LMFDB - Embedded newform 6011.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55964 q^{2} +0.828942 q^{3} +4.55177 q^{4} -3.75172 q^{5} -2.12180 q^{6} -2.60223 q^{7} -6.53163 q^{8} -2.31285 q^{9} +O(q^{10})$	\(q-2.55964 q^{2} +0.828942 q^{3} +4.55177 q^{4} -3.75172 q^{5} -2.12180 q^{6} -2.60223 q^{7} -6.53163 q^{8} -2.31285 q^{9} +9.60307 q^{10} -0.960243 q^{11} +3.77316 q^{12} +1.09941 q^{13} +6.66079 q^{14} -3.10996 q^{15} +7.61508 q^{16} +3.98534 q^{17} +5.92008 q^{18} -5.82523 q^{19} -17.0770 q^{20} -2.15710 q^{21} +2.45788 q^{22} +2.93972 q^{23} -5.41434 q^{24} +9.07542 q^{25} -2.81410 q^{26} -4.40405 q^{27} -11.8448 q^{28} +5.74232 q^{29} +7.96039 q^{30} -1.17251 q^{31} -6.42865 q^{32} -0.795986 q^{33} -10.2010 q^{34} +9.76285 q^{35} -10.5276 q^{36} -0.858185 q^{37} +14.9105 q^{38} +0.911348 q^{39} +24.5048 q^{40} +3.61399 q^{41} +5.52141 q^{42} -3.51054 q^{43} -4.37081 q^{44} +8.67719 q^{45} -7.52464 q^{46} -9.61662 q^{47} +6.31246 q^{48} -0.228386 q^{49} -23.2298 q^{50} +3.30362 q^{51} +5.00427 q^{52} -0.0846161 q^{53} +11.2728 q^{54} +3.60257 q^{55} +16.9968 q^{56} -4.82878 q^{57} -14.6983 q^{58} +9.87963 q^{59} -14.1558 q^{60} -5.70735 q^{61} +3.00120 q^{62} +6.01859 q^{63} +1.22487 q^{64} -4.12468 q^{65} +2.03744 q^{66} -15.7059 q^{67} +18.1404 q^{68} +2.43686 q^{69} -24.9894 q^{70} +14.2163 q^{71} +15.1067 q^{72} +14.0465 q^{73} +2.19665 q^{74} +7.52300 q^{75} -26.5151 q^{76} +2.49878 q^{77} -2.33272 q^{78} +10.9043 q^{79} -28.5697 q^{80} +3.28786 q^{81} -9.25053 q^{82} +5.16530 q^{83} -9.81863 q^{84} -14.9519 q^{85} +8.98572 q^{86} +4.76005 q^{87} +6.27195 q^{88} -8.58646 q^{89} -22.2105 q^{90} -2.86092 q^{91} +13.3809 q^{92} -0.971940 q^{93} +24.6151 q^{94} +21.8547 q^{95} -5.32898 q^{96} -6.97180 q^{97} +0.584587 q^{98} +2.22090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.55964	−1.80994	−0.904970	−	0.425474i	$-0.860107\pi$
$2$	−2.55964	−1.80994	−0.904970	+	0.425474i	$0.860107\pi$
$3$	0.828942	0.478590	0.239295	−	0.970947i	$-0.423084\pi$
$3$	0.828942	0.478590	0.239295	+	0.970947i	$0.423084\pi$
$4$	4.55177	2.27589
$5$	−3.75172	−1.67782	−0.838911	−	0.544269i	$-0.816807\pi$
$5$	−3.75172	−1.67782	−0.838911	+	0.544269i	$0.816807\pi$
$6$	−2.12180	−0.866220
$7$	−2.60223	−0.983551	−0.491776	−	0.870722i	$-0.663652\pi$
$7$	−2.60223	−0.983551	−0.491776	+	0.870722i	$0.663652\pi$
$8$	−6.53163	−2.30928
$9$	−2.31285	−0.770952
$10$	9.60307	3.03676
$11$	−0.960243	−0.289524	−0.144762	−	0.989466i	$-0.546242\pi$
$11$	−0.960243	−0.289524	−0.144762	+	0.989466i	$0.546242\pi$
$12$	3.77316	1.08922
$13$	1.09941	0.304922	0.152461	−	0.988310i	$-0.451280\pi$
$13$	1.09941	0.304922	0.152461	+	0.988310i	$0.451280\pi$
$14$	6.66079	1.78017
$15$	−3.10996	−0.802988
$16$	7.61508	1.90377
$17$	3.98534	0.966587	0.483294	−	0.875458i	$-0.339440\pi$
$17$	3.98534	0.966587	0.483294	+	0.875458i	$0.339440\pi$
$18$	5.92008	1.39538
$19$	−5.82523	−1.33640	−0.668200	−	0.743982i	$-0.732935\pi$
$19$	−5.82523	−1.33640	−0.668200	+	0.743982i	$0.732935\pi$
$20$	−17.0770	−3.81853
$21$	−2.15710	−0.470718
$22$	2.45788	0.524022
$23$	2.93972	0.612974	0.306487	−	0.951875i	$-0.400846\pi$
$23$	2.93972	0.612974	0.306487	+	0.951875i	$0.400846\pi$
$24$	−5.41434	−1.10520
$25$	9.07542	1.81508
$26$	−2.81410	−0.551890
$27$	−4.40405	−0.847560
$28$	−11.8448	−2.23845
$29$	5.74232	1.06632	0.533161	−	0.846014i	$-0.321004\pi$
$29$	5.74232	1.06632	0.533161	+	0.846014i	$0.321004\pi$
$30$	7.96039	1.45336
$31$	−1.17251	−0.210588	−0.105294	−	0.994441i	$-0.533578\pi$
$31$	−1.17251	−0.210588	−0.105294	+	0.994441i	$0.533578\pi$
$32$	−6.42865	−1.13643
$33$	−0.795986	−0.138563
$34$	−10.2010	−1.74947
$35$	9.76285	1.65022
$36$	−10.5276	−1.75460
$37$	−0.858185	−0.141085	−0.0705424	−	0.997509i	$-0.522473\pi$
$37$	−0.858185	−0.141085	−0.0705424	+	0.997509i	$0.522473\pi$
$38$	14.9105	2.41881
$39$	0.911348	0.145932
$40$	24.5048	3.87456
$41$	3.61399	0.564410	0.282205	−	0.959354i	$-0.408934\pi$
$41$	3.61399	0.564410	0.282205	+	0.959354i	$0.408934\pi$
$42$	5.52141	0.851971
$43$	−3.51054	−0.535352	−0.267676	−	0.963509i	$-0.586256\pi$
$43$	−3.51054	−0.535352	−0.267676	+	0.963509i	$0.586256\pi$
$44$	−4.37081	−0.658924
$45$	8.67719	1.29352
$46$	−7.52464	−1.10945
$47$	−9.61662	−1.40273	−0.701364	−	0.712803i	$-0.747425\pi$
$47$	−9.61662	−1.40273	−0.701364	+	0.712803i	$0.747425\pi$
$48$	6.31246	0.911126
$49$	−0.228386	−0.0326266
$50$	−23.2298	−3.28520
$51$	3.30362	0.462599
$52$	5.00427	0.693967
$53$	−0.0846161	−0.0116229	−0.00581146	−	0.999983i	$-0.501850\pi$
$53$	−0.0846161	−0.0116229	−0.00581146	+	0.999983i	$0.501850\pi$
$54$	11.2728	1.53403
$55$	3.60257	0.485770
$56$	16.9968	2.27129
$57$	−4.82878	−0.639588
$58$	−14.6983	−1.92998
$59$	9.87963	1.28622	0.643109	−	0.765775i	$-0.277644\pi$
$59$	9.87963	1.28622	0.643109	+	0.765775i	$0.277644\pi$
$60$	−14.1558	−1.82751
$61$	−5.70735	−0.730751	−0.365376	−	0.930860i	$-0.619059\pi$
$61$	−5.70735	−0.730751	−0.365376	+	0.930860i	$0.619059\pi$
$62$	3.00120	0.381152
$63$	6.01859	0.758271
$64$	1.22487	0.153109
$65$	−4.12468	−0.511604
$66$	2.03744	0.250792
$67$	−15.7059	−1.91879	−0.959393	−	0.282074i	$-0.908978\pi$
$67$	−15.7059	−1.91879	−0.959393	+	0.282074i	$0.908978\pi$
$68$	18.1404	2.19984
$69$	2.43686	0.293363
$70$	−24.9894	−2.98681
$71$	14.2163	1.68716	0.843580	−	0.537004i	$-0.180444\pi$
$71$	14.2163	1.68716	0.843580	+	0.537004i	$0.180444\pi$
$72$	15.1067	1.78034
$73$	14.0465	1.64401	0.822007	−	0.569478i	$-0.192854\pi$
$73$	14.0465	1.64401	0.822007	+	0.569478i	$0.192854\pi$
