LMFDB - Embedded newform 8017.2.a.b.1.8

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:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.67670 q^{2} -1.97751 q^{3} +5.16470 q^{4} -3.95415 q^{5} +5.29320 q^{6} -4.51333 q^{7} -8.47093 q^{8} +0.910563 q^{9} +O(q^{10})$	\(q-2.67670 q^{2} -1.97751 q^{3} +5.16470 q^{4} -3.95415 q^{5} +5.29320 q^{6} -4.51333 q^{7} -8.47093 q^{8} +0.910563 q^{9} +10.5841 q^{10} -0.730695 q^{11} -10.2133 q^{12} -0.533247 q^{13} +12.0808 q^{14} +7.81939 q^{15} +12.3447 q^{16} +6.82984 q^{17} -2.43730 q^{18} -3.35626 q^{19} -20.4220 q^{20} +8.92517 q^{21} +1.95585 q^{22} +3.41625 q^{23} +16.7514 q^{24} +10.6353 q^{25} +1.42734 q^{26} +4.13189 q^{27} -23.3100 q^{28} -1.87456 q^{29} -20.9301 q^{30} -6.52718 q^{31} -16.1012 q^{32} +1.44496 q^{33} -18.2814 q^{34} +17.8464 q^{35} +4.70278 q^{36} +11.4724 q^{37} +8.98368 q^{38} +1.05450 q^{39} +33.4954 q^{40} +5.43962 q^{41} -23.8900 q^{42} -1.37591 q^{43} -3.77382 q^{44} -3.60050 q^{45} -9.14425 q^{46} +11.2444 q^{47} -24.4118 q^{48} +13.3701 q^{49} -28.4675 q^{50} -13.5061 q^{51} -2.75406 q^{52} -2.91288 q^{53} -11.0598 q^{54} +2.88928 q^{55} +38.2321 q^{56} +6.63705 q^{57} +5.01763 q^{58} -5.86390 q^{59} +40.3848 q^{60} +2.09251 q^{61} +17.4713 q^{62} -4.10967 q^{63} +18.4085 q^{64} +2.10854 q^{65} -3.86772 q^{66} +15.4164 q^{67} +35.2741 q^{68} -6.75568 q^{69} -47.7693 q^{70} +15.3285 q^{71} -7.71332 q^{72} -10.6151 q^{73} -30.7082 q^{74} -21.0315 q^{75} -17.3341 q^{76} +3.29787 q^{77} -2.82258 q^{78} -7.22593 q^{79} -48.8129 q^{80} -10.9026 q^{81} -14.5602 q^{82} +11.0270 q^{83} +46.0958 q^{84} -27.0062 q^{85} +3.68288 q^{86} +3.70697 q^{87} +6.18967 q^{88} -13.5230 q^{89} +9.63745 q^{90} +2.40672 q^{91} +17.6439 q^{92} +12.9076 q^{93} -30.0979 q^{94} +13.2712 q^{95} +31.8403 q^{96} +5.58376 q^{97} -35.7878 q^{98} -0.665344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.67670	−1.89271	−0.946355	−	0.323130i	$-0.895265\pi$
$2$	−2.67670	−1.89271	−0.946355	+	0.323130i	$0.895265\pi$
$3$	−1.97751	−1.14172	−0.570859	−	0.821048i	$-0.693390\pi$
$3$	−1.97751	−1.14172	−0.570859	+	0.821048i	$0.693390\pi$
$4$	5.16470	2.58235
$5$	−3.95415	−1.76835	−0.884175	−	0.467155i	$-0.845279\pi$
$5$	−3.95415	−1.76835	−0.884175	+	0.467155i	$0.845279\pi$
$6$	5.29320	2.16094
$7$	−4.51333	−1.70588	−0.852939	−	0.522011i	$-0.825182\pi$
$7$	−4.51333	−1.70588	−0.852939	+	0.522011i	$0.825182\pi$
$8$	−8.47093	−2.99493
$9$	0.910563	0.303521
$10$	10.5841	3.34697
$11$	−0.730695	−0.220313	−0.110156	−	0.993914i	$-0.535135\pi$
$11$	−0.730695	−0.220313	−0.110156	+	0.993914i	$0.535135\pi$
$12$	−10.2133	−2.94832
$13$	−0.533247	−0.147896	−0.0739480	−	0.997262i	$-0.523560\pi$
$13$	−0.533247	−0.147896	−0.0739480	+	0.997262i	$0.523560\pi$
$14$	12.0808	3.22873
$15$	7.81939	2.01896
$16$	12.3447	3.08618
$17$	6.82984	1.65648	0.828240	−	0.560374i	$-0.189342\pi$
$17$	6.82984	1.65648	0.828240	+	0.560374i	$0.189342\pi$
$18$	−2.43730	−0.574477
$19$	−3.35626	−0.769978	−0.384989	−	0.922921i	$-0.625795\pi$
$19$	−3.35626	−0.769978	−0.384989	+	0.922921i	$0.625795\pi$
$20$	−20.4220	−4.56650
$21$	8.92517	1.94763
$22$	1.95585	0.416988
$23$	3.41625	0.712337	0.356168	−	0.934422i	$-0.384083\pi$
$23$	3.41625	0.712337	0.356168	+	0.934422i	$0.384083\pi$
$24$	16.7514	3.41936
$25$	10.6353	2.12706
$26$	1.42734	0.279924
$27$	4.13189	0.795183
$28$	−23.3100	−4.40517
$29$	−1.87456	−0.348097	−0.174049	−	0.984737i	$-0.555685\pi$
$29$	−1.87456	−0.348097	−0.174049	+	0.984737i	$0.555685\pi$
$30$	−20.9301	−3.82130
$31$	−6.52718	−1.17232	−0.586158	−	0.810197i	$-0.699360\pi$
$31$	−6.52718	−1.17232	−0.586158	+	0.810197i	$0.699360\pi$
$32$	−16.1012	−2.84631
$33$	1.44496	0.251535
$34$	−18.2814	−3.13523
$35$	17.8464	3.01659
$36$	4.70278	0.783797
$37$	11.4724	1.88605	0.943026	−	0.332718i	$-0.107966\pi$
$37$	11.4724	1.88605	0.943026	+	0.332718i	$0.107966\pi$
$38$	8.98368	1.45735
$39$	1.05450	0.168856
$40$	33.4954	5.29608
$41$	5.43962	0.849526	0.424763	−	0.905305i	$-0.360357\pi$
$41$	5.43962	0.849526	0.424763	+	0.905305i	$0.360357\pi$
$42$	−23.8900	−3.68630
$43$	−1.37591	−0.209824	−0.104912	−	0.994482i	$-0.533456\pi$
$43$	−1.37591	−0.209824	−0.104912	+	0.994482i	$0.533456\pi$
$44$	−3.77382	−0.568925
$45$	−3.60050	−0.536732
$46$	−9.14425	−1.34825
$47$	11.2444	1.64017	0.820083	−	0.572245i	$-0.193927\pi$
$47$	11.2444	1.64017	0.820083	+	0.572245i	$0.193927\pi$
$48$	−24.4118	−3.52355
$49$	13.3701	1.91002
$50$	−28.4675	−4.02591
$51$	−13.5061	−1.89123
$52$	−2.75406	−0.381919
$53$	−2.91288	−0.400115	−0.200058	−	0.979784i	$-0.564113\pi$
$53$	−2.91288	−0.400115	−0.200058	+	0.979784i	$0.564113\pi$
$54$	−11.0598	−1.50505
$55$	2.88928	0.389590
$56$	38.2321	5.10898
$57$	6.63705	0.879099
$58$	5.01763	0.658847
$59$	−5.86390	−0.763415	−0.381708	−	0.924283i	$-0.624664\pi$
$59$	−5.86390	−0.763415	−0.381708	+	0.924283i	$0.624664\pi$
$60$	40.3848	5.21366
$61$	2.09251	0.267919	0.133959	−	0.990987i	$-0.457231\pi$
$61$	2.09251	0.267919	0.133959	+	0.990987i	$0.457231\pi$
$62$	17.4713	2.21885
$63$	−4.10967	−0.517770
$64$	18.4085	2.30106
$65$	2.10854	0.261532
$66$	−3.86772	−0.476083
$67$	15.4164	1.88341	0.941707	−	0.336433i	$-0.109221\pi$
$67$	15.4164	1.88341	0.941707	+	0.336433i	$0.109221\pi$
$68$	35.2741	4.27761
$69$	−6.75568	−0.813288
$70$	−47.7693	−5.70953
$71$	15.3285	1.81916	0.909578	−	0.415532i	$-0.136405\pi$
$71$	15.3285	1.81916	0.909578	+	0.415532i	$0.136405\pi$
$72$	−7.71332	−0.909023
$73$	−10.6151	−1.24241	−0.621204	−	0.783649i	$-0.713356\pi$
