LMFDB - Embedded newform 3467.2.a.b.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3467,2,Mod(1,3467)] 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("3467.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3467, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3467.a (trivial)

Newform invariants

comment:select newform

sage:traces = [126] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$27.6841343808$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	3467.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.30915 q^{2} -2.10535 q^{3} +3.33217 q^{4} +0.0313740 q^{5} +4.86157 q^{6} +0.850976 q^{7} -3.07619 q^{8} +1.43250 q^{9} -0.0724474 q^{10} -3.50044 q^{11} -7.01539 q^{12} +3.38018 q^{13} -1.96503 q^{14} -0.0660534 q^{15} +0.439028 q^{16} +2.50571 q^{17} -3.30786 q^{18} -0.483045 q^{19} +0.104544 q^{20} -1.79160 q^{21} +8.08304 q^{22} +0.00571689 q^{23} +6.47645 q^{24} -4.99902 q^{25} -7.80535 q^{26} +3.30013 q^{27} +2.83560 q^{28} +5.87591 q^{29} +0.152527 q^{30} -2.04497 q^{31} +5.13859 q^{32} +7.36966 q^{33} -5.78606 q^{34} +0.0266986 q^{35} +4.77334 q^{36} -5.34220 q^{37} +1.11542 q^{38} -7.11647 q^{39} -0.0965124 q^{40} +3.80047 q^{41} +4.13708 q^{42} -8.46884 q^{43} -11.6641 q^{44} +0.0449434 q^{45} -0.0132012 q^{46} +7.93374 q^{47} -0.924308 q^{48} -6.27584 q^{49} +11.5435 q^{50} -5.27540 q^{51} +11.2634 q^{52} -12.8979 q^{53} -7.62051 q^{54} -0.109823 q^{55} -2.61776 q^{56} +1.01698 q^{57} -13.5684 q^{58} +9.96089 q^{59} -0.220101 q^{60} -3.99035 q^{61} +4.72215 q^{62} +1.21902 q^{63} -12.7438 q^{64} +0.106050 q^{65} -17.0176 q^{66} +7.75691 q^{67} +8.34945 q^{68} -0.0120361 q^{69} -0.0616510 q^{70} +3.20846 q^{71} -4.40664 q^{72} -12.3791 q^{73} +12.3359 q^{74} +10.5247 q^{75} -1.60959 q^{76} -2.97879 q^{77} +16.4330 q^{78} +5.27340 q^{79} +0.0137741 q^{80} -11.2454 q^{81} -8.77585 q^{82} -3.52953 q^{83} -5.96993 q^{84} +0.0786142 q^{85} +19.5558 q^{86} -12.3708 q^{87} +10.7680 q^{88} +8.06800 q^{89} -0.103781 q^{90} +2.87645 q^{91} +0.0190497 q^{92} +4.30539 q^{93} -18.3202 q^{94} -0.0151551 q^{95} -10.8185 q^{96} -8.39578 q^{97} +14.4919 q^{98} -5.01439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) $ 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * 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 $

$2$	−2.30915	−1.63282	−0.816408	−	0.577476i	$-0.804038\pi$
$2$	−2.30915	−1.63282	−0.816408	+	0.577476i	$0.804038\pi$
$3$	−2.10535	−1.21552	−0.607762	−	0.794119i	$-0.707933\pi$
$3$	−2.10535	−1.21552	−0.607762	+	0.794119i	$0.707933\pi$
$4$	3.33217	1.66609
$5$	0.0313740	0.0140309	0.00701545	−	0.999975i	$-0.497767\pi$
$5$	0.0313740	0.0140309	0.00701545	+	0.999975i	$0.497767\pi$
$6$	4.86157	1.98473
$7$	0.850976	0.321639	0.160819	−	0.986984i	$-0.448586\pi$
$7$	0.850976	0.321639	0.160819	+	0.986984i	$0.448586\pi$
$8$	−3.07619	−1.08760
$9$	1.43250	0.477500
$10$	−0.0724474	−0.0229099
$11$	−3.50044	−1.05542	−0.527711	−	0.849424i	$-0.676950\pi$
$11$	−3.50044	−1.05542	−0.527711	+	0.849424i	$0.676950\pi$
$12$	−7.01539	−2.02517
$13$	3.38018	0.937494	0.468747	−	0.883332i	$-0.344706\pi$
$13$	3.38018	0.937494	0.468747	+	0.883332i	$0.344706\pi$
$14$	−1.96503	−0.525176
$15$	−0.0660534	−0.0170549
$16$	0.439028	0.109757
$17$	2.50571	0.607724	0.303862	−	0.952716i	$-0.401724\pi$
$17$	2.50571	0.607724	0.303862	+	0.952716i	$0.401724\pi$
$18$	−3.30786	−0.779670
$19$	−0.483045	−0.110818	−0.0554090	−	0.998464i	$-0.517646\pi$
$19$	−0.483045	−0.110818	−0.0554090	+	0.998464i	$0.517646\pi$
$20$	0.104544	0.0233767
$21$	−1.79160	−0.390960
$22$	8.08304	1.72331
$23$	0.00571689	0.00119205	0.000596027	−	1.00000i	$-0.499810\pi$
$23$	0.00571689	0.00119205	0.000596027		1.00000i	$0.499810\pi$
$24$	6.47645	1.32200
$25$	−4.99902	−0.999803
$26$	−7.80535	−1.53076
$27$	3.30013	0.635111
$28$	2.83560	0.535878
$29$	5.87591	1.09113	0.545564	−	0.838069i	$-0.316315\pi$
$29$	5.87591	1.09113	0.545564	+	0.838069i	$0.316315\pi$
$30$	0.152527	0.0278475
$31$	−2.04497	−0.367288	−0.183644	−	0.982993i	$-0.558789\pi$
$31$	−2.04497	−0.367288	−0.183644	+	0.982993i	$0.558789\pi$
$32$	5.13859	0.908383
$33$	7.36966	1.28289
$34$	−5.78606	−0.992301
$35$	0.0266986	0.00451288
$36$	4.77334	0.795557
$37$	−5.34220	−0.878253	−0.439126	−	0.898425i	$-0.644712\pi$
$37$	−5.34220	−0.878253	−0.439126	+	0.898425i	$0.644712\pi$
$38$	1.11542	0.180945
$39$	−7.11647	−1.13955
$40$	−0.0965124	−0.0152599
$41$	3.80047	0.593534	0.296767	−	0.954950i	$-0.404092\pi$
$41$	3.80047	0.593534	0.296767	+	0.954950i	$0.404092\pi$
$42$	4.13708	0.638365
$43$	−8.46884	−1.29149	−0.645743	−	0.763555i	$-0.723452\pi$
$43$	−8.46884	−1.29149	−0.645743	+	0.763555i	$0.723452\pi$
$44$	−11.6641	−1.75843
$45$	0.0449434	0.00669976
$46$	−0.0132012	−0.00194640
$47$	7.93374	1.15725	0.578627	−	0.815592i	$-0.303589\pi$
$47$	7.93374	1.15725	0.578627	+	0.815592i	$0.303589\pi$
$48$	−0.924308	−0.133412
$49$	−6.27584	−0.896549
$50$	11.5435	1.63249
$51$	−5.27540	−0.738703
$52$	11.2634	1.56195
$53$	−12.8979	−1.77167	−0.885834	−	0.464003i	$-0.846413\pi$
$53$	−12.8979	−1.77167	−0.885834	+	0.464003i	$0.846413\pi$
$54$	−7.62051	−1.03702
$55$	−0.109823	−0.0148085
$56$	−2.61776	−0.349813
$57$	1.01698	0.134702
$58$	−13.5684	−1.78161
$59$	9.96089	1.29680	0.648399	−	0.761301i	$-0.275439\pi$
$59$	9.96089	1.29680	0.648399	+	0.761301i	$0.275439\pi$
$60$	−0.220101	−0.0284149
$61$	−3.99035	−0.510912	−0.255456	−	0.966821i	$-0.582226\pi$
$61$	−3.99035	−0.510912	−0.255456	+	0.966821i	$0.582226\pi$
$62$	4.72215	0.599714
$63$	1.21902	0.153583
$64$	−12.7438	−1.59298
$65$	0.106050	0.0131539
$66$	−17.0176	−2.09473
$67$	7.75691	0.947658	0.473829	−	0.880617i	$-0.342872\pi$