$74$	2.19665	0.255355
$75$	7.52300	0.868681
$76$	−26.5151	−3.04149
$77$	2.49878	0.284762
$78$	−2.33272	−0.264129
$79$	10.9043	1.22683	0.613413	−	0.789763i	$-0.289796\pi$
$79$	10.9043	1.22683	0.613413	+	0.789763i	$0.289796\pi$
$80$	−28.5697	−3.19419
$81$	3.28786	0.365318
$82$	−9.25053	−1.02155
$83$	5.16530	0.566965	0.283483	−	0.958977i	$-0.408510\pi$
$83$	5.16530	0.566965	0.283483	+	0.958977i	$0.408510\pi$
$84$	−9.81863	−1.07130
$85$	−14.9519	−1.62176
$86$	8.98572	0.968955
$87$	4.76005	0.510331
$88$	6.27195	0.668592
$89$	−8.58646	−0.910162	−0.455081	−	0.890450i	$-0.650390\pi$
$89$	−8.58646	−0.910162	−0.455081	+	0.890450i	$0.650390\pi$
$90$	−22.2105	−2.34119
$91$	−2.86092	−0.299906
$92$	13.3809	1.39506
$93$	−0.971940	−0.100785
$94$	24.6151	2.53886
$95$	21.8547	2.24224
$96$	−5.32898	−0.543886
$97$	−6.97180	−0.707879	−0.353939	−	0.935268i	$-0.615158\pi$
$97$	−6.97180	−0.707879	−0.353939	+	0.935268i	$0.615158\pi$
$98$	0.584587	0.0590522
$99$	2.22090	0.223209
$100$	41.3092	4.13092
$101$	19.1502	1.90552	0.952758	−	0.303731i	$-0.0982325\pi$
$101$	19.1502	1.90552	0.952758	+	0.303731i	$0.0982325\pi$
$102$	−8.45608	−0.837277
$103$	−6.13147	−0.604151	−0.302076	−	0.953284i	$-0.597680\pi$
$103$	−6.13147	−0.604151	−0.302076	+	0.953284i	$0.597680\pi$
$104$	−7.18094	−0.704149
$105$	8.09284	0.789780
$106$	0.216587	0.0210368
$107$	18.4096	1.77972	0.889859	−	0.456235i	$-0.150802\pi$
$107$	18.4096	1.77972	0.889859	+	0.456235i	$0.150802\pi$
$108$	−20.0462	−1.92895
$109$	4.50351	0.431358	0.215679	−	0.976464i	$-0.430803\pi$
$109$	4.50351	0.431358	0.215679	+	0.976464i	$0.430803\pi$
$110$	−9.22128	−0.879215
$111$	−0.711386	−0.0675218
$112$	−19.8162	−1.87246
$113$	16.3099	1.53430	0.767152	−	0.641465i	$-0.221673\pi$
$113$	16.3099	1.53430	0.767152	+	0.641465i	$0.221673\pi$
$114$	12.3600	1.15762
$115$	−11.0290	−1.02846
$116$	26.1377	2.42683
$117$	−2.54278	−0.235080
$118$	−25.2883	−2.32798
$119$	−10.3708	−0.950688
$120$	20.3131	1.85432
$121$	−10.0779	−0.916176
$122$	14.6088	1.32262
$123$	2.99579	0.270121
$124$	−5.33698	−0.479275
$125$	−15.2898	−1.36757
$126$	−15.4054	−1.37242
$127$	18.8588	1.67345	0.836724	−	0.547624i	$-0.184468\pi$
$127$	18.8588	1.67345	0.836724	+	0.547624i	$0.184468\pi$
$128$	9.72206	0.859317
$129$	−2.91003	−0.256214
$130$	10.5577	0.925973
$131$	−0.146203	−0.0127738	−0.00638691	−	0.999980i	$-0.502033\pi$
$131$	−0.146203	−0.0127738	−0.00638691	+	0.999980i	$0.502033\pi$
$132$	−3.62315	−0.315354
$133$	15.1586	1.31442
$134$	40.2016	3.47289
$135$	16.5228	1.42205
$136$	−26.0308	−2.23212
$137$	19.8729	1.69786	0.848930	−	0.528506i	$-0.177247\pi$
$137$	19.8729	1.69786	0.848930	+	0.528506i	$0.177247\pi$
$138$	−6.23749	−0.530970
$139$	18.0211	1.52853	0.764266	−	0.644901i	$-0.223102\pi$
$139$	18.0211	1.52853	0.764266	+	0.644901i	$0.223102\pi$
$140$	44.4383	3.75572
$141$	−7.97162	−0.671332
$142$	−36.3885	−3.05366
$143$	−1.05570	−0.0882822
$144$	−17.6126	−1.46772
$145$	−21.5436	−1.78910
$146$	−35.9539	−2.97557
$147$	−0.189319	−0.0156148
$148$	−3.90626	−0.321093
$149$	−18.1303	−1.48529	−0.742645	−	0.669686i	$-0.766429\pi$
$149$	−18.1303	−1.48529	−0.742645	+	0.669686i	$0.766429\pi$
$150$	−19.2562	−1.57226
$151$	−11.3999	−0.927712	−0.463856	−	0.885911i	$-0.653534\pi$
$151$	−11.3999	−0.927712	−0.463856	+	0.885911i	$0.653534\pi$
$152$	38.0482	3.08612
$153$	−9.21751	−0.745192
$154$	−6.39597	−0.515402
$155$	4.39892	0.353330
$156$	4.14825	0.332126
$157$	1.28277	0.102376	0.0511882	−	0.998689i	$-0.483699\pi$
$157$	1.28277	0.102376	0.0511882	+	0.998689i	$0.483699\pi$
$158$	−27.9110	−2.22048
$159$	−0.0701418	−0.00556261
$160$	24.1185	1.90673
$161$	−7.64984	−0.602892
$162$	−8.41576	−0.661204
$163$	15.9814	1.25176	0.625879	−	0.779920i	$-0.284740\pi$
$163$	15.9814	1.25176	0.625879	+	0.779920i	$0.284740\pi$
$164$	16.4501	1.28453
$165$	2.98632	0.232485
$166$	−13.2213	−1.02617
$167$	−16.3281	−1.26351	−0.631755	−	0.775168i	$-0.717665\pi$
$167$	−16.3281	−1.26351	−0.631755	+	0.775168i	$0.717665\pi$
$168$	14.0894	1.08702
$169$	−11.7913	−0.907023
$170$	38.2715	2.93529
$171$	13.4729	1.03030
$172$	−15.9792	−1.21840
$173$	6.23653	0.474155	0.237077	−	0.971491i	$-0.423810\pi$
$173$	6.23653	0.474155	0.237077	+	0.971491i	$0.423810\pi$
$174$	−12.1840	−0.923668
$175$	−23.6164	−1.78523
$176$	−7.31233	−0.551188
$177$	8.18964	0.615571
$178$	21.9783	1.64734
$179$	−6.12691	−0.457947	−0.228973	−	0.973433i	$-0.573537\pi$
$179$	−6.12691	−0.457947	−0.228973	+	0.973433i	$0.573537\pi$
$180$	39.4966	2.94390
$181$	−5.01771	−0.372963	−0.186482	−	0.982458i	$-0.559708\pi$
$181$	−5.01771	−0.372963	−0.186482	+	0.982458i	$0.559708\pi$
$182$	7.32294	0.542812
$183$	−4.73106	−0.349730
$184$	−19.2012	−1.41553
$185$	3.21967	0.236715
$186$	2.48782	0.182416
$187$	−3.82690	−0.279850
$188$	−43.7727	−3.19245
$189$	11.4604	0.833619
$190$	−55.9401	−4.05832
$191$	−18.9030	−1.36778	−0.683888	−	0.729587i	$-0.739712\pi$
$191$	−18.9030	−1.36778	−0.683888	+	0.729587i	$0.739712\pi$
$192$	1.01535	0.0732764
$193$	−12.0524	−0.867547	−0.433774	−	0.901022i	$-0.642818\pi$
$193$	−12.0524	−0.867547	−0.433774	+	0.901022i	$0.642818\pi$
$194$	17.8453	1.28122
$195$	−3.41912	−0.244849
$196$	−1.03956	−0.0742544
$197$	−19.4376	−1.38487	−0.692436	−	0.721479i	$-0.743463\pi$
$197$	−19.4376	−1.38487	−0.692436	+	0.721479i	$0.743463\pi$
$198$	−5.68472	−0.403995
$199$	−5.09502	−0.361176	−0.180588	−	0.983559i	$-0.557800\pi$
$199$	−5.09502	−0.361176	−0.180588	+	0.983559i	$0.557800\pi$
$200$	−59.2772	−4.19153
$201$	−13.0193	−0.918311
