LMFDB - Embedded newform 538.4.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,4,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	538.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:	$31.7430275831$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 189 x^{11} + 344 x^{10} + 12502 x^{9} - 15678 x^{8} - 385197 x^{7} + 263029 x^{6} + \cdots + 3268107 $ x^13 - 2x^12 - 189x^11 + 344x^10 + 12502x^9 - 15678x^8 - 385197x^7 + 263029x^6 + 5760126x^5 - 1326330x^4 - 37232298x^3 - 2190807x^2 + 62080182x + 3268107
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-4.40749$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +3.40749 q^{3} +4.00000 q^{4} -1.51765 q^{5} +6.81499 q^{6} -24.7241 q^{7} +8.00000 q^{8} -15.3890 q^{9} -3.03530 q^{10} -24.1415 q^{11} +13.6300 q^{12} +21.8956 q^{13} -49.4482 q^{14} -5.17139 q^{15} +16.0000 q^{16} +27.0456 q^{17} -30.7780 q^{18} +135.074 q^{19} -6.07061 q^{20} -84.2473 q^{21} -48.2830 q^{22} -191.404 q^{23} +27.2600 q^{24} -122.697 q^{25} +43.7912 q^{26} -144.440 q^{27} -98.8965 q^{28} -225.412 q^{29} -10.3428 q^{30} -330.532 q^{31} +32.0000 q^{32} -82.2621 q^{33} +54.0912 q^{34} +37.5226 q^{35} -61.5559 q^{36} +171.006 q^{37} +270.148 q^{38} +74.6091 q^{39} -12.1412 q^{40} -428.217 q^{41} -168.495 q^{42} +195.171 q^{43} -96.5661 q^{44} +23.3551 q^{45} -382.808 q^{46} +390.335 q^{47} +54.5199 q^{48} +268.282 q^{49} -245.393 q^{50} +92.1578 q^{51} +87.5823 q^{52} -150.141 q^{53} -288.880 q^{54} +36.6384 q^{55} -197.793 q^{56} +460.264 q^{57} -450.824 q^{58} -423.222 q^{59} -20.6856 q^{60} -142.383 q^{61} -661.065 q^{62} +380.479 q^{63} +64.0000 q^{64} -33.2299 q^{65} -164.524 q^{66} +249.793 q^{67} +108.182 q^{68} -652.208 q^{69} +75.0452 q^{70} +433.982 q^{71} -123.112 q^{72} +221.525 q^{73} +342.013 q^{74} -418.088 q^{75} +540.296 q^{76} +596.878 q^{77} +149.218 q^{78} +413.925 q^{79} -24.2824 q^{80} -76.6766 q^{81} -856.435 q^{82} -294.365 q^{83} -336.989 q^{84} -41.0458 q^{85} +390.341 q^{86} -768.090 q^{87} -193.132 q^{88} +1257.87 q^{89} +46.7102 q^{90} -541.349 q^{91} -765.616 q^{92} -1126.29 q^{93} +780.669 q^{94} -204.995 q^{95} +109.040 q^{96} -86.7492 q^{97} +536.564 q^{98} +371.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 26 q^{2} - 15 q^{3} + 52 q^{4} - 41 q^{5} - 30 q^{6} - 60 q^{7} + 104 q^{8} + 48 q^{9} - 82 q^{10} - 110 q^{11} - 60 q^{12} - 140 q^{13} - 120 q^{14} - 113 q^{15} + 208 q^{16} - 214 q^{17} + 96 q^{18}+ \cdots + 767 q^{99}+O(q^{100}) $ 13 * q + 26 * q^2 - 15 * q^3 + 52 * q^4 - 41 * q^5 - 30 * q^6 - 60 * q^7 + 104 * q^8 + 48 * q^9 - 82 * q^10 - 110 * q^11 - 60 * q^12 - 140 * q^13 - 120 * q^14 - 113 * q^15 + 208 * q^16 - 214 * q^17 + 96 * q^18 - 120 * q^19 - 164 * q^20 - 353 * q^21 - 220 * q^22 - 459 * q^23 - 120 * q^24 - 90 * q^25 - 280 * q^26 - 465 * q^27 - 240 * q^28 - 707 * q^29 - 226 * q^30 - 556 * q^31 + 416 * q^32 - 807 * q^33 - 428 * q^34 - 570 * q^35 + 192 * q^36 - 915 * q^37 - 240 * q^38 - 734 * q^39 - 328 * q^40 - 991 * q^41 - 706 * q^42 - 201 * q^43 - 440 * q^44 - 1154 * q^45 - 918 * q^46 - 686 * q^47 - 240 * q^48 - 407 * q^49 - 180 * q^50 - 251 * q^51 - 560 * q^52 - 2068 * q^53 - 930 * q^54 - 459 * q^55 - 480 * q^56 - 1982 * q^57 - 1414 * q^58 - 949 * q^59 - 452 * q^60 - 1731 * q^61 - 1112 * q^62 - 1856 * q^63 + 832 * q^64 - 2258 * q^65 - 1614 * q^66 - 1047 * q^67 - 856 * q^68 + 587 * q^69 - 1140 * q^70 - 2152 * q^71 + 384 * q^72 - 149 * q^73 - 1830 * q^74 + 441 * q^75 - 480 * q^76 + 886 * q^77 - 1468 * q^78 - 1608 * q^79 - 656 * q^80 + 1633 * q^81 - 1982 * q^82 + 2073 * q^83 - 1412 * q^84 - 465 * q^85 - 402 * q^86 + 4403 * q^87 - 880 * q^88 + 815 * q^89 - 2308 * q^90 + 2051 * q^91 - 1836 * q^92 - 2113 * q^93 - 1372 * q^94 - 158 * q^95 - 480 * q^96 - 1011 * q^97 - 814 * q^98 + 767 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.40749	0.655773	0.327886	−	0.944717i	$-0.393664\pi$
$3$	3.40749	0.655773	0.327886	+	0.944717i	$0.393664\pi$
$4$	4.00000	0.500000
$5$	−1.51765	−0.135743	−0.0678715	−	0.997694i	$-0.521621\pi$
$5$	−1.51765	−0.135743	−0.0678715	+	0.997694i	$0.521621\pi$
$6$	6.81499	0.463701
$7$	−24.7241	−1.33498	−0.667488	−	0.744620i	$-0.732631\pi$
$7$	−24.7241	−1.33498	−0.667488	+	0.744620i	$0.732631\pi$
$8$	8.00000	0.353553
$9$	−15.3890	−0.569962
$10$	−3.03530	−0.0959847
$11$	−24.1415	−0.661722	−0.330861	−	0.943679i	$-0.607339\pi$
$11$	−24.1415	−0.661722	−0.330861	+	0.943679i	$0.607339\pi$
$12$	13.6300	0.327886
$13$	21.8956	0.467134	0.233567	−	0.972341i	$-0.424960\pi$
$13$	21.8956	0.467134	0.233567	+	0.972341i	$0.424960\pi$
$14$	−49.4482	−0.943971
$15$	−5.17139	−0.0890165
$16$	16.0000	0.250000
$17$	27.0456	0.385854	0.192927	−	0.981213i	$-0.438202\pi$
$17$	27.0456	0.385854	0.192927	+	0.981213i	$0.438202\pi$
$18$	−30.7780	−0.403024
$19$	135.074	1.63095	0.815476	−	0.578791i	$-0.196475\pi$
$19$	135.074	1.63095	0.815476	+	0.578791i	$0.196475\pi$
$20$	−6.07061	−0.0678715
$21$	−84.2473	−0.875441
$22$	−48.2830	−0.467908
$23$	−191.404	−1.73524	−0.867620	−	0.497229i	$-0.834351\pi$
$23$	−191.404	−1.73524	−0.867620	+	0.497229i	$0.834351\pi$
$24$	27.2600	0.231851
$25$	−122.697	−0.981574
$26$	43.7912	0.330314
$27$	−144.440	−1.02954
$28$	−98.8965	−0.667488
$29$	−225.412	−1.44338	−0.721689	−	0.692217i	$-0.756634\pi$
$29$	−225.412	−1.44338	−0.721689	+	0.692217i	$0.756634\pi$
$30$	−10.3428	−0.0629442
$31$	−330.532	−1.91501	−0.957506	−	0.288414i	$-0.906872\pi$
$31$	−330.532	−1.91501	−0.957506	+	0.288414i	$0.906872\pi$
$32$	32.0000	0.176777
$33$	−82.2621	−0.433939
$34$	54.0912	0.272840
$35$	37.5226	0.181214
$36$	−61.5559	−0.284981
$37$	171.006	0.759818	0.379909	−	0.925024i	$-0.375955\pi$
$37$	171.006	0.759818	0.379909	+	0.925024i	$0.375955\pi$
$38$	270.148	1.15326
$39$	74.6091	0.306334
$40$	−12.1412	−0.0479924
$41$	−428.217	−1.63113	−0.815565	−	0.578666i	$-0.803574\pi$
$41$	−428.217	−1.63113	−0.815565	+	0.578666i	$0.803574\pi$
$42$	−168.495	−0.619030
