LMFDB - Embedded newform 867.4.a.w.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,4,Mod(1,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("867.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	867.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:	$51.1546559750$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 128 x^{18} + 6848 x^{16} - 198916 x^{14} - 1344 x^{13} + 3410877 x^{12} + 96960 x^{11} + \cdots - 2228224 $ x^20 - 128x^18 + 6848x^16 - 198916x^14 - 1344x^13 + 3410877x^12 + 96960x^11 - 35137604x^10 - 2571456x^9 + 211185834x^8 + 31654464x^7 - 675563376x^6 - 187186944x^5 + 908993040x^4 + 449577984x^3 - 207421440x^2 - 111083520x - 2228224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 17^{6} $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.0209109$ of defining polynomial
Character	$\chi$	$=$	867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.0209109 q^{2} +3.00000 q^{3} -7.99956 q^{4} +20.5423 q^{5} +0.0627328 q^{6} +6.44826 q^{7} -0.334566 q^{8} +9.00000 q^{9} +0.429559 q^{10} +18.2513 q^{11} -23.9987 q^{12} +63.8416 q^{13} +0.134839 q^{14} +61.6270 q^{15} +63.9895 q^{16} +0.188198 q^{18} -61.3281 q^{19} -164.330 q^{20} +19.3448 q^{21} +0.381651 q^{22} +106.234 q^{23} -1.00370 q^{24} +296.987 q^{25} +1.33499 q^{26} +27.0000 q^{27} -51.5833 q^{28} -112.532 q^{29} +1.28868 q^{30} -220.179 q^{31} +4.01460 q^{32} +54.7538 q^{33} +132.462 q^{35} -71.9961 q^{36} -187.746 q^{37} -1.28243 q^{38} +191.525 q^{39} -6.87276 q^{40} +198.268 q^{41} +0.404517 q^{42} +139.548 q^{43} -146.002 q^{44} +184.881 q^{45} +2.22145 q^{46} +575.652 q^{47} +191.969 q^{48} -301.420 q^{49} +6.21027 q^{50} -510.705 q^{52} -276.624 q^{53} +0.564595 q^{54} +374.923 q^{55} -2.15737 q^{56} -183.984 q^{57} -2.35315 q^{58} +48.2675 q^{59} -492.989 q^{60} +421.765 q^{61} -4.60415 q^{62} +58.0344 q^{63} -511.832 q^{64} +1311.46 q^{65} +1.14495 q^{66} -269.737 q^{67} +318.702 q^{69} +2.76991 q^{70} +699.900 q^{71} -3.01109 q^{72} -816.421 q^{73} -3.92594 q^{74} +890.961 q^{75} +490.598 q^{76} +117.689 q^{77} +4.00496 q^{78} -1116.41 q^{79} +1314.49 q^{80} +81.0000 q^{81} +4.14597 q^{82} -465.803 q^{83} -154.750 q^{84} +2.91808 q^{86} -337.597 q^{87} -6.10624 q^{88} -92.3664 q^{89} +3.86603 q^{90} +411.667 q^{91} -849.827 q^{92} -660.538 q^{93} +12.0374 q^{94} -1259.82 q^{95} +12.0438 q^{96} +1668.15 q^{97} -6.30297 q^{98} +164.261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 60 q^{3} + 96 q^{4} + 32 q^{5} + 56 q^{7} + 180 q^{9} + 80 q^{10} + 152 q^{11} + 288 q^{12} + 56 q^{13} + 112 q^{14} + 96 q^{15} + 512 q^{16} + 328 q^{19} + 192 q^{20} + 168 q^{21} - 104 q^{22} + 576 q^{23}+ \cdots + 1368 q^{99}+O(q^{100}) $ 20 * q + 60 * q^3 + 96 * q^4 + 32 * q^5 + 56 * q^7 + 180 * q^9 + 80 * q^10 + 152 * q^11 + 288 * q^12 + 56 * q^13 + 112 * q^14 + 96 * q^15 + 512 * q^16 + 328 * q^19 + 192 * q^20 + 168 * q^21 - 104 * q^22 + 576 * q^23 + 796 * q^25 + 540 * q^27 + 648 * q^28 + 1000 * q^29 + 240 * q^30 + 248 * q^31 + 456 * q^33 - 496 * q^35 + 864 * q^36 + 984 * q^37 - 352 * q^38 + 168 * q^39 + 1800 * q^40 + 1080 * q^41 + 336 * q^42 + 888 * q^43 + 2080 * q^44 + 288 * q^45 + 752 * q^46 - 368 * q^47 + 1536 * q^48 + 1444 * q^49 + 224 * q^50 + 480 * q^52 - 224 * q^53 + 1592 * q^55 - 352 * q^56 + 984 * q^57 + 3528 * q^58 + 576 * q^59 + 576 * q^60 + 2328 * q^61 + 368 * q^62 + 504 * q^63 + 1560 * q^64 + 4824 * q^65 - 312 * q^66 + 1136 * q^67 + 1728 * q^69 + 1224 * q^70 - 1224 * q^71 + 656 * q^73 + 1808 * q^74 + 2388 * q^75 + 1072 * q^76 - 1344 * q^77 + 648 * q^79 + 1280 * q^80 + 1620 * q^81 + 6712 * q^82 + 160 * q^83 + 1944 * q^84 - 7808 * q^86 + 3000 * q^87 + 576 * q^88 - 2128 * q^89 + 720 * q^90 + 1072 * q^91 + 9504 * q^92 + 744 * q^93 - 1952 * q^94 + 4632 * q^95 + 752 * q^97 - 10544 * q^98 + 1368 * q^99

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 $

$2$	0.0209109	0.00739313	0.00369656	−	0.999993i	$-0.498823\pi$
$2$	0.0209109	0.00739313	0.00369656	+	0.999993i	$0.498823\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.99956	−0.999945
$5$	20.5423	1.83736	0.918681	−	0.395001i	$-0.129256\pi$
$5$	20.5423	1.83736	0.918681	+	0.395001i	$0.129256\pi$
$6$	0.0627328	0.00426842
$7$	6.44826	0.348173	0.174087	−	0.984730i	$-0.444303\pi$
$7$	6.44826	0.348173	0.174087	+	0.984730i	$0.444303\pi$
$8$	−0.334566	−0.0147859
$9$	9.00000	0.333333
$10$	0.429559	0.0135838
$11$	18.2513	0.500269	0.250135	−	0.968211i	$-0.419525\pi$
$11$	18.2513	0.500269	0.250135	+	0.968211i	$0.419525\pi$
$12$	−23.9987	−0.577319
$13$	63.8416	1.36204	0.681018	−	0.732266i	$-0.261537\pi$
$13$	63.8416	1.36204	0.681018	+	0.732266i	$0.261537\pi$
$14$	0.134839	0.00257409
$15$	61.6270	1.06080
$16$	63.9895	0.999836
$17$	0	0
$17$	0	0
$18$	0.188198	0.00246438
$19$	−61.3281	−0.740507	−0.370254	−	0.928931i	$-0.620729\pi$
$19$	−61.3281	−0.740507	−0.370254	+	0.928931i	$0.620729\pi$
$20$	−164.330	−1.83726
$21$	19.3448	0.201018
$22$	0.381651	0.00369855
$23$	106.234	0.963102	0.481551	−	0.876418i	$-0.340074\pi$
$23$	106.234	0.963102	0.481551	+	0.876418i	$0.340074\pi$
$24$	−1.00370	−0.00853661
$25$	296.987	2.37590
$26$	1.33499	0.0100697
$27$	27.0000	0.192450
$28$	−51.5833	−0.348154
$29$	−112.532	−0.720577	−0.360288	−	0.932841i	$-0.617322\pi$
$29$	−112.532	−0.720577	−0.360288	+	0.932841i	$0.617322\pi$
$30$	1.28868	0.00784264
$31$	−220.179	−1.27566	−0.637829	−	0.770178i	$-0.720167\pi$
$31$	−220.179	−1.27566	−0.637829	+	0.770178i	$0.720167\pi$
$32$	4.01460	0.0221778
$33$	54.7538	0.288831
$34$	0	0
$35$	132.462	0.639720
$36$	−71.9961	−0.333315
$37$	−187.746	−0.834195	−0.417098	−	0.908862i	$-0.636953\pi$
$37$	−187.746	−0.834195	−0.417098	+	0.908862i	$0.636953\pi$
$38$	−1.28243	−0.00547467
$39$	191.525	0.786372
$40$	−6.87276	−0.0271670
$41$	198.268	0.755226	0.377613	−	0.925964i	$-0.376745\pi$
$41$	198.268	0.755226	0.377613	+	0.925964i	$0.376745\pi$
$42$	0.404517	0.00148615
$43$	139.548	0.494905	0.247452	−	0.968900i	$-0.420407\pi$
