LMFDB - Embedded newform 207.8.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.6637002752$
Analytic rank:	$1$
Dimension:	$8$
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} - 757x^{6} - 1170x^{5} + 170343x^{4} + 424132x^{3} - 9973075x^{2} - 5161010x + 130545120 $ x^8 - 757x^6 - 1170x^5 + 170343x^4 + 424132x^3 - 9973075x^2 - 5161010x + 130545120
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-14.7586$ 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)

$f(q)$	$=$	$q-17.7586 q^{2} +187.368 q^{4} -32.5148 q^{5} +1672.82 q^{7} -1054.29 q^{8} +O(q^{10})$	\(q-17.7586 q^{2} +187.368 q^{4} -32.5148 q^{5} +1672.82 q^{7} -1054.29 q^{8} +577.418 q^{10} +3105.35 q^{11} -7087.75 q^{13} -29707.0 q^{14} -5260.35 q^{16} -18708.2 q^{17} +34552.7 q^{19} -6092.24 q^{20} -55146.7 q^{22} -12167.0 q^{23} -77067.8 q^{25} +125869. q^{26} +313434. q^{28} -250815. q^{29} -81911.3 q^{31} +228366. q^{32} +332232. q^{34} -54391.6 q^{35} -413414. q^{37} -613608. q^{38} +34280.1 q^{40} +538737. q^{41} -430259. q^{43} +581843. q^{44} +216069. q^{46} +533167. q^{47} +1.97480e6 q^{49} +1.36862e6 q^{50} -1.32802e6 q^{52} +1.03569e6 q^{53} -100970. q^{55} -1.76364e6 q^{56} +4.45412e6 q^{58} -458111. q^{59} +1.16409e6 q^{61} +1.45463e6 q^{62} -3.38213e6 q^{64} +230457. q^{65} -4.02241e6 q^{67} -3.50532e6 q^{68} +965919. q^{70} -2.96942e6 q^{71} +12116.2 q^{73} +7.34166e6 q^{74} +6.47407e6 q^{76} +5.19470e6 q^{77} -5.33176e6 q^{79} +171039. q^{80} -9.56721e6 q^{82} +3.28547e6 q^{83} +608295. q^{85} +7.64081e6 q^{86} -3.27395e6 q^{88} +401235. q^{89} -1.18566e7 q^{91} -2.27971e6 q^{92} -9.46830e6 q^{94} -1.12348e6 q^{95} +1.54716e6 q^{97} -3.50696e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8}+O(q^{10}) $ 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8} + 11720 q^{10} - 6932 q^{11} + 12404 q^{13} - 30222 q^{14} + 27058 q^{16} - 24434 q^{17} - 14682 q^{19} + 3760 q^{20} + 36294 q^{22} - 97336 q^{23} + 144644 q^{25} - 325840 q^{26} - 21566 q^{28} - 255356 q^{29} + 450764 q^{31} - 647588 q^{32} + 191822 q^{34} - 1022616 q^{35} + 206240 q^{37} - 737372 q^{38} + 590028 q^{40} - 1053344 q^{41} + 1587806 q^{43} - 589366 q^{44} + 292008 q^{46} - 443336 q^{47} + 1944828 q^{49} + 1556112 q^{50} - 614236 q^{52} + 375530 q^{53} + 407792 q^{55} + 1316922 q^{56} - 1413384 q^{58} - 624008 q^{59} - 2005568 q^{61} + 3908272 q^{62} - 5082310 q^{64} - 646124 q^{65} - 2712286 q^{67} + 2289698 q^{68} - 16499468 q^{70} + 6287176 q^{71} - 10358312 q^{73} + 2000150 q^{74} - 25107464 q^{76} + 2156840 q^{77} - 8800574 q^{79} - 2384344 q^{80} - 31799800 q^{82} - 384948 q^{83} - 17826684 q^{85} + 11563928 q^{86} - 25202782 q^{88} + 3445530 q^{89} - 16316740 q^{91} - 6837854 q^{92} - 24237616 q^{94} - 26164288 q^{95} - 28043764 q^{97} + 9998012 q^{98}+O(q^{100}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8 + 11720 * q^10 - 6932 * q^11 + 12404 * q^13 - 30222 * q^14 + 27058 * q^16 - 24434 * q^17 - 14682 * q^19 + 3760 * q^20 + 36294 * q^22 - 97336 * q^23 + 144644 * q^25 - 325840 * q^26 - 21566 * q^28 - 255356 * q^29 + 450764 * q^31 - 647588 * q^32 + 191822 * q^34 - 1022616 * q^35 + 206240 * q^37 - 737372 * q^38 + 590028 * q^40 - 1053344 * q^41 + 1587806 * q^43 - 589366 * q^44 + 292008 * q^46 - 443336 * q^47 + 1944828 * q^49 + 1556112 * q^50 - 614236 * q^52 + 375530 * q^53 + 407792 * q^55 + 1316922 * q^56 - 1413384 * q^58 - 624008 * q^59 - 2005568 * q^61 + 3908272 * q^62 - 5082310 * q^64 - 646124 * q^65 - 2712286 * q^67 + 2289698 * q^68 - 16499468 * q^70 + 6287176 * q^71 - 10358312 * q^73 + 2000150 * q^74 - 25107464 * q^76 + 2156840 * q^77 - 8800574 * q^79 - 2384344 * q^80 - 31799800 * q^82 - 384948 * q^83 - 17826684 * q^85 + 11563928 * q^86 - 25202782 * q^88 + 3445530 * q^89 - 16316740 * q^91 - 6837854 * q^92 - 24237616 * q^94 - 26164288 * q^95 - 28043764 * q^97 + 9998012 * 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 $

$2$	−17.7586	−1.56965	−0.784827	−	0.619715i	$-0.787248\pi$
$2$	−17.7586	−1.56965	−0.784827	+	0.619715i	$0.787248\pi$
$3$	0	0
$3$	0	0
$4$	187.368	1.46381
$5$	−32.5148	−0.116329	−0.0581643	−	0.998307i	$-0.518525\pi$
$5$	−32.5148	−0.116329	−0.0581643	+	0.998307i	$0.518525\pi$
$6$	0	0
$7$	1672.82	1.84335	0.921674	−	0.387966i	$-0.126822\pi$
$7$	1672.82	1.84335	0.921674	+	0.387966i	$0.126822\pi$
$8$	−1054.29	−0.728024
$9$	0	0
$10$	577.418	0.182596
$11$	3105.35	0.703455	0.351727	−	0.936102i	$-0.385594\pi$
$11$	3105.35	0.703455	0.351727	+	0.936102i	$0.385594\pi$
$12$	0	0
$13$	−7087.75	−0.894760	−0.447380	−	0.894344i	$-0.647643\pi$
$13$	−7087.75	−0.894760	−0.447380	+	0.894344i	$0.647643\pi$
$14$	−29707.0	−2.89342
$15$	0	0
$16$	−5260.35	−0.321066
$17$	−18708.2	−0.923552	−0.461776	−	0.886997i	$-0.652788\pi$
$17$	−18708.2	−0.923552	−0.461776	+	0.886997i	$0.652788\pi$
$18$	0	0
$19$	34552.7	1.15570	0.577849	−	0.816143i	$-0.303892\pi$
$19$	34552.7	1.15570	0.577849	+	0.816143i	$0.303892\pi$
$20$	−6092.24	−0.170283
$21$	0	0
$22$	−55146.7	−1.10418
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−77067.8	−0.986468
$26$	125869.	1.40446
$27$	0	0
$28$	313434.	2.69831
$29$	−250815.	−1.90968	−0.954838	−	0.297127i	$-0.903972\pi$
$29$	−250815.	−1.90968	−0.954838	+	0.297127i	$0.903972\pi$
$30$	0	0
$31$	−81911.3	−0.493831	−0.246915	−	0.969037i	$-0.579417\pi$
$31$	−81911.3	−0.493831	−0.246915	+	0.969037i	$0.579417\pi$
$32$	228366.	1.23199
$33$	0	0
$34$	332232.	1.44966
$35$	−54391.6	−0.214434
$36$	0	0
$37$	−413414.	−1.34177	−0.670887	−	0.741560i	$-0.734086\pi$
$37$	−413414.	−1.34177	−0.670887	+	0.741560i	$0.734086\pi$
$38$	−613608.	−1.81405
$39$	0	0
