LMFDB - Embedded newform 1001.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(1,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, 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("1001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.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:	$7.99302524233$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.216637.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + x - 2 $ x^5 - 2x^4 - 4x^3 + 7*x^2 + x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.37067$ of defining polynomial
Character	$\chi$	$=$	1001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.37067 q^{2} +2.69782 q^{3} -0.121264 q^{4} -3.78629 q^{5} -3.69782 q^{6} -1.00000 q^{7} +2.90755 q^{8} +4.27822 q^{9} +O(q^{10})$	\(q-1.37067 q^{2} +2.69782 q^{3} -0.121264 q^{4} -3.78629 q^{5} -3.69782 q^{6} -1.00000 q^{7} +2.90755 q^{8} +4.27822 q^{9} +5.18975 q^{10} +1.00000 q^{11} -0.327148 q^{12} +1.00000 q^{13} +1.37067 q^{14} -10.2147 q^{15} -3.74277 q^{16} +0.414192 q^{17} -5.86403 q^{18} -5.01281 q^{19} +0.459141 q^{20} -2.69782 q^{21} -1.37067 q^{22} +1.90755 q^{23} +7.84405 q^{24} +9.33598 q^{25} -1.37067 q^{26} +3.44841 q^{27} +0.121264 q^{28} -3.25468 q^{29} +14.0010 q^{30} -5.00000 q^{31} -0.685007 q^{32} +2.69782 q^{33} -0.567720 q^{34} +3.78629 q^{35} -0.518794 q^{36} -8.27437 q^{37} +6.87091 q^{38} +2.69782 q^{39} -11.0088 q^{40} +0.347131 q^{41} +3.69782 q^{42} -12.9325 q^{43} -0.121264 q^{44} -16.1986 q^{45} -2.61463 q^{46} -7.99668 q^{47} -10.0973 q^{48} +1.00000 q^{49} -12.7966 q^{50} +1.11741 q^{51} -0.121264 q^{52} +1.18382 q^{53} -4.72663 q^{54} -3.78629 q^{55} -2.90755 q^{56} -13.5237 q^{57} +4.46110 q^{58} -3.98784 q^{59} +1.23868 q^{60} +0.450835 q^{61} +6.85335 q^{62} -4.27822 q^{63} +8.42445 q^{64} -3.78629 q^{65} -3.69782 q^{66} -10.5726 q^{67} -0.0502265 q^{68} +5.14623 q^{69} -5.18975 q^{70} -9.83864 q^{71} +12.4392 q^{72} +14.7599 q^{73} +11.3414 q^{74} +25.1868 q^{75} +0.607873 q^{76} -1.00000 q^{77} -3.69782 q^{78} -14.7540 q^{79} +14.1712 q^{80} -3.53148 q^{81} -0.475802 q^{82} +17.0680 q^{83} +0.327148 q^{84} -1.56825 q^{85} +17.7262 q^{86} -8.78054 q^{87} +2.90755 q^{88} +12.5296 q^{89} +22.2029 q^{90} -1.00000 q^{91} -0.231317 q^{92} -13.4891 q^{93} +10.9608 q^{94} +18.9799 q^{95} -1.84803 q^{96} -8.87974 q^{97} -1.37067 q^{98} +4.27822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^7 - 3 * q^8 - q^9	\( 5 q - 2 q^{2} + 2 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{7} - 3 q^{8} - q^{9} + 5 q^{10} + 5 q^{11} + 7 q^{12} + 5 q^{13} + 2 q^{14} - 8 q^{15} + q^{17} - 8 q^{18} - 7 q^{19} - 4 q^{20} - 2 q^{22} - 8 q^{23} + q^{24} + q^{25} - 2 q^{26} + 6 q^{27} - 2 q^{28} - 7 q^{29} + 12 q^{30} - 25 q^{31} - 8 q^{32} - 29 q^{34} + 4 q^{35} - 15 q^{36} - 17 q^{37} + 16 q^{38} - 18 q^{40} + 10 q^{41} + 5 q^{42} - 25 q^{43} + 2 q^{44} - 23 q^{45} + 6 q^{46} - 7 q^{47} - 12 q^{48} + 5 q^{49} - 3 q^{50} + q^{51} + 2 q^{52} + 6 q^{53} + 10 q^{54} - 4 q^{55} + 3 q^{56} - 24 q^{57} - 24 q^{58} - 24 q^{59} - q^{60} + 2 q^{61} + 10 q^{62} + q^{63} - 5 q^{64} - 4 q^{65} - 5 q^{66} - 23 q^{67} + 12 q^{68} + q^{69} - 5 q^{70} - q^{71} + 39 q^{72} + 12 q^{73} + 23 q^{74} + 28 q^{75} - 2 q^{76} - 5 q^{77} - 5 q^{78} - 29 q^{79} + 24 q^{80} + 5 q^{81} + 20 q^{82} + 16 q^{83} - 7 q^{84} - 3 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 2 q^{89} + 28 q^{90} - 5 q^{91} - 24 q^{92} + 26 q^{94} - 15 q^{95} + 10 q^{96} + 11 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^7 - 3 * q^8 - q^9 + 5 * q^10 + 5 * q^11 + 7 * q^12 + 5 * q^13 + 2 * q^14 - 8 * q^15 + q^17 - 8 * q^18 - 7 * q^19 - 4 * q^20 - 2 * q^22 - 8 * q^23 + q^24 + q^25 - 2 * q^26 + 6 * q^27 - 2 * q^28 - 7 * q^29 + 12 * q^30 - 25 * q^31 - 8 * q^32 - 29 * q^34 + 4 * q^35 - 15 * q^36 - 17 * q^37 + 16 * q^38 - 18 * q^40 + 10 * q^41 + 5 * q^42 - 25 * q^43 + 2 * q^44 - 23 * q^45 + 6 * q^46 - 7 * q^47 - 12 * q^48 + 5 * q^49 - 3 * q^50 + q^51 + 2 * q^52 + 6 * q^53 + 10 * q^54 - 4 * q^55 + 3 * q^56 - 24 * q^57 - 24 * q^58 - 24 * q^59 - q^60 + 2 * q^61 + 10 * q^62 + q^63 - 5 * q^64 - 4 * q^65 - 5 * q^66 - 23 * q^67 + 12 * q^68 + q^69 - 5 * q^70 - q^71 + 39 * q^72 + 12 * q^73 + 23 * q^74 + 28 * q^75 - 2 * q^76 - 5 * q^77 - 5 * q^78 - 29 * q^79 + 24 * q^80 + 5 * q^81 + 20 * q^82 + 16 * q^83 - 7 * q^84 - 3 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 2 * q^89 + 28 * q^90 - 5 * q^91 - 24 * q^92 + 26 * q^94 - 15 * q^95 + 10 * q^96 + 11 * q^97 - 2 * q^98 - 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 $

$2$	−1.37067	−0.969210	−0.484605	−	0.874733i	$-0.661037\pi$
$2$	−1.37067	−0.969210	−0.484605	+	0.874733i	$0.661037\pi$
$3$	2.69782	1.55759	0.778793	−	0.627281i	$-0.215832\pi$
$3$	2.69782	1.55759	0.778793	+	0.627281i	$0.215832\pi$
$4$	−0.121264	−0.0606320
$5$	−3.78629	−1.69328	−0.846640	−	0.532166i	$-0.821378\pi$
$5$	−3.78629	−1.69328	−0.846640	+	0.532166i	$0.821378\pi$
$6$	−3.69782	−1.50963
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.90755	1.02798
$9$	4.27822	1.42607
$10$	5.18975	1.64114
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.327148	−0.0944396
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.37067	0.366327
$15$	−10.2147	−2.63743
$16$	−3.74277	−0.935692
$17$	0.414192	0.100456	0.0502281	−	0.998738i	$-0.484005\pi$
$17$	0.414192	0.100456	0.0502281	+	0.998738i	$0.484005\pi$
$18$	−5.86403	−1.38217
$19$	−5.01281	−1.15002	−0.575009	−	0.818147i	$-0.695001\pi$
$19$	−5.01281	−1.15002	−0.575009	+	0.818147i	$0.695001\pi$
$20$	0.459141	0.102667
$21$	−2.69782	−0.588712
$22$	−1.37067	−0.292228
$23$	1.90755	0.397752	0.198876	−	0.980025i	$-0.436271\pi$
$23$	1.90755	0.397752	0.198876	+	0.980025i	$0.436271\pi$
$24$	7.84405	1.60116
$25$	9.33598	1.86720
$26$	−1.37067	−0.268810
$27$	3.44841	0.663647
$28$	0.121264	0.0229167
$29$	−3.25468	−0.604380	−0.302190	−	0.953248i	$-0.597718\pi$
$29$	−3.25468	−0.604380	−0.302190	+	0.953248i	$0.597718\pi$
$30$	14.0010	2.55622
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	−0.685007	−0.121093
$33$	2.69782	0.469630
$34$	−0.567720	−0.0973632
$35$	3.78629	0.640000
