LMFDB - Embedded newform 985.2.a.g.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [985,2,Mod(1,985)] 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("985.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(985, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 985 = 5 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	985.a (trivial)

Newform invariants

comment:select newform

sage:traces = [17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.86526459910$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 6 x^{16} - 8 x^{15} + 106 x^{14} - 60 x^{13} - 698 x^{12} + 877 x^{11} + 2076 x^{10} - 3556 x^{9} + \cdots + 2 $ x^17 - 6x^16 - 8x^15 + 106x^14 - 60x^13 - 698x^12 + 877x^11 + 2076x^10 - 3556x^9 - 2631x^8 + 5998x^7 + 1031x^6 - 4058x^5 - 119x^4 + 1073x^3 + 15x^2 - 75x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.369022$ of defining polynomial
Character	$\chi$	$=$	985.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.369022 q^{2} +3.16939 q^{3} -1.86382 q^{4} -1.00000 q^{5} -1.16957 q^{6} +3.62949 q^{7} +1.42584 q^{8} +7.04503 q^{9} +0.369022 q^{10} -3.32973 q^{11} -5.90718 q^{12} -2.49966 q^{13} -1.33936 q^{14} -3.16939 q^{15} +3.20148 q^{16} +3.99626 q^{17} -2.59977 q^{18} +0.544719 q^{19} +1.86382 q^{20} +11.5033 q^{21} +1.22874 q^{22} +8.11588 q^{23} +4.51903 q^{24} +1.00000 q^{25} +0.922428 q^{26} +12.8203 q^{27} -6.76472 q^{28} -3.01336 q^{29} +1.16957 q^{30} +0.641233 q^{31} -4.03309 q^{32} -10.5532 q^{33} -1.47471 q^{34} -3.62949 q^{35} -13.1307 q^{36} +2.21756 q^{37} -0.201013 q^{38} -7.92238 q^{39} -1.42584 q^{40} +7.30634 q^{41} -4.24496 q^{42} -12.1642 q^{43} +6.20603 q^{44} -7.04503 q^{45} -2.99494 q^{46} +5.63469 q^{47} +10.1467 q^{48} +6.17319 q^{49} -0.369022 q^{50} +12.6657 q^{51} +4.65891 q^{52} -11.4574 q^{53} -4.73097 q^{54} +3.32973 q^{55} +5.17505 q^{56} +1.72643 q^{57} +1.11200 q^{58} +12.0541 q^{59} +5.90718 q^{60} +5.18446 q^{61} -0.236629 q^{62} +25.5699 q^{63} -4.91466 q^{64} +2.49966 q^{65} +3.89437 q^{66} -7.98879 q^{67} -7.44832 q^{68} +25.7224 q^{69} +1.33936 q^{70} +6.47286 q^{71} +10.0451 q^{72} -10.1728 q^{73} -0.818327 q^{74} +3.16939 q^{75} -1.01526 q^{76} -12.0852 q^{77} +2.92353 q^{78} -10.1297 q^{79} -3.20148 q^{80} +19.4974 q^{81} -2.69620 q^{82} -1.50622 q^{83} -21.4400 q^{84} -3.99626 q^{85} +4.48884 q^{86} -9.55051 q^{87} -4.74765 q^{88} -1.60622 q^{89} +2.59977 q^{90} -9.07247 q^{91} -15.1266 q^{92} +2.03232 q^{93} -2.07932 q^{94} -0.544719 q^{95} -12.7824 q^{96} +9.03149 q^{97} -2.27804 q^{98} -23.4581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 17 q^{5} + 3 q^{6} + 7 q^{7} + 18 q^{8} + 22 q^{9} - 6 q^{10} + 7 q^{11} + 20 q^{12} + 3 q^{13} + 17 q^{14} - 5 q^{15} + 28 q^{16} + 6 q^{17} + 13 q^{18} - 23 q^{19}+ \cdots - 46 q^{99}+O(q^{100}) $ 17 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 17 * q^5 + 3 * q^6 + 7 * q^7 + 18 * q^8 + 22 * q^9 - 6 * q^10 + 7 * q^11 + 20 * q^12 + 3 * q^13 + 17 * q^14 - 5 * q^15 + 28 * q^16 + 6 * q^17 + 13 * q^18 - 23 * q^19 - 18 * q^20 - q^21 + 14 * q^22 + 49 * q^23 + q^24 + 17 * q^25 + 3 * q^26 + 29 * q^27 + 9 * q^28 + 19 * q^29 - 3 * q^30 - 18 * q^31 + 42 * q^32 + 14 * q^33 - 19 * q^34 - 7 * q^35 + 31 * q^36 + 10 * q^37 + 27 * q^38 + 21 * q^39 - 18 * q^40 + 14 * q^41 + 31 * q^42 + 22 * q^43 + 27 * q^44 - 22 * q^45 - 16 * q^46 + 51 * q^47 + 38 * q^48 + 8 * q^49 + 6 * q^50 + 7 * q^51 + 17 * q^52 + 37 * q^53 - 36 * q^54 - 7 * q^55 + 47 * q^56 - 11 * q^57 + 20 * q^58 + 23 * q^59 - 20 * q^60 - 15 * q^61 - 6 * q^62 + 37 * q^63 - 2 * q^64 - 3 * q^65 - 4 * q^66 + 24 * q^67 + 13 * q^68 + 6 * q^69 - 17 * q^70 + 68 * q^71 - 33 * q^72 - 10 * q^73 - 9 * q^74 + 5 * q^75 - 57 * q^76 - 16 * q^77 - 24 * q^78 + 3 * q^79 - 28 * q^80 + 33 * q^81 - 40 * q^82 + 29 * q^83 - 83 * q^84 - 6 * q^85 + 37 * q^86 + 23 * q^87 + 5 * q^88 - 11 * q^89 - 13 * q^90 - 82 * q^91 + 15 * q^93 - 39 * q^94 + 23 * q^95 + 2 * q^96 + 6 * q^97 + 15 * q^98 - 46 * 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 $

$2$	−0.369022	−0.260938	−0.130469	−	0.991452i	$-0.541648\pi$
$2$	−0.369022	−0.260938	−0.130469	+	0.991452i	$0.541648\pi$
$3$	3.16939	1.82985	0.914924	−	0.403626i	$-0.132250\pi$
$3$	3.16939	1.82985	0.914924	+	0.403626i	$0.132250\pi$
$4$	−1.86382	−0.931911
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.16957	−0.477477
$7$	3.62949	1.37182	0.685909	−	0.727687i	$-0.259405\pi$
$7$	3.62949	1.37182	0.685909	+	0.727687i	$0.259405\pi$
$8$	1.42584	0.504109
$9$	7.04503	2.34834
$10$	0.369022	0.116695
$11$	−3.32973	−1.00395	−0.501976	−	0.864882i	$-0.667393\pi$
$11$	−3.32973	−1.00395	−0.501976	+	0.864882i	$0.667393\pi$
$12$	−5.90718	−1.70526
$13$	−2.49966	−0.693280	−0.346640	−	0.937998i	$-0.612677\pi$
$13$	−2.49966	−0.693280	−0.346640	+	0.937998i	$0.612677\pi$
$14$	−1.33936	−0.357959
$15$	−3.16939	−0.818333
$16$	3.20148	0.800370
$17$	3.99626	0.969236	0.484618	−	0.874726i	$-0.338959\pi$
$17$	3.99626	0.969236	0.484618	+	0.874726i	$0.338959\pi$
$18$	−2.59977	−0.612772
$19$	0.544719	0.124967	0.0624835	−	0.998046i	$-0.480098\pi$
$19$	0.544719	0.124967	0.0624835	+	0.998046i	$0.480098\pi$
$20$	1.86382	0.416763
$21$	11.5033	2.51022
$22$	1.22874	0.261969
$23$	8.11588	1.69228	0.846139	−	0.532962i	$-0.178921\pi$
$23$	8.11588	1.69228	0.846139	+	0.532962i	$0.178921\pi$
$24$	4.51903	0.922443
$25$	1.00000	0.200000
$26$	0.922428	0.180903
$27$	12.8203	2.46726
$28$	−6.76472	−1.27841
$29$	−3.01336	−0.559567	−0.279783	−	0.960063i	$-0.590263\pi$
$29$	−3.01336	−0.559567	−0.279783	+	0.960063i	$0.590263\pi$
$30$	1.16957	0.213534
$31$	0.641233	0.115169	0.0575845	−	0.998341i	$-0.481660\pi$
$31$	0.641233	0.115169	0.0575845	+	0.998341i	$0.481660\pi$
$32$	−4.03309	−0.712956
$33$	−10.5532	−1.83708
$34$	−1.47471	−0.252910
$35$	−3.62949	−0.613496
$36$	−13.1307	−2.18845
$37$	2.21756	0.364564	0.182282	−	0.983246i	$-0.441652\pi$
$37$	2.21756	0.364564	0.182282	+	0.983246i	$0.441652\pi$
$38$	−0.201013	−0.0326086
