LMFDB - Embedded newform 2671.2.a.a.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55696 q^{2} +1.55375 q^{3} +0.424139 q^{4} -1.48943 q^{5} -2.41914 q^{6} -1.46054 q^{7} +2.45356 q^{8} -0.585849 q^{9} +O(q^{10})$	\(q-1.55696 q^{2} +1.55375 q^{3} +0.424139 q^{4} -1.48943 q^{5} -2.41914 q^{6} -1.46054 q^{7} +2.45356 q^{8} -0.585849 q^{9} +2.31899 q^{10} +1.81641 q^{11} +0.659007 q^{12} -4.47814 q^{13} +2.27401 q^{14} -2.31421 q^{15} -4.66838 q^{16} +2.03129 q^{17} +0.912147 q^{18} +2.37195 q^{19} -0.631726 q^{20} -2.26932 q^{21} -2.82809 q^{22} +9.19969 q^{23} +3.81223 q^{24} -2.78159 q^{25} +6.97230 q^{26} -5.57153 q^{27} -0.619471 q^{28} +8.73424 q^{29} +3.60314 q^{30} +2.88175 q^{31} +2.36139 q^{32} +2.82226 q^{33} -3.16265 q^{34} +2.17537 q^{35} -0.248481 q^{36} -9.73717 q^{37} -3.69304 q^{38} -6.95792 q^{39} -3.65441 q^{40} -3.23660 q^{41} +3.53325 q^{42} +12.4559 q^{43} +0.770411 q^{44} +0.872583 q^{45} -14.3236 q^{46} -9.82706 q^{47} -7.25352 q^{48} -4.86682 q^{49} +4.33084 q^{50} +3.15613 q^{51} -1.89935 q^{52} +5.77328 q^{53} +8.67467 q^{54} -2.70542 q^{55} -3.58352 q^{56} +3.68543 q^{57} -13.5989 q^{58} -6.76085 q^{59} -0.981546 q^{60} -3.29109 q^{61} -4.48679 q^{62} +0.855656 q^{63} +5.66017 q^{64} +6.66988 q^{65} -4.39416 q^{66} -4.88003 q^{67} +0.861550 q^{68} +14.2941 q^{69} -3.38698 q^{70} -10.1878 q^{71} -1.43742 q^{72} +6.59811 q^{73} +15.1604 q^{74} -4.32191 q^{75} +1.00604 q^{76} -2.65294 q^{77} +10.8332 q^{78} -9.26054 q^{79} +6.95324 q^{80} -6.89923 q^{81} +5.03928 q^{82} -17.4283 q^{83} -0.962506 q^{84} -3.02547 q^{85} -19.3934 q^{86} +13.5709 q^{87} +4.45668 q^{88} +4.16592 q^{89} -1.35858 q^{90} +6.54049 q^{91} +3.90194 q^{92} +4.47754 q^{93} +15.3004 q^{94} -3.53286 q^{95} +3.66902 q^{96} +1.27232 q^{97} +7.57747 q^{98} -1.06414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	−1.55696	−1.10094	−0.550470	−	0.834855i	$-0.685552\pi$
$2$	−1.55696	−1.10094	−0.550470	+	0.834855i	$0.685552\pi$
$3$	1.55375	0.897060	0.448530	−	0.893768i	$-0.351948\pi$
$3$	1.55375	0.897060	0.448530	+	0.893768i	$0.351948\pi$
$4$	0.424139	0.212069
$5$	−1.48943	−0.666094	−0.333047	−	0.942910i	$-0.608077\pi$
$5$	−1.48943	−0.666094	−0.333047	+	0.942910i	$0.608077\pi$
$6$	−2.41914	−0.987610
$7$	−1.46054	−0.552032	−0.276016	−	0.961153i	$-0.589014\pi$
$7$	−1.46054	−0.552032	−0.276016	+	0.961153i	$0.589014\pi$
$8$	2.45356	0.867465
$9$	−0.585849	−0.195283
$10$	2.31899	0.733330
$11$	1.81641	0.547669	0.273835	−	0.961777i	$-0.411708\pi$
$11$	1.81641	0.547669	0.273835	+	0.961777i	$0.411708\pi$
$12$	0.659007	0.190239
$13$	−4.47814	−1.24201	−0.621006	−	0.783806i	$-0.713276\pi$
$13$	−4.47814	−1.24201	−0.621006	+	0.783806i	$0.713276\pi$
$14$	2.27401	0.607754
$15$	−2.31421	−0.597527
$16$	−4.66838	−1.16710
$17$	2.03129	0.492661	0.246331	−	0.969186i	$-0.420775\pi$
$17$	2.03129	0.492661	0.246331	+	0.969186i	$0.420775\pi$
$18$	0.912147	0.214995
$19$	2.37195	0.544163	0.272081	−	0.962274i	$-0.412288\pi$
$19$	2.37195	0.544163	0.272081	+	0.962274i	$0.412288\pi$
$20$	−0.631726	−0.141258
$21$	−2.26932	−0.495206
$22$	−2.82809	−0.602951
$23$	9.19969	1.91827	0.959134	−	0.282953i	$-0.0913139\pi$
$23$	9.19969	1.91827	0.959134	+	0.282953i	$0.0913139\pi$
$24$	3.81223	0.778168
$25$	−2.78159	−0.556318
$26$	6.97230	1.36738
$27$	−5.57153	−1.07224
$28$	−0.619471	−0.117069
$29$	8.73424	1.62191	0.810953	−	0.585111i	$-0.198949\pi$
$29$	8.73424	1.62191	0.810953	+	0.585111i	$0.198949\pi$
$30$	3.60314	0.657841
$31$	2.88175	0.517578	0.258789	−	0.965934i	$-0.416677\pi$
$31$	2.88175	0.517578	0.258789	+	0.965934i	$0.416677\pi$
$32$	2.36139	0.417438
$33$	2.82226	0.491292
$34$	−3.16265	−0.542390
$35$	2.17537	0.367705
$36$	−0.248481	−0.0414136
$37$	−9.73717	−1.60078	−0.800390	−	0.599479i	$-0.795374\pi$
$37$	−9.73717	−1.60078	−0.800390	+	0.599479i	$0.795374\pi$
$38$	−3.69304	−0.599090
$39$	−6.95792	−1.11416
$40$	−3.65441	−0.577813
$41$	−3.23660	−0.505473	−0.252736	−	0.967535i	$-0.581331\pi$
$41$	−3.23660	−0.505473	−0.252736	+	0.967535i	$0.581331\pi$
$42$	3.53325	0.545192
$43$	12.4559	1.89950	0.949752	−	0.313003i	$-0.101335\pi$
$43$	12.4559	1.89950	0.949752	+	0.313003i	$0.101335\pi$
$44$	0.770411	0.116144
$45$	0.872583	0.130077
$46$	−14.3236	−2.11190
$47$	−9.82706	−1.43342	−0.716712	−	0.697369i	$-0.754354\pi$
$47$	−9.82706	−1.43342	−0.716712	+	0.697369i	$0.754354\pi$
$48$	−7.25352	−1.04696
$49$	−4.86682	−0.695261
$50$	4.33084	0.612473
$51$	3.15613	0.441947
$52$	−1.89935	−0.263393
$53$	5.77328	0.793021	0.396510	−	0.918030i	$-0.370221\pi$
$53$	5.77328	0.793021	0.396510	+	0.918030i	$0.370221\pi$
$54$	8.67467	1.18047
$55$	−2.70542	−0.364799
$56$	−3.58352	−0.478868
$57$	3.68543	0.488147
$58$	−13.5989	−1.78562
$59$	−6.76085	−0.880187	−0.440094	−	0.897952i	$-0.645055\pi$
$59$	−6.76085	−0.880187	−0.440094	+	0.897952i	$0.645055\pi$
$60$	−0.981546	−0.126717
$61$	−3.29109	−0.421380	−0.210690	−	0.977553i	$-0.567571\pi$
$61$	−3.29109	−0.421380	−0.210690	+	0.977553i	$0.567571\pi$
$62$	−4.48679	−0.569823
$63$	0.855656	0.107803
$64$	5.66017	0.707521
$65$	6.66988	0.827297
$66$	−4.39416	−0.540883
$67$	−4.88003	−0.596191	−0.298095	−	0.954536i	$-0.596351\pi$
$67$	−4.88003	−0.596191	−0.298095	+	0.954536i	$0.596351\pi$
$68$	0.861550	0.104478
$69$	14.2941	1.72080
$70$	−3.38698	−0.404822
$71$	−10.1878	−1.20906	−0.604532	−	0.796581i	$-0.706640\pi$
$71$	−10.1878	−1.20906	−0.604532	+	0.796581i	$0.706640\pi$
$72$	−1.43742	−0.169401
$73$	6.59811	0.772251	0.386125	−	0.922446i	$-0.373813\pi$
$73$	6.59811	0.772251	0.386125	+	0.922446i	$0.373813\pi$
