LMFDB - Embedded newform 8023.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44945 q^{2} -0.158730 q^{3} +3.99982 q^{4} -2.39064 q^{5} +0.388803 q^{6} -3.35946 q^{7} -4.89848 q^{8} -2.97480 q^{9} +O(q^{10})$	\(q-2.44945 q^{2} -0.158730 q^{3} +3.99982 q^{4} -2.39064 q^{5} +0.388803 q^{6} -3.35946 q^{7} -4.89848 q^{8} -2.97480 q^{9} +5.85577 q^{10} +4.88734 q^{11} -0.634894 q^{12} -5.94234 q^{13} +8.22884 q^{14} +0.379468 q^{15} +3.99895 q^{16} +3.33221 q^{17} +7.28665 q^{18} -1.30746 q^{19} -9.56215 q^{20} +0.533248 q^{21} -11.9713 q^{22} +1.99973 q^{23} +0.777538 q^{24} +0.715174 q^{25} +14.5555 q^{26} +0.948383 q^{27} -13.4372 q^{28} -0.726331 q^{29} -0.929489 q^{30} +2.51260 q^{31} +0.00171869 q^{32} -0.775769 q^{33} -8.16209 q^{34} +8.03127 q^{35} -11.8987 q^{36} -2.50928 q^{37} +3.20257 q^{38} +0.943230 q^{39} +11.7105 q^{40} -8.91593 q^{41} -1.30617 q^{42} -4.72724 q^{43} +19.5485 q^{44} +7.11170 q^{45} -4.89824 q^{46} +10.9668 q^{47} -0.634755 q^{48} +4.28597 q^{49} -1.75179 q^{50} -0.528923 q^{51} -23.7683 q^{52} -10.9709 q^{53} -2.32302 q^{54} -11.6839 q^{55} +16.4562 q^{56} +0.207534 q^{57} +1.77911 q^{58} -0.503774 q^{59} +1.51780 q^{60} +11.5932 q^{61} -6.15449 q^{62} +9.99373 q^{63} -8.00210 q^{64} +14.2060 q^{65} +1.90021 q^{66} +3.14243 q^{67} +13.3283 q^{68} -0.317417 q^{69} -19.6722 q^{70} +1.00000 q^{71} +14.5720 q^{72} -7.74868 q^{73} +6.14635 q^{74} -0.113520 q^{75} -5.22962 q^{76} -16.4188 q^{77} -2.31040 q^{78} -2.78944 q^{79} -9.56006 q^{80} +8.77388 q^{81} +21.8392 q^{82} -2.54731 q^{83} +2.13290 q^{84} -7.96612 q^{85} +11.5792 q^{86} +0.115291 q^{87} -23.9405 q^{88} +9.05381 q^{89} -17.4198 q^{90} +19.9630 q^{91} +7.99856 q^{92} -0.398826 q^{93} -26.8626 q^{94} +3.12568 q^{95} -0.000272808 q^{96} +8.43256 q^{97} -10.4983 q^{98} -14.5389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.44945	−1.73203	−0.866013	−	0.500022i	$-0.833325\pi$
$2$	−2.44945	−1.73203	−0.866013	+	0.500022i	$0.833325\pi$
$3$	−0.158730	−0.0916431	−0.0458215	−	0.998950i	$-0.514591\pi$
$3$	−0.158730	−0.0916431	−0.0458215	+	0.998950i	$0.514591\pi$
$4$	3.99982	1.99991
$5$	−2.39064	−1.06913	−0.534564	−	0.845128i	$-0.679524\pi$
$5$	−2.39064	−1.06913	−0.534564	+	0.845128i	$0.679524\pi$
$6$	0.388803	0.158728
$7$	−3.35946	−1.26976	−0.634878	−	0.772612i	$-0.718950\pi$
$7$	−3.35946	−1.26976	−0.634878	+	0.772612i	$0.718950\pi$
$8$	−4.89848	−1.73187
$9$	−2.97480	−0.991602
$10$	5.85577	1.85176
$11$	4.88734	1.47359	0.736794	−	0.676117i	$-0.236339\pi$
$11$	4.88734	1.47359	0.736794	+	0.676117i	$0.236339\pi$
$12$	−0.634894	−0.183278
$13$	−5.94234	−1.64811	−0.824054	−	0.566511i	$-0.808293\pi$
$13$	−5.94234	−1.64811	−0.824054	+	0.566511i	$0.808293\pi$
$14$	8.22884	2.19925
$15$	0.379468	0.0979782
$16$	3.99895	0.999737
$17$	3.33221	0.808179	0.404090	−	0.914719i	$-0.367588\pi$
$17$	3.33221	0.808179	0.404090	+	0.914719i	$0.367588\pi$
$18$	7.28665	1.71748
$19$	−1.30746	−0.299953	−0.149976	−	0.988690i	$-0.547920\pi$
$19$	−1.30746	−0.299953	−0.149976	+	0.988690i	$0.547920\pi$
$20$	−9.56215	−2.13816
$21$	0.533248	0.116364
$22$	−11.9713	−2.55229
$23$	1.99973	0.416972	0.208486	−	0.978025i	$-0.433146\pi$
$23$	1.99973	0.416972	0.208486	+	0.978025i	$0.433146\pi$
$24$	0.777538	0.158714
$25$	0.715174	0.143035
$26$	14.5555	2.85457
$27$	0.948383	0.182516
$28$	−13.4372	−2.53940
$29$	−0.726331	−0.134876	−0.0674381	−	0.997723i	$-0.521483\pi$
$29$	−0.726331	−0.134876	−0.0674381	+	0.997723i	$0.521483\pi$
$30$	−0.929489	−0.169701
$31$	2.51260	0.451276	0.225638	−	0.974211i	$-0.427553\pi$
$31$	2.51260	0.451276	0.225638	+	0.974211i	$0.427553\pi$
$32$	0.00171869	0.000303824 0
$33$	−0.775769	−0.135044
$34$	−8.16209	−1.39979
$35$	8.03127	1.35753
$36$	−11.8987	−1.98312
$37$	−2.50928	−0.412522	−0.206261	−	0.978497i	$-0.566130\pi$
$37$	−2.50928	−0.412522	−0.206261	+	0.978497i	$0.566130\pi$
$38$	3.20257	0.519526
$39$	0.943230	0.151038
$40$	11.7105	1.85159
$41$	−8.91593	−1.39243	−0.696217	−	0.717831i	$-0.745135\pi$
$41$	−8.91593	−1.39243	−0.696217	+	0.717831i	$0.745135\pi$
$42$	−1.30617	−0.201546
$43$	−4.72724	−0.720898	−0.360449	−	0.932779i	$-0.617376\pi$
$43$	−4.72724	−0.720898	−0.360449	+	0.932779i	$0.617376\pi$
$44$	19.5485	2.94705
$45$	7.11170	1.06015
$46$	−4.89824	−0.722206
$47$	10.9668	1.59967	0.799834	−	0.600221i	$-0.204921\pi$
$47$	10.9668	1.59967	0.799834	+	0.600221i	$0.204921\pi$
$48$	−0.634755	−0.0916190
$49$	4.28597	0.612281
$50$	−1.75179	−0.247740
$51$	−0.528923	−0.0740640
$52$	−23.7683	−3.29607
$53$	−10.9709	−1.50698	−0.753488	−	0.657462i	$-0.771630\pi$
$53$	−10.9709	−1.50698	−0.753488	+	0.657462i	$0.771630\pi$
$54$	−2.32302	−0.316123
$55$	−11.6839	−1.57545
$56$	16.4562	2.19906
$57$	0.207534	0.0274886
$58$	1.77911	0.233609
$59$	−0.503774	−0.0655858	−0.0327929	−	0.999462i	$-0.510440\pi$
$59$	−0.503774	−0.0655858	−0.0327929	+	0.999462i	$0.510440\pi$
$60$	1.51780	0.195948
$61$	11.5932	1.48435	0.742177	−	0.670204i	$-0.233793\pi$
$61$	11.5932	1.48435	0.742177	+	0.670204i	$0.233793\pi$
$62$	−6.15449	−0.781621
$63$	9.99373	1.25909
$64$	−8.00210	−1.00026
$65$	14.2060	1.76204
$66$	1.90021	0.233900
$67$	3.14243	0.383909	0.191954	−	0.981404i	$-0.438517\pi$
$67$	3.14243	0.383909	0.191954	+	0.981404i	$0.438517\pi$
$68$	13.3283	1.61629
$69$	−0.317417	−0.0382126
$70$	−19.6722	−2.35128
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	14.5720	1.71733
$73$	−7.74868	−0.906914	−0.453457	−	0.891278i	$-0.649809\pi$
$73$	−7.74868	−0.906914	−0.453457	+	0.891278i	$0.649809\pi$
$74$	6.14635	0.714499
$75$	−0.113520	−0.0131082
