LMFDB - Embedded newform 2667.2.a.p.1.11

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 = [18,-6,-18,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 $ x^18 - 6x^17 - 11x^16 + 123x^15 - 35x^14 - 982x^13 + 988x^12 + 3872x^11 - 5421x^10 - 7882x^9 + 13376x^8 + 7948x^7 - 15795x^6 - 3858x^5 + 8199x^4 + 1453x^3 - 1610x^2 - 380*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.375443$ 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)

$f(q)$	$=$	\(q+0.375443 q^{2} -1.00000 q^{3} -1.85904 q^{4} +2.49678 q^{5} -0.375443 q^{6} +1.00000 q^{7} -1.44885 q^{8} +1.00000 q^{9} +0.937397 q^{10} -0.0439826 q^{11} +1.85904 q^{12} +1.23685 q^{13} +0.375443 q^{14} -2.49678 q^{15} +3.17413 q^{16} -4.66254 q^{17} +0.375443 q^{18} -4.55600 q^{19} -4.64162 q^{20} -1.00000 q^{21} -0.0165129 q^{22} -5.31043 q^{23} +1.44885 q^{24} +1.23390 q^{25} +0.464365 q^{26} -1.00000 q^{27} -1.85904 q^{28} -5.23792 q^{29} -0.937397 q^{30} +0.715277 q^{31} +4.08940 q^{32} +0.0439826 q^{33} -1.75052 q^{34} +2.49678 q^{35} -1.85904 q^{36} +7.90706 q^{37} -1.71052 q^{38} -1.23685 q^{39} -3.61746 q^{40} -4.97134 q^{41} -0.375443 q^{42} +0.341392 q^{43} +0.0817655 q^{44} +2.49678 q^{45} -1.99376 q^{46} +11.4407 q^{47} -3.17413 q^{48} +1.00000 q^{49} +0.463260 q^{50} +4.66254 q^{51} -2.29935 q^{52} -4.41842 q^{53} -0.375443 q^{54} -0.109815 q^{55} -1.44885 q^{56} +4.55600 q^{57} -1.96654 q^{58} +9.78565 q^{59} +4.64162 q^{60} -9.42399 q^{61} +0.268546 q^{62} +1.00000 q^{63} -4.81291 q^{64} +3.08813 q^{65} +0.0165129 q^{66} +0.00811780 q^{67} +8.66785 q^{68} +5.31043 q^{69} +0.937397 q^{70} -4.91418 q^{71} -1.44885 q^{72} -11.8395 q^{73} +2.96865 q^{74} -1.23390 q^{75} +8.46980 q^{76} -0.0439826 q^{77} -0.464365 q^{78} -1.44620 q^{79} +7.92509 q^{80} +1.00000 q^{81} -1.86645 q^{82} -7.62022 q^{83} +1.85904 q^{84} -11.6413 q^{85} +0.128173 q^{86} +5.23792 q^{87} +0.0637241 q^{88} -11.8328 q^{89} +0.937397 q^{90} +1.23685 q^{91} +9.87232 q^{92} -0.715277 q^{93} +4.29534 q^{94} -11.3753 q^{95} -4.08940 q^{96} -8.97251 q^{97} +0.375443 q^{98} -0.0439826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

Coefficient data

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

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

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

$2$	0.375443	0.265478	0.132739	−	0.991151i	$-0.457623\pi$
$2$	0.375443	0.265478	0.132739	+	0.991151i	$0.457623\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.85904	−0.929521
$5$	2.49678	1.11659	0.558297	−	0.829641i	$-0.311455\pi$
$5$	2.49678	1.11659	0.558297	+	0.829641i	$0.311455\pi$
$6$	−0.375443	−0.153274
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.44885	−0.512246
$9$	1.00000	0.333333
$10$	0.937397	0.296431
$11$	−0.0439826	−0.0132612	−0.00663062	−	0.999978i	$-0.502111\pi$
$11$	−0.0439826	−0.0132612	−0.00663062	+	0.999978i	$0.502111\pi$
$12$	1.85904	0.536659
$13$	1.23685	0.343039	0.171520	−	0.985181i	$-0.445132\pi$
$13$	1.23685	0.343039	0.171520	+	0.985181i	$0.445132\pi$
$14$	0.375443	0.100341
$15$	−2.49678	−0.644665
$16$	3.17413	0.793531
$17$	−4.66254	−1.13083	−0.565416	−	0.824806i	$-0.691284\pi$
$17$	−4.66254	−1.13083	−0.565416	+	0.824806i	$0.691284\pi$
$18$	0.375443	0.0884927
$19$	−4.55600	−1.04522	−0.522609	−	0.852572i	$-0.675041\pi$
$19$	−4.55600	−1.04522	−0.522609	+	0.852572i	$0.675041\pi$
$20$	−4.64162	−1.03790
$21$	−1.00000	−0.218218
$22$	−0.0165129	−0.00352057
$23$	−5.31043	−1.10730	−0.553651	−	0.832749i	$-0.686766\pi$
$23$	−5.31043	−1.10730	−0.553651	+	0.832749i	$0.686766\pi$
$24$	1.44885	0.295745
$25$	1.23390	0.246780
$26$	0.464365	0.0910694
$27$	−1.00000	−0.192450
$28$	−1.85904	−0.351326
$29$	−5.23792	−0.972657	−0.486329	−	0.873776i	$-0.661664\pi$
$29$	−5.23792	−0.972657	−0.486329	+	0.873776i	$0.661664\pi$
$30$	−0.937397	−0.171145
$31$	0.715277	0.128468	0.0642338	−	0.997935i	$-0.479540\pi$
$31$	0.715277	0.128468	0.0642338	+	0.997935i	$0.479540\pi$
$32$	4.08940	0.722911
$33$	0.0439826	0.00765638
$34$	−1.75052	−0.300211
$35$	2.49678	0.422033
$36$	−1.85904	−0.309840
$37$	7.90706	1.29991	0.649956	−	0.759972i	$-0.274787\pi$
$37$	7.90706	1.29991	0.649956	+	0.759972i	$0.274787\pi$
$38$	−1.71052	−0.277483
$39$	−1.23685	−0.198054
$40$	−3.61746	−0.571970
$41$	−4.97134	−0.776393	−0.388197	−	0.921577i	$-0.626902\pi$
$41$	−4.97134	−0.776393	−0.388197	+	0.921577i	$0.626902\pi$
$42$	−0.375443	−0.0579321
$43$	0.341392	0.0520618	0.0260309	−	0.999661i	$-0.491713\pi$
$43$	0.341392	0.0520618	0.0260309	+	0.999661i	$0.491713\pi$
$44$	0.0817655	0.0123266
$45$	2.49678	0.372198
$46$	−1.99376	−0.293964
$47$	11.4407	1.66880	0.834402	−	0.551157i	$-0.185813\pi$
$47$	11.4407	1.66880	0.834402	+	0.551157i	$0.185813\pi$
$48$	−3.17413	−0.458145
$49$	1.00000	0.142857
$50$	0.463260	0.0655148
$51$	4.66254	0.652886
$52$	−2.29935	−0.318862
$53$	−4.41842	−0.606916	−0.303458	−	0.952845i	$-0.598141\pi$
$53$	−4.41842	−0.606916	−0.303458	+	0.952845i	$0.598141\pi$
$54$	−0.375443	−0.0510913
$55$	−0.109815	−0.0148074
$56$	−1.44885	−0.193611
$57$	4.55600	0.603457
$58$	−1.96654	−0.258219
$59$	9.78565	1.27398	0.636991	−	0.770871i	$-0.280179\pi$
$59$	9.78565	1.27398	0.636991	+	0.770871i	$0.280179\pi$
$60$	4.64162	0.599230
$61$	−9.42399	−1.20662	−0.603309	−	0.797508i	$-0.706151\pi$
$61$	−9.42399	−1.20662	−0.603309	+	0.797508i	$0.706151\pi$
$62$	0.268546	0.0341053
$63$	1.00000	0.125988
$64$	−4.81291	−0.601614
$65$	3.08813	0.383035
$66$	0.0165129	0.00203260
$67$	0.00811780	0.000991748 0	0.000495874	−	1.00000i	$-0.499842\pi$
$67$	0.00811780	0.000991748 0	0.000495874		1.00000i	$0.499842\pi$
$68$	8.66785	1.05113
$69$	5.31043	0.639301