$40$	34280.1	0.0846901
$41$	538737.	1.22077	0.610384	−	0.792106i	$-0.291015\pi$
$41$	538737.	1.22077	0.610384	+	0.792106i	$0.291015\pi$
$42$	0	0
$43$	−430259.	−0.825260	−0.412630	−	0.910899i	$-0.635390\pi$
$43$	−430259.	−0.825260	−0.412630	+	0.910899i	$0.635390\pi$
$44$	581843.	1.02973
$45$	0	0
$46$	216069.	0.327295
$47$	533167.	0.749067	0.374534	−	0.927213i	$-0.377803\pi$
$47$	533167.	0.749067	0.374534	+	0.927213i	$0.377803\pi$
$48$	0	0
$49$	1.97480e6	2.39793
$50$	1.36862e6	1.54841
$51$	0	0
$52$	−1.32802e6	−1.30976
$53$	1.03569e6	0.955576	0.477788	−	0.878475i	$-0.341439\pi$
$53$	1.03569e6	0.955576	0.477788	+	0.878475i	$0.341439\pi$
$54$	0	0
$55$	−100970.	−0.0818320
$56$	−1.76364e6	−1.34200
$57$	0	0
$58$	4.45412e6	2.99753
$59$	−458111.	−0.290395	−0.145197	−	0.989403i	$-0.546382\pi$
$59$	−458111.	−0.290395	−0.145197	+	0.989403i	$0.546382\pi$
$60$	0	0
$61$	1.16409e6	0.656647	0.328323	−	0.944565i	$-0.393516\pi$
$61$	1.16409e6	0.656647	0.328323	+	0.944565i	$0.393516\pi$
$62$	1.45463e6	0.775143
$63$	0	0
$64$	−3.38213e6	−1.61273
$65$	230457.	0.104086
$66$	0	0
$67$	−4.02241e6	−1.63390	−0.816949	−	0.576710i	$-0.804336\pi$
$67$	−4.02241e6	−1.63390	−0.816949	+	0.576710i	$0.804336\pi$
$68$	−3.50532e6	−1.35191
$69$	0	0
$70$	965919.	0.336587
$71$	−2.96942e6	−0.984616	−0.492308	−	0.870421i	$-0.663847\pi$
$71$	−2.96942e6	−0.984616	−0.492308	+	0.870421i	$0.663847\pi$
$72$	0	0
$73$	12116.2	0.00364532	0.00182266	−	0.999998i	$-0.499420\pi$
$73$	12116.2	0.00364532	0.00182266	+	0.999998i	$0.499420\pi$
$74$	7.34166e6	2.10612
$75$	0	0
$76$	6.47407e6	1.69173
$77$	5.19470e6	1.29671
$78$	0	0
$79$	−5.33176e6	−1.21668	−0.608339	−	0.793677i	$-0.708164\pi$
$79$	−5.33176e6	−1.21668	−0.608339	+	0.793677i	$0.708164\pi$
$80$	171039.	0.0373492
$81$	0	0
$82$	−9.56721e6	−1.91618
$83$	3.28547e6	0.630702	0.315351	−	0.948975i	$-0.397878\pi$
$83$	3.28547e6	0.630702	0.315351	+	0.948975i	$0.397878\pi$
$84$	0	0
$85$	608295.	0.107436
$86$	7.64081e6	1.29537
$87$	0	0
$88$	−3.27395e6	−0.512132
$89$	401235.	0.0603301	0.0301650	−	0.999545i	$-0.490397\pi$
$89$	401235.	0.0603301	0.0301650	+	0.999545i	$0.490397\pi$
$90$	0	0
$91$	−1.18566e7	−1.64935
$92$	−2.27971e6	−0.305226
$93$	0	0
$94$	−9.46830e6	−1.17578
$95$	−1.12348e6	−0.134441
$96$	0	0
$97$	1.54716e6	0.172121	0.0860606	−	0.996290i	$-0.472572\pi$
$97$	1.54716e6	0.172121	0.0860606	+	0.996290i	$0.472572\pi$
$98$	−3.50696e7	−3.76392
$99$	0	0
$100$	−1.44400e7	−1.44400
$101$	−1.09935e7	−1.06172	−0.530862	−	0.847458i	$-0.678132\pi$
$101$	−1.09935e7	−1.06172	−0.530862	+	0.847458i	$0.678132\pi$
$102$	0	0
$103$	−1.08340e7	−0.976916	−0.488458	−	0.872588i	$-0.662440\pi$
$103$	−1.08340e7	−0.976916	−0.488458	+	0.872588i	$0.662440\pi$
$104$	7.47256e6	0.651407
$105$	0	0
$106$	−1.83925e7	−1.49992
$107$	−1.48870e6	−0.117480	−0.0587399	−	0.998273i	$-0.518708\pi$
$107$	−1.48870e6	−0.117480	−0.0587399	+	0.998273i	$0.518708\pi$
$108$	0	0
$109$	1.41429e7	1.04603	0.523017	−	0.852322i	$-0.324807\pi$
$109$	1.41429e7	1.04603	0.523017	+	0.852322i	$0.324807\pi$
$110$	1.79309e6	0.128448
$111$	0	0
$112$	−8.79964e6	−0.591837
$113$	−1.47726e7	−0.963122	−0.481561	−	0.876413i	$-0.659930\pi$
$113$	−1.47726e7	−0.963122	−0.481561	+	0.876413i	$0.659930\pi$
$114$	0	0
$115$	395608.	0.0242562
$116$	−4.69946e7	−2.79541
$117$	0	0
$118$	8.13542e6	0.455819
$119$	−3.12956e7	−1.70243
$120$	0	0
$121$	−9.84397e6	−0.505151
$122$	−2.06726e7	−1.03071
$123$	0	0
$124$	−1.53476e7	−0.722875
$125$	5.04607e6	0.231083
$126$	0	0
$127$	1.42674e7	0.618061	0.309031	−	0.951052i	$-0.399995\pi$
$127$	1.42674e7	0.618061	0.309031	+	0.951052i	$0.399995\pi$
$128$	3.08311e7	1.29943
$129$	0	0
$130$	−4.09260e6	−0.163379
$131$	−2.80585e7	−1.09047	−0.545237	−	0.838282i	$-0.683560\pi$
$131$	−2.80585e7	−1.09047	−0.545237	+	0.838282i	$0.683560\pi$
$132$	0	0
$133$	5.78006e7	2.13035
$134$	7.14324e7	2.56465
$135$	0	0
$136$	1.97239e7	0.672368
$137$	−2.90657e7	−0.965736	−0.482868	−	0.875693i	$-0.660405\pi$
$137$	−2.90657e7	−0.965736	−0.482868	+	0.875693i	$0.660405\pi$
$138$	0	0
$139$	4.89962e7	1.54743	0.773714	−	0.633535i	$-0.218397\pi$
$139$	4.89962e7	1.54743	0.773714	+	0.633535i	$0.218397\pi$
$140$	−1.01912e7	−0.313891
$141$	0	0
$142$	5.27327e7	1.54551
$143$	−2.20099e7	−0.629423
$144$	0	0
$145$	8.15520e6	0.222150
$146$	−215166.	−0.00572189
$147$	0	0
$148$	−7.74606e7	−1.96410
$149$	−1.19196e7	−0.295194	−0.147597	−	0.989048i	$-0.547154\pi$
$149$	−1.19196e7	−0.295194	−0.147597	+	0.989048i	$0.547154\pi$
$150$	0	0
$151$	−4.94565e7	−1.16897	−0.584486	−	0.811404i	$-0.698704\pi$
$151$	−4.94565e7	−1.16897	−0.584486	+	0.811404i	$0.698704\pi$
$152$	−3.64286e7	−0.841377
$153$	0	0
$154$	−9.22507e7	−2.03539
$155$	2.66333e6	0.0574467
$156$	0	0
$157$	1.24765e7	0.257302	0.128651	−	0.991690i	$-0.458935\pi$
$157$	1.24765e7	0.257302	0.128651	+	0.991690i	$0.458935\pi$
$158$	9.46846e7	1.90976
$159$	0	0
$160$	−7.42528e6	−0.143315
$161$	−2.03533e7	−0.384364
$162$	0	0
$163$	2.14224e7	0.387446	0.193723	−	0.981056i	$-0.437944\pi$
$163$	2.14224e7	0.387446	0.193723	+	0.981056i	$0.437944\pi$
$164$	1.00942e8	1.78697
$165$	0	0
$166$	−5.83454e7	−0.989984
$167$	7.32594e7	1.21718	0.608591	−	0.793484i	$-0.291735\pi$
$167$	7.32594e7	1.21718	0.608591	+	0.793484i	$0.291735\pi$
$168$	0	0
$169$	−1.25123e7	−0.199404
$170$	−1.08025e7	−0.168637
$171$	0	0
$172$	−8.06168e7	−1.20803
$173$	7.87905e7	1.15694	0.578472	−	0.815702i	$-0.303649\pi$
$173$	7.87905e7	1.15694	0.578472	+	0.815702i	$0.303649\pi$
$174$	0	0
$175$	−1.28921e8	−1.81840
$176$	−1.63352e7	−0.225856
$177$	0	0
$178$	−7.12538e6	−0.0946974
$179$	−1.25066e8	−1.62988	−0.814938	−	0.579548i	$-0.803229\pi$
