LMFDB - Embedded newform 2667.2.a.o.1.8

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)

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);

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")

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

Newform invariants

comment:select newform

sage:traces = [16,5,-16,19] 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.298113$ 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)

$f(q)$	$=$	\(q+0.298113 q^{2} -1.00000 q^{3} -1.91113 q^{4} +2.54722 q^{5} -0.298113 q^{6} -1.00000 q^{7} -1.16596 q^{8} +1.00000 q^{9} +0.759360 q^{10} +6.15296 q^{11} +1.91113 q^{12} +4.68194 q^{13} -0.298113 q^{14} -2.54722 q^{15} +3.47467 q^{16} -4.41002 q^{17} +0.298113 q^{18} -5.03205 q^{19} -4.86807 q^{20} +1.00000 q^{21} +1.83427 q^{22} +9.11699 q^{23} +1.16596 q^{24} +1.48835 q^{25} +1.39575 q^{26} -1.00000 q^{27} +1.91113 q^{28} -4.28790 q^{29} -0.759360 q^{30} +0.0487464 q^{31} +3.36776 q^{32} -6.15296 q^{33} -1.31468 q^{34} -2.54722 q^{35} -1.91113 q^{36} +3.02081 q^{37} -1.50012 q^{38} -4.68194 q^{39} -2.96995 q^{40} -3.31879 q^{41} +0.298113 q^{42} +1.89550 q^{43} -11.7591 q^{44} +2.54722 q^{45} +2.71789 q^{46} -10.1769 q^{47} -3.47467 q^{48} +1.00000 q^{49} +0.443697 q^{50} +4.41002 q^{51} -8.94780 q^{52} +6.07411 q^{53} -0.298113 q^{54} +15.6730 q^{55} +1.16596 q^{56} +5.03205 q^{57} -1.27828 q^{58} -9.37602 q^{59} +4.86807 q^{60} +14.3700 q^{61} +0.0145319 q^{62} -1.00000 q^{63} -5.94537 q^{64} +11.9260 q^{65} -1.83427 q^{66} +5.59222 q^{67} +8.42813 q^{68} -9.11699 q^{69} -0.759360 q^{70} +7.54064 q^{71} -1.16596 q^{72} +5.40772 q^{73} +0.900543 q^{74} -1.48835 q^{75} +9.61689 q^{76} -6.15296 q^{77} -1.39575 q^{78} -8.18983 q^{79} +8.85077 q^{80} +1.00000 q^{81} -0.989374 q^{82} -12.5627 q^{83} -1.91113 q^{84} -11.2333 q^{85} +0.565072 q^{86} +4.28790 q^{87} -7.17408 q^{88} +17.6526 q^{89} +0.759360 q^{90} -4.68194 q^{91} -17.4237 q^{92} -0.0487464 q^{93} -3.03386 q^{94} -12.8178 q^{95} -3.36776 q^{96} -0.133391 q^{97} +0.298113 q^{98} +6.15296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * 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 $

$2$	0.298113	0.210797	0.105399	−	0.994430i	$-0.466388\pi$
$2$	0.298113	0.210797	0.105399	+	0.994430i	$0.466388\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.91113	−0.955564
$5$	2.54722	1.13915	0.569577	−	0.821938i	$-0.307107\pi$
$5$	2.54722	1.13915	0.569577	+	0.821938i	$0.307107\pi$
$6$	−0.298113	−0.121704
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.16596	−0.412228
$9$	1.00000	0.333333
$10$	0.759360	0.240131
$11$	6.15296	1.85519	0.927593	−	0.373592i	$-0.121874\pi$
$11$	6.15296	1.85519	0.927593	+	0.373592i	$0.121874\pi$
$12$	1.91113	0.551695
$13$	4.68194	1.29854	0.649269	−	0.760559i	$-0.275075\pi$
$13$	4.68194	1.29854	0.649269	+	0.760559i	$0.275075\pi$
$14$	−0.298113	−0.0796740
$15$	−2.54722	−0.657691
$16$	3.47467	0.868668
$17$	−4.41002	−1.06959	−0.534794	−	0.844982i	$-0.679611\pi$
$17$	−4.41002	−1.06959	−0.534794	+	0.844982i	$0.679611\pi$
$18$	0.298113	0.0702658
$19$	−5.03205	−1.15443	−0.577215	−	0.816592i	$-0.695861\pi$
$19$	−5.03205	−1.15443	−0.577215	+	0.816592i	$0.695861\pi$
$20$	−4.86807	−1.08853
$21$	1.00000	0.218218
$22$	1.83427	0.391069
$23$	9.11699	1.90102	0.950512	−	0.310688i	$-0.100559\pi$
$23$	9.11699	1.90102	0.950512	+	0.310688i	$0.100559\pi$
$24$	1.16596	0.238000
$25$	1.48835	0.297670
$26$	1.39575	0.273728
$27$	−1.00000	−0.192450
$28$	1.91113	0.361169
$29$	−4.28790	−0.796243	−0.398121	−	0.917333i	$-0.630338\pi$
$29$	−4.28790	−0.796243	−0.398121	+	0.917333i	$0.630338\pi$
$30$	−0.759360	−0.138639
$31$	0.0487464	0.00875512	0.00437756	−	0.999990i	$-0.498607\pi$
$31$	0.0487464	0.00875512	0.00437756	+	0.999990i	$0.498607\pi$
$32$	3.36776	0.595341
$33$	−6.15296	−1.07109
$34$	−1.31468	−0.225466
$35$	−2.54722	−0.430560
$36$	−1.91113	−0.318521
$37$	3.02081	0.496619	0.248309	−	0.968681i	$-0.420125\pi$
$37$	3.02081	0.496619	0.248309	+	0.968681i	$0.420125\pi$
$38$	−1.50012	−0.243351
$39$	−4.68194	−0.749711
$40$	−2.96995	−0.469591
$41$	−3.31879	−0.518309	−0.259154	−	0.965836i	$-0.583444\pi$
$41$	−3.31879	−0.518309	−0.259154	+	0.965836i	$0.583444\pi$
$42$	0.298113	0.0459998
$43$	1.89550	0.289061	0.144531	−	0.989500i	$-0.453833\pi$
$43$	1.89550	0.289061	0.144531	+	0.989500i	$0.453833\pi$
$44$	−11.7591	−1.77275
$45$	2.54722	0.379718
$46$	2.71789	0.400731
$47$	−10.1769	−1.48445	−0.742227	−	0.670149i	$-0.766230\pi$
$47$	−10.1769	−1.48445	−0.742227	+	0.670149i	$0.766230\pi$
$48$	−3.47467	−0.501526
$49$	1.00000	0.142857
$50$	0.443697	0.0627482
$51$	4.41002	0.617527
$52$	−8.94780	−1.24084
$53$	6.07411	0.834343	0.417171	−	0.908828i	$-0.363021\pi$
$53$	6.07411	0.834343	0.417171	+	0.908828i	$0.363021\pi$
$54$	−0.298113	−0.0405680
$55$	15.6730	2.11334
$56$	1.16596	0.155808
$57$	5.03205	0.666511
$58$	−1.27828	−0.167846
$59$	−9.37602	−1.22065	−0.610327	−	0.792150i	$-0.708962\pi$
$59$	−9.37602	−1.22065	−0.610327	+	0.792150i	$0.708962\pi$
$60$	4.86807	0.628466
$61$	14.3700	1.83989	0.919943	−	0.392052i	$-0.128235\pi$
$61$	14.3700	1.83989	0.919943	+	0.392052i	$0.128235\pi$
$62$	0.0145319	0.00184556
$63$	−1.00000	−0.125988
$64$	−5.94537	−0.743171
$65$	11.9260	1.47923
$66$	−1.83427	−0.225784
$67$	5.59222	0.683199	0.341599	−	0.939846i	$-0.389031\pi$
$67$	5.59222	0.683199	0.341599	+	0.939846i	$0.389031\pi$
$68$	8.42813	1.02206
$69$	−9.11699	−1.09756
$70$	−0.759360	−0.0907609
$71$	7.54064	0.894909	0.447455	−	0.894307i	$-0.352331\pi$
$71$	7.54064	0.894909	0.447455	+	0.894307i	$0.352331\pi$
