LMFDB - Embedded newform 8011.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75364 q^{2} -0.00102412 q^{3} +5.58256 q^{4} -3.57698 q^{5} +0.00282007 q^{6} +1.05818 q^{7} -9.86509 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.75364 q^{2} -0.00102412 q^{3} +5.58256 q^{4} -3.57698 q^{5} +0.00282007 q^{6} +1.05818 q^{7} -9.86509 q^{8} -3.00000 q^{9} +9.84973 q^{10} +1.12064 q^{11} -0.00571722 q^{12} +3.71956 q^{13} -2.91386 q^{14} +0.00366327 q^{15} +15.9998 q^{16} -4.93358 q^{17} +8.26093 q^{18} +5.04681 q^{19} -19.9687 q^{20} -0.00108371 q^{21} -3.08584 q^{22} +1.51598 q^{23} +0.0101031 q^{24} +7.79478 q^{25} -10.2423 q^{26} +0.00614473 q^{27} +5.90736 q^{28} +1.91463 q^{29} -0.0100873 q^{30} -1.66684 q^{31} -24.3277 q^{32} -0.00114767 q^{33} +13.5853 q^{34} -3.78509 q^{35} -16.7477 q^{36} +3.29072 q^{37} -13.8971 q^{38} -0.00380928 q^{39} +35.2872 q^{40} -5.99915 q^{41} +0.00298415 q^{42} -8.67231 q^{43} +6.25602 q^{44} +10.7309 q^{45} -4.17446 q^{46} +1.21334 q^{47} -0.0163858 q^{48} -5.88025 q^{49} -21.4641 q^{50} +0.00505259 q^{51} +20.7647 q^{52} +0.668065 q^{53} -0.0169204 q^{54} -4.00849 q^{55} -10.4391 q^{56} -0.00516855 q^{57} -5.27221 q^{58} -2.48011 q^{59} +0.0204504 q^{60} -5.18149 q^{61} +4.58989 q^{62} -3.17454 q^{63} +34.9902 q^{64} -13.3048 q^{65} +0.00316027 q^{66} +2.50599 q^{67} -27.5420 q^{68} -0.00155255 q^{69} +10.4228 q^{70} -0.521666 q^{71} +29.5953 q^{72} -9.31782 q^{73} -9.06147 q^{74} -0.00798281 q^{75} +28.1741 q^{76} +1.18584 q^{77} +0.0104894 q^{78} -1.37692 q^{79} -57.2311 q^{80} +8.99999 q^{81} +16.5195 q^{82} +9.43789 q^{83} -0.00604986 q^{84} +17.6473 q^{85} +23.8805 q^{86} -0.00196082 q^{87} -11.0552 q^{88} -10.8598 q^{89} -29.5492 q^{90} +3.93597 q^{91} +8.46303 q^{92} +0.00170705 q^{93} -3.34110 q^{94} -18.0523 q^{95} +0.0249145 q^{96} +15.7581 q^{97} +16.1921 q^{98} -3.36191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * 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 $

$2$	−2.75364	−1.94712	−0.973560	−	0.228430i	$-0.926641\pi$
$2$	−2.75364	−1.94712	−0.973560	+	0.228430i	$0.926641\pi$
$3$	−0.00102412	−0.000591277 0	−0.000295639	−	1.00000i	$-0.500094\pi$
$3$	−0.00102412	−0.000591277 0	−0.000295639		1.00000i	$0.500094\pi$
$4$	5.58256	2.79128
$5$	−3.57698	−1.59967	−0.799837	−	0.600217i	$-0.795081\pi$
$5$	−3.57698	−1.59967	−0.799837	+	0.600217i	$0.795081\pi$
$6$	0.00282007	0.00115129
$7$	1.05818	0.399955	0.199978	−	0.979800i	$-0.435913\pi$
$7$	1.05818	0.399955	0.199978	+	0.979800i	$0.435913\pi$
$8$	−9.86509	−3.48784
$9$	−3.00000	−1.00000
$10$	9.84973	3.11476
$11$	1.12064	0.337885	0.168942	−	0.985626i	$-0.445965\pi$
$11$	1.12064	0.337885	0.168942	+	0.985626i	$0.445965\pi$
$12$	−0.00571722	−0.00165042
$13$	3.71956	1.03162	0.515810	−	0.856703i	$-0.327491\pi$
$13$	3.71956	1.03162	0.515810	+	0.856703i	$0.327491\pi$
$14$	−2.91386	−0.778761
$15$	0.00366327	0.000945851 0
$16$	15.9998	3.99996
$17$	−4.93358	−1.19657	−0.598285	−	0.801284i	$-0.704151\pi$
$17$	−4.93358	−1.19657	−0.598285	+	0.801284i	$0.704151\pi$
$18$	8.26093	1.94712
$19$	5.04681	1.15782	0.578909	−	0.815392i	$-0.303479\pi$
$19$	5.04681	1.15782	0.578909	+	0.815392i	$0.303479\pi$
$20$	−19.9687	−4.46514
$21$	−0.00108371	−0.000236484 0
$22$	−3.08584	−0.657902
$23$	1.51598	0.316103	0.158052	−	0.987431i	$-0.449479\pi$
$23$	1.51598	0.316103	0.158052	+	0.987431i	$0.449479\pi$
$24$	0.0101031	0.00206228
$25$	7.79478	1.55896
$26$	−10.2423	−2.00869
$27$	0.00614473	0.00118255
$28$	5.90736	1.11639
$29$	1.91463	0.355538	0.177769	−	0.984072i	$-0.443112\pi$
$29$	1.91463	0.355538	0.177769	+	0.984072i	$0.443112\pi$
$30$	−0.0100873	−0.00184169
$31$	−1.66684	−0.299374	−0.149687	−	0.988733i	$-0.547827\pi$
$31$	−1.66684	−0.299374	−0.149687	+	0.988733i	$0.547827\pi$
$32$	−24.3277	−4.30057
$33$	−0.00114767	−0.000199784 0
$34$	13.5853	2.32987
$35$	−3.78509	−0.639798
$36$	−16.7477	−2.79128
$37$	3.29072	0.540991	0.270495	−	0.962721i	$-0.412813\pi$
$37$	3.29072	0.540991	0.270495	+	0.962721i	$0.412813\pi$
$38$	−13.8971	−2.25441
$39$	−0.00380928	−0.000609974 0
$40$	35.2872	5.57940
$41$	−5.99915	−0.936910	−0.468455	−	0.883487i	$-0.655189\pi$
$41$	−5.99915	−0.936910	−0.468455	+	0.883487i	$0.655189\pi$
$42$	0.00298415	0.000460464 0
$43$	−8.67231	−1.32252	−0.661258	−	0.750159i	$-0.729977\pi$
$43$	−8.67231	−1.32252	−0.661258	+	0.750159i	$0.729977\pi$
$44$	6.25602	0.943131
$45$	10.7309	1.59967
$46$	−4.17446	−0.615491
$47$	1.21334	0.176984	0.0884918	−	0.996077i	$-0.471795\pi$
$47$	1.21334	0.176984	0.0884918	+	0.996077i	$0.471795\pi$
$48$	−0.0163858	−0.00236509
$49$	−5.88025	−0.840036
$50$	−21.4641	−3.03548
$51$	0.00505259	0.000707504 0
$52$	20.7647	2.87954
$53$	0.668065	0.0917658	0.0458829	−	0.998947i	$-0.485390\pi$
$53$	0.668065	0.0917658	0.0458829	+	0.998947i	$0.485390\pi$
$54$	−0.0169204	−0.00230258
$55$	−4.00849	−0.540505
$56$	−10.4391	−1.39498
$57$	−0.00516855	−0.000684591 0
$58$	−5.27221	−0.692275
$59$	−2.48011	−0.322883	−0.161442	−	0.986882i	$-0.551614\pi$
$59$	−2.48011	−0.322883	−0.161442	+	0.986882i	$0.551614\pi$
$60$	0.0204504	0.00264013
$61$	−5.18149	−0.663421	−0.331711	−	0.943381i	$-0.607626\pi$
$61$	−5.18149	−0.663421	−0.331711	+	0.943381i	$0.607626\pi$
$62$	4.58989	0.582917
$63$	−3.17454	−0.399955
$64$	34.9902	4.37377
$65$	−13.3048	−1.65026
$66$	0.00316027	0.000389003 0
$67$	2.50599	0.306156	0.153078	−	0.988214i	$-0.451081\pi$
$67$	2.50599	0.306156	0.153078	+	0.988214i	$0.451081\pi$
$68$	−27.5420	−3.33996
$69$	−0.00155255	−0.000186905 0
$70$	10.4228	1.24576
$71$	−0.521666	−0.0619104	−0.0309552	−	0.999521i	$-0.509855\pi$
$71$	−0.521666	−0.0619104	−0.0309552	+	0.999521i	$0.509855\pi$
$72$	29.5953	3.48784
$73$	−9.31782	−1.09057	−0.545284	−	0.838251i	$-0.683578\pi$
