LMFDB - Embedded newform 207.8.a.h.1.4

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 1070 x^{10} + 4076 x^{9} + 403334 x^{8} - 1518684 x^{7} - 64710184 x^{6} + \cdots + 90709421512 $ x^12 - 4x^11 - 1070x^10 + 4076x^9 + 403334x^8 - 1518684x^7 - 64710184x^6 + 248484524x^5 + 4244585785x^4 - 14689737568x^3 - 89785869106x^2 + 190549532712*x + 90709421512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{7} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-9.27904$ 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)

$f(q)$	$=$	$q-8.27904 q^{2} -59.4574 q^{4} +230.336 q^{5} +754.718 q^{7} +1551.97 q^{8} +O(q^{10})$	\(q-8.27904 q^{2} -59.4574 q^{4} +230.336 q^{5} +754.718 q^{7} +1551.97 q^{8} -1906.96 q^{10} -4115.05 q^{11} +8274.99 q^{13} -6248.34 q^{14} -5238.26 q^{16} +33011.7 q^{17} +48539.1 q^{19} -13695.2 q^{20} +34068.7 q^{22} -12167.0 q^{23} -25070.2 q^{25} -68509.0 q^{26} -44873.6 q^{28} +75246.7 q^{29} -232682. q^{31} -155284. q^{32} -273305. q^{34} +173839. q^{35} -2857.50 q^{37} -401857. q^{38} +357475. q^{40} +13864.0 q^{41} -331623. q^{43} +244670. q^{44} +100731. q^{46} +182572. q^{47} -253943. q^{49} +207557. q^{50} -492010. q^{52} +943801. q^{53} -947846. q^{55} +1.17130e6 q^{56} -622971. q^{58} +1.66466e6 q^{59} -2.55605e6 q^{61} +1.92639e6 q^{62} +1.95610e6 q^{64} +1.90603e6 q^{65} -1.83091e6 q^{67} -1.96279e6 q^{68} -1.43922e6 q^{70} -2.39197e6 q^{71} +6.34234e6 q^{73} +23657.3 q^{74} -2.88601e6 q^{76} -3.10570e6 q^{77} -1.14136e6 q^{79} -1.20656e6 q^{80} -114780. q^{82} +9.04659e6 q^{83} +7.60378e6 q^{85} +2.74552e6 q^{86} -6.38643e6 q^{88} +6.35076e6 q^{89} +6.24529e6 q^{91} +723419. q^{92} -1.51152e6 q^{94} +1.11803e7 q^{95} +1.01526e7 q^{97} +2.10241e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8}+O(q^{10}) $ 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8} + 10270 q^{10} - 460 q^{11} - 21060 q^{13} + 4268 q^{14} + 56676 q^{16} + 73124 q^{17} + 8508 q^{19} + 170538 q^{20} + 124754 q^{22} - 146004 q^{23} + 194064 q^{25} + 206080 q^{26} - 390416 q^{28} + 268640 q^{29} - 191880 q^{31} + 1180172 q^{32} - 221436 q^{34} - 487244 q^{35} + 650332 q^{37} + 1432950 q^{38} + 1775722 q^{40} + 980088 q^{41} - 861276 q^{43} + 800666 q^{44} - 194672 q^{46} + 403868 q^{47} + 1699160 q^{49} + 2919092 q^{50} - 2369520 q^{52} - 201948 q^{53} - 1553512 q^{55} - 4848116 q^{56} + 3720672 q^{58} + 1302676 q^{59} + 2141364 q^{61} + 2160944 q^{62} + 9702136 q^{64} + 9099536 q^{65} - 6159260 q^{67} + 18442208 q^{68} - 10891632 q^{70} + 12584184 q^{71} + 7435872 q^{73} + 22491442 q^{74} + 5721386 q^{76} + 16450568 q^{77} + 3658028 q^{79} + 49905778 q^{80} - 5516316 q^{82} + 26137900 q^{83} + 5169556 q^{85} + 30678550 q^{86} + 14753046 q^{88} + 27235908 q^{89} - 7657216 q^{91} - 7786880 q^{92} - 23519352 q^{94} + 63623628 q^{95} + 22454720 q^{97} + 94951532 q^{98}+O(q^{100}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8 + 10270 * q^10 - 460 * q^11 - 21060 * q^13 + 4268 * q^14 + 56676 * q^16 + 73124 * q^17 + 8508 * q^19 + 170538 * q^20 + 124754 * q^22 - 146004 * q^23 + 194064 * q^25 + 206080 * q^26 - 390416 * q^28 + 268640 * q^29 - 191880 * q^31 + 1180172 * q^32 - 221436 * q^34 - 487244 * q^35 + 650332 * q^37 + 1432950 * q^38 + 1775722 * q^40 + 980088 * q^41 - 861276 * q^43 + 800666 * q^44 - 194672 * q^46 + 403868 * q^47 + 1699160 * q^49 + 2919092 * q^50 - 2369520 * q^52 - 201948 * q^53 - 1553512 * q^55 - 4848116 * q^56 + 3720672 * q^58 + 1302676 * q^59 + 2141364 * q^61 + 2160944 * q^62 + 9702136 * q^64 + 9099536 * q^65 - 6159260 * q^67 + 18442208 * q^68 - 10891632 * q^70 + 12584184 * q^71 + 7435872 * q^73 + 22491442 * q^74 + 5721386 * q^76 + 16450568 * q^77 + 3658028 * q^79 + 49905778 * q^80 - 5516316 * q^82 + 26137900 * q^83 + 5169556 * q^85 + 30678550 * q^86 + 14753046 * q^88 + 27235908 * q^89 - 7657216 * q^91 - 7786880 * q^92 - 23519352 * q^94 + 63623628 * q^95 + 22454720 * q^97 + 94951532 * 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 $

$2$	−8.27904	−0.731771	−0.365885	−	0.930660i	$-0.619234\pi$
$2$	−8.27904	−0.731771	−0.365885	+	0.930660i	$0.619234\pi$
$3$	0	0
$3$	0	0
$4$	−59.4574	−0.464511
$5$	230.336	0.824076	0.412038	−	0.911167i	$-0.364817\pi$
$5$	230.336	0.824076	0.412038	+	0.911167i	$0.364817\pi$
$6$	0	0
$7$	754.718	0.831652	0.415826	−	0.909444i	$-0.363493\pi$
$7$	754.718	0.831652	0.415826	+	0.909444i	$0.363493\pi$
$8$	1551.97	1.07169
$9$	0	0
$10$	−1906.96	−0.603035
$11$	−4115.05	−0.932182	−0.466091	−	0.884737i	$-0.654338\pi$
$11$	−4115.05	−0.932182	−0.466091	+	0.884737i	$0.654338\pi$
$12$	0	0
$13$	8274.99	1.04464	0.522319	−	0.852750i	$-0.325067\pi$
$13$	8274.99	1.04464	0.522319	+	0.852750i	$0.325067\pi$
$14$	−6248.34	−0.608579
$15$	0	0
$16$	−5238.26	−0.319718
$17$	33011.7	1.62966	0.814828	−	0.579702i	$-0.196831\pi$
$17$	33011.7	1.62966	0.814828	+	0.579702i	$0.196831\pi$
$18$	0	0
$19$	48539.1	1.62351	0.811753	−	0.584000i	$-0.198513\pi$
$19$	48539.1	1.62351	0.811753	+	0.584000i	$0.198513\pi$
$20$	−13695.2	−0.382793
$21$	0	0
$22$	34068.7	0.682144
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−25070.2	−0.320898
$26$	−68509.0	−0.764436
$27$	0	0
$28$	−44873.6	−0.386312
$29$	75246.7	0.572921	0.286460	−	0.958092i	$-0.407521\pi$
$29$	75246.7	0.572921	0.286460	+	0.958092i	$0.407521\pi$
$30$	0	0
$31$	−232682.	−1.40281	−0.701403	−	0.712765i	$-0.747443\pi$
$31$	−232682.	−1.40281	−0.701403	+	0.712765i	$0.747443\pi$
$32$	−155284.	−0.837726
$33$	0	0
$34$	−273305.	−1.19254
$35$	173839.	0.685345
$36$	0	0
$37$	−2857.50	−0.00927427	−0.00463713	−	0.999989i	$-0.501476\pi$