$72$	−1.16596	−0.137409
$73$	5.40772	0.632926	0.316463	−	0.948605i	$-0.397505\pi$
$73$	5.40772	0.632926	0.316463	+	0.948605i	$0.397505\pi$
$74$	0.900543	0.104686
$75$	−1.48835	−0.171860
$76$	9.61689	1.10313
$77$	−6.15296	−0.701195
$78$	−1.39575	−0.158037
$79$	−8.18983	−0.921427	−0.460714	−	0.887549i	$-0.652407\pi$
$79$	−8.18983	−0.921427	−0.460714	+	0.887549i	$0.652407\pi$
$80$	8.85077	0.989546
$81$	1.00000	0.111111
$82$	−0.989374	−0.109258
$83$	−12.5627	−1.37894	−0.689470	−	0.724314i	$-0.742157\pi$
$83$	−12.5627	−1.37894	−0.689470	+	0.724314i	$0.742157\pi$
$84$	−1.91113	−0.208521
$85$	−11.2333	−1.21842
$86$	0.565072	0.0609333
$87$	4.28790	0.459711
$88$	−7.17408	−0.764760
$89$	17.6526	1.87118	0.935588	−	0.353093i	$-0.114870\pi$
$89$	17.6526	1.87118	0.935588	+	0.353093i	$0.114870\pi$
$90$	0.759360	0.0800435
$91$	−4.68194	−0.490801
$92$	−17.4237	−1.81655
$93$	−0.0487464	−0.00505477
$94$	−3.03386	−0.312919
$95$	−12.8178	−1.31507
$96$	−3.36776	−0.343720
$97$	−0.133391	−0.0135438	−0.00677188	−	0.999977i	$-0.502156\pi$
$97$	−0.133391	−0.0135438	−0.00677188	+	0.999977i	$0.502156\pi$
$98$	0.298113	0.0301139
$99$	6.15296	0.618395
$100$	−2.84443	−0.284443
$101$	17.4204	1.73340	0.866699	−	0.498831i	$-0.166237\pi$
$101$	17.4204	1.73340	0.866699	+	0.498831i	$0.166237\pi$
$102$	1.31468	0.130173
$103$	5.99870	0.591069	0.295534	−	0.955332i	$-0.404502\pi$
$103$	5.99870	0.591069	0.295534	+	0.955332i	$0.404502\pi$
$104$	−5.45894	−0.535293
$105$	2.54722	0.248584
$106$	1.81077	0.175877
$107$	16.9503	1.63865	0.819323	−	0.573332i	$-0.194350\pi$
$107$	16.9503	1.63865	0.819323	+	0.573332i	$0.194350\pi$
$108$	1.91113	0.183898
$109$	−1.13699	−0.108904	−0.0544522	−	0.998516i	$-0.517341\pi$
$109$	−1.13699	−0.108904	−0.0544522	+	0.998516i	$0.517341\pi$
$110$	4.67231	0.445487
$111$	−3.02081	−0.286723
$112$	−3.47467	−0.328326
$113$	−7.37766	−0.694032	−0.347016	−	0.937859i	$-0.612805\pi$
$113$	−7.37766	−0.694032	−0.347016	+	0.937859i	$0.612805\pi$
$114$	1.50012	0.140499
$115$	23.2230	2.16556
$116$	8.19472	0.760861
$117$	4.68194	0.432846
$118$	−2.79511	−0.257311
$119$	4.41002	0.404266
$120$	2.96995	0.271118
$121$	26.8589	2.44172
$122$	4.28387	0.387843
$123$	3.31879	0.299246
$124$	−0.0931607	−0.00836608
$125$	−8.94496	−0.800061
$126$	−0.298113	−0.0265580
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−8.50790	−0.752000
$129$	−1.89550	−0.166889
$130$	3.55528	0.311819
$131$	−0.589991	−0.0515478	−0.0257739	−	0.999668i	$-0.508205\pi$
$131$	−0.589991	−0.0515478	−0.0257739	+	0.999668i	$0.508205\pi$
$132$	11.7591	1.02350
$133$	5.03205	0.436334
$134$	1.66711	0.144017
$135$	−2.54722	−0.219230
$136$	5.14190	0.440914
$137$	−6.88031	−0.587824	−0.293912	−	0.955832i	$-0.594957\pi$
$137$	−6.88031	−0.587824	−0.293912	+	0.955832i	$0.594957\pi$
$138$	−2.71789	−0.231362
$139$	23.2136	1.96895	0.984476	−	0.175521i	$-0.0561610\pi$
$139$	23.2136	1.96895	0.984476	+	0.175521i	$0.0561610\pi$
$140$	4.86807	0.411427
$141$	10.1769	0.857050
$142$	2.24796	0.188645
$143$	28.8078	2.40903
$144$	3.47467	0.289556
$145$	−10.9222	−0.907042
$146$	1.61211	0.133419
$147$	−1.00000	−0.0824786
$148$	−5.77316	−0.474551
$149$	−5.01259	−0.410647	−0.205324	−	0.978694i	$-0.565825\pi$
$149$	−5.01259	−0.410647	−0.205324	+	0.978694i	$0.565825\pi$
$150$	−0.443697	−0.0362277
$151$	10.9460	0.890769	0.445384	−	0.895339i	$-0.353067\pi$
$151$	10.9460	0.890769	0.445384	+	0.895339i	$0.353067\pi$
$152$	5.86715	0.475889
$153$	−4.41002	−0.356529
$154$	−1.83427	−0.147810
$155$	0.124168	0.00997342
$156$	8.94780	0.716397
$157$	4.71794	0.376532	0.188266	−	0.982118i	$-0.439713\pi$
$157$	4.71794	0.376532	0.188266	+	0.982118i	$0.439713\pi$
$158$	−2.44149	−0.194235
$159$	−6.07411	−0.481708
$160$	8.57843	0.678185
$161$	−9.11699	−0.718520
$162$	0.298113	0.0234219
$163$	−2.39560	−0.187638	−0.0938188	−	0.995589i	$-0.529907\pi$
$163$	−2.39560	−0.187638	−0.0938188	+	0.995589i	$0.529907\pi$
$164$	6.34264	0.495277
$165$	−15.6730	−1.22014
$166$	−3.74511	−0.290677
$167$	−6.18252	−0.478418	−0.239209	−	0.970968i	$-0.576888\pi$
$167$	−6.18252	−0.478418	−0.239209	+	0.970968i	$0.576888\pi$
$168$	−1.16596	−0.0899555
$169$	8.92059	0.686199
$170$	−3.34880	−0.256841
$171$	−5.03205	−0.384810
$172$	−3.62254	−0.276216
$173$	−16.3023	−1.23944	−0.619719	−	0.784824i	$-0.712753\pi$
$173$	−16.3023	−1.23944	−0.619719	+	0.784824i	$0.712753\pi$
$174$	1.27828	0.0969059
$175$	−1.48835	−0.112509
$176$	21.3795	1.61154
$177$	9.37602	0.704745
$178$	5.26248	0.394439
$179$	22.0264	1.64633	0.823166	−	0.567801i	$-0.192206\pi$
$179$	22.0264	1.64633	0.823166	+	0.567801i	$0.192206\pi$
$180$	−4.86807	−0.362845
$181$	7.90350	0.587463	0.293731	−	0.955888i	$-0.405103\pi$
$181$	7.90350	0.587463	0.293731	+	0.955888i	$0.405103\pi$
$182$	−1.39575	−0.103460
$183$	−14.3700	−1.06226
$184$	−10.6300	−0.783655
$185$	7.69469	0.565725
$186$	−0.0145319	−0.00106553
$187$	−27.1347	−1.98429
$188$	19.4494	1.41849
$189$	1.00000	0.0727393
$190$	−3.82113	−0.277214
$191$	−18.4005	−1.33141	−0.665707	−	0.746213i	$-0.731870\pi$
$191$	−18.4005	−1.33141	−0.665707	+	0.746213i	$0.731870\pi$
$192$	5.94537	0.429070
$193$	6.99017	0.503163	0.251582	−	0.967836i	$-0.419049\pi$
$193$	6.99017	0.503163	0.251582	+	0.967836i	$0.419049\pi$
$194$	−0.0397654	−0.00285499
$195$	−11.9260	−0.854036
$196$	−1.91113	−0.136509
$197$	19.1489	1.36430	0.682152	−	0.731210i	$-0.261044\pi$
$197$	19.1489	1.36430	0.682152	+	0.731210i	$0.261044\pi$
$198$	1.83427	0.130356
$199$	11.7831	0.835280	0.417640	−	0.908613i	$-0.362857\pi$
$199$	11.7831	0.835280	0.417640	+	0.908613i	$0.362857\pi$
