LMFDB - Embedded newform 8021.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79876 q^{2} -0.249621 q^{3} +5.83306 q^{4} +3.64528 q^{5} +0.698630 q^{6} +4.03852 q^{7} -10.7278 q^{8} -2.93769 q^{9} +O(q^{10})$	\(q-2.79876 q^{2} -0.249621 q^{3} +5.83306 q^{4} +3.64528 q^{5} +0.698630 q^{6} +4.03852 q^{7} -10.7278 q^{8} -2.93769 q^{9} -10.2023 q^{10} +5.65127 q^{11} -1.45606 q^{12} -1.00000 q^{13} -11.3028 q^{14} -0.909939 q^{15} +18.3585 q^{16} -2.53774 q^{17} +8.22189 q^{18} -4.75078 q^{19} +21.2631 q^{20} -1.00810 q^{21} -15.8165 q^{22} +8.67970 q^{23} +2.67789 q^{24} +8.28807 q^{25} +2.79876 q^{26} +1.48217 q^{27} +23.5569 q^{28} -6.52502 q^{29} +2.54670 q^{30} +9.29112 q^{31} -29.9253 q^{32} -1.41068 q^{33} +7.10254 q^{34} +14.7215 q^{35} -17.1357 q^{36} +3.91548 q^{37} +13.2963 q^{38} +0.249621 q^{39} -39.1059 q^{40} +6.76145 q^{41} +2.82143 q^{42} +4.27390 q^{43} +32.9642 q^{44} -10.7087 q^{45} -24.2924 q^{46} -6.37029 q^{47} -4.58266 q^{48} +9.30961 q^{49} -23.1963 q^{50} +0.633475 q^{51} -5.83306 q^{52} +8.64643 q^{53} -4.14825 q^{54} +20.6005 q^{55} -43.3245 q^{56} +1.18590 q^{57} +18.2620 q^{58} +2.89874 q^{59} -5.30773 q^{60} +8.42402 q^{61} -26.0036 q^{62} -11.8639 q^{63} +47.0369 q^{64} -3.64528 q^{65} +3.94815 q^{66} -6.22816 q^{67} -14.8028 q^{68} -2.16664 q^{69} -41.2020 q^{70} -3.84065 q^{71} +31.5150 q^{72} +1.53058 q^{73} -10.9585 q^{74} -2.06888 q^{75} -27.7116 q^{76} +22.8227 q^{77} -0.698630 q^{78} -5.14278 q^{79} +66.9218 q^{80} +8.44309 q^{81} -18.9237 q^{82} -14.7599 q^{83} -5.88030 q^{84} -9.25079 q^{85} -11.9616 q^{86} +1.62878 q^{87} -60.6258 q^{88} -3.27533 q^{89} +29.9711 q^{90} -4.03852 q^{91} +50.6292 q^{92} -2.31926 q^{93} +17.8289 q^{94} -17.3179 q^{95} +7.47000 q^{96} -4.10223 q^{97} -26.0554 q^{98} -16.6017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.79876	−1.97902	−0.989511	−	0.144456i	$-0.953857\pi$
$2$	−2.79876	−1.97902	−0.989511	+	0.144456i	$0.953857\pi$
$3$	−0.249621	−0.144119	−0.0720594	−	0.997400i	$-0.522957\pi$
$3$	−0.249621	−0.144119	−0.0720594	+	0.997400i	$0.522957\pi$
$4$	5.83306	2.91653
$5$	3.64528	1.63022	0.815110	−	0.579307i	$-0.196677\pi$
$5$	3.64528	1.63022	0.815110	+	0.579307i	$0.196677\pi$
$6$	0.698630	0.285215
$7$	4.03852	1.52642	0.763208	−	0.646153i	$-0.223623\pi$
$7$	4.03852	1.52642	0.763208	+	0.646153i	$0.223623\pi$
$8$	−10.7278	−3.79286
$9$	−2.93769	−0.979230
$10$	−10.2023	−3.22624
$11$	5.65127	1.70392	0.851961	−	0.523605i	$-0.175413\pi$
$11$	5.65127	1.70392	0.851961	+	0.523605i	$0.175413\pi$
$12$	−1.45606	−0.420327
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−11.3028	−3.02081
$15$	−0.909939	−0.234945
$16$	18.3585	4.58962
$17$	−2.53774	−0.615493	−0.307747	−	0.951468i	$-0.599575\pi$
$17$	−2.53774	−0.615493	−0.307747	+	0.951468i	$0.599575\pi$
$18$	8.22189	1.93792
$19$	−4.75078	−1.08990	−0.544952	−	0.838467i	$-0.683452\pi$
$19$	−4.75078	−1.08990	−0.544952	+	0.838467i	$0.683452\pi$
$20$	21.2631	4.75458
$21$	−1.00810	−0.219985
$22$	−15.8165	−3.37210
$23$	8.67970	1.80984	0.904922	−	0.425578i	$-0.139929\pi$
$23$	8.67970	1.80984	0.904922	+	0.425578i	$0.139929\pi$
$24$	2.67789	0.546622
$25$	8.28807	1.65761
$26$	2.79876	0.548882
$27$	1.48217	0.285244
$28$	23.5569	4.45184
$29$	−6.52502	−1.21167	−0.605833	−	0.795592i	$-0.707160\pi$
$29$	−6.52502	−1.21167	−0.605833	+	0.795592i	$0.707160\pi$
$30$	2.54670	0.464962
$31$	9.29112	1.66873	0.834367	−	0.551209i	$-0.185833\pi$
$31$	9.29112	1.66873	0.834367	+	0.551209i	$0.185833\pi$
$32$	−29.9253	−5.29010
$33$	−1.41068	−0.245567
$34$	7.10254	1.21808
$35$	14.7215	2.48839
$36$	−17.1357	−2.85595
$37$	3.91548	0.643700	0.321850	−	0.946791i	$-0.395695\pi$
$37$	3.91548	0.643700	0.321850	+	0.946791i	$0.395695\pi$
$38$	13.2963	2.15694
$39$	0.249621	0.0399714
$40$	−39.1059	−6.18319
$41$	6.76145	1.05596	0.527981	−	0.849256i	$-0.322949\pi$
$41$	6.76145	1.05596	0.527981	+	0.849256i	$0.322949\pi$
$42$	2.82143	0.435356
$43$	4.27390	0.651763	0.325882	−	0.945411i	$-0.394339\pi$
$43$	4.27390	0.651763	0.325882	+	0.945411i	$0.394339\pi$
$44$	32.9642	4.96954
$45$	−10.7087	−1.59636
$46$	−24.2924	−3.58172
$47$	−6.37029	−0.929202	−0.464601	−	0.885520i	$-0.653802\pi$
$47$	−6.37029	−0.929202	−0.464601	+	0.885520i	$0.653802\pi$
$48$	−4.58266	−0.661451
$49$	9.30961	1.32994
$50$	−23.1963	−3.28046
$51$	0.633475	0.0887042
$52$	−5.83306	−0.808900
$53$	8.64643	1.18768	0.593840	−	0.804583i	$-0.297611\pi$
$53$	8.64643	1.18768	0.593840	+	0.804583i	$0.297611\pi$
$54$	−4.14825	−0.564505
$55$	20.6005	2.77777
$56$	−43.3245	−5.78948
$57$	1.18590	0.157076
$58$	18.2620	2.39791
$59$	2.89874	0.377384	0.188692	−	0.982036i	$-0.439575\pi$
$59$	2.89874	0.377384	0.188692	+	0.982036i	$0.439575\pi$
$60$	−5.30773	−0.685225
$61$	8.42402	1.07858	0.539292	−	0.842119i	$-0.318692\pi$
$61$	8.42402	1.07858	0.539292	+	0.842119i	$0.318692\pi$
$62$	−26.0036	−3.30246
$63$	−11.8639	−1.49471
$64$	47.0369	5.87961
$65$	−3.64528	−0.452141
$66$	3.94815	0.485983
$67$	−6.22816	−0.760891	−0.380445	−	0.924803i	$-0.624229\pi$
$67$	−6.22816	−0.760891	−0.380445	+	0.924803i	$0.624229\pi$
$68$	−14.8028	−1.79511
$69$	−2.16664	−0.260833
$70$	−41.2020	−4.92458
$71$	−3.84065	−0.455802	−0.227901	−	0.973684i	$-0.573186\pi$
$71$	−3.84065	−0.455802	−0.227901	+	0.973684i	$0.573186\pi$
$72$	31.5150	3.71408
$73$	1.53058	0.179141	0.0895703	−	0.995981i	$-0.471451\pi$
$73$	1.53058	0.179141	0.0895703	+	0.995981i	$0.471451\pi$
$74$	−10.9585	−1.27390
$75$	−2.06888	−0.238894