$73$	−9.31782	−1.09057	−0.545284	+	0.838251i	$0.683578\pi$
$74$	−9.06147	−1.05337
$75$	−0.00798281	−0.000921776 0
$76$	28.1741	3.23179
$77$	1.18584	0.135139
$78$	0.0104894	0.00118769
$79$	−1.37692	−0.154916	−0.0774579	−	0.996996i	$-0.524680\pi$
$79$	−1.37692	−0.154916	−0.0774579	+	0.996996i	$0.524680\pi$
$80$	−57.2311	−6.39863
$81$	8.99999	0.999999
$82$	16.5195	1.82428
$83$	9.43789	1.03594	0.517971	−	0.855398i	$-0.326687\pi$
$83$	9.43789	1.03594	0.517971	+	0.855398i	$0.326687\pi$
$84$	−0.00604986	−0.000660094 0
$85$	17.6473	1.91412
$86$	23.8805	2.57510
$87$	−0.00196082	−0.000210221 0
$88$	−11.0552	−1.17849
$89$	−10.8598	−1.15113	−0.575566	−	0.817755i	$-0.695218\pi$
$89$	−10.8598	−1.15113	−0.575566	+	0.817755i	$0.695218\pi$
$90$	−29.5492	−3.11476
$91$	3.93597	0.412602
$92$	8.46303	0.882332
$93$	0.00170705	0.000177013 0
$94$	−3.34110	−0.344608
$95$	−18.0523	−1.85213
$96$	0.0249145	0.00254283
$97$	15.7581	1.59999	0.799996	−	0.600006i	$-0.204835\pi$
$97$	15.7581	1.59999	0.799996	+	0.600006i	$0.204835\pi$
$98$	16.1921	1.63565
$99$	−3.36191	−0.337885
$100$	43.5148	4.35148
$101$	8.79755	0.875389	0.437694	−	0.899124i	$-0.355795\pi$
$101$	8.79755	0.875389	0.437694	+	0.899124i	$0.355795\pi$
$102$	−0.0139130	−0.00137760
$103$	5.83894	0.575328	0.287664	−	0.957731i	$-0.407121\pi$
$103$	5.83894	0.575328	0.287664	+	0.957731i	$0.407121\pi$
$104$	−36.6938	−3.59812
$105$	0.00387640	0.000378298 0
$106$	−1.83961	−0.178679
$107$	8.19799	0.792529	0.396265	−	0.918136i	$-0.370306\pi$
$107$	8.19799	0.792529	0.396265	+	0.918136i	$0.370306\pi$
$108$	0.0343033	0.00330084
$109$	−18.9645	−1.81647	−0.908234	−	0.418463i	$-0.862569\pi$
$109$	−18.9645	−1.81647	−0.908234	+	0.418463i	$0.862569\pi$
$110$	11.0380	1.05243
$111$	−0.00337010	−0.000319876 0
$112$	16.9307	1.59980
$113$	11.6215	1.09326	0.546628	−	0.837375i	$-0.315911\pi$
$113$	11.6215	1.09326	0.546628	+	0.837375i	$0.315911\pi$
$114$	0.0142323	0.00133298
$115$	−5.42262	−0.505662
$116$	10.6885	0.992405
$117$	−11.1587	−1.03162
$118$	6.82935	0.628692
$119$	−5.22063	−0.478574
$120$	−0.0361385	−0.00329897
$121$	−9.74417	−0.885834
$122$	14.2680	1.29176
$123$	0.00614387	0.000553974 0
$124$	−9.30524	−0.835635
$125$	−9.99687	−0.894147
$126$	8.74157	0.778761
$127$	2.69020	0.238717	0.119358	−	0.992851i	$-0.461916\pi$
$127$	2.69020	0.238717	0.119358	+	0.992851i	$0.461916\pi$
$128$	−47.6951	−4.21569
$129$	0.00888151	0.000781974 0
$130$	36.6366	3.21325
$131$	15.8175	1.38198	0.690992	−	0.722863i	$-0.257174\pi$
$131$	15.8175	1.38198	0.690992	+	0.722863i	$0.257174\pi$
$132$	−0.00640693	−0.000557652 0
$133$	5.34044	0.463075
$134$	−6.90062	−0.596123
$135$	−0.0219796	−0.00189170
$136$	48.6703	4.17344
$137$	3.06338	0.261722	0.130861	−	0.991401i	$-0.458226\pi$
$137$	3.06338	0.261722	0.130861	+	0.991401i	$0.458226\pi$
$138$	0.00427516	0.000363926 0
$139$	−2.14301	−0.181768	−0.0908839	−	0.995861i	$-0.528969\pi$
$139$	−2.14301	−0.181768	−0.0908839	+	0.995861i	$0.528969\pi$
$140$	−21.1305	−1.78585
$141$	−0.00124261	−0.000104646 0
$142$	1.43648	0.120547
$143$	4.16827	0.348569
$144$	−47.9995	−3.99996
$145$	−6.84859	−0.568744
$146$	25.6580	2.12347
$147$	0.00602210	0.000496694 0
$148$	18.3706	1.51006
$149$	6.62073	0.542391	0.271196	−	0.962524i	$-0.412581\pi$
$149$	6.62073	0.542391	0.271196	+	0.962524i	$0.412581\pi$
$150$	0.0219818	0.00179481
$151$	6.27182	0.510394	0.255197	−	0.966889i	$-0.417860\pi$
$151$	6.27182	0.510394	0.255197	+	0.966889i	$0.417860\pi$
$152$	−49.7872	−4.03828
$153$	14.8007	1.19657
$154$	−3.26537	−0.263131
$155$	5.96226	0.478900
$156$	−0.0212656	−0.00170261
$157$	15.7361	1.25588	0.627940	−	0.778262i	$-0.283898\pi$
$157$	15.7361	1.25588	0.627940	+	0.778262i	$0.283898\pi$
$158$	3.79155	0.301640
$159$	−0.000684181 0	−5.42591e−5 0
$160$	87.0197	6.87951
$161$	1.60418	0.126427
$162$	−24.7828	−1.94712
$163$	8.05560	0.630964	0.315482	−	0.948932i	$-0.397834\pi$
$163$	8.05560	0.630964	0.315482	+	0.948932i	$0.397834\pi$
$164$	−33.4906	−2.61518
$165$	0.00410519	0.000319589 0
$166$	−25.9886	−2.01711
$167$	15.0217	1.16241	0.581207	−	0.813756i	$-0.302581\pi$
$167$	15.0217	1.16241	0.581207	+	0.813756i	$0.302581\pi$
$168$	0.0106909	0.000824819 0
$169$	0.835116	0.0642397
$170$	−48.5945	−3.72702
$171$	−15.1404	−1.15782
$172$	−48.4137	−3.69151
$173$	7.07465	0.537875	0.268938	−	0.963158i	$-0.413327\pi$
$173$	7.07465	0.537875	0.268938	+	0.963158i	$0.413327\pi$
$174$	0.00539939	0.000409327 0
$175$	8.24829	0.623512
$176$	17.9300	1.35153
$177$	0.00253994	0.000190913 0
$178$	29.9039	2.24139
$179$	15.2020	1.13625	0.568126	−	0.822942i	$-0.307669\pi$
$179$	15.2020	1.13625	0.568126	+	0.822942i	$0.307669\pi$
$180$	59.9061	4.46513
$181$	1.57660	0.117188	0.0585938	−	0.998282i	$-0.481338\pi$
$181$	1.57660	0.117188	0.0585938	+	0.998282i	$0.481338\pi$
$182$	−10.8383	−0.803385
$183$	0.00530648	0.000392266 0
$184$	−14.9553	−1.10252
$185$	−11.7708	−0.865409
$186$	−0.00470061	−0.000344665 0
$187$	−5.52875	−0.404302
$188$	6.77353	0.494011
$189$	0.00650224	0.000472969 0
$190$	49.7097	3.60632
$191$	4.40718	0.318892	0.159446	−	0.987207i	$-0.449029\pi$
$191$	4.40718	0.318892	0.159446	+	0.987207i	$0.449029\pi$
$192$	−0.0358342	−0.00258611
$193$	−0.849967	−0.0611820	−0.0305910	−	0.999532i	$-0.509739\pi$
$193$	−0.849967	−0.0611820	−0.0305910	+	0.999532i	$0.509739\pi$
$194$	−43.3922	−3.11538
$195$	0.0136257	0.000975759 0
$196$	−32.8269	−2.34478
$197$	19.7168	1.40476	0.702382	−	0.711800i	$-0.252120\pi$
$197$	19.7168	1.40476	0.702382	+	0.711800i	$0.252120\pi$
$198$	9.25750	0.657902
$199$	−0.357550	−0.0253461	−0.0126730	−	0.999920i	$-0.504034\pi$
$199$	−0.357550	−0.0253461	−0.0126730	+	0.999920i	$0.504034\pi$
$200$	−76.8962	−5.43739
$201$	−0.00256645	−0.000181023 0
$202$	−24.2253	−1.70449
