LMFDB - Embedded newform 1805.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 $ x^16 - 29x^14 + 339x^12 - 2038x^10 + 6639x^8 - 11261x^6 + 8701x^4 - 2592*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.51130$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51130 q^{2} -2.10371 q^{3} +4.30663 q^{4} +1.00000 q^{5} +5.28304 q^{6} +3.12429 q^{7} -5.79265 q^{8} +1.42558 q^{9} +O(q^{10})$	\(q-2.51130 q^{2} -2.10371 q^{3} +4.30663 q^{4} +1.00000 q^{5} +5.28304 q^{6} +3.12429 q^{7} -5.79265 q^{8} +1.42558 q^{9} -2.51130 q^{10} -4.95370 q^{11} -9.05989 q^{12} +5.68376 q^{13} -7.84604 q^{14} -2.10371 q^{15} +5.93383 q^{16} -1.64706 q^{17} -3.58006 q^{18} +4.30663 q^{20} -6.57260 q^{21} +12.4402 q^{22} +6.34734 q^{23} +12.1860 q^{24} +1.00000 q^{25} -14.2736 q^{26} +3.31212 q^{27} +13.4552 q^{28} -5.27521 q^{29} +5.28304 q^{30} +3.18951 q^{31} -3.31633 q^{32} +10.4211 q^{33} +4.13627 q^{34} +3.12429 q^{35} +6.13944 q^{36} +2.35365 q^{37} -11.9570 q^{39} -5.79265 q^{40} +5.55228 q^{41} +16.5058 q^{42} +2.47046 q^{43} -21.3338 q^{44} +1.42558 q^{45} -15.9401 q^{46} +1.64558 q^{47} -12.4830 q^{48} +2.76122 q^{49} -2.51130 q^{50} +3.46494 q^{51} +24.4779 q^{52} -11.2382 q^{53} -8.31773 q^{54} -4.95370 q^{55} -18.0980 q^{56} +13.2476 q^{58} +9.45450 q^{59} -9.05989 q^{60} +3.49701 q^{61} -8.00983 q^{62} +4.45393 q^{63} -3.53936 q^{64} +5.68376 q^{65} -26.1706 q^{66} +1.25927 q^{67} -7.09330 q^{68} -13.3529 q^{69} -7.84604 q^{70} -9.25071 q^{71} -8.25788 q^{72} -16.1903 q^{73} -5.91073 q^{74} -2.10371 q^{75} -15.4768 q^{77} +30.0275 q^{78} -1.92900 q^{79} +5.93383 q^{80} -11.2445 q^{81} -13.9434 q^{82} +8.15171 q^{83} -28.3058 q^{84} -1.64706 q^{85} -6.20408 q^{86} +11.0975 q^{87} +28.6951 q^{88} -0.254305 q^{89} -3.58006 q^{90} +17.7577 q^{91} +27.3357 q^{92} -6.70980 q^{93} -4.13254 q^{94} +6.97658 q^{96} -14.0882 q^{97} -6.93424 q^{98} -7.06188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.51130	−1.77576	−0.887879	−	0.460077i	$-0.847822\pi$
$2$	−2.51130	−1.77576	−0.887879	+	0.460077i	$0.847822\pi$
$3$	−2.10371	−1.21458	−0.607288	−	0.794482i	$-0.707742\pi$
$3$	−2.10371	−1.21458	−0.607288	+	0.794482i	$0.707742\pi$
$4$	4.30663	2.15332
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.28304	2.15679
$7$	3.12429	1.18087	0.590436	−	0.807084i	$-0.298956\pi$
$7$	3.12429	1.18087	0.590436	+	0.807084i	$0.298956\pi$
$8$	−5.79265	−2.04801
$9$	1.42558	0.475193
$10$	−2.51130	−0.794143
$11$	−4.95370	−1.49360	−0.746798	−	0.665051i	$-0.768410\pi$
$11$	−4.95370	−1.49360	−0.746798	+	0.665051i	$0.768410\pi$
$12$	−9.05989	−2.61537
$13$	5.68376	1.57639	0.788196	−	0.615424i	$-0.211015\pi$
$13$	5.68376	1.57639	0.788196	+	0.615424i	$0.211015\pi$
$14$	−7.84604	−2.09694
$15$	−2.10371	−0.543175
$16$	5.93383	1.48346
$17$	−1.64706	−0.399472	−0.199736	−	0.979850i	$-0.564008\pi$
$17$	−1.64706	−0.399472	−0.199736	+	0.979850i	$0.564008\pi$
$18$	−3.58006	−0.843827
$19$	0	0
$19$	0	0
$20$	4.30663	0.962993
$21$	−6.57260	−1.43426
$22$	12.4402	2.65227
$23$	6.34734	1.32351	0.661756	−	0.749720i	$-0.269812\pi$
$23$	6.34734	1.32351	0.661756	+	0.749720i	$0.269812\pi$
$24$	12.1860	2.48746
$25$	1.00000	0.200000
$26$	−14.2736	−2.79929
$27$	3.31212	0.637418
$28$	13.4552	2.54279
$29$	−5.27521	−0.979582	−0.489791	−	0.871840i	$-0.662927\pi$
$29$	−5.27521	−0.979582	−0.489791	+	0.871840i	$0.662927\pi$
$30$	5.28304	0.964547
$31$	3.18951	0.572854	0.286427	−	0.958102i	$-0.407532\pi$
$31$	3.18951	0.572854	0.286427	+	0.958102i	$0.407532\pi$
$32$	−3.31633	−0.586249
$33$	10.4211	1.81408
$34$	4.13627	0.709365
$35$	3.12429	0.528102
$36$	6.13944	1.02324
$37$	2.35365	0.386938	0.193469	−	0.981106i	$-0.438026\pi$
$37$	2.35365	0.386938	0.193469	+	0.981106i	$0.438026\pi$
$38$	0	0
$39$	−11.9570	−1.91465
$40$	−5.79265	−0.915899
$41$	5.55228	0.867120	0.433560	−	0.901125i	$-0.357257\pi$
$41$	5.55228	0.867120	0.433560	+	0.901125i	$0.357257\pi$
$42$	16.5058	2.54690
$43$	2.47046	0.376742	0.188371	−	0.982098i	$-0.439679\pi$
$43$	2.47046	0.376742	0.188371	+	0.982098i	$0.439679\pi$
$44$	−21.3338	−3.21619
$45$	1.42558	0.212513
$46$	−15.9401	−2.35024
$47$	1.64558	0.240032	0.120016	−	0.992772i	$-0.461705\pi$
$47$	1.64558	0.240032	0.120016	+	0.992772i	$0.461705\pi$
$48$	−12.4830	−1.80177
$49$	2.76122	0.394459
$50$	−2.51130	−0.355152
$51$	3.46494	0.485188
$52$	24.4779	3.39447
$53$	−11.2382	−1.54369	−0.771844	−	0.635812i	$-0.780666\pi$
$53$	−11.2382	−1.54369	−0.771844	+	0.635812i	$0.780666\pi$
$54$	−8.31773	−1.13190
$55$	−4.95370	−0.667957
$56$	−18.0980	−2.41844
$57$	0	0
$58$	13.2476	1.73950
$59$	9.45450	1.23087	0.615435	−	0.788187i	$-0.288980\pi$
$59$	9.45450	1.23087	0.615435	+	0.788187i	$0.288980\pi$
$60$	−9.05989	−1.16963
$61$	3.49701	0.447746	0.223873	−	0.974618i	$-0.428130\pi$
$61$	3.49701	0.447746	0.223873	+	0.974618i	$0.428130\pi$
$62$	−8.00983	−1.01725
$63$	4.45393	0.561142
$64$	−3.53936	−0.442420
$65$	5.68376	0.704984
$66$	−26.1706	−3.22138
$67$	1.25927	0.153844	0.0769219	−	0.997037i	$-0.475491\pi$
$67$	1.25927	0.153844	0.0769219	+	0.997037i	$0.475491\pi$
$68$	−7.09330	−0.860189
$69$	−13.3529	−1.60750
$70$	−7.84604	−0.937782
$71$	−9.25071	−1.09786	−0.548929	−	0.835869i	$-0.684964\pi$
$71$	−9.25071	−1.09786	−0.548929	+	0.835869i	$0.684964\pi$
$72$	−8.25788	−0.973201
$73$	−16.1903	−1.89494	−0.947468	−	0.319850i	$-0.896367\pi$
$73$	−16.1903	−1.89494	−0.947468	+	0.319850i	$0.896367\pi$
$74$	−5.91073	−0.687108