$76$	−27.7116	−3.17874
$77$	22.8227	2.60089
$78$	−0.698630	−0.0791043
$79$	−5.14278	−0.578608	−0.289304	−	0.957237i	$-0.593424\pi$
$79$	−5.14278	−0.578608	−0.289304	+	0.957237i	$0.593424\pi$
$80$	66.9218	7.48208
$81$	8.44309	0.938121
$82$	−18.9237	−2.08977
$83$	−14.7599	−1.62011	−0.810055	−	0.586354i	$-0.800563\pi$
$83$	−14.7599	−1.62011	−0.810055	+	0.586354i	$0.800563\pi$
$84$	−5.88030	−0.641594
$85$	−9.25079	−1.00339
$86$	−11.9616	−1.28985
$87$	1.62878	0.174624
$88$	−60.6258	−6.46273
$89$	−3.27533	−0.347185	−0.173592	−	0.984818i	$-0.555537\pi$
$89$	−3.27533	−0.347185	−0.173592	+	0.984818i	$0.555537\pi$
$90$	29.9711	3.15923
$91$	−4.03852	−0.423352
$92$	50.6292	5.27846
$93$	−2.31926	−0.240496
$94$	17.8289	1.83891
$95$	−17.3179	−1.77678
$96$	7.47000	0.762403
$97$	−4.10223	−0.416518	−0.208259	−	0.978074i	$-0.566780\pi$
$97$	−4.10223	−0.416518	−0.208259	+	0.978074i	$0.566780\pi$
$98$	−26.0554	−2.63199
$99$	−16.6017	−1.66853
$100$	48.3448	4.83448
$101$	−9.32431	−0.927804	−0.463902	−	0.885887i	$-0.653551\pi$
$101$	−9.32431	−0.927804	−0.463902	+	0.885887i	$0.653551\pi$
$102$	−1.77294	−0.175548
$103$	−14.9519	−1.47325	−0.736625	−	0.676301i	$-0.763582\pi$
$103$	−14.9519	−1.47325	−0.736625	+	0.676301i	$0.763582\pi$
$104$	10.7278	1.05195
$105$	−3.67481	−0.358624
$106$	−24.1993	−2.35044
$107$	−8.96295	−0.866481	−0.433240	−	0.901278i	$-0.642630\pi$
$107$	−8.96295	−0.866481	−0.433240	+	0.901278i	$0.642630\pi$
$108$	8.64561	0.831924
$109$	−4.19959	−0.402248	−0.201124	−	0.979566i	$-0.564459\pi$
$109$	−4.19959	−0.402248	−0.201124	+	0.979566i	$0.564459\pi$
$110$	−57.6558	−5.49726
$111$	−0.977386	−0.0927694
$112$	74.1410	7.00566
$113$	11.9235	1.12167	0.560836	−	0.827927i	$-0.310480\pi$
$113$	11.9235	1.12167	0.560836	+	0.827927i	$0.310480\pi$
$114$	−3.31904	−0.310856
$115$	31.6400	2.95044
$116$	−38.0608	−3.53386
$117$	2.93769	0.271589
$118$	−8.11288	−0.746851
$119$	−10.2487	−0.939499
$120$	9.76166	0.891114
$121$	20.9368	1.90335
$122$	−23.5768	−2.13454
$123$	−1.68780	−0.152184
$124$	54.1956	4.86691
$125$	11.9859	1.07206
$126$	33.2042	2.95807
$127$	11.7121	1.03928	0.519641	−	0.854385i	$-0.326066\pi$
$127$	11.7121	1.03928	0.519641	+	0.854385i	$0.326066\pi$
$128$	−71.7943	−6.34578
$129$	−1.06686	−0.0939314
$130$	10.2023	0.894798
$131$	3.73635	0.326446	0.163223	−	0.986589i	$-0.447811\pi$
$131$	3.73635	0.326446	0.163223	+	0.986589i	$0.447811\pi$
$132$	−8.22856	−0.716205
$133$	−19.1861	−1.66365
$134$	17.4311	1.50582
$135$	5.40294	0.465011
$136$	27.2245	2.33448
$137$	17.4776	1.49321	0.746604	−	0.665268i	$-0.231683\pi$
$137$	17.4776	1.49321	0.746604	+	0.665268i	$0.231683\pi$
$138$	6.06390	0.516194
$139$	2.74018	0.232419	0.116210	−	0.993225i	$-0.462926\pi$
$139$	2.74018	0.232419	0.116210	+	0.993225i	$0.462926\pi$
$140$	85.8715	7.25747
$141$	1.59016	0.133916
$142$	10.7491	0.902042
$143$	−5.65127	−0.472583
$144$	−53.9315	−4.49429
$145$	−23.7855	−1.97528
$146$	−4.28372	−0.354523
$147$	−2.32388	−0.191670
$148$	22.8392	1.87737
$149$	5.38669	0.441295	0.220647	−	0.975354i	$-0.429183\pi$
$149$	5.38669	0.441295	0.220647	+	0.975354i	$0.429183\pi$
$150$	5.79030	0.472776
$151$	0.355505	0.0289306	0.0144653	−	0.999895i	$-0.495395\pi$
$151$	0.355505	0.0289306	0.0144653	+	0.999895i	$0.495395\pi$
$152$	50.9655	4.13385
$153$	7.45510	0.602709
$154$	−63.8754	−5.14723
$155$	33.8687	2.72040
$156$	1.45606	0.116578
$157$	−4.87795	−0.389303	−0.194652	−	0.980872i	$-0.562358\pi$
$157$	−4.87795	−0.389303	−0.194652	+	0.980872i	$0.562358\pi$
$158$	14.3934	1.14508
$159$	−2.15833	−0.171167
$160$	−109.086	−8.62402
$161$	35.0531	2.76257
$162$	−23.6302	−1.85656
$163$	12.3761	0.969368	0.484684	−	0.874689i	$-0.338935\pi$
$163$	12.3761	0.969368	0.484684	+	0.874689i	$0.338935\pi$
$164$	39.4399	3.07974
$165$	−5.14231	−0.400329
$166$	41.3094	3.20623
$167$	2.44166	0.188941	0.0944705	−	0.995528i	$-0.469884\pi$
$167$	2.44166	0.188941	0.0944705	+	0.995528i	$0.469884\pi$
$168$	10.8147	0.834373
$169$	1.00000	0.0769231
$170$	25.8907	1.98573
$171$	13.9563	1.06727
$172$	24.9299	1.90089
$173$	−22.4956	−1.71031	−0.855156	−	0.518371i	$-0.826538\pi$
$173$	−22.4956	−1.71031	−0.855156	+	0.518371i	$0.826538\pi$
$174$	−4.55857	−0.345585
$175$	33.4715	2.53021
$176$	103.749	7.82035
$177$	−0.723587	−0.0543881
$178$	9.16687	0.687086
$179$	17.6430	1.31870	0.659351	−	0.751835i	$-0.270831\pi$
$179$	17.6430	1.31870	0.659351	+	0.751835i	$0.270831\pi$
$180$	−62.4645	−4.65583
$181$	−6.02414	−0.447771	−0.223885	−	0.974615i	$-0.571874\pi$
$181$	−6.02414	−0.447771	−0.223885	+	0.974615i	$0.571874\pi$
$182$	11.3028	0.837822
$183$	−2.10281	−0.155444
$184$	−93.1143	−6.86448
$185$	14.2730	1.04937
$186$	6.49105	0.475947
$187$	−14.3415	−1.04875
$188$	−37.1583	−2.71005
$189$	5.98578	0.435402
$190$	48.4687	3.51629
$191$	−0.643352	−0.0465513	−0.0232757	−	0.999729i	$-0.507410\pi$
$191$	−0.643352	−0.0465513	−0.0232757	+	0.999729i	$0.507410\pi$
$192$	−11.7414	−0.847363
$193$	16.9114	1.21731	0.608654	−	0.793436i	$-0.291710\pi$
$193$	16.9114	1.21731	0.608654	+	0.793436i	$0.291710\pi$
$194$	11.4812	0.824299
$195$	0.909939	0.0651621
$196$	54.3035	3.87882
$197$	−6.38570	−0.454962	−0.227481	−	0.973782i	$-0.573049\pi$
$197$	−6.38570	−0.454962	−0.227481	+	0.973782i	$0.573049\pi$
$198$	46.4641	3.30206
$199$	1.96650	0.139402	0.0697009	−	0.997568i	$-0.477796\pi$
$199$	1.96650	0.139402	0.0697009	+	0.997568i	$0.477796\pi$
$200$	−88.9129	−6.28709
$201$	1.55468	0.109659
$202$	26.0965	1.83614
$203$	−26.3514	−1.84951
$204$	3.69510	0.258709
