LMFDB - Embedded newform 8005.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, 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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$0$
Dimension:	$137$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57744 q^{2} +0.488387 q^{3} +4.64318 q^{4} -1.00000 q^{5} -1.25879 q^{6} +1.78000 q^{7} -6.81263 q^{8} -2.76148 q^{9} +O(q^{10})$	\(q-2.57744 q^{2} +0.488387 q^{3} +4.64318 q^{4} -1.00000 q^{5} -1.25879 q^{6} +1.78000 q^{7} -6.81263 q^{8} -2.76148 q^{9} +2.57744 q^{10} +2.29646 q^{11} +2.26767 q^{12} +4.97892 q^{13} -4.58783 q^{14} -0.488387 q^{15} +8.27277 q^{16} +6.11156 q^{17} +7.11754 q^{18} -2.99104 q^{19} -4.64318 q^{20} +0.869328 q^{21} -5.91897 q^{22} -1.24144 q^{23} -3.32720 q^{24} +1.00000 q^{25} -12.8329 q^{26} -2.81383 q^{27} +8.26485 q^{28} -0.529087 q^{29} +1.25879 q^{30} -8.66335 q^{31} -7.69728 q^{32} +1.12156 q^{33} -15.7522 q^{34} -1.78000 q^{35} -12.8220 q^{36} +4.01555 q^{37} +7.70923 q^{38} +2.43164 q^{39} +6.81263 q^{40} +8.36578 q^{41} -2.24064 q^{42} -7.16649 q^{43} +10.6629 q^{44} +2.76148 q^{45} +3.19973 q^{46} +6.68571 q^{47} +4.04032 q^{48} -3.83161 q^{49} -2.57744 q^{50} +2.98481 q^{51} +23.1180 q^{52} +0.136109 q^{53} +7.25248 q^{54} -2.29646 q^{55} -12.1265 q^{56} -1.46079 q^{57} +1.36369 q^{58} +4.45182 q^{59} -2.26767 q^{60} -0.514933 q^{61} +22.3292 q^{62} -4.91542 q^{63} +3.29372 q^{64} -4.97892 q^{65} -2.89075 q^{66} -6.15358 q^{67} +28.3771 q^{68} -0.606302 q^{69} +4.58783 q^{70} +15.6388 q^{71} +18.8129 q^{72} +7.19368 q^{73} -10.3498 q^{74} +0.488387 q^{75} -13.8880 q^{76} +4.08769 q^{77} -6.26741 q^{78} +8.06807 q^{79} -8.27277 q^{80} +6.91019 q^{81} -21.5623 q^{82} +9.08208 q^{83} +4.03645 q^{84} -6.11156 q^{85} +18.4712 q^{86} -0.258399 q^{87} -15.6449 q^{88} +14.9674 q^{89} -7.11754 q^{90} +8.86246 q^{91} -5.76422 q^{92} -4.23107 q^{93} -17.2320 q^{94} +2.99104 q^{95} -3.75926 q^{96} -15.6887 q^{97} +9.87574 q^{98} -6.34162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) $ 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * 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 $

$2$	−2.57744	−1.82252	−0.911262	−	0.411828i	$-0.864890\pi$
$2$	−2.57744	−1.82252	−0.911262	+	0.411828i	$0.864890\pi$
$3$	0.488387	0.281971	0.140985	−	0.990012i	$-0.454973\pi$
$3$	0.488387	0.281971	0.140985	+	0.990012i	$0.454973\pi$
$4$	4.64318	2.32159
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.25879	−0.513898
$7$	1.78000	0.672775	0.336388	−	0.941724i	$-0.390795\pi$
$7$	1.78000	0.672775	0.336388	+	0.941724i	$0.390795\pi$
$8$	−6.81263	−2.40863
$9$	−2.76148	−0.920493
$10$	2.57744	0.815057
$11$	2.29646	0.692408	0.346204	−	0.938159i	$-0.387471\pi$
$11$	2.29646	0.692408	0.346204	+	0.938159i	$0.387471\pi$
$12$	2.26767	0.654620
$13$	4.97892	1.38090	0.690452	−	0.723378i	$-0.257412\pi$
$13$	4.97892	1.38090	0.690452	+	0.723378i	$0.257412\pi$
$14$	−4.58783	−1.22615
$15$	−0.488387	−0.126101
$16$	8.27277	2.06819
$17$	6.11156	1.48227	0.741136	−	0.671355i	$-0.234287\pi$
$17$	6.11156	1.48227	0.741136	+	0.671355i	$0.234287\pi$
$18$	7.11754	1.67762
$19$	−2.99104	−0.686193	−0.343096	−	0.939300i	$-0.611476\pi$
$19$	−2.99104	−0.686193	−0.343096	+	0.939300i	$0.611476\pi$
$20$	−4.64318	−1.03825
$21$	0.869328	0.189703
$22$	−5.91897	−1.26193
$23$	−1.24144	−0.258858	−0.129429	−	0.991589i	$-0.541314\pi$
$23$	−1.24144	−0.258858	−0.129429	+	0.991589i	$0.541314\pi$
$24$	−3.32720	−0.679163
$25$	1.00000	0.200000
$26$	−12.8329	−2.51673
$27$	−2.81383	−0.541522
$28$	8.26485	1.56191
$29$	−0.529087	−0.0982490	−0.0491245	−	0.998793i	$-0.515643\pi$
$29$	−0.529087	−0.0982490	−0.0491245	+	0.998793i	$0.515643\pi$
$30$	1.25879	0.229822
$31$	−8.66335	−1.55598	−0.777992	−	0.628275i	$-0.783761\pi$
$31$	−8.66335	−1.55598	−0.777992	+	0.628275i	$0.783761\pi$
$32$	−7.69728	−1.36070
$33$	1.12156	0.195239
$34$	−15.7522	−2.70148
$35$	−1.78000	−0.300874
$36$	−12.8220	−2.13701
$37$	4.01555	0.660153	0.330077	−	0.943954i	$-0.392925\pi$
$37$	4.01555	0.660153	0.330077	+	0.943954i	$0.392925\pi$
$38$	7.70923	1.25060
$39$	2.43164	0.389374
$40$	6.81263	1.07717
$41$	8.36578	1.30652	0.653258	−	0.757135i	$-0.273402\pi$
$41$	8.36578	1.30652	0.653258	+	0.757135i	$0.273402\pi$
$42$	−2.24064	−0.345738
$43$	−7.16649	−1.09288	−0.546440	−	0.837498i	$-0.684017\pi$
$43$	−7.16649	−1.09288	−0.546440	+	0.837498i	$0.684017\pi$
$44$	10.6629	1.60749
$45$	2.76148	0.411657
$46$	3.19973	0.471774
$47$	6.68571	0.975212	0.487606	−	0.873064i	$-0.337870\pi$
$47$	6.68571	0.975212	0.487606	+	0.873064i	$0.337870\pi$
$48$	4.04032	0.583170
$49$	−3.83161	−0.547373
$50$	−2.57744	−0.364505
$51$	2.98481	0.417957
$52$	23.1180	3.20590
$53$	0.136109	0.0186960	0.00934798	−	0.999956i	$-0.497024\pi$
$53$	0.136109	0.0186960	0.00934798	+	0.999956i	$0.497024\pi$
$54$	7.25248	0.986937
$55$	−2.29646	−0.309654
$56$	−12.1265	−1.62047
$57$	−1.46079	−0.193486
$58$	1.36369	0.179061
$59$	4.45182	0.579578	0.289789	−	0.957091i	$-0.406415\pi$
$59$	4.45182	0.579578	0.289789	+	0.957091i	$0.406415\pi$
$60$	−2.26767	−0.292755
$61$	−0.514933	−0.0659304	−0.0329652	−	0.999457i	$-0.510495\pi$
$61$	−0.514933	−0.0659304	−0.0329652	+	0.999457i	$0.510495\pi$
$62$	22.3292	2.83582
$63$	−4.91542	−0.619285
$64$	3.29372	0.411715
$65$	−4.97892	−0.617559
$66$	−2.89075	−0.355827
$67$	−6.15358	−0.751779	−0.375890	−	0.926664i	$-0.622663\pi$
$67$	−6.15358	−0.751779	−0.375890	+	0.926664i	$0.622663\pi$
$68$	28.3771	3.44123
$69$	−0.606302	−0.0729902
$70$	4.58783	0.548350
$71$	15.6388	1.85599	0.927993	−	0.372599i	$-0.121533\pi$