$74$	15.1604	1.76236
$75$	−4.32191	−0.499051
$76$	1.00604	0.115400
$77$	−2.65294	−0.302331
$78$	10.8332	1.22662
$79$	−9.26054	−1.04189	−0.520946	−	0.853590i	$-0.674421\pi$
$79$	−9.26054	−1.04189	−0.520946	+	0.853590i	$0.674421\pi$
$80$	6.95324	0.777396
$81$	−6.89923	−0.766581
$82$	5.03928	0.556495
$83$	−17.4283	−1.91301	−0.956503	−	0.291723i	$-0.905771\pi$
$83$	−17.4283	−1.91301	−0.956503	+	0.291723i	$0.905771\pi$
$84$	−0.962506	−0.105018
$85$	−3.02547	−0.328159
$86$	−19.3934	−2.09124
$87$	13.5709	1.45495
$88$	4.45668	0.475084
$89$	4.16592	0.441587	0.220793	−	0.975321i	$-0.429135\pi$
$89$	4.16592	0.441587	0.220793	+	0.975321i	$0.429135\pi$
$90$	−1.35858	−0.143207
$91$	6.54049	0.685630
$92$	3.90194	0.406806
$93$	4.47754	0.464299
$94$	15.3004	1.57811
$95$	−3.53286	−0.362464
$96$	3.66902	0.374467
$97$	1.27232	0.129184	0.0645921	−	0.997912i	$-0.479425\pi$
$97$	1.27232	0.129184	0.0645921	+	0.997912i	$0.479425\pi$
$98$	7.57747	0.765440
$99$	−1.06414	−0.106951
$100$	−1.17978	−0.117978
$101$	7.40598	0.736923	0.368461	−	0.929643i	$-0.379885\pi$
$101$	7.40598	0.736923	0.368461	+	0.929643i	$0.379885\pi$
$102$	−4.91398	−0.486557
$103$	−0.871639	−0.0858852	−0.0429426	−	0.999078i	$-0.513673\pi$
$103$	−0.871639	−0.0858852	−0.0429426	+	0.999078i	$0.513673\pi$
$104$	−10.9874	−1.07740
$105$	3.38000	0.329854
$106$	−8.98879	−0.873068
$107$	5.74496	0.555386	0.277693	−	0.960670i	$-0.410430\pi$
$107$	5.74496	0.555386	0.277693	+	0.960670i	$0.410430\pi$
$108$	−2.36310	−0.227389
$109$	−5.78895	−0.554481	−0.277241	−	0.960801i	$-0.589420\pi$
$109$	−5.78895	−0.554481	−0.277241	+	0.960801i	$0.589420\pi$
$110$	4.21225	0.401622
$111$	−15.1292	−1.43600
$112$	6.81836	0.644274
$113$	−7.51913	−0.707340	−0.353670	−	0.935370i	$-0.615066\pi$
$113$	−7.51913	−0.707340	−0.353670	+	0.935370i	$0.615066\pi$
$114$	−5.73808	−0.537420
$115$	−13.7023	−1.27775
$116$	3.70453	0.343957
$117$	2.62351	0.242544
$118$	10.5264	0.969034
$119$	−2.96678	−0.271965
$120$	−5.67805	−0.518333
$121$	−7.70064	−0.700058
$122$	5.12410	0.463914
$123$	−5.02888	−0.453439
$124$	1.22226	0.109762
$125$	11.5902	1.03665
$126$	−1.33223	−0.118684
$127$	8.82692	0.783262	0.391631	−	0.920122i	$-0.371911\pi$
$127$	8.82692	0.783262	0.391631	+	0.920122i	$0.371911\pi$
$128$	−13.5355	−1.19638
$129$	19.3534	1.70397
$130$	−10.3848	−0.910804
$131$	−22.1354	−1.93398	−0.966991	−	0.254812i	$-0.917986\pi$
$131$	−22.1354	−1.93398	−0.966991	+	0.254812i	$0.917986\pi$
$132$	1.19703	0.104188
$133$	−3.46433	−0.300395
$134$	7.59804	0.656371
$135$	8.29841	0.714213
$136$	4.98390	0.427366
$137$	−18.8876	−1.61368	−0.806839	−	0.590772i	$-0.798823\pi$
$137$	−18.8876	−1.61368	−0.806839	+	0.590772i	$0.798823\pi$
$138$	−22.2553	−1.89450
$139$	−11.3511	−0.962792	−0.481396	−	0.876503i	$-0.659870\pi$
$139$	−11.3511	−0.962792	−0.481396	+	0.876503i	$0.659870\pi$
$140$	0.922660	0.0779790
$141$	−15.2688	−1.28587
$142$	15.8620	1.33111
$143$	−8.13414	−0.680211
$144$	2.73497	0.227914
$145$	−13.0091	−1.08034
$146$	−10.2730	−0.850202
$147$	−7.56185	−0.623691
$148$	−4.12991	−0.339476
$149$	−7.57924	−0.620915	−0.310458	−	0.950587i	$-0.600482\pi$
$149$	−7.57924	−0.620915	−0.310458	+	0.950587i	$0.600482\pi$
$150$	6.72906	0.549425
$151$	14.9705	1.21828	0.609140	−	0.793062i	$-0.291515\pi$
$151$	14.9705	1.21828	0.609140	+	0.793062i	$0.291515\pi$
$152$	5.81972	0.472042
$153$	−1.19003	−0.0962084
$154$	4.13054	0.332848
$155$	−4.29218	−0.344756
$156$	−2.95112	−0.236279
$157$	−5.31454	−0.424146	−0.212073	−	0.977254i	$-0.568022\pi$
$157$	−5.31454	−0.424146	−0.212073	+	0.977254i	$0.568022\pi$
$158$	14.4183	1.14706
$159$	8.97025	0.711387
$160$	−3.51713	−0.278053
$161$	−13.4365	−1.05895
$162$	10.7419	0.843960
$163$	−22.5185	−1.76378	−0.881892	−	0.471451i	$-0.843730\pi$
$163$	−22.5185	−1.76378	−0.881892	+	0.471451i	$0.843730\pi$
$164$	−1.37277	−0.107195
$165$	−4.20356	−0.327247
$166$	27.1353	2.10610
$167$	−9.31873	−0.721105	−0.360552	−	0.932739i	$-0.617412\pi$
$167$	−9.31873	−0.721105	−0.360552	+	0.932739i	$0.617412\pi$
$168$	−5.56791	−0.429574
$169$	7.05370	0.542592
$170$	4.71056	0.361283
$171$	−1.38961	−0.106266
$172$	5.28302	0.402827
$173$	4.60202	0.349885	0.174943	−	0.984579i	$-0.444026\pi$
$173$	4.60202	0.349885	0.174943	+	0.984579i	$0.444026\pi$
$174$	−21.1293	−1.60181
$175$	4.06263	0.307106
$176$	−8.47971	−0.639182
$177$	−10.5047	−0.789581
$178$	−6.48619	−0.486160
$179$	−19.8368	−1.48267	−0.741336	−	0.671135i	$-0.765807\pi$
$179$	−19.8368	−1.48267	−0.741336	+	0.671135i	$0.765807\pi$
$180$	0.370096	0.0275853
$181$	17.6461	1.31162	0.655811	−	0.754925i	$-0.272327\pi$
$181$	17.6461	1.31162	0.655811	+	0.754925i	$0.272327\pi$
$182$	−10.1833	−0.754838
$183$	−5.11354	−0.378003
$184$	22.5720	1.66403
$185$	14.5028	1.06627
$186$	−6.97136	−0.511165
$187$	3.68967	0.269815
$188$	−4.16804	−0.303985
$189$	8.13743	0.591911
$190$	5.50053	0.399051
$191$	7.85227	0.568171	0.284085	−	0.958799i	$-0.408310\pi$
$191$	7.85227	0.568171	0.284085	+	0.958799i	$0.408310\pi$
$192$	8.79451	0.634689
$193$	21.4543	1.54431	0.772157	−	0.635431i	$-0.219178\pi$
$193$	21.4543	1.54431	0.772157	+	0.635431i	$0.219178\pi$
$194$	−1.98095	−0.142224
$195$	10.3633	0.742135
$196$	−2.06421	−0.147443
$197$	9.19063	0.654805	0.327403	−	0.944885i	$-0.393827\pi$
$197$	9.19063	0.654805	0.327403	+	0.944885i	$0.393827\pi$
$198$	1.65684	0.117746
$199$	−8.66569	−0.614295	−0.307147	−	0.951662i	$-0.599374\pi$
$199$	−8.66569	−0.614295	−0.307147	+	0.951662i	$0.599374\pi$
$200$	−6.82480	−0.482587
$201$	−7.58237	−0.534819
$202$	−11.5309	−0.811308