$67$	7.75691	0.947658	0.473829	+	0.880617i	$0.342872\pi$
$68$	8.34945	1.01252
$69$	−0.0120361	−0.00144897
$70$	−0.0616510	−0.00736870
$71$	3.20846	0.380774	0.190387	−	0.981709i	$-0.439026\pi$
$71$	3.20846	0.380774	0.190387	+	0.981709i	$0.439026\pi$
$72$	−4.40664	−0.519327
$73$	−12.3791	−1.44886	−0.724432	−	0.689347i	$-0.757898\pi$
$73$	−12.3791	−1.44886	−0.724432	+	0.689347i	$0.757898\pi$
$74$	12.3359	1.43402
$75$	10.5247	1.21529
$76$	−1.60959	−0.184632
$77$	−2.97879	−0.339465
$78$	16.4330	1.86067
$79$	5.27340	0.593304	0.296652	−	0.954986i	$-0.404130\pi$
$79$	5.27340	0.593304	0.296652	+	0.954986i	$0.404130\pi$
$80$	0.0137741	0.00153999
$81$	−11.2454	−1.24949
$82$	−8.77585	−0.969131
$83$	−3.52953	−0.387416	−0.193708	−	0.981059i	$-0.562051\pi$
$83$	−3.52953	−0.387416	−0.193708	+	0.981059i	$0.562051\pi$
$84$	−5.96993	−0.651373
$85$	0.0786142	0.00852691
$86$	19.5558	2.10876
$87$	−12.3708	−1.32629
$88$	10.7680	1.14787
$89$	8.06800	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$89$	8.06800	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$90$	−0.103781	−0.0109395
$91$	2.87645	0.301534
$92$	0.0190497	0.00198606
$93$	4.30539	0.446448
$94$	−18.3202	−1.88958
$95$	−0.0151551	−0.00155488
$96$	−10.8185	−1.10416
$97$	−8.39578	−0.852463	−0.426231	−	0.904614i	$-0.640159\pi$
$97$	−8.39578	−0.852463	−0.426231	+	0.904614i	$0.640159\pi$
$98$	14.4919	1.46390
$99$	−5.01439	−0.503965
$100$	−16.6576	−1.66576
$101$	5.83991	0.581093	0.290546	−	0.956861i	$-0.406163\pi$
$101$	5.83991	0.581093	0.290546	+	0.956861i	$0.406163\pi$
$102$	12.1817	1.20617
$103$	11.2647	1.10994	0.554971	−	0.831870i	$-0.312729\pi$
$103$	11.2647	1.10994	0.554971	+	0.831870i	$0.312729\pi$
$104$	−10.3981	−1.01962
$105$	−0.0562098	−0.00548552
$106$	29.7833	2.89281
$107$	13.0070	1.25743	0.628715	−	0.777636i	$-0.283581\pi$
$107$	13.0070	1.25743	0.628715	+	0.777636i	$0.283581\pi$
$108$	10.9966	1.05815
$109$	−1.78442	−0.170916	−0.0854580	−	0.996342i	$-0.527235\pi$
$109$	−1.78442	−0.170916	−0.0854580	+	0.996342i	$0.527235\pi$
$110$	0.253598	0.0241796
$111$	11.2472	1.06754
$112$	0.373602	0.0353021
$113$	1.32158	0.124324	0.0621620	−	0.998066i	$-0.480200\pi$
$113$	1.32158	0.124324	0.0621620	+	0.998066i	$0.480200\pi$
$114$	−2.34835	−0.219944
$115$	0.000179362 0	1.67256e−5 0
$116$	19.5795	1.81791
$117$	4.84212	0.447654
$118$	−23.0012	−2.11743
$119$	2.13230	0.195467
$120$	0.203192	0.0185488
$121$	1.25309	0.113917
$122$	9.21432	0.834225
$123$	−8.00132	−0.721455
$124$	−6.81421	−0.611934
$125$	−0.313710	−0.0280590
$126$	−2.81491	−0.250772
$127$	1.69589	0.150485	0.0752427	−	0.997165i	$-0.476027\pi$
$127$	1.69589	0.150485	0.0752427	+	0.997165i	$0.476027\pi$
$128$	19.1502	1.69266
$129$	17.8299	1.56983
$130$	−0.244885	−0.0214779
$131$	11.2330	0.981430	0.490715	−	0.871320i	$-0.336736\pi$
$131$	11.2330	0.981430	0.490715	+	0.871320i	$0.336736\pi$
$132$	24.5570	2.13741
$133$	−0.411059	−0.0356434
$134$	−17.9119	−1.54735
$135$	0.103539	0.00891118
$136$	−7.70803	−0.660958
$137$	−4.31501	−0.368656	−0.184328	−	0.982865i	$-0.559011\pi$
$137$	−4.31501	−0.368656	−0.184328	+	0.982865i	$0.559011\pi$
$138$	0.0277931	0.00236590
$139$	8.97101	0.760911	0.380456	−	0.924799i	$-0.375767\pi$
$139$	8.97101	0.760911	0.380456	+	0.924799i	$0.375767\pi$
$140$	0.0889642	0.00751885
$141$	−16.7033	−1.40667
$142$	−7.40881	−0.621733
$143$	−11.8321	−0.989453
$144$	0.628908	0.0524090
$145$	0.184351	0.0153095
$146$	28.5852	2.36573
$147$	13.2128	1.08978
$148$	−17.8011	−1.46324
$149$	−1.07918	−0.0884100	−0.0442050	−	0.999022i	$-0.514075\pi$
$149$	−1.07918	−0.0884100	−0.0442050	+	0.999022i	$0.514075\pi$
$150$	−24.3031	−1.98434
$151$	−0.474939	−0.0386500	−0.0193250	−	0.999813i	$-0.506152\pi$
$151$	−0.474939	−0.0386500	−0.0193250	+	0.999813i	$0.506152\pi$
$152$	1.48593	0.120525
$153$	3.58943	0.290188
$154$	6.87847	0.554283
$155$	−0.0641591	−0.00515338
$156$	−23.7133	−1.89858
$157$	12.4231	0.991468	0.495734	−	0.868474i	$-0.334899\pi$
$157$	12.4231	0.991468	0.495734	+	0.868474i	$0.334899\pi$
$158$	−12.1771	−0.968756
$159$	27.1547	2.15351
$160$	0.161218	0.0127454
$161$	0.00486494	0.000383411 0
$162$	25.9674	2.04019
$163$	−8.79161	−0.688612	−0.344306	−	0.938858i	$-0.611886\pi$
$163$	−8.79161	−0.688612	−0.344306	+	0.938858i	$0.611886\pi$
$164$	12.6638	0.988878
$165$	0.231216	0.0180001
$166$	8.15021	0.632579
$167$	16.8378	1.30295	0.651474	−	0.758671i	$-0.274151\pi$
$167$	16.8378	1.30295	0.651474	+	0.758671i	$0.274151\pi$
$168$	5.51130	0.425206
$169$	−1.57435	−0.121104
$170$	−0.181532	−0.0139229
$171$	−0.691962	−0.0529156
$172$	−28.2196	−2.15173
$173$	−16.4974	−1.25427	−0.627137	−	0.778909i	$-0.715773\pi$
$173$	−16.4974	−1.25427	−0.627137	+	0.778909i	$0.715773\pi$
$174$	28.5661	2.16559
$175$	−4.25404	−0.321575
$176$	−1.53679	−0.115840
$177$	−20.9712	−1.57629
$178$	−18.6302	−1.39639
$179$	−3.51042	−0.262381	−0.131191	−	0.991357i	$-0.541880\pi$
$179$	−3.51042	−0.262381	−0.131191	+	0.991357i	$0.541880\pi$
$180$	0.149759	0.0111624
$181$	11.9668	0.889487	0.444743	−	0.895658i	$-0.353295\pi$
$181$	11.9668	0.889487	0.444743	+	0.895658i	$0.353295\pi$
$182$	−6.64217	−0.492350
$183$	8.40109	0.621026
$184$	−0.0175862	−0.00129647
$185$	−0.167606	−0.0123227
$186$	−9.94178	−0.728967
$187$	−8.77109	−0.641405
$188$	26.4366	1.92809
$189$	2.80833	0.204276
$190$	0.0349953	0.00253883
$191$	17.5167	1.26746	0.633732	−	0.773552i	$-0.281522\pi$
$191$	17.5167	1.26746	0.633732	+	0.773552i	$0.281522\pi$
$192$	26.8302	1.93630
$193$	6.18314	0.445072	0.222536	−	0.974924i	$-0.428567\pi$
$193$	6.18314	0.445072	0.222536	+	0.974924i	$0.428567\pi$
$194$	19.3871	1.39191
$195$	−0.223273	−0.0159889
$196$	−20.9122	−1.49373
$197$	−14.8597	−1.05871	−0.529355	−	0.848401i	$-0.677566\pi$
