LMFDB - Embedded newform 207.8.a.f.1.6

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			1.6
Root			$-7.41631$ 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)

$f(q)$	$=$	$q+7.41631 q^{2} -72.9984 q^{4} -376.733 q^{5} -902.074 q^{7} -1490.67 q^{8} +O(q^{10})$	\(q+7.41631 q^{2} -72.9984 q^{4} -376.733 q^{5} -902.074 q^{7} -1490.67 q^{8} -2793.97 q^{10} -7626.68 q^{11} +7028.41 q^{13} -6690.05 q^{14} -1711.44 q^{16} -27894.3 q^{17} -54578.2 q^{19} +27500.9 q^{20} -56561.8 q^{22} +12167.0 q^{23} +63802.7 q^{25} +52124.9 q^{26} +65849.9 q^{28} -55791.8 q^{29} +2175.47 q^{31} +178113. q^{32} -206872. q^{34} +339841. q^{35} -319241. q^{37} -404769. q^{38} +561583. q^{40} +1130.66 q^{41} -64643.1 q^{43} +556735. q^{44} +90234.2 q^{46} +743145. q^{47} -9806.08 q^{49} +473180. q^{50} -513063. q^{52} +1.21871e6 q^{53} +2.87322e6 q^{55} +1.34469e6 q^{56} -413769. q^{58} -1.29552e6 q^{59} +990092. q^{61} +16133.9 q^{62} +1.54000e6 q^{64} -2.64783e6 q^{65} -1.63534e6 q^{67} +2.03624e6 q^{68} +2.52036e6 q^{70} -1.25189e6 q^{71} +168373. q^{73} -2.36759e6 q^{74} +3.98412e6 q^{76} +6.87983e6 q^{77} -5.03956e6 q^{79} +644755. q^{80} +8385.33 q^{82} -9.63112e6 q^{83} +1.05087e7 q^{85} -479413. q^{86} +1.13688e7 q^{88} -2.11010e6 q^{89} -6.34015e6 q^{91} -888172. q^{92} +5.51139e6 q^{94} +2.05614e7 q^{95} -3.04753e6 q^{97} -72724.9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.41631	0.655515	0.327758	−	0.944762i	$-0.393707\pi$
$2$	7.41631	0.655515	0.327758	+	0.944762i	$0.393707\pi$
$3$	0	0
$3$	0	0
$4$	−72.9984	−0.570300
$5$	−376.733	−1.34784	−0.673920	−	0.738804i	$-0.735391\pi$
$5$	−376.733	−1.34784	−0.673920	+	0.738804i	$0.735391\pi$
$6$	0	0
$7$	−902.074	−0.994029	−0.497014	−	0.867742i	$-0.665570\pi$
$7$	−902.074	−0.994029	−0.497014	+	0.867742i	$0.665570\pi$
$8$	−1490.67	−1.02936
$9$	0	0
$10$	−2793.97	−0.883530
$11$	−7626.68	−1.72767	−0.863836	−	0.503774i	$-0.831945\pi$
$11$	−7626.68	−1.72767	−0.863836	+	0.503774i	$0.831945\pi$
$12$	0	0
$13$	7028.41	0.887270	0.443635	−	0.896208i	$-0.353689\pi$
$13$	7028.41	0.887270	0.443635	+	0.896208i	$0.353689\pi$
$14$	−6690.05	−0.651601
$15$	0	0
$16$	−1711.44	−0.104458
$17$	−27894.3	−1.37703	−0.688515	−	0.725222i	$-0.741737\pi$
$17$	−27894.3	−1.37703	−0.688515	+	0.725222i	$0.741737\pi$
$18$	0	0
$19$	−54578.2	−1.82550	−0.912750	−	0.408518i	$-0.866046\pi$
$19$	−54578.2	−1.82550	−0.912750	+	0.408518i	$0.866046\pi$
$20$	27500.9	0.768674
$21$	0	0
$22$	−56561.8	−1.13251
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	63802.7	0.816674
$26$	52124.9	0.581619
$27$	0	0
$28$	65849.9	0.566895
$29$	−55791.8	−0.424793	−0.212396	−	0.977184i	$-0.568127\pi$
$29$	−55791.8	−0.424793	−0.212396	+	0.977184i	$0.568127\pi$
$30$	0	0
$31$	2175.47	0.0131156	0.00655778	−	0.999978i	$-0.497913\pi$
$31$	2175.47	0.0131156	0.00655778	+	0.999978i	$0.497913\pi$
$32$	178113.	0.960882
$33$	0	0
$34$	−206872.	−0.902664
$35$	339841.	1.33979
$36$	0	0
$37$	−319241.	−1.03612	−0.518062	−	0.855343i	$-0.673346\pi$
$37$	−319241.	−1.03612	−0.518062	+	0.855343i	$0.673346\pi$
$38$	−404769.	−1.19664
$39$	0	0
$40$	561583.	1.38741
$41$	1130.66	0.00256206	0.00128103	−	0.999999i	$-0.499592\pi$
$41$	1130.66	0.00256206	0.00128103	+	0.999999i	$0.499592\pi$
$42$	0	0
$43$	−64643.1	−0.123989	−0.0619944	−	0.998076i	$-0.519746\pi$
$43$	−64643.1	−0.123989	−0.0619944	+	0.998076i	$0.519746\pi$
$44$	556735.	0.985291
$45$	0	0
$46$	90234.2	0.136684
$47$	743145.	1.04407	0.522036	−	0.852923i	$-0.325172\pi$
$47$	743145.	1.04407	0.522036	+	0.852923i	$0.325172\pi$
$48$	0	0
$49$	−9806.08	−0.0119072
$50$	473180.	0.535342
$51$	0	0
$52$	−513063.	−0.506010
$53$	1.21871e6	1.12444	0.562218	−	0.826989i	$-0.309948\pi$
$53$	1.21871e6	1.12444	0.562218	+	0.826989i	$0.309948\pi$
$54$	0	0
$55$	2.87322e6	2.32863
$56$	1.34469e6	1.02321
$57$	0	0
$58$	−413769.	−0.278458
$59$	−1.29552e6	−0.821222	−0.410611	−	0.911811i	$-0.634685\pi$
$59$	−1.29552e6	−0.821222	−0.410611	+	0.911811i	$0.634685\pi$
$60$	0	0
$61$	990092.	0.558497	0.279249	−	0.960219i	$-0.409915\pi$
$61$	990092.	0.558497	0.279249	+	0.960219i	$0.409915\pi$
$62$	16133.9	0.00859744
$63$	0	0
$64$	1.54000e6	0.734330
$65$	−2.64783e6	−1.19590
$66$	0	0
$67$	−1.63534e6	−0.664273	−0.332137	−	0.943231i	$-0.607769\pi$
$67$	−1.63534e6	−0.664273	−0.332137	+	0.943231i	$0.607769\pi$
$68$	2.03624e6	0.785321
$69$	0	0
$70$	2.52036e6	0.878254
$71$	−1.25189e6	−0.415110	−0.207555	−	0.978223i	$-0.566551\pi$
$71$	−1.25189e6	−0.415110	−0.207555	+	0.978223i	$0.566551\pi$
$72$	0	0
$73$	168373.	0.0506573	0.0253286	−	0.999679i	$-0.491937\pi$
$73$	168373.	0.0506573	0.0253286	+	0.999679i	$0.491937\pi$
$74$	−2.36759e6	−0.679195
$75$	0	0
$76$	3.98412e6	1.04108
$77$	6.87983e6	1.71735
$78$	0	0
$79$	−5.03956e6	−1.15000	−0.575000	−	0.818154i	$-0.694998\pi$
$79$	−5.03956e6	−1.15000	−0.575000	+	0.818154i	$0.694998\pi$
$80$	644755.	0.140793
$81$	0	0
$82$	8385.33	0.00167947
$83$	−9.63112e6	−1.84886	−0.924429	−	0.381355i	$-0.875458\pi$
$83$	−9.63112e6	−1.84886	−0.924429	+	0.381355i	$0.875458\pi$
$84$	0	0
$85$	1.05087e7	1.85602