$76$	−5.22962	−0.599879
$77$	−16.4188	−1.87110
$78$	−2.31040	−0.261601
$79$	−2.78944	−0.313836	−0.156918	−	0.987612i	$-0.550156\pi$
$79$	−2.78944	−0.313836	−0.156918	+	0.987612i	$0.550156\pi$
$80$	−9.56006	−1.06885
$81$	8.77388	0.974875
$82$	21.8392	2.41173
$83$	−2.54731	−0.279604	−0.139802	−	0.990179i	$-0.544647\pi$
$83$	−2.54731	−0.279604	−0.139802	+	0.990179i	$0.544647\pi$
$84$	2.13290	0.232718
$85$	−7.96612	−0.864047
$86$	11.5792	1.24861
$87$	0.115291	0.0123605
$88$	−23.9405	−2.55207
$89$	9.05381	0.959702	0.479851	−	0.877350i	$-0.340691\pi$
$89$	9.05381	0.959702	0.479851	+	0.877350i	$0.340691\pi$
$90$	−17.4198	−1.83621
$91$	19.9630	2.09270
$92$	7.99856	0.833907
$93$	−0.398826	−0.0413563
$94$	−26.8626	−2.77067
$95$	3.12568	0.320688
$96$	−0.000272808 0	−2.78434e−5 0
$97$	8.43256	0.856197	0.428098	−	0.903732i	$-0.359184\pi$
$97$	8.43256	0.856197	0.428098	+	0.903732i	$0.359184\pi$
$98$	−10.4983	−1.06049
$99$	−14.5389	−1.46121
$100$	2.86057	0.286057
$101$	4.84887	0.482481	0.241241	−	0.970465i	$-0.422446\pi$
$101$	4.84887	0.482481	0.241241	+	0.970465i	$0.422446\pi$
$102$	1.29557	0.128281
$103$	12.8483	1.26598	0.632992	−	0.774159i	$-0.281827\pi$
$103$	12.8483	1.26598	0.632992	+	0.774159i	$0.281827\pi$
$104$	29.1084	2.85431
$105$	−1.27481	−0.124408
$106$	26.8728	2.61012
$107$	−13.3646	−1.29201	−0.646003	−	0.763334i	$-0.723561\pi$
$107$	−13.3646	−1.29201	−0.646003	+	0.763334i	$0.723561\pi$
$108$	3.79337	0.365017
$109$	15.0694	1.44339	0.721693	−	0.692214i	$-0.243364\pi$
$109$	15.0694	1.44339	0.721693	+	0.692214i	$0.243364\pi$
$110$	28.6191	2.72873
$111$	0.398298	0.0378048
$112$	−13.4343	−1.26942
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−0.508346	−0.0476109
$115$	−4.78063	−0.445796
$116$	−2.90520	−0.269741
$117$	17.6773	1.63427
$118$	1.23397	0.113596
$119$	−11.1944	−1.02619
$120$	−1.85881	−0.169686
$121$	12.8861	1.17146
$122$	−28.3970	−2.57094
$123$	1.41523	0.127607
$124$	10.0500	0.902512
$125$	10.2435	0.916206
$126$	−24.4792	−2.18078
$127$	−2.81902	−0.250148	−0.125074	−	0.992147i	$-0.539917\pi$
$127$	−2.81902	−0.250148	−0.125074	+	0.992147i	$0.539917\pi$
$128$	19.5973	1.73218
$129$	0.750357	0.0660653
$130$	−34.7970	−3.05190
$131$	−1.49039	−0.130216	−0.0651079	−	0.997878i	$-0.520739\pi$
$131$	−1.49039	−0.130216	−0.0651079	+	0.997878i	$0.520739\pi$
$132$	−3.10294	−0.270076
$133$	4.39237	0.380867
$134$	−7.69723	−0.664939
$135$	−2.26725	−0.195133
$136$	−16.3228	−1.39966
$137$	11.2837	0.964034	0.482017	−	0.876162i	$-0.339904\pi$
$137$	11.2837	0.964034	0.482017	+	0.876162i	$0.339904\pi$
$138$	0.777500	0.0661852
$139$	1.32854	0.112685	0.0563425	−	0.998411i	$-0.482056\pi$
$139$	1.32854	0.112685	0.0563425	+	0.998411i	$0.482056\pi$
$140$	32.1237	2.71494
$141$	−1.74076	−0.146598
$142$	−2.44945	−0.205554
$143$	−29.0422	−2.42863
$144$	−11.8961	−0.991341
$145$	1.73640	0.144200
$146$	18.9800	1.57080
$147$	−0.680313	−0.0561113
$148$	−10.0367	−0.825008
$149$	−9.23464	−0.756531	−0.378265	−	0.925697i	$-0.623479\pi$
$149$	−9.23464	−0.756531	−0.378265	+	0.925697i	$0.623479\pi$
$150$	0.278062	0.0227037
$151$	11.8572	0.964925	0.482462	−	0.875917i	$-0.339742\pi$
$151$	11.8572	0.964925	0.482462	+	0.875917i	$0.339742\pi$
$152$	6.40458	0.519480
$153$	−9.91267	−0.801392
$154$	40.2171	3.24079
$155$	−6.00672	−0.482472
$156$	3.77275	0.302062
$157$	24.2083	1.93203	0.966015	−	0.258487i	$-0.0832240\pi$
$157$	24.2083	1.93203	0.966015	+	0.258487i	$0.0832240\pi$
$158$	6.83260	0.543572
$159$	1.74142	0.138104
$160$	−0.00410877	−0.000324827 0
$161$	−6.71800	−0.529453
$162$	−21.4912	−1.68851
$163$	8.67278	0.679304	0.339652	−	0.940551i	$-0.389691\pi$
$163$	8.67278	0.679304	0.339652	+	0.940551i	$0.389691\pi$
$164$	−35.6622	−2.78475
$165$	1.85459	0.144379
$166$	6.23953	0.484281
$167$	−13.6280	−1.05457	−0.527283	−	0.849690i	$-0.676789\pi$
$167$	−13.6280	−1.05457	−0.527283	+	0.849690i	$0.676789\pi$
$168$	−2.61211	−0.201528
$169$	22.3114	1.71626
$170$	19.5127	1.49655
$171$	3.88945	0.297434
$172$	−18.9081	−1.44173
$173$	17.5259	1.33247	0.666237	−	0.745740i	$-0.267904\pi$
$173$	17.5259	1.33247	0.666237	+	0.745740i	$0.267904\pi$
$174$	−0.282399	−0.0214087
$175$	−2.40260	−0.181619
$176$	19.5442	1.47320
$177$	0.0799643	0.00601049
$178$	−22.1769	−1.66223
$179$	13.0379	0.974498	0.487249	−	0.873263i	$-0.338000\pi$
$179$	13.0379	0.974498	0.487249	+	0.873263i	$0.338000\pi$
$180$	28.4455	2.12021
$181$	25.5596	1.89983	0.949915	−	0.312508i	$-0.101169\pi$
$181$	25.5596	1.89983	0.949915	+	0.312508i	$0.101169\pi$
$182$	−48.8986	−3.62460
$183$	−1.84019	−0.136031
$184$	−9.79562	−0.722142
$185$	5.99878	0.441039
$186$	0.976905	0.0716302
$187$	16.2856	1.19092
$188$	43.8652	3.19920
$189$	−3.18606	−0.231751
$190$	−7.65621	−0.555440
$191$	10.6564	0.771068	0.385534	−	0.922694i	$-0.374017\pi$
$191$	10.6564	0.771068	0.385534	+	0.922694i	$0.374017\pi$
$192$	1.27018	0.0916672
$193$	−2.24366	−0.161502	−0.0807511	−	0.996734i	$-0.525732\pi$
$193$	−2.24366	−0.161502	−0.0807511	+	0.996734i	$0.525732\pi$
$194$	−20.6552	−1.48295
$195$	−2.25493	−0.161479
$196$	17.1431	1.22451
$197$	−6.13678	−0.437227	−0.218614	−	0.975812i	$-0.570153\pi$
$197$	−6.13678	−0.437227	−0.218614	+	0.975812i	$0.570153\pi$
$198$	35.6123	2.53086
$199$	−4.72045	−0.334624	−0.167312	−	0.985904i	$-0.553509\pi$
$199$	−4.72045	−0.334624	−0.167312	+	0.985904i	$0.553509\pi$
$200$	−3.50327	−0.247718
$201$	−0.498799	−0.0351826
$202$	−11.8771	−0.835669
$203$	2.44008	0.171260
$204$	−2.11560	−0.148122
$205$	21.3148	1.48869
$206$	−31.4714	−2.19272
$207$	−5.94880	−0.413470
