LMFDB - Embedded newform 3023.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3023,2,Mod(1,3023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3023, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3023.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:	$24.1387765310$
Analytic rank:	$0$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	3023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22083 q^{2} +0.538465 q^{3} +2.93210 q^{4} +2.14893 q^{5} -1.19584 q^{6} -3.02689 q^{7} -2.07005 q^{8} -2.71006 q^{9} +O(q^{10})$	\(q-2.22083 q^{2} +0.538465 q^{3} +2.93210 q^{4} +2.14893 q^{5} -1.19584 q^{6} -3.02689 q^{7} -2.07005 q^{8} -2.71006 q^{9} -4.77242 q^{10} +1.72804 q^{11} +1.57883 q^{12} +3.14016 q^{13} +6.72222 q^{14} +1.15712 q^{15} -1.26697 q^{16} +7.60261 q^{17} +6.01858 q^{18} +5.55078 q^{19} +6.30088 q^{20} -1.62987 q^{21} -3.83769 q^{22} +3.18867 q^{23} -1.11465 q^{24} -0.382103 q^{25} -6.97378 q^{26} -3.07466 q^{27} -8.87516 q^{28} -0.465444 q^{29} -2.56978 q^{30} +8.00300 q^{31} +6.95384 q^{32} +0.930487 q^{33} -16.8841 q^{34} -6.50458 q^{35} -7.94617 q^{36} -1.53542 q^{37} -12.3274 q^{38} +1.69087 q^{39} -4.44839 q^{40} -2.53426 q^{41} +3.61968 q^{42} -11.5069 q^{43} +5.06679 q^{44} -5.82372 q^{45} -7.08150 q^{46} -7.90827 q^{47} -0.682221 q^{48} +2.16207 q^{49} +0.848586 q^{50} +4.09373 q^{51} +9.20728 q^{52} +9.25664 q^{53} +6.82832 q^{54} +3.71343 q^{55} +6.26581 q^{56} +2.98890 q^{57} +1.03367 q^{58} -3.46063 q^{59} +3.39280 q^{60} -8.35772 q^{61} -17.7733 q^{62} +8.20305 q^{63} -12.9094 q^{64} +6.74799 q^{65} -2.06646 q^{66} +3.30604 q^{67} +22.2916 q^{68} +1.71698 q^{69} +14.4456 q^{70} +15.1304 q^{71} +5.60995 q^{72} -5.18230 q^{73} +3.40991 q^{74} -0.205749 q^{75} +16.2755 q^{76} -5.23058 q^{77} -3.75513 q^{78} -4.24463 q^{79} -2.72264 q^{80} +6.47457 q^{81} +5.62816 q^{82} -6.82918 q^{83} -4.77896 q^{84} +16.3375 q^{85} +25.5549 q^{86} -0.250625 q^{87} -3.57712 q^{88} -3.84784 q^{89} +12.9335 q^{90} -9.50493 q^{91} +9.34950 q^{92} +4.30933 q^{93} +17.5630 q^{94} +11.9282 q^{95} +3.74440 q^{96} +7.80995 q^{97} -4.80161 q^{98} -4.68308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9}+O(q^{10}) $ 149 * q + 13 * q^2 + 16 * q^3 + 169 * q^4 + 15 * q^5 + 15 * q^6 + 59 * q^7 + 36 * q^8 + 189 * q^9	\( 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9} + 16 q^{10} + 17 q^{11} + 40 q^{12} + 65 q^{13} + 4 q^{14} + 19 q^{15} + 205 q^{16} + 55 q^{17} + 60 q^{18} + 33 q^{19} + 23 q^{20} + 30 q^{21} + 78 q^{22} + 31 q^{23} + 36 q^{24} + 280 q^{25} - 7 q^{26} + 52 q^{27} + 165 q^{28} + 34 q^{29} + 17 q^{30} + 30 q^{31} + 65 q^{32} + 86 q^{33} + 37 q^{34} + 12 q^{35} + 210 q^{36} + 138 q^{37} + 15 q^{38} + 37 q^{39} + 27 q^{40} + 57 q^{41} + 2 q^{42} + 92 q^{43} + 37 q^{44} + 50 q^{45} + 62 q^{46} + 26 q^{47} + 79 q^{48} + 266 q^{49} + 19 q^{50} + 28 q^{51} + 139 q^{52} + 44 q^{53} + 33 q^{54} + 36 q^{55} - 2 q^{56} + 207 q^{57} + 150 q^{58} + 13 q^{59} - 15 q^{60} + 87 q^{61} + 22 q^{62} + 161 q^{63} + 254 q^{64} + 137 q^{65} - 25 q^{66} + 87 q^{67} + 68 q^{68} - 16 q^{69} + 28 q^{70} + 32 q^{71} + 120 q^{72} + 329 q^{73} + 29 q^{74} + 37 q^{75} + 42 q^{76} + 45 q^{77} + 63 q^{79} - 17 q^{80} + 269 q^{81} + 29 q^{82} + 51 q^{83} + 6 q^{84} + 224 q^{85} - 20 q^{86} + 34 q^{87} + 199 q^{88} + 24 q^{89} - 103 q^{90} + 46 q^{91} + 22 q^{92} + 119 q^{93} + 18 q^{94} + 13 q^{95} - 6 q^{96} + 204 q^{97} - 22 q^{98} + 43 q^{99}+O(q^{100}) \) 149 * q + 13 * q^2 + 16 * q^3 + 169 * q^4 + 15 * q^5 + 15 * q^6 + 59 * q^7 + 36 * q^8 + 189 * q^9 + 16 * q^10 + 17 * q^11 + 40 * q^12 + 65 * q^13 + 4 * q^14 + 19 * q^15 + 205 * q^16 + 55 * q^17 + 60 * q^18 + 33 * q^19 + 23 * q^20 + 30 * q^21 + 78 * q^22 + 31 * q^23 + 36 * q^24 + 280 * q^25 - 7 * q^26 + 52 * q^27 + 165 * q^28 + 34 * q^29 + 17 * q^30 + 30 * q^31 + 65 * q^32 + 86 * q^33 + 37 * q^34 + 12 * q^35 + 210 * q^36 + 138 * q^37 + 15 * q^38 + 37 * q^39 + 27 * q^40 + 57 * q^41 + 2 * q^42 + 92 * q^43 + 37 * q^44 + 50 * q^45 + 62 * q^46 + 26 * q^47 + 79 * q^48 + 266 * q^49 + 19 * q^50 + 28 * q^51 + 139 * q^52 + 44 * q^53 + 33 * q^54 + 36 * q^55 - 2 * q^56 + 207 * q^57 + 150 * q^58 + 13 * q^59 - 15 * q^60 + 87 * q^61 + 22 * q^62 + 161 * q^63 + 254 * q^64 + 137 * q^65 - 25 * q^66 + 87 * q^67 + 68 * q^68 - 16 * q^69 + 28 * q^70 + 32 * q^71 + 120 * q^72 + 329 * q^73 + 29 * q^74 + 37 * q^75 + 42 * q^76 + 45 * q^77 + 63 * q^79 - 17 * q^80 + 269 * q^81 + 29 * q^82 + 51 * q^83 + 6 * q^84 + 224 * q^85 - 20 * q^86 + 34 * q^87 + 199 * q^88 + 24 * q^89 - 103 * q^90 + 46 * q^91 + 22 * q^92 + 119 * q^93 + 18 * q^94 + 13 * q^95 - 6 * q^96 + 204 * q^97 - 22 * q^98 + 43 * 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 $

$2$	−2.22083	−1.57037	−0.785183	−	0.619263i	$-0.787431\pi$
$2$	−2.22083	−1.57037	−0.785183	+	0.619263i	$0.787431\pi$
$3$	0.538465	0.310883	0.155441	−	0.987845i	$-0.450320\pi$
$3$	0.538465	0.310883	0.155441	+	0.987845i	$0.450320\pi$
$4$	2.93210	1.46605
$5$	2.14893	0.961030	0.480515	−	0.876986i	$-0.340450\pi$
$5$	2.14893	0.961030	0.480515	+	0.876986i	$0.340450\pi$
$6$	−1.19584	−0.488200
$7$	−3.02689	−1.14406	−0.572029	−	0.820234i	$-0.693843\pi$
$7$	−3.02689	−1.14406	−0.572029	+	0.820234i	$0.693843\pi$
$8$	−2.07005	−0.731872
$9$	−2.71006	−0.903352
$10$	−4.77242	−1.50917
$11$	1.72804	0.521023	0.260511	−	0.965471i	$-0.416109\pi$
$11$	1.72804	0.521023	0.260511	+	0.965471i	$0.416109\pi$
$12$	1.57883	0.455770
$13$	3.14016	0.870925	0.435462	−	0.900207i	$-0.356585\pi$
$13$	3.14016	0.870925	0.435462	+	0.900207i	$0.356585\pi$
$14$	6.72222	1.79659
$15$	1.15712	0.298768
$16$	−1.26697	−0.316744
$17$	7.60261	1.84390	0.921951	−	0.387305i	$-0.126594\pi$
$17$	7.60261	1.84390	0.921951	+	0.387305i	$0.126594\pi$
$18$	6.01858	1.41859
$19$	5.55078	1.27344	0.636718	−	0.771097i	$-0.280291\pi$
$19$	5.55078	1.27344	0.636718	+	0.771097i	$0.280291\pi$
$20$	6.30088	1.40892
$21$	−1.62987	−0.355668
$22$	−3.83769	−0.818197
$23$	3.18867	0.664883	0.332441	−	0.943124i	$-0.392128\pi$
$23$	3.18867	0.664883	0.332441	+	0.943124i	$0.392128\pi$