$36$	−0.518794	−0.0864657
$37$	−8.27437	−1.36030	−0.680149	−	0.733074i	$-0.738085\pi$
$37$	−8.27437	−1.36030	−0.680149	+	0.733074i	$0.738085\pi$
$38$	6.87091	1.11461
$39$	2.69782	0.431997
$40$	−11.0088	−1.74065
$41$	0.347131	0.0542127	0.0271064	−	0.999633i	$-0.491371\pi$
$41$	0.347131	0.0542127	0.0271064	+	0.999633i	$0.491371\pi$
$42$	3.69782	0.570586
$43$	−12.9325	−1.97219	−0.986095	−	0.166181i	$-0.946857\pi$
$43$	−12.9325	−1.97219	−0.986095	+	0.166181i	$0.946857\pi$
$44$	−0.121264	−0.0182812
$45$	−16.1986	−2.41474
$46$	−2.61463	−0.385505
$47$	−7.99668	−1.16644	−0.583218	−	0.812316i	$-0.698207\pi$
$47$	−7.99668	−1.16644	−0.583218	+	0.812316i	$0.698207\pi$
$48$	−10.0973	−1.45742
$49$	1.00000	0.142857
$50$	−12.7966	−1.80971
$51$	1.11741	0.156469
$52$	−0.121264	−0.0168163
$53$	1.18382	0.162610	0.0813050	−	0.996689i	$-0.474091\pi$
$53$	1.18382	0.162610	0.0813050	+	0.996689i	$0.474091\pi$
$54$	−4.72663	−0.643214
$55$	−3.78629	−0.510543
$56$	−2.90755	−0.388538
$57$	−13.5237	−1.79125
$58$	4.46110	0.585771
$59$	−3.98784	−0.519173	−0.259587	−	0.965720i	$-0.583586\pi$
$59$	−3.98784	−0.519173	−0.259587	+	0.965720i	$0.583586\pi$
$60$	1.23868	0.159913
$61$	0.450835	0.0577236	0.0288618	−	0.999583i	$-0.490812\pi$
$61$	0.450835	0.0577236	0.0288618	+	0.999583i	$0.490812\pi$
$62$	6.85335	0.870376
$63$	−4.27822	−0.539005
$64$	8.42445	1.05306
$65$	−3.78629	−0.469631
$66$	−3.69782	−0.455170
$67$	−10.5726	−1.29165	−0.645823	−	0.763487i	$-0.723486\pi$
$67$	−10.5726	−1.29165	−0.645823	+	0.763487i	$0.723486\pi$
$68$	−0.0502265	−0.00609086
$69$	5.14623	0.619533
$70$	−5.18975	−0.620294
$71$	−9.83864	−1.16763	−0.583816	−	0.811886i	$-0.698441\pi$
$71$	−9.83864	−1.16763	−0.583816	+	0.811886i	$0.698441\pi$
$72$	12.4392	1.46597
$73$	14.7599	1.72752	0.863758	−	0.503907i	$-0.168104\pi$
$73$	14.7599	1.72752	0.863758	+	0.503907i	$0.168104\pi$
$74$	11.3414	1.31841
$75$	25.1868	2.90832
$76$	0.607873	0.0697279
$77$	−1.00000	−0.113961
$78$	−3.69782	−0.418695
$79$	−14.7540	−1.65996	−0.829979	−	0.557795i	$-0.811648\pi$
$79$	−14.7540	−1.65996	−0.829979	+	0.557795i	$0.811648\pi$
$80$	14.1712	1.58439
$81$	−3.53148	−0.392387
$82$	−0.475802	−0.0525435
$83$	17.0680	1.87346	0.936729	−	0.350054i	$-0.113837\pi$
$83$	17.0680	1.87346	0.936729	+	0.350054i	$0.113837\pi$
$84$	0.327148	0.0356948
$85$	−1.56825	−0.170100
$86$	17.7262	1.91147
$87$	−8.78054	−0.941373
$88$	2.90755	0.309946
$89$	12.5296	1.32813	0.664067	−	0.747673i	$-0.268829\pi$
$89$	12.5296	1.32813	0.664067	+	0.747673i	$0.268829\pi$
$90$	22.2029	2.34039
$91$	−1.00000	−0.104828
$92$	−0.231317	−0.0241165
$93$	−13.4891	−1.39875
$94$	10.9608	1.13052
$95$	18.9799	1.94730
$96$	−1.84803	−0.188613
$97$	−8.87974	−0.901601	−0.450801	−	0.892625i	$-0.648861\pi$
$97$	−8.87974	−0.901601	−0.450801	+	0.892625i	$0.648861\pi$
$98$	−1.37067	−0.138459
$99$	4.27822	0.429978
$100$	−1.13212	−0.113212
$101$	14.7276	1.46546	0.732728	−	0.680522i	$-0.238247\pi$
$101$	14.7276	1.46546	0.732728	+	0.680522i	$0.238247\pi$
$102$	−1.53161	−0.151652
$103$	−8.27182	−0.815047	−0.407523	−	0.913195i	$-0.633608\pi$
$103$	−8.27182	−0.815047	−0.407523	+	0.913195i	$0.633608\pi$
$104$	2.90755	0.285109
$105$	10.2147	0.996854
$106$	−1.62263	−0.157603
$107$	16.0352	1.55018	0.775092	−	0.631848i	$-0.217703\pi$
$107$	16.0352	1.55018	0.775092	+	0.631848i	$0.217703\pi$
$108$	−0.418168	−0.0402383
$109$	6.81719	0.652968	0.326484	−	0.945203i	$-0.394136\pi$
$109$	6.81719	0.652968	0.326484	+	0.945203i	$0.394136\pi$
$110$	5.18975	0.494823
$111$	−22.3228	−2.11878
$112$	3.74277	0.353658
$113$	−13.0050	−1.22341	−0.611703	−	0.791088i	$-0.709515\pi$
$113$	−13.0050	−1.22341	−0.611703	+	0.791088i	$0.709515\pi$
$114$	18.5365	1.73610
$115$	−7.22255	−0.673506
$116$	0.394676	0.0366447
$117$	4.27822	0.395522
$118$	5.46602	0.503188
$119$	−0.414192	−0.0379689
$120$	−29.6998	−2.71121
$121$	1.00000	0.0909091
$122$	−0.617946	−0.0559462
$123$	0.936496	0.0844410
$124$	0.606320	0.0544491
$125$	−16.4173	−1.46841
$126$	5.86403	0.522409
$127$	−9.23868	−0.819800	−0.409900	−	0.912130i	$-0.634436\pi$
$127$	−9.23868	−0.819800	−0.409900	+	0.912130i	$0.634436\pi$
$128$	−10.1771	−0.899540
$129$	−34.8896	−3.07186
$130$	5.18975	0.455171
$131$	4.48411	0.391778	0.195889	−	0.980626i	$-0.437241\pi$
$131$	4.48411	0.391778	0.195889	+	0.980626i	$0.437241\pi$
$132$	−0.327148	−0.0284746
$133$	5.01281	0.434666
$134$	14.4915	1.25188
$135$	−13.0567	−1.12374
$136$	1.20428	0.103266
$137$	−15.6538	−1.33740	−0.668698	−	0.743534i	$-0.733148\pi$
$137$	−15.6538	−1.33740	−0.668698	+	0.743534i	$0.733148\pi$
$138$	−7.05378	−0.600458
$139$	2.79092	0.236723	0.118361	−	0.992971i	$-0.462236\pi$
$139$	2.79092	0.236723	0.118361	+	0.992971i	$0.462236\pi$
$140$	−0.459141	−0.0388045
$141$	−21.5736	−1.81682
$142$	13.4855	1.13168
$143$	1.00000	0.0836242
$144$	−16.0124	−1.33437
$145$	12.3232	1.02338
$146$	−20.2310	−1.67433
$147$	2.69782	0.222512
$148$	1.00338	0.0824776
$149$	−5.05858	−0.414415	−0.207207	−	0.978297i	$-0.566438\pi$
$149$	−5.05858	−0.414415	−0.207207	+	0.978297i	$0.566438\pi$
$150$	−34.5228	−2.81877
$151$	5.99188	0.487613	0.243806	−	0.969824i	$-0.421604\pi$
$151$	5.99188	0.487613	0.243806	+	0.969824i	$0.421604\pi$
$152$	−14.5750	−1.18219
$153$	1.77200	0.143258
$154$	1.37067	0.110452
$155$	18.9314	1.52061
$156$	−0.327148	−0.0261928
$157$	9.70276	0.774364	0.387182	−	0.922003i	$-0.373448\pi$
$157$	9.70276	0.774364	0.387182	+	0.922003i	$0.373448\pi$
$158$	20.2229	1.60885
$159$	3.19373	0.253279
$160$	2.59364	0.205045
$161$	−1.90755	−0.150336
$162$	4.84049	0.380305
$163$	15.4944	1.21362	0.606808	−	0.794848i	$-0.292450\pi$
$163$	15.4944	1.21362	0.606808	+	0.794848i	$0.292450\pi$
$164$	−0.0420945	−0.00328703
$165$	−10.2147	−0.795215
$166$	−23.3946	−1.81577
$167$	−3.20481	−0.247996	−0.123998	−	0.992282i	$-0.539572\pi$
$167$	−3.20481	−0.247996	−0.123998	+	0.992282i	$0.539572\pi$
$168$	−7.84405	−0.605181
$169$	1.00000	0.0769231
$170$	2.14955	0.164863
$171$	−21.4459	−1.64001
$172$	1.56825	0.119578
$173$	6.19995	0.471374	0.235687	−	0.971829i	$-0.424266\pi$
$173$	6.19995	0.471374	0.235687	+	0.971829i	$0.424266\pi$
$174$	12.0352	0.912388
