LMFDB - Embedded newform 8021.2.a.c.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.78389 q^{2} +2.33732 q^{3} +5.75006 q^{4} +3.09975 q^{5} -6.50684 q^{6} -2.32296 q^{7} -10.4398 q^{8} +2.46305 q^{9} +O(q^{10})$	\(q-2.78389 q^{2} +2.33732 q^{3} +5.75006 q^{4} +3.09975 q^{5} -6.50684 q^{6} -2.32296 q^{7} -10.4398 q^{8} +2.46305 q^{9} -8.62938 q^{10} +6.30075 q^{11} +13.4397 q^{12} -1.00000 q^{13} +6.46688 q^{14} +7.24510 q^{15} +17.5631 q^{16} +7.40726 q^{17} -6.85686 q^{18} +0.681595 q^{19} +17.8238 q^{20} -5.42949 q^{21} -17.5406 q^{22} -5.23409 q^{23} -24.4011 q^{24} +4.60846 q^{25} +2.78389 q^{26} -1.25503 q^{27} -13.3572 q^{28} +0.739462 q^{29} -20.1696 q^{30} -1.36413 q^{31} -28.0143 q^{32} +14.7268 q^{33} -20.6210 q^{34} -7.20060 q^{35} +14.1627 q^{36} +0.589819 q^{37} -1.89749 q^{38} -2.33732 q^{39} -32.3607 q^{40} -2.61654 q^{41} +15.1151 q^{42} -10.7425 q^{43} +36.2297 q^{44} +7.63483 q^{45} +14.5712 q^{46} +7.85875 q^{47} +41.0505 q^{48} -1.60385 q^{49} -12.8295 q^{50} +17.3131 q^{51} -5.75006 q^{52} -9.22754 q^{53} +3.49388 q^{54} +19.5308 q^{55} +24.2512 q^{56} +1.59310 q^{57} -2.05858 q^{58} +7.48241 q^{59} +41.6598 q^{60} -8.86669 q^{61} +3.79760 q^{62} -5.72156 q^{63} +42.8626 q^{64} -3.09975 q^{65} -40.9980 q^{66} +6.64496 q^{67} +42.5922 q^{68} -12.2337 q^{69} +20.0457 q^{70} +13.1387 q^{71} -25.7137 q^{72} +14.3271 q^{73} -1.64199 q^{74} +10.7714 q^{75} +3.91922 q^{76} -14.6364 q^{77} +6.50684 q^{78} +3.71795 q^{79} +54.4413 q^{80} -10.3225 q^{81} +7.28417 q^{82} +10.4126 q^{83} -31.2199 q^{84} +22.9607 q^{85} +29.9060 q^{86} +1.72836 q^{87} -65.7785 q^{88} +15.3356 q^{89} -21.2546 q^{90} +2.32296 q^{91} -30.0964 q^{92} -3.18841 q^{93} -21.8779 q^{94} +2.11278 q^{95} -65.4782 q^{96} +5.64189 q^{97} +4.46495 q^{98} +15.5190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.78389	−1.96851	−0.984255	−	0.176754i	$-0.943440\pi$
$2$	−2.78389	−1.96851	−0.984255	+	0.176754i	$0.943440\pi$
$3$	2.33732	1.34945	0.674725	−	0.738069i	$-0.264262\pi$
$3$	2.33732	1.34945	0.674725	+	0.738069i	$0.264262\pi$
$4$	5.75006	2.87503
$5$	3.09975	1.38625	0.693126	−	0.720817i	$-0.256233\pi$
$5$	3.09975	1.38625	0.693126	+	0.720817i	$0.256233\pi$
$6$	−6.50684	−2.65641
$7$	−2.32296	−0.877997	−0.438998	−	0.898488i	$-0.644667\pi$
$7$	−2.32296	−0.877997	−0.438998	+	0.898488i	$0.644667\pi$
$8$	−10.4398	−3.69102
$9$	2.46305	0.821015
$10$	−8.62938	−2.72885
$11$	6.30075	1.89975	0.949874	−	0.312633i	$-0.101211\pi$
$11$	6.30075	1.89975	0.949874	+	0.312633i	$0.101211\pi$
$12$	13.4397	3.87971
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	6.46688	1.72835
$15$	7.24510	1.87068
$16$	17.5631	4.39078
$17$	7.40726	1.79652	0.898262	−	0.439459i	$-0.144830\pi$
$17$	7.40726	1.79652	0.898262	+	0.439459i	$0.144830\pi$
$18$	−6.85686	−1.61618
$19$	0.681595	0.156369	0.0781843	−	0.996939i	$-0.475088\pi$
$19$	0.681595	0.156369	0.0781843	+	0.996939i	$0.475088\pi$
$20$	17.8238	3.98552
$21$	−5.42949	−1.18481
$22$	−17.5406	−3.73967
$23$	−5.23409	−1.09138	−0.545692	−	0.837986i	$-0.683733\pi$
$23$	−5.23409	−1.09138	−0.545692	+	0.837986i	$0.683733\pi$
$24$	−24.4011	−4.98085
$25$	4.60846	0.921692
$26$	2.78389	0.545966
$27$	−1.25503	−0.241531
$28$	−13.3572	−2.52427
$29$	0.739462	0.137315	0.0686573	−	0.997640i	$-0.478128\pi$
$29$	0.739462	0.137315	0.0686573	+	0.997640i	$0.478128\pi$
$30$	−20.1696	−3.68245
$31$	−1.36413	−0.245006	−0.122503	−	0.992468i	$-0.539092\pi$
$31$	−1.36413	−0.245006	−0.122503	+	0.992468i	$0.539092\pi$
$32$	−28.0143	−4.95227
$33$	14.7268	2.56362
$34$	−20.6210	−3.53648
$35$	−7.20060	−1.21712
$36$	14.1627	2.36045
$37$	0.589819	0.0969657	0.0484828	−	0.998824i	$-0.484561\pi$
$37$	0.589819	0.0969657	0.0484828	+	0.998824i	$0.484561\pi$
$38$	−1.89749	−0.307813
$39$	−2.33732	−0.374270
$40$	−32.3607	−5.11668
$41$	−2.61654	−0.408635	−0.204317	−	0.978905i	$-0.565497\pi$
$41$	−2.61654	−0.408635	−0.204317	+	0.978905i	$0.565497\pi$
$42$	15.1151	2.33232
$43$	−10.7425	−1.63822	−0.819109	−	0.573638i	$-0.805532\pi$
$43$	−10.7425	−1.63822	−0.819109	+	0.573638i	$0.805532\pi$
$44$	36.2297	5.46184
$45$	7.63483	1.13813
$46$	14.5712	2.14840
$47$	7.85875	1.14632	0.573158	−	0.819445i	$-0.305718\pi$
$47$	7.85875	1.14632	0.573158	+	0.819445i	$0.305718\pi$
$48$	41.0505	5.92514
$49$	−1.60385	−0.229122
$50$	−12.8295	−1.81436
$51$	17.3131	2.42432
$52$	−5.75006	−0.797391
$53$	−9.22754	−1.26750	−0.633750	−	0.773538i	$-0.718485\pi$
$53$	−9.22754	−1.26750	−0.633750	+	0.773538i	$0.718485\pi$
$54$	3.49388	0.475456
$55$	19.5308	2.63353
$56$	24.2512	3.24070
$57$	1.59310	0.211012
$58$	−2.05858	−0.270305
$59$	7.48241	0.974127	0.487064	−	0.873367i	$-0.338068\pi$
$59$	7.48241	0.974127	0.487064	+	0.873367i	$0.338068\pi$
$60$	41.6598	5.37826
$61$	−8.86669	−1.13526	−0.567632	−	0.823283i	$-0.692140\pi$
$61$	−8.86669	−1.13526	−0.567632	+	0.823283i	$0.692140\pi$
$62$	3.79760	0.482296
$63$	−5.72156	−0.720849
$64$	42.8626	5.35782
$65$	−3.09975	−0.384477
$66$	−40.9980	−5.04650
$67$	6.64496	0.811811	0.405906	−	0.913915i	$-0.366956\pi$
$67$	6.64496	0.811811	0.405906	+	0.913915i	$0.366956\pi$
$68$	42.5922	5.16507
$69$	−12.2337	−1.47277
$70$	20.0457	2.39592
$71$	13.1387	1.55928	0.779639	−	0.626229i	$-0.215403\pi$
$71$	13.1387	1.55928	0.779639	+	0.626229i	$0.215403\pi$
$72$	−25.7137	−3.03038
$73$	14.3271	1.67686	0.838429	−	0.545011i	$-0.183475\pi$
$73$	14.3271	1.67686	0.838429	+	0.545011i	$0.183475\pi$
$74$	−1.64199	−0.190878
$75$	10.7714	1.24378
$76$	3.91922	0.449565
