LMFDB - Embedded newform 8017.2.a.b.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.50135 q^{2} -2.46945 q^{3} +4.25678 q^{4} +1.14683 q^{5} +6.17696 q^{6} -1.51997 q^{7} -5.64500 q^{8} +3.09817 q^{9} +O(q^{10})$	\(q-2.50135 q^{2} -2.46945 q^{3} +4.25678 q^{4} +1.14683 q^{5} +6.17696 q^{6} -1.51997 q^{7} -5.64500 q^{8} +3.09817 q^{9} -2.86862 q^{10} +4.29850 q^{11} -10.5119 q^{12} +5.22369 q^{13} +3.80198 q^{14} -2.83203 q^{15} +5.60659 q^{16} -0.954242 q^{17} -7.74962 q^{18} -7.28082 q^{19} +4.88179 q^{20} +3.75348 q^{21} -10.7521 q^{22} -7.27620 q^{23} +13.9400 q^{24} -3.68478 q^{25} -13.0663 q^{26} -0.242422 q^{27} -6.47016 q^{28} -9.56432 q^{29} +7.08392 q^{30} -2.99062 q^{31} -2.73408 q^{32} -10.6149 q^{33} +2.38690 q^{34} -1.74314 q^{35} +13.1882 q^{36} -0.378497 q^{37} +18.2119 q^{38} -12.8996 q^{39} -6.47384 q^{40} -10.7657 q^{41} -9.38878 q^{42} -8.16165 q^{43} +18.2978 q^{44} +3.55307 q^{45} +18.2004 q^{46} -2.08513 q^{47} -13.8452 q^{48} -4.68970 q^{49} +9.21695 q^{50} +2.35645 q^{51} +22.2361 q^{52} -4.49261 q^{53} +0.606383 q^{54} +4.92964 q^{55} +8.58021 q^{56} +17.9796 q^{57} +23.9238 q^{58} +8.78761 q^{59} -12.0553 q^{60} -9.50510 q^{61} +7.48060 q^{62} -4.70911 q^{63} -4.37428 q^{64} +5.99068 q^{65} +26.5517 q^{66} +3.02326 q^{67} -4.06199 q^{68} +17.9682 q^{69} +4.36021 q^{70} +6.16004 q^{71} -17.4892 q^{72} +8.77757 q^{73} +0.946755 q^{74} +9.09938 q^{75} -30.9928 q^{76} -6.53358 q^{77} +32.2666 q^{78} -10.4141 q^{79} +6.42980 q^{80} -8.69586 q^{81} +26.9289 q^{82} +0.662144 q^{83} +15.9777 q^{84} -1.09435 q^{85} +20.4152 q^{86} +23.6186 q^{87} -24.2650 q^{88} -17.5166 q^{89} -8.88748 q^{90} -7.93984 q^{91} -30.9732 q^{92} +7.38517 q^{93} +5.21565 q^{94} -8.34985 q^{95} +6.75166 q^{96} +7.80008 q^{97} +11.7306 q^{98} +13.3175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50135	−1.76873	−0.884363	−	0.466801i	$-0.845407\pi$
$2$	−2.50135	−1.76873	−0.884363	+	0.466801i	$0.845407\pi$
$3$	−2.46945	−1.42574	−0.712868	−	0.701298i	$-0.752604\pi$
$3$	−2.46945	−1.42574	−0.712868	+	0.701298i	$0.752604\pi$
$4$	4.25678	2.12839
$5$	1.14683	0.512877	0.256439	−	0.966561i	$-0.417451\pi$
$5$	1.14683	0.512877	0.256439	+	0.966561i	$0.417451\pi$
$6$	6.17696	2.52173
$7$	−1.51997	−0.574493	−0.287247	−	0.957857i	$-0.592740\pi$
$7$	−1.51997	−0.574493	−0.287247	+	0.957857i	$0.592740\pi$
$8$	−5.64500	−1.99581
$9$	3.09817	1.03272
$10$	−2.86862	−0.907139
$11$	4.29850	1.29605	0.648023	−	0.761621i	$-0.275596\pi$
$11$	4.29850	1.29605	0.648023	+	0.761621i	$0.275596\pi$
$12$	−10.5119	−3.03452
$13$	5.22369	1.44879	0.724396	−	0.689384i	$-0.242119\pi$
$13$	5.22369	1.44879	0.724396	+	0.689384i	$0.242119\pi$
$14$	3.80198	1.01612
$15$	−2.83203	−0.731227
$16$	5.60659	1.40165
$17$	−0.954242	−0.231438	−0.115719	−	0.993282i	$-0.536917\pi$
$17$	−0.954242	−0.231438	−0.115719	+	0.993282i	$0.536917\pi$
$18$	−7.74962	−1.82660
$19$	−7.28082	−1.67033	−0.835167	−	0.549996i	$-0.814629\pi$
$19$	−7.28082	−1.67033	−0.835167	+	0.549996i	$0.814629\pi$
$20$	4.88179	1.09160
$21$	3.75348	0.819076
$22$	−10.7521	−2.29235
$23$	−7.27620	−1.51719	−0.758597	−	0.651561i	$-0.774115\pi$
$23$	−7.27620	−1.51719	−0.758597	+	0.651561i	$0.774115\pi$
$24$	13.9400	2.84550
$25$	−3.68478	−0.736957
$26$	−13.0663	−2.56251
$27$	−0.242422	−0.0466541
$28$	−6.47016	−1.22275
$29$	−9.56432	−1.77605	−0.888025	−	0.459796i	$-0.847923\pi$
$29$	−9.56432	−1.77605	−0.888025	+	0.459796i	$0.847923\pi$
$30$	7.08392	1.29334
$31$	−2.99062	−0.537131	−0.268565	−	0.963261i	$-0.586550\pi$
$31$	−2.99062	−0.537131	−0.268565	+	0.963261i	$0.586550\pi$
$32$	−2.73408	−0.483322
$33$	−10.6149	−1.84782
$34$	2.38690	0.409350
$35$	−1.74314	−0.294645
$36$	13.1882	2.19804
$37$	−0.378497	−0.0622245	−0.0311123	−	0.999516i	$-0.509905\pi$
$37$	−0.378497	−0.0622245	−0.0311123	+	0.999516i	$0.509905\pi$
$38$	18.2119	2.95436
$39$	−12.8996	−2.06559
$40$	−6.47384	−1.02360
$41$	−10.7657	−1.68132	−0.840662	−	0.541561i	$-0.817834\pi$
$41$	−10.7657	−1.68132	−0.840662	+	0.541561i	$0.817834\pi$
$42$	−9.38878	−1.44872
$43$	−8.16165	−1.24464	−0.622320	−	0.782763i	$-0.713810\pi$
$43$	−8.16165	−1.24464	−0.622320	+	0.782763i	$0.713810\pi$
$44$	18.2978	2.75849
$45$	3.55307	0.529660
$46$	18.2004	2.68350
$47$	−2.08513	−0.304147	−0.152074	−	0.988369i	$-0.548595\pi$
$47$	−2.08513	−0.304147	−0.152074	+	0.988369i	$0.548595\pi$
$48$	−13.8452	−1.99838
$49$	−4.68970	−0.669957
$50$	9.21695	1.30347
$51$	2.35645	0.329969
$52$	22.2361	3.08359
$53$	−4.49261	−0.617108	−0.308554	−	0.951207i	$-0.599845\pi$
$53$	−4.49261	−0.617108	−0.308554	+	0.951207i	$0.599845\pi$
$54$	0.606383	0.0825183
$55$	4.92964	0.664713
$56$	8.58021	1.14658
$57$	17.9796	2.38146
$58$	23.9238	3.14134
$59$	8.78761	1.14405	0.572025	−	0.820236i	$-0.306158\pi$
$59$	8.78761	1.14405	0.572025	+	0.820236i	$0.306158\pi$
$60$	−12.0553	−1.55634
$61$	−9.50510	−1.21700	−0.608501	−	0.793553i	$-0.708229\pi$
$61$	−9.50510	−1.21700	−0.608501	+	0.793553i	$0.708229\pi$
$62$	7.48060	0.950037
$63$	−4.70911	−0.593292
$64$	−4.37428	−0.546785
$65$	5.99068	0.743052
$66$	26.5517	3.26829
$67$	3.02326	0.369350	0.184675	−	0.982800i	$-0.440877\pi$
$67$	3.02326	0.369350	0.184675	+	0.982800i	$0.440877\pi$
$68$	−4.06199	−0.492589
$69$	17.9682	2.16312
$70$	4.36021	0.521145
$71$	6.16004	0.731062	0.365531	−	0.930799i	$-0.380887\pi$
$71$	6.16004	0.731062	0.365531	+	0.930799i	$0.380887\pi$
$72$	−17.4892	−2.06112
$73$	8.77757	1.02734	0.513668	−	0.857989i	$-0.328286\pi$
$73$	8.77757	1.02734	0.513668	+	0.857989i	$0.328286\pi$
