LMFDB - Embedded newform 8021.2.a.d.1.10

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:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.64790 q^{2} -2.80956 q^{3} +5.01138 q^{4} +2.16330 q^{5} +7.43944 q^{6} +3.49626 q^{7} -7.97383 q^{8} +4.89364 q^{9} +O(q^{10})$	\(q-2.64790 q^{2} -2.80956 q^{3} +5.01138 q^{4} +2.16330 q^{5} +7.43944 q^{6} +3.49626 q^{7} -7.97383 q^{8} +4.89364 q^{9} -5.72819 q^{10} +6.02925 q^{11} -14.0798 q^{12} +1.00000 q^{13} -9.25774 q^{14} -6.07792 q^{15} +11.0911 q^{16} -0.228765 q^{17} -12.9579 q^{18} +6.34290 q^{19} +10.8411 q^{20} -9.82295 q^{21} -15.9648 q^{22} +0.531904 q^{23} +22.4030 q^{24} -0.320150 q^{25} -2.64790 q^{26} -5.32030 q^{27} +17.5211 q^{28} +8.76346 q^{29} +16.0937 q^{30} -1.37536 q^{31} -13.4206 q^{32} -16.9395 q^{33} +0.605747 q^{34} +7.56344 q^{35} +24.5239 q^{36} -1.19078 q^{37} -16.7954 q^{38} -2.80956 q^{39} -17.2497 q^{40} -0.870904 q^{41} +26.0102 q^{42} -9.03405 q^{43} +30.2148 q^{44} +10.5864 q^{45} -1.40843 q^{46} -5.85132 q^{47} -31.1613 q^{48} +5.22382 q^{49} +0.847724 q^{50} +0.642730 q^{51} +5.01138 q^{52} -13.0641 q^{53} +14.0876 q^{54} +13.0430 q^{55} -27.8786 q^{56} -17.8208 q^{57} -23.2048 q^{58} -10.8614 q^{59} -30.4587 q^{60} +6.09692 q^{61} +3.64183 q^{62} +17.1094 q^{63} +13.3541 q^{64} +2.16330 q^{65} +44.8542 q^{66} -6.97733 q^{67} -1.14643 q^{68} -1.49442 q^{69} -20.0272 q^{70} +0.122416 q^{71} -39.0210 q^{72} +4.31860 q^{73} +3.15306 q^{74} +0.899480 q^{75} +31.7867 q^{76} +21.0798 q^{77} +7.43944 q^{78} -1.42583 q^{79} +23.9934 q^{80} +0.266801 q^{81} +2.30607 q^{82} +16.5628 q^{83} -49.2265 q^{84} -0.494887 q^{85} +23.9213 q^{86} -24.6215 q^{87} -48.0762 q^{88} +16.0574 q^{89} -28.0317 q^{90} +3.49626 q^{91} +2.66557 q^{92} +3.86417 q^{93} +15.4937 q^{94} +13.7216 q^{95} +37.7060 q^{96} +9.54110 q^{97} -13.8321 q^{98} +29.5050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.64790	−1.87235	−0.936174	−	0.351536i	$-0.885659\pi$
$2$	−2.64790	−1.87235	−0.936174	+	0.351536i	$0.885659\pi$
$3$	−2.80956	−1.62210	−0.811051	−	0.584976i	$-0.801104\pi$
$3$	−2.80956	−1.62210	−0.811051	+	0.584976i	$0.801104\pi$
$4$	5.01138	2.50569
$5$	2.16330	0.967455	0.483728	−	0.875219i	$-0.339282\pi$
$5$	2.16330	0.967455	0.483728	+	0.875219i	$0.339282\pi$
$6$	7.43944	3.03714
$7$	3.49626	1.32146	0.660731	−	0.750623i	$-0.270247\pi$
$7$	3.49626	1.32146	0.660731	+	0.750623i	$0.270247\pi$
$8$	−7.97383	−2.81917
$9$	4.89364	1.63121
$10$	−5.72819	−1.81141
$11$	6.02925	1.81789	0.908943	−	0.416921i	$-0.136891\pi$
$11$	6.02925	1.81789	0.908943	+	0.416921i	$0.136891\pi$
$12$	−14.0798	−4.06448
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−9.25774	−2.47424
$15$	−6.07792	−1.56931
$16$	11.0911	2.77279
$17$	−0.228765	−0.0554837	−0.0277419	−	0.999615i	$-0.508832\pi$
$17$	−0.228765	−0.0554837	−0.0277419	+	0.999615i	$0.508832\pi$
$18$	−12.9579	−3.05420
$19$	6.34290	1.45516	0.727580	−	0.686022i	$-0.240645\pi$
$19$	6.34290	1.45516	0.727580	+	0.686022i	$0.240645\pi$
$20$	10.8411	2.42414
$21$	−9.82295	−2.14354
$22$	−15.9648	−3.40372
$23$	0.531904	0.110910	0.0554548	−	0.998461i	$-0.482339\pi$
$23$	0.531904	0.110910	0.0554548	+	0.998461i	$0.482339\pi$
$24$	22.4030	4.57299
$25$	−0.320150	−0.0640299
$26$	−2.64790	−0.519296
$27$	−5.32030	−1.02389
$28$	17.5211	3.31117
$29$	8.76346	1.62733	0.813667	−	0.581331i	$-0.197468\pi$
$29$	8.76346	1.62733	0.813667	+	0.581331i	$0.197468\pi$
$30$	16.0937	2.93830
$31$	−1.37536	−0.247023	−0.123511	−	0.992343i	$-0.539416\pi$
$31$	−1.37536	−0.247023	−0.123511	+	0.992343i	$0.539416\pi$
$32$	−13.4206	−2.37245
$33$	−16.9395	−2.94880
$34$	0.605747	0.103885
$35$	7.56344	1.27845
$36$	24.5239	4.08731
$37$	−1.19078	−0.195762	−0.0978812	−	0.995198i	$-0.531207\pi$
$37$	−1.19078	−0.195762	−0.0978812	+	0.995198i	$0.531207\pi$
$38$	−16.7954	−2.72457
$39$	−2.80956	−0.449890
$40$	−17.2497	−2.72742
$41$	−0.870904	−0.136012	−0.0680061	−	0.997685i	$-0.521664\pi$
$41$	−0.870904	−0.136012	−0.0680061	+	0.997685i	$0.521664\pi$
$42$	26.0102	4.01346
$43$	−9.03405	−1.37768	−0.688840	−	0.724913i	$-0.741880\pi$
$43$	−9.03405	−1.37768	−0.688840	+	0.724913i	$0.741880\pi$
$44$	30.2148	4.55506
$45$	10.5864	1.57813
$46$	−1.40843	−0.207661
$47$	−5.85132	−0.853502	−0.426751	−	0.904369i	$-0.640342\pi$
$47$	−5.85132	−0.853502	−0.426751	+	0.904369i	$0.640342\pi$
$48$	−31.1613	−4.49774
$49$	5.22382	0.746259
$50$	0.847724	0.119886
$51$	0.642730	0.0900002
$52$	5.01138	0.694953
$53$	−13.0641	−1.79450	−0.897249	−	0.441526i	$-0.854437\pi$
$53$	−13.0641	−1.79450	−0.897249	+	0.441526i	$0.854437\pi$
$54$	14.0876	1.91708
$55$	13.0430	1.75872
$56$	−27.8786	−3.72543
$57$	−17.8208	−2.36042
$58$	−23.2048	−3.04694
$59$	−10.8614	−1.41403	−0.707016	−	0.707197i	$-0.749959\pi$
$59$	−10.8614	−1.41403	−0.707016	+	0.707197i	$0.749959\pi$
$60$	−30.4587	−3.93220
$61$	6.09692	0.780631	0.390315	−	0.920681i	$-0.372366\pi$
$61$	6.09692	0.780631	0.390315	+	0.920681i	$0.372366\pi$
$62$	3.64183	0.462512
$63$	17.1094	2.15559
$64$	13.3541	1.66926
$65$	2.16330	0.268324
$66$	44.8542	5.52117
$67$	−6.97733	−0.852417	−0.426208	−	0.904625i	$-0.640151\pi$
$67$	−6.97733	−0.852417	−0.426208	+	0.904625i	$0.640151\pi$
$68$	−1.14643	−0.139025
$69$	−1.49442	−0.179907
$70$	−20.0272	−2.39371
$71$	0.122416	0.0145281	0.00726405	−	0.999974i	$-0.497688\pi$
$71$	0.122416	0.0145281	0.00726405	+	0.999974i	$0.497688\pi$
$72$	−39.0210	−4.59867
$73$	4.31860	0.505454	0.252727	−	0.967538i	$-0.418673\pi$