$86$	−479413.	−0.0812766
$87$	0	0
$88$	1.13688e7	1.77839
$89$	−2.11010e6	−0.317276	−0.158638	−	0.987337i	$-0.550710\pi$
$89$	−2.11010e6	−0.317276	−0.158638	+	0.987337i	$0.550710\pi$
$90$	0	0
$91$	−6.34015e6	−0.881971
$92$	−888172.	−0.118916
$93$	0	0
$94$	5.51139e6	0.684406
$95$	2.05614e7	2.46048
$96$	0	0
$97$	−3.04753e6	−0.339037	−0.169518	−	0.985527i	$-0.554221\pi$
$97$	−3.04753e6	−0.339037	−0.169518	+	0.985527i	$0.554221\pi$
$98$	−72724.9	−0.00780534
$99$	0	0
$100$	−4.65749e6	−0.465749
$101$	1.58336e6	0.152917	0.0764583	−	0.997073i	$-0.475639\pi$
$101$	1.58336e6	0.152917	0.0764583	+	0.997073i	$0.475639\pi$
$102$	0	0
$103$	−1.20936e7	−1.09050	−0.545249	−	0.838274i	$-0.683565\pi$
$103$	−1.20936e7	−1.09050	−0.545249	+	0.838274i	$0.683565\pi$
$104$	−1.04770e7	−0.913316
$105$	0	0
$106$	9.03832e6	0.737084
$107$	−1.18754e7	−0.937140	−0.468570	−	0.883426i	$-0.655231\pi$
$107$	−1.18754e7	−0.937140	−0.468570	+	0.883426i	$0.655231\pi$
$108$	0	0
$109$	3.28058e6	0.242638	0.121319	−	0.992614i	$-0.461288\pi$
$109$	3.28058e6	0.242638	0.121319	+	0.992614i	$0.461288\pi$
$110$	2.13087e7	1.52645
$111$	0	0
$112$	1.54384e6	0.103834
$113$	−1.36981e7	−0.893073	−0.446536	−	0.894765i	$-0.647343\pi$
$113$	−1.36981e7	−0.893073	−0.446536	+	0.894765i	$0.647343\pi$
$114$	0	0
$115$	−4.58371e6	−0.281044
$116$	4.07271e6	0.242259
$117$	0	0
$118$	−9.60794e6	−0.538323
$119$	2.51627e7	1.36881
$120$	0	0
$121$	3.86791e7	1.98485
$122$	7.34282e6	0.366103
$123$	0	0
$124$	−158806.	−0.00747980
$125$	5.39569e6	0.247094
$126$	0	0
$127$	4.37621e6	0.189577	0.0947883	−	0.995497i	$-0.469783\pi$
$127$	4.37621e6	0.189577	0.0947883	+	0.995497i	$0.469783\pi$
$128$	−1.13773e7	−0.479517
$129$	0	0
$130$	−1.96372e7	−0.783929
$131$	3.88681e7	1.51058	0.755291	−	0.655390i	$-0.227496\pi$
$131$	3.88681e7	1.51058	0.755291	+	0.655390i	$0.227496\pi$
$132$	0	0
$133$	4.92336e7	1.81460
$134$	−1.21282e7	−0.435441
$135$	0	0
$136$	4.15810e7	1.41745
$137$	1.88290e7	0.625611	0.312805	−	0.949817i	$-0.398731\pi$
$137$	1.88290e7	0.625611	0.312805	+	0.949817i	$0.398731\pi$
$138$	0	0
$139$	−4.72630e7	−1.49269	−0.746345	−	0.665559i	$-0.768193\pi$
$139$	−4.72630e7	−1.49269	−0.746345	+	0.665559i	$0.768193\pi$
$140$	−2.48078e7	−0.764083
$141$	0	0
$142$	−9.28444e6	−0.272111
$143$	−5.36035e7	−1.53291
$144$	0	0
$145$	2.10186e7	0.572553
$146$	1.24870e6	0.0332066
$147$	0	0
$148$	2.33041e7	0.590902
$149$	−5.05967e7	−1.25306	−0.626528	−	0.779399i	$-0.715525\pi$
$149$	−5.05967e7	−1.25306	−0.626528	+	0.779399i	$0.715525\pi$
$150$	0	0
$151$	3.91785e6	0.0926038	0.0463019	−	0.998927i	$-0.485256\pi$
$151$	3.91785e6	0.0926038	0.0463019	+	0.998927i	$0.485256\pi$
$152$	8.13579e7	1.87909
$153$	0	0
$154$	5.10229e7	1.12575
$155$	−819570.	−0.0176777
$156$	0	0
$157$	−1.58413e7	−0.326694	−0.163347	−	0.986569i	$-0.552229\pi$
$157$	−1.58413e7	−0.326694	−0.163347	+	0.986569i	$0.552229\pi$
$158$	−3.73749e7	−0.753842
$159$	0	0
$160$	−6.71009e7	−1.29512
$161$	−1.09755e7	−0.207269
$162$	0	0
$163$	−4.32933e7	−0.783005	−0.391502	−	0.920177i	$-0.628045\pi$
$163$	−4.32933e7	−0.783005	−0.391502	+	0.920177i	$0.628045\pi$
$164$	−82536.5	−0.00146114
$165$	0	0
$166$	−7.14273e7	−1.21195
$167$	6.81498e6	0.113229	0.0566144	−	0.998396i	$-0.481969\pi$
$167$	6.81498e6	0.113229	0.0566144	+	0.998396i	$0.481969\pi$
$168$	0	0
$169$	−1.33499e7	−0.212753
$170$	7.79356e7	1.21665
$171$	0	0
$172$	4.71885e6	0.0707109
$173$	−9.61972e6	−0.141254	−0.0706270	−	0.997503i	$-0.522500\pi$
$173$	−9.61972e6	−0.141254	−0.0706270	+	0.997503i	$0.522500\pi$
$174$	0	0
$175$	−5.75547e7	−0.811798
$176$	1.30526e7	0.180469
$177$	0	0
$178$	−1.56491e7	−0.207979
$179$	−4.30258e7	−0.560716	−0.280358	−	0.959896i	$-0.590453\pi$
$179$	−4.30258e7	−0.560716	−0.280358	+	0.959896i	$0.590453\pi$
$180$	0	0
$181$	5.89816e7	0.739336	0.369668	−	0.929164i	$-0.379471\pi$
$181$	5.89816e7	0.739336	0.369668	+	0.929164i	$0.379471\pi$
$182$	−4.70205e7	−0.578145
$183$	0	0
$184$	−1.81369e7	−0.214635
$185$	1.20268e8	1.39653
$186$	0	0
$187$	2.12741e8	2.37906
$188$	−5.42484e7	−0.595435
$189$	0	0
$190$	1.52490e8	1.61288
$191$	7.80759e7	0.810774	0.405387	−	0.914145i	$-0.367137\pi$
$191$	7.80759e7	0.810774	0.405387	+	0.914145i	$0.367137\pi$
$192$	0	0
$193$	−1.06027e8	−1.06162	−0.530808	−	0.847492i	$-0.678111\pi$
$193$	−1.06027e8	−1.06162	−0.530808	+	0.847492i	$0.678111\pi$
$194$	−2.26014e7	−0.222244
$195$	0	0
$196$	715828.	0.00679067
$197$	−6.68123e7	−0.622622	−0.311311	−	0.950308i	$-0.600768\pi$
$197$	−6.68123e7	−0.622622	−0.311311	+	0.950308i	$0.600768\pi$
$198$	0	0
$199$	1.43281e8	1.28885	0.644426	−	0.764667i	$-0.277096\pi$
$199$	1.43281e8	1.28885	0.644426	+	0.764667i	$0.277096\pi$
$200$	−9.51085e7	−0.840648
$201$	0	0
$202$	1.17427e7	0.100239
$203$	5.03283e7	0.422256
$204$	0	0
$205$	−425957.	−0.00345325
$206$	−8.96897e7	−0.714837
$207$	0	0
$208$	−1.20287e7	−0.0926823
$209$	4.16251e8	3.15386
$210$	0	0
$211$	−9.05044e7	−0.663256	−0.331628	−	0.943410i	$-0.607598\pi$
$211$	−9.05044e7	−0.663256	−0.331628	+	0.943410i	$0.607598\pi$
$212$	−8.89638e7	−0.641266
$213$	0	0
$214$	−8.80715e7	−0.614309