$205$	24.6474	1.72145
$206$	41.8467	2.91560
$207$	−25.4983	−1.77225
$208$	−18.3585	−1.27293
$209$	−26.8479	−1.85711
$210$	10.2849	0.709726
$211$	20.8139	1.43288	0.716442	−	0.697646i	$-0.245769\pi$
$211$	20.8139	1.43288	0.716442	+	0.697646i	$0.245769\pi$
$212$	50.4352	3.46390
$213$	0.958709	0.0656896
$214$	25.0851	1.71479
$215$	15.5796	1.06252
$216$	−15.9005	−1.08189
$217$	37.5223	2.54718
$218$	11.7537	0.796058
$219$	−0.382065	−0.0258175
$220$	120.164	8.10144
$221$	2.53774	0.170707
$222$	2.73547	0.183593
$223$	2.59428	0.173726	0.0868631	−	0.996220i	$-0.472316\pi$
$223$	2.59428	0.173726	0.0868631	+	0.996220i	$0.472316\pi$
$224$	−120.854	−8.07489
$225$	−24.3478	−1.62319
$226$	−33.3711	−2.21982
$227$	−20.9297	−1.38916	−0.694578	−	0.719417i	$-0.744409\pi$
$227$	−20.9297	−1.38916	−0.694578	+	0.719417i	$0.744409\pi$
$228$	6.91740	0.458116
$229$	1.45256	0.0959878	0.0479939	−	0.998848i	$-0.484717\pi$
$229$	1.45256	0.0959878	0.0479939	+	0.998848i	$0.484717\pi$
$230$	−88.5527	−5.83899
$231$	−5.69704	−0.374838
$232$	69.9992	4.59567
$233$	−18.2670	−1.19671	−0.598357	−	0.801230i	$-0.704179\pi$
$233$	−18.2670	−1.19671	−0.598357	+	0.801230i	$0.704179\pi$
$234$	−8.22189	−0.537482
$235$	−23.2215	−1.51480
$236$	16.9085	1.10065
$237$	1.28375	0.0833883
$238$	28.6837	1.85929
$239$	−15.3561	−0.993304	−0.496652	−	0.867950i	$-0.665437\pi$
$239$	−15.3561	−0.993304	−0.496652	+	0.867950i	$0.665437\pi$
$240$	−16.7051	−1.07831
$241$	−20.0033	−1.28853	−0.644264	−	0.764803i	$-0.722836\pi$
$241$	−20.0033	−1.28853	−0.644264	+	0.764803i	$0.722836\pi$
$242$	−58.5972	−3.76677
$243$	−6.55409	−0.420445
$244$	49.1378	3.14572
$245$	33.9362	2.16810
$246$	4.72375	0.301175
$247$	4.75078	0.302285
$248$	−99.6734	−6.32927
$249$	3.68438	0.233488
$250$	−33.5458	−2.12162
$251$	−2.28191	−0.144033	−0.0720164	−	0.997403i	$-0.522943\pi$
$251$	−2.28191	−0.144033	−0.0720164	+	0.997403i	$0.522943\pi$
$252$	−69.2029	−4.35937
$253$	49.0513	3.08383
$254$	−32.7794	−2.05676
$255$	2.30919	0.144607
$256$	106.861	6.67883
$257$	−18.2059	−1.13565	−0.567827	−	0.823148i	$-0.692216\pi$
$257$	−18.2059	−1.13565	−0.567827	+	0.823148i	$0.692216\pi$
$258$	2.98587	0.185892
$259$	15.8127	0.982554
$260$	−21.2631	−1.31868
$261$	19.1685	1.18650
$262$	−10.4571	−0.646045
$263$	12.4193	0.765809	0.382905	−	0.923788i	$-0.374924\pi$
$263$	12.4193	0.765809	0.382905	+	0.923788i	$0.374924\pi$
$264$	15.1335	0.931402
$265$	31.5187	1.93618
$266$	53.6973	3.29239
$267$	0.817593	0.0500359
$268$	−36.3292	−2.21916
$269$	5.80024	0.353647	0.176824	−	0.984243i	$-0.443418\pi$
$269$	5.80024	0.353647	0.176824	+	0.984243i	$0.443418\pi$
$270$	−15.1215	−0.920267
$271$	−29.9539	−1.81957	−0.909784	−	0.415083i	$-0.863753\pi$
$271$	−29.9539	−1.81957	−0.909784	+	0.415083i	$0.863753\pi$
$272$	−46.5891	−2.82488
$273$	1.00810	0.0610130
$274$	−48.9155	−2.95509
$275$	46.8381	2.82445
$276$	−12.6381	−0.760726
$277$	28.1580	1.69185	0.845924	−	0.533304i	$-0.179050\pi$
$277$	28.1580	1.69185	0.845924	+	0.533304i	$0.179050\pi$
$278$	−7.66912	−0.459963
$279$	−27.2944	−1.63407
$280$	−157.930	−9.43811
$281$	11.5158	0.686977	0.343489	−	0.939157i	$-0.388391\pi$
$281$	11.5158	0.686977	0.343489	+	0.939157i	$0.388391\pi$
$282$	−4.45047	−0.265022
$283$	−1.92448	−0.114398	−0.0571991	−	0.998363i	$-0.518217\pi$
$283$	−1.92448	−0.114398	−0.0571991	+	0.998363i	$0.518217\pi$
$284$	−22.4028	−1.32936
$285$	4.32292	0.256068
$286$	15.8165	0.935252
$287$	27.3062	1.61184
$288$	87.9113	5.18022
$289$	−10.5599	−0.621168
$290$	66.5700	3.90912
$291$	1.02400	0.0600281
$292$	8.92795	0.522469
$293$	10.8790	0.635559	0.317780	−	0.948165i	$-0.397063\pi$
$293$	10.8790	0.635559	0.317780	+	0.948165i	$0.397063\pi$
$294$	6.50398	0.379320
$295$	10.5667	0.615218
$296$	−42.0045	−2.44146
$297$	8.37616	0.486034
$298$	−15.0760	−0.873332
$299$	−8.67970	−0.501960
$300$	−12.0679	−0.696740
$301$	17.2602	0.994861
$302$	−0.994972	−0.0572542
$303$	2.32755	0.133714
$304$	−87.2170	−5.00224
$305$	30.7079	1.75833
$306$	−20.8651	−1.19278
$307$	2.78709	0.159068	0.0795338	−	0.996832i	$-0.474657\pi$
$307$	2.78709	0.159068	0.0795338	+	0.996832i	$0.474657\pi$
$308$	133.126	7.58558
$309$	3.73230	0.212323
$310$	−94.7905	−5.38374
$311$	31.2358	1.77122	0.885611	−	0.464428i	$-0.153740\pi$
$311$	31.2358	1.77122	0.885611	+	0.464428i	$0.153740\pi$
$312$	−2.67789	−0.151606
$313$	3.12885	0.176853	0.0884264	−	0.996083i	$-0.471816\pi$
$313$	3.12885	0.176853	0.0884264	+	0.996083i	$0.471816\pi$
$314$	13.6522	0.770440
$315$	−43.2473	−2.43671
$316$	−29.9981	−1.68753
$317$	−25.7904	−1.44853	−0.724267	−	0.689519i	$-0.757822\pi$
$317$	−25.7904	−1.44853	−0.724267	+	0.689519i	$0.757822\pi$
$318$	6.04066	0.338743
$319$	−36.8746	−2.06458
$320$	171.463	9.58505
$321$	2.23734	0.124876
$322$	−98.1053	−5.46719
$323$	12.0563	0.670828
$324$	49.2490	2.73606
$325$	−8.28807	−0.459739
$326$	−34.6376	−1.91840
$327$	1.04831	0.0579715
$328$	−72.5356	−4.00511
$329$	−25.7265	−1.41835
$330$	14.3921	0.792259
$331$	16.5899	0.911861	0.455930	−	0.890015i	$-0.349307\pi$
$331$	16.5899	0.911861	0.455930	+	0.890015i	$0.349307\pi$
$332$	−86.0954	−4.72510
$333$	−11.5025	−0.630331
$334$	−6.83361	−0.373918
$335$	−22.7034	−1.24042
$336$	−18.5072	−1.00965
$337$	14.0897	0.767515	0.383757	−	0.923434i	$-0.374630\pi$
$337$	14.0897	0.767515	0.383757	+	0.923434i	$0.374630\pi$
$338$	−2.79876	−0.152233
$339$	−2.97637	−0.161654
$340$	−53.9604	−2.92641
$341$	52.5066	2.84339
$342$	−39.0604	−2.11214
$343$	9.32741	0.503633
$344$	−45.8496	−2.47204
