LMFDB - Embedded newform 207.8.a.b.1.1

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			1.1
Root			$8.86257$ 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)

$f(q)$	$=$	$q-13.7251 q^{2} +60.3796 q^{4} +364.747 q^{5} +165.110 q^{7} +928.099 q^{8} +O(q^{10})$	\(q-13.7251 q^{2} +60.3796 q^{4} +364.747 q^{5} +165.110 q^{7} +928.099 q^{8} -5006.20 q^{10} -31.8310 q^{11} +5670.88 q^{13} -2266.15 q^{14} -20466.9 q^{16} -10766.2 q^{17} -42639.9 q^{19} +22023.3 q^{20} +436.885 q^{22} -12167.0 q^{23} +54915.2 q^{25} -77833.7 q^{26} +9969.26 q^{28} -102406. q^{29} -202918. q^{31} +162114. q^{32} +147768. q^{34} +60223.2 q^{35} -165092. q^{37} +585239. q^{38} +338521. q^{40} +499932. q^{41} +221332. q^{43} -1921.94 q^{44} +166994. q^{46} +1.16280e6 q^{47} -796282. q^{49} -753719. q^{50} +342406. q^{52} +257314. q^{53} -11610.2 q^{55} +153238. q^{56} +1.40553e6 q^{58} -2.24767e6 q^{59} -2.82905e6 q^{61} +2.78508e6 q^{62} +394718. q^{64} +2.06844e6 q^{65} +3.03807e6 q^{67} -650060. q^{68} -826573. q^{70} -1.49374e6 q^{71} -512282. q^{73} +2.26592e6 q^{74} -2.57458e6 q^{76} -5255.60 q^{77} +5.82621e6 q^{79} -7.46523e6 q^{80} -6.86164e6 q^{82} +1.42467e6 q^{83} -3.92694e6 q^{85} -3.03781e6 q^{86} -29542.3 q^{88} -7.92006e6 q^{89} +936318. q^{91} -734639. q^{92} -1.59596e7 q^{94} -1.55528e7 q^{95} -1.76056e7 q^{97} +1.09291e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.7251	−1.21314	−0.606572	−	0.795029i	$-0.707456\pi$
$2$	−13.7251	−1.21314	−0.606572	+	0.795029i	$0.707456\pi$
$3$	0	0
$3$	0	0
$4$	60.3796	0.471716
$5$	364.747	1.30496	0.652479	−	0.757807i	$-0.273729\pi$
$5$	364.747	1.30496	0.652479	+	0.757807i	$0.273729\pi$
$6$	0	0
$7$	165.110	0.181941	0.0909703	−	0.995854i	$-0.471003\pi$
$7$	165.110	0.181941	0.0909703	+	0.995854i	$0.471003\pi$
$8$	928.099	0.640884
$9$	0	0
$10$	−5006.20	−1.58310
$11$	−31.8310	−0.00721066	−0.00360533	−	0.999994i	$-0.501148\pi$
$11$	−31.8310	−0.00721066	−0.00360533	+	0.999994i	$0.501148\pi$
$12$	0	0
$13$	5670.88	0.715894	0.357947	−	0.933742i	$-0.383477\pi$
$13$	5670.88	0.715894	0.357947	+	0.933742i	$0.383477\pi$
$14$	−2266.15	−0.220720
$15$	0	0
$16$	−20466.9	−1.24920
$17$	−10766.2	−0.531486	−0.265743	−	0.964044i	$-0.585617\pi$
$17$	−10766.2	−0.531486	−0.265743	+	0.964044i	$0.585617\pi$
$18$	0	0
$19$	−42639.9	−1.42619	−0.713097	−	0.701066i	$-0.752708\pi$
$19$	−42639.9	−1.42619	−0.713097	+	0.701066i	$0.752708\pi$
$20$	22023.3	0.615569
$21$	0	0
$22$	436.885	0.00874757
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	54915.2	0.702915
$26$	−77833.7	−0.868482
$27$	0	0
$28$	9969.26	0.0858242
$29$	−102406.	−0.779707	−0.389853	−	0.920877i	$-0.627474\pi$
$29$	−102406.	−0.779707	−0.389853	+	0.920877i	$0.627474\pi$
$30$	0	0
$31$	−202918.	−1.22336	−0.611681	−	0.791105i	$-0.709506\pi$
$31$	−202918.	−1.22336	−0.611681	+	0.791105i	$0.709506\pi$
$32$	162114.	0.874574
$33$	0	0
$34$	147768.	0.644769
$35$	60223.2	0.237425
$36$	0	0
$37$	−165092.	−0.535822	−0.267911	−	0.963444i	$-0.586333\pi$
$37$	−165092.	−0.535822	−0.267911	+	0.963444i	$0.586333\pi$
$38$	585239.	1.73018
$39$	0	0
$40$	338521.	0.836327
$41$	499932.	1.13284	0.566419	−	0.824118i	$-0.308329\pi$
$41$	499932.	1.13284	0.566419	+	0.824118i	$0.308329\pi$
$42$	0	0
$43$	221332.	0.424526	0.212263	−	0.977213i	$-0.431917\pi$
$43$	221332.	0.424526	0.212263	+	0.977213i	$0.431917\pi$
$44$	−1921.94	−0.00340139
$45$	0	0
$46$	166994.	0.252958
$47$	1.16280e6	1.63367	0.816833	−	0.576874i	$-0.195728\pi$
$47$	1.16280e6	1.63367	0.816833	+	0.576874i	$0.195728\pi$
$48$	0	0
$49$	−796282.	−0.966898
$50$	−753719.	−0.852736
$51$	0	0
$52$	342406.	0.337699
$53$	257314.	0.237409	0.118705	−	0.992930i	$-0.462126\pi$
$53$	257314.	0.237409	0.118705	+	0.992930i	$0.462126\pi$
$54$	0	0
$55$	−11610.2	−0.00940961
$56$	153238.	0.116603
$57$	0	0
$58$	1.40553e6	0.945896
$59$	−2.24767e6	−1.42479	−0.712395	−	0.701779i	$-0.752390\pi$
$59$	−2.24767e6	−1.42479	−0.712395	+	0.701779i	$0.752390\pi$
$60$	0	0
$61$	−2.82905e6	−1.59583	−0.797914	−	0.602771i	$-0.794063\pi$
$61$	−2.82905e6	−1.59583	−0.797914	+	0.602771i	$0.794063\pi$
$62$	2.78508e6	1.48411
$63$	0	0
$64$	394718.	0.188216
$65$	2.06844e6	0.934212
$66$	0	0
$67$	3.03807e6	1.23406	0.617030	−	0.786940i	$-0.288336\pi$
$67$	3.03807e6	1.23406	0.617030	+	0.786940i	$0.288336\pi$
$68$	−650060.	−0.250711
$69$	0	0
$70$	−826573.	−0.288030
$71$	−1.49374e6	−0.495303	−0.247652	−	0.968849i	$-0.579659\pi$
$71$	−1.49374e6	−0.495303	−0.247652	+	0.968849i	$0.579659\pi$
$72$	0	0
$73$	−512282.	−0.154127	−0.0770636	−	0.997026i	$-0.524554\pi$
$73$	−512282.	−0.154127	−0.0770636	+	0.997026i	$0.524554\pi$
$74$	2.26592e6	0.650029
$75$	0	0
$76$	−2.57458e6	−0.672758
$77$	−5255.60	−0.00131191
$78$	0	0
$79$	5.82621e6	1.32951	0.664754	−	0.747062i	$-0.268536\pi$
$79$	5.82621e6	1.32951	0.664754	+	0.747062i	$0.268536\pi$
$80$	−7.46523e6	−1.63015
$81$	0	0
$82$	−6.86164e6	−1.37429
$83$	1.42467e6	0.273490	0.136745	−	0.990606i	$-0.456336\pi$
$83$	1.42467e6	0.273490	0.136745	+	0.990606i	$0.456336\pi$
$84$	0	0
$85$	−3.92694e6	−0.693567
$86$	−3.03781e6	−0.515010