$202$	−49.0177	−3.44887
$203$	−14.9428	−1.04878
$204$	15.0373	1.05282
$205$	−13.5587	−0.946980
$206$	15.6944	1.09348
$207$	−6.79915	−0.472574
$208$	8.37210	0.580501
$209$	5.59364	0.386920
$210$	−20.7148	−1.42946
$211$	28.4452	1.95825	0.979124	−	0.203264i	$-0.0651551\pi$
$211$	28.4452	1.95825	0.979124	+	0.203264i	$0.0651551\pi$
$212$	−0.385153	−0.0264524
$213$	11.7845	0.807458
$214$	−47.1219	−3.22119
$215$	13.1706	0.898225
$216$	28.7656	1.95725
$217$	3.05113	0.207124
$218$	−11.5274	−0.780733
$219$	11.6437	0.786808
$220$	16.3981	1.10556
$221$	4.38153	0.294733
$222$	1.82089	0.122210
$223$	24.7914	1.66016	0.830078	−	0.557647i	$-0.188296\pi$
$223$	24.7914	1.66016	0.830078	+	0.557647i	$0.188296\pi$
$224$	16.7288	1.11774
$225$	−20.9901	−1.39934
$226$	−41.7475	−2.77700
$227$	8.58852	0.570040	0.285020	−	0.958522i	$-0.408000\pi$
$227$	8.58852	0.570040	0.285020	+	0.958522i	$0.408000\pi$
$228$	−21.9795	−1.45563
$229$	−9.92818	−0.656073	−0.328036	−	0.944665i	$-0.606387\pi$
$229$	−9.92818	−0.656073	−0.328036	+	0.944665i	$0.606387\pi$
$230$	28.2304	1.86145
$231$	2.07134	0.136284
$232$	−37.5067	−2.46243
$233$	−17.4972	−1.14628	−0.573140	−	0.819458i	$-0.694275\pi$
$233$	−17.4972	−1.14628	−0.573140	+	0.819458i	$0.694275\pi$
$234$	6.50860	0.425481
$235$	36.0789	2.35353
$236$	44.9698	2.92729
$237$	9.03900	0.587146
$238$	26.5455	1.72069
$239$	−23.4688	−1.51807	−0.759034	−	0.651051i	$-0.774328\pi$
$239$	−23.4688	−1.51807	−0.759034	+	0.651051i	$0.774328\pi$
$240$	−23.6826	−1.52871
$241$	0.452418	0.0291428	0.0145714	−	0.999894i	$-0.495362\pi$
$241$	0.452418	0.0291428	0.0145714	+	0.999894i	$0.495362\pi$
$242$	25.7959	1.65822
$243$	15.9376	1.02240
$244$	−25.9786	−1.66311
$245$	0.856841	0.0547416
$246$	−7.66815	−0.488903
$247$	−6.40432	−0.407497
$248$	7.65837	0.486307
$249$	4.28174	0.271344
$250$	39.1366	2.47521
$251$	−13.7898	−0.870402	−0.435201	−	0.900333i	$-0.643323\pi$
$251$	−13.7898	−0.870402	−0.435201	+	0.900333i	$0.643323\pi$
$252$	27.3952	1.72574
$253$	−2.82285	−0.177471
$254$	−48.2718	−3.02884
$255$	−12.3943	−0.776158
$256$	−27.3347	−1.70842
$257$	−15.3776	−0.959227	−0.479614	−	0.877480i	$-0.659223\pi$
$257$	−15.3776	−0.959227	−0.479614	+	0.877480i	$0.659223\pi$
$258$	7.44864	0.463732
$259$	2.23320	0.138764
$260$	−18.7746	−1.16435
$261$	−13.2811	−0.822082
$262$	0.374228	0.0231199
$263$	−18.4590	−1.13823	−0.569115	−	0.822258i	$-0.692714\pi$
$263$	−18.4590	−1.13823	−0.569115	+	0.822258i	$0.692714\pi$
$264$	5.19908	0.319981
$265$	0.317456	0.0195012
$266$	−38.8006	−2.37902
$267$	−7.11767	−0.435595
$268$	−71.4898	−4.36694
$269$	−31.0596	−1.89374	−0.946869	−	0.321620i	$-0.895773\pi$
$269$	−31.0596	−1.89374	−0.946869	+	0.321620i	$0.895773\pi$
$270$	−42.2924	−2.57383
$271$	9.22370	0.560300	0.280150	−	0.959956i	$-0.409616\pi$
$271$	9.22370	0.560300	0.280150	+	0.959956i	$0.409616\pi$
$272$	30.3487	1.84016
$273$	−2.37154	−0.143532
$274$	−50.8676	−3.07303
$275$	−8.71461	−0.525511
$276$	11.0920	0.667662
$277$	−13.0980	−0.786981	−0.393491	−	0.919329i	$-0.628733\pi$
$277$	−13.0980	−0.786981	−0.393491	+	0.919329i	$0.628733\pi$
$278$	−46.1276	−2.76655
$279$	2.71184	0.162353
$280$	−63.7673	−3.81083
$281$	−16.4723	−0.982657	−0.491328	−	0.870974i	$-0.663488\pi$
$281$	−16.4723	−0.982657	−0.491328	+	0.870974i	$0.663488\pi$
$282$	20.4045	1.21507
$283$	−6.53349	−0.388376	−0.194188	−	0.980964i	$-0.562207\pi$
$283$	−6.53349	−0.388376	−0.194188	+	0.980964i	$0.562207\pi$
$284$	64.7092	3.83978
$285$	18.1162	1.07311
$286$	2.70222	0.159786
$287$	−9.40444	−0.555127
$288$	14.8685	0.876136
$289$	−1.11706	−0.0657094
$290$	55.1439	3.23816
$291$	−5.77921	−0.338784
$292$	63.9363	3.74159
$293$	8.38719	0.489985	0.244992	−	0.969525i	$-0.421215\pi$
$293$	8.38719	0.489985	0.244992	+	0.969525i	$0.421215\pi$
$294$	0.484588	0.0282618
$295$	−37.0656	−2.15804
$296$	5.60535	0.325804
$297$	4.22896	0.245389
$298$	46.4070	2.68829
$299$	3.23196	0.186909
$300$	34.2430	1.97702
$301$	9.13523	0.526546
$302$	29.1797	1.67910
$303$	15.8744	0.911961
$304$	−44.3596	−2.54420
$305$	21.4124	1.22607
$306$	23.5935	1.34875
$307$	−8.52971	−0.486816	−0.243408	−	0.969924i	$-0.578265\pi$
$307$	−8.52971	−0.486816	−0.243408	+	0.969924i	$0.578265\pi$
$308$	11.3739	0.648086
$309$	−5.08263	−0.289141
$310$	−11.2597	−0.639506
$311$	29.4691	1.67104	0.835521	−	0.549459i	$-0.185166\pi$
$311$	29.4691	1.67104	0.835521	+	0.549459i	$0.185166\pi$
$312$	−5.95258	−0.336999
$313$	10.3352	0.584180	0.292090	−	0.956391i	$-0.405649\pi$
$313$	10.3352	0.584180	0.292090	+	0.956391i	$0.405649\pi$
$314$	−3.28344	−0.185295
$315$	−22.5801	−1.27224
$316$	49.6337	2.79211
$317$	0.131028	0.00735928	0.00367964	−	0.999993i	$-0.498829\pi$
$317$	0.131028	0.00735928	0.00367964	+	0.999993i	$0.498829\pi$
$318$	0.179538	0.0100680
$319$	−5.51402	−0.308726
$320$	−4.59538	−0.256889
$321$	15.2605	0.851755
$322$	19.5809	1.09120
$323$	−23.2155	−1.29175
$324$	14.9656	0.831422
$325$	9.97761	0.553458
$326$	−40.9066	−2.26561
$327$	3.73315	0.206444
$328$	−23.6052	−1.30338
$329$	25.0247	1.37966
$330$	−7.64391	−0.420783
$331$	29.2737	1.60903	0.804513	−	0.593935i	$-0.202426\pi$
$331$	29.2737	1.60903	0.804513	+	0.593935i	$0.202426\pi$
$332$	23.5113	1.29035
$333$	1.98486	0.108770
$334$	41.7942	2.28688
$335$	58.9243	3.21938
$336$	−16.4265	−0.896139
$337$	−17.1873	−0.936253	−0.468126	−	0.883662i	$-0.655071\pi$
$337$	−17.1873	−0.936253	−0.468126	+	0.883662i	$0.655071\pi$
$338$	30.1815	1.64166
$339$	13.5199	0.734303
$340$	−68.0576	−3.69094
$341$	1.12589	0.0609704
