LMFDB - Embedded newform 2667.2.a.k.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [11,-2,11,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 15 x^{9} + 25 x^{8} + 88 x^{7} - 112 x^{6} - 247 x^{5} + 215 x^{4} + 313 x^{3} + \cdots + 57 $ x^11 - 2x^10 - 15x^9 + 25x^8 + 88x^7 - 112x^6 - 247x^5 + 215x^4 + 313x^3 - 170x^2 - 121x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.455441$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.455441 q^{2} +1.00000 q^{3} -1.79257 q^{4} -0.749481 q^{5} -0.455441 q^{6} -1.00000 q^{7} +1.72729 q^{8} +1.00000 q^{9} +0.341344 q^{10} -1.95920 q^{11} -1.79257 q^{12} +2.51893 q^{13} +0.455441 q^{14} -0.749481 q^{15} +2.79847 q^{16} -1.75736 q^{17} -0.455441 q^{18} -3.76981 q^{19} +1.34350 q^{20} -1.00000 q^{21} +0.892299 q^{22} +7.74151 q^{23} +1.72729 q^{24} -4.43828 q^{25} -1.14723 q^{26} +1.00000 q^{27} +1.79257 q^{28} +1.80755 q^{29} +0.341344 q^{30} +7.78196 q^{31} -4.72912 q^{32} -1.95920 q^{33} +0.800374 q^{34} +0.749481 q^{35} -1.79257 q^{36} +2.63088 q^{37} +1.71693 q^{38} +2.51893 q^{39} -1.29457 q^{40} -8.09399 q^{41} +0.455441 q^{42} -11.7597 q^{43} +3.51201 q^{44} -0.749481 q^{45} -3.52580 q^{46} -3.25780 q^{47} +2.79847 q^{48} +1.00000 q^{49} +2.02137 q^{50} -1.75736 q^{51} -4.51538 q^{52} +0.297989 q^{53} -0.455441 q^{54} +1.46838 q^{55} -1.72729 q^{56} -3.76981 q^{57} -0.823230 q^{58} +0.440342 q^{59} +1.34350 q^{60} +4.23592 q^{61} -3.54422 q^{62} -1.00000 q^{63} -3.44310 q^{64} -1.88789 q^{65} +0.892299 q^{66} -13.5402 q^{67} +3.15020 q^{68} +7.74151 q^{69} -0.341344 q^{70} -1.44289 q^{71} +1.72729 q^{72} -2.90207 q^{73} -1.19821 q^{74} -4.43828 q^{75} +6.75767 q^{76} +1.95920 q^{77} -1.14723 q^{78} +2.11951 q^{79} -2.09740 q^{80} +1.00000 q^{81} +3.68633 q^{82} -4.47544 q^{83} +1.79257 q^{84} +1.31711 q^{85} +5.35583 q^{86} +1.80755 q^{87} -3.38411 q^{88} +2.94756 q^{89} +0.341344 q^{90} -2.51893 q^{91} -13.8772 q^{92} +7.78196 q^{93} +1.48374 q^{94} +2.82540 q^{95} -4.72912 q^{96} -9.80554 q^{97} -0.455441 q^{98} -1.95920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 2 q^{2} + 11 q^{3} + 12 q^{4} + q^{5} - 2 q^{6} - 11 q^{7} - 15 q^{8} + 11 q^{9} - 12 q^{10} - 7 q^{11} + 12 q^{12} - 24 q^{13} + 2 q^{14} + q^{15} - 6 q^{16} - 15 q^{17} - 2 q^{18} - 19 q^{19}+ \cdots - 7 q^{99}+O(q^{100}) $ 11 * q - 2 * q^2 + 11 * q^3 + 12 * q^4 + q^5 - 2 * q^6 - 11 * q^7 - 15 * q^8 + 11 * q^9 - 12 * q^10 - 7 * q^11 + 12 * q^12 - 24 * q^13 + 2 * q^14 + q^15 - 6 * q^16 - 15 * q^17 - 2 * q^18 - 19 * q^19 + 3 * q^20 - 11 * q^21 - 3 * q^22 - 11 * q^23 - 15 * q^24 + 10 * q^25 + 10 * q^26 + 11 * q^27 - 12 * q^28 - 10 * q^29 - 12 * q^30 - 20 * q^31 - 27 * q^32 - 7 * q^33 - 9 * q^34 - q^35 + 12 * q^36 - 22 * q^37 + 8 * q^38 - 24 * q^39 - 29 * q^40 + 9 * q^41 + 2 * q^42 - 17 * q^43 - 9 * q^44 + q^45 - 18 * q^46 - 7 * q^47 - 6 * q^48 + 11 * q^49 - 47 * q^50 - 15 * q^51 - 66 * q^52 - 28 * q^53 - 2 * q^54 - 24 * q^55 + 15 * q^56 - 19 * q^57 - 39 * q^58 + 35 * q^59 + 3 * q^60 - 6 * q^61 + 18 * q^62 - 11 * q^63 + 11 * q^64 - 43 * q^65 - 3 * q^66 - 22 * q^67 - 12 * q^68 - 11 * q^69 + 12 * q^70 - 22 * q^71 - 15 * q^72 - 29 * q^73 + 14 * q^74 + 10 * q^75 + 10 * q^76 + 7 * q^77 + 10 * q^78 - 20 * q^79 + 66 * q^80 + 11 * q^81 - 24 * q^82 + 17 * q^83 - 12 * q^84 - 50 * q^85 - 12 * q^86 - 10 * q^87 + 2 * q^88 - q^89 - 12 * q^90 + 24 * q^91 - 22 * q^92 - 20 * q^93 + q^94 + 10 * q^95 - 27 * q^96 - 45 * q^97 - 2 * q^98 - 7 * 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 $

$2$	−0.455441	−0.322045	−0.161023	−	0.986951i	$-0.551479\pi$
$2$	−0.455441	−0.322045	−0.161023	+	0.986951i	$0.551479\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.79257	−0.896287
$5$	−0.749481	−0.335178	−0.167589	−	0.985857i	$-0.553598\pi$
$5$	−0.749481	−0.335178	−0.167589	+	0.985857i	$0.553598\pi$
$6$	−0.455441	−0.185933
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.72729	0.610690
$9$	1.00000	0.333333
$10$	0.341344	0.107942
$11$	−1.95920	−0.590721	−0.295361	−	0.955386i	$-0.595440\pi$
$11$	−1.95920	−0.590721	−0.295361	+	0.955386i	$0.595440\pi$
$12$	−1.79257	−0.517471
$13$	2.51893	0.698627	0.349313	−	0.937006i	$-0.386415\pi$
$13$	2.51893	0.698627	0.349313	+	0.937006i	$0.386415\pi$
$14$	0.455441	0.121722
$15$	−0.749481	−0.193515
$16$	2.79847	0.699617
$17$	−1.75736	−0.426223	−0.213111	−	0.977028i	$-0.568360\pi$
$17$	−1.75736	−0.426223	−0.213111	+	0.977028i	$0.568360\pi$
$18$	−0.455441	−0.107348
$19$	−3.76981	−0.864854	−0.432427	−	0.901669i	$-0.642343\pi$
$19$	−3.76981	−0.864854	−0.432427	+	0.901669i	$0.642343\pi$
$20$	1.34350	0.300416
$21$	−1.00000	−0.218218
$22$	0.892299	0.190239
$23$	7.74151	1.61422	0.807108	−	0.590404i	$-0.201031\pi$
$23$	7.74151	1.61422	0.807108	+	0.590404i	$0.201031\pi$
$24$	1.72729	0.352582
$25$	−4.43828	−0.887656
$26$	−1.14723	−0.224989
$27$	1.00000	0.192450
$28$	1.79257	0.338765
$29$	1.80755	0.335653	0.167826	−	0.985817i	$-0.446325\pi$
$29$	1.80755	0.335653	0.167826	+	0.985817i	$0.446325\pi$
$30$	0.341344	0.0623206
$31$	7.78196	1.39768	0.698841	−	0.715277i	$-0.253700\pi$
$31$	7.78196	1.39768	0.698841	+	0.715277i	$0.253700\pi$
$32$	−4.72912	−0.835998
$33$	−1.95920	−0.341053
$34$	0.800374	0.137263
$35$	0.749481	0.126685
$36$	−1.79257	−0.298762
$37$	2.63088	0.432514	0.216257	−	0.976336i	$-0.430615\pi$
$37$	2.63088	0.432514	0.216257	+	0.976336i	$0.430615\pi$
$38$	1.71693	0.278522
$39$	2.51893	0.403352
$40$	−1.29457	−0.204690
$41$	−8.09399	−1.26407	−0.632034	−	0.774940i	$-0.717780\pi$
$41$	−8.09399	−1.26407	−0.632034	+	0.774940i	$0.717780\pi$
$42$	0.455441	0.0702760
$43$	−11.7597	−1.79333	−0.896667	−	0.442706i	$-0.854019\pi$
$43$	−11.7597	−1.79333	−0.896667	+	0.442706i	$0.854019\pi$
$44$	3.51201	0.529456
$45$	−0.749481	−0.111726
$46$	−3.52580	−0.519851
$47$	−3.25780	−0.475199	−0.237600	−	0.971363i	$-0.576361\pi$
$47$	−3.25780	−0.475199	−0.237600	+	0.971363i	$0.576361\pi$
$48$	2.79847	0.403924