$73$	−10.6151	−1.24241	−0.621204	+	0.783649i	$0.713356\pi$
$74$	−30.7082	−3.56975
$75$	−21.0315	−2.42851
$76$	−17.3341	−1.98835
$77$	3.29787	0.375827
$78$	−2.82258	−0.319595
$79$	−7.22593	−0.812981	−0.406490	−	0.913655i	$-0.633248\pi$
$79$	−7.22593	−0.812981	−0.406490	+	0.913655i	$0.633248\pi$
$80$	−48.8129	−5.45744
$81$	−10.9026	−1.21140
$82$	−14.5602	−1.60791
$83$	11.0270	1.21037	0.605184	−	0.796086i	$-0.293100\pi$
$83$	11.0270	1.21037	0.605184	+	0.796086i	$0.293100\pi$
$84$	46.0958	5.02947
$85$	−27.0062	−2.92924
$86$	3.68288	0.397135
$87$	3.70697	0.397429
$88$	6.18967	0.659821
$89$	−13.5230	−1.43344	−0.716720	−	0.697361i	$-0.754357\pi$
$89$	−13.5230	−1.43344	−0.716720	+	0.697361i	$0.754357\pi$
$90$	9.63745	1.01588
$91$	2.40672	0.252293
$92$	17.6439	1.83950
$93$	12.9076	1.33845
$94$	−30.0979	−3.10436
$95$	13.2712	1.36159
$96$	31.8403	3.24969
$97$	5.58376	0.566945	0.283473	−	0.958980i	$-0.408513\pi$
$97$	5.58376	0.566945	0.283473	+	0.958980i	$0.408513\pi$
$98$	−35.7878	−3.61511
$99$	−0.665344	−0.0668696
$100$	54.9282	5.49282
$101$	12.9150	1.28509	0.642545	−	0.766248i	$-0.277879\pi$
$101$	12.9150	1.28509	0.642545	+	0.766248i	$0.277879\pi$
$102$	36.1517	3.57956
$103$	−1.33070	−0.131118	−0.0655590	−	0.997849i	$-0.520883\pi$
$103$	−1.33070	−0.131118	−0.0655590	+	0.997849i	$0.520883\pi$
$104$	4.51710	0.442938
$105$	−35.2915	−3.44410
$106$	7.79690	0.757302
$107$	−3.02110	−0.292061	−0.146030	−	0.989280i	$-0.546650\pi$
$107$	−3.02110	−0.292061	−0.146030	+	0.989280i	$0.546650\pi$
$108$	21.3400	2.05344
$109$	−16.5179	−1.58213	−0.791066	−	0.611731i	$-0.790474\pi$
$109$	−16.5179	−1.58213	−0.791066	+	0.611731i	$0.790474\pi$
$110$	−7.73372	−0.737381
$111$	−22.6869	−2.15334
$112$	−55.7157	−5.26464
$113$	6.34564	0.596947	0.298474	−	0.954418i	$-0.403523\pi$
$113$	6.34564	0.596947	0.298474	+	0.954418i	$0.403523\pi$
$114$	−17.7654	−1.66388
$115$	−13.5084	−1.25966
$116$	−9.68155	−0.898909
$117$	−0.485555	−0.0448896
$118$	15.6959	1.44492
$119$	−30.8253	−2.82575
$120$	−66.2375	−6.04663
$121$	−10.4661	−0.951462
$122$	−5.60102	−0.507092
$123$	−10.7569	−0.969920
$124$	−33.7109	−3.02733
$125$	−22.2829	−1.99304
$126$	11.0003	0.979988
$127$	6.36857	0.565119	0.282560	−	0.959250i	$-0.408816\pi$
$127$	6.36857	0.565119	0.282560	+	0.959250i	$0.408816\pi$
$128$	−17.0716	−1.50893
$129$	2.72087	0.239560
$130$	−5.64392	−0.495004
$131$	16.6687	1.45635	0.728176	−	0.685390i	$-0.240368\pi$
$131$	16.6687	1.45635	0.728176	+	0.685390i	$0.240368\pi$
$132$	7.46278	0.649552
$133$	15.1479	1.31349
$134$	−41.2650	−3.56476
$135$	−16.3381	−1.40616
$136$	−57.8551	−4.96104
$137$	−12.9037	−1.10244	−0.551219	−	0.834361i	$-0.685837\pi$
$137$	−12.9037	−1.10244	−0.551219	+	0.834361i	$0.685837\pi$
$138$	18.0829	1.53932
$139$	1.52794	0.129598	0.0647992	−	0.997898i	$-0.479359\pi$
$139$	1.52794	0.129598	0.0647992	+	0.997898i	$0.479359\pi$
$140$	92.1712	7.78989
$141$	−22.2360	−1.87261
$142$	−41.0297	−3.44314
$143$	0.389641	0.0325834
$144$	11.2406	0.936720
$145$	7.41230	0.615558
$146$	28.4135	2.35152
$147$	−26.4396	−2.18070
$148$	59.2515	4.87045
$149$	−8.33182	−0.682569	−0.341285	−	0.939960i	$-0.610862\pi$
$149$	−8.33182	−0.682569	−0.341285	+	0.939960i	$0.610862\pi$
$150$	56.2949	4.59646
$151$	16.4940	1.34226	0.671130	−	0.741340i	$-0.265809\pi$
$151$	16.4940	1.34226	0.671130	+	0.741340i	$0.265809\pi$
$152$	28.4306	2.30603
$153$	6.21900	0.502776
$154$	−8.82738	−0.711331
$155$	25.8095	2.07307
$156$	5.44619	0.436044
$157$	−16.8550	−1.34517	−0.672586	−	0.740019i	$-0.734817\pi$
$157$	−16.8550	−1.34517	−0.672586	+	0.740019i	$0.734817\pi$
$158$	19.3416	1.53874
$159$	5.76026	0.456819
$160$	63.6664	5.03327
$161$	−15.4186	−1.21516
$162$	29.1828	2.29282
$163$	0.187181	0.0146611	0.00733056	−	0.999973i	$-0.497667\pi$
$163$	0.187181	0.0146611	0.00733056	+	0.999973i	$0.497667\pi$
$164$	28.0940	2.19377
$165$	−5.71359	−0.444802
$166$	−29.5159	−2.29087
$167$	10.6119	0.821175	0.410587	−	0.911821i	$-0.365324\pi$
$167$	10.6119	0.821175	0.410587	+	0.911821i	$0.365324\pi$
$168$	−75.6045	−5.83302
$169$	−12.7156	−0.978127
$170$	72.2875	5.54419
$171$	−3.05608	−0.233705
$172$	−7.10614	−0.541838
$173$	12.7380	0.968456	0.484228	−	0.874942i	$-0.339101\pi$
$173$	12.7380	0.968456	0.484228	+	0.874942i	$0.339101\pi$
$174$	−9.92244	−0.752218
$175$	−48.0007	−3.62851
$176$	−9.02022	−0.679924
$177$	11.5960	0.871605
$178$	36.1971	2.71308
$179$	−0.784198	−0.0586137	−0.0293069	−	0.999570i	$-0.509330\pi$
$179$	−0.784198	−0.0586137	−0.0293069	+	0.999570i	$0.509330\pi$
$180$	−18.5955	−1.38603
$181$	15.9206	1.18337	0.591686	−	0.806168i	$-0.298462\pi$
$181$	15.9206	1.18337	0.591686	+	0.806168i	$0.298462\pi$
$182$	−6.44205	−0.477517
$183$	−4.13797	−0.305888
$184$	−28.9388	−2.13340
$185$	−45.3637	−3.33520
$186$	−34.5497	−2.53331
$187$	−4.99053	−0.364944
$188$	58.0740	4.23548
$189$	−18.6486	−1.35648
$190$	−35.5228	−2.57710
$191$	−1.15938	−0.0838899	−0.0419450	−	0.999120i	$-0.513355\pi$
$191$	−1.15938	−0.0838899	−0.0419450	+	0.999120i	$0.513355\pi$
$192$	−36.4031	−2.62716
$193$	−14.5953	−1.05059	−0.525297	−	0.850919i	$-0.676046\pi$
$193$	−14.5953	−1.05059	−0.525297	+	0.850919i	$0.676046\pi$
$194$	−14.9460	−1.07306
$195$	−4.16967	−0.298596
$196$	69.0527	4.93233
$197$	11.5256	0.821167	0.410583	−	0.911823i	$-0.365325\pi$
$197$	11.5256	0.821167	0.410583	+	0.911823i	$0.365325\pi$
$198$	1.78092	0.126565
$199$	26.4500	1.87499	0.937496	−	0.347997i	$-0.113138\pi$
$199$	26.4500	1.87499	0.937496	+	0.347997i	$0.113138\pi$