$175$	−9.33598	−0.705734
$176$	−3.74277	−0.282122
$177$	−10.7585	−0.808657
$178$	−17.1739	−1.28724
$179$	7.08010	0.529191	0.264596	−	0.964359i	$-0.414762\pi$
$179$	7.08010	0.529191	0.264596	+	0.964359i	$0.414762\pi$
$180$	1.96431	0.146411
$181$	−17.9786	−1.33634	−0.668171	−	0.744008i	$-0.732923\pi$
$181$	−17.9786	−1.33634	−0.668171	+	0.744008i	$0.732923\pi$
$182$	1.37067	0.101601
$183$	1.21627	0.0899094
$184$	5.54631	0.408879
$185$	31.3292	2.30337
$186$	18.4891	1.35569
$187$	0.414192	0.0302887
$188$	0.969709	0.0707233
$189$	−3.44841	−0.250835
$190$	−26.0152	−1.88734
$191$	−10.8782	−0.787118	−0.393559	−	0.919299i	$-0.628756\pi$
$191$	−10.8782	−0.787118	−0.393559	+	0.919299i	$0.628756\pi$
$192$	22.7276	1.64023
$193$	−21.2432	−1.52912	−0.764559	−	0.644553i	$-0.777043\pi$
$193$	−21.2432	−1.52912	−0.764559	+	0.644553i	$0.777043\pi$
$194$	12.1712	0.873841
$195$	−10.2147	−0.731491
$196$	−0.121264	−0.00866171
$197$	4.68264	0.333624	0.166812	−	0.985989i	$-0.446653\pi$
$197$	4.68264	0.333624	0.166812	+	0.985989i	$0.446653\pi$
$198$	−5.86403	−0.416739
$199$	−1.94609	−0.137955	−0.0689774	−	0.997618i	$-0.521974\pi$
$199$	−1.94609	−0.137955	−0.0689774	+	0.997618i	$0.521974\pi$
$200$	27.1449	1.91943
$201$	−28.5229	−2.01185
$202$	−20.1867	−1.42033
$203$	3.25468	0.228434
$204$	−0.135502	−0.00948704
$205$	−1.31434	−0.0917973
$206$	11.3379	0.789952
$207$	8.16094	0.567224
$208$	−3.74277	−0.259514
$209$	−5.01281	−0.346743
$210$	−14.0010	−0.966161
$211$	21.4909	1.47949	0.739746	−	0.672886i	$-0.234946\pi$
$211$	21.4909	1.47949	0.739746	+	0.672886i	$0.234946\pi$
$212$	−0.143555	−0.00985937
$213$	−26.5429	−1.81869
$214$	−21.9790	−1.50245
$215$	48.9663	3.33947
$216$	10.0264	0.682213
$217$	5.00000	0.339422
$218$	−9.34411	−0.632863
$219$	39.8195	2.69076
$220$	0.459141	0.0309552
$221$	0.414192	0.0278615
$222$	30.5971	2.05354
$223$	5.78702	0.387528	0.193764	−	0.981048i	$-0.437930\pi$
$223$	5.78702	0.387528	0.193764	+	0.981048i	$0.437930\pi$
$224$	0.685007	0.0457690
$225$	39.9414	2.66276
$226$	17.8255	1.18574
$227$	1.20688	0.0801034	0.0400517	−	0.999198i	$-0.487248\pi$
$227$	1.20688	0.0801034	0.0400517	+	0.999198i	$0.487248\pi$
$228$	1.63993	0.108607
$229$	0.874114	0.0577631	0.0288815	−	0.999583i	$-0.490805\pi$
$229$	0.874114	0.0577631	0.0288815	+	0.999583i	$0.490805\pi$
$230$	9.89973	0.652769
$231$	−2.69782	−0.177503
$232$	−9.46316	−0.621287
$233$	−14.2068	−0.930719	−0.465360	−	0.885122i	$-0.654075\pi$
$233$	−14.2068	−0.930719	−0.465360	+	0.885122i	$0.654075\pi$
$234$	−5.86403	−0.383344
$235$	30.2777	1.97510
$236$	0.483582	0.0314785
$237$	−39.8037	−2.58553
$238$	0.567720	0.0367998
$239$	4.82022	0.311794	0.155897	−	0.987773i	$-0.450173\pi$
$239$	4.82022	0.311794	0.155897	+	0.987773i	$0.450173\pi$
$240$	38.2313	2.46782
$241$	−2.42557	−0.156244	−0.0781222	−	0.996944i	$-0.524892\pi$
$241$	−2.42557	−0.156244	−0.0781222	+	0.996944i	$0.524892\pi$
$242$	−1.37067	−0.0881100
$243$	−19.8725	−1.27482
$244$	−0.0546701	−0.00349989
$245$	−3.78629	−0.241897
$246$	−1.28363	−0.0818410
$247$	−5.01281	−0.318958
$248$	−14.5378	−0.923149
$249$	46.0464	2.91807
$250$	22.5027	1.42319
$251$	3.96280	0.250130	0.125065	−	0.992149i	$-0.460086\pi$
$251$	3.96280	0.250130	0.125065	+	0.992149i	$0.460086\pi$
$252$	0.518794	0.0326810
$253$	1.90755	0.119927
$254$	12.6632	0.794558
$255$	−4.23085	−0.264946
$256$	−2.89942	−0.181214
$257$	8.01294	0.499833	0.249917	−	0.968267i	$-0.419597\pi$
$257$	8.01294	0.499833	0.249917	+	0.968267i	$0.419597\pi$
$258$	47.8221	2.97727
$259$	8.27437	0.514144
$260$	0.459141	0.0284747
$261$	−13.9243	−0.861890
$262$	−6.14623	−0.379715
$263$	14.4266	0.889581	0.444791	−	0.895635i	$-0.353278\pi$
$263$	14.4266	0.889581	0.444791	+	0.895635i	$0.353278\pi$
$264$	7.84405	0.482768
$265$	−4.48228	−0.275344
$266$	−6.87091	−0.421282
$267$	33.8025	2.06868
$268$	1.28207	0.0783151
$269$	7.74121	0.471990	0.235995	−	0.971754i	$-0.424165\pi$
$269$	7.74121	0.471990	0.235995	+	0.971754i	$0.424165\pi$
$270$	17.8964	1.08914
$271$	−28.8319	−1.75141	−0.875706	−	0.482844i	$-0.839604\pi$
$271$	−28.8319	−1.75141	−0.875706	+	0.482844i	$0.839604\pi$
$272$	−1.55022	−0.0939961
$273$	−2.69782	−0.163279
$274$	21.4562	1.29622
$275$	9.33598	0.562981
$276$	−0.624052	−0.0375635
$277$	6.40338	0.384742	0.192371	−	0.981322i	$-0.438382\pi$
$277$	6.40338	0.384742	0.192371	+	0.981322i	$0.438382\pi$
$278$	−3.82543	−0.229434
$279$	−21.3911	−1.28065
$280$	11.0088	0.657904
$281$	13.0088	0.776039	0.388019	−	0.921651i	$-0.373159\pi$
$281$	13.0088	0.776039	0.388019	+	0.921651i	$0.373159\pi$
$282$	29.5703	1.76088
$283$	−30.2116	−1.79589	−0.897947	−	0.440103i	$-0.854942\pi$
$283$	−30.2116	−1.79589	−0.897947	+	0.440103i	$0.854942\pi$
$284$	1.19307	0.0707959
$285$	51.2045	3.03309
$286$	−1.37067	−0.0810494
$287$	−0.347131	−0.0204905
$288$	−2.93061	−0.172688
$289$	−16.8284	−0.989909
$290$	−16.8910	−0.991874
$291$	−23.9559	−1.40432
$292$	−1.78985	−0.104743
$293$	−5.17902	−0.302562	−0.151281	−	0.988491i	$-0.548340\pi$
$293$	−5.17902	−0.302562	−0.151281	+	0.988491i	$0.548340\pi$
$294$	−3.69782	−0.215661
$295$	15.0991	0.879105
$296$	−24.0582	−1.39835
$297$	3.44841	0.200097
$298$	6.93364	0.401655
$299$	1.90755	0.110317
$300$	−3.05425	−0.176337
$301$	12.9325	0.745418
$302$	−8.21289	−0.472599
$303$	39.7325	2.28257
$304$	18.7618	1.07606
$305$	−1.70699	−0.0977421
$306$	−2.42883	−0.138847
$307$	16.5059	0.942042	0.471021	−	0.882122i	$-0.343886\pi$
$307$	16.5059	0.942042	0.471021	+	0.882122i	$0.343886\pi$
$308$	0.121264	0.00690966
$309$	−22.3159	−1.26951
$310$	−25.9488	−1.47379
$311$	9.67274	0.548491	0.274245	−	0.961660i	$-0.411572\pi$
$311$	9.67274	0.548491	0.274245	+	0.961660i	$0.411572\pi$
$312$	7.84405	0.444082
$313$	−8.72603	−0.493224	−0.246612	−	0.969114i	$-0.579317\pi$
$313$	−8.72603	−0.493224	−0.246612	+	0.969114i	$0.579317\pi$
$314$	−13.2993	−0.750521
$315$	16.1986	0.912687
$316$	1.78913	0.100647
$317$	−7.11824	−0.399800	−0.199900	−	0.979816i	$-0.564062\pi$
$317$	−7.11824	−0.399800	−0.199900	+	0.979816i	$0.564062\pi$
$318$	−4.37755	−0.245481
$319$	−3.25468	−0.182227
$320$	−31.8974	−1.78312
$321$	43.2601	2.41454
$322$	2.61463	0.145707