$73$	4.31860	0.505454	0.252727	+	0.967538i	$0.418673\pi$
$74$	3.15306	0.366535
$75$	0.899480	0.103863
$76$	31.7867	3.64618
$77$	21.0798	2.40227
$78$	7.43944	0.842351
$79$	−1.42583	−0.160418	−0.0802091	−	0.996778i	$-0.525559\pi$
$79$	−1.42583	−0.160418	−0.0802091	+	0.996778i	$0.525559\pi$
$80$	23.9934	2.68255
$81$	0.266801	0.0296446
$82$	2.30607	0.254662
$83$	16.5628	1.81800	0.909000	−	0.416796i	$-0.136847\pi$
$83$	16.5628	1.81800	0.909000	+	0.416796i	$0.136847\pi$
$84$	−49.2265	−5.37105
$85$	−0.494887	−0.0536780
$86$	23.9213	2.57950
$87$	−24.6215	−2.63970
$88$	−48.0762	−5.12494
$89$	16.0574	1.70208	0.851039	−	0.525103i	$-0.175973\pi$
$89$	16.0574	1.70208	0.851039	+	0.525103i	$0.175973\pi$
$90$	−28.0317	−2.95480
$91$	3.49626	0.366507
$92$	2.66557	0.277905
$93$	3.86417	0.400696
$94$	15.4937	1.59805
$95$	13.7216	1.40780
$96$	37.7060	3.84835
$97$	9.54110	0.968752	0.484376	−	0.874860i	$-0.339047\pi$
$97$	9.54110	0.968752	0.484376	+	0.874860i	$0.339047\pi$
$98$	−13.8321	−1.39726
$99$	29.5050	2.96536
$100$	−1.60439	−0.160439
$101$	−17.6201	−1.75326	−0.876632	−	0.481161i	$-0.840215\pi$
$101$	−17.6201	−1.75326	−0.876632	+	0.481161i	$0.840215\pi$
$102$	−1.70189	−0.168512
$103$	4.95942	0.488667	0.244333	−	0.969691i	$-0.421431\pi$
$103$	4.95942	0.488667	0.244333	+	0.969691i	$0.421431\pi$
$104$	−7.97383	−0.781898
$105$	−21.2500	−2.07378
$106$	34.5925	3.35992
$107$	2.45512	0.237346	0.118673	−	0.992933i	$-0.462136\pi$
$107$	2.45512	0.237346	0.118673	+	0.992933i	$0.462136\pi$
$108$	−26.6620	−2.56556
$109$	13.8468	1.32628	0.663140	−	0.748496i	$-0.269224\pi$
$109$	13.8468	1.32628	0.663140	+	0.748496i	$0.269224\pi$
$110$	−34.5367	−3.29294
$111$	3.34556	0.317546
$112$	38.7775	3.66413
$113$	−18.3164	−1.72306	−0.861530	−	0.507706i	$-0.830494\pi$
$113$	−18.3164	−1.72306	−0.861530	+	0.507706i	$0.830494\pi$
$114$	47.1876	4.41953
$115$	1.15067	0.107300
$116$	43.9170	4.07759
$117$	4.89364	0.452417
$118$	28.7599	2.64756
$119$	−0.799822	−0.0733196
$120$	48.4642	4.42416
$121$	25.3518	2.30471
$122$	−16.1440	−1.46161
$123$	2.44686	0.220626
$124$	−6.89247	−0.618962
$125$	−11.5091	−1.02940
$126$	−45.3041	−4.03601
$127$	13.6547	1.21166	0.605829	−	0.795595i	$-0.292842\pi$
$127$	13.6547	1.21166	0.605829	+	0.795595i	$0.292842\pi$
$128$	−8.51917	−0.752995
$129$	25.3817	2.23474
$130$	−5.72819	−0.502396
$131$	−17.0505	−1.48971	−0.744854	−	0.667228i	$-0.767481\pi$
$131$	−17.0505	−1.48971	−0.744854	+	0.667228i	$0.767481\pi$
$132$	−84.8904	−7.38876
$133$	22.1764	1.92294
$134$	18.4753	1.59602
$135$	−11.5094	−0.990571
$136$	1.82413	0.156418
$137$	15.7948	1.34944	0.674721	−	0.738073i	$-0.264264\pi$
$137$	15.7948	1.34944	0.674721	+	0.738073i	$0.264264\pi$
$138$	3.95707	0.336848
$139$	21.5185	1.82517	0.912587	−	0.408883i	$-0.134082\pi$
$139$	21.5185	1.82517	0.912587	+	0.408883i	$0.134082\pi$
$140$	37.9033	3.20341
$141$	16.4396	1.38447
$142$	−0.324145	−0.0272017
$143$	6.02925	0.504191
$144$	54.2761	4.52301
$145$	18.9580	1.57437
$146$	−11.4352	−0.946385
$147$	−14.6766	−1.21051
$148$	−5.96743	−0.490519
$149$	14.7641	1.20953	0.604763	−	0.796406i	$-0.293268\pi$
$149$	14.7641	1.20953	0.604763	+	0.796406i	$0.293268\pi$
$150$	−2.38173	−0.194468
$151$	−18.6444	−1.51726	−0.758630	−	0.651522i	$-0.774131\pi$
$151$	−18.6444	−1.51726	−0.758630	+	0.651522i	$0.774131\pi$
$152$	−50.5772	−4.10235
$153$	−1.11949	−0.0905058
$154$	−55.8172	−4.49788
$155$	−2.97532	−0.238983
$156$	−14.0798	−1.12728
$157$	16.0033	1.27720	0.638599	−	0.769539i	$-0.279514\pi$
$157$	16.0033	1.27720	0.638599	+	0.769539i	$0.279514\pi$
$158$	3.77545	0.300359
$159$	36.7045	2.91086
$160$	−29.0327	−2.29524
$161$	1.85967	0.146563
$162$	−0.706463	−0.0555050
$163$	5.06390	0.396635	0.198318	−	0.980138i	$-0.436452\pi$
$163$	5.06390	0.396635	0.198318	+	0.980138i	$0.436452\pi$
$164$	−4.36443	−0.340804
$165$	−36.6452	−2.85283
$166$	−43.8566	−3.40393
$167$	10.2463	0.792883	0.396441	−	0.918060i	$-0.370245\pi$
$167$	10.2463	0.792883	0.396441	+	0.918060i	$0.370245\pi$
$168$	78.3265	6.04302
$169$	1.00000	0.0769231
$170$	1.31041	0.100504
$171$	31.0399	2.37368
$172$	−45.2731	−3.45204
$173$	−15.8934	−1.20835	−0.604177	−	0.796850i	$-0.706498\pi$
$173$	−15.8934	−1.20835	−0.604177	+	0.796850i	$0.706498\pi$
$174$	65.1953	4.94244
$175$	−1.11933	−0.0846131
$176$	66.8712	5.04061
$177$	30.5158	2.29371
$178$	−42.5183	−3.18688
$179$	−25.6890	−1.92009	−0.960045	−	0.279847i	$-0.909716\pi$
$179$	−25.6890	−1.92009	−0.960045	+	0.279847i	$0.909716\pi$
$180$	53.0524	3.95429
$181$	−5.61617	−0.417447	−0.208723	−	0.977975i	$-0.566931\pi$
$181$	−5.61617	−0.417447	−0.208723	+	0.977975i	$0.566931\pi$
$182$	−9.25774	−0.686229
$183$	−17.1297	−1.26626
$184$	−4.24131	−0.312673
$185$	−2.57600	−0.189391
$186$	−10.2319	−0.750242
$187$	−1.37928	−0.100863
$188$	−29.3231	−2.13861
$189$	−18.6012	−1.35303
$190$	−36.3333	−2.63590
$191$	−6.46245	−0.467606	−0.233803	−	0.972284i	$-0.575117\pi$
$191$	−6.46245	−0.467606	−0.233803	+	0.972284i	$0.575117\pi$
$192$	−37.5192	−2.70772
$193$	19.6122	1.41171	0.705857	−	0.708354i	$-0.250562\pi$
$193$	19.6122	1.41171	0.705857	+	0.708354i	$0.250562\pi$
$194$	−25.2639	−1.81384
$195$	−6.07792	−0.435249
$196$	26.1785	1.86989
$197$	10.9413	0.779536	0.389768	−	0.920913i	$-0.372555\pi$
$197$	10.9413	0.779536	0.389768	+	0.920913i	$0.372555\pi$
$198$	−78.1262	−5.55219
$199$	−0.375215	−0.0265983	−0.0132991	−	0.999912i	$-0.504233\pi$
$199$	−0.375215	−0.0265983	−0.0132991	+	0.999912i	$0.504233\pi$
$200$	2.55282	0.180511
$201$	19.6032	1.38271
$202$	46.6562	3.28272
