LMFDB - Embedded newform 8027.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75254 q^{2} -1.96907 q^{3} +5.57647 q^{4} -0.0473576 q^{5} +5.41994 q^{6} +2.07710 q^{7} -9.84438 q^{8} +0.877234 q^{9} +O(q^{10})$	\(q-2.75254 q^{2} -1.96907 q^{3} +5.57647 q^{4} -0.0473576 q^{5} +5.41994 q^{6} +2.07710 q^{7} -9.84438 q^{8} +0.877234 q^{9} +0.130354 q^{10} +0.121541 q^{11} -10.9805 q^{12} +1.39922 q^{13} -5.71730 q^{14} +0.0932504 q^{15} +15.9441 q^{16} +0.345935 q^{17} -2.41462 q^{18} -6.97282 q^{19} -0.264088 q^{20} -4.08996 q^{21} -0.334546 q^{22} -1.00000 q^{23} +19.3843 q^{24} -4.99776 q^{25} -3.85140 q^{26} +4.17987 q^{27} +11.5829 q^{28} -9.29989 q^{29} -0.256675 q^{30} +9.11747 q^{31} -24.1980 q^{32} -0.239323 q^{33} -0.952199 q^{34} -0.0983666 q^{35} +4.89187 q^{36} -9.82780 q^{37} +19.1930 q^{38} -2.75515 q^{39} +0.466206 q^{40} -1.67318 q^{41} +11.2578 q^{42} +1.91238 q^{43} +0.677770 q^{44} -0.0415437 q^{45} +2.75254 q^{46} -7.89257 q^{47} -31.3950 q^{48} -2.68565 q^{49} +13.7565 q^{50} -0.681169 q^{51} +7.80269 q^{52} -1.57193 q^{53} -11.5053 q^{54} -0.00575589 q^{55} -20.4478 q^{56} +13.7300 q^{57} +25.5983 q^{58} -10.2869 q^{59} +0.520008 q^{60} +10.0296 q^{61} -25.0962 q^{62} +1.82210 q^{63} +34.7177 q^{64} -0.0662636 q^{65} +0.658745 q^{66} +2.36703 q^{67} +1.92910 q^{68} +1.96907 q^{69} +0.270758 q^{70} -10.0204 q^{71} -8.63582 q^{72} -5.97182 q^{73} +27.0514 q^{74} +9.84093 q^{75} -38.8837 q^{76} +0.252453 q^{77} +7.58367 q^{78} -11.4072 q^{79} -0.755074 q^{80} -10.8622 q^{81} +4.60549 q^{82} +4.86353 q^{83} -22.8075 q^{84} -0.0163826 q^{85} -5.26391 q^{86} +18.3121 q^{87} -1.19650 q^{88} +7.46542 q^{89} +0.114351 q^{90} +2.90631 q^{91} -5.57647 q^{92} -17.9529 q^{93} +21.7246 q^{94} +0.330216 q^{95} +47.6475 q^{96} +0.302931 q^{97} +7.39236 q^{98} +0.106620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.75254	−1.94634	−0.973170	−	0.230089i	$-0.926098\pi$
$2$	−2.75254	−1.94634	−0.973170	+	0.230089i	$0.926098\pi$
$3$	−1.96907	−1.13684	−0.568421	−	0.822738i	$-0.692446\pi$
$3$	−1.96907	−1.13684	−0.568421	+	0.822738i	$0.692446\pi$
$4$	5.57647	2.78824
$5$	−0.0473576	−0.0211790	−0.0105895	−	0.999944i	$-0.503371\pi$
$5$	−0.0473576	−0.0211790	−0.0105895	+	0.999944i	$0.503371\pi$
$6$	5.41994	2.21268
$7$	2.07710	0.785070	0.392535	−	0.919737i	$-0.371598\pi$
$7$	2.07710	0.785070	0.392535	+	0.919737i	$0.371598\pi$
$8$	−9.84438	−3.48051
$9$	0.877234	0.292411
$10$	0.130354	0.0412215
$11$	0.121541	0.0366460	0.0183230	−	0.999832i	$-0.494167\pi$
$11$	0.121541	0.0366460	0.0183230	+	0.999832i	$0.494167\pi$
$12$	−10.9805	−3.16979
$13$	1.39922	0.388073	0.194036	−	0.980994i	$-0.437842\pi$
$13$	1.39922	0.388073	0.194036	+	0.980994i	$0.437842\pi$
$14$	−5.71730	−1.52801
$15$	0.0932504	0.0240772
$16$	15.9441	3.98602
$17$	0.345935	0.0839015	0.0419508	−	0.999120i	$-0.486643\pi$
$17$	0.345935	0.0839015	0.0419508	+	0.999120i	$0.486643\pi$
$18$	−2.41462	−0.569131
$19$	−6.97282	−1.59967	−0.799837	−	0.600217i	$-0.795081\pi$
$19$	−6.97282	−1.59967	−0.799837	+	0.600217i	$0.795081\pi$
$20$	−0.264088	−0.0590520
$21$	−4.08996	−0.892501
$22$	−0.334546	−0.0713255
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	19.3843	3.95680
$25$	−4.99776	−0.999551
$26$	−3.85140	−0.755321
$27$	4.17987	0.804417
$28$	11.5829	2.18896
$29$	−9.29989	−1.72695	−0.863473	−	0.504394i	$-0.831716\pi$
$29$	−9.29989	−1.72695	−0.863473	+	0.504394i	$0.831716\pi$
$30$	−0.256675	−0.0468623
$31$	9.11747	1.63755	0.818773	−	0.574118i	$-0.194655\pi$
$31$	9.11747	1.63755	0.818773	+	0.574118i	$0.194655\pi$
$32$	−24.1980	−4.27764
$33$	−0.239323	−0.0416607
$34$	−0.952199	−0.163301
$35$	−0.0983666	−0.0166270
$36$	4.89187	0.815311
$37$	−9.82780	−1.61568	−0.807840	−	0.589402i	$-0.799364\pi$
$37$	−9.82780	−1.61568	−0.807840	+	0.589402i	$0.799364\pi$
$38$	19.1930	3.11351
$39$	−2.75515	−0.441178
$40$	0.466206	0.0737137
$41$	−1.67318	−0.261307	−0.130653	−	0.991428i	$-0.541708\pi$
$41$	−1.67318	−0.261307	−0.130653	+	0.991428i	$0.541708\pi$
$42$	11.2578	1.73711
$43$	1.91238	0.291635	0.145818	−	0.989311i	$-0.453419\pi$
$43$	1.91238	0.291635	0.145818	+	0.989311i	$0.453419\pi$
$44$	0.677770	0.102178
$45$	−0.0415437	−0.00619297
$46$	2.75254	0.405840
$47$	−7.89257	−1.15125	−0.575625	−	0.817714i	$-0.695241\pi$
$47$	−7.89257	−1.15125	−0.575625	+	0.817714i	$0.695241\pi$
$48$	−31.3950	−4.53148
$49$	−2.68565	−0.383665
$50$	13.7565	1.94547
$51$	−0.681169	−0.0953828
$52$	7.80269	1.08204
$53$	−1.57193	−0.215921	−0.107961	−	0.994155i	$-0.534432\pi$
$53$	−1.57193	−0.215921	−0.107961	+	0.994155i	$0.534432\pi$
$54$	−11.5053	−1.56567
$55$	−0.00575589	−0.000776125 0
$56$	−20.4478	−2.73245
$57$	13.7300	1.81858
$58$	25.5983	3.36122
$59$	−10.2869	−1.33924	−0.669621	−	0.742703i	$-0.733544\pi$
$59$	−10.2869	−1.33924	−0.669621	+	0.742703i	$0.733544\pi$
$60$	0.520008	0.0671328
$61$	10.0296	1.28416	0.642080	−	0.766637i	$-0.278071\pi$
$61$	10.0296	1.28416	0.642080	+	0.766637i	$0.278071\pi$
$62$	−25.0962	−3.18722
$63$	1.82210	0.229563
$64$	34.7177	4.33972
$65$	−0.0662636	−0.00821898
$66$	0.658745	0.0810859
$67$	2.36703	0.289179	0.144590	−	0.989492i	$-0.453814\pi$
$67$	2.36703	0.289179	0.144590	+	0.989492i	$0.453814\pi$
$68$	1.92910	0.233937
$69$	1.96907	0.237048
$70$	0.270758	0.0323617
$71$	−10.0204	−1.18921	−0.594603	−	0.804019i	$-0.702691\pi$
$71$	−10.0204	−1.18921	−0.594603	+	0.804019i	$0.702691\pi$
$72$	−8.63582	−1.01774
$73$	−5.97182	−0.698948	−0.349474	−	0.936946i	$-0.613640\pi$
$73$	−5.97182	−0.698948	−0.349474	+	0.936946i	$0.613640\pi$
$74$	27.0514	3.14466
