LMFDB - Embedded newform 207.8.a.e.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:	$1$
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			1.4
Root			$-4.11469$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.11469 q^{2} -77.3812 q^{4} +244.007 q^{5} +549.357 q^{7} +1461.22 q^{8} +O(q^{10})$	\(q-7.11469 q^{2} -77.3812 q^{4} +244.007 q^{5} +549.357 q^{7} +1461.22 q^{8} -1736.03 q^{10} -6497.85 q^{11} +6328.07 q^{13} -3908.51 q^{14} -491.361 q^{16} -35620.9 q^{17} +10650.8 q^{19} -18881.5 q^{20} +46230.2 q^{22} -12167.0 q^{23} -18585.7 q^{25} -45022.3 q^{26} -42509.9 q^{28} +253060. q^{29} +138444. q^{31} -183541. q^{32} +253432. q^{34} +134047. q^{35} +86831.8 q^{37} -75777.1 q^{38} +356548. q^{40} -299642. q^{41} +283844. q^{43} +502811. q^{44} +86564.4 q^{46} -312235. q^{47} -521749. q^{49} +132232. q^{50} -489674. q^{52} -1.01632e6 q^{53} -1.58552e6 q^{55} +802734. q^{56} -1.80044e6 q^{58} -677210. q^{59} +2.34144e6 q^{61} -984986. q^{62} +1.36873e6 q^{64} +1.54409e6 q^{65} -3.15388e6 q^{67} +2.75639e6 q^{68} -953702. q^{70} +4.36034e6 q^{71} +2.79812e6 q^{73} -617781. q^{74} -824171. q^{76} -3.56964e6 q^{77} -6.51090e6 q^{79} -119895. q^{80} +2.13186e6 q^{82} +401787. q^{83} -8.69174e6 q^{85} -2.01946e6 q^{86} -9.49480e6 q^{88} -1.16894e7 q^{89} +3.47637e6 q^{91} +941497. q^{92} +2.22145e6 q^{94} +2.59887e6 q^{95} -1.24976e7 q^{97} +3.71208e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.11469	−0.628856	−0.314428	−	0.949281i	$-0.601813\pi$
$2$	−7.11469	−0.628856	−0.314428	+	0.949281i	$0.601813\pi$
$3$	0	0
$3$	0	0
$4$	−77.3812	−0.604540
$5$	244.007	0.872985	0.436493	−	0.899708i	$-0.356221\pi$
$5$	244.007	0.872985	0.436493	+	0.899708i	$0.356221\pi$
$6$	0	0
$7$	549.357	0.605357	0.302679	−	0.953093i	$-0.402119\pi$
$7$	549.357	0.605357	0.302679	+	0.953093i	$0.402119\pi$
$8$	1461.22	1.00902
$9$	0	0
$10$	−1736.03	−0.548982
$11$	−6497.85	−1.47196	−0.735978	−	0.677005i	$-0.763277\pi$
$11$	−6497.85	−1.47196	−0.735978	+	0.677005i	$0.763277\pi$
$12$	0	0
$13$	6328.07	0.798858	0.399429	−	0.916764i	$-0.369208\pi$
$13$	6328.07	0.798858	0.399429	+	0.916764i	$0.369208\pi$
$14$	−3908.51	−0.380683
$15$	0	0
$16$	−491.361	−0.0299903
$17$	−35620.9	−1.75847	−0.879233	−	0.476392i	$-0.841944\pi$
$17$	−35620.9	−1.75847	−0.879233	+	0.476392i	$0.841944\pi$
$18$	0	0
$19$	10650.8	0.356242	0.178121	−	0.984009i	$-0.442998\pi$
$19$	10650.8	0.356242	0.178121	+	0.984009i	$0.442998\pi$
$20$	−18881.5	−0.527755
$21$	0	0
$22$	46230.2	0.925648
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−18585.7	−0.237897
$26$	−45022.3	−0.502367
$27$	0	0
$28$	−42509.9	−0.365963
$29$	253060.	1.92677	0.963386	−	0.268119i	$-0.0864019\pi$
$29$	253060.	1.92677	0.963386	+	0.268119i	$0.0864019\pi$
$30$	0	0
$31$	138444.	0.834657	0.417329	−	0.908756i	$-0.362966\pi$
$31$	138444.	0.834657	0.417329	+	0.908756i	$0.362966\pi$
$32$	−183541.	−0.990165
$33$	0	0
$34$	253432.	1.10582
$35$	134047.	0.528468
$36$	0	0
$37$	86831.8	0.281821	0.140910	−	0.990022i	$-0.454997\pi$
$37$	86831.8	0.281821	0.140910	+	0.990022i	$0.454997\pi$
$38$	−75777.1	−0.224025
$39$	0	0
$40$	356548.	0.880863
$41$	−299642.	−0.678984	−0.339492	−	0.940609i	$-0.610255\pi$
$41$	−299642.	−0.678984	−0.339492	+	0.940609i	$0.610255\pi$
$42$	0	0
$43$	283844.	0.544428	0.272214	−	0.962237i	$-0.412244\pi$
$43$	283844.	0.544428	0.272214	+	0.962237i	$0.412244\pi$
$44$	502811.	0.889857
$45$	0	0
$46$	86564.4	0.131125
$47$	−312235.	−0.438671	−0.219335	−	0.975650i	$-0.570389\pi$
$47$	−312235.	−0.438671	−0.219335	+	0.975650i	$0.570389\pi$
$48$	0	0
$49$	−521749.	−0.633542
$50$	132232.	0.149603
$51$	0	0
$52$	−489674.	−0.482942
$53$	−1.01632e6	−0.937698	−0.468849	−	0.883278i	$-0.655331\pi$
$53$	−1.01632e6	−0.937698	−0.468849	+	0.883278i	$0.655331\pi$
$54$	0	0
$55$	−1.58552e6	−1.28500
$56$	802734.	0.610821
$57$	0	0
$58$	−1.80044e6	−1.21166
$59$	−677210.	−0.429281	−0.214640	−	0.976693i	$-0.568858\pi$
$59$	−677210.	−0.429281	−0.214640	+	0.976693i	$0.568858\pi$
$60$	0	0
$61$	2.34144e6	1.32077	0.660386	−	0.750926i	$-0.270392\pi$
$61$	2.34144e6	1.32077	0.660386	+	0.750926i	$0.270392\pi$
$62$	−984986.	−0.524879
$63$	0	0
$64$	1.36873e6	0.652661
$65$	1.54409e6	0.697391
$66$	0	0
$67$	−3.15388e6	−1.28110	−0.640551	−	0.767916i	$-0.721294\pi$
$67$	−3.15388e6	−1.28110	−0.640551	+	0.767916i	$0.721294\pi$
$68$	2.75639e6	1.06306
$69$	0	0
$70$	−953702.	−0.332330
$71$	4.36034e6	1.44583	0.722914	−	0.690939i	$-0.242802\pi$
$71$	4.36034e6	1.44583	0.722914	+	0.690939i	$0.242802\pi$
$72$	0	0
$73$	2.79812e6	0.841854	0.420927	−	0.907094i	$-0.361705\pi$
$73$	2.79812e6	0.841854	0.420927	+	0.907094i	$0.361705\pi$
$74$	−617781.	−0.177225
$75$	0	0
$76$	−824171.	−0.215362
$77$	−3.56964e6	−0.891060
$78$	0	0
$79$	−6.51090e6	−1.48575	−0.742875	−	0.669430i	$-0.766539\pi$
$79$	−6.51090e6	−1.48575	−0.742875	+	0.669430i	$0.766539\pi$
$80$	−119895.	−0.0261811
$81$	0	0
$82$	2.13186e6	0.426983
$83$	401787.	0.0771298	0.0385649	−	0.999256i	$-0.487721\pi$
$83$	401787.	0.0771298	0.0385649	+	0.999256i	$0.487721\pi$
$84$	0	0