$43$	139.548	0.494905	0.247452	+	0.968900i	$0.420407\pi$
$44$	−146.002	−0.500242
$45$	184.881	0.612454
$46$	2.22145	0.00712034
$47$	575.652	1.78654	0.893271	−	0.449519i	$-0.148405\pi$
$47$	575.652	1.78654	0.893271	+	0.449519i	$0.148405\pi$
$48$	191.969	0.577256
$49$	−301.420	−0.878775
$50$	6.21027	0.0175653
$51$	0	0
$52$	−510.705	−1.36196
$53$	−276.624	−0.716928	−0.358464	−	0.933544i	$-0.616699\pi$
$53$	−276.624	−0.716928	−0.358464	+	0.933544i	$0.616699\pi$
$54$	0.564595	0.00142281
$55$	374.923	0.919175
$56$	−2.15737	−0.00514804
$57$	−183.984	−0.427532
$58$	−2.35315	−0.00532732
$59$	48.2675	0.106507	0.0532533	−	0.998581i	$-0.483041\pi$
$59$	48.2675	0.106507	0.0532533	+	0.998581i	$0.483041\pi$
$60$	−492.989	−1.06074
$61$	421.765	0.885271	0.442636	−	0.896702i	$-0.354044\pi$
$61$	421.765	0.885271	0.442636	+	0.896702i	$0.354044\pi$
$62$	−4.60415	−0.00943110
$63$	58.0344	0.116058
$64$	−511.832	−0.999672
$65$	1311.46	2.50255
$66$	1.14495	0.00213536
$67$	−269.737	−0.491846	−0.245923	−	0.969289i	$-0.579091\pi$
$67$	−269.737	−0.491846	−0.245923	+	0.969289i	$0.579091\pi$
$68$	0	0
$69$	318.702	0.556047
$70$	2.76991	0.00472953
$71$	699.900	1.16990	0.584949	−	0.811070i	$-0.301114\pi$
$71$	699.900	1.16990	0.584949	+	0.811070i	$0.301114\pi$
$72$	−3.01109	−0.00492862
$73$	−816.421	−1.30897	−0.654485	−	0.756075i	$-0.727115\pi$
$73$	−816.421	−1.30897	−0.654485	+	0.756075i	$0.727115\pi$
$74$	−3.92594	−0.00616731
$75$	890.961	1.37172
$76$	490.598	0.740467
$77$	117.689	0.174180
$78$	4.00496	0.00581375
$79$	−1116.41	−1.58994	−0.794971	−	0.606648i	$-0.792514\pi$
$79$	−1116.41	−1.58994	−0.794971	+	0.606648i	$0.792514\pi$
$80$	1314.49	1.83706
$81$	81.0000	0.111111
$82$	4.14597	0.00558348
$83$	−465.803	−0.616007	−0.308003	−	0.951385i	$-0.599661\pi$
$83$	−465.803	−0.616007	−0.308003	+	0.951385i	$0.599661\pi$
$84$	−154.750	−0.201007
$85$	0	0
$86$	2.91808	0.00365889
$87$	−337.597	−0.416025
$88$	−6.10624	−0.00739691
$89$	−92.3664	−0.110009	−0.0550046	−	0.998486i	$-0.517517\pi$
$89$	−92.3664	−0.110009	−0.0550046	+	0.998486i	$0.517517\pi$
$90$	3.86603	0.00452795
$91$	411.667	0.474225
$92$	−849.827	−0.963050
$93$	−660.538	−0.736501
$94$	12.0374	0.0132081
$95$	−1259.82	−1.36058
$96$	12.0438	0.0128043
$97$	1668.15	1.74613	0.873066	−	0.487601i	$-0.162128\pi$
$97$	1668.15	1.74613	0.873066	+	0.487601i	$0.162128\pi$
$98$	−6.30297	−0.00649690
$99$	164.261	0.166756
$100$	−2375.77	−2.37577
$101$	669.102	0.659190	0.329595	−	0.944122i	$-0.393088\pi$
$101$	669.102	0.659190	0.329595	+	0.944122i	$0.393088\pi$
$102$	0	0
$103$	−692.734	−0.662690	−0.331345	−	0.943510i	$-0.607502\pi$
$103$	−692.734	−0.662690	−0.331345	+	0.943510i	$0.607502\pi$
$104$	−21.3592	−0.0201389
$105$	397.387	0.369343
$106$	−5.78446	−0.00530034
$107$	156.994	0.141843	0.0709215	−	0.997482i	$-0.477406\pi$
$107$	156.994	0.141843	0.0709215	+	0.997482i	$0.477406\pi$
$108$	−215.988	−0.192440
$109$	1166.37	1.02493	0.512466	−	0.858708i	$-0.328732\pi$
$109$	1166.37	1.02493	0.512466	+	0.858708i	$0.328732\pi$
$110$	7.83999	0.00679558
$111$	−563.238	−0.481623
$112$	412.621	0.348116
$113$	512.772	0.426881	0.213441	−	0.976956i	$-0.431533\pi$
$113$	512.772	0.426881	0.213441	+	0.976956i	$0.431533\pi$
$114$	−3.84728	−0.00316080
$115$	2182.30	1.76957
$116$	900.209	0.720537
$117$	574.575	0.454012
$118$	1.00932	0.000787417 0
$119$	0	0
$120$	−20.6183	−0.0156848
$121$	−997.892	−0.749731
$122$	8.81950	0.00654492
$123$	594.804	0.436030
$124$	1761.34	1.27559
$125$	3533.02	2.52802
$126$	1.21355	0.000858030 0
$127$	2060.12	1.43942	0.719708	−	0.694277i	$-0.244276\pi$
$127$	2060.12	1.43942	0.719708	+	0.694277i	$0.244276\pi$
$128$	−42.8197	−0.0295685
$129$	418.645	0.285733
$130$	27.4237	0.0185017
$131$	273.048	0.182110	0.0910548	−	0.995846i	$-0.470976\pi$
$131$	273.048	0.182110	0.0910548	+	0.995846i	$0.470976\pi$
$132$	−438.006	−0.288815
$133$	−395.460	−0.257825
$134$	−5.64046	−0.00363628
$135$	554.643	0.353600
$136$	0	0
$137$	2175.28	1.35654	0.678272	−	0.734811i	$-0.262729\pi$
$137$	2175.28	1.35654	0.678272	+	0.734811i	$0.262729\pi$
$138$	6.66436	0.00411093
$139$	−732.040	−0.446696	−0.223348	−	0.974739i	$-0.571699\pi$
$139$	−732.040	−0.446696	−0.223348	+	0.974739i	$0.571699\pi$
$140$	−1059.64	−0.639685
$141$	1726.96	1.03146
$142$	14.6355	0.00864921
$143$	1165.19	0.681385
$144$	575.906	0.333279
$145$	−2311.68	−1.32396
$146$	−17.0721	−0.00967739
$147$	−904.260	−0.507361
$148$	1501.88	0.834150
$149$	3003.88	1.65159	0.825796	−	0.563969i	$-0.190726\pi$
$149$	3003.88	1.65159	0.825796	+	0.563969i	$0.190726\pi$
$150$	18.6308	0.0101413
$151$	3176.88	1.71212	0.856061	−	0.516874i	$-0.172905\pi$
$151$	3176.88	1.71212	0.856061	+	0.516874i	$0.172905\pi$
$152$	20.5183	0.0109490
$153$	0	0
$154$	2.46098	0.00128774
$155$	−4523.00	−2.34384
$156$	−1532.11	−0.786329
$157$	−623.642	−0.317019	−0.158510	−	0.987357i	$-0.550669\pi$
$157$	−623.642	−0.317019	−0.158510	+	0.987357i	$0.550669\pi$
$158$	−23.3451	−0.0117546
$159$	−829.871	−0.413919
$160$	82.4693	0.0407486
$161$	685.026	0.335327
$162$	1.69378	0.000821459 0
$163$	−2247.34	−1.07991	−0.539954	−	0.841694i	$-0.681559\pi$
$163$	−2247.34	−1.07991	−0.539954	+	0.841694i	$0.681559\pi$
$164$	−1586.06	−0.755185
$165$	1124.77	0.530686
$166$	−9.74037	−0.00455422
$167$	−1887.30	−0.874511	−0.437256	−	0.899337i	$-0.644050\pi$
$167$	−1887.30	−0.874511	−0.437256	+	0.899337i	$0.644050\pi$
$168$	−6.47210	−0.00297222
$169$	1878.75	0.855144
$170$	0	0
$171$	−551.953	−0.246836
$172$	−1116.32	−0.494878
$173$	−2484.88	−1.09203	−0.546017	−	0.837774i	$-0.683856\pi$
$173$	−2484.88	−1.09203	−0.546017	+	0.837774i	$0.683856\pi$
$174$	−7.05946	−0.00307573
$175$	1915.05	0.827224
$176$	1167.89	0.500187
$177$	144.802	0.0614916
$178$	−1.93147	−0.000813312 0
$179$	1110.51	0.463708	0.231854	−	0.972751i	$-0.425521\pi$
$179$	1110.51	0.463708	0.231854	+	0.972751i	$0.425521\pi$
$180$	−1478.97	−0.612420
$181$	596.594	0.244997	0.122499	−	0.992469i	$-0.460909\pi$