$200$	−90.0911	−6.37040
$201$	−30.4862	−2.15033
$202$	−34.5695	−2.43230
$203$	8.46051	0.593812
$204$	−69.7550	−4.88383
$205$	−21.5091	−1.50226
$206$	3.56189	0.248168
$207$	3.11071	0.216209
$208$	−6.58278	−0.456434
$209$	2.45240	0.169636
$210$	94.4645	6.51867
$211$	−6.36317	−0.438059	−0.219029	−	0.975718i	$-0.570289\pi$
$211$	−6.36317	−0.438059	−0.219029	+	0.975718i	$0.570289\pi$
$212$	−15.0442	−1.03324
$213$	−30.3123	−2.07696
$214$	8.08656	0.552786
$215$	5.44054	0.371042
$216$	−35.0010	−2.38151
$217$	29.4593	1.99983
$218$	44.2135	2.99452
$219$	20.9916	1.41848
$220$	14.9223	1.00606
$221$	−3.64199	−0.244987
$222$	60.7258	4.07565
$223$	7.37719	0.494013	0.247007	−	0.969014i	$-0.420553\pi$
$223$	7.37719	0.494013	0.247007	+	0.969014i	$0.420553\pi$
$224$	72.6698	4.85546
$225$	9.68413	0.645609
$226$	−16.9853	−1.12985
$227$	−8.63120	−0.572873	−0.286436	−	0.958099i	$-0.592471\pi$
$227$	−8.63120	−0.572873	−0.286436	+	0.958099i	$0.592471\pi$
$228$	34.2784	2.27014
$229$	−21.0524	−1.39118	−0.695592	−	0.718437i	$-0.744858\pi$
$229$	−21.0524	−1.39118	−0.695592	+	0.718437i	$0.744858\pi$
$230$	36.1578	2.38417
$231$	−6.52158	−0.429088
$232$	15.8793	1.04253
$233$	22.8073	1.49416	0.747079	−	0.664735i	$-0.231456\pi$
$233$	22.8073	1.49416	0.747079	+	0.664735i	$0.231456\pi$
$234$	1.29968	0.0849629
$235$	−44.4621	−2.90039
$236$	−30.2853	−1.97140
$237$	14.2894	0.928195
$238$	82.5100	5.34833
$239$	18.5545	1.20019	0.600097	−	0.799927i	$-0.295129\pi$
$239$	18.5545	1.20019	0.600097	+	0.799927i	$0.295129\pi$
$240$	96.5281	6.23086
$241$	−3.03080	−0.195231	−0.0976154	−	0.995224i	$-0.531122\pi$
$241$	−3.03080	−0.195231	−0.0976154	+	0.995224i	$0.531122\pi$
$242$	28.0145	1.80084
$243$	9.16430	0.587890
$244$	10.8072	0.691860
$245$	−52.8675	−3.37758
$246$	28.7930	1.83578
$247$	1.78971	0.113877
$248$	55.2913	3.51100
$249$	−21.8060	−1.38190
$250$	59.6446	3.77225
$251$	3.23918	0.204455	0.102228	−	0.994761i	$-0.467403\pi$
$251$	3.23918	0.204455	0.102228	+	0.994761i	$0.467403\pi$
$252$	−21.2252	−1.33706
$253$	−2.49623	−0.156937
$254$	−17.0467	−1.06961
$255$	53.4052	3.34436
$256$	8.87847	0.554904
$257$	8.23585	0.513738	0.256869	−	0.966446i	$-0.417309\pi$
$257$	8.23585	0.513738	0.256869	+	0.966446i	$0.417309\pi$
$258$	−7.28295	−0.453417
$259$	−51.7788	−3.21738
$260$	10.8900	0.675367
$261$	−1.70691	−0.105655
$262$	−44.6171	−2.75645
$263$	16.9046	1.04238	0.521190	−	0.853441i	$-0.325488\pi$
$263$	16.9046	1.04238	0.521190	+	0.853441i	$0.325488\pi$
$264$	−12.2402	−0.753330
$265$	11.5180	0.707544
$266$	−40.5463	−2.48605
$267$	26.7420	1.63658
$268$	79.6211	4.86363
$269$	11.9089	0.726098	0.363049	−	0.931770i	$-0.381736\pi$
$269$	11.9089	0.726098	0.363049	+	0.931770i	$0.381736\pi$
$270$	43.7322	2.66146
$271$	−1.36761	−0.0830763	−0.0415382	−	0.999137i	$-0.513226\pi$
$271$	−1.36761	−0.0830763	−0.0415382	+	0.999137i	$0.513226\pi$
$272$	84.3124	5.11219
$273$	−4.75932	−0.288047
$274$	34.5393	2.08660
$275$	−7.77117	−0.468619
$276$	−34.8910	−2.10019
$277$	−4.67973	−0.281177	−0.140589	−	0.990068i	$-0.544900\pi$
$277$	−4.67973	−0.281177	−0.140589	+	0.990068i	$0.544900\pi$
$278$	−4.08984	−0.245292
$279$	−5.94341	−0.355823
$280$	−151.176	−9.03447
$281$	5.56893	0.332215	0.166107	−	0.986108i	$-0.446880\pi$
$281$	5.56893	0.332215	0.166107	+	0.986108i	$0.446880\pi$
$282$	59.5189	3.54430
$283$	10.6064	0.630487	0.315244	−	0.949011i	$-0.397914\pi$
$283$	10.6064	0.630487	0.315244	+	0.949011i	$0.397914\pi$
$284$	79.1670	4.69770
$285$	−26.2439	−1.55455
$286$	−1.04295	−0.0616709
$287$	−24.5508	−1.44919
$288$	−14.6611	−0.863915
$289$	29.6467	1.74393
$290$	−19.8405	−1.16507
$291$	−11.0420	−0.647292
$292$	−54.8240	−3.20833
$293$	−11.6252	−0.679153	−0.339576	−	0.940578i	$-0.610284\pi$
$293$	−11.6252	−0.679153	−0.339576	+	0.940578i	$0.610284\pi$
$294$	70.7708	4.12744
$295$	23.1868	1.34999
$296$	−97.1820	−5.64859
$297$	−3.01915	−0.175189
$298$	22.3017	1.29191
$299$	−1.82170	−0.105352
$300$	−108.621	−6.27125
$301$	6.20991	0.357933
$302$	−44.1493	−2.54051
$303$	−25.5396	−1.46721
$304$	−41.4320	−2.37629
$305$	−8.27411	−0.473774
$306$	−16.6464	−0.951610
$307$	15.8357	0.903791	0.451895	−	0.892071i	$-0.350748\pi$
$307$	15.8357	0.903791	0.451895	+	0.892071i	$0.350748\pi$
$308$	17.0325	0.970516
$309$	2.63148	0.149700
$310$	−69.0841	−3.92371
$311$	23.2079	1.31600	0.657999	−	0.753019i	$-0.271403\pi$
$311$	23.2079	1.31600	0.657999	+	0.753019i	$0.271403\pi$
$312$	−8.93263	−0.505710
$313$	−30.1615	−1.70483	−0.852415	−	0.522865i	$-0.824863\pi$
$313$	−30.1615	−1.70483	−0.852415	+	0.522865i	$0.824863\pi$
$314$	45.1156	2.54602
$315$	16.2503	0.915598
$316$	−37.3198	−2.09940
$317$	−34.8483	−1.95728	−0.978638	−	0.205591i	$-0.934088\pi$
$317$	−34.8483	−1.95728	−0.978638	+	0.205591i	$0.934088\pi$
$318$	−15.4185	−0.864625
$319$	1.36973	0.0766903
$320$	−72.7900	−4.06908
$321$	5.97427	0.333451
$322$	41.2710	2.29994
$323$	−22.9227	−1.27545
$324$	−56.3085	−3.12825
$325$	−5.67125	−0.314584
$326$	−0.501026	−0.0277492
$327$	32.6645	1.80635
$328$	−46.0787	−2.54427
$329$	−50.7497	−2.79792
$330$	15.2935	0.841882
$331$	−13.9975	−0.769372	−0.384686	−	0.923047i	$-0.625690\pi$
$331$	−13.9975	−0.769372	−0.384686	+	0.923047i	$0.625690\pi$
$332$	56.9510	3.12559
$333$	10.4464	0.572457
$334$	−28.4049	−1.55425
$335$	−60.9588	−3.33054
$336$	110.179	6.01074
$337$	4.12595	0.224755	0.112377	−	0.993666i	$-0.464153\pi$
$337$	4.12595	0.224755	0.112377	+	0.993666i	$0.464153\pi$
$338$	34.0359	1.85131
$339$	−12.5486	−0.681546
$340$	−139.479	−7.56431
