LMFDB - Embedded newform 8011.2.a.b.1.3

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:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.79545 q^{2} -2.80135 q^{3} +5.81452 q^{4} +0.0114194 q^{5} +7.83103 q^{6} +2.04645 q^{7} -10.6633 q^{8} +4.84758 q^{9} +O(q^{10})$	\(q-2.79545 q^{2} -2.80135 q^{3} +5.81452 q^{4} +0.0114194 q^{5} +7.83103 q^{6} +2.04645 q^{7} -10.6633 q^{8} +4.84758 q^{9} -0.0319223 q^{10} +2.83233 q^{11} -16.2885 q^{12} -4.48788 q^{13} -5.72075 q^{14} -0.0319897 q^{15} +18.1796 q^{16} +0.296507 q^{17} -13.5511 q^{18} -3.81702 q^{19} +0.0663982 q^{20} -5.73284 q^{21} -7.91763 q^{22} +2.26186 q^{23} +29.8716 q^{24} -4.99987 q^{25} +12.5456 q^{26} -5.17573 q^{27} +11.8991 q^{28} -8.53845 q^{29} +0.0894256 q^{30} -5.07961 q^{31} -29.4935 q^{32} -7.93436 q^{33} -0.828870 q^{34} +0.0233692 q^{35} +28.1863 q^{36} -4.77154 q^{37} +10.6703 q^{38} +12.5721 q^{39} -0.121768 q^{40} -4.60380 q^{41} +16.0258 q^{42} -8.56991 q^{43} +16.4686 q^{44} +0.0553564 q^{45} -6.32290 q^{46} -8.81606 q^{47} -50.9275 q^{48} -2.81203 q^{49} +13.9769 q^{50} -0.830622 q^{51} -26.0949 q^{52} +2.70133 q^{53} +14.4685 q^{54} +0.0323435 q^{55} -21.8219 q^{56} +10.6928 q^{57} +23.8688 q^{58} +4.17702 q^{59} -0.186005 q^{60} -9.11193 q^{61} +14.1998 q^{62} +9.92034 q^{63} +46.0883 q^{64} -0.0512489 q^{65} +22.1801 q^{66} -10.3243 q^{67} +1.72405 q^{68} -6.33626 q^{69} -0.0653274 q^{70} -7.07339 q^{71} -51.6911 q^{72} -16.4255 q^{73} +13.3386 q^{74} +14.0064 q^{75} -22.1941 q^{76} +5.79623 q^{77} -35.1448 q^{78} +10.4480 q^{79} +0.207600 q^{80} -0.0437062 q^{81} +12.8697 q^{82} -11.1628 q^{83} -33.3337 q^{84} +0.00338593 q^{85} +23.9567 q^{86} +23.9192 q^{87} -30.2019 q^{88} -10.5469 q^{89} -0.154746 q^{90} -9.18424 q^{91} +13.1516 q^{92} +14.2298 q^{93} +24.6448 q^{94} -0.0435880 q^{95} +82.6217 q^{96} -7.21992 q^{97} +7.86088 q^{98} +13.7300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.79545	−1.97668	−0.988339	−	0.152267i	$-0.951343\pi$
$2$	−2.79545	−1.97668	−0.988339	+	0.152267i	$0.951343\pi$
$3$	−2.80135	−1.61736	−0.808681	−	0.588247i	$-0.799818\pi$
$3$	−2.80135	−1.61736	−0.808681	+	0.588247i	$0.799818\pi$
$4$	5.81452	2.90726
$5$	0.0114194	0.00510690	0.00255345	−	0.999997i	$-0.499187\pi$
$5$	0.0114194	0.00510690	0.00255345	+	0.999997i	$0.499187\pi$
$6$	7.83103	3.19701
$7$	2.04645	0.773486	0.386743	−	0.922187i	$-0.373600\pi$
$7$	2.04645	0.773486	0.386743	+	0.922187i	$0.373600\pi$
$8$	−10.6633	−3.77004
$9$	4.84758	1.61586
$10$	−0.0319223	−0.0100947
$11$	2.83233	0.853980	0.426990	−	0.904256i	$-0.359574\pi$
$11$	2.83233	0.853980	0.426990	+	0.904256i	$0.359574\pi$
$12$	−16.2885	−4.70209
$13$	−4.48788	−1.24471	−0.622357	−	0.782733i	$-0.713825\pi$
$13$	−4.48788	−1.24471	−0.622357	+	0.782733i	$0.713825\pi$
$14$	−5.72075	−1.52893
$15$	−0.0319897	−0.00825971
$16$	18.1796	4.54490
$17$	0.296507	0.0719136	0.0359568	−	0.999353i	$-0.488552\pi$
$17$	0.296507	0.0719136	0.0359568	+	0.999353i	$0.488552\pi$
$18$	−13.5511	−3.19404
$19$	−3.81702	−0.875684	−0.437842	−	0.899052i	$-0.644257\pi$
$19$	−3.81702	−0.875684	−0.437842	+	0.899052i	$0.644257\pi$
$20$	0.0663982	0.0148471
$21$	−5.73284	−1.25101
$22$	−7.91763	−1.68804
$23$	2.26186	0.471630	0.235815	−	0.971798i	$-0.424224\pi$
$23$	2.26186	0.471630	0.235815	+	0.971798i	$0.424224\pi$
$24$	29.8716	6.09752
$25$	−4.99987	−0.999974
$26$	12.5456	2.46040
$27$	−5.17573	−0.996069
$28$	11.8991	2.24873
$29$	−8.53845	−1.58555	−0.792775	−	0.609514i	$-0.791364\pi$
$29$	−8.53845	−1.58555	−0.792775	+	0.609514i	$0.791364\pi$
$30$	0.0894256	0.0163268
$31$	−5.07961	−0.912325	−0.456162	−	0.889897i	$-0.650776\pi$
$31$	−5.07961	−0.912325	−0.456162	+	0.889897i	$0.650776\pi$
$32$	−29.4935	−5.21376
$33$	−7.93436	−1.38119
$34$	−0.828870	−0.142150
$35$	0.0233692	0.00395012
$36$	28.1863	4.69772
$37$	−4.77154	−0.784436	−0.392218	−	0.919872i	$-0.628292\pi$
$37$	−4.77154	−0.784436	−0.392218	+	0.919872i	$0.628292\pi$
$38$	10.6703	1.73095
$39$	12.5721	2.01315
$40$	−0.121768	−0.0192532
$41$	−4.60380	−0.718993	−0.359497	−	0.933146i	$-0.617052\pi$
$41$	−4.60380	−0.718993	−0.359497	+	0.933146i	$0.617052\pi$
$42$	16.0258	2.47284
$43$	−8.56991	−1.30690	−0.653450	−	0.756970i	$-0.726679\pi$
$43$	−8.56991	−1.30690	−0.653450	+	0.756970i	$0.726679\pi$
$44$	16.4686	2.48274
$45$	0.0553564	0.00825204
$46$	−6.32290	−0.932261
$47$	−8.81606	−1.28595	−0.642977	−	0.765886i	$-0.722301\pi$
$47$	−8.81606	−1.28595	−0.642977	+	0.765886i	$0.722301\pi$
$48$	−50.9275	−7.35075
$49$	−2.81203	−0.401719
$50$	13.9769	1.97663
$51$	−0.830622	−0.116310
$52$	−26.0949	−3.61871
$53$	2.70133	0.371056	0.185528	−	0.982639i	$-0.440600\pi$
$53$	2.70133	0.371056	0.185528	+	0.982639i	$0.440600\pi$
$54$	14.4685	1.96891
$55$	0.0323435	0.00436119
$56$	−21.8219	−2.91607
$57$	10.6928	1.41630
$58$	23.8688	3.13412
$59$	4.17702	0.543802	0.271901	−	0.962325i	$-0.412348\pi$
$59$	4.17702	0.543802	0.271901	+	0.962325i	$0.412348\pi$
$60$	−0.186005	−0.0240131
$61$	−9.11193	−1.16666	−0.583331	−	0.812234i	$-0.698251\pi$
$61$	−9.11193	−1.16666	−0.583331	+	0.812234i	$0.698251\pi$
$62$	14.1998	1.80337
$63$	9.92034	1.24985
$64$	46.0883	5.76104
$65$	−0.0512489	−0.00635664
$66$	22.1801	2.73018
$67$	−10.3243	−1.26132	−0.630659	−	0.776060i	$-0.717215\pi$
$67$	−10.3243	−1.26132	−0.630659	+	0.776060i	$0.717215\pi$
$68$	1.72405	0.209071
$69$	−6.33626	−0.762797
$70$	−0.0653274	−0.00780812
$71$	−7.07339	−0.839457	−0.419729	−	0.907650i	$-0.637875\pi$
$71$	−7.07339	−0.839457	−0.419729	+	0.907650i	$0.637875\pi$
$72$	−51.6911	−6.09186
$73$	−16.4255	−1.92246	−0.961232	−	0.275742i	$-0.911076\pi$
