LMFDB - Embedded newform 2001.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$0$
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} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.51124$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51124 q^{2} -1.00000 q^{3} +4.30634 q^{4} +2.07440 q^{5} +2.51124 q^{6} -0.329384 q^{7} -5.79178 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51124 q^{2} -1.00000 q^{3} +4.30634 q^{4} +2.07440 q^{5} +2.51124 q^{6} -0.329384 q^{7} -5.79178 q^{8} +1.00000 q^{9} -5.20933 q^{10} +4.89635 q^{11} -4.30634 q^{12} +2.21503 q^{13} +0.827164 q^{14} -2.07440 q^{15} +5.93189 q^{16} +4.14979 q^{17} -2.51124 q^{18} +0.434775 q^{19} +8.93309 q^{20} +0.329384 q^{21} -12.2959 q^{22} +1.00000 q^{23} +5.79178 q^{24} -0.696851 q^{25} -5.56247 q^{26} -1.00000 q^{27} -1.41844 q^{28} -1.00000 q^{29} +5.20933 q^{30} +11.0142 q^{31} -3.31286 q^{32} -4.89635 q^{33} -10.4211 q^{34} -0.683276 q^{35} +4.30634 q^{36} +0.655818 q^{37} -1.09182 q^{38} -2.21503 q^{39} -12.0145 q^{40} +7.37293 q^{41} -0.827164 q^{42} +0.463287 q^{43} +21.0853 q^{44} +2.07440 q^{45} -2.51124 q^{46} +4.14571 q^{47} -5.93189 q^{48} -6.89151 q^{49} +1.74996 q^{50} -4.14979 q^{51} +9.53866 q^{52} +2.30936 q^{53} +2.51124 q^{54} +10.1570 q^{55} +1.90772 q^{56} -0.434775 q^{57} +2.51124 q^{58} +9.22421 q^{59} -8.93309 q^{60} -12.4374 q^{61} -27.6594 q^{62} -0.329384 q^{63} -3.54439 q^{64} +4.59486 q^{65} +12.2959 q^{66} -14.6596 q^{67} +17.8704 q^{68} -1.00000 q^{69} +1.71587 q^{70} +12.1080 q^{71} -5.79178 q^{72} +7.93152 q^{73} -1.64692 q^{74} +0.696851 q^{75} +1.87229 q^{76} -1.61278 q^{77} +5.56247 q^{78} -6.32788 q^{79} +12.3051 q^{80} +1.00000 q^{81} -18.5152 q^{82} -16.4719 q^{83} +1.41844 q^{84} +8.60834 q^{85} -1.16343 q^{86} +1.00000 q^{87} -28.3586 q^{88} +7.88890 q^{89} -5.20933 q^{90} -0.729595 q^{91} +4.30634 q^{92} -11.0142 q^{93} -10.4109 q^{94} +0.901898 q^{95} +3.31286 q^{96} -15.8429 q^{97} +17.3062 q^{98} +4.89635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.51124	−1.77572	−0.887858	−	0.460117i	$-0.847808\pi$
$2$	−2.51124	−1.77572	−0.887858	+	0.460117i	$0.847808\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.30634	2.15317
$5$	2.07440	0.927701	0.463851	−	0.885913i	$-0.346467\pi$
$5$	2.07440	0.927701	0.463851	+	0.885913i	$0.346467\pi$
$6$	2.51124	1.02521
$7$	−0.329384	−0.124496	−0.0622478	−	0.998061i	$-0.519827\pi$
$7$	−0.329384	−0.124496	−0.0622478	+	0.998061i	$0.519827\pi$
$8$	−5.79178	−2.04770
$9$	1.00000	0.333333
$10$	−5.20933	−1.64733
$11$	4.89635	1.47630	0.738152	−	0.674635i	$-0.235699\pi$
$11$	4.89635	1.47630	0.738152	+	0.674635i	$0.235699\pi$
$12$	−4.30634	−1.24313
$13$	2.21503	0.614338	0.307169	−	0.951655i	$-0.400618\pi$
$13$	2.21503	0.614338	0.307169	+	0.951655i	$0.400618\pi$
$14$	0.827164	0.221069
$15$	−2.07440	−0.535609
$16$	5.93189	1.48297
$17$	4.14979	1.00647	0.503236	−	0.864149i	$-0.332143\pi$
$17$	4.14979	1.00647	0.503236	+	0.864149i	$0.332143\pi$
$18$	−2.51124	−0.591906
$19$	0.434775	0.0997441	0.0498721	−	0.998756i	$-0.484119\pi$
$19$	0.434775	0.0997441	0.0498721	+	0.998756i	$0.484119\pi$
$20$	8.93309	1.99750
$21$	0.329384	0.0718776
$22$	−12.2959	−2.62150
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	5.79178	1.18224
$25$	−0.696851	−0.139370
$26$	−5.56247	−1.09089
$27$	−1.00000	−0.192450
$28$	−1.41844	−0.268060
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	5.20933	0.951089
$31$	11.0142	1.97822	0.989108	−	0.147189i	$-0.0470227\pi$
$31$	11.0142	1.97822	0.989108	+	0.147189i	$0.0470227\pi$
$32$	−3.31286	−0.585636
$33$	−4.89635	−0.852344
$34$	−10.4211	−1.78721
$35$	−0.683276	−0.115495
$36$	4.30634	0.717724
$37$	0.655818	0.107816	0.0539079	−	0.998546i	$-0.482832\pi$
$37$	0.655818	0.107816	0.0539079	+	0.998546i	$0.482832\pi$
$38$	−1.09182	−0.177117
$39$	−2.21503	−0.354688
$40$	−12.0145	−1.89966
$41$	7.37293	1.15146	0.575729	−	0.817640i	$-0.304718\pi$
$41$	7.37293	1.15146	0.575729	+	0.817640i	$0.304718\pi$
$42$	−0.827164	−0.127634
$43$	0.463287	0.0706505	0.0353253	−	0.999376i	$-0.488753\pi$
$43$	0.463287	0.0706505	0.0353253	+	0.999376i	$0.488753\pi$
$44$	21.0853	3.17873
$45$	2.07440	0.309234
$46$	−2.51124	−0.370263
$47$	4.14571	0.604714	0.302357	−	0.953195i	$-0.402226\pi$
$47$	4.14571	0.604714	0.302357	+	0.953195i	$0.402226\pi$
$48$	−5.93189	−0.856195
$49$	−6.89151	−0.984501
$50$	1.74996	0.247482
$51$	−4.14979	−0.581087
$52$	9.53866	1.32277
$53$	2.30936	0.317215	0.158608	−	0.987342i	$-0.449300\pi$
$53$	2.30936	0.317215	0.158608	+	0.987342i	$0.449300\pi$
$54$	2.51124	0.341737
$55$	10.1570	1.36957
$56$	1.90772	0.254930
$57$	−0.434775	−0.0575873
$58$	2.51124	0.329742
$59$	9.22421	1.20089	0.600445	−	0.799666i	$-0.294990\pi$
$59$	9.22421	1.20089	0.600445	+	0.799666i	$0.294990\pi$
$60$	−8.93309	−1.15326
$61$	−12.4374	−1.59245	−0.796226	−	0.605000i	$-0.793173\pi$
$61$	−12.4374	−1.59245	−0.796226	+	0.605000i	$0.793173\pi$
$62$	−27.6594	−3.51275
$63$	−0.329384	−0.0414985
$64$	−3.54439	−0.443049
$65$	4.59486	0.569922
$66$	12.2959	1.51352
$67$	−14.6596	−1.79096	−0.895478	−	0.445106i	$-0.853166\pi$
$67$	−14.6596	−1.79096	−0.895478	+	0.445106i	$0.853166\pi$
$68$	17.8704	2.16711
$69$	−1.00000	−0.120386
$70$	1.71587	0.205086
$71$	12.1080	1.43695	0.718476	−	0.695552i	$-0.244840\pi$
$71$	12.1080	1.43695	0.718476	+	0.695552i	$0.244840\pi$
$72$	−5.79178	−0.682568
$73$	7.93152	0.928315	0.464157	−	0.885753i	$-0.346357\pi$
$73$	7.93152	0.928315	0.464157	+	0.885753i	$0.346357\pi$
$74$	−1.64692	−0.191450
$75$	0.696851	0.0804655
