	0.564159
$173$	6.90028e7	1.01322	0.506612	−	0.862174i	$-0.330898\pi$
$173$	6.90028e7	1.01322	0.506612	+	0.862174i	$0.330898\pi$
$174$	0	0
$175$	1.55667e7	0.219565
$176$	1.43167e6	0.0197947
$177$	0	0
$178$	640989.	0.00851884
$179$	−1.30669e8	−1.70289	−0.851447	−	0.524441i	$-0.824274\pi$
$179$	−1.30669e8	−1.70289	−0.851447	+	0.524441i	$0.824274\pi$
$180$	0	0
$181$	6.33783e7	0.794448	0.397224	−	0.917722i	$-0.369974\pi$
$181$	6.33783e7	0.794448	0.397224	+	0.917722i	$0.369974\pi$
$182$	−5.86256e6	−0.0720837
$183$	0	0
$184$	−1.67682e7	−0.198437
$185$	1.48763e8	1.72740
$186$	0	0
$187$	1.03767e7	0.116042
$188$	4.75380e7	0.521781
$189$	0	0
$190$	6.65969e7	0.704395
$191$	7.63479e7	0.792830	0.396415	−	0.918071i	$-0.370254\pi$
$191$	7.63479e7	0.792830	0.396415	+	0.918071i	$0.370254\pi$
$192$	0	0
$193$	3.45003e7	0.345440	0.172720	−	0.984971i	$-0.444744\pi$
$193$	3.45003e7	0.345440	0.172720	+	0.984971i	$0.444744\pi$
$194$	7.90170e7	0.776988
$195$	0	0
$196$	−9.26831e7	−0.879234
$197$	9.45693e7	0.881289	0.440645	−	0.897682i	$-0.354750\pi$
$197$	9.45693e7	0.881289	0.440645	+	0.897682i	$0.354750\pi$
$198$	0	0
$199$	9.61644e7	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$199$	9.61644e7	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$200$	−1.56025e7	−0.137908
$201$	0	0
$202$	1.65863e7	0.141586
$203$	−1.48525e8	−1.24613
$204$	0	0
$205$	−1.10034e8	−0.892044
$206$	−9.36627e7	−0.746503
$207$	0	0
$208$	−1.51381e6	−0.0116640
$209$	2.52522e7	0.191332
$210$	0	0
$211$	2.04103e8	1.49576	0.747878	−	0.663836i	$-0.231073\pi$
$211$	2.04103e8	1.49576	0.747878	+	0.663836i	$0.231073\pi$
$212$	−1.10740e8	−0.798234
$213$	0	0
$214$	−7.26699e7	−0.506881
$215$	1.12035e8	0.768810
$216$	0	0
$217$	−3.13788e8	−2.08462
$218$	−1.08782e7	−0.0711145
$219$	0	0
$220$	1.41124e7	0.0893553
$221$	−1.09720e7	−0.0683774
$222$	0	0
$223$	9.88109e7	0.596675	0.298337	−	0.954460i	$-0.403568\pi$
$223$	9.88109e7	0.596675	0.298337	+	0.954460i	$0.403568\pi$
$224$	2.62645e8	1.56135
$225$	0	0
$226$	1.71219e8	0.986668
$227$	5.16968e6	0.0293341	0.0146671	−	0.999892i	$-0.495331\pi$
$227$	5.16968e6	0.0293341	0.0146671	+	0.999892i	$0.495331\pi$
$228$	0	0
$229$	1.55922e7	0.0857990	0.0428995	−	0.999079i	$-0.486340\pi$
$229$	1.55922e7	0.0857990	0.0428995	+	0.999079i	$0.486340\pi$
$230$	−2.01716e7	−0.109318
$231$	0	0
$232$	1.48867e8	0.782692
$233$	−3.01968e8	−1.56392	−0.781960	−	0.623328i	$-0.785780\pi$
$233$	−3.01968e8	−1.56392	−0.781960	+	0.623328i	$0.785780\pi$
$234$	0	0
$235$	1.41463e8	0.711060
$236$	−7.55640e7	−0.374216
$237$	0	0
$238$	1.45585e8	0.700000
$239$	1.73522e8	0.822171	0.411085	−	0.911597i	$-0.365150\pi$
$239$	1.73522e8	0.822171	0.411085	+	0.911597i	$0.365150\pi$
$240$	0	0
$241$	2.78017e8	1.27942	0.639708	−	0.768618i	$-0.279055\pi$
$241$	2.78017e8	1.27942	0.639708	+	0.768618i	$0.279055\pi$
$242$	1.22463e8	0.555460
$243$	0	0
$244$	−1.26166e8	−0.556006
$245$	−2.75806e8	−1.19818
$246$	0	0
$247$	−2.67009e7	−0.112742
$248$	3.14509e8	1.30934
$249$	0	0
$250$	−1.48292e8	−0.600244
$251$	−4.45882e8	−1.77976	−0.889881	−	0.456194i	$-0.849212\pi$
$251$	−4.45882e8	−1.77976	−0.889881	+	0.456194i	$0.849212\pi$
$252$	0	0
$253$	−7.64865e6	−0.0296936
$254$	2.73863e8	1.04861
$255$	0	0
$256$	−2.37930e8	−0.886357
$257$	4.11457e8	1.51202	0.756011	−	0.654559i	$-0.227146\pi$
$257$	4.11457e8	1.51202	0.756011	+	0.654559i	$0.227146\pi$
$258$	0	0
$259$	7.91402e8	2.83040
$260$	−1.49220e7	−0.0526525
$261$	0	0
$262$	−1.37849e8	−0.473533
$263$	1.15343e8	0.390971	0.195486	−	0.980707i	$-0.437372\pi$
$263$	1.15343e8	0.390971	0.195486	+	0.980707i	$0.437372\pi$
$264$	0	0
$265$	−3.29540e8	−1.08780
$266$	3.54289e8	1.15418
$267$	0	0
$268$	2.15337e8	0.683356
$269$	1.38228e8	0.432976	0.216488	−	0.976285i	$-0.430540\pi$
$269$	1.38228e8	0.432976	0.216488	+	0.976285i	$0.430540\pi$
$270$	0	0
$271$	−5.05763e7	−0.154367	−0.0771836	−	0.997017i	$-0.524593\pi$
$271$	−5.05763e7	−0.154367	−0.0771836	+	0.997017i	$0.524593\pi$
$272$	3.75924e7	0.113269
$273$	0	0
$274$	1.53433e8	0.450601
$275$	−7.11695e6	−0.0206362
$276$	0	0
$277$	−5.24361e8	−1.48235	−0.741175	−	0.671311i	$-0.765731\pi$
$277$	−5.24361e8	−1.48235	−0.741175	+	0.671311i	$0.765731\pi$
$278$	8.94654e7	0.249746
$279$	0	0
$280$	4.89786e8	1.33338
$281$	−4.33802e8	−1.16632	−0.583162	−	0.812356i	$-0.698185\pi$