$74$	0.946755	0.110058
$75$	9.09938	1.05071
$76$	−30.9928	−3.55512
$77$	−6.53358	−0.744570
$78$	32.2666	3.65347
$79$	−10.4141	−1.17168	−0.585840	−	0.810426i	$-0.699235\pi$
$79$	−10.4141	−1.17168	−0.585840	+	0.810426i	$0.699235\pi$
$80$	6.42980	0.718873
$81$	−8.69586	−0.966206
$82$	26.9289	2.97380
$83$	0.662144	0.0726798	0.0363399	−	0.999339i	$-0.488430\pi$
$83$	0.662144	0.0726798	0.0363399	+	0.999339i	$0.488430\pi$
$84$	15.9777	1.74331
$85$	−1.09435	−0.118699
$86$	20.4152	2.20143
$87$	23.6186	2.53218
$88$	−24.2650	−2.58666
$89$	−17.5166	−1.85675	−0.928377	−	0.371639i	$-0.878796\pi$
$89$	−17.5166	−1.85675	−0.928377	+	0.371639i	$0.878796\pi$
$90$	−8.88748	−0.936823
$91$	−7.93984	−0.832321
$92$	−30.9732	−3.22918
$93$	7.38517	0.765807
$94$	5.21565	0.537953
$95$	−8.34985	−0.856677
$96$	6.75166	0.689089
$97$	7.80008	0.791978	0.395989	−	0.918255i	$-0.370402\pi$
$97$	7.80008	0.791978	0.395989	+	0.918255i	$0.370402\pi$
$98$	11.7306	1.18497
$99$	13.3175	1.33846
$100$	−15.6853	−1.56853
$101$	−4.88941	−0.486515	−0.243257	−	0.969962i	$-0.578216\pi$
$101$	−4.88941	−0.486515	−0.243257	+	0.969962i	$0.578216\pi$
$102$	−5.89432	−0.583624
$103$	14.5141	1.43011	0.715056	−	0.699067i	$-0.246401\pi$
$103$	14.5141	1.43011	0.715056	+	0.699067i	$0.246401\pi$
$104$	−29.4877	−2.89151
$105$	4.30459	0.420085
$106$	11.2376	1.09149
$107$	12.0952	1.16929	0.584643	−	0.811290i	$-0.301234\pi$
$107$	12.0952	1.16929	0.584643	+	0.811290i	$0.301234\pi$
$108$	−1.03194	−0.0992981
$109$	−12.1520	−1.16395	−0.581977	−	0.813205i	$-0.697721\pi$
$109$	−12.1520	−1.16395	−0.581977	+	0.813205i	$0.697721\pi$
$110$	−12.3308	−1.17569
$111$	0.934678	0.0887157
$112$	−8.52183	−0.805238
$113$	−7.99459	−0.752068	−0.376034	−	0.926606i	$-0.622712\pi$
$113$	−7.99459	−0.752068	−0.376034	+	0.926606i	$0.622712\pi$
$114$	−44.9734	−4.21214
$115$	−8.34456	−0.778134
$116$	−40.7132	−3.78012
$117$	16.1839	1.49620
$118$	−21.9809	−2.02351
$119$	1.45042	0.132959
$120$	15.9868	1.45939
$121$	7.47710	0.679737
$122$	23.7756	2.15254
$123$	26.5854	2.39712
$124$	−12.7304	−1.14322
$125$	−9.95996	−0.890846
$126$	11.7792	1.04937
$127$	7.59307	0.673776	0.336888	−	0.941545i	$-0.390626\pi$
$127$	7.59307	0.673776	0.336888	+	0.941545i	$0.390626\pi$
$128$	16.4098	1.45043
$129$	20.1548	1.77453
$130$	−14.9848	−1.31425
$131$	−5.66202	−0.494693	−0.247347	−	0.968927i	$-0.579559\pi$
$131$	−5.66202	−0.494693	−0.247347	+	0.968927i	$0.579559\pi$
$132$	−45.1853	−3.93288
$133$	11.0666	0.959596
$134$	−7.56225	−0.653279
$135$	−0.278016	−0.0239278
$136$	5.38669	0.461905
$137$	0.513255	0.0438503	0.0219252	−	0.999760i	$-0.493020\pi$
$137$	0.513255	0.0438503	0.0219252	+	0.999760i	$0.493020\pi$
$138$	−44.9448	−3.82596
$139$	17.6822	1.49978	0.749891	−	0.661562i	$-0.230106\pi$
$139$	17.6822	1.49978	0.749891	+	0.661562i	$0.230106\pi$
$140$	−7.42016	−0.627118
$141$	5.14912	0.433634
$142$	−15.4084	−1.29305
$143$	22.4540	1.87770
$144$	17.3702	1.44751
$145$	−10.9686	−0.910895
$146$	−21.9558	−1.81708
$147$	11.5810	0.955182
$148$	−1.61118	−0.132438
$149$	6.30923	0.516872	0.258436	−	0.966028i	$-0.416793\pi$
$149$	6.30923	0.516872	0.258436	+	0.966028i	$0.416793\pi$
$150$	−22.7608	−1.85841
$151$	−6.90161	−0.561645	−0.280823	−	0.959760i	$-0.590607\pi$
$151$	−6.90161	−0.561645	−0.280823	+	0.959760i	$0.590607\pi$
$152$	41.1002	3.33367
$153$	−2.95640	−0.239011
$154$	16.3428	1.31694
$155$	−3.42973	−0.275482
$156$	−54.9108	−4.39639
$157$	−11.7424	−0.937145	−0.468572	−	0.883425i	$-0.655231\pi$
$157$	−11.7424	−0.937145	−0.468572	+	0.883425i	$0.655231\pi$
$158$	26.0494	2.07238
$159$	11.0943	0.879833
$160$	−3.13552	−0.247885
$161$	11.0596	0.871618
$162$	21.7514	1.70895
$163$	7.73603	0.605933	0.302966	−	0.953001i	$-0.402023\pi$
$163$	7.73603	0.605933	0.302966	+	0.953001i	$0.402023\pi$
$164$	−45.8273	−3.57851
$165$	−12.1735	−0.947705
$166$	−1.65626	−0.128551
$167$	8.03602	0.621846	0.310923	−	0.950435i	$-0.399362\pi$
$167$	8.03602	0.621846	0.310923	+	0.950435i	$0.399362\pi$
$168$	−21.1884	−1.63472
$169$	14.2870	1.09900
$170$	2.73736	0.209946
$171$	−22.5572	−1.72499
$172$	−34.7423	−2.64908
$173$	12.7683	0.970756	0.485378	−	0.874304i	$-0.338682\pi$
$173$	12.7683	0.970756	0.485378	+	0.874304i	$0.338682\pi$
$174$	−59.0785	−4.47873
$175$	5.60075	0.423377
$176$	24.0999	1.81660
$177$	−21.7005	−1.63111
$178$	43.8152	3.28409
$179$	11.3745	0.850167	0.425084	−	0.905154i	$-0.360245\pi$
$179$	11.3745	0.850167	0.425084	+	0.905154i	$0.360245\pi$
$180$	15.1246	1.12732
$181$	19.8815	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$181$	19.8815	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$182$	19.8604	1.47215
$183$	23.4723	1.73512
$184$	41.0742	3.02803
$185$	−0.434071	−0.0319135
$186$	−18.4729	−1.35450
$187$	−4.10181	−0.299954
$188$	−8.87593	−0.647344
$189$	0.368473	0.0268025
$190$	20.8859	1.51523
$191$	14.0264	1.01492	0.507458	−	0.861676i	$-0.330585\pi$
$191$	14.0264	1.01492	0.507458	+	0.861676i	$0.330585\pi$
$192$	10.8021	0.779571
$193$	−7.07929	−0.509579	−0.254789	−	0.966997i	$-0.582006\pi$
$193$	−7.07929	−0.509579	−0.254789	+	0.966997i	$0.582006\pi$
$194$	−19.5108	−1.40079
$195$	−14.7937	−1.05940
$196$	−19.9630	−1.42593
$197$	17.7558	1.26505	0.632525	−	0.774540i	$-0.282019\pi$
$197$	17.7558	1.26505	0.632525	+	0.774540i	$0.282019\pi$
$198$	−33.3117	−2.36736
$199$	−5.43386	−0.385196	−0.192598	−	0.981278i	$-0.561691\pi$
$199$	−5.43386	−0.385196	−0.192598	+	0.981278i	$0.561691\pi$
$200$	20.8006	1.47082
$201$	−7.46579	−0.526596
