LMFDB - Embedded newform 8035.2.a.e.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.77624 q^{2} +1.54873 q^{3} +5.70752 q^{4} +1.00000 q^{5} -4.29965 q^{6} -0.285554 q^{7} -10.2930 q^{8} -0.601430 q^{9} +O(q^{10})$	\(q-2.77624 q^{2} +1.54873 q^{3} +5.70752 q^{4} +1.00000 q^{5} -4.29965 q^{6} -0.285554 q^{7} -10.2930 q^{8} -0.601430 q^{9} -2.77624 q^{10} +5.98927 q^{11} +8.83941 q^{12} -1.66116 q^{13} +0.792766 q^{14} +1.54873 q^{15} +17.1607 q^{16} +0.925145 q^{17} +1.66971 q^{18} +4.25042 q^{19} +5.70752 q^{20} -0.442246 q^{21} -16.6277 q^{22} +3.90313 q^{23} -15.9410 q^{24} +1.00000 q^{25} +4.61179 q^{26} -5.57765 q^{27} -1.62980 q^{28} +3.04199 q^{29} -4.29965 q^{30} +6.52521 q^{31} -27.0564 q^{32} +9.27578 q^{33} -2.56843 q^{34} -0.285554 q^{35} -3.43267 q^{36} +0.670341 q^{37} -11.8002 q^{38} -2.57270 q^{39} -10.2930 q^{40} +9.69421 q^{41} +1.22778 q^{42} +2.41354 q^{43} +34.1839 q^{44} -0.601430 q^{45} -10.8360 q^{46} -1.78921 q^{47} +26.5774 q^{48} -6.91846 q^{49} -2.77624 q^{50} +1.43280 q^{51} -9.48112 q^{52} +0.986060 q^{53} +15.4849 q^{54} +5.98927 q^{55} +2.93919 q^{56} +6.58276 q^{57} -8.44529 q^{58} +0.203441 q^{59} +8.83941 q^{60} -1.06783 q^{61} -18.1156 q^{62} +0.171740 q^{63} +40.7936 q^{64} -1.66116 q^{65} -25.7518 q^{66} +4.61177 q^{67} +5.28028 q^{68} +6.04491 q^{69} +0.792766 q^{70} +4.94620 q^{71} +6.19049 q^{72} +15.6211 q^{73} -1.86103 q^{74} +1.54873 q^{75} +24.2593 q^{76} -1.71026 q^{77} +7.14242 q^{78} +8.10983 q^{79} +17.1607 q^{80} -6.83399 q^{81} -26.9135 q^{82} -9.37155 q^{83} -2.52413 q^{84} +0.925145 q^{85} -6.70058 q^{86} +4.71122 q^{87} -61.6474 q^{88} -4.22230 q^{89} +1.66971 q^{90} +0.474351 q^{91} +22.2772 q^{92} +10.1058 q^{93} +4.96729 q^{94} +4.25042 q^{95} -41.9031 q^{96} -14.1713 q^{97} +19.2073 q^{98} -3.60213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77624	−1.96310	−0.981550	−	0.191208i	$-0.938760\pi$
$2$	−2.77624	−1.96310	−0.981550	+	0.191208i	$0.938760\pi$
$3$	1.54873	0.894161	0.447080	−	0.894494i	$-0.352464\pi$
$3$	1.54873	0.894161	0.447080	+	0.894494i	$0.352464\pi$
$4$	5.70752	2.85376
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.29965	−1.75533
$7$	−0.285554	−0.107929	−0.0539645	−	0.998543i	$-0.517186\pi$
$7$	−0.285554	−0.107929	−0.0539645	+	0.998543i	$0.517186\pi$
$8$	−10.2930	−3.63911
$9$	−0.601430	−0.200477
$10$	−2.77624	−0.877925
$11$	5.98927	1.80583	0.902917	−	0.429815i	$-0.141421\pi$
$11$	5.98927	1.80583	0.902917	+	0.429815i	$0.141421\pi$
$12$	8.83941	2.55172
$13$	−1.66116	−0.460724	−0.230362	−	0.973105i	$-0.573991\pi$
$13$	−1.66116	−0.460724	−0.230362	+	0.973105i	$0.573991\pi$
$14$	0.792766	0.211875
$15$	1.54873	0.399881
$16$	17.1607	4.29018
$17$	0.925145	0.224381	0.112190	−	0.993687i	$-0.464213\pi$
$17$	0.925145	0.224381	0.112190	+	0.993687i	$0.464213\pi$
$18$	1.66971	0.393555
$19$	4.25042	0.975113	0.487557	−	0.873091i	$-0.337888\pi$
$19$	4.25042	0.975113	0.487557	+	0.873091i	$0.337888\pi$
$20$	5.70752	1.27624
$21$	−0.442246	−0.0965059
$22$	−16.6277	−3.54503
$23$	3.90313	0.813860	0.406930	−	0.913459i	$-0.366599\pi$
$23$	3.90313	0.813860	0.406930	+	0.913459i	$0.366599\pi$
$24$	−15.9410	−3.25395
$25$	1.00000	0.200000
$26$	4.61179	0.904446
$27$	−5.57765	−1.07342
$28$	−1.62980	−0.308004
$29$	3.04199	0.564883	0.282441	−	0.959285i	$-0.408856\pi$
$29$	3.04199	0.564883	0.282441	+	0.959285i	$0.408856\pi$
$30$	−4.29965	−0.785006
$31$	6.52521	1.17196	0.585981	−	0.810325i	$-0.300709\pi$
$31$	6.52521	1.17196	0.585981	+	0.810325i	$0.300709\pi$
$32$	−27.0564	−4.78294
$33$	9.27578	1.61471
$34$	−2.56843	−0.440481
$35$	−0.285554	−0.0482674
$36$	−3.43267	−0.572112
$37$	0.670341	0.110203	0.0551017	−	0.998481i	$-0.482452\pi$
$37$	0.670341	0.110203	0.0551017	+	0.998481i	$0.482452\pi$
$38$	−11.8002	−1.91424
$39$	−2.57270	−0.411961
$40$	−10.2930	−1.62746
$41$	9.69421	1.51398	0.756991	−	0.653426i	$-0.226669\pi$
$41$	9.69421	1.51398	0.756991	+	0.653426i	$0.226669\pi$
$42$	1.22778	0.189451
$43$	2.41354	0.368062	0.184031	−	0.982920i	$-0.441085\pi$
$43$	2.41354	0.368062	0.184031	+	0.982920i	$0.441085\pi$
$44$	34.1839	5.15341
$45$	−0.601430	−0.0896558
$46$	−10.8360	−1.59769
$47$	−1.78921	−0.260984	−0.130492	−	0.991449i	$-0.541656\pi$
$47$	−1.78921	−0.260984	−0.130492	+	0.991449i	$0.541656\pi$
$48$	26.5774	3.83611
$49$	−6.91846	−0.988351
$50$	−2.77624	−0.392620
$51$	1.43280	0.200632
$52$	−9.48112	−1.31479
$53$	0.986060	0.135446	0.0677229	−	0.997704i	$-0.478427\pi$
$53$	0.986060	0.135446	0.0677229	+	0.997704i	$0.478427\pi$
$54$	15.4849	2.10723
$55$	5.98927	0.807594
$56$	2.93919	0.392766
$57$	6.58276	0.871908
$58$	−8.44529	−1.10892
$59$	0.203441	0.0264858	0.0132429	−	0.999912i	$-0.495785\pi$
$59$	0.203441	0.0264858	0.0132429	+	0.999912i	$0.495785\pi$
$60$	8.83941	1.14116
$61$	−1.06783	−0.136721	−0.0683605	−	0.997661i	$-0.521777\pi$
$61$	−1.06783	−0.136721	−0.0683605	+	0.997661i	$0.521777\pi$
$62$	−18.1156	−2.30068
$63$	0.171740	0.0216373
$64$	40.7936	5.09920
$65$	−1.66116	−0.206042
$66$	−25.7518	−3.16983
$67$	4.61177	0.563418	0.281709	−	0.959500i	$-0.409099\pi$
$67$	4.61177	0.563418	0.281709	+	0.959500i	$0.409099\pi$
$68$	5.28028	0.640328
$69$	6.04491	0.727721
$70$	0.792766	0.0947536
$71$	4.94620	0.587007	0.293503	−	0.955958i	$-0.405179\pi$
$71$	4.94620	0.587007	0.293503	+	0.955958i	$0.405179\pi$
$72$	6.19049	0.729557
$73$	15.6211	1.82831	0.914153	−	0.405369i	$-0.132857\pi$
$73$	15.6211	1.82831	0.914153	+	0.405369i	$0.132857\pi$
$74$	−1.86103	−0.216340
$75$	1.54873	0.178832
