LMFDB - Embedded newform 207.8.a.f.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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 832x^{6} - 1059x^{5} + 203052x^{4} + 678328x^{3} - 13424272x^{2} - 73308944x - 37372224 $ x^8 - 832x^6 - 1059x^5 + 203052x^4 + 678328x^3 - 13424272x^2 - 73308944x - 37372224
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$19.4241$ 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)

$f(q)$	$=$	$q-19.4241 q^{2} +249.296 q^{4} +31.9528 q^{5} -461.175 q^{7} -2356.08 q^{8} +O(q^{10})$	\(q-19.4241 q^{2} +249.296 q^{4} +31.9528 q^{5} -461.175 q^{7} -2356.08 q^{8} -620.655 q^{10} -4540.49 q^{11} -11191.4 q^{13} +8957.92 q^{14} +13854.8 q^{16} -14530.3 q^{17} +20739.4 q^{19} +7965.72 q^{20} +88195.1 q^{22} +12167.0 q^{23} -77104.0 q^{25} +217384. q^{26} -114969. q^{28} +31667.1 q^{29} +45528.3 q^{31} +32461.1 q^{32} +282238. q^{34} -14735.8 q^{35} -37949.6 q^{37} -402845. q^{38} -75283.2 q^{40} -662248. q^{41} +800333. q^{43} -1.13193e6 q^{44} -236333. q^{46} -952414. q^{47} -610860. q^{49} +1.49768e6 q^{50} -2.78998e6 q^{52} -639495. q^{53} -145081. q^{55} +1.08656e6 q^{56} -615105. q^{58} -1.79568e6 q^{59} -2.62433e6 q^{61} -884346. q^{62} -2.40394e6 q^{64} -357597. q^{65} +4.61394e6 q^{67} -3.62235e6 q^{68} +286231. q^{70} +1.45683e6 q^{71} +3.13913e6 q^{73} +737137. q^{74} +5.17027e6 q^{76} +2.09396e6 q^{77} -6.71170e6 q^{79} +442698. q^{80} +1.28636e7 q^{82} +8.16841e6 q^{83} -464284. q^{85} -1.55458e7 q^{86} +1.06977e7 q^{88} +4.59258e6 q^{89} +5.16121e6 q^{91} +3.03319e6 q^{92} +1.84998e7 q^{94} +662683. q^{95} -5.85762e6 q^{97} +1.18654e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 640 q^{4} - 444 q^{5} + 1446 q^{7} - 3177 q^{8}+O(q^{10}) $ 8 * q + 640 * q^4 - 444 * q^5 + 1446 * q^7 - 3177 * q^8	\( 8 q + 640 q^{4} - 444 q^{5} + 1446 q^{7} - 3177 q^{8} + 19502 q^{10} - 7588 q^{11} + 19862 q^{13} - 17544 q^{14} + 64336 q^{16} - 42070 q^{17} + 1050 q^{19} - 3364 q^{20} - 128220 q^{22} + 97336 q^{23} + 49496 q^{25} + 371761 q^{26} + 143050 q^{28} + 102578 q^{29} + 304172 q^{31} + 612824 q^{32} - 524530 q^{34} - 531048 q^{35} + 286472 q^{37} + 762932 q^{38} + 2105286 q^{40} - 1324414 q^{41} + 2052578 q^{43} + 867298 q^{44} - 675556 q^{47} - 55404 q^{49} - 1458528 q^{50} - 1695409 q^{52} - 203654 q^{53} - 1024444 q^{55} + 5766846 q^{56} - 5039991 q^{58} + 748892 q^{59} + 61822 q^{61} + 4939277 q^{62} + 2702267 q^{64} + 1571618 q^{65} + 3235604 q^{67} - 4914980 q^{68} + 10871764 q^{70} + 4951664 q^{71} + 11019370 q^{73} - 356954 q^{74} + 21973240 q^{76} + 5284888 q^{77} + 4202464 q^{79} - 8785886 q^{80} + 32636759 q^{82} - 518568 q^{83} + 9854220 q^{85} + 14681386 q^{86} + 20589740 q^{88} - 4203864 q^{89} + 2488406 q^{91} + 7786880 q^{92} + 12314327 q^{94} + 44485300 q^{95} + 18621134 q^{97} - 35756 q^{98}+O(q^{100}) \) 8 * q + 640 * q^4 - 444 * q^5 + 1446 * q^7 - 3177 * q^8 + 19502 * q^10 - 7588 * q^11 + 19862 * q^13 - 17544 * q^14 + 64336 * q^16 - 42070 * q^17 + 1050 * q^19 - 3364 * q^20 - 128220 * q^22 + 97336 * q^23 + 49496 * q^25 + 371761 * q^26 + 143050 * q^28 + 102578 * q^29 + 304172 * q^31 + 612824 * q^32 - 524530 * q^34 - 531048 * q^35 + 286472 * q^37 + 762932 * q^38 + 2105286 * q^40 - 1324414 * q^41 + 2052578 * q^43 + 867298 * q^44 - 675556 * q^47 - 55404 * q^49 - 1458528 * q^50 - 1695409 * q^52 - 203654 * q^53 - 1024444 * q^55 + 5766846 * q^56 - 5039991 * q^58 + 748892 * q^59 + 61822 * q^61 + 4939277 * q^62 + 2702267 * q^64 + 1571618 * q^65 + 3235604 * q^67 - 4914980 * q^68 + 10871764 * q^70 + 4951664 * q^71 + 11019370 * q^73 - 356954 * q^74 + 21973240 * q^76 + 5284888 * q^77 + 4202464 * q^79 - 8785886 * q^80 + 32636759 * q^82 - 518568 * q^83 + 9854220 * q^85 + 14681386 * q^86 + 20589740 * q^88 - 4203864 * q^89 + 2488406 * q^91 + 7786880 * q^92 + 12314327 * q^94 + 44485300 * q^95 + 18621134 * q^97 - 35756 * 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 $

$2$	−19.4241	−1.71687	−0.858433	−	0.512926i	$-0.828562\pi$
$2$	−19.4241	−1.71687	−0.858433	+	0.512926i	$0.828562\pi$
$3$	0	0
$3$	0	0
$4$	249.296	1.94763
$5$	31.9528	0.114318	0.0571589	−	0.998365i	$-0.481796\pi$
$5$	31.9528	0.114318	0.0571589	+	0.998365i	$0.481796\pi$
$6$	0	0
$7$	−461.175	−0.508186	−0.254093	−	0.967180i	$-0.581777\pi$
$7$	−461.175	−0.508186	−0.254093	+	0.967180i	$0.581777\pi$
$8$	−2356.08	−1.62695
$9$	0	0
$10$	−620.655	−0.196268
$11$	−4540.49	−1.02856	−0.514279	−	0.857623i	$-0.671940\pi$
$11$	−4540.49	−1.02856	−0.514279	+	0.857623i	$0.671940\pi$
$12$	0	0
$13$	−11191.4	−1.41281	−0.706405	−	0.707808i	$-0.749684\pi$
$13$	−11191.4	−1.41281	−0.706405	+	0.707808i	$0.749684\pi$
$14$	8957.92	0.872487
$15$	0	0
$16$	13854.8	0.845628
$17$	−14530.3	−0.717305	−0.358652	−	0.933471i	$-0.616764\pi$
$17$	−14530.3	−0.717305	−0.358652	+	0.933471i	$0.616764\pi$
$18$	0	0
$19$	20739.4	0.693680	0.346840	−	0.937924i	$-0.387255\pi$
$19$	20739.4	0.693680	0.346840	+	0.937924i	$0.387255\pi$
$20$	7965.72	0.222649
$21$	0	0
$22$	88195.1	1.76589
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	−77104.0	−0.986931
$26$	217384.	2.42561
$27$	0	0
$28$	−114969.	−0.989758
$29$	31667.1	0.241110	0.120555	−	0.992707i	$-0.461533\pi$
$29$	31667.1	0.241110	0.120555	+	0.992707i	$0.461533\pi$
$30$	0	0
$31$	45528.3	0.274483	0.137241	−	0.990538i	$-0.456176\pi$
$31$	45528.3	0.274483	0.137241	+	0.990538i	$0.456176\pi$
$32$	32461.1	0.175121
$33$	0	0
$34$	282238.	1.23152
$35$	−14735.8	−0.0580947
$36$	0	0
$37$	−37949.6	−0.123169	−0.0615844	−	0.998102i	$-0.519615\pi$
$37$	−37949.6	−0.123169	−0.0615844	+	0.998102i	$0.519615\pi$
$38$	−402845.	−1.19096
$39$	0	0