$203$	−12.7567	−0.895345
$204$	1.33864	0.0937233
$205$	4.82070	0.336692
$206$	1.35711	0.0945544
$207$	−5.38963	−0.374605
$208$	20.9057	1.44955
$209$	4.30844	0.298021
$210$	−5.26253	−0.363149
$211$	27.8310	1.91597	0.957983	−	0.286824i	$-0.0925996\pi$
$211$	27.8310	1.91597	0.957983	+	0.286824i	$0.0925996\pi$
$212$	2.44867	0.168175
$213$	−15.8293	−1.08460
$214$	−8.94470	−0.611447
$215$	−18.5522	−1.26525
$216$	−13.6701	−0.930131
$217$	−4.20892	−0.285720
$218$	9.01320	0.610451
$219$	10.2518	0.692755
$220$	−1.14748	−0.0773628
$221$	−9.09641	−0.611891
$222$	23.5556	1.58095
$223$	0.580098	0.0388462	0.0194231	−	0.999811i	$-0.493817\pi$
$223$	0.580098	0.0388462	0.0194231	+	0.999811i	$0.493817\pi$
$224$	−3.44890	−0.230439
$225$	1.62959	0.108640
$226$	11.7070	0.778739
$227$	−7.39647	−0.490921	−0.245461	−	0.969407i	$-0.578939\pi$
$227$	−7.39647	−0.490921	−0.245461	+	0.969407i	$0.578939\pi$
$228$	1.56313	0.103521
$229$	−3.04437	−0.201178	−0.100589	−	0.994928i	$-0.532073\pi$
$229$	−3.04437	−0.201178	−0.100589	+	0.994928i	$0.532073\pi$
$230$	21.3340	1.40672
$231$	−4.12202	−0.271209
$232$	21.4300	1.40695
$233$	14.3974	0.943206	0.471603	−	0.881811i	$-0.343675\pi$
$233$	14.3974	0.943206	0.471603	+	0.881811i	$0.343675\pi$
$234$	−4.08472	−0.267026
$235$	14.6367	0.954795
$236$	−2.86754	−0.186661
$237$	−14.3886	−0.934639
$238$	4.61918	0.299417
$239$	3.55790	0.230141	0.115071	−	0.993357i	$-0.463291\pi$
$239$	3.55790	0.230141	0.115071	+	0.993357i	$0.463291\pi$
$240$	10.8036	0.697371
$241$	−3.04582	−0.196199	−0.0980994	−	0.995177i	$-0.531276\pi$
$241$	−3.04582	−0.196199	−0.0980994	+	0.995177i	$0.531276\pi$
$242$	11.9896	0.770723
$243$	5.99487	0.384571
$244$	−1.39588	−0.0893618
$245$	7.24880	0.463109
$246$	7.82980	0.499210
$247$	−10.6219	−0.675856
$248$	7.07056	0.448981
$249$	−27.0793	−1.71608
$250$	−18.0455	−1.14129
$251$	−8.48403	−0.535507	−0.267754	−	0.963487i	$-0.586281\pi$
$251$	−8.48403	−0.535507	−0.267754	+	0.963487i	$0.586281\pi$
$252$	0.362917	0.0228616
$253$	16.7104	1.05058
$254$	−13.7432	−0.862325
$255$	−4.70084	−0.294378
$256$	9.75389	0.609618
$257$	−5.98473	−0.373317	−0.186659	−	0.982425i	$-0.559766\pi$
$257$	−5.98473	−0.373317	−0.186659	+	0.982425i	$0.559766\pi$
$258$	−30.1325	−1.87597
$259$	14.2215	0.883682
$260$	2.82895	0.175444
$261$	−5.11695	−0.316731
$262$	34.4641	2.12920
$263$	22.5067	1.38782	0.693910	−	0.720062i	$-0.255887\pi$
$263$	22.5067	1.38782	0.693910	+	0.720062i	$0.255887\pi$
$264$	6.92458	0.426179
$265$	−8.59890	−0.528226
$266$	5.39383	0.330717
$267$	6.47281	0.396130
$268$	−2.06981	−0.126434
$269$	−18.3385	−1.11812	−0.559058	−	0.829128i	$-0.688837\pi$
$269$	−18.3385	−1.11812	−0.559058	+	0.829128i	$0.688837\pi$
$270$	−12.9203	−0.786306
$271$	−19.5008	−1.18459	−0.592295	−	0.805721i	$-0.701778\pi$
$271$	−19.5008	−1.18459	−0.592295	+	0.805721i	$0.701778\pi$
$272$	−9.48286	−0.574983
$273$	10.1623	0.615051
$274$	29.4073	1.77656
$275$	−5.05252	−0.304678
$276$	6.06266	0.364929
$277$	−13.4208	−0.806380	−0.403190	−	0.915116i	$-0.632099\pi$
$277$	−13.4208	−0.806380	−0.403190	+	0.915116i	$0.632099\pi$
$278$	17.6733	1.05998
$279$	−1.68827	−0.101074
$280$	5.33741	0.318971
$281$	−28.0071	−1.67076	−0.835382	−	0.549670i	$-0.814753\pi$
$281$	−28.0071	−1.67076	−0.835382	+	0.549670i	$0.814753\pi$
$282$	23.7730	1.41566
$283$	−21.7144	−1.29079	−0.645394	−	0.763850i	$-0.723307\pi$
$283$	−21.7144	−1.29079	−0.645394	+	0.763850i	$0.723307\pi$
$284$	−4.32102	−0.256406
$285$	−5.48919	−0.325152
$286$	12.6646	0.748872
$287$	4.72719	0.279037
$288$	−1.38342	−0.0815187
$289$	−12.8738	−0.757285
$290$	20.2546	1.18939
$291$	1.97687	0.115886
$292$	2.79852	0.163771
$293$	−5.41767	−0.316504	−0.158252	−	0.987399i	$-0.550586\pi$
$293$	−5.41767	−0.316504	−0.158252	+	0.987399i	$0.550586\pi$
$294$	11.7735	0.686646
$295$	10.0698	0.586288
$296$	−23.8907	−1.38862
$297$	−10.1202	−0.587233
$298$	11.8006	0.683591
$299$	−41.1975	−2.38251
$300$	−1.83309	−0.105833
$301$	−18.1923	−1.04859
$302$	−23.3085	−1.34125
$303$	11.5071	0.661064
$304$	−11.0732	−0.635090
$305$	4.90185	0.280679
$306$	1.85284	0.105920
$307$	−15.0662	−0.859873	−0.429936	−	0.902859i	$-0.641464\pi$
$307$	−15.0662	−0.859873	−0.429936	+	0.902859i	$0.641464\pi$
$308$	−1.12522	−0.0641151
$309$	−1.35431	−0.0770442
$310$	6.68277	0.379556
$311$	5.55674	0.315094	0.157547	−	0.987511i	$-0.449641\pi$
$311$	5.55674	0.315094	0.157547	+	0.987511i	$0.449641\pi$
$312$	−17.0717	−0.966493
$313$	−13.2766	−0.750435	−0.375218	−	0.926937i	$-0.622432\pi$
$313$	−13.2766	−0.750435	−0.375218	+	0.926937i	$0.622432\pi$
$314$	8.27455	0.466960
$315$	−1.27444	−0.0718067
$316$	−3.92775	−0.220953
$317$	10.0600	0.565024	0.282512	−	0.959264i	$-0.408832\pi$
$317$	10.0600	0.565024	0.282512	+	0.959264i	$0.408832\pi$
$318$	−13.9664	−0.783195
$319$	15.8650	0.888268
$320$	−8.43044	−0.471276
$321$	8.92626	0.498215
$322$	20.9202	1.16584
$323$	4.81813	0.268088
$324$	−2.92623	−0.162568
$325$	12.4563	0.690954
$326$	35.0605	1.94182
$327$	−8.99461	−0.497403
$328$	−7.94120	−0.438480
$329$	14.3528	0.791296
$330$	6.54480	0.360279
$331$	3.01907	0.165943	0.0829716	−	0.996552i	$-0.473559\pi$
$331$	3.01907	0.165943	0.0829716	+	0.996552i	$0.473559\pi$
$332$	−7.39202	−0.405690
$333$	5.70451	0.312605
$334$	14.5089	0.793893
$335$	7.26848	0.397119
$336$	10.5940	0.577953
$337$	−4.89521	−0.266659	−0.133330	−	0.991072i	$-0.542567\pi$
$337$	−4.89521	−0.266659	−0.133330	+	0.991072i	$0.542567\pi$
$338$	−10.9824	−0.597362
$339$	−11.6829	−0.634527
$340$	−1.28322	−0.0695924
$341$	5.23446	0.283462
