LMFDB - Embedded newform 8017.2.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.67123 q^{2} -2.04696 q^{3} +5.13545 q^{4} +2.79534 q^{5} +5.46788 q^{6} -0.784684 q^{7} -8.37550 q^{8} +1.19003 q^{9} +O(q^{10})$	\(q-2.67123 q^{2} -2.04696 q^{3} +5.13545 q^{4} +2.79534 q^{5} +5.46788 q^{6} -0.784684 q^{7} -8.37550 q^{8} +1.19003 q^{9} -7.46698 q^{10} -1.87905 q^{11} -10.5120 q^{12} -1.74963 q^{13} +2.09607 q^{14} -5.72193 q^{15} +12.1020 q^{16} +0.780197 q^{17} -3.17884 q^{18} -0.705383 q^{19} +14.3553 q^{20} +1.60621 q^{21} +5.01938 q^{22} +2.69763 q^{23} +17.1443 q^{24} +2.81390 q^{25} +4.67365 q^{26} +3.70493 q^{27} -4.02971 q^{28} -3.16886 q^{29} +15.2846 q^{30} +3.31043 q^{31} -15.5761 q^{32} +3.84634 q^{33} -2.08408 q^{34} -2.19346 q^{35} +6.11134 q^{36} +10.7236 q^{37} +1.88424 q^{38} +3.58141 q^{39} -23.4123 q^{40} +8.65888 q^{41} -4.29056 q^{42} +10.6576 q^{43} -9.64979 q^{44} +3.32653 q^{45} -7.20599 q^{46} +6.13331 q^{47} -24.7722 q^{48} -6.38427 q^{49} -7.51657 q^{50} -1.59703 q^{51} -8.98513 q^{52} -6.68744 q^{53} -9.89671 q^{54} -5.25259 q^{55} +6.57212 q^{56} +1.44389 q^{57} +8.46474 q^{58} +9.41965 q^{59} -29.3847 q^{60} -7.89505 q^{61} -8.84292 q^{62} -0.933798 q^{63} +17.4033 q^{64} -4.89080 q^{65} -10.2744 q^{66} -6.38542 q^{67} +4.00667 q^{68} -5.52194 q^{69} +5.85922 q^{70} -12.1163 q^{71} -9.96710 q^{72} -4.19780 q^{73} -28.6451 q^{74} -5.75993 q^{75} -3.62246 q^{76} +1.47446 q^{77} -9.56677 q^{78} -17.3454 q^{79} +33.8291 q^{80} -11.1539 q^{81} -23.1298 q^{82} +15.6585 q^{83} +8.24863 q^{84} +2.18091 q^{85} -28.4688 q^{86} +6.48652 q^{87} +15.7380 q^{88} -5.80268 q^{89} -8.88593 q^{90} +1.37291 q^{91} +13.8536 q^{92} -6.77632 q^{93} -16.3835 q^{94} -1.97178 q^{95} +31.8836 q^{96} +9.52505 q^{97} +17.0538 q^{98} -2.23613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67123	−1.88884	−0.944421	−	0.328738i	$-0.893377\pi$
$2$	−2.67123	−1.88884	−0.944421	+	0.328738i	$0.893377\pi$
$3$	−2.04696	−1.18181	−0.590905	−	0.806741i	$-0.701229\pi$
$3$	−2.04696	−1.18181	−0.590905	+	0.806741i	$0.701229\pi$
$4$	5.13545	2.56773
$5$	2.79534	1.25011	0.625056	−	0.780580i	$-0.285076\pi$
$5$	2.79534	1.25011	0.625056	+	0.780580i	$0.285076\pi$
$6$	5.46788	2.23225
$7$	−0.784684	−0.296583	−0.148291	−	0.988944i	$-0.547377\pi$
$7$	−0.784684	−0.296583	−0.148291	+	0.988944i	$0.547377\pi$
$8$	−8.37550	−2.96119
$9$	1.19003	0.396677
$10$	−7.46698	−2.36126
$11$	−1.87905	−0.566556	−0.283278	−	0.959038i	$-0.591422\pi$
$11$	−1.87905	−0.566556	−0.283278	+	0.959038i	$0.591422\pi$
$12$	−10.5120	−3.03457
$13$	−1.74963	−0.485260	−0.242630	−	0.970119i	$-0.578010\pi$
$13$	−1.74963	−0.485260	−0.242630	+	0.970119i	$0.578010\pi$
$14$	2.09607	0.560198
$15$	−5.72193	−1.47740
$16$	12.1020	3.02549
$17$	0.780197	0.189226	0.0946128	−	0.995514i	$-0.469839\pi$
$17$	0.780197	0.189226	0.0946128	+	0.995514i	$0.469839\pi$
$18$	−3.17884	−0.749260
$19$	−0.705383	−0.161826	−0.0809130	−	0.996721i	$-0.525784\pi$
$19$	−0.705383	−0.161826	−0.0809130	+	0.996721i	$0.525784\pi$
$20$	14.3553	3.20995
$21$	1.60621	0.350505
$22$	5.01938	1.07014
$23$	2.69763	0.562496	0.281248	−	0.959635i	$-0.409252\pi$
$23$	2.69763	0.562496	0.281248	+	0.959635i	$0.409252\pi$
$24$	17.1443	3.49956
$25$	2.81390	0.562780
$26$	4.67365	0.916579
$27$	3.70493	0.713014
$28$	−4.02971	−0.761543
$29$	−3.16886	−0.588442	−0.294221	−	0.955737i	$-0.595060\pi$
$29$	−3.16886	−0.588442	−0.294221	+	0.955737i	$0.595060\pi$
$30$	15.2846	2.79057
$31$	3.31043	0.594572	0.297286	−	0.954789i	$-0.403919\pi$
$31$	3.31043	0.594572	0.297286	+	0.954789i	$0.403919\pi$
$32$	−15.5761	−2.75349
$33$	3.84634	0.669562
$34$	−2.08408	−0.357417
$35$	−2.19346	−0.370762
$36$	6.11134	1.01856
$37$	10.7236	1.76294	0.881472	−	0.472236i	$-0.156553\pi$
$37$	10.7236	1.76294	0.881472	+	0.472236i	$0.156553\pi$
$38$	1.88424	0.305664
$39$	3.58141	0.573485
$40$	−23.4123	−3.70182
$41$	8.65888	1.35229	0.676145	−	0.736769i	$-0.263649\pi$
$41$	8.65888	1.35229	0.676145	+	0.736769i	$0.263649\pi$
$42$	−4.29056	−0.662048
$43$	10.6576	1.62527	0.812634	−	0.582775i	$-0.198033\pi$
$43$	10.6576	1.62527	0.812634	+	0.582775i	$0.198033\pi$
$44$	−9.64979	−1.45476
$45$	3.32653	0.495890
$46$	−7.20599	−1.06247
$47$	6.13331	0.894636	0.447318	−	0.894375i	$-0.352379\pi$
$47$	6.13331	0.894636	0.447318	+	0.894375i	$0.352379\pi$
$48$	−24.7722	−3.57556
$49$	−6.38427	−0.912039
$50$	−7.51657	−1.06300
$51$	−1.59703	−0.223629
$52$	−8.98513	−1.24601
$53$	−6.68744	−0.918590	−0.459295	−	0.888284i	$-0.651898\pi$
$53$	−6.68744	−0.918590	−0.459295	+	0.888284i	$0.651898\pi$
$54$	−9.89671	−1.34677
$55$	−5.25259	−0.708259
$56$	6.57212	0.878237
$57$	1.44389	0.191248
$58$	8.46474	1.11148
$59$	9.41965	1.22633	0.613167	−	0.789953i	$-0.289895\pi$
$59$	9.41965	1.22633	0.613167	+	0.789953i	$0.289895\pi$
$60$	−29.3847	−3.79355
$61$	−7.89505	−1.01086	−0.505429	−	0.862868i	$-0.668666\pi$
$61$	−7.89505	−1.01086	−0.505429	+	0.862868i	$0.668666\pi$
$62$	−8.84292	−1.12305
$63$	−0.933798	−0.117647
$64$	17.4033	2.17542
$65$	−4.89080	−0.606629
$66$	−10.2744	−1.26470
$67$	−6.38542	−0.780103	−0.390051	−	0.920793i	$-0.627543\pi$
$67$	−6.38542	−0.780103	−0.390051	+	0.920793i	$0.627543\pi$
$68$	4.00667	0.485880
$69$	−5.52194	−0.664763
$70$	5.85922	0.700310
$71$	−12.1163	−1.43794	−0.718970	−	0.695041i	$-0.755386\pi$
$71$	−12.1163	−1.43794	−0.718970	+	0.695041i	$0.755386\pi$
$72$	−9.96710	−1.17463
$73$	−4.19780	−0.491316	−0.245658	−	0.969357i	$-0.579004\pi$
