LMFDB - Embedded newform 8023.2.a.d.1.33

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:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
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)

$f(q)$	$=$	$q-1.73632 q^{2} -3.22124 q^{3} +1.01482 q^{4} +2.56295 q^{5} +5.59311 q^{6} -4.40181 q^{7} +1.71059 q^{8} +7.37636 q^{9} +O(q^{10})$	\(q-1.73632 q^{2} -3.22124 q^{3} +1.01482 q^{4} +2.56295 q^{5} +5.59311 q^{6} -4.40181 q^{7} +1.71059 q^{8} +7.37636 q^{9} -4.45011 q^{10} +2.64872 q^{11} -3.26898 q^{12} +1.93717 q^{13} +7.64296 q^{14} -8.25586 q^{15} -4.99978 q^{16} +0.593698 q^{17} -12.8077 q^{18} -4.61459 q^{19} +2.60094 q^{20} +14.1793 q^{21} -4.59904 q^{22} +3.60105 q^{23} -5.51020 q^{24} +1.56871 q^{25} -3.36356 q^{26} -14.0973 q^{27} -4.46705 q^{28} -4.60963 q^{29} +14.3349 q^{30} -7.94895 q^{31} +5.26007 q^{32} -8.53215 q^{33} -1.03085 q^{34} -11.2816 q^{35} +7.48570 q^{36} -0.330732 q^{37} +8.01242 q^{38} -6.24009 q^{39} +4.38415 q^{40} +4.37547 q^{41} -24.6198 q^{42} +10.5211 q^{43} +2.68798 q^{44} +18.9052 q^{45} -6.25259 q^{46} -2.79019 q^{47} +16.1055 q^{48} +12.3759 q^{49} -2.72379 q^{50} -1.91244 q^{51} +1.96589 q^{52} -0.0874795 q^{53} +24.4774 q^{54} +6.78854 q^{55} -7.52967 q^{56} +14.8647 q^{57} +8.00381 q^{58} -3.73616 q^{59} -8.37824 q^{60} -2.97089 q^{61} +13.8020 q^{62} -32.4693 q^{63} +0.866376 q^{64} +4.96488 q^{65} +14.8146 q^{66} -0.652341 q^{67} +0.602498 q^{68} -11.5998 q^{69} +19.5885 q^{70} +1.00000 q^{71} +12.6179 q^{72} +6.40499 q^{73} +0.574259 q^{74} -5.05318 q^{75} -4.68299 q^{76} -11.6592 q^{77} +10.8348 q^{78} -4.73781 q^{79} -12.8142 q^{80} +23.2816 q^{81} -7.59724 q^{82} +10.8199 q^{83} +14.3894 q^{84} +1.52162 q^{85} -18.2680 q^{86} +14.8487 q^{87} +4.53087 q^{88} +7.01445 q^{89} -32.8256 q^{90} -8.52706 q^{91} +3.65442 q^{92} +25.6054 q^{93} +4.84467 q^{94} -11.8270 q^{95} -16.9439 q^{96} +9.24563 q^{97} -21.4886 q^{98} +19.5379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−1.73632	−1.22777	−0.613883	−	0.789397i	$-0.710394\pi$
$2$	−1.73632	−1.22777	−0.613883	+	0.789397i	$0.710394\pi$
$3$	−3.22124	−1.85978	−0.929890	−	0.367836i	$-0.880099\pi$
$3$	−3.22124	−1.85978	−0.929890	+	0.367836i	$0.880099\pi$
$4$	1.01482	0.507412
$5$	2.56295	1.14619	0.573093	−	0.819490i	$-0.305743\pi$
$5$	2.56295	1.14619	0.573093	+	0.819490i	$0.305743\pi$
$6$	5.59311	2.28338
$7$	−4.40181	−1.66373	−0.831863	−	0.554981i	$-0.812726\pi$
$7$	−4.40181	−1.66373	−0.831863	+	0.554981i	$0.812726\pi$
$8$	1.71059	0.604784
$9$	7.37636	2.45879
$10$	−4.45011	−1.40725
$11$	2.64872	0.798619	0.399310	−	0.916816i	$-0.369250\pi$
$11$	2.64872	0.798619	0.399310	+	0.916816i	$0.369250\pi$
$12$	−3.26898	−0.943674
$13$	1.93717	0.537275	0.268638	−	0.963241i	$-0.413427\pi$
$13$	1.93717	0.537275	0.268638	+	0.963241i	$0.413427\pi$
$14$	7.64296	2.04267
$15$	−8.25586	−2.13165
$16$	−4.99978	−1.24995
$17$	0.593698	0.143993	0.0719964	−	0.997405i	$-0.477063\pi$
$17$	0.593698	0.143993	0.0719964	+	0.997405i	$0.477063\pi$
$18$	−12.8077	−3.01882
$19$	−4.61459	−1.05866	−0.529330	−	0.848416i	$-0.677556\pi$
$19$	−4.61459	−1.05866	−0.529330	+	0.848416i	$0.677556\pi$
$20$	2.60094	0.581588
$21$	14.1793	3.09417
$22$	−4.59904	−0.980518
$23$	3.60105	0.750870	0.375435	−	0.926849i	$-0.377493\pi$
$23$	3.60105	0.750870	0.375435	+	0.926849i	$0.377493\pi$
$24$	−5.51020	−1.12477
$25$	1.56871	0.313742
$26$	−3.36356	−0.659649
$27$	−14.0973	−2.71302
$28$	−4.46705	−0.844194
$29$	−4.60963	−0.855986	−0.427993	−	0.903782i	$-0.640779\pi$
$29$	−4.60963	−0.855986	−0.427993	+	0.903782i	$0.640779\pi$
$30$	14.3349	2.61717
$31$	−7.94895	−1.42767	−0.713837	−	0.700312i	$-0.753044\pi$
$31$	−7.94895	−1.42767	−0.713837	+	0.700312i	$0.753044\pi$
$32$	5.26007	0.929857
$33$	−8.53215	−1.48526
$34$	−1.03085	−0.176790
$35$	−11.2816	−1.90694
$36$	7.48570	1.24762
$37$	−0.330732	−0.0543721	−0.0271860	−	0.999630i	$-0.508655\pi$
$37$	−0.330732	−0.0543721	−0.0271860	+	0.999630i	$0.508655\pi$
$38$	8.01242	1.29979
$39$	−6.24009	−0.999214
$40$	4.38415	0.693195
$41$	4.37547	0.683334	0.341667	−	0.939821i	$-0.389009\pi$
$41$	4.37547	0.683334	0.341667	+	0.939821i	$0.389009\pi$
$42$	−24.6198	−3.79892
$43$	10.5211	1.60445	0.802224	−	0.597023i	$-0.203650\pi$
$43$	10.5211	1.60445	0.802224	+	0.597023i	$0.203650\pi$
$44$	2.68798	0.405229
$45$	18.9052	2.81822
$46$	−6.25259	−0.921893
$47$	−2.79019	−0.406990	−0.203495	−	0.979076i	$-0.565230\pi$
$47$	−2.79019	−0.406990	−0.203495	+	0.979076i	$0.565230\pi$
$48$	16.1055	2.32462
$49$	12.3759	1.76799
$50$	−2.72379	−0.385202
$51$	−1.91244	−0.267795
$52$	1.96589	0.272620
$53$	−0.0874795	−0.0120162	−0.00600812	−	0.999982i	$-0.501912\pi$
$53$	−0.0874795	−0.0120162	−0.00600812	+	0.999982i	$0.501912\pi$
$54$	24.4774	3.33096
$55$	6.78854	0.915366
$56$	−7.52967	−1.00619
$57$	14.8647	1.96887
$58$	8.00381	1.05095
$59$	−3.73616	−0.486407	−0.243204	−	0.969975i	$-0.578198\pi$
$59$	−3.73616	−0.486407	−0.243204	+	0.969975i	$0.578198\pi$
$60$	−8.37824	−1.08163
$61$	−2.97089	−0.380383	−0.190191	−	0.981747i	$-0.560911\pi$
$61$	−2.97089	−0.380383	−0.190191	+	0.981747i	$0.560911\pi$
$62$	13.8020	1.75285
$63$	−32.4693	−4.09075
$64$	0.866376	0.108297
$65$	4.96488	0.615817
$66$	14.8146	1.82355
$67$	−0.652341	−0.0796961	−0.0398480	−	0.999206i	$-0.512687\pi$
$67$	−0.652341	−0.0796961	−0.0398480	+	0.999206i	$0.512687\pi$
$68$	0.602498	0.0730636
$69$	−11.5998	−1.39645
$70$	19.5885	2.34128
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	12.6179	1.48703