$342$	2.16357	0.116992
$343$	17.3320	0.935838
$344$	30.5613	1.64775
$345$	−21.2900	−1.14622
$346$	−7.16519	−0.385203
$347$	−18.8222	−1.01043	−0.505214	−	0.862994i	$-0.668586\pi$
$347$	−18.8222	−1.01043	−0.505214	+	0.862994i	$0.668586\pi$
$348$	5.75592	0.308550
$349$	18.0069	0.963888	0.481944	−	0.876202i	$-0.339931\pi$
$349$	18.0069	0.963888	0.481944	+	0.876202i	$0.339931\pi$
$350$	−6.32536	−0.338105
$351$	24.9501	1.33174
$352$	4.28926	0.228618
$353$	5.89494	0.313756	0.156878	−	0.987618i	$-0.449857\pi$
$353$	5.89494	0.313756	0.156878	+	0.987618i	$0.449857\pi$
$354$	16.3554	0.869282
$355$	15.1740	0.805351
$356$	1.76693	0.0936470
$357$	−4.60965	−0.243969
$358$	30.8852	1.63233
$359$	−16.7144	−0.882151	−0.441076	−	0.897470i	$-0.645403\pi$
$359$	−16.7144	−0.882151	−0.441076	+	0.897470i	$0.645403\pi$
$360$	2.14093	0.112837
$361$	−13.3739	−0.703887
$362$	−27.4743	−1.44402
$363$	−11.9649	−0.627995
$364$	2.77408	0.145401
$365$	−9.82744	−0.514392
$366$	7.96159	0.416159
$367$	−7.33537	−0.382903	−0.191452	−	0.981502i	$-0.561319\pi$
$367$	−7.33537	−0.382903	−0.191452	+	0.981502i	$0.561319\pi$
$368$	−42.9477	−2.23880
$369$	1.89616	0.0987103
$370$	−22.5804	−1.17390
$371$	−8.43210	−0.437773
$372$	1.89910	0.0984636
$373$	−31.4796	−1.62995	−0.814977	−	0.579494i	$-0.803250\pi$
$373$	−31.4796	−1.62995	−0.814977	+	0.579494i	$0.803250\pi$
$374$	−5.74468	−0.297051
$375$	18.0082	0.929942
$376$	−24.1113	−1.24344
$377$	−39.1131	−2.01443
$378$	−12.6697	−0.651659
$379$	6.54980	0.336441	0.168220	−	0.985749i	$-0.446198\pi$
$379$	6.54980	0.336441	0.168220	+	0.985749i	$0.446198\pi$
$380$	−1.49842	−0.0768674
$381$	13.7149	0.702633
$382$	−12.2257	−0.625522
$383$	−15.0168	−0.767321	−0.383660	−	0.923474i	$-0.625337\pi$
$383$	−15.0168	−0.767321	−0.383660	+	0.923474i	$0.625337\pi$
$384$	−21.0308	−1.07322
$385$	3.95138	0.201381
$386$	−33.4036	−1.70020
$387$	−7.29727	−0.370941
$388$	0.539639	0.0273960
$389$	12.3321	0.625265	0.312632	−	0.949874i	$-0.398789\pi$
$389$	12.3321	0.625265	0.312632	+	0.949874i	$0.398789\pi$
$390$	−16.1354	−0.817046
$391$	18.6873	0.945056
$392$	−11.9410	−0.603114
$393$	−34.3930	−1.73490
$394$	−14.3095	−0.720901
$395$	13.7929	0.693998
$396$	−0.451345	−0.0226809
$397$	−8.37698	−0.420429	−0.210214	−	0.977655i	$-0.567416\pi$
$397$	−8.37698	−0.420429	−0.210214	+	0.977655i	$0.567416\pi$
$398$	13.4922	0.676302
$399$	−5.38271	−0.269473
$400$	12.9855	0.649277
$401$	0.538064	0.0268696	0.0134348	−	0.999910i	$-0.495723\pi$
$401$	0.538064	0.0268696	0.0134348	+	0.999910i	$0.495723\pi$
$402$	11.8055	0.588804
$403$	−12.9049	−0.642838
$404$	3.14116	0.156279
$405$	10.2759	0.510615
$406$	19.8617	0.985721
$407$	−17.6867	−0.876698
$408$	7.74376	0.383373
$409$	−6.21465	−0.307295	−0.153647	−	0.988126i	$-0.549102\pi$
$409$	−6.21465	−0.307295	−0.153647	+	0.988126i	$0.549102\pi$
$410$	−7.50566	−0.370678
$411$	−29.3467	−1.44757
$412$	−0.369696	−0.0182136
$413$	9.87449	0.485892
$414$	8.39147	0.412418
$415$	25.9583	1.27424
$416$	−10.5746	−0.518463
$417$	−17.6369	−0.863682
$418$	−6.70809	−0.328103
$419$	35.7280	1.74543	0.872713	−	0.488234i	$-0.162359\pi$
$419$	35.7280	1.74543	0.872713	+	0.488234i	$0.162359\pi$
$420$	1.43359	0.0699519
$421$	−11.1258	−0.542239	−0.271120	−	0.962546i	$-0.587394\pi$
$421$	−11.1258	−0.542239	−0.271120	+	0.962546i	$0.587394\pi$
$422$	−43.3319	−2.10936
$423$	5.75718	0.279924
$424$	14.1651	0.687917
$425$	−5.65023	−0.274076
$426$	24.6456	1.19408
$427$	4.80676	0.232615
$428$	2.43666	0.117780
$429$	−12.6385	−0.610190
$430$	28.8851	1.39296
$431$	13.2287	0.637204	0.318602	−	0.947889i	$-0.396787\pi$
$431$	13.2287	0.637204	0.318602	+	0.947889i	$0.396787\pi$
$432$	26.0100	1.25141
$433$	16.3809	0.787218	0.393609	−	0.919278i	$-0.371226\pi$
$433$	16.3809	0.787218	0.393609	+	0.919278i	$0.371226\pi$
$434$	6.55313	0.314560
$435$	−20.2129	−0.969132
$436$	−2.45532	−0.117588
$437$	21.8212	1.04385
$438$	−15.9618	−0.762682
$439$	−25.6048	−1.22205	−0.611024	−	0.791612i	$-0.709242\pi$
$439$	−25.6048	−1.22205	−0.611024	+	0.791612i	$0.709242\pi$
$440$	−6.63792	−0.316450
$441$	2.85123	0.135773
$442$	14.1628	0.673655
$443$	−5.17365	−0.245807	−0.122904	−	0.992419i	$-0.539221\pi$
$443$	−5.17365	−0.245807	−0.122904	+	0.992419i	$0.539221\pi$
$444$	−6.41686	−0.304531
$445$	−6.20485	−0.294138
$446$	−0.903191	−0.0427674
$447$	−11.7763	−0.556998
$448$	−8.26690	−0.390574
$449$	−20.0912	−0.948164	−0.474082	−	0.880481i	$-0.657220\pi$
$449$	−20.0912	−0.948164	−0.474082	+	0.880481i	$0.657220\pi$
$450$	−2.53722	−0.119606
$451$	−5.87901	−0.276832
$452$	−3.18915	−0.150005
$453$	23.2604	1.09287
$454$	11.5160	0.540475
$455$	−9.74162	−0.456694
$456$	9.04241	0.423450
$457$	14.6701	0.686239	0.343119	−	0.939292i	$-0.388516\pi$
$457$	14.6701	0.686239	0.343119	+	0.939292i	$0.388516\pi$
$458$	4.73998	0.221485
$459$	−11.3174	−0.528251
$460$	−5.81168	−0.270971
$461$	3.91756	0.182459	0.0912295	−	0.995830i	$-0.470920\pi$
$461$	3.91756	0.182459	0.0912295	+	0.995830i	$0.470920\pi$
$462$	6.41784	0.298585
$463$	−2.96363	−0.137732	−0.0688658	−	0.997626i	$-0.521938\pi$
$463$	−2.96363	−0.137732	−0.0688658	+	0.997626i	$0.521938\pi$
$464$	−40.7748	−1.89292
$465$	−6.66898	−0.309267
$466$	−22.4163	−1.03841
$467$	17.5939	0.814147	0.407073	−	0.913395i	$-0.366549\pi$
$467$	17.5939	0.814147	0.407073	+	0.913395i	$0.366549\pi$
$468$	1.11273	0.0514361
$469$	7.12748	0.329116
$470$	−22.7889	−1.05117
$471$	−8.25748	−0.380485
$472$	−16.5881	−0.763531
$473$	22.6250	1.04030
$474$	22.4025	1.02898
$475$	−6.59780	−0.302728
$476$	−1.25833	−0.0576754
