LMFDB - Embedded newform 8017.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77418 q^{2} +0.313969 q^{3} +5.69607 q^{4} +4.29926 q^{5} -0.871005 q^{6} -0.431093 q^{7} -10.2536 q^{8} -2.90142 q^{9} +O(q^{10})$	\(q-2.77418 q^{2} +0.313969 q^{3} +5.69607 q^{4} +4.29926 q^{5} -0.871005 q^{6} -0.431093 q^{7} -10.2536 q^{8} -2.90142 q^{9} -11.9269 q^{10} +0.354716 q^{11} +1.78839 q^{12} +2.93477 q^{13} +1.19593 q^{14} +1.34983 q^{15} +17.0531 q^{16} -5.10306 q^{17} +8.04907 q^{18} +4.83298 q^{19} +24.4889 q^{20} -0.135350 q^{21} -0.984046 q^{22} -7.95390 q^{23} -3.21930 q^{24} +13.4836 q^{25} -8.14158 q^{26} -1.85286 q^{27} -2.45554 q^{28} -0.350992 q^{29} -3.74467 q^{30} +10.6156 q^{31} -26.8012 q^{32} +0.111370 q^{33} +14.1568 q^{34} -1.85338 q^{35} -16.5267 q^{36} -4.22629 q^{37} -13.4075 q^{38} +0.921426 q^{39} -44.0827 q^{40} -9.16232 q^{41} +0.375484 q^{42} -4.35603 q^{43} +2.02049 q^{44} -12.4740 q^{45} +22.0655 q^{46} -2.42343 q^{47} +5.35413 q^{48} -6.81416 q^{49} -37.4059 q^{50} -1.60220 q^{51} +16.7167 q^{52} -8.09704 q^{53} +5.14017 q^{54} +1.52502 q^{55} +4.42024 q^{56} +1.51740 q^{57} +0.973715 q^{58} -1.10074 q^{59} +7.68873 q^{60} -14.6136 q^{61} -29.4495 q^{62} +1.25078 q^{63} +40.2451 q^{64} +12.6173 q^{65} -0.308960 q^{66} +2.13735 q^{67} -29.0674 q^{68} -2.49728 q^{69} +5.14161 q^{70} -9.89421 q^{71} +29.7499 q^{72} -0.801202 q^{73} +11.7245 q^{74} +4.23343 q^{75} +27.5290 q^{76} -0.152916 q^{77} -2.55620 q^{78} +8.01462 q^{79} +73.3155 q^{80} +8.12253 q^{81} +25.4179 q^{82} -6.11770 q^{83} -0.770961 q^{84} -21.9393 q^{85} +12.0844 q^{86} -0.110201 q^{87} -3.63710 q^{88} -12.4195 q^{89} +34.6050 q^{90} -1.26516 q^{91} -45.3060 q^{92} +3.33296 q^{93} +6.72304 q^{94} +20.7782 q^{95} -8.41472 q^{96} +10.9842 q^{97} +18.9037 q^{98} -1.02918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.77418	−1.96164	−0.980820	−	0.194913i	$-0.937557\pi$
$2$	−2.77418	−1.96164	−0.980820	+	0.194913i	$0.937557\pi$
$3$	0.313969	0.181270	0.0906349	−	0.995884i	$-0.471110\pi$
$3$	0.313969	0.181270	0.0906349	+	0.995884i	$0.471110\pi$
$4$	5.69607	2.84803
$5$	4.29926	1.92269	0.961343	−	0.275355i	$-0.0887954\pi$
$5$	4.29926	1.92269	0.961343	+	0.275355i	$0.0887954\pi$
$6$	−0.871005	−0.355586
$7$	−0.431093	−0.162938	−0.0814689	−	0.996676i	$-0.525961\pi$
$7$	−0.431093	−0.162938	−0.0814689	+	0.996676i	$0.525961\pi$
$8$	−10.2536	−3.62518
$9$	−2.90142	−0.967141
$10$	−11.9269	−3.77162
$11$	0.354716	0.106951	0.0534755	−	0.998569i	$-0.482970\pi$
$11$	0.354716	0.106951	0.0534755	+	0.998569i	$0.482970\pi$
$12$	1.78839	0.516263
$13$	2.93477	0.813959	0.406980	−	0.913437i	$-0.366582\pi$
$13$	2.93477	0.813959	0.406980	+	0.913437i	$0.366582\pi$
$14$	1.19593	0.319626
$15$	1.34983	0.348525
$16$	17.0531	4.26327
$17$	−5.10306	−1.23767	−0.618836	−	0.785520i	$-0.712396\pi$
$17$	−5.10306	−1.23767	−0.618836	+	0.785520i	$0.712396\pi$
$18$	8.04907	1.89718
$19$	4.83298	1.10876	0.554381	−	0.832263i	$-0.312955\pi$
$19$	4.83298	1.10876	0.554381	+	0.832263i	$0.312955\pi$
$20$	24.4889	5.47587
$21$	−0.135350	−0.0295357
$22$	−0.984046	−0.209799
$23$	−7.95390	−1.65850	−0.829252	−	0.558876i	$-0.811233\pi$
$23$	−7.95390	−1.65850	−0.829252	+	0.558876i	$0.811233\pi$
$24$	−3.21930	−0.657136
$25$	13.4836	2.69672
$26$	−8.14158	−1.59670
$27$	−1.85286	−0.356583
$28$	−2.45554	−0.464053
$29$	−0.350992	−0.0651776	−0.0325888	−	0.999469i	$-0.510375\pi$
$29$	−0.350992	−0.0651776	−0.0325888	+	0.999469i	$0.510375\pi$
$30$	−3.74467	−0.683681
$31$	10.6156	1.90661	0.953307	−	0.302004i	$-0.0976557\pi$
$31$	10.6156	1.90661	0.953307	+	0.302004i	$0.0976557\pi$
$32$	−26.8012	−4.73782
$33$	0.111370	0.0193870
$34$	14.1568	2.42787
$35$	−1.85338	−0.313278
$36$	−16.5267	−2.75445
$37$	−4.22629	−0.694797	−0.347399	−	0.937718i	$-0.612935\pi$
$37$	−4.22629	−0.694797	−0.347399	+	0.937718i	$0.612935\pi$
$38$	−13.4075	−2.17499
$39$	0.921426	0.147546
$40$	−44.0827	−6.97008
$41$	−9.16232	−1.43091	−0.715457	−	0.698656i	$-0.753782\pi$
$41$	−9.16232	−1.43091	−0.715457	+	0.698656i	$0.753782\pi$
$42$	0.375484	0.0579385
$43$	−4.35603	−0.664288	−0.332144	−	0.943229i	$-0.607772\pi$
$43$	−4.35603	−0.664288	−0.332144	+	0.943229i	$0.607772\pi$
$44$	2.02049	0.304600
$45$	−12.4740	−1.85951
$46$	22.0655	3.25339
$47$	−2.42343	−0.353494	−0.176747	−	0.984256i	$-0.556557\pi$
$47$	−2.42343	−0.353494	−0.176747	+	0.984256i	$0.556557\pi$
$48$	5.35413	0.772802
$49$	−6.81416	−0.973451
$50$	−37.4059	−5.28999
$51$	−1.60220	−0.224353
$52$	16.7167	2.31818
$53$	−8.09704	−1.11221	−0.556107	−	0.831111i	$-0.687706\pi$
$53$	−8.09704	−1.11221	−0.556107	+	0.831111i	$0.687706\pi$
$54$	5.14017	0.699489
$55$	1.52502	0.205633
$56$	4.42024	0.590679
$57$	1.51740	0.200985
$58$	0.973715	0.127855
$59$	−1.10074	−0.143304	−0.0716518	−	0.997430i	$-0.522827\pi$
$59$	−1.10074	−0.143304	−0.0716518	+	0.997430i	$0.522827\pi$
$60$	7.68873	0.992611
$61$	−14.6136	−1.87108	−0.935539	−	0.353222i	$-0.885086\pi$
$61$	−14.6136	−1.87108	−0.935539	+	0.353222i	$0.885086\pi$
$62$	−29.4495	−3.74009
$63$	1.25078	0.157584
$64$	40.2451	5.03063
$65$	12.6173	1.56499
$66$	−0.308960	−0.0380303
$67$	2.13735	0.261119	0.130560	−	0.991440i	$-0.458323\pi$
$67$	2.13735	0.261119	0.130560	+	0.991440i	$0.458323\pi$
$68$	−29.0674	−3.52494
$69$	−2.49728	−0.300637
$70$	5.14161	0.614539
$71$	−9.89421	−1.17423	−0.587114	−	0.809505i	$-0.699736\pi$
$71$	−9.89421	−1.17423	−0.587114	+	0.809505i	$0.699736\pi$
$72$	29.7499	3.50606
$73$	−0.801202	−0.0937736	−0.0468868	−	0.998900i	$-0.514930\pi$