$345$	−7.89801	−0.425214
$346$	62.9599	3.38474
$347$	6.66631	0.357866	0.178933	−	0.983861i	$-0.442735\pi$
$347$	6.66631	0.357866	0.178933	+	0.983861i	$0.442735\pi$
$348$	9.50079	0.509296
$349$	14.0893	0.754184	0.377092	−	0.926176i	$-0.376924\pi$
$349$	14.0893	0.754184	0.377092	+	0.926176i	$0.376924\pi$
$350$	−93.6787	−5.00734
$351$	−1.48217	−0.0791126
$352$	−169.116	−9.01392
$353$	−10.6312	−0.565843	−0.282921	−	0.959143i	$-0.591304\pi$
$353$	−10.6312	−0.565843	−0.282921	+	0.959143i	$0.591304\pi$
$354$	2.02515	0.107635
$355$	−14.0003	−0.743057
$356$	−19.1052	−1.01257
$357$	2.55830	0.135400
$358$	−49.3786	−2.60974
$359$	−14.3484	−0.757280	−0.378640	−	0.925544i	$-0.623608\pi$
$359$	−14.3484	−0.757280	−0.378640	+	0.925544i	$0.623608\pi$
$360$	114.881	6.05476
$361$	3.56991	0.187890
$362$	16.8601	0.886148
$363$	−5.22628	−0.274309
$364$	−23.5569	−1.23472
$365$	5.57938	0.292038
$366$	5.88527	0.307628
$367$	−10.9086	−0.569425	−0.284713	−	0.958613i	$-0.591898\pi$
$367$	−10.9086	−0.569425	−0.284713	+	0.958613i	$0.591898\pi$
$368$	159.346	8.30649
$369$	−19.8630	−1.03403
$370$	−39.9467	−2.07673
$371$	34.9188	1.81289
$372$	−13.5284	−0.701414
$373$	0.484090	0.0250652	0.0125326	−	0.999921i	$-0.496011\pi$
$373$	0.484090	0.0250652	0.0125326	+	0.999921i	$0.496011\pi$
$374$	40.1384	2.07551
$375$	−2.99195	−0.154503
$376$	68.3393	3.52433
$377$	6.52502	0.336056
$378$	−16.7528	−0.861669
$379$	13.2729	0.681782	0.340891	−	0.940103i	$-0.389271\pi$
$379$	13.2729	0.681782	0.340891	+	0.940103i	$0.389271\pi$
$380$	−101.016	−5.18204
$381$	−2.92359	−0.149780
$382$	1.80059	0.0921261
$383$	−31.6591	−1.61771	−0.808853	−	0.588011i	$-0.799911\pi$
$383$	−31.6591	−1.61771	−0.808853	+	0.588011i	$0.799911\pi$
$384$	17.9214	0.914547
$385$	83.1953	4.24003
$386$	−47.3309	−2.40908
$387$	−12.5554	−0.638226
$388$	−23.9285	−1.21479
$389$	−26.3215	−1.33455	−0.667277	−	0.744809i	$-0.732540\pi$
$389$	−26.3215	−1.33455	−0.667277	+	0.744809i	$0.732540\pi$
$390$	−2.54670	−0.128957
$391$	−22.0269	−1.11395
$392$	−99.8718	−5.04429
$393$	−0.932672	−0.0470471
$394$	17.8721	0.900381
$395$	−18.7469	−0.943258
$396$	−96.8386	−4.86632
$397$	22.6925	1.13891	0.569453	−	0.822024i	$-0.307155\pi$
$397$	22.6925	1.13891	0.569453	+	0.822024i	$0.307155\pi$
$398$	−5.50377	−0.275879
$399$	4.78926	0.239763
$400$	152.156	7.60782
$401$	15.4422	0.771145	0.385573	−	0.922677i	$-0.374004\pi$
$401$	15.4422	0.771145	0.385573	+	0.922677i	$0.374004\pi$
$402$	−4.35118	−0.217017
$403$	−9.29112	−0.462823
$404$	−54.3893	−2.70597
$405$	30.7774	1.52934
$406$	73.7512	3.66021
$407$	22.1274	1.09682
$408$	−6.79580	−0.336442
$409$	26.9859	1.33437	0.667183	−	0.744894i	$-0.267500\pi$
$409$	26.9859	1.33437	0.667183	+	0.744894i	$0.267500\pi$
$410$	−68.9821	−3.40678
$411$	−4.36277	−0.215200
$412$	−87.2151	−4.29678
$413$	11.7066	0.576045
$414$	71.3636	3.50733
$415$	−53.8040	−2.64113
$416$	29.9253	1.46721
$417$	−0.684008	−0.0334960
$418$	75.1409	3.67526
$419$	−0.830255	−0.0405606	−0.0202803	−	0.999794i	$-0.506456\pi$
$419$	−0.830255	−0.0405606	−0.0202803	+	0.999794i	$0.506456\pi$
$420$	−21.4354	−1.04594
$421$	36.0106	1.75505	0.877525	−	0.479532i	$-0.159193\pi$
$421$	36.0106	1.75505	0.877525	+	0.479532i	$0.159193\pi$
$422$	−58.2530	−2.83571
$423$	18.7139	0.909902
$424$	−92.7574	−4.50470
$425$	−21.0330	−1.02025
$426$	−2.68320	−0.130001
$427$	34.0205	1.64637
$428$	−52.2814	−2.52712
$429$	1.41068	0.0681081
$430$	−43.6034	−2.10274
$431$	−36.1903	−1.74322	−0.871612	−	0.490196i	$-0.836925\pi$
$431$	−36.1903	−1.74322	−0.871612	+	0.490196i	$0.836925\pi$
$432$	27.2104	1.30916
$433$	−38.0950	−1.83073	−0.915365	−	0.402625i	$-0.868098\pi$
$433$	−38.0950	−1.83073	−0.915365	+	0.402625i	$0.868098\pi$
$434$	−105.016	−5.04093
$435$	5.93737	0.284675
$436$	−24.4965	−1.17317
$437$	−41.2354	−1.97255
$438$	1.06931	0.0510935
$439$	1.40990	0.0672908	0.0336454	−	0.999434i	$-0.489288\pi$
$439$	1.40990	0.0672908	0.0336454	+	0.999434i	$0.489288\pi$
$440$	−220.998	−10.5357
$441$	−27.3488	−1.30232
$442$	−7.10254	−0.337833
$443$	−4.46171	−0.211982	−0.105991	−	0.994367i	$-0.533801\pi$
$443$	−4.46171	−0.211982	−0.105991	+	0.994367i	$0.533801\pi$
$444$	−5.70115	−0.270565
$445$	−11.9395	−0.565987
$446$	−7.26078	−0.343808
$447$	−1.34463	−0.0635989
$448$	189.959	8.97473
$449$	9.82466	0.463655	0.231827	−	0.972757i	$-0.425530\pi$
$449$	9.82466	0.463655	0.231827	+	0.972757i	$0.425530\pi$
$450$	68.1436	3.21232
$451$	38.2108	1.79928
$452$	69.5508	3.27139
$453$	−0.0887415	−0.00416944
$454$	58.5774	2.74917
$455$	−14.7215	−0.690156
$456$	−12.7221	−0.595766
$457$	−4.84904	−0.226828	−0.113414	−	0.993548i	$-0.536179\pi$
$457$	−4.84904	−0.226828	−0.113414	+	0.993548i	$0.536179\pi$
$458$	−4.06537	−0.189962
$459$	−3.76138	−0.175566
$460$	184.558	8.60505
$461$	12.7766	0.595066	0.297533	−	0.954711i	$-0.403836\pi$
$461$	12.7766	0.595066	0.297533	+	0.954711i	$0.403836\pi$
$462$	15.9447	0.741812
$463$	−3.77488	−0.175433	−0.0877167	−	0.996145i	$-0.527957\pi$
$463$	−3.77488	−0.175433	−0.0877167	+	0.996145i	$0.527957\pi$
$464$	−119.789	−5.56108
$465$	−8.45435	−0.392061
$466$	51.1251	2.36832
$467$	−35.8634	−1.65956	−0.829781	−	0.558090i	$-0.811534\pi$
$467$	−35.8634	−1.65956	−0.829781	+	0.558090i	$0.811534\pi$
$468$	17.1357	0.792099
$469$	−25.1525	−1.16144
$470$	64.9914	2.99783
$471$	1.21764	0.0561059
$472$	−31.0972	−1.43136
$473$	24.1529	1.11055
$474$	−3.59290	−0.165027
$475$	−39.3748	−1.80664
$476$	−59.7814	−2.74008
$477$	−25.4005	−1.16301