$281$	−4.33802e8	−1.16632	−0.583162	+	0.812356i	$0.698185\pi$
$282$	0	0
$283$	−5.73790e8	−1.50488	−0.752438	−	0.658664i	$-0.771122\pi$
$283$	−5.73790e8	−1.50488	−0.752438	+	0.658664i	$0.771122\pi$
$284$	−3.25373e8	−0.842883
$285$	0	0
$286$	2.68031e6	0.00677490
$287$	−5.85367e8	−1.46164
$288$	0	0
$289$	−1.37870e8	−0.335992
$290$	1.79082e8	0.431181
$291$	0	0
$292$	−1.91529e8	−0.450189
$293$	6.54019e8	1.51899	0.759493	−	0.650516i	$-0.225447\pi$
$293$	6.54019e8	1.51899	0.759493	+	0.650516i	$0.225447\pi$
$294$	0	0
$295$	−2.24863e8	−0.509965
$296$	−7.93222e8	−1.77776
$297$	0	0
$298$	1.09189e8	0.239013
$299$	8.08744e6	0.0174969
$300$	0	0
$301$	5.96015e8	1.25972
$302$	−1.51742e8	−0.317017
$303$	0	0
$304$	9.14830e7	0.186760
$305$	−3.75445e8	−0.757700
$306$	0	0
$307$	−3.46850e8	−0.684159	−0.342080	−	0.939671i	$-0.611131\pi$
$307$	−3.46850e8	−0.684159	−0.342080	+	0.939671i	$0.611131\pi$
$308$	7.50764e7	0.146412
$309$	0	0
$310$	3.78345e8	0.721310
$311$	−6.84995e8	−1.29130	−0.645649	−	0.763635i	$-0.723413\pi$
$311$	−6.84995e8	−1.29130	−0.645649	+	0.763635i	$0.723413\pi$
$312$	0	0
$313$	−2.88666e8	−0.532096	−0.266048	−	0.963960i	$-0.585718\pi$
$313$	−2.88666e8	−0.532096	−0.266048	+	0.963960i	$0.585718\pi$
$314$	−1.27127e8	−0.231731
$315$	0	0
$316$	2.59907e8	0.463354
$317$	−9.31986e8	−1.64324	−0.821621	−	0.570034i	$-0.806930\pi$
$317$	−9.31986e8	−1.64324	−0.821621	+	0.570034i	$0.806930\pi$
$318$	0	0
$319$	6.79045e7	0.117120
$320$	−2.41335e8	−0.411714
$321$	0	0
$322$	−1.07311e8	−0.179121
$323$	6.63065e8	1.09483
$324$	0	0
$325$	7.52523e6	0.0121599
$326$	−6.88854e7	−0.110120
$327$	0	0
$328$	5.86714e8	0.918053
$329$	7.52571e8	1.16510
$330$	0	0
$331$	−1.02274e9	−1.55012	−0.775061	−	0.631886i	$-0.782281\pi$
$331$	−1.02274e9	−1.55012	−0.775061	+	0.631886i	$0.782281\pi$
$332$	6.20744e8	0.930956
$333$	0	0
$334$	1.66871e7	0.0245058
$335$	6.40798e8	0.931246
$336$	0	0
$337$	−1.98269e8	−0.282195	−0.141098	−	0.989996i	$-0.545063\pi$
$337$	−1.98269e8	−0.282195	−0.141098	+	0.989996i	$0.545063\pi$
$338$	3.99659e8	0.562965
$339$	0	0
$340$	3.70558e8	0.511305
$341$	1.43461e8	0.195926
$342$	0	0
$343$	−3.34883e8	−0.448089
$344$	−5.97386e8	−0.791226
$345$	0	0
$346$	−4.42611e8	−0.574454
$347$	6.40896e8	0.823444	0.411722	−	0.911309i	$-0.364927\pi$
$347$	6.40896e8	0.823444	0.411722	+	0.911309i	$0.364927\pi$
$348$	0	0
$349$	1.01822e9	1.28220	0.641098	−	0.767459i	$-0.278479\pi$
$349$	1.01822e9	1.28220	0.641098	+	0.767459i	$0.278479\pi$
$350$	−9.98508e7	−0.124484
$351$	0	0
$352$	−1.20079e8	−0.146746
$353$	9.17007e8	1.10959	0.554793	−	0.831988i	$-0.312797\pi$
$353$	9.17007e8	1.10959	0.554793	+	0.831988i	$0.312797\pi$
$354$	0	0
$355$	−9.68243e8	−1.14864
$356$	8.67946e6	0.0101957
$357$	0	0
$358$	8.38163e8	0.965468
$359$	1.16489e9	1.32879	0.664395	−	0.747382i	$-0.268689\pi$
$359$	1.16489e9	1.32879	0.664395	+	0.747382i	$0.268689\pi$
$360$	0	0
$361$	7.19729e8	0.805182
$362$	−4.06533e8	−0.450418
$363$	0	0
$364$	−7.93834e7	−0.0862730
$365$	−5.69951e8	−0.613497
$366$	0	0
$367$	−1.08158e9	−1.14216	−0.571079	−	0.820895i	$-0.693475\pi$
$367$	−1.08158e9	−1.14216	−0.571079	+	0.820895i	$0.693475\pi$
$368$	−2.77093e7	−0.0289840
$369$	0	0
$370$	−9.54221e8	−0.979361
$371$	−1.75312e9	−1.78239
$372$	0	0
$373$	−5.14748e8	−0.513587	−0.256793	−	0.966466i	$-0.582666\pi$
$373$	−5.14748e8	−0.513587	−0.256793	+	0.966466i	$0.582666\pi$
$374$	−6.65602e7	−0.0657906
$375$	0	0
$376$	−7.54302e8	−0.731792
$377$	−7.18000e7	−0.0690128
$378$	0	0
$379$	−9.80638e8	−0.925277	−0.462638	−	0.886547i	$-0.653097\pi$
$379$	−9.80638e8	−0.925277	−0.462638	+	0.886547i	$0.653097\pi$
$380$	9.01772e8	0.843051
$381$	0	0
$382$	−4.89725e8	−0.449501
$383$	−3.82765e8	−0.348126	−0.174063	−	0.984735i	$-0.555690\pi$
$383$	−3.82765e8	−0.348126	−0.174063	+	0.984735i	$0.555690\pi$
$384$	0	0
$385$	2.23412e8	0.199523
$386$	−2.21299e8	−0.195850
$387$	0	0
$388$	1.06995e9	0.929934
$389$	−2.07431e9	−1.78669	−0.893347	−	0.449368i	$-0.851649\pi$
$389$	−2.07431e9	−1.78669	−0.893347	+	0.449368i	$0.851649\pi$
$390$	0	0
$391$	−2.00836e8	−0.169912
$392$	1.47063e9	1.23311
$393$	0	0
$394$	−6.06604e8	−0.499653
$395$	7.73429e8	0.631438
$396$	0	0
$397$	−1.19403e8	−0.0957739	−0.0478870	−	0.998853i	$-0.515249\pi$
$397$	−1.19403e8	−0.0957739	−0.0478870	+	0.998853i	$0.515249\pi$