$76$	1.87229	0.214766
$77$	−1.61278	−0.183793
$78$	5.56247	0.629826
$79$	−6.32788	−0.711942	−0.355971	−	0.934497i	$-0.615850\pi$
$79$	−6.32788	−0.711942	−0.355971	+	0.934497i	$0.615850\pi$
$80$	12.3051	1.37576
$81$	1.00000	0.111111
$82$	−18.5152	−2.04467
$83$	−16.4719	−1.80803	−0.904014	−	0.427502i	$-0.859394\pi$
$83$	−16.4719	−1.80803	−0.904014	+	0.427502i	$0.859394\pi$
$84$	1.41844	0.154765
$85$	8.60834	0.933706
$86$	−1.16343	−0.125455
$87$	1.00000	0.107211
$88$	−28.3586	−3.02303
$89$	7.88890	0.836222	0.418111	−	0.908396i	$-0.362692\pi$
$89$	7.88890	0.836222	0.418111	+	0.908396i	$0.362692\pi$
$90$	−5.20933	−0.549112
$91$	−0.729595	−0.0764823
$92$	4.30634	0.448967
$93$	−11.0142	−1.14212
$94$	−10.4109	−1.07380
$95$	0.901898	0.0925328
$96$	3.31286	0.338117
$97$	−15.8429	−1.60861	−0.804303	−	0.594219i	$-0.797461\pi$
$97$	−15.8429	−1.60861	−0.804303	+	0.594219i	$0.797461\pi$
$98$	17.3062	1.74819
$99$	4.89635	0.492101
$100$	−3.00088	−0.300088
$101$	−12.1067	−1.20466	−0.602332	−	0.798246i	$-0.705761\pi$
$101$	−12.1067	−1.20466	−0.602332	+	0.798246i	$0.705761\pi$
$102$	10.4211	1.03185
$103$	−11.8721	−1.16979	−0.584895	−	0.811109i	$-0.698864\pi$
$103$	−11.8721	−1.16979	−0.584895	+	0.811109i	$0.698864\pi$
$104$	−12.8290	−1.25798
$105$	0.683276	0.0666809
$106$	−5.79937	−0.563284
$107$	−3.91344	−0.378327	−0.189163	−	0.981946i	$-0.560578\pi$
$107$	−3.91344	−0.378327	−0.189163	+	0.981946i	$0.560578\pi$
$108$	−4.30634	−0.414378
$109$	6.10250	0.584514	0.292257	−	0.956340i	$-0.405594\pi$
$109$	6.10250	0.584514	0.292257	+	0.956340i	$0.405594\pi$
$110$	−25.5067	−2.43197
$111$	−0.655818	−0.0622475
$112$	−1.95387	−0.184624
$113$	−3.69220	−0.347333	−0.173666	−	0.984805i	$-0.555561\pi$
$113$	−3.69220	−0.347333	−0.173666	+	0.984805i	$0.555561\pi$
$114$	1.09182	0.102259
$115$	2.07440	0.193439
$116$	−4.30634	−0.399834
$117$	2.21503	0.204779
$118$	−23.1642	−2.13244
$119$	−1.36688	−0.125301
$120$	12.0145	1.09677
$121$	12.9742	1.17947
$122$	31.2334	2.82774
$123$	−7.37293	−0.664795
$124$	47.4311	4.25944
$125$	−11.8176	−1.05700
$126$	0.827164	0.0736897
$127$	−11.0829	−0.983444	−0.491722	−	0.870752i	$-0.663632\pi$
$127$	−11.0829	−0.983444	−0.491722	+	0.870752i	$0.663632\pi$
$128$	15.5265	1.37237
$129$	−0.463287	−0.0407901
$130$	−11.5388	−1.01202
$131$	16.7632	1.46461	0.732304	−	0.680977i	$-0.238445\pi$
$131$	16.7632	1.46461	0.732304	+	0.680977i	$0.238445\pi$
$132$	−21.0853	−1.83524
$133$	−0.143208	−0.0124177
$134$	36.8138	3.18023
$135$	−2.07440	−0.178536
$136$	−24.0347	−2.06096
$137$	1.30482	0.111478	0.0557391	−	0.998445i	$-0.482248\pi$
$137$	1.30482	0.111478	0.0557391	+	0.998445i	$0.482248\pi$
$138$	2.51124	0.213771
$139$	0.506684	0.0429764	0.0214882	−	0.999769i	$-0.493160\pi$
$139$	0.506684	0.0429764	0.0214882	+	0.999769i	$0.493160\pi$
$140$	−2.94242	−0.248680
$141$	−4.14571	−0.349132
$142$	−30.4061	−2.55162
$143$	10.8455	0.906949
$144$	5.93189	0.494325
$145$	−2.07440	−0.172270
$146$	−19.9180	−1.64842
$147$	6.89151	0.568402
$148$	2.82418	0.232146
$149$	−12.4088	−1.01657	−0.508286	−	0.861188i	$-0.669721\pi$
$149$	−12.4088	−1.01657	−0.508286	+	0.861188i	$0.669721\pi$
$150$	−1.74996	−0.142884
$151$	17.4673	1.42147	0.710736	−	0.703459i	$-0.248362\pi$
$151$	17.4673	1.42147	0.710736	+	0.703459i	$0.248362\pi$
$152$	−2.51812	−0.204247
$153$	4.14979	0.335491
$154$	4.05008	0.326365
$155$	22.8480	1.83519
$156$	−9.53866	−0.763704
$157$	0.289576	0.0231107	0.0115553	−	0.999933i	$-0.496322\pi$
$157$	0.289576	0.0231107	0.0115553	+	0.999933i	$0.496322\pi$
$158$	15.8908	1.26421
$159$	−2.30936	−0.183144
$160$	−6.87221	−0.543296
$161$	−0.329384	−0.0259591
$162$	−2.51124	−0.197302
$163$	16.7973	1.31566	0.657832	−	0.753165i	$-0.271474\pi$
$163$	16.7973	1.31566	0.657832	+	0.753165i	$0.271474\pi$
$164$	31.7504	2.47929
$165$	−10.1570	−0.790721
$166$	41.3650	3.21055
$167$	10.5399	0.815598	0.407799	−	0.913072i	$-0.366296\pi$
$167$	10.5399	0.815598	0.407799	+	0.913072i	$0.366296\pi$
$168$	−1.90772	−0.147184
$169$	−8.09366	−0.622589
$170$	−21.6176	−1.65800
$171$	0.434775	0.0332480
$172$	1.99507	0.152123
$173$	−22.2051	−1.68822	−0.844112	−	0.536168i	$-0.819872\pi$
$173$	−22.2051	−1.68822	−0.844112	+	0.536168i	$0.819872\pi$
$174$	−2.51124	−0.190377
$175$	0.229532	0.0173510
$176$	29.0446	2.18932
$177$	−9.22421	−0.693334
$178$	−19.8109	−1.48489
$179$	5.20296	0.388887	0.194444	−	0.980914i	$-0.437710\pi$
$179$	5.20296	0.388887	0.194444	+	0.980914i	$0.437710\pi$
$180$	8.93309	0.665833
$181$	25.8911	1.92447	0.962235	−	0.272218i	$-0.0877573\pi$
$181$	25.8911	1.92447	0.962235	+	0.272218i	$0.0877573\pi$
$182$	1.83219	0.135811
$183$	12.4374	0.919402
$184$	−5.79178	−0.426976
$185$	1.36043	0.100021
$186$	27.6594	2.02809
$187$	20.3188	1.48586
$188$	17.8529	1.30205
$189$	0.329384	0.0239592
$190$	−2.26488	−0.164312
$191$	−18.1086	−1.31029	−0.655147	−	0.755501i	$-0.727393\pi$
$191$	−18.1086	−1.31029	−0.655147	+	0.755501i	$0.727393\pi$
$192$	3.54439	0.255794
$193$	21.6895	1.56124	0.780622	−	0.625003i	$-0.214902\pi$
$193$	21.6895	1.56124	0.780622	+	0.625003i	$0.214902\pi$
$194$	39.7855	2.85643
$195$	−4.59486	−0.329045
$196$	−29.6772	−2.11980
$197$	−12.8759	−0.917368	−0.458684	−	0.888600i	$-0.651679\pi$
$197$	−12.8759	−0.917368	−0.458684	+	0.888600i	$0.651679\pi$
$198$	−12.2959	−0.873833
$199$	9.73022	0.689757	0.344878	−	0.938647i	$-0.387920\pi$
$199$	9.73022	0.689757	0.344878	+	0.938647i	$0.387920\pi$
$200$	4.03601	0.285389
$201$	14.6596	1.03401
$202$	30.4029	2.13914
$203$	0.329384	0.0231183
$204$	−17.8704	−1.25118
$205$	15.2944	1.06821