$73$	−0.801202	−0.0937736	−0.0468868	+	0.998900i	$0.514930\pi$
$74$	11.7245	1.36294
$75$	4.23343	0.488834
$76$	27.5290	3.15779
$77$	−0.152916	−0.0174264
$78$	−2.55620	−0.289433
$79$	8.01462	0.901716	0.450858	−	0.892596i	$-0.351118\pi$
$79$	8.01462	0.901716	0.450858	+	0.892596i	$0.351118\pi$
$80$	73.3155	8.19692
$81$	8.12253	0.902503
$82$	25.4179	2.80694
$83$	−6.11770	−0.671505	−0.335752	−	0.941950i	$-0.608991\pi$
$83$	−6.11770	−0.671505	−0.335752	+	0.941950i	$0.608991\pi$
$84$	−0.770961	−0.0841188
$85$	−21.9393	−2.37966
$86$	12.0844	1.30309
$87$	−0.110201	−0.0118147
$88$	−3.63710	−0.387717
$89$	−12.4195	−1.31646	−0.658231	−	0.752816i	$-0.728695\pi$
$89$	−12.4195	−1.31646	−0.658231	+	0.752816i	$0.728695\pi$
$90$	34.6050	3.64769
$91$	−1.26516	−0.132625
$92$	−45.3060	−4.72347
$93$	3.33296	0.345612
$94$	6.72304	0.693428
$95$	20.7782	2.13180
$96$	−8.41472	−0.858824
$97$	10.9842	1.11528	0.557638	−	0.830084i	$-0.311708\pi$
$97$	10.9842	1.11528	0.557638	+	0.830084i	$0.311708\pi$
$98$	18.9037	1.90956
$99$	−1.02918	−0.103437
$100$	76.8035	7.68035
$101$	18.9244	1.88305	0.941524	−	0.336946i	$-0.109394\pi$
$101$	18.9244	1.88305	0.941524	+	0.336946i	$0.109394\pi$
$102$	4.44479	0.440100
$103$	−14.5437	−1.43303	−0.716516	−	0.697571i	$-0.754264\pi$
$103$	−14.5437	−1.43303	−0.716516	+	0.697571i	$0.754264\pi$
$104$	−30.0919	−2.95075
$105$	−0.581903	−0.0567879
$106$	22.4626	2.18176
$107$	2.60043	0.251393	0.125697	−	0.992069i	$-0.459883\pi$
$107$	2.60043	0.251393	0.125697	+	0.992069i	$0.459883\pi$
$108$	−10.5540	−1.01556
$109$	3.50421	0.335642	0.167821	−	0.985817i	$-0.446327\pi$
$109$	3.50421	0.335642	0.167821	+	0.985817i	$0.446327\pi$
$110$	−4.23067	−0.403378
$111$	−1.32692	−0.125946
$112$	−7.35146	−0.694648
$113$	−11.9693	−1.12598	−0.562989	−	0.826464i	$-0.690349\pi$
$113$	−11.9693	−1.12598	−0.562989	+	0.826464i	$0.690349\pi$
$114$	−4.20955	−0.394260
$115$	−34.1959	−3.18878
$116$	−1.99928	−0.185628
$117$	−8.51501	−0.787213
$118$	3.05364	0.281110
$119$	2.19989	0.201664
$120$	−13.8406	−1.26347
$121$	−10.8742	−0.988561
$122$	40.5407	3.67038
$123$	−2.87668	−0.259382
$124$	60.4670	5.43010
$125$	36.4731	3.26226
$126$	−3.46990	−0.309123
$127$	−9.43053	−0.836824	−0.418412	−	0.908257i	$-0.637413\pi$
$127$	−9.43053	−0.836824	−0.418412	+	0.908257i	$0.637413\pi$
$128$	−58.0447	−5.13048
$129$	−1.36766	−0.120415
$130$	−35.0027	−3.06994
$131$	9.51728	0.831528	0.415764	−	0.909472i	$-0.363514\pi$
$131$	9.51728	0.831528	0.415764	+	0.909472i	$0.363514\pi$
$132$	0.634370	0.0552148
$133$	−2.08346	−0.180659
$134$	−5.92940	−0.512222
$135$	−7.96593	−0.685598
$136$	52.3245	4.48679
$137$	4.34127	0.370899	0.185450	−	0.982654i	$-0.440626\pi$
$137$	4.34127	0.370899	0.185450	+	0.982654i	$0.440626\pi$
$138$	6.92789	0.589741
$139$	0.800322	0.0678824	0.0339412	−	0.999424i	$-0.489194\pi$
$139$	0.800322	0.0678824	0.0339412	+	0.999424i	$0.489194\pi$
$140$	−10.5570	−0.892227
$141$	−0.760882	−0.0640778
$142$	27.4483	2.30341
$143$	1.04101	0.0870537
$144$	−49.4782	−4.12318
$145$	−1.50901	−0.125316
$146$	2.22268	0.183950
$147$	−2.13943	−0.176457
$148$	−24.0732	−1.97881
$149$	−5.76046	−0.471915	−0.235958	−	0.971763i	$-0.575823\pi$
$149$	−5.76046	−0.471915	−0.235958	+	0.971763i	$0.575823\pi$
$150$	−11.7443	−0.958917
$151$	−16.1800	−1.31671	−0.658354	−	0.752708i	$-0.728747\pi$
$151$	−16.1800	−1.31671	−0.658354	+	0.752708i	$0.728747\pi$
$152$	−49.5552	−4.01946
$153$	14.8061	1.19700
$154$	0.424216	0.0341843
$155$	45.6391	3.66582
$156$	5.24851	0.420217
$157$	−8.56137	−0.683271	−0.341636	−	0.939832i	$-0.610981\pi$
$157$	−8.56137	−0.683271	−0.341636	+	0.939832i	$0.610981\pi$
$158$	−22.2340	−1.76884
$159$	−2.54222	−0.201611
$160$	−115.225	−9.10934
$161$	3.42887	0.270233
$162$	−22.5334	−1.77039
$163$	−12.0126	−0.940900	−0.470450	−	0.882427i	$-0.655908\pi$
$163$	−12.0126	−0.940900	−0.470450	+	0.882427i	$0.655908\pi$
$164$	−52.1892	−4.07530
$165$	0.478807	0.0372751
$166$	16.9716	1.31725
$167$	−9.19478	−0.711513	−0.355757	−	0.934579i	$-0.615777\pi$
$167$	−9.19478	−0.711513	−0.355757	+	0.934579i	$0.615777\pi$
$168$	1.38782	0.107072
$169$	−4.38712	−0.337471
$170$	60.8637	4.66803
$171$	−14.0225	−1.07233
$172$	−24.8122	−1.89191
$173$	−2.83660	−0.215663	−0.107831	−	0.994169i	$-0.534391\pi$
$173$	−2.83660	−0.215663	−0.107831	+	0.994169i	$0.534391\pi$
$174$	0.305716	0.0231763
$175$	−5.81268	−0.439398
$176$	6.04900	0.455961
$177$	−0.345597	−0.0259766
$178$	34.4539	2.58243
$179$	19.9744	1.49296	0.746478	−	0.665410i	$-0.231743\pi$
$179$	19.9744	1.49296	0.746478	+	0.665410i	$0.231743\pi$
$180$	−71.0526	−5.29594
$181$	−3.99247	−0.296758	−0.148379	−	0.988931i	$-0.547406\pi$
$181$	−3.99247	−0.296758	−0.148379	+	0.988931i	$0.547406\pi$
$182$	3.50978	0.260162
$183$	−4.58821	−0.339170
$184$	81.5558	6.01237
$185$	−18.1699	−1.33588
$186$	−9.24622	−0.677966
$187$	−1.81014	−0.132370
$188$	−13.8040	−1.00676
$189$	0.798756	0.0581010
$190$	−57.6425	−4.18182
$191$	7.31309	0.529157	0.264578	−	0.964364i	$-0.414767\pi$
$191$	7.31309	0.529157	0.264578	+	0.964364i	$0.414767\pi$
$192$	12.6357	0.911902
$193$	−13.4936	−0.971289	−0.485645	−	0.874156i	$-0.661415\pi$
$193$	−13.4936	−0.971289	−0.485645	+	0.874156i	$0.661415\pi$
$194$	−30.4721	−2.18777
$195$	3.96145	0.283685
$196$	−38.8139	−2.77242
$197$	11.3869	0.811286	0.405643	−	0.914032i	$-0.367048\pi$
$197$	11.3869	0.811286	0.405643	+	0.914032i	$0.367048\pi$
$198$	2.85514	0.202906
$199$	14.9765	1.06165	0.530827	−	0.847480i	$-0.321881\pi$
$199$	14.9765	1.06165	0.530827	+	0.847480i	$0.321881\pi$
$200$	−138.255	−9.77609
