LMFDB - Embedded newform 2299.2.a.u.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2299,2,Mod(1,2299)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2299.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2299, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,1,-2,7,-14,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$18.3576074247$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 17 x^{12} + 15 x^{11} + 107 x^{10} - 80 x^{9} - 310 x^{8} + 179 x^{7} + 415 x^{6} + \cdots - 1 $ x^14 - x^13 - 17x^12 + 15x^11 + 107x^10 - 80x^9 - 310x^8 + 179x^7 + 415x^6 - 151x^5 - 230x^4 + 43x^3 + 41*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.200027$ of defining polynomial
Character	$\chi$	$=$	2299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.200027 q^{2} +1.22622 q^{3} -1.95999 q^{4} +0.0816230 q^{5} -0.245277 q^{6} +0.895749 q^{7} +0.792103 q^{8} -1.49638 q^{9} -0.0163268 q^{10} -2.40338 q^{12} -4.65387 q^{13} -0.179174 q^{14} +0.100088 q^{15} +3.76154 q^{16} +2.44487 q^{17} +0.299316 q^{18} +1.00000 q^{19} -0.159980 q^{20} +1.09839 q^{21} +7.88800 q^{23} +0.971294 q^{24} -4.99334 q^{25} +0.930897 q^{26} -5.51356 q^{27} -1.75566 q^{28} +5.07424 q^{29} -0.0200202 q^{30} -7.80907 q^{31} -2.33661 q^{32} -0.489040 q^{34} +0.0731137 q^{35} +2.93289 q^{36} +1.43731 q^{37} -0.200027 q^{38} -5.70667 q^{39} +0.0646538 q^{40} +2.33889 q^{41} -0.219707 q^{42} -6.94775 q^{43} -0.122139 q^{45} -1.57781 q^{46} -4.95312 q^{47} +4.61248 q^{48} -6.19763 q^{49} +0.998800 q^{50} +2.99796 q^{51} +9.12153 q^{52} -9.73085 q^{53} +1.10286 q^{54} +0.709525 q^{56} +1.22622 q^{57} -1.01498 q^{58} -8.02085 q^{59} -0.196171 q^{60} -10.9682 q^{61} +1.56202 q^{62} -1.34038 q^{63} -7.05569 q^{64} -0.379863 q^{65} -13.3839 q^{67} -4.79193 q^{68} +9.67244 q^{69} -0.0146247 q^{70} +1.99737 q^{71} -1.18529 q^{72} +0.533747 q^{73} -0.287500 q^{74} -6.12294 q^{75} -1.95999 q^{76} +1.14149 q^{78} +11.0792 q^{79} +0.307028 q^{80} -2.27171 q^{81} -0.467840 q^{82} +16.1770 q^{83} -2.15283 q^{84} +0.199558 q^{85} +1.38974 q^{86} +6.22215 q^{87} -8.40759 q^{89} +0.0244310 q^{90} -4.16870 q^{91} -15.4604 q^{92} -9.57565 q^{93} +0.990755 q^{94} +0.0816230 q^{95} -2.86521 q^{96} -0.103308 q^{97} +1.23969 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} - 2 q^{3} + 7 q^{4} - 14 q^{5} - 8 q^{6} - 4 q^{7} + 3 q^{8} - 2 q^{9} + 6 q^{10} - 8 q^{12} + 5 q^{13} - 6 q^{14} - 10 q^{15} + 5 q^{16} - 10 q^{17} - 6 q^{18} + 14 q^{19} - 16 q^{20} + 9 q^{21}+ \cdots - 42 q^{98}+O(q^{100}) $ 14 * q + q^2 - 2 * q^3 + 7 * q^4 - 14 * q^5 - 8 * q^6 - 4 * q^7 + 3 * q^8 - 2 * q^9 + 6 * q^10 - 8 * q^12 + 5 * q^13 - 6 * q^14 - 10 * q^15 + 5 * q^16 - 10 * q^17 - 6 * q^18 + 14 * q^19 - 16 * q^20 + 9 * q^21 - 21 * q^23 + 22 * q^24 + 6 * q^25 - 28 * q^26 + 4 * q^27 - 15 * q^28 + 3 * q^29 + 20 * q^30 - 13 * q^31 + 2 * q^32 - 10 * q^34 + 3 * q^35 - 17 * q^36 - 31 * q^37 + q^38 - 33 * q^39 - 28 * q^40 + 10 * q^41 - 18 * q^42 + 6 * q^43 - 11 * q^45 + 23 * q^46 - 16 * q^47 - 16 * q^48 - 8 * q^49 - 16 * q^50 - 2 * q^51 - 7 * q^52 - 42 * q^53 - 30 * q^54 - 30 * q^56 - 2 * q^57 - 16 * q^58 - 26 * q^59 - 5 * q^60 - 34 * q^61 + 15 * q^62 + 33 * q^63 - 23 * q^64 - 13 * q^65 + 12 * q^67 + 32 * q^68 - 33 * q^69 - 27 * q^70 - 38 * q^71 - 14 * q^72 + 9 * q^73 - 26 * q^74 + 15 * q^75 + 7 * q^76 + 3 * q^78 + 6 * q^79 - 30 * q^80 - 22 * q^81 + 28 * q^82 - 35 * q^83 - 13 * q^84 + 12 * q^85 - 68 * q^86 + 17 * q^87 - 54 * q^89 + 39 * q^90 - 94 * q^92 - 26 * q^93 - 14 * q^95 + 5 * q^96 - 31 * q^97 - 42 * q^98

Coefficient data

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

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

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

$2$	−0.200027	−0.141440	−0.0707201	−	0.997496i	$-0.522530\pi$
$2$	−0.200027	−0.141440	−0.0707201	+	0.997496i	$0.522530\pi$
$3$	1.22622	0.707959	0.353980	−	0.935253i	$-0.384828\pi$
$3$	1.22622	0.707959	0.353980	+	0.935253i	$0.384828\pi$
$4$	−1.95999	−0.979995
$5$	0.0816230	0.0365029	0.0182515	−	0.999833i	$-0.494190\pi$
$5$	0.0816230	0.0365029	0.0182515	+	0.999833i	$0.494190\pi$
$6$	−0.245277	−0.100134
$7$	0.895749	0.338561	0.169281	−	0.985568i	$-0.445856\pi$
$7$	0.895749	0.338561	0.169281	+	0.985568i	$0.445856\pi$
$8$	0.792103	0.280051
$9$	−1.49638	−0.498793
$10$	−0.0163268	−0.00516298
$11$	0	0
$11$	0	0
$12$	−2.40338	−0.693796
$13$	−4.65387	−1.29075	−0.645375	−	0.763866i	$-0.723299\pi$
$13$	−4.65387	−1.29075	−0.645375	+	0.763866i	$0.723299\pi$
$14$	−0.179174	−0.0478861
$15$	0.100088	0.0258426
$16$	3.76154	0.940384
$17$	2.44487	0.592969	0.296485	−	0.955038i	$-0.404186\pi$
$17$	2.44487	0.592969	0.296485	+	0.955038i	$0.404186\pi$
$18$	0.299316	0.0705494
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.159980	−0.0357727
$21$	1.09839	0.239688
$22$	0	0
$23$	7.88800	1.64476	0.822381	−	0.568937i	$-0.192645\pi$
$23$	7.88800	1.64476	0.822381	+	0.568937i	$0.192645\pi$
$24$	0.971294	0.198265
$25$	−4.99334	−0.998668
$26$	0.930897	0.182564
$27$	−5.51356	−1.06108
$28$	−1.75566	−0.331788
$29$	5.07424	0.942263	0.471132	−	0.882063i	$-0.343846\pi$
$29$	5.07424	0.942263	0.471132	+	0.882063i	$0.343846\pi$
$30$	−0.0200202	−0.00365518
$31$	−7.80907	−1.40255	−0.701275	−	0.712891i	$-0.747385\pi$
$31$	−7.80907	−1.40255	−0.701275	+	0.712891i	$0.747385\pi$
$32$	−2.33661	−0.413059
$33$	0	0
$34$	−0.489040	−0.0838696
$35$	0.0731137	0.0123585
$36$	2.93289	0.488815
$37$	1.43731	0.236292	0.118146	−	0.992996i	$-0.462305\pi$
$37$	1.43731	0.236292	0.118146	+	0.992996i	$0.462305\pi$
$38$	−0.200027	−0.0324486
$39$	−5.70667	−0.913799
$40$	0.0646538	0.0102227
$41$	2.33889	0.365273	0.182636	−	0.983181i	$-0.441537\pi$
$41$	2.33889	0.365273	0.182636	+	0.983181i	$0.441537\pi$
$42$	−0.219707	−0.0339015
$43$	−6.94775	−1.05952	−0.529761	−	0.848147i	$-0.677719\pi$
