LMFDB - Embedded newform 4015.2.a.h.1.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72814 q^{2} -1.60784 q^{3} +5.44276 q^{4} +1.00000 q^{5} -4.38641 q^{6} +0.0202448 q^{7} +9.39234 q^{8} -0.414864 q^{9} +O(q^{10})$	\(q+2.72814 q^{2} -1.60784 q^{3} +5.44276 q^{4} +1.00000 q^{5} -4.38641 q^{6} +0.0202448 q^{7} +9.39234 q^{8} -0.414864 q^{9} +2.72814 q^{10} +1.00000 q^{11} -8.75107 q^{12} -5.65909 q^{13} +0.0552306 q^{14} -1.60784 q^{15} +14.7381 q^{16} +2.53163 q^{17} -1.13181 q^{18} +3.30165 q^{19} +5.44276 q^{20} -0.0325503 q^{21} +2.72814 q^{22} +3.06339 q^{23} -15.1013 q^{24} +1.00000 q^{25} -15.4388 q^{26} +5.49054 q^{27} +0.110187 q^{28} +0.877939 q^{29} -4.38641 q^{30} +7.95151 q^{31} +21.4230 q^{32} -1.60784 q^{33} +6.90665 q^{34} +0.0202448 q^{35} -2.25800 q^{36} -10.5501 q^{37} +9.00737 q^{38} +9.09889 q^{39} +9.39234 q^{40} +9.06315 q^{41} -0.0888018 q^{42} +9.08103 q^{43} +5.44276 q^{44} -0.414864 q^{45} +8.35735 q^{46} +7.34217 q^{47} -23.6965 q^{48} -6.99959 q^{49} +2.72814 q^{50} -4.07045 q^{51} -30.8011 q^{52} -0.627801 q^{53} +14.9790 q^{54} +1.00000 q^{55} +0.190146 q^{56} -5.30851 q^{57} +2.39514 q^{58} +10.3988 q^{59} -8.75107 q^{60} +9.37972 q^{61} +21.6928 q^{62} -0.00839882 q^{63} +28.9688 q^{64} -5.65909 q^{65} -4.38641 q^{66} +2.36861 q^{67} +13.7791 q^{68} -4.92542 q^{69} +0.0552306 q^{70} -11.1851 q^{71} -3.89654 q^{72} +1.00000 q^{73} -28.7821 q^{74} -1.60784 q^{75} +17.9701 q^{76} +0.0202448 q^{77} +24.8231 q^{78} -1.64616 q^{79} +14.7381 q^{80} -7.58330 q^{81} +24.7256 q^{82} -14.6348 q^{83} -0.177163 q^{84} +2.53163 q^{85} +24.7744 q^{86} -1.41158 q^{87} +9.39234 q^{88} -1.29715 q^{89} -1.13181 q^{90} -0.114567 q^{91} +16.6733 q^{92} -12.7847 q^{93} +20.0305 q^{94} +3.30165 q^{95} -34.4447 q^{96} +4.49947 q^{97} -19.0959 q^{98} -0.414864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	2.72814	1.92909	0.964544	−	0.263922i	$-0.0850163\pi$
$2$	2.72814	1.92909	0.964544	+	0.263922i	$0.0850163\pi$
$3$	−1.60784	−0.928284	−0.464142	−	0.885761i	$-0.653637\pi$
$3$	−1.60784	−0.928284	−0.464142	+	0.885761i	$0.653637\pi$
$4$	5.44276	2.72138
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.38641	−1.79074
$7$	0.0202448	0.00765180	0.00382590	−	0.999993i	$-0.498782\pi$
$7$	0.0202448	0.00765180	0.00382590	+	0.999993i	$0.498782\pi$
$8$	9.39234	3.32069
$9$	−0.414864	−0.138288
$10$	2.72814	0.862714
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−8.75107	−2.52621
$13$	−5.65909	−1.56955	−0.784775	−	0.619781i	$-0.787221\pi$
$13$	−5.65909	−1.56955	−0.784775	+	0.619781i	$0.787221\pi$
$14$	0.0552306	0.0147610
$15$	−1.60784	−0.415141
$16$	14.7381	3.68453
$17$	2.53163	0.614011	0.307005	−	0.951708i	$-0.400673\pi$
$17$	2.53163	0.614011	0.307005	+	0.951708i	$0.400673\pi$
$18$	−1.13181	−0.266770
$19$	3.30165	0.757450	0.378725	−	0.925509i	$-0.376363\pi$
$19$	3.30165	0.757450	0.378725	+	0.925509i	$0.376363\pi$
$20$	5.44276	1.21704
$21$	−0.0325503	−0.00710305
$22$	2.72814	0.581642
$23$	3.06339	0.638760	0.319380	−	0.947627i	$-0.396525\pi$
$23$	3.06339	0.638760	0.319380	+	0.947627i	$0.396525\pi$
$24$	−15.1013	−3.08255
$25$	1.00000	0.200000
$26$	−15.4388	−3.02780
$27$	5.49054	1.05666
$28$	0.110187	0.0208235
$29$	0.877939	0.163029	0.0815146	−	0.996672i	$-0.474024\pi$
$29$	0.877939	0.163029	0.0815146	+	0.996672i	$0.474024\pi$
$30$	−4.38641	−0.800844
$31$	7.95151	1.42813	0.714066	−	0.700078i	$-0.246851\pi$
$31$	7.95151	1.42813	0.714066	+	0.700078i	$0.246851\pi$
$32$	21.4230	3.78709
$33$	−1.60784	−0.279888
$34$	6.90665	1.18448
$35$	0.0202448	0.00342199
$36$	−2.25800	−0.376334
$37$	−10.5501	−1.73442	−0.867211	−	0.497941i	$-0.834090\pi$
$37$	−10.5501	−1.73442	−0.867211	+	0.497941i	$0.834090\pi$
$38$	9.00737	1.46119
$39$	9.09889	1.45699
$40$	9.39234	1.48506
$41$	9.06315	1.41543	0.707713	−	0.706500i	$-0.249727\pi$
$41$	9.06315	1.41543	0.707713	+	0.706500i	$0.249727\pi$
$42$	−0.0888018	−0.0137024
$43$	9.08103	1.38484	0.692422	−	0.721492i	$-0.256543\pi$
$43$	9.08103	1.38484	0.692422	+	0.721492i	$0.256543\pi$
$44$	5.44276	0.820527
$45$	−0.414864	−0.0618442
$46$	8.35735	1.23222
$47$	7.34217	1.07097	0.535483	−	0.844546i	$-0.320130\pi$
$47$	7.34217	1.07097	0.535483	+	0.844546i	$0.320130\pi$
$48$	−23.6965	−3.42029
$49$	−6.99959	−0.999941
$50$	2.72814	0.385818
$51$	−4.07045	−0.569976
$52$	−30.8011	−4.27134
$53$	−0.627801	−0.0862351	−0.0431175	−	0.999070i	$-0.513729\pi$
$53$	−0.627801	−0.0862351	−0.0431175	+	0.999070i	$0.513729\pi$
$54$	14.9790	2.03838
$55$	1.00000	0.134840
$56$	0.190146	0.0254093
$57$	−5.30851	−0.703129
$58$	2.39514	0.314498
$59$	10.3988	1.35381	0.676903	−	0.736072i	$-0.263322\pi$
$59$	10.3988	1.35381	0.676903	+	0.736072i	$0.263322\pi$
$60$	−8.75107	−1.12976
$61$	9.37972	1.20095	0.600475	−	0.799643i	$-0.294978\pi$
$61$	9.37972	1.20095	0.600475	+	0.799643i	$0.294978\pi$
$62$	21.6928	2.75499
$63$	−0.00839882	−0.00105815
$64$	28.9688	3.62110
$65$	−5.65909	−0.701924
$66$	−4.38641	−0.539929
$67$	2.36861	0.289371	0.144686	−	0.989478i	$-0.453783\pi$
$67$	2.36861	0.289371	0.144686	+	0.989478i	$0.453783\pi$
$68$	13.7791	1.67096
$69$	−4.92542	−0.592951
$70$	0.0552306	0.00660132
$71$	−11.1851	−1.32743	−0.663713	−	0.747988i	$-0.731020\pi$
$71$	−11.1851	−1.32743	−0.663713	+	0.747988i	$0.731020\pi$
$72$	−3.89654	−0.459212
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−28.7821	−3.34585
$75$	−1.60784	−0.185657
$76$	17.9701	2.06131
$77$	0.0202448	0.00230711
$78$	24.8231	2.81066
$79$	−1.64616	−0.185207	−0.0926036	−	0.995703i	$-0.529519\pi$