$342$	−34.4859	−1.86478
$343$	18.8099	1.01564
$344$	22.9295	1.23628
$345$	−9.14242	−0.492211
$346$	−15.9633	−0.858192
$347$	−20.5461	−1.10297	−0.551485	−	0.834185i	$-0.685939\pi$
$347$	−20.5461	−1.10297	−0.551485	+	0.834185i	$0.685939\pi$
$348$	21.6667	1.16145
$349$	−25.4276	−1.36111	−0.680555	−	0.732697i	$-0.738261\pi$
$349$	−25.4276	−1.36111	−0.680555	+	0.732697i	$0.738261\pi$
$350$	60.4494	3.23116
$351$	−4.84186	−0.258439
$352$	6.17306	0.329025
$353$	1.12083	0.0596560	0.0298280	−	0.999555i	$-0.490504\pi$
$353$	1.12083	0.0596560	0.0298280	+	0.999555i	$0.490504\pi$
$354$	−20.9626	−1.11415
$355$	−53.3355	−2.83075
$356$	−39.0836	−2.07143
$357$	−8.59678	−0.454990
$358$	15.6827	0.828856
$359$	23.9016	1.26148	0.630738	−	0.775996i	$-0.282752\pi$
$359$	23.9016	1.26148	0.630738	+	0.775996i	$0.282752\pi$
$360$	−56.6762	−2.98710
$361$	14.9333	0.785966
$362$	12.8435	0.675041
$363$	−8.35402	−0.438473
$364$	−13.0223	−0.682552
$365$	−52.6984	−2.75836
$366$	12.1098	0.632991
$367$	19.5968	1.02294	0.511472	−	0.859300i	$-0.329100\pi$
$367$	19.5968	1.02294	0.511472	+	0.859300i	$0.329100\pi$
$368$	22.3862	1.16696
$369$	−8.35864	−0.435133
$370$	−8.24121	−0.428440
$371$	0.220191	0.0114317
$372$	−4.42405	−0.229376
$373$	−13.3904	−0.693328	−0.346664	−	0.937989i	$-0.612686\pi$
$373$	−13.3904	−0.693328	−0.346664	+	0.937989i	$0.612686\pi$
$374$	9.79549	0.506513
$375$	−12.6744	−0.654503
$376$	62.8122	3.23929
$377$	6.31316	0.325144
$378$	−29.3344	−1.50880
$379$	−16.3314	−0.838887	−0.419443	−	0.907781i	$-0.637775\pi$
$379$	−16.3314	−0.838887	−0.419443	+	0.907781i	$0.637775\pi$
$380$	99.4774	5.10308
$381$	15.6329	0.800896
$382$	48.3850	2.47559
$383$	35.1677	1.79698	0.898492	−	0.438990i	$-0.144664\pi$
$383$	35.1677	1.79698	0.898492	+	0.438990i	$0.144664\pi$
$384$	8.05902	0.411260
$385$	−9.37471	−0.477780
$386$	30.8497	1.57021
$387$	8.11936	0.412730
$388$	−31.7340	−1.61105
$389$	4.54571	0.230477	0.115238	−	0.993338i	$-0.463237\pi$
$389$	4.54571	0.230477	0.115238	+	0.993338i	$0.463237\pi$
$390$	8.75173	0.443161
$391$	11.7158	0.592493
$392$	1.49173	0.0753438
$393$	−0.121194	−0.00611342
$394$	49.7533	2.50654
$395$	−40.9098	−2.05839
$396$	10.1090	0.507999
$397$	−24.9697	−1.25319	−0.626597	−	0.779343i	$-0.715553\pi$
$397$	−24.9697	−1.25319	−0.626597	+	0.779343i	$0.715553\pi$
$398$	13.0414	0.653708
$399$	12.5656	0.629067
$400$	69.1101	3.45550
$401$	15.9937	0.798686	0.399343	−	0.916802i	$-0.369238\pi$
$401$	15.9937	0.798686	0.399343	+	0.916802i	$0.369238\pi$
$402$	33.3248	1.66209
$403$	−1.28907	−0.0642129
$404$	87.1673	4.33674
$405$	−12.3351	−0.612938
$406$	38.2483	1.89823
$407$	0.824067	0.0408475
$408$	−21.5780	−1.06827
$409$	9.58725	0.474059	0.237029	−	0.971502i	$-0.423826\pi$
$409$	9.58725	0.474059	0.237029	+	0.971502i	$0.423826\pi$
$410$	34.7054	1.71398
$411$	16.4735	0.812579
$412$	−27.9090	−1.37498
$413$	−25.7091	−1.26506
$414$	17.4034	0.855330
$415$	−19.3788	−0.951267
$416$	−7.06772	−0.346524
$417$	14.9385	0.731540
$418$	−14.3177	−0.700303
$419$	−14.6435	−0.715379	−0.357690	−	0.933840i	$-0.616435\pi$
$419$	−14.6435	−0.715379	−0.357690	+	0.933840i	$0.616435\pi$
$420$	36.8368	1.79745
$421$	1.59339	0.0776570	0.0388285	−	0.999246i	$-0.487637\pi$
$421$	1.59339	0.0776570	0.0388285	+	0.999246i	$0.487637\pi$
$422$	−72.8095	−3.54431
$423$	22.2419	1.08144
$424$	0.552681	0.0268405
$425$	36.1686	1.75444
$426$	−30.1640	−1.46145
$427$	14.8518	0.718731
$428$	83.7961	4.05044
$429$	−0.875115	−0.0422510
$430$	−33.7119	−1.62573
$431$	−28.0942	−1.35325	−0.676624	−	0.736329i	$-0.736558\pi$
$431$	−28.0942	−1.35325	−0.676624	+	0.736329i	$0.736558\pi$
$432$	−33.5372	−1.61356
$433$	−33.7108	−1.62004	−0.810018	−	0.586405i	$-0.800543\pi$
$433$	−33.7108	−1.62004	−0.810018	+	0.586405i	$0.800543\pi$
$434$	−7.80981	−0.374883
$435$	−17.8584	−0.856244
$436$	20.4990	0.981722
$437$	−17.1246	−0.819179
$438$	−29.8037	−1.42408
$439$	−25.4019	−1.21236	−0.606182	−	0.795326i	$-0.707300\pi$
$439$	−25.4019	−1.21236	−0.606182	+	0.795326i	$0.707300\pi$
$440$	−23.5306	−1.12178
$441$	0.528224	0.0251535
$442$	−11.2151	−0.533450
$443$	−29.6707	−1.40970	−0.704848	−	0.709359i	$-0.748985\pi$
$443$	−29.6707	−1.40970	−0.704848	+	0.709359i	$0.748985\pi$
$444$	−3.23807	−0.153672
$445$	32.2140	1.52709
$446$	−63.4572	−3.00478
$447$	−15.0289	−0.710845
$448$	−3.18740	−0.150591
$449$	18.6857	0.881833	0.440916	−	0.897548i	$-0.354654\pi$
$449$	18.6857	0.881833	0.440916	+	0.897548i	$0.354654\pi$
$450$	53.7272	2.53273
$451$	−3.47031	−0.163411
$452$	74.2389	3.49190
$453$	−9.44987	−0.443994
$454$	−21.9835	−1.03174
$455$	10.7334	0.503189
$456$	31.5398	1.47699
$457$	−13.1844	−0.616742	−0.308371	−	0.951266i	$-0.599784\pi$
$457$	−13.1844	−0.616742	−0.308371	+	0.951266i	$0.599784\pi$
$458$	25.4126	1.18745
$459$	−17.5516	−0.819240
$460$	−50.2016	−2.34066
$461$	−16.1194	−0.750756	−0.375378	−	0.926872i	$-0.622487\pi$
$461$	−16.1194	−0.750756	−0.375378	+	0.926872i	$0.622487\pi$
$462$	−5.30189	−0.246666
$463$	11.6047	0.539314	0.269657	−	0.962956i	$-0.413090\pi$
$463$	11.6047	0.539314	0.269657	+	0.962956i	$0.413090\pi$
$464$	43.7282	2.03003
$465$	3.64645	0.169100
$466$	44.7866	2.07470
$467$	13.8512	0.640958	0.320479	−	0.947256i	$-0.396156\pi$
$467$	13.8512	0.640958	0.320479	+	0.947256i	$0.396156\pi$
$468$	−11.5741	−0.535015
$469$	40.8705	1.88722
$470$	−92.3491	−4.25975
$471$	1.06334	0.0489963
$472$	−64.5300	−2.97024
$473$	3.37097	0.154997
$474$	−23.1366	−1.06270
$475$	−52.8664	−2.42568
$476$	−47.2054	−2.16366
$477$	0.195705	0.00896071