$49$	1.00000	0.142857
$50$	2.02137	0.285865
$51$	−1.75736	−0.246080
$52$	−4.51538	−0.626170
$53$	0.297989	0.0409319	0.0204659	−	0.999791i	$-0.493485\pi$
$53$	0.297989	0.0409319	0.0204659	+	0.999791i	$0.493485\pi$
$54$	−0.455441	−0.0619776
$55$	1.46838	0.197997
$56$	−1.72729	−0.230819
$57$	−3.76981	−0.499324
$58$	−0.823230	−0.108095
$59$	0.440342	0.0573277	0.0286638	−	0.999589i	$-0.490875\pi$
$59$	0.440342	0.0573277	0.0286638	+	0.999589i	$0.490875\pi$
$60$	1.34350	0.173445
$61$	4.23592	0.542354	0.271177	−	0.962529i	$-0.412587\pi$
$61$	4.23592	0.542354	0.271177	+	0.962529i	$0.412587\pi$
$62$	−3.54422	−0.450117
$63$	−1.00000	−0.125988
$64$	−3.44310	−0.430388
$65$	−1.88789	−0.234164
$66$	0.892299	0.109834
$67$	−13.5402	−1.65420	−0.827101	−	0.562054i	$-0.810011\pi$
$67$	−13.5402	−1.65420	−0.827101	+	0.562054i	$0.810011\pi$
$68$	3.15020	0.382018
$69$	7.74151	0.931968
$70$	−0.341344	−0.0407984
$71$	−1.44289	−0.171239	−0.0856196	−	0.996328i	$-0.527287\pi$
$71$	−1.44289	−0.171239	−0.0856196	+	0.996328i	$0.527287\pi$
$72$	1.72729	0.203563
$73$	−2.90207	−0.339662	−0.169831	−	0.985473i	$-0.554322\pi$
$73$	−2.90207	−0.339662	−0.169831	+	0.985473i	$0.554322\pi$
$74$	−1.19821	−0.139289
$75$	−4.43828	−0.512488
$76$	6.75767	0.775158
$77$	1.95920	0.223272
$78$	−1.14723	−0.129898
$79$	2.11951	0.238464	0.119232	−	0.992866i	$-0.461957\pi$
$79$	2.11951	0.238464	0.119232	+	0.992866i	$0.461957\pi$
$80$	−2.09740	−0.234496
$81$	1.00000	0.111111
$82$	3.68633	0.407087
$83$	−4.47544	−0.491243	−0.245622	−	0.969366i	$-0.578992\pi$
$83$	−4.47544	−0.491243	−0.245622	+	0.969366i	$0.578992\pi$
$84$	1.79257	0.195586
$85$	1.31711	0.142860
$86$	5.35583	0.577535
$87$	1.80755	0.193789
$88$	−3.38411	−0.360747
$89$	2.94756	0.312441	0.156220	−	0.987722i	$-0.450069\pi$
$89$	2.94756	0.312441	0.156220	+	0.987722i	$0.450069\pi$
$90$	0.341344	0.0359808
$91$	−2.51893	−0.264056
$92$	−13.8772	−1.44680
$93$	7.78196	0.806952
$94$	1.48374	0.153036
$95$	2.82540	0.289880
$96$	−4.72912	−0.482664
$97$	−9.80554	−0.995602	−0.497801	−	0.867291i	$-0.665859\pi$
$97$	−9.80554	−0.995602	−0.497801	+	0.867291i	$0.665859\pi$
$98$	−0.455441	−0.0460065
$99$	−1.95920	−0.196907
$100$	7.95594	0.795594
$101$	−17.0317	−1.69472	−0.847360	−	0.531019i	$-0.821809\pi$
$101$	−17.0317	−1.69472	−0.847360	+	0.531019i	$0.821809\pi$
$102$	0.800374	0.0792488
$103$	9.72210	0.957947	0.478974	−	0.877829i	$-0.341009\pi$
$103$	9.72210	0.957947	0.478974	+	0.877829i	$0.341009\pi$
$104$	4.35094	0.426644
$105$	0.749481	0.0731418
$106$	−0.135716	−0.0131819
$107$	−8.65396	−0.836610	−0.418305	−	0.908307i	$-0.637376\pi$
$107$	−8.65396	−0.836610	−0.418305	+	0.908307i	$0.637376\pi$
$108$	−1.79257	−0.172490
$109$	−12.5836	−1.20529	−0.602647	−	0.798008i	$-0.705887\pi$
$109$	−12.5836	−1.20529	−0.602647	+	0.798008i	$0.705887\pi$
$110$	−0.668761	−0.0637639
$111$	2.63088	0.249712
$112$	−2.79847	−0.264430
$113$	4.54886	0.427921	0.213960	−	0.976842i	$-0.431364\pi$
$113$	4.54886	0.427921	0.213960	+	0.976842i	$0.431364\pi$
$114$	1.71693	0.160805
$115$	−5.80211	−0.541050
$116$	−3.24016	−0.300841
$117$	2.51893	0.232876
$118$	−0.200550	−0.0184621
$119$	1.75736	0.161097
$120$	−1.29457	−0.118178
$121$	−7.16153	−0.651049
$122$	−1.92921	−0.174663
$123$	−8.09399	−0.729810
$124$	−13.9497	−1.25272
$125$	7.07381	0.632701
$126$	0.455441	0.0405739
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	11.0264	0.974603
$129$	−11.7597	−1.03538
$130$	0.859823	0.0754115
$131$	3.88980	0.339853	0.169927	−	0.985457i	$-0.445647\pi$
$131$	3.88980	0.339853	0.169927	+	0.985457i	$0.445647\pi$
$132$	3.51201	0.305681
$133$	3.76981	0.326884
$134$	6.16677	0.532727
$135$	−0.749481	−0.0645050
$136$	−3.03548	−0.260290
$137$	12.5423	1.07156	0.535779	−	0.844358i	$-0.320018\pi$
$137$	12.5423	1.07156	0.535779	+	0.844358i	$0.320018\pi$
$138$	−3.52580	−0.300136
$139$	−21.1389	−1.79298	−0.896488	−	0.443069i	$-0.853890\pi$
$139$	−21.1389	−1.79298	−0.896488	+	0.443069i	$0.853890\pi$
$140$	−1.34350	−0.113546
$141$	−3.25780	−0.274357
$142$	0.657149	0.0551468
$143$	−4.93510	−0.412694
$144$	2.79847	0.233206
$145$	−1.35472	−0.112504
$146$	1.32172	0.109386
$147$	1.00000	0.0824786
$148$	−4.71605	−0.387657
$149$	−18.2486	−1.49498	−0.747492	−	0.664271i	$-0.768742\pi$
$149$	−18.2486	−1.49498	−0.747492	+	0.664271i	$0.768742\pi$
$150$	2.02137	0.165044
$151$	−4.00291	−0.325752	−0.162876	−	0.986647i	$-0.552077\pi$
$151$	−4.00291	−0.325752	−0.162876	+	0.986647i	$0.552077\pi$
$152$	−6.51157	−0.528158
$153$	−1.75736	−0.142074
$154$	−0.892299	−0.0719035
$155$	−5.83243	−0.468472
$156$	−4.51538	−0.361519
$157$	−3.26752	−0.260776	−0.130388	−	0.991463i	$-0.541622\pi$
$157$	−3.26752	−0.260776	−0.130388	+	0.991463i	$0.541622\pi$
$158$	−0.965313	−0.0767961
$159$	0.297989	0.0236320
$160$	3.54439	0.280208
$161$	−7.74151	−0.610116
$162$	−0.455441	−0.0357828
$163$	−5.99201	−0.469331	−0.234665	−	0.972076i	$-0.575399\pi$
$163$	−5.99201	−0.469331	−0.234665	+	0.972076i	$0.575399\pi$
$164$	14.5091	1.13297
$165$	1.46838	0.114313
$166$	2.03830	0.158202
$167$	−21.2819	−1.64684	−0.823421	−	0.567431i	$-0.807937\pi$
$167$	−21.2819	−1.64684	−0.823421	+	0.567431i	$0.807937\pi$
$168$	−1.72729	−0.133263
$169$	−6.65497	−0.511921
$170$	−0.599865	−0.0460075
$171$	−3.76981	−0.288285
$172$	21.0801	1.60734
$173$	2.41503	0.183612	0.0918058	−	0.995777i	$-0.470736\pi$
$173$	2.41503	0.183612	0.0918058	+	0.995777i	$0.470736\pi$
$174$	−0.823230	−0.0624089
$175$	4.43828	0.335502
$176$	−5.48276	−0.413279
$177$	0.440342	0.0330982
$178$	−1.34244	−0.100620
$179$	14.3890	1.07548	0.537741	−	0.843110i	$-0.319278\pi$
$179$	14.3890	1.07548	0.537741	+	0.843110i	$0.319278\pi$
$180$	1.34350	0.100139
$181$	6.74044	0.501013	0.250506	−	0.968115i	$-0.419403\pi$
$181$	6.74044	0.501013	0.250506	+	0.968115i	$0.419403\pi$
$182$	1.14723	0.0850380
$183$	4.23592	0.313128
$184$	13.3719	0.985786
$185$	−1.97179	−0.144969
$186$	−3.54422	−0.259875
$187$	3.44302	0.251779