$206$	29.8136	2.07721
$207$	1.00000	0.0695048
$208$	13.1393	0.911047
$209$	2.12881	0.147253
$210$	−1.71587	−0.118406
$211$	21.1320	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$211$	21.1320	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$212$	9.94490	0.683018
$213$	−12.1080	−0.829625
$214$	9.82760	0.671801
$215$	0.961043	0.0655426
$216$	5.79178	0.394081
$217$	−3.62792	−0.246279
$218$	−15.3249	−1.03793
$219$	−7.93152	−0.535963
$220$	43.7395	2.94892
$221$	9.19190	0.618314
$222$	1.64692	0.110534
$223$	18.3905	1.23152	0.615759	−	0.787934i	$-0.288849\pi$
$223$	18.3905	1.23152	0.615759	+	0.787934i	$0.288849\pi$
$224$	1.09120	0.0729092
$225$	−0.696851	−0.0464568
$226$	9.27201	0.616765
$227$	20.9143	1.38813	0.694066	−	0.719912i	$-0.255818\pi$
$227$	20.9143	1.38813	0.694066	+	0.719912i	$0.255818\pi$
$228$	−1.87229	−0.123995
$229$	6.61855	0.437366	0.218683	−	0.975796i	$-0.429824\pi$
$229$	6.61855	0.437366	0.218683	+	0.975796i	$0.429824\pi$
$230$	−5.20933	−0.343493
$231$	1.61278	0.106113
$232$	5.79178	0.380249
$233$	−17.6336	−1.15522	−0.577608	−	0.816314i	$-0.696014\pi$
$233$	−17.6336	−1.15522	−0.577608	+	0.816314i	$0.696014\pi$
$234$	−5.56247	−0.363630
$235$	8.59988	0.560994
$236$	39.7226	2.58572
$237$	6.32788	0.411040
$238$	3.43256	0.222500
$239$	−3.61613	−0.233908	−0.116954	−	0.993137i	$-0.537313\pi$
$239$	−3.61613	−0.233908	−0.116954	+	0.993137i	$0.537313\pi$
$240$	−12.3051	−0.794293
$241$	−27.5459	−1.77439	−0.887193	−	0.461398i	$-0.847348\pi$
$241$	−27.5459	−1.77439	−0.887193	+	0.461398i	$0.847348\pi$
$242$	−32.5814	−2.09441
$243$	−1.00000	−0.0641500
$244$	−53.5599	−3.42882
$245$	−14.2958	−0.913323
$246$	18.5152	1.18049
$247$	0.963037	0.0612766
$248$	−63.7921	−4.05080
$249$	16.4719	1.04387
$250$	29.6768	1.87692
$251$	8.21398	0.518462	0.259231	−	0.965815i	$-0.416531\pi$
$251$	8.21398	0.518462	0.259231	+	0.965815i	$0.416531\pi$
$252$	−1.41844	−0.0893534
$253$	4.89635	0.307831
$254$	27.8317	1.74632
$255$	−8.60834	−0.539075
$256$	−31.9022	−1.99388
$257$	10.5170	0.656034	0.328017	−	0.944672i	$-0.393620\pi$
$257$	10.5170	0.656034	0.328017	+	0.944672i	$0.393620\pi$
$258$	1.16343	0.0724317
$259$	−0.216016	−0.0134226
$260$	19.7870	1.22714
$261$	−1.00000	−0.0618984
$262$	−42.0965	−2.60073
$263$	−2.77438	−0.171076	−0.0855378	−	0.996335i	$-0.527261\pi$
$263$	−2.77438	−0.171076	−0.0855378	+	0.996335i	$0.527261\pi$
$264$	28.3586	1.74535
$265$	4.79055	0.294281
$266$	0.359630	0.0220503
$267$	−7.88890	−0.482793
$268$	−63.1293	−3.85623
$269$	23.7005	1.44505	0.722524	−	0.691346i	$-0.242982\pi$
$269$	23.7005	1.44505	0.722524	+	0.691346i	$0.242982\pi$
$270$	5.20933	0.317030
$271$	7.94842	0.482832	0.241416	−	0.970422i	$-0.422388\pi$
$271$	7.94842	0.482832	0.241416	+	0.970422i	$0.422388\pi$
$272$	24.6161	1.49257
$273$	0.729595	0.0441571
$274$	−3.27672	−0.197954
$275$	−3.41202	−0.205753
$276$	−4.30634	−0.259211
$277$	−3.94280	−0.236900	−0.118450	−	0.992960i	$-0.537793\pi$
$277$	−3.94280	−0.236900	−0.118450	+	0.992960i	$0.537793\pi$
$278$	−1.27241	−0.0763139
$279$	11.0142	0.659406
$280$	3.95739	0.236499
$281$	19.7692	1.17933	0.589667	−	0.807647i	$-0.299259\pi$
$281$	19.7692	1.17933	0.589667	+	0.807647i	$0.299259\pi$
$282$	10.4109	0.619960
$283$	−19.5488	−1.16205	−0.581027	−	0.813885i	$-0.697349\pi$
$283$	−19.5488	−1.16205	−0.581027	+	0.813885i	$0.697349\pi$
$284$	52.1411	3.09400
$285$	−0.901898	−0.0534238
$286$	−27.2358	−1.61048
$287$	−2.42853	−0.143352
$288$	−3.31286	−0.195212
$289$	0.220779	0.0129870
$290$	5.20933	0.305902
$291$	15.8429	0.928730
$292$	34.1558	1.99882
$293$	10.8038	0.631162	0.315581	−	0.948899i	$-0.397801\pi$
$293$	10.8038	0.631162	0.315581	+	0.948899i	$0.397801\pi$
$294$	−17.3062	−1.00932
$295$	19.1347	1.11407
$296$	−3.79836	−0.220775
$297$	−4.89635	−0.284115
$298$	31.1616	1.80514
$299$	2.21503	0.128098
$300$	3.00088	0.173256
$301$	−0.152599	−0.00879568
$302$	−43.8647	−2.52413
$303$	12.1067	0.695513
$304$	2.57904	0.147918
$305$	−25.8003	−1.47732
$306$	−10.4211	−0.595737
$307$	4.16574	0.237751	0.118876	−	0.992909i	$-0.462071\pi$
$307$	4.16574	0.237751	0.118876	+	0.992909i	$0.462071\pi$
$308$	−6.94518	−0.395738
$309$	11.8721	0.675378
$310$	−57.3768	−3.25879
$311$	−8.17076	−0.463321	−0.231661	−	0.972797i	$-0.574416\pi$
$311$	−8.17076	−0.463321	−0.231661	+	0.972797i	$0.574416\pi$
$312$	12.8290	0.726296
$313$	13.6902	0.773819	0.386909	−	0.922118i	$-0.373543\pi$
$313$	13.6902	0.773819	0.386909	+	0.922118i	$0.373543\pi$
$314$	−0.727195	−0.0410380
$315$	−0.683276	−0.0384983
$316$	−27.2500	−1.53293
$317$	−19.5419	−1.09758	−0.548792	−	0.835959i	$-0.684912\pi$
$317$	−19.5419	−1.09758	−0.548792	+	0.835959i	$0.684912\pi$
$318$	5.79937	0.325212
$319$	−4.89635	−0.274143
$320$	−7.35250	−0.411017
$321$	3.91344	0.218427
$322$	0.827164	0.0460961
$323$	1.80422	0.100390
$324$	4.30634	0.239241
$325$	−1.54354	−0.0856204
$326$	−42.1820	−2.33625
$327$	−6.10250	−0.337469
$328$	−42.7024	−2.35785
$329$	−1.36553	−0.0752843
$330$	25.5067	1.40410
$331$	−11.9595	−0.657352	−0.328676	−	0.944443i	$-0.606602\pi$
$331$	−11.9595	−0.657352	−0.328676	+	0.944443i	$0.606602\pi$
$332$	−70.9337	−3.89299
$333$	0.655818	0.0359386
$334$	−26.4681	−1.44827
$335$	−30.4099	−1.66147
$336$	1.95387	0.106593
$337$	−14.1312	−0.769773	−0.384887	−	0.922964i	$-0.625759\pi$
$337$	−14.1312	−0.769773	−0.384887	+	0.922964i	$0.625759\pi$
$338$	20.3251	1.10554
$339$	3.69220	0.200533
$340$	37.0705	2.01043
$341$	53.9295	2.92045
$342$	−1.09182	−0.0590391
$343$	4.57565	0.247062
$344$	−2.68326	−0.144671
$345$	−2.07440	−0.111682