$73$	−16.4255	−1.92246	−0.961232	+	0.275742i	$0.911076\pi$
$74$	13.3386	1.55058
$75$	14.0064	1.61732
$76$	−22.1941	−2.54584
$77$	5.79623	0.660542
$78$	−35.1448	−3.97936
$79$	10.4480	1.17549	0.587746	−	0.809045i	$-0.300015\pi$
$79$	10.4480	1.17549	0.587746	+	0.809045i	$0.300015\pi$
$80$	0.207600	0.0232104
$81$	−0.0437062	−0.00485624
$82$	12.8697	1.42122
$83$	−11.1628	−1.22527	−0.612636	−	0.790365i	$-0.709891\pi$
$83$	−11.1628	−1.22527	−0.612636	+	0.790365i	$0.709891\pi$
$84$	−33.3337	−3.63700
$85$	0.00338593	0.000367256 0
$86$	23.9567	2.58332
$87$	23.9192	2.56441
$88$	−30.2019	−3.21954
$89$	−10.5469	−1.11797	−0.558983	−	0.829179i	$-0.688808\pi$
$89$	−10.5469	−1.11797	−0.558983	+	0.829179i	$0.688808\pi$
$90$	−0.154746	−0.0163116
$91$	−9.18424	−0.962770
$92$	13.1516	1.37115
$93$	14.2298	1.47556
$94$	24.6448	2.54192
$95$	−0.0435880	−0.00447203
$96$	82.6217	8.43254
$97$	−7.21992	−0.733072	−0.366536	−	0.930404i	$-0.619456\pi$
$97$	−7.21992	−0.733072	−0.366536	+	0.930404i	$0.619456\pi$
$98$	7.86088	0.794069
$99$	13.7300	1.37991
$100$	−29.0718	−2.90718
$101$	15.5294	1.54523	0.772617	−	0.634873i	$-0.218947\pi$
$101$	15.5294	1.54523	0.772617	+	0.634873i	$0.218947\pi$
$102$	2.32196	0.229908
$103$	0.195042	0.0192181	0.00960905	−	0.999954i	$-0.496941\pi$
$103$	0.195042	0.0192181	0.00960905	+	0.999954i	$0.496941\pi$
$104$	47.8556	4.69262
$105$	−0.0654655	−0.00638877
$106$	−7.55142	−0.733459
$107$	7.14254	0.690495	0.345248	−	0.938512i	$-0.387795\pi$
$107$	7.14254	0.690495	0.345248	+	0.938512i	$0.387795\pi$
$108$	−30.0944	−2.89583
$109$	14.1909	1.35924	0.679622	−	0.733563i	$-0.262144\pi$
$109$	14.1909	1.35924	0.679622	+	0.733563i	$0.262144\pi$
$110$	−0.0904144	−0.00862068
$111$	13.3668	1.26872
$112$	37.2037	3.51542
$113$	6.39714	0.601792	0.300896	−	0.953657i	$-0.402714\pi$
$113$	6.39714	0.601792	0.300896	+	0.953657i	$0.402714\pi$
$114$	−29.8912	−2.79957
$115$	0.0258290	0.00240857
$116$	−49.6470	−4.60960
$117$	−21.7554	−2.01129
$118$	−11.6766	−1.07492
$119$	0.606788	0.0556242
$120$	0.341115	0.0311394
$121$	−2.97790	−0.270718
$122$	25.4719	2.30612
$123$	12.8969	1.16287
$124$	−29.5355	−2.65236
$125$	−0.114192	−0.0102137
$126$	−27.7318	−2.47054
$127$	−2.13941	−0.189842	−0.0949210	−	0.995485i	$-0.530260\pi$
$127$	−2.13941	−0.189842	−0.0949210	+	0.995485i	$0.530260\pi$
$128$	−69.8504	−6.17396
$129$	24.0074	2.11373
$130$	0.143263	0.0125650
$131$	5.86256	0.512214	0.256107	−	0.966648i	$-0.417560\pi$
$131$	5.86256	0.512214	0.256107	+	0.966648i	$0.417560\pi$
$132$	−46.1345	−4.01549
$133$	−7.81135	−0.677330
$134$	28.8611	2.49322
$135$	−0.0591036	−0.00508683
$136$	−3.16174	−0.271117
$137$	0.439957	0.0375880	0.0187940	−	0.999823i	$-0.494017\pi$
$137$	0.439957	0.0375880	0.0187940	+	0.999823i	$0.494017\pi$
$138$	17.7127	1.50780
$139$	15.0205	1.27402	0.637010	−	0.770855i	$-0.280171\pi$
$139$	15.0205	1.27402	0.637010	+	0.770855i	$0.280171\pi$
$140$	0.135881	0.0114840
$141$	24.6969	2.07985
$142$	19.7733	1.65934
$143$	−12.7112	−1.06296
$144$	88.1270	7.34392
$145$	−0.0975038	−0.00809725
$146$	45.9167	3.80009
$147$	7.87750	0.649725
$148$	−27.7442	−2.28056
$149$	16.3800	1.34190	0.670951	−	0.741502i	$-0.265886\pi$
$149$	16.3800	1.34190	0.670951	+	0.741502i	$0.265886\pi$
$150$	−39.1541	−3.19692
$151$	−4.54505	−0.369871	−0.184935	−	0.982751i	$-0.559208\pi$
$151$	−4.54505	−0.369871	−0.184935	+	0.982751i	$0.559208\pi$
$152$	40.7019	3.30136
$153$	1.43734	0.116202
$154$	−16.2031	−1.30568
$155$	−0.0580060	−0.00465915
$156$	73.1010	5.85276
$157$	17.0652	1.36195	0.680975	−	0.732306i	$-0.261556\pi$
$157$	17.0652	1.36195	0.680975	+	0.732306i	$0.261556\pi$
$158$	−29.2068	−2.32357
$159$	−7.56738	−0.600132
$160$	−0.336798	−0.0266262
$161$	4.62879	0.364799
$162$	0.122178	0.00959923
$163$	−0.317234	−0.0248477	−0.0124238	−	0.999923i	$-0.503955\pi$
$163$	−0.317234	−0.0248477	−0.0124238	+	0.999923i	$0.503955\pi$
$164$	−26.7689	−2.09030
$165$	−0.0906055	−0.00705363
$166$	31.2049	2.42197
$167$	−17.2292	−1.33323	−0.666616	−	0.745401i	$-0.732258\pi$
$167$	−17.2292	−1.33323	−0.666616	+	0.745401i	$0.732258\pi$
$168$	61.1308	4.71635
$169$	7.14109	0.549315
$170$	−0.00946519	−0.000725947 0
$171$	−18.5033	−1.41498
$172$	−49.8299	−3.79950
$173$	8.01130	0.609088	0.304544	−	0.952498i	$-0.401496\pi$
$173$	8.01130	0.609088	0.304544	+	0.952498i	$0.401496\pi$
$174$	−66.8649	−5.06901
$175$	−10.2320	−0.773466
$176$	51.4906	3.88125
$177$	−11.7013	−0.879524
$178$	29.4832	2.20986
$179$	23.2943	1.74110	0.870548	−	0.492083i	$-0.163764\pi$
$179$	23.2943	1.74110	0.870548	+	0.492083i	$0.163764\pi$
$180$	0.321871	0.0239908
$181$	−5.16127	−0.383634	−0.191817	−	0.981431i	$-0.561438\pi$
$181$	−5.16127	−0.383634	−0.191817	+	0.981431i	$0.561438\pi$
$182$	25.6740	1.90309
$183$	25.5257	1.88692
$184$	−24.1188	−1.77806
$185$	−0.0544880	−0.00400604
$186$	−39.7786	−2.91671
$187$	0.839807	0.0614128
$188$	−51.2611	−3.73860
$189$	−10.5919	−0.770446
$190$	0.121848	0.00883978
$191$	12.9250	0.935220	0.467610	−	0.883935i	$-0.345115\pi$
$191$	12.9250	0.935220	0.467610	+	0.883935i	$0.345115\pi$
$192$	−129.110	−9.31769
$193$	3.16917	0.228122	0.114061	−	0.993474i	$-0.463614\pi$
$193$	3.16917	0.228122	0.114061	+	0.993474i	$0.463614\pi$
$194$	20.1829	1.44905
$195$	0.143566	0.0102810
$196$	−16.3506	−1.16790
$197$	5.10470	0.363695	0.181848	−	0.983327i	$-0.441792\pi$
$197$	5.10470	0.363695	0.181848	+	0.983327i	$0.441792\pi$
$198$	−38.3813	−2.72764
$199$	22.3335	1.58318	0.791589	−	0.611053i	$-0.209254\pi$
$199$	22.3335	1.58318	0.791589	+	0.611053i	$0.209254\pi$
$200$	53.3150	3.76994
