LMFDB - Embedded newform 4027.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44784 q^{2} +0.695688 q^{3} +3.99191 q^{4} +2.35878 q^{5} -1.70293 q^{6} +2.06757 q^{7} -4.87586 q^{8} -2.51602 q^{9} +O(q^{10})$	\(q-2.44784 q^{2} +0.695688 q^{3} +3.99191 q^{4} +2.35878 q^{5} -1.70293 q^{6} +2.06757 q^{7} -4.87586 q^{8} -2.51602 q^{9} -5.77391 q^{10} -1.68683 q^{11} +2.77712 q^{12} +5.70876 q^{13} -5.06107 q^{14} +1.64098 q^{15} +3.95150 q^{16} -3.66221 q^{17} +6.15880 q^{18} -1.93861 q^{19} +9.41603 q^{20} +1.43838 q^{21} +4.12907 q^{22} -6.40949 q^{23} -3.39208 q^{24} +0.563847 q^{25} -13.9741 q^{26} -3.83743 q^{27} +8.25354 q^{28} -0.205540 q^{29} -4.01684 q^{30} -4.10533 q^{31} +0.0790922 q^{32} -1.17350 q^{33} +8.96450 q^{34} +4.87694 q^{35} -10.0437 q^{36} +3.69075 q^{37} +4.74541 q^{38} +3.97152 q^{39} -11.5011 q^{40} -3.58873 q^{41} -3.52093 q^{42} -3.50143 q^{43} -6.73365 q^{44} -5.93473 q^{45} +15.6894 q^{46} +3.66653 q^{47} +2.74901 q^{48} -2.72516 q^{49} -1.38021 q^{50} -2.54776 q^{51} +22.7888 q^{52} -12.1912 q^{53} +9.39340 q^{54} -3.97885 q^{55} -10.0812 q^{56} -1.34867 q^{57} +0.503127 q^{58} +4.00175 q^{59} +6.55062 q^{60} -4.78005 q^{61} +10.0492 q^{62} -5.20204 q^{63} -8.09661 q^{64} +13.4657 q^{65} +2.87255 q^{66} +7.11138 q^{67} -14.6192 q^{68} -4.45901 q^{69} -11.9380 q^{70} -15.9379 q^{71} +12.2678 q^{72} +11.6981 q^{73} -9.03435 q^{74} +0.392262 q^{75} -7.73876 q^{76} -3.48763 q^{77} -9.72162 q^{78} +1.65660 q^{79} +9.32072 q^{80} +4.87840 q^{81} +8.78464 q^{82} -12.5143 q^{83} +5.74189 q^{84} -8.63836 q^{85} +8.57093 q^{86} -0.142991 q^{87} +8.22473 q^{88} -10.5121 q^{89} +14.5273 q^{90} +11.8032 q^{91} -25.5861 q^{92} -2.85603 q^{93} -8.97508 q^{94} -4.57276 q^{95} +0.0550235 q^{96} -18.2708 q^{97} +6.67076 q^{98} +4.24408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * 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 $

$2$	−2.44784	−1.73088	−0.865441	−	0.501011i	$-0.832962\pi$
$2$	−2.44784	−1.73088	−0.865441	+	0.501011i	$0.832962\pi$
$3$	0.695688	0.401656	0.200828	−	0.979627i	$-0.435637\pi$
$3$	0.695688	0.401656	0.200828	+	0.979627i	$0.435637\pi$
$4$	3.99191	1.99595
$5$	2.35878	1.05488	0.527439	−	0.849593i	$-0.323152\pi$
$5$	2.35878	1.05488	0.527439	+	0.849593i	$0.323152\pi$
$6$	−1.70293	−0.695219
$7$	2.06757	0.781467	0.390734	−	0.920504i	$-0.372221\pi$
$7$	2.06757	0.781467	0.390734	+	0.920504i	$0.372221\pi$
$8$	−4.87586	−1.72388
$9$	−2.51602	−0.838673
$10$	−5.77391	−1.82587
$11$	−1.68683	−0.508597	−0.254298	−	0.967126i	$-0.581845\pi$
$11$	−1.68683	−0.508597	−0.254298	+	0.967126i	$0.581845\pi$
$12$	2.77712	0.801686
$13$	5.70876	1.58332	0.791662	−	0.610959i	$-0.209216\pi$
$13$	5.70876	1.58332	0.791662	+	0.610959i	$0.209216\pi$
$14$	−5.06107	−1.35263
$15$	1.64098	0.423698
$16$	3.95150	0.987875
$17$	−3.66221	−0.888217	−0.444109	−	0.895973i	$-0.646480\pi$
$17$	−3.66221	−0.888217	−0.444109	+	0.895973i	$0.646480\pi$
$18$	6.15880	1.45164
$19$	−1.93861	−0.444748	−0.222374	−	0.974961i	$-0.571381\pi$
$19$	−1.93861	−0.444748	−0.222374	+	0.974961i	$0.571381\pi$
$20$	9.41603	2.10549
$21$	1.43838	0.313881
$22$	4.12907	0.880321
$23$	−6.40949	−1.33647	−0.668235	−	0.743950i	$-0.732950\pi$
$23$	−6.40949	−1.33647	−0.668235	+	0.743950i	$0.732950\pi$
$24$	−3.39208	−0.692405
$25$	0.563847	0.112769
$26$	−13.9741	−2.74055
$27$	−3.83743	−0.738514
$28$	8.25354	1.55977
$29$	−0.205540	−0.0381677	−0.0190839	−	0.999818i	$-0.506075\pi$
$29$	−0.205540	−0.0381677	−0.0190839	+	0.999818i	$0.506075\pi$
$30$	−4.01684	−0.733372
$31$	−4.10533	−0.737339	−0.368669	−	0.929561i	$-0.620187\pi$
$31$	−4.10533	−0.737339	−0.368669	+	0.929561i	$0.620187\pi$
$32$	0.0790922	0.0139817
$33$	−1.17350	−0.204281
$34$	8.96450	1.53740
$35$	4.87694	0.824353
$36$	−10.0437	−1.67395
$37$	3.69075	0.606755	0.303377	−	0.952870i	$-0.401886\pi$
$37$	3.69075	0.606755	0.303377	+	0.952870i	$0.401886\pi$
$38$	4.74541	0.769807
$39$	3.97152	0.635951
$40$	−11.5011	−1.81848
$41$	−3.58873	−0.560466	−0.280233	−	0.959932i	$-0.590412\pi$
$41$	−3.58873	−0.560466	−0.280233	+	0.959932i	$0.590412\pi$
$42$	−3.52093	−0.543291
$43$	−3.50143	−0.533963	−0.266981	−	0.963702i	$-0.586026\pi$
$43$	−3.50143	−0.533963	−0.266981	+	0.963702i	$0.586026\pi$
$44$	−6.73365	−1.01514
$45$	−5.93473	−0.884698
$46$	15.6894	2.31327
$47$	3.66653	0.534819	0.267409	−	0.963583i	$-0.413832\pi$
$47$	3.66653	0.534819	0.267409	+	0.963583i	$0.413832\pi$
$48$	2.74901	0.396786
$49$	−2.72516	−0.389309
$50$	−1.38021	−0.195191
$51$	−2.54776	−0.356758
$52$	22.7888	3.16024
$53$	−12.1912	−1.67459	−0.837297	−	0.546748i	$-0.815866\pi$
$53$	−12.1912	−1.67459	−0.837297	+	0.546748i	$0.815866\pi$
$54$	9.39340	1.27828
$55$	−3.97885	−0.536508
$56$	−10.0812	−1.34715
$57$	−1.34867	−0.178636
$58$	0.503127	0.0660638
$59$	4.00175	0.520983	0.260491	−	0.965476i	$-0.416115\pi$
$59$	4.00175	0.520983	0.260491	+	0.965476i	$0.416115\pi$
$60$	6.55062	0.845682
$61$	−4.78005	−0.612022	−0.306011	−	0.952028i	$-0.598994\pi$
$61$	−4.78005	−0.612022	−0.306011	+	0.952028i	$0.598994\pi$
$62$	10.0492	1.27625
$63$	−5.20204	−0.655395
$64$	−8.09661	−1.01208
$65$	13.4657	1.67021
$66$	2.87255	0.353586
$67$	7.11138	0.868793	0.434397	−	0.900722i	$-0.356962\pi$
$67$	7.11138	0.868793	0.434397	+	0.900722i	$0.356962\pi$
$68$	−14.6192	−1.77284
$69$	−4.45901	−0.536801
$70$	−11.9380	−1.42686
$71$	−15.9379	−1.89148	−0.945741	−	0.324920i	$-0.894662\pi$
$71$	−15.9379	−1.89148	−0.945741	+	0.324920i	$0.894662\pi$
$72$	12.2678	1.44577
$73$	11.6981	1.36916	0.684578	−	0.728939i	$-0.259986\pi$