$341$	4.76938	0.258276
$342$	8.18021	0.442335
$343$	−28.7505	−1.55238
$344$	11.6552	0.628407
$345$	26.7130	1.43818
$346$	−34.0959	−1.83301
$347$	−23.6124	−1.26758	−0.633791	−	0.773504i	$-0.718502\pi$
$347$	−23.6124	−1.26758	−0.633791	+	0.773504i	$0.718502\pi$
$348$	19.1454	1.02630
$349$	27.5222	1.47323	0.736614	−	0.676314i	$-0.236424\pi$
$349$	27.5222	1.47323	0.736614	+	0.676314i	$0.236424\pi$
$350$	128.483	6.86772
$351$	−2.20332	−0.117604
$352$	11.7650	0.627079
$353$	−6.70117	−0.356667	−0.178334	−	0.983970i	$-0.557071\pi$
$353$	−6.70117	−0.356667	−0.178334	+	0.983970i	$0.557071\pi$
$354$	−31.0388	−1.64970
$355$	−60.6112	−3.21691
$356$	−69.8424	−3.70164
$357$	60.9575	3.22621
$358$	2.09906	0.110939
$359$	16.2448	0.857369	0.428684	−	0.903454i	$-0.358977\pi$
$359$	16.2448	0.857369	0.428684	+	0.903454i	$0.358977\pi$
$360$	30.4996	1.60747
$361$	−7.73553	−0.407133
$362$	−42.6147	−2.23978
$363$	20.6968	1.08630
$364$	12.4300	0.651508
$365$	41.9739	2.19701
$366$	11.0761	0.578957
$367$	23.6572	1.23490	0.617449	−	0.786611i	$-0.288166\pi$
$367$	23.6572	1.23490	0.617449	+	0.786611i	$0.288166\pi$
$368$	42.1726	2.19840
$369$	4.95312	0.257849
$370$	121.425	6.31257
$371$	13.1468	0.682547
$372$	66.6638	3.45636
$373$	17.9130	0.927499	0.463749	−	0.885966i	$-0.346504\pi$
$373$	17.9130	0.927499	0.463749	+	0.885966i	$0.346504\pi$
$374$	13.3581	0.690732
$375$	44.0648	2.27549
$376$	−95.2506	−4.91218
$377$	0.999604	0.0514822
$378$	49.9166	2.56743
$379$	−8.60392	−0.441954	−0.220977	−	0.975279i	$-0.570924\pi$
$379$	−8.60392	−0.441954	−0.220977	+	0.975279i	$0.570924\pi$
$380$	68.5415	3.51611
$381$	−12.5939	−0.645207
$382$	3.10331	0.158779
$383$	−24.4446	−1.24906	−0.624530	−	0.781001i	$-0.714709\pi$
$383$	−24.4446	−1.24906	−0.624530	+	0.781001i	$0.714709\pi$
$384$	33.7593	1.72277
$385$	−13.0403	−0.664593
$386$	39.0672	1.98847
$387$	−1.25285	−0.0636859
$388$	28.8385	1.46405
$389$	−36.2507	−1.83798	−0.918991	−	0.394278i	$-0.870995\pi$
$389$	−36.2507	−1.83798	−0.918991	+	0.394278i	$0.870995\pi$
$390$	11.1609	0.565156
$391$	23.3324	1.17997
$392$	−113.257	−5.72037
$393$	−32.9626	−1.66274
$394$	−30.8506	−1.55423
$395$	28.5724	1.43764
$396$	−3.43630	−0.172681
$397$	−5.48245	−0.275156	−0.137578	−	0.990491i	$-0.543932\pi$
$397$	−5.48245	−0.275156	−0.137578	+	0.990491i	$0.543932\pi$
$398$	−70.7986	−3.54881
$399$	−29.9552	−1.49963
$400$	131.290	6.56450
$401$	−14.5160	−0.724894	−0.362447	−	0.932004i	$-0.618059\pi$
$401$	−14.5160	−0.724894	−0.362447	+	0.932004i	$0.618059\pi$
$402$	81.6022	4.06995
$403$	3.48060	0.173381
$404$	66.7020	3.31855
$405$	43.1104	2.14217
$406$	−22.6462	−1.12391
$407$	−8.38283	−0.415522
$408$	114.409	5.66411
$409$	4.98872	0.246676	0.123338	−	0.992365i	$-0.460640\pi$
$409$	4.98872	0.246676	0.123338	+	0.992365i	$0.460640\pi$
$410$	57.5733	2.84334
$411$	25.5173	1.25867
$412$	−6.87268	−0.338592
$413$	26.4657	1.30229
$414$	−8.32642	−0.409221
$415$	−43.6023	−2.14035
$416$	8.58590	0.420958
$417$	−3.02153	−0.147965
$418$	−6.56433	−0.321072
$419$	15.0518	0.735328	0.367664	−	0.929959i	$-0.380158\pi$
$419$	15.0518	0.735328	0.367664	+	0.929959i	$0.380158\pi$
$420$	−182.270	−8.89386
$421$	−20.3628	−0.992421	−0.496211	−	0.868202i	$-0.665276\pi$
$421$	−20.3628	−0.992421	−0.496211	+	0.868202i	$0.665276\pi$
$422$	17.0323	0.829118
$423$	10.2387	0.497825
$424$	24.6748	1.19832
$425$	72.6375	3.52344
$426$	81.1368	3.93109
$427$	−9.44419	−0.457037
$428$	−15.6031	−0.754203
$429$	−0.770520	−0.0372011
$430$	−14.5627	−0.702274
$431$	16.6148	0.800304	0.400152	−	0.916449i	$-0.368957\pi$
$431$	16.6148	0.800304	0.400152	+	0.916449i	$0.368957\pi$
$432$	51.0070	2.45408
$433$	−0.495924	−0.0238326	−0.0119163	−	0.999929i	$-0.503793\pi$
$433$	−0.495924	−0.0238326	−0.0119163	+	0.999929i	$0.503793\pi$
$434$	−78.8536	−3.78509
$435$	−14.6579	−0.702794
$436$	−85.3102	−4.08562
$437$	−11.4658	−0.548484
$438$	−56.1881	−2.68477
$439$	−12.6499	−0.603747	−0.301873	−	0.953348i	$-0.597612\pi$
$439$	−12.6499	−0.603747	−0.301873	+	0.953348i	$0.597612\pi$
$440$	−24.4749	−1.16679
$441$	12.1743	0.579731
$442$	9.74850	0.463689
$443$	−8.60211	−0.408698	−0.204349	−	0.978898i	$-0.565508\pi$
$443$	−8.60211	−0.408698	−0.204349	+	0.978898i	$0.565508\pi$
$444$	−117.171	−5.56068
$445$	53.4721	2.53482
$446$	−19.7465	−0.935024
$447$	16.4763	0.779302
$448$	−83.0835	−3.92533
$449$	−19.3363	−0.912535	−0.456267	−	0.889843i	$-0.650814\pi$
$449$	−19.3363	−0.912535	−0.456267	+	0.889843i	$0.650814\pi$
$450$	−25.9215	−1.22195
$451$	−3.97470	−0.187161
$452$	32.7733	1.54153
$453$	−32.6170	−1.53248
$454$	23.1031	1.08428
$455$	−9.51653	−0.446142
$456$	−56.2220	−2.63284
$457$	25.8586	1.20962	0.604808	−	0.796371i	$-0.293250\pi$
$457$	25.8586	1.20962	0.604808	+	0.796371i	$0.293250\pi$
$458$	56.3510	2.63311
$459$	28.2202	1.31720
$460$	−69.7666	−3.25288
$461$	−10.8844	−0.506939	−0.253469	−	0.967343i	$-0.581572\pi$
$461$	−10.8844	−0.506939	−0.253469	+	0.967343i	$0.581572\pi$
$462$	17.4563	0.812139
$463$	−22.2984	−1.03629	−0.518146	−	0.855292i	$-0.673378\pi$
$463$	−22.2984	−1.03629	−0.518146	+	0.855292i	$0.673378\pi$
$464$	−23.1409	−1.07429
$465$	−51.0386	−2.36686
$466$	−61.0483	−2.82801
$467$	4.21862	0.195214	0.0976071	−	0.995225i	$-0.468881\pi$
$467$	4.21862	0.195214	0.0976071	+	0.995225i	$0.468881\pi$
$468$	−2.50774	−0.115921
$469$	−69.5793	−3.21288
$470$	119.012	5.48959
$471$	33.3309	1.53581
$472$	49.6727	2.28637
$473$	1.00537	0.0462268
$474$	−38.2483	−1.75680
$475$	−35.6949	−1.63779
$476$	−159.203	−7.29708