$203$	30.6393	2.15046
$204$	3.22096	0.225512
$205$	−1.88402	−0.131586
$206$	−13.1321	−0.914954
$207$	2.60295	0.180917
$208$	11.0911	0.769033
$209$	38.2429	2.64532
$210$	56.2678	3.88285
$211$	−13.1750	−0.907001	−0.453501	−	0.891256i	$-0.649825\pi$
$211$	−13.1750	−0.907001	−0.453501	+	0.891256i	$0.649825\pi$
$212$	−65.4693	−4.49645
$213$	−0.343935	−0.0235661
$214$	−6.50092	−0.444394
$215$	−19.5433	−1.33284
$216$	42.4232	2.88653
$217$	−4.80863	−0.326431
$218$	−36.6648	−2.48326
$219$	−12.1334	−0.819897
$220$	65.3636	4.40681
$221$	−0.228765	−0.0153884
$222$	−8.85871	−0.594557
$223$	11.6834	0.782377	0.391189	−	0.920311i	$-0.372064\pi$
$223$	11.6834	0.782377	0.391189	+	0.920311i	$0.372064\pi$
$224$	−46.9219	−3.13510
$225$	−1.56670	−0.104446
$226$	48.5000	3.22617
$227$	1.08857	0.0722508	0.0361254	−	0.999347i	$-0.488498\pi$
$227$	1.08857	0.0722508	0.0361254	+	0.999347i	$0.488498\pi$
$228$	−89.3066	−5.91447
$229$	5.07487	0.335357	0.167678	−	0.985842i	$-0.446373\pi$
$229$	5.07487	0.335357	0.167678	+	0.985842i	$0.446373\pi$
$230$	−3.04685	−0.200903
$231$	−59.2250	−3.89672
$232$	−69.8783	−4.58774
$233$	2.65552	0.173969	0.0869845	−	0.996210i	$-0.472277\pi$
$233$	2.65552	0.173969	0.0869845	+	0.996210i	$0.472277\pi$
$234$	−12.9579	−0.847083
$235$	−12.6581	−0.825725
$236$	−54.4305	−3.54313
$237$	4.00595	0.260215
$238$	2.11785	0.137280
$239$	24.3741	1.57663	0.788316	−	0.615270i	$-0.210953\pi$
$239$	24.3741	1.57663	0.788316	+	0.615270i	$0.210953\pi$
$240$	−67.4110	−4.35136
$241$	22.8244	1.47025	0.735124	−	0.677933i	$-0.237124\pi$
$241$	22.8244	1.47025	0.735124	+	0.677933i	$0.237124\pi$
$242$	−67.1290	−4.31522
$243$	15.2113	0.975806
$244$	30.5540	1.95602
$245$	11.3007	0.721973
$246$	−6.47904	−0.413088
$247$	6.34290	0.403589
$248$	10.9669	0.696400
$249$	−46.5341	−2.94898
$250$	30.4748	1.92740
$251$	5.15437	0.325341	0.162670	−	0.986680i	$-0.447989\pi$
$251$	5.15437	0.325341	0.162670	+	0.986680i	$0.447989\pi$
$252$	85.7418	5.40123
$253$	3.20698	0.201621
$254$	−36.1562	−2.26864
$255$	1.39042	0.0870712
$256$	−4.15032	−0.259395
$257$	−18.9086	−1.17949	−0.589745	−	0.807590i	$-0.700772\pi$
$257$	−18.9086	−1.17949	−0.589745	+	0.807590i	$0.700772\pi$
$258$	−67.2083	−4.18421
$259$	−4.16326	−0.258692
$260$	10.8411	0.672336
$261$	42.8852	2.65453
$262$	45.1480	2.78925
$263$	−12.4196	−0.765823	−0.382912	−	0.923785i	$-0.625079\pi$
$263$	−12.4196	−0.765823	−0.382912	+	0.923785i	$0.625079\pi$
$264$	135.073	8.31317
$265$	−28.2616	−1.73610
$266$	−58.7209	−3.60041
$267$	−45.1142	−2.76094
$268$	−34.9660	−2.13589
$269$	−3.73143	−0.227509	−0.113755	−	0.993509i	$-0.536288\pi$
$269$	−3.73143	−0.227509	−0.113755	+	0.993509i	$0.536288\pi$
$270$	30.4757	1.85469
$271$	11.5096	0.699160	0.349580	−	0.936906i	$-0.386324\pi$
$271$	11.5096	0.699160	0.349580	+	0.936906i	$0.386324\pi$
$272$	−2.53727	−0.153844
$273$	−9.82295	−0.594512
$274$	−41.8231	−2.52662
$275$	−1.93026	−0.116399
$276$	−7.48909	−0.450790
$277$	4.56733	0.274424	0.137212	−	0.990542i	$-0.456186\pi$
$277$	4.56733	0.274424	0.137212	+	0.990542i	$0.456186\pi$
$278$	−56.9788	−3.41736
$279$	−6.73054	−0.402947
$280$	−60.3096	−3.60419
$281$	13.0929	0.781057	0.390528	−	0.920591i	$-0.372292\pi$
$281$	13.0929	0.781057	0.390528	+	0.920591i	$0.372292\pi$
$282$	−43.5305	−2.59220
$283$	32.5539	1.93513	0.967564	−	0.252625i	$-0.0812938\pi$
$283$	32.5539	1.93513	0.967564	+	0.252625i	$0.0812938\pi$
$284$	0.613472	0.0364029
$285$	−38.5516	−2.28360
$286$	−15.9648	−0.944021
$287$	−3.04490	−0.179735
$288$	−65.6756	−3.86997
$289$	−16.9477	−0.996922
$290$	−50.1988	−2.94778
$291$	−26.8063	−1.57141
$292$	21.6421	1.26651
$293$	6.92781	0.404727	0.202363	−	0.979310i	$-0.435138\pi$
$293$	6.92781	0.404727	0.202363	+	0.979310i	$0.435138\pi$
$294$	38.8623	2.26649
$295$	−23.4964	−1.36801
$296$	9.49504	0.551888
$297$	−32.0774	−1.86132
$298$	−39.0940	−2.26465
$299$	0.531904	0.0307608
$300$	4.50763	0.260248
$301$	−31.5854	−1.82055
$302$	49.3685	2.84084
$303$	49.5047	2.84397
$304$	70.3500	4.03485
$305$	13.1894	0.755226
$306$	2.96431	0.169458
$307$	21.1522	1.20722	0.603610	−	0.797279i	$-0.293728\pi$
$307$	21.1522	1.20722	0.603610	+	0.797279i	$0.293728\pi$
$308$	105.639	6.01933
$309$	−13.9338	−0.792667
$310$	7.87835	0.447460
$311$	15.7350	0.892251	0.446126	−	0.894970i	$-0.352803\pi$
$311$	15.7350	0.892251	0.446126	+	0.894970i	$0.352803\pi$
$312$	22.4030	1.26832
$313$	−22.7265	−1.28458	−0.642289	−	0.766462i	$-0.722015\pi$
$313$	−22.7265	−1.28458	−0.642289	+	0.766462i	$0.722015\pi$
$314$	−42.3750	−2.39136
$315$	37.0128	2.08543
$316$	−7.14536	−0.401958
$317$	5.31369	0.298446	0.149223	−	0.988804i	$-0.452323\pi$
$317$	5.31369	0.298446	0.149223	+	0.988804i	$0.452323\pi$
$318$	−97.1899	−5.45014
$319$	52.8371	2.95831
$320$	28.8889	1.61494
$321$	−6.89782	−0.384999
$322$	−4.92423	−0.274416
$323$	−1.45103	−0.0807377
$324$	1.33704	0.0742801
$325$	−0.320150	−0.0177587
$326$	−13.4087	−0.742640
$327$	−38.9033	−2.15136
$328$	6.94443	0.383442
$329$	−20.4577	−1.12787
$330$	97.0330	5.34149
$331$	14.3033	0.786182	0.393091	−	0.919500i	$-0.371406\pi$
$331$	14.3033	0.786182	0.393091	+	0.919500i	$0.371406\pi$
$332$	83.0023	4.55534
$333$	−5.82723	−0.319330
$334$	−27.1312	−1.48455
$335$	−15.0940	−0.824675
$336$	−108.948	−5.94359
$337$	−2.14765	−0.116990	−0.0584950	−	0.998288i	$-0.518630\pi$
$337$	−2.14765	−0.116990	−0.0584950	+	0.998288i	$0.518630\pi$
$338$	−2.64790	−0.144027
$339$	51.4610	2.79498
$340$	−2.48006	−0.134500
$341$	−8.29240	−0.449059
$342$	−82.1905	−4.44435