$73$	11.6981	1.36916	0.684578	+	0.728939i	$0.259986\pi$
$74$	−9.03435	−1.05022
$75$	0.392262	0.0452945
$76$	−7.73876	−0.887697
$77$	−3.48763	−0.397452
$78$	−9.72162	−1.10076
$79$	1.65660	0.186383	0.0931913	−	0.995648i	$-0.470293\pi$
$79$	1.65660	0.186383	0.0931913	+	0.995648i	$0.470293\pi$
$80$	9.32072	1.04209
$81$	4.87840	0.542044
$82$	8.78464	0.970101
$83$	−12.5143	−1.37362	−0.686811	−	0.726836i	$-0.740990\pi$
$83$	−12.5143	−1.37362	−0.686811	+	0.726836i	$0.740990\pi$
$84$	5.74189	0.626491
$85$	−8.63836	−0.936961
$86$	8.57093	0.924227
$87$	−0.142991	−0.0153303
$88$	8.22473	0.876759
$89$	−10.5121	−1.11428	−0.557142	−	0.830417i	$-0.688102\pi$
$89$	−10.5121	−1.11428	−0.557142	+	0.830417i	$0.688102\pi$
$90$	14.5273	1.53131
$91$	11.8032	1.23732
$92$	−25.5861	−2.66753
$93$	−2.85603	−0.296156
$94$	−8.97508	−0.925709
$95$	−4.57276	−0.469156
$96$	0.0550235	0.00561582
$97$	−18.2708	−1.85512	−0.927560	−	0.373674i	$-0.878098\pi$
$97$	−18.2708	−1.85512	−0.927560	+	0.373674i	$0.878098\pi$
$98$	6.67076	0.673848
$99$	4.24408	0.426546
$100$	2.25083	0.225083
$101$	−4.84281	−0.481877	−0.240939	−	0.970540i	$-0.577455\pi$
$101$	−4.84281	−0.481877	−0.240939	+	0.970540i	$0.577455\pi$
$102$	6.23650	0.617505
$103$	0.826503	0.0814378	0.0407189	−	0.999171i	$-0.487035\pi$
$103$	0.826503	0.0814378	0.0407189	+	0.999171i	$0.487035\pi$
$104$	−27.8351	−2.72946
$105$	3.39283	0.331106
$106$	29.8421	2.89853
$107$	9.72554	0.940203	0.470101	−	0.882612i	$-0.344217\pi$
$107$	9.72554	0.940203	0.470101	+	0.882612i	$0.344217\pi$
$108$	−15.3187	−1.47404
$109$	−20.7646	−1.98889	−0.994443	−	0.105274i	$-0.966428\pi$
$109$	−20.7646	−1.98889	−0.994443	+	0.105274i	$0.966428\pi$
$110$	9.73958	0.928632
$111$	2.56761	0.243707
$112$	8.17000	0.771992
$113$	1.13478	0.106751	0.0533756	−	0.998575i	$-0.483002\pi$
$113$	1.13478	0.106751	0.0533756	+	0.998575i	$0.483002\pi$
$114$	3.30133	0.309198
$115$	−15.1186	−1.40981
$116$	−0.820494	−0.0761810
$117$	−14.3633	−1.32789
$118$	−9.79562	−0.901760
$119$	−7.57187	−0.694112
$120$	−8.00117	−0.730404
$121$	−8.15462	−0.741329
$122$	11.7008	1.05934
$123$	−2.49664	−0.225115
$124$	−16.3881	−1.47169
$125$	−10.4639	−0.935921
$126$	12.7337	1.13441
$127$	19.3629	1.71818	0.859088	−	0.511827i	$-0.171031\pi$
$127$	19.3629	1.71818	0.859088	+	0.511827i	$0.171031\pi$
$128$	19.6610	1.73780
$129$	−2.43590	−0.214469
$130$	−32.9618	−2.89095
$131$	−1.69776	−0.148334	−0.0741670	−	0.997246i	$-0.523630\pi$
$131$	−1.69776	−0.148334	−0.0741670	+	0.997246i	$0.523630\pi$
$132$	−4.68452	−0.407735
$133$	−4.00821	−0.347556
$134$	−17.4075	−1.50378
$135$	−9.05166	−0.779042
$136$	17.8564	1.53118
$137$	−8.52511	−0.728350	−0.364175	−	0.931331i	$-0.618649\pi$
$137$	−8.52511	−0.728350	−0.364175	+	0.931331i	$0.618649\pi$
$138$	10.9149	0.929140
$139$	−13.4598	−1.14165	−0.570823	−	0.821073i	$-0.693376\pi$
$139$	−13.4598	−1.14165	−0.570823	+	0.821073i	$0.693376\pi$
$140$	19.4683	1.64537
$141$	2.55077	0.214813
$142$	39.0134	3.27393
$143$	−9.62967	−0.805274
$144$	−9.94205	−0.828504
$145$	−0.484823	−0.0402623
$146$	−28.6350	−2.36985
$147$	−1.89586	−0.156368
$148$	14.7331	1.21105
$149$	17.9295	1.46884	0.734422	−	0.678694i	$-0.237454\pi$
$149$	17.9295	1.46884	0.734422	+	0.678694i	$0.237454\pi$
$150$	−0.960194	−0.0783995
$151$	3.52266	0.286670	0.143335	−	0.989674i	$-0.454217\pi$
$151$	3.52266	0.286670	0.143335	+	0.989674i	$0.454217\pi$
$152$	9.45241	0.766692
$153$	9.21419	0.744923
$154$	8.53714	0.687942
$155$	−9.68357	−0.777803
$156$	15.8539	1.26933
$157$	9.49435	0.757732	0.378866	−	0.925452i	$-0.376314\pi$
$157$	9.49435	0.757732	0.378866	+	0.925452i	$0.376314\pi$
$158$	−4.05510	−0.322606
$159$	−8.48130	−0.672611
$160$	0.186561	0.0147490
$161$	−13.2520	−1.04441
$162$	−11.9415	−0.938215
$163$	9.81595	0.768845	0.384422	−	0.923157i	$-0.374401\pi$
$163$	9.81595	0.768845	0.384422	+	0.923157i	$0.374401\pi$
$164$	−14.3259	−1.11866
$165$	−2.76804	−0.215492
$166$	30.6329	2.37758
$167$	−18.3482	−1.41982	−0.709912	−	0.704291i	$-0.751265\pi$
$167$	−18.3482	−1.41982	−0.709912	+	0.704291i	$0.751265\pi$
$168$	−7.01335	−0.541092
$169$	19.5899	1.50691
$170$	21.1453	1.62177
$171$	4.87759	0.372998
$172$	−13.9774	−1.06576
$173$	13.8732	1.05476	0.527379	−	0.849630i	$-0.323175\pi$
$173$	13.8732	1.05476	0.527379	+	0.849630i	$0.323175\pi$
$174$	0.350020	0.0265349
$175$	1.16579	0.0881256
$176$	−6.66549	−0.502430
$177$	2.78397	0.209256
$178$	25.7320	1.92870
$179$	5.16634	0.386150	0.193075	−	0.981184i	$-0.438154\pi$
$179$	5.16634	0.386150	0.193075	+	0.981184i	$0.438154\pi$
$180$	−23.6909	−1.76582
$181$	−1.71928	−0.127793	−0.0638965	−	0.997957i	$-0.520353\pi$
$181$	−1.71928	−0.127793	−0.0638965	+	0.997957i	$0.520353\pi$
$182$	−28.8924	−2.14165
$183$	−3.32542	−0.245822
$184$	31.2518	2.30391
$185$	8.70566	0.640053
$186$	6.99109	0.512612
$187$	6.17751	0.451745
$188$	14.6365	1.06747
$189$	−7.93415	−0.577124
$190$	11.1934	0.812053
$191$	20.7644	1.50246	0.751230	−	0.660040i	$-0.229461\pi$
$191$	20.7644	1.50246	0.751230	+	0.660040i	$0.229461\pi$
$192$	−5.63272	−0.406506
$193$	−16.0115	−1.15253	−0.576266	−	0.817262i	$-0.695491\pi$
$193$	−16.0115	−1.15253	−0.576266	+	0.817262i	$0.695491\pi$
$194$	44.7240	3.21099
$195$	9.36793	0.670852
$196$	−10.8786	−0.777043
$197$	16.7066	1.19030	0.595149	−	0.803615i	$-0.297093\pi$
$197$	16.7066	1.19030	0.595149	+	0.803615i	$0.297093\pi$
$198$	−10.3888	−0.738301
$199$	22.0671	1.56429	0.782147	−	0.623094i	$-0.214125\pi$
$199$	22.0671	1.56429	0.782147	+	0.623094i	$0.214125\pi$
$200$	−2.74924	−0.194401
