LMFDB - Embedded newform 8021.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66546 q^{2} +1.20306 q^{3} +5.10470 q^{4} -3.76588 q^{5} -3.20671 q^{6} -2.98135 q^{7} -8.27547 q^{8} -1.55265 q^{9} +O(q^{10})$	\(q-2.66546 q^{2} +1.20306 q^{3} +5.10470 q^{4} -3.76588 q^{5} -3.20671 q^{6} -2.98135 q^{7} -8.27547 q^{8} -1.55265 q^{9} +10.0378 q^{10} +4.22537 q^{11} +6.14126 q^{12} -1.00000 q^{13} +7.94667 q^{14} -4.53058 q^{15} +11.8486 q^{16} +1.00920 q^{17} +4.13853 q^{18} -6.97539 q^{19} -19.2237 q^{20} -3.58674 q^{21} -11.2626 q^{22} -0.183999 q^{23} -9.95588 q^{24} +9.18187 q^{25} +2.66546 q^{26} -5.47711 q^{27} -15.2189 q^{28} -0.624176 q^{29} +12.0761 q^{30} +2.79672 q^{31} -15.0310 q^{32} +5.08337 q^{33} -2.69000 q^{34} +11.2274 q^{35} -7.92580 q^{36} -1.48513 q^{37} +18.5926 q^{38} -1.20306 q^{39} +31.1644 q^{40} -4.32631 q^{41} +9.56032 q^{42} +7.69958 q^{43} +21.5692 q^{44} +5.84709 q^{45} +0.490442 q^{46} +7.56614 q^{47} +14.2545 q^{48} +1.88843 q^{49} -24.4739 q^{50} +1.21413 q^{51} -5.10470 q^{52} +13.2572 q^{53} +14.5990 q^{54} -15.9123 q^{55} +24.6720 q^{56} -8.39181 q^{57} +1.66372 q^{58} -1.60794 q^{59} -23.1273 q^{60} +3.65823 q^{61} -7.45457 q^{62} +4.62898 q^{63} +16.3674 q^{64} +3.76588 q^{65} -13.5495 q^{66} -5.32435 q^{67} +5.15168 q^{68} -0.221361 q^{69} -29.9262 q^{70} -3.21676 q^{71} +12.8489 q^{72} +8.12012 q^{73} +3.95857 q^{74} +11.0463 q^{75} -35.6073 q^{76} -12.5973 q^{77} +3.20671 q^{78} -6.61597 q^{79} -44.6203 q^{80} -1.93134 q^{81} +11.5316 q^{82} +5.16366 q^{83} -18.3092 q^{84} -3.80054 q^{85} -20.5230 q^{86} -0.750921 q^{87} -34.9669 q^{88} -8.59771 q^{89} -15.5852 q^{90} +2.98135 q^{91} -0.939257 q^{92} +3.36463 q^{93} -20.1673 q^{94} +26.2685 q^{95} -18.0832 q^{96} +3.49262 q^{97} -5.03354 q^{98} -6.56051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.66546	−1.88477	−0.942384	−	0.334533i	$-0.891421\pi$
$2$	−2.66546	−1.88477	−0.942384	+	0.334533i	$0.891421\pi$
$3$	1.20306	0.694587	0.347293	−	0.937757i	$-0.387101\pi$
$3$	1.20306	0.694587	0.347293	+	0.937757i	$0.387101\pi$
$4$	5.10470	2.55235
$5$	−3.76588	−1.68415	−0.842077	−	0.539357i	$-0.818667\pi$
$5$	−3.76588	−1.68415	−0.842077	+	0.539357i	$0.818667\pi$
$6$	−3.20671	−1.30913
$7$	−2.98135	−1.12684	−0.563422	−	0.826170i	$-0.690515\pi$
$7$	−2.98135	−1.12684	−0.563422	+	0.826170i	$0.690515\pi$
$8$	−8.27547	−2.92582
$9$	−1.55265	−0.517549
$10$	10.0378	3.17424
$11$	4.22537	1.27400	0.636999	−	0.770865i	$-0.280176\pi$
$11$	4.22537	1.27400	0.636999	+	0.770865i	$0.280176\pi$
$12$	6.14126	1.77283
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.94667	2.12384
$15$	−4.53058	−1.16979
$16$	11.8486	2.96214
$17$	1.00920	0.244768	0.122384	−	0.992483i	$-0.460946\pi$
$17$	1.00920	0.244768	0.122384	+	0.992483i	$0.460946\pi$
$18$	4.13853	0.975460
$19$	−6.97539	−1.60026	−0.800132	−	0.599824i	$-0.795237\pi$
$19$	−6.97539	−1.60026	−0.800132	+	0.599824i	$0.795237\pi$
$20$	−19.2237	−4.29855
$21$	−3.58674	−0.782691
$22$	−11.2626	−2.40119
$23$	−0.183999	−0.0383664	−0.0191832	−	0.999816i	$-0.506107\pi$
$23$	−0.183999	−0.0383664	−0.0191832	+	0.999816i	$0.506107\pi$
$24$	−9.95588	−2.03224
$25$	9.18187	1.83637
$26$	2.66546	0.522741
$27$	−5.47711	−1.05407
$28$	−15.2189	−2.87610
$29$	−0.624176	−0.115907	−0.0579533	−	0.998319i	$-0.518457\pi$
$29$	−0.624176	−0.115907	−0.0579533	+	0.998319i	$0.518457\pi$
$30$	12.0761	2.20478
$31$	2.79672	0.502307	0.251153	−	0.967947i	$-0.419190\pi$
$31$	2.79672	0.502307	0.251153	+	0.967947i	$0.419190\pi$
$32$	−15.0310	−2.65713
$33$	5.08337	0.884902
$34$	−2.69000	−0.461331
$35$	11.2274	1.89778
$36$	−7.92580	−1.32097
$37$	−1.48513	−0.244154	−0.122077	−	0.992521i	$-0.538956\pi$
$37$	−1.48513	−0.244154	−0.122077	+	0.992521i	$0.538956\pi$
$38$	18.5926	3.01613
$39$	−1.20306	−0.192644
$40$	31.1644	4.92753
$41$	−4.32631	−0.675656	−0.337828	−	0.941208i	$-0.609692\pi$
$41$	−4.32631	−0.675656	−0.337828	+	0.941208i	$0.609692\pi$
$42$	9.56032	1.47519
$43$	7.69958	1.17418	0.587088	−	0.809523i	$-0.300274\pi$
$43$	7.69958	1.17418	0.587088	+	0.809523i	$0.300274\pi$
$44$	21.5692	3.25169
$45$	5.84709	0.871632
$46$	0.490442	0.0723117
$47$	7.56614	1.10364	0.551818	−	0.833965i	$-0.313934\pi$
$47$	7.56614	1.10364	0.551818	+	0.833965i	$0.313934\pi$
$48$	14.2545	2.05746
$49$	1.88843	0.269776
$50$	−24.4739	−3.46114
$51$	1.21413	0.170013
$52$	−5.10470	−0.707894
$53$	13.2572	1.82102	0.910508	−	0.413491i	$-0.135691\pi$
$53$	13.2572	1.82102	0.910508	+	0.413491i	$0.135691\pi$
$54$	14.5990	1.98668
$55$	−15.9123	−2.14561
$56$	24.6720	3.29694
$57$	−8.39181	−1.11152
$58$	1.66372	0.218457
$59$	−1.60794	−0.209336	−0.104668	−	0.994507i	$-0.533378\pi$
$59$	−1.60794	−0.209336	−0.104668	+	0.994507i	$0.533378\pi$
$60$	−23.1273	−2.98572
$61$	3.65823	0.468388	0.234194	−	0.972190i	$-0.424755\pi$
$61$	3.65823	0.468388	0.234194	+	0.972190i	$0.424755\pi$
$62$	−7.45457	−0.946731
$63$	4.62898	0.583197
$64$	16.3674	2.04593
$65$	3.76588	0.467100
$66$	−13.5495	−1.66783
$67$	−5.32435	−0.650473	−0.325236	−	0.945633i	$-0.605444\pi$
$67$	−5.32435	−0.650473	−0.325236	+	0.945633i	$0.605444\pi$
$68$	5.15168	0.624733
$69$	−0.221361	−0.0266488
$70$	−29.9262	−3.57687
$71$	−3.21676	−0.381759	−0.190880	−	0.981613i	$-0.561134\pi$
$71$	−3.21676	−0.381759	−0.190880	+	0.981613i	$0.561134\pi$
$72$	12.8489	1.51425
$73$	8.12012	0.950388	0.475194	−	0.879881i	$-0.342378\pi$
$73$	8.12012	0.950388	0.475194	+	0.879881i	$0.342378\pi$
$74$	3.95857	0.460174
$75$	11.0463	1.27552