$202$	12.2302	0.860511
$203$	14.5374	1.02033
$204$	10.0309	0.702302
$205$	−12.3464	−0.862312
$206$	−36.3048	−2.52948
$207$	−22.5429	−1.56684
$208$	29.2871	2.03070
$209$	−31.2966	−2.16483
$210$	−10.7673	−0.743015
$211$	14.3473	0.987710	0.493855	−	0.869544i	$-0.335587\pi$
$211$	14.3473	0.987710	0.493855	+	0.869544i	$0.335587\pi$
$212$	−19.1241	−1.31345
$213$	−15.2119	−1.04230
$214$	−30.2544	−2.06815
$215$	−9.36001	−0.638347
$216$	1.36847	0.0931127
$217$	4.54564	0.308578
$218$	30.3965	2.05871
$219$	−21.6757	−1.46471
$220$	20.9844	1.41477
$221$	−4.98466	−0.335305
$222$	−2.33796	−0.156914
$223$	−12.8031	−0.857362	−0.428681	−	0.903456i	$-0.641022\pi$
$223$	−12.8031	−0.857362	−0.428681	+	0.903456i	$0.641022\pi$
$224$	4.15571	0.277665
$225$	−11.4161	−0.761072
$226$	19.9973	1.33020
$227$	12.6129	0.837149	0.418575	−	0.908182i	$-0.362530\pi$
$227$	12.6129	0.837149	0.418575	+	0.908182i	$0.362530\pi$
$228$	76.5351	5.06866
$229$	−14.7034	−0.971627	−0.485813	−	0.874063i	$-0.661476\pi$
$229$	−14.7034	−0.971627	−0.485813	+	0.874063i	$0.661476\pi$
$230$	20.8727	1.37630
$231$	16.1343	1.06156
$232$	53.9906	3.54465
$233$	6.50926	0.426435	0.213218	−	0.977005i	$-0.431606\pi$
$233$	6.50926	0.426435	0.213218	+	0.977005i	$0.431606\pi$
$234$	−40.4816	−2.64637
$235$	−2.39129	−0.155990
$236$	37.4069	2.43498
$237$	25.7171	1.67051
$238$	−3.62800	−0.235169
$239$	4.96030	0.320855	0.160427	−	0.987048i	$-0.448713\pi$
$239$	4.96030	0.320855	0.160427	+	0.987048i	$0.448713\pi$
$240$	−15.8780	−1.02492
$241$	−13.5426	−0.872353	−0.436176	−	0.899861i	$-0.643668\pi$
$241$	−13.5426	−0.872353	−0.436176	+	0.899861i	$0.643668\pi$
$242$	−18.7029	−1.20227
$243$	22.2012	1.42421
$244$	−40.4611	−2.59025
$245$	−5.37828	−0.343606
$246$	−66.4995	−4.23985
$247$	−38.0328	−2.41997
$248$	16.8820	1.07201
$249$	−1.63513	−0.103622
$250$	24.9134	1.57566
$251$	15.8050	0.997604	0.498802	−	0.866716i	$-0.333773\pi$
$251$	15.8050	0.997604	0.498802	+	0.866716i	$0.333773\pi$
$252$	−20.0456	−1.26276
$253$	−31.2768	−1.96635
$254$	−18.9930	−1.19172
$255$	2.70244	0.169234
$256$	−32.2981	−2.01863
$257$	−24.8269	−1.54866	−0.774329	−	0.632783i	$-0.781913\pi$
$257$	−24.8269	−1.54866	−0.774329	+	0.632783i	$0.781913\pi$
$258$	−50.4142	−3.13865
$259$	0.575303	0.0357476
$260$	25.5010	1.58150
$261$	−29.6319	−1.83417
$262$	14.1627	0.874976
$263$	11.2174	0.691697	0.345849	−	0.938290i	$-0.387591\pi$
$263$	11.2174	0.691697	0.345849	+	0.938290i	$0.387591\pi$
$264$	59.9212	3.68789
$265$	−5.15226	−0.316501
$266$	−27.6815	−1.69726
$267$	43.2563	2.64724
$268$	12.8694	0.786121
$269$	9.97752	0.608340	0.304170	−	0.952618i	$-0.401621\pi$
$269$	9.97752	0.608340	0.304170	+	0.952618i	$0.401621\pi$
$270$	0.695417	0.0423217
$271$	−15.6620	−0.951397	−0.475698	−	0.879609i	$-0.657805\pi$
$271$	−15.6620	−0.951397	−0.475698	+	0.879609i	$0.657805\pi$
$272$	−5.35004	−0.324394
$273$	19.6070	1.18667
$274$	−1.28383	−0.0775592
$275$	−15.8390	−0.955131
$276$	76.4866	4.60395
$277$	6.28913	0.377877	0.188939	−	0.981989i	$-0.439495\pi$
$277$	6.28913	0.377877	0.188939	+	0.981989i	$0.439495\pi$
$278$	−44.2294	−2.65270
$279$	−9.26544	−0.554707
$280$	9.84003	0.588054
$281$	27.9467	1.66716	0.833579	−	0.552400i	$-0.186288\pi$
$281$	27.9467	1.66716	0.833579	+	0.552400i	$0.186288\pi$
$282$	−12.8798	−0.766979
$283$	11.7187	0.696605	0.348302	−	0.937382i	$-0.386758\pi$
$283$	11.7187	0.696605	0.348302	+	0.937382i	$0.386758\pi$
$284$	26.2219	1.55598
$285$	20.6195	1.22139
$286$	−56.1655	−3.32114
$287$	16.3635	0.965909
$288$	−8.47064	−0.499137
$289$	−16.0894	−0.946437
$290$	27.4364	1.61112
$291$	−19.2619	−1.12915
$292$	37.3641	2.18657
$293$	27.6261	1.61393	0.806966	−	0.590598i	$-0.201108\pi$
$293$	27.6261	1.61393	0.806966	+	0.590598i	$0.201108\pi$
$294$	−28.9681	−1.68945
$295$	10.0779	0.586757
$296$	2.13661	0.124188
$297$	−1.04205	−0.0604659
$298$	−15.7816	−0.914204
$299$	−38.0086	−2.19810
$300$	38.7340	2.23631
$301$	12.4054	0.715037
$302$	17.2634	0.993396
$303$	12.0741	0.693641
$304$	−40.8206	−2.34122
$305$	−10.9007	−0.624173
$306$	7.39501	0.422745
$307$	−16.2683	−0.928482	−0.464241	−	0.885709i	$-0.653673\pi$
$307$	−16.2683	−0.928482	−0.464241	+	0.885709i	$0.653673\pi$
$308$	−27.8120	−1.58473
$309$	−35.8417	−2.03896
$310$	8.57896	0.487252
$311$	−5.67284	−0.321677	−0.160838	−	0.986981i	$-0.551420\pi$
$311$	−5.67284	−0.321677	−0.160838	+	0.986981i	$0.551420\pi$
$312$	72.8184	4.12253
$313$	−27.9182	−1.57803	−0.789014	−	0.614375i	$-0.789408\pi$
$313$	−27.9182	−1.57803	−0.789014	+	0.614375i	$0.789408\pi$
$314$	29.3719	1.65755
$315$	−5.40054	−0.304286
$316$	−44.3306	−2.49379
$317$	−22.0148	−1.23647	−0.618236	−	0.785993i	$-0.712152\pi$
$317$	−22.0148	−1.23647	−0.618236	+	0.785993i	$0.712152\pi$
$318$	−27.7507	−1.55618
$319$	−41.1122	−2.30184
$320$	−5.01655	−0.280434
$321$	−29.8684	−1.66709
$322$	−27.6640	−1.54165
$323$	6.94766	0.386578
$324$	−37.0163	−2.05646
$325$	−19.2482	−1.06770
$326$	−19.3506	−1.07173
$327$	30.0088	1.65949
$328$	60.7725	3.35560
$329$	3.16933	0.174731
$330$	30.4502	1.67623
$331$	11.3874	0.625908	0.312954	−	0.949768i	$-0.398681\pi$
$331$	11.3874	0.625908	0.312954	+	0.949768i	$0.398681\pi$
$332$	2.81860	0.154691
$333$	−1.17265	−0.0642607
$334$	−20.1009	−1.09987
$335$	3.46716	0.189431
$336$	21.0442	1.14806
$337$	−15.2148	−0.828801	−0.414400	−	0.910095i	$-0.636009\pi$
$337$	−15.2148	−0.828801	−0.414400	+	0.910095i	$0.636009\pi$
$338$	−35.7367	−1.94382
$339$	19.7422	1.07225
$340$	−4.65841	−0.252638
$341$	−12.8552	−0.696147