$201$	4.94731	0.348956
$202$	11.8544	0.834073
$203$	−0.424967	−0.0298268
$204$	−10.1704	−0.712071
$205$	−8.46504	−0.591224
$206$	−2.02315	−0.140959
$207$	16.1264	1.12086
$208$	22.5582	1.56413
$209$	3.27010	0.226198
$210$	−8.30510	−0.573106
$211$	4.18395	0.288035	0.144018	−	0.989575i	$-0.453998\pi$
$211$	4.18395	0.288035	0.144018	+	0.989575i	$0.453998\pi$
$212$	−48.6662	−3.34241
$213$	−11.0878	−0.759725
$214$	−23.8065	−1.62738
$215$	−8.25910	−0.563266
$216$	18.7108	1.27311
$217$	−8.48804	−0.576206
$218$	50.8283	3.44253
$219$	8.13822	0.549930
$220$	−15.8832	−1.07085
$221$	−20.9067	−1.40634
$222$	−6.28509	−0.421828
$223$	9.22700	0.617886	0.308943	−	0.951081i	$-0.400025\pi$
$223$	9.22700	0.617886	0.308943	+	0.951081i	$0.400025\pi$
$224$	0.163529	0.0109262
$225$	−1.41865	−0.0945767
$226$	−2.77776	−0.184774
$227$	−20.4001	−1.35401	−0.677003	−	0.735981i	$-0.736721\pi$
$227$	−20.4001	−1.35401	−0.677003	+	0.735981i	$0.736721\pi$
$228$	−5.38377	−0.356549
$229$	−12.9115	−0.853214	−0.426607	−	0.904437i	$-0.640291\pi$
$229$	−12.9115	−0.853214	−0.426607	+	0.904437i	$0.640291\pi$
$230$	37.0078	2.44022
$231$	−2.42630	−0.159639
$232$	1.00218	0.0657965
$233$	23.7973	1.55901	0.779505	−	0.626396i	$-0.215471\pi$
$233$	23.7973	1.55901	0.779505	+	0.626396i	$0.215471\pi$
$234$	35.1591	2.29842
$235$	8.64855	0.564169
$236$	15.9746	1.03986
$237$	1.15248	0.0748616
$238$	18.5347	1.20143
$239$	14.9401	0.966398	0.483199	−	0.875511i	$-0.339475\pi$
$239$	14.9401	0.966398	0.483199	+	0.875511i	$0.339475\pi$
$240$	6.48432	0.418561
$241$	−1.45252	−0.0935651	−0.0467826	−	0.998905i	$-0.514897\pi$
$241$	−1.45252	−0.0935651	−0.0467826	+	0.998905i	$0.514897\pi$
$242$	19.9612	1.28315
$243$	14.9061	0.956229
$244$	−19.0815	−1.22157
$245$	−6.42806	−0.410674
$246$	6.11137	0.389647
$247$	−11.0671	−0.704181
$248$	20.0170	1.27108
$249$	−8.70605	−0.551723
$250$	25.6140	1.61997
$251$	13.8322	0.873080	0.436540	−	0.899685i	$-0.356204\pi$
$251$	13.8322	0.873080	0.436540	+	0.899685i	$0.356204\pi$
$252$	−20.7660	−1.30814
$253$	10.8117	0.679725
$254$	−47.3971	−2.97396
$255$	−6.00961	−0.376336
$256$	−31.9337	−1.99585
$257$	−21.2557	−1.32589	−0.662947	−	0.748666i	$-0.730695\pi$
$257$	−21.2557	−1.32589	−0.662947	+	0.748666i	$0.730695\pi$
$258$	5.96269	0.371221
$259$	7.63087	0.474159
$260$	53.7538	3.33367
$261$	0.517141	0.0320102
$262$	4.15584	0.256749
$263$	3.34054	0.205986	0.102993	−	0.994682i	$-0.467158\pi$
$263$	3.34054	0.205986	0.102993	+	0.994682i	$0.467158\pi$
$264$	5.72185	0.352155
$265$	−28.7564	−1.76649
$266$	9.81146	0.601579
$267$	−7.31317	−0.447559
$268$	28.3880	1.73407
$269$	12.7553	0.777707	0.388854	−	0.921300i	$-0.372871\pi$
$269$	12.7553	0.777707	0.388854	+	0.921300i	$0.372871\pi$
$270$	22.1570	1.34843
$271$	−26.8588	−1.63155	−0.815777	−	0.578366i	$-0.803690\pi$
$271$	−26.8588	−1.63155	−0.815777	+	0.578366i	$0.803690\pi$
$272$	−14.4712	−0.877448
$273$	8.21138	0.496975
$274$	20.8681	1.26069
$275$	−0.951112	−0.0573542
$276$	−17.7999	−1.07143
$277$	17.7698	1.06768	0.533841	−	0.845585i	$-0.320748\pi$
$277$	17.7698	1.06768	0.533841	+	0.845585i	$0.320748\pi$
$278$	32.9474	1.97606
$279$	10.3291	0.618386
$280$	−23.7793	−1.42108
$281$	1.34428	0.0801931	0.0400965	−	0.999196i	$-0.487233\pi$
$281$	1.34428	0.0801931	0.0400965	+	0.999196i	$0.487233\pi$
$282$	−6.24386	−0.371816
$283$	24.1961	1.43831	0.719155	−	0.694850i	$-0.244529\pi$
$283$	24.1961	1.43831	0.719155	+	0.694850i	$0.244529\pi$
$284$	−63.6227	−3.77531
$285$	−3.18122	−0.188439
$286$	23.5719	1.39383
$287$	−7.41995	−0.437986
$288$	−0.198997	−0.0117260
$289$	−3.58820	−0.211070
$290$	1.18677	0.0696894
$291$	−12.7108	−0.745120
$292$	46.6976	2.73277
$293$	−19.2158	−1.12260	−0.561300	−	0.827612i	$-0.689699\pi$
$293$	−19.2158	−1.12260	−0.561300	+	0.827612i	$0.689699\pi$
$294$	4.64077	0.270655
$295$	9.43924	0.549574
$296$	−17.9956	−1.04597
$297$	6.47307	0.375606
$298$	−43.8885	−2.54239
$299$	−36.5902	−2.11607
$300$	1.56587	0.0904057
$301$	−7.23944	−0.417274
$302$	−8.62291	−0.496192
$303$	−3.36908	−0.193549
$304$	−7.66043	−0.439356
$305$	−11.2751	−0.645609
$306$	−22.5548	−1.28937
$307$	6.09731	0.347992	0.173996	−	0.984746i	$-0.444332\pi$
$307$	6.09731	0.347992	0.173996	+	0.984746i	$0.444332\pi$
$308$	−13.9223	−0.793295
$309$	0.574989	0.0327100
$310$	23.7038	1.34629
$311$	9.38813	0.532352	0.266176	−	0.963924i	$-0.414240\pi$
$311$	9.38813	0.532352	0.266176	+	0.963924i	$0.414240\pi$
$312$	−19.3646	−1.09630
$313$	−8.53531	−0.482444	−0.241222	−	0.970470i	$-0.577548\pi$
$313$	−8.53531	−0.482444	−0.241222	+	0.970470i	$0.577548\pi$
$314$	−23.2406	−1.31154
$315$	−12.2705	−0.691362
$316$	6.61301	0.372011
$317$	11.0295	0.619480	0.309740	−	0.950821i	$-0.399758\pi$
$317$	11.0295	0.619480	0.309740	+	0.950821i	$0.399758\pi$
$318$	20.7608	1.16421
$319$	0.346709	0.0194120
$320$	−19.0981	−1.06762
$321$	6.76594	0.377638
$322$	32.4389	1.80775
$323$	7.09962	0.395033
$324$	19.4741	1.08189
$325$	3.21887	0.178551
$326$	−24.0279	−1.33078
$327$	−14.4457	−0.798848
$328$	17.4982	0.966175
$329$	7.58081	0.417943
$330$	6.77571	0.372991
$331$	31.5412	1.73366	0.866829	−	0.498605i	$-0.166154\pi$
$331$	31.5412	1.73366	0.866829	+	0.498605i	$0.166154\pi$
$332$	−49.9559	−2.74168
$333$	−9.28598	−0.508869
$334$	44.9133	2.45755
$335$	16.7742	0.916472
$336$	5.68377	0.310075
$337$	−14.3608	−0.782282	−0.391141	−	0.920331i	$-0.627920\pi$
$337$	−14.3608	−0.782282	−0.391141	+	0.920331i	$0.627920\pi$
$338$	−47.9529	−2.60829
$339$	0.789454	0.0428772
$340$	−34.4835	−1.87013
$341$	6.92497	0.375008