$201$	0.671062	0.0473330
$202$	−52.4997	−3.69386
$203$	0.151310	0.0106199
$204$	−9.12624	−0.638965
$205$	−39.3912	−2.75120
$206$	40.3468	2.81109
$207$	23.0776	1.60401
$208$	50.0469	3.47013
$209$	1.71434	0.118583
$210$	1.61430	0.111397
$211$	−10.7124	−0.737472	−0.368736	−	0.929534i	$-0.620209\pi$
$211$	−10.7124	−0.737472	−0.368736	+	0.929534i	$0.620209\pi$
$212$	−46.1213	−3.16762
$213$	−3.10647	−0.212852
$214$	−7.21406	−0.493143
$215$	−18.7277	−1.27722
$216$	18.9984	1.29268
$217$	−4.57630	−0.310660
$218$	−9.72130	−0.658410
$219$	−0.251552	−0.0169983
$220$	8.68659	0.585650
$221$	−14.9763	−1.00741
$222$	3.68112	0.247060
$223$	5.53011	0.370324	0.185162	−	0.982708i	$-0.440719\pi$
$223$	5.53011	0.370324	0.185162	+	0.982708i	$0.440719\pi$
$224$	11.5538	0.771970
$225$	−39.1216	−2.60811
$226$	33.2050	2.20877
$227$	−12.0992	−0.803055	−0.401528	−	0.915847i	$-0.631521\pi$
$227$	−12.0992	−0.803055	−0.401528	+	0.915847i	$0.631521\pi$
$228$	8.64324	0.572412
$229$	28.5959	1.88967	0.944837	−	0.327542i	$-0.106220\pi$
$229$	28.5959	1.88967	0.944837	+	0.327542i	$0.106220\pi$
$230$	94.8654	6.25524
$231$	−0.0480107	−0.00315887
$232$	3.59892	0.236281
$233$	17.9704	1.17728	0.588640	−	0.808395i	$-0.299664\pi$
$233$	17.9704	1.17728	0.588640	+	0.808395i	$0.299664\pi$
$234$	23.6222	1.54423
$235$	−10.4190	−0.679658
$236$	−6.26987	−0.408134
$237$	2.51634	0.163454
$238$	−6.10290	−0.395592
$239$	−17.9084	−1.15840	−0.579200	−	0.815186i	$-0.696635\pi$
$239$	−17.9084	−1.15840	−0.579200	+	0.815186i	$0.696635\pi$
$240$	23.0188	1.48586
$241$	−0.707006	−0.0455423	−0.0227711	−	0.999741i	$-0.507249\pi$
$241$	−0.707006	−0.0455423	−0.0227711	+	0.999741i	$0.507249\pi$
$242$	30.1669	1.93920
$243$	8.10881	0.520180
$244$	−83.2400	−5.32890
$245$	−29.2958	−1.87164
$246$	7.98043	0.508814
$247$	14.1837	0.902486
$248$	−108.847	−6.91182
$249$	−1.92077	−0.121724
$250$	−101.183	−6.39938
$251$	3.90870	0.246715	0.123357	−	0.992362i	$-0.460634\pi$
$251$	3.90870	0.246715	0.123357	+	0.992362i	$0.460634\pi$
$252$	7.12455	0.448805
$253$	−2.82138	−0.177378
$254$	26.1620	1.64155
$255$	−6.88826	−0.431360
$256$	80.5363	5.03352
$257$	17.9329	1.11863	0.559313	−	0.828957i	$-0.311065\pi$
$257$	17.9329	1.11863	0.559313	+	0.828957i	$0.311065\pi$
$258$	3.79412	0.236212
$259$	1.82192	0.113209
$260$	71.8692	4.45714
$261$	1.01838	0.0630360
$262$	−26.4026	−1.63116
$263$	−5.39146	−0.332452	−0.166226	−	0.986088i	$-0.553158\pi$
$263$	−5.39146	−0.332452	−0.166226	+	0.986088i	$0.553158\pi$
$264$	−1.14194	−0.0702813
$265$	−34.8112	−2.13844
$266$	5.77990	0.354388
$267$	−3.89933	−0.238635
$268$	12.1745	0.743676
$269$	5.16711	0.315044	0.157522	−	0.987515i	$-0.449649\pi$
$269$	5.16711	0.315044	0.157522	+	0.987515i	$0.449649\pi$
$270$	22.0989	1.34490
$271$	−24.1550	−1.46731	−0.733657	−	0.679520i	$-0.762188\pi$
$271$	−24.1550	−1.46731	−0.733657	+	0.679520i	$0.762188\pi$
$272$	−87.0228	−5.27653
$273$	−0.397220	−0.0240409
$274$	−12.0434	−0.727571
$275$	4.78285	0.288417
$276$	−14.2247	−0.856224
$277$	−4.19890	−0.252288	−0.126144	−	0.992012i	$-0.540260\pi$
$277$	−4.19890	−0.252288	−0.126144	+	0.992012i	$0.540260\pi$
$278$	−2.22024	−0.133161
$279$	−30.8003	−1.84396
$280$	19.0037	1.13569
$281$	−21.4551	−1.27990	−0.639951	−	0.768416i	$-0.721045\pi$
$281$	−21.4551	−1.27990	−0.639951	+	0.768416i	$0.721045\pi$
$282$	2.11082	0.125698
$283$	9.70926	0.577156	0.288578	−	0.957456i	$-0.406818\pi$
$283$	9.70926	0.577156	0.288578	+	0.957456i	$0.406818\pi$
$284$	−56.3581	−3.34424
$285$	6.52371	0.386431
$286$	−2.88795	−0.170768
$287$	3.94982	0.233150
$288$	77.7615	4.58214
$289$	9.04118	0.531834
$290$	4.18625	0.245825
$291$	3.44869	0.202166
$292$	−4.56370	−0.267070
$293$	4.17558	0.243940	0.121970	−	0.992534i	$-0.461079\pi$
$293$	4.17558	0.243940	0.121970	+	0.992534i	$0.461079\pi$
$294$	5.93517	0.346146
$295$	−4.73235	−0.275528
$296$	43.3345	2.51877
$297$	−0.657240	−0.0381369
$298$	15.9805	0.925728
$299$	−23.3429	−1.34995
$300$	24.1139	1.39222
$301$	1.87785	0.108238
$302$	44.8862	2.58291
$303$	5.94167	0.341340
$304$	82.4171	4.72695
$305$	−62.8276	−3.59750
$306$	−41.0748	−2.34809
$307$	−3.56765	−0.203617	−0.101808	−	0.994804i	$-0.532463\pi$
$307$	−3.56765	−0.203617	−0.101808	+	0.994804i	$0.532463\pi$
$308$	−0.871019	−0.0496309
$309$	−4.56626	−0.259766
$310$	−126.611	−7.19102
$311$	2.80911	0.159290	0.0796450	−	0.996823i	$-0.474621\pi$
$311$	2.80911	0.159290	0.0796450	+	0.996823i	$0.474621\pi$
$312$	−9.44790	−0.534882
$313$	21.3699	1.20790	0.603950	−	0.797022i	$-0.293593\pi$
$313$	21.3699	1.20790	0.603950	+	0.797022i	$0.293593\pi$
$314$	23.7508	1.34033
$315$	5.37744	0.302984
$316$	45.6519	2.56812
$317$	22.4354	1.26010	0.630050	−	0.776555i	$-0.283034\pi$
$317$	22.4354	1.26010	0.630050	+	0.776555i	$0.283034\pi$
$318$	7.05256	0.395488
$319$	−0.124503	−0.00697081
$320$	173.024	9.67232
$321$	0.816454	0.0455700
$322$	−9.51231	−0.530100
$323$	−24.6630	−1.37228
$324$	46.2665	2.57036
$325$	39.5713	2.19502
$326$	33.3251	1.84571
$327$	1.10021	0.0608419
$328$	93.9464	5.18732
$329$	1.04473	0.0575976
$330$	−1.32830	−0.0731203
$331$	−1.95831	−0.107638	−0.0538192	−	0.998551i	$-0.517139\pi$
$331$	−1.95831	−0.107638	−0.0538192	+	0.998551i	$0.517139\pi$
$332$	−34.8468	−1.91247
$333$	12.2622	0.671967
$334$	25.5080	1.39573
$335$	9.18902	0.502050
$336$	−2.30813	−0.125919
$337$	−19.4304	−1.05844	−0.529220	−	0.848484i	$-0.677516\pi$
$337$	−19.4304	−1.05844	−0.529220	+	0.848484i	$0.677516\pi$
$338$	12.1707	0.661996
$339$	−3.75799	−0.204106
$340$	−124.968	−6.77734
$341$	3.76552	0.203914