$77$	−14.6364	−1.66797
$78$	6.50684	0.736754
$79$	3.71795	0.418302	0.209151	−	0.977883i	$-0.432930\pi$
$79$	3.71795	0.418302	0.209151	+	0.977883i	$0.432930\pi$
$80$	54.4413	6.08672
$81$	−10.3225	−1.14695
$82$	7.28417	0.804402
$83$	10.4126	1.14293	0.571466	−	0.820626i	$-0.306375\pi$
$83$	10.4126	1.14293	0.571466	+	0.820626i	$0.306375\pi$
$84$	−31.2199	−3.40638
$85$	22.9607	2.49043
$86$	29.9060	3.22485
$87$	1.72836	0.185299
$88$	−65.7785	−7.01201
$89$	15.3356	1.62557	0.812786	−	0.582563i	$-0.197950\pi$
$89$	15.3356	1.62557	0.812786	+	0.582563i	$0.197950\pi$
$90$	−21.2546	−2.24043
$91$	2.32296	0.243512
$92$	−30.0964	−3.13776
$93$	−3.18841	−0.330623
$94$	−21.8779	−2.25654
$95$	2.11278	0.216766
$96$	−65.4782	−6.68284
$97$	5.64189	0.572847	0.286423	−	0.958103i	$-0.407534\pi$
$97$	5.64189	0.572847	0.286423	+	0.958103i	$0.407534\pi$
$98$	4.46495	0.451028
$99$	15.5190	1.55972
$100$	26.4990	2.64990
$101$	7.58428	0.754664	0.377332	−	0.926078i	$-0.376842\pi$
$101$	7.58428	0.754664	0.377332	+	0.926078i	$0.376842\pi$
$102$	−48.1979	−4.77230
$103$	0.320308	0.0315608	0.0157804	−	0.999875i	$-0.494977\pi$
$103$	0.320308	0.0315608	0.0157804	+	0.999875i	$0.494977\pi$
$104$	10.4398	1.02370
$105$	−16.8301	−1.64245
$106$	25.6885	2.49509
$107$	−1.92523	−0.186119	−0.0930595	−	0.995661i	$-0.529665\pi$
$107$	−1.92523	−0.186119	−0.0930595	+	0.995661i	$0.529665\pi$
$108$	−7.21652	−0.694410
$109$	−3.90414	−0.373949	−0.186974	−	0.982365i	$-0.559868\pi$
$109$	−3.90414	−0.373949	−0.186974	+	0.982365i	$0.559868\pi$
$110$	−54.3716	−5.18413
$111$	1.37859	0.130850
$112$	−40.7984	−3.85509
$113$	16.7957	1.58000	0.790002	−	0.613105i	$-0.210080\pi$
$113$	16.7957	1.58000	0.790002	+	0.613105i	$0.210080\pi$
$114$	−4.43503	−0.415379
$115$	−16.2244	−1.51293
$116$	4.25195	0.394784
$117$	−2.46305	−0.227709
$118$	−20.8302	−1.91758
$119$	−17.2068	−1.57734
$120$	−75.6373	−6.90471
$121$	28.6995	2.60904
$122$	24.6839	2.23478
$123$	−6.11568	−0.551432
$124$	−7.84386	−0.704399
$125$	−1.21367	−0.108554
$126$	15.9282	1.41900
$127$	−4.26505	−0.378462	−0.189231	−	0.981933i	$-0.560600\pi$
$127$	−4.26505	−0.378462	−0.189231	+	0.981933i	$0.560600\pi$
$128$	−63.2963	−5.59465
$129$	−25.1086	−2.21069
$130$	8.62938	0.756847
$131$	14.7243	1.28647	0.643233	−	0.765671i	$-0.277593\pi$
$131$	14.7243	1.28647	0.643233	+	0.765671i	$0.277593\pi$
$132$	84.6803	7.37048
$133$	−1.58332	−0.137291
$134$	−18.4989	−1.59806
$135$	−3.89029	−0.334823
$136$	−77.3302	−6.63101
$137$	−5.83636	−0.498634	−0.249317	−	0.968422i	$-0.580206\pi$
$137$	−5.83636	−0.498634	−0.249317	+	0.968422i	$0.580206\pi$
$138$	34.0574	2.89916
$139$	−2.90224	−0.246165	−0.123082	−	0.992396i	$-0.539278\pi$
$139$	−2.90224	−0.246165	−0.123082	+	0.992396i	$0.539278\pi$
$140$	−41.4039	−3.49927
$141$	18.3684	1.54690
$142$	−36.5768	−3.06946
$143$	−6.30075	−0.526895
$144$	43.2588	3.60490
$145$	2.29215	0.190353
$146$	−39.8851	−3.30091
$147$	−3.74871	−0.309188
$148$	3.39150	0.278779
$149$	−0.385776	−0.0316040	−0.0158020	−	0.999875i	$-0.505030\pi$
$149$	−0.385776	−0.0316040	−0.0158020	+	0.999875i	$0.505030\pi$
$150$	−29.9865	−2.44839
$151$	1.47203	0.119792	0.0598959	−	0.998205i	$-0.480923\pi$
$151$	1.47203	0.119792	0.0598959	+	0.998205i	$0.480923\pi$
$152$	−7.11571	−0.577160
$153$	18.2444	1.47497
$154$	40.7462	3.28342
$155$	−4.22848	−0.339639
$156$	−13.4397	−1.07604
$157$	13.3717	1.06718	0.533588	−	0.845745i	$-0.320843\pi$
$157$	13.3717	1.06718	0.533588	+	0.845745i	$0.320843\pi$
$158$	−10.3504	−0.823432
$159$	−21.5677	−1.71043
$160$	−86.8373	−6.86509
$161$	12.1586	0.958231
$162$	28.7369	2.25778
$163$	4.49172	0.351819	0.175909	−	0.984406i	$-0.443713\pi$
$163$	4.49172	0.351819	0.175909	+	0.984406i	$0.443713\pi$
$164$	−15.0453	−1.17484
$165$	45.6496	3.55381
$166$	−28.9876	−2.24987
$167$	−19.3436	−1.49685	−0.748425	−	0.663219i	$-0.769190\pi$
$167$	−19.3436	−1.49685	−0.748425	+	0.663219i	$0.769190\pi$
$168$	56.6827	4.37317
$169$	1.00000	0.0769231
$170$	−63.9201	−4.90245
$171$	1.67880	0.128381
$172$	−61.7702	−4.70993
$173$	−10.8146	−0.822222	−0.411111	−	0.911585i	$-0.634859\pi$
$173$	−10.8146	−0.822222	−0.411111	+	0.911585i	$0.634859\pi$
$174$	−4.81156	−0.364763
$175$	−10.7053	−0.809243
$176$	110.661	8.34137
$177$	17.4888	1.31454
$178$	−42.6927	−3.19995
$179$	−7.45678	−0.557346	−0.278673	−	0.960386i	$-0.589895\pi$
$179$	−7.45678	−0.557346	−0.278673	+	0.960386i	$0.589895\pi$
$180$	43.9008	3.27217
$181$	23.8535	1.77302	0.886508	−	0.462712i	$-0.153124\pi$
$181$	23.8535	1.77302	0.886508	+	0.462712i	$0.153124\pi$
$182$	−6.46688	−0.479357
$183$	−20.7243	−1.53198
$184$	54.6428	4.02832
$185$	1.82829	0.134419
$186$	8.87620	0.650834
$187$	46.6713	3.41295
$188$	45.1883	3.29570
$189$	2.91539	0.212063
$190$	−5.88174	−0.426707
$191$	6.86260	0.496560	0.248280	−	0.968688i	$-0.420135\pi$
$191$	6.86260	0.496560	0.248280	+	0.968688i	$0.420135\pi$
$192$	100.183	7.23011
$193$	21.5422	1.55064	0.775319	−	0.631569i	$-0.217589\pi$
$193$	21.5422	1.55064	0.775319	+	0.631569i	$0.217589\pi$
$194$	−15.7064	−1.12765
$195$	−7.24510	−0.518832
$196$	−9.22225	−0.658732
$197$	−14.3521	−1.02255	−0.511273	−	0.859418i	$-0.670826\pi$
$197$	−14.3521	−1.02255	−0.511273	+	0.859418i	$0.670826\pi$
$198$	−43.2034	−3.07033
$199$	11.8406	0.839361	0.419680	−	0.907672i	$-0.362142\pi$
$199$	11.8406	0.839361	0.419680	+	0.907672i	$0.362142\pi$
$200$	−48.1113	−3.40199
$201$	15.5314	1.09550
$202$	−21.1138	−1.48556
$203$	−1.71774	−0.120562
$204$	99.5515	6.97000