$203$	2.02603	0.142199
$204$	0.0282064	0.00197484
$205$	21.4588	1.49875
$206$	−16.0784	−1.12023
$207$	−4.54793	−0.316103
$208$	59.5124	4.12644
$209$	5.65564	0.391209
$210$	−0.0106742	−0.000736592 0
$211$	−8.82070	−0.607242	−0.303621	−	0.952793i	$-0.598196\pi$
$211$	−8.82070	−0.607242	−0.303621	+	0.952793i	$0.598196\pi$
$212$	3.72951	0.256144
$213$	0.000534250 0	3.66062e−5 0
$214$	−22.5743	−1.54315
$215$	31.0207	2.11559
$216$	−0.0606184	−0.00412456
$217$	−1.76382	−0.119736
$218$	52.2214	3.53688
$219$	0.00954259	0.000644829 0
$220$	−22.3777	−1.50870
$221$	−18.3507	−1.23440
$222$	0.00928006	0.000622837 0
$223$	−16.9325	−1.13389	−0.566944	−	0.823757i	$-0.691874\pi$
$223$	−16.9325	−1.13389	−0.566944	+	0.823757i	$0.691874\pi$
$224$	−25.7431	−1.72004
$225$	−23.3843	−1.55896
$226$	−32.0014	−2.12870
$227$	−9.90977	−0.657735	−0.328867	−	0.944376i	$-0.606667\pi$
$227$	−9.90977	−0.657735	−0.328867	+	0.944376i	$0.606667\pi$
$228$	−0.0288537	−0.00191089
$229$	9.05410	0.598312	0.299156	−	0.954204i	$-0.403295\pi$
$229$	9.05410	0.598312	0.299156	+	0.954204i	$0.403295\pi$
$230$	14.9320	0.984585
$231$	−0.00121444	−7.99045e−5 0
$232$	−18.8880	−1.24006
$233$	−5.41132	−0.354508	−0.177254	−	0.984165i	$-0.556721\pi$
$233$	−5.41132	−0.354508	−0.177254	+	0.984165i	$0.556721\pi$
$234$	30.7270	2.00869
$235$	−4.34009	−0.283116
$236$	−13.8454	−0.901257
$237$	0.00141014	9.15982e−5 0
$238$	14.3757	0.931841
$239$	−3.79226	−0.245301	−0.122650	−	0.992450i	$-0.539139\pi$
$239$	−3.79226	−0.245301	−0.122650	+	0.992450i	$0.539139\pi$
$240$	0.0586117	0.00378337
$241$	−21.5186	−1.38614	−0.693069	−	0.720871i	$-0.743742\pi$
$241$	−21.5186	−1.38614	−0.693069	+	0.720871i	$0.743742\pi$
$242$	26.8320	1.72483
$243$	−0.0276513	−0.00177383
$244$	−28.9260	−1.85179
$245$	21.0335	1.34378
$246$	−0.0169180	−0.00107865
$247$	18.7719	1.19443
$248$	16.4435	1.04417
$249$	−0.00966555	−0.000612530 0
$250$	27.5278	1.74101
$251$	−23.9430	−1.51127	−0.755636	−	0.654992i	$-0.772672\pi$
$251$	−23.9430	−1.51127	−0.755636	+	0.654992i	$0.772672\pi$
$252$	−17.7221	−1.11639
$253$	1.69886	0.106806
$254$	−7.40786	−0.464811
$255$	−0.0180730	−0.00113178
$256$	61.3549	3.83468
$257$	−26.5751	−1.65771	−0.828854	−	0.559465i	$-0.811007\pi$
$257$	−26.5751	−1.65771	−0.828854	+	0.559465i	$0.811007\pi$
$258$	−0.0244565	−0.00152260
$259$	3.48218	0.216372
$260$	−74.2747	−4.60632
$261$	−5.74389	−0.355538
$262$	−43.5558	−2.69089
$263$	−13.2504	−0.817058	−0.408529	−	0.912745i	$-0.633958\pi$
$263$	−13.2504	−0.817058	−0.408529	+	0.912745i	$0.633958\pi$
$264$	0.0113219	0.000696813 0
$265$	−2.38966	−0.146795
$266$	−14.7057	−0.901663
$267$	0.0111217	0.000680638 0
$268$	13.9899	0.854567
$269$	7.05049	0.429876	0.214938	−	0.976628i	$-0.431045\pi$
$269$	7.05049	0.429876	0.214938	+	0.976628i	$0.431045\pi$
$270$	0.0605240	0.00368337
$271$	−22.9213	−1.39237	−0.696186	−	0.717862i	$-0.745121\pi$
$271$	−22.9213	−1.39237	−0.696186	+	0.717862i	$0.745121\pi$
$272$	−78.9366	−4.78623
$273$	−0.00403091	−0.000243962 0
$274$	−8.43545	−0.509604
$275$	8.73512	0.526747
$276$	−0.00866718	−0.000521703 0
$277$	1.70432	0.102403	0.0512014	−	0.998688i	$-0.483695\pi$
$277$	1.70432	0.102403	0.0512014	+	0.998688i	$0.483695\pi$
$278$	5.90109	0.353924
$279$	5.00052	0.299373
$280$	37.3403	2.23151
$281$	3.67539	0.219256	0.109628	−	0.993973i	$-0.465034\pi$
$281$	3.67539	0.219256	0.109628	+	0.993973i	$0.465034\pi$
$282$	0.00342170	0.000203759 0
$283$	2.60223	0.154687	0.0773433	−	0.997005i	$-0.475356\pi$
$283$	2.60223	0.154687	0.0773433	+	0.997005i	$0.475356\pi$
$284$	−2.91223	−0.172809
$285$	0.0184878	0.00109512
$286$	−11.4779	−0.678705
$287$	−6.34819	−0.374722
$288$	72.9831	4.30057
$289$	7.34023	0.431778
$290$	18.8586	1.10741
$291$	−0.0161382	−0.000946039 0
$292$	−52.0173	−3.04408
$293$	10.2148	0.596755	0.298378	−	0.954448i	$-0.403555\pi$
$293$	10.2148	0.596755	0.298378	+	0.954448i	$0.403555\pi$
$294$	−0.0165827	−0.000967124 0
$295$	8.87131	0.516508
$296$	−32.4633	−1.88689
$297$	0.00688601	0.000399567 0
$298$	−18.2311	−1.05610
$299$	5.63877	0.326098
$300$	−0.0445645	−0.00257293
$301$	−9.17688	−0.528947
$302$	−17.2704	−0.993798
$303$	−0.00900977	−0.000517598 0
$304$	80.7481	4.63122
$305$	18.5341	1.06126
$306$	−40.7560	−2.32986
$307$	0.199172	0.0113674	0.00568368	−	0.999984i	$-0.498191\pi$
$307$	0.199172	0.0113674	0.00568368	+	0.999984i	$0.498191\pi$
$308$	6.62001	0.377210
$309$	−0.00597979	−0.000340179 0
$310$	−16.4179	−0.932476
$311$	8.16345	0.462907	0.231453	−	0.972846i	$-0.425652\pi$
$311$	8.16345	0.462907	0.231453	+	0.972846i	$0.425652\pi$
$312$	0.0375789	0.00212749
$313$	−22.5820	−1.27641	−0.638206	−	0.769866i	$-0.720323\pi$
$313$	−22.5820	−1.27641	−0.638206	+	0.769866i	$0.720323\pi$
$314$	−43.3317	−2.44535
$315$	11.3553	0.639797
$316$	−7.68674	−0.432413
$317$	−22.0878	−1.24058	−0.620288	−	0.784374i	$-0.712984\pi$
$317$	−22.0878	−1.24058	−0.620288	+	0.784374i	$0.712984\pi$
$318$	0.00188399	0.000105649 0
$319$	2.14560	0.120131
$320$	−125.159	−6.99660
$321$	−0.00839574	−0.000468605 0
$322$	−4.41734	−0.246169
$323$	−24.8988	−1.38541
$324$	50.2430	2.79128
$325$	28.9931	1.60825
$326$	−22.1823	−1.22856
$327$	0.0194220	0.00107404
$328$	59.1822	3.26779
$329$	1.28393	0.0707855
$330$	−0.0113042	−0.000622278 0
$331$	−17.4510	−0.959195	−0.479597	−	0.877489i	$-0.659217\pi$
$331$	−17.4510	−0.959195	−0.479597	+	0.877489i	$0.659217\pi$
$332$	52.6876	2.89161
$333$	−9.87215	−0.540991
$334$	−41.3644	−2.26336
$335$	−8.96389	−0.489750
$336$	−0.0173392	−0.000945928 0
$337$	−3.73514	−0.203466	−0.101733	−	0.994812i	$-0.532439\pi$
$337$	−3.73514	−0.203466	−0.101733	+	0.994812i	$0.532439\pi$
$338$	−2.29961	−0.125083
$339$	−0.0119018	−0.000646418 0
$340$	98.5172	5.34285
$341$	−1.86792	−0.101154