$87$	0	0
$88$	−29542.3	−0.00462120
$89$	−7.92006e6	−1.19087	−0.595434	−	0.803404i	$-0.703020\pi$
$89$	−7.92006e6	−1.19087	−0.595434	+	0.803404i	$0.703020\pi$
$90$	0	0
$91$	936318.	0.130250
$92$	−734639.	−0.0983596
$93$	0	0
$94$	−1.59596e7	−1.98187
$95$	−1.55528e7	−1.86112
$96$	0	0
$97$	−1.76056e7	−1.95862	−0.979308	−	0.202374i	$-0.935134\pi$
$97$	−1.76056e7	−1.95862	−0.979308	+	0.202374i	$0.935134\pi$
$98$	1.09291e7	1.17299
$99$	0	0
$100$	3.31576e6	0.331576
$101$	−828399.	−0.0800046	−0.0400023	−	0.999200i	$-0.512737\pi$
$101$	−828399.	−0.0800046	−0.0400023	+	0.999200i	$0.512737\pi$
$102$	0	0
$103$	3.32839e6	0.300126	0.150063	−	0.988676i	$-0.452052\pi$
$103$	3.32839e6	0.300126	0.150063	+	0.988676i	$0.452052\pi$
$104$	5.26314e6	0.458805
$105$	0	0
$106$	−3.53167e6	−0.288012
$107$	−1.21513e7	−0.958913	−0.479456	−	0.877566i	$-0.659166\pi$
$107$	−1.21513e7	−0.958913	−0.479456	+	0.877566i	$0.659166\pi$
$108$	0	0
$109$	6.44543e6	0.476716	0.238358	−	0.971177i	$-0.423391\pi$
$109$	6.44543e6	0.476716	0.238358	+	0.971177i	$0.423391\pi$
$110$	159352.	0.0114152
$111$	0	0
$112$	−3.37928e6	−0.227280
$113$	−1.73550e7	−1.13149	−0.565743	−	0.824582i	$-0.691411\pi$
$113$	−1.73550e7	−1.13149	−0.565743	+	0.824582i	$0.691411\pi$
$114$	0	0
$115$	−4.43787e6	−0.272102
$116$	−6.18322e6	−0.367800
$117$	0	0
$118$	3.08496e7	1.72847
$119$	−1.77761e6	−0.0966988
$120$	0	0
$121$	−1.94862e7	−0.999948
$122$	3.88291e7	1.93597
$123$	0	0
$124$	−1.22521e7	−0.577079
$125$	−8.46570e6	−0.387684
$126$	0	0
$127$	−3.56482e7	−1.54427	−0.772137	−	0.635456i	$-0.780812\pi$
$127$	−3.56482e7	−1.54427	−0.772137	+	0.635456i	$0.780812\pi$
$128$	−2.61682e7	−1.10291
$129$	0	0
$130$	−2.83896e7	−1.13333
$131$	2.55304e7	0.992219	0.496110	−	0.868260i	$-0.334761\pi$
$131$	2.55304e7	0.992219	0.496110	+	0.868260i	$0.334761\pi$
$132$	0	0
$133$	−7.04026e6	−0.259482
$134$	−4.16980e7	−1.49709
$135$	0	0
$136$	−9.99212e6	−0.340621
$137$	3.24969e7	1.07974	0.539871	−	0.841748i	$-0.318473\pi$
$137$	3.24969e7	1.07974	0.539871	+	0.841748i	$0.318473\pi$
$138$	0	0
$139$	−3.81088e7	−1.20358	−0.601788	−	0.798656i	$-0.705545\pi$
$139$	−3.81088e7	−1.20358	−0.601788	+	0.798656i	$0.705545\pi$
$140$	3.63626e6	0.111997
$141$	0	0
$142$	2.05018e7	0.600874
$143$	−180510.	−0.00516207
$144$	0	0
$145$	−3.73522e7	−1.01748
$146$	7.03115e6	0.186978
$147$	0	0
$148$	−9.96821e6	−0.252756
$149$	−2.97747e7	−0.737388	−0.368694	−	0.929551i	$-0.620195\pi$
$149$	−2.97747e7	−0.737388	−0.368694	+	0.929551i	$0.620195\pi$
$150$	0	0
$151$	−9.80561e6	−0.231769	−0.115884	−	0.993263i	$-0.536970\pi$
$151$	−9.80561e6	−0.231769	−0.115884	+	0.993263i	$0.536970\pi$
$152$	−3.95741e7	−0.914025
$153$	0	0
$154$	72133.9	0.00159154
$155$	−7.40137e7	−1.59644
$156$	0	0
$157$	5.70394e7	1.17632	0.588161	−	0.808744i	$-0.299852\pi$
$157$	5.70394e7	1.17632	0.588161	+	0.808744i	$0.299852\pi$
$158$	−7.99656e7	−1.61288
$159$	0	0
$160$	5.91307e7	1.14128
$161$	−2.00889e6	−0.0379372
$162$	0	0
$163$	1.04716e8	1.89389	0.946947	−	0.321389i	$-0.104150\pi$
$163$	1.04716e8	1.89389	0.946947	+	0.321389i	$0.104150\pi$
$164$	3.01857e7	0.534377
$165$	0	0
$166$	−1.95538e7	−0.331782
$167$	2.05048e7	0.340681	0.170340	−	0.985385i	$-0.445513\pi$
$167$	2.05048e7	0.340681	0.170340	+	0.985385i	$0.445513\pi$
$168$	0	0
$169$	−3.05896e7	−0.487495
$170$	5.38979e7	0.841396
$171$	0	0
$172$	1.33639e7	0.200256
$173$	1.33900e8	1.96617	0.983083	−	0.183158i	$-0.0586320\pi$
$173$	1.33900e8	1.96617	0.983083	+	0.183158i	$0.0586320\pi$
$174$	0	0
$175$	9.06703e6	0.127889
$176$	651481.	0.00900756
$177$	0	0
$178$	1.08704e8	1.44469
$179$	8.02166e7	1.04539	0.522695	−	0.852519i	$-0.324927\pi$
$179$	8.02166e7	1.04539	0.522695	+	0.852519i	$0.324927\pi$
$180$	0	0
$181$	−1.25221e8	−1.56965	−0.784823	−	0.619720i	$-0.787246\pi$
$181$	−1.25221e8	−1.56965	−0.784823	+	0.619720i	$0.787246\pi$
$182$	−1.28511e7	−0.158012
$183$	0	0
$184$	−1.12922e7	−0.133634
$185$	−6.02169e7	−0.699225
$186$	0	0
$187$	342699.	0.00383237
$188$	7.02096e7	0.770626
$189$	0	0
$190$	2.13464e8	2.25781
$191$	−3.24582e6	−0.0337060	−0.0168530	−	0.999858i	$-0.505365\pi$
$191$	−3.24582e6	−0.0337060	−0.0168530	+	0.999858i	$0.505365\pi$
$192$	0	0
$193$	−1.07685e8	−1.07822	−0.539109	−	0.842236i	$-0.681239\pi$
$193$	−1.07685e8	−1.07822	−0.539109	+	0.842236i	$0.681239\pi$
$194$	2.41639e8	2.37608
$195$	0	0
$196$	−4.80792e7	−0.456101
$197$	6.15574e7	0.573652	0.286826	−	0.957983i	$-0.407400\pi$
$197$	6.15574e7	0.573652	0.286826	+	0.957983i	$0.407400\pi$
$198$	0	0
$199$	5.44216e7	0.489537	0.244769	−	0.969581i	$-0.421288\pi$
$199$	5.44216e7	0.489537	0.244769	+	0.969581i	$0.421288\pi$
$200$	5.09668e7	0.450487
$201$	0	0
$202$	1.13699e7	0.0970570
$203$	−1.69082e7	−0.141860
$204$	0	0
$205$	1.82349e8	1.47830
$206$	−4.56826e7	−0.364095
$207$	0	0
$208$	−1.16065e8	−0.894295
$209$	1.35727e6	0.0102838
$210$	0	0
$211$	−5.76976e7	−0.422833	−0.211417	−	0.977396i	$-0.567808\pi$
$211$	−5.76976e7	−0.422833	−0.211417	+	0.977396i	$0.567808\pi$
$212$	1.55365e7	0.111990
$213$	0	0
$214$	1.66778e8	1.16330
$215$	8.07300e7	0.553988
$216$	0	0