$85$	−8.69174e6	−1.53511
$86$	−2.01946e6	−0.342367
$87$	0	0
$88$	−9.49480e6	−1.48524
$89$	−1.16894e7	−1.75762	−0.878811	−	0.477170i	$-0.841662\pi$
$89$	−1.16894e7	−1.75762	−0.878811	+	0.477170i	$0.841662\pi$
$90$	0	0
$91$	3.47637e6	0.483595
$92$	941497.	0.126055
$93$	0	0
$94$	2.22145e6	0.275861
$95$	2.59887e6	0.310994
$96$	0	0
$97$	−1.24976e7	−1.39036	−0.695179	−	0.718836i	$-0.744675\pi$
$97$	−1.24976e7	−1.39036	−0.695179	+	0.718836i	$0.744675\pi$
$98$	3.71208e6	0.398407
$99$	0	0
$100$	1.43818e6	0.143818
$101$	−1.27743e6	−0.123371	−0.0616856	−	0.998096i	$-0.519648\pi$
$101$	−1.27743e6	−0.123371	−0.0616856	+	0.998096i	$0.519648\pi$
$102$	0	0
$103$	−9.61010e6	−0.866558	−0.433279	−	0.901260i	$-0.642643\pi$
$103$	−9.61010e6	−0.866558	−0.433279	+	0.901260i	$0.642643\pi$
$104$	9.24673e6	0.806067
$105$	0	0
$106$	7.23077e6	0.589677
$107$	−1.26586e7	−0.998948	−0.499474	−	0.866329i	$-0.666473\pi$
$107$	−1.26586e7	−0.998948	−0.499474	+	0.866329i	$0.666473\pi$
$108$	0	0
$109$	−8.26222e6	−0.611088	−0.305544	−	0.952178i	$-0.598838\pi$
$109$	−8.26222e6	−0.611088	−0.305544	+	0.952178i	$0.598838\pi$
$110$	1.12805e7	0.808077
$111$	0	0
$112$	−269933.	−0.0181549
$113$	3.78609e6	0.246841	0.123420	−	0.992354i	$-0.460614\pi$
$113$	3.78609e6	0.246841	0.123420	+	0.992354i	$0.460614\pi$
$114$	0	0
$115$	−2.96883e6	−0.182030
$116$	−1.95821e7	−1.16481
$117$	0	0
$118$	4.81814e6	0.269956
$119$	−1.95686e7	−1.06450
$120$	0	0
$121$	2.27348e7	1.16666
$122$	−1.66586e7	−0.830576
$123$	0	0
$124$	−1.07130e7	−0.504584
$125$	−2.35981e7	−1.08067
$126$	0	0
$127$	2.79370e7	1.21023	0.605114	−	0.796139i	$-0.293128\pi$
$127$	2.79370e7	1.21023	0.605114	+	0.796139i	$0.293128\pi$
$128$	1.37551e7	0.579735
$129$	0	0
$130$	−1.09857e7	−0.438559
$131$	−2.68577e7	−1.04380	−0.521902	−	0.853006i	$-0.674777\pi$
$131$	−2.68577e7	−1.04380	−0.521902	+	0.853006i	$0.674777\pi$
$132$	0	0
$133$	5.85110e6	0.215653
$134$	2.24389e7	0.805628
$135$	0	0
$136$	−5.20501e7	−1.77433
$137$	−5.57360e7	−1.85189	−0.925943	−	0.377664i	$-0.876727\pi$
$137$	−5.57360e7	−1.85189	−0.925943	+	0.377664i	$0.876727\pi$
$138$	0	0
$139$	−4.66115e7	−1.47211	−0.736057	−	0.676919i	$-0.763315\pi$
$139$	−4.66115e7	−1.47211	−0.736057	+	0.676919i	$0.763315\pi$
$140$	−1.03727e7	−0.319480
$141$	0	0
$142$	−3.10225e7	−0.909217
$143$	−4.11188e7	−1.17588
$144$	0	0
$145$	6.17483e7	1.68204
$146$	−1.99078e7	−0.529405
$147$	0	0
$148$	−6.71915e6	−0.170372
$149$	1.38043e7	0.341870	0.170935	−	0.985282i	$-0.445321\pi$
$149$	1.38043e7	0.341870	0.170935	+	0.985282i	$0.445321\pi$
$150$	0	0
$151$	4.84217e6	0.114451	0.0572257	−	0.998361i	$-0.481775\pi$
$151$	4.84217e6	0.114451	0.0572257	+	0.998361i	$0.481775\pi$
$152$	1.55632e7	0.359456
$153$	0	0
$154$	2.53969e7	0.560348
$155$	3.37813e7	0.728643
$156$	0	0
$157$	−6.95253e7	−1.43382	−0.716909	−	0.697167i	$-0.754444\pi$
$157$	−6.95253e7	−1.43382	−0.716909	+	0.697167i	$0.754444\pi$
$158$	4.63230e7	0.934323
$159$	0	0
$160$	−4.47852e7	−0.864399
$161$	−6.68403e6	−0.126226
$162$	0	0
$163$	1.11737e7	0.202087	0.101044	−	0.994882i	$-0.467782\pi$
$163$	1.11737e7	0.202087	0.101044	+	0.994882i	$0.467782\pi$
$164$	2.31867e7	0.410474
$165$	0	0
$166$	−2.85859e6	−0.0485035
$167$	1.09499e8	1.81930	0.909648	−	0.415379i	$-0.136351\pi$
$167$	1.09499e8	1.81930	0.909648	+	0.415379i	$0.136351\pi$
$168$	0	0
$169$	−2.27040e7	−0.361826
$170$	6.18391e7	0.965365
$171$	0	0
$172$	−2.19642e7	−0.329129
$173$	−4.92182e7	−0.722710	−0.361355	−	0.932428i	$-0.617686\pi$
$173$	−4.92182e7	−0.722710	−0.361355	+	0.932428i	$0.617686\pi$
$174$	0	0
$175$	−1.02102e7	−0.144013
$176$	3.19279e6	0.0441444
$177$	0	0
$178$	8.31661e7	1.10529
$179$	2.98184e7	0.388596	0.194298	−	0.980943i	$-0.437757\pi$
$179$	2.98184e7	0.388596	0.194298	+	0.980943i	$0.437757\pi$
$180$	0	0
$181$	−4.59690e7	−0.576222	−0.288111	−	0.957597i	$-0.593027\pi$
$181$	−4.59690e7	−0.576222	−0.288111	+	0.957597i	$0.593027\pi$
$182$	−2.47333e7	−0.304111
$183$	0	0
$184$	−1.77787e7	−0.210396
$185$	2.11875e7	0.246025
$186$	0	0
$187$	2.31459e8	2.58838
$188$	2.41611e7	0.265194
$189$	0	0
$190$	−1.84901e7	−0.195570
$191$	1.04506e8	1.08524	0.542621	−	0.839978i	$-0.317432\pi$
$191$	1.04506e8	1.08524	0.542621	+	0.839978i	$0.317432\pi$
$192$	0	0
$193$	1.63523e8	1.63730	0.818652	−	0.574289i	$-0.194722\pi$
$193$	1.63523e8	1.63730	0.818652	+	0.574289i	$0.194722\pi$
$194$	8.89168e7	0.874335
$195$	0	0
$196$	4.03736e7	0.383002
$197$	−1.04340e8	−0.972342	−0.486171	−	0.873864i	$-0.661607\pi$
$197$	−1.04340e8	−0.972342	−0.486171	+	0.873864i	$0.661607\pi$
$198$	0	0
$199$	−6.79329e7	−0.611075	−0.305538	−	0.952180i	$-0.598836\pi$
$199$	−6.79329e7	−0.611075	−0.305538	+	0.952180i	$0.598836\pi$
$200$	−2.71579e7	−0.240044
$201$	0	0
$202$	9.08855e6	0.0775827
$203$	1.39020e8	1.16639
$204$	0	0
$205$	−7.31148e7	−0.592743
$206$	6.83729e7	0.544940
$207$	0	0
$208$	−3.10937e6	−0.0239580
$209$	−6.92072e7	−0.524372
$210$	0	0
$211$	−1.07654e8	−0.788935	−0.394468	−	0.918910i	$-0.629071\pi$
$211$	−1.07654e8	−0.788935	−0.394468	+	0.918910i	$0.629071\pi$
$212$	7.86437e7	0.566877