$70$	0.937397	0.112040
$71$	−4.91418	−0.583206	−0.291603	−	0.956539i	$-0.594189\pi$
$71$	−4.91418	−0.583206	−0.291603	+	0.956539i	$0.594189\pi$
$72$	−1.44885	−0.170749
$73$	−11.8395	−1.38571	−0.692856	−	0.721076i	$-0.743648\pi$
$73$	−11.8395	−1.38571	−0.692856	+	0.721076i	$0.743648\pi$
$74$	2.96865	0.345098
$75$	−1.23390	−0.142479
$76$	8.46980	0.971553
$77$	−0.0439826	−0.00501228
$78$	−0.464365	−0.0525790
$79$	−1.44620	−0.162710	−0.0813552	−	0.996685i	$-0.525925\pi$
$79$	−1.44620	−0.162710	−0.0813552	+	0.996685i	$0.525925\pi$
$80$	7.92509	0.886052
$81$	1.00000	0.111111
$82$	−1.86645	−0.206115
$83$	−7.62022	−0.836428	−0.418214	−	0.908349i	$-0.637344\pi$
$83$	−7.62022	−0.836428	−0.418214	+	0.908349i	$0.637344\pi$
$84$	1.85904	0.202838
$85$	−11.6413	−1.26268
$86$	0.128173	0.0138213
$87$	5.23792	0.561564
$88$	0.0637241	0.00679301
$89$	−11.8328	−1.25427	−0.627137	−	0.778909i	$-0.715773\pi$
$89$	−11.8328	−1.25427	−0.627137	+	0.778909i	$0.715773\pi$
$90$	0.937397	0.0988104
$91$	1.23685	0.129657
$92$	9.87232	1.02926
$93$	−0.715277	−0.0741708
$94$	4.29534	0.443031
$95$	−11.3753	−1.16708
$96$	−4.08940	−0.417373
$97$	−8.97251	−0.911020	−0.455510	−	0.890231i	$-0.650543\pi$
$97$	−8.97251	−0.911020	−0.455510	+	0.890231i	$0.650543\pi$
$98$	0.375443	0.0379255
$99$	−0.0439826	−0.00442041
$100$	−2.29388	−0.229388
$101$	11.8979	1.18389	0.591943	−	0.805980i	$-0.298361\pi$
$101$	11.8979	1.18389	0.591943	+	0.805980i	$0.298361\pi$
$102$	1.75052	0.173327
$103$	3.32884	0.328000	0.164000	−	0.986460i	$-0.447560\pi$
$103$	3.32884	0.328000	0.164000	+	0.986460i	$0.447560\pi$
$104$	−1.79200	−0.175720
$105$	−2.49678	−0.243661
$106$	−1.65886	−0.161123
$107$	−11.7272	−1.13371	−0.566856	−	0.823817i	$-0.691841\pi$
$107$	−11.7272	−1.13371	−0.566856	+	0.823817i	$0.691841\pi$
$108$	1.85904	0.178886
$109$	−12.3647	−1.18432	−0.592161	−	0.805820i	$-0.701725\pi$
$109$	−12.3647	−1.18432	−0.592161	+	0.805820i	$0.701725\pi$
$110$	−0.0412291	−0.00393104
$111$	−7.90706	−0.750505
$112$	3.17413	0.299927
$113$	−11.5463	−1.08618	−0.543092	−	0.839673i	$-0.682747\pi$
$113$	−11.5463	−1.08618	−0.543092	+	0.839673i	$0.682747\pi$
$114$	1.71052	0.160205
$115$	−13.2590	−1.23641
$116$	9.73752	0.904106
$117$	1.23685	0.114346
$118$	3.67395	0.338215
$119$	−4.66254	−0.427414
$120$	3.61746	0.330227
$121$	−10.9981	−0.999824
$122$	−3.53817	−0.320331
$123$	4.97134	0.448251
$124$	−1.32973	−0.119413
$125$	−9.40311	−0.841040
$126$	0.375443	0.0334471
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−9.98578	−0.882626
$129$	−0.341392	−0.0300579
$130$	1.15942	0.101688
$131$	1.63563	0.142906	0.0714529	−	0.997444i	$-0.477236\pi$
$131$	1.63563	0.142906	0.0714529	+	0.997444i	$0.477236\pi$
$132$	−0.0817655	−0.00711677
$133$	−4.55600	−0.395056
$134$	0.00304777	0.000263287 0
$135$	−2.49678	−0.214888
$136$	6.75531	0.579263
$137$	4.20337	0.359118	0.179559	−	0.983747i	$-0.442533\pi$
$137$	4.20337	0.359118	0.179559	+	0.983747i	$0.442533\pi$
$138$	1.99376	0.169720
$139$	−1.83457	−0.155606	−0.0778030	−	0.996969i	$-0.524791\pi$
$139$	−1.83457	−0.155606	−0.0778030	+	0.996969i	$0.524791\pi$
$140$	−4.64162	−0.392288
$141$	−11.4407	−0.963484
$142$	−1.84499	−0.154828
$143$	−0.0543996	−0.00454913
$144$	3.17413	0.264510
$145$	−13.0779	−1.08606
$146$	−4.44506	−0.367876
$147$	−1.00000	−0.0824786
$148$	−14.6996	−1.20830
$149$	−14.6708	−1.20188	−0.600940	−	0.799294i	$-0.705207\pi$
$149$	−14.6708	−1.20188	−0.600940	+	0.799294i	$0.705207\pi$
$150$	−0.463260	−0.0378250
$151$	7.31356	0.595169	0.297585	−	0.954695i	$-0.403819\pi$
$151$	7.31356	0.595169	0.297585	+	0.954695i	$0.403819\pi$
$152$	6.60096	0.535409
$153$	−4.66254	−0.376944
$154$	−0.0165129	−0.00133065
$155$	1.78589	0.143446
$156$	2.29935	0.184095
$157$	5.65707	0.451483	0.225742	−	0.974187i	$-0.427519\pi$
$157$	5.65707	0.451483	0.225742	+	0.974187i	$0.427519\pi$
$158$	−0.542966	−0.0431961
$159$	4.41842	0.350403
$160$	10.2103	0.807198
$161$	−5.31043	−0.418521
$162$	0.375443	0.0294976
$163$	16.3284	1.27894	0.639470	−	0.768816i	$-0.279154\pi$
$163$	16.3284	1.27894	0.639470	+	0.768816i	$0.279154\pi$
$164$	9.24194	0.721674
$165$	0.109815	0.00854906
$166$	−2.86096	−0.222053
$167$	−12.9310	−1.00063	−0.500314	−	0.865844i	$-0.666782\pi$
$167$	−12.9310	−1.00063	−0.500314	+	0.865844i	$0.666782\pi$
$168$	1.44885	0.111781
$169$	−11.4702	−0.882324
$170$	−4.37065	−0.335213
$171$	−4.55600	−0.348406
$172$	−0.634663	−0.0483926
$173$	9.17036	0.697209	0.348605	−	0.937270i	$-0.386656\pi$
$173$	9.17036	0.697209	0.348605	+	0.937270i	$0.386656\pi$
$174$	1.96654	0.149083
$175$	1.23390	0.0932742
$176$	−0.139606	−0.0105232
$177$	−9.78565	−0.735534
$178$	−4.44254	−0.332982
$179$	−4.47476	−0.334459	−0.167230	−	0.985918i	$-0.553482\pi$
$179$	−4.47476	−0.334459	−0.167230	+	0.985918i	$0.553482\pi$
$180$	−4.64162	−0.345966
$181$	−10.6152	−0.789023	−0.394511	−	0.918891i	$-0.629086\pi$
$181$	−10.6152	−0.789023	−0.394511	+	0.918891i	$0.629086\pi$
$182$	0.464365	0.0344210
$183$	9.42399	0.696641
$184$	7.69402	0.567210
$185$	19.7422	1.45147
$186$	−0.268546	−0.0196907
$187$	0.205070	0.0149962
$188$	−21.2688	−1.55119
$189$	−1.00000	−0.0727393
$190$	−4.27079	−0.309835
$191$	10.6972	0.774020	0.387010	−	0.922075i	$-0.373508\pi$
$191$	10.6972	0.774020	0.387010	+	0.922075i	$0.373508\pi$
$192$	4.81291	0.347342
$193$	3.42294	0.246388	0.123194	−	0.992383i	$-0.460686\pi$
$193$	3.42294	0.246388	0.123194	+	0.992383i	$0.460686\pi$
$194$	−3.36866	−0.241856
$195$	−3.08813	−0.221146
$196$	−1.85904	−0.132789
$197$	12.6206	0.899181	0.449591	−	0.893235i	$-0.351570\pi$
$197$	12.6206	0.899181	0.449591	+	0.893235i	$0.351570\pi$
$198$	−0.0165129	−0.00117352