$76$	−35.6073	−4.08443
$77$	−12.5973	−1.43560
$78$	3.20671	0.363089
$79$	−6.61597	−0.744355	−0.372177	−	0.928162i	$-0.621389\pi$
$79$	−6.61597	−0.744355	−0.372177	+	0.928162i	$0.621389\pi$
$80$	−44.6203	−4.98870
$81$	−1.93134	−0.214594
$82$	11.5316	1.27346
$83$	5.16366	0.566785	0.283393	−	0.959004i	$-0.408540\pi$
$83$	5.16366	0.566785	0.283393	+	0.959004i	$0.408540\pi$
$84$	−18.3092	−1.99770
$85$	−3.80054	−0.412227
$86$	−20.5230	−2.21305
$87$	−0.750921	−0.0805072
$88$	−34.9669	−3.72749
$89$	−8.59771	−0.911356	−0.455678	−	0.890145i	$-0.650603\pi$
$89$	−8.59771	−0.911356	−0.455678	+	0.890145i	$0.650603\pi$
$90$	−15.5852	−1.64282
$91$	2.98135	0.312530
$92$	−0.939257	−0.0979243
$93$	3.36463	0.348896
$94$	−20.1673	−2.08010
$95$	26.2685	2.69509
$96$	−18.0832	−1.84560
$97$	3.49262	0.354622	0.177311	−	0.984155i	$-0.443260\pi$
$97$	3.49262	0.354622	0.177311	+	0.984155i	$0.443260\pi$
$98$	−5.03354	−0.508465
$99$	−6.56051	−0.659356
$100$	46.8707	4.68707
$101$	13.0363	1.29716	0.648582	−	0.761144i	$-0.275362\pi$
$101$	13.0363	1.29716	0.648582	+	0.761144i	$0.275362\pi$
$102$	−3.23623	−0.320434
$103$	−13.2314	−1.30373	−0.651863	−	0.758337i	$-0.726012\pi$
$103$	−13.2314	−1.30373	−0.651863	+	0.758337i	$0.726012\pi$
$104$	8.27547	0.811476
$105$	13.5072	1.31817
$106$	−35.3366	−3.43219
$107$	1.19240	0.115273	0.0576366	−	0.998338i	$-0.481644\pi$
$107$	1.19240	0.115273	0.0576366	+	0.998338i	$0.481644\pi$
$108$	−27.9590	−2.69035
$109$	13.7085	1.31304	0.656518	−	0.754310i	$-0.272028\pi$
$109$	13.7085	1.31304	0.656518	+	0.754310i	$0.272028\pi$
$110$	42.4135	4.04397
$111$	−1.78670	−0.169586
$112$	−35.3247	−3.33787
$113$	6.84134	0.643579	0.321790	−	0.946811i	$-0.395716\pi$
$113$	6.84134	0.643579	0.321790	+	0.946811i	$0.395716\pi$
$114$	22.3681	2.09496
$115$	0.692917	0.0646148
$116$	−3.18623	−0.295834
$117$	1.55265	0.143542
$118$	4.28590	0.394549
$119$	−3.00879	−0.275815
$120$	37.4927	3.42260
$121$	6.85376	0.623069
$122$	−9.75087	−0.882802
$123$	−5.20481	−0.469302
$124$	14.2764	1.28206
$125$	−15.7484	−1.40858
$126$	−12.3384	−1.09919
$127$	−3.21659	−0.285426	−0.142713	−	0.989764i	$-0.545583\pi$
$127$	−3.21659	−0.285426	−0.142713	+	0.989764i	$0.545583\pi$
$128$	−13.5648	−1.19897
$129$	9.26306	0.815567
$130$	−10.0378	−0.880376
$131$	14.5778	1.27366	0.636832	−	0.771002i	$-0.280244\pi$
$131$	14.5778	1.27366	0.636832	+	0.771002i	$0.280244\pi$
$132$	25.9491	2.25858
$133$	20.7960	1.80325
$134$	14.1919	1.22599
$135$	20.6261	1.77522
$136$	−8.35163	−0.716146
$137$	−8.33224	−0.711871	−0.355936	−	0.934510i	$-0.615838\pi$
$137$	−8.33224	−0.711871	−0.355936	+	0.934510i	$0.615838\pi$
$138$	0.590030	0.0502267
$139$	−14.2275	−1.20676	−0.603382	−	0.797452i	$-0.706181\pi$
$139$	−14.2275	−1.20676	−0.603382	+	0.797452i	$0.706181\pi$
$140$	57.3125	4.84379
$141$	9.10252	0.766571
$142$	8.57416	0.719528
$143$	−4.22537	−0.353343
$144$	−18.3966	−1.53305
$145$	2.35057	0.195204
$146$	−21.6439	−1.79126
$147$	2.27189	0.187383
$148$	−7.58116	−0.623167
$149$	21.9534	1.79849	0.899244	−	0.437446i	$-0.144117\pi$
$149$	21.9534	1.79849	0.899244	+	0.437446i	$0.144117\pi$
$150$	−29.4436	−2.40406
$151$	−17.4567	−1.42060	−0.710302	−	0.703897i	$-0.751442\pi$
$151$	−17.4567	−1.42060	−0.710302	+	0.703897i	$0.751442\pi$
$152$	57.7246	4.68208
$153$	−1.56694	−0.126679
$154$	33.5776	2.70576
$155$	−10.5321	−0.845962
$156$	−6.14126	−0.491694
$157$	−7.63165	−0.609072	−0.304536	−	0.952501i	$-0.598501\pi$
$157$	−7.63165	−0.609072	−0.304536	+	0.952501i	$0.598501\pi$
$158$	17.6346	1.40294
$159$	15.9492	1.26485
$160$	56.6049	4.47501
$161$	0.548564	0.0432329
$162$	5.14793	0.404459
$163$	11.3849	0.891736	0.445868	−	0.895099i	$-0.352895\pi$
$163$	11.3849	0.891736	0.445868	+	0.895099i	$0.352895\pi$
$164$	−22.0845	−1.72451
$165$	−19.1434	−1.49031
$166$	−13.7636	−1.06826
$167$	13.6322	1.05489	0.527446	−	0.849589i	$-0.323150\pi$
$167$	13.6322	1.05489	0.527446	+	0.849589i	$0.323150\pi$
$168$	29.6819	2.29001
$169$	1.00000	0.0769231
$170$	10.1302	0.776952
$171$	10.8303	0.828215
$172$	39.3041	2.99691
$173$	8.50513	0.646633	0.323316	−	0.946291i	$-0.395202\pi$
$173$	8.50513	0.646633	0.323316	+	0.946291i	$0.395202\pi$
$174$	2.00155	0.151737
$175$	−27.3743	−2.06931
$176$	50.0645	3.77376
$177$	−1.93445	−0.145402
$178$	22.9169	1.71769
$179$	7.52219	0.562235	0.281117	−	0.959673i	$-0.409295\pi$
$179$	7.52219	0.562235	0.281117	+	0.959673i	$0.409295\pi$
$180$	29.8476	2.22471
$181$	5.78859	0.430262	0.215131	−	0.976585i	$-0.430982\pi$
$181$	5.78859	0.430262	0.215131	+	0.976585i	$0.430982\pi$
$182$	−7.94667	−0.589047
$183$	4.40107	0.325336
$184$	1.52267	0.112253
$185$	5.59284	0.411193
$186$	−8.96829	−0.657587
$187$	4.26426	0.311834
$188$	38.6229	2.81686
$189$	16.3292	1.18777
$190$	−70.0177	−5.07962
$191$	−23.3562	−1.68999	−0.844996	−	0.534773i	$-0.820397\pi$
$191$	−23.3562	−1.68999	−0.844996	+	0.534773i	$0.820397\pi$
$192$	19.6910	1.42107
$193$	−24.6470	−1.77413	−0.887064	−	0.461647i	$-0.847259\pi$
$193$	−24.6470	−1.77413	−0.887064	+	0.461647i	$0.847259\pi$
$194$	−9.30946	−0.668380
$195$	4.53058	0.324442
$196$	9.63987	0.688562
$197$	6.20993	0.442439	0.221220	−	0.975224i	$-0.428996\pi$
$197$	6.20993	0.442439	0.221220	+	0.975224i	$0.428996\pi$
$198$	17.4868	1.24273
$199$	19.0577	1.35096	0.675481	−	0.737378i	$-0.263936\pi$
$199$	19.0577	1.35096	0.675481	+	0.737378i	$0.263936\pi$
$200$	−75.9843	−5.37290
$201$	−6.40551	−0.451810
$202$	−34.7479	−2.44485
$203$	1.86088	0.130609
$204$	6.19778	0.433931
$205$	16.2924	1.13791