$201$	28.9221	2.04001
$202$	−43.4116	−3.05443
$203$	−17.4735	−1.22640
$204$	−4.82967	−0.338144
$205$	−0.0525726	−0.00367183
$206$	−0.545230	−0.0379880
$207$	10.9645	0.762088
$208$	−81.5879	−5.65710
$209$	−10.8111	−0.747817
$210$	0.183005	0.0126286
$211$	−2.93558	−0.202094	−0.101047	−	0.994882i	$-0.532219\pi$
$211$	−2.93558	−0.202094	−0.101047	+	0.994882i	$0.532219\pi$
$212$	15.7069	1.07876
$213$	19.8151	1.35771
$214$	−19.9666	−1.36489
$215$	−0.0978631	−0.00667421
$216$	55.1902	3.75522
$217$	−10.3952	−0.705671
$218$	−39.6699	−2.68679
$219$	46.0137	3.10932
$220$	0.188062	0.0126791
$221$	−1.33069	−0.0895119
$222$	−37.3661	−2.50785
$223$	−19.9098	−1.33326	−0.666629	−	0.745390i	$-0.732263\pi$
$223$	−19.9098	−1.33326	−0.666629	+	0.745390i	$0.732263\pi$
$224$	−60.3570	−4.03277
$225$	−24.2373	−1.61582
$226$	−17.8829	−1.18955
$227$	25.5590	1.69641	0.848205	−	0.529668i	$-0.177683\pi$
$227$	25.5590	1.69641	0.848205	+	0.529668i	$0.177683\pi$
$228$	62.1736	4.11755
$229$	−29.2406	−1.93227	−0.966137	−	0.258031i	$-0.916926\pi$
$229$	−29.2406	−1.93227	−0.966137	+	0.258031i	$0.916926\pi$
$230$	−0.0722037	−0.00476097
$231$	−16.2373	−1.06834
$232$	91.0479	5.97759
$233$	15.9418	1.04438	0.522192	−	0.852828i	$-0.325115\pi$
$233$	15.9418	1.04438	0.522192	+	0.852828i	$0.325115\pi$
$234$	60.8160	3.97566
$235$	−0.100674	−0.00656724
$236$	24.2874	1.58097
$237$	−29.2685	−1.90120
$238$	−1.69624	−0.109951
$239$	7.60391	0.491856	0.245928	−	0.969288i	$-0.420907\pi$
$239$	7.60391	0.491856	0.245928	+	0.969288i	$0.420907\pi$
$240$	−0.581560	−0.0375395
$241$	19.3748	1.24804	0.624021	−	0.781407i	$-0.285498\pi$
$241$	19.3748	1.24804	0.624021	+	0.781407i	$0.285498\pi$
$242$	8.32456	0.535123
$243$	15.6496	1.00392
$244$	−52.9815	−3.39179
$245$	−0.0321117	−0.00205154
$246$	−36.0525	−2.29863
$247$	17.1303	1.08998
$248$	54.1653	3.43950
$249$	31.2708	1.98171
$250$	0.319219	0.0201892
$251$	−9.34290	−0.589719	−0.294859	−	0.955541i	$-0.595273\pi$
$251$	−9.34290	−0.589719	−0.294859	+	0.955541i	$0.595273\pi$
$252$	57.6820	3.63363
$253$	6.40633	0.402763
$254$	5.98060	0.375256
$255$	−0.00948519	−0.000593985 0
$256$	103.086	6.44290
$257$	−23.3233	−1.45487	−0.727435	−	0.686176i	$-0.759288\pi$
$257$	−23.3233	−1.45487	−0.727435	+	0.686176i	$0.759288\pi$
$258$	−67.1113	−4.17817
$259$	−9.76473	−0.606751
$260$	−0.297987	−0.0184804
$261$	−41.3908	−2.56203
$262$	−16.3885	−1.01248
$263$	10.1041	0.623048	0.311524	−	0.950238i	$-0.399161\pi$
$263$	10.1041	0.623048	0.311524	+	0.950238i	$0.399161\pi$
$264$	84.6063	5.20716
$265$	0.0308475	0.00189495
$266$	21.8362	1.33886
$267$	29.5455	1.80816
$268$	−60.0310	−3.66698
$269$	−20.9829	−1.27935	−0.639676	−	0.768645i	$-0.720931\pi$
$269$	−20.9829	−1.27935	−0.639676	+	0.768645i	$0.720931\pi$
$270$	0.165221	0.0100550
$271$	−8.31265	−0.504958	−0.252479	−	0.967602i	$-0.581246\pi$
$271$	−8.31265	−0.504958	−0.252479	+	0.967602i	$0.581246\pi$
$272$	5.39038	0.326840
$273$	25.7283	1.55715
$274$	−1.22988	−0.0742995
$275$	−14.1613	−0.853958
$276$	−36.8423	−2.21765
$277$	−14.6574	−0.880680	−0.440340	−	0.897831i	$-0.645142\pi$
$277$	−14.6574	−0.880680	−0.440340	+	0.897831i	$0.645142\pi$
$278$	−41.9890	−2.51833
$279$	−24.6238	−1.47419
$280$	−0.249193	−0.0148921
$281$	−7.22490	−0.431001	−0.215501	−	0.976504i	$-0.569138\pi$
$281$	−7.22490	−0.431001	−0.215501	+	0.976504i	$0.569138\pi$
$282$	−69.0388	−4.11120
$283$	8.03331	0.477531	0.238765	−	0.971077i	$-0.423257\pi$
$283$	8.03331	0.477531	0.238765	+	0.971077i	$0.423257\pi$
$284$	−41.1284	−2.44052
$285$	0.122105	0.00723290
$286$	35.5334	2.10113
$287$	−9.42146	−0.556131
$288$	−142.972	−8.42471
$289$	−16.9121	−0.994828
$290$	0.272567	0.0160057
$291$	20.2256	1.18564
$292$	−95.5066	−5.58910
$293$	−10.0692	−0.588249	−0.294124	−	0.955767i	$-0.595028\pi$
$293$	−10.0692	−0.588249	−0.294124	+	0.955767i	$0.595028\pi$
$294$	−22.0211	−1.28430
$295$	0.0476990	0.00277714
$296$	50.8803	2.95736
$297$	−14.6594	−0.850623
$298$	−45.7894	−2.65251
$299$	−10.1510	−0.587045
$300$	81.4405	4.70197
$301$	−17.5379	−1.01087
$302$	12.7054	0.731116
$303$	−43.5034	−2.49920
$304$	−69.3918	−3.97989
$305$	−0.104053	−0.00595803
$306$	−4.01801	−0.229695
$307$	−33.3082	−1.90100	−0.950498	−	0.310729i	$-0.899427\pi$
$307$	−33.3082	−1.90100	−0.950498	+	0.310729i	$0.899427\pi$
$308$	33.7023	1.92037
$309$	−0.546383	−0.0310826
$310$	0.162153	0.00920965
$311$	23.5089	1.33307	0.666533	−	0.745475i	$-0.267777\pi$
$311$	23.5089	1.33307	0.666533	+	0.745475i	$0.267777\pi$
$312$	−134.060	−7.58967
$313$	8.74768	0.494448	0.247224	−	0.968958i	$-0.420482\pi$
$313$	8.74768	0.494448	0.247224	+	0.968958i	$0.420482\pi$
$314$	−47.7048	−2.69214
$315$	0.113284	0.00638284
$316$	60.7501	3.41746
$317$	20.1567	1.13211	0.566056	−	0.824367i	$-0.308469\pi$
$317$	20.1567	1.13211	0.566056	+	0.824367i	$0.308469\pi$
$318$	21.1542	1.18627
$319$	−24.1837	−1.35403
$320$	0.526300	0.0294211
$321$	−20.0088	−1.11678
$322$	−12.9395	−0.721091
$323$	−1.13177	−0.0629736
$324$	−0.254130	−0.0141184
$325$	22.4388	1.24468
$326$	0.886810	0.0491159
$327$	−39.7538	−2.19839
$328$	49.0916	2.71063
$329$	−18.0416	−0.994668
$330$	0.253283	0.0139428
$331$	22.3708	1.22961	0.614805	−	0.788679i	$-0.289235\pi$
$331$	22.3708	1.22961	0.614805	+	0.788679i	$0.289235\pi$
$332$	−64.9061	−3.56218
$333$	−23.1304	−1.26754
$334$	48.1632	2.63537
$335$	−0.117897	−0.00644143
$336$	−104.221	−5.68570
$337$	−16.8980	−0.920495	−0.460247	−	0.887791i	$-0.652239\pi$
$337$	−16.8980	−0.920495	−0.460247	+	0.887791i	$0.652239\pi$
$338$	−19.9625	−1.08582
$339$	−17.9206	−0.973316
$340$	0.0196876	0.00106771