$24$	−1.11465	−0.227526
$25$	−0.382103	−0.0764205
$26$	−6.97378	−1.36767
$27$	−3.07466	−0.591719
$28$	−8.87516	−1.67725
$29$	−0.465444	−0.0864307	−0.0432154	−	0.999066i	$-0.513760\pi$
$29$	−0.465444	−0.0864307	−0.0432154	+	0.999066i	$0.513760\pi$
$30$	−2.56978	−0.469175
$31$	8.00300	1.43738	0.718691	−	0.695330i	$-0.244742\pi$
$31$	8.00300	1.43738	0.718691	+	0.695330i	$0.244742\pi$
$32$	6.95384	1.22928
$33$	0.930487	0.161977
$34$	−16.8841	−2.89560
$35$	−6.50458	−1.09947
$36$	−7.94617	−1.32436
$37$	−1.53542	−0.252421	−0.126211	−	0.992003i	$-0.540282\pi$
$37$	−1.53542	−0.252421	−0.126211	+	0.992003i	$0.540282\pi$
$38$	−12.3274	−1.99976
$39$	1.69087	0.270755
$40$	−4.44839	−0.703352
$41$	−2.53426	−0.395784	−0.197892	−	0.980224i	$-0.563410\pi$
$41$	−2.53426	−0.395784	−0.197892	+	0.980224i	$0.563410\pi$
$42$	3.61968	0.558529
$43$	−11.5069	−1.75479	−0.877393	−	0.479772i	$-0.840719\pi$
$43$	−11.5069	−1.75479	−0.877393	+	0.479772i	$0.840719\pi$
$44$	5.06679	0.763847
$45$	−5.82372	−0.868149
$46$	−7.08150	−1.04411
$47$	−7.90827	−1.15354	−0.576770	−	0.816907i	$-0.695687\pi$
$47$	−7.90827	−1.15354	−0.576770	+	0.816907i	$0.695687\pi$
$48$	−0.682221	−0.0984701
$49$	2.16207	0.308868
$50$	0.848586	0.120008
$51$	4.09373	0.573238
$52$	9.20728	1.27682
$53$	9.25664	1.27150	0.635748	−	0.771896i	$-0.280692\pi$
$53$	9.25664	1.27150	0.635748	+	0.771896i	$0.280692\pi$
$54$	6.82832	0.929216
$55$	3.71343	0.500719
$56$	6.26581	0.837304
$57$	2.98890	0.395889
$58$	1.03367	0.135728
$59$	−3.46063	−0.450535	−0.225268	−	0.974297i	$-0.572326\pi$
$59$	−3.46063	−0.450535	−0.225268	+	0.974297i	$0.572326\pi$
$60$	3.39280	0.438009
$61$	−8.35772	−1.07010	−0.535048	−	0.844822i	$-0.679706\pi$
$61$	−8.35772	−1.07010	−0.535048	+	0.844822i	$0.679706\pi$
$62$	−17.7733	−2.25722
$63$	8.20305	1.03349
$64$	−12.9094	−1.61367
$65$	6.74799	0.836985
$66$	−2.06646	−0.254363
$67$	3.30604	0.403898	0.201949	−	0.979396i	$-0.435273\pi$
$67$	3.30604	0.403898	0.201949	+	0.979396i	$0.435273\pi$
$68$	22.2916	2.70326
$69$	1.71698	0.206701
$70$	14.4456	1.72658
$71$	15.1304	1.79565	0.897823	−	0.440357i	$-0.145148\pi$
$71$	15.1304	1.79565	0.897823	+	0.440357i	$0.145148\pi$
$72$	5.60995	0.661138
$73$	−5.18230	−0.606542	−0.303271	−	0.952904i	$-0.598079\pi$
$73$	−5.18230	−0.606542	−0.303271	+	0.952904i	$0.598079\pi$
$74$	3.40991	0.396394
$75$	−0.205749	−0.0237578
$76$	16.2755	1.86692
$77$	−5.23058	−0.596080
$78$	−3.75513	−0.425185
$79$	−4.24463	−0.477558	−0.238779	−	0.971074i	$-0.576747\pi$
$79$	−4.24463	−0.477558	−0.238779	+	0.971074i	$0.576747\pi$
$80$	−2.72264	−0.304400
$81$	6.47457	0.719397
$82$	5.62816	0.621527
$83$	−6.82918	−0.749600	−0.374800	−	0.927106i	$-0.622289\pi$
$83$	−6.82918	−0.749600	−0.374800	+	0.927106i	$0.622289\pi$
$84$	−4.77896	−0.521427
$85$	16.3375	1.77205
$86$	25.5549	2.75566
$87$	−0.250625	−0.0268698
$88$	−3.57712	−0.381322
$89$	−3.84784	−0.407870	−0.203935	−	0.978984i	$-0.565373\pi$
$89$	−3.84784	−0.407870	−0.203935	+	0.978984i	$0.565373\pi$
$90$	12.9335	1.36331
$91$	−9.50493	−0.996388
$92$	9.34950	0.974753
$93$	4.30933	0.446857
$94$	17.5630	1.81148
$95$	11.9282	1.22381
$96$	3.74440	0.382161
$97$	7.80995	0.792981	0.396490	−	0.918039i	$-0.370228\pi$
$97$	7.80995	0.792981	0.396490	+	0.918039i	$0.370228\pi$
$98$	−4.80161	−0.485036
$99$	−4.68308	−0.470667
$100$	−1.12036	−0.112036
$101$	18.0886	1.79989	0.899943	−	0.436008i	$-0.143608\pi$
$101$	18.0886	1.79989	0.899943	+	0.436008i	$0.143608\pi$
$102$	−9.09151	−0.900193
$103$	9.87559	0.973071	0.486535	−	0.873661i	$-0.338260\pi$
$103$	9.87559	0.973071	0.486535	+	0.873661i	$0.338260\pi$
$104$	−6.50029	−0.637406
$105$	−3.50248	−0.341808
$106$	−20.5575	−1.99672
$107$	−6.67887	−0.645671	−0.322836	−	0.946455i	$-0.604636\pi$
$107$	−6.67887	−0.645671	−0.322836	+	0.946455i	$0.604636\pi$
$108$	−9.01523	−0.867491
$109$	10.4231	0.998353	0.499177	−	0.866500i	$-0.333636\pi$
$109$	10.4231	0.998353	0.499177	+	0.866500i	$0.333636\pi$
$110$	−8.24691	−0.786312
$111$	−0.826768	−0.0784734
$112$	3.83500	0.362373
$113$	11.3193	1.06483	0.532413	−	0.846485i	$-0.321285\pi$
$113$	11.3193	1.06483	0.532413	+	0.846485i	$0.321285\pi$
$114$	−6.63785	−0.621691
$115$	6.85222	0.638973
$116$	−1.36473	−0.126712
$117$	−8.51002	−0.786751
$118$	7.68548	0.707506
$119$	−23.0123	−2.10953
$120$	−2.39530	−0.218660
$121$	−8.01389	−0.728535
$122$	18.5611	1.68044
$123$	−1.36461	−0.123043
$124$	23.4656	2.10728
$125$	−11.5658	−1.03447
$126$	−18.2176	−1.62295
$127$	20.7636	1.84247	0.921236	−	0.389004i	$-0.127181\pi$
$127$	20.7636	1.84247	0.921236	+	0.389004i	$0.127181\pi$
$128$	14.7619	1.30478
$129$	−6.19606	−0.545533
$130$	−14.9862	−1.31437
$131$	−10.8238	−0.945681	−0.472840	−	0.881148i	$-0.656771\pi$
$131$	−10.8238	−0.945681	−0.472840	+	0.881148i	$0.656771\pi$
$132$	2.72829	0.237467
$133$	−16.8016	−1.45688
$134$	−7.34217	−0.634267
$135$	−6.60723	−0.568660
$136$	−15.7378	−1.34950
$137$	8.61889	0.736361	0.368181	−	0.929754i	$-0.379981\pi$
$137$	8.61889	0.736361	0.368181	+	0.929754i	$0.379981\pi$
$138$	−3.81314	−0.324596
$139$	−2.15287	−0.182604	−0.0913020	−	0.995823i	$-0.529103\pi$
$139$	−2.15287	−0.182604	−0.0913020	+	0.995823i	$0.529103\pi$
$140$	−19.0721	−1.61189
$141$	−4.25832	−0.358616
$142$	−33.6021	−2.81982
$143$	5.42632	0.453772
$144$	3.43357	0.286131
$145$	−1.00021	−0.0830625
$146$	11.5090	0.952493
$147$	1.16420	0.0960216
$148$	−4.50201	−0.370063
$149$	−13.8493	−1.13458	−0.567291	−	0.823518i	$-0.692008\pi$
$149$	−13.8493	−1.13458	−0.567291	+	0.823518i	$0.692008\pi$
$150$	0.456934	0.0373085
$151$	15.1810	1.23541	0.617706	−	0.786409i	$-0.288062\pi$
$151$	15.1810	1.23541	0.617706	+	0.786409i	$0.288062\pi$
$152$	−11.4904	−0.931993
$153$	−20.6035	−1.66569
$154$	11.6163	0.936065
$155$	17.1979	1.38137
$156$	4.95780	0.396941
$157$	14.8218	1.18291	0.591454	−	0.806339i	$-0.298554\pi$
$157$	14.8218	1.18291	0.591454	+	0.806339i	$0.298554\pi$
$158$	9.42661	0.749941
$159$	4.98437	0.395286
$160$	14.9433	1.18137
$161$	−9.65175	−0.760664
$162$	−14.3789	−1.12972
$163$	−16.7376	−1.31099	−0.655495	−	0.755200i	$-0.727540\pi$