$206$	35.2678	2.45722
$207$	0.285685	0.0198565
$208$	−11.8486	−0.821550
$209$	−29.4736	−2.03873
$210$	−36.0031	−2.48445
$211$	7.54090	0.519137	0.259568	−	0.965725i	$-0.416420\pi$
$211$	7.54090	0.519137	0.259568	+	0.965725i	$0.416420\pi$
$212$	67.6740	4.64787
$213$	−3.86996	−0.265165
$214$	−3.17829	−0.217263
$215$	−28.9957	−1.97749
$216$	45.3256	3.08402
$217$	−8.33801	−0.566021
$218$	−36.5395	−2.47477
$219$	9.76899	0.660127
$220$	−81.2273	−5.47634
$221$	−1.00920	−0.0678864
$222$	4.76239	0.319631
$223$	−4.51989	−0.302675	−0.151337	−	0.988482i	$-0.548358\pi$
$223$	−4.51989	−0.302675	−0.151337	+	0.988482i	$0.548358\pi$
$224$	44.8126	2.99416
$225$	−14.2562	−0.950414
$226$	−18.2353	−1.21300
$227$	4.06257	0.269642	0.134821	−	0.990870i	$-0.456954\pi$
$227$	4.06257	0.269642	0.134821	+	0.990870i	$0.456954\pi$
$228$	−42.8376	−2.83699
$229$	−2.74703	−0.181529	−0.0907644	−	0.995872i	$-0.528931\pi$
$229$	−2.74703	−0.181529	−0.0907644	+	0.995872i	$0.528931\pi$
$230$	−1.84695	−0.121784
$231$	−15.1553	−0.997146
$232$	5.16535	0.339122
$233$	10.1238	0.663235	0.331617	−	0.943414i	$-0.392406\pi$
$233$	10.1238	0.663235	0.331617	+	0.943414i	$0.392406\pi$
$234$	−4.13853	−0.270544
$235$	−28.4932	−1.85869
$236$	−8.20804	−0.534298
$237$	−7.95941	−0.517019
$238$	8.01981	0.519847
$239$	6.02458	0.389697	0.194849	−	0.980833i	$-0.437578\pi$
$239$	6.02458	0.389697	0.194849	+	0.980833i	$0.437578\pi$
$240$	−53.6809	−3.46508
$241$	−10.7384	−0.691724	−0.345862	−	0.938285i	$-0.612413\pi$
$241$	−10.7384	−0.691724	−0.345862	+	0.938285i	$0.612413\pi$
$242$	−18.2685	−1.17434
$243$	14.1078	0.905016
$244$	18.6741	1.19549
$245$	−7.11161	−0.454344
$246$	13.8732	0.884525
$247$	6.97539	0.443833
$248$	−23.1442	−1.46966
$249$	6.21219	0.393682
$250$	41.9769	2.65485
$251$	−14.2380	−0.898696	−0.449348	−	0.893357i	$-0.648344\pi$
$251$	−14.2380	−0.898696	−0.449348	+	0.893357i	$0.648344\pi$
$252$	23.6296	1.48852
$253$	−0.777462	−0.0488786
$254$	8.57371	0.537962
$255$	−4.57228	−0.286327
$256$	3.42166	0.213854
$257$	−21.9012	−1.36616	−0.683079	−	0.730345i	$-0.739359\pi$
$257$	−21.9012	−1.36616	−0.683079	+	0.730345i	$0.739359\pi$
$258$	−24.6903	−1.53715
$259$	4.42770	0.275124
$260$	19.2237	1.19220
$261$	0.969125	0.0599873
$262$	−38.8565	−2.40056
$263$	10.8672	0.670100	0.335050	−	0.942200i	$-0.391247\pi$
$263$	10.8672	0.670100	0.335050	+	0.942200i	$0.391247\pi$
$264$	−42.0673	−2.58906
$265$	−49.9251	−3.06687
$266$	−55.4311	−3.39870
$267$	−10.3436	−0.633016
$268$	−27.1792	−1.66023
$269$	19.4081	1.18333	0.591666	−	0.806183i	$-0.298471\pi$
$269$	19.4081	1.18333	0.591666	+	0.806183i	$0.298471\pi$
$270$	−54.9782	−3.34587
$271$	6.42397	0.390228	0.195114	−	0.980781i	$-0.437492\pi$
$271$	6.42397	0.390228	0.195114	+	0.980781i	$0.437492\pi$
$272$	11.9576	0.725036
$273$	3.58674	0.217079
$274$	22.2093	1.34171
$275$	38.7968	2.33954
$276$	−1.12998	−0.0680170
$277$	−3.51928	−0.211453	−0.105726	−	0.994395i	$-0.533717\pi$
$277$	−3.51928	−0.211453	−0.105726	+	0.994395i	$0.533717\pi$
$278$	37.9230	2.27447
$279$	−4.34233	−0.259968
$280$	−92.9120	−5.55255
$281$	−25.6253	−1.52868	−0.764338	−	0.644816i	$-0.776934\pi$
$281$	−25.6253	−1.52868	−0.764338	+	0.644816i	$0.776934\pi$
$282$	−24.2624	−1.44481
$283$	−11.8030	−0.701617	−0.350809	−	0.936447i	$-0.614093\pi$
$283$	−11.8030	−0.701617	−0.350809	+	0.936447i	$0.614093\pi$
$284$	−16.4206	−0.974383
$285$	31.6026	1.87197
$286$	11.2626	0.665970
$287$	12.8982	0.761359
$288$	23.3378	1.37519
$289$	−15.9815	−0.940089
$290$	−6.26537	−0.367915
$291$	4.20183	0.246316
$292$	41.4508	2.42572
$293$	21.6855	1.26688	0.633441	−	0.773791i	$-0.281642\pi$
$293$	21.6855	1.26688	0.633441	+	0.773791i	$0.281642\pi$
$294$	−6.05565	−0.353173
$295$	6.05531	0.352554
$296$	12.2902	0.714351
$297$	−23.1428	−1.34288
$298$	−58.5159	−3.38973
$299$	0.183999	0.0106409
$300$	56.3882	3.25558
$301$	−22.9551	−1.32311
$302$	46.5301	2.67751
$303$	15.6835	0.900994
$304$	−82.6483	−4.74020
$305$	−13.7765	−0.788837
$306$	4.17662	0.238761
$307$	8.92811	0.509554	0.254777	−	0.967000i	$-0.417998\pi$
$307$	8.92811	0.509554	0.254777	+	0.967000i	$0.417998\pi$
$308$	−64.3054	−3.66414
$309$	−15.9181	−0.905551
$310$	28.0730	1.59444
$311$	−20.0115	−1.13475	−0.567375	−	0.823460i	$-0.692041\pi$
$311$	−20.0115	−1.13475	−0.567375	+	0.823460i	$0.692041\pi$
$312$	9.95588	0.563641
$313$	−1.96184	−0.110890	−0.0554450	−	0.998462i	$-0.517658\pi$
$313$	−1.96184	−0.110890	−0.0554450	+	0.998462i	$0.517658\pi$
$314$	20.3419	1.14796
$315$	−17.4322	−0.982193
$316$	−33.7725	−1.89985
$317$	16.8968	0.949017	0.474509	−	0.880251i	$-0.342626\pi$
$317$	16.8968	0.949017	0.474509	+	0.880251i	$0.342626\pi$
$318$	−42.5120	−2.38396
$319$	−2.63737	−0.147665
$320$	−61.6377	−3.44565
$321$	1.43452	0.0800673
$322$	−1.46218	−0.0814839
$323$	−7.03959	−0.391693
$324$	−9.85893	−0.547718
$325$	−9.18187	−0.509319
$326$	−30.3461	−1.68072
$327$	16.4921	0.912018
$328$	35.8022	1.97685
$329$	−22.5573	−1.24362
$330$	51.0260	2.80889
$331$	−26.8452	−1.47555	−0.737774	−	0.675048i	$-0.764123\pi$
$331$	−26.8452	−1.47555	−0.737774	+	0.675048i	$0.764123\pi$
$332$	26.3589	1.44663
$333$	2.30589	0.126362
$334$	−36.3361	−1.98822
$335$	20.0509	1.09550
$336$	−42.4977	−2.31844
$337$	14.3773	0.783180	0.391590	−	0.920140i	$-0.371925\pi$
$337$	14.3773	0.783180	0.391590	+	0.920140i	$0.371925\pi$
$338$	−2.66546	−0.144982
$339$	8.23054	0.447022
$340$	−19.4006	−1.05215
$341$	11.8172	0.639937
$342$	−28.8678	−1.56099
$343$	15.2394	0.822848
$344$	−63.7176	−3.43542