$342$	−11.9395	−0.645616
$343$	−20.1074	−1.08570
$344$	17.0725	0.920486
$345$	−10.5178	−0.566260
$346$	−33.9593	−1.82566
$347$	−33.4857	−1.79760	−0.898802	−	0.438354i	$-0.855562\pi$
$347$	−33.4857	−1.79760	−0.898802	+	0.438354i	$0.855562\pi$
$348$	−0.570808	−0.0305985
$349$	15.5699	0.833437	0.416719	−	0.909036i	$-0.363180\pi$
$349$	15.5699	0.833437	0.416719	+	0.909036i	$0.363180\pi$
$350$	−2.85367	−0.152535
$351$	−21.9069	−1.16931
$352$	−0.133415	−0.00711103
$353$	−21.2103	−1.12891	−0.564454	−	0.825464i	$-0.690913\pi$
$353$	−21.2103	−1.12891	−0.564454	+	0.825464i	$0.690913\pi$
$354$	−6.81470	−0.362197
$355$	−37.5941	−1.99529
$356$	−41.9635	−2.22406
$357$	−5.26766	−0.278794
$358$	−12.6463	−0.668380
$359$	−6.08405	−0.321104	−0.160552	−	0.987027i	$-0.551327\pi$
$359$	−6.08405	−0.321104	−0.160552	+	0.987027i	$0.551327\pi$
$360$	28.9369	1.52511
$361$	−15.2418	−0.802199
$362$	4.20852	0.221195
$363$	−5.67308	−0.297759
$364$	47.1174	2.46962
$365$	27.5932	1.44429
$366$	8.14009	0.425489
$367$	−10.2651	−0.535835	−0.267918	−	0.963442i	$-0.586336\pi$
$367$	−10.2651	−0.535835	−0.267918	+	0.963442i	$0.586336\pi$
$368$	−25.3271	−1.32027
$369$	9.02932	0.470048
$370$	−21.3100	−1.10786
$371$	−25.2062	−1.30864
$372$	−11.4010	−0.591114
$373$	−18.4701	−0.956345	−0.478173	−	0.878266i	$-0.658701\pi$
$373$	−18.4701	−0.956345	−0.478173	+	0.878266i	$0.658701\pi$
$374$	−15.1215	−0.781917
$375$	−7.27962	−0.375918
$376$	−17.8775	−0.921962
$377$	−1.17337	−0.0604319
$378$	19.4215	0.998934
$379$	11.6565	0.598756	0.299378	−	0.954135i	$-0.403221\pi$
$379$	11.6565	0.598756	0.299378	+	0.954135i	$0.403221\pi$
$380$	−18.2540	−0.936413
$381$	13.4705	0.690116
$382$	−50.8279	−2.60058
$383$	−4.19503	−0.214356	−0.107178	−	0.994240i	$-0.534182\pi$
$383$	−4.19503	−0.214356	−0.107178	+	0.994240i	$0.534182\pi$
$384$	13.6779	0.697999
$385$	−8.22654	−0.419264
$386$	39.1935	1.99490
$387$	8.80966	0.447820
$388$	−72.9354	−3.70273
$389$	−24.5521	−1.24484	−0.622421	−	0.782683i	$-0.713851\pi$
$389$	−24.5521	−1.24484	−0.622421	+	0.782683i	$0.713851\pi$
$390$	−22.9312	−1.16117
$391$	23.4729	1.18708
$392$	13.2875	0.671121
$393$	−1.18111	−0.0595793
$394$	−40.8951	−2.06027
$395$	3.90757	0.196611
$396$	16.9420	0.851366
$397$	33.2312	1.66783	0.833914	−	0.551894i	$-0.186095\pi$
$397$	33.2312	1.66783	0.833914	+	0.551894i	$0.186095\pi$
$398$	−54.0166	−2.70761
$399$	−2.78847	−0.139598
$400$	2.22804	0.111402
$401$	−20.6620	−1.03181	−0.515906	−	0.856645i	$-0.672545\pi$
$401$	−20.6620	−1.03181	−0.515906	+	0.856645i	$0.672545\pi$
$402$	−12.1102	−0.604002
$403$	−23.4363	−1.16745
$404$	−19.3320	−0.961804
$405$	11.5071	0.571791
$406$	1.04025	0.0516267
$407$	−6.22564	−0.308594
$408$	12.4225	0.615006
$409$	14.1775	0.701034	0.350517	−	0.936556i	$-0.386006\pi$
$409$	14.1775	0.701034	0.350517	+	0.936556i	$0.386006\pi$
$410$	20.7210	1.02334
$411$	−5.93082	−0.292546
$412$	3.29932	0.162546
$413$	8.27388	0.407131
$414$	−39.4748	−1.94008
$415$	−29.5185	−1.44900
$416$	0.451518	0.0221375
$417$	−9.36384	−0.458549
$418$	−8.00468	−0.391522
$419$	−7.24452	−0.353918	−0.176959	−	0.984218i	$-0.556626\pi$
$419$	−7.24452	−0.353918	−0.176959	+	0.984218i	$0.556626\pi$
$420$	13.5439	0.660873
$421$	30.0085	1.46252	0.731262	−	0.682096i	$-0.238932\pi$
$421$	30.0085	1.46252	0.731262	+	0.682096i	$0.238932\pi$
$422$	−10.2416	−0.498555
$423$	−9.22506	−0.448538
$424$	59.4427	2.88679
$425$	−2.06493	−0.100164
$426$	27.1412	1.31499
$427$	−9.88307	−0.478275
$428$	38.8234	1.87660
$429$	−6.69925	−0.323443
$430$	20.2169	0.974947
$431$	24.9839	1.20343	0.601716	−	0.798710i	$-0.294484\pi$
$431$	24.9839	1.20343	0.601716	+	0.798710i	$0.294484\pi$
$432$	−15.1636	−0.729559
$433$	16.6412	0.799725	0.399862	−	0.916575i	$-0.369058\pi$
$433$	16.6412	0.799725	0.399862	+	0.916575i	$0.369058\pi$
$434$	20.7773	0.997344
$435$	−0.337286	−0.0161716
$436$	−82.8903	−3.96972
$437$	12.4255	0.594393
$438$	−19.9210	−0.951864
$439$	−12.7010	−0.606186	−0.303093	−	0.952961i	$-0.598019\pi$
$439$	−12.7010	−0.606186	−0.303093	+	0.952961i	$0.598019\pi$
$440$	19.4003	0.924874
$441$	6.85656	0.326503
$442$	51.1761	2.43420
$443$	9.45430	0.449188	0.224594	−	0.974452i	$-0.427894\pi$
$443$	9.45430	0.449188	0.224594	+	0.974452i	$0.427894\pi$
$444$	10.2497	0.486427
$445$	−24.7958	−1.17544
$446$	−22.5862	−1.06949
$447$	12.4734	0.589970
$448$	−16.7403	−0.790904
$449$	−11.1070	−0.524171	−0.262086	−	0.965045i	$-0.584410\pi$
$449$	−11.1070	−0.524171	−0.262086	+	0.965045i	$0.584410\pi$
$450$	3.47262	0.163701
$451$	6.05357	0.285051
$452$	4.52994	0.213070
$453$	2.45068	0.115143
$454$	49.9362	2.34362
$455$	27.8413	1.30522
$456$	6.57593	0.307946
$457$	−13.8160	−0.646284	−0.323142	−	0.946350i	$-0.604739\pi$
$457$	−13.8160	−0.646284	−0.323142	+	0.946350i	$0.604739\pi$
$458$	31.6052	1.47681
$459$	14.0535	0.655960
$460$	−60.3519	−2.81392
$461$	4.17016	0.194224	0.0971118	−	0.995273i	$-0.469040\pi$
$461$	4.17016	0.194224	0.0971118	+	0.995273i	$0.469040\pi$
$462$	5.93919	0.276316
$463$	−31.8562	−1.48048	−0.740240	−	0.672342i	$-0.765288\pi$
$463$	−31.8562	−1.48048	−0.740240	+	0.672342i	$0.765288\pi$
$464$	−0.812190	−0.0377050
$465$	−6.73675	−0.312409
$466$	−58.2518	−2.69846
$467$	35.9136	1.66188	0.830942	−	0.556359i	$-0.187802\pi$
$467$	35.9136	1.66188	0.830942	+	0.556359i	$0.187802\pi$
$468$	−57.3371	−2.65041
$469$	14.7033	0.678933
$470$	−21.1702	−0.976510
$471$	6.60511	0.304347
$472$	−19.5120	−0.898110
$473$	5.90630	0.271572
$474$	−2.82108	−0.129577
$475$	−1.09308	−0.0501540
$476$	−30.2262	−1.38542
$477$	30.6733	1.40444