$200$	−1.73535	−0.122708
$201$	−5.59222	−0.394445
$202$	5.19325	0.365396
$203$	4.28790	0.300951
$204$	−8.42813	−0.590087
$205$	−8.45371	−0.590433
$206$	1.78829	0.124596
$207$	9.11699	0.633675
$208$	16.2682	1.12800
$209$	−30.9620	−2.14168
$210$	0.759360	0.0524008
$211$	−25.5442	−1.75854	−0.879268	−	0.476327i	$-0.841968\pi$
$211$	−25.5442	−1.75854	−0.879268	+	0.476327i	$0.841968\pi$
$212$	−11.6084	−0.797268
$213$	−7.54064	−0.516676
$214$	5.05309	0.345422
$215$	4.82826	0.329285
$216$	1.16596	0.0793333
$217$	−0.0487464	−0.00330912
$218$	−0.338953	−0.0229568
$219$	−5.40772	−0.365420
$220$	−29.9531	−2.01943
$221$	−20.6475	−1.38890
$222$	−0.900543	−0.0604405
$223$	−17.0666	−1.14286	−0.571432	−	0.820650i	$-0.693612\pi$
$223$	−17.0666	−1.14286	−0.571432	+	0.820650i	$0.693612\pi$
$224$	−3.36776	−0.225018
$225$	1.48835	0.0992235
$226$	−2.19937	−0.146300
$227$	19.1172	1.26885	0.634427	−	0.772982i	$-0.281236\pi$
$227$	19.1172	1.26885	0.634427	+	0.772982i	$0.281236\pi$
$228$	−9.61689	−0.636894
$229$	−17.4537	−1.15337	−0.576686	−	0.816966i	$-0.695654\pi$
$229$	−17.4537	−1.15337	−0.576686	+	0.816966i	$0.695654\pi$
$230$	6.92308	0.456494
$231$	6.15296	0.404835
$232$	4.99950	0.328233
$233$	18.3373	1.20132	0.600659	−	0.799506i	$-0.294905\pi$
$233$	18.3373	1.20132	0.600659	+	0.799506i	$0.294905\pi$
$234$	1.39575	0.0912428
$235$	−25.9229	−1.69102
$236$	17.9188	1.16641
$237$	8.18983	0.531986
$238$	1.31468	0.0852183
$239$	12.5721	0.813222	0.406611	−	0.913601i	$-0.366710\pi$
$239$	12.5721	0.813222	0.406611	+	0.913601i	$0.366710\pi$
$240$	−8.85077	−0.571315
$241$	1.76945	0.113980	0.0569900	−	0.998375i	$-0.481850\pi$
$241$	1.76945	0.113980	0.0569900	+	0.998375i	$0.481850\pi$
$242$	8.00697	0.514708
$243$	−1.00000	−0.0641500
$244$	−27.4629	−1.75813
$245$	2.54722	0.162736
$246$	0.989374	0.0630802
$247$	−23.5598	−1.49907
$248$	−0.0568362	−0.00360910
$249$	12.5627	0.796132
$250$	−2.66660	−0.168651
$251$	−30.8131	−1.94491	−0.972453	−	0.233099i	$-0.925114\pi$
$251$	−30.8131	−1.94491	−0.972453	+	0.233099i	$0.925114\pi$
$252$	1.91113	0.120390
$253$	56.0965	3.52675
$254$	0.298113	0.0187052
$255$	11.2333	0.703458
$256$	9.35443	0.584652
$257$	13.9647	0.871092	0.435546	−	0.900166i	$-0.356555\pi$
$257$	13.9647	0.871092	0.435546	+	0.900166i	$0.356555\pi$
$258$	−0.565072	−0.0351799
$259$	−3.02081	−0.187704
$260$	−22.7920	−1.41350
$261$	−4.28790	−0.265414
$262$	−0.175884	−0.0108661
$263$	2.37995	0.146754	0.0733770	−	0.997304i	$-0.476622\pi$
$263$	2.37995	0.146754	0.0733770	+	0.997304i	$0.476622\pi$
$264$	7.17408	0.441534
$265$	15.4721	0.950445
$266$	1.50012	0.0919781
$267$	−17.6526	−1.08032
$268$	−10.6875	−0.652840
$269$	6.90652	0.421098	0.210549	−	0.977583i	$-0.432475\pi$
$269$	6.90652	0.421098	0.210549	+	0.977583i	$0.432475\pi$
$270$	−0.759360	−0.0462132
$271$	−15.2627	−0.927141	−0.463570	−	0.886060i	$-0.653432\pi$
$271$	−15.2627	−0.927141	−0.463570	+	0.886060i	$0.653432\pi$
$272$	−15.3234	−0.929117
$273$	4.68194	0.283364
$274$	−2.05111	−0.123912
$275$	9.15777	0.552234
$276$	17.4237	1.04879
$277$	−20.0356	−1.20382	−0.601910	−	0.798564i	$-0.705593\pi$
$277$	−20.0356	−1.20382	−0.601910	+	0.798564i	$0.705593\pi$
$278$	6.92027	0.415050
$279$	0.0487464	0.00291837
$280$	2.96995	0.177489
$281$	19.7110	1.17586	0.587929	−	0.808912i	$-0.299943\pi$
$281$	19.7110	1.17586	0.587929	+	0.808912i	$0.299943\pi$
$282$	3.03386	0.180664
$283$	−16.3259	−0.970473	−0.485236	−	0.874383i	$-0.661266\pi$
$283$	−16.3259	−0.970473	−0.485236	+	0.874383i	$0.661266\pi$
$284$	−14.4111	−0.855143
$285$	12.8178	0.759258
$286$	8.58797	0.507817
$287$	3.31879	0.195902
$288$	3.36776	0.198447
$289$	2.44832	0.144019
$290$	−3.25606	−0.191202
$291$	0.133391	0.00781949
$292$	−10.3349	−0.604802
$293$	−7.46323	−0.436006	−0.218003	−	0.975948i	$-0.569954\pi$
$293$	−7.46323	−0.436006	−0.218003	+	0.975948i	$0.569954\pi$
$294$	−0.298113	−0.0173863
$295$	−23.8828	−1.39051
$296$	−3.52214	−0.204720
$297$	−6.15296	−0.357031
$298$	−1.49432	−0.0865634
$299$	42.6852	2.46855
$300$	2.84443	0.164223
$301$	−1.89550	−0.109255
$302$	3.26313	0.187772
$303$	−17.4204	−1.00078
$304$	−17.4847	−1.00282
$305$	36.6035	2.09591
$306$	−1.31468	−0.0751555
$307$	10.3378	0.590010	0.295005	−	0.955496i	$-0.404679\pi$
$307$	10.3378	0.590010	0.295005	+	0.955496i	$0.404679\pi$
$308$	11.7591	0.670037
$309$	−5.99870	−0.341254
$310$	0.0370161	0.00210237
$311$	18.9888	1.07676	0.538379	−	0.842703i	$-0.319037\pi$
$311$	18.9888	1.07676	0.538379	+	0.842703i	$0.319037\pi$
$312$	5.45894	0.309052
$313$	21.6377	1.22304	0.611519	−	0.791230i	$-0.290559\pi$
$313$	21.6377	1.22304	0.611519	+	0.791230i	$0.290559\pi$
$314$	1.40648	0.0793720
$315$	−2.54722	−0.143520
$316$	15.6518	0.880483
$317$	5.64090	0.316824	0.158412	−	0.987373i	$-0.449363\pi$
$317$	5.64090	0.316824	0.158412	+	0.987373i	$0.449363\pi$
$318$	−1.81077	−0.101543
$319$	−26.3832	−1.47718
$320$	−15.1442	−0.846586
$321$	−16.9503	−0.946073
$322$	−2.71789	−0.151462
$323$	22.1915	1.23477
$324$	−1.91113	−0.106174
$325$	6.96838	0.386536
$326$	−0.714158	−0.0395535
$327$	1.13699	0.0628760
$328$	3.86957	0.213661
$329$	10.1769	0.561071
$330$	−4.67231	−0.257202
$331$	−11.1486	−0.612781	−0.306391	−	0.951906i	$-0.599121\pi$
$331$	−11.1486	−0.612781	−0.306391	+	0.951906i	$0.599121\pi$
$332$	24.0090	1.31767
$333$	3.02081	0.165540
$334$	−1.84309	−0.100849
$335$	14.2446	0.778268
$336$	3.47467	0.189559
$337$	26.5229	1.44480	0.722398	−	0.691477i	$-0.243040\pi$
$337$	26.5229	1.44480	0.722398	+	0.691477i	$0.243040\pi$
$338$	2.65934	0.144649
$339$	7.37766	0.400700
$340$	21.4683	1.16428