$163$	−16.7376	−1.31099	−0.655495	+	0.755200i	$0.727540\pi$
$164$	−7.43071	−0.580241
$165$	1.99955	0.155665
$166$	15.1665	1.17715
$167$	−8.63834	−0.668455	−0.334228	−	0.942492i	$-0.608475\pi$
$167$	−8.63834	−0.668455	−0.334228	+	0.942492i	$0.608475\pi$
$168$	3.37392	0.260303
$169$	−3.13938	−0.241490
$170$	−36.2828	−2.78276
$171$	−15.0429	−1.15036
$172$	−33.7394	−2.57261
$173$	8.84659	0.672594	0.336297	−	0.941756i	$-0.390825\pi$
$173$	8.84659	0.672594	0.336297	+	0.941756i	$0.390825\pi$
$174$	0.556596	0.0421955
$175$	1.15658	0.0874295
$176$	−2.18938	−0.165031
$177$	−1.86343	−0.140064
$178$	8.54542	0.640506
$179$	2.51959	0.188323	0.0941615	−	0.995557i	$-0.469983\pi$
$179$	2.51959	0.188323	0.0941615	+	0.995557i	$0.469983\pi$
$180$	−17.0757	−1.27275
$181$	9.09400	0.675952	0.337976	−	0.941155i	$-0.390258\pi$
$181$	9.09400	0.675952	0.337976	+	0.941155i	$0.390258\pi$
$182$	21.1089	1.56469
$183$	−4.50033	−0.332674
$184$	−6.60069	−0.486609
$185$	−3.29950	−0.242584
$186$	−9.57032	−0.701730
$187$	13.1376	0.960716
$188$	−23.1879	−1.69115
$189$	9.30667	0.676961
$190$	−26.4906	−1.92183
$191$	18.7762	1.35860	0.679300	−	0.733861i	$-0.262284\pi$
$191$	18.7762	1.35860	0.679300	+	0.733861i	$0.262284\pi$
$192$	−6.95124	−0.501662
$193$	23.6400	1.70165	0.850823	−	0.525452i	$-0.176104\pi$
$193$	23.6400	1.70165	0.850823	+	0.525452i	$0.176104\pi$
$194$	−17.3446	−1.24527
$195$	3.63355	0.260204
$196$	6.33942	0.452816
$197$	−13.3249	−0.949358	−0.474679	−	0.880159i	$-0.657436\pi$
$197$	−13.3249	−0.949358	−0.474679	+	0.880159i	$0.657436\pi$
$198$	10.4003	0.739120
$199$	7.53099	0.533858	0.266929	−	0.963716i	$-0.413991\pi$
$199$	7.53099	0.533858	0.266929	+	0.963716i	$0.413991\pi$
$200$	0.790971	0.0559301
$201$	1.78019	0.125565
$202$	−40.1718	−2.82648
$203$	1.40885	0.0988817
$204$	12.0033	0.840396
$205$	−5.44594	−0.380361
$206$	−21.9320	−1.52808
$207$	−8.64146	−0.600623
$208$	−3.97851	−0.275860
$209$	9.59196	0.663490
$210$	7.77844	0.536763
$211$	18.0311	1.24131	0.620656	−	0.784083i	$-0.286866\pi$
$211$	18.0311	1.24131	0.620656	+	0.784083i	$0.286866\pi$
$212$	27.1414	1.86408
$213$	8.14717	0.558235
$214$	14.8327	1.01394
$215$	−24.7275	−1.68640
$216$	6.36470	0.433063
$217$	−24.2242	−1.64445
$218$	−23.1480	−1.56778
$219$	−2.79048	−0.188563
$220$	10.8882	0.734080
$221$	23.8734	1.60590
$222$	1.83612	0.123232
$223$	2.84006	0.190185	0.0950923	−	0.995468i	$-0.469685\pi$
$223$	2.84006	0.190185	0.0950923	+	0.995468i	$0.469685\pi$
$224$	−21.0485	−1.40636
$225$	1.03552	0.0690346
$226$	−25.1382	−1.67217
$227$	−27.8808	−1.85052	−0.925258	−	0.379339i	$-0.876152\pi$
$227$	−27.8808	−1.85052	−0.925258	+	0.379339i	$0.876152\pi$
$228$	8.76376	0.580394
$229$	−25.4075	−1.67898	−0.839488	−	0.543379i	$-0.817145\pi$
$229$	−25.4075	−1.67898	−0.839488	+	0.543379i	$0.817145\pi$
$230$	−15.2176	−1.00342
$231$	−2.81648	−0.185311
$232$	0.963491	0.0632563
$233$	25.5669	1.67494	0.837470	−	0.546483i	$-0.184034\pi$
$233$	25.5669	1.67494	0.837470	+	0.546483i	$0.184034\pi$
$234$	18.8993	1.23549
$235$	−16.9943	−1.10859
$236$	−10.1469	−0.660508
$237$	−2.28558	−0.148464
$238$	51.1064	3.31274
$239$	0.420456	0.0271970	0.0135985	−	0.999908i	$-0.495671\pi$
$239$	0.420456	0.0271970	0.0135985	+	0.999908i	$0.495671\pi$
$240$	−1.46605	−0.0946328
$241$	12.2342	0.788074	0.394037	−	0.919095i	$-0.371078\pi$
$241$	12.2342	0.788074	0.394037	+	0.919095i	$0.371078\pi$
$242$	17.7975	1.14407
$243$	12.7103	0.815367
$244$	−24.5057	−1.56882
$245$	4.64614	0.296831
$246$	3.03057	0.193222
$247$	17.4304	1.10907
$248$	−16.5666	−1.05198
$249$	−3.67727	−0.233038
$250$	25.6856	1.62450
$251$	−3.48824	−0.220176	−0.110088	−	0.993922i	$-0.535113\pi$
$251$	−3.48824	−0.220176	−0.110088	+	0.993922i	$0.535113\pi$
$252$	24.0522	1.51515
$253$	5.51014	0.346419
$254$	−46.1125	−2.89336
$255$	8.79715	0.550899
$256$	−6.96497	−0.435311
$257$	18.6762	1.16499	0.582496	−	0.812834i	$-0.302076\pi$
$257$	18.6762	1.16499	0.582496	+	0.812834i	$0.302076\pi$
$258$	13.7604	0.856687
$259$	4.64754	0.288784
$260$	19.7858	1.22706
$261$	1.26138	0.0780774
$262$	24.0379	1.48507
$263$	8.56310	0.528023	0.264012	−	0.964519i	$-0.414954\pi$
$263$	8.56310	0.528023	0.264012	+	0.964519i	$0.414954\pi$
$264$	−1.92615	−0.118547
$265$	19.8919	1.22195
$266$	37.3136	2.28784
$267$	−2.07193	−0.126800
$268$	9.69366	0.592135
$269$	−26.8580	−1.63756	−0.818782	−	0.574105i	$-0.805350\pi$
$269$	−26.8580	−1.63756	−0.818782	+	0.574105i	$0.805350\pi$
$270$	14.6736	0.893005
$271$	−0.00161485	−9.80953e−5 0	−4.90476e−5	−	1.00000i	$-0.500016\pi$
$271$	−0.00161485	−9.80953e−5 0	−4.90476e−5		1.00000i	$0.500016\pi$
$272$	−9.63231	−0.584045
$273$	−5.11807	−0.309760
$274$	−19.1411	−1.15636
$275$	−0.660288	−0.0398168
$276$	5.03438	0.303034
$277$	32.8331	1.97275	0.986374	−	0.164519i	$-0.0526073\pi$
$277$	32.8331	1.97275	0.986374	+	0.164519i	$0.0526073\pi$
$278$	4.78116	0.286755
$279$	−21.6886	−1.29846
$280$	13.4648	0.804675
$281$	26.6453	1.58953	0.794763	−	0.606920i	$-0.207595\pi$
$281$	26.6453	1.58953	0.794763	+	0.606920i	$0.207595\pi$
$282$	9.45703	0.563158
$283$	3.87916	0.230592	0.115296	−	0.993331i	$-0.463218\pi$
$283$	3.87916	0.230592	0.115296	+	0.993331i	$0.463218\pi$
$284$	44.3638	2.63251
$285$	6.42293	0.380462
$286$	−12.0510	−0.712588
$287$	7.67092	0.452800
$288$	−18.8453	−1.11047
$289$	40.7996	2.39998
$290$	2.22129	0.130439
$291$	4.20538	0.246524
$292$	−15.1950	−0.889222
$293$	22.0914	1.29060	0.645298	−	0.763931i	$-0.276733\pi$
$293$	22.0914	1.29060	0.645298	+	0.763931i	$0.276733\pi$
$294$	−2.58550	−0.150789
$295$	−7.43665	−0.432978
$296$	3.17839	0.184740
$297$	−5.31313	−0.308299
$298$	30.7571	1.78171
$299$	10.0129	0.579063
$300$	−0.603277	−0.0348302
$301$	34.8302	2.00758
$302$	−33.7145	−1.94005
$303$	9.74009	0.559553
$304$	−7.03270	−0.403353
$305$	−17.9601	−1.02839
$306$	45.7569	2.61575
$307$	30.0014	1.71227	0.856136	−	0.516751i	$-0.172859\pi$
$307$	30.0014	1.71227	0.856136	+	0.516751i	$0.172859\pi$
$308$	−15.3366	−0.873885
$309$	5.31766	0.302511
$310$	−38.1937	−2.16925
$311$	−21.1564	−1.19967	−0.599833	−	0.800125i	$-0.704766\pi$