$213$	0	0
$214$	9.00621e7	0.628194
$215$	6.92599e7	0.475277
$216$	0	0
$217$	7.60553e7	0.505266
$218$	5.87831e7	0.384286
$219$	0	0
$220$	1.22689e8	0.776832
$221$	−2.25412e8	−1.40476
$222$	0	0
$223$	1.24220e8	0.750108	0.375054	−	0.927003i	$-0.377624\pi$
$223$	1.24220e8	0.750108	0.375054	+	0.927003i	$0.377624\pi$
$224$	−1.00829e8	−0.599404
$225$	0	0
$226$	−2.69369e7	−0.155227
$227$	−2.29102e8	−1.29998	−0.649992	−	0.759941i	$-0.725228\pi$
$227$	−2.29102e8	−1.29998	−0.649992	+	0.759941i	$0.725228\pi$
$228$	0	0
$229$	−4.81263e7	−0.264824	−0.132412	−	0.991195i	$-0.542272\pi$
$229$	−4.81263e7	−0.264824	−0.132412	+	0.991195i	$0.542272\pi$
$230$	2.11223e7	0.114471
$231$	0	0
$232$	3.69777e8	1.94416
$233$	3.32165e8	1.72031	0.860157	−	0.510030i	$-0.170366\pi$
$233$	3.32165e8	1.72031	0.860157	+	0.510030i	$0.170366\pi$
$234$	0	0
$235$	−7.61874e7	−0.382953
$236$	5.24033e7	0.259518
$237$	0	0
$238$	1.39225e8	0.669417
$239$	−1.03958e8	−0.492568	−0.246284	−	0.969198i	$-0.579210\pi$
$239$	−1.03958e8	−0.492568	−0.246284	+	0.969198i	$0.579210\pi$
$240$	0	0
$241$	−1.94440e8	−0.894802	−0.447401	−	0.894333i	$-0.647650\pi$
$241$	−1.94440e8	−0.894802	−0.447401	+	0.894333i	$0.647650\pi$
$242$	−1.61751e8	−0.733658
$243$	0	0
$244$	−1.81183e8	−0.798461
$245$	−1.27310e8	−0.553073
$246$	0	0
$247$	6.73990e7	0.284586
$248$	2.02298e8	0.842190
$249$	0	0
$250$	1.67893e8	0.679583
$251$	−1.51886e8	−0.606261	−0.303130	−	0.952949i	$-0.598032\pi$
$251$	−1.51886e8	−0.606261	−0.303130	+	0.952949i	$0.598032\pi$
$252$	0	0
$253$	7.90593e7	0.306924
$254$	−1.98763e8	−0.761059
$255$	0	0
$256$	−2.73061e8	−1.01723
$257$	−1.66995e8	−0.613675	−0.306837	−	0.951762i	$-0.599271\pi$
$257$	−1.66995e8	−0.613675	−0.306837	+	0.951762i	$0.599271\pi$
$258$	0	0
$259$	4.77017e7	0.170602
$260$	−1.19484e8	−0.421601
$261$	0	0
$262$	1.91084e8	0.656402
$263$	2.50981e7	0.0850737	0.0425369	−	0.999095i	$-0.486456\pi$
$263$	2.50981e7	0.0850737	0.0425369	+	0.999095i	$0.486456\pi$
$264$	0	0
$265$	−2.47988e8	−0.818597
$266$	−4.16287e7	−0.135615
$267$	0	0
$268$	2.44051e8	0.774477
$269$	−1.92309e7	−0.0602375	−0.0301188	−	0.999546i	$-0.509589\pi$
$269$	−1.92309e7	−0.0602375	−0.0301188	+	0.999546i	$0.509589\pi$
$270$	0	0
$271$	8.71110e7	0.265877	0.132938	−	0.991124i	$-0.457559\pi$
$271$	8.71110e7	0.265877	0.132938	+	0.991124i	$0.457559\pi$
$272$	1.75027e7	0.0527369
$273$	0	0
$274$	3.96545e8	1.16457
$275$	1.20767e8	0.350174
$276$	0	0
$277$	−5.71631e8	−1.61598	−0.807991	−	0.589195i	$-0.799445\pi$
$277$	−5.71631e8	−1.61598	−0.807991	+	0.589195i	$0.799445\pi$
$278$	3.31627e8	0.925748
$279$	0	0
$280$	1.95873e8	0.533237
$281$	6.95246e8	1.86925	0.934623	−	0.355639i	$-0.115737\pi$
$281$	6.95246e8	1.86925	0.934623	+	0.355639i	$0.115737\pi$
$282$	0	0
$283$	−2.27178e8	−0.595817	−0.297909	−	0.954594i	$-0.596289\pi$
$283$	−2.27178e8	−0.595817	−0.297909	+	0.954594i	$0.596289\pi$
$284$	−3.37408e8	−0.874061
$285$	0	0
$286$	2.92548e8	0.739462
$287$	−1.64611e8	−0.411028
$288$	0	0
$289$	8.58511e8	2.09220
$290$	−4.39320e8	−1.05776
$291$	0	0
$292$	−2.16522e8	−0.508935
$293$	8.01165e7	0.186074	0.0930369	−	0.995663i	$-0.470343\pi$
$293$	8.01165e7	0.186074	0.0930369	+	0.995663i	$0.470343\pi$
$294$	0	0
$295$	−1.65244e8	−0.374756
$296$	1.26881e8	0.284364
$297$	0	0
$298$	−9.82131e7	−0.214987
$299$	−7.69937e7	−0.166573
$300$	0	0
$301$	1.55932e8	0.329573
$302$	−3.44506e7	−0.0719734
$303$	0	0
$304$	−5.23339e6	−0.0106838
$305$	5.71327e8	1.15302
$306$	0	0
$307$	5.88460e8	1.16073	0.580367	−	0.814355i	$-0.302909\pi$
$307$	5.88460e8	1.16073	0.580367	+	0.814355i	$0.302909\pi$
$308$	2.76223e8	0.538682
$309$	0	0
$310$	−2.40343e8	−0.458212
$311$	−1.30155e8	−0.245358	−0.122679	−	0.992446i	$-0.539149\pi$
$311$	−1.30155e8	−0.245358	−0.122679	+	0.992446i	$0.539149\pi$
$312$	0	0
$313$	−3.53675e8	−0.651927	−0.325964	−	0.945382i	$-0.605689\pi$
$313$	−3.53675e8	−0.651927	−0.325964	+	0.945382i	$0.605689\pi$
$314$	4.94651e8	0.901665
$315$	0	0
$316$	5.03821e8	0.898197
$317$	−3.97105e7	−0.0700161	−0.0350080	−	0.999387i	$-0.511146\pi$
$317$	−3.97105e7	−0.0700161	−0.0350080	+	0.999387i	$0.511146\pi$
$318$	0	0
$319$	−1.64434e9	−2.83612
$320$	3.33979e8	0.569763
$321$	0	0
$322$	4.75548e7	0.0793778
$323$	−3.79391e8	−0.626438
$324$	0	0
$325$	−1.17612e8	−0.190046
$326$	−7.94971e7	−0.127084
$327$	0	0
$328$	−4.37845e8	−0.685112
$329$	−1.71528e8	−0.265553
$330$	0	0
$331$	−1.13474e9	−1.71988	−0.859938	−	0.510398i	$-0.829498\pi$
$331$	−1.13474e9	−1.71988	−0.859938	+	0.510398i	$0.829498\pi$
$332$	−3.10907e7	−0.0466281
$333$	0	0
$334$	−7.79053e8	−1.14408
$335$	−7.69568e8	−1.11838
$336$	0	0
$337$	−3.16562e8	−0.450561	−0.225281	−	0.974294i	$-0.572330\pi$
$337$	−3.16562e8	−0.450561	−0.225281	+	0.974294i	$0.572330\pi$
$338$	1.61532e8	0.227536
$339$	0	0
$340$	6.72577e8	0.928039
$341$	−8.99588e8	−1.22858
$342$	0	0
$343$	−7.39046e8	−0.988877
$344$	4.14760e8	0.549341
$345$	0	0
$346$	3.50172e8	0.454480
$347$	8.24599e8	1.05947	0.529736	−	0.848162i	$-0.322291\pi$
$347$	8.24599e8	1.05947	0.529736	+	0.848162i	$0.322291\pi$
$348$	0	0