$181$	596.594	0.244997	0.122499	+	0.992469i	$0.460909\pi$
$182$	8.60835	0.00350601
$183$	1265.30	0.511111
$184$	−35.5423	−0.0142403
$185$	−3856.74	−1.53272
$186$	−13.8125	−0.00544505
$187$	0	0
$188$	−4604.96	−1.78644
$189$	174.103	0.0670060
$190$	−26.3441	−0.0100589
$191$	−2220.92	−0.841363	−0.420681	−	0.907209i	$-0.638209\pi$
$191$	−2220.92	−0.841363	−0.420681	+	0.907209i	$0.638209\pi$
$192$	−1535.50	−0.577161
$193$	−1156.23	−0.431229	−0.215615	−	0.976479i	$-0.569175\pi$
$193$	−1156.23	−0.431229	−0.215615	+	0.976479i	$0.569175\pi$
$194$	34.8825	0.0129094
$195$	3934.37	1.44485
$196$	2411.23	0.878727
$197$	3490.60	1.26241	0.631205	−	0.775616i	$-0.282561\pi$
$197$	3490.60	1.26241	0.631205	+	0.775616i	$0.282561\pi$
$198$	3.43486	0.00123285
$199$	−2736.58	−0.974831	−0.487415	−	0.873170i	$-0.662060\pi$
$199$	−2736.58	−0.974831	−0.487415	+	0.873170i	$0.662060\pi$
$200$	−99.3617	−0.0351297
$201$	−809.212	−0.283967
$202$	13.9915	0.00487347
$203$	−725.638	−0.250886
$204$	0	0
$205$	4072.89	1.38762
$206$	−14.4857	−0.00489935
$207$	956.107	0.321034
$208$	4085.19	1.36181
$209$	−1119.32	−0.370453
$210$	8.30973	0.00273060
$211$	4456.34	1.45397	0.726984	−	0.686654i	$-0.240921\pi$
$211$	4456.34	1.45397	0.726984	+	0.686654i	$0.240921\pi$
$212$	2212.87	0.716889
$213$	2099.70	0.675441
$214$	3.28289	0.00104866
$215$	2866.64	0.909319
$216$	−9.03327	−0.00284554
$217$	−1419.77	−0.444150
$218$	24.3898	0.00757745
$219$	−2449.26	−0.755735
$220$	−2999.22	−0.919125
$221$	0	0
$222$	−11.7778	−0.00356070
$223$	638.518	0.191741	0.0958707	−	0.995394i	$-0.469436\pi$
$223$	638.518	0.191741	0.0958707	+	0.995394i	$0.469436\pi$
$224$	25.8872	0.00772171
$225$	2672.88	0.791966
$226$	10.7225	0.00315599
$227$	−1101.58	−0.322090	−0.161045	−	0.986947i	$-0.551487\pi$
$227$	−1101.58	−0.322090	−0.161045	+	0.986947i	$0.551487\pi$
$228$	1471.80	0.427509
$229$	−3603.12	−1.03974	−0.519871	−	0.854244i	$-0.674020\pi$
$229$	−3603.12	−1.03974	−0.519871	+	0.854244i	$0.674020\pi$
$230$	45.6338	0.0130826
$231$	353.067	0.100563
$232$	37.6494	0.0106543
$233$	1977.85	0.556110	0.278055	−	0.960565i	$-0.410310\pi$
$233$	1977.85	0.556110	0.278055	+	0.960565i	$0.410310\pi$
$234$	12.0149	0.00335657
$235$	11825.2	3.28252
$236$	−386.119	−0.106501
$237$	−3349.22	−0.917953
$238$	0	0
$239$	−5104.03	−1.38139	−0.690694	−	0.723147i	$-0.742695\pi$
$239$	−5104.03	−1.38139	−0.690694	+	0.723147i	$0.742695\pi$
$240$	3943.48	1.06063
$241$	−163.071	−0.0435864	−0.0217932	−	0.999762i	$-0.506938\pi$
$241$	−163.071	−0.0435864	−0.0217932	+	0.999762i	$0.506938\pi$
$242$	−20.8668	−0.00554285
$243$	243.000	0.0641500
$244$	−3373.94	−0.885223
$245$	−6191.87	−1.61463
$246$	12.4379	0.00322362
$247$	−3915.29	−1.00860
$248$	73.6644	0.0188617
$249$	−1397.41	−0.355652
$250$	73.8786	0.0186900
$251$	−4032.94	−1.01417	−0.507085	−	0.861896i	$-0.669277\pi$
$251$	−4032.94	−1.01417	−0.507085	+	0.861896i	$0.669277\pi$
$252$	−464.250	−0.116051
$253$	1938.91	0.481810
$254$	43.0790	0.0106418
$255$	0	0
$256$	4093.76	0.999453
$257$	−2385.61	−0.579029	−0.289515	−	0.957174i	$-0.593494\pi$
$257$	−2385.61	−0.579029	−0.289515	+	0.957174i	$0.593494\pi$
$258$	8.75425	0.00211246
$259$	−1210.63	−0.290445
$260$	−10491.1	−2.50242
$261$	−1012.79	−0.240192
$262$	5.70969	0.00134636
$263$	−7312.21	−1.71441	−0.857206	−	0.514974i	$-0.827802\pi$
$263$	−7312.21	−1.71441	−0.857206	+	0.514974i	$0.827802\pi$
$264$	−18.3187	−0.00427061
$265$	−5682.49	−1.31726
$266$	−8.26943	−0.00190613
$267$	−277.099	−0.0635138
$268$	2157.78	0.491819
$269$	−1272.89	−0.288511	−0.144255	−	0.989540i	$-0.546079\pi$
$269$	−1272.89	−0.288511	−0.144255	+	0.989540i	$0.546079\pi$
$270$	11.5981	0.00261421
$271$	269.767	0.0604693	0.0302346	−	0.999543i	$-0.490375\pi$
$271$	269.767	0.0604693	0.0302346	+	0.999543i	$0.490375\pi$
$272$	0	0
$273$	1235.00	0.273794
$274$	45.4871	0.0100291
$275$	5420.39	1.18859
$276$	−2549.48	−0.556017
$277$	3470.76	0.752843	0.376422	−	0.926448i	$-0.377154\pi$
$277$	3470.76	0.752843	0.376422	+	0.926448i	$0.377154\pi$
$278$	−15.3076	−0.00330248
$279$	−1981.61	−0.425219
$280$	−44.3173	−0.00945881
$281$	−721.579	−0.153188	−0.0765940	−	0.997062i	$-0.524405\pi$
$281$	−721.579	−0.153188	−0.0765940	+	0.997062i	$0.524405\pi$
$282$	36.1122	0.00762572
$283$	−1017.08	−0.213636	−0.106818	−	0.994279i	$-0.534066\pi$
$283$	−1017.08	−0.213636	−0.106818	+	0.994279i	$0.534066\pi$
$284$	−5598.89	−1.16983
$285$	−3779.47	−0.785531
$286$	24.3652	0.00503757
$287$	1278.48	0.262950
$288$	36.1314	0.00739259
$289$	0	0
$290$	−48.3393	−0.00978820
$291$	5004.45	1.00813
$292$	6531.01	1.30890
$293$	2776.30	0.553560	0.276780	−	0.960933i	$-0.410733\pi$
$293$	2776.30	0.553560	0.276780	+	0.960933i	$0.410733\pi$
$294$	−18.9089	−0.00375099
$295$	991.527	0.195691
$296$	62.8133	0.0123343
$297$	492.784	0.0962769
$298$	62.8138	0.0122104
$299$	6782.16	1.31178
$300$	−7127.30	−1.37165
$301$	899.844	0.172313
$302$	66.4314	0.0126579
$303$	2007.31	0.380583
$304$	−3924.36	−0.740386
$305$	8664.04	1.62656
$306$	0	0
$307$	−727.432	−0.135234	−0.0676168	−	0.997711i	$-0.521540\pi$
$307$	−727.432	−0.135234	−0.0676168	+	0.997711i	$0.521540\pi$
$308$	−941.460	−0.174171
$309$	−2078.20	−0.382604
$310$	−94.5800	−0.0173283
$311$	−1184.60	−0.215989	−0.107994	−	0.994152i	$-0.534443\pi$
$311$	−1184.60	−0.215989	−0.107994	+	0.994152i	$0.534443\pi$
$312$	−64.0776	−0.0116272
$313$	254.466	0.0459529	0.0229765	−	0.999736i	$-0.492686\pi$
$313$	254.466	0.0459529	0.0229765	+	0.999736i	$0.492686\pi$
$314$	−13.0409	−0.00234376
$315$	1192.16	0.213240
$316$	8930.75	1.58985
$317$	8638.25	1.53051	0.765256	−	0.643726i	$-0.222612\pi$
$317$	8638.25	1.53051	0.765256	+	0.643726i	$0.222612\pi$
$318$	−17.3534	−0.00306015
$319$	−2053.86	−0.360482
$320$	−10514.2	−1.83676
$321$	470.983	0.0818931
$322$	14.3245	0.00247911
$323$	0	0
$324$	−647.965	−0.111105
$325$	18960.1	3.23606
$326$	−46.9939	−0.00798390
$327$	3499.10	0.591744
$328$	−66.3337	−0.0111667