$346$	55.7624	2.99781
$347$	−5.12769	−0.275269	−0.137635	−	0.990483i	$-0.543950\pi$
$347$	−5.12769	−0.275269	−0.137635	+	0.990483i	$0.543950\pi$
$348$	4.30634	0.230844
$349$	−24.1423	−1.29231	−0.646154	−	0.763207i	$-0.723624\pi$
$349$	−24.1423	−1.29231	−0.646154	+	0.763207i	$0.723624\pi$
$350$	−0.576411	−0.0308104
$351$	−2.21503	−0.118229
$352$	−16.2209	−0.864577
$353$	15.5988	0.830241	0.415121	−	0.909766i	$-0.363739\pi$
$353$	15.5988	0.830241	0.415121	+	0.909766i	$0.363739\pi$
$354$	23.1642	1.23116
$355$	25.1168	1.33306
$356$	33.9723	1.80053
$357$	1.36688	0.0723428
$358$	−13.0659	−0.690554
$359$	16.0554	0.847370	0.423685	−	0.905810i	$-0.360736\pi$
$359$	16.0554	0.847370	0.423685	+	0.905810i	$0.360736\pi$
$360$	−12.0145	−0.633220
$361$	−18.8110	−0.990051
$362$	−65.0189	−3.41732
$363$	−12.9742	−0.680969
$364$	−3.14189	−0.164680
$365$	16.4532	0.861199
$366$	−31.2334	−1.63260
$367$	24.1708	1.26170	0.630852	−	0.775903i	$-0.282706\pi$
$367$	24.1708	1.26170	0.630852	+	0.775903i	$0.282706\pi$
$368$	5.93189	0.309221
$369$	7.37293	0.383820
$370$	−3.41637	−0.177609
$371$	−0.760668	−0.0394919
$372$	−47.4311	−2.45919
$373$	0.418763	0.0216827	0.0108414	−	0.999941i	$-0.496549\pi$
$373$	0.418763	0.0216827	0.0108414	+	0.999941i	$0.496549\pi$
$374$	−51.0255	−2.63847
$375$	11.8176	0.610257
$376$	−24.0111	−1.23828
$377$	−2.21503	−0.114080
$378$	−0.827164	−0.0425447
$379$	−12.9349	−0.664419	−0.332209	−	0.943206i	$-0.607794\pi$
$379$	−12.9349	−0.664419	−0.332209	+	0.943206i	$0.607794\pi$
$380$	3.88388	0.199239
$381$	11.0829	0.567792
$382$	45.4752	2.32671
$383$	19.4317	0.992912	0.496456	−	0.868062i	$-0.334634\pi$
$383$	19.4317	0.992912	0.496456	+	0.868062i	$0.334634\pi$
$384$	−15.5265	−0.792336
$385$	−3.34556	−0.170505
$386$	−54.4676	−2.77233
$387$	0.463287	0.0235502
$388$	−68.2251	−3.46361
$389$	12.7146	0.644655	0.322327	−	0.946628i	$-0.395535\pi$
$389$	12.7146	0.644655	0.322327	+	0.946628i	$0.395535\pi$
$390$	11.5388	0.584290
$391$	4.14979	0.209864
$392$	39.9141	2.01597
$393$	−16.7632	−0.845592
$394$	32.3344	1.62899
$395$	−13.1266	−0.660470
$396$	21.0853	1.05958
$397$	−3.82487	−0.191965	−0.0959824	−	0.995383i	$-0.530599\pi$
$397$	−3.82487	−0.191965	−0.0959824	+	0.995383i	$0.530599\pi$
$398$	−24.4349	−1.22481
$399$	0.143208	0.00716937
$400$	−4.13365	−0.206682
$401$	−25.7050	−1.28364	−0.641822	−	0.766853i	$-0.721821\pi$
$401$	−25.7050	−1.28364	−0.641822	+	0.766853i	$0.721821\pi$
$402$	−36.8138	−1.83611
$403$	24.3968	1.21529
$404$	−52.1356	−2.59385
$405$	2.07440	0.103078
$406$	−0.827164	−0.0410515
$407$	3.21111	0.159169
$408$	24.0347	1.18990
$409$	−3.42184	−0.169199	−0.0845996	−	0.996415i	$-0.526961\pi$
$409$	−3.42184	−0.169199	−0.0845996	+	0.996415i	$0.526961\pi$
$410$	−38.4081	−1.89684
$411$	−1.30482	−0.0643620
$412$	−51.1252	−2.51876
$413$	−3.03831	−0.149505
$414$	−2.51124	−0.123421
$415$	−34.1694	−1.67731
$416$	−7.33807	−0.359779
$417$	−0.506684	−0.0248124
$418$	−5.34595	−0.261479
$419$	−6.84345	−0.334324	−0.167162	−	0.985929i	$-0.553460\pi$
$419$	−6.84345	−0.334324	−0.167162	+	0.985929i	$0.553460\pi$
$420$	2.94242	0.143575
$421$	30.2672	1.47513	0.737567	−	0.675273i	$-0.235974\pi$
$421$	30.2672	1.47513	0.737567	+	0.675273i	$0.235974\pi$
$422$	−53.0676	−2.58329
$423$	4.14571	0.201571
$424$	−13.3753	−0.649563
$425$	−2.89179	−0.140272
$426$	30.4061	1.47318
$427$	4.09670	0.198253
$428$	−16.8526	−0.814602
$429$	−10.8455	−0.523627
$430$	−2.41341	−0.116385
$431$	−23.8381	−1.14824	−0.574120	−	0.818771i	$-0.694656\pi$
$431$	−23.8381	−1.14824	−0.574120	+	0.818771i	$0.694656\pi$
$432$	−5.93189	−0.285398
$433$	−32.3113	−1.55278	−0.776392	−	0.630250i	$-0.782952\pi$
$433$	−32.3113	−1.55278	−0.776392	+	0.630250i	$0.782952\pi$
$434$	9.11059	0.437322
$435$	2.07440	0.0994600
$436$	26.2795	1.25856
$437$	0.434775	0.0207981
$438$	19.9180	0.951718
$439$	−3.14005	−0.149866	−0.0749332	−	0.997189i	$-0.523874\pi$
$439$	−3.14005	−0.149866	−0.0749332	+	0.997189i	$0.523874\pi$
$440$	−58.8271	−2.80447
$441$	−6.89151	−0.328167
$442$	−23.0831	−1.09795
$443$	20.0935	0.954673	0.477336	−	0.878721i	$-0.341602\pi$
$443$	20.0935	0.954673	0.477336	+	0.878721i	$0.341602\pi$
$444$	−2.82418	−0.134030
$445$	16.3648	0.775764
$446$	−46.1830	−2.18683
$447$	12.4088	0.586918
$448$	1.16747	0.0551577
$449$	−26.5247	−1.25178	−0.625890	−	0.779911i	$-0.715264\pi$
$449$	−26.5247	−1.25178	−0.625890	+	0.779911i	$0.715264\pi$
$450$	1.74996	0.0824940
$451$	36.1004	1.69990
$452$	−15.8999	−0.747867
$453$	−17.4673	−0.820687
$454$	−52.5209	−2.46493
$455$	−1.51347	−0.0709528
$456$	2.51812	0.117922
$457$	24.8925	1.16442	0.582211	−	0.813038i	$-0.302188\pi$
$457$	24.8925	1.16442	0.582211	+	0.813038i	$0.302188\pi$
$458$	−16.6208	−0.776638
$459$	−4.14979	−0.193696
$460$	8.93309	0.416507
$461$	14.3135	0.666645	0.333323	−	0.942813i	$-0.391830\pi$
$461$	14.3135	0.666645	0.333323	+	0.942813i	$0.391830\pi$
$462$	−4.05008	−0.188427
$463$	−11.6147	−0.539782	−0.269891	−	0.962891i	$-0.586988\pi$
$463$	−11.6147	−0.539782	−0.269891	+	0.962891i	$0.586988\pi$
$464$	−5.93189	−0.275381
$465$	−22.8480	−1.05955
$466$	44.2823	2.05134
$467$	7.84693	0.363113	0.181556	−	0.983381i	$-0.441887\pi$
$467$	7.84693	0.363113	0.181556	+	0.983381i	$0.441887\pi$
$468$	9.53866	0.440925
$469$	4.82865	0.222966
$470$	−21.5964	−0.996167
$471$	−0.289576	−0.0133429
$472$	−53.4246	−2.45907
$473$	2.26841	0.104302
$474$	−15.8908	−0.729891
$475$	−0.302973	−0.0139014
$476$	−5.88624	−0.269795
$477$	2.30936	0.105738
$478$	9.08098	0.415354
$479$	−9.05712	−0.413831	−0.206915	−	0.978359i	$-0.566342\pi$