$39$	−7.92238	−1.26860
$40$	−1.42584	−0.225444
$41$	7.30634	1.14106	0.570529	−	0.821277i	$-0.306738\pi$
$41$	7.30634	1.14106	0.570529	+	0.821277i	$0.306738\pi$
$42$	−4.24496	−0.655011
$43$	−12.1642	−1.85502	−0.927508	−	0.373803i	$-0.878054\pi$
$43$	−12.1642	−1.85502	−0.927508	+	0.373803i	$0.878054\pi$
$44$	6.20603	0.935594
$45$	−7.04503	−1.05021
$46$	−2.99494	−0.441580
$47$	5.63469	0.821904	0.410952	−	0.911657i	$-0.365196\pi$
$47$	5.63469	0.821904	0.410952	+	0.911657i	$0.365196\pi$
$48$	10.1467	1.46456
$49$	6.17319	0.881884
$50$	−0.369022	−0.0521876
$51$	12.6657	1.77355
$52$	4.65891	0.646075
$53$	−11.4574	−1.57379	−0.786895	−	0.617087i	$-0.788313\pi$
$53$	−11.4574	−1.57379	−0.786895	+	0.617087i	$0.788313\pi$
$54$	−4.73097	−0.643803
$55$	3.32973	0.448981
$56$	5.17505	0.691546
$57$	1.72643	0.228671
$58$	1.11200	0.146012
$59$	12.0541	1.56931	0.784654	−	0.619935i	$-0.212841\pi$
$59$	12.0541	1.56931	0.784654	+	0.619935i	$0.212841\pi$
$60$	5.90718	0.762614
$61$	5.18446	0.663802	0.331901	−	0.943314i	$-0.392310\pi$
$61$	5.18446	0.663802	0.331901	+	0.943314i	$0.392310\pi$
$62$	−0.236629	−0.0300519
$63$	25.5699	3.22150
$64$	−4.91466	−0.614333
$65$	2.49966	0.310044
$66$	3.89437	0.479364
$67$	−7.98879	−0.975986	−0.487993	−	0.872848i	$-0.662271\pi$
$67$	−7.98879	−0.975986	−0.487993	+	0.872848i	$0.662271\pi$
$68$	−7.44832	−0.903242
$69$	25.7224	3.09661
$70$	1.33936	0.160084
$71$	6.47286	0.768188	0.384094	−	0.923294i	$-0.374514\pi$
$71$	6.47286	0.768188	0.384094	+	0.923294i	$0.374514\pi$
$72$	10.0451	1.18382
$73$	−10.1728	−1.19064	−0.595319	−	0.803489i	$-0.702974\pi$
$73$	−10.1728	−1.19064	−0.595319	+	0.803489i	$0.702974\pi$
$74$	−0.818327	−0.0951286
$75$	3.16939	0.365970
$76$	−1.01526	−0.116458
$77$	−12.0852	−1.37724
$78$	2.92353	0.331025
$79$	−10.1297	−1.13968	−0.569839	−	0.821757i	$-0.692994\pi$
$79$	−10.1297	−1.13968	−0.569839	+	0.821757i	$0.692994\pi$
$80$	−3.20148	−0.357936
$81$	19.4974	2.16638
$82$	−2.69620	−0.297745
$83$	−1.50622	−0.165329	−0.0826645	−	0.996577i	$-0.526343\pi$
$83$	−1.50622	−0.165329	−0.0826645	+	0.996577i	$0.526343\pi$
$84$	−21.4400	−2.33930
$85$	−3.99626	−0.433455
$86$	4.48884	0.484044
$87$	−9.55051	−1.02392
$88$	−4.74765	−0.506101
$89$	−1.60622	−0.170259	−0.0851296	−	0.996370i	$-0.527130\pi$
$89$	−1.60622	−0.170259	−0.0851296	+	0.996370i	$0.527130\pi$
$90$	2.59977	0.274040
$91$	−9.07247	−0.951054
$92$	−15.1266	−1.57705
$93$	2.03232	0.210742
$94$	−2.07932	−0.214466
$95$	−0.544719	−0.0558869
$96$	−12.7824	−1.30460
$97$	9.03149	0.917009	0.458505	−	0.888692i	$-0.348385\pi$
$97$	9.03149	0.917009	0.458505	+	0.888692i	$0.348385\pi$
$98$	−2.27804	−0.230117
$99$	−23.4581	−2.35762
$100$	−1.86382	−0.186382
$101$	18.2527	1.81622	0.908108	−	0.418736i	$-0.137527\pi$
$101$	18.2527	1.81622	0.908108	+	0.418736i	$0.137527\pi$
$102$	−4.67393	−0.462788
$103$	12.0874	1.19101	0.595504	−	0.803353i	$-0.296953\pi$
$103$	12.0874	1.19101	0.595504	+	0.803353i	$0.296953\pi$
$104$	−3.56410	−0.349489
$105$	−11.5033	−1.12260
$106$	4.22802	0.410662
$107$	1.43376	0.138607	0.0693034	−	0.997596i	$-0.477922\pi$
$107$	1.43376	0.138607	0.0693034	+	0.997596i	$0.477922\pi$
$108$	−23.8947	−2.29927
$109$	−13.0840	−1.25322	−0.626610	−	0.779333i	$-0.715558\pi$
$109$	−13.0840	−1.25322	−0.626610	+	0.779333i	$0.715558\pi$
$110$	−1.22874	−0.117156
$111$	7.02830	0.667097
$112$	11.6197	1.09796
$113$	−9.16102	−0.861797	−0.430898	−	0.902400i	$-0.641803\pi$
$113$	−9.16102	−0.861797	−0.430898	+	0.902400i	$0.641803\pi$
$114$	−0.637089	−0.0596688
$115$	−8.11588	−0.756810
$116$	5.61637	0.521467
$117$	−17.6102	−1.62806
$118$	−4.44822	−0.409492
$119$	14.5044	1.32962
$120$	−4.51903	−0.412529
$121$	0.0871140	0.00791945
$122$	−1.91318	−0.173211
$123$	23.1566	2.08796
$124$	−1.19515	−0.107327
$125$	−1.00000	−0.0894427
$126$	−9.43584	−0.840612
$127$	6.16467	0.547026	0.273513	−	0.961868i	$-0.411814\pi$
$127$	6.16467	0.547026	0.273513	+	0.961868i	$0.411814\pi$
$128$	9.87979	0.873259
$129$	−38.5529	−3.39440
$130$	−0.922428	−0.0809023
$131$	−12.2174	−1.06744	−0.533721	−	0.845661i	$-0.679207\pi$
$131$	−12.2174	−1.06744	−0.533721	+	0.845661i	$0.679207\pi$
$132$	19.6693	1.71200
$133$	1.97705	0.171432
$134$	2.94804	0.254672
$135$	−12.8203	−1.10339
$136$	5.69801	0.488601
$137$	−20.5447	−1.75525	−0.877626	−	0.479347i	$-0.840874\pi$
$137$	−20.5447	−1.75525	−0.877626	+	0.479347i	$0.840874\pi$
$138$	−9.49213	−0.808024
$139$	−16.4704	−1.39700	−0.698500	−	0.715610i	$-0.746149\pi$
$139$	−16.4704	−1.39700	−0.698500	+	0.715610i	$0.746149\pi$
$140$	6.76472	0.571724
$141$	17.8585	1.50396
$142$	−2.38863	−0.200449
$143$	8.32318	0.696019
$144$	22.5545	1.87954
$145$	3.01336	0.250246
$146$	3.75399	0.310683
$147$	19.5652	1.61371
$148$	−4.13313	−0.339741
$149$	−10.9722	−0.898880	−0.449440	−	0.893311i	$-0.648376\pi$
$149$	−10.9722	−0.898880	−0.449440	+	0.893311i	$0.648376\pi$
$150$	−1.16957	−0.0954954
$151$	−2.19462	−0.178596	−0.0892979	−	0.996005i	$-0.528462\pi$
$151$	−2.19462	−0.178596	−0.0892979	+	0.996005i	$0.528462\pi$
$152$	0.776679	0.0629970
$153$	28.1538	2.27610
$154$	4.45971	0.359374
$155$	−0.641233	−0.0515051
$156$	14.7659	1.18222
$157$	10.5396	0.841148	0.420574	−	0.907258i	$-0.361829\pi$
$157$	10.5396	0.841148	0.420574	+	0.907258i	$0.361829\pi$
$158$	3.73807	0.297385
$159$	−36.3129	−2.87980
$160$	4.03309	0.318844
$161$	29.4565	2.32150
$162$	−7.19496	−0.565289
$163$	−20.5710	−1.61125	−0.805624	−	0.592427i	$-0.798170\pi$
$163$	−20.5710	−1.61125	−0.805624	+	0.592427i	$0.798170\pi$
$164$	−13.6177	−1.06337
$165$	10.5532	0.821567
$166$	0.555828	0.0431406
$167$	−15.3918	−1.19105	−0.595527	−	0.803335i	$-0.703057\pi$
$167$	−15.3918	−1.19105	−0.595527	+	0.803335i	$0.703057\pi$
$168$	16.4018	1.26542
$169$	−6.75172	−0.519363
$170$	1.47471	0.113105
$171$	3.83756	0.293466
$172$	22.6718	1.72871
$173$	14.0591	1.06889	0.534447	−	0.845202i	$-0.320520\pi$
$173$	14.0591	1.06889	0.534447	+	0.845202i	$0.320520\pi$
$174$	3.52435	0.267180
$175$	3.62949	0.274364
$176$	−10.6601	−0.803533