$76$	24.2593	2.78274
$77$	−1.71026	−0.194902
$78$	7.14242	0.808720
$79$	8.10983	0.912428	0.456214	−	0.889870i	$-0.349205\pi$
$79$	8.10983	0.912428	0.456214	+	0.889870i	$0.349205\pi$
$80$	17.1607	1.91863
$81$	−6.83399	−0.759333
$82$	−26.9135	−2.97210
$83$	−9.37155	−1.02866	−0.514330	−	0.857592i	$-0.671959\pi$
$83$	−9.37155	−1.02866	−0.514330	+	0.857592i	$0.671959\pi$
$84$	−2.52413	−0.275405
$85$	0.925145	0.100346
$86$	−6.70058	−0.722542
$87$	4.71122	0.505096
$88$	−61.6474	−6.57163
$89$	−4.22230	−0.447563	−0.223782	−	0.974639i	$-0.571840\pi$
$89$	−4.22230	−0.447563	−0.223782	+	0.974639i	$0.571840\pi$
$90$	1.66971	0.176003
$91$	0.474351	0.0497255
$92$	22.2772	2.32256
$93$	10.1058	1.04792
$94$	4.96729	0.512337
$95$	4.25042	0.436084
$96$	−41.9031	−4.27671
$97$	−14.1713	−1.43887	−0.719437	−	0.694558i	$-0.755600\pi$
$97$	−14.1713	−1.43887	−0.719437	+	0.694558i	$0.755600\pi$
$98$	19.2073	1.94023
$99$	−3.60213	−0.362027
$100$	5.70752	0.570752
$101$	−19.1738	−1.90786	−0.953932	−	0.300022i	$-0.903006\pi$
$101$	−19.1738	−1.90786	−0.953932	+	0.300022i	$0.903006\pi$
$102$	−3.97780	−0.393861
$103$	−14.6688	−1.44536	−0.722679	−	0.691184i	$-0.757090\pi$
$103$	−14.6688	−1.44536	−0.722679	+	0.691184i	$0.757090\pi$
$104$	17.0983	1.67663
$105$	−0.442246	−0.0431588
$106$	−2.73754	−0.265893
$107$	8.32461	0.804770	0.402385	−	0.915471i	$-0.368181\pi$
$107$	8.32461	0.804770	0.402385	+	0.915471i	$0.368181\pi$
$108$	−31.8345	−3.06328
$109$	−2.74202	−0.262638	−0.131319	−	0.991340i	$-0.541921\pi$
$109$	−2.74202	−0.262638	−0.131319	+	0.991340i	$0.541921\pi$
$110$	−16.6277	−1.58539
$111$	1.03818	0.0985396
$112$	−4.90030	−0.463035
$113$	−2.07193	−0.194910	−0.0974552	−	0.995240i	$-0.531070\pi$
$113$	−2.07193	−0.194910	−0.0974552	+	0.995240i	$0.531070\pi$
$114$	−18.2753	−1.71164
$115$	3.90313	0.363969
$116$	17.3622	1.61204
$117$	0.999073	0.0923643
$118$	−0.564802	−0.0519942
$119$	−0.264178	−0.0242172
$120$	−15.9410	−1.45521
$121$	24.8714	2.26104
$122$	2.96454	0.268397
$123$	15.0137	1.35374
$124$	37.2427	3.34450
$125$	1.00000	0.0894427
$126$	−0.476793	−0.0424761
$127$	6.73285	0.597444	0.298722	−	0.954340i	$-0.403440\pi$
$127$	6.73285	0.597444	0.298722	+	0.954340i	$0.403440\pi$
$128$	−59.1401	−5.22730
$129$	3.73793	0.329106
$130$	4.61179	0.404481
$131$	8.03671	0.702171	0.351086	−	0.936343i	$-0.385813\pi$
$131$	8.03671	0.702171	0.351086	+	0.936343i	$0.385813\pi$
$132$	52.9417	4.60798
$133$	−1.21372	−0.105243
$134$	−12.8034	−1.10605
$135$	−5.57765	−0.480048
$136$	−9.52248	−0.816546
$137$	−3.80919	−0.325441	−0.162721	−	0.986672i	$-0.552027\pi$
$137$	−3.80919	−0.325441	−0.162721	+	0.986672i	$0.552027\pi$
$138$	−16.7821	−1.42859
$139$	−19.8425	−1.68302	−0.841508	−	0.540244i	$-0.818332\pi$
$139$	−19.8425	−1.68302	−0.841508	+	0.540244i	$0.818332\pi$
$140$	−1.62980	−0.137743
$141$	−2.77101	−0.233361
$142$	−13.7319	−1.15235
$143$	−9.94916	−0.831990
$144$	−10.3210	−0.860080
$145$	3.04199	0.252623
$146$	−43.3678	−3.58915
$147$	−10.7148	−0.883745
$148$	3.82598	0.314494
$149$	−12.3976	−1.01565	−0.507826	−	0.861460i	$-0.669551\pi$
$149$	−12.3976	−1.01565	−0.507826	+	0.861460i	$0.669551\pi$
$150$	−4.29965	−0.351065
$151$	−4.22393	−0.343739	−0.171869	−	0.985120i	$-0.554981\pi$
$151$	−4.22393	−0.343739	−0.171869	+	0.985120i	$0.554981\pi$
$152$	−43.7494	−3.54855
$153$	−0.556410	−0.0449831
$154$	4.74809	0.382612
$155$	6.52521	0.524117
$156$	−14.6837	−1.17564
$157$	−10.3033	−0.822295	−0.411147	−	0.911569i	$-0.634872\pi$
$157$	−10.3033	−0.822295	−0.411147	+	0.911569i	$0.634872\pi$
$158$	−22.5149	−1.79119
$159$	1.52714	0.121110
$160$	−27.0564	−2.13899
$161$	−1.11455	−0.0878391
$162$	18.9728	1.49065
$163$	−16.8917	−1.32306	−0.661528	−	0.749920i	$-0.730092\pi$
$163$	−16.8917	−1.32306	−0.661528	+	0.749920i	$0.730092\pi$
$164$	55.3299	4.32054
$165$	9.27578	0.722118
$166$	26.0177	2.01936
$167$	10.1238	0.783404	0.391702	−	0.920092i	$-0.371886\pi$
$167$	10.1238	0.783404	0.391702	+	0.920092i	$0.371886\pi$
$168$	4.55202	0.351196
$169$	−10.2405	−0.787734
$170$	−2.56843	−0.196989
$171$	−2.55633	−0.195487
$172$	13.7753	1.05036
$173$	8.72403	0.663276	0.331638	−	0.943407i	$-0.392399\pi$
$173$	8.72403	0.663276	0.331638	+	0.943407i	$0.392399\pi$
$174$	−13.0795	−0.991553
$175$	−0.285554	−0.0215858
$176$	102.780	7.74735
$177$	0.315076	0.0236825
$178$	11.7221	0.878611
$179$	−4.29841	−0.321278	−0.160639	−	0.987013i	$-0.551356\pi$
$179$	−4.29841	−0.321278	−0.160639	+	0.987013i	$0.551356\pi$
$180$	−3.43267	−0.255856
$181$	−6.53585	−0.485806	−0.242903	−	0.970051i	$-0.578100\pi$
$181$	−6.53585	−0.485806	−0.242903	+	0.970051i	$0.578100\pi$
$182$	−1.31691	−0.0976161
$183$	−1.65378	−0.122251
$184$	−40.1748	−2.96173
$185$	0.670341	0.0492845
$186$	−28.0561	−2.05718
$187$	5.54095	0.405194
$188$	−10.2120	−0.744785
$189$	1.59272	0.115853
$190$	−11.8002	−0.856076
$191$	24.6316	1.78228	0.891141	−	0.453726i	$-0.149906\pi$
$191$	24.6316	1.78228	0.891141	+	0.453726i	$0.149906\pi$
$192$	63.1783	4.55950
$193$	−11.0658	−0.796537	−0.398268	−	0.917269i	$-0.630389\pi$
$193$	−11.0658	−0.796537	−0.398268	+	0.917269i	$0.630389\pi$
$194$	39.3429	2.82465
$195$	−2.57270	−0.184235
$196$	−39.4872	−2.82052
$197$	22.9506	1.63517	0.817583	−	0.575811i	$-0.195314\pi$
$197$	22.9506	1.63517	0.817583	+	0.575811i	$0.195314\pi$
$198$	10.0004	0.710696
$199$	−8.38036	−0.594068	−0.297034	−	0.954867i	$-0.595997\pi$
$199$	−8.38036	−0.594068	−0.297034	+	0.954867i	$0.595997\pi$
$200$	−10.2930	−0.727822
$201$	7.14240	0.503786
$202$	53.2311	3.74533
$203$	−0.868650	−0.0609673