$188$	5.83985	0.425915
$189$	−1.00000	−0.0727393
$190$	−1.28680	−0.0933545
$191$	17.9119	1.29606	0.648031	−	0.761614i	$-0.275593\pi$
$191$	17.9119	1.29606	0.648031	+	0.761614i	$0.275593\pi$
$192$	−3.44310	−0.248485
$193$	8.61234	0.619930	0.309965	−	0.950748i	$-0.399683\pi$
$193$	8.61234	0.619930	0.309965	+	0.950748i	$0.399683\pi$
$194$	4.46584	0.320629
$195$	−1.88789	−0.135195
$196$	−1.79257	−0.128041
$197$	−26.3709	−1.87885	−0.939423	−	0.342759i	$-0.888639\pi$
$197$	−26.3709	−1.87885	−0.939423	+	0.342759i	$0.888639\pi$
$198$	0.892299	0.0634130
$199$	−12.3460	−0.875185	−0.437593	−	0.899173i	$-0.644169\pi$
$199$	−12.3460	−0.875185	−0.437593	+	0.899173i	$0.644169\pi$
$200$	−7.66620	−0.542082
$201$	−13.5402	−0.955053
$202$	7.75694	0.545776
$203$	−1.80755	−0.126865
$204$	3.15020	0.220558
$205$	6.06629	0.423688
$206$	−4.42784	−0.308502
$207$	7.74151	0.538072
$208$	7.04916	0.488771
$209$	7.38582	0.510888
$210$	−0.341344	−0.0235550
$211$	−28.4545	−1.95889	−0.979445	−	0.201711i	$-0.935350\pi$
$211$	−28.4545	−1.95889	−0.979445	+	0.201711i	$0.935350\pi$
$212$	−0.534167	−0.0366867
$213$	−1.44289	−0.0988650
$214$	3.94136	0.269426
$215$	8.81365	0.601086
$216$	1.72729	0.117527
$217$	−7.78196	−0.528274
$218$	5.73110	0.388159
$219$	−2.90207	−0.196104
$220$	−2.63219	−0.177462
$221$	−4.42668	−0.297771
$222$	−1.19821	−0.0804186
$223$	5.39195	0.361071	0.180536	−	0.983568i	$-0.442217\pi$
$223$	5.39195	0.361071	0.180536	+	0.983568i	$0.442217\pi$
$224$	4.72912	0.315978
$225$	−4.43828	−0.295885
$226$	−2.07174	−0.137810
$227$	10.8739	0.721729	0.360865	−	0.932618i	$-0.382482\pi$
$227$	10.8739	0.721729	0.360865	+	0.932618i	$0.382482\pi$
$228$	6.75767	0.447537
$229$	3.50976	0.231932	0.115966	−	0.993253i	$-0.463004\pi$
$229$	3.50976	0.231932	0.115966	+	0.993253i	$0.463004\pi$
$230$	2.64252	0.174243
$231$	1.95920	0.128906
$232$	3.12216	0.204980
$233$	2.48327	0.162685	0.0813424	−	0.996686i	$-0.474079\pi$
$233$	2.48327	0.162685	0.0813424	+	0.996686i	$0.474079\pi$
$234$	−1.14723	−0.0749965
$235$	2.44166	0.159276
$236$	−0.789346	−0.0513821
$237$	2.11951	0.137677
$238$	−0.800374	−0.0518805
$239$	21.1743	1.36965	0.684826	−	0.728706i	$-0.259878\pi$
$239$	21.1743	1.36965	0.684826	+	0.728706i	$0.259878\pi$
$240$	−2.09740	−0.135387
$241$	−17.1342	−1.10371	−0.551854	−	0.833941i	$-0.686080\pi$
$241$	−17.1342	−1.10371	−0.551854	+	0.833941i	$0.686080\pi$
$242$	3.26165	0.209667
$243$	1.00000	0.0641500
$244$	−7.59321	−0.486105
$245$	−0.749481	−0.0478826
$246$	3.68633	0.235032
$247$	−9.49591	−0.604210
$248$	13.4417	0.853550
$249$	−4.47544	−0.283619
$250$	−3.22170	−0.203758
$251$	−2.98515	−0.188421	−0.0942104	−	0.995552i	$-0.530033\pi$
$251$	−2.98515	−0.188421	−0.0942104	+	0.995552i	$0.530033\pi$
$252$	1.79257	0.112922
$253$	−15.1672	−0.953552
$254$	−0.455441	−0.0285769
$255$	1.31711	0.0824805
$256$	1.86435	0.116522
$257$	−14.2653	−0.889845	−0.444923	−	0.895569i	$-0.646769\pi$
$257$	−14.2653	−0.889845	−0.444923	+	0.895569i	$0.646769\pi$
$258$	5.35583	0.333440
$259$	−2.63088	−0.163475
$260$	3.38419	0.209878
$261$	1.80755	0.111884
$262$	−1.77157	−0.109448
$263$	−6.23379	−0.384392	−0.192196	−	0.981357i	$-0.561561\pi$
$263$	−6.23379	−0.384392	−0.192196	+	0.981357i	$0.561561\pi$
$264$	−3.38411	−0.208278
$265$	−0.223337	−0.0137195
$266$	−1.71693	−0.105271
$267$	2.94756	0.180388
$268$	24.2718	1.48264
$269$	9.49493	0.578916	0.289458	−	0.957191i	$-0.406525\pi$
$269$	9.49493	0.578916	0.289458	+	0.957191i	$0.406525\pi$
$270$	0.341344	0.0207735
$271$	−24.8348	−1.50860	−0.754302	−	0.656528i	$-0.772025\pi$
$271$	−24.8348	−1.50860	−0.754302	+	0.656528i	$0.772025\pi$
$272$	−4.91792	−0.298193
$273$	−2.51893	−0.152453
$274$	−5.71225	−0.345090
$275$	8.69548	0.524357
$276$	−13.8772	−0.835311
$277$	16.1475	0.970208	0.485104	−	0.874457i	$-0.338782\pi$
$277$	16.1475	0.970208	0.485104	+	0.874457i	$0.338782\pi$
$278$	9.62750	0.577419
$279$	7.78196	0.465894
$280$	1.29457	0.0773655
$281$	−9.45191	−0.563854	−0.281927	−	0.959436i	$-0.590974\pi$
$281$	−9.45191	−0.563854	−0.281927	+	0.959436i	$0.590974\pi$
$282$	1.48374	0.0883552
$283$	14.1920	0.843625	0.421812	−	0.906683i	$-0.361394\pi$
$283$	14.1920	0.843625	0.421812	+	0.906683i	$0.361394\pi$
$284$	2.58648	0.153479
$285$	2.82540	0.167362
$286$	2.24764	0.132906
$287$	8.09399	0.477773
$288$	−4.72912	−0.278666
$289$	−13.9117	−0.818334
$290$	0.616995	0.0362312
$291$	−9.80554	−0.574811
$292$	5.20218	0.304434
$293$	18.0263	1.05311	0.526554	−	0.850141i	$-0.323484\pi$
$293$	18.0263	1.05311	0.526554	+	0.850141i	$0.323484\pi$
$294$	−0.455441	−0.0265618
$295$	−0.330028	−0.0192150
$296$	4.54430	0.264132
$297$	−1.95920	−0.113684
$298$	8.31115	0.481452
$299$	19.5004	1.12773
$300$	7.95594	0.459337
$301$	11.7597	0.677817
$302$	1.82309	0.104907
$303$	−17.0317	−0.978447
$304$	−10.5497	−0.605067
$305$	−3.17474	−0.181785
$306$	0.800374	0.0457543
$307$	16.0943	0.918552	0.459276	−	0.888294i	$-0.348109\pi$
$307$	16.0943	0.918552	0.459276	+	0.888294i	$0.348109\pi$
$308$	−3.51201	−0.200115
$309$	9.72210	0.553071
$310$	2.65633	0.150869
$311$	19.3077	1.09484	0.547421	−	0.836857i	$-0.315610\pi$
$311$	19.3077	1.09484	0.547421	+	0.836857i	$0.315610\pi$
$312$	4.35094	0.246323
$313$	−30.8613	−1.74438	−0.872191	−	0.489166i	$-0.837301\pi$
$313$	−30.8613	−1.74438	−0.872191	+	0.489166i	$0.837301\pi$
$314$	1.48816	0.0839817
$315$	0.749481	0.0422285
$316$	−3.79938	−0.213732
$317$	30.6756	1.72291	0.861457	−	0.507831i	$-0.169553\pi$
$317$	30.6756	1.72291	0.861457	+	0.507831i	$0.169553\pi$
$318$	−0.135716	−0.00761058
$319$	−3.54135	−0.198277
$320$	2.58054	0.144257
$321$	−8.65396	−0.483017
$322$	3.52580	0.196485
$323$	6.62492	0.368621
$324$	−1.79257	−0.0995874
$325$	−11.1797	−0.620140
$326$	2.72901	0.151146
$327$	−12.5836	−0.695876
$328$	−13.9807	−0.771954
$329$	3.25780	0.179608
$330$	−0.668761	−0.0368141
$331$	−10.2450	−0.563114	−0.281557	−	0.959544i	$-0.590851\pi$
$331$	−10.2450	−0.563114	−0.281557	+	0.959544i	$0.590851\pi$