$311$	−21.1564	−1.19967	−0.599833	+	0.800125i	$0.704766\pi$
$312$	−3.50018	−0.198158
$313$	16.7943	0.949270	0.474635	−	0.880183i	$-0.342580\pi$
$313$	16.7943	0.949270	0.474635	+	0.880183i	$0.342580\pi$
$314$	−32.9167	−1.85760
$315$	17.6278	0.993212
$316$	−12.4457	−0.700124
$317$	−2.06671	−0.116078	−0.0580390	−	0.998314i	$-0.518485\pi$
$317$	−2.06671	−0.116078	−0.0580390	+	0.998314i	$0.518485\pi$
$318$	−11.0695	−0.620745
$319$	−0.804304	−0.0450324
$320$	−27.7413	−1.55079
$321$	−3.59634	−0.200728
$322$	21.4349	1.19452
$323$	42.2004	2.34809
$324$	18.9841	1.05467
$325$	−1.19986	−0.0665565
$326$	37.1714	2.05873
$327$	5.61248	0.310371
$328$	5.24603	0.289664
$329$	23.9375	1.31972
$330$	−4.44067	−0.244451
$331$	−24.0859	−1.32388	−0.661940	−	0.749557i	$-0.730267\pi$
$331$	−24.0859	−1.32388	−0.661940	+	0.749557i	$0.730267\pi$
$332$	−20.0239	−1.09895
$333$	4.16107	0.228025
$334$	19.1843	1.04972
$335$	7.10445	0.388158
$336$	2.06501	0.112656
$337$	6.86511	0.373966	0.186983	−	0.982363i	$-0.440129\pi$
$337$	6.86511	0.373966	0.186983	+	0.982363i	$0.440129\pi$
$338$	6.97203	0.379229
$339$	6.09502	0.331036
$340$	47.9031	2.59791
$341$	13.8295	0.748909
$342$	33.4078	1.80649
$343$	14.6439	0.790695
$344$	23.8198	1.28428
$345$	3.68968	0.198646
$346$	−19.6468	−1.05622
$347$	−24.0184	−1.28937	−0.644687	−	0.764447i	$-0.723012\pi$
$347$	−24.0184	−1.28937	−0.644687	+	0.764447i	$0.723012\pi$
$348$	−0.734858	−0.0393925
$349$	−11.4291	−0.611784	−0.305892	−	0.952066i	$-0.598955\pi$
$349$	−11.4291	−0.611784	−0.305892	+	0.952066i	$0.598955\pi$
$350$	−2.56858	−0.137296
$351$	−9.65494	−0.515343
$352$	12.0165	0.640481
$353$	−7.87572	−0.419182	−0.209591	−	0.977789i	$-0.567213\pi$
$353$	−7.87572	−0.419182	−0.209591	+	0.977789i	$0.567213\pi$
$354$	4.13836	0.219951
$355$	32.5141	1.72567
$356$	−11.2823	−0.597959
$357$	−12.3913	−0.655817
$358$	−5.59559	−0.295736
$359$	−13.1723	−0.695206	−0.347603	−	0.937642i	$-0.613004\pi$
$359$	−13.1723	−0.695206	−0.347603	+	0.937642i	$0.613004\pi$
$360$	12.0554	0.635374
$361$	11.8112	0.621640
$362$	−20.1963	−1.06149
$363$	−4.31519	−0.226489
$364$	−27.8695	−1.46076
$365$	−11.1364	−0.582905
$366$	9.99450	0.522421
$367$	−21.4732	−1.12089	−0.560446	−	0.828191i	$-0.689370\pi$
$367$	−21.4732	−1.12089	−0.560446	+	0.828191i	$0.689370\pi$
$368$	−4.03996	−0.210597
$369$	6.86798	0.357533
$370$	7.32765	0.380947
$371$	−28.0188	−1.45467
$372$	12.6354	0.655116
$373$	−9.72183	−0.503377	−0.251689	−	0.967808i	$-0.580986\pi$
$373$	−9.72183	−0.503377	−0.251689	+	0.967808i	$0.580986\pi$
$374$	−29.1764	−1.50868
$375$	−6.22775	−0.321600
$376$	16.3705	0.844244
$377$	−1.46157	−0.0752746
$378$	−20.6686	−1.06308
$379$	−13.6311	−0.700182	−0.350091	−	0.936716i	$-0.613849\pi$
$379$	−13.6311	−0.700182	−0.350091	+	0.936716i	$0.613849\pi$
$380$	34.9748	1.79417
$381$	11.1805	0.572793
$382$	−41.6989	−2.13350
$383$	−36.5368	−1.86694	−0.933472	−	0.358651i	$-0.883237\pi$
$383$	−36.5368	−1.86694	−0.933472	+	0.358651i	$0.883237\pi$
$384$	7.94876	0.405633
$385$	−11.2402	−0.572851
$386$	−52.5006	−2.67221
$387$	31.1844	1.58519
$388$	22.8996	1.16255
$389$	−28.2080	−1.43020	−0.715101	−	0.699021i	$-0.753619\pi$
$389$	−28.2080	−1.43020	−0.715101	+	0.699021i	$0.753619\pi$
$390$	−8.06952	−0.408616
$391$	24.2422	1.22598
$392$	−4.47560	−0.226052
$393$	−5.82824	−0.293996
$394$	29.5923	1.49084
$395$	−9.12140	−0.458947
$396$	−13.7313	−0.690022
$397$	2.63815	0.132405	0.0662024	−	0.997806i	$-0.478912\pi$
$397$	2.63815	0.132405	0.0662024	+	0.997806i	$0.478912\pi$
$398$	−16.7251	−0.838353
$399$	−9.04707	−0.452920
$400$	0.484114	0.0242057
$401$	−20.7096	−1.03419	−0.517094	−	0.855929i	$-0.672986\pi$
$401$	−20.7096	−1.03419	−0.517094	+	0.855929i	$0.672986\pi$
$402$	−3.95350	−0.197183
$403$	25.1307	1.25185
$404$	53.0377	2.63873
$405$	13.9134	0.691362
$406$	−3.12882	−0.155281
$407$	−2.65326	−0.131517
$408$	−8.47423	−0.419537
$409$	18.7594	0.927594	0.463797	−	0.885942i	$-0.346487\pi$
$409$	18.7594	0.927594	0.463797	+	0.885942i	$0.346487\pi$
$410$	12.0945	0.597306
$411$	4.64097	0.228922
$412$	28.9563	1.42657
$413$	10.4749	0.515438
$414$	19.1913	0.943199
$415$	−14.6754	−0.720388
$416$	21.8362	1.07061
$417$	−1.15924	−0.0567684
$418$	−21.3021	−1.04192
$419$	18.0701	0.882782	0.441391	−	0.897315i	$-0.354485\pi$
$419$	18.0701	0.882782	0.441391	+	0.897315i	$0.354485\pi$
$420$	−10.2696	−0.501108
$421$	−24.9752	−1.21722	−0.608609	−	0.793471i	$-0.708272\pi$
$421$	−24.9752	−1.21722	−0.608609	+	0.793471i	$0.708272\pi$
$422$	−40.0441	−1.94932
$423$	21.4319	1.04205
$424$	−19.1617	−0.930573
$425$	−2.90498	−0.140912
$426$	−18.0935	−0.876634
$427$	25.2979	1.22425
$428$	−19.5832	−0.946587
$429$	2.92188	0.141070
$430$	54.9157	2.64827
$431$	26.7986	1.29084	0.645421	−	0.763827i	$-0.276682\pi$
$431$	26.7986	1.29084	0.645421	+	0.763827i	$0.276682\pi$
$432$	3.89552	0.187423
$433$	20.5293	0.986576	0.493288	−	0.869866i	$-0.335795\pi$
$433$	20.5293	0.986576	0.493288	+	0.869866i	$0.335795\pi$
$434$	53.7980	2.58239
$435$	−0.538575	−0.0258227
$436$	30.5617	1.46364
$437$	17.6996	0.846686
$438$	6.19720	0.296114
$439$	16.6071	0.792612	0.396306	−	0.918119i	$-0.370292\pi$
$439$	16.6071	0.792612	0.396306	+	0.918119i	$0.370292\pi$
$440$	−7.68698	−0.366462
$441$	−5.85934	−0.279016
$442$	−53.0189	−2.52185
$443$	−32.5471	−1.54636	−0.773180	−	0.634187i	$-0.781335\pi$
$443$	−32.5471	−1.54636	−0.773180	+	0.634187i	$0.781335\pi$
$444$	−2.42417	−0.115046
$445$	−8.26874	−0.391976
$446$	−6.30731	−0.298660
$447$	−7.45737	−0.352722
$448$	39.0753	1.84613
$449$	16.8153	0.793564	0.396782	−	0.917913i	$-0.370127\pi$
$449$	16.8153	0.793564	0.396782	+	0.917913i	$0.370127\pi$
$450$	−2.29972	−0.108410
$451$	−4.37929	−0.206213
$452$	33.1892	1.56109
$453$	8.17443	0.384068
$454$	61.9187	2.90599
$455$	−20.4254	−0.957559
$456$	−6.18716	−0.289741
$457$	28.6808	1.34163	0.670816	−	0.741624i	$-0.265944\pi$
$457$	28.6808	1.34163	0.670816	+	0.741624i	$0.265944\pi$
$458$	56.4258	2.63661
$459$	−23.3755	−1.09107
$460$	20.0914	0.936767
$461$	29.1801	1.35905	0.679526	−	0.733652i	$-0.262186\pi$