$40$	−75283.2	−0.185989
$41$	−662248.	−1.50064	−0.750321	−	0.661074i	$-0.770101\pi$
$41$	−662248.	−1.50064	−0.750321	+	0.661074i	$0.770101\pi$
$42$	0	0
$43$	800333.	1.53508	0.767540	−	0.641001i	$-0.221481\pi$
$43$	800333.	1.53508	0.767540	+	0.641001i	$0.221481\pi$
$44$	−1.13193e6	−2.00325
$45$	0	0
$46$	−236333.	−0.357991
$47$	−952414.	−1.33808	−0.669042	−	0.743225i	$-0.733295\pi$
$47$	−952414.	−1.33808	−0.669042	+	0.743225i	$0.733295\pi$
$48$	0	0
$49$	−610860.	−0.741747
$50$	1.49768e6	1.69443
$51$	0	0
$52$	−2.78998e6	−2.75163
$53$	−639495.	−0.590026	−0.295013	−	0.955493i	$-0.595324\pi$
$53$	−639495.	−0.590026	−0.295013	+	0.955493i	$0.595324\pi$
$54$	0	0
$55$	−145081.	−0.117582
$56$	1.08656e6	0.826794
$57$	0	0
$58$	−615105.	−0.413953
$59$	−1.79568e6	−1.13827	−0.569137	−	0.822243i	$-0.692723\pi$
$59$	−1.79568e6	−1.13827	−0.569137	+	0.822243i	$0.692723\pi$
$60$	0	0
$61$	−2.62433e6	−1.48035	−0.740175	−	0.672414i	$-0.765257\pi$
$61$	−2.62433e6	−1.48035	−0.740175	+	0.672414i	$0.765257\pi$
$62$	−884346.	−0.471250
$63$	0	0
$64$	−2.40394e6	−1.14629
$65$	−357597.	−0.161509
$66$	0	0
$67$	4.61394e6	1.87417	0.937087	−	0.349097i	$-0.113512\pi$
$67$	4.61394e6	1.87417	0.937087	+	0.349097i	$0.113512\pi$
$68$	−3.62235e6	−1.39704
$69$	0	0
$70$	286231.	0.0997408
$71$	1.45683e6	0.483066	0.241533	−	0.970393i	$-0.422350\pi$
$71$	1.45683e6	0.483066	0.241533	+	0.970393i	$0.422350\pi$
$72$	0	0
$73$	3.13913e6	0.944450	0.472225	−	0.881478i	$-0.343451\pi$
$73$	3.13913e6	0.944450	0.472225	+	0.881478i	$0.343451\pi$
$74$	737137.	0.211464
$75$	0	0
$76$	5.17027e6	1.35103
$77$	2.09396e6	0.522699
$78$	0	0
$79$	−6.71170e6	−1.53157	−0.765787	−	0.643094i	$-0.777650\pi$
$79$	−6.71170e6	−1.53157	−0.765787	+	0.643094i	$0.777650\pi$
$80$	442698.	0.0966703
$81$	0	0
$82$	1.28636e7	2.57640
$83$	8.16841e6	1.56806	0.784032	−	0.620720i	$-0.213160\pi$
$83$	8.16841e6	1.56806	0.784032	+	0.620720i	$0.213160\pi$
$84$	0	0
$85$	−464284.	−0.0820006
$86$	−1.55458e7	−2.63553
$87$	0	0
$88$	1.06977e7	1.67341
$89$	4.59258e6	0.690544	0.345272	−	0.938503i	$-0.387787\pi$
$89$	4.59258e6	0.690544	0.345272	+	0.938503i	$0.387787\pi$
$90$	0	0
$91$	5.16121e6	0.717971
$92$	3.03319e6	0.406109
$93$	0	0
$94$	1.84998e7	2.29731
$95$	662683.	0.0793000
$96$	0	0
$97$	−5.85762e6	−0.651658	−0.325829	−	0.945429i	$-0.605643\pi$
$97$	−5.85762e6	−0.651658	−0.325829	+	0.945429i	$0.605643\pi$
$98$	1.18654e7	1.27348
$99$	0	0
$100$	−1.92218e7	−1.92218
$101$	−1.05558e7	−1.01945	−0.509724	−	0.860338i	$-0.670253\pi$
$101$	−1.05558e7	−1.01945	−0.509724	+	0.860338i	$0.670253\pi$
$102$	0	0
$103$	5.72955e6	0.516642	0.258321	−	0.966059i	$-0.416831\pi$
$103$	5.72955e6	0.516642	0.258321	+	0.966059i	$0.416831\pi$
$104$	2.63679e7	2.29857
$105$	0	0
$106$	1.24216e7	1.01300
$107$	9.53116e6	0.752147	0.376074	−	0.926590i	$-0.377274\pi$
$107$	9.53116e6	0.752147	0.376074	+	0.926590i	$0.377274\pi$
$108$	0	0
$109$	1.22213e7	0.903911	0.451955	−	0.892041i	$-0.350727\pi$
$109$	1.22213e7	0.903911	0.451955	+	0.892041i	$0.350727\pi$
$110$	2.81808e6	0.201873
$111$	0	0
$112$	−6.38947e6	−0.429736
$113$	1.23119e7	0.802695	0.401348	−	0.915926i	$-0.368542\pi$
$113$	1.23119e7	0.802695	0.401348	+	0.915926i	$0.368542\pi$
$114$	0	0
$115$	388770.	0.0238369
$116$	7.89449e6	0.469593
$117$	0	0
$118$	3.48795e7	1.95426
$119$	6.70102e6	0.364524
$120$	0	0
$121$	1.12890e6	0.0579302
$122$	5.09753e7	2.54156
$123$	0	0
$124$	1.13500e7	0.534590
$125$	−4.96000e6	−0.227142
$126$	0	0
$127$	−3.71495e7	−1.60931	−0.804656	−	0.593742i	$-0.797650\pi$
$127$	−3.71495e7	−1.60931	−0.804656	+	0.593742i	$0.797650\pi$
$128$	4.25394e7	1.79290
$129$	0	0
$130$	6.94602e6	0.277290
$131$	1.33795e7	0.519985	0.259993	−	0.965611i	$-0.416280\pi$
$131$	1.33795e7	0.519985	0.259993	+	0.965611i	$0.416280\pi$
$132$	0	0
$133$	−9.56451e6	−0.352519
$134$	−8.96216e7	−3.21770
$135$	0	0
$136$	3.42345e7	1.16702
$137$	−3.68311e7	−1.22375	−0.611875	−	0.790954i	$-0.709585\pi$
$137$	−3.68311e7	−1.22375	−0.611875	+	0.790954i	$0.709585\pi$
$138$	0	0
$139$	2.10570e7	0.665034	0.332517	−	0.943097i	$-0.392102\pi$
$139$	2.10570e7	0.665034	0.332517	+	0.943097i	$0.392102\pi$
$140$	−3.67359e6	−0.113147
$141$	0	0
$142$	−2.82977e7	−0.829359
$143$	5.08146e7	1.45316
$144$	0	0
$145$	1.01185e6	0.0275632
$146$	−6.09748e7	−1.62149
$147$	0	0
$148$	−9.46069e6	−0.239887
$149$	5.53228e7	1.37010	0.685050	−	0.728496i	$-0.259780\pi$
$149$	5.53228e7	1.37010	0.685050	+	0.728496i	$0.259780\pi$
$150$	0	0
$151$	−7.90397e6	−0.186821	−0.0934105	−	0.995628i	$-0.529777\pi$
$151$	−7.90397e6	−0.186821	−0.0934105	+	0.995628i	$0.529777\pi$
$152$	−4.88637e7	−1.12858
$153$	0	0
$154$	−4.06734e7	−0.897403
$155$	1.45475e6	0.0313783
$156$	0	0
$157$	5.83484e7	1.20332	0.601658	−	0.798754i	$-0.294507\pi$
$157$	5.83484e7	1.20332	0.601658	+	0.798754i	$0.294507\pi$
$158$	1.30369e8	2.62951
$159$	0	0
$160$	1.03722e6	0.0200194
$161$	−5.61112e6	−0.105964
$162$	0	0
$163$	−5.25424e7	−0.950285	−0.475142	−	0.879909i	$-0.657603\pi$
$163$	−5.25424e7	−0.950285	−0.475142	+	0.879909i	$0.657603\pi$
$164$	−1.65096e8	−2.92269
$165$	0	0
$166$	−1.58664e8	−2.69216
$167$	−2.29173e7	−0.380763	−0.190382	−	0.981710i	$-0.560973\pi$
$167$	−2.29173e7	−0.380763	−0.190382	+	0.981710i	$0.560973\pi$
$168$	0	0
$169$	6.24997e7	0.996034
$170$	9.01830e6	0.140784
$171$	0	0
$172$	1.99520e8	2.98976
$173$	5.20840e7	0.764792	0.382396	−	0.923999i	$-0.375099\pi$
$173$	5.20840e7	0.764792	0.382396	+	0.923999i	$0.375099\pi$
$174$	0	0
$175$	3.55585e7	0.501545
$176$	−6.29075e7	−0.869777
$177$	0	0
$178$	−8.92068e7	−1.18557
$179$	6.93616e7	0.903927	0.451964	−	0.892036i	$-0.350724\pi$
$179$	6.93616e7	0.903927	0.451964	+	0.892036i	$0.350724\pi$