$345$	0.833620	0.0448806
$346$	−22.6701	−1.21875
$347$	−18.4782	−0.991960	−0.495980	−	0.868334i	$-0.665191\pi$
$347$	−18.4782	−0.991960	−0.495980	+	0.868334i	$0.665191\pi$
$348$	−3.83322	−0.205482
$349$	−24.8530	−1.33035	−0.665177	−	0.746686i	$-0.731644\pi$
$349$	−24.8530	−1.33035	−0.665177	+	0.746686i	$0.731644\pi$
$350$	72.9653	3.90016
$351$	5.47711	0.292346
$352$	−63.5114	−3.38517
$353$	26.7337	1.42289	0.711445	−	0.702742i	$-0.248041\pi$
$353$	26.7337	1.42289	0.711445	+	0.702742i	$0.248041\pi$
$354$	5.15620	0.274049
$355$	12.1139	0.642941
$356$	−43.8887	−2.32610
$357$	−3.61975	−0.191577
$358$	−20.0501	−1.05968
$359$	−20.2552	−1.06903	−0.534513	−	0.845160i	$-0.679505\pi$
$359$	−20.2552	−1.06903	−0.534513	+	0.845160i	$0.679505\pi$
$360$	−48.3874	−2.55024
$361$	29.6560	1.56084
$362$	−15.4293	−0.810945
$363$	8.24548	0.432776
$364$	15.2189	0.797686
$365$	−30.5794	−1.60060
$366$	−11.7309	−0.613183
$367$	10.3417	0.539832	0.269916	−	0.962884i	$-0.413004\pi$
$367$	10.3417	0.539832	0.269916	+	0.962884i	$0.413004\pi$
$368$	−2.18012	−0.113646
$369$	6.71723	0.349685
$370$	−14.9075	−0.775004
$371$	−39.5243	−2.05200
$372$	17.1754	0.890503
$373$	−24.4486	−1.26590	−0.632951	−	0.774192i	$-0.718157\pi$
$373$	−24.4486	−1.26590	−0.632951	+	0.774192i	$0.718157\pi$
$374$	−11.3662	−0.587734
$375$	−18.9463	−0.978383
$376$	−62.6134	−3.22904
$377$	0.624176	0.0321467
$378$	−43.5248	−2.23867
$379$	−25.7339	−1.32186	−0.660931	−	0.750447i	$-0.729838\pi$
$379$	−25.7339	−1.32186	−0.660931	+	0.750447i	$0.729838\pi$
$380$	134.093	6.87881
$381$	−3.86975	−0.198253
$382$	62.2550	3.18524
$383$	5.40669	0.276269	0.138135	−	0.990413i	$-0.455889\pi$
$383$	5.40669	0.276269	0.138135	+	0.990413i	$0.455889\pi$
$384$	−16.3193	−0.832789
$385$	47.4399	2.41776
$386$	65.6956	3.34382
$387$	−11.9547	−0.607693
$388$	17.8288	0.905119
$389$	−16.6649	−0.844942	−0.422471	−	0.906376i	$-0.638837\pi$
$389$	−16.6649	−0.844942	−0.422471	+	0.906376i	$0.638837\pi$
$390$	−12.0761	−0.611497
$391$	−0.185692	−0.00939085
$392$	−15.6276	−0.789315
$393$	17.5379	0.884671
$394$	−16.5523	−0.833895
$395$	24.9150	1.25361
$396$	−33.4894	−1.68291
$397$	−0.291144	−0.0146121	−0.00730606	−	0.999973i	$-0.502326\pi$
$397$	−0.291144	−0.0146121	−0.00730606	+	0.999973i	$0.502326\pi$
$398$	−50.7975	−2.54625
$399$	25.0189	1.25251
$400$	108.792	5.43960
$401$	−3.09330	−0.154472	−0.0772361	−	0.997013i	$-0.524610\pi$
$401$	−3.09330	−0.154472	−0.0772361	+	0.997013i	$0.524610\pi$
$402$	17.0737	0.851557
$403$	−2.79672	−0.139315
$404$	66.5466	3.31082
$405$	7.27321	0.361409
$406$	−4.96012	−0.246167
$407$	−6.27524	−0.311052
$408$	−10.0475	−0.497426
$409$	32.3877	1.60147	0.800735	−	0.599019i	$-0.204443\pi$
$409$	32.3877	1.60147	0.800735	+	0.599019i	$0.204443\pi$
$410$	−43.4267	−2.14469
$411$	−10.0242	−0.494456
$412$	−67.5422	−3.32756
$413$	4.79382	0.235889
$414$	−0.761483	−0.0374248
$415$	−19.4457	−0.954554
$416$	15.0310	0.736954
$417$	−17.1166	−0.838203
$418$	78.5608	3.84254
$419$	17.6139	0.860494	0.430247	−	0.902711i	$-0.358427\pi$
$419$	17.6139	0.860494	0.430247	+	0.902711i	$0.358427\pi$
$420$	68.9504	3.36443
$421$	−18.2660	−0.890233	−0.445116	−	0.895473i	$-0.646838\pi$
$421$	−18.2660	−0.890233	−0.445116	+	0.895473i	$0.646838\pi$
$422$	−20.1000	−0.978452
$423$	−11.7476	−0.571186
$424$	−109.709	−5.32796
$425$	9.26638	0.449485
$426$	10.3152	0.499774
$427$	−10.9064	−0.527800
$428$	6.08682	0.294218
$429$	−5.08337	−0.245428
$430$	77.2871	3.72711
$431$	6.32392	0.304612	0.152306	−	0.988333i	$-0.451330\pi$
$431$	6.32392	0.304612	0.152306	+	0.988333i	$0.451330\pi$
$432$	−64.8958	−3.12230
$433$	12.2563	0.589001	0.294501	−	0.955651i	$-0.404847\pi$
$433$	12.2563	0.589001	0.294501	+	0.955651i	$0.404847\pi$
$434$	22.2247	1.06682
$435$	2.82788	0.135586
$436$	69.9778	3.35133
$437$	1.28346	0.0613963
$438$	−26.0389	−1.24419
$439$	15.4616	0.737940	0.368970	−	0.929441i	$-0.379710\pi$
$439$	15.4616	0.737940	0.368970	+	0.929441i	$0.379710\pi$
$440$	131.681	6.27766
$441$	−2.93207	−0.139622
$442$	2.69000	0.127950
$443$	−31.2966	−1.48695	−0.743473	−	0.668766i	$-0.766823\pi$
$443$	−31.2966	−1.48695	−0.743473	+	0.668766i	$0.766823\pi$
$444$	−9.12058	−0.432844
$445$	32.3780	1.53486
$446$	12.0476	0.570471
$447$	26.4112	1.24921
$448$	−48.7969	−2.30544
$449$	5.07356	0.239436	0.119718	−	0.992808i	$-0.461801\pi$
$449$	5.07356	0.239436	0.119718	+	0.992808i	$0.461801\pi$
$450$	37.9994	1.79131
$451$	−18.2803	−0.860784
$452$	34.9230	1.64264
$453$	−21.0014	−0.986733
$454$	−10.8286	−0.508213
$455$	−11.2274	−0.526349
$456$	69.4461	3.25211
$457$	17.0198	0.796153	0.398076	−	0.917352i	$-0.369678\pi$
$457$	17.0198	0.796153	0.398076	+	0.917352i	$0.369678\pi$
$458$	7.32211	0.342140
$459$	−5.52752	−0.258002
$460$	3.53713	0.164920
$461$	38.4512	1.79085	0.895424	−	0.445214i	$-0.146872\pi$
$461$	38.4512	1.79085	0.895424	+	0.445214i	$0.146872\pi$
$462$	40.3959	1.87939
$463$	−25.1778	−1.17011	−0.585056	−	0.810993i	$-0.698927\pi$
$463$	−25.1778	−1.17011	−0.585056	+	0.810993i	$0.698927\pi$
$464$	−7.39558	−0.343331
$465$	−12.6708	−0.587594
$466$	−26.9847	−1.25004
$467$	14.3613	0.664560	0.332280	−	0.943181i	$-0.392182\pi$
$467$	14.3613	0.664560	0.332280	+	0.943181i	$0.392182\pi$
$468$	7.92580	0.366370
$469$	15.8737	0.732981
$470$	75.9476	3.50320
$471$	−9.18133	−0.423053
$472$	13.3064	0.612479
$473$	32.5336	1.49590
$474$	21.2155	0.974461
$475$	−64.0471	−2.93868
$476$	−15.3590	−0.703976
$477$	−20.5838	−0.942465
$478$	−16.0583	−0.734489