$332$	8.02255	0.440295
$333$	2.63088	0.144171
$334$	9.69263	0.530357
$335$	10.1481	0.554452
$336$	−2.79847	−0.152669
$337$	−1.30395	−0.0710307	−0.0355154	−	0.999369i	$-0.511307\pi$
$337$	−1.30395	−0.0710307	−0.0355154	+	0.999369i	$0.511307\pi$
$338$	3.03094	0.164862
$339$	4.54886	0.247060
$340$	−2.36101	−0.128044
$341$	−15.2464	−0.825640
$342$	1.71693	0.0928407
$343$	−1.00000	−0.0539949
$344$	−20.3124	−1.09517
$345$	−5.80211	−0.312375
$346$	−1.09990	−0.0591312
$347$	18.6437	1.00085	0.500424	−	0.865780i	$-0.333177\pi$
$347$	18.6437	1.00085	0.500424	+	0.865780i	$0.333177\pi$
$348$	−3.24016	−0.173691
$349$	7.47368	0.400057	0.200029	−	0.979790i	$-0.435897\pi$
$349$	7.47368	0.400057	0.200029	+	0.979790i	$0.435897\pi$
$350$	−2.02137	−0.108047
$351$	2.51893	0.134451
$352$	9.26529	0.493842
$353$	−10.4557	−0.556502	−0.278251	−	0.960508i	$-0.589755\pi$
$353$	−10.4557	−0.556502	−0.278251	+	0.960508i	$0.589755\pi$
$354$	−0.200550	−0.0106591
$355$	1.08142	0.0573956
$356$	−5.28372	−0.280037
$357$	1.75736	0.0930094
$358$	−6.55332	−0.346354
$359$	35.8946	1.89444	0.947222	−	0.320579i	$-0.103877\pi$
$359$	35.8946	1.89444	0.947222	+	0.320579i	$0.103877\pi$
$360$	−1.29457	−0.0682300
$361$	−4.78851	−0.252027
$362$	−3.06987	−0.161349
$363$	−7.16153	−0.375883
$364$	4.51538	0.236670
$365$	2.17505	0.113847
$366$	−1.92921	−0.100842
$367$	3.15632	0.164758	0.0823792	−	0.996601i	$-0.473748\pi$
$367$	3.15632	0.164758	0.0823792	+	0.996601i	$0.473748\pi$
$368$	21.6644	1.12933
$369$	−8.09399	−0.421356
$370$	0.898035	0.0466866
$371$	−0.297989	−0.0154708
$372$	−13.9497	−0.723260
$373$	−4.08938	−0.211740	−0.105870	−	0.994380i	$-0.533763\pi$
$373$	−4.08938	−0.211740	−0.105870	+	0.994380i	$0.533763\pi$
$374$	−1.56809	−0.0810841
$375$	7.07381	0.365290
$376$	−5.62718	−0.290200
$377$	4.55309	0.234496
$378$	0.455441	0.0234253
$379$	−34.1819	−1.75581	−0.877903	−	0.478839i	$-0.841058\pi$
$379$	−34.1819	−1.75581	−0.877903	+	0.478839i	$0.841058\pi$
$380$	−5.06474	−0.259816
$381$	1.00000	0.0512316
$382$	−8.15782	−0.417391
$383$	35.9813	1.83856	0.919279	−	0.393606i	$-0.128772\pi$
$383$	35.9813	1.83856	0.919279	+	0.393606i	$0.128772\pi$
$384$	11.0264	0.562687
$385$	−1.46838	−0.0748357
$386$	−3.92241	−0.199645
$387$	−11.7597	−0.597778
$388$	17.5772	0.892345
$389$	−10.0249	−0.508281	−0.254141	−	0.967167i	$-0.581793\pi$
$389$	−10.0249	−0.508281	−0.254141	+	0.967167i	$0.581793\pi$
$390$	0.859823	0.0435389
$391$	−13.6046	−0.688016
$392$	1.72729	0.0872414
$393$	3.88980	0.196214
$394$	12.0104	0.605074
$395$	−1.58853	−0.0799279
$396$	3.51201	0.176485
$397$	−33.3894	−1.67576	−0.837882	−	0.545852i	$-0.816206\pi$
$397$	−33.3894	−1.67576	−0.837882	+	0.545852i	$0.816206\pi$
$398$	5.62287	0.281849
$399$	3.76981	0.188727
$400$	−12.4204	−0.621019
$401$	38.9495	1.94505	0.972524	−	0.232804i	$-0.0747901\pi$
$401$	38.9495	1.94505	0.972524	+	0.232804i	$0.0747901\pi$
$402$	6.16677	0.307570
$403$	19.6023	0.976458
$404$	30.5306	1.51896
$405$	−0.749481	−0.0372420
$406$	0.823230	0.0408562
$407$	−5.15442	−0.255495
$408$	−3.03548	−0.150278
$409$	−27.7656	−1.37292	−0.686461	−	0.727167i	$-0.740837\pi$
$409$	−27.7656	−1.37292	−0.686461	+	0.727167i	$0.740837\pi$
$410$	−2.76283	−0.136447
$411$	12.5423	0.618664
$412$	−17.4276	−0.858596
$413$	−0.440342	−0.0216678
$414$	−3.52580	−0.173284
$415$	3.35425	0.164654
$416$	−11.9123	−0.584051
$417$	−21.1389	−1.03517
$418$	−3.36380	−0.164529
$419$	31.9442	1.56058	0.780288	−	0.625420i	$-0.215072\pi$
$419$	31.9442	1.56058	0.780288	+	0.625420i	$0.215072\pi$
$420$	−1.34350	−0.0655561
$421$	16.0201	0.780771	0.390386	−	0.920651i	$-0.372342\pi$
$421$	16.0201	0.780771	0.390386	+	0.920651i	$0.372342\pi$
$422$	12.9593	0.630851
$423$	−3.25780	−0.158400
$424$	0.514713	0.0249967
$425$	7.79966	0.378339
$426$	0.657149	0.0318390
$427$	−4.23592	−0.204991
$428$	15.5129	0.749842
$429$	−4.93510	−0.238269
$430$	−4.01410	−0.193577
$431$	−30.1897	−1.45419	−0.727094	−	0.686537i	$-0.759130\pi$
$431$	−30.1897	−1.45419	−0.727094	+	0.686537i	$0.759130\pi$
$432$	2.79847	0.134641
$433$	22.6091	1.08652	0.543262	−	0.839563i	$-0.317189\pi$
$433$	22.6091	1.08652	0.543262	+	0.839563i	$0.317189\pi$
$434$	3.54422	0.170128
$435$	−1.35472	−0.0649539
$436$	22.5571	1.08029
$437$	−29.1840	−1.39606
$438$	1.32172	0.0631543
$439$	30.2295	1.44278	0.721389	−	0.692530i	$-0.243504\pi$
$439$	30.2295	1.44278	0.721389	+	0.692530i	$0.243504\pi$
$440$	2.53633	0.120915
$441$	1.00000	0.0476190
$442$	2.01609	0.0958956
$443$	−4.67658	−0.222191	−0.111096	−	0.993810i	$-0.535436\pi$
$443$	−4.67658	−0.222191	−0.111096	+	0.993810i	$0.535436\pi$
$444$	−4.71605	−0.223814
$445$	−2.20914	−0.104723
$446$	−2.45571	−0.116281
$447$	−18.2486	−0.863129
$448$	3.44310	0.162671
$449$	−1.91605	−0.0904240	−0.0452120	−	0.998977i	$-0.514396\pi$
$449$	−1.91605	−0.0904240	−0.0452120	+	0.998977i	$0.514396\pi$
$450$	2.02137	0.0952884
$451$	15.8577	0.746712
$452$	−8.15417	−0.383540
$453$	−4.00291	−0.188073
$454$	−4.95244	−0.232429
$455$	1.88789	0.0885058
$456$	−6.51157	−0.304932
$457$	−8.96919	−0.419561	−0.209780	−	0.977749i	$-0.567275\pi$
$457$	−8.96919	−0.419561	−0.209780	+	0.977749i	$0.567275\pi$
$458$	−1.59849	−0.0746924
$459$	−1.75736	−0.0820266
$460$	10.4007	0.484936
$461$	−40.4148	−1.88231	−0.941153	−	0.337979i	$-0.890257\pi$
$461$	−40.4148	−1.88231	−0.941153	+	0.337979i	$0.890257\pi$
$462$	−0.892299	−0.0415135
$463$	18.4440	0.857165	0.428582	−	0.903503i	$-0.359013\pi$
$463$	18.4440	0.857165	0.428582	+	0.903503i	$0.359013\pi$
$464$	5.05836	0.234829
$465$	−5.83243	−0.270473
$466$	−1.13098	−0.0523918
$467$	1.77695	0.0822273	0.0411136	−	0.999154i	$-0.486909\pi$
$467$	1.77695	0.0822273	0.0411136	+	0.999154i	$0.486909\pi$
$468$	−4.51538	−0.208723
$469$	13.5402	0.625229
$470$	−1.11203	−0.0512942
$471$	−3.26752	−0.150559
$472$	0.760600	0.0350094
$473$	23.0396	1.05936
$474$	−0.965313	−0.0443383
$475$	16.7315	0.767693
$476$	−3.15020	−0.144389