$479$	−9.05712	−0.413831	−0.206915	+	0.978359i	$0.566342\pi$
$480$	6.87221	0.313672
$481$	1.45265	0.0662353
$482$	69.1744	3.15081
$483$	0.329384	0.0149875
$484$	55.8713	2.53961
$485$	−32.8646	−1.49231
$486$	2.51124	0.113912
$487$	20.1934	0.915052	0.457526	−	0.889196i	$-0.348736\pi$
$487$	20.1934	0.915052	0.457526	+	0.889196i	$0.348736\pi$
$488$	72.0350	3.26087
$489$	−16.7973	−0.759599
$490$	35.9001	1.62180
$491$	1.20309	0.0542945	0.0271472	−	0.999631i	$-0.491358\pi$
$491$	1.20309	0.0542945	0.0271472	+	0.999631i	$0.491358\pi$
$492$	−31.7504	−1.43142
$493$	−4.14979	−0.186897
$494$	−2.41842	−0.108810
$495$	10.1570	0.456523
$496$	65.3353	2.93364
$497$	−3.98818	−0.178894
$498$	−41.3650	−1.85361
$499$	13.6638	0.611674	0.305837	−	0.952084i	$-0.401064\pi$
$499$	13.6638	0.611674	0.305837	+	0.952084i	$0.401064\pi$
$500$	−50.8905	−2.27589
$501$	−10.5399	−0.470886
$502$	−20.6273	−0.920642
$503$	−17.6204	−0.785656	−0.392828	−	0.919612i	$-0.628503\pi$
$503$	−17.6204	−0.785656	−0.392828	+	0.919612i	$0.628503\pi$
$504$	1.90772	0.0849768
$505$	−25.1142	−1.11757
$506$	−12.2959	−0.546620
$507$	8.09366	0.359452
$508$	−47.7266	−2.11752
$509$	38.6815	1.71453	0.857264	−	0.514877i	$-0.172162\pi$
$509$	38.6815	1.71453	0.857264	+	0.514877i	$0.172162\pi$
$510$	21.6176	0.957245
$511$	−2.61252	−0.115571
$512$	49.0610	2.16821
$513$	−0.434775	−0.0191958
$514$	−26.4108	−1.16493
$515$	−24.6274	−1.08521
$516$	−1.99507	−0.0878281
$517$	20.2988	0.892742
$518$	0.542470	0.0238347
$519$	22.2051	0.974696
$520$	−26.6124	−1.16703
$521$	3.48891	0.152852	0.0764259	−	0.997075i	$-0.475649\pi$
$521$	3.48891	0.152852	0.0764259	+	0.997075i	$0.475649\pi$
$522$	2.51124	0.109914
$523$	1.19981	0.0524641	0.0262321	−	0.999656i	$-0.491649\pi$
$523$	1.19981	0.0524641	0.0262321	+	0.999656i	$0.491649\pi$
$524$	72.1881	3.15355
$525$	−0.229532	−0.0100176
$526$	6.96714	0.303782
$527$	45.7068	1.99102
$528$	−29.0446	−1.26400
$529$	1.00000	0.0434783
$530$	−12.0302	−0.522560
$531$	9.22421	0.400296
$532$	−0.616703	−0.0267374
$533$	16.3312	0.707385
$534$	19.8109	0.857304
$535$	−8.11805	−0.350974
$536$	84.9053	3.66735
$537$	−5.20296	−0.224524
$538$	−59.5178	−2.56600
$539$	−33.7432	−1.45342
$540$	−8.93309	−0.384419
$541$	−23.3264	−1.00288	−0.501439	−	0.865193i	$-0.667196\pi$
$541$	−23.3264	−1.00288	−0.501439	+	0.865193i	$0.667196\pi$
$542$	−19.9604	−0.857373
$543$	−25.8911	−1.11109
$544$	−13.7477	−0.589427
$545$	12.6590	0.542254
$546$	−1.83219	−0.0784105
$547$	4.42366	0.189142	0.0945711	−	0.995518i	$-0.469852\pi$
$547$	4.42366	0.189142	0.0945711	+	0.995518i	$0.469852\pi$
$548$	5.61900	0.240032
$549$	−12.4374	−0.530817
$550$	8.56842	0.365359
$551$	−0.434775	−0.0185220
$552$	5.79178	0.246515
$553$	2.08431	0.0886337
$554$	9.90134	0.420668
$555$	−1.36043	−0.0577471
$556$	2.18196	0.0925355
$557$	2.29640	0.0973014	0.0486507	−	0.998816i	$-0.484508\pi$
$557$	2.29640	0.0973014	0.0486507	+	0.998816i	$0.484508\pi$
$558$	−27.6594	−1.17092
$559$	1.02619	0.0434033
$560$	−4.05312	−0.171276
$561$	−20.3188	−0.857861
$562$	−49.6453	−2.09416
$563$	9.63174	0.405929	0.202965	−	0.979186i	$-0.434942\pi$
$563$	9.63174	0.405929	0.202965	+	0.979186i	$0.434942\pi$
$564$	−17.8529	−0.751741
$565$	−7.65911	−0.322221
$566$	49.0917	2.06348
$567$	−0.329384	−0.0138328
$568$	−70.1268	−2.94245
$569$	−19.6362	−0.823191	−0.411596	−	0.911367i	$-0.635028\pi$
$569$	−19.6362	−0.823191	−0.411596	+	0.911367i	$0.635028\pi$
$570$	2.26488	0.0948656
$571$	−0.0358829	−0.00150165	−0.000750827	−	1.00000i	$-0.500239\pi$
$571$	−0.0358829	−0.00150165	−0.000750827		1.00000i	$0.500239\pi$
$572$	46.7046	1.95282
$573$	18.1086	0.756499
$574$	6.09863	0.254552
$575$	−0.696851	−0.0290607
$576$	−3.54439	−0.147683
$577$	20.4917	0.853082	0.426541	−	0.904468i	$-0.359732\pi$
$577$	20.4917	0.853082	0.426541	+	0.904468i	$0.359732\pi$
$578$	−0.554430	−0.0230613
$579$	−21.6895	−0.901385
$580$	−8.93309	−0.370926
$581$	5.42560	0.225092
$582$	−39.7855	−1.64916
$583$	11.3074	0.468306
$584$	−45.9377	−1.90091
$585$	4.59486	0.189974
$586$	−27.1309	−1.12077
$587$	39.7227	1.63953	0.819766	−	0.572698i	$-0.194103\pi$
$587$	39.7227	1.63953	0.819766	+	0.572698i	$0.194103\pi$
$588$	29.6772	1.22387
$589$	4.78871	0.197316
$590$	−48.0519	−1.97827
$591$	12.8759	0.529642
$592$	3.89024	0.159888
$593$	18.9906	0.779849	0.389925	−	0.920847i	$-0.372501\pi$
$593$	18.9906	0.779849	0.389925	+	0.920847i	$0.372501\pi$
$594$	12.2959	0.504507
$595$	−2.83545	−0.116242
$596$	−53.4367	−2.18885
$597$	−9.73022	−0.398231
$598$	−5.56247	−0.227466
$599$	−15.1699	−0.619823	−0.309912	−	0.950765i	$-0.600300\pi$
$599$	−15.1699	−0.619823	−0.309912	+	0.950765i	$0.600300\pi$
$600$	−4.03601	−0.164770
$601$	−15.7115	−0.640885	−0.320442	−	0.947268i	$-0.603832\pi$
$601$	−15.7115	−0.640885	−0.320442	+	0.947268i	$0.603832\pi$
$602$	0.383214	0.0156186
$603$	−14.6596	−0.596985
$604$	75.2203	3.06067
$605$	26.9137	1.09420
$606$	−30.4029	−1.23503
$607$	16.9322	0.687257	0.343628	−	0.939106i	$-0.388344\pi$
$607$	16.9322	0.687257	0.343628	+	0.939106i	$0.388344\pi$
$608$	−1.44035	−0.0584138
$609$	−0.329384	−0.0133473
$610$	64.7907	2.62330
$611$	9.18286	0.371499
$612$	17.8704	0.722369
$613$	−41.5232	−1.67710	−0.838552	−	0.544821i	$-0.816598\pi$
$613$	−41.5232	−1.67710	−0.838552	+	0.544821i	$0.816598\pi$
$614$	−10.4612	−0.422179
$615$	−15.2944	−0.616731
$616$	9.34087	0.376355
$617$	−15.0521	−0.605975	−0.302988	−	0.952994i	$-0.597984\pi$
$617$	−15.0521	−0.605975	−0.302988	+	0.952994i	$0.597984\pi$
$618$	−29.8136	−1.19928