$217$	−3.35037e7	−0.222579
$218$	−8.84645e7	−0.578324
$219$	0	0
$220$	−701022.	−0.00443866
$221$	−6.10540e7	−0.380488
$222$	0	0
$223$	7.40469e7	0.447136	0.223568	−	0.974688i	$-0.428229\pi$
$223$	7.40469e7	0.447136	0.223568	+	0.974688i	$0.428229\pi$
$224$	2.67667e7	0.159120
$225$	0	0
$226$	2.38199e8	1.37265
$227$	−2.72026e8	−1.54355	−0.771774	−	0.635897i	$-0.780630\pi$
$227$	−2.72026e8	−1.54355	−0.771774	+	0.635897i	$0.780630\pi$
$228$	0	0
$229$	−2.28178e8	−1.25559	−0.627797	−	0.778377i	$-0.716043\pi$
$229$	−2.28178e8	−1.25559	−0.627797	+	0.778377i	$0.716043\pi$
$230$	6.09105e7	0.330099
$231$	0	0
$232$	−9.50427e7	−0.499702
$233$	3.52957e8	1.82800	0.914000	−	0.405714i	$-0.132977\pi$
$233$	3.52957e8	1.82800	0.914000	+	0.405714i	$0.132977\pi$
$234$	0	0
$235$	4.24128e8	2.13187
$236$	−1.35714e8	−0.672096
$237$	0	0
$238$	2.43979e7	0.117310
$239$	−1.58503e8	−0.751007	−0.375504	−	0.926821i	$-0.622530\pi$
$239$	−1.58503e8	−0.751007	−0.375504	+	0.926821i	$0.622530\pi$
$240$	0	0
$241$	2.05090e8	0.943811	0.471905	−	0.881649i	$-0.343566\pi$
$241$	2.05090e8	0.943811	0.471905	+	0.881649i	$0.343566\pi$
$242$	2.67450e8	1.21308
$243$	0	0
$244$	−1.70817e8	−0.752778
$245$	−2.90441e8	−1.26176
$246$	0	0
$247$	−2.41806e8	−1.02100
$248$	−1.88328e8	−0.784033
$249$	0	0
$250$	1.16193e8	0.470316
$251$	−2.93965e8	−1.17338	−0.586688	−	0.809813i	$-0.699569\pi$
$251$	−2.93965e8	−1.17338	−0.586688	+	0.809813i	$0.699569\pi$
$252$	0	0
$253$	387287.	0.00150353
$254$	4.89276e8	1.87342
$255$	0	0
$256$	3.08639e8	1.14977
$257$	−3.01645e8	−1.10848	−0.554242	−	0.832355i	$-0.686992\pi$
$257$	−3.01645e8	−1.10848	−0.554242	+	0.832355i	$0.686992\pi$
$258$	0	0
$259$	−2.72583e7	−0.0974878
$260$	1.24891e8	0.440683
$261$	0	0
$262$	−3.50408e8	−1.20370
$263$	2.44871e8	0.830027	0.415013	−	0.909815i	$-0.363777\pi$
$263$	2.44871e8	0.830027	0.415013	+	0.909815i	$0.363777\pi$
$264$	0	0
$265$	9.38545e7	0.309809
$266$	9.66286e7	0.314789
$267$	0	0
$268$	1.83438e8	0.582125
$269$	−5.08963e8	−1.59424	−0.797119	−	0.603823i	$-0.793644\pi$
$269$	−5.08963e8	−1.59424	−0.797119	+	0.603823i	$0.793644\pi$
$270$	0	0
$271$	2.81631e8	0.859582	0.429791	−	0.902928i	$-0.358587\pi$
$271$	2.81631e8	0.859582	0.429791	+	0.902928i	$0.358587\pi$
$272$	2.20351e8	0.663932
$273$	0	0
$274$	−4.46025e8	−1.30988
$275$	−1.74800e6	−0.00506848
$276$	0	0
$277$	−9.11506e7	−0.257680	−0.128840	−	0.991665i	$-0.541125\pi$
$277$	−9.11506e7	−0.257680	−0.128840	+	0.991665i	$0.541125\pi$
$278$	5.23049e8	1.46011
$279$	0	0
$280$	5.58931e7	0.152162
$281$	−2.84061e8	−0.763730	−0.381865	−	0.924218i	$-0.624718\pi$
$281$	−2.84061e8	−0.763730	−0.381865	+	0.924218i	$0.624718\pi$
$282$	0	0
$283$	−5.73111e8	−1.50309	−0.751547	−	0.659680i	$-0.770692\pi$
$283$	−5.73111e8	−1.50309	−0.751547	+	0.659680i	$0.770692\pi$
$284$	−9.01915e7	−0.233642
$285$	0	0
$286$	2.47752e6	0.00626233
$287$	8.25436e7	0.206109
$288$	0	0
$289$	−2.94427e8	−0.717523
$290$	5.12664e8	1.23435
$291$	0	0
$292$	−3.09314e7	−0.0727043
$293$	−2.76652e8	−0.642536	−0.321268	−	0.946988i	$-0.604109\pi$
$293$	−2.76652e8	−0.642536	−0.321268	+	0.946988i	$0.604109\pi$
$294$	0	0
$295$	−8.19831e8	−1.85929
$296$	−1.53222e8	−0.343400
$297$	0	0
$298$	4.08663e8	0.894557
$299$	−6.89976e7	−0.149274
$300$	0	0
$301$	3.65440e7	0.0772384
$302$	1.34583e8	0.281169
$303$	0	0
$304$	8.72706e8	1.78160
$305$	−1.03189e9	−2.08249
$306$	0	0
$307$	−1.05781e7	−0.0208653	−0.0104327	−	0.999946i	$-0.503321\pi$
$307$	−1.05781e7	−0.0208653	−0.0104327	+	0.999946i	$0.503321\pi$
$308$	−317331.	−0.000618850 0
$309$	0	0
$310$	1.01585e9	1.93670
$311$	5.64572e7	0.106429	0.0532143	−	0.998583i	$-0.483053\pi$
$311$	5.64572e7	0.106429	0.0532143	+	0.998583i	$0.483053\pi$
$312$	0	0
$313$	−7.00757e8	−1.29170	−0.645851	−	0.763463i	$-0.723497\pi$
$313$	−7.00757e8	−1.29170	−0.645851	+	0.763463i	$0.723497\pi$
$314$	−7.82874e8	−1.42705
$315$	0	0
$316$	3.51784e8	0.627151
$317$	4.05544e8	0.715041	0.357520	−	0.933905i	$-0.383622\pi$
$317$	4.05544e8	0.715041	0.357520	+	0.933905i	$0.383622\pi$
$318$	0	0
$319$	3.25967e6	0.00562220
$320$	1.43972e8	0.245614
$321$	0	0
$322$	2.75723e7	0.0460233
$323$	4.59070e8	0.758002
$324$	0	0
$325$	3.11418e8	0.503213
$326$	−1.43724e9	−2.29757
$327$	0	0
$328$	4.63987e8	0.726017
$329$	1.91990e8	0.297230
$330$	0	0
$331$	4.73572e8	0.717775	0.358887	−	0.933381i	$-0.383156\pi$
$331$	4.73572e8	0.717775	0.358887	+	0.933381i	$0.383156\pi$
$332$	8.60210e7	0.129009
$333$	0	0
$334$	−2.81431e8	−0.413294
$335$	1.10813e9	1.61039
$336$	0	0
$337$	−3.83572e8	−0.545937	−0.272969	−	0.962023i	$-0.588005\pi$
$337$	−3.83572e8	−0.545937	−0.272969	+	0.962023i	$0.588005\pi$
$338$	4.19847e8	0.591401
$339$	0	0
$340$	−2.37107e8	−0.327167
$341$	6.45908e6	0.00882125
$342$	0	0
$343$	−2.67449e8	−0.357858
$344$	2.05418e8	0.272072
$345$	0	0
$346$	−1.83780e9	−2.38524
$347$	−2.62821e8	−0.337681	−0.168841	−	0.985643i	$-0.554002\pi$
$347$	−2.62821e8	−0.337681	−0.168841	+	0.985643i	$0.554002\pi$
$348$	0	0
$349$	−5.33512e8	−0.671823	−0.335912	−	0.941894i	$-0.609044\pi$
$349$	−5.33512e8	−0.671823	−0.335912	+	0.941894i	$0.609044\pi$