$37$	−2857.50	−0.00927427	−0.00463713	+	0.999989i	$0.501476\pi$
$38$	−401857.	−1.18804
$39$	0	0
$40$	357475.	0.883152
$41$	13864.0	0.0314155	0.0157077	−	0.999877i	$-0.495000\pi$
$41$	13864.0	0.0314155	0.0157077	+	0.999877i	$0.495000\pi$
$42$	0	0
$43$	−331623.	−0.636070	−0.318035	−	0.948079i	$-0.603023\pi$
$43$	−331623.	−0.636070	−0.318035	+	0.948079i	$0.603023\pi$
$44$	244670.	0.433009
$45$	0	0
$46$	100731.	0.152585
$47$	182572.	0.256502	0.128251	−	0.991742i	$-0.459064\pi$
$47$	182572.	0.256502	0.128251	+	0.991742i	$0.459064\pi$
$48$	0	0
$49$	−253943.	−0.308355
$50$	207557.	0.234824
$51$	0	0
$52$	−492010.	−0.485246
$53$	943801.	0.870793	0.435397	−	0.900239i	$-0.356608\pi$
$53$	943801.	0.870793	0.435397	+	0.900239i	$0.356608\pi$
$54$	0	0
$55$	−947846.	−0.768189
$56$	1.17130e6	0.891271
$57$	0	0
$58$	−622971.	−0.419247
$59$	1.66466e6	1.05522	0.527610	−	0.849487i	$-0.323088\pi$
$59$	1.66466e6	1.05522	0.527610	+	0.849487i	$0.323088\pi$
$60$	0	0
$61$	−2.55605e6	−1.44183	−0.720916	−	0.693022i	$-0.756279\pi$
$61$	−2.55605e6	−1.44183	−0.720916	+	0.693022i	$0.756279\pi$
$62$	1.92639e6	1.02653
$63$	0	0
$64$	1.95610e6	0.932742
$65$	1.90603e6	0.860862
$66$	0	0
$67$	−1.83091e6	−0.743714	−0.371857	−	0.928290i	$-0.621279\pi$
$67$	−1.83091e6	−0.743714	−0.371857	+	0.928290i	$0.621279\pi$
$68$	−1.96279e6	−0.756994
$69$	0	0
$70$	−1.43922e6	−0.501515
$71$	−2.39197e6	−0.793143	−0.396571	−	0.918004i	$-0.629800\pi$
$71$	−2.39197e6	−0.793143	−0.396571	+	0.918004i	$0.629800\pi$
$72$	0	0
$73$	6.34234e6	1.90818	0.954090	−	0.299519i	$-0.0968261\pi$
$73$	6.34234e6	1.90818	0.954090	+	0.299519i	$0.0968261\pi$
$74$	23657.3	0.00678664
$75$	0	0
$76$	−2.88601e6	−0.754137
$77$	−3.10570e6	−0.775251
$78$	0	0
$79$	−1.14136e6	−0.260453	−0.130226	−	0.991484i	$-0.541570\pi$
$79$	−1.14136e6	−0.260453	−0.130226	+	0.991484i	$0.541570\pi$
$80$	−1.20656e6	−0.263472
$81$	0	0
$82$	−114780.	−0.0229889
$83$	9.04659e6	1.73665	0.868324	−	0.495998i	$-0.165198\pi$
$83$	9.04659e6	1.73665	0.868324	+	0.495998i	$0.165198\pi$
$84$	0	0
$85$	7.60378e6	1.34296
$86$	2.74552e6	0.465457
$87$	0	0
$88$	−6.38643e6	−0.999007
$89$	6.35076e6	0.954907	0.477453	−	0.878657i	$-0.341560\pi$
$89$	6.35076e6	0.954907	0.477453	+	0.878657i	$0.341560\pi$
$90$	0	0
$91$	6.24529e6	0.868775
$92$	723419.	0.0968573
$93$	0	0
$94$	−1.51152e6	−0.187701
$95$	1.11803e7	1.33789
$96$	0	0
$97$	1.01526e7	1.12947	0.564736	−	0.825271i	$-0.308978\pi$
$97$	1.01526e7	1.12947	0.564736	+	0.825271i	$0.308978\pi$
$98$	2.10241e6	0.225645
$99$	0	0
$100$	1.49061e6	0.149061
$101$	4.22741e6	0.408272	0.204136	−	0.978943i	$-0.434562\pi$
$101$	4.22741e6	0.408272	0.204136	+	0.978943i	$0.434562\pi$
$102$	0	0
$103$	−4.52490e6	−0.408018	−0.204009	−	0.978969i	$-0.565397\pi$
$103$	−4.52490e6	−0.408018	−0.204009	+	0.978969i	$0.565397\pi$
$104$	1.28425e7	1.11952
$105$	0	0
$106$	−7.81377e6	−0.637221
$107$	−7.27785e6	−0.574328	−0.287164	−	0.957881i	$-0.592713\pi$
$107$	−7.27785e6	−0.574328	−0.287164	+	0.957881i	$0.592713\pi$
$108$	0	0
$109$	1.53664e7	1.13652	0.568262	−	0.822848i	$-0.307616\pi$
$109$	1.53664e7	1.13652	0.568262	+	0.822848i	$0.307616\pi$
$110$	7.84726e6	0.562139
$111$	0	0
$112$	−3.95341e6	−0.265894
$113$	−4.65400e6	−0.303425	−0.151713	−	0.988425i	$-0.548479\pi$
$113$	−4.65400e6	−0.303425	−0.151713	+	0.988425i	$0.548479\pi$
$114$	0	0
$115$	−2.80250e6	−0.171832
$116$	−4.47398e6	−0.266128
$117$	0	0
$118$	−1.37818e7	−0.772179
$119$	2.49145e7	1.35531
$120$	0	0
$121$	−2.55354e6	−0.131037
$122$	2.11616e7	1.05509
$123$	0	0
$124$	1.38347e7	0.651619
$125$	−2.37696e7	−1.08852
$126$	0	0
$127$	−4.16201e7	−1.80298	−0.901489	−	0.432801i	$-0.857525\pi$
$127$	−4.16201e7	−1.80298	−0.901489	+	0.432801i	$0.857525\pi$
$128$	3.68172e6	0.155173
$129$	0	0
$130$	−1.57801e7	−0.629954
$131$	3.75725e7	1.46023	0.730113	−	0.683327i	$-0.239467\pi$
$131$	3.75725e7	1.46023	0.730113	+	0.683327i	$0.239467\pi$
$132$	0	0
$133$	3.66333e7	1.35019
$134$	1.51582e7	0.544228
$135$	0	0
$136$	5.12330e7	1.74648
$137$	5.36242e7	1.78172	0.890859	−	0.454280i	$-0.150104\pi$
$137$	5.36242e7	1.78172	0.890859	+	0.454280i	$0.150104\pi$
$138$	0	0
$139$	5.00758e7	1.58152	0.790762	−	0.612123i	$-0.209684\pi$
$139$	5.00758e7	1.58152	0.790762	+	0.612123i	$0.209684\pi$
$140$	−1.03360e7	−0.318350
$141$	0	0
$142$	1.98032e7	0.580399
$143$	−3.40520e7	−0.973793
$144$	0	0
$145$	1.73321e7	0.472130
$146$	−5.25085e7	−1.39635
$147$	0	0
$148$	169899.	0.00430800
$149$	4.80205e7	1.18925	0.594627	−	0.804001i	$-0.297300\pi$
$149$	4.80205e7	1.18925	0.594627	+	0.804001i	$0.297300\pi$
$150$	0	0
$151$	1.70099e7	0.402052	0.201026	−	0.979586i	$-0.435572\pi$
$151$	1.70099e7	0.402052	0.201026	+	0.979586i	$0.435572\pi$
$152$	7.53312e7	1.73989
$153$	0	0
$154$	2.57122e7	0.567306
$155$	−5.35952e7	−1.15602
$156$	0	0
$157$	−7.58262e7	−1.56376	−0.781881	−	0.623428i	$-0.785740\pi$
$157$	−7.58262e7	−1.56376	−0.781881	+	0.623428i	$0.785740\pi$
$158$	9.44940e6	0.190592
$159$	0	0
$160$	−3.57676e7	−0.690351
$161$	−9.18266e6	−0.173411
$162$	0	0
$163$	−4.18051e7	−0.756088	−0.378044	−	0.925788i	$-0.623403\pi$
$163$	−4.18051e7	−0.756088	−0.378044	+	0.925788i	$0.623403\pi$
$164$	−824315.	−0.0145928
$165$	0	0
$166$	−7.48971e7	−1.27083
$167$	−1.23505e7	−0.205199	−0.102600	−	0.994723i	$-0.532716\pi$
$167$	−1.23505e7	−0.205199	−0.102600	+	0.994723i	$0.532716\pi$
$168$	0	0
$169$	5.72698e6	0.0912688
$170$	−6.29521e7	−0.982740
$171$	0	0
$172$	1.97174e7	0.295462
$173$	3.88347e7	0.570241	0.285120	−	0.958492i	$-0.407966\pi$
$173$	3.88347e7	0.570241	0.285120	+	0.958492i	$0.407966\pi$
$174$	0	0
$175$	−1.89209e7	−0.266875
$176$	2.15557e7	0.298035
$177$	0	0
$178$	−5.25783e7	−0.698773