$205$	−8.11063	−0.566471
$206$	−0.891702	−0.0621279
$207$	−12.8918	−0.896042
$208$	−17.5631	−1.21778
$209$	4.29456	0.297061
$210$	46.8532	3.23318
$211$	−7.31411	−0.503524	−0.251762	−	0.967789i	$-0.581010\pi$
$211$	−7.31411	−0.503524	−0.251762	+	0.967789i	$0.581010\pi$
$212$	−53.0590	−3.64410
$213$	30.7093	2.10417
$214$	5.35963	0.366377
$215$	−33.2991	−2.27098
$216$	13.1023	0.891496
$217$	3.16883	0.215114
$218$	10.8687	0.736122
$219$	33.4869	2.26284
$220$	112.303	7.57148
$221$	−7.40726	−0.498266
$222$	−3.83786	−0.257580
$223$	25.1557	1.68455	0.842276	−	0.539047i	$-0.181215\pi$
$223$	25.1557	1.68455	0.842276	+	0.539047i	$0.181215\pi$
$224$	65.0761	4.34808
$225$	11.3509	0.756723
$226$	−46.7574	−3.11025
$227$	−16.2086	−1.07580	−0.537901	−	0.843008i	$-0.680782\pi$
$227$	−16.2086	−1.07580	−0.537901	+	0.843008i	$0.680782\pi$
$228$	9.16045	0.606665
$229$	−17.2694	−1.14119	−0.570596	−	0.821231i	$-0.693288\pi$
$229$	−17.2694	−1.14119	−0.570596	+	0.821231i	$0.693288\pi$
$230$	45.1670	2.97822
$231$	−34.2099	−2.25085
$232$	−7.71982	−0.506831
$233$	−9.39380	−0.615408	−0.307704	−	0.951482i	$-0.599561\pi$
$233$	−9.39380	−0.615408	−0.307704	+	0.951482i	$0.599561\pi$
$234$	6.85686	0.448247
$235$	24.3602	1.58908
$236$	43.0244	2.80065
$237$	8.69002	0.564478
$238$	47.9019	3.10502
$239$	2.62953	0.170090	0.0850450	−	0.996377i	$-0.472897\pi$
$239$	2.62953	0.170090	0.0850450	+	0.996377i	$0.472897\pi$
$240$	127.247	8.21373
$241$	−28.7650	−1.85292	−0.926458	−	0.376399i	$-0.877162\pi$
$241$	−28.7650	−1.85292	−0.926458	+	0.376399i	$0.877162\pi$
$242$	−79.8963	−5.13593
$243$	−20.3619	−1.30622
$244$	−50.9841	−3.26392
$245$	−4.97154	−0.317620
$246$	17.0254	1.08550
$247$	−0.681595	−0.0433689
$248$	14.2413	0.904321
$249$	24.3375	1.54233
$250$	3.37873	0.213690
$251$	12.5677	0.793269	0.396635	−	0.917977i	$-0.370178\pi$
$251$	12.5677	0.793269	0.396635	+	0.917977i	$0.370178\pi$
$252$	−32.8993	−2.07246
$253$	−32.9787	−2.07335
$254$	11.8735	0.745007
$255$	53.6663	3.36072
$256$	90.4849	5.65531
$257$	24.9566	1.55675	0.778375	−	0.627800i	$-0.216044\pi$
$257$	24.9566	1.55675	0.778375	+	0.627800i	$0.216044\pi$
$258$	69.8998	4.35177
$259$	−1.37013	−0.0851355
$260$	−17.8238	−1.10538
$261$	1.82133	0.112737
$262$	−40.9908	−2.53242
$263$	0.862442	0.0531804	0.0265902	−	0.999646i	$-0.491535\pi$
$263$	0.862442	0.0531804	0.0265902	+	0.999646i	$0.491535\pi$
$264$	−153.745	−9.46236
$265$	−28.6031	−1.75707
$266$	4.40779	0.270259
$267$	35.8442	2.19363
$268$	38.2090	2.33398
$269$	−26.0142	−1.58612	−0.793058	−	0.609146i	$-0.791512\pi$
$269$	−26.0142	−1.58612	−0.793058	+	0.609146i	$0.791512\pi$
$270$	10.8301	0.659102
$271$	24.6631	1.49818	0.749088	−	0.662470i	$-0.230492\pi$
$271$	24.6631	1.49818	0.749088	+	0.662470i	$0.230492\pi$
$272$	130.095	7.88814
$273$	5.42949	0.328608
$274$	16.2478	0.981566
$275$	29.0368	1.75098
$276$	−70.3447	−4.23425
$277$	12.9146	0.775964	0.387982	−	0.921667i	$-0.373172\pi$
$277$	12.9146	0.775964	0.387982	+	0.921667i	$0.373172\pi$
$278$	8.07953	0.484578
$279$	−3.35992	−0.201153
$280$	75.1727	4.49243
$281$	18.2430	1.08829	0.544144	−	0.838992i	$-0.316855\pi$
$281$	18.2430	1.08829	0.544144	+	0.838992i	$0.316855\pi$
$282$	−51.1356	−3.04508
$283$	−9.32662	−0.554410	−0.277205	−	0.960811i	$-0.589408\pi$
$283$	−9.32662	−0.554410	−0.277205	+	0.960811i	$0.589408\pi$
$284$	75.5484	4.48298
$285$	4.93823	0.292515
$286$	17.5406	1.03720
$287$	6.07812	0.358780
$288$	−69.0005	−4.06589
$289$	37.8675	2.22750
$290$	−6.38110	−0.374711
$291$	13.1869	0.773028
$292$	82.3816	4.82102
$293$	−27.6039	−1.61263	−0.806317	−	0.591483i	$-0.798542\pi$
$293$	−27.6039	−1.61263	−0.806317	+	0.591483i	$0.798542\pi$
$294$	10.4360	0.608640
$295$	23.1936	1.35038
$296$	−6.15758	−0.357902
$297$	−7.90765	−0.458848
$298$	1.07396	0.0622129
$299$	5.23409	0.302695
$300$	61.9364	3.57590
$301$	24.9544	1.43835
$302$	−4.09797	−0.235811
$303$	17.7269	1.01838
$304$	11.9709	0.686580
$305$	−27.4845	−1.57376
$306$	−50.7905	−2.90350
$307$	−21.7504	−1.24136	−0.620679	−	0.784065i	$-0.713143\pi$
$307$	−21.7504	−1.24136	−0.620679	+	0.784065i	$0.713143\pi$
$308$	−84.1603	−4.79548
$309$	0.748660	0.0425898
$310$	11.7716	0.668584
$311$	−10.8596	−0.615792	−0.307896	−	0.951420i	$-0.599625\pi$
$311$	−10.8596	−0.615792	−0.307896	+	0.951420i	$0.599625\pi$
$312$	24.4011	1.38144
$313$	−16.4751	−0.931230	−0.465615	−	0.884987i	$-0.654167\pi$
$313$	−16.4751	−0.931230	−0.465615	+	0.884987i	$0.654167\pi$
$314$	−37.2253	−2.10075
$315$	−17.7354	−0.999277
$316$	21.3785	1.20263
$317$	−8.13973	−0.457173	−0.228586	−	0.973524i	$-0.573410\pi$
$317$	−8.13973	−0.457173	−0.228586	+	0.973524i	$0.573410\pi$
$318$	60.0421	3.36700
$319$	4.65917	0.260863
$320$	132.863	7.42728
$321$	−4.49987	−0.251158
$322$	−33.8482	−1.88629
$323$	5.04875	0.280920
$324$	−59.3553	−3.29752
$325$	−4.60846	−0.255631
$326$	−12.5045	−0.692559
$327$	−9.12520	−0.504625
$328$	27.3161	1.50828
$329$	−18.2556	−1.00646
$330$	−127.084	−6.99572
$331$	−8.73498	−0.480118	−0.240059	−	0.970758i	$-0.577167\pi$
$331$	−8.73498	−0.480118	−0.240059	+	0.970758i	$0.577167\pi$
$332$	59.8732	3.28597
$333$	1.45275	0.0796103
$334$	53.8504	2.94656
$335$	20.5977	1.12537
$336$	−95.3588	−5.20225
$337$	−22.9402	−1.24963	−0.624816	−	0.780772i	$-0.714826\pi$
$337$	−22.9402	−1.24963	−0.624816	+	0.780772i	$0.714826\pi$
$338$	−2.78389	−0.151424
$339$	39.2568	2.13214
$340$	132.025	7.16008
$341$	−8.59507	−0.465449
$342$	−4.67360	−0.252719
$343$	19.9864	1.07916
$344$	112.150	6.04670