$43$	−6.94775	−1.05952	−0.529761	+	0.848147i	$0.677719\pi$
$44$	0	0
$45$	−0.122139	−0.0182074
$46$	−1.57781	−0.232635
$47$	−4.95312	−0.722486	−0.361243	−	0.932472i	$-0.617648\pi$
$47$	−4.95312	−0.722486	−0.361243	+	0.932472i	$0.617648\pi$
$48$	4.61248	0.665754
$49$	−6.19763	−0.885376
$50$	0.998800	0.141252
$51$	2.99796	0.419798
$52$	9.12153	1.26493
$53$	−9.73085	−1.33663	−0.668317	−	0.743876i	$-0.732985\pi$
$53$	−9.73085	−1.33663	−0.668317	+	0.743876i	$0.732985\pi$
$54$	1.10286	0.150080
$55$	0	0
$56$	0.709525	0.0948143
$57$	1.22622	0.162417
$58$	−1.01498	−0.133274
$59$	−8.02085	−1.04423	−0.522113	−	0.852876i	$-0.674856\pi$
$59$	−8.02085	−1.04423	−0.522113	+	0.852876i	$0.674856\pi$
$60$	−0.196171	−0.0253256
$61$	−10.9682	−1.40433	−0.702165	−	0.712014i	$-0.747783\pi$
$61$	−10.9682	−1.40433	−0.702165	+	0.712014i	$0.747783\pi$
$62$	1.56202	0.198377
$63$	−1.34038	−0.168872
$64$	−7.05569	−0.881961
$65$	−0.379863	−0.0471162
$66$	0	0
$67$	−13.3839	−1.63511	−0.817554	−	0.575852i	$-0.804670\pi$
$67$	−13.3839	−1.63511	−0.817554	+	0.575852i	$0.804670\pi$
$68$	−4.79193	−0.581107
$69$	9.67244	1.16443
$70$	−0.0146247	−0.00174798
$71$	1.99737	0.237044	0.118522	−	0.992951i	$-0.462184\pi$
$71$	1.99737	0.237044	0.118522	+	0.992951i	$0.462184\pi$
$72$	−1.18529	−0.139687
$73$	0.533747	0.0624703	0.0312352	−	0.999512i	$-0.490056\pi$
$73$	0.533747	0.0624703	0.0312352	+	0.999512i	$0.490056\pi$
$74$	−0.287500	−0.0334212
$75$	−6.12294	−0.707016
$76$	−1.95999	−0.224826
$77$	0	0
$78$	1.14149	0.129248
$79$	11.0792	1.24651	0.623254	−	0.782020i	$-0.285810\pi$
$79$	11.0792	1.24651	0.623254	+	0.782020i	$0.285810\pi$
$80$	0.307028	0.0343268
$81$	−2.27171	−0.252412
$82$	−0.467840	−0.0516642
$83$	16.1770	1.77565	0.887827	−	0.460178i	$-0.152215\pi$
$83$	16.1770	1.77565	0.887827	+	0.460178i	$0.152215\pi$
$84$	−2.15283	−0.234893
$85$	0.199558	0.0216451
$86$	1.38974	0.149859
$87$	6.22215	0.667084
$88$	0	0
$89$	−8.40759	−0.891203	−0.445602	−	0.895231i	$-0.647010\pi$
$89$	−8.40759	−0.891203	−0.445602	+	0.895231i	$0.647010\pi$
$90$	0.0244310	0.00257526
$91$	−4.16870	−0.436998
$92$	−15.4604	−1.61186
$93$	−9.57565	−0.992948
$94$	0.990755	0.102189
$95$	0.0816230	0.00837434
$96$	−2.86521	−0.292429
$97$	−0.103308	−0.0104894	−0.00524469	−	0.999986i	$-0.501669\pi$
$97$	−0.103308	−0.0104894	−0.00524469	+	0.999986i	$0.501669\pi$
$98$	1.23969	0.125228
$99$	0	0
$100$	9.78689	0.978689
$101$	−10.3789	−1.03274	−0.516370	−	0.856366i	$-0.672717\pi$
$101$	−10.3789	−1.03274	−0.516370	+	0.856366i	$0.672717\pi$
$102$	−0.599671	−0.0593763
$103$	−3.48528	−0.343415	−0.171708	−	0.985148i	$-0.554928\pi$
$103$	−3.48528	−0.343415	−0.171708	+	0.985148i	$0.554928\pi$
$104$	−3.68634	−0.361476
$105$	0.0896536	0.00874930
$106$	1.94643	0.189054
$107$	7.57460	0.732265	0.366132	−	0.930563i	$-0.380682\pi$
$107$	7.57460	0.732265	0.366132	+	0.930563i	$0.380682\pi$
$108$	10.8065	1.03986
$109$	14.3006	1.36975	0.684875	−	0.728661i	$-0.259857\pi$
$109$	14.3006	1.36975	0.684875	+	0.728661i	$0.259857\pi$
$110$	0	0
$111$	1.76246	0.167285
$112$	3.36939	0.318378
$113$	14.5393	1.36774	0.683870	−	0.729604i	$-0.260295\pi$
$113$	14.5393	1.36774	0.683870	+	0.729604i	$0.260295\pi$
$114$	−0.245277	−0.0229723
$115$	0.643842	0.0600386
$116$	−9.94546	−0.923413
$117$	6.96396	0.643818
$118$	1.60438	0.147695
$119$	2.18999	0.200756
$120$	0.0792799	0.00723723
$121$	0	0
$122$	2.19393	0.198629
$123$	2.86799	0.258598
$124$	15.3057	1.37449
$125$	−0.815686	−0.0729572
$126$	0.268112	0.0238853
$127$	−19.6947	−1.74762	−0.873811	−	0.486266i	$-0.838358\pi$
$127$	−19.6947	−1.74762	−0.873811	+	0.486266i	$0.838358\pi$
$128$	6.08455	0.537803
$129$	−8.51949	−0.750099
$130$	0.0759826	0.00666412
$131$	−14.6793	−1.28253	−0.641267	−	0.767318i	$-0.721591\pi$
$131$	−14.6793	−1.28253	−0.641267	+	0.767318i	$0.721591\pi$
$132$	0	0
$133$	0.895749	0.0776713
$134$	2.67714	0.231270
$135$	−0.450033	−0.0387327
$136$	1.93659	0.166061
$137$	−12.5169	−1.06939	−0.534695	−	0.845045i	$-0.679573\pi$
$137$	−12.5169	−1.06939	−0.534695	+	0.845045i	$0.679573\pi$
$138$	−1.93474	−0.164696
$139$	−6.90711	−0.585853	−0.292927	−	0.956135i	$-0.594629\pi$
$139$	−6.90711	−0.585853	−0.292927	+	0.956135i	$0.594629\pi$
$140$	−0.143302	−0.0121112
$141$	−6.07362	−0.511491
$142$	−0.399526	−0.0335275
$143$	0	0
$144$	−5.62869	−0.469058
$145$	0.414175	0.0343954
$146$	−0.106764	−0.00883581
$147$	−7.59967	−0.626810
$148$	−2.81711	−0.231565
$149$	−15.2444	−1.24887	−0.624433	−	0.781078i	$-0.714670\pi$
$149$	−15.2444	−1.24887	−0.624433	+	0.781078i	$0.714670\pi$
$150$	1.22475	0.100000
$151$	−6.13838	−0.499535	−0.249767	−	0.968306i	$-0.580354\pi$
$151$	−6.13838	−0.499535	−0.249767	+	0.968306i	$0.580354\pi$
$152$	0.792103	0.0642480
$153$	−3.65846	−0.295769
$154$	0	0
$155$	−0.637399	−0.0511971
$156$	11.1850	0.895518
$157$	−4.13567	−0.330063	−0.165031	−	0.986288i	$-0.552773\pi$
$157$	−4.13567	−0.330063	−0.165031	+	0.986288i	$0.552773\pi$
$158$	−2.21613	−0.176306
$159$	−11.9322	−0.946283
$160$	−0.190721	−0.0150778
$161$	7.06567	0.556853
$162$	0.454401	0.0357011
$163$	−15.9329	−1.24796	−0.623982	−	0.781439i	$-0.714486\pi$
$163$	−15.9329	−1.24796	−0.623982	+	0.781439i	$0.714486\pi$
$164$	−4.58419	−0.357965
$165$	0	0
$166$	−3.23582	−0.251149
$167$	−1.46039	−0.113008	−0.0565041	−	0.998402i	$-0.517995\pi$
$167$	−1.46039	−0.113008	−0.0565041	+	0.998402i	$0.517995\pi$
$168$	0.870035	0.0671247
$169$	8.65849	0.666037
$170$	−0.0399169	−0.00306149
$171$	−1.49638	−0.114431
$172$	13.6175	1.03833
$173$	14.6398	1.11304	0.556522	−	0.830833i	$-0.312135\pi$
$173$	14.6398	1.11304	0.556522	+	0.830833i	$0.312135\pi$
$174$	−1.24459	−0.0943525
$175$	−4.47278	−0.338110
$176$	0	0
$177$	−9.83534	−0.739270
$178$	1.68174	0.126052
$179$	−13.9305	−1.04121	−0.520606	−	0.853797i	$-0.674294\pi$
$179$	−13.9305	−1.04121	−0.520606	+	0.853797i	$0.674294\pi$