$398$	−6.16836e8	−0.490432
$399$	0	0
$400$	−2.57831e7	−0.0201430
$401$	−8.62416e8	−0.667900	−0.333950	−	0.942591i	$-0.608382\pi$
$401$	−8.62416e8	−0.667900	−0.333950	+	0.942591i	$0.608382\pi$
$402$	0	0
$403$	−1.51691e8	−0.115449
$404$	2.24591e8	0.169456
$405$	0	0
$406$	9.52700e8	0.706505
$407$	−3.61821e8	−0.266020
$408$	0	0
$409$	−2.72783e9	−1.97145	−0.985725	−	0.168361i	$-0.946153\pi$
$409$	−2.72783e9	−1.97145	−0.985725	+	0.168361i	$0.946153\pi$
$410$	7.05798e8	0.505751
$411$	0	0
$412$	−1.26826e9	−0.893448
$413$	−1.19625e9	−0.835595
$414$	0	0
$415$	1.84721e9	1.26866
$416$	1.26967e8	0.0864700
$417$	0	0
$418$	−1.61978e8	−0.108477
$419$	−1.89767e9	−1.26029	−0.630147	−	0.776476i	$-0.717005\pi$
$419$	−1.89767e9	−1.26029	−0.630147	+	0.776476i	$0.717005\pi$
$420$	0	0
$421$	−1.38932e9	−0.907433	−0.453716	−	0.891146i	$-0.649902\pi$
$421$	−1.38932e9	−0.907433	−0.453716	+	0.891146i	$0.649902\pi$
$422$	−1.30920e9	−0.848029
$423$	0	0
$424$	1.75715e9	1.11951
$425$	−1.86875e8	−0.118083
$426$	0	0
$427$	−1.99733e9	−1.24152
$428$	−9.84004e8	−0.606658
$429$	0	0
$430$	−7.18636e8	−0.435883
$431$	−3.19103e8	−0.191982	−0.0959911	−	0.995382i	$-0.530602\pi$
$431$	−3.19103e8	−0.191982	−0.0959911	+	0.995382i	$0.530602\pi$
$432$	0	0
$433$	1.46973e9	0.870019	0.435010	−	0.900426i	$-0.356745\pi$
$433$	1.46973e9	0.870019	0.435010	+	0.900426i	$0.356745\pi$
$434$	2.01276e9	1.18189
$435$	0	0
$436$	−1.47299e8	−0.0851130
$437$	−4.88744e8	−0.280154
$438$	0	0
$439$	3.49428e9	1.97120	0.985601	−	0.169086i	$-0.0540815\pi$
$439$	3.49428e9	1.97120	0.985601	+	0.169086i	$0.0540815\pi$
$440$	−2.23926e8	−0.125320
$441$	0	0
$442$	7.03786e7	0.0387671
$443$	2.24240e9	1.22546	0.612730	−	0.790292i	$-0.290071\pi$
$443$	2.24240e9	1.22546	0.612730	+	0.790292i	$0.290071\pi$
$444$	0	0
$445$	2.58283e7	0.0138943
$446$	−6.33811e8	−0.338289
$447$	0	0
$448$	−1.28388e9	−0.674607
$449$	2.86545e9	1.49393	0.746965	−	0.664863i	$-0.231510\pi$
$449$	2.86545e9	1.49393	0.746965	+	0.664863i	$0.231510\pi$
$450$	0	0
$451$	2.67624e8	0.137375
$452$	2.31843e9	1.18089
$453$	0	0
$454$	−3.31603e7	−0.0166312
$455$	−2.36228e8	−0.117569
$456$	0	0
$457$	−5.18060e8	−0.253906	−0.126953	−	0.991909i	$-0.540520\pi$
$457$	−5.18060e8	−0.253906	−0.126953	+	0.991909i	$0.540520\pi$
$458$	−1.00014e8	−0.0486444
$459$	0	0
$460$	−2.73138e8	−0.130837
$461$	−5.60254e8	−0.266337	−0.133169	−	0.991093i	$-0.542515\pi$
$461$	−5.60254e8	−0.266337	−0.133169	+	0.991093i	$0.542515\pi$
$462$	0	0
$463$	−1.95481e9	−0.915315	−0.457657	−	0.889129i	$-0.651311\pi$
$463$	−1.95481e9	−0.915315	−0.457657	+	0.889129i	$0.651311\pi$
$464$	2.46002e8	0.114321
$465$	0	0
$466$	1.93694e9	0.886676
$467$	−7.33604e7	−0.0333313	−0.0166657	−	0.999861i	$-0.505305\pi$
$467$	−7.33604e7	−0.0333313	−0.0166657	+	0.999861i	$0.505305\pi$
$468$	0	0
$469$	3.40898e9	1.52588
$470$	−9.07401e8	−0.403141
$471$	0	0
$472$	1.19900e9	0.524834
$473$	−2.72493e8	−0.118397
$474$	0	0
$475$	−4.54769e8	−0.194699
$476$	1.97133e9	0.837791
$477$	0	0
$478$	−1.11304e9	−0.466136
$479$	1.55935e9	0.648290	0.324145	−	0.946007i	$-0.394923\pi$
$479$	1.55935e9	0.648290	0.324145	+	0.946007i	$0.394923\pi$
$480$	0	0
$481$	3.82578e8	0.156752
$482$	−1.78331e9	−0.725374
$483$	0	0
$484$	1.65825e9	0.664799
$485$	3.18395e9	1.26727
$486$	0	0
$487$	−6.54145e8	−0.256639	−0.128320	−	0.991733i	$-0.540958\pi$
$487$	−6.54145e8	−0.256639	−0.128320	+	0.991733i	$0.540958\pi$
$488$	2.00193e9	0.779792
$489$	0	0
$490$	1.76912e9	0.679317
$491$	−1.65065e9	−0.629316	−0.314658	−	0.949205i	$-0.601890\pi$
$491$	−1.65065e9	−0.629316	−0.314658	+	0.949205i	$0.601890\pi$
$492$	0	0
$493$	1.78301e9	0.670179
$494$	1.71270e8	0.0639200
$495$	0	0
$496$	5.19726e8	0.191244
$497$	−5.15095e9	−1.88209
$498$	0	0
$499$	−4.10867e9	−1.48030	−0.740149	−	0.672443i	$-0.765245\pi$
$499$	−4.10867e9	−1.48030	−0.740149	+	0.672443i	$0.765245\pi$
$500$	−2.00798e9	−0.718398
$501$	0	0
$502$	2.86006e9	1.00905
$503$	−1.25134e9	−0.438418	−0.219209	−	0.975678i	$-0.570348\pi$
$503$	−1.25134e9	−0.438418	−0.219209	+	0.975678i	$0.570348\pi$
$504$	0	0
$505$	6.68336e8	0.230927
$506$	4.90614e7	0.0168350
$507$	0	0
$508$	3.70830e9	1.25502
$509$	−6.49677e7	−0.0218366	−0.0109183	−	0.999940i	$-0.503475\pi$
$509$	−6.49677e7	−0.0218366	−0.0109183	+	0.999940i	$0.503475\pi$