$75$	−2.10371	−0.242915
$76$	0	0
$77$	−15.4768	−1.76375
$78$	30.0275	3.39995
$79$	−1.92900	−0.217029	−0.108515	−	0.994095i	$-0.534609\pi$
$79$	−1.92900	−0.217029	−0.108515	+	0.994095i	$0.534609\pi$
$80$	5.93383	0.663422
$81$	−11.2445	−1.24938
$82$	−13.9434	−1.53980
$83$	8.15171	0.894767	0.447383	−	0.894342i	$-0.352356\pi$
$83$	8.15171	0.894767	0.447383	+	0.894342i	$0.352356\pi$
$84$	−28.3058	−3.08841
$85$	−1.64706	−0.178649
$86$	−6.20408	−0.669003
$87$	11.0975	1.18978
$88$	28.6951	3.05890
$89$	−0.254305	−0.0269562	−0.0134781	−	0.999909i	$-0.504290\pi$
$89$	−0.254305	−0.0269562	−0.0134781	+	0.999909i	$0.504290\pi$
$90$	−3.58006	−0.377371
$91$	17.7577	1.86152
$92$	27.3357	2.84994
$93$	−6.70980	−0.695774
$94$	−4.13254	−0.426239
$95$	0	0
$96$	6.97658	0.712044
$97$	−14.0882	−1.43044	−0.715221	−	0.698899i	$-0.753674\pi$
$97$	−14.0882	−1.43044	−0.715221	+	0.698899i	$0.753674\pi$
$98$	−6.93424	−0.700464
$99$	−7.06188	−0.709746
$100$	4.30663	0.430663
$101$	9.12025	0.907498	0.453749	−	0.891129i	$-0.350086\pi$
$101$	9.12025	0.907498	0.453749	+	0.891129i	$0.350086\pi$
$102$	−8.70150	−0.861577
$103$	10.1415	0.999274	0.499637	−	0.866235i	$-0.333467\pi$
$103$	10.1415	0.999274	0.499637	+	0.866235i	$0.333467\pi$
$104$	−32.9241	−3.22847
$105$	−6.57260	−0.641420
$106$	28.2226	2.74122
$107$	15.5854	1.50669	0.753347	−	0.657623i	$-0.228438\pi$
$107$	15.5854	1.50669	0.753347	+	0.657623i	$0.228438\pi$
$108$	14.2641	1.37256
$109$	−4.47986	−0.429093	−0.214546	−	0.976714i	$-0.568827\pi$
$109$	−4.47986	−0.429093	−0.214546	+	0.976714i	$0.568827\pi$
$110$	12.4402	1.18613
$111$	−4.95139	−0.469965
$112$	18.5390	1.75177
$113$	−2.93493	−0.276095	−0.138047	−	0.990426i	$-0.544083\pi$
$113$	−2.93493	−0.276095	−0.138047	+	0.990426i	$0.544083\pi$
$114$	0	0
$115$	6.34734	0.591892
$116$	−22.7184	−2.10935
$117$	8.10265	0.749090
$118$	−23.7431	−2.18573
$119$	−5.14591	−0.471725
$120$	12.1860	1.11243
$121$	13.5391	1.23083
$122$	−8.78205	−0.795089
$123$	−11.6804	−1.05318
$124$	13.7361	1.23354
$125$	1.00000	0.0894427
$126$	−11.1852	−0.996452
$127$	−6.79799	−0.603224	−0.301612	−	0.953431i	$-0.597525\pi$
$127$	−6.79799	−0.603224	−0.301612	+	0.953431i	$0.597525\pi$
$128$	15.5211	1.37188
$129$	−5.19713	−0.457582
$130$	−14.2736	−1.25188
$131$	9.41038	0.822188	0.411094	−	0.911593i	$-0.365147\pi$
$131$	9.41038	0.822188	0.411094	+	0.911593i	$0.365147\pi$
$132$	44.8800	3.90630
$133$	0	0
$134$	−3.16240	−0.273189
$135$	3.31212	0.285062
$136$	9.54087	0.818123
$137$	1.05674	0.0902837	0.0451419	−	0.998981i	$-0.485626\pi$
$137$	1.05674	0.0902837	0.0451419	+	0.998981i	$0.485626\pi$
$138$	33.5332	2.85454
$139$	4.77821	0.405282	0.202641	−	0.979253i	$-0.435048\pi$
$139$	4.77821	0.405282	0.202641	+	0.979253i	$0.435048\pi$
$140$	13.4552	1.13717
$141$	−3.46181	−0.291537
$142$	23.2313	1.94953
$143$	−28.1556	−2.35449
$144$	8.45914	0.704928
$145$	−5.27521	−0.438083
$146$	40.6588	3.36495
$147$	−5.80878	−0.479100
$148$	10.1363	0.833200
$149$	8.37678	0.686252	0.343126	−	0.939289i	$-0.388514\pi$
$149$	8.37678	0.686252	0.343126	+	0.939289i	$0.388514\pi$
$150$	5.28304	0.431358
$151$	−13.6896	−1.11404	−0.557021	−	0.830498i	$-0.688056\pi$
$151$	−13.6896	−1.11404	−0.557021	+	0.830498i	$0.688056\pi$
$152$	0	0
$153$	−2.34802	−0.189826
$154$	38.8669	3.13199
$155$	3.18951	0.256188
$156$	−51.4943	−4.12284
$157$	9.01310	0.719324	0.359662	−	0.933083i	$-0.382892\pi$
$157$	9.01310	0.719324	0.359662	+	0.933083i	$0.382892\pi$
$158$	4.84430	0.385392
$159$	23.6419	1.87493
$160$	−3.31633	−0.262179
$161$	19.8309	1.56290
$162$	28.2382	2.21860
$163$	14.1259	1.10643	0.553215	−	0.833039i	$-0.313401\pi$
$163$	14.1259	1.10643	0.553215	+	0.833039i	$0.313401\pi$
$164$	23.9116	1.86719
$165$	10.4211	0.811283
$166$	−20.4714	−1.58889
$167$	6.96322	0.538830	0.269415	−	0.963024i	$-0.413170\pi$
$167$	6.96322	0.538830	0.269415	+	0.963024i	$0.413170\pi$
$168$	38.0728	2.93738
$169$	19.3052	1.48501
$170$	4.13627	0.317238
$171$	0	0
$172$	10.6394	0.811246
$173$	−3.24026	−0.246352	−0.123176	−	0.992385i	$-0.539308\pi$
$173$	−3.24026	−0.246352	−0.123176	+	0.992385i	$0.539308\pi$
$174$	−27.8692	−2.11276
$175$	3.12429	0.236174
$176$	−29.3944	−2.21569
$177$	−19.8895	−1.49498
$178$	0.638636	0.0478678
$179$	17.2783	1.29144	0.645721	−	0.763574i	$-0.276557\pi$
$179$	17.2783	1.29144	0.645721	+	0.763574i	$0.276557\pi$
$180$	6.13944	0.457607
$181$	6.74026	0.501000	0.250500	−	0.968117i	$-0.419405\pi$
$181$	6.74026	0.501000	0.250500	+	0.968117i	$0.419405\pi$
$182$	−44.5951	−3.30561
$183$	−7.35668	−0.543822
$184$	−36.7679	−2.71057
$185$	2.35365	0.173044
$186$	16.8503	1.23553
$187$	8.15906	0.596649
$188$	7.08690	0.516865
$189$	10.3480	0.752709
$190$	0	0
$191$	−17.3734	−1.25709	−0.628546	−	0.777772i	$-0.716350\pi$
$191$	−17.3734	−1.25709	−0.628546	+	0.777772i	$0.716350\pi$
$192$	7.44578	0.537353
$193$	−0.543637	−0.0391318	−0.0195659	−	0.999809i	$-0.506228\pi$
$193$	−0.543637	−0.0391318	−0.0195659	+	0.999809i	$0.506228\pi$
$194$	35.3797	2.54012
$195$	−11.9570	−0.856256
$196$	11.8915	0.849396
$197$	13.6826	0.974844	0.487422	−	0.873167i	$-0.337937\pi$
$197$	13.6826	0.974844	0.487422	+	0.873167i	$0.337937\pi$
$198$	17.7345	1.26034
$199$	10.5803	0.750015	0.375008	−	0.927022i	$-0.377640\pi$
$199$	10.5803	0.750015	0.375008	+	0.927022i	$0.377640\pi$
$200$	−5.79265	−0.409602
$201$	−2.64913	−0.186855
$202$	−22.9037	−1.61150
$203$	−16.4813	−1.15676
$204$	14.9222	1.04476