$204$	8.17774	0.572556
$205$	9.69421	0.677073
$206$	40.7241	2.83738
$207$	−2.34746	−0.163160
$208$	−28.5067	−1.97659
$209$	25.4569	1.76089
$210$	1.22778	0.0847250
$211$	19.8566	1.36698	0.683491	−	0.729959i	$-0.260461\pi$
$211$	19.8566	1.36698	0.683491	+	0.729959i	$0.260461\pi$
$212$	5.62795	0.386529
$213$	7.66034	0.524878
$214$	−23.1111	−1.57984
$215$	2.41354	0.164602
$216$	57.4105	3.90629
$217$	−1.86330	−0.126489
$218$	7.61251	0.515584
$219$	24.1928	1.63480
$220$	34.1839	2.30468
$221$	−1.53682	−0.103377
$222$	−2.88224	−0.193443
$223$	9.91011	0.663630	0.331815	−	0.943345i	$-0.392339\pi$
$223$	9.91011	0.663630	0.331815	+	0.943345i	$0.392339\pi$
$224$	7.72604	0.516218
$225$	−0.601430	−0.0400953
$226$	5.75217	0.382629
$227$	24.9432	1.65554	0.827770	−	0.561067i	$-0.189609\pi$
$227$	24.9432	1.65554	0.827770	+	0.561067i	$0.189609\pi$
$228$	37.5712	2.48821
$229$	−8.65945	−0.572232	−0.286116	−	0.958195i	$-0.592364\pi$
$229$	−8.65945	−0.572232	−0.286116	+	0.958195i	$0.592364\pi$
$230$	−10.8360	−0.714508
$231$	−2.64873	−0.174274
$232$	−31.3111	−2.05567
$233$	7.37154	0.482925	0.241463	−	0.970410i	$-0.422373\pi$
$233$	7.37154	0.482925	0.241463	+	0.970410i	$0.422373\pi$
$234$	−2.77367	−0.181320
$235$	−1.78921	−0.116715
$236$	1.16114	0.0755840
$237$	12.5600	0.815857
$238$	0.733423	0.0475408
$239$	19.0190	1.23024	0.615118	−	0.788435i	$-0.289108\pi$
$239$	19.0190	1.23024	0.615118	+	0.788435i	$0.289108\pi$
$240$	26.5774	1.71556
$241$	−15.6589	−1.00868	−0.504338	−	0.863506i	$-0.668264\pi$
$241$	−15.6589	−1.00868	−0.504338	+	0.863506i	$0.668264\pi$
$242$	−69.0490	−4.43864
$243$	6.14892	0.394454
$244$	−6.09463	−0.390169
$245$	−6.91846	−0.442004
$246$	−41.6817	−2.65753
$247$	−7.06064	−0.449258
$248$	−67.1637	−4.26490
$249$	−14.5140	−0.919788
$250$	−2.77624	−0.175585
$251$	26.6085	1.67952	0.839758	−	0.542960i	$-0.182697\pi$
$251$	26.6085	1.67952	0.839758	+	0.542960i	$0.182697\pi$
$252$	0.980211	0.0617475
$253$	23.3769	1.46970
$254$	−18.6920	−1.17284
$255$	1.43280	0.0897255
$256$	82.6001	5.16250
$257$	−2.12996	−0.132863	−0.0664315	−	0.997791i	$-0.521161\pi$
$257$	−2.12996	−0.132863	−0.0664315	+	0.997791i	$0.521161\pi$
$258$	−10.3774	−0.646068
$259$	−0.191418	−0.0118942
$260$	−9.48112	−0.587994
$261$	−1.82954	−0.113246
$262$	−22.3119	−1.37843
$263$	−0.257515	−0.0158791	−0.00793954	−	0.999968i	$-0.502527\pi$
$263$	−0.257515	−0.0158791	−0.00793954	+	0.999968i	$0.502527\pi$
$264$	−95.4753	−5.87610
$265$	0.986060	0.0605732
$266$	3.36959	0.206603
$267$	−6.53922	−0.400193
$268$	26.3218	1.60786
$269$	−11.5733	−0.705639	−0.352819	−	0.935691i	$-0.614777\pi$
$269$	−11.5733	−0.705639	−0.352819	+	0.935691i	$0.614777\pi$
$270$	15.4849	0.942381
$271$	9.51253	0.577845	0.288922	−	0.957352i	$-0.406703\pi$
$271$	9.51253	0.577845	0.288922	+	0.957352i	$0.406703\pi$
$272$	15.8762	0.962633
$273$	0.734642	0.0444626
$274$	10.5752	0.638874
$275$	5.98927	0.361167
$276$	34.5014	2.07674
$277$	24.3908	1.46550	0.732750	−	0.680498i	$-0.238236\pi$
$277$	24.3908	1.46550	0.732750	+	0.680498i	$0.238236\pi$
$278$	55.0875	3.30393
$279$	−3.92445	−0.234951
$280$	2.93919	0.175650
$281$	5.23052	0.312026	0.156013	−	0.987755i	$-0.450136\pi$
$281$	5.23052	0.312026	0.156013	+	0.987755i	$0.450136\pi$
$282$	7.69300	0.458112
$283$	−8.55517	−0.508552	−0.254276	−	0.967132i	$-0.581837\pi$
$283$	−8.55517	−0.508552	−0.254276	+	0.967132i	$0.581837\pi$
$284$	28.2305	1.67517
$285$	6.58276	0.389929
$286$	27.6213	1.63328
$287$	−2.76822	−0.163403
$288$	16.2725	0.958867
$289$	−16.1441	−0.949653
$290$	−8.44529	−0.495924
$291$	−21.9475	−1.28658
$292$	89.1575	5.21755
$293$	15.9010	0.928948	0.464474	−	0.885587i	$-0.346243\pi$
$293$	15.9010	0.928948	0.464474	+	0.885587i	$0.346243\pi$
$294$	29.7470	1.73488
$295$	0.203441	0.0118448
$296$	−6.89980	−0.401043
$297$	−33.4061	−1.93842
$298$	34.4188	1.99383
$299$	−6.48374	−0.374964
$300$	8.83941	0.510344
$301$	−0.689195	−0.0397246
$302$	11.7267	0.674793
$303$	−29.6951	−1.70594
$304$	72.9403	4.18341
$305$	−1.06783	−0.0611435
$306$	1.54473	0.0883062
$307$	−10.8588	−0.619746	−0.309873	−	0.950778i	$-0.600287\pi$
$307$	−10.8588	−0.619746	−0.309873	+	0.950778i	$0.600287\pi$
$308$	−9.76133	−0.556203
$309$	−22.7180	−1.29238
$310$	−18.1156	−1.02889
$311$	4.38222	0.248493	0.124247	−	0.992251i	$-0.460349\pi$
$311$	4.38222	0.248493	0.124247	+	0.992251i	$0.460349\pi$
$312$	26.4807	1.49917
$313$	−17.5973	−0.994659	−0.497330	−	0.867562i	$-0.665686\pi$
$313$	−17.5973	−0.994659	−0.497330	+	0.867562i	$0.665686\pi$
$314$	28.6045	1.61425
$315$	0.171740	0.00967647
$316$	46.2870	2.60385
$317$	25.6921	1.44301	0.721507	−	0.692407i	$-0.243450\pi$
$317$	25.6921	1.44301	0.721507	+	0.692407i	$0.243450\pi$
$318$	−4.23972	−0.237751
$319$	18.2193	1.02008
$320$	40.7936	2.28043
$321$	12.8926	0.719594
$322$	3.09427	0.172437
$323$	3.93226	0.218797
$324$	−39.0051	−2.16695
$325$	−1.66116	−0.0921447
$326$	46.8953	2.59729
$327$	−4.24665	−0.234841
$328$	−99.7821	−5.50955
$329$	0.510916	0.0281677
$330$	−25.7518	−1.41759
$331$	−20.8353	−1.14521	−0.572606	−	0.819831i	$-0.694068\pi$
$331$	−20.8353	−1.14521	−0.572606	+	0.819831i	$0.694068\pi$
$332$	−53.4883	−2.93555
$333$	−0.403163	−0.0220932
$334$	−28.1061	−1.53790
$335$	4.61177	0.251968
$336$	−7.58926	−0.414028
$337$	−18.5133	−1.00848	−0.504242	−	0.863562i	$-0.668228\pi$
$337$	−18.5133	−1.00848	−0.504242	+	0.863562i	$0.668228\pi$
$338$	28.4302	1.54640
$339$	−3.20886	−0.174281
$340$	5.28028	0.286363
$341$	39.0813	2.11637
$342$	7.09699	0.383761