$345$	−37.9215	−2.04163
$346$	30.1068	1.61855
$347$	0.0164978	0.000885647 0	0.000442824	−	1.00000i	$-0.499859\pi$
$347$	0.0164978	0.000885647 0	0.000442824		1.00000i	$0.499859\pi$
$348$	9.93816	0.532741
$349$	−13.1484	−0.703815	−0.351908	−	0.936035i	$-0.614467\pi$
$349$	−13.1484	−0.703815	−0.351908	+	0.936035i	$0.614467\pi$
$350$	29.8024	1.59300
$351$	1.25503	0.0669887
$352$	−176.511	−9.40807
$353$	3.53401	0.188096	0.0940482	−	0.995568i	$-0.470019\pi$
$353$	3.53401	0.188096	0.0940482	+	0.995568i	$0.470019\pi$
$354$	−48.6869	−2.58768
$355$	40.7267	2.16155
$356$	88.1808	4.67357
$357$	−40.2177	−2.12855
$358$	20.7589	1.09714
$359$	−25.4651	−1.34399	−0.671997	−	0.740554i	$-0.734563\pi$
$359$	−25.4651	−1.34399	−0.671997	+	0.740554i	$0.734563\pi$
$360$	−79.7060	−4.20087
$361$	−18.5354	−0.975549
$362$	−66.4056	−3.49020
$363$	67.0797	3.52077
$364$	13.3572	0.700106
$365$	44.4104	2.32455
$366$	57.6941	3.01572
$367$	−33.0957	−1.72758	−0.863790	−	0.503851i	$-0.831916\pi$
$367$	−33.0957	−1.72758	−0.863790	+	0.503851i	$0.831916\pi$
$368$	−91.9270	−4.79202
$369$	−6.44466	−0.335496
$370$	−5.08977	−0.264605
$371$	21.4352	1.11286
$372$	−18.3336	−0.950551
$373$	−33.4737	−1.73320	−0.866602	−	0.499000i	$-0.833701\pi$
$373$	−33.4737	−1.73320	−0.866602	+	0.499000i	$0.833701\pi$
$374$	−129.928	−6.71842
$375$	−2.83673	−0.146488
$376$	−82.0436	−4.23108
$377$	−0.739462	−0.0380842
$378$	−8.11614	−0.417449
$379$	1.42937	0.0734216	0.0367108	−	0.999326i	$-0.488312\pi$
$379$	1.42937	0.0734216	0.0367108	+	0.999326i	$0.488312\pi$
$380$	12.1486	0.623210
$381$	−9.96878	−0.510716
$382$	−19.1047	−0.977483
$383$	−22.5810	−1.15384	−0.576918	−	0.816802i	$-0.695745\pi$
$383$	−22.5810	−1.15384	−0.576918	+	0.816802i	$0.695745\pi$
$384$	−147.943	−7.54970
$385$	−45.3692	−2.31223
$386$	−59.9711	−3.05245
$387$	−26.4593	−1.34500
$388$	32.4412	1.64695
$389$	0.795002	0.0403082	0.0201541	−	0.999797i	$-0.493584\pi$
$389$	0.795002	0.0403082	0.0201541	+	0.999797i	$0.493584\pi$
$390$	20.1696	1.02133
$391$	−38.7703	−1.96070
$392$	16.7439	0.845693
$393$	34.4153	1.73602
$394$	39.9548	2.01289
$395$	11.5247	0.579872
$396$	89.2355	4.48425
$397$	0.166320	0.00834735	0.00417368	−	0.999991i	$-0.498671\pi$
$397$	0.166320	0.00834735	0.00417368	+	0.999991i	$0.498671\pi$
$398$	−32.9631	−1.65229
$399$	−3.70072	−0.185268
$400$	80.9389	4.04695
$401$	−32.0601	−1.60101	−0.800503	−	0.599329i	$-0.795434\pi$
$401$	−32.0601	−1.60101	−0.800503	+	0.599329i	$0.795434\pi$
$402$	−43.2377	−2.15650
$403$	1.36413	0.0679523
$404$	43.6101	2.16968
$405$	−31.9973	−1.58996
$406$	4.78201	0.237327
$407$	3.71630	0.184210
$408$	−180.745	−8.94822
$409$	12.1009	0.598351	0.299176	−	0.954198i	$-0.403288\pi$
$409$	12.1009	0.598351	0.299176	+	0.954198i	$0.403288\pi$
$410$	22.5791	1.11510
$411$	−13.6414	−0.672881
$412$	1.84179	0.0907385
$413$	−17.3814	−0.855280
$414$	35.8894	1.76387
$415$	32.2765	1.58439
$416$	28.0143	1.37351
$417$	−6.78345	−0.332187
$418$	−11.9556	−0.584768
$419$	4.17270	0.203850	0.101925	−	0.994792i	$-0.467500\pi$
$419$	4.17270	0.203850	0.101925	+	0.994792i	$0.467500\pi$
$420$	−96.7741	−4.72209
$421$	0.00411092	0.000200354 0	0.000100177	−	1.00000i	$-0.499968\pi$
$421$	0.00411092	0.000200354 0	0.000100177		1.00000i	$0.499968\pi$
$422$	20.3617	0.991192
$423$	19.3565	0.941143
$424$	96.3335	4.67837
$425$	34.1361	1.65584
$426$	−85.4915	−4.14208
$427$	20.5970	0.996758
$428$	−11.0702	−0.535098
$429$	−14.7268	−0.711019
$430$	92.7012	4.47045
$431$	15.7748	0.759847	0.379924	−	0.925018i	$-0.375950\pi$
$431$	15.7748	0.759847	0.379924	+	0.925018i	$0.375950\pi$
$432$	−22.0423	−1.06051
$433$	−17.1344	−0.823425	−0.411712	−	0.911314i	$-0.635069\pi$
$433$	−17.1344	−0.823425	−0.411712	+	0.911314i	$0.635069\pi$
$434$	−8.82169	−0.423454
$435$	5.35748	0.256871
$436$	−22.4490	−1.07511
$437$	−3.56753	−0.170658
$438$	−93.2240	−4.45441
$439$	16.0886	0.767866	0.383933	−	0.923361i	$-0.374569\pi$
$439$	16.0886	0.767866	0.383933	+	0.923361i	$0.374569\pi$
$440$	−203.897	−9.72041
$441$	−3.95036	−0.188112
$442$	20.6210	0.980842
$443$	17.3407	0.823882	0.411941	−	0.911210i	$-0.364851\pi$
$443$	17.3407	0.823882	0.411941	+	0.911210i	$0.364851\pi$
$444$	7.92700	0.376199
$445$	47.5366	2.25345
$446$	−70.0309	−3.31606
$447$	−0.901681	−0.0426481
$448$	−99.5681	−4.70415
$449$	−6.15732	−0.290582	−0.145291	−	0.989389i	$-0.546412\pi$
$449$	−6.15732	−0.290582	−0.145291	+	0.989389i	$0.546412\pi$
$450$	−31.5996	−1.48962
$451$	−16.4862	−0.776304
$452$	96.5762	4.54256
$453$	3.44059	0.161653
$454$	45.1230	2.11773
$455$	7.20060	0.337569
$456$	−16.6317	−0.778848
$457$	−15.7549	−0.736984	−0.368492	−	0.929631i	$-0.620126\pi$
$457$	−15.7549	−0.736984	−0.368492	+	0.929631i	$0.620126\pi$
$458$	48.0761	2.24645
$459$	−9.29635	−0.433916
$460$	−93.2913	−4.34973
$461$	25.1789	1.17270	0.586350	−	0.810058i	$-0.300564\pi$
$461$	25.1789	1.17270	0.586350	+	0.810058i	$0.300564\pi$
$462$	95.2367	4.43081
$463$	8.82413	0.410092	0.205046	−	0.978752i	$-0.434266\pi$
$463$	8.82413	0.410092	0.205046	+	0.978752i	$0.434266\pi$
$464$	12.9873	0.602918
$465$	−9.88328	−0.458326
$466$	26.1513	1.21144
$467$	−30.5223	−1.41241	−0.706203	−	0.708010i	$-0.749593\pi$
$467$	−30.5223	−1.41241	−0.706203	+	0.708010i	$0.749593\pi$
$468$	−14.1627	−0.654670
$469$	−15.4360	−0.712768
$470$	−67.8161	−3.12813
$471$	31.2538	1.44010
$472$	−78.1147	−3.59552
$473$	−67.6859	−3.11220
$474$	−24.1921	−1.11118
$475$	3.14111	0.144124
$476$	−98.9401	−4.53491
$477$	−22.7279	−1.04064
