LMFDB - Embedded newform 8035.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} +O(q^{10})$	\(q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} -2.69988 q^{10} +2.05516 q^{11} -2.61642 q^{12} -4.61042 q^{13} -9.33708 q^{14} -0.494659 q^{15} +13.3984 q^{16} +0.0376674 q^{17} +7.43900 q^{18} -6.34243 q^{19} +5.28933 q^{20} -1.71070 q^{21} -5.54869 q^{22} -5.72394 q^{23} +4.39297 q^{24} +1.00000 q^{25} +12.4476 q^{26} +2.84692 q^{27} +18.2923 q^{28} +7.38384 q^{29} +1.33552 q^{30} +0.978803 q^{31} -18.4124 q^{32} -1.01661 q^{33} -0.101697 q^{34} +3.45834 q^{35} -14.5738 q^{36} -2.58132 q^{37} +17.1238 q^{38} +2.28059 q^{39} -8.88080 q^{40} -1.56398 q^{41} +4.61868 q^{42} +2.20743 q^{43} +10.8705 q^{44} -2.75531 q^{45} +15.4539 q^{46} -11.2376 q^{47} -6.62764 q^{48} +4.96010 q^{49} -2.69988 q^{50} -0.0186325 q^{51} -24.3860 q^{52} +10.5759 q^{53} -7.68633 q^{54} +2.05516 q^{55} -30.7128 q^{56} +3.13734 q^{57} -19.9355 q^{58} -1.30853 q^{59} -2.61642 q^{60} -8.58263 q^{61} -2.64265 q^{62} -9.52880 q^{63} +22.9144 q^{64} -4.61042 q^{65} +2.74471 q^{66} -13.5641 q^{67} +0.199236 q^{68} +2.83140 q^{69} -9.33708 q^{70} +0.0361528 q^{71} +24.4694 q^{72} -6.51047 q^{73} +6.96925 q^{74} -0.494659 q^{75} -33.5472 q^{76} +7.10745 q^{77} -6.15730 q^{78} +8.52645 q^{79} +13.3984 q^{80} +6.85768 q^{81} +4.22256 q^{82} +6.10541 q^{83} -9.04846 q^{84} +0.0376674 q^{85} -5.95980 q^{86} -3.65248 q^{87} -18.2515 q^{88} +12.1970 q^{89} +7.43900 q^{90} -15.9444 q^{91} -30.2758 q^{92} -0.484174 q^{93} +30.3400 q^{94} -6.34243 q^{95} +9.10787 q^{96} -6.54569 q^{97} -13.3917 q^{98} -5.66262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.69988	−1.90910	−0.954551	−	0.298049i	$-0.903664\pi$
$2$	−2.69988	−1.90910	−0.954551	+	0.298049i	$0.903664\pi$
$3$	−0.494659	−0.285592	−0.142796	−	0.989752i	$-0.545609\pi$
$3$	−0.494659	−0.285592	−0.142796	+	0.989752i	$0.545609\pi$
$4$	5.28933	2.64467
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.33552	0.545223
$7$	3.45834	1.30713	0.653564	−	0.756871i	$-0.273273\pi$
$7$	3.45834	1.30713	0.653564	+	0.756871i	$0.273273\pi$
$8$	−8.88080	−3.13984
$9$	−2.75531	−0.918437
$10$	−2.69988	−0.853776
$11$	2.05516	0.619655	0.309828	−	0.950793i	$-0.399729\pi$
$11$	2.05516	0.619655	0.309828	+	0.950793i	$0.399729\pi$
$12$	−2.61642	−0.755295
$13$	−4.61042	−1.27870	−0.639350	−	0.768916i	$-0.720796\pi$
$13$	−4.61042	−1.27870	−0.639350	+	0.768916i	$0.720796\pi$
$14$	−9.33708	−2.49544
$15$	−0.494659	−0.127720
$16$	13.3984	3.34960
$17$	0.0376674	0.00913569	0.00456785	−	0.999990i	$-0.498546\pi$
$17$	0.0376674	0.00913569	0.00456785	+	0.999990i	$0.498546\pi$
$18$	7.43900	1.75339
$19$	−6.34243	−1.45505	−0.727526	−	0.686080i	$-0.759330\pi$
$19$	−6.34243	−1.45505	−0.727526	+	0.686080i	$0.759330\pi$
$20$	5.28933	1.18273
$21$	−1.71070	−0.373305
$22$	−5.54869	−1.18298
$23$	−5.72394	−1.19352	−0.596762	−	0.802418i	$-0.703546\pi$
$23$	−5.72394	−1.19352	−0.596762	+	0.802418i	$0.703546\pi$
$24$	4.39297	0.896711
$25$	1.00000	0.200000
$26$	12.4476	2.44117
$27$	2.84692	0.547890
$28$	18.2923	3.45692
$29$	7.38384	1.37114	0.685572	−	0.728005i	$-0.259552\pi$
$29$	7.38384	1.37114	0.685572	+	0.728005i	$0.259552\pi$
$30$	1.33552	0.243831
$31$	0.978803	0.175798	0.0878991	−	0.996129i	$-0.471985\pi$
$31$	0.978803	0.175798	0.0878991	+	0.996129i	$0.471985\pi$
$32$	−18.4124	−3.25488
$33$	−1.01661	−0.176968
$34$	−0.101697	−0.0174410
$35$	3.45834	0.584566
$36$	−14.5738	−2.42896
$37$	−2.58132	−0.424367	−0.212183	−	0.977230i	$-0.568057\pi$
$37$	−2.58132	−0.424367	−0.212183	+	0.977230i	$0.568057\pi$
$38$	17.1238	2.77784
$39$	2.28059	0.365186
$40$	−8.88080	−1.40418
$41$	−1.56398	−0.244253	−0.122127	−	0.992515i	$-0.538971\pi$
$41$	−1.56398	−0.244253	−0.122127	+	0.992515i	$0.538971\pi$
$42$	4.61868	0.712677
$43$	2.20743	0.336631	0.168315	−	0.985733i	$-0.446167\pi$
$43$	2.20743	0.336631	0.168315	+	0.985733i	$0.446167\pi$
$44$	10.8705	1.63878
$45$	−2.75531	−0.410738
$46$	15.4539	2.27856
$47$	−11.2376	−1.63917	−0.819583	−	0.572960i	$-0.805795\pi$
$47$	−11.2376	−1.63917	−0.819583	+	0.572960i	$0.805795\pi$
$48$	−6.62764	−0.956617
$49$	4.96010	0.708585
$50$	−2.69988	−0.381820
$51$	−0.0186325	−0.00260908
$52$	−24.3860	−3.38174
$53$	10.5759	1.45271	0.726356	−	0.687318i	$-0.241212\pi$
$53$	10.5759	1.45271	0.726356	+	0.687318i	$0.241212\pi$
$54$	−7.68633	−1.04598
$55$	2.05516	0.277118
$56$	−30.7128	−4.10417
$57$	3.13734	0.415551
$58$	−19.9355	−2.61765
$59$	−1.30853	−0.170357	−0.0851783	−	0.996366i	$-0.527146\pi$
$59$	−1.30853	−0.170357	−0.0851783	+	0.996366i	$0.527146\pi$
$60$	−2.61642	−0.337778
$61$	−8.58263	−1.09889	−0.549447	−	0.835529i	$-0.685161\pi$
$61$	−8.58263	−1.09889	−0.549447	+	0.835529i	$0.685161\pi$
$62$	−2.64265	−0.335616
$63$	−9.52880	−1.20052
$64$	22.9144	2.86431
$65$	−4.61042	−0.571852
$66$	2.74471	0.337851
$67$	−13.5641	−1.65712	−0.828559	−	0.559902i	$-0.810839\pi$
$67$	−13.5641	−1.65712	−0.828559	+	0.559902i	$0.810839\pi$
$68$	0.199236	0.0241609
$69$	2.83140	0.340861
$70$	−9.33708	−1.11600
$71$	0.0361528	0.00429054	0.00214527	−	0.999998i	$-0.499317\pi$
$71$	0.0361528	0.00429054	0.00214527	+	0.999998i	$0.499317\pi$
$72$	24.4694	2.88374
$73$	−6.51047	−0.761993	−0.380996	−	0.924576i	$-0.624419\pi$
$73$	−6.51047	−0.761993	−0.380996	+	0.924576i	$0.624419\pi$
$74$	6.96925	0.810159
$75$	−0.494659	−0.0571183
$76$	−33.5472	−3.84813
$77$	7.10745	0.809969
$78$	−6.15730	−0.697177
$79$	8.52645	0.959301	0.479650	−	0.877460i	$-0.340764\pi$