$341$	−14.3871	−0.779107
$342$	51.7250	2.79697
$343$	−20.0799	−1.08421
$344$	91.3834	4.92706
$345$	−0.0723562	−0.00389553
$346$	−22.3952	−1.20397
$347$	28.0395	1.50524	0.752620	−	0.658455i	$-0.228790\pi$
$347$	28.0395	1.50524	0.752620	+	0.658455i	$0.228790\pi$
$348$	139.079	7.45540
$349$	8.43495	0.451513	0.225756	−	0.974184i	$-0.427515\pi$
$349$	8.43495	0.451513	0.225756	+	0.974184i	$0.427515\pi$
$350$	28.6030	1.52889
$351$	23.2280	1.23982
$352$	−83.5354	−4.45245
$353$	−14.2815	−0.760128	−0.380064	−	0.924960i	$-0.624098\pi$
$353$	−14.2815	−0.760128	−0.380064	+	0.924960i	$0.624098\pi$
$354$	32.7104	1.73854
$355$	−0.0807738	−0.00428703
$356$	−61.3250	−3.25022
$357$	−1.69983	−0.0899644
$358$	−65.1179	−3.44159
$359$	3.99165	0.210671	0.105336	−	0.994437i	$-0.466408\pi$
$359$	3.99165	0.210671	0.105336	+	0.994437i	$0.466408\pi$
$360$	−0.590281	−0.0311105
$361$	−4.43037	−0.233177
$362$	14.4280	0.758321
$363$	8.34215	0.437849
$364$	−53.4019	−2.79902
$365$	−0.187569	−0.00981783
$366$	−71.3558	−3.72983
$367$	−26.2953	−1.37261	−0.686303	−	0.727316i	$-0.740767\pi$
$367$	−26.2953	−1.37261	−0.686303	+	0.727316i	$0.740767\pi$
$368$	41.1197	2.14351
$369$	−22.3173	−1.16179
$370$	0.152318	0.00791866
$371$	5.52814	0.287007
$372$	82.7393	4.28983
$373$	33.1377	1.71581	0.857903	−	0.513812i	$-0.171767\pi$
$373$	33.1377	1.71581	0.857903	+	0.513812i	$0.171767\pi$
$374$	−2.34763	−0.121393
$375$	0.319893	0.0165192
$376$	94.0081	4.84810
$377$	38.3196	1.97356
$378$	29.6090	1.52292
$379$	−0.235235	−0.0120832	−0.00604160	−	0.999982i	$-0.501923\pi$
$379$	−0.235235	−0.0120832	−0.00604160	+	0.999982i	$0.501923\pi$
$380$	−0.253443	−0.0130014
$381$	5.99324	0.307043
$382$	−36.1311	−1.84863
$383$	−10.5833	−0.540779	−0.270390	−	0.962751i	$-0.587153\pi$
$383$	−10.5833	−0.540779	−0.270390	+	0.962751i	$0.587153\pi$
$384$	195.676	9.98553
$385$	0.0661894	0.00337332
$386$	−8.85924	−0.450924
$387$	−41.5433	−2.11177
$388$	−41.9804	−2.13123
$389$	0.890161	0.0451329	0.0225665	−	0.999745i	$-0.492816\pi$
$389$	0.890161	0.0451329	0.0225665	+	0.999745i	$0.492816\pi$
$390$	−0.401331	−0.0203222
$391$	0.670657	0.0339166
$392$	29.9855	1.51450
$393$	−16.4231	−0.828435
$394$	−14.2699	−0.718908
$395$	0.119310	0.00600313
$396$	79.8331	4.01176
$397$	14.2263	0.713997	0.356999	−	0.934105i	$-0.383800\pi$
$397$	14.2263	0.713997	0.356999	+	0.934105i	$0.383800\pi$
$398$	−62.4321	−3.12944
$399$	21.8823	1.09549
$400$	−90.8956	−4.54478
$401$	16.7337	0.835643	0.417822	−	0.908529i	$-0.362794\pi$
$401$	16.7337	0.835643	0.417822	+	0.908529i	$0.362794\pi$
$402$	−80.8501	−4.03244
$403$	22.7967	1.13558
$404$	90.2960	4.49240
$405$	−0.000499098 0	−2.48004e−5 0
$406$	48.8463	2.42420
$407$	−13.5146	−0.669893
$408$	8.85715	0.438494
$409$	4.10538	0.202998	0.101499	−	0.994836i	$-0.467636\pi$
$409$	4.10538	0.202998	0.101499	+	0.994836i	$0.467636\pi$
$410$	0.146964	0.00725803
$411$	−1.23247	−0.0607935
$412$	1.13408	0.0558720
$413$	8.54807	0.420623
$414$	−30.6508	−1.50640
$415$	−0.127472	−0.00625735
$416$	132.363	6.48965
$417$	−42.0777	−2.06055
$418$	30.2217	1.47819
$419$	28.0980	1.37268	0.686338	−	0.727283i	$-0.259217\pi$
$419$	28.0980	1.37268	0.686338	+	0.727283i	$0.259217\pi$
$420$	−0.380650	−0.0185738
$421$	17.2177	0.839139	0.419569	−	0.907723i	$-0.362181\pi$
$421$	17.2177	0.839139	0.419569	+	0.907723i	$0.362181\pi$
$422$	8.20627	0.399475
$423$	−42.7365	−2.07792
$424$	−28.8050	−1.39890
$425$	−1.48250	−0.0719117
$426$	−55.3920	−2.68375
$427$	−18.6471	−0.902398
$428$	41.5304	2.00745
$429$	35.6085	1.71919
$430$	0.273571	0.0131928
$431$	−37.4389	−1.80337	−0.901685	−	0.432393i	$-0.857669\pi$
$431$	−37.4389	−1.80337	−0.901685	+	0.432393i	$0.857669\pi$
$432$	−94.0926	−4.52703
$433$	30.5454	1.46792	0.733958	−	0.679195i	$-0.237671\pi$
$433$	30.5454	1.46792	0.733958	+	0.679195i	$0.237671\pi$
$434$	29.0592	1.39488
$435$	0.273143	0.0130962
$436$	82.5133	3.95167
$437$	−8.63355	−0.412999
$438$	−128.629	−6.14613
$439$	3.44668	0.164501	0.0822505	−	0.996612i	$-0.473789\pi$
$439$	3.44668	0.164501	0.0822505	+	0.996612i	$0.473789\pi$
$440$	−0.344888	−0.0164419
$441$	−13.6316	−0.649122
$442$	3.71987	0.176936
$443$	−10.1765	−0.483501	−0.241750	−	0.970338i	$-0.577721\pi$
$443$	−10.1765	−0.483501	−0.241750	+	0.970338i	$0.577721\pi$
$444$	77.7213	3.68849
$445$	−0.120439	−0.00570934
$446$	55.6567	2.63542
$447$	−45.8862	−2.17034
$448$	94.3175	4.45608
$449$	18.5161	0.873828	0.436914	−	0.899503i	$-0.356071\pi$
$449$	18.5161	0.873828	0.436914	+	0.899503i	$0.356071\pi$
$450$	67.7540	3.19395
$451$	−13.0395	−0.614006
$452$	37.1963	1.74957
$453$	12.7323	0.598215
$454$	−71.4488	−3.35326
$455$	−0.104878	−0.00491677
$456$	−114.021	−5.33950
$457$	39.9782	1.87010	0.935050	−	0.354516i	$-0.115354\pi$
$457$	39.9782	1.87010	0.935050	+	0.354516i	$0.115354\pi$
$458$	81.7405	3.81948
$459$	−1.53464	−0.0716309
$460$	0.150183	0.00700234
$461$	2.48689	0.115826	0.0579130	−	0.998322i	$-0.481555\pi$
$461$	2.48689	0.115826	0.0579130	+	0.998322i	$0.481555\pi$
$462$	45.3905	2.11176
$463$	−39.9679	−1.85746	−0.928732	−	0.370751i	$-0.879100\pi$
$463$	−39.9679	−1.85746	−0.928732	+	0.370751i	$0.879100\pi$
$464$	−155.225	−7.20616
$465$	0.162495	0.00753554
$466$	−44.5645	−2.06441
$467$	−15.8949	−0.735527	−0.367763	−	0.929919i	$-0.619876\pi$
$467$	−15.8949	−0.735527	−0.367763	+	0.929919i	$0.619876\pi$
$468$	−126.497	−5.84733
$469$	−21.1282	−0.975612
$470$	0.281429	0.0129813
$471$	−47.8056	−2.20277
$472$	−44.5407	−2.05015
$473$	−24.2728	−1.11607
$474$	81.8186	3.75806
$475$	19.0846	0.875661
$476$	3.52818	0.161714
$477$	13.0949	0.599575