$73$	−4.19780	−0.491316	−0.245658	+	0.969357i	$0.579004\pi$
$74$	−28.6451	−3.32992
$75$	−5.75993	−0.665100
$76$	−3.62246	−0.415525
$77$	1.47446	0.168031
$78$	−9.56677	−1.08322
$79$	−17.3454	−1.95152	−0.975758	−	0.218854i	$-0.929768\pi$
$79$	−17.3454	−1.95152	−0.975758	+	0.218854i	$0.929768\pi$
$80$	33.8291	3.78220
$81$	−11.1539	−1.23932
$82$	−23.1298	−2.55426
$83$	15.6585	1.71874	0.859369	−	0.511355i	$-0.170856\pi$
$83$	15.6585	1.71874	0.859369	+	0.511355i	$0.170856\pi$
$84$	8.24863	0.900000
$85$	2.18091	0.236553
$86$	−28.4688	−3.06987
$87$	6.48652	0.695428
$88$	15.7380	1.67768
$89$	−5.80268	−0.615083	−0.307541	−	0.951535i	$-0.599506\pi$
$89$	−5.80268	−0.615083	−0.307541	+	0.951535i	$0.599506\pi$
$90$	−8.88593	−0.936659
$91$	1.37291	0.143920
$92$	13.8536	1.44433
$93$	−6.77632	−0.702671
$94$	−16.3835	−1.68983
$95$	−1.97178	−0.202301
$96$	31.8836	3.25410
$97$	9.52505	0.967123	0.483561	−	0.875310i	$-0.339343\pi$
$97$	9.52505	0.967123	0.483561	+	0.875310i	$0.339343\pi$
$98$	17.0538	1.72270
$99$	−2.23613	−0.224740
$100$	14.4507	1.44507
$101$	8.03755	0.799766	0.399883	−	0.916566i	$-0.369051\pi$
$101$	8.03755	0.799766	0.399883	+	0.916566i	$0.369051\pi$
$102$	4.26603	0.422400
$103$	1.11532	0.109896	0.0549479	−	0.998489i	$-0.482501\pi$
$103$	1.11532	0.109896	0.0549479	+	0.998489i	$0.482501\pi$
$104$	14.6540	1.43694
$105$	4.48991	0.438170
$106$	17.8637	1.73507
$107$	18.5120	1.78963	0.894813	−	0.446441i	$-0.147309\pi$
$107$	18.5120	1.78963	0.894813	+	0.446441i	$0.147309\pi$
$108$	19.0265	1.83082
$109$	12.4556	1.19303	0.596516	−	0.802601i	$-0.296551\pi$
$109$	12.4556	1.19303	0.596516	+	0.802601i	$0.296551\pi$
$110$	14.0308	1.33779
$111$	−21.9507	−2.08347
$112$	−9.49622	−0.897308
$113$	−18.5753	−1.74742	−0.873711	−	0.486446i	$-0.838293\pi$
$113$	−18.5753	−1.74742	−0.873711	+	0.486446i	$0.838293\pi$
$114$	−3.85695	−0.361237
$115$	7.54079	0.703183
$116$	−16.2735	−1.51096
$117$	−2.08211	−0.192491
$118$	−25.1620	−2.31635
$119$	−0.612208	−0.0561210
$120$	47.9240	4.37485
$121$	−7.46916	−0.679014
$122$	21.0895	1.90935
$123$	−17.7243	−1.59815
$124$	17.0006	1.52670
$125$	−6.11088	−0.546574
$126$	2.49439	0.222218
$127$	−13.2530	−1.17601	−0.588007	−	0.808856i	$-0.700087\pi$
$127$	−13.2530	−1.17601	−0.588007	+	0.808856i	$0.700087\pi$
$128$	−15.3360	−1.35553
$129$	−21.8156	−1.92076
$130$	13.0644	1.14583
$131$	−6.08836	−0.531942	−0.265971	−	0.963981i	$-0.585693\pi$
$131$	−6.08836	−0.531942	−0.265971	+	0.963981i	$0.585693\pi$
$132$	19.7527	1.71925
$133$	0.553503	0.0479948
$134$	17.0569	1.47349
$135$	10.3565	0.891347
$136$	−6.53455	−0.560333
$137$	−0.592433	−0.0506150	−0.0253075	−	0.999680i	$-0.508056\pi$
$137$	−0.592433	−0.0506150	−0.0253075	+	0.999680i	$0.508056\pi$
$138$	14.7504	1.25563
$139$	−3.37469	−0.286238	−0.143119	−	0.989706i	$-0.545713\pi$
$139$	−3.37469	−0.286238	−0.143119	+	0.989706i	$0.545713\pi$
$140$	−11.2644	−0.952014
$141$	−12.5546	−1.05729
$142$	32.3654	2.71604
$143$	3.28765	0.274927
$144$	14.4017	1.20014
$145$	−8.85803	−0.735619
$146$	11.2133	0.928018
$147$	13.0683	1.07786
$148$	55.0704	4.52676
$149$	15.9902	1.30997	0.654983	−	0.755644i	$-0.272676\pi$
$149$	15.9902	1.30997	0.654983	+	0.755644i	$0.272676\pi$
$150$	15.3861	1.25627
$151$	10.2207	0.831749	0.415875	−	0.909422i	$-0.363475\pi$
$151$	10.2207	0.831749	0.415875	+	0.909422i	$0.363475\pi$
$152$	5.90794	0.479197
$153$	0.928458	0.0750614
$154$	−3.93863	−0.317384
$155$	9.25378	0.743281
$156$	18.3922	1.47255
$157$	−5.53044	−0.441377	−0.220689	−	0.975344i	$-0.570830\pi$
$157$	−5.53044	−0.441377	−0.220689	+	0.975344i	$0.570830\pi$
$158$	46.3336	3.68610
$159$	13.6889	1.08560
$160$	−43.5404	−3.44217
$161$	−2.11679	−0.166826
$162$	29.7946	2.34089
$163$	8.95433	0.701357	0.350679	−	0.936496i	$-0.385951\pi$
$163$	8.95433	0.701357	0.350679	+	0.936496i	$0.385951\pi$
$164$	44.4672	3.47231
$165$	10.7518	0.837028
$166$	−41.8273	−3.24643
$167$	−18.0667	−1.39804	−0.699022	−	0.715100i	$-0.746381\pi$
$167$	−18.0667	−1.39804	−0.699022	+	0.715100i	$0.746381\pi$
$168$	−13.4528	−1.03791
$169$	−9.93880	−0.764523
$170$	−5.82571	−0.446812
$171$	−0.839427	−0.0641926
$172$	54.7315	4.17324
$173$	−4.88863	−0.371675	−0.185838	−	0.982580i	$-0.559500\pi$
$173$	−4.88863	−0.371675	−0.185838	+	0.982580i	$0.559500\pi$
$174$	−17.3270	−1.31355
$175$	−2.20802	−0.166911
$176$	−22.7402	−1.71411
$177$	−19.2816	−1.44929
$178$	15.5003	1.16179
$179$	−17.5671	−1.31303	−0.656514	−	0.754313i	$-0.727970\pi$
$179$	−17.5671	−1.31303	−0.656514	+	0.754313i	$0.727970\pi$
$180$	17.0833	1.27331
$181$	−4.47088	−0.332318	−0.166159	−	0.986099i	$-0.553137\pi$
$181$	−4.47088	−0.332318	−0.166159	+	0.986099i	$0.553137\pi$
$182$	−3.66734	−0.271841
$183$	16.1608	1.19464
$184$	−22.5940	−1.66565
$185$	29.9760	2.20388
$186$	18.1011	1.32724
$187$	−1.46603	−0.107207
$188$	31.4973	2.29718
$189$	−2.90720	−0.211468
$190$	5.26708	0.382114
$191$	15.8934	1.15001	0.575004	−	0.818151i	$-0.305001\pi$
$191$	15.8934	1.15001	0.575004	+	0.818151i	$0.305001\pi$
$192$	−35.6238	−2.57093
$193$	19.2169	1.38326	0.691632	−	0.722250i	$-0.256892\pi$
$193$	19.2169	1.38326	0.691632	+	0.722250i	$0.256892\pi$
$194$	−25.4436	−1.82674
$195$	10.0113	0.716921
$196$	−32.7861	−2.34187
$197$	1.40847	0.100349	0.0501745	−	0.998740i	$-0.484022\pi$
$197$	1.40847	0.100349	0.0501745	+	0.998740i	$0.484022\pi$
$198$	5.97321	0.424498
$199$	−22.6248	−1.60383	−0.801916	−	0.597437i	$-0.796186\pi$
$199$	−22.6248	−1.60383	−0.801916	+	0.597437i	$0.796186\pi$
$200$	−23.5678	−1.66650
