LMFDB - Embedded newform 2667.2.a.q.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [19,4,19,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.782325$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.782325 q^{2} +1.00000 q^{3} -1.38797 q^{4} -2.85652 q^{5} -0.782325 q^{6} +1.00000 q^{7} +2.65049 q^{8} +1.00000 q^{9} +2.23472 q^{10} -5.95291 q^{11} -1.38797 q^{12} -2.24308 q^{13} -0.782325 q^{14} -2.85652 q^{15} +0.702387 q^{16} +0.355250 q^{17} -0.782325 q^{18} +4.58452 q^{19} +3.96475 q^{20} +1.00000 q^{21} +4.65711 q^{22} +1.77438 q^{23} +2.65049 q^{24} +3.15968 q^{25} +1.75482 q^{26} +1.00000 q^{27} -1.38797 q^{28} -9.18000 q^{29} +2.23472 q^{30} -2.61888 q^{31} -5.85048 q^{32} -5.95291 q^{33} -0.277921 q^{34} -2.85652 q^{35} -1.38797 q^{36} +0.446439 q^{37} -3.58659 q^{38} -2.24308 q^{39} -7.57117 q^{40} -5.55748 q^{41} -0.782325 q^{42} -3.81437 q^{43} +8.26245 q^{44} -2.85652 q^{45} -1.38814 q^{46} -4.89679 q^{47} +0.702387 q^{48} +1.00000 q^{49} -2.47190 q^{50} +0.355250 q^{51} +3.11332 q^{52} +12.9711 q^{53} -0.782325 q^{54} +17.0046 q^{55} +2.65049 q^{56} +4.58452 q^{57} +7.18175 q^{58} +5.34918 q^{59} +3.96475 q^{60} +3.71025 q^{61} +2.04882 q^{62} +1.00000 q^{63} +3.17221 q^{64} +6.40739 q^{65} +4.65711 q^{66} +10.3248 q^{67} -0.493075 q^{68} +1.77438 q^{69} +2.23472 q^{70} +1.31960 q^{71} +2.65049 q^{72} -8.85675 q^{73} -0.349261 q^{74} +3.15968 q^{75} -6.36316 q^{76} -5.95291 q^{77} +1.75482 q^{78} +13.1696 q^{79} -2.00638 q^{80} +1.00000 q^{81} +4.34776 q^{82} +15.2753 q^{83} -1.38797 q^{84} -1.01478 q^{85} +2.98408 q^{86} -9.18000 q^{87} -15.7782 q^{88} -2.60509 q^{89} +2.23472 q^{90} -2.24308 q^{91} -2.46278 q^{92} -2.61888 q^{93} +3.83088 q^{94} -13.0958 q^{95} -5.85048 q^{96} -3.10938 q^{97} -0.782325 q^{98} -5.95291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Coefficient data

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

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

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

$2$	−0.782325	−0.553188	−0.276594	−	0.960987i	$-0.589206\pi$
$2$	−0.782325	−0.553188	−0.276594	+	0.960987i	$0.589206\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.38797	−0.693984
$5$	−2.85652	−1.27747	−0.638736	−	0.769426i	$-0.720543\pi$
$5$	−2.85652	−1.27747	−0.638736	+	0.769426i	$0.720543\pi$
$6$	−0.782325	−0.319383
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.65049	0.937091
$9$	1.00000	0.333333
$10$	2.23472	0.706682
$11$	−5.95291	−1.79487	−0.897435	−	0.441146i	$-0.854572\pi$
$11$	−5.95291	−1.79487	−0.897435	+	0.441146i	$0.854572\pi$
$12$	−1.38797	−0.400672
$13$	−2.24308	−0.622118	−0.311059	−	0.950391i	$-0.600684\pi$
$13$	−2.24308	−0.622118	−0.311059	+	0.950391i	$0.600684\pi$
$14$	−0.782325	−0.209085
$15$	−2.85652	−0.737549
$16$	0.702387	0.175597
$17$	0.355250	0.0861607	0.0430803	−	0.999072i	$-0.486283\pi$
$17$	0.355250	0.0861607	0.0430803	+	0.999072i	$0.486283\pi$
$18$	−0.782325	−0.184396
$19$	4.58452	1.05176	0.525881	−	0.850558i	$-0.323736\pi$
$19$	4.58452	1.05176	0.525881	+	0.850558i	$0.323736\pi$
$20$	3.96475	0.886545
$21$	1.00000	0.218218
$22$	4.65711	0.992900
$23$	1.77438	0.369984	0.184992	−	0.982740i	$-0.440774\pi$
$23$	1.77438	0.369984	0.184992	+	0.982740i	$0.440774\pi$
$24$	2.65049	0.541030
$25$	3.15968	0.631936
$26$	1.75482	0.344148
$27$	1.00000	0.192450
$28$	−1.38797	−0.262301
$29$	−9.18000	−1.70468	−0.852342	−	0.522985i	$-0.824818\pi$
$29$	−9.18000	−1.70468	−0.852342	+	0.522985i	$0.824818\pi$
$30$	2.23472	0.408003
$31$	−2.61888	−0.470365	−0.235183	−	0.971951i	$-0.575569\pi$
$31$	−2.61888	−0.470365	−0.235183	+	0.971951i	$0.575569\pi$
$32$	−5.85048	−1.03423
$33$	−5.95291	−1.03627
$34$	−0.277921	−0.0476630
$35$	−2.85652	−0.482839
$36$	−1.38797	−0.231328
$37$	0.446439	0.0733942	0.0366971	−	0.999326i	$-0.488316\pi$
$37$	0.446439	0.0733942	0.0366971	+	0.999326i	$0.488316\pi$
$38$	−3.58659	−0.581821
$39$	−2.24308	−0.359180
$40$	−7.57117	−1.19711
$41$	−5.55748	−0.867932	−0.433966	−	0.900929i	$-0.642886\pi$
$41$	−5.55748	−0.867932	−0.433966	+	0.900929i	$0.642886\pi$
$42$	−0.782325	−0.120715
$43$	−3.81437	−0.581685	−0.290843	−	0.956771i	$-0.593936\pi$
$43$	−3.81437	−0.581685	−0.290843	+	0.956771i	$0.593936\pi$
$44$	8.26245	1.24561
$45$	−2.85652	−0.425824
$46$	−1.38814	−0.204671
$47$	−4.89679	−0.714271	−0.357135	−	0.934053i	$-0.616246\pi$
$47$	−4.89679	−0.714271	−0.357135	+	0.934053i	$0.616246\pi$
$48$	0.702387	0.101381
$49$	1.00000	0.142857
$50$	−2.47190	−0.349579
$51$	0.355250	0.0497449
$52$	3.11332	0.431740
$53$	12.9711	1.78171	0.890856	−	0.454286i	$-0.150106\pi$
$53$	12.9711	1.78171	0.890856	+	0.454286i	$0.150106\pi$
$54$	−0.782325	−0.106461
$55$	17.0046	2.29290
$56$	2.65049	0.354187
$57$	4.58452	0.607235
$58$	7.18175	0.943010
$59$	5.34918	0.696403	0.348202	−	0.937420i	$-0.386792\pi$
$59$	5.34918	0.696403	0.348202	+	0.937420i	$0.386792\pi$
$60$	3.96475	0.511847
$61$	3.71025	0.475049	0.237524	−	0.971382i	$-0.423664\pi$
$61$	3.71025	0.475049	0.237524	+	0.971382i	$0.423664\pi$
$62$	2.04882	0.260200
$63$	1.00000	0.125988
$64$	3.17221	0.396526
$65$	6.40739	0.794739
$66$	4.65711	0.573251
$67$	10.3248	1.26138	0.630689	−	0.776035i	$-0.282772\pi$
$67$	10.3248	1.26138	0.630689	+	0.776035i	$0.282772\pi$
$68$	−0.493075	−0.0597941
$69$	1.77438	0.213610
$70$	2.23472	0.267101
$71$	1.31960	0.156608	0.0783041	−	0.996930i	$-0.475050\pi$
$71$	1.31960	0.156608	0.0783041	+	0.996930i	$0.475050\pi$
$72$	2.65049	0.312364
$73$	−8.85675	−1.03660	−0.518302	−	0.855198i	$-0.673436\pi$