$180$	0	0
$181$	8.66347e7	1.08597	0.542984	−	0.839743i	$-0.317294\pi$
$181$	8.66347e7	1.08597	0.542984	+	0.839743i	$0.317294\pi$
$182$	−1.00252e8	−1.23266
$183$	0	0
$184$	−2.86664e7	−0.339243
$185$	−1.21259e6	−0.0140804
$186$	0	0
$187$	6.59747e7	0.737789
$188$	−2.37433e8	−2.60609
$189$	0	0
$190$	−1.28720e7	−0.136147
$191$	7.02747e6	0.0729764	0.0364882	−	0.999334i	$-0.488383\pi$
$191$	7.02747e6	0.0729764	0.0364882	+	0.999334i	$0.488383\pi$
$192$	0	0
$193$	−2.73465e7	−0.273811	−0.136905	−	0.990584i	$-0.543716\pi$
$193$	−2.73465e7	−0.273811	−0.136905	+	0.990584i	$0.543716\pi$
$194$	1.13779e8	1.11881
$195$	0	0
$196$	−1.52285e8	−1.44465
$197$	−6.75894e6	−0.0629864	−0.0314932	−	0.999504i	$-0.510026\pi$
$197$	−6.75894e6	−0.0629864	−0.0314932	+	0.999504i	$0.510026\pi$
$198$	0	0
$199$	−6.19972e7	−0.557682	−0.278841	−	0.960337i	$-0.589950\pi$
$199$	−6.19972e7	−0.557682	−0.278841	+	0.960337i	$0.589950\pi$
$200$	1.81663e8	1.60569
$201$	0	0
$202$	2.05037e8	1.75026
$203$	−1.46041e7	−0.122529
$204$	0	0
$205$	−2.11607e7	−0.171550
$206$	−1.11291e8	−0.887005
$207$	0	0
$208$	−1.55055e8	−1.19471
$209$	−9.41673e7	−0.713490
$210$	0	0
$211$	−1.33317e8	−0.977003	−0.488502	−	0.872563i	$-0.662456\pi$
$211$	−1.33317e8	−0.977003	−0.488502	+	0.872563i	$0.662456\pi$
$212$	−1.59424e8	−1.14915
$213$	0	0
$214$	−1.85134e8	−1.29134
$215$	2.55729e7	0.175487
$216$	0	0
$217$	−2.09965e7	−0.139488
$218$	−2.37388e8	−1.55189
$219$	0	0
$220$	−3.61683e7	−0.229007
$221$	1.62615e8	1.01342
$222$	0	0
$223$	−5.61487e7	−0.339057	−0.169529	−	0.985525i	$-0.554224\pi$
$223$	−5.61487e7	−0.339057	−0.169529	+	0.985525i	$0.554224\pi$
$224$	−1.49703e7	−0.0889941
$225$	0	0
$226$	−2.39148e8	−1.37812
$227$	−1.95292e8	−1.10814	−0.554069	−	0.832471i	$-0.686925\pi$
$227$	−1.95292e8	−1.10814	−0.554069	+	0.832471i	$0.686925\pi$
$228$	0	0
$229$	3.07484e8	1.69199	0.845995	−	0.533191i	$-0.179007\pi$
$229$	3.07484e8	1.69199	0.845995	+	0.533191i	$0.179007\pi$
$230$	−7.55151e6	−0.0409248
$231$	0	0
$232$	−7.46101e7	−0.392274
$233$	3.20423e8	1.65950	0.829752	−	0.558132i	$-0.188482\pi$
$233$	3.20423e8	1.65950	0.829752	+	0.558132i	$0.188482\pi$
$234$	0	0
$235$	−3.04323e7	−0.152967
$236$	−4.47657e8	−2.21694
$237$	0	0
$238$	−1.30161e8	−0.625839
$239$	1.07806e8	0.510801	0.255400	−	0.966835i	$-0.417793\pi$
$239$	1.07806e8	0.510801	0.255400	+	0.966835i	$0.417793\pi$
$240$	0	0
$241$	1.98145e8	0.911849	0.455924	−	0.890019i	$-0.349309\pi$
$241$	1.98145e8	0.911849	0.455924	+	0.890019i	$0.349309\pi$
$242$	−2.19278e7	−0.0994584
$243$	0	0
$244$	−6.54237e8	−2.88317
$245$	−1.95187e7	−0.0847948
$246$	0	0
$247$	−2.32104e8	−0.980039
$248$	−1.07268e8	−0.446570
$249$	0	0
$250$	9.63436e7	0.389972
$251$	1.69055e8	0.674794	0.337397	−	0.941362i	$-0.390454\pi$
$251$	1.69055e8	0.674794	0.337397	+	0.941362i	$0.390454\pi$
$252$	0	0
$253$	−5.52442e7	−0.214469
$254$	7.21596e8	2.76297
$255$	0	0
$256$	−5.18586e8	−1.93188
$257$	5.75630e7	0.211533	0.105766	−	0.994391i	$-0.466270\pi$
$257$	5.75630e7	0.211533	0.105766	+	0.994391i	$0.466270\pi$
$258$	0	0
$259$	1.75014e7	0.0625927
$260$	−8.91478e7	−0.314560
$261$	0	0
$262$	−2.59885e8	−0.892745
$263$	2.19210e8	0.743046	0.371523	−	0.928424i	$-0.378836\pi$
$263$	2.19210e8	0.743046	0.371523	+	0.928424i	$0.378836\pi$
$264$	0	0
$265$	−2.04336e7	−0.0674505
$266$	1.85782e8	0.605227
$267$	0	0
$268$	1.15024e9	3.65019
$269$	3.76409e7	0.117904	0.0589518	−	0.998261i	$-0.481224\pi$
$269$	3.76409e7	0.117904	0.0589518	+	0.998261i	$0.481224\pi$
$270$	0	0
$271$	1.33250e8	0.406701	0.203350	−	0.979106i	$-0.434817\pi$
$271$	1.33250e8	0.406701	0.203350	+	0.979106i	$0.434817\pi$
$272$	−2.01314e8	−0.606573
$273$	0	0
$274$	7.15412e8	2.10102
$275$	3.50090e8	1.01512
$276$	0	0
$277$	5.61404e8	1.58707	0.793535	−	0.608524i	$-0.208238\pi$
$277$	5.61404e8	1.58707	0.793535	+	0.608524i	$0.208238\pi$
$278$	−4.09013e8	−1.14177
$279$	0	0
$280$	3.47187e7	0.0945172
$281$	−5.62980e8	−1.51364	−0.756818	−	0.653626i	$-0.773247\pi$
$281$	−5.62980e8	−1.51364	−0.756818	+	0.653626i	$0.773247\pi$
$282$	0	0
$283$	6.66508e8	1.74805	0.874023	−	0.485884i	$-0.161502\pi$
$283$	6.66508e8	1.74805	0.874023	+	0.485884i	$0.161502\pi$
$284$	3.63184e8	0.940832
$285$	0	0
$286$	−9.87029e8	−2.49488
$287$	3.05412e8	0.762605
$288$	0	0
$289$	−1.99209e8	−0.485474
$290$	−1.96543e7	−0.0473222
$291$	0	0
$292$	7.82573e8	1.83944
$293$	6.90546e8	1.60382	0.801911	−	0.597444i	$-0.203817\pi$
$293$	6.90546e8	1.60382	0.801911	+	0.597444i	$0.203817\pi$
$294$	0	0
$295$	−5.73770e7	−0.130125
$296$	8.94120e7	0.200390
$297$	0	0
$298$	−1.07460e9	−2.35228
$299$	−1.36166e8	−0.294591
$300$	0	0
$301$	−3.69094e8	−0.780106
$302$	1.53528e8	0.320747
$303$	0	0
$304$	2.87340e8	0.586595
$305$	−8.38547e7	−0.169230
$306$	0	0
$307$	2.93174e8	0.578283	0.289142	−	0.957286i	$-0.406630\pi$
$307$	2.93174e8	0.578283	0.289142	+	0.957286i	$0.406630\pi$
$308$	5.22017e8	1.01802
$309$	0	0
$310$	−2.82573e7	−0.0538722
$311$	5.93648e8	1.11910	0.559548	−	0.828798i	$-0.310975\pi$
$311$	5.93648e8	1.11910	0.559548	+	0.828798i	$0.310975\pi$
$312$	0	0
$313$	8.91246e8	1.64283	0.821414	−	0.570332i	$-0.193185\pi$
$313$	8.91246e8	1.64283	0.821414	+	0.570332i	$0.193185\pi$
$314$	−1.13337e9	−2.06593
$315$	0	0
$316$	−1.67320e9	−2.98294
$317$	−1.02837e9	−1.81319	−0.906596	−	0.421999i	$-0.861329\pi$
$317$	−1.02837e9	−1.81319	−0.906596	+	0.421999i	$0.861329\pi$
$318$	0	0
$319$	−1.43784e8	−0.247995
$320$	−7.68125e7	−0.131041
$321$	0	0
$322$	1.08991e8	0.181926
$323$	−3.01350e8	−0.497580
$324$	0	0
$325$	8.62904e8	1.39435
$326$	1.02059e9	1.63151
$327$	0	0
$328$	1.56031e9	2.44147
$329$	4.39230e8	0.679996
$330$	0	0