$350$	−1.24446e8	−0.155147
$351$	0	0
$352$	−5.16026e6	−0.00630626
$353$	−3.57541e8	−0.432628	−0.216314	−	0.976324i	$-0.569404\pi$
$353$	−3.57541e8	−0.432628	−0.216314	+	0.976324i	$0.569404\pi$
$354$	0	0
$355$	−5.44837e8	−0.646350
$356$	−4.78211e8	−0.561751
$357$	0	0
$358$	−1.10098e9	−1.26821
$359$	−7.42830e8	−0.847342	−0.423671	−	0.905816i	$-0.639259\pi$
$359$	−7.42830e8	−0.847342	−0.423671	+	0.905816i	$0.639259\pi$
$360$	0	0
$361$	9.24289e8	1.03403
$362$	1.71867e9	1.90420
$363$	0	0
$364$	5.65345e7	0.0614411
$365$	−1.86853e8	−0.201129
$366$	0	0
$367$	−9.86306e8	−1.04155	−0.520775	−	0.853694i	$-0.674357\pi$
$367$	−9.86306e8	−1.04155	−0.520775	+	0.853694i	$0.674357\pi$
$368$	2.49021e8	0.260476
$369$	0	0
$370$	8.26485e8	0.848260
$371$	4.24850e7	0.0431944
$372$	0	0
$373$	−1.02745e8	−0.102513	−0.0512566	−	0.998686i	$-0.516323\pi$
$373$	−1.02745e8	−0.102513	−0.0512566	+	0.998686i	$0.516323\pi$
$374$	−4.70359e6	−0.00464921
$375$	0	0
$376$	1.07920e9	1.04699
$377$	−5.80731e8	−0.558188
$378$	0	0
$379$	1.60090e9	1.51052	0.755262	−	0.655423i	$-0.227510\pi$
$379$	1.60090e9	1.51052	0.755262	+	0.655423i	$0.227510\pi$
$380$	−9.39070e8	−0.877921
$381$	0	0
$382$	4.45494e7	0.0408902
$383$	6.54385e8	0.595165	0.297583	−	0.954696i	$-0.403820\pi$
$383$	6.54385e8	0.595165	0.297583	+	0.954696i	$0.403820\pi$
$384$	0	0
$385$	−1.91696e6	−0.00171199
$386$	1.47800e9	1.30803
$387$	0	0
$388$	−1.06302e9	−0.923911
$389$	−5.47686e8	−0.471746	−0.235873	−	0.971784i	$-0.575795\pi$
$389$	−5.47686e8	−0.471746	−0.235873	+	0.971784i	$0.575795\pi$
$390$	0	0
$391$	1.30993e8	0.110823
$392$	−7.39029e8	−0.619669
$393$	0	0
$394$	−8.44884e8	−0.695921
$395$	2.12509e9	1.73495
$396$	0	0
$397$	−6.70333e8	−0.537680	−0.268840	−	0.963185i	$-0.586640\pi$
$397$	−6.70333e8	−0.537680	−0.268840	+	0.963185i	$0.586640\pi$
$398$	−7.46945e8	−0.593879
$399$	0	0
$400$	−1.12394e9	−0.878081
$401$	1.96156e9	1.51914	0.759569	−	0.650427i	$-0.225410\pi$
$401$	1.96156e9	1.51914	0.759569	+	0.650427i	$0.225410\pi$
$402$	0	0
$403$	−1.15072e9	−0.875798
$404$	−5.00185e7	−0.0377395
$405$	0	0
$406$	2.32067e8	0.172097
$407$	5.25504e6	0.00386363
$408$	0	0
$409$	1.11366e9	0.804858	0.402429	−	0.915451i	$-0.368166\pi$
$409$	1.11366e9	0.804858	0.402429	+	0.915451i	$0.368166\pi$
$410$	−2.50276e9	−1.79340
$411$	0	0
$412$	2.00967e8	0.141574
$413$	−3.71112e8	−0.259227
$414$	0	0
$415$	5.19644e8	0.356892
$416$	9.19332e8	0.626103
$417$	0	0
$418$	−1.86287e7	−0.0124757
$419$	1.56650e9	1.04035	0.520176	−	0.854059i	$-0.325866\pi$
$419$	1.56650e9	1.04035	0.520176	+	0.854059i	$0.325866\pi$
$420$	0	0
$421$	6.66031e8	0.435018	0.217509	−	0.976058i	$-0.430207\pi$
$421$	6.66031e8	0.435018	0.217509	+	0.976058i	$0.430207\pi$
$422$	7.91908e8	0.512957
$423$	0	0
$424$	2.38813e8	0.152152
$425$	−5.91229e8	−0.373589
$426$	0	0
$427$	−4.67104e8	−0.290346
$428$	−7.33690e8	−0.452334
$429$	0	0
$430$	−1.10803e9	−0.672067
$431$	−2.09866e9	−1.26262	−0.631310	−	0.775531i	$-0.717482\pi$
$431$	−2.09866e9	−1.26262	−0.631310	+	0.775531i	$0.717482\pi$
$432$	0	0
$433$	6.94969e6	0.00411394	0.00205697	−	0.999998i	$-0.499345\pi$
$433$	6.94969e6	0.00411394	0.00205697	+	0.999998i	$0.499345\pi$
$434$	4.59844e8	0.270020
$435$	0	0
$436$	3.89173e8	0.224874
$437$	5.18800e8	0.297382
$438$	0	0
$439$	−2.01271e9	−1.13541	−0.567707	−	0.823231i	$-0.692169\pi$
$439$	−2.01271e9	−1.13541	−0.567707	+	0.823231i	$0.692169\pi$
$440$	−1.07755e7	−0.00603047
$441$	0	0
$442$	8.37975e8	0.461586
$443$	4.14786e7	0.0226679	0.0113340	−	0.999936i	$-0.496392\pi$
$443$	4.14786e7	0.0226679	0.0113340	+	0.999936i	$0.496392\pi$
$444$	0	0
$445$	−2.88882e9	−1.55403
$446$	−1.01631e9	−0.542441
$447$	0	0
$448$	6.51718e7	0.0342442
$449$	8.30315e8	0.432893	0.216447	−	0.976294i	$-0.430553\pi$
$449$	8.30315e8	0.432893	0.216447	+	0.976294i	$0.430553\pi$
$450$	0	0
$451$	−1.59133e7	−0.00816851
$452$	−1.04789e9	−0.533740
$453$	0	0
$454$	3.73360e9	1.87255
$455$	3.41519e8	0.169971
$456$	0	0
$457$	6.85053e7	0.0335751	0.0167876	−	0.999859i	$-0.494656\pi$
$457$	6.85053e7	0.0335751	0.0167876	+	0.999859i	$0.494656\pi$
$458$	3.13177e9	1.52321
$459$	0	0
$460$	−2.67957e8	−0.128355
$461$	−3.77005e9	−1.79223	−0.896114	−	0.443824i	$-0.853622\pi$
$461$	−3.77005e9	−1.79223	−0.896114	+	0.443824i	$0.853622\pi$
$462$	0	0
$463$	5.54935e8	0.259841	0.129921	−	0.991524i	$-0.458528\pi$
$463$	5.54935e8	0.259841	0.129921	+	0.991524i	$0.458528\pi$
$464$	2.09593e9	0.974010
$465$	0	0
$466$	−4.84439e9	−2.21763
$467$	2.27560e9	1.03392	0.516959	−	0.856010i	$-0.327064\pi$
$467$	2.27560e9	1.03392	0.516959	+	0.856010i	$0.327064\pi$
$468$	0	0
$469$	5.01615e8	0.224525
$470$	−5.82122e9	−2.58626
$471$	0	0
$472$	−2.08606e9	−0.913125
$473$	−7.04520e6	−0.00306111
$474$	0	0
$475$	−2.34158e9	−1.00249
$476$	−1.07331e8	−0.0456144
$477$	0	0
$478$	2.17547e9	0.911079
$479$	−2.27144e9	−0.944337	−0.472168	−	0.881508i	$-0.656529\pi$
$479$	−2.27144e9	−0.944337	−0.472168	+	0.881508i	$0.656529\pi$
$480$	0	0
$481$	−9.36219e8	−0.383592
$482$	−2.81489e9	−1.14498
$483$	0	0
$484$	−1.17657e9	−0.471691
$485$	−6.42158e9	−2.55591
$486$	0	0