$342$	38.9010	2.10352
$343$	5.95519	0.321550
$344$	44.6648	2.40816
$345$	−10.7364	−0.578030
$346$	7.86925	0.423053
$347$	−24.1118	−1.29439	−0.647194	−	0.762325i	$-0.724058\pi$
$347$	−24.1118	−1.29439	−0.647194	+	0.762325i	$0.724058\pi$
$348$	−0.627710	−0.0336488
$349$	−30.1195	−1.61226	−0.806131	−	0.591737i	$-0.798442\pi$
$349$	−30.1195	−1.61226	−0.806131	+	0.591737i	$0.798442\pi$
$350$	16.1254	0.861940
$351$	−5.43773	−0.290244
$352$	−9.50680	−0.506714
$353$	24.8944	1.32500	0.662499	−	0.749063i	$-0.269496\pi$
$353$	24.8944	1.32500	0.662499	+	0.749063i	$0.269496\pi$
$354$	0.958747	0.0509568
$355$	−42.5378	−2.25767
$356$	−70.7422	−3.74933
$357$	0.690697	0.0365556
$358$	−55.4125	−2.92864
$359$	−18.6932	−0.986589	−0.493295	−	0.869862i	$-0.664208\pi$
$359$	−18.6932	−0.986589	−0.493295	+	0.869862i	$0.664208\pi$
$360$	127.903	6.74105
$361$	4.35768	0.229351
$362$	11.0758	0.582132
$363$	−3.41415	−0.179196
$364$	−7.20644	−0.377720
$365$	−3.44457	−0.180297
$366$	12.7285	0.665330
$367$	−13.1508	−0.686468	−0.343234	−	0.939250i	$-0.611522\pi$
$367$	−13.1508	−0.686468	−0.343234	+	0.939250i	$0.611522\pi$
$368$	−135.638	−7.07064
$369$	26.5838	1.38390
$370$	50.4065	2.62051
$371$	3.49058	0.181222
$372$	18.9848	0.984314
$373$	20.9584	1.08519	0.542594	−	0.839995i	$-0.317442\pi$
$373$	20.9584	1.08519	0.542594	+	0.839995i	$0.317442\pi$
$374$	5.02164	0.259663
$375$	11.4514	0.591349
$376$	24.8488	1.28148
$377$	−1.03008	−0.0530519
$378$	−2.21589	−0.113973
$379$	32.3703	1.66275	0.831375	−	0.555712i	$-0.187554\pi$
$379$	32.3703	1.66275	0.831375	+	0.555712i	$0.187554\pi$
$380$	118.354	6.07144
$381$	−2.96089	−0.151691
$382$	−20.2878	−1.03802
$383$	−13.5999	−0.694921	−0.347461	−	0.937695i	$-0.612956\pi$
$383$	−13.5999	−0.694921	−0.347461	+	0.937695i	$0.612956\pi$
$384$	−18.2242	−0.930001
$385$	−0.657424	−0.0335054
$386$	37.4336	1.90532
$387$	12.6387	0.642460
$388$	62.5667	3.17634
$389$	20.1108	1.01966	0.509828	−	0.860276i	$-0.329709\pi$
$389$	20.1108	1.01966	0.509828	+	0.860276i	$0.329709\pi$
$390$	−10.9898	−0.556488
$391$	40.5892	2.05268
$392$	69.8694	3.52894
$393$	2.98813	0.150731
$394$	−31.5894	−1.59145
$395$	34.4569	1.73372
$396$	−5.86229	−0.294591
$397$	1.50104	0.0753351	0.0376675	−	0.999290i	$-0.488007\pi$
$397$	1.50104	0.0753351	0.0376675	+	0.999290i	$0.488007\pi$
$398$	−41.5474	−2.08258
$399$	−0.654142	−0.0327481
$400$	229.937	11.4968
$401$	−7.24962	−0.362029	−0.181014	−	0.983480i	$-0.557938\pi$
$401$	−7.24962	−0.362029	−0.181014	+	0.983480i	$0.557938\pi$
$402$	−1.86164	−0.0928504
$403$	31.1543	1.55191
$404$	107.795	5.36299
$405$	34.9208	1.73523
$406$	−0.419762	−0.0208324
$407$	−1.49913	−0.0743092
$408$	16.4282	0.813319
$409$	37.5215	1.85532	0.927660	−	0.373427i	$-0.121817\pi$
$409$	37.5215	1.85532	0.927660	+	0.373427i	$0.121817\pi$
$410$	109.278	5.39686
$411$	1.36302	0.0672329
$412$	−82.8419	−4.08133
$413$	0.474520	0.0233496
$414$	−64.0215	−3.14649
$415$	−26.3015	−1.29109
$416$	−78.6553	−3.85639
$417$	0.251276	0.0123050
$418$	−4.75587	−0.232617
$419$	0.480647	0.0234812	0.0117406	−	0.999931i	$-0.496263\pi$
$419$	0.480647	0.0234812	0.0117406	+	0.999931i	$0.496263\pi$
$420$	−3.31456	−0.161734
$421$	1.24525	0.0606898	0.0303449	−	0.999539i	$-0.490339\pi$
$421$	1.24525	0.0606898	0.0303449	+	0.999539i	$0.490339\pi$
$422$	29.7181	1.44666
$423$	7.03141	0.341879
$424$	83.0235	4.03198
$425$	−68.8075	−3.33766
$426$	8.61791	0.417539
$427$	6.29982	0.304870
$428$	14.8122	0.715977
$429$	0.326845	0.0157802
$430$	51.9539	2.50544
$431$	−22.3280	−1.07550	−0.537751	−	0.843104i	$-0.680726\pi$
$431$	−22.3280	−1.07550	−0.537751	+	0.843104i	$0.680726\pi$
$432$	−31.5970	−1.52021
$433$	21.1383	1.01584	0.507921	−	0.861404i	$-0.330414\pi$
$433$	21.1383	1.01584	0.507921	+	0.861404i	$0.330414\pi$
$434$	12.6955	0.609402
$435$	−0.473780	−0.0227160
$436$	19.9602	0.955921
$437$	−38.4410	−1.83888
$438$	0.697851	0.0333446
$439$	−25.0872	−1.19735	−0.598674	−	0.800993i	$-0.704305\pi$
$439$	−25.0872	−1.19735	−0.598674	+	0.800993i	$0.704305\pi$
$440$	−15.6368	−0.745457
$441$	19.7708	0.941465
$442$	41.5469	1.97619
$443$	18.4343	0.875838	0.437919	−	0.899015i	$-0.355716\pi$
$443$	18.4343	0.875838	0.437919	+	0.899015i	$0.355716\pi$
$444$	−7.55824	−0.358698
$445$	−53.3945	−2.53114
$446$	−15.3415	−0.726442
$447$	−1.80860	−0.0855440
$448$	−17.3494	−0.819681
$449$	3.46585	0.163563	0.0817817	−	0.996650i	$-0.473939\pi$
$449$	3.46585	0.163563	0.0817817	+	0.996650i	$0.473939\pi$
$450$	108.530	5.11617
$451$	−3.25002	−0.153038
$452$	−68.1781	−3.20683
$453$	−5.08001	−0.238680
$454$	33.5655	1.57531
$455$	−5.43924	−0.254996
$456$	−15.5588	−0.728607
$457$	−11.7905	−0.551538	−0.275769	−	0.961224i	$-0.588933\pi$
$457$	−11.7905	−0.551538	−0.275769	+	0.961224i	$0.588933\pi$
$458$	−79.3303	−3.70686
$459$	9.45526	0.441334
$460$	−194.782	−9.08176
$461$	−10.5280	−0.490338	−0.245169	−	0.969480i	$-0.578843\pi$
$461$	−10.5280	−0.490338	−0.245169	+	0.969480i	$0.578843\pi$
$462$	0.133190	0.00619658
$463$	4.80992	0.223536	0.111768	−	0.993734i	$-0.464349\pi$
$463$	4.80992	0.223536	0.111768	+	0.993734i	$0.464349\pi$
$464$	−5.98550	−0.277870
$465$	14.3292	0.664502
$466$	−49.8531	−2.30940
$467$	−1.03843	−0.0480529	−0.0240265	−	0.999711i	$-0.507649\pi$
$467$	−1.03843	−0.0480529	−0.0240265	+	0.999711i	$0.507649\pi$
$468$	−48.5021	−2.24201
$469$	−0.921398	−0.0425462
$470$	28.9041	1.33324
$471$	−2.68800	−0.123857
$472$	11.2865	0.519502
$473$	−1.54515	−0.0710462
$474$	−6.98078	−0.320638
$475$	65.1659	2.99002
$476$	12.5307	0.574346
$477$	23.4929	1.07567