$342$	56.4236	3.05104
$343$	17.7680	0.959379
$344$	46.0725	2.48406
$345$	20.6064	1.10941
$346$	−31.9381	−1.71700
$347$	21.0867	1.13199	0.565997	−	0.824407i	$-0.308491\pi$
$347$	21.0867	1.13199	0.565997	+	0.824407i	$0.308491\pi$
$348$	100.539	5.38946
$349$	27.8010	1.48815	0.744076	−	0.668095i	$-0.232890\pi$
$349$	27.8010	1.48815	0.744076	+	0.668095i	$0.232890\pi$
$350$	−14.0095	−0.748837
$351$	−1.26634	−0.0675921
$352$	−11.7524	−0.626407
$353$	−0.489071	−0.0260306	−0.0130153	−	0.999915i	$-0.504143\pi$
$353$	−0.489071	−0.0260306	−0.0130153	+	0.999915i	$0.504143\pi$
$354$	54.2808	2.88499
$355$	7.06450	0.374945
$356$	−74.5642	−3.95189
$357$	−3.58172	−0.189565
$358$	−28.4516	−1.50371
$359$	13.9075	0.734012	0.367006	−	0.930219i	$-0.380383\pi$
$359$	13.9075	0.734012	0.367006	+	0.930219i	$0.380383\pi$
$360$	−20.0571	−1.05710
$361$	34.0104	1.79002
$362$	−49.7308	−2.61379
$363$	−18.4643	−0.969125
$364$	−33.7981	−1.77150
$365$	10.0664	0.526898
$366$	−58.7126	−3.06896
$367$	−19.6090	−1.02358	−0.511790	−	0.859110i	$-0.671018\pi$
$367$	−19.6090	−1.02358	−0.511790	+	0.859110i	$0.671018\pi$
$368$	−40.7947	−2.12657
$369$	−33.3540	−1.73634
$370$	1.08577	0.0564463
$371$	6.82862	0.354524
$372$	31.4370	1.62993
$373$	−34.6828	−1.79581	−0.897903	−	0.440194i	$-0.854910\pi$
$373$	−34.6828	−1.79581	−0.897903	+	0.440194i	$0.854910\pi$
$374$	10.2601	0.530536
$375$	24.5956	1.27011
$376$	11.7706	0.607020
$377$	−49.9611	−2.57313
$378$	−0.921682	−0.0474062
$379$	27.1768	1.39598	0.697989	−	0.716108i	$-0.254078\pi$
$379$	27.1768	1.39598	0.697989	+	0.716108i	$0.254078\pi$
$380$	−35.5434	−1.82334
$381$	−18.7507	−0.960627
$382$	−35.0851	−1.79511
$383$	−5.15061	−0.263184	−0.131592	−	0.991304i	$-0.542009\pi$
$383$	−5.15061	−0.263184	−0.131592	+	0.991304i	$0.542009\pi$
$384$	−40.5231	−2.06794
$385$	−7.49289	−0.381873
$386$	17.7078	0.901305
$387$	−25.2862	−1.28537
$388$	33.2032	1.68564
$389$	26.3215	1.33455	0.667276	−	0.744811i	$-0.267460\pi$
$389$	26.3215	1.33455	0.667276	+	0.744811i	$0.267460\pi$
$390$	37.0042	1.87378
$391$	6.94326	0.351136
$392$	26.4734	1.33711
$393$	13.9821	0.705302
$394$	−44.4136	−2.23753
$395$	−11.9432	−0.600928
$396$	56.6895	2.84876
$397$	15.1147	0.758587	0.379294	−	0.925276i	$-0.376167\pi$
$397$	15.1147	0.758587	0.379294	+	0.925276i	$0.376167\pi$
$398$	13.5920	0.681306
$399$	−27.3284	−1.36813
$400$	−20.6591	−1.03295
$401$	−2.86941	−0.143292	−0.0716458	−	0.997430i	$-0.522825\pi$
$401$	−2.86941	−0.143292	−0.0716458	+	0.997430i	$0.522825\pi$
$402$	18.6746	0.931403
$403$	−15.6221	−0.778191
$404$	−20.8131	−1.03549
$405$	−9.97266	−0.495545
$406$	−36.3633	−1.80468
$407$	−1.62697	−0.0806459
$408$	−13.3022	−0.658555
$409$	−3.64109	−0.180041	−0.0900203	−	0.995940i	$-0.528693\pi$
$409$	−3.64109	−0.180041	−0.0900203	+	0.995940i	$0.528693\pi$
$410$	30.8828	1.52519
$411$	−1.26746	−0.0625190
$412$	61.7831	3.04383
$413$	−13.3569	−0.657249
$414$	56.3878	2.77131
$415$	0.759366	0.0372758
$416$	−14.2820	−0.700232
$417$	−43.6652	−2.13829
$418$	78.2839	3.82899
$419$	−28.0946	−1.37251	−0.686255	−	0.727361i	$-0.740746\pi$
$419$	−28.0946	−1.37251	−0.686255	+	0.727361i	$0.740746\pi$
$420$	18.3237	0.894105
$421$	7.96720	0.388297	0.194149	−	0.980972i	$-0.437806\pi$
$421$	7.96720	0.388297	0.194149	+	0.980972i	$0.437806\pi$
$422$	−35.8877	−1.74699
$423$	−6.46008	−0.314100
$424$	25.3608	1.23163
$425$	3.51618	0.170560
$426$	38.0503	1.84354
$427$	14.4474	0.699160
$428$	51.4865	2.48870
$429$	−55.4491	−2.67711
$430$	23.4127	1.12906
$431$	31.9521	1.53908	0.769539	−	0.638600i	$-0.220486\pi$
$431$	31.9521	1.53908	0.769539	+	0.638600i	$0.220486\pi$
$432$	−1.35916	−0.0653926
$433$	−21.0502	−1.01161	−0.505804	−	0.862648i	$-0.668804\pi$
$433$	−21.0502	−1.01161	−0.505804	+	0.862648i	$0.668804\pi$
$434$	−11.3703	−0.545790
$435$	27.0865	1.29870
$436$	−51.7285	−2.47735
$437$	52.9767	2.53422
$438$	54.2187	2.59067
$439$	−22.3981	−1.06901	−0.534503	−	0.845167i	$-0.679501\pi$
$439$	−22.3981	−1.06901	−0.534503	+	0.845167i	$0.679501\pi$
$440$	−27.8278	−1.32664
$441$	−14.5295	−0.691880
$442$	12.4684	0.593062
$443$	−0.906897	−0.0430880	−0.0215440	−	0.999768i	$-0.506858\pi$
$443$	−0.906897	−0.0430880	−0.0215440	+	0.999768i	$0.506858\pi$
$444$	3.97871	0.188821
$445$	−20.0885	−0.952287
$446$	32.0252	1.51644
$447$	−15.5803	−0.736923
$448$	6.64876	0.314124
$449$	−0.621704	−0.0293400	−0.0146700	−	0.999892i	$-0.504670\pi$
$449$	−0.621704	−0.0293400	−0.0146700	+	0.999892i	$0.504670\pi$
$450$	28.5557	1.34613
$451$	−46.2765	−2.17907
$452$	−34.0312	−1.60069
$453$	17.0432	0.800758
$454$	−31.5494	−1.48069
$455$	−9.10563	−0.426879
$456$	−101.495	−4.75293
$457$	35.3714	1.65460	0.827302	−	0.561758i	$-0.189875\pi$
$457$	35.3714	1.65460	0.827302	+	0.561758i	$0.189875\pi$
$458$	36.7784	1.71854
$459$	0.231329	0.0107975
$460$	−35.5209	−1.65617
$461$	1.83567	0.0854957	0.0427479	−	0.999086i	$-0.486389\pi$
$461$	1.83567	0.0854957	0.0427479	+	0.999086i	$0.486389\pi$
$462$	−40.3577	−1.87761
$463$	23.9737	1.11415	0.557077	−	0.830461i	$-0.311923\pi$
$463$	23.9737	1.11415	0.557077	+	0.830461i	$0.311923\pi$
$464$	−53.6232	−2.48940
$465$	8.46953	0.392765
$466$	−16.2820	−0.754247
$467$	41.0501	1.89957	0.949785	−	0.312903i	$-0.101302\pi$
$467$	41.0501	1.89957	0.949785	+	0.312903i	$0.101302\pi$
$468$	68.8911	3.18449
$469$	−4.59526	−0.212189
$470$	5.98145	0.275904
$471$	28.9972	1.33612
$472$	−49.6061	−2.28330
$473$	−35.0828	−1.61311
$474$	−64.3277	−2.95467
$475$	26.8283	1.23096
$476$	6.17410	0.282989
$477$	−13.9189	−0.637302