$329$	3711.95	0.622026
$330$	23.5200	0.00392343
$331$	931.174	0.154628	0.0773141	−	0.997007i	$-0.475366\pi$
$331$	931.174	0.154628	0.0773141	+	0.997007i	$0.475366\pi$
$332$	3726.22	0.615973
$333$	−1689.71	−0.278065
$334$	−39.4651	−0.00646537
$335$	−5541.03	−0.903699
$336$	1237.86	0.200985
$337$	−8125.43	−1.31341	−0.656707	−	0.754146i	$-0.728051\pi$
$337$	−8125.43	−1.31341	−0.656707	+	0.754146i	$0.728051\pi$
$338$	39.2864	0.00632219
$339$	1538.32	0.246460
$340$	0	0
$341$	−4018.55	−0.638172
$342$	−11.5419	−0.00182489
$343$	−4155.39	−0.654140
$344$	−46.6880	−0.00731759
$345$	6546.89	1.02166
$346$	−51.9611	−0.00807354
$347$	−10952.1	−1.69435	−0.847177	−	0.531310i	$-0.821700\pi$
$347$	−10952.1	−1.69435	−0.847177	+	0.531310i	$0.821700\pi$
$348$	2700.63	0.416002
$349$	−4845.63	−0.743212	−0.371606	−	0.928391i	$-0.621193\pi$
$349$	−4845.63	−0.743212	−0.371606	+	0.928391i	$0.621193\pi$
$350$	40.0455	0.00611577
$351$	1723.72	0.262124
$352$	73.2716	0.0110949
$353$	−1814.62	−0.273605	−0.136802	−	0.990598i	$-0.543683\pi$
$353$	−1814.62	−0.273605	−0.136802	+	0.990598i	$0.543683\pi$
$354$	3.02795	0.000454616 0
$355$	14377.6	2.14953
$356$	738.891	0.110003
$357$	0	0
$358$	23.2219	0.00342825
$359$	−10174.2	−1.49575	−0.747874	−	0.663840i	$-0.768925\pi$
$359$	−10174.2	−1.49575	−0.747874	+	0.663840i	$0.768925\pi$
$360$	−61.8548	−0.00905565
$361$	−3097.86	−0.451649
$362$	12.4753	0.00181130
$363$	−2993.67	−0.432857
$364$	−3293.16	−0.474199
$365$	−16771.2	−2.40505
$366$	26.4585	0.00377871
$367$	−4544.86	−0.646430	−0.323215	−	0.946326i	$-0.604764\pi$
$367$	−4544.86	−0.646430	−0.323215	+	0.946326i	$0.604764\pi$
$368$	6797.87	0.962944
$369$	1784.41	0.251742
$370$	−80.6479	−0.0113316
$371$	−1783.74	−0.249615
$372$	5284.02	0.736461
$373$	−549.941	−0.0763402	−0.0381701	−	0.999271i	$-0.512153\pi$
$373$	−549.941	−0.0763402	−0.0381701	+	0.999271i	$0.512153\pi$
$374$	0	0
$375$	10599.0	1.45955
$376$	−192.593	−0.0264155
$377$	−7184.24	−0.981452
$378$	3.64066	0.000495384 0
$379$	2072.61	0.280905	0.140452	−	0.990087i	$-0.455144\pi$
$379$	2072.61	0.280905	0.140452	+	0.990087i	$0.455144\pi$
$380$	10078.0	1.36051
$381$	6180.35	0.831047
$382$	−46.4415	−0.00622030
$383$	−12705.2	−1.69506	−0.847530	−	0.530748i	$-0.821911\pi$
$383$	−12705.2	−1.69506	−0.847530	+	0.530748i	$0.821911\pi$
$384$	−128.459	−0.0170714
$385$	2417.60	0.320032
$386$	−24.1778	−0.00318813
$387$	1255.93	0.164968
$388$	−13344.5	−1.74604
$389$	6157.69	0.802589	0.401295	−	0.915949i	$-0.368560\pi$
$389$	6157.69	0.802589	0.401295	+	0.915949i	$0.368560\pi$
$390$	82.2712	0.0106820
$391$	0	0
$392$	100.845	0.0129934
$393$	819.145	0.105141
$394$	72.9916	0.00933316
$395$	−22933.6	−2.92130
$396$	−1314.02	−0.166747
$397$	−7088.92	−0.896178	−0.448089	−	0.893989i	$-0.647895\pi$
$397$	−7088.92	−0.896178	−0.448089	+	0.893989i	$0.647895\pi$
$398$	−57.2245	−0.00720705
$399$	−1186.38	−0.148855
$400$	19004.1	2.37551
$401$	877.750	0.109309	0.0546543	−	0.998505i	$-0.482594\pi$
$401$	877.750	0.109309	0.0546543	+	0.998505i	$0.482594\pi$
$402$	−16.9214	−0.00209941
$403$	−14056.6	−1.73749
$404$	−5352.52	−0.659154
$405$	1663.93	0.204151
$406$	−15.1738	−0.00185483
$407$	−3426.60	−0.417322
$408$	0	0
$409$	7333.73	0.886625	0.443313	−	0.896367i	$-0.353803\pi$
$409$	7333.73	0.886625	0.443313	+	0.896367i	$0.353803\pi$
$410$	85.1678	0.0102589
$411$	6525.84	0.783201
$412$	5541.57	0.662654
$413$	311.241	0.0370828
$414$	19.9931	0.00237345
$415$	−9568.68	−1.13183
$416$	256.299	0.0302069
$417$	−2196.12	−0.257900
$418$	−23.4059	−0.00273881
$419$	−1047.46	−0.122129	−0.0610643	−	0.998134i	$-0.519449\pi$
$419$	−1047.46	−0.122129	−0.0610643	+	0.998134i	$0.519449\pi$
$420$	−3178.92	−0.369323
$421$	−15517.0	−1.79632	−0.898162	−	0.439665i	$-0.855097\pi$
$421$	−15517.0	−1.79632	−0.898162	+	0.439665i	$0.855097\pi$
$422$	93.1863	0.0107494
$423$	5180.87	0.595514
$424$	92.5488	0.0106004
$425$	0	0
$426$	43.9066	0.00499362
$427$	2719.65	0.308228
$428$	−1255.89	−0.141835
$429$	3495.57	0.393398
$430$	59.9442	0.00672271
$431$	−7274.46	−0.812989	−0.406495	−	0.913653i	$-0.633249\pi$
$431$	−7274.46	−0.812989	−0.406495	+	0.913653i	$0.633249\pi$
$432$	1727.72	0.192419
$433$	5853.31	0.649635	0.324818	−	0.945777i	$-0.394697\pi$
$433$	5853.31	0.649635	0.324818	+	0.945777i	$0.394697\pi$
$434$	−29.6888	−0.00328366
$435$	−6935.03	−0.764389
$436$	−9330.41	−1.02488
$437$	−6515.14	−0.713184
$438$	−51.2164	−0.00558724
$439$	−4390.59	−0.477338	−0.238669	−	0.971101i	$-0.576711\pi$
$439$	−4390.59	−0.477338	−0.238669	+	0.971101i	$0.576711\pi$
$440$	−125.436	−0.0135908
$441$	−2712.78	−0.292925
$442$	0	0
$443$	−698.038	−0.0748641	−0.0374320	−	0.999299i	$-0.511918\pi$
$443$	−698.038	−0.0748641	−0.0374320	+	0.999299i	$0.511918\pi$
$444$	4505.65	0.481597
$445$	−1897.42	−0.202127
$446$	13.3520	0.00141757
$447$	9011.63	0.953547
$448$	−3300.43	−0.348059
$449$	5550.98	0.583445	0.291723	−	0.956503i	$-0.405772\pi$
$449$	5550.98	0.583445	0.291723	+	0.956503i	$0.405772\pi$
$450$	55.8925	0.00585510
$451$	3618.64	0.377816
$452$	−4101.95	−0.426858
$453$	9530.63	0.988495
$454$	−23.0351	−0.00238126
$455$	8456.61	0.871323
$456$	61.5549	0.00632143
$457$	−6755.97	−0.691534	−0.345767	−	0.938320i	$-0.612381\pi$
$457$	−6755.97	−0.691534	−0.345767	+	0.938320i	$0.612381\pi$
$458$	−75.3446	−0.00768695
$459$	0	0
$460$	−17457.4	−1.76947
$461$	1187.20	0.119942	0.0599710	−	0.998200i	$-0.480899\pi$
$461$	1187.20	0.119942	0.0599710	+	0.998200i	$0.480899\pi$
$462$	7.38295	0.000743476 0
$463$	3496.16	0.350930	0.175465	−	0.984486i	$-0.443857\pi$
$463$	3496.16	0.350930	0.175465	+	0.984486i	$0.443857\pi$
$464$	−7200.89	−0.720459
$465$	−13569.0	−1.35322
$466$	41.3588	0.00411139
$467$	−18552.6	−1.83835	−0.919175	−	0.393848i	$-0.871144\pi$
$467$	−18552.6	−1.83835	−0.919175	+	0.393848i	$0.871144\pi$
$468$	−4596.34	−0.453987
$469$	−1739.34	−0.171248
$470$	247.276	0.0242681
$471$	−1870.93	−0.183031
$472$	−16.1486	−0.00157479
$473$	2546.93	0.247586