$478$	49.6812	2.27236
$479$	−30.9487	−1.41408	−0.707042	−	0.707172i	$-0.749971\pi$
$479$	−30.9487	−1.41408	−0.707042	+	0.707172i	$0.749971\pi$
$480$	−36.1770	−1.65125
$481$	−12.4032	−0.565537
$482$	1.96136	0.0893375
$483$	1.07656	0.0489851
$484$	−61.9401	−2.81546
$485$	47.2238	2.14432
$486$	−22.4953	−1.02041
$487$	22.2814	1.00967	0.504833	−	0.863217i	$-0.331554\pi$
$487$	22.2814	1.00967	0.504833	+	0.863217i	$0.331554\pi$
$488$	149.841	6.78300
$489$	−3.77158	−0.170557
$490$	81.2718	3.67149
$491$	9.58549	0.432587	0.216294	−	0.976328i	$-0.430603\pi$
$491$	9.58549	0.432587	0.216294	+	0.976328i	$0.430603\pi$
$492$	−16.3858	−0.738728
$493$	1.79113	0.0806686
$494$	−39.3481	−1.77035
$495$	−4.42472	−0.198876
$496$	181.028	8.12840
$497$	4.26533	0.191326
$498$	5.32855	0.238778
$499$	−17.3697	−0.777576	−0.388788	−	0.921327i	$-0.627106\pi$
$499$	−17.3697	−0.777576	−0.388788	+	0.921327i	$0.627106\pi$
$500$	207.754	9.29102
$501$	−2.88687	−0.128976
$502$	−10.8434	−0.483966
$503$	−30.2673	−1.34955	−0.674776	−	0.738023i	$-0.735760\pi$
$503$	−30.2673	−1.34955	−0.674776	+	0.738023i	$0.735760\pi$
$504$	−12.8250	−0.571270
$505$	81.3608	3.62051
$506$	7.82701	0.347953
$507$	−1.37742	−0.0611733
$508$	−53.7170	−2.38331
$509$	−35.9906	−1.59526	−0.797628	−	0.603150i	$-0.793912\pi$
$509$	−35.9906	−1.59526	−0.797628	+	0.603150i	$0.793912\pi$
$510$	19.1093	0.846173
$511$	0.345393	0.0152793
$512$	−107.333	−4.74348
$513$	−8.95484	−0.395366
$514$	−49.7492	−2.19434
$515$	−62.5270	−2.75527
$516$	−7.79026	−0.342947
$517$	−0.859631	−0.0378065
$518$	−5.05434	−0.222075
$519$	−0.890605	−0.0390932
$520$	−129.373	−5.67336
$521$	10.1922	0.446529	0.223264	−	0.974758i	$-0.428329\pi$
$521$	10.1922	0.446529	0.223264	+	0.974758i	$0.428329\pi$
$522$	−2.82516	−0.123654
$523$	1.11933	0.0489451	0.0244725	−	0.999701i	$-0.492209\pi$
$523$	1.11933	0.0489451	0.0244725	+	0.999701i	$0.492209\pi$
$524$	54.2111	2.36822
$525$	−1.82500	−0.0796496
$526$	14.9569	0.652151
$527$	−54.1719	−2.35976
$528$	1.89920	0.0826519
$529$	40.2645	1.75063
$530$	96.5726	4.19485
$531$	3.19370	0.138595
$532$	−11.8676	−0.514524
$533$	−26.8893	−1.16471
$534$	10.8174	0.468116
$535$	11.1799	0.483350
$536$	−21.9155	−0.946604
$537$	6.27133	0.270628
$538$	−14.3345	−0.618003
$539$	−2.41709	−0.104112
$540$	−45.3745	−1.95261
$541$	27.4355	1.17955	0.589773	−	0.807569i	$-0.299217\pi$
$541$	27.4355	1.17955	0.589773	+	0.807569i	$0.299217\pi$
$542$	67.0104	2.87834
$543$	−1.25351	−0.0537933
$544$	136.768	5.86387
$545$	15.0655	0.645335
$546$	1.10196	0.0471596
$547$	−25.8853	−1.10677	−0.553387	−	0.832924i	$-0.686665\pi$
$547$	−25.8853	−1.10677	−0.553387	+	0.832924i	$0.686665\pi$
$548$	24.7281	1.05633
$549$	42.4002	1.80960
$550$	−13.2685	−0.565770
$551$	−1.69634	−0.0722664
$552$	25.6060	1.08986
$553$	−3.45505	−0.146924
$554$	11.6485	0.494898
$555$	−5.70477	−0.242154
$556$	4.55869	0.193332
$557$	11.7719	0.498790	0.249395	−	0.968402i	$-0.419768\pi$
$557$	11.7719	0.498790	0.249395	+	0.968402i	$0.419768\pi$
$558$	85.4455	3.61720
$559$	−12.7839	−0.540703
$560$	−31.6058	−1.33559
$561$	−0.568326	−0.0239947
$562$	59.5202	2.51071
$563$	25.0679	1.05649	0.528243	−	0.849093i	$-0.322851\pi$
$563$	25.0679	1.05649	0.528243	+	0.849093i	$0.322851\pi$
$564$	−4.33404	−0.182496
$565$	−51.4591	−2.16490
$566$	−26.9352	−1.13217
$567$	−3.50157	−0.147052
$568$	101.451	4.25679
$569$	2.65509	0.111307	0.0556536	−	0.998450i	$-0.482276\pi$
$569$	2.65509	0.111307	0.0556536	+	0.998450i	$0.482276\pi$
$570$	−18.0979	−0.758039
$571$	−20.6631	−0.864724	−0.432362	−	0.901700i	$-0.642320\pi$
$571$	−20.6631	−0.864724	−0.432362	+	0.901700i	$0.642320\pi$
$572$	5.92967	0.247932
$573$	2.29608	0.0959202
$574$	−10.9575	−0.457357
$575$	−107.247	−4.47252
$576$	−116.768	−4.86533
$577$	0.469457	0.0195437	0.00977187	−	0.999952i	$-0.496889\pi$
$577$	0.469457	0.0195437	0.00977187	+	0.999952i	$0.496889\pi$
$578$	−25.0818	−1.04327
$579$	−4.23656	−0.176065
$580$	−8.59540	−0.356905
$581$	2.63730	0.109414
$582$	−9.56729	−0.396577
$583$	−2.87215	−0.118952
$584$	8.21517	0.339946
$585$	−36.6082	−1.51356
$586$	−11.5838	−0.478522
$587$	6.08792	0.251276	0.125638	−	0.992076i	$-0.459902\pi$
$587$	6.08792	0.251276	0.125638	+	0.992076i	$0.459902\pi$
$588$	−12.1864	−0.502557
$589$	51.3048	2.11398
$590$	13.1284	0.540487
$591$	3.57514	0.147062
$592$	−72.0712	−2.96211
$593$	−22.0393	−0.905045	−0.452523	−	0.891753i	$-0.649476\pi$
$593$	−22.0393	−0.905045	−0.452523	+	0.891753i	$0.649476\pi$
$594$	1.82330	0.0748110
$595$	9.45790	0.387736
$596$	−32.8120	−1.34403
$597$	4.70214	0.192446
$598$	64.7573	2.64812
$599$	44.7516	1.82850	0.914250	−	0.405151i	$-0.132781\pi$
$599$	44.7516	1.82850	0.914250	+	0.405151i	$0.132781\pi$
$600$	−43.4077	−1.77211
$601$	45.0076	1.83590	0.917949	−	0.396698i	$-0.129844\pi$
$601$	45.0076	1.83590	0.917949	+	0.396698i	$0.129844\pi$
$602$	−5.20950	−0.212323
$603$	−6.20136	−0.252539
$604$	−92.1623	−3.75003
$605$	−46.7509	−1.90069
$606$	−16.4832	−0.669586
$607$	−36.1651	−1.46790	−0.733949	−	0.679205i	$-0.762325\pi$
$607$	−36.1651	−1.46790	−0.733949	+	0.679205i	$0.762325\pi$
$608$	−129.529	−5.25311
$609$	0.0475067	0.00192507
$610$	174.295	7.05699
$611$	−7.11222	−0.287730
$612$	84.3367	3.40911
$613$	15.7607	0.636568	0.318284	−	0.947995i	$-0.396893\pi$
$613$	15.7607	0.636568	0.318284	+	0.947995i	$0.396893\pi$
$614$	9.89730	0.399422
$615$	−12.3676	−0.498709
$616$	1.56793	0.0631737
$617$	12.8105	0.515730	0.257865	−	0.966181i	$-0.416981\pi$
$617$	12.8105	0.515730	0.257865	+	0.966181i	$0.416981\pi$