$323$	−2.07626	−0.115526
$324$	0.428241	0.0237912
$325$	9.33598	0.517867
$326$	−21.2377	−1.17625
$327$	18.3915	1.01705
$328$	1.00930	0.0557293
$329$	7.99668	0.440871
$330$	14.0010	0.770730
$331$	−2.10810	−0.115872	−0.0579359	−	0.998320i	$-0.518452\pi$
$331$	−2.10810	−0.115872	−0.0579359	+	0.998320i	$0.518452\pi$
$332$	−2.06974	−0.113592
$333$	−35.3996	−1.93989
$334$	4.39274	0.240360
$335$	40.0308	2.18712
$336$	10.0973	0.550853
$337$	3.73814	0.203630	0.101815	−	0.994803i	$-0.467535\pi$
$337$	3.73814	0.203630	0.101815	+	0.994803i	$0.467535\pi$
$338$	−1.37067	−0.0745546
$339$	−35.0851	−1.90556
$340$	0.190172	0.0103135
$341$	−5.00000	−0.270765
$342$	29.3953	1.58951
$343$	−1.00000	−0.0539949
$344$	−37.6020	−2.02736
$345$	−19.4851	−1.04904
$346$	−8.49809	−0.456860
$347$	−20.5073	−1.10089	−0.550445	−	0.834871i	$-0.685542\pi$
$347$	−20.5073	−1.10089	−0.550445	+	0.834871i	$0.685542\pi$
$348$	1.06476	0.0570773
$349$	9.28576	0.497055	0.248528	−	0.968625i	$-0.420053\pi$
$349$	9.28576	0.497055	0.248528	+	0.968625i	$0.420053\pi$
$350$	12.7966	0.684004
$351$	3.44841	0.184063
$352$	−0.685007	−0.0365110
$353$	18.2261	0.970078	0.485039	−	0.874493i	$-0.338805\pi$
$353$	18.2261	0.970078	0.485039	+	0.874493i	$0.338805\pi$
$354$	14.7463	0.783758
$355$	37.2519	1.97713
$356$	−1.51939	−0.0805274
$357$	−1.11741	−0.0591398
$358$	−9.70448	−0.512898
$359$	0.107387	0.00566769	0.00283385	−	0.999996i	$-0.499098\pi$
$359$	0.107387	0.00566769	0.00283385	+	0.999996i	$0.499098\pi$
$360$	−47.0982	−2.48230
$361$	6.12827	0.322541
$362$	24.6428	1.29520
$363$	2.69782	0.141599
$364$	0.121264	0.00635596
$365$	−55.8853	−2.92517
$366$	−1.66711	−0.0871411
$367$	9.44389	0.492967	0.246484	−	0.969147i	$-0.420725\pi$
$367$	9.44389	0.492967	0.246484	+	0.969147i	$0.420725\pi$
$368$	−7.13953	−0.372173
$369$	1.48510	0.0773114
$370$	−42.9419	−2.23245
$371$	−1.18382	−0.0614608
$372$	1.63574	0.0848092
$373$	24.2349	1.25483	0.627417	−	0.778683i	$-0.284112\pi$
$373$	24.2349	1.25483	0.627417	+	0.778683i	$0.284112\pi$
$374$	−0.567720	−0.0293561
$375$	−44.2908	−2.28717
$376$	−23.2508	−1.19907
$377$	−3.25468	−0.167625
$378$	4.72663	0.243112
$379$	29.0836	1.49392	0.746961	−	0.664868i	$-0.231512\pi$
$379$	29.0836	1.49392	0.746961	+	0.664868i	$0.231512\pi$
$380$	−2.30158	−0.118069
$381$	−24.9243	−1.27691
$382$	14.9104	0.762883
$383$	−25.6050	−1.30835	−0.654177	−	0.756341i	$-0.726985\pi$
$383$	−25.6050	−1.30835	−0.654177	+	0.756341i	$0.726985\pi$
$384$	−27.4560	−1.40111
$385$	3.78629	0.192967
$386$	29.1174	1.48204
$387$	−55.3282	−2.81249
$388$	1.07679	0.0546659
$389$	−8.35502	−0.423616	−0.211808	−	0.977311i	$-0.567935\pi$
$389$	−8.35502	−0.423616	−0.211808	+	0.977311i	$0.567935\pi$
$390$	14.0010	0.708969
$391$	0.790092	0.0399567
$392$	2.90755	0.146854
$393$	12.0973	0.610228
$394$	−6.41835	−0.323352
$395$	55.8630	2.81077
$396$	−0.518794	−0.0260704
$397$	34.7027	1.74168	0.870838	−	0.491570i	$-0.163577\pi$
$397$	34.7027	1.74168	0.870838	+	0.491570i	$0.163577\pi$
$398$	2.66745	0.133707
$399$	13.5237	0.677029
$400$	−34.9424	−1.74712
$401$	32.3766	1.61681	0.808405	−	0.588627i	$-0.200331\pi$
$401$	32.3766	1.61681	0.808405	+	0.588627i	$0.200331\pi$
$402$	39.0955	1.94990
$403$	−5.00000	−0.249068
$404$	−1.78593	−0.0888535
$405$	13.3712	0.664420
$406$	−4.46110	−0.221401
$407$	−8.27437	−0.410145
$408$	3.24894	0.160846
$409$	−10.3140	−0.509994	−0.254997	−	0.966942i	$-0.582075\pi$
$409$	−10.3140	−0.509994	−0.254997	+	0.966942i	$0.582075\pi$
$410$	1.80152	0.0889709
$411$	−42.2312	−2.08311
$412$	1.00307	0.0494179
$413$	3.98784	0.196229
$414$	−11.1859	−0.549759
$415$	−64.6245	−3.17229
$416$	−0.685007	−0.0335852
$417$	7.52940	0.368716
$418$	6.87091	0.336067
$419$	24.4795	1.19590	0.597952	−	0.801532i	$-0.295981\pi$
$419$	24.4795	1.19590	0.597952	+	0.801532i	$0.295981\pi$
$420$	−1.23868	−0.0604413
$421$	−39.6956	−1.93465	−0.967323	−	0.253548i	$-0.918403\pi$
$421$	−39.6956	−1.93465	−0.967323	+	0.253548i	$0.918403\pi$
$422$	−29.4569	−1.43394
$423$	−34.2116	−1.66342
$424$	3.44202	0.167159
$425$	3.86689	0.187571
$426$	36.3815	1.76269
$427$	−0.450835	−0.0218175
$428$	−1.94450	−0.0939908
$429$	2.69782	0.130252
$430$	−67.1166	−3.23665
$431$	−35.3752	−1.70396	−0.851981	−	0.523573i	$-0.824599\pi$
$431$	−35.3752	−1.70396	−0.851981	+	0.523573i	$0.824599\pi$
$432$	−12.9066	−0.620969
$433$	20.7040	0.994969	0.497485	−	0.867473i	$-0.334257\pi$
$433$	20.7040	0.994969	0.497485	+	0.867473i	$0.334257\pi$
$434$	−6.85335	−0.328971
$435$	33.2457	1.59401
$436$	−0.826679	−0.0395908
$437$	−9.56220	−0.457422
$438$	−54.5794	−2.60791
$439$	13.0733	0.623957	0.311978	−	0.950089i	$-0.399008\pi$
$439$	13.0733	0.623957	0.311978	+	0.950089i	$0.399008\pi$
$440$	−11.0088	−0.524826
$441$	4.27822	0.203725
$442$	−0.567720	−0.0270037
$443$	−8.12901	−0.386221	−0.193110	−	0.981177i	$-0.561858\pi$
$443$	−8.12901	−0.386221	−0.193110	+	0.981177i	$0.561858\pi$
$444$	2.70695	0.128466
$445$	−47.4406	−2.24890
$446$	−7.93210	−0.375596
$447$	−13.6471	−0.645487
$448$	−8.42445	−0.398018
$449$	36.4247	1.71899	0.859495	−	0.511144i	$-0.170778\pi$
$449$	36.4247	1.71899	0.859495	+	0.511144i	$0.170778\pi$
$450$	−54.7465	−2.58077
$451$	0.347131	0.0163458
$452$	1.57704	0.0741776
$453$	16.1650	0.759498
$454$	−1.65423	−0.0776371
$455$	3.78629	0.177504
$456$	−39.3207	−1.84136
$457$	4.64482	0.217275	0.108638	−	0.994081i	$-0.465351\pi$
$457$	4.64482	0.217275	0.108638	+	0.994081i	$0.465351\pi$
$458$	−1.19812	−0.0559845
$459$	1.42830	0.0666675
$460$	0.875835	0.0408360
$461$	31.0498	1.44613	0.723067	−	0.690778i	$-0.242732\pi$
$461$	31.0498	1.44613	0.723067	+	0.690778i	$0.242732\pi$
$462$	3.69782	0.172038
$463$	−11.9230	−0.554110	−0.277055	−	0.960854i	$-0.589358\pi$
$463$	−11.9230	−0.554110	−0.277055	+	0.960854i	$0.589358\pi$
$464$	12.1815	0.565513
$465$	51.0736	2.36848
$466$	19.4728	0.902062
$467$	−35.9542	−1.66376	−0.831880	−	0.554955i	$-0.812735\pi$
$467$	−35.9542	−1.66376	−0.831880	+	0.554955i	$0.812735\pi$
$468$	−0.518794	−0.0239813
$469$	10.5726	0.488196
$470$	−41.5008	−1.91429
$471$	26.1763	1.20614
$472$	−11.5949	−0.533697
$473$	−12.9325	−0.594638
$474$	54.5577	2.50592
$475$	−46.7995	−2.14731