$71$	15.6388	1.85599	0.927993	+	0.372599i	$0.121533\pi$
$72$	18.8129	2.21713
$73$	7.19368	0.841957	0.420979	−	0.907071i	$-0.361687\pi$
$73$	7.19368	0.841957	0.420979	+	0.907071i	$0.361687\pi$
$74$	−10.3498	−1.20314
$75$	0.488387	0.0563941
$76$	−13.8880	−1.59306
$77$	4.08769	0.465835
$78$	−6.26741	−0.709644
$79$	8.06807	0.907729	0.453864	−	0.891071i	$-0.350045\pi$
$79$	8.06807	0.907729	0.453864	+	0.891071i	$0.350045\pi$
$80$	−8.27277	−0.924924
$81$	6.91019	0.767799
$82$	−21.5623	−2.38116
$83$	9.08208	0.996888	0.498444	−	0.866922i	$-0.333905\pi$
$83$	9.08208	0.996888	0.498444	+	0.866922i	$0.333905\pi$
$84$	4.03645	0.440412
$85$	−6.11156	−0.662892
$86$	18.4712	1.99180
$87$	−0.258399	−0.0277033
$88$	−15.6449	−1.66775
$89$	14.9674	1.58654	0.793269	−	0.608871i	$-0.208377\pi$
$89$	14.9674	1.58654	0.793269	+	0.608871i	$0.208377\pi$
$90$	−7.11754	−0.750254
$91$	8.86246	0.929038
$92$	−5.76422	−0.600961
$93$	−4.23107	−0.438742
$94$	−17.2320	−1.77735
$95$	2.99104	0.306875
$96$	−3.75926	−0.383678
$97$	−15.6887	−1.59294	−0.796471	−	0.604676i	$-0.793303\pi$
$97$	−15.6887	−1.59294	−0.796471	+	0.604676i	$0.793303\pi$
$98$	9.87574	0.997601
$99$	−6.34162	−0.637356
$100$	4.64318	0.464318
$101$	−7.00641	−0.697164	−0.348582	−	0.937278i	$-0.613337\pi$
$101$	−7.00641	−0.697164	−0.348582	+	0.937278i	$0.613337\pi$
$102$	−7.69316	−0.761737
$103$	4.25975	0.419725	0.209863	−	0.977731i	$-0.432698\pi$
$103$	4.25975	0.419725	0.209863	+	0.977731i	$0.432698\pi$
$104$	−33.9196	−3.32609
$105$	−0.869328	−0.0848377
$106$	−0.350812	−0.0340738
$107$	−10.3047	−0.996191	−0.498096	−	0.867122i	$-0.665967\pi$
$107$	−10.3047	−0.996191	−0.498096	+	0.867122i	$0.665967\pi$
$108$	−13.0651	−1.25719
$109$	20.5469	1.96804	0.984020	−	0.178059i	$-0.0569817\pi$
$109$	20.5469	1.96804	0.984020	+	0.178059i	$0.0569817\pi$
$110$	5.91897	0.564352
$111$	1.96115	0.186144
$112$	14.7255	1.39143
$113$	−18.9972	−1.78711	−0.893555	−	0.448954i	$-0.851797\pi$
$113$	−18.9972	−1.78711	−0.893555	+	0.448954i	$0.851797\pi$
$114$	3.76509	0.352633
$115$	1.24144	0.115765
$116$	−2.45665	−0.228094
$117$	−13.7492	−1.27111
$118$	−11.4743	−1.05629
$119$	10.8786	0.997236
$120$	3.32720	0.303731
$121$	−5.72628	−0.520571
$122$	1.32721	0.120160
$123$	4.08574	0.368399
$124$	−40.2255	−3.61236
$125$	−1.00000	−0.0894427
$126$	12.6692	1.12866
$127$	−2.92044	−0.259147	−0.129573	−	0.991570i	$-0.541361\pi$
$127$	−2.92044	−0.259147	−0.129573	+	0.991570i	$0.541361\pi$
$128$	6.90522	0.610341
$129$	−3.50002	−0.308160
$130$	12.8329	1.12552
$131$	9.74604	0.851516	0.425758	−	0.904837i	$-0.360008\pi$
$131$	9.74604	0.851516	0.425758	+	0.904837i	$0.360008\pi$
$132$	5.20761	0.453264
$133$	−5.32405	−0.461653
$134$	15.8605	1.37014
$135$	2.81383	0.242176
$136$	−41.6359	−3.57025
$137$	−15.2091	−1.29940	−0.649702	−	0.760189i	$-0.725106\pi$
$137$	−15.2091	−1.29940	−0.649702	+	0.760189i	$0.725106\pi$
$138$	1.56271	0.133026
$139$	−6.49824	−0.551173	−0.275587	−	0.961276i	$-0.588872\pi$
$139$	−6.49824	−0.551173	−0.275587	+	0.961276i	$0.588872\pi$
$140$	−8.26485	−0.698507
$141$	3.26522	0.274981
$142$	−40.3080	−3.38258
$143$	11.4339	0.956149
$144$	−22.8451	−1.90376
$145$	0.529087	0.0439383
$146$	−18.5413	−1.53449
$147$	−1.87131	−0.154343
$148$	18.6449	1.53261
$149$	7.59360	0.622092	0.311046	−	0.950395i	$-0.399321\pi$
$149$	7.59360	0.622092	0.311046	+	0.950395i	$0.399321\pi$
$150$	−1.25879	−0.102780
$151$	18.2197	1.48270	0.741350	−	0.671119i	$-0.234186\pi$
$151$	18.2197	1.48270	0.741350	+	0.671119i	$0.234186\pi$
$152$	20.3769	1.65278
$153$	−16.8769	−1.36442
$154$	−10.5358	−0.848995
$155$	8.66335	0.695857
$156$	11.2906	0.903968
$157$	−2.33009	−0.185961	−0.0929806	−	0.995668i	$-0.529639\pi$
$157$	−2.33009	−0.185961	−0.0929806	+	0.995668i	$0.529639\pi$
$158$	−20.7949	−1.65436
$159$	0.0664738	0.00527171
$160$	7.69728	0.608524
$161$	−2.20975	−0.174153
$162$	−17.8106	−1.39933
$163$	−3.62337	−0.283804	−0.141902	−	0.989881i	$-0.545322\pi$
$163$	−3.62337	−0.283804	−0.141902	+	0.989881i	$0.545322\pi$
$164$	38.8439	3.03320
$165$	−1.12156	−0.0873134
$166$	−23.4085	−1.81685
$167$	−8.92068	−0.690303	−0.345151	−	0.938547i	$-0.612172\pi$
$167$	−8.92068	−0.690303	−0.345151	+	0.938547i	$0.612172\pi$
$168$	−5.92241	−0.456924
$169$	11.7897	0.906897
$170$	15.7522	1.20814
$171$	8.25970	0.631635
$172$	−33.2753	−2.53722
$173$	16.9719	1.29035	0.645176	−	0.764034i	$-0.276784\pi$
$173$	16.9719	1.29035	0.645176	+	0.764034i	$0.276784\pi$
$174$	0.666008	0.0504900
$175$	1.78000	0.134555
$176$	18.9981	1.43203
$177$	2.17421	0.163424
$178$	−38.5775	−2.89150
$179$	6.46074	0.482899	0.241449	−	0.970413i	$-0.422377\pi$
$179$	6.46074	0.482899	0.241449	+	0.970413i	$0.422377\pi$
$180$	12.8220	0.955699
$181$	−4.76691	−0.354322	−0.177161	−	0.984182i	$-0.556691\pi$
$181$	−4.76691	−0.354322	−0.177161	+	0.984182i	$0.556691\pi$
$182$	−22.8424	−1.69319
$183$	−0.251487	−0.0185904
$184$	8.45746	0.623492
$185$	−4.01555	−0.295229
$186$	10.9053	0.799617
$187$	14.0349	1.02634
$188$	31.0430	2.26404
$189$	−5.00861	−0.364323
$190$	−7.70923	−0.559286
$191$	11.6719	0.844553	0.422276	−	0.906467i	$-0.361231\pi$
$191$	11.6719	0.844553	0.422276	+	0.906467i	$0.361231\pi$
$192$	1.60861	0.116091
$193$	−21.6448	−1.55803	−0.779015	−	0.627005i	$-0.784280\pi$
$193$	−21.6448	−1.55803	−0.779015	+	0.627005i	$0.784280\pi$
$194$	40.4366	2.90318
$195$	−2.43164	−0.174134
$196$	−17.7909	−1.27078
$197$	10.9071	0.777097	0.388548	−	0.921428i	$-0.372977\pi$
$197$	10.9071	0.777097	0.388548	+	0.921428i	$0.372977\pi$
$198$	16.3451	1.16160