$343$	3.97446	0.214601
$344$	−24.8425	−1.33942
$345$	6.04491	0.325447
$346$	−24.2200	−1.30208
$347$	34.0030	1.82538	0.912688	−	0.408657i	$-0.134003\pi$
$347$	34.0030	1.82538	0.912688	+	0.408657i	$0.134003\pi$
$348$	26.8894	1.44142
$349$	14.8203	0.793314	0.396657	−	0.917967i	$-0.370170\pi$
$349$	14.8203	0.793314	0.396657	+	0.917967i	$0.370170\pi$
$350$	0.792766	0.0423751
$351$	9.26538	0.494550
$352$	−162.048	−8.63719
$353$	−3.33345	−0.177422	−0.0887109	−	0.996057i	$-0.528275\pi$
$353$	−3.33345	−0.177422	−0.0887109	+	0.996057i	$0.528275\pi$
$354$	−0.874726	−0.0464912
$355$	4.94620	0.262517
$356$	−24.0989	−1.27724
$357$	−0.409142	−0.0216541
$358$	11.9334	0.630701
$359$	−21.3772	−1.12825	−0.564123	−	0.825691i	$-0.690785\pi$
$359$	−21.3772	−1.12825	−0.564123	+	0.825691i	$0.690785\pi$
$360$	6.19049	0.326268
$361$	−0.933929	−0.0491542
$362$	18.1451	0.953685
$363$	38.5191	2.02173
$364$	2.70737	0.141905
$365$	15.6211	0.817644
$366$	4.59128	0.239990
$367$	−22.0047	−1.14863	−0.574317	−	0.818633i	$-0.694732\pi$
$367$	−22.0047	−1.14863	−0.574317	+	0.818633i	$0.694732\pi$
$368$	66.9806	3.49160
$369$	−5.83039	−0.303518
$370$	−1.86103	−0.0967503
$371$	−0.281573	−0.0146185
$372$	57.6790	2.99052
$373$	29.3077	1.51750	0.758748	−	0.651384i	$-0.225811\pi$
$373$	29.3077	1.51750	0.758748	+	0.651384i	$0.225811\pi$
$374$	−15.3830	−0.795436
$375$	1.54873	0.0799762
$376$	18.4163	0.949749
$377$	−5.05323	−0.260255
$378$	−4.42177	−0.227431
$379$	36.3492	1.86713	0.933566	−	0.358406i	$-0.116680\pi$
$379$	36.3492	1.86713	0.933566	+	0.358406i	$0.116680\pi$
$380$	24.2593	1.24448
$381$	10.4274	0.534211
$382$	−68.3833	−3.49880
$383$	9.47282	0.484039	0.242019	−	0.970271i	$-0.422190\pi$
$383$	9.47282	0.484039	0.242019	+	0.970271i	$0.422190\pi$
$384$	−91.5922	−4.67404
$385$	−1.71026	−0.0871628
$386$	30.7215	1.56368
$387$	−1.45158	−0.0737877
$388$	−80.8827	−4.10620
$389$	0.647709	0.0328402	0.0164201	−	0.999865i	$-0.494773\pi$
$389$	0.647709	0.0328402	0.0164201	+	0.999865i	$0.494773\pi$
$390$	7.14242	0.361671
$391$	3.61097	0.182614
$392$	71.2114	3.59672
$393$	12.4467	0.627854
$394$	−63.7165	−3.20999
$395$	8.10983	0.408050
$396$	−20.5592	−1.03314
$397$	−31.0776	−1.55974	−0.779871	−	0.625940i	$-0.784715\pi$
$397$	−31.0776	−1.55974	−0.779871	+	0.625940i	$0.784715\pi$
$398$	23.2659	1.16621
$399$	−1.87973	−0.0941042
$400$	17.1607	0.858036
$401$	−12.2679	−0.612627	−0.306314	−	0.951931i	$-0.599096\pi$
$401$	−12.2679	−0.612627	−0.306314	+	0.951931i	$0.599096\pi$
$402$	−19.8290	−0.988982
$403$	−10.8394	−0.539951
$404$	−109.435	−5.44458
$405$	−6.83399	−0.339584
$406$	2.41158	0.119685
$407$	4.01486	0.199009
$408$	−14.7478	−0.730124
$409$	−28.9145	−1.42973	−0.714865	−	0.699262i	$-0.753512\pi$
$409$	−28.9145	−1.42973	−0.714865	+	0.699262i	$0.753512\pi$
$410$	−26.9135	−1.32916
$411$	−5.89942	−0.290997
$412$	−83.7223	−4.12470
$413$	−0.0580933	−0.00285859
$414$	6.51712	0.320299
$415$	−9.37155	−0.460031
$416$	44.9450	2.20361
$417$	−30.7307	−1.50489
$418$	−70.6746	−3.45681
$419$	1.38654	0.0677371	0.0338686	−	0.999426i	$-0.489217\pi$
$419$	1.38654	0.0677371	0.0338686	+	0.999426i	$0.489217\pi$
$420$	−2.52413	−0.123165
$421$	13.5491	0.660340	0.330170	−	0.943921i	$-0.392894\pi$
$421$	13.5491	0.660340	0.330170	+	0.943921i	$0.392894\pi$
$422$	−55.1266	−2.68352
$423$	1.07609	0.0523211
$424$	−10.1495	−0.492902
$425$	0.925145	0.0448761
$426$	−21.2670	−1.03039
$427$	0.304921	0.0147562
$428$	47.5128	2.29662
$429$	−15.4086	−0.743933
$430$	−6.70058	−0.323130
$431$	18.5687	0.894422	0.447211	−	0.894428i	$-0.352417\pi$
$431$	18.5687	0.894422	0.447211	+	0.894428i	$0.352417\pi$
$432$	−95.7165	−4.60516
$433$	−39.0352	−1.87591	−0.937955	−	0.346756i	$-0.887283\pi$
$433$	−39.0352	−1.87591	−0.937955	+	0.346756i	$0.887283\pi$
$434$	5.17296	0.248310
$435$	4.71122	0.225886
$436$	−15.6501	−0.749505
$437$	16.5900	0.793605
$438$	−67.1651	−3.20927
$439$	1.26087	0.0601782	0.0300891	−	0.999547i	$-0.490421\pi$
$439$	1.26087	0.0601782	0.0300891	+	0.999547i	$0.490421\pi$
$440$	−61.6474	−2.93892
$441$	4.16097	0.198141
$442$	4.26657	0.202940
$443$	−10.5450	−0.501009	−0.250504	−	0.968115i	$-0.580596\pi$
$443$	−10.5450	−0.501009	−0.250504	+	0.968115i	$0.580596\pi$
$444$	5.92542	0.281208
$445$	−4.22230	−0.200156
$446$	−27.5128	−1.30277
$447$	−19.2006	−0.908156
$448$	−11.6488	−0.550352
$449$	39.4969	1.86397	0.931986	−	0.362494i	$-0.118075\pi$
$449$	39.4969	1.86397	0.931986	+	0.362494i	$0.118075\pi$
$450$	1.66971	0.0787111
$451$	58.0613	2.73400
$452$	−11.8256	−0.556228
$453$	−6.54174	−0.307358
$454$	−69.2485	−3.24999
$455$	0.474351	0.0222379
$456$	−67.7561	−3.17297
$457$	17.4277	0.815232	0.407616	−	0.913153i	$-0.366360\pi$
$457$	17.4277	0.815232	0.407616	+	0.913153i	$0.366360\pi$
$458$	24.0407	1.12335
$459$	−5.16013	−0.240854
$460$	22.2772	1.03868
$461$	−14.5109	−0.675838	−0.337919	−	0.941175i	$-0.609723\pi$
$461$	−14.5109	−0.675838	−0.337919	+	0.941175i	$0.609723\pi$
$462$	7.35352	0.342117
$463$	36.2033	1.68251	0.841255	−	0.540638i	$-0.181817\pi$
$463$	36.2033	1.68251	0.841255	+	0.540638i	$0.181817\pi$
$464$	52.2027	2.42345
$465$	10.1058	0.468645
$466$	−20.4652	−0.948030
$467$	−15.9154	−0.736475	−0.368238	−	0.929732i	$-0.620039\pi$
$467$	−15.9154	−0.736475	−0.368238	+	0.929732i	$0.620039\pi$
$468$	5.70222	0.263585
$469$	−1.31691	−0.0608092
$470$	4.96729	0.229124
$471$	−15.9571	−0.735264
$472$	−2.09401	−0.0963847
$473$	14.4554	0.664658
$474$	−34.8695	−1.60161
$475$	4.25042	0.195023
$476$	−1.50780	−0.0691100
$477$	−0.593046	−0.0271537