$208$	−23.7631	−1.64767
$209$	−6.39002	−0.442007
$210$	3.12258	0.215479
$211$	−18.7784	−1.29276	−0.646378	−	0.763017i	$-0.723717\pi$
$211$	−18.7784	−1.29276	−0.646378	+	0.763017i	$0.723717\pi$
$212$	−43.8819	−3.01382
$213$	−0.158730	−0.0108760
$214$	32.7360	2.23779
$215$	11.3011	0.770732
$216$	−4.64564	−0.316095
$217$	−8.44097	−0.573010
$218$	−36.9118	−2.49998
$219$	1.22995	0.0831124
$220$	−46.7335	−3.15077
$221$	−19.8011	−1.33197
$222$	−0.975613	−0.0654789
$223$	−28.5096	−1.90914	−0.954570	−	0.297985i	$-0.903685\pi$
$223$	−28.5096	−1.90914	−0.954570	+	0.297985i	$0.903685\pi$
$224$	−0.00577386	−0.000385782 0
$225$	−2.12750	−0.141834
$226$	−2.44945	−0.162935
$227$	−8.32095	−0.552281	−0.276140	−	0.961117i	$-0.589055\pi$
$227$	−8.32095	−0.552281	−0.276140	+	0.961117i	$0.589055\pi$
$228$	0.830101	0.0549748
$229$	2.42329	0.160135	0.0800676	−	0.996789i	$-0.474486\pi$
$229$	2.42329	0.160135	0.0800676	+	0.996789i	$0.474486\pi$
$230$	11.7099	0.772131
$231$	2.60617	0.171473
$232$	3.55792	0.233589
$233$	−21.6026	−1.41523	−0.707615	−	0.706598i	$-0.750229\pi$
$233$	−21.6026	−1.41523	−0.707615	+	0.706598i	$0.750229\pi$
$234$	−43.2997	−2.83059
$235$	−26.2176	−1.71025
$236$	−2.01501	−0.131166
$237$	0.442769	0.0287609
$238$	27.4202	1.77739
$239$	23.0374	1.49016	0.745082	−	0.666973i	$-0.232410\pi$
$239$	23.0374	1.49016	0.745082	+	0.666973i	$0.232410\pi$
$240$	1.51747	0.0979524
$241$	−0.216438	−0.0139420	−0.00697099	−	0.999976i	$-0.502219\pi$
$241$	−0.216438	−0.0139420	−0.00697099	+	0.999976i	$0.502219\pi$
$242$	−31.5639	−2.02900
$243$	−4.23783	−0.271857
$244$	46.3707	2.96858
$245$	−10.2462	−0.654607
$246$	−3.46654	−0.221018
$247$	7.76939	0.494354
$248$	−12.3079	−0.781553
$249$	0.404336	0.0256238
$250$	−25.0910	−1.58689
$251$	−23.8485	−1.50530	−0.752651	−	0.658419i	$-0.771225\pi$
$251$	−23.8485	−1.50530	−0.752651	+	0.658419i	$0.771225\pi$
$252$	39.9732	2.51807
$253$	9.77334	0.614445
$254$	6.90507	0.433262
$255$	1.26447	0.0791839
$256$	−31.9986	−1.99991
$257$	9.39341	0.585945	0.292972	−	0.956121i	$-0.405356\pi$
$257$	9.39341	0.585945	0.292972	+	0.956121i	$0.405356\pi$
$258$	−1.83797	−0.114427
$259$	8.42981	0.523803
$260$	56.8215	3.52392
$261$	2.16069	0.133743
$262$	3.65064	0.225537
$263$	−27.4575	−1.69310	−0.846551	−	0.532308i	$-0.821325\pi$
$263$	−27.4575	−1.69310	−0.846551	+	0.532308i	$0.821325\pi$
$264$	3.80009	0.233879
$265$	26.2276	1.61115
$266$	−10.7589	−0.659671
$267$	−1.43712	−0.0879500
$268$	12.5692	0.767784
$269$	21.4405	1.30725	0.653626	−	0.756818i	$-0.273247\pi$
$269$	21.4405	1.30725	0.653626	+	0.756818i	$0.273247\pi$
$270$	5.55352	0.337976
$271$	−18.0327	−1.09541	−0.547705	−	0.836672i	$-0.684498\pi$
$271$	−18.0327	−1.09541	−0.547705	+	0.836672i	$0.684498\pi$
$272$	13.3253	0.807967
$273$	−3.16874	−0.191781
$274$	−27.6390	−1.66973
$275$	3.49530	0.210774
$276$	−1.26961	−0.0764218
$277$	18.5001	1.11156	0.555781	−	0.831329i	$-0.312419\pi$
$277$	18.5001	1.11156	0.555781	+	0.831329i	$0.312419\pi$
$278$	−3.25419	−0.195173
$279$	−7.47449	−0.447486
$280$	−39.3410	−2.35107
$281$	0.579362	0.0345619	0.0172809	−	0.999851i	$-0.494499\pi$
$281$	0.579362	0.0345619	0.0172809	+	0.999851i	$0.494499\pi$
$282$	4.26391	0.253912
$283$	−0.352249	−0.0209390	−0.0104695	−	0.999945i	$-0.503333\pi$
$283$	−0.352249	−0.0209390	−0.0104695	+	0.999945i	$0.503333\pi$
$284$	3.99982	0.237346
$285$	−0.496140	−0.0293888
$286$	71.1376	4.20645
$287$	29.9527	1.76805
$288$	−0.00511276	−0.000301272 0
$289$	−5.89638	−0.346846
$290$	−4.25323	−0.249758
$291$	−1.33850	−0.0784645
$292$	−30.9933	−1.81375
$293$	−14.6522	−0.855993	−0.427996	−	0.903780i	$-0.640780\pi$
$293$	−14.6522	−0.855993	−0.427996	+	0.903780i	$0.640780\pi$
$294$	1.66640	0.0971862
$295$	1.20434	0.0701197
$296$	12.2916	0.714436
$297$	4.63507	0.268954
$298$	22.6198	1.31033
$299$	−11.8831	−0.687215
$300$	−0.454060	−0.0262152
$301$	15.8810	0.915364
$302$	−29.0437	−1.67127
$303$	−0.769664	−0.0442160
$304$	−5.22848	−0.299874
$305$	−27.7151	−1.58696
$306$	24.2806	1.38803
$307$	−23.0133	−1.31344	−0.656719	−	0.754136i	$-0.728056\pi$
$307$	−23.0133	−1.31344	−0.656719	+	0.754136i	$0.728056\pi$
$308$	−65.6724	−3.74203
$309$	−2.03942	−0.116019
$310$	14.7132	0.835653
$311$	6.23125	0.353342	0.176671	−	0.984270i	$-0.443467\pi$
$311$	6.23125	0.353342	0.176671	+	0.984270i	$0.443467\pi$
$312$	−4.62039	−0.261578
$313$	−1.37417	−0.0776726	−0.0388363	−	0.999246i	$-0.512365\pi$
$313$	−1.37417	−0.0776726	−0.0388363	+	0.999246i	$0.512365\pi$
$314$	−59.2970	−3.34632
$315$	−23.8915	−1.34613
$316$	−11.1573	−0.627645
$317$	−30.0303	−1.68667	−0.843336	−	0.537386i	$-0.819412\pi$
$317$	−30.0303	−1.68667	−0.843336	+	0.537386i	$0.819412\pi$
$318$	−4.26554	−0.239199
$319$	−3.54982	−0.198752
$320$	19.1302	1.06941
$321$	2.12137	0.118403
$322$	16.4554	0.917025
$323$	−4.35674	−0.242416
$324$	35.0940	1.94966
$325$	−4.24981	−0.235737
$326$	−21.2436	−1.17657
$327$	−2.39197	−0.132276
$328$	43.6745	2.41152
$329$	−36.8424	−2.03119
$330$	−4.54273	−0.250069
$331$	8.01583	0.440590	0.220295	−	0.975433i	$-0.429298\pi$
$331$	8.01583	0.440590	0.220295	+	0.975433i	$0.429298\pi$
$332$	−10.1888	−0.559183
$333$	7.46460	0.409058
$334$	33.3812	1.82654
$335$	−7.51242	−0.410447
$336$	2.13243	0.116334
$337$	−11.7493	−0.640024	−0.320012	−	0.947414i	$-0.603687\pi$
$337$	−11.7493	−0.640024	−0.320012	+	0.947414i	$0.603687\pi$
$338$	−54.6507	−2.97261
$339$	−0.158730	−0.00862105
$340$	−31.8631	−1.72802
$341$	12.2799	0.664995
$342$	−9.52702	−0.515162
$343$	9.11769	0.492309
$344$	23.1563	1.24850
$345$	0.758832	0.0408541