$477$	−3.38227	−0.154864
$478$	−5.53952	−0.253372
$479$	40.0671	1.83071	0.915357	−	0.402644i	$-0.131909\pi$
$479$	40.0671	1.83071	0.915357	+	0.402644i	$0.131909\pi$
$480$	−5.46475	−0.249431
$481$	43.6044	1.98819
$482$	4.74224	0.216003
$483$	−20.8770	−0.949938
$484$	−3.26614	−0.148461
$485$	−1.89503	−0.0860488
$486$	−9.33381	−0.423390
$487$	21.8717	0.991099	0.495550	−	0.868580i	$-0.334967\pi$
$487$	21.8717	0.991099	0.495550	+	0.868580i	$0.334967\pi$
$488$	−8.07488	−0.365532
$489$	−34.9882	−1.58222
$490$	−11.2861	−0.509855
$491$	−31.8368	−1.43678	−0.718388	−	0.695643i	$-0.755120\pi$
$491$	−31.8368	−1.43678	−0.718388	+	0.695643i	$0.755120\pi$
$492$	−2.13294	−0.0961606
$493$	17.7418	0.799050
$494$	16.5379	0.744077
$495$	1.58497	0.0712392
$496$	−13.4531	−0.604064
$497$	14.8796	0.667442
$498$	42.1615	1.88930
$499$	19.3091	0.864393	0.432196	−	0.901780i	$-0.357739\pi$
$499$	19.3091	0.864393	0.432196	+	0.901780i	$0.357739\pi$
$500$	4.91583	0.219843
$501$	−14.4790	−0.646874
$502$	13.2093	0.589561
$503$	−44.4327	−1.98116	−0.990579	−	0.136942i	$-0.956273\pi$
$503$	−44.4327	−1.98116	−0.990579	+	0.136942i	$0.956273\pi$
$504$	2.09940	0.0935149
$505$	−11.0307	−0.490860
$506$	−26.0176	−1.15662
$507$	10.9597	0.486738
$508$	3.74384	0.166106
$509$	13.3178	0.590302	0.295151	−	0.955451i	$-0.404630\pi$
$509$	13.3178	0.590302	0.295151	+	0.955451i	$0.404630\pi$
$510$	7.31904	0.324093
$511$	−9.63680	−0.426307
$512$	11.8845	0.525224
$513$	−13.2154	−0.583473
$514$	9.31801	0.411000
$515$	1.29825	0.0572076
$516$	8.20852	0.361360
$517$	−17.8500	−0.785042
$518$	−22.1424	−0.972881
$519$	7.15041	0.313868
$520$	16.3649	0.717650
$521$	37.1711	1.62850	0.814248	−	0.580517i	$-0.197149\pi$
$521$	37.1711	1.62850	0.814248	+	0.580517i	$0.197149\pi$
$522$	7.96691	0.348702
$523$	8.88819	0.388653	0.194327	−	0.980937i	$-0.437748\pi$
$523$	8.88819	0.388653	0.194327	+	0.980937i	$0.437748\pi$
$524$	−9.38849	−0.410138
$525$	6.31232	0.275492
$526$	−35.0421	−1.52791
$527$	5.85369	0.254991
$528$	−13.1754	−0.573385
$529$	61.6343	2.67975
$530$	13.3882	0.581546
$531$	3.96084	0.171886
$532$	−1.46935	−0.0637046
$533$	14.4939	0.627803
$534$	−10.0779	−0.436115
$535$	−8.55673	−0.369940
$536$	−11.9735	−0.517174
$537$	−30.8215	−1.33005
$538$	28.5524	1.23098
$539$	−8.84016	−0.380773
$540$	3.51968	0.151463
$541$	−21.3525	−0.918016	−0.459008	−	0.888432i	$-0.651795\pi$
$541$	−21.3525	−0.918016	−0.459008	+	0.888432i	$0.651795\pi$
$542$	30.3621	1.30416
$543$	27.4176	1.17660
$544$	4.79667	0.205656
$545$	8.62225	0.369337
$546$	−15.8224	−0.677135
$547$	4.21529	0.180233	0.0901165	−	0.995931i	$-0.471276\pi$
$547$	4.21529	0.180233	0.0901165	+	0.995931i	$0.471276\pi$
$548$	−8.01097	−0.342212
$549$	1.92808	0.0822885
$550$	7.86660	0.335433
$551$	20.7172	0.882581
$552$	35.0713	1.49273
$553$	13.5254	0.575158
$554$	20.8958	0.887776
$555$	22.5339	0.956509
$556$	−4.81446	−0.204179
$557$	39.1213	1.65762	0.828810	−	0.559530i	$-0.189018\pi$
$557$	39.1213	1.65762	0.828810	+	0.559530i	$0.189018\pi$
$558$	2.62858	0.111277
$559$	−55.7791	−2.35921
$560$	−10.1555	−0.429147
$561$	5.73284	0.242041
$562$	43.6061	1.83941
$563$	−23.4373	−0.987766	−0.493883	−	0.869528i	$-0.664423\pi$
$563$	−23.4373	−0.987766	−0.493883	+	0.869528i	$0.664423\pi$
$564$	−6.47610	−0.272693
$565$	11.1992	0.471155
$566$	33.8086	1.42108
$567$	10.0766	0.423177
$568$	−24.9963	−1.04882
$569$	5.61024	0.235194	0.117597	−	0.993061i	$-0.462481\pi$
$569$	5.61024	0.235194	0.117597	+	0.993061i	$0.462481\pi$
$570$	8.54648	0.357972
$571$	0.313645	0.0131256	0.00656282	−	0.999978i	$-0.497911\pi$
$571$	0.313645	0.0131256	0.00656282	+	0.999978i	$0.497911\pi$
$572$	−3.45001	−0.144252
$573$	12.2005	0.509683
$574$	−7.36006	−0.307203
$575$	−25.5898	−1.06717
$576$	−3.31601	−0.138167
$577$	−16.9118	−0.704046	−0.352023	−	0.935991i	$-0.614506\pi$
$577$	−16.9118	−0.704046	−0.352023	+	0.935991i	$0.614506\pi$
$578$	20.0441	0.833726
$579$	33.3347	1.38534
$580$	−5.51764	−0.229108
$581$	25.4547	1.05604
$582$	−3.07791	−0.127583
$583$	10.4867	0.434313
$584$	16.1889	0.669900
$585$	−3.90754	−0.161557
$586$	8.43512	0.348452
$587$	19.1327	0.789690	0.394845	−	0.918748i	$-0.370798\pi$
$587$	19.1327	0.789690	0.394845	+	0.918748i	$0.370798\pi$
$588$	−3.20727	−0.132266
$589$	6.83538	0.281647
$590$	−15.6784	−0.645468
$591$	14.2800	0.587400
$592$	45.4568	1.86826
$593$	−12.0489	−0.494790	−0.247395	−	0.968915i	$-0.579575\pi$
$593$	−12.0489	−0.494790	−0.247395	+	0.968915i	$0.579575\pi$
$594$	15.7568	0.646509
$595$	4.41882	0.181154
$596$	−3.21465	−0.131677
$597$	−13.4644	−0.551059
$598$	64.1430	2.62300
$599$	−4.88716	−0.199684	−0.0998421	−	0.995003i	$-0.531834\pi$
$599$	−4.88716	−0.199684	−0.0998421	+	0.995003i	$0.531834\pi$
$600$	−10.6041	−0.432909
$601$	−30.4366	−1.24153	−0.620767	−	0.783995i	$-0.713179\pi$
$601$	−30.4366	−1.24153	−0.620767	+	0.783995i	$0.713179\pi$
$602$	28.3248	1.15443
$603$	2.85896	0.116426
$604$	6.34956	0.258360
$605$	11.4696	0.466305
$606$	−17.9161	−0.727792
$607$	−17.8739	−0.725478	−0.362739	−	0.931891i	$-0.618158\pi$
$607$	−17.8739	−0.725478	−0.362739	+	0.931891i	$0.618158\pi$
$608$	5.60109	0.227154
$609$	−19.8208	−0.803178
$610$	−7.63200	−0.309011
$611$	44.0069	1.78033
$612$	−0.504739	−0.0204029
$613$	44.4239	1.79426	0.897132	−	0.441762i	$-0.145646\pi$
$613$	44.4239	1.79426	0.897132	+	0.441762i	$0.145646\pi$
$614$	23.4575	0.946668
$615$	7.49018	0.302033
$616$	−6.50916	−0.262261
$617$	−32.7378	−1.31798	−0.658988	−	0.752154i	$-0.729015\pi$
$617$	−32.7378	−1.31798	−0.658988	+	0.752154i	$0.729015\pi$