$75$	9.84093	1.13633
$76$	−38.8837	−4.46027
$77$	0.252453	0.0287697
$78$	7.58367	0.858682
$79$	−11.4072	−1.28341	−0.641704	−	0.766953i	$-0.721772\pi$
$79$	−11.4072	−1.28341	−0.641704	+	0.766953i	$0.721772\pi$
$80$	−0.755074	−0.0844199
$81$	−10.8622	−1.20691
$82$	4.60549	0.508592
$83$	4.86353	0.533842	0.266921	−	0.963718i	$-0.413994\pi$
$83$	4.86353	0.533842	0.266921	+	0.963718i	$0.413994\pi$
$84$	−22.8075	−2.48850
$85$	−0.0163826	−0.00177695
$86$	−5.26391	−0.567622
$87$	18.3121	1.96327
$88$	−1.19650	−0.127547
$89$	7.46542	0.791333	0.395666	−	0.918394i	$-0.370514\pi$
$89$	7.46542	0.791333	0.395666	+	0.918394i	$0.370514\pi$
$90$	0.114351	0.0120536
$91$	2.90631	0.304665
$92$	−5.57647	−0.581387
$93$	−17.9529	−1.86163
$94$	21.7246	2.24072
$95$	0.330216	0.0338795
$96$	47.6475	4.86300
$97$	0.302931	0.0307580	0.0153790	−	0.999882i	$-0.495105\pi$
$97$	0.302931	0.0307580	0.0153790	+	0.999882i	$0.495105\pi$
$98$	7.39236	0.746741
$99$	0.106620	0.0107157
$100$	−27.8699	−2.78699
$101$	−11.3221	−1.12659	−0.563296	−	0.826255i	$-0.690467\pi$
$101$	−11.3221	−1.12659	−0.563296	+	0.826255i	$0.690467\pi$
$102$	1.87495	0.185647
$103$	5.24921	0.517220	0.258610	−	0.965982i	$-0.416735\pi$
$103$	5.24921	0.517220	0.258610	+	0.965982i	$0.416735\pi$
$104$	−13.7744	−1.35069
$105$	0.193691	0.0189023
$106$	4.32680	0.420256
$107$	1.81304	0.175273	0.0876365	−	0.996153i	$-0.472069\pi$
$107$	1.81304	0.175273	0.0876365	+	0.996153i	$0.472069\pi$
$108$	23.3090	2.24290
$109$	8.34392	0.799202	0.399601	−	0.916689i	$-0.369149\pi$
$109$	8.34392	0.799202	0.399601	+	0.916689i	$0.369149\pi$
$110$	0.0158433	0.00151060
$111$	19.3516	1.83677
$112$	33.1175	3.12931
$113$	8.60918	0.809884	0.404942	−	0.914342i	$-0.367292\pi$
$113$	8.60918	0.809884	0.404942	+	0.914342i	$0.367292\pi$
$114$	−37.7923	−3.53957
$115$	0.0473576	0.00441612
$116$	−51.8606	−4.81513
$117$	1.22744	0.113477
$118$	28.3151	2.60662
$119$	0.718541	0.0658686
$120$	−0.917993	−0.0838009
$121$	−10.9852	−0.998657
$122$	−27.6069	−2.49941
$123$	3.29461	0.297065
$124$	50.8433	4.56586
$125$	0.473470	0.0423484
$126$	−5.01541	−0.446808
$127$	16.7879	1.48968	0.744841	−	0.667242i	$-0.232525\pi$
$127$	16.7879	1.48968	0.744841	+	0.667242i	$0.232525\pi$
$128$	−47.1659	−4.16892
$129$	−3.76561	−0.331544
$130$	0.182393	0.0159969
$131$	−0.337600	−0.0294962	−0.0147481	−	0.999891i	$-0.504695\pi$
$131$	−0.337600	−0.0294962	−0.0147481	+	0.999891i	$0.504695\pi$
$132$	−1.33458	−0.116160
$133$	−14.4832	−1.25586
$134$	−6.51536	−0.562841
$135$	−0.197949	−0.0170367
$136$	−3.40551	−0.292020
$137$	−0.966139	−0.0825428	−0.0412714	−	0.999148i	$-0.513141\pi$
$137$	−0.966139	−0.0825428	−0.0412714	+	0.999148i	$0.513141\pi$
$138$	−5.41994	−0.461376
$139$	5.84906	0.496111	0.248055	−	0.968746i	$-0.420209\pi$
$139$	5.84906	0.496111	0.248055	+	0.968746i	$0.420209\pi$
$140$	−0.548538	−0.0463600
$141$	15.5410	1.30879
$142$	27.5816	2.31460
$143$	0.170062	0.0142213
$144$	13.9867	1.16556
$145$	0.440421	0.0365750
$146$	16.4377	1.36039
$147$	5.28823	0.436166
$148$	−54.8044	−4.50490
$149$	14.4815	1.18637	0.593184	−	0.805067i	$-0.297871\pi$
$149$	14.4815	1.18637	0.593184	+	0.805067i	$0.297871\pi$
$150$	−27.0875	−2.21169
$151$	12.0196	0.978140	0.489070	−	0.872244i	$-0.337336\pi$
$151$	12.0196	0.978140	0.489070	+	0.872244i	$0.337336\pi$
$152$	68.6431	5.56769
$153$	0.303466	0.0245337
$154$	−0.694887	−0.0559956
$155$	−0.431782	−0.0346815
$156$	−15.3640	−1.23011
$157$	0.560194	0.0447084	0.0223542	−	0.999750i	$-0.492884\pi$
$157$	0.560194	0.0447084	0.0223542	+	0.999750i	$0.492884\pi$
$158$	31.3987	2.49795
$159$	3.09524	0.245469
$160$	1.14596	0.0905960
$161$	−2.07710	−0.163698
$162$	29.8985	2.34905
$163$	−5.99691	−0.469714	−0.234857	−	0.972030i	$-0.575462\pi$
$163$	−5.99691	−0.469714	−0.234857	+	0.972030i	$0.575462\pi$
$164$	−9.33044	−0.728585
$165$	0.0113338	0.000882332 0
$166$	−13.3871	−1.03904
$167$	9.93777	0.769008	0.384504	−	0.923123i	$-0.374373\pi$
$167$	9.93777	0.769008	0.384504	+	0.923123i	$0.374373\pi$
$168$	40.2631	3.10636
$169$	−11.0422	−0.849399
$170$	0.0450939	0.00345854
$171$	−6.11679	−0.467763
$172$	10.6643	0.813149
$173$	−7.09918	−0.539741	−0.269870	−	0.962897i	$-0.586981\pi$
$173$	−7.09918	−0.539741	−0.269870	+	0.962897i	$0.586981\pi$
$174$	−50.4049	−3.82118
$175$	−10.3808	−0.784718
$176$	1.93786	0.146072
$177$	20.2557	1.52251
$178$	−20.5489	−1.54020
$179$	8.95732	0.669501	0.334751	−	0.942307i	$-0.391348\pi$
$179$	8.95732	0.669501	0.334751	+	0.942307i	$0.391348\pi$
$180$	−0.231667	−0.0172675
$181$	25.4270	1.88997	0.944986	−	0.327111i	$-0.106075\pi$
$181$	25.4270	1.88997	0.944986	+	0.327111i	$0.106075\pi$
$182$	−7.99974	−0.592980
$183$	−19.7490	−1.45989
$184$	9.84438	0.725737
$185$	0.465421	0.0342184
$186$	49.4161	3.62337
$187$	0.0420453	0.00307465
$188$	−44.0127	−3.20996
$189$	8.68202	0.631524
$190$	−0.908933	−0.0659409
$191$	−17.2483	−1.24805	−0.624023	−	0.781406i	$-0.714503\pi$
$191$	−17.2483	−1.24805	−0.624023	+	0.781406i	$0.714503\pi$
$192$	−68.3616	−4.93357
$193$	12.3714	0.890516	0.445258	−	0.895402i	$-0.353112\pi$
$193$	12.3714	0.890516	0.445258	+	0.895402i	$0.353112\pi$
$194$	−0.833830	−0.0598655
$195$	0.130478	0.00934369
$196$	−14.9765	−1.06975
$197$	12.5249	0.892363	0.446181	−	0.894943i	$-0.352784\pi$
$197$	12.5249	0.892363	0.446181	+	0.894943i	$0.352784\pi$
$198$	−0.293475	−0.0208564
$199$	−12.4130	−0.879934	−0.439967	−	0.898014i	$-0.645010\pi$
$199$	−12.4130	−0.879934	−0.439967	+	0.898014i	$0.645010\pi$
$200$	49.1998	3.47895
$201$	−4.66086	−0.328751
$202$	31.1646	2.19273
$203$	−19.3168	−1.35577