$331$	−3.04610e8	−0.461686	−0.230843	−	0.972991i	$-0.574148\pi$
$331$	−3.04610e8	−0.461686	−0.230843	+	0.972991i	$0.574148\pi$
$332$	2.03635e9	3.05401
$333$	0	0
$334$	4.45148e8	0.653720
$335$	1.47428e8	0.214251
$336$	0	0
$337$	7.38290e8	1.05081	0.525403	−	0.850853i	$-0.323915\pi$
$337$	7.38290e8	1.05081	0.525403	+	0.850853i	$0.323915\pi$
$338$	−1.21400e9	−1.71006
$339$	0	0
$340$	−1.15744e8	−0.159707
$341$	−2.06721e8	−0.282321
$342$	0	0
$343$	6.61511e8	0.885132
$344$	−1.88564e9	−2.49750
$345$	0	0
$346$	−1.01169e9	−1.31304
$347$	−1.19490e9	−1.53525	−0.767625	−	0.640899i	$-0.778562\pi$
$347$	−1.19490e9	−1.53525	−0.767625	+	0.640899i	$0.778562\pi$
$348$	0	0
$349$	−3.33144e8	−0.419511	−0.209755	−	0.977754i	$-0.567267\pi$
$349$	−3.33144e8	−0.419511	−0.209755	+	0.977754i	$0.567267\pi$
$350$	−6.90692e8	−0.861085
$351$	0	0
$352$	−1.47389e8	−0.180122
$353$	4.06593e8	0.491981	0.245990	−	0.969272i	$-0.420887\pi$
$353$	4.06593e8	0.491981	0.245990	+	0.969272i	$0.420887\pi$
$354$	0	0
$355$	4.65499e7	0.0552230
$356$	1.14491e9	1.34492
$357$	0	0
$358$	−1.34729e9	−1.55192
$359$	−4.07962e8	−0.465361	−0.232680	−	0.972553i	$-0.574750\pi$
$359$	−4.07962e8	−0.465361	−0.232680	+	0.972553i	$0.574750\pi$
$360$	0	0
$361$	−4.63747e8	−0.518808
$362$	−1.68280e9	−1.86446
$363$	0	0
$364$	1.28667e9	1.39834
$365$	1.00304e8	0.107967
$366$	0	0
$367$	−9.75739e8	−1.03039	−0.515196	−	0.857072i	$-0.672281\pi$
$367$	−9.75739e8	−1.03039	−0.515196	+	0.857072i	$0.672281\pi$
$368$	1.68571e8	0.176326
$369$	0	0
$370$	2.35536e7	0.0241741
$371$	2.94919e8	0.299843
$372$	0	0
$373$	−9.40794e8	−0.938671	−0.469336	−	0.883020i	$-0.655507\pi$
$373$	−9.40794e8	−0.938671	−0.469336	+	0.883020i	$0.655507\pi$
$374$	−1.28150e9	−1.26668
$375$	0	0
$376$	2.24396e9	2.17700
$377$	−3.54400e8	−0.340643
$378$	0	0
$379$	2.18628e8	0.206286	0.103143	−	0.994667i	$-0.467110\pi$
$379$	2.18628e8	0.206286	0.103143	+	0.994667i	$0.467110\pi$
$380$	1.65204e8	0.154447
$381$	0	0
$382$	−1.36502e8	−0.125291
$383$	3.44641e7	0.0313452	0.0156726	−	0.999877i	$-0.495011\pi$
$383$	3.44641e7	0.0313452	0.0156726	+	0.999877i	$0.495011\pi$
$384$	0	0
$385$	6.69079e7	0.0597537
$386$	5.31181e8	0.470097
$387$	0	0
$388$	−1.46028e9	−1.26919
$389$	1.06655e9	0.918667	0.459334	−	0.888264i	$-0.348088\pi$
$389$	1.06655e9	0.918667	0.459334	+	0.888264i	$0.348088\pi$
$390$	0	0
$391$	−1.76790e8	−0.149568
$392$	1.43923e9	1.20679
$393$	0	0
$394$	1.31286e8	0.108139
$395$	−2.14458e8	−0.175086
$396$	0	0
$397$	−1.68869e9	−1.35451	−0.677257	−	0.735746i	$-0.736832\pi$
$397$	−1.68869e9	−1.35451	−0.677257	+	0.735746i	$0.736832\pi$
$398$	1.20424e9	0.957465
$399$	0	0
$400$	−1.06826e9	−0.834577
$401$	−1.57434e9	−1.21925	−0.609626	−	0.792689i	$-0.708680\pi$
$401$	−1.57434e9	−1.21925	−0.609626	+	0.792689i	$0.708680\pi$
$402$	0	0
$403$	−5.09526e8	−0.387792
$404$	−2.63152e9	−1.98551
$405$	0	0
$406$	2.83671e8	0.210365
$407$	1.72310e8	0.126686
$408$	0	0
$409$	4.48861e8	0.324399	0.162200	−	0.986758i	$-0.448141\pi$
$409$	4.48861e8	0.324399	0.162200	+	0.986758i	$0.448141\pi$
$410$	4.11027e8	0.294528
$411$	0	0
$412$	1.42836e9	1.00623
$413$	8.28123e8	0.578455
$414$	0	0
$415$	2.61003e8	0.179258
$416$	−3.63286e8	−0.247413
$417$	0	0
$418$	1.82912e9	1.22497
$419$	−2.11622e9	−1.40544	−0.702719	−	0.711468i	$-0.748031\pi$
$419$	−2.11622e9	−1.40544	−0.702719	+	0.711468i	$0.748031\pi$
$420$	0	0
$421$	−1.61505e9	−1.05487	−0.527434	−	0.849596i	$-0.676846\pi$
$421$	−1.61505e9	−1.05487	−0.527434	+	0.849596i	$0.676846\pi$
$422$	2.58956e9	1.67738
$423$	0	0
$424$	1.50670e9	0.959944
$425$	1.12035e9	0.707930
$426$	0	0
$427$	1.21028e9	0.752293
$428$	2.37609e9	1.46490
$429$	0	0
$430$	−4.96730e8	−0.301287
$431$	2.26873e8	0.136494	0.0682469	−	0.997668i	$-0.478259\pi$
$431$	2.26873e8	0.136494	0.0682469	+	0.997668i	$0.478259\pi$
$432$	0	0
$433$	−1.34072e9	−0.793653	−0.396826	−	0.917894i	$-0.629889\pi$
$433$	−1.34072e9	−0.793653	−0.396826	+	0.917894i	$0.629889\pi$
$434$	4.07839e8	0.239483
$435$	0	0
$436$	3.04673e9	1.76048
$437$	2.52337e8	0.144642
$438$	0	0
$439$	2.47801e9	1.39790	0.698951	−	0.715169i	$-0.253650\pi$
$439$	2.47801e9	1.39790	0.698951	+	0.715169i	$0.253650\pi$
$440$	3.41823e8	0.191301
$441$	0	0
$442$	−3.15865e9	−1.73990
$443$	3.45535e9	1.88833	0.944167	−	0.329467i	$-0.106869\pi$
$443$	3.45535e9	1.88833	0.944167	+	0.329467i	$0.106869\pi$
$444$	0	0
$445$	1.46746e8	0.0789415
$446$	1.09064e9	0.582116
$447$	0	0
$448$	1.10864e9	0.582527
$449$	3.65410e9	1.90510	0.952551	−	0.304379i	$-0.0984488\pi$
$449$	3.65410e9	1.90510	0.952551	+	0.304379i	$0.0984488\pi$
$450$	0	0
$451$	3.00693e9	1.54350
$452$	3.06931e9	1.56335
$453$	0	0
$454$	3.79337e9	1.90252
$455$	1.64915e8	0.0820768
$456$	0	0
$457$	3.34179e9	1.63784	0.818921	−	0.573906i	$-0.194573\pi$
$457$	3.34179e9	1.63784	0.818921	+	0.573906i	$0.194573\pi$
$458$	−5.97260e9	−2.90492
$459$	0	0
$460$	9.69189e7	0.0464254
$461$	−2.79653e9	−1.32943	−0.664715	−	0.747097i	$-0.731447\pi$
$461$	−2.79653e9	−1.32943	−0.664715	+	0.747097i	$0.731447\pi$
$462$	0	0
$463$	2.91958e9	1.36706	0.683530	−	0.729923i	$-0.260444\pi$
$463$	2.91958e9	1.36706	0.683530	+	0.729923i	$0.260444\pi$
$464$	4.38740e8	0.203889
$465$	0	0
$466$	−6.22394e9	−2.84915
$467$	−3.07316e9	−1.39629	−0.698146	−	0.715955i	$-0.745991\pi$
$467$	−3.07316e9	−1.39629	−0.698146	+	0.715955i	$0.745991\pi$
$468$	0	0
$469$	−2.12783e9	−0.952429
$470$	5.91120e8	0.262623
$471$	0	0
$472$	4.23076e9	1.85192
$473$	−3.63390e9	−1.57892
$474$	0	0
$475$	−1.59909e9	−0.684615
$476$	1.67054e9	0.709958
$477$	0	0
$478$	−2.09404e9	−0.876976
$479$	−3.39636e8	−0.141202	−0.0706008	−	0.997505i	$-0.522492\pi$
$479$	−3.39636e8	−0.141202	−0.0706008	+	0.997505i	$0.522492\pi$