$197$	−14.8597	−1.05871	−0.529355	+	0.848401i	$0.677566\pi$
$198$	11.5790	0.822881
$199$	−5.54256	−0.392901	−0.196451	−	0.980514i	$-0.562942\pi$
$199$	−5.54256	−0.392901	−0.196451	+	0.980514i	$0.562942\pi$
$200$	15.3779	1.08738
$201$	−16.3310	−1.15190
$202$	−13.4852	−0.948817
$203$	5.00026	0.350949
$204$	−17.5785	−1.23074
$205$	0.119236	0.00832781
$206$	−26.0118	−1.81233
$207$	0.00818945	0.000569206 0
$208$	1.48400	0.102897
$209$	1.69087	0.116960
$210$	0.129797	0.00895684
$211$	16.4168	1.13018	0.565089	−	0.825030i	$-0.308842\pi$
$211$	16.4168	1.13018	0.565089	+	0.825030i	$0.308842\pi$
$212$	−42.9781	−2.95175
$213$	−6.75493	−0.462840
$214$	−30.0350	−2.05315
$215$	−0.265702	−0.0181207
$216$	−10.1518	−0.690744
$217$	−1.74022	−0.118134
$218$	4.12048	0.279074
$219$	26.0623	1.76113
$220$	−0.365949	−0.0246723
$221$	8.46976	0.569738
$222$	−25.9715	−1.74309
$223$	10.0930	0.675880	0.337940	−	0.941168i	$-0.390270\pi$
$223$	10.0930	0.675880	0.337940	+	0.941168i	$0.390270\pi$
$224$	4.37281	0.292171
$225$	−7.16110	−0.477406
$226$	−3.05173	−0.202998
$227$	−29.1594	−1.93538	−0.967690	−	0.252142i	$-0.918865\pi$
$227$	−29.1594	−1.93538	−0.967690	+	0.252142i	$0.918865\pi$
$228$	3.38875	0.224425
$229$	0.688399	0.0454907	0.0227454	−	0.999741i	$-0.492759\pi$
$229$	0.688399	0.0454907	0.0227454	+	0.999741i	$0.492759\pi$
$230$	−0.000414174 0	−2.73098e−5 0
$231$	6.27140	0.412628
$232$	−18.0754	−1.18671
$233$	−5.57374	−0.365148	−0.182574	−	0.983192i	$-0.558443\pi$
$233$	−5.57374	−0.365148	−0.182574	+	0.983192i	$0.558443\pi$
$234$	−11.1812	−0.730936
$235$	0.248913	0.0162373
$236$	33.1914	2.16058
$237$	−11.1024	−0.721176
$238$	−4.92379	−0.319162
$239$	−7.54397	−0.487979	−0.243989	−	0.969778i	$-0.578456\pi$
$239$	−7.54397	−0.487979	−0.243989	+	0.969778i	$0.578456\pi$
$240$	−0.0289993	−0.00187190
$241$	−10.1273	−0.652354	−0.326177	−	0.945309i	$-0.605761\pi$
$241$	−10.1273	−0.652354	−0.326177	+	0.945309i	$0.605761\pi$
$242$	−2.89357	−0.186006
$243$	13.7752	0.883679
$244$	−13.2965	−0.851224
$245$	−0.196899	−0.0125794
$246$	18.4763	1.17800
$247$	−1.63278	−0.103891
$248$	6.29072	0.399461
$249$	7.43089	0.470914
$250$	0.724402	0.0458152
$251$	16.4740	1.03983	0.519915	−	0.854218i	$-0.325964\pi$
$251$	16.4740	1.03983	0.519915	+	0.854218i	$0.325964\pi$
$252$	4.06200	0.255882
$253$	−0.0200116	−0.00125812
$254$	−3.91605	−0.245715
$255$	−0.165511	−0.0103647
$256$	−18.7331	−1.17082
$257$	−2.82751	−0.176375	−0.0881877	−	0.996104i	$-0.528108\pi$
$257$	−2.82751	−0.176375	−0.0881877	+	0.996104i	$0.528108\pi$
$258$	−41.1718	−2.56325
$259$	−4.54608	−0.282480
$260$	0.353377	0.0219155
$261$	8.41725	0.521014
$262$	−25.9386	−1.60249
$263$	−30.5709	−1.88508	−0.942541	−	0.334090i	$-0.891571\pi$
$263$	−30.5709	−1.88508	−0.942541	+	0.334090i	$0.891571\pi$
$264$	−22.6704	−1.39527
$265$	−0.404660	−0.0248581
$266$	0.949197	0.0581990
$267$	−16.9860	−1.03952
$268$	25.8474	1.57888
$269$	−15.5972	−0.950978	−0.475489	−	0.879722i	$-0.657729\pi$
$269$	−15.5972	−0.950978	−0.475489	+	0.879722i	$0.657729\pi$
$270$	−0.239086	−0.0145503
$271$	−2.99917	−0.182186	−0.0910932	−	0.995842i	$-0.529036\pi$
$271$	−2.99917	−0.182186	−0.0910932	+	0.995842i	$0.529036\pi$
$272$	1.10008	0.0667019
$273$	−6.05595	−0.366523
$274$	9.96400	0.601948
$275$	17.4988	1.05522
$276$	−0.0401062	−0.00241411
$277$	−15.0480	−0.904149	−0.452074	−	0.891980i	$-0.649316\pi$
$277$	−15.0480	−0.904149	−0.452074	+	0.891980i	$0.649316\pi$
$278$	−20.7154	−1.24243
$279$	−2.92943	−0.175380
$280$	−0.0821297	−0.00490819
$281$	11.3460	0.676846	0.338423	−	0.940994i	$-0.390107\pi$
$281$	11.3460	0.676846	0.338423	+	0.940994i	$0.390107\pi$
$282$	38.5704	2.29683
$283$	−22.4749	−1.33599	−0.667996	−	0.744165i	$-0.732848\pi$
$283$	−22.4749	−1.33599	−0.667996	+	0.744165i	$0.732848\pi$
$284$	10.6911	0.634402
$285$	0.0319067	0.00188999
$286$	27.3222	1.61559
$287$	3.23411	0.190903
$288$	7.36103	0.433753
$289$	−10.7214	−0.630672
$290$	−0.425694	−0.0249976
$291$	17.6761	1.03619
$292$	−41.2493	−2.41393
$293$	−16.0381	−0.936956	−0.468478	−	0.883475i	$-0.655198\pi$
$293$	−16.0381	−0.936956	−0.468478	+	0.883475i	$0.655198\pi$
$294$	−30.5104	−1.77940
$295$	0.312514	0.0181952
$296$	16.4336	0.955184
$297$	−11.5519	−0.670311
$298$	2.49199	0.144357
$299$	0.0193241	0.00111754
$300$	35.0701	2.02477
$301$	−7.20678	−0.415392
$302$	1.09671	0.0631084
$303$	−12.2951	−0.706333
$304$	−0.212070	−0.0121631
$305$	−0.125194	−0.00716856
$306$	−8.28853	−0.473824
$307$	−6.96631	−0.397588	−0.198794	−	0.980041i	$-0.563703\pi$
$307$	−6.96631	−0.397588	−0.198794	+	0.980041i	$0.563703\pi$
$308$	−9.92584	−0.565577
$309$	−23.7161	−1.34916
$310$	0.148153	0.00841453
$311$	−13.4057	−0.760170	−0.380085	−	0.924952i	$-0.624105\pi$
$311$	−13.4057	−0.760170	−0.380085	+	0.924952i	$0.624105\pi$
$312$	21.8916	1.23937
$313$	34.7186	1.96241	0.981207	−	0.192958i	$-0.0618081\pi$
$313$	34.7186	1.96241	0.981207	+	0.192958i	$0.0618081\pi$
$314$	−28.6867	−1.61888
$315$	0.0382457	0.00215490
$316$	17.5719	0.988496
$317$	−32.1515	−1.80581	−0.902905	−	0.429840i	$-0.858570\pi$
$317$	−32.1515	−1.80581	−0.902905	+	0.429840i	$0.858570\pi$
$318$	−62.7042	−3.51628
$319$	−20.5683	−1.15160
$320$	−0.399826	−0.0223509
$321$	−27.3842	−1.52844
$322$	−0.0112339	−0.000626039 0
$323$	−1.21037	−0.0673467
$324$	−37.4718	−2.08176
$325$	−16.8976	−0.937310
$326$	20.3011	1.12438
$327$	3.75682	0.207753
$328$	−11.6910	−0.645525
$329$	6.75142	0.372218
$330$	−0.533912	−0.0293909
$331$	−24.8668	−1.36680	−0.683401	−	0.730044i	$-0.739500\pi$
$331$	−24.8668	−1.36680	−0.683401	+	0.730044i	$0.739500\pi$
$332$	−11.7610	−0.645468
$333$	−7.65271	−0.419366
$334$	−38.8810	−2.12747