$478$	−52.8013	−2.41508
$479$	−6.84437	−0.312727	−0.156364	−	0.987700i	$-0.549977\pi$
$479$	−6.84437	−0.312727	−0.156364	+	0.987700i	$0.549977\pi$
$480$	−41.9031	−1.91260
$481$	−1.11355	−0.0507733
$482$	43.4728	1.98013
$483$	−1.72614	−0.0785423
$484$	141.954	6.45245
$485$	−14.1713	−0.643484
$486$	−17.0709	−0.774352
$487$	10.1919	0.461840	0.230920	−	0.972973i	$-0.425826\pi$
$487$	10.1919	0.461840	0.230920	+	0.972973i	$0.425826\pi$
$488$	10.9911	0.497543
$489$	−26.1606	−1.18303
$490$	19.2073	0.867698
$491$	−5.36581	−0.242155	−0.121078	−	0.992643i	$-0.538635\pi$
$491$	−5.36581	−0.242155	−0.121078	+	0.992643i	$0.538635\pi$
$492$	85.6911	3.86325
$493$	2.81428	0.126749
$494$	19.6020	0.881938
$495$	−3.60213	−0.161904
$496$	111.977	5.02793
$497$	−1.41241	−0.0633551
$498$	40.2944	1.80564
$499$	−6.64210	−0.297341	−0.148671	−	0.988887i	$-0.547499\pi$
$499$	−6.64210	−0.297341	−0.148671	+	0.988887i	$0.547499\pi$
$500$	5.70752	0.255248
$501$	15.6791	0.700489
$502$	−73.8718	−3.29706
$503$	−14.8976	−0.664253	−0.332126	−	0.943235i	$-0.607766\pi$
$503$	−14.8976	−0.664253	−0.332126	+	0.943235i	$0.607766\pi$
$504$	−1.76772	−0.0787404
$505$	−19.1738	−0.853223
$506$	−64.9000	−2.88516
$507$	−15.8598	−0.704361
$508$	38.4279	1.70496
$509$	−10.3839	−0.460260	−0.230130	−	0.973160i	$-0.573915\pi$
$509$	−10.3839	−0.460260	−0.230130	+	0.973160i	$0.573915\pi$
$510$	−3.97780	−0.176140
$511$	−4.46065	−0.197327
$512$	−111.038	−4.90721
$513$	−23.7074	−1.04671
$514$	5.91328	0.260823
$515$	−14.6688	−0.646384
$516$	21.3343	0.939190
$517$	−10.7161	−0.471293
$518$	0.531423	0.0233494
$519$	13.5112	0.593075
$520$	17.0983	0.749810
$521$	29.3053	1.28389	0.641945	−	0.766751i	$-0.278128\pi$
$521$	29.3053	1.28389	0.641945	+	0.766751i	$0.278128\pi$
$522$	5.07925	0.222313
$523$	−2.15564	−0.0942595	−0.0471297	−	0.998889i	$-0.515007\pi$
$523$	−2.15564	−0.0942595	−0.0471297	+	0.998889i	$0.515007\pi$
$524$	45.8697	2.00383
$525$	−0.442246	−0.0193012
$526$	0.714925	0.0311722
$527$	6.03677	0.262966
$528$	159.179	6.92738
$529$	−7.76554	−0.337632
$530$	−2.73754	−0.118911
$531$	−0.122356	−0.00530978
$532$	−6.92734	−0.300338
$533$	−16.1037	−0.697527
$534$	18.1544	0.785619
$535$	8.32461	0.359904
$536$	−47.4688	−2.05034
$537$	−6.65709	−0.287275
$538$	32.1304	1.38524
$539$	−41.4365	−1.78480
$540$	−31.8345	−1.36994
$541$	−30.3456	−1.30466	−0.652330	−	0.757935i	$-0.726208\pi$
$541$	−30.3456	−1.30466	−0.652330	+	0.757935i	$0.726208\pi$
$542$	−26.4091	−1.13437
$543$	−10.1223	−0.434388
$544$	−25.0311	−1.07320
$545$	−2.74202	−0.117455
$546$	−2.03954	−0.0872844
$547$	−1.54945	−0.0662497	−0.0331249	−	0.999451i	$-0.510546\pi$
$547$	−1.54945	−0.0662497	−0.0331249	+	0.999451i	$0.510546\pi$
$548$	−21.7410	−0.928731
$549$	0.642222	0.0274094
$550$	−16.6277	−0.709006
$551$	12.9297	0.550825
$552$	−62.2200	−2.64826
$553$	−2.31579	−0.0984775
$554$	−67.7147	−2.87692
$555$	1.03818	0.0440682
$556$	−113.251	−4.80292
$557$	0.441314	0.0186991	0.00934954	−	0.999956i	$-0.497024\pi$
$557$	0.441314	0.0186991	0.00934954	+	0.999956i	$0.497024\pi$
$558$	10.8952	0.461232
$559$	−4.00929	−0.169575
$560$	−4.90030	−0.207076
$561$	8.58144	0.362309
$562$	−14.5212	−0.612539
$563$	−17.7172	−0.746690	−0.373345	−	0.927693i	$-0.621789\pi$
$563$	−17.7172	−0.746690	−0.373345	+	0.927693i	$0.621789\pi$
$564$	−15.8156	−0.665957
$565$	−2.07193	−0.0871666
$566$	23.7512	0.998339
$567$	1.95147	0.0819541
$568$	−50.9111	−2.13618
$569$	−3.16538	−0.132700	−0.0663498	−	0.997796i	$-0.521135\pi$
$569$	−3.16538	−0.132700	−0.0663498	+	0.997796i	$0.521135\pi$
$570$	−18.2753	−0.765470
$571$	19.8078	0.828930	0.414465	−	0.910065i	$-0.363969\pi$
$571$	19.8078	0.828930	0.414465	+	0.910065i	$0.363969\pi$
$572$	−56.7850	−2.37430
$573$	38.1478	1.59365
$574$	7.68524	0.320776
$575$	3.90313	0.162772
$576$	−24.5345	−1.02227
$577$	−11.9990	−0.499524	−0.249762	−	0.968307i	$-0.580352\pi$
$577$	−11.9990	−0.499524	−0.249762	+	0.968307i	$0.580352\pi$
$578$	44.8199	1.86426
$579$	−17.1380	−0.712232
$580$	17.3622	0.720926
$581$	2.67608	0.111022
$582$	60.9315	2.52569
$583$	5.90578	0.244592
$584$	−160.787	−6.65341
$585$	0.999073	0.0413066
$586$	−44.1451	−1.82362
$587$	−6.58103	−0.271628	−0.135814	−	0.990734i	$-0.543365\pi$
$587$	−6.58103	−0.271628	−0.135814	+	0.990734i	$0.543365\pi$
$588$	−61.1551	−2.52199
$589$	27.7349	1.14280
$590$	−0.564802	−0.0232525
$591$	35.5444	1.46210
$592$	11.5035	0.472793
$593$	−30.9072	−1.26921	−0.634603	−	0.772838i	$-0.718836\pi$
$593$	−30.9072	−1.26921	−0.634603	+	0.772838i	$0.718836\pi$
$594$	92.7433	3.80530
$595$	−0.264178	−0.0108303
$596$	−70.7596	−2.89843
$597$	−12.9789	−0.531192
$598$	18.0004	0.736092
$599$	35.8813	1.46607	0.733035	−	0.680191i	$-0.238103\pi$
$599$	35.8813	1.46607	0.733035	+	0.680191i	$0.238103\pi$
$600$	−15.9410	−0.650790
$601$	32.8710	1.34084	0.670419	−	0.741983i	$-0.266115\pi$
$601$	32.8710	1.34084	0.670419	+	0.741983i	$0.266115\pi$
$602$	1.91337	0.0779833
$603$	−2.77366	−0.112952
$604$	−24.1082	−0.980947
$605$	24.8714	1.01117
$606$	82.4407	3.34892
$607$	39.8301	1.61665	0.808326	−	0.588735i	$-0.200374\pi$
$607$	39.8301	1.61665	0.808326	+	0.588735i	$0.200374\pi$
$608$	−115.001	−4.66390
$609$	−1.34531	−0.0545145
$610$	2.96454	0.120031
$611$	2.97218	0.120241
$612$	−3.17572	−0.128371
$613$	38.7089	1.56344	0.781719	−	0.623631i	$-0.214343\pi$
$613$	38.7089	1.56344	0.781719	+	0.623631i	$0.214343\pi$
$614$	30.1467	1.21662
$615$	15.0137	0.605412
$616$	17.6036	0.709270
$617$	−1.97709	−0.0795948	−0.0397974	−	0.999208i	$-0.512671\pi$