$73$	6.40499	0.749648	0.374824	−	0.927096i	$-0.377703\pi$
$73$	6.40499	0.749648	0.374824	+	0.927096i	$0.377703\pi$
$74$	0.574259	0.0667562
$75$	−5.05318	−0.583491
$76$	−4.68299	−0.537176
$77$	−11.6592	−1.32868
$78$	10.8348	1.22680
$79$	−4.73781	−0.533045	−0.266522	−	0.963829i	$-0.585875\pi$
$79$	−4.73781	−0.533045	−0.266522	+	0.963829i	$0.585875\pi$
$80$	−12.8142	−1.43267
$81$	23.2816	2.58684
$82$	−7.59724	−0.838974
$83$	10.8199	1.18764	0.593820	−	0.804598i	$-0.297619\pi$
$83$	10.8199	1.18764	0.593820	+	0.804598i	$0.297619\pi$
$84$	14.3894	1.57002
$85$	1.52162	0.165043
$86$	−18.2680	−1.96989
$87$	14.8487	1.59195
$88$	4.53087	0.482992
$89$	7.01445	0.743530	0.371765	−	0.928327i	$-0.378753\pi$
$89$	7.01445	0.743530	0.371765	+	0.928327i	$0.378753\pi$
$90$	−32.8256	−3.46012
$91$	−8.52706	−0.893879
$92$	3.65442	0.381000
$93$	25.6054	2.65516
$94$	4.84467	0.499689
$95$	−11.8270	−1.21342
$96$	−16.9439	−1.72933
$97$	9.24563	0.938751	0.469376	−	0.882999i	$-0.344479\pi$
$97$	9.24563	0.938751	0.469376	+	0.882999i	$0.344479\pi$
$98$	−21.4886	−2.17067
$99$	19.5379	1.96363
$100$	1.59196	0.159196
$101$	−11.4260	−1.13693	−0.568466	−	0.822707i	$-0.692463\pi$
$101$	−11.4260	−1.13693	−0.568466	+	0.822707i	$0.692463\pi$
$102$	3.32062	0.328790
$103$	14.3095	1.40995	0.704977	−	0.709230i	$-0.250957\pi$
$103$	14.3095	1.40995	0.704977	+	0.709230i	$0.250957\pi$
$104$	3.31370	0.324935
$105$	36.3407	3.54649
$106$	0.151893	0.0147531
$107$	−14.8188	−1.43259	−0.716295	−	0.697798i	$-0.754163\pi$
$107$	−14.8188	−1.43259	−0.716295	+	0.697798i	$0.754163\pi$
$108$	−14.3062	−1.37662
$109$	−1.89454	−0.181464	−0.0907320	−	0.995875i	$-0.528921\pi$
$109$	−1.89454	−0.181464	−0.0907320	+	0.995875i	$0.528921\pi$
$110$	−11.7871	−1.12386
$111$	1.06537	0.101120
$112$	22.0081	2.07957
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−25.8099	−2.41732
$115$	9.22930	0.860637
$116$	−4.67796	−0.434337
$117$	14.2893	1.32104
$118$	6.48719	0.597195
$119$	−2.61334	−0.239565
$120$	−14.1224	−1.28919
$121$	−3.98428	−0.362207
$122$	5.15842	0.467022
$123$	−14.0944	−1.27085
$124$	−8.06678	−0.724418
$125$	−8.79423	−0.786579
$126$	56.3772	5.02248
$127$	3.16221	0.280601	0.140301	−	0.990109i	$-0.455193\pi$
$127$	3.16221	0.280601	0.140301	+	0.990109i	$0.455193\pi$
$128$	−12.0244	−1.06282
$129$	−33.8909	−2.98392
$130$	−8.62064	−0.756080
$131$	−0.0694870	−0.00607111	−0.00303556	−	0.999995i	$-0.500966\pi$
$131$	−0.0694870	−0.00607111	−0.00303556	+	0.999995i	$0.500966\pi$
$132$	−8.65862	−0.753637
$133$	20.3125	1.76132
$134$	1.13267	0.0978482
$135$	−36.1306	−3.10963
$136$	1.01557	0.0870846
$137$	14.5204	1.24056	0.620280	−	0.784380i	$-0.287019\pi$
$137$	14.5204	1.24056	0.620280	+	0.784380i	$0.287019\pi$
$138$	20.1410	1.71452
$139$	−13.0893	−1.11022	−0.555109	−	0.831778i	$-0.687323\pi$
$139$	−13.0893	−1.11022	−0.555109	+	0.831778i	$0.687323\pi$
$140$	−11.4488	−0.967603
$141$	8.98784	0.756913
$142$	−1.73632	−0.145709
$143$	5.13103	0.429078
$144$	−36.8802	−3.07335
$145$	−11.8142	−0.981119
$146$	−11.1211	−0.920393
$147$	−39.8657	−3.28807
$148$	−0.335635	−0.0275890
$149$	6.27240	0.513855	0.256927	−	0.966431i	$-0.417290\pi$
$149$	6.27240	0.513855	0.256927	+	0.966431i	$0.417290\pi$
$150$	8.77396	0.716391
$151$	13.6644	1.11199	0.555996	−	0.831185i	$-0.312337\pi$
$151$	13.6644	1.11199	0.555996	+	0.831185i	$0.312337\pi$
$152$	−7.89365	−0.640260
$153$	4.37933	0.354048
$154$	20.2441	1.63131
$155$	−20.3728	−1.63638
$156$	−6.33259	−0.507013
$157$	11.3753	0.907847	0.453923	−	0.891041i	$-0.350024\pi$
$157$	11.3753	0.907847	0.453923	+	0.891041i	$0.350024\pi$
$158$	8.22637	0.654455
$159$	0.281792	0.0223476
$160$	13.4813	1.06579
$161$	−15.8511	−1.24924
$162$	−40.4243	−3.17604
$163$	−14.6217	−1.14526	−0.572630	−	0.819814i	$-0.694077\pi$
$163$	−14.6217	−1.14526	−0.572630	+	0.819814i	$0.694077\pi$
$164$	4.44033	0.346731
$165$	−21.8675	−1.70238
$166$	−18.7869	−1.45814
$167$	−1.41058	−0.109154	−0.0545769	−	0.998510i	$-0.517381\pi$
$167$	−1.41058	−0.109154	−0.0545769	+	0.998510i	$0.517381\pi$
$168$	24.2548	1.87130
$169$	−9.24736	−0.711335
$170$	−2.64202	−0.202634
$171$	−34.0388	−2.60302
$172$	10.6770	0.814116
$173$	9.02743	0.686343	0.343171	−	0.939273i	$-0.388499\pi$
$173$	9.02743	0.686343	0.343171	+	0.939273i	$0.388499\pi$
$174$	−25.7822	−1.95454
$175$	−6.90515	−0.521980
$176$	−13.2430	−0.998230
$177$	12.0351	0.904611
$178$	−12.1794	−0.912882
$179$	14.1428	1.05708	0.528541	−	0.848908i	$-0.322739\pi$
$179$	14.1428	1.05708	0.528541	+	0.848908i	$0.322739\pi$
$180$	19.1855	1.43000
$181$	7.69648	0.572075	0.286037	−	0.958218i	$-0.407662\pi$
$181$	7.69648	0.572075	0.286037	+	0.958218i	$0.407662\pi$
$182$	14.8057	1.09747
$183$	9.56992	0.707429
$184$	6.15990	0.454114
$185$	−0.847650	−0.0623205
$186$	−44.4594	−3.25992
$187$	1.57254	0.114995
$188$	−2.83154	−0.206512
$189$	62.0535	4.51373
$190$	20.5354	1.48980
$191$	−12.6620	−0.916191	−0.458096	−	0.888903i	$-0.651468\pi$
$191$	−12.6620	−0.916191	−0.458096	+	0.888903i	$0.651468\pi$
$192$	−2.79080	−0.201409
$193$	6.96385	0.501269	0.250634	−	0.968082i	$-0.419361\pi$
$193$	6.96385	0.501269	0.250634	+	0.968082i	$0.419361\pi$
$194$	−16.0534	−1.15257
$195$	−15.9930	−1.14528
$196$	12.5593	0.897096
$197$	−20.5561	−1.46456	−0.732280	−	0.681004i	$-0.761544\pi$
$197$	−20.5561	−1.46456	−0.732280	+	0.681004i	$0.761544\pi$
$198$	−33.9241	−2.41088
$199$	−4.98255	−0.353203	−0.176602	−	0.984282i	$-0.556510\pi$
$199$	−4.98255	−0.353203	−0.176602	+	0.984282i	$0.556510\pi$
$200$	2.68341	0.189746
$201$	2.10134	0.148217