$215$	2.43532e7	0.167117
$216$	0	0
$217$	−1.96243e6	−0.0130372
$218$	2.43298e7	0.159053
$219$	0	0
$220$	−2.09741e8	−1.32802
$221$	−1.96052e8	−1.22180
$222$	0	0
$223$	−2.67712e8	−1.61659	−0.808297	−	0.588775i	$-0.799610\pi$
$223$	−2.67712e8	−1.61659	−0.808297	+	0.588775i	$0.799610\pi$
$224$	−1.60671e8	−0.955144
$225$	0	0
$226$	−1.01590e8	−0.585423
$227$	−3.38479e8	−1.92062	−0.960311	−	0.278932i	$-0.910019\pi$
$227$	−3.38479e8	−1.92062	−0.960311	+	0.278932i	$0.910019\pi$
$228$	0	0
$229$	−1.93202e8	−1.06313	−0.531566	−	0.847017i	$-0.678396\pi$
$229$	−1.93202e8	−1.06313	−0.531566	+	0.847017i	$0.678396\pi$
$230$	−3.39942e7	−0.184229
$231$	0	0
$232$	8.31669e7	0.437263
$233$	−8.77640e7	−0.454538	−0.227269	−	0.973832i	$-0.572980\pi$
$233$	−8.77640e7	−0.454538	−0.227269	+	0.973832i	$0.572980\pi$
$234$	0	0
$235$	−2.79967e8	−1.40724
$236$	9.45706e7	0.468343
$237$	0	0
$238$	1.86614e8	0.897274
$239$	9.29015e7	0.440180	0.220090	−	0.975480i	$-0.429365\pi$
$239$	9.29015e7	0.440180	0.220090	+	0.975480i	$0.429365\pi$
$240$	0	0
$241$	2.01589e8	0.927699	0.463850	−	0.885914i	$-0.346468\pi$
$241$	2.01589e8	0.927699	0.463850	+	0.885914i	$0.346468\pi$
$242$	2.86856e8	1.30110
$243$	0	0
$244$	−7.22751e7	−0.318511
$245$	3.69427e6	0.0160490
$246$	0	0
$247$	−3.83598e8	−1.61971
$248$	−3.24289e6	−0.0135006
$249$	0	0
$250$	4.00161e7	0.161974
$251$	−1.61812e8	−0.645881	−0.322940	−	0.946419i	$-0.604671\pi$
$251$	−1.61812e8	−0.645881	−0.322940	+	0.946419i	$0.604671\pi$
$252$	0	0
$253$	−9.27938e7	−0.360244
$254$	3.24553e7	0.124270
$255$	0	0
$256$	−2.81498e8	−1.04866
$257$	−4.84885e8	−1.78186	−0.890928	−	0.454144i	$-0.849945\pi$
$257$	−4.84885e8	−1.78186	−0.890928	+	0.454144i	$0.849945\pi$
$258$	0	0
$259$	2.87978e8	1.02994
$260$	1.93288e8	0.682021
$261$	0	0
$262$	2.88258e8	0.990209
$263$	3.24801e8	1.10096	0.550481	−	0.834848i	$-0.314444\pi$
$263$	3.24801e8	1.10096	0.550481	+	0.834848i	$0.314444\pi$
$264$	0	0
$265$	−4.59128e8	−1.51556
$266$	3.65131e8	1.18950
$267$	0	0
$268$	1.19377e8	0.378835
$269$	4.32058e7	0.135335	0.0676674	−	0.997708i	$-0.478444\pi$
$269$	4.32058e7	0.135335	0.0676674	+	0.997708i	$0.478444\pi$
$270$	0	0
$271$	−6.50483e8	−1.98538	−0.992689	−	0.120698i	$-0.961487\pi$
$271$	−6.50483e8	−1.98538	−0.992689	+	0.120698i	$0.961487\pi$
$272$	4.77393e7	0.143842
$273$	0	0
$274$	1.39641e8	0.410097
$275$	−4.86603e8	−1.41095
$276$	0	0
$277$	5.37378e8	1.51915	0.759575	−	0.650419i	$-0.225407\pi$
$277$	5.37378e8	1.51915	0.759575	+	0.650419i	$0.225407\pi$
$278$	−3.50517e8	−0.978481
$279$	0	0
$280$	−5.06589e8	−1.37912
$281$	−4.15058e8	−1.11593	−0.557964	−	0.829865i	$-0.688417\pi$
$281$	−4.15058e8	−1.11593	−0.557964	+	0.829865i	$0.688417\pi$
$282$	0	0
$283$	6.53012e8	1.71265	0.856325	−	0.516437i	$-0.172742\pi$
$283$	6.53012e8	1.71265	0.856325	+	0.516437i	$0.172742\pi$
$284$	9.13863e7	0.236738
$285$	0	0
$286$	−3.97540e8	−1.00485
$287$	−1.01994e6	−0.00254676
$288$	0	0
$289$	3.67751e8	0.896214
$290$	1.55880e8	0.375317
$291$	0	0
$292$	−1.22909e7	−0.0288899
$293$	−5.88056e8	−1.36578	−0.682892	−	0.730520i	$-0.739278\pi$
$293$	−5.88056e8	−1.36578	−0.682892	+	0.730520i	$0.739278\pi$
$294$	0	0
$295$	4.88063e8	1.10688
$296$	4.75881e8	1.06654
$297$	0	0
$298$	−3.75241e8	−0.821397
$299$	8.55147e7	0.185008
$300$	0	0
$301$	5.83129e7	0.123248
$302$	2.90560e7	0.0607032
$303$	0	0
$304$	9.34072e7	0.190688
$305$	−3.73000e8	−0.752765
$306$	0	0
$307$	−2.36913e8	−0.467309	−0.233654	−	0.972320i	$-0.575068\pi$
$307$	−2.36913e8	−0.467309	−0.233654	+	0.972320i	$0.575068\pi$
$308$	−5.02216e8	−0.979407
$309$	0	0
$310$	−6.07818e6	−0.0115880
$311$	7.77890e8	1.46641	0.733207	−	0.680005i	$-0.238023\pi$
$311$	7.77890e8	1.46641	0.733207	+	0.680005i	$0.238023\pi$
$312$	0	0
$313$	−1.79054e8	−0.330049	−0.165024	−	0.986290i	$-0.552770\pi$
$313$	−1.79054e8	−0.330049	−0.165024	+	0.986290i	$0.552770\pi$
$314$	−1.17484e8	−0.214153
$315$	0	0
$316$	3.67880e8	0.655845
$317$	4.64965e7	0.0819809	0.0409905	−	0.999160i	$-0.486949\pi$
$317$	4.64965e7	0.0819809	0.0409905	+	0.999160i	$0.486949\pi$
$318$	0	0
$319$	4.25506e8	0.733902
$320$	−5.80169e8	−0.989760
$321$	0	0
$322$	−8.13979e7	−0.135868
$323$	1.52242e9	2.51377
$324$	0	0
$325$	4.48432e8	0.724610
$326$	−3.21077e8	−0.513271
$327$	0	0
$328$	−1.68544e6	−0.00263727
$329$	−6.70371e8	−1.03784
$330$	0	0
$331$	−6.50765e7	−0.0986339	−0.0493169	−	0.998783i	$-0.515704\pi$
$331$	−6.50765e7	−0.0986339	−0.0493169	+	0.998783i	$0.515704\pi$
$332$	7.03056e8	1.05440
$333$	0	0
$334$	5.05419e7	0.0742231
$335$	6.16087e8	0.895334
$336$	0	0
$337$	5.16934e8	0.735750	0.367875	−	0.929875i	$-0.380085\pi$
$337$	5.16934e8	0.735750	0.367875	+	0.929875i	$0.380085\pi$
$338$	−9.90071e7	−0.139463
$339$	0	0
$340$	−7.67117e8	−1.05849
$341$	−1.65916e7	−0.0226594
$342$	0	0
$343$	7.51742e8	1.00586
$344$	9.63613e7	0.127629
$345$	0	0
$346$	−7.13428e7	−0.0925941
$347$	−3.21796e8	−0.413454	−0.206727	−	0.978399i	$-0.566281\pi$
$347$	−3.21796e8	−0.413454	−0.206727	+	0.978399i	$0.566281\pi$
$348$	0	0
$349$	−1.40297e8	−0.176669	−0.0883346	−	0.996091i	$-0.528154\pi$