$79$	−1.64616	−0.185207	−0.0926036	+	0.995703i	$0.529519\pi$
$80$	14.7381	1.64777
$81$	−7.58330	−0.842589
$82$	24.7256	2.73048
$83$	−14.6348	−1.60638	−0.803190	−	0.595723i	$-0.796866\pi$
$83$	−14.6348	−1.60638	−0.803190	+	0.595723i	$0.796866\pi$
$84$	−0.177163	−0.0193301
$85$	2.53163	0.274594
$86$	24.7744	2.67149
$87$	−1.41158	−0.151338
$88$	9.39234	1.00123
$89$	−1.29715	−0.137498	−0.0687489	−	0.997634i	$-0.521901\pi$
$89$	−1.29715	−0.137498	−0.0687489	+	0.997634i	$0.521901\pi$
$90$	−1.13181	−0.119303
$91$	−0.114567	−0.0120099
$92$	16.6733	1.73831
$93$	−12.7847	−1.32571
$94$	20.0305	2.06599
$95$	3.30165	0.338742
$96$	−34.4447	−3.51549
$97$	4.49947	0.456852	0.228426	−	0.973561i	$-0.426642\pi$
$97$	4.49947	0.456852	0.228426	+	0.973561i	$0.426642\pi$
$98$	−19.0959	−1.92897
$99$	−0.414864	−0.0416954
$100$	5.44276	0.544276
$101$	−13.1908	−1.31253	−0.656267	−	0.754529i	$-0.727865\pi$
$101$	−13.1908	−1.31253	−0.656267	+	0.754529i	$0.727865\pi$
$102$	−11.1048	−1.09953
$103$	−3.43734	−0.338691	−0.169346	−	0.985557i	$-0.554165\pi$
$103$	−3.43734	−0.338691	−0.169346	+	0.985557i	$0.554165\pi$
$104$	−53.1521	−5.21199
$105$	−0.0325503	−0.00317658
$106$	−1.71273	−0.166355
$107$	−8.37143	−0.809296	−0.404648	−	0.914472i	$-0.632606\pi$
$107$	−8.37143	−0.809296	−0.404648	+	0.914472i	$0.632606\pi$
$108$	29.8837	2.87556
$109$	−6.72410	−0.644052	−0.322026	−	0.946731i	$-0.604364\pi$
$109$	−6.72410	−0.644052	−0.322026	+	0.946731i	$0.604364\pi$
$110$	2.72814	0.260118
$111$	16.9628	1.61004
$112$	0.298370	0.0281933
$113$	−14.0809	−1.32462	−0.662311	−	0.749229i	$-0.730424\pi$
$113$	−14.0809	−1.32462	−0.662311	+	0.749229i	$0.730424\pi$
$114$	−14.4824	−1.35640
$115$	3.06339	0.285662
$116$	4.77841	0.443664
$117$	2.34775	0.217050
$118$	28.3694	2.61161
$119$	0.0512523	0.00469829
$120$	−15.1013	−1.37856
$121$	1.00000	0.0909091
$122$	25.5892	2.31674
$123$	−14.5721	−1.31392
$124$	43.2781	3.88649
$125$	1.00000	0.0894427
$126$	−0.0229132	−0.00204127
$127$	−17.0513	−1.51306	−0.756528	−	0.653962i	$-0.773106\pi$
$127$	−17.0513	−1.51306	−0.756528	+	0.653962i	$0.773106\pi$
$128$	36.1849	3.19832
$129$	−14.6008	−1.28553
$130$	−15.4388	−1.35407
$131$	−21.8689	−1.91069	−0.955347	−	0.295487i	$-0.904518\pi$
$131$	−21.8689	−1.91069	−0.955347	+	0.295487i	$0.904518\pi$
$132$	−8.75107	−0.761682
$133$	0.0668411	0.00579586
$134$	6.46190	0.558223
$135$	5.49054	0.472550
$136$	23.7779	2.03894
$137$	19.7008	1.68315	0.841576	−	0.540139i	$-0.181628\pi$
$137$	19.7008	1.68315	0.841576	+	0.540139i	$0.181628\pi$
$138$	−13.4373	−1.14385
$139$	19.1454	1.62389	0.811947	−	0.583731i	$-0.198408\pi$
$139$	19.1454	1.62389	0.811947	+	0.583731i	$0.198408\pi$
$140$	0.110187	0.00931254
$141$	−11.8050	−0.994161
$142$	−30.5145	−2.56072
$143$	−5.65909	−0.473237
$144$	−6.11431	−0.509526
$145$	0.877939	0.0729089
$146$	2.72814	0.225783
$147$	11.2542	0.928230
$148$	−57.4215	−4.72002
$149$	18.8469	1.54400	0.771999	−	0.635623i	$-0.219257\pi$
$149$	18.8469	1.54400	0.771999	+	0.635623i	$0.219257\pi$
$150$	−4.38641	−0.358148
$151$	10.0911	0.821202	0.410601	−	0.911815i	$-0.365319\pi$
$151$	10.0911	0.821202	0.410601	+	0.911815i	$0.365319\pi$
$152$	31.0102	2.51526
$153$	−1.05028	−0.0849102
$154$	0.0552306	0.00445061
$155$	7.95151	0.638680
$156$	49.5231	3.96502
$157$	−1.01358	−0.0808921	−0.0404461	−	0.999182i	$-0.512878\pi$
$157$	−1.01358	−0.0808921	−0.0404461	+	0.999182i	$0.512878\pi$
$158$	−4.49095	−0.357281
$159$	1.00940	0.0800507
$160$	21.4230	1.69364
$161$	0.0620175	0.00488767
$162$	−20.6883	−1.62543
$163$	−15.7345	−1.23242	−0.616209	−	0.787583i	$-0.711332\pi$
$163$	−15.7345	−1.23242	−0.616209	+	0.787583i	$0.711332\pi$
$164$	49.3285	3.85191
$165$	−1.60784	−0.125170
$166$	−39.9259	−3.09885
$167$	22.2434	1.72124	0.860622	−	0.509244i	$-0.170075\pi$
$167$	22.2434	1.72124	0.860622	+	0.509244i	$0.170075\pi$
$168$	−0.305723	−0.0235871
$169$	19.0253	1.46348
$170$	6.90665	0.529716
$171$	−1.36973	−0.104746
$172$	49.4259	3.76869
$173$	−1.36747	−0.103967	−0.0519833	−	0.998648i	$-0.516554\pi$
$173$	−1.36747	−0.103967	−0.0519833	+	0.998648i	$0.516554\pi$
$174$	−3.85100	−0.291943
$175$	0.0202448	0.00153036
$176$	14.7381	1.11093
$177$	−16.7195	−1.25672
$178$	−3.53882	−0.265246
$179$	18.5897	1.38946	0.694729	−	0.719271i	$-0.255524\pi$
$179$	18.5897	1.38946	0.694729	+	0.719271i	$0.255524\pi$
$180$	−2.25800	−0.168302
$181$	−5.36088	−0.398471	−0.199236	−	0.979952i	$-0.563846\pi$
$181$	−5.36088	−0.398471	−0.199236	+	0.979952i	$0.563846\pi$
$182$	−0.312555	−0.0231681
$183$	−15.0811	−1.11482
$184$	28.7724	2.12113
$185$	−10.5501	−0.775657
$186$	−34.8785	−2.55742
$187$	2.53163	0.185131
$188$	39.9617	2.91451
$189$	0.111155	0.00808532
$190$	9.00737	0.653463
$191$	−20.9088	−1.51291	−0.756453	−	0.654048i	$-0.773069\pi$
$191$	−20.9088	−1.51291	−0.756453	+	0.654048i	$0.773069\pi$
$192$	−46.5770	−3.36141
$193$	1.01599	0.0731326	0.0365663	−	0.999331i	$-0.488358\pi$
$193$	1.01599	0.0731326	0.0365663	+	0.999331i	$0.488358\pi$
$194$	12.2752	0.881308
$195$	9.09889	0.651585
$196$	−38.0971	−2.72122
$197$	−20.9700	−1.49405	−0.747025	−	0.664796i	$-0.768518\pi$
$197$	−20.9700	−1.49405	−0.747025	+	0.664796i	$0.768518\pi$
$198$	−1.13181	−0.0804340
$199$	7.08708	0.502390	0.251195	−	0.967937i	$-0.419176\pi$
$199$	7.08708	0.502390	0.251195	+	0.967937i	$0.419176\pi$
$200$	9.39234	0.664139
$201$	−3.80833	−0.268619
$202$	−35.9864	−2.53199
$203$	0.0177737	0.00124747
$204$	−22.1545	−1.55112
$205$	9.06315	0.632998
$206$	−9.37756	−0.653366
$207$	−1.27089	−0.0883328
$208$	−83.4043	−5.78305
$209$	3.30165	0.228380