$335$	0.243366	0.0132965
$336$	−0.786564	−0.0429106
$337$	−14.4171	−0.785349	−0.392674	−	0.919678i	$-0.628450\pi$
$337$	−14.4171	−0.785349	−0.392674	+	0.919678i	$0.628450\pi$
$338$	3.63542	0.197741
$339$	−2.78239	−0.151119
$340$	0.261956	0.0142066
$341$	7.15831	0.387644
$342$	1.59784	0.0864015
$343$	−11.2974	−0.610003
$344$	26.0517	1.40461
$345$	−0.000377620 0	−2.03304e−5 0
$346$	38.0949	2.04800
$347$	−32.3591	−1.73713	−0.868563	−	0.495578i	$-0.834956\pi$
$347$	−32.3591	−1.73713	−0.868563	+	0.495578i	$0.834956\pi$
$348$	−41.2218	−2.20972
$349$	−5.73602	−0.307042	−0.153521	−	0.988145i	$-0.549061\pi$
$349$	−5.73602	−0.307042	−0.153521	+	0.988145i	$0.549061\pi$
$350$	9.82322	0.525073
$351$	11.1551	0.595413
$352$	−17.9873	−0.958728
$353$	12.2471	0.651848	0.325924	−	0.945396i	$-0.394325\pi$
$353$	12.2471	0.651848	0.325924	+	0.945396i	$0.394325\pi$
$354$	48.4256	2.57379
$355$	0.100662	0.00534260
$356$	26.8840	1.42485
$357$	−4.48923	−0.237595
$358$	8.10608	0.428420
$359$	28.5202	1.50524	0.752618	−	0.658457i	$-0.228791\pi$
$359$	28.5202	1.50524	0.752618	+	0.658457i	$0.228791\pi$
$360$	−0.138254	−0.00728663
$361$	−18.7667	−0.987719
$362$	−27.6332	−1.45237
$363$	−2.63819	−0.138469
$364$	9.58484	0.502382
$365$	−0.388382	−0.0203289
$366$	−19.3994	−1.01402
$367$	32.3879	1.69064	0.845319	−	0.534263i	$-0.179411\pi$
$367$	32.3879	1.69064	0.845319	+	0.534263i	$0.179411\pi$
$368$	0.00250988	0.000130836 0
$369$	5.44418	0.283413
$370$	0.387028	0.0201207
$371$	−10.9758	−0.569837
$372$	14.3463	0.743821
$373$	5.82162	0.301432	0.150716	−	0.988577i	$-0.451842\pi$
$373$	5.82162	0.301432	0.150716	+	0.988577i	$0.451842\pi$
$374$	20.2538	1.04730
$375$	0.660469	0.0341065
$376$	−24.4056	−1.25863
$377$	19.8617	1.02293
$378$	−6.48487	−0.333545
$379$	−33.5658	−1.72416	−0.862080	−	0.506772i	$-0.830839\pi$
$379$	−33.5658	−1.72416	−0.862080	+	0.506772i	$0.830839\pi$
$380$	−0.0504993	−0.00259056
$381$	−3.57043	−0.182919
$382$	−40.4487	−2.06954
$383$	−34.3158	−1.75346	−0.876729	−	0.480985i	$-0.840279\pi$
$383$	−34.3158	−1.75346	−0.876729	+	0.480985i	$0.840279\pi$
$384$	−40.3179	−2.05747
$385$	−0.0934567	−0.00476300
$386$	−14.2778	−0.726720
$387$	−12.1316	−0.616685
$388$	−27.9762	−1.42028
$389$	−4.49554	−0.227933	−0.113966	−	0.993485i	$-0.536356\pi$
$389$	−4.49554	−0.227933	−0.113966	+	0.993485i	$0.536356\pi$
$390$	0.515570	0.0261069
$391$	0.0143249	0.000724439 0
$392$	19.3056	0.975083
$393$	−23.6494	−1.19295
$394$	34.3133	1.72868
$395$	0.165448	0.00832459
$396$	−16.7088	−0.839649
$397$	21.3964	1.07386	0.536928	−	0.843628i	$-0.319584\pi$
$397$	21.3964	1.07386	0.536928	+	0.843628i	$0.319584\pi$
$398$	12.7986	0.641535
$399$	0.865424	0.0433254
$400$	−2.19471	−0.109735
$401$	−13.1318	−0.655769	−0.327885	−	0.944718i	$-0.606336\pi$
$401$	−13.1318	−0.655769	−0.327885	+	0.944718i	$0.606336\pi$
$402$	37.7108	1.88084
$403$	−6.91239	−0.344331
$404$	19.4596	0.968151
$405$	−0.352815	−0.0175315
$406$	−11.5463	−0.573035
$407$	18.7001	0.926928
$408$	16.2281	0.803410
$409$	27.2151	1.34570	0.672850	−	0.739779i	$-0.265070\pi$
$409$	27.2151	1.34570	0.672850	+	0.739779i	$0.265070\pi$
$410$	−0.275334	−0.0135978
$411$	9.08461	0.448111
$412$	37.5358	1.84926
$413$	8.47648	0.417100
$414$	−0.0189107	−0.000929409 0
$415$	−0.110736	−0.00543580
$416$	17.3694	0.851604
$417$	−18.8871	−0.924906
$418$	−3.90447	−0.190974
$419$	19.8345	0.968978	0.484489	−	0.874797i	$-0.339006\pi$
$419$	19.8345	0.968978	0.484489	+	0.874797i	$0.339006\pi$
$420$	−0.187301	−0.00913934
$421$	−2.89331	−0.141011	−0.0705057	−	0.997511i	$-0.522461\pi$
$421$	−2.89331	−0.141011	−0.0705057	+	0.997511i	$0.522461\pi$
$422$	−37.9088	−1.84537
$423$	11.3651	0.552589
$424$	39.6764	1.92686
$425$	−12.5261	−0.607604
$426$	15.5981	0.755732
$427$	−3.39569	−0.164329
$428$	43.3414	2.09499
$429$	24.9108	1.20270
$430$	0.613545	0.0295878
$431$	−24.6017	−1.18502	−0.592512	−	0.805562i	$-0.701864\pi$
$431$	−24.6017	−1.18502	−0.592512	+	0.805562i	$0.701864\pi$
$432$	1.44885	0.0697079
$433$	8.63694	0.415065	0.207532	−	0.978228i	$-0.433457\pi$
$433$	8.63694	0.415065	0.207532	+	0.978228i	$0.433457\pi$
$434$	4.01844	0.192891
$435$	−0.388124	−0.0186091
$436$	−5.94598	−0.284761
$437$	−0.00276151	−0.000132101 0
$438$	−60.1818	−2.87560
$439$	10.4518	0.498837	0.249418	−	0.968396i	$-0.419761\pi$
$439$	10.4518	0.498837	0.249418	+	0.968396i	$0.419761\pi$
$440$	0.337836	0.0161057
$441$	−8.99015	−0.428102
$442$	−19.5579	−0.930276
$443$	−32.2811	−1.53372	−0.766860	−	0.641815i	$-0.778182\pi$
$443$	−32.2811	−1.53372	−0.766860	+	0.641815i	$0.778182\pi$
$444$	37.4776	1.77861
$445$	0.253126	0.0119993
$446$	−23.3063	−1.10359
$447$	2.27205	0.107464
$448$	−10.8447	−0.512363
$449$	−11.1492	−0.526163	−0.263082	−	0.964774i	$-0.584739\pi$
$449$	−11.1492	−0.526163	−0.263082	+	0.964774i	$0.584739\pi$
$450$	16.5360	0.779516
$451$	−13.3033	−0.626429
$452$	4.40374	0.207134
$453$	0.999914	0.0469801
$454$	67.3335	3.16012
$455$	0.0902460	0.00423080
$456$	−3.12841	−0.146501
$457$	−15.5700	−0.728336	−0.364168	−	0.931333i	$-0.618647\pi$
$457$	−15.5700	−0.728336	−0.364168	+	0.931333i	$0.618647\pi$
$458$	−1.58962	−0.0742779
$459$	8.26918	0.385972
$460$	0.000597665 0	2.78663e−5 0
$461$	−2.93696	−0.136788	−0.0683940	−	0.997658i	$-0.521787\pi$
$461$	−2.93696	−0.136788	−0.0683940	+	0.997658i	$0.521787\pi$
$462$	−14.4816	−0.673745
$463$	−23.9879	−1.11481	−0.557407	−	0.830239i	$-0.688204\pi$
$463$	−23.9879	−1.11481	−0.557407	+	0.830239i	$0.688204\pi$
$464$	2.57969	0.119759
$465$	0.135077	0.00626407
$466$	12.8706	0.596219
$467$	3.77256	0.174573	0.0872867	−	0.996183i	$-0.472180\pi$
$467$	3.77256	0.174573	0.0872867	+	0.996183i	$0.472180\pi$
$468$	16.1348	0.745830