$618$	2.10862	0.0848210
$619$	−8.97677	−0.360807	−0.180403	−	0.983593i	$-0.557740\pi$
$619$	−8.97677	−0.360807	−0.180403	+	0.983593i	$0.557740\pi$
$620$	−1.82048	−0.0731122
$621$	−51.2563	−2.05685
$622$	−8.65165	−0.346900
$623$	−6.08449	−0.243770
$624$	32.4822	1.30033
$625$	−3.35478	−0.134191
$626$	20.6711	0.826184
$627$	6.69426	0.267343
$628$	−2.25410	−0.0899485
$629$	−19.7790	−0.788642
$630$	1.98426	0.0790548
$631$	5.41581	0.215600	0.107800	−	0.994173i	$-0.465619\pi$
$631$	5.41581	0.215600	0.107800	+	0.994173i	$0.465619\pi$
$632$	−22.7213	−0.903804
$633$	43.2426	1.71874
$634$	−15.6630	−0.622058
$635$	−13.1471	−0.521726
$636$	3.80463	0.150863
$637$	21.7943	0.863522
$638$	−24.7012	−0.977930
$639$	5.96849	0.236110
$640$	20.1601	0.796900
$641$	4.77140	0.188459	0.0942295	−	0.995551i	$-0.469961\pi$
$641$	4.77140	0.188459	0.0942295	+	0.995551i	$0.469961\pi$
$642$	−13.8979	−0.548505
$643$	25.7708	1.01630	0.508150	−	0.861269i	$-0.330330\pi$
$643$	25.7708	1.01630	0.508150	+	0.861269i	$0.330330\pi$
$644$	−5.69894	−0.224570
$645$	−28.8255	−1.13500
$646$	−7.50165	−0.295149
$647$	−19.3208	−0.759580	−0.379790	−	0.925073i	$-0.624004\pi$
$647$	−19.3208	−0.759580	−0.379790	+	0.925073i	$0.624004\pi$
$648$	−16.9277	−0.664982
$649$	−12.2805	−0.482052
$650$	−19.3941	−0.760699
$651$	−6.53962	−0.256308
$652$	−9.55096	−0.374045
$653$	28.0957	1.09947	0.549735	−	0.835339i	$-0.314729\pi$
$653$	28.0957	1.09947	0.549735	+	0.835339i	$0.314729\pi$
$654$	14.0043	0.547611
$655$	32.9692	1.28821
$656$	15.1097	0.589935
$657$	−3.86550	−0.150808
$658$	−22.3468	−0.871170
$659$	10.6687	0.415595	0.207797	−	0.978172i	$-0.433371\pi$
$659$	10.6687	0.415595	0.207797	+	0.978172i	$0.433371\pi$
$660$	−1.78289	−0.0693990
$661$	17.3402	0.674455	0.337228	−	0.941423i	$-0.390511\pi$
$661$	17.3402	0.674455	0.337228	+	0.941423i	$0.390511\pi$
$662$	−4.70059	−0.182694
$663$	−14.1336	−0.548903
$664$	−42.7614	−1.65946
$665$	5.15988	0.200091
$666$	−8.88173	−0.344160
$667$	80.3523	3.11125
$668$	−3.95243	−0.152924
$669$	0.901329	0.0348474
$670$	−11.3168	−0.437205
$671$	−5.97797	−0.230777
$672$	−5.35874	−0.206718
$673$	12.7249	0.490508	0.245254	−	0.969459i	$-0.421129\pi$
$673$	12.7249	0.490508	0.245254	+	0.969459i	$0.421129\pi$
$674$	7.62167	0.293576
$675$	15.4977	0.596507
$676$	2.99175	0.115067
$677$	42.7671	1.64367	0.821836	−	0.569724i	$-0.192950\pi$
$677$	42.7671	1.64367	0.821836	+	0.569724i	$0.192950\pi$
$678$	18.1898	0.698576
$679$	−1.85827	−0.0713138
$680$	−7.42318	−0.284666
$681$	−11.4923	−0.440386
$682$	−8.14986	−0.312074
$683$	21.6427	0.828134	0.414067	−	0.910246i	$-0.364108\pi$
$683$	21.6427	0.828134	0.414067	+	0.910246i	$0.364108\pi$
$684$	−0.589386	−0.0225357
$685$	28.1318	1.07486
$686$	−26.9853	−1.03030
$687$	−4.73021	−0.180469
$688$	−58.1489	−2.21690
$689$	−25.8535	−0.984941
$690$	33.1478	1.26192
$691$	5.43439	0.206734	0.103367	−	0.994643i	$-0.467038\pi$
$691$	5.43439	0.206734	0.103367	+	0.994643i	$0.467038\pi$
$692$	1.95190	0.0741999
$693$	1.55423	0.0590401
$694$	29.3055	1.11242
$695$	16.9068	0.641310
$696$	33.2969	1.26212
$697$	−6.57449	−0.249027
$698$	−28.0361	−1.06118
$699$	22.3700	0.846113
$700$	1.72312	0.0651277
$701$	2.46953	0.0932727	0.0466363	−	0.998912i	$-0.485150\pi$
$701$	2.46953	0.0932727	0.0466363	+	0.998912i	$0.485150\pi$
$702$	−38.8463	−1.46616
$703$	−23.0961	−0.871085
$704$	10.2812	0.387488
$705$	22.7419	0.856509
$706$	−9.17822	−0.345427
$707$	−10.8167	−0.406805
$708$	−4.45545	−0.167446
$709$	−8.41212	−0.315924	−0.157962	−	0.987445i	$-0.550492\pi$
$709$	−8.41212	−0.315924	−0.157962	+	0.987445i	$0.550492\pi$
$710$	−23.6253	−0.886643
$711$	5.42528	0.203464
$712$	10.2213	0.383061
$713$	26.5112	0.992854
$714$	7.17707	0.268595
$715$	12.1153	0.453085
$716$	−8.41355	−0.314429
$717$	5.52810	0.206451
$718$	26.0237	0.971196
$719$	−16.4109	−0.612023	−0.306011	−	0.952028i	$-0.598995\pi$
$719$	−16.4109	−0.612023	−0.306011	+	0.952028i	$0.598995\pi$
$720$	−4.07355	−0.151812
$721$	1.27306	0.0474114
$722$	20.8226	0.774938
$723$	−4.73246	−0.176002
$724$	7.48438	0.278155
$725$	−24.2951	−0.902297
$726$	18.6289	0.691384
$727$	18.2471	0.676748	0.338374	−	0.941012i	$-0.390123\pi$
$727$	18.2471	0.676748	0.338374	+	0.941012i	$0.390123\pi$
$728$	16.0475	0.594760
$729$	30.0123	1.11156
$730$	15.3010	0.566315
$731$	25.3016	0.935812
$732$	−2.16885	−0.0801629
$733$	−4.16265	−0.153751	−0.0768754	−	0.997041i	$-0.524494\pi$
$733$	−4.16265	−0.153751	−0.0768754	+	0.997041i	$0.524494\pi$
$734$	11.4209	0.421554
$735$	11.2629	0.415437
$736$	21.7240	0.800759
$737$	−8.86416	−0.326515
$738$	−2.95226	−0.108674
$739$	0.144464	0.00531419	0.00265710	−	0.999996i	$-0.499154\pi$
$739$	0.144464	0.00531419	0.00265710	+	0.999996i	$0.499154\pi$
$740$	6.15122	0.226123
$741$	−16.5038	−0.606284
$742$	13.1285	0.481962
$743$	−16.4859	−0.604810	−0.302405	−	0.953180i	$-0.597789\pi$
$743$	−16.4859	−0.604810	−0.302405	+	0.953180i	$0.597789\pi$
$744$	10.9859	0.402763
$745$	11.2888	0.413588
$746$	49.0127	1.79448
$747$	10.2104	0.373578
$748$	1.56493	0.0572196
$749$	−8.39074	−0.306591
$750$	−28.0382	−1.02381
$751$	−11.6790	−0.426173	−0.213086	−	0.977033i	$-0.568352\pi$
$751$	−11.6790	−0.426173	−0.213086	+	0.977033i	$0.568352\pi$
$752$	45.8765	1.67294
$753$	−13.1821	−0.480382
$754$	60.8977	2.21776
$755$	−22.2975	−0.811490
$756$	3.45140	0.125526
$757$	6.33534	0.230262	0.115131	−	0.993350i	$-0.463271\pi$
$757$	6.33534	0.230262	0.115131	+	0.993350i	$0.463271\pi$
$758$	−10.1978	−0.370401
$759$	25.9639	0.942430
$760$	−8.66808	−0.314424