$477$	0.297989	0.0136440
$478$	−9.64364	−0.441090
$479$	−5.47638	−0.250222	−0.125111	−	0.992143i	$-0.539929\pi$
$479$	−5.47638	−0.250222	−0.125111	+	0.992143i	$0.539929\pi$
$480$	3.54439	0.161778
$481$	6.62702	0.302166
$482$	7.80359	0.355444
$483$	−7.74151	−0.352251
$484$	12.8376	0.583526
$485$	7.34907	0.333704
$486$	−0.455441	−0.0206592
$487$	−34.6833	−1.57165	−0.785826	−	0.618448i	$-0.787762\pi$
$487$	−34.6833	−1.57165	−0.785826	+	0.618448i	$0.787762\pi$
$488$	7.31668	0.331210
$489$	−5.99201	−0.270968
$490$	0.341344	0.0154204
$491$	5.81719	0.262526	0.131263	−	0.991348i	$-0.458097\pi$
$491$	5.81719	0.262526	0.131263	+	0.991348i	$0.458097\pi$
$492$	14.5091	0.654119
$493$	−3.17651	−0.143063
$494$	4.32482	0.194583
$495$	1.46838	0.0659989
$496$	21.7776	0.977842
$497$	1.44289	0.0647223
$498$	2.03830	0.0913382
$499$	−2.83170	−0.126764	−0.0633822	−	0.997989i	$-0.520189\pi$
$499$	−2.83170	−0.126764	−0.0633822	+	0.997989i	$0.520189\pi$
$500$	−12.6803	−0.567081
$501$	−21.2819	−0.950804
$502$	1.35956	0.0606800
$503$	−11.1295	−0.496242	−0.248121	−	0.968729i	$-0.579813\pi$
$503$	−11.1295	−0.496242	−0.248121	+	0.968729i	$0.579813\pi$
$504$	−1.72729	−0.0769397
$505$	12.7650	0.568033
$506$	6.90774	0.307087
$507$	−6.65497	−0.295558
$508$	−1.79257	−0.0795326
$509$	0.0947118	0.00419803	0.00209901	−	0.999998i	$-0.499332\pi$
$509$	0.0947118	0.00419803	0.00209901	+	0.999998i	$0.499332\pi$
$510$	−0.599865	−0.0265625
$511$	2.90207	0.128380
$512$	−22.9018	−1.01213
$513$	−3.76981	−0.166441
$514$	6.49700	0.286570
$515$	−7.28653	−0.321083
$516$	21.0801	0.927999
$517$	6.38269	0.280710
$518$	1.19821	0.0526463
$519$	2.41503	0.106008
$520$	−3.26094	−0.143002
$521$	17.2116	0.754054	0.377027	−	0.926202i	$-0.376946\pi$
$521$	17.2116	0.754054	0.377027	+	0.926202i	$0.376946\pi$
$522$	−0.823230	−0.0360318
$523$	−30.7334	−1.34388	−0.671938	−	0.740607i	$-0.734538\pi$
$523$	−30.7334	−1.34388	−0.671938	+	0.740607i	$0.734538\pi$
$524$	−6.97275	−0.304606
$525$	4.43828	0.193702
$526$	2.83912	0.123791
$527$	−13.6757	−0.595724
$528$	−5.48276	−0.238607
$529$	36.9310	1.60569
$530$	0.101717	0.00441829
$531$	0.440342	0.0191092
$532$	−6.75767	−0.292982
$533$	−20.3882	−0.883112
$534$	−1.34244	−0.0580930
$535$	6.48598	0.280413
$536$	−23.3879	−1.01020
$537$	14.3890	0.620930
$538$	−4.32438	−0.186437
$539$	−1.95920	−0.0843887
$540$	1.34350	0.0578150
$541$	−45.4903	−1.95578	−0.977891	−	0.209117i	$-0.932941\pi$
$541$	−45.4903	−1.95578	−0.977891	+	0.209117i	$0.932941\pi$
$542$	11.3108	0.485839
$543$	6.74044	0.289260
$544$	8.31077	0.356321
$545$	9.43119	0.403988
$546$	1.14723	0.0490967
$547$	−2.40242	−0.102720	−0.0513599	−	0.998680i	$-0.516356\pi$
$547$	−2.40242	−0.102720	−0.0513599	+	0.998680i	$0.516356\pi$
$548$	−22.4829	−0.960423
$549$	4.23592	0.180785
$550$	−3.96027	−0.168867
$551$	−6.81411	−0.290291
$552$	13.3719	0.569144
$553$	−2.11951	−0.0901309
$554$	−7.35422	−0.312451
$555$	−1.97179	−0.0836980
$556$	37.8930	1.60702
$557$	−14.6511	−0.620788	−0.310394	−	0.950608i	$-0.600461\pi$
$557$	−14.6511	−0.620788	−0.310394	+	0.950608i	$0.600461\pi$
$558$	−3.54422	−0.150039
$559$	−29.6219	−1.25287
$560$	2.09740	0.0886313
$561$	3.44302	0.145365
$562$	4.30478	0.181586
$563$	−37.5930	−1.58436	−0.792178	−	0.610291i	$-0.791053\pi$
$563$	−37.5930	−1.58436	−0.792178	+	0.610291i	$0.791053\pi$
$564$	5.83985	0.245902
$565$	−3.40929	−0.143430
$566$	−6.46360	−0.271685
$567$	−1.00000	−0.0419961
$568$	−2.49229	−0.104574
$569$	3.82876	0.160510	0.0802550	−	0.996774i	$-0.474427\pi$
$569$	3.82876	0.160510	0.0802550	+	0.996774i	$0.474427\pi$
$570$	−1.28680	−0.0538983
$571$	17.2172	0.720519	0.360260	−	0.932852i	$-0.382688\pi$
$571$	17.2172	0.720519	0.360260	+	0.932852i	$0.382688\pi$
$572$	8.84653	0.369892
$573$	17.9119	0.748282
$574$	−3.68633	−0.153864
$575$	−34.3590	−1.43287
$576$	−3.44310	−0.143463
$577$	17.9929	0.749055	0.374527	−	0.927216i	$-0.377805\pi$
$577$	17.9929	0.749055	0.374527	+	0.927216i	$0.377805\pi$
$578$	6.33595	0.263541
$579$	8.61234	0.357917
$580$	2.42844	0.100835
$581$	4.47544	0.185672
$582$	4.46584	0.185115
$583$	−0.583819	−0.0241793
$584$	−5.01273	−0.207428
$585$	−1.88789	−0.0780548
$586$	−8.20992	−0.339149
$587$	−15.1685	−0.626070	−0.313035	−	0.949742i	$-0.601346\pi$
$587$	−15.1685	−0.626070	−0.313035	+	0.949742i	$0.601346\pi$
$588$	−1.79257	−0.0739245
$589$	−29.3365	−1.20879
$590$	0.150308	0.00618809
$591$	−26.3709	−1.08475
$592$	7.36244	0.302594
$593$	29.4625	1.20988	0.604940	−	0.796271i	$-0.293197\pi$
$593$	29.4625	1.20988	0.604940	+	0.796271i	$0.293197\pi$
$594$	0.892299	0.0366115
$595$	−1.31711	−0.0539962
$596$	32.7120	1.33993
$597$	−12.3460	−0.505289
$598$	−8.88126	−0.363182
$599$	6.27754	0.256493	0.128247	−	0.991742i	$-0.459065\pi$
$599$	6.27754	0.256493	0.128247	+	0.991742i	$0.459065\pi$
$600$	−7.66620	−0.312971
$601$	21.5091	0.877373	0.438687	−	0.898640i	$-0.355444\pi$
$601$	21.5091	0.877373	0.438687	+	0.898640i	$0.355444\pi$
$602$	−5.35583	−0.218288
$603$	−13.5402	−0.551400
$604$	7.17551	0.291967
$605$	5.36743	0.218217
$606$	7.75694	0.315104
$607$	36.2458	1.47117	0.735586	−	0.677431i	$-0.236907\pi$
$607$	36.2458	1.47117	0.735586	+	0.677431i	$0.236907\pi$
$608$	17.8279	0.723017
$609$	−1.80755	−0.0732455
$610$	1.44591	0.0585431
$611$	−8.20619	−0.331987
$612$	3.15020	0.127339
$613$	4.88666	0.197370	0.0986851	−	0.995119i	$-0.468536\pi$
$613$	4.88666	0.197370	0.0986851	+	0.995119i	$0.468536\pi$
$614$	−7.33001	−0.295815
$615$	6.06629	0.244616
$616$	3.38411	0.136350
$617$	4.27798	0.172225	0.0861126	−	0.996285i	$-0.472556\pi$
$617$	4.27798	0.172225	0.0861126	+	0.996285i	$0.472556\pi$
$618$	−4.42784	−0.178114
$619$	32.3159	1.29888	0.649442	−	0.760411i	$-0.275003\pi$
$619$	32.3159	1.29888	0.649442	+	0.760411i	$0.275003\pi$
$620$	10.4551	0.419886
$621$	7.74151	0.310656
$622$	−8.79353	−0.352589
$623$	−2.94756	−0.118092
$624$	7.04916	0.282192
$625$	16.8897	0.675588
$626$	14.0555	0.561770