$349$	−1.40297e8	−0.176669	−0.0883346	+	0.996091i	$0.528154\pi$
$350$	−4.26843e8	−0.532146
$351$	0	0
$352$	−1.35841e9	−1.66009
$353$	1.14999e8	0.139149	0.0695747	−	0.997577i	$-0.477836\pi$
$353$	1.14999e8	0.139149	0.0695747	+	0.997577i	$0.477836\pi$
$354$	0	0
$355$	4.71630e8	0.559503
$356$	1.54034e8	0.180943
$357$	0	0
$358$	−3.19092e8	−0.367558
$359$	1.78108e8	0.203167	0.101583	−	0.994827i	$-0.467609\pi$
$359$	1.78108e8	0.203167	0.101583	+	0.994827i	$0.467609\pi$
$360$	0	0
$361$	2.08491e9	2.33245
$362$	4.37426e8	0.484646
$363$	0	0
$364$	4.62821e8	0.502988
$365$	−6.34316e7	−0.0682780
$366$	0	0
$367$	1.57710e9	1.66543	0.832717	−	0.553699i	$-0.186784\pi$
$367$	1.57710e9	1.66543	0.832717	+	0.553699i	$0.186784\pi$
$368$	−2.08231e7	−0.0217810
$369$	0	0
$370$	8.91947e8	0.915447
$371$	−1.09937e9	−1.11772
$372$	0	0
$373$	5.57282e8	0.556025	0.278013	−	0.960577i	$-0.410324\pi$
$373$	5.57282e8	0.556025	0.278013	+	0.960577i	$0.410324\pi$
$374$	1.57775e9	1.55951
$375$	0	0
$376$	−1.10778e9	−1.07472
$377$	−3.92128e8	−0.376906
$378$	0	0
$379$	8.27613e8	0.780890	0.390445	−	0.920626i	$-0.372321\pi$
$379$	8.27613e8	0.780890	0.390445	+	0.920626i	$0.372321\pi$
$380$	−1.50095e9	−1.40321
$381$	0	0
$382$	5.79034e8	0.531475
$383$	1.17119e9	1.06520	0.532602	−	0.846366i	$-0.321214\pi$
$383$	1.17119e9	1.06520	0.532602	+	0.846366i	$0.321214\pi$
$384$	0	0
$385$	−2.59186e9	−2.31472
$386$	−7.86332e8	−0.695905
$387$	0	0
$388$	2.22465e8	0.193353
$389$	1.70087e9	1.46503	0.732515	−	0.680751i	$-0.238346\pi$
$389$	1.70087e9	1.46503	0.732515	+	0.680751i	$0.238346\pi$
$390$	0	0
$391$	−3.39390e8	−0.287131
$392$	1.46176e7	0.0122567
$393$	0	0
$394$	−4.95501e8	−0.408138
$395$	1.89857e9	1.55002
$396$	0	0
$397$	5.38011e8	0.431543	0.215772	−	0.976444i	$-0.430773\pi$
$397$	5.38011e8	0.431543	0.215772	+	0.976444i	$0.430773\pi$
$398$	1.06262e9	0.844862
$399$	0	0
$400$	−1.09194e8	−0.0853080
$401$	−1.74431e7	−0.0135089	−0.00675443	−	0.999977i	$-0.502150\pi$
$401$	−1.74431e7	−0.0135089	−0.00675443	+	0.999977i	$0.502150\pi$
$402$	0	0
$403$	1.52901e7	0.0116370
$404$	−1.15583e8	−0.0872084
$405$	0	0
$406$	3.73250e8	0.276795
$407$	2.43475e9	1.79008
$408$	0	0
$409$	−1.51659e9	−1.09607	−0.548035	−	0.836456i	$-0.684624\pi$
$409$	−1.51659e9	−1.09607	−0.548035	+	0.836456i	$0.684624\pi$
$410$	−3.15903e6	−0.00226366
$411$	0	0
$412$	8.82812e8	0.621911
$413$	1.16865e9	0.816318
$414$	0	0
$415$	3.62836e9	2.49197
$416$	1.25185e9	0.852561
$417$	0	0
$418$	3.08704e9	2.06741
$419$	−2.53748e8	−0.168521	−0.0842603	−	0.996444i	$-0.526853\pi$
$419$	−2.53748e8	−0.168521	−0.0842603	+	0.996444i	$0.526853\pi$
$420$	0	0
$421$	−7.78971e8	−0.508784	−0.254392	−	0.967101i	$-0.581875\pi$
$421$	−7.78971e8	−0.508784	−0.254392	+	0.967101i	$0.581875\pi$
$422$	−6.71208e8	−0.434774
$423$	0	0
$424$	−1.81669e9	−1.15744
$425$	−1.77973e9	−1.12459
$426$	0	0
$427$	−8.93136e8	−0.555162
$428$	8.66884e8	0.534451
$429$	0	0
$430$	1.80611e8	0.109548
$431$	1.40312e9	0.844161	0.422080	−	0.906558i	$-0.361300\pi$
$431$	1.40312e9	0.844161	0.422080	+	0.906558i	$0.361300\pi$
$432$	0	0
$433$	5.75394e8	0.340610	0.170305	−	0.985391i	$-0.445525\pi$
$433$	5.75394e8	0.340610	0.170305	+	0.985391i	$0.445525\pi$
$434$	−1.45540e7	−0.00854610
$435$	0	0
$436$	−2.39477e8	−0.138376
$437$	−6.64053e8	−0.380643
$438$	0	0
$439$	−1.69516e9	−0.956280	−0.478140	−	0.878284i	$-0.658689\pi$
$439$	−1.69516e9	−0.956280	−0.478140	+	0.878284i	$0.658689\pi$
$440$	−4.28301e9	−2.39698
$441$	0	0
$442$	−1.45398e9	−0.800907
$443$	−1.83805e9	−1.00449	−0.502244	−	0.864726i	$-0.667492\pi$
$443$	−1.83805e9	−1.00449	−0.502244	+	0.864726i	$0.667492\pi$
$444$	0	0
$445$	7.94943e8	0.427638
$446$	−1.98543e9	−1.05970
$447$	0	0
$448$	−1.38920e9	−0.729945
$449$	−1.41972e9	−0.740186	−0.370093	−	0.928995i	$-0.620674\pi$
$449$	−1.41972e9	−0.740186	−0.370093	+	0.928995i	$0.620674\pi$
$450$	0	0
$451$	−8.62319e6	−0.00442639
$452$	9.99942e8	0.509319
$453$	0	0
$454$	−2.51027e9	−1.25900
$455$	2.38854e9	1.18876
$456$	0	0
$457$	3.08293e9	1.51097	0.755487	−	0.655164i	$-0.227400\pi$
$457$	3.08293e9	1.51097	0.755487	+	0.655164i	$0.227400\pi$
$458$	−1.43284e9	−0.696898
$459$	0	0
$460$	3.34603e8	0.160280
$461$	3.66779e9	1.74362	0.871810	−	0.489845i	$-0.162947\pi$
$461$	3.66779e9	1.74362	0.871810	+	0.489845i	$0.162947\pi$
$462$	0	0
$463$	−1.56614e9	−0.733328	−0.366664	−	0.930353i	$-0.619500\pi$
$463$	−1.56614e9	−0.733328	−0.366664	+	0.930353i	$0.619500\pi$
$464$	9.54841e7	0.0443729
$465$	0	0
$466$	−6.50885e8	−0.297957
$467$	−3.62021e9	−1.64484	−0.822421	−	0.568879i	$-0.807377\pi$
$467$	−3.62021e9	−1.64484	−0.822421	+	0.568879i	$0.807377\pi$
$468$	0	0
$469$	1.47520e9	0.660306
$470$	−2.07632e9	−0.922470
$471$	0	0
$472$	1.93118e9	0.845329
$473$	4.93012e8	0.214212
$474$	0	0
$475$	−3.48224e9	−1.49084
$476$	−1.83684e9	−0.780631
$477$	0	0
$478$	6.88986e8	0.288544
$479$	1.07598e9	0.447331	0.223665	−	0.974666i	$-0.428198\pi$
$479$	1.07598e9	0.447331	0.223665	+	0.974666i	$0.428198\pi$
$480$	0	0
$481$	−2.24375e9	−0.919322
$482$	1.49505e9	0.608121
$483$	0	0
$484$	−2.82351e9	−1.13196
$485$	1.14811e9	0.456968
$486$	0	0