$342$	41.6913	2.25441
$343$	−13.6296	−0.735932
$344$	85.5532	4.61272
$345$	0.00555343	0.000298986 0
$346$	−19.4811	−1.04731
$347$	−20.3418	−1.09200	−0.546002	−	0.837784i	$-0.683851\pi$
$347$	−20.3418	−1.09200	−0.546002	+	0.837784i	$0.683851\pi$
$348$	−0.0109464	−0.000586787 0
$349$	15.4986	0.829621	0.414810	−	0.909908i	$-0.363848\pi$
$349$	15.4986	0.829621	0.414810	+	0.909908i	$0.363848\pi$
$350$	−22.7129	−1.21405
$351$	0.0228557	0.00121995
$352$	−27.2625	−1.45310
$353$	15.4448	0.822045	0.411022	−	0.911625i	$-0.365172\pi$
$353$	15.4448	0.822045	0.411022	+	0.911625i	$0.365172\pi$
$354$	−0.00699409	−0.000371732 0
$355$	1.86599	0.0990364
$356$	−60.6252	−3.21313
$357$	0.00534656	0.000282970 0
$358$	−41.8609	−2.21242
$359$	−25.3802	−1.33951	−0.669757	−	0.742581i	$-0.733602\pi$
$359$	−25.3802	−1.33951	−0.669757	+	0.742581i	$0.733602\pi$
$360$	−105.862	−5.57940
$361$	6.47027	0.340540
$362$	−4.34139	−0.228179
$363$	0.00997923	0.000523774 0
$364$	21.9728	1.15169
$365$	33.3297	1.74455
$366$	−0.0146122	−0.000763789 0
$367$	11.5878	0.604877	0.302438	−	0.953169i	$-0.402199\pi$
$367$	11.5878	0.604877	0.302438	+	0.953169i	$0.402199\pi$
$368$	24.2554	1.26440
$369$	17.9975	0.936910
$370$	32.4127	1.68506
$371$	0.706934	0.0367022
$372$	0.00952971	0.000494092 0
$373$	2.26634	0.117347	0.0586733	−	0.998277i	$-0.481313\pi$
$373$	2.26634	0.117347	0.0586733	+	0.998277i	$0.481313\pi$
$374$	15.2242	0.787226
$375$	0.0102380	0.000528689 0
$376$	−11.9697	−0.617290
$377$	7.12158	0.366780
$378$	−0.0179049	−0.000920927 0
$379$	13.9325	0.715663	0.357832	−	0.933786i	$-0.383516\pi$
$379$	13.9325	0.715663	0.357832	+	0.933786i	$0.383516\pi$
$380$	−100.778	−5.16981
$381$	−0.00275510	−0.000141148 0
$382$	−12.1358	−0.620922
$383$	−9.46492	−0.483635	−0.241817	−	0.970322i	$-0.577744\pi$
$383$	−9.46492	−0.483635	−0.241817	+	0.970322i	$0.577744\pi$
$384$	0.0488456	0.00249264
$385$	−4.24171	−0.216178
$386$	2.34051	0.119129
$387$	26.0169	1.32252
$388$	87.9704	4.46602
$389$	19.5389	0.990660	0.495330	−	0.868705i	$-0.335047\pi$
$389$	19.5389	0.990660	0.495330	+	0.868705i	$0.335047\pi$
$390$	−0.0375204	−0.00189992
$391$	−7.47920	−0.378239
$392$	58.0092	2.92991
$393$	−0.0161991	−0.000817136 0
$394$	−54.2931	−2.73525
$395$	4.92522	0.247815
$396$	−18.7681	−0.943130
$397$	13.8591	0.695569	0.347784	−	0.937575i	$-0.386934\pi$
$397$	13.8591	0.695569	0.347784	+	0.937575i	$0.386934\pi$
$398$	0.984566	0.0493519
$399$	−0.00546926	−0.000273806 0
$400$	124.715	6.23576
$401$	9.74807	0.486795	0.243398	−	0.969927i	$-0.421738\pi$
$401$	9.74807	0.486795	0.243398	+	0.969927i	$0.421738\pi$
$402$	0.00706708	0.000352474 0
$403$	−6.19991	−0.308840
$404$	49.1128	2.44345
$405$	−32.1928	−1.59967
$406$	−5.57895	−0.276879
$407$	3.68770	0.182793
$408$	−0.0498443	−0.00246766
$409$	37.3649	1.84757	0.923787	−	0.382906i	$-0.125077\pi$
$409$	37.3649	1.84757	0.923787	+	0.382906i	$0.125077\pi$
$410$	−59.0900	−2.91825
$411$	−0.00313727	−0.000154750 0
$412$	32.5962	1.60590
$413$	−2.62441	−0.129139
$414$	12.5234	0.615491
$415$	−33.7591	−1.65717
$416$	−90.4883	−4.43655
$417$	0.00219470	0.000107475 0
$418$	−15.5736	−0.761730
$419$	39.4272	1.92615	0.963073	−	0.269242i	$-0.0867731\pi$
$419$	39.4272	1.92615	0.963073	+	0.269242i	$0.0867731\pi$
$420$	0.0216402	0.00105594
$421$	−25.6528	−1.25024	−0.625121	−	0.780528i	$-0.714950\pi$
$421$	−25.6528	−1.25024	−0.625121	+	0.780528i	$0.714950\pi$
$422$	24.2891	1.18237
$423$	−3.64001	−0.176983
$424$	−6.59053	−0.320064
$425$	−38.4562	−1.86540
$426$	−0.00147113	−7.12767e−5 0
$427$	−5.48295	−0.265339
$428$	45.7658	2.21217
$429$	−0.00426882	−0.000206101 0
$430$	−85.4199	−4.11932
$431$	22.0071	1.06005	0.530023	−	0.847984i	$-0.322183\pi$
$431$	22.0071	1.06005	0.530023	+	0.847984i	$0.322183\pi$
$432$	0.0983148	0.00473017
$433$	26.5614	1.27646	0.638230	−	0.769845i	$-0.279667\pi$
$433$	26.5614	1.27646	0.638230	+	0.769845i	$0.279667\pi$
$434$	4.85694	0.233140
$435$	0.00701380	0.000336286 0
$436$	−105.870	−5.07027
$437$	7.65085	0.365990
$438$	−0.0262769	−0.00125556
$439$	−28.8109	−1.37507	−0.687534	−	0.726152i	$-0.741307\pi$
$439$	−28.8109	−1.37507	−0.687534	+	0.726152i	$0.741307\pi$
$440$	39.5442	1.88519
$441$	17.6407	0.840036
$442$	50.5314	2.40354
$443$	12.3633	0.587397	0.293699	−	0.955898i	$-0.405114\pi$
$443$	12.3633	0.587397	0.293699	+	0.955898i	$0.405114\pi$
$444$	−0.0188138	−0.000892862 0
$445$	38.8451	1.84144
$446$	46.6262	2.20782
$447$	−0.00678044	−0.000320704 0
$448$	37.0259	1.74931
$449$	30.4236	1.43578	0.717889	−	0.696157i	$-0.245108\pi$
$449$	30.4236	1.43578	0.717889	+	0.696157i	$0.245108\pi$
$450$	64.3921	3.03547
$451$	−6.72287	−0.316568
$452$	64.8776	3.05159
$453$	−0.00642311	−0.000301784 0
$454$	27.2880	1.28069
$455$	−14.0789	−0.660028
$456$	0.0509882	0.00238774
$457$	−13.0611	−0.610973	−0.305487	−	0.952196i	$-0.598819\pi$
$457$	−13.0611	−0.610973	−0.305487	+	0.952196i	$0.598819\pi$
$458$	−24.9318	−1.16499
$459$	−0.0303156	−0.00141501
$460$	−30.2721	−1.41144
$461$	20.3143	0.946130	0.473065	−	0.881027i	$-0.343148\pi$
$461$	20.3143	0.946130	0.473065	+	0.881027i	$0.343148\pi$
$462$	0.00334414	0.000155584 0
$463$	26.1012	1.21303	0.606513	−	0.795074i	$-0.292568\pi$
$463$	26.1012	1.21303	0.606513	+	0.795074i	$0.292568\pi$
$464$	30.6338	1.42214
$465$	−0.00610608	−0.000283163 0
$466$	14.9009	0.690269
$467$	−25.6555	−1.18720	−0.593598	−	0.804762i	$-0.702293\pi$
$467$	−25.6555	−1.18720	−0.593598	+	0.804762i	$0.702293\pi$
$468$	−62.2939	−2.87954
$469$	2.65180	0.122449
$470$	11.9511	0.551261
$471$	−0.0161157	−0.000742574 0
$472$	24.4665	1.12616
$473$	−9.71851	−0.446858
$474$	−0.00388301	−0.000178353 0
$475$	39.3388	1.80499
$476$	−29.1445	−1.33583
$477$	−2.00420	−0.0917658
$478$	10.4425	0.477630
