LMFDB - Embedded newform 8021.2.a.a.1.16

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:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +O(q^{10})$	\(q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +5.27718 q^{10} +0.876358 q^{11} +6.10997 q^{12} +1.00000 q^{13} +4.02425 q^{14} -4.60042 q^{15} -0.578545 q^{16} -4.07944 q^{17} -1.98301 q^{18} -0.618616 q^{19} -7.24844 q^{20} -3.50816 q^{21} -1.97962 q^{22} +1.84925 q^{23} -4.90529 q^{24} +0.457608 q^{25} -2.25892 q^{26} -4.17898 q^{27} -5.52748 q^{28} -2.44360 q^{29} +10.3920 q^{30} -2.19500 q^{31} +6.28883 q^{32} +1.72575 q^{33} +9.21513 q^{34} +4.16183 q^{35} +2.72375 q^{36} +7.05873 q^{37} +1.39741 q^{38} +1.96923 q^{39} +5.81929 q^{40} +9.83684 q^{41} +7.92466 q^{42} +9.85045 q^{43} +2.71910 q^{44} -2.05081 q^{45} -4.17731 q^{46} +5.03215 q^{47} -1.13929 q^{48} -3.82629 q^{49} -1.03370 q^{50} -8.03334 q^{51} +3.10273 q^{52} +0.650174 q^{53} +9.43999 q^{54} -2.04731 q^{55} +4.43764 q^{56} -1.21820 q^{57} +5.51990 q^{58} +12.9876 q^{59} -14.2738 q^{60} +8.84685 q^{61} +4.95832 q^{62} -1.56390 q^{63} -13.0489 q^{64} -2.33615 q^{65} -3.89833 q^{66} -4.47938 q^{67} -12.6574 q^{68} +3.64159 q^{69} -9.40126 q^{70} +12.2604 q^{71} -2.18672 q^{72} +9.32880 q^{73} -15.9451 q^{74} +0.901134 q^{75} -1.91940 q^{76} -1.56122 q^{77} -4.44833 q^{78} -5.45394 q^{79} +1.35157 q^{80} -10.8629 q^{81} -22.2206 q^{82} -4.47644 q^{83} -10.8849 q^{84} +9.53019 q^{85} -22.2514 q^{86} -4.81200 q^{87} -2.18298 q^{88} -3.76320 q^{89} +4.63262 q^{90} -1.78149 q^{91} +5.73771 q^{92} -4.32245 q^{93} -11.3672 q^{94} +1.44518 q^{95} +12.3841 q^{96} -4.39280 q^{97} +8.64329 q^{98} +0.769319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.25892	−1.59730	−0.798649	−	0.601797i	$-0.794452\pi$
$2$	−2.25892	−1.59730	−0.798649	+	0.601797i	$0.794452\pi$
$3$	1.96923	1.13693	0.568467	−	0.822706i	$-0.307537\pi$
$3$	1.96923	1.13693	0.568467	+	0.822706i	$0.307537\pi$
$4$	3.10273	1.55136
$5$	−2.33615	−1.04476	−0.522380	−	0.852713i	$-0.674956\pi$
$5$	−2.33615	−1.04476	−0.522380	+	0.852713i	$0.674956\pi$
$6$	−4.44833	−1.81602
$7$	−1.78149	−0.673340	−0.336670	−	0.941623i	$-0.609301\pi$
$7$	−1.78149	−0.673340	−0.336670	+	0.941623i	$0.609301\pi$
$8$	−2.49097	−0.880691
$9$	0.877859	0.292620
$10$	5.27718	1.66879
$11$	0.876358	0.264232	0.132116	−	0.991234i	$-0.457823\pi$
$11$	0.876358	0.264232	0.132116	+	0.991234i	$0.457823\pi$
$12$	6.10997	1.76380
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.02425	1.07553
$15$	−4.60042	−1.18782
$16$	−0.578545	−0.144636
$17$	−4.07944	−0.989409	−0.494704	−	0.869061i	$-0.664724\pi$
$17$	−4.07944	−0.989409	−0.494704	+	0.869061i	$0.664724\pi$
$18$	−1.98301	−0.467401
$19$	−0.618616	−0.141920	−0.0709602	−	0.997479i	$-0.522606\pi$
$19$	−0.618616	−0.141920	−0.0709602	+	0.997479i	$0.522606\pi$
$20$	−7.24844	−1.62080
$21$	−3.50816	−0.765544
$22$	−1.97962	−0.422057
$23$	1.84925	0.385595	0.192798	−	0.981239i	$-0.438244\pi$
$23$	1.84925	0.385595	0.192798	+	0.981239i	$0.438244\pi$
$24$	−4.90529	−1.00129
$25$	0.457608	0.0915216
$26$	−2.25892	−0.443011
$27$	−4.17898	−0.804245
$28$	−5.52748	−1.04460
$29$	−2.44360	−0.453765	−0.226882	−	0.973922i	$-0.572853\pi$
$29$	−2.44360	−0.453765	−0.226882	+	0.973922i	$0.572853\pi$
$30$	10.3920	1.89731
$31$	−2.19500	−0.394233	−0.197116	−	0.980380i	$-0.563158\pi$
$31$	−2.19500	−0.394233	−0.197116	+	0.980380i	$0.563158\pi$
$32$	6.28883	1.11172
$33$	1.72575	0.300414
$34$	9.21513	1.58038
$35$	4.16183	0.703478
$36$	2.72375	0.453959
$37$	7.05873	1.16045	0.580224	−	0.814457i	$-0.302965\pi$
$37$	7.05873	1.16045	0.580224	+	0.814457i	$0.302965\pi$
$38$	1.39741	0.226689
$39$	1.96923	0.315329
$40$	5.81929	0.920110
$41$	9.83684	1.53626	0.768128	−	0.640296i	$-0.221188\pi$
$41$	9.83684	1.53626	0.768128	+	0.640296i	$0.221188\pi$
$42$	7.92466	1.22280
$43$	9.85045	1.50218	0.751090	−	0.660200i	$-0.229528\pi$
$43$	9.85045	1.50218	0.751090	+	0.660200i	$0.229528\pi$
$44$	2.71910	0.409920
$45$	−2.05081	−0.305717
$46$	−4.17731	−0.615911
$47$	5.03215	0.734014	0.367007	−	0.930218i	$-0.380382\pi$
$47$	5.03215	0.734014	0.367007	+	0.930218i	$0.380382\pi$
$48$	−1.13929	−0.164442
$49$	−3.82629	−0.546613
$50$	−1.03370	−0.146187
$51$	−8.03334	−1.12489
$52$	3.10273	0.430271
$53$	0.650174	0.0893083	0.0446542	−	0.999003i	$-0.485781\pi$
$53$	0.650174	0.0893083	0.0446542	+	0.999003i	$0.485781\pi$
$54$	9.43999	1.28462
$55$	−2.04731	−0.276059
$56$	4.43764	0.593005
$57$	−1.21820	−0.161354
$58$	5.51990	0.724798
$59$	12.9876	1.69084	0.845421	−	0.534101i	$-0.179350\pi$
$59$	12.9876	1.69084	0.845421	+	0.534101i	$0.179350\pi$
$60$	−14.2738	−1.84274
$61$	8.84685	1.13272	0.566361	−	0.824157i	$-0.308351\pi$
$61$	8.84685	1.13272	0.566361	+	0.824157i	$0.308351\pi$
$62$	4.95832	0.629708
$63$	−1.56390	−0.197033
$64$	−13.0489	−1.63111
$65$	−2.33615	−0.289764
$66$	−3.89833	−0.479851
$67$	−4.47938	−0.547244	−0.273622	−	0.961837i	$-0.588222\pi$
$67$	−4.47938	−0.547244	−0.273622	+	0.961837i	$0.588222\pi$
$68$	−12.6574	−1.53493
$69$	3.64159	0.438396
$70$	−9.40126	−1.12367
$71$	12.2604	1.45504	0.727519	−	0.686087i	$-0.240673\pi$
$71$	12.2604	1.45504	0.727519	+	0.686087i	$0.240673\pi$
$72$	−2.18672	−0.257707
$73$	9.32880	1.09185	0.545927	−	0.837833i	$-0.316178\pi$
$73$	9.32880	1.09185	0.545927	+	0.837833i	$0.316178\pi$
$74$	−15.9451	−1.85358
$75$	0.901134	0.104054
$76$	−1.91940	−0.220170
$77$	−1.56122	−0.177918
$78$	−4.44833	−0.503674
$79$	−5.45394	−0.613616	−0.306808	−	0.951771i	$-0.599261\pi$