$341$	0.299935	0.0162424
$342$	−1.50012	−0.0811170
$343$	−1.00000	−0.0539949
$344$	−2.21007	−0.119159
$345$	−23.2230	−1.25029
$346$	−4.85991	−0.261270
$347$	8.02759	0.430944	0.215472	−	0.976510i	$-0.430871\pi$
$347$	8.02759	0.430944	0.215472	+	0.976510i	$0.430871\pi$
$348$	−8.19472	−0.439283
$349$	4.22025	0.225905	0.112952	−	0.993600i	$-0.463969\pi$
$349$	4.22025	0.225905	0.112952	+	0.993600i	$0.463969\pi$
$350$	−0.443697	−0.0237166
$351$	−4.68194	−0.249904
$352$	20.7217	1.10447
$353$	27.0656	1.44056	0.720278	−	0.693686i	$-0.244014\pi$
$353$	27.0656	1.44056	0.720278	+	0.693686i	$0.244014\pi$
$354$	2.79511	0.148558
$355$	19.2077	1.01944
$356$	−33.7365	−1.78803
$357$	−4.41002	−0.233403
$358$	6.56636	0.347043
$359$	−20.6950	−1.09224	−0.546121	−	0.837706i	$-0.683896\pi$
$359$	−20.6950	−1.09224	−0.546121	+	0.837706i	$0.683896\pi$
$360$	−2.96995	−0.156530
$361$	6.32150	0.332711
$362$	2.35613	0.123836
$363$	−26.8589	−1.40973
$364$	8.94780	0.468992
$365$	13.7747	0.721000
$366$	−4.28387	−0.223921
$367$	−0.789317	−0.0412020	−0.0206010	−	0.999788i	$-0.506558\pi$
$367$	−0.789317	−0.0412020	−0.0206010	+	0.999788i	$0.506558\pi$
$368$	31.6785	1.65136
$369$	−3.31879	−0.172770
$370$	2.29388	0.119253
$371$	−6.07411	−0.315352
$372$	0.0931607	0.00483016
$373$	−6.27308	−0.324808	−0.162404	−	0.986724i	$-0.551925\pi$
$373$	−6.27308	−0.324808	−0.162404	+	0.986724i	$0.551925\pi$
$374$	−8.08919	−0.418282
$375$	8.94496	0.461916
$376$	11.8658	0.611934
$377$	−20.0757	−1.03395
$378$	0.298113	0.0153333
$379$	−25.4550	−1.30754	−0.653768	−	0.756695i	$-0.726813\pi$
$379$	−25.4550	−1.30754	−0.653768	+	0.756695i	$0.726813\pi$
$380$	24.4964	1.25664
$381$	−1.00000	−0.0512316
$382$	−5.48542	−0.280659
$383$	−1.91780	−0.0979952	−0.0489976	−	0.998799i	$-0.515603\pi$
$383$	−1.91780	−0.0979952	−0.0489976	+	0.998799i	$0.515603\pi$
$384$	8.50790	0.434167
$385$	−15.6730	−0.798768
$386$	2.08386	0.106066
$387$	1.89550	0.0963537
$388$	0.254926	0.0129419
$389$	−30.4853	−1.54567	−0.772833	−	0.634610i	$-0.781161\pi$
$389$	−30.4853	−1.54567	−0.772833	+	0.634610i	$0.781161\pi$
$390$	−3.55528	−0.180029
$391$	−40.2062	−2.03331
$392$	−1.16596	−0.0588897
$393$	0.589991	0.0297611
$394$	5.70853	0.287592
$395$	−20.8613	−1.04965
$396$	−11.7591	−0.590917
$397$	−1.00903	−0.0506415	−0.0253208	−	0.999679i	$-0.508061\pi$
$397$	−1.00903	−0.0506415	−0.0253208	+	0.999679i	$0.508061\pi$
$398$	3.51268	0.176075
$399$	−5.03205	−0.251917
$400$	5.17153	0.258577
$401$	18.9677	0.947203	0.473602	−	0.880739i	$-0.342954\pi$
$401$	18.9677	0.947203	0.473602	+	0.880739i	$0.342954\pi$
$402$	−1.66711	−0.0831480
$403$	0.228228	0.0113688
$404$	−33.2927	−1.65637
$405$	2.54722	0.126573
$406$	1.27828	0.0634398
$407$	18.5869	0.921320
$408$	−5.14190	−0.254562
$409$	21.3336	1.05488	0.527439	−	0.849593i	$-0.323152\pi$
$409$	21.3336	1.05488	0.527439	+	0.849593i	$0.323152\pi$
$410$	−2.52016	−0.124462
$411$	6.88031	0.339381
$412$	−11.4643	−0.564805
$413$	9.37602	0.461364
$414$	2.71789	0.133577
$415$	−32.0001	−1.57083
$416$	15.7676	0.773072
$417$	−23.2136	−1.13677
$418$	−9.23015	−0.451462
$419$	1.91650	0.0936270	0.0468135	−	0.998904i	$-0.485093\pi$
$419$	1.91650	0.0936270	0.0468135	+	0.998904i	$0.485093\pi$
$420$	−4.86807	−0.237538
$421$	−11.1631	−0.544055	−0.272028	−	0.962289i	$-0.587694\pi$
$421$	−11.1631	−0.544055	−0.272028	+	0.962289i	$0.587694\pi$
$422$	−7.61505	−0.370695
$423$	−10.1769	−0.494818
$424$	−7.08215	−0.343940
$425$	−6.56367	−0.318385
$426$	−2.24796	−0.108914
$427$	−14.3700	−0.695412
$428$	−32.3942	−1.56583
$429$	−28.8078	−1.39085
$430$	1.43937	0.0694124
$431$	25.2766	1.21753	0.608766	−	0.793350i	$-0.291665\pi$
$431$	25.2766	1.21753	0.608766	+	0.793350i	$0.291665\pi$
$432$	−3.47467	−0.167175
$433$	−24.4814	−1.17650	−0.588251	−	0.808678i	$-0.700183\pi$
$433$	−24.4814	−1.17650	−0.588251	+	0.808678i	$0.700183\pi$
$434$	−0.0145319	−0.000697555 0
$435$	10.9222	0.523681
$436$	2.17294	0.104065
$437$	−45.8771	−2.19460
$438$	−1.61211	−0.0770296
$439$	−33.1662	−1.58294	−0.791469	−	0.611209i	$-0.790683\pi$
$439$	−33.1662	−1.58294	−0.791469	+	0.611209i	$0.790683\pi$
$440$	−18.2740	−0.871179
$441$	1.00000	0.0476190
$442$	−6.15528	−0.292777
$443$	22.9199	1.08896	0.544478	−	0.838775i	$-0.316728\pi$
$443$	22.9199	1.08896	0.544478	+	0.838775i	$0.316728\pi$
$444$	5.77316	0.273982
$445$	44.9652	2.13156
$446$	−5.08777	−0.240913
$447$	5.01259	0.237087
$448$	5.94537	0.280892
$449$	−10.8422	−0.511676	−0.255838	−	0.966720i	$-0.582351\pi$
$449$	−10.8422	−0.511676	−0.255838	+	0.966720i	$0.582351\pi$
$450$	0.443697	0.0209161
$451$	−20.4204	−0.961559
$452$	14.0997	0.663192
$453$	−10.9460	−0.514286
$454$	5.69909	0.267471
$455$	−11.9260	−0.559098
$456$	−5.86715	−0.274755
$457$	20.5538	0.961466	0.480733	−	0.876867i	$-0.340371\pi$
$457$	20.5538	0.961466	0.480733	+	0.876867i	$0.340371\pi$
$458$	−5.20317	−0.243128
$459$	4.41002	0.205842
$460$	−44.3822	−2.06933
$461$	−30.0440	−1.39929	−0.699645	−	0.714491i	$-0.746658\pi$
$461$	−30.0440	−1.39929	−0.699645	+	0.714491i	$0.746658\pi$
$462$	1.83427	0.0853382
$463$	−25.9689	−1.20688	−0.603439	−	0.797409i	$-0.706203\pi$
$463$	−25.9689	−1.20688	−0.603439	+	0.797409i	$0.706203\pi$
$464$	−14.8990	−0.691670
$465$	−0.124168	−0.00575816
$466$	5.46659	0.253235
$467$	−28.5728	−1.32219	−0.661096	−	0.750301i	$-0.729909\pi$
$467$	−28.5728	−1.32219	−0.661096	+	0.750301i	$0.729909\pi$
$468$	−8.94780	−0.413612
$469$	−5.59222	−0.258225
$470$	−7.72793	−0.356463
$471$	−4.71794	−0.217391
$472$	10.9320	0.503188
$473$	11.6629	0.536262
$474$	2.44149	0.112141
$475$	−7.48946	−0.343640
$476$	−8.42813	−0.386302