$461$	29.1801	1.35905	0.679526	+	0.733652i	$0.262186\pi$
$462$	6.25494	0.291006
$463$	8.33566	0.387391	0.193695	−	0.981062i	$-0.437953\pi$
$463$	8.33566	0.387391	0.193695	+	0.981062i	$0.437953\pi$
$464$	0.589705	0.0273764
$465$	9.26046	0.429443
$466$	−56.7798	−2.63027
$467$	21.6506	1.00187	0.500935	−	0.865485i	$-0.332989\pi$
$467$	21.6506	1.00187	0.500935	+	0.865485i	$0.332989\pi$
$468$	−24.9523	−1.15342
$469$	−10.0070	−0.462082
$470$	37.7416	1.74089
$471$	7.98101	0.367746
$472$	7.16367	0.329734
$473$	−19.8844	−0.914284
$474$	5.07590	0.233144
$475$	−2.12097	−0.0973167
$476$	−67.4744	−3.09268
$477$	−25.0860	−1.14861
$478$	−0.933763	−0.0427093
$479$	−10.5654	−0.482745	−0.241373	−	0.970433i	$-0.577598\pi$
$479$	−10.5654	−0.482745	−0.241373	+	0.970433i	$0.577598\pi$
$480$	8.04644	0.367268
$481$	−4.82146	−0.219840
$482$	−27.1701	−1.23756
$483$	−5.19713	−0.236477
$484$	−23.4975	−1.06807
$485$	16.7830	0.762079
$486$	−28.2275	−1.28043
$487$	−8.56661	−0.388190	−0.194095	−	0.980983i	$-0.562177\pi$
$487$	−8.56661	−0.388190	−0.194095	+	0.980983i	$0.562177\pi$
$488$	17.3009	0.783174
$489$	−9.01260	−0.407564
$490$	−10.3183	−0.466134
$491$	−15.6703	−0.707191	−0.353595	−	0.935399i	$-0.615041\pi$
$491$	−15.6703	−0.707191	−0.353595	+	0.935399i	$0.615041\pi$
$492$	−4.00117	−0.180387
$493$	−3.53858	−0.159370
$494$	−38.7099	−1.74164
$495$	−10.0636	−0.452325
$496$	−10.1396	−0.455282
$497$	−45.7980	−2.05432
$498$	8.16661	0.365955
$499$	16.4391	0.735916	0.367958	−	0.929842i	$-0.380057\pi$
$499$	16.4391	0.735916	0.367958	+	0.929842i	$0.380057\pi$
$500$	−33.9120	−1.51659
$501$	−4.65144	−0.207811
$502$	7.74681	0.345757
$503$	−30.7708	−1.37200	−0.686001	−	0.727600i	$-0.740636\pi$
$503$	−30.7708	−1.37200	−0.686001	+	0.727600i	$0.740636\pi$
$504$	−16.9807	−0.756380
$505$	38.8712	1.72974
$506$	−12.2371	−0.544005
$507$	−1.69044	−0.0750752
$508$	60.8810	2.70116
$509$	2.47723	0.109801	0.0549007	−	0.998492i	$-0.482516\pi$
$509$	2.47723	0.109801	0.0549007	+	0.998492i	$0.482516\pi$
$510$	−19.5370	−0.865113
$511$	15.6863	0.693919
$512$	−14.0557	−0.621181
$513$	−17.0668	−0.753517
$514$	−41.4768	−1.82946
$515$	21.2219	0.935150
$516$	−18.1675	−0.799779
$517$	−13.6658	−0.601021
$518$	−10.3214	−0.453497
$519$	4.76358	0.209098
$520$	−13.9687	−0.612566
$521$	−41.4469	−1.81582	−0.907911	−	0.419163i	$-0.862324\pi$
$521$	−41.4469	−1.81582	−0.907911	+	0.419163i	$0.862324\pi$
$522$	−2.80131	−0.122610
$523$	−8.50784	−0.372022	−0.186011	−	0.982548i	$-0.559556\pi$
$523$	−8.50784	−0.372022	−0.186011	+	0.982548i	$0.559556\pi$
$524$	−31.7365	−1.38642
$525$	0.622779	0.0271803
$526$	−19.0172	−0.829190
$527$	60.8437	2.65039
$528$	−1.17890	−0.0513052
$529$	−12.8324	−0.557931
$530$	−44.1765	−1.91891
$531$	9.37850	0.406992
$532$	−49.2641	−2.13587
$533$	−7.95798	−0.344698
$534$	4.60141	0.199122
$535$	−14.3524	−0.620510
$536$	−6.84367	−0.295601
$537$	1.35671	0.0585463
$538$	59.6472	2.57158
$539$	3.73615	0.160927
$540$	−19.3731	−0.833685
$541$	6.61719	0.284495	0.142248	−	0.989831i	$-0.454567\pi$
$541$	6.61719	0.284495	0.142248	+	0.989831i	$0.454567\pi$
$542$	0.00358632	0.000154046 0
$543$	4.89680	0.210142
$544$	52.8673	2.26667
$545$	22.3985	0.959448
$546$	11.3664	0.486436
$547$	−10.1270	−0.432999	−0.216499	−	0.976283i	$-0.569464\pi$
$547$	−10.1270	−0.432999	−0.216499	+	0.976283i	$0.569464\pi$
$548$	25.2715	1.07954
$549$	22.6499	0.966673
$550$	1.46639	0.0625271
$551$	−2.58358	−0.110064
$552$	−3.55424	−0.151278
$553$	12.8480	0.546353
$554$	−72.9168	−3.09794
$555$	−1.77667	−0.0754153
$556$	−6.31244	−0.267707
$557$	15.0203	0.636431	0.318216	−	0.948018i	$-0.396916\pi$
$557$	15.0203	0.636431	0.318216	+	0.948018i	$0.396916\pi$
$558$	48.1667	2.03906
$559$	−36.1336	−1.52829
$560$	8.24113	0.348251
$561$	7.07413	0.298670
$562$	−59.1748	−2.49614
$563$	38.6443	1.62866	0.814331	−	0.580401i	$-0.197104\pi$
$563$	38.6443	1.62866	0.814331	+	0.580401i	$0.197104\pi$
$564$	−12.4858	−0.525749
$565$	24.3243	1.02333
$566$	−8.61496	−0.362114
$567$	−19.5978	−0.823031
$568$	−31.3206	−1.31418
$569$	−19.2767	−0.808119	−0.404060	−	0.914733i	$-0.632401\pi$
$569$	−19.2767	−0.808119	−0.404060	+	0.914733i	$0.632401\pi$
$570$	−14.2643	−0.597464
$571$	−33.1316	−1.38651	−0.693257	−	0.720690i	$-0.743825\pi$
$571$	−33.1316	−1.38651	−0.693257	+	0.720690i	$0.743825\pi$
$572$	15.9105	0.665253
$573$	10.1103	0.422365
$574$	−17.0358	−0.711062
$575$	−1.21840	−0.0508107
$576$	34.9851	1.45771
$577$	24.8657	1.03517	0.517586	−	0.855631i	$-0.326831\pi$
$577$	24.8657	1.03517	0.517586	+	0.855631i	$0.326831\pi$
$578$	−90.6092	−3.76885
$579$	12.7293	0.529013
$580$	−2.93271	−0.121774
$581$	20.6712	0.857585
$582$	−9.33946	−0.387133
$583$	15.9958	0.662479
$584$	10.7276	0.443911
$585$	−18.2874	−0.756092
$586$	−49.0614	−2.02671
$587$	15.5636	0.642379	0.321190	−	0.947015i	$-0.395917\pi$
$587$	15.5636	0.642379	0.321190	+	0.947015i	$0.395917\pi$
$588$	3.41356	0.140773
$589$	44.4229	1.83041
$590$	16.5156	0.679935
$591$	−7.17497	−0.295139
$592$	1.94534	0.0799528
$593$	6.21442	0.255195	0.127598	−	0.991826i	$-0.459273\pi$
$593$	6.21442	0.255195	0.127598	+	0.991826i	$0.459273\pi$
$594$	11.7996	0.484143
$595$	−49.4517	−2.02732
$596$	−40.6077	−1.66335
$597$	4.05517	0.165967
$598$	−22.2371	−0.909341
$599$	−21.2395	−0.867822	−0.433911	−	0.900956i	$-0.642867\pi$
$599$	−21.2395	−0.867822	−0.433911	+	0.900956i	$0.642867\pi$
$600$	0.425910	0.0173877
$601$	−6.69526	−0.273105	−0.136553	−	0.990633i	$-0.543602\pi$
$601$	−6.69526	−0.273105	−0.136553	+	0.990633i	$0.543602\pi$
$602$	−77.3520	−3.15263
$603$	−8.95956	−0.364862
$604$	44.5123	1.81118
$605$	−17.2213	−0.700144
$606$	−21.6311	−0.878704
$607$	45.3486	1.84064	0.920321	−	0.391163i	$-0.127927\pi$
$607$	45.3486	1.84064	0.920321	+	0.391163i	$0.127927\pi$
$608$	38.5992	1.56541
$609$	0.758615	0.0307406
$610$	39.8865	1.61496
$611$	−24.8333	−1.00465
$612$	−60.4116	−2.44199
$613$	−19.0678	−0.770141	−0.385070	−	0.922887i	$-0.625823\pi$
$613$	−19.0678	−0.770141	−0.385070	+	0.922887i	$0.625823\pi$
$614$	−66.6282	−2.68889
$615$	−2.93245	−0.118248
$616$	10.8276	0.436255