$79$	−5.45394	−0.613616	−0.306808	+	0.951771i	$0.599261\pi$
$80$	1.35157	0.151110
$81$	−10.8629	−1.20699
$82$	−22.2206	−2.45386
$83$	−4.47644	−0.491353	−0.245677	−	0.969352i	$-0.579010\pi$
$83$	−4.47644	−0.491353	−0.245677	+	0.969352i	$0.579010\pi$
$84$	−10.8849	−1.18764
$85$	9.53019	1.03369
$86$	−22.2514	−2.39943
$87$	−4.81200	−0.515901
$88$	−2.18298	−0.232707
$89$	−3.76320	−0.398898	−0.199449	−	0.979908i	$-0.563915\pi$
$89$	−3.76320	−0.398898	−0.199449	+	0.979908i	$0.563915\pi$
$90$	4.63262	0.488321
$91$	−1.78149	−0.186751
$92$	5.73771	0.598198
$93$	−4.32245	−0.448217
$94$	−11.3672	−1.17244
$95$	1.44518	0.148273
$96$	12.3841	1.26395
$97$	−4.39280	−0.446021	−0.223011	−	0.974816i	$-0.571588\pi$
$97$	−4.39280	−0.446021	−0.223011	+	0.974816i	$0.571588\pi$
$98$	8.64329	0.873104
$99$	0.769319	0.0773194
$100$	1.41983	0.141983
$101$	−11.1496	−1.10943	−0.554715	−	0.832040i	$-0.687173\pi$
$101$	−11.1496	−1.10943	−0.554715	+	0.832040i	$0.687173\pi$
$102$	18.1467	1.79679
$103$	−16.4044	−1.61638	−0.808188	−	0.588924i	$-0.799552\pi$
$103$	−16.4044	−1.61638	−0.808188	+	0.588924i	$0.799552\pi$
$104$	−2.49097	−0.244260
$105$	8.19560	0.799809
$106$	−1.46869	−0.142652
$107$	4.15832	0.402000	0.201000	−	0.979591i	$-0.435581\pi$
$107$	4.15832	0.402000	0.201000	+	0.979591i	$0.435581\pi$
$108$	−12.9662	−1.24768
$109$	−13.5478	−1.29765	−0.648823	−	0.760939i	$-0.724739\pi$
$109$	−13.5478	−1.29765	−0.648823	+	0.760939i	$0.724739\pi$
$110$	4.62470	0.440948
$111$	13.9003	1.31935
$112$	1.03067	0.0973894
$113$	−12.3110	−1.15812	−0.579060	−	0.815285i	$-0.696580\pi$
$113$	−12.3110	−1.15812	−0.579060	+	0.815285i	$0.696580\pi$
$114$	2.75181	0.257731
$115$	−4.32013	−0.402854
$116$	−7.58182	−0.703954
$117$	0.877859	0.0811581
$118$	−29.3380	−2.70078
$119$	7.26748	0.666209
$120$	11.4595	1.04610
$121$	−10.2320	−0.930181
$122$	−19.9843	−1.80930
$123$	19.3710	1.74662
$124$	−6.81047	−0.611598
$125$	10.6117	0.949141
$126$	3.53272	0.314720
$127$	−19.2315	−1.70652	−0.853258	−	0.521488i	$-0.825377\pi$
$127$	−19.2315	−1.70652	−0.853258	+	0.521488i	$0.825377\pi$
$128$	16.8987	1.49365
$129$	19.3978	1.70788
$130$	5.27718	0.462840
$131$	7.93404	0.693200	0.346600	−	0.938013i	$-0.387336\pi$
$131$	7.93404	0.693200	0.346600	+	0.938013i	$0.387336\pi$
$132$	5.35453	0.466052
$133$	1.10206	0.0955607
$134$	10.1186	0.874112
$135$	9.76273	0.840242
$136$	10.1618	0.871363
$137$	−1.72942	−0.147754	−0.0738770	−	0.997267i	$-0.523537\pi$
$137$	−1.72942	−0.147754	−0.0738770	+	0.997267i	$0.523537\pi$
$138$	−8.22607	−0.700250
$139$	−22.9671	−1.94805	−0.974023	−	0.226449i	$-0.927288\pi$
$139$	−22.9671	−1.94805	−0.974023	+	0.226449i	$0.927288\pi$
$140$	12.9130	1.09135
$141$	9.90944	0.834526
$142$	−27.6952	−2.32413
$143$	0.876358	0.0732848
$144$	−0.507881	−0.0423234
$145$	5.70862	0.474075
$146$	−21.0730	−1.74402
$147$	−7.53484	−0.621463
$148$	21.9013	1.80028
$149$	−5.89663	−0.483071	−0.241535	−	0.970392i	$-0.577651\pi$
$149$	−5.89663	−0.483071	−0.241535	+	0.970392i	$0.577651\pi$
$150$	−2.03559	−0.166205
$151$	20.5433	1.67179	0.835894	−	0.548890i	$-0.184950\pi$
$151$	20.5433	1.67179	0.835894	+	0.548890i	$0.184950\pi$
$152$	1.54096	0.124988
$153$	−3.58117	−0.289520
$154$	3.52668	0.284188
$155$	5.12785	0.411879
$156$	6.10997	0.489189
$157$	4.33920	0.346306	0.173153	−	0.984895i	$-0.444604\pi$
$157$	4.33920	0.346306	0.173153	+	0.984895i	$0.444604\pi$
$158$	12.3200	0.980128
$159$	1.28034	0.101538
$160$	−14.6917	−1.16148
$161$	−3.29442	−0.259637
$162$	24.5385	1.92793
$163$	−6.85601	−0.537004	−0.268502	−	0.963279i	$-0.586529\pi$
$163$	−6.85601	−0.537004	−0.268502	+	0.963279i	$0.586529\pi$
$164$	30.5210	2.38329
$165$	−4.03161	−0.313861
$166$	10.1119	0.784838
$167$	−5.81311	−0.449832	−0.224916	−	0.974378i	$-0.572211\pi$
$167$	−5.81311	−0.449832	−0.224916	+	0.974378i	$0.572211\pi$
$168$	8.73873	0.674207
$169$	1.00000	0.0769231
$170$	−21.5279	−1.65112
$171$	−0.543058	−0.0415287
$172$	30.5633	2.33043
$173$	16.8780	1.28321	0.641606	−	0.767034i	$-0.278268\pi$
$173$	16.8780	1.28321	0.641606	+	0.767034i	$0.278268\pi$
$174$	10.8699	0.824048
$175$	−0.815224	−0.0616252
$176$	−0.507013	−0.0382175
$177$	25.5755	1.92238
$178$	8.50077	0.637160
$179$	2.57803	0.192691	0.0963455	−	0.995348i	$-0.469285\pi$
$179$	2.57803	0.192691	0.0963455	+	0.995348i	$0.469285\pi$
$180$	−6.36311	−0.474278
$181$	10.5920	0.787299	0.393649	−	0.919261i	$-0.371212\pi$
$181$	10.5920	0.787299	0.393649	+	0.919261i	$0.371212\pi$
$182$	4.02425	0.298297
$183$	17.4215	1.28783
$184$	−4.60643	−0.339590
$185$	−16.4903	−1.21239
$186$	9.76407	0.715936
$187$	−3.57505	−0.261433
$188$	15.6134	1.13872
$189$	7.44482	0.541531
$190$	−3.26455	−0.236836
$191$	10.1881	0.737185	0.368593	−	0.929591i	$-0.379840\pi$
$191$	10.1881	0.737185	0.368593	+	0.929591i	$0.379840\pi$
$192$	−25.6962	−1.85446
$193$	−3.07177	−0.221111	−0.110556	−	0.993870i	$-0.535263\pi$
$193$	−3.07177	−0.221111	−0.110556	+	0.993870i	$0.535263\pi$
$194$	9.92299	0.712429
$195$	−4.60042	−0.329443
$196$	−11.8719	−0.847995
$197$	−18.3263	−1.30569	−0.652847	−	0.757490i	$-0.726426\pi$
$197$	−18.3263	−1.30569	−0.652847	+	0.757490i	$0.726426\pi$
$198$	−1.73783	−0.123502
$199$	7.67756	0.544247	0.272124	−	0.962262i	$-0.412274\pi$
$199$	7.67756	0.544247	0.272124	+	0.962262i	$0.412274\pi$
$200$	−1.13989	−0.0806022
$201$	−8.82093	−0.622180
$202$	25.1862	1.77209
$203$	4.35325	0.305538
$204$	−24.9253	−1.74512
$205$	−22.9803	−1.60502
$206$	37.0563	2.58184
$207$	1.62338	0.112833