$179$	−1.25066e8	−1.62988	−0.814938	+	0.579548i	$0.803229\pi$
$180$	0	0
$181$	9.63252e7	1.20744	0.603719	−	0.797197i	$-0.293685\pi$
$181$	9.63252e7	1.20744	0.603719	+	0.797197i	$0.293685\pi$
$182$	2.10556e8	2.58891
$183$	0	0
$184$	1.28276e7	0.151804
$185$	1.34421e7	0.156087
$186$	0	0
$187$	−5.80956e7	−0.649677
$188$	9.98984e7	1.09649
$189$	0	0
$190$	1.99514e7	0.211026
$191$	−5.43389e7	−0.564279	−0.282140	−	0.959373i	$-0.591044\pi$
$191$	−5.43389e7	−0.564279	−0.282140	+	0.959373i	$0.591044\pi$
$192$	0	0
$193$	−7.87494e7	−0.788491	−0.394245	−	0.919005i	$-0.628994\pi$
$193$	−7.87494e7	−0.788491	−0.394245	+	0.919005i	$0.628994\pi$
$194$	−2.74754e7	−0.270171
$195$	0	0
$196$	3.70014e8	3.51012
$197$	−1.24009e8	−1.15564	−0.577819	−	0.816165i	$-0.696096\pi$
$197$	−1.24009e8	−1.15564	−0.577819	+	0.816165i	$0.696096\pi$
$198$	0	0
$199$	1.93717e8	1.74254	0.871268	−	0.490807i	$-0.163298\pi$
$199$	1.93717e8	1.74254	0.871268	+	0.490807i	$0.163298\pi$
$200$	8.12519e7	0.718172
$201$	0	0
$202$	1.95230e8	1.66654
$203$	−4.19569e8	−3.52020
$204$	0	0
$205$	−1.75169e7	−0.142010
$206$	1.92396e8	1.53342
$207$	0	0
$208$	3.72840e7	0.287277
$209$	1.07298e8	0.812982
$210$	0	0
$211$	3.81020e7	0.279228	0.139614	−	0.990206i	$-0.455414\pi$
$211$	3.81020e7	0.279228	0.139614	+	0.990206i	$0.455414\pi$
$212$	1.94056e8	1.39878
$213$	0	0
$214$	2.64372e7	0.184403
$215$	1.39898e7	0.0960014
$216$	0	0
$217$	−1.37023e8	−0.910301
$218$	−2.51158e8	−1.64191
$219$	0	0
$220$	−1.89185e7	−0.119787
$221$	1.32599e8	0.826357
$222$	0	0
$223$	−2.83677e8	−1.71300	−0.856499	−	0.516149i	$-0.827365\pi$
$223$	−2.83677e8	−1.71300	−0.856499	+	0.516149i	$0.827365\pi$
$224$	3.82016e8	2.27098
$225$	0	0
$226$	2.62340e8	1.51177
$227$	3.20198e8	1.81689	0.908445	−	0.418004i	$-0.137270\pi$
$227$	3.20198e8	1.81689	0.908445	+	0.418004i	$0.137270\pi$
$228$	0	0
$229$	2.11267e8	1.16254	0.581269	−	0.813712i	$-0.302556\pi$
$229$	2.11267e8	1.16254	0.581269	+	0.813712i	$0.302556\pi$
$230$	−7.02545e6	−0.0380738
$231$	0	0
$232$	2.64432e8	1.39029
$233$	−1.21921e8	−0.631441	−0.315721	−	0.948852i	$-0.602246\pi$
$233$	−1.21921e8	−0.631441	−0.315721	+	0.948852i	$0.602246\pi$
$234$	0	0
$235$	−1.73359e7	−0.0871380
$236$	−8.58354e7	−0.425084
$237$	0	0
$238$	5.55765e8	2.67222
$239$	−2.27248e8	−1.07673	−0.538367	−	0.842711i	$-0.680958\pi$
$239$	−2.27248e8	−1.07673	−0.538367	+	0.842711i	$0.680958\pi$
$240$	0	0
$241$	−2.85965e8	−1.31599	−0.657996	−	0.753022i	$-0.728596\pi$
$241$	−2.85965e8	−1.31599	−0.657996	+	0.753022i	$0.728596\pi$
$242$	1.74815e8	0.792913
$243$	0	0
$244$	2.18113e8	0.961207
$245$	−6.42102e7	−0.278948
$246$	0	0
$247$	−2.44901e8	−1.03407
$248$	8.63584e7	0.359521
$249$	0	0
$250$	−8.96111e7	−0.362720
$251$	2.37970e8	0.949868	0.474934	−	0.880021i	$-0.342472\pi$
$251$	2.37970e8	0.949868	0.474934	+	0.880021i	$0.342472\pi$
$252$	0	0
$253$	−3.77828e7	−0.146680
$254$	−2.53369e8	−0.970142
$255$	0	0
$256$	−1.14605e8	−0.426936
$257$	−2.33952e8	−0.859726	−0.429863	−	0.902894i	$-0.641438\pi$
$257$	−2.33952e8	−0.859726	−0.429863	+	0.902894i	$0.641438\pi$
$258$	0	0
$259$	−6.91569e8	−2.47335
$260$	4.31803e7	0.152363
$261$	0	0
$262$	4.98281e8	1.71167
$263$	−2.83534e7	−0.0961082	−0.0480541	−	0.998845i	$-0.515302\pi$
$263$	−2.83534e7	−0.0961082	−0.0480541	+	0.998845i	$0.515302\pi$
$264$	0	0
$265$	−3.36754e7	−0.111161
$266$	−1.02646e9	−3.34392
$267$	0	0
$268$	−7.53671e8	−2.39172
$269$	−2.33693e8	−0.732002	−0.366001	−	0.930615i	$-0.619273\pi$
$269$	−2.33693e8	−0.732002	−0.366001	+	0.930615i	$0.619273\pi$
$270$	0	0
$271$	3.27606e8	0.999906	0.499953	−	0.866053i	$-0.333351\pi$
$271$	3.27606e8	0.999906	0.499953	+	0.866053i	$0.333351\pi$
$272$	9.84118e7	0.296521
$273$	0	0
$274$	5.16166e8	1.51587
$275$	−2.39322e8	−0.693935
$276$	0	0
$277$	4.83558e8	1.36700	0.683502	−	0.729949i	$-0.260456\pi$
$277$	4.83558e8	1.36700	0.683502	+	0.729949i	$0.260456\pi$
$278$	−8.70104e8	−2.42893
$279$	0	0
$280$	5.73446e7	0.156113
$281$	4.37393e8	1.17598	0.587990	−	0.808868i	$-0.299919\pi$
$281$	4.37393e8	1.17598	0.587990	+	0.808868i	$0.299919\pi$
$282$	0	0
$283$	−2.22456e8	−0.583434	−0.291717	−	0.956505i	$-0.594227\pi$
$283$	−2.22456e8	−0.583434	−0.291717	+	0.956505i	$0.594227\pi$
$284$	−5.56373e8	−1.44129
$285$	0	0
$286$	3.90866e8	0.987977
$287$	9.01212e8	2.25030
$288$	0	0
$289$	−6.03412e7	−0.147052
$290$	−1.44825e8	−0.348699
$291$	0	0
$292$	2.27018e6	0.00533606
$293$	−1.81014e8	−0.420413	−0.210207	−	0.977657i	$-0.567414\pi$
$293$	−1.81014e8	−0.420413	−0.210207	+	0.977657i	$0.567414\pi$
$294$	0	0
$295$	1.48954e7	0.0337812
$296$	4.35859e8	0.976844
$297$	0	0
$298$	2.11675e8	0.463353
$299$	8.62367e7	0.186570
$300$	0	0
$301$	−7.19748e8	−1.52124
$302$	8.78278e8	1.83488
$303$	0	0
$304$	−1.81759e8	−0.371056
$305$	−3.78502e7	−0.0763868
$306$	0	0
$307$	−3.98750e8	−0.786533	−0.393266	−	0.919425i	$-0.628655\pi$
$307$	−3.98750e8	−0.786533	−0.393266	+	0.919425i	$0.628655\pi$
$308$	9.73321e8	1.89814
$309$	0	0
$310$	−4.72971e7	−0.0901713
$311$	−5.26090e8	−0.991743	−0.495871	−	0.868396i	$-0.665151\pi$
$311$	−5.26090e8	−0.991743	−0.495871	+	0.868396i	$0.665151\pi$
$312$	0	0
$313$	2.70320e8	0.498279	0.249140	−	0.968468i	$-0.419852\pi$
$313$	2.70320e8	0.498279	0.249140	+	0.968468i	$0.419852\pi$
$314$	−2.21565e8	−0.403876
$315$	0	0
$316$	−9.99001e8	−1.78099
$317$	−7.35356e8	−1.29655	−0.648276	−	0.761405i	$-0.724510\pi$
$317$	−7.35356e8	−1.29655	−0.648276	+	0.761405i	$0.724510\pi$
$318$	0	0
$319$	−7.78867e8	−1.34337
$320$	1.09970e8	0.187606
$321$	0	0
$322$	3.61445e8	0.603319
$323$	−6.46420e8	−1.06735
$324$	0	0
$325$	5.46237e8	0.882652
$326$	−3.80432e8	−0.608156