$477$	6.07411	0.278114
$478$	3.74791	0.171425
$479$	−29.2436	−1.33618	−0.668088	−	0.744082i	$-0.732887\pi$
$479$	−29.2436	−1.33618	−0.668088	+	0.744082i	$0.732887\pi$
$480$	−8.57843	−0.391550
$481$	14.1433	0.644878
$482$	0.527494	0.0240267
$483$	9.11699	0.414837
$484$	−51.3308	−2.33322
$485$	−0.339776	−0.0154284
$486$	−0.298113	−0.0135227
$487$	−18.8801	−0.855537	−0.427769	−	0.903888i	$-0.640700\pi$
$487$	−18.8801	−0.855537	−0.427769	+	0.903888i	$0.640700\pi$
$488$	−16.7548	−0.758453
$489$	2.39560	0.108333
$490$	0.759360	0.0343044
$491$	24.1789	1.09118	0.545589	−	0.838053i	$-0.316306\pi$
$491$	24.1789	1.09118	0.545589	+	0.838053i	$0.316306\pi$
$492$	−6.34264	−0.285948
$493$	18.9097	0.851652
$494$	−7.02346	−0.316000
$495$	15.6730	0.704447
$496$	0.169378	0.00760529
$497$	−7.54064	−0.338244
$498$	3.74511	0.167823
$499$	−6.67434	−0.298784	−0.149392	−	0.988778i	$-0.547732\pi$
$499$	−6.67434	−0.298784	−0.149392	+	0.988778i	$0.547732\pi$
$500$	17.0950	0.764510
$501$	6.18252	0.276215
$502$	−9.18578	−0.409981
$503$	8.56876	0.382062	0.191031	−	0.981584i	$-0.438817\pi$
$503$	8.56876	0.382062	0.191031	+	0.981584i	$0.438817\pi$
$504$	1.16596	0.0519358
$505$	44.3738	1.97461
$506$	16.7231	0.743431
$507$	−8.92059	−0.396177
$508$	−1.91113	−0.0847926
$509$	22.5337	0.998791	0.499395	−	0.866374i	$-0.333556\pi$
$509$	22.5337	0.998791	0.499395	+	0.866374i	$0.333556\pi$
$510$	3.34880	0.148287
$511$	−5.40772	−0.239224
$512$	19.8045	0.875243
$513$	5.03205	0.222170
$514$	4.16305	0.183624
$515$	15.2800	0.673318
$516$	3.62254	0.159474
$517$	−62.6181	−2.75394
$518$	−0.900543	−0.0395676
$519$	16.3023	0.715590
$520$	−13.9052	−0.609781
$521$	−32.0705	−1.40503	−0.702516	−	0.711668i	$-0.747940\pi$
$521$	−32.0705	−1.40503	−0.702516	+	0.711668i	$0.747940\pi$
$522$	−1.27828	−0.0559486
$523$	−36.3672	−1.59023	−0.795113	−	0.606461i	$-0.792589\pi$
$523$	−36.3672	−1.59023	−0.795113	+	0.606461i	$0.792589\pi$
$524$	1.12755	0.0492572
$525$	1.48835	0.0649570
$526$	0.709493	0.0309354
$527$	−0.214973	−0.00936437
$528$	−21.3795	−0.930423
$529$	60.1195	2.61389
$530$	4.61243	0.200351
$531$	−9.37602	−0.406885
$532$	−9.61689	−0.416945
$533$	−15.5384	−0.673043
$534$	−5.26248	−0.227730
$535$	43.1762	1.86667
$536$	−6.52029	−0.281634
$537$	−22.0264	−0.950510
$538$	2.05892	0.0887664
$539$	6.15296	0.265027
$540$	4.86807	0.209489
$541$	−35.7283	−1.53608	−0.768039	−	0.640403i	$-0.778767\pi$
$541$	−35.7283	−1.53608	−0.768039	+	0.640403i	$0.778767\pi$
$542$	−4.54999	−0.195439
$543$	−7.90350	−0.339172
$544$	−14.8519	−0.636770
$545$	−2.89618	−0.124059
$546$	1.39575	0.0597324
$547$	6.53314	0.279337	0.139668	−	0.990198i	$-0.455396\pi$
$547$	6.53314	0.279337	0.139668	+	0.990198i	$0.455396\pi$
$548$	13.1492	0.561704
$549$	14.3700	0.613295
$550$	2.73005	0.116410
$551$	21.5769	0.919207
$552$	10.6300	0.452444
$553$	8.18983	0.348267
$554$	−5.97285	−0.253762
$555$	−7.69469	−0.326621
$556$	−44.3642	−1.88146
$557$	22.4418	0.950891	0.475446	−	0.879745i	$-0.342287\pi$
$557$	22.4418	0.950891	0.475446	+	0.879745i	$0.342287\pi$
$558$	0.0145319	0.000615185 0
$559$	8.87462	0.375356
$560$	−8.85077	−0.374013
$561$	27.1347	1.14563
$562$	5.87609	0.247868
$563$	1.91786	0.0808282	0.0404141	−	0.999183i	$-0.487132\pi$
$563$	1.91786	0.0808282	0.0404141	+	0.999183i	$0.487132\pi$
$564$	−19.4494	−0.818966
$565$	−18.7926	−0.790609
$566$	−4.86695	−0.204573
$567$	−1.00000	−0.0419961
$568$	−8.79206	−0.368907
$569$	−5.35626	−0.224546	−0.112273	−	0.993677i	$-0.535813\pi$
$569$	−5.35626	−0.224546	−0.112273	+	0.993677i	$0.535813\pi$
$570$	3.82113	0.160050
$571$	9.68343	0.405239	0.202619	−	0.979258i	$-0.435055\pi$
$571$	9.68343	0.405239	0.202619	+	0.979258i	$0.435055\pi$
$572$	−55.0554	−2.30198
$573$	18.4005	0.768692
$574$	0.989374	0.0412957
$575$	13.5693	0.565879
$576$	−5.94537	−0.247724
$577$	−25.6603	−1.06825	−0.534127	−	0.845404i	$-0.679360\pi$
$577$	−25.6603	−1.06825	−0.534127	+	0.845404i	$0.679360\pi$
$578$	0.729874	0.0303588
$579$	−6.99017	−0.290502
$580$	20.8738	0.866737
$581$	12.5627	0.521191
$582$	0.0397654	0.00164833
$583$	37.3737	1.54786
$584$	−6.30517	−0.260910
$585$	11.9260	0.493078
$586$	−2.22488	−0.0919091
$587$	−15.0132	−0.619663	−0.309832	−	0.950791i	$-0.600273\pi$
$587$	−15.0132	−0.619663	−0.309832	+	0.950791i	$0.600273\pi$
$588$	1.91113	0.0788136
$589$	−0.245294	−0.0101072
$590$	−7.11977	−0.293116
$591$	−19.1489	−0.787681
$592$	10.4963	0.431397
$593$	25.4740	1.04609	0.523046	−	0.852305i	$-0.324796\pi$
$593$	25.4740	1.04609	0.523046	+	0.852305i	$0.324796\pi$
$594$	−1.83427	−0.0752612
$595$	11.2333	0.460521
$596$	9.57970	0.392400
$597$	−11.7831	−0.482249
$598$	12.7250	0.520364
$599$	−43.7657	−1.78822	−0.894109	−	0.447850i	$-0.852190\pi$
$599$	−43.7657	−1.78822	−0.894109	+	0.447850i	$0.852190\pi$
$600$	1.73535	0.0708455
$601$	31.5090	1.28528	0.642640	−	0.766168i	$-0.277839\pi$
$601$	31.5090	1.28528	0.642640	+	0.766168i	$0.277839\pi$
$602$	−0.565072	−0.0230306
$603$	5.59222	0.227733
$604$	−20.9191	−0.851187
$605$	68.4156	2.78149
$606$	−5.19325	−0.210961
$607$	25.6191	1.03985	0.519923	−	0.854213i	$-0.325961\pi$
$607$	25.6191	1.03985	0.519923	+	0.854213i	$0.325961\pi$
$608$	−16.9467	−0.687280
$609$	−4.28790	−0.173754
$610$	10.9120	0.441813
$611$	−47.6477	−1.92762
$612$	8.42813	0.340687
$613$	14.1667	0.572188	0.286094	−	0.958201i	$-0.407643\pi$
$613$	14.1667	0.572188	0.286094	+	0.958201i	$0.407643\pi$
$614$	3.08183	0.124373
$615$	8.45371	0.340887
$616$	7.17408	0.289052
$617$	31.0958	1.25187	0.625934	−	0.779876i	$-0.284718\pi$
$617$	31.0958	1.25187	0.625934	+	0.779876i	$0.284718\pi$