$205$	5.55228	0.387788
$206$	−25.4684	−1.77447
$207$	9.04863	0.628923
$208$	33.7265	2.33851
$209$	0	0
$210$	16.5058	1.13901
$211$	−11.4128	−0.785687	−0.392844	−	0.919605i	$-0.628509\pi$
$211$	−11.4128	−0.785687	−0.392844	+	0.919605i	$0.628509\pi$
$212$	−48.3989	−3.32405
$213$	19.4608	1.33343
$214$	−39.1395	−2.67552
$215$	2.47046	0.168484
$216$	−19.1860	−1.30544
$217$	9.96498	0.676467
$218$	11.2503	0.761965
$219$	34.0597	2.30154
$220$	−21.3338	−1.43832
$221$	−9.36152	−0.629724
$222$	12.4344	0.834544
$223$	14.5808	0.976403	0.488202	−	0.872731i	$-0.337653\pi$
$223$	14.5808	0.976403	0.488202	+	0.872731i	$0.337653\pi$
$224$	−10.3612	−0.692286
$225$	1.42558	0.0950386
$226$	7.37048	0.490277
$227$	12.5892	0.835577	0.417789	−	0.908544i	$-0.362805\pi$
$227$	12.5892	0.835577	0.417789	+	0.908544i	$0.362805\pi$
$228$	0	0
$229$	15.4825	1.02311	0.511556	−	0.859250i	$-0.329069\pi$
$229$	15.4825	1.02311	0.511556	+	0.859250i	$0.329069\pi$
$230$	−15.9401	−1.05106
$231$	32.5587	2.14220
$232$	30.5575	2.00620
$233$	−24.3790	−1.59712	−0.798562	−	0.601912i	$-0.794406\pi$
$233$	−24.3790	−1.59712	−0.798562	+	0.601912i	$0.794406\pi$
$234$	−20.3482	−1.33020
$235$	1.64558	0.107346
$236$	40.7171	2.65045
$237$	4.05805	0.263598
$238$	12.9229	0.837670
$239$	−9.46971	−0.612544	−0.306272	−	0.951944i	$-0.599082\pi$
$239$	−9.46971	−0.612544	−0.306272	+	0.951944i	$0.599082\pi$
$240$	−12.4830	−0.805776
$241$	−13.6179	−0.877209	−0.438605	−	0.898680i	$-0.644527\pi$
$241$	−13.6179	−0.877209	−0.438605	+	0.898680i	$0.644527\pi$
$242$	−34.0008	−2.18566
$243$	13.7187	0.880054
$244$	15.0603	0.964140
$245$	2.76122	0.176408
$246$	29.3329	1.87020
$247$	0	0
$248$	−18.4758	−1.17321
$249$	−17.1488	−1.08676
$250$	−2.51130	−0.158829
$251$	−11.0705	−0.698761	−0.349381	−	0.936981i	$-0.613608\pi$
$251$	−11.0705	−0.698761	−0.349381	+	0.936981i	$0.613608\pi$
$252$	19.1814	1.20832
$253$	−31.4428	−1.97679
$254$	17.0718	1.07118
$255$	3.46494	0.216983
$256$	−31.8993	−1.99371
$257$	26.1626	1.63198	0.815990	−	0.578066i	$-0.196192\pi$
$257$	26.1626	1.63198	0.815990	+	0.578066i	$0.196192\pi$
$258$	13.0516	0.812555
$259$	7.35350	0.456924
$260$	24.4779	1.51805
$261$	−7.52023	−0.465491
$262$	−23.6323	−1.46001
$263$	−2.64467	−0.163078	−0.0815388	−	0.996670i	$-0.525983\pi$
$263$	−2.64467	−0.163078	−0.0815388	+	0.996670i	$0.525983\pi$
$264$	−60.3660	−3.71527
$265$	−11.2382	−0.690359
$266$	0	0
$267$	0.534982	0.0327404
$268$	5.42320	0.331275
$269$	8.50727	0.518698	0.259349	−	0.965784i	$-0.416492\pi$
$269$	8.50727	0.518698	0.259349	+	0.965784i	$0.416492\pi$
$270$	−8.31773	−0.506201
$271$	11.5872	0.703874	0.351937	−	0.936024i	$-0.385523\pi$
$271$	11.5872	0.703874	0.351937	+	0.936024i	$0.385523\pi$
$272$	−9.77340	−0.592599
$273$	−37.3571	−2.26095
$274$	−2.65380	−0.160322
$275$	−4.95370	−0.298719
$276$	−57.5062	−3.46147
$277$	11.4882	0.690257	0.345129	−	0.938555i	$-0.387835\pi$
$277$	11.4882	0.690257	0.345129	+	0.938555i	$0.387835\pi$
$278$	−11.9995	−0.719683
$279$	4.54690	0.272216
$280$	−18.0980	−1.08156
$281$	−9.08056	−0.541701	−0.270850	−	0.962621i	$-0.587305\pi$
$281$	−9.08056	−0.541701	−0.270850	+	0.962621i	$0.587305\pi$
$282$	8.69365	0.517699
$283$	−0.517991	−0.0307914	−0.0153957	−	0.999881i	$-0.504901\pi$
$283$	−0.517991	−0.0307914	−0.0153957	+	0.999881i	$0.504901\pi$
$284$	−39.8394	−2.36404
$285$	0	0
$286$	70.7073	4.18101
$287$	17.3470	1.02396
$288$	−4.72769	−0.278582
$289$	−14.2872	−0.840422
$290$	13.2476	0.777929
$291$	29.6375	1.73738
$292$	−69.7259	−4.08040
$293$	10.4819	0.612362	0.306181	−	0.951973i	$-0.400949\pi$
$293$	10.4819	0.612362	0.306181	+	0.951973i	$0.400949\pi$
$294$	14.5876	0.850767
$295$	9.45450	0.550462
$296$	−13.6339	−0.792453
$297$	−16.4072	−0.952045
$298$	−21.0366	−1.21862
$299$	36.0768	2.08637
$300$	−9.05989	−0.523073
$301$	7.71846	0.444885
$302$	34.3787	1.97827
$303$	−19.1863	−1.10223
$304$	0	0
$305$	3.49701	0.200238
$306$	5.89658	0.337085
$307$	8.66142	0.494334	0.247167	−	0.968973i	$-0.420500\pi$
$307$	8.66142	0.494334	0.247167	+	0.968973i	$0.420500\pi$
$308$	−66.6530	−3.79791
$309$	−21.3348	−1.21369
$310$	−8.00983	−0.454928
$311$	6.34099	0.359564	0.179782	−	0.983706i	$-0.442461\pi$
$311$	6.34099	0.359564	0.179782	+	0.983706i	$0.442461\pi$
$312$	69.2626	3.92122
$313$	16.9153	0.956109	0.478055	−	0.878330i	$-0.341342\pi$
$313$	16.9153	0.956109	0.478055	+	0.878330i	$0.341342\pi$
$314$	−22.6346	−1.27734
$315$	4.45393	0.250950
$316$	−8.30749	−0.467333
$317$	20.0369	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$317$	20.0369	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$318$	−59.3720	−3.32942
$319$	26.1318	1.46310
$320$	−3.53936	−0.197856
$321$	−32.7870	−1.82999
$322$	−49.8015	−2.77533
$323$	0	0
$324$	−48.4258	−2.69032
$325$	5.68376	0.315278
$326$	−35.4745	−1.96475
$327$	9.42431	0.521165
$328$	−32.1624	−1.77587
$329$	5.14127	0.283447
$330$	−26.1706	−1.44064
$331$	−27.0350	−1.48598	−0.742989	−	0.669304i	$-0.766593\pi$
$331$	−27.0350	−1.48598	−0.742989	+	0.669304i	$0.766593\pi$
$332$	35.1065	1.92672
$333$	3.35531	0.183870
$334$	−17.4868	−0.956833
$335$	1.25927	0.0688011
$336$	−39.0007	−2.12766
$337$	31.6620	1.72474	0.862368	−	0.506282i	$-0.168980\pi$
$337$	31.6620	1.72474	0.862368	+	0.506282i	$0.168980\pi$
$338$	−48.4811	−2.63702
$339$	6.17422	0.335338
$340$	−7.09330	−0.384688
$341$	−15.7999	−0.855612
$342$	0	0
$343$	−13.2432	−0.715066
$344$	−14.3105	−0.771573
$345$	−13.3529	−0.718898