$346$	−42.9290	−2.30788
$347$	19.0321	1.02170	0.510849	−	0.859670i	$-0.329331\pi$
$347$	19.0321	1.02170	0.510849	+	0.859670i	$0.329331\pi$
$348$	0.461143	0.0247199
$349$	25.4471	1.36215	0.681075	−	0.732214i	$-0.261513\pi$
$349$	25.4471	1.36215	0.681075	+	0.732214i	$0.261513\pi$
$350$	5.88505	0.314569
$351$	−5.63561	−0.300807
$352$	0.00839981	0.000447711 0
$353$	−17.8787	−0.951588	−0.475794	−	0.879557i	$-0.657839\pi$
$353$	−17.8787	−0.951588	−0.475794	+	0.879557i	$0.657839\pi$
$354$	−0.195869	−0.0104103
$355$	−2.39064	−0.126882
$356$	36.2136	1.91932
$357$	1.77690	0.0940433
$358$	−31.9357	−1.68786
$359$	5.13216	0.270865	0.135432	−	0.990787i	$-0.456758\pi$
$359$	5.13216	0.270865	0.135432	+	0.990787i	$0.456758\pi$
$360$	−34.8365	−1.83604
$361$	−17.2905	−0.910028
$362$	−62.6071	−3.29055
$363$	−2.04541	−0.107356
$364$	79.8487	4.18521
$365$	18.5243	0.969607
$366$	4.50746	0.235609
$367$	22.4653	1.17268	0.586341	−	0.810065i	$-0.300568\pi$
$367$	22.4653	1.17268	0.586341	+	0.810065i	$0.300568\pi$
$368$	7.99680	0.416862
$369$	26.5232	1.38074
$370$	−14.6937	−0.763891
$371$	36.8565	1.91349
$372$	−1.59523	−0.0827090
$373$	32.5591	1.68584	0.842922	−	0.538036i	$-0.180833\pi$
$373$	32.5591	1.68584	0.842922	+	0.538036i	$0.180833\pi$
$374$	−39.8909	−2.06271
$375$	−1.62595	−0.0839639
$376$	−53.7205	−2.77042
$377$	4.31610	0.222291
$378$	7.80410	0.401399
$379$	3.67599	0.188823	0.0944113	−	0.995533i	$-0.469903\pi$
$379$	3.67599	0.188823	0.0944113	+	0.995533i	$0.469903\pi$
$380$	12.5022	0.641348
$381$	0.447465	0.0229243
$382$	−26.1023	−1.33551
$383$	−18.8606	−0.963732	−0.481866	−	0.876245i	$-0.660041\pi$
$383$	−18.8606	−0.963732	−0.481866	+	0.876245i	$0.660041\pi$
$384$	−3.11070	−0.158742
$385$	39.2515	2.00044
$386$	5.49574	0.279726
$387$	14.0626	0.714843
$388$	33.7288	1.71232
$389$	−35.5486	−1.80238	−0.901192	−	0.433419i	$-0.857307\pi$
$389$	−35.5486	−1.80238	−0.901192	+	0.433419i	$0.857307\pi$
$390$	5.52334	0.279685
$391$	6.66351	0.336988
$392$	−20.9947	−1.06039
$393$	0.236570	0.0119334
$394$	15.0317	0.757289
$395$	6.66855	0.335531
$396$	−58.1530	−2.92230
$397$	−29.3459	−1.47283	−0.736415	−	0.676530i	$-0.763483\pi$
$397$	−29.3459	−1.47283	−0.736415	+	0.676530i	$0.763483\pi$
$398$	11.5625	0.579577
$399$	−0.697203	−0.0349038
$400$	2.85994	0.142997
$401$	35.1485	1.75523	0.877616	−	0.479364i	$-0.159133\pi$
$401$	35.1485	1.75523	0.877616	+	0.479364i	$0.159133\pi$
$402$	1.22178	0.0609371
$403$	−14.9307	−0.743751
$404$	19.3946	0.964920
$405$	−20.9752	−1.04227
$406$	−5.97686	−0.296627
$407$	−12.2637	−0.607888
$408$	2.59092	0.128270
$409$	6.47922	0.320377	0.160188	−	0.987086i	$-0.448790\pi$
$409$	6.47922	0.320377	0.160188	+	0.987086i	$0.448790\pi$
$410$	−52.2096	−2.57845
$411$	−1.79107	−0.0883471
$412$	51.3911	2.53186
$413$	1.69241	0.0832780
$414$	14.5713	0.716140
$415$	6.08972	0.298932
$416$	−0.0102130	−0.000500735 0
$417$	−0.210879	−0.0103268
$418$	15.6521	0.765567
$419$	−8.39372	−0.410060	−0.205030	−	0.978756i	$-0.565729\pi$
$419$	−8.39372	−0.410060	−0.205030	+	0.978756i	$0.565729\pi$
$420$	−5.09900	−0.248806
$421$	−13.1434	−0.640569	−0.320284	−	0.947321i	$-0.603778\pi$
$421$	−13.1434	−0.640569	−0.320284	+	0.947321i	$0.603778\pi$
$422$	45.9968	2.23909
$423$	−32.6240	−1.58623
$424$	53.7410	2.60989
$425$	2.38311	0.115598
$426$	0.388803	0.0188376
$427$	−38.9468	−1.88477
$428$	−53.4562	−2.58390
$429$	4.60988	0.222567
$430$	−27.6816	−1.33493
$431$	2.66161	0.128205	0.0641027	−	0.997943i	$-0.479581\pi$
$431$	2.66161	0.128205	0.0641027	+	0.997943i	$0.479581\pi$
$432$	3.79254	0.182468
$433$	−11.8732	−0.570588	−0.285294	−	0.958440i	$-0.592091\pi$
$433$	−11.8732	−0.570588	−0.285294	+	0.958440i	$0.592091\pi$
$434$	20.6758	0.992469
$435$	−0.275619	−0.0132149
$436$	60.2749	2.88664
$437$	−2.61457	−0.125072
$438$	−3.01271	−0.143953
$439$	18.3609	0.876320	0.438160	−	0.898897i	$-0.355630\pi$
$439$	18.3609	0.876320	0.438160	+	0.898897i	$0.355630\pi$
$440$	57.2332	2.72849
$441$	−12.7499	−0.607139
$442$	48.5019	2.30700
$443$	11.9330	0.566952	0.283476	−	0.958979i	$-0.408512\pi$
$443$	11.9330	0.566952	0.283476	+	0.958979i	$0.408512\pi$
$444$	1.59312	0.0756063
$445$	−21.6444	−1.02604
$446$	69.8328	3.30668
$447$	1.46582	0.0693308
$448$	26.8827	1.27009
$449$	−5.79121	−0.273304	−0.136652	−	0.990619i	$-0.543634\pi$
$449$	−5.79121	−0.273304	−0.136652	+	0.990619i	$0.543634\pi$
$450$	5.21122	0.245659
$451$	−43.5752	−2.05187
$452$	3.99982	0.188136
$453$	−1.88210	−0.0884287
$454$	20.3818	0.956564
$455$	−47.7245	−2.23736
$456$	−1.01660	−0.0476068
$457$	−16.3015	−0.762553	−0.381277	−	0.924461i	$-0.624515\pi$
$457$	−16.3015	−0.762553	−0.381277	+	0.924461i	$0.624515\pi$
$458$	−5.93573	−0.277358
$459$	3.16021	0.147506
$460$	−19.1217	−0.891553
$461$	22.1666	1.03240	0.516201	−	0.856468i	$-0.327346\pi$
$461$	22.1666	1.03240	0.516201	+	0.856468i	$0.327346\pi$
$462$	−6.38368	−0.296996
$463$	−1.42282	−0.0661243	−0.0330621	−	0.999453i	$-0.510526\pi$
$463$	−1.42282	−0.0661243	−0.0330621	+	0.999453i	$0.510526\pi$
$464$	−2.90456	−0.134841
$465$	0.953450	0.0442152
$466$	52.9145	2.45122
$467$	17.7911	0.823273	0.411636	−	0.911348i	$-0.364957\pi$
$467$	17.7911	0.823273	0.411636	+	0.911348i	$0.364957\pi$
$468$	70.7061	3.26839
$469$	−10.5569	−0.487470
$470$	64.2189	2.96220
$471$	−3.84259	−0.177057
$472$	2.46773	0.113586
$473$	−23.1036	−1.06231
$474$	−1.08454	−0.0498146
$475$	−0.935064	−0.0429037
$476$	−44.7757	−2.05229
$477$	32.6364	1.49432
$478$	−56.4290	−2.58100
$479$	22.8176	1.04256	0.521282	−	0.853384i	$-0.325454\pi$