$478$	60.0716	2.74761
$479$	38.9362	1.77904	0.889519	−	0.456898i	$-0.151039\pi$
$479$	38.9362	1.77904	0.889519	+	0.456898i	$0.151039\pi$
$480$	19.9928	0.912544
$481$	−0.943498	−0.0430198
$482$	−1.15803	−0.0527468
$483$	−6.34127	−0.288538
$484$	−45.8725	−2.08511
$485$	26.1562	1.18769
$486$	−40.7946	−1.85048
$487$	10.9066	0.494227	0.247113	−	0.968987i	$-0.420518\pi$
$487$	10.9066	0.494227	0.247113	+	0.968987i	$0.420518\pi$
$488$	37.2783	1.68751
$489$	13.2476	0.599079
$490$	−2.19321	−0.0990790
$491$	−30.4346	−1.37350	−0.686748	−	0.726896i	$-0.740962\pi$
$491$	−30.4346	−1.37350	−0.686748	+	0.726896i	$0.740962\pi$
$492$	13.6361	0.614765
$493$	22.8851	1.03069
$494$	16.3928	0.737546
$495$	−8.33221	−0.374505
$496$	−8.92873	−0.400912
$497$	−36.9940	−1.65941
$498$	−10.9597	−0.491117
$499$	−11.3276	−0.507093	−0.253547	−	0.967323i	$-0.581597\pi$
$499$	−11.3276	−0.507093	−0.253547	+	0.967323i	$0.581597\pi$
$500$	−69.5959	−3.11242
$501$	−13.5351	−0.604703
$502$	35.2969	1.57538
$503$	15.3106	0.682664	0.341332	−	0.939943i	$-0.389122\pi$
$503$	15.3106	0.682664	0.341332	+	0.939943i	$0.389122\pi$
$504$	−39.3112	−1.75106
$505$	−71.8462	−3.19711
$506$	7.22548	0.321212
$507$	−9.77430	−0.434092
$508$	85.8410	3.80858
$509$	−41.3790	−1.83409	−0.917046	−	0.398780i	$-0.869434\pi$
$509$	−41.3790	−1.83409	−0.917046	+	0.398780i	$0.869434\pi$
$510$	31.7249	1.40480
$511$	−36.5522	−1.61697
$512$	50.5231	2.23283
$513$	25.6546	1.13268
$514$	39.3611	1.73614
$515$	23.0036	1.01366
$516$	−13.2458	−0.583114
$517$	9.23430	0.406124
$518$	−5.71619	−0.251155
$519$	5.16973	0.226926
$520$	26.9409	1.18144
$521$	12.9728	0.568347	0.284174	−	0.958773i	$-0.408281\pi$
$521$	12.9728	0.568347	0.284174	+	0.958773i	$0.408281\pi$
$522$	33.9950	1.48792
$523$	−15.1135	−0.660866	−0.330433	−	0.943829i	$-0.607195\pi$
$523$	−15.1135	−0.660866	−0.330433	+	0.943829i	$0.607195\pi$
$524$	−0.665483	−0.0290718
$525$	−19.5766	−0.854393
$526$	47.2485	2.06013
$527$	−4.67284	−0.203552
$528$	−6.06150	−0.263793
$529$	−14.3580	−0.624262
$530$	−0.812574	−0.0352960
$531$	−22.8502	−0.991612
$532$	68.9985	2.99147
$533$	3.97326	0.172101
$534$	18.2187	0.788401
$535$	−69.0675	−2.98605
$536$	102.585	4.43101
$537$	−5.07885	−0.219169
$538$	79.5015	3.42755
$539$	0.219306	0.00944618
$540$	75.2079	3.23643
$541$	7.02349	0.301963	0.150982	−	0.988537i	$-0.451757\pi$
$541$	7.02349	0.301963	0.150982	+	0.988537i	$0.451757\pi$
$542$	−23.6094	−1.01411
$543$	−4.15939	−0.178496
$544$	−25.6203	−1.09846
$545$	−16.8959	−0.723742
$546$	6.07029	0.259784
$547$	−15.0296	−0.642621	−0.321310	−	0.946974i	$-0.604123\pi$
$547$	−15.0296	−0.642621	−0.321310	+	0.946974i	$0.604123\pi$
$548$	90.4571	3.86414
$549$	13.2003	0.563374
$550$	22.3063	0.951144
$551$	−33.4503	−1.42503
$552$	−15.9167	−0.677458
$553$	−28.3754	−1.20665
$554$	33.5261	1.42439
$555$	2.66892	0.113289
$556$	82.0280	3.47876
$557$	5.78844	0.245264	0.122632	−	0.992452i	$-0.460866\pi$
$557$	5.78844	0.245264	0.122632	+	0.992452i	$0.460866\pi$
$558$	−6.94133	−0.293850
$559$	−3.85952	−0.163240
$560$	74.3450	3.14165
$561$	−3.17228	−0.133934
$562$	42.1633	1.77855
$563$	0.889911	0.0375053	0.0187526	−	0.999824i	$-0.494030\pi$
$563$	0.889911	0.0375053	0.0187526	+	0.999824i	$0.494030\pi$
$564$	−36.2850	−1.52787
$565$	−61.1901	−2.57429
$566$	16.7234	0.702937
$567$	−8.55578	−0.359309
$568$	−92.8553	−3.89612
$569$	28.9171	1.21227	0.606135	−	0.795362i	$-0.292719\pi$
$569$	28.9171	1.21227	0.606135	+	0.795362i	$0.292719\pi$
$570$	−46.3711	−1.94227
$571$	−25.1376	−1.05198	−0.525988	−	0.850492i	$-0.676304\pi$
$571$	−25.1376	−1.05198	−0.525988	+	0.850492i	$0.676304\pi$
$572$	−4.80531	−0.200920
$573$	−15.6695	−0.654604
$574$	24.0720	1.00475
$575$	26.6792	1.11260
$576$	−2.83295	−0.118040
$577$	7.58133	0.315615	0.157807	−	0.987470i	$-0.449557\pi$
$577$	7.58133	0.315615	0.157807	+	0.987470i	$0.449557\pi$
$578$	2.85927	0.118930
$579$	−9.99070	−0.415199
$580$	−98.0614	−4.07178
$581$	−13.4413	−0.557640
$582$	14.7927	0.613178
$583$	0.0812520	0.00336512
$584$	−91.7462	−3.79649
$585$	9.53979	0.394422
$586$	−21.4682	−0.886844
$587$	22.4413	0.926253	0.463127	−	0.886292i	$-0.346728\pi$
$587$	22.4413	0.926253	0.463127	+	0.886292i	$0.346728\pi$
$588$	−0.861736	−0.0355374
$589$	6.83012	0.281430
$590$	94.8748	3.90593
$591$	−16.1127	−0.662786
$592$	−6.53515	−0.268593
$593$	16.1703	0.664036	0.332018	−	0.943273i	$-0.392270\pi$
$593$	16.1703	0.664036	0.332018	+	0.943273i	$0.392270\pi$
$594$	−10.8246	−0.444140
$595$	38.9083	1.59508
$596$	−82.5248	−3.38035
$597$	−4.22347	−0.172855
$598$	−8.27267	−0.338294
$599$	−35.2525	−1.44038	−0.720189	−	0.693777i	$-0.755945\pi$
$599$	−35.2525	−1.44038	−0.720189	+	0.693777i	$0.755945\pi$
$600$	−49.1374	−2.00603
$601$	33.2029	1.35437	0.677187	−	0.735811i	$-0.263199\pi$
$601$	33.2029	1.35437	0.677187	+	0.735811i	$0.263199\pi$
$602$	−23.3829	−0.953017
$603$	36.3255	1.47929
$604$	−51.8898	−2.11137
$605$	37.8096	1.53718
$606$	−40.6328	−1.65059
$607$	39.7635	1.61395	0.806976	−	0.590584i	$-0.201103\pi$
$607$	39.7635	1.61395	0.806976	+	0.590584i	$0.201103\pi$
$608$	37.4484	1.51873
$609$	−12.3868	−0.501936
$610$	−54.8081	−2.21911
$611$	−10.5726	−0.427722
$612$	−41.9560	−1.69597
$613$	16.0740	0.649221	0.324611	−	0.945848i	$-0.394767\pi$
$613$	16.0740	0.649221	0.324611	+	0.945848i	$0.394767\pi$
$614$	21.8330	0.881109
$615$	−11.2394	−0.453215
$616$	−16.3211	−0.657595
$617$	−8.18887	−0.329672	−0.164836	−	0.986321i	$-0.552709\pi$
$617$	−8.18887	−0.329672	−0.164836	+	0.986321i	$0.552709\pi$
$618$	13.0097	0.523328