$201$	13.0707	0.921934
$202$	−21.4701	−1.51063
$203$	2.48655	0.174522
$204$	−8.20147	−0.574218
$205$	24.2045	1.69051
$206$	−2.97928	−0.207576
$207$	3.21027	0.223129
$208$	−21.1739	−1.46815
$209$	1.32545	0.0916835
$210$	−11.9936	−0.827634
$211$	8.76960	0.603724	0.301862	−	0.953352i	$-0.402392\pi$
$211$	8.76960	0.603724	0.301862	+	0.953352i	$0.402392\pi$
$212$	−34.3430	−2.35869
$213$	24.8015	1.69937
$214$	−49.4498	−3.38032
$215$	29.7915	2.03177
$216$	−31.0306	−2.11137
$217$	−2.59764	−0.176340
$218$	−33.2718	−2.25345
$219$	8.59272	0.580642
$220$	−26.9744	−1.81861
$221$	−1.36506	−0.0918236
$222$	58.6353	3.93534
$223$	−5.27353	−0.353141	−0.176571	−	0.984288i	$-0.556500\pi$
$223$	−5.27353	−0.353141	−0.176571	+	0.984288i	$0.556500\pi$
$224$	12.2223	0.816637
$225$	3.34863	0.223242
$226$	49.6190	3.30060
$227$	14.6953	0.975363	0.487681	−	0.873022i	$-0.337843\pi$
$227$	14.6953	0.975363	0.487681	+	0.873022i	$0.337843\pi$
$228$	7.41502	0.491072
$229$	14.4413	0.954308	0.477154	−	0.878820i	$-0.341668\pi$
$229$	14.4413	0.954308	0.477154	+	0.878820i	$0.341668\pi$
$230$	−20.1432	−1.32820
$231$	−3.01816	−0.198580
$232$	26.5408	1.74249
$233$	−10.8598	−0.711446	−0.355723	−	0.934591i	$-0.615765\pi$
$233$	−10.8598	−0.711446	−0.355723	+	0.934591i	$0.615765\pi$
$234$	5.56179	0.363586
$235$	17.1447	1.11839
$236$	48.3742	3.14889
$237$	35.5054	2.30632
$238$	1.63535	0.106004
$239$	27.0599	1.75036	0.875181	−	0.483795i	$-0.160742\pi$
$239$	27.0599	1.75036	0.875181	+	0.483795i	$0.160742\pi$
$240$	−69.2466	−4.46985
$241$	6.06052	0.390392	0.195196	−	0.980764i	$-0.437466\pi$
$241$	6.06052	0.390392	0.195196	+	0.980764i	$0.437466\pi$
$242$	19.9518	1.28255
$243$	11.7168	0.751633
$244$	−40.5447	−2.59561
$245$	−17.8462	−1.14015
$246$	47.3457	3.01865
$247$	1.23416	0.0785276
$248$	−27.7266	−1.76064
$249$	−32.0522	−2.03122
$250$	16.3235	1.03239
$251$	10.6776	0.673966	0.336983	−	0.941511i	$-0.390593\pi$
$251$	10.6776	0.673966	0.336983	+	0.941511i	$0.390593\pi$
$252$	−4.79547	−0.302086
$253$	−5.06900	−0.318685
$254$	35.4018	2.22130
$255$	−4.46423	−0.279561
$256$	6.15942	0.384964
$257$	−16.4417	−1.02561	−0.512803	−	0.858506i	$-0.671393\pi$
$257$	−16.4417	−1.02561	−0.512803	+	0.858506i	$0.671393\pi$
$258$	58.2745	3.62801
$259$	−8.41462	−0.522859
$260$	−25.1165	−1.55766
$261$	−3.77104	−0.233421
$262$	16.2634	1.00476
$263$	−4.26752	−0.263147	−0.131573	−	0.991306i	$-0.542003\pi$
$263$	−4.26752	−0.263147	−0.131573	+	0.991306i	$0.542003\pi$
$264$	−32.2150	−1.98270
$265$	−18.6936	−1.14834
$266$	−1.47853	−0.0906546
$267$	11.8778	0.726911
$268$	−32.7920	−2.00309
$269$	−27.1615	−1.65606	−0.828032	−	0.560681i	$-0.810539\pi$
$269$	−27.1615	−1.65606	−0.828032	+	0.560681i	$0.810539\pi$
$270$	−27.6646	−1.68361
$271$	3.20014	0.194394	0.0971972	−	0.995265i	$-0.469012\pi$
$271$	3.20014	0.194394	0.0971972	+	0.995265i	$0.469012\pi$
$272$	9.44192	0.572500
$273$	−2.81028	−0.170086
$274$	1.58252	0.0956037
$275$	−5.28747	−0.318847
$276$	−28.3577	−1.70693
$277$	27.9150	1.67725	0.838623	−	0.544712i	$-0.183361\pi$
$277$	27.9150	1.67725	0.838623	+	0.544712i	$0.183361\pi$
$278$	9.01456	0.540658
$279$	3.93952	0.235853
$280$	18.3713	1.09789
$281$	15.3092	0.913270	0.456635	−	0.889654i	$-0.349055\pi$
$281$	15.3092	0.913270	0.456635	+	0.889654i	$0.349055\pi$
$282$	33.5362	1.99705
$283$	5.90061	0.350755	0.175377	−	0.984501i	$-0.443885\pi$
$283$	5.90061	0.350755	0.175377	+	0.984501i	$0.443885\pi$
$284$	−62.2227	−3.69224
$285$	4.03615	0.239081
$286$	−8.78205	−0.519293
$287$	−6.79448	−0.401066
$288$	−18.5360	−1.09224
$289$	−16.3913	−0.964194
$290$	23.6618	1.38947
$291$	−19.4974	−1.14296
$292$	−21.5576	−1.26156
$293$	−15.8405	−0.925412	−0.462706	−	0.886512i	$-0.653121\pi$
$293$	−15.8405	−0.925412	−0.462706	+	0.886512i	$0.653121\pi$
$294$	−34.9085	−2.03590
$295$	26.3311	1.53306
$296$	−89.8153	−5.22041
$297$	−6.96176	−0.403962
$298$	−42.7134	−2.47432
$299$	−4.71986	−0.272956
$300$	−29.5799	−1.70779
$301$	−8.36284	−0.482026
$302$	−27.3018	−1.57104
$303$	−16.4525	−0.945172
$304$	−8.53652	−0.489603
$305$	−22.0693	−1.26369
$306$	−2.48012	−0.141779
$307$	−17.7343	−1.01215	−0.506074	−	0.862490i	$-0.668904\pi$
$307$	−17.7343	−1.01215	−0.506074	+	0.862490i	$0.668904\pi$
$308$	7.57204	0.431457
$309$	−2.28301	−0.129876
$310$	−24.7189	−1.40394
$311$	24.5276	1.39083	0.695416	−	0.718608i	$-0.255220\pi$
$311$	24.5276	1.39083	0.695416	+	0.718608i	$0.255220\pi$
$312$	−29.9961	−1.69820
$313$	35.0495	1.98112	0.990558	−	0.137093i	$-0.0437759\pi$
$313$	35.0495	1.98112	0.990558	+	0.137093i	$0.0437759\pi$
$314$	14.7731	0.833693
$315$	−2.61028	−0.147072
$316$	−89.0767	−5.01096
$317$	8.68556	0.487830	0.243915	−	0.969797i	$-0.421568\pi$
$317$	8.68556	0.487830	0.243915	+	0.969797i	$0.421568\pi$
$318$	−36.5661	−2.05053
$319$	5.95446	0.333386
$320$	48.6481	2.71951
$321$	−37.8933	−2.11500
$322$	5.65443	0.315109
$323$	−0.550338	−0.0306216
$324$	−57.2804	−3.18225
$325$	−4.92328	−0.273095
$326$	−23.9191	−1.32475
$327$	−25.4961	−1.40994
$328$	−72.5224	−4.00438
$329$	−4.81271	−0.265333
$330$	−28.7205	−1.58101
$331$	−7.39410	−0.406416	−0.203208	−	0.979136i	$-0.565137\pi$
$331$	−7.39410	−0.406416	−0.203208	+	0.979136i	$0.565137\pi$
$332$	80.4133	4.41325
$333$	12.7614	0.699319
$334$	48.2603	2.64069
$335$	−17.8494	−0.975216
$336$	19.4383	1.06045
$337$	−14.3596	−0.782216	−0.391108	−	0.920345i	$-0.627908\pi$
$337$	−14.3596	−0.782216	−0.391108	+	0.920345i	$0.627908\pi$
$338$	26.5488	1.44406
$339$	38.0229	2.06512
$340$	11.2000	0.607404