$476$	0.0502265	0.00230213
$477$	5.06464	0.231894
$478$	−6.60692	−0.302194
$479$	15.6136	0.713406	0.356703	−	0.934218i	$-0.383901\pi$
$479$	15.6136	0.713406	0.356703	+	0.934218i	$0.383901\pi$
$480$	6.99716	0.319375
$481$	−8.27437	−0.377279
$482$	3.32465	0.151434
$483$	−5.14623	−0.234162
$484$	−0.121264	−0.00551200
$485$	33.6213	1.52666
$486$	27.2387	1.23557
$487$	3.52941	0.159933	0.0799664	−	0.996798i	$-0.474519\pi$
$487$	3.52941	0.159933	0.0799664	+	0.996798i	$0.474519\pi$
$488$	1.31083	0.0593384
$489$	41.8011	1.89031
$490$	5.18975	0.234449
$491$	−27.1123	−1.22356	−0.611780	−	0.791028i	$-0.709546\pi$
$491$	−27.1123	−1.22356	−0.611780	+	0.791028i	$0.709546\pi$
$492$	−0.113563	−0.00511983
$493$	−1.34806	−0.0607137
$494$	6.87091	0.309137
$495$	−16.1986	−0.728072
$496$	18.7138	0.840276
$497$	9.83864	0.441324
$498$	−63.1144	−2.82823
$499$	30.8058	1.37906	0.689528	−	0.724259i	$-0.257818\pi$
$499$	30.8058	1.37906	0.689528	+	0.724259i	$0.257818\pi$
$500$	1.99083	0.0890324
$501$	−8.64599	−0.386274
$502$	−5.43169	−0.242428
$503$	30.7215	1.36980	0.684902	−	0.728635i	$-0.259845\pi$
$503$	30.7215	1.36980	0.684902	+	0.728635i	$0.259845\pi$
$504$	−12.4392	−0.554084
$505$	−55.7631	−2.48143
$506$	−2.61463	−0.116234
$507$	2.69782	0.119814
$508$	1.12032	0.0497061
$509$	−40.7476	−1.80611	−0.903053	−	0.429529i	$-0.858680\pi$
$509$	−40.7476	−1.80611	−0.903053	+	0.429529i	$0.858680\pi$
$510$	5.79910	0.256788
$511$	−14.7599	−0.652940
$512$	24.3284	1.07517
$513$	−17.2862	−0.763206
$514$	−10.9831	−0.484443
$515$	31.3195	1.38010
$516$	4.23085	0.186253
$517$	−7.99668	−0.351694
$518$	−11.3414	−0.498314
$519$	16.7263	0.734205
$520$	−11.0088	−0.482769
$521$	−22.6396	−0.991861	−0.495930	−	0.868362i	$-0.665173\pi$
$521$	−22.6396	−0.991861	−0.495930	+	0.868362i	$0.665173\pi$
$522$	19.0856	0.835352
$523$	32.7380	1.43153	0.715767	−	0.698340i	$-0.246077\pi$
$523$	32.7380	1.43153	0.715767	+	0.698340i	$0.246077\pi$
$524$	−0.543761	−0.0237543
$525$	−25.1868	−1.09924
$526$	−19.7741	−0.862191
$527$	−2.07096	−0.0902123
$528$	−10.0973	−0.439429
$529$	−19.3612	−0.841793
$530$	6.14373	0.266866
$531$	−17.0609	−0.740379
$532$	−0.607873	−0.0263547
$533$	0.347131	0.0150359
$534$	−46.3321	−2.00499
$535$	−60.7140	−2.62490
$536$	−30.7403	−1.32778
$537$	19.1008	0.824261
$538$	−10.6106	−0.457458
$539$	1.00000	0.0430730
$540$	1.58331	0.0681346
$541$	16.1649	0.694985	0.347492	−	0.937683i	$-0.387033\pi$
$541$	16.1649	0.694985	0.347492	+	0.937683i	$0.387033\pi$
$542$	39.5190	1.69749
$543$	−48.5031	−2.08147
$544$	−0.283724	−0.0121646
$545$	−25.8118	−1.10566
$546$	3.69782	0.158252
$547$	−18.3782	−0.785794	−0.392897	−	0.919583i	$-0.628527\pi$
$547$	−18.3782	−0.785794	−0.392897	+	0.919583i	$0.628527\pi$
$548$	1.89825	0.0810890
$549$	1.92877	0.0823181
$550$	−12.7966	−0.545647
$551$	16.3151	0.695047
$552$	14.9629	0.636865
$553$	14.7540	0.627405
$554$	−8.77693	−0.372896
$555$	84.5204	3.58769
$556$	−0.338438	−0.0143530
$557$	−4.77622	−0.202375	−0.101187	−	0.994867i	$-0.532264\pi$
$557$	−4.77622	−0.202375	−0.101187	+	0.994867i	$0.532264\pi$
$558$	29.3202	1.24122
$559$	−12.9325	−0.546987
$560$	−14.1712	−0.598842
$561$	1.11741	0.0471772
$562$	−17.8307	−0.752145
$563$	−38.9338	−1.64086	−0.820431	−	0.571745i	$-0.806267\pi$
$563$	−38.9338	−1.64086	−0.820431	+	0.571745i	$0.806267\pi$
$564$	2.61610	0.110158
$565$	49.2406	2.07157
$566$	41.4102	1.74060
$567$	3.53148	0.148308
$568$	−28.6064	−1.20030
$569$	−28.6294	−1.20020	−0.600102	−	0.799923i	$-0.704874\pi$
$569$	−28.6294	−1.20020	−0.600102	+	0.799923i	$0.704874\pi$
$570$	−70.1844	−2.93970
$571$	−29.6805	−1.24209	−0.621045	−	0.783775i	$-0.713292\pi$
$571$	−29.6805	−1.24209	−0.621045	+	0.783775i	$0.713292\pi$
$572$	−0.121264	−0.00507030
$573$	−29.3474	−1.22600
$574$	0.475802	0.0198596
$575$	17.8089	0.742682
$576$	36.0417	1.50174
$577$	−8.51496	−0.354482	−0.177241	−	0.984167i	$-0.556717\pi$
$577$	−8.51496	−0.354482	−0.177241	+	0.984167i	$0.556717\pi$
$578$	23.0662	0.959429
$579$	−57.3103	−2.38173
$580$	−1.49436	−0.0620498
$581$	−17.0680	−0.708101
$582$	32.8357	1.36108
$583$	1.18382	0.0490288
$584$	42.9152	1.77584
$585$	−16.1986	−0.669729
$586$	7.09873	0.293246
$587$	29.3465	1.21126	0.605630	−	0.795746i	$-0.292921\pi$
$587$	29.3465	1.21126	0.605630	+	0.795746i	$0.292921\pi$
$588$	−0.327148	−0.0134914
$589$	25.0641	1.03275
$590$	−20.6959	−0.852038
$591$	12.6329	0.519648
$592$	30.9690	1.27282
$593$	−16.7245	−0.686794	−0.343397	−	0.939190i	$-0.611578\pi$
$593$	−16.7245	−0.686794	−0.343397	+	0.939190i	$0.611578\pi$
$594$	−4.72663	−0.193936
$595$	1.56825	0.0642919
$596$	0.613423	0.0251268
$597$	−5.25020	−0.214876
$598$	−2.61463	−0.106920
$599$	−46.1571	−1.88593	−0.942964	−	0.332894i	$-0.891975\pi$
$599$	−46.1571	−1.88593	−0.942964	+	0.332894i	$0.891975\pi$
$600$	73.2319	2.98968
$601$	9.30579	0.379591	0.189796	−	0.981824i	$-0.439217\pi$
$601$	9.30579	0.379591	0.189796	+	0.981824i	$0.439217\pi$
$602$	−17.7262	−0.722467
$603$	−45.2318	−1.84198
$604$	−0.726600	−0.0295649
$605$	−3.78629	−0.153935
$606$	−54.4601	−2.21229
$607$	17.2482	0.700081	0.350041	−	0.936735i	$-0.386168\pi$
$607$	17.2482	0.700081	0.350041	+	0.936735i	$0.386168\pi$
$608$	3.43381	0.139259
$609$	8.78054	0.355806
$610$	2.33972	0.0947326
$611$	−7.99668	−0.323511
$612$	−0.214880	−0.00868602
$613$	19.2976	0.779423	0.389712	−	0.920937i	$-0.372575\pi$
$613$	19.2976	0.779423	0.389712	+	0.920937i	$0.372575\pi$
$614$	−22.6242	−0.913037
$615$	−3.54584	−0.142982
$616$	−2.90755	−0.117149
$617$	−20.8055	−0.837596	−0.418798	−	0.908079i	$-0.637548\pi$
$617$	−20.8055	−0.837596	−0.418798	+	0.908079i	$0.637548\pi$
$618$	30.5877	1.23042
$619$	−32.4257	−1.30330	−0.651650	−	0.758520i	$-0.725923\pi$
$619$	−32.4257	−1.30330	−0.651650	+	0.758520i	$0.725923\pi$
$620$	−2.29570	−0.0921976
$621$	6.57803	0.263967
$622$	−13.2581	−0.531603
$623$	−12.5296	−0.501987
$624$	−10.0973	−0.404216
$625$	15.4807	0.619226
$626$	11.9605	0.478038
$627$	−13.5237	−0.540083
$628$	−1.17659	−0.0469512
$629$	−3.42718	−0.136650
$630$	−22.2029	−0.884585
$631$	36.5675	1.45573	0.727864	−	0.685721i	$-0.240513\pi$
$631$	36.5675	1.45573	0.727864	+	0.685721i	$0.240513\pi$