$479$	−11.8431	−0.541126	−0.270563	−	0.962702i	$-0.587210\pi$
$479$	−11.8431	−0.541126	−0.270563	+	0.962702i	$0.587210\pi$
$480$	−0.0891188	−0.00406770
$481$	12.2400	0.558097
$482$	59.2547	2.69898
$483$	−0.00164288	−7.47534e−5 0
$484$	−54.3974	−2.47261
$485$	−56.3663	−2.55946
$486$	0.0761418	0.00345386
$487$	−14.2819	−0.647175	−0.323587	−	0.946198i	$-0.604889\pi$
$487$	−14.2819	−0.647175	−0.323587	+	0.946198i	$0.604889\pi$
$488$	51.1159	2.31391
$489$	−0.00824992	−0.000373074 0
$490$	−57.9189	−2.61651
$491$	20.6828	0.933402	0.466701	−	0.884415i	$-0.345442\pi$
$491$	20.6828	0.933402	0.466701	+	0.884415i	$0.345442\pi$
$492$	0.0342985	0.00154630
$493$	−9.44598	−0.425426
$494$	−51.6911	−2.32569
$495$	12.0255	0.540505
$496$	−26.6692	−1.19748
$497$	−0.552017	−0.0247614
$498$	0.0266155	0.00119267
$499$	−34.6901	−1.55294	−0.776471	−	0.630153i	$-0.782992\pi$
$499$	−34.6901	−1.55294	−0.776471	+	0.630153i	$0.782992\pi$
$500$	−55.8081	−2.49582
$501$	−0.0153840	−0.000687309 0
$502$	65.9306	2.94263
$503$	−12.7272	−0.567478	−0.283739	−	0.958902i	$-0.591575\pi$
$503$	−12.7272	−0.567478	−0.283739	+	0.958902i	$0.591575\pi$
$504$	31.3172	1.39498
$505$	−31.4686	−1.40034
$506$	−4.67806	−0.207965
$507$	−0.000855262 0	−3.79835e−5 0
$508$	15.0182	0.666326
$509$	−5.90528	−0.261747	−0.130873	−	0.991399i	$-0.541778\pi$
$509$	−5.90528	−0.261747	−0.130873	+	0.991399i	$0.541778\pi$
$510$	0.0497667	0.00220371
$511$	−9.85995	−0.436178
$512$	−73.5595	−3.25090
$513$	0.0310113	0.00136918
$514$	73.1783	3.22776
$515$	−20.8858	−0.920337
$516$	0.0495816	0.00218271
$517$	1.35971	0.0598000
$518$	−9.58868	−0.421302
$519$	−0.00724531	−0.000318034 0
$520$	131.253	5.75582
$521$	−33.1775	−1.45353	−0.726767	−	0.686884i	$-0.758978\pi$
$521$	−33.1775	−1.45353	−0.726767	+	0.686884i	$0.758978\pi$
$522$	15.8166	0.692275
$523$	39.5374	1.72885	0.864425	−	0.502761i	$-0.167683\pi$
$523$	39.5374	1.72885	0.864425	+	0.502761i	$0.167683\pi$
$524$	88.3023	3.85750
$525$	−0.00844726	−0.000368669 0
$526$	36.4870	1.59091
$527$	8.22350	0.358221
$528$	−0.0183625	−0.000799127 0
$529$	−20.7018	−0.900079
$530$	6.58026	0.285828
$531$	7.44033	0.322883
$532$	29.8133	1.29257
$533$	−22.3142	−0.966536
$534$	−0.0306253	−0.00132529
$535$	−29.3240	−1.26779
$536$	−24.7219	−1.06782
$537$	−0.0155687	−0.000671840 0
$538$	−19.4145	−0.837020
$539$	−6.58963	−0.283835
$540$	−0.122702	−0.00528027
$541$	2.25655	0.0970166	0.0485083	−	0.998823i	$-0.484553\pi$
$541$	2.25655	0.0970166	0.0485083	+	0.998823i	$0.484553\pi$
$542$	63.1172	2.71112
$543$	−0.00161463	−6.92904e−5 0
$544$	120.023	5.14593
$545$	67.8356	2.90576
$546$	0.0110997	0.000475024 0
$547$	−40.7039	−1.74037	−0.870185	−	0.492724i	$-0.836001\pi$
$547$	−40.7039	−1.74037	−0.870185	+	0.492724i	$0.836001\pi$
$548$	17.1015	0.730539
$549$	15.5445	0.663421
$550$	−24.0534	−1.02564
$551$	9.66277	0.411648
$552$	0.0153160	0.000651893 0
$553$	−1.45703	−0.0619593
$554$	−4.69310	−0.199391
$555$	0.0120548	0.000511697 0
$556$	−11.9635	−0.507365
$557$	−25.2934	−1.07171	−0.535857	−	0.844308i	$-0.680012\pi$
$557$	−25.2934	−1.07171	−0.535857	+	0.844308i	$0.680012\pi$
$558$	−13.7697	−0.582916
$559$	−32.2572	−1.36433
$560$	−60.5609	−2.55917
$561$	0.00566212	0.000239055 0
$562$	−10.1207	−0.426917
$563$	−35.6912	−1.50420	−0.752102	−	0.659046i	$-0.770960\pi$
$563$	−35.6912	−1.50420	−0.752102	+	0.659046i	$0.770960\pi$
$564$	−0.00693693	−0.000292097 0
$565$	−41.5698	−1.74885
$566$	−7.16562	−0.301194
$567$	9.52362	0.399955
$568$	5.14628	0.215933
$569$	−42.4181	−1.77826	−0.889130	−	0.457654i	$-0.848690\pi$
$569$	−42.4181	−1.77826	−0.889130	+	0.457654i	$0.848690\pi$
$570$	−0.0509088	−0.00213234
$571$	−46.7357	−1.95583	−0.977915	−	0.209003i	$-0.932978\pi$
$571$	−46.7357	−1.95583	−0.977915	+	0.209003i	$0.932978\pi$
$572$	23.2696	0.972952
$573$	−0.00451349	−0.000188554 0
$574$	17.4807	0.729629
$575$	11.8167	0.492791
$576$	−104.970	−4.37377
$577$	−14.7132	−0.612517	−0.306258	−	0.951948i	$-0.599077\pi$
$577$	−14.7132	−0.612517	−0.306258	+	0.951948i	$0.599077\pi$
$578$	−20.2124	−0.840725
$579$	0.000870471 0	3.61755e−5 0
$580$	−38.2327	−1.58752
$581$	9.98700	0.414331
$582$	0.0444389	0.00184205
$583$	0.748658	0.0310063
$584$	91.9212	3.80373
$585$	39.9143	1.65025
$586$	−28.1279	−1.16195
$587$	−18.3658	−0.758038	−0.379019	−	0.925389i	$-0.623739\pi$
$587$	−18.3658	−0.758038	−0.379019	+	0.925389i	$0.623739\pi$
$588$	0.0336187	0.00138641
$589$	−8.41223	−0.346620
$590$	−24.4284	−1.00570
$591$	−0.0201924	−0.000830605 0
$592$	52.6510	2.16394
$593$	−5.48753	−0.225346	−0.112673	−	0.993632i	$-0.535941\pi$
$593$	−5.48753	−0.225346	−0.112673	+	0.993632i	$0.535941\pi$
$594$	−0.0189616	−0.000778005 0
$595$	18.6741	0.765562
$596$	36.9606	1.51397
$597$	0.000366175 0	1.49866e−5 0
$598$	−15.5272	−0.634953
$599$	−42.5735	−1.73950	−0.869752	−	0.493489i	$-0.835721\pi$
$599$	−42.5735	−1.73950	−0.869752	+	0.493489i	$0.835721\pi$
$600$	0.0787512	0.00321500
$601$	−5.83223	−0.237902	−0.118951	−	0.992900i	$-0.537953\pi$
$601$	−5.83223	−0.237902	−0.118951	+	0.992900i	$0.537953\pi$
$602$	25.2699	1.02992
$603$	−7.51798	−0.306156
$604$	35.0128	1.42465
$605$	34.8547	1.41705
$606$	0.0248097	0.00100783
$607$	5.98587	0.242959	0.121480	−	0.992594i	$-0.461236\pi$
$607$	5.98587	0.242959	0.121480	+	0.992594i	$0.461236\pi$
$608$	−122.777	−4.97927
$609$	−0.00207490	−8.40791e−5 0
$610$	−51.0362	−2.06640
$611$	4.51308	0.182580
$612$	82.6260	3.33996
$613$	−9.10084	−0.367579	−0.183790	−	0.982966i	$-0.558837\pi$
$613$	−9.10084	−0.367579	−0.183790	+	0.982966i	$0.558837\pi$
$614$	−0.548450	−0.0221336
$615$	−0.0219765	−0.000886178 0
$616$	−11.6984	−0.471342
$617$	−14.8184	−0.596564	−0.298282	−	0.954478i	$-0.596414\pi$
$617$	−14.8184	−0.596564	−0.298282	+	0.954478i	$0.596414\pi$