$73$	−8.85675	−1.03660	−0.518302	+	0.855198i	$0.673436\pi$
$74$	−0.349261	−0.0406007
$75$	3.15968	0.364849
$76$	−6.36316	−0.729905
$77$	−5.95291	−0.678397
$78$	1.75482	0.198694
$79$	13.1696	1.48169	0.740847	−	0.671673i	$-0.234424\pi$
$79$	13.1696	1.48169	0.740847	+	0.671673i	$0.234424\pi$
$80$	−2.00638	−0.224320
$81$	1.00000	0.111111
$82$	4.34776	0.480129
$83$	15.2753	1.67668	0.838342	−	0.545145i	$-0.183525\pi$
$83$	15.2753	1.67668	0.838342	+	0.545145i	$0.183525\pi$
$84$	−1.38797	−0.151440
$85$	−1.01478	−0.110068
$86$	2.98408	0.321781
$87$	−9.18000	−0.984199
$88$	−15.7782	−1.68196
$89$	−2.60509	−0.276139	−0.138070	−	0.990423i	$-0.544090\pi$
$89$	−2.60509	−0.276139	−0.138070	+	0.990423i	$0.544090\pi$
$90$	2.23472	0.235561
$91$	−2.24308	−0.235139
$92$	−2.46278	−0.256763
$93$	−2.61888	−0.271565
$94$	3.83088	0.395126
$95$	−13.0958	−1.34360
$96$	−5.85048	−0.597112
$97$	−3.10938	−0.315709	−0.157855	−	0.987462i	$-0.550458\pi$
$97$	−3.10938	−0.315709	−0.157855	+	0.987462i	$0.550458\pi$
$98$	−0.782325	−0.0790268
$99$	−5.95291	−0.598290
$100$	−4.38553	−0.438553
$101$	2.36661	0.235487	0.117743	−	0.993044i	$-0.462434\pi$
$101$	2.36661	0.235487	0.117743	+	0.993044i	$0.462434\pi$
$102$	−0.277921	−0.0275183
$103$	3.24902	0.320135	0.160068	−	0.987106i	$-0.448829\pi$
$103$	3.24902	0.320135	0.160068	+	0.987106i	$0.448829\pi$
$104$	−5.94526	−0.582981
$105$	−2.85652	−0.278767
$106$	−10.1476	−0.985621
$107$	−0.104034	−0.0100573	−0.00502866	−	0.999987i	$-0.501601\pi$
$107$	−0.104034	−0.0100573	−0.00502866	+	0.999987i	$0.501601\pi$
$108$	−1.38797	−0.133557
$109$	19.8237	1.89877	0.949383	−	0.314120i	$-0.101710\pi$
$109$	19.8237	1.89877	0.949383	+	0.314120i	$0.101710\pi$
$110$	−13.3031	−1.26840
$111$	0.446439	0.0423741
$112$	0.702387	0.0663693
$113$	−13.2923	−1.25043	−0.625216	−	0.780452i	$-0.714989\pi$
$113$	−13.2923	−1.25043	−0.625216	+	0.780452i	$0.714989\pi$
$114$	−3.58659	−0.335915
$115$	−5.06855	−0.472645
$116$	12.7415	1.18302
$117$	−2.24308	−0.207373
$118$	−4.18480	−0.385242
$119$	0.355250	0.0325657
$120$	−7.57117	−0.691150
$121$	24.4372	2.22156
$122$	−2.90262	−0.262791
$123$	−5.55748	−0.501101
$124$	3.63492	0.326426
$125$	5.25690	0.470191
$126$	−0.782325	−0.0696951
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	9.21926	0.814875
$129$	−3.81437	−0.335836
$130$	−5.01266	−0.439640
$131$	1.48402	0.129660	0.0648298	−	0.997896i	$-0.479350\pi$
$131$	1.48402	0.129660	0.0648298	+	0.997896i	$0.479350\pi$
$132$	8.26245	0.719154
$133$	4.58452	0.397528
$134$	−8.07738	−0.697779
$135$	−2.85652	−0.245850
$136$	0.941587	0.0807404
$137$	3.92401	0.335251	0.167626	−	0.985851i	$-0.446390\pi$
$137$	3.92401	0.335251	0.167626	+	0.985851i	$0.446390\pi$
$138$	−1.38814	−0.118167
$139$	−1.61387	−0.136887	−0.0684435	−	0.997655i	$-0.521803\pi$
$139$	−1.61387	−0.136887	−0.0684435	+	0.997655i	$0.521803\pi$
$140$	3.96475	0.335082
$141$	−4.89679	−0.412384
$142$	−1.03236	−0.0866337
$143$	13.3529	1.11662
$144$	0.702387	0.0585322
$145$	26.2228	2.17769
$146$	6.92886	0.573437
$147$	1.00000	0.0824786
$148$	−0.619643	−0.0509343
$149$	9.10778	0.746138	0.373069	−	0.927804i	$-0.378305\pi$
$149$	9.10778	0.746138	0.373069	+	0.927804i	$0.378305\pi$
$150$	−2.47190	−0.201830
$151$	−9.73474	−0.792202	−0.396101	−	0.918207i	$-0.629637\pi$
$151$	−9.73474	−0.792202	−0.396101	+	0.918207i	$0.629637\pi$
$152$	12.1512	0.985595
$153$	0.355250	0.0287202
$154$	4.65711	0.375281
$155$	7.48088	0.600879
$156$	3.11332	0.249265
$157$	10.5542	0.842315	0.421158	−	0.906987i	$-0.361624\pi$
$157$	10.5542	0.842315	0.421158	+	0.906987i	$0.361624\pi$
$158$	−10.3029	−0.819655
$159$	12.9711	1.02867
$160$	16.7120	1.32120
$161$	1.77438	0.139841
$162$	−0.782325	−0.0614653
$163$	6.03292	0.472534	0.236267	−	0.971688i	$-0.424076\pi$
$163$	6.03292	0.472534	0.236267	+	0.971688i	$0.424076\pi$
$164$	7.71360	0.602331
$165$	17.0046	1.32381
$166$	−11.9503	−0.927520
$167$	1.24770	0.0965497	0.0482748	−	0.998834i	$-0.484628\pi$
$167$	1.24770	0.0965497	0.0482748	+	0.998834i	$0.484628\pi$
$168$	2.65049	0.204490
$169$	−7.96860	−0.612969
$170$	0.793885	0.0608882
$171$	4.58452	0.350587
$172$	5.29421	0.403680
$173$	−7.02419	−0.534039	−0.267020	−	0.963691i	$-0.586039\pi$
$173$	−7.02419	−0.534039	−0.267020	+	0.963691i	$0.586039\pi$
$174$	7.18175	0.544447
$175$	3.15968	0.238849
$176$	−4.18125	−0.315173
$177$	5.34918	0.402069
$178$	2.03803	0.152757
$179$	−16.0501	−1.19964	−0.599822	−	0.800134i	$-0.704762\pi$
$179$	−16.0501	−1.19964	−0.599822	+	0.800134i	$0.704762\pi$
$180$	3.96475	0.295515
$181$	−10.0388	−0.746181	−0.373091	−	0.927795i	$-0.621702\pi$
$181$	−10.0388	−0.746181	−0.373091	+	0.927795i	$0.621702\pi$
$182$	1.75482	0.130076
$183$	3.71025	0.274269
$184$	4.70299	0.346709
$185$	−1.27526	−0.0937590
$186$	2.04882	0.150227
$187$	−2.11477	−0.154647
$188$	6.79659	0.495692
$189$	1.00000	0.0727393
$190$	10.2451	0.743260
$191$	12.8858	0.932386	0.466193	−	0.884683i	$-0.345625\pi$
$191$	12.8858	0.932386	0.466193	+	0.884683i	$0.345625\pi$
$192$	3.17221	0.228934
$193$	15.5417	1.11871	0.559357	−	0.828927i	$-0.311048\pi$
$193$	15.5417	1.11871	0.559357	+	0.828927i	$0.311048\pi$
$194$	2.43254	0.174647
$195$	6.40739	0.458843
$196$	−1.38797	−0.0991405
$197$	−9.10451	−0.648669	−0.324335	−	0.945942i	$-0.605140\pi$
$197$	−9.10451	−0.648669	−0.324335	+	0.945942i	$0.605140\pi$
$198$	4.65711	0.330967
$199$	20.7799	1.47305	0.736524	−	0.676411i	$-0.236466\pi$
$199$	20.7799	1.47305	0.736524	+	0.676411i	$0.236466\pi$
$200$	8.37471	0.592181
$201$	10.3248	0.728257
$202$	−1.85146	−0.130268
$203$	−9.18000	−0.644310
$204$	−0.493075	−0.0345221