$632$	−42.8981	−1.70639
$633$	57.9785	2.30444
$634$	9.75675	0.387490
$635$	34.9803	1.38815
$636$	−0.387284	−0.0153568
$637$	1.00000	0.0396214
$638$	4.46110	0.176617
$639$	−42.0919	−1.66513
$640$	38.5336	1.52317
$641$	47.1457	1.86214	0.931071	−	0.364837i	$-0.118875\pi$
$641$	47.1457	1.86214	0.931071	+	0.364837i	$0.118875\pi$
$642$	−59.2954	−2.34020
$643$	−10.9998	−0.433790	−0.216895	−	0.976195i	$-0.569593\pi$
$643$	−10.9998	−0.433790	−0.216895	+	0.976195i	$0.569593\pi$
$644$	0.231317	0.00911519
$645$	132.102	5.20151
$646$	2.84587	0.111969
$647$	39.6249	1.55782	0.778908	−	0.627138i	$-0.215774\pi$
$647$	39.6249	1.55782	0.778908	+	0.627138i	$0.215774\pi$
$648$	−10.2680	−0.403364
$649$	−3.98784	−0.156537
$650$	−12.7966	−0.501922
$651$	13.4891	0.528679
$652$	−1.87891	−0.0735840
$653$	−25.4626	−0.996430	−0.498215	−	0.867054i	$-0.666011\pi$
$653$	−25.4626	−0.996430	−0.498215	+	0.867054i	$0.666011\pi$
$654$	−25.2087	−0.985739
$655$	−16.9781	−0.663390
$656$	−1.29923	−0.0507264
$657$	63.1462	2.46357
$658$	−10.9608	−0.427297
$659$	16.7732	0.653391	0.326695	−	0.945130i	$-0.394065\pi$
$659$	16.7732	0.653391	0.326695	+	0.945130i	$0.394065\pi$
$660$	1.23868	0.0482155
$661$	10.2041	0.396894	0.198447	−	0.980112i	$-0.436410\pi$
$661$	10.2041	0.396894	0.198447	+	0.980112i	$0.436410\pi$
$662$	2.88951	0.112304
$663$	1.11741	0.0433967
$664$	49.6262	1.92587
$665$	−18.9799	−0.736011
$666$	48.5212	1.88016
$667$	−6.20848	−0.240393
$668$	0.388628	0.0150365
$669$	15.6123	0.603608
$670$	−54.8691	−2.11978
$671$	0.450835	0.0174043
$672$	1.84803	0.0712891
$673$	−31.1252	−1.19979	−0.599894	−	0.800079i	$-0.704791\pi$
$673$	−31.1252	−1.19979	−0.599894	+	0.800079i	$0.704791\pi$
$674$	−5.12376	−0.197360
$675$	32.1943	1.23916
$676$	−0.121264	−0.00466400
$677$	−2.61795	−0.100616	−0.0503079	−	0.998734i	$-0.516020\pi$
$677$	−2.61795	−0.100616	−0.0503079	+	0.998734i	$0.516020\pi$
$678$	48.0901	1.84689
$679$	8.87974	0.340773
$680$	−4.55977	−0.174859
$681$	3.25594	0.124768
$682$	6.85335	0.262428
$683$	28.9215	1.10665	0.553326	−	0.832965i	$-0.313359\pi$
$683$	28.9215	1.10665	0.553326	+	0.832965i	$0.313359\pi$
$684$	2.60062	0.0994371
$685$	59.2699	2.26459
$686$	1.37067	0.0523324
$687$	2.35820	0.0899709
$688$	48.4034	1.84536
$689$	1.18382	0.0450999
$690$	26.7077	1.01674
$691$	−25.4655	−0.968753	−0.484376	−	0.874860i	$-0.660953\pi$
$691$	−25.4655	−0.968753	−0.484376	+	0.874860i	$0.660953\pi$
$692$	−0.751831	−0.0285803
$693$	−4.27822	−0.162516
$694$	28.1087	1.06699
$695$	−10.5672	−0.400838
$696$	−25.5299	−0.967708
$697$	0.143779	0.00544600
$698$	−12.7277	−0.481751
$699$	−38.3274	−1.44968
$700$	1.13212	0.0427901
$701$	5.35852	0.202388	0.101194	−	0.994867i	$-0.467734\pi$
$701$	5.35852	0.202388	0.101194	+	0.994867i	$0.467734\pi$
$702$	−4.72663	−0.178395
$703$	41.4779	1.56437
$704$	8.42445	0.317509
$705$	81.6838	3.07639
$706$	−24.9820	−0.940209
$707$	−14.7276	−0.553890
$708$	1.30462	0.0490305
$709$	−21.2505	−0.798080	−0.399040	−	0.916933i	$-0.630657\pi$
$709$	−21.2505	−0.798080	−0.399040	+	0.916933i	$0.630657\pi$
$710$	−51.0601	−1.91625
$711$	−63.1210	−2.36722
$712$	36.4304	1.36529
$713$	−9.53776	−0.357192
$714$	1.53161	0.0573189
$715$	−3.78629	−0.141599
$716$	−0.858561	−0.0320859
$717$	13.0041	0.485646
$718$	−0.147193	−0.00549318
$719$	−42.1816	−1.57311	−0.786554	−	0.617521i	$-0.788137\pi$
$719$	−42.1816	−1.57311	−0.786554	+	0.617521i	$0.788137\pi$
$720$	60.6275	2.25945
$721$	8.27182	0.308059
$722$	−8.39984	−0.312610
$723$	−6.54373	−0.243364
$724$	2.18016	0.0810251
$725$	−30.3857	−1.12850
$726$	−3.69782	−0.137239
$727$	−38.6270	−1.43260	−0.716298	−	0.697795i	$-0.754165\pi$
$727$	−38.6270	−1.43260	−0.716298	+	0.697795i	$0.754165\pi$
$728$	−2.90755	−0.107761
$729$	−43.0180	−1.59326
$730$	76.6003	2.83510
$731$	−5.35654	−0.198119
$732$	−0.147490	−0.00545139
$733$	5.43963	0.200917	0.100459	−	0.994941i	$-0.467969\pi$
$733$	5.43963	0.200917	0.100459	+	0.994941i	$0.467969\pi$
$734$	−12.9445	−0.477789
$735$	−10.2147	−0.376776
$736$	−1.30669	−0.0481651
$737$	−10.5726	−0.389446
$738$	−2.03559	−0.0749309
$739$	−29.0722	−1.06944	−0.534719	−	0.845030i	$-0.679583\pi$
$739$	−29.0722	−1.06944	−0.534719	+	0.845030i	$0.679583\pi$
$740$	−3.79910	−0.139658
$741$	−13.5237	−0.496804
$742$	1.62263	0.0595684
$743$	48.0629	1.76326	0.881629	−	0.471943i	$-0.156447\pi$
$743$	48.0629	1.76326	0.881629	+	0.471943i	$0.156447\pi$
$744$	−39.2202	−1.43788
$745$	19.1532	0.701720
$746$	−33.2180	−1.21620
$747$	73.0208	2.67169
$748$	−0.0502265	−0.00183646
$749$	−16.0352	−0.585914
$750$	60.7081	2.21675
$751$	−31.6230	−1.15394	−0.576970	−	0.816765i	$-0.695765\pi$
$751$	−31.6230	−1.15394	−0.576970	+	0.816765i	$0.695765\pi$
$752$	29.9297	1.09142
$753$	10.6909	0.389598
$754$	4.46110	0.162464
$755$	−22.6870	−0.825664
$756$	0.418168	0.0152086
$757$	6.45666	0.234671	0.117336	−	0.993092i	$-0.462565\pi$
$757$	6.45666	0.234671	0.117336	+	0.993092i	$0.462565\pi$
$758$	−39.8640	−1.44792
$759$	5.14623	0.186796
$760$	55.1852	2.00178
$761$	7.19805	0.260929	0.130465	−	0.991453i	$-0.458353\pi$
$761$	7.19805	0.260929	0.130465	+	0.991453i	$0.458353\pi$
$762$	34.1629	1.23759
$763$	−6.81719	−0.246799
$764$	1.31913	0.0477245
$765$	−6.70932	−0.242576
$766$	35.0960	1.26807
$767$	−3.98784	−0.143993
$768$	−7.82211	−0.282256
$769$	−14.6589	−0.528612	−0.264306	−	0.964439i	$-0.585143\pi$
$769$	−14.6589	−0.528612	−0.264306	+	0.964439i	$0.585143\pi$
$770$	−5.18975	−0.187026
$771$	21.6174	0.778533
$772$	2.57603	0.0927135
$773$	50.5119	1.81679	0.908393	−	0.418118i	$-0.137310\pi$
$773$	50.5119	1.81679	0.908393	+	0.418118i	$0.137310\pi$
$774$	75.8367	2.72589
$775$	−46.6799	−1.67679
$776$	−25.8183	−0.926824
$777$	22.3228	0.800824
$778$	11.4520	0.410573
$779$	−1.74010	−0.0623456
$780$	1.23868	0.0443518
$781$	−9.83864	−0.352054
$782$	−1.08296	−0.0387264
$783$	−11.2235	−0.401095
$784$	−3.74277	−0.133670
$785$	−36.7374	−1.31122
$786$	−16.5814	−0.591439
$787$	5.81864	0.207412	0.103706	−	0.994608i	$-0.466930\pi$
$787$	5.81864	0.207412	0.103706	+	0.994608i	$0.466930\pi$
$788$	−0.567835	−0.0202283
$789$	38.9203	1.38560
$790$	−76.5697	−2.72423