$346$	8.13727	0.437462
$347$	30.8808	1.65777	0.828883	−	0.559422i	$-0.188977\pi$
$347$	30.8808	1.65777	0.828883	+	0.559422i	$0.188977\pi$
$348$	47.7929	2.56197
$349$	25.7784	1.37989	0.689944	−	0.723863i	$-0.257635\pi$
$349$	25.7784	1.37989	0.689944	+	0.723863i	$0.257635\pi$
$350$	−7.84604	−0.419389
$351$	18.8253	1.00482
$352$	16.4281	0.875620
$353$	12.3807	0.658958	0.329479	−	0.944163i	$-0.393127\pi$
$353$	12.3807	0.658958	0.329479	+	0.944163i	$0.393127\pi$
$354$	49.9485	2.65473
$355$	−9.25071	−0.490977
$356$	−1.09520	−0.0580453
$357$	10.8255	0.572945
$358$	−43.3910	−2.29329
$359$	−3.73114	−0.196922	−0.0984611	−	0.995141i	$-0.531392\pi$
$359$	−3.73114	−0.196922	−0.0984611	+	0.995141i	$0.531392\pi$
$360$	−8.25788	−0.435229
$361$	0	0
$362$	−16.9268	−0.889654
$363$	−28.4823	−1.49493
$364$	76.4761	4.00844
$365$	−16.1903	−0.847441
$366$	18.4748	0.965696
$367$	37.7390	1.96996	0.984979	−	0.172675i	$-0.0552411\pi$
$367$	37.7390	1.96996	0.984979	+	0.172675i	$0.0552411\pi$
$368$	37.6640	1.96337
$369$	7.91521	0.412049
$370$	−5.91073	−0.307284
$371$	−35.1115	−1.82290
$372$	−28.8967	−1.49822
$373$	−3.45498	−0.178892	−0.0894460	−	0.995992i	$-0.528510\pi$
$373$	−3.45498	−0.178892	−0.0894460	+	0.995992i	$0.528510\pi$
$374$	−20.4899	−1.05950
$375$	−2.10371	−0.108635
$376$	−9.53226	−0.491589
$377$	−29.9831	−1.54421
$378$	−25.9870	−1.33663
$379$	33.7181	1.73198	0.865992	−	0.500057i	$-0.166688\pi$
$379$	33.7181	1.73198	0.865992	+	0.500057i	$0.166688\pi$
$380$	0	0
$381$	14.3010	0.732661
$382$	43.6298	2.23229
$383$	30.2493	1.54567	0.772833	−	0.634610i	$-0.218839\pi$
$383$	30.2493	1.54567	0.772833	+	0.634610i	$0.218839\pi$
$384$	−32.6517	−1.66625
$385$	−15.4768	−0.788771
$386$	1.36524	0.0694887
$387$	3.52184	0.179025
$388$	−60.6728	−3.08019
$389$	−36.4027	−1.84569	−0.922846	−	0.385169i	$-0.874143\pi$
$389$	−36.4027	−1.84569	−0.922846	+	0.385169i	$0.874143\pi$
$390$	30.0275	1.52050
$391$	−10.4545	−0.528705
$392$	−15.9948	−0.807857
$393$	−19.7967	−0.998610
$394$	−34.3611	−1.73109
$395$	−1.92900	−0.0970585
$396$	−30.4130	−1.52831
$397$	−5.39732	−0.270884	−0.135442	−	0.990785i	$-0.543245\pi$
$397$	−5.39732	−0.270884	−0.135442	+	0.990785i	$0.543245\pi$
$398$	−26.5702	−1.33185
$399$	0	0
$400$	5.93383	0.296691
$401$	6.14232	0.306733	0.153366	−	0.988169i	$-0.450989\pi$
$401$	6.14232	0.306733	0.153366	+	0.988169i	$0.450989\pi$
$402$	6.65275	0.331809
$403$	18.1284	0.903042
$404$	39.2776	1.95413
$405$	−11.2445	−0.558742
$406$	41.3896	2.05413
$407$	−11.6593	−0.577929
$408$	−20.0712	−0.993672
$409$	−6.59785	−0.326243	−0.163121	−	0.986606i	$-0.552156\pi$
$409$	−6.59785	−0.326243	−0.163121	+	0.986606i	$0.552156\pi$
$410$	−13.9434	−0.688618
$411$	−2.22308	−0.109656
$412$	43.6758	2.15175
$413$	29.5386	1.45350
$414$	−22.7238	−1.11682
$415$	8.15171	0.400152
$416$	−18.8492	−0.924159
$417$	−10.0519	−0.492246
$418$	0	0
$419$	0.620825	0.0303293	0.0151646	−	0.999885i	$-0.495173\pi$
$419$	0.620825	0.0303293	0.0151646	+	0.999885i	$0.495173\pi$
$420$	−28.3058	−1.38118
$421$	−36.6340	−1.78543	−0.892717	−	0.450619i	$-0.851203\pi$
$421$	−36.6340	−1.78543	−0.892717	+	0.450619i	$0.851203\pi$
$422$	28.6609	1.39519
$423$	2.34590	0.114062
$424$	65.0991	3.16149
$425$	−1.64706	−0.0798943
$426$	−48.8719	−2.36785
$427$	10.9257	0.528731
$428$	67.1204	3.24439
$429$	59.2312	2.85971
$430$	−6.20408	−0.299187
$431$	−23.2448	−1.11966	−0.559831	−	0.828607i	$-0.689134\pi$
$431$	−23.2448	−1.11966	−0.559831	+	0.828607i	$0.689134\pi$
$432$	19.6536	0.945582
$433$	−7.40310	−0.355770	−0.177885	−	0.984051i	$-0.556926\pi$
$433$	−7.40310	−0.355770	−0.177885	+	0.984051i	$0.556926\pi$
$434$	−25.0251	−1.20124
$435$	11.0975	0.532084
$436$	−19.2931	−0.923973
$437$	0	0
$438$	−85.5342	−4.08698
$439$	31.5811	1.50729	0.753643	−	0.657284i	$-0.228295\pi$
$439$	31.5811	1.50729	0.753643	+	0.657284i	$0.228295\pi$
$440$	28.6951	1.36798
$441$	3.93633	0.187444
$442$	23.5096	1.11824
$443$	−11.3146	−0.537574	−0.268787	−	0.963200i	$-0.586623\pi$
$443$	−11.3146	−0.537574	−0.268787	+	0.963200i	$0.586623\pi$
$444$	−21.3238	−1.01198
$445$	−0.254305	−0.0120552
$446$	−36.6168	−1.73386
$447$	−17.6223	−0.833505
$448$	−11.0580	−0.522442
$449$	16.1601	0.762642	0.381321	−	0.924443i	$-0.375469\pi$
$449$	16.1601	0.762642	0.381321	+	0.924443i	$0.375469\pi$
$450$	−3.58006	−0.168765
$451$	−27.5043	−1.29513
$452$	−12.6397	−0.594519
$453$	28.7989	1.35309
$454$	−31.6154	−1.48378
$455$	17.7577	0.832496
$456$	0	0
$457$	−17.8117	−0.833196	−0.416598	−	0.909091i	$-0.636778\pi$
$457$	−17.8117	−0.833196	−0.416598	+	0.909091i	$0.636778\pi$
$458$	−38.8812	−1.81680
$459$	−5.45527	−0.254630
$460$	27.3357	1.27453
$461$	28.9495	1.34831	0.674156	−	0.738589i	$-0.264508\pi$
$461$	28.9495	1.34831	0.674156	+	0.738589i	$0.264508\pi$
$462$	−81.7646	−3.80403
$463$	−1.91583	−0.0890363	−0.0445181	−	0.999009i	$-0.514175\pi$
$463$	−1.91583	−0.0890363	−0.0445181	+	0.999009i	$0.514175\pi$
$464$	−31.3022	−1.45317
$465$	−6.70980	−0.311160
$466$	61.2231	2.83611
$467$	−27.8213	−1.28742	−0.643709	−	0.765270i	$-0.722605\pi$
$467$	−27.8213	−1.28742	−0.643709	+	0.765270i	$0.722605\pi$
$468$	34.8951	1.61303
$469$	3.93432	0.181670
$470$	−4.13254	−0.190620
$471$	−18.9609	−0.873672
$472$	−54.7666	−2.52084
$473$	−12.2379	−0.562701
$474$	−10.1910	−0.468087
$475$	0	0
$476$	−22.1616	−1.01577
$477$	−16.0210	−0.733550
$478$	23.7813	1.08773
$479$	−5.36777	−0.245260	−0.122630	−	0.992452i	$-0.539133\pi$