$627$	7.38582	0.294961
$628$	5.85726	0.233730
$629$	−4.62341	−0.184347
$630$	−0.341344	−0.0135995
$631$	−0.860434	−0.0342533	−0.0171267	−	0.999853i	$-0.505452\pi$
$631$	−0.860434	−0.0342533	−0.0171267	+	0.999853i	$0.505452\pi$
$632$	3.66102	0.145628
$633$	−28.4545	−1.13097
$634$	−13.9709	−0.554856
$635$	−0.749481	−0.0297422
$636$	−0.534167	−0.0211811
$637$	2.51893	0.0998038
$638$	1.61287	0.0638542
$639$	−1.44289	−0.0570797
$640$	−8.26405	−0.326665
$641$	1.41230	0.0557827	0.0278913	−	0.999611i	$-0.491121\pi$
$641$	1.41230	0.0557827	0.0278913	+	0.999611i	$0.491121\pi$
$642$	3.94136	0.155553
$643$	−11.5508	−0.455518	−0.227759	−	0.973718i	$-0.573140\pi$
$643$	−11.5508	−0.455518	−0.227759	+	0.973718i	$0.573140\pi$
$644$	13.8772	0.546839
$645$	8.81365	0.347037
$646$	−3.01726	−0.118712
$647$	1.61666	0.0635574	0.0317787	−	0.999495i	$-0.489883\pi$
$647$	1.61666	0.0635574	0.0317787	+	0.999495i	$0.489883\pi$
$648$	1.72729	0.0678544
$649$	−0.862719	−0.0338647
$650$	5.09170	0.199713
$651$	−7.78196	−0.304999
$652$	10.7411	0.420655
$653$	−14.8742	−0.582071	−0.291035	−	0.956712i	$-0.594000\pi$
$653$	−14.8742	−0.582071	−0.291035	+	0.956712i	$0.594000\pi$
$654$	5.73110	0.224104
$655$	−2.91533	−0.113911
$656$	−22.6508	−0.884364
$657$	−2.90207	−0.113221
$658$	−1.48374	−0.0578420
$659$	19.5325	0.760878	0.380439	−	0.924806i	$-0.375773\pi$
$659$	19.5325	0.760878	0.380439	+	0.924806i	$0.375773\pi$
$660$	−2.63219	−0.102458
$661$	36.3289	1.41303	0.706516	−	0.707697i	$-0.250266\pi$
$661$	36.3289	1.41303	0.706516	+	0.707697i	$0.250266\pi$
$662$	4.66597	0.181348
$663$	−4.42668	−0.171918
$664$	−7.73039	−0.299997
$665$	−2.82540	−0.109564
$666$	−1.19821	−0.0464297
$667$	13.9931	0.541817
$668$	38.1493	1.47604
$669$	5.39195	0.208465
$670$	−4.62187	−0.178559
$671$	−8.29902	−0.320380
$672$	4.72912	0.182430
$673$	6.49459	0.250348	0.125174	−	0.992135i	$-0.460051\pi$
$673$	6.49459	0.250348	0.125174	+	0.992135i	$0.460051\pi$
$674$	0.593872	0.0228751
$675$	−4.43828	−0.170829
$676$	11.9295	0.458828
$677$	47.4029	1.82184	0.910921	−	0.412582i	$-0.135373\pi$
$677$	47.4029	1.82184	0.910921	+	0.412582i	$0.135373\pi$
$678$	−2.07174	−0.0795646
$679$	9.80554	0.376302
$680$	2.27503	0.0872435
$681$	10.8739	0.416691
$682$	6.94384	0.265893
$683$	−32.5349	−1.24491	−0.622456	−	0.782655i	$-0.713865\pi$
$683$	−32.5349	−1.24491	−0.622456	+	0.782655i	$0.713865\pi$
$684$	6.75767	0.258386
$685$	−9.40018	−0.359163
$686$	0.455441	0.0173888
$687$	3.50976	0.133906
$688$	−32.9091	−1.25465
$689$	0.750614	0.0285961
$690$	2.64252	0.100599
$691$	−1.09394	−0.0416155	−0.0208078	−	0.999783i	$-0.506624\pi$
$691$	−1.09394	−0.0416155	−0.0208078	+	0.999783i	$0.506624\pi$
$692$	−4.32912	−0.164569
$693$	1.95920	0.0744239
$694$	−8.49112	−0.322318
$695$	15.8432	0.600966
$696$	3.12216	0.118345
$697$	14.2241	0.538775
$698$	−3.40382	−0.128836
$699$	2.48327	0.0939261
$700$	−7.95594	−0.300706
$701$	37.3987	1.41253	0.706264	−	0.707949i	$-0.250379\pi$
$701$	37.3987	1.41253	0.706264	+	0.707949i	$0.250379\pi$
$702$	−1.14723	−0.0432992
$703$	−9.91793	−0.374062
$704$	6.74573	0.254239
$705$	2.44166	0.0919583
$706$	4.76196	0.179219
$707$	17.0317	0.640544
$708$	−0.789346	−0.0296654
$709$	27.4538	1.03105	0.515524	−	0.856875i	$-0.327597\pi$
$709$	27.4538	1.03105	0.515524	+	0.856875i	$0.327597\pi$
$710$	−0.492521	−0.0184840
$711$	2.11951	0.0794880
$712$	5.09130	0.190804
$713$	60.2441	2.25616
$714$	−0.800374	−0.0299532
$715$	3.69876	0.138326
$716$	−25.7933	−0.963941
$717$	21.1743	0.790769
$718$	−16.3479	−0.610096
$719$	14.8902	0.555312	0.277656	−	0.960681i	$-0.410443\pi$
$719$	14.8902	0.555312	0.277656	+	0.960681i	$0.410443\pi$
$720$	−2.09740	−0.0781654
$721$	−9.72210	−0.362070
$722$	2.18088	0.0811641
$723$	−17.1342	−0.637226
$724$	−12.0827	−0.449051
$725$	−8.02239	−0.297944
$726$	3.26165	0.121051
$727$	8.84554	0.328063	0.164032	−	0.986455i	$-0.447550\pi$
$727$	8.84554	0.328063	0.164032	+	0.986455i	$0.447550\pi$
$728$	−4.35094	−0.161256
$729$	1.00000	0.0370370
$730$	−0.990605	−0.0366639
$731$	20.6660	0.764360
$732$	−7.59321	−0.280653
$733$	51.0985	1.88737	0.943683	−	0.330851i	$-0.107336\pi$
$733$	51.0985	1.88737	0.943683	+	0.330851i	$0.107336\pi$
$734$	−1.43752	−0.0530597
$735$	−0.749481	−0.0276450
$736$	−36.6105	−1.34948
$737$	26.5280	0.977171
$738$	3.68633	0.135696
$739$	1.57429	0.0579112	0.0289556	−	0.999581i	$-0.490782\pi$
$739$	1.57429	0.0579112	0.0289556	+	0.999581i	$0.490782\pi$
$740$	3.53459	0.129934
$741$	−9.49591	−0.348841
$742$	0.135716	0.00498230
$743$	39.0343	1.43203	0.716015	−	0.698085i	$-0.245964\pi$
$743$	39.0343	1.43203	0.716015	+	0.698085i	$0.245964\pi$
$744$	13.4417	0.492797
$745$	13.6770	0.501086
$746$	1.86247	0.0681899
$747$	−4.47544	−0.163748
$748$	−6.17187	−0.225666
$749$	8.65396	0.316209
$750$	−3.22170	−0.117640
$751$	9.74428	0.355574	0.177787	−	0.984069i	$-0.443106\pi$
$751$	9.74428	0.355574	0.177787	+	0.984069i	$0.443106\pi$
$752$	−9.11686	−0.332458
$753$	−2.98515	−0.108785
$754$	−2.07366	−0.0755183
$755$	3.00010	0.109185
$756$	1.79257	0.0651953
$757$	−17.7563	−0.645363	−0.322682	−	0.946508i	$-0.604584\pi$
$757$	−17.7563	−0.645363	−0.322682	+	0.946508i	$0.604584\pi$
$758$	15.5678	0.565449
$759$	−15.1672	−0.550533
$760$	4.88030	0.177027
$761$	−14.0688	−0.509994	−0.254997	−	0.966942i	$-0.582075\pi$
$761$	−14.0688	−0.509994	−0.254997	+	0.966942i	$0.582075\pi$
$762$	−0.455441	−0.0164989
$763$	12.5836	0.455558
$764$	−32.1085	−1.16164
$765$	1.31711	0.0476202
$766$	−16.3873	−0.592099
$767$	1.10919	0.0400507
$768$	1.86435	0.0672739
$769$	−2.66067	−0.0959461	−0.0479730	−	0.998849i	$-0.515276\pi$
$769$	−2.66067	−0.0959461	−0.0479730	+	0.998849i	$0.515276\pi$
$770$	0.668761	0.0241005
$771$	−14.2653	−0.513752
$772$	−15.4383	−0.555635
$773$	−3.52993	−0.126963	−0.0634814	−	0.997983i	$-0.520220\pi$
$773$	−3.52993	−0.126963	−0.0634814	+	0.997983i	$0.520220\pi$
$774$	5.35583	0.192512
$775$	−34.5385	−1.24066
$776$	−16.9370	−0.608004