$208$	−0.578545	−0.0401149
$209$	−0.542130	−0.0374999
$210$	−18.5132	−1.27753
$211$	−0.622270	−0.0428388	−0.0214194	−	0.999771i	$-0.506819\pi$
$211$	−0.622270	−0.0428388	−0.0214194	+	0.999771i	$0.506819\pi$
$212$	2.01731	0.138550
$213$	24.1435	1.65428
$214$	−9.39333	−0.642115
$215$	−23.0122	−1.56942
$216$	10.4097	0.708291
$217$	3.91037	0.265453
$218$	30.6035	2.07273
$219$	18.3705	1.24137
$220$	−6.35223	−0.428267
$221$	−4.07944	−0.274413
$222$	−31.3996	−2.10740
$223$	7.29827	0.488728	0.244364	−	0.969684i	$-0.421421\pi$
$223$	7.29827	0.488728	0.244364	+	0.969684i	$0.421421\pi$
$224$	−11.2035	−0.748565
$225$	0.401715	0.0267810
$226$	27.8095	1.84986
$227$	−24.4719	−1.62426	−0.812130	−	0.583477i	$-0.801692\pi$
$227$	−24.4719	−1.62426	−0.812130	+	0.583477i	$0.801692\pi$
$228$	−3.77973	−0.250319
$229$	−9.11998	−0.602665	−0.301333	−	0.953519i	$-0.597431\pi$
$229$	−9.11998	−0.602665	−0.301333	+	0.953519i	$0.597431\pi$
$230$	9.75883	0.643478
$231$	−3.07441	−0.202281
$232$	6.08693	0.399627
$233$	−11.6853	−0.765527	−0.382763	−	0.923846i	$-0.625028\pi$
$233$	−11.6853	−0.765527	−0.382763	+	0.923846i	$0.625028\pi$
$234$	−1.98301	−0.129634
$235$	−11.7559	−0.766868
$236$	40.2970	2.62311
$237$	−10.7400	−0.697641
$238$	−16.4167	−1.06413
$239$	0.221982	0.0143588	0.00717942	−	0.999974i	$-0.497715\pi$
$239$	0.221982	0.0143588	0.00717942	+	0.999974i	$0.497715\pi$
$240$	2.66155	0.171802
$241$	−15.4671	−0.996325	−0.498163	−	0.867084i	$-0.665992\pi$
$241$	−15.4671	−0.996325	−0.498163	+	0.867084i	$0.665992\pi$
$242$	23.1133	1.48578
$243$	−8.85466	−0.568027
$244$	27.4493	1.75726
$245$	8.93880	0.571079
$246$	−43.7575	−2.78988
$247$	−0.618616	−0.0393616
$248$	5.46767	0.347197
$249$	−8.81513	−0.558636
$250$	−23.9710	−1.51606
$251$	−1.07569	−0.0678971	−0.0339486	−	0.999424i	$-0.510808\pi$
$251$	−1.07569	−0.0678971	−0.0339486	+	0.999424i	$0.510808\pi$
$252$	−4.85234	−0.305669
$253$	1.62061	0.101887
$254$	43.4424	2.72582
$255$	18.7671	1.17524
$256$	−12.0752	−0.754697
$257$	25.8401	1.61186	0.805930	−	0.592011i	$-0.201666\pi$
$257$	25.8401	1.61186	0.805930	+	0.592011i	$0.201666\pi$
$258$	−43.8181	−2.72799
$259$	−12.5751	−0.781377
$260$	−7.24844	−0.449529
$261$	−2.14513	−0.132780
$262$	−17.9224	−1.10725
$263$	−31.2144	−1.92476	−0.962380	−	0.271706i	$-0.912412\pi$
$263$	−31.2144	−1.92476	−0.962380	+	0.271706i	$0.912412\pi$
$264$	−4.29879	−0.264572
$265$	−1.51891	−0.0933057
$266$	−2.48947	−0.152639
$267$	−7.41060	−0.453521
$268$	−13.8983	−0.848974
$269$	−22.5719	−1.37623	−0.688116	−	0.725601i	$-0.741562\pi$
$269$	−22.5719	−1.37623	−0.688116	+	0.725601i	$0.741562\pi$
$270$	−22.0532	−1.34212
$271$	−24.9509	−1.51566	−0.757830	−	0.652453i	$-0.773740\pi$
$271$	−24.9509	−1.51566	−0.757830	+	0.652453i	$0.773740\pi$
$272$	2.36014	0.143104
$273$	−3.50816	−0.212324
$274$	3.90662	0.236007
$275$	0.401029	0.0241829
$276$	11.2989	0.680112
$277$	−18.8341	−1.13163	−0.565816	−	0.824532i	$-0.691439\pi$
$277$	−18.8341	−1.13163	−0.565816	+	0.824532i	$0.691439\pi$
$278$	51.8809	3.11161
$279$	−1.92690	−0.115360
$280$	−10.3670	−0.619547
$281$	10.5244	0.627830	0.313915	−	0.949451i	$-0.398359\pi$
$281$	10.5244	0.627830	0.313915	+	0.949451i	$0.398359\pi$
$282$	−22.3847	−1.33299
$283$	30.1203	1.79047	0.895234	−	0.445597i	$-0.147008\pi$
$283$	30.1203	1.79047	0.895234	+	0.445597i	$0.147008\pi$
$284$	38.0406	2.25729
$285$	2.84589	0.168576
$286$	−1.97962	−0.117058
$287$	−17.5242	−1.03442
$288$	5.52070	0.325310
$289$	−0.358192	−0.0210701
$290$	−12.8953	−0.757239
$291$	−8.65042	−0.507097
$292$	28.9447	1.69386
$293$	11.8053	0.689674	0.344837	−	0.938663i	$-0.387934\pi$
$293$	11.8053	0.689674	0.344837	+	0.938663i	$0.387934\pi$
$294$	17.0206	0.992662
$295$	−30.3410	−1.76652
$296$	−17.5831	−1.02200
$297$	−3.66228	−0.212507
$298$	13.3200	0.771609
$299$	1.84925	0.106945
$300$	2.79597	0.161426
$301$	−17.5485	−1.01148
$302$	−46.4057	−2.67035
$303$	−21.9562	−1.26135
$304$	0.357897	0.0205268
$305$	−20.6676	−1.18342
$306$	8.08958	0.462450
$307$	−19.8524	−1.13303	−0.566517	−	0.824050i	$-0.691709\pi$
$307$	−19.8524	−1.13303	−0.566517	+	0.824050i	$0.691709\pi$
$308$	−4.84405	−0.276015
$309$	−32.3041	−1.83771
$310$	−11.5834	−0.657893
$311$	10.8085	0.612896	0.306448	−	0.951887i	$-0.400860\pi$
$311$	10.8085	0.612896	0.306448	+	0.951887i	$0.400860\pi$
$312$	−4.90529	−0.277707
$313$	25.2964	1.42984	0.714919	−	0.699208i	$-0.246464\pi$
$313$	25.2964	1.42984	0.714919	+	0.699208i	$0.246464\pi$
$314$	−9.80192	−0.553154
$315$	3.65350	0.205852
$316$	−16.9221	−0.951941
$317$	3.78100	0.212362	0.106181	−	0.994347i	$-0.466138\pi$
$317$	3.78100	0.212362	0.106181	+	0.994347i	$0.466138\pi$
$318$	−2.89219	−0.162186
$319$	−2.14147	−0.119899
$320$	30.4842	1.70412
$321$	8.18869	0.457048
$322$	7.44184	0.414717
$323$	2.52361	0.140417
$324$	−33.7047	−1.87248
$325$	0.457608	0.0253835
$326$	15.4872	0.857755
$327$	−26.6788	−1.47534
$328$	−24.5033	−1.35297
$329$	−8.96472	−0.494241
$330$	9.10710	0.501329
$331$	−5.29120	−0.290831	−0.145415	−	0.989371i	$-0.546452\pi$
$331$	−5.29120	−0.290831	−0.145415	+	0.989371i	$0.546452\pi$
$332$	−13.8892	−0.762267
$333$	6.19657	0.339570
$334$	13.1313	0.718516
$335$	10.4645	0.571738
$336$	2.02963	0.110725
$337$	9.27317	0.505142	0.252571	−	0.967578i	$-0.418724\pi$
$337$	9.27317	0.505142	0.252571	+	0.967578i	$0.418724\pi$
$338$	−2.25892	−0.122869
$339$	−24.2431	−1.31671
$340$	29.5696	1.60363
$341$	−1.92360	−0.104169
$342$	1.22672	0.0663337
$343$	19.2869	1.04140
$344$	−24.5372	−1.32296