$349$	−9.77269e8	−1.23062	−0.615312	−	0.788284i	$-0.710970\pi$
$349$	−9.77269e8	−1.23062	−0.615312	+	0.788284i	$0.710970\pi$
$350$	7.26424e7	0.0905632
$351$	0	0
$352$	1.19262e9	1.45748
$353$	−4.67249e8	−0.565376	−0.282688	−	0.959212i	$-0.591226\pi$
$353$	−4.67249e8	−0.565376	−0.282688	+	0.959212i	$0.591226\pi$
$354$	0	0
$355$	1.06395e9	1.26219
$356$	9.04536e8	1.06255
$357$	0	0
$358$	−2.12149e8	−0.244371
$359$	1.08943e8	0.124271	0.0621356	−	0.998068i	$-0.480209\pi$
$359$	1.08943e8	0.124271	0.0621356	+	0.998068i	$0.480209\pi$
$360$	0	0
$361$	−7.80432e8	−0.873092
$362$	3.27055e8	0.362361
$363$	0	0
$364$	−2.69006e8	−0.292353
$365$	6.82761e8	0.734926
$366$	0	0
$367$	2.72618e8	0.287888	0.143944	−	0.989586i	$-0.454022\pi$
$367$	2.72618e8	0.287888	0.143944	+	0.989586i	$0.454022\pi$
$368$	5.97839e6	0.00625341
$369$	0	0
$370$	−1.50743e8	−0.154714
$371$	−5.58321e8	−0.567643
$372$	0	0
$373$	8.25069e8	0.823208	0.411604	−	0.911363i	$-0.364969\pi$
$373$	8.25069e8	0.823208	0.411604	+	0.911363i	$0.364969\pi$
$374$	−1.64676e9	−1.62772
$375$	0	0
$376$	−4.56245e8	−0.442629
$377$	1.60138e9	1.53922
$378$	0	0
$379$	−5.98480e8	−0.564693	−0.282347	−	0.959312i	$-0.591113\pi$
$379$	−5.98480e8	−0.564693	−0.282347	+	0.959312i	$0.591113\pi$
$380$	−2.01103e8	−0.188008
$381$	0	0
$382$	−7.43531e8	−0.682460
$383$	−1.50205e9	−1.36612	−0.683062	−	0.730361i	$-0.739352\pi$
$383$	−1.50205e9	−1.36612	−0.683062	+	0.730361i	$0.739352\pi$
$384$	0	0
$385$	−8.71016e8	−0.777882
$386$	−1.16342e9	−1.02963
$387$	0	0
$388$	9.67082e8	0.840528
$389$	−4.18026e8	−0.360064	−0.180032	−	0.983661i	$-0.557620\pi$
$389$	−4.18026e8	−0.360064	−0.180032	+	0.983661i	$0.557620\pi$
$390$	0	0
$391$	4.33400e8	0.366665
$392$	−7.62392e8	−0.639260
$393$	0	0
$394$	7.42347e8	0.611463
$395$	−1.58870e9	−1.29704
$396$	0	0
$397$	−4.57774e8	−0.367184	−0.183592	−	0.983002i	$-0.558773\pi$
$397$	−4.57774e8	−0.367184	−0.183592	+	0.983002i	$0.558773\pi$
$398$	4.83322e8	0.384278
$399$	0	0
$400$	9.13229e6	0.00713460
$401$	−4.25900e8	−0.329839	−0.164920	−	0.986307i	$-0.552736\pi$
$401$	−4.25900e8	−0.329839	−0.164920	+	0.986307i	$0.552736\pi$
$402$	0	0
$403$	8.76084e8	0.666773
$404$	9.88494e7	0.0745829
$405$	0	0
$406$	−9.89087e8	−0.733488
$407$	−5.64220e8	−0.414828
$408$	0	0
$409$	−1.12075e8	−0.0809982	−0.0404991	−	0.999180i	$-0.512895\pi$
$409$	−1.12075e8	−0.0809982	−0.0404991	+	0.999180i	$0.512895\pi$
$410$	5.20189e8	0.372750
$411$	0	0
$412$	7.43641e8	0.523869
$413$	−3.72031e8	−0.259868
$414$	0	0
$415$	9.80387e7	0.0673332
$416$	−1.16146e9	−0.791001
$417$	0	0
$418$	4.92388e8	0.329754
$419$	1.93151e9	1.28277	0.641384	−	0.767220i	$-0.278361\pi$
$419$	1.93151e9	1.28277	0.641384	+	0.767220i	$0.278361\pi$
$420$	0	0
$421$	6.61902e7	0.0432321	0.0216161	−	0.999766i	$-0.493119\pi$
$421$	6.61902e7	0.0432321	0.0216161	+	0.999766i	$0.493119\pi$
$422$	7.65925e8	0.496126
$423$	0	0
$424$	−1.48506e9	−0.946160
$425$	6.62040e8	0.418334
$426$	0	0
$427$	1.28629e9	0.799540
$428$	9.79539e8	0.603905
$429$	0	0
$430$	−4.92763e8	−0.298881
$431$	2.55963e9	1.53995	0.769975	−	0.638075i	$-0.220269\pi$
$431$	2.55963e9	1.53995	0.769975	+	0.638075i	$0.220269\pi$
$432$	0	0
$433$	1.29063e9	0.764001	0.382000	−	0.924162i	$-0.375235\pi$
$433$	1.29063e9	0.764001	0.382000	+	0.924162i	$0.375235\pi$
$434$	−5.41110e8	−0.317739
$435$	0	0
$436$	6.39340e8	0.369428
$437$	−1.29588e8	−0.0742815
$438$	0	0
$439$	−1.48653e8	−0.0838588	−0.0419294	−	0.999121i	$-0.513350\pi$
$439$	−1.48653e8	−0.0838588	−0.0419294	+	0.999121i	$0.513350\pi$
$440$	−2.31680e9	−1.29659
$441$	0	0
$442$	1.60373e9	0.883394
$443$	−6.67331e8	−0.364693	−0.182347	−	0.983234i	$-0.558369\pi$
$443$	−6.67331e8	−0.364693	−0.182347	+	0.983234i	$0.558369\pi$
$444$	0	0
$445$	−2.85228e9	−1.53438
$446$	−8.83785e8	−0.471710
$447$	0	0
$448$	7.51922e8	0.395093
$449$	1.40061e9	0.730223	0.365112	−	0.930964i	$-0.381031\pi$
$449$	1.40061e9	0.730223	0.365112	+	0.930964i	$0.381031\pi$
$450$	0	0
$451$	1.94703e9	0.999435
$452$	−2.92972e8	−0.149225
$453$	0	0
$454$	1.62999e9	0.817502
$455$	8.48259e8	0.422171
$456$	0	0
$457$	−3.43054e9	−1.68134	−0.840671	−	0.541547i	$-0.817839\pi$
$457$	−3.43054e9	−1.68134	−0.840671	+	0.541547i	$0.817839\pi$
$458$	3.42403e8	0.166536
$459$	0	0
$460$	2.29732e8	0.110044
$461$	−1.46443e9	−0.696171	−0.348085	−	0.937463i	$-0.613168\pi$
$461$	−1.46443e9	−0.696171	−0.348085	+	0.937463i	$0.613168\pi$
$462$	0	0
$463$	−4.82051e8	−0.225714	−0.112857	−	0.993611i	$-0.536000\pi$
$463$	−4.82051e8	−0.225714	−0.112857	+	0.993611i	$0.536000\pi$
$464$	−1.24344e8	−0.0577845
$465$	0	0
$466$	−2.36325e9	−1.08183
$467$	4.21545e8	0.191529	0.0957645	−	0.995404i	$-0.469470\pi$
$467$	4.21545e8	0.191529	0.0957645	+	0.995404i	$0.469470\pi$
$468$	0	0
$469$	−1.73261e9	−0.775524
$470$	5.42050e8	0.240822
$471$	0	0
$472$	−9.89556e8	−0.433155
$473$	−1.84438e9	−0.801374
$474$	0	0
$475$	−1.97953e8	−0.0847488
$476$	1.51424e9	0.643534
$477$	0	0
$478$	7.39631e8	0.309754
$479$	5.85826e8	0.243553	0.121777	−	0.992558i	$-0.461141\pi$
$479$	5.85826e8	0.243553	0.121777	+	0.992558i	$0.461141\pi$