$479$	−5.36777	−0.245260	−0.122630	+	0.992452i	$0.539133\pi$
$480$	6.97658	0.318436
$481$	13.3776	0.609966
$482$	34.1988	1.55771
$483$	−41.7185	−1.89826
$484$	58.3081	2.65037
$485$	−14.0882	−0.639713
$486$	−34.4517	−1.56276
$487$	27.4702	1.24479	0.622396	−	0.782702i	$-0.286159\pi$
$487$	27.4702	1.24479	0.622396	+	0.782702i	$0.286159\pi$
$488$	−20.2570	−0.916990
$489$	−29.7168	−1.34384
$490$	−6.93424	−0.313257
$491$	16.7520	0.756007	0.378003	−	0.925804i	$-0.376611\pi$
$491$	16.7520	0.756007	0.378003	+	0.925804i	$0.376611\pi$
$492$	−50.3030	−2.26784
$493$	8.68861	0.391315
$494$	0	0
$495$	−7.06188	−0.317408
$496$	18.9260	0.849804
$497$	−28.9020	−1.29643
$498$	43.0658	1.92983
$499$	34.4373	1.54162	0.770812	−	0.637063i	$-0.219851\pi$
$499$	34.4373	1.54162	0.770812	+	0.637063i	$0.219851\pi$
$500$	4.30663	0.192599
$501$	−14.6486	−0.654450
$502$	27.8013	1.24083
$503$	−35.5634	−1.58569	−0.792847	−	0.609421i	$-0.791402\pi$
$503$	−35.5634	−1.58569	−0.792847	+	0.609421i	$0.791402\pi$
$504$	−25.8001	−1.14923
$505$	9.12025	0.405846
$506$	78.9623	3.51030
$507$	−40.6124	−1.80366
$508$	−29.2764	−1.29893
$509$	−14.2156	−0.630094	−0.315047	−	0.949076i	$-0.602020\pi$
$509$	−14.2156	−0.630094	−0.315047	+	0.949076i	$0.602020\pi$
$510$	−8.70150	−0.385309
$511$	−50.5834	−2.23768
$512$	49.0667	2.16846
$513$	0	0
$514$	−65.7022	−2.89800
$515$	10.1415	0.446889
$516$	−22.3821	−0.985319
$517$	−8.15169	−0.358511
$518$	−18.4669	−0.811387
$519$	6.81655	0.299213
$520$	−32.9241	−1.44382
$521$	29.3515	1.28591	0.642956	−	0.765903i	$-0.277708\pi$
$521$	29.3515	1.28591	0.642956	+	0.765903i	$0.277708\pi$
$522$	18.8856	0.826599
$523$	−3.11084	−0.136028	−0.0680138	−	0.997684i	$-0.521666\pi$
$523$	−3.11084	−0.136028	−0.0680138	+	0.997684i	$0.521666\pi$
$524$	40.5271	1.77043
$525$	−6.57260	−0.286852
$526$	6.64157	0.289586
$527$	−5.25333	−0.228839
$528$	61.8372	2.69112
$529$	17.2887	0.751682
$530$	28.2226	1.22591
$531$	13.4781	0.584901
$532$	0	0
$533$	31.5578	1.36692
$534$	−1.34350	−0.0581390
$535$	15.5854	0.673814
$536$	−7.29449	−0.315074
$537$	−36.3485	−1.56855
$538$	−21.3643	−0.921082
$539$	−13.6782	−0.589163
$540$	14.2641	0.613829
$541$	31.8726	1.37031	0.685156	−	0.728397i	$-0.259734\pi$
$541$	31.8726	1.37031	0.685156	+	0.728397i	$0.259734\pi$
$542$	−29.0990	−1.24991
$543$	−14.1795	−0.608502
$544$	5.46220	0.234190
$545$	−4.47986	−0.191896
$546$	93.8149	4.01491
$547$	−39.8253	−1.70281	−0.851403	−	0.524512i	$-0.824248\pi$
$547$	−39.8253	−1.70281	−0.851403	+	0.524512i	$0.824248\pi$
$548$	4.55101	0.194409
$549$	4.98526	0.212766
$550$	12.4402	0.530453
$551$	0	0
$552$	77.3489	3.29219
$553$	−6.02676	−0.256284
$554$	−28.8503	−1.22573
$555$	−4.95139	−0.210175
$556$	20.5780	0.872701
$557$	31.0713	1.31653	0.658267	−	0.752785i	$-0.271290\pi$
$557$	31.0713	1.31653	0.658267	+	0.752785i	$0.271290\pi$
$558$	−11.4186	−0.483390
$559$	14.0415	0.593894
$560$	18.5390	0.783417
$561$	−17.1643	−0.724675
$562$	22.8040	0.961930
$563$	−14.6493	−0.617394	−0.308697	−	0.951160i	$-0.599893\pi$
$563$	−14.6493	−0.617394	−0.308697	+	0.951160i	$0.599893\pi$
$564$	−14.9088	−0.627772
$565$	−2.93493	−0.123473
$566$	1.30083	0.0546780
$567$	−35.1310	−1.47536
$568$	53.5862	2.24843
$569$	12.4441	0.521684	0.260842	−	0.965381i	$-0.416000\pi$
$569$	12.4441	0.521684	0.260842	+	0.965381i	$0.416000\pi$
$570$	0	0
$571$	−1.00373	−0.0420047	−0.0210023	−	0.999779i	$-0.506686\pi$
$571$	−1.00373	−0.0420047	−0.0210023	+	0.999779i	$0.506686\pi$
$572$	−121.256	−5.06997
$573$	36.5484	1.52683
$574$	−43.5634	−1.81830
$575$	6.34734	0.264702
$576$	−5.04564	−0.210235
$577$	−26.5136	−1.10378	−0.551888	−	0.833918i	$-0.686092\pi$
$577$	−26.5136	−1.10378	−0.551888	+	0.833918i	$0.686092\pi$
$578$	35.8794	1.49239
$579$	1.14365	0.0475285
$580$	−22.7184	−0.943331
$581$	25.4684	1.05661
$582$	−74.4286	−3.08516
$583$	55.6708	2.30565
$584$	93.7850	3.88085
$585$	8.10265	0.335003
$586$	−26.3233	−1.08741
$587$	3.05673	0.126165	0.0630824	−	0.998008i	$-0.479907\pi$
$587$	3.05673	0.126165	0.0630824	+	0.998008i	$0.479907\pi$
$588$	−25.0163	−1.03166
$589$	0	0
$590$	−23.7431	−0.977487
$591$	−28.7841	−1.18402
$592$	13.9662	0.574006
$593$	28.4444	1.16807	0.584036	−	0.811728i	$-0.301473\pi$
$593$	28.4444	1.16807	0.584036	+	0.811728i	$0.301473\pi$
$594$	41.2035	1.69060
$595$	−5.14591	−0.210962
$596$	36.0757	1.47772
$597$	−22.2578	−0.910950
$598$	−90.5996	−3.70489
$599$	5.70853	0.233244	0.116622	−	0.993176i	$-0.462793\pi$
$599$	5.70853	0.233244	0.116622	+	0.993176i	$0.462793\pi$
$600$	12.1860	0.497493
$601$	11.4603	0.467475	0.233737	−	0.972300i	$-0.424904\pi$
$601$	11.4603	0.467475	0.233737	+	0.972300i	$0.424904\pi$
$602$	−19.3834	−0.790008
$603$	1.79518	0.0731055
$604$	−58.9560	−2.39889
$605$	13.5391	0.550444
$606$	48.1826	1.95729
$607$	44.5740	1.80920	0.904601	−	0.426260i	$-0.140169\pi$
$607$	44.5740	1.80920	0.904601	+	0.426260i	$0.140169\pi$
$608$	0	0
$609$	34.6718	1.40497
$610$	−8.78205	−0.355575
$611$	9.35307	0.378385
$612$	−10.1121	−0.408756
$613$	14.3027	0.577681	0.288840	−	0.957377i	$-0.406730\pi$
$613$	14.3027	0.577681	0.288840	+	0.957377i	$0.406730\pi$
$614$	−21.7514	−0.877817
$615$	−11.6804	−0.470998
$616$	89.6518	3.61217
$617$	−30.5611	−1.23034	−0.615171	−	0.788394i	$-0.710913\pi$
$617$	−30.5611	−1.23034	−0.615171	+	0.788394i	$0.710913\pi$
$618$	53.5781	2.15523
$619$	−23.5855	−0.947980	−0.473990	−	0.880530i	$-0.657187\pi$