$477$	−2.65236	−0.121443
$478$	−49.6649	−2.27162
$479$	40.9948	1.87310	0.936551	−	0.350531i	$-0.113999\pi$
$479$	40.9948	1.87310	0.936551	+	0.350531i	$0.113999\pi$
$480$	−125.901	−5.74658
$481$	−6.11763	−0.278940
$482$	8.11252	0.369515
$483$	30.4906	1.38737
$484$	−54.0542	−2.45701
$485$	−22.0791	−1.00256
$486$	−24.5300	−1.11271
$487$	−35.7804	−1.62137	−0.810683	−	0.585485i	$-0.800904\pi$
$487$	−35.7804	−1.62137	−0.810683	+	0.585485i	$0.800904\pi$
$488$	−17.7255	−0.802397
$489$	−0.370152	−0.0167389
$490$	141.510	6.39278
$491$	20.7272	0.935404	0.467702	−	0.883886i	$-0.345082\pi$
$491$	20.7272	0.935404	0.467702	+	0.883886i	$0.345082\pi$
$492$	−55.5563	−2.50467
$493$	−12.8030	−0.576616
$494$	−4.79052	−0.215536
$495$	2.63087	0.118249
$496$	−80.5761	−3.61798
$497$	−69.1825	−3.10326
$498$	58.3680	2.61553
$499$	−16.7697	−0.750717	−0.375358	−	0.926880i	$-0.622480\pi$
$499$	−16.7697	−0.750717	−0.375358	+	0.926880i	$0.622480\pi$
$500$	−115.084	−5.14673
$501$	−20.9852	−0.937550
$502$	−8.67030	−0.386974
$503$	30.9605	1.38046	0.690231	−	0.723590i	$-0.257509\pi$
$503$	30.9605	1.38046	0.690231	+	0.723590i	$0.257509\pi$
$504$	34.8127	1.55068
$505$	−51.0679	−2.27249
$506$	6.68166	0.297036
$507$	25.1454	1.11675
$508$	32.8918	1.45934
$509$	24.9953	1.10790	0.553948	−	0.832551i	$-0.313121\pi$
$509$	24.9953	1.10790	0.553948	+	0.832551i	$0.313121\pi$
$510$	−142.949	−6.32991
$511$	47.9096	2.11940
$512$	10.3782	0.458657
$513$	−13.8677	−0.612274
$514$	−22.0449	−0.972357
$515$	5.26180	0.231863
$516$	14.0525	0.618626
$517$	−8.21623	−0.361350
$518$	138.596	6.08956
$519$	−25.1897	−1.10570
$520$	−17.8613	−0.783270
$521$	21.4203	0.938441	0.469220	−	0.883081i	$-0.344535\pi$
$521$	21.4203	0.938441	0.469220	+	0.883081i	$0.344535\pi$
$522$	4.56887	0.199974
$523$	12.4243	0.543278	0.271639	−	0.962399i	$-0.412434\pi$
$523$	12.4243	0.543278	0.271639	+	0.962399i	$0.412434\pi$
$524$	86.0889	3.76081
$525$	94.9220	4.14274
$526$	−45.2484	−1.97292
$527$	−44.5796	−1.94192
$528$	17.8376	0.776282
$529$	−11.3293	−0.492577
$530$	−30.8301	−1.33917
$531$	−5.33945	−0.231713
$532$	78.2343	3.39189
$533$	−2.90066	−0.125642
$534$	−71.5802	−3.09758
$535$	11.9459	0.516466
$536$	−130.591	−5.64069
$537$	1.55076	0.0669204
$538$	−31.8765	−1.37429
$539$	−9.76949	−0.420802
$540$	−84.3815	−3.63120
$541$	21.5855	0.928031	0.464016	−	0.885827i	$-0.346408\pi$
$541$	21.5855	0.928031	0.464016	+	0.885827i	$0.346408\pi$
$542$	3.66067	0.157239
$543$	−31.4833	−1.35108
$544$	−109.968	−4.71486
$545$	65.3145	2.79776
$546$	12.7392	0.545190
$547$	22.6098	0.966724	0.483362	−	0.875420i	$-0.339415\pi$
$547$	22.6098	0.966724	0.483362	+	0.875420i	$0.339415\pi$
$548$	−66.6438	−2.84688
$549$	1.90536	0.0813190
$550$	20.8011	0.886960
$551$	6.29151	0.268027
$552$	57.2269	2.43574
$553$	32.6130	1.38685
$554$	12.5262	0.532187
$555$	89.7073	3.80786
$556$	7.89136	0.334668
$557$	−32.6067	−1.38159	−0.690796	−	0.723050i	$-0.742740\pi$
$557$	−32.6067	−1.38159	−0.690796	+	0.723050i	$0.742740\pi$
$558$	15.9087	0.673469
$559$	0.733697	0.0310321
$560$	220.308	9.30973
$561$	9.86885	0.416663
$562$	−14.9063	−0.628786
$563$	25.5982	1.07883	0.539417	−	0.842039i	$-0.318645\pi$
$563$	25.5982	1.07883	0.539417	+	0.842039i	$0.318645\pi$
$564$	−114.842	−4.83573
$565$	−25.0916	−1.05561
$566$	−28.3902	−1.19333
$567$	49.2068	2.06649
$568$	−129.847	−5.44824
$569$	−47.6625	−1.99812	−0.999059	−	0.0433803i	$-0.986187\pi$
$569$	−47.6625	−1.99812	−0.999059	+	0.0433803i	$0.986187\pi$
$570$	70.2469	2.94232
$571$	−11.4494	−0.479142	−0.239571	−	0.970879i	$-0.577007\pi$
$571$	−11.4494	−0.479142	−0.239571	+	0.970879i	$0.577007\pi$
$572$	2.01238	0.0841417
$573$	2.29269	0.0957787
$574$	65.7150	2.74289
$575$	36.3329	1.51519
$576$	16.7621	0.698420
$577$	22.8560	0.951510	0.475755	−	0.879578i	$-0.342175\pi$
$577$	22.8560	0.951510	0.475755	+	0.879578i	$0.342175\pi$
$578$	−79.3553	−3.30074
$579$	28.8625	1.19948
$580$	38.2823	1.58959
$581$	−49.7684	−2.06474
$582$	29.5560	1.22514
$583$	2.12843	0.0881505
$584$	89.9201	3.72092
$585$	1.91996	0.0793805
$586$	31.1172	1.28544
$587$	−35.3471	−1.45893	−0.729465	−	0.684019i	$-0.760231\pi$
$587$	−35.3471	−1.45893	−0.729465	+	0.684019i	$0.760231\pi$
$588$	−136.553	−5.63134
$589$	21.9069	0.902658
$590$	−62.0639	−2.55513
$591$	−22.7921	−0.937541
$592$	141.624	5.82069
$593$	35.5899	1.46150	0.730751	−	0.682644i	$-0.239170\pi$
$593$	35.5899	1.46150	0.730751	+	0.682644i	$0.239170\pi$
$594$	8.08135	0.331582
$595$	121.888	4.99692
$596$	−43.0313	−1.76263
$597$	−52.3053	−2.14071
$598$	4.87614	0.199400
$599$	43.9678	1.79648	0.898238	−	0.439510i	$-0.144848\pi$
$599$	43.9678	1.79648	0.898238	+	0.439510i	$0.144848\pi$
$600$	178.156	7.27320
$601$	−1.98671	−0.0810396	−0.0405198	−	0.999179i	$-0.512901\pi$
$601$	−1.98671	−0.0810396	−0.0405198	+	0.999179i	$0.512901\pi$
$602$	−16.6220	−0.677464
$603$	14.0376	0.571656
$604$	85.1863	3.46618
$605$	41.3845	1.68252
$606$	68.3617	2.77700
$607$	−14.0200	−0.569054	−0.284527	−	0.958668i	$-0.591837\pi$
$607$	−14.0200	−0.569054	−0.284527	+	0.958668i	$0.591837\pi$
$608$	54.0397	2.19160
$609$	−16.7308	−0.677966
$610$	22.1473	0.896717
$611$	−5.99605	−0.242574
$612$	32.1193	1.29834
$613$	29.7541	1.20176	0.600878	−	0.799341i	$-0.294818\pi$
$613$	29.7541	1.20176	0.600878	+	0.799341i	$0.294818\pi$
$614$	−42.3873	−1.71061
$615$	42.5345	1.71516
$616$	−27.9360	−1.12557
$617$	29.9540	1.20590	0.602951	−	0.797778i	$-0.293991\pi$
$617$	29.9540	1.20590	0.602951	+	0.797778i	$0.293991\pi$
$618$	−7.04368	−0.283338