$478$	−36.5710	−1.67272
$479$	−41.9697	−1.91765	−0.958823	−	0.284005i	$-0.908337\pi$
$479$	−41.9697	−1.91765	−0.958823	+	0.284005i	$0.908337\pi$
$480$	0.129788	0.00592401
$481$	21.0696	0.960690
$482$	3.55553	0.161950
$483$	−9.21930	−0.419492
$484$	−32.5525	−1.47966
$485$	−43.0969	−1.95693
$486$	−36.4878	−1.65512
$487$	31.3299	1.41969	0.709847	−	0.704356i	$-0.248764\pi$
$487$	31.3299	1.41969	0.709847	+	0.704356i	$0.248764\pi$
$488$	23.3068	1.05505
$489$	6.82884	0.308811
$490$	15.7349	0.710828
$491$	3.86084	0.174237	0.0871187	−	0.996198i	$-0.472234\pi$
$491$	3.86084	0.174237	0.0871187	+	0.996198i	$0.472234\pi$
$492$	−9.96636	−0.449318
$493$	0.752729	0.0339012
$494$	27.0904	1.21885
$495$	10.0109	0.449955
$496$	−16.2222	−0.728398
$497$	−32.9527	−1.47813
$498$	21.3110	0.954968
$499$	10.3075	0.461429	0.230715	−	0.973021i	$-0.425894\pi$
$499$	10.3075	0.461429	0.230715	+	0.973021i	$0.425894\pi$
$500$	−41.7710	−1.86805
$501$	−12.7646	−0.570280
$502$	−33.8589	−1.51120
$503$	2.19104	0.0976937	0.0488468	−	0.998806i	$-0.484445\pi$
$503$	2.19104	0.0976937	0.0488468	+	0.998806i	$0.484445\pi$
$504$	25.3644	1.12982
$505$	−11.4231	−0.508322
$506$	−26.4652	−1.17652
$507$	13.6285	0.605261
$508$	77.2948	3.42940
$509$	8.88080	0.393635	0.196817	−	0.980440i	$-0.436939\pi$
$509$	8.88080	0.393635	0.196817	+	0.980440i	$0.436939\pi$
$510$	14.7105	0.651393
$511$	24.1866	1.06995
$512$	38.8465	1.71679
$513$	7.43929	0.328453
$514$	52.0305	2.29497
$515$	1.94954	0.0859070
$516$	−9.72390	−0.428071
$517$	−6.18480	−0.272007
$518$	−18.6791	−0.820713
$519$	9.65141	0.423650
$520$	−65.6569	−2.87925
$521$	−20.2195	−0.885831	−0.442916	−	0.896563i	$-0.646056\pi$
$521$	−20.2195	−0.885831	−0.442916	+	0.896563i	$0.646056\pi$
$522$	−1.26588	−0.0554059
$523$	−6.99472	−0.305858	−0.152929	−	0.988237i	$-0.548871\pi$
$523$	−6.99472	−0.305858	−0.152929	+	0.988237i	$0.548871\pi$
$524$	−6.77730	−0.296068
$525$	0.811028	0.0353962
$526$	−8.17709	−0.356538
$527$	15.0346	0.654917
$528$	−4.63711	−0.201804
$529$	18.0815	0.786153
$530$	70.3911	3.05759
$531$	−10.0685	−0.436934
$532$	−16.0004	−0.693706
$533$	−20.4872	−0.887399
$534$	17.9015	0.774672
$535$	22.9404	0.991800
$536$	−34.6741	−1.49769
$537$	3.59416	0.155099
$538$	−31.2230	−1.34612
$539$	4.59688	0.198001
$540$	−36.1334	−1.55493
$541$	17.9978	0.773787	0.386894	−	0.922124i	$-0.373548\pi$
$541$	17.9978	0.773787	0.386894	+	0.922124i	$0.373548\pi$
$542$	65.7459	2.82403
$543$	−1.19608	−0.0513288
$544$	−0.289653	−0.0124188
$545$	−48.9791	−2.09803
$546$	−20.1001	−0.860205
$547$	−34.2669	−1.46515	−0.732574	−	0.680687i	$-0.761681\pi$
$547$	−34.2669	−1.46515	−0.732574	+	0.680687i	$0.761681\pi$
$548$	−34.0314	−1.45375
$549$	12.0267	0.513286
$550$	2.32817	0.0992734
$551$	0.398462	0.0169750
$552$	21.7415	0.925379
$553$	3.42514	0.145652
$554$	−43.4975	−1.84803
$555$	6.05643	0.257081
$556$	−53.7303	−2.27867
$557$	−41.0213	−1.73813	−0.869065	−	0.494698i	$-0.835279\pi$
$557$	−41.0213	−1.73813	−0.869065	+	0.494698i	$0.835279\pi$
$558$	−25.2839	−1.07035
$559$	−19.9888	−0.845436
$560$	19.2712	0.814358
$561$	4.29762	0.181446
$562$	−3.29058	−0.138805
$563$	18.9973	0.800643	0.400321	−	0.916375i	$-0.368899\pi$
$563$	18.9973	0.800643	0.400321	+	0.916375i	$0.368899\pi$
$564$	10.1824	0.428757
$565$	2.67670	0.112610
$566$	−59.2281	−2.48954
$567$	10.0864	0.423590
$568$	77.7111	3.26068
$569$	−5.38831	−0.225890	−0.112945	−	0.993601i	$-0.536028\pi$
$569$	−5.38831	−0.225890	−0.112945	+	0.993601i	$0.536028\pi$
$570$	7.78711	0.326166
$571$	−32.1832	−1.34682	−0.673412	−	0.739267i	$-0.735172\pi$
$571$	−32.1832	−1.34682	−0.673412	+	0.739267i	$0.735172\pi$
$572$	−38.4407	−1.60729
$573$	14.4456	0.603472
$574$	18.1628	0.758102
$575$	−3.61397	−0.150713
$576$	20.3712	0.848800
$577$	−27.8574	−1.15972	−0.579860	−	0.814716i	$-0.696893\pi$
$577$	−27.8574	−1.15972	−0.579860	+	0.814716i	$0.696893\pi$
$578$	8.78332	0.365338
$579$	−11.1390	−0.462922
$580$	−1.93537	−0.0803617
$581$	−25.8741	−1.07344
$582$	31.1140	1.28971
$583$	20.5645	0.851694
$584$	−57.0382	−2.36026
$585$	−33.8799	−1.40076
$586$	47.0372	1.94309
$587$	−36.2273	−1.49526	−0.747631	−	0.664114i	$-0.768809\pi$
$587$	−36.2273	−1.49526	−0.747631	+	0.664114i	$0.768809\pi$
$588$	−7.56811	−0.312104
$589$	7.95864	0.327930
$590$	−23.1057	−0.951248
$591$	11.6226	0.478090
$592$	14.5840	0.599398
$593$	4.49511	0.184592	0.0922960	−	0.995732i	$-0.470579\pi$
$593$	4.49511	0.184592	0.0922960	+	0.995732i	$0.470579\pi$
$594$	−15.8450	−0.650129
$595$	−17.8604	−0.732205
$596$	71.5729	2.93174
$597$	15.3518	0.628308
$598$	89.5668	3.66266
$599$	13.9301	0.569167	0.284583	−	0.958651i	$-0.408145\pi$
$599$	13.9301	0.569167	0.284583	+	0.958651i	$0.408145\pi$
$600$	−1.91262	−0.0780822
$601$	−5.39701	−0.220149	−0.110074	−	0.993923i	$-0.535109\pi$
$601$	−5.39701	−0.220149	−0.110074	+	0.993923i	$0.535109\pi$
$602$	17.7210	0.722253
$603$	−17.8924	−0.728633
$604$	14.0621	0.572180
$605$	−19.2350	−0.782012
$606$	8.24697	0.335010
$607$	−42.7122	−1.73363	−0.866817	−	0.498627i	$-0.833838\pi$
$607$	−42.7122	−1.73363	−0.866817	+	0.498627i	$0.833838\pi$
$608$	−0.153329	−0.00621832
$609$	−0.295645	−0.0119801
$610$	27.5996	1.11747
$611$	20.9313	0.846792
$612$	36.7822	1.48683
$613$	31.7344	1.28174	0.640870	−	0.767650i	$-0.278574\pi$
$613$	31.7344	1.28174	0.640870	+	0.767650i	$0.278574\pi$
$614$	−14.9252	−0.602333
$615$	−5.88903	−0.237469
$616$	17.0052	0.685158
$617$	−19.6620	−0.791561	−0.395781	−	0.918345i	$-0.629526\pi$
$617$	−19.6620	−0.791561	−0.395781	+	0.918345i	$0.629526\pi$