$510$	0	0
$511$	−3.03208e9	−1.00524
$512$	−8.36766e8	−0.275524
$513$	0	0
$514$	−2.63924e9	−0.857252
$515$	−3.77409e9	−1.21755
$516$	0	0
$517$	−3.44068e8	−0.109503
$518$	−5.07636e9	−1.60472
$519$	0	0
$520$	2.36772e8	0.0738446
$521$	2.87506e9	0.890666	0.445333	−	0.895365i	$-0.353085\pi$
$521$	2.87506e9	0.890666	0.445333	+	0.895365i	$0.353085\pi$
$522$	0	0
$523$	−1.33531e9	−0.408157	−0.204079	−	0.978954i	$-0.565420\pi$
$523$	−1.33531e9	−0.408157	−0.204079	+	0.978954i	$0.565420\pi$
$524$	−1.86658e9	−0.566745
$525$	0	0
$526$	−7.39853e8	−0.221664
$527$	3.76695e9	1.12112
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	2.11380e9	0.616734
$531$	0	0
$532$	4.79733e9	1.38137
$533$	−2.82978e8	−0.0809481
$534$	0	0
$535$	−2.92819e9	−0.826726
$536$	−3.41683e9	−0.958398
$537$	0	0
$538$	−8.86650e8	−0.245479
$539$	6.70817e8	0.184520
$540$	0	0
$541$	−1.21649e9	−0.330308	−0.165154	−	0.986268i	$-0.552812\pi$
$541$	−1.21649e9	−0.330308	−0.165154	+	0.986268i	$0.552812\pi$
$542$	3.24416e8	0.0875196
$543$	0	0
$544$	−3.15299e9	−0.839704
$545$	−4.38330e8	−0.115988
$546$	0	0
$547$	2.19724e7	0.00574013	0.00287007	−	0.999996i	$-0.499086\pi$
$547$	2.19724e7	0.00574013	0.00287007	+	0.999996i	$0.499086\pi$
$548$	2.07760e9	0.539299
$549$	0	0
$550$	4.56509e7	0.0116998
$551$	4.33905e9	1.10501
$552$	0	0
$553$	4.11456e9	1.03463
$554$	3.36345e9	0.840429
$555$	0	0
$556$	1.21143e9	0.298907
$557$	4.57323e9	1.12132	0.560660	−	0.828046i	$-0.310547\pi$
$557$	4.57323e9	1.12132	0.560660	+	0.828046i	$0.310547\pi$
$558$	0	0
$559$	2.88125e8	0.0697653
$560$	8.09370e8	0.194755
$561$	0	0
$562$	2.78257e9	0.661256
$563$	3.99570e9	0.943656	0.471828	−	0.881691i	$-0.343594\pi$
$563$	3.99570e9	0.943656	0.471828	+	0.881691i	$0.343594\pi$
$564$	0	0
$565$	6.89916e9	1.60926
$566$	3.68051e9	0.853200
$567$	0	0
$568$	5.16280e9	1.18213
$569$	−1.93234e9	−0.439734	−0.219867	−	0.975530i	$-0.570562\pi$
$569$	−1.93234e9	−0.439734	−0.219867	+	0.975530i	$0.570562\pi$
$570$	0	0
$571$	−5.02820e9	−1.13028	−0.565140	−	0.824995i	$-0.691178\pi$
$571$	−5.02820e9	−1.13028	−0.565140	+	0.824995i	$0.691178\pi$
$572$	3.62933e7	0.00810850
$573$	0	0
$574$	3.75477e9	0.828690
$575$	1.37745e8	0.0302161
$576$	0	0
$577$	−7.01087e9	−1.51935	−0.759673	−	0.650306i	$-0.774641\pi$
$577$	−7.01087e9	−1.51935	−0.759673	+	0.650306i	$0.774641\pi$
$578$	8.84355e8	0.190493
$579$	0	0
$580$	2.42491e9	0.516057
$581$	9.82695e9	2.07875
$582$	0	0
$583$	8.01511e8	0.167521
$584$	3.03906e9	0.631385
$585$	0	0
$586$	−4.19513e9	−0.861200
$587$	−8.62743e9	−1.76055	−0.880275	−	0.474464i	$-0.842642\pi$
$587$	−8.62743e9	−1.76055	−0.880275	+	0.474464i	$0.842642\pi$
$588$	0	0
$589$	9.16706e9	1.84853
$590$	1.44236e9	0.289128
$591$	0	0
$592$	−1.31080e9	−0.259663
$593$	−2.64789e8	−0.0521446	−0.0260723	−	0.999660i	$-0.508300\pi$
$593$	−2.64789e8	−0.0521446	−0.0260723	+	0.999660i	$0.508300\pi$
$594$	0	0
$595$	5.86628e9	1.14170
$596$	1.47850e9	0.286061
$597$	0	0
$598$	−5.18760e7	−0.00992001
$599$	−8.16746e9	−1.55272	−0.776360	−	0.630289i	$-0.782936\pi$
$599$	−8.16746e9	−1.55272	−0.776360	+	0.630289i	$0.782936\pi$
$600$	0	0
$601$	−9.33408e9	−1.75392	−0.876962	−	0.480559i	$-0.840434\pi$
$601$	−9.33408e9	−1.75392	−0.876962	+	0.480559i	$0.840434\pi$
$602$	−3.82307e9	−0.714208
$603$	0	0
$604$	−2.05471e9	−0.379420
$605$	4.93460e9	0.905958
$606$	0	0
$607$	7.02465e9	1.27487	0.637433	−	0.770506i	$-0.279996\pi$
$607$	7.02465e9	1.27487	0.637433	+	0.770506i	$0.279996\pi$
$608$	−7.67295e9	−1.38452
$609$	0	0
$610$	2.40825e9	0.429583
$611$	3.63807e8	0.0645248
$612$	0	0
$613$	5.41176e9	0.948914	0.474457	−	0.880279i	$-0.342644\pi$
$613$	5.41176e9	0.948914	0.474457	+	0.880279i	$0.342644\pi$
$614$	2.22483e9	0.387889
$615$	0	0
$616$	−1.19126e9	−0.205341
$617$	2.48099e9	0.425233	0.212616	−	0.977136i	$-0.431802\pi$
$617$	2.48099e9	0.425233	0.212616	+	0.977136i	$0.431802\pi$
$618$	0	0
$619$	3.11577e9	0.528017	0.264008	−	0.964520i	$-0.414955\pi$
$619$	3.11577e9	0.528017	0.264008	+	0.964520i	$0.414955\pi$
$620$	5.12307e9	0.863295
$621$	0	0
$622$	4.39383e9	0.732110
$623$	1.37404e8	0.0227662
$624$	0	0
$625$	−5.09088e9	−0.834089
$626$	1.85161e9	0.301676
$627$	0	0
$628$	−1.72139e9	−0.277345
$629$	−9.50060e9	−1.52221
$630$	0	0
$631$	9.05069e9	1.43410	0.717049	−	0.697022i	$-0.245492\pi$