$474$	−70.0352	−0.00678654
$475$	−18213.7	−1.75937
$476$	0	0
$477$	−2489.61	−0.238976
$478$	−106.730	−0.0102128
$479$	18512.5	1.76588	0.882941	−	0.469483i	$-0.155560\pi$
$479$	18512.5	1.76588	0.882941	+	0.469483i	$0.155560\pi$
$480$	247.408	0.0235262
$481$	−11986.0	−1.13620
$482$	−3.40997	−0.000322240 0
$483$	2055.08	0.193601
$484$	7982.70	0.749690
$485$	34267.7	3.20828
$486$	5.08135	0.000474269 0
$487$	−13830.9	−1.28693	−0.643466	−	0.765475i	$-0.722504\pi$
$487$	−13830.9	−1.28693	−0.643466	+	0.765475i	$0.722504\pi$
$488$	−141.108	−0.0130895
$489$	−6742.01	−0.623486
$490$	−129.478	−0.0119371
$491$	2710.45	0.249126	0.124563	−	0.992212i	$-0.460247\pi$
$491$	2710.45	0.249126	0.124563	+	0.992212i	$0.460247\pi$
$492$	−4758.17	−0.436006
$493$	0	0
$494$	−81.8723	−0.00745670
$495$	3374.31	0.306392
$496$	−14089.2	−1.27545
$497$	4513.14	0.407328
$498$	−29.2211	−0.00262938
$499$	−8787.23	−0.788317	−0.394159	−	0.919042i	$-0.628964\pi$
$499$	−8787.23	−0.788317	−0.394159	+	0.919042i	$0.628964\pi$
$500$	−28262.6	−2.52788
$501$	−5661.89	−0.504899
$502$	−84.3325	−0.00749789
$503$	4482.62	0.397356	0.198678	−	0.980065i	$-0.436335\pi$
$503$	4482.62	0.397356	0.198678	+	0.980065i	$0.436335\pi$
$504$	−19.4163	−0.00171601
$505$	13744.9	1.21117
$506$	40.5443	0.00356209
$507$	5636.25	0.493718
$508$	−16480.0	−1.43934
$509$	−17537.7	−1.52720	−0.763599	−	0.645691i	$-0.776569\pi$
$509$	−17537.7	−1.52720	−0.763599	+	0.645691i	$0.776569\pi$
$510$	0	0
$511$	−5264.50	−0.455749
$512$	428.162	0.0369576
$513$	−1655.86	−0.142511
$514$	−49.8854	−0.00428084
$515$	−14230.4	−1.21760
$516$	−3348.97	−0.285718
$517$	10506.4	0.893752
$518$	−25.3155	−0.00214729
$519$	−7454.63	−0.630486
$520$	−438.768	−0.0370024
$521$	21557.7	1.81278	0.906390	−	0.422441i	$-0.138827\pi$
$521$	21557.7	1.81278	0.906390	+	0.422441i	$0.138827\pi$
$522$	−21.1784	−0.00177577
$523$	−8765.00	−0.732823	−0.366412	−	0.930453i	$-0.619414\pi$
$523$	−8765.00	−0.732823	−0.366412	+	0.930453i	$0.619414\pi$
$524$	−2184.27	−0.182100
$525$	5745.15	0.477598
$526$	−152.905	−0.0126749
$527$	0	0
$528$	3503.67	0.288783
$529$	−881.307	−0.0724342
$530$	−118.826	−0.00973864
$531$	434.407	0.0355022
$532$	3163.51	0.257811
$533$	12657.7	1.02865
$534$	−5.79440	−0.000469566 0
$535$	3225.03	0.260617
$536$	90.2449	0.00727236
$537$	3331.54	0.267722
$538$	−26.6173	−0.00213300
$539$	−5501.29	−0.439624
$540$	−4436.90	−0.353581
$541$	5971.04	0.474519	0.237260	−	0.971446i	$-0.423751\pi$
$541$	5971.04	0.474519	0.237260	+	0.971446i	$0.423751\pi$
$542$	5.64107	0.000447057 0
$543$	1789.78	0.141449
$544$	0	0
$545$	23959.9	1.88317
$546$	25.8250	0.00202419
$547$	17281.6	1.35084	0.675419	−	0.737434i	$-0.263963\pi$
$547$	17281.6	1.35084	0.675419	+	0.737434i	$0.263963\pi$
$548$	−17401.3	−1.35647
$549$	3795.89	0.295090
$550$	113.345	0.00878738
$551$	6901.40	0.533592
$552$	−106.627	−0.00822163
$553$	−7198.87	−0.553575
$554$	72.5767	0.00556587
$555$	−11570.2	−0.884915
$556$	5856.00	0.446672
$557$	−6265.83	−0.476646	−0.238323	−	0.971186i	$-0.576598\pi$
$557$	−6265.83	−0.476646	−0.238323	+	0.971186i	$0.576598\pi$
$558$	−41.4374	−0.00314370
$559$	8908.98	0.674078
$560$	8476.20	0.639616
$561$	0	0
$562$	−15.0889	−0.00113254
$563$	−3685.25	−0.275870	−0.137935	−	0.990441i	$-0.544046\pi$
$563$	−3685.25	−0.275870	−0.137935	+	0.990441i	$0.544046\pi$
$564$	−13814.9	−1.03140
$565$	10533.5	0.784335
$566$	−21.2680	−0.00157944
$567$	522.309	0.0386859
$568$	−234.162	−0.0172979
$569$	−3570.81	−0.263086	−0.131543	−	0.991310i	$-0.541993\pi$
$569$	−3570.81	−0.263086	−0.131543	+	0.991310i	$0.541993\pi$
$570$	−79.0322	−0.00580753
$571$	8578.53	0.628722	0.314361	−	0.949304i	$-0.398210\pi$
$571$	8578.53	0.628722	0.314361	+	0.949304i	$0.398210\pi$
$572$	−9321.01	−0.681348
$573$	−6662.76	−0.485761
$574$	26.7343	0.00194402
$575$	31550.2	2.28823
$576$	−4606.49	−0.333224
$577$	15119.3	1.09086	0.545429	−	0.838157i	$-0.316367\pi$
$577$	15119.3	1.09086	0.545429	+	0.838157i	$0.316367\pi$
$578$	0	0
$579$	−3468.69	−0.248970
$580$	18492.4	1.32389
$581$	−3003.62	−0.214477
$582$	104.648	0.00745323
$583$	−5048.73	−0.358657
$584$	273.146	0.0193542
$585$	11803.1	0.834185
$586$	58.0550	0.00409254
$587$	−15700.9	−1.10399	−0.551997	−	0.833846i	$-0.686134\pi$
$587$	−15700.9	−1.10399	−0.551997	+	0.833846i	$0.686134\pi$
$588$	7233.68	0.507333
$589$	13503.2	0.944634
$590$	20.7337	0.00144677
$591$	10471.8	0.728853
$592$	−12013.8	−0.834059
$593$	−12196.6	−0.844614	−0.422307	−	0.906453i	$-0.638780\pi$
$593$	−12196.6	−0.844614	−0.422307	+	0.906453i	$0.638780\pi$
$594$	10.3046	0.000711787 0
$595$	0	0
$596$	−24029.7	−1.65150
$597$	−8209.75	−0.562819
$598$	141.821	0.00969816
$599$	19363.2	1.32080	0.660400	−	0.750914i	$-0.270387\pi$
$599$	19363.2	1.32080	0.660400	+	0.750914i	$0.270387\pi$
$600$	−298.085	−0.0202821
$601$	−12765.4	−0.866406	−0.433203	−	0.901296i	$-0.642617\pi$
$601$	−12765.4	−0.866406	−0.433203	+	0.901296i	$0.642617\pi$
$602$	18.8166	0.00127393
$603$	−2427.64	−0.163949
$604$	−25413.6	−1.71203
$605$	−20499.0	−1.37753
$606$	41.9746	0.00281370
$607$	−15295.8	−1.02279	−0.511397	−	0.859344i	$-0.670872\pi$
$607$	−15295.8	−1.02279	−0.511397	+	0.859344i	$0.670872\pi$
$608$	−246.208	−0.0164228
$609$	−2176.91	−0.144849
$610$	181.173	0.0120254
$611$	36750.5	2.43333
$612$	0	0
$613$	11554.2	0.761291	0.380646	−	0.924721i	$-0.375702\pi$
$613$	11554.2	0.761291	0.380646	+	0.924721i	$0.375702\pi$
$614$	−15.2113	−0.000999800 0
$615$	12218.7	0.801144
$616$	−39.3747	−0.00257541
$617$	7681.67	0.501220	0.250610	−	0.968088i	$-0.419369\pi$
$617$	7681.67	0.501220	0.250610	+	0.968088i	$0.419369\pi$
$618$	−43.4571	−0.00282864
$619$	18736.0	1.21658	0.608292	−	0.793713i	$-0.291855\pi$
$619$	18736.0	1.21658	0.608292	+	0.793713i	$0.291855\pi$
$620$	36182.0	2.34372
$621$	2868.32	0.185349
$622$	−24.7711	−0.00159683
$623$	−595.603	−0.0383023
$624$	12255.6	0.786243
$625$	35453.0	2.26899
$626$	5.32112	0.000339736 0
$627$	−3357.95	−0.213881