$618$	−1.40748	−0.0566171
$619$	−20.6156	−0.828613	−0.414306	−	0.910138i	$-0.635976\pi$
$619$	−20.6156	−0.828613	−0.414306	+	0.910138i	$0.635976\pi$
$620$	−38.6559	−1.55246
$621$	24.5960	0.987002
$622$	−22.9806	−0.921438
$623$	−21.7346	−0.870777
$624$	15.6934	0.628241
$625$	−27.5013	−1.10005
$626$	20.8931	0.835054
$627$	2.27497	0.0908536
$628$	37.9006	1.51240
$629$	−13.5163	−0.538930
$630$	30.0361	1.19667
$631$	4.22036	0.168010	0.0840050	−	0.996465i	$-0.473229\pi$
$631$	4.22036	0.168010	0.0840050	+	0.996465i	$0.473229\pi$
$632$	−8.07737	−0.321301
$633$	2.91073	0.115691
$634$	−26.9985	−1.07225
$635$	45.6728	1.81247
$636$	−33.8565	−1.34250
$637$	−15.5573	−0.616402
$638$	−0.848688	−0.0335999
$639$	40.1001	1.58633
$640$	46.3760	1.83317
$641$	−37.7265	−1.49011	−0.745054	−	0.667004i	$-0.767576\pi$
$641$	−37.7265	−1.49011	−0.745054	+	0.667004i	$0.767576\pi$
$642$	−16.5619	−0.653647
$643$	−3.88626	−0.153259	−0.0766296	−	0.997060i	$-0.524416\pi$
$643$	−3.88626	−0.153259	−0.0766296	+	0.997060i	$0.524416\pi$
$644$	−52.9009	−2.08459
$645$	−5.74576	−0.226239
$646$	−17.3787	−0.683756
$647$	−12.3337	−0.484888	−0.242444	−	0.970165i	$-0.577949\pi$
$647$	−12.3337	−0.484888	−0.242444	+	0.970165i	$0.577949\pi$
$648$	−23.7864	−0.934418
$649$	−6.75025	−0.264970
$650$	−7.87926	−0.309050
$651$	−5.90503	−0.231436
$652$	39.1844	1.53458
$653$	41.0720	1.60727	0.803637	−	0.595120i	$-0.202896\pi$
$653$	41.0720	1.60727	0.803637	+	0.595120i	$0.202896\pi$
$654$	35.3607	1.38271
$655$	−4.00465	−0.156474
$656$	−14.1809	−0.553671
$657$	−29.4326	−1.14827
$658$	−18.5566	−0.723411
$659$	−17.8385	−0.694888	−0.347444	−	0.937701i	$-0.612950\pi$
$659$	−17.8385	−0.694888	−0.347444	+	0.937701i	$0.612950\pi$
$660$	−11.0498	−0.430111
$661$	−4.79986	−0.186693	−0.0933466	−	0.995634i	$-0.529756\pi$
$661$	−4.79986	−0.186693	−0.0933466	+	0.995634i	$0.529756\pi$
$662$	−77.2076	−3.00076
$663$	−14.5445	−0.564863
$664$	61.0179	2.36795
$665$	−9.45450	−0.366630
$666$	22.7306	0.880792
$667$	1.31740	0.0510100
$668$	−73.2441	−2.83390
$669$	6.41912	0.248177
$670$	−41.0605	−1.58630
$671$	8.06310	0.311273
$672$	0.113765	0.00438858
$673$	−15.1035	−0.582196	−0.291098	−	0.956693i	$-0.594021\pi$
$673$	−15.1035	−0.582196	−0.291098	+	0.956693i	$0.594021\pi$
$674$	35.1529	1.35404
$675$	−2.16372	−0.0832818
$676$	78.2010	3.00773
$677$	34.7527	1.33565	0.667827	−	0.744317i	$-0.267225\pi$
$677$	34.7527	1.33565	0.667827	+	0.744317i	$0.267225\pi$
$678$	−1.93245	−0.0742154
$679$	−37.7762	−1.44972
$680$	42.1194	1.61521
$681$	−14.1921	−0.543844
$682$	−16.9512	−0.649095
$683$	−18.0649	−0.691235	−0.345617	−	0.938376i	$-0.612330\pi$
$683$	−18.0649	−0.691235	−0.345617	+	0.938376i	$0.612330\pi$
$684$	19.4709	0.744487
$685$	−20.1089	−0.768321
$686$	49.2197	1.87922
$687$	−8.98236	−0.342698
$688$	−13.8359	−0.527489
$689$	−69.5968	−2.65143
$690$	25.7459	0.980130
$691$	15.2713	0.580948	0.290474	−	0.956883i	$-0.406187\pi$
$691$	15.2713	0.580948	0.290474	+	0.956883i	$0.406187\pi$
$692$	55.3804	2.10525
$693$	8.77493	0.333332
$694$	81.9675	3.11144
$695$	−31.7488	−1.20430
$696$	0.697206	0.0264275
$697$	13.1427	0.497816
$698$	−38.1126	−1.44258
$699$	16.5555	0.626186
$700$	4.65373	0.175895
$701$	43.8120	1.65476	0.827378	−	0.561645i	$-0.189831\pi$
$701$	43.8120	1.65476	0.827378	+	0.561645i	$0.189831\pi$
$702$	53.6246	2.02393
$703$	−7.15493	−0.269853
$704$	13.6576	0.514739
$705$	6.01670	0.226602
$706$	51.9193	1.95401
$707$	−10.0128	−0.376571
$708$	11.1133	0.417665
$709$	37.3863	1.40407	0.702035	−	0.712142i	$-0.252275\pi$
$709$	37.3863	1.40407	0.702035	+	0.712142i	$0.252275\pi$
$710$	92.0241	3.45360
$711$	−4.16804	−0.156314
$712$	51.2557	1.92089
$713$	26.3130	0.985431
$714$	12.8944	0.482560
$715$	−22.7143	−0.849466
$716$	20.6235	0.770737
$717$	10.3937	0.388159
$718$	14.8928	0.555793
$719$	19.0571	0.710711	0.355356	−	0.934731i	$-0.384360\pi$
$719$	19.0571	0.710711	0.355356	+	0.934731i	$0.384360\pi$
$720$	−23.4511	−0.873971
$721$	1.70885	0.0636410
$722$	37.3094	1.38851
$723$	−1.01050	−0.0375810
$724$	−6.86320	−0.255069
$725$	−0.115893	−0.00430415
$726$	13.8868	0.515386
$727$	−7.36926	−0.273311	−0.136655	−	0.990619i	$-0.543635\pi$
$727$	−7.36926	−0.273311	−0.136655	+	0.990619i	$0.543635\pi$
$728$	−57.5509	−2.13298
$729$	−4.26517	−0.157969
$730$	−67.5437	−2.49990
$731$	12.8230	0.474275
$732$	−13.2748	−0.490650
$733$	−45.2827	−1.67255	−0.836277	−	0.548307i	$-0.815273\pi$
$733$	−45.2827	−1.67255	−0.836277	+	0.548307i	$0.815273\pi$
$734$	25.1274	0.927468
$735$	−4.47193	−0.164950
$736$	−0.506941	−0.0186861
$737$	−11.9957	−0.441866
$738$	−22.1023	−0.813597
$739$	32.0061	1.17736	0.588681	−	0.808365i	$-0.299647\pi$
$739$	32.0061	1.17736	0.588681	+	0.808365i	$0.299647\pi$
$740$	34.7522	1.27752
$741$	−7.69923	−0.282838
$742$	61.7007	2.26510
$743$	−16.3470	−0.599712	−0.299856	−	0.953984i	$-0.596939\pi$
$743$	−16.3470	−0.599712	−0.299856	+	0.953984i	$0.596939\pi$
$744$	13.9256	0.510537
$745$	42.2918	1.54945
$746$	45.2118	1.65532
$747$	31.4862	1.15202
$748$	24.6601	0.901661
$749$	20.1082	0.734738
$750$	17.8193	0.650670
$751$	32.0384	1.16910	0.584549	−	0.811358i	$-0.301271\pi$
$751$	32.0384	1.16910	0.584549	+	0.811358i	$0.301271\pi$
$752$	14.4883	0.528334
$753$	9.62289	0.350678
$754$	2.87223	0.104600
$755$	8.30919	0.302402
$756$	−31.6724	−1.15191
$757$	10.8591	0.394682	0.197341	−	0.980335i	$-0.436769\pi$
$757$	10.8591	0.394682	0.197341	+	0.980335i	$0.436769\pi$
$758$	−28.5333	−1.03638
$759$	7.52156	0.273015
$760$	22.2962	0.808767
$761$	−21.0114	−0.761661	−0.380830	−	0.924645i	$-0.624362\pi$