$469$	6.60094	0.304803
$470$	−0.574778	−0.0265126
$471$	−26.1549	−1.20515
$472$	−30.6416	−1.41039
$473$	29.6447	1.36306
$474$	25.6370	1.17755
$475$	2.41475	0.110796
$476$	7.10518	0.325666
$477$	−18.4763	−0.845972
$478$	17.4201	0.796779
$479$	29.8844	1.36545	0.682726	−	0.730674i	$-0.260794\pi$
$479$	29.8844	1.36545	0.682726	+	0.730674i	$0.260794\pi$
$480$	−0.339421	−0.0154924
$481$	−18.0576	−0.823357
$482$	23.3854	1.06517
$483$	−0.0102424	−0.000466045 0
$484$	4.17551	0.189796
$485$	−0.263410	−0.0119608
$486$	−31.8090	−1.44289
$487$	−14.1002	−0.638939	−0.319470	−	0.947597i	$-0.603505\pi$
$487$	−14.1002	−0.638939	−0.319470	+	0.947597i	$0.603505\pi$
$488$	12.2751	0.555666
$489$	18.5094	0.837025
$490$	0.454668	0.0205398
$491$	−35.0558	−1.58205	−0.791023	−	0.611787i	$-0.790451\pi$
$491$	−35.0558	−1.58205	−0.791023	+	0.611787i	$0.790451\pi$
$492$	−26.6618	−1.20201
$493$	14.7233	0.663105
$494$	3.77033	0.169635
$495$	−0.157322	−0.00707108
$496$	−0.897801	−0.0403125
$497$	2.73032	0.122472
$498$	−17.1590	−0.768915
$499$	14.9534	0.669407	0.334704	−	0.942323i	$-0.391364\pi$
$499$	14.9534	0.669407	0.334704	+	0.942323i	$0.391364\pi$
$500$	−1.04533	−0.0467488
$501$	−35.4495	−1.58377
$502$	−38.0410	−1.69785
$503$	−2.06959	−0.0922786	−0.0461393	−	0.998935i	$-0.514692\pi$
$503$	−2.06959	−0.0922786	−0.0461393	+	0.998935i	$0.514692\pi$
$504$	−3.74994	−0.167036
$505$	0.183222	0.00815325
$506$	0.0462099	0.00205428
$507$	3.31457	0.147205
$508$	5.65098	0.250722
$509$	−16.2756	−0.721405	−0.360703	−	0.932681i	$-0.617463\pi$
$509$	−16.2756	−0.721405	−0.360703	+	0.932681i	$0.617463\pi$
$510$	0.382189	0.0169236
$511$	−10.5343	−0.466010
$512$	4.95705	0.219073
$513$	−1.59411	−0.0703818
$514$	6.52915	0.287988
$515$	0.353418	0.0155735
$516$	59.4122	2.61548
$517$	−27.7716	−1.22139
$518$	10.4976	0.461238
$519$	34.7328	1.52460
$520$	−0.326230	−0.0143061
$521$	45.1948	1.98002	0.990010	−	0.141000i	$-0.0450316\pi$
$521$	45.1948	1.98002	0.990010	+	0.141000i	$0.0450316\pi$
$522$	−19.4367	−0.850720
$523$	2.41891	0.105772	0.0528858	−	0.998601i	$-0.483158\pi$
$523$	2.41891	0.105772	0.0528858	+	0.998601i	$0.483158\pi$
$524$	37.4302	1.63515
$525$	8.95625	0.390883
$526$	70.5928	3.07799
$527$	−5.12411	−0.223210
$528$	3.23549	0.140806
$529$	−23.0000	−0.999999
$530$	0.934421	0.0405887
$531$	14.2690	0.619221
$532$	−1.36972	−0.0593849
$533$	12.8463	0.556435
$534$	39.2231	1.69735
$535$	0.408081	0.0176429
$536$	−23.8617	−1.03067
$537$	7.39066	0.318931
$538$	36.0163	1.55277
$539$	21.9682	0.946238
$540$	0.345008	0.0148468
$541$	27.8204	1.19609	0.598046	−	0.801462i	$-0.295944\pi$
$541$	27.8204	1.19609	0.598046	+	0.801462i	$0.295944\pi$
$542$	6.92553	0.297477
$543$	−25.1944	−1.08119
$544$	12.8758	0.552046
$545$	−0.0559843	−0.00239811
$546$	13.9841	0.598464
$547$	−9.01289	−0.385363	−0.192682	−	0.981261i	$-0.561718\pi$
$547$	−9.01289	−0.385363	−0.192682	+	0.981261i	$0.561718\pi$
$548$	−14.3784	−0.614213
$549$	−5.71618	−0.243961
$550$	−40.4073	−1.72297
$551$	−2.83833	−0.120917
$552$	0.0370252	0.00157590
$553$	4.48754	0.190830
$554$	34.7482	1.47631
$555$	0.352870	0.0149785
$556$	29.8930	1.26774
$557$	−22.9196	−0.971134	−0.485567	−	0.874199i	$-0.661387\pi$
$557$	−22.9196	−0.971134	−0.485567	+	0.874199i	$0.661387\pi$
$558$	6.76449	0.286364
$559$	−28.6262	−1.21076
$560$	0.0117214	0.000495320 0
$561$	18.4662	0.779644
$562$	−26.1996	−1.10516
$563$	5.76141	0.242814	0.121407	−	0.992603i	$-0.461259\pi$
$563$	5.76141	0.242814	0.121407	+	0.992603i	$0.461259\pi$
$564$	−55.6583	−2.34364
$565$	0.0414634	0.00174438
$566$	51.8978	2.18143
$567$	−9.56960	−0.401885
$568$	−9.86981	−0.414128
$569$	−17.2528	−0.723274	−0.361637	−	0.932319i	$-0.617782\pi$
$569$	−17.2528	−0.723274	−0.361637	+	0.932319i	$0.617782\pi$
$570$	−0.0736774	−0.00308601
$571$	−29.8928	−1.25097	−0.625487	−	0.780235i	$-0.715100\pi$
$571$	−29.8928	−1.25097	−0.625487	+	0.780235i	$0.715100\pi$
$572$	−39.4267	−1.64851
$573$	−36.8788	−1.54063
$574$	−7.46804	−0.311710
$575$	−0.0285788	−0.00119182
$576$	−18.2555	−0.760648
$577$	−24.4489	−1.01782	−0.508910	−	0.860820i	$-0.669951\pi$
$577$	−24.4489	−1.01782	−0.508910	+	0.860820i	$0.669951\pi$
$578$	24.7574	1.02977
$579$	−13.0177	−0.540996
$580$	0.614289	0.0255070
$581$	−3.00354	−0.124608
$582$	−40.8167	−1.69191
$583$	45.1485	1.86986
$584$	38.0804	1.57578
$585$	0.151917	0.00628099
$586$	37.0344	1.52988
$587$	29.5460	1.21950	0.609748	−	0.792595i	$-0.291271\pi$
$587$	29.5460	1.21950	0.609748	+	0.792595i	$0.291271\pi$
$588$	44.0275	1.81566
$589$	0.987814	0.0407022
$590$	−0.721641	−0.0297095
$591$	31.2849	1.28689
$592$	−2.34538	−0.0963944
$593$	−8.66498	−0.355828	−0.177914	−	0.984046i	$-0.556935\pi$
$593$	−8.66498	−0.355828	−0.177914	+	0.984046i	$0.556935\pi$
$594$	26.6751	1.09449
$595$	0.0668988	0.00274258
$596$	−3.59602	−0.147299
$597$	11.6690	0.477581
$598$	−0.0446223	−0.00182474
$599$	−37.6852	−1.53977	−0.769887	−	0.638180i	$-0.779687\pi$
$599$	−37.6852	−1.53977	−0.769887	+	0.638180i	$0.779687\pi$
$600$	−32.3759	−1.32174
$601$	−0.819509	−0.0334285	−0.0167142	−	0.999860i	$-0.505321\pi$
$601$	−0.819509	−0.0334285	−0.0167142	+	0.999860i	$0.505321\pi$
$602$	16.6415	0.678258
$603$	11.1118	0.452507
$604$	−1.58258	−0.0643943
$605$	0.0393145	0.00159836
$606$	28.3911	1.15331
$607$	−12.9692	−0.526402	−0.263201	−	0.964741i	$-0.584778\pi$
$607$	−12.9692	−0.526402	−0.263201	+	0.964741i	$0.584778\pi$
$608$	−2.48217	−0.100665
$609$	−10.5273	−0.426587
$610$	0.289091	0.0117049
$611$	26.8175	1.08492
$612$	11.9606	0.483479
$613$	−12.5116	−0.505338	−0.252669	−	0.967553i	$-0.581308\pi$
$613$	−12.5116	−0.505338	−0.252669	+	0.967553i	$0.581308\pi$
$614$	16.0863	0.649189
$615$	−0.251034	−0.0101227