$199$	21.2114	1.50364	0.751819	−	0.659369i	$-0.229177\pi$
$199$	21.2114	1.50364	0.751819	+	0.659369i	$0.229177\pi$
$200$	−1.78774	−0.126412
$201$	−0.00811780	−0.000572586 0
$202$	4.46699	0.314296
$203$	−5.23792	−0.367630
$204$	−8.66785	−0.606871
$205$	−12.4123	−0.866915
$206$	1.24979	0.0870769
$207$	−5.31043	−0.369100
$208$	3.92590	0.272212
$209$	0.200385	0.0138609
$210$	−0.937397	−0.0646866
$211$	1.41420	0.0973575	0.0486788	−	0.998814i	$-0.484499\pi$
$211$	1.41420	0.0973575	0.0486788	+	0.998814i	$0.484499\pi$
$212$	8.21403	0.564142
$213$	4.91418	0.336714
$214$	−4.40290	−0.300976
$215$	0.852381	0.0581319
$216$	1.44885	0.0985817
$217$	0.715277	0.0485562
$218$	−4.64223	−0.314411
$219$	11.8395	0.800041
$220$	0.204150	0.0137638
$221$	−5.76684	−0.387919
$222$	−2.96865	−0.199243
$223$	−11.6705	−0.781512	−0.390756	−	0.920494i	$-0.627786\pi$
$223$	−11.6705	−0.781512	−0.390756	+	0.920494i	$0.627786\pi$
$224$	4.08940	0.273235
$225$	1.23390	0.0822601
$226$	−4.33497	−0.288358
$227$	−6.98427	−0.463562	−0.231781	−	0.972768i	$-0.574455\pi$
$227$	−6.98427	−0.463562	−0.231781	+	0.972768i	$0.574455\pi$
$228$	−8.46980	−0.560926
$229$	3.76335	0.248689	0.124345	−	0.992239i	$-0.460317\pi$
$229$	3.76335	0.248689	0.124345	+	0.992239i	$0.460317\pi$
$230$	−4.97798	−0.328239
$231$	0.0439826	0.00289384
$232$	7.58896	0.498240
$233$	−6.17050	−0.404243	−0.202121	−	0.979360i	$-0.564784\pi$
$233$	−6.17050	−0.404243	−0.202121	+	0.979360i	$0.564784\pi$
$234$	0.464365	0.0303565
$235$	28.5650	1.86337
$236$	−18.1919	−1.18419
$237$	1.44620	0.0939409
$238$	−1.75052	−0.113469
$239$	5.01726	0.324540	0.162270	−	0.986746i	$-0.448118\pi$
$239$	5.01726	0.324540	0.162270	+	0.986746i	$0.448118\pi$
$240$	−7.92509	−0.511562
$241$	−4.66693	−0.300623	−0.150312	−	0.988639i	$-0.548028\pi$
$241$	−4.66693	−0.300623	−0.150312	+	0.988639i	$0.548028\pi$
$242$	−4.12914	−0.265431
$243$	−1.00000	−0.0641500
$244$	17.5196	1.12158
$245$	2.49678	0.159513
$246$	1.86645	0.119001
$247$	−5.63507	−0.358551
$248$	−1.03633	−0.0658070
$249$	7.62022	0.482912
$250$	−3.53033	−0.223278
$251$	−14.9362	−0.942765	−0.471382	−	0.881929i	$-0.656245\pi$
$251$	−14.9362	−0.942765	−0.471382	+	0.881929i	$0.656245\pi$
$252$	−1.85904	−0.117109
$253$	0.233566	0.0146842
$254$	0.375443	0.0235574
$255$	11.6413	0.729008
$256$	5.87674	0.367296
$257$	2.50206	0.156074	0.0780370	−	0.996950i	$-0.475135\pi$
$257$	2.50206	0.156074	0.0780370	+	0.996950i	$0.475135\pi$
$258$	−0.128173	−0.00797972
$259$	7.90706	0.491321
$260$	−5.74096	−0.356040
$261$	−5.23792	−0.324219
$262$	0.614086	0.0379383
$263$	−3.74847	−0.231141	−0.115570	−	0.993299i	$-0.536870\pi$
$263$	−3.74847	−0.231141	−0.115570	+	0.993299i	$0.536870\pi$
$264$	−0.0637241	−0.00392195
$265$	−11.0318	−0.677679
$266$	−1.71052	−0.104879
$267$	11.8328	0.724155
$268$	−0.0150913	−0.000921851 0
$269$	8.16292	0.497702	0.248851	−	0.968542i	$-0.419947\pi$
$269$	8.16292	0.497702	0.248851	+	0.968542i	$0.419947\pi$
$270$	−0.937397	−0.0570482
$271$	−8.16035	−0.495706	−0.247853	−	0.968798i	$-0.579725\pi$
$271$	−8.16035	−0.495706	−0.247853	+	0.968798i	$0.579725\pi$
$272$	−14.7995	−0.897350
$273$	−1.23685	−0.0748573
$274$	1.57812	0.0953380
$275$	−0.0542702	−0.00327261
$276$	−9.87232	−0.594244
$277$	−19.5232	−1.17304	−0.586519	−	0.809935i	$-0.699502\pi$
$277$	−19.5232	−1.17304	−0.586519	+	0.809935i	$0.699502\pi$
$278$	−0.688775	−0.0413100
$279$	0.715277	0.0428225
$280$	−3.61746	−0.216184
$281$	−13.5957	−0.811052	−0.405526	−	0.914084i	$-0.632912\pi$
$281$	−13.5957	−0.811052	−0.405526	+	0.914084i	$0.632912\pi$
$282$	−4.29534	−0.255784
$283$	24.0199	1.42783	0.713917	−	0.700230i	$-0.246919\pi$
$283$	24.0199	1.42783	0.713917	+	0.700230i	$0.246919\pi$
$284$	9.13567	0.542102
$285$	11.3753	0.673816
$286$	−0.0204240	−0.00120769
$287$	−4.97134	−0.293449
$288$	4.08940	0.240970
$289$	4.73924	0.278779
$290$	−4.91001	−0.288326
$291$	8.97251	0.525978
$292$	22.0102	1.28805
$293$	−27.5825	−1.61138	−0.805692	−	0.592334i	$-0.798206\pi$
$293$	−27.5825	−1.61138	−0.805692	+	0.592334i	$0.798206\pi$
$294$	−0.375443	−0.0218963
$295$	24.4326	1.42252
$296$	−11.4561	−0.665875
$297$	0.0439826	0.00255213
$298$	−5.50806	−0.319073
$299$	−6.56818	−0.379848
$300$	2.29388	0.132437
$301$	0.341392	0.0196775
$302$	2.74582	0.158004
$303$	−11.8979	−0.683517
$304$	−14.4613	−0.829414
$305$	−23.5296	−1.34730
$306$	−1.75052	−0.100070
$307$	−24.8153	−1.41629	−0.708143	−	0.706069i	$-0.750467\pi$
$307$	−24.8153	−1.41629	−0.708143	+	0.706069i	$0.750467\pi$
$308$	0.0817655	0.00465902
$309$	−3.32884	−0.189371
$310$	0.670499	0.0380818
$311$	−0.788961	−0.0447379	−0.0223689	−	0.999750i	$-0.507121\pi$
$311$	−0.788961	−0.0447379	−0.0223689	+	0.999750i	$0.507121\pi$
$312$	1.79200	0.101452
$313$	16.4791	0.931453	0.465727	−	0.884929i	$-0.345793\pi$
$313$	16.4791	0.931453	0.465727	+	0.884929i	$0.345793\pi$
$314$	2.12391	0.119859
$315$	2.49678	0.140678
$316$	2.68855	0.151243
$317$	15.2893	0.858735	0.429367	−	0.903130i	$-0.358737\pi$
$317$	15.2893	0.858735	0.429367	+	0.903130i	$0.358737\pi$
$318$	1.65886	0.0930244
$319$	0.230377	0.0128986
$320$	−12.0168	−0.671758
$321$	11.7272	0.654549
$322$	−1.99376	−0.111108
$323$	21.2425	1.18197
$324$	−1.85904	−0.103280
$325$	1.52615	0.0846554
$326$	6.13039	0.339531
$327$	12.3647	0.683768
$328$	7.20273	0.397704
$329$	11.4407	0.630748
$330$	0.0412291	0.00226959
$331$	−8.79412	−0.483369	−0.241684	−	0.970355i	$-0.577700\pi$
$331$	−8.79412	−0.483369	−0.241684	+	0.970355i	$0.577700\pi$
$332$	14.1663	0.777477
$333$	7.90706	0.433304
$334$	−4.85484	−0.265645
$335$	0.0202684	0.00110738
$336$	−3.17413	−0.173163
$337$	10.3907	0.566015	0.283008	−	0.959118i	$-0.408668\pi$