$478$	−12.4075	−0.567504
$479$	18.2207	0.832526	0.416263	−	0.909244i	$-0.363340\pi$
$479$	18.2207	0.832526	0.416263	+	0.909244i	$0.363340\pi$
$480$	7.74300	0.353418
$481$	−1.97715	−0.0901503
$482$	33.8747	1.54295
$483$	−27.3111	−1.24270
$484$	31.8284	1.44674
$485$	8.94536	0.406188
$486$	−55.5331	−2.51903
$487$	−15.2117	−0.689309	−0.344654	−	0.938730i	$-0.612004\pi$
$487$	−15.2117	−0.689309	−0.344654	+	0.938730i	$0.612004\pi$
$488$	53.6562	2.42890
$489$	−19.1037	−0.863900
$490$	13.4530	0.607744
$491$	−8.76298	−0.395468	−0.197734	−	0.980256i	$-0.563358\pi$
$491$	−8.76298	−0.395468	−0.197734	+	0.980256i	$0.563358\pi$
$492$	113.168	5.10201
$493$	9.12667	0.411045
$494$	95.1334	4.28026
$495$	15.2729	0.686464
$496$	−16.7672	−0.752868
$497$	−9.36305	−0.419990
$498$	4.09004	0.183279
$499$	−23.3100	−1.04350	−0.521750	−	0.853098i	$-0.674721\pi$
$499$	−23.3100	−1.04350	−0.521750	+	0.853098i	$0.674721\pi$
$500$	−42.3973	−1.89607
$501$	−19.8445	−0.886588
$502$	−39.5340	−1.76449
$503$	−34.1276	−1.52167	−0.760837	−	0.648943i	$-0.775211\pi$
$503$	−34.1276	−1.52167	−0.760837	+	0.648943i	$0.775211\pi$
$504$	26.5829	1.18410
$505$	−5.60732	−0.249522
$506$	78.2343	3.47794
$507$	−35.2809	−1.56688
$508$	32.3220	1.43406
$509$	−22.1359	−0.981157	−0.490579	−	0.871397i	$-0.663215\pi$
$509$	−22.1359	−0.981157	−0.490579	+	0.871397i	$0.663215\pi$
$510$	−6.75977	−0.299328
$511$	−13.3416	−0.590198
$512$	47.9695	2.11997
$513$	1.76503	0.0779280
$514$	62.1009	2.73915
$515$	16.6451	0.733472
$516$	85.7943	3.77688
$517$	−8.96293	−0.394189
$518$	−1.43904	−0.0632276
$519$	−31.5307	−1.38404
$520$	−33.8174	−1.48299
$521$	−10.9170	−0.478283	−0.239142	−	0.970985i	$-0.576866\pi$
$521$	−10.9170	−0.478283	−0.239142	+	0.970985i	$0.576866\pi$
$522$	74.1198	3.24414
$523$	−37.9029	−1.65738	−0.828688	−	0.559710i	$-0.810912\pi$
$523$	−37.9029	−1.65738	−0.828688	+	0.559710i	$0.810912\pi$
$524$	−24.1020	−1.05290
$525$	−13.8308	−0.603624
$526$	−28.0588	−1.22342
$527$	2.85377	0.124312
$528$	−59.5135	−2.58999
$529$	29.9431	1.30188
$530$	12.8876	0.559803
$531$	27.2255	1.18149
$532$	47.1081	2.04239
$533$	−56.2368	−2.43589
$534$	−108.199	−4.68224
$535$	13.8711	0.599701
$536$	−17.0663	−0.737152
$537$	−28.0886	−1.21211
$538$	−24.9573	−1.07599
$539$	−20.1587	−0.868296
$540$	−1.18345	−0.0509277
$541$	36.4672	1.56785	0.783924	−	0.620857i	$-0.213215\pi$
$541$	36.4672	1.56785	0.783924	+	0.620857i	$0.213215\pi$
$542$	39.1761	1.68276
$543$	−49.0964	−2.10693
$544$	2.60897	0.111859
$545$	−13.9363	−0.596965
$546$	−49.0441	−2.09889
$547$	3.17288	0.135662	0.0678312	−	0.997697i	$-0.478392\pi$
$547$	3.17288	0.135662	0.0678312	+	0.997697i	$0.478392\pi$
$548$	2.18481	0.0933305
$549$	−29.4484	−1.25683
$550$	39.6191	1.68936
$551$	69.6361	2.96660
$552$	−101.430	−4.31717
$553$	15.8291	0.673123
$554$	−15.7313	−0.668361
$555$	1.07192	0.0455003
$556$	75.2690	3.19212
$557$	30.0460	1.27309	0.636544	−	0.771240i	$-0.280363\pi$
$557$	30.0460	1.27309	0.636544	+	0.771240i	$0.280363\pi$
$558$	23.1762	0.981125
$559$	−42.6339	−1.80322
$560$	−9.77308	−0.412988
$561$	10.1292	0.427655
$562$	−69.9045	−2.94874
$563$	−14.1674	−0.597083	−0.298541	−	0.954397i	$-0.596500\pi$
$563$	−14.1674	−0.597083	−0.298541	+	0.954397i	$0.596500\pi$
$564$	21.9186	0.922941
$565$	−9.16842	−0.385718
$566$	−29.3126	−1.23210
$567$	13.2174	0.555079
$568$	−34.7734	−1.45906
$569$	16.0676	0.673588	0.336794	−	0.941578i	$-0.390657\pi$
$569$	16.0676	0.673588	0.336794	+	0.941578i	$0.390657\pi$
$570$	−51.5767	−2.16031
$571$	−13.2800	−0.555749	−0.277875	−	0.960617i	$-0.589630\pi$
$571$	−13.2800	−0.555749	−0.277875	+	0.960617i	$0.589630\pi$
$572$	95.5818	3.99648
$573$	−34.6375	−1.44700
$574$	−40.9310	−1.70843
$575$	26.8112	1.11811
$576$	−13.5523	−0.564677
$577$	−1.91689	−0.0798013	−0.0399006	−	0.999204i	$-0.512704\pi$
$577$	−1.91689	−0.0798013	−0.0399006	+	0.999204i	$0.512704\pi$
$578$	40.2454	1.67399
$579$	17.4819	0.726525
$580$	−46.6910	−1.93874
$581$	−1.00644	−0.0417540
$582$	48.1808	1.99716
$583$	−19.3115	−0.799801
$584$	−49.5494	−2.05037
$585$	18.5601	0.767367
$586$	−69.1026	−2.85460
$587$	−4.09362	−0.168962	−0.0844809	−	0.996425i	$-0.526923\pi$
$587$	−4.09362	−0.168962	−0.0844809	+	0.996425i	$0.526923\pi$
$588$	49.2976	2.03300
$589$	21.7742	0.897188
$590$	−25.2084	−1.03781
$591$	−43.8471	−1.80363
$592$	−2.12208	−0.0872168
$593$	23.3231	0.957766	0.478883	−	0.877879i	$-0.341042\pi$
$593$	23.3231	0.957766	0.478883	+	0.877879i	$0.341042\pi$
$594$	2.60654	0.106948
$595$	1.66338	0.0681918
$596$	26.8570	1.10010
$597$	13.4186	0.549188
$598$	95.0731	3.88783
$599$	−7.78770	−0.318197	−0.159098	−	0.987263i	$-0.550859\pi$
$599$	−7.78770	−0.318197	−0.159098	+	0.987263i	$0.550859\pi$
$600$	−51.3660	−2.09701
$601$	24.9476	1.01764	0.508818	−	0.860874i	$-0.330083\pi$
$601$	24.9476	1.01764	0.508818	+	0.860874i	$0.330083\pi$
$602$	−31.0304	−1.26470
$603$	9.36658	0.381436
$604$	−29.3786	−1.19540
$605$	8.57495	0.348621
$606$	−30.2017	−1.22686
$607$	−1.87093	−0.0759388	−0.0379694	−	0.999279i	$-0.512089\pi$
$607$	−1.87093	−0.0759388	−0.0379694	+	0.999279i	$0.512089\pi$
$608$	19.9063	0.807309
$609$	−35.8995	−1.45472
$610$	27.2665	1.10399
$611$	−10.8921	−0.440646
$612$	−12.5847	−0.508708
$613$	19.9108	0.804190	0.402095	−	0.915598i	$-0.368282\pi$
$613$	19.9108	0.804190	0.402095	+	0.915598i	$0.368282\pi$
$614$	40.6928	1.64223
$615$	30.4889	1.22943
$616$	36.8820	1.48602
$617$	−33.9817	−1.36805	−0.684026	−	0.729457i	$-0.739773\pi$
$617$	−33.9817	−1.36805	−0.684026	+	0.729457i	$0.739773\pi$