$478$	42.9780	1.96577
$479$	23.7059	1.08315	0.541575	−	0.840653i	$-0.317828\pi$
$479$	23.7059	1.08315	0.541575	+	0.840653i	$0.317828\pi$
$480$	27.2302	1.24288
$481$	−3.91548	−0.178530
$482$	55.9846	2.55003
$483$	−8.75000	−0.398139
$484$	122.126	5.55118
$485$	−14.9538	−0.679016
$486$	18.3433	0.832071
$487$	−25.1373	−1.13908	−0.569540	−	0.821963i	$-0.692879\pi$
$487$	−25.1373	−1.13908	−0.569540	+	0.821963i	$0.692879\pi$
$488$	−90.3713	−4.09092
$489$	−3.08933	−0.139704
$490$	−94.9792	−4.29072
$491$	−27.1844	−1.22682	−0.613408	−	0.789766i	$-0.710202\pi$
$491$	−27.1844	−1.22682	−0.613408	+	0.789766i	$0.710202\pi$
$492$	−9.84505	−0.443849
$493$	16.5588	0.745772
$494$	−13.2963	−0.598229
$495$	−60.5178	−2.72007
$496$	170.571	7.65885
$497$	−15.5105	−0.695743
$498$	−10.3117	−0.462079
$499$	−21.3264	−0.954701	−0.477350	−	0.878713i	$-0.658403\pi$
$499$	−21.3264	−0.954701	−0.477350	+	0.878713i	$0.658403\pi$
$500$	69.9147	3.12668
$501$	−0.609489	−0.0272300
$502$	6.38652	0.285044
$503$	−12.7885	−0.570213	−0.285106	−	0.958496i	$-0.592029\pi$
$503$	−12.7885	−0.570213	−0.285106	+	0.958496i	$0.592029\pi$
$504$	127.274	5.66923
$505$	−33.9897	−1.51252
$506$	−137.283	−6.10297
$507$	−0.249621	−0.0110861
$508$	68.3175	3.03110
$509$	0.649179	0.0287744	0.0143872	−	0.999896i	$-0.495420\pi$
$509$	0.649179	0.0287744	0.0143872	+	0.999896i	$0.495420\pi$
$510$	−6.46288	−0.286181
$511$	6.18126	0.273443
$512$	−155.491	−6.87178
$513$	−7.04148	−0.310889
$514$	50.9540	2.24749
$515$	−54.5037	−2.40172
$516$	−6.22303	−0.273954
$517$	−36.0002	−1.58329
$518$	−44.2560	−1.94450
$519$	5.61539	0.246488
$520$	39.1059	1.71491
$521$	3.26143	0.142886	0.0714429	−	0.997445i	$-0.477240\pi$
$521$	3.26143	0.142886	0.0714429	+	0.997445i	$0.477240\pi$
$522$	−53.6480	−2.34811
$523$	32.1371	1.40526	0.702628	−	0.711558i	$-0.252010\pi$
$523$	32.1371	1.40526	0.702628	+	0.711558i	$0.252010\pi$
$524$	21.7944	0.952091
$525$	−8.35520	−0.364651
$526$	−34.7587	−1.51555
$527$	−23.5785	−1.02709
$528$	−25.8979	−1.12706
$529$	52.3373	2.27553
$530$	−88.2132	−3.83174
$531$	−8.51560	−0.369545
$532$	−111.914	−4.85207
$533$	−6.76145	−0.292871
$534$	−2.28825	−0.0990221
$535$	−32.6725	−1.41255
$536$	66.8146	2.88595
$537$	−4.40407	−0.190050
$538$	−16.2335	−0.699876
$539$	52.6111	2.26612
$540$	31.5157	1.35622
$541$	21.4061	0.920321	0.460161	−	0.887836i	$-0.347792\pi$
$541$	21.4061	0.920321	0.460161	+	0.887836i	$0.347792\pi$
$542$	83.8337	3.60096
$543$	1.50375	0.0645322
$544$	75.9428	3.25602
$545$	−15.3087	−0.655752
$546$	−2.82143	−0.120746
$547$	19.5219	0.834697	0.417349	−	0.908747i	$-0.362959\pi$
$547$	19.5219	0.834697	0.417349	+	0.908747i	$0.362959\pi$
$548$	101.948	4.35499
$549$	−24.7471	−1.05618
$550$	−131.089	−5.58964
$551$	30.9989	1.32060
$552$	23.2433	0.989301
$553$	−20.7692	−0.883196
$554$	−78.8074	−3.34820
$555$	−3.56285	−0.151234
$556$	15.9837	0.677858
$557$	−16.1656	−0.684960	−0.342480	−	0.939525i	$-0.611267\pi$
$557$	−16.1656	−0.684960	−0.342480	+	0.939525i	$0.611267\pi$
$558$	76.3905	3.23387
$559$	−4.27390	−0.180767
$560$	270.265	11.4208
$561$	3.57994	0.151145
$562$	−32.2301	−1.35954
$563$	17.8441	0.752039	0.376020	−	0.926612i	$-0.377292\pi$
$563$	17.8441	0.752039	0.376020	+	0.926612i	$0.377292\pi$
$564$	9.27549	0.390569
$565$	43.4647	1.82857
$566$	5.38615	0.226397
$567$	34.0975	1.43196
$568$	41.2018	1.72879
$569$	17.1313	0.718182	0.359091	−	0.933303i	$-0.383087\pi$
$569$	17.1313	0.718182	0.359091	+	0.933303i	$0.383087\pi$
$570$	−12.0988	−0.506764
$571$	32.8416	1.37438	0.687190	−	0.726478i	$-0.258844\pi$
$571$	32.8416	1.37438	0.687190	+	0.726478i	$0.258844\pi$
$572$	−32.9642	−1.37830
$573$	0.160594	0.00670893
$574$	−76.4236	−3.18986
$575$	71.9380	3.00002
$576$	−138.180	−5.75749
$577$	21.6057	0.899456	0.449728	−	0.893166i	$-0.351521\pi$
$577$	21.6057	0.899456	0.449728	+	0.893166i	$0.351521\pi$
$578$	29.5545	1.22931
$579$	−4.22144	−0.175437
$580$	−138.742	−5.76096
$581$	−59.6081	−2.47296
$582$	−2.86594	−0.118797
$583$	48.8633	2.02371
$584$	−16.4198	−0.679454
$585$	10.7087	0.442750
$586$	−30.4478	−1.25779
$587$	22.1686	0.914995	0.457498	−	0.889211i	$-0.348746\pi$
$587$	22.1686	0.914995	0.457498	+	0.889211i	$0.348746\pi$
$588$	−13.5553	−0.559012
$589$	−44.1400	−1.81876
$590$	−29.5737	−1.21753
$591$	1.59401	0.0655687
$592$	71.8822	2.95434
$593$	−16.9183	−0.694753	−0.347376	−	0.937726i	$-0.612927\pi$
$593$	−16.9183	−0.694753	−0.347376	+	0.937726i	$0.612927\pi$
$594$	−23.4429	−0.961873
$595$	−37.3595	−1.53159
$596$	31.4209	1.28705
$597$	−0.490881	−0.0200904
$598$	24.2924	0.993391
$599$	−47.1197	−1.92526	−0.962629	−	0.270823i	$-0.912704\pi$
$599$	−47.1197	−1.92526	−0.962629	+	0.270823i	$0.912704\pi$
$600$	22.1946	0.906089
$601$	−0.663865	−0.0270796	−0.0135398	−	0.999908i	$-0.504310\pi$
$601$	−0.663865	−0.0270796	−0.0135398	+	0.999908i	$0.504310\pi$
$602$	−48.3072	−1.96885
$603$	18.2964	0.745087
$604$	2.07368	0.0843768
$605$	76.3207	3.10288
$606$	−6.51424	−0.264623
$607$	−18.7344	−0.760408	−0.380204	−	0.924903i	$-0.624146\pi$
$607$	−18.7344	−0.760408	−0.380204	+	0.924903i	$0.624146\pi$
$608$	142.169	5.76570
$609$	6.57787	0.266549
$610$	−85.9441	−3.47977
$611$	6.37029	0.257714
$612$	43.4861	1.75782
$613$	20.1780	0.814980	0.407490	−	0.913210i	$-0.366404\pi$
$613$	20.1780	0.814980	0.407490	+	0.913210i	$0.366404\pi$
$614$	−7.80039	−0.314798
$615$	−6.15251	−0.248093
$616$	−244.838	−9.86481
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−10.4458	−0.420192