$210$	−0.0888018	−0.00612790
$211$	−24.2105	−1.66672	−0.833358	−	0.552733i	$-0.813585\pi$
$211$	−24.2105	−1.66672	−0.833358	+	0.552733i	$0.813585\pi$
$212$	−3.41697	−0.234678
$213$	17.9838	1.23223
$214$	−22.8384	−1.56120
$215$	9.08103	0.619321
$216$	51.5690	3.50883
$217$	0.160976	0.0109278
$218$	−18.3443	−1.24243
$219$	−1.60784	−0.108647
$220$	5.44276	0.366951
$221$	−14.3267	−0.963720
$222$	46.2769	3.10590
$223$	−4.65428	−0.311674	−0.155837	−	0.987783i	$-0.549807\pi$
$223$	−4.65428	−0.311674	−0.155837	+	0.987783i	$0.549807\pi$
$224$	0.433704	0.0289781
$225$	−0.414864	−0.0276576
$226$	−38.4147	−2.55531
$227$	−20.5006	−1.36067	−0.680336	−	0.732901i	$-0.738166\pi$
$227$	−20.5006	−1.36067	−0.680336	+	0.732901i	$0.738166\pi$
$228$	−28.8929	−1.91348
$229$	10.0276	0.662639	0.331320	−	0.943519i	$-0.392506\pi$
$229$	10.0276	0.662639	0.331320	+	0.943519i	$0.392506\pi$
$230$	8.35735	0.551067
$231$	−0.0325503	−0.00214165
$232$	8.24590	0.541370
$233$	−20.1525	−1.32024	−0.660118	−	0.751161i	$-0.729494\pi$
$233$	−20.1525	−1.32024	−0.660118	+	0.751161i	$0.729494\pi$
$234$	6.40500	0.418708
$235$	7.34217	0.478951
$236$	56.5981	3.68422
$237$	2.64675	0.171925
$238$	0.139824	0.00906341
$239$	−13.3447	−0.863196	−0.431598	−	0.902066i	$-0.642050\pi$
$239$	−13.3447	−0.863196	−0.431598	+	0.902066i	$0.642050\pi$
$240$	−23.6965	−1.52960
$241$	21.6886	1.39708	0.698542	−	0.715569i	$-0.253832\pi$
$241$	21.6886	1.39708	0.698542	+	0.715569i	$0.253832\pi$
$242$	2.72814	0.175372
$243$	−4.27892	−0.274493
$244$	51.0516	3.26824
$245$	−6.99959	−0.447187
$246$	−39.7546	−2.53466
$247$	−18.6843	−1.18886
$248$	74.6832	4.74239
$249$	23.5304	1.49118
$250$	2.72814	0.172543
$251$	1.13251	0.0714832	0.0357416	−	0.999361i	$-0.488621\pi$
$251$	1.13251	0.0714832	0.0357416	+	0.999361i	$0.488621\pi$
$252$	−0.0457128	−0.00287963
$253$	3.06339	0.192593
$254$	−46.5183	−2.91882
$255$	−4.07045	−0.254901
$256$	40.7800	2.54875
$257$	−3.07116	−0.191574	−0.0957869	−	0.995402i	$-0.530537\pi$
$257$	−3.07116	−0.191574	−0.0957869	+	0.995402i	$0.530537\pi$
$258$	−39.8331	−2.47990
$259$	−0.213584	−0.0132715
$260$	−30.8011	−1.91020
$261$	−0.364225	−0.0225450
$262$	−59.6614	−3.68590
$263$	−8.74819	−0.539436	−0.269718	−	0.962939i	$-0.586931\pi$
$263$	−8.74819	−0.539436	−0.269718	+	0.962939i	$0.586931\pi$
$264$	−15.1013	−0.929423
$265$	−0.627801	−0.0385655
$266$	0.182352	0.0111807
$267$	2.08561	0.127637
$268$	12.8918	0.787490
$269$	−17.2518	−1.05186	−0.525929	−	0.850529i	$-0.676282\pi$
$269$	−17.2518	−1.05186	−0.525929	+	0.850529i	$0.676282\pi$
$270$	14.9790	0.911591
$271$	−6.69507	−0.406697	−0.203348	−	0.979106i	$-0.565182\pi$
$271$	−6.69507	−0.406697	−0.203348	+	0.979106i	$0.565182\pi$
$272$	37.3115	2.26234
$273$	0.184205	0.0111486
$274$	53.7466	3.24695
$275$	1.00000	0.0603023
$276$	−26.8079	−1.61365
$277$	10.6207	0.638134	0.319067	−	0.947732i	$-0.396631\pi$
$277$	10.6207	0.638134	0.319067	+	0.947732i	$0.396631\pi$
$278$	52.2315	3.13264
$279$	−3.29879	−0.197493
$280$	0.190146	0.0113634
$281$	17.8227	1.06321	0.531607	−	0.846991i	$-0.321588\pi$
$281$	17.8227	1.06321	0.531607	+	0.846991i	$0.321588\pi$
$282$	−32.2058	−1.91782
$283$	−0.0709677	−0.00421859	−0.00210930	−	0.999998i	$-0.500671\pi$
$283$	−0.0709677	−0.00421859	−0.00210930	+	0.999998i	$0.500671\pi$
$284$	−60.8777	−3.61243
$285$	−5.30851	−0.314449
$286$	−15.4388	−0.912916
$287$	0.183481	0.0108306
$288$	−8.88763	−0.523708
$289$	−10.5908	−0.622991
$290$	2.39514	0.140648
$291$	−7.23441	−0.424089
$292$	5.44276	0.318513
$293$	−18.2285	−1.06492	−0.532461	−	0.846455i	$-0.678733\pi$
$293$	−18.2285	−1.06492	−0.532461	+	0.846455i	$0.678733\pi$
$294$	30.7030	1.79064
$295$	10.3988	0.605441
$296$	−99.0899	−5.75948
$297$	5.49054	0.318593
$298$	51.4170	2.97851
$299$	−17.3360	−1.00257
$300$	−8.75107	−0.505243
$301$	0.183843	0.0105966
$302$	27.5300	1.58417
$303$	21.2086	1.21840
$304$	48.6601	2.79085
$305$	9.37972	0.537081
$306$	−2.86532	−0.163799
$307$	10.5732	0.603445	0.301722	−	0.953396i	$-0.402438\pi$
$307$	10.5732	0.603445	0.301722	+	0.953396i	$0.402438\pi$
$308$	0.110187	0.00627851
$309$	5.52668	0.314402
$310$	21.6928	1.23207
$311$	3.79446	0.215164	0.107582	−	0.994196i	$-0.465689\pi$
$311$	3.79446	0.215164	0.107582	+	0.994196i	$0.465689\pi$
$312$	85.4598	4.83821
$313$	19.9559	1.12798	0.563988	−	0.825783i	$-0.309266\pi$
$313$	19.9559	1.12798	0.563988	+	0.825783i	$0.309266\pi$
$314$	−2.76518	−0.156048
$315$	−0.00839882	−0.000473220 0
$316$	−8.95964	−0.504019
$317$	26.6890	1.49900	0.749501	−	0.662003i	$-0.230293\pi$
$317$	26.6890	1.49900	0.749501	+	0.662003i	$0.230293\pi$
$318$	2.75379	0.154425
$319$	0.877939	0.0491552
$320$	28.9688	1.61940
$321$	13.4599	0.751257
$322$	0.169193	0.00942874
$323$	8.35855	0.465082
$324$	−41.2741	−2.29300
$325$	−5.65909	−0.313910
$326$	−42.9258	−2.37744
$327$	10.8113	0.597864
$328$	85.1242	4.70020
$329$	0.148641	0.00819482
$330$	−4.38641	−0.241464
$331$	−24.1084	−1.32512	−0.662559	−	0.749010i	$-0.730530\pi$
$331$	−24.1084	−1.32512	−0.662559	+	0.749010i	$0.730530\pi$
$332$	−79.6538	−4.37157
$333$	4.37684	0.239850
$334$	60.6831	3.32043
$335$	2.36861	0.129411
$336$	−0.479730	−0.0261714
$337$	29.8467	1.62585	0.812925	−	0.582368i	$-0.197874\pi$
$337$	29.8467	1.62585	0.812925	+	0.582368i	$0.197874\pi$
$338$	51.9037	2.82319
$339$	22.6398	1.22963
$340$	13.7791	0.747274
$341$	7.95151	0.430598
$342$	−3.73683	−0.202065
$343$	−0.283419	−0.0153032
$344$	85.2922	4.59865
$345$	−4.92542	−0.265176
$346$	−3.73065	−0.200561
$347$	25.1609	1.35071	0.675354	−	0.737494i	$-0.263991\pi$