$43$	195.171	0.692169	0.346084	−	0.938203i	$-0.387511\pi$
$43$	195.171	0.692169	0.346084	+	0.938203i	$0.387511\pi$
$44$	−96.5661	−0.330861
$45$	23.3551	0.0773684
$46$	−382.808	−1.22700
$47$	390.335	1.21141	0.605704	−	0.795690i	$-0.292892\pi$
$47$	390.335	1.21141	0.605704	+	0.795690i	$0.292892\pi$
$48$	54.5199	0.163943
$49$	268.282	0.782163
$50$	−245.393	−0.694078
$51$	92.1578	0.253033
$52$	87.5823	0.233567
$53$	−150.141	−0.389122	−0.194561	−	0.980890i	$-0.562328\pi$
$53$	−150.141	−0.389122	−0.194561	+	0.980890i	$0.562328\pi$
$54$	−288.880	−0.727993
$55$	36.6384	0.0898241
$56$	−197.793	−0.471986
$57$	460.264	1.06953
$58$	−450.824	−1.02062
$59$	−423.222	−0.933878	−0.466939	−	0.884290i	$-0.654643\pi$
$59$	−423.222	−0.933878	−0.466939	+	0.884290i	$0.654643\pi$
$60$	−20.6856	−0.0445082
$61$	−142.383	−0.298857	−0.149428	−	0.988773i	$-0.547743\pi$
$61$	−142.383	−0.298857	−0.149428	+	0.988773i	$0.547743\pi$
$62$	−661.065	−1.35412
$63$	380.479	0.760886
$64$	64.0000	0.125000
$65$	−33.2299	−0.0634101
$66$	−164.524	−0.306841
$67$	249.793	0.455478	0.227739	−	0.973722i	$-0.426867\pi$
$67$	249.793	0.455478	0.227739	+	0.973722i	$0.426867\pi$
$68$	108.182	0.192927
$69$	−652.208	−1.13792
$70$	75.0452	0.128137
$71$	433.982	0.725412	0.362706	−	0.931904i	$-0.381853\pi$
$71$	433.982	0.725412	0.362706	+	0.931904i	$0.381853\pi$
$72$	−123.112	−0.201512
$73$	221.525	0.355172	0.177586	−	0.984105i	$-0.443171\pi$
$73$	221.525	0.355172	0.177586	+	0.984105i	$0.443171\pi$
$74$	342.013	0.537273
$75$	−418.088	−0.643689
$76$	540.296	0.815476
$77$	596.878	0.883383
$78$	149.218	0.216611
$79$	413.925	0.589496	0.294748	−	0.955575i	$-0.404764\pi$
$79$	413.925	0.589496	0.294748	+	0.955575i	$0.404764\pi$
$80$	−24.2824	−0.0339357
$81$	−76.6766	−0.105181
$82$	−856.435	−1.15338
$83$	−294.365	−0.389286	−0.194643	−	0.980874i	$-0.562355\pi$
$83$	−294.365	−0.389286	−0.194643	+	0.980874i	$0.562355\pi$
$84$	−336.989	−0.437721
$85$	−41.0458	−0.0523770
$86$	390.341	0.489437
$87$	−768.090	−0.946528
$88$	−193.132	−0.233954
$89$	1257.87	1.49813	0.749067	−	0.662494i	$-0.230502\pi$
$89$	1257.87	1.49813	0.749067	+	0.662494i	$0.230502\pi$
$90$	46.7102	0.0547077
$91$	−541.349	−0.623613
$92$	−765.616	−0.867620
$93$	−1126.29	−1.25581
$94$	780.669	0.856595
$95$	−204.995	−0.221390
$96$	109.040	0.115925
$97$	−86.7492	−0.0908047	−0.0454023	−	0.998969i	$-0.514457\pi$
$97$	−86.7492	−0.0908047	−0.0454023	+	0.998969i	$0.514457\pi$
$98$	536.564	0.553072
$99$	371.513	0.377157
$100$	−490.787	−0.490787
$101$	−1948.85	−1.91997	−0.959987	−	0.280045i	$-0.909651\pi$
$101$	−1948.85	−1.91997	−0.959987	+	0.280045i	$0.909651\pi$
$102$	184.316	0.178921
$103$	900.399	0.861349	0.430675	−	0.902507i	$-0.358276\pi$
$103$	900.399	0.861349	0.430675	+	0.902507i	$0.358276\pi$
$104$	175.165	0.165157
$105$	127.858	0.118835
$106$	−300.282	−0.275151
$107$	686.009	0.619804	0.309902	−	0.950769i	$-0.399704\pi$
$107$	686.009	0.619804	0.309902	+	0.950769i	$0.399704\pi$
$108$	−577.761	−0.514769
$109$	−213.561	−0.187664	−0.0938322	−	0.995588i	$-0.529912\pi$
$109$	−213.561	−0.187664	−0.0938322	+	0.995588i	$0.529912\pi$
$110$	73.2768	0.0635152
$111$	582.703	0.498268
$112$	−395.586	−0.333744
$113$	1136.58	0.946196	0.473098	−	0.881010i	$-0.343136\pi$
$113$	1136.58	0.946196	0.473098	+	0.881010i	$0.343136\pi$
$114$	920.528	0.756275
$115$	290.485	0.235546
$116$	−901.648	−0.721689
$117$	−336.951	−0.266249
$118$	−846.444	−0.660351
$119$	−668.679	−0.515107
$120$	−41.3711	−0.0314721
$121$	−748.187	−0.562124
$122$	−284.766	−0.211323
$123$	−1459.15	−1.06965
$124$	−1322.13	−0.957506
$125$	375.917	0.268985
$126$	760.958	0.538028
$127$	17.7360	0.0123922	0.00619611	−	0.999981i	$-0.498028\pi$
$127$	17.7360	0.0123922	0.00619611	+	0.999981i	$0.498028\pi$
$128$	128.000	0.0883883
$129$	665.043	0.453905
$130$	−66.4597	−0.0448377
$131$	2653.46	1.76972	0.884862	−	0.465853i	$-0.154252\pi$
$131$	2653.46	1.76972	0.884862	+	0.465853i	$0.154252\pi$
$132$	−329.048	−0.216970
$133$	−3339.58	−2.17728
$134$	499.585	0.322072
$135$	219.210	0.139753
$136$	216.365	0.136420
$137$	1700.75	1.06062	0.530308	−	0.847805i	$-0.322076\pi$
$137$	1700.75	1.06062	0.530308	+	0.847805i	$0.322076\pi$
$138$	−1304.42	−0.804633
$139$	−1504.11	−0.917823	−0.458911	−	0.888482i	$-0.651760\pi$
$139$	−1504.11	−0.917823	−0.458911	+	0.888482i	$0.651760\pi$
$140$	150.090	0.0906068
$141$	1330.06	0.794408
$142$	867.965	0.512944
$143$	−528.593	−0.309113
$144$	−246.224	−0.142491
$145$	342.097	0.195928
$146$	443.050	0.251144
$147$	914.169	0.512921
$148$	684.026	0.379909
$149$	1525.33	0.838657	0.419329	−	0.907834i	$-0.362265\pi$
$149$	1525.33	0.838657	0.419329	+	0.907834i	$0.362265\pi$
$150$	−836.177	−0.455157
$151$	673.096	0.362754	0.181377	−	0.983414i	$-0.441945\pi$
$151$	673.096	0.362754	0.181377	+	0.983414i	$0.441945\pi$
$152$	1080.59	0.576629
$153$	−416.204	−0.219922
$154$	1193.76	0.624646
$155$	501.633	0.259949
$156$	298.436	0.153167
$157$	−1025.10	−0.521095	−0.260547	−	0.965461i	$-0.583903\pi$
$157$	−1025.10	−0.521095	−0.260547	+	0.965461i	$0.583903\pi$
$158$	827.850	0.416837
$159$	−511.605	−0.255175
$160$	−48.5649	−0.0239962
$161$	4732.30	2.31650
$162$	−153.353	−0.0743739
$163$	2223.46	1.06843	0.534217	−	0.845347i	$-0.320606\pi$
$163$	2223.46	1.06843	0.534217	+	0.845347i	$0.320606\pi$
$164$	−1712.87	−0.815565
$165$	124.845	0.0589042
$166$	−588.730	−0.275267
$167$	−3816.65	−1.76851	−0.884256	−	0.467003i	$-0.845334\pi$
$167$	−3816.65	−1.76851	−0.884256	+	0.467003i	$0.845334\pi$
$168$	−673.978	−0.309515
$169$	−1717.58	−0.781786
$170$	−82.0916	−0.0370361
$171$	−2078.65	−0.929581
$172$	780.683	0.346084
$173$	−4212.25	−1.85116	−0.925581	−	0.378549i	$-0.876423\pi$
$173$	−4212.25	−1.85116	−0.925581	+	0.378549i	$0.876423\pi$
$174$	−1536.18	−0.669296
$175$	3033.57	1.31038
$176$	−386.264	−0.165431
$177$	−1442.13	−0.612412
$178$	2515.74	1.05934
$179$	−2141.00	−0.893998	−0.446999	−	0.894534i	$-0.647507\pi$
$179$	−2141.00	−0.893998	−0.446999	+	0.894534i	$0.647507\pi$