$337$	10.3907	0.566015	0.283008	+	0.959118i	$0.408668\pi$
$338$	−4.30641	−0.234238
$339$	11.5463	0.627109
$340$	21.6417	1.17369
$341$	−0.0314597	−0.00170364
$342$	−1.71052	−0.0924943
$343$	1.00000	0.0539949
$344$	−0.494626	−0.0266684
$345$	13.2590	0.713839
$346$	3.44294	0.185094
$347$	−3.73798	−0.200665	−0.100333	−	0.994954i	$-0.531991\pi$
$347$	−3.73798	−0.200665	−0.100333	+	0.994954i	$0.531991\pi$
$348$	−9.73752	−0.521986
$349$	13.8895	0.743487	0.371744	−	0.928335i	$-0.378760\pi$
$349$	13.8895	0.743487	0.371744	+	0.928335i	$0.378760\pi$
$350$	0.463260	0.0247623
$351$	−1.23685	−0.0660179
$352$	−0.179862	−0.00958670
$353$	−29.3769	−1.56357	−0.781787	−	0.623546i	$-0.785691\pi$
$353$	−29.3769	−1.56357	−0.781787	+	0.623546i	$0.785691\pi$
$354$	−3.67395	−0.195268
$355$	−12.2696	−0.651204
$356$	21.9977	1.16587
$357$	4.66254	0.246768
$358$	−1.68002	−0.0887917
$359$	−3.99547	−0.210873	−0.105436	−	0.994426i	$-0.533624\pi$
$359$	−3.99547	−0.210873	−0.105436	+	0.994426i	$0.533624\pi$
$360$	−3.61746	−0.190657
$361$	1.75716	0.0924823
$362$	−3.98541	−0.209468
$363$	10.9981	0.577249
$364$	−2.29935	−0.120519
$365$	−29.5607	−1.54728
$366$	3.53817	0.184943
$367$	−15.8689	−0.828348	−0.414174	−	0.910198i	$-0.635929\pi$
$367$	−15.8689	−0.828348	−0.414174	+	0.910198i	$0.635929\pi$
$368$	−16.8560	−0.878678
$369$	−4.97134	−0.258798
$370$	7.41206	0.385335
$371$	−4.41842	−0.229393
$372$	1.32973	0.0689434
$373$	−1.79342	−0.0928595	−0.0464298	−	0.998922i	$-0.514784\pi$
$373$	−1.79342	−0.0928595	−0.0464298	+	0.998922i	$0.514784\pi$
$374$	0.0769922	0.00398117
$375$	9.40311	0.485575
$376$	−16.5759	−0.854837
$377$	−6.47850	−0.333660
$378$	−0.375443	−0.0193107
$379$	30.6924	1.57656	0.788280	−	0.615316i	$-0.210972\pi$
$379$	30.6924	1.57656	0.788280	+	0.615316i	$0.210972\pi$
$380$	21.1472	1.08483
$381$	−1.00000	−0.0512316
$382$	4.01618	0.205485
$383$	−13.9575	−0.713194	−0.356597	−	0.934258i	$-0.616063\pi$
$383$	−13.9575	−0.713194	−0.356597	+	0.934258i	$0.616063\pi$
$384$	9.98578	0.509585
$385$	−0.109815	−0.00559668
$386$	1.28512	0.0654107
$387$	0.341392	0.0173539
$388$	16.6803	0.846813
$389$	31.4166	1.59288	0.796442	−	0.604715i	$-0.206713\pi$
$389$	31.4166	1.59288	0.796442	+	0.604715i	$0.206713\pi$
$390$	−1.15942	−0.0587093
$391$	24.7601	1.25217
$392$	−1.44885	−0.0731780
$393$	−1.63563	−0.0825067
$394$	4.73832	0.238713
$395$	−3.61085	−0.181681
$396$	0.0817655	0.00410887
$397$	4.14664	0.208114	0.104057	−	0.994571i	$-0.466818\pi$
$397$	4.14664	0.208114	0.104057	+	0.994571i	$0.466818\pi$
$398$	7.96368	0.399183
$399$	4.55600	0.228085
$400$	3.91656	0.195828
$401$	23.0458	1.15085	0.575427	−	0.817853i	$-0.304836\pi$
$401$	23.0458	1.15085	0.575427	+	0.817853i	$0.304836\pi$
$402$	−0.00304777	−0.000152009 0
$403$	0.884688	0.0440694
$404$	−22.1187	−1.10045
$405$	2.49678	0.124066
$406$	−1.96654	−0.0975977
$407$	−0.347773	−0.0172385
$408$	−6.75531	−0.334438
$409$	10.6304	0.525639	0.262819	−	0.964845i	$-0.415348\pi$
$409$	10.6304	0.525639	0.262819	+	0.964845i	$0.415348\pi$
$410$	−4.66012	−0.230147
$411$	−4.20337	−0.207337
$412$	−6.18845	−0.304883
$413$	9.78565	0.481520
$414$	−1.99376	−0.0979881
$415$	−19.0260	−0.933950
$416$	5.05796	0.247987
$417$	1.83457	0.0898391
$418$	0.0752330	0.00367977
$419$	0.439830	0.0214871	0.0107436	−	0.999942i	$-0.496580\pi$
$419$	0.439830	0.0214871	0.0107436	+	0.999942i	$0.496580\pi$
$420$	4.64162	0.226488
$421$	30.3492	1.47913	0.739564	−	0.673087i	$-0.235032\pi$
$421$	30.3492	1.47913	0.739564	+	0.673087i	$0.235032\pi$
$422$	0.530951	0.0258463
$423$	11.4407	0.556268
$424$	6.40162	0.310890
$425$	−5.75311	−0.279067
$426$	1.84499	0.0893903
$427$	−9.42399	−0.456059
$428$	21.8014	1.05381
$429$	0.0543996	0.00262644
$430$	0.320020	0.0154327
$431$	8.63673	0.416017	0.208008	−	0.978127i	$-0.433302\pi$
$431$	8.63673	0.416017	0.208008	+	0.978127i	$0.433302\pi$
$432$	−3.17413	−0.152715
$433$	9.34002	0.448853	0.224426	−	0.974491i	$-0.427949\pi$
$433$	9.34002	0.448853	0.224426	+	0.974491i	$0.427949\pi$
$434$	0.268546	0.0128906
$435$	13.0779	0.627038
$436$	22.9865	1.10085
$437$	24.1943	1.15737
$438$	4.44506	0.212393
$439$	4.79533	0.228869	0.114434	−	0.993431i	$-0.463494\pi$
$439$	4.79533	0.228869	0.114434	+	0.993431i	$0.463494\pi$
$440$	0.159105	0.00758503
$441$	1.00000	0.0476190
$442$	−2.16512	−0.102984
$443$	−9.57969	−0.455145	−0.227572	−	0.973761i	$-0.573079\pi$
$443$	−9.57969	−0.455145	−0.227572	+	0.973761i	$0.573079\pi$
$444$	14.6996	0.697610
$445$	−29.5439	−1.40051
$446$	−4.38159	−0.207474
$447$	14.6708	0.693906
$448$	−4.81291	−0.227389
$449$	−22.2178	−1.04852	−0.524262	−	0.851557i	$-0.675659\pi$
$449$	−22.2178	−1.04852	−0.524262	+	0.851557i	$0.675659\pi$
$450$	0.463260	0.0218383
$451$	0.218652	0.0102959
$452$	21.4651	1.00963
$453$	−7.31356	−0.343621
$454$	−2.62219	−0.123066
$455$	3.08813	0.144774
$456$	−6.60096	−0.309118
$457$	32.8310	1.53577	0.767884	−	0.640589i	$-0.221310\pi$
$457$	32.8310	1.53577	0.767884	+	0.640589i	$0.221310\pi$
$458$	1.41292	0.0660216
$459$	4.66254	0.217629
$460$	24.6490	1.14927
$461$	−7.65926	−0.356727	−0.178364	−	0.983965i	$-0.557080\pi$
$461$	−7.65926	−0.356727	−0.178364	+	0.983965i	$0.557080\pi$
$462$	0.0165129	0.000768251 0
$463$	38.3105	1.78044	0.890220	−	0.455530i	$-0.150550\pi$
$463$	38.3105	1.78044	0.890220	+	0.455530i	$0.150550\pi$
$464$	−16.6258	−0.771834
$465$	−1.78589	−0.0828186
$466$	−2.31667	−0.107318
$467$	−35.9613	−1.66409	−0.832046	−	0.554707i	$-0.812830\pi$
$467$	−35.9613	−1.66409	−0.832046	+	0.554707i	$0.812830\pi$
$468$	−2.29935	−0.106287
$469$	0.00811780	0.000374845 0
$470$	10.7245	0.494685
$471$	−5.65707	−0.260664
$472$	−14.1779	−0.652592