$761$	5.96227	0.216132	0.108066	−	0.994144i	$-0.465534\pi$
$761$	5.96227	0.216132	0.108066	+	0.994144i	$0.465534\pi$
$762$	−21.3535	−0.773557
$763$	8.45500	0.306091
$764$	3.33045	0.120492
$765$	1.77247	0.0640839
$766$	23.3806	0.844775
$767$	30.2760	1.09320
$768$	15.1551	0.546864
$769$	−9.22243	−0.332569	−0.166285	−	0.986078i	$-0.553177\pi$
$769$	−9.22243	−0.332569	−0.166285	+	0.986078i	$0.553177\pi$
$770$	−6.15216	−0.221708
$771$	−9.29880	−0.334888
$772$	9.09960	0.327502
$773$	−36.6083	−1.31671	−0.658355	−	0.752708i	$-0.728747\pi$
$773$	−36.6083	−1.31671	−0.658355	+	0.752708i	$0.728747\pi$
$774$	11.3616	0.408384
$775$	−8.01586	−0.287938
$776$	3.12170	0.112063
$777$	22.0967	0.792716
$778$	−19.2007	−0.688379
$779$	−7.67706	−0.275059
$780$	4.39550	0.157384
$781$	−18.5052	−0.662167
$782$	−29.0954	−1.04045
$783$	−48.6630	−1.73907
$784$	22.7202	0.811436
$785$	7.91564	0.282521
$786$	53.5487	1.91002
$787$	−31.4559	−1.12128	−0.560641	−	0.828059i	$-0.689445\pi$
$787$	−31.4559	−1.12128	−0.560641	+	0.828059i	$0.689445\pi$
$788$	3.89810	0.138864
$789$	34.9698	1.24496
$790$	−21.4751	−0.764050
$791$	10.9820	0.390474
$792$	−2.61094	−0.0927758
$793$	14.7379	0.523359
$794$	13.0427	0.462867
$795$	−13.3606	−0.473851
$796$	−3.67546	−0.130273
$797$	8.59379	0.304408	0.152204	−	0.988349i	$-0.451363\pi$
$797$	8.59379	0.304408	0.152204	+	0.988349i	$0.451363\pi$
$798$	8.38069	0.296673
$799$	−19.9616	−0.706192
$800$	−6.56842	−0.232229
$801$	−2.44060	−0.0862344
$802$	−0.837746	−0.0295818
$803$	11.9849	0.422938
$804$	−3.21598	−0.113419
$805$	20.0128	0.705357
$806$	20.0924	0.707726
$807$	−28.4935	−1.00302
$808$	18.1710	0.639254
$809$	−25.0921	−0.882192	−0.441096	−	0.897460i	$-0.645410\pi$
$809$	−25.0921	−0.882192	−0.441096	+	0.897460i	$0.645410\pi$
$810$	−15.9993	−0.562157
$811$	17.8400	0.626446	0.313223	−	0.949680i	$-0.398591\pi$
$811$	17.8400	0.626446	0.313223	+	0.949680i	$0.398591\pi$
$812$	−5.41061	−0.189875
$813$	−30.2995	−1.06265
$814$	27.5376	0.965192
$815$	33.5398	1.17485
$816$	−14.7340	−0.515794
$817$	29.5447	1.03364
$818$	9.67600	0.338313
$819$	−3.83174	−0.133892
$820$	2.04465	0.0714021
$821$	−29.1488	−1.01730	−0.508650	−	0.860973i	$-0.669855\pi$
$821$	−29.1488	−1.01730	−0.508650	+	0.860973i	$0.669855\pi$
$822$	45.6918	1.59368
$823$	51.0931	1.78099	0.890497	−	0.454990i	$-0.150357\pi$
$823$	51.0931	1.78099	0.890497	+	0.454990i	$0.150357\pi$
$824$	−2.13862	−0.0745023
$825$	−7.85037	−0.273315
$826$	−15.3742	−0.534938
$827$	42.6499	1.48308	0.741541	−	0.670907i	$-0.234095\pi$
$827$	42.6499	1.48308	0.741541	+	0.670907i	$0.234095\pi$
$828$	−2.28595	−0.0794423
$829$	50.2835	1.74642	0.873208	−	0.487347i	$-0.162035\pi$
$829$	50.2835	1.74642	0.873208	+	0.487347i	$0.162035\pi$
$830$	−40.4161	−1.40286
$831$	−20.8527	−0.723371
$832$	−25.3470	−0.878749
$833$	−9.88595	−0.342528
$834$	27.4600	0.950862
$835$	13.8796	0.480324
$836$	1.82738	0.0632011
$837$	−16.0558	−0.554969
$838$	−55.6272	−1.92161
$839$	9.33529	0.322290	0.161145	−	0.986931i	$-0.448481\pi$
$839$	9.33529	0.322290	0.161145	+	0.986931i	$0.448481\pi$
$840$	8.29302	0.286136
$841$	47.2869	1.63058
$842$	17.3225	0.596973
$843$	−43.5161	−1.49878
$844$	11.8042	0.406318
$845$	−10.5060	−0.361418
$846$	−8.96372	−0.308179
$847$	11.2471	0.386455
$848$	−26.9519	−0.925531
$849$	−33.7389	−1.15792
$850$	8.79721	0.301742
$851$	−89.5789	−3.07073
$852$	−6.71381	−0.230011
$853$	−20.4688	−0.700837	−0.350419	−	0.936593i	$-0.613961\pi$
$853$	−20.4688	−0.700837	−0.350419	+	0.936593i	$0.613961\pi$
$854$	−7.48395	−0.256096
$855$	2.06972	0.0707830
$856$	14.0956	0.481778
$857$	45.6302	1.55870	0.779348	−	0.626591i	$-0.215550\pi$
$857$	45.6302	1.55870	0.779348	+	0.626591i	$0.215550\pi$
$858$	19.6776	0.671783
$859$	−17.5396	−0.598445	−0.299222	−	0.954183i	$-0.596727\pi$
$859$	−17.5396	−0.598445	−0.299222	+	0.954183i	$0.596727\pi$
$860$	−7.86870	−0.268321
$861$	7.34488	0.250313
$862$	−20.5966	−0.701523
$863$	−45.5665	−1.55110	−0.775551	−	0.631285i	$-0.782528\pi$
$863$	−45.5665	−1.55110	−0.775551	+	0.631285i	$0.782528\pi$
$864$	−13.1565	−0.447594
$865$	−6.85440	−0.233057
$866$	−25.5045	−0.866680
$867$	−20.0028	−0.679330
$868$	−1.78516	−0.0605924
$869$	−16.8210	−0.570612
$870$	31.4707	1.06696
$871$	21.8535	0.740476
$872$	−14.2035	−0.480993
$873$	−0.745386	−0.0252275
$874$	−33.9748	−1.14922
$875$	−16.9279	−0.572267
$876$	4.34820	0.146912
$877$	14.4126	0.486679	0.243340	−	0.969941i	$-0.421757\pi$
$877$	14.4126	0.486679	0.243340	+	0.969941i	$0.421757\pi$
$878$	39.8657	1.34540
$879$	−8.41773	−0.283923
$880$	12.6300	0.425756
$881$	−24.4578	−0.824005	−0.412003	−	0.911183i	$-0.635171\pi$
$881$	−24.4578	−0.824005	−0.412003	+	0.911183i	$0.635171\pi$
$882$	−4.43926	−0.149478
$883$	35.4403	1.19266	0.596331	−	0.802739i	$-0.296625\pi$
$883$	35.4403	1.19266	0.596331	+	0.802739i	$0.296625\pi$
$884$	−3.85814	−0.129763
$885$	15.6460	0.525935
$886$	8.05519	0.270619
$887$	31.8434	1.06920	0.534598	−	0.845106i	$-0.320463\pi$
$887$	31.8434	1.06920	0.534598	+	0.845106i	$0.320463\pi$
$888$	−37.1203	−1.24568
$889$	−12.8921	−0.432386
$890$	9.66074	0.323829
$891$	−12.5319	−0.419833
$892$	0.246042	0.00823809
$893$	−23.3093	−0.780016
$894$	18.3352	0.613222
$895$	29.5455	0.987599
$896$	19.7691	0.660438
$897$	−64.0107	−2.13726
$898$	31.2813	1.04387
$899$	25.1699	0.839464
$900$	0.691174	0.0230391
$901$	11.7272	0.390690
$902$	9.15341	0.304775
$903$	−28.2664	−0.940646
$904$	−18.4486	−0.613593
$905$	−26.2826	−0.873664
$906$	−36.2157	−1.20319
$907$	33.4314	1.11007	0.555036	−	0.831826i	$-0.312705\pi$