$180$	93.4205	0.0386842
$181$	2106.29	0.864970	0.432485	−	0.901641i	$-0.357637\pi$
$181$	2106.29	0.864970	0.432485	+	0.901641i	$0.357637\pi$
$182$	−1082.70	−0.440961
$183$	−485.169	−0.195982
$184$	−1531.23	−0.613500
$185$	−259.528	−0.103140
$186$	−2252.57	−0.887993
$187$	−652.922	−0.255328
$188$	1561.34	0.605704
$189$	3571.16	1.37441
$190$	−409.991	−0.156547
$191$	1583.77	0.599986	0.299993	−	0.953941i	$-0.403016\pi$
$191$	1583.77	0.599986	0.299993	+	0.953941i	$0.403016\pi$
$192$	218.080	0.0819716
$193$	1310.02	0.488589	0.244294	−	0.969701i	$-0.421444\pi$
$193$	1310.02	0.488589	0.244294	+	0.969701i	$0.421444\pi$
$194$	−173.498	−0.0642086
$195$	−113.231	−0.0415826
$196$	1073.13	0.391081
$197$	2597.84	0.939535	0.469767	−	0.882790i	$-0.344338\pi$
$197$	2597.84	0.939535	0.469767	+	0.882790i	$0.344338\pi$
$198$	743.027	0.266690
$199$	−1392.63	−0.496086	−0.248043	−	0.968749i	$-0.579787\pi$
$199$	−1392.63	−0.496086	−0.248043	+	0.968749i	$0.579787\pi$
$200$	−981.574	−0.347039
$201$	851.167	0.298690
$202$	−3897.69	−1.35763
$203$	5573.11	1.92688
$204$	368.631	0.126516
$205$	649.885	0.221414
$206$	1800.80	0.609066
$207$	2945.51	0.989021
$208$	350.329	0.116783
$209$	−3260.89	−1.07924
$210$	255.716	0.0840290
$211$	−1159.68	−0.378368	−0.189184	−	0.981942i	$-0.560584\pi$
$211$	−1159.68	−0.378368	−0.189184	+	0.981942i	$0.560584\pi$
$212$	−600.564	−0.194561
$213$	1478.79	0.475705
$214$	1372.02	0.438268
$215$	−296.201	−0.0939570
$216$	−1155.52	−0.363997
$217$	8172.12	2.55650
$218$	−427.121	−0.132699
$219$	754.845	0.232912
$220$	146.554	0.0449120
$221$	592.179	0.180246
$222$	1165.41	0.352329
$223$	−5018.57	−1.50703	−0.753516	−	0.657429i	$-0.771644\pi$
$223$	−5018.57	−1.50703	−0.753516	+	0.657429i	$0.771644\pi$
$224$	−791.172	−0.235993
$225$	1888.18	0.559460
$226$	2273.15	0.669061
$227$	−3008.73	−0.879719	−0.439860	−	0.898067i	$-0.644972\pi$
$227$	−3008.73	−0.879719	−0.439860	+	0.898067i	$0.644972\pi$
$228$	1841.06	0.534767
$229$	−1551.16	−0.447613	−0.223806	−	0.974634i	$-0.571848\pi$
$229$	−1551.16	−0.447613	−0.223806	+	0.974634i	$0.571848\pi$
$230$	580.969	0.166556
$231$	2033.86	0.579299
$232$	−1803.30	−0.510311
$233$	431.719	0.121386	0.0606928	−	0.998156i	$-0.480669\pi$
$233$	431.719	0.121386	0.0606928	+	0.998156i	$0.480669\pi$
$234$	−673.901	−0.188266
$235$	−592.392	−0.164440
$236$	−1692.89	−0.466939
$237$	1410.45	0.386575
$238$	−1337.36	−0.364235
$239$	−1896.08	−0.513169	−0.256585	−	0.966522i	$-0.582597\pi$
$239$	−1896.08	−0.513169	−0.256585	+	0.966522i	$0.582597\pi$
$240$	−82.7422	−0.0222541
$241$	−1082.80	−0.289416	−0.144708	−	0.989474i	$-0.546224\pi$
$241$	−1082.80	−0.289416	−0.144708	+	0.989474i	$0.546224\pi$
$242$	−1496.37	−0.397482
$243$	3638.61	0.960564
$244$	−569.531	−0.149428
$245$	−407.158	−0.106173
$246$	−2918.30	−0.756357
$247$	2957.52	0.761873
$248$	−2644.26	−0.677059
$249$	−1003.05	−0.255283
$250$	751.835	0.190201
$251$	−1482.51	−0.372809	−0.186405	−	0.982473i	$-0.559684\pi$
$251$	−1482.51	−0.372809	−0.186405	+	0.982473i	$0.559684\pi$
$252$	1521.92	0.380443
$253$	4620.78	1.14825
$254$	35.4719	0.00876262
$255$	−139.863	−0.0343474
$256$	256.000	0.0625000
$257$	−2290.18	−0.555865	−0.277932	−	0.960601i	$-0.589649\pi$
$257$	−2290.18	−0.555865	−0.277932	+	0.960601i	$0.589649\pi$
$258$	1330.09	0.320959
$259$	−4227.98	−1.01434
$260$	−132.919	−0.0317051
$261$	3468.86	0.822671
$262$	5306.92	1.25138
$263$	−2815.61	−0.660144	−0.330072	−	0.943956i	$-0.607073\pi$
$263$	−2815.61	−0.660144	−0.330072	+	0.943956i	$0.607073\pi$
$264$	−658.097	−0.153421
$265$	227.862	0.0528205
$266$	−6679.17	−1.53957
$267$	4286.18	0.982435
$268$	999.171	0.227739
$269$	−269.000	−0.0609711
$269$	−269.000	−0.0609711
$270$	438.420	0.0988200
$271$	−1744.89	−0.391123	−0.195561	−	0.980691i	$-0.562653\pi$
$271$	−1744.89	−0.391123	−0.195561	+	0.980691i	$0.562653\pi$
$272$	432.730	0.0964636
$273$	−1844.64	−0.408948
$274$	3401.49	0.749969
$275$	2962.09	0.649529
$276$	−2608.83	−0.568961
$277$	1768.88	0.383689	0.191844	−	0.981425i	$-0.438553\pi$
$277$	1768.88	0.383689	0.191844	+	0.981425i	$0.438553\pi$
$278$	−3008.23	−0.648999
$279$	5086.56	1.09148
$280$	300.181	0.0640687
$281$	1532.69	0.325384	0.162692	−	0.986677i	$-0.447982\pi$
$281$	1532.69	0.325384	0.162692	+	0.986677i	$0.447982\pi$
$282$	2660.13	0.561731
$283$	2210.03	0.464213	0.232107	−	0.972690i	$-0.425438\pi$
$283$	2210.03	0.464213	0.232107	+	0.972690i	$0.425438\pi$
$284$	1735.93	0.362706
$285$	−698.520	−0.145182
$286$	−1057.19	−0.218576
$287$	10587.3	2.17752
$288$	−492.447	−0.100756
$289$	−4181.54	−0.851116
$290$	684.194	0.138542
$291$	−295.598	−0.0595472
$292$	886.100	0.177586
$293$	−8946.98	−1.78392	−0.891960	−	0.452115i	$-0.850670\pi$
$293$	−8946.98	−1.78392	−0.891960	+	0.452115i	$0.850670\pi$
$294$	1828.34	0.362690
$295$	642.304	0.126767
$296$	1368.05	0.268636
$297$	3487.01	0.681268
$298$	3050.66	0.593020
$299$	−4190.90	−0.810589
$300$	−1672.35	−0.321845
$301$	−4825.42	−0.924029
$302$	1346.19	0.256505
$303$	−6640.68	−1.25907
$304$	2161.18	0.407738
$305$	216.088	0.0405677
$306$	−832.409	−0.155509
$307$	8186.79	1.52197	0.760985	−	0.648770i	$-0.224716\pi$
$307$	8186.79	1.52197	0.760985	+	0.648770i	$0.224716\pi$
$308$	2387.51	0.441692
$309$	3068.10	0.564849
$310$	1003.27	0.183812
$311$	7960.72	1.45148	0.725742	−	0.687967i	$-0.241497\pi$
$311$	7960.72	1.45148	0.725742	+	0.687967i	$0.241497\pi$
$312$	596.872	0.108305
$313$	1823.64	0.329324	0.164662	−	0.986350i	$-0.447347\pi$
$313$	1823.64	0.329324	0.164662	+	0.986350i	$0.447347\pi$
$314$	−2050.20	−0.368470
$315$	−577.435	−0.103285
$316$	1655.70	0.294748
$317$	−3619.11	−0.641228	−0.320614	−	0.947210i	$-0.603889\pi$
$317$	−3619.11	−0.641228	−0.320614	+	0.947210i	$0.603889\pi$
$318$	−1023.21	−0.180436
$319$	5441.79	0.955115
$320$	−97.1297	−0.0169679
$321$	2337.57	0.406450
$322$	9464.59	1.63802
$323$	3653.16	0.629310
$324$	−306.706	−0.0525903
$325$	−2686.52	−0.458526
$326$	4446.92	0.755498