$480$	0	0
$481$	4.24710e8	0.174014
$482$	−3.84879e9	−1.56552
$483$	0	0
$484$	2.81430e8	0.112827
$485$	−1.87167e8	−0.0744961
$486$	0	0
$487$	7.38660e8	0.289796	0.144898	−	0.989447i	$-0.453715\pi$
$487$	7.38660e8	0.289796	0.144898	+	0.989447i	$0.453715\pi$
$488$	6.18313e9	2.40846
$489$	0	0
$490$	3.79133e8	0.145581
$491$	−2.52875e8	−0.0964097	−0.0482049	−	0.998837i	$-0.515350\pi$
$491$	−2.52875e8	−0.0964097	−0.0482049	+	0.998837i	$0.515350\pi$
$492$	0	0
$493$	−4.60133e8	−0.172949
$494$	4.50842e9	1.68260
$495$	0	0
$496$	6.30783e8	0.232110
$497$	−6.71856e8	−0.245487
$498$	0	0
$499$	−2.88385e9	−1.03901	−0.519507	−	0.854466i	$-0.673884\pi$
$499$	−2.88385e9	−1.03901	−0.519507	+	0.854466i	$0.673884\pi$
$500$	−1.23651e9	−0.442387
$501$	0	0
$502$	−3.28375e9	−1.15853
$503$	−2.74533e9	−0.961849	−0.480925	−	0.876762i	$-0.659699\pi$
$503$	−2.74533e9	−0.961849	−0.480925	+	0.876762i	$0.659699\pi$
$504$	0	0
$505$	−3.37286e8	−0.116541
$506$	1.07307e9	0.368215
$507$	0	0
$508$	−9.26124e9	−3.13434
$509$	1.01298e9	0.340477	0.170238	−	0.985403i	$-0.445546\pi$
$509$	1.01298e9	0.340477	0.170238	+	0.985403i	$0.445546\pi$
$510$	0	0
$511$	−1.44769e9	−0.479956
$512$	4.62803e9	1.52388
$513$	0	0
$514$	−1.11811e9	−0.363173
$515$	1.83075e8	0.0590614
$516$	0	0
$517$	4.32443e9	1.37630
$518$	−3.39949e8	−0.107463
$519$	0	0
$520$	8.42527e8	0.262768
$521$	−2.83889e9	−0.879459	−0.439730	−	0.898130i	$-0.644926\pi$
$521$	−2.83889e9	−0.879459	−0.439730	+	0.898130i	$0.644926\pi$
$522$	0	0
$523$	−1.90587e9	−0.582555	−0.291278	−	0.956639i	$-0.594080\pi$
$523$	−1.90587e9	−0.582555	−0.291278	+	0.956639i	$0.594080\pi$
$524$	3.33547e9	1.01274
$525$	0	0
$526$	−4.25797e9	−1.27571
$527$	−6.61539e8	−0.196888
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	3.96905e8	0.115803
$531$	0	0
$532$	−2.38440e9	−0.686575
$533$	7.41150e9	2.12012
$534$	0	0
$535$	3.04547e8	0.0859838
$536$	−1.08708e10	−3.04919
$537$	0	0
$538$	−7.31141e8	−0.202425
$539$	2.77361e9	0.762929
$540$	0	0
$541$	−3.17124e9	−0.861070	−0.430535	−	0.902574i	$-0.641675\pi$
$541$	−3.17124e9	−0.861070	−0.430535	+	0.902574i	$0.641675\pi$
$542$	−2.58827e9	−0.698251
$543$	0	0
$544$	−4.71670e8	−0.125615
$545$	3.90505e8	0.103333
$546$	0	0
$547$	5.19778e9	1.35788	0.678941	−	0.734193i	$-0.262439\pi$
$547$	5.19778e9	1.35788	0.678941	+	0.734193i	$0.262439\pi$
$548$	−9.18187e9	−2.38341
$549$	0	0
$550$	−6.80019e9	−1.74282
$551$	6.56758e8	0.167253
$552$	0	0
$553$	3.09527e9	0.778325
$554$	−1.09048e10	−2.72479
$555$	0	0
$556$	5.24943e9	1.29524
$557$	−1.45144e8	−0.0355882	−0.0177941	−	0.999842i	$-0.505664\pi$
$557$	−1.45144e8	−0.0355882	−0.0177941	+	0.999842i	$0.505664\pi$
$558$	0	0
$559$	−8.95687e9	−2.16878
$560$	−2.04162e8	−0.0491265
$561$	0	0
$562$	1.09354e10	2.59871
$563$	4.84897e9	1.14517	0.572585	−	0.819845i	$-0.305940\pi$
$563$	4.84897e9	1.14517	0.572585	+	0.819845i	$0.305940\pi$
$564$	0	0
$565$	3.93400e8	0.0917623
$566$	−1.29463e10	−3.00116
$567$	0	0
$568$	−3.43241e9	−0.785924
$569$	−3.67260e9	−0.835759	−0.417879	−	0.908503i	$-0.637227\pi$
$569$	−3.67260e9	−0.835759	−0.417879	+	0.908503i	$0.637227\pi$
$570$	0	0
$571$	−3.48704e9	−0.783845	−0.391922	−	0.919998i	$-0.628190\pi$
$571$	−3.48704e9	−0.783845	−0.391922	+	0.919998i	$0.628190\pi$
$572$	1.26679e10	2.83021
$573$	0	0
$574$	−5.93236e9	−1.30929
$575$	−9.38125e8	−0.205789
$576$	0	0
$577$	3.61850e9	0.784175	0.392087	−	0.919928i	$-0.371753\pi$
$577$	3.61850e9	0.784175	0.392087	+	0.919928i	$0.371753\pi$
$578$	3.86946e9	0.833494
$579$	0	0
$580$	2.52251e8	0.0536828
$581$	−3.76707e9	−0.796869
$582$	0	0
$583$	2.90362e9	0.606876
$584$	−7.39602e9	−1.53657
$585$	0	0
$586$	−1.34132e10	−2.75355
$587$	−6.71119e7	−0.0136951	−0.00684757	−	0.999977i	$-0.502180\pi$
$587$	−6.71119e7	−0.0136951	−0.00684757	+	0.999977i	$0.502180\pi$
$588$	0	0
$589$	9.44230e8	0.190403
$590$	1.11450e9	0.223407
$591$	0	0
$592$	−5.25782e8	−0.104155
$593$	−1.87365e9	−0.368976	−0.184488	−	0.982835i	$-0.559063\pi$
$593$	−1.87365e9	−0.368976	−0.184488	+	0.982835i	$0.559063\pi$
$594$	0	0
$595$	2.14116e8	0.0416716
$596$	1.37918e10	2.66845
$597$	0	0
$598$	2.64491e9	0.505774
$599$	−8.95545e9	−1.70253	−0.851263	−	0.524739i	$-0.824163\pi$
$599$	−8.95545e9	−1.70253	−0.851263	+	0.524739i	$0.824163\pi$
$600$	0	0
$601$	7.89076e9	1.48272	0.741358	−	0.671110i	$-0.234182\pi$
$601$	7.89076e9	1.48272	0.741358	+	0.671110i	$0.234182\pi$
$602$	7.16932e9	1.33934
$603$	0	0
$604$	−1.97043e9	−0.363858
$605$	3.60714e7	0.00662245
$606$	0	0
$607$	2.38885e9	0.433540	0.216770	−	0.976223i	$-0.430448\pi$
$607$	2.38885e9	0.433540	0.216770	+	0.976223i	$0.430448\pi$
$608$	6.73225e8	0.121478
$609$	0	0
$610$	1.62880e9	0.290546
$611$	1.06589e10	1.89046
$612$	0	0
$613$	−6.37578e9	−1.11795	−0.558974	−	0.829185i	$-0.688805\pi$
$613$	−6.37578e9	−1.11795	−0.558974	+	0.829185i	$0.688805\pi$
$614$	−5.69464e9	−0.992835
$615$	0	0
$616$	−4.93353e9	−0.850405
$617$	−3.95188e9	−0.677339	−0.338669	−	0.940905i	$-0.609977\pi$
$617$	−3.95188e9	−0.677339	−0.338669	+	0.940905i	$0.609977\pi$
$618$	0	0
$619$	−5.24085e9	−0.888147	−0.444073	−	0.895990i	$-0.646467\pi$
$619$	−5.24085e9	−0.888147	−0.444073	+	0.895990i	$0.646467\pi$
$620$	3.62665e8	0.0611132
$621$	0	0
$622$	−1.15311e10	−1.92134
$623$	−2.11798e9	−0.350925
$624$	0	0
$625$	5.86527e9	0.960965
$626$	−1.73117e10	−2.82052
$627$	0	0
$628$	1.45460e10	2.34361
$629$	5.51419e8	0.0883495
$630$	0	0
$631$	−3.53246e9	−0.559725	−0.279862	−	0.960040i	$-0.590289\pi$
$631$	−3.53246e9	−0.559725	−0.279862	+	0.960040i	$0.590289\pi$
$632$	1.58133e10	2.49180
$633$	0	0
$634$	1.99753e10	3.11301
$635$	−1.18703e9	−0.183973
$636$	0	0
$637$	6.83640e9	1.04795