$180$	0.239391	0.0178432
$181$	18.4877	1.37418	0.687090	−	0.726573i	$-0.258888\pi$
$181$	18.4877	1.37418	0.687090	+	0.726573i	$0.258888\pi$
$182$	0.833850	0.0618091
$183$	−13.4494	−0.994209
$184$	6.24811	0.460617
$185$	0.117318	0.00862536
$186$	1.91538	0.140443
$187$	0	0
$188$	9.70806	0.708033
$189$	−4.93876	−0.359242
$190$	−0.0163268	−0.00118447
$191$	−4.36556	−0.315881	−0.157941	−	0.987449i	$-0.550485\pi$
$191$	−4.36556	−0.315881	−0.157941	+	0.987449i	$0.550485\pi$
$192$	−8.65184	−0.624393
$193$	6.81018	0.490208	0.245104	−	0.969497i	$-0.421178\pi$
$193$	6.81018	0.490208	0.245104	+	0.969497i	$0.421178\pi$
$194$	0.0206644	0.00148362
$195$	−0.465796	−0.0333563
$196$	12.1473	0.867664
$197$	−10.5905	−0.754542	−0.377271	−	0.926103i	$-0.623137\pi$
$197$	−10.5905	−0.754542	−0.377271	+	0.926103i	$0.623137\pi$
$198$	0	0
$199$	2.81828	0.199782	0.0998911	−	0.994998i	$-0.468151\pi$
$199$	2.81828	0.199782	0.0998911	+	0.994998i	$0.468151\pi$
$200$	−3.95524	−0.279678
$201$	−16.4117	−1.15759
$202$	2.07606	0.146071
$203$	4.54525	0.319014
$204$	−5.87597	−0.411400
$205$	0.190907	0.0133335
$206$	0.697149	0.0485727
$207$	−11.8035	−0.820397
$208$	−17.5057	−1.21380
$209$	0	0
$210$	−0.0179331	−0.00123750
$211$	−10.7387	−0.739284	−0.369642	−	0.929174i	$-0.620520\pi$
$211$	−10.7387	−0.739284	−0.369642	+	0.929174i	$0.620520\pi$
$212$	19.0724	1.30990
$213$	2.44921	0.167817
$214$	−1.51512	−0.103572
$215$	−0.567097	−0.0386757
$216$	−4.36731	−0.297158
$217$	−6.99496	−0.474849
$218$	−2.86050	−0.193737
$219$	0.654492	0.0442265
$220$	0	0
$221$	−11.3781	−0.765376
$222$	−0.352539	−0.0236609
$223$	3.99759	0.267698	0.133849	−	0.991002i	$-0.457266\pi$
$223$	3.99759	0.267698	0.133849	+	0.991002i	$0.457266\pi$
$224$	−2.09302	−0.139846
$225$	7.47193	0.498129
$226$	−2.90824	−0.193453
$227$	−21.4664	−1.42477	−0.712387	−	0.701787i	$-0.752386\pi$
$227$	−21.4664	−1.42477	−0.712387	+	0.701787i	$0.752386\pi$
$228$	−2.40338	−0.159168
$229$	4.99717	0.330223	0.165111	−	0.986275i	$-0.447202\pi$
$229$	4.99717	0.330223	0.165111	+	0.986275i	$0.447202\pi$
$230$	−0.128786	−0.00849187
$231$	0	0
$232$	4.01932	0.263882
$233$	13.3691	0.875841	0.437920	−	0.899014i	$-0.355715\pi$
$233$	13.3691	0.875841	0.437920	+	0.899014i	$0.355715\pi$
$234$	−1.39298	−0.0910617
$235$	−0.404288	−0.0263729
$236$	15.7208	1.02334
$237$	13.5856	0.882477
$238$	−0.438057	−0.0283950
$239$	12.0780	0.781263	0.390632	−	0.920547i	$-0.372257\pi$
$239$	12.0780	0.781263	0.390632	+	0.920547i	$0.372257\pi$
$240$	0.376484	0.0243020
$241$	22.7610	1.46617	0.733083	−	0.680139i	$-0.238080\pi$
$241$	22.7610	1.46617	0.733083	+	0.680139i	$0.238080\pi$
$242$	0	0
$243$	13.7551	0.882388
$244$	21.4975	1.37624
$245$	−0.505869	−0.0323188
$246$	−0.573675	−0.0365762
$247$	−4.65387	−0.296119
$248$	−6.18558	−0.392785
$249$	19.8366	1.25709
$250$	0.163159	0.0103191
$251$	14.3292	0.904449	0.452224	−	0.891904i	$-0.350631\pi$
$251$	14.3292	0.904449	0.452224	+	0.891904i	$0.350631\pi$
$252$	2.62713	0.165494
$253$	0	0
$254$	3.93946	0.247184
$255$	0.244702	0.0153239
$256$	12.8943	0.805894
$257$	−4.54396	−0.283445	−0.141722	−	0.989906i	$-0.545264\pi$
$257$	−4.54396	−0.283445	−0.141722	+	0.989906i	$0.545264\pi$
$258$	1.70412	0.106094
$259$	1.28747	0.0799994
$260$	0.744527	0.0461736
$261$	−7.59300	−0.469995
$262$	2.93625	0.181402
$263$	−7.21456	−0.444869	−0.222434	−	0.974948i	$-0.571400\pi$
$263$	−7.21456	−0.444869	−0.222434	+	0.974948i	$0.571400\pi$
$264$	0	0
$265$	−0.794261	−0.0487911
$266$	−0.179174	−0.0109858
$267$	−10.3096	−0.630936
$268$	26.2324	1.60240
$269$	9.71941	0.592603	0.296302	−	0.955094i	$-0.404247\pi$
$269$	9.71941	0.592603	0.296302	+	0.955094i	$0.404247\pi$
$270$	0.0900186	0.00547836
$271$	17.5875	1.06837	0.534183	−	0.845369i	$-0.320619\pi$
$271$	17.5875	1.06837	0.534183	+	0.845369i	$0.320619\pi$
$272$	9.19649	0.557619
$273$	−5.11175	−0.309377
$274$	2.50371	0.151255
$275$	0	0
$276$	−18.9579	−1.14113
$277$	−0.995539	−0.0598161	−0.0299081	−	0.999553i	$-0.509521\pi$
$277$	−0.995539	−0.0598161	−0.0299081	+	0.999553i	$0.509521\pi$
$278$	1.38160	0.0828631
$279$	11.6853	0.699583
$280$	0.0579136	0.00346100
$281$	14.7235	0.878333	0.439166	−	0.898406i	$-0.355274\pi$
$281$	14.7235	0.878333	0.439166	+	0.898406i	$0.355274\pi$
$282$	1.21489	0.0723454
$283$	−5.04060	−0.299632	−0.149816	−	0.988714i	$-0.547868\pi$
$283$	−5.04060	−0.299632	−0.149816	+	0.988714i	$0.547868\pi$
$284$	−3.91481	−0.232301
$285$	0.100088	0.00592869
$286$	0	0
$287$	2.09506	0.123667
$288$	3.49646	0.206031
$289$	−11.0226	−0.648387
$290$	−0.0828460	−0.00486488
$291$	−0.126679	−0.00742605
$292$	−1.04614	−0.0612206
$293$	14.5677	0.851056	0.425528	−	0.904945i	$-0.360088\pi$
$293$	14.5677	0.851056	0.425528	+	0.904945i	$0.360088\pi$
$294$	1.52014	0.0886562
$295$	−0.654686	−0.0381173
$296$	1.13850	0.0661738
$297$	0	0
$298$	3.04928	0.176640
$299$	−36.7097	−2.12298
$300$	12.0009	0.692872
$301$	−6.22344	−0.358713
$302$	1.22784	0.0706542
$303$	−12.7268	−0.731138
$304$	3.76154	0.215739
$305$	−0.895255	−0.0512622
$306$	0.731790	0.0418336
$307$	4.11852	0.235056	0.117528	−	0.993070i	$-0.462503\pi$
$307$	4.11852	0.235056	0.117528	+	0.993070i	$0.462503\pi$
$308$	0	0
$309$	−4.27373	−0.243124
$310$	0.127497	0.00724133
$311$	2.68101	0.152026	0.0760131	−	0.997107i	$-0.475781\pi$
$311$	2.68101	0.152026	0.0760131	+	0.997107i	$0.475781\pi$
$312$	−4.52027	−0.255910
$313$	−4.69992	−0.265655	−0.132827	−	0.991139i	$-0.542406\pi$
$313$	−4.69992	−0.265655	−0.132827	+	0.991139i	$0.542406\pi$
$314$	0.827244	0.0466841
$315$	−0.109406	−0.00616432
$316$	−21.7151	−1.22157
$317$	−1.77929	−0.0999348	−0.0499674	−	0.998751i	$-0.515912\pi$
$317$	−1.77929	−0.0999348	−0.0499674	+	0.998751i	$0.515912\pi$
$318$	2.38675	0.133842
$319$	0	0
$320$	−0.575907	−0.0321942
$321$	9.28814	0.518414
$322$	−1.41332	−0.0787613