$618$	−1.78829	−0.0719354
$619$	−1.80860	−0.0726939	−0.0363469	−	0.999339i	$-0.511572\pi$
$619$	−1.80860	−0.0726939	−0.0363469	+	0.999339i	$0.511572\pi$
$620$	−0.237301	−0.00953024
$621$	−9.11699	−0.365852
$622$	5.66081	0.226978
$623$	−17.6526	−0.707238
$624$	−16.2682	−0.651250
$625$	−30.2266	−1.20906
$626$	6.45049	0.257813
$627$	30.9620	1.23650
$628$	−9.01658	−0.359801
$629$	−13.3219	−0.531177
$630$	−0.759360	−0.0302536
$631$	4.27550	0.170205	0.0851025	−	0.996372i	$-0.472878\pi$
$631$	4.27550	0.170205	0.0851025	+	0.996372i	$0.472878\pi$
$632$	9.54898	0.379838
$633$	25.5442	1.01529
$634$	1.68162	0.0667858
$635$	2.54722	0.101084
$636$	11.6084	0.460303
$637$	4.68194	0.185505
$638$	−7.86518	−0.311385
$639$	7.54064	0.298303
$640$	−21.6715	−0.856643
$641$	−21.0567	−0.831688	−0.415844	−	0.909436i	$-0.636514\pi$
$641$	−21.0567	−0.831688	−0.415844	+	0.909436i	$0.636514\pi$
$642$	−5.05309	−0.199430
$643$	−23.4286	−0.923935	−0.461968	−	0.886897i	$-0.652856\pi$
$643$	−23.4286	−0.923935	−0.461968	+	0.886897i	$0.652856\pi$
$644$	17.4237	0.686592
$645$	−4.82826	−0.190113
$646$	6.61555	0.260285
$647$	−30.4852	−1.19850	−0.599248	−	0.800564i	$-0.704533\pi$
$647$	−30.4852	−1.19850	−0.599248	+	0.800564i	$0.704533\pi$
$648$	−1.16596	−0.0458031
$649$	−57.6903	−2.26454
$650$	2.07736	0.0814808
$651$	0.0487464	0.00191052
$652$	4.57829	0.179300
$653$	−11.7448	−0.459609	−0.229805	−	0.973237i	$-0.573809\pi$
$653$	−11.7448	−0.459609	−0.229805	+	0.973237i	$0.573809\pi$
$654$	0.338953	0.0132541
$655$	−1.50284	−0.0587208
$656$	−11.5317	−0.450238
$657$	5.40772	0.210975
$658$	3.03386	0.118272
$659$	−23.1760	−0.902809	−0.451405	−	0.892319i	$-0.649077\pi$
$659$	−23.1760	−0.902809	−0.451405	+	0.892319i	$0.649077\pi$
$660$	29.9531	1.16592
$661$	−11.9144	−0.463416	−0.231708	−	0.972785i	$-0.574431\pi$
$661$	−11.9144	−0.463416	−0.231708	+	0.972785i	$0.574431\pi$
$662$	−3.32353	−0.129173
$663$	20.6475	0.801882
$664$	14.6476	0.568438
$665$	12.8178	0.497051
$666$	0.900543	0.0348953
$667$	−39.0927	−1.51368
$668$	11.8156	0.457159
$669$	17.0666	0.659833
$670$	4.24651	0.164057
$671$	88.4178	3.41333
$672$	3.36776	0.129914
$673$	−12.2102	−0.470668	−0.235334	−	0.971915i	$-0.575618\pi$
$673$	−12.2102	−0.470668	−0.235334	+	0.971915i	$0.575618\pi$
$674$	7.90682	0.304559
$675$	−1.48835	−0.0572867
$676$	−17.0484	−0.655707
$677$	30.4234	1.16927	0.584633	−	0.811298i	$-0.301239\pi$
$677$	30.4234	1.16927	0.584633	+	0.811298i	$0.301239\pi$
$678$	2.19937	0.0844664
$679$	0.133391	0.00511906
$680$	13.0976	0.502269
$681$	−19.1172	−0.732574
$682$	0.0894143	0.00342385
$683$	−10.7503	−0.411349	−0.205674	−	0.978620i	$-0.565939\pi$
$683$	−10.7503	−0.411349	−0.205674	+	0.978620i	$0.565939\pi$
$684$	9.61689	0.367711
$685$	−17.5257	−0.669622
$686$	−0.298113	−0.0113820
$687$	17.4537	0.665900
$688$	6.58624	0.251098
$689$	28.4386	1.08343
$690$	−6.92308	−0.263557
$691$	−24.4202	−0.928987	−0.464493	−	0.885577i	$-0.653764\pi$
$691$	−24.4202	−0.928987	−0.464493	+	0.885577i	$0.653764\pi$
$692$	31.1557	1.18436
$693$	−6.15296	−0.233732
$694$	2.39313	0.0908418
$695$	59.1302	2.24294
$696$	−4.99950	−0.189506
$697$	14.6360	0.554377
$698$	1.25811	0.0476201
$699$	−18.3373	−0.693581
$700$	2.84443	0.107509
$701$	−10.6603	−0.402636	−0.201318	−	0.979526i	$-0.564522\pi$
$701$	−10.6603	−0.402636	−0.201318	+	0.979526i	$0.564522\pi$
$702$	−1.39575	−0.0526790
$703$	−15.2009	−0.573312
$704$	−36.5816	−1.37872
$705$	25.9229	0.976311
$706$	8.06859	0.303665
$707$	−17.4204	−0.655163
$708$	−17.9188	−0.673429
$709$	8.83062	0.331641	0.165820	−	0.986156i	$-0.446973\pi$
$709$	8.83062	0.331641	0.165820	+	0.986156i	$0.446973\pi$
$710$	5.72606	0.214895
$711$	−8.18983	−0.307142
$712$	−20.5822	−0.771351
$713$	0.444421	0.0166437
$714$	−1.31468	−0.0492008
$715$	73.3799	2.74425
$716$	−42.0953	−1.57318
$717$	−12.5721	−0.469514
$718$	−6.16945	−0.230242
$719$	−11.2112	−0.418109	−0.209054	−	0.977904i	$-0.567039\pi$
$719$	−11.2112	−0.418109	−0.209054	+	0.977904i	$0.567039\pi$
$720$	8.85077	0.329849
$721$	−5.99870	−0.223403
$722$	1.88452	0.0701346
$723$	−1.76945	−0.0658064
$724$	−15.1046	−0.561359
$725$	−6.38190	−0.237018
$726$	−8.00697	−0.297167
$727$	−30.6785	−1.13780	−0.568901	−	0.822406i	$-0.692631\pi$
$727$	−30.6785	−1.13780	−0.568901	+	0.822406i	$0.692631\pi$
$728$	5.45894	0.202322
$729$	1.00000	0.0370370
$730$	4.10641	0.151985
$731$	−8.35920	−0.309176
$732$	27.4629	1.01506
$733$	42.1689	1.55754	0.778772	−	0.627307i	$-0.215843\pi$
$733$	42.1689	1.55754	0.778772	+	0.627307i	$0.215843\pi$
$734$	−0.235305	−0.00868528
$735$	−2.54722	−0.0939558
$736$	30.7038	1.13176
$737$	34.4087	1.26746
$738$	−0.989374	−0.0364194
$739$	−21.9476	−0.807354	−0.403677	−	0.914902i	$-0.632268\pi$
$739$	−21.9476	−0.807354	−0.403677	+	0.914902i	$0.632268\pi$
$740$	−14.7055	−0.540587
$741$	23.5598	0.865489
$742$	−1.81077	−0.0664754
$743$	34.0869	1.25053	0.625264	−	0.780414i	$-0.284991\pi$
$743$	34.0869	1.25053	0.625264	+	0.780414i	$0.284991\pi$
$744$	0.0568362	0.00208372
$745$	−12.7682	−0.467790
$746$	−1.87008	−0.0684686
$747$	−12.5627	−0.459647
$748$	51.8579	1.89611
$749$	−16.9503	−0.619350
$750$	2.66660	0.0973706
$751$	3.36757	0.122884	0.0614422	−	0.998111i	$-0.480430\pi$
$751$	3.36757	0.122884	0.0614422	+	0.998111i	$0.480430\pi$
$752$	−35.3614	−1.28950
$753$	30.8131	1.12289
$754$	−5.98482	−0.217954
$755$	27.8818	1.01472
$756$	−1.91113	−0.0695071
$757$	4.97069	0.180663	0.0903315	−	0.995912i	$-0.471207\pi$
$757$	4.97069	0.180663	0.0903315	+	0.995912i	$0.471207\pi$
$758$	−7.58846	−0.275625
$759$	−56.0965	−2.03617