$479$	22.8176	1.04256	0.521282	+	0.853384i	$0.325454\pi$
$480$	0.000652187 0	2.97681e−5 0
$481$	14.9110	0.679881
$482$	0.530154	0.0241479
$483$	1.06635	0.0485207
$484$	51.5421	2.34282
$485$	−20.1592	−0.915384
$486$	10.3804	0.470863
$487$	4.29236	0.194506	0.0972528	−	0.995260i	$-0.468994\pi$
$487$	4.29236	0.194506	0.0972528	+	0.995260i	$0.468994\pi$
$488$	−56.7889	−2.57071
$489$	−1.37663	−0.0622535
$490$	25.0976	1.13380
$491$	39.4724	1.78137	0.890683	−	0.454626i	$-0.150227\pi$
$491$	39.4724	1.78137	0.890683	+	0.454626i	$0.150227\pi$
$492$	5.66067	0.255203
$493$	−2.42029	−0.109004
$494$	−19.0308	−0.856235
$495$	34.7573	1.56222
$496$	10.0477	0.451157
$497$	−3.35946	−0.150692
$498$	−0.990403	−0.0443810
$499$	25.4986	1.14147	0.570737	−	0.821133i	$-0.306658\pi$
$499$	25.4986	1.14147	0.570737	+	0.821133i	$0.306658\pi$
$500$	40.9722	1.83233
$501$	2.16318	0.0966437
$502$	58.4158	2.60722
$503$	−11.0315	−0.491872	−0.245936	−	0.969286i	$-0.579095\pi$
$503$	−11.0315	−0.491872	−0.245936	+	0.969286i	$0.579095\pi$
$504$	−48.9541	−2.18059
$505$	−11.5919	−0.515834
$506$	−23.9393	−1.06423
$507$	−3.54150	−0.157283
$508$	−11.2756	−0.500274
$509$	−3.70037	−0.164016	−0.0820081	−	0.996632i	$-0.526133\pi$
$509$	−3.70037	−0.164016	−0.0820081	+	0.996632i	$0.526133\pi$
$510$	−3.09725	−0.137149
$511$	26.0314	1.15156
$512$	39.1844	1.73172
$513$	−1.23998	−0.0547463
$514$	−23.0087	−1.01487
$515$	−30.7158	−1.35350
$516$	3.00130	0.132125
$517$	53.5983	2.35725
$518$	−20.6484	−0.907240
$519$	−2.78190	−0.122112
$520$	−69.5878	−3.05163
$521$	−20.5234	−0.899147	−0.449574	−	0.893243i	$-0.648424\pi$
$521$	−20.5234	−0.899147	−0.449574	+	0.893243i	$0.648424\pi$
$522$	−5.29252	−0.231647
$523$	−15.4891	−0.677292	−0.338646	−	0.940914i	$-0.609969\pi$
$523$	−15.4891	−0.677292	−0.338646	+	0.940914i	$0.609969\pi$
$524$	−5.96129	−0.260420
$525$	0.381366	0.0166442
$526$	67.2559	2.93249
$527$	8.37250	0.364712
$528$	−3.10226	−0.135009
$529$	−19.0011	−0.826135
$530$	−64.2434	−2.79055
$531$	1.49863	0.0650350
$532$	17.5687	0.761700
$533$	52.9815	2.29488
$534$	3.52015	0.152332
$535$	31.9500	1.38132
$536$	−15.3931	−0.664881
$537$	−2.06951	−0.0893060
$538$	−52.5176	−2.26419
$539$	20.9470	0.902250
$540$	−9.06859	−0.390250
$541$	−34.8658	−1.49900	−0.749499	−	0.662005i	$-0.769706\pi$
$541$	−34.8658	−1.49900	−0.749499	+	0.662005i	$0.769706\pi$
$542$	44.1703	1.89728
$543$	−4.05709	−0.174106
$544$	0.00572703	0.000245544 0
$545$	−36.0255	−1.54316
$546$	7.76169	0.332170
$547$	3.92828	0.167961	0.0839806	−	0.996467i	$-0.473237\pi$
$547$	3.92828	0.167961	0.0839806	+	0.996467i	$0.473237\pi$
$548$	45.1329	1.92798
$549$	−34.4874	−1.47189
$550$	−8.56157	−0.365067
$551$	0.949651	0.0404565
$552$	1.55486	0.0661793
$553$	9.37100	0.398496
$554$	−45.3151	−1.92525
$555$	−0.952189	−0.0404182
$556$	5.31392	0.225360
$557$	19.5849	0.829841	0.414920	−	0.909858i	$-0.363809\pi$
$557$	19.5849	0.829841	0.414920	+	0.909858i	$0.363809\pi$
$558$	18.3084	0.775057
$559$	28.0909	1.18812
$560$	32.1166	1.35717
$561$	−2.58503	−0.109140
$562$	−1.41912	−0.0598620
$563$	9.54227	0.402159	0.201079	−	0.979575i	$-0.435555\pi$
$563$	9.54227	0.402159	0.201079	+	0.979575i	$0.435555\pi$
$564$	−6.96274	−0.293184
$565$	−2.39064	−0.100575
$566$	0.862818	0.0362670
$567$	−29.4755	−1.23785
$568$	−4.89848	−0.205536
$569$	−24.6013	−1.03134	−0.515669	−	0.856788i	$-0.672457\pi$
$569$	−24.6013	−1.03134	−0.515669	+	0.856788i	$0.672457\pi$
$570$	1.21527	0.0509022
$571$	41.6159	1.74157	0.870785	−	0.491663i	$-0.163611\pi$
$571$	41.6159	1.74157	0.870785	+	0.491663i	$0.163611\pi$
$572$	−116.164	−4.85705
$573$	−1.69149	−0.0706630
$574$	−73.3678	−3.06231
$575$	1.43015	0.0596415
$576$	23.8047	0.991862
$577$	−33.3333	−1.38768	−0.693842	−	0.720128i	$-0.744083\pi$
$577$	−33.3333	−1.38768	−0.693842	+	0.720128i	$0.744083\pi$
$578$	14.4429	0.600746
$579$	0.356137	0.0148006
$580$	6.94529	0.288387
$581$	8.55759	0.355029
$582$	3.27860	0.135902
$583$	−53.6187	−2.22066
$584$	37.9567	1.57066
$585$	−42.2601	−1.74724
$586$	35.8900	1.48260
$587$	−37.1941	−1.53517	−0.767583	−	0.640950i	$-0.778541\pi$
$587$	−37.1941	−1.53517	−0.767583	+	0.640950i	$0.778541\pi$
$588$	−2.72113	−0.112218
$589$	−3.28513	−0.135361
$590$	−2.94999	−0.121449
$591$	0.974093	0.0400688
$592$	−10.0345	−0.412414
$593$	−4.62659	−0.189991	−0.0949955	−	0.995478i	$-0.530284\pi$
$593$	−4.62659	−0.189991	−0.0949955	+	0.995478i	$0.530284\pi$
$594$	−11.3534	−0.465835
$595$	26.7619	1.09713
$596$	−36.9369	−1.51300
$597$	0.749279	0.0306660
$598$	29.1070	1.19027
$599$	−15.3177	−0.625865	−0.312933	−	0.949775i	$-0.601311\pi$
$599$	−15.3177	−0.625865	−0.312933	+	0.949775i	$0.601311\pi$
$600$	0.556075	0.0227017
$601$	36.8202	1.50193	0.750963	−	0.660344i	$-0.229590\pi$
$601$	36.8202	1.50193	0.750963	+	0.660344i	$0.229590\pi$
$602$	−38.8997	−1.58543
$603$	−9.34811	−0.380684
$604$	47.4267	1.92977
$605$	−30.8060	−1.25244
$606$	1.88526	0.0765833
$607$	−15.1378	−0.614423	−0.307211	−	0.951641i	$-0.599396\pi$
$607$	−15.1378	−0.614423	−0.307211	+	0.951641i	$0.599396\pi$
$608$	−0.00224712	−9.11328e−5 0
$609$	−0.387315	−0.0156948
$610$	67.8870	2.74866
$611$	−65.1683	−2.63643
$612$	−39.6489	−1.60271
$613$	25.5844	1.03335	0.516673	−	0.856183i	$-0.327170\pi$
$613$	25.5844	1.03335	0.516673	+	0.856183i	$0.327170\pi$
$614$	56.3700	2.27491
$615$	−3.38331	−0.136428
$616$	80.4272	3.24050
$617$	45.8916	1.84753	0.923763	−	0.382965i	$-0.125097\pi$
$617$	45.8916	1.84753	0.923763	+	0.382965i	$0.125097\pi$
$618$	4.99547	0.200947
$619$	−39.1368	−1.57304	−0.786521	−	0.617564i	$-0.788120\pi$