$327$	0	0
$328$	−5.67986e8	−0.888748
$329$	8.91895e8	1.38079
$330$	0	0
$331$	−8.38584e8	−1.27101	−0.635505	−	0.772097i	$-0.719208\pi$
$331$	−8.38584e8	−1.27101	−0.635505	+	0.772097i	$0.719208\pi$
$332$	6.15592e8	0.923230
$333$	0	0
$334$	−1.30098e9	−1.91055
$335$	1.30788e8	0.190069
$336$	0	0
$337$	1.13260e8	0.161203	0.0806015	−	0.996746i	$-0.474316\pi$
$337$	1.13260e8	0.161203	0.0806015	+	0.996746i	$0.474316\pi$
$338$	2.22201e8	0.312995
$339$	0	0
$340$	1.13975e8	0.157265
$341$	−2.54363e8	−0.347388
$342$	0	0
$343$	1.92585e9	2.57687
$344$	4.53619e8	0.600809
$345$	0	0
$346$	−1.39921e9	−1.81600
$347$	−1.44981e9	−1.86276	−0.931381	−	0.364046i	$-0.881395\pi$
$347$	−1.44981e9	−1.86276	−0.931381	+	0.364046i	$0.881395\pi$
$348$	0	0
$349$	−3.64693e8	−0.459239	−0.229620	−	0.973280i	$-0.573748\pi$
$349$	−3.64693e8	−0.459239	−0.229620	+	0.973280i	$0.573748\pi$
$350$	2.28945e9	2.85426
$351$	0	0
$352$	7.09156e8	0.866647
$353$	1.99838e8	0.241805	0.120903	−	0.992664i	$-0.461421\pi$
$353$	1.99838e8	0.241805	0.120903	+	0.992664i	$0.461421\pi$
$354$	0	0
$355$	9.65501e7	0.114539
$356$	7.51786e7	0.0883119
$357$	0	0
$358$	2.22100e9	2.55834
$359$	−7.71291e6	−0.00879808	−0.00439904	−	0.999990i	$-0.501400\pi$
$359$	−7.71291e6	−0.00879808	−0.00439904	+	0.999990i	$0.501400\pi$
$360$	0	0
$361$	3.00018e8	0.335639
$362$	−1.71060e9	−1.89526
$363$	0	0
$364$	−2.22154e9	−2.41434
$365$	−393956.	−0.000424055 0
$366$	0	0
$367$	5.29899e8	0.559580	0.279790	−	0.960061i	$-0.409735\pi$
$367$	5.29899e8	0.559580	0.279790	+	0.960061i	$0.409735\pi$
$368$	6.40027e7	0.0669470
$369$	0	0
$370$	−2.38713e8	−0.245002
$371$	1.73253e9	1.76146
$372$	0	0
$373$	−1.47849e9	−1.47515	−0.737577	−	0.675263i	$-0.764030\pi$
$373$	−1.47849e9	−1.47515	−0.737577	+	0.675263i	$0.764030\pi$
$374$	1.03170e9	1.01977
$375$	0	0
$376$	−5.62114e8	−0.545339
$377$	1.77771e9	1.70870
$378$	0	0
$379$	4.26713e8	0.402623	0.201312	−	0.979527i	$-0.435480\pi$
$379$	4.26713e8	0.402623	0.201312	+	0.979527i	$0.435480\pi$
$380$	−2.10503e8	−0.196796
$381$	0	0
$382$	9.64983e8	0.885723
$383$	−1.13179e9	−1.02937	−0.514683	−	0.857381i	$-0.672090\pi$
$383$	−1.13179e9	−1.02937	−0.514683	+	0.857381i	$0.672090\pi$
$384$	0	0
$385$	−1.68905e8	−0.150845
$386$	1.39848e9	1.23766
$387$	0	0
$388$	2.89888e8	0.251953
$389$	1.02164e9	0.879981	0.439991	−	0.898002i	$-0.354982\pi$
$389$	1.02164e9	0.879981	0.439991	+	0.898002i	$0.354982\pi$
$390$	0	0
$391$	2.27623e8	0.192574
$392$	−2.08201e9	−1.74575
$393$	0	0
$394$	2.20223e9	1.81395
$395$	1.73361e8	0.141535
$396$	0	0
$397$	−2.88404e7	−0.0231331	−0.0115666	−	0.999933i	$-0.503682\pi$
$397$	−2.88404e7	−0.0231331	−0.0115666	+	0.999933i	$0.503682\pi$
$398$	−3.44014e9	−2.73518
$399$	0	0
$400$	4.05404e8	0.316722
$401$	1.62456e9	1.25815	0.629073	−	0.777346i	$-0.283435\pi$
$401$	1.62456e9	1.25815	0.629073	+	0.777346i	$0.283435\pi$
$402$	0	0
$403$	5.80567e8	0.441860
$404$	−2.05983e9	−1.55417
$405$	0	0
$406$	7.45095e9	5.52549
$407$	−1.28380e9	−0.943877
$408$	0	0
$409$	−2.35821e9	−1.70432	−0.852159	−	0.523284i	$-0.824707\pi$
$409$	−2.35821e9	−1.70432	−0.852159	+	0.523284i	$0.824707\pi$
$410$	3.11076e8	0.222907
$411$	0	0
$412$	−2.02994e9	−1.43002
$413$	−7.66340e8	−0.535299
$414$	0	0
$415$	−1.06827e8	−0.0733688
$416$	−1.61860e9	−1.10233
$417$	0	0
$418$	−1.90547e9	−1.27610
$419$	−1.67574e9	−1.11290	−0.556451	−	0.830881i	$-0.687837\pi$
$419$	−1.67574e9	−1.11290	−0.556451	+	0.830881i	$0.687837\pi$
$420$	0	0
$421$	−1.67013e9	−1.09085	−0.545423	−	0.838161i	$-0.683631\pi$
$421$	−1.67013e9	−1.09085	−0.545423	+	0.838161i	$0.683631\pi$
$422$	−6.76639e8	−0.438292
$423$	0	0
$424$	−1.09192e9	−0.695683
$425$	1.44180e9	0.911054
$426$	0	0
$427$	1.94732e9	1.21043
$428$	−2.78934e8	−0.171968
$429$	0	0
$430$	−2.48440e8	−0.150689
$431$	−1.45319e9	−0.874285	−0.437142	−	0.899392i	$-0.644009\pi$
$431$	−1.45319e9	−0.874285	−0.437142	+	0.899392i	$0.644009\pi$
$432$	0	0
$433$	−1.74251e9	−1.03150	−0.515748	−	0.856740i	$-0.672486\pi$
$433$	−1.74251e9	−1.03150	−0.515748	+	0.856740i	$0.672486\pi$
$434$	2.43334e9	1.42886
$435$	0	0
$436$	2.64993e9	1.53120
$437$	−4.20403e8	−0.240980
$438$	0	0
$439$	1.03334e9	0.582932	0.291466	−	0.956581i	$-0.405857\pi$
$439$	1.03334e9	0.582932	0.291466	+	0.956581i	$0.405857\pi$
$440$	1.06452e8	0.0595756
$441$	0	0
$442$	−2.35478e9	−1.29709
$443$	−2.81649e8	−0.153920	−0.0769601	−	0.997034i	$-0.524521\pi$
$443$	−2.81649e8	−0.153920	−0.0769601	+	0.997034i	$0.524521\pi$
$444$	0	0
$445$	−1.30461e7	−0.00701812
$446$	5.03770e9	2.68881
$447$	0	0
$448$	−5.65771e9	−2.97281
$449$	−4.17577e8	−0.217708	−0.108854	−	0.994058i	$-0.534718\pi$
$449$	−4.17577e8	−0.217708	−0.108854	+	0.994058i	$0.534718\pi$
$450$	0	0
$451$	1.67297e9	0.858755
$452$	−2.76790e9	−1.40983
$453$	0	0
$454$	−5.68628e9	−2.85189
$455$	3.85514e8	0.191867
$456$	0	0
$457$	−1.24124e9	−0.608341	−0.304171	−	0.952618i	$-0.598379\pi$
$457$	−1.24124e9	−0.608341	−0.304171	+	0.952618i	$0.598379\pi$
$458$	−3.75180e9	−1.82478
$459$	0	0
$460$	7.41243e7	0.0355065
$461$	1.87145e9	0.889663	0.444832	−	0.895614i	$-0.353264\pi$
$461$	1.87145e9	0.889663	0.444832	+	0.895614i	$0.353264\pi$
$462$	0	0
$463$	−3.16121e9	−1.48020	−0.740100	−	0.672497i	$-0.765222\pi$
$463$	−3.16121e9	−1.48020	−0.740100	+	0.672497i	$0.765222\pi$
$464$	1.31937e9	0.613133
$465$	0	0
$466$	2.16515e9	0.991144
$467$	−3.42208e9	−1.55482	−0.777412	−	0.628992i	$-0.783468\pi$
$467$	−3.42208e9	−1.55482	−0.777412	+	0.628992i	$0.783468\pi$
$468$	0	0
$469$	−6.72879e9	−3.01184
$470$	3.07860e8	0.136776
$471$	0	0
$472$	4.82983e8	0.211415
$473$	−1.33611e9	−0.580533
$474$	0	0
$475$	−2.66290e9	−1.14006