$760$	14.9449	0.542110
$761$	−34.7856	−1.26098	−0.630489	−	0.776198i	$-0.717146\pi$
$761$	−34.7856	−1.26098	−0.630489	+	0.776198i	$0.717146\pi$
$762$	−0.298113	−0.0107995
$763$	1.13699	0.0411620
$764$	35.1657	1.27225
$765$	−11.2333	−0.406142
$766$	−0.571721	−0.0206571
$767$	−43.8980	−1.58506
$768$	−9.35443	−0.337549
$769$	9.55583	0.344592	0.172296	−	0.985045i	$-0.444881\pi$
$769$	9.55583	0.344592	0.172296	+	0.985045i	$0.444881\pi$
$770$	−4.67231	−0.168378
$771$	−13.9647	−0.502925
$772$	−13.3591	−0.480805
$773$	28.8187	1.03654	0.518268	−	0.855218i	$-0.326577\pi$
$773$	28.8187	1.03654	0.518268	+	0.855218i	$0.326577\pi$
$774$	0.565072	0.0203111
$775$	0.0725518	0.00260614
$776$	0.155528	0.00558312
$777$	3.02081	0.108371
$778$	−9.08805	−0.325822
$779$	16.7003	0.598351
$780$	22.7920	0.816086
$781$	46.3972	1.66022
$782$	−11.9860	−0.428617
$783$	4.28790	0.153237
$784$	3.47467	0.124095
$785$	12.0176	0.428928
$786$	0.175884	0.00627357
$787$	−16.4957	−0.588009	−0.294004	−	0.955804i	$-0.594988\pi$
$787$	−16.4957	−0.588009	−0.294004	+	0.955804i	$0.594988\pi$
$788$	−36.5960	−1.30368
$789$	−2.37995	−0.0847285
$790$	−6.21902	−0.221263
$791$	7.37766	0.262319
$792$	−7.17408	−0.254920
$793$	67.2794	2.38916
$794$	−0.300803	−0.0106751
$795$	−15.4721	−0.548739
$796$	−22.5190	−0.798164
$797$	−38.3239	−1.35750	−0.678752	−	0.734368i	$-0.737479\pi$
$797$	−38.3239	−1.35750	−0.678752	+	0.734368i	$0.737479\pi$
$798$	−1.50012	−0.0531036
$799$	44.8804	1.58775
$800$	5.01241	0.177215
$801$	17.6526	0.623725
$802$	5.65452	0.199668
$803$	33.2735	1.17420
$804$	10.6875	0.376918
$805$	−23.2230	−0.818504
$806$	0.0680376	0.00239652
$807$	−6.90652	−0.243121
$808$	−20.3115	−0.714555
$809$	1.14289	0.0401819	0.0200910	−	0.999798i	$-0.493604\pi$
$809$	1.14289	0.0401819	0.0200910	+	0.999798i	$0.493604\pi$
$810$	0.759360	0.0266812
$811$	3.16944	0.111294	0.0556471	−	0.998450i	$-0.482278\pi$
$811$	3.16944	0.111294	0.0556471	+	0.998450i	$0.482278\pi$
$812$	−8.19472	−0.287578
$813$	15.2627	0.535285
$814$	5.54100	0.194212
$815$	−6.10212	−0.213748
$816$	15.3234	0.536426
$817$	−9.53825	−0.333701
$818$	6.35981	0.222365
$819$	−4.68194	−0.163600
$820$	16.1561	0.564197
$821$	−14.3760	−0.501725	−0.250863	−	0.968023i	$-0.580714\pi$
$821$	−14.3760	−0.501725	−0.250863	+	0.968023i	$0.580714\pi$
$822$	2.05111	0.0715406
$823$	12.2041	0.425409	0.212705	−	0.977117i	$-0.431773\pi$
$823$	12.2041	0.425409	0.212705	+	0.977117i	$0.431773\pi$
$824$	−6.99422	−0.243655
$825$	−9.15777	−0.318833
$826$	2.79511	0.0972543
$827$	17.7731	0.618030	0.309015	−	0.951057i	$-0.400001\pi$
$827$	17.7731	0.618030	0.309015	+	0.951057i	$0.400001\pi$
$828$	−17.4237	−0.605517
$829$	12.9454	0.449613	0.224807	−	0.974403i	$-0.427825\pi$
$829$	12.9454	0.449613	0.224807	+	0.974403i	$0.427825\pi$
$830$	−9.53965	−0.331126
$831$	20.0356	0.695026
$832$	−27.8359	−0.965036
$833$	−4.41002	−0.152798
$834$	−6.92027	−0.239629
$835$	−15.7483	−0.544991
$836$	59.1723	2.04652
$837$	−0.0487464	−0.00168492
$838$	0.571332	0.0197363
$839$	35.7687	1.23487	0.617437	−	0.786621i	$-0.288171\pi$
$839$	35.7687	1.23487	0.617437	+	0.786621i	$0.288171\pi$
$840$	−2.96995	−0.102473
$841$	−10.6139	−0.365998
$842$	−3.32786	−0.114685
$843$	−19.7110	−0.678882
$844$	48.8183	1.68039
$845$	22.7227	0.781686
$846$	−3.03386	−0.104306
$847$	−26.8589	−0.922882
$848$	21.1055	0.724767
$849$	16.3259	0.560303
$850$	−1.95671	−0.0671147
$851$	27.5407	0.944084
$852$	14.4111	0.493717
$853$	−42.0346	−1.43924	−0.719619	−	0.694370i	$-0.755683\pi$
$853$	−42.0346	−1.43924	−0.719619	+	0.694370i	$0.755683\pi$
$854$	−4.28387	−0.146591
$855$	−12.8178	−0.438358
$856$	−19.7633	−0.675496
$857$	39.5497	1.35099	0.675496	−	0.737364i	$-0.263930\pi$
$857$	39.5497	1.35099	0.675496	+	0.737364i	$0.263930\pi$
$858$	−8.58797	−0.293188
$859$	5.41594	0.184789	0.0923947	−	0.995722i	$-0.470548\pi$
$859$	5.41594	0.184789	0.0923947	+	0.995722i	$0.470548\pi$
$860$	−9.22743	−0.314653
$861$	−3.31879	−0.113104
$862$	7.53527	0.256652
$863$	30.5858	1.04115	0.520576	−	0.853815i	$-0.325717\pi$
$863$	30.5858	1.04115	0.520576	+	0.853815i	$0.325717\pi$
$864$	−3.36776	−0.114573
$865$	−41.5255	−1.41191
$866$	−7.29822	−0.248004
$867$	−2.44832	−0.0831492
$868$	0.0931607	0.00316208
$869$	−50.3916	−1.70942
$870$	3.25606	0.110391
$871$	26.1825	0.887159
$872$	1.32569	0.0448934
$873$	−0.133391	−0.00451459
$874$	−13.6766	−0.462616
$875$	8.94496	0.302395
$876$	10.3349	0.349183
$877$	40.7400	1.37569	0.687846	−	0.725857i	$-0.258556\pi$
$877$	40.7400	1.37569	0.687846	+	0.725857i	$0.258556\pi$
$878$	−9.88727	−0.333679
$879$	7.46323	0.251728
$880$	54.4584	1.83579
$881$	−13.0783	−0.440620	−0.220310	−	0.975430i	$-0.570707\pi$
$881$	−13.0783	−0.440620	−0.220310	+	0.975430i	$0.570707\pi$
$882$	0.298113	0.0100380
$883$	−46.1932	−1.55452	−0.777262	−	0.629177i	$-0.783392\pi$
$883$	−46.1932	−1.55452	−0.777262	+	0.629177i	$0.783392\pi$
$884$	39.4600	1.32718
$885$	23.8828	0.802812
$886$	6.83270	0.229549
$887$	23.4042	0.785838	0.392919	−	0.919573i	$-0.371465\pi$
$887$	23.4042	0.785838	0.392919	+	0.919573i	$0.371465\pi$
$888$	3.52214	0.118195
$889$	−1.00000	−0.0335389
$890$	13.4047	0.449327
$891$	6.15296	0.206132
$892$	32.6165	1.09208
$893$	51.2107	1.71370
$894$	1.49432	0.0499774
$895$	56.1062	1.87542
$896$	8.50790	0.284229
$897$	−42.6852	−1.42522
$898$	−3.23220	−0.107860
$899$	−0.209020	−0.00697119
$900$	−2.84443	−0.0948144
$901$	−26.7870	−0.892403
$902$	−6.08758	−0.202694
$903$	1.89550	0.0630783
$904$	8.60203	0.286099
$905$	20.1320	0.669210
$906$	−3.26313	−0.108410
$907$	−0.601645	−0.0199773	−0.00998864	−	0.999950i	$-0.503180\pi$