$79$	8.52645	0.959301	0.479650	+	0.877460i	$0.340764\pi$
$80$	13.3984	1.49799
$81$	6.85768	0.761965
$82$	4.22256	0.466304
$83$	6.10541	0.670155	0.335078	−	0.942190i	$-0.391237\pi$
$83$	6.10541	0.670155	0.335078	+	0.942190i	$0.391237\pi$
$84$	−9.04846	−0.987268
$85$	0.0376674	0.00408561
$86$	−5.95980	−0.642662
$87$	−3.65248	−0.391587
$88$	−18.2515	−1.94562
$89$	12.1970	1.29287	0.646437	−	0.762967i	$-0.276258\pi$
$89$	12.1970	1.29287	0.646437	+	0.762967i	$0.276258\pi$
$90$	7.43900	0.784140
$91$	−15.9444	−1.67143
$92$	−30.2758	−3.15648
$93$	−0.484174	−0.0502065
$94$	30.3400	3.12933
$95$	−6.34243	−0.650719
$96$	9.10787	0.929568
$97$	−6.54569	−0.664614	−0.332307	−	0.943171i	$-0.607827\pi$
$97$	−6.54569	−0.664614	−0.332307	+	0.943171i	$0.607827\pi$
$98$	−13.3917	−1.35276
$99$	−5.66262	−0.569115
$100$	5.28933	0.528933
$101$	8.78624	0.874263	0.437132	−	0.899397i	$-0.355994\pi$
$101$	8.78624	0.874263	0.437132	+	0.899397i	$0.355994\pi$
$102$	0.0503056	0.00498099
$103$	12.3705	1.21890	0.609452	−	0.792823i	$-0.291389\pi$
$103$	12.3705	1.21890	0.609452	+	0.792823i	$0.291389\pi$
$104$	40.9442	4.01491
$105$	−1.71070	−0.166947
$106$	−28.5536	−2.77338
$107$	−2.16198	−0.209006	−0.104503	−	0.994525i	$-0.533325\pi$
$107$	−2.16198	−0.209006	−0.104503	+	0.994525i	$0.533325\pi$
$108$	15.0583	1.44899
$109$	−0.912287	−0.0873813	−0.0436906	−	0.999045i	$-0.513912\pi$
$109$	−0.912287	−0.0873813	−0.0436906	+	0.999045i	$0.513912\pi$
$110$	−5.54869	−0.529047
$111$	1.27687	0.121196
$112$	46.3361	4.37835
$113$	14.2056	1.33635	0.668177	−	0.744002i	$-0.267075\pi$
$113$	14.2056	1.33635	0.668177	+	0.744002i	$0.267075\pi$
$114$	−8.47043	−0.793329
$115$	−5.72394	−0.533760
$116$	39.0556	3.62622
$117$	12.7031	1.17441
$118$	3.53288	0.325228
$119$	0.130267	0.0119415
$120$	4.39297	0.401021
$121$	−6.77630	−0.616027
$122$	23.1721	2.09790
$123$	0.773639	0.0697567
$124$	5.17721	0.464928
$125$	1.00000	0.0894427
$126$	25.7266	2.29191
$127$	4.80654	0.426512	0.213256	−	0.976996i	$-0.431593\pi$
$127$	4.80654	0.426512	0.213256	+	0.976996i	$0.431593\pi$
$128$	−25.0414	−2.21336
$129$	−1.09193	−0.0961389
$130$	12.4476	1.09172
$131$	−7.86193	−0.686900	−0.343450	−	0.939171i	$-0.611596\pi$
$131$	−7.86193	−0.686900	−0.343450	+	0.939171i	$0.611596\pi$
$132$	−5.37717	−0.468023
$133$	−21.9343	−1.90194
$134$	36.6214	3.16360
$135$	2.84692	0.245024
$136$	−0.334517	−0.0286846
$137$	8.31193	0.710136	0.355068	−	0.934841i	$-0.384458\pi$
$137$	8.31193	0.710136	0.355068	+	0.934841i	$0.384458\pi$
$138$	−7.64443	−0.650737
$139$	22.1095	1.87530	0.937651	−	0.347578i	$-0.112996\pi$
$139$	22.1095	1.87530	0.937651	+	0.347578i	$0.112996\pi$
$140$	18.2923	1.54598
$141$	5.55876	0.468132
$142$	−0.0976080	−0.00819108
$143$	−9.47517	−0.792353
$144$	−36.9167	−3.07640
$145$	7.38384	0.613194
$146$	17.5775	1.45472
$147$	−2.45356	−0.202366
$148$	−13.6535	−1.12231
$149$	−0.359147	−0.0294225	−0.0147112	−	0.999892i	$-0.504683\pi$
$149$	−0.359147	−0.0294225	−0.0147112	+	0.999892i	$0.504683\pi$
$150$	1.33552	0.109045
$151$	−19.1965	−1.56219	−0.781095	−	0.624413i	$-0.785338\pi$
$151$	−19.1965	−1.56219	−0.781095	+	0.624413i	$0.785338\pi$
$152$	56.3258	4.56863
$153$	−0.103786	−0.00839056
$154$	−19.1892	−1.54631
$155$	0.978803	0.0786193
$156$	12.0628	0.965795
$157$	2.06065	0.164458	0.0822289	−	0.996613i	$-0.473796\pi$
$157$	2.06065	0.164458	0.0822289	+	0.996613i	$0.473796\pi$
$158$	−23.0204	−1.83140
$159$	−5.23147	−0.414883
$160$	−18.4124	−1.45563
$161$	−19.7953	−1.56009
$162$	−18.5149	−1.45467
$163$	−15.9314	−1.24784	−0.623922	−	0.781487i	$-0.714462\pi$
$163$	−15.9314	−1.24784	−0.623922	+	0.781487i	$0.714462\pi$
$164$	−8.27243	−0.645969
$165$	−1.01661	−0.0791427
$166$	−16.4838	−1.27939
$167$	−23.3184	−1.80443	−0.902217	−	0.431283i	$-0.858061\pi$
$167$	−23.3184	−1.80443	−0.902217	+	0.431283i	$0.858061\pi$
$168$	15.1924	1.17212
$169$	8.25595	0.635073
$170$	−0.101697	−0.00779984
$171$	17.4754	1.33637
$172$	11.6759	0.890276
$173$	18.2523	1.38770	0.693849	−	0.720120i	$-0.255913\pi$
$173$	18.2523	1.38770	0.693849	+	0.720120i	$0.255913\pi$
$174$	9.86126	0.747580
$175$	3.45834	0.261426
$176$	27.5359	2.07560
$177$	0.647278	0.0486524
$178$	−32.9303	−2.46823
$179$	20.3194	1.51874	0.759371	−	0.650658i	$-0.225507\pi$
$179$	20.3194	1.51874	0.759371	+	0.650658i	$0.225507\pi$
$180$	−14.5738	−1.08626
$181$	−6.31209	−0.469174	−0.234587	−	0.972095i	$-0.575374\pi$
$181$	−6.31209	−0.469174	−0.234587	+	0.972095i	$0.575374\pi$
$182$	43.0479	3.19092
$183$	4.24548	0.313835
$184$	50.8332	3.74747
$185$	−2.58132	−0.189782
$186$	1.30721	0.0958493
$187$	0.0774128	0.00566098
$188$	−59.4392	−4.33505
$189$	9.84560	0.716162
$190$	17.1238	1.24229
$191$	17.1489	1.24085	0.620425	−	0.784266i	$-0.286960\pi$
$191$	17.1489	1.24085	0.620425	+	0.784266i	$0.286960\pi$
$192$	−11.3348	−0.818022
$193$	19.0249	1.36944	0.684721	−	0.728805i	$-0.259924\pi$
$193$	19.0249	1.36944	0.684721	+	0.728805i	$0.259924\pi$
$194$	17.6726	1.26882
$195$	2.28059	0.163316
$196$	26.2356	1.87397
$197$	1.77564	0.126509	0.0632546	−	0.997997i	$-0.479852\pi$
$197$	1.77564	0.126509	0.0632546	+	0.997997i	$0.479852\pi$
$198$	15.2884	1.08650
$199$	26.8200	1.90122	0.950610	−	0.310389i	$-0.100459\pi$
$199$	26.8200	1.90122	0.950610	+	0.310389i	$0.100459\pi$
$200$	−8.88080	−0.627967
$201$	6.70960	0.473259
$202$	−23.7218	−1.66906
$203$	25.5358	1.79226
$204$	−0.0985537	−0.00690014
$205$	−1.56398	−0.109233
$206$	−33.3989	−2.32701
$207$	15.7712	1.09618
$208$	−61.7722	−4.28313