$478$	−21.2563	−0.972241
$479$	−9.25773	−0.422997	−0.211498	−	0.977378i	$-0.567834\pi$
$479$	−9.25773	−0.422997	−0.211498	+	0.977378i	$0.567834\pi$
$480$	0.943489	0.0430642
$481$	21.4141	0.976399
$482$	−54.1613	−2.46698
$483$	−12.9669	−0.590013
$484$	−17.3151	−0.787048
$485$	−0.0824471	−0.00374373
$486$	−43.7476	−1.98443
$487$	−6.90361	−0.312833	−0.156416	−	0.987691i	$-0.549994\pi$
$487$	−6.90361	−0.312833	−0.156416	+	0.987691i	$0.549994\pi$
$488$	97.1630	4.39836
$489$	0.888684	0.0401877
$490$	0.0897665	0.00405524
$491$	−29.3402	−1.32411	−0.662053	−	0.749457i	$-0.730315\pi$
$491$	−29.3402	−1.32411	−0.662053	+	0.749457i	$0.730315\pi$
$492$	74.9891	3.38077
$493$	−2.53171	−0.114023
$494$	−47.8869	−2.15453
$495$	0.156788	0.00704708
$496$	−92.3452	−4.14642
$497$	−14.4754	−0.649309
$498$	−87.4159	−3.91720
$499$	−18.0955	−0.810068	−0.405034	−	0.914302i	$-0.632740\pi$
$499$	−18.0955	−0.810068	−0.405034	+	0.914302i	$0.632740\pi$
$500$	−0.663974	−0.0296938
$501$	48.2650	2.15632
$502$	26.1176	1.16568
$503$	27.4886	1.22566	0.612828	−	0.790217i	$-0.290032\pi$
$503$	27.4886	1.22566	0.612828	+	0.790217i	$0.290032\pi$
$504$	−105.783	−4.71197
$505$	0.177336	0.00789136
$506$	−17.9086	−0.796132
$507$	−20.0047	−0.888441
$508$	−12.4396	−0.551920
$509$	−21.8882	−0.970178	−0.485089	−	0.874465i	$-0.661213\pi$
$509$	−21.8882	−0.970178	−0.485089	+	0.874465i	$0.661213\pi$
$510$	0.0265153	0.00117412
$511$	−33.6141	−1.48700
$512$	−148.472	−6.56158
$513$	19.7558	0.872242
$514$	65.1992	2.87581
$515$	0.00222726	9.81450e−5 0
$516$	139.591	6.14516
$517$	−24.9700	−1.09818
$518$	27.2968	1.19935
$519$	−22.4425	−0.985116
$520$	0.546481	0.0239648
$521$	−19.6099	−0.859126	−0.429563	−	0.903037i	$-0.641332\pi$
$521$	−19.6099	−0.859126	−0.429563	+	0.903037i	$0.641332\pi$
$522$	115.706	5.06430
$523$	28.6317	1.25198	0.625989	−	0.779832i	$-0.284695\pi$
$523$	28.6317	1.25198	0.625989	+	0.779832i	$0.284695\pi$
$524$	34.0879	1.48914
$525$	28.6634	1.25097
$526$	−28.2456	−1.23157
$527$	−1.50614	−0.0656085
$528$	−144.243	−6.27739
$529$	−17.8840	−0.777565
$530$	−0.0862326	−0.00374570
$531$	20.2484	0.878707
$532$	−45.4192	−1.96917
$533$	20.6613	0.894941
$534$	−82.5929	−3.57414
$535$	0.0815634	0.00352629
$536$	110.091	4.75522
$537$	−65.2555	−2.81598
$538$	58.6567	2.52887
$539$	−7.96461	−0.343060
$540$	−0.343659	−0.0147887
$541$	15.6578	0.673180	0.336590	−	0.941651i	$-0.390726\pi$
$541$	15.6578	0.673180	0.336590	+	0.941651i	$0.390726\pi$
$542$	23.2376	0.998139
$543$	14.4585	0.620475
$544$	−8.74504	−0.374940
$545$	0.162051	0.00694152
$546$	−71.9221	−3.07798
$547$	15.5171	0.663461	0.331731	−	0.943374i	$-0.392367\pi$
$547$	15.5171	0.663461	0.331731	+	0.943374i	$0.392367\pi$
$548$	2.55814	0.109278
$549$	−44.1708	−1.88516
$550$	39.5871	1.68800
$551$	32.5914	1.38844
$552$	67.5654	2.87577
$553$	21.3813	0.909227
$554$	40.9741	1.74082
$555$	0.152640	0.00647922
$556$	87.3369	3.70391
$557$	−4.22462	−0.179003	−0.0895014	−	0.995987i	$-0.528527\pi$
$557$	−4.22462	−0.179003	−0.0895014	+	0.995987i	$0.528527\pi$
$558$	68.8345	2.91400
$559$	38.4608	1.62672
$560$	0.424843	0.0179529
$561$	−2.35260	−0.0993267
$562$	20.1968	0.851951
$563$	17.1645	0.723396	0.361698	−	0.932295i	$-0.382197\pi$
$563$	17.1645	0.723396	0.361698	+	0.932295i	$0.382197\pi$
$564$	143.601	6.04667
$565$	0.0730514	0.00307329
$566$	−22.4567	−0.943925
$567$	−0.0894426	−0.00375624
$568$	75.4256	3.16479
$569$	−3.76276	−0.157743	−0.0788716	−	0.996885i	$-0.525132\pi$
$569$	−3.76276	−0.157743	−0.0788716	+	0.996885i	$0.525132\pi$
$570$	−0.341339	−0.0142971
$571$	29.9350	1.25274	0.626370	−	0.779526i	$-0.284540\pi$
$571$	29.9350	1.25274	0.626370	+	0.779526i	$0.284540\pi$
$572$	−73.9093	−3.09030
$573$	−36.2075	−1.51259
$574$	26.3372	1.09929
$575$	−11.3090	−0.471618
$576$	223.417	9.30903
$577$	19.8565	0.826636	0.413318	−	0.910587i	$-0.364370\pi$
$577$	19.8565	0.826636	0.413318	+	0.910587i	$0.364370\pi$
$578$	47.2768	1.96646
$579$	−8.87796	−0.368956
$580$	−0.566938	−0.0235408
$581$	−22.8441	−0.947731
$582$	−56.5395	−2.34364
$583$	7.65106	0.316875
$584$	175.150	7.24776
$585$	−0.248433	−0.0102714
$586$	28.1479	1.16278
$587$	−8.15324	−0.336520	−0.168260	−	0.985743i	$-0.553815\pi$
$587$	−8.15324	−0.336520	−0.168260	+	0.985743i	$0.553815\pi$
$588$	45.8038	1.88892
$589$	19.3890	0.798908
$590$	−0.133340	−0.00548952
$591$	−14.3001	−0.588227
$592$	−86.7446	−3.56518
$593$	47.0412	1.93175	0.965876	−	0.259004i	$-0.0833944\pi$
$593$	47.0412	1.93175	0.965876	+	0.259004i	$0.0833944\pi$
$594$	40.9795	1.68141
$595$	0.00692915	0.000284067 0
$596$	95.2418	3.90126
$597$	−62.5640	−2.56057
$598$	28.3764	1.16040
$599$	2.63317	0.107589	0.0537943	−	0.998552i	$-0.482868\pi$
$599$	2.63317	0.107589	0.0537943	+	0.998552i	$0.482868\pi$
$600$	−149.354	−6.09736
$601$	−28.5421	−1.16426	−0.582128	−	0.813097i	$-0.697780\pi$
$601$	−28.5421	−1.16426	−0.582128	+	0.813097i	$0.697780\pi$
$602$	49.0263	1.99816
$603$	−50.0480	−2.03811
$604$	−26.4273	−1.07531
$605$	−0.0340058	−0.00138253
$606$	121.611	4.94012
$607$	43.3050	1.75770	0.878848	−	0.477101i	$-0.158312\pi$
$607$	43.3050	1.75770	0.878848	+	0.477101i	$0.158312\pi$
$608$	112.577	4.56561
$609$	48.9495	1.98353
$610$	0.290873	0.0117771
$611$	39.5654	1.60065
$612$	8.35746	0.337830
$613$	−2.75874	−0.111425	−0.0557123	−	0.998447i	$-0.517743\pi$
$613$	−2.75874	−0.111425	−0.0557123	+	0.998447i	$0.517743\pi$
$614$	93.1112	3.75766
$615$	0.147274	0.00593868
$616$	−61.8068	−2.49027
$617$	15.5746	0.627010	0.313505	−	0.949587i	$-0.398497\pi$
$617$	15.5746	0.627010	0.313505	+	0.949587i	$0.398497\pi$