$618$	89.6528	3.60636
$619$	43.3364	1.74184	0.870918	−	0.491428i	$-0.163525\pi$
$619$	43.3364	1.74184	0.870918	+	0.491428i	$0.163525\pi$
$620$	−14.5996	−0.586333
$621$	1.76391	0.0707833
$622$	14.1898	0.568958
$623$	26.6246	1.06669
$624$	−72.3230	−2.89524
$625$	7.00156	0.280063
$626$	69.8332	2.79110
$627$	77.2853	3.08648
$628$	−49.9847	−1.99461
$629$	0.361178	0.0144011
$630$	13.5087	0.538199
$631$	28.9267	1.15155	0.575777	−	0.817607i	$-0.304700\pi$
$631$	28.9267	1.15155	0.575777	+	0.817607i	$0.304700\pi$
$632$	58.7877	2.33845
$633$	−35.4299	−1.40821
$634$	55.0667	2.18698
$635$	8.70795	0.345564
$636$	47.2258	1.87263
$637$	−24.4976	−0.970628
$638$	102.836	4.07133
$639$	19.0848	0.754984
$640$	18.8192	0.743895
$641$	38.1046	1.50504	0.752521	−	0.658568i	$-0.228837\pi$
$641$	38.1046	1.50504	0.752521	+	0.658568i	$0.228837\pi$
$642$	74.7116	2.94863
$643$	19.7648	0.779446	0.389723	−	0.920932i	$-0.372571\pi$
$643$	19.7648	0.779446	0.389723	+	0.920932i	$0.372571\pi$
$644$	47.0782	1.85514
$645$	23.1140	0.910115
$646$	−17.3786	−0.683751
$647$	13.7037	0.538747	0.269373	−	0.963036i	$-0.413183\pi$
$647$	13.7037	0.538747	0.269373	+	0.963036i	$0.413183\pi$
$648$	49.0881	1.92836
$649$	37.7736	1.48274
$650$	48.1465	1.88846
$651$	−11.2252	−0.439951
$652$	32.9305	1.28966
$653$	−3.32342	−0.130056	−0.0650278	−	0.997883i	$-0.520714\pi$
$653$	−3.32342	−0.130056	−0.0650278	+	0.997883i	$0.520714\pi$
$654$	−75.0627	−2.93518
$655$	−6.49337	−0.253717
$656$	−60.3590	−2.35662
$657$	27.1944	1.06095
$658$	−7.92761	−0.309051
$659$	−30.8379	−1.20127	−0.600637	−	0.799522i	$-0.705086\pi$
$659$	−30.8379	−1.20127	−0.600637	+	0.799522i	$0.705086\pi$
$660$	−51.8198	−2.01708
$661$	1.51322	0.0588573	0.0294287	−	0.999567i	$-0.490631\pi$
$661$	1.51322	0.0588573	0.0294287	+	0.999567i	$0.490631\pi$
$662$	−28.4839	−1.10706
$663$	12.3094	0.478056
$664$	−3.73780	−0.145055
$665$	12.6915	0.492155
$666$	2.93321	0.113659
$667$	69.5919	2.69461
$668$	34.2076	1.32353
$669$	31.6167	1.22237
$670$	−8.67260	−0.335052
$671$	−40.8577	−1.57729
$672$	−10.2623	−0.395877
$673$	−18.1084	−0.698028	−0.349014	−	0.937118i	$-0.613483\pi$
$673$	−18.1084	−0.698028	−0.349014	+	0.937118i	$0.613483\pi$
$674$	38.0575	1.46592
$675$	0.893272	0.0343821
$676$	60.8164	2.33909
$677$	26.9799	1.03692	0.518461	−	0.855101i	$-0.326505\pi$
$677$	26.9799	1.03692	0.518461	+	0.855101i	$0.326505\pi$
$678$	−49.3823	−1.89652
$679$	−11.8559	−0.454986
$680$	6.17761	0.236901
$681$	−31.1469	−1.19355
$682$	32.1554	1.23129
$683$	−12.8714	−0.492509	−0.246254	−	0.969205i	$-0.579200\pi$
$683$	−12.8714	−0.492509	−0.246254	+	0.969205i	$0.579200\pi$
$684$	−96.0210	−3.67145
$685$	0.588615	0.0224898
$686$	−44.4440	−1.69688
$687$	36.3092	1.38528
$688$	−45.7590	−1.74455
$689$	−23.4680	−0.894061
$690$	−51.5440	−1.96225
$691$	−11.7803	−0.448143	−0.224071	−	0.974573i	$-0.571935\pi$
$691$	−11.7803	−0.448143	−0.224071	+	0.974573i	$0.571935\pi$
$692$	54.3518	2.06615
$693$	−20.2421	−0.768935
$694$	−52.7454	−2.00219
$695$	20.2784	0.769204
$696$	−133.327	−5.05374
$697$	10.2731	0.389122
$698$	−69.5401	−2.63213
$699$	−16.0743	−0.607984
$700$	23.8411	0.901110
$701$	0.937512	0.0354093	0.0177047	−	0.999843i	$-0.494364\pi$
$701$	0.937512	0.0354093	0.0177047	+	0.999843i	$0.494364\pi$
$702$	3.16756	0.119552
$703$	2.75577	0.103936
$704$	−18.8028	−0.708659
$705$	5.90515	0.222401
$706$	1.22334	0.0460411
$707$	7.43174	0.279500
$708$	−92.3744	−3.47164
$709$	1.12744	0.0423418	0.0211709	−	0.999776i	$-0.493261\pi$
$709$	1.12744	0.0423418	0.0211709	+	0.999776i	$0.493261\pi$
$710$	−17.6708	−0.663174
$711$	−32.2647	−1.21002
$712$	98.8811	3.70573
$713$	21.7603	0.814931
$714$	8.95917	0.335288
$715$	25.7509	0.963030
$716$	48.4185	1.80949
$717$	−12.2492	−0.457454
$718$	−34.7877	−1.29827
$719$	−1.85839	−0.0693064	−0.0346532	−	0.999399i	$-0.511033\pi$
$719$	−1.85839	−0.0693064	−0.0346532	+	0.999399i	$0.511033\pi$
$720$	19.9206	0.742397
$721$	−22.0609	−0.821590
$722$	−85.0720	−3.16605
$723$	33.4426	1.24374
$724$	84.6313	3.14530
$725$	35.2425	1.30887
$726$	46.1858	1.71412
$727$	26.2379	0.973110	0.486555	−	0.873650i	$-0.338253\pi$
$727$	26.2379	0.973110	0.486555	+	0.873650i	$0.338253\pi$
$728$	44.8204	1.66115
$729$	−28.7372	−1.06434
$730$	−25.1796	−0.931937
$731$	7.78819	0.288056
$732$	99.9165	3.69302
$733$	−25.5859	−0.945037	−0.472518	−	0.881321i	$-0.656655\pi$
$733$	−25.5859	−0.945037	−0.472518	+	0.881321i	$0.656655\pi$
$734$	49.0490	1.81043
$735$	13.2814	0.489891
$736$	19.8937	0.733292
$737$	12.9955	0.478695
$738$	83.4302	3.07111
$739$	22.6496	0.833178	0.416589	−	0.909095i	$-0.363225\pi$
$739$	22.6496	0.833178	0.416589	+	0.909095i	$0.363225\pi$
$740$	−1.84774	−0.0679244
$741$	93.9199	3.45023
$742$	−17.0808	−0.627056
$743$	−22.6262	−0.830076	−0.415038	−	0.909804i	$-0.636232\pi$
$743$	−22.6262	−0.830076	−0.415038	+	0.909804i	$0.636232\pi$
$744$	−41.6893	−1.52840
$745$	7.23560	0.265092
$746$	86.7539	3.17629
$747$	2.05143	0.0750581
$748$	−17.4605	−0.638418
$749$	−18.3843	−0.671748
$750$	−61.5223	−2.24648
$751$	−24.7330	−0.902518	−0.451259	−	0.892393i	$-0.649025\pi$
$751$	−24.7330	−0.902518	−0.451259	+	0.892393i	$0.649025\pi$
$752$	−11.6905	−0.426308
$753$	−39.0297	−1.42232
$754$	124.970	4.55115
$755$	−7.91497	−0.288055
$756$	1.56851	0.0570461
$757$	21.9185	0.796641	0.398320	−	0.917246i	$-0.369593\pi$
$757$	21.9185	0.796641	0.398320	+	0.917246i	$0.369593\pi$
$758$	−67.9788	−2.46910
$759$	77.2363	2.80350
$760$	47.1349	1.70976