$209$	−13.0347	−0.901631
$210$	4.61868	0.318719
$211$	25.8950	1.78268	0.891341	−	0.453333i	$-0.149765\pi$
$211$	25.8950	1.78268	0.891341	+	0.453333i	$0.149765\pi$
$212$	55.9395	3.84194
$213$	−0.0178833	−0.00122534
$214$	5.83707	0.399014
$215$	2.20743	0.150546
$216$	−25.2829	−1.72028
$217$	3.38503	0.229791
$218$	2.46306	0.166820
$219$	3.22046	0.217619
$220$	10.8705	0.732886
$221$	−0.173663	−0.0116818
$222$	−3.44740	−0.231375
$223$	3.32004	0.222326	0.111163	−	0.993802i	$-0.464542\pi$
$223$	3.32004	0.222326	0.111163	+	0.993802i	$0.464542\pi$
$224$	−63.6763	−4.25455
$225$	−2.75531	−0.183687
$226$	−38.3535	−2.55123
$227$	9.56720	0.634997	0.317499	−	0.948259i	$-0.397157\pi$
$227$	9.56720	0.634997	0.317499	+	0.948259i	$0.397157\pi$
$228$	16.5944	1.09899
$229$	21.4191	1.41541	0.707706	−	0.706507i	$-0.249730\pi$
$229$	21.4191	1.41541	0.707706	+	0.706507i	$0.249730\pi$
$230$	15.4539	1.01900
$231$	−3.51577	−0.231320
$232$	−65.5744	−4.30517
$233$	5.54978	0.363578	0.181789	−	0.983338i	$-0.441811\pi$
$233$	5.54978	0.363578	0.181789	+	0.983338i	$0.441811\pi$
$234$	−34.2969	−2.24206
$235$	−11.2376	−0.733057
$236$	−6.92127	−0.450536
$237$	−4.21769	−0.273968
$238$	−0.351704	−0.0227976
$239$	24.1435	1.56171	0.780855	−	0.624712i	$-0.214784\pi$
$239$	24.1435	1.56171	0.780855	+	0.624712i	$0.214784\pi$
$240$	−6.62764	−0.427812
$241$	23.4184	1.50851	0.754255	−	0.656582i	$-0.227998\pi$
$241$	23.4184	1.50851	0.754255	+	0.656582i	$0.227998\pi$
$242$	18.2952	1.17606
$243$	−11.9330	−0.765500
$244$	−45.3964	−2.90621
$245$	4.96010	0.316889
$246$	−2.08873	−0.133173
$247$	29.2412	1.86058
$248$	−8.69255	−0.551977
$249$	−3.02010	−0.191391
$250$	−2.69988	−0.170755
$251$	30.4654	1.92296	0.961481	−	0.274872i	$-0.0886354\pi$
$251$	30.4654	1.92296	0.961481	+	0.274872i	$0.0886354\pi$
$252$	−50.4010	−3.17496
$253$	−11.7636	−0.739574
$254$	−12.9771	−0.814254
$255$	−0.0186325	−0.00116681
$256$	21.7797	1.36123
$257$	−11.1355	−0.694614	−0.347307	−	0.937751i	$-0.612904\pi$
$257$	−11.1355	−0.694614	−0.347307	+	0.937751i	$0.612904\pi$
$258$	2.94807	0.183539
$259$	−8.92708	−0.554702
$260$	−24.3860	−1.51236
$261$	−20.3448	−1.25931
$262$	21.2262	1.31136
$263$	7.04524	0.434428	0.217214	−	0.976124i	$-0.430303\pi$
$263$	7.04524	0.434428	0.217214	+	0.976124i	$0.430303\pi$
$264$	9.02827	0.555652
$265$	10.5759	0.649673
$266$	59.2198	3.63100
$267$	−6.03334	−0.369234
$268$	−71.7450	−4.38252
$269$	2.59721	0.158355	0.0791773	−	0.996861i	$-0.474771\pi$
$269$	2.59721	0.158355	0.0791773	+	0.996861i	$0.474771\pi$
$270$	−7.68633	−0.467775
$271$	−12.0230	−0.730345	−0.365173	−	0.930940i	$-0.618990\pi$
$271$	−12.0230	−0.730345	−0.365173	+	0.930940i	$0.618990\pi$
$272$	0.504683	0.0306009
$273$	7.88703	0.477345
$274$	−22.4412	−1.35572
$275$	2.05516	0.123931
$276$	14.9762	0.901463
$277$	−9.03660	−0.542956	−0.271478	−	0.962445i	$-0.587512\pi$
$277$	−9.03660	−0.542956	−0.271478	+	0.962445i	$0.587512\pi$
$278$	−59.6929	−3.58014
$279$	−2.69691	−0.161460
$280$	−30.7128	−1.83544
$281$	1.34202	0.0800582	0.0400291	−	0.999199i	$-0.487255\pi$
$281$	1.34202	0.0800582	0.0400291	+	0.999199i	$0.487255\pi$
$282$	−15.0080	−0.893712
$283$	1.80348	0.107206	0.0536028	−	0.998562i	$-0.482930\pi$
$283$	1.80348	0.107206	0.0536028	+	0.998562i	$0.482930\pi$
$284$	0.191224	0.0113471
$285$	3.13734	0.185840
$286$	25.5818	1.51268
$287$	−5.40878	−0.319270
$288$	50.7319	2.98941
$289$	−16.9986	−0.999917
$290$	−19.9355	−1.17065
$291$	3.23789	0.189808
$292$	−34.4361	−2.01522
$293$	−13.6782	−0.799089	−0.399545	−	0.916714i	$-0.630832\pi$
$293$	−13.6782	−0.799089	−0.399545	+	0.916714i	$0.630832\pi$
$294$	6.62430	0.386337
$295$	−1.30853	−0.0761858
$296$	22.9242	1.33244
$297$	5.85089	0.339503
$298$	0.969654	0.0561705
$299$	26.3898	1.52616
$300$	−2.61642	−0.151059
$301$	7.63405	0.440020
$302$	51.8282	2.98238
$303$	−4.34619	−0.249682
$304$	−84.9783	−4.87384
$305$	−8.58263	−0.491440
$306$	0.280208	0.0160184
$307$	−13.0469	−0.744624	−0.372312	−	0.928108i	$-0.621435\pi$
$307$	−13.0469	−0.744624	−0.372312	+	0.928108i	$0.621435\pi$
$308$	37.5937	2.14210
$309$	−6.11919	−0.348109
$310$	−2.64265	−0.150092
$311$	3.04693	0.172776	0.0863878	−	0.996262i	$-0.472468\pi$
$311$	3.04693	0.172776	0.0863878	+	0.996262i	$0.472468\pi$
$312$	−20.2534	−1.14662
$313$	−9.70956	−0.548817	−0.274409	−	0.961613i	$-0.588482\pi$
$313$	−9.70956	−0.548817	−0.274409	+	0.961613i	$0.588482\pi$
$314$	−5.56350	−0.313966
$315$	−9.52880	−0.536887
$316$	45.0992	2.53703
$317$	−22.9909	−1.29130	−0.645649	−	0.763634i	$-0.723413\pi$
$317$	−22.9909	−1.29130	−0.645649	+	0.763634i	$0.723413\pi$
$318$	14.1243	0.792053
$319$	15.1750	0.849637
$320$	22.9144	1.28096
$321$	1.06944	0.0596904
$322$	53.4449	2.97837
$323$	−0.238903	−0.0132929
$324$	36.2726	2.01514
$325$	−4.61042	−0.255740
$326$	43.0128	2.38226
$327$	0.451271	0.0249554
$328$	13.8894	0.766915
$329$	−38.8633	−2.14260
$330$	2.74471	0.151091
$331$	−8.73695	−0.480226	−0.240113	−	0.970745i	$-0.577185\pi$
$331$	−8.73695	−0.480226	−0.240113	+	0.970745i	$0.577185\pi$
$332$	32.2935	1.77234
$333$	7.11235	0.389754
$334$	62.9569	3.44485
$335$	−13.5641	−0.741085
$336$	−22.9206	−1.25042
$337$	17.7358	0.966128	0.483064	−	0.875585i	$-0.339524\pi$
$337$	17.7358	0.966128	0.483064	+	0.875585i	$0.339524\pi$
$338$	−22.2900	−1.21242
$339$	−7.02695	−0.381651
$340$	0.199236	0.0108051
$341$	2.01160	0.108934
$342$	−47.1813	−2.55127
$343$	−7.05467	−0.380916
$344$	−19.6038	−1.05696
$345$	2.83140	0.152438
$346$	−49.2790	−2.64926