$479$	−31.4156	−1.43542	−0.717708	−	0.696344i	$-0.754809\pi$
$479$	−31.4156	−1.43542	−0.717708	+	0.696344i	$0.754809\pi$
$480$	68.0991	3.10828
$481$	1.48513	0.0677162
$482$	28.6229	1.30374
$483$	0.659955	0.0300290
$484$	34.9864	1.59029
$485$	−13.1528	−0.597238
$486$	−37.6038	−1.70574
$487$	33.3583	1.51161	0.755804	−	0.654798i	$-0.227246\pi$
$487$	33.3583	1.51161	0.755804	+	0.654798i	$0.227246\pi$
$488$	−30.2735	−1.37042
$489$	13.6967	0.619388
$490$	18.9557	0.856333
$491$	−27.2180	−1.22833	−0.614165	−	0.789178i	$-0.710507\pi$
$491$	−27.2180	−1.22833	−0.614165	+	0.789178i	$0.710507\pi$
$492$	−26.5690	−1.19782
$493$	−0.629921	−0.0283702
$494$	−18.5926	−0.836523
$495$	24.7061	1.11046
$496$	33.1372	1.48790
$497$	9.59028	0.430183
$498$	−16.5584	−0.741999
$499$	−42.0844	−1.88396	−0.941979	−	0.335672i	$-0.891037\pi$
$499$	−42.0844	−1.88396	−0.941979	+	0.335672i	$0.891037\pi$
$500$	−80.3910	−3.59520
$501$	16.4003	0.732714
$502$	37.9509	1.69383
$503$	−5.97410	−0.266372	−0.133186	−	0.991091i	$-0.542521\pi$
$503$	−5.97410	−0.266372	−0.133186	+	0.991091i	$0.542521\pi$
$504$	−38.3070	−1.70633
$505$	−49.0933	−2.18463
$506$	2.07230	0.0921249
$507$	1.20306	0.0534298
$508$	−16.4197	−0.728508
$509$	15.5420	0.688885	0.344443	−	0.938807i	$-0.388068\pi$
$509$	15.5420	0.688885	0.344443	+	0.938807i	$0.388068\pi$
$510$	12.1872	0.539660
$511$	−24.2089	−1.07094
$512$	18.0093	0.795905
$513$	38.2049	1.68679
$514$	58.3768	2.57489
$515$	49.8278	2.19568
$516$	47.2851	2.08161
$517$	31.9698	1.40603
$518$	−11.8019	−0.518544
$519$	10.2322	0.449143
$520$	−31.1644	−1.36665
$521$	−32.9927	−1.44544	−0.722719	−	0.691142i	$-0.757108\pi$
$521$	−32.9927	−1.44544	−0.722719	+	0.691142i	$0.757108\pi$
$522$	−2.58317	−0.113062
$523$	0.276737	0.0121008	0.00605042	−	0.999982i	$-0.498074\pi$
$523$	0.276737	0.0121008	0.00605042	+	0.999982i	$0.498074\pi$
$524$	74.4151	3.25084
$525$	−32.9330	−1.43731
$526$	−28.9661	−1.26298
$527$	2.82246	0.122948
$528$	60.2306	2.62120
$529$	−22.9661	−0.998528
$530$	133.073	5.78034
$531$	2.49656	0.108342
$532$	106.158	4.60251
$533$	4.32631	0.187393
$534$	27.5704	1.19309
$535$	−4.49042	−0.194138
$536$	44.0615	1.90317
$537$	9.04964	0.390521
$538$	−51.7315	−2.23030
$539$	7.97932	0.343694
$540$	105.290	4.53097
$541$	38.1387	1.63971	0.819856	−	0.572569i	$-0.194053\pi$
$541$	38.1387	1.63971	0.819856	+	0.572569i	$0.194053\pi$
$542$	−17.1229	−0.735490
$543$	6.96402	0.298855
$544$	−15.1693	−0.650379
$545$	−51.6246	−2.21136
$546$	−9.56032	−0.409144
$547$	−6.85327	−0.293025	−0.146512	−	0.989209i	$-0.546805\pi$
$547$	−6.85327	−0.293025	−0.146512	+	0.989209i	$0.546805\pi$
$548$	−42.5336	−1.81694
$549$	−5.67994	−0.242414
$550$	−103.412	−4.40948
$551$	4.35387	0.185481
$552$	1.83187	0.0779694
$553$	19.7245	0.838771
$554$	9.38051	0.398540
$555$	6.72852	0.285610
$556$	−72.6273	−3.08008
$557$	−22.6247	−0.958639	−0.479319	−	0.877641i	$-0.659116\pi$
$557$	−22.6247	−0.958639	−0.479319	+	0.877641i	$0.659116\pi$
$558$	11.5743	0.489980
$559$	−7.69958	−0.325658
$560$	133.029	5.62148
$561$	5.13016	0.216595
$562$	68.3033	2.88120
$563$	29.4938	1.24302	0.621509	−	0.783407i	$-0.286520\pi$
$563$	29.4938	1.24302	0.621509	+	0.783407i	$0.286520\pi$
$564$	46.4656	1.95656
$565$	−25.7637	−1.08389
$566$	31.4605	1.32239
$567$	5.75801	0.241814
$568$	26.6202	1.11696
$569$	−45.1497	−1.89278	−0.946388	−	0.323033i	$-0.895297\pi$
$569$	−45.1497	−1.89278	−0.946388	+	0.323033i	$0.895297\pi$
$570$	−84.2355	−3.52824
$571$	−11.9477	−0.499995	−0.249998	−	0.968246i	$-0.580430\pi$
$571$	−11.9477	−0.499995	−0.249998	+	0.968246i	$0.580430\pi$
$572$	−21.5692	−0.901856
$573$	−28.0988	−1.17385
$574$	−34.3798	−1.43498
$575$	−1.68945	−0.0704550
$576$	−25.4128	−1.05887
$577$	−37.3576	−1.55522	−0.777609	−	0.628748i	$-0.783568\pi$
$577$	−37.3576	−1.55522	−0.777609	+	0.628748i	$0.783568\pi$
$578$	42.5981	1.77185
$579$	−29.6518	−1.23229
$580$	11.9990	0.498230
$581$	−15.3947	−0.638678
$582$	−11.1998	−0.464248
$583$	56.0166	2.31997
$584$	−67.1978	−2.78066
$585$	−5.84709	−0.241747
$586$	−57.8020	−2.38778
$587$	−43.4141	−1.79189	−0.895946	−	0.444163i	$-0.853501\pi$
$587$	−43.4141	−1.79189	−0.895946	+	0.444163i	$0.853501\pi$
$588$	11.5973	0.478266
$589$	−19.5082	−0.803823
$590$	−16.1402	−0.664482
$591$	7.47091	0.307312
$592$	−17.5967	−0.723219
$593$	−16.8739	−0.692929	−0.346464	−	0.938063i	$-0.612618\pi$
$593$	−16.8739	−0.692929	−0.346464	+	0.938063i	$0.612618\pi$
$594$	61.6863	2.53102
$595$	11.3307	0.464515
$596$	112.065	4.59037
$597$	22.9275	0.938360
$598$	−0.490442	−0.0200556
$599$	−31.0767	−1.26976	−0.634880	−	0.772611i	$-0.718950\pi$
$599$	−31.0767	−1.26976	−0.634880	+	0.772611i	$0.718950\pi$
$600$	−91.4136	−3.73194
$601$	40.8892	1.66790	0.833952	−	0.551837i	$-0.186073\pi$
$601$	40.8892	1.66790	0.833952	+	0.551837i	$0.186073\pi$
$602$	61.1861	2.49376
$603$	8.26684	0.336652
$604$	−89.1111	−3.62588
$605$	−25.8105	−1.04934
$606$	−41.8038	−1.69816
$607$	23.7699	0.964789	0.482395	−	0.875954i	$-0.339767\pi$
$607$	23.7699	0.964789	0.482395	+	0.875954i	$0.339767\pi$
$608$	104.847	4.25210
$609$	2.23876	0.0907189
$610$	36.7206	1.48678
$611$	−7.56614	−0.306093
$612$	−7.99874	−0.323330
$613$	−14.1485	−0.571453	−0.285726	−	0.958311i	$-0.592235\pi$
$613$	−14.1485	−0.571453	−0.285726	+	0.958311i	$0.592235\pi$
$614$	−23.7975	−0.960391
$615$	19.6007	0.790377
$616$	104.248	4.20029
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	42.4292	1.70675
$619$	−30.3947	−1.22167	−0.610833	−	0.791760i	$-0.709165\pi$