$628$	4988.86	0.317002
$629$	0	0
$630$	24.9292	0.00157651
$631$	−15516.0	−0.978892	−0.489446	−	0.872034i	$-0.662801\pi$
$631$	−15516.0	−0.978892	−0.489446	+	0.872034i	$0.662801\pi$
$632$	373.511	0.0235086
$633$	13369.0	0.839449
$634$	180.634	0.0113153
$635$	42319.6	2.64473
$636$	6638.61	0.413896
$637$	−19243.1	−1.19692
$638$	−42.9480	−0.00266509
$639$	6299.10	0.389966
$640$	−879.617	−0.0543280
$641$	12592.6	0.775940	0.387970	−	0.921672i	$-0.373176\pi$
$641$	12592.6	0.775940	0.387970	+	0.921672i	$0.373176\pi$
$642$	9.84868	0.000605446 0
$643$	8183.85	0.501928	0.250964	−	0.967996i	$-0.419252\pi$
$643$	8183.85	0.501928	0.250964	+	0.967996i	$0.419252\pi$
$644$	−5479.91	−0.335308
$645$	8599.93	0.524996
$646$	0	0
$647$	−2042.87	−0.124132	−0.0620661	−	0.998072i	$-0.519769\pi$
$647$	−2042.87	−0.124132	−0.0620661	+	0.998072i	$0.519769\pi$
$648$	−27.0998	−0.00164287
$649$	880.943	0.0532820
$650$	396.474	0.0239246
$651$	−4259.32	−0.256430
$652$	17977.7	1.07985
$653$	−17805.3	−1.06704	−0.533518	−	0.845789i	$-0.679130\pi$
$653$	−17805.3	−1.06704	−0.533518	+	0.845789i	$0.679130\pi$
$654$	73.1693	0.00437484
$655$	5609.05	0.334601
$656$	12687.1	0.755102
$657$	−7347.79	−0.436324
$658$	77.6204	0.00459872
$659$	24705.9	1.46040	0.730202	−	0.683231i	$-0.239426\pi$
$659$	24705.9	1.46040	0.730202	+	0.683231i	$0.239426\pi$
$660$	−8997.67	−0.530657
$661$	14655.1	0.862354	0.431177	−	0.902267i	$-0.358098\pi$
$661$	14655.1	0.862354	0.431177	+	0.902267i	$0.358098\pi$
$662$	19.4717	0.00114319
$663$	0	0
$664$	155.842	0.00910818
$665$	−8123.67	−0.473718
$666$	−35.3335	−0.00205577
$667$	−11954.8	−0.693989
$668$	15097.5	0.874464
$669$	1915.55	0.110702
$670$	−115.868	−0.00668116
$671$	7697.75	0.442874
$672$	77.6617	0.00445813
$673$	22375.5	1.28159	0.640797	−	0.767711i	$-0.278604\pi$
$673$	22375.5	1.28159	0.640797	+	0.767711i	$0.278604\pi$
$674$	−169.910	−0.00971023
$675$	8018.65	0.457242
$676$	−15029.2	−0.855097
$677$	−18940.5	−1.07525	−0.537623	−	0.843185i	$-0.680678\pi$
$677$	−18940.5	−1.07525	−0.537623	+	0.843185i	$0.680678\pi$
$678$	32.1676	0.00182211
$679$	10756.7	0.607957
$680$	0	0
$681$	−3304.74	−0.185959
$682$	−84.0316	−0.00471809
$683$	−9489.30	−0.531622	−0.265811	−	0.964025i	$-0.585640\pi$
$683$	−9489.30	−0.531622	−0.265811	+	0.964025i	$0.585640\pi$
$684$	4415.39	0.246822
$685$	44685.3	2.49246
$686$	−86.8930	−0.00483614
$687$	−10809.4	−0.600296
$688$	8929.62	0.494824
$689$	−17660.1	−0.976482
$690$	136.901	0.00755326
$691$	4564.16	0.251272	0.125636	−	0.992076i	$-0.459903\pi$
$691$	4564.16	0.251272	0.125636	+	0.992076i	$0.459903\pi$
$692$	19877.9	1.09197
$693$	1059.20	0.0580602
$694$	−229.019	−0.0125266
$695$	−15037.8	−0.820742
$696$	112.948	0.00615129
$697$	0	0
$698$	−101.327	−0.00549466
$699$	5933.56	0.321070
$700$	−15319.6	−0.827179
$701$	−25637.7	−1.38135	−0.690673	−	0.723167i	$-0.742686\pi$
$701$	−25637.7	−1.38135	−0.690673	+	0.723167i	$0.742686\pi$
$702$	36.0446	0.00193792
$703$	11514.1	0.617728
$704$	−9341.58	−0.500105
$705$	35475.7	1.89516
$706$	−37.9454	−0.00202279
$707$	4314.55	0.229512
$708$	−1158.36	−0.0614883
$709$	15590.0	0.825804	0.412902	−	0.910775i	$-0.364515\pi$
$709$	15590.0	0.825804	0.412902	+	0.910775i	$0.364515\pi$
$710$	300.648	0.0158917
$711$	−10047.6	−0.529980
$712$	30.9026	0.00162658
$713$	−23390.6	−1.22859
$714$	0	0
$715$	23935.7	1.25195
$716$	−8883.63	−0.463683
$717$	−15312.1	−0.797545
$718$	−212.752	−0.0110583
$719$	−27501.9	−1.42649	−0.713247	−	0.700913i	$-0.752776\pi$
$719$	−27501.9	−1.42649	−0.713247	+	0.700913i	$0.752776\pi$
$720$	11830.4	0.612353
$721$	−4466.93	−0.230731
$722$	−64.7791	−0.00333910
$723$	−489.213	−0.0251646
$724$	−4772.49	−0.244984
$725$	−33420.6	−1.71202
$726$	−62.6005	−0.00320017
$727$	27457.0	1.40072	0.700360	−	0.713790i	$-0.253023\pi$
$727$	27457.0	1.40072	0.700360	+	0.713790i	$0.253023\pi$
$728$	−137.730	−0.00701182
$729$	729.000	0.0370370
$730$	−350.701	−0.0177809
$731$	0	0
$732$	−10121.8	−0.511084
$733$	−22002.0	−1.10868	−0.554340	−	0.832290i	$-0.687029\pi$
$733$	−22002.0	−1.10868	−0.554340	+	0.832290i	$0.687029\pi$
$734$	−95.0373	−0.00477914
$735$	−18575.6	−0.932206
$736$	426.488	0.0213595
$737$	−4923.05	−0.246055
$738$	37.3137	0.00186116
$739$	7294.60	0.363107	0.181554	−	0.983381i	$-0.441887\pi$
$739$	7294.60	0.363107	0.181554	+	0.983381i	$0.441887\pi$
$740$	30852.2	1.53263
$741$	−11745.9	−0.582315
$742$	−37.2997	−0.00184544
$743$	−2257.31	−0.111457	−0.0557286	−	0.998446i	$-0.517748\pi$
$743$	−2257.31	−0.111457	−0.0557286	+	0.998446i	$0.517748\pi$
$744$	220.993	0.0108898
$745$	61706.6	3.03457
$746$	−11.4998	−0.000564393 0
$747$	−4192.23	−0.205336
$748$	0	0
$749$	1012.34	0.0493860
$750$	221.636	0.0107907
$751$	−3350.03	−0.162776	−0.0813878	−	0.996683i	$-0.525935\pi$
$751$	−3350.03	−0.162776	−0.0813878	+	0.996683i	$0.525935\pi$
$752$	36835.7	1.78625
$753$	−12098.8	−0.585532
$754$	−150.229	−0.00725600
$755$	65260.4	3.14579
$756$	−1392.75	−0.0670023
$757$	−27564.3	−1.32344	−0.661718	−	0.749753i	$-0.730172\pi$
$757$	−27564.3	−1.32344	−0.661718	+	0.749753i	$0.730172\pi$
$758$	43.3402	0.00207676
$759$	5816.72	0.278173
$760$	421.493	0.0201173
$761$	27697.8	1.31937	0.659687	−	0.751541i	$-0.270689\pi$
$761$	27697.8	1.31937	0.659687	+	0.751541i	$0.270689\pi$
$762$	129.237	0.00614404
$763$	7521.03	0.356854
$764$	17766.4	0.841317
$765$	0	0
$766$	−265.678	−0.0125318
$767$	3081.47	0.145066
$768$	12281.3	0.577035
$769$	34530.8	1.61926	0.809632	−	0.586938i	$-0.199667\pi$
$769$	34530.8	1.61926	0.809632	+	0.586938i	$0.199667\pi$
$770$	50.5543	0.00236604
$771$	−7156.84	−0.334303
$772$	9249.33	0.431206
$773$	−3723.24	−0.173241	−0.0866206	−	0.996241i	$-0.527607\pi$
$773$	−3723.24	−0.173241	−0.0866206	+	0.996241i	$0.527607\pi$
$774$	26.2627	0.00121963
$775$	−65390.4	−3.03083
$776$	−558.105	−0.0258181
$777$	−3631.90	−0.167688
$778$	128.763	0.00593365
$779$	−12159.4	−0.559250
$780$	−31473.2	−1.44477
$781$	12774.0	0.585264
$782$	0	0
$783$	−3038.37	−0.138675