$631$	9.05069e9	1.43410	0.717049	+	0.697022i	$0.245492\pi$
$632$	−4.12403e9	−0.649848
$633$	0	0
$634$	5.97812e9	0.931648
$635$	1.10351e10	1.71029
$636$	0	0
$637$	−7.09300e8	−0.108728
$638$	−4.35566e8	−0.0664020
$639$	0	0
$640$	−4.77137e9	−0.719471
$641$	−7.70954e9	−1.15618	−0.578090	−	0.815973i	$-0.696202\pi$
$641$	−7.70954e9	−1.15618	−0.578090	+	0.815973i	$0.696202\pi$
$642$	0	0
$643$	−4.41619e9	−0.655102	−0.327551	−	0.944833i	$-0.606223\pi$
$643$	−4.41619e9	−0.655102	−0.327551	+	0.944833i	$0.606223\pi$
$644$	−1.45307e9	−0.214380
$645$	0	0
$646$	−4.25316e9	−0.620723
$647$	1.16052e9	0.168457	0.0842283	−	0.996446i	$-0.473157\pi$
$647$	1.16052e9	0.168457	0.0842283	+	0.996446i	$0.473157\pi$
$648$	0	0
$649$	5.46913e8	0.0785348
$650$	−4.82698e7	−0.00689412
$651$	0	0
$652$	−9.32760e8	−0.131796
$653$	−1.22436e9	−0.172073	−0.0860366	−	0.996292i	$-0.527420\pi$
$653$	−1.22436e9	−0.172073	−0.0860366	+	0.996292i	$0.527420\pi$
$654$	0	0
$655$	−5.55456e9	−0.772334
$656$	9.69543e8	0.134092
$657$	0	0
$658$	−4.82728e9	−0.660559
$659$	−2.00612e9	−0.273060	−0.136530	−	0.990636i	$-0.543595\pi$
$659$	−2.00612e9	−0.273060	−0.136530	+	0.990636i	$0.543595\pi$
$660$	0	0
$661$	−1.31936e10	−1.77688	−0.888439	−	0.458995i	$-0.848210\pi$
$661$	−1.31936e10	−1.77688	−0.888439	+	0.458995i	$0.848210\pi$
$662$	6.56023e9	0.878853
$663$	0	0
$664$	−9.84955e9	−1.30565
$665$	1.42759e10	1.88247
$666$	0	0
$667$	−1.31426e9	−0.171490
$668$	2.25956e8	0.0293296
$669$	0	0
$670$	−4.11033e9	−0.527977
$671$	9.13161e8	0.116686
$672$	0	0
$673$	−6.38937e9	−0.807989	−0.403995	−	0.914761i	$-0.632379\pi$
$673$	−6.38937e9	−0.807989	−0.403995	+	0.914761i	$0.632379\pi$
$674$	1.27177e9	0.159993
$675$	0	0
$676$	5.41169e9	0.673782
$677$	−8.25794e9	−1.02285	−0.511424	−	0.859328i	$-0.670882\pi$
$677$	−8.25794e9	−1.02285	−0.511424	+	0.859328i	$0.670882\pi$
$678$	0	0
$679$	1.69383e10	2.07647
$680$	−5.87977e9	−0.717099
$681$	0	0
$682$	−9.20213e8	−0.111082
$683$	−3.90289e9	−0.468721	−0.234360	−	0.972150i	$-0.575300\pi$
$683$	−3.90289e9	−0.468721	−0.234360	+	0.972150i	$0.575300\pi$
$684$	0	0
$685$	6.18250e9	0.734932
$686$	2.14807e9	0.254047
$687$	0	0
$688$	−9.87179e8	−0.115568
$689$	−8.47492e8	−0.0987116
$690$	0	0
$691$	4.78440e9	0.551638	0.275819	−	0.961210i	$-0.411051\pi$
$691$	4.78440e9	0.551638	0.275819	+	0.961210i	$0.411051\pi$
$692$	−5.99328e9	−0.687532
$693$	0	0
$694$	−4.11095e9	−0.466858
$695$	3.60496e9	0.407337
$696$	0	0
$697$	7.02720e9	0.786082
$698$	−6.53129e9	−0.726951
$699$	0	0
$700$	−1.35205e9	−0.148988
$701$	−1.15430e10	−1.26563	−0.632813	−	0.774305i	$-0.718100\pi$
$701$	−1.15430e10	−1.26563	−0.632813	+	0.774305i	$0.718100\pi$
$702$	0	0
$703$	−2.31202e10	−2.50985
$704$	5.86977e8	0.0634040
$705$	0	0
$706$	−5.88204e9	−0.629088
$707$	3.55548e9	0.378382
$708$	0	0
$709$	−8.22369e9	−0.866573	−0.433286	−	0.901256i	$-0.642646\pi$
$709$	−8.22369e9	−0.866573	−0.433286	+	0.901256i	$0.642646\pi$
$710$	6.21069e9	0.651231
$711$	0	0
$712$	−1.37720e8	−0.0142994
$713$	−2.77661e9	−0.286881
$714$	0	0
$715$	1.08001e8	0.0110499
$716$	1.13494e10	1.15551
$717$	0	0
$718$	−7.47209e9	−0.753367
$719$	−1.41230e10	−1.41702	−0.708510	−	0.705701i	$-0.750632\pi$
$719$	−1.41230e10	−1.41702	−0.708510	+	0.705701i	$0.750632\pi$
$720$	0	0
$721$	−2.00778e10	−1.99500
$722$	−4.61662e9	−0.456504
$723$	0	0
$724$	−5.50476e9	−0.539080
$725$	−1.22290e9	−0.119181
$726$	0	0
$727$	1.99093e10	1.92170	0.960848	−	0.277077i	$-0.0893658\pi$
$727$	1.99093e10	1.92170	0.960848	+	0.277077i	$0.0893658\pi$
$728$	1.25960e9	0.120997
$729$	0	0
$730$	3.65589e9	0.347827
$731$	−7.15502e9	−0.677486
$732$	0	0
$733$	3.99037e9	0.374239	0.187120	−	0.982337i	$-0.440085\pi$
$733$	3.99037e9	0.374239	0.187120	+	0.982337i	$0.440085\pi$
$734$	6.93766e9	0.647555
$735$	0	0
$736$	2.32406e9	0.214870
$737$	−1.55856e9	−0.143412
$738$	0	0
$739$	1.10404e10	1.00630	0.503151	−	0.864198i	$-0.332174\pi$
$739$	1.10404e10	1.00630	0.503151	+	0.864198i	$0.332174\pi$
$740$	−1.29209e10	−1.17214
$741$	0	0
$742$	1.12452e10	1.01054
$743$	−9.61216e9	−0.859726	−0.429863	−	0.902894i	$-0.641438\pi$
$743$	−9.61216e9	−0.859726	−0.429863	+	0.902894i	$0.641438\pi$
$744$	0	0
$745$	4.39971e9	0.389831
$746$	3.30179e9	0.291182
$747$	0	0
$748$	−9.01275e8	−0.0787411
$749$	−1.55777e10	−1.35462
$750$	0	0