$487$	4.79757e9	1.88222	0.941109	−	0.338103i	$-0.109785\pi$
$487$	4.79757e9	1.88222	0.941109	+	0.338103i	$0.109785\pi$
$488$	−1.47590e9	−0.574892
$489$	0	0
$490$	2.73979e7	0.0105204
$491$	−3.90095e9	−1.48725	−0.743627	−	0.668595i	$-0.766896\pi$
$491$	−3.90095e9	−1.48725	−0.743627	+	0.668595i	$0.766896\pi$
$492$	0	0
$493$	1.55627e9	0.584953
$494$	−2.84488e9	−1.06174
$495$	0	0
$496$	−3.72318e6	−0.00137002
$497$	1.12930e9	0.412632
$498$	0	0
$499$	−3.71148e9	−1.33720	−0.668599	−	0.743624i	$-0.733106\pi$
$499$	−3.71148e9	−1.33720	−0.668599	+	0.743624i	$0.733106\pi$
$500$	−3.93876e8	−0.140918
$501$	0	0
$502$	−1.20005e9	−0.423385
$503$	−8.97097e8	−0.314305	−0.157153	−	0.987574i	$-0.550231\pi$
$503$	−8.97097e8	−0.314305	−0.157153	+	0.987574i	$0.550231\pi$
$504$	0	0
$505$	−5.96504e8	−0.206107
$506$	−6.88187e8	−0.236146
$507$	0	0
$508$	−3.19456e8	−0.108116
$509$	−9.62066e8	−0.323365	−0.161682	−	0.986843i	$-0.551692\pi$
$509$	−9.62066e8	−0.323365	−0.161682	+	0.986843i	$0.551692\pi$
$510$	0	0
$511$	−1.51885e8	−0.0503548
$512$	−6.31380e8	−0.207896
$513$	0	0
$514$	−3.59605e9	−1.16803
$515$	4.55605e9	1.46982
$516$	0	0
$517$	−5.66773e9	−1.80381
$518$	2.13574e9	0.675140
$519$	0	0
$520$	3.94704e9	1.23100
$521$	−1.79750e9	−0.556848	−0.278424	−	0.960458i	$-0.589812\pi$
$521$	−1.79750e9	−0.556848	−0.278424	+	0.960458i	$0.589812\pi$
$522$	0	0
$523$	3.06457e9	0.936727	0.468363	−	0.883536i	$-0.344844\pi$
$523$	3.06457e9	0.936727	0.468363	+	0.883536i	$0.344844\pi$
$524$	−2.83731e9	−0.861485
$525$	0	0
$526$	2.40882e9	0.721697
$527$	−6.06831e7	−0.0180605
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−3.40503e9	−0.993472
$531$	0	0
$532$	−3.59397e9	−1.03487
$533$	7.94676e6	0.00227324
$534$	0	0
$535$	4.47385e9	1.26312
$536$	2.43775e9	0.683773
$537$	0	0
$538$	3.20428e8	0.0887140
$539$	7.47879e7	0.0205717
$540$	0	0
$541$	3.57698e9	0.971238	0.485619	−	0.874171i	$-0.338594\pi$
$541$	3.57698e9	0.971238	0.485619	+	0.874171i	$0.338594\pi$
$542$	−4.82418e9	−1.30145
$543$	0	0
$544$	−4.96832e9	−1.32316
$545$	−1.23590e9	−0.327037
$546$	0	0
$547$	−3.67029e9	−0.958838	−0.479419	−	0.877586i	$-0.659153\pi$
$547$	−3.67029e9	−0.958838	−0.479419	+	0.877586i	$0.659153\pi$
$548$	−1.37448e9	−0.356786
$549$	0	0
$550$	−3.60879e9	−0.924896
$551$	3.04502e9	0.775459
$552$	0	0
$553$	4.54605e9	1.14313
$554$	3.98536e9	0.995826
$555$	0	0
$556$	3.45013e9	0.851281
$557$	6.60186e8	0.161872	0.0809362	−	0.996719i	$-0.474209\pi$
$557$	6.60186e8	0.161872	0.0809362	+	0.996719i	$0.474209\pi$
$558$	0	0
$559$	−4.54339e8	−0.110012
$560$	−5.81616e8	−0.139952
$561$	0	0
$562$	−3.07820e9	−0.731508
$563$	1.82891e9	0.431931	0.215965	−	0.976401i	$-0.430710\pi$
$563$	1.82891e9	0.431931	0.215965	+	0.976401i	$0.430710\pi$
$564$	0	0
$565$	5.16054e9	1.20372
$566$	4.84294e9	1.12267
$567$	0	0
$568$	1.86616e9	0.427296
$569$	−8.08639e6	−0.00184019	−0.000920093	−	1.00000i	$-0.500293\pi$
$569$	−8.08639e6	−0.00184019	−0.000920093		1.00000i	$0.500293\pi$
$570$	0	0
$571$	5.07946e9	1.14180	0.570902	−	0.821018i	$-0.306594\pi$
$571$	5.07946e9	1.14180	0.570902	+	0.821018i	$0.306594\pi$
$572$	3.91297e9	0.874219
$573$	0	0
$574$	−7.56419e6	−0.00166944
$575$	7.76287e8	0.170288
$576$	0	0
$577$	−5.38743e9	−1.16753	−0.583763	−	0.811924i	$-0.698420\pi$
$577$	−5.38743e9	−1.16753	−0.583763	+	0.811924i	$0.698420\pi$
$578$	2.72736e9	0.587482
$579$	0	0
$580$	−1.53432e9	−0.326527
$581$	8.68798e9	1.83782
$582$	0	0
$583$	−9.29471e9	−1.94266
$584$	−2.50988e8	−0.0521444
$585$	0	0
$586$	−4.36120e9	−0.895291
$587$	−2.67277e8	−0.0545416	−0.0272708	−	0.999628i	$-0.508682\pi$
$587$	−2.67277e8	−0.0545416	−0.0272708	+	0.999628i	$0.508682\pi$
$588$	0	0
$589$	−1.18733e8	−0.0239424
$590$	3.61963e9	0.725574
$591$	0	0
$592$	5.46360e8	0.108231
$593$	−1.39914e9	−0.275531	−0.137766	−	0.990465i	$-0.543992\pi$
$593$	−1.39914e9	−0.275531	−0.137766	+	0.990465i	$0.543992\pi$
$594$	0	0
$595$	−9.47961e9	−1.84494
$596$	3.69348e9	0.714618
$597$	0	0
$598$	6.34203e8	0.121276
$599$	−9.72526e9	−1.84887	−0.924437	−	0.381335i	$-0.875464\pi$
$599$	−9.72526e9	−1.84887	−0.924437	+	0.381335i	$0.875464\pi$
$600$	0	0
$601$	2.35451e9	0.442426	0.221213	−	0.975226i	$-0.428998\pi$
$601$	2.35451e9	0.442426	0.221213	+	0.975226i	$0.428998\pi$
$602$	4.32466e8	0.0807912
$603$	0	0
$604$	−2.85997e8	−0.0528120
$605$	−1.45717e10	−2.67526
$606$	0	0
$607$	−4.08085e9	−0.740611	−0.370306	−	0.928910i	$-0.620747\pi$
$607$	−4.08085e9	−0.740611	−0.370306	+	0.928910i	$0.620747\pi$
$608$	−9.72108e9	−1.75409
$609$	0	0
$610$	−2.76628e9	−0.493449
$611$	5.22313e9	0.926374
$612$	0	0
$613$	2.81411e9	0.493434	0.246717	−	0.969088i	$-0.420648\pi$
$613$	2.81411e9	0.493434	0.246717	+	0.969088i	$0.420648\pi$
$614$	−1.75702e9	−0.306328
$615$	0	0
$616$	−1.02555e10	−1.76777
$617$	1.81164e9	0.310509	0.155255	−	0.987875i	$-0.450380\pi$
$617$	1.81164e9	0.310509	0.155255	+	0.987875i	$0.450380\pi$
$618$	0	0
$619$	6.68480e9	1.13285	0.566423	−	0.824114i	$-0.308327\pi$
$619$	6.68480e9	1.13285	0.566423	+	0.824114i	$0.308327\pi$
$620$	5.98273e7	0.0100816
$621$	0	0
$622$	5.76907e9	0.961257