$177$	38.2041	2.87159
$178$	0.592731	0.0444271
$179$	−4.10194	−0.306593	−0.153297	−	0.988180i	$-0.548989\pi$
$179$	−4.10194	−0.306593	−0.153297	+	0.988180i	$0.548989\pi$
$180$	13.1307	0.978704
$181$	−6.72689	−0.500006	−0.250003	−	0.968245i	$-0.580432\pi$
$181$	−6.72689	−0.500006	−0.250003	+	0.968245i	$0.580432\pi$
$182$	3.34794	0.248166
$183$	16.4316	1.21466
$184$	11.5719	0.853093
$185$	−2.21756	−0.163038
$186$	−0.749970	−0.0549905
$187$	−13.3065	−0.973066
$188$	−10.5021	−0.765941
$189$	46.5311	3.38464
$190$	0.201013	0.0145830
$191$	−18.9292	−1.36967	−0.684835	−	0.728698i	$-0.740126\pi$
$191$	−18.9292	−1.36967	−0.684835	+	0.728698i	$0.740126\pi$
$192$	−15.5765	−1.12414
$193$	−0.433778	−0.0312240	−0.0156120	−	0.999878i	$-0.504970\pi$
$193$	−0.433778	−0.0312240	−0.0156120	+	0.999878i	$0.504970\pi$
$194$	−3.33282	−0.239282
$195$	7.92238	0.567334
$196$	−11.5057	−0.821838
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	8.65654	0.615194
$199$	7.77869	0.551417	0.275708	−	0.961241i	$-0.411088\pi$
$199$	7.77869	0.551417	0.275708	+	0.961241i	$0.411088\pi$
$200$	1.42584	0.100822
$201$	−25.3196	−1.78591
$202$	−6.73566	−0.473920
$203$	−10.9370	−0.767624
$204$	−23.6066	−1.65280
$205$	−7.30634	−0.510297
$206$	−4.46052	−0.310779
$207$	57.1767	3.97405
$208$	−8.00260	−0.554880
$209$	−1.81377	−0.125461
$210$	4.24496	0.292930
$211$	1.45253	0.0999966	0.0499983	−	0.998749i	$-0.484078\pi$
$211$	1.45253	0.0999966	0.0499983	+	0.998749i	$0.484078\pi$
$212$	21.3545	1.46663
$213$	20.5150	1.40567
$214$	−0.529089	−0.0361678
$215$	12.1642	0.829588
$216$	18.2796	1.24377
$217$	2.32735	0.157991
$218$	4.82828	0.327012
$219$	−32.2416	−2.17869
$220$	−6.20603	−0.418410
$221$	−9.98928	−0.671952
$222$	−2.59360	−0.174071
$223$	−22.2099	−1.48728	−0.743641	−	0.668579i	$-0.766903\pi$
$223$	−22.2099	−1.48728	−0.743641	+	0.668579i	$0.766903\pi$
$224$	−14.6380	−0.978046
$225$	7.04503	0.469669
$226$	3.38062	0.224875
$227$	−21.4704	−1.42504	−0.712520	−	0.701651i	$-0.752446\pi$
$227$	−21.4704	−1.42504	−0.712520	+	0.701651i	$0.752446\pi$
$228$	−3.21775	−0.213101
$229$	20.4485	1.35127	0.675636	−	0.737235i	$-0.263869\pi$
$229$	20.4485	1.35127	0.675636	+	0.737235i	$0.263869\pi$
$230$	2.99494	0.197480
$231$	−38.3028	−2.52014
$232$	−4.29655	−0.282083
$233$	4.59751	0.301193	0.150596	−	0.988595i	$-0.451881\pi$
$233$	4.59751	0.301193	0.150596	+	0.988595i	$0.451881\pi$
$234$	6.49853	0.424822
$235$	−5.63469	−0.367566
$236$	−22.4667	−1.46246
$237$	−32.1049	−2.08544
$238$	−5.35244	−0.346947
$239$	5.11573	0.330909	0.165454	−	0.986217i	$-0.447091\pi$
$239$	5.11573	0.330909	0.165454	+	0.986217i	$0.447091\pi$
$240$	−10.1467	−0.654969
$241$	−15.1695	−0.977151	−0.488575	−	0.872522i	$-0.662483\pi$
$241$	−15.1695	−0.977151	−0.488575	+	0.872522i	$0.662483\pi$
$242$	−0.0321470	−0.00206649
$243$	23.3339	1.49687
$244$	−9.66291	−0.618604
$245$	−6.17319	−0.394391
$246$	−8.54531	−0.544829
$247$	−1.36161	−0.0866371
$248$	0.914293	0.0580577
$249$	−4.77380	−0.302527
$250$	0.369022	0.0233390
$251$	5.40983	0.341465	0.170733	−	0.985317i	$-0.445387\pi$
$251$	5.40983	0.341465	0.170733	+	0.985317i	$0.445387\pi$
$252$	−47.6577	−3.00215
$253$	−27.0237	−1.69897
$254$	−2.27490	−0.142740
$255$	−12.6657	−0.793158
$256$	6.18347	0.386467
$257$	29.8866	1.86427	0.932137	−	0.362106i	$-0.117942\pi$
$257$	29.8866	1.86427	0.932137	+	0.362106i	$0.117942\pi$
$258$	14.2269	0.885727
$259$	8.04860	0.500116
$260$	−4.65891	−0.288934
$261$	−21.2292	−1.31406
$262$	4.50850	0.278536
$263$	−23.3117	−1.43746	−0.718731	−	0.695289i	$-0.755277\pi$
$263$	−23.3117	−1.43746	−0.718731	+	0.695289i	$0.755277\pi$
$264$	−15.0472	−0.926088
$265$	11.4574	0.703821
$266$	−0.729575	−0.0447331
$267$	−5.09074	−0.311548
$268$	14.8897	0.909532
$269$	9.82140	0.598821	0.299411	−	0.954124i	$-0.403210\pi$
$269$	9.82140	0.598821	0.299411	+	0.954124i	$0.403210\pi$
$270$	4.73097	0.287917
$271$	−8.43747	−0.512540	−0.256270	−	0.966605i	$-0.582494\pi$
$271$	−8.43747	−0.512540	−0.256270	+	0.966605i	$0.582494\pi$
$272$	12.7940	0.775748
$273$	−28.7542	−1.74028
$274$	7.58144	0.458012
$275$	−3.32973	−0.200790
$276$	−47.9420	−2.88577
$277$	9.36468	0.562669	0.281334	−	0.959610i	$-0.409223\pi$
$277$	9.36468	0.562669	0.281334	+	0.959610i	$0.409223\pi$
$278$	6.07794	0.364531
$279$	4.51751	0.270456
$280$	−5.17505	−0.309269
$281$	17.2537	1.02927	0.514636	−	0.857409i	$-0.327927\pi$
$281$	17.2537	1.02927	0.514636	+	0.857409i	$0.327927\pi$
$282$	−6.59019	−0.392440
$283$	8.50540	0.505593	0.252797	−	0.967519i	$-0.418650\pi$
$283$	8.50540	0.505593	0.252797	+	0.967519i	$0.418650\pi$
$284$	−12.0643	−0.715883
$285$	−1.72643	−0.102265
$286$	−3.07144	−0.181618
$287$	26.5183	1.56532
$288$	−28.4132	−1.67427
$289$	−1.02989	−0.0605817
$290$	−1.11200	−0.0652986
$291$	28.6243	1.67799
$292$	18.9603	1.10957
$293$	−9.44646	−0.551868	−0.275934	−	0.961177i	$-0.588987\pi$
$293$	−9.44646	−0.551868	−0.275934	+	0.961177i	$0.588987\pi$
$294$	−7.22001	−0.421079
$295$	−12.0541	−0.701815
$296$	3.16187	0.183780
$297$	−42.6881	−2.47701
$298$	4.04899	0.234552
$299$	−20.2869	−1.17322
$300$	−5.90718	−0.341051
$301$	−44.1497	−2.54474
$302$	0.809863	0.0466024
$303$	57.8501	3.32340
$304$	1.74391	0.100020
$305$	−5.18446	−0.296861
$306$	−10.3894	−0.593921
$307$	8.89433	0.507626	0.253813	−	0.967253i	$-0.418315\pi$
$307$	8.89433	0.507626	0.253813	+	0.967253i	$0.418315\pi$
$308$	22.5247	1.28346
$309$	38.3097	2.17936
$310$	0.236629	0.0134396
$311$	−3.24151	−0.183809	−0.0919045	−	0.995768i	$-0.529295\pi$
$311$	−3.24151	−0.183809	−0.0919045	+	0.995768i	$0.529295\pi$
$312$	−11.2960	−0.639511
$313$	8.12235	0.459102	0.229551	−	0.973297i	$-0.426274\pi$
$313$	8.12235	0.459102	0.229551	+	0.973297i	$0.426274\pi$
$314$	−3.88933	−0.219488
$315$	−25.5699	−1.44070
$316$	18.8799	1.06208
$317$	−18.3808	−1.03237	−0.516185	−	0.856477i	$-0.672648\pi$
$317$	−18.3808	−1.03237	−0.516185	+	0.856477i	$0.672648\pi$
$318$	13.4002	0.751448
$319$	10.0337	0.561778
$320$	4.91466	0.274738