$327$	−727.707	−0.123065
$328$	−3425.74	−0.576691
$329$	−9650.68	−1.61720
$330$	249.690	0.0416515
$331$	−1597.41	−0.265262	−0.132631	−	0.991165i	$-0.542343\pi$
$331$	−1597.41	−0.265262	−0.132631	+	0.991165i	$0.542343\pi$
$332$	−1177.46	−0.194643
$333$	−2631.61	−0.433068
$334$	−7633.31	−1.25053
$335$	−379.098	−0.0618279
$336$	−1347.96	−0.218860
$337$	−10728.5	−1.73418	−0.867091	−	0.498149i	$-0.834013\pi$
$337$	−10728.5	−1.73418	−0.867091	+	0.498149i	$0.834013\pi$
$338$	−3435.17	−0.552806
$339$	3872.88	0.620489
$340$	−164.183	−0.0261885
$341$	7979.55	1.26721
$342$	−4157.30	−0.657313
$343$	1847.34	0.290808
$344$	1561.37	0.244719
$345$	989.825	0.154465
$346$	−8424.49	−1.30897
$347$	−8540.79	−1.32131	−0.660654	−	0.750691i	$-0.729721\pi$
$347$	−8540.79	−1.32131	−0.660654	+	0.750691i	$0.729721\pi$
$348$	−3072.36	−0.473264
$349$	10888.5	1.67004	0.835022	−	0.550216i	$-0.185455\pi$
$349$	10888.5	1.67004	0.835022	+	0.550216i	$0.185455\pi$
$350$	6067.14	0.926577
$351$	−3162.60	−0.480932
$352$	−772.529	−0.116977
$353$	−1760.03	−0.265373	−0.132687	−	0.991158i	$-0.542360\pi$
$353$	−1760.03	−0.265373	−0.132687	+	0.991158i	$0.542360\pi$
$354$	−2884.25	−0.433040
$355$	−658.634	−0.0984695
$356$	5031.48	0.749067
$357$	−2278.52	−0.337793
$358$	−4281.99	−0.632152
$359$	−6463.46	−0.950218	−0.475109	−	0.879927i	$-0.657591\pi$
$359$	−6463.46	−0.950218	−0.475109	+	0.879927i	$0.657591\pi$
$360$	186.841	0.0273538
$361$	11386.0	1.66001
$362$	4212.59	0.611626
$363$	−2549.44	−0.368625
$364$	−2165.39	−0.311806
$365$	−336.198	−0.0482121
$366$	−970.337	−0.138580
$367$	6456.84	0.918376	0.459188	−	0.888339i	$-0.348140\pi$
$367$	6456.84	0.918376	0.459188	+	0.888339i	$0.348140\pi$
$368$	−3062.46	−0.433810
$369$	6589.83	0.929683
$370$	−519.056	−0.0729310
$371$	3712.10	0.519468
$372$	−4505.15	−0.627906
$373$	−7517.75	−1.04358	−0.521788	−	0.853075i	$-0.674735\pi$
$373$	−7517.75	−1.04358	−0.521788	+	0.853075i	$0.674735\pi$
$374$	−1305.84	−0.180544
$375$	1280.94	0.176393
$376$	3122.68	0.428297
$377$	−4935.53	−0.674251
$378$	7142.31	0.971854
$379$	−12664.4	−1.71643	−0.858214	−	0.513291i	$-0.828426\pi$
$379$	−12664.4	−1.71643	−0.858214	+	0.513291i	$0.828426\pi$
$380$	−819.981	−0.110695
$381$	60.4352	0.00812648
$382$	3167.53	0.424254
$383$	6954.46	0.927824	0.463912	−	0.885881i	$-0.346445\pi$
$383$	6954.46	0.927824	0.463912	+	0.885881i	$0.346445\pi$
$384$	436.159	0.0579627
$385$	−905.853	−0.119913
$386$	2620.05	0.345484
$387$	−3003.48	−0.394510
$388$	−346.997	−0.0454023
$389$	1671.13	0.217815	0.108907	−	0.994052i	$-0.465265\pi$
$389$	1671.13	0.217815	0.108907	+	0.994052i	$0.465265\pi$
$390$	−226.461	−0.0294033
$391$	−5176.64	−0.669550
$392$	2146.25	0.276536
$393$	9041.65	1.16054
$394$	5195.68	0.664351
$395$	−628.194	−0.0800199
$396$	1486.05	0.188578
$397$	−12233.3	−1.54653	−0.773267	−	0.634081i	$-0.781379\pi$
$397$	−12233.3	−1.54653	−0.773267	+	0.634081i	$0.781379\pi$
$398$	−2785.27	−0.350786
$399$	−11379.6	−1.42780
$400$	−1963.15	−0.245393
$401$	−13185.9	−1.64208	−0.821038	−	0.570873i	$-0.806605\pi$
$401$	−13185.9	−1.64208	−0.821038	+	0.570873i	$0.806605\pi$
$402$	1702.33	0.211206
$403$	−7237.20	−0.894567
$404$	−7795.38	−0.959987
$405$	116.368	0.0142775
$406$	11146.2	1.36251
$407$	−4128.35	−0.502789
$408$	737.262	0.0894606
$409$	9059.62	1.09528	0.547640	−	0.836714i	$-0.315527\pi$
$409$	9059.62	1.09528	0.547640	+	0.836714i	$0.315527\pi$
$410$	1299.77	0.156564
$411$	5795.28	0.695523
$412$	3601.60	0.430675
$413$	10463.8	1.24671
$414$	5891.03	0.699343
$415$	446.744	0.0528429
$416$	700.659	0.0825784
$417$	−5125.26	−0.601883
$418$	−6521.78	−0.763136
$419$	−9398.92	−1.09586	−0.547932	−	0.836523i	$-0.684585\pi$
$419$	−9398.92	−1.09586	−0.547932	+	0.836523i	$0.684585\pi$
$420$	511.432	0.0594175
$421$	−10004.8	−1.15820	−0.579102	−	0.815255i	$-0.696597\pi$
$421$	−10004.8	−1.15820	−0.579102	+	0.815255i	$0.696597\pi$
$422$	−2319.36	−0.267547
$423$	−6006.85	−0.690457
$424$	−1201.13	−0.137575
$425$	−3318.41	−0.378745
$426$	2957.58	0.336374
$427$	3520.29	0.398966
$428$	2744.04	0.309902
$429$	−1801.18	−0.202708
$430$	−592.402	−0.0664376
$431$	15243.5	1.70360	0.851801	−	0.523865i	$-0.175510\pi$
$431$	15243.5	1.70360	0.851801	+	0.523865i	$0.175510\pi$
$432$	−2311.04	−0.257385
$433$	−1116.95	−0.123966	−0.0619828	−	0.998077i	$-0.519742\pi$
$433$	−1116.95	−0.123966	−0.0619828	+	0.998077i	$0.519742\pi$
$434$	16344.2	1.80772
$435$	1165.69	0.128484
$436$	−854.243	−0.0938322
$437$	−25853.7	−2.83009
$438$	1509.69	0.164694
$439$	9000.27	0.978495	0.489248	−	0.872145i	$-0.337271\pi$
$439$	9000.27	0.978495	0.489248	+	0.872145i	$0.337271\pi$
$440$	293.107	0.0317576
$441$	−4128.58	−0.445803
$442$	1184.36	0.127453
$443$	−5418.87	−0.581170	−0.290585	−	0.956849i	$-0.593850\pi$
$443$	−5418.87	−0.581170	−0.290585	+	0.956849i	$0.593850\pi$
$444$	2330.81	0.249134
$445$	−1909.01	−0.203361
$446$	−10037.1	−1.06563
$447$	5197.56	0.549969
$448$	−1582.34	−0.166872
$449$	−11304.0	−1.18812	−0.594062	−	0.804419i	$-0.702477\pi$
$449$	−11304.0	−1.18812	−0.594062	+	0.804419i	$0.702477\pi$
$450$	3776.36	0.395598
$451$	10337.8	1.07935
$452$	4546.30	0.473098
$453$	2293.57	0.237884
$454$	−6017.46	−0.622056
$455$	821.579	0.0846510
$456$	3682.11	0.378137
$457$	16511.4	1.69009	0.845043	−	0.534698i	$-0.179575\pi$
$457$	16511.4	1.69009	0.845043	+	0.534698i	$0.179575\pi$
$458$	−3102.31	−0.316510
$459$	−3906.47	−0.397252
$460$	1161.94	0.117773
$461$	5205.28	0.525888	0.262944	−	0.964811i	$-0.415307\pi$
$461$	5205.28	0.525888	0.262944	+	0.964811i	$0.415307\pi$
$462$	4067.71	0.409626
$463$	6418.22	0.644233	0.322116	−	0.946700i	$-0.395606\pi$
$463$	6418.22	0.644233	0.322116	+	0.946700i	$0.395606\pi$
$464$	−3606.59	−0.360845
$465$	1709.31	0.170468
$466$	863.438	0.0858326
$467$	14037.9	1.39100	0.695502	−	0.718524i	$-0.255182\pi$
$467$	14037.9	1.39100	0.695502	+	0.718524i	$0.255182\pi$
$468$	−1347.80	−0.133124
$469$	−6175.90	−0.608053
$470$	−1184.78	−0.116277
$471$	−3493.02	−0.341720