$199$	3.83565	0.271902	0.135951	−	0.990716i	$-0.456591\pi$
$199$	3.83565	0.271902	0.135951	+	0.990716i	$0.456591\pi$
$200$	−6.81263	−0.481726
$201$	−3.00533	−0.211980
$202$	18.0586	1.27060
$203$	−0.941773	−0.0660995
$204$	13.8590	0.970326
$205$	−8.36578	−0.584292
$206$	−10.9792	−0.764959
$207$	3.42820	0.238276
$208$	41.1895	2.85598
$209$	−6.86881	−0.475125
$210$	2.24064	0.154619
$211$	−8.43601	−0.580759	−0.290380	−	0.956912i	$-0.593782\pi$
$211$	−8.43601	−0.580759	−0.290380	+	0.956912i	$0.593782\pi$
$212$	0.631977	0.0434044
$213$	7.63780	0.523333
$214$	26.5597	1.81558
$215$	7.16649	0.488751
$216$	19.1696	1.30433
$217$	−15.4207	−1.04683
$218$	−52.9584	−3.58680
$219$	3.51330	0.237407
$220$	−10.6629	−0.718891
$221$	30.4290	2.04688
$222$	−5.05473	−0.339251
$223$	0.374846	0.0251016	0.0125508	−	0.999921i	$-0.496005\pi$
$223$	0.374846	0.0251016	0.0125508	+	0.999921i	$0.496005\pi$
$224$	−13.7011	−0.915446
$225$	−2.76148	−0.184099
$226$	48.9642	3.25705
$227$	22.0734	1.46506	0.732531	−	0.680733i	$-0.238339\pi$
$227$	22.0734	1.46506	0.732531	+	0.680733i	$0.238339\pi$
$228$	−6.78271	−0.449196
$229$	−27.6640	−1.82809	−0.914044	−	0.405615i	$-0.867058\pi$
$229$	−27.6640	−1.82809	−0.914044	+	0.405615i	$0.867058\pi$
$230$	−3.19973	−0.210984
$231$	1.99637	0.131352
$232$	3.60448	0.236645
$233$	28.8675	1.89117	0.945587	−	0.325369i	$-0.105488\pi$
$233$	28.8675	1.89117	0.945587	+	0.325369i	$0.105488\pi$
$234$	35.4376	2.31663
$235$	−6.68571	−0.436128
$236$	20.6706	1.34554
$237$	3.94034	0.255953
$238$	−28.0388	−1.81749
$239$	−17.5120	−1.13275	−0.566377	−	0.824146i	$-0.691655\pi$
$239$	−17.5120	−1.13275	−0.566377	+	0.824146i	$0.691655\pi$
$240$	−4.04032	−0.260801
$241$	12.1621	0.783433	0.391716	−	0.920086i	$-0.371881\pi$
$241$	12.1621	0.783433	0.391716	+	0.920086i	$0.371881\pi$
$242$	14.7591	0.948753
$243$	11.8164	0.758019
$244$	−2.39093	−0.153063
$245$	3.83161	0.244793
$246$	−10.5307	−0.671416
$247$	−14.8922	−0.947566
$248$	59.0202	3.74779
$249$	4.43557	0.281093
$250$	2.57744	0.163011
$251$	−12.4202	−0.783956	−0.391978	−	0.919975i	$-0.628209\pi$
$251$	−12.4202	−0.783956	−0.391978	+	0.919975i	$0.628209\pi$
$252$	−22.8232	−1.43773
$253$	−2.85091	−0.179235
$254$	7.52724	0.472301
$255$	−2.98481	−0.186916
$256$	−24.3852	−1.52408
$257$	−24.8601	−1.55073	−0.775364	−	0.631515i	$-0.782434\pi$
$257$	−24.8601	−1.55073	−0.775364	+	0.631515i	$0.782434\pi$
$258$	9.02109	0.561629
$259$	7.14767	0.444135
$260$	−23.1180	−1.43372
$261$	1.46106	0.0904375
$262$	−25.1198	−1.55191
$263$	−15.6832	−0.967064	−0.483532	−	0.875327i	$-0.660646\pi$
$263$	−15.6832	−0.967064	−0.483532	+	0.875327i	$0.660646\pi$
$264$	−7.64078	−0.470258
$265$	−0.136109	−0.00836109
$266$	13.7224	0.841374
$267$	7.30988	0.447357
$268$	−28.5722	−1.74532
$269$	−15.9900	−0.974926	−0.487463	−	0.873144i	$-0.662078\pi$
$269$	−15.9900	−0.974926	−0.487463	+	0.873144i	$0.662078\pi$
$270$	−7.25248	−0.441372
$271$	18.2581	1.10910	0.554551	−	0.832149i	$-0.312890\pi$
$271$	18.2581	1.10910	0.554551	+	0.832149i	$0.312890\pi$
$272$	50.5596	3.06563
$273$	4.32831	0.261962
$274$	39.2006	2.36819
$275$	2.29646	0.138482
$276$	−2.81517	−0.169453
$277$	20.4471	1.22855	0.614274	−	0.789093i	$-0.289449\pi$
$277$	20.4471	1.22855	0.614274	+	0.789093i	$0.289449\pi$
$278$	16.7488	1.00453
$279$	23.9236	1.43227
$280$	12.1265	0.724695
$281$	8.23540	0.491283	0.245642	−	0.969361i	$-0.421001\pi$
$281$	8.23540	0.491283	0.245642	+	0.969361i	$0.421001\pi$
$282$	−8.41589	−0.501159
$283$	32.6336	1.93986	0.969932	−	0.243376i	$-0.0782548\pi$
$283$	32.6336	1.93986	0.969932	+	0.243376i	$0.0782548\pi$
$284$	72.6138	4.30884
$285$	1.46079	0.0865296
$286$	−29.4701	−1.74260
$287$	14.8911	0.878992
$288$	21.2559	1.25251
$289$	20.3512	1.19713
$290$	−1.36369	−0.0800785
$291$	−7.66215	−0.449163
$292$	33.4016	1.95468
$293$	−21.4308	−1.25200	−0.626001	−	0.779822i	$-0.715309\pi$
$293$	−21.4308	−1.25200	−0.626001	+	0.779822i	$0.715309\pi$
$294$	4.82319	0.281294
$295$	−4.45182	−0.259195
$296$	−27.3565	−1.59006
$297$	−6.46185	−0.374954
$298$	−19.5720	−1.13378
$299$	−6.18102	−0.357458
$300$	2.26767	0.130924
$301$	−12.7563	−0.735262
$302$	−46.9602	−2.70225
$303$	−3.42184	−0.196580
$304$	−24.7442	−1.41918
$305$	0.514933	0.0294850
$306$	43.4993	2.48669
$307$	10.9930	0.627404	0.313702	−	0.949522i	$-0.398431\pi$
$307$	10.9930	0.627404	0.313702	+	0.949522i	$0.398431\pi$
$308$	18.9799	1.08148
$309$	2.08041	0.118350
$310$	−22.3292	−1.26822
$311$	30.9309	1.75393	0.876965	−	0.480553i	$-0.159564\pi$
$311$	30.9309	1.75393	0.876965	+	0.480553i	$0.159564\pi$
$312$	−16.5659	−0.937859
$313$	−30.8267	−1.74243	−0.871215	−	0.490902i	$-0.836667\pi$
$313$	−30.8267	−1.74243	−0.871215	+	0.490902i	$0.836667\pi$
$314$	6.00566	0.338919
$315$	4.91542	0.276953
$316$	37.4615	2.10737
$317$	−14.5540	−0.817433	−0.408716	−	0.912661i	$-0.634024\pi$
$317$	−14.5540	−0.817433	−0.408716	+	0.912661i	$0.634024\pi$
$318$	−0.171332	−0.00960782
$319$	−1.21503	−0.0680284
$320$	−3.29372	−0.184124
$321$	−5.03268	−0.280897
$322$	5.69550	0.317398
$323$	−18.2800	−1.01712
$324$	32.0853	1.78252
$325$	4.97892	0.276181
$326$	9.33901	0.517240
$327$	10.0349	0.554929
$328$	−56.9930	−3.14691
$329$	11.9005	0.656098
$330$	2.89075	0.159131
$331$	8.66560	0.476304	0.238152	−	0.971228i	$-0.423458\pi$
$331$	8.66560	0.476304	0.238152	+	0.971228i	$0.423458\pi$
$332$	42.1697	2.31437
$333$	−11.0889	−0.607666
$334$	22.9925	1.25809
$335$	6.15358	0.336206
$336$	7.19175	0.392342
$337$	17.9455	0.977556	0.488778	−	0.872408i	$-0.337443\pi$
$337$	17.9455	0.977556	0.488778	+	0.872408i	$0.337443\pi$