$202$	19.8393	1.39589
$203$	20.2907	1.42413
$204$	−1.94079	−0.135882
$205$	11.2141	0.783227
$206$	−24.8459	−1.73110
$207$	26.5626	1.84623
$208$	−9.68544	−0.671564
$209$	−12.2228	−0.845466
$210$	−63.0993	−4.35426
$211$	11.9233	0.820833	0.410416	−	0.911898i	$-0.365383\pi$
$211$	11.9233	0.820833	0.410416	+	0.911898i	$0.365383\pi$
$212$	−0.0887762	−0.00609717
$213$	−3.22124	−0.220715
$214$	25.7303	1.75889
$215$	26.9650	1.83900
$216$	−24.1146	−1.64079
$217$	34.9898	2.37526
$218$	3.28954	0.222796
$219$	−20.6320	−1.39418
$220$	6.88916	0.464467
$221$	1.15010	0.0773638
$222$	−1.84982	−0.124152
$223$	9.28592	0.621831	0.310916	−	0.950437i	$-0.399364\pi$
$223$	9.28592	0.621831	0.310916	+	0.950437i	$0.399364\pi$
$224$	−23.1538	−1.54703
$225$	11.5714	0.771424
$226$	1.73632	0.115499
$227$	−12.1785	−0.808314	−0.404157	−	0.914690i	$-0.632435\pi$
$227$	−12.1785	−0.808314	−0.404157	+	0.914690i	$0.632435\pi$
$228$	15.0850	0.999029
$229$	−9.53180	−0.629879	−0.314939	−	0.949112i	$-0.601984\pi$
$229$	−9.53180	−0.629879	−0.314939	+	0.949112i	$0.601984\pi$
$230$	−16.0251	−1.05666
$231$	37.5569	2.47106
$232$	−7.88517	−0.517687
$233$	−7.82486	−0.512624	−0.256312	−	0.966594i	$-0.582507\pi$
$233$	−7.82486	−0.512624	−0.256312	+	0.966594i	$0.582507\pi$
$234$	−24.8108	−1.62193
$235$	−7.15110	−0.466487
$236$	−3.79155	−0.246809
$237$	15.2616	0.991347
$238$	4.53761	0.294130
$239$	−8.00153	−0.517576	−0.258788	−	0.965934i	$-0.583323\pi$
$239$	−8.00153	−0.517576	−0.258788	+	0.965934i	$0.583323\pi$
$240$	41.2775	2.66445
$241$	−3.26830	−0.210530	−0.105265	−	0.994444i	$-0.533569\pi$
$241$	−3.26830	−0.210530	−0.105265	+	0.994444i	$0.533569\pi$
$242$	6.91800	0.444706
$243$	−32.7036	−2.09793
$244$	−3.01492	−0.193011
$245$	31.7188	2.02644
$246$	24.4725	1.56031
$247$	−8.93926	−0.568791
$248$	−13.5974	−0.863434
$249$	−34.8535	−2.20875
$250$	15.2696	0.965736
$251$	−5.14227	−0.324577	−0.162289	−	0.986743i	$-0.551888\pi$
$251$	−5.14227	−0.324577	−0.162289	+	0.986743i	$0.551888\pi$
$252$	−32.9506	−2.07569
$253$	9.53817	0.599659
$254$	−5.49063	−0.344513
$255$	−4.90149	−0.306943
$256$	19.1456	1.19660
$257$	16.6051	1.03580	0.517899	−	0.855442i	$-0.326714\pi$
$257$	16.6051	1.03580	0.517899	+	0.855442i	$0.326714\pi$
$258$	58.8455	3.66356
$259$	1.45582	0.0904603
$260$	5.03847	0.312473
$261$	−34.0023	−2.10469
$262$	0.120652	0.00745391
$263$	−21.1214	−1.30240	−0.651201	−	0.758905i	$-0.725735\pi$
$263$	−21.1214	−1.30240	−0.651201	+	0.758905i	$0.725735\pi$
$264$	−14.5950	−0.898259
$265$	−0.224205	−0.0137728
$266$	−35.2691	−2.16249
$267$	−22.5952	−1.38280
$268$	−0.662010	−0.0404387
$269$	−16.9655	−1.03441	−0.517203	−	0.855863i	$-0.673027\pi$
$269$	−16.9655	−1.03441	−0.517203	+	0.855863i	$0.673027\pi$
$270$	62.7344	3.81790
$271$	−19.1959	−1.16607	−0.583035	−	0.812447i	$-0.698135\pi$
$271$	−19.1959	−1.16607	−0.583035	+	0.812447i	$0.698135\pi$
$272$	−2.96836	−0.179983
$273$	27.4677	1.66242
$274$	−25.2121	−1.52312
$275$	4.15507	0.250560
$276$	−11.7718	−0.708577
$277$	0.164845	0.00990458	0.00495229	−	0.999988i	$-0.498424\pi$
$277$	0.164845	0.00990458	0.00495229	+	0.999988i	$0.498424\pi$
$278$	22.7272	1.36309
$279$	−58.6343	−3.51034
$280$	−19.2982	−1.15329
$281$	18.9887	1.13277	0.566386	−	0.824140i	$-0.308341\pi$
$281$	18.9887	1.13277	0.566386	+	0.824140i	$0.308341\pi$
$282$	−15.6058	−0.929313
$283$	20.7761	1.23501	0.617505	−	0.786567i	$-0.288143\pi$
$283$	20.7761	1.23501	0.617505	+	0.786567i	$0.288143\pi$
$284$	1.01482	0.0602187
$285$	38.0974	2.25670
$286$	−8.90913	−0.526808
$287$	−19.2600	−1.13688
$288$	38.8001	2.28632
$289$	−16.6475	−0.979266
$290$	20.5134	1.20459
$291$	−29.7823	−1.74587
$292$	6.49994	0.380380
$293$	16.7032	0.975810	0.487905	−	0.872897i	$-0.337761\pi$
$293$	16.7032	0.975810	0.487905	+	0.872897i	$0.337761\pi$
$294$	69.2198	4.03698
$295$	−9.57560	−0.557513
$296$	−0.565747	−0.0328834
$297$	−37.3397	−2.16667
$298$	−10.8909	−0.630894
$299$	6.97585	0.403424
$300$	−5.12808	−0.296070
$301$	−46.3117	−2.66936
$302$	−23.7258	−1.36527
$303$	36.8059	2.11444
$304$	23.0719	1.32327
$305$	−7.61423	−0.435990
$306$	−7.60393	−0.434688
$307$	25.6506	1.46395	0.731977	−	0.681329i	$-0.238598\pi$
$307$	25.6506	1.46395	0.731977	+	0.681329i	$0.238598\pi$
$308$	−11.8320	−0.674190
$309$	−46.0942	−2.62221
$310$	35.3737	2.00909
$311$	−9.65551	−0.547514	−0.273757	−	0.961799i	$-0.588266\pi$
$311$	−9.65551	−0.547514	−0.273757	+	0.961799i	$0.588266\pi$
$312$	−10.6742	−0.604309
$313$	4.16923	0.235659	0.117829	−	0.993034i	$-0.462406\pi$
$313$	4.16923	0.235659	0.117829	+	0.993034i	$0.462406\pi$
$314$	−19.7512	−1.11462
$315$	−83.2171	−4.68875
$316$	−4.80804	−0.270473
$317$	−21.4965	−1.20736	−0.603682	−	0.797225i	$-0.706301\pi$
$317$	−21.4965	−1.20736	−0.603682	+	0.797225i	$0.706301\pi$
$318$	−0.489282	−0.0274376
$319$	−12.2096	−0.683607
$320$	2.22048	0.124128
$321$	47.7349	2.66430
$322$	27.5227	1.53378
$323$	−2.73967	−0.152439
$324$	23.6267	1.31259
$325$	3.03886	0.168566
$326$	25.3880	1.40611
$327$	6.10276	0.337483
$328$	7.48462	0.413269
$329$	12.2819	0.677121
$330$	37.9690	2.09013
$331$	9.37726	0.515421	0.257710	−	0.966222i	$-0.417032\pi$
$331$	9.37726	0.515421	0.257710	+	0.966222i	$0.417032\pi$
$332$	10.9803	0.602622
$333$	−2.43960	−0.133689
$334$	2.44922	0.134015
$335$	−1.67192	−0.0913465
$336$	−70.8932	−3.86754
$337$	−10.0184	−0.545739	−0.272870	−	0.962051i	$-0.587973\pi$
$337$	−10.0184	−0.545739	−0.272870	+	0.962051i	$0.587973\pi$
$338$	16.0564	0.873354
$339$	3.22124	0.174953
$340$	1.54417	0.0837445
$341$	−21.0546	−1.14017