$618$	0.0164662	0.000662369 0
$619$	19.3505	0.777761	0.388881	−	0.921288i	$-0.372862\pi$
$619$	19.3505	0.777761	0.388881	+	0.921288i	$0.372862\pi$
$620$	33.2847	1.33674
$621$	0.00931528	0.000373809 0
$622$	−22.4792	−0.901336
$623$	−11.4916	−0.460401
$624$	−0.0609480	−0.00243987
$625$	−3.21530	−0.128612
$626$	62.1829	2.48533
$627$	−0.00579207	−0.000231313 0
$628$	87.8479	3.50551
$629$	−16.2350	−0.647333
$630$	−31.2684	−1.24576
$631$	−17.2331	−0.686038	−0.343019	−	0.939329i	$-0.611449\pi$
$631$	−17.2331	−0.686038	−0.343019	+	0.939329i	$0.611449\pi$
$632$	13.5835	0.540321
$633$	0.00903347	0.000359048 0
$634$	60.8220	2.41555
$635$	−9.62280	−0.381869
$636$	−0.00381948	−0.000151452 0
$637$	−21.8719	−0.866598
$638$	−5.90823	−0.233909
$639$	1.56500	0.0619103
$640$	170.604	6.74372
$641$	−8.84162	−0.349223	−0.174611	−	0.984637i	$-0.555867\pi$
$641$	−8.84162	−0.349223	−0.174611	+	0.984637i	$0.555867\pi$
$642$	0.0231189	0.000912430 0
$643$	−27.6545	−1.09059	−0.545294	−	0.838245i	$-0.683582\pi$
$643$	−27.6545	−1.09059	−0.545294	+	0.838245i	$0.683582\pi$
$644$	8.95542	0.352893
$645$	−0.0317690	−0.00125090
$646$	68.5626	2.69756
$647$	15.7630	0.619708	0.309854	−	0.950784i	$-0.399720\pi$
$647$	15.7630	0.619708	0.309854	+	0.950784i	$0.399720\pi$
$648$	−88.7858	−3.48783
$649$	−2.77930	−0.109097
$650$	−79.8368	−3.13146
$651$	0.00180637	7.07972e−5 0
$652$	44.9709	1.76120
$653$	9.62727	0.376744	0.188372	−	0.982098i	$-0.439679\pi$
$653$	9.62727	0.376744	0.188372	+	0.982098i	$0.439679\pi$
$654$	−0.0534812	−0.00209128
$655$	−56.5790	−2.21072
$656$	−95.9855	−3.74761
$657$	27.9535	1.09057
$658$	−3.53549	−0.137828
$659$	−2.07885	−0.0809805	−0.0404902	−	0.999180i	$-0.512892\pi$
$659$	−2.07885	−0.0809805	−0.0404902	+	0.999180i	$0.512892\pi$
$660$	0.0229175	0.000892061 0
$661$	36.1601	1.40646	0.703231	−	0.710961i	$-0.251740\pi$
$661$	36.1601	1.40646	0.703231	+	0.710961i	$0.251740\pi$
$662$	48.0539	1.86767
$663$	0.0187934	0.000729876 0
$664$	−93.1057	−3.61320
$665$	−19.1026	−0.740769
$666$	27.1844	1.05337
$667$	2.90253	0.112387
$668$	83.8595	3.24462
$669$	0.0173410	0.000670442 0
$670$	24.6834	0.953602
$671$	−5.80656	−0.224160
$672$	0.0263641	0.00101702
$673$	35.9885	1.38725	0.693627	−	0.720335i	$-0.256012\pi$
$673$	35.9885	1.38725	0.693627	+	0.720335i	$0.256012\pi$
$674$	10.2852	0.396173
$675$	0.0478969	0.00184355
$676$	4.66209	0.179311
$677$	−29.6214	−1.13844	−0.569222	−	0.822184i	$-0.692756\pi$
$677$	−29.6214	−1.13844	−0.569222	+	0.822184i	$0.692756\pi$
$678$	0.0327734	0.00125865
$679$	16.6749	0.639925
$680$	−174.092	−6.67614
$681$	0.0101488	0.000388904 0
$682$	5.14360	0.196959
$683$	25.2912	0.967742	0.483871	−	0.875139i	$-0.339230\pi$
$683$	25.2912	0.967742	0.483871	+	0.875139i	$0.339230\pi$
$684$	−84.5223	−3.23179
$685$	−10.9576	−0.418670
$686$	37.5312	1.43295
$687$	−0.00927251	−0.000353768 0
$688$	−138.756	−5.29001
$689$	2.48491	0.0946675
$690$	−0.0152922	−0.000582163 0
$691$	24.9051	0.947434	0.473717	−	0.880677i	$-0.342912\pi$
$691$	24.9051	0.947434	0.473717	+	0.880677i	$0.342912\pi$
$692$	39.4946	1.50136
$693$	−3.55751	−0.135139
$694$	56.0140	2.12626
$695$	7.66550	0.290769
$696$	0.0193436	0.000733218 0
$697$	29.5973	1.12108
$698$	−42.6776	−1.61537
$699$	0.00554186	0.000209612 0
$700$	46.0466	1.74040
$701$	35.9673	1.35847	0.679233	−	0.733923i	$-0.262313\pi$
$701$	35.9673	1.35847	0.679233	+	0.733923i	$0.262313\pi$
$702$	−0.0629365	−0.00237538
$703$	16.6076	0.626368
$704$	39.2113	1.47783
$705$	0.00444478	0.000167400 0
$706$	−42.5295	−1.60062
$707$	9.30940	0.350116
$708$	0.0141794	0.000532893 0
$709$	49.9585	1.87623	0.938115	−	0.346325i	$-0.112570\pi$
$709$	49.9585	1.87623	0.938115	+	0.346325i	$0.112570\pi$
$710$	−5.13827	−0.192836
$711$	4.13076	0.154916
$712$	107.133	4.01496
$713$	−2.52689	−0.0946329
$714$	−0.0147225	−0.000550977 0
$715$	−14.9098	−0.557596
$716$	84.8661	3.17160
$717$	0.00388374	0.000145041 0
$718$	69.8879	2.60819
$719$	−44.4042	−1.65600	−0.827999	−	0.560729i	$-0.810521\pi$
$719$	−44.4042	−1.65600	−0.827999	+	0.560729i	$0.810521\pi$
$720$	171.693	6.39863
$721$	6.17866	0.230105
$722$	−17.8168	−0.663073
$723$	0.0220377	0.000819592 0
$724$	8.80145	0.327103
$725$	14.9241	0.554268
$726$	−0.0274792	−0.00101985
$727$	−47.8407	−1.77431	−0.887156	−	0.461470i	$-0.847322\pi$
$727$	−47.8407	−1.77431	−0.887156	+	0.461470i	$0.847322\pi$
$728$	−38.8287	−1.43909
$729$	−26.9999	−0.999998
$730$	−91.7780	−3.39686
$731$	42.7856	1.58248
$732$	0.0296237	0.00109492
$733$	31.6661	1.16962	0.584808	−	0.811172i	$-0.301170\pi$
$733$	31.6661	1.16962	0.584808	+	0.811172i	$0.301170\pi$
$734$	−31.9086	−1.17777
$735$	−0.0215409	−0.000794549 0
$736$	−36.8802	−1.35942
$737$	2.80831	0.103445
$738$	−49.5586	−1.82428
$739$	11.3232	0.416532	0.208266	−	0.978072i	$-0.433218\pi$
$739$	11.3232	0.416532	0.208266	+	0.978072i	$0.433218\pi$
$740$	−65.7114	−2.41560
$741$	−0.0192247	−0.000706238 0
$742$	−1.94665	−0.0714636
$743$	27.2577	0.999989	0.499994	−	0.866029i	$-0.333335\pi$
$743$	27.2577	0.999989	0.499994	+	0.866029i	$0.333335\pi$
$744$	−0.0168402	−0.000617392 0
$745$	−23.6822	−0.867649
$746$	−6.24070	−0.228488
$747$	−28.3137	−1.03594
$748$	−30.8646	−1.12852
$749$	8.67496	0.316976
$750$	−0.0281919	−0.00102942
$751$	−22.7829	−0.831358	−0.415679	−	0.909511i	$-0.636456\pi$
$751$	−22.7829	−0.831358	−0.415679	+	0.909511i	$0.636456\pi$
$752$	19.4132	0.707927
$753$	0.0245206	0.000893581 0
$754$	−19.6103	−0.714165
$755$	−22.4342	−0.816463
$756$	0.0362992	0.00132019
$757$	29.2048	1.06147	0.530733	−	0.847539i	$-0.321917\pi$
$757$	29.2048	1.06147	0.530733	+	0.847539i	$0.321917\pi$
$758$	−38.3651	−1.39348
$759$	−0.00173984	−6.31522e−5 0
$760$	178.088	6.45993
$761$	−22.3133	−0.808857	−0.404429	−	0.914570i	$-0.632530\pi$