$347$	−23.7116	−1.27291	−0.636453	−	0.771316i	$-0.719599\pi$
$347$	−23.7116	−1.27291	−0.636453	+	0.771316i	$0.719599\pi$
$348$	−19.3192	−1.03562
$349$	−14.4329	−0.772574	−0.386287	−	0.922379i	$-0.626243\pi$
$349$	−14.4329	−0.772574	−0.386287	+	0.922379i	$0.626243\pi$
$350$	−9.33708	−0.499088
$351$	−13.1255	−0.700586
$352$	−37.8405	−2.01691
$353$	4.71838	0.251134	0.125567	−	0.992085i	$-0.459925\pi$
$353$	4.71838	0.251134	0.125567	+	0.992085i	$0.459925\pi$
$354$	−1.74757	−0.0928823
$355$	0.0361528	0.00191879
$356$	64.5138	3.41922
$357$	−0.0644376	−0.00341040
$358$	−54.8598	−2.89943
$359$	36.7926	1.94184	0.970919	−	0.239407i	$-0.0769530\pi$
$359$	36.7926	1.94184	0.970919	+	0.239407i	$0.0769530\pi$
$360$	24.4694	1.28965
$361$	21.2264	1.11718
$362$	17.0419	0.895700
$363$	3.35196	0.175932
$364$	−84.3352	−4.42036
$365$	−6.51047	−0.340774
$366$	−11.4623	−0.599142
$367$	5.52458	0.288381	0.144190	−	0.989550i	$-0.453942\pi$
$367$	5.52458	0.288381	0.144190	+	0.989550i	$0.453942\pi$
$368$	−76.6916	−3.99783
$369$	4.30926	0.224331
$370$	6.96925	0.362314
$371$	36.5751	1.89888
$372$	−2.56096	−0.132779
$373$	22.2820	1.15372	0.576860	−	0.816843i	$-0.304278\pi$
$373$	22.2820	1.15372	0.576860	+	0.816843i	$0.304278\pi$
$374$	−0.209005	−0.0108074
$375$	−0.494659	−0.0255441
$376$	99.7985	5.14671
$377$	−34.0426	−1.75328
$378$	−26.5819	−1.36723
$379$	−17.5074	−0.899296	−0.449648	−	0.893206i	$-0.648451\pi$
$379$	−17.5074	−0.899296	−0.449648	+	0.893206i	$0.648451\pi$
$380$	−33.5472	−1.72094
$381$	−2.37760	−0.121808
$382$	−46.2999	−2.36891
$383$	24.4038	1.24698	0.623488	−	0.781833i	$-0.285715\pi$
$383$	24.4038	1.24698	0.623488	+	0.781833i	$0.285715\pi$
$384$	12.3869	0.632118
$385$	7.10745	0.362229
$386$	−51.3649	−2.61440
$387$	−6.08217	−0.309174
$388$	−34.6224	−1.75768
$389$	8.79603	0.445977	0.222988	−	0.974821i	$-0.428419\pi$
$389$	8.79603	0.445977	0.222988	+	0.974821i	$0.428419\pi$
$390$	−6.15730	−0.311787
$391$	−0.215606	−0.0109037
$392$	−44.0496	−2.22484
$393$	3.88898	0.196173
$394$	−4.79401	−0.241519
$395$	8.52645	0.429012
$396$	−29.9515	−1.50512
$397$	−23.4910	−1.17898	−0.589491	−	0.807775i	$-0.700671\pi$
$397$	−23.4910	−1.17898	−0.589491	+	0.807775i	$0.700671\pi$
$398$	−72.4107	−3.62962
$399$	10.8500	0.543178
$400$	13.3984	0.669919
$401$	−31.6820	−1.58212	−0.791061	−	0.611737i	$-0.790471\pi$
$401$	−31.6820	−1.58212	−0.791061	+	0.611737i	$0.790471\pi$
$402$	−18.1151	−0.903499
$403$	−4.51269	−0.224793
$404$	46.4734	2.31214
$405$	6.85768	0.340761
$406$	−68.9435	−3.42161
$407$	−5.30504	−0.262961
$408$	0.165472	0.00819208
$409$	11.6817	0.577622	0.288811	−	0.957386i	$-0.406740\pi$
$409$	11.6817	0.577622	0.288811	+	0.957386i	$0.406740\pi$
$410$	4.22256	0.208538
$411$	−4.11157	−0.202809
$412$	65.4318	3.22360
$413$	−4.52535	−0.222678
$414$	−42.5804	−2.09271
$415$	6.10541	0.299703
$416$	84.8889	4.16202
$417$	−10.9367	−0.535571
$418$	35.1922	1.72131
$419$	−12.2576	−0.598822	−0.299411	−	0.954124i	$-0.596790\pi$
$419$	−12.2576	−0.598822	−0.299411	+	0.954124i	$0.596790\pi$
$420$	−9.04846	−0.441519
$421$	10.7425	0.523557	0.261779	−	0.965128i	$-0.415691\pi$
$421$	10.7425	0.523557	0.261779	+	0.965128i	$0.415691\pi$
$422$	−69.9132	−3.40332
$423$	30.9630	1.50547
$424$	−93.9225	−4.56128
$425$	0.0376674	0.00182714
$426$	0.0482827	0.00233930
$427$	−29.6816	−1.43640
$428$	−11.4354	−0.552751
$429$	4.68698	0.226289
$430$	−5.95980	−0.287407
$431$	−24.7757	−1.19340	−0.596702	−	0.802463i	$-0.703523\pi$
$431$	−24.7757	−1.19340	−0.596702	+	0.802463i	$0.703523\pi$
$432$	38.1441	1.83521
$433$	−27.4946	−1.32130	−0.660652	−	0.750692i	$-0.729720\pi$
$433$	−27.4946	−1.32130	−0.660652	+	0.750692i	$0.729720\pi$
$434$	−9.13916	−0.438694
$435$	−3.65248	−0.175123
$436$	−4.82539	−0.231094
$437$	36.3037	1.73664
$438$	−8.69486	−0.415456
$439$	13.5808	0.648174	0.324087	−	0.946027i	$-0.394943\pi$
$439$	13.5808	0.648174	0.324087	+	0.946027i	$0.394943\pi$
$440$	−18.2515	−0.870106
$441$	−13.6666	−0.650791
$442$	0.468867	0.0223018
$443$	4.57912	0.217561	0.108780	−	0.994066i	$-0.465305\pi$
$443$	4.57912	0.217561	0.108780	+	0.994066i	$0.465305\pi$
$444$	6.75381	0.320522
$445$	12.1970	0.578191
$446$	−8.96369	−0.424443
$447$	0.177656	0.00840282
$448$	79.2459	3.74402
$449$	19.4625	0.918492	0.459246	−	0.888309i	$-0.348120\pi$
$449$	19.4625	0.918492	0.459246	+	0.888309i	$0.348120\pi$
$450$	7.43900	0.350678
$451$	−3.21424	−0.151353
$452$	75.1383	3.53421
$453$	9.49573	0.446148
$454$	−25.8303	−1.21227
$455$	−15.9444	−0.747484
$456$	−27.8621	−1.30476
$457$	−8.80778	−0.412011	−0.206005	−	0.978551i	$-0.566046\pi$
$457$	−8.80778	−0.412011	−0.206005	+	0.978551i	$0.566046\pi$
$458$	−57.8288	−2.70216
$459$	0.107236	0.00500535
$460$	−30.2758	−1.41162
$461$	−20.5626	−0.957698	−0.478849	−	0.877897i	$-0.658946\pi$
$461$	−20.5626	−0.957698	−0.478849	+	0.877897i	$0.658946\pi$
$462$	9.49214	0.441614
$463$	6.53896	0.303891	0.151946	−	0.988389i	$-0.451446\pi$
$463$	6.53896	0.303891	0.151946	+	0.988389i	$0.451446\pi$
$464$	98.9315	4.59278
$465$	−0.484174	−0.0224530
$466$	−14.9837	−0.694107
$467$	11.8221	0.547060	0.273530	−	0.961864i	$-0.411809\pi$
$467$	11.8221	0.547060	0.273530	+	0.961864i	$0.411809\pi$
$468$	67.1912	3.10591
$469$	−46.9092	−2.16607
$470$	30.3400	1.39948
$471$	−1.01932	−0.0469678
$472$	11.6208	0.534892
$473$	4.53664	0.208595
$474$	11.3872	0.523033
$475$	−6.34243	−0.291011
$476$	0.689024	0.0315814
$477$	−29.1399	−1.33423
$478$	−65.1844	−2.98146