$761$	−21.0114	−0.761661	−0.380830	+	0.924645i	$0.624362\pi$
$762$	−32.9736	−1.19451
$763$	−42.9322	−1.55425
$764$	82.8896	2.99884
$765$	21.7343	0.785804
$766$	10.2688	0.371025
$767$	22.8450	0.824885
$768$	−22.2159	−0.801647
$769$	27.6589	0.997405	0.498702	−	0.866773i	$-0.333810\pi$
$769$	27.6589	0.997405	0.498702	+	0.866773i	$0.333810\pi$
$770$	20.1372	0.725696
$771$	−14.7873	−0.532553
$772$	−63.9164	−2.30040
$773$	−10.3590	−0.372588	−0.186294	−	0.982494i	$-0.559648\pi$
$773$	−10.3590	−0.372588	−0.186294	+	0.982494i	$0.559648\pi$
$774$	−21.5646	−0.775124
$775$	−2.31478	−0.0831493
$776$	89.0860	3.19800
$777$	5.30871	0.190449
$778$	60.0996	2.15467
$779$	6.95717	0.249266
$780$	37.3959	1.33899
$781$	26.8845	0.962002
$782$	−57.4578	−2.05469
$783$	0.788743	0.0281874
$784$	−10.7685	−0.384589
$785$	22.3951	0.799315
$786$	2.89117	0.103125
$787$	8.07368	0.287795	0.143898	−	0.989593i	$-0.454036\pi$
$787$	8.07368	0.287795	0.143898	+	0.989593i	$0.454036\pi$
$788$	66.6913	2.37578
$789$	2.32397	0.0827356
$790$	−9.56508	−0.340310
$791$	2.34624	0.0834225
$792$	−20.6936	−0.735313
$793$	−27.2881	−0.969029
$794$	−81.3447	−2.88681
$795$	−20.0055	−0.709523
$796$	88.0897	3.12226
$797$	−41.9585	−1.48625	−0.743123	−	0.669155i	$-0.766656\pi$
$797$	−41.9585	−1.48625	−0.743123	+	0.669155i	$0.766656\pi$
$798$	6.82572	0.241628
$799$	−13.4276	−0.475035
$800$	0.0445959	0.00157670
$801$	26.4487	0.934520
$802$	50.5773	1.78594
$803$	−19.7326	−0.696349
$804$	19.7492	0.696500
$805$	−31.2587	−1.10172
$806$	57.3683	2.02071
$807$	8.87375	0.312371
$808$	23.6129	0.830697
$809$	−3.03884	−0.106840	−0.0534199	−	0.998572i	$-0.517012\pi$
$809$	−3.03884	−0.106840	−0.0534199	+	0.998572i	$0.517012\pi$
$810$	−28.1674	−0.989703
$811$	45.6225	1.60202	0.801011	−	0.598650i	$-0.204296\pi$
$811$	45.6225	1.60202	0.801011	+	0.598650i	$0.204296\pi$
$812$	−1.69643	−0.0595329
$813$	−18.6853	−0.655323
$814$	15.2394	0.534139
$815$	23.1537	0.811038
$816$	−10.0675	−0.352432
$817$	6.78792	0.237479
$818$	−34.7043	−1.21341
$819$	−29.6972	−1.03770
$820$	−33.7916	−1.18006
$821$	5.36218	0.187141	0.0935707	−	0.995613i	$-0.470172\pi$
$821$	5.36218	0.187141	0.0935707	+	0.995613i	$0.470172\pi$
$822$	14.5177	0.506362
$823$	50.6240	1.76464	0.882321	−	0.470649i	$-0.155980\pi$
$823$	50.6240	1.76464	0.882321	+	0.470649i	$0.155980\pi$
$824$	−4.02992	−0.140389
$825$	−0.661678	−0.0230367
$826$	−20.2531	−0.704696
$827$	−20.7119	−0.720223	−0.360112	−	0.932909i	$-0.617261\pi$
$827$	−20.7119	−0.720223	−0.360112	+	0.932909i	$0.617261\pi$
$828$	64.3750	2.23719
$829$	30.9002	1.07321	0.536605	−	0.843834i	$-0.319707\pi$
$829$	30.9002	1.07321	0.536605	+	0.843834i	$0.319707\pi$
$830$	72.2564	2.50806
$831$	12.3622	0.428841
$832$	−46.2215	−1.60244
$833$	9.98013	0.345791
$834$	22.9212	0.793695
$835$	−43.2793	−1.49774
$836$	13.0539	0.451480
$837$	15.7539	0.544535
$838$	17.7334	0.612590
$839$	−11.9054	−0.411020	−0.205510	−	0.978655i	$-0.565885\pi$
$839$	−11.9054	−0.411020	−0.205510	+	0.978655i	$0.565885\pi$
$840$	−16.5430	−0.570787
$841$	−28.9578	−0.998543
$842$	−73.4559	−2.53146
$843$	0.935200	0.0322100
$844$	16.7020	0.574905
$845$	46.2083	1.58961
$846$	22.5815	0.776366
$847$	−16.8602	−0.579324
$848$	−48.1737	−1.65429
$849$	16.8330	0.577705
$850$	5.05461	0.173372
$851$	−23.6558	−0.810910
$852$	−44.2615	−1.51638
$853$	14.0839	0.482222	0.241111	−	0.970498i	$-0.422488\pi$
$853$	14.0839	0.482222	0.241111	+	0.970498i	$0.422488\pi$
$854$	24.1921	0.827838
$855$	11.5052	0.393468
$856$	−47.4204	−1.62079
$857$	−50.7906	−1.73497	−0.867487	−	0.497459i	$-0.834266\pi$
$857$	−50.7906	−1.73497	−0.867487	+	0.497459i	$0.834266\pi$
$858$	16.3987	0.559842
$859$	−48.9920	−1.67159	−0.835793	−	0.549044i	$-0.814992\pi$
$859$	−48.9920	−1.67159	−0.835793	+	0.549044i	$0.814992\pi$
$860$	−32.9696	−1.12425
$861$	−5.16197	−0.175920
$862$	−61.1566	−2.08300
$863$	−9.69351	−0.329971	−0.164985	−	0.986296i	$-0.552758\pi$
$863$	−9.69351	−0.329971	−0.164985	+	0.986296i	$0.552758\pi$
$864$	−0.303511	−0.0103256
$865$	32.7238	1.11264
$866$	−40.7349	−1.38423
$867$	−2.49627	−0.0847777
$868$	−33.8835	−1.15008
$869$	−2.79440	−0.0947936
$870$	0.825620	0.0279911
$871$	40.5971	1.37558
$872$	101.245	3.42860
$873$	45.9697	1.55584
$874$	−30.4156	−1.02882
$875$	−21.6348	−0.731391
$876$	32.4870	1.09763
$877$	48.5059	1.63793	0.818964	−	0.573845i	$-0.194549\pi$
$877$	48.5059	1.63793	0.818964	+	0.573845i	$0.194549\pi$
$878$	31.0900	1.04924
$879$	−13.3682	−0.450899
$880$	−15.7224	−0.530003
$881$	30.1917	1.01718	0.508592	−	0.861008i	$-0.330166\pi$
$881$	30.1917	1.01718	0.508592	+	0.861008i	$0.330166\pi$
$882$	−16.7837	−0.565138
$883$	16.4321	0.552985	0.276492	−	0.961016i	$-0.410828\pi$
$883$	16.4321	0.552985	0.276492	+	0.961016i	$0.410828\pi$
$884$	−83.4575	−2.80698
$885$	6.56677	0.220740
$886$	−23.1426	−0.777491
$887$	−40.7947	−1.36975	−0.684876	−	0.728659i	$-0.740144\pi$
$887$	−40.7947	−1.36975	−0.684876	+	0.728659i	$0.740144\pi$
$888$	−12.5193	−0.420120
$889$	40.0340	1.34270
$890$	60.6962	2.03454
$891$	−8.22900	−0.275682
$892$	36.8333	1.23327
$893$	−7.10799	−0.237860
$894$	−30.5327	−1.02117
$895$	12.1863	0.407341
$896$	40.6504	1.35804
$897$	−25.4554	−0.849930
$898$	27.1881	0.907279
$899$	0.843807	0.0281425
$900$	−5.66312	−0.188771
$901$	44.6469	1.48740
$902$	−14.8181	−0.493390
$903$	−5.03640	−0.167601
$904$	−5.53303	−0.184026
$905$	−4.05540	−0.134806
$906$	−5.99886	−0.199299
$907$	−26.4933	−0.879695	−0.439848	−	0.898072i	$-0.644968\pi$
$907$	−26.4933	−0.879695	−0.439848	+	0.898072i	$0.644968\pi$