$345$	−8.50732	−0.458019
$346$	−38.1261	−2.04967
$347$	24.1782	1.29796	0.648978	−	0.760807i	$-0.275197\pi$
$347$	24.1782	1.29796	0.648978	+	0.760807i	$0.275197\pi$
$348$	−14.9303	−0.800349
$349$	−18.5285	−0.991807	−0.495904	−	0.868378i	$-0.665163\pi$
$349$	−18.5285	−0.991807	−0.495904	+	0.868378i	$0.665163\pi$
$350$	1.84153	0.0984338
$351$	−4.17898	−0.223057
$352$	5.51127	0.293752
$353$	−22.1816	−1.18061	−0.590303	−	0.807182i	$-0.700992\pi$
$353$	−22.1816	−1.18061	−0.590303	+	0.807182i	$0.700992\pi$
$354$	−57.7731	−3.07061
$355$	−28.6421	−1.52017
$356$	−11.6762	−0.618836
$357$	14.3113	0.757436
$358$	−5.82357	−0.307785
$359$	−0.818977	−0.0432240	−0.0216120	−	0.999766i	$-0.506880\pi$
$359$	−0.818977	−0.0432240	−0.0216120	+	0.999766i	$0.506880\pi$
$360$	5.10851	0.269242
$361$	−18.6173	−0.979859
$362$	−23.9265	−1.25755
$363$	−20.1491	−1.05756
$364$	−5.52748	−0.289719
$365$	−21.7935	−1.14072
$366$	−39.3537	−2.05705
$367$	−33.2391	−1.73507	−0.867535	−	0.497377i	$-0.834297\pi$
$367$	−33.2391	−1.73507	−0.867535	+	0.497377i	$0.834297\pi$
$368$	−1.06987	−0.0557711
$369$	8.63535	0.449538
$370$	37.2502	1.93655
$371$	−1.15828	−0.0601349
$372$	−13.4114	−0.695347
$373$	3.45866	0.179083	0.0895413	−	0.995983i	$-0.471460\pi$
$373$	3.45866	0.179083	0.0895413	+	0.995983i	$0.471460\pi$
$374$	8.07575	0.417587
$375$	20.8969	1.07911
$376$	−12.5349	−0.646440
$377$	−2.44360	−0.125852
$378$	−16.8173	−0.864986
$379$	18.5826	0.954522	0.477261	−	0.878762i	$-0.341630\pi$
$379$	18.5826	0.954522	0.477261	+	0.878762i	$0.341630\pi$
$380$	4.48400	0.230025
$381$	−37.8711	−1.94020
$382$	−23.0141	−1.17750
$383$	−26.9089	−1.37498	−0.687491	−	0.726193i	$-0.741288\pi$
$383$	−26.9089	−1.37498	−0.687491	+	0.726193i	$0.741288\pi$
$384$	33.2775	1.69818
$385$	3.64726	0.185881
$386$	6.93889	0.353180
$387$	8.64730	0.439567
$388$	−13.6296	−0.691941
$389$	4.87333	0.247088	0.123544	−	0.992339i	$-0.460574\pi$
$389$	4.87333	0.247088	0.123544	+	0.992339i	$0.460574\pi$
$390$	10.3920	0.526218
$391$	−7.54390	−0.381511
$392$	9.53118	0.481397
$393$	15.6239	0.788123
$394$	41.3977	2.08558
$395$	12.7412	0.641081
$396$	2.38698	0.119950
$397$	34.9142	1.75229	0.876146	−	0.482046i	$-0.160106\pi$
$397$	34.9142	1.75229	0.876146	+	0.482046i	$0.160106\pi$
$398$	−17.3430	−0.869326
$399$	2.17021	0.108646
$400$	−0.264747	−0.0132373
$401$	10.5754	0.528108	0.264054	−	0.964508i	$-0.414940\pi$
$401$	10.5754	0.528108	0.264054	+	0.964508i	$0.414940\pi$
$402$	19.9258	0.993807
$403$	−2.19500	−0.109341
$404$	−34.5943	−1.72113
$405$	25.3775	1.26102
$406$	−9.83365	−0.488036
$407$	6.18598	0.306628
$408$	20.0108	0.990683
$409$	−23.6292	−1.16839	−0.584195	−	0.811614i	$-0.698589\pi$
$409$	−23.6292	−1.16839	−0.584195	+	0.811614i	$0.698589\pi$
$410$	51.9108	2.56369
$411$	−3.40561	−0.167987
$412$	−50.8984	−2.50759
$413$	−23.1373	−1.13851
$414$	−3.66709	−0.180227
$415$	10.4577	0.513346
$416$	6.28883	0.308335
$417$	−45.2275	−2.21480
$418$	1.22463	0.0598985
$419$	−7.03590	−0.343726	−0.171863	−	0.985121i	$-0.554979\pi$
$419$	−7.03590	−0.343726	−0.171863	+	0.985121i	$0.554979\pi$
$420$	25.4287	1.24079
$421$	−4.81078	−0.234463	−0.117232	−	0.993105i	$-0.537402\pi$
$421$	−4.81078	−0.234463	−0.117232	+	0.993105i	$0.537402\pi$
$422$	1.40566	0.0684264
$423$	4.41751	0.214787
$424$	−1.61957	−0.0786530
$425$	−1.86678	−0.0905523
$426$	−54.5382	−2.64238
$427$	−15.7606	−0.762708
$428$	12.9021	0.623649
$429$	1.72575	0.0833200
$430$	51.9827	2.50683
$431$	32.0861	1.54553	0.772766	−	0.634691i	$-0.218873\pi$
$431$	32.0861	1.54553	0.772766	+	0.634691i	$0.218873\pi$
$432$	2.41773	0.116323
$433$	−31.1169	−1.49538	−0.747692	−	0.664046i	$-0.768838\pi$
$433$	−31.1169	−1.49538	−0.747692	+	0.664046i	$0.768838\pi$
$434$	−8.83321	−0.424008
$435$	11.2416	0.538992
$436$	−42.0352	−2.01312
$437$	−1.14398	−0.0547238
$438$	−41.4976	−1.98283
$439$	28.2858	1.35001	0.675005	−	0.737813i	$-0.264142\pi$
$439$	28.2858	1.35001	0.675005	+	0.737813i	$0.264142\pi$
$440$	5.09978	0.243122
$441$	−3.35894	−0.159950
$442$	9.21513	0.438319
$443$	34.5892	1.64338	0.821691	−	0.569933i	$-0.193031\pi$
$443$	34.5892	1.64338	0.821691	+	0.569933i	$0.193031\pi$
$444$	43.1287	2.04680
$445$	8.79141	0.416753
$446$	−16.4862	−0.780645
$447$	−11.6118	−0.549220
$448$	23.2465	1.09829
$449$	−30.1250	−1.42168	−0.710842	−	0.703351i	$-0.751686\pi$
$449$	−30.1250	−1.42168	−0.710842	+	0.703351i	$0.751686\pi$
$450$	−0.907443	−0.0427773
$451$	8.62059	0.405928
$452$	−38.1976	−1.79666
$453$	40.4544	1.90071
$454$	55.2802	2.59443
$455$	4.16183	0.195110
$456$	3.03449	0.142103
$457$	−0.372412	−0.0174207	−0.00871035	−	0.999962i	$-0.502773\pi$
$457$	−0.372412	−0.0174207	−0.00871035	+	0.999962i	$0.502773\pi$
$458$	20.6013	0.962636
$459$	17.0479	0.795727
$460$	−13.4042	−0.624973
$461$	−19.8356	−0.923837	−0.461918	−	0.886922i	$-0.652839\pi$
$461$	−19.8356	−0.923837	−0.461918	+	0.886922i	$0.652839\pi$
$462$	6.94484	0.323103
$463$	−22.2138	−1.03236	−0.516181	−	0.856479i	$-0.672647\pi$
$463$	−22.2138	−1.03236	−0.516181	+	0.856479i	$0.672647\pi$
$464$	1.41373	0.0656309
$465$	10.0979	0.468279
$466$	26.3961	1.22277
$467$	−12.7511	−0.590052	−0.295026	−	0.955489i	$-0.595328\pi$
$467$	−12.7511	−0.590052	−0.295026	+	0.955489i	$0.595328\pi$
$468$	2.72375	0.125906
$469$	7.97998	0.368481
$470$	26.5556	1.22492
$471$	8.54488	0.393727
$472$	−32.3517	−1.48911
$473$	8.63253	0.396924
$474$	24.2609	1.11434
$475$	−0.283084	−0.0129888
$476$	22.5490	1.03353
$477$	0.570761	0.0261334
$478$	−0.501441	−0.0229354