$323$	2.44487	0.136036
$324$	4.45252	0.247362
$325$	23.2383	1.28903
$326$	3.18701	0.176512
$327$	17.5357	0.969727
$328$	1.85264	0.102295
$329$	−4.43675	−0.244606
$330$	0	0
$331$	18.2118	1.00101	0.500505	−	0.865734i	$-0.333148\pi$
$331$	18.2118	1.00101	0.500505	+	0.865734i	$0.333148\pi$
$332$	−31.7067	−1.74013
$333$	−2.15076	−0.117861
$334$	0.292117	0.0159839
$335$	−1.09244	−0.0596862
$336$	4.13162	0.225398
$337$	−1.76331	−0.0960537	−0.0480268	−	0.998846i	$-0.515293\pi$
$337$	−1.76331	−0.0960537	−0.0480268	+	0.998846i	$0.515293\pi$
$338$	−1.73193	−0.0942044
$339$	17.8284	0.968305
$340$	−0.391132	−0.0212121
$341$	0	0
$342$	0.299316	0.0161851
$343$	−11.8218	−0.638315
$344$	−5.50334	−0.296720
$345$	0.789494	0.0425049
$346$	−2.92835	−0.157429
$347$	34.2534	1.83882	0.919408	−	0.393304i	$-0.128668\pi$
$347$	34.2534	1.83882	0.919408	+	0.393304i	$0.128668\pi$
$348$	−12.1953	−0.653739
$349$	−23.0038	−1.23136	−0.615682	−	0.787995i	$-0.711119\pi$
$349$	−23.0038	−1.23136	−0.615682	+	0.787995i	$0.711119\pi$
$350$	0.894674	0.0478223
$351$	25.6594	1.36960
$352$	0	0
$353$	7.46659	0.397407	0.198703	−	0.980060i	$-0.436327\pi$
$353$	7.46659	0.397407	0.198703	+	0.980060i	$0.436327\pi$
$354$	1.96733	0.104562
$355$	0.163031	0.00865278
$356$	16.4788	0.873374
$357$	2.68542	0.142127
$358$	2.78646	0.147269
$359$	−34.5410	−1.82301	−0.911503	−	0.411293i	$-0.865077\pi$
$359$	−34.5410	−1.82301	−0.911503	+	0.411293i	$0.865077\pi$
$360$	−0.0967467	−0.00509900
$361$	1.00000	0.0526316
$362$	−3.69803	−0.194364
$363$	0	0
$364$	8.17060	0.428256
$365$	0.0435660	0.00228035
$366$	2.69024	0.140621
$367$	−8.73460	−0.455942	−0.227971	−	0.973668i	$-0.573209\pi$
$367$	−8.73460	−0.455942	−0.227971	+	0.973668i	$0.573209\pi$
$368$	29.6710	1.54671
$369$	−3.49986	−0.182196
$370$	−0.0234666	−0.00121997
$371$	−8.71640	−0.452533
$372$	18.7682	0.973084
$373$	−29.9452	−1.55050	−0.775251	−	0.631654i	$-0.782376\pi$
$373$	−29.9452	−1.55050	−0.775251	+	0.631654i	$0.782376\pi$
$374$	0	0
$375$	−1.00021	−0.0516507
$376$	−3.92338	−0.202333
$377$	−23.6149	−1.21623
$378$	0.987884	0.0508113
$379$	−7.49446	−0.384965	−0.192482	−	0.981300i	$-0.561654\pi$
$379$	−7.49446	−0.384965	−0.192482	+	0.981300i	$0.561654\pi$
$380$	−0.159980	−0.00820681
$381$	−24.1501	−1.23724
$382$	0.873228	0.0446783
$383$	4.01152	0.204979	0.102489	−	0.994734i	$-0.467319\pi$
$383$	4.01152	0.204979	0.102489	+	0.994734i	$0.467319\pi$
$384$	7.46101	0.380743
$385$	0	0
$386$	−1.36222	−0.0693350
$387$	10.3965	0.528483
$388$	0.202483	0.0102795
$389$	30.6954	1.55632	0.778159	−	0.628067i	$-0.216154\pi$
$389$	30.6954	1.55632	0.778159	+	0.628067i	$0.216154\pi$
$390$	0.0931715	0.00471792
$391$	19.2852	0.975294
$392$	−4.90916	−0.247950
$393$	−18.0001	−0.907982
$394$	2.11838	0.106722
$395$	0.904318	0.0455012
$396$	0	0
$397$	−1.79554	−0.0901158	−0.0450579	−	0.998984i	$-0.514347\pi$
$397$	−1.79554	−0.0901158	−0.0450579	+	0.998984i	$0.514347\pi$
$398$	−0.563730	−0.0282572
$399$	1.09839	0.0549881
$400$	−18.7826	−0.939131
$401$	−6.42021	−0.320610	−0.160305	−	0.987068i	$-0.551248\pi$
$401$	−6.42021	−0.320610	−0.160305	+	0.987068i	$0.551248\pi$
$402$	3.28277	0.163730
$403$	36.3424	1.81034
$404$	20.3425	1.01208
$405$	−0.185423	−0.00921376
$406$	−0.909170	−0.0451214
$407$	0	0
$408$	2.37469	0.117565
$409$	4.28533	0.211896	0.105948	−	0.994372i	$-0.466212\pi$
$409$	4.28533	0.211896	0.105948	+	0.994372i	$0.466212\pi$
$410$	−0.0381865	−0.00188590
$411$	−15.3485	−0.757084
$412$	6.83112	0.336545
$413$	−7.18467	−0.353534
$414$	2.36100	0.116037
$415$	1.32041	0.0648165
$416$	10.8743	0.533156
$417$	−8.46964	−0.414760
$418$	0	0
$419$	17.0735	0.834094	0.417047	−	0.908885i	$-0.363065\pi$
$419$	17.0735	0.834094	0.417047	+	0.908885i	$0.363065\pi$
$420$	−0.175720	−0.00857426
$421$	−34.8218	−1.69711	−0.848557	−	0.529105i	$-0.822528\pi$
$421$	−34.8218	−1.69711	−0.848557	+	0.529105i	$0.822528\pi$
$422$	2.14803	0.104564
$423$	7.41175	0.360371
$424$	−7.70783	−0.374326
$425$	−12.2081	−0.592179
$426$	−0.489907	−0.0237361
$427$	−9.82473	−0.475452
$428$	−14.8461	−0.717615
$429$	0	0
$430$	0.113434	0.00547029
$431$	−4.79973	−0.231195	−0.115597	−	0.993296i	$-0.536878\pi$
$431$	−4.79973	−0.231195	−0.115597	+	0.993296i	$0.536878\pi$
$432$	−20.7395	−0.997828
$433$	28.2849	1.35928	0.679642	−	0.733544i	$-0.262135\pi$
$433$	28.2849	1.35928	0.679642	+	0.733544i	$0.262135\pi$
$434$	1.39918	0.0671627
$435$	0.507870	0.0243505
$436$	−28.0290	−1.34235
$437$	7.88800	0.377334
$438$	−0.130916	−0.00625540
$439$	29.2851	1.39770	0.698850	−	0.715268i	$-0.253696\pi$
$439$	29.2851	1.39770	0.698850	+	0.715268i	$0.253696\pi$
$440$	0	0
$441$	9.27402	0.441620
$442$	2.27593	0.108255
$443$	9.86786	0.468836	0.234418	−	0.972136i	$-0.424682\pi$
$443$	9.86786	0.468836	0.234418	+	0.972136i	$0.424682\pi$
$444$	−3.45441	−0.163939
$445$	−0.686253	−0.0325315
$446$	−0.799624	−0.0378633
$447$	−18.6930	−0.884147
$448$	−6.32013	−0.298598
$449$	4.70980	0.222269	0.111135	−	0.993805i	$-0.464552\pi$
$449$	4.70980	0.222269	0.111135	+	0.993805i	$0.464552\pi$
$450$	−1.49458	−0.0704554
$451$	0	0
$452$	−28.4968	−1.34038
$453$	−7.52702	−0.353650
$454$	4.29384	0.201520
$455$	−0.340262	−0.0159517
$456$	0.971294	0.0454850
$457$	−1.15519	−0.0540375	−0.0270187	−	0.999635i	$-0.508601\pi$
$457$	−1.15519	−0.0540375	−0.0270187	+	0.999635i	$0.508601\pi$
$458$	−0.999568	−0.0467067
$459$	−13.4800	−0.629191
$460$	−1.26192	−0.0588375
$461$	41.3195	1.92444	0.962221	−	0.272271i	$-0.0877747\pi$
$461$	41.3195	1.92444	0.962221	+	0.272271i	$0.0877747\pi$
$462$	0	0
$463$	−8.31946	−0.386638	−0.193319	−	0.981136i	$-0.561925\pi$
$463$	−8.31946	−0.386638	−0.193319	+	0.981136i	$0.561925\pi$
$464$	19.0870	0.886090
$465$	−0.781593	−0.0362455
$466$	−2.67418	−0.123879
$467$	7.11539	0.329261	0.164630	−	0.986355i	$-0.447357\pi$
$467$	7.11539	0.329261	0.164630	+	0.986355i	$0.447357\pi$