$473$	−0.0150153	−0.000690404 0
$474$	0.542966	0.0249393
$475$	−5.62166	−0.257939
$476$	8.66785	0.397290
$477$	−4.41842	−0.202305
$478$	1.88370	0.0861582
$479$	9.37274	0.428251	0.214126	−	0.976806i	$-0.431310\pi$
$479$	9.37274	0.428251	0.214126	+	0.976806i	$0.431310\pi$
$480$	−10.2103	−0.466036
$481$	9.77981	0.445921
$482$	−1.75217	−0.0798089
$483$	5.31043	0.241633
$484$	20.4459	0.929358
$485$	−22.4024	−1.01724
$486$	−0.375443	−0.0170304
$487$	41.8227	1.89517	0.947584	−	0.319507i	$-0.103517\pi$
$487$	41.8227	1.89517	0.947584	+	0.319507i	$0.103517\pi$
$488$	13.6539	0.618085
$489$	−16.3284	−0.738397
$490$	0.937397	0.0423473
$491$	15.2407	0.687802	0.343901	−	0.939006i	$-0.388252\pi$
$491$	15.2407	0.687802	0.343901	+	0.939006i	$0.388252\pi$
$492$	−9.24194	−0.416659
$493$	24.4220	1.09991
$494$	−2.11565	−0.0951875
$495$	−0.109815	−0.00493580
$496$	2.27038	0.101943
$497$	−4.91418	−0.220431
$498$	2.86096	0.128203
$499$	18.6214	0.833608	0.416804	−	0.908996i	$-0.363150\pi$
$499$	18.6214	0.833608	0.416804	+	0.908996i	$0.363150\pi$
$500$	17.4808	0.781765
$501$	12.9310	0.577713
$502$	−5.60769	−0.250283
$503$	−40.6766	−1.81368	−0.906841	−	0.421474i	$-0.861513\pi$
$503$	−40.6766	−1.81368	−0.906841	+	0.421474i	$0.861513\pi$
$504$	−1.44885	−0.0645369
$505$	29.7064	1.32192
$506$	0.0876908	0.00389833
$507$	11.4702	0.509410
$508$	−1.85904	−0.0824817
$509$	33.9922	1.50668	0.753340	−	0.657631i	$-0.228442\pi$
$509$	33.9922	1.50668	0.753340	+	0.657631i	$0.228442\pi$
$510$	4.37065	0.193536
$511$	−11.8395	−0.523750
$512$	22.1779	0.980136
$513$	4.55600	0.201152
$514$	0.939379	0.0414342
$515$	8.31137	0.366243
$516$	0.634663	0.0279395
$517$	−0.503193	−0.0221304
$518$	2.96865	0.130435
$519$	−9.17036	−0.402534
$520$	−4.47424	−0.196208
$521$	−1.31867	−0.0577722	−0.0288861	−	0.999583i	$-0.509196\pi$
$521$	−1.31867	−0.0577722	−0.0288861	+	0.999583i	$0.509196\pi$
$522$	−1.96654	−0.0860731
$523$	−30.7412	−1.34422	−0.672109	−	0.740452i	$-0.734611\pi$
$523$	−30.7412	−1.34422	−0.672109	+	0.740452i	$0.734611\pi$
$524$	−3.04071	−0.132834
$525$	−1.23390	−0.0538519
$526$	−1.40734	−0.0613628
$527$	−3.33501	−0.145275
$528$	0.139606	0.00607558
$529$	5.20068	0.226116
$530$	−4.14181	−0.179909
$531$	9.78565	0.424661
$532$	8.46980	0.367213
$533$	−6.14878	−0.266333
$534$	4.44254	0.192247
$535$	−29.2803	−1.26590
$536$	−0.0117615	−0.000508019 0
$537$	4.47476	0.193100
$538$	3.06471	0.132129
$539$	−0.0439826	−0.00189446
$540$	4.64162	0.199743
$541$	16.8366	0.723860	0.361930	−	0.932205i	$-0.382118\pi$
$541$	16.8366	0.723860	0.361930	+	0.932205i	$0.382118\pi$
$542$	−3.06374	−0.131599
$543$	10.6152	0.455542
$544$	−19.0670	−0.817490
$545$	−30.8719	−1.32241
$546$	−0.464365	−0.0198730
$547$	16.8752	0.721531	0.360766	−	0.932656i	$-0.382515\pi$
$547$	16.8752	0.721531	0.360766	+	0.932656i	$0.382515\pi$
$548$	−7.81424	−0.333808
$549$	−9.42399	−0.402206
$550$	−0.0203753	−0.000868807 0
$551$	23.8640	1.01664
$552$	−7.69402	−0.327479
$553$	−1.44620	−0.0614988
$554$	−7.32986	−0.311416
$555$	−19.7422	−0.838009
$556$	3.41054	0.144639
$557$	−31.2255	−1.32307	−0.661534	−	0.749915i	$-0.730094\pi$
$557$	−31.2255	−1.32307	−0.661534	+	0.749915i	$0.730094\pi$
$558$	0.268546	0.0113684
$559$	0.422249	0.0178592
$560$	7.92509	0.334896
$561$	−0.205070	−0.00865807
$562$	−5.10441	−0.215317
$563$	−12.2339	−0.515595	−0.257798	−	0.966199i	$-0.582997\pi$
$563$	−12.2339	−0.515595	−0.257798	+	0.966199i	$0.582997\pi$
$564$	21.2688	0.895579
$565$	−28.8285	−1.21283
$566$	9.01810	0.379059
$567$	1.00000	0.0419961
$568$	7.11991	0.298745
$569$	−16.3199	−0.684164	−0.342082	−	0.939670i	$-0.611132\pi$
$569$	−16.3199	−0.684164	−0.342082	+	0.939670i	$0.611132\pi$
$570$	4.27079	0.178884
$571$	0.774915	0.0324292	0.0162146	−	0.999869i	$-0.494839\pi$
$571$	0.774915	0.0324292	0.0162146	+	0.999869i	$0.494839\pi$
$572$	0.101131	0.00422851
$573$	−10.6972	−0.446881
$574$	−1.86645	−0.0779043
$575$	−6.55255	−0.273260
$576$	−4.81291	−0.200538
$577$	13.3038	0.553845	0.276922	−	0.960892i	$-0.410685\pi$
$577$	13.3038	0.553845	0.276922	+	0.960892i	$0.410685\pi$
$578$	1.77931	0.0740097
$579$	−3.42294	−0.142252
$580$	24.3124	1.00952
$581$	−7.62022	−0.316140
$582$	3.36866	0.139636
$583$	0.194333	0.00804846
$584$	17.1537	0.709825
$585$	3.08813	0.127678
$586$	−10.3556	−0.427787
$587$	1.02046	0.0421187	0.0210594	−	0.999778i	$-0.493296\pi$
$587$	1.02046	0.0421187	0.0210594	+	0.999778i	$0.493296\pi$
$588$	1.85904	0.0766656
$589$	−3.25881	−0.134277
$590$	9.17304	0.377648
$591$	−12.6206	−0.519143
$592$	25.0980	1.03152
$593$	−22.7116	−0.932655	−0.466327	−	0.884612i	$-0.654423\pi$
$593$	−22.7116	−0.932655	−0.466327	+	0.884612i	$0.654423\pi$
$594$	0.0165129	0.000677534 0
$595$	−11.6413	−0.477248
$596$	27.2737	1.11717
$597$	−21.2114	−0.868126
$598$	−2.46598	−0.100841
$599$	25.5601	1.04436	0.522180	−	0.852835i	$-0.325119\pi$
$599$	25.5601	1.04436	0.522180	+	0.852835i	$0.325119\pi$
$600$	1.78774	0.0729841
$601$	−26.9352	−1.09871	−0.549355	−	0.835589i	$-0.685127\pi$
$601$	−26.9352	−1.09871	−0.549355	+	0.835589i	$0.685127\pi$
$602$	0.128173	0.00522395
$603$	0.00811780	0.000330583 0
$604$	−13.5962	−0.553222
$605$	−27.4597	−1.11640
$606$	−4.46699	−0.181459
$607$	37.3334	1.51532	0.757659	−	0.652651i	$-0.226343\pi$
$607$	37.3334	1.51532	0.757659	+	0.652651i	$0.226343\pi$
$608$	−18.6313	−0.755600
$609$	5.23792	0.212251
$610$	−8.83402	−0.357679
$611$	14.1504	0.572465
$612$	8.66785	0.350377
$613$	24.7374	0.999135	0.499568	−	0.866275i	$-0.333492\pi$
$613$	24.7374	0.999135	0.499568	+	0.866275i	$0.333492\pi$
$614$	−9.31674	−0.375993
$615$	12.4123	0.500514
$616$	0.0637241	0.00256752