$347$	25.1609	1.35071	0.675354	+	0.737494i	$0.263991\pi$
$348$	−7.68290	−0.411847
$349$	19.2035	1.02794	0.513971	−	0.857808i	$-0.328174\pi$
$349$	19.2035	1.02794	0.513971	+	0.857808i	$0.328174\pi$
$350$	0.0552306	0.00295220
$351$	−31.0715	−1.65847
$352$	21.4230	1.14185
$353$	−1.53605	−0.0817556	−0.0408778	−	0.999164i	$-0.513015\pi$
$353$	−1.53605	−0.0817556	−0.0408778	+	0.999164i	$0.513015\pi$
$354$	−45.6133	−2.42432
$355$	−11.1851	−0.593643
$356$	−7.06009	−0.374184
$357$	−0.0824053	−0.00436135
$358$	50.7153	2.68039
$359$	15.5703	0.821771	0.410885	−	0.911687i	$-0.365220\pi$
$359$	15.5703	0.821771	0.410885	+	0.911687i	$0.365220\pi$
$360$	−3.89654	−0.205366
$361$	−8.09912	−0.426269
$362$	−14.6252	−0.768686
$363$	−1.60784	−0.0843895
$364$	−0.623561	−0.0326835
$365$	1.00000	0.0523424
$366$	−41.1433	−2.15059
$367$	1.71540	0.0895433	0.0447717	−	0.998997i	$-0.485744\pi$
$367$	1.71540	0.0895433	0.0447717	+	0.998997i	$0.485744\pi$
$368$	45.1485	2.35353
$369$	−3.75997	−0.195736
$370$	−28.7821	−1.49631
$371$	−0.0127097	−0.000659854 0
$372$	−69.5841	−3.60777
$373$	−21.2658	−1.10110	−0.550551	−	0.834802i	$-0.685582\pi$
$373$	−21.2658	−1.10110	−0.550551	+	0.834802i	$0.685582\pi$
$374$	6.90665	0.357134
$375$	−1.60784	−0.0830283
$376$	68.9602	3.55635
$377$	−4.96834	−0.255882
$378$	0.303246	0.0155973
$379$	−33.1128	−1.70089	−0.850445	−	0.526065i	$-0.823667\pi$
$379$	−33.1128	−1.70089	−0.850445	+	0.526065i	$0.823667\pi$
$380$	17.9701	0.921846
$381$	27.4156	1.40455
$382$	−57.0421	−2.91853
$383$	−10.3209	−0.527375	−0.263688	−	0.964608i	$-0.584939\pi$
$383$	−10.3209	−0.527375	−0.263688	+	0.964608i	$0.584939\pi$
$384$	−58.1794	−2.96895
$385$	0.0202448	0.00103177
$386$	2.77177	0.141079
$387$	−3.76739	−0.191507
$388$	24.4895	1.24327
$389$	−8.26030	−0.418814	−0.209407	−	0.977829i	$-0.567153\pi$
$389$	−8.26030	−0.418814	−0.209407	+	0.977829i	$0.567153\pi$
$390$	24.8231	1.25696
$391$	7.75536	0.392205
$392$	−65.7425	−3.32050
$393$	35.1616	1.77367
$394$	−57.2091	−2.88215
$395$	−1.64616	−0.0828272
$396$	−2.25800	−0.113469
$397$	−8.40135	−0.421651	−0.210826	−	0.977524i	$-0.567615\pi$
$397$	−8.40135	−0.421651	−0.210826	+	0.977524i	$0.567615\pi$
$398$	19.3346	0.969154
$399$	−0.107470	−0.00538021
$400$	14.7381	0.736906
$401$	−13.6460	−0.681449	−0.340725	−	0.940163i	$-0.610672\pi$
$401$	−13.6460	−0.681449	−0.340725	+	0.940163i	$0.610672\pi$
$402$	−10.3897	−0.518190
$403$	−44.9983	−2.24152
$404$	−71.7944	−3.57190
$405$	−7.58330	−0.376817
$406$	0.0484891	0.00240648
$407$	−10.5501	−0.522948
$408$	−38.2310	−1.89272
$409$	5.47668	0.270804	0.135402	−	0.990791i	$-0.456767\pi$
$409$	5.47668	0.270804	0.135402	+	0.990791i	$0.456767\pi$
$410$	24.7256	1.22111
$411$	−31.6756	−1.56244
$412$	−18.7086	−0.921708
$413$	0.210521	0.0103591
$414$	−3.46716	−0.170402
$415$	−14.6348	−0.718395
$416$	−121.235	−5.94402
$417$	−30.7827	−1.50744
$418$	9.00737	0.440565
$419$	4.96199	0.242409	0.121204	−	0.992628i	$-0.461324\pi$
$419$	4.96199	0.242409	0.121204	+	0.992628i	$0.461324\pi$
$420$	−0.177163	−0.00864468
$421$	21.8345	1.06415	0.532074	−	0.846698i	$-0.321413\pi$
$421$	21.8345	1.06415	0.532074	+	0.846698i	$0.321413\pi$
$422$	−66.0496	−3.21524
$423$	−3.04600	−0.148102
$424$	−5.89652	−0.286360
$425$	2.53163	0.122802
$426$	49.0623	2.37708
$427$	0.189890	0.00918944
$428$	−45.5637	−2.20240
$429$	9.09889	0.439298
$430$	24.7744	1.19473
$431$	−27.4566	−1.32254	−0.661269	−	0.750149i	$-0.729982\pi$
$431$	−27.4566	−1.32254	−0.661269	+	0.750149i	$0.729982\pi$
$432$	80.9202	3.89328
$433$	33.3470	1.60255	0.801277	−	0.598294i	$-0.204154\pi$
$433$	33.3470	1.60255	0.801277	+	0.598294i	$0.204154\pi$
$434$	0.439167	0.0210807
$435$	−1.41158	−0.0676802
$436$	−36.5977	−1.75271
$437$	10.1142	0.483829
$438$	−4.38641	−0.209591
$439$	0.0175384	0.000837060 0	0.000418530	−	1.00000i	$-0.499867\pi$
$439$	0.0175384	0.000837060 0	0.000418530		1.00000i	$0.499867\pi$
$440$	9.39234	0.447762
$441$	2.90388	0.138280
$442$	−39.0853	−1.85910
$443$	29.6692	1.40963	0.704814	−	0.709392i	$-0.251031\pi$
$443$	29.6692	1.40963	0.704814	+	0.709392i	$0.251031\pi$
$444$	92.3244	4.38152
$445$	−1.29715	−0.0614909
$446$	−12.6975	−0.601246
$447$	−30.3027	−1.43327
$448$	0.586466	0.0277079
$449$	0.182072	0.00859253	0.00429626	−	0.999991i	$-0.498632\pi$
$449$	0.182072	0.00859253	0.00429626	+	0.999991i	$0.498632\pi$
$450$	−1.13181	−0.0533539
$451$	9.06315	0.426767
$452$	−76.6390	−3.60480
$453$	−16.2248	−0.762309
$454$	−55.9285	−2.62485
$455$	−0.114567	−0.00537098
$456$	−49.8593	−2.33488
$457$	−25.3419	−1.18545	−0.592723	−	0.805406i	$-0.701947\pi$
$457$	−25.3419	−1.18545	−0.592723	+	0.805406i	$0.701947\pi$
$458$	27.3566	1.27829
$459$	13.9000	0.648797
$460$	16.6733	0.777395
$461$	2.56282	0.119362	0.0596811	−	0.998217i	$-0.480992\pi$
$461$	2.56282	0.119362	0.0596811	+	0.998217i	$0.480992\pi$
$462$	−0.0888018	−0.00413143
$463$	−25.5894	−1.18924	−0.594621	−	0.804006i	$-0.702698\pi$
$463$	−25.5894	−1.18924	−0.594621	+	0.804006i	$0.702698\pi$
$464$	12.9392	0.600686
$465$	−12.7847	−0.592877
$466$	−54.9790	−2.54685
$467$	−24.0867	−1.11460	−0.557300	−	0.830311i	$-0.688163\pi$
$467$	−24.0867	−1.11460	−0.557300	+	0.830311i	$0.688163\pi$
$468$	12.7782	0.590675
$469$	0.0479519	0.00221421
$470$	20.0305	0.923938
$471$	1.62966	0.0750909
$472$	97.6689	4.49558
$473$	9.08103	0.417546
$474$	7.22072	0.331658
$475$	3.30165	0.151490
$476$	0.278954	0.0127858
$477$	0.260452	0.0119253
$478$	−36.4062	−1.66518
$479$	−15.6921	−0.716988	−0.358494	−	0.933532i	$-0.616710\pi$