$338$	−30.3871	−1.65284
$339$	−9.27801	−0.503912
$340$	−28.3771	−1.53896
$341$	−19.8950	−1.07738
$342$	−21.2889	−1.15117
$343$	−19.2802	−1.04103
$344$	48.8227	2.63234
$345$	0.606302	0.0326422
$346$	−43.7441	−2.35170
$347$	12.8853	0.691719	0.345859	−	0.938286i	$-0.387587\pi$
$347$	12.8853	0.691719	0.345859	+	0.938286i	$0.387587\pi$
$348$	−1.19980	−0.0643158
$349$	−15.4394	−0.826452	−0.413226	−	0.910629i	$-0.635598\pi$
$349$	−15.4394	−0.826452	−0.413226	+	0.910629i	$0.635598\pi$
$350$	−4.58783	−0.245230
$351$	−14.0099	−0.747791
$352$	−17.6765	−0.942160
$353$	17.1417	0.912360	0.456180	−	0.889888i	$-0.349217\pi$
$353$	17.1417	0.912360	0.456180	+	0.889888i	$0.349217\pi$
$354$	−5.60390	−0.297844
$355$	−15.6388	−0.830022
$356$	69.4962	3.68329
$357$	5.31295	0.281191
$358$	−16.6522	−0.880094
$359$	13.6705	0.721501	0.360750	−	0.932662i	$-0.382521\pi$
$359$	13.6705	0.721501	0.360750	+	0.932662i	$0.382521\pi$
$360$	−18.8129	−0.991529
$361$	−10.0537	−0.529140
$362$	12.2864	0.645760
$363$	−2.79664	−0.146786
$364$	41.1500	2.15685
$365$	−7.19368	−0.376535
$366$	0.648191	0.0338815
$367$	27.5469	1.43794	0.718969	−	0.695042i	$-0.244614\pi$
$367$	27.5469	1.43794	0.718969	+	0.695042i	$0.244614\pi$
$368$	−10.2701	−0.535367
$369$	−23.1019	−1.20264
$370$	10.3498	0.538062
$371$	0.242273	0.0125782
$372$	−19.6456	−1.01858
$373$	27.3172	1.41443	0.707216	−	0.706998i	$-0.249951\pi$
$373$	27.3172	1.41443	0.707216	+	0.706998i	$0.249951\pi$
$374$	−36.1742	−1.87052
$375$	−0.488387	−0.0252202
$376$	−45.5473	−2.34892
$377$	−2.63428	−0.135672
$378$	12.9094	0.663987
$379$	−28.1855	−1.44779	−0.723896	−	0.689909i	$-0.757650\pi$
$379$	−28.1855	−1.44779	−0.723896	+	0.689909i	$0.757650\pi$
$380$	13.8880	0.712437
$381$	−1.42630	−0.0730718
$382$	−30.0837	−1.53922
$383$	−26.5446	−1.35637	−0.678183	−	0.734893i	$-0.737233\pi$
$383$	−26.5446	−1.35637	−0.678183	+	0.734893i	$0.737233\pi$
$384$	3.37242	0.172098
$385$	−4.08769	−0.208328
$386$	55.7882	2.83955
$387$	19.7901	1.00599
$388$	−72.8453	−3.69816
$389$	−21.3044	−1.08018	−0.540088	−	0.841609i	$-0.681609\pi$
$389$	−21.3044	−1.08018	−0.540088	+	0.841609i	$0.681609\pi$
$390$	6.26741	0.317362
$391$	−7.58712	−0.383697
$392$	26.1034	1.31842
$393$	4.75985	0.240102
$394$	−28.1123	−1.41628
$395$	−8.06807	−0.405949
$396$	−29.4453	−1.47968
$397$	26.7372	1.34190	0.670951	−	0.741502i	$-0.265886\pi$
$397$	26.7372	1.34190	0.670951	+	0.741502i	$0.265886\pi$
$398$	−9.88614	−0.495548
$399$	−2.60020	−0.130173
$400$	8.27277	0.413639
$401$	−13.9929	−0.698770	−0.349385	−	0.936979i	$-0.613609\pi$
$401$	−13.9929	−0.698770	−0.349385	+	0.936979i	$0.613609\pi$
$402$	7.74605	0.386338
$403$	−43.1341	−2.14866
$404$	−32.5321	−1.61853
$405$	−6.91019	−0.343370
$406$	2.42736	0.120468
$407$	9.22155	0.457095
$408$	−20.3344	−1.00670
$409$	−21.1215	−1.04439	−0.522196	−	0.852825i	$-0.674887\pi$
$409$	−21.1215	−1.04439	−0.522196	+	0.852825i	$0.674887\pi$
$410$	21.5623	1.06489
$411$	−7.42795	−0.366394
$412$	19.7788	0.974430
$413$	7.92423	0.389926
$414$	−8.83597	−0.434264
$415$	−9.08208	−0.445822
$416$	−38.3242	−1.87900
$417$	−3.17366	−0.155415
$418$	17.7039	0.865927
$419$	25.1045	1.22644	0.613219	−	0.789913i	$-0.289875\pi$
$419$	25.1045	1.22644	0.613219	+	0.789913i	$0.289875\pi$
$420$	−4.03645	−0.196958
$421$	32.4776	1.58286	0.791430	−	0.611260i	$-0.209337\pi$
$421$	32.4776	1.58286	0.791430	+	0.611260i	$0.209337\pi$
$422$	21.7433	1.05845
$423$	−18.4624	−0.897675
$424$	−0.927259	−0.0450317
$425$	6.11156	0.296454
$426$	−19.6859	−0.953787
$427$	−0.916578	−0.0443563
$428$	−47.8465	−2.31275
$429$	5.58416	0.269606
$430$	−18.4712	−0.890759
$431$	−5.96735	−0.287437	−0.143719	−	0.989619i	$-0.545906\pi$
$431$	−5.96735	−0.287437	−0.143719	+	0.989619i	$0.545906\pi$
$432$	−23.2782	−1.11997
$433$	−40.4040	−1.94169	−0.970846	−	0.239703i	$-0.922950\pi$
$433$	−40.4040	−1.94169	−0.970846	+	0.239703i	$0.922950\pi$
$434$	39.7460	1.90787
$435$	0.258399	0.0123893
$436$	95.4032	4.56898
$437$	3.71319	0.177626
$438$	−9.05532	−0.432680
$439$	−16.2213	−0.774201	−0.387101	−	0.922037i	$-0.626523\pi$
$439$	−16.2213	−0.774201	−0.387101	+	0.922037i	$0.626523\pi$
$440$	15.6449	0.745843
$441$	10.5809	0.503853
$442$	−78.4288	−3.73048
$443$	−17.5884	−0.835650	−0.417825	−	0.908528i	$-0.637207\pi$
$443$	−17.5884	−0.835650	−0.417825	+	0.908528i	$0.637207\pi$
$444$	9.10596	0.432150
$445$	−14.9674	−0.709521
$446$	−0.966143	−0.0457482
$447$	3.70862	0.175412
$448$	5.86280	0.276991
$449$	−21.2021	−1.00059	−0.500294	−	0.865856i	$-0.666775\pi$
$449$	−21.2021	−1.00059	−0.500294	+	0.865856i	$0.666775\pi$
$450$	7.11754	0.335524
$451$	19.2117	0.904642
$452$	−88.2076	−4.14894
$453$	8.89828	0.418078
$454$	−56.8928	−2.67011
$455$	−8.86246	−0.415479
$456$	9.95182	0.466037
$457$	18.8795	0.883144	0.441572	−	0.897226i	$-0.354421\pi$
$457$	18.8795	0.883144	0.441572	+	0.897226i	$0.354421\pi$
$458$	71.3022	3.33173
$459$	−17.1969	−0.802684
$460$	5.76422	0.268758
$461$	−7.07267	−0.329407	−0.164703	−	0.986343i	$-0.552667\pi$
$461$	−7.07267	−0.329407	−0.164703	+	0.986343i	$0.552667\pi$
$462$	−5.14553	−0.239392
$463$	−4.34025	−0.201708	−0.100854	−	0.994901i	$-0.532158\pi$
$463$	−4.34025	−0.201708	−0.100854	+	0.994901i	$0.532158\pi$
$464$	−4.37702	−0.203198
$465$	4.23107	0.196211
$466$	−74.4042	−3.44671
$467$	13.7317	0.635426	0.317713	−	0.948187i	$-0.397085\pi$
$467$	13.7317	0.635426	0.317713	+	0.948187i	$0.397085\pi$
$468$	−63.8399	−2.95100
$469$	−10.9533	−0.505779
$470$	17.2320	0.794853
$471$	−1.13799	−0.0524356
$472$	−30.3286	−1.39599
$473$	−16.4575	−0.756719