$342$	59.1025	3.19590
$343$	−23.6637	−1.27772
$344$	17.9972	0.970345
$345$	−29.7297	−1.60060
$346$	−15.6745	−0.842669
$347$	−33.2567	−1.78532	−0.892658	−	0.450735i	$-0.851162\pi$
$347$	−33.2567	−1.78532	−0.892658	+	0.450735i	$0.851162\pi$
$348$	15.0688	0.807772
$349$	−1.29124	−0.0691183	−0.0345591	−	0.999403i	$-0.511003\pi$
$349$	−1.29124	−0.0691183	−0.0345591	+	0.999403i	$0.511003\pi$
$350$	11.9896	0.640870
$351$	−27.3089	−1.45764
$352$	13.9324	0.742602
$353$	−7.47354	−0.397776	−0.198888	−	0.980022i	$-0.563733\pi$
$353$	−7.47354	−0.397776	−0.198888	+	0.980022i	$0.563733\pi$
$354$	−20.8968	−1.11065
$355$	2.56295	0.136027
$356$	7.11843	0.377276
$357$	8.41819	0.445538
$358$	−24.5565	−1.29785
$359$	−19.0211	−1.00390	−0.501949	−	0.864897i	$-0.667383\pi$
$359$	−19.0211	−1.00390	−0.501949	+	0.864897i	$0.667383\pi$
$360$	32.3390	1.70442
$361$	2.29443	0.120759
$362$	−13.3636	−0.702374
$363$	12.8343	0.673626
$364$	−8.65346	−0.453564
$365$	16.4157	0.859236
$366$	−16.6165	−0.868558
$367$	−14.2350	−0.743062	−0.371531	−	0.928420i	$-0.621167\pi$
$367$	−14.2350	−0.743062	−0.371531	+	0.928420i	$0.621167\pi$
$368$	−18.0044	−0.938546
$369$	32.2750	1.68017
$370$	1.47180	0.0765150
$371$	0.385068	0.0199917
$372$	25.9850	1.34726
$373$	11.7284	0.607273	0.303637	−	0.952788i	$-0.401799\pi$
$373$	11.7284	0.607273	0.303637	+	0.952788i	$0.401799\pi$
$374$	−2.73044	−0.141188
$375$	28.3283	1.46287
$376$	−4.77285	−0.246141
$377$	−8.92965	−0.459900
$378$	−107.745	−5.54180
$379$	−3.48896	−0.179216	−0.0896080	−	0.995977i	$-0.528561\pi$
$379$	−3.48896	−0.179216	−0.0896080	+	0.995977i	$0.528561\pi$
$380$	−12.0023	−0.615703
$381$	−10.1862	−0.521857
$382$	21.9854	1.12487
$383$	−27.3972	−1.39993	−0.699966	−	0.714176i	$-0.746801\pi$
$383$	−27.3972	−1.39993	−0.699966	+	0.714176i	$0.746801\pi$
$384$	38.7336	1.97661
$385$	−29.8818	−1.52292
$386$	−12.0915	−0.615441
$387$	77.6072	3.94500
$388$	9.38268	0.476333
$389$	32.5246	1.64906	0.824532	−	0.565815i	$-0.191438\pi$
$389$	32.5246	1.64906	0.824532	+	0.565815i	$0.191438\pi$
$390$	27.7691	1.40614
$391$	2.13793	0.108120
$392$	21.1701	1.06925
$393$	0.223834	0.0112909
$394$	35.6920	1.79814
$395$	−12.1428	−0.610969
$396$	19.8275	0.996370
$397$	−19.9633	−1.00193	−0.500964	−	0.865468i	$-0.667021\pi$
$397$	−19.9633	−1.00193	−0.500964	+	0.865468i	$0.667021\pi$
$398$	8.65132	0.433651
$399$	−65.4314	−3.27567
$400$	−7.84320	−0.392160
$401$	−33.9389	−1.69483	−0.847413	−	0.530934i	$-0.821841\pi$
$401$	−33.9389	−1.69483	−0.847413	+	0.530934i	$0.821841\pi$
$402$	−3.64861	−0.181976
$403$	−15.3985	−0.767054
$404$	−11.5954	−0.576892
$405$	59.6695	2.96500
$406$	−35.2312	−1.74850
$407$	−0.876018	−0.0434226
$408$	−3.27140	−0.161958
$409$	23.9223	1.18288	0.591440	−	0.806349i	$-0.298559\pi$
$409$	23.9223	1.18288	0.591440	+	0.806349i	$0.298559\pi$
$410$	−19.4713	−0.961621
$411$	−46.7736	−2.30717
$412$	14.5216	0.715427
$413$	16.4459	0.809249
$414$	−46.1213	−2.26674
$415$	27.7309	1.36125
$416$	10.1897	0.499589
$417$	42.1636	2.06476
$418$	21.2227	1.03803
$419$	9.64620	0.471248	0.235624	−	0.971844i	$-0.424287\pi$
$419$	9.64620	0.471248	0.235624	+	0.971844i	$0.424287\pi$
$420$	36.8794	1.79953
$421$	−21.8041	−1.06266	−0.531332	−	0.847163i	$-0.678308\pi$
$421$	−21.8041	−1.06266	−0.531332	+	0.847163i	$0.678308\pi$
$422$	−20.7027	−1.00779
$423$	−20.5814	−1.00070
$424$	−0.149641	−0.00726722
$425$	0.931339	0.0451766
$426$	5.59311	0.270987
$427$	13.0773	0.632853
$428$	−15.0385	−0.726912
$429$	−16.5283	−0.797992
$430$	−46.8200	−2.25786
$431$	39.4412	1.89981	0.949907	−	0.312533i	$-0.101178\pi$
$431$	39.4412	1.89981	0.949907	+	0.312533i	$0.101178\pi$
$432$	70.4833	3.39113
$433$	−6.20604	−0.298243	−0.149122	−	0.988819i	$-0.547645\pi$
$433$	−6.20604	−0.298243	−0.149122	+	0.988819i	$0.547645\pi$
$434$	−60.7536	−2.91626
$435$	38.0565	1.82467
$436$	−1.92262	−0.0920770
$437$	−16.6173	−0.794915
$438$	35.8238	1.71173
$439$	21.4044	1.02158	0.510789	−	0.859706i	$-0.329353\pi$
$439$	21.4044	1.02158	0.510789	+	0.859706i	$0.329353\pi$
$440$	11.6124	0.553599
$441$	91.2890	4.34710
$442$	−1.99694	−0.0949847
$443$	29.5898	1.40585	0.702927	−	0.711262i	$-0.251876\pi$
$443$	29.5898	1.40585	0.702927	+	0.711262i	$0.251876\pi$
$444$	1.08116	0.0513095
$445$	17.9777	0.852224
$446$	−16.1234	−0.763464
$447$	−20.2049	−0.955657
$448$	−3.81362	−0.180177
$449$	24.6613	1.16384	0.581919	−	0.813247i	$-0.302302\pi$
$449$	24.6613	1.16384	0.581919	+	0.813247i	$0.302302\pi$
$450$	−20.0916	−0.947128
$451$	11.5894	0.545723
$452$	−1.01482	−0.0477333
$453$	−44.0162	−2.06806
$454$	21.1458	0.992421
$455$	−21.8544	−1.02455
$456$	25.4273	1.19074
$457$	8.65132	0.404692	0.202346	−	0.979314i	$-0.435143\pi$
$457$	8.65132	0.404692	0.202346	+	0.979314i	$0.435143\pi$
$458$	16.5503	0.773344
$459$	−8.36952	−0.390656
$460$	9.36610	0.436697
$461$	33.9169	1.57967	0.789833	−	0.613321i	$-0.210167\pi$
$461$	33.9169	1.57967	0.789833	+	0.613321i	$0.210167\pi$
$462$	−65.2109	−3.03389
$463$	15.3345	0.712653	0.356326	−	0.934362i	$-0.384029\pi$
$463$	15.3345	0.712653	0.356326	+	0.934362i	$0.384029\pi$
$464$	23.0471	1.06994
$465$	65.6255	3.04331
$466$	13.5865	0.629383
$467$	−8.57802	−0.396943	−0.198472	−	0.980107i	$-0.563598\pi$
$467$	−8.57802	−0.396943	−0.198472	+	0.980107i	$0.563598\pi$
$468$	14.5011	0.670313
$469$	2.87148	0.132592
$470$	12.4166	0.572737
$471$	−36.6425	−1.68840
$472$	−6.39103	−0.294171
$473$	27.8674	1.28134
$474$	−26.4991	−1.21714
$475$	−7.23895	−0.332146
$476$	−2.65208	−0.121558
$477$	−0.645280	−0.0295453