$487$	1.35084e9	0.529972	0.264986	−	0.964252i	$-0.414633\pi$
$487$	1.35084e9	0.529972	0.264986	+	0.964252i	$0.414633\pi$
$488$	−2.62564e9	−1.02274
$489$	0	0
$490$	3.98635e9	1.53070
$491$	4.17684e9	1.59244	0.796220	−	0.605007i	$-0.206830\pi$
$491$	4.17684e9	1.59244	0.796220	+	0.605007i	$0.206830\pi$
$492$	0	0
$493$	1.10252e9	0.414403
$494$	3.31882e9	1.23862
$495$	0	0
$496$	4.15310e9	1.52822
$497$	−2.46631e8	−0.0901157
$498$	0	0
$499$	−4.43292e8	−0.159712	−0.0798562	−	0.996806i	$-0.525446\pi$
$499$	−4.43292e8	−0.159712	−0.0798562	+	0.996806i	$0.525446\pi$
$500$	−5.11156e8	−0.182877
$501$	0	0
$502$	4.03471e9	1.42347
$503$	−1.62588e9	−0.569640	−0.284820	−	0.958581i	$-0.591934\pi$
$503$	−1.62588e9	−0.569640	−0.284820	+	0.958581i	$0.591934\pi$
$504$	0	0
$505$	−3.02156e8	−0.104403
$506$	−5.31557e6	−0.00182399
$507$	0	0
$508$	−2.15242e9	−0.728459
$509$	−3.90930e9	−1.31398	−0.656988	−	0.753901i	$-0.728170\pi$
$509$	−3.90930e9	−1.31398	−0.656988	+	0.753901i	$0.728170\pi$
$510$	0	0
$511$	−8.45827e7	−0.0280420
$512$	−8.86579e8	−0.291926
$513$	0	0
$514$	4.14012e9	1.34475
$515$	1.21402e9	0.391651
$516$	0	0
$517$	−3.70131e7	−0.0117798
$518$	3.74125e8	0.118267
$519$	0	0
$520$	1.91971e9	0.598722
$521$	6.02035e9	1.86505	0.932523	−	0.361111i	$-0.117603\pi$
$521$	6.02035e9	1.86505	0.932523	+	0.361111i	$0.117603\pi$
$522$	0	0
$523$	4.68995e9	1.43355	0.716774	−	0.697306i	$-0.245618\pi$
$523$	4.68995e9	1.43355	0.716774	+	0.697306i	$0.245618\pi$
$524$	1.54152e9	0.468046
$525$	0	0
$526$	−3.36089e9	−1.00694
$527$	2.18466e9	0.650200
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−1.28817e9	−0.375843
$531$	0	0
$532$	−4.25088e8	−0.122402
$533$	2.83506e9	0.810992
$534$	0	0
$535$	−4.43214e9	−1.25134
$536$	2.81963e9	0.790889
$537$	0	0
$538$	6.98559e9	1.93404
$539$	2.53464e7	0.00697197
$540$	0	0
$541$	2.20440e9	0.598550	0.299275	−	0.954167i	$-0.403255\pi$
$541$	2.20440e9	0.598550	0.299275	+	0.954167i	$0.403255\pi$
$542$	−3.86542e9	−1.04280
$543$	0	0
$544$	−1.74536e9	−0.464824
$545$	2.35095e9	0.622094
$546$	0	0
$547$	1.29680e9	0.338779	0.169390	−	0.985549i	$-0.445820\pi$
$547$	1.29680e9	0.338779	0.169390	+	0.985549i	$0.445820\pi$
$548$	1.96215e9	0.509331
$549$	0	0
$550$	2.39916e7	0.00614879
$551$	4.36657e9	1.11201
$552$	0	0
$553$	9.61963e8	0.241891
$554$	1.25105e9	0.312602
$555$	0	0
$556$	−2.30100e9	−0.567746
$557$	−1.66581e9	−0.408444	−0.204222	−	0.978925i	$-0.565466\pi$
$557$	−1.66581e9	−0.408444	−0.204222	+	0.978925i	$0.565466\pi$
$558$	0	0
$559$	1.25515e9	0.303916
$560$	−1.23258e9	−0.296591
$561$	0	0
$562$	3.89878e9	0.926514
$563$	2.66413e9	0.629181	0.314590	−	0.949228i	$-0.398133\pi$
$563$	2.66413e9	0.629181	0.314590	+	0.949228i	$0.398133\pi$
$564$	0	0
$565$	−6.33017e9	−1.47654
$566$	7.86603e9	1.82347
$567$	0	0
$568$	−1.38634e9	−0.317432
$569$	4.86641e9	1.10743	0.553714	−	0.832707i	$-0.313210\pi$
$569$	4.86641e9	1.10743	0.553714	+	0.832707i	$0.313210\pi$
$570$	0	0
$571$	−4.12268e9	−0.926731	−0.463365	−	0.886167i	$-0.653358\pi$
$571$	−4.12268e9	−0.926731	−0.463365	+	0.886167i	$0.653358\pi$
$572$	−1.08991e7	−0.00243503
$573$	0	0
$574$	−1.13292e9	−0.250040
$575$	−6.68153e8	−0.146568
$576$	0	0
$577$	−4.73370e9	−1.02585	−0.512927	−	0.858432i	$-0.671439\pi$
$577$	−4.73370e9	−1.02585	−0.512927	+	0.858432i	$0.671439\pi$
$578$	4.04106e9	0.870457
$579$	0	0
$580$	−2.25531e9	−0.479964
$581$	2.35227e8	0.0497588
$582$	0	0
$583$	−8.19055e6	−0.00171188
$584$	−4.75449e8	−0.0987776
$585$	0	0
$586$	3.79709e9	0.779488
$587$	−5.07303e8	−0.103522	−0.0517612	−	0.998659i	$-0.516483\pi$
$587$	−5.07303e8	−0.103522	−0.0517612	+	0.998659i	$0.516483\pi$
$588$	0	0
$589$	8.65240e9	1.74475
$590$	1.12523e10	2.25559
$591$	0	0
$592$	3.37893e9	0.669349
$593$	−2.80919e9	−0.553210	−0.276605	−	0.960984i	$-0.589209\pi$
$593$	−2.80919e9	−0.553210	−0.276605	+	0.960984i	$0.589209\pi$
$594$	0	0
$595$	−6.48376e8	−0.126188
$596$	−1.79779e9	−0.347838
$597$	0	0
$598$	9.47003e8	0.181091
$599$	−7.18428e9	−1.36581	−0.682904	−	0.730508i	$-0.739283\pi$
$599$	−7.18428e9	−1.36581	−0.682904	+	0.730508i	$0.739283\pi$
$600$	0	0
$601$	5.67050e9	1.06552	0.532759	−	0.846267i	$-0.321155\pi$
$601$	5.67050e9	1.06552	0.532759	+	0.846267i	$0.321155\pi$
$602$	−5.01572e8	−0.0937012
$603$	0	0
$604$	−5.92059e8	−0.109329
$605$	−7.10751e9	−1.30489
$606$	0	0
$607$	9.85285e8	0.178814	0.0894070	−	0.995995i	$-0.471503\pi$
$607$	9.85285e8	0.178814	0.0894070	+	0.995995i	$0.471503\pi$
$608$	−6.91254e9	−1.24731
$609$	0	0
$610$	1.41628e10	2.52636
$611$	6.59411e9	1.16953
$612$	0	0
$613$	8.22759e9	1.44265	0.721325	−	0.692597i	$-0.243533\pi$
$613$	8.22759e9	1.44265	0.721325	+	0.692597i	$0.243533\pi$
$614$	1.45187e8	0.0253126
$615$	0	0
$616$	−4.87772e6	−0.000840783 0
$617$	6.50643e9	1.11518	0.557590	−	0.830117i	$-0.311726\pi$
$617$	6.50643e9	1.11518	0.557590	+	0.830117i	$0.311726\pi$
$618$	0	0
$619$	−2.33559e9	−0.395803	−0.197901	−	0.980222i	$-0.563413\pi$
$619$	−2.33559e9	−0.395803	−0.197901	+	0.980222i	$0.563413\pi$
$620$	−4.46892e9	−0.753064
$621$	0	0
$622$	−7.74884e8	−0.129113
$623$	−1.30768e9	−0.216667
$624$	0	0