$474$	−10.1560	−0.466480
$475$	−2.99104	−0.137239
$476$	50.5111	2.31517
$477$	−0.375861	−0.0172095
$478$	45.1360	2.06447
$479$	4.15871	0.190016	0.0950082	−	0.995476i	$-0.469712\pi$
$479$	4.15871	0.190016	0.0950082	+	0.995476i	$0.469712\pi$
$480$	3.75926	0.171586
$481$	19.9931	0.911608
$482$	−31.3472	−1.42782
$483$	−1.07922	−0.0491060
$484$	−26.5882	−1.20855
$485$	15.6887	0.712386
$486$	−30.4559	−1.38151
$487$	−21.2925	−0.964857	−0.482429	−	0.875935i	$-0.660245\pi$
$487$	−21.2925	−0.964857	−0.482429	+	0.875935i	$0.660245\pi$
$488$	3.50805	0.158802
$489$	−1.76961	−0.0800245
$490$	−9.87574	−0.446141
$491$	−15.3882	−0.694458	−0.347229	−	0.937780i	$-0.612877\pi$
$491$	−15.3882	−0.694458	−0.347229	+	0.937780i	$0.612877\pi$
$492$	18.9709	0.855272
$493$	−3.23355	−0.145632
$494$	38.3836	1.72696
$495$	6.34162	0.285034
$496$	−71.6699	−3.21807
$497$	27.8370	1.24866
$498$	−11.4324	−0.512299
$499$	27.0996	1.21315	0.606573	−	0.795028i	$-0.292544\pi$
$499$	27.0996	1.21315	0.606573	+	0.795028i	$0.292544\pi$
$500$	−4.64318	−0.207649
$501$	−4.35675	−0.194645
$502$	32.0123	1.42878
$503$	38.2802	1.70683	0.853415	−	0.521233i	$-0.174528\pi$
$503$	38.2802	1.70683	0.853415	+	0.521233i	$0.174528\pi$
$504$	33.4870	1.49163
$505$	7.00641	0.311781
$506$	7.34804	0.326660
$507$	5.75792	0.255718
$508$	−13.5601	−0.601633
$509$	−11.5135	−0.510328	−0.255164	−	0.966898i	$-0.582129\pi$
$509$	−11.5135	−0.510328	−0.255164	+	0.966898i	$0.582129\pi$
$510$	7.69316	0.340659
$511$	12.8047	0.566448
$512$	49.0409	2.16732
$513$	8.41630	0.371589
$514$	64.0752	2.82624
$515$	−4.25975	−0.187707
$516$	−16.2512	−0.715421
$517$	15.3535	0.675244
$518$	−18.4227	−0.809446
$519$	8.28888	0.363841
$520$	33.9196	1.48747
$521$	22.6458	0.992131	0.496066	−	0.868285i	$-0.334778\pi$
$521$	22.6458	0.992131	0.496066	+	0.868285i	$0.334778\pi$
$522$	−3.76580	−0.164824
$523$	6.05672	0.264842	0.132421	−	0.991194i	$-0.457725\pi$
$523$	6.05672	0.264842	0.132421	+	0.991194i	$0.457725\pi$
$524$	45.2527	1.97687
$525$	0.869328	0.0379406
$526$	40.4223	1.76250
$527$	−52.9466	−2.30639
$528$	9.27842	0.403791
$529$	−21.4588	−0.932993
$530$	0.350812	0.0152383
$531$	−12.2936	−0.533497
$532$	−24.7205	−1.07177
$533$	41.6526	1.80417
$534$	−18.8407	−0.815319
$535$	10.3047	0.445510
$536$	41.9221	1.81076
$537$	3.15535	0.136163
$538$	41.2131	1.77682
$539$	−8.79914	−0.379006
$540$	13.0651	0.562234
$541$	13.7917	0.592952	0.296476	−	0.955040i	$-0.404189\pi$
$541$	13.7917	0.592952	0.296476	+	0.955040i	$0.404189\pi$
$542$	−47.0592	−2.02137
$543$	−2.32810	−0.0999083
$544$	−47.0424	−2.01693
$545$	−20.5469	−0.880134
$546$	−11.1560	−0.477431
$547$	42.8022	1.83009	0.915046	−	0.403351i	$-0.132154\pi$
$547$	42.8022	1.83009	0.915046	+	0.403351i	$0.132154\pi$
$548$	−70.6187	−3.01668
$549$	1.42197	0.0606884
$550$	−5.91897	−0.252386
$551$	1.58252	0.0674177
$552$	4.13052	0.175806
$553$	14.3611	0.610697
$554$	−52.7012	−2.23906
$555$	−1.96115	−0.0832460
$556$	−30.1725	−1.27960
$557$	−3.81167	−0.161506	−0.0807528	−	0.996734i	$-0.525732\pi$
$557$	−3.81167	−0.161506	−0.0807528	+	0.996734i	$0.525732\pi$
$558$	−61.6617	−2.61035
$559$	−35.6814	−1.50916
$560$	−14.7255	−0.622266
$561$	6.85449	0.289397
$562$	−21.2262	−0.895375
$563$	31.2079	1.31526	0.657628	−	0.753343i	$-0.271560\pi$
$563$	31.2079	1.31526	0.657628	+	0.753343i	$0.271560\pi$
$564$	15.1610	0.638393
$565$	18.9972	0.799220
$566$	−84.1110	−3.53545
$567$	12.3001	0.516556
$568$	−106.541	−4.47038
$569$	22.4944	0.943013	0.471507	−	0.881862i	$-0.343710\pi$
$569$	22.4944	0.943013	0.471507	+	0.881862i	$0.343710\pi$
$570$	−3.76509	−0.157702
$571$	26.9917	1.12957	0.564783	−	0.825240i	$-0.308960\pi$
$571$	26.9917	1.12957	0.564783	+	0.825240i	$0.308960\pi$
$572$	53.0896	2.21979
$573$	5.70043	0.238139
$574$	−38.3808	−1.60198
$575$	−1.24144	−0.0517715
$576$	−9.09553	−0.378980
$577$	4.85344	0.202051	0.101026	−	0.994884i	$-0.467788\pi$
$577$	4.85344	0.202051	0.101026	+	0.994884i	$0.467788\pi$
$578$	−52.4540	−2.18180
$579$	−10.5711	−0.439319
$580$	2.45665	0.102007
$581$	16.1661	0.670681
$582$	19.7487	0.818610
$583$	0.312568	0.0129452
$584$	−49.0079	−2.02796
$585$	13.7492	0.568459
$586$	55.2366	2.28180
$587$	−6.04904	−0.249671	−0.124835	−	0.992177i	$-0.539840\pi$
$587$	−6.04904	−0.249671	−0.124835	+	0.992177i	$0.539840\pi$
$588$	−8.68884	−0.358322
$589$	25.9125	1.06770
$590$	11.4743	0.472389
$591$	5.32688	0.219118
$592$	33.2198	1.36532
$593$	−18.2171	−0.748087	−0.374044	−	0.927411i	$-0.622029\pi$
$593$	−18.2171	−0.748087	−0.374044	+	0.927411i	$0.622029\pi$
$594$	16.6550	0.683363
$595$	−10.8786	−0.445978
$596$	35.2584	1.44424
$597$	1.87328	0.0766683
$598$	15.9312	0.651475
$599$	21.9935	0.898630	0.449315	−	0.893373i	$-0.351668\pi$
$599$	21.9935	0.898630	0.449315	+	0.893373i	$0.351668\pi$
$600$	−3.32720	−0.135833
$601$	48.2538	1.96831	0.984157	−	0.177298i	$-0.0567358\pi$
$601$	48.2538	1.96831	0.984157	+	0.177298i	$0.0567358\pi$
$602$	32.8786	1.34003
$603$	16.9930	0.692007
$604$	84.5975	3.44222
$605$	5.72628	0.232807
$606$	8.81959	0.358271
$607$	−6.65251	−0.270017	−0.135009	−	0.990844i	$-0.543106\pi$
$607$	−6.65251	−0.270017	−0.135009	+	0.990844i	$0.543106\pi$
$608$	23.0229	0.933703
$609$	−0.459950	−0.0186381
$610$	−1.32721	−0.0537370
$611$	33.2876	1.34667
$612$	−78.3627	−3.16763
$613$	−4.33031	−0.174900	−0.0874498	−	0.996169i	$-0.527872\pi$
$613$	−4.33031	−0.174900	−0.0874498	+	0.996169i	$0.527872\pi$
$614$	−28.3338	−1.14346
$615$	−4.08574	−0.164753
$616$	−27.8479	−1.12202
$617$	1.43094	0.0576075	0.0288038	−	0.999585i	$-0.490830\pi$