$623$	1.90346e9	0.315382
$624$	0	0
$625$	−7.01732e9	−1.14972
$626$	−1.32792e9	−0.216352
$627$	0	0
$628$	1.15639e9	0.186313
$629$	8.90498e9	1.42678
$630$	0	0
$631$	−2.44991e9	−0.388192	−0.194096	−	0.980982i	$-0.562177\pi$
$631$	−2.44991e9	−0.388192	−0.194096	+	0.980982i	$0.562177\pi$
$632$	7.51230e9	1.18376
$633$	0	0
$634$	3.44832e8	0.0537397
$635$	−1.64866e9	−0.255519
$636$	0	0
$637$	−6.89212e7	−0.0105649
$638$	3.15568e9	0.481084
$639$	0	0
$640$	4.28620e9	0.646313
$641$	3.35413e9	0.503010	0.251505	−	0.967856i	$-0.419074\pi$
$641$	3.35413e9	0.503010	0.251505	+	0.967856i	$0.419074\pi$
$642$	0	0
$643$	−4.40659e9	−0.653679	−0.326840	−	0.945080i	$-0.605984\pi$
$643$	−4.40659e9	−0.653679	−0.326840	+	0.945080i	$0.605984\pi$
$644$	8.01196e8	0.118206
$645$	0	0
$646$	1.12907e10	1.64781
$647$	−6.70695e9	−0.973554	−0.486777	−	0.873526i	$-0.661828\pi$
$647$	−6.70695e9	−0.973554	−0.486777	+	0.873526i	$0.661828\pi$
$648$	0	0
$649$	9.88048e9	1.41880
$650$	3.32571e9	0.474993
$651$	0	0
$652$	3.16034e9	0.446548
$653$	−3.88510e9	−0.546017	−0.273009	−	0.962012i	$-0.588019\pi$
$653$	−3.88510e9	−0.546017	−0.273009	+	0.962012i	$0.588019\pi$
$654$	0	0
$655$	−1.46429e10	−2.03602
$656$	−1.93506e6	−0.000267627 0
$657$	0	0
$658$	−4.97168e9	−0.680319
$659$	5.53120e9	0.752871	0.376435	−	0.926443i	$-0.377150\pi$
$659$	5.53120e9	0.752871	0.376435	+	0.926443i	$0.377150\pi$
$660$	0	0
$661$	5.60384e9	0.754711	0.377355	−	0.926069i	$-0.376834\pi$
$661$	5.60384e9	0.754711	0.377355	+	0.926069i	$0.376834\pi$
$662$	−4.82627e8	−0.0646560
$663$	0	0
$664$	1.43568e10	1.90313
$665$	−1.85479e10	−2.44579
$666$	0	0
$667$	−6.78818e8	−0.0885754
$668$	−4.97482e8	−0.0645744
$669$	0	0
$670$	4.56909e9	0.586905
$671$	−7.55111e9	−0.964899
$672$	0	0
$673$	1.01343e10	1.28156	0.640782	−	0.767723i	$-0.278610\pi$
$673$	1.01343e10	1.28156	0.640782	+	0.767723i	$0.278610\pi$
$674$	3.83374e9	0.482295
$675$	0	0
$676$	9.74523e8	0.121333
$677$	7.14863e9	0.885447	0.442724	−	0.896658i	$-0.354012\pi$
$677$	7.14863e9	0.885447	0.442724	+	0.896658i	$0.354012\pi$
$678$	0	0
$679$	2.74910e9	0.337012
$680$	−1.56649e10	−1.91050
$681$	0	0
$682$	−1.23048e8	−0.0148536
$683$	−7.53628e9	−0.905075	−0.452538	−	0.891745i	$-0.649481\pi$
$683$	−7.53628e9	−0.905075	−0.452538	+	0.891745i	$0.649481\pi$
$684$	0	0
$685$	−7.09349e9	−0.843224
$686$	5.57515e9	0.659359
$687$	0	0
$688$	1.10633e8	0.0129516
$689$	8.56559e9	0.997677
$690$	0	0
$691$	4.75530e9	0.548283	0.274142	−	0.961689i	$-0.411606\pi$
$691$	4.75530e9	0.548283	0.274142	+	0.961689i	$0.411606\pi$
$692$	7.02224e8	0.0805572
$693$	0	0
$694$	−2.38654e9	−0.271025
$695$	1.78055e10	2.01191
$696$	0	0
$697$	−3.15390e7	−0.00352803
$698$	−1.04049e9	−0.115809
$699$	0	0
$700$	4.20140e9	0.462968
$701$	−1.29238e10	−1.41703	−0.708514	−	0.705697i	$-0.750634\pi$
$701$	−1.29238e10	−1.41703	−0.708514	+	0.705697i	$0.750634\pi$
$702$	0	0
$703$	1.74236e10	1.89145
$704$	−1.17451e10	−1.26868
$705$	0	0
$706$	8.52865e8	0.0912145
$707$	−1.42831e9	−0.152003
$708$	0	0
$709$	−9.39908e9	−0.990429	−0.495215	−	0.868771i	$-0.664911\pi$
$709$	−9.39908e9	−0.990429	−0.495215	+	0.868771i	$0.664911\pi$
$710$	3.49775e9	0.366762
$711$	0	0
$712$	3.14545e9	0.326590
$713$	2.64689e7	0.00273478
$714$	0	0
$715$	2.01942e10	2.06612
$716$	3.14081e9	0.319776
$717$	0	0
$718$	1.32090e9	0.133179
$719$	6.36863e8	0.0638991	0.0319496	−	0.999489i	$-0.489828\pi$
$719$	6.36863e8	0.0638991	0.0319496	+	0.999489i	$0.489828\pi$
$720$	0	0
$721$	1.09093e10	1.08399
$722$	1.54624e10	1.52896
$723$	0	0
$724$	−4.30557e9	−0.421643
$725$	−3.55966e9	−0.346917
$726$	0	0
$727$	−1.55580e10	−1.50170	−0.750850	−	0.660473i	$-0.770356\pi$
$727$	−1.55580e10	−1.50170	−0.750850	+	0.660473i	$0.770356\pi$
$728$	9.45104e9	0.907862
$729$	0	0
$730$	−4.70428e8	−0.0447572
$731$	1.80317e9	0.170737
$732$	0	0
$733$	−5.81058e9	−0.544949	−0.272475	−	0.962163i	$-0.587842\pi$
$733$	−5.81058e9	−0.544949	−0.272475	+	0.962163i	$0.587842\pi$
$734$	1.16962e10	1.09172
$735$	0	0
$736$	2.16710e9	0.200358
$737$	1.24722e10	1.14765
$738$	0	0
$739$	1.90719e10	1.73836	0.869178	−	0.494500i	$-0.164649\pi$
$739$	1.90719e10	1.73836	0.869178	+	0.494500i	$0.164649\pi$
$740$	−8.77940e9	−0.796442
$741$	0	0
$742$	−8.15323e9	−0.732683
$743$	−2.32518e9	−0.207968	−0.103984	−	0.994579i	$-0.533159\pi$
$743$	−2.32518e9	−0.207968	−0.103984	+	0.994579i	$0.533159\pi$
$744$	0	0
$745$	1.90614e10	1.68892
$746$	4.13298e9	0.364483
$747$	0	0
$748$	−1.55297e10	−1.35678
$749$	1.07125e10	0.931544
$750$	0	0
$751$	−8.44159e9	−0.727251	−0.363625	−	0.931545i	$-0.618461\pi$
$751$	−8.44159e9	−0.727251	−0.363625	+	0.931545i	$0.618461\pi$
$752$	−1.27185e9	−0.109062
$753$	0	0
$754$	−2.90814e9	−0.247067
$755$	−1.47598e9	−0.124815
$756$	0	0
$757$	8.83237e8	0.0740017	0.0370009	−	0.999315i	$-0.488220\pi$
$757$	8.83237e8	0.0740017	0.0370009	+	0.999315i	$0.488220\pi$
$758$	6.13783e9	0.511885
$759$	0	0
$760$	−3.06502e10	−2.53271
$761$	−6.01891e9	−0.495076	−0.247538	−	0.968878i	$-0.579622\pi$
$761$	−6.01891e9	−0.495076	−0.247538	+	0.968878i	$0.579622\pi$
$762$	0	0
$763$	−2.95933e9	−0.241189
$764$	−5.69941e9	−0.462385