$619$	14.6008	0.586856	0.293428	−	0.955981i	$-0.405204\pi$
$619$	14.6008	0.586856	0.293428	+	0.955981i	$0.405204\pi$
$620$	197.558	7.93413
$621$	12.8648	0.516248
$622$	−87.4216	−3.50529
$623$	−13.2275	−0.529948
$624$	4.58266	0.183453
$625$	2.25177	0.0900708
$626$	−8.75689	−0.349996
$627$	6.70181	0.267645
$628$	−28.4534	−1.13541
$629$	−9.93648	−0.396193
$630$	121.039	4.82230
$631$	26.9213	1.07172	0.535861	−	0.844306i	$-0.319987\pi$
$631$	26.9213	1.07172	0.535861	+	0.844306i	$0.319987\pi$
$632$	55.1708	2.19458
$633$	−5.19558	−0.206506
$634$	72.1812	2.86668
$635$	42.6940	1.69426
$636$	−12.5897	−0.499214
$637$	−9.30961	−0.368860
$638$	103.203	4.08586
$639$	11.2826	0.446335
$640$	−261.710	−10.3450
$641$	11.0865	0.437889	0.218945	−	0.975737i	$-0.429739\pi$
$641$	11.0865	0.437889	0.218945	+	0.975737i	$0.429739\pi$
$642$	−6.26178	−0.247133
$643$	−19.4797	−0.768205	−0.384102	−	0.923291i	$-0.625489\pi$
$643$	−19.4797	−0.768205	−0.384102	+	0.923291i	$0.625489\pi$
$644$	204.467	8.05713
$645$	−3.88899	−0.153129
$646$	−33.7426	−1.32758
$647$	−26.3364	−1.03539	−0.517696	−	0.855564i	$-0.673210\pi$
$647$	−26.3364	−1.03539	−0.517696	+	0.855564i	$0.673210\pi$
$648$	−90.5759	−3.55816
$649$	16.3816	0.643033
$650$	23.1963	0.909835
$651$	−9.36637	−0.367097
$652$	72.1903	2.82719
$653$	−39.3982	−1.54177	−0.770885	−	0.636974i	$-0.780186\pi$
$653$	−39.3982	−1.54177	−0.770885	+	0.636974i	$0.780186\pi$
$654$	−2.93396	−0.114727
$655$	13.6200	0.532179
$656$	124.130	4.84646
$657$	−4.49636	−0.175420
$658$	72.0023	2.80694
$659$	18.3857	0.716204	0.358102	−	0.933683i	$-0.383424\pi$
$659$	18.3857	0.716204	0.358102	+	0.933683i	$0.383424\pi$
$660$	−29.9954	−1.16757
$661$	25.5956	0.995554	0.497777	−	0.867305i	$-0.334150\pi$
$661$	25.5956	0.995554	0.497777	+	0.867305i	$0.334150\pi$
$662$	−46.4310	−1.80459
$663$	−0.633475	−0.0246021
$664$	158.342	6.14484
$665$	−69.9387	−2.71211
$666$	32.1926	1.24744
$667$	−56.6352	−2.19292
$668$	14.2423	0.551052
$669$	−0.647588	−0.0250372
$670$	63.5414	2.45482
$671$	47.6064	1.83782
$672$	30.1677	1.16374
$673$	−12.6930	−0.489279	−0.244640	−	0.969614i	$-0.578670\pi$
$673$	−12.6930	−0.489279	−0.244640	+	0.969614i	$0.578670\pi$
$674$	−39.4337	−1.51893
$675$	12.2844	0.472825
$676$	5.83306	0.224348
$677$	−18.4612	−0.709521	−0.354760	−	0.934957i	$-0.615438\pi$
$677$	−18.4612	−0.709521	−0.354760	+	0.934957i	$0.615438\pi$
$678$	8.33015	0.319917
$679$	−16.5669	−0.635780
$680$	99.2408	3.80571
$681$	5.22451	0.200204
$682$	−146.953	−5.62714
$683$	7.36041	0.281638	0.140819	−	0.990035i	$-0.455026\pi$
$683$	7.36041	0.281638	0.140819	+	0.990035i	$0.455026\pi$
$684$	81.4080	3.11271
$685$	63.7106	2.43426
$686$	−26.1052	−0.996701
$687$	−0.362590	−0.0138337
$688$	78.4622	2.99134
$689$	−8.64643	−0.329403
$690$	22.1046	0.841509
$691$	4.36567	0.166078	0.0830390	−	0.996546i	$-0.473537\pi$
$691$	4.36567	0.166078	0.0830390	+	0.996546i	$0.473537\pi$
$692$	−131.218	−4.98817
$693$	−67.0461	−2.54687
$694$	−18.6574	−0.708226
$695$	9.98874	0.378894
$696$	−17.4733	−0.662323
$697$	−17.1588	−0.649937
$698$	−39.4326	−1.49255
$699$	4.55984	0.172469
$700$	195.241	7.37943
$701$	−6.61924	−0.250005	−0.125003	−	0.992156i	$-0.539894\pi$
$701$	−6.61924	−0.250005	−0.125003	+	0.992156i	$0.539894\pi$
$702$	4.14825	0.156566
$703$	−18.6016	−0.701571
$704$	265.818	10.0184
$705$	5.79658	0.218312
$706$	29.7542	1.11982
$707$	−37.6564	−1.41621
$708$	−4.22073	−0.158625
$709$	42.6609	1.60217	0.801083	−	0.598554i	$-0.204258\pi$
$709$	42.6609	1.60217	0.801083	+	0.598554i	$0.204258\pi$
$710$	39.1834	1.47053
$711$	15.1079	0.566590
$712$	35.1372	1.31682
$713$	80.6441	3.02015
$714$	−7.16007	−0.267959
$715$	−20.6005	−0.770414
$716$	102.913	3.84603
$717$	3.83321	0.143154
$718$	40.1578	1.49867
$719$	−20.8123	−0.776170	−0.388085	−	0.921624i	$-0.626863\pi$
$719$	−20.8123	−0.776170	−0.388085	+	0.921624i	$0.626863\pi$
$720$	−196.595	−7.32668
$721$	−60.3833	−2.24879
$722$	−9.99131	−0.371838
$723$	4.99326	0.185701
$724$	−35.1392	−1.30594
$725$	−54.0798	−2.00847
$726$	14.6271	0.542863
$727$	35.4719	1.31558	0.657790	−	0.753202i	$-0.271492\pi$
$727$	35.4719	1.31558	0.657790	+	0.753202i	$0.271492\pi$
$728$	43.3245	1.60571
$729$	−23.6932	−0.877527
$730$	−15.6154	−0.577950
$731$	−10.8461	−0.401156
$732$	−12.2658	−0.453358
$733$	−51.0080	−1.88402	−0.942011	−	0.335581i	$-0.891067\pi$
$733$	−51.0080	−1.88402	−0.942011	+	0.335581i	$0.891067\pi$
$734$	30.5306	1.12691
$735$	−8.47119	−0.312464
$736$	−259.743	−9.57425
$737$	−35.1970	−1.29650
$738$	55.5919	2.04637
$739$	51.4652	1.89318	0.946589	−	0.322443i	$-0.104504\pi$
$739$	51.4652	1.89318	0.946589	+	0.322443i	$0.104504\pi$
$740$	83.2553	3.06053
$741$	−1.18590	−0.0435650
$742$	−97.7293	−3.58775
$743$	17.1238	0.628210	0.314105	−	0.949388i	$-0.398296\pi$
$743$	17.1238	0.628210	0.314105	+	0.949388i	$0.398296\pi$
$744$	24.8806	0.912167
$745$	19.6360	0.719407
$746$	−1.35485	−0.0496047
$747$	43.3600	1.58646
$748$	−83.6547	−3.05872
$749$	−36.1970	−1.32261
$750$	8.37374	0.305766
$751$	−8.19981	−0.299215	−0.149608	−	0.988745i	$-0.547801\pi$
$751$	−8.19981	−0.299215	−0.149608	+	0.988745i	$0.547801\pi$
$752$	−116.949	−4.26468
$753$	0.569613	0.0207579
$754$	−18.2620	−0.665062
$755$	1.29591	0.0471631
$756$	34.9154	1.26986
$757$	10.1711	0.369676	0.184838	−	0.982769i	$-0.440824\pi$
$757$	10.1711	0.369676	0.184838	+	0.982769i	$0.440824\pi$
$758$	−37.1476	−1.34926
$759$	−12.2443	−0.444438
$760$	185.784	6.73908
$761$	28.2407	1.02373	0.511863	−	0.859067i	$-0.328956\pi$