$617$	1.43094	0.0576075	0.0288038	+	0.999585i	$0.490830\pi$
$618$	−5.36212	−0.215696
$619$	−12.2409	−0.492004	−0.246002	−	0.969269i	$-0.579117\pi$
$619$	−12.2409	−0.492004	−0.246002	+	0.969269i	$0.579117\pi$
$620$	40.2255	1.61550
$621$	3.49320	0.140177
$622$	−79.7225	−3.19658
$623$	26.6419	1.06738
$624$	20.1164	0.805302
$625$	1.00000	0.0400000
$626$	79.4539	3.17562
$627$	−3.35464	−0.133971
$628$	−10.8190	−0.431726
$629$	24.5413	0.978526
$630$	−12.6692	−0.504752
$631$	18.4145	0.733071	0.366535	−	0.930404i	$-0.380544\pi$
$631$	18.4145	0.733071	0.366535	+	0.930404i	$0.380544\pi$
$632$	−54.9648	−2.18638
$633$	−4.12004	−0.163757
$634$	37.5120	1.48979
$635$	2.92044	0.115894
$636$	0.308650	0.0122388
$637$	−19.0773	−0.755870
$638$	3.13165	0.123983
$639$	−43.1862	−1.70842
$640$	−6.90522	−0.272953
$641$	−5.75593	−0.227346	−0.113673	−	0.993518i	$-0.536262\pi$
$641$	−5.75593	−0.227346	−0.113673	+	0.993518i	$0.536262\pi$
$642$	12.9714	0.511941
$643$	17.9931	0.709580	0.354790	−	0.934946i	$-0.384552\pi$
$643$	17.9931	0.709580	0.354790	+	0.934946i	$0.384552\pi$
$644$	−10.2603	−0.404312
$645$	3.50002	0.137813
$646$	47.1155	1.85373
$647$	−48.6669	−1.91329	−0.956646	−	0.291252i	$-0.905928\pi$
$647$	−48.6669	−1.91329	−0.956646	+	0.291252i	$0.905928\pi$
$648$	−47.0766	−1.84934
$649$	10.2234	0.401304
$650$	−12.8329	−0.503346
$651$	−7.53129	−0.295174
$652$	−16.8240	−0.658878
$653$	−11.8870	−0.465174	−0.232587	−	0.972576i	$-0.574719\pi$
$653$	−11.8870	−0.465174	−0.232587	+	0.972576i	$0.574719\pi$
$654$	−25.8642	−1.01137
$655$	−9.74604	−0.380809
$656$	69.2082	2.70213
$657$	−19.8652	−0.775015
$658$	−30.6729	−1.19575
$659$	−31.8515	−1.24076	−0.620379	−	0.784303i	$-0.713021\pi$
$659$	−31.8515	−1.24076	−0.620379	+	0.784303i	$0.713021\pi$
$660$	−5.20761	−0.202706
$661$	20.2201	0.786470	0.393235	−	0.919438i	$-0.371356\pi$
$661$	20.2201	0.786470	0.393235	+	0.919438i	$0.371356\pi$
$662$	−22.3350	−0.868075
$663$	14.8611	0.577159
$664$	−61.8729	−2.40113
$665$	5.32405	0.206458
$666$	28.5808	1.10749
$667$	0.656828	0.0254325
$668$	−41.4203	−1.60260
$669$	0.183070	0.00707790
$670$	−15.8605	−0.612743
$671$	−1.18252	−0.0456507
$672$	−6.69146	−0.258129
$673$	29.3143	1.12998	0.564992	−	0.825096i	$-0.308879\pi$
$673$	29.3143	1.12998	0.564992	+	0.825096i	$0.308879\pi$
$674$	−46.2535	−1.78162
$675$	−2.81383	−0.108304
$676$	54.7415	2.10544
$677$	−36.5624	−1.40521	−0.702604	−	0.711581i	$-0.747980\pi$
$677$	−36.5624	−1.40521	−0.702604	+	0.711581i	$0.747980\pi$
$678$	23.9135	0.918392
$679$	−27.9258	−1.07169
$680$	41.6359	1.59666
$681$	10.7804	0.413105
$682$	51.2781	1.96354
$683$	−7.24206	−0.277110	−0.138555	−	0.990355i	$-0.544246\pi$
$683$	−7.24206	−0.277110	−0.138555	+	0.990355i	$0.544246\pi$
$684$	38.3513	1.46640
$685$	15.2091	0.581111
$686$	49.6936	1.89731
$687$	−13.5107	−0.515467
$688$	−59.2868	−2.26029
$689$	0.677674	0.0258173
$690$	−1.56271	−0.0594912
$691$	9.92260	0.377474	0.188737	−	0.982028i	$-0.439561\pi$
$691$	9.92260	0.377474	0.188737	+	0.982028i	$0.439561\pi$
$692$	78.8037	2.99567
$693$	−11.2881	−0.428798
$694$	−33.2110	−1.26067
$695$	6.49824	0.246492
$696$	1.76038	0.0667271
$697$	51.1280	1.93661
$698$	39.7941	1.50623
$699$	14.0985	0.533256
$700$	8.26485	0.312382
$701$	45.9379	1.73505	0.867526	−	0.497392i	$-0.165709\pi$
$701$	45.9379	1.73505	0.867526	+	0.497392i	$0.165709\pi$
$702$	36.1095	1.36287
$703$	−12.0107	−0.452992
$704$	7.56388	0.285075
$705$	−3.26522	−0.122975
$706$	−44.1816	−1.66280
$707$	−12.4714	−0.469035
$708$	10.0953	0.379404
$709$	17.7879	0.668038	0.334019	−	0.942566i	$-0.391595\pi$
$709$	17.7879	0.668038	0.334019	+	0.942566i	$0.391595\pi$
$710$	40.3080	1.51273
$711$	−22.2798	−0.835558
$712$	−101.967	−3.82138
$713$	10.7550	0.402778
$714$	−13.6938	−0.512478
$715$	−11.4339	−0.427603
$716$	29.9984	1.12109
$717$	−8.55262	−0.319403
$718$	−35.2348	−1.31495
$719$	41.5726	1.55040	0.775199	−	0.631717i	$-0.217650\pi$
$719$	41.5726	1.55040	0.775199	+	0.631717i	$0.217650\pi$
$720$	22.8451	0.851386
$721$	7.58233	0.282381
$722$	25.9127	0.964369
$723$	5.93984	0.220905
$724$	−22.1336	−0.822590
$725$	−0.529087	−0.0196498
$726$	7.20818	0.267520
$727$	22.2309	0.824498	0.412249	−	0.911071i	$-0.364743\pi$
$727$	22.2309	0.824498	0.412249	+	0.911071i	$0.364743\pi$
$728$	−60.3767	−2.23771
$729$	−14.9596	−0.554060
$730$	18.5413	0.686243
$731$	−43.7985	−1.61994
$732$	−1.16770	−0.0431594
$733$	−31.5325	−1.16468	−0.582340	−	0.812945i	$-0.697863\pi$
$733$	−31.5325	−1.16468	−0.582340	+	0.812945i	$0.697863\pi$
$734$	−71.0005	−2.62067
$735$	1.87131	0.0690244
$736$	9.55569	0.352228
$737$	−14.1314	−0.520538
$738$	59.5438	2.19184
$739$	4.11209	0.151266	0.0756329	−	0.997136i	$-0.475902\pi$
$739$	4.11209	0.151266	0.0756329	+	0.997136i	$0.475902\pi$
$740$	−18.6449	−0.685402
$741$	−7.27315	−0.267186
$742$	−0.624443	−0.0229240
$743$	−9.60140	−0.352241	−0.176121	−	0.984369i	$-0.556355\pi$
$743$	−9.60140	−0.352241	−0.176121	+	0.984369i	$0.556355\pi$
$744$	28.8247	1.05677
$745$	−7.59360	−0.278208
$746$	−70.4084	−2.57783
$747$	−25.0800	−0.917628
$748$	65.1668	2.38273
$749$	−18.3423	−0.670213
$750$	1.25879	0.0459644
$751$	11.7751	0.429680	0.214840	−	0.976649i	$-0.431077\pi$
$751$	11.7751	0.429680	0.214840	+	0.976649i	$0.431077\pi$
$752$	55.3094	2.01693
$753$	−6.06587	−0.221053
$754$	6.78970	0.247266
$755$	−18.2197	−0.663083
$756$	−23.2559	−0.845809
$757$	34.7349	1.26246	0.631230	−	0.775596i	$-0.282550\pi$
$757$	34.7349	1.26246	0.631230	+	0.775596i	$0.282550\pi$
$758$	72.6464	2.63863
$759$	−1.39235	−0.0505390
$760$	−20.3769	−0.739148