$478$	−7.32033	−0.334824
$479$	−5.41846	−0.247576	−0.123788	−	0.992309i	$-0.539504\pi$
$479$	−5.41846	−0.247576	−0.123788	+	0.992309i	$0.539504\pi$
$480$	−202.966	−9.26410
$481$	−0.589819	−0.0268934
$482$	80.0787	3.64748
$483$	28.4185	1.29309
$484$	165.024	7.50108
$485$	17.4884	0.794110
$486$	56.6855	2.57131
$487$	22.6460	1.02619	0.513094	−	0.858332i	$-0.328499\pi$
$487$	22.6460	1.02619	0.513094	+	0.858332i	$0.328499\pi$
$488$	92.5663	4.19028
$489$	10.4986	0.474762
$490$	13.8402	0.625238
$491$	−13.0804	−0.590310	−0.295155	−	0.955449i	$-0.595371\pi$
$491$	−13.0804	−0.590310	−0.295155	+	0.955449i	$0.595371\pi$
$492$	−35.1656	−1.58539
$493$	5.47739	0.246689
$494$	1.89749	0.0853721
$495$	48.1052	2.16217
$496$	−23.9584	−1.07577
$497$	−30.5207	−1.36904
$498$	−67.7531	−3.03609
$499$	4.36479	0.195395	0.0976973	−	0.995216i	$-0.468852\pi$
$499$	4.36479	0.195395	0.0976973	+	0.995216i	$0.468852\pi$
$500$	−6.97869	−0.312097
$501$	−45.2120	−2.01992
$502$	−34.9873	−1.56156
$503$	0.928025	0.0413786	0.0206893	−	0.999786i	$-0.493414\pi$
$503$	0.928025	0.0413786	0.0206893	+	0.999786i	$0.493414\pi$
$504$	59.7318	2.66067
$505$	23.5094	1.04615
$506$	91.8092	4.08142
$507$	2.33732	0.103804
$508$	−24.5243	−1.08809
$509$	34.5377	1.53086	0.765429	−	0.643520i	$-0.222527\pi$
$509$	34.5377	1.53086	0.765429	+	0.643520i	$0.222527\pi$
$510$	−149.401	−6.61561
$511$	−33.2812	−1.47228
$512$	−125.308	−5.53788
$513$	−0.855424	−0.0377679
$514$	−69.4765	−3.06448
$515$	0.992874	0.0437513
$516$	−144.376	−6.35581
$517$	49.5160	2.17771
$518$	3.81429	0.167590
$519$	−25.2772	−1.10955
$520$	32.3607	1.41911
$521$	11.0233	0.482941	0.241471	−	0.970408i	$-0.422370\pi$
$521$	11.0233	0.482941	0.241471	+	0.970408i	$0.422370\pi$
$522$	−5.07039	−0.221925
$523$	17.1079	0.748078	0.374039	−	0.927413i	$-0.377973\pi$
$523$	17.1079	0.748078	0.374039	+	0.927413i	$0.377973\pi$
$524$	84.6655	3.69863
$525$	−25.0216	−1.09203
$526$	−2.40095	−0.104686
$527$	−10.1045	−0.440159
$528$	258.649	11.2563
$529$	4.39571	0.191118
$530$	79.6280	3.45882
$531$	18.4295	0.799773
$532$	−9.10419	−0.394717
$533$	2.61654	0.113335
$534$	−99.7864	−4.31818
$535$	−5.96773	−0.258008
$536$	−69.3720	−2.99641
$537$	−17.4288	−0.752110
$538$	72.4209	3.12229
$539$	−10.1055	−0.435273
$540$	−22.3694	−0.962626
$541$	1.96650	0.0845465	0.0422732	−	0.999106i	$-0.486540\pi$
$541$	1.96650	0.0845465	0.0422732	+	0.999106i	$0.486540\pi$
$542$	−68.6594	−2.94918
$543$	55.7532	2.39260
$544$	−207.509	−8.89688
$545$	−12.1019	−0.518387
$546$	−15.1151	−0.646868
$547$	36.8936	1.57746	0.788729	−	0.614741i	$-0.210739\pi$
$547$	36.8936	1.57746	0.788729	+	0.614741i	$0.210739\pi$
$548$	−33.5594	−1.43359
$549$	−21.8391	−0.932069
$550$	−80.8353	−3.44683
$551$	0.504014	0.0214717
$552$	127.717	5.43601
$553$	−8.63665	−0.367268
$554$	−35.9529	−1.52749
$555$	4.27330	0.181391
$556$	−16.6881	−0.707732
$557$	22.4139	0.949707	0.474854	−	0.880065i	$-0.342501\pi$
$557$	22.4139	0.949707	0.474854	+	0.880065i	$0.342501\pi$
$558$	9.35367	0.395972
$559$	10.7425	0.454360
$560$	−126.465	−5.34412
$561$	109.086	4.60560
$562$	−50.7866	−2.14231
$563$	1.78039	0.0750347	0.0375173	−	0.999296i	$-0.488055\pi$
$563$	1.78039	0.0750347	0.0375173	+	0.999296i	$0.488055\pi$
$564$	105.619	4.44738
$565$	52.0624	2.19028
$566$	25.9643	1.09136
$567$	23.9789	1.00702
$568$	−137.165	−5.75533
$569$	12.9104	0.541234	0.270617	−	0.962687i	$-0.412772\pi$
$569$	12.9104	0.541234	0.270617	+	0.962687i	$0.412772\pi$
$570$	−13.7475	−0.575819
$571$	32.4902	1.35967	0.679837	−	0.733364i	$-0.262051\pi$
$571$	32.4902	1.35967	0.679837	+	0.733364i	$0.262051\pi$
$572$	−36.2297	−1.51484
$573$	16.0401	0.670083
$574$	−16.9208	−0.706263
$575$	−24.1211	−1.00592
$576$	105.572	4.39885
$577$	7.96911	0.331758	0.165879	−	0.986146i	$-0.446954\pi$
$577$	7.96911	0.331758	0.165879	+	0.986146i	$0.446954\pi$
$578$	−105.419	−4.38486
$579$	50.3508	2.09251
$580$	13.1800	0.547270
$581$	−24.1881	−1.00349
$582$	−36.7109	−1.52171
$583$	−58.1405	−2.40793
$584$	−149.572	−6.18932
$585$	−7.63483	−0.315661
$586$	76.8462	3.17449
$587$	33.9010	1.39924	0.699622	−	0.714513i	$-0.253352\pi$
$587$	33.9010	1.39924	0.699622	+	0.714513i	$0.253352\pi$
$588$	−21.5553	−0.888926
$589$	−0.929787	−0.0383112
$590$	−64.5686	−2.65825
$591$	−33.5454	−1.37987
$592$	10.3591	0.425755
$593$	0.484025	0.0198765	0.00993826	−	0.999951i	$-0.496837\pi$
$593$	0.484025	0.0198765	0.00993826	+	0.999951i	$0.496837\pi$
$594$	22.0140	0.903247
$595$	−53.3368	−2.18659
$596$	−2.21824	−0.0908626
$597$	27.6753	1.13268
$598$	−14.5712	−0.595859
$599$	−23.2582	−0.950304	−0.475152	−	0.879904i	$-0.657607\pi$
$599$	−23.2582	−0.950304	−0.475152	+	0.879904i	$0.657607\pi$
$600$	−112.451	−4.59081
$601$	−15.2688	−0.622826	−0.311413	−	0.950275i	$-0.600802\pi$
$601$	−15.2688	−0.622826	−0.311413	+	0.950275i	$0.600802\pi$
$602$	−69.4705	−2.83141
$603$	16.3668	0.666509
$604$	8.46425	0.344405
$605$	88.9613	3.61679
$606$	−49.3497	−2.00469
$607$	16.4422	0.667368	0.333684	−	0.942685i	$-0.391708\pi$
$607$	16.4422	0.667368	0.333684	+	0.942685i	$0.391708\pi$
$608$	−19.0944	−0.774380
$609$	−4.01490	−0.162692
$610$	76.5141	3.09796
$611$	−7.85875	−0.317931
$612$	104.907	4.24060
$613$	27.7891	1.12239	0.561196	−	0.827683i	$-0.310341\pi$
$613$	27.7891	1.12239	0.561196	+	0.827683i	$0.310341\pi$
$614$	60.5507	2.44363
$615$	−18.9571	−0.764424
$616$	152.801	6.15652
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−2.08419	−0.0838384
$619$	−10.6357	−0.427487	−0.213743	−	0.976890i	$-0.568566\pi$