$321$	4.54415	0.253629
$322$	−10.8701	−0.605767
$323$	2.17684	0.121123
$324$	−36.3397	−2.01887
$325$	−2.49966	−0.138656
$326$	7.59117	0.420436
$327$	−41.4683	−2.29320
$328$	10.4176	0.575218
$329$	20.4510	1.12750
$330$	−3.89437	−0.214378
$331$	−27.4223	−1.50727	−0.753633	−	0.657296i	$-0.771700\pi$
$331$	−27.4223	−1.50727	−0.753633	+	0.657296i	$0.771700\pi$
$332$	2.80733	0.154072
$333$	15.6228	0.856122
$334$	5.67992	0.310791
$335$	7.98879	0.436474
$336$	36.8275	2.00910
$337$	28.3356	1.54354	0.771770	−	0.635901i	$-0.219372\pi$
$337$	28.3356	1.54354	0.771770	+	0.635901i	$0.219372\pi$
$338$	2.49153	0.135522
$339$	−29.0349	−1.57696
$340$	7.44832	0.403942
$341$	−2.13514	−0.115624
$342$	−1.41614	−0.0765763
$343$	−3.00089	−0.162033
$344$	−17.3441	−0.935130
$345$	−25.7224	−1.38485
$346$	−5.18811	−0.278915
$347$	32.3894	1.73875	0.869377	−	0.494149i	$-0.164520\pi$
$347$	32.3894	1.73875	0.869377	+	0.494149i	$0.164520\pi$
$348$	17.8005	0.954205
$349$	14.1356	0.756664	0.378332	−	0.925670i	$-0.376498\pi$
$349$	14.1356	0.756664	0.378332	+	0.925670i	$0.376498\pi$
$350$	−1.33936	−0.0715919
$351$	−32.0463	−1.71050
$352$	13.4291	0.715773
$353$	9.86104	0.524850	0.262425	−	0.964952i	$-0.415478\pi$
$353$	9.86104	0.524850	0.262425	+	0.964952i	$0.415478\pi$
$354$	−14.0981	−0.749308
$355$	−6.47286	−0.343544
$356$	2.99371	0.158666
$357$	45.9701	2.43299
$358$	1.51371	0.0800018
$359$	24.4102	1.28832	0.644161	−	0.764890i	$-0.277207\pi$
$359$	24.4102	1.28832	0.644161	+	0.764890i	$0.277207\pi$
$360$	−10.0451	−0.529421
$361$	−18.7033	−0.984383
$362$	2.48237	0.130470
$363$	0.276098	0.0144914
$364$	16.9095	0.886298
$365$	10.1728	0.532470
$366$	−6.06361	−0.316950
$367$	−14.6178	−0.763043	−0.381521	−	0.924360i	$-0.624600\pi$
$367$	−14.6178	−0.763043	−0.381521	+	0.924360i	$0.624600\pi$
$368$	25.9828	1.35445
$369$	51.4734	2.67960
$370$	0.818327	0.0425428
$371$	−41.5844	−2.15895
$372$	−3.78788	−0.196393
$373$	−11.2438	−0.582184	−0.291092	−	0.956695i	$-0.594018\pi$
$373$	−11.2438	−0.582184	−0.291092	+	0.956695i	$0.594018\pi$
$374$	4.91038	0.253910
$375$	−3.16939	−0.163667
$376$	8.03414	0.414329
$377$	7.53236	0.387936
$378$	−17.1710	−0.883180
$379$	−32.9033	−1.69013	−0.845065	−	0.534664i	$-0.820438\pi$
$379$	−32.9033	−1.69013	−0.845065	+	0.534664i	$0.820438\pi$
$380$	1.01526	0.0520817
$381$	19.5382	1.00097
$382$	6.98529	0.357399
$383$	−20.2629	−1.03539	−0.517694	−	0.855566i	$-0.673209\pi$
$383$	−20.2629	−1.03539	−0.517694	+	0.855566i	$0.673209\pi$
$384$	31.3129	1.59793
$385$	12.0852	0.615920
$386$	0.160074	0.00814753
$387$	−85.6969	−4.35622
$388$	−16.8331	−0.854571
$389$	−0.422252	−0.0214091	−0.0107045	−	0.999943i	$-0.503407\pi$
$389$	−0.422252	−0.0214091	−0.0107045	+	0.999943i	$0.503407\pi$
$390$	−2.92353	−0.148039
$391$	32.4332	1.64022
$392$	8.80195	0.444566
$393$	−38.7218	−1.95326
$394$	−0.369022	−0.0185911
$395$	10.1297	0.509679
$396$	43.7217	2.19710
$397$	−32.6880	−1.64056	−0.820282	−	0.571959i	$-0.806184\pi$
$397$	−32.6880	−1.64056	−0.820282	+	0.571959i	$0.806184\pi$
$398$	−2.87051	−0.143886
$399$	6.26604	0.313694
$400$	3.20148	0.160074
$401$	36.7998	1.83770	0.918848	−	0.394612i	$-0.129121\pi$
$401$	36.7998	1.83770	0.918848	+	0.394612i	$0.129121\pi$
$402$	9.34348	0.466010
$403$	−1.60286	−0.0798443
$404$	−34.0199	−1.69255
$405$	−19.4974	−0.968832
$406$	4.03598	0.200302
$407$	−7.38387	−0.366005
$408$	18.0592	0.894065
$409$	−20.3060	−1.00407	−0.502034	−	0.864848i	$-0.667415\pi$
$409$	−20.3060	−1.00407	−0.502034	+	0.864848i	$0.667415\pi$
$410$	2.69620	0.133156
$411$	−65.1141	−3.21184
$412$	−22.5288	−1.10991
$413$	43.7501	2.15280
$414$	−21.0994	−1.03698
$415$	1.50622	0.0739374
$416$	10.0813	0.494278
$417$	−52.2011	−2.55630
$418$	0.669320	0.0327375
$419$	−16.7906	−0.820274	−0.410137	−	0.912024i	$-0.634519\pi$
$419$	−16.7906	−0.820274	−0.410137	+	0.912024i	$0.634519\pi$
$420$	21.4400	1.04617
$421$	−3.86925	−0.188576	−0.0942880	−	0.995545i	$-0.530057\pi$
$421$	−3.86925	−0.188576	−0.0942880	+	0.995545i	$0.530057\pi$
$422$	−0.536017	−0.0260929
$423$	39.6965	1.93011
$424$	−16.3363	−0.793362
$425$	3.99626	0.193847
$426$	−7.57050	−0.366792
$427$	18.8169	0.910615
$428$	−2.67228	−0.129169
$429$	26.3794	1.27361
$430$	−4.48884	−0.216471
$431$	10.2805	0.495193	0.247597	−	0.968863i	$-0.420359\pi$
$431$	10.2805	0.495193	0.247597	+	0.968863i	$0.420359\pi$
$432$	41.0439	1.97473
$433$	4.55826	0.219056	0.109528	−	0.993984i	$-0.465066\pi$
$433$	4.55826	0.219056	0.109528	+	0.993984i	$0.465066\pi$
$434$	−0.858843	−0.0412258
$435$	9.55051	0.457912
$436$	24.3862	1.16789
$437$	4.42087	0.211479
$438$	11.8979	0.568502
$439$	30.1153	1.43733	0.718663	−	0.695359i	$-0.244755\pi$
$439$	30.1153	1.43733	0.718663	+	0.695359i	$0.244755\pi$
$440$	4.74765	0.226335
$441$	43.4903	2.07097
$442$	3.68626	0.175338
$443$	34.5931	1.64357	0.821783	−	0.569801i	$-0.192980\pi$
$443$	34.5931	1.64357	0.821783	+	0.569801i	$0.192980\pi$
$444$	−13.0995	−0.621675
$445$	1.60622	0.0761422
$446$	8.19593	0.388088
$447$	−34.7753	−1.64481
$448$	−17.8377	−0.842753
$449$	20.4992	0.967416	0.483708	−	0.875230i	$-0.339290\pi$
$449$	20.4992	0.967416	0.483708	+	0.875230i	$0.339290\pi$
$450$	−2.59977	−0.122554
$451$	−24.3282	−1.14557
$452$	17.0745	0.803118
$453$	−6.95561	−0.326803
$454$	7.92305	0.371847
$455$	9.07247	0.425324
$456$	2.46160	0.115275
$457$	−32.9485	−1.54127	−0.770633	−	0.637279i	$-0.780060\pi$
$457$	−32.9485	−1.54127	−0.770633	+	0.637279i	$0.780060\pi$
$458$	−7.54593	−0.352598
$459$	51.2332	2.39136
$460$	15.1266	0.705280
$461$	7.00086	0.326063	0.163031	−	0.986621i	$-0.447873\pi$
$461$	7.00086	0.326063	0.163031	+	0.986621i	$0.447873\pi$
$462$	14.1346	0.657600
$463$	27.4431	1.27539	0.637694	−	0.770290i	$-0.279889\pi$
$463$	27.4431	1.27539	0.637694	+	0.770290i	$0.279889\pi$
$464$	−9.64721	−0.447861
$465$	−2.03232	−0.0942465
$466$	−1.69658	−0.0785926
$467$	28.8035	1.33287	0.666434	−	0.745564i	$-0.267820\pi$
$467$	28.8035	1.33287	0.666434	+	0.745564i	$0.267820\pi$