$476$	−5.86378e9	−2.49203
$477$	0	0
$478$	4.03561e9	1.69010
$479$	2.03897e9	0.847691	0.423845	−	0.905735i	$-0.360680\pi$
$479$	2.03897e9	0.847691	0.423845	+	0.905735i	$0.360680\pi$
$480$	0	0
$481$	2.93018e9	1.20057
$482$	5.07834e9	2.06565
$483$	0	0
$484$	−1.84444e9	−0.739447
$485$	−5.03057e7	−0.0200226
$486$	0	0
$487$	1.92494e9	0.755208	0.377604	−	0.925967i	$-0.376748\pi$
$487$	1.92494e9	0.755208	0.377604	+	0.925967i	$0.376748\pi$
$488$	−1.22729e9	−0.478055
$489$	0	0
$490$	1.14028e9	0.437851
$491$	−4.53370e8	−0.172849	−0.0864246	−	0.996258i	$-0.527544\pi$
$491$	−4.53370e8	−0.172849	−0.0864246	+	0.996258i	$0.527544\pi$
$492$	0	0
$493$	4.69229e9	1.76368
$494$	4.34910e9	1.62314
$495$	0	0
$496$	4.30882e8	0.158552
$497$	−4.96731e9	−1.81499
$498$	0	0
$499$	−1.01960e9	−0.367348	−0.183674	−	0.982987i	$-0.558799\pi$
$499$	−1.01960e9	−0.367348	−0.183674	+	0.982987i	$0.558799\pi$
$500$	9.45472e8	0.338262
$501$	0	0
$502$	−4.22601e9	−1.49096
$503$	5.25300e9	1.84043	0.920215	−	0.391413i	$-0.128014\pi$
$503$	5.25300e9	1.84043	0.920215	+	0.391413i	$0.128014\pi$
$504$	0	0
$505$	3.57453e8	0.123509
$506$	6.70970e8	0.230238
$507$	0	0
$508$	2.67325e9	0.904725
$509$	3.47786e9	1.16896	0.584481	−	0.811408i	$-0.301298\pi$
$509$	3.47786e9	1.16896	0.584481	+	0.811408i	$0.301298\pi$
$510$	0	0
$511$	2.02682e7	0.00671959
$512$	−1.91116e9	−0.629294
$513$	0	0
$514$	4.15465e9	1.34947
$515$	3.52265e8	0.113643
$516$	0	0
$517$	1.65567e9	0.526935
$518$	1.22813e10	3.88231
$519$	0	0
$520$	−2.42969e8	−0.0757773
$521$	−1.14363e9	−0.354287	−0.177143	−	0.984185i	$-0.556686\pi$
$521$	−1.14363e9	−0.354287	−0.177143	+	0.984185i	$0.556686\pi$
$522$	0	0
$523$	3.78149e9	1.15587	0.577933	−	0.816084i	$-0.303860\pi$
$523$	3.78149e9	1.15587	0.577933	+	0.816084i	$0.303860\pi$
$524$	−5.25727e9	−1.59625
$525$	0	0
$526$	5.03517e8	0.150857
$527$	1.53242e9	0.456078
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	5.98028e8	0.174484
$531$	0	0
$532$	1.08300e10	3.11844
$533$	−3.81843e9	−1.09229
$534$	0	0
$535$	4.84048e7	0.0136663
$536$	4.24080e9	1.18952
$537$	0	0
$538$	4.15005e9	1.14899
$539$	6.13244e9	1.68683
$540$	0	0
$541$	3.46679e9	0.941320	0.470660	−	0.882315i	$-0.344016\pi$
$541$	3.46679e9	0.941320	0.470660	+	0.882315i	$0.344016\pi$
$542$	−5.81782e9	−1.56951
$543$	0	0
$544$	−4.27232e9	−1.13780
$545$	−4.59854e8	−0.121684
$546$	0	0
$547$	3.72645e9	0.973507	0.486754	−	0.873539i	$-0.338181\pi$
$547$	3.72645e9	0.973507	0.486754	+	0.873539i	$0.338181\pi$
$548$	−5.44598e9	−1.41366
$549$	0	0
$550$	4.25003e9	1.08924
$551$	−8.66632e9	−2.20701
$552$	0	0
$553$	−8.91910e9	−2.24276
$554$	−8.58732e9	−2.14572
$555$	0	0
$556$	9.18032e9	2.26514
$557$	−6.64263e8	−0.162872	−0.0814360	−	0.996679i	$-0.525951\pi$
$557$	−6.64263e8	−0.162872	−0.0814360	+	0.996679i	$0.525951\pi$
$558$	0	0
$559$	3.04957e9	0.738410
$560$	2.86119e8	0.0688476
$561$	0	0
$562$	−7.76749e9	−1.84588
$563$	6.14488e9	1.45122	0.725612	−	0.688104i	$-0.241557\pi$
$563$	6.14488e9	1.45122	0.725612	+	0.688104i	$0.241557\pi$
$564$	0	0
$565$	4.80327e8	0.112039
$566$	3.95051e9	0.915789
$567$	0	0
$568$	3.13063e9	0.716824
$569$	7.57121e9	1.72295	0.861474	−	0.507801i	$-0.169542\pi$
$569$	7.57121e9	1.72295	0.861474	+	0.507801i	$0.169542\pi$
$570$	0	0
$571$	6.99906e9	1.57331	0.786654	−	0.617395i	$-0.211812\pi$
$571$	6.99906e9	1.57331	0.786654	+	0.617395i	$0.211812\pi$
$572$	−4.12396e9	−0.921358
$573$	0	0
$574$	−1.60043e10	−3.53219
$575$	9.37684e8	0.205693
$576$	0	0
$577$	−4.05834e9	−0.879495	−0.439747	−	0.898121i	$-0.644932\pi$
$577$	−4.05834e9	−0.879495	−0.439747	+	0.898121i	$0.644932\pi$
$578$	1.07157e9	0.230821
$579$	0	0
$580$	1.52802e9	0.325186
$581$	5.49602e9	1.16260
$582$	0	0
$583$	3.21619e9	0.672205
$584$	−1.27740e7	−0.00265388
$585$	0	0
$586$	3.21456e9	0.659903
$587$	−4.47493e9	−0.913172	−0.456586	−	0.889679i	$-0.650928\pi$
$587$	−4.47493e9	−0.913172	−0.456586	+	0.889679i	$0.650928\pi$
$588$	0	0
$589$	−2.83026e9	−0.570719
$590$	−2.64522e8	−0.0530249
$591$	0	0
$592$	2.17470e9	0.430798
$593$	2.72369e9	0.536373	0.268186	−	0.963367i	$-0.413576\pi$
$593$	2.72369e9	0.536373	0.268186	+	0.963367i	$0.413576\pi$
$594$	0	0
$595$	1.01757e9	0.198041
$596$	−2.23334e9	−0.432109
$597$	0	0
$598$	−1.53144e9	−0.292851
$599$	−5.09808e9	−0.969199	−0.484600	−	0.874736i	$-0.661035\pi$
$599$	−5.09808e9	−0.969199	−0.484600	+	0.874736i	$0.661035\pi$
$600$	0	0
$601$	−1.25245e9	−0.235343	−0.117671	−	0.993053i	$-0.537543\pi$
$601$	−1.25245e9	−0.235343	−0.117671	+	0.993053i	$0.537543\pi$
$602$	1.27817e10	2.38782
$603$	0	0
$604$	−9.26656e9	−1.71116
$605$	3.20075e8	0.0587636
$606$	0	0
$607$	−4.63329e9	−0.840870	−0.420435	−	0.907323i	$-0.638123\pi$
$607$	−4.63329e9	−0.840870	−0.420435	+	0.907323i	$0.638123\pi$
$608$	7.89066e9	1.42381
$609$	0	0
$610$	6.72166e8	0.119901
$611$	−3.77896e9	−0.670236
$612$	0	0
$613$	2.89197e9	0.507086	0.253543	−	0.967324i	$-0.418404\pi$
$613$	2.89197e9	0.507086	0.253543	+	0.967324i	$0.418404\pi$
$614$	7.08125e9	1.23458
$615$	0	0
$616$	−5.47673e9	−0.944037
$617$	−6.68525e9	−1.14583	−0.572914	−	0.819615i	$-0.694187\pi$
$617$	−6.68525e9	−1.14583	−0.572914	+	0.819615i	$0.694187\pi$
$618$	0	0
$619$	6.61297e9	1.12067	0.560337	−	0.828265i	$-0.310672\pi$
$619$	6.61297e9	1.12067	0.560337	+	0.828265i	$0.310672\pi$
$620$	4.99023e8	0.0840911
$621$	0	0
$622$	9.34263e9	1.55669
$623$	6.71196e8	0.111209
$624$	0	0
$625$	5.85685e9	0.959586
$626$	−4.80050e9	−0.782126
$627$	0	0
$628$	2.33769e9	0.376642
$629$	7.73424e9	1.23920
$630$	0	0
$631$	4.18438e9	0.663023	0.331511	−	0.943451i	$-0.392441\pi$
$631$	4.18438e9	0.663023	0.331511	+	0.943451i	$0.392441\pi$