$343$	−6.21000	−0.335308
$344$	72.0360	3.88392
$345$	−3.23287	−0.174052
$346$	42.0842	2.26246
$347$	5.93945	0.318846	0.159423	−	0.987210i	$-0.449037\pi$
$347$	5.93945	0.318846	0.159423	+	0.987210i	$0.449037\pi$
$348$	−123.388	−6.61427
$349$	−34.5180	−1.84771	−0.923853	−	0.382748i	$-0.874978\pi$
$349$	−34.5180	−1.84771	−0.923853	+	0.382748i	$0.874978\pi$
$350$	2.96386	0.158425
$351$	−5.32030	−0.283977
$352$	−80.9161	−4.31284
$353$	−33.8239	−1.80026	−0.900132	−	0.435617i	$-0.856530\pi$
$353$	−33.8239	−1.80026	−0.900132	+	0.435617i	$0.856530\pi$
$354$	−80.8027	−4.29461
$355$	0.264822	0.0140553
$356$	80.4695	4.26487
$357$	2.24715	0.118932
$358$	68.0220	3.59508
$359$	12.1768	0.642669	0.321335	−	0.946966i	$-0.395869\pi$
$359$	12.1768	0.642669	0.321335	+	0.946966i	$0.395869\pi$
$360$	−84.4141	−4.44901
$361$	21.2324	1.11749
$362$	14.8711	0.781606
$363$	−71.2275	−3.73847
$364$	17.5211	0.918353
$365$	9.34240	0.489004
$366$	45.3577	2.37089
$367$	36.8830	1.92527	0.962637	−	0.270793i	$-0.0872860\pi$
$367$	36.8830	1.92527	0.962637	+	0.270793i	$0.0872860\pi$
$368$	5.89942	0.307529
$369$	−4.26189	−0.221865
$370$	6.82099	0.354607
$371$	−45.6756	−2.37136
$372$	19.3648	1.00402
$373$	−19.7138	−1.02074	−0.510371	−	0.859954i	$-0.670492\pi$
$373$	−19.7138	−1.02074	−0.510371	+	0.859954i	$0.670492\pi$
$374$	3.65220	0.188851
$375$	32.3354	1.66979
$376$	46.6574	2.40617
$377$	8.76346	0.451341
$378$	49.2540	2.53335
$379$	−1.45062	−0.0745132	−0.0372566	−	0.999306i	$-0.511862\pi$
$379$	−1.45062	−0.0745132	−0.0372566	+	0.999306i	$0.511862\pi$
$380$	68.7639	3.52752
$381$	−38.3637	−1.96543
$382$	17.1119	0.875522
$383$	−18.3354	−0.936895	−0.468447	−	0.883491i	$-0.655186\pi$
$383$	−18.3354	−0.936895	−0.468447	+	0.883491i	$0.655186\pi$
$384$	23.9351	1.22143
$385$	45.6018	2.32408
$386$	−51.9311	−2.64322
$387$	−44.2094	−2.24729
$388$	47.8140	2.42739
$389$	−8.02946	−0.407110	−0.203555	−	0.979064i	$-0.565250\pi$
$389$	−8.02946	−0.407110	−0.203555	+	0.979064i	$0.565250\pi$
$390$	16.0937	0.814937
$391$	−0.121681	−0.00615368
$392$	−41.6538	−2.10383
$393$	47.9044	2.41646
$394$	−28.9715	−1.45956
$395$	−3.08449	−0.155197
$396$	147.860	7.43027
$397$	7.95160	0.399080	0.199540	−	0.979890i	$-0.436055\pi$
$397$	7.95160	0.399080	0.199540	+	0.979890i	$0.436055\pi$
$398$	0.993532	0.0498012
$399$	−62.3060	−3.11920
$400$	−3.55083	−0.177541
$401$	−8.93879	−0.446382	−0.223191	−	0.974775i	$-0.571647\pi$
$401$	−8.93879	−0.446382	−0.223191	+	0.974775i	$0.571647\pi$
$402$	−51.9075	−2.58891
$403$	−1.37536	−0.0685117
$404$	−88.3009	−4.39314
$405$	0.577170	0.0286798
$406$	−81.1299	−4.02641
$407$	−7.17948	−0.355874
$408$	−5.12502	−0.253726
$409$	−0.430421	−0.0212829	−0.0106415	−	0.999943i	$-0.503387\pi$
$409$	−0.430421	−0.0212829	−0.0106415	+	0.999943i	$0.503387\pi$
$410$	4.98870	0.246375
$411$	−44.3765	−2.18893
$412$	24.8535	1.22445
$413$	−37.9742	−1.86859
$414$	−6.89234	−0.338740
$415$	35.8302	1.75883
$416$	−13.4206	−0.657999
$417$	−60.4575	−2.96062
$418$	−101.263	−4.95295
$419$	−15.8979	−0.776662	−0.388331	−	0.921520i	$-0.626948\pi$
$419$	−15.8979	−0.776662	−0.388331	+	0.921520i	$0.626948\pi$
$420$	−106.492	−5.19626
$421$	3.79096	0.184760	0.0923801	−	0.995724i	$-0.470553\pi$
$421$	3.79096	0.184760	0.0923801	+	0.995724i	$0.470553\pi$
$422$	34.8860	1.69822
$423$	−28.6342	−1.39224
$424$	104.171	5.05900
$425$	0.0732391	0.00355262
$426$	0.910706	0.0441239
$427$	21.3164	1.03157
$428$	12.3035	0.594714
$429$	−16.9395	−0.817849
$430$	51.7488	2.49555
$431$	−18.3634	−0.884536	−0.442268	−	0.896883i	$-0.645826\pi$
$431$	−18.3634	−0.884536	−0.442268	+	0.896883i	$0.645826\pi$
$432$	−59.0083	−2.83904
$433$	−23.3287	−1.12110	−0.560552	−	0.828119i	$-0.689411\pi$
$433$	−23.3287	−1.12110	−0.560552	+	0.828119i	$0.689411\pi$
$434$	12.7328	0.611192
$435$	−53.2636	−2.55379
$436$	69.3913	3.32324
$437$	3.37381	0.161391
$438$	32.1280	1.53513
$439$	0.750035	0.0357972	0.0178986	−	0.999840i	$-0.494302\pi$
$439$	0.750035	0.0357972	0.0178986	+	0.999840i	$0.494302\pi$
$440$	−104.003	−4.95815
$441$	25.5635	1.21731
$442$	0.605747	0.0288125
$443$	16.4156	0.779929	0.389965	−	0.920830i	$-0.372487\pi$
$443$	16.4156	0.779929	0.389965	+	0.920830i	$0.372487\pi$
$444$	16.7659	0.795672
$445$	34.7368	1.64668
$446$	−30.9364	−1.46488
$447$	−41.4808	−1.96197
$448$	46.6894	2.20587
$449$	−1.14302	−0.0539422	−0.0269711	−	0.999636i	$-0.508586\pi$
$449$	−1.14302	−0.0539422	−0.0269711	+	0.999636i	$0.508586\pi$
$450$	4.14846	0.195560
$451$	−5.25089	−0.247255
$452$	−91.7903	−4.31745
$453$	52.3826	2.46115
$454$	−2.88242	−0.135279
$455$	7.56344	0.354580
$456$	142.100	6.65443
$457$	−15.0470	−0.703868	−0.351934	−	0.936025i	$-0.614476\pi$
$457$	−15.0470	−0.703868	−0.351934	+	0.936025i	$0.614476\pi$
$458$	−13.4377	−0.627904
$459$	1.21710	0.0568094
$460$	5.76642	0.268861
$461$	−26.5257	−1.23542	−0.617712	−	0.786405i	$-0.711940\pi$
$461$	−26.5257	−1.23542	−0.617712	+	0.786405i	$0.711940\pi$
$462$	156.822	7.29601
$463$	27.8938	1.29634	0.648169	−	0.761497i	$-0.275535\pi$
$463$	27.8938	1.29634	0.648169	+	0.761497i	$0.275535\pi$
$464$	97.1968	4.51225
$465$	8.35934	0.387655
$466$	−7.03156	−0.325731
$467$	6.74879	0.312297	0.156148	−	0.987734i	$-0.450092\pi$
$467$	6.74879	0.312297	0.156148	+	0.987734i	$0.450092\pi$
$468$	24.5239	1.13362
$469$	−24.3945	−1.12644
$470$	33.5175	1.54605
$471$	−44.9622	−2.07175
$472$	86.6069	3.98640
$473$	−54.4685	−2.50447
$474$	−10.6074	−0.487212
$475$	−2.03068	−0.0931738
$476$	−4.00821	−0.183716