$617$	32.1227	1.29321	0.646606	−	0.762824i	$-0.276188\pi$
$617$	32.1227	1.29321	0.646606	+	0.762824i	$0.276188\pi$
$618$	−11.8096	−0.475053
$619$	−22.1935	−0.892031	−0.446015	−	0.895025i	$-0.647157\pi$
$619$	−22.1935	−0.892031	−0.446015	+	0.895025i	$0.647157\pi$
$620$	50.4260	2.02516
$621$	−9.80407	−0.393424
$622$	46.9847	1.88392
$623$	11.6470	0.466627
$624$	−2.14229	−0.0857601
$625$	−22.9435	−0.917739
$626$	−37.2974	−1.49070
$627$	5.16493	0.206267
$628$	43.4590	1.73420
$629$	−11.6732	−0.465440
$630$	−39.1483	−1.55971
$631$	−48.4256	−1.92779	−0.963897	−	0.266276i	$-0.914207\pi$
$631$	−48.4256	−1.92779	−0.963897	+	0.266276i	$0.914207\pi$
$632$	8.78658	0.349511
$633$	9.70911	0.385903
$634$	4.58982	0.182285
$635$	44.6195	1.77067
$636$	14.6147	0.579510
$637$	6.78926	0.269000
$638$	1.78623	0.0707174
$639$	−41.0042	−1.62210
$640$	31.7223	1.25393
$641$	33.7797	1.33422	0.667108	−	0.744961i	$-0.267532\pi$
$641$	33.7797	1.33422	0.667108	+	0.744961i	$0.267532\pi$
$642$	7.98687	0.315217
$643$	46.0268	1.81512	0.907559	−	0.419924i	$-0.137943\pi$
$643$	46.0268	1.81512	0.907559	+	0.419924i	$0.137943\pi$
$644$	−28.2999	−1.11517
$645$	−13.3149	−0.524274
$646$	−93.7201	−3.68737
$647$	−17.2081	−0.676519	−0.338259	−	0.941053i	$-0.609838\pi$
$647$	−17.2081	−0.676519	−0.338259	+	0.941053i	$0.609838\pi$
$648$	−13.4027	−0.526507
$649$	−5.98010	−0.234739
$650$	2.66470	0.104518
$651$	−13.0439	−0.511230
$652$	−49.0764	−1.92198
$653$	−0.831460	−0.0325375	−0.0162688	−	0.999868i	$-0.505179\pi$
$653$	−0.831460	−0.0325375	−0.0162688	+	0.999868i	$0.505179\pi$
$654$	−12.4644	−0.487396
$655$	−23.2596	−0.908828
$656$	3.21084	0.125362
$657$	14.0443	0.547921
$658$	−53.1612	−2.07244
$659$	−20.7946	−0.810044	−0.405022	−	0.914307i	$-0.632736\pi$
$659$	−20.7946	−0.810044	−0.405022	+	0.914307i	$0.632736\pi$
$660$	5.86289	0.228213
$661$	9.05262	0.352106	0.176053	−	0.984381i	$-0.443667\pi$
$661$	9.05262	0.352106	0.176053	+	0.984381i	$0.443667\pi$
$662$	53.4907	2.07898
$663$	12.8550	0.499247
$664$	14.1367	0.548611
$665$	−36.1055	−1.40011
$666$	−9.24104	−0.358083
$667$	−1.48414	−0.0574663
$668$	−25.3285	−0.979990
$669$	1.52927	0.0591251
$670$	−15.7778	−0.609550
$671$	−14.4424	−0.557545
$672$	−11.3339	−0.437214
$673$	−20.3960	−0.786208	−0.393104	−	0.919494i	$-0.628599\pi$
$673$	−20.3960	−0.786208	−0.393104	+	0.919494i	$0.628599\pi$
$674$	−15.2463	−0.587264
$675$	1.17484	0.0452195
$676$	−9.20498	−0.354038
$677$	4.32547	0.166241	0.0831206	−	0.996539i	$-0.473511\pi$
$677$	4.32547	0.166241	0.0831206	+	0.996539i	$0.473511\pi$
$678$	−13.5360	−0.519848
$679$	−23.6399	−0.907216
$680$	−33.8193	−1.29691
$681$	−15.0128	−0.575293
$682$	−30.7130	−1.17606
$683$	7.46372	0.285591	0.142796	−	0.989752i	$-0.454391\pi$
$683$	7.46372	0.285591	0.142796	+	0.989752i	$0.454391\pi$
$684$	−44.1074	−1.68649
$685$	18.5214	0.707665
$686$	−32.5216	−1.24168
$687$	−13.6810	−0.521964
$688$	14.5790	0.555818
$689$	29.0673	1.10738
$690$	−8.19416	−0.311946
$691$	25.9084	0.985601	0.492800	−	0.870142i	$-0.335973\pi$
$691$	25.9084	0.985601	0.492800	+	0.870142i	$0.335973\pi$
$692$	25.9391	0.986057
$693$	14.1752	0.538470
$694$	53.3408	2.02479
$695$	−4.62636	−0.175488
$696$	0.518806	0.0196653
$697$	−19.2670	−0.729788
$698$	25.3821	0.960726
$699$	13.7669	0.520710
$700$	3.39122	0.128176
$701$	−48.9971	−1.85059	−0.925297	−	0.379244i	$-0.876184\pi$
$701$	−48.9971	−1.85059	−0.925297	+	0.379244i	$0.876184\pi$
$702$	21.4420	0.809277
$703$	−8.52277	−0.321442
$704$	−22.3079	−0.840760
$705$	−9.15084	−0.344641
$706$	17.4907	0.658270
$707$	−54.7523	−2.05917
$708$	−5.46376	−0.205341
$709$	−41.5691	−1.56116	−0.780580	−	0.625056i	$-0.785076\pi$
$709$	−41.5691	−1.56116	−0.780580	+	0.625056i	$0.785076\pi$
$710$	−72.2085	−2.70993
$711$	11.5032	0.431403
$712$	7.96522	0.298509
$713$	25.5189	0.955691
$714$	27.5190	1.02987
$715$	11.6608	0.436088
$716$	7.38770	0.276091
$717$	0.226401	0.00845509
$718$	29.2534	1.09173
$719$	7.44690	0.277723	0.138861	−	0.990312i	$-0.455656\pi$
$719$	7.44690	0.277723	0.138861	+	0.990312i	$0.455656\pi$
$720$	7.37850	0.274981
$721$	−29.8923	−1.11325
$722$	−26.2306	−0.976203
$723$	6.58768	0.244998
$724$	26.6645	0.990980
$725$	0.177847	0.00660508
$726$	9.58333	0.355671
$727$	−33.0324	−1.22510	−0.612551	−	0.790431i	$-0.709857\pi$
$727$	−33.0324	−1.22510	−0.612551	+	0.790431i	$0.709857\pi$
$728$	19.6757	0.729229
$729$	−12.5797	−0.465913
$730$	24.7321	0.915375
$731$	−87.4825	−3.23566
$732$	−13.1954	−0.487718
$733$	28.5504	1.05453	0.527266	−	0.849700i	$-0.323217\pi$
$733$	28.5504	1.05453	0.527266	+	0.849700i	$0.323217\pi$
$734$	47.6884	1.76021
$735$	2.50178	0.0922797
$736$	22.1735	0.817325
$737$	5.71297	0.210440
$738$	−15.2526	−0.561457
$739$	2.42161	0.0890805	0.0445403	−	0.999008i	$-0.485818\pi$
$739$	2.42161	0.0890805	0.0445403	+	0.999008i	$0.485818\pi$
$740$	−9.67449	−0.355641
$741$	9.38563	0.344790
$742$	62.2252	2.28436
$743$	6.97604	0.255926	0.127963	−	0.991779i	$-0.459156\pi$
$743$	6.97604	0.255926	0.127963	+	0.991779i	$0.459156\pi$
$744$	−8.92053	−0.327042
$745$	−29.7612	−1.09037
$746$	21.5906	0.790487
$747$	18.5075	0.677152
$748$	38.5208	1.40846
$749$	20.2162	0.738685
$750$	13.8308	0.505030
$751$	−19.4133	−0.708403	−0.354201	−	0.935169i	$-0.615247\pi$
$751$	−19.4133	−0.708403	−0.354201	+	0.935169i	$0.615247\pi$
$752$	10.0196	0.365377
$753$	−1.87830	−0.0684489
$754$	3.24590	0.118209
$755$	32.6229	1.18727
$756$	27.2881	0.992460
$757$	47.8956	1.74080	0.870398	−	0.492349i	$-0.163862\pi$
$757$	47.8956	1.74080	0.870398	+	0.492349i	$0.163862\pi$
$758$	30.2724	1.09954
$759$	2.96701	0.107696
$760$	−24.6920	−0.895674
$761$	34.5212	1.25139	0.625696	−	0.780067i	$-0.284815\pi$
$761$	34.5212	1.25139	0.625696	+	0.780067i	$0.284815\pi$
$762$	−24.8300	−0.899495
$763$	−31.5496	−1.14217
$764$	55.0538	1.99178
$765$	−44.2754	−1.60078
$766$	81.1422	2.93179
$767$	−10.8669	−0.392382
$768$	−3.75039	−0.135331
$769$	−8.80864	−0.317648	−0.158824	−	0.987307i	$-0.550770\pi$
$769$	−8.80864	−0.317648	−0.158824	+	0.987307i	$0.550770\pi$
$770$	24.9625	0.899587
$771$	10.0565	0.362176