$619$	−39.1368	−1.57304	−0.786521	+	0.617564i	$0.788120\pi$
$620$	−24.0258	−0.964901
$621$	1.89651	0.0761042
$622$	−15.2632	−0.611997
$623$	−30.4159	−1.21859
$624$	3.77193	0.150998
$625$	−28.0644	−1.12258
$626$	3.36596	0.134531
$627$	1.01429	0.0405068
$628$	96.8288	3.86389
$629$	−8.36143	−0.333392
$630$	58.5210	2.33153
$631$	−22.6416	−0.901348	−0.450674	−	0.892689i	$-0.648816\pi$
$631$	−22.6416	−0.901348	−0.450674	+	0.892689i	$0.648816\pi$
$632$	13.6640	0.543525
$633$	2.98070	0.118472
$634$	73.5579	2.92136
$635$	6.73928	0.267440
$636$	6.96539	0.276196
$637$	−25.4687	−1.00910
$638$	8.69513	0.344244
$639$	−2.97480	−0.117681
$640$	−46.8503	−1.85192
$641$	−27.1577	−1.07266	−0.536332	−	0.844007i	$-0.680191\pi$
$641$	−27.1577	−1.07266	−0.536332	+	0.844007i	$0.680191\pi$
$642$	−5.19620	−0.205078
$643$	16.7950	0.662332	0.331166	−	0.943573i	$-0.392558\pi$
$643$	16.7950	0.662332	0.331166	+	0.943573i	$0.392558\pi$
$644$	−26.8708	−1.05886
$645$	−1.79384	−0.0706322
$646$	10.6716	0.419870
$647$	27.7957	1.09276	0.546382	−	0.837536i	$-0.316005\pi$
$647$	27.7957	1.09276	0.546382	+	0.837536i	$0.316005\pi$
$648$	−42.9786	−1.68836
$649$	−2.46212	−0.0966465
$650$	10.4097	0.408302
$651$	1.33984	0.0525124
$652$	34.6896	1.35855
$653$	−18.9576	−0.741869	−0.370935	−	0.928659i	$-0.620963\pi$
$653$	−18.9576	−0.741869	−0.370935	+	0.928659i	$0.620963\pi$
$654$	5.85902	0.229106
$655$	3.56299	0.139217
$656$	−35.6543	−1.39207
$657$	23.0508	0.899297
$658$	90.2438	3.51807
$659$	34.9849	1.36282	0.681409	−	0.731903i	$-0.261368\pi$
$659$	34.9849	1.36282	0.681409	+	0.731903i	$0.261368\pi$
$660$	7.41803	0.288746
$661$	0.744278	0.0289490	0.0144745	−	0.999895i	$-0.495392\pi$
$661$	0.744278	0.0289490	0.0144745	+	0.999895i	$0.495392\pi$
$662$	−19.6344	−0.763113
$663$	3.14304	0.122066
$664$	12.4780	0.484239
$665$	−10.5006	−0.407195
$666$	−18.2842	−0.708498
$667$	−1.45246	−0.0562396
$668$	−54.5096	−2.10904
$669$	4.52533	0.174960
$670$	18.4013	0.710905
$671$	56.6598	2.18733
$672$	0.000916487 0	3.53543e−5 0
$673$	−41.5269	−1.60074	−0.800372	−	0.599503i	$-0.795365\pi$
$673$	−41.5269	−1.60074	−0.800372	+	0.599503i	$0.795365\pi$
$674$	28.7793	1.10854
$675$	0.678259	0.0261062
$676$	89.2416	3.43237
$677$	−26.8692	−1.03267	−0.516334	−	0.856387i	$-0.672704\pi$
$677$	−26.8692	−1.03267	−0.516334	+	0.856387i	$0.672704\pi$
$678$	0.388803	0.0149319
$679$	−28.3288	−1.08716
$680$	39.0219	1.49642
$681$	1.32079	0.0506127
$682$	−30.0791	−1.15179
$683$	14.9272	0.571174	0.285587	−	0.958353i	$-0.407811\pi$
$683$	14.9272	0.571174	0.285587	+	0.958353i	$0.407811\pi$
$684$	15.5571	0.594841
$685$	−26.9754	−1.03068
$686$	−22.3334	−0.852691
$687$	−0.384649	−0.0146753
$688$	−18.9040	−0.720708
$689$	65.1931	2.48366
$690$	−1.85872	−0.0707604
$691$	−32.8179	−1.24845	−0.624227	−	0.781243i	$-0.714586\pi$
$691$	−32.8179	−1.24845	−0.624227	+	0.781243i	$0.714586\pi$
$692$	70.1007	2.66483
$693$	48.8428	1.85538
$694$	−46.6183	−1.76961
$695$	−3.17606	−0.120475
$696$	−0.564749	−0.0214068
$697$	−29.7097	−1.12534
$698$	−62.3314	−2.35928
$699$	3.42898	0.129696
$700$	−9.60997	−0.363223
$701$	6.31768	0.238616	0.119308	−	0.992857i	$-0.461932\pi$
$701$	6.31768	0.238616	0.119308	+	0.992857i	$0.461932\pi$
$702$	13.8042	0.521005
$703$	3.28079	0.123737
$704$	−39.1090	−1.47398
$705$	4.16154	0.156733
$706$	43.7931	1.64817
$707$	−16.2896	−0.612633
$708$	0.319843	0.0120204
$709$	23.7312	0.891242	0.445621	−	0.895222i	$-0.352983\pi$
$709$	23.7312	0.891242	0.445621	+	0.895222i	$0.352983\pi$
$710$	5.85577	0.219763
$711$	8.29803	0.311201
$712$	−44.3499	−1.66208
$713$	5.02451	0.188169
$714$	−4.35242	−0.162885
$715$	69.4296	2.59652
$716$	52.1493	1.94891
$717$	−3.65673	−0.136563
$718$	−12.5710	−0.469145
$719$	−10.1117	−0.377102	−0.188551	−	0.982063i	$-0.560379\pi$
$719$	−10.1117	−0.377102	−0.188551	+	0.982063i	$0.560379\pi$
$720$	28.4393	1.05987
$721$	−43.1634	−1.60749
$722$	42.3524	1.57619
$723$	0.0343553	0.00127769
$724$	102.234	3.79949
$725$	−0.519453	−0.0192920
$726$	5.01015	0.185944
$727$	−39.7385	−1.47382	−0.736910	−	0.675991i	$-0.763716\pi$
$727$	−39.7385	−1.47382	−0.736910	+	0.675991i	$0.763716\pi$
$728$	−97.7885	−3.62428
$729$	−25.6490	−0.949961
$730$	−45.3745	−1.67938
$731$	−15.7522	−0.582615
$732$	−7.36044	−0.272050
$733$	10.2889	0.380028	0.190014	−	0.981781i	$-0.439147\pi$
$733$	10.2889	0.380028	0.190014	+	0.981781i	$0.439147\pi$
$734$	−55.0278	−2.03111
$735$	1.62639	0.0599902
$736$	0.00343691	0.000126686 0
$737$	15.3581	0.565723
$738$	−64.9672	−2.39148
$739$	−27.5261	−1.01256	−0.506282	−	0.862368i	$-0.668981\pi$
$739$	−27.5261	−1.01256	−0.506282	+	0.862368i	$0.668981\pi$
$740$	23.9941	0.882040
$741$	−1.23324	−0.0453042
$742$	−90.2782	−3.31422
$743$	−35.9403	−1.31852	−0.659261	−	0.751915i	$-0.729131\pi$
$743$	−35.9403	−1.31852	−0.659261	+	0.751915i	$0.729131\pi$
$744$	1.95364	0.0716239
$745$	22.0767	0.808828
$746$	−79.7519	−2.91992
$747$	7.57776	0.277256
$748$	65.1397	2.38174
$749$	44.8979	1.64053
$750$	3.98270	0.145428
$751$	8.96426	0.327110	0.163555	−	0.986534i	$-0.447704\pi$
$751$	8.96426	0.327110	0.163555	+	0.986534i	$0.447704\pi$
$752$	43.8555	1.59925
$753$	3.78548	0.137951
$754$	−10.5721	−0.385013
$755$	−28.3463	−1.03163
$756$	−12.7437	−0.463483
$757$	21.4206	0.778544	0.389272	−	0.921123i	$-0.372727\pi$
$757$	21.4206	0.778544	0.389272	+	0.921123i	$0.372727\pi$
$758$	−9.00416	−0.327046
$759$	−1.55133	−0.0563096
$760$	−15.3111	−0.555391
$761$	44.1348	1.59988	0.799942	−	0.600077i	$-0.204864\pi$
$761$	44.1348	1.59988	0.799942	+	0.600077i	$0.204864\pi$