$618$	1.52738	0.0614404
$619$	−7.12769	−0.286486	−0.143243	−	0.989688i	$-0.545753\pi$
$619$	−7.12769	−0.286486	−0.143243	+	0.989688i	$0.545753\pi$
$620$	−0.337277	−0.0135454
$621$	−11.7068	−0.469776
$622$	−65.7178	−2.63505
$623$	−21.5837	−0.864731
$624$	228.556	9.14958
$625$	24.9980	0.999922
$626$	−24.4537	−0.977365
$627$	30.2856	1.20949
$628$	99.2259	3.95954
$629$	−1.41480	−0.0564116
$630$	−0.316680	−0.0126168
$631$	−36.5200	−1.45384	−0.726918	−	0.686724i	$-0.759048\pi$
$631$	−36.5200	−1.45384	−0.726918	+	0.686724i	$0.759048\pi$
$632$	−111.410	−4.43165
$633$	8.22361	0.326859
$634$	−56.3469	−2.23782
$635$	−0.0244307	−0.000969504 0
$636$	−44.0007	−1.74474
$637$	12.6201	0.500025
$638$	67.6043	2.67648
$639$	−34.2888	−1.35645
$640$	−0.797648	−0.0315298
$641$	8.97926	0.354660	0.177330	−	0.984151i	$-0.443254\pi$
$641$	8.97926	0.354660	0.177330	+	0.984151i	$0.443254\pi$
$642$	55.9335	2.20752
$643$	6.43155	0.253636	0.126818	−	0.991926i	$-0.459524\pi$
$643$	6.43155	0.253636	0.126818	+	0.991926i	$0.459524\pi$
$644$	26.9142	1.06057
$645$	0.274149	0.0107946
$646$	3.16381	0.124479
$647$	−30.9828	−1.21806	−0.609029	−	0.793148i	$-0.708441\pi$
$647$	−30.9828	−1.21806	−0.609029	+	0.793148i	$0.708441\pi$
$648$	0.466051	0.0183082
$649$	11.8307	0.464396
$650$	−62.7265	−2.46034
$651$	29.1206	1.14132
$652$	−1.84456	−0.0722386
$653$	26.9923	1.05629	0.528144	−	0.849155i	$-0.322888\pi$
$653$	26.9923	1.05629	0.528144	+	0.849155i	$0.322888\pi$
$654$	111.130	4.34551
$655$	0.0669468	0.00261583
$656$	−83.6952	−3.26775
$657$	−79.6241	−3.10643
$658$	50.4344	1.96614
$659$	−16.3289	−0.636082	−0.318041	−	0.948077i	$-0.603025\pi$
$659$	−16.3289	−0.636082	−0.318041	+	0.948077i	$0.603025\pi$
$660$	−0.526827	−0.0205067
$661$	7.11354	0.276685	0.138342	−	0.990384i	$-0.455823\pi$
$661$	7.11354	0.276685	0.138342	+	0.990384i	$0.455823\pi$
$662$	−62.5364	−2.43054
$663$	3.72773	0.144773
$664$	119.032	4.61932
$665$	−0.0892008	−0.00345906
$666$	64.6598	2.50552
$667$	−19.3128	−0.747793
$668$	−100.179	−3.87605
$669$	55.7743	2.15636
$670$	0.329576	0.0127326
$671$	−25.8080	−0.996307
$672$	169.081	6.52246
$673$	11.8750	0.457747	0.228873	−	0.973456i	$-0.426496\pi$
$673$	11.8750	0.457747	0.228873	+	0.973456i	$0.426496\pi$
$674$	47.2375	1.81952
$675$	25.8780	0.996043
$676$	41.5220	1.59700
$677$	5.95851	0.229004	0.114502	−	0.993423i	$-0.463473\pi$
$677$	5.95851	0.229004	0.114502	+	0.993423i	$0.463473\pi$
$678$	50.0962	1.92393
$679$	−14.7752	−0.567021
$680$	−0.0361051	−0.00138457
$681$	−71.5998	−2.74371
$682$	40.2185	1.54004
$683$	3.46453	0.132567	0.0662833	−	0.997801i	$-0.478886\pi$
$683$	3.46453	0.132567	0.0662833	+	0.997801i	$0.478886\pi$
$684$	−107.588	−4.11372
$685$	0.00502404	0.000191959 0
$686$	56.1322	2.14314
$687$	81.9132	3.12519
$688$	−155.798	−5.93973
$689$	−12.1233	−0.461859
$690$	0.202268	0.00770021
$691$	−29.8821	−1.13677	−0.568384	−	0.822763i	$-0.692431\pi$
$691$	−29.8821	−1.13677	−0.568384	+	0.822763i	$0.692431\pi$
$692$	46.5819	1.77078
$693$	28.0977	1.06734
$694$	−78.3830	−2.97538
$695$	0.171525	0.00650630
$696$	−255.057	−9.66792
$697$	−1.36506	−0.0517054
$698$	−23.5794	−0.892495
$699$	−44.6587	−1.68915
$700$	−59.4941	−2.24867
$701$	19.8498	0.749718	0.374859	−	0.927082i	$-0.377691\pi$
$701$	19.8498	0.749718	0.374859	+	0.927082i	$0.377691\pi$
$702$	−64.9328	−2.45073
$703$	18.2131	0.686918
$704$	130.537	4.91981
$705$	0.282023	0.0106216
$706$	39.9232	1.50253
$707$	31.7802	1.19522
$708$	−68.0375	−2.55700
$709$	−41.3929	−1.55454	−0.777271	−	0.629166i	$-0.783397\pi$
$709$	−41.3929	−1.55454	−0.777271	+	0.629166i	$0.783397\pi$
$710$	0.225799	0.00847408
$711$	50.6475	1.89943
$712$	112.464	4.21478
$713$	−11.4894	−0.430280
$714$	4.75178	0.177831
$715$	−0.145154	−0.00542844
$716$	135.445	5.06182
$717$	−21.3012	−0.795509
$718$	−11.1584	−0.416429
$719$	26.9170	1.00383	0.501917	−	0.864916i	$-0.332628\pi$
$719$	26.9170	1.00383	0.501917	+	0.864916i	$0.332628\pi$
$720$	1.00636	0.0375047
$721$	0.399145	0.0148649
$722$	12.3849	0.460917
$723$	−54.2758	−2.01854
$724$	−30.0103	−1.11532
$725$	42.6911	1.58551
$726$	−23.3200	−0.865487
$727$	−17.1819	−0.637241	−0.318620	−	0.947882i	$-0.603219\pi$
$727$	−17.1819	−0.637241	−0.318620	+	0.947882i	$0.603219\pi$
$728$	97.9341	3.62968
$729$	−43.7090	−1.61885
$730$	0.524340	0.0194067
$731$	−2.54104	−0.0939838
$732$	148.420	5.48575
$733$	−23.9574	−0.884889	−0.442444	−	0.896796i	$-0.645889\pi$
$733$	−23.9574	−0.884889	−0.442444	+	0.896796i	$0.645889\pi$
$734$	73.5072	2.71320
$735$	0.0899561	0.00331808
$736$	−66.7101	−2.45897
$737$	−29.2419	−1.07714
$738$	62.3868	2.29649
$739$	33.6922	1.23939	0.619694	−	0.784843i	$-0.287257\pi$
$739$	33.6922	1.23939	0.619694	+	0.784843i	$0.287257\pi$
$740$	−0.316822	−0.0116466
$741$	−47.9881	−1.76289
$742$	−15.4536	−0.567320
$743$	−27.6938	−1.01599	−0.507994	−	0.861361i	$-0.669613\pi$
$743$	−27.6938	−1.01599	−0.507994	+	0.861361i	$0.669613\pi$
$744$	−151.736	−5.56292
$745$	0.187049	0.00685296
$746$	−92.6347	−3.39160
$747$	−54.1124	−1.97987
$748$	4.88307	0.178543
$749$	14.6169	0.534089
$750$	−0.894244	−0.0326532
$751$	−25.6372	−0.935516	−0.467758	−	0.883857i	$-0.654938\pi$
$751$	−25.6372	−0.935516	−0.467758	+	0.883857i	$0.654938\pi$
$752$	−160.272	−5.84453
$753$	26.1728	0.953788
$754$	−107.120	−3.90109
$755$	−0.0519016	−0.00188889
$756$	−61.5867	−2.23989
$757$	−4.76737	−0.173273	−0.0866366	−	0.996240i	$-0.527612\pi$
$757$	−4.76737	−0.173273	−0.0866366	+	0.996240i	$0.527612\pi$
$758$	0.657587	0.0238846
$759$	−17.9464	−0.651413
$760$	0.464791	0.0168597
$761$	30.0482	1.08925	0.544623	−	0.838681i	$-0.316673\pi$