$205$	15.8750	1.10876
$206$	−2.54179	−0.177095
$207$	1.77438	0.123328
$208$	−1.57551	−0.109242
$209$	−27.2912	−1.88778
$210$	2.23472	0.154211
$211$	−7.23948	−0.498387	−0.249193	−	0.968454i	$-0.580165\pi$
$211$	−7.23948	−0.498387	−0.249193	+	0.968454i	$0.580165\pi$
$212$	−18.0034	−1.23648
$213$	1.31960	0.0904177
$214$	0.0813882	0.00556358
$215$	10.8958	0.743087
$216$	2.65049	0.180343
$217$	−2.61888	−0.177781
$218$	−15.5086	−1.05037
$219$	−8.85675	−0.598484
$220$	−23.6018	−1.59123
$221$	−0.796853	−0.0536021
$222$	−0.349261	−0.0234408
$223$	−16.9713	−1.13648	−0.568241	−	0.822862i	$-0.692376\pi$
$223$	−16.9713	−1.13648	−0.568241	+	0.822862i	$0.692376\pi$
$224$	−5.85048	−0.390902
$225$	3.15968	0.210645
$226$	10.3989	0.691723
$227$	26.3750	1.75057	0.875285	−	0.483607i	$-0.160674\pi$
$227$	26.3750	1.75057	0.875285	+	0.483607i	$0.160674\pi$
$228$	−6.36316	−0.421411
$229$	22.6839	1.49900	0.749498	−	0.662006i	$-0.230295\pi$
$229$	22.6839	1.49900	0.749498	+	0.662006i	$0.230295\pi$
$230$	3.96525	0.261461
$231$	−5.95291	−0.391673
$232$	−24.3315	−1.59744
$233$	19.9035	1.30392	0.651960	−	0.758253i	$-0.273947\pi$
$233$	19.9035	1.30392	0.651960	+	0.758253i	$0.273947\pi$
$234$	1.75482	0.114716
$235$	13.9878	0.912461
$236$	−7.42448	−0.483292
$237$	13.1696	0.855457
$238$	−0.277921	−0.0180149
$239$	14.8701	0.961870	0.480935	−	0.876756i	$-0.340297\pi$
$239$	14.8701	0.961870	0.480935	+	0.876756i	$0.340297\pi$
$240$	−2.00638	−0.129511
$241$	29.5656	1.90449	0.952245	−	0.305335i	$-0.0987685\pi$
$241$	29.5656	1.90449	0.952245	+	0.305335i	$0.0987685\pi$
$242$	−19.1178	−1.22894
$243$	1.00000	0.0641500
$244$	−5.14970	−0.329676
$245$	−2.85652	−0.182496
$246$	4.34776	0.277203
$247$	−10.2834	−0.654320
$248$	−6.94133	−0.440775
$249$	15.2753	0.968034
$250$	−4.11261	−0.260104
$251$	20.0199	1.26364	0.631821	−	0.775114i	$-0.282308\pi$
$251$	20.0199	1.26364	0.631821	+	0.775114i	$0.282308\pi$
$252$	−1.38797	−0.0874337
$253$	−10.5627	−0.664074
$254$	−0.782325	−0.0490875
$255$	−1.01478	−0.0635477
$256$	−13.5569	−0.847305
$257$	−26.4101	−1.64742	−0.823709	−	0.567012i	$-0.808099\pi$
$257$	−26.4101	−1.64742	−0.823709	+	0.567012i	$0.808099\pi$
$258$	2.98408	0.185780
$259$	0.446439	0.0277404
$260$	−8.89325	−0.551536
$261$	−9.18000	−0.568228
$262$	−1.16099	−0.0717261
$263$	−18.5090	−1.14131	−0.570656	−	0.821189i	$-0.693311\pi$
$263$	−18.5090	−1.14131	−0.570656	+	0.821189i	$0.693311\pi$
$264$	−15.7782	−0.971078
$265$	−37.0520	−2.27609
$266$	−3.58659	−0.219908
$267$	−2.60509	−0.159429
$268$	−14.3305	−0.875376
$269$	0.573334	0.0349568	0.0174784	−	0.999847i	$-0.494436\pi$
$269$	0.573334	0.0349568	0.0174784	+	0.999847i	$0.494436\pi$
$270$	2.23472	0.136001
$271$	7.26958	0.441595	0.220798	−	0.975320i	$-0.429134\pi$
$271$	7.26958	0.441595	0.220798	+	0.975320i	$0.429134\pi$
$272$	0.249523	0.0151295
$273$	−2.24308	−0.135757
$274$	−3.06986	−0.185457
$275$	−18.8093	−1.13424
$276$	−2.46278	−0.148242
$277$	−16.1927	−0.972924	−0.486462	−	0.873702i	$-0.661713\pi$
$277$	−16.1927	−0.972924	−0.486462	+	0.873702i	$0.661713\pi$
$278$	1.26257	0.0757242
$279$	−2.61888	−0.156788
$280$	−7.57117	−0.452464
$281$	−0.461522	−0.0275321	−0.0137661	−	0.999905i	$-0.504382\pi$
$281$	−0.461522	−0.0275321	−0.0137661	+	0.999905i	$0.504382\pi$
$282$	3.83088	0.228126
$283$	3.00080	0.178379	0.0891895	−	0.996015i	$-0.471572\pi$
$283$	3.00080	0.178379	0.0891895	+	0.996015i	$0.471572\pi$
$284$	−1.83157	−0.108683
$285$	−13.0958	−0.775725
$286$	−10.4463	−0.617701
$287$	−5.55748	−0.328048
$288$	−5.85048	−0.344743
$289$	−16.8738	−0.992576
$290$	−20.5148	−1.20467
$291$	−3.10938	−0.182275
$292$	12.2929	0.719386
$293$	14.8706	0.868752	0.434376	−	0.900732i	$-0.356969\pi$
$293$	14.8706	0.868752	0.434376	+	0.900732i	$0.356969\pi$
$294$	−0.782325	−0.0456261
$295$	−15.2800	−0.889636
$296$	1.18328	0.0687770
$297$	−5.95291	−0.345423
$298$	−7.12524	−0.412754
$299$	−3.98008	−0.230174
$300$	−4.38553	−0.253199
$301$	−3.81437	−0.219856
$302$	7.61573	0.438236
$303$	2.36661	0.135958
$304$	3.22011	0.184686
$305$	−10.5984	−0.606862
$306$	−0.277921	−0.0158877
$307$	20.0380	1.14363	0.571815	−	0.820383i	$-0.306240\pi$
$307$	20.0380	1.14363	0.571815	+	0.820383i	$0.306240\pi$
$308$	8.26245	0.470797
$309$	3.24902	0.184830
$310$	−5.85248	−0.332399
$311$	−1.42299	−0.0806904	−0.0403452	−	0.999186i	$-0.512846\pi$
$311$	−1.42299	−0.0806904	−0.0403452	+	0.999186i	$0.512846\pi$
$312$	−5.94526	−0.336584
$313$	8.24182	0.465855	0.232928	−	0.972494i	$-0.425170\pi$
$313$	8.24182	0.465855	0.232928	+	0.972494i	$0.425170\pi$
$314$	−8.25680	−0.465958
$315$	−2.85652	−0.160946
$316$	−18.2790	−1.02827
$317$	22.8267	1.28208	0.641038	−	0.767509i	$-0.278504\pi$
$317$	22.8267	1.28208	0.641038	+	0.767509i	$0.278504\pi$
$318$	−10.1476	−0.569048
$319$	54.6477	3.05969
$320$	−9.06145	−0.506551
$321$	−0.104034	−0.00580660
$322$	−1.38814	−0.0773582
$323$	1.62865	0.0906205
$324$	−1.38797	−0.0771093
$325$	−7.08741	−0.393139
$326$	−4.71970	−0.261400
$327$	19.8237	1.09625
$328$	−14.7301	−0.813331
$329$	−4.89679	−0.269969
$330$	−13.3031	−0.732313
$331$	23.7844	1.30731	0.653656	−	0.756792i	$-0.273235\pi$
$331$	23.7844	1.30731	0.653656	+	0.756792i	$0.273235\pi$
$332$	−21.2016	−1.16359
$333$	0.446439	0.0244647
$334$	−0.976105	−0.0534101
$335$	−29.4930	−1.61138
$336$	0.702387	0.0383183
$337$	−6.16356	−0.335750	−0.167875	−	0.985808i	$-0.553691\pi$
$337$	−6.16356	−0.335750	−0.167875	+	0.985808i	$0.553691\pi$
$338$	6.23403	0.339087
$339$	−13.2923	−0.721937
$340$	1.40848	0.0763853
$341$	15.5900	0.844245
$342$	−3.58659	−0.193940