$478$	13.8932	0.635462
$479$	−19.2498	−0.879547	−0.439774	−	0.898109i	$-0.644941\pi$
$479$	−19.2498	−0.879547	−0.439774	+	0.898109i	$0.644941\pi$
$480$	−43.4264	−1.98213
$481$	−0.640686	−0.0292128
$482$	5.67483	0.258481
$483$	51.0601	2.32332
$484$	−4.04334	−0.183788
$485$	23.6961	1.07598
$486$	56.7840	2.57577
$487$	−41.6402	−1.88690	−0.943449	−	0.331516i	$-0.892440\pi$
$487$	−41.6402	−1.88690	−0.943449	+	0.331516i	$0.892440\pi$
$488$	−5.08196	−0.230049
$489$	47.1000	2.12993
$490$	−55.0741	−2.48800
$491$	0.247681	0.0111777	0.00558884	−	0.999984i	$-0.498221\pi$
$491$	0.247681	0.0111777	0.00558884	+	0.999984i	$0.498221\pi$
$492$	−14.3033	−0.644844
$493$	−2.73673	−0.123256
$494$	15.5215	0.698343
$495$	50.0747	2.25069
$496$	39.7430	1.78451
$497$	−4.40181	−0.197448
$498$	60.5169	2.71183
$499$	−19.3735	−0.867276	−0.433638	−	0.901087i	$-0.642770\pi$
$499$	−19.3735	−0.867276	−0.433638	+	0.901087i	$0.642770\pi$
$500$	−8.92458	−0.399119
$501$	4.54380	0.203002
$502$	8.92866	0.398505
$503$	27.9510	1.24627	0.623136	−	0.782113i	$-0.285858\pi$
$503$	27.9510	1.24627	0.623136	+	0.782113i	$0.285858\pi$
$504$	−55.5415	−2.47402
$505$	−29.2843	−1.30314
$506$	−16.5614	−0.736242
$507$	29.7879	1.32293
$508$	3.20909	0.142380
$509$	36.0924	1.59977	0.799884	−	0.600155i	$-0.204894\pi$
$509$	36.0924	1.59977	0.799884	+	0.600155i	$0.204894\pi$
$510$	8.51057	0.376854
$511$	−28.1935	−1.24721
$512$	−9.19406	−0.406324
$513$	65.0531	2.87216
$514$	−28.8319	−1.27172
$515$	36.6745	1.61607
$516$	−34.3932	−1.51408
$517$	−7.39042	−0.325030
$518$	−2.52778	−0.111064
$519$	−29.0795	−1.27645
$520$	8.49285	0.372436
$521$	10.3695	0.454297	0.227149	−	0.973860i	$-0.427060\pi$
$521$	10.3695	0.454297	0.227149	+	0.973860i	$0.427060\pi$
$522$	59.0390	2.58406
$523$	29.0072	1.26840	0.634198	−	0.773171i	$-0.281330\pi$
$523$	29.0072	1.26840	0.634198	+	0.773171i	$0.281330\pi$
$524$	−0.0705170	−0.00308055
$525$	22.2431	0.970769
$526$	36.6736	1.59905
$527$	−4.71928	−0.205575
$528$	42.6589	1.85649
$529$	−10.0325	−0.436194
$530$	0.389293	0.0169098
$531$	−27.5593	−1.19597
$532$	20.6136	0.893714
$533$	8.47604	0.367138
$534$	39.2326	1.69776
$535$	−37.9799	−1.64201
$536$	−1.11589	−0.0481989
$537$	−45.5573	−1.96594
$538$	29.4577	1.27001
$539$	32.7803	1.41195
$540$	−36.6662	−1.57786
$541$	−21.3720	−0.918855	−0.459427	−	0.888215i	$-0.651945\pi$
$541$	−21.3720	−0.918855	−0.459427	+	0.888215i	$0.651945\pi$
$542$	33.3304	1.43166
$543$	−24.7922	−1.06393
$544$	3.12289	0.133893
$545$	−4.85561	−0.207992
$546$	−47.6928	−2.04106
$547$	12.8992	0.551529	0.275764	−	0.961225i	$-0.411069\pi$
$547$	12.8992	0.551529	0.275764	+	0.961225i	$0.411069\pi$
$548$	14.7356	0.629475
$549$	−21.9143	−0.935280
$550$	−7.21455	−0.307630
$551$	21.2715	0.906198
$552$	−19.8425	−0.844553
$553$	20.8549	0.886841
$554$	−0.286224	−0.0121605
$555$	2.73048	0.115902
$556$	−13.2833	−0.563337
$557$	15.7889	0.668998	0.334499	−	0.942396i	$-0.391433\pi$
$557$	15.7889	0.668998	0.334499	+	0.942396i	$0.391433\pi$
$558$	101.808	4.30988
$559$	20.3811	0.862031
$560$	56.4056	2.38357
$561$	−5.06552	−0.213866
$562$	−32.9706	−1.39078
$563$	7.29090	0.307275	0.153637	−	0.988127i	$-0.450901\pi$
$563$	7.29090	0.307275	0.153637	+	0.988127i	$0.450901\pi$
$564$	9.12107	0.384066
$565$	−2.56295	−0.107824
$566$	−36.0740	−1.51631
$567$	−102.481	−4.30379
$568$	1.71059	0.0717746
$569$	−26.8569	−1.12590	−0.562949	−	0.826491i	$-0.690333\pi$
$569$	−26.8569	−1.12590	−0.562949	+	0.826491i	$0.690333\pi$
$570$	−66.1495	−2.77070
$571$	8.36148	0.349917	0.174959	−	0.984576i	$-0.444021\pi$
$571$	8.36148	0.349917	0.174959	+	0.984576i	$0.444021\pi$
$572$	5.20709	0.217719
$573$	40.7873	1.70392
$574$	33.4416	1.39582
$575$	5.64899	0.235579
$576$	6.39070	0.266279
$577$	7.27676	0.302935	0.151468	−	0.988462i	$-0.451600\pi$
$577$	7.27676	0.302935	0.151468	+	0.988462i	$0.451600\pi$
$578$	28.9055	1.20231
$579$	−22.4322	−0.932250
$580$	−11.9894	−0.497831
$581$	−47.6271	−1.97591
$582$	51.7118	2.14352
$583$	−0.231709	−0.00959639
$584$	10.9563	0.453375
$585$	36.6227	1.51416
$586$	−29.0021	−1.19807
$587$	−14.4473	−0.596304	−0.298152	−	0.954518i	$-0.596370\pi$
$587$	−14.4473	−0.596304	−0.298152	+	0.954518i	$0.596370\pi$
$588$	−40.4566	−1.66840
$589$	36.6811	1.51142
$590$	16.6264	0.684496
$591$	66.2159	2.72376
$592$	1.65359	0.0679621
$593$	30.7307	1.26196	0.630980	−	0.775799i	$-0.282653\pi$
$593$	30.7307	1.26196	0.630980	+	0.775799i	$0.282653\pi$
$594$	64.8339	2.66017
$595$	−6.69786	−0.274586
$596$	6.36537	0.260736
$597$	16.0500	0.656881
$598$	−12.1123	−0.495310
$599$	44.4152	1.81476	0.907378	−	0.420317i	$-0.138081\pi$
$599$	44.4152	1.81476	0.907378	+	0.420317i	$0.138081\pi$
$600$	−8.64390	−0.352886
$601$	44.1887	1.80249	0.901247	−	0.433305i	$-0.142653\pi$
$601$	44.1887	1.80249	0.901247	+	0.433305i	$0.142653\pi$
$602$	80.4122	3.27736
$603$	−4.81190	−0.195956
$604$	13.8669	0.564237
$605$	−10.2115	−0.415157
$606$	−63.9070	−2.59605
$607$	−5.83249	−0.236733	−0.118367	−	0.992970i	$-0.537766\pi$
$607$	−5.83249	−0.236733	−0.118367	+	0.992970i	$0.537766\pi$
$608$	−24.2730	−0.984402
$609$	−65.3611	−2.64856
$610$	13.2208	0.535293
$611$	−5.40507	−0.218666
$612$	4.44424	0.179648
$613$	−37.9406	−1.53241	−0.766203	−	0.642598i	$-0.777856\pi$
$613$	−37.9406	−1.53241	−0.766203	+	0.642598i	$0.777856\pi$
$614$	−44.5377	−1.79740
$615$	−36.1233	−1.45663
$616$	−19.9440	−0.803567
$617$	−25.5180	−1.02732	−0.513658	−	0.857995i	$-0.671710\pi$
$617$	−25.5180	−1.02732	−0.513658	+	0.857995i	$0.671710\pi$