$619$	−23.5855	−0.947980	−0.473990	+	0.880530i	$0.657187\pi$
$620$	13.7361	0.551654
$621$	21.0231	0.843630
$622$	−15.9241	−0.638499
$623$	−0.794523	−0.0318319
$624$	−70.9506	−2.84030
$625$	1.00000	0.0400000
$626$	−42.4794	−1.69782
$627$	0	0
$628$	38.8161	1.54893
$629$	−3.87661	−0.154571
$630$	−11.1852	−0.445627
$631$	39.8496	1.58639	0.793194	−	0.608969i	$-0.208417\pi$
$631$	39.8496	1.58639	0.793194	+	0.608969i	$0.208417\pi$
$632$	11.1740	0.444479
$633$	24.0091	0.954276
$634$	−50.3186	−1.99841
$635$	−6.79799	−0.269770
$636$	101.817	4.03731
$637$	15.6941	0.621823
$638$	−65.6249	−2.59811
$639$	−13.1876	−0.521694
$640$	15.5211	0.613524
$641$	17.0425	0.673139	0.336570	−	0.941659i	$-0.390733\pi$
$641$	17.0425	0.673139	0.336570	+	0.941659i	$0.390733\pi$
$642$	82.3381	3.24962
$643$	−6.92053	−0.272919	−0.136460	−	0.990646i	$-0.543572\pi$
$643$	−6.92053	−0.272919	−0.136460	+	0.990646i	$0.543572\pi$
$644$	85.4046	3.36541
$645$	−5.19713	−0.204637
$646$	0	0
$647$	46.2327	1.81760	0.908798	−	0.417237i	$-0.137001\pi$
$647$	46.2327	1.81760	0.908798	+	0.417237i	$0.137001\pi$
$648$	65.1353	2.55876
$649$	−46.8347	−1.83842
$650$	−14.2736	−0.559858
$651$	−20.9634	−0.821620
$652$	60.8353	2.38249
$653$	−17.4643	−0.683429	−0.341715	−	0.939804i	$-0.611008\pi$
$653$	−17.4643	−0.683429	−0.341715	+	0.939804i	$0.611008\pi$
$654$	−23.6673	−0.925464
$655$	9.41038	0.367694
$656$	32.9463	1.28634
$657$	−23.0806	−0.900460
$658$	−12.9113	−0.503334
$659$	−2.57667	−0.100373	−0.0501864	−	0.998740i	$-0.515982\pi$
$659$	−2.57667	−0.100373	−0.0501864	+	0.998740i	$0.515982\pi$
$660$	44.8800	1.74695
$661$	−30.6967	−1.19396	−0.596981	−	0.802255i	$-0.703633\pi$
$661$	−30.6967	−1.19396	−0.596981	+	0.802255i	$0.703633\pi$
$662$	67.8930	2.63874
$663$	19.6939	0.764847
$664$	−47.2201	−1.83249
$665$	0	0
$666$	−8.42620	−0.326509
$667$	−33.4836	−1.29649
$668$	29.9881	1.16027
$669$	−30.6737	−1.18591
$670$	−3.16240	−0.122174
$671$	−17.3231	−0.668752
$672$	21.7969	0.840833
$673$	−41.3838	−1.59523	−0.797614	−	0.603168i	$-0.793905\pi$
$673$	−41.3838	−1.59523	−0.797614	+	0.603168i	$0.793905\pi$
$674$	−79.5127	−3.06271
$675$	3.31212	0.127484
$676$	83.1403	3.19770
$677$	7.40965	0.284776	0.142388	−	0.989811i	$-0.454522\pi$
$677$	7.40965	0.284776	0.142388	+	0.989811i	$0.454522\pi$
$678$	−15.5053	−0.595479
$679$	−44.0157	−1.68917
$680$	9.54087	0.365876
$681$	−26.4841	−1.01487
$682$	39.6783	1.51936
$683$	−36.1799	−1.38439	−0.692193	−	0.721712i	$-0.743355\pi$
$683$	−36.1799	−1.38439	−0.692193	+	0.721712i	$0.743355\pi$
$684$	0	0
$685$	1.05674	0.0403761
$686$	33.2577	1.26978
$687$	−32.5706	−1.24265
$688$	14.6593	0.558881
$689$	−63.8754	−2.43346
$690$	33.5332	1.27659
$691$	−30.9212	−1.17630	−0.588150	−	0.808752i	$-0.700143\pi$
$691$	−30.9212	−1.17630	−0.588150	+	0.808752i	$0.700143\pi$
$692$	−13.9546	−0.530475
$693$	−22.0634	−0.838120
$694$	−77.5509	−2.94379
$695$	4.77821	0.181248
$696$	−64.2840	−2.43668
$697$	−9.14496	−0.346390
$698$	−64.7374	−2.45035
$699$	51.2863	1.93983
$700$	13.4552	0.508558
$701$	−39.0955	−1.47662	−0.738308	−	0.674463i	$-0.764375\pi$
$701$	−39.0955	−1.47662	−0.738308	+	0.674463i	$0.764375\pi$
$702$	−47.2760	−1.78432
$703$	0	0
$704$	17.5329	0.660797
$705$	−3.46181	−0.130379
$706$	−31.0917	−1.17015
$707$	28.4943	1.07164
$708$	−85.6567	−3.21918
$709$	−31.3976	−1.17916	−0.589580	−	0.807710i	$-0.700707\pi$
$709$	−31.3976	−1.17916	−0.589580	+	0.807710i	$0.700707\pi$
$710$	23.2313	0.871856
$711$	−2.74994	−0.103131
$712$	1.47310	0.0552067
$713$	20.2449	0.758178
$714$	−27.1861	−1.01741
$715$	−28.1556	−1.05296
$716$	74.4113	2.78088
$717$	19.9215	0.743981
$718$	9.37003	0.349686
$719$	22.8519	0.852234	0.426117	−	0.904668i	$-0.359881\pi$
$719$	22.8519	0.852234	0.426117	+	0.904668i	$0.359881\pi$
$720$	8.45914	0.315254
$721$	31.6851	1.18002
$722$	0	0
$723$	28.6482	1.06544
$724$	29.0278	1.07881
$725$	−5.27521	−0.195916
$726$	71.5277	2.65464
$727$	−37.8752	−1.40471	−0.702356	−	0.711825i	$-0.747869\pi$
$727$	−37.8752	−1.40471	−0.702356	+	0.711825i	$0.747869\pi$
$728$	−102.864	−3.81241
$729$	4.87332	0.180493
$730$	40.6588	1.50485
$731$	−4.06901	−0.150498
$732$	−31.6825	−1.17102
$733$	49.0665	1.81231	0.906156	−	0.422943i	$-0.139003\pi$
$733$	49.0665	1.81231	0.906156	+	0.422943i	$0.139003\pi$
$734$	−94.7739	−3.49817
$735$	−5.80878	−0.214260
$736$	−21.0498	−0.775908
$737$	−6.23802	−0.229781
$738$	−19.8775	−0.731700
$739$	−24.8489	−0.914083	−0.457041	−	0.889445i	$-0.651091\pi$
$739$	−24.8489	−0.914083	−0.457041	+	0.889445i	$0.651091\pi$
$740$	10.1363	0.372618
$741$	0	0
$742$	88.1756	3.23703
$743$	−3.38789	−0.124290	−0.0621449	−	0.998067i	$-0.519794\pi$
$743$	−3.38789	−0.124290	−0.0621449	+	0.998067i	$0.519794\pi$
$744$	38.8675	1.42495
$745$	8.37678	0.306901
$746$	8.67649	0.317669
$747$	11.6209	0.425187
$748$	35.1381	1.28478
$749$	48.6932	1.77921
$750$	5.28304	0.192909
$751$	36.3549	1.32661	0.663305	−	0.748349i	$-0.269153\pi$
$751$	36.3549	1.32661	0.663305	+	0.748349i	$0.269153\pi$
$752$	9.76458	0.356077
$753$	23.2890	0.848698
$754$	75.2965	2.74214
$755$	−13.6896	−0.498215
$756$	44.5652	1.62082
$757$	43.1009	1.56653	0.783264	−	0.621689i	$-0.213553\pi$
$757$	43.1009	1.56653	0.783264	+	0.621689i	$0.213553\pi$
$758$	−84.6764	−3.07559
$759$	66.1464	2.40096
$760$	0	0
$761$	−23.4043	−0.848406	−0.424203	−	0.905567i	$-0.639446\pi$
$761$	−23.4043	−0.848406	−0.424203	+	0.905567i	$0.639446\pi$
$762$	−35.9140	−1.30103
$763$	−13.9964	−0.506704