$343$	1.00000	0.0539949
$344$	−10.1099	−0.545092
$345$	−5.06855	−0.272882
$346$	5.49520	0.295424
$347$	−10.9479	−0.587716	−0.293858	−	0.955849i	$-0.594939\pi$
$347$	−10.9479	−0.587716	−0.293858	+	0.955849i	$0.594939\pi$
$348$	12.7415	0.683018
$349$	−4.35089	−0.232898	−0.116449	−	0.993197i	$-0.537151\pi$
$349$	−4.35089	−0.232898	−0.116449	+	0.993197i	$0.537151\pi$
$350$	−2.47190	−0.132129
$351$	−2.24308	−0.119727
$352$	34.8274	1.85631
$353$	−23.5716	−1.25459	−0.627294	−	0.778782i	$-0.715838\pi$
$353$	−23.5716	−1.25459	−0.627294	+	0.778782i	$0.715838\pi$
$354$	−4.18480	−0.222419
$355$	−3.76947	−0.200063
$356$	3.61578	0.191636
$357$	0.355250	0.0188018
$358$	12.5564	0.663628
$359$	−10.7509	−0.567412	−0.283706	−	0.958911i	$-0.591564\pi$
$359$	−10.7509	−0.567412	−0.283706	+	0.958911i	$0.591564\pi$
$360$	−7.57117	−0.399036
$361$	2.01782	0.106201
$362$	7.85364	0.412778
$363$	24.4372	1.28262
$364$	3.11332	0.163182
$365$	25.2995	1.32423
$366$	−2.90262	−0.151722
$367$	13.4042	0.699694	0.349847	−	0.936807i	$-0.386234\pi$
$367$	13.4042	0.699694	0.349847	+	0.936807i	$0.386234\pi$
$368$	1.24630	0.0649680
$369$	−5.55748	−0.289311
$370$	0.997669	0.0518663
$371$	12.9711	0.673424
$372$	3.63492	0.188462
$373$	2.43314	0.125983	0.0629915	−	0.998014i	$-0.479936\pi$
$373$	2.43314	0.125983	0.0629915	+	0.998014i	$0.479936\pi$
$374$	1.65444	0.0855490
$375$	5.25690	0.271465
$376$	−12.9789	−0.669336
$377$	20.5915	1.06051
$378$	−0.782325	−0.0402385
$379$	1.12262	0.0576652	0.0288326	−	0.999584i	$-0.490821\pi$
$379$	1.12262	0.0576652	0.0288326	+	0.999584i	$0.490821\pi$
$380$	18.1765	0.932433
$381$	1.00000	0.0512316
$382$	−10.0809	−0.515784
$383$	−12.1235	−0.619484	−0.309742	−	0.950821i	$-0.600243\pi$
$383$	−12.1235	−0.619484	−0.309742	+	0.950821i	$0.600243\pi$
$384$	9.21926	0.470469
$385$	17.0046	0.866634
$386$	−12.1586	−0.618858
$387$	−3.81437	−0.193895
$388$	4.31571	0.219097
$389$	−7.49818	−0.380173	−0.190086	−	0.981767i	$-0.560877\pi$
$389$	−7.49818	−0.380173	−0.190086	+	0.981767i	$0.560877\pi$
$390$	−5.01266	−0.253826
$391$	0.630349	0.0318781
$392$	2.65049	0.133870
$393$	1.48402	0.0748590
$394$	7.12268	0.358836
$395$	−37.6191	−1.89282
$396$	8.26245	0.415204
$397$	2.60531	0.130757	0.0653785	−	0.997861i	$-0.479175\pi$
$397$	2.60531	0.130757	0.0653785	+	0.997861i	$0.479175\pi$
$398$	−16.2566	−0.814872
$399$	4.58452	0.229513
$400$	2.21932	0.110966
$401$	−34.5142	−1.72356	−0.861778	−	0.507285i	$-0.830649\pi$
$401$	−34.5142	−1.72356	−0.861778	+	0.507285i	$0.830649\pi$
$402$	−8.07738	−0.402863
$403$	5.87436	0.292623
$404$	−3.28478	−0.163424
$405$	−2.85652	−0.141941
$406$	7.18175	0.356424
$407$	−2.65761	−0.131733
$408$	0.941587	0.0466155
$409$	−18.5829	−0.918864	−0.459432	−	0.888213i	$-0.651947\pi$
$409$	−18.5829	−0.918864	−0.459432	+	0.888213i	$0.651947\pi$
$410$	−12.4194	−0.613352
$411$	3.92401	0.193557
$412$	−4.50953	−0.222168
$413$	5.34918	0.263216
$414$	−1.38814	−0.0682236
$415$	−43.6342	−2.14192
$416$	13.1231	0.643412
$417$	−1.61387	−0.0790317
$418$	21.3506	1.04429
$419$	−34.4281	−1.68192	−0.840962	−	0.541094i	$-0.818010\pi$
$419$	−34.4281	−1.68192	−0.840962	+	0.541094i	$0.818010\pi$
$420$	3.96475	0.193460
$421$	10.5543	0.514383	0.257191	−	0.966360i	$-0.417203\pi$
$421$	10.5543	0.514383	0.257191	+	0.966360i	$0.417203\pi$
$422$	5.66363	0.275701
$423$	−4.89679	−0.238090
$424$	34.3797	1.66963
$425$	1.12248	0.0544481
$426$	−1.03236	−0.0500180
$427$	3.71025	0.179552
$428$	0.144395	0.00697961
$429$	13.3529	0.644682
$430$	−8.52406	−0.411067
$431$	23.7306	1.14306	0.571531	−	0.820581i	$-0.306350\pi$
$431$	23.7306	1.14306	0.571531	+	0.820581i	$0.306350\pi$
$432$	0.702387	0.0337936
$433$	3.32779	0.159923	0.0799617	−	0.996798i	$-0.474520\pi$
$433$	3.32779	0.159923	0.0799617	+	0.996798i	$0.474520\pi$
$434$	2.04882	0.0983464
$435$	26.2228	1.25729
$436$	−27.5146	−1.31771
$437$	8.13469	0.389135
$438$	6.92886	0.331074
$439$	20.6852	0.987252	0.493626	−	0.869674i	$-0.335671\pi$
$439$	20.6852	0.987252	0.493626	+	0.869674i	$0.335671\pi$
$440$	45.0705	2.14865
$441$	1.00000	0.0476190
$442$	0.623398	0.0296520
$443$	−40.0896	−1.90472	−0.952358	−	0.304981i	$-0.901350\pi$
$443$	−40.0896	−1.90472	−0.952358	+	0.304981i	$0.901350\pi$
$444$	−0.619643	−0.0294070
$445$	7.44149	0.352760
$446$	13.2771	0.628687
$447$	9.10778	0.430783
$448$	3.17221	0.149873
$449$	−20.3346	−0.959648	−0.479824	−	0.877365i	$-0.659300\pi$
$449$	−20.3346	−0.959648	−0.479824	+	0.877365i	$0.659300\pi$
$450$	−2.47190	−0.116526
$451$	33.0832	1.55783
$452$	18.4492	0.867779
$453$	−9.73474	−0.457378
$454$	−20.6338	−0.968394
$455$	6.40739	0.300383
$456$	12.1512	0.569034
$457$	−11.4154	−0.533991	−0.266996	−	0.963698i	$-0.586031\pi$
$457$	−11.4154	−0.533991	−0.266996	+	0.963698i	$0.586031\pi$
$458$	−17.7462	−0.829226
$459$	0.355250	0.0165816
$460$	7.03498	0.328008
$461$	−35.1107	−1.63527	−0.817634	−	0.575738i	$-0.804715\pi$
$461$	−35.1107	−1.63527	−0.817634	+	0.575738i	$0.804715\pi$
$462$	4.65711	0.216669
$463$	−9.61602	−0.446894	−0.223447	−	0.974716i	$-0.571731\pi$
$463$	−9.61602	−0.446894	−0.223447	+	0.974716i	$0.571731\pi$
$464$	−6.44791	−0.299337
$465$	7.48088	0.346917
$466$	−15.5710	−0.721313
$467$	32.7492	1.51545	0.757725	−	0.652574i	$-0.226311\pi$
$467$	32.7492	1.51545	0.757725	+	0.652574i	$0.226311\pi$
$468$	3.11332	0.143913
$469$	10.3248	0.476756
$470$	−10.9430	−0.504762
$471$	10.5542	0.486311
$472$	14.1780	0.652593
$473$	22.7066	1.04405
$474$	−10.3029	−0.473228
$475$	14.4856	0.664646
$476$	−0.493075	−0.0226000
$477$	12.9711	0.593904
$478$	−11.6333	−0.532095