$751$	−7.47557e9	−0.644028	−0.322014	−	0.946735i	$-0.604360\pi$
$751$	−7.47557e9	−0.644028	−0.322014	+	0.946735i	$0.604360\pi$
$752$	−1.24648e9	−0.106887
$753$	0	0
$754$	4.60553e8	0.0391273
$755$	−6.11438e9	−0.517057
$756$	0	0
$757$	−2.64497e9	−0.221608	−0.110804	−	0.993842i	$-0.535343\pi$
$757$	−2.64497e9	−0.221608	−0.110804	+	0.993842i	$0.535343\pi$
$758$	6.29019e9	0.524592
$759$	0	0
$760$	−1.43087e10	−1.18237
$761$	5.88932e9	0.484417	0.242208	−	0.970224i	$-0.422128\pi$
$761$	5.88932e9	0.484417	0.242208	+	0.970224i	$0.422128\pi$
$762$	0	0
$763$	−2.33187e9	−0.190051
$764$	−6.63124e9	−0.537982
$765$	0	0
$766$	2.45520e9	0.197372
$767$	−5.78289e8	−0.0462765
$768$	0	0
$769$	−2.44979e10	−1.94262	−0.971309	−	0.237822i	$-0.923567\pi$
$769$	−2.44979e10	−1.94262	−0.971309	+	0.237822i	$0.923567\pi$
$770$	−1.43305e9	−0.113121
$771$	0	0
$772$	−2.99655e9	−0.234402
$773$	−2.04519e10	−1.59260	−0.796298	−	0.604905i	$-0.793211\pi$
$773$	−2.04519e10	−1.59260	−0.796298	+	0.604905i	$0.793211\pi$
$774$	0	0
$775$	−2.58359e9	−0.199374
$776$	−1.69772e10	−1.30422
$777$	0	0
$778$	1.33054e10	1.01298
$779$	1.71010e10	1.29611
$780$	0	0
$781$	2.35497e9	0.176891
$782$	1.28824e9	0.0963326
$783$	0	0
$784$	2.43022e9	0.180110
$785$	−5.12250e9	−0.377954
$786$	0	0
$787$	4.33951e9	0.317343	0.158672	−	0.987331i	$-0.449279\pi$
$787$	4.33951e9	0.317343	0.158672	+	0.987331i	$0.449279\pi$
$788$	−8.21387e9	−0.598007
$789$	0	0
$790$	−4.96107e9	−0.357998
$791$	3.67028e10	2.63683
$792$	0	0
$793$	−9.65548e8	−0.0687571
$794$	7.65895e8	0.0542997
$795$	0	0
$796$	−8.35242e9	−0.586971
$797$	2.36953e9	0.165790	0.0828951	−	0.996558i	$-0.473583\pi$
$797$	2.36953e9	0.165790	0.0828951	+	0.996558i	$0.473583\pi$
$798$	0	0
$799$	−9.03444e9	−0.626596
$800$	2.16250e9	0.149328
$801$	0	0
$802$	5.53187e9	0.378671
$803$	1.38624e9	0.0944787
$804$	0	0
$805$	−4.32402e9	−0.292148
$806$	9.73004e8	0.0654549
$807$	0	0
$808$	−3.56366e9	−0.237660
$809$	1.81515e10	1.20529	0.602647	−	0.798008i	$-0.294113\pi$
$809$	1.81515e10	1.20529	0.602647	+	0.798008i	$0.294113\pi$
$810$	0	0
$811$	−1.43566e10	−0.945102	−0.472551	−	0.881303i	$-0.656667\pi$
$811$	−1.43566e10	−0.945102	−0.472551	+	0.881303i	$0.656667\pi$
$812$	1.29003e10	0.845576
$813$	0	0
$814$	2.32086e9	0.150822
$815$	−2.77570e9	−0.179606
$816$	0	0
$817$	−1.74121e10	−1.11705
$818$	1.74974e10	1.11773
$819$	0	0
$820$	9.55703e9	0.605305
$821$	−1.71884e10	−1.08402	−0.542008	−	0.840374i	$-0.682336\pi$
$821$	−1.71884e10	−1.08402	−0.542008	+	0.840374i	$0.682336\pi$
$822$	0	0
$823$	1.30653e10	0.816994	0.408497	−	0.912760i	$-0.366053\pi$
$823$	1.30653e10	0.816994	0.408497	+	0.912760i	$0.366053\pi$
$824$	2.01240e10	1.25305
$825$	0	0
$826$	7.67320e9	0.473747
$827$	1.10411e9	0.0678804	0.0339402	−	0.999424i	$-0.489194\pi$
$827$	1.10411e9	0.0678804	0.0339402	+	0.999424i	$0.489194\pi$
$828$	0	0
$829$	−6.95576e9	−0.424037	−0.212018	−	0.977266i	$-0.568004\pi$
$829$	−6.95576e9	−0.424037	−0.212018	+	0.977266i	$0.568004\pi$
$830$	−1.18487e10	−0.719279
$831$	0	0
$832$	−6.20651e8	−0.0373608
$833$	1.76141e10	1.05585
$834$	0	0
$835$	6.72399e8	0.0399691
$836$	−2.19330e9	−0.129830
$837$	0	0
$838$	1.21724e10	0.714532
$839$	−1.74955e10	−1.02272	−0.511362	−	0.859365i	$-0.670859\pi$
$839$	−1.74955e10	−1.02272	−0.511362	+	0.859365i	$0.670859\pi$
$840$	0	0
$841$	−5.58195e9	−0.323593
$842$	8.91163e9	0.514476
$843$	0	0
$844$	−1.77275e10	−1.01496
$845$	1.61041e10	0.918199
$846$	0	0
$847$	2.62516e10	1.48444
$848$	2.90369e9	0.163518
$849$	0	0
$850$	1.19869e9	0.0669483
$851$	7.00288e9	0.389514
$852$	0	0
$853$	1.02759e10	0.566889	0.283444	−	0.958989i	$-0.408523\pi$
$853$	1.02759e10	0.566889	0.283444	+	0.958989i	$0.408523\pi$
$854$	1.28117e10	0.703887
$855$	0	0
$856$	1.56135e10	0.850830
$857$	−9.38878e9	−0.509538	−0.254769	−	0.967002i	$-0.581999\pi$
$857$	−9.38878e9	−0.509538	−0.254769	+	0.967002i	$0.581999\pi$
$858$	0	0
$859$	1.60522e10	0.864090	0.432045	−	0.901852i	$-0.357792\pi$
$859$	1.60522e10	0.864090	0.432045	+	0.901852i	$0.357792\pi$
$860$	−9.73087e9	−0.521684
$861$	0	0
$862$	2.04685e9	0.108846
$863$	2.10300e10	1.11378	0.556891	−	0.830585i	$-0.311994\pi$
$863$	2.10300e10	1.11378	0.556891	+	0.830585i	$0.311994\pi$
$864$	0	0
$865$	−1.78348e10	−0.936938
$866$	−9.42740e9	−0.493264
$867$	0	0
$868$	2.72542e10	1.41454