$761$	−22.3133	−0.808857	−0.404429	+	0.914570i	$0.632530\pi$
$762$	0.00758656	0.000274832 0
$763$	−20.0679	−0.726506
$764$	24.6033	0.890118
$765$	−52.9419	−1.91412
$766$	26.0630	0.941695
$767$	−9.22492	−0.333093
$768$	−0.0628350	−0.00226736
$769$	31.3592	1.13084	0.565421	−	0.824803i	$-0.308714\pi$
$769$	31.3592	1.13084	0.565421	+	0.824803i	$0.308714\pi$
$770$	11.6802	0.420924
$771$	0.0272161	0.000980165 0
$772$	−4.74499	−0.170776
$773$	−13.3046	−0.478535	−0.239267	−	0.970954i	$-0.576907\pi$
$773$	−13.3046	−0.478535	−0.239267	+	0.970954i	$0.576907\pi$
$774$	−71.6414	−2.57510
$775$	−12.9927	−0.466710
$776$	−155.455	−5.58051
$777$	−0.00356618	−0.000127936 0
$778$	−53.8031	−1.92893
$779$	−30.2766	−1.08477
$780$	0.0760664	0.00272362
$781$	−0.584598	−0.0209186
$782$	20.5951	0.736478
$783$	0.0117649	0.000420443 0
$784$	−94.0831	−3.36011
$785$	−56.2878	−2.00900
$786$	0.0446065	0.00159106
$787$	−45.0714	−1.60662	−0.803311	−	0.595560i	$-0.796930\pi$
$787$	−45.0714	−1.60662	−0.803311	+	0.595560i	$0.796930\pi$
$788$	110.070	3.92109
$789$	0.0135701	0.000483108 0
$790$	−13.5623	−0.482525
$791$	12.2976	0.437254
$792$	33.1655	1.17849
$793$	−19.2728	−0.684399
$794$	−38.1631	−1.35436
$795$	0.00244730	8.67968e−5 0
$796$	−1.99605	−0.0707480
$797$	0.214721	0.00760580	0.00380290	−	0.999993i	$-0.498789\pi$
$797$	0.214721	0.00760580	0.00380290	+	0.999993i	$0.498789\pi$
$798$	0.0150604	0.000533133 0
$799$	−5.98610	−0.211773
$800$	−189.629	−6.70440
$801$	32.5793	1.15113
$802$	−26.8427	−0.947849
$803$	−10.4419	−0.368486
$804$	−0.0143273	−0.000505286 0
$805$	−5.73812	−0.202242
$806$	17.0724	0.601348
$807$	−0.00722057	−0.000254176 0
$808$	−86.7886	−3.05321
$809$	16.2001	0.569564	0.284782	−	0.958592i	$-0.408079\pi$
$809$	16.2001	0.569564	0.284782	+	0.958592i	$0.408079\pi$
$810$	88.6475	3.11475
$811$	28.8992	1.01479	0.507394	−	0.861714i	$-0.330609\pi$
$811$	28.8992	1.01479	0.507394	+	0.861714i	$0.330609\pi$
$812$	11.3104	0.396917
$813$	0.0234743	0.000823278 0
$814$	−10.1546	−0.355919
$815$	−28.8147	−1.00934
$816$	0.0808407	0.00282999
$817$	−43.7675	−1.53123
$818$	−102.890	−3.59745
$819$	−11.8079	−0.412601
$820$	119.795	4.18343
$821$	28.2273	0.985140	0.492570	−	0.870273i	$-0.336058\pi$
$821$	28.2273	0.985140	0.492570	+	0.870273i	$0.336058\pi$
$822$	0.00863893	0.000301317 0
$823$	22.4922	0.784029	0.392014	−	0.919959i	$-0.371778\pi$
$823$	22.4922	0.784029	0.392014	+	0.919959i	$0.371778\pi$
$824$	−57.6017	−2.00665
$825$	−0.00894583	−0.000311454 0
$826$	7.22669	0.251449
$827$	−23.7645	−0.826374	−0.413187	−	0.910646i	$-0.635584\pi$
$827$	−23.7645	−0.826374	−0.413187	+	0.910646i	$0.635584\pi$
$828$	−25.3891	−0.882332
$829$	−27.9799	−0.971781	−0.485890	−	0.874020i	$-0.661505\pi$
$829$	−27.9799	−0.971781	−0.485890	+	0.874020i	$0.661505\pi$
$830$	92.9606	3.22671
$831$	−0.00174544	−6.05485e−5 0
$832$	130.148	4.51207
$833$	29.0107	1.00516
$834$	−0.00604344	−0.000209267 0
$835$	−53.7323	−1.85948
$836$	31.5729	1.09197
$837$	−0.0102423	−0.000354026 0
$838$	−108.569	−3.75044
$839$	−20.1404	−0.695323	−0.347662	−	0.937620i	$-0.613024\pi$
$839$	−20.1404	−0.695323	−0.347662	+	0.937620i	$0.613024\pi$
$840$	−0.0382410	−0.00131944
$841$	−25.3342	−0.873593
$842$	70.6388	2.43437
$843$	−0.00376405	−0.000129641 0
$844$	−49.2421	−1.69498
$845$	−2.98719	−0.102763
$846$	10.0233	0.344608
$847$	−10.3111	−0.354294
$848$	10.6889	0.367060
$849$	−0.00266500	−9.14627e−5 0
$850$	105.895	3.63216
$851$	4.98865	0.171009
$852$	0.00298248	0.000102178 0
$853$	−14.5695	−0.498849	−0.249424	−	0.968394i	$-0.580241\pi$
$853$	−14.5695	−0.498849	−0.249424	+	0.968394i	$0.580241\pi$
$854$	15.0981	0.516647
$855$	54.1570	1.85213
$856$	−80.8739	−2.76421
$857$	16.6515	0.568806	0.284403	−	0.958705i	$-0.408205\pi$
$857$	16.6515	0.568806	0.284403	+	0.958705i	$0.408205\pi$
$858$	0.0117548	0.000401303 0
$859$	−47.5804	−1.62342	−0.811711	−	0.584059i	$-0.801464\pi$
$859$	−47.5804	−1.62342	−0.811711	+	0.584059i	$0.801464\pi$
$860$	173.175	5.90521
$861$	0.00650133	0.000221565 0
$862$	−60.5998	−2.06404
$863$	32.0205	1.08999	0.544995	−	0.838439i	$-0.316531\pi$
$863$	32.0205	1.08999	0.544995	+	0.838439i	$0.316531\pi$
$864$	−0.149487	−0.00508566
$865$	−25.3059	−0.860425
$866$	−73.1407	−2.48542
$867$	−0.00751730	−0.000255301 0
$868$	−9.84663	−0.334217
$869$	−1.54303	−0.0523437
$870$	−0.0193135	−0.000654789 0
$871$	9.32119	0.315837
$872$	187.086	6.33555
$873$	−47.2742	−1.59999
$874$	−21.0677	−0.712626
$875$	−10.5785	−0.357619
$876$	0.0532721	0.00179990
$877$	31.2185	1.05417	0.527086	−	0.849812i	$-0.323284\pi$
$877$	31.2185	1.05417	0.527086	+	0.849812i	$0.323284\pi$
$878$	79.3349	2.67742
$879$	−0.0104612	−0.000352848 0
$880$	−64.1353	−2.16200
$881$	−43.2924	−1.45856	−0.729279	−	0.684216i	$-0.760144\pi$
$881$	−43.2924	−1.45856	−0.729279	+	0.684216i	$0.760144\pi$
$882$	−48.5764	−1.63565
$883$	5.48623	0.184626	0.0923132	−	0.995730i	$-0.470574\pi$
$883$	5.48623	0.184626	0.0923132	+	0.995730i	$0.470574\pi$
$884$	−102.444	−3.44557
$885$	−0.00908531	−0.000305399 0
$886$	−34.0441	−1.14373
$887$	−55.4269	−1.86105	−0.930526	−	0.366226i	$-0.880650\pi$
$887$	−55.4269	−1.86105	−0.930526	+	0.366226i	$0.880650\pi$
$888$	0.0332463	0.00111567
$889$	2.84672	0.0954760
$890$	−106.966	−3.58550
$891$	10.0857	0.337884
$892$	−94.5269	−3.16500
$893$	6.12348	0.204915
$894$	0.0186709	0.000624449 0
$895$	−54.3773	−1.81763
$896$	−50.4700	−1.68609
$897$	−0.00577479	−0.000192815 0
$898$	−83.7758	−2.79563
$899$	−3.19138	−0.106439
$900$	−130.544	−4.35148
$901$	−3.29595	−0.109804
$902$	18.5124	0.616396
$903$	0.00939825	0.000312754 0
$904$	−114.647	−3.81310
$905$	−5.63946	−0.187462
$906$	0.0176870	0.000587610 0
$907$	−6.15403	−0.204341	−0.102171	−	0.994767i	$-0.532579\pi$