$468$	−13.6493	−0.630938
$469$	−11.9886	−0.553584
$470$	0.0808684	0.00373018
$471$	−5.07125	−0.233671
$472$	−6.35334	−0.292436
$473$	0	0
$474$	−2.71747	−0.124818
$475$	−4.99334	−0.229110
$476$	−4.29237	−0.196740
$477$	14.5610	0.666705
$478$	−2.41593	−0.110502
$479$	20.8922	0.954588	0.477294	−	0.878744i	$-0.341618\pi$
$479$	20.8922	0.954588	0.477294	+	0.878744i	$0.341618\pi$
$480$	−0.233867	−0.0106745
$481$	−6.68905	−0.304995
$482$	−4.55281	−0.207375
$483$	8.66408	0.394229
$484$	0	0
$485$	−0.00843234	−0.000382893 0
$486$	−2.75138	−0.124805
$487$	1.11750	0.0506388	0.0253194	−	0.999679i	$-0.491940\pi$
$487$	1.11750	0.0506388	0.0253194	+	0.999679i	$0.491940\pi$
$488$	−8.68792	−0.393284
$489$	−19.5373	−0.883508
$490$	0.101187	0.00457118
$491$	−29.0965	−1.31311	−0.656553	−	0.754280i	$-0.727986\pi$
$491$	−29.0965	−1.31311	−0.656553	+	0.754280i	$0.727986\pi$
$492$	−5.62124	−0.253425
$493$	12.4059	0.558733
$494$	0.930897	0.0418830
$495$	0	0
$496$	−29.3741	−1.31894
$497$	1.78914	0.0802538
$498$	−3.96784	−0.177803
$499$	−2.95731	−0.132387	−0.0661937	−	0.997807i	$-0.521086\pi$
$499$	−2.95731	−0.132387	−0.0661937	+	0.997807i	$0.521086\pi$
$500$	1.59874	0.0714977
$501$	−1.79076	−0.0800053
$502$	−2.86621	−0.127925
$503$	23.9236	1.06670	0.533350	−	0.845895i	$-0.320933\pi$
$503$	23.9236	1.06670	0.533350	+	0.845895i	$0.320933\pi$
$504$	−1.06172	−0.0472928
$505$	−0.847157	−0.0376980
$506$	0	0
$507$	10.6172	0.471528
$508$	38.6014	1.71266
$509$	9.84805	0.436507	0.218254	−	0.975892i	$-0.429964\pi$
$509$	9.84805	0.436507	0.218254	+	0.975892i	$0.429964\pi$
$510$	−0.0489470	−0.00216741
$511$	0.478103	0.0211500
$512$	−14.7483	−0.651789
$513$	−5.51356	−0.243430
$514$	0.908913	0.0400904
$515$	−0.284479	−0.0125357
$516$	16.6981	0.735093
$517$	0	0
$518$	−0.257528	−0.0113151
$519$	17.9517	0.787991
$520$	−0.300890	−0.0131949
$521$	−24.5361	−1.07495	−0.537474	−	0.843280i	$-0.680621\pi$
$521$	−24.5361	−1.07495	−0.537474	+	0.843280i	$0.680621\pi$
$522$	1.51880	0.0664761
$523$	44.1499	1.93054	0.965270	−	0.261254i	$-0.0841360\pi$
$523$	44.1499	1.93054	0.965270	+	0.261254i	$0.0841360\pi$
$524$	28.7712	1.25688
$525$	−5.48462	−0.239368
$526$	1.44310	0.0629223
$527$	−19.0922	−0.831669
$528$	0	0
$529$	39.2206	1.70524
$530$	0.158873	0.00690101
$531$	12.0022	0.520853
$532$	−1.75566	−0.0761174
$533$	−10.8849	−0.471476
$534$	2.06219	0.0892396
$535$	0.618262	0.0267298
$536$	−10.6015	−0.457913
$537$	−17.0818	−0.737135
$538$	−1.94414	−0.0838178
$539$	0	0
$540$	0.882060	0.0379578
$541$	5.41726	0.232906	0.116453	−	0.993196i	$-0.462848\pi$
$541$	5.41726	0.232906	0.116453	+	0.993196i	$0.462848\pi$
$542$	−3.51797	−0.151110
$543$	22.6700	0.972863
$544$	−5.71273	−0.244931
$545$	1.16726	0.0499998
$546$	1.02249	0.0437583
$547$	1.20892	0.0516897	0.0258448	−	0.999666i	$-0.491772\pi$
$547$	1.20892	0.0516897	0.0258448	+	0.999666i	$0.491772\pi$
$548$	24.5330	1.04800
$549$	16.4126	0.700471
$550$	0	0
$551$	5.07424	0.216170
$552$	7.66157	0.326098
$553$	9.92418	0.422019
$554$	0.199134	0.00846040
$555$	0.143857	0.00610641
$556$	13.5379	0.574133
$557$	−28.4168	−1.20406	−0.602030	−	0.798473i	$-0.705641\pi$
$557$	−28.4168	−1.20406	−0.602030	+	0.798473i	$0.705641\pi$
$558$	−2.33738	−0.0989490
$559$	32.3339	1.36758
$560$	0.275020	0.0116217
$561$	0	0
$562$	−2.94510	−0.124232
$563$	−25.2933	−1.06599	−0.532994	−	0.846119i	$-0.678933\pi$
$563$	−25.2933	−1.06599	−0.532994	+	0.846119i	$0.678933\pi$
$564$	11.9042	0.501258
$565$	1.18674	0.0499265
$566$	1.00825	0.0423800
$567$	−2.03488	−0.0854568
$568$	1.58212	0.0663842
$569$	−8.81909	−0.369716	−0.184858	−	0.982765i	$-0.559182\pi$
$569$	−8.81909	−0.369716	−0.184858	+	0.982765i	$0.559182\pi$
$570$	−0.0200202	−0.000838555 0
$571$	28.4197	1.18933	0.594663	−	0.803975i	$-0.297285\pi$
$571$	28.4197	1.18933	0.594663	+	0.803975i	$0.297285\pi$
$572$	0	0
$573$	−5.35315	−0.223631
$574$	−0.419067	−0.0174915
$575$	−39.3875	−1.64257
$576$	10.5580	0.439916
$577$	28.2626	1.17659	0.588294	−	0.808647i	$-0.299800\pi$
$577$	28.2626	1.17659	0.588294	+	0.808647i	$0.299800\pi$
$578$	2.20481	0.0917080
$579$	8.35080	0.347047
$580$	−0.811779	−0.0337073
$581$	14.4905	0.601167
$582$	0.0253391	0.00105034
$583$	0	0
$584$	0.422782	0.0174949
$585$	0.568419	0.0235012
$586$	−2.91393	−0.120373
$587$	−34.2658	−1.41430	−0.707151	−	0.707063i	$-0.750020\pi$
$587$	−34.2658	−1.41430	−0.707151	+	0.707063i	$0.750020\pi$
$588$	14.8953	0.614271
$589$	−7.80907	−0.321767
$590$	0.130955	0.00539131
$591$	−12.9863	−0.534185
$592$	5.40650	0.222206
$593$	25.9391	1.06519	0.532595	−	0.846370i	$-0.321217\pi$
$593$	25.9391	1.06519	0.532595	+	0.846370i	$0.321217\pi$
$594$	0	0
$595$	0.178754	0.00732819
$596$	29.8788	1.22388
$597$	3.45583	0.141438
$598$	7.34292	0.300274
$599$	11.9624	0.488771	0.244386	−	0.969678i	$-0.421414\pi$
$599$	11.9624	0.488771	0.244386	+	0.969678i	$0.421414\pi$
$600$	−4.85000	−0.198000
$601$	−47.9051	−1.95409	−0.977044	−	0.213037i	$-0.931664\pi$
$601$	−47.9051	−1.95409	−0.977044	+	0.213037i	$0.931664\pi$
$602$	1.24485	0.0507365
$603$	20.0275	0.815581
$604$	12.0312	0.489541
$605$	0	0
$606$	2.54570	0.103412
$607$	−37.6440	−1.52792	−0.763961	−	0.645262i	$-0.776748\pi$
$607$	−37.6440	−1.52792	−0.763961	+	0.645262i	$0.776748\pi$
$608$	−2.33661	−0.0947622
$609$	5.57348	0.225849
$610$	0.179075	0.00725053
$611$	23.0512	0.932550
$612$	7.17055	0.289852
$613$	−29.7321	−1.20087	−0.600435	−	0.799674i	$-0.705006\pi$
$613$	−29.7321	−1.20087	−0.600435	+	0.799674i	$0.705006\pi$
$614$	−0.823813	−0.0332464
$615$	0.234094	0.00943959
$616$	0	0
$617$	−31.2183	−1.25680	−0.628401	−	0.777890i	$-0.716290\pi$
$617$	−31.2183	−1.25680	−0.628401	+	0.777890i	$0.716290\pi$
$618$	0.854860	0.0343875
$619$	26.9286	1.08235	0.541176	−	0.840909i	$-0.317979\pi$
$619$	26.9286	1.08235	0.541176	+	0.840909i	$0.317979\pi$