$479$	20.3005	0.927555	0.463777	−	0.885952i	$-0.346494\pi$
$479$	20.3005	0.927555	0.463777	+	0.885952i	$0.346494\pi$
$480$	9.10787	0.415715
$481$	11.9010	0.542637
$482$	−63.2267	−2.87990
$483$	9.79194	0.445549
$484$	−35.8421	−1.62919
$485$	−6.54569	−0.297225
$486$	32.2176	1.46142
$487$	9.14739	0.414508	0.207254	−	0.978287i	$-0.433547\pi$
$487$	9.14739	0.414508	0.207254	+	0.978287i	$0.433547\pi$
$488$	76.2206	3.45035
$489$	7.88062	0.356374
$490$	−13.3917	−0.604973
$491$	−12.3373	−0.556774	−0.278387	−	0.960469i	$-0.589800\pi$
$491$	−12.3373	−0.556774	−0.278387	+	0.960469i	$0.589800\pi$
$492$	4.09204	0.184483
$493$	0.278130	0.0125264
$494$	−78.9477	−3.55203
$495$	−5.66262	−0.254516
$496$	13.1144	0.588853
$497$	0.125028	0.00560829
$498$	8.15389	0.365384
$499$	−11.2217	−0.502353	−0.251176	−	0.967941i	$-0.580817\pi$
$499$	−11.2217	−0.502353	−0.251176	+	0.967941i	$0.580817\pi$
$500$	5.28933	0.236546
$501$	11.5347	0.515331
$502$	−82.2529	−3.67113
$503$	−24.6211	−1.09780	−0.548901	−	0.835887i	$-0.684954\pi$
$503$	−24.6211	−1.09780	−0.548901	+	0.835887i	$0.684954\pi$
$504$	84.6233	3.76942
$505$	8.78624	0.390982
$506$	31.7604	1.41192
$507$	−4.08388	−0.181372
$508$	25.4234	1.12798
$509$	29.2776	1.29771	0.648854	−	0.760913i	$-0.275248\pi$
$509$	29.2776	1.29771	0.648854	+	0.760913i	$0.275248\pi$
$510$	0.0503056	0.00222757
$511$	−22.5154	−0.996023
$512$	−8.71979	−0.385364
$513$	−18.0564	−0.797208
$514$	30.0645	1.32609
$515$	12.3705	0.545110
$516$	−5.77557	−0.254255
$517$	−23.0950	−1.01572
$518$	24.1020	1.05898
$519$	−9.02868	−0.396315
$520$	40.9442	1.79552
$521$	12.5853	0.551370	0.275685	−	0.961248i	$-0.411095\pi$
$521$	12.5853	0.551370	0.275685	+	0.961248i	$0.411095\pi$
$522$	54.9284	2.40415
$523$	−9.66475	−0.422610	−0.211305	−	0.977420i	$-0.567771\pi$
$523$	−9.66475	−0.422610	−0.211305	+	0.977420i	$0.567771\pi$
$524$	−41.5844	−1.81662
$525$	−1.71070	−0.0746610
$526$	−19.0213	−0.829367
$527$	0.0368690	0.00160604
$528$	−13.6209	−0.592773
$529$	9.76352	0.424501
$530$	−28.5536	−1.24029
$531$	3.60542	0.156462
$532$	−116.018	−5.03000
$533$	7.21062	0.312327
$534$	16.2893	0.704906
$535$	−2.16198	−0.0934703
$536$	120.460	5.20308
$537$	−10.0512	−0.433740
$538$	−7.01214	−0.302315
$539$	10.1938	0.439079
$540$	15.0583	0.648006
$541$	14.9162	0.641297	0.320648	−	0.947198i	$-0.396099\pi$
$541$	14.9162	0.641297	0.320648	+	0.947198i	$0.396099\pi$
$542$	32.4606	1.39430
$543$	3.12233	0.133992
$544$	−0.693548	−0.0297356
$545$	−0.912287	−0.0390781
$546$	−21.2940	−0.911300
$547$	7.80378	0.333666	0.166833	−	0.985985i	$-0.446646\pi$
$547$	7.80378	0.333666	0.166833	+	0.985985i	$0.446646\pi$
$548$	43.9646	1.87807
$549$	23.6478	1.00926
$550$	−5.54869	−0.236597
$551$	−46.8315	−1.99509
$552$	−25.1451	−1.07025
$553$	29.4873	1.25393
$554$	24.3977	1.03656
$555$	1.27687	0.0542003
$556$	116.944	4.95955
$557$	−27.1701	−1.15124	−0.575618	−	0.817719i	$-0.695238\pi$
$557$	−27.1701	−1.15124	−0.575618	+	0.817719i	$0.695238\pi$
$558$	7.28132	0.308243
$559$	−10.1772	−0.430450
$560$	46.3361	1.95806
$561$	−0.0382929	−0.00161673
$562$	−3.62329	−0.152839
$563$	34.7229	1.46340	0.731698	−	0.681629i	$-0.238728\pi$
$563$	34.7229	1.46340	0.731698	+	0.681629i	$0.238728\pi$
$564$	29.4021	1.23805
$565$	14.2056	0.597636
$566$	−4.86917	−0.204666
$567$	23.7162	0.995986
$568$	−0.321065	−0.0134716
$569$	−5.59082	−0.234379	−0.117190	−	0.993110i	$-0.537389\pi$
$569$	−5.59082	−0.234379	−0.117190	+	0.993110i	$0.537389\pi$
$570$	−8.47043	−0.354787
$571$	28.0726	1.17480	0.587401	−	0.809296i	$-0.300151\pi$
$571$	28.0726	1.17480	0.587401	+	0.809296i	$0.300151\pi$
$572$	−50.1173	−2.09551
$573$	−8.48285	−0.354376
$574$	14.6030	0.609520
$575$	−5.72394	−0.238705
$576$	−63.1364	−2.63068
$577$	−14.1695	−0.589884	−0.294942	−	0.955515i	$-0.595300\pi$
$577$	−14.1695	−0.589884	−0.294942	+	0.955515i	$0.595300\pi$
$578$	45.8941	1.90894
$579$	−9.41084	−0.391101
$580$	39.0556	1.62170
$581$	21.1146	0.875979
$582$	−8.74190	−0.362363
$583$	21.7352	0.900181
$584$	57.8182	2.39253
$585$	12.7031	0.525210
$586$	36.9295	1.52554
$587$	10.0003	0.412757	0.206379	−	0.978472i	$-0.433832\pi$
$587$	10.0003	0.412757	0.206379	+	0.978472i	$0.433832\pi$
$588$	−12.9777	−0.535191
$589$	−6.20799	−0.255796
$590$	3.53288	0.145446
$591$	−0.878337	−0.0361300
$592$	−34.5855	−1.42146
$593$	−4.59197	−0.188570	−0.0942848	−	0.995545i	$-0.530056\pi$
$593$	−4.59197	−0.188570	−0.0942848	+	0.995545i	$0.530056\pi$
$594$	−15.7967	−0.648145
$595$	0.130267	0.00534041
$596$	−1.89965	−0.0778127
$597$	−13.2668	−0.542972
$598$	−71.2491	−2.91359
$599$	4.41617	0.180440	0.0902200	−	0.995922i	$-0.471243\pi$
$599$	4.41617	0.180440	0.0902200	+	0.995922i	$0.471243\pi$
$600$	4.39297	0.179342
$601$	41.5314	1.69410	0.847051	−	0.531512i	$-0.178376\pi$
$601$	41.5314	1.69410	0.847051	+	0.531512i	$0.178376\pi$
$602$	−20.6110	−0.840042
$603$	37.3733	1.52196
$604$	−101.537	−4.13147
$605$	−6.77630	−0.275496
$606$	11.7342	0.476669
$607$	−15.6479	−0.635128	−0.317564	−	0.948237i	$-0.602865\pi$
$607$	−15.6479	−0.635128	−0.317564	+	0.948237i	$0.602865\pi$
$608$	116.779	4.73603
$609$	−12.6315	−0.511855
$610$	23.1721	0.938209
$611$	51.8098	2.09600
$612$	−0.548956	−0.0221902
$613$	3.21572	0.129882	0.0649409	−	0.997889i	$-0.479314\pi$
$613$	3.21572	0.129882	0.0649409	+	0.997889i	$0.479314\pi$
$614$	35.2249	1.42156
$615$	0.773639	0.0311961
$616$	−63.1198	−2.54317
$617$	10.4263	0.419746	0.209873	−	0.977729i	$-0.432695\pi$
$617$	10.4263	0.419746	0.209873	+	0.977729i	$0.432695\pi$