$638$	2.79288e9	0.425775
$639$	0	0
$640$	1.35925e9	0.204960
$641$	1.22614e9	0.183881	0.0919404	−	0.995765i	$-0.470693\pi$
$641$	1.22614e9	0.183881	0.0919404	+	0.995765i	$0.470693\pi$
$642$	0	0
$643$	−4.95336e9	−0.734787	−0.367394	−	0.930066i	$-0.619750\pi$
$643$	−4.95336e9	−0.734787	−0.367394	+	0.930066i	$0.619750\pi$
$644$	−1.39883e9	−0.206379
$645$	0	0
$646$	5.85347e9	0.854278
$647$	5.83163e9	0.846496	0.423248	−	0.906014i	$-0.360890\pi$
$647$	5.83163e9	0.846496	0.423248	+	0.906014i	$0.360890\pi$
$648$	0	0
$649$	8.15327e9	1.17078
$650$	−1.67612e10	−2.39391
$651$	0	0
$652$	−1.30986e10	−1.85080
$653$	−4.46418e9	−0.627402	−0.313701	−	0.949522i	$-0.601569\pi$
$653$	−4.46418e9	−0.627402	−0.313701	+	0.949522i	$0.601569\pi$
$654$	0	0
$655$	4.27513e8	0.0594435
$656$	−9.17529e9	−1.26898
$657$	0	0
$658$	−8.53165e9	−1.16746
$659$	2.01518e9	0.274294	0.137147	−	0.990551i	$-0.456207\pi$
$659$	2.01518e9	0.274294	0.137147	+	0.990551i	$0.456207\pi$
$660$	0	0
$661$	−1.19004e10	−1.60271	−0.801355	−	0.598189i	$-0.795887\pi$
$661$	−1.19004e10	−1.60271	−0.801355	+	0.598189i	$0.795887\pi$
$662$	5.91679e9	0.792653
$663$	0	0
$664$	−1.92454e10	−2.55116
$665$	−3.05613e8	−0.0402991
$666$	0	0
$667$	3.85294e8	0.0502749
$668$	−5.71319e9	−0.741586
$669$	0	0
$670$	−2.86366e9	−0.367841
$671$	1.19158e10	1.52262
$672$	0	0
$673$	8.49880e7	0.0107474	0.00537372	−	0.999986i	$-0.498289\pi$
$673$	8.49880e7	0.0107474	0.00537372	+	0.999986i	$0.498289\pi$
$674$	−1.43406e10	−1.80409
$675$	0	0
$676$	1.55809e10	1.93990
$677$	1.24072e10	1.53679	0.768393	−	0.639979i	$-0.221057\pi$
$677$	1.24072e10	1.53679	0.768393	+	0.639979i	$0.221057\pi$
$678$	0	0
$679$	2.70139e9	0.331164
$680$	1.09389e9	0.133411
$681$	0	0
$682$	4.01537e9	0.484708
$683$	−9.35039e9	−1.12294	−0.561471	−	0.827496i	$-0.689764\pi$
$683$	−9.35039e9	−1.12294	−0.561471	+	0.827496i	$0.689764\pi$
$684$	0	0
$685$	−1.17686e9	−0.139896
$686$	−1.28493e10	−1.51965
$687$	0	0
$688$	1.10884e10	1.29811
$689$	7.15686e9	0.833596
$690$	0	0
$691$	−2.51962e9	−0.290511	−0.145255	−	0.989394i	$-0.546400\pi$
$691$	−2.51962e9	−0.290511	−0.145255	+	0.989394i	$0.546400\pi$
$692$	1.29844e10	1.48953
$693$	0	0
$694$	2.32099e10	2.63582
$695$	6.72829e8	0.0760252
$696$	0	0
$697$	9.62266e9	1.07642
$698$	6.47103e9	0.720243
$699$	0	0
$700$	8.86460e9	0.976823
$701$	8.81005e9	0.965973	0.482987	−	0.875628i	$-0.339552\pi$
$701$	8.81005e9	0.965973	0.482987	+	0.875628i	$0.339552\pi$
$702$	0	0
$703$	−7.87052e8	−0.0854398
$704$	1.09151e10	1.17902
$705$	0	0
$706$	−7.89770e9	−0.844665
$707$	4.86806e9	0.518069
$708$	0	0
$709$	−1.59837e10	−1.68428	−0.842142	−	0.539256i	$-0.818705\pi$
$709$	−1.59837e10	−1.68428	−0.842142	+	0.539256i	$0.818705\pi$
$710$	−9.04191e8	−0.0948104
$711$	0	0
$712$	−1.08205e10	−1.12348
$713$	5.53942e8	0.0572336
$714$	0	0
$715$	1.62367e9	0.166122
$716$	1.72916e10	1.76051
$717$	0	0
$718$	7.92431e9	0.798962
$719$	1.38835e10	1.39299	0.696496	−	0.717561i	$-0.254742\pi$
$719$	1.38835e10	1.39299	0.696496	+	0.717561i	$0.254742\pi$
$720$	0	0
$721$	−2.64232e9	−0.262550
$722$	9.00789e9	0.890723
$723$	0	0
$724$	2.15977e10	2.11506
$725$	−2.44166e9	−0.237959
$726$	0	0
$727$	−9.03760e9	−0.872334	−0.436167	−	0.899866i	$-0.643664\pi$
$727$	−9.03760e9	−0.872334	−0.436167	+	0.899866i	$0.643664\pi$
$728$	−1.21602e10	−1.16810
$729$	0	0
$730$	−1.94831e9	−0.185366
$731$	−1.16291e10	−1.10112
$732$	0	0
$733$	9.91766e9	0.930133	0.465067	−	0.885276i	$-0.346030\pi$
$733$	9.91766e9	0.930133	0.465067	+	0.885276i	$0.346030\pi$
$734$	1.89529e10	1.76905
$735$	0	0
$736$	3.94954e8	0.0365153
$737$	−2.09495e10	−1.92769
$738$	0	0
$739$	−9.63558e9	−0.878258	−0.439129	−	0.898424i	$-0.644713\pi$
$739$	−9.63558e9	−0.878258	−0.439129	+	0.898424i	$0.644713\pi$
$740$	−3.02295e8	−0.0274233
$741$	0	0
$742$	−5.72854e9	−0.514791
$743$	1.25237e10	1.12013	0.560067	−	0.828447i	$-0.310775\pi$
$743$	1.25237e10	1.12013	0.560067	+	0.828447i	$0.310775\pi$
$744$	0	0
$745$	1.76772e9	0.156627
$746$	1.82741e10	1.61157
$747$	0	0
$748$	1.64473e10	1.43694
$749$	−4.39554e9	−0.382231
$750$	0	0
$751$	1.22905e10	1.05884	0.529420	−	0.848360i	$-0.322410\pi$
$751$	1.22905e10	1.05884	0.529420	+	0.848360i	$0.322410\pi$
$752$	−1.31955e10	−1.13152
$753$	0	0
$754$	6.88391e9	0.584838
$755$	−2.52554e8	−0.0213570
$756$	0	0
$757$	1.22456e10	1.02600	0.512998	−	0.858390i	$-0.328535\pi$
$757$	1.22456e10	1.02600	0.512998	+	0.858390i	$0.328535\pi$
$758$	−4.24666e9	−0.354165
$759$	0	0
$760$	−1.56133e9	−0.129017
$761$	−5.82263e9	−0.478931	−0.239465	−	0.970905i	$-0.576972\pi$
$761$	−5.82263e9	−0.478931	−0.239465	+	0.970905i	$0.576972\pi$
$762$	0	0
$763$	−5.63617e9	−0.459355
$764$	1.75192e9	0.142131
$765$	0	0
$766$	−6.69435e8	−0.0538155
$767$	2.00962e10	1.60817
$768$	0	0
$769$	1.85949e9	0.147452	0.0737260	−	0.997279i	$-0.476511\pi$
$769$	1.85949e9	0.147452	0.0737260	+	0.997279i	$0.476511\pi$
$770$	−1.29963e9	−0.102589
$771$	0	0
$772$	−6.81738e9	−0.533282
$773$	−1.40809e10	−1.09649	−0.548243	−	0.836319i	$-0.684703\pi$
$773$	−1.40809e10	−1.09649	−0.548243	+	0.836319i	$0.684703\pi$
$774$	0	0
$775$	−3.51041e9	−0.270896
$776$	1.38010e10	1.06022
$777$	0	0
$778$	−2.07168e10	−1.57723
$779$	−1.37346e10	−1.04097
$780$	0	0
$781$	−6.61475e9	−0.496861
$782$	3.43399e9	0.256789
$783$	0	0
$784$	−8.46333e9	−0.627242
$785$	1.86439e9	0.137560
$786$	0	0
$787$	1.00606e10	0.735717	0.367858	−	0.929882i	$-0.380091\pi$
$787$	1.00606e10	0.735717	0.367858	+	0.929882i	$0.380091\pi$
$788$	−1.68498e9	−0.122674
$789$	0	0
$790$	4.16565e9	0.300599
$791$	−5.67795e9	−0.407919
$792$	0	0
$793$	2.93700e10	2.09145
$794$	3.28014e10	2.32552
$795$	0	0
$796$	−1.54557e10	−1.08616