$179$	7.88803e7	1.02798	0.513988	−	0.857797i	$-0.328168\pi$
$179$	7.88803e7	1.02798	0.513988	+	0.857797i	$0.328168\pi$
$180$	0	0
$181$	1.03433e8	1.29653	0.648266	−	0.761414i	$-0.275495\pi$
$181$	1.03433e8	1.29653	0.648266	+	0.761414i	$0.275495\pi$
$182$	−5.17050e7	−0.635745
$183$	0	0
$184$	−1.88828e7	−0.223462
$185$	−658185.	−0.00764270
$186$	0	0
$187$	−1.35845e8	−1.51914
$188$	−1.08552e7	−0.119148
$189$	0	0
$190$	−9.25624e7	−0.979032
$191$	−1.50405e8	−1.56187	−0.780935	−	0.624613i	$-0.785257\pi$
$191$	−1.50405e8	−1.56187	−0.780935	+	0.624613i	$0.785257\pi$
$192$	0	0
$193$	−1.70982e7	−0.171198	−0.0855992	−	0.996330i	$-0.527280\pi$
$193$	−1.70982e7	−0.171198	−0.0855992	+	0.996330i	$0.527280\pi$
$194$	−8.40537e7	−0.826515
$195$	0	0
$196$	1.50988e7	0.143234
$197$	−7.28798e7	−0.679165	−0.339583	−	0.940576i	$-0.610286\pi$
$197$	−7.28798e7	−0.679165	−0.339583	+	0.940576i	$0.610286\pi$
$198$	0	0
$199$	3.31117e7	0.297849	0.148924	−	0.988849i	$-0.452419\pi$
$199$	3.31117e7	0.297849	0.148924	+	0.988849i	$0.452419\pi$
$200$	−3.89081e7	−0.343902
$201$	0	0
$202$	−3.49989e7	−0.298761
$203$	5.67900e7	0.476471
$204$	0	0
$205$	3.19337e6	0.0258888
$206$	3.74619e7	0.298576
$207$	0	0
$208$	−4.33466e7	−0.333990
$209$	−1.99741e8	−1.51340
$210$	0	0
$211$	8.39274e7	0.615057	0.307528	−	0.951539i	$-0.400498\pi$
$211$	8.39274e7	0.615057	0.307528	+	0.951539i	$0.400498\pi$
$212$	−5.61160e7	−0.404493
$213$	0	0
$214$	6.02537e7	0.420277
$215$	−7.63848e7	−0.524170
$216$	0	0
$217$	−1.75610e8	−1.16665
$218$	−1.27219e8	−0.831675
$219$	0	0
$220$	5.63565e7	0.356833
$221$	2.73171e8	1.70240
$222$	0	0
$223$	−2.98634e7	−0.180332	−0.0901660	−	0.995927i	$-0.528740\pi$
$223$	−2.98634e7	−0.180332	−0.0901660	+	0.995927i	$0.528740\pi$
$224$	−1.17196e8	−0.696697
$225$	0	0
$226$	3.85307e7	0.222038
$227$	2.07159e7	0.117547	0.0587737	−	0.998271i	$-0.481281\pi$
$227$	2.07159e7	0.117547	0.0587737	+	0.998271i	$0.481281\pi$
$228$	0	0
$229$	−1.00664e7	−0.0553925	−0.0276963	−	0.999616i	$-0.508817\pi$
$229$	−1.00664e7	−0.0553925	−0.0276963	+	0.999616i	$0.508817\pi$
$230$	2.32020e7	0.125742
$231$	0	0
$232$	1.16780e8	0.613991
$233$	−2.03064e8	−1.05169	−0.525845	−	0.850580i	$-0.676251\pi$
$233$	−2.03064e8	−1.05169	−0.525845	+	0.850580i	$0.676251\pi$
$234$	0	0
$235$	4.20529e7	0.211377
$236$	−9.89763e7	−0.490162
$237$	0	0
$238$	−2.06268e8	−0.991774
$239$	−1.24450e8	−0.589662	−0.294831	−	0.955549i	$-0.595263\pi$
$239$	−1.24450e8	−0.589662	−0.294831	+	0.955549i	$0.595263\pi$
$240$	0	0
$241$	3.24479e8	1.49323	0.746616	−	0.665256i	$-0.231677\pi$
$241$	3.24479e8	1.49323	0.746616	+	0.665256i	$0.231677\pi$
$242$	2.11408e7	0.0958889
$243$	0	0
$244$	1.51976e8	0.669747
$245$	−5.84924e7	−0.254108
$246$	0	0
$247$	4.01661e8	1.69598
$248$	−3.61116e8	−1.50337
$249$	0	0
$250$	1.96790e8	0.796548
$251$	4.12639e8	1.64707	0.823535	−	0.567265i	$-0.191998\pi$
$251$	4.12639e8	1.64707	0.823535	+	0.567265i	$0.191998\pi$
$252$	0	0
$253$	5.00678e7	0.194373
$254$	3.44575e8	1.31937
$255$	0	0
$256$	−2.80862e8	−1.04629
$257$	−2.41861e8	−0.888791	−0.444396	−	0.895831i	$-0.646582\pi$
$257$	−2.41861e8	−0.888791	−0.444396	+	0.895831i	$0.646582\pi$
$258$	0	0
$259$	−2.15660e6	−0.00771296
$260$	−1.13328e8	−0.399880
$261$	0	0
$262$	−3.11064e8	−1.06855
$263$	2.50721e8	0.849858	0.424929	−	0.905227i	$-0.360299\pi$
$263$	2.50721e8	0.849858	0.424929	+	0.905227i	$0.360299\pi$
$264$	0	0
$265$	2.17392e8	0.717600
$266$	−3.03289e8	−0.988032
$267$	0	0
$268$	1.08861e8	0.345463
$269$	3.46340e7	0.108485	0.0542425	−	0.998528i	$-0.482726\pi$
$269$	3.46340e7	0.108485	0.0542425	+	0.998528i	$0.482726\pi$
$270$	0	0
$271$	−3.57248e8	−1.09038	−0.545189	−	0.838313i	$-0.683542\pi$
$271$	−3.57248e8	−1.09038	−0.545189	+	0.838313i	$0.683542\pi$
$272$	−1.72924e8	−0.521031
$273$	0	0
$274$	−4.43957e8	−1.30381
$275$	1.03165e8	0.299135
$276$	0	0
$277$	1.87394e8	0.529758	0.264879	−	0.964282i	$-0.414668\pi$
$277$	1.87394e8	0.529758	0.264879	+	0.964282i	$0.414668\pi$
$278$	−4.14580e8	−1.15731
$279$	0	0
$280$	2.69793e8	0.734475
$281$	1.91336e8	0.514428	0.257214	−	0.966354i	$-0.417195\pi$
$281$	1.91336e8	0.514428	0.257214	+	0.966354i	$0.417195\pi$
$282$	0	0
$283$	−3.55697e8	−0.932883	−0.466441	−	0.884552i	$-0.654464\pi$
$283$	−3.55697e8	−0.932883	−0.466441	+	0.884552i	$0.654464\pi$
$284$	1.42220e8	0.368424
$285$	0	0
$286$	2.81918e8	0.712593
$287$	1.04634e7	0.0261267
$288$	0	0
$289$	6.79431e8	1.65578
$290$	−1.43493e8	−0.345491
$291$	0	0
$292$	−3.77099e8	−0.886372
$293$	−6.34027e8	−1.47255	−0.736277	−	0.676680i	$-0.763418\pi$
$293$	−6.34027e8	−1.47255	−0.736277	+	0.676680i	$0.763418\pi$
$294$	0	0
$295$	3.83431e8	0.869582
$296$	−4.43474e6	−0.00993911
$297$	0	0
$298$	−3.97564e8	−0.870262
$299$	−1.00682e8	−0.217822
$300$	0	0
$301$	−2.50282e8	−0.528989
$302$	−1.40826e8	−0.294210
$303$	0	0
$304$	−2.54260e8	−0.519064
$305$	−5.88751e8	−1.18818
$306$	0	0
$307$	9.26232e8	1.82699	0.913494	−	0.406853i	$-0.133374\pi$
$307$	9.26232e8	1.82699	0.913494	+	0.406853i	$0.133374\pi$
$308$	1.84657e8	0.360113
$309$	0	0
$310$	4.43717e8	0.845942
$311$	3.99629e8	0.753348	0.376674	−	0.926346i	$-0.377068\pi$
$311$	3.99629e8	0.753348	0.376674	+	0.926346i	$0.377068\pi$
$312$	0	0
$313$	−6.48164e8	−1.19476	−0.597379	−	0.801959i	$-0.703791\pi$
$313$	−6.48164e8	−1.19476	−0.597379	+	0.801959i	$0.703791\pi$
$314$	6.27769e8	1.14432
$315$	0	0
$316$	6.78626e7	0.120983
$317$	−8.23337e8	−1.45168	−0.725839	−	0.687865i	$-0.758548\pi$
$317$	−8.23337e8	−1.45168	−0.725839	+	0.687865i	$0.758548\pi$
$318$	0	0
$319$	−3.09644e8	−0.534066
$320$	4.50561e8	0.768651
$321$	0	0
$322$	7.60236e7	0.126897
$323$	1.60236e9	2.64576
$324$	0	0