$479$	4.11326	0.187940	0.0939698	−	0.995575i	$-0.470044\pi$
$479$	4.11326	0.187940	0.0939698	+	0.995575i	$0.470044\pi$
$480$	16.7120	0.762794
$481$	−1.00140	−0.0456598
$482$	−23.1299	−1.05354
$483$	1.77438	0.0807372
$484$	−33.9180	−1.54173
$485$	8.88199	0.403310
$486$	−0.782325	−0.0354870
$487$	−10.3942	−0.471007	−0.235504	−	0.971873i	$-0.575674\pi$
$487$	−10.3942	−0.471007	−0.235504	+	0.971873i	$0.575674\pi$
$488$	9.83399	0.445164
$489$	6.03292	0.272818
$490$	2.23472	0.100955
$491$	11.6309	0.524895	0.262447	−	0.964946i	$-0.415470\pi$
$491$	11.6309	0.524895	0.262447	+	0.964946i	$0.415470\pi$
$492$	7.71360	0.347756
$493$	−3.26119	−0.146877
$494$	8.04500	0.361961
$495$	17.0046	0.764299
$496$	−1.83947	−0.0825946
$497$	1.31960	0.0591923
$498$	−11.9503	−0.535504
$499$	18.6834	0.836384	0.418192	−	0.908359i	$-0.362664\pi$
$499$	18.6834	0.836384	0.418192	+	0.908359i	$0.362664\pi$
$500$	−7.29640	−0.326305
$501$	1.24770	0.0557430
$502$	−15.6620	−0.699031
$503$	−37.2918	−1.66276	−0.831380	−	0.555705i	$-0.812449\pi$
$503$	−37.2918	−1.66276	−0.831380	+	0.555705i	$0.812449\pi$
$504$	2.65049	0.118062
$505$	−6.76026	−0.300828
$506$	8.26350	0.367357
$507$	−7.96860	−0.353898
$508$	−1.38797	−0.0615811
$509$	30.3885	1.34695	0.673474	−	0.739211i	$-0.264801\pi$
$509$	30.3885	1.34695	0.673474	+	0.739211i	$0.264801\pi$
$510$	0.793885	0.0351538
$511$	−8.85675	−0.391800
$512$	−7.83264	−0.346157
$513$	4.58452	0.202412
$514$	20.6613	0.911331
$515$	−9.28086	−0.408964
$516$	5.29421	0.233065
$517$	29.1502	1.28202
$518$	−0.349261	−0.0153456
$519$	−7.02419	−0.308328
$520$	16.9827	0.744742
$521$	13.9497	0.611146	0.305573	−	0.952169i	$-0.401152\pi$
$521$	13.9497	0.611146	0.305573	+	0.952169i	$0.401152\pi$
$522$	7.18175	0.314337
$523$	−22.2163	−0.971450	−0.485725	−	0.874112i	$-0.661444\pi$
$523$	−22.2163	−0.971450	−0.485725	+	0.874112i	$0.661444\pi$
$524$	−2.05977	−0.0899816
$525$	3.15968	0.137900
$526$	14.4800	0.631360
$527$	−0.930357	−0.0405270
$528$	−4.18125	−0.181965
$529$	−19.8516	−0.863112
$530$	28.9867	1.25910
$531$	5.34918	0.232134
$532$	−6.36316	−0.275878
$533$	12.4659	0.539957
$534$	2.03803	0.0881942
$535$	0.297174	0.0128479
$536$	27.3659	1.18203
$537$	−16.0501	−0.692614
$538$	−0.448534	−0.0193377
$539$	−5.95291	−0.256410
$540$	3.96475	0.170616
$541$	25.9878	1.11730	0.558651	−	0.829403i	$-0.311319\pi$
$541$	25.9878	1.11730	0.558651	+	0.829403i	$0.311319\pi$
$542$	−5.68718	−0.244285
$543$	−10.0388	−0.430808
$544$	−2.07838	−0.0891098
$545$	−56.6267	−2.42562
$546$	1.75482	0.0750993
$547$	−38.7425	−1.65651	−0.828254	−	0.560352i	$-0.810666\pi$
$547$	−38.7425	−1.65651	−0.828254	+	0.560352i	$0.810666\pi$
$548$	−5.44640	−0.232659
$549$	3.71025	0.158350
$550$	14.7150	0.627450
$551$	−42.0859	−1.79292
$552$	4.70299	0.200172
$553$	13.1696	0.560028
$554$	12.6679	0.538209
$555$	−1.27526	−0.0541318
$556$	2.24000	0.0949973
$557$	−13.2224	−0.560252	−0.280126	−	0.959963i	$-0.590376\pi$
$557$	−13.2224	−0.560252	−0.280126	+	0.959963i	$0.590376\pi$
$558$	2.04882	0.0867334
$559$	8.55592	0.361877
$560$	−2.00638	−0.0847850
$561$	−2.11477	−0.0892857
$562$	0.361061	0.0152304
$563$	−12.5799	−0.530180	−0.265090	−	0.964224i	$-0.585402\pi$
$563$	−12.5799	−0.530180	−0.265090	+	0.964224i	$0.585402\pi$
$564$	6.79659	0.286188
$565$	37.9696	1.59739
$566$	−2.34760	−0.0986771
$567$	1.00000	0.0419961
$568$	3.49760	0.146756
$569$	22.4858	0.942653	0.471326	−	0.881959i	$-0.343775\pi$
$569$	22.4858	0.942653	0.471326	+	0.881959i	$0.343775\pi$
$570$	10.2451	0.429122
$571$	10.9617	0.458733	0.229366	−	0.973340i	$-0.426335\pi$
$571$	10.9617	0.458733	0.229366	+	0.973340i	$0.426335\pi$
$572$	−18.5333	−0.774917
$573$	12.8858	0.538313
$574$	4.34776	0.181472
$575$	5.60648	0.233806
$576$	3.17221	0.132175
$577$	−7.86167	−0.327286	−0.163643	−	0.986520i	$-0.552324\pi$
$577$	−7.86167	−0.327286	−0.163643	+	0.986520i	$0.552324\pi$
$578$	13.2008	0.549081
$579$	15.5417	0.645889
$580$	−36.3964	−1.51128
$581$	15.2753	0.633727
$582$	2.43254	0.100832
$583$	−77.2156	−3.19794
$584$	−23.4748	−0.971392
$585$	6.40739	0.264913
$586$	−11.6337	−0.480583
$587$	45.8628	1.89296	0.946479	−	0.322764i	$-0.104612\pi$
$587$	45.8628	1.89296	0.946479	+	0.322764i	$0.104612\pi$
$588$	−1.38797	−0.0572388
$589$	−12.0063	−0.494712
$590$	11.9539	0.492136
$591$	−9.10451	−0.374509
$592$	0.313573	0.0128878
$593$	19.8056	0.813319	0.406660	−	0.913580i	$-0.366693\pi$
$593$	19.8056	0.813319	0.406660	+	0.913580i	$0.366693\pi$
$594$	4.65711	0.191084
$595$	−1.01478	−0.0416018
$596$	−12.6413	−0.517808
$597$	20.7799	0.850465
$598$	3.11372	0.127329
$599$	34.5952	1.41352	0.706761	−	0.707452i	$-0.250156\pi$
$599$	34.5952	1.41352	0.706761	+	0.707452i	$0.250156\pi$
$600$	8.37471	0.341896
$601$	10.5867	0.431840	0.215920	−	0.976411i	$-0.430725\pi$
$601$	10.5867	0.431840	0.215920	+	0.976411i	$0.430725\pi$
$602$	2.98408	0.121622
$603$	10.3248	0.420460
$604$	13.5115	0.549775
$605$	−69.8052	−2.83798
$606$	−1.85146	−0.0752104
$607$	−28.2830	−1.14797	−0.573986	−	0.818865i	$-0.694604\pi$
$607$	−28.2830	−1.14797	−0.573986	+	0.818865i	$0.694604\pi$
$608$	−26.8216	−1.08776
$609$	−9.18000	−0.371992
$610$	8.29138	0.335708
$611$	10.9839	0.444361
$612$	−0.493075	−0.0199314
$613$	−8.39067	−0.338896	−0.169448	−	0.985539i	$-0.554198\pi$
$613$	−8.39067	−0.338896	−0.169448	+	0.985539i	$0.554198\pi$
$614$	−15.6762	−0.632642
$615$	15.8750	0.640143
$616$	−15.7782	−0.635720
$617$	1.54113	0.0620437	0.0310219	−	0.999519i	$-0.490124\pi$
$617$	1.54113	0.0620437	0.0310219	+	0.999519i	$0.490124\pi$
$618$	−2.54179	−0.102246