$479$	−28.8385	−1.31766	−0.658832	−	0.752290i	$-0.728949\pi$
$479$	−28.8385	−1.31766	−0.658832	+	0.752290i	$0.728949\pi$
$480$	−28.9312	−1.32052
$481$	7.05873	0.321850
$482$	34.9390	1.59143
$483$	−6.48747	−0.295190
$484$	−31.7471	−1.44305
$485$	10.2622	0.465985
$486$	20.0020	0.907309
$487$	−0.966908	−0.0438148	−0.0219074	−	0.999760i	$-0.506974\pi$
$487$	−0.966908	−0.0438148	−0.0219074	+	0.999760i	$0.506974\pi$
$488$	−22.0372	−0.997579
$489$	−13.5010	−0.610538
$490$	−20.1920	−0.912183
$491$	15.3629	0.693316	0.346658	−	0.937992i	$-0.387316\pi$
$491$	15.3629	0.693316	0.346658	+	0.937992i	$0.387316\pi$
$492$	60.1028	2.70964
$493$	9.96851	0.448959
$494$	1.39741	0.0628723
$495$	−1.79725	−0.0807802
$496$	1.26990	0.0570204
$497$	−21.8417	−0.979736
$498$	19.9127	0.892309
$499$	−3.14340	−0.140718	−0.0703591	−	0.997522i	$-0.522415\pi$
$499$	−3.14340	−0.140718	−0.0703591	+	0.997522i	$0.522415\pi$
$500$	32.9253	1.47246
$501$	−11.4473	−0.511429
$502$	2.42991	0.108452
$503$	36.1941	1.61382	0.806908	−	0.590677i	$-0.201139\pi$
$503$	36.1941	1.61382	0.806908	+	0.590677i	$0.201139\pi$
$504$	3.89562	0.173525
$505$	26.0473	1.15909
$506$	−3.66082	−0.162743
$507$	1.96923	0.0874565
$508$	−59.6700	−2.64743
$509$	2.01204	0.0891820	0.0445910	−	0.999005i	$-0.485802\pi$
$509$	2.01204	0.0891820	0.0445910	+	0.999005i	$0.485802\pi$
$510$	−42.3934	−1.87721
$511$	−16.6192	−0.735189
$512$	−6.52065	−0.288175
$513$	2.58519	0.114139
$514$	−58.3707	−2.57462
$515$	38.3232	1.68872
$516$	60.1860	2.64954
$517$	4.40996	0.193950
$518$	28.4061	1.24809
$519$	33.2367	1.45893
$520$	5.81929	0.255193
$521$	13.6550	0.598237	0.299119	−	0.954216i	$-0.403307\pi$
$521$	13.6550	0.598237	0.299119	+	0.954216i	$0.403307\pi$
$522$	4.84569	0.212090
$523$	−9.58464	−0.419107	−0.209554	−	0.977797i	$-0.567201\pi$
$523$	−9.58464	−0.419107	−0.209554	+	0.977797i	$0.567201\pi$
$524$	24.6172	1.07541
$525$	−1.60536	−0.0700638
$526$	70.5108	3.07442
$527$	8.95435	0.390058
$528$	−0.998424	−0.0434508
$529$	−19.5803	−0.851316
$530$	3.43109	0.149037
$531$	11.4013	0.494773
$532$	3.41939	0.148249
$533$	9.83684	0.426081
$534$	16.7400	0.724409
$535$	−9.71448	−0.419994
$536$	11.1580	0.481953
$537$	5.07673	0.219077
$538$	50.9881	2.19825
$539$	−3.35320	−0.144433
$540$	30.2911	1.30352
$541$	−7.44070	−0.319901	−0.159950	−	0.987125i	$-0.551133\pi$
$541$	−7.44070	−0.319901	−0.159950	+	0.987125i	$0.551133\pi$
$542$	56.3621	2.42096
$543$	20.8581	0.895107
$544$	−25.6549	−1.09994
$545$	31.6498	1.35573
$546$	7.92466	0.339144
$547$	−14.0384	−0.600240	−0.300120	−	0.953901i	$-0.597027\pi$
$547$	−14.0384	−0.600240	−0.300120	+	0.953901i	$0.597027\pi$
$548$	−5.36590	−0.229220
$549$	7.76628	0.331457
$550$	−0.905892	−0.0386274
$551$	1.51165	0.0643985
$552$	−9.07110	−0.386092
$553$	9.71614	0.413172
$554$	42.5447	1.80755
$555$	−32.4731	−1.37841
$556$	−71.2607	−3.02213
$557$	10.9468	0.463829	0.231915	−	0.972736i	$-0.425501\pi$
$557$	10.9468	0.463829	0.231915	+	0.972736i	$0.425501\pi$
$558$	4.35271	0.184265
$559$	9.85045	0.416630
$560$	−2.40781	−0.101748
$561$	−7.04009	−0.297233
$562$	−23.7737	−1.00283
$563$	−5.34071	−0.225084	−0.112542	−	0.993647i	$-0.535899\pi$
$563$	−5.34071	−0.225084	−0.112542	+	0.993647i	$0.535899\pi$
$564$	30.7463	1.29465
$565$	28.7603	1.20996
$566$	−68.0395	−2.85991
$567$	19.3522	0.812717
$568$	−30.5402	−1.28144
$569$	−7.26970	−0.304762	−0.152381	−	0.988322i	$-0.548694\pi$
$569$	−7.26970	−0.304762	−0.152381	+	0.988322i	$0.548694\pi$
$570$	−6.42865	−0.269266
$571$	29.3167	1.22686	0.613432	−	0.789747i	$-0.289788\pi$
$571$	29.3167	1.22686	0.613432	+	0.789747i	$0.289788\pi$
$572$	2.71910	0.113691
$573$	20.0627	0.838131
$574$	39.5859	1.65228
$575$	0.846231	0.0352903
$576$	−11.4551	−0.477295
$577$	−18.7341	−0.779909	−0.389955	−	0.920834i	$-0.627509\pi$
$577$	−18.7341	−0.779909	−0.389955	+	0.920834i	$0.627509\pi$
$578$	0.809128	0.0336553
$579$	−6.04902	−0.251389
$580$	17.7123	0.735462
$581$	7.97474	0.330848
$582$	19.5406	0.809985
$583$	0.569786	0.0235981
$584$	−23.2378	−0.961585
$585$	−2.05081	−0.0847906
$586$	−26.6673	−1.10162
$587$	8.76337	0.361703	0.180852	−	0.983510i	$-0.442115\pi$
$587$	8.76337	0.361703	0.180852	+	0.983510i	$0.442115\pi$
$588$	−23.3785	−0.964114
$589$	1.35786	0.0559497
$590$	68.5380	2.82166
$591$	−36.0886	−1.48449
$592$	−4.08379	−0.167843
$593$	−14.8228	−0.608700	−0.304350	−	0.952560i	$-0.598439\pi$
$593$	−14.8228	−0.608700	−0.304350	+	0.952560i	$0.598439\pi$
$594$	8.27281	0.339438
$595$	−16.9779	−0.696028
$596$	−18.2956	−0.749418
$597$	15.1189	0.618774
$598$	−4.17731	−0.170823
$599$	−47.4191	−1.93749	−0.968745	−	0.248057i	$-0.920208\pi$
$599$	−47.4191	−1.93749	−0.968745	+	0.248057i	$0.920208\pi$
$600$	−2.24470	−0.0916395
$601$	−2.15857	−0.0880498	−0.0440249	−	0.999030i	$-0.514018\pi$
$601$	−2.15857	−0.0880498	−0.0440249	+	0.999030i	$0.514018\pi$
$602$	39.6407	1.61563
$603$	−3.93226	−0.160134
$604$	63.7402	2.59355
$605$	23.9035	0.971816
$606$	49.5973	2.01475
$607$	−24.8346	−1.00801	−0.504003	−	0.863702i	$-0.668140\pi$
$607$	−24.8346	−1.00801	−0.504003	+	0.863702i	$0.668140\pi$
$608$	−3.89037	−0.157775
$609$	8.57254	0.347377
$610$	46.6864	1.89028
$611$	5.03215	0.203579
$612$	−11.1114	−0.449151
$613$	−34.4569	−1.39170	−0.695851	−	0.718186i	$-0.744973\pi$
$613$	−34.4569	−1.39170	−0.695851	+	0.718186i	$0.744973\pi$
$614$	44.8449	1.80979
$615$	−45.2535	−1.82480
$616$	3.88896	0.156691
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	72.9723	2.93538