$617$	1.99796	0.0804347	0.0402173	−	0.999191i	$-0.487195\pi$
$617$	1.99796	0.0804347	0.0402173	+	0.999191i	$0.487195\pi$
$618$	−1.24979	−0.0502739
$619$	−12.8044	−0.514654	−0.257327	−	0.966324i	$-0.582842\pi$
$619$	−12.8044	−0.514654	−0.257327	+	0.966324i	$0.582842\pi$
$620$	−3.32004	−0.133336
$621$	5.31043	0.213100
$622$	−0.296210	−0.0118769
$623$	−11.8328	−0.474071
$624$	−3.92590	−0.157162
$625$	−29.6470	−1.18588
$626$	6.18696	0.247280
$627$	−0.200385	−0.00800259
$628$	−10.5167	−0.419663
$629$	−36.8670	−1.46998
$630$	0.937397	0.0373468
$631$	48.1211	1.91567	0.957836	−	0.287315i	$-0.0927625\pi$
$631$	48.1211	1.91567	0.957836	+	0.287315i	$0.0927625\pi$
$632$	2.09533	0.0833477
$633$	−1.41420	−0.0562094
$634$	5.74027	0.227975
$635$	2.49678	0.0990816
$636$	−8.21403	−0.325707
$637$	1.23685	0.0490056
$638$	0.0864934	0.00342431
$639$	−4.91418	−0.194402
$640$	−24.9323	−0.985535
$641$	−27.7591	−1.09642	−0.548209	−	0.836341i	$-0.684690\pi$
$641$	−27.7591	−1.09642	−0.548209	+	0.836341i	$0.684690\pi$
$642$	4.40290	0.173769
$643$	10.3622	0.408647	0.204323	−	0.978903i	$-0.434501\pi$
$643$	10.3622	0.408647	0.204323	+	0.978903i	$0.434501\pi$
$644$	9.87232	0.389024
$645$	−0.852381	−0.0335625
$646$	7.97535	0.313786
$647$	27.9465	1.09869	0.549345	−	0.835596i	$-0.314877\pi$
$647$	27.9465	1.09869	0.549345	+	0.835596i	$0.314877\pi$
$648$	−1.44885	−0.0569162
$649$	−0.430398	−0.0168946
$650$	0.572981	0.0224741
$651$	−0.715277	−0.0280339
$652$	−30.3552	−1.18880
$653$	28.5640	1.11780	0.558898	−	0.829237i	$-0.311225\pi$
$653$	28.5640	1.11780	0.558898	+	0.829237i	$0.311225\pi$
$654$	4.64223	0.181526
$655$	4.08381	0.159568
$656$	−15.7797	−0.616092
$657$	−11.8395	−0.461904
$658$	4.29534	0.167450
$659$	−21.4088	−0.833967	−0.416983	−	0.908914i	$-0.636913\pi$
$659$	−21.4088	−0.833967	−0.416983	+	0.908914i	$0.636913\pi$
$660$	−0.204150	−0.00794654
$661$	−9.97679	−0.388052	−0.194026	−	0.980996i	$-0.562155\pi$
$661$	−9.97679	−0.388052	−0.194026	+	0.980996i	$0.562155\pi$
$662$	−3.30169	−0.128324
$663$	5.76684	0.223965
$664$	11.0406	0.428457
$665$	−11.3753	−0.441116
$666$	2.96865	0.115033
$667$	27.8156	1.07702
$668$	24.0392	0.930105
$669$	11.6705	0.451206
$670$	0.00760961	0.000293985 0
$671$	0.414491	0.0160012
$672$	−4.08940	−0.157752
$673$	13.9270	0.536846	0.268423	−	0.963301i	$-0.413498\pi$
$673$	13.9270	0.536846	0.268423	+	0.963301i	$0.413498\pi$
$674$	3.90110	0.150265
$675$	−1.23390	−0.0474929
$676$	21.3236	0.820139
$677$	36.3413	1.39671	0.698355	−	0.715752i	$-0.253916\pi$
$677$	36.3413	1.39671	0.698355	+	0.715752i	$0.253916\pi$
$678$	4.33497	0.166484
$679$	−8.97251	−0.344333
$680$	16.8665	0.646802
$681$	6.98427	0.267638
$682$	−0.0118113	−0.000452279 0
$683$	29.4074	1.12524	0.562621	−	0.826715i	$-0.309793\pi$
$683$	29.4074	1.12524	0.562621	+	0.826715i	$0.309793\pi$
$684$	8.46980	0.323851
$685$	10.4949	0.400989
$686$	0.375443	0.0143345
$687$	−3.76335	−0.143581
$688$	1.08362	0.0413127
$689$	−5.46490	−0.208196
$690$	4.97798	0.189509
$691$	−30.7917	−1.17137	−0.585685	−	0.810539i	$-0.699175\pi$
$691$	−30.7917	−1.17137	−0.585685	+	0.810539i	$0.699175\pi$
$692$	−17.0481	−0.648071
$693$	−0.0439826	−0.00167076
$694$	−1.40340	−0.0532722
$695$	−4.58051	−0.173749
$696$	−7.58896	−0.287659
$697$	23.1791	0.877970
$698$	5.21471	0.197380
$699$	6.17050	0.233390
$700$	−2.29388	−0.0867004
$701$	18.0737	0.682636	0.341318	−	0.939948i	$-0.389127\pi$
$701$	18.0737	0.682636	0.341318	+	0.939948i	$0.389127\pi$
$702$	−0.464365	−0.0175263
$703$	−36.0246	−1.35869
$704$	0.211684	0.00797815
$705$	−28.5650	−1.07582
$706$	−11.0293	−0.415095
$707$	11.8979	0.447467
$708$	18.1919	0.683695
$709$	−16.5066	−0.619919	−0.309960	−	0.950750i	$-0.600316\pi$
$709$	−16.5066	−0.619919	−0.309960	+	0.950750i	$0.600316\pi$
$710$	−4.60654	−0.172880
$711$	−1.44620	−0.0542368
$712$	17.1439	0.642496
$713$	−3.79843	−0.142252
$714$	1.75052	0.0655114
$715$	−0.135824	−0.00507952
$716$	8.31878	0.310887
$717$	−5.01726	−0.187373
$718$	−1.50007	−0.0559821
$719$	−28.8143	−1.07459	−0.537296	−	0.843394i	$-0.680554\pi$
$719$	−28.8143	−1.07459	−0.537296	+	0.843394i	$0.680554\pi$
$720$	7.92509	0.295351
$721$	3.32884	0.123972
$722$	0.659715	0.0245520
$723$	4.66693	0.173565
$724$	19.7341	0.733413
$725$	−6.46308	−0.240033
$726$	4.12914	0.153247
$727$	37.2045	1.37984	0.689920	−	0.723886i	$-0.257646\pi$
$727$	37.2045	1.37984	0.689920	+	0.723886i	$0.257646\pi$
$728$	−1.79200	−0.0664161
$729$	1.00000	0.0370370
$730$	−11.0983	−0.410768
$731$	−1.59175	−0.0588731
$732$	−17.5196	−0.647543
$733$	17.7329	0.654980	0.327490	−	0.944855i	$-0.393797\pi$
$733$	17.7329	0.654980	0.327490	+	0.944855i	$0.393797\pi$
$734$	−5.95785	−0.219908
$735$	−2.49678	−0.0920951
$736$	−21.7165	−0.800480
$737$	−0.000357042 0	−1.31518e−5 0
$738$	−1.86645	−0.0687052
$739$	−15.1053	−0.555658	−0.277829	−	0.960631i	$-0.589615\pi$
$739$	−15.1053	−0.555658	−0.277829	+	0.960631i	$0.589615\pi$
$740$	−36.7015	−1.34918
$741$	5.63507	0.207010
$742$	−1.65886	−0.0608988
$743$	−47.6088	−1.74660	−0.873299	−	0.487184i	$-0.838024\pi$
$743$	−47.6088	−1.74660	−0.873299	+	0.487184i	$0.838024\pi$
$744$	1.03633	0.0379937
$745$	−36.6298	−1.34201
$746$	−0.673325	−0.0246522
$747$	−7.62022	−0.278809
$748$	−0.381234	−0.0139393
$749$	−11.7272	−0.428503
$750$	3.53033	0.128909
$751$	7.36875	0.268890	0.134445	−	0.990921i	$-0.457075\pi$
$751$	7.36875	0.268890	0.134445	+	0.990921i	$0.457075\pi$
$752$	36.3143	1.32425
$753$	14.9362	0.544306
$754$	−2.43231	−0.0885793
$755$	18.2603	0.664562
$756$	1.85904	0.0676127
$757$	−2.31274	−0.0840581	−0.0420291	−	0.999116i	$-0.513382\pi$
$757$	−2.31274	−0.0840581	−0.0420291	+	0.999116i	$0.513382\pi$
$758$	11.5232	0.418543