$480$	0	0
$481$	5.49478e8	0.225135
$482$	1.38338e9	0.562702
$483$	0	0
$484$	−1.75925e9	−0.705291
$485$	−3.04951e9	−1.21376
$486$	0	0
$487$	3.35256e9	1.31530	0.657651	−	0.753323i	$-0.271550\pi$
$487$	3.35256e9	1.31530	0.657651	+	0.753323i	$0.271550\pi$
$488$	3.42136e9	1.33269
$489$	0	0
$490$	9.05774e8	0.347803
$491$	−3.71490e9	−1.41632	−0.708161	−	0.706051i	$-0.750475\pi$
$491$	−3.71490e9	−1.41632	−0.708161	+	0.706051i	$0.750475\pi$
$492$	0	0
$493$	−9.01422e9	−3.38816
$494$	−4.79523e8	−0.178964
$495$	0	0
$496$	−6.80260e7	−0.0250316
$497$	2.39539e9	0.875242
$498$	0	0
$499$	3.12811e9	1.12702	0.563509	−	0.826110i	$-0.309451\pi$
$499$	3.12811e9	1.12702	0.563509	+	0.826110i	$0.309451\pi$
$500$	1.82605e9	0.653306
$501$	0	0
$502$	1.08062e9	0.381250
$503$	1.14943e9	0.402713	0.201356	−	0.979518i	$-0.435465\pi$
$503$	1.14943e9	0.402713	0.201356	+	0.979518i	$0.435465\pi$
$504$	0	0
$505$	−3.11703e8	−0.107701
$506$	−5.62482e8	−0.193011
$507$	0	0
$508$	−2.16180e9	−0.731632
$509$	3.96039e9	1.33115	0.665573	−	0.746333i	$-0.268187\pi$
$509$	3.96039e9	1.33115	0.665573	+	0.746333i	$0.268187\pi$
$510$	0	0
$511$	1.53717e9	0.509623
$512$	1.82087e8	0.0599563
$513$	0	0
$514$	1.18812e9	0.385913
$515$	−2.34493e9	−0.756492
$516$	0	0
$517$	2.02885e9	0.645704
$518$	−3.39383e8	−0.107284
$519$	0	0
$520$	2.25626e9	0.703685
$521$	−1.89506e8	−0.0587071	−0.0293535	−	0.999569i	$-0.509345\pi$
$521$	−1.89506e8	−0.0587071	−0.0293535	+	0.999569i	$0.509345\pi$
$522$	0	0
$523$	−3.32527e8	−0.101642	−0.0508208	−	0.998708i	$-0.516184\pi$
$523$	−3.32527e8	−0.101642	−0.0508208	+	0.998708i	$0.516184\pi$
$524$	2.07828e9	0.631021
$525$	0	0
$526$	−1.78565e8	−0.0534991
$527$	−4.93150e9	−1.46772
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	1.76436e9	0.514779
$531$	0	0
$532$	−4.52765e8	−0.130371
$533$	−1.89616e9	−0.542412
$534$	0	0
$535$	−3.08879e9	−0.872067
$536$	−4.60852e9	−1.29266
$537$	0	0
$538$	1.36822e8	0.0378807
$539$	3.39025e9	0.932547
$540$	0	0
$541$	4.30263e9	1.16827	0.584135	−	0.811656i	$-0.301434\pi$
$541$	4.30263e9	1.16827	0.584135	+	0.811656i	$0.301434\pi$
$542$	−6.19768e8	−0.167198
$543$	0	0
$544$	6.53789e9	1.74117
$545$	−2.01604e9	−0.533471
$546$	0	0
$547$	7.00466e9	1.82992	0.914958	−	0.403549i	$-0.132223\pi$
$547$	7.00466e9	1.82992	0.914958	+	0.403549i	$0.132223\pi$
$548$	4.31292e9	1.11954
$549$	0	0
$550$	−8.59220e8	−0.220209
$551$	2.69529e9	0.686396
$552$	0	0
$553$	−3.57681e9	−0.899410
$554$	4.06697e9	1.01622
$555$	0	0
$556$	3.60686e9	0.889953
$557$	−2.99900e9	−0.735331	−0.367666	−	0.929958i	$-0.619843\pi$
$557$	−2.99900e9	−0.735331	−0.367666	+	0.929958i	$0.619843\pi$
$558$	0	0
$559$	1.79619e9	0.434921
$560$	−6.58654e7	−0.0158489
$561$	0	0
$562$	−4.94646e9	−1.17549
$563$	−1.11595e9	−0.263551	−0.131775	−	0.991280i	$-0.542068\pi$
$563$	−1.11595e9	−0.263551	−0.131775	+	0.991280i	$0.542068\pi$
$564$	0	0
$565$	9.23832e8	0.215488
$566$	1.61630e9	0.374683
$567$	0	0
$568$	6.37143e9	1.45887
$569$	8.66803e8	0.197255	0.0986273	−	0.995124i	$-0.468555\pi$
$569$	8.66803e8	0.197255	0.0986273	+	0.995124i	$0.468555\pi$
$570$	0	0
$571$	2.93241e9	0.659172	0.329586	−	0.944126i	$-0.393091\pi$
$571$	2.93241e9	0.659172	0.329586	+	0.944126i	$0.393091\pi$
$572$	3.18182e9	0.710870
$573$	0	0
$574$	1.17115e9	0.258477
$575$	2.26132e8	0.0496050
$576$	0	0
$577$	4.78530e9	1.03704	0.518518	−	0.855067i	$-0.326484\pi$
$577$	4.78530e9	1.03704	0.518518	+	0.855067i	$0.326484\pi$
$578$	−6.10804e9	−1.31569
$579$	0	0
$580$	−4.77816e9	−1.01686
$581$	2.20725e8	0.0466911
$582$	0	0
$583$	6.60386e9	1.38025
$584$	4.08868e9	0.849451
$585$	0	0
$586$	−5.70004e8	−0.117014
$587$	−2.22146e8	−0.0453320	−0.0226660	−	0.999743i	$-0.507215\pi$
$587$	−2.22146e8	−0.0453320	−0.0226660	+	0.999743i	$0.507215\pi$
$588$	0	0
$589$	1.47454e9	0.297340
$590$	1.17566e9	0.235667
$591$	0	0
$592$	−4.26658e7	−0.00845189
$593$	6.63984e9	1.30757	0.653787	−	0.756679i	$-0.273179\pi$
$593$	6.63984e9	1.30757	0.653787	+	0.756679i	$0.273179\pi$
$594$	0	0
$595$	−4.77487e9	−0.929293
$596$	−1.06819e9	−0.206674
$597$	0	0
$598$	5.47786e8	0.104751
$599$	6.78244e9	1.28941	0.644706	−	0.764430i	$-0.276980\pi$
$599$	6.78244e9	1.28941	0.644706	+	0.764430i	$0.276980\pi$
$600$	0	0
$601$	6.88273e9	1.29330	0.646651	−	0.762786i	$-0.276169\pi$
$601$	6.88273e9	1.29330	0.646651	+	0.762786i	$0.276169\pi$
$602$	−1.10941e9	−0.207254
$603$	0	0
$604$	−3.74693e8	−0.0691905
$605$	5.54745e9	1.01847
$606$	0	0
$607$	−6.20980e9	−1.12698	−0.563491	−	0.826122i	$-0.690542\pi$
$607$	−6.20980e9	−1.12698	−0.563491	+	0.826122i	$0.690542\pi$
$608$	−1.95486e9	−0.352738
$609$	0	0
$610$	−4.06481e9	−0.725080
$611$	−1.97584e9	−0.350436
$612$	0	0
$613$	−5.45404e8	−0.0956327	−0.0478164	−	0.998856i	$-0.515226\pi$
$613$	−5.45404e8	−0.0956327	−0.0478164	+	0.998856i	$0.515226\pi$
$614$	−4.18671e9	−0.729934
$615$	0	0
$616$	−5.21604e9	−0.899101
$617$	−4.84884e9	−0.831073	−0.415537	−	0.909576i	$-0.636406\pi$
$617$	−4.84884e9	−0.831073	−0.415537	+	0.909576i	$0.636406\pi$
$618$	0	0
$619$	8.95916e9	1.51827	0.759137	−	0.650931i	$-0.225621\pi$