$625$	−7.37809e9	−1.20883
$626$	9.61800e9	1.56702
$627$	0	0
$628$	3.44402e9	0.554889
$629$	1.77742e9	0.284782
$630$	0	0
$631$	5.24733e9	0.831449	0.415725	−	0.909490i	$-0.363528\pi$
$631$	5.24733e9	0.831449	0.415725	+	0.909490i	$0.363528\pi$
$632$	5.40730e9	0.852061
$633$	0	0
$634$	−5.56615e9	−0.867447
$635$	−1.30026e10	−2.01521
$636$	0	0
$637$	−4.51562e9	−0.692197
$638$	−4.47395e7	−0.00682054
$639$	0	0
$640$	−9.54477e9	−1.43925
$641$	−9.28633e8	−0.139265	−0.0696324	−	0.997573i	$-0.522183\pi$
$641$	−9.28633e8	−0.139265	−0.0696324	+	0.997573i	$0.522183\pi$
$642$	0	0
$643$	−1.05720e10	−1.56827	−0.784133	−	0.620593i	$-0.786892\pi$
$643$	−1.05720e10	−1.56827	−0.784133	+	0.620593i	$0.786892\pi$
$644$	−1.21296e8	−0.0178956
$645$	0	0
$646$	−6.30081e9	−0.919565
$647$	7.21397e9	1.04715	0.523576	−	0.851979i	$-0.324598\pi$
$647$	7.21397e9	1.04715	0.523576	+	0.851979i	$0.324598\pi$
$648$	0	0
$649$	7.15456e7	0.0102737
$650$	−4.27425e9	−0.610469
$651$	0	0
$652$	6.32271e9	0.893380
$653$	2.53937e9	0.356886	0.178443	−	0.983950i	$-0.442894\pi$
$653$	2.53937e9	0.356886	0.178443	+	0.983950i	$0.442894\pi$
$654$	0	0
$655$	9.31212e9	1.29480
$656$	−1.02321e10	−1.41514
$657$	0	0
$658$	−2.63509e9	−0.360583
$659$	−8.08492e9	−1.10047	−0.550233	−	0.835011i	$-0.685461\pi$
$659$	−8.08492e9	−1.10047	−0.550233	+	0.835011i	$0.685461\pi$
$660$	0	0
$661$	−1.08284e10	−1.45834	−0.729169	−	0.684333i	$-0.760093\pi$
$661$	−1.08284e10	−1.45834	−0.729169	+	0.684333i	$0.760093\pi$
$662$	−6.49985e9	−0.870764
$663$	0	0
$664$	1.32223e9	0.175275
$665$	−2.56791e9	−0.338614
$666$	0	0
$667$	1.24597e9	0.162580
$668$	1.23807e9	0.160705
$669$	0	0
$670$	−1.52092e10	−1.95364
$671$	9.00514e7	0.0115070
$672$	0	0
$673$	−2.97284e9	−0.375941	−0.187970	−	0.982175i	$-0.560191\pi$
$673$	−2.97284e9	−0.375941	−0.187970	+	0.982175i	$0.560191\pi$
$674$	5.26459e9	0.662300
$675$	0	0
$676$	−1.84699e9	−0.229959
$677$	−4.49801e9	−0.557135	−0.278567	−	0.960417i	$-0.589860\pi$
$677$	−4.49801e9	−0.557135	−0.278567	+	0.960417i	$0.589860\pi$
$678$	0	0
$679$	−2.90685e9	−0.356352
$680$	−3.64459e9	−0.444496
$681$	0	0
$682$	−8.86518e7	−0.0107014
$683$	−2.98727e9	−0.358759	−0.179379	−	0.983780i	$-0.557409\pi$
$683$	−2.98727e9	−0.358759	−0.179379	+	0.983780i	$0.557409\pi$
$684$	0	0
$685$	1.18531e10	1.40902
$686$	3.67077e9	0.434133
$687$	0	0
$688$	−4.52997e9	−0.530317
$689$	1.45920e9	0.169960
$690$	0	0
$691$	1.94984e9	0.224815	0.112408	−	0.993662i	$-0.464144\pi$
$691$	1.94984e9	0.224815	0.112408	+	0.993662i	$0.464144\pi$
$692$	8.08486e9	0.927472
$693$	0	0
$694$	3.60726e9	0.409656
$695$	−1.39001e10	−1.57062
$696$	0	0
$697$	−5.38238e9	−0.602087
$698$	7.32253e9	0.815018
$699$	0	0
$700$	5.47464e8	0.0603271
$701$	5.22279e9	0.572650	0.286325	−	0.958133i	$-0.407566\pi$
$701$	5.22279e9	0.572650	0.286325	+	0.958133i	$0.407566\pi$
$702$	0	0
$703$	7.03952e9	0.764186
$704$	−1.25643e7	−0.00135716
$705$	0	0
$706$	4.90731e9	0.524840
$707$	−1.36777e8	−0.0145561
$708$	0	0
$709$	−5.14916e9	−0.542594	−0.271297	−	0.962496i	$-0.587452\pi$
$709$	−5.14916e9	−0.542594	−0.271297	+	0.962496i	$0.587452\pi$
$710$	7.47797e9	0.784115
$711$	0	0
$712$	−7.35060e9	−0.763208
$713$	2.46890e9	0.255089
$714$	0	0
$715$	−6.58403e7	−0.00673629
$716$	4.84345e9	0.493128
$717$	0	0
$718$	1.01955e10	1.02795
$719$	−1.08945e9	−0.109309	−0.0546543	−	0.998505i	$-0.517406\pi$
$719$	−1.08945e9	−0.109309	−0.0546543	+	0.998505i	$0.517406\pi$
$720$	0	0
$721$	5.49549e8	0.0546050
$722$	−1.26860e10	−1.25442
$723$	0	0
$724$	−7.56079e9	−0.740427
$725$	−5.62363e9	−0.548067
$726$	0	0
$727$	−7.46975e9	−0.721000	−0.360500	−	0.932759i	$-0.617394\pi$
$727$	−7.46975e9	−0.721000	−0.360500	+	0.932759i	$0.617394\pi$
$728$	8.68996e8	0.0834753
$729$	0	0
$730$	2.56459e9	0.243999
$731$	−2.38290e9	−0.225629
$732$	0	0
$733$	−5.34556e9	−0.501337	−0.250668	−	0.968073i	$-0.580650\pi$
$733$	−5.34556e9	−0.501337	−0.250668	+	0.968073i	$0.580650\pi$
$734$	1.35372e10	1.26355
$735$	0	0
$736$	−1.97245e9	−0.182361
$737$	−9.67047e7	−0.00889839
$738$	0	0
$739$	−2.81976e9	−0.257014	−0.128507	−	0.991709i	$-0.541019\pi$
$739$	−2.81976e9	−0.257014	−0.128507	+	0.991709i	$0.541019\pi$
$740$	−3.63587e9	−0.329836
$741$	0	0
$742$	−5.83113e8	−0.0524010
$743$	−1.06791e10	−0.955155	−0.477578	−	0.878590i	$-0.658485\pi$
$743$	−1.06791e10	−0.955155	−0.477578	+	0.878590i	$0.658485\pi$
$744$	0	0
$745$	−1.08602e10	−0.962260
$746$	1.41019e9	0.124363
$747$	0	0
$748$	2.06920e7	0.00180779
$749$	−2.00629e9	−0.174465
$750$	0	0
$751$	1.65038e10	1.42181	0.710907	−	0.703286i	$-0.248284\pi$
$751$	1.65038e10	1.42181	0.710907	+	0.703286i	$0.248284\pi$
$752$	−2.37989e10	−2.04078
$753$	0	0
$754$	7.97062e9	0.677162
$755$	−3.57656e9	−0.302449
$756$	0	0
$757$	−6.98732e8	−0.0585430	−0.0292715	−	0.999571i	$-0.509319\pi$
$757$	−6.98732e8	−0.0585430	−0.0292715	+	0.999571i	$0.509319\pi$
$758$	−2.19726e10	−1.83248
$759$	0	0
$760$	−1.44345e10	−1.19276
$761$	−6.64496e9	−0.546570	−0.273285	−	0.961933i	$-0.588110\pi$
$761$	−6.64496e9	−0.546570	−0.273285	+	0.961933i	$0.588110\pi$
$762$	0	0
$763$	1.06420e9	0.0867339
$764$	−1.95981e8	−0.0158997