$204$	−3.79852	−0.265950
$205$	0.0792378	0.00553421
$206$	−14.4487	−1.00669
$207$	−0.877234	−0.0609720
$208$	22.3092	1.54687
$209$	−0.847483	−0.0586217
$210$	−0.533141	−0.0367902
$211$	19.5733	1.34748	0.673740	−	0.738969i	$-0.264687\pi$
$211$	19.5733	1.34748	0.673740	+	0.738969i	$0.264687\pi$
$212$	−8.76583	−0.602040
$213$	19.7309	1.35194
$214$	−4.99046	−0.341141
$215$	−0.0905659	−0.00617654
$216$	−41.1483	−2.79978
$217$	18.9379	1.28559
$218$	−22.9670	−1.55552
$219$	11.7589	0.794594
$220$	−0.0320976	−0.00216402
$221$	0.484038	0.0325599
$222$	−53.2661	−3.57499
$223$	26.2544	1.75812	0.879061	−	0.476708i	$-0.158170\pi$
$223$	26.2544	1.75812	0.879061	+	0.476708i	$0.158170\pi$
$224$	−50.2617	−3.35825
$225$	−4.38420	−0.292280
$226$	−23.6971	−1.57631
$227$	17.4787	1.16010	0.580050	−	0.814581i	$-0.303033\pi$
$227$	17.4787	1.16010	0.580050	+	0.814581i	$0.303033\pi$
$228$	76.5647	5.07062
$229$	−16.7238	−1.10514	−0.552570	−	0.833467i	$-0.686353\pi$
$229$	−16.7238	−1.10514	−0.552570	+	0.833467i	$0.686353\pi$
$230$	−0.130354	−0.00859527
$231$	−0.497097	−0.0327066
$232$	91.5517	6.01066
$233$	−3.11526	−0.204088	−0.102044	−	0.994780i	$-0.532538\pi$
$233$	−3.11526	−0.204088	−0.102044	+	0.994780i	$0.532538\pi$
$234$	−3.37858	−0.220864
$235$	0.373773	0.0243823
$236$	−57.3647	−3.73412
$237$	22.4615	1.45903
$238$	−1.97781	−0.128203
$239$	−2.12366	−0.137368	−0.0686841	−	0.997638i	$-0.521880\pi$
$239$	−2.12366	−0.137368	−0.0686841	+	0.997638i	$0.521880\pi$
$240$	1.48679	0.0959721
$241$	−13.4428	−0.865926	−0.432963	−	0.901412i	$-0.642532\pi$
$241$	−13.4428	−0.865926	−0.432963	+	0.901412i	$0.642532\pi$
$242$	30.2373	1.94373
$243$	8.84873	0.567646
$244$	55.9299	3.58054
$245$	0.127186	0.00812562
$246$	−9.06854	−0.578189
$247$	−9.75648	−0.620790
$248$	−89.7558	−5.69950
$249$	−9.57663	−0.606894
$250$	−1.30324	−0.0824244
$251$	21.9849	1.38767	0.693836	−	0.720133i	$-0.255919\pi$
$251$	21.9849	1.38767	0.693836	+	0.720133i	$0.255919\pi$
$252$	10.1609	0.640077
$253$	−0.121541	−0.00764122
$254$	−46.2092	−2.89942
$255$	0.0322586	0.00202011
$256$	60.3906	3.77441
$257$	12.1861	0.760149	0.380074	−	0.924956i	$-0.375898\pi$
$257$	12.1861	0.760149	0.380074	+	0.924956i	$0.375898\pi$
$258$	10.3650	0.645296
$259$	−20.4133	−1.26842
$260$	−0.369517	−0.0229165
$261$	−8.15818	−0.504979
$262$	0.929257	0.0574097
$263$	−20.2645	−1.24956	−0.624781	−	0.780800i	$-0.714812\pi$
$263$	−20.2645	−1.24956	−0.624781	+	0.780800i	$0.714812\pi$
$264$	2.35598	0.145001
$265$	0.0744429	0.00457299
$266$	39.8657	2.44432
$267$	−14.6999	−0.899621
$268$	13.1997	0.806300
$269$	−13.2925	−0.810457	−0.405228	−	0.914216i	$-0.632808\pi$
$269$	−13.2925	−0.810457	−0.405228	+	0.914216i	$0.632808\pi$
$270$	0.544862	0.0331593
$271$	0.156975	0.00953555	0.00476777	−	0.999989i	$-0.498482\pi$
$271$	0.156975	0.00953555	0.00476777	+	0.999989i	$0.498482\pi$
$272$	5.51562	0.334433
$273$	−5.72273	−0.346356
$274$	2.65934	0.160656
$275$	−0.607433	−0.0366296
$276$	10.9805	0.660946
$277$	−1.07842	−0.0647961	−0.0323981	−	0.999475i	$-0.510314\pi$
$277$	−1.07842	−0.0647961	−0.0323981	+	0.999475i	$0.510314\pi$
$278$	−16.0998	−0.965600
$279$	7.99815	0.478837
$280$	0.968358	0.0578704
$281$	−26.2402	−1.56536	−0.782680	−	0.622424i	$-0.786148\pi$
$281$	−26.2402	−1.56536	−0.782680	+	0.622424i	$0.786148\pi$
$282$	−42.7773	−2.54735
$283$	−10.3757	−0.616772	−0.308386	−	0.951261i	$-0.599789\pi$
$283$	−10.3757	−0.616772	−0.308386	+	0.951261i	$0.599789\pi$
$284$	−55.8786	−3.31579
$285$	−0.650218	−0.0385156
$286$	−0.468103	−0.0276795
$287$	−3.47536	−0.205144
$288$	−21.2273	−1.25083
$289$	−16.8803	−0.992961
$290$	−1.21228	−0.0711873
$291$	−0.596492	−0.0349670
$292$	−33.3017	−1.94883
$293$	9.93367	0.580331	0.290166	−	0.956976i	$-0.406290\pi$
$293$	9.93367	0.580331	0.290166	+	0.956976i	$0.406290\pi$
$294$	−14.5561	−0.848927
$295$	0.487164	0.0283638
$296$	96.7486	5.62340
$297$	0.508026	0.0294787
$298$	−39.8608	−2.30907
$299$	−1.39922	−0.0809188
$300$	54.8777	3.16836
$301$	3.97221	0.228954
$302$	−33.0844	−1.90379
$303$	22.2940	1.28076
$304$	−111.175	−6.37634
$305$	−0.474979	−0.0271972
$306$	−0.835301	−0.0477510
$307$	16.8271	0.960376	0.480188	−	0.877166i	$-0.340569\pi$
$307$	16.8271	0.960376	0.480188	+	0.877166i	$0.340569\pi$
$308$	1.40780	0.0802167
$309$	−10.3361	−0.587998
$310$	1.18850	0.0675020
$311$	−3.30084	−0.187173	−0.0935867	−	0.995611i	$-0.529833\pi$
$311$	−3.30084	−0.187173	−0.0935867	+	0.995611i	$0.529833\pi$
$312$	27.1228	1.53553
$313$	−3.71011	−0.209708	−0.104854	−	0.994488i	$-0.533438\pi$
$313$	−3.71011	−0.209708	−0.104854	+	0.994488i	$0.533438\pi$
$314$	−1.54196	−0.0870176
$315$	−0.0862905	−0.00486192
$316$	−63.6118	−3.57844
$317$	13.3621	0.750489	0.375244	−	0.926926i	$-0.377559\pi$
$317$	13.3621	0.750489	0.375244	+	0.926926i	$0.377559\pi$
$318$	−8.51977	−0.477765
$319$	−1.13032	−0.0632857
$320$	−1.64415	−0.0919107
$321$	−3.57000	−0.199258
$322$	5.71730	0.318613
$323$	−2.41214	−0.134215
$324$	−60.5725	−3.36514
$325$	−6.99295	−0.387899
$326$	16.5067	0.914222
$327$	−16.4298	−0.908567
$328$	16.4714	0.909482
$329$	−16.3937	−0.903812
$330$	−0.0311966	−0.00171732
$331$	−8.10109	−0.445276	−0.222638	−	0.974901i	$-0.571467\pi$
$331$	−8.10109	−0.445276	−0.222638	+	0.974901i	$0.571467\pi$
$332$	27.1213	1.48848
$333$	−8.62128	−0.472443
$334$	−27.3541	−1.49675
$335$	−0.112097	−0.00612452
$336$	−65.2106	−3.55753
$337$	14.3455	0.781449	0.390724	−	0.920508i	$-0.372225\pi$
$337$	14.3455	0.781449	0.390724	+	0.920508i	$0.372225\pi$
$338$	30.3941	1.65322
$339$	−16.9521	−0.920711
$340$	−0.0913574	−0.00495455