$764$	−74.8207	−2.70692
$765$	−2.34802	−0.0848928
$766$	−75.9650	−2.74473
$767$	53.7371	1.94033
$768$	67.1068	2.42151
$769$	31.7097	1.14348	0.571740	−	0.820435i	$-0.306269\pi$
$769$	31.7097	1.14348	0.571740	+	0.820435i	$0.306269\pi$
$770$	38.8669	1.40067
$771$	−55.0385	−1.98216
$772$	−2.34124	−0.0842632
$773$	−32.9231	−1.18416	−0.592081	−	0.805878i	$-0.701694\pi$
$773$	−32.9231	−1.18416	−0.592081	+	0.805878i	$0.701694\pi$
$774$	−8.84440	−0.317906
$775$	3.18951	0.114571
$776$	81.6081	2.92956
$777$	−15.4696	−0.554969
$778$	91.4182	3.27750
$779$	0	0
$780$	−51.4943	−1.84379
$781$	45.8252	1.63976
$782$	26.2543	0.938853
$783$	−17.4721	−0.624403
$784$	16.3846	0.585164
$785$	9.01310	0.321691
$786$	49.7154	1.77329
$787$	−4.80345	−0.171224	−0.0856122	−	0.996329i	$-0.527285\pi$
$787$	−4.80345	−0.171224	−0.0856122	+	0.996329i	$0.527285\pi$
$788$	58.9259	2.09915
$789$	5.56361	0.198070
$790$	4.84430	0.172352
$791$	−9.16957	−0.326032
$792$	40.9071	1.45357
$793$	19.8762	0.705824
$794$	13.5543	0.481024
$795$	23.6419	0.838492
$796$	45.5654	1.61502
$797$	7.86016	0.278421	0.139211	−	0.990263i	$-0.455544\pi$
$797$	7.86016	0.278421	0.139211	+	0.990263i	$0.455544\pi$
$798$	0	0
$799$	−2.71037	−0.0958860
$800$	−3.31633	−0.117250
$801$	−0.362531	−0.0128094
$802$	−15.4252	−0.544683
$803$	80.2021	2.83027
$804$	−11.4088	−0.402358
$805$	19.8309	0.698949
$806$	−45.5260	−1.60358
$807$	−17.8968	−0.629997
$808$	−52.8304	−1.85857
$809$	−49.1777	−1.72899	−0.864497	−	0.502637i	$-0.832363\pi$
$809$	−49.1777	−1.72899	−0.864497	+	0.502637i	$0.832363\pi$
$810$	28.2382	0.992190
$811$	−17.8049	−0.625216	−0.312608	−	0.949882i	$-0.601203\pi$
$811$	−17.8049	−0.625216	−0.312608	+	0.949882i	$0.601203\pi$
$812$	−70.9790	−2.49087
$813$	−24.3761	−0.854908
$814$	29.2800	1.02626
$815$	14.1259	0.494810
$816$	20.5604	0.719756
$817$	0	0
$818$	16.5692	0.579328
$819$	25.3151	0.884580
$820$	23.9116	0.835031
$821$	6.65278	0.232184	0.116092	−	0.993238i	$-0.462963\pi$
$821$	6.65278	0.232184	0.116092	+	0.993238i	$0.462963\pi$
$822$	5.58282	0.194723
$823$	43.1112	1.50276	0.751382	−	0.659868i	$-0.229388\pi$
$823$	43.1112	1.50276	0.751382	+	0.659868i	$0.229388\pi$
$824$	−58.7464	−2.04653
$825$	10.4211	0.362817
$826$	−74.1804	−2.58107
$827$	−2.01975	−0.0702336	−0.0351168	−	0.999383i	$-0.511180\pi$
$827$	−2.01975	−0.0702336	−0.0351168	+	0.999383i	$0.511180\pi$
$828$	38.9691	1.35427
$829$	43.1834	1.49982	0.749911	−	0.661538i	$-0.230096\pi$
$829$	43.1834	1.49982	0.749911	+	0.661538i	$0.230096\pi$
$830$	−20.4714	−0.710573
$831$	−24.1677	−0.838369
$832$	−20.1169	−0.697428
$833$	−4.54790	−0.157575
$834$	25.2435	0.874109
$835$	6.96322	0.240972
$836$	0	0
$837$	10.5641	0.365147
$838$	−1.55908	−0.0538575
$839$	−23.5701	−0.813730	−0.406865	−	0.913488i	$-0.633378\pi$
$839$	−23.5701	−0.813730	−0.406865	+	0.913488i	$0.633378\pi$
$840$	38.0728	1.31364
$841$	−1.17213	−0.0404183
$842$	91.9991	3.17050
$843$	19.1028	0.657936
$844$	−49.1506	−1.69183
$845$	19.3052	0.664118
$846$	−5.89126	−0.202546
$847$	42.3002	1.45345
$848$	−66.6857	−2.29000
$849$	1.08970	0.0373984
$850$	4.13627	0.141873
$851$	14.9394	0.512117
$852$	83.8105	2.87130
$853$	2.00073	0.0685038	0.0342519	−	0.999413i	$-0.489095\pi$
$853$	2.00073	0.0685038	0.0342519	+	0.999413i	$0.489095\pi$
$854$	−27.4377	−0.938899
$855$	0	0
$856$	−90.2806	−3.08573
$857$	36.0257	1.23061	0.615307	−	0.788288i	$-0.289032\pi$
$857$	36.0257	1.23061	0.615307	+	0.788288i	$0.289032\pi$
$858$	−148.747	−5.07815
$859$	−4.72013	−0.161049	−0.0805244	−	0.996753i	$-0.525659\pi$
$859$	−4.72013	−0.161049	−0.0805244	+	0.996753i	$0.525659\pi$
$860$	10.6394	0.362800
$861$	−36.4929	−1.24367
$862$	58.3746	1.98825
$863$	−46.1578	−1.57123	−0.785615	−	0.618716i	$-0.787653\pi$
$863$	−46.1578	−1.57123	−0.785615	+	0.618716i	$0.787653\pi$
$864$	−10.9841	−0.373686
$865$	−3.24026	−0.110172
$866$	18.5914	0.631762
$867$	30.0560	1.02076
$868$	42.9155	1.45665
$869$	9.55568	0.324154
$870$	−27.8692	−0.944853
$871$	7.15737	0.242518
$872$	25.9503	0.878787
$873$	−20.0839	−0.679735
$874$	0	0
$875$	3.12429	0.105620
$876$	146.683	4.95595
$877$	6.34689	0.214319	0.107160	−	0.994242i	$-0.465824\pi$
$877$	6.34689	0.214319	0.107160	+	0.994242i	$0.465824\pi$
$878$	−79.3097	−2.67657
$879$	−22.0509	−0.743759
$880$	−29.3944	−0.990885
$881$	−24.9919	−0.841999	−0.421000	−	0.907061i	$-0.638321\pi$
$881$	−24.9919	−0.841999	−0.421000	+	0.907061i	$0.638321\pi$
$882$	−9.88531	−0.332856
$883$	16.1645	0.543978	0.271989	−	0.962300i	$-0.412319\pi$
$883$	16.1645	0.543978	0.271989	+	0.962300i	$0.412319\pi$
$884$	−40.3166	−1.35600
$885$	−19.8895	−0.668577
$886$	28.4144	0.954601
$887$	15.2451	0.511881	0.255940	−	0.966693i	$-0.417615\pi$
$887$	15.2451	0.511881	0.255940	+	0.966693i	$0.417615\pi$
$888$	28.6817	0.962494
$889$	−21.2389	−0.712330
$890$	0.638636	0.0214071
$891$	55.7017	1.86608
$892$	62.7942	2.10251
$893$	0	0
$894$	44.2549	1.48010
$895$	17.2783	0.577550
$896$	48.4924	1.62002
$897$	−75.8949	−2.53406
$898$	−40.5829	−1.35427
$899$	−16.8254	−0.561157
$900$	6.13944	0.204648
$901$	18.5101	0.616660
$902$	69.0716	2.29983
$903$	−16.2374	−0.540346
$904$	17.0010	0.565445
$905$	6.74026	0.224054
$906$	−72.3226	−2.40276
$907$	12.7982	0.424957	0.212479	−	0.977166i	$-0.431846\pi$
$907$	12.7982	0.424957	0.212479	+	0.977166i	$0.431846\pi$
$908$	54.2173	1.79926
$909$	13.0016	0.431237
$910$	−44.5951	−1.47831
$911$	24.3164	0.805640	0.402820	−	0.915279i	$-0.368030\pi$