$761$	30.0482	1.08925	0.544623	+	0.838681i	$0.316673\pi$
$762$	−16.7538	−0.606926
$763$	29.0410	1.05136
$764$	75.1527	2.71893
$765$	0.0164136	0.000593434 0
$766$	29.5849	1.06895
$767$	−18.7460	−0.676878
$768$	−288.781	−10.4205
$769$	32.0385	1.15534	0.577668	−	0.816272i	$-0.303963\pi$
$769$	32.0385	1.15534	0.577668	+	0.816272i	$0.303963\pi$
$770$	−0.185029	−0.00666798
$771$	65.3369	2.35305
$772$	18.4272	0.663209
$773$	−6.70720	−0.241241	−0.120621	−	0.992699i	$-0.538488\pi$
$773$	−6.70720	−0.241241	−0.120621	+	0.992699i	$0.538488\pi$
$774$	116.132	4.17429
$775$	25.3974	0.912301
$776$	76.9881	2.76371
$777$	27.3545	0.981336
$778$	−2.48840	−0.0892133
$779$	17.5728	0.629611
$780$	0.834768	0.0298895
$781$	−20.0342	−0.716880
$782$	−1.87479	−0.0670422
$783$	44.1927	1.57932
$784$	−51.1216	−1.82577
$785$	0.194874	0.00695535
$786$	45.9099	1.63755
$787$	−41.6414	−1.48435	−0.742177	−	0.670204i	$-0.766207\pi$
$787$	−41.6414	−1.48435	−0.742177	+	0.670204i	$0.766207\pi$
$788$	29.6814	1.05736
$789$	−28.3053	−1.00769
$790$	−0.333524	−0.0118663
$791$	13.0914	0.465478
$792$	−146.406	−5.20232
$793$	40.8933	1.45216
$794$	−39.7688	−1.41134
$795$	−0.0864148	−0.00306482
$796$	129.858	4.60271
$797$	11.4007	0.403833	0.201917	−	0.979403i	$-0.435283\pi$
$797$	11.4007	0.403833	0.201917	+	0.979403i	$0.435283\pi$
$798$	−61.1709	−2.16543
$799$	−2.61402	−0.0924775
$800$	147.464	5.21363
$801$	−51.1268	−1.80648
$802$	−46.7783	−1.65180
$803$	−46.5225	−1.64175
$804$	168.168	5.93083
$805$	0.0528579	0.00186300
$806$	−63.7269	−2.24468
$807$	58.7806	2.06918
$808$	−165.594	−5.82559
$809$	−8.79100	−0.309075	−0.154538	−	0.987987i	$-0.549389\pi$
$809$	−8.79100	−0.309075	−0.154538	+	0.987987i	$0.549389\pi$
$810$	0.00139520	4.90224e−5 0
$811$	41.3019	1.45031	0.725153	−	0.688587i	$-0.241769\pi$
$811$	41.3019	1.45031	0.725153	+	0.688587i	$0.241769\pi$
$812$	−101.600	−3.56547
$813$	23.2867	0.816700
$814$	37.7793	1.32416
$815$	−0.00362261	−0.000126895 0
$816$	−15.1004	−0.528618
$817$	32.7115	1.14443
$818$	−11.4764	−0.401262
$819$	−44.5213	−1.55570
$820$	−0.305684	−0.0106750
$821$	14.0404	0.490013	0.245006	−	0.969521i	$-0.421210\pi$
$821$	14.0404	0.490013	0.245006	+	0.969521i	$0.421210\pi$
$822$	3.44532	0.120169
$823$	−17.2200	−0.600250	−0.300125	−	0.953900i	$-0.597028\pi$
$823$	−17.2200	−0.600250	−0.300125	+	0.953900i	$0.597028\pi$
$824$	−2.07979	−0.0724530
$825$	39.6708	1.38116
$826$	−23.8957	−0.831437
$827$	54.9549	1.91097	0.955485	−	0.295041i	$-0.0953334\pi$
$827$	54.9549	1.91097	0.955485	+	0.295041i	$0.0953334\pi$
$828$	63.7535	2.21559
$829$	5.78512	0.200925	0.100463	−	0.994941i	$-0.467968\pi$
$829$	5.78512	0.200925	0.100463	+	0.994941i	$0.467968\pi$
$830$	0.356341	0.0123688
$831$	41.0606	1.42438
$832$	−206.839	−7.17085
$833$	−0.833788	−0.0288890
$834$	117.626	4.07305
$835$	−0.196746	−0.00680869
$836$	−62.8611	−2.17410
$837$	26.2907	0.908738
$838$	−78.5464	−2.71334
$839$	41.4352	1.43050	0.715251	−	0.698868i	$-0.246313\pi$
$839$	41.4352	1.43050	0.715251	+	0.698868i	$0.246313\pi$
$840$	0.698077	0.0240859
$841$	43.9051	1.51397
$842$	−48.1311	−1.65871
$843$	20.2395	0.697085
$844$	−17.0690	−0.587540
$845$	0.0815469	0.00280530
$846$	119.468	4.10738
$847$	−6.09413	−0.209397
$848$	49.1091	1.68641
$849$	−22.5041	−0.772340
$850$	4.14424	0.142146
$851$	−10.7925	−0.369964
$852$	115.215	3.94720
$853$	48.4532	1.65901	0.829503	−	0.558502i	$-0.188624\pi$
$853$	48.4532	1.65901	0.829503	+	0.558502i	$0.188624\pi$
$854$	52.1270	1.78375
$855$	−0.211296	−0.00722618
$856$	−76.1629	−2.60319
$857$	−14.4670	−0.494184	−0.247092	−	0.968992i	$-0.579475\pi$
$857$	−14.4670	−0.494184	−0.247092	+	0.968992i	$0.579475\pi$
$858$	−99.5416	−3.39829
$859$	16.8019	0.573272	0.286636	−	0.958040i	$-0.407463\pi$
$859$	16.8019	0.573272	0.286636	+	0.958040i	$0.407463\pi$
$860$	−0.569027	−0.0194037
$861$	26.3928	0.899466
$862$	104.659	3.56468
$863$	−34.2698	−1.16656	−0.583278	−	0.812272i	$-0.698230\pi$
$863$	−34.2698	−1.16656	−0.583278	+	0.812272i	$0.698230\pi$
$864$	152.650	5.19327
$865$	0.0914841	0.00311055
$866$	−85.3879	−2.90160
$867$	47.3767	1.60900
$868$	−60.4429	−2.05157
$869$	29.5922	1.00385
$870$	−0.763555	−0.0258870
$871$	46.3344	1.56998
$872$	−151.322	−5.12440
$873$	−34.9992	−1.18454
$874$	24.1346	0.816366
$875$	−0.233689	−0.00790014
$876$	267.548	9.03960
$877$	6.39451	0.215927	0.107964	−	0.994155i	$-0.465567\pi$
$877$	6.39451	0.215927	0.107964	+	0.994155i	$0.465567\pi$
$878$	−9.63500	−0.325166
$879$	28.2074	0.951411
$880$	0.587991	0.0198212
$881$	−14.6581	−0.493844	−0.246922	−	0.969035i	$-0.579419\pi$
$881$	−14.6581	−0.493844	−0.246922	+	0.969035i	$0.579419\pi$
$882$	38.1063	1.28310
$883$	−21.1515	−0.711805	−0.355903	−	0.934523i	$-0.615827\pi$
$883$	−21.1515	−0.711805	−0.355903	+	0.934523i	$0.615827\pi$
$884$	−7.73732	−0.260234
$885$	−0.133622	−0.00449164
$886$	28.4479	0.955726
$887$	−36.3024	−1.21891	−0.609457	−	0.792819i	$-0.708613\pi$
$887$	−36.3024	−1.21891	−0.609457	+	0.792819i	$0.708613\pi$
$888$	−142.534	−4.78311
$889$	−4.37820	−0.146840
$890$	0.336680	0.0112855
$891$	−0.123790	−0.00414713
$892$	−115.766	−3.87613
$893$	33.6510	1.12609
$894$	128.272	4.29007
$895$	0.266006	0.00889161
$896$	−142.946	−4.77547
$897$	28.4364	0.949464
$898$	−51.7607	−1.72728
$899$	43.3720	1.44654
$900$	−140.928	−4.69760
$901$	0.800964	0.0266840
$902$	36.4512	1.21369
$903$	49.1299	1.63494
$904$	−68.2145	−2.26878
$905$	−0.0589385	−0.00195918
$906$	−35.5924	−1.18248
$907$	−35.7582	−1.18733	−0.593665	−	0.804712i	$-0.702320\pi$
$907$	−35.7582	−1.18733	−0.593665	+	0.804712i	$0.702320\pi$