$479$	−15.6921	−0.716988	−0.358494	+	0.933532i	$0.616710\pi$
$480$	−34.4447	−1.57218
$481$	59.7038	2.72226
$482$	59.1695	2.69510
$483$	−0.0997140	−0.00453715
$484$	5.44276	0.247398
$485$	4.49947	0.204310
$486$	−11.6735	−0.529521
$487$	14.2991	0.647955	0.323977	−	0.946065i	$-0.394980\pi$
$487$	14.2991	0.647955	0.323977	+	0.946065i	$0.394980\pi$
$488$	88.0975	3.98799
$489$	25.2984	1.14403
$490$	−19.0959	−0.862664
$491$	5.88734	0.265692	0.132846	−	0.991137i	$-0.457588\pi$
$491$	5.88734	0.265692	0.132846	+	0.991137i	$0.457588\pi$
$492$	−79.3122	−3.57567
$493$	2.22262	0.100102
$494$	−50.9735	−2.29341
$495$	−0.414864	−0.0186467
$496$	117.190	5.26200
$497$	−0.226439	−0.0101572
$498$	64.1942	2.87661
$499$	23.2658	1.04152	0.520761	−	0.853703i	$-0.325648\pi$
$499$	23.2658	1.04152	0.520761	+	0.853703i	$0.325648\pi$
$500$	5.44276	0.243408
$501$	−35.7637	−1.59780
$502$	3.08964	0.137897
$503$	−21.5961	−0.962922	−0.481461	−	0.876468i	$-0.659894\pi$
$503$	−21.5961	−0.962922	−0.481461	+	0.876468i	$0.659894\pi$
$504$	−0.0788846	−0.00351380
$505$	−13.1908	−0.586983
$506$	8.35735	0.371530
$507$	−30.5896	−1.35853
$508$	−92.8060	−4.11760
$509$	7.51595	0.333139	0.166569	−	0.986030i	$-0.446731\pi$
$509$	7.51595	0.333139	0.166569	+	0.986030i	$0.446731\pi$
$510$	−11.1048	−0.491727
$511$	0.0202448	0.000895576 0
$512$	38.8839	1.71844
$513$	18.1278	0.800363
$514$	−8.37857	−0.369563
$515$	−3.43734	−0.151467
$516$	−79.4687	−3.49842
$517$	7.34217	0.322908
$518$	−0.582687	−0.0256018
$519$	2.19866	0.0965107
$520$	−53.1521	−2.33087
$521$	15.4966	0.678916	0.339458	−	0.940621i	$-0.389756\pi$
$521$	15.4966	0.678916	0.339458	+	0.940621i	$0.389756\pi$
$522$	−0.993658	−0.0434912
$523$	−28.6723	−1.25375	−0.626877	−	0.779118i	$-0.715667\pi$
$523$	−28.6723	−1.25375	−0.626877	+	0.779118i	$0.715667\pi$
$524$	−119.027	−5.19972
$525$	−0.0325503	−0.00142061
$526$	−23.8663	−1.04062
$527$	20.1303	0.876888
$528$	−23.6965	−1.03126
$529$	−13.6157	−0.591986
$530$	−1.71273	−0.0743962
$531$	−4.31408	−0.187215
$532$	0.363800	0.0157727
$533$	−51.2892	−2.22158
$534$	5.68984	0.246223
$535$	−8.37143	−0.361928
$536$	22.2468	0.960914
$537$	−29.8892	−1.28981
$538$	−47.0652	−2.02913
$539$	−6.99959	−0.301494
$540$	29.8837	1.28599
$541$	5.74640	0.247057	0.123529	−	0.992341i	$-0.460579\pi$
$541$	5.74640	0.247057	0.123529	+	0.992341i	$0.460579\pi$
$542$	−18.2651	−0.784554
$543$	8.61942	0.369895
$544$	54.2351	2.32531
$545$	−6.72410	−0.288029
$546$	0.502537	0.0215066
$547$	−12.8587	−0.549800	−0.274900	−	0.961473i	$-0.588645\pi$
$547$	−12.8587	−0.549800	−0.274900	+	0.961473i	$0.588645\pi$
$548$	107.227	4.58050
$549$	−3.89131	−0.166077
$550$	2.72814	0.116328
$551$	2.89865	0.123486
$552$	−46.2612	−1.96901
$553$	−0.0333261	−0.00141717
$554$	28.9747	1.23102
$555$	16.9628	0.720030
$556$	104.204	4.41924
$557$	−44.6693	−1.89270	−0.946349	−	0.323147i	$-0.895259\pi$
$557$	−44.6693	−1.89270	−0.946349	+	0.323147i	$0.895259\pi$
$558$	−8.99957	−0.380982
$559$	−51.3904	−2.17358
$560$	0.298370	0.0126084
$561$	−4.07045	−0.171854
$562$	48.6229	2.05104
$563$	11.6233	0.489865	0.244932	−	0.969540i	$-0.421234\pi$
$563$	11.6233	0.489865	0.244932	+	0.969540i	$0.421234\pi$
$564$	−64.2518	−2.70549
$565$	−14.0809	−0.592389
$566$	−0.193610	−0.00813803
$567$	−0.153522	−0.00644732
$568$	−105.054	−4.40797
$569$	35.1404	1.47316	0.736582	−	0.676348i	$-0.236439\pi$
$569$	35.1404	1.47316	0.736582	+	0.676348i	$0.236439\pi$
$570$	−14.4824	−0.606600
$571$	14.3073	0.598742	0.299371	−	0.954137i	$-0.403223\pi$
$571$	14.3073	0.598742	0.299371	+	0.954137i	$0.403223\pi$
$572$	−30.8011	−1.28786
$573$	33.6179	1.40441
$574$	0.500563	0.0208931
$575$	3.06339	0.127752
$576$	−12.0181	−0.500754
$577$	−47.1678	−1.96362	−0.981811	−	0.189861i	$-0.939196\pi$
$577$	−47.1678	−1.96362	−0.981811	+	0.189861i	$0.939196\pi$
$578$	−28.8933	−1.20180
$579$	−1.63355	−0.0678879
$580$	4.77841	0.198413
$581$	−0.296278	−0.0122917
$582$	−19.7365	−0.818104
$583$	−0.627801	−0.0260008
$584$	9.39234	0.388658
$585$	2.34775	0.0970676
$586$	−49.7300	−2.05433
$587$	−18.6217	−0.768602	−0.384301	−	0.923208i	$-0.625557\pi$
$587$	−18.6217	−0.768602	−0.384301	+	0.923208i	$0.625557\pi$
$588$	61.2539	2.52607
$589$	26.2531	1.08174
$590$	28.3694	1.16795
$591$	33.7163	1.38690
$592$	−155.488	−6.39053
$593$	−35.6941	−1.46578	−0.732890	−	0.680347i	$-0.761829\pi$
$593$	−35.6941	−1.46578	−0.732890	+	0.680347i	$0.761829\pi$
$594$	14.9790	0.614595
$595$	0.0512523	0.00210114
$596$	102.579	4.20181
$597$	−11.3949	−0.466361
$598$	−47.2950	−1.93404
$599$	−13.0601	−0.533622	−0.266811	−	0.963749i	$-0.585970\pi$
$599$	−13.0601	−0.533622	−0.266811	+	0.963749i	$0.585970\pi$
$600$	−15.1013	−0.616510
$601$	3.10099	0.126492	0.0632459	−	0.997998i	$-0.479855\pi$
$601$	3.10099	0.126492	0.0632459	+	0.997998i	$0.479855\pi$
$602$	0.501551	0.0204417
$603$	−0.982649	−0.0400166
$604$	54.9234	2.23480
$605$	1.00000	0.0406558
$606$	57.8602	2.35041
$607$	32.1321	1.30420	0.652102	−	0.758132i	$-0.273888\pi$
$607$	32.1321	1.30420	0.652102	+	0.758132i	$0.273888\pi$
$608$	70.7312	2.86853
$609$	−0.0285772	−0.00115801
$610$	25.5892	1.03608
$611$	−41.5500	−1.68093
$612$	−5.71643	−0.231073
$613$	−6.00202	−0.242419	−0.121210	−	0.992627i	$-0.538677\pi$
$613$	−6.00202	−0.242419	−0.121210	+	0.992627i	$0.538677\pi$
$614$	28.8452	1.16410
$615$	−14.5721	−0.587602
$616$	0.190146	0.00766119
$617$	−29.4537	−1.18576	−0.592880	−	0.805291i	$-0.702009\pi$
$617$	−29.4537	−1.18576	−0.592880	+	0.805291i	$0.702009\pi$
$618$	15.0776	0.606509
$619$	1.93577	0.0778050	0.0389025	−	0.999243i	$-0.487614\pi$