$619$	−33.7558	−1.35676	−0.678381	−	0.734711i	$-0.737318\pi$
$619$	−33.7558	−1.35676	−0.678381	+	0.734711i	$0.737318\pi$
$620$	98.3912	3.95149
$621$	−1.00000	−0.0401286
$622$	20.5188	0.822727
$623$	−2.59848	−0.104106
$624$	−13.1393	−0.525993
$625$	−21.0301	−0.841206
$626$	−34.3795	−1.37408
$627$	−2.12881	−0.0850164
$628$	1.24701	0.0497612
$629$	2.72151	0.108514
$630$	1.71587	0.0683620
$631$	25.8463	1.02893	0.514463	−	0.857513i	$-0.327991\pi$
$631$	25.8463	1.02893	0.514463	+	0.857513i	$0.327991\pi$
$632$	36.6497	1.45785
$633$	−21.1320	−0.839922
$634$	49.0745	1.94900
$635$	−22.9903	−0.912342
$636$	−9.94490	−0.394341
$637$	−15.2649	−0.604816
$638$	12.2959	0.486800
$639$	12.1080	0.478984
$640$	32.2083	1.27315
$641$	11.5642	0.456757	0.228378	−	0.973572i	$-0.426658\pi$
$641$	11.5642	0.456757	0.228378	+	0.973572i	$0.426658\pi$
$642$	−9.82760	−0.387864
$643$	−19.5700	−0.771766	−0.385883	−	0.922548i	$-0.626103\pi$
$643$	−19.5700	−0.771766	−0.385883	+	0.922548i	$0.626103\pi$
$644$	−1.41844	−0.0558944
$645$	−0.961043	−0.0378410
$646$	−4.53085	−0.178264
$647$	7.87567	0.309624	0.154812	−	0.987944i	$-0.450523\pi$
$647$	7.87567	0.309624	0.154812	+	0.987944i	$0.450523\pi$
$648$	−5.79178	−0.227523
$649$	45.1649	1.77288
$650$	3.87621	0.152038
$651$	3.62792	0.142189
$652$	72.3348	2.83285
$653$	−11.7165	−0.458503	−0.229251	−	0.973367i	$-0.573628\pi$
$653$	−11.7165	−0.458503	−0.229251	+	0.973367i	$0.573628\pi$
$654$	15.3249	0.599250
$655$	34.7737	1.35872
$656$	43.7355	1.70758
$657$	7.93152	0.309438
$658$	3.42919	0.133684
$659$	23.7139	0.923761	0.461881	−	0.886942i	$-0.347175\pi$
$659$	23.7139	0.923761	0.461881	+	0.886942i	$0.347175\pi$
$660$	−43.7395	−1.70256
$661$	9.06231	0.352483	0.176242	−	0.984347i	$-0.443606\pi$
$661$	9.06231	0.352483	0.176242	+	0.984347i	$0.443606\pi$
$662$	30.0332	1.16727
$663$	−9.19190	−0.356984
$664$	95.4018	3.70231
$665$	−0.297071	−0.0115199
$666$	−1.64692	−0.0638168
$667$	−1.00000	−0.0387202
$668$	45.3882	1.75612
$669$	−18.3905	−0.711018
$670$	76.3667	2.95030
$671$	−60.8980	−2.35094
$672$	−1.09120	−0.0420941
$673$	12.5398	0.483374	0.241687	−	0.970354i	$-0.422299\pi$
$673$	12.5398	0.483374	0.241687	+	0.970354i	$0.422299\pi$
$674$	35.4868	1.36690
$675$	0.696851	0.0268218
$676$	−34.8541	−1.34054
$677$	−13.0087	−0.499964	−0.249982	−	0.968250i	$-0.580425\pi$
$677$	−13.0087	−0.499964	−0.249982	+	0.968250i	$0.580425\pi$
$678$	−9.27201	−0.356089
$679$	5.21842	0.200265
$680$	−49.8577	−1.91195
$681$	−20.9143	−0.801438
$682$	−135.430	−5.18589
$683$	−24.1598	−0.924449	−0.462225	−	0.886763i	$-0.652949\pi$
$683$	−24.1598	−0.924449	−0.462225	+	0.886763i	$0.652949\pi$
$684$	1.87229	0.0715887
$685$	2.70672	0.103419
$686$	−11.4906	−0.438712
$687$	−6.61855	−0.252513
$688$	2.74817	0.104773
$689$	5.11530	0.194877
$690$	5.20933	0.198316
$691$	−8.79410	−0.334543	−0.167272	−	0.985911i	$-0.553496\pi$
$691$	−8.79410	−0.334543	−0.167272	+	0.985911i	$0.553496\pi$
$692$	−95.6228	−3.63503
$693$	−1.61278	−0.0612645
$694$	12.8769	0.488800
$695$	1.05107	0.0398693
$696$	−5.79178	−0.219537
$697$	30.5961	1.15891
$698$	60.6272	2.29477
$699$	17.6336	0.666965
$700$	0.988443	0.0373596
$701$	−17.1365	−0.647238	−0.323619	−	0.946188i	$-0.604900\pi$
$701$	−17.1365	−0.647238	−0.323619	+	0.946188i	$0.604900\pi$
$702$	5.56247	0.209942
$703$	0.285133	0.0107540
$704$	−17.3546	−0.654075
$705$	−8.59988	−0.323890
$706$	−39.1724	−1.47427
$707$	3.98776	0.149975
$708$	−39.7226	−1.49287
$709$	11.6715	0.438331	0.219166	−	0.975688i	$-0.429666\pi$
$709$	11.6715	0.438331	0.219166	+	0.975688i	$0.429666\pi$
$710$	−63.0744	−2.36714
$711$	−6.32788	−0.237314
$712$	−45.6908	−1.71234
$713$	11.0142	0.412487
$714$	−3.43256	−0.128460
$715$	22.4980	0.841378
$716$	22.4057	0.837341
$717$	3.61613	0.135047
$718$	−40.3189	−1.50469
$719$	−43.8644	−1.63587	−0.817933	−	0.575313i	$-0.804880\pi$
$719$	−43.8644	−1.63587	−0.817933	+	0.575313i	$0.804880\pi$
$720$	12.3051	0.458586
$721$	3.91047	0.145634
$722$	47.2389	1.75805
$723$	27.5459	1.02444
$724$	111.496	4.14371
$725$	0.696851	0.0258804
$726$	32.5814	1.20921
$727$	50.0227	1.85524	0.927620	−	0.373526i	$-0.121851\pi$
$727$	50.0227	1.85524	0.927620	+	0.373526i	$0.121851\pi$
$728$	4.22566	0.156613
$729$	1.00000	0.0370370
$730$	−41.3179	−1.52925
$731$	1.92254	0.0711078
$732$	53.5599	1.97963
$733$	−8.42563	−0.311208	−0.155604	−	0.987820i	$-0.549732\pi$
$733$	−8.42563	−0.311208	−0.155604	+	0.987820i	$0.549732\pi$
$734$	−60.6987	−2.24043
$735$	14.2958	0.527307
$736$	−3.31286	−0.122114
$737$	−71.7785	−2.64399
$738$	−18.5152	−0.681555
$739$	−34.3160	−1.26234	−0.631168	−	0.775646i	$-0.717424\pi$
$739$	−34.3160	−1.26234	−0.631168	+	0.775646i	$0.717424\pi$
$740$	5.85848	0.215362
$741$	−0.963037	−0.0353780
$742$	1.91022	0.0701264
$743$	−26.1566	−0.959594	−0.479797	−	0.877380i	$-0.659290\pi$
$743$	−26.1566	−0.959594	−0.479797	+	0.877380i	$0.659290\pi$
$744$	63.7921	2.33873
$745$	−25.7409	−0.943075
$746$	−1.05162	−0.0385024
$747$	−16.4719	−0.602676
$748$	87.4998	3.19931
$749$	1.28903	0.0471000
$750$	−29.6768	−1.08364
$751$	−2.94242	−0.107370	−0.0536852	−	0.998558i	$-0.517097\pi$
$751$	−2.94242	−0.107370	−0.0536852	+	0.998558i	$0.517097\pi$
$752$	24.5919	0.896775
$753$	−8.21398	−0.299334
$754$	5.56247	0.202573
$755$	36.2343	1.31870
$756$	1.41844	0.0515882
$757$	−30.5553	−1.11055	−0.555276	−	0.831666i	$-0.687388\pi$
$757$	−30.5553	−1.11055	−0.555276	+	0.831666i	$0.687388\pi$
$758$	32.4826	1.17982
$759$	−4.89635	−0.177726
$760$	−5.22360	−0.189480
$761$	7.04354	0.255328	0.127664	−	0.991817i	$-0.459252\pi$