$759$	−0.233566	−0.00847792
$760$	16.4811	0.597834
$761$	−34.4910	−1.25030	−0.625149	−	0.780506i	$-0.714962\pi$
$761$	−34.4910	−1.25030	−0.625149	+	0.780506i	$0.714962\pi$
$762$	−0.375443	−0.0136009
$763$	−12.3647	−0.447631
$764$	−19.8865	−0.719468
$765$	−11.6413	−0.420893
$766$	−5.24024	−0.189337
$767$	12.1033	0.437026
$768$	−5.87674	−0.212059
$769$	−42.3387	−1.52677	−0.763387	−	0.645941i	$-0.776465\pi$
$769$	−42.3387	−1.52677	−0.763387	+	0.645941i	$0.776465\pi$
$770$	−0.0412291	−0.00148580
$771$	−2.50206	−0.0901093
$772$	−6.36339	−0.229023
$773$	−35.6992	−1.28401	−0.642006	−	0.766700i	$-0.721898\pi$
$773$	−35.6992	−1.28401	−0.642006	+	0.766700i	$0.721898\pi$
$774$	0.128173	0.00460709
$775$	0.882582	0.0317033
$776$	12.9998	0.466666
$777$	−7.90706	−0.283664
$778$	11.7951	0.422876
$779$	22.6495	0.811501
$780$	5.74096	0.205560
$781$	0.216138	0.00773404
$782$	9.29599	0.332424
$783$	5.23792	0.187188
$784$	3.17413	0.113362
$785$	14.1244	0.504123
$786$	−0.614086	−0.0219037
$787$	−43.8015	−1.56135	−0.780677	−	0.624935i	$-0.785125\pi$
$787$	−43.8015	−1.56135	−0.780677	+	0.624935i	$0.785125\pi$
$788$	−23.4623	−0.835808
$789$	3.74847	0.133449
$790$	−1.35567	−0.0482324
$791$	−11.5463	−0.410539
$792$	0.0637241	0.00226434
$793$	−11.6560	−0.413917
$794$	1.55683	0.0552497
$795$	11.0318	0.391258
$796$	−39.4329	−1.39766
$797$	−31.2751	−1.10782	−0.553910	−	0.832577i	$-0.686865\pi$
$797$	−31.2751	−1.10782	−0.553910	+	0.832577i	$0.686865\pi$
$798$	1.71052	0.0605517
$799$	−53.3428	−1.88713
$800$	5.04592	0.178400
$801$	−11.8328	−0.418091
$802$	8.65240	0.305527
$803$	0.520733	0.0183763
$804$	0.0150913	0.000532231 0
$805$	−13.2590	−0.467317
$806$	0.332150	0.0116995
$807$	−8.16292	−0.287348
$808$	−17.2383	−0.606441
$809$	15.2691	0.536834	0.268417	−	0.963303i	$-0.413499\pi$
$809$	15.2691	0.536834	0.268417	+	0.963303i	$0.413499\pi$
$810$	0.937397	0.0329368
$811$	12.6537	0.444332	0.222166	−	0.975009i	$-0.428687\pi$
$811$	12.6537	0.444332	0.222166	+	0.975009i	$0.428687\pi$
$812$	9.73752	0.341720
$813$	8.16035	0.286196
$814$	−0.130569	−0.00457643
$815$	40.7684	1.42806
$816$	14.7995	0.518085
$817$	−1.55538	−0.0544160
$818$	3.99110	0.139546
$819$	1.23685	0.0432189
$820$	23.0751	0.805816
$821$	34.4322	1.20169	0.600846	−	0.799365i	$-0.294831\pi$
$821$	34.4322	1.20169	0.600846	+	0.799365i	$0.294831\pi$
$822$	−1.57812	−0.0550434
$823$	−37.0847	−1.29269	−0.646346	−	0.763044i	$-0.723704\pi$
$823$	−37.0847	−1.29269	−0.646346	+	0.763044i	$0.723704\pi$
$824$	−4.82299	−0.168017
$825$	0.0542702	0.00188944
$826$	3.67395	0.127833
$827$	40.9578	1.42424	0.712120	−	0.702057i	$-0.247735\pi$
$827$	40.9578	1.42424	0.712120	+	0.702057i	$0.247735\pi$
$828$	9.87232	0.343087
$829$	38.7169	1.34469	0.672346	−	0.740237i	$-0.265287\pi$
$829$	38.7169	1.34469	0.672346	+	0.740237i	$0.265287\pi$
$830$	−7.14317	−0.247943
$831$	19.5232	0.677254
$832$	−5.95283	−0.206377
$833$	−4.66254	−0.161547
$834$	0.688775	0.0238503
$835$	−32.2857	−1.11729
$836$	−0.372524	−0.0128840
$837$	−0.715277	−0.0247236
$838$	0.165131	0.00570436
$839$	41.1323	1.42005	0.710023	−	0.704179i	$-0.248685\pi$
$839$	41.1323	1.42005	0.710023	+	0.704179i	$0.248685\pi$
$840$	3.61746	0.124814
$841$	−1.56420	−0.0539380
$842$	11.3944	0.392676
$843$	13.5957	0.468261
$844$	−2.62906	−0.0904959
$845$	−28.6386	−0.985197
$846$	4.29534	0.147677
$847$	−10.9981	−0.377898
$848$	−14.0246	−0.481607
$849$	−24.0199	−0.824360
$850$	−2.15996	−0.0740862
$851$	−41.9899	−1.43940
$852$	−9.13567	−0.312983
$853$	−17.8259	−0.610348	−0.305174	−	0.952297i	$-0.598715\pi$
$853$	−17.8259	−0.610348	−0.305174	+	0.952297i	$0.598715\pi$
$854$	−3.53817	−0.121074
$855$	−11.3753	−0.389028
$856$	16.9910	0.580739
$857$	−52.7623	−1.80233	−0.901164	−	0.433479i	$-0.857286\pi$
$857$	−52.7623	−1.80233	−0.901164	+	0.433479i	$0.857286\pi$
$858$	0.0204240	0.000697262 0
$859$	−52.2180	−1.78166	−0.890828	−	0.454341i	$-0.849875\pi$
$859$	−52.2180	−1.78166	−0.890828	+	0.454341i	$0.849875\pi$
$860$	−1.58461	−0.0540348
$861$	4.97134	0.169423
$862$	3.24260	0.110443
$863$	−16.7285	−0.569446	−0.284723	−	0.958610i	$-0.591902\pi$
$863$	−16.7285	−0.569446	−0.284723	+	0.958610i	$0.591902\pi$
$864$	−4.08940	−0.139124
$865$	22.8963	0.778499
$866$	3.50664	0.119161
$867$	−4.73924	−0.160953
$868$	−1.32973	−0.0451340
$869$	0.0636077	0.00215774
$870$	4.91001	0.166465
$871$	0.0100405	0.000340208 0
$872$	17.9146	0.606664
$873$	−8.97251	−0.303673
$874$	9.08359	0.307257
$875$	−9.40311	−0.317883
$876$	−22.0102	−0.743655
$877$	−3.86764	−0.130601	−0.0653005	−	0.997866i	$-0.520801\pi$
$877$	−3.86764	−0.130601	−0.0653005	+	0.997866i	$0.520801\pi$
$878$	1.80037	0.0607596
$879$	27.5825	0.930333
$880$	−0.348566	−0.0117501
$881$	22.2193	0.748586	0.374293	−	0.927311i	$-0.377885\pi$
$881$	22.2193	0.748586	0.374293	+	0.927311i	$0.377885\pi$
$882$	0.375443	0.0126418
$883$	−3.75514	−0.126370	−0.0631852	−	0.998002i	$-0.520126\pi$
$883$	−3.75514	−0.126370	−0.0631852	+	0.998002i	$0.520126\pi$
$884$	10.7208	0.360579
$885$	−24.4326	−0.821293
$886$	−3.59662	−0.120831
$887$	54.5326	1.83102	0.915512	−	0.402291i	$-0.131786\pi$
$887$	54.5326	1.83102	0.915512	+	0.402291i	$0.131786\pi$
$888$	11.4561	0.384443
$889$	1.00000	0.0335389
$890$	−11.0920	−0.371806
$891$	−0.0439826	−0.00147347
$892$	21.6959	0.726432
$893$	−52.1240	−1.74426
$894$	5.50806	0.184217
$895$	−11.1725	−0.373455
$896$	−9.98578	−0.333601
$897$	6.56818	0.219305
$898$	−8.34152	−0.278360
$899$	−3.74657	−0.124955
$900$	−2.29388	−0.0764625
$901$	20.6010	0.686320
$902$	0.0820915	0.00273335
$903$	−0.341392	−0.0113608
$904$	16.7288	0.556393
$905$	−26.5038	−0.881017
$906$	−2.74582	−0.0912239