$341$	−6.22048	−0.336858
$342$	2.24230	0.121250
$343$	10.5024	0.567078
$344$	−89.2627	−4.81272
$345$	−15.4357	−0.831029
$346$	13.0586	0.702036
$347$	32.5441	1.74706	0.873529	−	0.486772i	$-0.161826\pi$
$347$	32.5441	1.74706	0.873529	+	0.486772i	$0.161826\pi$
$348$	33.3112	1.78567
$349$	−33.6713	−1.80238	−0.901191	−	0.433423i	$-0.857306\pi$
$349$	−33.6713	−1.80238	−0.901191	+	0.433423i	$0.857306\pi$
$350$	5.89813	0.315268
$351$	−6.48225	−0.345997
$352$	29.2683	1.56001
$353$	3.05670	0.162692	0.0813459	−	0.996686i	$-0.474078\pi$
$353$	3.05670	0.162692	0.0813459	+	0.996686i	$0.474078\pi$
$354$	51.5056	2.73749
$355$	−33.8691	−1.79759
$356$	−29.7994	−1.57936
$357$	1.25316	0.0663245
$358$	46.9258	2.48010
$359$	−25.9713	−1.37071	−0.685356	−	0.728208i	$-0.740353\pi$
$359$	−25.9713	−1.37071	−0.685356	+	0.728208i	$0.740353\pi$
$360$	−27.8614	−1.46842
$361$	−18.5024	−0.973812
$362$	11.9427	0.627697
$363$	15.2890	0.802466
$364$	7.05049	0.369546
$365$	−11.7343	−0.614199
$366$	−43.1692	−2.25649
$367$	−32.3747	−1.68994	−0.844972	−	0.534811i	$-0.820383\pi$
$367$	−32.3747	−1.68994	−0.844972	+	0.534811i	$0.820383\pi$
$368$	32.6467	1.70183
$369$	10.3043	0.536422
$370$	−80.0727	−4.16278
$371$	5.24753	0.272438
$372$	−34.7994	−1.80427
$373$	15.7305	0.814495	0.407248	−	0.913318i	$-0.366489\pi$
$373$	15.7305	0.814495	0.407248	+	0.913318i	$0.366489\pi$
$374$	3.91611	0.202497
$375$	12.5087	0.645947
$376$	−51.3696	−2.64918
$377$	5.54433	0.285547
$378$	7.76579	0.399429
$379$	−20.6487	−1.06065	−0.530325	−	0.847794i	$-0.677930\pi$
$379$	−20.6487	−1.06065	−0.530325	+	0.847794i	$0.677930\pi$
$380$	−10.1260	−0.519453
$381$	27.1283	1.38982
$382$	−42.4549	−2.17218
$383$	22.7939	1.16471	0.582356	−	0.812934i	$-0.302131\pi$
$383$	22.7939	1.16471	0.582356	+	0.812934i	$0.302131\pi$
$384$	31.3922	1.60198
$385$	4.12162	0.210057
$386$	−51.3328	−2.61277
$387$	12.6829	0.644706
$388$	48.9155	2.48331
$389$	−35.5931	−1.80464	−0.902321	−	0.431066i	$-0.858138\pi$
$389$	−35.5931	−1.80464	−0.902321	+	0.431066i	$0.858138\pi$
$390$	−26.7423	−1.35415
$391$	2.10469	0.106439
$392$	53.4715	2.70072
$393$	12.4626	0.628655
$394$	−3.76233	−0.189543
$395$	−48.4863	−2.43961
$396$	−11.4835	−0.577070
$397$	−3.27590	−0.164413	−0.0822063	−	0.996615i	$-0.526197\pi$
$397$	−3.27590	−0.164413	−0.0822063	+	0.996615i	$0.526197\pi$
$398$	60.4361	3.02939
$399$	−1.13300	−0.0567208
$400$	34.0537	1.70269
$401$	21.0571	1.05154	0.525771	−	0.850626i	$-0.323777\pi$
$401$	21.0571	1.05154	0.525771	+	0.850626i	$0.323777\pi$
$402$	−34.9147	−1.74139
$403$	−5.79203	−0.288522
$404$	41.2764	2.05358
$405$	−31.1789	−1.54929
$406$	−6.64215	−0.329644
$407$	−20.1502	−0.998807
$408$	13.3759	0.662207
$409$	−0.635258	−0.0314115	−0.0157058	−	0.999877i	$-0.505000\pi$
$409$	−0.635258	−0.0314115	−0.0157058	+	0.999877i	$0.505000\pi$
$410$	−64.6556	−3.19311
$411$	1.21268	0.0598173
$412$	5.72768	0.282182
$413$	−7.39145	−0.363709
$414$	−8.57535	−0.421455
$415$	43.7706	2.14862
$416$	27.2524	1.33616
$417$	6.90784	0.338279
$418$	−3.54058	−0.173176
$419$	19.0867	0.932445	0.466222	−	0.884668i	$-0.345615\pi$
$419$	19.0867	0.932445	0.466222	+	0.884668i	$0.345615\pi$
$420$	23.0577	1.12510
$421$	−8.19478	−0.399389	−0.199694	−	0.979858i	$-0.563995\pi$
$421$	−8.19478	−0.399389	−0.199694	+	0.979858i	$0.563995\pi$
$422$	−23.4256	−1.14034
$423$	7.29883	0.354881
$424$	56.0107	2.72012
$425$	2.19540	0.106492
$426$	−66.2505	−3.20985
$427$	6.19512	0.299803
$428$	95.0677	4.59527
$429$	−6.72967	−0.324911
$430$	−79.5800	−3.83769
$431$	34.4804	1.66086	0.830432	−	0.557119i	$-0.188093\pi$
$431$	34.4804	1.66086	0.830432	+	0.557119i	$0.188093\pi$
$432$	44.8369	2.15722
$433$	−26.5425	−1.27555	−0.637776	−	0.770222i	$-0.720145\pi$
$433$	−26.5425	−1.27555	−0.637776	+	0.770222i	$0.720145\pi$
$434$	6.93890	0.333078
$435$	18.1320	0.869363
$436$	63.9652	3.06338
$437$	−1.90287	−0.0910264
$438$	−22.9531	−1.09674
$439$	22.3368	1.06608	0.533039	−	0.846091i	$-0.321050\pi$
$439$	22.3368	1.06608	0.533039	+	0.846091i	$0.321050\pi$
$440$	43.9930	2.09729
$441$	−7.59748	−0.361785
$442$	3.64637	0.173440
$443$	19.0899	0.906989	0.453494	−	0.891259i	$-0.350177\pi$
$443$	19.0899	0.906989	0.453494	+	0.891259i	$0.350177\pi$
$444$	−112.727	−5.34977
$445$	−16.2204	−0.768922
$446$	14.0868	0.667029
$447$	−32.7312	−1.54813
$448$	−13.6561	−0.645190
$449$	21.0093	0.991488	0.495744	−	0.868469i	$-0.334895\pi$
$449$	21.0093	0.991488	0.495744	+	0.868469i	$0.334895\pi$
$450$	−8.94494	−0.421669
$451$	−16.2705	−0.766148
$452$	−95.3928	−4.48690
$453$	−20.9213	−0.982970
$454$	−39.2545	−1.84231
$455$	3.83773	0.179916
$456$	−12.0933	−0.566320
$457$	13.2971	0.622011	0.311006	−	0.950408i	$-0.399334\pi$
$457$	13.2971	0.622011	0.311006	+	0.950408i	$0.399334\pi$
$458$	−38.5760	−1.80254
$459$	2.89058	0.134921
$460$	38.7254	1.80558
$461$	37.3304	1.73865	0.869326	−	0.494239i	$-0.164553\pi$
$461$	37.3304	1.73865	0.869326	+	0.494239i	$0.164553\pi$
$462$	8.06220	0.375087
$463$	13.9703	0.649255	0.324627	−	0.945842i	$-0.394761\pi$
$463$	13.9703	0.649255	0.324627	+	0.945842i	$0.394761\pi$
$464$	−38.3494	−1.78033
$465$	−18.9421	−0.878418
$466$	29.0089	1.34381
$467$	−2.18887	−0.101289	−0.0506445	−	0.998717i	$-0.516128\pi$
$467$	−2.18887	−0.101289	−0.0506445	+	0.998717i	$0.516128\pi$
$468$	−10.6926	−0.494265
$469$	5.01053	0.231365
$470$	−45.7973	−2.11247
$471$	11.3206	0.521625
$472$	−78.8943	−3.63141
$473$	−20.0262	−0.920805
$474$	−94.8429	−4.35628
$475$	−1.98488	−0.0910725
$476$	−3.14397	−0.144103