$619$	−25.8396	−1.03858	−0.519290	−	0.854598i	$-0.673804\pi$
$619$	−25.8396	−1.03858	−0.519290	+	0.854598i	$0.673804\pi$
$620$	133.298	5.35338
$621$	14.1156	0.566438
$622$	−62.1204	−2.49080
$623$	61.0339	2.44527
$624$	13.0175	0.521119
$625$	34.9334	1.39734
$626$	80.7332	3.22675
$627$	−4.84966	−0.193677
$628$	−87.0508	−3.47370
$629$	78.3547	3.12421
$630$	−43.4970	−1.73296
$631$	26.7276	1.06401	0.532004	−	0.846742i	$-0.321439\pi$
$631$	26.7276	1.06401	0.532004	+	0.846742i	$0.321439\pi$
$632$	61.2104	2.43482
$633$	12.5833	0.500140
$634$	93.2783	3.70455
$635$	−25.1823	−0.999329
$636$	29.7500	1.17967
$637$	−7.12958	−0.282484
$638$	−3.66636	−0.145152
$639$	13.9576	0.552152
$640$	67.5037	2.66832
$641$	38.1989	1.50877	0.754384	−	0.656433i	$-0.227936\pi$
$641$	38.1989	1.50877	0.754384	+	0.656433i	$0.227936\pi$
$642$	−15.9913	−0.631126
$643$	−33.2621	−1.31173	−0.655864	−	0.754879i	$-0.727696\pi$
$643$	−33.2621	−1.31173	−0.655864	+	0.754879i	$0.727696\pi$
$644$	−79.6326	−3.13796
$645$	−10.7587	−0.423625
$646$	61.3571	2.41406
$647$	−28.9161	−1.13681	−0.568405	−	0.822749i	$-0.692439\pi$
$647$	−28.9161	−1.13681	−0.568405	+	0.822749i	$0.692439\pi$
$648$	92.3549	3.62804
$649$	4.28472	0.168190
$650$	15.1802	0.595417
$651$	−58.2562	−2.28324
$652$	0.966732	0.0378601
$653$	−15.5883	−0.610018	−0.305009	−	0.952349i	$-0.598660\pi$
$653$	−15.5883	−0.610018	−0.305009	+	0.952349i	$0.598660\pi$
$654$	−87.4328	−3.41889
$655$	−65.9106	−2.57534
$656$	67.1505	2.62179
$657$	−9.66575	−0.377097
$658$	135.841	5.29565
$659$	−16.3509	−0.636942	−0.318471	−	0.947933i	$-0.603169\pi$
$659$	−16.3509	−0.636942	−0.318471	+	0.947933i	$0.603169\pi$
$660$	−29.5090	−1.14864
$661$	38.7899	1.50875	0.754376	−	0.656443i	$-0.227940\pi$
$661$	38.7899	1.50875	0.754376	+	0.656443i	$0.227940\pi$
$662$	37.4671	1.45620
$663$	7.20209	0.279706
$664$	−93.4088	−3.62496
$665$	−59.8971	−2.32271
$666$	−27.9617	−1.08349
$667$	−6.40396	−0.247962
$668$	54.8073	2.12056
$669$	−14.5885	−0.564024
$670$	163.168	6.30374
$671$	−1.52899	−0.0590259
$672$	−143.706	−5.54357
$673$	−43.8639	−1.69083	−0.845414	−	0.534111i	$-0.820646\pi$
$673$	−43.8639	−1.69083	−0.845414	+	0.534111i	$0.820646\pi$
$674$	−11.0439	−0.425396
$675$	43.9440	1.69140
$676$	−65.6725	−2.52586
$677$	−23.5691	−0.905836	−0.452918	−	0.891552i	$-0.649617\pi$
$677$	−23.5691	−0.905836	−0.452918	+	0.891552i	$0.649617\pi$
$678$	33.5887	1.28997
$679$	−25.2014	−0.967139
$680$	228.768	8.77285
$681$	17.0683	0.654059
$682$	−12.7662	−0.488842
$683$	−44.9350	−1.71939	−0.859695	−	0.510807i	$-0.829347\pi$
$683$	−44.9350	−1.71939	−0.859695	+	0.510807i	$0.829347\pi$
$684$	−15.7838	−0.603507
$685$	51.0232	1.94950
$686$	76.9563	2.93820
$687$	41.6315	1.58834
$688$	−16.9852	−0.647553
$689$	1.55328	0.0591754
$690$	−71.5025	−2.72205
$691$	13.3031	0.506075	0.253038	−	0.967456i	$-0.418570\pi$
$691$	13.3031	0.506075	0.253038	+	0.967456i	$0.418570\pi$
$692$	65.7882	2.50089
$693$	3.00291	0.114071
$694$	63.2033	2.39917
$695$	−6.04171	−0.229175
$696$	−31.4015	−1.19027
$697$	37.1517	1.40722
$698$	−73.6685	−2.78839
$699$	−45.1018	−1.70591
$700$	−247.909	−9.37008
$701$	0.00222685	8.41071e−5 0	4.20535e−5	−	1.00000i	$-0.499987\pi$
$701$	0.00222685	8.41071e−5 0	4.20535e−5		1.00000i	$0.499987\pi$
$702$	5.89761	0.222591
$703$	−38.5044	−1.45222
$704$	−13.4510	−0.506953
$705$	87.9244	3.31143
$706$	17.9370	0.675068
$707$	−58.2896	−2.19221
$708$	59.8896	2.25079
$709$	12.7186	0.477655	0.238828	−	0.971062i	$-0.423237\pi$
$709$	12.7186	0.477655	0.238828	+	0.971062i	$0.423237\pi$
$710$	162.238	6.08867
$711$	−6.57967	−0.246757
$712$	114.553	4.29305
$713$	−22.2985	−0.835084
$714$	−163.165	−6.10628
$715$	−1.54070	−0.0576189
$716$	−4.05015	−0.151361
$717$	−36.6919	−1.37028
$718$	−43.4824	−1.62275
$719$	21.3774	0.797244	0.398622	−	0.917115i	$-0.369489\pi$
$719$	21.3774	0.797244	0.398622	+	0.917115i	$0.369489\pi$
$720$	−44.4472	−1.65645
$721$	6.00590	0.223671
$722$	20.7057	0.770585
$723$	5.99344	0.222899
$724$	82.2253	3.05588
$725$	−19.9366	−0.740425
$726$	−55.3991	−2.05605
$727$	14.7576	0.547329	0.273665	−	0.961825i	$-0.411764\pi$
$727$	14.7576	0.547329	0.273665	+	0.961825i	$0.411764\pi$
$728$	−20.3871	−0.755598
$729$	14.5852	0.540191
$730$	−112.351	−4.15831
$731$	−9.39722	−0.347569
$732$	−21.3714	−0.789909
$733$	29.8104	1.10107	0.550535	−	0.834812i	$-0.314424\pi$
$733$	29.8104	1.10107	0.550535	+	0.834812i	$0.314424\pi$
$734$	−63.3232	−2.33730
$735$	104.546	3.85625
$736$	−55.0055	−2.02753
$737$	−11.2647	−0.414940
$738$	−13.2580	−0.488033
$739$	−18.7976	−0.691480	−0.345740	−	0.938330i	$-0.612372\pi$
$739$	−18.7976	−0.691480	−0.345740	+	0.938330i	$0.612372\pi$
$740$	−234.290	−8.61266
$741$	−3.53919	−0.130015
$742$	−35.1899	−1.29186
$743$	31.7905	1.16628	0.583140	−	0.812372i	$-0.301824\pi$
$743$	31.7905	1.16628	0.583140	+	0.812372i	$0.301824\pi$
$744$	−109.339	−4.00857
$745$	32.9453	1.20702
$746$	−47.9476	−1.75549
$747$	10.0408	0.367372
$748$	−25.7746	−0.942412
$749$	13.6352	0.498220
$750$	−117.948	−4.30685
$751$	18.5044	0.675236	0.337618	−	0.941283i	$-0.390379\pi$
$751$	18.5044	0.675236	0.337618	+	0.941283i	$0.390379\pi$
$752$	138.809	5.06184
$753$	−6.40553	−0.233430
$754$	−2.67564	−0.0974409
$755$	−65.2196	−2.37358
$756$	−96.3143	−3.50292
$757$	35.7023	1.29762	0.648811	−	0.760950i	$-0.275267\pi$
$757$	35.7023	1.29762	0.648811	+	0.760950i	$0.275267\pi$
$758$	23.0301	0.836490
$759$	4.93634	0.179178
$760$	−112.419	−4.07787
$761$	−25.8762	−0.938013	−0.469007	−	0.883195i	$-0.655388\pi$