$632$	5.62123e9	0.885772
$633$	0	0
$634$	1.30589e10	2.03514
$635$	−4.63902e8	−0.0718982
$636$	0	0
$637$	−1.39969e10	−2.14557
$638$	1.38316e10	2.10863
$639$	0	0
$640$	−1.00247e9	−0.151162
$641$	−4.58753e9	−0.687980	−0.343990	−	0.938973i	$-0.611779\pi$
$641$	−4.58753e9	−0.687980	−0.343990	+	0.938973i	$0.611779\pi$
$642$	0	0
$643$	−1.08232e10	−1.60552	−0.802762	−	0.596300i	$-0.796637\pi$
$643$	−1.08232e10	−1.60552	−0.802762	+	0.596300i	$0.796637\pi$
$644$	−3.81355e9	−0.562637
$645$	0	0
$646$	1.14795e10	1.67537
$647$	−2.87142e9	−0.416804	−0.208402	−	0.978043i	$-0.566826\pi$
$647$	−2.87142e9	−0.416804	−0.208402	+	0.978043i	$0.566826\pi$
$648$	0	0
$649$	−1.42260e9	−0.204280
$650$	−9.70041e9	−1.38546
$651$	0	0
$652$	4.01387e9	0.567148
$653$	−1.04014e10	−1.46183	−0.730914	−	0.682470i	$-0.760906\pi$
$653$	−1.04014e10	−1.46183	−0.730914	+	0.682470i	$0.760906\pi$
$654$	0	0
$655$	9.12319e8	0.126853
$656$	−2.83394e9	−0.391947
$657$	0	0
$658$	−1.58388e10	−2.16736
$659$	1.11771e9	0.152135	0.0760677	−	0.997103i	$-0.475763\pi$
$659$	1.11771e9	0.152135	0.0760677	+	0.997103i	$0.475763\pi$
$660$	0	0
$661$	−8.43061e9	−1.13541	−0.567706	−	0.823231i	$-0.692169\pi$
$661$	−8.43061e9	−1.13541	−0.567706	+	0.823231i	$0.692169\pi$
$662$	1.48921e10	1.99504
$663$	0	0
$664$	−3.46385e9	−0.459167
$665$	−1.87938e9	−0.247821
$666$	0	0
$667$	3.05166e9	0.398195
$668$	1.37265e10	1.78173
$669$	0	0
$670$	−2.32262e9	−0.298343
$671$	3.61490e9	0.461921
$672$	0	0
$673$	8.81023e9	1.11413	0.557063	−	0.830470i	$-0.311928\pi$
$673$	8.81023e9	1.11413	0.557063	+	0.830470i	$0.311928\pi$
$674$	−2.01135e9	−0.253033
$675$	0	0
$676$	−2.34441e9	−0.291890
$677$	6.28975e9	0.779064	0.389532	−	0.921013i	$-0.372637\pi$
$677$	6.28975e9	0.779064	0.389532	+	0.921013i	$0.372637\pi$
$678$	0	0
$679$	2.58813e9	0.317279
$680$	−6.41320e8	−0.0782157
$681$	0	0
$682$	4.51714e9	0.545278
$683$	−9.76407e9	−1.17262	−0.586311	−	0.810086i	$-0.699420\pi$
$683$	−9.76407e9	−1.17262	−0.586311	+	0.810086i	$0.699420\pi$
$684$	0	0
$685$	9.45066e8	0.112343
$686$	−3.42003e10	−4.04479
$687$	0	0
$688$	2.26332e9	0.264963
$689$	−7.34073e9	−0.855012
$690$	0	0
$691$	−7.16059e9	−0.825611	−0.412806	−	0.910819i	$-0.635451\pi$
$691$	−7.16059e9	−0.825611	−0.412806	+	0.910819i	$0.635451\pi$
$692$	1.47628e10	1.69355
$693$	0	0
$694$	2.57466e10	2.92389
$695$	−1.59310e9	−0.180010
$696$	0	0
$697$	−1.00788e10	−1.12744
$698$	6.47644e9	0.720846
$699$	0	0
$700$	−2.41556e10	−2.66180
$701$	9.03880e7	0.00991055	0.00495527	−	0.999988i	$-0.498423\pi$
$701$	9.03880e7	0.00991055	0.00495527	+	0.999988i	$0.498423\pi$
$702$	0	0
$703$	−1.42846e10	−1.55069
$704$	−1.05027e10	−1.13448
$705$	0	0
$706$	−3.54884e9	−0.379551
$707$	−1.83902e10	−1.95713
$708$	0	0
$709$	1.66026e10	1.74950	0.874751	−	0.484573i	$-0.161025\pi$
$709$	1.66026e10	1.74950	0.874751	+	0.484573i	$0.161025\pi$
$710$	−1.71460e9	−0.179787
$711$	0	0
$712$	−4.23019e8	−0.0439218
$713$	9.96615e8	0.102971
$714$	0	0
$715$	7.15650e8	0.0732200
$716$	−2.34334e10	−2.38583
$717$	0	0
$718$	1.36971e8	0.0138099
$719$	1.35703e10	1.36156	0.680782	−	0.732486i	$-0.261640\pi$
$719$	1.35703e10	1.36156	0.680782	+	0.732486i	$0.261640\pi$
$720$	0	0
$721$	−1.81233e10	−1.80079
$722$	−5.32791e9	−0.526837
$723$	0	0
$724$	1.80483e10	1.76746
$725$	1.93297e10	1.88383
$726$	0	0
$727$	−1.71708e10	−1.65737	−0.828685	−	0.559715i	$-0.810911\pi$
$727$	−1.71708e10	−1.65737	−0.828685	+	0.559715i	$0.810911\pi$
$728$	1.25003e10	1.20077
$729$	0	0
$730$	6.99610e6	0.000665619 0
$731$	8.04939e9	0.762170
$732$	0	0
$733$	−1.40815e10	−1.32064	−0.660322	−	0.750983i	$-0.729580\pi$
$733$	−1.40815e10	−1.32064	−0.660322	+	0.750983i	$0.729580\pi$
$734$	−9.41026e9	−0.878346
$735$	0	0
$736$	−2.77853e9	−0.256887
$737$	−1.24910e10	−1.14937
$738$	0	0
$739$	1.44525e10	1.31731	0.658656	−	0.752444i	$-0.271125\pi$
$739$	1.44525e10	1.31731	0.658656	+	0.752444i	$0.271125\pi$
$740$	2.51862e9	0.228482
$741$	0	0
$742$	−3.07673e10	−2.76488
$743$	−1.88767e10	−1.68836	−0.844181	−	0.536059i	$-0.819912\pi$
$743$	−1.88767e10	−1.68836	−0.844181	+	0.536059i	$0.819912\pi$
$744$	0	0
$745$	3.87562e8	0.0343396
$746$	2.62559e10	2.31548
$747$	0	0
$748$	−1.08852e10	−0.951005
$749$	−2.49033e9	−0.216556
$750$	0	0
$751$	−9.16087e9	−0.789218	−0.394609	−	0.918849i	$-0.629120\pi$
$751$	−9.16087e9	−0.789218	−0.394609	+	0.918849i	$0.629120\pi$
$752$	−2.80465e9	−0.240500
$753$	0	0
$754$	−3.15697e10	−2.68207
$755$	1.60807e9	0.135985
$756$	0	0
$757$	−1.77258e10	−1.48515	−0.742573	−	0.669765i	$-0.766395\pi$
$757$	−1.77258e10	−1.48515	−0.742573	+	0.669765i	$0.766395\pi$
$758$	−7.57783e9	−0.631979
$759$	0	0
$760$	1.18447e9	0.0978762
$761$	−8.48556e9	−0.697966	−0.348983	−	0.937129i	$-0.613473\pi$
$761$	−8.48556e9	−0.697966	−0.348983	+	0.937129i	$0.613473\pi$
$762$	0	0
$763$	2.36586e10	1.92820
$764$	−1.01814e10	−0.825999
$765$	0	0
$766$	2.00990e10	1.61575
$767$	3.24698e9	0.259834
$768$	0	0
$769$	1.80190e10	1.42886	0.714430	−	0.699707i	$-0.246686\pi$
$769$	1.80190e10	1.42886	0.714430	+	0.699707i	$0.246686\pi$
$770$	2.99952e9	0.236774
$771$	0	0
$772$	−1.47551e10	−1.15420
$773$	1.25368e10	0.976246	0.488123	−	0.872775i	$-0.337682\pi$
$773$	1.25368e10	0.976246	0.488123	+	0.872775i	$0.337682\pi$
$774$	0	0
$775$	6.31272e9	0.487148
$776$	−1.63116e9	−0.125308
$777$	0	0
$778$	−1.81429e10	−1.38127
$779$	1.86148e10	1.41084
$780$	0	0
$781$	−9.22108e9	−0.692633
$782$	−4.04226e9	−0.302274
$783$	0	0
$784$	−1.03881e10	−0.769894
$785$	−4.05671e8	−0.0299316
$786$	0	0
$787$	1.06633e10	0.779797	0.389899	−	0.920858i	$-0.372510\pi$
$787$	1.06633e10	0.779797	0.389899	+	0.920858i	$0.372510\pi$
$788$	−2.32353e10	−1.69164