$761$	35.9777	1.30419	0.652095	−	0.758137i	$-0.273890\pi$
$761$	35.9777	1.30419	0.652095	+	0.758137i	$0.273890\pi$
$762$	3.67621	0.133175
$763$	36.5735	1.32405
$764$	54.1950	1.96071
$765$	16.8769	0.610187
$766$	68.4171	2.47201
$767$	22.1653	0.800342
$768$	−11.9094	−0.429744
$769$	23.0230	0.830232	0.415116	−	0.909769i	$-0.363741\pi$
$769$	23.0230	0.830232	0.415116	+	0.909769i	$0.363741\pi$
$770$	10.5358	0.379682
$771$	−12.1413	−0.437260
$772$	−100.501	−3.61711
$773$	−52.8908	−1.90235	−0.951176	−	0.308650i	$-0.900123\pi$
$773$	−52.8908	−1.90235	−0.951176	+	0.308650i	$0.900123\pi$
$774$	−51.0078	−1.83344
$775$	−8.66335	−0.311197
$776$	106.881	3.83681
$777$	3.49083	0.125233
$778$	54.9107	1.96864
$779$	−25.0224	−0.896522
$780$	−11.2906	−0.404267
$781$	35.9139	1.28510
$782$	19.5553	0.699297
$783$	1.48876	0.0532040
$784$	−31.6981	−1.13207
$785$	2.33009	0.0831644
$786$	−12.2682	−0.437592
$787$	−17.1236	−0.610390	−0.305195	−	0.952290i	$-0.598722\pi$
$787$	−17.1236	−0.610390	−0.305195	+	0.952290i	$0.598722\pi$
$788$	50.6435	1.80410
$789$	−7.65945	−0.272684
$790$	20.7949	0.739851
$791$	−33.8150	−1.20232
$792$	43.2031	1.53516
$793$	−2.56381	−0.0910435
$794$	−68.9135	−2.44565
$795$	−0.0664738	−0.00235758
$796$	17.8096	0.631245
$797$	−5.36610	−0.190077	−0.0950386	−	0.995474i	$-0.530297\pi$
$797$	−5.36610	−0.190077	−0.0950386	+	0.995474i	$0.530297\pi$
$798$	6.70185	0.237243
$799$	40.8602	1.44553
$800$	−7.69728	−0.272140
$801$	−41.3321	−1.46040
$802$	36.0657	1.27352
$803$	16.5200	0.582978
$804$	−13.9543	−0.492130
$805$	2.20975	0.0778836
$806$	111.176	3.91599
$807$	−7.80930	−0.274900
$808$	47.7321	1.67921
$809$	7.18652	0.252665	0.126332	−	0.991988i	$-0.459679\pi$
$809$	7.18652	0.252665	0.126332	+	0.991988i	$0.459679\pi$
$810$	17.8106	0.625800
$811$	−9.27263	−0.325606	−0.162803	−	0.986659i	$-0.552054\pi$
$811$	−9.27263	−0.325606	−0.162803	+	0.986659i	$0.552054\pi$
$812$	−4.37282	−0.153456
$813$	8.91704	0.312734
$814$	−23.7680	−0.833067
$815$	3.62337	0.126921
$816$	24.6927	0.864416
$817$	21.4353	0.749926
$818$	54.4394	1.90343
$819$	−24.4735	−0.855173
$820$	−38.8439	−1.35649
$821$	−0.324145	−0.0113128	−0.00565638	−	0.999984i	$-0.501800\pi$
$821$	−0.324145	−0.0113128	−0.00565638	+	0.999984i	$0.501800\pi$
$822$	19.1451	0.667761
$823$	35.3439	1.23201	0.616006	−	0.787742i	$-0.288750\pi$
$823$	35.3439	1.23201	0.616006	+	0.787742i	$0.288750\pi$
$824$	−29.0201	−1.01096
$825$	1.12156	0.0390477
$826$	−20.4242	−0.710649
$827$	34.9085	1.21389	0.606944	−	0.794745i	$-0.292395\pi$
$827$	34.9085	1.21389	0.606944	+	0.794745i	$0.292395\pi$
$828$	15.9178	0.553180
$829$	−0.378469	−0.0131448	−0.00657238	−	0.999978i	$-0.502092\pi$
$829$	−0.378469	−0.0131448	−0.00657238	+	0.999978i	$0.502092\pi$
$830$	23.4085	0.812520
$831$	9.98612	0.346415
$832$	16.3992	0.568539
$833$	−23.4172	−0.811356
$834$	8.17990	0.283247
$835$	8.92068	0.308713
$836$	−31.8931	−1.10305
$837$	24.3772	0.842600
$838$	−64.7054	−2.23521
$839$	−30.5214	−1.05372	−0.526858	−	0.849953i	$-0.676630\pi$
$839$	−30.5214	−1.05372	−0.526858	+	0.849953i	$0.676630\pi$
$840$	5.92241	0.204343
$841$	−28.7201	−0.990347
$842$	−83.7089	−2.88480
$843$	4.02207	0.138527
$844$	−39.1699	−1.34829
$845$	−11.7897	−0.405577
$846$	47.5858	1.63603
$847$	−10.1928	−0.350227
$848$	1.12600	0.0386669
$849$	15.9378	0.546985
$850$	−15.7522	−0.540295
$851$	−4.98506	−0.170886
$852$	35.4637	1.21497
$853$	−23.1313	−0.792001	−0.396001	−	0.918250i	$-0.629602\pi$
$853$	−23.1313	−0.792001	−0.396001	+	0.918250i	$0.629602\pi$
$854$	2.36242	0.0808404
$855$	−8.25970	−0.282476
$856$	70.2020	2.39946
$857$	−4.48896	−0.153340	−0.0766700	−	0.997057i	$-0.524429\pi$
$857$	−4.48896	−0.153340	−0.0766700	+	0.997057i	$0.524429\pi$
$858$	−14.3928	−0.491363
$859$	−34.6287	−1.18152	−0.590759	−	0.806848i	$-0.701171\pi$
$859$	−34.6287	−1.18152	−0.590759	+	0.806848i	$0.701171\pi$
$860$	33.2753	1.13468
$861$	7.27261	0.247850
$862$	15.3805	0.523861
$863$	33.9567	1.15590	0.577949	−	0.816073i	$-0.303853\pi$
$863$	33.9567	1.15590	0.577949	+	0.816073i	$0.303853\pi$
$864$	21.6589	0.736850
$865$	−16.9719	−0.577063
$866$	104.139	3.53878
$867$	9.93928	0.337556
$868$	−71.6012	−2.43030
$869$	18.5280	0.628519
$870$	−0.666008	−0.0225798
$871$	−30.6382	−1.03814
$872$	−139.979	−4.74028
$873$	43.3239	1.46629
$874$	−9.57052	−0.323728
$875$	−1.78000	−0.0601749
$876$	16.3129	0.551162
$877$	30.7761	1.03924	0.519618	−	0.854399i	$-0.326074\pi$
$877$	30.7761	1.03924	0.519618	+	0.854399i	$0.326074\pi$
$878$	41.8094	1.41100
$879$	−10.4665	−0.353028
$880$	−18.9981	−0.640425
$881$	21.7307	0.732125	0.366063	−	0.930590i	$-0.380706\pi$
$881$	21.7307	0.732125	0.366063	+	0.930590i	$0.380706\pi$
$882$	−27.2716	−0.918284
$883$	30.9595	1.04187	0.520935	−	0.853596i	$-0.325583\pi$
$883$	30.9595	1.04187	0.520935	+	0.853596i	$0.325583\pi$
$884$	141.287	4.75201
$885$	−2.17421	−0.0730854
$886$	45.3330	1.52299
$887$	50.3052	1.68908	0.844541	−	0.535490i	$-0.179873\pi$
$887$	50.3052	1.68908	0.844541	+	0.535490i	$0.179873\pi$
$888$	−13.3606	−0.448351
$889$	−5.19837	−0.174348
$890$	38.5775	1.29312
$891$	15.8690	0.531630
$892$	1.74048	0.0582756
$893$	−19.9973	−0.669183
$894$	−9.55873	−0.319692
$895$	−6.46074	−0.215959
$896$	12.2913	0.410622
$897$	−3.01873	−0.100793
$898$	54.6470	1.82359
$899$	4.58367	0.152874
$900$	−12.8220	−0.427401
$901$	0.831837	0.0277125
$902$	−49.5169	−1.64873
$903$	−6.23003	−0.207322
$904$	129.421	4.30449
$905$	4.76691	0.158457
$906$	−22.9348	−0.761956
$907$	35.8178	1.18931	0.594655	−	0.803981i	$-0.297289\pi$