$619$	−30.3947	−1.22167	−0.610833	+	0.791760i	$0.709165\pi$
$620$	−53.7634	−2.15919
$621$	1.00778	0.0404408
$622$	53.3400	2.13874
$623$	25.6328	1.02696
$624$	−14.2545	−0.570638
$625$	13.3974	0.535896
$626$	5.22922	0.209002
$627$	−35.4585	−1.41608
$628$	−38.9573	−1.55456
$629$	−1.49880	−0.0597611
$630$	46.4649	1.85121
$631$	−20.1376	−0.801664	−0.400832	−	0.916152i	$-0.631279\pi$
$631$	−20.1376	−0.801664	−0.400832	+	0.916152i	$0.631279\pi$
$632$	54.7502	2.17785
$633$	9.07215	0.360586
$634$	−45.0377	−1.78868
$635$	12.1133	0.480702
$636$	81.4159	3.22835
$637$	−1.88843	−0.0748223
$638$	7.02983	0.278314
$639$	4.99450	0.197579
$640$	51.0834	2.01925
$641$	−1.25884	−0.0497212	−0.0248606	−	0.999691i	$-0.507914\pi$
$641$	−1.25884	−0.0497212	−0.0248606	+	0.999691i	$0.507914\pi$
$642$	−3.82367	−0.150908
$643$	−10.1200	−0.399093	−0.199546	−	0.979888i	$-0.563947\pi$
$643$	−10.1200	−0.399093	−0.199546	+	0.979888i	$0.563947\pi$
$644$	2.80025	0.110345
$645$	−34.8836	−1.37354
$646$	18.7638	0.738250
$647$	14.2708	0.561041	0.280521	−	0.959848i	$-0.409493\pi$
$647$	14.2708	0.561041	0.280521	+	0.959848i	$0.409493\pi$
$648$	15.9828	0.627862
$649$	−6.79414	−0.266693
$650$	24.4739	0.959947
$651$	−10.0311	−0.393151
$652$	58.1166	2.27602
$653$	−2.32792	−0.0910986	−0.0455493	−	0.998962i	$-0.514504\pi$
$653$	−2.32792	−0.0910986	−0.0455493	+	0.998962i	$0.514504\pi$
$654$	−43.9592	−1.71894
$655$	−54.8981	−2.14505
$656$	−51.2605	−2.00139
$657$	−12.6077	−0.491873
$658$	60.1257	2.34394
$659$	21.2004	0.825850	0.412925	−	0.910765i	$-0.364507\pi$
$659$	21.2004	0.825850	0.412925	+	0.910765i	$0.364507\pi$
$660$	−97.7212	−3.80379
$661$	25.0040	0.972543	0.486271	−	0.873808i	$-0.338357\pi$
$661$	25.0040	0.972543	0.486271	+	0.873808i	$0.338357\pi$
$662$	71.5550	2.78106
$663$	−1.21413	−0.0471530
$664$	−42.7317	−1.65831
$665$	−78.3155	−3.03694
$666$	−6.14626	−0.238163
$667$	0.114847	0.00444691
$668$	69.5883	2.69245
$669$	−5.43770	−0.210234
$670$	−53.4449	−2.06476
$671$	15.4574	0.596725
$672$	53.9122	2.07971
$673$	5.05472	0.194845	0.0974225	−	0.995243i	$-0.468940\pi$
$673$	5.05472	0.194845	0.0974225	+	0.995243i	$0.468940\pi$
$674$	−38.3221	−1.47611
$675$	−50.2901	−1.93567
$676$	5.10470	0.196335
$677$	−6.16768	−0.237043	−0.118522	−	0.992951i	$-0.537815\pi$
$677$	−6.16768	−0.237043	−0.118522	+	0.992951i	$0.537815\pi$
$678$	−21.9382	−0.842532
$679$	−10.4127	−0.399603
$680$	31.4513	1.20610
$681$	4.88752	0.187290
$682$	−31.4983	−1.20613
$683$	8.01944	0.306855	0.153428	−	0.988160i	$-0.450969\pi$
$683$	8.01944	0.306855	0.153428	+	0.988160i	$0.450969\pi$
$684$	55.2855	2.11389
$685$	31.3782	1.19890
$686$	−40.6200	−1.55088
$687$	−3.30484	−0.126088
$688$	91.2289	3.47807
$689$	−13.2572	−0.505059
$690$	−2.22199	−0.0845895
$691$	4.94694	0.188190	0.0940952	−	0.995563i	$-0.470004\pi$
$691$	4.94694	0.188190	0.0940952	+	0.995563i	$0.470004\pi$
$692$	43.4161	1.65043
$693$	19.5592	0.742991
$694$	49.2529	1.86961
$695$	53.5793	2.03238
$696$	6.21422	0.235549
$697$	−4.36613	−0.165379
$698$	66.2449	2.50741
$699$	12.1796	0.460674
$700$	−139.738	−5.28159
$701$	−22.1711	−0.837392	−0.418696	−	0.908126i	$-0.637513\pi$
$701$	−22.1711	−0.837392	−0.418696	+	0.908126i	$0.637513\pi$
$702$	−14.5990	−0.551005
$703$	10.3594	0.390711
$704$	69.1584	2.60650
$705$	−34.2790	−1.29102
$706$	−71.2577	−2.68182
$707$	−38.8659	−1.46170
$708$	−9.87477	−0.371116
$709$	25.8348	0.970248	0.485124	−	0.874446i	$-0.338775\pi$
$709$	25.8348	0.970248	0.485124	+	0.874446i	$0.338775\pi$
$710$	−32.2893	−1.21180
$711$	10.2723	0.385240
$712$	71.1501	2.66646
$713$	−0.514593	−0.0192717
$714$	9.64831	0.361079
$715$	15.9123	0.595084
$716$	38.3985	1.43502
$717$	7.24793	0.270679
$718$	53.9894	2.01487
$719$	49.6907	1.85315	0.926575	−	0.376110i	$-0.122738\pi$
$719$	49.6907	1.85315	0.926575	+	0.376110i	$0.122738\pi$
$720$	69.2796	2.58190
$721$	39.4473	1.46909
$722$	−79.0471	−2.94183
$723$	−12.9190	−0.480462
$724$	29.5490	1.09818
$725$	−5.73110	−0.212848
$726$	−21.9780	−0.815681
$727$	24.9393	0.924946	0.462473	−	0.886633i	$-0.346962\pi$
$727$	24.9393	0.924946	0.462473	+	0.886633i	$0.346962\pi$
$728$	−24.6720	−0.914406
$729$	22.7666	0.843206
$730$	81.5083	3.01676
$731$	7.77045	0.287400
$732$	22.4661	0.830371
$733$	15.2614	0.563691	0.281845	−	0.959460i	$-0.409053\pi$
$733$	15.2614	0.563691	0.281845	+	0.959460i	$0.409053\pi$
$734$	−27.5654	−1.01746
$735$	−8.55569	−0.315581
$736$	2.76568	0.101944
$737$	−22.4974	−0.828701
$738$	−17.9045	−0.659076
$739$	−36.6495	−1.34817	−0.674087	−	0.738652i	$-0.735463\pi$
$739$	−36.6495	−1.34817	−0.674087	+	0.738652i	$0.735463\pi$
$740$	28.5497	1.04951
$741$	8.39181	0.308281
$742$	105.351	3.86754
$743$	15.6771	0.575135	0.287568	−	0.957760i	$-0.407153\pi$
$743$	15.6771	0.575135	0.287568	+	0.957760i	$0.407153\pi$
$744$	−27.8438	−1.02081
$745$	−82.6738	−3.02893
$746$	65.1669	2.38593
$747$	−8.01734	−0.293339
$748$	21.7678	0.795908
$749$	−3.55495	−0.129895
$750$	50.5007	1.84403
$751$	−22.7667	−0.830770	−0.415385	−	0.909646i	$-0.636353\pi$
$751$	−22.7667	−0.830770	−0.415385	+	0.909646i	$0.636353\pi$
$752$	89.6479	3.26912
$753$	−17.1292	−0.624222
$754$	−1.66372	−0.0605890
$755$	65.7398	2.39252
$756$	83.3554	3.03161
$757$	−47.1088	−1.71220	−0.856100	−	0.516810i	$-0.827119\pi$
$757$	−47.1088	−1.71220	−0.856100	+	0.516810i	$0.827119\pi$
$758$	68.5928	2.49140
$759$	−0.935333	−0.0339505
$760$	−217.384	−7.88534
$761$	−12.3258	−0.446811	−0.223405	−	0.974726i	$-0.571717\pi$
$761$	−12.3258	−0.446811	−0.223405	+	0.974726i	$0.571717\pi$