$619$	−4.65486	−0.187095	−0.0935473	−	0.995615i	$-0.529821\pi$
$619$	−4.65486	−0.187095	−0.0935473	+	0.995615i	$0.529821\pi$
$620$	20.0229	0.804138
$621$	−12.9467	−0.519532
$622$	−75.4305	−3.02449
$623$	22.3440	0.895192
$624$	6.93999	0.277822
$625$	11.9862	0.479446
$626$	−26.4544	−1.05733
$627$	4.63680	0.185176
$628$	5.83889	0.232997
$629$	−3.42016	−0.136371
$630$	57.7969	2.30268
$631$	−10.6427	−0.423678	−0.211839	−	0.977305i	$-0.567945\pi$
$631$	−10.6427	−0.423678	−0.211839	+	0.977305i	$0.567945\pi$
$632$	−71.2226	−2.83308
$633$	23.5794	0.937198
$634$	−0.335385	−0.0133199
$635$	−70.7530	−2.80775
$636$	−0.319270	−0.0126599
$637$	−0.251090	−0.00994855
$638$	14.1139	0.558776
$639$	−32.8801	−1.30072
$640$	−36.4745	−1.44178
$641$	−0.952893	−0.0376370	−0.0188185	−	0.999823i	$-0.505990\pi$
$641$	−0.952893	−0.0376370	−0.0188185	+	0.999823i	$0.505990\pi$
$642$	−39.0613	−1.54163
$643$	2.86136	0.112841	0.0564206	−	0.998407i	$-0.482031\pi$
$643$	2.86136	0.112841	0.0564206	+	0.998407i	$0.482031\pi$
$644$	−34.8203	−1.37211
$645$	10.9176	0.429881
$646$	59.4235	2.33799
$647$	11.0996	0.436368	0.218184	−	0.975908i	$-0.429987\pi$
$647$	11.0996	0.436368	0.218184	+	0.975908i	$0.429987\pi$
$648$	−21.4751	−0.843621
$649$	−9.48685	−0.372391
$650$	−25.5391	−1.00173
$651$	2.52921	0.0991277
$652$	72.7436	2.84886
$653$	−8.50096	−0.332668	−0.166334	−	0.986069i	$-0.553193\pi$
$653$	−8.50096	−0.332668	−0.166334	+	0.986069i	$0.553193\pi$
$654$	−9.55553	−0.373651
$655$	0.548513	0.0214322
$656$	27.5208	1.07451
$657$	−32.4874	−1.26746
$658$	−64.0543	−2.49710
$659$	−40.5205	−1.57846	−0.789228	−	0.614100i	$-0.789519\pi$
$659$	−40.5205	−1.57846	−0.789228	+	0.614100i	$0.789519\pi$
$660$	13.5930	0.529108
$661$	−18.9621	−0.737541	−0.368770	−	0.929520i	$-0.620221\pi$
$661$	−18.9621	−0.737541	−0.368770	+	0.929520i	$0.620221\pi$
$662$	−74.9301	−2.91224
$663$	3.63203	0.141056
$664$	−33.7378	−1.30928
$665$	−56.8709	−2.20536
$666$	−5.08053	−0.196866
$667$	16.8808	0.653628
$668$	−74.3220	−2.87560
$669$	20.5506	0.794534
$670$	−150.825	−5.82688
$671$	5.48044	0.211570
$672$	13.8672	0.534940
$673$	33.4877	1.29085	0.645427	−	0.763822i	$-0.276679\pi$
$673$	33.4877	1.29085	0.645427	+	0.763822i	$0.276679\pi$
$674$	43.9934	1.69456
$675$	−39.9686	−1.53839
$676$	−53.6713	−2.06428
$677$	9.72165	0.373633	0.186817	−	0.982395i	$-0.440183\pi$
$677$	9.72165	0.373633	0.186817	+	0.982395i	$0.440183\pi$
$678$	−34.6062	−1.32904
$679$	18.1422	0.696235
$680$	97.6602	3.74510
$681$	7.11938	0.272815
$682$	−2.88188	−0.110353
$683$	4.80577	0.183887	0.0919437	−	0.995764i	$-0.470692\pi$
$683$	4.80577	0.183887	0.0919437	+	0.995764i	$0.470692\pi$
$684$	61.3257	2.34485
$685$	−74.5577	−2.84871
$686$	−48.1467	−1.83825
$687$	−8.22989	−0.313990
$688$	−26.7330	−1.01919
$689$	−0.0930278	−0.00354408
$690$	23.4013	0.890873
$691$	48.4328	1.84247	0.921235	−	0.389005i	$-0.127181\pi$
$691$	48.4328	1.84247	0.921235	+	0.389005i	$0.127181\pi$
$692$	28.3873	1.07912
$693$	−5.77931	−0.219538
$694$	52.5906	1.99631
$695$	−67.6102	−2.56460
$696$	−31.0908	−1.17850
$697$	14.4030	0.545552
$698$	65.0856	2.46353
$699$	−14.5042	−0.548598
$700$	−107.496	−4.06298
$701$	−19.6126	−0.740757	−0.370379	−	0.928881i	$-0.620772\pi$
$701$	−19.6126	−0.740757	−0.370379	+	0.928881i	$0.620772\pi$
$702$	12.3934	0.467760
$703$	4.99913	0.188546
$704$	−1.17617	−0.0443287
$705$	29.9073	1.12637
$706$	−2.86894	−0.107974
$707$	−49.8333	−1.87417
$708$	37.2774	1.40097
$709$	−29.4666	−1.10664	−0.553320	−	0.832969i	$-0.686639\pi$
$709$	−29.4666	−1.10664	−0.553320	+	0.832969i	$0.686639\pi$
$710$	136.520	5.12349
$711$	−25.2200	−0.945823
$712$	56.0835	2.10182
$713$	−3.44684	−0.129085
$714$	22.0047	0.823505
$715$	3.96070	0.148122
$716$	−27.8883	−1.04223
$717$	−19.4542	−0.726532
$718$	−61.1795	−2.28320
$719$	−26.5758	−0.991110	−0.495555	−	0.868577i	$-0.665035\pi$
$719$	−26.5758	−0.991110	−0.495555	+	0.868577i	$0.665035\pi$
$720$	66.0775	2.46256
$721$	15.9555	0.594214
$722$	−38.2240	−1.42255
$723$	0.375029	0.0139475
$724$	−22.8395	−0.848822
$725$	52.1139	1.93546
$726$	21.3833	0.793609
$727$	1.13765	0.0421932	0.0210966	−	0.999777i	$-0.493284\pi$
$727$	1.13765	0.0421932	0.0210966	+	0.999777i	$0.493284\pi$
$728$	18.6865	0.692567
$729$	3.34776	0.123991
$730$	134.889	4.99247
$731$	−13.9907	−0.517464
$732$	−21.5347	−0.795946
$733$	−23.4981	−0.867921	−0.433961	−	0.900932i	$-0.642884\pi$
$733$	−23.4981	−0.867921	−0.433961	+	0.900932i	$0.642884\pi$
$734$	−50.1608	−1.85147
$735$	0.710272	0.0261988
$736$	−18.8984	−0.696605
$737$	15.0815	0.555535
$738$	21.3951	0.787565
$739$	−4.13357	−0.152056	−0.0760280	−	0.997106i	$-0.524224\pi$
$739$	−4.13357	−0.152056	−0.0760280	+	0.997106i	$0.524224\pi$
$740$	14.6552	0.538737
$741$	−5.30881	−0.195024
$742$	−0.563610	−0.0206908
$743$	3.78557	0.138879	0.0694396	−	0.997586i	$-0.477879\pi$
$743$	3.78557	0.138879	0.0694396	+	0.997586i	$0.477879\pi$
$744$	6.34835	0.232742
$745$	68.0197	2.49205
$746$	34.2746	1.25488
$747$	−11.9466	−0.437103
$748$	−17.4192	−0.636908
$749$	−47.9059	−1.75044
$750$	32.4419	1.18461
$751$	−8.63589	−0.315128	−0.157564	−	0.987509i	$-0.550364\pi$
$751$	−8.63589	−0.315128	−0.157564	+	0.987509i	$0.550364\pi$
$752$	−73.2314	−2.67047
$753$	−11.4309	−0.416566
$754$	−16.1594	−0.588492
$755$	42.7693	1.55653
$756$	52.1649	1.89722
$757$	24.0859	0.875416	0.437708	−	0.899117i	$-0.355790\pi$
$757$	24.0859	0.875416	0.437708	+	0.899117i	$0.355790\pi$
$758$	41.8025	1.51834
$759$	−2.33998	−0.0849358
$760$	−142.746	−5.17796