$761$	7.04354	0.255328	0.127664	+	0.991817i	$0.459252\pi$
$762$	−27.8317	−1.00824
$763$	−2.01007	−0.0727694
$764$	−77.9819	−2.82129
$765$	8.60834	0.311235
$766$	−48.7977	−1.76313
$767$	20.4319	0.737752
$768$	31.9022	1.15117
$769$	−38.3769	−1.38391	−0.691954	−	0.721942i	$-0.743250\pi$
$769$	−38.3769	−1.38391	−0.691954	+	0.721942i	$0.743250\pi$
$770$	8.40150	0.302769
$771$	−10.5170	−0.378761
$772$	93.4024	3.36163
$773$	−16.3163	−0.586858	−0.293429	−	0.955981i	$-0.594796\pi$
$773$	−16.3163	−0.586858	−0.293429	+	0.955981i	$0.594796\pi$
$774$	−1.16343	−0.0418184
$775$	−7.67529	−0.275705
$776$	91.7589	3.29395
$777$	0.216016	0.00774954
$778$	−31.9294	−1.14472
$779$	3.20556	0.114851
$780$	−19.7870	−0.708489
$781$	59.2848	2.12138
$782$	−10.4211	−0.372659
$783$	1.00000	0.0357371
$784$	−40.8797	−1.45999
$785$	0.600697	0.0214398
$786$	42.0965	1.50153
$787$	−34.1348	−1.21677	−0.608387	−	0.793640i	$-0.708183\pi$
$787$	−34.1348	−1.21677	−0.608387	+	0.793640i	$0.708183\pi$
$788$	−55.4479	−1.97525
$789$	2.77438	0.0987705
$790$	32.9640	1.17281
$791$	1.21615	0.0432414
$792$	−28.3586	−1.00768
$793$	−27.5493	−0.978303
$794$	9.60519	0.340875
$795$	−4.79055	−0.169903
$796$	41.9016	1.48516
$797$	2.65681	0.0941091	0.0470546	−	0.998892i	$-0.485017\pi$
$797$	2.65681	0.0941091	0.0470546	+	0.998892i	$0.485017\pi$
$798$	−0.359630	−0.0127308
$799$	17.2038	0.608628
$800$	2.30857	0.0816203
$801$	7.88890	0.278741
$802$	64.5514	2.27939
$803$	38.8355	1.37047
$804$	63.1293	2.22640
$805$	−0.683276	−0.0240823
$806$	−61.2664	−2.15802
$807$	−23.7005	−0.834299
$808$	70.1195	2.46679
$809$	1.46905	0.0516491	0.0258246	−	0.999666i	$-0.491779\pi$
$809$	1.46905	0.0516491	0.0258246	+	0.999666i	$0.491779\pi$
$810$	−5.20933	−0.183037
$811$	−10.8251	−0.380119	−0.190060	−	0.981773i	$-0.560868\pi$
$811$	−10.8251	−0.380119	−0.190060	+	0.981773i	$0.560868\pi$
$812$	1.41844	0.0497776
$813$	−7.94842	−0.278763
$814$	−8.06389	−0.282639
$815$	34.8443	1.22054
$816$	−24.6161	−0.861737
$817$	0.201425	0.00704698
$818$	8.59308	0.300450
$819$	−0.729595	−0.0254941
$820$	65.8631	2.30004
$821$	−11.6328	−0.405988	−0.202994	−	0.979180i	$-0.565067\pi$
$821$	−11.6328	−0.405988	−0.202994	+	0.979180i	$0.565067\pi$
$822$	3.27672	0.114289
$823$	41.5811	1.44942	0.724712	−	0.689051i	$-0.241973\pi$
$823$	41.5811	1.44942	0.724712	+	0.689051i	$0.241973\pi$
$824$	68.7604	2.39538
$825$	3.41202	0.118791
$826$	7.62994	0.265479
$827$	26.0406	0.905521	0.452760	−	0.891632i	$-0.350439\pi$
$827$	26.0406	0.905521	0.452760	+	0.891632i	$0.350439\pi$
$828$	4.30634	0.149656
$829$	−7.98370	−0.277285	−0.138643	−	0.990342i	$-0.544274\pi$
$829$	−7.98370	−0.277285	−0.138643	+	0.990342i	$0.544274\pi$
$830$	85.8077	2.97843
$831$	3.94280	0.136774
$832$	−7.85092	−0.272182
$833$	−28.5983	−0.990873
$834$	1.27241	0.0440599
$835$	21.8639	0.756632
$836$	9.16737	0.317060
$837$	−11.0142	−0.380708
$838$	17.1856	0.593666
$839$	−47.9200	−1.65438	−0.827191	−	0.561920i	$-0.810063\pi$
$839$	−47.9200	−1.65438	−0.827191	+	0.561920i	$0.810063\pi$
$840$	−3.95739	−0.136543
$841$	1.00000	0.0344828
$842$	−76.0084	−2.61942
$843$	−19.7692	−0.680888
$844$	91.0017	3.13241
$845$	−16.7895	−0.577577
$846$	−10.4109	−0.357934
$847$	−4.27350	−0.146839
$848$	13.6989	0.470422
$849$	19.5488	0.670912
$850$	7.26198	0.249084
$851$	0.655818	0.0224812
$852$	−52.1411	−1.78632
$853$	−9.80607	−0.335753	−0.167877	−	0.985808i	$-0.553691\pi$
$853$	−9.80607	−0.335753	−0.167877	+	0.985808i	$0.553691\pi$
$854$	−10.2878	−0.352042
$855$	0.901898	0.0308443
$856$	22.6658	0.774701
$857$	1.34916	0.0460864	0.0230432	−	0.999734i	$-0.492664\pi$
$857$	1.34916	0.0460864	0.0230432	+	0.999734i	$0.492664\pi$
$858$	27.2358	0.929814
$859$	−0.248201	−0.00846852	−0.00423426	−	0.999991i	$-0.501348\pi$
$859$	−0.248201	−0.00846852	−0.00423426	+	0.999991i	$0.501348\pi$
$860$	4.13858	0.141124
$861$	2.42853	0.0827641
$862$	59.8633	2.03895
$863$	−47.4175	−1.61411	−0.807055	−	0.590476i	$-0.798940\pi$
$863$	−47.4175	−1.61411	−0.807055	+	0.590476i	$0.798940\pi$
$864$	3.31286	0.112706
$865$	−46.0623	−1.56617
$866$	81.1416	2.75731
$867$	−0.220779	−0.00749805
$868$	−15.6231	−0.530281
$869$	−30.9835	−1.05104
$870$	−5.20933	−0.176613
$871$	−32.4714	−1.10025
$872$	−35.3444	−1.19691
$873$	−15.8429	−0.536202
$874$	−1.09182	−0.0369315
$875$	3.89252	0.131591
$876$	−34.1558	−1.15402
$877$	−24.3089	−0.820852	−0.410426	−	0.911894i	$-0.634620\pi$
$877$	−24.3089	−0.820852	−0.410426	+	0.911894i	$0.634620\pi$
$878$	7.88543	0.266120
$879$	−10.8038	−0.364402
$880$	60.2502	2.03103
$881$	−27.4357	−0.924332	−0.462166	−	0.886793i	$-0.652928\pi$
$881$	−27.4357	−0.924332	−0.462166	+	0.886793i	$0.652928\pi$
$882$	17.3062	0.582732
$883$	−24.8918	−0.837676	−0.418838	−	0.908061i	$-0.637562\pi$
$883$	−24.8918	−0.837676	−0.418838	+	0.908061i	$0.637562\pi$
$884$	39.5835	1.33134
$885$	−19.1347	−0.643207
$886$	−50.4597	−1.69523
$887$	12.2114	0.410019	0.205009	−	0.978760i	$-0.434277\pi$
$887$	12.2114	0.410019	0.205009	+	0.978760i	$0.434277\pi$
$888$	3.79836	0.127465
$889$	3.65052	0.122434
$890$	−41.0959	−1.37754
$891$	4.89635	0.164034
$892$	79.1958	2.65167
$893$	1.80245	0.0603167
$894$	−31.1616	−1.04220
$895$	10.7930	0.360771
$896$	−5.11420	−0.170854
$897$	−2.21503	−0.0739576
$898$	66.6101	2.22281
$899$	−11.0142	−0.367346
$900$	−3.00088	−0.100029
$901$	9.58337	0.319268
$902$	−90.6570	−3.01855
$903$	0.152599	0.00507819
$904$	21.3844	0.711235
$905$	53.7086	1.78533
$906$	43.8647	1.45731
$907$	−22.2846	−0.739949	−0.369975	−	0.929042i	$-0.620634\pi$
$907$	−22.2846	−0.739949	−0.369975	+	0.929042i	$0.620634\pi$