$341$	1.10815	0.0600095
$342$	16.8367	0.910425
$343$	−20.1181	−1.08627
$344$	−18.8262	−1.01504
$345$	−0.0932504	−0.00502043
$346$	19.5408	1.05052
$347$	−26.6677	−1.43160	−0.715798	−	0.698308i	$-0.753937\pi$
$347$	−26.6677	−1.43160	−0.715798	+	0.698308i	$0.753937\pi$
$348$	102.117	5.47405
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	28.5737	1.52733
$351$	5.84855	0.312172
$352$	−2.94105	−0.156758
$353$	16.4056	0.873183	0.436592	−	0.899660i	$-0.356185\pi$
$353$	16.4056	0.873183	0.436592	+	0.899660i	$0.356185\pi$
$354$	−55.7545	−2.96332
$355$	0.474544	0.0251862
$356$	41.6307	2.20642
$357$	−1.41486	−0.0748822
$358$	−24.6554	−1.30308
$359$	−21.3863	−1.12872	−0.564362	−	0.825527i	$-0.690878\pi$
$359$	−21.3863	−1.12872	−0.564362	+	0.825527i	$0.690878\pi$
$360$	0.408972	0.0215547
$361$	29.6202	1.55896
$362$	−69.9887	−3.67853
$363$	21.6307	1.13532
$364$	16.2070	0.849477
$365$	0.282811	0.0148030
$366$	54.3599	2.84144
$367$	−16.2224	−0.846803	−0.423401	−	0.905942i	$-0.639164\pi$
$367$	−16.2224	−0.846803	−0.423401	+	0.905942i	$0.639164\pi$
$368$	−15.9441	−0.831143
$369$	−1.46777	−0.0764090
$370$	−1.28109	−0.0666007
$371$	−3.26506	−0.169513
$372$	−100.114	−5.19067
$373$	27.4549	1.42156	0.710781	−	0.703413i	$-0.248342\pi$
$373$	27.4549	1.42156	0.710781	+	0.703413i	$0.248342\pi$
$374$	−0.115731	−0.00598432
$375$	−0.932295	−0.0481435
$376$	77.6975	4.00694
$377$	−13.0126	−0.670181
$378$	−23.8976	−1.22916
$379$	−13.5893	−0.698035	−0.349018	−	0.937116i	$-0.613485\pi$
$379$	−13.5893	−0.698035	−0.349018	+	0.937116i	$0.613485\pi$
$380$	1.84144	0.0944639
$381$	−33.0564	−1.69353
$382$	47.4767	2.42912
$383$	−14.3085	−0.731132	−0.365566	−	0.930785i	$-0.619125\pi$
$383$	−14.3085	−0.731132	−0.365566	+	0.930785i	$0.619125\pi$
$384$	92.8730	4.73940
$385$	−0.0119556	−0.000609312 0
$386$	−34.0529	−1.73325
$387$	1.67761	0.0852775
$388$	1.68929	0.0857605
$389$	28.1038	1.42492	0.712460	−	0.701713i	$-0.247581\pi$
$389$	28.1038	1.42492	0.712460	+	0.701713i	$0.247581\pi$
$390$	−0.359145	−0.0181860
$391$	−0.345935	−0.0174947
$392$	26.4386	1.33535
$393$	0.664758	0.0335326
$394$	−34.4753	−1.73684
$395$	0.540217	0.0271813
$396$	0.594563	0.0298779
$397$	24.2615	1.21765	0.608824	−	0.793305i	$-0.291641\pi$
$397$	24.2615	1.21765	0.608824	+	0.793305i	$0.291641\pi$
$398$	34.1673	1.71265
$399$	28.5185	1.42771
$400$	−79.6847	−3.98424
$401$	−26.4851	−1.32260	−0.661302	−	0.750120i	$-0.729996\pi$
$401$	−26.4851	−1.32260	−0.661302	+	0.750120i	$0.729996\pi$
$402$	12.8292	0.639862
$403$	12.7573	0.635487
$404$	−63.1375	−3.14121
$405$	0.514406	0.0255610
$406$	53.1703	2.63880
$407$	−1.19448	−0.0592082
$408$	6.70569	0.331981
$409$	24.9234	1.23238	0.616192	−	0.787596i	$-0.288675\pi$
$409$	24.9234	1.23238	0.616192	+	0.787596i	$0.288675\pi$
$410$	−0.218105	−0.0107714
$411$	1.90239	0.0938382
$412$	29.2721	1.44213
$413$	−21.3670	−1.05140
$414$	2.41462	0.118672
$415$	−0.230325	−0.0113062
$416$	−33.8582	−1.66004
$417$	−11.5172	−0.564000
$418$	2.33273	0.114098
$419$	−6.03026	−0.294597	−0.147299	−	0.989092i	$-0.547058\pi$
$419$	−6.03026	−0.294597	−0.147299	+	0.989092i	$0.547058\pi$
$420$	1.08011	0.0527040
$421$	−22.6768	−1.10520	−0.552599	−	0.833447i	$-0.686364\pi$
$421$	−22.6768	−1.10520	−0.552599	+	0.833447i	$0.686364\pi$
$422$	−53.8762	−2.62265
$423$	−6.92363	−0.336638
$424$	15.4747	0.751517
$425$	−1.72890	−0.0838639
$426$	−54.3101	−2.63133
$427$	20.8325	1.00816
$428$	10.1104	0.488703
$429$	−0.334864	−0.0161674
$430$	0.249286	0.0120216
$431$	−13.4647	−0.648572	−0.324286	−	0.945959i	$-0.605124\pi$
$431$	−13.4647	−0.648572	−0.324286	+	0.945959i	$0.605124\pi$
$432$	66.6443	3.20643
$433$	−9.09789	−0.437217	−0.218608	−	0.975813i	$-0.570152\pi$
$433$	−9.09789	−0.437217	−0.218608	+	0.975813i	$0.570152\pi$
$434$	−52.1273	−2.50219
$435$	−0.867219	−0.0415800
$436$	46.5296	2.22836
$437$	6.97282	0.333555
$438$	−32.3669	−1.54655
$439$	−3.43798	−0.164086	−0.0820430	−	0.996629i	$-0.526144\pi$
$439$	−3.43798	−0.164086	−0.0820430	+	0.996629i	$0.526144\pi$
$440$	0.0566632	0.00270131
$441$	−2.35594	−0.112188
$442$	−1.33233	−0.0633726
$443$	−17.6921	−0.840579	−0.420290	−	0.907390i	$-0.638072\pi$
$443$	−17.6921	−0.840579	−0.420290	+	0.907390i	$0.638072\pi$
$444$	107.914	5.12136
$445$	−0.353544	−0.0167596
$446$	−72.2662	−3.42190
$447$	−28.5150	−1.34871
$448$	72.1122	3.40698
$449$	23.4221	1.10536	0.552678	−	0.833395i	$-0.313606\pi$
$449$	23.4221	1.10536	0.552678	+	0.833395i	$0.313606\pi$
$450$	12.0677	0.568876
$451$	−0.203360	−0.00957585
$452$	48.0089	2.25815
$453$	−23.6674	−1.11199
$454$	−48.1107	−2.25795
$455$	−0.137636	−0.00645248
$456$	−135.163	−6.32958
$457$	−32.6173	−1.52577	−0.762887	−	0.646532i	$-0.776219\pi$
$457$	−32.6173	−1.52577	−0.762887	+	0.646532i	$0.776219\pi$
$458$	46.0329	2.15098
$459$	1.44596	0.0674918
$460$	0.264088	0.0123132
$461$	−17.4279	−0.811699	−0.405849	−	0.913940i	$-0.633024\pi$
$461$	−17.4279	−0.811699	−0.405849	+	0.913940i	$0.633024\pi$
$462$	1.36828	0.0636582
$463$	−27.3737	−1.27216	−0.636082	−	0.771621i	$-0.719446\pi$
$463$	−27.3737	−1.27216	−0.636082	+	0.771621i	$0.719446\pi$
$464$	−148.278	−6.88365
$465$	0.850208	0.0394274
$466$	8.57488	0.397224
$467$	21.1442	0.978439	0.489219	−	0.872161i	$-0.337282\pi$
$467$	21.1442	0.978439	0.489219	+	0.872161i	$0.337282\pi$
$468$	6.84478	0.316400
$469$	4.91657	0.227026
$470$	−1.02883	−0.0474562
$471$	−1.10306	−0.0508264
$472$	101.268	4.66125
$473$	0.232433	0.0106873
$474$	−61.8262	−2.83977
$475$	34.8484	1.59896
$476$	4.00693	0.183657
$477$	−1.37895	−0.0631378
$478$	5.84546	0.267365