$761$	29.1603	1.05706	0.528530	−	0.848915i	$-0.322743\pi$
$761$	29.1603	1.05706	0.528530	+	0.848915i	$0.322743\pi$
$762$	−40.0145	−1.44957
$763$	−11.7192	−0.424263
$764$	−86.0424	−3.11290
$765$	34.5816	1.25030
$766$	−90.0167	−3.25243
$767$	10.8618	0.392196
$768$	−22.6589	−0.817633
$769$	−37.1901	−1.34111	−0.670554	−	0.741861i	$-0.733944\pi$
$769$	−37.1901	−1.34111	−0.670554	+	0.741861i	$0.733944\pi$
$770$	23.9959	0.864753
$771$	−12.7471	−0.459077
$772$	−54.8596	−1.97444
$773$	14.8608	0.534507	0.267254	−	0.963626i	$-0.413884\pi$
$773$	14.8608	0.534507	0.267254	+	0.963626i	$0.413884\pi$
$774$	−20.7827	−0.747018
$775$	−10.6410	−0.382236
$776$	45.5372	1.63469
$777$	1.85119	0.0664111
$778$	−11.6354	−0.417149
$779$	−21.0523	−0.754278
$780$	−15.5631	−0.557247
$781$	−13.6511	−0.488474
$782$	−29.9882	−1.07238
$783$	−25.2894	−0.903771
$784$	−1.73918	−0.0621135
$785$	−4.81260	−0.171769
$786$	0.310213	0.0110649
$787$	−32.0842	−1.14368	−0.571839	−	0.820366i	$-0.693770\pi$
$787$	−32.0842	−1.14368	−0.571839	+	0.820366i	$0.693770\pi$
$788$	−88.4756	−3.15181
$789$	−15.3014	−0.544746
$790$	104.714	3.72557
$791$	−42.4421	−1.50907
$792$	−14.5061	−0.515452
$793$	−6.27472	−0.222822
$794$	63.9136	2.26821
$795$	0.263153	0.00933307
$796$	−23.1914	−0.821996
$797$	18.9823	0.672387	0.336194	−	0.941793i	$-0.390860\pi$
$797$	18.9823	0.672387	0.336194	+	0.941793i	$0.390860\pi$
$798$	−32.1635	−1.13857
$799$	−38.3255	−1.35586
$800$	−58.3427	−2.06273
$801$	19.8592	0.701691
$802$	−40.9381	−1.44557
$803$	−13.4880	−0.475982
$804$	−59.2609	−2.08997
$805$	28.7001	1.01154
$806$	3.29955	0.116222
$807$	−25.7466	−0.906324
$808$	−125.082	−4.40037
$809$	−2.14378	−0.0753712	−0.0376856	−	0.999290i	$-0.511999\pi$
$809$	−2.14378	−0.0753712	−0.0376856	+	0.999290i	$0.511999\pi$
$810$	31.5736	1.10938
$811$	2.01134	0.0706279	0.0353139	−	0.999376i	$-0.488757\pi$
$811$	2.01134	0.0706279	0.0353139	+	0.999376i	$0.488757\pi$
$812$	−68.0164	−2.38691
$813$	7.64591	0.268154
$814$	−2.10932	−0.0739315
$815$	−59.9577	−2.10023
$816$	25.1573	0.880682
$817$	20.4497	0.715444
$818$	−24.5399	−0.858019
$819$	6.61690	0.231213
$820$	−61.7161	−2.15522
$821$	18.6908	0.652314	0.326157	−	0.945316i	$-0.394246\pi$
$821$	18.6908	0.652314	0.326157	+	0.945316i	$0.394246\pi$
$822$	−42.1663	−1.47072
$823$	45.7675	1.59535	0.797677	−	0.603086i	$-0.206062\pi$
$823$	45.7675	1.59535	0.797677	+	0.603086i	$0.206062\pi$
$824$	40.0484	1.39515
$825$	−7.22391	−0.251504
$826$	65.8061	2.28969
$827$	26.8064	0.932149	0.466075	−	0.884745i	$-0.345668\pi$
$827$	26.8064	0.932149	0.466075	+	0.884745i	$0.345668\pi$
$828$	−30.9482	−1.07552
$829$	1.53089	0.0531699	0.0265850	−	0.999647i	$-0.491537\pi$
$829$	1.53089	0.0531699	0.0265850	+	0.999647i	$0.491537\pi$
$830$	49.6027	1.72174
$831$	−10.8575	−0.376641
$832$	1.34664	0.0466862
$833$	−0.910196	−0.0315364
$834$	−38.2371	−1.32404
$835$	61.2587	2.11994
$836$	25.4610	0.880586
$837$	5.16377	0.178486
$838$	37.4820	1.29479
$839$	−23.4659	−0.810135	−0.405067	−	0.914287i	$-0.632752\pi$
$839$	−23.4659	−0.810135	−0.405067	+	0.914287i	$0.632752\pi$
$840$	−52.8594	−1.82382
$841$	3.97419	0.137041
$842$	−4.07850	−0.140555
$843$	−13.6546	−0.470290
$844$	129.476	4.45675
$845$	44.2377	1.52182
$846$	−56.9312	−1.95734
$847$	26.2251	0.901106
$848$	−0.644359	−0.0221274
$849$	−5.41589	−0.185873
$850$	−92.5788	−3.17543
$851$	−2.52283	−0.0864814
$852$	53.6402	1.83768
$853$	−41.3426	−1.41555	−0.707773	−	0.706440i	$-0.750300\pi$
$853$	−41.3426	−1.41555	−0.707773	+	0.706440i	$0.750300\pi$
$854$	−38.0154	−1.30086
$855$	−50.5467	−1.72866
$856$	−120.244	−4.10987
$857$	18.6800	0.638097	0.319049	−	0.947738i	$-0.396637\pi$
$857$	18.6800	0.638097	0.319049	+	0.947738i	$0.396637\pi$
$858$	2.23998	0.0764718
$859$	−24.5203	−0.836622	−0.418311	−	0.908304i	$-0.637378\pi$
$859$	−24.5203	−0.836622	−0.418311	+	0.908304i	$0.637378\pi$
$860$	59.9494	2.04426
$861$	−7.79574	−0.265678
$862$	71.9110	2.44930
$863$	25.7495	0.876522	0.438261	−	0.898848i	$-0.355595\pi$
$863$	25.7495	0.876522	0.438261	+	0.898848i	$0.355595\pi$
$864$	28.3121	0.963196
$865$	−23.3977	−0.795547
$866$	86.2875	2.93217
$867$	−0.925978	−0.0314479
$868$	13.8881	0.471392
$869$	−10.4707	−0.355196
$870$	45.7111	1.54975
$871$	−17.2673	−0.585079
$872$	−29.4153	−0.996126
$873$	16.1248	0.545740
$874$	43.8328	1.48267
$875$	39.7877	1.34507
$876$	52.9995	1.79069
$877$	−57.4102	−1.93860	−0.969302	−	0.245874i	$-0.920925\pi$
$877$	−57.4102	−1.93860	−0.969302	+	0.245874i	$0.920925\pi$
$878$	65.0197	2.19431
$879$	6.95249	0.234502
$880$	27.4338	0.924795
$881$	−1.38687	−0.0467247	−0.0233624	−	0.999727i	$-0.507437\pi$
$881$	−1.38687	−0.0467247	−0.0233624	+	0.999727i	$0.507437\pi$
$882$	−1.35206	−0.0455264
$883$	48.8841	1.64508	0.822540	−	0.568707i	$-0.192556\pi$
$883$	48.8841	1.64508	0.822540	+	0.568707i	$0.192556\pi$
$884$	19.9437	0.670779
$885$	−30.7253	−1.03282
$886$	75.9463	2.55147
$887$	−17.9292	−0.602005	−0.301003	−	0.953623i	$-0.597321\pi$
$887$	−17.9292	−0.602005	−0.301003	+	0.953623i	$0.597321\pi$
$888$	4.64651	0.155927
$889$	−49.0750	−1.64592
$890$	−82.4563	−2.76394
$891$	−3.15715	−0.105768
$892$	112.845	3.77833
$893$	56.0191	1.87461
$894$	38.4687	1.28659
$895$	22.9865	0.768353
$896$	−25.2991	−0.845182
$897$	2.67911	0.0894528
$898$	−47.8287	−1.59607
$899$	−6.73290	−0.224555
$900$	−95.5423	−3.18474
$901$	−0.337224	−0.0112346
$902$	8.88275	0.295763
$903$	7.57258	0.252000
$904$	−106.530	−3.54314
$905$	18.8250	0.625766
$906$	24.1883	0.803602
$907$	6.85951	0.227766	0.113883	−	0.993494i	$-0.463671\pi$