$765$	0	0
$766$	8.68593e9	0.698258
$767$	−9.10542e9	−0.728645
$768$	0	0
$769$	−4.25596e9	−0.337485	−0.168743	−	0.985660i	$-0.553971\pi$
$769$	−4.25596e9	−0.337485	−0.168743	+	0.985660i	$0.553971\pi$
$770$	−1.92220e10	−1.51733
$771$	0	0
$772$	7.73983e9	0.605440
$773$	−1.06123e10	−0.826387	−0.413193	−	0.910643i	$-0.635587\pi$
$773$	−1.06123e10	−0.826387	−0.413193	+	0.910643i	$0.635587\pi$
$774$	0	0
$775$	1.38801e8	0.0107111
$776$	4.54285e9	0.348990
$777$	0	0
$778$	1.26141e10	0.960350
$779$	−6.17095e7	−0.00467704
$780$	0	0
$781$	9.54780e9	0.717174
$782$	−2.51702e9	−0.188219
$783$	0	0
$784$	1.67825e7	0.00124380
$785$	5.96792e9	0.440331
$786$	0	0
$787$	−2.71674e10	−1.98672	−0.993358	−	0.115062i	$-0.963293\pi$
$787$	−2.71674e10	−1.98672	−0.993358	+	0.115062i	$0.963293\pi$
$788$	4.87719e9	0.355082
$789$	0	0
$790$	1.40804e10	1.01606
$791$	1.23567e10	0.887740
$792$	0	0
$793$	6.95877e9	0.495537
$794$	3.99005e9	0.282883
$795$	0	0
$796$	−1.04593e10	−0.735033
$797$	−1.84161e10	−1.28852	−0.644262	−	0.764805i	$-0.722835\pi$
$797$	−1.84161e10	−1.28852	−0.644262	+	0.764805i	$0.722835\pi$
$798$	0	0
$799$	−2.07295e10	−1.43772
$800$	1.13641e10	0.784727
$801$	0	0
$802$	−1.29363e8	−0.00885526
$803$	−1.28413e9	−0.0875192
$804$	0	0
$805$	4.13484e9	0.279366
$806$	1.13396e8	0.00762825
$807$	0	0
$808$	−2.36026e9	−0.157406
$809$	−2.81026e10	−1.86606	−0.933032	−	0.359794i	$-0.882847\pi$
$809$	−2.81026e10	−1.86606	−0.933032	+	0.359794i	$0.882847\pi$
$810$	0	0
$811$	8.67752e9	0.571246	0.285623	−	0.958342i	$-0.407800\pi$
$811$	8.67752e9	0.571246	0.285623	+	0.958342i	$0.407800\pi$
$812$	−3.67388e9	−0.240813
$813$	0	0
$814$	1.80568e10	1.17343
$815$	1.63100e10	1.05537
$816$	0	0
$817$	3.52811e9	0.226342
$818$	−1.12475e10	−0.718490
$819$	0	0
$820$	3.10942e7	0.00196939
$821$	1.19593e10	0.754230	0.377115	−	0.926166i	$-0.376916\pi$
$821$	1.19593e10	0.754230	0.377115	+	0.926166i	$0.376916\pi$
$822$	0	0
$823$	1.36366e10	0.852718	0.426359	−	0.904554i	$-0.359796\pi$
$823$	1.36366e10	0.852718	0.426359	+	0.904554i	$0.359796\pi$
$824$	1.80275e10	1.12251
$825$	0	0
$826$	8.66707e9	0.535109
$827$	−5.45503e9	−0.335373	−0.167686	−	0.985840i	$-0.553630\pi$
$827$	−5.45503e9	−0.335373	−0.167686	+	0.985840i	$0.553630\pi$
$828$	0	0
$829$	1.05123e10	0.640852	0.320426	−	0.947274i	$-0.396174\pi$
$829$	1.05123e10	0.640852	0.320426	+	0.947274i	$0.396174\pi$
$830$	2.69090e10	1.63352
$831$	0	0
$832$	1.08238e10	0.651549
$833$	2.73533e8	0.0163966
$834$	0	0
$835$	−2.56743e9	−0.152614
$836$	−3.03856e10	−1.79865
$837$	0	0
$838$	−1.88187e9	−0.110468
$839$	8.52891e9	0.498571	0.249285	−	0.968430i	$-0.419804\pi$
$839$	8.52891e9	0.498571	0.249285	+	0.968430i	$0.419804\pi$
$840$	0	0
$841$	−1.41372e10	−0.819551
$842$	−5.77708e9	−0.333516
$843$	0	0
$844$	6.60667e9	0.378255
$845$	5.02935e9	0.286757
$846$	0	0
$847$	−3.48914e10	−1.97300
$848$	−2.08574e9	−0.117456
$849$	0	0
$850$	−1.31990e10	−0.737183
$851$	−3.88420e9	−0.216047
$852$	0	0
$853$	−3.05748e10	−1.68671	−0.843357	−	0.537353i	$-0.819424\pi$
$853$	−3.05748e10	−1.68671	−0.843357	+	0.537353i	$0.819424\pi$
$854$	−6.62377e9	−0.363917
$855$	0	0
$856$	1.77022e10	0.964650
$857$	2.13202e10	1.15707	0.578534	−	0.815659i	$-0.303625\pi$
$857$	2.13202e10	1.15707	0.578534	+	0.815659i	$0.303625\pi$
$858$	0	0
$859$	7.34663e9	0.395469	0.197734	−	0.980256i	$-0.436642\pi$
$859$	7.34663e9	0.395469	0.197734	+	0.980256i	$0.436642\pi$
$860$	−1.77774e9	−0.0953070
$861$	0	0
$862$	1.04060e10	0.553360
$863$	−1.52367e10	−0.806964	−0.403482	−	0.914988i	$-0.632200\pi$
$863$	−1.52367e10	−0.806964	−0.403482	+	0.914988i	$0.632200\pi$
$864$	0	0
$865$	3.62406e9	0.190388
$866$	4.26730e9	0.223275
$867$	0	0
$868$	1.43254e8	0.00743513
$869$	3.84351e10	1.98682
$870$	0	0
$871$	−1.14939e10	−0.589389
$872$	−4.89026e9	−0.249761
$873$	0	0
$874$	−4.92482e9	−0.249517
$875$	−4.86731e9	−0.245618
$876$	0	0
$877$	5.97975e9	0.299354	0.149677	−	0.988735i	$-0.452177\pi$
$877$	5.97975e9	0.299354	0.149677	+	0.988735i	$0.452177\pi$
$878$	−1.25718e10	−0.626856
$879$	0	0
$880$	−4.91734e9	−0.243243
$881$	2.59747e10	1.27978	0.639890	−	0.768467i	$-0.278980\pi$
$881$	2.59747e10	1.27978	0.639890	+	0.768467i	$0.278980\pi$
$882$	0	0
$883$	−3.74577e10	−1.83096	−0.915478	−	0.402367i	$-0.868188\pi$
$883$	−3.74577e10	−1.83096	−0.915478	+	0.402367i	$0.868188\pi$
$884$	1.43115e10	0.696791
$885$	0	0
$886$	−1.36315e10	−0.658457
$887$	−1.64110e10	−0.789592	−0.394796	−	0.918769i	$-0.629185\pi$
$887$	−1.64110e10	−0.789592	−0.394796	+	0.918769i	$0.629185\pi$
$888$	0	0
$889$	−3.94766e9	−0.188445
$890$	5.89554e9	0.280323
$891$	0	0
$892$	1.95425e10	0.921943
$893$	−4.05595e10	−1.90596
$894$	0	0
$895$	1.62092e10	0.755756
$896$	1.02632e10	0.476654
$897$	0	0
$898$	−1.05291e10	−0.485203
$899$	−1.21373e8	−0.00557139
$900$	0	0
$901$	−3.39950e10	−1.54838
$902$	−6.39522e7	−0.00290157
$903$	0	0
$904$	2.04193e10	0.919289
$905$	−2.22203e10	−0.996507
$906$	0	0
$907$	−3.48138e10	−1.54927	−0.774633	−	0.632410i	$-0.782066\pi$
$907$	−3.48138e10	−1.54927	−0.774633	+	0.632410i	$0.782066\pi$
$908$	2.47085e10	1.09533