$618$	12.6676	0.509567
$619$	−29.2164	−1.17431	−0.587154	−	0.809475i	$-0.699752\pi$
$619$	−29.2164	−1.17431	−0.587154	+	0.809475i	$0.699752\pi$
$620$	259.963	10.4404
$621$	14.7375	0.591395
$622$	−7.79298	−0.312470
$623$	5.35395	0.214502
$624$	15.7131	0.629029
$625$	89.3893	3.57557
$626$	−59.2840	−2.36947
$627$	0.538248	0.0214955
$628$	−48.7661	−1.94598
$629$	21.5670	0.859932
$630$	−14.9180	−0.594346
$631$	−22.1902	−0.883378	−0.441689	−	0.897168i	$-0.645621\pi$
$631$	−22.1902	−0.883378	−0.441689	+	0.897168i	$0.645621\pi$
$632$	−82.1784	−3.26888
$633$	−3.36336	−0.133682
$634$	−62.2399	−2.47186
$635$	−40.5443	−1.60895
$636$	−14.4806	−0.574195
$637$	−19.9980	−0.792349
$638$	0.345393	0.0136742
$639$	28.7073	1.13564
$640$	−249.549	−9.86429
$641$	19.5694	0.772945	0.386473	−	0.922301i	$-0.373693\pi$
$641$	19.5694	0.772945	0.386473	+	0.922301i	$0.373693\pi$
$642$	−2.26499	−0.0893920
$643$	9.66900	0.381308	0.190654	−	0.981657i	$-0.438939\pi$
$643$	9.66900	0.381308	0.190654	+	0.981657i	$0.438939\pi$
$644$	19.5311	0.769633
$645$	−5.87990	−0.231521
$646$	68.4195	2.69193
$647$	−46.3681	−1.82292	−0.911458	−	0.411392i	$-0.865043\pi$
$647$	−46.3681	−1.82292	−0.911458	+	0.411392i	$0.865043\pi$
$648$	−83.2849	−3.27174
$649$	−0.390449	−0.0153265
$650$	−109.778	−4.30584
$651$	−1.43681	−0.0563132
$652$	−68.4246	−2.67972
$653$	20.2649	0.793027	0.396513	−	0.918029i	$-0.370220\pi$
$653$	20.2649	0.793027	0.396513	+	0.918029i	$0.370220\pi$
$654$	−3.05218	−0.119350
$655$	40.9172	1.59877
$656$	−156.246	−6.10037
$657$	2.32463	0.0906923
$658$	−2.89826	−0.112986
$659$	2.73307	0.106465	0.0532327	−	0.998582i	$-0.483048\pi$
$659$	2.73307	0.106465	0.0532327	+	0.998582i	$0.483048\pi$
$660$	2.72732	0.106161
$661$	−2.71454	−0.105583	−0.0527916	−	0.998606i	$-0.516812\pi$
$661$	−2.71454	−0.105583	−0.0527916	+	0.998606i	$0.516812\pi$
$662$	5.43270	0.211148
$663$	−4.70209	−0.182614
$664$	62.7282	2.43433
$665$	−8.95734	−0.347351
$666$	−34.0177	−1.31816
$667$	2.79176	0.108097
$668$	−52.3741	−2.02641
$669$	1.73628	0.0671285
$670$	−25.4920	−0.984842
$671$	−5.18368	−0.200114
$672$	3.62753	0.139935
$673$	−42.3449	−1.63228	−0.816138	−	0.577858i	$-0.803889\pi$
$673$	−42.3449	−1.63228	−0.816138	+	0.577858i	$0.803889\pi$
$674$	53.9034	2.07628
$675$	−24.9832	−0.961605
$676$	−24.9893	−0.961128
$677$	−44.7514	−1.71994	−0.859968	−	0.510348i	$-0.829517\pi$
$677$	−44.7514	−1.71994	−0.859968	+	0.510348i	$0.829517\pi$
$678$	10.4253	0.400383
$679$	−4.73521	−0.181721
$680$	224.956	8.62668
$681$	−3.79879	−0.145570
$682$	−10.4462	−0.400006
$683$	9.25429	0.354106	0.177053	−	0.984201i	$-0.443344\pi$
$683$	9.25429	0.354106	0.177053	+	0.984201i	$0.443344\pi$
$684$	−79.8732	−3.05403
$685$	18.6642	0.713123
$686$	−16.5208	−0.630766
$687$	8.97823	0.342541
$688$	−74.2836	−2.83204
$689$	−23.7630	−0.905297
$690$	29.7848	1.13389
$691$	13.6915	0.520849	0.260425	−	0.965494i	$-0.416137\pi$
$691$	13.6915	0.520849	0.260425	+	0.965494i	$0.416137\pi$
$692$	−16.1575	−0.614216
$693$	0.443673	0.0168538
$694$	66.8904	2.53913
$695$	3.44079	0.130517
$696$	1.12995	0.0428306
$697$	46.7559	1.77100
$698$	83.5570	3.16268
$699$	5.64214	0.213405
$700$	−33.1095	−1.25142
$701$	30.2094	1.14099	0.570497	−	0.821300i	$-0.306751\pi$
$701$	30.2094	1.14099	0.570497	+	0.821300i	$0.306751\pi$
$702$	15.0852	0.569355
$703$	−20.4256	−0.770364
$704$	14.2756	0.538031
$705$	−3.27123	−0.123201
$706$	−69.0616	−2.59917
$707$	−8.15818	−0.306820
$708$	−1.96854	−0.0739824
$709$	−0.260472	−0.00978223	−0.00489112	−	0.999988i	$-0.501557\pi$
$709$	−0.260472	−0.00978223	−0.00489112	+	0.999988i	$0.501557\pi$
$710$	118.007	4.42874
$711$	−23.2538	−0.872086
$712$	127.344	4.77241
$713$	−84.4352	−3.16212
$714$	−1.91612	−0.0717089
$715$	4.47557	0.167377
$716$	113.776	4.25199
$717$	−5.62268	−0.209983
$718$	51.8583	1.93533
$719$	−48.6629	−1.81482	−0.907410	−	0.420245i	$-0.861944\pi$
$719$	−48.6629	−1.81482	−0.907410	+	0.420245i	$0.861944\pi$
$720$	−212.719	−7.92758
$721$	6.26968	0.233495
$722$	−12.0890	−0.449905
$723$	−0.221978	−0.00825544
$724$	−22.7414	−0.845177
$725$	−4.73264	−0.175766
$726$	9.47146	0.351519
$727$	−19.6156	−0.727502	−0.363751	−	0.931496i	$-0.618504\pi$
$727$	−19.6156	−0.727502	−0.363751	+	0.931496i	$0.618504\pi$
$728$	12.9724	0.480789
$729$	−21.8217	−0.808210
$730$	9.55586	0.353678
$731$	22.2290	0.822171
$732$	−26.1348	−0.965969
$733$	−31.2568	−1.15450	−0.577248	−	0.816569i	$-0.695873\pi$
$733$	−31.2568	−1.15450	−0.577248	+	0.816569i	$0.695873\pi$
$734$	36.4828	1.34660
$735$	−9.19796	−0.339272
$736$	213.174	7.85769
$737$	0.758153	0.0279269
$738$	−73.7482	−2.71471
$739$	−31.8053	−1.16998	−0.584989	−	0.811041i	$-0.698901\pi$
$739$	−31.8053	−1.16998	−0.584989	+	0.811041i	$0.698901\pi$
$740$	−103.497	−3.80462
$741$	4.45323	0.163594
$742$	−9.68349	−0.355492
$743$	51.2405	1.87983	0.939917	−	0.341404i	$-0.110903\pi$
$743$	51.2405	1.87983	0.939917	+	0.341404i	$0.110903\pi$
$744$	−34.1747	−1.25290
$745$	−24.7657	−0.907344
$746$	−58.1425	−2.12875
$747$	17.7500	0.649440
$748$	−10.3107	−0.376995
$749$	−1.12103	−0.0409615
$750$	−31.7683	−1.16001
$751$	−45.5539	−1.66229	−0.831143	−	0.556058i	$-0.812313\pi$
$751$	−45.5539	−1.66229	−0.831143	+	0.556058i	$0.812313\pi$
$752$	−41.3270	−1.50704
$753$	1.22721	0.0447219
$754$	2.85763	0.104069
$755$	−69.5619	−2.53162
$756$	4.54977	0.165474
$757$	7.21999	0.262415	0.131207	−	0.991355i	$-0.458115\pi$
$757$	7.21999	0.262415	0.131207	+	0.991355i	$0.458115\pi$
$758$	−89.8009	−3.26172
$759$	−0.885824	−0.0321534
$760$	−213.051	−7.72816