$619$	−17.4726	−0.702282	−0.351141	−	0.936323i	$-0.614206\pi$
$619$	−17.4726	−0.702282	−0.351141	+	0.936323i	$0.614206\pi$
$620$	15.9103	0.638973
$621$	−7.72798	−0.310113
$622$	−24.4156	−0.978977
$623$	6.70411	0.268594
$624$	−1.13929	−0.0456080
$625$	−27.0786	−1.08315
$626$	−57.1426	−2.28388
$627$	−1.06758	−0.0426349
$628$	13.4634	0.537246
$629$	−28.7957	−1.14816
$630$	−8.25297	−0.328806
$631$	−26.2695	−1.04577	−0.522886	−	0.852403i	$-0.675144\pi$
$631$	−26.2695	−1.04577	−0.522886	+	0.852403i	$0.675144\pi$
$632$	13.5856	0.540406
$633$	−1.22539	−0.0487049
$634$	−8.54099	−0.339206
$635$	44.9276	1.78290
$636$	3.97255	0.157522
$637$	−3.82629	−0.151603
$638$	4.83741	0.191515
$639$	10.7629	0.425773
$640$	−39.4780	−1.56051
$641$	−39.1106	−1.54478	−0.772389	−	0.635150i	$-0.780938\pi$
$641$	−39.1106	−1.54478	−0.772389	+	0.635150i	$0.780938\pi$
$642$	−18.4976	−0.730042
$643$	−43.8249	−1.72829	−0.864144	−	0.503245i	$-0.832139\pi$
$643$	−43.8249	−1.72829	−0.864144	+	0.503245i	$0.832139\pi$
$644$	−10.2217	−0.402791
$645$	−45.3162	−1.78432
$646$	−5.70063	−0.224288
$647$	21.1081	0.829845	0.414923	−	0.909857i	$-0.363809\pi$
$647$	21.1081	0.829845	0.414923	+	0.909857i	$0.363809\pi$
$648$	27.0593	1.06299
$649$	11.3818	0.446774
$650$	−1.03370	−0.0405451
$651$	7.70040	0.301803
$652$	−21.2723	−0.833088
$653$	38.2859	1.49824	0.749121	−	0.662433i	$-0.230476\pi$
$653$	38.2859	1.49824	0.749121	+	0.662433i	$0.230476\pi$
$654$	60.2652	2.35656
$655$	−18.5351	−0.724227
$656$	−5.69105	−0.222198
$657$	8.18936	0.319498
$658$	20.2506	0.789451
$659$	−24.0208	−0.935719	−0.467860	−	0.883803i	$-0.654975\pi$
$659$	−24.0208	−0.935719	−0.467860	+	0.883803i	$0.654975\pi$
$660$	−12.5090	−0.486912
$661$	−49.3872	−1.92094	−0.960471	−	0.278381i	$-0.910202\pi$
$661$	−49.3872	−1.92094	−0.960471	+	0.278381i	$0.910202\pi$
$662$	11.9524	0.464544
$663$	−8.03334	−0.311989
$664$	11.1507	0.432730
$665$	−2.57458	−0.0998379
$666$	−13.9976	−0.542394
$667$	−4.51882	−0.174970
$668$	−18.0365	−0.697852
$669$	14.3720	0.555652
$670$	−23.6385	−0.913236
$671$	7.75301	0.299301
$672$	−22.0622	−0.851069
$673$	39.3540	1.51699	0.758493	−	0.651681i	$-0.225936\pi$
$673$	39.3540	1.51699	0.758493	+	0.651681i	$0.225936\pi$
$674$	−20.9474	−0.806863
$675$	−1.91233	−0.0736058
$676$	3.10273	0.119336
$677$	25.4560	0.978353	0.489177	−	0.872185i	$-0.337297\pi$
$677$	25.4560	0.978353	0.489177	+	0.872185i	$0.337297\pi$
$678$	54.7633	2.10317
$679$	7.82573	0.300324
$680$	−23.7394	−0.910365
$681$	−48.1908	−1.84668
$682$	4.34527	0.166389
$683$	2.30538	0.0882128	0.0441064	−	0.999027i	$-0.485956\pi$
$683$	2.30538	0.0882128	0.0441064	+	0.999027i	$0.485956\pi$
$684$	−1.68496	−0.0644260
$685$	4.04018	0.154367
$686$	−43.5677	−1.66342
$687$	−17.9593	−0.685191
$688$	−5.69893	−0.217270
$689$	0.650174	0.0247697
$690$	19.2174	0.731593
$691$	4.29295	0.163312	0.0816558	−	0.996661i	$-0.473979\pi$
$691$	4.29295	0.163312	0.0816558	+	0.996661i	$0.473979\pi$
$692$	52.3679	1.99073
$693$	−1.37053	−0.0520623
$694$	−54.6167	−2.07322
$695$	53.6547	2.03524
$696$	11.9866	0.454349
$697$	−40.1288	−1.51999
$698$	41.8544	1.58421
$699$	−23.0109	−0.870353
$700$	−2.52942	−0.0956030
$701$	11.0922	0.418946	0.209473	−	0.977814i	$-0.432825\pi$
$701$	11.0922	0.418946	0.209473	+	0.977814i	$0.432825\pi$
$702$	9.43999	0.356289
$703$	−4.36665	−0.164691
$704$	−11.4355	−0.430991
$705$	−23.1500	−0.871878
$706$	50.1064	1.88578
$707$	19.8630	0.747024
$708$	79.3539	2.98230
$709$	47.2640	1.77504	0.887518	−	0.460774i	$-0.152428\pi$
$709$	47.2640	1.77504	0.887518	+	0.460774i	$0.152428\pi$
$710$	64.7003	2.42816
$711$	−4.78778	−0.179556
$712$	9.37402	0.351306
$713$	−4.05910	−0.152014
$714$	−32.3282	−1.20985
$715$	−2.04731	−0.0765649
$716$	7.99892	0.298934
$717$	0.437134	0.0163251
$718$	1.85001	0.0690416
$719$	−47.1308	−1.75768	−0.878842	−	0.477113i	$-0.841683\pi$
$719$	−47.1308	−1.75768	−0.878842	+	0.477113i	$0.841683\pi$
$720$	1.18649	0.0442178
$721$	29.2243	1.08837
$722$	42.0550	1.56513
$723$	−30.4583	−1.13276
$724$	32.8641	1.22139
$725$	−1.11821	−0.0415293
$726$	45.5153	1.68923
$727$	−22.2968	−0.826942	−0.413471	−	0.910517i	$-0.635684\pi$
$727$	−22.2968	−0.826942	−0.413471	+	0.910517i	$0.635684\pi$
$728$	4.43764	0.164470
$729$	15.1520	0.561184
$730$	49.2298	1.82208
$731$	−40.1843	−1.48627
$732$	54.0540	1.99789
$733$	0.922949	0.0340899	0.0170450	−	0.999855i	$-0.494574\pi$
$733$	0.922949	0.0340899	0.0170450	+	0.999855i	$0.494574\pi$
$734$	75.0846	2.77142
$735$	17.6025	0.649279
$736$	11.6296	0.428673
$737$	−3.92554	−0.144599
$738$	−19.5066	−0.718047
$739$	14.0292	0.516072	0.258036	−	0.966135i	$-0.416925\pi$
$739$	14.0292	0.516072	0.258036	+	0.966135i	$0.416925\pi$
$740$	−51.1648	−1.88086
$741$	−1.21820	−0.0447516
$742$	2.61646	0.0960534
$743$	49.3715	1.81126	0.905632	−	0.424064i	$-0.139397\pi$
$743$	49.3715	1.81126	0.905632	+	0.424064i	$0.139397\pi$
$744$	10.7671	0.394741
$745$	13.7754	0.504693
$746$	−7.81284	−0.286048
$747$	−3.92968	−0.143780
$748$	−11.0924	−0.405578
$749$	−7.40802	−0.270683
$750$	−47.2044	−1.72366
$751$	40.6390	1.48294	0.741470	−	0.670986i	$-0.234129\pi$
$751$	40.6390	1.48294	0.741470	+	0.670986i	$0.234129\pi$
$752$	−2.91132	−0.106165
$753$	−2.11828	−0.0771946
$754$	5.51990	0.201023
$755$	−47.9922	−1.74662
$756$	23.0992	0.840110
$757$	−46.7699	−1.69988	−0.849941	−	0.526878i	$-0.823362\pi$
$757$	−46.7699	−1.69988	−0.849941	+	0.526878i	$0.823362\pi$
$758$	−41.9765	−1.52466
$759$	3.19134	0.115838
$760$	−3.59991	−0.130582
$761$	−15.4921	−0.561587	−0.280794	−	0.959768i	$-0.590598\pi$