$619$	1.93577	0.0778050	0.0389025	+	0.999243i	$0.487614\pi$
$620$	43.2781	1.73809
$621$	16.8196	0.674949
$622$	10.3518	0.415070
$623$	−0.0262606	−0.00105211
$624$	134.100	5.36832
$625$	1.00000	0.0400000
$626$	54.4426	2.17596
$627$	−5.30851	−0.212001
$628$	−5.51665	−0.220138
$629$	−26.7089	−1.06495
$630$	−0.0229132	−0.000912883 0
$631$	−30.4264	−1.21126	−0.605628	−	0.795748i	$-0.707078\pi$
$631$	−30.4264	−1.21126	−0.605628	+	0.795748i	$0.707078\pi$
$632$	−15.4613	−0.615016
$633$	38.9264	1.54719
$634$	72.8113	2.89171
$635$	−17.0513	−0.676659
$636$	5.49392	0.217848
$637$	39.6113	1.56946
$638$	2.39514	0.0948246
$639$	4.64028	0.183567
$640$	36.1849	1.43033
$641$	26.4313	1.04397	0.521987	−	0.852953i	$-0.325191\pi$
$641$	26.4313	1.04397	0.521987	+	0.852953i	$0.325191\pi$
$642$	36.7205	1.44924
$643$	25.1631	0.992335	0.496168	−	0.868227i	$-0.334740\pi$
$643$	25.1631	0.992335	0.496168	+	0.868227i	$0.334740\pi$
$644$	0.337547	0.0133012
$645$	−14.6008	−0.574906
$646$	22.8033	0.897185
$647$	12.2291	0.480776	0.240388	−	0.970677i	$-0.422725\pi$
$647$	12.2291	0.480776	0.240388	+	0.970677i	$0.422725\pi$
$648$	−71.2249	−2.79798
$649$	10.3988	0.408188
$650$	−15.4388	−0.605560
$651$	−0.258824	−0.0101441
$652$	−85.6389	−3.35388
$653$	−30.6945	−1.20117	−0.600584	−	0.799561i	$-0.705065\pi$
$653$	−30.6945	−1.20117	−0.600584	+	0.799561i	$0.705065\pi$
$654$	29.4946	1.15333
$655$	−21.8689	−0.854488
$656$	133.574	5.21518
$657$	−0.414864	−0.0161854
$658$	0.405513	0.0158085
$659$	7.92067	0.308545	0.154273	−	0.988028i	$-0.450697\pi$
$659$	7.92067	0.308545	0.154273	+	0.988028i	$0.450697\pi$
$660$	−8.75107	−0.340635
$661$	−17.2769	−0.671993	−0.335997	−	0.941863i	$-0.609073\pi$
$661$	−17.2769	−0.671993	−0.335997	+	0.941863i	$0.609073\pi$
$662$	−65.7712	−2.55627
$663$	23.0350	0.894606
$664$	−137.455	−5.33429
$665$	0.0668411	0.00259199
$666$	11.9407	0.462691
$667$	2.68947	0.104137
$668$	121.065	4.68416
$669$	7.48332	0.289322
$670$	6.46190	0.249645
$671$	9.37972	0.362100
$672$	−0.697325	−0.0268999
$673$	27.2091	1.04884	0.524418	−	0.851461i	$-0.324283\pi$
$673$	27.2091	1.04884	0.524418	+	0.851461i	$0.324283\pi$
$674$	81.4259	3.13641
$675$	5.49054	0.211331
$676$	103.550	3.98270
$677$	−42.8321	−1.64617	−0.823085	−	0.567919i	$-0.807749\pi$
$677$	−42.8321	−1.64617	−0.823085	+	0.567919i	$0.807749\pi$
$678$	61.7646	2.37206
$679$	0.0910908	0.00349574
$680$	23.7779	0.911842
$681$	32.9616	1.26309
$682$	21.6928	0.830662
$683$	25.8300	0.988357	0.494179	−	0.869360i	$-0.335469\pi$
$683$	25.8300	0.988357	0.494179	+	0.869360i	$0.335469\pi$
$684$	−7.45513	−0.285054
$685$	19.7008	0.752729
$686$	−0.773206	−0.0295211
$687$	−16.1227	−0.615118
$688$	133.837	5.10250
$689$	3.55278	0.135350
$690$	−13.4373	−0.511547
$691$	−4.81022	−0.182989	−0.0914946	−	0.995806i	$-0.529164\pi$
$691$	−4.81022	−0.182989	−0.0914946	+	0.995806i	$0.529164\pi$
$692$	−7.44280	−0.282933
$693$	−0.00839882	−0.000319045 0
$694$	68.6425	2.60563
$695$	19.1454	0.726228
$696$	−13.2581	−0.502545
$697$	22.9445	0.869087
$698$	52.3900	1.98299
$699$	32.4020	1.22556
$700$	0.110187	0.00416469
$701$	29.8387	1.12699	0.563496	−	0.826119i	$-0.309456\pi$
$701$	29.8387	1.12699	0.563496	+	0.826119i	$0.309456\pi$
$702$	−84.7674	−3.19934
$703$	−34.8326	−1.31374
$704$	28.9688	1.09180
$705$	−11.8050	−0.444602
$706$	−4.19056	−0.157714
$707$	−0.267045	−0.0100433
$708$	−91.0004	−3.42001
$709$	−23.8980	−0.897507	−0.448754	−	0.893656i	$-0.648132\pi$
$709$	−23.8980	−0.897507	−0.448754	+	0.893656i	$0.648132\pi$
$710$	−30.5145	−1.14519
$711$	0.682931	0.0256119
$712$	−12.1833	−0.456588
$713$	24.3585	0.912234
$714$	−0.224813	−0.00841342
$715$	−5.65909	−0.211638
$716$	101.179	3.78125
$717$	21.4561	0.801291
$718$	42.4781	1.58527
$719$	−43.8019	−1.63353	−0.816767	−	0.576968i	$-0.804236\pi$
$719$	−43.8019	−1.63353	−0.816767	+	0.576968i	$0.804236\pi$
$720$	−6.11431	−0.227867
$721$	−0.0695882	−0.00259160
$722$	−22.0955	−0.822311
$723$	−34.8717	−1.29689
$724$	−29.1780	−1.08439
$725$	0.877939	0.0326058
$726$	−4.38641	−0.162795
$727$	−30.9195	−1.14674	−0.573370	−	0.819296i	$-0.694364\pi$
$727$	−30.9195	−1.14674	−0.573370	+	0.819296i	$0.694364\pi$
$728$	−1.07605	−0.0398811
$729$	29.6297	1.09740
$730$	2.72814	0.100973
$731$	22.9898	0.850309
$732$	−82.0826	−3.03386
$733$	−43.4191	−1.60372	−0.801860	−	0.597511i	$-0.796156\pi$
$733$	−43.4191	−1.60372	−0.801860	+	0.597511i	$0.796156\pi$
$734$	4.67986	0.172737
$735$	11.2542	0.415117
$736$	65.6269	2.41904
$737$	2.36861	0.0872488
$738$	−10.2577	−0.377593
$739$	−15.6949	−0.577347	−0.288673	−	0.957428i	$-0.593214\pi$
$739$	−15.6949	−0.577347	−0.288673	+	0.957428i	$0.593214\pi$
$740$	−57.4215	−2.11086
$741$	30.0413	1.10360
$742$	−0.0346738	−0.00127292
$743$	10.5974	0.388779	0.194390	−	0.980924i	$-0.437727\pi$
$743$	10.5974	0.388779	0.194390	+	0.980924i	$0.437727\pi$
$744$	−120.078	−4.40229
$745$	18.8469	0.690497
$746$	−58.0162	−2.12412
$747$	6.07145	0.222143
$748$	13.7791	0.503812
$749$	−0.169478	−0.00619258
$750$	−4.38641	−0.160169
$751$	41.0570	1.49819	0.749096	−	0.662461i	$-0.230488\pi$
$751$	41.0570	1.49819	0.749096	+	0.662461i	$0.230488\pi$
$752$	108.210	3.94601
$753$	−1.82089	−0.0663568
$754$	−13.5543	−0.493620
$755$	10.0911	0.367253
$756$	0.604989	0.0220032
$757$	30.5742	1.11124	0.555619	−	0.831437i	$-0.312481\pi$
$757$	30.5742	1.11124	0.555619	+	0.831437i	$0.312481\pi$
$758$	−90.3364	−3.28116
$759$	−4.92542	−0.178781
$760$	31.0102	1.12486
$761$	−25.6763	−0.930766	−0.465383	−	0.885109i	$-0.654083\pi$
$761$	−25.6763	−0.930766	−0.465383	+	0.885109i	$0.654083\pi$