$791$	13.0050	0.462404
$792$	12.4392	0.442006
$793$	0.450835	0.0160096
$794$	−47.5659	−1.68805
$795$	−12.0924	−0.428872
$796$	0.235991	0.00836447
$797$	−14.3946	−0.509882	−0.254941	−	0.966957i	$-0.582056\pi$
$797$	−14.3946	−0.509882	−0.254941	+	0.966957i	$0.582056\pi$
$798$	−18.5365	−0.656184
$799$	−3.31216	−0.117176
$800$	−6.39522	−0.226105
$801$	53.6044	1.89402
$802$	−44.3776	−1.56703
$803$	14.7599	0.520866
$804$	3.45880	0.121982
$805$	7.22255	0.254561
$806$	6.85335	0.241399
$807$	20.8844	0.735165
$808$	42.8214	1.50645
$809$	1.35504	0.0476406	0.0238203	−	0.999716i	$-0.492417\pi$
$809$	1.35504	0.0476406	0.0238203	+	0.999716i	$0.492417\pi$
$810$	−18.3275	−0.643963
$811$	−3.19639	−0.112241	−0.0561203	−	0.998424i	$-0.517873\pi$
$811$	−3.19639	−0.112241	−0.0561203	+	0.998424i	$0.517873\pi$
$812$	−0.394676	−0.0138504
$813$	−77.7832	−2.72798
$814$	11.3414	0.397517
$815$	−58.6663	−2.05499
$816$	−4.18222	−0.146407
$817$	64.8283	2.26805
$818$	14.1371	0.494292
$819$	−4.27822	−0.149493
$820$	0.159382	0.00556585
$821$	10.4495	0.364692	0.182346	−	0.983234i	$-0.441631\pi$
$821$	10.4495	0.364692	0.182346	+	0.983234i	$0.441631\pi$
$822$	57.8850	2.01897
$823$	−43.8490	−1.52848	−0.764240	−	0.644932i	$-0.776885\pi$
$823$	−43.8490	−1.52848	−0.764240	+	0.644932i	$0.776885\pi$
$824$	−24.0508	−0.837848
$825$	25.1868	0.876891
$826$	−5.46602	−0.190187
$827$	36.3525	1.26410	0.632050	−	0.774927i	$-0.282214\pi$
$827$	36.3525	1.26410	0.632050	+	0.774927i	$0.282214\pi$
$828$	−0.989628	−0.0343919
$829$	−15.4149	−0.535383	−0.267691	−	0.963505i	$-0.586261\pi$
$829$	−15.4149	−0.535383	−0.267691	+	0.963505i	$0.586261\pi$
$830$	88.5788	3.07461
$831$	17.2752	0.599269
$832$	8.42445	0.292065
$833$	0.414192	0.0143509
$834$	−10.3203	−0.357363
$835$	12.1343	0.419926
$836$	0.607873	0.0210237
$837$	−17.2421	−0.595973
$838$	−33.5534	−1.15908
$839$	−43.2075	−1.49169	−0.745845	−	0.666120i	$-0.767954\pi$
$839$	−43.2075	−1.49169	−0.745845	+	0.666120i	$0.767954\pi$
$840$	29.6998	1.02474
$841$	−18.4070	−0.634725
$842$	54.4096	1.87508
$843$	35.0953	1.20875
$844$	−2.60607	−0.0897046
$845$	−3.78629	−0.130252
$846$	46.8928	1.61221
$847$	−1.00000	−0.0343604
$848$	−4.43076	−0.152153
$849$	−81.5055	−2.79726
$850$	−5.30022	−0.181796
$851$	−15.7838	−0.541062
$852$	3.21870	0.110271
$853$	−12.8284	−0.439237	−0.219619	−	0.975586i	$-0.570481\pi$
$853$	−12.8284	−0.439237	−0.219619	+	0.975586i	$0.570481\pi$
$854$	0.617946	0.0211457
$855$	81.2004	2.77700
$856$	46.6233	1.59355
$857$	41.9686	1.43362	0.716811	−	0.697268i	$-0.245601\pi$
$857$	41.9686	1.43362	0.716811	+	0.697268i	$0.245601\pi$
$858$	−3.69782	−0.126241
$859$	9.78348	0.333808	0.166904	−	0.985973i	$-0.446623\pi$
$859$	9.78348	0.333808	0.166904	+	0.985973i	$0.446623\pi$
$860$	−5.93784	−0.202479
$861$	−0.936496	−0.0319157
$862$	48.4877	1.65150
$863$	36.8325	1.25379	0.626897	−	0.779102i	$-0.284325\pi$
$863$	36.8325	1.25379	0.626897	+	0.779102i	$0.284325\pi$
$864$	−2.36219	−0.0803633
$865$	−23.4748	−0.798167
$866$	−28.3783	−0.964334
$867$	−45.4001	−1.54187
$868$	−0.606320	−0.0205798
$869$	−14.7540	−0.500496
$870$	−45.5688	−1.54493
$871$	−10.5726	−0.358238
$872$	19.8213	0.671235
$873$	−37.9895	−1.28575
$874$	13.1066	0.443338
$875$	16.4173	0.555005
$876$	−4.82868	−0.163146
$877$	29.9082	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$877$	29.9082	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$878$	−17.9192	−0.604745
$879$	−13.9721	−0.471266
$880$	14.1712	0.477711
$881$	−17.2886	−0.582466	−0.291233	−	0.956652i	$-0.594066\pi$
$881$	−17.2886	−0.582466	−0.291233	+	0.956652i	$0.594066\pi$
$882$	−5.86403	−0.197452
$883$	−19.2080	−0.646400	−0.323200	−	0.946331i	$-0.604759\pi$
$883$	−19.2080	−0.646400	−0.323200	+	0.946331i	$0.604759\pi$
$884$	−0.0502265	−0.00168930
$885$	40.7347	1.36928
$886$	11.1422	0.374329
$887$	−42.7841	−1.43655	−0.718275	−	0.695759i	$-0.755068\pi$
$887$	−42.7841	−1.43655	−0.718275	+	0.695759i	$0.755068\pi$
$888$	−64.9046	−2.17805
$889$	9.23868	0.309855
$890$	65.0254	2.17966
$891$	−3.53148	−0.118309
$892$	−0.701758	−0.0234966
$893$	40.0858	1.34142
$894$	18.7057	0.625612
$895$	−26.8073	−0.896069
$896$	10.1771	0.339994
$897$	5.14623	0.171828
$898$	−49.9263	−1.66606
$899$	16.2734	0.542749
$900$	−4.84346	−0.161449
$901$	0.490328	0.0163352
$902$	−0.475802	−0.0158425
$903$	34.8896	1.16105
$904$	−37.8127	−1.25763
$905$	68.0724	2.26280
$906$	−22.1569	−0.736114
$907$	54.3168	1.80356	0.901779	−	0.432197i	$-0.142261\pi$
$907$	54.3168	1.80356	0.901779	+	0.432197i	$0.142261\pi$
$908$	−0.146351	−0.00485683
$909$	63.0081	2.08985
$910$	−5.18975	−0.172039
$911$	−16.5393	−0.547971	−0.273986	−	0.961734i	$-0.588342\pi$
$911$	−16.5393	−0.547971	−0.273986	+	0.961734i	$0.588342\pi$
$912$	50.6159	1.67606
$913$	17.0680	0.564869
$914$	−6.36651	−0.210586
$915$	−4.60516	−0.152242
$916$	−0.105999	−0.00350229
$917$	−4.48411	−0.148078
$918$	−1.95773	−0.0646148
$919$	−25.0863	−0.827519	−0.413760	−	0.910386i	$-0.635785\pi$
$919$	−25.0863	−0.827519	−0.413760	+	0.910386i	$0.635785\pi$
$920$	−20.9999	−0.692347
$921$	44.5300	1.46731
$922$	−42.5590	−1.40161
$923$	−9.83864	−0.323843
$924$	0.327148	0.0107624
$925$	−77.2494	−2.53994
$926$	16.3425	0.537049
$927$	−35.3887	−1.16232
$928$	2.22948	0.0731863
$929$	−53.8463	−1.76664	−0.883319	−	0.468772i	$-0.844697\pi$
$929$	−53.8463	−1.76664	−0.883319	+	0.468772i	$0.844697\pi$
$930$	−70.0050	−2.29556
$931$	−5.01281	−0.164288
$932$	1.72277	0.0564314
$933$	26.0953	0.854321
$934$	49.2813	1.61253
$935$	−1.56825	−0.0512872
$936$	12.4392	0.406587
$937$	28.3993	0.927763	0.463882	−	0.885897i	$-0.346456\pi$
$937$	28.3993	0.927763	0.463882	+	0.885897i	$0.346456\pi$
$938$	−14.4915	−0.473165
$939$	−23.5412	−0.768239
$940$	−3.67160	−0.119754
$941$	0.933696	0.0304376	0.0152188	−	0.999884i	$-0.495156\pi$
$941$	0.933696	0.0304376	0.0152188	+	0.999884i	$0.495156\pi$
$942$	−35.8790	−1.16900
$943$	0.662170	0.0215632
$944$	14.9256	0.485786
$945$	13.0567	0.424734
$946$	17.7262	0.576329
$947$	4.91998	0.159878	0.0799390	−	0.996800i	$-0.474527\pi$
$947$	4.91998	0.159878	0.0799390	+	0.996800i	$0.474527\pi$
$948$	4.82675	0.156766
$949$	14.7599	0.479127