$772$	69.3150	2.49470
$773$	35.0938	1.26224	0.631118	−	0.775687i	$-0.282596\pi$
$773$	35.0938	1.26224	0.631118	+	0.775687i	$0.282596\pi$
$774$	−69.2553	−2.48933
$775$	−3.05797	−0.109845
$776$	−16.1670	−0.580361
$777$	2.50254	0.0897781
$778$	62.6453	2.24594
$779$	−14.0671	−0.504006
$780$	10.6540	0.381473
$781$	26.1459	0.935573
$782$	−53.8378	−1.92524
$783$	1.43108	0.0511427
$784$	−2.73929	−0.0978319
$785$	31.8510	1.13681
$786$	12.9436	0.461681
$787$	−20.5942	−0.734105	−0.367052	−	0.930200i	$-0.619633\pi$
$787$	−20.5942	−0.734105	−0.367052	+	0.930200i	$0.619633\pi$
$788$	−39.0699	−1.39181
$789$	4.61093	0.164153
$790$	20.2571	0.720716
$791$	−34.2622	−1.21822
$792$	9.69420	0.344468
$793$	−26.2446	−0.931973
$794$	−5.85889	−0.207924
$795$	10.7111	0.379882
$796$	22.0817	0.782664
$797$	−41.4422	−1.46796	−0.733979	−	0.679172i	$-0.762339\pi$
$797$	−41.4422	−1.46796	−0.733979	+	0.679172i	$0.762339\pi$
$798$	20.0920	0.711251
$799$	−60.1235	−2.12702
$800$	−2.65708	−0.0939419
$801$	10.4279	0.368451
$802$	45.9925	1.62405
$803$	−8.95521	−0.316022
$804$	5.21970	0.184084
$805$	−20.7409	−0.731022
$806$	−55.8112	−1.96587
$807$	−14.4621	−0.509090
$808$	−37.4443	−1.31729
$809$	29.4107	1.03402	0.517012	−	0.855978i	$-0.327044\pi$
$809$	29.4107	1.03402	0.517012	+	0.855978i	$0.327044\pi$
$810$	−30.8993	−1.08569
$811$	16.1173	0.565954	0.282977	−	0.959127i	$-0.408678\pi$
$811$	16.1173	0.565954	0.282977	+	0.959127i	$0.408678\pi$
$812$	4.13089	0.144966
$813$	−0.000869541 0	−3.04961e−5 0
$814$	5.89245	0.206530
$815$	−35.9679	−1.25990
$816$	−5.18666	−0.181569
$817$	−63.8723	−2.23461
$818$	−41.6616	−1.45666
$819$	25.7589	0.900089
$820$	−15.9681	−0.557629
$821$	50.0375	1.74632	0.873160	−	0.487433i	$-0.162067\pi$
$821$	50.0375	1.74632	0.873160	+	0.487433i	$0.162067\pi$
$822$	−10.3068	−0.359491
$823$	39.8345	1.38854	0.694271	−	0.719713i	$-0.255727\pi$
$823$	39.8345	1.38854	0.694271	+	0.719713i	$0.255727\pi$
$824$	−20.4429	−0.712164
$825$	−0.355542	−0.0123784
$826$	−23.2631	−0.809427
$827$	−10.4689	−0.364038	−0.182019	−	0.983295i	$-0.558263\pi$
$827$	−10.4689	−0.364038	−0.182019	+	0.983295i	$0.558263\pi$
$828$	−25.3377	−0.880545
$829$	−22.1038	−0.767697	−0.383849	−	0.923396i	$-0.625402\pi$
$829$	−22.1038	−0.767697	−0.383849	+	0.923396i	$0.625402\pi$
$830$	32.5917	1.13127
$831$	17.6794	0.613293
$832$	−40.5375	−1.40539
$833$	16.4374	0.569522
$834$	2.57449	0.0891472
$835$	−18.5632	−0.642406
$836$	28.1246	0.972710
$837$	−24.6065	−0.850526
$838$	−40.1307	−1.38629
$839$	11.9289	0.411833	0.205916	−	0.978570i	$-0.433982\pi$
$839$	11.9289	0.411833	0.205916	+	0.978570i	$0.433982\pi$
$840$	7.25031	0.250159
$841$	−28.7834	−0.992530
$842$	55.4658	1.91148
$843$	14.3476	0.494156
$844$	52.8691	1.81983
$845$	−6.74630	−0.232080
$846$	−47.5966	−1.63640
$847$	24.2572	0.833486
$848$	−11.7279	−0.402739
$849$	2.08879	0.0716870
$850$	6.45147	0.221284
$851$	−4.89594	−0.167831
$852$	23.8884	0.818402
$853$	19.1025	0.654059	0.327029	−	0.945014i	$-0.393952\pi$
$853$	19.1025	0.654059	0.327029	+	0.945014i	$0.393952\pi$
$854$	−56.1824	−1.92252
$855$	−32.3262	−1.10553
$856$	13.8256	0.472549
$857$	10.8229	0.369702	0.184851	−	0.982767i	$-0.440820\pi$
$857$	10.8229	0.369702	0.184851	+	0.982767i	$0.440820\pi$
$858$	−6.48901	−0.221531
$859$	12.8514	0.438485	0.219243	−	0.975670i	$-0.429641\pi$
$859$	12.8514	0.438485	0.219243	+	0.975670i	$0.429641\pi$
$860$	−72.5037	−2.47235
$861$	4.13052	0.140768
$862$	−59.5152	−2.02710
$863$	−46.0704	−1.56825	−0.784127	−	0.620601i	$-0.786889\pi$
$863$	−46.0704	−1.56825	−0.784127	+	0.620601i	$0.786889\pi$
$864$	−21.3807	−0.727386
$865$	19.0107	0.646383
$866$	−45.5922	−1.54929
$867$	21.9692	0.746112
$868$	−71.0279	−2.41085
$869$	−7.33487	−0.248819
$870$	1.19609	0.0405511
$871$	10.3815	0.351764
$872$	−21.5763	−0.730667
$873$	−21.1654	−0.716341
$874$	−39.3078	−1.32961
$875$	35.0083	1.18350
$876$	−8.18199	−0.276444
$877$	−3.57284	−0.120646	−0.0603232	−	0.998179i	$-0.519213\pi$
$877$	−3.57284	−0.120646	−0.0603232	+	0.998179i	$0.519213\pi$
$878$	−36.8815	−1.24469
$879$	11.8955	0.401224
$880$	−4.70482	−0.158600
$881$	21.6244	0.728544	0.364272	−	0.931293i	$-0.381318\pi$
$881$	21.6244	0.728544	0.364272	+	0.931293i	$0.381318\pi$
$882$	13.0126	0.438158
$883$	−27.9123	−0.939322	−0.469661	−	0.882847i	$-0.655624\pi$
$883$	−27.9123	−0.939322	−0.469661	+	0.882847i	$0.655624\pi$
$884$	69.9994	2.35433
$885$	−4.00437	−0.134605
$886$	72.2817	2.42835
$887$	−36.8709	−1.23800	−0.619002	−	0.785390i	$-0.712463\pi$
$887$	−36.8709	−1.23800	−0.619002	+	0.785390i	$0.712463\pi$
$888$	1.71145	0.0574325
$889$	−62.8492	−2.10789
$890$	18.3635	0.615546
$891$	11.1883	0.374822
$892$	8.32736	0.278821
$893$	−43.8971	−1.46896
$894$	16.5616	0.553902
$895$	5.41442	0.180984
$896$	−44.6826	−1.49274
$897$	5.39161	0.180021
$898$	−37.3440	−1.24619
$899$	−3.72495	−0.124234
$900$	3.03625	0.101208
$901$	70.3746	2.34452
$902$	9.72568	0.323830
$903$	18.7548	0.624121
$904$	−23.4314	−0.779317
$905$	19.5424	0.649610
$906$	−18.1541	−0.603128
$907$	−4.96631	−0.164904	−0.0824518	−	0.996595i	$-0.526275\pi$
$907$	−4.96631	−0.164904	−0.0824518	+	0.996595i	$0.526275\pi$
$908$	−81.7495	−2.71295
$909$	−49.0212	−1.62593
$910$	45.3615	1.50372
$911$	−40.6003	−1.34515	−0.672573	−	0.740031i	$-0.734811\pi$
$911$	−40.6003	−1.34515	−0.672573	+	0.740031i	$0.734811\pi$
$912$	−3.78686	−0.125395
$913$	−11.8011	−0.390559
$914$	−63.6953	−2.10685
$915$	−9.67090	−0.319710
$916$	−74.4974	−2.46146
$917$	32.7625	1.08191
$918$	51.9130	1.71338
$919$	−12.7161	−0.419466	−0.209733	−	0.977759i	$-0.567259\pi$
$919$	−12.7161	−0.419466	−0.209733	+	0.977759i	$0.567259\pi$
$920$	−14.1844	−0.467647
$921$	16.1547	0.532315
$922$	−64.8041	−2.13421
$923$	47.5119	1.56387
$924$	−8.25822	−0.271676
$925$	0.586687	0.0192902
$926$	−18.5121	−0.608346
$927$	−26.7634	−0.879025
$928$	−3.23662	−0.106247
$929$	−32.8769	−1.07865	−0.539327	−	0.842096i	$-0.681321\pi$
$929$	−32.8769	−1.07865	−0.539327	+	0.842096i	$0.681321\pi$
$930$	−20.5659	−0.674384
$931$	12.0012	0.393323
$932$	74.9647	2.45555
$933$	−11.3919	−0.372956