$777$	−2.63088	−0.0943823
$778$	4.56573	0.163690
$779$	30.5128	1.09324
$780$	3.38419	0.121173
$781$	2.82690	0.101155
$782$	6.19610	0.221572
$783$	1.80755	0.0645964
$784$	2.79847	0.0999453
$785$	2.44894	0.0874065
$786$	−1.77157	−0.0631899
$787$	9.63057	0.343293	0.171646	−	0.985159i	$-0.445091\pi$
$787$	9.63057	0.343293	0.171646	+	0.985159i	$0.445091\pi$
$788$	47.2717	1.68399
$789$	−6.23379	−0.221929
$790$	0.723483	0.0257404
$791$	−4.54886	−0.161739
$792$	−3.38411	−0.120249
$793$	10.6700	0.378903
$794$	15.2069	0.539672
$795$	−0.223337	−0.00792094
$796$	22.1311	0.784417
$797$	−5.94571	−0.210608	−0.105304	−	0.994440i	$-0.533582\pi$
$797$	−5.94571	−0.210608	−0.105304	+	0.994440i	$0.533582\pi$
$798$	−1.71693	−0.0607785
$799$	5.72514	0.202541
$800$	20.9892	0.742079
$801$	2.94756	0.104147
$802$	−17.7392	−0.626393
$803$	5.68574	0.200645
$804$	24.2718	0.856002
$805$	5.80211	0.204498
$806$	−8.92766	−0.314464
$807$	9.49493	0.334237
$808$	−29.4188	−1.03495
$809$	−38.1282	−1.34051	−0.670257	−	0.742129i	$-0.733816\pi$
$809$	−38.1282	−1.34051	−0.670257	+	0.742129i	$0.733816\pi$
$810$	0.341344	0.0119936
$811$	21.9571	0.771018	0.385509	−	0.922704i	$-0.374026\pi$
$811$	21.9571	0.771018	0.385509	+	0.922704i	$0.374026\pi$
$812$	3.24016	0.113707
$813$	−24.8348	−0.870993
$814$	2.34753	0.0822810
$815$	4.49090	0.157309
$816$	−4.91792	−0.172162
$817$	44.3318	1.55097
$818$	12.6456	0.442143
$819$	−2.51893	−0.0880187
$820$	−10.8743	−0.379746
$821$	31.2927	1.09212	0.546061	−	0.837746i	$-0.316127\pi$
$821$	31.2927	1.09212	0.546061	+	0.837746i	$0.316127\pi$
$822$	−5.71225	−0.199238
$823$	18.8063	0.655547	0.327773	−	0.944756i	$-0.393702\pi$
$823$	18.8063	0.655547	0.327773	+	0.944756i	$0.393702\pi$
$824$	16.7929	0.585009
$825$	8.69548	0.302738
$826$	0.200550	0.00697802
$827$	−23.1897	−0.806386	−0.403193	−	0.915115i	$-0.632100\pi$
$827$	−23.1897	−0.806386	−0.403193	+	0.915115i	$0.632100\pi$
$828$	−13.8772	−0.482267
$829$	−56.7692	−1.97168	−0.985838	−	0.167700i	$-0.946366\pi$
$829$	−56.7692	−1.97168	−0.985838	+	0.167700i	$0.946366\pi$
$830$	−1.52766	−0.0530260
$831$	16.1475	0.560150
$832$	−8.67295	−0.300681
$833$	−1.75736	−0.0608890
$834$	9.62750	0.333373
$835$	15.9504	0.551985
$836$	−13.2396	−0.457902
$837$	7.78196	0.268984
$838$	−14.5487	−0.502576
$839$	−28.5757	−0.986542	−0.493271	−	0.869876i	$-0.664199\pi$
$839$	−28.5757	−0.986542	−0.493271	+	0.869876i	$0.664199\pi$
$840$	1.29457	0.0446670
$841$	−25.7328	−0.887337
$842$	−7.29620	−0.251444
$843$	−9.45191	−0.325541
$844$	51.0068	1.75573
$845$	4.98777	0.171585
$846$	1.48374	0.0510119
$847$	7.16153	0.246073
$848$	0.833912	0.0286366
$849$	14.1920	0.487067
$850$	−3.55228	−0.121842
$851$	20.3670	0.698171
$852$	2.58648	0.0886114
$853$	17.4300	0.596792	0.298396	−	0.954442i	$-0.403548\pi$
$853$	17.4300	0.596792	0.298396	+	0.954442i	$0.403548\pi$
$854$	1.92921	0.0660163
$855$	2.82540	0.0966267
$856$	−14.9479	−0.510909
$857$	−31.4574	−1.07456	−0.537282	−	0.843403i	$-0.680549\pi$
$857$	−31.4574	−1.07456	−0.537282	+	0.843403i	$0.680549\pi$
$858$	2.24764	0.0767333
$859$	−17.7552	−0.605799	−0.302900	−	0.953022i	$-0.597955\pi$
$859$	−17.7552	−0.605799	−0.302900	+	0.953022i	$0.597955\pi$
$860$	−15.7991	−0.538746
$861$	8.09399	0.275842
$862$	13.7496	0.468315
$863$	16.9150	0.575793	0.287897	−	0.957661i	$-0.407044\pi$
$863$	16.9150	0.575793	0.287897	+	0.957661i	$0.407044\pi$
$864$	−4.72912	−0.160888
$865$	−1.81002	−0.0615426
$866$	−10.2971	−0.349910
$867$	−13.9117	−0.472465
$868$	13.9497	0.473485
$869$	−4.15255	−0.140866
$870$	0.616995	0.0209181
$871$	−34.1069	−1.15567
$872$	−21.7356	−0.736060
$873$	−9.80554	−0.331867
$874$	13.2916	0.449595
$875$	−7.07381	−0.239138
$876$	5.20218	0.175765
$877$	−13.3300	−0.450121	−0.225061	−	0.974345i	$-0.572258\pi$
$877$	−13.3300	−0.450121	−0.225061	+	0.974345i	$0.572258\pi$
$878$	−13.7678	−0.464639
$879$	18.0263	0.608013
$880$	4.10922	0.138522
$881$	−31.1651	−1.04998	−0.524990	−	0.851109i	$-0.675931\pi$
$881$	−31.1651	−1.04998	−0.524990	+	0.851109i	$0.675931\pi$
$882$	−0.455441	−0.0153355
$883$	20.0110	0.673422	0.336711	−	0.941608i	$-0.390685\pi$
$883$	20.0110	0.673422	0.336711	+	0.941608i	$0.390685\pi$
$884$	7.93515	0.266888
$885$	−0.330028	−0.0110938
$886$	2.12991	0.0715556
$887$	−10.0796	−0.338441	−0.169221	−	0.985578i	$-0.554125\pi$
$887$	−10.0796	−0.338441	−0.169221	+	0.985578i	$0.554125\pi$
$888$	4.54430	0.152497
$889$	−1.00000	−0.0335389
$890$	1.00613	0.0337256
$891$	−1.95920	−0.0656357
$892$	−9.66546	−0.323624
$893$	12.2813	0.410978
$894$	8.31115	0.277967
$895$	−10.7843	−0.360478
$896$	−11.0264	−0.368365
$897$	19.5004	0.651098
$898$	0.872647	0.0291206
$899$	14.0663	0.469136
$900$	7.95594	0.265198
$901$	−0.523674	−0.0174461
$902$	−7.22226	−0.240475
$903$	11.7597	0.391338
$904$	7.85721	0.261327
$905$	−5.05183	−0.167928
$906$	1.82309	0.0605680
$907$	32.5788	1.08176	0.540880	−	0.841100i	$-0.318091\pi$
$907$	32.5788	1.08176	0.540880	+	0.841100i	$0.318091\pi$
$908$	−19.4924	−0.646876
$909$	−17.0317	−0.564907
$910$	−0.859823	−0.0285029
$911$	−34.9407	−1.15764	−0.578819	−	0.815456i	$-0.696486\pi$
$911$	−34.9407	−1.15764	−0.578819	+	0.815456i	$0.696486\pi$
$912$	−10.5497	−0.349336
$913$	8.76828	0.290188
$914$	4.08493	0.135118
$915$	−3.17474	−0.104954
$916$	−6.29151	−0.207877
$917$	−3.88980	−0.128453
$918$	0.800374	0.0264163
$919$	−36.5952	−1.20716	−0.603582	−	0.797301i	$-0.706260\pi$
$919$	−36.5952	−1.20716	−0.603582	+	0.797301i	$0.706260\pi$
$920$	−10.0219	−0.330414
$921$	16.0943	0.530326
$922$	18.4066	0.606188
$923$	−3.63454	−0.119632
$924$	−3.51201	−0.115537
$925$	−11.6766	−0.383924
$926$	−8.40014	−0.276046
$927$	9.72210	0.319316
$928$	−8.54811	−0.280605
$929$	4.37077	0.143400	0.0717002	−	0.997426i	$-0.477158\pi$
$929$	4.37077	0.143400	0.0717002	+	0.997426i	$0.477158\pi$
$930$	2.65633	0.0871044
$931$	−3.76981	−0.123551
$932$	−4.45145	−0.145812
$933$	19.3077	0.632107
$934$	−0.809294	−0.0264809