$784$	−19287.7	−0.878631
$785$	−12811.1	−0.582479
$786$	17.1291	0.000777321 0
$787$	5397.77	0.244485	0.122243	−	0.992500i	$-0.460991\pi$
$787$	5397.77	0.244485	0.122243	+	0.992500i	$0.460991\pi$
$788$	−27923.3	−1.26234
$789$	−21936.6	−0.989816
$790$	−479.562	−0.0215975
$791$	3306.49	0.148629
$792$	−54.9562	−0.00246564
$793$	26926.2	1.20577
$794$	−148.236	−0.00662556
$795$	−17047.5	−0.760518
$796$	21891.5	0.974778
$797$	−6133.78	−0.272609	−0.136305	−	0.990667i	$-0.543523\pi$
$797$	−6133.78	−0.272609	−0.136305	+	0.990667i	$0.543523\pi$
$798$	−24.8083	−0.00110051
$799$	0	0
$800$	1192.29	0.0526921
$801$	−831.298	−0.0366697
$802$	18.3546	0.000808133 0
$803$	−14900.7	−0.654838
$804$	6473.34	0.283952
$805$	14072.0	0.616116
$806$	−293.937	−0.0128455
$807$	−3818.67	−0.166572
$808$	−223.859	−0.00974668
$809$	2078.87	0.0903453	0.0451726	−	0.998979i	$-0.485616\pi$
$809$	2078.87	0.0903453	0.0451726	+	0.998979i	$0.485616\pi$
$810$	34.7943	0.00150932
$811$	29163.4	1.26272	0.631361	−	0.775489i	$-0.282497\pi$
$811$	29163.4	1.26272	0.631361	+	0.775489i	$0.282497\pi$
$812$	5804.79	0.250872
$813$	809.301	0.0349119
$814$	−71.6533	−0.00308532
$815$	−46165.6	−1.98418
$816$	0	0
$817$	−8558.23	−0.366481
$818$	153.355	0.00655493
$819$	3705.01	0.158075
$820$	−32581.3	−1.38755
$821$	11121.7	0.472775	0.236388	−	0.971659i	$-0.424036\pi$
$821$	11121.7	0.472775	0.236388	+	0.971659i	$0.424036\pi$
$822$	136.461	0.00579031
$823$	38055.6	1.61183	0.805914	−	0.592033i	$-0.201674\pi$
$823$	38055.6	1.61183	0.805914	+	0.592033i	$0.201674\pi$
$824$	231.765	0.00979844
$825$	16261.2	0.686232
$826$	6.50835	0.000274158 0
$827$	−1391.63	−0.0585146	−0.0292573	−	0.999572i	$-0.509314\pi$
$827$	−1391.63	−0.0585146	−0.0292573	+	0.999572i	$0.509314\pi$
$828$	−7648.44	−0.321017
$829$	−28005.4	−1.17330	−0.586651	−	0.809840i	$-0.699554\pi$
$829$	−28005.4	−1.17330	−0.586651	+	0.809840i	$0.699554\pi$
$830$	−200.090	−0.00836774
$831$	10412.3	0.434654
$832$	−32676.2	−1.36159
$833$	0	0
$834$	−45.9229	−0.00190669
$835$	−38769.5	−1.60679
$836$	8954.04	0.370433
$837$	−5944.84	−0.245500
$838$	−21.9034	−0.000902912 0
$839$	−26495.8	−1.09027	−0.545135	−	0.838348i	$-0.683521\pi$
$839$	−26495.8	−1.09027	−0.545135	+	0.838348i	$0.683521\pi$
$840$	−132.952	−0.00546105
$841$	−11725.5	−0.480769
$842$	−324.475	−0.0132804
$843$	−2164.74	−0.0884431
$844$	−35648.8	−1.45389
$845$	38593.9	1.57121
$846$	108.337	0.00440271
$847$	−6434.67	−0.261036
$848$	−17701.0	−0.716811
$849$	−3051.24	−0.123343
$850$	0	0
$851$	−19945.0	−0.803415
$852$	−16796.7	−0.675404
$853$	47429.5	1.90381	0.951907	−	0.306386i	$-0.0991198\pi$
$853$	47429.5	1.90381	0.951907	+	0.306386i	$0.0991198\pi$
$854$	56.8705	0.00227877
$855$	−11338.4	−0.453527
$856$	−52.5249	−0.00209727
$857$	2113.73	0.0842516	0.0421258	−	0.999112i	$-0.486587\pi$
$857$	2113.73	0.0842516	0.0421258	+	0.999112i	$0.486587\pi$
$858$	73.0956	0.00290844
$859$	35271.0	1.40097	0.700483	−	0.713669i	$-0.252968\pi$
$859$	35271.0	1.40097	0.700483	+	0.713669i	$0.252968\pi$
$860$	−22931.9	−0.909269
$861$	3835.45	0.151814
$862$	−152.116	−0.00601053
$863$	−46110.0	−1.81877	−0.909387	−	0.415951i	$-0.863449\pi$
$863$	−46110.0	−1.81877	−0.909387	+	0.415951i	$0.863449\pi$
$864$	108.394	0.00426811
$865$	−51045.2	−2.00646
$866$	122.398	0.00480284
$867$	0	0
$868$	11357.6	0.444126
$869$	−20375.8	−0.795399
$870$	−145.018	−0.00565122
$871$	−17220.5	−0.669912
$872$	−390.226	−0.0151545
$873$	15013.3	0.582044
$874$	−136.238	−0.00527266
$875$	22781.8	0.880189
$876$	19593.0	0.755693
$877$	20985.3	0.808008	0.404004	−	0.914757i	$-0.367618\pi$
$877$	20985.3	0.808008	0.404004	+	0.914757i	$0.367618\pi$
$878$	−91.8112	−0.00352902
$879$	8328.90	0.319598
$880$	23991.2	0.919025
$881$	33923.6	1.29729	0.648646	−	0.761090i	$-0.275336\pi$
$881$	33923.6	1.29729	0.648646	+	0.761090i	$0.275336\pi$
$882$	−56.7267	−0.00216563
$883$	−31168.8	−1.18790	−0.593948	−	0.804503i	$-0.702432\pi$
$883$	−31168.8	−1.18790	−0.593948	+	0.804503i	$0.702432\pi$
$884$	0	0
$885$	2974.58	0.112982
$886$	−14.5966	−0.000553480 0
$887$	−35032.5	−1.32613	−0.663064	−	0.748563i	$-0.730744\pi$
$887$	−35032.5	−1.32613	−0.663064	+	0.748563i	$0.730744\pi$
$888$	188.440	0.00712120
$889$	13284.2	0.501167
$890$	−39.6768	−0.00149435
$891$	1478.35	0.0555855
$892$	−5107.87	−0.191731
$893$	−35303.7	−1.32295
$894$	188.441	0.00704969
$895$	22812.5	0.851999
$896$	−276.113	−0.0102950
$897$	20346.5	0.757357
$898$	116.076	0.00431349
$899$	24777.3	0.919209
$900$	−21381.9	−0.791922
$901$	0	0
$902$	75.6691	0.00279324
$903$	2699.53	0.0994848
$904$	−171.556	−0.00631180
$905$	12255.4	0.450149
$906$	199.294	0.00730807
$907$	−23052.2	−0.843921	−0.421960	−	0.906614i	$-0.638658\pi$
$907$	−23052.2	−0.843921	−0.421960	+	0.906614i	$0.638658\pi$
$908$	8812.17	0.322073
$909$	6021.92	0.219730
$910$	176.835	0.00644180
$911$	18173.2	0.660927	0.330463	−	0.943819i	$-0.392795\pi$
$911$	18173.2	0.660927	0.330463	+	0.943819i	$0.392795\pi$
$912$	−11773.1	−0.427462
$913$	−8501.50	−0.308169
$914$	−141.274	−0.00511260
$915$	25992.1	0.939096
$916$	28823.4	1.03969
$917$	1760.69	0.0634057
$918$	0	0
$919$	−13457.8	−0.483061	−0.241530	−	0.970393i	$-0.577649\pi$
$919$	−13457.8	−0.483061	−0.241530	+	0.970393i	$0.577649\pi$
$920$	−730.121	−0.0261645
$921$	−2182.30	−0.0780772
$922$	24.8254	0.000886746 0
$923$	44682.7	1.59344
$924$	−2824.38	−0.100558
$925$	−55758.1	−1.98196
$926$	73.1080	0.00259447
$927$	−6234.61	−0.220897
$928$	−451.773	−0.0159808
$929$	−33883.2	−1.19663	−0.598316	−	0.801260i	$-0.704163\pi$
$929$	−33883.2	−1.19663	−0.598316	+	0.801260i	$0.704163\pi$
$930$	−283.740	−0.0100045
$931$	18485.5	0.650740
$932$	−15822.0	−0.556079
$933$	−3553.80	−0.124701
$934$	−387.951	−0.0135912
$935$	0	0
$936$	−192.233	−0.00671296
$937$	21838.9	0.761414	0.380707	−	0.924696i	$-0.375681\pi$
$937$	21838.9	0.761414	0.380707	+	0.924696i	$0.375681\pi$
$938$	−36.3712	−0.00126606
$939$	763.398	0.0265309
$940$	−94596.6	−3.28234