$479$	−34.2112	−1.56315	−0.781574	−	0.623813i	$-0.785583\pi$
$479$	−34.2112	−1.56315	−0.781574	+	0.623813i	$0.785583\pi$
$480$	−2.25647	−0.102993
$481$	−13.7512	−0.627002
$482$	37.0018	1.68539
$483$	4.08996	0.186099
$484$	−61.2588	−2.78449
$485$	−0.0143461	−0.000651423 0
$486$	−24.3565	−1.10483
$487$	27.9635	1.26715	0.633573	−	0.773683i	$-0.281588\pi$
$487$	27.9635	1.26715	0.633573	+	0.773683i	$0.281588\pi$
$488$	−98.7354	−4.46954
$489$	11.8083	0.533991
$490$	−0.350085	−0.0158152
$491$	−19.0238	−0.858532	−0.429266	−	0.903178i	$-0.641228\pi$
$491$	−19.0238	−0.858532	−0.429266	+	0.903178i	$0.641228\pi$
$492$	18.3723	0.828287
$493$	−3.21716	−0.144893
$494$	26.8551	1.20827
$495$	−0.00504926	−0.000226948 0
$496$	145.370	6.52730
$497$	−20.8134	−0.933610
$498$	26.3600	1.18122
$499$	−21.1878	−0.948494	−0.474247	−	0.880392i	$-0.657280\pi$
$499$	−21.1878	−0.948494	−0.474247	+	0.880392i	$0.657280\pi$
$500$	2.64029	0.118077
$501$	−19.5682	−0.874241
$502$	−60.5142	−2.70088
$503$	−0.373698	−0.0166624	−0.00833120	−	0.999965i	$-0.502652\pi$
$503$	−0.373698	−0.0166624	−0.00833120	+	0.999965i	$0.502652\pi$
$504$	−17.9375	−0.798998
$505$	0.536188	0.0238601
$506$	0.334546	0.0148724
$507$	21.7428	0.965634
$508$	93.6170	4.15358
$509$	20.1134	0.891511	0.445756	−	0.895155i	$-0.352935\pi$
$509$	20.1134	0.891511	0.445756	+	0.895155i	$0.352935\pi$
$510$	−0.0887930	−0.00393182
$511$	−12.4041	−0.548724
$512$	−71.8956	−3.17737
$513$	−29.1455	−1.28681
$514$	−33.5428	−1.47951
$515$	−0.248590	−0.0109542
$516$	−20.9988	−0.924422
$517$	−0.959271	−0.0421887
$518$	56.1885	2.46878
$519$	13.9788	0.613600
$520$	0.652324	0.0286063
$521$	9.63029	0.421911	0.210955	−	0.977496i	$-0.432343\pi$
$521$	9.63029	0.421911	0.210955	+	0.977496i	$0.432343\pi$
$522$	22.4557	0.982860
$523$	−4.85415	−0.212257	−0.106128	−	0.994352i	$-0.533845\pi$
$523$	−4.85415	−0.212257	−0.106128	+	0.994352i	$0.533845\pi$
$524$	−1.88262	−0.0822425
$525$	20.4406	0.892101
$526$	55.7788	2.43207
$527$	3.15405	0.137393
$528$	−3.81578	−0.166061
$529$	1.00000	0.0434783
$530$	−0.204907	−0.00890059
$531$	−9.02403	−0.391610
$532$	−80.7654	−3.50162
$533$	−2.34114	−0.101406
$534$	40.4621	1.75097
$535$	−0.0858612	−0.00371210
$536$	−23.3020	−1.00649
$537$	−17.6376	−0.761118
$538$	36.5881	1.57742
$539$	−0.326417	−0.0140598
$540$	−1.10386	−0.0475024
$541$	22.3129	0.959307	0.479653	−	0.877458i	$-0.340762\pi$
$541$	22.3129	0.959307	0.479653	+	0.877458i	$0.340762\pi$
$542$	−0.432080	−0.0185594
$543$	−50.0675	−2.14860
$544$	−8.37093	−0.358900
$545$	−0.395148	−0.0169263
$546$	15.7520	0.674125
$547$	26.0423	1.11349	0.556744	−	0.830684i	$-0.312050\pi$
$547$	26.0423	1.11349	0.556744	+	0.830684i	$0.312050\pi$
$548$	−5.38765	−0.230149
$549$	8.79832	0.375503
$550$	1.67198	0.0712936
$551$	64.8465	2.76255
$552$	−19.3843	−0.825049
$553$	−23.6939	−1.00757
$554$	2.96840	0.126115
$555$	−0.916447	−0.0389010
$556$	32.6171	1.38327
$557$	−11.5053	−0.487494	−0.243747	−	0.969839i	$-0.578377\pi$
$557$	−11.5053	−0.487494	−0.243747	+	0.969839i	$0.578377\pi$
$558$	−22.0152	−0.931979
$559$	2.67584	0.113176
$560$	−1.56837	−0.0662756
$561$	−0.0827900	−0.00349540
$562$	72.2272	3.04672
$563$	−31.6628	−1.33443	−0.667214	−	0.744866i	$-0.732513\pi$
$563$	−31.6628	−1.33443	−0.667214	+	0.744866i	$0.732513\pi$
$564$	86.6641	3.64922
$565$	−0.407711	−0.0171525
$566$	28.5596	1.20045
$567$	−22.5618	−0.947507
$568$	98.6449	4.13905
$569$	1.88109	0.0788592	0.0394296	−	0.999222i	$-0.487446\pi$
$569$	1.88109	0.0788592	0.0394296	+	0.999222i	$0.487446\pi$
$570$	1.78975	0.0749644
$571$	0.390181	0.0163286	0.00816428	−	0.999967i	$-0.497401\pi$
$571$	0.390181	0.0163286	0.00816428	+	0.999967i	$0.497401\pi$
$572$	0.948347	0.0396524
$573$	33.9632	1.41883
$574$	9.56607	0.399280
$575$	4.99776	0.208421
$576$	30.4556	1.26898
$577$	29.3985	1.22388	0.611938	−	0.790905i	$-0.290390\pi$
$577$	29.3985	1.22388	0.611938	+	0.790905i	$0.290390\pi$
$578$	46.4638	1.93264
$579$	−24.3602	−1.01238
$580$	2.45599	0.101980
$581$	10.1020	0.419103
$582$	1.64187	0.0680576
$583$	−0.191054	−0.00791265
$584$	58.7888	2.43270
$585$	−0.0581286	−0.00240332
$586$	−27.3428	−1.12952
$587$	44.2009	1.82437	0.912183	−	0.409784i	$-0.134396\pi$
$587$	44.2009	1.82437	0.912183	+	0.409784i	$0.134396\pi$
$588$	29.4897	1.21613
$589$	−63.5744	−2.61954
$590$	−1.34094	−0.0552055
$591$	−24.6624	−1.01448
$592$	−156.695	−6.44014
$593$	8.71160	0.357742	0.178871	−	0.983872i	$-0.442755\pi$
$593$	8.71160	0.357742	0.178871	+	0.983872i	$0.442755\pi$
$594$	−1.39836	−0.0573755
$595$	−0.0340284	−0.00139503
$596$	80.7555	3.30787
$597$	24.4421	1.00035
$598$	3.85140	0.157495
$599$	4.93572	0.201668	0.100834	−	0.994903i	$-0.467849\pi$
$599$	4.93572	0.201668	0.100834	+	0.994903i	$0.467849\pi$
$600$	−96.8778	−3.95502
$601$	−29.7790	−1.21471	−0.607355	−	0.794430i	$-0.707770\pi$
$601$	−29.7790	−1.21471	−0.607355	+	0.794430i	$0.707770\pi$
$602$	−10.9337	−0.445623
$603$	2.07644	0.0845593
$604$	67.0269	2.72729
$605$	0.520234	0.0211505
$606$	−61.3652	−2.49279
$607$	9.63152	0.390931	0.195466	−	0.980711i	$-0.437378\pi$
$607$	9.63152	0.390931	0.195466	+	0.980711i	$0.437378\pi$
$608$	168.728	6.84283
$609$	38.0361	1.54130
$610$	1.30740	0.0529350
$611$	−11.0434	−0.446769
$612$	1.69227	0.0684059
$613$	−8.92866	−0.360625	−0.180313	−	0.983609i	$-0.557711\pi$
$613$	−8.92866	−0.360625	−0.180313	+	0.983609i	$0.557711\pi$
$614$	−46.3174	−1.86922
$615$	−0.156025	−0.00629153
$616$	−2.48524	−0.100133
$617$	33.4387	1.34619	0.673096	−	0.739555i	$-0.264964\pi$
$617$	33.4387	1.34619	0.673096	+	0.739555i	$0.264964\pi$