$869$	−1.88114e9	−0.0972415
$870$	0	0
$871$	1.64797e9	0.0845055
$872$	2.33724e9	0.119370
$873$	0	0
$874$	3.13500e9	0.158835
$875$	−3.17882e10	−1.60413
$876$	0	0
$877$	2.42580e8	0.0121439	0.00607193	−	0.999982i	$-0.498067\pi$
$877$	2.42580e8	0.0121439	0.00607193	+	0.999982i	$0.498067\pi$
$878$	−2.24136e10	−1.11759
$879$	0	0
$880$	−3.70036e8	−0.0183044
$881$	1.59632e10	0.786510	0.393255	−	0.919430i	$-0.371349\pi$
$881$	1.59632e10	0.786510	0.393255	+	0.919430i	$0.371349\pi$
$882$	0	0
$883$	−1.76696e10	−0.863704	−0.431852	−	0.901945i	$-0.642140\pi$
$883$	−1.76696e10	−0.863704	−0.431852	+	0.901945i	$0.642140\pi$
$884$	9.52979e8	0.0463981
$885$	0	0
$886$	−1.43836e10	−0.694783
$887$	2.57850e10	1.24061	0.620304	−	0.784362i	$-0.287009\pi$
$887$	2.57850e10	1.24061	0.620304	+	0.784362i	$0.287009\pi$
$888$	0	0
$889$	5.87059e10	2.80237
$890$	−1.65673e8	−0.00787745
$891$	0	0
$892$	−8.58228e9	−0.404879
$893$	−2.19857e10	−1.03314
$894$	0	0
$895$	3.37733e10	1.57468
$896$	−2.53832e10	−1.17888
$897$	0	0
$898$	−1.83801e10	−0.846995
$899$	2.46507e10	1.13154
$900$	0	0
$901$	2.10458e10	0.958582
$902$	−1.71665e9	−0.0778858
$903$	0	0
$904$	−3.67873e10	−1.65618
$905$	−1.63810e10	−0.734634
$906$	0	0
$907$	3.53695e9	0.157400	0.0786998	−	0.996898i	$-0.474923\pi$
$907$	3.53695e9	0.157400	0.0786998	+	0.996898i	$0.474923\pi$
$908$	−4.49016e8	−0.0199050
$909$	0	0
$910$	1.51526e9	0.0666565
$911$	1.88154e10	0.824516	0.412258	−	0.911067i	$-0.364740\pi$
$911$	1.88154e10	0.824516	0.412258	+	0.911067i	$0.364740\pi$
$912$	0	0
$913$	−4.49279e9	−0.195375
$914$	3.32304e9	0.143954
$915$	0	0
$916$	−1.35427e9	−0.0582198
$917$	−2.95497e10	−1.26550
$918$	0	0
$919$	4.95571e8	0.0210621	0.0105311	−	0.999945i	$-0.496648\pi$
$919$	4.95571e8	0.0210621	0.0105311	+	0.999945i	$0.496648\pi$
$920$	4.33397e9	0.183497
$921$	0	0
$922$	3.59369e9	0.151002
$923$	−2.49007e9	−0.104233
$924$	0	0
$925$	6.51606e9	0.270701
$926$	1.25389e10	0.518944
$927$	0	0
$928$	−2.06330e10	−0.847507
$929$	1.67054e10	0.683600	0.341800	−	0.939773i	$-0.388964\pi$
$929$	1.67054e10	0.683600	0.341800	+	0.939773i	$0.388964\pi$
$930$	0	0
$931$	4.28648e10	1.74091
$932$	2.62276e10	1.06121
$933$	0	0
$934$	4.70562e8	0.0188974
$935$	−2.68201e9	−0.107305
$936$	0	0
$937$	2.60835e10	1.03580	0.517902	−	0.855440i	$-0.326713\pi$
$937$	2.60835e10	1.03580	0.517902	+	0.855440i	$0.326713\pi$
$938$	−2.18665e10	−0.865108
$939$	0	0
$940$	−1.22869e10	−0.482497
$941$	−3.52314e10	−1.37837	−0.689185	−	0.724585i	$-0.742031\pi$
$941$	−3.52314e10	−1.37837	−0.689185	+	0.724585i	$0.742031\pi$
$942$	0	0
$943$	−5.17974e9	−0.201149
$944$	1.98134e9	0.0766580
$945$	0	0
$946$	1.74787e9	0.0671260
$947$	1.39583e10	0.534081	0.267040	−	0.963685i	$-0.413954\pi$
$947$	1.39583e10	0.534081	0.267040	+	0.963685i	$0.413954\pi$
$948$	0	0
$949$	−1.46577e9	−0.0556715
$950$	2.91706e9	0.110386
$951$	0	0
$952$	−3.12798e10	−1.17499
$953$	2.30442e10	0.862457	0.431228	−	0.902243i	$-0.358080\pi$
$953$	2.30442e10	0.862457	0.431228	+	0.902243i	$0.358080\pi$
$954$	0	0
$955$	−1.97332e10	−0.733138
$956$	−1.50714e10	−0.557892
$957$	0	0
$958$	−1.00023e10	−0.367553
$959$	3.28903e10	1.20421
$960$	0	0
$961$	2.45665e10	0.892917
$962$	−2.45401e9	−0.0888716
$963$	0	0
$964$	−2.41473e10	−0.868160
$965$	−8.91711e9	−0.319432
$966$	0	0
$967$	−1.73599e10	−0.617382	−0.308691	−	0.951162i	$-0.599891\pi$
$967$	−1.73599e10	−0.617382	−0.308691	+	0.951162i	$0.599891\pi$
$968$	−2.63120e10	−0.932372
$969$	0	0
$970$	−2.04231e10	−0.718489
$971$	2.31551e10	0.811670	0.405835	−	0.913946i	$-0.366981\pi$
$971$	2.31551e10	0.811670	0.405835	+	0.913946i	$0.366981\pi$
$972$	0	0
$973$	1.91780e10	0.667435
$974$	4.19594e9	0.145503
$975$	0	0
$976$	3.30818e9	0.113897
$977$	−6.79406e9	−0.233076	−0.116538	−	0.993186i	$-0.537180\pi$
$977$	−6.79406e9	−0.233076	−0.116538	+	0.993186i	$0.537180\pi$
$978$	0	0
$979$	−6.28198e7	−0.00213972
$980$	2.39553e10	0.813036
$981$	0	0
$982$	1.05879e10	0.356795
$983$	2.85219e10	0.957725	0.478863	−	0.877890i	$-0.341049\pi$
$983$	2.85219e10	0.957725	0.478863	+	0.877890i	$0.341049\pi$
$984$	0	0
$985$	−2.44428e10	−0.814937
$986$	−1.14369e10	−0.379963
$987$	0	0
$988$	2.31912e9	0.0765023
$989$	5.27396e9	0.173360
$990$	0	0
$991$	2.55537e10	0.834057	0.417029	−	0.908893i	$-0.363071\pi$