$761$	19.1465	0.694061	0.347031	−	0.937854i	$-0.387190\pi$
$761$	19.1465	0.694061	0.347031	+	0.937854i	$0.387190\pi$
$762$	46.9021	1.69909
$763$	18.4707	0.668684
$764$	59.7074	2.16014
$765$	−3.39049	−0.122583
$766$	12.8835	0.465500
$767$	45.9038	1.65749
$768$	79.7586	2.87804
$769$	1.41399	0.0509899	0.0254950	−	0.999675i	$-0.491884\pi$
$769$	1.41399	0.0509899	0.0254950	+	0.999675i	$0.491884\pi$
$770$	18.7424	0.675428
$771$	61.3087	2.20798
$772$	−30.1350	−1.08458
$773$	31.3078	1.12606	0.563031	−	0.826436i	$-0.309635\pi$
$773$	31.3078	1.12606	0.563031	+	0.826436i	$0.309635\pi$
$774$	63.2497	2.27346
$775$	11.0198	0.395842
$776$	−44.0315	−1.58064
$777$	−1.42068	−0.0509666
$778$	−65.8393	−2.36045
$779$	78.3833	2.80837
$780$	−62.9733	−2.25481
$781$	26.4789	0.947490
$782$	−17.3676	−0.621062
$783$	2.31860	0.0828600
$784$	−26.2932	−0.939044
$785$	−13.4665	−0.480640
$786$	−34.9741	−1.24748
$787$	16.7058	0.595499	0.297749	−	0.954644i	$-0.403764\pi$
$787$	16.7058	0.595499	0.297749	+	0.954644i	$0.403764\pi$
$788$	75.5826	2.69252
$789$	−27.7009	−0.986177
$790$	29.8742	1.06288
$791$	12.1515	0.432058
$792$	−75.1771	−2.67130
$793$	−49.6517	−1.76318
$794$	−37.8073	−1.34173
$795$	12.7232	0.451246
$796$	−23.1307	−0.819847
$797$	−39.0352	−1.38270	−0.691349	−	0.722521i	$-0.742983\pi$
$797$	−39.0352	−1.38270	−0.691349	+	0.722521i	$0.742983\pi$
$798$	68.3580	2.41985
$799$	1.98972	0.0703912
$800$	10.0745	0.356187
$801$	−54.2693	−1.91751
$802$	7.17742	0.253444
$803$	37.7304	1.33148
$804$	−31.7802	−1.12080
$805$	12.6834	0.447033
$806$	39.0763	1.37641
$807$	−24.6390	−0.867333
$808$	27.6007	0.970990
$809$	44.9543	1.58051	0.790254	−	0.612779i	$-0.209948\pi$
$809$	44.9543	1.58051	0.790254	+	0.612779i	$0.209948\pi$
$810$	24.9451	0.876483
$811$	−26.1932	−0.919767	−0.459884	−	0.887979i	$-0.652109\pi$
$811$	−26.1932	−0.919767	−0.459884	+	0.887979i	$0.652109\pi$
$812$	61.8827	2.17166
$813$	38.6764	1.35644
$814$	4.06963	0.142640
$815$	8.87190	0.310769
$816$	13.2117	0.462500
$817$	59.4235	2.07897
$818$	9.10767	0.318442
$819$	−24.5990	−0.859557
$820$	−52.5560	−1.83534
$821$	1.33782	0.0466902	0.0233451	−	0.999727i	$-0.492568\pi$
$821$	1.33782	0.0466902	0.0233451	+	0.999727i	$0.492568\pi$
$822$	3.17036	0.110579
$823$	−12.5967	−0.439092	−0.219546	−	0.975602i	$-0.570458\pi$
$823$	−12.5967	−0.439092	−0.219546	+	0.975602i	$0.570458\pi$
$824$	−81.9318	−2.85423
$825$	39.1137	1.36176
$826$	33.4103	1.16249
$827$	21.9545	0.763433	0.381717	−	0.924279i	$-0.375333\pi$
$827$	21.9545	0.763433	0.381717	+	0.924279i	$0.375333\pi$
$828$	−95.9601	−3.33484
$829$	−26.5542	−0.922266	−0.461133	−	0.887331i	$-0.652557\pi$
$829$	−26.5542	−0.922266	−0.461133	+	0.887331i	$0.652557\pi$
$830$	−1.89944	−0.0659306
$831$	−15.5307	−0.538753
$832$	−22.8499	−0.792178
$833$	4.47511	0.155053
$834$	109.222	3.78205
$835$	9.21594	0.318931
$836$	−133.223	−4.60760
$837$	0.724991	0.0250594
$838$	70.2745	2.42759
$839$	52.0072	1.79549	0.897744	−	0.440517i	$-0.145205\pi$
$839$	52.0072	1.79549	0.897744	+	0.440517i	$0.145205\pi$
$840$	−24.2994	−0.838410
$841$	62.4762	2.15435
$842$	−19.9288	−0.686791
$843$	−69.0128	−2.37693
$844$	61.0733	2.10223
$845$	16.3847	0.563650
$846$	16.1590	0.555556
$847$	−11.3649	−0.390504
$848$	−25.1883	−0.864968
$849$	−28.9387	−0.993174
$850$	−8.79520	−0.301673
$851$	2.75402	0.0944066
$852$	−64.7536	−2.21842
$853$	41.2847	1.41356	0.706780	−	0.707433i	$-0.250147\pi$
$853$	41.2847	1.41356	0.706780	+	0.707433i	$0.250147\pi$
$854$	−36.1381	−1.23662
$855$	−25.8692	−0.884710
$856$	−68.2774	−2.33367
$857$	−22.2581	−0.760322	−0.380161	−	0.924920i	$-0.624131\pi$
$857$	−22.2581	−0.760322	−0.380161	+	0.924920i	$0.624131\pi$
$858$	138.698	4.73506
$859$	−50.9050	−1.73685	−0.868427	−	0.495816i	$-0.834869\pi$
$859$	−50.9050	−1.73685	−0.868427	+	0.495816i	$0.834869\pi$
$860$	−39.8435	−1.35865
$861$	−40.4089	−1.37713
$862$	−79.9235	−2.72221
$863$	27.2241	0.926720	0.463360	−	0.886170i	$-0.346644\pi$
$863$	27.2241	0.926720	0.463360	+	0.886170i	$0.346644\pi$
$864$	0.662801	0.0225489
$865$	14.6431	0.497879
$866$	52.6540	1.78926
$867$	39.7320	1.34937
$868$	19.3498	0.656774
$869$	−44.7651	−1.51855
$870$	−67.7528	−2.29704
$871$	15.7926	0.535111
$872$	68.5982	2.32303
$873$	24.1660	0.817894
$874$	−132.514	−4.48234
$875$	15.1388	0.511785
$876$	−92.2688	−3.11747
$877$	4.46508	0.150775	0.0753875	−	0.997154i	$-0.475981\pi$
$877$	4.46508	0.150775	0.0753875	+	0.997154i	$0.475981\pi$
$878$	56.0257	1.89078
$879$	−68.2211	−2.30104
$880$	27.6385	0.931693
$881$	−46.1718	−1.55557	−0.777784	−	0.628531i	$-0.783656\pi$
$881$	−46.1718	−1.55557	−0.777784	+	0.628531i	$0.783656\pi$
$882$	36.3434	1.22375
$883$	−6.31339	−0.212462	−0.106231	−	0.994341i	$-0.533878\pi$
$883$	−6.31339	−0.212462	−0.106231	+	0.994341i	$0.533878\pi$
$884$	−21.2186	−0.713659
$885$	−24.8868	−0.836561
$886$	2.26847	0.0762108
$887$	−2.81780	−0.0946124	−0.0473062	−	0.998880i	$-0.515064\pi$
$887$	−2.81780	−0.0946124	−0.0473062	+	0.998880i	$0.515064\pi$
$888$	−5.27626	−0.177060
$889$	−11.5412	−0.387080
$890$	50.2485	1.68433
$891$	−37.3791	−1.25225
$892$	−54.5001	−1.82480
$893$	15.1815	0.508028
$894$	38.9719	1.30341
$895$	13.0446	0.436031
$896$	−24.9423	−0.833265
$897$	93.8603	3.13391
$898$	1.55510	0.0518944
$899$	28.6032	0.953971
$900$	−48.5957	−1.61986
$901$	4.28704	0.142822
$902$	115.754	3.85418
$903$	−30.6346	−1.01945
$904$	45.1295	1.50098
$905$	22.8007	0.757922
$906$	−42.6310	−1.41632
$907$	−23.4053	−0.777159	−0.388580	−	0.921415i	$-0.627034\pi$