$468$	32.8222	1.51721
$469$	−28.9952	−1.33887
$470$	2.07932	0.0959120
$471$	33.4040	1.53917
$472$	17.1871	0.791102
$473$	40.5034	1.86235
$474$	11.8474	0.544169
$475$	0.544719	0.0249934
$476$	−27.0336	−1.23908
$477$	−80.7175	−3.69580
$478$	−1.88782	−0.0863467
$479$	11.8621	0.541991	0.270996	−	0.962581i	$-0.412647\pi$
$479$	11.8621	0.541991	0.270996	+	0.962581i	$0.412647\pi$
$480$	12.7824	0.583435
$481$	−5.54313	−0.252745
$482$	5.59786	0.254976
$483$	93.3592	4.24799
$484$	−0.162365	−0.00738023
$485$	−9.03149	−0.410099
$486$	−8.61074	−0.390591
$487$	27.2745	1.23592	0.617962	−	0.786208i	$-0.287959\pi$
$487$	27.2745	1.23592	0.617962	+	0.786208i	$0.287959\pi$
$488$	7.39218	0.334628
$489$	−65.1976	−2.94834
$490$	2.27804	0.102911
$491$	9.40640	0.424505	0.212252	−	0.977215i	$-0.431920\pi$
$491$	9.40640	0.424505	0.212252	+	0.977215i	$0.431920\pi$
$492$	−43.1599	−1.94580
$493$	−12.0422	−0.542352
$494$	0.502464	0.0226069
$495$	23.4581	1.05436
$496$	2.05290	0.0921778
$497$	23.4932	1.05381
$498$	1.76164	0.0789408
$499$	22.0773	0.988314	0.494157	−	0.869373i	$-0.335477\pi$
$499$	22.0773	0.988314	0.494157	+	0.869373i	$0.335477\pi$
$500$	1.86382	0.0833527
$501$	−48.7826	−2.17945
$502$	−1.99634	−0.0891012
$503$	8.84249	0.394267	0.197133	−	0.980377i	$-0.436837\pi$
$503$	8.84249	0.394267	0.197133	+	0.980377i	$0.436837\pi$
$504$	36.4584	1.62399
$505$	−18.2527	−0.812236
$506$	9.97235	0.443325
$507$	−21.3988	−0.950356
$508$	−11.4899	−0.509780
$509$	−6.64300	−0.294446	−0.147223	−	0.989103i	$-0.547033\pi$
$509$	−6.64300	−0.294446	−0.147223	+	0.989103i	$0.547033\pi$
$510$	4.67393	0.206965
$511$	−36.9221	−1.63334
$512$	−22.0414	−0.974103
$513$	6.98345	0.308327
$514$	−11.0288	−0.486460
$515$	−12.0874	−0.532635
$516$	71.8559	3.16328
$517$	−18.7620	−0.825152
$518$	−2.97011	−0.130499
$519$	44.5588	1.95591
$520$	3.56410	0.156296
$521$	23.3371	1.02242	0.511208	−	0.859457i	$-0.329198\pi$
$521$	23.3371	1.02242	0.511208	+	0.859457i	$0.329198\pi$
$522$	7.83405	0.342887
$523$	−2.26374	−0.0989864	−0.0494932	−	0.998774i	$-0.515761\pi$
$523$	−2.26374	−0.0989864	−0.0494932	+	0.998774i	$0.515761\pi$
$524$	22.7711	0.994761
$525$	11.5033	0.502044
$526$	8.60253	0.375088
$527$	2.56254	0.111626
$528$	−33.7859	−1.47034
$529$	42.8676	1.86381
$530$	−4.22802	−0.183653
$531$	84.9214	3.68527
$532$	−3.68487	−0.159759
$533$	−18.2633	−0.791073
$534$	1.87860	0.0812948
$535$	−1.43376	−0.0619869
$536$	−11.3907	−0.492003
$537$	−13.0006	−0.561019
$538$	−3.62431	−0.156255
$539$	−20.5551	−0.885370
$540$	23.8947	1.02827
$541$	11.5584	0.496934	0.248467	−	0.968640i	$-0.420073\pi$
$541$	11.5584	0.496934	0.248467	+	0.968640i	$0.420073\pi$
$542$	3.11361	0.133741
$543$	−21.3201	−0.914934
$544$	−16.1173	−0.691022
$545$	13.0840	0.560457
$546$	10.6109	0.454106
$547$	14.0004	0.598612	0.299306	−	0.954157i	$-0.403245\pi$
$547$	14.0004	0.598612	0.299306	+	0.954157i	$0.403245\pi$
$548$	38.2917	1.63574
$549$	36.5247	1.55883
$550$	1.22874	0.0523938
$551$	−1.64143	−0.0699274
$552$	36.6759	1.56103
$553$	−36.7655	−1.56343
$554$	−3.45577	−0.146822
$555$	−7.02830	−0.298335
$556$	30.6979	1.30188
$557$	13.3440	0.565405	0.282702	−	0.959208i	$-0.408769\pi$
$557$	13.3440	0.565405	0.282702	+	0.959208i	$0.408769\pi$
$558$	−1.66706	−0.0705723
$559$	30.4062	1.28605
$560$	−11.6197	−0.491024
$561$	−42.1734	−1.78056
$562$	−6.36701	−0.268576
$563$	3.87985	0.163516	0.0817581	−	0.996652i	$-0.473946\pi$
$563$	3.87985	0.163516	0.0817581	+	0.996652i	$0.473946\pi$
$564$	−33.2851	−1.40156
$565$	9.16102	0.385407
$566$	−3.13868	−0.131928
$567$	70.7655	2.97187
$568$	9.22924	0.387250
$569$	−44.6070	−1.87002	−0.935012	−	0.354617i	$-0.884611\pi$
$569$	−44.6070	−1.87002	−0.935012	+	0.354617i	$0.884611\pi$
$570$	0.637089	0.0266847
$571$	−14.4771	−0.605848	−0.302924	−	0.953015i	$-0.597963\pi$
$571$	−14.4771	−0.605848	−0.302924	+	0.953015i	$0.597963\pi$
$572$	−15.5129	−0.648628
$573$	−59.9940	−2.50629
$574$	−9.78583	−0.408453
$575$	8.11588	0.338456
$576$	−34.6240	−1.44267
$577$	36.9803	1.53951	0.769754	−	0.638340i	$-0.220379\pi$
$577$	36.9803	1.53951	0.769754	+	0.638340i	$0.220379\pi$
$578$	0.380052	0.0158081
$579$	−1.37481	−0.0571352
$580$	−5.61637	−0.233207
$581$	−5.46681	−0.226801
$582$	−10.5630	−0.437851
$583$	38.1500	1.58001
$584$	−14.5048	−0.600211
$585$	17.6102	0.728090
$586$	3.48595	0.144003
$587$	2.84496	0.117424	0.0587121	−	0.998275i	$-0.481301\pi$
$587$	2.84496	0.117424	0.0587121	+	0.998275i	$0.481301\pi$
$588$	−36.4662	−1.50384
$589$	0.349292	0.0143923
$590$	4.44822	0.183130
$591$	3.16939	0.130371
$592$	7.09947	0.291786
$593$	−23.8491	−0.979365	−0.489683	−	0.871901i	$-0.662887\pi$
$593$	−23.8491	−0.979365	−0.489683	+	0.871901i	$0.662887\pi$
$594$	15.7528	0.646347
$595$	−14.5044	−0.594622
$596$	20.4503	0.837676
$597$	24.6537	1.00901
$598$	7.48632	0.306138
$599$	25.3852	1.03721	0.518606	−	0.855013i	$-0.326451\pi$
$599$	25.3852	1.03721	0.518606	+	0.855013i	$0.326451\pi$
$600$	4.51903	0.184489
$601$	−10.2857	−0.419561	−0.209780	−	0.977749i	$-0.567275\pi$
$601$	−10.2857	−0.419561	−0.209780	+	0.977749i	$0.567275\pi$
$602$	16.2922	0.664020
$603$	−56.2813	−2.29195
$604$	4.09038	0.166435
$605$	−0.0871140	−0.00354169
$606$	−21.3479	−0.867201
$607$	27.0073	1.09619	0.548096	−	0.836415i	$-0.315353\pi$
$607$	27.0073	1.09619	0.548096	+	0.836415i	$0.315353\pi$
$608$	−2.19690	−0.0890960
$609$	−34.6635	−1.40463
$610$	1.91318	0.0774623
$611$	−14.0848	−0.569809
$612$	−52.4737	−2.12112
$613$	−2.25781	−0.0911919	−0.0455959	−	0.998960i	$-0.514519\pi$
$613$	−2.25781	−0.0911919	−0.0455959	+	0.998960i	$0.514519\pi$
$614$	−3.28220	−0.132459
$615$	−23.1566	−0.933766
$616$	−17.2315	−0.694279
$617$	−15.0149	−0.604477	−0.302239	−	0.953232i	$-0.597734\pi$
$617$	−15.0149	−0.604477	−0.302239	+	0.953232i	$0.597734\pi$
$618$	−14.1371	−0.568678
$619$	−26.9543	−1.08338	−0.541692	−	0.840577i	$-0.682216\pi$
$619$	−26.9543	−1.08338	−0.541692	+	0.840577i	$0.682216\pi$
$620$	1.19515	0.0479982
$621$	104.048	4.17530