$765$	0	0
$766$	−8.98153e9	−0.722021
$767$	−1.27463e10	−1.02000
$768$	0	0
$769$	2.08487e10	1.65324	0.826620	−	0.562761i	$-0.190261\pi$
$769$	2.08487e10	1.65324	0.826620	+	0.562761i	$0.190261\pi$
$770$	2.63106e7	0.00207689
$771$	0	0
$772$	−6.50201e9	−0.508613
$773$	1.95781e10	1.52455	0.762274	−	0.647254i	$-0.224083\pi$
$773$	1.95781e10	1.52455	0.762274	+	0.647254i	$0.224083\pi$
$774$	0	0
$775$	−1.11433e10	−0.859919
$776$	−1.63397e10	−1.25525
$777$	0	0
$778$	7.51708e9	0.572295
$779$	−2.13171e10	−1.61565
$780$	0	0
$781$	4.75472e7	0.00357146
$782$	−1.79789e9	−0.134444
$783$	0	0
$784$	1.62974e10	1.20785
$785$	2.08049e10	1.53505
$786$	0	0
$787$	−4.00363e9	−0.292781	−0.146390	−	0.989227i	$-0.546766\pi$
$787$	−4.00363e9	−0.292781	−0.146390	+	0.989227i	$0.546766\pi$
$788$	3.71681e9	0.270601
$789$	0	0
$790$	−2.91672e10	−2.10475
$791$	−2.86547e9	−0.205863
$792$	0	0
$793$	−1.60432e10	−1.14244
$794$	9.20041e9	0.652282
$795$	0	0
$796$	3.28596e9	0.230923
$797$	−2.37163e10	−1.65937	−0.829685	−	0.558232i	$-0.811480\pi$
$797$	−2.37163e10	−1.65937	−0.829685	+	0.558232i	$0.811480\pi$
$798$	0	0
$799$	−1.25190e10	−0.868271
$800$	8.90255e9	0.614751
$801$	0	0
$802$	−2.69227e10	−1.84293
$803$	1.63064e7	0.00111136
$804$	0	0
$805$	−7.32736e8	−0.0495065
$806$	1.57939e10	1.06247
$807$	0	0
$808$	−7.68837e8	−0.0512737
$809$	1.29604e10	0.860592	0.430296	−	0.902688i	$-0.358409\pi$
$809$	1.29604e10	0.860592	0.430296	+	0.902688i	$0.358409\pi$
$810$	0	0
$811$	−1.64248e10	−1.08125	−0.540625	−	0.841264i	$-0.681812\pi$
$811$	−1.64248e10	−1.08125	−0.540625	+	0.841264i	$0.681812\pi$
$812$	−1.02091e9	−0.0669177
$813$	0	0
$814$	−7.21263e7	−0.00468714
$815$	3.81948e10	2.47145
$816$	0	0
$817$	−9.43756e9	−0.605456
$818$	−1.52851e10	−0.976408
$819$	0	0
$820$	1.10101e10	0.697340
$821$	2.05578e10	1.29651	0.648256	−	0.761423i	$-0.275499\pi$
$821$	2.05578e10	1.29651	0.648256	+	0.761423i	$0.275499\pi$
$822$	0	0
$823$	−1.10026e10	−0.688011	−0.344006	−	0.938968i	$-0.611784\pi$
$823$	−1.10026e10	−0.688011	−0.344006	+	0.938968i	$0.611784\pi$
$824$	3.08907e9	0.192346
$825$	0	0
$826$	5.09357e9	0.314480
$827$	−9.32463e9	−0.573274	−0.286637	−	0.958039i	$-0.592537\pi$
$827$	−9.32463e9	−0.573274	−0.286637	+	0.958039i	$0.592537\pi$
$828$	0	0
$829$	2.18659e10	1.33299	0.666493	−	0.745511i	$-0.267795\pi$
$829$	2.18659e10	1.33299	0.666493	+	0.745511i	$0.267795\pi$
$830$	−7.13218e9	−0.432961
$831$	0	0
$832$	2.23840e9	0.134743
$833$	8.57294e9	0.513893
$834$	0	0
$835$	7.47905e9	0.444574
$836$	8.19514e7	0.00485103
$837$	0	0
$838$	−2.15004e10	−1.26210
$839$	1.18840e10	0.694700	0.347350	−	0.937736i	$-0.387082\pi$
$839$	1.18840e10	0.694700	0.347350	+	0.937736i	$0.387082\pi$
$840$	0	0
$841$	−6.76294e9	−0.392057
$842$	−9.14138e9	−0.527739
$843$	0	0
$844$	−3.48376e9	−0.199457
$845$	−1.11575e10	−0.636161
$846$	0	0
$847$	−3.21735e9	−0.181931
$848$	−5.26642e9	−0.296572
$849$	0	0
$850$	8.11471e9	0.453217
$851$	2.00868e9	0.111727
$852$	0	0
$853$	2.26976e10	1.25216	0.626078	−	0.779761i	$-0.284659\pi$
$853$	2.26976e10	1.25216	0.626078	+	0.779761i	$0.284659\pi$
$854$	6.41106e9	0.352231
$855$	0	0
$856$	−1.12776e10	−0.614552
$857$	−1.71504e10	−0.930768	−0.465384	−	0.885109i	$-0.654084\pi$
$857$	−1.71504e10	−0.930768	−0.465384	+	0.885109i	$0.654084\pi$
$858$	0	0
$859$	2.14474e9	0.115451	0.0577255	−	0.998332i	$-0.481615\pi$
$859$	2.14474e9	0.115451	0.0577255	+	0.998332i	$0.481615\pi$
$860$	4.87445e9	0.261325
$861$	0	0
$862$	2.88045e10	1.53174
$863$	2.64750e10	1.40216	0.701081	−	0.713082i	$-0.252701\pi$
$863$	2.64750e10	1.40216	0.701081	+	0.713082i	$0.252701\pi$
$864$	0	0
$865$	4.88397e10	2.56576
$866$	−9.53855e7	−0.00499080
$867$	0	0
$868$	−2.02294e9	−0.104994
$869$	−1.85454e8	−0.00958664
$870$	0	0
$871$	1.72285e10	0.883456
$872$	5.98200e9	0.305519
$873$	0	0
$874$	−7.12060e9	−0.360767
$875$	−1.39777e9	−0.0705354
$876$	0	0
$877$	2.88546e10	1.44450	0.722249	−	0.691633i	$-0.243108\pi$
$877$	2.88546e10	1.44450	0.722249	+	0.691633i	$0.243108\pi$
$878$	2.76247e10	1.37742
$879$	0	0
$880$	2.37625e8	0.0117545
$881$	1.83638e10	0.904790	0.452395	−	0.891818i	$-0.350570\pi$
$881$	1.83638e10	0.904790	0.452395	+	0.891818i	$0.350570\pi$
$882$	0	0
$883$	1.95197e10	0.954135	0.477067	−	0.878867i	$-0.341700\pi$
$883$	1.95197e10	0.954135	0.477067	+	0.878867i	$0.341700\pi$
$884$	−3.68642e9	−0.179482
$885$	0	0
$886$	−5.69300e8	−0.0274994
$887$	3.57604e10	1.72056	0.860280	−	0.509822i	$-0.170289\pi$
$887$	3.57604e10	1.72056	0.860280	+	0.509822i	$0.170289\pi$
$888$	0	0
$889$	−5.88586e9	−0.280966
$890$	3.96494e10	1.88526
$891$	0	0
$892$	4.47093e9	0.210921
$893$	−4.95818e10	−2.32992
$894$	0	0
$895$	2.92587e10	1.36419
$896$	−4.32062e9	−0.200664
$897$	0	0
$898$	−1.13962e10	−0.525161
$899$	2.07800e10	0.953863
$900$	0	0
$901$	−2.77030e9	−0.126180
$902$	2.18413e8	0.00990957
$903$	0	0
$904$	−1.61071e10	−0.725151
$905$	−4.56739e10	−2.04832
$906$	0	0
$907$	1.33486e10	0.594033	0.297016	−	0.954872i	$-0.404008\pi$
$907$	1.33486e10	0.594033	0.297016	+	0.954872i	$0.404008\pi$
$908$	−1.64248e10	−0.728117
$909$	0	0
$910$	−4.68740e9	−0.206199