$619$	8.95916e9	1.51827	0.759137	+	0.650931i	$0.225621\pi$
$620$	−2.61403e9	−0.440494
$621$	0	0
$622$	9.26014e8	0.154295
$623$	−6.42163e9	−1.06399
$624$	0	0
$625$	−4.30608e9	−0.705508
$626$	2.51629e9	0.409968
$627$	0	0
$628$	5.37995e9	0.866801
$629$	−3.09303e9	−0.495572
$630$	0	0
$631$	4.66301e9	0.738862	0.369431	−	0.929258i	$-0.379553\pi$
$631$	4.66301e9	0.738862	0.369431	+	0.929258i	$0.379553\pi$
$632$	−9.51388e9	−1.49916
$633$	0	0
$634$	2.82528e8	0.0440300
$635$	6.81682e9	1.05651
$636$	0	0
$637$	−3.30167e9	−0.506110
$638$	1.16990e10	1.78351
$639$	0	0
$640$	3.35634e9	0.506100
$641$	−9.05541e9	−1.35802	−0.679008	−	0.734131i	$-0.737590\pi$
$641$	−9.05541e9	−1.35802	−0.679008	+	0.734131i	$0.737590\pi$
$642$	0	0
$643$	−6.14386e9	−0.911387	−0.455694	−	0.890137i	$-0.650609\pi$
$643$	−6.14386e9	−0.911387	−0.455694	+	0.890137i	$0.650609\pi$
$644$	5.17218e8	0.0763086
$645$	0	0
$646$	2.69925e9	0.393939
$647$	−1.34542e10	−1.95295	−0.976476	−	0.215626i	$-0.930821\pi$
$647$	−1.34542e10	−1.95295	−0.976476	+	0.215626i	$0.930821\pi$
$648$	0	0
$649$	4.40041e9	0.631883
$650$	8.36771e8	0.119511
$651$	0	0
$652$	−8.64630e8	−0.122170
$653$	8.77081e9	1.23266	0.616330	−	0.787488i	$-0.288619\pi$
$653$	8.77081e9	1.23266	0.616330	+	0.787488i	$0.288619\pi$
$654$	0	0
$655$	−6.55345e9	−0.911225
$656$	1.47233e8	0.0203629
$657$	0	0
$658$	1.22037e9	0.166994
$659$	1.25720e10	1.71122	0.855612	−	0.517618i	$-0.173181\pi$
$659$	1.25720e10	1.71122	0.855612	+	0.517618i	$0.173181\pi$
$660$	0	0
$661$	−1.17733e10	−1.58560	−0.792798	−	0.609485i	$-0.791376\pi$
$661$	−1.17733e10	−1.58560	−0.792798	+	0.609485i	$0.791376\pi$
$662$	8.07330e9	1.08155
$663$	0	0
$664$	5.87100e8	0.0778259
$665$	1.42771e9	0.188262
$666$	0	0
$667$	−3.07898e9	−0.401760
$668$	−8.47318e9	−1.09984
$669$	0	0
$670$	5.47524e9	0.703301
$671$	−1.52143e10	−1.94412
$672$	0	0
$673$	−1.27645e10	−1.61418	−0.807088	−	0.590432i	$-0.798958\pi$
$673$	−1.27645e10	−1.61418	−0.807088	+	0.590432i	$0.798958\pi$
$674$	2.25224e9	0.283338
$675$	0	0
$676$	1.75686e9	0.218738
$677$	1.31090e10	1.62371	0.811854	−	0.583861i	$-0.198459\pi$
$677$	1.31090e10	1.62371	0.811854	+	0.583861i	$0.198459\pi$
$678$	0	0
$679$	−6.86567e9	−0.841664
$680$	−1.27006e10	−1.54897
$681$	0	0
$682$	6.40029e9	0.772599
$683$	5.12267e9	0.615210	0.307605	−	0.951514i	$-0.400472\pi$
$683$	5.12267e9	0.615210	0.307605	+	0.951514i	$0.400472\pi$
$684$	0	0
$685$	−1.36000e10	−1.61667
$686$	5.25809e9	0.621861
$687$	0	0
$688$	−1.39470e8	−0.0163276
$689$	−6.43132e9	−0.749088
$690$	0	0
$691$	3.65593e9	0.421527	0.210763	−	0.977537i	$-0.432405\pi$
$691$	3.65593e9	0.421527	0.210763	+	0.977537i	$0.432405\pi$
$692$	3.80856e9	0.436908
$693$	0	0
$694$	−5.86677e9	−0.666256
$695$	−1.13735e10	−1.28513
$696$	0	0
$697$	1.06735e10	1.19397
$698$	6.95297e9	0.773885
$699$	0	0
$700$	7.90077e8	0.0870615
$701$	1.62181e10	1.77822	0.889112	−	0.457691i	$-0.151323\pi$
$701$	1.62181e10	1.77822	0.889112	+	0.457691i	$0.151323\pi$
$702$	0	0
$703$	9.24828e8	0.100396
$704$	−8.89379e9	−0.960689
$705$	0	0
$706$	3.32433e9	0.355540
$707$	−7.01768e8	−0.0746837
$708$	0	0
$709$	−3.99511e9	−0.420986	−0.210493	−	0.977595i	$-0.567507\pi$
$709$	−3.99511e9	−0.420986	−0.210493	+	0.977595i	$0.567507\pi$
$710$	−7.56970e9	−0.793733
$711$	0	0
$712$	−1.70808e10	−1.77348
$713$	−1.68445e9	−0.174038
$714$	0	0
$715$	−1.00333e10	−1.02653
$716$	−2.30738e9	−0.234922
$717$	0	0
$718$	−7.75098e8	−0.0781486
$719$	−5.04375e9	−0.506060	−0.253030	−	0.967458i	$-0.581427\pi$
$719$	−5.04375e9	−0.506060	−0.253030	+	0.967458i	$0.581427\pi$
$720$	0	0
$721$	−5.27938e9	−0.524577
$722$	5.55253e9	0.549049
$723$	0	0
$724$	3.55713e9	0.348350
$725$	−4.70330e9	−0.458373
$726$	0	0
$727$	−8.20105e9	−0.791588	−0.395794	−	0.918339i	$-0.629530\pi$
$727$	−8.20105e9	−0.791588	−0.395794	+	0.918339i	$0.629530\pi$
$728$	5.07976e9	0.487959
$729$	0	0
$730$	−4.85763e9	−0.462162
$731$	−1.01108e10	−0.957358
$732$	0	0
$733$	−3.11182e9	−0.291844	−0.145922	−	0.989296i	$-0.546615\pi$
$733$	−3.11182e9	−0.291844	−0.145922	+	0.989296i	$0.546615\pi$
$734$	−1.93959e9	−0.181040
$735$	0	0
$736$	2.23314e9	0.206464
$737$	2.04934e10	1.88572
$738$	0	0
$739$	2.45017e9	0.223326	0.111663	−	0.993746i	$-0.464382\pi$
$739$	2.45017e9	0.223326	0.111663	+	0.993746i	$0.464382\pi$
$740$	−1.63952e9	−0.148732
$741$	0	0
$742$	3.97228e9	0.356965
$743$	−1.47214e10	−1.31670	−0.658350	−	0.752712i	$-0.728745\pi$
$743$	−1.47214e10	−1.31670	−0.658350	+	0.752712i	$0.728745\pi$
$744$	0	0
$745$	3.36833e9	0.298448
$746$	−5.87011e9	−0.517679
$747$	0	0
$748$	−1.79106e10	−1.56478
$749$	−6.95411e9	−0.604721
$750$	0	0
$751$	−1.60115e10	−1.37941	−0.689703	−	0.724092i	$-0.742259\pi$
$751$	−1.60115e10	−1.37941	−0.689703	+	0.724092i	$0.742259\pi$
$752$	1.53420e8	0.0131559
$753$	0	0
$754$	−1.13933e10	−0.967946
$755$	1.18152e9	0.0999144
$756$	0	0
$757$	1.69878e10	1.42332	0.711660	−	0.702524i	$-0.247944\pi$
$757$	1.69878e10	1.42332	0.711660	+	0.702524i	$0.247944\pi$
$758$	4.25800e9	0.355111
$759$	0	0
$760$	3.79753e9	0.313800
$761$	2.21862e10	1.82489	0.912447	−	0.409195i	$-0.134191\pi$