$620$	1.24930	0.0501729
$621$	−43.4910	−1.74523
$622$	−0.536274	−0.0215026
$623$	−7.53109	−0.301727
$624$	−21.4659	−0.859322
$625$	24.9001	0.996004
$626$	0.940108	0.0375743
$627$	0	0
$628$	8.10587	0.323460
$629$	3.51404	0.140114
$630$	0.0218841	0.000871883 0
$631$	19.4266	0.773360	0.386680	−	0.922214i	$-0.373622\pi$
$631$	19.4266	0.773360	0.386680	+	0.922214i	$0.373622\pi$
$632$	8.77587	0.349085
$633$	−13.1680	−0.523383
$634$	0.355905	0.0141348
$635$	−1.60754	−0.0637933
$636$	23.3869	0.927353
$637$	28.8430	1.14280
$638$	0	0
$639$	−2.98882	−0.118236
$640$	0.496639	0.0196314
$641$	−3.38404	−0.133661	−0.0668307	−	0.997764i	$-0.521289\pi$
$641$	−3.38404	−0.133661	−0.0668307	+	0.997764i	$0.521289\pi$
$642$	−1.85788	−0.0733245
$643$	20.2841	0.799926	0.399963	−	0.916531i	$-0.369023\pi$
$643$	20.2841	0.799926	0.399963	+	0.916531i	$0.369023\pi$
$644$	−13.8486	−0.545713
$645$	−0.695386	−0.0273808
$646$	−0.489040	−0.0192410
$647$	3.45406	0.135793	0.0678966	−	0.997692i	$-0.478371\pi$
$647$	3.45406	0.135793	0.0678966	+	0.997692i	$0.478371\pi$
$648$	−1.79942	−0.0706881
$649$	0	0
$650$	−4.64828	−0.182321
$651$	−8.57737	−0.336174
$652$	31.2284	1.22300
$653$	−25.9226	−1.01443	−0.507215	−	0.861820i	$-0.669325\pi$
$653$	−25.9226	−1.01443	−0.507215	+	0.861820i	$0.669325\pi$
$654$	−3.50761	−0.137158
$655$	−1.19817	−0.0468162
$656$	8.79781	0.343497
$657$	−0.798688	−0.0311598
$658$	0.887468	0.0345971
$659$	−39.0302	−1.52040	−0.760201	−	0.649688i	$-0.774899\pi$
$659$	−39.0302	−1.52040	−0.760201	+	0.649688i	$0.774899\pi$
$660$	0	0
$661$	−12.0694	−0.469444	−0.234722	−	0.972063i	$-0.575418\pi$
$661$	−12.0694	−0.469444	−0.234722	+	0.972063i	$0.575418\pi$
$662$	−3.64284	−0.141583
$663$	−13.9521	−0.541855
$664$	12.8138	0.497273
$665$	0.0731137	0.00283523
$666$	0.430210	0.0166703
$667$	40.0257	1.54980
$668$	2.86235	0.110748
$669$	4.90193	0.189520
$670$	0.218516	0.00844202
$671$	0	0
$672$	−2.56651	−0.0990051
$673$	35.2196	1.35762	0.678808	−	0.734316i	$-0.262497\pi$
$673$	35.2196	1.35762	0.678808	+	0.734316i	$0.262497\pi$
$674$	0.352709	0.0135858
$675$	27.5311	1.05967
$676$	−16.9705	−0.652713
$677$	14.8411	0.570391	0.285196	−	0.958469i	$-0.407941\pi$
$677$	14.8411	0.570391	0.285196	+	0.958469i	$0.407941\pi$
$678$	−3.56615	−0.136957
$679$	−0.0925383	−0.00355130
$680$	0.158070	0.00606173
$681$	−26.3225	−1.00868
$682$	0	0
$683$	−31.1026	−1.19011	−0.595054	−	0.803686i	$-0.702869\pi$
$683$	−31.1026	−1.19011	−0.595054	+	0.803686i	$0.702869\pi$
$684$	2.93289	0.112142
$685$	−1.02167	−0.0390358
$686$	2.36467	0.0902834
$687$	6.12764	0.233784
$688$	−26.1342	−0.996358
$689$	45.2861	1.72526
$690$	−0.157920	−0.00601190
$691$	48.6258	1.84981	0.924907	−	0.380194i	$-0.124143\pi$
$691$	48.6258	1.84981	0.924907	+	0.380194i	$0.124143\pi$
$692$	−28.6939	−1.09078
$693$	0	0
$694$	−6.85158	−0.260082
$695$	−0.563779	−0.0213853
$696$	4.92858	0.186817
$697$	5.71829	0.216596
$698$	4.60137	0.174164
$699$	16.3935	0.620060
$700$	8.76660	0.331346
$701$	17.3353	0.654747	0.327373	−	0.944895i	$-0.393836\pi$
$701$	17.3353	0.654747	0.327373	+	0.944895i	$0.393836\pi$
$702$	−5.13256	−0.193716
$703$	1.43731	0.0542092
$704$	0	0
$705$	−0.495747	−0.0186709
$706$	−1.49352	−0.0562093
$707$	−9.29689	−0.349646
$708$	19.2772	0.724480
$709$	17.7875	0.668025	0.334012	−	0.942569i	$-0.391597\pi$
$709$	17.7875	0.668025	0.334012	+	0.942569i	$0.391597\pi$
$710$	−0.0326105	−0.00122385
$711$	−16.5787	−0.621750
$712$	−6.65968	−0.249582
$713$	−61.5979	−2.30686
$714$	−0.537155	−0.0201025
$715$	0	0
$716$	27.3035	1.02038
$717$	14.8104	0.553103
$718$	6.90912	0.257846
$719$	−48.7880	−1.81949	−0.909743	−	0.415173i	$-0.863721\pi$
$719$	−48.7880	−1.81949	−0.909743	+	0.415173i	$0.863721\pi$
$720$	−0.459431	−0.0171220
$721$	−3.12194	−0.116267
$722$	−0.200027	−0.00744422
$723$	27.9101	1.03799
$724$	−36.2357	−1.34669
$725$	−25.3374	−0.941008
$726$	0	0
$727$	−11.3288	−0.420162	−0.210081	−	0.977684i	$-0.567373\pi$
$727$	−11.3288	−0.420162	−0.210081	+	0.977684i	$0.567373\pi$
$728$	−3.30204	−0.122382
$729$	23.6819	0.877106
$730$	−0.00871436	−0.000322533 0
$731$	−16.9864	−0.628264
$732$	26.3607	0.974320
$733$	−14.3227	−0.529023	−0.264511	−	0.964383i	$-0.585211\pi$
$733$	−14.3227	−0.529023	−0.264511	+	0.964383i	$0.585211\pi$
$734$	1.74715	0.0644885
$735$	−0.620308	−0.0228804
$736$	−18.4312	−0.679383
$737$	0	0
$738$	0.700066	0.0257698
$739$	−42.5999	−1.56706	−0.783532	−	0.621351i	$-0.786584\pi$
$739$	−42.5999	−1.56706	−0.783532	+	0.621351i	$0.786584\pi$
$740$	−0.229941	−0.00845281
$741$	−5.70667	−0.209640
$742$	1.74351	0.0640063
$743$	25.5536	0.937470	0.468735	−	0.883339i	$-0.344710\pi$
$743$	25.5536	0.937470	0.468735	+	0.883339i	$0.344710\pi$
$744$	−7.58490	−0.278076
$745$	−1.24429	−0.0455873
$746$	5.98983	0.219303
$747$	−24.2069	−0.885684
$748$	0	0
$749$	6.78494	0.247916
$750$	0.200069	0.00730549
$751$	42.8191	1.56249	0.781246	−	0.624223i	$-0.214584\pi$
$751$	42.8191	1.56249	0.781246	+	0.624223i	$0.214584\pi$
$752$	−18.6313	−0.679415
$753$	17.5707	0.640313
$754$	4.72360	0.172023
$755$	−0.501033	−0.0182345
$756$	9.67993	0.352056
$757$	−31.5166	−1.14549	−0.572744	−	0.819734i	$-0.694121\pi$
$757$	−31.5166	−1.14549	−0.572744	+	0.819734i	$0.694121\pi$
$758$	1.49909	0.0544494
$759$	0	0
$760$	0.0646538	0.00234524
$761$	35.2163	1.27659	0.638296	−	0.769791i	$-0.279640\pi$
$761$	35.2163	1.27659	0.638296	+	0.769791i	$0.279640\pi$
$762$	4.83065	0.174996
$763$	12.8097	0.463744
$764$	8.55646	0.309562
$765$	−0.298615	−0.0107964
$766$	−0.802410	−0.0289922
$767$	37.3280	1.34784
$768$	15.8113	0.570540
$769$	−9.89036	−0.356655	−0.178328	−	0.983971i	$-0.557069\pi$
$769$	−9.89036	−0.356655	−0.178328	+	0.983971i	$0.557069\pi$
$770$	0	0
$771$	−5.57191	−0.200667
$772$	−13.3479	−0.480401
$773$	−32.8434	−1.18130	−0.590648	−	0.806930i	$-0.701128\pi$