$761$	28.0165	1.01560	0.507799	−	0.861475i	$-0.330459\pi$
$761$	28.0165	1.01560	0.507799	+	0.861475i	$0.330459\pi$
$762$	8.21404	0.297563
$763$	−1.51064	−0.0546889
$764$	41.6559	1.50706
$765$	63.6553	2.30146
$766$	37.7285	1.36319
$767$	−3.23041	−0.116643
$768$	25.2859	0.912425
$769$	−23.9520	−0.863732	−0.431866	−	0.901938i	$-0.642145\pi$
$769$	−23.9520	−0.863732	−0.431866	+	0.901938i	$0.642145\pi$
$770$	1.82381	0.0657256
$771$	5.63038	0.202773
$772$	−76.8604	−2.76627
$773$	19.0913	0.686667	0.343334	−	0.939214i	$-0.388444\pi$
$773$	19.0913	0.686667	0.343334	+	0.939214i	$0.388444\pi$
$774$	−35.0620	−1.26028
$775$	143.136	5.14160
$776$	−112.627	−4.04308
$777$	0.572027	0.0205213
$778$	−55.7909	−2.00020
$779$	−44.2813	−1.58654
$780$	22.5647	0.807945
$781$	−3.50964	−0.125585
$782$	−112.602	−4.02663
$783$	0.650340	0.0232413
$784$	−116.202	−4.15008
$785$	−36.8075	−1.31372
$786$	−8.28960	−0.295680
$787$	−51.3504	−1.83044	−0.915222	−	0.402951i	$-0.867985\pi$
$787$	−51.3504	−1.83044	−0.915222	+	0.402951i	$0.867985\pi$
$788$	64.8608	2.31057
$789$	−1.69275	−0.0602635
$790$	−95.5897	−3.40093
$791$	5.15989	0.183465
$792$	10.5528	0.374977
$793$	−42.8875	−1.52298
$794$	−4.16416	−0.147780
$795$	−10.9296	−0.387634
$796$	85.3070	3.02363
$797$	−0.697748	−0.0247155	−0.0123577	−	0.999924i	$-0.503934\pi$
$797$	−0.697748	−0.0247155	−0.0123577	+	0.999924i	$0.503934\pi$
$798$	1.81471	0.0642400
$799$	12.3669	0.437510
$800$	−361.376	−12.7766
$801$	36.0342	1.27321
$802$	20.1118	0.710171
$803$	−0.284199	−0.0100292
$804$	3.82241	0.134806
$805$	14.7416	0.519573
$806$	−86.4275	−3.04428
$807$	1.62231	0.0571080
$808$	−194.042	−6.82639
$809$	9.02924	0.317451	0.158726	−	0.987323i	$-0.449262\pi$
$809$	9.02924	0.317451	0.158726	+	0.987323i	$0.449262\pi$
$810$	−96.8766	−3.40390
$811$	15.5100	0.544631	0.272315	−	0.962208i	$-0.412211\pi$
$811$	15.5100	0.544631	0.272315	+	0.962208i	$0.412211\pi$
$812$	0.861874	0.0302459
$813$	−7.58392	−0.265980
$814$	4.15886	0.145768
$815$	−51.6453	−1.80905
$816$	−27.3224	−0.956476
$817$	−21.0526	−0.736537
$818$	−104.091	−3.63947
$819$	3.67076	0.128267
$820$	−224.375	−7.83551
$821$	−51.9336	−1.81249	−0.906247	−	0.422749i	$-0.861065\pi$
$821$	−51.9336	−1.81249	−0.906247	+	0.422749i	$0.861065\pi$
$822$	−3.78126	−0.131887
$823$	34.5369	1.20388	0.601940	−	0.798542i	$-0.294395\pi$
$823$	34.5369	1.20388	0.601940	+	0.798542i	$0.294395\pi$
$824$	149.125	5.19500
$825$	1.50166	0.0522813
$826$	−1.31640	−0.0458035
$827$	48.4761	1.68568	0.842839	−	0.538166i	$-0.180882\pi$
$827$	48.4761	1.68568	0.842839	+	0.538166i	$0.180882\pi$
$828$	131.452	4.56827
$829$	6.10554	0.212054	0.106027	−	0.994363i	$-0.466187\pi$
$829$	6.10554	0.212054	0.106027	+	0.994363i	$0.466187\pi$
$830$	72.9652	2.53266
$831$	−1.31832	−0.0457321
$832$	118.110	4.09473
$833$	34.7730	1.20481
$834$	−0.697085	−0.0241381
$835$	−39.5307	−1.36802
$836$	9.76498	0.337729
$837$	−19.6692	−0.679867
$838$	−1.33340	−0.0460616
$839$	25.0915	0.866255	0.433127	−	0.901333i	$-0.357410\pi$
$839$	25.0915	0.866255	0.433127	+	0.901333i	$0.357410\pi$
$840$	5.96658	0.205866
$841$	−28.8768	−0.995752
$842$	−3.45455	−0.119052
$843$	−6.73622	−0.232008
$844$	−61.0186	−2.10035
$845$	−18.8613	−0.648850
$846$	−19.5064	−0.670643
$847$	4.68778	0.161074
$848$	−138.079	−4.74167
$849$	3.04840	0.104621
$850$	190.884	6.54728
$851$	33.6155	1.15232
$852$	−17.6947	−0.606210
$853$	−12.0492	−0.412556	−0.206278	−	0.978493i	$-0.566135\pi$
$853$	−12.0492	−0.412556	−0.206278	+	0.978493i	$0.566135\pi$
$854$	−17.4768	−0.598045
$855$	−60.2864	−2.06175
$856$	−26.6637	−0.911346
$857$	36.0585	1.23174	0.615868	−	0.787849i	$-0.288805\pi$
$857$	36.0585	1.23174	0.615868	+	0.787849i	$0.288805\pi$
$858$	−0.906726	−0.0309551
$859$	−5.63952	−0.192418	−0.0962090	−	0.995361i	$-0.530672\pi$
$859$	−5.63952	−0.192418	−0.0962090	+	0.995361i	$0.530672\pi$
$860$	−106.674	−3.63756
$861$	1.24012	0.0422631
$862$	61.9418	2.10975
$863$	−36.3532	−1.23748	−0.618738	−	0.785597i	$-0.712356\pi$
$863$	−36.3532	−1.23748	−0.618738	+	0.785597i	$0.712356\pi$
$864$	49.6588	1.68943
$865$	−12.1953	−0.414652
$866$	−58.6414	−1.99272
$867$	2.83865	0.0964055
$868$	−26.0669	−0.884769
$869$	2.84292	0.0964394
$870$	1.31435	0.0445607
$871$	6.27264	0.212540
$872$	−35.9306	−1.21676
$873$	−31.8698	−1.07863
$874$	106.642	3.60723
$875$	−15.7233	−0.531545
$876$	−1.43286	−0.0484118
$877$	28.8280	0.973452	0.486726	−	0.873555i	$-0.338191\pi$
$877$	28.8280	0.973452	0.486726	+	0.873555i	$0.338191\pi$
$878$	69.5964	2.34876
$879$	1.31100	0.0442190
$880$	26.0062	0.876669
$881$	−30.8328	−1.03878	−0.519392	−	0.854536i	$-0.673842\pi$
$881$	−30.8328	−1.03878	−0.519392	+	0.854536i	$0.673842\pi$
$882$	−54.8476	−1.84682
$883$	−48.5784	−1.63479	−0.817396	−	0.576076i	$-0.804583\pi$
$883$	−48.5784	−1.63479	−0.817396	+	0.576076i	$0.804583\pi$
$884$	−85.3061	−2.86915
$885$	−1.48581	−0.0499449
$886$	−51.1399	−1.71808
$887$	22.8615	0.767616	0.383808	−	0.923413i	$-0.374612\pi$
$887$	22.8615	0.767616	0.383808	+	0.923413i	$0.374612\pi$
$888$	13.6057	0.456576
$889$	4.06544	0.136350
$890$	148.126	4.96519
$891$	2.88119	0.0965236
$892$	31.4999	1.05469
$893$	−11.7124	−0.391941
$894$	5.01739	0.167807
$895$	85.8750	2.87049
$896$	25.0227	0.835949
$897$	−7.32893	−0.244706
$898$	−9.61488	−0.320853
$899$	−3.72598	−0.124269
$900$	−222.839	−7.42798
$901$	41.3196	1.37656
$902$	9.01615	0.300205
$903$	0.589587	0.0196202
$904$	122.728	4.08188
$905$	−17.1646	−0.570572
$906$	14.0929	0.468204
$907$	56.3592	1.87138	0.935689	−	0.352827i	$-0.114779\pi$