$619$	−18.5681	−0.746313	−0.373157	−	0.927768i	$-0.621725\pi$
$619$	−18.5681	−0.746313	−0.373157	+	0.927768i	$0.621725\pi$
$620$	−10.3832	−0.417000
$621$	1.77438	0.0712035
$622$	1.11324	0.0446369
$623$	−2.60509	−0.104371
$624$	−1.57551	−0.0630708
$625$	−30.8148	−1.23259
$626$	−6.44778	−0.257705
$627$	−27.2912	−1.08991
$628$	−14.6489	−0.584553
$629$	0.158597	0.00632369
$630$	2.23472	0.0890336
$631$	34.2361	1.36292	0.681459	−	0.731857i	$-0.261346\pi$
$631$	34.2361	1.36292	0.681459	+	0.731857i	$0.261346\pi$
$632$	34.9059	1.38848
$633$	−7.23948	−0.287744
$634$	−17.8579	−0.709229
$635$	−2.85652	−0.113357
$636$	−18.0034	−0.713881
$637$	−2.24308	−0.0888740
$638$	−42.7523	−1.69258
$639$	1.31960	0.0522027
$640$	−26.3350	−1.04098
$641$	0.674416	0.0266378	0.0133189	−	0.999911i	$-0.495760\pi$
$641$	0.674416	0.0266378	0.0133189	+	0.999911i	$0.495760\pi$
$642$	0.0813882	0.00321214
$643$	29.7807	1.17444	0.587219	−	0.809428i	$-0.300223\pi$
$643$	29.7807	1.17444	0.587219	+	0.809428i	$0.300223\pi$
$644$	−2.46278	−0.0970473
$645$	10.8958	0.429022
$646$	−1.27413	−0.0501301
$647$	19.3926	0.762401	0.381200	−	0.924492i	$-0.375511\pi$
$647$	19.3926	0.762401	0.381200	+	0.924492i	$0.375511\pi$
$648$	2.65049	0.104121
$649$	−31.8432	−1.24995
$650$	5.54466	0.217480
$651$	−2.61888	−0.102642
$652$	−8.37349	−0.327931
$653$	−7.50126	−0.293547	−0.146773	−	0.989170i	$-0.546889\pi$
$653$	−7.50126	−0.293547	−0.146773	+	0.989170i	$0.546889\pi$
$654$	−15.5086	−0.606434
$655$	−4.23913	−0.165637
$656$	−3.90350	−0.152406
$657$	−8.85675	−0.345535
$658$	3.83088	0.149343
$659$	−1.97123	−0.0767882	−0.0383941	−	0.999263i	$-0.512224\pi$
$659$	−1.97123	−0.0767882	−0.0383941	+	0.999263i	$0.512224\pi$
$660$	−23.6018	−0.918699
$661$	−24.4180	−0.949750	−0.474875	−	0.880053i	$-0.657507\pi$
$661$	−24.4180	−0.949750	−0.474875	+	0.880053i	$0.657507\pi$
$662$	−18.6072	−0.723188
$663$	−0.796853	−0.0309472
$664$	40.4871	1.57120
$665$	−13.0958	−0.507831
$666$	−0.349261	−0.0135336
$667$	−16.2888	−0.630706
$668$	−1.73176	−0.0670039
$669$	−16.9713	−0.656148
$670$	23.0732	0.891394
$671$	−22.0868	−0.852651
$672$	−5.85048	−0.225687
$673$	−39.0533	−1.50539	−0.752697	−	0.658367i	$-0.771247\pi$
$673$	−39.0533	−1.50539	−0.752697	+	0.658367i	$0.771247\pi$
$674$	4.82191	0.185733
$675$	3.15968	0.121616
$676$	11.0601	0.425390
$677$	−37.5231	−1.44213	−0.721065	−	0.692868i	$-0.756347\pi$
$677$	−37.5231	−1.44213	−0.721065	+	0.692868i	$0.756347\pi$
$678$	10.3989	0.399366
$679$	−3.10938	−0.119327
$680$	−2.68966	−0.103144
$681$	26.3750	1.01069
$682$	−12.1964	−0.467026
$683$	−42.5582	−1.62845	−0.814223	−	0.580552i	$-0.802837\pi$
$683$	−42.5582	−1.62845	−0.814223	+	0.580552i	$0.802837\pi$
$684$	−6.36316	−0.243302
$685$	−11.2090	−0.428274
$686$	−0.782325	−0.0298693
$687$	22.6839	0.865446
$688$	−2.67916	−0.102142
$689$	−29.0951	−1.10844
$690$	3.96525	0.150955
$691$	8.50252	0.323451	0.161726	−	0.986836i	$-0.448294\pi$
$691$	8.50252	0.323451	0.161726	+	0.986836i	$0.448294\pi$
$692$	9.74934	0.370614
$693$	−5.95291	−0.226132
$694$	8.56485	0.325117
$695$	4.61006	0.174869
$696$	−24.3315	−0.922284
$697$	−1.97429	−0.0747817
$698$	3.40381	0.128836
$699$	19.9035	0.752819
$700$	−4.38553	−0.165758
$701$	41.0282	1.54962	0.774808	−	0.632197i	$-0.217847\pi$
$701$	41.0282	1.54962	0.774808	+	0.632197i	$0.217847\pi$
$702$	1.75482	0.0662313
$703$	2.04671	0.0771931
$704$	−18.8839	−0.711712
$705$	13.9878	0.526810
$706$	18.4406	0.694023
$707$	2.36661	0.0890055
$708$	−7.42448	−0.279029
$709$	−27.8419	−1.04563	−0.522813	−	0.852448i	$-0.675117\pi$
$709$	−27.8419	−1.04563	−0.522813	+	0.852448i	$0.675117\pi$
$710$	2.94895	0.110672
$711$	13.1696	0.493898
$712$	−6.90478	−0.258767
$713$	−4.64690	−0.174028
$714$	−0.277921	−0.0104009
$715$	−38.1426	−1.42645
$716$	22.2771	0.832533
$717$	14.8701	0.555336
$718$	8.41072	0.313885
$719$	35.7992	1.33509	0.667543	−	0.744572i	$-0.267346\pi$
$719$	35.7992	1.33509	0.667543	+	0.744572i	$0.267346\pi$
$720$	−2.00638	−0.0747733
$721$	3.24902	0.121000
$722$	−1.57859	−0.0587492
$723$	29.5656	1.09956
$724$	13.9336	0.517838
$725$	−29.0059	−1.07725
$726$	−19.1178	−0.709529
$727$	28.1120	1.04262	0.521308	−	0.853369i	$-0.325444\pi$
$727$	28.1120	1.04262	0.521308	+	0.853369i	$0.325444\pi$
$728$	−5.94526	−0.220346
$729$	1.00000	0.0370370
$730$	−19.7924	−0.732550
$731$	−1.35505	−0.0501184
$732$	−5.14970	−0.190339
$733$	−3.35859	−0.124053	−0.0620263	−	0.998075i	$-0.519756\pi$
$733$	−3.35859	−0.124053	−0.0620263	+	0.998075i	$0.519756\pi$
$734$	−10.4865	−0.387062
$735$	−2.85652	−0.105364
$736$	−10.3810	−0.382648
$737$	−61.4628	−2.26401
$738$	4.34776	0.160043
$739$	−8.81699	−0.324338	−0.162169	−	0.986763i	$-0.551849\pi$
$739$	−8.81699	−0.324338	−0.162169	+	0.986763i	$0.551849\pi$
$740$	1.77002	0.0650672
$741$	−10.2834	−0.377772
$742$	−10.1476	−0.372530
$743$	−33.5929	−1.23240	−0.616201	−	0.787589i	$-0.711329\pi$
$743$	−33.5929	−1.23240	−0.616201	+	0.787589i	$0.711329\pi$
$744$	−6.94133	−0.254481
$745$	−26.0165	−0.953171
$746$	−1.90350	−0.0696922
$747$	15.2753	0.558895
$748$	2.93523	0.107323
$749$	−0.104034	−0.00380131
$750$	−4.11261	−0.150171
$751$	38.7986	1.41578	0.707891	−	0.706321i	$-0.249647\pi$
$751$	38.7986	1.41578	0.707891	+	0.706321i	$0.249647\pi$
$752$	−3.43944	−0.125424
$753$	20.0199	0.729564
$754$	−16.1092	−0.586663
$755$	27.8074	1.01202
$756$	−1.38797	−0.0504799
$757$	13.6304	0.495406	0.247703	−	0.968836i	$-0.420324\pi$
$757$	13.6304	0.495406	0.247703	+	0.968836i	$0.420324\pi$
$758$	−0.878256	−0.0318997
$759$	−10.5627	−0.383403
$760$	−34.7102	−1.25907