$991$	2.55537e10	0.834057	0.417029	+	0.908893i	$0.363071\pi$
$992$	−4.35909e10	−1.41777
$993$	0	0
$994$	3.30402e10	1.06706
$995$	−2.48551e10	−0.799897
$996$	0	0
$997$	3.78798e10	1.21053	0.605264	−	0.796025i	$-0.293068\pi$
$997$	3.78798e10	1.21053	0.605264	+	0.796025i	$0.293068\pi$
$998$	2.63546e10	0.839266
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.b.1.2		5
3.2	odd	2		23.8.a.a.1.4	✓	5
12.11	even	2		368.8.a.e.1.3		5
15.14	odd	2		575.8.a.a.1.2		5
69.68	even	2		529.8.a.b.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.a.a.1.4	✓	5	3.2	odd	2
207.8.a.b.1.2		5	1.1	even	1	trivial
368.8.a.e.1.3		5	12.11	even	2
529.8.a.b.1.4		5	69.68	even	2
575.8.a.a.1.2		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q-6.41439 q^{2} -86.8556 q^{4} -258.464 q^{5} -1375.00 q^{7} +1378.17 q^{8} +O(q^{10})\)	\(q-6.41439 q^{2} -86.8556 q^{4} -258.464 q^{5} -1375.00 q^{7} +1378.17 q^{8} +1657.89 q^{10} +628.639 q^{11} -664.703 q^{13} +8819.81 q^{14} +2277.42 q^{16} +16506.6 q^{17} +40169.7 q^{19} +22449.1 q^{20} -4032.34 q^{22} -12167.0 q^{23} -11321.2 q^{25} +4263.66 q^{26} +119427. q^{28} +108018. q^{29} +228208. q^{31} -191014. q^{32} -105880. q^{34} +355390. q^{35} -575563. q^{37} -257664. q^{38} -356207. q^{40} +425720. q^{41} -433464. q^{43} -54600.8 q^{44} +78043.9 q^{46} -547322. q^{47} +1.06709e6 q^{49} +72618.6 q^{50} +57733.2 q^{52} +1.27499e6 q^{53} -162481. q^{55} -1.89499e6 q^{56} -692871. q^{58} +869996. q^{59} +1.45260e6 q^{61} -1.46382e6 q^{62} +933727. q^{64} +171802. q^{65} -2.47925e6 q^{67} -1.43369e6 q^{68} -2.27961e6 q^{70} +3.74614e6 q^{71} +2.20514e6 q^{73} +3.69189e6 q^{74} -3.48896e6 q^{76} -864381. q^{77} -2.99240e6 q^{79} -588631. q^{80} -2.73074e6 q^{82} -7.14685e6 q^{83} -4.26637e6 q^{85} +2.78041e6 q^{86} +866370. q^{88} -99929.8 q^{89} +913969. q^{91} +1.05677e6 q^{92} +3.51074e6 q^{94} -1.03824e7 q^{95} -1.23187e7 q^{97} -6.84475e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 256 q^{4} + 56 q^{5} - 1156 q^{7} + 5952 q^{8}+O(q^{10}) \) 5 * q + 16 * q^2 + 256 * q^4 + 56 * q^5 - 1156 * q^7 + 5952 * q^8	\( 5 q + 16 q^{2} + 256 q^{4} + 56 q^{5} - 1156 q^{7} + 5952 q^{8} - 11260 q^{10} + 1318 q^{11} - 19662 q^{13} + 6848 q^{14} + 32448 q^{16} + 5002 q^{17} - 38314 q^{19} - 104440 q^{20} - 74872 q^{22} - 60835 q^{23} + 54959 q^{25} - 345430 q^{26} + 90800 q^{28} + 150634 q^{29} - 179940 q^{31} + 404032 q^{32} + 32116 q^{34} + 374032 q^{35} - 752672 q^{37} - 456808 q^{38} - 1082576 q^{40} + 1192910 q^{41} - 932646 q^{43} - 2467104 q^{44} - 194672 q^{46} + 1008460 q^{47} - 2005219 q^{49} - 1571224 q^{50} - 1740516 q^{52} - 897104 q^{53} + 1203168 q^{55} - 3050144 q^{56} + 5685090 q^{58} - 1020972 q^{59} - 2758364 q^{61} - 2661794 q^{62} + 5173248 q^{64} + 1350472 q^{65} - 1523138 q^{67} - 2501304 q^{68} - 2794240 q^{70} - 3044884 q^{71} - 8872022 q^{73} - 1408492 q^{74} - 17963952 q^{76} + 3501672 q^{77} - 4437540 q^{79} - 12197536 q^{80} - 7738154 q^{82} + 4637362 q^{83} - 8625728 q^{85} + 3025868 q^{86} - 41815040 q^{88} - 6381402 q^{89} + 3240808 q^{91} - 3114752 q^{92} - 13893974 q^{94} - 15762704 q^{95} - 6432034 q^{97} - 22652640 q^{98}+O(q^{100}) \) 5 * q + 16 * q^2 + 256 * q^4 + 56 * q^5 - 1156 * q^7 + 5952 * q^8 - 11260 * q^10 + 1318 * q^11 - 19662 * q^13 + 6848 * q^14 + 32448 * q^16 + 5002 * q^17 - 38314 * q^19 - 104440 * q^20 - 74872 * q^22 - 60835 * q^23 + 54959 * q^25 - 345430 * q^26 + 90800 * q^28 + 150634 * q^29 - 179940 * q^31 + 404032 * q^32 + 32116 * q^34 + 374032 * q^35 - 752672 * q^37 - 456808 * q^38 - 1082576 * q^40 + 1192910 * q^41 - 932646 * q^43 - 2467104 * q^44 - 194672 * q^46 + 1008460 * q^47 - 2005219 * q^49 - 1571224 * q^50 - 1740516 * q^52 - 897104 * q^53 + 1203168 * q^55 - 3050144 * q^56 + 5685090 * q^58 - 1020972 * q^59 - 2758364 * q^61 - 2661794 * q^62 + 5173248 * q^64 + 1350472 * q^65 - 1523138 * q^67 - 2501304 * q^68 - 2794240 * q^70 - 3044884 * q^71 - 8872022 * q^73 - 1408492 * q^74 - 17963952 * q^76 + 3501672 * q^77 - 4437540 * q^79 - 12197536 * q^80 - 7738154 * q^82 + 4637362 * q^83 - 8625728 * q^85 + 3025868 * q^86 - 41815040 * q^88 - 6381402 * q^89 + 3240808 * q^91 - 3114752 * q^92 - 13893974 * q^94 - 15762704 * q^95 - 6432034 * q^97 - 22652640 * q^98

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