$472$	−3385.78	−0.330176
$473$	−4711.72	−0.458023
$474$	2820.89	0.273350
$475$	−16573.1	−1.60090
$476$	−2674.71	−0.257553
$477$	2310.52	0.221785
$478$	−3792.17	−0.362865
$479$	6783.14	0.647035	0.323517	−	0.946222i	$-0.395135\pi$
$479$	6783.14	0.647035	0.323517	+	0.946222i	$0.395135\pi$
$480$	−165.484	−0.0157360
$481$	3744.28	0.354937
$482$	−2165.60	−0.204648
$483$	16125.3	1.51910
$484$	−2992.75	−0.281062
$485$	131.655	0.0123261
$486$	7277.22	0.679221
$487$	−959.214	−0.0892528	−0.0446264	−	0.999004i	$-0.514210\pi$
$487$	−959.214	−0.0892528	−0.0446264	+	0.999004i	$0.514210\pi$
$488$	−1139.06	−0.105662
$489$	7576.43	0.700650
$490$	−814.317	−0.0750757
$491$	7370.51	0.677447	0.338723	−	0.940886i	$-0.390005\pi$
$491$	7370.51	0.677447	0.338723	+	0.940886i	$0.390005\pi$
$492$	−5836.59	−0.534825
$493$	−6096.41	−0.556934
$494$	5915.05	0.538726
$495$	−563.828	−0.0511963
$496$	−5288.52	−0.478753
$497$	−10729.8	−0.968408
$498$	−2006.10	−0.180513
$499$	−159.784	−0.0143345	−0.00716725	−	0.999974i	$-0.502281\pi$
$499$	−159.784	−0.0143345	−0.00716725	+	0.999974i	$0.502281\pi$
$500$	1503.67	0.134492
$501$	−13005.2	−1.15974
$502$	−2965.02	−0.263616
$503$	−6117.45	−0.542274	−0.271137	−	0.962541i	$-0.587400\pi$
$503$	−6117.45	−0.542274	−0.271137	+	0.962541i	$0.587400\pi$
$504$	3043.83	0.269014
$505$	2957.67	0.260623
$506$	9241.57	0.811933
$507$	−5852.66	−0.512674
$508$	70.9438	0.00619611
$509$	−2953.79	−0.257219	−0.128610	−	0.991695i	$-0.541051\pi$
$509$	−2953.79	−0.257219	−0.128610	+	0.991695i	$0.541051\pi$
$510$	−279.727	−0.0242873
$511$	−5477.01	−0.474146
$512$	512.000	0.0441942
$513$	−19510.1	−1.67913
$514$	−4580.35	−0.393056
$515$	−1366.49	−0.116922
$516$	2660.17	0.226953
$517$	−9423.27	−0.801615
$518$	−8455.96	−0.717247
$519$	−14353.2	−1.21394
$520$	−265.839	−0.0224189
$521$	−6433.70	−0.541009	−0.270504	−	0.962719i	$-0.587190\pi$
$521$	−6433.70	−0.541009	−0.270504	+	0.962719i	$0.587190\pi$
$522$	6937.72	0.581716
$523$	−9670.04	−0.808492	−0.404246	−	0.914650i	$-0.632466\pi$
$523$	−9670.04	−0.808492	−0.404246	+	0.914650i	$0.632466\pi$
$524$	10613.8	0.884862
$525$	10336.9	0.859310
$526$	−5631.22	−0.466792
$527$	−8939.45	−0.738915
$528$	−1316.19	−0.108485
$529$	24468.5	2.01106
$530$	455.724	0.0373497
$531$	6512.95	0.532275
$532$	−13358.3	−1.08864
$533$	−9376.07	−0.761956
$534$	8572.37	0.694686
$535$	−1041.12	−0.0841340
$536$	1998.34	0.161036
$537$	−7295.44	−0.586259
$538$	−538.000	−0.0431131
$539$	−6476.73	−0.517574
$540$	876.840	0.0698763
$541$	−9497.13	−0.754739	−0.377369	−	0.926063i	$-0.623171\pi$
$541$	−9497.13	−0.754739	−0.377369	+	0.926063i	$0.623171\pi$
$542$	−3489.77	−0.276566
$543$	7177.18	0.567224
$544$	865.459	0.0682101
$545$	324.111	0.0254741
$546$	−3689.29	−0.289170
$547$	−13128.8	−1.02623	−0.513115	−	0.858320i	$-0.671509\pi$
$547$	−13128.8	−1.02623	−0.513115	+	0.858320i	$0.671509\pi$
$548$	6802.98	0.530308
$549$	2191.13	0.170337
$550$	5924.17	0.459286
$551$	−30447.3	−2.35408
$552$	−5217.67	−0.402316
$553$	−10233.9	−0.786963
$554$	3537.76	0.271309
$555$	−884.341	−0.0676364
$556$	−6016.46	−0.458911
$557$	−25580.9	−1.94595	−0.972976	−	0.230905i	$-0.925831\pi$
$557$	−25580.9	−1.94595	−0.972976	+	0.230905i	$0.925831\pi$
$558$	10173.1	0.771796
$559$	4273.38	0.323335
$560$	600.362	0.0453034
$561$	−2224.83	−0.167437
$562$	3065.39	0.230081
$563$	3109.95	0.232804	0.116402	−	0.993202i	$-0.462864\pi$
$563$	3109.95	0.232804	0.116402	+	0.993202i	$0.462864\pi$
$564$	5320.25	0.397204
$565$	−1724.93	−0.128439
$566$	4420.05	0.328248
$567$	1895.76	0.140414
$568$	3471.86	0.256472
$569$	−23750.3	−1.74985	−0.874925	−	0.484258i	$-0.839090\pi$
$569$	−23750.3	−1.74985	−0.874925	+	0.484258i	$0.839090\pi$
$570$	−1397.04	−0.102659
$571$	2105.75	0.154331	0.0771654	−	0.997018i	$-0.475413\pi$
$571$	2105.75	0.154331	0.0771654	+	0.997018i	$0.475413\pi$
$572$	−2114.37	−0.154556
$573$	5396.67	0.393454
$574$	21174.6	1.53974
$575$	23484.7	1.70327
$576$	−984.895	−0.0712453
$577$	−116.705	−0.00842028	−0.00421014	−	0.999991i	$-0.501340\pi$
$577$	−116.705	−0.00842028	−0.00421014	+	0.999991i	$0.501340\pi$
$578$	−8363.07	−0.601830
$579$	4463.90	0.320403
$580$	1368.39	0.0979642
$581$	7277.92	0.519688
$582$	−591.195	−0.0421062
$583$	3624.63	0.257490
$584$	1772.20	0.125572
$585$	511.374	0.0361414
$586$	−17894.0	−1.26142
$587$	14628.0	1.02856	0.514278	−	0.857624i	$-0.328060\pi$
$587$	14628.0	1.02856	0.514278	+	0.857624i	$0.328060\pi$
$588$	3656.67	0.256460
$589$	−44646.3	−3.12329
$590$	1284.61	0.0896380
$591$	8852.12	0.616121
$592$	2736.10	0.189955
$593$	3363.86	0.232946	0.116473	−	0.993194i	$-0.462841\pi$
$593$	3363.86	0.232946	0.116473	+	0.993194i	$0.462841\pi$
$594$	6974.01	0.481729
$595$	1014.82	0.0699221
$596$	6101.32	0.419329
$597$	−4745.39	−0.325320
$598$	−8381.80	−0.573173
$599$	19587.8	1.33612	0.668059	−	0.744108i	$-0.267125\pi$
$599$	19587.8	1.33612	0.668059	+	0.744108i	$0.267125\pi$
$600$	−3344.71	−0.227578
$601$	−26502.6	−1.79877	−0.899387	−	0.437153i	$-0.855987\pi$
$601$	−26502.6	−1.79877	−0.899387	+	0.437153i	$0.855987\pi$
$602$	−9650.84	−0.653387
$603$	−3844.06	−0.259605
$604$	2692.38	0.181377
$605$	1135.49	0.0763044
$606$	−13281.4	−0.890294
$607$	−22872.0	−1.52940	−0.764698	−	0.644388i	$-0.777112\pi$
$607$	−22872.0	−1.52940	−0.764698	+	0.644388i	$0.777112\pi$
$608$	4322.37	0.288314
$609$	18990.3	1.26359
$610$	432.175	0.0286857
$611$	8546.60	0.565890
$612$	−1664.82	−0.109961
$613$	−18154.1	−1.19615	−0.598073	−	0.801442i	$-0.704067\pi$
$613$	−18154.1	−1.19615	−0.598073	+	0.801442i	$0.704067\pi$
$614$	16373.6	1.07619
$615$	2214.48	0.145197
$616$	4775.02	0.312323
$617$	−15347.7	−1.00142	−0.500708	−	0.865616i	$-0.666927\pi$
$617$	−15347.7	−1.00142	−0.500708	+	0.865616i	$0.666927\pi$
$618$	6136.21	0.399409
$619$	25371.4	1.64743	0.823717	−	0.567001i	$-0.191897\pi$
$619$	25371.4	1.64743	0.823717	+	0.567001i	$0.191897\pi$
$620$	2006.53	0.129975
$621$	27646.4	1.78650
$622$	15921.4	1.02635
$623$	−31099.7	−1.99997