$325$	−2.07455e8	−0.335222
$326$	3.46106e8	0.553284
$327$	0	0
$328$	2.15164e7	0.0336676
$329$	1.37790e8	0.213320
$330$	0	0
$331$	2.06477e8	0.312949	0.156475	−	0.987682i	$-0.449987\pi$
$331$	2.06477e8	0.312949	0.156475	+	0.987682i	$0.449987\pi$
$332$	−5.37887e8	−0.806692
$333$	0	0
$334$	1.02250e8	0.150159
$335$	−4.21726e8	−0.612877
$336$	0	0
$337$	8.59787e8	1.22373	0.611866	−	0.790961i	$-0.290419\pi$
$337$	8.59787e8	1.22373	0.611866	+	0.790961i	$0.290419\pi$
$338$	−4.74139e7	−0.0667879
$339$	0	0
$340$	−4.52102e8	−0.623821
$341$	9.57500e8	1.30767
$342$	0	0
$343$	−8.13199e8	−1.08810
$344$	−5.14668e8	−0.681667
$345$	0	0
$346$	−3.21514e8	−0.417286
$347$	1.16313e9	1.49443	0.747214	−	0.664584i	$-0.231391\pi$
$347$	1.16313e9	1.49443	0.747214	+	0.664584i	$0.231391\pi$
$348$	0	0
$349$	−3.96456e8	−0.499236	−0.249618	−	0.968344i	$-0.580305\pi$
$349$	−3.96456e8	−0.499236	−0.249618	+	0.968344i	$0.580305\pi$
$350$	1.56647e8	0.195292
$351$	0	0
$352$	6.39002e8	0.780913
$353$	1.13106e9	1.36860	0.684298	−	0.729203i	$-0.260109\pi$
$353$	1.13106e9	1.36860	0.684298	+	0.729203i	$0.260109\pi$
$354$	0	0
$355$	−5.50958e8	−0.653610
$356$	−3.77600e8	−0.443565
$357$	0	0
$358$	−6.53054e8	−0.752243
$359$	−1.01215e8	−0.115456	−0.0577279	−	0.998332i	$-0.518386\pi$
$359$	−1.01215e8	−0.115456	−0.0577279	+	0.998332i	$0.518386\pi$
$360$	0	0
$361$	1.46217e9	1.63577
$362$	−8.56324e8	−0.948764
$363$	0	0
$364$	−3.71329e8	−0.403556
$365$	1.46087e9	1.57249
$366$	0	0
$367$	−6.95735e8	−0.734704	−0.367352	−	0.930082i	$-0.619736\pi$
$367$	−6.95735e8	−0.734704	−0.367352	+	0.930082i	$0.619736\pi$
$368$	6.37339e7	0.0666658
$369$	0	0
$370$	5.44914e6	0.00559271
$371$	7.12304e8	0.724197
$372$	0	0
$373$	−1.35531e9	−1.35225	−0.676127	−	0.736785i	$-0.736343\pi$
$373$	−1.35531e9	−1.35225	−0.676127	+	0.736785i	$0.736343\pi$
$374$	1.12466e9	1.11166
$375$	0	0
$376$	2.83345e8	0.274890
$377$	6.22666e8	0.598495
$378$	0	0
$379$	−5.43056e8	−0.512398	−0.256199	−	0.966624i	$-0.582470\pi$
$379$	−5.43056e8	−0.512398	−0.256199	+	0.966624i	$0.582470\pi$
$380$	−6.64753e8	−0.621467
$381$	0	0
$382$	1.24521e9	1.14293
$383$	6.55701e8	0.596362	0.298181	−	0.954509i	$-0.403620\pi$
$383$	6.55701e8	0.596362	0.298181	+	0.954509i	$0.403620\pi$
$384$	0	0
$385$	−7.15356e8	−0.638866
$386$	1.41557e8	0.125278
$387$	0	0
$388$	−6.03647e8	−0.524653
$389$	1.86302e9	1.60470	0.802350	−	0.596854i	$-0.203583\pi$
$389$	1.86302e9	1.60470	0.802350	+	0.596854i	$0.203583\pi$
$390$	0	0
$391$	−4.01653e8	−0.339807
$392$	−3.94112e8	−0.330460
$393$	0	0
$394$	6.03375e8	0.496994
$395$	−2.62898e8	−0.214633
$396$	0	0
$397$	1.01806e9	0.816595	0.408298	−	0.912849i	$-0.366123\pi$
$397$	1.01806e9	0.816595	0.408298	+	0.912849i	$0.366123\pi$
$398$	−2.74133e8	−0.217957
$399$	0	0
$400$	1.31324e8	0.102597
$401$	6.12164e8	0.474092	0.237046	−	0.971498i	$-0.423821\pi$
$401$	6.12164e8	0.474092	0.237046	+	0.971498i	$0.423821\pi$
$402$	0	0
$403$	−1.92545e9	−1.46543
$404$	−2.51351e8	−0.189647
$405$	0	0
$406$	−4.70167e8	−0.348667
$407$	1.17587e7	0.00864530
$408$	0	0
$409$	7.49787e8	0.541884	0.270942	−	0.962596i	$-0.412665\pi$
$409$	7.49787e8	0.541884	0.270942	+	0.962596i	$0.412665\pi$
$410$	−2.64381e7	−0.0189446
$411$	0	0
$412$	2.69039e8	0.189529
$413$	1.25635e9	0.877576
$414$	0	0
$415$	2.08376e9	1.43113
$416$	−1.28498e9	−0.875121
$417$	0	0
$418$	1.65366e9	1.10747
$419$	−2.75885e9	−1.83222	−0.916112	−	0.400922i	$-0.868690\pi$
$419$	−2.75885e9	−1.83222	−0.916112	+	0.400922i	$0.868690\pi$
$420$	0	0
$421$	−1.64458e9	−1.07416	−0.537079	−	0.843532i	$-0.680472\pi$
$421$	−1.64458e9	−1.07416	−0.537079	+	0.843532i	$0.680472\pi$
$422$	−6.94839e8	−0.450081
$423$	0	0
$424$	1.46475e9	0.933217
$425$	−8.27607e8	−0.522954
$426$	0	0
$427$	−1.92910e9	−1.19910
$428$	4.32723e8	0.266782
$429$	0	0
$430$	6.32393e8	0.383572
$431$	−5.81864e8	−0.350067	−0.175034	−	0.984562i	$-0.556003\pi$
$431$	−5.81864e8	−0.350067	−0.175034	+	0.984562i	$0.556003\pi$
$432$	0	0
$433$	7.96319e8	0.471389	0.235694	−	0.971827i	$-0.424264\pi$
$433$	7.96319e8	0.471389	0.235694	+	0.971827i	$0.424264\pi$
$434$	1.45388e9	0.853718
$435$	0	0
$436$	−9.13645e8	−0.527928
$437$	−5.90575e8	−0.338525
$438$	0	0
$439$	−2.22269e9	−1.25387	−0.626937	−	0.779070i	$-0.715692\pi$
$439$	−2.22269e9	−1.25387	−0.626937	+	0.779070i	$0.715692\pi$
$440$	−1.47103e9	−0.823258
$441$	0	0
$442$	−2.26160e9	−1.24577
$443$	2.58868e9	1.41470	0.707352	−	0.706861i	$-0.249890\pi$
$443$	2.58868e9	1.41470	0.707352	+	0.706861i	$0.249890\pi$
$444$	0	0
$445$	1.46281e9	0.786916
$446$	2.47241e8	0.131962
$447$	0	0
$448$	1.47631e9	0.775717
$449$	2.27545e9	1.18633	0.593164	−	0.805081i	$-0.297878\pi$
$449$	2.27545e9	1.18633	0.593164	+	0.805081i	$0.297878\pi$
$450$	0	0
$451$	−5.70509e7	−0.0292849
$452$	2.76715e8	0.140945
$453$	0	0
$454$	−1.71508e8	−0.0860177
$455$	1.43852e9	0.715937
$456$	0	0
$457$	−2.19813e9	−1.07732	−0.538662	−	0.842522i	$-0.681070\pi$
$457$	−2.19813e9	−1.07732	−0.538662	+	0.842522i	$0.681070\pi$
$458$	8.33404e7	0.0405346
$459$	0	0
$460$	1.66630e8	0.0798178
$461$	6.14119e8	0.291944	0.145972	−	0.989289i	$-0.453369\pi$
$461$	6.14119e8	0.291944	0.145972	+	0.989289i	$0.453369\pi$
$462$	0	0
$463$	1.25933e9	0.589667	0.294833	−	0.955549i	$-0.404736\pi$
$463$	1.25933e9	0.589667	0.294833	+	0.955549i	$0.404736\pi$
$464$	−3.94162e8	−0.183173
$465$	0	0
$466$	1.68118e9	0.769597
$467$	3.93421e8	0.178751	0.0893755	−	0.995998i	$-0.471513\pi$
$467$	3.93421e8	0.178751	0.0893755	+	0.995998i	$0.471513\pi$
$468$	0	0
$469$	−1.38182e9	−0.618511
$470$	−3.48158e8	−0.154680
$471$	0	0
$472$	2.58350e9	1.13087
$473$	1.36464e9	0.592933
$474$	0	0
$475$	−1.21688e9	−0.520980