$477$	−7.95825	−0.364383
$478$	−72.2832	−3.30616
$479$	39.8642	1.82144	0.910722	−	0.413020i	$-0.135526\pi$
$479$	39.8642	1.82144	0.910722	+	0.413020i	$0.135526\pi$
$480$	89.1253	4.06799
$481$	−18.7623	−0.855486
$482$	−16.1890	−0.737389
$483$	4.33298	0.197157
$484$	−38.3575	−1.74352
$485$	26.6257	1.20901
$486$	−31.2982	−1.41972
$487$	27.6433	1.25264	0.626318	−	0.779568i	$-0.284561\pi$
$487$	27.6433	1.25264	0.626318	+	0.779568i	$0.284561\pi$
$488$	66.1250	2.99334
$489$	−18.3291	−0.828872
$490$	47.6712	2.15356
$491$	−6.30804	−0.284678	−0.142339	−	0.989818i	$-0.545462\pi$
$491$	−6.30804	−0.284678	−0.142339	+	0.989818i	$0.545462\pi$
$492$	−91.0225	−4.10361
$493$	−2.47234	−0.111348
$494$	−3.29672	−0.148326
$495$	−6.25074	−0.280950
$496$	40.0628	1.79887
$497$	9.50746	0.426468
$498$	85.6186	3.83666
$499$	−34.8071	−1.55818	−0.779090	−	0.626912i	$-0.784318\pi$
$499$	−34.8071	−1.55818	−0.779090	+	0.626912i	$0.784318\pi$
$500$	−31.3821	−1.40345
$501$	36.9818	1.65222
$502$	−28.5224	−1.27302
$503$	3.26688	0.145663	0.0728315	−	0.997344i	$-0.476796\pi$
$503$	3.26688	0.145663	0.0728315	+	0.997344i	$0.476796\pi$
$504$	7.82103	0.348376
$505$	22.4676	0.999797
$506$	13.5404	0.601946
$507$	20.3443	0.903522
$508$	−68.0601	−3.01968
$509$	21.4915	0.952596	0.476298	−	0.879284i	$-0.341978\pi$
$509$	21.4915	0.952596	0.476298	+	0.879284i	$0.341978\pi$
$510$	11.9250	0.528047
$511$	3.29395	0.145716
$512$	14.2189	0.628392
$513$	−2.61339	−0.115384
$514$	43.9196	1.93721
$515$	3.11770	0.137382
$516$	−112.033	−4.93198
$517$	−11.5248	−0.506861
$518$	22.4773	0.987598
$519$	10.0068	0.439250
$520$	40.9629	1.79634
$521$	−37.7881	−1.65553	−0.827763	−	0.561077i	$-0.810387\pi$
$521$	−37.7881	−1.65553	−0.827763	+	0.561077i	$0.810387\pi$
$522$	10.0733	0.440896
$523$	−14.8127	−0.647712	−0.323856	−	0.946106i	$-0.604979\pi$
$523$	−14.8127	−0.647712	−0.323856	+	0.946106i	$0.604979\pi$
$524$	−31.2665	−1.36588
$525$	4.51973	0.197257
$526$	11.3995	0.497043
$527$	2.58279	0.112508
$528$	46.5483	2.02575
$529$	−15.7228	−0.683599
$530$	49.9349	2.16903
$531$	11.2097	0.486458
$532$	2.84249	0.123237
$533$	−15.1498	−0.656211
$534$	−31.7284	−1.37302
$535$	51.7473	2.23723
$536$	53.4811	2.31003
$537$	35.9591	1.55175
$538$	72.5544	3.12804
$539$	11.9964	0.516721
$540$	53.1854	2.28874
$541$	−13.0182	−0.559696	−0.279848	−	0.960044i	$-0.590284\pi$
$541$	−13.0182	−0.559696	−0.279848	+	0.960044i	$0.590284\pi$
$542$	−8.54829	−0.367180
$543$	9.15170	0.392737
$544$	−12.1524	−0.521031
$545$	34.8176	1.49142
$546$	7.50689	0.321265
$547$	31.0999	1.32973	0.664867	−	0.746962i	$-0.268488\pi$
$547$	31.0999	1.32973	0.664867	+	0.746962i	$0.268488\pi$
$548$	−3.04241	−0.129965
$549$	−9.39535	−0.400984
$550$	14.1240	0.602251
$551$	2.23526	0.0952253
$552$	46.2490	1.96849
$553$	13.6107	0.578786
$554$	−74.5672	−3.16806
$555$	−61.3595	−2.60457
$556$	−17.3306	−0.734980
$557$	40.5524	1.71826	0.859131	−	0.511755i	$-0.171005\pi$
$557$	40.5524	1.71826	0.859131	+	0.511755i	$0.171005\pi$
$558$	−10.5233	−0.445489
$559$	−18.6468	−0.788677
$560$	−26.5451	−1.12174
$561$	3.00090	0.126698
$562$	−40.8943	−1.72502
$563$	25.6405	1.08062	0.540310	−	0.841466i	$-0.318307\pi$
$563$	25.6405	1.08062	0.540310	+	0.841466i	$0.318307\pi$
$564$	−64.4737	−2.71483
$565$	−51.9243	−2.18447
$566$	−15.7619	−0.662521
$567$	8.75230	0.367562
$568$	101.480	4.25801
$569$	−8.71989	−0.365557	−0.182778	−	0.983154i	$-0.558509\pi$
$569$	−8.71989	−0.365557	−0.182778	+	0.983154i	$0.558509\pi$
$570$	−10.7815	−0.451586
$571$	31.9462	1.33691	0.668454	−	0.743754i	$-0.266956\pi$
$571$	31.9462	1.33691	0.668454	+	0.743754i	$0.266956\pi$
$572$	16.8835	0.705937
$573$	−32.5331	−1.35909
$574$	18.1496	0.757550
$575$	7.59088	0.316561
$576$	20.7105	0.862937
$577$	0.182546	0.00759950	0.00379975	−	0.999993i	$-0.498790\pi$
$577$	0.182546	0.00759950	0.00379975	+	0.999993i	$0.498790\pi$
$578$	43.7849	1.82121
$579$	−39.3362	−1.63476
$580$	−45.4900	−1.88887
$581$	−12.2869	−0.509748
$582$	52.0819	2.15886
$583$	12.5661	0.520433
$584$	35.1587	1.45488
$585$	−5.82020	−0.240636
$586$	42.3136	1.74796
$587$	14.4665	0.597095	0.298548	−	0.954395i	$-0.403498\pi$
$587$	14.4665	0.597095	0.298548	+	0.954395i	$0.403498\pi$
$588$	67.1118	2.76764
$589$	−2.33512	−0.0962171
$590$	−70.3363	−2.89570
$591$	−2.88307	−0.118594
$592$	129.776	5.33377
$593$	−9.55278	−0.392286	−0.196143	−	0.980575i	$-0.562842\pi$
$593$	−9.55278	−0.392286	−0.196143	+	0.980575i	$0.562842\pi$
$594$	18.5964	0.763021
$595$	−1.71133	−0.0701576
$596$	82.1167	3.36363
$597$	46.3121	1.89543
$598$	12.6078	0.515572
$599$	30.2790	1.23717	0.618583	−	0.785719i	$-0.287707\pi$
$599$	30.2790	1.23717	0.618583	+	0.785719i	$0.287707\pi$
$600$	48.2423	1.96949
$601$	1.44295	0.0588592	0.0294296	−	0.999567i	$-0.490631\pi$
$601$	1.44295	0.0588592	0.0294296	+	0.999567i	$0.490631\pi$
$602$	22.3390	0.910471
$603$	−7.59884	−0.309449
$604$	52.4880	2.13570
$605$	−20.8788	−0.848844
$606$	43.9484	1.78528
$607$	−5.36121	−0.217605	−0.108802	−	0.994063i	$-0.534702\pi$
$607$	−5.36121	−0.217605	−0.108802	+	0.994063i	$0.534702\pi$
$608$	10.9871	0.445586
$609$	−5.08987	−0.206252
$610$	58.9522	2.38690
$611$	−10.7310	−0.434131
$612$	4.76805	0.192737
$613$	23.6854	0.956643	0.478321	−	0.878185i	$-0.341245\pi$
$613$	23.6854	0.956643	0.478321	+	0.878185i	$0.341245\pi$
$614$	47.3722	1.91179
$615$	−49.5455	−1.99787
$616$	−12.3494	−0.497570
$617$	37.6900	1.51734	0.758671	−	0.651473i	$-0.225849\pi$
$617$	37.6900	1.51734	0.758671	+	0.651473i	$0.225849\pi$