$773$	−32.8434	−1.18130	−0.590648	+	0.806930i	$0.701128\pi$
$774$	−2.07957	−0.0747487
$775$	38.9933	1.40068
$776$	−0.0818308	−0.00293756
$777$	1.57872	0.0566364
$778$	−6.13990	−0.220126
$779$	2.33889	0.0837993
$780$	0.912955	0.0326890
$781$	0	0
$782$	−3.85755	−0.137946
$783$	−27.9771	−0.999822
$784$	−23.3126	−0.832594
$785$	−0.337566	−0.0120482
$786$	3.60049	0.128425
$787$	−52.3773	−1.86705	−0.933524	−	0.358516i	$-0.883283\pi$
$787$	−52.3773	−1.86705	−0.933524	+	0.358516i	$0.883283\pi$
$788$	20.7573	0.739447
$789$	−8.84665	−0.314949
$790$	−0.180888	−0.00643569
$791$	13.0235	0.463064
$792$	0	0
$793$	51.0444	1.81264
$794$	0.359157	0.0127460
$795$	−0.973940	−0.0345421
$796$	−5.52379	−0.195786
$797$	−17.7908	−0.630181	−0.315091	−	0.949062i	$-0.602035\pi$
$797$	−17.7908	−0.630181	−0.315091	+	0.949062i	$0.602035\pi$
$798$	−0.219707	−0.00777753
$799$	−12.1098	−0.428412
$800$	11.6675	0.412508
$801$	12.5810	0.444526
$802$	1.28421	0.0453471
$803$	0	0
$804$	32.1667	1.13443
$805$	0.576721	0.0203268
$806$	−7.26944	−0.256055
$807$	11.9182	0.419539
$808$	−8.22116	−0.289219
$809$	−36.7305	−1.29137	−0.645687	−	0.763602i	$-0.723429\pi$
$809$	−36.7305	−1.29137	−0.645687	+	0.763602i	$0.723429\pi$
$810$	0.0370896	0.00130320
$811$	38.5485	1.35362	0.676811	−	0.736157i	$-0.263361\pi$
$811$	38.5485	1.35362	0.676811	+	0.736157i	$0.263361\pi$
$812$	−8.90864	−0.312632
$813$	21.5662	0.756360
$814$	0	0
$815$	−1.30049	−0.0455543
$816$	11.2769	0.394772
$817$	−6.94775	−0.243071
$818$	−0.857179	−0.0299706
$819$	6.23796	0.217972
$820$	−0.374176	−0.0130668
$821$	−25.8360	−0.901683	−0.450842	−	0.892604i	$-0.648876\pi$
$821$	−25.8360	−0.901683	−0.450842	+	0.892604i	$0.648876\pi$
$822$	3.07010	0.107082
$823$	−21.3234	−0.743289	−0.371644	−	0.928375i	$-0.621206\pi$
$823$	−21.3234	−0.743289	−0.371644	+	0.928375i	$0.621206\pi$
$824$	−2.76070	−0.0961737
$825$	0	0
$826$	1.43712	0.0500040
$827$	−12.2015	−0.424289	−0.212144	−	0.977238i	$-0.568045\pi$
$827$	−12.2015	−0.424289	−0.212144	+	0.977238i	$0.568045\pi$
$828$	23.1346	0.803984
$829$	53.2814	1.85054	0.925270	−	0.379308i	$-0.123838\pi$
$829$	53.2814	1.85054	0.925270	+	0.379308i	$0.123838\pi$
$830$	−0.264118	−0.00916766
$831$	−1.22075	−0.0423474
$832$	32.8362	1.13839
$833$	−15.1524	−0.525001
$834$	1.69415	0.0586637
$835$	−0.119201	−0.00412513
$836$	0	0
$837$	43.0557	1.48822
$838$	−3.41515	−0.117974
$839$	−8.39932	−0.289977	−0.144988	−	0.989433i	$-0.546314\pi$
$839$	−8.39932	−0.289977	−0.144988	+	0.989433i	$0.546314\pi$
$840$	0.0710149	0.00245025
$841$	−3.25205	−0.112140
$842$	6.96529	0.240040
$843$	18.0543	0.621824
$844$	21.0478	0.724494
$845$	0.706732	0.0243123
$846$	−1.48255	−0.0509710
$847$	0	0
$848$	−36.6029	−1.25695
$849$	−6.18089	−0.212128
$850$	2.44194	0.0837579
$851$	11.3375	0.388645
$852$	−4.80043	−0.164460
$853$	−53.4755	−1.83097	−0.915484	−	0.402355i	$-0.868192\pi$
$853$	−53.4755	−1.83097	−0.915484	+	0.402355i	$0.868192\pi$
$854$	1.96521	0.0672480
$855$	−0.122139	−0.00417707
$856$	5.99987	0.205071
$857$	26.7668	0.914335	0.457168	−	0.889381i	$-0.348864\pi$
$857$	26.7668	0.914335	0.457168	+	0.889381i	$0.348864\pi$
$858$	0	0
$859$	20.6673	0.705158	0.352579	−	0.935782i	$-0.385305\pi$
$859$	20.6673	0.705158	0.352579	+	0.935782i	$0.385305\pi$
$860$	1.11150	0.0379019
$861$	2.56900	0.0875514
$862$	0.960074	0.0327002
$863$	37.9184	1.29076	0.645379	−	0.763863i	$-0.276700\pi$
$863$	37.9184	1.29076	0.645379	+	0.763863i	$0.276700\pi$
$864$	12.8831	0.438290
$865$	1.19495	0.0406294
$866$	−5.65773	−0.192257
$867$	−13.5161	−0.459032
$868$	13.7101	0.465349
$869$	0	0
$870$	−0.101588	−0.00344414
$871$	62.2871	2.11052
$872$	11.3275	0.383599
$873$	0.154589	0.00523203
$874$	−1.57781	−0.0533702
$875$	−0.730650	−0.0247005
$876$	−1.28280	−0.0433417
$877$	0.729467	0.0246324	0.0123162	−	0.999924i	$-0.496080\pi$
$877$	0.729467	0.0246324	0.0123162	+	0.999924i	$0.496080\pi$
$878$	−5.85779	−0.197691
$879$	17.8633	0.602513
$880$	0	0
$881$	−42.5972	−1.43514	−0.717569	−	0.696488i	$-0.754745\pi$
$881$	−42.5972	−1.43514	−0.717569	+	0.696488i	$0.754745\pi$
$882$	−1.85505	−0.0624628
$883$	1.36806	0.0460390	0.0230195	−	0.999735i	$-0.492672\pi$
$883$	1.36806	0.0460390	0.0230195	+	0.999735i	$0.492672\pi$
$884$	22.3010	0.750064
$885$	−0.802790	−0.0269855
$886$	−1.97383	−0.0663122
$887$	−22.5442	−0.756960	−0.378480	−	0.925610i	$-0.623553\pi$
$887$	−22.5442	−0.756960	−0.378480	+	0.925610i	$0.623553\pi$
$888$	1.39605	0.0468484
$889$	−17.6415	−0.591677
$890$	0.137269	0.00460126
$891$	0	0
$892$	−7.83523	−0.262343
$893$	−4.95312	−0.165750
$894$	3.73909	0.125054
$895$	−1.13705	−0.0380072
$896$	5.45023	0.182079
$897$	−45.0143	−1.50298
$898$	−0.942084	−0.0314378
$899$	−39.6251	−1.32157
$900$	−14.6449	−0.488164
$901$	−23.7907	−0.792583
$902$	0	0
$903$	−7.63132	−0.253954
$904$	11.5166	0.383037
$905$	1.50902	0.0501616
$906$	1.50560	0.0500203
$907$	−22.1263	−0.734691	−0.367346	−	0.930084i	$-0.619733\pi$
$907$	−22.1263	−0.734691	−0.367346	+	0.930084i	$0.619733\pi$
$908$	42.0739	1.39627
$909$	15.5308	0.515124
$910$	0.0680613	0.00225621
$911$	13.8428	0.458632	0.229316	−	0.973352i	$-0.426351\pi$
$911$	13.8428	0.458632	0.229316	+	0.973352i	$0.426351\pi$
$912$	4.61248	0.152734
$913$	0	0
$914$	0.231068	0.00764307
$915$	−1.09778	−0.0362915
$916$	−9.79441	−0.323616
$917$	−13.1489	−0.434217
$918$	2.69635	0.0889928
$919$	14.3933	0.474792	0.237396	−	0.971413i	$-0.423706\pi$
$919$	14.3933	0.474792	0.237396	+	0.971413i	$0.423706\pi$
$920$	0.509990	0.0168139
$921$	5.05022	0.166410
$922$	−8.26500	−0.272193
$923$	−9.29547	−0.305964
$924$	0	0
$925$	−7.17698	−0.235978
$926$	1.66411	0.0546861
$927$	5.21531	0.171293
$928$	−11.8565	−0.389210
$929$	23.1287	0.758827	0.379413	−	0.925227i	$-0.376126\pi$
$929$	23.1287	0.758827	0.379413	+	0.925227i	$0.376126\pi$
$930$	0.156339	0.00512657
$931$	−6.19763	−0.203119