$619$	−10.6357	−0.427487	−0.213743	+	0.976890i	$0.568566\pi$
$620$	−24.3140	−0.976474
$621$	6.56895	0.263603
$622$	30.2320	1.21219
$623$	−35.6240	−1.42725
$624$	−41.0505	−1.64334
$625$	−26.8044	−1.07218
$626$	45.8650	1.83314
$627$	10.0377	0.400869
$628$	76.8880	3.06816
$629$	4.36894	0.174201
$630$	49.3735	1.96709
$631$	28.1013	1.11869	0.559347	−	0.828933i	$-0.311052\pi$
$631$	28.1013	1.11869	0.559347	+	0.828933i	$0.311052\pi$
$632$	−38.8146	−1.54396
$633$	−17.0954	−0.679480
$634$	22.6601	0.899949
$635$	−13.2206	−0.524644
$636$	−124.016	−4.91754
$637$	1.60385	0.0635469
$638$	−12.9706	−0.513512
$639$	32.3612	1.28019
$640$	−196.203	−7.75559
$641$	−13.4828	−0.532540	−0.266270	−	0.963898i	$-0.585791\pi$
$641$	−13.4828	−0.532540	−0.266270	+	0.963898i	$0.585791\pi$
$642$	12.5272	0.494408
$643$	−12.6051	−0.497096	−0.248548	−	0.968620i	$-0.579953\pi$
$643$	−12.6051	−0.497096	−0.248548	+	0.968620i	$0.579953\pi$
$644$	69.9127	2.75495
$645$	−77.8306	−3.06458
$646$	−14.0552	−0.552994
$647$	15.1478	0.595520	0.297760	−	0.954641i	$-0.403761\pi$
$647$	15.1478	0.595520	0.297760	+	0.954641i	$0.403761\pi$
$648$	107.765	4.23341
$649$	47.1448	1.85060
$650$	12.8295	0.503213
$651$	7.40656	0.290286
$652$	25.8277	1.01149
$653$	−21.4006	−0.837472	−0.418736	−	0.908108i	$-0.637527\pi$
$653$	−21.4006	−0.837472	−0.418736	+	0.908108i	$0.637527\pi$
$654$	25.4036	0.993359
$655$	45.6416	1.78336
$656$	−45.9546	−1.79423
$657$	35.2882	1.37673
$658$	50.8216	1.98123
$659$	18.3375	0.714327	0.357163	−	0.934042i	$-0.383744\pi$
$659$	18.3375	0.714327	0.357163	+	0.934042i	$0.383744\pi$
$660$	262.488	10.2173
$661$	−18.8681	−0.733884	−0.366942	−	0.930244i	$-0.619595\pi$
$661$	−18.8681	−0.733884	−0.366942	+	0.930244i	$0.619595\pi$
$662$	24.3172	0.945117
$663$	−17.3131	−0.672386
$664$	−108.705	−4.21858
$665$	−4.90790	−0.190320
$666$	−4.04431	−0.156714
$667$	−3.87041	−0.149863
$668$	−111.227	−4.30349
$669$	58.7969	2.27322
$670$	−57.3419	−2.21531
$671$	−55.8668	−2.15672
$672$	152.103	5.86752
$673$	−12.2414	−0.471873	−0.235936	−	0.971769i	$-0.575816\pi$
$673$	−12.2414	−0.471873	−0.235936	+	0.971769i	$0.575816\pi$
$674$	63.8630	2.45991
$675$	−5.78377	−0.222617
$676$	5.75006	0.221156
$677$	−4.43478	−0.170442	−0.0852211	−	0.996362i	$-0.527160\pi$
$677$	−4.43478	−0.170442	−0.0852211	+	0.996362i	$0.527160\pi$
$678$	−109.287	−4.19713
$679$	−13.1059	−0.502958
$680$	−239.704	−9.19225
$681$	−37.8846	−1.45174
$682$	23.9278	0.916241
$683$	−37.0897	−1.41920	−0.709599	−	0.704605i	$-0.751124\pi$
$683$	−37.0897	−1.41920	−0.709599	+	0.704605i	$0.751124\pi$
$684$	9.65321	0.369100
$685$	−18.0913	−0.691232
$686$	−55.6401	−2.12435
$687$	−40.3640	−1.53998
$688$	−188.672	−7.19305
$689$	9.22754	0.351541
$690$	105.569	4.01896
$691$	−6.69151	−0.254557	−0.127278	−	0.991867i	$-0.540624\pi$
$691$	−6.69151	−0.254557	−0.127278	+	0.991867i	$0.540624\pi$
$692$	−62.1849	−2.36391
$693$	−36.0501	−1.36943
$694$	−0.0459281	−0.00174341
$695$	−8.99622	−0.341246
$696$	−18.0437	−0.683943
$697$	−19.3814	−0.734123
$698$	36.6036	1.38547
$699$	−21.9563	−0.830463
$700$	−61.5560	−2.32660
$701$	−20.9071	−0.789650	−0.394825	−	0.918756i	$-0.629195\pi$
$701$	−20.9071	−0.789650	−0.394825	+	0.918756i	$0.629195\pi$
$702$	−3.49388	−0.131868
$703$	0.402018	0.0151624
$704$	270.066	10.1785
$705$	56.9374	2.14439
$706$	−9.83831	−0.370270
$707$	−17.6180	−0.662592
$708$	100.562	3.77933
$709$	17.3375	0.651125	0.325563	−	0.945520i	$-0.394446\pi$
$709$	17.3375	0.651125	0.325563	+	0.945520i	$0.394446\pi$
$710$	−113.379	−4.25504
$711$	9.15748	0.343432
$712$	−160.100	−6.00002
$713$	7.14000	0.267395
$714$	111.962	4.19006
$715$	−19.5308	−0.730409
$716$	−42.8770	−1.60239
$717$	6.14604	0.229528
$718$	70.8920	2.64567
$719$	36.2597	1.35226	0.676129	−	0.736783i	$-0.263656\pi$
$719$	36.2597	1.35226	0.676129	+	0.736783i	$0.263656\pi$
$720$	134.091	4.99729
$721$	−0.744062	−0.0277103
$722$	51.6007	1.92038
$723$	−67.2328	−2.50042
$724$	137.159	5.09748
$725$	3.40778	0.126562
$726$	−186.743	−6.93068
$727$	13.8083	0.512122	0.256061	−	0.966661i	$-0.417575\pi$
$727$	13.8083	0.512122	0.256061	+	0.966661i	$0.417575\pi$
$728$	−24.2512	−0.898810
$729$	−16.6247	−0.615729
$730$	−123.634	−4.57589
$731$	−79.5726	−2.94310
$732$	−119.166	−4.40450
$733$	−37.7871	−1.39570	−0.697850	−	0.716244i	$-0.745860\pi$
$733$	−37.7871	−1.39570	−0.697850	+	0.716244i	$0.745860\pi$
$734$	92.1349	3.40076
$735$	−11.6201	−0.428612
$736$	146.629	5.40483
$737$	41.8683	1.54224
$738$	17.9412	0.660426
$739$	21.3086	0.783848	0.391924	−	0.919998i	$-0.371810\pi$
$739$	21.3086	0.783848	0.391924	+	0.919998i	$0.371810\pi$
$740$	10.5128	0.386458
$741$	−1.59310	−0.0585241
$742$	−59.6734	−2.19068
$743$	−49.2839	−1.80805	−0.904025	−	0.427479i	$-0.859402\pi$
$743$	−49.2839	−1.80805	−0.904025	+	0.427479i	$0.859402\pi$
$744$	33.2863	1.22034
$745$	−1.19581	−0.0438111
$746$	93.1873	3.41183
$747$	25.6467	0.938364
$748$	268.363	9.81233
$749$	4.47223	0.163412
$750$	7.89717	0.288364
$751$	−7.15033	−0.260919	−0.130460	−	0.991454i	$-0.541645\pi$
$751$	−7.15033	−0.260919	−0.130460	+	0.991454i	$0.541645\pi$
$752$	138.024	5.03322
$753$	29.3748	1.07048
$754$	2.05858	0.0749692
$755$	4.56292	0.166062
$756$	16.7637	0.609689
$757$	41.8781	1.52208	0.761042	−	0.648702i	$-0.224688\pi$
$757$	41.8781	1.52208	0.761042	+	0.648702i	$0.224688\pi$
$758$	−3.97920	−0.144531
$759$	−77.0817	−2.79789
$760$	−22.0569	−0.800089
$761$	23.2718	0.843603	0.421801	−	0.906688i	$-0.361398\pi$