$762$	−1.09604	−0.0397055
$763$	−50.6250	−1.83275
$764$	42.6236	1.54207
$765$	23.6977	0.856791
$766$	46.1982	1.66921
$767$	2.99360	0.108093
$768$	5.07915	0.183278
$769$	−46.0216	−1.65958	−0.829790	−	0.558075i	$-0.811540\pi$
$769$	−46.0216	−1.65958	−0.829790	+	0.558075i	$0.811540\pi$
$770$	−96.1448	−3.46482
$771$	−1.49102	−0.0536978
$772$	−8.97425	−0.322990
$773$	−30.2075	−1.08649	−0.543244	−	0.839575i	$-0.682804\pi$
$773$	−30.2075	−1.08649	−0.543244	+	0.839575i	$0.682804\pi$
$774$	−34.4457	−1.23813
$775$	1.79695	0.0645482
$776$	−41.3067	−1.48282
$777$	−1.33807	−0.0480029
$778$	87.0746	3.12178
$779$	11.6573	0.417664
$780$	−9.01931	−0.322943
$781$	4.88734	0.174883
$782$	−16.3220	−0.583672
$783$	−0.688840	−0.0246171
$784$	17.1394	0.612120
$785$	−57.8733	−2.06559
$786$	−0.579468	−0.0206689
$787$	−13.0282	−0.464406	−0.232203	−	0.972667i	$-0.574593\pi$
$787$	−13.0282	−0.464406	−0.232203	+	0.972667i	$0.574593\pi$
$788$	−24.5460	−0.874416
$789$	4.35834	0.155161
$790$	−16.3343	−0.581149
$791$	−3.35946	−0.119449
$792$	71.2184	2.53063
$793$	−68.8906	−2.44638
$794$	71.8815	2.55098
$795$	−4.16312	−0.147651
$796$	−18.8810	−0.669218
$797$	−21.6442	−0.766676	−0.383338	−	0.923608i	$-0.625226\pi$
$797$	−21.6442	−0.766676	−0.383338	+	0.923608i	$0.625226\pi$
$798$	1.70777	0.0604543
$799$	36.5436	1.29282
$800$	0.00122916	4.34574e−5 0
$801$	−26.9333	−0.951642
$802$	−86.0946	−3.04011
$803$	−37.8704	−1.33642
$804$	−1.99511	−0.0703620
$805$	16.0603	0.566053
$806$	36.5721	1.28820
$807$	−3.40326	−0.119801
$808$	−23.7521	−0.835596
$809$	9.06885	0.318844	0.159422	−	0.987211i	$-0.449037\pi$
$809$	9.06885	0.318844	0.159422	+	0.987211i	$0.449037\pi$
$810$	51.3778	1.80523
$811$	−28.6443	−1.00584	−0.502918	−	0.864334i	$-0.667740\pi$
$811$	−28.6443	−1.00584	−0.502918	+	0.864334i	$0.667740\pi$
$812$	9.75989	0.342505
$813$	2.86234	0.100387
$814$	30.0393	1.05288
$815$	−20.7335	−0.726263
$816$	−2.11514	−0.0740446
$817$	6.18070	0.216235
$818$	−15.8705	−0.554901
$819$	−59.3862	−2.07512
$820$	85.2555	2.97725
$821$	−25.2333	−0.880649	−0.440325	−	0.897839i	$-0.645137\pi$
$821$	−25.2333	−0.880649	−0.440325	+	0.897839i	$0.645137\pi$
$822$	4.38715	0.153019
$823$	48.2507	1.68191	0.840957	−	0.541102i	$-0.181993\pi$
$823$	48.2507	1.68191	0.840957	+	0.541102i	$0.181993\pi$
$824$	−62.9373	−2.19252
$825$	−0.554810	−0.0193160
$826$	−4.14548	−0.144240
$827$	−42.7910	−1.48799	−0.743995	−	0.668185i	$-0.767071\pi$
$827$	−42.7910	−1.48799	−0.743995	+	0.668185i	$0.767071\pi$
$828$	−23.7941	−0.826904
$829$	44.1594	1.53372	0.766860	−	0.641815i	$-0.221818\pi$
$829$	44.1594	1.53372	0.766860	+	0.641815i	$0.221818\pi$
$830$	−14.9165	−0.517759
$831$	−2.93653	−0.101867
$832$	47.5512	1.64854
$833$	14.2817	0.494833
$834$	0.516539	0.0178863
$835$	32.5797	1.12747
$836$	−25.5589	−0.883975
$837$	2.38291	0.0823653
$838$	20.5600	0.710234
$839$	−7.57475	−0.261509	−0.130755	−	0.991415i	$-0.541740\pi$
$839$	−7.57475	−0.261509	−0.130755	+	0.991415i	$0.541740\pi$
$840$	6.24461	0.215460
$841$	−28.4724	−0.981808
$842$	32.1941	1.10948
$843$	−0.0919625	−0.00316736
$844$	−75.1102	−2.58540
$845$	−53.3386	−1.83490
$846$	79.9110	2.74740
$847$	−43.2903	−1.48747
$848$	−43.8722	−1.50658
$849$	0.0559127	0.00191892
$850$	−5.83732	−0.200218
$851$	−5.01786	−0.172010
$852$	−0.634894	−0.0217511
$853$	−42.3800	−1.45106	−0.725532	−	0.688188i	$-0.758406\pi$
$853$	−42.3800	−1.45106	−0.725532	+	0.688188i	$0.758406\pi$
$854$	95.3984	3.26447
$855$	−9.29828	−0.317995
$856$	65.4663	2.23759
$857$	−20.2411	−0.691424	−0.345712	−	0.938341i	$-0.612363\pi$
$857$	−20.2411	−0.691424	−0.345712	+	0.938341i	$0.612363\pi$
$858$	−11.2917	−0.385492
$859$	−21.9697	−0.749596	−0.374798	−	0.927106i	$-0.622288\pi$
$859$	−21.9697	−0.749596	−0.374798	+	0.927106i	$0.622288\pi$
$860$	45.2026	1.54140
$861$	−4.75441	−0.162030
$862$	−6.51949	−0.222055
$863$	46.7906	1.59277	0.796386	−	0.604789i	$-0.206743\pi$
$863$	46.7906	1.59277	0.796386	+	0.604789i	$0.206743\pi$
$864$	0.00162997	5.54529e−5 0
$865$	−41.8983	−1.42458
$866$	29.0828	0.988274
$867$	0.935935	0.0317860
$868$	−33.7624	−1.14597
$869$	−13.6329	−0.462465
$870$	0.675116	0.0228886
$871$	−18.6734	−0.632723
$872$	−73.8170	−2.49976
$873$	−25.0852	−0.849006
$874$	6.40427	0.216628
$875$	−34.4126	−1.16336
$876$	4.91959	0.166217
$877$	−32.3763	−1.09327	−0.546635	−	0.837371i	$-0.684092\pi$
$877$	−32.3763	−1.09327	−0.546635	+	0.837371i	$0.684092\pi$
$878$	−44.9743	−1.51781
$879$	2.32576	0.0784458
$880$	−46.7232	−1.57504
$881$	25.6352	0.863672	0.431836	−	0.901952i	$-0.357866\pi$
$881$	25.6352	0.863672	0.431836	+	0.901952i	$0.357866\pi$
$882$	31.2303	1.05158
$883$	−4.61027	−0.155148	−0.0775740	−	0.996987i	$-0.524717\pi$
$883$	−4.61027	−0.155148	−0.0775740	+	0.996987i	$0.524717\pi$
$884$	−79.2010	−2.66382
$885$	−0.191166	−0.00642598
$886$	−29.2292	−0.981976
$887$	5.40850	0.181600	0.0907999	−	0.995869i	$-0.471058\pi$
$887$	5.40850	0.181600	0.0907999	+	0.995869i	$0.471058\pi$
$888$	−1.95106	−0.0654731
$889$	9.47039	0.317627
$890$	53.0170	1.77713
$891$	42.8809	1.43656
$892$	−114.033	−3.81811
$893$	−14.3387	−0.479825
$894$	−3.59045	−0.120083
$895$	−31.1690	−1.04186
$896$	−65.8365	−2.19944
$897$	1.88620	0.0629785
$898$	14.1853	0.473370
$899$	−1.82498	−0.0608664
$900$	−8.50964	−0.283655
$901$	−36.5575	−1.21791
$902$	106.735	3.55390
$903$	−2.52079	−0.0838868
$904$	−4.89848	−0.162921
$905$	−61.1039	−2.03116
$906$	4.61011	0.153161
$907$	24.2079	0.803811	0.401906	−	0.915681i	$-0.368348\pi$
$907$	24.2079	0.803811	0.401906	+	0.915681i	$0.368348\pi$