$617$	−1.97709	−0.0795948	−0.0397974	+	0.999208i	$0.512671\pi$
$618$	63.0707	2.53708
$619$	28.1183	1.13017	0.565085	−	0.825033i	$-0.308843\pi$
$619$	28.1183	1.13017	0.565085	+	0.825033i	$0.308843\pi$
$620$	37.2427	1.49570
$621$	−21.7703	−0.873613
$622$	−12.1661	−0.487817
$623$	1.20569	0.0483051
$624$	−44.1493	−1.76739
$625$	1.00000	0.0400000
$626$	48.8544	1.95261
$627$	39.4260	1.57452
$628$	−58.8064	−2.34663
$629$	0.620163	0.0247275
$630$	−0.476793	−0.0189959
$631$	−45.6834	−1.81863	−0.909315	−	0.416109i	$-0.863393\pi$
$631$	−45.6834	−1.81863	−0.909315	+	0.416109i	$0.863393\pi$
$632$	−83.4742	−3.32043
$633$	30.7525	1.22230
$634$	−71.3276	−2.83278
$635$	6.73285	0.267185
$636$	8.71619	0.345619
$637$	11.4927	0.455357
$638$	−50.5812	−2.00253
$639$	−2.97479	−0.117681
$640$	−59.1401	−2.33772
$641$	13.6467	0.539014	0.269507	−	0.962998i	$-0.413139\pi$
$641$	13.6467	0.539014	0.269507	+	0.962998i	$0.413139\pi$
$642$	−35.7929	−1.41263
$643$	−12.5653	−0.495527	−0.247764	−	0.968820i	$-0.579696\pi$
$643$	−12.5653	−0.495527	−0.247764	+	0.968820i	$0.579696\pi$
$644$	−6.36133	−0.250672
$645$	3.73793	0.147181
$646$	−10.9169	−0.429519
$647$	−2.83106	−0.111300	−0.0556502	−	0.998450i	$-0.517723\pi$
$647$	−2.83106	−0.111300	−0.0556502	+	0.998450i	$0.517723\pi$
$648$	70.3420	2.76330
$649$	1.21846	0.0478289
$650$	4.61179	0.180889
$651$	−2.88575	−0.113101
$652$	−96.4094	−3.77568
$653$	−5.24539	−0.205268	−0.102634	−	0.994719i	$-0.532727\pi$
$653$	−5.24539	−0.205268	−0.102634	+	0.994719i	$0.532727\pi$
$654$	11.7897	0.461015
$655$	8.03671	0.314020
$656$	166.360	6.49525
$657$	−9.39497	−0.366533
$658$	−1.41843	−0.0552961
$659$	32.8830	1.28094	0.640470	−	0.767983i	$-0.278739\pi$
$659$	32.8830	1.28094	0.640470	+	0.767983i	$0.278739\pi$
$660$	52.9417	2.06075
$661$	−13.1534	−0.511610	−0.255805	−	0.966728i	$-0.582340\pi$
$661$	−13.1534	−0.511610	−0.255805	+	0.966728i	$0.582340\pi$
$662$	57.8438	2.24816
$663$	−2.38012	−0.0924361
$664$	96.4610	3.74341
$665$	−1.21372	−0.0470661
$666$	1.11928	0.0433712
$667$	11.8733	0.459735
$668$	57.7818	2.23565
$669$	15.3481	0.593392
$670$	−12.8034	−0.494638
$671$	−6.39550	−0.246895
$672$	11.9656	0.461582
$673$	−18.3678	−0.708026	−0.354013	−	0.935241i	$-0.615183\pi$
$673$	−18.3678	−0.708026	−0.354013	+	0.935241i	$0.615183\pi$
$674$	51.3974	1.97976
$675$	−5.57765	−0.214684
$676$	−58.4480	−2.24800
$677$	−32.0777	−1.23285	−0.616423	−	0.787415i	$-0.711419\pi$
$677$	−32.0777	−1.23285	−0.616423	+	0.787415i	$0.711419\pi$
$678$	8.90857	0.342132
$679$	4.04665	0.155296
$680$	−9.52248	−0.365171
$681$	38.6304	1.48032
$682$	−108.499	−4.15464
$683$	37.8885	1.44976	0.724881	−	0.688874i	$-0.241895\pi$
$683$	37.8885	1.44976	0.724881	+	0.688874i	$0.241895\pi$
$684$	−14.5903	−0.557874
$685$	−3.80919	−0.145542
$686$	−11.0341	−0.421283
$687$	−13.4112	−0.511668
$688$	41.4181	1.57905
$689$	−1.63801	−0.0624030
$690$	−16.7821	−0.638885
$691$	44.8339	1.70556	0.852781	−	0.522269i	$-0.174914\pi$
$691$	44.8339	1.70556	0.852781	+	0.522269i	$0.174914\pi$
$692$	49.7926	1.89283
$693$	1.02860	0.0390733
$694$	−94.4005	−3.58339
$695$	−19.8425	−0.752668
$696$	−48.4924	−1.83810
$697$	8.96855	0.339708
$698$	−41.1448	−1.55735
$699$	11.4165	0.431813
$700$	−1.62980	−0.0616007
$701$	−18.6258	−0.703489	−0.351744	−	0.936096i	$-0.614411\pi$
$701$	−18.6258	−0.703489	−0.351744	+	0.936096i	$0.614411\pi$
$702$	−25.7229	−0.970850
$703$	2.84923	0.107461
$704$	244.324	9.20831
$705$	−2.77101	−0.104362
$706$	9.25447	0.348297
$707$	5.47515	0.205914
$708$	1.79830	0.0675843
$709$	−12.6545	−0.475248	−0.237624	−	0.971357i	$-0.576369\pi$
$709$	−12.6545	−0.475248	−0.237624	+	0.971357i	$0.576369\pi$
$710$	−13.7319	−0.515348
$711$	−4.87749	−0.182920
$712$	43.4600	1.62873
$713$	25.4688	0.953813
$714$	1.13588	0.0425091
$715$	−9.94916	−0.372077
$716$	−24.5333	−0.916851
$717$	29.4553	1.10003
$718$	59.3483	2.21486
$719$	−1.92185	−0.0716729	−0.0358365	−	0.999358i	$-0.511410\pi$
$719$	−1.92185	−0.0716729	−0.0358365	+	0.999358i	$0.511410\pi$
$720$	−10.3210	−0.384640
$721$	4.18872	0.155996
$722$	2.59281	0.0964945
$723$	−24.2514	−0.901919
$724$	−37.3035	−1.38637
$725$	3.04199	0.112977
$726$	−106.938	−3.96886
$727$	30.5601	1.13341	0.566706	−	0.823920i	$-0.308218\pi$
$727$	30.5601	1.13341	0.566706	+	0.823920i	$0.308218\pi$
$728$	−4.88248	−0.180957
$729$	30.0250	1.11204
$730$	−43.3678	−1.60512
$731$	2.23288	0.0825859
$732$	−9.43895	−0.348874
$733$	−2.21924	−0.0819696	−0.0409848	−	0.999160i	$-0.513050\pi$
$733$	−2.21924	−0.0819696	−0.0409848	+	0.999160i	$0.513050\pi$
$734$	61.0903	2.25488
$735$	−10.7148	−0.395223
$736$	−105.605	−3.89264
$737$	27.6212	1.01744
$738$	16.1866	0.595835
$739$	3.72729	0.137110	0.0685552	−	0.997647i	$-0.478161\pi$
$739$	3.72729	0.137110	0.0685552	+	0.997647i	$0.478161\pi$
$740$	3.82598	0.140646
$741$	−10.9350	−0.401709
$742$	0.781714	0.0286976
$743$	44.4285	1.62992	0.814962	−	0.579514i	$-0.196758\pi$
$743$	44.4285	1.62992	0.814962	+	0.579514i	$0.196758\pi$
$744$	−104.019	−3.81351
$745$	−12.3976	−0.454213
$746$	−81.3653	−2.97900
$747$	5.63633	0.206222
$748$	31.6251	1.15633
$749$	−2.37712	−0.0868581
$750$	−4.29965	−0.157001
$751$	26.2193	0.956757	0.478378	−	0.878154i	$-0.341225\pi$
$751$	26.2193	0.956757	0.478378	+	0.878154i	$0.341225\pi$
$752$	−30.7042	−1.11967
$753$	41.2095	1.50176
$754$	14.0290	0.510906
$755$	−4.22393	−0.153725
$756$	9.09046	0.330617
$757$	2.50635	0.0910949	0.0455474	−	0.998962i	$-0.485497\pi$
$757$	2.50635	0.0910949	0.0455474	+	0.998962i	$0.485497\pi$
$758$	−100.914	−3.66536