$762$	74.7938	2.70949
$763$	−0.136128	−0.00492816
$764$	−113.801	−4.11719
$765$	−1.05028	−0.0379730
$766$	−28.1570	−1.01735
$767$	−58.8477	−2.12487
$768$	−65.5676	−2.36597
$769$	42.3263	1.52632	0.763162	−	0.646207i	$-0.223646\pi$
$769$	42.3263	1.52632	0.763162	+	0.646207i	$0.223646\pi$
$770$	0.0552306	0.00199037
$771$	4.93792	0.177835
$772$	5.52980	0.199022
$773$	27.3682	0.984366	0.492183	−	0.870492i	$-0.336199\pi$
$773$	27.3682	0.984366	0.492183	+	0.870492i	$0.336199\pi$
$774$	−10.2780	−0.369434
$775$	7.95151	0.285627
$776$	42.2606	1.51707
$777$	0.343408	0.0123197
$778$	−22.5353	−0.807929
$779$	29.9233	1.07211
$780$	49.5231	1.77321
$781$	−11.1851	−0.400234
$782$	21.1577	0.756599
$783$	4.82036	0.172266
$784$	−103.161	−3.68431
$785$	−1.01358	−0.0361761
$786$	95.9258	3.42156
$787$	7.10865	0.253396	0.126698	−	0.991941i	$-0.459562\pi$
$787$	7.10865	0.253396	0.126698	+	0.991941i	$0.459562\pi$
$788$	−114.135	−4.06588
$789$	14.0657	0.500751
$790$	−4.49095	−0.159781
$791$	−0.285065	−0.0101357
$792$	−3.89654	−0.138458
$793$	−53.0807	−1.88495
$794$	−22.9201	−0.813403
$795$	1.00940	0.0357997
$796$	38.5733	1.36719
$797$	−22.3204	−0.790630	−0.395315	−	0.918546i	$-0.629364\pi$
$797$	−22.3204	−0.790630	−0.395315	+	0.918546i	$0.629364\pi$
$798$	−0.293192	−0.0103789
$799$	18.5877	0.657585
$800$	21.4230	0.757418
$801$	0.538141	0.0190143
$802$	−37.2283	−1.31458
$803$	1.00000	0.0352892
$804$	−20.7278	−0.731014
$805$	0.0620175	0.00218583
$806$	−122.762	−4.32410
$807$	27.7380	0.976423
$808$	−123.892	−4.35852
$809$	26.5928	0.934951	0.467476	−	0.884006i	$-0.345164\pi$
$809$	26.5928	0.934951	0.467476	+	0.884006i	$0.345164\pi$
$810$	−20.6883	−0.726913
$811$	−5.85142	−0.205471	−0.102736	−	0.994709i	$-0.532760\pi$
$811$	−5.85142	−0.205471	−0.102736	+	0.994709i	$0.532760\pi$
$812$	0.0967379	0.00339483
$813$	10.7646	0.377530
$814$	−28.7821	−1.00881
$815$	−15.7345	−0.551154
$816$	−59.9907	−2.10009
$817$	29.9824	1.04895
$818$	14.9412	0.522405
$819$	0.0475297	0.00166082
$820$	49.3285	1.72263
$821$	−14.3841	−0.502008	−0.251004	−	0.967986i	$-0.580761\pi$
$821$	−14.3841	−0.502008	−0.251004	+	0.967986i	$0.580761\pi$
$822$	−86.4157	−3.01409
$823$	10.5061	0.366220	0.183110	−	0.983092i	$-0.441384\pi$
$823$	10.5061	0.366220	0.183110	+	0.983092i	$0.441384\pi$
$824$	−32.2847	−1.12469
$825$	−1.60784	−0.0559777
$826$	0.574331	0.0199835
$827$	53.3710	1.85589	0.927946	−	0.372714i	$-0.121573\pi$
$827$	53.3710	1.85589	0.927946	+	0.372714i	$0.121573\pi$
$828$	−6.91714	−0.240387
$829$	3.07102	0.106661	0.0533305	−	0.998577i	$-0.483016\pi$
$829$	3.07102	0.106661	0.0533305	+	0.998577i	$0.483016\pi$
$830$	−39.9259	−1.38585
$831$	−17.0763	−0.592370
$832$	−163.937	−5.68349
$833$	−17.7204	−0.613975
$834$	−83.9796	−2.90798
$835$	22.2434	0.769764
$836$	17.9701	0.621508
$837$	43.6581	1.50904
$838$	13.5370	0.467628
$839$	14.8021	0.511024	0.255512	−	0.966806i	$-0.417756\pi$
$839$	14.8021	0.511024	0.255512	+	0.966806i	$0.417756\pi$
$840$	−0.305723	−0.0105485
$841$	−28.2292	−0.973421
$842$	59.5676	2.05283
$843$	−28.6560	−0.986966
$844$	−131.772	−4.53577
$845$	19.0253	0.654490
$846$	−8.30993	−0.285701
$847$	0.0202448	0.000695619 0
$848$	−9.25260	−0.317736
$849$	0.114104	0.00391605
$850$	6.90665	0.236896
$851$	−32.3189	−1.10788
$852$	97.8814	3.35336
$853$	14.3825	0.492446	0.246223	−	0.969213i	$-0.420810\pi$
$853$	14.3825	0.492446	0.246223	+	0.969213i	$0.420810\pi$
$854$	0.518048	0.0177272
$855$	−1.36973	−0.0468439
$856$	−78.6273	−2.68743
$857$	30.6645	1.04748	0.523739	−	0.851879i	$-0.324537\pi$
$857$	30.6645	1.04748	0.523739	+	0.851879i	$0.324537\pi$
$858$	24.8231	0.847445
$859$	−21.3067	−0.726975	−0.363487	−	0.931599i	$-0.618414\pi$
$859$	−21.3067	−0.726975	−0.363487	+	0.931599i	$0.618414\pi$
$860$	49.4259	1.68541
$861$	−0.295008	−0.0100538
$862$	−74.9055	−2.55129
$863$	47.9363	1.63177	0.815886	−	0.578213i	$-0.196250\pi$
$863$	47.9363	1.63177	0.815886	+	0.578213i	$0.196250\pi$
$864$	117.624	4.00165
$865$	−1.36747	−0.0464953
$866$	90.9753	3.09147
$867$	17.0283	0.578313
$868$	0.876156	0.0297387
$869$	−1.64616	−0.0558421
$870$	−3.85100	−0.130561
$871$	−13.4042	−0.454183
$872$	−63.1550	−2.13870
$873$	−1.86667	−0.0631771
$874$	27.5930	0.933348
$875$	0.0202448	0.000684398 0
$876$	−8.75107	−0.295671
$877$	−15.6489	−0.528426	−0.264213	−	0.964464i	$-0.585112\pi$
$877$	−15.6489	−0.528426	−0.264213	+	0.964464i	$0.585112\pi$
$878$	0.0478471	0.00161476
$879$	29.3085	0.988550
$880$	14.7381	0.496822
$881$	−17.7355	−0.597525	−0.298763	−	0.954327i	$-0.596574\pi$
$881$	−17.7355	−0.597525	−0.298763	+	0.954327i	$0.596574\pi$
$882$	7.92219	0.266754
$883$	−45.7682	−1.54022	−0.770112	−	0.637909i	$-0.779800\pi$
$883$	−45.7682	−1.54022	−0.770112	+	0.637909i	$0.779800\pi$
$884$	−77.9769	−2.62265
$885$	−16.7195	−0.562021
$886$	80.9419	2.71930
$887$	18.7808	0.630598	0.315299	−	0.948992i	$-0.397895\pi$
$887$	18.7808	0.630598	0.315299	+	0.948992i	$0.397895\pi$
$888$	159.320	5.34644
$889$	−0.345199	−0.0115776
$890$	−3.53882	−0.118621
$891$	−7.58330	−0.254050
$892$	−25.3321	−0.848183
$893$	24.2413	0.811203
$894$	−82.6702	−2.76490
$895$	18.5897	0.621385
$896$	0.732555	0.0244729
$897$	27.8734	0.930666
$898$	0.496719	0.0165757
$899$	6.98094	0.232827
$900$	−2.25800	−0.0752668
$901$	−1.58936	−0.0529492
$902$	24.7256	0.823271
$903$	−0.295590	−0.00983662
$904$	−132.253	−4.39866
$905$	−5.36088	−0.178202
$906$	−44.2636	−1.47056
$907$	−36.6525	−1.21703	−0.608513	−	0.793544i	$-0.708234\pi$
$907$	−36.6525	−1.21703	−0.608513	+	0.793544i	$0.708234\pi$