$616$	9.16331	0.369200
$617$	−38.8652	−1.56465	−0.782327	−	0.622868i	$-0.785967\pi$
$617$	−38.8652	−1.56465	−0.782327	+	0.622868i	$0.785967\pi$
$618$	54.7640	2.20293
$619$	−2.49439	−0.100258	−0.0501290	−	0.998743i	$-0.515963\pi$
$619$	−2.49439	−0.100258	−0.0501290	+	0.998743i	$0.515963\pi$
$620$	−0.213789	−0.00858598
$621$	0.0188665	0.000757087 0
$622$	30.9559	1.24122
$623$	6.86567	0.275067
$624$	−3.12433	−0.125073
$625$	24.9852	0.999409
$626$	−80.1706	−3.20426
$627$	−3.55987	−0.142168
$628$	41.3958	1.65187
$629$	−13.3860	−0.533735
$630$	−0.0883151	−0.00351856
$631$	1.84167	0.0733156	0.0366578	−	0.999328i	$-0.488329\pi$
$631$	1.84167	0.0733156	0.0366578	+	0.999328i	$0.488329\pi$
$632$	−16.2220	−0.645275
$633$	−34.5631	−1.37376
$634$	74.2427	2.94856
$635$	0.0532068	0.00211145
$636$	90.4840	3.58793
$637$	−21.2135	−0.840509
$638$	47.4952	1.88035
$639$	4.59612	0.181820
$640$	0.600820	0.0237495
$641$	12.6011	0.497712	0.248856	−	0.968540i	$-0.419945\pi$
$641$	12.6011	0.497712	0.248856	+	0.968540i	$0.419945\pi$
$642$	63.2342	2.49566
$643$	8.69311	0.342823	0.171411	−	0.985200i	$-0.445167\pi$
$643$	8.69311	0.342823	0.171411	+	0.985200i	$0.445167\pi$
$644$	0.0162108	0.000638795 0
$645$	0.559395	0.0220262
$646$	2.79492	0.109965
$647$	29.2401	1.14955	0.574773	−	0.818313i	$-0.305090\pi$
$647$	29.2401	1.14955	0.574773	+	0.818313i	$0.305090\pi$
$648$	34.5931	1.35894
$649$	−34.8675	−1.36867
$650$	39.0191	1.53045
$651$	3.66378	0.143595
$652$	−29.2951	−1.14729
$653$	−11.4327	−0.447396	−0.223698	−	0.974658i	$-0.571813\pi$
$653$	−11.4327	−0.447396	−0.223698	+	0.974658i	$0.571813\pi$
$654$	−8.67506	−0.339222
$655$	0.352424	0.0137704
$656$	1.66851	0.0651445
$657$	−17.7331	−0.691833
$658$	−15.5900	−0.607763
$659$	−10.8036	−0.420848	−0.210424	−	0.977610i	$-0.567484\pi$
$659$	−10.8036	−0.420848	−0.210424	+	0.977610i	$0.567484\pi$
$660$	0.770451	0.0299898
$661$	32.1299	1.24971	0.624853	−	0.780742i	$-0.285159\pi$
$661$	32.1299	1.24971	0.624853	+	0.780742i	$0.285159\pi$
$662$	57.4211	2.23173
$663$	−17.8318	−0.692530
$664$	10.8575	0.421352
$665$	−0.0128966	−0.000500108 0
$666$	17.6713	0.684747
$667$	0.0335919	0.00130068
$668$	56.1064	2.17082
$669$	−21.2494	−0.821548
$670$	−0.561968	−0.0217107
$671$	13.9680	0.539228
$672$	−9.20631	−0.355141
$673$	−19.4205	−0.748604	−0.374302	−	0.927307i	$-0.622118\pi$
$673$	−19.4205	−0.748604	−0.374302	+	0.927307i	$0.622118\pi$
$674$	33.2912	1.28233
$675$	−16.4974	−0.634986
$676$	−5.24602	−0.201770
$677$	10.2595	0.394304	0.197152	−	0.980373i	$-0.436831\pi$
$677$	10.2595	0.394304	0.197152	+	0.980373i	$0.436831\pi$
$678$	6.42496	0.246749
$679$	−7.14461	−0.274185
$680$	−0.241832	−0.00927383
$681$	61.3909	2.35250
$682$	−16.5296	−0.632952
$683$	−39.9611	−1.52907	−0.764534	−	0.644584i	$-0.777031\pi$
$683$	−39.9611	−1.52907	−0.764534	+	0.644584i	$0.777031\pi$
$684$	−2.30574	−0.0881620
$685$	−0.135379	−0.00517258
$686$	26.0874	0.996023
$687$	−1.44932	−0.0552951
$688$	−3.71806	−0.141750
$689$	−43.5974	−1.66093
$690$	0.000871981 0	3.31957e−5 0
$691$	−43.7881	−1.66578	−0.832889	−	0.553440i	$-0.813315\pi$
$691$	−43.7881	−1.66578	−0.832889	+	0.553440i	$0.813315\pi$
$692$	−54.9721	−2.08973
$693$	−4.26712	−0.162095
$694$	74.7220	2.83641
$695$	0.281457	0.0106763
$696$	38.0550	1.44247
$697$	9.52287	0.360704
$698$	13.2453	0.501343
$699$	11.7347	0.443846
$700$	−14.1752	−0.535772
$701$	−37.8684	−1.43027	−0.715135	−	0.698987i	$-0.753635\pi$
$701$	−37.8684	−1.43027	−0.715135	+	0.698987i	$0.753635\pi$
$702$	−25.7587	−0.972200
$703$	2.58052	0.0973262
$704$	44.6090	1.68127
$705$	−0.524050	−0.0197369
$706$	−28.2804	−1.06435
$707$	4.96962	0.186902
$708$	−69.8796	−2.62623
$709$	4.39983	0.165239	0.0826196	−	0.996581i	$-0.473671\pi$
$709$	4.39983	0.165239	0.0826196	+	0.996581i	$0.473671\pi$
$710$	−0.232444	−0.00872348
$711$	7.55416	0.283303
$712$	−24.8187	−0.930119
$713$	−0.0116909	−0.000437827 0
$714$	10.3663	0.387950
$715$	−0.371222	−0.0138829
$716$	−11.6973	−0.437149
$717$	15.8827	0.593150
$718$	−65.8573	−2.45777
$719$	47.5950	1.77500	0.887498	−	0.460812i	$-0.152442\pi$
$719$	47.5950	1.77500	0.887498	+	0.460812i	$0.152442\pi$
$720$	0.0197314	0.000735346 0
$721$	9.58596	0.357000
$722$	43.3350	1.61276
$723$	21.3214	0.792953
$724$	39.8755	1.48196
$725$	−29.3738	−1.09091
$726$	6.09199	0.226095
$727$	−38.7897	−1.43863	−0.719315	−	0.694684i	$-0.755544\pi$
$727$	−38.7897	−1.43863	−0.719315	+	0.694684i	$0.755544\pi$
$728$	−8.84851	−0.327948
$729$	4.73471	0.175360
$730$	0.896833	0.0331933
$731$	−21.2204	−0.784866
$732$	27.9939	1.03468
$733$	−36.3333	−1.34200	−0.671001	−	0.741456i	$-0.734135\pi$
$733$	−36.3333	−1.34200	−0.671001	+	0.741456i	$0.734135\pi$
$734$	−74.7886	−2.76050
$735$	0.414540	0.0152906
$736$	0.0293768	0.00108284
$737$	−27.1526	−1.00018
$738$	−12.5714	−0.462760
$739$	2.59369	0.0954104	0.0477052	−	0.998861i	$-0.484809\pi$
$739$	2.59369	0.0954104	0.0477052	+	0.998861i	$0.484809\pi$
$740$	−0.558494	−0.0205306
$741$	3.43757	0.126282
$742$	25.3448	0.930438
$743$	34.8933	1.28011	0.640056	−	0.768328i	$-0.278911\pi$
$743$	34.8933	1.28011	0.640056	+	0.768328i	$0.278911\pi$
$744$	−13.2442	−0.485555
$745$	−0.0338583	−0.00124047
$746$	−13.4430	−0.492183
$747$	−5.05605	−0.184991
$748$	−29.2268	−1.06864
$749$	11.0686	0.404438
$750$	−1.52512	−0.0556895
$751$	43.4881	1.58690	0.793451	−	0.608634i	$-0.208282\pi$
$751$	43.4881	1.58690	0.793451	+	0.608634i	$0.208282\pi$
$752$	3.48313	0.127017
$753$	−34.6836	−1.26394
$754$	−45.8635	−1.67025
$755$	−0.0149008	−0.000542295 0
$756$	9.35786	0.340342
$757$	22.9586	0.834443	0.417222	−	0.908805i	$-0.363004\pi$
$757$	22.9586	0.834443	0.417222	+	0.908805i	$0.363004\pi$
$758$	77.5085	2.81524