$797$	1.12447e10	0.786764	0.393382	−	0.919375i	$-0.371305\pi$
$797$	1.12447e10	0.786764	0.393382	+	0.919375i	$0.371305\pi$
$798$	0	0
$799$	1.38389e10	0.959814
$800$	−2.50288e9	−0.172833
$801$	0	0
$802$	3.05802e10	2.09329
$803$	−1.42532e10	−0.971421
$804$	0	0
$805$	−1.79291e8	−0.0121136
$806$	9.89710e9	0.665787
$807$	0	0
$808$	2.48702e10	1.65859
$809$	1.46201e10	0.970804	0.485402	−	0.874291i	$-0.338673\pi$
$809$	1.46201e10	0.970804	0.485402	+	0.874291i	$0.338673\pi$
$810$	0	0
$811$	7.54458e9	0.496663	0.248332	−	0.968675i	$-0.420118\pi$
$811$	7.54458e9	0.496663	0.248332	+	0.968675i	$0.420118\pi$
$812$	−3.64074e9	−0.238640
$813$	0	0
$814$	−3.34696e9	−0.217503
$815$	−1.67888e9	−0.108634
$816$	0	0
$817$	1.65984e10	1.06485
$818$	−8.71873e9	−0.556950
$819$	0	0
$820$	−5.27528e9	−0.334116
$821$	−1.11248e10	−0.701601	−0.350800	−	0.936450i	$-0.614090\pi$
$821$	−1.11248e10	−0.701601	−0.350800	+	0.936450i	$0.614090\pi$
$822$	0	0
$823$	7.31892e9	0.457665	0.228833	−	0.973466i	$-0.426509\pi$
$823$	7.31892e9	0.457665	0.228833	+	0.973466i	$0.426509\pi$
$824$	−1.34992e10	−0.840551
$825$	0	0
$826$	−1.60856e10	−0.993130
$827$	3.81082e9	0.234288	0.117144	−	0.993115i	$-0.462626\pi$
$827$	3.81082e9	0.234288	0.117144	+	0.993115i	$0.462626\pi$
$828$	0	0
$829$	−7.19105e9	−0.438381	−0.219190	−	0.975682i	$-0.570342\pi$
$829$	−7.19105e9	−0.438381	−0.219190	+	0.975682i	$0.570342\pi$
$830$	−5.06976e9	−0.307761
$831$	0	0
$832$	2.69035e10	1.61949
$833$	8.87599e9	0.532058
$834$	0	0
$835$	−7.32271e8	−0.0435280
$836$	−2.34756e10	−1.38961
$837$	0	0
$838$	4.11057e10	2.41295
$839$	1.28144e10	0.749085	0.374543	−	0.927210i	$-0.377800\pi$
$839$	1.28144e10	0.749085	0.374543	+	0.927210i	$0.377800\pi$
$840$	0	0
$841$	−1.62471e10	−0.941866
$842$	3.13709e10	1.81107
$843$	0	0
$844$	−3.32354e10	−1.90284
$845$	1.99704e9	0.113864
$846$	0	0
$847$	−5.20619e8	−0.0294393
$848$	−8.86005e9	−0.498943
$849$	0	0
$850$	−2.17617e10	−1.21542
$851$	−4.61732e8	−0.0256825
$852$	0	0
$853$	−1.63523e10	−0.902103	−0.451052	−	0.892498i	$-0.648951\pi$
$853$	−1.63523e10	−0.902103	−0.451052	+	0.892498i	$0.648951\pi$
$854$	−2.35086e10	−1.29159
$855$	0	0
$856$	−2.24562e10	−1.22371
$857$	1.26845e10	0.688401	0.344201	−	0.938896i	$-0.388150\pi$
$857$	1.26845e10	0.688401	0.344201	+	0.938896i	$0.388150\pi$
$858$	0	0
$859$	−1.07437e10	−0.578334	−0.289167	−	0.957279i	$-0.593378\pi$
$859$	−1.07437e10	−0.578334	−0.289167	+	0.957279i	$0.593378\pi$
$860$	6.37522e9	0.341783
$861$	0	0
$862$	−4.40681e9	−0.234341
$863$	−3.31964e9	−0.175814	−0.0879070	−	0.996129i	$-0.528018\pi$
$863$	−3.31964e9	−0.175814	−0.0879070	+	0.996129i	$0.528018\pi$
$864$	0	0
$865$	1.66423e9	0.0874293
$866$	2.60423e10	1.36260
$867$	0	0
$868$	−5.23435e9	−0.271671
$869$	3.04744e10	1.57531
$870$	0	0
$871$	−5.16365e10	−2.64785
$872$	−2.87944e10	−1.47062
$873$	0	0
$874$	−4.90142e9	−0.248332
$875$	2.28743e9	0.115430
$876$	0	0
$877$	1.15145e9	0.0576431	0.0288215	−	0.999585i	$-0.490825\pi$
$877$	1.15145e9	0.0576431	0.0288215	+	0.999585i	$0.490825\pi$
$878$	−4.81331e10	−2.40001
$879$	0	0
$880$	−2.01007e9	−0.0994309
$881$	−2.47306e10	−1.21848	−0.609242	−	0.792984i	$-0.708526\pi$
$881$	−2.47306e10	−1.21848	−0.609242	+	0.792984i	$0.708526\pi$
$882$	0	0
$883$	6.69486e9	0.327250	0.163625	−	0.986523i	$-0.447681\pi$
$883$	6.69486e9	0.327250	0.163625	+	0.986523i	$0.447681\pi$
$884$	4.05393e10	1.97376
$885$	0	0
$886$	−6.71171e10	−3.24202
$887$	−2.11862e10	−1.01934	−0.509672	−	0.860369i	$-0.670233\pi$
$887$	−2.11862e10	−1.01934	−0.509672	+	0.860369i	$0.670233\pi$
$888$	0	0
$889$	1.71324e10	0.817830
$890$	−2.85041e9	−0.135532
$891$	0	0
$892$	−1.39977e10	−0.660357
$893$	−1.97525e10	−0.928203
$894$	0	0
$895$	2.21630e9	0.103335
$896$	−1.96181e10	−0.911127
$897$	0	0
$898$	−7.09777e10	−3.27080
$899$	1.44175e9	0.0661805
$900$	0	0
$901$	9.29205e9	0.423229
$902$	−5.84070e10	−2.64998
$903$	0	0
$904$	−2.90078e10	−1.30595
$905$	2.76822e9	0.124145
$906$	0	0
$907$	−1.42788e10	−0.635426	−0.317713	−	0.948187i	$-0.602915\pi$
$907$	−1.42788e10	−0.635426	−0.317713	+	0.948187i	$0.602915\pi$
$908$	−4.86855e10	−2.15824
$909$	0	0
$910$	−3.20333e9	−0.140915
$911$	−2.63971e10	−1.15676	−0.578379	−	0.815768i	$-0.696315\pi$
$911$	−2.63971e10	−1.15676	−0.578379	+	0.815768i	$0.696315\pi$
$912$	0	0
$913$	−3.70886e10	−1.61284
$914$	−6.49113e10	−2.81195
$915$	0	0
$916$	7.66545e10	3.29537
$917$	−6.17030e9	−0.264249
$918$	0	0
$919$	−1.25404e10	−0.532976	−0.266488	−	0.963838i	$-0.585863\pi$
$919$	−1.25404e10	−0.532976	−0.266488	+	0.963838i	$0.585863\pi$
$920$	−9.15971e8	−0.0387815
$921$	0	0
$922$	5.43201e10	2.28245
$923$	−1.63041e10	−0.682480
$924$	0	0
$925$	2.92606e9	0.121559
$926$	−5.67103e10	−2.34706
$927$	0	0
$928$	1.02795e9	0.0422234
$929$	2.25667e9	0.0923450	0.0461725	−	0.998933i	$-0.485298\pi$
$929$	2.25667e9	0.0923450	0.0461725	+	0.998933i	$0.485298\pi$
$930$	0	0
$931$	−1.26689e10	−0.514535
$932$	7.98804e10	3.23210
$933$	0	0
$934$	5.96934e10	2.39725
$935$	2.10808e9	0.0843424
$936$	0	0
$937$	−4.10624e10	−1.63063	−0.815315	−	0.579017i	$-0.803436\pi$
$937$	−4.10624e10	−1.63063	−0.815315	+	0.579017i	$0.803436\pi$
$938$	4.13313e10	1.63519
$939$	0	0
$940$	−7.58666e9	−0.297922
$941$	2.83833e10	1.11045	0.555225	−	0.831700i	$-0.312632\pi$
$941$	2.83833e10	1.11045	0.555225	+	0.831700i	$0.312632\pi$
$942$	0	0
$943$	−8.05757e9	−0.312905
$944$	−2.48787e10	−0.962557
$945$	0	0
$946$	7.05854e10	2.71079
$947$	−2.68264e9	−0.102645	−0.0513225	−	0.998682i	$-0.516344\pi$
$947$	−2.68264e9	−0.102645	−0.0513225	+	0.998682i	$0.516344\pi$
$948$	0	0
$949$	−3.51313e10	−1.33433
$950$	3.10610e10	1.17539
$951$	0	0
$952$	−1.57881e10	−0.593063