$761$	−7.00438	−0.253909	−0.126954	−	0.991909i	$-0.540520\pi$
$761$	−7.00438	−0.253909	−0.126954	+	0.991909i	$0.540520\pi$
$762$	−0.782325	−0.0283407
$763$	19.8237	0.717666
$764$	−17.8851	−0.647061
$765$	−1.01478	−0.0366893
$766$	9.48456	0.342691
$767$	−11.9986	−0.433245
$768$	−13.5569	−0.489192
$769$	−25.3807	−0.915251	−0.457625	−	0.889145i	$-0.651300\pi$
$769$	−25.3807	−0.915251	−0.457625	+	0.889145i	$0.651300\pi$
$770$	−13.3031	−0.479411
$771$	−26.4101	−0.951137
$772$	−21.5713	−0.776368
$773$	45.1789	1.62497	0.812485	−	0.582982i	$-0.198114\pi$
$773$	45.1789	1.62497	0.812485	+	0.582982i	$0.198114\pi$
$774$	2.98408	0.107260
$775$	−8.27483	−0.297241
$776$	−8.24138	−0.295848
$777$	0.446439	0.0160159
$778$	5.86601	0.210307
$779$	−25.4784	−0.912857
$780$	−8.89325	−0.318429
$781$	−7.85548	−0.281091
$782$	−0.493138	−0.0176346
$783$	−9.18000	−0.328066
$784$	0.702387	0.0250852
$785$	−30.1482	−1.07603
$786$	−1.16099	−0.0414111
$787$	17.2345	0.614344	0.307172	−	0.951654i	$-0.400617\pi$
$787$	17.2345	0.614344	0.307172	+	0.951654i	$0.400617\pi$
$788$	12.6368	0.450166
$789$	−18.5090	−0.658937
$790$	29.4304	1.04709
$791$	−13.2923	−0.472619
$792$	−15.7782	−0.560652
$793$	−8.32238	−0.295536
$794$	−2.03820	−0.0723331
$795$	−37.0520	−1.31410
$796$	−28.8418	−1.02227
$797$	11.1590	0.395273	0.197636	−	0.980275i	$-0.436673\pi$
$797$	11.1590	0.395273	0.197636	+	0.980275i	$0.436673\pi$
$798$	−3.58659	−0.126964
$799$	−1.73958	−0.0615420
$800$	−18.4856	−0.653566
$801$	−2.60509	−0.0920464
$802$	27.0013	0.953450
$803$	52.7235	1.86057
$804$	−14.3305	−0.505399
$805$	−5.06855	−0.178643
$806$	−4.59566	−0.161875
$807$	0.573334	0.0201823
$808$	6.27268	0.220672
$809$	−8.81764	−0.310012	−0.155006	−	0.987914i	$-0.549540\pi$
$809$	−8.81764	−0.310012	−0.155006	+	0.987914i	$0.549540\pi$
$810$	2.23472	0.0785202
$811$	23.6575	0.830726	0.415363	−	0.909656i	$-0.363655\pi$
$811$	23.6575	0.830726	0.415363	+	0.909656i	$0.363655\pi$
$812$	12.7415	0.447140
$813$	7.26958	0.254955
$814$	2.07912	0.0728731
$815$	−17.2331	−0.603650
$816$	0.249523	0.00873504
$817$	−17.4870	−0.611794
$818$	14.5379	0.508304
$819$	−2.24308	−0.0783795
$820$	−22.0340	−0.769461
$821$	−10.4013	−0.363006	−0.181503	−	0.983390i	$-0.558096\pi$
$821$	−10.4013	−0.363006	−0.181503	+	0.983390i	$0.558096\pi$
$822$	−3.06986	−0.107074
$823$	−55.3493	−1.92935	−0.964677	−	0.263434i	$-0.915145\pi$
$823$	−55.3493	−1.92935	−0.964677	+	0.263434i	$0.915145\pi$
$824$	8.61149	0.299996
$825$	−18.8093	−0.654856
$826$	−4.18480	−0.145608
$827$	48.9737	1.70298	0.851491	−	0.524369i	$-0.175699\pi$
$827$	48.9737	1.70298	0.851491	+	0.524369i	$0.175699\pi$
$828$	−2.46278	−0.0855876
$829$	13.1541	0.456859	0.228430	−	0.973560i	$-0.426641\pi$
$829$	13.1541	0.456859	0.228430	+	0.973560i	$0.426641\pi$
$830$	34.1361	1.18488
$831$	−16.1927	−0.561718
$832$	−7.11551	−0.246686
$833$	0.355250	0.0123087
$834$	1.26257	0.0437194
$835$	−3.56407	−0.123340
$836$	37.8794	1.31008
$837$	−2.61888	−0.0905218
$838$	26.9340	0.930420
$839$	−22.3972	−0.773237	−0.386618	−	0.922240i	$-0.626357\pi$
$839$	−22.3972	−0.773237	−0.386618	+	0.922240i	$0.626357\pi$
$840$	−7.57117	−0.261230
$841$	55.2724	1.90594
$842$	−8.25686	−0.284550
$843$	−0.461522	−0.0158957
$844$	10.0482	0.345872
$845$	22.7624	0.783051
$846$	3.83088	0.131709
$847$	24.4372	0.839671
$848$	9.11070	0.312863
$849$	3.00080	0.102987
$850$	−0.878141	−0.0301200
$851$	0.792154	0.0271547
$852$	−1.83157	−0.0627484
$853$	6.45732	0.221094	0.110547	−	0.993871i	$-0.464740\pi$
$853$	6.45732	0.221094	0.110547	+	0.993871i	$0.464740\pi$
$854$	−2.90262	−0.0993257
$855$	−13.0958	−0.447865
$856$	−0.275741	−0.00942462
$857$	−2.95220	−0.100845	−0.0504226	−	0.998728i	$-0.516057\pi$
$857$	−2.95220	−0.100845	−0.0504226	+	0.998728i	$0.516057\pi$
$858$	−10.4463	−0.356630
$859$	−36.7317	−1.25327	−0.626634	−	0.779314i	$-0.715568\pi$
$859$	−36.7317	−1.25327	−0.626634	+	0.779314i	$0.715568\pi$
$860$	−15.1230	−0.515690
$861$	−5.55748	−0.189398
$862$	−18.5650	−0.632327
$863$	20.3620	0.693131	0.346565	−	0.938026i	$-0.387348\pi$
$863$	20.3620	0.693131	0.346565	+	0.938026i	$0.387348\pi$
$864$	−5.85048	−0.199037
$865$	20.0647	0.682220
$866$	−2.60342	−0.0884677
$867$	−16.8738	−0.573064
$868$	3.63492	0.123377
$869$	−78.3974	−2.65945
$870$	−20.5148	−0.695516
$871$	−23.1594	−0.784727
$872$	52.5426	1.77932
$873$	−3.10938	−0.105236
$874$	−6.36397	−0.215265
$875$	5.25690	0.177716
$876$	12.2929	0.415338
$877$	24.0567	0.812338	0.406169	−	0.913798i	$-0.366864\pi$
$877$	24.0567	0.812338	0.406169	+	0.913798i	$0.366864\pi$
$878$	−16.1826	−0.546136
$879$	14.8706	0.501574
$880$	11.9438	0.402625
$881$	46.6478	1.57161	0.785803	−	0.618477i	$-0.212250\pi$
$881$	46.6478	1.57161	0.785803	+	0.618477i	$0.212250\pi$
$882$	−0.782325	−0.0263423
$883$	25.3836	0.854225	0.427112	−	0.904198i	$-0.359531\pi$
$883$	25.3836	0.854225	0.427112	+	0.904198i	$0.359531\pi$
$884$	1.10601	0.0371990
$885$	−15.2800	−0.513632
$886$	31.3631	1.05367
$887$	25.9636	0.871771	0.435886	−	0.900002i	$-0.356435\pi$
$887$	25.9636	0.871771	0.435886	+	0.900002i	$0.356435\pi$
$888$	1.18328	0.0397084
$889$	1.00000	0.0335389
$890$	−5.82166	−0.195143
$891$	−5.95291	−0.199430
$892$	23.5556	0.788699
$893$	−22.4494	−0.751242
$894$	−7.12524	−0.238304
$895$	45.8475	1.53251
$896$	9.21926	0.307994
$897$	−3.98008	−0.132891
$898$	15.9083	0.530866
$899$	24.0413	0.801824
$900$	−4.38553	−0.146184
$901$	4.60796	0.153514
$902$	−25.8818	−0.861770
$903$	−3.81437	−0.126934
$904$	−35.2310	−1.17177
$905$	28.6761	0.953226
$906$	7.61573	0.253016