$624$	1193.74	0.0765834
$625$	14766.6	0.945061
$626$	3647.29	0.232867
$627$	−11111.5	−0.707734
$628$	−4100.40	−0.260547
$629$	4624.97	0.293179
$630$	−1154.87	−0.0730335
$631$	−8022.02	−0.506104	−0.253052	−	0.967453i	$-0.581434\pi$
$631$	−8022.02	−0.506104	−0.253052	+	0.967453i	$0.581434\pi$
$632$	3311.40	0.208418
$633$	−3951.61	−0.248124
$634$	−7238.21	−0.453417
$635$	−26.9170	−0.00168216
$636$	−2046.42	−0.127588
$637$	5874.18	0.365375
$638$	10883.6	0.675368
$639$	−6678.55	−0.413457
$640$	−194.259	−0.0119981
$641$	21454.8	1.32202	0.661010	−	0.750377i	$-0.270128\pi$
$641$	21454.8	1.32202	0.661010	+	0.750377i	$0.270128\pi$
$642$	4675.15	0.287404
$643$	23631.8	1.44937	0.724686	−	0.689080i	$-0.241985\pi$
$643$	23631.8	1.44937	0.724686	+	0.689080i	$0.241985\pi$
$644$	18929.2	1.15825
$645$	−1009.30	−0.0616144
$646$	7306.32	0.444989
$647$	6347.20	0.385679	0.192840	−	0.981230i	$-0.438230\pi$
$647$	6347.20	0.385679	0.192840	+	0.981230i	$0.438230\pi$
$648$	−613.413	−0.0371869
$649$	10217.2	0.617968
$650$	−5373.03	−0.324227
$651$	27846.4	1.67648
$652$	8893.84	0.534217
$653$	2481.65	0.148721	0.0743603	−	0.997231i	$-0.476308\pi$
$653$	2481.65	0.148721	0.0743603	+	0.997231i	$0.476308\pi$
$654$	−1455.41	−0.0870202
$655$	−4027.03	−0.240228
$656$	−6851.48	−0.407782
$657$	−3409.05	−0.202435
$658$	−19301.4	−1.14353
$659$	−10707.7	−0.632951	−0.316475	−	0.948601i	$-0.602499\pi$
$659$	−10707.7	−0.632951	−0.316475	+	0.948601i	$0.602499\pi$
$660$	499.381	0.0294521
$661$	−32837.0	−1.93224	−0.966120	−	0.258093i	$-0.916906\pi$
$661$	−32837.0	−1.93224	−0.966120	+	0.258093i	$0.916906\pi$
$662$	−3194.82	−0.187568
$663$	2017.85	0.118200
$664$	−2354.92	−0.137634
$665$	5068.33	0.295551
$666$	−5263.23	−0.306225
$667$	43144.8	2.50461
$668$	−15266.6	−0.884256
$669$	−17100.8	−0.988271
$670$	−758.197	−0.0437189
$671$	3437.34	0.197760
$672$	−2695.91	−0.154758
$673$	13069.6	0.748583	0.374291	−	0.927311i	$-0.377886\pi$
$673$	13069.6	0.748583	0.374291	+	0.927311i	$0.377886\pi$
$674$	−21457.0	−1.22625
$675$	17722.3	1.01057
$676$	−6870.33	−0.390893
$677$	−27617.9	−1.56786	−0.783932	−	0.620847i	$-0.786789\pi$
$677$	−27617.9	−1.56786	−0.783932	+	0.620847i	$0.786789\pi$
$678$	7745.75	0.438752
$679$	2144.80	0.121222
$680$	−328.367	−0.0185181
$681$	−10252.2	−0.576896
$682$	15959.1	0.896049
$683$	−8519.21	−0.477275	−0.238637	−	0.971109i	$-0.576701\pi$
$683$	−8519.21	−0.477275	−0.238637	+	0.971109i	$0.576701\pi$
$684$	−8314.60	−0.464791
$685$	−2581.14	−0.143971
$686$	3694.68	0.205632
$687$	−5285.56	−0.293532
$688$	3122.73	0.173042
$689$	−3287.42	−0.181772
$690$	1979.65	0.109223
$691$	31072.6	1.71065	0.855323	−	0.518096i	$-0.173359\pi$
$691$	31072.6	1.71065	0.855323	+	0.518096i	$0.173359\pi$
$692$	−16849.0	−0.925581
$693$	−9185.34	−0.503495
$694$	−17081.6	−0.934305
$695$	2282.72	0.124588
$696$	−6144.72	−0.334648
$697$	−11581.4	−0.629378
$698$	21776.9	1.18090
$699$	1471.08	0.0796014
$700$	12134.3	0.655189
$701$	662.282	0.0356834	0.0178417	−	0.999841i	$-0.494321\pi$
$701$	662.282	0.0356834	0.0178417	+	0.999841i	$0.494321\pi$
$702$	−6325.20	−0.340070
$703$	23098.5	1.23923
$704$	−1545.06	−0.0827153
$705$	−2018.57	−0.107835
$706$	−3520.05	−0.187647
$707$	48183.5	2.56312
$708$	−5768.50	−0.306206
$709$	9426.56	0.499326	0.249663	−	0.968333i	$-0.419680\pi$
$709$	9426.56	0.499326	0.249663	+	0.968333i	$0.419680\pi$
$710$	−1317.27	−0.0696285
$711$	−6369.88	−0.335991
$712$	10063.0	0.529670
$713$	63265.2	3.32300
$714$	−4557.04	−0.238856
$715$	802.219	0.0419599
$716$	−8563.99	−0.446999
$717$	−6460.89	−0.336522
$718$	−12926.9	−0.671906
$719$	−30710.1	−1.59290	−0.796450	−	0.604705i	$-0.793291\pi$
$719$	−30710.1	−1.59290	−0.796450	+	0.604705i	$0.793291\pi$
$720$	373.682	0.0193421
$721$	−22261.6	−1.14988
$722$	22772.0	1.17380
$723$	−3689.64	−0.189791
$724$	8425.17	0.432485
$725$	27657.3	1.41678
$726$	−5098.89	−0.260658
$727$	22568.5	1.15133	0.575667	−	0.817684i	$-0.304742\pi$
$727$	22568.5	1.15133	0.575667	+	0.817684i	$0.304742\pi$
$728$	−4330.79	−0.220480
$729$	14468.8	0.735092
$730$	−672.396	−0.0340911
$731$	5278.51	0.267076
$732$	−1940.67	−0.0979909
$733$	4535.51	0.228544	0.114272	−	0.993449i	$-0.463546\pi$
$733$	4535.51	0.228544	0.114272	+	0.993449i	$0.463546\pi$
$734$	12913.7	0.649390
$735$	−1387.39	−0.0696254
$736$	−6124.93	−0.306750
$737$	−6030.37	−0.301400
$738$	13179.7	0.657385
$739$	31404.5	1.56324	0.781619	−	0.623756i	$-0.214394\pi$
$739$	31404.5	1.56324	0.781619	+	0.623756i	$0.214394\pi$
$740$	−1038.11	−0.0515700
$741$	10077.7	0.499616
$742$	7424.21	0.367320
$743$	12752.7	0.629677	0.314838	−	0.949145i	$-0.398050\pi$
$743$	12752.7	0.629677	0.314838	+	0.949145i	$0.398050\pi$
$744$	−9010.29	−0.443997
$745$	−2314.92	−0.113842
$746$	−15035.5	−0.737920
$747$	4529.98	0.221879
$748$	−2611.69	−0.127664
$749$	−16961.0	−0.827424
$750$	2561.87	0.124728
$751$	−2887.72	−0.140312	−0.0701560	−	0.997536i	$-0.522350\pi$
$751$	−2887.72	−0.140312	−0.0701560	+	0.997536i	$0.522350\pi$
$752$	6245.36	0.302852
$753$	−5051.64	−0.244478
$754$	−9871.05	−0.476767
$755$	−1021.53	−0.0492412
$756$	14284.6	0.687205
$757$	6581.74	0.316007	0.158004	−	0.987439i	$-0.449494\pi$
$757$	6581.74	0.316007	0.158004	+	0.987439i	$0.449494\pi$
$758$	−25328.8	−1.21370
$759$	15745.3	0.752988
$760$	−1639.96	−0.0782733
$761$	−3453.84	−0.164523	−0.0822613	−	0.996611i	$-0.526214\pi$
$761$	−3453.84	−0.164523	−0.0822613	+	0.996611i	$0.526214\pi$
$762$	120.870	0.00574629
$763$	5280.10	0.250527
$764$	6335.06	0.299993
$765$	631.653	0.0298529
$766$	13908.9	0.656070
$767$	−9266.69	−0.436246
$768$	872.319	0.0409858
$769$	30668.7	1.43816	0.719079	−	0.694928i	$-0.244564\pi$
$769$	30668.7	1.43816	0.719079	+	0.694928i	$0.244564\pi$
$770$	−1811.71	−0.0847913
$771$	−7803.76	−0.364521
$772$	5240.10	0.244294
$773$	9792.34	0.455635	0.227818	−	0.973704i	$-0.426841\pi$
$773$	9792.34	0.455635	0.227818	+	0.973704i	$0.426841\pi$
$774$	−6006.96	−0.278961
$775$	40555.2	1.87973