$941$	−34598.1	−1.19858	−0.599291	−	0.800531i	$-0.704551\pi$
$941$	−34598.1	−1.19858	−0.599291	+	0.800531i	$0.704551\pi$
$942$	−39.1228	−0.00135317
$943$	21062.8	0.727360
$944$	3088.61	0.106489
$945$	3576.48	0.123114
$946$	53.2587	0.00183043
$947$	−7753.79	−0.266066	−0.133033	−	0.991112i	$-0.542472\pi$
$947$	−7753.79	−0.266066	−0.133033	+	0.991112i	$0.542472\pi$
$948$	26792.3	0.917903
$949$	−52121.6	−1.78287
$950$	−380.865	−0.0130072
$951$	25914.8	0.883642
$952$	0	0
$953$	−32189.4	−1.09414	−0.547071	−	0.837086i	$-0.684257\pi$
$953$	−32189.4	−1.09414	−0.547071	+	0.837086i	$0.684257\pi$
$954$	−52.0601	−0.00176678
$955$	−45622.9	−1.54589
$956$	40830.0	1.38131
$957$	−6161.57	−0.208125
$958$	387.113	0.0130554
$959$	14026.8	0.472313
$960$	−31542.7	−1.06045
$961$	18688.0	0.627302
$962$	−250.638	−0.00840011
$963$	1412.95	0.0472810
$964$	1304.50	0.0435840
$965$	−23751.6	−0.792324
$966$	42.9736	0.00143132
$967$	−8790.83	−0.292341	−0.146171	−	0.989259i	$-0.546695\pi$
$967$	−8790.83	−0.292341	−0.146171	+	0.989259i	$0.546695\pi$
$968$	333.860	0.0110854
$969$	0	0
$970$	716.568	0.0237192
$971$	30609.1	1.01163	0.505815	−	0.862642i	$-0.331192\pi$
$971$	30609.1	1.01163	0.505815	+	0.862642i	$0.331192\pi$
$972$	−1943.89	−0.0641465
$973$	−4720.38	−0.155528
$974$	−289.216	−0.00951445
$975$	56880.4	1.86834
$976$	26988.6	0.885126
$977$	19095.9	0.625314	0.312657	−	0.949866i	$-0.398781\pi$
$977$	19095.9	0.625314	0.312657	+	0.949866i	$0.398781\pi$
$978$	−140.982	−0.00460951
$979$	−1685.80	−0.0550342
$980$	49532.2	1.61454
$981$	10497.3	0.341644
$982$	56.6780	0.00184182
$983$	−2465.89	−0.0800100	−0.0400050	−	0.999199i	$-0.512737\pi$
$983$	−2465.89	−0.0800100	−0.0400050	+	0.999199i	$0.512737\pi$
$984$	−199.001	−0.00644707
$985$	71705.0	2.31950
$986$	0	0
$987$	11135.9	0.359127
$988$	31320.6	1.00854
$989$	14824.8	0.476644
$990$	70.5599	0.00226519
$991$	21369.6	0.684994	0.342497	−	0.939519i	$-0.388727\pi$
$991$	21369.6	0.684994	0.342497	+	0.939519i	$0.388727\pi$
$992$	−883.933	−0.0282912
$993$	2793.52	0.0892747
$994$	94.3738	0.00301142
$995$	−56215.8	−1.79112
$996$	11178.7	0.355632
$997$	−25866.7	−0.821670	−0.410835	−	0.911710i	$-0.634763\pi$
$997$	−25866.7	−0.821670	−0.410835	+	0.911710i	$0.634763\pi$
$998$	−183.749	−0.00582813
$999$	−5069.14	−0.160541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.4.a.w.1.10		20
17.5	odd	16		51.4.h.a.25.5	✓	40
17.7	odd	16		51.4.h.a.49.5	yes	40
17.16	even	2		867.4.a.v.1.10		20
51.5	even	16		153.4.l.c.127.6		40
51.41	even	16		153.4.l.c.100.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.25.5	✓	40	17.5	odd	16
51.4.h.a.49.5	yes	40	17.7	odd	16
153.4.l.c.100.6		40	51.41	even	16
153.4.l.c.127.6		40	51.5	even	16
867.4.a.v.1.10		20	17.16	even	2
867.4.a.w.1.10		20	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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	867.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0209109 q^{2} +3.00000 q^{3} -7.99956 q^{4} +20.5423 q^{5} +0.0627328 q^{6} +6.44826 q^{7} -0.334566 q^{8} +9.00000 q^{9} +0.429559 q^{10} +18.2513 q^{11} -23.9987 q^{12} +63.8416 q^{13} +0.134839 q^{14} +61.6270 q^{15} +63.9895 q^{16} +0.188198 q^{18} -61.3281 q^{19} -164.330 q^{20} +19.3448 q^{21} +0.381651 q^{22} +106.234 q^{23} -1.00370 q^{24} +296.987 q^{25} +1.33499 q^{26} +27.0000 q^{27} -51.5833 q^{28} -112.532 q^{29} +1.28868 q^{30} -220.179 q^{31} +4.01460 q^{32} +54.7538 q^{33} +132.462 q^{35} -71.9961 q^{36} -187.746 q^{37} -1.28243 q^{38} +191.525 q^{39} -6.87276 q^{40} +198.268 q^{41} +0.404517 q^{42} +139.548 q^{43} -146.002 q^{44} +184.881 q^{45} +2.22145 q^{46} +575.652 q^{47} +191.969 q^{48} -301.420 q^{49} +6.21027 q^{50} -510.705 q^{52} -276.624 q^{53} +0.564595 q^{54} +374.923 q^{55} -2.15737 q^{56} -183.984 q^{57} -2.35315 q^{58} +48.2675 q^{59} -492.989 q^{60} +421.765 q^{61} -4.60415 q^{62} +58.0344 q^{63} -511.832 q^{64} +1311.46 q^{65} +1.14495 q^{66} -269.737 q^{67} +318.702 q^{69} +2.76991 q^{70} +699.900 q^{71} -3.01109 q^{72} -816.421 q^{73} -3.92594 q^{74} +890.961 q^{75} +490.598 q^{76} +117.689 q^{77} +4.00496 q^{78} -1116.41 q^{79} +1314.49 q^{80} +81.0000 q^{81} +4.14597 q^{82} -465.803 q^{83} -154.750 q^{84} +2.91808 q^{86} -337.597 q^{87} -6.10624 q^{88} -92.3664 q^{89} +3.86603 q^{90} +411.667 q^{91} -849.827 q^{92} -660.538 q^{93} +12.0374 q^{94} -1259.82 q^{95} +12.0438 q^{96} +1668.15 q^{97} -6.30297 q^{98} +164.261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 60 q^{3} + 96 q^{4} + 32 q^{5} + 56 q^{7} + 180 q^{9} + 80 q^{10} + 152 q^{11} + 288 q^{12} + 56 q^{13} + 112 q^{14} + 96 q^{15} + 512 q^{16} + 328 q^{19} + 192 q^{20} + 168 q^{21} - 104 q^{22} + 576 q^{23}+ \cdots + 1368 q^{99}+O(q^{100}) \) 20 * q + 60 * q^3 + 96 * q^4 + 32 * q^5 + 56 * q^7 + 180 * q^9 + 80 * q^10 + 152 * q^11 + 288 * q^12 + 56 * q^13 + 112 * q^14 + 96 * q^15 + 512 * q^16 + 328 * q^19 + 192 * q^20 + 168 * q^21 - 104 * q^22 + 576 * q^23 + 796 * q^25 + 540 * q^27 + 648 * q^28 + 1000 * q^29 + 240 * q^30 + 248 * q^31 + 456 * q^33 - 496 * q^35 + 864 * q^36 + 984 * q^37 - 352 * q^38 + 168 * q^39 + 1800 * q^40 + 1080 * q^41 + 336 * q^42 + 888 * q^43 + 2080 * q^44 + 288 * q^45 + 752 * q^46 - 368 * q^47 + 1536 * q^48 + 1444 * q^49 + 224 * q^50 + 480 * q^52 - 224 * q^53 + 1592 * q^55 - 352 * q^56 + 984 * q^57 + 3528 * q^58 + 576 * q^59 + 576 * q^60 + 2328 * q^61 + 368 * q^62 + 504 * q^63 + 1560 * q^64 + 4824 * q^65 - 312 * q^66 + 1136 * q^67 + 1728 * q^69 + 1224 * q^70 - 1224 * q^71 + 656 * q^73 + 1808 * q^74 + 2388 * q^75 + 1072 * q^76 - 1344 * q^77 + 648 * q^79 + 1280 * q^80 + 1620 * q^81 + 6712 * q^82 + 160 * q^83 + 1944 * q^84 - 7808 * q^86 + 3000 * q^87 + 576 * q^88 - 2128 * q^89 + 720 * q^90 + 1072 * q^91 + 9504 * q^92 + 744 * q^93 - 1952 * q^94 + 4632 * q^95 + 752 * q^97 - 10544 * q^98 + 1368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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