$908$	148.613	4.93191
$909$	75.2800	2.49688
$910$	0.293182	0.00971888
$911$	−36.5844	−1.21210	−0.606048	−	0.795428i	$-0.707246\pi$
$911$	−36.5844	−1.21210	−0.606048	+	0.795428i	$0.707246\pi$
$912$	194.391	6.43693
$913$	−31.6166	−1.04636
$914$	−111.757	−3.69659
$915$	0.291488	0.00963630
$916$	−170.020	−5.61762
$917$	11.9974	0.396190
$918$	4.29000	0.141591
$919$	−41.9150	−1.38265	−0.691324	−	0.722545i	$-0.742972\pi$
$919$	−41.9150	−1.38265	−0.691324	+	0.722545i	$0.742972\pi$
$920$	−0.275422	−0.00908040
$921$	93.3079	3.07460
$922$	−6.95196	−0.228951
$923$	31.7446	1.04488
$924$	−94.4120	−3.10593
$925$	23.8571	0.784416
$926$	111.728	3.67161
$927$	0.945484	0.0310538
$928$	251.829	8.26668
$929$	9.59368	0.314759	0.157379	−	0.987538i	$-0.449695\pi$
$929$	9.59368	0.314759	0.157379	+	0.987538i	$0.449695\pi$
$930$	−0.454247	−0.0148953
$931$	10.7336	0.351779
$932$	92.6940	3.03629
$933$	−65.8567	−2.15605
$934$	44.4332	1.45390
$935$	0.00959008	0.000313629 0
$936$	231.984	7.58262
$937$	−0.277619	−0.00906940	−0.00453470	−	0.999990i	$-0.501443\pi$
$937$	−0.277619	−0.00906940	−0.00453470	+	0.999990i	$0.501443\pi$
$938$	59.0629	1.92847
$939$	−24.5053	−0.799701
$940$	−0.585370	−0.0190927
$941$	−20.6316	−0.672571	−0.336285	−	0.941760i	$-0.609171\pi$
$941$	−20.6316	−0.672571	−0.336285	+	0.941760i	$0.609171\pi$
$942$	133.638	4.35416
$943$	−10.4131	−0.339099
$944$	75.9365	2.47152
$945$	−0.120953	−0.00393459
$946$	67.8534	2.20610
$947$	13.2042	0.429078	0.214539	−	0.976715i	$-0.431175\pi$
$947$	13.2042	0.429078	0.214539	+	0.976715i	$0.431175\pi$
$948$	−170.183	−5.52727
$949$	73.7159	2.39292
$950$	−53.3500	−1.73090
$951$	−56.4660	−1.83103
$952$	−6.47035	−0.209705
$953$	11.9856	0.388251	0.194126	−	0.980977i	$-0.437813\pi$
$953$	11.9856	0.388251	0.194126	+	0.980977i	$0.437813\pi$
$954$	−36.6061	−1.18517
$955$	0.147596	0.00477608
$956$	44.2131	1.42995
$957$	67.7471	2.18995
$958$	25.8795	0.836129
$959$	0.900351	0.0290738
$960$	−1.47435	−0.0475845
$961$	−5.19758	−0.167664
$962$	−59.8620	−1.93003
$963$	34.6240	1.11574
$964$	112.655	3.62838
$965$	0.0361900	0.00116500
$966$	36.2482	1.16627
$967$	−1.11335	−0.0358029	−0.0179014	−	0.999840i	$-0.505699\pi$
$967$	−1.11335	−0.0358029	−0.0179014	+	0.999840i	$0.505699\pi$
$968$	31.7542	1.02062
$969$	3.17050	0.101851
$970$	0.230476	0.00740015
$971$	18.7273	0.600989	0.300494	−	0.953784i	$-0.402848\pi$
$971$	18.7273	0.600989	0.300494	+	0.953784i	$0.402848\pi$
$972$	90.9950	2.91866
$973$	30.7387	0.985438
$974$	19.2987	0.618370
$975$	−62.8591	−2.01310
$976$	−165.651	−5.30236
$977$	−24.4749	−0.783023	−0.391511	−	0.920173i	$-0.628048\pi$
$977$	−24.4749	−0.783023	−0.391511	+	0.920173i	$0.628048\pi$
$978$	−2.48427	−0.0794381
$979$	−29.8722	−0.954721
$980$	−0.186714	−0.00596436
$981$	68.7916	2.19635
$982$	82.0191	2.61733
$983$	−26.4161	−0.842544	−0.421272	−	0.906934i	$-0.638416\pi$
$983$	−26.4161	−0.842544	−0.421272	+	0.906934i	$0.638416\pi$
$984$	−137.523	−4.38407
$985$	0.0582926	0.00185736
$986$	7.07726	0.225386
$987$	50.5410	1.60874
$988$	99.6046	3.16885
$989$	−19.3839	−0.616373
$990$	−0.438291	−0.0139298
$991$	−23.4603	−0.745240	−0.372620	−	0.927984i	$-0.621540\pi$
$991$	−23.4603	−0.745240	−0.372620	+	0.927984i	$0.621540\pi$
$992$	149.815	4.75664
$993$	−62.6685	−1.98872
$994$	40.4651	1.28347
$995$	0.255035	0.00808514
$996$	181.825	5.76134
$997$	21.5343	0.681999	0.340999	−	0.940064i	$-0.389235\pi$
$997$	21.5343	0.681999	0.340999	+	0.940064i	$0.389235\pi$
$998$	50.5851	1.60124
$999$	24.6962	0.781352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.3	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.3	✓	358	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)

\(f(q)\)	\(=\)	\(q-2.79545 q^{2} -2.80135 q^{3} +5.81452 q^{4} +0.0114194 q^{5} +7.83103 q^{6} +2.04645 q^{7} -10.6633 q^{8} +4.84758 q^{9} +O(q^{10})\)	\(q-2.79545 q^{2} -2.80135 q^{3} +5.81452 q^{4} +0.0114194 q^{5} +7.83103 q^{6} +2.04645 q^{7} -10.6633 q^{8} +4.84758 q^{9} -0.0319223 q^{10} +2.83233 q^{11} -16.2885 q^{12} -4.48788 q^{13} -5.72075 q^{14} -0.0319897 q^{15} +18.1796 q^{16} +0.296507 q^{17} -13.5511 q^{18} -3.81702 q^{19} +0.0663982 q^{20} -5.73284 q^{21} -7.91763 q^{22} +2.26186 q^{23} +29.8716 q^{24} -4.99987 q^{25} +12.5456 q^{26} -5.17573 q^{27} +11.8991 q^{28} -8.53845 q^{29} +0.0894256 q^{30} -5.07961 q^{31} -29.4935 q^{32} -7.93436 q^{33} -0.828870 q^{34} +0.0233692 q^{35} +28.1863 q^{36} -4.77154 q^{37} +10.6703 q^{38} +12.5721 q^{39} -0.121768 q^{40} -4.60380 q^{41} +16.0258 q^{42} -8.56991 q^{43} +16.4686 q^{44} +0.0553564 q^{45} -6.32290 q^{46} -8.81606 q^{47} -50.9275 q^{48} -2.81203 q^{49} +13.9769 q^{50} -0.830622 q^{51} -26.0949 q^{52} +2.70133 q^{53} +14.4685 q^{54} +0.0323435 q^{55} -21.8219 q^{56} +10.6928 q^{57} +23.8688 q^{58} +4.17702 q^{59} -0.186005 q^{60} -9.11193 q^{61} +14.1998 q^{62} +9.92034 q^{63} +46.0883 q^{64} -0.0512489 q^{65} +22.1801 q^{66} -10.3243 q^{67} +1.72405 q^{68} -6.33626 q^{69} -0.0653274 q^{70} -7.07339 q^{71} -51.6911 q^{72} -16.4255 q^{73} +13.3386 q^{74} +14.0064 q^{75} -22.1941 q^{76} +5.79623 q^{77} -35.1448 q^{78} +10.4480 q^{79} +0.207600 q^{80} -0.0437062 q^{81} +12.8697 q^{82} -11.1628 q^{83} -33.3337 q^{84} +0.00338593 q^{85} +23.9567 q^{86} +23.9192 q^{87} -30.2019 q^{88} -10.5469 q^{89} -0.154746 q^{90} -9.18424 q^{91} +13.1516 q^{92} +14.2298 q^{93} +24.6448 q^{94} -0.0435880 q^{95} +82.6217 q^{96} -7.21992 q^{97} +7.86088 q^{98} +13.7300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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