$907$	35.8178	1.18931	0.594655	+	0.803981i	$0.297289\pi$
$908$	102.491	3.40128
$909$	19.3481	0.641735
$910$	22.8424	0.757219
$911$	43.8061	1.45136	0.725681	−	0.688031i	$-0.241525\pi$
$911$	43.8061	1.45136	0.725681	+	0.688031i	$0.241525\pi$
$912$	−12.0848	−0.400167
$913$	20.8566	0.690253
$914$	−48.6606	−1.60955
$915$	0.251487	0.00831389
$916$	−128.449	−4.24407
$917$	17.3479	0.572879
$918$	44.3240	1.46291
$919$	−44.8765	−1.48034	−0.740170	−	0.672420i	$-0.765255\pi$
$919$	−44.8765	−1.48034	−0.740170	+	0.672420i	$0.765255\pi$
$920$	−8.45746	−0.278834
$921$	5.36884	0.176909
$922$	18.2294	0.600352
$923$	77.8644	2.56294
$924$	9.26953	0.304945
$925$	4.01555	0.132031
$926$	11.1867	0.367618
$927$	−11.7632	−0.386354
$928$	4.07253	0.133687
$929$	29.8407	0.979042	0.489521	−	0.871992i	$-0.337172\pi$
$929$	29.8407	0.979042	0.489521	+	0.871992i	$0.337172\pi$
$930$	−10.9053	−0.357599
$931$	11.4605	0.375604
$932$	134.037	4.39053
$933$	15.1063	0.494557
$934$	−35.3925	−1.15808
$935$	−14.0349	−0.458992
$936$	93.6681	3.06164
$937$	−29.7592	−0.972192	−0.486096	−	0.873905i	$-0.661579\pi$
$937$	−29.7592	−0.972192	−0.486096	+	0.873905i	$0.661579\pi$
$938$	28.2316	0.921793
$939$	−15.0554	−0.491314
$940$	−31.0430	−1.01251
$941$	−30.7767	−1.00329	−0.501646	−	0.865073i	$-0.667272\pi$
$941$	−30.7767	−1.00329	−0.501646	+	0.865073i	$0.667272\pi$
$942$	2.93309	0.0955651
$943$	−10.3856	−0.338202
$944$	36.8289	1.19868
$945$	5.00861	0.162930
$946$	42.4183	1.37914
$947$	20.8394	0.677189	0.338594	−	0.940932i	$-0.390049\pi$
$947$	20.8394	0.677189	0.338594	+	0.940932i	$0.390049\pi$
$948$	18.2957	0.594218
$949$	35.8168	1.16266
$950$	7.70923	0.250120
$951$	−7.10798	−0.230492
$952$	−74.1117	−2.40197
$953$	−12.8538	−0.416376	−0.208188	−	0.978089i	$-0.566757\pi$
$953$	−12.8538	−0.416376	−0.208188	+	0.978089i	$0.566757\pi$
$954$	0.968758	0.0313647
$955$	−11.6719	−0.377695
$956$	−81.3112	−2.62979
$957$	−0.593403	−0.0191820
$958$	−10.7188	−0.346309
$959$	−27.0722	−0.874207
$960$	−1.60861	−0.0519177
$961$	44.0536	1.42108
$962$	−51.5310	−1.66143
$963$	28.4562	0.916987
$964$	56.4710	1.81881
$965$	21.6448	0.696772
$966$	2.78161	0.0894969
$967$	−13.4839	−0.433613	−0.216807	−	0.976215i	$-0.569564\pi$
$967$	−13.4839	−0.433613	−0.216807	+	0.976215i	$0.569564\pi$
$968$	39.0111	1.25386
$969$	−8.92770	−0.286799
$970$	−40.4366	−1.29834
$971$	35.8101	1.14920	0.574600	−	0.818434i	$-0.305158\pi$
$971$	35.8101	1.14920	0.574600	+	0.818434i	$0.305158\pi$
$972$	54.8655	1.75981
$973$	−11.5668	−0.370816
$974$	54.8802	1.75848
$975$	2.43164	0.0778749
$976$	−4.25992	−0.136357
$977$	12.9093	0.413006	0.206503	−	0.978446i	$-0.433792\pi$
$977$	12.9093	0.413006	0.206503	+	0.978446i	$0.433792\pi$
$978$	4.56106	0.145846
$979$	34.3719	1.09853
$980$	17.7909	0.568309
$981$	−56.7399	−1.81157
$982$	39.6620	1.26567
$983$	−29.2468	−0.932828	−0.466414	−	0.884567i	$-0.654454\pi$
$983$	−29.2468	−0.932828	−0.466414	+	0.884567i	$0.654454\pi$
$984$	−27.8347	−0.887337
$985$	−10.9071	−0.347528
$986$	8.33427	0.265417
$987$	5.81208	0.185000
$988$	−69.1471	−2.19986
$989$	8.89675	0.282900
$990$	−16.3451	−0.519482
$991$	−0.574385	−0.0182459	−0.00912296	−	0.999958i	$-0.502904\pi$
$991$	−0.574385	−0.0182459	−0.00912296	+	0.999958i	$0.502904\pi$
$992$	66.6843	2.11723
$993$	4.23217	0.134304
$994$	−71.7482	−2.27571
$995$	−3.83565	−0.121598
$996$	20.5952	0.652583
$997$	17.3701	0.550117	0.275059	−	0.961427i	$-0.411303\pi$
$997$	17.3701	0.550117	0.275059	+	0.961427i	$0.411303\pi$
$998$	−69.8475	−2.21099
$999$	−11.2991	−0.357488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.g.1.5	✓	137

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.g.1.5	✓	137	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57744 q^{2} +0.488387 q^{3} +4.64318 q^{4} -1.00000 q^{5} -1.25879 q^{6} +1.78000 q^{7} -6.81263 q^{8} -2.76148 q^{9} +O(q^{10})\)	\(q-2.57744 q^{2} +0.488387 q^{3} +4.64318 q^{4} -1.00000 q^{5} -1.25879 q^{6} +1.78000 q^{7} -6.81263 q^{8} -2.76148 q^{9} +2.57744 q^{10} +2.29646 q^{11} +2.26767 q^{12} +4.97892 q^{13} -4.58783 q^{14} -0.488387 q^{15} +8.27277 q^{16} +6.11156 q^{17} +7.11754 q^{18} -2.99104 q^{19} -4.64318 q^{20} +0.869328 q^{21} -5.91897 q^{22} -1.24144 q^{23} -3.32720 q^{24} +1.00000 q^{25} -12.8329 q^{26} -2.81383 q^{27} +8.26485 q^{28} -0.529087 q^{29} +1.25879 q^{30} -8.66335 q^{31} -7.69728 q^{32} +1.12156 q^{33} -15.7522 q^{34} -1.78000 q^{35} -12.8220 q^{36} +4.01555 q^{37} +7.70923 q^{38} +2.43164 q^{39} +6.81263 q^{40} +8.36578 q^{41} -2.24064 q^{42} -7.16649 q^{43} +10.6629 q^{44} +2.76148 q^{45} +3.19973 q^{46} +6.68571 q^{47} +4.04032 q^{48} -3.83161 q^{49} -2.57744 q^{50} +2.98481 q^{51} +23.1180 q^{52} +0.136109 q^{53} +7.25248 q^{54} -2.29646 q^{55} -12.1265 q^{56} -1.46079 q^{57} +1.36369 q^{58} +4.45182 q^{59} -2.26767 q^{60} -0.514933 q^{61} +22.3292 q^{62} -4.91542 q^{63} +3.29372 q^{64} -4.97892 q^{65} -2.89075 q^{66} -6.15358 q^{67} +28.3771 q^{68} -0.606302 q^{69} +4.58783 q^{70} +15.6388 q^{71} +18.8129 q^{72} +7.19368 q^{73} -10.3498 q^{74} +0.488387 q^{75} -13.8880 q^{76} +4.08769 q^{77} -6.26741 q^{78} +8.06807 q^{79} -8.27277 q^{80} +6.91019 q^{81} -21.5623 q^{82} +9.08208 q^{83} +4.03645 q^{84} -6.11156 q^{85} +18.4712 q^{86} -0.258399 q^{87} -15.6449 q^{88} +14.9674 q^{89} -7.11754 q^{90} +8.86246 q^{91} -5.76422 q^{92} -4.23107 q^{93} -17.2320 q^{94} +2.99104 q^{95} -3.75926 q^{96} -15.6887 q^{97} +9.87574 q^{98} -6.34162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * q^99

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