$907$	−0.601645	−0.0199773	−0.00998864	+	0.999950i	$0.503180\pi$
$908$	−36.5355	−1.21247
$909$	17.4204	0.577799
$910$	−3.55528	−0.117856
$911$	−55.2607	−1.83087	−0.915435	−	0.402467i	$-0.868153\pi$
$911$	−55.2607	−1.83087	−0.915435	+	0.402467i	$0.868153\pi$
$912$	17.4847	0.578977
$913$	−77.2980	−2.55819
$914$	6.12734	0.202675
$915$	−36.6035	−1.21008
$916$	33.3563	1.10212
$917$	0.589991	0.0194832
$918$	1.31468	0.0433910
$919$	40.3608	1.33138	0.665689	−	0.746229i	$-0.268138\pi$
$919$	40.3608	1.33138	0.665689	+	0.746229i	$0.268138\pi$
$920$	−27.0770	−0.892704
$921$	−10.3378	−0.340642
$922$	−8.95650	−0.294967
$923$	35.3048	1.16207
$924$	−11.7591	−0.386846
$925$	4.49603	0.147829
$926$	−7.74166	−0.254407
$927$	5.99870	0.197023
$928$	−14.4406	−0.474036
$929$	−17.1233	−0.561798	−0.280899	−	0.959737i	$-0.590633\pi$
$929$	−17.1233	−0.561798	−0.280899	+	0.959737i	$0.590633\pi$
$930$	−0.0370161	−0.00121380
$931$	−5.03205	−0.164919
$932$	−35.0450	−1.14794
$933$	−18.9888	−0.621667
$934$	−8.51792	−0.278715
$935$	−69.1181	−2.26041
$936$	−5.45894	−0.178431
$937$	−27.9645	−0.913560	−0.456780	−	0.889580i	$-0.650997\pi$
$937$	−27.9645	−0.913560	−0.456780	+	0.889580i	$0.650997\pi$
$938$	−1.66711	−0.0544331
$939$	−21.6377	−0.706121
$940$	49.5419	1.61588
$941$	−37.0801	−1.20878	−0.604389	−	0.796689i	$-0.706583\pi$
$941$	−37.0801	−1.20878	−0.604389	+	0.796689i	$0.706583\pi$
$942$	−1.40648	−0.0458255
$943$	−30.2574	−0.985317
$944$	−32.5786	−1.06034
$945$	2.54722	0.0828612
$946$	3.47687	0.113043
$947$	−47.2707	−1.53609	−0.768045	−	0.640396i	$-0.778770\pi$
$947$	−47.2707	−1.53609	−0.768045	+	0.640396i	$0.778770\pi$
$948$	−15.6518	−0.508347
$949$	25.3187	0.821878
$950$	−2.23270	−0.0724384
$951$	−5.64090	−0.182919
$952$	−5.14190	−0.166650
$953$	1.78295	0.0577553	0.0288776	−	0.999583i	$-0.490807\pi$
$953$	1.78295	0.0577553	0.0288776	+	0.999583i	$0.490807\pi$
$954$	1.81077	0.0586258
$955$	−46.8702	−1.51668
$956$	−24.0269	−0.777086
$957$	26.3832	0.852849
$958$	−8.71790	−0.281663
$959$	6.88031	0.222177
$960$	15.1442	0.488777
$961$	−30.9976	−0.999923
$962$	4.21629	0.135939
$963$	16.9503	0.546215
$964$	−3.38164	−0.108915
$965$	17.8055	0.573180
$966$	2.71789	0.0874467
$967$	19.3686	0.622851	0.311426	−	0.950271i	$-0.399194\pi$
$967$	19.3686	0.622851	0.311426	+	0.950271i	$0.399194\pi$
$968$	−31.3163	−1.00654
$969$	−22.1915	−0.712892
$970$	−0.101291	−0.00325227
$971$	−56.6777	−1.81888	−0.909438	−	0.415840i	$-0.863487\pi$
$971$	−56.6777	−1.81888	−0.909438	+	0.415840i	$0.863487\pi$
$972$	1.91113	0.0612995
$973$	−23.2136	−0.744194
$974$	−5.62838	−0.180345
$975$	−6.96838	−0.223167
$976$	49.9309	1.59825
$977$	−34.5076	−1.10400	−0.551998	−	0.833845i	$-0.686134\pi$
$977$	−34.5076	−1.10400	−0.551998	+	0.833845i	$0.686134\pi$
$978$	0.714158	0.0228362
$979$	108.616	3.47138
$980$	−4.86807	−0.155505
$981$	−1.13699	−0.0363015
$982$	7.20803	0.230018
$983$	30.3657	0.968514	0.484257	−	0.874926i	$-0.339090\pi$
$983$	30.3657	0.968514	0.484257	+	0.874926i	$0.339090\pi$
$984$	−3.86957	−0.123357
$985$	48.7766	1.55415
$986$	5.63723	0.179526
$987$	−10.1769	−0.323934
$988$	45.0257	1.43246
$989$	17.2813	0.549512
$990$	4.67231	0.148496
$991$	−25.7213	−0.817063	−0.408532	−	0.912744i	$-0.633959\pi$
$991$	−25.7213	−0.817063	−0.408532	+	0.912744i	$0.633959\pi$
$992$	0.164166	0.00521228
$993$	11.1486	0.353789
$994$	−2.24796	−0.0713009
$995$	30.0141	0.951512
$996$	−24.0090	−0.760755
$997$	13.4555	0.426139	0.213069	−	0.977037i	$-0.431654\pi$
$997$	13.4555	0.426139	0.213069	+	0.977037i	$0.431654\pi$
$998$	−1.98970	−0.0629830
$999$	−3.02081	−0.0955743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.8	✓	16
3.2	odd	2		8001.2.a.r.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.8	✓	16	1.1	even	1	trivial
8001.2.a.r.1.9		16	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)

\(f(q)\)	\(=\)	\(q+0.298113 q^{2} -1.00000 q^{3} -1.91113 q^{4} +2.54722 q^{5} -0.298113 q^{6} -1.00000 q^{7} -1.16596 q^{8} +1.00000 q^{9} +0.759360 q^{10} +6.15296 q^{11} +1.91113 q^{12} +4.68194 q^{13} -0.298113 q^{14} -2.54722 q^{15} +3.47467 q^{16} -4.41002 q^{17} +0.298113 q^{18} -5.03205 q^{19} -4.86807 q^{20} +1.00000 q^{21} +1.83427 q^{22} +9.11699 q^{23} +1.16596 q^{24} +1.48835 q^{25} +1.39575 q^{26} -1.00000 q^{27} +1.91113 q^{28} -4.28790 q^{29} -0.759360 q^{30} +0.0487464 q^{31} +3.36776 q^{32} -6.15296 q^{33} -1.31468 q^{34} -2.54722 q^{35} -1.91113 q^{36} +3.02081 q^{37} -1.50012 q^{38} -4.68194 q^{39} -2.96995 q^{40} -3.31879 q^{41} +0.298113 q^{42} +1.89550 q^{43} -11.7591 q^{44} +2.54722 q^{45} +2.71789 q^{46} -10.1769 q^{47} -3.47467 q^{48} +1.00000 q^{49} +0.443697 q^{50} +4.41002 q^{51} -8.94780 q^{52} +6.07411 q^{53} -0.298113 q^{54} +15.6730 q^{55} +1.16596 q^{56} +5.03205 q^{57} -1.27828 q^{58} -9.37602 q^{59} +4.86807 q^{60} +14.3700 q^{61} +0.0145319 q^{62} -1.00000 q^{63} -5.94537 q^{64} +11.9260 q^{65} -1.83427 q^{66} +5.59222 q^{67} +8.42813 q^{68} -9.11699 q^{69} -0.759360 q^{70} +7.54064 q^{71} -1.16596 q^{72} +5.40772 q^{73} +0.900543 q^{74} -1.48835 q^{75} +9.61689 q^{76} -6.15296 q^{77} -1.39575 q^{78} -8.18983 q^{79} +8.85077 q^{80} +1.00000 q^{81} -0.989374 q^{82} -12.5627 q^{83} -1.91113 q^{84} -11.2333 q^{85} +0.565072 q^{86} +4.28790 q^{87} -7.17408 q^{88} +17.6526 q^{89} +0.759360 q^{90} -4.68194 q^{91} -17.4237 q^{92} -0.0487464 q^{93} -3.03386 q^{94} -12.8178 q^{95} -3.36776 q^{96} -0.133391 q^{97} +0.298113 q^{98} +6.15296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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