$907$	6.85951	0.227766	0.113883	+	0.993494i	$0.463671\pi$
$908$	39.0930	1.29735
$909$	−44.2916	−1.46906
$910$	−27.4736	−0.910742
$911$	−29.2337	−0.968555	−0.484278	−	0.874914i	$-0.660918\pi$
$911$	−29.2337	−0.968555	−0.484278	+	0.874914i	$0.660918\pi$
$912$	−36.7716	−1.21763
$913$	−4.95995	−0.164150
$914$	33.7475	1.11627
$915$	17.7496	0.586785
$916$	−45.1908	−1.49315
$917$	0.380454	0.0125637
$918$	44.9259	1.48278
$919$	−34.2369	−1.12937	−0.564686	−	0.825306i	$-0.691003\pi$
$919$	−34.2369	−1.12937	−0.564686	+	0.825306i	$0.691003\pi$
$920$	72.0374	2.37500
$921$	−7.07064	−0.232985
$922$	41.2599	1.35882
$923$	15.6295	0.514451
$924$	9.42827	0.310167
$925$	−7.78839	−0.256081
$926$	−29.7038	−0.976126
$927$	14.1812	0.465771
$928$	−36.9153	−1.21180
$929$	31.9214	1.04731	0.523654	−	0.851931i	$-0.324568\pi$
$929$	31.9214	1.04731	0.523654	+	0.851931i	$0.324568\pi$
$930$	−9.33360	−0.306061
$931$	1.33040	0.0436022
$932$	−79.6433	−2.60880
$933$	24.4282	0.799743
$934$	−35.4542	−1.16010
$935$	14.3575	0.469539
$936$	16.6085	0.542865
$937$	−44.4376	−1.45171	−0.725856	−	0.687847i	$-0.758556\pi$
$937$	−44.4376	−1.45171	−0.725856	+	0.687847i	$0.758556\pi$
$938$	−104.614	−3.41576
$939$	8.56728	0.279582
$940$	164.223	5.35636
$941$	15.7050	0.511969	0.255984	−	0.966681i	$-0.417600\pi$
$941$	15.7050	0.511969	0.255984	+	0.966681i	$0.417600\pi$
$942$	−2.72178	−0.0886804
$943$	10.6241	0.345969
$944$	75.2342	2.44867
$945$	−42.9961	−1.39866
$946$	−8.62848	−0.280536
$947$	9.51684	0.309256	0.154628	−	0.987973i	$-0.450582\pi$
$947$	9.51684	0.309256	0.154628	+	0.987973i	$0.450582\pi$
$948$	41.1435	1.33628
$949$	15.4428	0.501295
$950$	135.319	4.39034
$951$	0.108615	0.00352208
$952$	67.7381	2.19540
$953$	12.6096	0.408465	0.204233	−	0.978922i	$-0.434530\pi$
$953$	12.6096	0.408465	0.204233	+	0.978922i	$0.434530\pi$
$954$	−0.500934	−0.0162183
$955$	70.9190	2.29488
$956$	−106.824	−3.45495
$957$	−4.57080	−0.147753
$958$	−99.6627	−3.21995
$959$	−51.7140	−1.66993
$960$	−3.80930	−0.122945
$961$	−29.6252	−0.955653
$962$	2.41502	0.0778633
$963$	−42.5786	−1.37208
$964$	2.05931	0.0663258
$965$	45.2171	1.45559
$966$	16.2314	0.522237
$967$	17.5571	0.564597	0.282299	−	0.959327i	$-0.408903\pi$
$967$	17.5571	0.564597	0.282299	+	0.959327i	$0.408903\pi$
$968$	65.8253	2.11570
$969$	−19.2443	−0.618217
$970$	−66.9506	−2.14966
$971$	55.0910	1.76795	0.883977	−	0.467530i	$-0.154856\pi$
$971$	55.0910	1.76795	0.883977	+	0.467530i	$0.154856\pi$
$972$	72.5443	2.32686
$973$	−46.8951	−1.50339
$974$	−27.9171	−0.894522
$975$	8.27086	0.264880
$976$	−43.4619	−1.39118
$977$	−2.49293	−0.0797559	−0.0398780	−	0.999205i	$-0.512697\pi$
$977$	−2.49293	−0.0797559	−0.0398780	+	0.999205i	$0.512697\pi$
$978$	−33.9092	−1.08430
$979$	8.24509	0.263514
$980$	3.90014	0.124586
$981$	−10.4160	−0.332556
$982$	77.9018	2.48595
$983$	−5.27202	−0.168151	−0.0840757	−	0.996459i	$-0.526794\pi$
$983$	−5.27202	−0.168151	−0.0840757	+	0.996459i	$0.526794\pi$
$984$	−19.5674	−0.623785
$985$	72.9245	2.32357
$986$	−58.5776	−1.86549
$987$	20.7440	0.660289
$988$	−29.1510	−0.927417
$989$	−10.3200	−0.328157
$990$	21.3275	0.677832
$991$	−54.9770	−1.74640	−0.873200	−	0.487361i	$-0.837959\pi$
$991$	−54.9770	−1.74640	−0.873200	+	0.487361i	$0.837959\pi$
$992$	7.53763	0.239320
$993$	24.2662	0.770064
$994$	94.6915	3.00343
$995$	19.1151	0.605989
$996$	19.4895	0.617548
$997$	28.6258	0.906590	0.453295	−	0.891361i	$-0.350248\pi$
$997$	28.6258	0.906590	0.453295	+	0.891361i	$0.350248\pi$
$998$	28.9946	0.917809
$999$	3.77949	0.119578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.10	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.10	✓	221	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55964 q^{2} +0.828942 q^{3} +4.55177 q^{4} -3.75172 q^{5} -2.12180 q^{6} -2.60223 q^{7} -6.53163 q^{8} -2.31285 q^{9} +O(q^{10})\)	\(q-2.55964 q^{2} +0.828942 q^{3} +4.55177 q^{4} -3.75172 q^{5} -2.12180 q^{6} -2.60223 q^{7} -6.53163 q^{8} -2.31285 q^{9} +9.60307 q^{10} -0.960243 q^{11} +3.77316 q^{12} +1.09941 q^{13} +6.66079 q^{14} -3.10996 q^{15} +7.61508 q^{16} +3.98534 q^{17} +5.92008 q^{18} -5.82523 q^{19} -17.0770 q^{20} -2.15710 q^{21} +2.45788 q^{22} +2.93972 q^{23} -5.41434 q^{24} +9.07542 q^{25} -2.81410 q^{26} -4.40405 q^{27} -11.8448 q^{28} +5.74232 q^{29} +7.96039 q^{30} -1.17251 q^{31} -6.42865 q^{32} -0.795986 q^{33} -10.2010 q^{34} +9.76285 q^{35} -10.5276 q^{36} -0.858185 q^{37} +14.9105 q^{38} +0.911348 q^{39} +24.5048 q^{40} +3.61399 q^{41} +5.52141 q^{42} -3.51054 q^{43} -4.37081 q^{44} +8.67719 q^{45} -7.52464 q^{46} -9.61662 q^{47} +6.31246 q^{48} -0.228386 q^{49} -23.2298 q^{50} +3.30362 q^{51} +5.00427 q^{52} -0.0846161 q^{53} +11.2728 q^{54} +3.60257 q^{55} +16.9968 q^{56} -4.82878 q^{57} -14.6983 q^{58} +9.87963 q^{59} -14.1558 q^{60} -5.70735 q^{61} +3.00120 q^{62} +6.01859 q^{63} +1.22487 q^{64} -4.12468 q^{65} +2.03744 q^{66} -15.7059 q^{67} +18.1404 q^{68} +2.43686 q^{69} -24.9894 q^{70} +14.2163 q^{71} +15.1067 q^{72} +14.0465 q^{73} +2.19665 q^{74} +7.52300 q^{75} -26.5151 q^{76} +2.49878 q^{77} -2.33272 q^{78} +10.9043 q^{79} -28.5697 q^{80} +3.28786 q^{81} -9.25053 q^{82} +5.16530 q^{83} -9.81863 q^{84} -14.9519 q^{85} +8.98572 q^{86} +4.76005 q^{87} +6.27195 q^{88} -8.58646 q^{89} -22.2105 q^{90} -2.86092 q^{91} +13.3809 q^{92} -0.971940 q^{93} +24.6151 q^{94} +21.8547 q^{95} -5.32898 q^{96} -6.97180 q^{97} +0.584587 q^{98} +2.22090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more