$618$	6.09845	0.245316
$619$	−26.8805	−1.08042	−0.540210	−	0.841530i	$-0.681655\pi$
$619$	−26.8805	−1.08042	−0.540210	+	0.841530i	$0.681655\pi$
$620$	47.5223	1.90854
$621$	9.99454	0.401067
$622$	−65.5187	−2.62706
$623$	4.55327	0.182423
$624$	43.3421	1.73507
$625$	−31.1515	−1.24606
$626$	−93.6252	−3.74202
$627$	−2.71314	−0.108353
$628$	−28.4013	−1.13334
$629$	8.36650	0.333594
$630$	6.97264	0.277797
$631$	44.6764	1.77854	0.889270	−	0.457383i	$-0.151213\pi$
$631$	44.6764	1.77854	0.889270	+	0.457383i	$0.151213\pi$
$632$	145.277	5.77880
$633$	−17.9510	−0.713488
$634$	−23.2011	−0.921434
$635$	−37.0466	−1.47015
$636$	70.2987	2.78752
$637$	11.1701	0.442576
$638$	−15.9057	−0.629713
$639$	−14.4188	−0.570397
$640$	−42.8694	−1.69456
$641$	−38.5782	−1.52375	−0.761874	−	0.647726i	$-0.775720\pi$
$641$	−38.5782	−1.52375	−0.761874	+	0.647726i	$0.775720\pi$
$642$	101.222	3.99490
$643$	2.78435	0.109804	0.0549020	−	0.998492i	$-0.482515\pi$
$643$	2.78435	0.109804	0.0549020	+	0.998492i	$0.482515\pi$
$644$	−10.8707	−0.428365
$645$	−60.9820	−2.40116
$646$	1.47008	0.0578394
$647$	10.5242	0.413750	0.206875	−	0.978367i	$-0.433671\pi$
$647$	10.5242	0.413750	0.206875	+	0.978367i	$0.433671\pi$
$648$	93.4197	3.66987
$649$	−17.7000	−0.694787
$650$	13.1512	0.515833
$651$	5.31727	0.208400
$652$	45.9845	1.80089
$653$	−29.9603	−1.17244	−0.586218	−	0.810153i	$-0.699384\pi$
$653$	−29.9603	−1.17244	−0.586218	+	0.810153i	$0.699384\pi$
$654$	68.1058	2.66315
$655$	−17.0190	−0.664988
$656$	104.789	4.09134
$657$	−4.99551	−0.194893
$658$	12.8558	0.501173
$659$	39.4951	1.53851	0.769255	−	0.638942i	$-0.220627\pi$
$659$	39.4951	1.53851	0.769255	+	0.638942i	$0.220627\pi$
$660$	55.2154	2.14926
$661$	−2.72745	−0.106086	−0.0530428	−	0.998592i	$-0.516892\pi$
$661$	−2.72745	−0.106086	−0.0530428	+	0.998592i	$0.516892\pi$
$662$	19.7513	0.767656
$663$	2.79421	0.108518
$664$	−131.147	−5.08951
$665$	1.54723	0.0599989
$666$	−34.0885	−1.32090
$667$	−8.54842	−0.330996
$668$	−92.7808	−3.58980
$669$	10.7947	0.417346
$670$	47.6797	1.84203
$671$	14.8352	0.572708
$672$	−25.0185	−0.965110
$673$	27.5215	1.06087	0.530437	−	0.847724i	$-0.322028\pi$
$673$	27.5215	1.06087	0.530437	+	0.847724i	$0.322028\pi$
$674$	38.3577	1.47748
$675$	10.4253	0.401270
$676$	−51.0402	−1.96309
$677$	0.739791	0.0284325	0.0142162	−	0.999899i	$-0.495475\pi$
$677$	0.739791	0.0284325	0.0142162	+	0.999899i	$0.495475\pi$
$678$	−101.568	−3.90069
$679$	−7.47416	−0.286832
$680$	−18.2662	−0.700479
$681$	−30.0807	−1.15269
$682$	16.6163	0.636272
$683$	8.00832	0.306430	0.153215	−	0.988193i	$-0.451037\pi$
$683$	8.00832	0.306430	0.153215	+	0.988193i	$0.451037\pi$
$684$	−4.31084	−0.164829
$685$	−1.65605	−0.0632744
$686$	−28.0544	−1.07112
$687$	−29.5607	−1.12781
$688$	128.978	4.91723
$689$	11.7005	0.445755
$690$	41.2322	1.56968
$691$	29.9271	1.13848	0.569241	−	0.822171i	$-0.307237\pi$
$691$	29.9271	1.13848	0.569241	+	0.822171i	$0.307237\pi$
$692$	−25.1053	−0.954360
$693$	1.75466	0.0666539
$694$	−86.9326	−3.29992
$695$	−9.43339	−0.357829
$696$	−54.3279	−2.05929
$697$	6.75563	0.255888
$698$	89.9436	3.40441
$699$	22.2294	0.840795
$700$	−11.3392	−0.428581
$701$	−11.4624	−0.432928	−0.216464	−	0.976291i	$-0.569452\pi$
$701$	−11.4624	−0.432928	−0.216464	+	0.976291i	$0.569452\pi$
$702$	17.3156	0.653534
$703$	−7.56423	−0.285290
$704$	−32.7018	−1.23249
$705$	−35.0944	−1.32173
$706$	−8.16515	−0.307299
$707$	−6.30693	−0.237197
$708$	−99.0198	−3.72139
$709$	7.01682	0.263522	0.131761	−	0.991282i	$-0.457937\pi$
$709$	7.01682	0.263522	0.131761	+	0.991282i	$0.457937\pi$
$710$	90.4721	3.39536
$711$	−20.6416	−0.774121
$712$	48.6004	1.82138
$713$	8.93034	0.334444
$714$	−3.34748	−0.125276
$715$	9.19007	0.343689
$716$	−90.2151	−3.37150
$717$	−55.3905	−2.06860
$718$	69.3752	2.58906
$719$	30.9959	1.15595	0.577976	−	0.816054i	$-0.303843\pi$
$719$	30.9959	1.15595	0.577976	+	0.816054i	$0.303843\pi$
$720$	40.2576	1.50031
$721$	−0.875175	−0.0325932
$722$	49.4242	1.83938
$723$	−12.4056	−0.461370
$724$	−22.9600	−0.853302
$725$	−8.91686	−0.331164
$726$	−40.8405	−1.51573
$727$	−16.2463	−0.602541	−0.301270	−	0.953539i	$-0.597411\pi$
$727$	−16.2463	−0.602541	−0.301270	+	0.953539i	$0.597411\pi$
$728$	−11.4988	−0.426173
$729$	9.47798	0.351036
$730$	31.3449	1.16013
$731$	8.31502	0.307542
$732$	82.9932	3.06752
$733$	4.60282	0.170009	0.0850045	−	0.996381i	$-0.472910\pi$
$733$	4.60282	0.170009	0.0850045	+	0.996381i	$0.472910\pi$
$734$	86.4800	3.19204
$735$	36.5304	1.34744
$736$	−42.0186	−1.54883
$737$	11.9985	0.441972
$738$	−27.5252	−1.01322
$739$	−49.2365	−1.81119	−0.905596	−	0.424140i	$-0.860576\pi$
$739$	−49.2365	−1.81119	−0.905596	+	0.424140i	$0.860576\pi$
$740$	153.940	5.65896
$741$	−2.52627	−0.0928048
$742$	−14.0173	−0.514592
$743$	−5.79323	−0.212533	−0.106266	−	0.994338i	$-0.533890\pi$
$743$	−5.79323	−0.212533	−0.106266	+	0.994338i	$0.533890\pi$
$744$	56.7551	2.08074
$745$	44.6979	1.63760
$746$	−42.0198	−1.53845
$747$	18.6340	0.681784
$748$	−7.52874	−0.275278
$749$	−14.5261	−0.530772
$750$	−33.4136	−1.22009
$751$	15.3491	0.560096	0.280048	−	0.959986i	$-0.409650\pi$
$751$	15.3491	0.560096	0.280048	+	0.959986i	$0.409650\pi$
$752$	74.2251	2.70671
$753$	−21.8567	−0.796501
$754$	−14.8102	−0.539354
$755$	28.5703	1.03978
$756$	−14.9298	−0.542991
$757$	25.9113	0.941761	0.470881	−	0.882197i	$-0.343936\pi$
$757$	25.9113	0.941761	0.470881	+	0.882197i	$0.343936\pi$
$758$	55.1572	2.00340
$759$	10.3760	0.376626
$760$	16.5147	0.599050