$776$	−693.994	−0.0321043
$777$	−14406.8	−0.665176
$778$	3342.27	0.154018
$779$	−57841.0	−2.66029
$780$	−452.922	−0.0207913
$781$	−10477.0	−0.480021
$782$	−10353.3	−0.473443
$783$	32558.6	1.48601
$784$	4292.51	0.195541
$785$	1555.74	0.0707349
$786$	18083.3	0.820623
$787$	38453.8	1.74171	0.870857	−	0.491536i	$-0.163564\pi$
$787$	38453.8	1.74171	0.870857	+	0.491536i	$0.163564\pi$
$788$	10391.4	0.469767
$789$	−9594.17	−0.432904
$790$	−1256.39	−0.0565826
$791$	−28100.8	−1.26315
$792$	2972.11	0.133345
$793$	−3117.55	−0.139606
$794$	−24466.7	−1.09356
$795$	776.438	0.0346382
$796$	−5570.53	−0.248043
$797$	−1335.78	−0.0593674	−0.0296837	−	0.999559i	$-0.509450\pi$
$797$	−1335.78	−0.0593674	−0.0296837	+	0.999559i	$0.509450\pi$
$798$	−22759.2	−1.00961
$799$	10556.8	0.467427
$800$	−3926.30	−0.173519
$801$	−19357.3	−0.853880
$802$	−26371.8	−1.16112
$803$	−5347.95	−0.235025
$804$	3404.67	0.149345
$805$	−7181.98	−0.314449
$806$	−14474.4	−0.632554
$807$	−916.616	−0.0399832
$808$	−15590.8	−0.678813
$809$	8481.43	0.368592	0.184296	−	0.982871i	$-0.440999\pi$
$809$	8481.43	0.368592	0.184296	+	0.982871i	$0.440999\pi$
$810$	232.737	0.0100957
$811$	−28127.1	−1.21785	−0.608925	−	0.793228i	$-0.708399\pi$
$811$	−28127.1	−1.21785	−0.608925	+	0.793228i	$0.708399\pi$
$812$	22292.5	0.963438
$813$	−5945.69	−0.256488
$814$	−8256.71	−0.355525
$815$	−3374.44	−0.145032
$816$	1474.52	0.0632582
$817$	26362.5	1.12889
$818$	18119.2	0.774479
$819$	8330.81	0.355436
$820$	2599.54	0.110707
$821$	−16757.1	−0.712337	−0.356168	−	0.934422i	$-0.615917\pi$
$821$	−16757.1	−0.712337	−0.356168	+	0.934422i	$0.615917\pi$
$822$	11590.6	0.491809
$823$	26047.5	1.10323	0.551614	−	0.834099i	$-0.314012\pi$
$823$	26047.5	1.10323	0.551614	+	0.834099i	$0.314012\pi$
$824$	7203.19	0.304533
$825$	10093.3	0.425943
$826$	20927.6	0.881554
$827$	−23807.6	−1.00105	−0.500526	−	0.865721i	$-0.666860\pi$
$827$	−23807.6	−1.00105	−0.500526	+	0.865721i	$0.666860\pi$
$828$	11782.1	0.494511
$829$	−11270.9	−0.472201	−0.236101	−	0.971729i	$-0.575869\pi$
$829$	−11270.9	−0.472201	−0.236101	+	0.971729i	$0.575869\pi$
$830$	893.488	0.0373656
$831$	6027.45	0.251612
$832$	1401.32	0.0583917
$833$	7255.84	0.301801
$834$	−10250.5	−0.425595
$835$	5792.35	0.240063
$836$	−13043.6	−0.539619
$837$	47742.2	1.97158
$838$	−18797.8	−0.774893
$839$	−33284.4	−1.36961	−0.684807	−	0.728725i	$-0.740113\pi$
$839$	−33284.4	−1.36961	−0.684807	+	0.728725i	$0.740113\pi$
$840$	1022.86	0.0420145
$841$	26421.6	1.08334
$842$	−20009.6	−0.818974
$843$	5222.65	0.213378
$844$	−4638.72	−0.189184
$845$	2606.69	0.106122
$846$	−12013.7	−0.488227
$847$	18498.3	0.750422
$848$	−2402.26	−0.0972804
$849$	7530.65	0.304418
$850$	−6636.82	−0.267813
$851$	−32731.3	−1.31847
$852$	5915.17	0.237853
$853$	15920.5	0.639049	0.319524	−	0.947578i	$-0.396477\pi$
$853$	15920.5	0.639049	0.319524	+	0.947578i	$0.396477\pi$
$854$	7040.58	0.282112
$855$	3154.67	0.126184
$856$	5488.08	0.219134
$857$	−35133.4	−1.40039	−0.700196	−	0.713951i	$-0.746904\pi$
$857$	−35133.4	−1.40039	−0.700196	+	0.713951i	$0.746904\pi$
$858$	−3602.35	−0.143336
$859$	−33334.7	−1.32406	−0.662029	−	0.749478i	$-0.730305\pi$
$859$	−33334.7	−1.32406	−0.662029	+	0.749478i	$0.730305\pi$
$860$	−1184.80	−0.0469785
$861$	36076.1	1.42796
$862$	30487.0	1.20463
$863$	28167.7	1.11105	0.555527	−	0.831498i	$-0.312516\pi$
$863$	28167.7	1.11105	0.555527	+	0.831498i	$0.312516\pi$
$864$	−4622.09	−0.181998
$865$	6392.72	0.251282
$866$	−2233.90	−0.0876570
$867$	−14248.6	−0.558139
$868$	32688.5	1.27825
$869$	−9992.77	−0.390082
$870$	2331.39	0.0908522
$871$	5469.36	0.212769
$872$	−1708.49	−0.0663494
$873$	1334.98	0.0517552
$874$	−51707.4	−2.00118
$875$	−9294.23	−0.359088
$876$	3019.38	0.116456
$877$	−20115.1	−0.774501	−0.387251	−	0.921974i	$-0.626575\pi$
$877$	−20115.1	−0.774501	−0.387251	+	0.921974i	$0.626575\pi$
$878$	18000.5	0.691901
$879$	−30486.8	−1.16985
$880$	586.215	0.0224560
$881$	28290.6	1.08188	0.540938	−	0.841062i	$-0.318069\pi$
$881$	28290.6	1.08188	0.540938	+	0.841062i	$0.318069\pi$
$882$	−8257.17	−0.315230
$883$	33470.4	1.27561	0.637807	−	0.770196i	$-0.279842\pi$
$883$	33470.4	1.27561	0.637807	+	0.770196i	$0.279842\pi$
$884$	2368.72	0.0901228
$885$	2188.65	0.0831305
$886$	−10837.7	−0.410949
$887$	−28668.7	−1.08523	−0.542616	−	0.839981i	$-0.682566\pi$
$887$	−28668.7	−1.08523	−0.542616	+	0.839981i	$0.682566\pi$
$888$	4661.63	0.176164
$889$	−438.506	−0.0165433
$890$	−3818.02	−0.143798
$891$	1851.09	0.0696003
$892$	−20074.3	−0.753516
$893$	52724.1	1.97575
$894$	10395.1	0.388886
$895$	3249.29	0.121354
$896$	−3164.69	−0.117996
$897$	−14280.5	−0.531562
$898$	−22608.0	−0.840131
$899$	74506.0	2.76409
$900$	7552.71	0.279730
$901$	−4060.65	−0.150144
$902$	20675.6	0.763219
$903$	−16442.6	−0.605953
$904$	9092.61	0.334531
$905$	−3196.62	−0.117414
$906$	4587.14	0.168209
$907$	17672.9	0.646988	0.323494	−	0.946230i	$-0.395143\pi$
$907$	17672.9	0.646988	0.323494	+	0.946230i	$0.395143\pi$
$908$	−12034.9	−0.439860
$909$	29990.8	1.09431
$910$	1643.16	0.0598573
$911$	−26005.8	−0.945784	−0.472892	−	0.881120i	$-0.656790\pi$
$911$	−26005.8	−0.945784	−0.472892	+	0.881120i	$0.656790\pi$
$912$	7364.22	0.267383
$913$	7106.42	0.257599
$914$	33022.7	1.19507
$915$	736.317	0.0266032
$916$	−6204.63	−0.223806
$917$	−65604.4	−2.36254
$918$	−7812.95	−0.280899
$919$	25914.6	0.930187	0.465094	−	0.885261i	$-0.346021\pi$
$919$	25914.6	0.930187	0.465094	+	0.885261i	$0.346021\pi$
$920$	2323.88	0.0832782
$921$	27896.4	0.998066
$922$	10410.6	0.371859
$923$	9502.30	0.338864
$924$	8135.43	0.289649
$925$	−20981.9	−0.745818
$926$	12836.4	0.455541
$927$	−13856.2	−0.490937
$928$	−7213.19	−0.255156
$929$	1775.24	0.0626951	0.0313476	−	0.999509i	$-0.490020\pi$
$929$	1775.24	0.0626951	0.0313476	+	0.999509i	$0.490020\pi$
$930$	3418.62	0.120539
$931$	36237.9	1.27567
$932$	1726.88	0.0606928
$933$	27126.1	0.951843
$934$	28075.9	0.983588
$935$	990.909	0.0346590
$936$	−2695.61	−0.0941331