$622$	1.19619	0.0479627
$623$	−5.82976	−0.233565
$624$	−25.3634	−1.01535
$625$	1.00000	0.0400000
$626$	−2.99732	−0.119797
$627$	−5.74853	−0.229574
$628$	−19.6439	−0.783876
$629$	8.86194	0.353349
$630$	9.43584	0.375933
$631$	5.72444	0.227887	0.113943	−	0.993487i	$-0.463652\pi$
$631$	5.72444	0.227887	0.113943	+	0.993487i	$0.463652\pi$
$632$	−14.4432	−0.574522
$633$	4.60365	0.182979
$634$	6.78293	0.269384
$635$	−6.16467	−0.244638
$636$	67.6807	2.68372
$637$	−15.4309	−0.611393
$638$	−3.70265	−0.146589
$639$	45.6015	1.80397
$640$	−9.87979	−0.390533
$641$	−20.4206	−0.806564	−0.403282	−	0.915076i	$-0.632131\pi$
$641$	−20.4206	−0.806564	−0.403282	+	0.915076i	$0.632131\pi$
$642$	−1.67689	−0.0661815
$643$	32.5966	1.28549	0.642743	−	0.766082i	$-0.277796\pi$
$643$	32.5966	1.28549	0.642743	+	0.766082i	$0.277796\pi$
$644$	−54.9017	−2.16343
$645$	38.5529	1.51802
$646$	−0.803301	−0.0316055
$647$	24.6732	0.970004	0.485002	−	0.874513i	$-0.338819\pi$
$647$	24.6732	0.970004	0.485002	+	0.874513i	$0.338819\pi$
$648$	27.8001	1.09209
$649$	−40.1368	−1.57551
$650$	0.922428	0.0361806
$651$	7.37628	0.289099
$652$	38.3408	1.50154
$653$	18.9700	0.742352	0.371176	−	0.928562i	$-0.378955\pi$
$653$	18.9700	0.742352	0.371176	+	0.928562i	$0.378955\pi$
$654$	15.3027	0.598383
$655$	12.2174	0.477374
$656$	23.3911	0.913269
$657$	−71.6678	−2.79603
$658$	−7.54688	−0.294208
$659$	−6.15252	−0.239668	−0.119834	−	0.992794i	$-0.538236\pi$
$659$	−6.15252	−0.239668	−0.119834	+	0.992794i	$0.538236\pi$
$660$	−19.6693	−0.765628
$661$	46.7725	1.81924	0.909619	−	0.415443i	$-0.136374\pi$
$661$	46.7725	1.81924	0.909619	+	0.415443i	$0.136374\pi$
$662$	10.1194	0.393303
$663$	−31.6599	−1.22957
$664$	−2.14762	−0.0833439
$665$	−1.97705	−0.0766667
$666$	−5.76514	−0.223395
$667$	−24.4561	−0.946943
$668$	28.6876	1.10996
$669$	−70.3917	−2.72150
$670$	−2.94804	−0.113893
$671$	−17.2629	−0.666425
$672$	−46.3937	−1.78968
$673$	−50.3018	−1.93899	−0.969496	−	0.245106i	$-0.921177\pi$
$673$	−50.3018	−1.93899	−0.969496	+	0.245106i	$0.921177\pi$
$674$	−10.4565	−0.402768
$675$	12.8203	0.493453
$676$	12.5840	0.484001
$677$	11.6359	0.447204	0.223602	−	0.974681i	$-0.428219\pi$
$677$	11.6359	0.447204	0.223602	+	0.974681i	$0.428219\pi$
$678$	10.7145	0.411488
$679$	32.7797	1.25797
$680$	−5.69801	−0.218509
$681$	−68.0481	−2.60761
$682$	0.787912	0.0301707
$683$	−18.6346	−0.713033	−0.356517	−	0.934289i	$-0.616036\pi$
$683$	−18.6346	−0.713033	−0.356517	+	0.934289i	$0.616036\pi$
$684$	−7.15253	−0.273484
$685$	20.5447	0.784972
$686$	1.10740	0.0422806
$687$	64.8092	2.47262
$688$	−38.9433	−1.48470
$689$	28.6395	1.09108
$690$	9.49213	0.361359
$691$	−10.8788	−0.413851	−0.206925	−	0.978357i	$-0.566346\pi$
$691$	−10.8788	−0.413851	−0.206925	+	0.978357i	$0.566346\pi$
$692$	−26.2037	−0.996114
$693$	−85.1408	−3.23423
$694$	−11.9524	−0.453707
$695$	16.4704	0.624758
$696$	−13.6175	−0.516168
$697$	29.1980	1.10595
$698$	−5.21636	−0.197442
$699$	14.5713	0.551137
$700$	−6.76472	−0.255683
$701$	−8.56606	−0.323536	−0.161768	−	0.986829i	$-0.551720\pi$
$701$	−8.56606	−0.323536	−0.161768	+	0.986829i	$0.551720\pi$
$702$	11.8258	0.446335
$703$	1.20794	0.0455585
$704$	16.3645	0.616761
$705$	−17.8585	−0.672591
$706$	−3.63894	−0.136953
$707$	66.2481	2.49152
$708$	−71.2056	−2.67607
$709$	−38.2856	−1.43785	−0.718923	−	0.695089i	$-0.755365\pi$
$709$	−38.2856	−1.43785	−0.718923	+	0.695089i	$0.755365\pi$
$710$	2.38863	0.0896436
$711$	−71.3639	−2.67635
$712$	−2.29021	−0.0858292
$713$	5.20418	0.194898
$714$	−16.9640	−0.634860
$715$	−8.32318	−0.311269
$716$	7.64529	0.285718
$717$	16.2137	0.605513
$718$	−9.00791	−0.336172
$719$	39.1245	1.45910	0.729549	−	0.683928i	$-0.239730\pi$
$719$	39.1245	1.45910	0.729549	+	0.683928i	$0.239730\pi$
$720$	−22.5545	−0.840558
$721$	43.8711	1.63384
$722$	6.90192	0.256863
$723$	−48.0779	−1.78804
$724$	12.5377	0.465961
$725$	−3.01336	−0.111913
$726$	−0.101886	−0.00378136
$727$	−19.8848	−0.737487	−0.368744	−	0.929531i	$-0.620212\pi$
$727$	−19.8848	−0.737487	−0.368744	+	0.929531i	$0.620212\pi$
$728$	−12.9359	−0.479435
$729$	15.4622	0.572675
$730$	−3.75399	−0.138942
$731$	−48.6111	−1.79795
$732$	−30.6255	−1.13195
$733$	41.0835	1.51745	0.758726	−	0.651410i	$-0.225822\pi$
$733$	41.0835	1.51745	0.758726	+	0.651410i	$0.225822\pi$
$734$	5.39429	0.199107
$735$	−19.5652	−0.721675
$736$	−32.7321	−1.20652
$737$	26.6005	0.979843
$738$	−18.9948	−0.699209
$739$	30.8980	1.13660	0.568300	−	0.822821i	$-0.307601\pi$
$739$	30.8980	1.13660	0.568300	+	0.822821i	$0.307601\pi$
$740$	4.13313	0.151937
$741$	−4.31547	−0.158533
$742$	15.3456	0.563353
$743$	25.5831	0.938551	0.469276	−	0.883052i	$-0.344515\pi$
$743$	25.5831	0.938551	0.469276	+	0.883052i	$0.344515\pi$
$744$	2.89775	0.106237
$745$	10.9722	0.401991
$746$	4.14922	0.151914
$747$	−10.6114	−0.388250
$748$	24.8009	0.906812
$749$	5.20382	0.190143
$750$	1.16957	0.0427068
$751$	6.05935	0.221109	0.110554	−	0.993870i	$-0.464737\pi$
$751$	6.05935	0.221109	0.110554	+	0.993870i	$0.464737\pi$
$752$	18.0393	0.657827
$753$	17.1458	0.624829
$754$	−2.77961	−0.101227
$755$	2.19462	0.0798704
$756$	−86.7257	−3.15418
$757$	1.09916	0.0399497	0.0199749	−	0.999800i	$-0.493641\pi$
$757$	1.09916	0.0399497	0.0199749	+	0.999800i	$0.493641\pi$
$758$	12.1420	0.441019
$759$	−85.6487	−3.10885
$760$	−0.776679	−0.0281731
$761$	−38.0673	−1.37994	−0.689970	−	0.723838i	$-0.742376\pi$
$761$	−38.0673	−1.37994	−0.689970	+	0.723838i	$0.742376\pi$
$762$	−7.21004	−0.261192
$763$	−47.4882	−1.71919
$764$	35.2807	1.27641
$765$	−28.1538	−1.01790
$766$	7.47747	0.270172
$767$	−30.1310	−1.08797
$768$	19.5978	0.707175
$769$	−22.0829	−0.796328	−0.398164	−	0.917314i	$-0.630353\pi$
$769$	−22.0829	−0.796328	−0.398164	+	0.917314i	$0.630353\pi$
$770$	−4.45971	−0.160717
$771$	94.7222	3.41134
$772$	0.808485	0.0290980
$773$	0.552136	0.0198590	0.00992948	−	0.999951i	$-0.496839\pi$
$773$	0.552136	0.0198590	0.00992948	+	0.999951i	$0.496839\pi$
$774$	31.6240	1.13670
$775$	0.641233	0.0230338