$935$	−2.58048	−0.0843907
$936$	4.35094	0.142215
$937$	36.0803	1.17869	0.589346	−	0.807881i	$-0.299386\pi$
$937$	36.0803	1.17869	0.589346	+	0.807881i	$0.299386\pi$
$938$	−6.16677	−0.201352
$939$	−30.8613	−1.00712
$940$	−4.37686	−0.142757
$941$	17.2953	0.563810	0.281905	−	0.959442i	$-0.409034\pi$
$941$	17.2953	0.563810	0.281905	+	0.959442i	$0.409034\pi$
$942$	1.48816	0.0484869
$943$	−62.6597	−2.04048
$944$	1.23228	0.0401074
$945$	0.749481	0.0243806
$946$	−10.4932	−0.341162
$947$	28.8863	0.938679	0.469340	−	0.883018i	$-0.344492\pi$
$947$	28.8863	0.938679	0.469340	+	0.883018i	$0.344492\pi$
$948$	−3.79938	−0.123398
$949$	−7.31013	−0.237297
$950$	−7.62020	−0.247232
$951$	30.6756	0.994724
$952$	3.03548	0.0983804
$953$	−45.3794	−1.46998	−0.734992	−	0.678076i	$-0.762814\pi$
$953$	−45.3794	−1.46998	−0.734992	+	0.678076i	$0.762814\pi$
$954$	−0.135716	−0.00439397
$955$	−13.4247	−0.434412
$956$	−37.9565	−1.22760
$957$	−3.54135	−0.114475
$958$	2.49417	0.0805828
$959$	−12.5423	−0.405011
$960$	2.58054	0.0832866
$961$	29.5589	0.953514
$962$	−3.01821	−0.0973111
$963$	−8.65396	−0.278870
$964$	30.7142	0.989239
$965$	−6.45479	−0.207787
$966$	3.52580	0.113441
$967$	−9.53966	−0.306775	−0.153387	−	0.988166i	$-0.549018\pi$
$967$	−9.53966	−0.306775	−0.153387	+	0.988166i	$0.549018\pi$
$968$	−12.3701	−0.397589
$969$	6.62492	0.212823
$970$	−3.34706	−0.107468
$971$	48.0293	1.54133	0.770667	−	0.637239i	$-0.219923\pi$
$971$	48.0293	1.54133	0.770667	+	0.637239i	$0.219923\pi$
$972$	−1.79257	−0.0574968
$973$	21.1389	0.677681
$974$	15.7962	0.506143
$975$	−11.1797	−0.358038
$976$	11.8541	0.379440
$977$	−10.7980	−0.345460	−0.172730	−	0.984969i	$-0.555259\pi$
$977$	−10.7980	−0.345460	−0.172730	+	0.984969i	$0.555259\pi$
$978$	2.72901	0.0872640
$979$	−5.77486	−0.184565
$980$	1.34350	0.0429165
$981$	−12.5836	−0.401764
$982$	−2.64939	−0.0845453
$983$	−3.04790	−0.0972130	−0.0486065	−	0.998818i	$-0.515478\pi$
$983$	−3.04790	−0.0972130	−0.0486065	+	0.998818i	$0.515478\pi$
$984$	−13.9807	−0.445688
$985$	19.7645	0.629748
$986$	1.44671	0.0460727
$987$	3.25780	0.103697
$988$	17.0221	0.541546
$989$	−91.0377	−2.89483
$990$	−0.668761	−0.0212546
$991$	−44.1141	−1.40133	−0.700665	−	0.713491i	$-0.747113\pi$
$991$	−44.1141	−1.40133	−0.700665	+	0.713491i	$0.747113\pi$
$992$	−36.8018	−1.16846
$993$	−10.2450	−0.325114
$994$	−0.657149	−0.0208435
$995$	9.25310	0.293343
$996$	8.02255	0.254204
$997$	−60.8537	−1.92726	−0.963629	−	0.267245i	$-0.913887\pi$
$997$	−60.8537	−1.92726	−0.963629	+	0.267245i	$0.913887\pi$
$998$	1.28967	0.0408239
$999$	2.63088	0.0832374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.k.1.6	✓	11
3.2	odd	2		8001.2.a.m.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.k.1.6	✓	11	1.1	even	1	trivial
8001.2.a.m.1.6		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.455441 q^{2} +1.00000 q^{3} -1.79257 q^{4} -0.749481 q^{5} -0.455441 q^{6} -1.00000 q^{7} +1.72729 q^{8} +1.00000 q^{9} +0.341344 q^{10} -1.95920 q^{11} -1.79257 q^{12} +2.51893 q^{13} +0.455441 q^{14} -0.749481 q^{15} +2.79847 q^{16} -1.75736 q^{17} -0.455441 q^{18} -3.76981 q^{19} +1.34350 q^{20} -1.00000 q^{21} +0.892299 q^{22} +7.74151 q^{23} +1.72729 q^{24} -4.43828 q^{25} -1.14723 q^{26} +1.00000 q^{27} +1.79257 q^{28} +1.80755 q^{29} +0.341344 q^{30} +7.78196 q^{31} -4.72912 q^{32} -1.95920 q^{33} +0.800374 q^{34} +0.749481 q^{35} -1.79257 q^{36} +2.63088 q^{37} +1.71693 q^{38} +2.51893 q^{39} -1.29457 q^{40} -8.09399 q^{41} +0.455441 q^{42} -11.7597 q^{43} +3.51201 q^{44} -0.749481 q^{45} -3.52580 q^{46} -3.25780 q^{47} +2.79847 q^{48} +1.00000 q^{49} +2.02137 q^{50} -1.75736 q^{51} -4.51538 q^{52} +0.297989 q^{53} -0.455441 q^{54} +1.46838 q^{55} -1.72729 q^{56} -3.76981 q^{57} -0.823230 q^{58} +0.440342 q^{59} +1.34350 q^{60} +4.23592 q^{61} -3.54422 q^{62} -1.00000 q^{63} -3.44310 q^{64} -1.88789 q^{65} +0.892299 q^{66} -13.5402 q^{67} +3.15020 q^{68} +7.74151 q^{69} -0.341344 q^{70} -1.44289 q^{71} +1.72729 q^{72} -2.90207 q^{73} -1.19821 q^{74} -4.43828 q^{75} +6.75767 q^{76} +1.95920 q^{77} -1.14723 q^{78} +2.11951 q^{79} -2.09740 q^{80} +1.00000 q^{81} +3.68633 q^{82} -4.47544 q^{83} +1.79257 q^{84} +1.31711 q^{85} +5.35583 q^{86} +1.80755 q^{87} -3.38411 q^{88} +2.94756 q^{89} +0.341344 q^{90} -2.51893 q^{91} -13.8772 q^{92} +7.78196 q^{93} +1.48374 q^{94} +2.82540 q^{95} -4.72912 q^{96} -9.80554 q^{97} -0.455441 q^{98} -1.95920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 2 q^{2} + 11 q^{3} + 12 q^{4} + q^{5} - 2 q^{6} - 11 q^{7} - 15 q^{8} + 11 q^{9} - 12 q^{10} - 7 q^{11} + 12 q^{12} - 24 q^{13} + 2 q^{14} + q^{15} - 6 q^{16} - 15 q^{17} - 2 q^{18} - 19 q^{19}+ \cdots - 7 q^{99}+O(q^{100}) \) 11 * q - 2 * q^2 + 11 * q^3 + 12 * q^4 + q^5 - 2 * q^6 - 11 * q^7 - 15 * q^8 + 11 * q^9 - 12 * q^10 - 7 * q^11 + 12 * q^12 - 24 * q^13 + 2 * q^14 + q^15 - 6 * q^16 - 15 * q^17 - 2 * q^18 - 19 * q^19 + 3 * q^20 - 11 * q^21 - 3 * q^22 - 11 * q^23 - 15 * q^24 + 10 * q^25 + 10 * q^26 + 11 * q^27 - 12 * q^28 - 10 * q^29 - 12 * q^30 - 20 * q^31 - 27 * q^32 - 7 * q^33 - 9 * q^34 - q^35 + 12 * q^36 - 22 * q^37 + 8 * q^38 - 24 * q^39 - 29 * q^40 + 9 * q^41 + 2 * q^42 - 17 * q^43 - 9 * q^44 + q^45 - 18 * q^46 - 7 * q^47 - 6 * q^48 + 11 * q^49 - 47 * q^50 - 15 * q^51 - 66 * q^52 - 28 * q^53 - 2 * q^54 - 24 * q^55 + 15 * q^56 - 19 * q^57 - 39 * q^58 + 35 * q^59 + 3 * q^60 - 6 * q^61 + 18 * q^62 - 11 * q^63 + 11 * q^64 - 43 * q^65 - 3 * q^66 - 22 * q^67 - 12 * q^68 - 11 * q^69 + 12 * q^70 - 22 * q^71 - 15 * q^72 - 29 * q^73 + 14 * q^74 + 10 * q^75 + 10 * q^76 + 7 * q^77 + 10 * q^78 - 20 * q^79 + 66 * q^80 + 11 * q^81 - 24 * q^82 + 17 * q^83 - 12 * q^84 - 50 * q^85 - 12 * q^86 - 10 * q^87 + 2 * q^88 - q^89 - 12 * q^90 + 24 * q^91 - 22 * q^92 - 20 * q^93 + q^94 + 10 * q^95 - 27 * q^96 - 45 * q^97 - 2 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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