$908$	−33.2823	−1.10451
$909$	−14.4245	−0.478429
$910$	116.899	3.87516
$911$	−45.5069	−1.50771	−0.753855	−	0.657041i	$-0.771808\pi$
$911$	−45.5069	−1.50771	−0.753855	+	0.657041i	$0.771808\pi$
$912$	0.829919	0.0274814
$913$	−12.4496	−0.412021
$914$	39.9298	1.32076
$915$	4.39924	0.145434
$916$	9.69272	0.320256
$917$	5.00690	0.165342
$918$	−7.74079	−0.255484
$919$	−12.3261	−0.406602	−0.203301	−	0.979116i	$-0.565167\pi$
$919$	−12.3261	−0.406602	−0.203301	+	0.979116i	$0.565167\pi$
$920$	23.4178	0.772063
$921$	3.65291	0.120367
$922$	−54.2961	−1.78815
$923$	−5.94234	−0.195594
$924$	10.4242	0.342931
$925$	−1.79457	−0.0590051
$926$	3.48514	0.114529
$927$	−38.2213	−1.25535
$928$	−0.00124834	−4.09786e−5 0
$929$	−8.02838	−0.263402	−0.131701	−	0.991289i	$-0.542044\pi$
$929$	−8.02838	−0.263402	−0.131701	+	0.991289i	$0.542044\pi$
$930$	−2.33543	−0.0765818
$931$	−5.60374	−0.183655
$932$	−86.4064	−2.83034
$933$	−0.989090	−0.0323813
$934$	−43.5784	−1.42593
$935$	−38.9331	−1.27325
$936$	−86.5918	−2.83034
$937$	41.0656	1.34156	0.670778	−	0.741659i	$-0.265961\pi$
$937$	41.0656	1.34156	0.670778	+	0.741659i	$0.265961\pi$
$938$	25.8585	0.844311
$939$	0.218122	0.00711816
$940$	−104.866	−3.42035
$941$	−24.8124	−0.808862	−0.404431	−	0.914569i	$-0.632530\pi$
$941$	−24.8124	−0.808862	−0.404431	+	0.914569i	$0.632530\pi$
$942$	9.41224	0.306667
$943$	−17.8294	−0.580606
$944$	−2.01457	−0.0655686
$945$	7.61672	0.247772
$946$	56.5913	1.83994
$947$	−40.7508	−1.32422	−0.662111	−	0.749406i	$-0.730339\pi$
$947$	−40.7508	−1.32422	−0.662111	+	0.749406i	$0.730339\pi$
$948$	1.77100	0.0575193
$949$	46.0452	1.49469
$950$	2.29040	0.0743103
$951$	4.76673	0.154572
$952$	54.8356	1.77723
$953$	−20.1204	−0.651764	−0.325882	−	0.945410i	$-0.605661\pi$
$953$	−20.1204	−0.651764	−0.325882	+	0.945410i	$0.605661\pi$
$954$	−79.9414	−2.58820
$955$	−25.4756	−0.824370
$956$	92.1454	2.98020
$957$	0.563465	0.0182142
$958$	−55.8907	−1.80575
$959$	−37.9072	−1.22409
$960$	−3.03654	−0.0980040
$961$	−24.6869	−0.796350
$962$	−36.5237	−1.17757
$963$	39.7571	1.28116
$964$	−0.865713	−0.0278827
$965$	5.36379	0.172667
$966$	−2.61198	−0.0840390
$967$	−10.0777	−0.324078	−0.162039	−	0.986784i	$-0.551807\pi$
$967$	−10.0777	−0.324078	−0.162039	+	0.986784i	$0.551807\pi$
$968$	−63.1222	−2.02882
$969$	0.691548	0.0222157
$970$	49.3791	1.58547
$971$	−45.3701	−1.45600	−0.727998	−	0.685579i	$-0.759549\pi$
$971$	−45.3701	−1.45600	−0.727998	+	0.685579i	$0.759549\pi$
$972$	−16.9506	−0.543690
$973$	−4.46317	−0.143083
$974$	−10.5139	−0.336889
$975$	0.674574	0.0216036
$976$	46.3605	1.48396
$977$	2.24138	0.0717081	0.0358540	−	0.999357i	$-0.488585\pi$
$977$	2.24138	0.0717081	0.0358540	+	0.999357i	$0.488585\pi$
$978$	3.37200	0.107825
$979$	44.2490	1.41421
$980$	−40.9831	−1.30916
$981$	−44.8285	−1.43126
$982$	−96.6859	−3.08537
$983$	−6.32560	−0.201755	−0.100878	−	0.994899i	$-0.532165\pi$
$983$	−6.32560	−0.201755	−0.100878	+	0.994899i	$0.532165\pi$
$984$	−6.93247	−0.220999
$985$	14.6708	0.467452
$986$	5.92838	0.188798
$987$	5.84801	0.186144
$988$	31.0762	0.988666
$989$	−9.45319	−0.300594
$990$	−85.1363	−2.70581
$991$	18.7185	0.594614	0.297307	−	0.954782i	$-0.403911\pi$
$991$	18.7185	0.594614	0.297307	+	0.954782i	$0.403911\pi$
$992$	0.00431837	0.000137108 0
$993$	−1.27236	−0.0403770
$994$	8.22884	0.261003
$995$	11.2849	0.357756
$996$	1.61727	0.0512453
$997$	5.38757	0.170626	0.0853130	−	0.996354i	$-0.472811\pi$
$997$	5.38757	0.170626	0.0853130	+	0.996354i	$0.472811\pi$
$998$	−62.4576	−1.97706
$999$	−2.37975	−0.0752921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.18	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.18	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44945 q^{2} -0.158730 q^{3} +3.99982 q^{4} -2.39064 q^{5} +0.388803 q^{6} -3.35946 q^{7} -4.89848 q^{8} -2.97480 q^{9} +O(q^{10})\)	\(q-2.44945 q^{2} -0.158730 q^{3} +3.99982 q^{4} -2.39064 q^{5} +0.388803 q^{6} -3.35946 q^{7} -4.89848 q^{8} -2.97480 q^{9} +5.85577 q^{10} +4.88734 q^{11} -0.634894 q^{12} -5.94234 q^{13} +8.22884 q^{14} +0.379468 q^{15} +3.99895 q^{16} +3.33221 q^{17} +7.28665 q^{18} -1.30746 q^{19} -9.56215 q^{20} +0.533248 q^{21} -11.9713 q^{22} +1.99973 q^{23} +0.777538 q^{24} +0.715174 q^{25} +14.5555 q^{26} +0.948383 q^{27} -13.4372 q^{28} -0.726331 q^{29} -0.929489 q^{30} +2.51260 q^{31} +0.00171869 q^{32} -0.775769 q^{33} -8.16209 q^{34} +8.03127 q^{35} -11.8987 q^{36} -2.50928 q^{37} +3.20257 q^{38} +0.943230 q^{39} +11.7105 q^{40} -8.91593 q^{41} -1.30617 q^{42} -4.72724 q^{43} +19.5485 q^{44} +7.11170 q^{45} -4.89824 q^{46} +10.9668 q^{47} -0.634755 q^{48} +4.28597 q^{49} -1.75179 q^{50} -0.528923 q^{51} -23.7683 q^{52} -10.9709 q^{53} -2.32302 q^{54} -11.6839 q^{55} +16.4562 q^{56} +0.207534 q^{57} +1.77911 q^{58} -0.503774 q^{59} +1.51780 q^{60} +11.5932 q^{61} -6.15449 q^{62} +9.99373 q^{63} -8.00210 q^{64} +14.2060 q^{65} +1.90021 q^{66} +3.14243 q^{67} +13.3283 q^{68} -0.317417 q^{69} -19.6722 q^{70} +1.00000 q^{71} +14.5720 q^{72} -7.74868 q^{73} +6.14635 q^{74} -0.113520 q^{75} -5.22962 q^{76} -16.4188 q^{77} -2.31040 q^{78} -2.78944 q^{79} -9.56006 q^{80} +8.77388 q^{81} +21.8392 q^{82} -2.54731 q^{83} +2.13290 q^{84} -7.96612 q^{85} +11.5792 q^{86} +0.115291 q^{87} -23.9405 q^{88} +9.05381 q^{89} -17.4198 q^{90} +19.9630 q^{91} +7.99856 q^{92} -0.398826 q^{93} -26.8626 q^{94} +3.12568 q^{95} -0.000272808 q^{96} +8.43256 q^{97} -10.4983 q^{98} -14.5389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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