$776$	12.8774	0.462273
$777$	25.5091	0.915135
$778$	0.155820	0.00558643
$779$	3.97990	0.142595
$780$	−14.7659	−0.528705
$781$	−21.5529	−0.771223
$782$	−11.9686	−0.427995
$783$	−38.6321	−1.38060
$784$	19.7634	0.705834
$785$	−10.5396	−0.376173
$786$	14.2892	0.509679
$787$	23.2969	0.830446	0.415223	−	0.909720i	$-0.363704\pi$
$787$	23.2969	0.830446	0.415223	+	0.909720i	$0.363704\pi$
$788$	−1.86382	−0.0663959
$789$	−73.8839	−2.63034
$790$	−3.73807	−0.132995
$791$	−33.2498	−1.18223
$792$	−33.4473	−1.18850
$793$	−12.9594	−0.460200
$794$	12.0626	0.428086
$795$	36.3129	1.28788
$796$	−14.4981	−0.513871
$797$	36.6840	1.29941	0.649707	−	0.760185i	$-0.274892\pi$
$797$	36.6840	1.29941	0.649707	+	0.760185i	$0.274892\pi$
$798$	−2.31231	−0.0818548
$799$	22.5177	0.796618
$800$	−4.03309	−0.142591
$801$	−11.3159	−0.399827
$802$	−13.5799	−0.479525
$803$	33.8728	1.19534
$804$	47.1912	1.66431
$805$	−29.4565	−1.03821
$806$	0.591492	0.0208344
$807$	31.1279	1.09575
$808$	26.0254	0.915571
$809$	27.4076	0.963601	0.481800	−	0.876281i	$-0.339983\pi$
$809$	27.4076	0.963601	0.481800	+	0.876281i	$0.339983\pi$
$810$	7.19496	0.252805
$811$	−13.9367	−0.489385	−0.244693	−	0.969601i	$-0.578687\pi$
$811$	−13.9367	−0.489385	−0.244693	+	0.969601i	$0.578687\pi$
$812$	20.3845	0.715357
$813$	−26.7416	−0.937870
$814$	2.72481	0.0955045
$815$	20.5710	0.720572
$816$	40.5490	1.41950
$817$	−6.62604	−0.231816
$818$	7.49337	0.262000
$819$	−63.9159	−2.23340
$820$	13.6177	0.475551
$821$	31.5126	1.09980	0.549899	−	0.835231i	$-0.314666\pi$
$821$	31.5126	1.09980	0.549899	+	0.835231i	$0.314666\pi$
$822$	24.0285	0.838092
$823$	18.7233	0.652653	0.326326	−	0.945257i	$-0.394189\pi$
$823$	18.7233	0.652653	0.326326	+	0.945257i	$0.394189\pi$
$824$	17.2346	0.600397
$825$	−10.5532	−0.367416
$826$	−16.1448	−0.561748
$827$	−49.5562	−1.72324	−0.861620	−	0.507554i	$-0.830550\pi$
$827$	−49.5562	−1.72324	−0.861620	+	0.507554i	$0.830550\pi$
$828$	−106.567	−3.70346
$829$	16.6379	0.577858	0.288929	−	0.957351i	$-0.406701\pi$
$829$	16.6379	0.577858	0.288929	+	0.957351i	$0.406701\pi$
$830$	−0.555828	−0.0192931
$831$	29.6803	1.02960
$832$	12.2850	0.425905
$833$	24.6697	0.854754
$834$	19.2634	0.667035
$835$	15.3918	0.532656
$836$	3.38054	0.116918
$837$	8.22079	0.284152
$838$	6.19610	0.214041
$839$	10.7175	0.370009	0.185004	−	0.982738i	$-0.440770\pi$
$839$	10.7175	0.370009	0.185004	+	0.982738i	$0.440770\pi$
$840$	−16.4018	−0.565915
$841$	−19.9197	−0.686885
$842$	1.42784	0.0492066
$843$	54.6838	1.88341
$844$	−2.70727	−0.0931880
$845$	6.75172	0.232266
$846$	−14.6489	−0.503639
$847$	0.316179	0.0108641
$848$	−36.6805	−1.25962
$849$	26.9569	0.925159
$850$	−1.47471	−0.0505821
$851$	17.9974	0.616944
$852$	−38.2364	−1.30996
$853$	−28.8204	−0.986791	−0.493395	−	0.869805i	$-0.664244\pi$
$853$	−28.8204	−0.986791	−0.493395	+	0.869805i	$0.664244\pi$
$854$	−6.94386	−0.237614
$855$	−3.83756	−0.131242
$856$	2.04431	0.0698730
$857$	−10.7662	−0.367766	−0.183883	−	0.982948i	$-0.558867\pi$
$857$	−10.7662	−0.367766	−0.183883	+	0.982948i	$0.558867\pi$
$858$	−9.73458	−0.332333
$859$	−35.9060	−1.22510	−0.612549	−	0.790433i	$-0.709856\pi$
$859$	−35.9060	−1.22510	−0.612549	+	0.790433i	$0.709856\pi$
$860$	−22.6718	−0.773103
$861$	84.0468	2.86431
$862$	−3.79372	−0.129215
$863$	28.0912	0.956236	0.478118	−	0.878296i	$-0.341319\pi$
$863$	28.0912	0.956236	0.478118	+	0.878296i	$0.341319\pi$
$864$	−51.7053	−1.75905
$865$	−14.0591	−0.478024
$866$	−1.68210	−0.0571600
$867$	−3.26412	−0.110855
$868$	−4.33777	−0.147233
$869$	33.7291	1.14418
$870$	−3.52435	−0.119487
$871$	19.9692	0.676631
$872$	−18.6556	−0.631759
$873$	63.6272	2.15345
$874$	−1.63140	−0.0551829
$875$	−3.62949	−0.122699
$876$	60.0927	2.03034
$877$	−35.1007	−1.18527	−0.592633	−	0.805473i	$-0.701911\pi$
$877$	−35.1007	−1.18527	−0.592633	+	0.805473i	$0.701911\pi$
$878$	−11.1132	−0.375053
$879$	−29.9395	−1.00983
$880$	10.6601	0.359351
$881$	−30.2865	−1.02038	−0.510189	−	0.860062i	$-0.670425\pi$
$881$	−30.2865	−1.02038	−0.510189	+	0.860062i	$0.670425\pi$
$882$	−16.0489	−0.540394
$883$	−30.4056	−1.02323	−0.511616	−	0.859214i	$-0.670953\pi$
$883$	−30.4056	−1.02323	−0.511616	+	0.859214i	$0.670953\pi$
$884$	18.6182	0.626199
$885$	−38.2041	−1.28422
$886$	−12.7656	−0.428869
$887$	−42.2061	−1.41714	−0.708572	−	0.705639i	$-0.750660\pi$
$887$	−42.2061	−1.41714	−0.708572	+	0.705639i	$0.750660\pi$
$888$	10.0212	0.336290
$889$	22.3746	0.750420
$890$	−0.592731	−0.0198684
$891$	−64.9210	−2.17494
$892$	41.3952	1.38602
$893$	3.06932	0.102711
$894$	12.8328	0.429194
$895$	4.10194	0.137113
$896$	35.8586	1.19795
$897$	−64.2971	−2.14682
$898$	−7.56464	−0.252435
$899$	−1.93227	−0.0644447
$900$	−13.1307	−0.437690
$901$	−45.7866	−1.52537
$902$	8.97762	0.298922
$903$	−139.927	−4.65650
$904$	−13.0621	−0.434439
$905$	6.72689	0.223609
$906$	2.56677	0.0852753
$907$	−21.4748	−0.713061	−0.356530	−	0.934284i	$-0.616040\pi$
$907$	−21.4748	−0.713061	−0.356530	+	0.934284i	$0.616040\pi$
$908$	40.0170	1.32801
$909$	128.591	4.26510
$910$	−3.34794	−0.110983
$911$	29.1475	0.965698	0.482849	−	0.875704i	$-0.339602\pi$
$911$	29.1475	0.965698	0.482849	+	0.875704i	$0.339602\pi$
$912$	5.52712	0.183021
$913$	5.01531	0.165982
$914$	12.1587	0.402175
$915$	−16.4316	−0.543211
$916$	−38.1123	−1.25927
$917$	−44.3430	−1.46434
$918$	−18.9062	−0.623997
$919$	21.6813	0.715199	0.357600	−	0.933875i	$-0.383595\pi$
$919$	21.6813	0.715199	0.357600	+	0.933875i	$0.383595\pi$
$920$	−11.5719	−0.381515
$921$	28.1896	0.928879
$922$	−2.58347	−0.0850821
$923$	−16.1799	−0.532569
$924$	71.3896	2.34855
$925$	2.21756	0.0729128
$926$	−10.1271	−0.332797
$927$	85.1561	2.79689
$928$	12.1531	0.398946
$929$	−19.1445	−0.628111	−0.314056	−	0.949405i	$-0.601688\pi$
$929$	−19.1445	−0.628111	−0.314056	+	0.949405i	$0.601688\pi$
$930$	0.749970	0.0245925
$931$	3.36265	0.110206
$932$	−8.56894	−0.280685
$933$	−10.2736	−0.336343
$934$	−10.6291	−0.347796
$935$	13.3065	0.435168
$936$	−25.1092	−0.820719