$761$	2.21862e10	1.82489	0.912447	+	0.409195i	$0.134191\pi$
$762$	0	0
$763$	−4.53891e9	−0.369927
$764$	−8.08683e9	−0.656072
$765$	0	0
$766$	1.06867e10	0.859095
$767$	−4.28544e9	−0.342935
$768$	0	0
$769$	−4.74577e9	−0.376326	−0.188163	−	0.982138i	$-0.560253\pi$
$769$	−4.74577e9	−0.376326	−0.188163	+	0.982138i	$0.560253\pi$
$770$	6.19701e9	0.489176
$771$	0	0
$772$	−1.26536e10	−0.989817
$773$	9.43919e9	0.735032	0.367516	−	0.930017i	$-0.380208\pi$
$773$	9.43919e9	0.735032	0.367516	+	0.930017i	$0.380208\pi$
$774$	0	0
$775$	−2.57308e9	−0.198562
$776$	−1.82618e10	−1.40291
$777$	0	0
$778$	2.97412e9	0.226428
$779$	−3.19143e9	−0.241882
$780$	0	0
$781$	−2.83328e10	−2.12819
$782$	−3.08350e9	−0.230580
$783$	0	0
$784$	2.56367e8	0.0190001
$785$	−1.69646e10	−1.25170
$786$	0	0
$787$	2.24683e10	1.64308	0.821538	−	0.570154i	$-0.193116\pi$
$787$	2.24683e10	1.64308	0.821538	+	0.570154i	$0.193116\pi$
$788$	8.07396e9	0.587820
$789$	0	0
$790$	1.13031e10	0.815650
$791$	2.07992e9	0.149427
$792$	0	0
$793$	1.48168e10	1.05511
$794$	3.25692e9	0.230906
$795$	0	0
$796$	5.25673e9	0.369420
$797$	−1.09382e9	−0.0765314	−0.0382657	−	0.999268i	$-0.512183\pi$
$797$	−1.09382e9	−0.0765314	−0.0382657	+	0.999268i	$0.512183\pi$
$798$	0	0
$799$	1.11221e10	0.771387
$800$	3.41123e9	0.235557
$801$	0	0
$802$	3.03015e9	0.207421
$803$	−1.81818e10	−1.23917
$804$	0	0
$805$	−1.63095e9	−0.110193
$806$	−6.23306e9	−0.419304
$807$	0	0
$808$	−1.86662e9	−0.124485
$809$	−1.21344e10	−0.805748	−0.402874	−	0.915255i	$-0.631989\pi$
$809$	−1.21344e10	−0.805748	−0.402874	+	0.915255i	$0.631989\pi$
$810$	0	0
$811$	1.02343e10	0.673730	0.336865	−	0.941553i	$-0.390633\pi$
$811$	1.02343e10	0.673730	0.336865	+	0.941553i	$0.390633\pi$
$812$	−1.07576e10	−0.705127
$813$	0	0
$814$	4.01425e9	0.260867
$815$	2.72645e9	0.176419
$816$	0	0
$817$	3.02317e9	0.193948
$818$	7.97376e8	0.0509362
$819$	0	0
$820$	5.65771e9	0.358337
$821$	−2.57619e10	−1.62472	−0.812358	−	0.583159i	$-0.801816\pi$
$821$	−2.57619e10	−1.62472	−0.812358	+	0.583159i	$0.801816\pi$
$822$	0	0
$823$	−1.12632e10	−0.704307	−0.352154	−	0.935942i	$-0.614551\pi$
$823$	−1.12632e10	−0.704307	−0.352154	+	0.935942i	$0.614551\pi$
$824$	−1.40425e10	−0.874378
$825$	0	0
$826$	2.64688e9	0.163420
$827$	1.88055e10	1.15615	0.578077	−	0.815982i	$-0.303803\pi$
$827$	1.88055e10	1.15615	0.578077	+	0.815982i	$0.303803\pi$
$828$	0	0
$829$	−1.31492e9	−0.0801600	−0.0400800	−	0.999196i	$-0.512761\pi$
$829$	−1.31492e9	−0.0801600	−0.0400800	+	0.999196i	$0.512761\pi$
$830$	−6.97515e8	−0.0423429
$831$	0	0
$832$	8.66142e9	0.521384
$833$	1.85852e10	1.11406
$834$	0	0
$835$	2.67186e10	1.58822
$836$	5.35534e9	0.317004
$837$	0	0
$838$	−1.37421e10	−0.806675
$839$	5.54224e9	0.323980	0.161990	−	0.986792i	$-0.448209\pi$
$839$	5.54224e9	0.323980	0.161990	+	0.986792i	$0.448209\pi$
$840$	0	0
$841$	4.67894e10	2.71245
$842$	−4.70923e8	−0.0271868
$843$	0	0
$844$	8.33039e9	0.476943
$845$	−5.53993e9	−0.315868
$846$	0	0
$847$	1.24895e10	0.706244
$848$	4.99378e8	0.0281219
$849$	0	0
$850$	−4.71021e9	−0.263072
$851$	−1.05648e9	−0.0587637
$852$	0	0
$853$	−1.06408e10	−0.587021	−0.293511	−	0.955956i	$-0.594824\pi$
$853$	−1.06408e10	−0.587021	−0.293511	+	0.955956i	$0.594824\pi$
$854$	−9.15153e9	−0.502795
$855$	0	0
$856$	−1.84971e10	−1.00796
$857$	4.28265e9	0.232423	0.116212	−	0.993224i	$-0.462925\pi$
$857$	4.28265e9	0.232423	0.116212	+	0.993224i	$0.462925\pi$
$858$	0	0
$859$	−3.28556e10	−1.76862	−0.884309	−	0.466903i	$-0.845370\pi$
$859$	−3.28556e10	−1.76862	−0.884309	+	0.466903i	$0.845370\pi$
$860$	−5.35941e9	−0.287324
$861$	0	0
$862$	−1.82110e10	−0.968406
$863$	2.96741e10	1.57159	0.785796	−	0.618486i	$-0.212254\pi$
$863$	2.96741e10	1.57159	0.785796	+	0.618486i	$0.212254\pi$
$864$	0	0
$865$	−1.20096e10	−0.630915
$866$	−9.18242e9	−0.480446
$867$	0	0
$868$	−5.88525e9	−0.305454
$869$	4.23068e10	2.18696
$870$	0	0
$871$	−1.99580e10	−1.02342
$872$	−1.20729e10	−0.616603
$873$	0	0
$874$	9.21980e8	0.0467123
$875$	−1.29638e10	−0.654189
$876$	0	0
$877$	1.68956e10	0.845814	0.422907	−	0.906173i	$-0.361010\pi$
$877$	1.68956e10	0.845814	0.422907	+	0.906173i	$0.361010\pi$
$878$	1.05762e9	0.0527351
$879$	0	0
$880$	7.79062e8	0.0385374
$881$	−8.75880e9	−0.431548	−0.215774	−	0.976443i	$-0.569227\pi$
$881$	−8.75880e9	−0.431548	−0.215774	+	0.976443i	$0.569227\pi$
$882$	0	0
$883$	2.43303e10	1.18928	0.594641	−	0.803991i	$-0.297294\pi$
$883$	2.43303e10	1.18928	0.594641	+	0.803991i	$0.297294\pi$
$884$	1.74426e10	0.849237
$885$	0	0
$886$	4.74785e9	0.229340
$887$	9.17722e9	0.441548	0.220774	−	0.975325i	$-0.429142\pi$
$887$	9.17722e9	0.441548	0.220774	+	0.975325i	$0.429142\pi$
$888$	0	0
$889$	1.53474e10	0.732620
$890$	2.02931e10	0.964902
$891$	0	0
$892$	−9.61227e9	−0.453471
$893$	−3.32555e9	−0.156273
$894$	0	0
$895$	7.27589e9	0.339239
$896$	7.55648e9	0.350947
$897$	0	0
$898$	−9.96492e9	−0.459205
$899$	3.50346e10	1.60819
$900$	0	0
$901$	3.62021e10	1.64891
$902$	−1.38525e10	−0.628501
$903$	0	0
$904$	5.53233e9	0.249068
$905$	−1.12167e10	−0.503033
$906$	0	0