$618$	28.4504	1.14444
$619$	20.5091	0.824330	0.412165	−	0.911109i	$-0.364773\pi$
$619$	20.5091	0.824330	0.412165	+	0.911109i	$0.364773\pi$
$620$	−2.40782	−0.0967003
$621$	−4.17987	−0.167733
$622$	9.08569	0.364303
$623$	15.5064	0.621252
$624$	−43.9284	−1.75855
$625$	24.9664	0.998655
$626$	10.2122	0.408163
$627$	1.66875	0.0666436
$628$	3.12391	0.124657
$629$	−3.39978	−0.135558
$630$	0.237518	0.00946294
$631$	21.1312	0.841221	0.420611	−	0.907241i	$-0.361816\pi$
$631$	21.1312	0.841221	0.420611	+	0.907241i	$0.361816\pi$
$632$	112.297	4.46692
$633$	−38.5411	−1.53187
$634$	−36.7796	−1.46071
$635$	−0.795033	−0.0315499
$636$	17.2605	0.684424
$637$	−3.75781	−0.148890
$638$	3.11125	0.123175
$639$	−8.79026	−0.347737
$640$	2.23367	0.0882934
$641$	−31.4491	−1.24217	−0.621083	−	0.783745i	$-0.713307\pi$
$641$	−31.4491	−1.24217	−0.621083	+	0.783745i	$0.713307\pi$
$642$	9.82656	0.387823
$643$	12.1901	0.480731	0.240365	−	0.970683i	$-0.422733\pi$
$643$	12.1901	0.480731	0.240365	+	0.970683i	$0.422733\pi$
$644$	−11.5829	−0.456430
$645$	0.178330	0.00702175
$646$	6.63951	0.261228
$647$	25.9772	1.02127	0.510635	−	0.859797i	$-0.329410\pi$
$647$	25.9772	1.02127	0.510635	+	0.859797i	$0.329410\pi$
$648$	106.931	4.20066
$649$	−1.25028	−0.0490779
$650$	19.2484	0.754983
$651$	−37.2900	−1.46151
$652$	−33.4416	−1.30967
$653$	4.31069	0.168690	0.0843452	−	0.996437i	$-0.473120\pi$
$653$	4.31069	0.168690	0.0843452	+	0.996437i	$0.473120\pi$
$654$	45.2235	1.76838
$655$	0.0159879	0.000624700 0
$656$	−26.6773	−1.04158
$657$	−5.23868	−0.204380
$658$	45.1242	1.75913
$659$	−16.5483	−0.644631	−0.322316	−	0.946632i	$-0.604461\pi$
$659$	−16.5483	−0.644631	−0.322316	+	0.946632i	$0.604461\pi$
$660$	0.0632024	0.00246015
$661$	39.8877	1.55145	0.775725	−	0.631071i	$-0.217384\pi$
$661$	39.8877	1.55145	0.775725	+	0.631071i	$0.217384\pi$
$662$	22.2986	0.866658
$663$	−0.953104	−0.0370155
$664$	−47.8784	−1.85804
$665$	0.685892	0.0265978
$666$	23.7304	0.919534
$667$	9.29989	0.360093
$668$	55.4177	2.14417
$669$	−51.6967	−1.99871
$670$	0.308552	0.0119204
$671$	1.21901	0.0470594
$672$	98.9687	3.81780
$673$	−48.6133	−1.87390	−0.936952	−	0.349457i	$-0.886366\pi$
$673$	−48.6133	−1.87390	−0.936952	+	0.349457i	$0.886366\pi$
$674$	−39.4865	−1.52096
$675$	−20.8900	−0.804056
$676$	−61.5765	−2.36833
$677$	19.8513	0.762946	0.381473	−	0.924380i	$-0.375417\pi$
$677$	19.8513	0.762946	0.381473	+	0.924380i	$0.375417\pi$
$678$	46.6613	1.79202
$679$	0.629218	0.0241472
$680$	0.161277	0.00618469
$681$	−34.4167	−1.31885
$682$	−3.05022	−0.116799
$683$	24.0119	0.918791	0.459396	−	0.888232i	$-0.348066\pi$
$683$	24.0119	0.918791	0.459396	+	0.888232i	$0.348066\pi$
$684$	−34.1101	−1.30423
$685$	0.0457540	0.00174817
$686$	55.3758	2.11426
$687$	32.9303	1.25637
$688$	30.4912	1.16247
$689$	−2.19947	−0.0837932
$690$	0.256675	0.00977147
$691$	1.97425	0.0751041	0.0375520	−	0.999295i	$-0.488044\pi$
$691$	1.97425	0.0751041	0.0375520	+	0.999295i	$0.488044\pi$
$692$	−39.5884	−1.50492
$693$	0.221460	0.00841258
$694$	73.4038	2.78637
$695$	−0.276998	−0.0105071
$696$	−180.272	−6.83318
$697$	−0.578811	−0.0219240
$698$	−2.75254	−0.104185
$699$	6.13417	0.232015
$700$	−57.8885	−2.18798
$701$	48.4352	1.82937	0.914685	−	0.404167i	$-0.132439\pi$
$701$	48.4352	1.82937	0.914685	+	0.404167i	$0.132439\pi$
$702$	−16.0984	−0.607593
$703$	68.5274	2.58456
$704$	4.21963	0.159033
$705$	−0.735986	−0.0277188
$706$	−45.1571	−1.69951
$707$	−23.5172	−0.884454
$708$	112.955	4.24511
$709$	41.3751	1.55387	0.776937	−	0.629578i	$-0.216772\pi$
$709$	41.3751	1.55387	0.776937	+	0.629578i	$0.216772\pi$
$710$	−1.30620	−0.0490208
$711$	−10.0068	−0.375283
$712$	−73.4924	−2.75424
$713$	−9.11747	−0.341452
$714$	3.89445	0.145746
$715$	−0.00805374	−0.000301193 0
$716$	49.9502	1.86673
$717$	4.18164	0.156166
$718$	58.8666	2.19688
$719$	37.9985	1.41710	0.708552	−	0.705659i	$-0.249349\pi$
$719$	37.9985	1.41710	0.708552	+	0.705659i	$0.249349\pi$
$720$	−0.662377	−0.0246853
$721$	10.9031	0.406054
$722$	−81.5307	−3.03426
$723$	26.4698	0.984422
$724$	141.793	5.26969
$725$	46.4786	1.72617
$726$	−59.5393	−2.20971
$727$	11.6097	0.430580	0.215290	−	0.976550i	$-0.430930\pi$
$727$	11.6097	0.430580	0.215290	+	0.976550i	$0.430930\pi$
$728$	−28.6109	−1.06039
$729$	15.1627	0.561583
$730$	−0.778449	−0.0288117
$731$	0.661559	0.0244687
$732$	−110.130	−4.07051
$733$	16.7897	0.620141	0.310071	−	0.950714i	$-0.399647\pi$
$733$	16.7897	0.620141	0.310071	+	0.950714i	$0.399647\pi$
$734$	44.6528	1.64817
$735$	−0.250438	−0.00923755
$736$	24.1980	0.891950
$737$	0.287692	0.0105973
$738$	4.04009	0.148718
$739$	−25.1770	−0.926150	−0.463075	−	0.886319i	$-0.653254\pi$
$739$	−25.1770	−0.926150	−0.463075	+	0.886319i	$0.653254\pi$
$740$	2.59541	0.0954091
$741$	19.2112	0.705741
$742$	8.98721	0.329931
$743$	33.9835	1.24673	0.623367	−	0.781929i	$-0.285764\pi$
$743$	33.9835	1.24673	0.623367	+	0.781929i	$0.285764\pi$
$744$	176.735	6.47943
$745$	−0.685808	−0.0251261
$746$	−75.5708	−2.76684
$747$	4.26645	0.156101
$748$	0.234464	0.00857286
$749$	3.76586	0.137602
$750$	2.56618	0.0937036
$751$	5.74398	0.209601	0.104800	−	0.994493i	$-0.466580\pi$
$751$	5.74398	0.209601	0.104800	+	0.994493i	$0.466580\pi$
$752$	−125.840	−4.58891
$753$	−43.2897	−1.57757
$754$	35.8176	1.30440
$755$	−0.569219	−0.0207160
$756$	48.4150	1.76084
$757$	21.2309	0.771650	0.385825	−	0.922572i	$-0.373917\pi$
$757$	21.2309	0.771650	0.385825	+	0.922572i	$0.373917\pi$
$758$	37.4051	1.35861
$759$	0.239323	0.00868686
$760$	−3.25077	−0.117918
$761$	−9.07674	−0.329032	−0.164516	−	0.986374i	$-0.552606\pi$