$761$	−25.8762	−0.938013	−0.469007	+	0.883195i	$0.655388\pi$
$762$	33.7101	1.22119
$763$	74.5509	2.69892
$764$	−5.98786	−0.216633
$765$	−24.5909	−0.889085
$766$	65.4307	2.36411
$767$	3.12691	0.112906
$768$	−17.5573	−0.633544
$769$	−7.35690	−0.265296	−0.132648	−	0.991163i	$-0.542348\pi$
$769$	−7.35690	−0.265296	−0.132648	+	0.991163i	$0.542348\pi$
$770$	34.9048	1.25788
$771$	−16.2865	−0.586544
$772$	−75.3804	−2.71300
$773$	21.2949	0.765926	0.382963	−	0.923764i	$-0.374904\pi$
$773$	21.2949	0.765926	0.382963	+	0.923764i	$0.374904\pi$
$774$	3.35349	0.120539
$775$	−69.4186	−2.49359
$776$	−47.2997	−1.69796
$777$	102.393	3.67334
$778$	97.0320	3.47877
$779$	−18.2568	−0.654117
$780$	−21.5351	−0.771079
$781$	−11.2004	−0.400784
$782$	−62.4538	−2.23334
$783$	−7.74549	−0.276801
$784$	165.050	5.89466
$785$	66.6471	2.37874
$786$	88.2309	3.14709
$787$	30.6652	1.09310	0.546549	−	0.837427i	$-0.315941\pi$
$787$	30.6652	1.09310	0.546549	+	0.837427i	$0.315941\pi$
$788$	59.5264	2.12054
$789$	−33.4290	−1.19010
$790$	−76.4797	−2.72103
$791$	−28.6399	−1.01832
$792$	5.63608	0.200269
$793$	−1.11583	−0.0396241
$794$	14.6748	0.520791
$795$	−22.7770	−0.807816
$796$	136.606	4.84188
$797$	3.76434	0.133340	0.0666698	−	0.997775i	$-0.478763\pi$
$797$	3.76434	0.133340	0.0666698	+	0.997775i	$0.478763\pi$
$798$	80.1809	2.83837
$799$	76.7975	2.71690
$800$	−171.241	−6.05428
$801$	−12.3136	−0.435079
$802$	38.8549	1.37201
$803$	7.75643	0.273718
$804$	−157.452	−5.55290
$805$	60.9676	2.14883
$806$	−9.31650	−0.328160
$807$	−23.5500	−0.828999
$808$	−109.402	−3.84875
$809$	−24.3278	−0.855320	−0.427660	−	0.903940i	$-0.640662\pi$
$809$	−24.3278	−0.855320	−0.427660	+	0.903940i	$0.640662\pi$
$810$	−115.393	−4.05451
$811$	−15.4792	−0.543550	−0.271775	−	0.962361i	$-0.587611\pi$
$811$	−15.4792	−0.543550	−0.271775	+	0.962361i	$0.587611\pi$
$812$	43.6960	1.53343
$813$	2.70447	0.0948498
$814$	22.4383	0.786462
$815$	−0.740141	−0.0259260
$816$	−166.729	−5.83668
$817$	4.61789	0.161560
$818$	−13.3533	−0.466887
$819$	2.19147	0.0765761
$820$	−111.088	−3.87936
$821$	−10.8681	−0.379299	−0.189649	−	0.981852i	$-0.560735\pi$
$821$	−10.8681	−0.379299	−0.189649	+	0.981852i	$0.560735\pi$
$822$	−68.3020	−2.38230
$823$	−51.5850	−1.79814	−0.899071	−	0.437803i	$-0.855757\pi$
$823$	−51.5850	−1.79814	−0.899071	+	0.437803i	$0.855757\pi$
$824$	11.2723	0.392689
$825$	15.3676	0.535031
$826$	−70.8407	−2.46486
$827$	19.6937	0.684818	0.342409	−	0.939551i	$-0.388757\pi$
$827$	19.6937	0.684818	0.342409	+	0.939551i	$0.388757\pi$
$828$	16.0659	0.558327
$829$	−29.7168	−1.03211	−0.516053	−	0.856557i	$-0.672599\pi$
$829$	−29.7168	−1.03211	−0.516053	+	0.856557i	$0.672599\pi$
$830$	116.710	4.05107
$831$	9.25422	0.321025
$832$	−9.81627	−0.340318
$833$	91.3159	3.16391
$834$	8.08771	0.280054
$835$	−41.9611	−1.45212
$836$	12.6659	0.438060
$837$	−26.9696	−0.932206
$838$	−40.2890	−1.39176
$839$	−39.4607	−1.36233	−0.681167	−	0.732128i	$-0.738527\pi$
$839$	−39.4607	−1.36233	−0.681167	+	0.732128i	$0.738527\pi$
$840$	298.952	10.3148
$841$	−25.4860	−0.878828
$842$	54.5050	1.87836
$843$	−11.0126	−0.379296
$844$	−32.8639	−1.13122
$845$	50.2796	1.72967
$846$	−27.4060	−0.942238
$847$	47.2369	1.62308
$848$	−35.9587	−1.23483
$849$	−20.9744	−0.719839
$850$	−194.429	−6.66884
$851$	39.1926	1.34350
$852$	−156.554	−5.36345
$853$	−5.72740	−0.196102	−0.0980512	−	0.995181i	$-0.531261\pi$
$853$	−5.72740	−0.196102	−0.0980512	+	0.995181i	$0.531261\pi$
$854$	25.2792	0.865037
$855$	12.0842	0.413272
$856$	25.5915	0.874701
$857$	44.6922	1.52666	0.763328	−	0.646011i	$-0.223564\pi$
$857$	44.6922	1.52666	0.763328	+	0.646011i	$0.223564\pi$
$858$	2.06245	0.0704108
$859$	5.74160	0.195901	0.0979504	−	0.995191i	$-0.468771\pi$
$859$	5.74160	0.195901	0.0979504	+	0.995191i	$0.468771\pi$
$860$	28.0988	0.958159
$861$	48.5495	1.65456
$862$	−44.4726	−1.51474
$863$	−29.7740	−1.01352	−0.506759	−	0.862088i	$-0.669157\pi$
$863$	−29.7740	−1.01352	−0.506759	+	0.862088i	$0.669157\pi$
$864$	−66.5283	−2.26334
$865$	−50.3682	−1.71257
$866$	1.32744	0.0451082
$867$	−58.6268	−1.99107
$868$	152.148	5.16425
$869$	5.27995	0.179110
$870$	39.2348	1.33019
$871$	−8.22076	−0.278550
$872$	139.922	4.73837
$873$	5.08437	0.172080
$874$	30.6905	1.03812
$875$	100.570	3.39989
$876$	108.415	3.66301
$877$	34.5222	1.16573	0.582866	−	0.812568i	$-0.301931\pi$
$877$	34.5222	1.16573	0.582866	+	0.812568i	$0.301931\pi$
$878$	33.8599	1.14272
$879$	22.9890	0.775401
$880$	35.6673	1.20234
$881$	34.0521	1.14725	0.573623	−	0.819120i	$-0.305538\pi$
$881$	34.0521	1.14725	0.573623	+	0.819120i	$0.305538\pi$
$882$	−32.5870	−1.09726
$883$	16.2441	0.546656	0.273328	−	0.961921i	$-0.411876\pi$
$883$	16.2441	0.546656	0.273328	+	0.961921i	$0.411876\pi$
$884$	−18.8098	−0.632642
$885$	−45.8522	−1.54130
$886$	23.0252	0.773547
$887$	−14.8249	−0.497773	−0.248886	−	0.968533i	$-0.580065\pi$
$887$	−14.8249	−0.497773	−0.248886	+	0.968533i	$0.580065\pi$
$888$	192.179	6.44910
$889$	−28.7435	−0.964025
$890$	−143.129	−4.79768
$891$	7.96645	0.266886
$892$	38.1010	1.27571
$893$	−37.7391	−1.26289
$894$	−44.1020	−1.47499
$895$	3.10084	0.103650
$896$	77.0497	2.57405
$897$	3.60244	0.120282
$898$	51.7573	1.72716
$899$	12.2356	0.408080
$900$	50.0156	1.66719
$901$	−19.8945	−0.662782
$902$	10.6391	0.354242
$903$	−12.2802	−0.408659
$904$	−53.7534	−1.78781
$905$	−62.9527	−2.09262
$906$	87.3059	2.90054
$907$	−3.70404	−0.122991	−0.0614953	−	0.998107i	$-0.519587\pi$
$907$	−3.70404	−0.122991	−0.0614953	+	0.998107i	$0.519587\pi$