$907$	1.69074e10	0.752405	0.376202	−	0.926538i	$-0.377230\pi$
$907$	1.69074e10	0.752405	0.376202	+	0.926538i	$0.377230\pi$
$908$	1.77282e10	0.785893
$909$	0	0
$910$	−6.03510e9	−0.265485
$911$	−7.71107e9	−0.337910	−0.168955	−	0.985624i	$-0.554039\pi$
$911$	−7.71107e9	−0.337910	−0.168955	+	0.985624i	$0.554039\pi$
$912$	0	0
$913$	−2.61075e9	−0.113532
$914$	2.44072e10	1.05732
$915$	0	0
$916$	3.72407e9	0.160097
$917$	−1.47545e10	−0.631874
$918$	0	0
$919$	−2.07829e10	−0.883287	−0.441644	−	0.897191i	$-0.645604\pi$
$919$	−2.07829e10	−0.883287	−0.441644	+	0.897191i	$0.645604\pi$
$920$	−4.33812e9	−0.183673
$921$	0	0
$922$	1.04190e10	0.437791
$923$	2.75926e10	1.15501
$924$	0	0
$925$	−1.61383e9	−0.0670443
$926$	3.42964e9	0.141942
$927$	0	0
$928$	−4.64468e10	−1.90782
$929$	−2.73426e10	−1.11888	−0.559442	−	0.828870i	$-0.688985\pi$
$929$	−2.73426e10	−1.11888	−0.559442	+	0.828870i	$0.688985\pi$
$930$	0	0
$931$	−5.55705e9	−0.225694
$932$	−2.57033e10	−1.04000
$933$	0	0
$934$	−2.99916e9	−0.120444
$935$	5.64776e10	2.25962
$936$	0	0
$937$	−2.65430e10	−1.05405	−0.527026	−	0.849849i	$-0.676693\pi$
$937$	−2.65430e10	−1.05405	−0.527026	+	0.849849i	$0.676693\pi$
$938$	1.23270e10	0.487693
$939$	0	0
$940$	5.89547e9	0.231511
$941$	2.60897e10	1.02072	0.510358	−	0.859962i	$-0.329513\pi$
$941$	2.60897e10	1.02072	0.510358	+	0.859962i	$0.329513\pi$
$942$	0	0
$943$	3.64575e9	0.141578
$944$	3.32755e8	0.0128743
$945$	0	0
$946$	1.31222e10	0.503949
$947$	−2.11552e10	−0.809454	−0.404727	−	0.914438i	$-0.632633\pi$
$947$	−2.11552e10	−0.809454	−0.404727	+	0.914438i	$0.632633\pi$
$948$	0	0
$949$	1.77067e10	0.672522
$950$	1.40837e9	0.0532948
$951$	0	0
$952$	−2.85941e10	−1.07411
$953$	2.33959e10	0.875619	0.437810	−	0.899068i	$-0.355754\pi$
$953$	2.33959e10	0.875619	0.437810	+	0.899068i	$0.355754\pi$
$954$	0	0
$955$	2.55003e10	0.947399
$956$	8.04441e9	0.297777
$957$	0	0
$958$	−4.16797e9	−0.153160
$959$	−3.06190e10	−1.12105
$960$	0	0
$961$	−8.34587e9	−0.303347
$962$	−3.90937e9	−0.141577
$963$	0	0
$964$	1.50460e10	0.540944
$965$	3.99008e10	1.42934
$966$	0	0
$967$	2.79465e10	0.993882	0.496941	−	0.867784i	$-0.334456\pi$
$967$	2.79465e10	0.993882	0.496941	+	0.867784i	$0.334456\pi$
$968$	3.32207e10	1.17718
$969$	0	0
$970$	2.16963e10	0.763281
$971$	−2.96781e10	−1.04033	−0.520163	−	0.854067i	$-0.674129\pi$
$971$	−2.96781e10	−1.04033	−0.520163	+	0.854067i	$0.674129\pi$
$972$	0	0
$973$	−2.56064e10	−0.891156
$974$	−2.38524e10	−0.827135
$975$	0	0
$976$	−1.15049e9	−0.0396104
$977$	−3.47537e10	−1.19226	−0.596128	−	0.802889i	$-0.703295\pi$
$977$	−3.47537e10	−1.19226	−0.596128	+	0.802889i	$0.703295\pi$
$978$	0	0
$979$	7.59556e10	2.58714
$980$	9.85143e9	0.334355
$981$	0	0
$982$	2.64304e10	0.890662
$983$	3.56697e10	1.19774	0.598870	−	0.800846i	$-0.295617\pi$
$983$	3.56697e10	1.19774	0.598870	+	0.800846i	$0.295617\pi$
$984$	0	0
$985$	−2.54597e10	−0.848840
$986$	6.41334e10	2.13066
$987$	0	0
$988$	−5.21542e9	−0.172044
$989$	−3.45353e9	−0.113521
$990$	0	0
$991$	2.52813e10	0.825166	0.412583	−	0.910920i	$-0.364627\pi$
$991$	2.52813e10	0.825166	0.412583	+	0.910920i	$0.364627\pi$
$992$	−2.54101e10	−0.826448
$993$	0	0
$994$	−1.70424e10	−0.550401
$995$	−1.65761e10	−0.533460
$996$	0	0
$997$	−1.68122e10	−0.537268	−0.268634	−	0.963242i	$-0.586572\pi$
$997$	−1.68122e10	−0.537268	−0.268634	+	0.963242i	$0.586572\pi$
$998$	−2.22556e10	−0.708731
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.e.1.4		8
3.2	odd	2		69.8.a.d.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.d.1.5	✓	8	3.2	odd	2
207.8.a.e.1.4		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)

\(f(q)\)	\(=\)	\(q-7.11469 q^{2} -77.3812 q^{4} +244.007 q^{5} +549.357 q^{7} +1461.22 q^{8} +O(q^{10})\)	\(q-7.11469 q^{2} -77.3812 q^{4} +244.007 q^{5} +549.357 q^{7} +1461.22 q^{8} -1736.03 q^{10} -6497.85 q^{11} +6328.07 q^{13} -3908.51 q^{14} -491.361 q^{16} -35620.9 q^{17} +10650.8 q^{19} -18881.5 q^{20} +46230.2 q^{22} -12167.0 q^{23} -18585.7 q^{25} -45022.3 q^{26} -42509.9 q^{28} +253060. q^{29} +138444. q^{31} -183541. q^{32} +253432. q^{34} +134047. q^{35} +86831.8 q^{37} -75777.1 q^{38} +356548. q^{40} -299642. q^{41} +283844. q^{43} +502811. q^{44} +86564.4 q^{46} -312235. q^{47} -521749. q^{49} +132232. q^{50} -489674. q^{52} -1.01632e6 q^{53} -1.58552e6 q^{55} +802734. q^{56} -1.80044e6 q^{58} -677210. q^{59} +2.34144e6 q^{61} -984986. q^{62} +1.36873e6 q^{64} +1.54409e6 q^{65} -3.15388e6 q^{67} +2.75639e6 q^{68} -953702. q^{70} +4.36034e6 q^{71} +2.79812e6 q^{73} -617781. q^{74} -824171. q^{76} -3.56964e6 q^{77} -6.51090e6 q^{79} -119895. q^{80} +2.13186e6 q^{82} +401787. q^{83} -8.69174e6 q^{85} -2.01946e6 q^{86} -9.49480e6 q^{88} -1.16894e7 q^{89} +3.47637e6 q^{91} +941497. q^{92} +2.22145e6 q^{94} +2.59887e6 q^{95} -1.24976e7 q^{97} +3.71208e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8}+O(q^{10}) \) 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

Varieties

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Database

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