$761$	−9.07674	−0.329032	−0.164516	+	0.986374i	$0.552606\pi$
$762$	90.9892	3.29619
$763$	17.3312	0.627430
$764$	−96.1849	−3.47985
$765$	−0.0143714	−0.000519599 0
$766$	39.3848	1.42303
$767$	−14.3936	−0.519724
$768$	−118.913	−4.29091
$769$	−44.5637	−1.60701	−0.803504	−	0.595300i	$-0.797033\pi$
$769$	−44.5637	−1.60701	−0.803504	+	0.595300i	$0.797033\pi$
$770$	0.0329082	0.00118593
$771$	−23.9953	−0.864170
$772$	68.9890	2.48297
$773$	14.5306	0.522629	0.261314	−	0.965254i	$-0.415844\pi$
$773$	14.5306	0.522629	0.261314	+	0.965254i	$0.415844\pi$
$774$	−4.61768	−0.165979
$775$	−45.5669	−1.63681
$776$	−2.98217	−0.107054
$777$	40.1953	1.44200
$778$	−77.3569	−2.77338
$779$	11.6668	0.418006
$780$	0.727604	0.0260524
$781$	−1.21789	−0.0435796
$782$	0.952199	0.0340506
$783$	−38.8724	−1.38919
$784$	−42.8203	−1.52930
$785$	−0.0265295	−0.000946877 0
$786$	−1.82977	−0.0652658
$787$	7.82889	0.279070	0.139535	−	0.990217i	$-0.455439\pi$
$787$	7.82889	0.279070	0.139535	+	0.990217i	$0.455439\pi$
$788$	69.8448	2.48812
$789$	39.9022	1.42056
$790$	−1.48697	−0.0529039
$791$	17.8821	0.635816
$792$	−1.04961	−0.0372961
$793$	14.0336	0.498348
$794$	−66.7807	−2.36996
$795$	−0.146583	−0.00519877
$796$	−69.2208	−2.45346
$797$	10.1030	0.357865	0.178932	−	0.983861i	$-0.442736\pi$
$797$	10.1030	0.357865	0.178932	+	0.983861i	$0.442736\pi$
$798$	−78.4983	−2.77881
$799$	−2.73032	−0.0965916
$800$	120.936	4.27572
$801$	6.54891	0.231395
$802$	72.9013	2.57424
$803$	−0.725821	−0.0256137
$804$	−25.9911	−0.916636
$805$	0.0983666	0.00346697
$806$	−35.1150	−1.23687
$807$	26.1738	0.921362
$808$	111.459	3.92112
$809$	10.1385	0.356452	0.178226	−	0.983990i	$-0.442964\pi$
$809$	10.1385	0.356452	0.178226	+	0.983990i	$0.442964\pi$
$810$	−1.41592	−0.0497505
$811$	35.0989	1.23249	0.616245	−	0.787554i	$-0.288653\pi$
$811$	35.0989	1.23249	0.616245	+	0.787554i	$0.288653\pi$
$812$	−107.720	−3.78022
$813$	−0.309094	−0.0108404
$814$	3.28786	0.115239
$815$	0.283999	0.00994806
$816$	−10.8606	−0.380198
$817$	−13.3347	−0.466522
$818$	−68.6027	−2.39864
$819$	2.54952	0.0890873
$820$	0.441868	0.0154307
$821$	7.28355	0.254198	0.127099	−	0.991890i	$-0.459433\pi$
$821$	7.28355	0.254198	0.127099	+	0.991890i	$0.459433\pi$
$822$	−5.23641	−0.182641
$823$	−16.3147	−0.568695	−0.284347	−	0.958721i	$-0.591777\pi$
$823$	−16.3147	−0.568695	−0.284347	+	0.958721i	$0.591777\pi$
$824$	−51.6753	−1.80019
$825$	1.19608	0.0416421
$826$	58.8134	2.04638
$827$	5.52157	0.192004	0.0960020	−	0.995381i	$-0.469394\pi$
$827$	5.52157	0.192004	0.0960020	+	0.995381i	$0.469394\pi$
$828$	−4.89187	−0.170004
$829$	−27.4692	−0.954043	−0.477022	−	0.878891i	$-0.658284\pi$
$829$	−27.4692	−0.954043	−0.477022	+	0.878891i	$0.658284\pi$
$830$	0.633979	0.0220057
$831$	2.12349	0.0736630
$832$	48.5776	1.68413
$833$	−0.929060	−0.0321900
$834$	31.7015	1.09773
$835$	−0.470629	−0.0162868
$836$	−4.72597	−0.163451
$837$	38.1099	1.31727
$838$	16.5985	0.573386
$839$	−40.6799	−1.40443	−0.702213	−	0.711967i	$-0.747804\pi$
$839$	−40.6799	−1.40443	−0.702213	+	0.711967i	$0.747804\pi$
$840$	−1.90676	−0.0657896
$841$	57.4880	1.98234
$842$	62.4187	2.15109
$843$	51.6688	1.77957
$844$	109.150	3.75709
$845$	0.522932	0.0179894
$846$	19.0576	0.655212
$847$	−22.8174	−0.784016
$848$	−25.0630	−0.860668
$849$	20.4305	0.701173
$850$	4.75886	0.163228
$851$	9.82780	0.336893
$852$	110.029	3.76953
$853$	9.35510	0.320313	0.160156	−	0.987092i	$-0.448800\pi$
$853$	9.35510	0.320313	0.160156	+	0.987092i	$0.448800\pi$
$854$	−57.3424	−1.96221
$855$	0.289677	0.00990673
$856$	−17.8482	−0.610040
$857$	−6.59658	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$857$	−6.59658	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$858$	0.921727	0.0314672
$859$	−21.2294	−0.724339	−0.362170	−	0.932112i	$-0.617964\pi$
$859$	−21.2294	−0.724339	−0.362170	+	0.932112i	$0.617964\pi$
$860$	−0.505038	−0.0172217
$861$	6.84323	0.233217
$862$	37.0621	1.26234
$863$	0.889591	0.0302820	0.0151410	−	0.999885i	$-0.495180\pi$
$863$	0.889591	0.0302820	0.0151410	+	0.999885i	$0.495180\pi$
$864$	−101.145	−3.44101
$865$	0.336200	0.0114312
$866$	25.0423	0.850972
$867$	33.2385	1.12884
$868$	105.607	3.58452
$869$	−1.38644	−0.0470318
$870$	2.38705	0.0809287
$871$	3.31199	0.112223
$872$	−82.1407	−2.78163
$873$	0.265741	0.00899398
$874$	−19.1930	−0.649211
$875$	0.983445	0.0332465
$876$	65.5733	2.21552
$877$	−2.64914	−0.0894551	−0.0447275	−	0.998999i	$-0.514242\pi$
$877$	−2.64914	−0.0894551	−0.0447275	+	0.998999i	$0.514242\pi$
$878$	9.46318	0.319367
$879$	−19.5601	−0.659746
$880$	−0.0917725	−0.00309365
$881$	47.8387	1.61173	0.805864	−	0.592100i	$-0.201701\pi$
$881$	47.8387	1.61173	0.805864	+	0.592100i	$0.201701\pi$
$882$	6.48483	0.218356
$883$	−1.25431	−0.0422108	−0.0211054	−	0.999777i	$-0.506719\pi$
$883$	−1.25431	−0.0422108	−0.0211054	+	0.999777i	$0.506719\pi$
$884$	2.69922	0.0907847
$885$	−0.959260	−0.0322452
$886$	48.6983	1.63605
$887$	−34.6289	−1.16273	−0.581363	−	0.813644i	$-0.697480\pi$
$887$	−34.6289	−1.16273	−0.581363	+	0.813644i	$0.697480\pi$
$888$	−190.505	−6.39292
$889$	34.8701	1.16950
$890$	0.973145	0.0326199
$891$	−1.32020	−0.0442283
$892$	146.407	4.90206
$893$	55.0335	1.84162
$894$	78.4887	2.62505
$895$	−0.424197	−0.0141794
$896$	−97.9684	−3.27289
$897$	2.75515	0.0919919
$898$	−64.4702	−2.15140
$899$	−84.7915	−2.82795
$900$	−24.4484	−0.814946
$901$	−0.543786	−0.0181161
$902$	0.559756	0.0186379
$903$	−7.82156	−0.260285
$904$	−84.7521	−2.81881
$905$	−1.20416	−0.0400277
$906$	65.1455	2.16431
$907$	33.6600	1.11766	0.558831	−	0.829281i	$-0.311250\pi$