$907$	−23.4053	−0.777159	−0.388580	+	0.921415i	$0.627034\pi$
$908$	53.6904	1.78178
$909$	−15.1482	−0.502435
$910$	22.7764	0.755031
$911$	−38.5067	−1.27578	−0.637892	−	0.770126i	$-0.720194\pi$
$911$	−38.5067	−1.27578	−0.637892	+	0.770126i	$0.720194\pi$
$912$	100.804	3.33796
$913$	2.84623	0.0941964
$914$	−88.4764	−2.92654
$915$	26.9187	0.889906
$916$	−62.5890	−2.06800
$917$	8.60608	0.284198
$918$	−0.578636	−0.0190978
$919$	8.46133	0.279114	0.139557	−	0.990214i	$-0.455432\pi$
$919$	8.46133	0.279114	0.139557	+	0.990214i	$0.455432\pi$
$920$	47.1050	1.55301
$921$	40.1737	1.32377
$922$	−4.59167	−0.151218
$923$	32.1781	1.05916
$924$	68.6802	2.25941
$925$	1.39468	0.0458568
$926$	−59.9668	−1.97063
$927$	44.9670	1.47691
$928$	26.1496	0.858403
$929$	23.4160	0.768253	0.384127	−	0.923280i	$-0.374503\pi$
$929$	23.4160	0.768253	0.384127	+	0.923280i	$0.374503\pi$
$930$	−21.1853	−0.694693
$931$	34.1449	1.11905
$932$	27.7084	0.907620
$933$	14.0088	0.458626
$934$	−102.681	−3.35982
$935$	−4.70407	−0.153840
$936$	−91.3580	−2.98613
$937$	−3.32143	−0.108506	−0.0542532	−	0.998527i	$-0.517278\pi$
$937$	−3.32143	−0.108506	−0.0542532	+	0.998527i	$0.517278\pi$
$938$	11.4944	0.375305
$939$	68.9424	2.24985
$940$	−10.1792	−0.332008
$941$	59.4056	1.93657	0.968283	−	0.249856i	$-0.0803833\pi$
$941$	59.4056	1.93657	0.968283	+	0.249856i	$0.0803833\pi$
$942$	−72.5323	−2.36323
$943$	78.3336	2.55089
$944$	49.2686	1.60356
$945$	0.422575	0.0137464
$946$	87.7547	2.85315
$947$	39.8468	1.29485	0.647424	−	0.762130i	$-0.275846\pi$
$947$	39.8468	1.29485	0.647424	+	0.762130i	$0.275846\pi$
$948$	109.472	3.55549
$949$	45.8513	1.48840
$950$	−67.1070	−2.17724
$951$	54.3643	1.76288
$952$	−8.18760	−0.265361
$953$	−25.5502	−0.827651	−0.413825	−	0.910356i	$-0.635808\pi$
$953$	−25.5502	−0.827651	−0.413825	+	0.910356i	$0.635808\pi$
$954$	34.8160	1.12721
$955$	16.0859	0.520528
$956$	21.1149	0.682904
$957$	101.524	3.28182
$958$	−45.5765	−1.47251
$959$	−0.780130	−0.0251917
$960$	12.3881	0.399824
$961$	−22.0562	−0.711490
$962$	4.94556	0.159451
$963$	37.4730	1.20755
$964$	−57.6476	−1.85671
$965$	−8.11873	−0.261351
$966$	68.3147	2.19799
$967$	−35.9016	−1.15452	−0.577259	−	0.816561i	$-0.695878\pi$
$967$	−35.9016	−1.15452	−0.577259	+	0.816561i	$0.695878\pi$
$968$	−42.2082	−1.35662
$969$	−17.1569	−0.551159
$970$	−22.3755	−0.718434
$971$	1.57454	0.0505295	0.0252647	−	0.999681i	$-0.491957\pi$
$971$	1.57454	0.0505295	0.0252647	+	0.999681i	$0.491957\pi$
$972$	94.5056	3.03127
$973$	−26.8763	−0.861615
$974$	38.0499	1.21920
$975$	47.5324	1.52225
$976$	−53.2912	−1.70581
$977$	−16.7855	−0.537015	−0.268507	−	0.963278i	$-0.586530\pi$
$977$	−16.7855	−0.537015	−0.268507	+	0.963278i	$0.586530\pi$
$978$	47.7852	1.52800
$979$	−75.2951	−2.40644
$980$	−22.8941	−0.731327
$981$	−37.6490	−1.20204
$982$	21.9193	0.699474
$983$	12.4342	0.396588	0.198294	−	0.980143i	$-0.436460\pi$
$983$	12.4342	0.396588	0.198294	+	0.980143i	$0.436460\pi$
$984$	−150.074	−4.78420
$985$	20.3629	0.648815
$986$	−22.8290	−0.727025
$987$	−7.82649	−0.249120
$988$	−161.897	−5.15063
$989$	59.3858	1.88836
$990$	−38.2028	−1.21417
$991$	−31.1547	−0.989662	−0.494831	−	0.868989i	$-0.664770\pi$
$991$	−31.1547	−0.989662	−0.494831	+	0.868989i	$0.664770\pi$
$992$	8.17659	0.259607
$993$	−28.1206	−0.892379
$994$	23.4203	0.742847
$995$	−6.23171	−0.197558
$996$	−6.96038	−0.220548
$997$	16.0283	0.507621	0.253810	−	0.967254i	$-0.418316\pi$
$997$	16.0283	0.507621	0.253810	+	0.967254i	$0.418316\pi$
$998$	58.3067	1.84567
$999$	0.0917559	0.00290303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.20	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.50135 q^{2} -2.46945 q^{3} +4.25678 q^{4} +1.14683 q^{5} +6.17696 q^{6} -1.51997 q^{7} -5.64500 q^{8} +3.09817 q^{9} +O(q^{10})\)	\(q-2.50135 q^{2} -2.46945 q^{3} +4.25678 q^{4} +1.14683 q^{5} +6.17696 q^{6} -1.51997 q^{7} -5.64500 q^{8} +3.09817 q^{9} -2.86862 q^{10} +4.29850 q^{11} -10.5119 q^{12} +5.22369 q^{13} +3.80198 q^{14} -2.83203 q^{15} +5.60659 q^{16} -0.954242 q^{17} -7.74962 q^{18} -7.28082 q^{19} +4.88179 q^{20} +3.75348 q^{21} -10.7521 q^{22} -7.27620 q^{23} +13.9400 q^{24} -3.68478 q^{25} -13.0663 q^{26} -0.242422 q^{27} -6.47016 q^{28} -9.56432 q^{29} +7.08392 q^{30} -2.99062 q^{31} -2.73408 q^{32} -10.6149 q^{33} +2.38690 q^{34} -1.74314 q^{35} +13.1882 q^{36} -0.378497 q^{37} +18.2119 q^{38} -12.8996 q^{39} -6.47384 q^{40} -10.7657 q^{41} -9.38878 q^{42} -8.16165 q^{43} +18.2978 q^{44} +3.55307 q^{45} +18.2004 q^{46} -2.08513 q^{47} -13.8452 q^{48} -4.68970 q^{49} +9.21695 q^{50} +2.35645 q^{51} +22.2361 q^{52} -4.49261 q^{53} +0.606383 q^{54} +4.92964 q^{55} +8.58021 q^{56} +17.9796 q^{57} +23.9238 q^{58} +8.78761 q^{59} -12.0553 q^{60} -9.50510 q^{61} +7.48060 q^{62} -4.70911 q^{63} -4.37428 q^{64} +5.99068 q^{65} +26.5517 q^{66} +3.02326 q^{67} -4.06199 q^{68} +17.9682 q^{69} +4.36021 q^{70} +6.16004 q^{71} -17.4892 q^{72} +8.77757 q^{73} +0.946755 q^{74} +9.09938 q^{75} -30.9928 q^{76} -6.53358 q^{77} +32.2666 q^{78} -10.4141 q^{79} +6.42980 q^{80} -8.69586 q^{81} +26.9289 q^{82} +0.662144 q^{83} +15.9777 q^{84} -1.09435 q^{85} +20.4152 q^{86} +23.6186 q^{87} -24.2650 q^{88} -17.5166 q^{89} -8.88748 q^{90} -7.93984 q^{91} -30.9732 q^{92} +7.38517 q^{93} +5.21565 q^{94} -8.34985 q^{95} +6.75166 q^{96} +7.80008 q^{97} +11.7306 q^{98} +13.3175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 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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