$907$	−6.15403	−0.204341	−0.102171	+	0.994767i	$0.532579\pi$
$908$	−55.3219	−1.83592
$909$	−26.3926	−0.875388
$910$	38.7682	1.28515
$911$	6.90940	0.228919	0.114459	−	0.993428i	$-0.463486\pi$
$911$	6.90940	0.228919	0.114459	+	0.993428i	$0.463486\pi$
$912$	−0.0826960	−0.00273834
$913$	10.5764	0.350029
$914$	35.9657	1.18964
$915$	−0.0189812	−0.000627498 0
$916$	50.5451	1.67006
$917$	16.7378	0.552731
$918$	0.0834783	0.00275519
$919$	−47.5377	−1.56813	−0.784063	−	0.620681i	$-0.786856\pi$
$919$	−47.5377	−1.56813	−0.784063	+	0.620681i	$0.786856\pi$
$920$	53.4946	1.76367
$921$	−0.000203977 0	−6.72126e−6 0
$922$	−55.9383	−1.84223
$923$	−1.94037	−0.0638680
$924$	−0.00677970	−0.000223036 0
$925$	25.6504	0.843381
$926$	−71.8734	−2.36191
$927$	−17.5168	−0.575328
$928$	−46.5785	−1.52902
$929$	−40.9710	−1.34421	−0.672107	−	0.740454i	$-0.734611\pi$
$929$	−40.9710	−1.34421	−0.672107	+	0.740454i	$0.734611\pi$
$930$	0.0168140	0.000551352 0
$931$	−29.6765	−0.972608
$932$	−30.2090	−0.989530
$933$	−0.00836038	−0.000273706 0
$934$	70.6462	2.31161
$935$	19.7762	0.646752
$936$	110.081	3.59812
$937$	50.5632	1.65183	0.825914	−	0.563797i	$-0.190660\pi$
$937$	50.5632	1.65183	0.825914	+	0.563797i	$0.190660\pi$
$938$	−7.30211	−0.238422
$939$	0.0231268	0.000754714 0
$940$	−24.2288	−0.790256
$941$	8.79487	0.286704	0.143352	−	0.989672i	$-0.454212\pi$
$941$	8.79487	0.286704	0.143352	+	0.989672i	$0.454212\pi$
$942$	0.0443770	0.00144588
$943$	−9.09458	−0.296160
$944$	−39.6814	−1.29152
$945$	−0.0232584	−0.000756596 0
$946$	26.7613	0.870086
$947$	10.4108	0.338304	0.169152	−	0.985590i	$-0.445897\pi$
$947$	10.4108	0.338304	0.169152	+	0.985590i	$0.445897\pi$
$948$	0.00787217	0.000255676 0
$949$	−34.6582	−1.12505
$950$	−108.325	−3.51453
$951$	0.0226206	0.000733524 0
$952$	51.5020	1.66919
$953$	−43.2718	−1.40171	−0.700856	−	0.713303i	$-0.747198\pi$
$953$	−43.2718	−1.40171	−0.700856	+	0.713303i	$0.747198\pi$
$954$	5.51884	0.178679
$955$	−15.7644	−0.510124
$956$	−21.1705	−0.684703
$957$	−0.00219736	−7.10306e−5 0
$958$	32.6118	1.05364
$959$	3.24161	0.104677
$960$	0.128178	0.00413693
$961$	−28.2216	−0.910375
$962$	−33.7047	−1.08668
$963$	−24.5940	−0.792529
$964$	−120.129	−3.86910
$965$	3.04031	0.0978712
$966$	0.00452390	0.000145554 0
$967$	5.41354	0.174088	0.0870438	−	0.996204i	$-0.472258\pi$
$967$	5.41354	0.174088	0.0870438	+	0.996204i	$0.472258\pi$
$968$	96.1272	3.08964
$969$	0.0254995	0.000819161 0
$970$	155.213	4.98359
$971$	−36.6382	−1.17578	−0.587888	−	0.808943i	$-0.700040\pi$
$971$	−36.6382	−1.17578	−0.587888	+	0.808943i	$0.700040\pi$
$972$	−0.154365	−0.00495126
$973$	−2.26769	−0.0726989
$974$	39.3273	1.26013
$975$	−0.0296925	−0.000950922 0
$976$	−82.9030	−2.65366
$977$	−39.3517	−1.25897	−0.629487	−	0.777011i	$-0.716735\pi$
$977$	−39.3517	−1.25897	−0.629487	+	0.777011i	$0.716735\pi$
$978$	0.0227174	0.000726421 0
$979$	−12.1698	−0.388950
$980$	117.421	3.75088
$981$	56.8934	1.81647
$982$	−56.9531	−1.81745
$983$	29.2889	0.934171	0.467085	−	0.884212i	$-0.345304\pi$
$983$	29.2889	0.934171	0.467085	+	0.884212i	$0.345304\pi$
$984$	−0.0606098	−0.00193217
$985$	−70.5266	−2.24716
$986$	26.0109	0.828355
$987$	−0.00131490	−4.18538e−5 0
$988$	104.795	3.33398
$989$	−13.1470	−0.418051
$990$	−33.1139	−1.05243
$991$	−8.15791	−0.259144	−0.129572	−	0.991570i	$-0.541360\pi$
$991$	−8.15791	−0.259144	−0.129572	+	0.991570i	$0.541360\pi$
$992$	40.5504	1.28748
$993$	0.0178720	0.000567150 0
$994$	1.52006	0.0482134
$995$	1.27895	0.0405454
$996$	−0.0539585	−0.00170974
$997$	11.6400	0.368643	0.184322	−	0.982866i	$-0.440991\pi$
$997$	11.6400	0.368643	0.184322	+	0.982866i	$0.440991\pi$
$998$	95.5242	3.02377
$999$	0.0202206	0.000639751 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.4	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.4	✓	309	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75364 q^{2} -0.00102412 q^{3} +5.58256 q^{4} -3.57698 q^{5} +0.00282007 q^{6} +1.05818 q^{7} -9.86509 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.75364 q^{2} -0.00102412 q^{3} +5.58256 q^{4} -3.57698 q^{5} +0.00282007 q^{6} +1.05818 q^{7} -9.86509 q^{8} -3.00000 q^{9} +9.84973 q^{10} +1.12064 q^{11} -0.00571722 q^{12} +3.71956 q^{13} -2.91386 q^{14} +0.00366327 q^{15} +15.9998 q^{16} -4.93358 q^{17} +8.26093 q^{18} +5.04681 q^{19} -19.9687 q^{20} -0.00108371 q^{21} -3.08584 q^{22} +1.51598 q^{23} +0.0101031 q^{24} +7.79478 q^{25} -10.2423 q^{26} +0.00614473 q^{27} +5.90736 q^{28} +1.91463 q^{29} -0.0100873 q^{30} -1.66684 q^{31} -24.3277 q^{32} -0.00114767 q^{33} +13.5853 q^{34} -3.78509 q^{35} -16.7477 q^{36} +3.29072 q^{37} -13.8971 q^{38} -0.00380928 q^{39} +35.2872 q^{40} -5.99915 q^{41} +0.00298415 q^{42} -8.67231 q^{43} +6.25602 q^{44} +10.7309 q^{45} -4.17446 q^{46} +1.21334 q^{47} -0.0163858 q^{48} -5.88025 q^{49} -21.4641 q^{50} +0.00505259 q^{51} +20.7647 q^{52} +0.668065 q^{53} -0.0169204 q^{54} -4.00849 q^{55} -10.4391 q^{56} -0.00516855 q^{57} -5.27221 q^{58} -2.48011 q^{59} +0.0204504 q^{60} -5.18149 q^{61} +4.58989 q^{62} -3.17454 q^{63} +34.9902 q^{64} -13.3048 q^{65} +0.00316027 q^{66} +2.50599 q^{67} -27.5420 q^{68} -0.00155255 q^{69} +10.4228 q^{70} -0.521666 q^{71} +29.5953 q^{72} -9.31782 q^{73} -9.06147 q^{74} -0.00798281 q^{75} +28.1741 q^{76} +1.18584 q^{77} +0.0104894 q^{78} -1.37692 q^{79} -57.2311 q^{80} +8.99999 q^{81} +16.5195 q^{82} +9.43789 q^{83} -0.00604986 q^{84} +17.6473 q^{85} +23.8805 q^{86} -0.00196082 q^{87} -11.0552 q^{88} -10.8598 q^{89} -29.5492 q^{90} +3.93597 q^{91} +8.46303 q^{92} +0.00170705 q^{93} -3.34110 q^{94} -18.0523 q^{95} +0.0249145 q^{96} +15.7581 q^{97} +16.1921 q^{98} -3.36191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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