$907$	33.4314	1.11007	0.555036	+	0.831826i	$0.312705\pi$
$908$	−3.13713	−0.104109
$909$	−4.33879	−0.143909
$910$	15.1674	0.502793
$911$	−53.6380	−1.77711	−0.888554	−	0.458772i	$-0.848289\pi$
$911$	−53.6380	−1.77711	−0.888554	+	0.458772i	$0.848289\pi$
$912$	−17.2050	−0.569714
$913$	−31.6570	−1.04769
$914$	−22.8408	−0.755508
$915$	7.61626	0.251786
$916$	−1.29124	−0.0426637
$917$	32.3297	1.06762
$918$	17.6208	0.581573
$919$	20.5741	0.678676	0.339338	−	0.940665i	$-0.389797\pi$
$919$	20.5741	0.678676	0.339338	+	0.940665i	$0.389797\pi$
$920$	−33.6194	−1.10840
$921$	−23.4091	−0.771357
$922$	−6.09950	−0.200876
$923$	45.6222	1.50167
$924$	−1.74831	−0.0575151
$925$	27.0848	0.890544
$926$	4.61427	0.151634
$927$	0.510649	0.0167719
$928$	20.6249	0.677046
$929$	−54.0022	−1.77175	−0.885877	−	0.463920i	$-0.846443\pi$
$929$	−54.0022	−1.77175	−0.885877	+	0.463920i	$0.846443\pi$
$930$	10.3834	0.340484
$931$	−11.5439	−0.378335
$932$	6.10650	0.200025
$933$	8.63381	0.282658
$934$	−27.3930	−0.896327
$935$	−5.49551	−0.179722
$936$	6.43695	0.210398
$937$	51.6049	1.68586	0.842929	−	0.538025i	$-0.180829\pi$
$937$	51.6049	1.68586	0.842929	+	0.538025i	$0.180829\pi$
$938$	−11.0972	−0.362338
$939$	−20.6285	−0.673186
$940$	6.20801	0.202483
$941$	−18.9004	−0.616134	−0.308067	−	0.951365i	$-0.599682\pi$
$941$	−18.9004	−0.616134	−0.308067	+	0.951365i	$0.599682\pi$
$942$	12.8566	0.418891
$943$	−29.7757	−0.969632
$944$	31.5622	1.02726
$945$	−12.1202	−0.394269
$946$	−35.2264	−1.14531
$947$	−1.10661	−0.0359600	−0.0179800	−	0.999838i	$-0.505724\pi$
$947$	−1.10661	−0.0359600	−0.0179800	+	0.999838i	$0.505724\pi$
$948$	−6.10276	−0.198208
$949$	−29.5472	−0.959144
$950$	10.2725	0.333285
$951$	15.6307	0.506860
$952$	−7.27918	−0.235920
$953$	−0.975076	−0.0315858	−0.0157929	−	0.999875i	$-0.505027\pi$
$953$	−0.975076	−0.0315858	−0.0157929	+	0.999875i	$0.505027\pi$
$954$	5.26608	0.170496
$955$	−11.6954	−0.378455
$956$	1.50904	0.0488059
$957$	24.6503	0.796830
$958$	−62.3831	−2.01551
$959$	27.5861	0.890802
$960$	−13.0988	−0.422763
$961$	−22.6955	−0.732113
$962$	−67.8904	−2.18888
$963$	−3.36568	−0.108458
$964$	−1.29185	−0.0416078
$965$	−31.9547	−1.02866
$966$	32.5048	1.04582
$967$	−12.7376	−0.409613	−0.204806	−	0.978802i	$-0.565657\pi$
$967$	−12.7376	−0.409613	−0.204806	+	0.978802i	$0.565657\pi$
$968$	−18.8940	−0.607276
$969$	7.48618	0.240491
$970$	2.95049	0.0947346
$971$	14.8248	0.475749	0.237875	−	0.971296i	$-0.423549\pi$
$971$	14.8248	0.475749	0.237875	+	0.971296i	$0.423549\pi$
$972$	2.54266	0.0815558
$973$	16.5788	0.531492
$974$	−34.0534	−1.09114
$975$	19.3541	0.619827
$976$	15.3640	0.491791
$977$	30.9603	0.990509	0.495254	−	0.868748i	$-0.335075\pi$
$977$	30.9603	0.990509	0.495254	+	0.868748i	$0.335075\pi$
$978$	54.4754	1.74193
$979$	7.56703	0.241843
$980$	3.07450	0.0982113
$981$	3.39146	0.108281
$982$	49.5688	1.58180
$983$	17.3209	0.552450	0.276225	−	0.961093i	$-0.410916\pi$
$983$	17.3209	0.552450	0.276225	+	0.961093i	$0.410916\pi$
$984$	−12.3387	−0.393342
$985$	−13.6888	−0.436162
$986$	−27.6234	−0.879707
$987$	22.3007	0.709840
$988$	−4.50516	−0.143328
$989$	114.590	3.64376
$990$	−2.46774	−0.0784301
$991$	8.10122	0.257344	0.128672	−	0.991687i	$-0.458929\pi$
$991$	8.10122	0.257344	0.128672	+	0.991687i	$0.458929\pi$
$992$	6.80494	0.216057
$993$	4.69090	0.148861
$994$	−23.1671	−0.734814
$995$	12.9070	0.409178
$996$	−11.4854	−0.363928
$997$	−38.9705	−1.23421	−0.617104	−	0.786881i	$-0.711694\pi$
$997$	−38.9705	−1.23421	−0.617104	+	0.786881i	$0.711694\pi$
$998$	−30.0635	−0.951645
$999$	54.2509	1.71642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.30	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.30	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55696 q^{2} +1.55375 q^{3} +0.424139 q^{4} -1.48943 q^{5} -2.41914 q^{6} -1.46054 q^{7} +2.45356 q^{8} -0.585849 q^{9} +O(q^{10})\)	\(q-1.55696 q^{2} +1.55375 q^{3} +0.424139 q^{4} -1.48943 q^{5} -2.41914 q^{6} -1.46054 q^{7} +2.45356 q^{8} -0.585849 q^{9} +2.31899 q^{10} +1.81641 q^{11} +0.659007 q^{12} -4.47814 q^{13} +2.27401 q^{14} -2.31421 q^{15} -4.66838 q^{16} +2.03129 q^{17} +0.912147 q^{18} +2.37195 q^{19} -0.631726 q^{20} -2.26932 q^{21} -2.82809 q^{22} +9.19969 q^{23} +3.81223 q^{24} -2.78159 q^{25} +6.97230 q^{26} -5.57153 q^{27} -0.619471 q^{28} +8.73424 q^{29} +3.60314 q^{30} +2.88175 q^{31} +2.36139 q^{32} +2.82226 q^{33} -3.16265 q^{34} +2.17537 q^{35} -0.248481 q^{36} -9.73717 q^{37} -3.69304 q^{38} -6.95792 q^{39} -3.65441 q^{40} -3.23660 q^{41} +3.53325 q^{42} +12.4559 q^{43} +0.770411 q^{44} +0.872583 q^{45} -14.3236 q^{46} -9.82706 q^{47} -7.25352 q^{48} -4.86682 q^{49} +4.33084 q^{50} +3.15613 q^{51} -1.89935 q^{52} +5.77328 q^{53} +8.67467 q^{54} -2.70542 q^{55} -3.58352 q^{56} +3.68543 q^{57} -13.5989 q^{58} -6.76085 q^{59} -0.981546 q^{60} -3.29109 q^{61} -4.48679 q^{62} +0.855656 q^{63} +5.66017 q^{64} +6.66988 q^{65} -4.39416 q^{66} -4.88003 q^{67} +0.861550 q^{68} +14.2941 q^{69} -3.38698 q^{70} -10.1878 q^{71} -1.43742 q^{72} +6.59811 q^{73} +15.1604 q^{74} -4.32191 q^{75} +1.00604 q^{76} -2.65294 q^{77} +10.8332 q^{78} -9.26054 q^{79} +6.95324 q^{80} -6.89923 q^{81} +5.03928 q^{82} -17.4283 q^{83} -0.962506 q^{84} -3.02547 q^{85} -19.3934 q^{86} +13.5709 q^{87} +4.45668 q^{88} +4.16592 q^{89} -1.35858 q^{90} +6.54049 q^{91} +3.90194 q^{92} +4.47754 q^{93} +15.3004 q^{94} -3.53286 q^{95} +3.66902 q^{96} +1.27232 q^{97} +7.57747 q^{98} -1.06414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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