$618$	16.5211	0.664575
$619$	−30.7181	−1.23466	−0.617331	−	0.786703i	$-0.711786\pi$
$619$	−30.7181	−1.23466	−0.617331	+	0.786703i	$0.711786\pi$
$620$	5.17721	0.207922
$621$	−16.2956	−0.653920
$622$	−8.22634	−0.329846
$623$	42.1812	1.68995
$624$	30.5562	1.22323
$625$	1.00000	0.0400000
$626$	26.2146	1.04775
$627$	6.44775	0.257498
$628$	10.8995	0.434936
$629$	−0.0972317	−0.00387688
$630$	25.7266	1.02497
$631$	−44.9682	−1.79016	−0.895078	−	0.445910i	$-0.852880\pi$
$631$	−44.9682	−1.79016	−0.895078	+	0.445910i	$0.852880\pi$
$632$	−75.7217	−3.01205
$633$	−12.8092	−0.509119
$634$	62.0727	2.46522
$635$	4.80654	0.190742
$636$	−27.6710	−1.09723
$637$	−22.8681	−0.906068
$638$	−40.9706	−1.62204
$639$	−0.0996121	−0.00394059
$640$	−25.0414	−0.989847
$641$	−4.38997	−0.173394	−0.0866968	−	0.996235i	$-0.527631\pi$
$641$	−4.38997	−0.173394	−0.0866968	+	0.996235i	$0.527631\pi$
$642$	−2.88736	−0.113955
$643$	49.6659	1.95863	0.979316	−	0.202335i	$-0.0648529\pi$
$643$	49.6659	1.95863	0.979316	+	0.202335i	$0.0648529\pi$
$644$	−104.704	−4.12592
$645$	−1.09193	−0.0429946
$646$	0.645008	0.0253775
$647$	−25.4735	−1.00147	−0.500734	−	0.865601i	$-0.666936\pi$
$647$	−25.4735	−1.00147	−0.500734	+	0.865601i	$0.666936\pi$
$648$	−60.9017	−2.39244
$649$	−2.68925	−0.105562
$650$	12.4476	0.488233
$651$	−1.67444	−0.0656263
$652$	−84.2665	−3.30013
$653$	11.8937	0.465437	0.232718	−	0.972544i	$-0.425238\pi$
$653$	11.8937	0.465437	0.232718	+	0.972544i	$0.425238\pi$
$654$	−1.21838	−0.0476423
$655$	−7.86193	−0.307191
$656$	−20.9549	−0.818150
$657$	17.9384	0.699843
$658$	104.926	4.09044
$659$	−18.3202	−0.713653	−0.356827	−	0.934171i	$-0.616141\pi$
$659$	−18.3202	−0.713653	−0.356827	+	0.934171i	$0.616141\pi$
$660$	−5.37717	−0.209306
$661$	34.7971	1.35345	0.676726	−	0.736235i	$-0.263398\pi$
$661$	34.7971	1.35345	0.676726	+	0.736235i	$0.263398\pi$
$662$	23.5887	0.916800
$663$	0.0859038	0.00333623
$664$	−54.2209	−2.10418
$665$	−21.9343	−0.850574
$666$	−19.2025	−0.744080
$667$	−42.2647	−1.63649
$668$	−123.339	−4.77213
$669$	−1.64229	−0.0634945
$670$	36.6214	1.41481
$671$	−17.6387	−0.680935
$672$	31.4981	1.21506
$673$	42.3762	1.63348	0.816742	−	0.577003i	$-0.195778\pi$
$673$	42.3762	1.63348	0.816742	+	0.577003i	$0.195778\pi$
$674$	−47.8844	−1.84444
$675$	2.84692	0.109578
$676$	43.6685	1.67956
$677$	−4.07445	−0.156594	−0.0782970	−	0.996930i	$-0.524948\pi$
$677$	−4.07445	−0.156594	−0.0782970	+	0.996930i	$0.524948\pi$
$678$	18.9719	0.728611
$679$	−22.6372	−0.868736
$680$	−0.334517	−0.0128281
$681$	−4.73250	−0.181350
$682$	−5.43107	−0.207967
$683$	−3.39848	−0.130039	−0.0650196	−	0.997884i	$-0.520711\pi$
$683$	−3.39848	−0.130039	−0.0650196	+	0.997884i	$0.520711\pi$
$684$	92.4331	3.53427
$685$	8.31193	0.317582
$686$	19.0467	0.727208
$687$	−10.5951	−0.404230
$688$	29.5761	1.12758
$689$	−48.7593	−1.85758
$690$	−7.64443	−0.291019
$691$	−42.3141	−1.60970	−0.804852	−	0.593476i	$-0.797755\pi$
$691$	−42.3141	−1.60970	−0.804852	+	0.593476i	$0.797755\pi$
$692$	96.5426	3.67000
$693$	−19.5833	−0.743906
$694$	64.0184	2.43011
$695$	22.1095	0.838661
$696$	32.4370	1.22952
$697$	−0.0589112	−0.00223142
$698$	38.9670	1.47492
$699$	−2.74525	−0.103835
$700$	18.2923	0.691384
$701$	−2.31169	−0.0873113	−0.0436557	−	0.999047i	$-0.513900\pi$
$701$	−2.31169	−0.0873113	−0.0436557	+	0.999047i	$0.513900\pi$
$702$	35.4372	1.33749
$703$	16.3718	0.617476
$704$	47.0929	1.77488
$705$	5.55876	0.209355
$706$	−12.7390	−0.479440
$707$	30.3858	1.14277
$708$	3.42367	0.128669
$709$	14.2956	0.536882	0.268441	−	0.963296i	$-0.413492\pi$
$709$	14.2956	0.536882	0.268441	+	0.963296i	$0.413492\pi$
$710$	−0.0976080	−0.00366316
$711$	−23.4930	−0.881058
$712$	−108.319	−4.05941
$713$	−5.60261	−0.209819
$714$	0.173974	0.00651080
$715$	−9.47517	−0.354351
$716$	107.476	4.01657
$717$	−11.9428	−0.446012
$718$	−99.3355	−3.70717
$719$	21.2871	0.793876	0.396938	−	0.917845i	$-0.370073\pi$
$719$	21.2871	0.793876	0.396938	+	0.917845i	$0.370073\pi$
$720$	−36.9167	−1.37581
$721$	42.7814	1.59326
$722$	−57.3086	−2.13281
$723$	−11.5841	−0.430818
$724$	−33.3867	−1.24081
$725$	7.38384	0.274229
$726$	−9.04988	−0.335872
$727$	−4.22454	−0.156679	−0.0783397	−	0.996927i	$-0.524962\pi$
$727$	−4.22454	−0.156679	−0.0783397	+	0.996927i	$0.524962\pi$
$728$	141.599	5.24800
$729$	−14.6703	−0.543344
$730$	17.5775	0.650571
$731$	0.0831484	0.00307535
$732$	22.4558	0.829989
$733$	−35.7796	−1.32155	−0.660775	−	0.750584i	$-0.729772\pi$
$733$	−35.7796	−1.32155	−0.660775	+	0.750584i	$0.729772\pi$
$734$	−14.9157	−0.550548
$735$	−2.45356	−0.0905009
$736$	105.392	3.88478
$737$	−27.8764	−1.02684
$738$	−11.6345	−0.428271
$739$	−5.33288	−0.196173	−0.0980866	−	0.995178i	$-0.531272\pi$
$739$	−5.33288	−0.196173	−0.0980866	+	0.995178i	$0.531272\pi$
$740$	−13.6535	−0.501912
$741$	−14.4644	−0.531365
$742$	−98.7481	−3.62516
$743$	48.4887	1.77888	0.889439	−	0.457054i	$-0.151095\pi$
$743$	48.4887	1.77888	0.889439	+	0.457054i	$0.151095\pi$
$744$	4.29985	0.157640
$745$	−0.359147	−0.0131581
$746$	−60.1587	−2.20257
$747$	−16.8223	−0.615496
$748$	0.409462	0.0149714
$749$	−7.47684	−0.273198
$750$	1.33552	0.0487663
$751$	1.63587	0.0596939	0.0298469	−	0.999554i	$-0.490498\pi$
$751$	1.63587	0.0596939	0.0298469	+	0.999554i	$0.490498\pi$
$752$	−150.565	−5.49055
$753$	−15.0700	−0.549182
$754$	91.9108	3.34719
$755$	−19.1965	−0.698632
$756$	52.0767	1.89401
$757$	51.0030	1.85374	0.926869	−	0.375386i	$-0.122490\pi$
$757$	51.0030	1.85374	0.926869	+	0.375386i	$0.122490\pi$