$761$	23.2718	0.843603	0.421801	+	0.906688i	$0.361398\pi$
$762$	27.7520	1.00535
$763$	9.06916	0.328326
$764$	39.4604	1.42763
$765$	56.5532	2.04468
$766$	62.8631	2.27134
$767$	−7.48241	−0.270174
$768$	211.492	7.63155
$769$	12.6584	0.456474	0.228237	−	0.973606i	$-0.426704\pi$
$769$	12.6584	0.456474	0.228237	+	0.973606i	$0.426704\pi$
$770$	126.303	4.55165
$771$	58.3315	2.10076
$772$	123.869	4.45814
$773$	−50.5008	−1.81639	−0.908193	−	0.418552i	$-0.862538\pi$
$773$	−50.5008	−1.81639	−0.908193	+	0.418552i	$0.862538\pi$
$774$	73.6599	2.64765
$775$	−6.28656	−0.225820
$776$	−58.9001	−2.11439
$777$	−3.20242	−0.114886
$778$	−2.21320	−0.0793471
$779$	−1.78342	−0.0638977
$780$	−41.6598	−1.49166
$781$	82.7838	2.96224
$782$	107.932	3.85965
$783$	−0.928048	−0.0331657
$784$	−28.1686	−1.00602
$785$	41.4489	1.47937
$786$	−95.8085	−3.41737
$787$	31.3947	1.11910	0.559550	−	0.828797i	$-0.310974\pi$
$787$	31.3947	1.11910	0.559550	+	0.828797i	$0.310974\pi$
$788$	−82.5256	−2.93985
$789$	2.01580	0.0717643
$790$	−32.0836	−1.14148
$791$	−39.0157	−1.38724
$792$	−162.015	−5.75697
$793$	8.86669	0.314865
$794$	−0.463017	−0.0164318
$795$	−66.8545	−2.37108
$796$	68.0845	2.41319
$797$	−6.82237	−0.241661	−0.120830	−	0.992673i	$-0.538556\pi$
$797$	−6.82237	−0.241661	−0.120830	+	0.992673i	$0.538556\pi$
$798$	10.3024	0.364701
$799$	58.2118	2.05939
$800$	−129.103	−4.56447
$801$	37.7723	1.33462
$802$	89.2519	3.15159
$803$	90.2714	3.18561
$804$	89.3064	3.14959
$805$	37.6886	1.32835
$806$	−3.79760	−0.133765
$807$	−60.8035	−2.14038
$808$	−79.1782	−2.78548
$809$	−41.6611	−1.46473	−0.732364	−	0.680914i	$-0.761583\pi$
$809$	−41.6611	−1.46473	−0.732364	+	0.680914i	$0.761583\pi$
$810$	89.0771	3.12985
$811$	34.4243	1.20880	0.604401	−	0.796680i	$-0.293413\pi$
$811$	34.4243	1.20880	0.604401	+	0.796680i	$0.293413\pi$
$812$	−9.87712	−0.346619
$813$	57.6455	2.02171
$814$	−10.3458	−0.362620
$815$	13.9232	0.487709
$816$	304.072	10.6447
$817$	−7.32205	−0.256166
$818$	−33.6876	−1.17786
$819$	5.72156	0.199927
$820$	−46.6366	−1.62862
$821$	−20.2909	−0.708156	−0.354078	−	0.935216i	$-0.615205\pi$
$821$	−20.2909	−0.708156	−0.354078	+	0.935216i	$0.615205\pi$
$822$	37.9763	1.32457
$823$	12.7159	0.443248	0.221624	−	0.975132i	$-0.428864\pi$
$823$	12.7159	0.443248	0.221624	+	0.975132i	$0.428864\pi$
$824$	−3.34394	−0.116492
$825$	67.8681	2.36286
$826$	48.3878	1.68363
$827$	−19.4707	−0.677062	−0.338531	−	0.940955i	$-0.609930\pi$
$827$	−19.4707	−0.677062	−0.338531	+	0.940955i	$0.609930\pi$
$828$	−74.1287	−2.57615
$829$	29.0207	1.00793	0.503965	−	0.863724i	$-0.331874\pi$
$829$	29.0207	1.00793	0.503965	+	0.863724i	$0.331874\pi$
$830$	−89.8543	−3.11889
$831$	30.1855	1.04712
$832$	−42.8626	−1.48599
$833$	−11.8801	−0.411623
$834$	18.8844	0.653914
$835$	−59.9603	−2.07501
$836$	24.6940	0.854060
$837$	1.71203	0.0591765
$838$	−11.6164	−0.401280
$839$	14.8005	0.510972	0.255486	−	0.966813i	$-0.417765\pi$
$839$	14.8005	0.510972	0.255486	+	0.966813i	$0.417765\pi$
$840$	175.702	6.06231
$841$	−28.4532	−0.981145
$842$	−0.0114444	−0.000394399 0
$843$	42.6397	1.46859
$844$	−42.0566	−1.44765
$845$	3.09975	0.106635
$846$	−53.8863	−1.85265
$847$	−66.6678	−2.29073
$848$	−162.064	−5.56531
$849$	−21.7993	−0.748149
$850$	−95.0312	−3.25954
$851$	−3.08717	−0.105827
$852$	176.581	6.04955
$853$	18.4688	0.632359	0.316179	−	0.948699i	$-0.397600\pi$
$853$	18.4688	0.632359	0.316179	+	0.948699i	$0.397600\pi$
$854$	−57.3398	−1.96213
$855$	5.20386	0.177968
$856$	20.0990	0.686969
$857$	−54.4577	−1.86024	−0.930119	−	0.367258i	$-0.880296\pi$
$857$	−54.4577	−1.86024	−0.930119	+	0.367258i	$0.880296\pi$
$858$	40.9980	1.39965
$859$	18.6043	0.634769	0.317384	−	0.948297i	$-0.397195\pi$
$859$	18.6043	0.634769	0.317384	+	0.948297i	$0.397195\pi$
$860$	−191.472	−6.52915
$861$	14.2065	0.484156
$862$	−43.9155	−1.49577
$863$	−39.9385	−1.35952	−0.679762	−	0.733433i	$-0.737917\pi$
$863$	−39.9385	−1.35952	−0.679762	+	0.733433i	$0.737917\pi$
$864$	35.1588	1.19613
$865$	−33.5227	−1.13981
$866$	47.7002	1.62092
$867$	88.5084	3.00590
$868$	18.2210	0.618460
$869$	23.4259	0.794669
$870$	−14.9146	−0.505654
$871$	−6.64496	−0.225156
$872$	40.7584	1.38025
$873$	13.8962	0.470316
$874$	9.93163	0.335942
$875$	2.81931	0.0953102
$876$	192.552	6.50573
$877$	−35.5897	−1.20178	−0.600889	−	0.799332i	$-0.705187\pi$
$877$	−35.5897	−1.20178	−0.600889	+	0.799332i	$0.705187\pi$
$878$	−44.7889	−1.51155
$879$	−64.5189	−2.17617
$880$	343.021	11.5632
$881$	20.8002	0.700775	0.350388	−	0.936605i	$-0.386050\pi$
$881$	20.8002	0.700775	0.350388	+	0.936605i	$0.386050\pi$
$882$	10.9974	0.370301
$883$	55.6716	1.87350	0.936749	−	0.350002i	$-0.113819\pi$
$883$	55.6716	1.87350	0.936749	+	0.350002i	$0.113819\pi$
$884$	−42.5922	−1.43253
$885$	54.2108	1.82228
$886$	−48.2747	−1.62182
$887$	−25.1462	−0.844327	−0.422163	−	0.906520i	$-0.638729\pi$
$887$	−25.1462	−0.844327	−0.422163	+	0.906520i	$0.638729\pi$
$888$	−14.3922	−0.482971
$889$	9.90756	0.332289
$890$	−132.337	−4.43594
$891$	−65.0398	−2.17891
$892$	144.647	4.84314
$893$	5.35649	0.179248
$894$	2.51018	0.0839531
$895$	−23.1142	−0.772621
$896$	147.035	4.91209
$897$	12.2337	0.408472
$898$	17.1413	0.572013
$899$	−1.00873	−0.0336429
$900$	65.2681	2.17560
$901$	−68.3508	−2.27710
$902$	45.8958	1.52816
$903$	58.3264	1.94098
$904$	−175.343	−5.83183
$905$	73.9399	2.45785
$906$	−9.57824	−0.318216
$907$	46.7436	1.55209	0.776047	−	0.630675i	$-0.217222\pi$
$907$	46.7436	1.55209	0.776047	+	0.630675i	$0.217222\pi$