$761$	26.0664	0.944907	0.472453	−	0.881356i	$-0.343369\pi$
$761$	26.0664	0.944907	0.472453	+	0.881356i	$0.343369\pi$
$762$	−72.4658	−2.62516
$763$	−9.77372	−0.353832
$764$	81.6199	2.95290
$765$	2.59535	0.0938352
$766$	−60.8876	−2.19996
$767$	−16.4809	−0.595090
$768$	−12.6081	−0.454955
$769$	26.2294	0.945857	0.472929	−	0.881101i	$-0.343197\pi$
$769$	26.2294	0.945857	0.472929	+	0.881101i	$0.343197\pi$
$770$	−11.0098	−0.396765
$771$	33.6555	1.21207
$772$	98.6876	3.55185
$773$	−31.3911	−1.12906	−0.564529	−	0.825413i	$-0.690942\pi$
$773$	−31.3911	−1.12906	−0.564529	+	0.825413i	$0.690942\pi$
$774$	−33.8788	−1.21775
$775$	9.31524	0.334613
$776$	−79.7771	−2.86383
$777$	17.2244	0.617920
$778$	95.0772	3.40868
$779$	−6.10782	−0.218836
$780$	51.4123	1.84086
$781$	22.7672	0.814673
$782$	−5.62210	−0.201046
$783$	−11.7404	−0.419568
$784$	−77.2622	−2.75937
$785$	−15.4594	−0.551771
$786$	−33.2904	−1.18743
$787$	−30.3766	−1.08281	−0.541405	−	0.840762i	$-0.682107\pi$
$787$	−30.3766	−1.08281	−0.541405	+	0.840762i	$0.682107\pi$
$788$	7.23311	0.257669
$789$	8.73543	0.310990
$790$	129.518	4.60804
$791$	14.5758	0.518255
$792$	18.7287	0.665496
$793$	13.8134	0.490529
$794$	8.75067	0.310550
$795$	38.2650	1.35712
$796$	−116.189	−4.11820
$797$	31.4370	1.11356	0.556778	−	0.830661i	$-0.312037\pi$
$797$	31.4370	1.11356	0.556778	+	0.830661i	$0.312037\pi$
$798$	3.02649	0.107137
$799$	4.78519	0.169288
$800$	−43.8296	−1.54961
$801$	−6.90536	−0.243989
$802$	−56.2483	−1.98620
$803$	7.88789	0.278358
$804$	67.1238	2.36727
$805$	−5.91714	−0.208552
$806$	15.4718	0.544972
$807$	55.5983	1.95715
$808$	−67.3185	−2.36826
$809$	14.6691	0.515737	0.257869	−	0.966180i	$-0.416980\pi$
$809$	14.6691	0.515737	0.257869	+	0.966180i	$0.416980\pi$
$810$	83.2860	2.92637
$811$	−25.5673	−0.897788	−0.448894	−	0.893585i	$-0.648182\pi$
$811$	−25.5673	−0.897788	−0.448894	+	0.893585i	$0.648182\pi$
$812$	12.7696	0.448124
$813$	−6.55054	−0.229737
$814$	53.8257	1.88659
$815$	25.0304	0.876775
$816$	−19.3272	−0.676587
$817$	−7.51768	−0.263010
$818$	1.69692	0.0593314
$819$	1.63380	0.0570896
$820$	124.301	4.34077
$821$	20.3599	0.710566	0.355283	−	0.934759i	$-0.384384\pi$
$821$	20.3599	0.710566	0.355283	+	0.934759i	$0.384384\pi$
$822$	−3.23936	−0.112985
$823$	19.4543	0.678133	0.339066	−	0.940762i	$-0.389889\pi$
$823$	19.4543	0.678133	0.339066	+	0.940762i	$0.389889\pi$
$824$	−9.34138	−0.325422
$825$	10.8232	0.376816
$826$	19.7442	0.686990
$827$	21.6263	0.752020	0.376010	−	0.926616i	$-0.377296\pi$
$827$	21.6263	0.752020	0.376010	+	0.926616i	$0.377296\pi$
$828$	16.4862	0.572934
$829$	14.9148	0.518013	0.259006	−	0.965876i	$-0.416605\pi$
$829$	14.9148	0.518013	0.259006	+	0.965876i	$0.416605\pi$
$830$	−116.921	−4.05840
$831$	−57.1407	−1.98219
$832$	−30.4493	−1.05564
$833$	−4.98099	−0.172581
$834$	−18.4524	−0.638955
$835$	−50.5025	−1.74771
$836$	6.80680	0.235418
$837$	12.2649	0.423938
$838$	−50.9848	−1.76124
$839$	−32.5745	−1.12459	−0.562297	−	0.826935i	$-0.690082\pi$
$839$	−32.5745	−1.12459	−0.562297	+	0.826935i	$0.690082\pi$
$840$	−37.6052	−1.29750
$841$	−18.9583	−0.653735
$842$	21.8901	0.754383
$843$	−31.3373	−1.07931
$844$	45.0359	1.55020
$845$	−27.7823	−0.955740
$846$	−19.4968	−0.670315
$847$	5.86093	0.201384
$848$	−80.9311	−2.77919
$849$	−12.0783	−0.414526
$850$	−5.86441	−0.201147
$851$	28.9283	0.991649
$852$	127.367	4.36352
$853$	−55.5403	−1.90166	−0.950832	−	0.309707i	$-0.899769\pi$
$853$	−55.5403	−1.90166	−0.950832	+	0.309707i	$0.899769\pi$
$854$	−16.5486	−0.566280
$855$	−2.34648	−0.0802480
$856$	−155.048	−5.29942
$857$	−27.3740	−0.935078	−0.467539	−	0.883973i	$-0.654859\pi$
$857$	−27.3740	−0.935078	−0.467539	+	0.883973i	$0.654859\pi$
$858$	17.9765	0.613706
$859$	39.4064	1.34453	0.672265	−	0.740310i	$-0.265321\pi$
$859$	39.4064	1.34453	0.672265	+	0.740310i	$0.265321\pi$
$860$	152.993	5.21702
$861$	13.9080	0.473984
$862$	−92.1051	−3.13711
$863$	38.7000	1.31736	0.658681	−	0.752422i	$-0.271115\pi$
$863$	38.7000	1.31736	0.658681	+	0.752422i	$0.271115\pi$
$864$	−57.7083	−1.96328
$865$	−13.6653	−0.464636
$866$	70.9011	2.40932
$867$	33.5523	1.13949
$868$	−13.3401	−0.452792
$869$	32.5930	1.10564
$870$	−48.4347	−1.64209
$871$	11.1721	0.378552
$872$	−104.322	−3.53279
$873$	11.3351	0.383635
$874$	5.08299	0.171935
$875$	4.79511	0.162104
$876$	44.1275	1.49093
$877$	−39.9690	−1.34966	−0.674829	−	0.737975i	$-0.735782\pi$
$877$	−39.9690	−1.34966	−0.674829	+	0.737975i	$0.735782\pi$
$878$	−59.6666	−2.01365
$879$	32.4248	1.09366
$880$	−63.5666	−2.14283
$881$	35.8282	1.20708	0.603542	−	0.797331i	$-0.293756\pi$
$881$	35.8282	1.20708	0.603542	+	0.797331i	$0.293756\pi$
$882$	20.2946	0.683354
$883$	−12.1692	−0.409528	−0.204764	−	0.978811i	$-0.565643\pi$
$883$	−12.1692	−0.409528	−0.204764	+	0.978811i	$0.565643\pi$
$884$	−7.01018	−0.235778
$885$	−53.8986	−1.81178
$886$	−50.9935	−1.71316
$887$	−31.6523	−1.06278	−0.531391	−	0.847127i	$-0.678330\pi$
$887$	−31.6523	−1.06278	−0.531391	+	0.847127i	$0.678330\pi$
$888$	183.848	6.16954
$889$	10.3994	0.348785
$890$	43.3285	1.45237
$891$	20.9588	0.702147
$892$	−27.0819	−0.906770
$893$	−4.32633	−0.144775
$894$	87.4324	2.92418
$895$	−49.1060	−1.64143
$896$	12.0340	0.402026
$897$	9.66134	0.322583
$898$	−56.1205	−1.87277
$899$	−10.4903	−0.349871
$900$	17.1967	0.573224
$901$	−5.21752	−0.173821
$902$	43.4622	1.44713
$903$	17.1184	0.569664
$904$	155.578	5.17444
$905$	−12.4976	−0.415435
$906$	55.8856	1.85668
$907$	−48.4847	−1.60991	−0.804954	−	0.593338i	$-0.797810\pi$