$911$	−1.44202e10	−0.631913	−0.315957	−	0.948774i	$-0.602325\pi$
$911$	−1.44202e10	−0.631913	−0.315957	+	0.948774i	$0.602325\pi$
$912$	0	0
$913$	−4.53486e7	−0.00197204
$914$	−9.40246e8	−0.0407314
$915$	0	0
$916$	−1.37773e10	−0.592283
$917$	4.21531e9	0.180525
$918$	0	0
$919$	2.38461e10	1.01347	0.506737	−	0.862101i	$-0.330852\pi$
$919$	2.38461e10	1.01347	0.506737	+	0.862101i	$0.330852\pi$
$920$	−4.11879e9	−0.174386
$921$	0	0
$922$	5.17444e10	2.17423
$923$	−8.47083e9	−0.354585
$924$	0	0
$925$	−9.06608e9	−0.376637
$926$	−7.61656e9	−0.315225
$927$	0	0
$928$	−1.66014e10	−0.681911
$929$	3.57952e10	1.46477	0.732386	−	0.680890i	$-0.238407\pi$
$929$	3.57952e10	1.46477	0.732386	+	0.680890i	$0.238407\pi$
$930$	0	0
$931$	3.39534e10	1.37898
$932$	2.13114e10	0.862297
$933$	0	0
$934$	−3.12329e10	−1.25429
$935$	1.24998e8	0.00500108
$936$	0	0
$937$	−3.70969e10	−1.47316	−0.736578	−	0.676352i	$-0.763560\pi$
$937$	−3.70969e10	−1.47316	−0.736578	+	0.676352i	$0.763560\pi$
$938$	−6.88474e9	−0.272381
$939$	0	0
$940$	2.56087e10	1.00563
$941$	−1.06625e9	−0.0417152	−0.0208576	−	0.999782i	$-0.506640\pi$
$941$	−1.06625e9	−0.0417152	−0.0208576	+	0.999782i	$0.506640\pi$
$942$	0	0
$943$	−6.08267e9	−0.236213
$944$	4.60029e10	1.77985
$945$	0	0
$946$	9.66964e7	0.00371357
$947$	1.45973e10	0.558530	0.279265	−	0.960214i	$-0.409909\pi$
$947$	1.45973e10	0.558530	0.279265	+	0.960214i	$0.409909\pi$
$948$	0	0
$949$	−2.90509e9	−0.110339
$950$	3.21385e10	1.21617
$951$	0	0
$952$	−1.64980e9	−0.0619727
$953$	2.80924e10	1.05139	0.525694	−	0.850673i	$-0.323806\pi$
$953$	2.80924e10	1.05139	0.525694	+	0.850673i	$0.323806\pi$
$954$	0	0
$955$	−1.18390e9	−0.0439850
$956$	−9.57034e9	−0.354262
$957$	0	0
$958$	3.11758e10	1.14562
$959$	5.36555e9	0.196449
$960$	0	0
$961$	1.36631e10	0.496613
$962$	1.28497e10	0.465352
$963$	0	0
$964$	1.23833e10	0.445211
$965$	−3.92779e10	−1.40703
$966$	0	0
$967$	−5.05633e10	−1.79822	−0.899110	−	0.437723i	$-0.855785\pi$
$967$	−5.05633e10	−1.79822	−0.899110	+	0.437723i	$0.855785\pi$
$968$	−1.80851e10	−0.640851
$969$	0	0
$970$	8.81371e10	3.10069
$971$	3.90879e10	1.37017	0.685085	−	0.728463i	$-0.259765\pi$
$971$	3.90879e10	1.37017	0.685085	+	0.728463i	$0.259765\pi$
$972$	0	0
$973$	−6.29214e9	−0.218979
$974$	−1.85405e10	−0.642932
$975$	0	0
$976$	5.79019e10	1.99351
$977$	−2.06771e9	−0.0709348	−0.0354674	−	0.999371i	$-0.511292\pi$
$977$	−2.06771e9	−0.0709348	−0.0354674	+	0.999371i	$0.511292\pi$
$978$	0	0
$979$	2.52103e8	0.00858695
$980$	−1.75367e10	−0.595193
$981$	0	0
$982$	−5.73278e10	−1.93186
$983$	−4.38211e10	−1.47145	−0.735725	−	0.677280i	$-0.763159\pi$
$983$	−4.38211e10	−1.47145	−0.735725	+	0.677280i	$0.763159\pi$
$984$	0	0
$985$	2.24529e10	0.748591
$986$	−1.51323e10	−0.502730
$987$	0	0
$988$	−1.46002e10	−0.481624
$989$	−2.69294e9	−0.0885197
$990$	0	0
$991$	−4.54621e10	−1.48386	−0.741928	−	0.670479i	$-0.766088\pi$
$991$	−4.54621e10	−1.48386	−0.741928	+	0.670479i	$0.766088\pi$
$992$	−3.28959e10	−1.06992
$993$	0	0
$994$	3.38505e9	0.109323
$995$	1.98501e10	0.638826
$996$	0	0
$997$	−2.21452e10	−0.707696	−0.353848	−	0.935303i	$-0.615127\pi$
$997$	−2.21452e10	−0.707696	−0.353848	+	0.935303i	$0.615127\pi$
$998$	6.08425e9	0.193754
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.b.1.1		5
3.2	odd	2		23.8.a.a.1.5	✓	5
12.11	even	2		368.8.a.e.1.4		5
15.14	odd	2		575.8.a.a.1.1		5
69.68	even	2		529.8.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.a.a.1.5	✓	5	3.2	odd	2
207.8.a.b.1.1		5	1.1	even	1	trivial
368.8.a.e.1.4		5	12.11	even	2
529.8.a.b.1.5		5	69.68	even	2
575.8.a.a.1.1		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)

\(f(q)\)	\(=\)	\(q-13.7251 q^{2} +60.3796 q^{4} +364.747 q^{5} +165.110 q^{7} +928.099 q^{8} +O(q^{10})\)	\(q-13.7251 q^{2} +60.3796 q^{4} +364.747 q^{5} +165.110 q^{7} +928.099 q^{8} -5006.20 q^{10} -31.8310 q^{11} +5670.88 q^{13} -2266.15 q^{14} -20466.9 q^{16} -10766.2 q^{17} -42639.9 q^{19} +22023.3 q^{20} +436.885 q^{22} -12167.0 q^{23} +54915.2 q^{25} -77833.7 q^{26} +9969.26 q^{28} -102406. q^{29} -202918. q^{31} +162114. q^{32} +147768. q^{34} +60223.2 q^{35} -165092. q^{37} +585239. q^{38} +338521. q^{40} +499932. q^{41} +221332. q^{43} -1921.94 q^{44} +166994. q^{46} +1.16280e6 q^{47} -796282. q^{49} -753719. q^{50} +342406. q^{52} +257314. q^{53} -11610.2 q^{55} +153238. q^{56} +1.40553e6 q^{58} -2.24767e6 q^{59} -2.82905e6 q^{61} +2.78508e6 q^{62} +394718. q^{64} +2.06844e6 q^{65} +3.03807e6 q^{67} -650060. q^{68} -826573. q^{70} -1.49374e6 q^{71} -512282. q^{73} +2.26592e6 q^{74} -2.57458e6 q^{76} -5255.60 q^{77} +5.82621e6 q^{79} -7.46523e6 q^{80} -6.86164e6 q^{82} +1.42467e6 q^{83} -3.92694e6 q^{85} -3.03781e6 q^{86} -29542.3 q^{88} -7.92006e6 q^{89} +936318. q^{91} -734639. q^{92} -1.59596e7 q^{94} -1.55528e7 q^{95} -1.76056e7 q^{97} +1.09291e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 16 q^{2} + 256 q^{4} + 56 q^{5} - 1156 q^{7} + 5952 q^{8}+O(q^{10}) \) 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

Introduction

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