$908$	−44.5775	−1.47936
$909$	11.7599	0.390052
$910$	25.4729	0.844417
$911$	44.2182	1.46501	0.732507	−	0.680759i	$-0.238350\pi$
$911$	44.2182	1.46501	0.732507	+	0.680759i	$0.238350\pi$
$912$	81.9324	2.71305
$913$	−8.05736	−0.266660
$914$	−69.2157	−2.28945
$915$	16.3622	0.540917
$916$	−108.729	−3.59252
$917$	−75.2314	−2.48436
$918$	−75.5368	−2.49309
$919$	−0.690343	−0.0227723	−0.0113862	−	0.999935i	$-0.503624\pi$
$919$	−0.690343	−0.0227723	−0.0113862	+	0.999935i	$0.503624\pi$
$920$	114.428	3.77259
$921$	−31.3153	−1.03187
$922$	29.1343	0.959488
$923$	−8.17387	−0.269046
$924$	−33.6820	−1.10806
$925$	122.013	4.01175
$926$	59.6859	1.96140
$927$	−1.21169	−0.0397971
$928$	30.1826	0.990793
$929$	4.45993	0.146326	0.0731628	−	0.997320i	$-0.476691\pi$
$929$	4.45993	0.146326	0.0731628	+	0.997320i	$0.476691\pi$
$930$	136.615	4.47977
$931$	−44.8736	−1.47067
$932$	117.793	3.85844
$933$	−45.8939	−1.50250
$934$	−11.2919	−0.369484
$935$	19.7333	0.645348
$936$	4.11310	0.134441
$937$	11.6960	0.382093	0.191046	−	0.981581i	$-0.438812\pi$
$937$	11.6960	0.382093	0.191046	+	0.981581i	$0.438812\pi$
$938$	186.243	6.08104
$939$	59.6449	1.94644
$940$	−229.633	−7.48981
$941$	−19.7883	−0.645080	−0.322540	−	0.946556i	$-0.604537\pi$
$941$	−19.7883	−0.645080	−0.322540	+	0.946556i	$0.604537\pi$
$942$	−89.2167	−2.90684
$943$	18.5831	0.605148
$944$	−72.3882	−2.35603
$945$	73.7393	2.39874
$946$	−2.69106	−0.0874940
$947$	6.71253	0.218128	0.109064	−	0.994035i	$-0.465215\pi$
$947$	6.71253	0.218128	0.109064	+	0.994035i	$0.465215\pi$
$948$	73.8004	2.39692
$949$	5.66049	0.183747
$950$	95.5443	3.09987
$951$	68.9130	2.23466
$952$	261.119	8.46292
$953$	3.55514	0.115162	0.0575811	−	0.998341i	$-0.481661\pi$
$953$	3.55514	0.115162	0.0575811	+	0.998341i	$0.481661\pi$
$954$	7.09957	0.229857
$955$	4.58437	0.148347
$956$	95.8286	3.09932
$957$	−2.70867	−0.0875587
$958$	−109.731	−3.54524
$959$	58.2387	1.88062
$960$	143.943	4.64575
$961$	11.6041	0.374325
$962$	16.3750	0.527952
$963$	−2.75090	−0.0886466
$964$	−15.6531	−0.504154
$965$	57.7121	1.85782
$966$	−81.6140	−2.62589
$967$	30.3926	0.977360	0.488680	−	0.872463i	$-0.337479\pi$
$967$	30.3926	0.977360	0.488680	+	0.872463i	$0.337479\pi$
$968$	88.6575	2.84956
$969$	45.3300	1.45621
$970$	59.0989	1.89755
$971$	−20.2126	−0.648652	−0.324326	−	0.945945i	$-0.605137\pi$
$971$	−20.2126	−0.648652	−0.324326	+	0.945945i	$0.605137\pi$
$972$	47.3309	1.51814
$973$	−6.89610	−0.221079
$974$	95.7734	3.06878
$975$	11.2150	0.359167
$976$	25.8315	0.826845
$977$	−13.0731	−0.418244	−0.209122	−	0.977890i	$-0.567061\pi$
$977$	−13.0731	−0.418244	−0.209122	+	0.977890i	$0.567061\pi$
$978$	0.990785	0.0316818
$979$	9.88122	0.315805
$980$	−273.045	−8.72210
$981$	−15.0406	−0.480210
$982$	−55.4803	−1.77045
$983$	32.3004	1.03022	0.515111	−	0.857123i	$-0.327751\pi$
$983$	32.3004	1.03022	0.515111	+	0.857123i	$0.327751\pi$
$984$	91.1212	2.90484
$985$	−45.5741	−1.45211
$986$	34.2696	1.09137
$987$	100.358	3.19444
$988$	9.24333	0.294070
$989$	−4.70043	−0.149465
$990$	−7.04204	−0.223811
$991$	−1.78951	−0.0568457	−0.0284229	−	0.999596i	$-0.509048\pi$
$991$	−1.78951	−0.0568457	−0.0284229	+	0.999596i	$0.509048\pi$
$992$	105.095	3.33678
$993$	27.6803	0.878407
$994$	185.180	5.87357
$995$	−104.587	−3.31564
$996$	−112.621	−3.56855
$997$	−29.4538	−0.932812	−0.466406	−	0.884571i	$-0.654451\pi$
$997$	−29.4538	−0.932812	−0.466406	+	0.884571i	$0.654451\pi$
$998$	44.8875	1.42089
$999$	47.4028	1.49976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.8	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.8	✓	340	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)

\(f(q)\)	\(=\)	\(q-2.67670 q^{2} -1.97751 q^{3} +5.16470 q^{4} -3.95415 q^{5} +5.29320 q^{6} -4.51333 q^{7} -8.47093 q^{8} +0.910563 q^{9} +O(q^{10})\)	\(q-2.67670 q^{2} -1.97751 q^{3} +5.16470 q^{4} -3.95415 q^{5} +5.29320 q^{6} -4.51333 q^{7} -8.47093 q^{8} +0.910563 q^{9} +10.5841 q^{10} -0.730695 q^{11} -10.2133 q^{12} -0.533247 q^{13} +12.0808 q^{14} +7.81939 q^{15} +12.3447 q^{16} +6.82984 q^{17} -2.43730 q^{18} -3.35626 q^{19} -20.4220 q^{20} +8.92517 q^{21} +1.95585 q^{22} +3.41625 q^{23} +16.7514 q^{24} +10.6353 q^{25} +1.42734 q^{26} +4.13189 q^{27} -23.3100 q^{28} -1.87456 q^{29} -20.9301 q^{30} -6.52718 q^{31} -16.1012 q^{32} +1.44496 q^{33} -18.2814 q^{34} +17.8464 q^{35} +4.70278 q^{36} +11.4724 q^{37} +8.98368 q^{38} +1.05450 q^{39} +33.4954 q^{40} +5.43962 q^{41} -23.8900 q^{42} -1.37591 q^{43} -3.77382 q^{44} -3.60050 q^{45} -9.14425 q^{46} +11.2444 q^{47} -24.4118 q^{48} +13.3701 q^{49} -28.4675 q^{50} -13.5061 q^{51} -2.75406 q^{52} -2.91288 q^{53} -11.0598 q^{54} +2.88928 q^{55} +38.2321 q^{56} +6.63705 q^{57} +5.01763 q^{58} -5.86390 q^{59} +40.3848 q^{60} +2.09251 q^{61} +17.4713 q^{62} -4.10967 q^{63} +18.4085 q^{64} +2.10854 q^{65} -3.86772 q^{66} +15.4164 q^{67} +35.2741 q^{68} -6.75568 q^{69} -47.7693 q^{70} +15.3285 q^{71} -7.71332 q^{72} -10.6151 q^{73} -30.7082 q^{74} -21.0315 q^{75} -17.3341 q^{76} +3.29787 q^{77} -2.82258 q^{78} -7.22593 q^{79} -48.8129 q^{80} -10.9026 q^{81} -14.5602 q^{82} +11.0270 q^{83} +46.0958 q^{84} -27.0062 q^{85} +3.68288 q^{86} +3.70697 q^{87} +6.18967 q^{88} -13.5230 q^{89} +9.63745 q^{90} +2.40672 q^{91} +17.6439 q^{92} +12.9076 q^{93} -30.0979 q^{94} +13.2712 q^{95} +31.8403 q^{96} +5.58376 q^{97} -35.7878 q^{98} -0.665344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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