$759$	0.0421315	0.00152928
$760$	0.0466198	0.00169108
$761$	7.51600	0.272455	0.136227	−	0.990678i	$-0.456502\pi$
$761$	7.51600	0.272455	0.136227	+	0.990678i	$0.456502\pi$
$762$	8.24466	0.298673
$763$	−1.51849	−0.0549732
$764$	58.3687	2.11171
$765$	0.112615	0.00407160
$766$	79.2404	2.86307
$767$	33.6697	1.21574
$768$	39.4397	1.42316
$769$	−44.6033	−1.60843	−0.804217	−	0.594335i	$-0.797415\pi$
$769$	−44.6033	−1.60843	−0.804217	+	0.594335i	$0.797415\pi$
$770$	0.215806	0.00777709
$771$	5.95290	0.214389
$772$	20.6033	0.741528
$773$	−17.8751	−0.642924	−0.321462	−	0.946922i	$-0.604174\pi$
$773$	−17.8751	−0.642924	−0.321462	+	0.946922i	$0.604174\pi$
$774$	28.0137	1.00693
$775$	10.2229	0.367216
$776$	25.8270	0.927135
$777$	9.57110	0.343361
$778$	10.3809	0.372172
$779$	−1.83580	−0.0657742
$780$	−0.743983	−0.0266389
$781$	−11.2310	−0.401877
$782$	−0.0330783	−0.00118288
$783$	19.3913	0.692988
$784$	−2.75527	−0.0984025
$785$	0.389762	0.0139112
$786$	54.6099	1.94787
$787$	−29.6328	−1.05629	−0.528147	−	0.849153i	$-0.677113\pi$
$787$	−29.6328	−1.05629	−0.528147	+	0.849153i	$0.677113\pi$
$788$	−49.5151	−1.76390
$789$	64.3625	2.29136
$790$	−0.382044	−0.0135925
$791$	1.12463	0.0399874
$792$	15.4252	0.548110
$793$	−13.4881	−0.478977
$794$	−49.4076	−1.75341
$795$	0.851952	0.0302156
$796$	−18.4688	−0.654608
$797$	30.8240	1.09184	0.545921	−	0.837837i	$-0.316180\pi$
$797$	30.8240	1.09184	0.545921	+	0.837837i	$0.316180\pi$
$798$	−1.99839	−0.0707423
$799$	19.8796	0.703291
$800$	−25.6879	−0.908204
$801$	11.5574	0.408361
$802$	30.3232	1.07075
$803$	43.3323	1.52916
$804$	−54.4178	−1.91917
$805$	0.000152633 0	5.37960e−6 0
$806$	15.9617	0.562228
$807$	32.8376	1.15594
$808$	−17.9646	−0.631994
$809$	44.3153	1.55804	0.779021	−	0.626998i	$-0.215717\pi$
$809$	44.3153	1.55804	0.779021	+	0.626998i	$0.215717\pi$
$810$	0.814703	0.0286257
$811$	−3.98585	−0.139962	−0.0699810	−	0.997548i	$-0.522294\pi$
$811$	−3.98585	−0.139962	−0.0699810	+	0.997548i	$0.522294\pi$
$812$	16.6617	0.584712
$813$	6.31430	0.221452
$814$	−43.1812	−1.51350
$815$	−0.275828	−0.00966184
$816$	−2.31605	−0.0810779
$817$	4.09083	0.143120
$818$	−62.8438	−2.19728
$819$	4.12052	0.143983
$820$	0.397315	0.0138749
$821$	2.11376	0.0737708	0.0368854	−	0.999320i	$-0.488256\pi$
$821$	2.11376	0.0737708	0.0368854	+	0.999320i	$0.488256\pi$
$822$	−20.9777	−0.731682
$823$	−21.8687	−0.762296	−0.381148	−	0.924514i	$-0.624471\pi$
$823$	−21.8687	−0.762296	−0.381148	+	0.924514i	$0.624471\pi$
$824$	−34.6522	−1.20717
$825$	−36.8410	−1.28264
$826$	−19.5735	−0.681048
$827$	23.8993	0.831060	0.415530	−	0.909579i	$-0.363596\pi$
$827$	23.8993	0.831060	0.415530	+	0.909579i	$0.363596\pi$
$828$	0.0272887	0.000948347 0
$829$	21.0239	0.730191	0.365095	−	0.930970i	$-0.381036\pi$
$829$	21.0239	0.730191	0.365095	+	0.930970i	$0.381036\pi$
$830$	0.255705	0.00887565
$831$	31.6814	1.09902
$832$	−43.0765	−1.49341
$833$	−15.7254	−0.544854
$834$	43.6132	1.51020
$835$	0.528270	0.0182815
$836$	5.63427	0.194865
$837$	−6.74869	−0.233269
$838$	−45.8008	−1.58216
$839$	31.6822	1.09379	0.546895	−	0.837201i	$-0.315810\pi$
$839$	31.6822	1.09379	0.546895	+	0.837201i	$0.315810\pi$
$840$	0.172912	0.00596602
$841$	5.52630	0.190562
$842$	6.68109	0.230246
$843$	−23.8873	−0.822722
$844$	54.7035	1.88297
$845$	−0.0493938	−0.00169920
$846$	−26.2437	−0.902276
$847$	1.06635	0.0366402
$848$	−5.66255	−0.194453
$849$	47.3174	1.62393
$850$	28.9246	0.992105
$851$	−0.0305408	−0.00104692
$852$	−22.5086	−0.771131
$853$	6.97227	0.238726	0.119363	−	0.992851i	$-0.461915\pi$
$853$	6.97227	0.238726	0.119363	+	0.992851i	$0.461915\pi$
$854$	7.84116	0.268319
$855$	−0.0217096	−0.000742454 0
$856$	−40.0118	−1.36758
$857$	−12.5886	−0.430018	−0.215009	−	0.976612i	$-0.568978\pi$
$857$	−12.5886	−0.430018	−0.215009	+	0.976612i	$0.568978\pi$
$858$	−57.5228	−1.96379
$859$	−23.7901	−0.811707	−0.405854	−	0.913938i	$-0.633026\pi$
$859$	−23.7901	−0.811707	−0.405854	+	0.913938i	$0.633026\pi$
$860$	−0.885364	−0.0301907
$861$	−6.80893	−0.232048
$862$	56.8091	1.93492
$863$	8.43989	0.287297	0.143649	−	0.989629i	$-0.454117\pi$
$863$	8.43989	0.287297	0.143649	+	0.989629i	$0.454117\pi$
$864$	16.9580	0.576924
$865$	−0.517590	−0.0175986
$866$	−19.9440	−0.677724
$867$	22.5724	0.766597
$868$	−5.79872	−0.196822
$869$	−18.4592	−0.626187
$870$	0.896235	0.0303852
$871$	26.2198	0.888424
$872$	5.48919	0.185888
$873$	−12.0270	−0.407051
$874$	0.00637675	0.000215697 0
$875$	−0.266959	−0.00902487
$876$	86.8442	2.93419
$877$	−35.0556	−1.18374	−0.591871	−	0.806033i	$-0.701610\pi$
$877$	−35.0556	−1.18374	−0.591871	+	0.806033i	$0.701610\pi$
$878$	−24.1348	−0.814509
$879$	33.7658	1.13889
$880$	−0.0482154	−0.00162534
$881$	25.3400	0.853725	0.426863	−	0.904316i	$-0.359619\pi$
$881$	25.3400	0.853725	0.426863	+	0.904316i	$0.359619\pi$
$882$	20.7596	0.699012
$883$	5.99355	0.201699	0.100849	−	0.994902i	$-0.467844\pi$
$883$	5.99355	0.201699	0.100849	+	0.994902i	$0.467844\pi$
$884$	28.2227	0.949232
$885$	−0.657951	−0.0221168
$886$	74.5418	2.50428
$887$	−41.2741	−1.38585	−0.692924	−	0.721011i	$-0.743678\pi$
$887$	−41.2741	−1.38585	−0.692924	+	0.721011i	$0.743678\pi$
$888$	−34.5985	−1.16105
$889$	1.44316	0.0484019
$890$	−0.584505	−0.0195927
$891$	39.3640	1.31874
$892$	33.6317	1.12607
$893$	−3.83235	−0.128245
$894$	−5.24651	−0.175470
$895$	−0.110136	−0.00368144
$896$	16.2964	0.544424
$897$	−0.0406841	−0.00135840
$898$	25.7452	0.859127
$899$	−12.0161	−0.400759
$900$	−23.8620	−0.795400
$901$	−32.3185	−1.07668
$902$	30.7194	1.02284
$903$	15.1728	0.504919
$904$	−4.06543	−0.135214
$905$	0.375448	0.0124803
$906$	−2.30895	−0.0767098
$907$	−7.58946	−0.252004	−0.126002	−	0.992030i	$-0.540215\pi$