$476$	−1.48135e9	−0.629555
$477$	0	0
$478$	1.03033e9	0.431498
$479$	−1.22994e9	−0.511341	−0.255671	−	0.966764i	$-0.582296\pi$
$479$	−1.22994e9	−0.511341	−0.255671	+	0.966764i	$0.582296\pi$
$480$	0	0
$481$	−2.36458e7	−0.00968825
$482$	−2.68638e9	−1.09270
$483$	0	0
$484$	1.51827e8	0.0608681
$485$	2.33851e9	0.930772
$486$	0	0
$487$	4.43712e9	1.74080	0.870401	−	0.492343i	$-0.163860\pi$
$487$	4.43712e9	1.74080	0.870401	+	0.492343i	$0.163860\pi$
$488$	−3.96691e9	−1.54519
$489$	0	0
$490$	4.84261e8	0.185949
$491$	−4.32988e9	−1.65078	−0.825392	−	0.564560i	$-0.809046\pi$
$491$	−4.32988e9	−1.65078	−0.825392	+	0.564560i	$0.809046\pi$
$492$	0	0
$493$	2.48402e9	0.933664
$494$	−3.32537e9	−1.24107
$495$	0	0
$496$	1.21885e9	0.448503
$497$	−1.80526e9	−0.659619
$498$	0	0
$499$	4.37581e8	0.157655	0.0788273	−	0.996888i	$-0.474882\pi$
$499$	4.37581e8	0.157655	0.0788273	+	0.996888i	$0.474882\pi$
$500$	1.41328e9	0.505630
$501$	0	0
$502$	−3.41626e9	−1.20528
$503$	1.94933e9	0.682963	0.341481	−	0.939889i	$-0.389071\pi$
$503$	1.94933e9	0.682963	0.341481	+	0.939889i	$0.389071\pi$
$504$	0	0
$505$	9.73725e8	0.336447
$506$	−4.14514e8	−0.142237
$507$	0	0
$508$	2.47463e9	0.837504
$509$	3.98497e9	1.33941	0.669704	−	0.742628i	$-0.266421\pi$
$509$	3.98497e9	1.33941	0.669704	+	0.742628i	$0.266421\pi$
$510$	0	0
$511$	4.78668e9	1.58694
$512$	1.85401e9	0.610474
$513$	0	0
$514$	2.00238e9	0.650392
$515$	−1.04225e9	−0.336238
$516$	0	0
$517$	−7.51291e8	−0.239107
$518$	1.78546e7	0.00564412
$519$	0	0
$520$	2.95810e9	0.922574
$521$	−3.81438e9	−1.18166	−0.590830	−	0.806796i	$-0.701199\pi$
$521$	−3.81438e9	−1.18166	−0.590830	+	0.806796i	$0.701199\pi$
$522$	0	0
$523$	−1.84543e9	−0.564081	−0.282040	−	0.959403i	$-0.591011\pi$
$523$	−1.84543e9	−0.564081	−0.282040	+	0.959403i	$0.591011\pi$
$524$	−2.23396e9	−0.678291
$525$	0	0
$526$	−2.07573e9	−0.621901
$527$	−7.68123e9	−2.28609
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−1.79980e9	−0.525119
$531$	0	0
$532$	−2.17812e9	−0.627180
$533$	1.14724e8	0.0328178
$534$	0	0
$535$	−1.67635e9	−0.473290
$536$	−2.84152e9	−0.797028
$537$	0	0
$538$	−2.86736e8	−0.0793861
$539$	1.04499e9	0.287443
$540$	0	0
$541$	−2.23015e9	−0.605541	−0.302770	−	0.953064i	$-0.597912\pi$
$541$	−2.23015e9	−0.605541	−0.302770	+	0.953064i	$0.597912\pi$
$542$	2.95767e9	0.797908
$543$	0	0
$544$	−5.12619e9	−1.36521
$545$	3.53943e9	0.936583
$546$	0	0
$547$	−6.73527e8	−0.175954	−0.0879770	−	0.996123i	$-0.528040\pi$
$547$	−6.73527e8	−0.175954	−0.0879770	+	0.996123i	$0.528040\pi$
$548$	−3.18836e9	−0.827628
$549$	0	0
$550$	−8.54107e8	−0.218899
$551$	3.65241e9	0.930141
$552$	0	0
$553$	−8.61408e8	−0.216606
$554$	−1.55145e9	−0.387661
$555$	0	0
$556$	−2.97738e9	−0.734636
$557$	−2.84289e9	−0.697056	−0.348528	−	0.937298i	$-0.613318\pi$
$557$	−2.84289e9	−0.697056	−0.348528	+	0.937298i	$0.613318\pi$
$558$	0	0
$559$	−2.74418e9	−0.664463
$560$	−9.10614e8	−0.219117
$561$	0	0
$562$	−1.58408e9	−0.376444
$563$	−3.66816e8	−0.0866302	−0.0433151	−	0.999061i	$-0.513792\pi$
$563$	−3.66816e8	−0.0866302	−0.0433151	+	0.999061i	$0.513792\pi$
$564$	0	0
$565$	−1.07199e9	−0.250046
$566$	2.94483e9	0.682657
$567$	0	0
$568$	−3.71226e9	−0.850001
$569$	−5.20650e9	−1.18482	−0.592411	−	0.805636i	$-0.701824\pi$
$569$	−5.20650e9	−1.18482	−0.592411	+	0.805636i	$0.701824\pi$
$570$	0	0
$571$	−2.65236e9	−0.596220	−0.298110	−	0.954532i	$-0.596356\pi$
$571$	−2.65236e9	−0.596220	−0.298110	+	0.954532i	$0.596356\pi$
$572$	2.02465e9	0.452338
$573$	0	0
$574$	−8.66268e7	−0.0191188
$575$	3.05029e8	0.0669119
$576$	0	0
$577$	6.12313e9	1.32696	0.663480	−	0.748194i	$-0.269079\pi$
$577$	6.12313e9	1.32696	0.663480	+	0.748194i	$0.269079\pi$
$578$	−5.62504e9	−1.21165
$579$	0	0
$580$	−1.03052e9	−0.219310
$581$	6.82763e9	1.44429
$582$	0	0
$583$	−3.88379e9	−0.811738
$584$	9.84311e9	2.04497
$585$	0	0
$586$	5.24914e9	1.07757
$587$	−4.30258e9	−0.878002	−0.439001	−	0.898487i	$-0.644668\pi$
$587$	−4.30258e9	−0.878002	−0.439001	+	0.898487i	$0.644668\pi$
$588$	0	0
$589$	−1.12942e10	−2.27747
$590$	−3.17444e9	−0.636335
$591$	0	0
$592$	1.49683e7	0.00296515
$593$	−6.32366e9	−1.24531	−0.622654	−	0.782497i	$-0.713946\pi$
$593$	−6.32366e9	−1.24531	−0.622654	+	0.782497i	$0.713946\pi$
$594$	0	0
$595$	5.73871e9	1.11688
$596$	−2.85518e9	−0.552422
$597$	0	0
$598$	8.33549e8	0.159396
$599$	−5.31827e8	−0.101106	−0.0505530	−	0.998721i	$-0.516098\pi$
$599$	−5.31827e8	−0.101106	−0.0505530	+	0.998721i	$0.516098\pi$
$600$	0	0
$601$	7.02936e9	1.32085	0.660427	−	0.750890i	$-0.270375\pi$
$601$	7.02936e9	1.32085	0.660427	+	0.750890i	$0.270375\pi$
$602$	2.07209e9	0.387099
$603$	0	0
$604$	−1.01136e9	−0.186758
$605$	−5.88172e8	−0.107984
$606$	0	0
$607$	−6.62784e9	−1.20285	−0.601425	−	0.798929i	$-0.705400\pi$
$607$	−6.62784e9	−1.20285	−0.601425	+	0.798929i	$0.705400\pi$
$608$	−7.53735e9	−1.36005
$609$	0	0
$610$	4.87430e9	0.869476
$611$	1.51078e9	0.267952
$612$	0	0
$613$	5.85988e9	1.02749	0.513744	−	0.857943i	$-0.328258\pi$
$613$	5.85988e9	1.02749	0.513744	+	0.857943i	$0.328258\pi$
$614$	−7.66832e9	−1.33694
$615$	0	0
$616$	−4.81995e9	−0.830826
$617$	−2.58683e8	−0.0443374	−0.0221687	−	0.999754i	$-0.507057\pi$
$617$	−2.58683e8	−0.0443374	−0.0221687	+	0.999754i	$0.507057\pi$
$618$	0	0
$619$	1.78962e9	0.303280	0.151640	−	0.988436i	$-0.451544\pi$
$619$	1.78962e9	0.303280	0.151640	+	0.988436i	$0.451544\pi$
$620$	3.18664e9	0.536984
$621$	0	0
$622$	−3.30854e9	−0.551278
$623$	4.79304e9	0.794150
$624$	0	0
$625$	−3.51640e9	−0.576126
$626$	5.36618e9	0.874289
$627$	0	0
$628$	4.50843e9	0.726385
$629$	−9.43307e7	−0.0151139
$630$	0	0
$631$	4.73769e9	0.750695	0.375348	−	0.926884i	$-0.377523\pi$