$908$	−93.2004	−3.09296
$909$	18.6804	0.619591
$910$	−20.0457	−0.664509
$911$	2.96265	0.0981569	0.0490785	−	0.998795i	$-0.484372\pi$
$911$	2.96265	0.0981569	0.0490785	+	0.998795i	$0.484372\pi$
$912$	27.9799	0.926506
$913$	65.6072	2.17128
$914$	43.8600	1.45076
$915$	−64.2401	−2.12371
$916$	−99.3000	−3.28097
$917$	−34.2039	−1.12951
$918$	25.8801	0.854169
$919$	−35.7897	−1.18059	−0.590297	−	0.807186i	$-0.700989\pi$
$919$	−35.7897	−1.18059	−0.590297	+	0.807186i	$0.700989\pi$
$920$	169.379	5.58426
$921$	−50.8375	−1.67515
$922$	−70.0955	−2.30847
$923$	−13.1387	−0.432466
$924$	−196.709	−6.47126
$925$	2.71816	0.0893725
$926$	−24.5655	−0.807271
$927$	0.788932	0.0259119
$928$	−20.7155	−0.680020
$929$	−6.02510	−0.197677	−0.0988386	−	0.995103i	$-0.531513\pi$
$929$	−6.02510	−0.197677	−0.0988386	+	0.995103i	$0.531513\pi$
$930$	27.5140	0.902220
$931$	−1.09318	−0.0358274
$932$	−54.0150	−1.76932
$933$	−25.3823	−0.830980
$934$	84.9710	2.78034
$935$	144.670	4.73120
$936$	25.7137	0.840477
$937$	−35.0487	−1.14499	−0.572496	−	0.819908i	$-0.694025\pi$
$937$	−35.0487	−1.14499	−0.572496	+	0.819908i	$0.694025\pi$
$938$	42.9722	1.40309
$939$	−38.5076	−1.25665
$940$	140.073	4.56866
$941$	−22.7053	−0.740173	−0.370086	−	0.928997i	$-0.620672\pi$
$941$	−22.7053	−0.740173	−0.370086	+	0.928997i	$0.620672\pi$
$942$	−87.0073	−2.83485
$943$	13.6952	0.445977
$944$	131.414	4.27718
$945$	9.03699	0.293973
$946$	188.430	6.12640
$947$	−2.09905	−0.0682098	−0.0341049	−	0.999418i	$-0.510858\pi$
$947$	−2.09905	−0.0682098	−0.0341049	+	0.999418i	$0.510858\pi$
$948$	49.9682	1.62289
$949$	−14.3271	−0.465077
$950$	−8.74450	−0.283709
$951$	−19.0251	−0.616932
$952$	179.635	5.82201
$953$	−1.77479	−0.0574910	−0.0287455	−	0.999587i	$-0.509151\pi$
$953$	−1.77479	−0.0574910	−0.0287455	+	0.999587i	$0.509151\pi$
$954$	63.2719	2.04850
$955$	21.2723	0.688357
$956$	15.1200	0.489014
$957$	10.8899	0.352022
$958$	15.0844	0.487355
$959$	13.5576	0.437799
$960$	310.544	10.0227
$961$	−29.1391	−0.939972
$962$	1.64199	0.0529400
$963$	−4.74193	−0.152807
$964$	−165.401	−5.32719
$965$	66.7754	2.14957
$966$	−79.1140	−2.54545
$967$	−11.4719	−0.368911	−0.184455	−	0.982841i	$-0.559052\pi$
$967$	−11.4719	−0.368911	−0.184455	+	0.982841i	$0.559052\pi$
$968$	−299.616	−9.63003
$969$	11.8005	0.379088
$970$	−48.6860	−1.56321
$971$	−39.1623	−1.25678	−0.628388	−	0.777900i	$-0.716285\pi$
$971$	−39.1623	−1.25678	−0.628388	+	0.777900i	$0.716285\pi$
$972$	−117.083	−3.75542
$973$	6.74179	0.216132
$974$	−63.0441	−2.02006
$975$	−10.7714	−0.344962
$976$	−155.727	−4.98469
$977$	40.2686	1.28831	0.644153	−	0.764897i	$-0.277210\pi$
$977$	40.2686	1.28831	0.644153	+	0.764897i	$0.277210\pi$
$978$	−29.2269	−0.934573
$979$	96.6259	3.08818
$980$	−28.5867	−0.913168
$981$	−9.61607	−0.307018
$982$	36.4144	1.16203
$983$	−32.8023	−1.04623	−0.523115	−	0.852262i	$-0.675230\pi$
$983$	−32.8023	−1.04623	−0.523115	+	0.852262i	$0.675230\pi$
$984$	63.8464	2.03535
$985$	−44.4880	−1.41751
$986$	−15.2485	−0.485610
$987$	−42.6690	−1.35817
$988$	−3.91922	−0.124687
$989$	56.2273	1.78792
$990$	−133.920	−4.25625
$991$	1.98461	0.0630431	0.0315215	−	0.999503i	$-0.489965\pi$
$991$	1.98461	0.0630431	0.0315215	+	0.999503i	$0.489965\pi$
$992$	38.2152	1.21333
$993$	−20.4164	−0.647895
$994$	84.9664	2.69497
$995$	36.7031	1.16357
$996$	139.942	4.43425
$997$	50.2711	1.59210	0.796050	−	0.605230i	$-0.206919\pi$
$997$	50.2711	1.59210	0.796050	+	0.605230i	$0.206919\pi$
$998$	−12.1511	−0.384636
$999$	−0.740242	−0.0234202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.3	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.78389 q^{2} +2.33732 q^{3} +5.75006 q^{4} +3.09975 q^{5} -6.50684 q^{6} -2.32296 q^{7} -10.4398 q^{8} +2.46305 q^{9} +O(q^{10})\)	\(q-2.78389 q^{2} +2.33732 q^{3} +5.75006 q^{4} +3.09975 q^{5} -6.50684 q^{6} -2.32296 q^{7} -10.4398 q^{8} +2.46305 q^{9} -8.62938 q^{10} +6.30075 q^{11} +13.4397 q^{12} -1.00000 q^{13} +6.46688 q^{14} +7.24510 q^{15} +17.5631 q^{16} +7.40726 q^{17} -6.85686 q^{18} +0.681595 q^{19} +17.8238 q^{20} -5.42949 q^{21} -17.5406 q^{22} -5.23409 q^{23} -24.4011 q^{24} +4.60846 q^{25} +2.78389 q^{26} -1.25503 q^{27} -13.3572 q^{28} +0.739462 q^{29} -20.1696 q^{30} -1.36413 q^{31} -28.0143 q^{32} +14.7268 q^{33} -20.6210 q^{34} -7.20060 q^{35} +14.1627 q^{36} +0.589819 q^{37} -1.89749 q^{38} -2.33732 q^{39} -32.3607 q^{40} -2.61654 q^{41} +15.1151 q^{42} -10.7425 q^{43} +36.2297 q^{44} +7.63483 q^{45} +14.5712 q^{46} +7.85875 q^{47} +41.0505 q^{48} -1.60385 q^{49} -12.8295 q^{50} +17.3131 q^{51} -5.75006 q^{52} -9.22754 q^{53} +3.49388 q^{54} +19.5308 q^{55} +24.2512 q^{56} +1.59310 q^{57} -2.05858 q^{58} +7.48241 q^{59} +41.6598 q^{60} -8.86669 q^{61} +3.79760 q^{62} -5.72156 q^{63} +42.8626 q^{64} -3.09975 q^{65} -40.9980 q^{66} +6.64496 q^{67} +42.5922 q^{68} -12.2337 q^{69} +20.0457 q^{70} +13.1387 q^{71} -25.7137 q^{72} +14.3271 q^{73} -1.64199 q^{74} +10.7714 q^{75} +3.91922 q^{76} -14.6364 q^{77} +6.50684 q^{78} +3.71795 q^{79} +54.4413 q^{80} -10.3225 q^{81} +7.28417 q^{82} +10.4126 q^{83} -31.2199 q^{84} +22.9607 q^{85} +29.9060 q^{86} +1.72836 q^{87} -65.7785 q^{88} +15.3356 q^{89} -21.2546 q^{90} +2.32296 q^{91} -30.0964 q^{92} -3.18841 q^{93} -21.8779 q^{94} +2.11278 q^{95} -65.4782 q^{96} +5.64189 q^{97} +4.46495 q^{98} +15.5190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 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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