$761$	−15.4921	−0.561587	−0.280794	+	0.959768i	$0.590598\pi$
$762$	85.5479	3.09907
$763$	24.1353	0.873758
$764$	31.6109	1.14364
$765$	8.36616	0.302479
$766$	60.7852	2.19626
$767$	12.9876	0.468955
$768$	−23.7787	−0.858041
$769$	8.02649	0.289443	0.144721	−	0.989472i	$-0.453771\pi$
$769$	8.02649	0.289443	0.144721	+	0.989472i	$0.453771\pi$
$770$	−8.23887	−0.296908
$771$	50.8850	1.83258
$772$	−9.53087	−0.343023
$773$	−3.64341	−0.131045	−0.0655223	−	0.997851i	$-0.520871\pi$
$773$	−3.64341	−0.131045	−0.0655223	+	0.997851i	$0.520871\pi$
$774$	−19.5336	−0.702120
$775$	−1.00445	−0.0360808
$776$	10.9423	0.392807
$777$	−24.7632	−0.888374
$778$	−11.0085	−0.394673
$779$	−6.08523	−0.218026
$780$	−14.2738	−0.511085
$781$	10.7445	0.384468
$782$	17.0411	0.609387
$783$	10.2118	0.364938
$784$	2.21368	0.0790601
$785$	−10.1370	−0.361806
$786$	−35.2932	−1.25887
$787$	−26.5431	−0.946158	−0.473079	−	0.881020i	$-0.656858\pi$
$787$	−26.5431	−0.946158	−0.473079	+	0.881020i	$0.656858\pi$
$788$	−56.8615	−2.02561
$789$	−61.4682	−2.18833
$790$	−28.7814	−1.02400
$791$	21.9319	0.779809
$792$	−1.91635	−0.0680945
$793$	8.84685	0.314161
$794$	−78.8684	−2.79893
$795$	−2.99107	−0.106082
$796$	23.8213	0.844325
$797$	6.65834	0.235850	0.117925	−	0.993022i	$-0.462376\pi$
$797$	6.65834	0.235850	0.117925	+	0.993022i	$0.462376\pi$
$798$	−4.90233	−0.173540
$799$	−20.5283	−0.726240
$800$	2.87782	0.101746
$801$	−3.30356	−0.116725
$802$	−23.8889	−0.843547
$803$	8.17537	0.288502
$804$	−27.3689	−0.965227
$805$	7.69627	0.271258
$806$	4.95832	0.174650
$807$	−44.4492	−1.56468
$808$	27.7734	0.977066
$809$	−50.8010	−1.78607	−0.893035	−	0.449987i	$-0.851428\pi$
$809$	−50.8010	−1.78607	−0.893035	+	0.449987i	$0.851428\pi$
$810$	−57.3257	−2.01422
$811$	−11.8194	−0.415035	−0.207517	−	0.978231i	$-0.566538\pi$
$811$	−11.8194	−0.415035	−0.207517	+	0.978231i	$0.566538\pi$
$812$	13.5069	0.474001
$813$	−49.1340	−1.72320
$814$	−13.9736	−0.489776
$815$	16.0167	0.561040
$816$	4.64765	0.162700
$817$	−6.09365	−0.213190
$818$	53.3765	1.86627
$819$	−1.56390	−0.0546470
$820$	−71.3017	−2.48996
$821$	36.9398	1.28921	0.644604	−	0.764517i	$-0.277022\pi$
$821$	36.9398	1.28921	0.644604	+	0.764517i	$0.277022\pi$
$822$	7.69302	0.268325
$823$	−39.9145	−1.39133	−0.695666	−	0.718365i	$-0.744891\pi$
$823$	−39.9145	−1.39133	−0.695666	+	0.718365i	$0.744891\pi$
$824$	40.8629	1.42353
$825$	0.789717	0.0274944
$826$	52.2653	1.81854
$827$	−11.7627	−0.409029	−0.204515	−	0.978863i	$-0.565562\pi$
$827$	−11.7627	−0.409029	−0.204515	+	0.978863i	$0.565562\pi$
$828$	5.03690	0.175044
$829$	11.4351	0.397157	0.198578	−	0.980085i	$-0.436368\pi$
$829$	11.4351	0.397157	0.198578	+	0.980085i	$0.436368\pi$
$830$	−23.6230	−0.819967
$831$	−37.0886	−1.28659
$832$	−13.0489	−0.452388
$833$	15.6091	0.540824
$834$	102.165	3.53770
$835$	13.5803	0.469966
$836$	−1.68208	−0.0581759
$837$	9.17285	0.317060
$838$	15.8935	0.549033
$839$	27.9130	0.963664	0.481832	−	0.876264i	$-0.339972\pi$
$839$	27.9130	0.963664	0.481832	+	0.876264i	$0.339972\pi$
$840$	−20.4150	−0.704384
$841$	−23.0288	−0.794097
$842$	10.8672	0.374508
$843$	20.7248	0.713802
$844$	−1.93073	−0.0664585
$845$	−2.33615	−0.0803661
$846$	−9.97882	−0.343079
$847$	18.2282	0.626329
$848$	−0.376155	−0.0129172
$849$	59.3138	2.03564
$850$	4.21692	0.144639
$851$	13.0534	0.447463
$852$	74.9106	2.56639
$853$	51.5658	1.76558	0.882789	−	0.469769i	$-0.155663\pi$
$853$	51.5658	1.76558	0.882789	+	0.469769i	$0.155663\pi$
$854$	35.6019	1.21827
$855$	1.26867	0.0433874
$856$	−10.3583	−0.354038
$857$	−32.5871	−1.11315	−0.556577	−	0.830796i	$-0.687886\pi$
$857$	−32.5871	−1.11315	−0.556577	+	0.830796i	$0.687886\pi$
$858$	−3.89833	−0.133087
$859$	−50.2963	−1.71609	−0.858044	−	0.513576i	$-0.828320\pi$
$859$	−50.2963	−1.71609	−0.858044	+	0.513576i	$0.828320\pi$
$860$	−71.4004	−2.43473
$861$	−34.5092	−1.17607
$862$	−72.4799	−2.46868
$863$	48.3426	1.64560	0.822801	−	0.568329i	$-0.192410\pi$
$863$	48.3426	1.64560	0.822801	+	0.568329i	$0.192410\pi$
$864$	−26.2809	−0.894094
$865$	−39.4296	−1.34065
$866$	70.2907	2.38857
$867$	−0.705362	−0.0239553
$868$	12.1328	0.411814
$869$	−4.77960	−0.162137
$870$	−25.3938	−0.860931
$871$	−4.47938	−0.151778
$872$	33.7472	1.14283
$873$	−3.85626	−0.130514
$874$	2.58415	0.0874102
$875$	−18.9047	−0.639095
$876$	56.9987	1.92581
$877$	2.49265	0.0841707	0.0420854	−	0.999114i	$-0.486600\pi$
$877$	2.49265	0.0841707	0.0420854	+	0.999114i	$0.486600\pi$
$878$	−63.8955	−2.15637
$879$	23.2474	0.784114
$880$	1.18446	0.0399281
$881$	−31.6659	−1.06685	−0.533426	−	0.845847i	$-0.679096\pi$
$881$	−31.6659	−1.06685	−0.533426	+	0.845847i	$0.679096\pi$
$882$	7.58758	0.255487
$883$	6.22698	0.209554	0.104777	−	0.994496i	$-0.466587\pi$
$883$	6.22698	0.209554	0.104777	+	0.994496i	$0.466587\pi$
$884$	−12.6574	−0.425714
$885$	−59.7484	−2.00842
$886$	−78.1343	−2.62497
$887$	16.1820	0.543337	0.271669	−	0.962391i	$-0.412425\pi$
$887$	16.1820	0.543337	0.271669	+	0.962391i	$0.412425\pi$
$888$	−34.6251	−1.16194
$889$	34.2607	1.14907
$890$	−19.8591	−0.665679
$891$	−9.51983	−0.318926
$892$	22.6445	0.758195
$893$	−3.11297	−0.104172
$894$	26.2302	0.877268
$895$	−6.02267	−0.201316
$896$	−30.1049	−1.00574
$897$	3.64159	0.121589
$898$	68.0499	2.27086
$899$	5.36369	0.178889
$900$	1.24641	0.0415471
$901$	−2.65235	−0.0883624
$902$	−19.4732	−0.648388
$903$	−34.5570	−1.14998
$904$	30.6663	1.01995
$905$	−24.7446	−0.822537
$906$	−91.3833	−3.03601
$907$	0.520372	0.0172787	0.00863933	−	0.999963i	$-0.497250\pi$