$908$	90.0641	2.98888
$909$	−12.1067	−0.401554
$910$	3.80070	0.125992
$911$	24.4401	0.809736	0.404868	−	0.914375i	$-0.367318\pi$
$911$	24.4401	0.809736	0.404868	+	0.914375i	$0.367318\pi$
$912$	−2.57904	−0.0854004
$913$	−80.6522	−2.66920
$914$	−62.5111	−2.06768
$915$	25.8003	0.852931
$916$	28.5017	0.941723
$917$	−5.52154	−0.182337
$918$	10.4211	0.343949
$919$	−32.0653	−1.05774	−0.528869	−	0.848704i	$-0.677384\pi$
$919$	−32.0653	−1.05774	−0.528869	+	0.848704i	$0.677384\pi$
$920$	−12.0145	−0.396106
$921$	−4.16574	−0.137266
$922$	−35.9446	−1.18377
$923$	26.8195	0.882774
$924$	6.94518	0.228480
$925$	−0.457008	−0.0150263
$926$	29.1674	0.958501
$927$	−11.8721	−0.389930
$928$	3.31286	0.108750
$929$	58.1912	1.90919	0.954596	−	0.297902i	$-0.0962868\pi$
$929$	58.1912	1.90919	0.954596	+	0.297902i	$0.0962868\pi$
$930$	57.3768	1.88146
$931$	−2.99625	−0.0981982
$932$	−75.9364	−2.48738
$933$	8.17076	0.267499
$934$	−19.7055	−0.644785
$935$	42.1494	1.37843
$936$	−12.8290	−0.419327
$937$	23.5858	0.770515	0.385258	−	0.922809i	$-0.374113\pi$
$937$	23.5858	0.770515	0.385258	+	0.922809i	$0.374113\pi$
$938$	−12.1259	−0.395925
$939$	−13.6902	−0.446764
$940$	37.0340	1.20792
$941$	20.4455	0.666503	0.333252	−	0.942838i	$-0.391854\pi$
$941$	20.4455	0.666503	0.333252	+	0.942838i	$0.391854\pi$
$942$	0.727195	0.0236933
$943$	7.37293	0.240096
$944$	54.7170	1.78089
$945$	0.683276	0.0222270
$946$	−5.69653	−0.185210
$947$	7.80239	0.253544	0.126772	−	0.991932i	$-0.459538\pi$
$947$	7.80239	0.253544	0.126772	+	0.991932i	$0.459538\pi$
$948$	27.2500	0.885040
$949$	17.5685	0.570299
$950$	0.760839	0.0246849
$951$	19.5419	0.633690
$952$	7.91666	0.256580
$953$	23.6780	0.767007	0.383504	−	0.923539i	$-0.374717\pi$
$953$	23.6780	0.767007	0.383504	+	0.923539i	$0.374717\pi$
$954$	−5.79937	−0.187761
$955$	−37.5646	−1.21556
$956$	−15.5723	−0.503644
$957$	4.89635	0.158276
$958$	22.7446	0.734846
$959$	−0.429787	−0.0138786
$960$	7.35250	0.237301
$961$	90.3136	2.91334
$962$	−3.64797	−0.117615
$963$	−3.91344	−0.126109
$964$	−118.622	−3.82056
$965$	44.9928	1.44837
$966$	−0.827164	−0.0266136
$967$	37.1140	1.19350	0.596752	−	0.802425i	$-0.296457\pi$
$967$	37.1140	1.19350	0.596752	+	0.802425i	$0.296457\pi$
$968$	−75.1438	−2.41521
$969$	−1.80422	−0.0579600
$970$	82.5311	2.64991
$971$	3.64698	0.117037	0.0585185	−	0.998286i	$-0.481362\pi$
$971$	3.64698	0.117037	0.0585185	+	0.998286i	$0.481362\pi$
$972$	−4.30634	−0.138126
$973$	−0.166894	−0.00535037
$974$	−50.7106	−1.62487
$975$	1.54354	0.0494330
$976$	−73.7776	−2.36156
$977$	18.3292	0.586403	0.293201	−	0.956051i	$-0.405279\pi$
$977$	18.3292	0.586403	0.293201	+	0.956051i	$0.405279\pi$
$978$	42.1820	1.34883
$979$	38.6268	1.23452
$980$	−61.5624	−1.96654
$981$	6.10250	0.194838
$982$	−3.02124	−0.0964116
$983$	−11.7224	−0.373885	−0.186943	−	0.982371i	$-0.559858\pi$
$983$	−11.7224	−0.373885	−0.186943	+	0.982371i	$0.559858\pi$
$984$	42.7024	1.36130
$985$	−26.7097	−0.851043
$986$	10.4211	0.331877
$987$	1.36553	0.0434654
$988$	4.14717	0.131939
$989$	0.463287	0.0147317
$990$	−25.5067	−0.810656
$991$	31.0791	0.987260	0.493630	−	0.869672i	$-0.335670\pi$
$991$	31.0791	0.987260	0.493630	+	0.869672i	$0.335670\pi$
$992$	−36.4886	−1.15852
$993$	11.9595	0.379523
$994$	10.0153	0.317665
$995$	20.1844	0.639888
$996$	70.9337	2.24762
$997$	−46.6959	−1.47887	−0.739437	−	0.673226i	$-0.764908\pi$
$997$	−46.6959	−1.47887	−0.739437	+	0.673226i	$0.764908\pi$
$998$	−34.3130	−1.08616
$999$	−0.655818	−0.0207492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.1	✓	11
3.2	odd	2		6003.2.a.m.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.1	✓	11	1.1	even	1	trivial
6003.2.a.m.1.11		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51124 q^{2} -1.00000 q^{3} +4.30634 q^{4} +2.07440 q^{5} +2.51124 q^{6} -0.329384 q^{7} -5.79178 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51124 q^{2} -1.00000 q^{3} +4.30634 q^{4} +2.07440 q^{5} +2.51124 q^{6} -0.329384 q^{7} -5.79178 q^{8} +1.00000 q^{9} -5.20933 q^{10} +4.89635 q^{11} -4.30634 q^{12} +2.21503 q^{13} +0.827164 q^{14} -2.07440 q^{15} +5.93189 q^{16} +4.14979 q^{17} -2.51124 q^{18} +0.434775 q^{19} +8.93309 q^{20} +0.329384 q^{21} -12.2959 q^{22} +1.00000 q^{23} +5.79178 q^{24} -0.696851 q^{25} -5.56247 q^{26} -1.00000 q^{27} -1.41844 q^{28} -1.00000 q^{29} +5.20933 q^{30} +11.0142 q^{31} -3.31286 q^{32} -4.89635 q^{33} -10.4211 q^{34} -0.683276 q^{35} +4.30634 q^{36} +0.655818 q^{37} -1.09182 q^{38} -2.21503 q^{39} -12.0145 q^{40} +7.37293 q^{41} -0.827164 q^{42} +0.463287 q^{43} +21.0853 q^{44} +2.07440 q^{45} -2.51124 q^{46} +4.14571 q^{47} -5.93189 q^{48} -6.89151 q^{49} +1.74996 q^{50} -4.14979 q^{51} +9.53866 q^{52} +2.30936 q^{53} +2.51124 q^{54} +10.1570 q^{55} +1.90772 q^{56} -0.434775 q^{57} +2.51124 q^{58} +9.22421 q^{59} -8.93309 q^{60} -12.4374 q^{61} -27.6594 q^{62} -0.329384 q^{63} -3.54439 q^{64} +4.59486 q^{65} +12.2959 q^{66} -14.6596 q^{67} +17.8704 q^{68} -1.00000 q^{69} +1.71587 q^{70} +12.1080 q^{71} -5.79178 q^{72} +7.93152 q^{73} -1.64692 q^{74} +0.696851 q^{75} +1.87229 q^{76} -1.61278 q^{77} +5.56247 q^{78} -6.32788 q^{79} +12.3051 q^{80} +1.00000 q^{81} -18.5152 q^{82} -16.4719 q^{83} +1.41844 q^{84} +8.60834 q^{85} -1.16343 q^{86} +1.00000 q^{87} -28.3586 q^{88} +7.88890 q^{89} -5.20933 q^{90} -0.729595 q^{91} +4.30634 q^{92} -11.0142 q^{93} -10.4109 q^{94} +0.901898 q^{95} +3.31286 q^{96} -15.8429 q^{97} +17.3062 q^{98} +4.89635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more