$907$	−7.58946	−0.252004	−0.126002	+	0.992030i	$0.540215\pi$
$908$	−97.1643	−3.22451
$909$	8.36568	0.277472
$910$	−0.208392	−0.00690811
$911$	24.4133	0.808847	0.404424	−	0.914572i	$-0.367472\pi$
$911$	24.4133	0.808847	0.404424	+	0.914572i	$0.367472\pi$
$912$	0.446482	0.0147845
$913$	12.3549	0.408888
$914$	35.9535	1.18924
$915$	0.263576	0.00871356
$916$	2.29387	0.0757915
$917$	9.55900	0.315666
$918$	−19.0948	−0.630221
$919$	−17.8182	−0.587769	−0.293885	−	0.955841i	$-0.594948\pi$
$919$	−17.8182	−0.587769	−0.293885	+	0.955841i	$0.594948\pi$
$920$	−0.000551751 0	−1.81907e−5 0
$921$	14.6665	0.483279
$922$	6.78189	0.223350
$923$	10.8452	0.356973
$924$	20.8974	0.687473
$925$	26.7057	0.878080
$926$	55.3918	1.82029
$927$	16.1367	0.529997
$928$	30.1939	0.991163
$929$	31.5496	1.03511	0.517555	−	0.855650i	$-0.326842\pi$
$929$	31.5496	1.03511	0.517555	+	0.855650i	$0.326842\pi$
$930$	−0.311914	−0.0102281
$931$	3.03151	0.0993538
$932$	−18.5726	−0.608367
$933$	28.2238	0.924005
$934$	−8.71142	−0.285046
$935$	−0.275185	−0.00899950
$936$	−14.8953	−0.486867
$937$	−53.3153	−1.74174	−0.870868	−	0.491518i	$-0.836442\pi$
$937$	−53.3153	−1.74174	−0.870868	+	0.491518i	$0.836442\pi$
$938$	−15.2426	−0.497687
$939$	−73.0949	−2.38536
$940$	0.829422	0.0270528
$941$	55.2514	1.80114	0.900571	−	0.434708i	$-0.143149\pi$
$941$	55.2514	1.80114	0.900571	+	0.434708i	$0.143149\pi$
$942$	60.3956	1.96779
$943$	0.0217269	0.000707524 0
$944$	4.37311	0.142333
$945$	0.0881088	0.00286618
$946$	−68.4540	−2.22563
$947$	17.5276	0.569570	0.284785	−	0.958591i	$-0.408078\pi$
$947$	17.5276	0.569570	0.284785	+	0.958591i	$0.408078\pi$
$948$	−36.9950	−1.20154
$949$	−41.8436	−1.35830
$950$	−5.57601	−0.180910
$951$	67.6903	2.19501
$952$	−6.55934	−0.212590
$953$	−9.63561	−0.312128	−0.156064	−	0.987747i	$-0.549881\pi$
$953$	−9.63561	−0.312128	−0.156064	+	0.987747i	$0.549881\pi$
$954$	42.6645	1.38132
$955$	0.549570	0.0177837
$956$	−25.1378	−0.813015
$957$	43.3034	1.39980
$958$	−69.0075	−2.22953
$959$	−3.67197	−0.118574
$960$	0.841773	0.0271681
$961$	−26.8181	−0.865099
$962$	41.6978	1.34439
$963$	18.6325	0.600423
$964$	−33.7458	−1.08688
$965$	0.193990	0.00624476
$966$	0.0236512	0.000760966 0
$967$	48.8910	1.57223	0.786114	−	0.618081i	$-0.212090\pi$
$967$	48.8910	1.57223	0.786114	+	0.618081i	$0.212090\pi$
$968$	−3.85474	−0.123896
$969$	2.54825	0.0818616
$970$	0.608252	0.0195298
$971$	−59.9879	−1.92510	−0.962552	−	0.271097i	$-0.912614\pi$
$971$	−59.9879	−1.92510	−0.962552	+	0.271097i	$0.912614\pi$
$972$	45.9013	1.47229
$973$	7.63411	0.244738
$974$	32.5594	1.04327
$975$	35.5754	1.13932
$976$	−1.75188	−0.0560762
$977$	38.5937	1.23472	0.617360	−	0.786680i	$-0.288202\pi$
$977$	38.5937	1.23472	0.617360	+	0.786680i	$0.288202\pi$
$978$	−42.7410	−1.36671
$979$	−28.2416	−0.902604
$980$	−0.656100	−0.0209583
$981$	−2.55618	−0.0816125
$982$	80.9491	2.58319
$983$	0.452103	0.0144199	0.00720993	−	0.999974i	$-0.497705\pi$
$983$	0.452103	0.0144199	0.00720993	+	0.999974i	$0.497705\pi$
$984$	24.6136	0.784651
$985$	−0.466209	−0.0148547
$986$	−33.9983	−1.08273
$987$	−14.2141	−0.452440
$988$	−5.44070	−0.173092
$989$	−0.0484154	−0.00153952
$990$	0.363279	0.0115458
$991$	−51.9560	−1.65044	−0.825219	−	0.564813i	$-0.808948\pi$
$991$	−51.9560	−1.65044	−0.825219	+	0.564813i	$0.808948\pi$
$992$	−10.5083	−0.333638
$993$	52.3533	1.66138
$994$	−6.30472	−0.199973
$995$	−0.173892	−0.00551276
$996$	24.7610	0.784583
$997$	−8.48431	−0.268701	−0.134350	−	0.990934i	$-0.542895\pi$
$997$	−8.48431	−0.268701	−0.134350	+	0.990934i	$0.542895\pi$
$998$	−34.5297	−1.09302
$999$	−17.6300	−0.557788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.2.a.b.1.14	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.2.a.b.1.14	✓	126	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3467.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30915 q^{2} -2.10535 q^{3} +3.33217 q^{4} +0.0313740 q^{5} +4.86157 q^{6} +0.850976 q^{7} -3.07619 q^{8} +1.43250 q^{9} -0.0724474 q^{10} -3.50044 q^{11} -7.01539 q^{12} +3.38018 q^{13} -1.96503 q^{14} -0.0660534 q^{15} +0.439028 q^{16} +2.50571 q^{17} -3.30786 q^{18} -0.483045 q^{19} +0.104544 q^{20} -1.79160 q^{21} +8.08304 q^{22} +0.00571689 q^{23} +6.47645 q^{24} -4.99902 q^{25} -7.80535 q^{26} +3.30013 q^{27} +2.83560 q^{28} +5.87591 q^{29} +0.152527 q^{30} -2.04497 q^{31} +5.13859 q^{32} +7.36966 q^{33} -5.78606 q^{34} +0.0266986 q^{35} +4.77334 q^{36} -5.34220 q^{37} +1.11542 q^{38} -7.11647 q^{39} -0.0965124 q^{40} +3.80047 q^{41} +4.13708 q^{42} -8.46884 q^{43} -11.6641 q^{44} +0.0449434 q^{45} -0.0132012 q^{46} +7.93374 q^{47} -0.924308 q^{48} -6.27584 q^{49} +11.5435 q^{50} -5.27540 q^{51} +11.2634 q^{52} -12.8979 q^{53} -7.62051 q^{54} -0.109823 q^{55} -2.61776 q^{56} +1.01698 q^{57} -13.5684 q^{58} +9.96089 q^{59} -0.220101 q^{60} -3.99035 q^{61} +4.72215 q^{62} +1.21902 q^{63} -12.7438 q^{64} +0.106050 q^{65} -17.0176 q^{66} +7.75691 q^{67} +8.34945 q^{68} -0.0120361 q^{69} -0.0616510 q^{70} +3.20846 q^{71} -4.40664 q^{72} -12.3791 q^{73} +12.3359 q^{74} +10.5247 q^{75} -1.60959 q^{76} -2.97879 q^{77} +16.4330 q^{78} +5.27340 q^{79} +0.0137741 q^{80} -11.2454 q^{81} -8.77585 q^{82} -3.52953 q^{83} -5.96993 q^{84} +0.0786142 q^{85} +19.5558 q^{86} -12.3708 q^{87} +10.7680 q^{88} +8.06800 q^{89} -0.103781 q^{90} +2.87645 q^{91} +0.0190497 q^{92} +4.30539 q^{93} -18.3202 q^{94} -0.0151551 q^{95} -10.8185 q^{96} -8.39578 q^{97} +14.4919 q^{98} -5.01439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) \) 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * q^97 + 4 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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