$907$	−48.4847	−1.60991	−0.804954	+	0.593338i	$0.797810\pi$
$908$	75.4671	2.50446
$909$	9.56492	0.317248
$910$	−10.2515	−0.339832
$911$	32.6235	1.08087	0.540433	−	0.841387i	$-0.318261\pi$
$911$	32.6235	1.08087	0.540433	+	0.841387i	$0.318261\pi$
$912$	17.4739	0.578618
$913$	−29.4231	−0.973762
$914$	−35.5195	−1.17488
$915$	45.1749	1.49344
$916$	74.1626	2.45040
$917$	4.77744	0.157765
$918$	−7.72138	−0.254844
$919$	50.0535	1.65111	0.825557	−	0.564319i	$-0.190861\pi$
$919$	50.0535	1.65111	0.825557	+	0.564319i	$0.190861\pi$
$920$	−63.1579	−2.08226
$921$	36.3013	1.19617
$922$	−99.7181	−3.28404
$923$	21.1990	0.697774
$924$	−15.4996	−0.509900
$925$	30.1751	0.992150
$926$	−37.3178	−1.22634
$927$	1.32727	0.0435931
$928$	49.3584	1.62027
$929$	−34.2137	−1.12252	−0.561258	−	0.827641i	$-0.689683\pi$
$929$	−34.2137	−1.12252	−0.561258	+	0.827641i	$0.689683\pi$
$930$	50.5986	1.65919
$931$	4.50336	0.147592
$932$	−55.7697	−1.82680
$933$	−50.2069	−1.64370
$934$	5.84698	0.191319
$935$	−4.09805	−0.134021
$936$	17.4387	0.570003
$937$	23.6513	0.772655	0.386327	−	0.922362i	$-0.373743\pi$
$937$	23.6513	0.772655	0.386327	+	0.922362i	$0.373743\pi$
$938$	−13.3843	−0.437012
$939$	−71.7449	−2.34130
$940$	88.0456	2.87173
$941$	−41.2278	−1.34399	−0.671995	−	0.740556i	$-0.734562\pi$
$941$	−41.2278	−1.34399	−0.671995	+	0.740556i	$0.734562\pi$
$942$	−30.2398	−0.985267
$943$	23.3585	0.760657
$944$	113.996	3.71026
$945$	−8.12660	−0.264358
$946$	53.4945	1.73926
$947$	16.0280	0.520840	0.260420	−	0.965495i	$-0.416139\pi$
$947$	16.0280	0.520840	0.260420	+	0.965495i	$0.416139\pi$
$948$	182.336	5.92200
$949$	7.34459	0.238416
$950$	5.30206	0.172022
$951$	−17.7790	−0.576522
$952$	5.12755	0.166185
$953$	3.87716	0.125593	0.0627967	−	0.998026i	$-0.479998\pi$
$953$	3.87716	0.125593	0.0627967	+	0.998026i	$0.479998\pi$
$954$	21.2583	0.688263
$955$	44.4275	1.43764
$956$	138.965	4.49445
$957$	−12.1885	−0.393999
$958$	−106.486	−3.44042
$959$	0.464873	0.0150115
$960$	−99.5806	−3.21395
$961$	−20.0410	−0.646485
$962$	50.1183	1.61588
$963$	22.0299	0.709903
$964$	31.1235	1.00242
$965$	53.7178	1.72924
$966$	−11.5744	−0.372399
$967$	17.8851	0.575145	0.287573	−	0.957759i	$-0.407152\pi$
$967$	17.8851	0.575145	0.287573	+	0.957759i	$0.407152\pi$
$968$	62.5580	2.01069
$969$	1.12652	0.0361890
$970$	−71.1233	−2.28363
$971$	25.7632	0.826781	0.413391	−	0.910554i	$-0.364344\pi$
$971$	25.7632	0.826781	0.413391	+	0.910554i	$0.364344\pi$
$972$	60.1711	1.92999
$973$	2.64807	0.0848931
$974$	−73.8415	−2.36603
$975$	10.0777	0.322746
$976$	−95.5456	−3.05834
$977$	−40.1477	−1.28444	−0.642219	−	0.766521i	$-0.721986\pi$
$977$	−40.1477	−1.28444	−0.642219	+	0.766521i	$0.721986\pi$
$978$	48.9613	1.56561
$979$	10.9035	0.348479
$980$	−91.6482	−2.92759
$981$	14.8226	0.473248
$982$	16.8502	0.537712
$983$	3.50899	0.111919	0.0559597	−	0.998433i	$-0.482178\pi$
$983$	3.50899	0.111919	0.0559597	+	0.998433i	$0.482178\pi$
$984$	148.450	4.73242
$985$	3.93713	0.125448
$986$	6.60417	0.210320
$987$	9.85141	0.313574
$988$	6.33796	0.201637
$989$	28.7503	0.914206
$990$	16.6971	0.530670
$991$	−56.6562	−1.79974	−0.899872	−	0.436153i	$-0.856341\pi$
$991$	−56.6562	−1.79974	−0.899872	+	0.436153i	$0.856341\pi$
$992$	−51.5636	−1.63715
$993$	15.1354	0.480307
$994$	−25.3966	−0.805531
$995$	−63.2440	−2.00497
$996$	−164.602	−5.21563
$997$	−11.4034	−0.361148	−0.180574	−	0.983561i	$-0.557796\pi$
$997$	−11.4034	−0.361148	−0.180574	+	0.983561i	$0.557796\pi$
$998$	92.9776	2.94316
$999$	39.7301	1.25700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.9	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.67123 q^{2} -2.04696 q^{3} +5.13545 q^{4} +2.79534 q^{5} +5.46788 q^{6} -0.784684 q^{7} -8.37550 q^{8} +1.19003 q^{9} +O(q^{10})\)	\(q-2.67123 q^{2} -2.04696 q^{3} +5.13545 q^{4} +2.79534 q^{5} +5.46788 q^{6} -0.784684 q^{7} -8.37550 q^{8} +1.19003 q^{9} -7.46698 q^{10} -1.87905 q^{11} -10.5120 q^{12} -1.74963 q^{13} +2.09607 q^{14} -5.72193 q^{15} +12.1020 q^{16} +0.780197 q^{17} -3.17884 q^{18} -0.705383 q^{19} +14.3553 q^{20} +1.60621 q^{21} +5.01938 q^{22} +2.69763 q^{23} +17.1443 q^{24} +2.81390 q^{25} +4.67365 q^{26} +3.70493 q^{27} -4.02971 q^{28} -3.16886 q^{29} +15.2846 q^{30} +3.31043 q^{31} -15.5761 q^{32} +3.84634 q^{33} -2.08408 q^{34} -2.19346 q^{35} +6.11134 q^{36} +10.7236 q^{37} +1.88424 q^{38} +3.58141 q^{39} -23.4123 q^{40} +8.65888 q^{41} -4.29056 q^{42} +10.6576 q^{43} -9.64979 q^{44} +3.32653 q^{45} -7.20599 q^{46} +6.13331 q^{47} -24.7722 q^{48} -6.38427 q^{49} -7.51657 q^{50} -1.59703 q^{51} -8.98513 q^{52} -6.68744 q^{53} -9.89671 q^{54} -5.25259 q^{55} +6.57212 q^{56} +1.44389 q^{57} +8.46474 q^{58} +9.41965 q^{59} -29.3847 q^{60} -7.89505 q^{61} -8.84292 q^{62} -0.933798 q^{63} +17.4033 q^{64} -4.89080 q^{65} -10.2744 q^{66} -6.38542 q^{67} +4.00667 q^{68} -5.52194 q^{69} +5.85922 q^{70} -12.1163 q^{71} -9.96710 q^{72} -4.19780 q^{73} -28.6451 q^{74} -5.75993 q^{75} -3.62246 q^{76} +1.47446 q^{77} -9.56677 q^{78} -17.3454 q^{79} +33.8291 q^{80} -11.1539 q^{81} -23.1298 q^{82} +15.6585 q^{83} +8.24863 q^{84} +2.18091 q^{85} -28.4688 q^{86} +6.48652 q^{87} +15.7380 q^{88} -5.80268 q^{89} -8.88593 q^{90} +1.37291 q^{91} +13.8536 q^{92} -6.77632 q^{93} -16.3835 q^{94} -1.97178 q^{95} +31.8836 q^{96} +9.52505 q^{97} +17.0538 q^{98} -2.23613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 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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