$759$	36.2046	1.31414
$760$	−43.7494	−1.58696
$761$	−43.1566	−1.56443	−0.782213	−	0.623012i	$-0.785909\pi$
$761$	−43.1566	−1.56443	−0.782213	+	0.623012i	$0.785909\pi$
$762$	−28.9489	−1.04871
$763$	0.782994	0.0283463
$764$	140.585	5.08620
$765$	−0.556410	−0.0201170
$766$	−26.2988	−0.950216
$767$	−0.337949	−0.0122026
$768$	127.925	4.61611
$769$	10.2971	0.371321	0.185661	−	0.982614i	$-0.440558\pi$
$769$	10.2971	0.371321	0.185661	+	0.982614i	$0.440558\pi$
$770$	4.74809	0.171109
$771$	−3.29873	−0.118801
$772$	−63.1585	−2.27312
$773$	−40.3745	−1.45217	−0.726086	−	0.687604i	$-0.758662\pi$
$773$	−40.3745	−1.45217	−0.726086	+	0.687604i	$0.758662\pi$
$774$	4.02993	0.144853
$775$	6.52521	0.234392
$776$	145.864	5.23622
$777$	−0.296456	−0.0106353
$778$	−1.79820	−0.0644685
$779$	41.2045	1.47630
$780$	−14.6837	−0.525761
$781$	29.6242	1.06004
$782$	−10.0249	−0.358490
$783$	−16.9671	−0.606356
$784$	−118.726	−4.24020
$785$	−10.3033	−0.367741
$786$	−34.5551	−1.23254
$787$	−30.9322	−1.10261	−0.551307	−	0.834303i	$-0.685871\pi$
$787$	−30.9322	−1.10261	−0.551307	+	0.834303i	$0.685871\pi$
$788$	130.991	4.66637
$789$	−0.398822	−0.0141984
$790$	−22.5149	−0.801043
$791$	0.591646	0.0210365
$792$	37.0766	1.31746
$793$	1.77383	0.0629906
$794$	86.2790	3.06193
$795$	1.52714	0.0541621
$796$	−47.8310	−1.69533
$797$	−51.6555	−1.82973	−0.914866	−	0.403758i	$-0.867704\pi$
$797$	−51.6555	−1.82973	−0.914866	+	0.403758i	$0.867704\pi$
$798$	5.21859	0.184736
$799$	−1.65528	−0.0585597
$800$	−27.0564	−0.956587
$801$	2.53942	0.0897259
$802$	34.0585	1.20265
$803$	93.5588	3.30162
$804$	40.7654	1.43768
$805$	−1.11455	−0.0392829
$806$	30.0929	1.05998
$807$	−17.9240	−0.630955
$808$	197.355	6.94293
$809$	35.2649	1.23985	0.619923	−	0.784662i	$-0.287164\pi$
$809$	35.2649	1.23985	0.619923	+	0.784662i	$0.287164\pi$
$810$	18.9728	0.666637
$811$	0.700052	0.0245821	0.0122911	−	0.999924i	$-0.496088\pi$
$811$	0.700052	0.0245821	0.0122911	+	0.999924i	$0.496088\pi$
$812$	−4.95783	−0.173986
$813$	14.7324	0.516686
$814$	−11.1462	−0.390675
$815$	−16.8917	−0.591689
$816$	24.5879	0.860749
$817$	10.2586	0.358902
$818$	80.2736	2.80670
$819$	−0.285289	−0.00996879
$820$	55.3299	1.93220
$821$	−44.8393	−1.56490	−0.782451	−	0.622712i	$-0.786031\pi$
$821$	−44.8393	−1.56490	−0.782451	+	0.622712i	$0.786031\pi$
$822$	16.3782	0.571256
$823$	13.9672	0.486867	0.243434	−	0.969918i	$-0.421726\pi$
$823$	13.9672	0.486867	0.243434	+	0.969918i	$0.421726\pi$
$824$	150.985	5.25982
$825$	9.27578	0.322941
$826$	0.161281	0.00561169
$827$	−17.3792	−0.604335	−0.302168	−	0.953255i	$-0.597710\pi$
$827$	−17.3792	−0.604335	−0.302168	+	0.953255i	$0.597710\pi$
$828$	−13.3982	−0.465619
$829$	−26.9205	−0.934987	−0.467494	−	0.883996i	$-0.654843\pi$
$829$	−26.9205	−0.934987	−0.467494	+	0.883996i	$0.654843\pi$
$830$	26.0177	0.903087
$831$	37.7748	1.31039
$832$	−67.7648	−2.34932
$833$	−6.40058	−0.221767
$834$	85.3158	2.95424
$835$	10.1238	0.350349
$836$	145.296	5.02516
$837$	−36.3953	−1.25801
$838$	−3.84938	−0.132975
$839$	15.9222	0.549695	0.274847	−	0.961488i	$-0.411373\pi$
$839$	15.9222	0.549695	0.274847	+	0.961488i	$0.411373\pi$
$840$	4.55202	0.157060
$841$	−19.7463	−0.680908
$842$	−37.6154	−1.29631
$843$	8.10067	0.279002
$844$	113.332	3.90104
$845$	−10.2405	−0.352285
$846$	−2.98748	−0.102712
$847$	−7.10212	−0.244032
$848$	16.9215	0.581086
$849$	−13.2497	−0.454727
$850$	−2.56843	−0.0880963
$851$	2.61643	0.0896901
$852$	43.7216	1.49788
$853$	4.35922	0.149257	0.0746285	−	0.997211i	$-0.476223\pi$
$853$	4.35922	0.149257	0.0746285	+	0.997211i	$0.476223\pi$
$854$	−0.846535	−0.0289678
$855$	−2.55633	−0.0874246
$856$	−85.6849	−2.92865
$857$	−9.40077	−0.321124	−0.160562	−	0.987026i	$-0.551331\pi$
$857$	−9.40077	−0.321124	−0.160562	+	0.987026i	$0.551331\pi$
$858$	42.7779	1.46041
$859$	−7.95490	−0.271418	−0.135709	−	0.990749i	$-0.543331\pi$
$859$	−7.95490	−0.271418	−0.135709	+	0.990749i	$0.543331\pi$
$860$	13.7753	0.469735
$861$	−4.28722	−0.146108
$862$	−51.5512	−1.75584
$863$	−10.3495	−0.352302	−0.176151	−	0.984363i	$-0.556365\pi$
$863$	−10.3495	−0.352302	−0.176151	+	0.984363i	$0.556365\pi$
$864$	150.911	5.13409
$865$	8.72403	0.296626
$866$	108.371	3.68260
$867$	−25.0029	−0.849143
$868$	−10.6348	−0.360969
$869$	48.5720	1.64769
$870$	−13.0795	−0.443436
$871$	−7.66091	−0.259580
$872$	28.2235	0.955769
$873$	8.52302	0.288460
$874$	−46.0577	−1.55793
$875$	−0.285554	−0.00965347
$876$	138.081	4.66532
$877$	−7.22609	−0.244008	−0.122004	−	0.992530i	$-0.538932\pi$
$877$	−7.22609	−0.244008	−0.122004	+	0.992530i	$0.538932\pi$
$878$	−3.50049	−0.118136
$879$	24.6264	0.830629
$880$	102.780	3.46472
$881$	9.10623	0.306797	0.153398	−	0.988164i	$-0.450978\pi$
$881$	9.10623	0.306797	0.153398	+	0.988164i	$0.450978\pi$
$882$	−11.5518	−0.388971
$883$	48.6147	1.63602	0.818008	−	0.575207i	$-0.195079\pi$
$883$	48.6147	1.63602	0.818008	+	0.575207i	$0.195079\pi$
$884$	−8.77141	−0.295014
$885$	0.315076	0.0105912
$886$	29.2755	0.983530
$887$	−56.2648	−1.88919	−0.944593	−	0.328244i	$-0.893543\pi$
$887$	−56.2648	−1.88919	−0.944593	+	0.328244i	$0.893543\pi$
$888$	−10.6859	−0.358597
$889$	−1.92259	−0.0644816
$890$	11.7221	0.392927
$891$	−40.9307	−1.37123
$892$	56.5621	1.89384
$893$	−7.60491	−0.254489
$894$	53.3054	1.78280
$895$	−4.29841	−0.143680
$896$	16.8877	0.564177
$897$	−10.0416	−0.335278
$898$	−109.653	−3.65916
$899$	19.8496	0.662021
$900$	−3.43267	−0.114422
$901$	0.912248	0.0303914
$902$	−161.192	−5.36711
$903$	−1.06738	−0.0355201
$904$	21.3263	0.709301