$761$	28.2407	1.02373	0.511863	+	0.859067i	$0.328956\pi$
$762$	8.18244	0.296419
$763$	−16.9601	−0.613998
$764$	−3.75271	−0.135768
$765$	27.1759	0.982548
$766$	88.6063	3.20148
$767$	−2.89874	−0.104667
$768$	−26.6749	−0.962546
$769$	−13.2812	−0.478932	−0.239466	−	0.970905i	$-0.576972\pi$
$769$	−13.2812	−0.478932	−0.239466	+	0.970905i	$0.576972\pi$
$770$	−232.844	−8.39111
$771$	4.54459	0.163669
$772$	98.6451	3.55032
$773$	3.96562	0.142633	0.0713166	−	0.997454i	$-0.477280\pi$
$773$	3.96562	0.142633	0.0713166	+	0.997454i	$0.477280\pi$
$774$	35.1395	1.26306
$775$	77.0054	2.76612
$776$	44.0079	1.57979
$777$	−3.94719	−0.141605
$778$	73.6677	2.64111
$779$	−32.1222	−1.15090
$780$	5.30773	0.190047
$781$	−21.7046	−0.776650
$782$	61.6479	2.20453
$783$	−9.67121	−0.345621
$784$	170.910	6.10394
$785$	−17.7815	−0.634649
$786$	2.61033	0.0931073
$787$	20.9259	0.745929	0.372965	−	0.927846i	$-0.378341\pi$
$787$	20.9259	0.745929	0.372965	+	0.927846i	$0.378341\pi$
$788$	−37.2482	−1.32691
$789$	−3.10013	−0.110368
$790$	52.4680	1.86673
$791$	48.1534	1.71214
$792$	178.100	6.32850
$793$	−8.42402	−0.299146
$794$	−63.5110	−2.25392
$795$	−7.86773	−0.279040
$796$	11.4707	0.406569
$797$	−2.60869	−0.0924045	−0.0462022	−	0.998932i	$-0.514712\pi$
$797$	−2.60869	−0.0924045	−0.0462022	+	0.998932i	$0.514712\pi$
$798$	−13.4040	−0.474496
$799$	16.1662	0.571918
$800$	−248.023	−8.76895
$801$	9.62191	0.339973
$802$	−43.2189	−1.52611
$803$	8.64970	0.305241
$804$	9.06855	0.319823
$805$	127.778	4.50360
$806$	26.0036	0.915938
$807$	−1.44786	−0.0509672
$808$	100.030	3.51903
$809$	54.6657	1.92194	0.960971	−	0.276649i	$-0.0892238\pi$
$809$	54.6657	1.92194	0.960971	+	0.276649i	$0.0892238\pi$
$810$	−86.1386	−3.02660
$811$	−31.2754	−1.09823	−0.549114	−	0.835747i	$-0.685035\pi$
$811$	−31.2754	−1.09823	−0.549114	+	0.835747i	$0.685035\pi$
$812$	−153.709	−5.39414
$813$	7.47712	0.262234
$814$	−61.9293	−2.17062
$815$	45.1142	1.58028
$816$	11.6296	0.407119
$817$	−20.3043	−0.710359
$818$	−75.5271	−2.64074
$819$	11.8639	0.414558
$820$	143.770	5.02065
$821$	−20.1017	−0.701555	−0.350778	−	0.936459i	$-0.614083\pi$
$821$	−20.1017	−0.701555	−0.350778	+	0.936459i	$0.614083\pi$
$822$	12.2103	0.425885
$823$	21.6377	0.754242	0.377121	−	0.926164i	$-0.376914\pi$
$823$	21.6377	0.754242	0.377121	+	0.926164i	$0.376914\pi$
$824$	160.401	5.58783
$825$	−11.6918	−0.407056
$826$	−32.7640	−1.14001
$827$	−2.72874	−0.0948876	−0.0474438	−	0.998874i	$-0.515108\pi$
$827$	−2.72874	−0.0948876	−0.0474438	+	0.998874i	$0.515108\pi$
$828$	−148.733	−5.16883
$829$	−55.2550	−1.91909	−0.959543	−	0.281563i	$-0.909147\pi$
$829$	−55.2550	−1.91909	−0.959543	+	0.281563i	$0.909147\pi$
$830$	150.584	5.22686
$831$	−7.02882	−0.243827
$832$	−47.0369	−1.63071
$833$	−23.6254	−0.818572
$834$	1.91437	0.0662894
$835$	8.90052	0.308015
$836$	−156.606	−5.41632
$837$	13.7710	0.475997
$838$	2.32368	0.0802703
$839$	38.6463	1.33422	0.667110	−	0.744959i	$-0.267531\pi$
$839$	38.6463	1.33422	0.667110	+	0.744959i	$0.267531\pi$
$840$	39.4226	1.36021
$841$	13.5759	0.468133
$842$	−100.785	−3.47328
$843$	−2.87460	−0.0990064
$844$	121.408	4.17905
$845$	3.64528	0.125401
$846$	−52.3758	−1.80072
$847$	84.5538	2.90530
$848$	158.735	5.45099
$849$	0.480390	0.0164870
$850$	58.8663	2.01910
$851$	33.9852	1.16500
$852$	5.59221	0.191586
$853$	−45.2388	−1.54895	−0.774473	−	0.632607i	$-0.781985\pi$
$853$	−45.2388	−1.54895	−0.774473	+	0.632607i	$0.781985\pi$
$854$	−95.2153	−3.25820
$855$	50.8747	1.73988
$856$	96.1529	3.28644
$857$	−19.3906	−0.662370	−0.331185	−	0.943566i	$-0.607448\pi$
$857$	−19.3906	−0.662370	−0.331185	+	0.943566i	$0.607448\pi$
$858$	−3.94815	−0.134788
$859$	−22.9523	−0.783122	−0.391561	−	0.920152i	$-0.628065\pi$
$859$	−22.9523	−0.783122	−0.391561	+	0.920152i	$0.628065\pi$
$860$	90.8765	3.09886
$861$	−6.81621	−0.232296
$862$	101.288	3.44988
$863$	−7.34538	−0.250040	−0.125020	−	0.992154i	$-0.539899\pi$
$863$	−7.34538	−0.250040	−0.125020	+	0.992154i	$0.539899\pi$
$864$	−44.3545	−1.50897
$865$	−82.0029	−2.78818
$866$	106.619	3.62306
$867$	2.63596	0.0895220
$868$	218.870	7.42893
$869$	−29.0632	−0.985903
$870$	−16.6173	−0.563379
$871$	6.22816	0.211033
$872$	45.0525	1.52567
$873$	12.0511	0.407867
$874$	115.408	3.90373
$875$	48.4054	1.63640
$876$	−2.22861	−0.0752976
$877$	−1.39746	−0.0471890	−0.0235945	−	0.999722i	$-0.507511\pi$
$877$	−1.39746	−0.0471890	−0.0235945	+	0.999722i	$0.507511\pi$
$878$	−3.94597	−0.133170
$879$	−2.71563	−0.0915961
$880$	378.193	12.7489
$881$	25.7105	0.866210	0.433105	−	0.901343i	$-0.357418\pi$
$881$	25.7105	0.866210	0.433105	+	0.901343i	$0.357418\pi$
$882$	76.5426	2.57732
$883$	−49.3584	−1.66104	−0.830521	−	0.556987i	$-0.811957\pi$
$883$	−49.3584	−1.66104	−0.830521	+	0.556987i	$0.811957\pi$
$884$	14.8028	0.497873
$885$	−2.63768	−0.0886646
$886$	12.4873	0.419517
$887$	4.46588	0.149950	0.0749748	−	0.997185i	$-0.476112\pi$
$887$	4.46588	0.149950	0.0749748	+	0.997185i	$0.476112\pi$
$888$	10.4852	0.351861
$889$	47.2996	1.58638
$890$	33.4158	1.12010
$891$	47.7142	1.59848
$892$	15.1326	0.506677
$893$	30.2638	1.01274
$894$	3.76330	0.125864
$895$	64.3138	2.14977
$896$	−289.943	−9.68630
$897$	2.16664	0.0723420
$898$	−27.4969	−0.917583
$899$	−60.6247	−2.02195
$900$	−142.022	−4.73407
$901$	−21.9424	−0.731009
$902$	−106.943	−3.56081
$903$	−4.30851	−0.143378
$904$	−127.914	−4.25434
$905$	−21.9597	−0.729964
$906$	0.248366	0.00825141
$907$	23.1098	0.767347	0.383673	−	0.923469i	$-0.374659\pi$
$907$	23.1098	0.767347	0.383673	+	0.923469i	$0.374659\pi$