$758$	47.2679	1.71685
$759$	5.81899	0.211216
$760$	56.3258	2.04315
$761$	−22.1501	−0.802942	−0.401471	−	0.915872i	$-0.631501\pi$
$761$	−22.1501	−0.802942	−0.401471	+	0.915872i	$0.631501\pi$
$762$	6.41923	0.232544
$763$	−3.15500	−0.114219
$764$	90.7062	3.28163
$765$	−0.103786	−0.00375237
$766$	−65.8873	−2.38060
$767$	6.03288	0.217835
$768$	−10.7735	−0.388756
$769$	4.45711	0.160727	0.0803637	−	0.996766i	$-0.474392\pi$
$769$	4.45711	0.160727	0.0803637	+	0.996766i	$0.474392\pi$
$770$	−19.1892	−0.691532
$771$	5.50828	0.198376
$772$	100.629	3.62172
$773$	36.9116	1.32762	0.663809	−	0.747902i	$-0.268939\pi$
$773$	36.9116	1.32762	0.663809	+	0.747902i	$0.268939\pi$
$774$	16.4211	0.590245
$775$	0.978803	0.0351596
$776$	58.1310	2.08678
$777$	4.41586	0.158418
$778$	−23.7482	−0.851414
$779$	9.91945	0.355401
$780$	12.0628	0.431917
$781$	0.0742999	0.00265866
$782$	0.582110	0.0208162
$783$	21.0212	0.751236
$784$	66.4573	2.37348
$785$	2.06065	0.0735477
$786$	−10.4998	−0.374514
$787$	27.7929	0.990709	0.495355	−	0.868691i	$-0.335038\pi$
$787$	27.7929	0.990709	0.495355	+	0.868691i	$0.335038\pi$
$788$	9.39196	0.334575
$789$	−3.48499	−0.124069
$790$	−23.0204	−0.819028
$791$	49.1279	1.74679
$792$	50.2886	1.78693
$793$	39.5695	1.40515
$794$	63.4229	2.25079
$795$	−5.23147	−0.185541
$796$	141.860	5.02809
$797$	−8.65304	−0.306506	−0.153253	−	0.988187i	$-0.548975\pi$
$797$	−8.65304	−0.306506	−0.153253	+	0.988187i	$0.548975\pi$
$798$	−29.2936	−1.03698
$799$	−0.423290	−0.0149749
$800$	−18.4124	−0.650977
$801$	−33.6064	−1.18742
$802$	85.5374	3.02043
$803$	−13.3801	−0.472173
$804$	35.4893	1.25161
$805$	−19.7953	−0.697694
$806$	12.1837	0.429153
$807$	−1.28473	−0.0452247
$808$	−78.0288	−2.74504
$809$	27.0759	0.951938	0.475969	−	0.879462i	$-0.342097\pi$
$809$	27.0759	0.951938	0.475969	+	0.879462i	$0.342097\pi$
$810$	−18.5149	−0.650547
$811$	−28.1103	−0.987085	−0.493543	−	0.869722i	$-0.664298\pi$
$811$	−28.1103	−0.987085	−0.493543	+	0.869722i	$0.664298\pi$
$812$	135.067	4.73994
$813$	5.94729	0.208580
$814$	14.3230	0.502019
$815$	−15.9314	−0.558053
$816$	−0.249646	−0.00873936
$817$	−14.0005	−0.489815
$818$	−31.5391	−1.10274
$819$	43.9317	1.53510
$820$	−8.27243	−0.288886
$821$	−23.2022	−0.809761	−0.404881	−	0.914370i	$-0.632687\pi$
$821$	−23.2022	−0.809761	−0.404881	+	0.914370i	$0.632687\pi$
$822$	11.1007	0.387183
$823$	−30.7176	−1.07075	−0.535374	−	0.844615i	$-0.679829\pi$
$823$	−30.7176	−1.07075	−0.535374	+	0.844615i	$0.679829\pi$
$824$	−109.860	−3.82716
$825$	−1.01661	−0.0353937
$826$	12.2179	0.425115
$827$	53.9267	1.87521	0.937607	−	0.347696i	$-0.113036\pi$
$827$	53.9267	1.87521	0.937607	+	0.347696i	$0.113036\pi$
$828$	83.4194	2.89902
$829$	−26.1499	−0.908225	−0.454113	−	0.890944i	$-0.650044\pi$
$829$	−26.1499	−0.908225	−0.454113	+	0.890944i	$0.650044\pi$
$830$	−16.4838	−0.572163
$831$	4.47004	0.155064
$832$	−105.645	−3.66259
$833$	0.186834	0.00647342
$834$	29.5276	1.02246
$835$	−23.3184	−0.806967
$836$	−68.9451	−2.38451
$837$	2.78657	0.0963180
$838$	33.0940	1.14321
$839$	−23.1411	−0.798921	−0.399461	−	0.916750i	$-0.630803\pi$
$839$	−23.1411	−0.798921	−0.399461	+	0.916750i	$0.630803\pi$
$840$	15.1924	0.524186
$841$	25.5211	0.880037
$842$	−29.0034	−0.999524
$843$	−0.663843	−0.0228640
$844$	136.967	4.71460
$845$	8.25595	0.284013
$846$	−83.5962	−2.87410
$847$	−23.4347	−0.805227
$848$	141.700	4.86600
$849$	−0.892107	−0.0306170
$850$	−0.101697	−0.00348819
$851$	14.7753	0.506492
$852$	−0.0945907	−0.00324062
$853$	32.2512	1.10426	0.552130	−	0.833758i	$-0.313815\pi$
$853$	32.2512	1.10426	0.552130	+	0.833758i	$0.313815\pi$
$854$	80.1368	2.74222
$855$	17.4754	0.597645
$856$	19.2001	0.656245
$857$	54.1109	1.84839	0.924197	−	0.381915i	$-0.124735\pi$
$857$	54.1109	1.84839	0.924197	+	0.381915i	$0.124735\pi$
$858$	−12.6543	−0.432009
$859$	14.6440	0.499646	0.249823	−	0.968292i	$-0.419628\pi$
$859$	14.6440	0.499646	0.249823	+	0.968292i	$0.419628\pi$
$860$	11.6759	0.398144
$861$	2.67550	0.0911810
$862$	66.8914	2.27833
$863$	26.6152	0.905991	0.452996	−	0.891513i	$-0.350355\pi$
$863$	26.6152	0.905991	0.452996	+	0.891513i	$0.350355\pi$
$864$	−52.4186	−1.78332
$865$	18.2523	0.620598
$866$	74.2319	2.52250
$867$	8.40851	0.285568
$868$	17.9046	0.607720
$869$	17.5233	0.594436
$870$	9.86126	0.334328
$871$	62.5361	2.11896
$872$	8.10184	0.274363
$873$	18.0354	0.610407
$874$	−98.0155	−3.31542
$875$	3.45834	0.116913
$876$	17.0341	0.575529
$877$	−52.3344	−1.76721	−0.883604	−	0.468236i	$-0.844890\pi$
$877$	−52.3344	−1.76721	−0.883604	+	0.468236i	$0.844890\pi$
$878$	−36.6664	−1.23743
$879$	6.76605	0.228213
$880$	27.5359	0.928235
$881$	16.6091	0.559575	0.279788	−	0.960062i	$-0.409736\pi$
$881$	16.6091	0.559575	0.279788	+	0.960062i	$0.409736\pi$
$882$	36.8982	1.24243
$883$	−1.52258	−0.0512389	−0.0256194	−	0.999672i	$-0.508156\pi$
$883$	−1.52258	−0.0512389	−0.0256194	+	0.999672i	$0.508156\pi$
$884$	−0.918559	−0.0308945
$885$	0.647278	0.0217580
$886$	−12.3631	−0.415345
$887$	−10.8814	−0.365363	−0.182681	−	0.983172i	$-0.558478\pi$
$887$	−10.8814	−0.365363	−0.182681	+	0.983172i	$0.558478\pi$
$888$	−11.3397	−0.380534
$889$	16.6226	0.557506
$890$	−32.9303	−1.10383
$891$	14.0937	0.472156
$892$	17.5608	0.587979
$893$	71.2734	2.38507
$894$	−0.479648	−0.0160418
$895$	20.3194	0.679202
$896$	−86.6015	−2.89315
$897$	−13.0539	−0.435858
$898$	−52.5463	−1.75349
$899$	7.22732	0.241045
$900$	−14.5738	−0.485792
$901$	0.398367	0.0132715
$902$	8.67806	0.288948
$903$	−3.77626	−0.125666