$631$	4.73769e9	0.750695	0.375348	+	0.926884i	$0.377523\pi$
$632$	−1.77136e9	−0.279124
$633$	0	0
$634$	6.81644e9	1.06230
$635$	−9.58663e9	−1.48579
$636$	0	0
$637$	−2.10138e9	−0.322119
$638$	2.56356e9	0.390814
$639$	0	0
$640$	8.48034e8	0.127874
$641$	−3.39484e9	−0.509115	−0.254558	−	0.967058i	$-0.581930\pi$
$641$	−3.39484e9	−0.509115	−0.254558	+	0.967058i	$0.581930\pi$
$642$	0	0
$643$	−2.32292e9	−0.344585	−0.172292	−	0.985046i	$-0.555117\pi$
$643$	−2.32292e9	−0.344585	−0.172292	+	0.985046i	$0.555117\pi$
$644$	5.45977e8	0.0805516
$645$	0	0
$646$	−1.32660e10	−1.93609
$647$	4.82089e9	0.699781	0.349891	−	0.936791i	$-0.386219\pi$
$647$	4.82089e9	0.699781	0.349891	+	0.936791i	$0.386219\pi$
$648$	0	0
$649$	−6.85015e9	−0.983657
$650$	1.71753e9	0.245306
$651$	0	0
$652$	2.48562e9	0.351212
$653$	−4.99311e9	−0.701738	−0.350869	−	0.936425i	$-0.614114\pi$
$653$	−4.99311e9	−0.701738	−0.350869	+	0.936425i	$0.614114\pi$
$654$	0	0
$655$	8.65430e9	1.20334
$656$	−7.26230e7	−0.0100441
$657$	0	0
$658$	−1.14077e9	−0.156102
$659$	−5.39303e9	−0.734064	−0.367032	−	0.930208i	$-0.619626\pi$
$659$	−5.39303e9	−0.734064	−0.367032	+	0.930208i	$0.619626\pi$
$660$	0	0
$661$	3.07114e8	0.0413613	0.0206807	−	0.999786i	$-0.493417\pi$
$661$	3.07114e8	0.0413613	0.0206807	+	0.999786i	$0.493417\pi$
$662$	−1.70943e9	−0.229007
$663$	0	0
$664$	1.40400e10	1.86114
$665$	8.43799e9	1.11266
$666$	0	0
$667$	−9.15527e8	−0.119462
$668$	7.34328e8	0.0953175
$669$	0	0
$670$	3.49149e9	0.448486
$671$	1.05183e10	1.34405
$672$	0	0
$673$	−4.75222e9	−0.600958	−0.300479	−	0.953788i	$-0.597146\pi$
$673$	−4.75222e9	−0.600958	−0.300479	+	0.953788i	$0.597146\pi$
$674$	−7.11822e9	−0.895492
$675$	0	0
$676$	−3.40512e8	−0.0423954
$677$	9.05541e9	1.12162	0.560812	−	0.827943i	$-0.310489\pi$
$677$	9.05541e9	1.12162	0.560812	+	0.827943i	$0.310489\pi$
$678$	0	0
$679$	7.66234e9	0.939328
$680$	1.18008e10	1.43923
$681$	0	0
$682$	−7.92718e9	−0.956916
$683$	1.03421e10	1.24204	0.621019	−	0.783795i	$-0.286719\pi$
$683$	1.03421e10	1.24204	0.621019	+	0.783795i	$0.286719\pi$
$684$	0	0
$685$	1.23516e10	1.46827
$686$	6.73251e9	0.796237
$687$	0	0
$688$	1.73713e9	0.203363
$689$	7.80995e9	0.909664
$690$	0	0
$691$	−8.96571e9	−1.03374	−0.516870	−	0.856064i	$-0.672903\pi$
$691$	−8.96571e9	−1.03374	−0.516870	+	0.856064i	$0.672903\pi$
$692$	−2.30901e9	−0.264883
$693$	0	0
$694$	−9.62960e9	−1.09358
$695$	1.15343e10	1.30330
$696$	0	0
$697$	4.57672e8	0.0511964
$698$	3.28227e9	0.365326
$699$	0	0
$700$	1.12499e9	0.123967
$701$	−2.90654e9	−0.318686	−0.159343	−	0.987223i	$-0.550938\pi$
$701$	−2.90654e9	−0.318686	−0.159343	+	0.987223i	$0.550938\pi$
$702$	0	0
$703$	−1.38700e8	−0.0150568
$704$	−8.04946e9	−0.869485
$705$	0	0
$706$	−9.36411e9	−1.00150
$707$	3.19050e9	0.339540
$708$	0	0
$709$	3.11906e9	0.328671	0.164335	−	0.986405i	$-0.447452\pi$
$709$	3.11906e9	0.328671	0.164335	+	0.986405i	$0.447452\pi$
$710$	4.56140e9	0.478293
$711$	0	0
$712$	9.85618e9	1.02336
$713$	2.83105e9	0.292505
$714$	0	0
$715$	−7.84342e9	−0.802480
$716$	−4.69002e9	−0.477506
$717$	0	0
$718$	8.37966e8	0.0844871
$719$	6.74098e9	0.676351	0.338175	−	0.941083i	$-0.390190\pi$
$719$	6.74098e9	0.676351	0.338175	+	0.941083i	$0.390190\pi$
$720$	0	0
$721$	−3.41503e9	−0.339329
$722$	−1.21054e10	−1.19701
$723$	0	0
$724$	−6.14985e9	−0.602253
$725$	−1.88645e9	−0.183849
$726$	0	0
$727$	7.66111e8	0.0739472	0.0369736	−	0.999316i	$-0.488228\pi$
$727$	7.66111e8	0.0739472	0.0369736	+	0.999316i	$0.488228\pi$
$728$	9.69249e9	0.931055
$729$	0	0
$730$	−1.20946e10	−1.15070
$731$	−1.09474e10	−1.03658
$732$	0	0
$733$	9.36723e9	0.878511	0.439255	−	0.898362i	$-0.355242\pi$
$733$	9.36723e9	0.878511	0.439255	+	0.898362i	$0.355242\pi$
$734$	5.76002e9	0.537635
$735$	0	0
$736$	1.88934e9	0.174678
$737$	7.53430e9	0.693276
$738$	0	0
$739$	−2.03255e8	−0.0185262	−0.00926310	−	0.999957i	$-0.502949\pi$
$739$	−2.03255e8	−0.0185262	−0.00926310	+	0.999957i	$0.502949\pi$
$740$	3.91340e7	0.00355012
$741$	0	0
$742$	−5.89719e9	−0.529946
$743$	−1.22714e10	−1.09757	−0.548786	−	0.835963i	$-0.684910\pi$
$743$	−1.22714e10	−1.09757	−0.548786	+	0.835963i	$0.684910\pi$
$744$	0	0
$745$	1.10609e10	0.980037
$746$	1.12207e10	0.989541
$747$	0	0
$748$	8.07697e9	0.705656
$749$	−5.49273e9	−0.477641
$750$	0	0
$751$	1.38569e10	1.19379	0.596893	−	0.802321i	$-0.296402\pi$
$751$	1.38569e10	1.19379	0.596893	+	0.802321i	$0.296402\pi$
$752$	−9.56357e8	−0.0820083
$753$	0	0
$754$	−5.15508e9	−0.437961
$755$	3.91800e9	0.331322
$756$	0	0
$757$	1.37394e10	1.15115	0.575574	−	0.817750i	$-0.304779\pi$
$757$	1.37394e10	1.15115	0.575574	+	0.817750i	$0.304779\pi$
$758$	4.49598e9	0.374958
$759$	0	0
$760$	1.73515e10	1.43380
$761$	2.26204e10	1.86061	0.930303	−	0.366792i	$-0.119544\pi$
$761$	2.26204e10	1.86061	0.930303	+	0.366792i	$0.119544\pi$
$762$	0	0
$763$	1.15973e10	0.945193
$764$	8.94268e9	0.725506
$765$	0	0
$766$	−5.42858e9	−0.436401
$767$	1.37750e10	1.10232
$768$	0	0
$769$	−1.45410e10	−1.15306	−0.576528	−	0.817077i	$-0.695593\pi$
$769$	−1.45410e10	−1.15306	−0.576528	+	0.817077i	$0.695593\pi$
$770$	5.92247e9	0.467504
$771$	0	0
$772$	1.01662e9	0.0795236
$773$	1.39990e9	0.109011	0.0545053	−	0.998513i	$-0.482642\pi$
$773$	1.39990e9	0.109011	0.0545053	+	0.998513i	$0.482642\pi$
$774$	0	0
$775$	5.83339e9	0.450158
$776$	1.57565e10	1.21044
$777$	0	0
$778$	−1.54240e10	−1.17427
$779$	6.72944e8	0.0510032
$780$	0	0
$781$	9.84307e9	0.739354
$782$	3.32530e9	0.248661
$783$	0	0
$784$	1.33022e9	0.0985866
$785$	−1.74655e10	−1.28866
$786$	0	0
$787$	2.28181e10	1.66866	0.834329	−	0.551267i	$-0.185856\pi$
$787$	2.28181e10	1.66866	0.834329	+	0.551267i	$0.185856\pi$