$908$	−81.4355	−2.70253
$909$	12.1846	0.404137
$910$	−68.1509	−2.25918
$911$	−2.26131	−0.0749205	−0.0374603	−	0.999298i	$-0.511927\pi$
$911$	−2.26131	−0.0749205	−0.0374603	+	0.999298i	$0.511927\pi$
$912$	−5.32927	−0.176470
$913$	21.1094	0.698620
$914$	33.8192	1.11864
$915$	−7.84394	−0.259313
$916$	−51.5414	−1.70298
$917$	−3.51024	−0.115918
$918$	−34.4006	−1.13539
$919$	−12.8115	−0.422614	−0.211307	−	0.977420i	$-0.567772\pi$
$919$	−12.8115	−0.422614	−0.211307	+	0.977420i	$0.567772\pi$
$920$	73.7161	2.43035
$921$	4.24183	0.139773
$922$	−10.2079	−0.336178
$923$	−90.9857	−2.99483
$924$	−9.68556	−0.318632
$925$	2.08102	0.0684234
$926$	77.9787	2.56254
$927$	−2.07950	−0.0682996
$928$	−0.0162566	−0.000533648 0
$929$	−13.4315	−0.440673	−0.220336	−	0.975424i	$-0.570715\pi$
$929$	−13.4315	−0.440673	−0.220336	+	0.975424i	$0.570715\pi$
$930$	16.4905	0.540743
$931$	5.28304	0.173145
$932$	94.9964	3.11171
$933$	6.53121	0.213822
$934$	−87.9107	−2.87652
$935$	14.5714	0.476536
$936$	70.0336	2.28912
$937$	−45.8736	−1.49863	−0.749313	−	0.662216i	$-0.769616\pi$
$937$	−45.8736	−1.49863	−0.749313	+	0.662216i	$0.769616\pi$
$938$	−35.9912	−1.17515
$939$	−5.93792	−0.193777
$940$	34.5242	1.12606
$941$	2.73301	0.0890935	0.0445468	−	0.999007i	$-0.485816\pi$
$941$	2.73301	0.0890935	0.0445468	+	0.999007i	$0.485816\pi$
$942$	−16.1682	−0.526790
$943$	23.0019	0.749046
$944$	15.8129	0.514666
$945$	−18.7149	−0.608796
$946$	−14.4577	−0.470059
$947$	22.3141	0.725111	0.362555	−	0.931962i	$-0.381904\pi$
$947$	22.3141	0.725111	0.362555	+	0.931962i	$0.381904\pi$
$948$	4.60059	0.149420
$949$	66.7815	2.16782
$950$	2.67569	0.0868107
$951$	7.67312	0.248818
$952$	36.9194	1.19656
$953$	−4.81827	−0.156079	−0.0780396	−	0.996950i	$-0.524866\pi$
$953$	−4.81827	−0.156079	−0.0780396	+	0.996950i	$0.524866\pi$
$954$	−75.0834	−2.43091
$955$	48.9787	1.58491
$956$	59.6396	1.92888
$957$	0.241202	0.00779694
$958$	102.735	3.31922
$959$	−17.6262	−0.569181
$960$	−13.2863	−0.428815
$961$	−14.1463	−0.456332
$962$	−51.5749	−1.66284
$963$	−24.4696	−0.788522
$964$	−5.79833	−0.186752
$965$	−37.7676	−1.21578
$966$	22.5673	0.726092
$967$	19.9674	0.642110	0.321055	−	0.947061i	$-0.395963\pi$
$967$	19.9674	0.642110	0.321055	+	0.947061i	$0.395963\pi$
$968$	39.7608	1.27796
$969$	4.93912	0.158667
$970$	105.494	3.38721
$971$	8.70014	0.279201	0.139600	−	0.990208i	$-0.455418\pi$
$971$	8.70014	0.279201	0.139600	+	0.990208i	$0.455418\pi$
$972$	59.5039	1.90859
$973$	−27.8291	−0.892160
$974$	−76.6905	−2.45732
$975$	2.23933	0.0717159
$976$	−18.8884	−0.604602
$977$	27.3861	0.876159	0.438080	−	0.898936i	$-0.355659\pi$
$977$	27.3861	0.876159	0.438080	+	0.898936i	$0.355659\pi$
$978$	−16.7159	−0.534516
$979$	17.7321	0.566722
$980$	−25.6602	−0.819686
$981$	52.2441	1.66802
$982$	−9.45071	−0.301584
$983$	20.2173	0.644833	0.322417	−	0.946598i	$-0.395505\pi$
$983$	20.2173	0.644833	0.322417	+	0.946598i	$0.395505\pi$
$984$	12.1733	0.388070
$985$	39.4073	1.25562
$986$	−1.84256	−0.0586790
$987$	5.27388	0.167869
$988$	−44.1787	−1.40551
$989$	22.4424	0.713626
$990$	−24.5050	−0.778819
$991$	−27.8732	−0.885421	−0.442710	−	0.896665i	$-0.645983\pi$
$991$	−27.8732	−0.885421	−0.442710	+	0.896665i	$0.645983\pi$
$992$	−0.324699	−0.0103092
$993$	21.9428	0.696334
$994$	80.6629	2.55847
$995$	52.0514	1.65014
$996$	−34.7537	−1.10121
$997$	−28.2238	−0.893856	−0.446928	−	0.894570i	$-0.647482\pi$
$997$	−28.2238	−0.893856	−0.446928	+	0.894570i	$0.647482\pi$
$998$	−25.2312	−0.798679
$999$	−14.1630	−0.448097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.18	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.18	✓	159	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44784 q^{2} +0.695688 q^{3} +3.99191 q^{4} +2.35878 q^{5} -1.70293 q^{6} +2.06757 q^{7} -4.87586 q^{8} -2.51602 q^{9} +O(q^{10})\)	\(q-2.44784 q^{2} +0.695688 q^{3} +3.99191 q^{4} +2.35878 q^{5} -1.70293 q^{6} +2.06757 q^{7} -4.87586 q^{8} -2.51602 q^{9} -5.77391 q^{10} -1.68683 q^{11} +2.77712 q^{12} +5.70876 q^{13} -5.06107 q^{14} +1.64098 q^{15} +3.95150 q^{16} -3.66221 q^{17} +6.15880 q^{18} -1.93861 q^{19} +9.41603 q^{20} +1.43838 q^{21} +4.12907 q^{22} -6.40949 q^{23} -3.39208 q^{24} +0.563847 q^{25} -13.9741 q^{26} -3.83743 q^{27} +8.25354 q^{28} -0.205540 q^{29} -4.01684 q^{30} -4.10533 q^{31} +0.0790922 q^{32} -1.17350 q^{33} +8.96450 q^{34} +4.87694 q^{35} -10.0437 q^{36} +3.69075 q^{37} +4.74541 q^{38} +3.97152 q^{39} -11.5011 q^{40} -3.58873 q^{41} -3.52093 q^{42} -3.50143 q^{43} -6.73365 q^{44} -5.93473 q^{45} +15.6894 q^{46} +3.66653 q^{47} +2.74901 q^{48} -2.72516 q^{49} -1.38021 q^{50} -2.54776 q^{51} +22.7888 q^{52} -12.1912 q^{53} +9.39340 q^{54} -3.97885 q^{55} -10.0812 q^{56} -1.34867 q^{57} +0.503127 q^{58} +4.00175 q^{59} +6.55062 q^{60} -4.78005 q^{61} +10.0492 q^{62} -5.20204 q^{63} -8.09661 q^{64} +13.4657 q^{65} +2.87255 q^{66} +7.11138 q^{67} -14.6192 q^{68} -4.45901 q^{69} -11.9380 q^{70} -15.9379 q^{71} +12.2678 q^{72} +11.6981 q^{73} -9.03435 q^{74} +0.392262 q^{75} -7.73876 q^{76} -3.48763 q^{77} -9.72162 q^{78} +1.65660 q^{79} +9.32072 q^{80} +4.87840 q^{81} +8.78464 q^{82} -12.5143 q^{83} +5.74189 q^{84} -8.63836 q^{85} +8.57093 q^{86} -0.142991 q^{87} +8.22473 q^{88} -10.5121 q^{89} +14.5273 q^{90} +11.8032 q^{91} -25.5861 q^{92} -2.85603 q^{93} -8.97508 q^{94} -4.57276 q^{95} +0.0550235 q^{96} -18.2708 q^{97} +6.67076 q^{98} +4.24408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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