$618$	80.0345	3.21946
$619$	42.7689	1.71903	0.859514	−	0.511111i	$-0.170766\pi$
$619$	42.7689	1.71903	0.859514	+	0.511111i	$0.170766\pi$
$620$	−20.6748	−0.830318
$621$	−50.7649	−2.03713
$622$	16.7651	0.672219
$623$	−30.8763	−1.23703
$624$	31.1991	1.24896
$625$	−30.3827	−1.21531
$626$	−7.23914	−0.289334
$627$	39.3724	1.57238
$628$	11.5439	0.460652
$629$	−0.196355	−0.00782919
$630$	144.492	5.75670
$631$	−16.0478	−0.638853	−0.319426	−	0.947611i	$-0.603490\pi$
$631$	−16.0478	−0.638853	−0.319426	+	0.947611i	$0.603490\pi$
$632$	−8.10443	−0.322377
$633$	−38.4077	−1.52657
$634$	37.3249	1.48236
$635$	8.10459	0.321621
$636$	0.285969	0.0113394
$637$	23.9743	0.949895
$638$	21.1999	0.839310
$639$	7.37636	0.291804
$640$	−30.8180	−1.21819
$641$	−15.1421	−0.598078	−0.299039	−	0.954241i	$-0.596666\pi$
$641$	−15.1421	−0.598078	−0.299039	+	0.954241i	$0.596666\pi$
$642$	−82.8833	−3.27114
$643$	42.4136	1.67263	0.836315	−	0.548250i	$-0.184706\pi$
$643$	42.4136	1.67263	0.836315	+	0.548250i	$0.184706\pi$
$644$	−16.0861	−0.633880
$645$	−86.8605	−3.42013
$646$	4.75696	0.187160
$647$	28.7600	1.13067	0.565337	−	0.824860i	$-0.308746\pi$
$647$	28.7600	1.13067	0.565337	+	0.824860i	$0.308746\pi$
$648$	39.8251	1.56448
$649$	−9.89606	−0.388454
$650$	−5.27645	−0.206959
$651$	−112.710	−4.41746
$652$	−14.8384	−0.581119
$653$	31.4789	1.23187	0.615933	−	0.787799i	$-0.288779\pi$
$653$	31.4789	1.23187	0.615933	+	0.787799i	$0.288779\pi$
$654$	−10.5964	−0.414351
$655$	−0.178092	−0.00695862
$656$	−21.8764	−0.854130
$657$	47.2455	1.84322
$658$	−21.3253	−0.831346
$659$	−14.3997	−0.560934	−0.280467	−	0.959864i	$-0.590489\pi$
$659$	−14.3997	−0.560934	−0.280467	+	0.959864i	$0.590489\pi$
$660$	−22.1916	−0.863807
$661$	−2.09563	−0.0815104	−0.0407552	−	0.999169i	$-0.512976\pi$
$661$	−2.09563	−0.0815104	−0.0407552	+	0.999169i	$0.512976\pi$
$662$	−16.2820	−0.632817
$663$	−3.70473	−0.143880
$664$	18.5084	0.718265
$665$	52.0600	2.01880
$666$	4.23594	0.164139
$667$	−16.5995	−0.642735
$668$	−1.43149	−0.0553859
$669$	−29.9121	−1.15647
$670$	2.90299	0.112152
$671$	−7.86905	−0.303781
$672$	74.5838	2.87713
$673$	21.8571	0.842531	0.421265	−	0.906937i	$-0.361586\pi$
$673$	21.8571	0.842531	0.421265	+	0.906937i	$0.361586\pi$
$674$	17.3953	0.670041
$675$	−22.1145	−0.851188
$676$	−9.38443	−0.360940
$677$	−14.4050	−0.553631	−0.276815	−	0.960923i	$-0.589279\pi$
$677$	−14.4050	−0.553631	−0.276815	+	0.960923i	$0.589279\pi$
$678$	−5.59311	−0.214802
$679$	−40.6975	−1.56183
$680$	2.60286	0.0998151
$681$	39.2297	1.50329
$682$	36.5575	1.39986
$683$	−20.3732	−0.779558	−0.389779	−	0.920908i	$-0.627449\pi$
$683$	−20.3732	−0.779558	−0.389779	+	0.920908i	$0.627449\pi$
$684$	−34.5434	−1.32080
$685$	37.2150	1.42191
$686$	41.0878	1.56874
$687$	30.7042	1.17144
$688$	−52.6031	−2.00547
$689$	−0.169463	−0.00645602
$690$	51.6205	1.96516
$691$	−43.4953	−1.65464	−0.827319	−	0.561733i	$-0.810135\pi$
$691$	−43.4953	−1.65464	−0.827319	+	0.561733i	$0.810135\pi$
$692$	9.16124	0.348258
$693$	−86.0021	−3.26695
$694$	57.7445	2.19195
$695$	−33.5472	−1.27252
$696$	25.4000	0.962784
$697$	2.59771	0.0983952
$698$	2.24201	0.0848611
$699$	25.2057	0.953368
$700$	−7.00751	−0.264859
$701$	−29.9755	−1.13216	−0.566080	−	0.824350i	$-0.691541\pi$
$701$	−29.9755	−1.13216	−0.566080	+	0.824350i	$0.691541\pi$
$702$	47.4170	1.78964
$703$	1.52619	0.0575615
$704$	2.29479	0.0864881
$705$	23.0354	0.867563
$706$	12.9765	0.488377
$707$	50.2952	1.89154
$708$	12.2135	0.459010
$709$	10.5733	0.397090	0.198545	−	0.980092i	$-0.436378\pi$
$709$	10.5733	0.397090	0.198545	+	0.980092i	$0.436378\pi$
$710$	−4.45011	−0.167010
$711$	−34.9478	−1.31064
$712$	11.9988	0.449675
$713$	−28.6245	−1.07200
$714$	−14.6167	−0.547017
$715$	13.1506	0.491803
$716$	14.3524	0.536376
$717$	25.7748	0.962577
$718$	33.0269	1.23255
$719$	−18.3814	−0.685511	−0.342756	−	0.939425i	$-0.611360\pi$
$719$	−18.3814	−0.685511	−0.342756	+	0.939425i	$0.611360\pi$
$720$	−94.5220	−3.52263
$721$	−62.9875	−2.34578
$722$	−3.98387	−0.148264
$723$	10.5280	0.391539
$724$	7.81056	0.290277
$725$	−7.23116	−0.268559
$726$	−22.2845	−0.827056
$727$	32.1723	1.19321	0.596603	−	0.802537i	$-0.296517\pi$
$727$	32.1723	1.19321	0.596603	+	0.802537i	$0.296517\pi$
$728$	−14.5863	−0.540603
$729$	35.5012	1.31486
$730$	−28.5029	−1.05494
$731$	6.24634	0.231029
$732$	9.71178	0.358958
$733$	12.1835	0.450008	0.225004	−	0.974358i	$-0.427760\pi$
$733$	12.1835	0.450008	0.225004	+	0.974358i	$0.427760\pi$
$734$	24.7166	0.912307
$735$	−102.174	−3.76873
$736$	18.9417	0.698202
$737$	−1.72787	−0.0636468
$738$	−56.0399	−2.06286
$739$	41.6559	1.53234	0.766169	−	0.642640i	$-0.222161\pi$
$739$	41.6559	1.53234	0.766169	+	0.642640i	$0.222161\pi$
$740$	−0.860215	−0.0316221
$741$	28.7954	1.05783
$742$	−0.668603	−0.0245452
$743$	−21.2234	−0.778609	−0.389305	−	0.921109i	$-0.627285\pi$
$743$	−21.2234	−0.778609	−0.389305	+	0.921109i	$0.627285\pi$
$744$	43.8003	1.60580
$745$	16.0758	0.588973
$746$	−20.3643	−0.745590
$747$	79.8115	2.92015
$748$	1.59585	0.0583500
$749$	65.2296	2.38344
$750$	−49.1871	−1.79606
$751$	18.6533	0.680669	0.340334	−	0.940304i	$-0.389460\pi$
$751$	18.6533	0.680669	0.340334	+	0.940304i	$0.389460\pi$
$752$	13.9503	0.508716
$753$	16.5645	0.603643
$754$	15.5048	0.564650
$755$	35.0211	1.27455
$756$	62.9733	2.29032
$757$	32.3423	1.17550	0.587751	−	0.809042i	$-0.300013\pi$
$757$	32.3423	1.17550	0.587751	+	0.809042i	$0.300013\pi$
$758$	6.05797	0.220035
$759$	−30.7247	−1.11524
$760$	−20.2310	−0.733857
$761$	14.5861	0.528746	0.264373	−	0.964421i	$-0.414835\pi$