$953$	−2.13426e10	−0.798770	−0.399385	−	0.916783i	$-0.630776\pi$
$953$	−2.13426e10	−0.798770	−0.399385	+	0.916783i	$0.630776\pi$
$954$	0	0
$955$	2.24547e8	0.00834250
$956$	2.68757e10	0.994850
$957$	0	0
$958$	6.59714e9	0.242424
$959$	1.69856e10	0.621893
$960$	0	0
$961$	−2.54398e10	−0.924659
$962$	−8.24962e9	−0.298759
$963$	0	0
$964$	4.93968e10	1.77594
$965$	−8.73796e8	−0.0313015
$966$	0	0
$967$	3.65959e10	1.30149	0.650743	−	0.759298i	$-0.274458\pi$
$967$	3.65959e10	1.30149	0.650743	+	0.759298i	$0.274458\pi$
$968$	−2.65977e9	−0.0942496
$969$	0	0
$970$	3.63556e9	0.127900
$971$	3.22880e10	1.13181	0.565905	−	0.824471i	$-0.308527\pi$
$971$	3.22880e10	1.13181	0.565905	+	0.824471i	$0.308527\pi$
$972$	0	0
$973$	−9.71095e9	−0.337961
$974$	−1.43478e10	−0.497542
$975$	0	0
$976$	−3.63595e10	−1.25183
$977$	−2.74321e10	−0.941082	−0.470541	−	0.882378i	$-0.655941\pi$
$977$	−2.74321e10	−0.941082	−0.470541	+	0.882378i	$0.655941\pi$
$978$	0	0
$979$	−2.08526e10	−0.710264
$980$	−4.86594e9	−0.165149
$981$	0	0
$982$	4.91188e9	0.165523
$983$	−2.14416e10	−0.719980	−0.359990	−	0.932956i	$-0.617220\pi$
$983$	−2.14416e10	−0.719980	−0.359990	+	0.932956i	$0.617220\pi$
$984$	0	0
$985$	−2.15967e8	−0.00720046
$986$	8.93767e9	0.296931
$987$	0	0
$988$	−5.78627e10	−1.90875
$989$	9.73765e9	0.320086
$990$	0	0
$991$	−1.93552e10	−0.631743	−0.315872	−	0.948802i	$-0.602297\pi$
$991$	−1.93552e10	−0.631743	−0.315872	+	0.948802i	$0.602297\pi$
$992$	1.47790e9	0.0480677
$993$	0	0
$994$	1.30502e10	0.421469
$995$	−1.98098e9	−0.0637529
$996$	0	0
$997$	−2.41358e10	−0.771311	−0.385655	−	0.922643i	$-0.626025\pi$
$997$	−2.41358e10	−0.771311	−0.385655	+	0.922643i	$0.626025\pi$
$998$	5.60163e10	1.78385
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.f.1.2		8
3.2	odd	2		23.8.a.b.1.7	✓	8
12.11	even	2		368.8.a.h.1.4		8
15.14	odd	2		575.8.a.b.1.2		8
69.68	even	2		529.8.a.c.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.a.b.1.7	✓	8	3.2	odd	2
207.8.a.f.1.2		8	1.1	even	1	trivial
368.8.a.h.1.4		8	12.11	even	2
529.8.a.c.1.7		8	69.68	even	2
575.8.a.b.1.2		8	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)

\(f(q)\)	\(=\)	\(q-19.4241 q^{2} +249.296 q^{4} +31.9528 q^{5} -461.175 q^{7} -2356.08 q^{8} +O(q^{10})\)	\(q-19.4241 q^{2} +249.296 q^{4} +31.9528 q^{5} -461.175 q^{7} -2356.08 q^{8} -620.655 q^{10} -4540.49 q^{11} -11191.4 q^{13} +8957.92 q^{14} +13854.8 q^{16} -14530.3 q^{17} +20739.4 q^{19} +7965.72 q^{20} +88195.1 q^{22} +12167.0 q^{23} -77104.0 q^{25} +217384. q^{26} -114969. q^{28} +31667.1 q^{29} +45528.3 q^{31} +32461.1 q^{32} +282238. q^{34} -14735.8 q^{35} -37949.6 q^{37} -402845. q^{38} -75283.2 q^{40} -662248. q^{41} +800333. q^{43} -1.13193e6 q^{44} -236333. q^{46} -952414. q^{47} -610860. q^{49} +1.49768e6 q^{50} -2.78998e6 q^{52} -639495. q^{53} -145081. q^{55} +1.08656e6 q^{56} -615105. q^{58} -1.79568e6 q^{59} -2.62433e6 q^{61} -884346. q^{62} -2.40394e6 q^{64} -357597. q^{65} +4.61394e6 q^{67} -3.62235e6 q^{68} +286231. q^{70} +1.45683e6 q^{71} +3.13913e6 q^{73} +737137. q^{74} +5.17027e6 q^{76} +2.09396e6 q^{77} -6.71170e6 q^{79} +442698. q^{80} +1.28636e7 q^{82} +8.16841e6 q^{83} -464284. q^{85} -1.55458e7 q^{86} +1.06977e7 q^{88} +4.59258e6 q^{89} +5.16121e6 q^{91} +3.03319e6 q^{92} +1.84998e7 q^{94} +662683. q^{95} -5.85762e6 q^{97} +1.18654e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 640 q^{4} - 444 q^{5} + 1446 q^{7} - 3177 q^{8}+O(q^{10}) \) 8 * q + 640 * q^4 - 444 * q^5 + 1446 * q^7 - 3177 * q^8	\( 8 q + 640 q^{4} - 444 q^{5} + 1446 q^{7} - 3177 q^{8} + 19502 q^{10} - 7588 q^{11} + 19862 q^{13} - 17544 q^{14} + 64336 q^{16} - 42070 q^{17} + 1050 q^{19} - 3364 q^{20} - 128220 q^{22} + 97336 q^{23} + 49496 q^{25} + 371761 q^{26} + 143050 q^{28} + 102578 q^{29} + 304172 q^{31} + 612824 q^{32} - 524530 q^{34} - 531048 q^{35} + 286472 q^{37} + 762932 q^{38} + 2105286 q^{40} - 1324414 q^{41} + 2052578 q^{43} + 867298 q^{44} - 675556 q^{47} - 55404 q^{49} - 1458528 q^{50} - 1695409 q^{52} - 203654 q^{53} - 1024444 q^{55} + 5766846 q^{56} - 5039991 q^{58} + 748892 q^{59} + 61822 q^{61} + 4939277 q^{62} + 2702267 q^{64} + 1571618 q^{65} + 3235604 q^{67} - 4914980 q^{68} + 10871764 q^{70} + 4951664 q^{71} + 11019370 q^{73} - 356954 q^{74} + 21973240 q^{76} + 5284888 q^{77} + 4202464 q^{79} - 8785886 q^{80} + 32636759 q^{82} - 518568 q^{83} + 9854220 q^{85} + 14681386 q^{86} + 20589740 q^{88} - 4203864 q^{89} + 2488406 q^{91} + 7786880 q^{92} + 12314327 q^{94} + 44485300 q^{95} + 18621134 q^{97} - 35756 q^{98}+O(q^{100}) \) 8 * q + 640 * q^4 - 444 * q^5 + 1446 * q^7 - 3177 * q^8 + 19502 * q^10 - 7588 * q^11 + 19862 * q^13 - 17544 * q^14 + 64336 * q^16 - 42070 * q^17 + 1050 * q^19 - 3364 * q^20 - 128220 * q^22 + 97336 * q^23 + 49496 * q^25 + 371761 * q^26 + 143050 * q^28 + 102578 * q^29 + 304172 * q^31 + 612824 * q^32 - 524530 * q^34 - 531048 * q^35 + 286472 * q^37 + 762932 * q^38 + 2105286 * q^40 - 1324414 * q^41 + 2052578 * q^43 + 867298 * q^44 - 675556 * q^47 - 55404 * q^49 - 1458528 * q^50 - 1695409 * q^52 - 203654 * q^53 - 1024444 * q^55 + 5766846 * q^56 - 5039991 * q^58 + 748892 * q^59 + 61822 * q^61 + 4939277 * q^62 + 2702267 * q^64 + 1571618 * q^65 + 3235604 * q^67 - 4914980 * q^68 + 10871764 * q^70 + 4951664 * q^71 + 11019370 * q^73 - 356954 * q^74 + 21973240 * q^76 + 5284888 * q^77 + 4202464 * q^79 - 8785886 * q^80 + 32636759 * q^82 - 518568 * q^83 + 9854220 * q^85 + 14681386 * q^86 + 20589740 * q^88 - 4203864 * q^89 + 2488406 * q^91 + 7786880 * q^92 + 12314327 * q^94 + 44485300 * q^95 + 18621134 * q^97 - 35756 * q^98

Introduction

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