$908$	−111.580	−3.70290
$909$	5.47238	0.181508
$910$	−0.312555	−0.0103611
$911$	27.5244	0.911926	0.455963	−	0.889999i	$-0.349295\pi$
$911$	27.5244	0.911926	0.455963	+	0.889999i	$0.349295\pi$
$912$	−78.2374	−2.59070
$913$	−14.6348	−0.484342
$914$	−69.1364	−2.28683
$915$	−15.0811	−0.498564
$916$	54.5776	1.80329
$917$	−0.442731	−0.0146203
$918$	37.9212	1.25159
$919$	−14.9457	−0.493015	−0.246507	−	0.969141i	$-0.579283\pi$
$919$	−14.9457	−0.493015	−0.246507	+	0.969141i	$0.579283\pi$
$920$	28.7724	0.948597
$921$	−17.0000	−0.560169
$922$	6.99173	0.230260
$923$	63.2974	2.08346
$924$	−0.177163	−0.00582825
$925$	−10.5501	−0.346884
$926$	−69.8116	−2.29415
$927$	1.42603	0.0468369
$928$	18.8081	0.617406
$929$	14.8001	0.485577	0.242789	−	0.970079i	$-0.421938\pi$
$929$	14.8001	0.485577	0.242789	+	0.970079i	$0.421938\pi$
$930$	−34.8785	−1.14371
$931$	−23.1102	−0.757406
$932$	−109.685	−3.59287
$933$	−6.10087	−0.199733
$934$	−65.7120	−2.15016
$935$	2.53163	0.0827932
$936$	22.0509	0.720755
$937$	−23.8888	−0.780413	−0.390207	−	0.920727i	$-0.627596\pi$
$937$	−23.8888	−0.780413	−0.390207	+	0.920727i	$0.627596\pi$
$938$	0.130820	0.00427141
$939$	−32.0859	−1.04708
$940$	39.9617	1.30341
$941$	−19.8837	−0.648189	−0.324094	−	0.946025i	$-0.605060\pi$
$941$	−19.8837	−0.648189	−0.324094	+	0.946025i	$0.605060\pi$
$942$	4.44595	0.144857
$943$	27.7639	0.904118
$944$	153.259	4.98814
$945$	0.111155	0.00361586
$946$	24.7744	0.805484
$947$	−14.1639	−0.460265	−0.230132	−	0.973159i	$-0.573916\pi$
$947$	−14.1639	−0.460265	−0.230132	+	0.973159i	$0.573916\pi$
$948$	14.4056	0.467873
$949$	−5.65909	−0.183702
$950$	9.00737	0.292238
$951$	−42.9115	−1.39150
$952$	0.481379	0.0156016
$953$	−7.70434	−0.249568	−0.124784	−	0.992184i	$-0.539824\pi$
$953$	−7.70434	−0.249568	−0.124784	+	0.992184i	$0.539824\pi$
$954$	0.710549	0.0230049
$955$	−20.9088	−0.676592
$956$	−72.6319	−2.34908
$957$	−1.41158	−0.0456300
$958$	−42.8102	−1.38313
$959$	0.398838	0.0128792
$960$	−46.5770	−1.50327
$961$	32.2264	1.03956
$962$	162.881	5.25148
$963$	3.47300	0.111916
$964$	118.046	3.80200
$965$	1.01599	0.0327059
$966$	−0.272034	−0.00875255
$967$	−22.8296	−0.734150	−0.367075	−	0.930191i	$-0.619641\pi$
$967$	−22.8296	−0.734150	−0.367075	+	0.930191i	$0.619641\pi$
$968$	9.39234	0.301881
$969$	−13.4392	−0.431729
$970$	12.2752	0.394133
$971$	16.1047	0.516823	0.258412	−	0.966035i	$-0.416801\pi$
$971$	16.1047	0.516823	0.258412	+	0.966035i	$0.416801\pi$
$972$	−23.2892	−0.747000
$973$	0.387595	0.0124257
$974$	39.0100	1.24996
$975$	9.09889	0.291398
$976$	138.239	4.42494
$977$	−27.8595	−0.891304	−0.445652	−	0.895206i	$-0.647028\pi$
$977$	−27.8595	−0.891304	−0.445652	+	0.895206i	$0.647028\pi$
$978$	69.0177	2.20694
$979$	−1.29715	−0.0414572
$980$	−38.0971	−1.21697
$981$	2.78959	0.0890646
$982$	16.0615	0.512543
$983$	−30.1361	−0.961193	−0.480597	−	0.876942i	$-0.659580\pi$
$983$	−30.1361	−0.961193	−0.480597	+	0.876942i	$0.659580\pi$
$984$	−136.866	−4.36312
$985$	−20.9700	−0.668159
$986$	6.06362	0.193105
$987$	−0.238990	−0.00760713
$988$	−101.694	−3.23533
$989$	27.8187	0.884584
$990$	−1.13181	−0.0359712
$991$	11.9136	0.378449	0.189224	−	0.981934i	$-0.439403\pi$
$991$	11.9136	0.378449	0.189224	+	0.981934i	$0.439403\pi$
$992$	170.345	5.40846
$993$	38.7624	1.23009
$994$	−0.617759	−0.0195941
$995$	7.08708	0.224676
$996$	128.070	4.05806
$997$	−14.5722	−0.461505	−0.230753	−	0.973012i	$-0.574119\pi$
$997$	−14.5722	−0.461505	−0.230753	+	0.973012i	$0.574119\pi$
$998$	63.4725	2.00919
$999$	−57.9256	−1.83269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.37	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.37	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.72814 q^{2} -1.60784 q^{3} +5.44276 q^{4} +1.00000 q^{5} -4.38641 q^{6} +0.0202448 q^{7} +9.39234 q^{8} -0.414864 q^{9} +O(q^{10})\)	\(q+2.72814 q^{2} -1.60784 q^{3} +5.44276 q^{4} +1.00000 q^{5} -4.38641 q^{6} +0.0202448 q^{7} +9.39234 q^{8} -0.414864 q^{9} +2.72814 q^{10} +1.00000 q^{11} -8.75107 q^{12} -5.65909 q^{13} +0.0552306 q^{14} -1.60784 q^{15} +14.7381 q^{16} +2.53163 q^{17} -1.13181 q^{18} +3.30165 q^{19} +5.44276 q^{20} -0.0325503 q^{21} +2.72814 q^{22} +3.06339 q^{23} -15.1013 q^{24} +1.00000 q^{25} -15.4388 q^{26} +5.49054 q^{27} +0.110187 q^{28} +0.877939 q^{29} -4.38641 q^{30} +7.95151 q^{31} +21.4230 q^{32} -1.60784 q^{33} +6.90665 q^{34} +0.0202448 q^{35} -2.25800 q^{36} -10.5501 q^{37} +9.00737 q^{38} +9.09889 q^{39} +9.39234 q^{40} +9.06315 q^{41} -0.0888018 q^{42} +9.08103 q^{43} +5.44276 q^{44} -0.414864 q^{45} +8.35735 q^{46} +7.34217 q^{47} -23.6965 q^{48} -6.99959 q^{49} +2.72814 q^{50} -4.07045 q^{51} -30.8011 q^{52} -0.627801 q^{53} +14.9790 q^{54} +1.00000 q^{55} +0.190146 q^{56} -5.30851 q^{57} +2.39514 q^{58} +10.3988 q^{59} -8.75107 q^{60} +9.37972 q^{61} +21.6928 q^{62} -0.00839882 q^{63} +28.9688 q^{64} -5.65909 q^{65} -4.38641 q^{66} +2.36861 q^{67} +13.7791 q^{68} -4.92542 q^{69} +0.0552306 q^{70} -11.1851 q^{71} -3.89654 q^{72} +1.00000 q^{73} -28.7821 q^{74} -1.60784 q^{75} +17.9701 q^{76} +0.0202448 q^{77} +24.8231 q^{78} -1.64616 q^{79} +14.7381 q^{80} -7.58330 q^{81} +24.7256 q^{82} -14.6348 q^{83} -0.177163 q^{84} +2.53163 q^{85} +24.7744 q^{86} -1.41158 q^{87} +9.39234 q^{88} -1.29715 q^{89} -1.13181 q^{90} -0.114567 q^{91} +16.6733 q^{92} -12.7847 q^{93} +20.0305 q^{94} +3.30165 q^{95} -34.4447 q^{96} +4.49947 q^{97} -19.0959 q^{98} -0.414864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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