$761$	14.5861	0.528746	0.264373	+	0.964421i	$0.414835\pi$
$762$	17.6866	0.640718
$763$	8.33940	0.301907
$764$	−12.8497	−0.464886
$765$	11.2240	0.405804
$766$	47.5704	1.71879
$767$	−7.23760	−0.261335
$768$	−61.6724	−2.22541
$769$	3.69132	0.133113	0.0665563	−	0.997783i	$-0.478799\pi$
$769$	3.69132	0.133113	0.0665563	+	0.997783i	$0.478799\pi$
$770$	51.8845	1.86979
$771$	−53.4889	−1.92636
$772$	7.06708	0.254350
$773$	−7.71074	−0.277336	−0.138668	−	0.990339i	$-0.544282\pi$
$773$	−7.71074	−0.277336	−0.138668	+	0.990339i	$0.544282\pi$
$774$	−134.751	−4.84353
$775$	−12.4696	−0.447921
$776$	15.8155	0.567742
$777$	−4.68954	−0.168236
$778$	−56.4733	−2.02467
$779$	−20.1910	−0.723417
$780$	−16.2301	−0.581131
$781$	2.64872	0.0947787
$782$	−3.71215	−0.132746
$783$	64.9832	2.32231
$784$	−61.8768	−2.20988
$785$	29.1543	1.04056
$786$	−0.388649	−0.0138626
$787$	9.64129	0.343675	0.171837	−	0.985125i	$-0.445030\pi$
$787$	9.64129	0.343675	0.171837	+	0.985125i	$0.445030\pi$
$788$	−20.8608	−0.743134
$789$	68.0370	2.42218
$790$	21.0838	0.750127
$791$	4.40181	0.156510
$792$	33.4213	1.18757
$793$	−5.75512	−0.204370
$794$	34.6627	1.23013
$795$	0.722219	0.0256145
$796$	−5.05640	−0.179219
$797$	33.6381	1.19152	0.595761	−	0.803162i	$-0.296850\pi$
$797$	33.6381	1.19152	0.595761	+	0.803162i	$0.296850\pi$
$798$	113.610	4.02176
$799$	−1.65653	−0.0586037
$800$	8.25151	0.291735
$801$	51.7411	1.82818
$802$	58.9289	2.08085
$803$	16.9650	0.598683
$804$	2.13249	0.0752071
$805$	−40.6256	−1.43186
$806$	26.7368	0.941763
$807$	54.6500	1.92377
$808$	−19.5452	−0.687598
$809$	−8.68405	−0.305315	−0.152657	−	0.988279i	$-0.548783\pi$
$809$	−8.68405	−0.305315	−0.152657	+	0.988279i	$0.548783\pi$
$810$	−103.606	−3.64033
$811$	−26.0020	−0.913055	−0.456528	−	0.889709i	$-0.650907\pi$
$811$	−26.0020	−0.913055	−0.456528	+	0.889709i	$0.650907\pi$
$812$	20.5915	0.722619
$813$	61.8346	2.16864
$814$	1.52105	0.0533128
$815$	−37.4747	−1.31268
$816$	9.56178	0.334729
$817$	−48.5504	−1.69856
$818$	−41.5369	−1.45230
$819$	−62.8986	−2.19786
$820$	11.3803	0.397419
$821$	5.93274	0.207054	0.103527	−	0.994627i	$-0.466987\pi$
$821$	5.93274	0.207054	0.103527	+	0.994627i	$0.466987\pi$
$822$	81.2141	2.83267
$823$	15.4695	0.539233	0.269616	−	0.962968i	$-0.413103\pi$
$823$	15.4695	0.539233	0.269616	+	0.962968i	$0.413103\pi$
$824$	24.4776	0.852718
$825$	−13.3845	−0.465987
$826$	−28.5554	−0.993569
$827$	44.7364	1.55564	0.777819	−	0.628489i	$-0.216326\pi$
$827$	44.7364	1.55564	0.777819	+	0.628489i	$0.216326\pi$
$828$	26.9563	0.936797
$829$	−43.1614	−1.49906	−0.749529	−	0.661972i	$-0.769720\pi$
$829$	−43.1614	−1.49906	−0.749529	+	0.661972i	$0.769720\pi$
$830$	−48.1498	−1.67130
$831$	−0.531005	−0.0184203
$832$	1.67832	0.0581853
$833$	7.34754	0.254577
$834$	−73.2098	−2.53505
$835$	−3.61524	−0.125110
$836$	−12.4039	−0.428999
$837$	112.059	3.87331
$838$	−16.7489	−0.578582
$839$	47.6679	1.64568	0.822839	−	0.568274i	$-0.192389\pi$
$839$	47.6679	1.64568	0.822839	+	0.568274i	$0.192389\pi$
$840$	62.1639	2.14486
$841$	−7.75133	−0.267287
$842$	37.8589	1.30470
$843$	−61.1671	−2.10671
$844$	12.1000	0.416500
$845$	−23.7005	−0.815323
$846$	35.7360	1.22863
$847$	17.5380	0.602614
$848$	0.437378	0.0150196
$849$	−66.9247	−2.29685
$850$	−1.61711	−0.0554663
$851$	−1.19098	−0.0408264
$852$	−3.26898	−0.111994
$853$	−21.1698	−0.724842	−0.362421	−	0.932015i	$-0.618050\pi$
$853$	−21.1698	−0.724842	−0.362421	+	0.932015i	$0.618050\pi$
$854$	−22.7064	−0.776996
$855$	−87.2398	−2.98354
$856$	−25.3489	−0.866407
$857$	−25.0755	−0.856564	−0.428282	−	0.903645i	$-0.640881\pi$
$857$	−25.0755	−0.856564	−0.428282	+	0.903645i	$0.640881\pi$
$858$	28.6984	0.979748
$859$	−51.0913	−1.74321	−0.871607	−	0.490206i	$-0.836922\pi$
$859$	−51.0913	−1.74321	−0.871607	+	0.490206i	$0.836922\pi$
$860$	27.3647	0.933128
$861$	62.0409	2.11435
$862$	−68.4826	−2.33253
$863$	−28.0316	−0.954206	−0.477103	−	0.878847i	$-0.658313\pi$
$863$	−28.0316	−0.954206	−0.477103	+	0.878847i	$0.658313\pi$
$864$	−74.1526	−2.52272
$865$	23.1368	0.786676
$866$	10.7757	0.366173
$867$	53.6256	1.82122
$868$	35.5084	1.20523
$869$	−12.5491	−0.425700
$870$	−66.0784	−2.24027
$871$	−1.26370	−0.0428187
$872$	−3.24078	−0.109747
$873$	68.1990	2.30819
$874$	28.8531	0.975971
$875$	38.7105	1.30865
$876$	−20.9378	−0.707423
$877$	−41.5826	−1.40414	−0.702072	−	0.712106i	$-0.747741\pi$
$877$	−41.5826	−1.40414	−0.702072	+	0.712106i	$0.747741\pi$
$878$	−37.1651	−1.25426
$879$	−53.8049	−1.81479
$880$	−33.9412	−1.14416
$881$	46.8965	1.57998	0.789991	−	0.613118i	$-0.210085\pi$
$881$	46.8965	1.57998	0.789991	+	0.613118i	$0.210085\pi$
$882$	−158.507	−5.33722
$883$	27.9577	0.940851	0.470425	−	0.882440i	$-0.344100\pi$
$883$	27.9577	0.940851	0.470425	+	0.882440i	$0.344100\pi$
$884$	1.16714	0.0392553
$885$	30.8453	1.03685
$886$	−51.3775	−1.72606
$887$	−11.0613	−0.371402	−0.185701	−	0.982606i	$-0.559456\pi$
$887$	−11.0613	−0.371402	−0.185701	+	0.982606i	$0.559456\pi$
$888$	1.82240	0.0611558
$889$	−13.9195	−0.466843
$890$	−31.2151	−1.04633
$891$	61.6663	2.06590
$892$	9.42357	0.315524
$893$	12.8756	0.430864
$894$	35.0822	1.17332
$895$	36.2473	1.21161
$896$	52.9293	1.76824
$897$	−22.4709	−0.750280
$898$	−42.8200	−1.42892
$899$	36.6417	1.22207
$900$	11.7429	0.391429
$901$	−0.0519364	−0.00173025
$902$	−20.1230	−0.670021
$903$	149.181	4.96443
$904$	−1.71059	−0.0568933
$905$	19.7257	0.655704
$906$	76.4263	2.53910
$907$	−14.6889	−0.487736	−0.243868	−	0.969808i	$-0.578416\pi$
$907$	−14.6889	−0.487736	−0.243868	+	0.969808i	$0.578416\pi$