$762$	10.3147	0.373662
$763$	−40.8698	−1.47959
$764$	−119.226	−4.31345
$765$	5.90090	0.213348
$766$	−14.4113	−0.520703
$767$	1.60794	0.0580593
$768$	4.11646	0.148540
$769$	−12.7825	−0.460950	−0.230475	−	0.973078i	$-0.574028\pi$
$769$	−12.7825	−0.460950	−0.230475	+	0.973078i	$0.574028\pi$
$770$	−126.449	−4.55692
$771$	−26.3484	−0.948915
$772$	−125.815	−4.52819
$773$	−2.22766	−0.0801232	−0.0400616	−	0.999197i	$-0.512755\pi$
$773$	−2.22766	−0.0801232	−0.0400616	+	0.999197i	$0.512755\pi$
$774$	31.8649	1.14536
$775$	25.6792	0.922423
$776$	−28.9031	−1.03756
$777$	5.32678	0.191097
$778$	44.4196	1.59252
$779$	30.1777	1.08123
$780$	23.1273	0.828089
$781$	−13.5920	−0.486360
$782$	0.494955	0.0176996
$783$	3.41868	0.122174
$784$	22.3752	0.799114
$785$	28.7399	1.02577
$786$	−46.7467	−1.66740
$787$	−0.970357	−0.0345895	−0.0172948	−	0.999850i	$-0.505505\pi$
$787$	−0.970357	−0.0345895	−0.0172948	+	0.999850i	$0.505505\pi$
$788$	31.6998	1.12926
$789$	13.0739	0.465443
$790$	−66.4099	−2.36276
$791$	−20.3964	−0.725213
$792$	54.2913	1.92916
$793$	−3.65823	−0.129907
$794$	0.776035	0.0275405
$795$	−60.0628	−2.13021
$796$	97.2836	3.44813
$797$	−39.1689	−1.38743	−0.693717	−	0.720248i	$-0.744028\pi$
$797$	−39.1689	−1.38743	−0.693717	+	0.720248i	$0.744028\pi$
$798$	−66.6870	−2.36069
$799$	7.63578	0.270135
$800$	−138.012	−4.87948
$801$	13.3492	0.471671
$802$	8.24509	0.291144
$803$	34.3105	1.21079
$804$	−32.6982	−1.15318
$805$	−2.06583	−0.0728108
$806$	7.45457	0.262576
$807$	23.3491	0.821926
$808$	−107.882	−3.79527
$809$	−2.57379	−0.0904898	−0.0452449	−	0.998976i	$-0.514407\pi$
$809$	−2.57379	−0.0904898	−0.0452449	+	0.998976i	$0.514407\pi$
$810$	−19.3865	−0.681172
$811$	−18.5552	−0.651563	−0.325781	−	0.945445i	$-0.605627\pi$
$811$	−18.5552	−0.651563	−0.325781	+	0.945445i	$0.605627\pi$
$812$	9.49926	0.333359
$813$	7.72842	0.271048
$814$	16.7264	0.586261
$815$	−42.8743	−1.50182
$816$	14.3857	0.503601
$817$	−53.7076	−1.87899
$818$	−86.3283	−3.01840
$819$	−4.62898	−0.161750
$820$	83.1677	2.90434
$821$	−36.5921	−1.27707	−0.638536	−	0.769592i	$-0.720460\pi$
$821$	−36.5921	−1.27707	−0.638536	+	0.769592i	$0.720460\pi$
$822$	26.7191	0.931936
$823$	−6.13004	−0.213680	−0.106840	−	0.994276i	$-0.534073\pi$
$823$	−6.13004	−0.213680	−0.106840	+	0.994276i	$0.534073\pi$
$824$	109.496	3.81447
$825$	46.6749	1.62501
$826$	−12.7778	−0.444595
$827$	−40.9214	−1.42298	−0.711488	−	0.702698i	$-0.751978\pi$
$827$	−40.9214	−1.42298	−0.711488	+	0.702698i	$0.751978\pi$
$828$	1.45834	0.0506807
$829$	−31.7328	−1.10212	−0.551062	−	0.834464i	$-0.685777\pi$
$829$	−31.7328	−1.10212	−0.551062	+	0.834464i	$0.685777\pi$
$830$	51.8319	1.79911
$831$	−4.23390	−0.146872
$832$	−16.3674	−0.567438
$833$	1.90581	0.0660324
$834$	45.6236	1.57982
$835$	−51.3373	−1.77660
$836$	−150.454	−5.20356
$837$	−15.3180	−0.529466
$838$	−46.9491	−1.62183
$839$	44.5593	1.53836	0.769179	−	0.639034i	$-0.220666\pi$
$839$	44.5593	1.53836	0.769179	+	0.639034i	$0.220666\pi$
$840$	−111.779	−3.85673
$841$	−28.6104	−0.986566
$842$	48.6875	1.67788
$843$	−30.8287	−1.06180
$844$	38.4940	1.32502
$845$	−3.76588	−0.129550
$846$	31.3127	1.07655
$847$	−20.4334	−0.702101
$848$	157.079	5.39410
$849$	−14.1997	−0.487334
$850$	−24.6992	−0.847176
$851$	0.273262	0.00936731
$852$	−19.7550	−0.676794
$853$	36.3239	1.24371	0.621853	−	0.783134i	$-0.286380\pi$
$853$	36.3239	1.24371	0.621853	+	0.783134i	$0.286380\pi$
$854$	29.0707	0.994780
$855$	−40.7857	−1.39484
$856$	−9.86763	−0.337269
$857$	−29.7146	−1.01503	−0.507516	−	0.861642i	$-0.669436\pi$
$857$	−29.7146	−1.01503	−0.507516	+	0.861642i	$0.669436\pi$
$858$	13.5495	0.462574
$859$	−52.6214	−1.79542	−0.897709	−	0.440589i	$-0.854769\pi$
$859$	−52.6214	−1.79542	−0.897709	+	0.440589i	$0.854769\pi$
$860$	−148.014	−5.04725
$861$	15.5173	0.528830
$862$	−16.8562	−0.574124
$863$	36.4827	1.24188	0.620942	−	0.783856i	$-0.286750\pi$
$863$	36.4827	1.24188	0.620942	+	0.783856i	$0.286750\pi$
$864$	82.3262	2.80080
$865$	−32.0293	−1.08903
$866$	−32.6688	−1.11013
$867$	−19.2267	−0.652973
$868$	−42.5630	−1.44468
$869$	−27.9549	−0.948306
$870$	−7.53761	−0.255549
$871$	5.32435	0.180409
$872$	−113.444	−3.84171
$873$	−5.42281	−0.183534
$874$	−3.42102	−0.115718
$875$	46.9516	1.58725
$876$	49.8678	1.68488
$877$	36.8245	1.24347	0.621737	−	0.783226i	$-0.286427\pi$
$877$	36.8245	1.24347	0.621737	+	0.783226i	$0.286427\pi$
$878$	−41.2122	−1.39085
$879$	26.0890	0.879960
$880$	−188.537	−6.35559
$881$	−6.17428	−0.208017	−0.104008	−	0.994576i	$-0.533167\pi$
$881$	−6.17428	−0.208017	−0.104008	+	0.994576i	$0.533167\pi$
$882$	7.81532	0.263155
$883$	23.1169	0.777945	0.388972	−	0.921249i	$-0.372830\pi$
$883$	23.1169	0.777945	0.388972	+	0.921249i	$0.372830\pi$
$884$	−5.15168	−0.173270
$885$	7.28490	0.244879
$886$	83.4199	2.80255
$887$	−49.2547	−1.65381	−0.826905	−	0.562341i	$-0.809901\pi$
$887$	−49.2547	−1.65381	−0.826905	+	0.562341i	$0.809901\pi$
$888$	14.7858	0.496179
$889$	9.58977	0.321631
$890$	−86.3024	−2.89286
$891$	−8.16064	−0.273392
$892$	−23.0727	−0.772531
$893$	−52.7768	−1.76611
$894$	−70.3981	−2.35446
$895$	−28.3277	−0.946890
$896$	40.4414	1.35105
$897$	0.221361	0.00739104
$898$	−13.5234	−0.451281
$899$	−1.74565	−0.0582206
$900$	−72.7737	−2.42579
$901$	13.3792	0.445726
$902$	48.7254	1.62238
$903$	−27.6164	−0.919016
$904$	−56.6153	−1.88300
$905$	−21.7991	−0.724628
$906$	55.9785	1.85976
$907$	25.6304	0.851043	0.425522	−	0.904948i	$-0.360091\pi$
$907$	25.6304	0.851043	0.425522	+	0.904948i	$0.360091\pi$