$932$	−26.2033	−0.858319
$933$	3.28752	0.107628
$934$	−1.42327	−0.0465707
$935$	0	0
$936$	5.51617	0.180302
$937$	4.99511	0.163183	0.0815916	−	0.996666i	$-0.474000\pi$
$937$	4.99511	0.163183	0.0815916	+	0.996666i	$0.474000\pi$
$938$	2.39805	0.0782990
$939$	−5.76314	−0.188073
$940$	0.792401	0.0258453
$941$	57.5285	1.87538	0.937688	−	0.347479i	$-0.112962\pi$
$941$	57.5285	1.87538	0.937688	+	0.347479i	$0.112962\pi$
$942$	1.01438	0.0330504
$943$	18.4492	0.600787
$944$	−30.1707	−0.981974
$945$	−0.403117	−0.0131134
$946$	0	0
$947$	26.9892	0.877032	0.438516	−	0.898723i	$-0.355504\pi$
$947$	26.9892	0.877032	0.438516	+	0.898723i	$0.355504\pi$
$948$	−26.6275	−0.864822
$949$	−2.48399	−0.0806336
$950$	0.998800	0.0324054
$951$	−2.18180	−0.0707498
$952$	1.73470	0.0562220
$953$	44.7439	1.44940	0.724699	−	0.689066i	$-0.241979\pi$
$953$	44.7439	1.44940	0.724699	+	0.689066i	$0.241979\pi$
$954$	−2.91260	−0.0942988
$955$	−0.356330	−0.0115306
$956$	−23.6728	−0.765634
$957$	0	0
$958$	−4.17899	−0.135017
$959$	−11.2120	−0.362054
$960$	−0.706189	−0.0227922
$961$	29.9815	0.967145
$962$	1.33799	0.0431385
$963$	−11.3345	−0.365249
$964$	−44.6114	−1.43684
$965$	0.555868	0.0178940
$966$	−1.73305	−0.0557598
$967$	−15.9104	−0.511644	−0.255822	−	0.966724i	$-0.582346\pi$
$967$	−15.9104	−0.511644	−0.255822	+	0.966724i	$0.582346\pi$
$968$	0	0
$969$	2.99796	0.0963083
$970$	0.00168669	5.41564e−5 0
$971$	31.3050	1.00462	0.502312	−	0.864686i	$-0.332483\pi$
$971$	31.3050	1.00462	0.502312	+	0.864686i	$0.332483\pi$
$972$	−26.9598	−0.864735
$973$	−6.18703	−0.198347
$974$	−0.223530	−0.00716236
$975$	28.4954	0.912582
$976$	−41.2572	−1.32061
$977$	16.4925	0.527643	0.263821	−	0.964572i	$-0.415017\pi$
$977$	16.4925	0.527643	0.263821	+	0.964572i	$0.415017\pi$
$978$	3.90798	0.124964
$979$	0	0
$980$	0.991499	0.0316723
$981$	−21.3991	−0.683222
$982$	5.82007	0.185726
$983$	−27.7320	−0.884514	−0.442257	−	0.896888i	$-0.645822\pi$
$983$	−27.7320	−0.884514	−0.442257	+	0.896888i	$0.645822\pi$
$984$	2.27175	0.0724206
$985$	−0.864428	−0.0275430
$986$	−2.48151	−0.0790273
$987$	−5.44044	−0.173171
$988$	9.12153	0.290195
$989$	−54.8039	−1.74266
$990$	0	0
$991$	36.0016	1.14363	0.571815	−	0.820383i	$-0.306240\pi$
$991$	36.0016	1.14363	0.571815	+	0.820383i	$0.306240\pi$
$992$	18.2468	0.579335
$993$	22.3317	0.708674
$994$	−0.357875	−0.0113511
$995$	0.230036	0.00729263
$996$	−38.8794	−1.23194
$997$	27.1016	0.858317	0.429158	−	0.903229i	$-0.358810\pi$
$997$	27.1016	0.858317	0.429158	+	0.903229i	$0.358810\pi$
$998$	0.591541	0.0187249
$999$	−7.92470	−0.250726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.u.1.7		14
11.2	odd	10		209.2.f.b.191.4	yes	28
11.6	odd	10		209.2.f.b.58.4	✓	28
11.10	odd	2		2299.2.a.t.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.b.58.4	✓	28	11.6	odd	10
209.2.f.b.191.4	yes	28	11.2	odd	10
2299.2.a.t.1.8		14	11.10	odd	2
2299.2.a.u.1.7		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

\(f(q)\)	\(=\)	\(q-0.200027 q^{2} +1.22622 q^{3} -1.95999 q^{4} +0.0816230 q^{5} -0.245277 q^{6} +0.895749 q^{7} +0.792103 q^{8} -1.49638 q^{9} -0.0163268 q^{10} -2.40338 q^{12} -4.65387 q^{13} -0.179174 q^{14} +0.100088 q^{15} +3.76154 q^{16} +2.44487 q^{17} +0.299316 q^{18} +1.00000 q^{19} -0.159980 q^{20} +1.09839 q^{21} +7.88800 q^{23} +0.971294 q^{24} -4.99334 q^{25} +0.930897 q^{26} -5.51356 q^{27} -1.75566 q^{28} +5.07424 q^{29} -0.0200202 q^{30} -7.80907 q^{31} -2.33661 q^{32} -0.489040 q^{34} +0.0731137 q^{35} +2.93289 q^{36} +1.43731 q^{37} -0.200027 q^{38} -5.70667 q^{39} +0.0646538 q^{40} +2.33889 q^{41} -0.219707 q^{42} -6.94775 q^{43} -0.122139 q^{45} -1.57781 q^{46} -4.95312 q^{47} +4.61248 q^{48} -6.19763 q^{49} +0.998800 q^{50} +2.99796 q^{51} +9.12153 q^{52} -9.73085 q^{53} +1.10286 q^{54} +0.709525 q^{56} +1.22622 q^{57} -1.01498 q^{58} -8.02085 q^{59} -0.196171 q^{60} -10.9682 q^{61} +1.56202 q^{62} -1.34038 q^{63} -7.05569 q^{64} -0.379863 q^{65} -13.3839 q^{67} -4.79193 q^{68} +9.67244 q^{69} -0.0146247 q^{70} +1.99737 q^{71} -1.18529 q^{72} +0.533747 q^{73} -0.287500 q^{74} -6.12294 q^{75} -1.95999 q^{76} +1.14149 q^{78} +11.0792 q^{79} +0.307028 q^{80} -2.27171 q^{81} -0.467840 q^{82} +16.1770 q^{83} -2.15283 q^{84} +0.199558 q^{85} +1.38974 q^{86} +6.22215 q^{87} -8.40759 q^{89} +0.0244310 q^{90} -4.16870 q^{91} -15.4604 q^{92} -9.57565 q^{93} +0.990755 q^{94} +0.0816230 q^{95} -2.86521 q^{96} -0.103308 q^{97} +1.23969 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} - 2 q^{3} + 7 q^{4} - 14 q^{5} - 8 q^{6} - 4 q^{7} + 3 q^{8} - 2 q^{9} + 6 q^{10} - 8 q^{12} + 5 q^{13} - 6 q^{14} - 10 q^{15} + 5 q^{16} - 10 q^{17} - 6 q^{18} + 14 q^{19} - 16 q^{20} + 9 q^{21}+ \cdots - 42 q^{98}+O(q^{100}) \) 14 * q + q^2 - 2 * q^3 + 7 * q^4 - 14 * q^5 - 8 * q^6 - 4 * q^7 + 3 * q^8 - 2 * q^9 + 6 * q^10 - 8 * q^12 + 5 * q^13 - 6 * q^14 - 10 * q^15 + 5 * q^16 - 10 * q^17 - 6 * q^18 + 14 * q^19 - 16 * q^20 + 9 * q^21 - 21 * q^23 + 22 * q^24 + 6 * q^25 - 28 * q^26 + 4 * q^27 - 15 * q^28 + 3 * q^29 + 20 * q^30 - 13 * q^31 + 2 * q^32 - 10 * q^34 + 3 * q^35 - 17 * q^36 - 31 * q^37 + q^38 - 33 * q^39 - 28 * q^40 + 10 * q^41 - 18 * q^42 + 6 * q^43 - 11 * q^45 + 23 * q^46 - 16 * q^47 - 16 * q^48 - 8 * q^49 - 16 * q^50 - 2 * q^51 - 7 * q^52 - 42 * q^53 - 30 * q^54 - 30 * q^56 - 2 * q^57 - 16 * q^58 - 26 * q^59 - 5 * q^60 - 34 * q^61 + 15 * q^62 + 33 * q^63 - 23 * q^64 - 13 * q^65 + 12 * q^67 + 32 * q^68 - 33 * q^69 - 27 * q^70 - 38 * q^71 - 14 * q^72 + 9 * q^73 - 26 * q^74 + 15 * q^75 + 7 * q^76 + 3 * q^78 + 6 * q^79 - 30 * q^80 - 22 * q^81 + 28 * q^82 - 35 * q^83 - 13 * q^84 + 12 * q^85 - 68 * q^86 + 17 * q^87 - 54 * q^89 + 39 * q^90 - 94 * q^92 - 26 * q^93 - 14 * q^95 + 5 * q^96 - 31 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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