$908$	−12.3590	−0.410148
$909$	−84.2824	−2.79547
$910$	37.9464	1.25791
$911$	39.7902	1.31831	0.659155	−	0.752007i	$-0.270914\pi$
$911$	39.7902	1.31831	0.659155	+	0.752007i	$0.270914\pi$
$912$	−74.3201	−2.46098
$913$	28.6589	0.948472
$914$	−15.0215	−0.496867
$915$	24.5272	0.810845
$916$	−9.67309	−0.319608
$917$	0.305868	0.0101007
$918$	14.5322	0.479634
$919$	1.88387	0.0621432	0.0310716	−	0.999517i	$-0.490108\pi$
$919$	1.88387	0.0621432	0.0310716	+	0.999517i	$0.490108\pi$
$920$	15.7875	0.520499
$921$	−82.6265	−2.72264
$922$	−58.8907	−1.93946
$923$	1.93717	0.0637628
$924$	38.1136	1.25385
$925$	−0.518823	−0.0170588
$926$	−26.6256	−0.874971
$927$	105.552	3.46677
$928$	−24.2470	−0.795945
$929$	25.9911	0.852739	0.426370	−	0.904549i	$-0.359792\pi$
$929$	25.9911	0.852739	0.426370	+	0.904549i	$0.359792\pi$
$930$	−113.947	−3.73647
$931$	−57.1097	−1.87169
$932$	−7.94085	−0.260111
$933$	31.1027	1.01826
$934$	14.8942	0.487354
$935$	4.03034	0.131806
$936$	24.4431	0.798946
$937$	4.24329	0.138622	0.0693111	−	0.997595i	$-0.477920\pi$
$937$	4.24329	0.138622	0.0693111	+	0.997595i	$0.477920\pi$
$938$	−4.98582	−0.162793
$939$	−13.4301	−0.438274
$940$	−7.25710	−0.236701
$941$	53.4776	1.74332	0.871660	−	0.490111i	$-0.163044\pi$
$941$	53.4776	1.74332	0.871660	+	0.490111i	$0.163044\pi$
$942$	63.6232	2.07296
$943$	15.7563	0.513095
$944$	18.6800	0.607982
$945$	159.040	5.17357
$946$	−48.3868	−1.57319
$947$	−37.4364	−1.21652	−0.608260	−	0.793738i	$-0.708132\pi$
$947$	−37.4364	−1.21652	−0.608260	+	0.793738i	$0.708132\pi$
$948$	15.4878	0.503021
$949$	12.4076	0.402767
$950$	12.5692	0.407797
$951$	69.2454	2.24543
$952$	−4.47035	−0.144885
$953$	−33.8764	−1.09737	−0.548683	−	0.836031i	$-0.684870\pi$
$953$	−33.8764	−1.09737	−0.548683	+	0.836031i	$0.684870\pi$
$954$	1.12042	0.0362748
$955$	−32.4521	−1.05013
$956$	−8.12013	−0.262624
$957$	39.3300	1.27136
$958$	33.4239	1.07988
$959$	−63.9159	−2.06395
$960$	−7.15268	−0.230852
$961$	32.1859	1.03825
$962$	1.11244	0.0358665
$963$	−109.309	−3.52243
$964$	−3.31674	−0.106825
$965$	17.8480	0.574547
$966$	−88.6570	−2.85249
$967$	−20.6288	−0.663378	−0.331689	−	0.943389i	$-0.607619\pi$
$967$	−20.6288	−0.663378	−0.331689	+	0.943389i	$0.607619\pi$
$968$	−6.81546	−0.219057
$969$	8.82512	0.283504
$970$	−41.1441	−1.32106
$971$	46.3070	1.48606	0.743031	−	0.669257i	$-0.233388\pi$
$971$	46.3070	1.48606	0.743031	+	0.669257i	$0.233388\pi$
$972$	−33.1883	−1.06452
$973$	57.6165	1.84710
$974$	72.3010	2.31667
$975$	−9.78888	−0.313495
$976$	14.8538	0.475458
$977$	53.4850	1.71114	0.855568	−	0.517690i	$-0.173208\pi$
$977$	53.4850	1.71114	0.855568	+	0.517690i	$0.173208\pi$
$978$	−81.7808	−2.61506
$979$	18.5793	0.593798
$980$	32.1890	1.02824
$981$	−13.9748	−0.446181
$982$	−0.430055	−0.0137236
$983$	16.4493	0.524652	0.262326	−	0.964979i	$-0.415511\pi$
$983$	16.4493	0.524652	0.262326	+	0.964979i	$0.415511\pi$
$984$	−24.1097	−0.768590
$985$	−52.6842	−1.67866
$986$	4.75184	0.151330
$987$	−39.5627	−1.25930
$988$	−9.07176	−0.288611
$989$	37.8869	1.20473
$990$	−86.9459	−2.76332
$991$	32.4332	1.03028	0.515138	−	0.857108i	$-0.327741\pi$
$991$	32.4332	1.03028	0.515138	+	0.857108i	$0.327741\pi$
$992$	−41.8120	−1.32753
$993$	−30.2064	−0.958570
$994$	7.64296	0.242420
$995$	−12.7700	−0.404837
$996$	−35.3701	−1.12074
$997$	31.0535	0.983474	0.491737	−	0.870744i	$-0.336362\pi$
$997$	31.0535	0.983474	0.491737	+	0.870744i	$0.336362\pi$
$998$	33.6387	1.06481
$999$	4.66243	0.147513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.33	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.33	✓	165	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)

\(f(q)\)	\(=\)	\(q-1.73632 q^{2} -3.22124 q^{3} +1.01482 q^{4} +2.56295 q^{5} +5.59311 q^{6} -4.40181 q^{7} +1.71059 q^{8} +7.37636 q^{9} +O(q^{10})\)	\(q-1.73632 q^{2} -3.22124 q^{3} +1.01482 q^{4} +2.56295 q^{5} +5.59311 q^{6} -4.40181 q^{7} +1.71059 q^{8} +7.37636 q^{9} -4.45011 q^{10} +2.64872 q^{11} -3.26898 q^{12} +1.93717 q^{13} +7.64296 q^{14} -8.25586 q^{15} -4.99978 q^{16} +0.593698 q^{17} -12.8077 q^{18} -4.61459 q^{19} +2.60094 q^{20} +14.1793 q^{21} -4.59904 q^{22} +3.60105 q^{23} -5.51020 q^{24} +1.56871 q^{25} -3.36356 q^{26} -14.0973 q^{27} -4.46705 q^{28} -4.60963 q^{29} +14.3349 q^{30} -7.94895 q^{31} +5.26007 q^{32} -8.53215 q^{33} -1.03085 q^{34} -11.2816 q^{35} +7.48570 q^{36} -0.330732 q^{37} +8.01242 q^{38} -6.24009 q^{39} +4.38415 q^{40} +4.37547 q^{41} -24.6198 q^{42} +10.5211 q^{43} +2.68798 q^{44} +18.9052 q^{45} -6.25259 q^{46} -2.79019 q^{47} +16.1055 q^{48} +12.3759 q^{49} -2.72379 q^{50} -1.91244 q^{51} +1.96589 q^{52} -0.0874795 q^{53} +24.4774 q^{54} +6.78854 q^{55} -7.52967 q^{56} +14.8647 q^{57} +8.00381 q^{58} -3.73616 q^{59} -8.37824 q^{60} -2.97089 q^{61} +13.8020 q^{62} -32.4693 q^{63} +0.866376 q^{64} +4.96488 q^{65} +14.8146 q^{66} -0.652341 q^{67} +0.602498 q^{68} -11.5998 q^{69} +19.5885 q^{70} +1.00000 q^{71} +12.6179 q^{72} +6.40499 q^{73} +0.574259 q^{74} -5.05318 q^{75} -4.68299 q^{76} -11.6592 q^{77} +10.8348 q^{78} -4.73781 q^{79} -12.8142 q^{80} +23.2816 q^{81} -7.59724 q^{82} +10.8199 q^{83} +14.3894 q^{84} +1.52162 q^{85} -18.2680 q^{86} +14.8487 q^{87} +4.53087 q^{88} +7.01445 q^{89} -32.8256 q^{90} -8.52706 q^{91} +3.65442 q^{92} +25.6054 q^{93} +4.84467 q^{94} -11.8270 q^{95} -16.9439 q^{96} +9.24563 q^{97} -21.4886 q^{98} +19.5379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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