$908$	−122.084	−4.05152
$909$	27.3919	0.908533
$910$	41.2020	1.36583
$911$	−20.4921	−0.678933	−0.339467	−	0.940618i	$-0.610247\pi$
$911$	−20.4921	−0.678933	−0.339467	+	0.940618i	$0.610247\pi$
$912$	21.7712	0.720917
$913$	−83.4122	−2.76054
$914$	13.5713	0.448898
$915$	−7.66535	−0.253408
$916$	8.47287	0.279951
$917$	15.0893	0.498293
$918$	10.5272	0.347449
$919$	−41.4593	−1.36762	−0.683808	−	0.729662i	$-0.739677\pi$
$919$	−41.4593	−1.36762	−0.683808	+	0.729662i	$0.739677\pi$
$920$	−339.428	−11.1906
$921$	−0.695717	−0.0229246
$922$	−35.7587	−1.17765
$923$	3.84065	0.126417
$924$	−33.2312	−1.09323
$925$	32.4518	1.06701
$926$	10.5650	0.347187
$927$	43.9239	1.44265
$928$	195.263	6.40983
$929$	−58.3011	−1.91280	−0.956399	−	0.292063i	$-0.905658\pi$
$929$	−58.3011	−1.91280	−0.956399	+	0.292063i	$0.905658\pi$
$930$	23.6617	0.775898
$931$	−44.2279	−1.44951
$932$	−106.553	−3.49025
$933$	−7.79713	−0.255266
$934$	100.373	3.28431
$935$	−52.2787	−1.70970
$936$	−31.5150	−1.03010
$937$	−12.4528	−0.406816	−0.203408	−	0.979094i	$-0.565202\pi$
$937$	−12.4528	−0.406816	−0.203408	+	0.979094i	$0.565202\pi$
$938$	70.3959	2.29851
$939$	−0.781026	−0.0254878
$940$	−135.452	−4.41797
$941$	13.9003	0.453136	0.226568	−	0.973995i	$-0.427249\pi$
$941$	13.9003	0.453136	0.226568	+	0.973995i	$0.427249\pi$
$942$	−3.40789	−0.111035
$943$	58.6874	1.91112
$944$	53.2164	1.73205
$945$	21.8199	0.709800
$946$	−67.5983	−2.19781
$947$	8.34523	0.271183	0.135592	−	0.990765i	$-0.456706\pi$
$947$	8.34523	0.271183	0.135592	+	0.990765i	$0.456706\pi$
$948$	7.48817	0.243205
$949$	−1.53058	−0.0496846
$950$	110.201	3.57538
$951$	6.43784	0.208761
$952$	109.946	3.56338
$953$	−27.5259	−0.891650	−0.445825	−	0.895120i	$-0.647090\pi$
$953$	−27.5259	−0.891650	−0.445825	+	0.895120i	$0.647090\pi$
$954$	71.0900	2.30162
$955$	−2.34520	−0.0758889
$956$	−89.5731	−2.89700
$957$	9.20469	0.297545
$958$	−66.3471	−2.14358
$959$	70.5834	2.27926
$960$	−42.8007	−1.38139
$961$	55.3248	1.78467
$962$	10.9585	0.353316
$963$	26.3304	0.848484
$964$	−116.681	−3.75803
$965$	61.6467	1.98448
$966$	24.4892	0.787926
$967$	55.8429	1.79579	0.897893	−	0.440215i	$-0.145098\pi$
$967$	55.8429	1.79579	0.897893	+	0.440215i	$0.145098\pi$
$968$	−224.607	−7.21913
$969$	−3.00950	−0.0966791
$970$	41.8520	1.34379
$971$	0.153456	0.00492465	0.00246233	−	0.999997i	$-0.499216\pi$
$971$	0.153456	0.00492465	0.00246233	+	0.999997i	$0.499216\pi$
$972$	−38.2304	−1.22624
$973$	11.0663	0.354768
$974$	70.3533	2.25427
$975$	2.06888	0.0662571
$976$	154.652	4.95029
$977$	−7.65904	−0.245034	−0.122517	−	0.992466i	$-0.539097\pi$
$977$	−7.65904	−0.245034	−0.122517	+	0.992466i	$0.539097\pi$
$978$	8.64629	0.276478
$979$	−18.5098	−0.591575
$980$	197.952	6.32333
$981$	12.3371	0.393893
$982$	76.0827	2.42790
$983$	36.4922	1.16392	0.581960	−	0.813217i	$-0.302286\pi$
$983$	36.4922	1.16392	0.581960	+	0.813217i	$0.302286\pi$
$984$	18.1064	0.577212
$985$	−23.2777	−0.741688
$986$	−46.3442	−1.47590
$987$	6.42188	0.204411
$988$	27.7116	0.881623
$989$	37.0962	1.17959
$990$	169.375	5.38308
$991$	−30.4478	−0.967206	−0.483603	−	0.875287i	$-0.660672\pi$
$991$	−30.4478	−0.967206	−0.483603	+	0.875287i	$0.660672\pi$
$992$	−278.040	−8.82777
$993$	−4.14118	−0.131416
$994$	43.4103	1.37689
$995$	7.16846	0.227255
$996$	21.4912	0.680976
$997$	31.9048	1.01044	0.505218	−	0.862992i	$-0.331412\pi$
$997$	31.9048	1.01044	0.505218	+	0.862992i	$0.331412\pi$
$998$	59.6875	1.88937
$999$	5.80342	0.183612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.2	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.2	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79876 q^{2} -0.249621 q^{3} +5.83306 q^{4} +3.64528 q^{5} +0.698630 q^{6} +4.03852 q^{7} -10.7278 q^{8} -2.93769 q^{9} +O(q^{10})\)	\(q-2.79876 q^{2} -0.249621 q^{3} +5.83306 q^{4} +3.64528 q^{5} +0.698630 q^{6} +4.03852 q^{7} -10.7278 q^{8} -2.93769 q^{9} -10.2023 q^{10} +5.65127 q^{11} -1.45606 q^{12} -1.00000 q^{13} -11.3028 q^{14} -0.909939 q^{15} +18.3585 q^{16} -2.53774 q^{17} +8.22189 q^{18} -4.75078 q^{19} +21.2631 q^{20} -1.00810 q^{21} -15.8165 q^{22} +8.67970 q^{23} +2.67789 q^{24} +8.28807 q^{25} +2.79876 q^{26} +1.48217 q^{27} +23.5569 q^{28} -6.52502 q^{29} +2.54670 q^{30} +9.29112 q^{31} -29.9253 q^{32} -1.41068 q^{33} +7.10254 q^{34} +14.7215 q^{35} -17.1357 q^{36} +3.91548 q^{37} +13.2963 q^{38} +0.249621 q^{39} -39.1059 q^{40} +6.76145 q^{41} +2.82143 q^{42} +4.27390 q^{43} +32.9642 q^{44} -10.7087 q^{45} -24.2924 q^{46} -6.37029 q^{47} -4.58266 q^{48} +9.30961 q^{49} -23.1963 q^{50} +0.633475 q^{51} -5.83306 q^{52} +8.64643 q^{53} -4.14825 q^{54} +20.6005 q^{55} -43.3245 q^{56} +1.18590 q^{57} +18.2620 q^{58} +2.89874 q^{59} -5.30773 q^{60} +8.42402 q^{61} -26.0036 q^{62} -11.8639 q^{63} +47.0369 q^{64} -3.64528 q^{65} +3.94815 q^{66} -6.22816 q^{67} -14.8028 q^{68} -2.16664 q^{69} -41.2020 q^{70} -3.84065 q^{71} +31.5150 q^{72} +1.53058 q^{73} -10.9585 q^{74} -2.06888 q^{75} -27.7116 q^{76} +22.8227 q^{77} -0.698630 q^{78} -5.14278 q^{79} +66.9218 q^{80} +8.44309 q^{81} -18.9237 q^{82} -14.7599 q^{83} -5.88030 q^{84} -9.25079 q^{85} -11.9616 q^{86} +1.62878 q^{87} -60.6258 q^{88} -3.27533 q^{89} +29.9711 q^{90} -4.03852 q^{91} +50.6292 q^{92} -2.31926 q^{93} +17.8289 q^{94} -17.3179 q^{95} +7.47000 q^{96} -4.10223 q^{97} -26.0554 q^{98} -16.6017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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