$907$	0.520372	0.0172787	0.00863933	+	0.999963i	$0.497250\pi$
$908$	−75.9297	−2.51982
$909$	−9.78781	−0.324641
$910$	−9.40126	−0.311649
$911$	−25.1969	−0.834810	−0.417405	−	0.908721i	$-0.637060\pi$
$911$	−25.1969	−0.834810	−0.417405	+	0.908721i	$0.637060\pi$
$912$	0.704782	0.0233377
$913$	−3.92297	−0.129831
$914$	0.841250	0.0278261
$915$	−40.6992	−1.34547
$916$	−28.2968	−0.934953
$917$	−14.1344	−0.466760
$918$	−38.5098	−1.27101
$919$	46.8070	1.54402	0.772010	−	0.635611i	$-0.219252\pi$
$919$	46.8070	1.54402	0.772010	+	0.635611i	$0.219252\pi$
$920$	10.7613	0.354790
$921$	−39.0938	−1.28819
$922$	44.8071	1.47564
$923$	12.2604	0.403555
$924$	−9.53904	−0.313811
$925$	3.23013	0.106206
$926$	50.1792	1.64899
$927$	−14.4008	−0.472983
$928$	−15.3674	−0.504459
$929$	−29.9787	−0.983569	−0.491785	−	0.870717i	$-0.663655\pi$
$929$	−29.9787	−0.983569	−0.491785	+	0.870717i	$0.663655\pi$
$930$	−22.8104	−0.747981
$931$	2.36701	0.0775755
$932$	−36.2561	−1.18761
$933$	21.2845	0.696822
$934$	28.8038	0.942489
$935$	8.35186	0.273135
$936$	−2.18672	−0.0714752
$937$	−17.9571	−0.586632	−0.293316	−	0.956016i	$-0.594759\pi$
$937$	−17.9571	−0.586632	−0.293316	+	0.956016i	$0.594759\pi$
$938$	−18.0261	−0.588575
$939$	49.8144	1.62563
$940$	−36.4752	−1.18969
$941$	−0.830816	−0.0270838	−0.0135419	−	0.999908i	$-0.504311\pi$
$941$	−0.830816	−0.0270838	−0.0135419	+	0.999908i	$0.504311\pi$
$942$	−19.3022	−0.628900
$943$	18.1908	0.592373
$944$	−7.51391	−0.244557
$945$	−17.3922	−0.565769
$946$	−19.5002	−0.634006
$947$	25.4657	0.827524	0.413762	−	0.910385i	$-0.364215\pi$
$947$	25.4657	0.827524	0.413762	+	0.910385i	$0.364215\pi$
$948$	−33.3234	−1.08229
$949$	9.32880	0.302826
$950$	0.639464	0.0207470
$951$	7.44566	0.241442
$952$	−18.1031	−0.586724
$953$	20.3880	0.660432	0.330216	−	0.943905i	$-0.392878\pi$
$953$	20.3880	0.660432	0.330216	+	0.943905i	$0.392878\pi$
$954$	−1.28930	−0.0417428
$955$	−23.8010	−0.770181
$956$	0.688750	0.0222758
$957$	−4.21704	−0.136317
$958$	65.1439	2.10470
$959$	3.08094	0.0994887
$960$	60.0303	1.93747
$961$	−26.1820	−0.844580
$962$	−15.9451	−0.514091
$963$	3.65042	0.117633
$964$	−47.9902	−1.54566
$965$	7.17613	0.231008
$966$	14.6547	0.471507
$967$	55.1711	1.77418	0.887092	−	0.461592i	$-0.152722\pi$
$967$	55.1711	1.77418	0.887092	+	0.461592i	$0.152722\pi$
$968$	25.4876	0.819202
$969$	4.96956	0.159645
$970$	−23.1816	−0.744317
$971$	−9.35303	−0.300153	−0.150077	−	0.988674i	$-0.547952\pi$
$971$	−9.35303	−0.300153	−0.150077	+	0.988674i	$0.547952\pi$
$972$	−27.4736	−0.881216
$973$	40.9157	1.31170
$974$	2.18417	0.0699853
$975$	0.901134	0.0288594
$976$	−5.11830	−0.163833
$977$	16.8767	0.539934	0.269967	−	0.962870i	$-0.412987\pi$
$977$	16.8767	0.539934	0.269967	+	0.962870i	$0.412987\pi$
$978$	30.4978	0.975212
$979$	−3.29791	−0.105402
$980$	27.7346	0.885950
$981$	−11.8931	−0.379717
$982$	−34.7035	−1.10743
$983$	31.5291	1.00562	0.502810	−	0.864397i	$-0.332299\pi$
$983$	31.5291	1.00562	0.502810	+	0.864397i	$0.332299\pi$
$984$	−48.2525	−1.53823
$985$	42.8130	1.36414
$986$	−22.5181	−0.717122
$987$	−17.6536	−0.561920
$988$	−1.91940	−0.0610641
$989$	18.2159	0.579233
$990$	4.05984	0.129030
$991$	−36.9207	−1.17283	−0.586413	−	0.810012i	$-0.699460\pi$
$991$	−36.9207	−1.17283	−0.586413	+	0.810012i	$0.699460\pi$
$992$	−13.8040	−0.438276
$993$	−10.4196	−0.330656
$994$	49.3388	1.56493
$995$	−17.9359	−0.568608
$996$	−27.3509	−0.866648
$997$	31.1725	0.987244	0.493622	−	0.869677i	$-0.335673\pi$
$997$	31.1725	0.987244	0.493622	+	0.869677i	$0.335673\pi$
$998$	7.10070	0.224769
$999$	−29.4983	−0.933285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.16	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.16	✓	134	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)

\(f(q)\)	\(=\)	\(q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +O(q^{10})\)	\(q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +5.27718 q^{10} +0.876358 q^{11} +6.10997 q^{12} +1.00000 q^{13} +4.02425 q^{14} -4.60042 q^{15} -0.578545 q^{16} -4.07944 q^{17} -1.98301 q^{18} -0.618616 q^{19} -7.24844 q^{20} -3.50816 q^{21} -1.97962 q^{22} +1.84925 q^{23} -4.90529 q^{24} +0.457608 q^{25} -2.25892 q^{26} -4.17898 q^{27} -5.52748 q^{28} -2.44360 q^{29} +10.3920 q^{30} -2.19500 q^{31} +6.28883 q^{32} +1.72575 q^{33} +9.21513 q^{34} +4.16183 q^{35} +2.72375 q^{36} +7.05873 q^{37} +1.39741 q^{38} +1.96923 q^{39} +5.81929 q^{40} +9.83684 q^{41} +7.92466 q^{42} +9.85045 q^{43} +2.71910 q^{44} -2.05081 q^{45} -4.17731 q^{46} +5.03215 q^{47} -1.13929 q^{48} -3.82629 q^{49} -1.03370 q^{50} -8.03334 q^{51} +3.10273 q^{52} +0.650174 q^{53} +9.43999 q^{54} -2.04731 q^{55} +4.43764 q^{56} -1.21820 q^{57} +5.51990 q^{58} +12.9876 q^{59} -14.2738 q^{60} +8.84685 q^{61} +4.95832 q^{62} -1.56390 q^{63} -13.0489 q^{64} -2.33615 q^{65} -3.89833 q^{66} -4.47938 q^{67} -12.6574 q^{68} +3.64159 q^{69} -9.40126 q^{70} +12.2604 q^{71} -2.18672 q^{72} +9.32880 q^{73} -15.9451 q^{74} +0.901134 q^{75} -1.91940 q^{76} -1.56122 q^{77} -4.44833 q^{78} -5.45394 q^{79} +1.35157 q^{80} -10.8629 q^{81} -22.2206 q^{82} -4.47644 q^{83} -10.8849 q^{84} +9.53019 q^{85} -22.2514 q^{86} -4.81200 q^{87} -2.18298 q^{88} -3.76320 q^{89} +4.63262 q^{90} -1.78149 q^{91} +5.73771 q^{92} -4.32245 q^{93} -11.3672 q^{94} +1.44518 q^{95} +12.3841 q^{96} -4.39280 q^{97} +8.64329 q^{98} +0.769319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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