$909$	0	0
$910$	1.77142e10	0.779248
$911$	3.41705e10	1.49740	0.748699	−	0.662911i	$-0.230679\pi$
$911$	3.41705e10	1.49740	0.748699	+	0.662911i	$0.230679\pi$
$912$	0	0
$913$	7.34535e10	3.19422
$914$	2.28640e10	0.990466
$915$	0	0
$916$	1.41034e10	0.606304
$917$	−3.50619e10	−1.50156
$918$	0	0
$919$	5.31876e9	0.226051	0.113025	−	0.993592i	$-0.463946\pi$
$919$	5.31876e9	0.226051	0.113025	+	0.993592i	$0.463946\pi$
$920$	6.83278e9	0.289294
$921$	0	0
$922$	2.72015e10	1.14297
$923$	−8.79884e9	−0.368315
$924$	0	0
$925$	−2.03684e10	−0.846177
$926$	−1.16150e10	−0.480708
$927$	0	0
$928$	−9.93722e9	−0.408176
$929$	1.55224e10	0.635190	0.317595	−	0.948226i	$-0.397125\pi$
$929$	1.55224e10	0.635190	0.317595	+	0.948226i	$0.397125\pi$
$930$	0	0
$931$	5.35199e8	0.0217366
$932$	6.40663e9	0.259223
$933$	0	0
$934$	−2.68486e10	−1.07822
$935$	−8.01464e10	−3.20659
$936$	0	0
$937$	9.15750e9	0.363654	0.181827	−	0.983331i	$-0.441799\pi$
$937$	9.15750e9	0.363654	0.181827	+	0.983331i	$0.441799\pi$
$938$	1.09405e10	0.432841
$939$	0	0
$940$	2.04371e10	0.802551
$941$	3.71210e10	1.45230	0.726150	−	0.687536i	$-0.241308\pi$
$941$	3.71210e10	1.45230	0.726150	+	0.687536i	$0.241308\pi$
$942$	0	0
$943$	1.37568e7	0.000534226 0
$944$	2.21719e9	0.0857831
$945$	0	0
$946$	3.65633e9	0.140419
$947$	−1.03990e10	−0.397894	−0.198947	−	0.980010i	$-0.563752\pi$
$947$	−1.03990e10	−0.397894	−0.198947	+	0.980010i	$0.563752\pi$
$948$	0	0
$949$	1.18339e9	0.0449467
$950$	−2.58253e10	−0.977268
$951$	0	0
$952$	−3.75091e10	−1.40899
$953$	1.55816e10	0.583161	0.291580	−	0.956546i	$-0.405819\pi$
$953$	1.55816e10	0.583161	0.291580	+	0.956546i	$0.405819\pi$
$954$	0	0
$955$	−2.94137e10	−1.09279
$956$	−6.78166e9	−0.251034
$957$	0	0
$958$	7.97978e9	0.293232
$959$	−1.69851e10	−0.621875
$960$	0	0
$961$	−2.75079e10	−0.999828
$962$	−1.66404e10	−0.602629
$963$	0	0
$964$	−1.47157e10	−0.529067
$965$	3.99440e10	1.43089
$966$	0	0
$967$	−1.71000e9	−0.0608140	−0.0304070	−	0.999538i	$-0.509680\pi$
$967$	−1.71000e9	−0.0608140	−0.0304070	+	0.999538i	$0.509680\pi$
$968$	−5.76576e10	−2.04311
$969$	0	0
$970$	8.51470e9	0.299549
$971$	−1.30801e10	−0.458503	−0.229252	−	0.973367i	$-0.573628\pi$
$971$	−1.30801e10	−0.458503	−0.229252	+	0.973367i	$0.573628\pi$
$972$	0	0
$973$	4.26347e10	1.48378
$974$	3.55802e10	1.23382
$975$	0	0
$976$	−1.69448e9	−0.0583394
$977$	−1.00204e10	−0.343758	−0.171879	−	0.985118i	$-0.554984\pi$
$977$	−1.00204e10	−0.343758	−0.171879	+	0.985118i	$0.554984\pi$
$978$	0	0
$979$	1.60930e10	0.548149
$980$	−2.69676e8	−0.00915274
$981$	0	0
$982$	−2.89306e10	−0.974917
$983$	2.71157e10	0.910509	0.455254	−	0.890361i	$-0.349548\pi$
$983$	2.71157e10	0.910509	0.455254	+	0.890361i	$0.349548\pi$
$984$	0	0
$985$	2.51704e10	0.839196
$986$	1.15418e10	0.383445
$987$	0	0
$988$	2.80021e10	0.923721
$989$	−7.86513e8	−0.0258535
$990$	0	0
$991$	−5.01084e10	−1.63551	−0.817755	−	0.575567i	$-0.804781\pi$
$991$	−5.01084e10	−1.63551	−0.817755	+	0.575567i	$0.804781\pi$
$992$	3.87478e8	0.0126025
$993$	0	0
$994$	8.37525e9	0.270486
$995$	−5.39787e10	−1.73717
$996$	0	0
$997$	−1.93448e10	−0.618203	−0.309101	−	0.951029i	$-0.600028\pi$
$997$	−1.93448e10	−0.618203	−0.309101	+	0.951029i	$0.600028\pi$
$998$	−2.75255e10	−0.876553
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.f.1.6		8
3.2	odd	2		23.8.a.b.1.3	✓	8
12.11	even	2		368.8.a.h.1.2		8
15.14	odd	2		575.8.a.b.1.6		8
69.68	even	2		529.8.a.c.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.a.b.1.3	✓	8	3.2	odd	2
207.8.a.f.1.6		8	1.1	even	1	trivial
368.8.a.h.1.2		8	12.11	even	2
529.8.a.c.1.3		8	69.68	even	2
575.8.a.b.1.6		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)

\(f(q)\)	\(=\)	\(q+7.41631 q^{2} -72.9984 q^{4} -376.733 q^{5} -902.074 q^{7} -1490.67 q^{8} +O(q^{10})\)	\(q+7.41631 q^{2} -72.9984 q^{4} -376.733 q^{5} -902.074 q^{7} -1490.67 q^{8} -2793.97 q^{10} -7626.68 q^{11} +7028.41 q^{13} -6690.05 q^{14} -1711.44 q^{16} -27894.3 q^{17} -54578.2 q^{19} +27500.9 q^{20} -56561.8 q^{22} +12167.0 q^{23} +63802.7 q^{25} +52124.9 q^{26} +65849.9 q^{28} -55791.8 q^{29} +2175.47 q^{31} +178113. q^{32} -206872. q^{34} +339841. q^{35} -319241. q^{37} -404769. q^{38} +561583. q^{40} +1130.66 q^{41} -64643.1 q^{43} +556735. q^{44} +90234.2 q^{46} +743145. q^{47} -9806.08 q^{49} +473180. q^{50} -513063. q^{52} +1.21871e6 q^{53} +2.87322e6 q^{55} +1.34469e6 q^{56} -413769. q^{58} -1.29552e6 q^{59} +990092. q^{61} +16133.9 q^{62} +1.54000e6 q^{64} -2.64783e6 q^{65} -1.63534e6 q^{67} +2.03624e6 q^{68} +2.52036e6 q^{70} -1.25189e6 q^{71} +168373. q^{73} -2.36759e6 q^{74} +3.98412e6 q^{76} +6.87983e6 q^{77} -5.03956e6 q^{79} +644755. q^{80} +8385.33 q^{82} -9.63112e6 q^{83} +1.05087e7 q^{85} -479413. q^{86} +1.13688e7 q^{88} -2.11010e6 q^{89} -6.34015e6 q^{91} -888172. q^{92} +5.51139e6 q^{94} +2.05614e7 q^{95} -3.04753e6 q^{97} -72724.9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 640 q^{4} - 444 q^{5} + 1446 q^{7} - 3177 q^{8}+O(q^{10}) \) 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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