$477$	−63.9312	−2.92721
$478$	−64.5403	−2.95201
$479$	32.7181	1.49493	0.747463	−	0.664303i	$-0.231272\pi$
$479$	32.7181	1.49493	0.747463	+	0.664303i	$0.231272\pi$
$480$	81.5692	3.72311
$481$	−1.19078	−0.0542947
$482$	−60.4367	−2.75281
$483$	−5.22487	−0.237740
$484$	127.047	5.77488
$485$	20.6402	0.937224
$486$	−40.2780	−1.82705
$487$	−10.2854	−0.466074	−0.233037	−	0.972468i	$-0.574866\pi$
$487$	−10.2854	−0.466074	−0.233037	+	0.972468i	$0.574866\pi$
$488$	−48.6158	−2.20073
$489$	−14.2274	−0.643383
$490$	−29.9230	−1.35178
$491$	9.44721	0.426346	0.213173	−	0.977014i	$-0.431620\pi$
$491$	9.44721	0.426346	0.213173	+	0.977014i	$0.431620\pi$
$492$	12.2621	0.552819
$493$	−2.00478	−0.0902905
$494$	−16.7954	−0.755659
$495$	63.8280	2.86885
$496$	−15.2544	−0.684941
$497$	0.427998	0.0191983
$498$	123.218	5.52152
$499$	24.1563	1.08139	0.540693	−	0.841220i	$-0.318162\pi$
$499$	24.1563	1.08139	0.540693	+	0.841220i	$0.318162\pi$
$500$	−57.6762	−2.57936
$501$	−28.7876	−1.28614
$502$	−13.6483	−0.609151
$503$	9.50538	0.423824	0.211912	−	0.977289i	$-0.432031\pi$
$503$	9.50538	0.423824	0.211912	+	0.977289i	$0.432031\pi$
$504$	−136.428	−6.07697
$505$	−38.1175	−1.69621
$506$	−8.49176	−0.377505
$507$	−2.80956	−0.124777
$508$	68.4288	3.03604
$509$	6.80502	0.301627	0.150814	−	0.988562i	$-0.451811\pi$
$509$	6.80502	0.301627	0.150814	+	0.988562i	$0.451811\pi$
$510$	−3.68168	−0.163028
$511$	15.0989	0.667937
$512$	28.0280	1.23867
$513$	−33.7461	−1.48993
$514$	50.0682	2.20841
$515$	10.7287	0.472763
$516$	127.197	5.59956
$517$	−35.2790	−1.55157
$518$	11.0239	0.484362
$519$	44.6535	1.96007
$520$	−17.2497	−0.756452
$521$	−29.7391	−1.30290	−0.651448	−	0.758694i	$-0.725838\pi$
$521$	−29.7391	−1.30290	−0.651448	+	0.758694i	$0.725838\pi$
$522$	−113.556	−4.97021
$523$	22.9084	1.00171	0.500857	−	0.865530i	$-0.333018\pi$
$523$	22.9084	1.00171	0.500857	+	0.865530i	$0.333018\pi$
$524$	−85.4464	−3.73274
$525$	3.14481	0.137251
$526$	32.8858	1.43389
$527$	0.314635	0.0137057
$528$	−187.879	−8.17638
$529$	−22.7171	−0.987699
$530$	74.8339	3.25058
$531$	−53.1518	−2.30659
$532$	111.134	4.81828
$533$	−0.870904	−0.0377230
$534$	119.458	5.16945
$535$	5.31115	0.229621
$536$	55.6360	2.40311
$537$	72.1750	3.11458
$538$	9.88045	0.425977
$539$	31.4957	1.35661
$540$	−57.6779	−2.48206
$541$	−0.660818	−0.0284108	−0.0142054	−	0.999899i	$-0.504522\pi$
$541$	−0.660818	−0.0284108	−0.0142054	+	0.999899i	$0.504522\pi$
$542$	−30.4764	−1.30907
$543$	15.7790	0.677141
$544$	3.07016	0.131632
$545$	29.9546	1.28312
$546$	26.0102	1.11313
$547$	−6.06931	−0.259505	−0.129753	−	0.991546i	$-0.541418\pi$
$547$	−6.06931	−0.259505	−0.129753	+	0.991546i	$0.541418\pi$
$548$	79.1537	3.38128
$549$	29.8362	1.27338
$550$	5.11114	0.217940
$551$	55.5858	2.36803
$552$	11.9162	0.507188
$553$	−4.98506	−0.211986
$554$	−12.0938	−0.513818
$555$	7.23743	0.307212
$556$	107.837	4.57332
$557$	26.5790	1.12619	0.563093	−	0.826393i	$-0.309611\pi$
$557$	26.5790	1.12619	0.563093	+	0.826393i	$0.309611\pi$
$558$	17.8218	0.754457
$559$	−9.03405	−0.382100
$560$	83.8872	3.54488
$561$	3.87518	0.163610
$562$	−34.6687	−1.46241
$563$	−6.00678	−0.253155	−0.126578	−	0.991957i	$-0.540399\pi$
$563$	−6.00678	−0.253155	−0.126578	+	0.991957i	$0.540399\pi$
$564$	82.3852	3.46904
$565$	−39.6238	−1.66698
$566$	−86.1995	−3.62324
$567$	0.932806	0.0391742
$568$	−0.976123	−0.0409572
$569$	18.8394	0.789788	0.394894	−	0.918727i	$-0.370781\pi$
$569$	18.8394	0.789788	0.394894	+	0.918727i	$0.370781\pi$
$570$	102.081	4.27569
$571$	31.4581	1.31648	0.658240	−	0.752808i	$-0.271301\pi$
$571$	31.4581	1.31648	0.658240	+	0.752808i	$0.271301\pi$
$572$	30.2148	1.26335
$573$	18.1567	0.758505
$574$	8.06260	0.336526
$575$	−0.170289	−0.00710153
$576$	65.3502	2.72293
$577$	−27.9249	−1.16253	−0.581265	−	0.813714i	$-0.697442\pi$
$577$	−27.9249	−1.16253	−0.581265	+	0.813714i	$0.697442\pi$
$578$	44.8757	1.86658
$579$	−55.1016	−2.28995
$580$	95.0055	3.94489
$581$	57.9077	2.40242
$582$	70.9804	2.94223
$583$	−78.7669	−3.26219
$584$	−34.4357	−1.42496
$585$	10.5864	0.437694
$586$	−18.3441	−0.757790
$587$	29.4491	1.21549	0.607747	−	0.794131i	$-0.292074\pi$
$587$	29.4491	1.21549	0.607747	+	0.794131i	$0.292074\pi$
$588$	−73.5502	−3.03316
$589$	−8.72379	−0.359458
$590$	62.2162	2.56140
$591$	−30.7403	−1.26449
$592$	−13.2071	−0.542807
$593$	−9.87811	−0.405645	−0.202823	−	0.979215i	$-0.565011\pi$
$593$	−9.87811	−0.405645	−0.202823	+	0.979215i	$0.565011\pi$
$594$	84.9378	3.48504
$595$	−1.73025	−0.0709334
$596$	73.9887	3.03069
$597$	1.05419	0.0431451
$598$	−1.40843	−0.0575949
$599$	22.6768	0.926551	0.463275	−	0.886214i	$-0.346674\pi$
$599$	22.6768	0.926551	0.463275	+	0.886214i	$0.346674\pi$
$600$	−7.17230	−0.292808
$601$	31.4960	1.28475	0.642373	−	0.766392i	$-0.277950\pi$
$601$	31.4960	1.28475	0.642373	+	0.766392i	$0.277950\pi$
$602$	83.6349	3.40871
$603$	−34.1446	−1.39047
$604$	−93.4341	−3.80178
$605$	54.8434	2.22970
$606$	−131.084	−5.32491
$607$	−1.36200	−0.0552817	−0.0276408	−	0.999618i	$-0.508799\pi$
$607$	−1.36200	−0.0552817	−0.0276408	+	0.999618i	$0.508799\pi$
$608$	−85.1255	−3.45229
$609$	−86.0831	−3.48826
$610$	−34.9244	−1.41405
$611$	−5.85132	−0.236719
$612$	−5.61021	−0.226779
$613$	5.10469	0.206177	0.103088	−	0.994672i	$-0.467128\pi$
$613$	5.10469	0.206177	0.103088	+	0.994672i	$0.467128\pi$
$614$	−56.0090	−2.26034
$615$	5.29328	0.213446
$616$	−168.087	−6.77240
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	36.8953	1.48415
$619$	−6.86535	−0.275942	−0.137971	−	0.990436i	$-0.544058\pi$