$911$	24.3164	0.805640	0.402820	+	0.915279i	$0.368030\pi$
$912$	0	0
$913$	−40.3811	−1.33642
$914$	44.7305	1.47955
$915$	−7.35668	−0.243204
$916$	66.6774	2.20308
$917$	29.4008	0.970900
$918$	13.6998	0.452162
$919$	−39.6895	−1.30924	−0.654619	−	0.755959i	$-0.727171\pi$
$919$	−39.6895	−1.30924	−0.654619	+	0.755959i	$0.727171\pi$
$920$	−36.7679	−1.21220
$921$	−18.2211	−0.600405
$922$	−72.7009	−2.39428
$923$	−52.5789	−1.73065
$924$	140.218	4.61284
$925$	2.35365	0.0773876
$926$	4.81123	0.158107
$927$	14.4575	0.474848
$928$	17.4943	0.574280
$929$	48.2685	1.58364	0.791819	−	0.610756i	$-0.209134\pi$
$929$	48.2685	1.58364	0.791819	+	0.610756i	$0.209134\pi$
$930$	16.8503	0.552544
$931$	0	0
$932$	−104.992	−3.43912
$933$	−13.3396	−0.436718
$934$	69.8678	2.28614
$935$	8.15906	0.266830
$936$	−46.9358	−1.53415
$937$	−42.6931	−1.39472	−0.697362	−	0.716719i	$-0.745643\pi$
$937$	−42.6931	−1.39472	−0.697362	+	0.716719i	$0.745643\pi$
$938$	−9.88026	−0.322602
$939$	−35.5848	−1.16127
$940$	7.08690	0.231149
$941$	7.87499	0.256717	0.128359	−	0.991728i	$-0.459029\pi$
$941$	7.87499	0.256717	0.128359	+	0.991728i	$0.459029\pi$
$942$	47.6165	1.55143
$943$	35.2422	1.14764
$944$	56.1014	1.82594
$945$	10.3480	0.336622
$946$	30.7331	0.999221
$947$	1.37526	0.0446899	0.0223449	−	0.999750i	$-0.492887\pi$
$947$	1.37526	0.0446899	0.0223449	+	0.999750i	$0.492887\pi$
$948$	17.4765	0.567611
$949$	−92.0221	−2.98716
$950$	0	0
$951$	−42.1517	−1.36686
$952$	29.8085	0.966099
$953$	−15.2382	−0.493612	−0.246806	−	0.969065i	$-0.579381\pi$
$953$	−15.2382	−0.493612	−0.246806	+	0.969065i	$0.579381\pi$
$954$	40.2335	1.30261
$955$	−17.3734	−0.562189
$956$	−40.7826	−1.31900
$957$	−54.9736	−1.77705
$958$	13.4801	0.435522
$959$	3.30158	0.106614
$960$	7.44578	0.240311
$961$	−20.8270	−0.671839
$962$	−33.5952	−1.08315
$963$	22.2182	0.715970
$964$	−58.6475	−1.88891
$965$	−0.543637	−0.0175003
$966$	104.768	3.37084
$967$	8.20129	0.263736	0.131868	−	0.991267i	$-0.457903\pi$
$967$	8.20129	0.263736	0.131868	+	0.991267i	$0.457903\pi$
$968$	−78.4275	−2.52075
$969$	0	0
$970$	35.3797	1.13598
$971$	−26.5480	−0.851967	−0.425983	−	0.904731i	$-0.640072\pi$
$971$	−26.5480	−0.851967	−0.425983	+	0.904731i	$0.640072\pi$
$972$	59.0813	1.89503
$973$	14.9285	0.478587
$974$	−68.9859	−2.21045
$975$	−11.9570	−0.382929
$976$	20.7507	0.664213
$977$	−24.9918	−0.799559	−0.399780	−	0.916611i	$-0.630913\pi$
$977$	−24.9918	−0.799559	−0.399780	+	0.916611i	$0.630913\pi$
$978$	74.6279	2.38634
$979$	1.25975	0.0402617
$980$	11.8915	0.379861
$981$	−6.38639	−0.203902
$982$	−42.0693	−1.34249
$983$	−33.0198	−1.05317	−0.526584	−	0.850123i	$-0.676527\pi$
$983$	−33.0198	−1.05317	−0.526584	+	0.850123i	$0.676527\pi$
$984$	67.6603	2.15693
$985$	13.6826	0.435963
$986$	−21.8197	−0.694882
$987$	−10.8157	−0.344268
$988$	0	0
$989$	15.6809	0.498623
$990$	17.7345	0.563640
$991$	−20.2980	−0.644787	−0.322394	−	0.946606i	$-0.604487\pi$
$991$	−20.2980	−0.644787	−0.322394	+	0.946606i	$0.604487\pi$
$992$	−10.5775	−0.335835
$993$	56.8737	1.80483
$994$	72.5815	2.30215
$995$	10.5803	0.335417
$996$	−73.8537	−2.34014
$997$	−57.6736	−1.82654	−0.913270	−	0.407354i	$-0.866451\pi$
$997$	−57.6736	−1.82654	−0.913270	+	0.407354i	$0.866451\pi$
$998$	−86.4824	−2.73755
$999$	7.79557	0.246641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.w.1.2	✓	16
5.4	even	2		9025.2.a.cm.1.15		16
19.18	odd	2	inner	1805.2.a.w.1.15	yes	16
95.94	odd	2		9025.2.a.cm.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.w.1.2	✓	16	1.1	even	1	trivial
1805.2.a.w.1.15	yes	16	19.18	odd	2	inner
9025.2.a.cm.1.2		16	95.94	odd	2
9025.2.a.cm.1.15		16	5.4	even	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51130 q^{2} -2.10371 q^{3} +4.30663 q^{4} +1.00000 q^{5} +5.28304 q^{6} +3.12429 q^{7} -5.79265 q^{8} +1.42558 q^{9} +O(q^{10})\)	\(q-2.51130 q^{2} -2.10371 q^{3} +4.30663 q^{4} +1.00000 q^{5} +5.28304 q^{6} +3.12429 q^{7} -5.79265 q^{8} +1.42558 q^{9} -2.51130 q^{10} -4.95370 q^{11} -9.05989 q^{12} +5.68376 q^{13} -7.84604 q^{14} -2.10371 q^{15} +5.93383 q^{16} -1.64706 q^{17} -3.58006 q^{18} +4.30663 q^{20} -6.57260 q^{21} +12.4402 q^{22} +6.34734 q^{23} +12.1860 q^{24} +1.00000 q^{25} -14.2736 q^{26} +3.31212 q^{27} +13.4552 q^{28} -5.27521 q^{29} +5.28304 q^{30} +3.18951 q^{31} -3.31633 q^{32} +10.4211 q^{33} +4.13627 q^{34} +3.12429 q^{35} +6.13944 q^{36} +2.35365 q^{37} -11.9570 q^{39} -5.79265 q^{40} +5.55228 q^{41} +16.5058 q^{42} +2.47046 q^{43} -21.3338 q^{44} +1.42558 q^{45} -15.9401 q^{46} +1.64558 q^{47} -12.4830 q^{48} +2.76122 q^{49} -2.51130 q^{50} +3.46494 q^{51} +24.4779 q^{52} -11.2382 q^{53} -8.31773 q^{54} -4.95370 q^{55} -18.0980 q^{56} +13.2476 q^{58} +9.45450 q^{59} -9.05989 q^{60} +3.49701 q^{61} -8.00983 q^{62} +4.45393 q^{63} -3.53936 q^{64} +5.68376 q^{65} -26.1706 q^{66} +1.25927 q^{67} -7.09330 q^{68} -13.3529 q^{69} -7.84604 q^{70} -9.25071 q^{71} -8.25788 q^{72} -16.1903 q^{73} -5.91073 q^{74} -2.10371 q^{75} -15.4768 q^{77} +30.0275 q^{78} -1.92900 q^{79} +5.93383 q^{80} -11.2445 q^{81} -13.9434 q^{82} +8.15171 q^{83} -28.3058 q^{84} -1.64706 q^{85} -6.20408 q^{86} +11.0975 q^{87} +28.6951 q^{88} -0.254305 q^{89} -3.58006 q^{90} +17.7577 q^{91} +27.3357 q^{92} -6.70980 q^{93} -4.13254 q^{94} +6.97658 q^{96} -14.0882 q^{97} -6.93424 q^{98} -7.06188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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