$907$	33.6600	1.11766	0.558831	+	0.829281i	$0.311250\pi$
$908$	97.4693	3.23463
$909$	−9.93214	−0.329428
$910$	0.378849	0.0125587
$911$	−50.6052	−1.67663	−0.838313	−	0.545190i	$-0.816458\pi$
$911$	−50.6052	−1.67663	−0.838313	+	0.545190i	$0.816458\pi$
$912$	218.912	7.24889
$913$	0.591119	0.0195632
$914$	89.7804	2.96967
$915$	0.935266	0.0309189
$916$	−93.2598	−3.08139
$917$	−0.701229	−0.0231566
$918$	−3.98007	−0.131362
$919$	48.2157	1.59049	0.795245	−	0.606289i	$-0.207342\pi$
$919$	48.2157	1.59049	0.795245	+	0.606289i	$0.207342\pi$
$920$	−0.466206	−0.0153704
$921$	−33.1338	−1.09180
$922$	47.9710	1.57984
$923$	−14.0207	−0.461499
$924$	−2.77205	−0.0911937
$925$	49.1170	1.61496
$926$	75.3472	2.47606
$927$	4.60479	0.151241
$928$	225.039	7.38726
$929$	13.1516	0.431491	0.215746	−	0.976450i	$-0.430782\pi$
$929$	13.1516	0.431491	0.215746	+	0.976450i	$0.430782\pi$
$930$	−2.34023	−0.0767392
$931$	18.7266	0.613738
$932$	−17.3722	−0.569044
$933$	6.49958	0.212787
$934$	−58.2004	−1.90437
$935$	−0.00199116	−6.51180e−5 0
$936$	−12.0834	−0.394958
$937$	45.2686	1.47886	0.739431	−	0.673233i	$-0.235095\pi$
$937$	45.2686	1.47886	0.739431	+	0.673233i	$0.235095\pi$
$938$	−13.5331	−0.441870
$939$	7.30547	0.238405
$940$	2.08434	0.0679836
$941$	10.6599	0.347501	0.173751	−	0.984790i	$-0.444411\pi$
$941$	10.6599	0.347501	0.173751	+	0.984790i	$0.444411\pi$
$942$	3.03622	0.0989254
$943$	1.67318	0.0544862
$944$	−164.016	−5.33825
$945$	−0.411160	−0.0133750
$946$	−0.639781	−0.0208011
$947$	4.55497	0.148016	0.0740082	−	0.997258i	$-0.476421\pi$
$947$	4.55497	0.148016	0.0740082	+	0.997258i	$0.476421\pi$
$948$	125.256	4.06813
$949$	−8.35587	−0.271243
$950$	−95.9217	−3.11211
$951$	−26.3108	−0.853188
$952$	−7.07359	−0.229257
$953$	1.23814	0.0401074	0.0200537	−	0.999799i	$-0.493616\pi$
$953$	1.23814	0.0401074	0.0200537	+	0.999799i	$0.493616\pi$
$954$	3.79562	0.122888
$955$	0.816840	0.0264323
$956$	−11.8425	−0.383015
$957$	2.22568	0.0719459
$958$	94.1676	3.04242
$959$	−2.00677	−0.0648019
$960$	3.23744	0.104488
$961$	52.1282	1.68156
$962$	37.8508	1.22036
$963$	1.59046	0.0512518
$964$	−74.9633	−2.41441
$965$	−0.585882	−0.0188602
$966$	−11.2578	−0.362213
$967$	−7.33393	−0.235843	−0.117922	−	0.993023i	$-0.537623\pi$
$967$	−7.33393	−0.235843	−0.117922	+	0.993023i	$0.537623\pi$
$968$	108.143	3.47584
$969$	4.74967	0.152581
$970$	0.0394882	0.00126789
$971$	−31.8586	−1.02239	−0.511196	−	0.859464i	$-0.670797\pi$
$971$	−31.8586	−1.02239	−0.511196	+	0.859464i	$0.670797\pi$
$972$	49.3447	1.58273
$973$	12.1491	0.389482
$974$	−76.9706	−2.46630
$975$	13.7696	0.440980
$976$	159.913	5.11870
$977$	−20.5102	−0.656179	−0.328090	−	0.944647i	$-0.606405\pi$
$977$	−20.5102	−0.656179	−0.328090	+	0.944647i	$0.606405\pi$
$978$	−32.5029	−1.03933
$979$	0.907355	0.0289992
$980$	0.709250	0.0226561
$981$	7.31956	0.233696
$982$	52.3637	1.67099
$983$	35.9111	1.14539	0.572694	−	0.819769i	$-0.305898\pi$
$983$	35.9111	1.14539	0.572694	+	0.819769i	$0.305898\pi$
$984$	−32.4334	−1.03394
$985$	−0.593150	−0.0188993
$986$	8.85535	0.282012
$987$	32.2803	1.02749
$988$	−54.4067	−1.73091
$989$	−1.91238	−0.0608102
$990$	0.0138983	0.000441717 0
$991$	17.7821	0.564865	0.282433	−	0.959287i	$-0.408859\pi$
$991$	17.7821	0.564865	0.282433	+	0.959287i	$0.408859\pi$
$992$	−220.624	−7.00483
$993$	15.9516	0.506209
$994$	57.2898	1.81712
$995$	0.587850	0.0186361
$996$	−53.4038	−1.69216
$997$	−54.4988	−1.72599	−0.862997	−	0.505209i	$-0.831415\pi$
$997$	−54.4988	−1.72599	−0.862997	+	0.505209i	$0.831415\pi$
$998$	58.3201	1.84609
$999$	−41.0790	−1.29968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.2	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.2	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75254 q^{2} -1.96907 q^{3} +5.57647 q^{4} -0.0473576 q^{5} +5.41994 q^{6} +2.07710 q^{7} -9.84438 q^{8} +0.877234 q^{9} +O(q^{10})\)	\(q-2.75254 q^{2} -1.96907 q^{3} +5.57647 q^{4} -0.0473576 q^{5} +5.41994 q^{6} +2.07710 q^{7} -9.84438 q^{8} +0.877234 q^{9} +0.130354 q^{10} +0.121541 q^{11} -10.9805 q^{12} +1.39922 q^{13} -5.71730 q^{14} +0.0932504 q^{15} +15.9441 q^{16} +0.345935 q^{17} -2.41462 q^{18} -6.97282 q^{19} -0.264088 q^{20} -4.08996 q^{21} -0.334546 q^{22} -1.00000 q^{23} +19.3843 q^{24} -4.99776 q^{25} -3.85140 q^{26} +4.17987 q^{27} +11.5829 q^{28} -9.29989 q^{29} -0.256675 q^{30} +9.11747 q^{31} -24.1980 q^{32} -0.239323 q^{33} -0.952199 q^{34} -0.0983666 q^{35} +4.89187 q^{36} -9.82780 q^{37} +19.1930 q^{38} -2.75515 q^{39} +0.466206 q^{40} -1.67318 q^{41} +11.2578 q^{42} +1.91238 q^{43} +0.677770 q^{44} -0.0415437 q^{45} +2.75254 q^{46} -7.89257 q^{47} -31.3950 q^{48} -2.68565 q^{49} +13.7565 q^{50} -0.681169 q^{51} +7.80269 q^{52} -1.57193 q^{53} -11.5053 q^{54} -0.00575589 q^{55} -20.4478 q^{56} +13.7300 q^{57} +25.5983 q^{58} -10.2869 q^{59} +0.520008 q^{60} +10.0296 q^{61} -25.0962 q^{62} +1.82210 q^{63} +34.7177 q^{64} -0.0662636 q^{65} +0.658745 q^{66} +2.36703 q^{67} +1.92910 q^{68} +1.96907 q^{69} +0.270758 q^{70} -10.0204 q^{71} -8.63582 q^{72} -5.97182 q^{73} +27.0514 q^{74} +9.84093 q^{75} -38.8837 q^{76} +0.252453 q^{77} +7.58367 q^{78} -11.4072 q^{79} -0.755074 q^{80} -10.8622 q^{81} +4.60549 q^{82} +4.86353 q^{83} -22.8075 q^{84} -0.0163826 q^{85} -5.26391 q^{86} +18.3121 q^{87} -1.19650 q^{88} +7.46542 q^{89} +0.114351 q^{90} +2.90631 q^{91} -5.57647 q^{92} -17.9529 q^{93} +21.7246 q^{94} +0.330216 q^{95} +47.6475 q^{96} +0.302931 q^{97} +7.39236 q^{98} +0.106620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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