$905$	−6.53585	−0.217259
$906$	18.1614	0.603374
$907$	38.0406	1.26312	0.631560	−	0.775327i	$-0.282415\pi$
$907$	38.0406	1.26312	0.631560	+	0.775327i	$0.282415\pi$
$908$	142.364	4.72451
$909$	11.5317	0.382482
$910$	−1.31691	−0.0436552
$911$	21.4882	0.711937	0.355969	−	0.934498i	$-0.384151\pi$
$911$	21.4882	0.711937	0.355969	+	0.934498i	$0.384151\pi$
$912$	112.965	3.74064
$913$	−56.1288	−1.85759
$914$	−48.3834	−1.60038
$915$	−1.65378	−0.0546721
$916$	−49.4239	−1.63301
$917$	−2.29491	−0.0757847
$918$	14.3258	0.472821
$919$	34.3064	1.13166	0.565831	−	0.824521i	$-0.308555\pi$
$919$	34.3064	1.13166	0.565831	+	0.824521i	$0.308555\pi$
$920$	−40.1748	−1.32452
$921$	−16.8174	−0.554153
$922$	40.2857	1.32674
$923$	−8.21645	−0.270448
$924$	−15.1177	−0.497335
$925$	0.670341	0.0220407
$926$	−100.509	−3.30293
$927$	8.82224	0.289760
$928$	−82.3051	−2.70180
$929$	−36.7886	−1.20699	−0.603497	−	0.797365i	$-0.706227\pi$
$929$	−36.7886	−1.20699	−0.603497	+	0.797365i	$0.706227\pi$
$930$	−28.0561	−0.919997
$931$	−29.4064	−0.963754
$932$	42.0732	1.37815
$933$	6.78689	0.222193
$934$	44.1849	1.44577
$935$	5.54095	0.181208
$936$	−10.2834	−0.336124
$937$	57.2491	1.87025	0.935124	−	0.354321i	$-0.115288\pi$
$937$	57.2491	1.87025	0.935124	+	0.354321i	$0.115288\pi$
$938$	3.65605	0.119374
$939$	−27.2535	−0.889385
$940$	−10.2120	−0.333078
$941$	19.4172	0.632983	0.316491	−	0.948595i	$-0.397495\pi$
$941$	19.4172	0.632983	0.316491	+	0.948595i	$0.397495\pi$
$942$	44.3007	1.44340
$943$	37.8378	1.23217
$944$	3.49120	0.113629
$945$	1.59272	0.0518111
$946$	−40.1316	−1.30479
$947$	−34.1457	−1.10959	−0.554793	−	0.831988i	$-0.687203\pi$
$947$	−34.1457	−1.10959	−0.554793	+	0.831988i	$0.687203\pi$
$948$	71.6862	2.32826
$949$	−25.9491	−0.842344
$950$	−11.8002	−0.382849
$951$	39.7902	1.29029
$952$	2.71918	0.0881291
$953$	−20.7739	−0.672933	−0.336467	−	0.941695i	$-0.609232\pi$
$953$	−20.7739	−0.672933	−0.336467	+	0.941695i	$0.609232\pi$
$954$	1.64644	0.0533054
$955$	24.6316	0.797061
$956$	108.551	3.51080
$957$	28.2168	0.912119
$958$	19.0016	0.613915
$959$	1.08773	0.0351246
$960$	63.1783	2.03907
$961$	11.5784	0.373496
$962$	3.09147	0.0996731
$963$	−5.00667	−0.161338
$964$	−89.3733	−2.87852
$965$	−11.0658	−0.356222
$966$	4.79219	0.154186
$967$	−55.1610	−1.77386	−0.886929	−	0.461906i	$-0.847166\pi$
$967$	−55.1610	−1.77386	−0.886929	+	0.461906i	$0.847166\pi$
$968$	−256.000	−8.22817
$969$	6.09001	0.195639
$970$	39.3429	1.26322
$971$	−3.33609	−0.107060	−0.0535301	−	0.998566i	$-0.517047\pi$
$971$	−3.33609	−0.107060	−0.0535301	+	0.998566i	$0.517047\pi$
$972$	35.0951	1.12568
$973$	5.66609	0.181646
$974$	−28.2952	−0.906637
$975$	−2.57270	−0.0823922
$976$	−18.3247	−0.586558
$977$	21.0890	0.674697	0.337348	−	0.941380i	$-0.390470\pi$
$977$	21.0890	0.674697	0.337348	+	0.941380i	$0.390470\pi$
$978$	72.6283	2.32240
$979$	−25.2885	−0.808225
$980$	−39.4872	−1.26137
$981$	1.64913	0.0526528
$982$	14.8968	0.475375
$983$	43.9875	1.40298	0.701491	−	0.712678i	$-0.252518\pi$
$983$	43.9875	1.40298	0.701491	+	0.712678i	$0.252518\pi$
$984$	−154.536	−4.92642
$985$	22.9506	0.731268
$986$	−7.81312	−0.248820
$987$	0.791273	0.0251865
$988$	−40.2987	−1.28207
$989$	9.42038	0.299551
$990$	10.0004	0.317833
$991$	45.5447	1.44678	0.723388	−	0.690442i	$-0.242584\pi$
$991$	45.5447	1.44678	0.723388	+	0.690442i	$0.242584\pi$
$992$	−176.549	−5.60542
$993$	−32.2683	−1.02400
$994$	3.92118	0.124372
$995$	−8.38036	−0.265675
$996$	−82.8390	−2.62485
$997$	53.0497	1.68010	0.840051	−	0.542508i	$-0.182525\pi$
$997$	53.0497	1.68010	0.840051	+	0.542508i	$0.182525\pi$
$998$	18.4401	0.583710
$999$	−3.73893	−0.118294

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.77624 q^{2} +1.54873 q^{3} +5.70752 q^{4} +1.00000 q^{5} -4.29965 q^{6} -0.285554 q^{7} -10.2930 q^{8} -0.601430 q^{9} +O(q^{10})\)	\(q-2.77624 q^{2} +1.54873 q^{3} +5.70752 q^{4} +1.00000 q^{5} -4.29965 q^{6} -0.285554 q^{7} -10.2930 q^{8} -0.601430 q^{9} -2.77624 q^{10} +5.98927 q^{11} +8.83941 q^{12} -1.66116 q^{13} +0.792766 q^{14} +1.54873 q^{15} +17.1607 q^{16} +0.925145 q^{17} +1.66971 q^{18} +4.25042 q^{19} +5.70752 q^{20} -0.442246 q^{21} -16.6277 q^{22} +3.90313 q^{23} -15.9410 q^{24} +1.00000 q^{25} +4.61179 q^{26} -5.57765 q^{27} -1.62980 q^{28} +3.04199 q^{29} -4.29965 q^{30} +6.52521 q^{31} -27.0564 q^{32} +9.27578 q^{33} -2.56843 q^{34} -0.285554 q^{35} -3.43267 q^{36} +0.670341 q^{37} -11.8002 q^{38} -2.57270 q^{39} -10.2930 q^{40} +9.69421 q^{41} +1.22778 q^{42} +2.41354 q^{43} +34.1839 q^{44} -0.601430 q^{45} -10.8360 q^{46} -1.78921 q^{47} +26.5774 q^{48} -6.91846 q^{49} -2.77624 q^{50} +1.43280 q^{51} -9.48112 q^{52} +0.986060 q^{53} +15.4849 q^{54} +5.98927 q^{55} +2.93919 q^{56} +6.58276 q^{57} -8.44529 q^{58} +0.203441 q^{59} +8.83941 q^{60} -1.06783 q^{61} -18.1156 q^{62} +0.171740 q^{63} +40.7936 q^{64} -1.66116 q^{65} -25.7518 q^{66} +4.61177 q^{67} +5.28028 q^{68} +6.04491 q^{69} +0.792766 q^{70} +4.94620 q^{71} +6.19049 q^{72} +15.6211 q^{73} -1.86103 q^{74} +1.54873 q^{75} +24.2593 q^{76} -1.71026 q^{77} +7.14242 q^{78} +8.10983 q^{79} +17.1607 q^{80} -6.83399 q^{81} -26.9135 q^{82} -9.37155 q^{83} -2.52413 q^{84} +0.925145 q^{85} -6.70058 q^{86} +4.71122 q^{87} -61.6474 q^{88} -4.22230 q^{89} +1.66971 q^{90} +0.474351 q^{91} +22.2772 q^{92} +10.1058 q^{93} +4.96729 q^{94} +4.25042 q^{95} -41.9031 q^{96} -14.1713 q^{97} +19.2073 q^{98} -3.60213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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