$904$	−126.157	−4.19593
$905$	−6.31209	−0.209821
$906$	−25.6373	−0.851742
$907$	48.6254	1.61458	0.807290	−	0.590154i	$-0.200933\pi$
$907$	48.6254	1.61458	0.807290	+	0.590154i	$0.200933\pi$
$908$	50.6041	1.67936
$909$	−24.2088	−0.802956
$910$	43.0479	1.42702
$911$	28.3575	0.939524	0.469762	−	0.882793i	$-0.344340\pi$
$911$	28.3575	0.939524	0.469762	+	0.882793i	$0.344340\pi$
$912$	42.0353	1.39193
$913$	12.5476	0.415265
$914$	23.7799	0.786570
$915$	4.24548	0.140351
$916$	113.293	3.74329
$917$	−27.1892	−0.897867
$918$	−0.289524	−0.00955572
$919$	−20.9148	−0.689917	−0.344959	−	0.938618i	$-0.612107\pi$
$919$	−20.9148	−0.689917	−0.344959	+	0.938618i	$0.612107\pi$
$920$	50.8332	1.67592
$921$	6.45375	0.212658
$922$	55.5166	1.82834
$923$	−0.166679	−0.00548632
$924$	−18.5961	−0.611766
$925$	−2.58132	−0.0848733
$926$	−17.6544	−0.580159
$927$	−34.0847	−1.11949
$928$	−135.954	−4.46292
$929$	−30.0134	−0.984708	−0.492354	−	0.870395i	$-0.663863\pi$
$929$	−30.0134	−0.984708	−0.492354	+	0.870395i	$0.663863\pi$
$930$	1.30721	0.0428651
$931$	−31.4591	−1.03103
$932$	29.3546	0.961543
$933$	−1.50719	−0.0493433
$934$	−31.9181	−1.04439
$935$	0.0774128	0.00253167
$936$	−112.814	−3.68744
$937$	−37.2078	−1.21552	−0.607762	−	0.794119i	$-0.707933\pi$
$937$	−37.2078	−1.21552	−0.607762	+	0.794119i	$0.707933\pi$
$938$	126.649	4.13524
$939$	4.80293	0.156738
$940$	−59.4392	−1.93869
$941$	5.92644	0.193196	0.0965982	−	0.995323i	$-0.469204\pi$
$941$	5.92644	0.193196	0.0965982	+	0.995323i	$0.469204\pi$
$942$	2.75204	0.0896662
$943$	8.95215	0.291522
$944$	−17.5322	−0.570626
$945$	9.84560	0.320278
$946$	−12.2484	−0.398229
$947$	47.5559	1.54536	0.772679	−	0.634797i	$-0.218916\pi$
$947$	47.5559	1.54536	0.772679	+	0.634797i	$0.218916\pi$
$948$	−22.3088	−0.724555
$949$	30.0160	0.974360
$950$	17.1238	0.555569
$951$	11.3727	0.368784
$952$	−1.15687	−0.0374944
$953$	45.6961	1.48024	0.740121	−	0.672473i	$-0.234768\pi$
$953$	45.6961	1.48024	0.740121	+	0.672473i	$0.234768\pi$
$954$	78.6742	2.54717
$955$	17.1489	0.554925
$956$	127.703	4.13021
$957$	−7.50646	−0.242649
$958$	−54.8089	−1.77080
$959$	28.7454	0.928239
$960$	−11.3348	−0.365830
$961$	−30.0419	−0.969095
$962$	−32.1311	−1.03595
$963$	5.95692	0.191959
$964$	123.868	3.98951
$965$	19.0249	0.612433
$966$	−26.4370	−0.850598
$967$	26.0762	0.838553	0.419277	−	0.907859i	$-0.362284\pi$
$967$	26.0762	0.838553	0.419277	+	0.907859i	$0.362284\pi$
$968$	60.1789	1.93422
$969$	0.118176	0.00379635
$970$	17.6726	0.567432
$971$	−8.82536	−0.283219	−0.141610	−	0.989923i	$-0.545228\pi$
$971$	−8.82536	−0.283219	−0.141610	+	0.989923i	$0.545228\pi$
$972$	−63.1175	−2.02449
$973$	76.4621	2.45126
$974$	−24.6968	−0.791337
$975$	2.28059	0.0730372
$976$	−114.993	−3.68085
$977$	47.2630	1.51208	0.756039	−	0.654526i	$-0.227132\pi$
$977$	47.2630	1.51208	0.756039	+	0.654526i	$0.227132\pi$
$978$	−21.2767	−0.680354
$979$	25.0668	0.801137
$980$	26.2356	0.838066
$981$	2.51364	0.0802542
$982$	33.3091	1.06294
$983$	−28.2186	−0.900033	−0.450016	−	0.893020i	$-0.648582\pi$
$983$	−28.2186	−0.900033	−0.450016	+	0.893020i	$0.648582\pi$
$984$	−6.87053	−0.219025
$985$	1.77564	0.0565766
$986$	−0.750917	−0.0239141
$987$	19.2241	0.611909
$988$	154.667	4.92060
$989$	−12.6352	−0.401777
$990$	15.2884	0.485896
$991$	19.9285	0.633050	0.316525	−	0.948584i	$-0.397484\pi$
$991$	19.9285	0.633050	0.316525	+	0.948584i	$0.397484\pi$
$992$	−18.0221	−0.572203
$993$	4.32181	0.137149
$994$	−0.337561	−0.0107068
$995$	26.8200	0.850251
$996$	−15.9743	−0.506165
$997$	55.6230	1.76160	0.880799	−	0.473491i	$-0.157006\pi$
$997$	55.6230	1.76160	0.880799	+	0.473491i	$0.157006\pi$
$998$	30.2972	0.959043
$999$	−7.34881	−0.232506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.3	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.3	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} +O(q^{10})\)	\(q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} -2.69988 q^{10} +2.05516 q^{11} -2.61642 q^{12} -4.61042 q^{13} -9.33708 q^{14} -0.494659 q^{15} +13.3984 q^{16} +0.0376674 q^{17} +7.43900 q^{18} -6.34243 q^{19} +5.28933 q^{20} -1.71070 q^{21} -5.54869 q^{22} -5.72394 q^{23} +4.39297 q^{24} +1.00000 q^{25} +12.4476 q^{26} +2.84692 q^{27} +18.2923 q^{28} +7.38384 q^{29} +1.33552 q^{30} +0.978803 q^{31} -18.4124 q^{32} -1.01661 q^{33} -0.101697 q^{34} +3.45834 q^{35} -14.5738 q^{36} -2.58132 q^{37} +17.1238 q^{38} +2.28059 q^{39} -8.88080 q^{40} -1.56398 q^{41} +4.61868 q^{42} +2.20743 q^{43} +10.8705 q^{44} -2.75531 q^{45} +15.4539 q^{46} -11.2376 q^{47} -6.62764 q^{48} +4.96010 q^{49} -2.69988 q^{50} -0.0186325 q^{51} -24.3860 q^{52} +10.5759 q^{53} -7.68633 q^{54} +2.05516 q^{55} -30.7128 q^{56} +3.13734 q^{57} -19.9355 q^{58} -1.30853 q^{59} -2.61642 q^{60} -8.58263 q^{61} -2.64265 q^{62} -9.52880 q^{63} +22.9144 q^{64} -4.61042 q^{65} +2.74471 q^{66} -13.5641 q^{67} +0.199236 q^{68} +2.83140 q^{69} -9.33708 q^{70} +0.0361528 q^{71} +24.4694 q^{72} -6.51047 q^{73} +6.96925 q^{74} -0.494659 q^{75} -33.5472 q^{76} +7.10745 q^{77} -6.15730 q^{78} +8.52645 q^{79} +13.3984 q^{80} +6.85768 q^{81} +4.22256 q^{82} +6.10541 q^{83} -9.04846 q^{84} +0.0376674 q^{85} -5.95980 q^{86} -3.65248 q^{87} -18.2515 q^{88} +12.1970 q^{89} +7.43900 q^{90} -15.9444 q^{91} -30.2758 q^{92} -0.484174 q^{93} +30.3400 q^{94} -6.34243 q^{95} +9.10787 q^{96} -6.54569 q^{97} -13.3917 q^{98} -5.66262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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