$788$	4.33325e9	0.315480
$789$	0	0
$790$	2.17654e9	0.157062
$791$	−3.51246e9	−0.252344
$792$	0	0
$793$	−2.11513e10	−1.50619
$794$	−8.42857e9	−0.597561
$795$	0	0
$796$	−1.96874e9	−0.138354
$797$	−1.59030e10	−1.11269	−0.556345	−	0.830951i	$-0.687797\pi$
$797$	−1.59030e10	−1.11269	−0.556345	+	0.830951i	$0.687797\pi$
$798$	0	0
$799$	6.02699e9	0.418010
$800$	3.89300e9	0.268825
$801$	0	0
$802$	−5.06813e9	−0.346927
$803$	−2.60990e10	−1.77877
$804$	0	0
$805$	−2.11510e9	−0.142904
$806$	1.59408e10	1.07236
$807$	0	0
$808$	6.56080e9	0.437539
$809$	−1.86254e10	−1.23676	−0.618382	−	0.785878i	$-0.712212\pi$
$809$	−1.86254e10	−1.23676	−0.618382	+	0.785878i	$0.712212\pi$
$810$	0	0
$811$	−3.12454e9	−0.205690	−0.102845	−	0.994697i	$-0.532795\pi$
$811$	−3.12454e9	−0.205690	−0.102845	+	0.994697i	$0.532795\pi$
$812$	−3.37659e9	−0.221326
$813$	0	0
$814$	−9.73511e7	−0.00632638
$815$	−9.62923e9	−0.623075
$816$	0	0
$817$	−1.60967e10	−1.03266
$818$	−6.20752e9	−0.396535
$819$	0	0
$820$	−1.89870e8	−0.0120256
$821$	1.64768e10	1.03913	0.519566	−	0.854430i	$-0.326094\pi$
$821$	1.64768e10	1.03913	0.519566	+	0.854430i	$0.326094\pi$
$822$	0	0
$823$	−1.90558e9	−0.119159	−0.0595797	−	0.998224i	$-0.518976\pi$
$823$	−1.90558e9	−0.119159	−0.0595797	+	0.998224i	$0.518976\pi$
$824$	−7.02251e9	−0.437267
$825$	0	0
$826$	−1.04014e10	−0.642185
$827$	1.64287e10	1.01003	0.505014	−	0.863111i	$-0.331487\pi$
$827$	1.64287e10	1.01003	0.505014	+	0.863111i	$0.331487\pi$
$828$	0	0
$829$	−2.75444e10	−1.67916	−0.839581	−	0.543235i	$-0.817199\pi$
$829$	−2.75444e10	−1.67916	−0.839581	+	0.543235i	$0.817199\pi$
$830$	−1.72515e10	−1.04726
$831$	0	0
$832$	1.61867e10	0.974378
$833$	−8.38310e9	−0.502513
$834$	0	0
$835$	−2.84477e9	−0.169100
$836$	1.18761e10	0.702993
$837$	0	0
$838$	2.28406e10	1.34077
$839$	−2.38175e10	−1.39229	−0.696145	−	0.717901i	$-0.745103\pi$
$839$	−2.38175e10	−1.39229	−0.696145	+	0.717901i	$0.745103\pi$
$840$	0	0
$841$	−1.15878e10	−0.671762
$842$	1.36156e10	0.786038
$843$	0	0
$844$	−4.99011e9	−0.285701
$845$	1.31913e9	0.0752125
$846$	0	0
$847$	−1.92720e9	−0.108977
$848$	−4.94388e9	−0.278408
$849$	0	0
$850$	6.85180e9	0.382682
$851$	3.47672e7	0.00193382
$852$	0	0
$853$	−2.20575e10	−1.21684	−0.608422	−	0.793614i	$-0.708197\pi$
$853$	−2.20575e10	−1.21684	−0.608422	+	0.793614i	$0.708197\pi$
$854$	1.59711e10	0.877469
$855$	0	0
$856$	−1.12950e10	−0.615500
$857$	−2.22968e10	−1.21007	−0.605035	−	0.796199i	$-0.706841\pi$
$857$	−2.22968e10	−1.21007	−0.605035	+	0.796199i	$0.706841\pi$
$858$	0	0
$859$	2.41019e10	1.29740	0.648702	−	0.761042i	$-0.275312\pi$
$859$	2.41019e10	1.29740	0.648702	+	0.761042i	$0.275312\pi$
$860$	4.54164e9	0.243483
$861$	0	0
$862$	4.81728e9	0.256169
$863$	2.81619e10	1.49150	0.745752	−	0.666224i	$-0.232090\pi$
$863$	2.81619e10	1.49150	0.745752	+	0.666224i	$0.232090\pi$
$864$	0	0
$865$	8.94504e9	0.469922
$866$	−6.59276e9	−0.344949
$867$	0	0
$868$	1.04413e10	0.541921
$869$	4.69677e9	0.242789
$870$	0	0
$871$	−1.51508e10	−0.776912
$872$	2.38481e10	1.21800
$873$	0	0
$874$	4.88940e9	0.247722
$875$	−1.79393e10	−0.905271
$876$	0	0
$877$	1.60300e9	0.0802483	0.0401241	−	0.999195i	$-0.487225\pi$
$877$	1.60300e9	0.0802483	0.0401241	+	0.999195i	$0.487225\pi$
$878$	1.84018e10	0.917549
$879$	0	0
$880$	4.96506e9	0.245604
$881$	1.31584e10	0.648316	0.324158	−	0.946003i	$-0.394919\pi$
$881$	1.31584e10	0.648316	0.324158	+	0.946003i	$0.394919\pi$
$882$	0	0
$883$	−3.44816e9	−0.168549	−0.0842743	−	0.996443i	$-0.526857\pi$
$883$	−3.44816e9	−0.168549	−0.0842743	+	0.996443i	$0.526857\pi$
$884$	−1.62421e10	−0.790785
$885$	0	0
$886$	−2.14318e10	−1.03524
$887$	−3.55622e10	−1.71102	−0.855512	−	0.517782i	$-0.826758\pi$
$887$	−3.55622e10	−1.71102	−0.855512	+	0.517782i	$0.826758\pi$
$888$	0	0
$889$	−3.14115e10	−1.49945
$890$	−1.21107e10	−0.575842
$891$	0	0
$892$	1.77560e9	0.0837662
$893$	8.86186e9	0.416433
$894$	0	0
$895$	1.81690e10	0.847131
$896$	2.77866e9	0.129050
$897$	0	0
$898$	−1.88385e10	−0.868121
$899$	−1.75086e10	−0.803697
$900$	0	0
$901$	3.11564e10	1.41909
$902$	4.72327e8	0.0214299
$903$	0	0
$904$	−7.22286e9	−0.325177
$905$	2.38243e10	1.06844
$906$	0	0
$907$	−4.21633e9	−0.187633	−0.0938165	−	0.995590i	$-0.529907\pi$
$907$	−4.21633e9	−0.187633	−0.0938165	+	0.995590i	$0.529907\pi$
$908$	−1.23171e9	−0.0546021
$909$	0	0
$910$	−1.19095e10	−0.523902
$911$	−3.08748e10	−1.35297	−0.676487	−	0.736455i	$-0.736498\pi$
$911$	−3.08748e10	−1.35297	−0.676487	+	0.736455i	$0.736498\pi$
$912$	0	0
$913$	−3.72272e10	−1.61887
$914$	1.81984e10	0.788354
$915$	0	0
$916$	5.98524e8	0.0257305
$917$	2.83566e10	1.21440
$918$	0	0
$919$	−1.02154e10	−0.434163	−0.217082	−	0.976153i	$-0.569654\pi$
$919$	−1.02154e10	−0.434163	−0.217082	+	0.976153i	$0.569654\pi$
$920$	−4.34940e9	−0.184150
$921$	0	0
$922$	−5.08432e9	−0.213636
$923$	−1.97935e10	−0.828547
$924$	0	0
$925$	7.16379e7	0.00297609
$926$	−1.04261e10	−0.431501
$927$	0	0
$928$	−1.16846e10	−0.479951
$929$	−1.51656e10	−0.620591	−0.310295	−	0.950640i	$-0.600428\pi$
$929$	−1.51656e10	−0.620591	−0.310295	+	0.950640i	$0.600428\pi$
$930$	0	0
$931$	−1.23262e10	−0.500616
$932$	1.20737e10	0.488522
$933$	0	0
$934$	−3.25715e9	−0.130805
$935$	−3.12900e10	−1.25188
$936$	0	0
$937$	−6.54065e9	−0.259736	−0.129868	−	0.991531i	$-0.541455\pi$
$937$	−6.54065e9	−0.259736	−0.129868	+	0.991531i	$0.541455\pi$
$938$	1.14402e10	0.452608
$939$	0	0
$940$	−2.50036e9	−0.0981871
$941$	−4.48310e10	−1.75394	−0.876970	−	0.480546i	$-0.840439\pi$
$941$	−4.48310e10	−1.75394	−0.876970	+	0.480546i	$0.840439\pi$
$942$	0	0
$943$	−1.68683e8	−0.00655058
$944$	−8.71991e9	−0.337373
$945$	0	0
$946$	−1.12979e10	−0.433891