$789$	0	0
$790$	−3.07866e9	−0.222160
$791$	−2.47119e10	−1.77537
$792$	0	0
$793$	−8.25077e9	−0.587541
$794$	5.12165e8	0.0363110
$795$	0	0
$796$	3.62963e10	2.55075
$797$	1.99461e10	1.39558	0.697789	−	0.716303i	$-0.254167\pi$
$797$	1.99461e10	1.39558	0.697789	+	0.716303i	$0.254167\pi$
$798$	0	0
$799$	−9.97461e9	−0.691803
$800$	−1.75996e10	−1.21532
$801$	0	0
$802$	−2.88499e10	−1.97485
$803$	3.76250e7	0.00256432
$804$	0	0
$805$	6.61783e8	0.0447126
$806$	−1.03101e10	−0.693567
$807$	0	0
$808$	1.15904e10	0.772961
$809$	2.22638e10	1.47836	0.739179	−	0.673509i	$-0.235214\pi$
$809$	2.22638e10	1.47836	0.739179	+	0.673509i	$0.235214\pi$
$810$	0	0
$811$	8.40970e9	0.553615	0.276807	−	0.960925i	$-0.410724\pi$
$811$	8.40970e9	0.553615	0.276807	+	0.960925i	$0.410724\pi$
$812$	−7.86137e10	−5.15291
$813$	0	0
$814$	2.27984e10	1.48156
$815$	−6.96546e8	−0.0450711
$816$	0	0
$817$	−1.48666e10	−0.953752
$818$	4.18785e10	2.67519
$819$	0	0
$820$	−3.28211e9	−0.207876
$821$	1.15961e10	0.731324	0.365662	−	0.930748i	$-0.380843\pi$
$821$	1.15961e10	0.731324	0.365662	+	0.930748i	$0.380843\pi$
$822$	0	0
$823$	1.52874e10	0.955951	0.477975	−	0.878373i	$-0.341371\pi$
$823$	1.52874e10	0.955951	0.477975	+	0.878373i	$0.341371\pi$
$824$	1.14222e10	0.711218
$825$	0	0
$826$	1.36091e10	0.840233
$827$	−3.33339e9	−0.204935	−0.102468	−	0.994736i	$-0.532674\pi$
$827$	−3.33339e9	−0.204935	−0.102468	+	0.994736i	$0.532674\pi$
$828$	0	0
$829$	2.92842e10	1.78522	0.892612	−	0.450825i	$-0.148870\pi$
$829$	2.92842e10	1.78522	0.892612	+	0.450825i	$0.148870\pi$
$830$	1.89709e9	0.115164
$831$	0	0
$832$	2.39717e10	1.44300
$833$	−3.69449e10	−2.21461
$834$	0	0
$835$	−2.38202e9	−0.141593
$836$	2.01043e10	1.19005
$837$	0	0
$838$	2.97587e10	1.74687
$839$	4.45381e9	0.260355	0.130177	−	0.991491i	$-0.458445\pi$
$839$	4.45381e9	0.260355	0.130177	+	0.991491i	$0.458445\pi$
$840$	0	0
$841$	4.56581e10	2.64686
$842$	2.96592e10	1.71225
$843$	0	0
$844$	7.13910e9	0.408738
$845$	4.06836e8	0.0231964
$846$	0	0
$847$	−1.64672e10	−0.931169
$848$	−5.44811e9	−0.306803
$849$	0	0
$850$	−2.56044e10	−1.43004
$851$	5.03001e9	0.279779
$852$	0	0
$853$	−2.71758e10	−1.49921	−0.749603	−	0.661887i	$-0.769756\pi$
$853$	−2.71758e10	−1.49921	−0.749603	+	0.661887i	$0.769756\pi$
$854$	−3.45816e10	−1.89995
$855$	0	0
$856$	1.56952e9	0.0855282
$857$	−1.59445e10	−0.865323	−0.432662	−	0.901556i	$-0.642426\pi$
$857$	−1.59445e10	−0.865323	−0.432662	+	0.901556i	$0.642426\pi$
$858$	0	0
$859$	−3.19563e10	−1.72020	−0.860102	−	0.510122i	$-0.829600\pi$
$859$	−3.19563e10	−1.72020	−0.860102	+	0.510122i	$0.829600\pi$
$860$	2.62124e9	0.140528
$861$	0	0
$862$	2.58067e10	1.37232
$863$	1.24014e10	0.656800	0.328400	−	0.944539i	$-0.393491\pi$
$863$	1.24014e10	0.656800	0.328400	+	0.944539i	$0.393491\pi$
$864$	0	0
$865$	−2.56186e9	−0.134586
$866$	3.09446e10	1.61909
$867$	0	0
$868$	−2.56738e10	−1.33251
$869$	−1.65570e10	−0.855879
$870$	0	0
$871$	2.85099e10	1.46195
$872$	−1.49107e10	−0.761538
$873$	0	0
$874$	7.46577e9	0.378255
$875$	8.44119e9	0.425966
$876$	0	0
$877$	−9.66888e9	−0.484036	−0.242018	−	0.970272i	$-0.577809\pi$
$877$	−9.66888e9	−0.484036	−0.242018	+	0.970272i	$0.577809\pi$
$878$	−1.83507e10	−0.915001
$879$	0	0
$880$	5.31138e8	0.0262735
$881$	1.13975e10	0.561556	0.280778	−	0.959773i	$-0.409408\pi$
$881$	1.13975e10	0.561556	0.280778	+	0.959773i	$0.409408\pi$
$882$	0	0
$883$	−6.25195e9	−0.305600	−0.152800	−	0.988257i	$-0.548829\pi$
$883$	−6.25195e9	−0.305600	−0.152800	+	0.988257i	$0.548829\pi$
$884$	2.48448e10	1.20963
$885$	0	0
$886$	5.00170e9	0.241601
$887$	4.13242e9	0.198826	0.0994128	−	0.995046i	$-0.468304\pi$
$887$	4.13242e9	0.198826	0.0994128	+	0.995046i	$0.468304\pi$
$888$	0	0
$889$	2.38668e10	1.13930
$890$	2.31681e8	0.0110160
$891$	0	0
$892$	−5.31519e10	−2.50751
$893$	1.84224e10	0.865696
$894$	0	0
$895$	4.06651e9	0.189601
$896$	5.15750e10	2.39531
$897$	0	0
$898$	7.41559e9	0.341726
$899$	2.05446e10	0.943057
$900$	0	0
$901$	−1.93760e10	−0.882524
$902$	−2.97095e10	−1.34795
$903$	0	0
$904$	1.55746e10	0.701176
$905$	−3.13200e9	−0.140460
$906$	0	0
$907$	1.64191e10	0.730674	0.365337	−	0.930875i	$-0.380954\pi$
$907$	1.64191e10	0.730674	0.365337	+	0.930875i	$0.380954\pi$
$908$	5.99949e10	2.65959
$909$	0	0
$910$	−6.84619e9	−0.301165
$911$	2.35385e10	1.03149	0.515745	−	0.856742i	$-0.327515\pi$
$911$	2.35385e10	1.03149	0.515745	+	0.856742i	$0.327515\pi$
$912$	0	0
$913$	1.02025e10	0.443671
$914$	2.20426e10	0.954885
$915$	0	0
$916$	3.95846e10	1.70174
$917$	−4.69370e10	−2.01012
$918$	0	0
$919$	−2.89668e10	−1.23111	−0.615554	−	0.788095i	$-0.711068\pi$
$919$	−2.89668e10	−1.23111	−0.615554	+	0.788095i	$0.711068\pi$
$920$	−4.17086e8	−0.0176591
$921$	0	0
$922$	−3.32344e10	−1.39646
$923$	2.10465e10	0.880995
$924$	0	0
$925$	3.18609e10	1.32362
$926$	5.61387e10	2.32340
$927$	0	0
$928$	−5.72775e10	−2.35270
$929$	2.22692e10	0.911277	0.455638	−	0.890165i	$-0.349411\pi$
$929$	2.22692e10	0.911277	0.455638	+	0.890165i	$0.349411\pi$
$930$	0	0
$931$	6.82346e10	2.77128
$932$	−2.28441e10	−0.924312
$933$	0	0
$934$	6.07713e10	2.44053
$935$	1.88897e9	0.0755760
$936$	0	0
$937$	3.15430e10	1.25261	0.626303	−	0.779580i	$-0.284567\pi$
$937$	3.15430e10	1.25261	0.626303	+	0.779580i	$0.284567\pi$
$938$	1.19494e11	4.72755
$939$	0	0
$940$	−3.24818e9	−0.127554
$941$	1.49779e10	0.585987	0.292993	−	0.956114i	$-0.405349\pi$
$941$	1.49779e10	0.585987	0.292993	+	0.956114i	$0.405349\pi$
$942$	0	0
$943$	−6.55481e9	−0.254548
$944$	2.40983e9	0.0932360
$945$	0	0
$946$	2.37274e10	0.911236
$947$	−2.53390e10	−0.969539	−0.484769	−	0.874642i	$-0.661096\pi$
$947$	−2.53390e10	−0.969539	−0.484769	+	0.874642i	$0.661096\pi$