$907$	42.1002	1.39791	0.698957	−	0.715163i	$-0.253648\pi$
$907$	42.1002	1.39791	0.698957	+	0.715163i	$0.253648\pi$
$908$	12.9841	0.430891
$909$	11.8979	0.394629
$910$	1.15942	0.0384343
$911$	25.1777	0.834173	0.417086	−	0.908867i	$-0.363051\pi$
$911$	25.1777	0.834173	0.417086	+	0.908867i	$0.363051\pi$
$912$	14.4613	0.478862
$913$	0.335157	0.0110921
$914$	12.3261	0.407713
$915$	23.5296	0.777865
$916$	−6.99624	−0.231162
$917$	1.63563	0.0540133
$918$	1.75052	0.0577756
$919$	3.16307	0.104340	0.0521699	−	0.998638i	$-0.483386\pi$
$919$	3.16307	0.104340	0.0521699	+	0.998638i	$0.483386\pi$
$920$	19.2103	0.633343
$921$	24.8153	0.817693
$922$	−2.87561	−0.0947033
$923$	−6.07808	−0.200063
$924$	−0.0817655	−0.00268989
$925$	9.75654	0.320793
$926$	14.3834	0.472668
$927$	3.32884	0.109333
$928$	−21.4200	−0.703145
$929$	14.3412	0.470519	0.235260	−	0.971933i	$-0.424406\pi$
$929$	14.3412	0.470519	0.235260	+	0.971933i	$0.424406\pi$
$930$	−0.670499	−0.0219865
$931$	−4.55600	−0.149317
$932$	11.4712	0.375752
$933$	0.788961	0.0258294
$934$	−13.5014	−0.441780
$935$	0.512015	0.0167447
$936$	−1.79200	−0.0585735
$937$	42.7371	1.39616	0.698080	−	0.716020i	$-0.254038\pi$
$937$	42.7371	1.39616	0.698080	+	0.716020i	$0.254038\pi$
$938$	0.00304777	9.95133e−5 0
$939$	−16.4791	−0.537775
$940$	−53.1035	−1.73205
$941$	−4.82197	−0.157192	−0.0785958	−	0.996907i	$-0.525044\pi$
$941$	−4.82197	−0.157192	−0.0785958	+	0.996907i	$0.525044\pi$
$942$	−2.12391	−0.0692006
$943$	26.4000	0.859701
$944$	31.0609	1.01095
$945$	−2.49678	−0.0812202
$946$	−0.00563739	−0.000183287 0
$947$	14.0659	0.457080	0.228540	−	0.973535i	$-0.426605\pi$
$947$	14.0659	0.457080	0.228540	+	0.973535i	$0.426605\pi$
$948$	−2.68855	−0.0873201
$949$	−14.6437	−0.475354
$950$	−2.11061	−0.0684773
$951$	−15.2893	−0.495791
$952$	6.75531	0.218941
$953$	37.8805	1.22707	0.613534	−	0.789668i	$-0.289747\pi$
$953$	37.8805	1.22707	0.613534	+	0.789668i	$0.289747\pi$
$954$	−1.65886	−0.0537077
$955$	26.7085	0.864266
$956$	−9.32731	−0.301667
$957$	−0.230377	−0.00744703
$958$	3.51893	0.113691
$959$	4.20337	0.135734
$960$	12.0168	0.387840
$961$	−30.4884	−0.983496
$962$	3.67176	0.118382
$963$	−11.7272	−0.377904
$964$	8.67602	0.279436
$965$	8.54631	0.275116
$966$	1.99376	0.0641483
$967$	−4.19261	−0.134825	−0.0674126	−	0.997725i	$-0.521474\pi$
$967$	−4.19261	−0.134825	−0.0674126	+	0.997725i	$0.521474\pi$
$968$	15.9345	0.512156
$969$	−21.2425	−0.682408
$970$	−8.41081	−0.270055
$971$	48.6618	1.56163	0.780815	−	0.624762i	$-0.214804\pi$
$971$	48.6618	1.56163	0.780815	+	0.624762i	$0.214804\pi$
$972$	1.85904	0.0596288
$973$	−1.83457	−0.0588135
$974$	15.7020	0.503126
$975$	−1.52615	−0.0488758
$976$	−29.9129	−0.957489
$977$	−9.44891	−0.302297	−0.151149	−	0.988511i	$-0.548297\pi$
$977$	−9.44891	−0.302297	−0.151149	+	0.988511i	$0.548297\pi$
$978$	−6.13039	−0.196028
$979$	0.520437	0.0166332
$980$	−4.64162	−0.148271
$981$	−12.3647	−0.394774
$982$	5.72200	0.182596
$983$	−41.1626	−1.31288	−0.656441	−	0.754377i	$-0.727939\pi$
$983$	−41.1626	−1.31288	−0.656441	+	0.754377i	$0.727939\pi$
$984$	−7.20273	−0.229615
$985$	31.5109	1.00402
$986$	9.16906	0.292002
$987$	−11.4407	−0.364163
$988$	10.4758	0.333281
$989$	−1.81294	−0.0576481
$990$	−0.0412291	−0.00131035
$991$	−24.3889	−0.774740	−0.387370	−	0.921924i	$-0.626616\pi$
$991$	−24.3889	−0.774740	−0.387370	+	0.921924i	$0.626616\pi$
$992$	2.92506	0.0928707
$993$	8.79412	0.279073
$994$	−1.84499	−0.0585197
$995$	52.9602	1.67895
$996$	−14.1663	−0.448877
$997$	2.58240	0.0817855	0.0408927	−	0.999164i	$-0.486980\pi$
$997$	2.58240	0.0817855	0.0408927	+	0.999164i	$0.486980\pi$
$998$	6.99127	0.221305
$999$	−7.90706	−0.250168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.p.1.11	✓	18
3.2	odd	2		8001.2.a.u.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.11	✓	18	1.1	even	1	trivial
8001.2.a.u.1.8		18	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)

\(f(q)\)	\(=\)	\(q+0.375443 q^{2} -1.00000 q^{3} -1.85904 q^{4} +2.49678 q^{5} -0.375443 q^{6} +1.00000 q^{7} -1.44885 q^{8} +1.00000 q^{9} +0.937397 q^{10} -0.0439826 q^{11} +1.85904 q^{12} +1.23685 q^{13} +0.375443 q^{14} -2.49678 q^{15} +3.17413 q^{16} -4.66254 q^{17} +0.375443 q^{18} -4.55600 q^{19} -4.64162 q^{20} -1.00000 q^{21} -0.0165129 q^{22} -5.31043 q^{23} +1.44885 q^{24} +1.23390 q^{25} +0.464365 q^{26} -1.00000 q^{27} -1.85904 q^{28} -5.23792 q^{29} -0.937397 q^{30} +0.715277 q^{31} +4.08940 q^{32} +0.0439826 q^{33} -1.75052 q^{34} +2.49678 q^{35} -1.85904 q^{36} +7.90706 q^{37} -1.71052 q^{38} -1.23685 q^{39} -3.61746 q^{40} -4.97134 q^{41} -0.375443 q^{42} +0.341392 q^{43} +0.0817655 q^{44} +2.49678 q^{45} -1.99376 q^{46} +11.4407 q^{47} -3.17413 q^{48} +1.00000 q^{49} +0.463260 q^{50} +4.66254 q^{51} -2.29935 q^{52} -4.41842 q^{53} -0.375443 q^{54} -0.109815 q^{55} -1.44885 q^{56} +4.55600 q^{57} -1.96654 q^{58} +9.78565 q^{59} +4.64162 q^{60} -9.42399 q^{61} +0.268546 q^{62} +1.00000 q^{63} -4.81291 q^{64} +3.08813 q^{65} +0.0165129 q^{66} +0.00811780 q^{67} +8.66785 q^{68} +5.31043 q^{69} +0.937397 q^{70} -4.91418 q^{71} -1.44885 q^{72} -11.8395 q^{73} +2.96865 q^{74} -1.23390 q^{75} +8.46980 q^{76} -0.0439826 q^{77} -0.464365 q^{78} -1.44620 q^{79} +7.92509 q^{80} +1.00000 q^{81} -1.86645 q^{82} -7.62022 q^{83} +1.85904 q^{84} -11.6413 q^{85} +0.128173 q^{86} +5.23792 q^{87} +0.0637241 q^{88} -11.8328 q^{89} +0.937397 q^{90} +1.23685 q^{91} +9.87232 q^{92} -0.715277 q^{93} +4.29534 q^{94} -11.3753 q^{95} -4.08940 q^{96} -8.97251 q^{97} +0.375443 q^{98} -0.0439826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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