$947$	−4.44963e10	−1.70255	−0.851274	−	0.524722i	$-0.824169\pi$
$947$	−4.44963e10	−1.70255	−0.851274	+	0.524722i	$0.824169\pi$
$948$	0	0
$949$	5.24828e10	1.99336
$950$	1.00746e10	0.381238
$951$	0	0
$952$	3.86665e10	1.45246
$953$	−4.58181e10	−1.71479	−0.857397	−	0.514655i	$-0.827920\pi$
$953$	−4.58181e10	−1.71479	−0.857397	+	0.514655i	$0.827920\pi$
$954$	0	0
$955$	−3.46437e10	−1.28710
$956$	7.39950e9	0.273905
$957$	0	0
$958$	1.01828e10	0.374185
$959$	4.04712e10	1.48177
$960$	0	0
$961$	2.66285e10	0.967866
$962$	1.95764e8	0.00708958
$963$	0	0
$964$	−1.92927e10	−0.693623
$965$	−3.93834e9	−0.141081
$966$	0	0
$967$	9.38045e9	0.333604	0.166802	−	0.985990i	$-0.446656\pi$
$967$	9.38045e9	0.333604	0.166802	+	0.985990i	$0.446656\pi$
$968$	−3.96301e9	−0.140430
$969$	0	0
$970$	−1.93606e10	−0.681112
$971$	−4.17079e10	−1.46201	−0.731007	−	0.682370i	$-0.760949\pi$
$971$	−4.17079e10	−1.46201	−0.731007	+	0.682370i	$0.760949\pi$
$972$	0	0
$973$	3.77931e10	1.31528
$974$	−3.67351e10	−1.27387
$975$	0	0
$976$	1.33893e10	0.460980
$977$	3.51002e10	1.20414	0.602072	−	0.798442i	$-0.294342\pi$
$977$	3.51002e10	1.20414	0.602072	+	0.798442i	$0.294342\pi$
$978$	0	0
$979$	−2.61337e10	−0.890147
$980$	3.47781e9	0.118036
$981$	0	0
$982$	3.58472e10	1.20800
$983$	−9.51453e9	−0.319485	−0.159742	−	0.987159i	$-0.551066\pi$
$983$	−9.51453e9	−0.319485	−0.159742	+	0.987159i	$0.551066\pi$
$984$	0	0
$985$	−1.67869e10	−0.559684
$986$	−2.05653e10	−0.683228
$987$	0	0
$988$	−2.38817e10	−0.787801
$989$	4.03485e9	0.132630
$990$	0	0
$991$	4.12180e10	1.34533	0.672666	−	0.739946i	$-0.265149\pi$
$991$	4.12180e10	1.34533	0.672666	+	0.739946i	$0.265149\pi$
$992$	3.61319e10	1.17517
$993$	0	0
$994$	1.49459e10	0.482690
$995$	7.62683e9	0.245450
$996$	0	0
$997$	3.96827e10	1.26814	0.634071	−	0.773275i	$-0.281383\pi$
$997$	3.96827e10	1.26814	0.634071	+	0.773275i	$0.281383\pi$
$998$	−3.62275e9	−0.115367
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.h.1.4	yes	12
3.2	odd	2		207.8.a.g.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.8.a.g.1.9	✓	12	3.2	odd	2
207.8.a.h.1.4	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-8.27904 q^{2} -59.4574 q^{4} +230.336 q^{5} +754.718 q^{7} +1551.97 q^{8} +O(q^{10})\)	\(q-8.27904 q^{2} -59.4574 q^{4} +230.336 q^{5} +754.718 q^{7} +1551.97 q^{8} -1906.96 q^{10} -4115.05 q^{11} +8274.99 q^{13} -6248.34 q^{14} -5238.26 q^{16} +33011.7 q^{17} +48539.1 q^{19} -13695.2 q^{20} +34068.7 q^{22} -12167.0 q^{23} -25070.2 q^{25} -68509.0 q^{26} -44873.6 q^{28} +75246.7 q^{29} -232682. q^{31} -155284. q^{32} -273305. q^{34} +173839. q^{35} -2857.50 q^{37} -401857. q^{38} +357475. q^{40} +13864.0 q^{41} -331623. q^{43} +244670. q^{44} +100731. q^{46} +182572. q^{47} -253943. q^{49} +207557. q^{50} -492010. q^{52} +943801. q^{53} -947846. q^{55} +1.17130e6 q^{56} -622971. q^{58} +1.66466e6 q^{59} -2.55605e6 q^{61} +1.92639e6 q^{62} +1.95610e6 q^{64} +1.90603e6 q^{65} -1.83091e6 q^{67} -1.96279e6 q^{68} -1.43922e6 q^{70} -2.39197e6 q^{71} +6.34234e6 q^{73} +23657.3 q^{74} -2.88601e6 q^{76} -3.10570e6 q^{77} -1.14136e6 q^{79} -1.20656e6 q^{80} -114780. q^{82} +9.04659e6 q^{83} +7.60378e6 q^{85} +2.74552e6 q^{86} -6.38643e6 q^{88} +6.35076e6 q^{89} +6.24529e6 q^{91} +723419. q^{92} -1.51152e6 q^{94} +1.11803e7 q^{95} +1.01526e7 q^{97} +2.10241e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8}+O(q^{10}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8} + 10270 q^{10} - 460 q^{11} - 21060 q^{13} + 4268 q^{14} + 56676 q^{16} + 73124 q^{17} + 8508 q^{19} + 170538 q^{20} + 124754 q^{22} - 146004 q^{23} + 194064 q^{25} + 206080 q^{26} - 390416 q^{28} + 268640 q^{29} - 191880 q^{31} + 1180172 q^{32} - 221436 q^{34} - 487244 q^{35} + 650332 q^{37} + 1432950 q^{38} + 1775722 q^{40} + 980088 q^{41} - 861276 q^{43} + 800666 q^{44} - 194672 q^{46} + 403868 q^{47} + 1699160 q^{49} + 2919092 q^{50} - 2369520 q^{52} - 201948 q^{53} - 1553512 q^{55} - 4848116 q^{56} + 3720672 q^{58} + 1302676 q^{59} + 2141364 q^{61} + 2160944 q^{62} + 9702136 q^{64} + 9099536 q^{65} - 6159260 q^{67} + 18442208 q^{68} - 10891632 q^{70} + 12584184 q^{71} + 7435872 q^{73} + 22491442 q^{74} + 5721386 q^{76} + 16450568 q^{77} + 3658028 q^{79} + 49905778 q^{80} - 5516316 q^{82} + 26137900 q^{83} + 5169556 q^{85} + 30678550 q^{86} + 14753046 q^{88} + 27235908 q^{89} - 7657216 q^{91} - 7786880 q^{92} - 23519352 q^{94} + 63623628 q^{95} + 22454720 q^{97} + 94951532 q^{98}+O(q^{100}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8 + 10270 * q^10 - 460 * q^11 - 21060 * q^13 + 4268 * q^14 + 56676 * q^16 + 73124 * q^17 + 8508 * q^19 + 170538 * q^20 + 124754 * q^22 - 146004 * q^23 + 194064 * q^25 + 206080 * q^26 - 390416 * q^28 + 268640 * q^29 - 191880 * q^31 + 1180172 * q^32 - 221436 * q^34 - 487244 * q^35 + 650332 * q^37 + 1432950 * q^38 + 1775722 * q^40 + 980088 * q^41 - 861276 * q^43 + 800666 * q^44 - 194672 * q^46 + 403868 * q^47 + 1699160 * q^49 + 2919092 * q^50 - 2369520 * q^52 - 201948 * q^53 - 1553512 * q^55 - 4848116 * q^56 + 3720672 * q^58 + 1302676 * q^59 + 2141364 * q^61 + 2160944 * q^62 + 9702136 * q^64 + 9099536 * q^65 - 6159260 * q^67 + 18442208 * q^68 - 10891632 * q^70 + 12584184 * q^71 + 7435872 * q^73 + 22491442 * q^74 + 5721386 * q^76 + 16450568 * q^77 + 3658028 * q^79 + 49905778 * q^80 - 5516316 * q^82 + 26137900 * q^83 + 5169556 * q^85 + 30678550 * q^86 + 14753046 * q^88 + 27235908 * q^89 - 7657216 * q^91 - 7786880 * q^92 - 23519352 * q^94 + 63623628 * q^95 + 22454720 * q^97 + 94951532 * q^98

Introduction

L-functions

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