$908$	20.7382	0.688222
$909$	−20.2408	−0.671347
$910$	29.9262	0.992045
$911$	−24.1082	−0.798741	−0.399370	−	0.916790i	$-0.630771\pi$
$911$	−24.1082	−0.798741	−0.399370	+	0.916790i	$0.630771\pi$
$912$	−99.4308	−3.29248
$913$	21.8184	0.722083
$914$	−45.3657	−1.50056
$915$	−16.5739	−0.547916
$916$	−14.0228	−0.463325
$917$	−43.4614	−1.43522
$918$	14.7334	0.486275
$919$	17.6777	0.583134	0.291567	−	0.956550i	$-0.405823\pi$
$919$	17.6777	0.583134	0.291567	+	0.956550i	$0.405823\pi$
$920$	−5.73421	−0.189051
$921$	10.7410	0.353929
$922$	−102.490	−3.37533
$923$	3.21676	0.105881
$924$	−77.3633	−2.54506
$925$	−13.6363	−0.448359
$926$	67.1105	2.20539
$927$	20.5437	0.674742
$928$	9.38197	0.307978
$929$	−9.15564	−0.300387	−0.150193	−	0.988657i	$-0.547990\pi$
$929$	−9.15564	−0.300387	−0.150193	+	0.988657i	$0.547990\pi$
$930$	33.7735	1.10748
$931$	−13.1725	−0.431712
$932$	51.6792	1.69281
$933$	−24.0751	−0.788182
$934$	−38.2794	−1.25254
$935$	−16.0587	−0.525176
$936$	−12.8489	−0.419979
$937$	46.5639	1.52118	0.760588	−	0.649235i	$-0.224911\pi$
$937$	46.5639	1.52118	0.760588	+	0.649235i	$0.224911\pi$
$938$	−42.3109	−1.38150
$939$	−2.36021	−0.0770227
$940$	−145.449	−4.74403
$941$	16.5134	0.538322	0.269161	−	0.963095i	$-0.413254\pi$
$941$	16.5134	0.538322	0.269161	+	0.963095i	$0.413254\pi$
$942$	24.4725	0.797357
$943$	0.796035	0.0259225
$944$	−19.0518	−0.620082
$945$	−61.4937	−2.00039
$946$	−86.7171	−2.81942
$947$	25.2570	0.820742	0.410371	−	0.911919i	$-0.365399\pi$
$947$	25.2570	0.820742	0.410371	+	0.911919i	$0.365399\pi$
$948$	−40.6304	−1.31961
$949$	−8.12012	−0.263590
$950$	170.715	5.53873
$951$	20.3278	0.659175
$952$	24.8991	0.806985
$953$	7.09903	0.229960	0.114980	−	0.993368i	$-0.463320\pi$
$953$	7.09903	0.229960	0.114980	+	0.993368i	$0.463320\pi$
$954$	54.8653	1.77633
$955$	87.9565	2.84621
$956$	30.7537	0.994644
$957$	−3.17292	−0.102566
$958$	83.7372	2.70543
$959$	24.8413	0.802167
$960$	−74.1539	−2.39331
$961$	−23.1783	−0.747688
$962$	−3.95857	−0.127629
$963$	−1.85137	−0.0596596
$964$	−54.8165	−1.76552
$965$	92.8176	2.98790
$966$	−1.75909	−0.0565977
$967$	−40.4812	−1.30179	−0.650894	−	0.759169i	$-0.725606\pi$
$967$	−40.4812	−1.30179	−0.650894	+	0.759169i	$0.725606\pi$
$968$	−56.7180	−1.82299
$969$	−8.46904	−0.272065
$970$	35.0583	1.12566
$971$	35.0396	1.12448	0.562238	−	0.826976i	$-0.309941\pi$
$971$	35.0396	1.12448	0.562238	+	0.826976i	$0.309941\pi$
$972$	72.0161	2.30992
$973$	42.4172	1.35983
$974$	−88.9153	−2.84903
$975$	−11.0463	−0.353766
$976$	43.3447	1.38743
$977$	−12.9923	−0.415662	−0.207831	−	0.978165i	$-0.566640\pi$
$977$	−12.9923	−0.415662	−0.207831	+	0.978165i	$0.566640\pi$
$978$	−36.5082	−1.16740
$979$	−36.3285	−1.16106
$980$	−36.3026	−1.15964
$981$	−21.2845	−0.679561
$982$	72.5485	2.31512
$983$	8.33816	0.265946	0.132973	−	0.991120i	$-0.457548\pi$
$983$	8.33816	0.265946	0.132973	+	0.991120i	$0.457548\pi$
$984$	43.0722	1.37309
$985$	−23.3859	−0.745135
$986$	1.67903	0.0534712
$987$	−27.1378	−0.863805
$988$	35.6073	1.13282
$989$	−1.41671	−0.0450488
$990$	−65.8533	−2.09295
$991$	−36.4031	−1.15638	−0.578192	−	0.815901i	$-0.696242\pi$
$991$	−36.4031	−1.15638	−0.578192	+	0.815901i	$0.696242\pi$
$992$	−42.0375	−1.33469
$993$	−32.2964	−1.02490
$994$	−25.5626	−0.810795
$995$	−71.7689	−2.27523
$996$	31.7114	1.00481
$997$	−26.8748	−0.851134	−0.425567	−	0.904927i	$-0.639925\pi$
$997$	−26.8748	−0.851134	−0.425567	+	0.904927i	$0.639925\pi$
$998$	112.175	3.55082
$999$	8.13423	0.257356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.3	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.3	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66546 q^{2} +1.20306 q^{3} +5.10470 q^{4} -3.76588 q^{5} -3.20671 q^{6} -2.98135 q^{7} -8.27547 q^{8} -1.55265 q^{9} +O(q^{10})\)	\(q-2.66546 q^{2} +1.20306 q^{3} +5.10470 q^{4} -3.76588 q^{5} -3.20671 q^{6} -2.98135 q^{7} -8.27547 q^{8} -1.55265 q^{9} +10.0378 q^{10} +4.22537 q^{11} +6.14126 q^{12} -1.00000 q^{13} +7.94667 q^{14} -4.53058 q^{15} +11.8486 q^{16} +1.00920 q^{17} +4.13853 q^{18} -6.97539 q^{19} -19.2237 q^{20} -3.58674 q^{21} -11.2626 q^{22} -0.183999 q^{23} -9.95588 q^{24} +9.18187 q^{25} +2.66546 q^{26} -5.47711 q^{27} -15.2189 q^{28} -0.624176 q^{29} +12.0761 q^{30} +2.79672 q^{31} -15.0310 q^{32} +5.08337 q^{33} -2.69000 q^{34} +11.2274 q^{35} -7.92580 q^{36} -1.48513 q^{37} +18.5926 q^{38} -1.20306 q^{39} +31.1644 q^{40} -4.32631 q^{41} +9.56032 q^{42} +7.69958 q^{43} +21.5692 q^{44} +5.84709 q^{45} +0.490442 q^{46} +7.56614 q^{47} +14.2545 q^{48} +1.88843 q^{49} -24.4739 q^{50} +1.21413 q^{51} -5.10470 q^{52} +13.2572 q^{53} +14.5990 q^{54} -15.9123 q^{55} +24.6720 q^{56} -8.39181 q^{57} +1.66372 q^{58} -1.60794 q^{59} -23.1273 q^{60} +3.65823 q^{61} -7.45457 q^{62} +4.62898 q^{63} +16.3674 q^{64} +3.76588 q^{65} -13.5495 q^{66} -5.32435 q^{67} +5.15168 q^{68} -0.221361 q^{69} -29.9262 q^{70} -3.21676 q^{71} +12.8489 q^{72} +8.12012 q^{73} +3.95857 q^{74} +11.0463 q^{75} -35.6073 q^{76} -12.5973 q^{77} +3.20671 q^{78} -6.61597 q^{79} -44.6203 q^{80} -1.93134 q^{81} +11.5316 q^{82} +5.16366 q^{83} -18.3092 q^{84} -3.80054 q^{85} -20.5230 q^{86} -0.750921 q^{87} -34.9669 q^{88} -8.59771 q^{89} -15.5852 q^{90} +2.98135 q^{91} -0.939257 q^{92} +3.36463 q^{93} -20.1673 q^{94} +26.2685 q^{95} -18.0832 q^{96} +3.49262 q^{97} -5.03354 q^{98} -6.56051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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