$619$	−6.86535	−0.275942	−0.137971	+	0.990436i	$0.544058\pi$
$620$	−14.9104	−0.598818
$621$	−2.82989	−0.113560
$622$	−41.6648	−1.67061
$623$	56.1407	2.24923
$624$	−31.1613	−1.24745
$625$	−23.2968	−0.931870
$626$	60.1776	2.40518
$627$	−107.446	−4.29097
$628$	80.1984	3.20026
$629$	0.272408	0.0108616
$630$	−98.0061	−3.90466
$631$	16.1592	0.643286	0.321643	−	0.946861i	$-0.395765\pi$
$631$	16.1592	0.643286	0.321643	+	0.946861i	$0.395765\pi$
$632$	11.3693	0.452247
$633$	37.0159	1.47125
$634$	−14.0701	−0.558796
$635$	29.5391	1.17222
$636$	183.940	7.29370
$637$	5.22382	0.206975
$638$	−139.907	−5.53898
$639$	0.599060	0.0236984
$640$	−18.4295	−0.728489
$641$	−0.882729	−0.0348657	−0.0174328	−	0.999848i	$-0.505549\pi$
$641$	−0.882729	−0.0348657	−0.0174328	+	0.999848i	$0.505549\pi$
$642$	18.2647	0.720851
$643$	−13.9748	−0.551112	−0.275556	−	0.961285i	$-0.588862\pi$
$643$	−13.9748	−0.551112	−0.275556	+	0.961285i	$0.588862\pi$
$644$	9.31952	0.367241
$645$	54.9082	2.16201
$646$	3.84219	0.151169
$647$	−7.86224	−0.309097	−0.154548	−	0.987985i	$-0.549392\pi$
$647$	−7.86224	−0.309097	−0.154548	+	0.987985i	$0.549392\pi$
$648$	−2.12743	−0.0835733
$649$	−65.4860	−2.57055
$650$	0.847724	0.0332505
$651$	13.5101	0.529504
$652$	25.3771	0.993845
$653$	8.93487	0.349649	0.174824	−	0.984600i	$-0.444064\pi$
$653$	8.93487	0.349649	0.174824	+	0.984600i	$0.444064\pi$
$654$	103.012	4.02809
$655$	−36.8852	−1.44123
$656$	−9.65932	−0.377133
$657$	21.1337	0.824503
$658$	54.1700	2.11177
$659$	0.401191	0.0156282	0.00781410	−	0.999969i	$-0.497513\pi$
$659$	0.401191	0.0156282	0.00781410	+	0.999969i	$0.497513\pi$
$660$	−183.643	−7.14830
$661$	−3.01222	−0.117162	−0.0585808	−	0.998283i	$-0.518658\pi$
$661$	−3.01222	−0.117162	−0.0585808	+	0.998283i	$0.518658\pi$
$662$	−37.8738	−1.47201
$663$	0.642730	0.0249616
$664$	−132.069	−5.12526
$665$	47.9741	1.86036
$666$	15.4299	0.597897
$667$	4.66132	0.180487
$668$	51.3481	1.98672
$669$	−32.8252	−1.26910
$670$	39.9675	1.54408
$671$	36.7598	1.41910
$672$	131.830	5.08545
$673$	28.5158	1.09920	0.549602	−	0.835426i	$-0.314779\pi$
$673$	28.5158	1.09920	0.549602	+	0.835426i	$0.314779\pi$
$674$	5.68676	0.219046
$675$	1.70329	0.0655598
$676$	5.01138	0.192745
$677$	35.1563	1.35117	0.675584	−	0.737283i	$-0.263892\pi$
$677$	35.1563	1.35117	0.675584	+	0.737283i	$0.263892\pi$
$678$	−136.264	−5.23318
$679$	33.3581	1.28017
$680$	3.94614	0.151328
$681$	−3.05840	−0.117198
$682$	21.9575	0.840795
$683$	−37.6194	−1.43947	−0.719733	−	0.694251i	$-0.755736\pi$
$683$	−37.6194	−1.43947	−0.719733	+	0.694251i	$0.755736\pi$
$684$	155.552	5.94770
$685$	34.1688	1.30552
$686$	16.4435	0.627814
$687$	−14.2582	−0.543983
$688$	−100.198	−3.82001
$689$	−13.0641	−0.497704
$690$	8.56031	0.325885
$691$	43.3337	1.64849	0.824246	−	0.566232i	$-0.191599\pi$
$691$	43.3337	1.64849	0.824246	+	0.566232i	$0.191599\pi$
$692$	−79.6479	−3.02776
$693$	103.157	3.91861
$694$	−15.7271	−0.596991
$695$	46.5508	1.76577
$696$	196.328	7.44178
$697$	0.199232	0.00754647
$698$	91.4002	3.45955
$699$	−7.46086	−0.282196
$700$	−5.60936	−0.212014
$701$	−10.7051	−0.404325	−0.202163	−	0.979352i	$-0.564797\pi$
$701$	−10.7051	−0.404325	−0.202163	+	0.979352i	$0.564797\pi$
$702$	14.0876	0.531703
$703$	−7.55297	−0.284866
$704$	80.5152	3.03453
$705$	35.5638	1.33941
$706$	89.5623	3.37072
$707$	−61.6044	−2.31687
$708$	152.926	5.74731
$709$	1.28918	0.0484161	0.0242081	−	0.999707i	$-0.492294\pi$
$709$	1.28918	0.0484161	0.0242081	+	0.999707i	$0.492294\pi$
$710$	−0.701222	−0.0263164
$711$	−6.97749	−0.261676
$712$	−128.039	−4.79845
$713$	−0.731561	−0.0273972
$714$	−5.95023	−0.222682
$715$	13.0430	0.487782
$716$	−128.737	−4.81114
$717$	−68.4807	−2.55746
$718$	−32.2431	−1.20330
$719$	−15.3168	−0.571221	−0.285610	−	0.958346i	$-0.592196\pi$
$719$	−15.3168	−0.571221	−0.285610	+	0.958346i	$0.592196\pi$
$720$	117.415	4.37581
$721$	17.3394	0.645754
$722$	−56.2212	−2.09234
$723$	−64.1265	−2.38489
$724$	−28.1448	−1.04599
$725$	−2.80562	−0.104198
$726$	188.603	6.99972
$727$	−1.01096	−0.0374945	−0.0187473	−	0.999824i	$-0.505968\pi$
$727$	−1.01096	−0.0374945	−0.0187473	+	0.999824i	$0.505968\pi$
$728$	−27.8786	−1.03325
$729$	−43.5375	−1.61250
$730$	−24.7378	−0.915585
$731$	2.06668	0.0764388
$732$	−85.8433	−3.17286
$733$	−31.4862	−1.16297	−0.581484	−	0.813558i	$-0.697528\pi$
$733$	−31.4862	−1.16297	−0.581484	+	0.813558i	$0.697528\pi$
$734$	−97.6624	−3.60479
$735$	−31.7499	−1.17111
$736$	−7.13847	−0.263127
$737$	−42.0680	−1.54960
$738$	11.2851	0.415409
$739$	22.9263	0.843358	0.421679	−	0.906745i	$-0.361441\pi$
$739$	22.9263	0.843358	0.421679	+	0.906745i	$0.361441\pi$
$740$	−12.9093	−0.474556
$741$	−17.8208	−0.654662
$742$	120.944	4.44001
$743$	13.4845	0.494697	0.247349	−	0.968927i	$-0.420441\pi$
$743$	13.4845	0.494697	0.247349	+	0.968927i	$0.420441\pi$
$744$	−30.8122	−1.12963
$745$	31.9392	1.17016
$746$	52.2002	1.91118
$747$	81.0523	2.96555
$748$	−6.91210	−0.252731
$749$	8.58374	0.313643
$750$	−85.6210	−3.12644
$751$	13.3728	0.487979	0.243990	−	0.969778i	$-0.421544\pi$
$751$	13.3728	0.487979	0.243990	+	0.969778i	$0.421544\pi$
$752$	−64.8978	−2.36658
$753$	−14.4815	−0.527736
$754$	−23.2048	−0.845068
$755$	−40.3333	−1.46788
$756$	−93.2174	−3.39028
$757$	−40.8248	−1.48380	−0.741901	−	0.670509i	$-0.766076\pi$
$757$	−40.8248	−1.48380	−0.741901	+	0.670509i	$0.766076\pi$
$758$	3.84109	0.139515
$759$	−9.01021	−0.327050
$760$	−109.413	−3.96884
$761$	24.0057	0.870205	0.435103	−	0.900381i	$-0.356712\pi$