$950$	64.1467	2.08119
$951$	−19.2037	−0.622723
$952$	−1.20428	−0.0390311
$953$	−26.5012	−0.858458	−0.429229	−	0.903196i	$-0.641215\pi$
$953$	−26.5012	−0.858458	−0.429229	+	0.903196i	$0.641215\pi$
$954$	−6.94195	−0.224754
$955$	41.1880	1.33281
$956$	−0.584519	−0.0189047
$957$	−8.78054	−0.283835
$958$	−21.4012	−0.691440
$959$	15.6538	0.505489
$960$	−86.0534	−2.77736
$961$	−6.00000	−0.193548
$962$	11.3414	0.365662
$963$	68.6023	2.21068
$964$	0.294134	0.00947341
$965$	80.4329	2.58923
$966$	7.05378	0.226952
$967$	−31.9403	−1.02713	−0.513565	−	0.858051i	$-0.671675\pi$
$967$	−31.9403	−1.02713	−0.513565	+	0.858051i	$0.671675\pi$
$968$	2.90755	0.0934523
$969$	−5.60138	−0.179942
$970$	−46.0837	−1.47966
$971$	−32.6593	−1.04809	−0.524043	−	0.851692i	$-0.675577\pi$
$971$	−32.6593	−1.04809	−0.524043	+	0.851692i	$0.675577\pi$
$972$	2.40982	0.0772951
$973$	−2.79092	−0.0894728
$974$	−4.83765	−0.155008
$975$	25.1868	0.806623
$976$	−1.68737	−0.0540115
$977$	30.5877	0.978586	0.489293	−	0.872119i	$-0.337255\pi$
$977$	30.5877	0.978586	0.489293	+	0.872119i	$0.337255\pi$
$978$	−57.2955	−1.83211
$979$	12.5296	0.400447
$980$	0.459141	0.0146667
$981$	29.1654	0.931181
$982$	37.1620	1.18589
$983$	33.1014	1.05577	0.527886	−	0.849315i	$-0.322985\pi$
$983$	33.1014	1.05577	0.527886	+	0.849315i	$0.322985\pi$
$984$	2.72291	0.0868032
$985$	−17.7298	−0.564919
$986$	1.84775	0.0588443
$987$	21.5736	0.686695
$988$	0.607873	0.0193390
$989$	−24.6695	−0.784443
$990$	22.2029	0.705655
$991$	19.8529	0.630649	0.315325	−	0.948984i	$-0.397887\pi$
$991$	19.8529	0.630649	0.315325	+	0.948984i	$0.397887\pi$
$992$	3.42504	0.108745
$993$	−5.68727	−0.180480
$994$	−13.4855	−0.427735
$995$	7.36846	0.233596
$996$	−5.58377	−0.176929
$997$	−26.8793	−0.851277	−0.425639	−	0.904893i	$-0.639951\pi$
$997$	−26.8793	−0.851277	−0.425639	+	0.904893i	$0.639951\pi$
$998$	−42.2246	−1.33660
$999$	−28.5334	−0.902758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.a.j.1.2	✓	5
3.2	odd	2		9009.2.a.bb.1.4		5
7.6	odd	2		7007.2.a.o.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.j.1.2	✓	5	1.1	even	1	trivial
7007.2.a.o.1.2		5	7.6	odd	2
9009.2.a.bb.1.4		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.37067 q^{2} +2.69782 q^{3} -0.121264 q^{4} -3.78629 q^{5} -3.69782 q^{6} -1.00000 q^{7} +2.90755 q^{8} +4.27822 q^{9} +O(q^{10})\)	\(q-1.37067 q^{2} +2.69782 q^{3} -0.121264 q^{4} -3.78629 q^{5} -3.69782 q^{6} -1.00000 q^{7} +2.90755 q^{8} +4.27822 q^{9} +5.18975 q^{10} +1.00000 q^{11} -0.327148 q^{12} +1.00000 q^{13} +1.37067 q^{14} -10.2147 q^{15} -3.74277 q^{16} +0.414192 q^{17} -5.86403 q^{18} -5.01281 q^{19} +0.459141 q^{20} -2.69782 q^{21} -1.37067 q^{22} +1.90755 q^{23} +7.84405 q^{24} +9.33598 q^{25} -1.37067 q^{26} +3.44841 q^{27} +0.121264 q^{28} -3.25468 q^{29} +14.0010 q^{30} -5.00000 q^{31} -0.685007 q^{32} +2.69782 q^{33} -0.567720 q^{34} +3.78629 q^{35} -0.518794 q^{36} -8.27437 q^{37} +6.87091 q^{38} +2.69782 q^{39} -11.0088 q^{40} +0.347131 q^{41} +3.69782 q^{42} -12.9325 q^{43} -0.121264 q^{44} -16.1986 q^{45} -2.61463 q^{46} -7.99668 q^{47} -10.0973 q^{48} +1.00000 q^{49} -12.7966 q^{50} +1.11741 q^{51} -0.121264 q^{52} +1.18382 q^{53} -4.72663 q^{54} -3.78629 q^{55} -2.90755 q^{56} -13.5237 q^{57} +4.46110 q^{58} -3.98784 q^{59} +1.23868 q^{60} +0.450835 q^{61} +6.85335 q^{62} -4.27822 q^{63} +8.42445 q^{64} -3.78629 q^{65} -3.69782 q^{66} -10.5726 q^{67} -0.0502265 q^{68} +5.14623 q^{69} -5.18975 q^{70} -9.83864 q^{71} +12.4392 q^{72} +14.7599 q^{73} +11.3414 q^{74} +25.1868 q^{75} +0.607873 q^{76} -1.00000 q^{77} -3.69782 q^{78} -14.7540 q^{79} +14.1712 q^{80} -3.53148 q^{81} -0.475802 q^{82} +17.0680 q^{83} +0.327148 q^{84} -1.56825 q^{85} +17.7262 q^{86} -8.78054 q^{87} +2.90755 q^{88} +12.5296 q^{89} +22.2029 q^{90} -1.00000 q^{91} -0.231317 q^{92} -13.4891 q^{93} +10.9608 q^{94} +18.9799 q^{95} -1.84803 q^{96} -8.87974 q^{97} -1.37067 q^{98} +4.27822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^7 - 3 * q^8 - q^9	\( 5 q - 2 q^{2} + 2 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{7} - 3 q^{8} - q^{9} + 5 q^{10} + 5 q^{11} + 7 q^{12} + 5 q^{13} + 2 q^{14} - 8 q^{15} + q^{17} - 8 q^{18} - 7 q^{19} - 4 q^{20} - 2 q^{22} - 8 q^{23} + q^{24} + q^{25} - 2 q^{26} + 6 q^{27} - 2 q^{28} - 7 q^{29} + 12 q^{30} - 25 q^{31} - 8 q^{32} - 29 q^{34} + 4 q^{35} - 15 q^{36} - 17 q^{37} + 16 q^{38} - 18 q^{40} + 10 q^{41} + 5 q^{42} - 25 q^{43} + 2 q^{44} - 23 q^{45} + 6 q^{46} - 7 q^{47} - 12 q^{48} + 5 q^{49} - 3 q^{50} + q^{51} + 2 q^{52} + 6 q^{53} + 10 q^{54} - 4 q^{55} + 3 q^{56} - 24 q^{57} - 24 q^{58} - 24 q^{59} - q^{60} + 2 q^{61} + 10 q^{62} + q^{63} - 5 q^{64} - 4 q^{65} - 5 q^{66} - 23 q^{67} + 12 q^{68} + q^{69} - 5 q^{70} - q^{71} + 39 q^{72} + 12 q^{73} + 23 q^{74} + 28 q^{75} - 2 q^{76} - 5 q^{77} - 5 q^{78} - 29 q^{79} + 24 q^{80} + 5 q^{81} + 20 q^{82} + 16 q^{83} - 7 q^{84} - 3 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 2 q^{89} + 28 q^{90} - 5 q^{91} - 24 q^{92} + 26 q^{94} - 15 q^{95} + 10 q^{96} + 11 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^7 - 3 * q^8 - q^9 + 5 * q^10 + 5 * q^11 + 7 * q^12 + 5 * q^13 + 2 * q^14 - 8 * q^15 + q^17 - 8 * q^18 - 7 * q^19 - 4 * q^20 - 2 * q^22 - 8 * q^23 + q^24 + q^25 - 2 * q^26 + 6 * q^27 - 2 * q^28 - 7 * q^29 + 12 * q^30 - 25 * q^31 - 8 * q^32 - 29 * q^34 + 4 * q^35 - 15 * q^36 - 17 * q^37 + 16 * q^38 - 18 * q^40 + 10 * q^41 + 5 * q^42 - 25 * q^43 + 2 * q^44 - 23 * q^45 + 6 * q^46 - 7 * q^47 - 12 * q^48 + 5 * q^49 - 3 * q^50 + q^51 + 2 * q^52 + 6 * q^53 + 10 * q^54 - 4 * q^55 + 3 * q^56 - 24 * q^57 - 24 * q^58 - 24 * q^59 - q^60 + 2 * q^61 + 10 * q^62 + q^63 - 5 * q^64 - 4 * q^65 - 5 * q^66 - 23 * q^67 + 12 * q^68 + q^69 - 5 * q^70 - q^71 + 39 * q^72 + 12 * q^73 + 23 * q^74 + 28 * q^75 - 2 * q^76 - 5 * q^77 - 5 * q^78 - 29 * q^79 + 24 * q^80 + 5 * q^81 + 20 * q^82 + 16 * q^83 - 7 * q^84 - 3 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 2 * q^89 + 28 * q^90 - 5 * q^91 - 24 * q^92 + 26 * q^94 - 15 * q^95 + 10 * q^96 + 11 * q^97 - 2 * q^98 - q^99

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