$907$	56.3592	1.87138	0.935689	+	0.352827i	$0.114779\pi$
$908$	−68.9182	−2.28713
$909$	−54.9077	−1.82117
$910$	15.0894	0.500210
$911$	46.4972	1.54052	0.770261	−	0.637729i	$-0.220126\pi$
$911$	46.4972	1.54052	0.770261	+	0.637729i	$0.220126\pi$
$912$	25.8764	0.856853
$913$	−2.17005	−0.0718181
$914$	32.7091	1.08192
$915$	−19.7259	−0.652118
$916$	162.885	5.38186
$917$	−4.10283	−0.135487
$918$	−26.2306	−0.865738
$919$	1.85713	0.0612610	0.0306305	−	0.999531i	$-0.490248\pi$
$919$	1.85713	0.0612610	0.0306305	+	0.999531i	$0.490248\pi$
$920$	350.629	11.5599
$921$	−1.12013	−0.0369095
$922$	29.2066	0.961867
$923$	−29.0373	−0.955773
$924$	−0.273473	−0.00899659
$925$	−56.9855	−1.87367
$926$	−13.3436	−0.438498
$927$	42.1974	1.38594
$928$	9.40700	0.308800
$929$	−38.8298	−1.27396	−0.636982	−	0.770878i	$-0.719818\pi$
$929$	−38.8298	−1.27396	−0.636982	+	0.770878i	$0.719818\pi$
$930$	−39.7519	−1.30351
$931$	−32.9327	−1.07933
$932$	102.361	3.35293
$933$	0.881973	0.0288745
$934$	2.88080	0.0942626
$935$	−7.78224	−0.254506
$936$	87.3092	2.85379
$937$	2.94887	0.0963355	0.0481677	−	0.998839i	$-0.484662\pi$
$937$	2.94887	0.0963355	0.0481677	+	0.998839i	$0.484662\pi$
$938$	2.55612	0.0834604
$939$	6.70949	0.218956
$940$	−59.3471	−1.93569
$941$	42.1955	1.37554	0.687768	−	0.725931i	$-0.258591\pi$
$941$	42.1955	1.37554	0.687768	+	0.725931i	$0.258591\pi$
$942$	7.45699	0.242962
$943$	72.8762	2.37318
$944$	−18.7709	−0.610942
$945$	3.43406	0.111710
$946$	4.28653	0.139367
$947$	−14.7613	−0.479677	−0.239838	−	0.970813i	$-0.577094\pi$
$947$	−14.7613	−0.479677	−0.239838	+	0.970813i	$0.577094\pi$
$948$	14.3333	0.465522
$949$	−2.35134	−0.0763279
$950$	−180.782	−5.86534
$951$	7.04403	0.228418
$952$	−22.5567	−0.731068
$953$	4.89773	0.158653	0.0793265	−	0.996849i	$-0.474723\pi$
$953$	4.89773	0.158653	0.0793265	+	0.996849i	$0.474723\pi$
$954$	−65.1736	−2.11007
$955$	31.4409	1.01740
$956$	−102.008	−3.29916
$957$	−0.0390899	−0.00126360
$958$	85.8573	2.77392
$959$	−1.87149	−0.0604335
$960$	54.3241	1.75330
$961$	81.6904	2.63517
$962$	34.4087	1.10938
$963$	−7.54495	−0.243133
$964$	−4.02715	−0.129706
$965$	−58.0123	−1.86748
$966$	−2.98657	−0.0960912
$967$	43.2481	1.39077	0.695383	−	0.718639i	$-0.255235\pi$
$967$	43.2481	1.39077	0.695383	+	0.718639i	$0.255235\pi$
$968$	111.499	3.58371
$969$	−7.74340	−0.248754
$970$	−131.007	−4.20639
$971$	15.2484	0.489343	0.244671	−	0.969606i	$-0.421320\pi$
$971$	15.2484	0.489343	0.244671	+	0.969606i	$0.421320\pi$
$972$	46.1883	1.48149
$973$	−0.345013	−0.0110606
$974$	−61.8126	−1.98060
$975$	12.4241	0.397891
$976$	−249.207	−7.97691
$977$	−33.4915	−1.07149	−0.535744	−	0.844381i	$-0.679969\pi$
$977$	−33.4915	−1.07149	−0.535744	+	0.844381i	$0.679969\pi$
$978$	10.4630	0.334571
$979$	−4.40539	−0.140797
$980$	−166.871	−5.33050
$981$	−10.1672	−0.324614
$982$	−26.5919	−0.848580
$983$	48.4566	1.54553	0.772763	−	0.634695i	$-0.218874\pi$
$983$	48.4566	1.54553	0.772763	+	0.634695i	$0.218874\pi$
$984$	29.4962	0.940306
$985$	48.9554	1.55985
$986$	−4.96892	−0.158243
$987$	0.328011	0.0104407
$988$	80.7913	2.57031
$989$	34.6474	1.10172
$990$	12.2750	0.390124
$991$	−59.0123	−1.87459	−0.937293	−	0.348541i	$-0.886677\pi$
$991$	−59.0123	−1.87459	−0.937293	+	0.348541i	$0.886677\pi$
$992$	−284.510	−9.03319
$993$	−0.614848	−0.0195116
$994$	−11.8328	−0.375313
$995$	64.3877	2.04123
$996$	−10.9408	−0.346673
$997$	−22.2894	−0.705912	−0.352956	−	0.935640i	$-0.614824\pi$
$997$	−22.2894	−0.705912	−0.352956	+	0.935640i	$0.614824\pi$
$998$	48.1867	1.52532
$999$	7.83073	0.247753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.3	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.3	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77418 q^{2} +0.313969 q^{3} +5.69607 q^{4} +4.29926 q^{5} -0.871005 q^{6} -0.431093 q^{7} -10.2536 q^{8} -2.90142 q^{9} +O(q^{10})\)	\(q-2.77418 q^{2} +0.313969 q^{3} +5.69607 q^{4} +4.29926 q^{5} -0.871005 q^{6} -0.431093 q^{7} -10.2536 q^{8} -2.90142 q^{9} -11.9269 q^{10} +0.354716 q^{11} +1.78839 q^{12} +2.93477 q^{13} +1.19593 q^{14} +1.34983 q^{15} +17.0531 q^{16} -5.10306 q^{17} +8.04907 q^{18} +4.83298 q^{19} +24.4889 q^{20} -0.135350 q^{21} -0.984046 q^{22} -7.95390 q^{23} -3.21930 q^{24} +13.4836 q^{25} -8.14158 q^{26} -1.85286 q^{27} -2.45554 q^{28} -0.350992 q^{29} -3.74467 q^{30} +10.6156 q^{31} -26.8012 q^{32} +0.111370 q^{33} +14.1568 q^{34} -1.85338 q^{35} -16.5267 q^{36} -4.22629 q^{37} -13.4075 q^{38} +0.921426 q^{39} -44.0827 q^{40} -9.16232 q^{41} +0.375484 q^{42} -4.35603 q^{43} +2.02049 q^{44} -12.4740 q^{45} +22.0655 q^{46} -2.42343 q^{47} +5.35413 q^{48} -6.81416 q^{49} -37.4059 q^{50} -1.60220 q^{51} +16.7167 q^{52} -8.09704 q^{53} +5.14017 q^{54} +1.52502 q^{55} +4.42024 q^{56} +1.51740 q^{57} +0.973715 q^{58} -1.10074 q^{59} +7.68873 q^{60} -14.6136 q^{61} -29.4495 q^{62} +1.25078 q^{63} +40.2451 q^{64} +12.6173 q^{65} -0.308960 q^{66} +2.13735 q^{67} -29.0674 q^{68} -2.49728 q^{69} +5.14161 q^{70} -9.89421 q^{71} +29.7499 q^{72} -0.801202 q^{73} +11.7245 q^{74} +4.23343 q^{75} +27.5290 q^{76} -0.152916 q^{77} -2.55620 q^{78} +8.01462 q^{79} +73.3155 q^{80} +8.12253 q^{81} +25.4179 q^{82} -6.11770 q^{83} -0.770961 q^{84} -21.9393 q^{85} +12.0844 q^{86} -0.110201 q^{87} -3.63710 q^{88} -12.4195 q^{89} +34.6050 q^{90} -1.26516 q^{91} -45.3060 q^{92} +3.33296 q^{93} +6.72304 q^{94} +20.7782 q^{95} -8.41472 q^{96} +10.9842 q^{97} +18.9037 q^{98} -1.02918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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