$761$	24.0057	0.870205	0.435103	+	0.900381i	$0.356712\pi$
$762$	101.583	3.67997
$763$	48.4118	1.75263
$764$	−32.3858	−1.17168
$765$	−2.42180	−0.0875603
$766$	48.5503	1.75419
$767$	−10.8614	−0.392182
$768$	11.6606	0.420765
$769$	4.69856	0.169434	0.0847171	−	0.996405i	$-0.473001\pi$
$769$	4.69856	0.169434	0.0847171	+	0.996405i	$0.473001\pi$
$770$	−120.749	−4.35150
$771$	53.1250	1.91325
$772$	98.2840	3.53732
$773$	15.8823	0.571248	0.285624	−	0.958342i	$-0.407799\pi$
$773$	15.8823	0.571248	0.285624	+	0.958342i	$0.407799\pi$
$774$	117.062	4.20771
$775$	0.440322	0.0158168
$776$	−76.0791	−2.73108
$777$	11.6969	0.419625
$778$	21.2612	0.762251
$779$	−5.52405	−0.197920
$780$	−30.4587	−1.09060
$781$	0.738076	0.0264104
$782$	0.322199	0.0115218
$783$	−46.6243	−1.66622
$784$	57.9381	2.06922
$785$	34.6198	1.23563
$786$	−126.846	−4.52445
$787$	−14.6536	−0.522344	−0.261172	−	0.965292i	$-0.584109\pi$
$787$	−14.6536	−0.522344	−0.261172	+	0.965292i	$0.584109\pi$
$788$	54.8310	1.95327
$789$	34.8935	1.24224
$790$	8.16742	0.290584
$791$	−64.0388	−2.27696
$792$	−235.267	−8.35986
$793$	6.09692	0.216508
$794$	−21.0551	−0.747216
$795$	79.4027	2.81612
$796$	−1.88034	−0.0666470
$797$	−53.8039	−1.90583	−0.952916	−	0.303233i	$-0.901934\pi$
$797$	−53.8039	−1.90583	−0.952916	+	0.303233i	$0.901934\pi$
$798$	164.980	5.84023
$799$	1.33858	0.0473555
$800$	4.29660	0.151908
$801$	78.5790	2.77645
$802$	23.6690	0.835782
$803$	26.0379	0.918857
$804$	98.2393	3.46463
$805$	4.02302	0.141793
$806$	3.64183	0.128278
$807$	10.4837	0.369043
$808$	140.500	4.94276
$809$	20.6047	0.724422	0.362211	−	0.932096i	$-0.382022\pi$
$809$	20.6047	0.724422	0.362211	+	0.932096i	$0.382022\pi$
$810$	−1.52829	−0.0536986
$811$	17.3068	0.607724	0.303862	−	0.952716i	$-0.401724\pi$
$811$	17.3068	0.607724	0.303862	+	0.952716i	$0.401724\pi$
$812$	153.545	5.38838
$813$	−32.3370	−1.13411
$814$	19.0105	0.666319
$815$	10.9547	0.383727
$816$	7.12861	0.249551
$817$	−57.3021	−2.00475
$818$	1.13971	0.0398491
$819$	17.1094	0.597852
$820$	−9.44155	−0.329713
$821$	−29.9714	−1.04601	−0.523005	−	0.852330i	$-0.675189\pi$
$821$	−29.9714	−1.04601	−0.523005	+	0.852330i	$0.675189\pi$
$822$	117.505	4.09844
$823$	33.4487	1.16595	0.582974	−	0.812491i	$-0.301889\pi$
$823$	33.4487	1.16595	0.582974	+	0.812491i	$0.301889\pi$
$824$	−39.5456	−1.37764
$825$	5.42319	0.188811
$826$	100.552	3.49865
$827$	10.1021	0.351285	0.175642	−	0.984454i	$-0.443800\pi$
$827$	10.1021	0.351285	0.175642	+	0.984454i	$0.443800\pi$
$828$	13.0443	0.453322
$829$	−18.4707	−0.641515	−0.320757	−	0.947161i	$-0.603937\pi$
$829$	−18.4707	−0.641515	−0.320757	+	0.947161i	$0.603937\pi$
$830$	−94.8748	−3.29315
$831$	−12.8322	−0.445144
$832$	13.3541	0.462970
$833$	−1.19503	−0.0414052
$834$	160.085	5.54331
$835$	22.1658	0.767079
$836$	191.650	6.62834
$837$	7.31735	0.252925
$838$	42.0960	1.45418
$839$	54.4945	1.88136	0.940679	−	0.339297i	$-0.110189\pi$
$839$	54.4945	1.88136	0.940679	+	0.339297i	$0.110189\pi$
$840$	169.443	5.84636
$841$	47.7983	1.64822
$842$	−10.0381	−0.345936
$843$	−36.7853	−1.26695
$844$	−66.0247	−2.27266
$845$	2.16330	0.0744197
$846$	75.8206	2.60677
$847$	88.6364	3.04558
$848$	−144.896	−4.97576
$849$	−91.4622	−3.13898
$850$	−0.193930	−0.00665174
$851$	−0.633378	−0.0217119
$852$	−1.72359	−0.0590492
$853$	21.2932	0.729067	0.364533	−	0.931190i	$-0.381229\pi$
$853$	21.2932	0.729067	0.364533	+	0.931190i	$0.381229\pi$
$854$	−56.4437	−1.93146
$855$	67.1484	2.29643
$856$	−19.5767	−0.669118
$857$	11.3589	0.388011	0.194006	−	0.981000i	$-0.437852\pi$
$857$	11.3589	0.388011	0.194006	+	0.981000i	$0.437852\pi$
$858$	44.8542	1.53130
$859$	−19.4269	−0.662836	−0.331418	−	0.943484i	$-0.607527\pi$
$859$	−19.4269	−0.662836	−0.331418	+	0.943484i	$0.607527\pi$
$860$	−97.9390	−3.33969
$861$	8.55485	0.291548
$862$	48.6246	1.65616
$863$	50.2857	1.71175	0.855873	−	0.517186i	$-0.173020\pi$
$863$	50.2857	1.71175	0.855873	+	0.517186i	$0.173020\pi$
$864$	71.4016	2.42913
$865$	−34.3822	−1.16903
$866$	61.7720	2.09910
$867$	47.6155	1.61711
$868$	−24.0978	−0.817934
$869$	−8.59666	−0.291622
$870$	141.037	4.78159
$871$	−6.97733	−0.236418
$872$	−110.412	−3.73901
$873$	46.6907	1.58024
$874$	−8.93352	−0.302181
$875$	−40.2386	−1.36031
$876$	−60.8049	−2.05441
$877$	−5.39858	−0.182297	−0.0911486	−	0.995837i	$-0.529054\pi$
$877$	−5.39858	−0.182297	−0.0911486	+	0.995837i	$0.529054\pi$
$878$	−1.98602	−0.0670249
$879$	−19.4641	−0.656508
$880$	144.662	4.87656
$881$	22.2206	0.748633	0.374316	−	0.927301i	$-0.377877\pi$
$881$	22.2206	0.748633	0.374316	+	0.927301i	$0.377877\pi$
$882$	−67.6896	−2.27923
$883$	−49.3514	−1.66081	−0.830404	−	0.557162i	$-0.811890\pi$
$883$	−49.3514	−1.66081	−0.830404	+	0.557162i	$0.811890\pi$
$884$	−1.14643	−0.0385586
$885$	66.0146	2.21906
$886$	−43.4669	−1.46030
$887$	−38.2465	−1.28419	−0.642096	−	0.766624i	$-0.721935\pi$
$887$	−38.2465	−1.28419	−0.642096	+	0.766624i	$0.721935\pi$
$888$	−26.6769	−0.895218
$889$	47.7403	1.60116
$890$	−91.9797	−3.08317
$891$	1.60861	0.0538905
$892$	58.5498	1.96039
$893$	−37.1143	−1.24198
$894$	109.837	3.67350
$895$	−55.5730	−1.85760
$896$	−29.7852	−0.995054
$897$	−1.49442	−0.0498971
$898$	3.02659	0.100999
$899$	−12.0529	−0.401988
$900$	−7.85131	−0.261710
$901$	2.98862	0.0995654
$902$	13.9038	0.462947
$903$	88.7411	2.95312
$904$	146.052	4.85761
$905$	−12.1494	−0.403861
$906$	−138.704	−4.60813
$907$	1.07719	0.0357675	0.0178838	−	0.999840i	$-0.494307\pi$
$907$	1.07719	0.0357675	0.0178838	+	0.999840i	$0.494307\pi$