$937$	24.8331	0.811261	0.405631	−	0.914037i	$-0.367052\pi$
$937$	24.8331	0.811261	0.405631	+	0.914037i	$0.367052\pi$
$938$	10.6999	0.349363
$939$	25.7429	0.840087
$940$	10.5021	0.342539
$941$	−14.9389	−0.486994	−0.243497	−	0.969902i	$-0.578295\pi$
$941$	−14.9389	−0.486994	−0.243497	+	0.969902i	$0.578295\pi$
$942$	−12.3268	−0.401629
$943$	59.2974	1.93099
$944$	38.5909	1.25603
$945$	−46.5311	−1.51366
$946$	−14.9466	−0.485957
$947$	−50.7152	−1.64802	−0.824011	−	0.566574i	$-0.808268\pi$
$947$	−50.7152	−1.64802	−0.824011	+	0.566574i	$0.808268\pi$
$948$	59.8378	1.94344
$949$	25.4285	0.825445
$950$	−0.201013	−0.00652173
$951$	−58.2560	−1.88908
$952$	20.6809	0.670271
$953$	−52.6966	−1.70701	−0.853505	−	0.521085i	$-0.825528\pi$
$953$	−52.6966	−1.70701	−0.853505	+	0.521085i	$0.825528\pi$
$954$	29.7865	0.964375
$955$	18.9292	0.612535
$956$	−9.53481	−0.308378
$957$	31.8006	1.02797
$958$	−4.37736	−0.141426
$959$	−74.5667	−2.40789
$960$	15.5765	0.502729
$961$	−30.5888	−0.986736
$962$	2.04554	0.0659507
$963$	10.1009	0.325497
$964$	28.2732	0.910618
$965$	0.433778	0.0139638
$966$	−34.4516	−1.10846
$967$	−47.7016	−1.53398	−0.766990	−	0.641659i	$-0.778246\pi$
$967$	−47.7016	−1.53398	−0.766990	+	0.641659i	$0.778246\pi$
$968$	0.124210	0.00399227
$969$	6.89925	0.221636
$970$	3.33282	0.107010
$971$	35.9972	1.15520	0.577602	−	0.816318i	$-0.303988\pi$
$971$	35.9972	1.15520	0.577602	+	0.816318i	$0.303988\pi$
$972$	−43.4903	−1.39495
$973$	−59.7791	−1.91643
$974$	−10.0649	−0.322499
$975$	−7.92238	−0.253719
$976$	16.5979	0.531287
$977$	−23.9826	−0.767270	−0.383635	−	0.923485i	$-0.625328\pi$
$977$	−23.9826	−0.767270	−0.383635	+	0.923485i	$0.625328\pi$
$978$	24.0594	0.769334
$979$	5.34829	0.170932
$980$	11.5057	0.367537
$981$	−92.1771	−2.94299
$982$	−3.47117	−0.110769
$983$	−23.0414	−0.734905	−0.367453	−	0.930042i	$-0.619770\pi$
$983$	−23.0414	−0.734905	−0.367453	+	0.930042i	$0.619770\pi$
$984$	33.0176	1.05256
$985$	−1.00000	−0.0318626
$986$	4.44383	0.141520
$987$	64.8173	2.06316
$988$	2.53780	0.0807381
$989$	−98.7229	−3.13920
$990$	−8.65654	−0.275123
$991$	44.7215	1.42062	0.710312	−	0.703887i	$-0.248554\pi$
$991$	44.7215	1.42062	0.710312	+	0.703887i	$0.248554\pi$
$992$	−2.58615	−0.0821104
$993$	−86.9119	−2.75807
$994$	−8.66950	−0.274980
$995$	−7.77869	−0.246601
$996$	8.89751	0.281928
$997$	61.0998	1.93505	0.967524	−	0.252777i	$-0.0813440\pi$
$997$	61.0998	1.93505	0.967524	+	0.252777i	$0.0813440\pi$
$998$	−8.14699	−0.257889
$999$	28.4297	0.899476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	985.2.a.g.1.7	✓	17
3.2	odd	2		8865.2.a.z.1.11		17
5.4	even	2		4925.2.a.l.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
985.2.a.g.1.7	✓	17	1.1	even	1	trivial
4925.2.a.l.1.11		17	5.4	even	2
8865.2.a.z.1.11		17	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:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.a (trivial)

\(f(q)\)	\(=\)	\(q-0.369022 q^{2} +3.16939 q^{3} -1.86382 q^{4} -1.00000 q^{5} -1.16957 q^{6} +3.62949 q^{7} +1.42584 q^{8} +7.04503 q^{9} +0.369022 q^{10} -3.32973 q^{11} -5.90718 q^{12} -2.49966 q^{13} -1.33936 q^{14} -3.16939 q^{15} +3.20148 q^{16} +3.99626 q^{17} -2.59977 q^{18} +0.544719 q^{19} +1.86382 q^{20} +11.5033 q^{21} +1.22874 q^{22} +8.11588 q^{23} +4.51903 q^{24} +1.00000 q^{25} +0.922428 q^{26} +12.8203 q^{27} -6.76472 q^{28} -3.01336 q^{29} +1.16957 q^{30} +0.641233 q^{31} -4.03309 q^{32} -10.5532 q^{33} -1.47471 q^{34} -3.62949 q^{35} -13.1307 q^{36} +2.21756 q^{37} -0.201013 q^{38} -7.92238 q^{39} -1.42584 q^{40} +7.30634 q^{41} -4.24496 q^{42} -12.1642 q^{43} +6.20603 q^{44} -7.04503 q^{45} -2.99494 q^{46} +5.63469 q^{47} +10.1467 q^{48} +6.17319 q^{49} -0.369022 q^{50} +12.6657 q^{51} +4.65891 q^{52} -11.4574 q^{53} -4.73097 q^{54} +3.32973 q^{55} +5.17505 q^{56} +1.72643 q^{57} +1.11200 q^{58} +12.0541 q^{59} +5.90718 q^{60} +5.18446 q^{61} -0.236629 q^{62} +25.5699 q^{63} -4.91466 q^{64} +2.49966 q^{65} +3.89437 q^{66} -7.98879 q^{67} -7.44832 q^{68} +25.7224 q^{69} +1.33936 q^{70} +6.47286 q^{71} +10.0451 q^{72} -10.1728 q^{73} -0.818327 q^{74} +3.16939 q^{75} -1.01526 q^{76} -12.0852 q^{77} +2.92353 q^{78} -10.1297 q^{79} -3.20148 q^{80} +19.4974 q^{81} -2.69620 q^{82} -1.50622 q^{83} -21.4400 q^{84} -3.99626 q^{85} +4.48884 q^{86} -9.55051 q^{87} -4.74765 q^{88} -1.60622 q^{89} +2.59977 q^{90} -9.07247 q^{91} -15.1266 q^{92} +2.03232 q^{93} -2.07932 q^{94} -0.544719 q^{95} -12.7824 q^{96} +9.03149 q^{97} -2.27804 q^{98} -23.4581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 17 q^{5} + 3 q^{6} + 7 q^{7} + 18 q^{8} + 22 q^{9} - 6 q^{10} + 7 q^{11} + 20 q^{12} + 3 q^{13} + 17 q^{14} - 5 q^{15} + 28 q^{16} + 6 q^{17} + 13 q^{18} - 23 q^{19}+ \cdots - 46 q^{99}+O(q^{100}) \) 17 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 17 * q^5 + 3 * q^6 + 7 * q^7 + 18 * q^8 + 22 * q^9 - 6 * q^10 + 7 * q^11 + 20 * q^12 + 3 * q^13 + 17 * q^14 - 5 * q^15 + 28 * q^16 + 6 * q^17 + 13 * q^18 - 23 * q^19 - 18 * q^20 - q^21 + 14 * q^22 + 49 * q^23 + q^24 + 17 * q^25 + 3 * q^26 + 29 * q^27 + 9 * q^28 + 19 * q^29 - 3 * q^30 - 18 * q^31 + 42 * q^32 + 14 * q^33 - 19 * q^34 - 7 * q^35 + 31 * q^36 + 10 * q^37 + 27 * q^38 + 21 * q^39 - 18 * q^40 + 14 * q^41 + 31 * q^42 + 22 * q^43 + 27 * q^44 - 22 * q^45 - 16 * q^46 + 51 * q^47 + 38 * q^48 + 8 * q^49 + 6 * q^50 + 7 * q^51 + 17 * q^52 + 37 * q^53 - 36 * q^54 - 7 * q^55 + 47 * q^56 - 11 * q^57 + 20 * q^58 + 23 * q^59 - 20 * q^60 - 15 * q^61 - 6 * q^62 + 37 * q^63 - 2 * q^64 - 3 * q^65 - 4 * q^66 + 24 * q^67 + 13 * q^68 + 6 * q^69 - 17 * q^70 + 68 * q^71 - 33 * q^72 - 10 * q^73 - 9 * q^74 + 5 * q^75 - 57 * q^76 - 16 * q^77 - 24 * q^78 + 3 * q^79 - 28 * q^80 + 33 * q^81 - 40 * q^82 + 29 * q^83 - 83 * q^84 - 6 * q^85 + 37 * q^86 + 23 * q^87 + 5 * q^88 - 11 * q^89 - 13 * q^90 - 82 * q^91 + 15 * q^93 - 39 * q^94 + 23 * q^95 + 2 * q^96 + 6 * q^97 + 15 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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