$937$	−15444.3	−0.538466	−0.269233	−	0.963075i	$-0.586770\pi$
$937$	−15444.3	−0.538466	−0.269233	+	0.963075i	$0.586770\pi$
$938$	−12351.8	−0.429958
$939$	6214.06	0.215962
$940$	−2369.57	−0.0822200
$941$	32278.7	1.11823	0.559115	−	0.829090i	$-0.311141\pi$
$941$	32278.7	1.11823	0.559115	+	0.829090i	$0.311141\pi$
$942$	−6986.04	−0.241632
$943$	81962.5	2.83040
$944$	−6771.55	−0.233469
$945$	−5419.77	−0.186566
$946$	−9423.43	−0.323871
$947$	2548.59	0.0874529	0.0437265	−	0.999044i	$-0.486077\pi$
$947$	2548.59	0.0874529	0.0437265	+	0.999044i	$0.486077\pi$
$948$	5641.79	0.193288
$949$	4850.42	0.165913
$950$	−33146.3	−1.13201
$951$	−12332.1	−0.420500
$952$	−5349.43	−0.182118
$953$	−22955.4	−0.780271	−0.390136	−	0.920757i	$-0.627572\pi$
$953$	−22955.4	−0.780271	−0.390136	+	0.920757i	$0.627572\pi$
$954$	4621.03	0.156825
$955$	−2403.60	−0.0814438
$956$	−7584.33	−0.256585
$957$	18542.9	0.626338
$958$	13566.3	0.457523
$959$	−42049.4	−1.41590
$960$	−330.969	−0.0111271
$961$	79460.6	2.66727
$962$	7488.57	0.250978
$963$	−10557.0	−0.353265
$964$	−4331.21	−0.144708
$965$	−1988.16	−0.0663224
$966$	32250.5	1.07417
$967$	54820.1	1.82306	0.911528	−	0.411237i	$-0.134903\pi$
$967$	54820.1	1.82306	0.911528	+	0.411237i	$0.134903\pi$
$968$	−5985.50	−0.198741
$969$	12448.1	0.412684
$970$	263.310	0.00871586
$971$	2907.74	0.0961007	0.0480504	−	0.998845i	$-0.484699\pi$
$971$	2907.74	0.0961007	0.0480504	+	0.998845i	$0.484699\pi$
$972$	14554.4	0.480282
$973$	37187.9	1.22527
$974$	−1918.43	−0.0631113
$975$	−9154.29	−0.300689
$976$	−2278.12	−0.0747141
$977$	−43351.2	−1.41958	−0.709789	−	0.704415i	$-0.751210\pi$
$977$	−43351.2	−1.41958	−0.709789	+	0.704415i	$0.751210\pi$
$978$	15152.9	0.495435
$979$	−30366.9	−0.991348
$980$	−1628.63	−0.0530865
$981$	3286.48	0.106962
$982$	14741.0	0.479027
$983$	−11683.0	−0.379074	−0.189537	−	0.981874i	$-0.560699\pi$
$983$	−11683.0	−0.379074	−0.189537	+	0.981874i	$0.560699\pi$
$984$	−11673.2	−0.378178
$985$	−3942.61	−0.127535
$986$	−12192.8	−0.393812
$987$	−32884.6	−1.06052
$988$	11830.1	0.380937
$989$	−37356.5	−1.20108
$990$	−1127.66	−0.0362013
$991$	−44062.4	−1.41240	−0.706200	−	0.708013i	$-0.749592\pi$
$991$	−44062.4	−1.41240	−0.706200	+	0.708013i	$0.749592\pi$
$992$	−10577.0	−0.338529
$993$	−5443.17	−0.173951
$994$	−21459.7	−0.684768
$995$	2113.53	0.0673402
$996$	−4012.19	−0.127642
$997$	−30706.1	−0.975398	−0.487699	−	0.873012i	$-0.662164\pi$
$997$	−30706.1	−0.975398	−0.487699	+	0.873012i	$0.662164\pi$
$998$	−319.568	−0.0101360
$999$	−24700.2	−0.782262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.4.a.a.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.4.a.a.1.10	✓	13	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.40749 q^{3} +4.00000 q^{4} -1.51765 q^{5} +6.81499 q^{6} -24.7241 q^{7} +8.00000 q^{8} -15.3890 q^{9} -3.03530 q^{10} -24.1415 q^{11} +13.6300 q^{12} +21.8956 q^{13} -49.4482 q^{14} -5.17139 q^{15} +16.0000 q^{16} +27.0456 q^{17} -30.7780 q^{18} +135.074 q^{19} -6.07061 q^{20} -84.2473 q^{21} -48.2830 q^{22} -191.404 q^{23} +27.2600 q^{24} -122.697 q^{25} +43.7912 q^{26} -144.440 q^{27} -98.8965 q^{28} -225.412 q^{29} -10.3428 q^{30} -330.532 q^{31} +32.0000 q^{32} -82.2621 q^{33} +54.0912 q^{34} +37.5226 q^{35} -61.5559 q^{36} +171.006 q^{37} +270.148 q^{38} +74.6091 q^{39} -12.1412 q^{40} -428.217 q^{41} -168.495 q^{42} +195.171 q^{43} -96.5661 q^{44} +23.3551 q^{45} -382.808 q^{46} +390.335 q^{47} +54.5199 q^{48} +268.282 q^{49} -245.393 q^{50} +92.1578 q^{51} +87.5823 q^{52} -150.141 q^{53} -288.880 q^{54} +36.6384 q^{55} -197.793 q^{56} +460.264 q^{57} -450.824 q^{58} -423.222 q^{59} -20.6856 q^{60} -142.383 q^{61} -661.065 q^{62} +380.479 q^{63} +64.0000 q^{64} -33.2299 q^{65} -164.524 q^{66} +249.793 q^{67} +108.182 q^{68} -652.208 q^{69} +75.0452 q^{70} +433.982 q^{71} -123.112 q^{72} +221.525 q^{73} +342.013 q^{74} -418.088 q^{75} +540.296 q^{76} +596.878 q^{77} +149.218 q^{78} +413.925 q^{79} -24.2824 q^{80} -76.6766 q^{81} -856.435 q^{82} -294.365 q^{83} -336.989 q^{84} -41.0458 q^{85} +390.341 q^{86} -768.090 q^{87} -193.132 q^{88} +1257.87 q^{89} +46.7102 q^{90} -541.349 q^{91} -765.616 q^{92} -1126.29 q^{93} +780.669 q^{94} -204.995 q^{95} +109.040 q^{96} -86.7492 q^{97} +536.564 q^{98} +371.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 26 q^{2} - 15 q^{3} + 52 q^{4} - 41 q^{5} - 30 q^{6} - 60 q^{7} + 104 q^{8} + 48 q^{9} - 82 q^{10} - 110 q^{11} - 60 q^{12} - 140 q^{13} - 120 q^{14} - 113 q^{15} + 208 q^{16} - 214 q^{17} + 96 q^{18}+ \cdots + 767 q^{99}+O(q^{100}) \) 13 * q + 26 * q^2 - 15 * q^3 + 52 * q^4 - 41 * q^5 - 30 * q^6 - 60 * q^7 + 104 * q^8 + 48 * q^9 - 82 * q^10 - 110 * q^11 - 60 * q^12 - 140 * q^13 - 120 * q^14 - 113 * q^15 + 208 * q^16 - 214 * q^17 + 96 * q^18 - 120 * q^19 - 164 * q^20 - 353 * q^21 - 220 * q^22 - 459 * q^23 - 120 * q^24 - 90 * q^25 - 280 * q^26 - 465 * q^27 - 240 * q^28 - 707 * q^29 - 226 * q^30 - 556 * q^31 + 416 * q^32 - 807 * q^33 - 428 * q^34 - 570 * q^35 + 192 * q^36 - 915 * q^37 - 240 * q^38 - 734 * q^39 - 328 * q^40 - 991 * q^41 - 706 * q^42 - 201 * q^43 - 440 * q^44 - 1154 * q^45 - 918 * q^46 - 686 * q^47 - 240 * q^48 - 407 * q^49 - 180 * q^50 - 251 * q^51 - 560 * q^52 - 2068 * q^53 - 930 * q^54 - 459 * q^55 - 480 * q^56 - 1982 * q^57 - 1414 * q^58 - 949 * q^59 - 452 * q^60 - 1731 * q^61 - 1112 * q^62 - 1856 * q^63 + 832 * q^64 - 2258 * q^65 - 1614 * q^66 - 1047 * q^67 - 856 * q^68 + 587 * q^69 - 1140 * q^70 - 2152 * q^71 + 384 * q^72 - 149 * q^73 - 1830 * q^74 + 441 * q^75 - 480 * q^76 + 886 * q^77 - 1468 * q^78 - 1608 * q^79 - 656 * q^80 + 1633 * q^81 - 1982 * q^82 + 2073 * q^83 - 1412 * q^84 - 465 * q^85 - 402 * q^86 + 4403 * q^87 - 880 * q^88 + 815 * q^89 - 2308 * q^90 + 2051 * q^91 - 1836 * q^92 - 2113 * q^93 - 1372 * q^94 - 158 * q^95 - 480 * q^96 - 1011 * q^97 - 814 * q^98 + 767 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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