$908$	5.45523	0.181038
$909$	−86.2264	−2.85995
$910$	−20.0272	−0.663896
$911$	29.0415	0.962189	0.481095	−	0.876669i	$-0.340239\pi$
$911$	29.0415	0.962189	0.481095	+	0.876669i	$0.340239\pi$
$912$	−197.653	−6.54494
$913$	99.8610	3.30492
$914$	39.8429	1.31789
$915$	−37.0566	−1.22505
$916$	25.4321	0.840299
$917$	−59.6129	−1.96859
$918$	−3.22276	−0.106367
$919$	2.85908	0.0943123	0.0471562	−	0.998888i	$-0.484984\pi$
$919$	2.85908	0.0943123	0.0471562	+	0.998888i	$0.484984\pi$
$920$	−9.17521	−0.302498
$921$	−59.4285	−1.95823
$922$	70.2373	2.31314
$923$	0.122416	0.00402937
$924$	−296.799	−9.76396
$925$	0.381226	0.0125346
$926$	−73.8601	−2.42719
$927$	24.2696	0.797120
$928$	−117.611	−3.86077
$929$	−26.8954	−0.882411	−0.441205	−	0.897406i	$-0.645449\pi$
$929$	−26.8954	−0.882411	−0.441205	+	0.897406i	$0.645449\pi$
$930$	−22.1347	−0.725826
$931$	33.1341	1.08593
$932$	13.3078	0.435912
$933$	−44.2085	−1.44732
$934$	−17.8701	−0.584728
$935$	−2.98379	−0.0975805
$936$	−39.0210	−1.27544
$937$	23.2777	0.760449	0.380225	−	0.924894i	$-0.375847\pi$
$937$	23.2777	0.760449	0.380225	+	0.924894i	$0.375847\pi$
$938$	64.5943	2.10908
$939$	63.8516	2.08372
$940$	−63.4347	−2.06901
$941$	−9.40594	−0.306625	−0.153313	−	0.988178i	$-0.548994\pi$
$941$	−9.40594	−0.306625	−0.153313	+	0.988178i	$0.548994\pi$
$942$	119.055	3.87903
$943$	−0.463237	−0.0150851
$944$	−120.465	−3.92081
$945$	−40.2398	−1.30900
$946$	144.227	4.68923
$947$	19.2001	0.623919	0.311960	−	0.950095i	$-0.399015\pi$
$947$	19.2001	0.623919	0.311960	+	0.950095i	$0.399015\pi$
$948$	20.0753	0.652017
$949$	4.31860	0.140188
$950$	5.37703	0.174454
$951$	−14.9291	−0.484110
$952$	6.37764	0.206701
$953$	−5.86106	−0.189858	−0.0949291	−	0.995484i	$-0.530262\pi$
$953$	−5.86106	−0.189858	−0.0949291	+	0.995484i	$0.530262\pi$
$954$	169.283	5.48075
$955$	−13.9802	−0.452388
$956$	122.148	3.95055
$957$	−148.449	−4.79868
$958$	−86.6342	−2.79902
$959$	55.2227	1.78323
$960$	−81.1652	−2.61959
$961$	−29.1084	−0.938980
$962$	3.15306	0.101659
$963$	12.0145	0.387161
$964$	114.382	3.68398
$965$	42.4269	1.36577
$966$	13.8349	0.445131
$967$	29.9357	0.962666	0.481333	−	0.876538i	$-0.340153\pi$
$967$	29.9357	0.962666	0.481333	+	0.876538i	$0.340153\pi$
$968$	−202.151	−6.49737
$969$	4.07677	0.130965
$970$	−54.6532	−1.75481
$971$	15.1953	0.487640	0.243820	−	0.969820i	$-0.421599\pi$
$971$	15.1953	0.487640	0.243820	+	0.969820i	$0.421599\pi$
$972$	76.2296	2.44507
$973$	75.2341	2.41190
$974$	27.2346	0.872654
$975$	0.899480	0.0288064
$976$	67.6219	2.16452
$977$	34.1628	1.09296	0.546482	−	0.837471i	$-0.315967\pi$
$977$	34.1628	1.09296	0.546482	+	0.837471i	$0.315967\pi$
$978$	37.6726	1.20464
$979$	96.8138	3.09418
$980$	56.6319	1.80904
$981$	67.7611	2.16344
$982$	−25.0153	−0.798269
$983$	−23.6077	−0.752969	−0.376484	−	0.926423i	$-0.622867\pi$
$983$	−23.6077	−0.752969	−0.376484	+	0.926423i	$0.622867\pi$
$984$	−19.5108	−0.621982
$985$	23.6693	0.754167
$986$	5.30845	0.169055
$987$	57.4772	1.82952
$988$	31.7867	1.01127
$989$	−4.80525	−0.152798
$990$	−169.010	−5.37149
$991$	−17.0167	−0.540553	−0.270276	−	0.962783i	$-0.587115\pi$
$991$	−17.0167	−0.540553	−0.270276	+	0.962783i	$0.587115\pi$
$992$	18.4582	0.586048
$993$	−40.1861	−1.27527
$994$	−1.13330	−0.0359459
$995$	−0.811701	−0.0257326
$996$	−233.200	−7.38923
$997$	−28.5190	−0.903206	−0.451603	−	0.892219i	$-0.649148\pi$
$997$	−28.5190	−0.903206	−0.451603	+	0.892219i	$0.649148\pi$
$998$	−63.9635	−2.02473
$999$	6.33529	0.200440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.10	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.10	✓	174	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)

\(f(q)\)	\(=\)	\(q-2.64790 q^{2} -2.80956 q^{3} +5.01138 q^{4} +2.16330 q^{5} +7.43944 q^{6} +3.49626 q^{7} -7.97383 q^{8} +4.89364 q^{9} +O(q^{10})\)	\(q-2.64790 q^{2} -2.80956 q^{3} +5.01138 q^{4} +2.16330 q^{5} +7.43944 q^{6} +3.49626 q^{7} -7.97383 q^{8} +4.89364 q^{9} -5.72819 q^{10} +6.02925 q^{11} -14.0798 q^{12} +1.00000 q^{13} -9.25774 q^{14} -6.07792 q^{15} +11.0911 q^{16} -0.228765 q^{17} -12.9579 q^{18} +6.34290 q^{19} +10.8411 q^{20} -9.82295 q^{21} -15.9648 q^{22} +0.531904 q^{23} +22.4030 q^{24} -0.320150 q^{25} -2.64790 q^{26} -5.32030 q^{27} +17.5211 q^{28} +8.76346 q^{29} +16.0937 q^{30} -1.37536 q^{31} -13.4206 q^{32} -16.9395 q^{33} +0.605747 q^{34} +7.56344 q^{35} +24.5239 q^{36} -1.19078 q^{37} -16.7954 q^{38} -2.80956 q^{39} -17.2497 q^{40} -0.870904 q^{41} +26.0102 q^{42} -9.03405 q^{43} +30.2148 q^{44} +10.5864 q^{45} -1.40843 q^{46} -5.85132 q^{47} -31.1613 q^{48} +5.22382 q^{49} +0.847724 q^{50} +0.642730 q^{51} +5.01138 q^{52} -13.0641 q^{53} +14.0876 q^{54} +13.0430 q^{55} -27.8786 q^{56} -17.8208 q^{57} -23.2048 q^{58} -10.8614 q^{59} -30.4587 q^{60} +6.09692 q^{61} +3.64183 q^{62} +17.1094 q^{63} +13.3541 q^{64} +2.16330 q^{65} +44.8542 q^{66} -6.97733 q^{67} -1.14643 q^{68} -1.49442 q^{69} -20.0272 q^{70} +0.122416 q^{71} -39.0210 q^{72} +4.31860 q^{73} +3.15306 q^{74} +0.899480 q^{75} +31.7867 q^{76} +21.0798 q^{77} +7.43944 q^{78} -1.42583 q^{79} +23.9934 q^{80} +0.266801 q^{81} +2.30607 q^{82} +16.5628 q^{83} -49.2265 q^{84} -0.494887 q^{85} +23.9213 q^{86} -24.6215 q^{87} -48.0762 q^{88} +16.0574 q^{89} -28.0317 q^{90} +3.49626 q^{91} +2.66557 q^{92} +3.86417 q^{93} +15.4937 q^{94} +13.7216 q^{95} +37.7060 q^{96} +9.54110 q^{97} -13.8321 q^{98} +29.5050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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