$948$	0	0
$949$	−8.58764e7	−0.00326169
$950$	4.72894e10	1.78950
$951$	0	0
$952$	3.29946e10	1.23941
$953$	−7.27301e9	−0.272201	−0.136100	−	0.990695i	$-0.543457\pi$
$953$	−7.27301e9	−0.272201	−0.136100	+	0.990695i	$0.543457\pi$
$954$	0	0
$955$	1.76682e9	0.0656419
$956$	−4.25791e10	−1.57614
$957$	0	0
$958$	−3.62093e10	−1.33058
$959$	−4.86218e10	−1.78019
$960$	0	0
$961$	−2.08031e10	−0.756131
$962$	−5.20358e10	−1.88447
$963$	0	0
$964$	−5.35807e10	−1.92636
$965$	2.56052e9	0.0917241
$966$	0	0
$967$	−4.43467e10	−1.57714	−0.788568	−	0.614948i	$-0.789177\pi$
$967$	−4.43467e10	−1.57714	−0.788568	+	0.614948i	$0.789177\pi$
$968$	1.03784e10	0.367762
$969$	0	0
$970$	8.93359e8	0.0314286
$971$	4.92204e9	0.172535	0.0862675	−	0.996272i	$-0.472506\pi$
$971$	4.92204e9	0.172535	0.0862675	+	0.996272i	$0.472506\pi$
$972$	0	0
$973$	8.19620e10	2.85245
$974$	−3.41843e10	−1.18542
$975$	0	0
$976$	−6.12352e9	−0.210827
$977$	3.86252e10	1.32507	0.662537	−	0.749029i	$-0.269480\pi$
$977$	3.86252e10	1.32507	0.662537	+	0.749029i	$0.269480\pi$
$978$	0	0
$979$	1.24598e9	0.0424395
$980$	−1.20309e10	−0.408327
$981$	0	0
$982$	8.05121e9	0.271313
$983$	−1.46424e10	−0.491673	−0.245836	−	0.969311i	$-0.579063\pi$
$983$	−1.46424e10	−0.491673	−0.245836	+	0.969311i	$0.579063\pi$
$984$	0	0
$985$	4.03214e9	0.134434
$986$	−8.33286e10	−2.76837
$987$	0	0
$988$	−4.58866e10	−1.51369
$989$	5.23497e9	0.172079
$990$	0	0
$991$	8.70242e9	0.284042	0.142021	−	0.989864i	$-0.454640\pi$
$991$	8.70242e9	0.284042	0.142021	+	0.989864i	$0.454640\pi$
$992$	−1.87057e10	−0.608393
$993$	0	0
$994$	8.82125e10	2.84890
$995$	−6.29868e9	−0.202707
$996$	0	0
$997$	−2.46012e10	−0.786182	−0.393091	−	0.919500i	$-0.628594\pi$
$997$	−2.46012e10	−0.786182	−0.393091	+	0.919500i	$0.628594\pi$
$998$	1.81067e10	0.576609
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.e.1.2		8
3.2	odd	2		69.8.a.d.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.d.1.7	✓	8	3.2	odd	2
207.8.a.e.1.2		8	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)

\(f(q)\)	\(=\)	\(q-17.7586 q^{2} +187.368 q^{4} -32.5148 q^{5} +1672.82 q^{7} -1054.29 q^{8} +O(q^{10})\)	\(q-17.7586 q^{2} +187.368 q^{4} -32.5148 q^{5} +1672.82 q^{7} -1054.29 q^{8} +577.418 q^{10} +3105.35 q^{11} -7087.75 q^{13} -29707.0 q^{14} -5260.35 q^{16} -18708.2 q^{17} +34552.7 q^{19} -6092.24 q^{20} -55146.7 q^{22} -12167.0 q^{23} -77067.8 q^{25} +125869. q^{26} +313434. q^{28} -250815. q^{29} -81911.3 q^{31} +228366. q^{32} +332232. q^{34} -54391.6 q^{35} -413414. q^{37} -613608. q^{38} +34280.1 q^{40} +538737. q^{41} -430259. q^{43} +581843. q^{44} +216069. q^{46} +533167. q^{47} +1.97480e6 q^{49} +1.36862e6 q^{50} -1.32802e6 q^{52} +1.03569e6 q^{53} -100970. q^{55} -1.76364e6 q^{56} +4.45412e6 q^{58} -458111. q^{59} +1.16409e6 q^{61} +1.45463e6 q^{62} -3.38213e6 q^{64} +230457. q^{65} -4.02241e6 q^{67} -3.50532e6 q^{68} +965919. q^{70} -2.96942e6 q^{71} +12116.2 q^{73} +7.34166e6 q^{74} +6.47407e6 q^{76} +5.19470e6 q^{77} -5.33176e6 q^{79} +171039. q^{80} -9.56721e6 q^{82} +3.28547e6 q^{83} +608295. q^{85} +7.64081e6 q^{86} -3.27395e6 q^{88} +401235. q^{89} -1.18566e7 q^{91} -2.27971e6 q^{92} -9.46830e6 q^{94} -1.12348e6 q^{95} +1.54716e6 q^{97} -3.50696e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8}+O(q^{10}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8} + 11720 q^{10} - 6932 q^{11} + 12404 q^{13} - 30222 q^{14} + 27058 q^{16} - 24434 q^{17} - 14682 q^{19} + 3760 q^{20} + 36294 q^{22} - 97336 q^{23} + 144644 q^{25} - 325840 q^{26} - 21566 q^{28} - 255356 q^{29} + 450764 q^{31} - 647588 q^{32} + 191822 q^{34} - 1022616 q^{35} + 206240 q^{37} - 737372 q^{38} + 590028 q^{40} - 1053344 q^{41} + 1587806 q^{43} - 589366 q^{44} + 292008 q^{46} - 443336 q^{47} + 1944828 q^{49} + 1556112 q^{50} - 614236 q^{52} + 375530 q^{53} + 407792 q^{55} + 1316922 q^{56} - 1413384 q^{58} - 624008 q^{59} - 2005568 q^{61} + 3908272 q^{62} - 5082310 q^{64} - 646124 q^{65} - 2712286 q^{67} + 2289698 q^{68} - 16499468 q^{70} + 6287176 q^{71} - 10358312 q^{73} + 2000150 q^{74} - 25107464 q^{76} + 2156840 q^{77} - 8800574 q^{79} - 2384344 q^{80} - 31799800 q^{82} - 384948 q^{83} - 17826684 q^{85} + 11563928 q^{86} - 25202782 q^{88} + 3445530 q^{89} - 16316740 q^{91} - 6837854 q^{92} - 24237616 q^{94} - 26164288 q^{95} - 28043764 q^{97} + 9998012 q^{98}+O(q^{100}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8 + 11720 * q^10 - 6932 * q^11 + 12404 * q^13 - 30222 * q^14 + 27058 * q^16 - 24434 * q^17 - 14682 * q^19 + 3760 * q^20 + 36294 * q^22 - 97336 * q^23 + 144644 * q^25 - 325840 * q^26 - 21566 * q^28 - 255356 * q^29 + 450764 * q^31 - 647588 * q^32 + 191822 * q^34 - 1022616 * q^35 + 206240 * q^37 - 737372 * q^38 + 590028 * q^40 - 1053344 * q^41 + 1587806 * q^43 - 589366 * q^44 + 292008 * q^46 - 443336 * q^47 + 1944828 * q^49 + 1556112 * q^50 - 614236 * q^52 + 375530 * q^53 + 407792 * q^55 + 1316922 * q^56 - 1413384 * q^58 - 624008 * q^59 - 2005568 * q^61 + 3908272 * q^62 - 5082310 * q^64 - 646124 * q^65 - 2712286 * q^67 + 2289698 * q^68 - 16499468 * q^70 + 6287176 * q^71 - 10358312 * q^73 + 2000150 * q^74 - 25107464 * q^76 + 2156840 * q^77 - 8800574 * q^79 - 2384344 * q^80 - 31799800 * q^82 - 384948 * q^83 - 17826684 * q^85 + 11563928 * q^86 - 25202782 * q^88 + 3445530 * q^89 - 16316740 * q^91 - 6837854 * q^92 - 24237616 * q^94 - 26164288 * q^95 - 28043764 * q^97 + 9998012 * q^98

Introduction

L-functions

Modular forms

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Database

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