$907$	−16.6421	−0.552591	−0.276296	−	0.961073i	$-0.589107\pi$
$907$	−16.6421	−0.552591	−0.276296	+	0.961073i	$0.589107\pi$
$908$	−36.6076	−1.21487
$909$	2.36661	0.0784955
$910$	−5.01266	−0.166168
$911$	23.3831	0.774717	0.387358	−	0.921929i	$-0.373388\pi$
$911$	23.3831	0.774717	0.387358	+	0.921929i	$0.373388\pi$
$912$	3.22011	0.106628
$913$	−90.9326	−3.00943
$914$	8.93058	0.295397
$915$	−10.5984	−0.350372
$916$	−31.4845	−1.04028
$917$	1.48402	0.0490067
$918$	−0.277921	−0.00917275
$919$	24.1039	0.795114	0.397557	−	0.917578i	$-0.369858\pi$
$919$	24.1039	0.795114	0.397557	+	0.917578i	$0.369858\pi$
$920$	−13.4342	−0.442911
$921$	20.0380	0.660275
$922$	27.4680	0.904610
$923$	−2.95997	−0.0974288
$924$	8.26245	0.271815
$925$	1.41061	0.0463804
$926$	7.52286	0.247216
$927$	3.24902	0.106712
$928$	53.7074	1.76303
$929$	−11.7991	−0.387117	−0.193559	−	0.981089i	$-0.562003\pi$
$929$	−11.7991	−0.387117	−0.193559	+	0.981089i	$0.562003\pi$
$930$	−5.85248	−0.191910
$931$	4.58452	0.150252
$932$	−27.6254	−0.904899
$933$	−1.42299	−0.0465866
$934$	−25.6205	−0.838328
$935$	6.04087	0.197558
$936$	−5.94526	−0.194327
$937$	−13.8473	−0.452371	−0.226186	−	0.974084i	$-0.572626\pi$
$937$	−13.8473	−0.452371	−0.226186	+	0.974084i	$0.572626\pi$
$938$	−8.07738	−0.263736
$939$	8.24182	0.268962
$940$	−19.4146	−0.633233
$941$	44.6036	1.45404	0.727018	−	0.686618i	$-0.240905\pi$
$941$	44.6036	1.45404	0.727018	+	0.686618i	$0.240905\pi$
$942$	−8.25680	−0.269021
$943$	−9.86109	−0.321121
$944$	3.75719	0.122286
$945$	−2.85652	−0.0929225
$946$	−17.7639	−0.577555
$947$	23.5909	0.766601	0.383301	−	0.923624i	$-0.374787\pi$
$947$	23.5909	0.766601	0.383301	+	0.923624i	$0.374787\pi$
$948$	−18.2790	−0.593673
$949$	19.8664	0.644891
$950$	−11.3325	−0.367674
$951$	22.8267	0.740207
$952$	0.941587	0.0305170
$953$	22.2076	0.719374	0.359687	−	0.933073i	$-0.382884\pi$
$953$	22.2076	0.719374	0.359687	+	0.933073i	$0.382884\pi$
$954$	−10.1476	−0.328540
$955$	−36.8086	−1.19110
$956$	−20.6393	−0.667522
$957$	54.6477	1.76651
$958$	−3.21791	−0.103966
$959$	3.92401	0.126713
$960$	−9.06145	−0.292457
$961$	−24.1415	−0.778757
$962$	0.783419	0.0252585
$963$	−0.104034	−0.00335244
$964$	−41.0361	−1.32168
$965$	−44.3950	−1.42913
$966$	−1.38814	−0.0446628
$967$	−15.9265	−0.512161	−0.256081	−	0.966655i	$-0.582431\pi$
$967$	−15.9265	−0.512161	−0.256081	+	0.966655i	$0.582431\pi$
$968$	64.7705	2.08180
$969$	1.62865	0.0523197
$970$	−6.94860	−0.223106
$971$	−34.2446	−1.09896	−0.549480	−	0.835507i	$-0.685174\pi$
$971$	−34.2446	−1.09896	−0.549480	+	0.835507i	$0.685174\pi$
$972$	−1.38797	−0.0445191
$973$	−1.61387	−0.0517384
$974$	8.13166	0.260555
$975$	−7.08741	−0.226979
$976$	2.60603	0.0834170
$977$	6.04555	0.193414	0.0967072	−	0.995313i	$-0.469169\pi$
$977$	6.04555	0.193414	0.0967072	+	0.995313i	$0.469169\pi$
$978$	−4.71970	−0.150919
$979$	15.5079	0.495634
$980$	3.96475	0.126649
$981$	19.8237	0.632922
$982$	−9.09914	−0.290365
$983$	50.1818	1.60055	0.800275	−	0.599633i	$-0.204687\pi$
$983$	50.1818	1.60055	0.800275	+	0.599633i	$0.204687\pi$
$984$	−14.7301	−0.469577
$985$	26.0072	0.828657
$986$	2.55131	0.0812504
$987$	−4.89679	−0.155867
$988$	14.2731	0.454087
$989$	−6.76814	−0.215214
$990$	−13.3031	−0.422801
$991$	34.7358	1.10342	0.551710	−	0.834036i	$-0.313976\pi$
$991$	34.7358	1.10342	0.551710	+	0.834036i	$0.313976\pi$
$992$	15.3217	0.486465
$993$	23.7844	0.754776
$994$	−1.03236	−0.0327444
$995$	−59.3581	−1.88178
$996$	−21.2016	−0.671799
$997$	−28.1054	−0.890108	−0.445054	−	0.895504i	$-0.646815\pi$
$997$	−28.1054	−0.890108	−0.445054	+	0.895504i	$0.646815\pi$
$998$	−14.6165	−0.462677
$999$	0.446439	0.0141247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.7	✓	19
3.2	odd	2		8001.2.a.v.1.13		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.7	✓	19	1.1	even	1	trivial
8001.2.a.v.1.13		19	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.782325 q^{2} +1.00000 q^{3} -1.38797 q^{4} -2.85652 q^{5} -0.782325 q^{6} +1.00000 q^{7} +2.65049 q^{8} +1.00000 q^{9} +2.23472 q^{10} -5.95291 q^{11} -1.38797 q^{12} -2.24308 q^{13} -0.782325 q^{14} -2.85652 q^{15} +0.702387 q^{16} +0.355250 q^{17} -0.782325 q^{18} +4.58452 q^{19} +3.96475 q^{20} +1.00000 q^{21} +4.65711 q^{22} +1.77438 q^{23} +2.65049 q^{24} +3.15968 q^{25} +1.75482 q^{26} +1.00000 q^{27} -1.38797 q^{28} -9.18000 q^{29} +2.23472 q^{30} -2.61888 q^{31} -5.85048 q^{32} -5.95291 q^{33} -0.277921 q^{34} -2.85652 q^{35} -1.38797 q^{36} +0.446439 q^{37} -3.58659 q^{38} -2.24308 q^{39} -7.57117 q^{40} -5.55748 q^{41} -0.782325 q^{42} -3.81437 q^{43} +8.26245 q^{44} -2.85652 q^{45} -1.38814 q^{46} -4.89679 q^{47} +0.702387 q^{48} +1.00000 q^{49} -2.47190 q^{50} +0.355250 q^{51} +3.11332 q^{52} +12.9711 q^{53} -0.782325 q^{54} +17.0046 q^{55} +2.65049 q^{56} +4.58452 q^{57} +7.18175 q^{58} +5.34918 q^{59} +3.96475 q^{60} +3.71025 q^{61} +2.04882 q^{62} +1.00000 q^{63} +3.17221 q^{64} +6.40739 q^{65} +4.65711 q^{66} +10.3248 q^{67} -0.493075 q^{68} +1.77438 q^{69} +2.23472 q^{70} +1.31960 q^{71} +2.65049 q^{72} -8.85675 q^{73} -0.349261 q^{74} +3.15968 q^{75} -6.36316 q^{76} -5.95291 q^{77} +1.75482 q^{78} +13.1696 q^{79} -2.00638 q^{80} +1.00000 q^{81} +4.34776 q^{82} +15.2753 q^{83} -1.38797 q^{84} -1.01478 q^{85} +2.98408 q^{86} -9.18000 q^{87} -15.7782 q^{88} -2.60509 q^{89} +2.23472 q^{90} -2.24308 q^{91} -2.46278 q^{92} -2.61888 q^{93} +3.83088 q^{94} -13.0958 q^{95} -5.85048 q^{96} -3.10938 q^{97} -0.782325 q^{98} -5.95291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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