$934$	−48.0824	−1.57330
$935$	28.2318	0.923277
$936$	17.6161	0.575802
$937$	−33.4881	−1.09401	−0.547005	−	0.837129i	$-0.684232\pi$
$937$	−33.4881	−1.09401	−0.547005	+	0.837129i	$0.684232\pi$
$938$	22.2240	0.725638
$939$	9.04314	0.295112
$940$	−49.8291	−1.62525
$941$	21.5161	0.701406	0.350703	−	0.936487i	$-0.385943\pi$
$941$	21.5161	0.701406	0.350703	+	0.936487i	$0.385943\pi$
$942$	−17.7245	−0.577495
$943$	−8.08090	−0.263150
$944$	4.38453	0.142704
$945$	19.9994	0.650580
$946$	44.1599	1.43576
$947$	26.5788	0.863694	0.431847	−	0.901947i	$-0.357862\pi$
$947$	26.5788	0.863694	0.431847	+	0.901947i	$0.357862\pi$
$948$	−6.70156	−0.217657
$949$	−16.2733	−0.528252
$950$	4.71032	0.152823
$951$	−1.11285	−0.0360867
$952$	47.6365	1.54391
$953$	17.5374	0.568094	0.284047	−	0.958810i	$-0.408323\pi$
$953$	17.5374	0.568094	0.284047	+	0.958810i	$0.408323\pi$
$954$	55.7118	1.80374
$955$	40.3488	1.30566
$956$	1.23282	0.0398723
$957$	−0.433089	−0.0139998
$958$	23.4640	0.758087
$959$	−26.0884	−0.842440
$960$	−14.9377	−0.482113
$961$	33.0481	1.06607
$962$	10.7077	0.345229
$963$	18.1001	0.583268
$964$	35.8719	1.15536
$965$	50.8008	1.63533
$966$	11.5420	0.371356
$967$	3.93359	0.126496	0.0632478	−	0.997998i	$-0.479854\pi$
$967$	3.93359	0.126496	0.0632478	+	0.997998i	$0.479854\pi$
$968$	16.5891	0.533195
$969$	22.7234	0.729981
$970$	−37.2723	−1.19674
$971$	−44.8558	−1.43949	−0.719746	−	0.694238i	$-0.755742\pi$
$971$	−44.8558	−1.43949	−0.719746	+	0.694238i	$0.755742\pi$
$972$	37.2680	1.19537
$973$	6.51650	0.208909
$974$	19.0250	0.609601
$975$	−0.646085	−0.0206913
$976$	10.5890	0.338946
$977$	−43.4251	−1.38929	−0.694646	−	0.719352i	$-0.744439\pi$
$977$	−43.4251	−1.38929	−0.694646	+	0.719352i	$0.744439\pi$
$978$	20.0155	0.640025
$979$	−6.64922	−0.212510
$980$	13.6230	0.435170
$981$	−28.2472	−0.901865
$982$	34.8011	1.11055
$983$	52.4123	1.67169	0.835846	−	0.548964i	$-0.184978\pi$
$983$	52.4123	1.67169	0.835846	+	0.548964i	$0.184978\pi$
$984$	2.82480	0.0900515
$985$	−28.6342	−0.912362
$986$	7.85861	0.250269
$987$	12.8895	0.410277
$988$	51.1076	1.62595
$989$	−36.6917	−1.16673
$990$	22.3496	0.710317
$991$	10.4746	0.332738	0.166369	−	0.986064i	$-0.446796\pi$
$991$	10.4746	0.332738	0.166369	+	0.986064i	$0.446796\pi$
$992$	55.6516	1.76694
$993$	−12.9694	−0.411571
$994$	101.710	3.22604
$995$	16.1836	0.513054
$996$	−10.7821	−0.341645
$997$	−41.5065	−1.31452	−0.657261	−	0.753663i	$-0.728285\pi$
$997$	−41.5065	−1.31452	−0.657261	+	0.753663i	$0.728285\pi$
$998$	−36.5086	−1.15566
$999$	4.72089	0.149362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3023.2.a.c.1.20	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3023.2.a.c.1.20	✓	149	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:	\( N \)	\(=\)	\( 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22083 q^{2} +0.538465 q^{3} +2.93210 q^{4} +2.14893 q^{5} -1.19584 q^{6} -3.02689 q^{7} -2.07005 q^{8} -2.71006 q^{9} +O(q^{10})\)	\(q-2.22083 q^{2} +0.538465 q^{3} +2.93210 q^{4} +2.14893 q^{5} -1.19584 q^{6} -3.02689 q^{7} -2.07005 q^{8} -2.71006 q^{9} -4.77242 q^{10} +1.72804 q^{11} +1.57883 q^{12} +3.14016 q^{13} +6.72222 q^{14} +1.15712 q^{15} -1.26697 q^{16} +7.60261 q^{17} +6.01858 q^{18} +5.55078 q^{19} +6.30088 q^{20} -1.62987 q^{21} -3.83769 q^{22} +3.18867 q^{23} -1.11465 q^{24} -0.382103 q^{25} -6.97378 q^{26} -3.07466 q^{27} -8.87516 q^{28} -0.465444 q^{29} -2.56978 q^{30} +8.00300 q^{31} +6.95384 q^{32} +0.930487 q^{33} -16.8841 q^{34} -6.50458 q^{35} -7.94617 q^{36} -1.53542 q^{37} -12.3274 q^{38} +1.69087 q^{39} -4.44839 q^{40} -2.53426 q^{41} +3.61968 q^{42} -11.5069 q^{43} +5.06679 q^{44} -5.82372 q^{45} -7.08150 q^{46} -7.90827 q^{47} -0.682221 q^{48} +2.16207 q^{49} +0.848586 q^{50} +4.09373 q^{51} +9.20728 q^{52} +9.25664 q^{53} +6.82832 q^{54} +3.71343 q^{55} +6.26581 q^{56} +2.98890 q^{57} +1.03367 q^{58} -3.46063 q^{59} +3.39280 q^{60} -8.35772 q^{61} -17.7733 q^{62} +8.20305 q^{63} -12.9094 q^{64} +6.74799 q^{65} -2.06646 q^{66} +3.30604 q^{67} +22.2916 q^{68} +1.71698 q^{69} +14.4456 q^{70} +15.1304 q^{71} +5.60995 q^{72} -5.18230 q^{73} +3.40991 q^{74} -0.205749 q^{75} +16.2755 q^{76} -5.23058 q^{77} -3.75513 q^{78} -4.24463 q^{79} -2.72264 q^{80} +6.47457 q^{81} +5.62816 q^{82} -6.82918 q^{83} -4.77896 q^{84} +16.3375 q^{85} +25.5549 q^{86} -0.250625 q^{87} -3.57712 q^{88} -3.84784 q^{89} +12.9335 q^{90} -9.50493 q^{91} +9.34950 q^{92} +4.30933 q^{93} +17.5630 q^{94} +11.9282 q^{95} +3.74440 q^{96} +7.80995 q^{97} -4.80161 q^{98} -4.68308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9}+O(q^{10}) \) 149 * q + 13 * q^2 + 16 * q^3 + 169 * q^4 + 15 * q^5 + 15 * q^6 + 59 * q^7 + 36 * q^8 + 189 * q^9	\( 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9} + 16 q^{10} + 17 q^{11} + 40 q^{12} + 65 q^{13} + 4 q^{14} + 19 q^{15} + 205 q^{16} + 55 q^{17} + 60 q^{18} + 33 q^{19} + 23 q^{20} + 30 q^{21} + 78 q^{22} + 31 q^{23} + 36 q^{24} + 280 q^{25} - 7 q^{26} + 52 q^{27} + 165 q^{28} + 34 q^{29} + 17 q^{30} + 30 q^{31} + 65 q^{32} + 86 q^{33} + 37 q^{34} + 12 q^{35} + 210 q^{36} + 138 q^{37} + 15 q^{38} + 37 q^{39} + 27 q^{40} + 57 q^{41} + 2 q^{42} + 92 q^{43} + 37 q^{44} + 50 q^{45} + 62 q^{46} + 26 q^{47} + 79 q^{48} + 266 q^{49} + 19 q^{50} + 28 q^{51} + 139 q^{52} + 44 q^{53} + 33 q^{54} + 36 q^{55} - 2 q^{56} + 207 q^{57} + 150 q^{58} + 13 q^{59} - 15 q^{60} + 87 q^{61} + 22 q^{62} + 161 q^{63} + 254 q^{64} + 137 q^{65} - 25 q^{66} + 87 q^{67} + 68 q^{68} - 16 q^{69} + 28 q^{70} + 32 q^{71} + 120 q^{72} + 329 q^{73} + 29 q^{74} + 37 q^{75} + 42 q^{76} + 45 q^{77} + 63 q^{79} - 17 q^{80} + 269 q^{81} + 29 q^{82} + 51 q^{83} + 6 q^{84} + 224 q^{85} - 20 q^{86} + 34 q^{87} + 199 q^{88} + 24 q^{89} - 103 q^{90} + 46 q^{91} + 22 q^{92} + 119 q^{93} + 18 q^{94} + 13 q^{95} - 6 q^{96} + 204 q^{97} - 22 q^{98} + 43 q^{99}+O(q^{100}) \) 149 * q + 13 * q^2 + 16 * q^3 + 169 * q^4 + 15 * q^5 + 15 * q^6 + 59 * q^7 + 36 * q^8 + 189 * q^9 + 16 * q^10 + 17 * q^11 + 40 * q^12 + 65 * q^13 + 4 * q^14 + 19 * q^15 + 205 * q^16 + 55 * q^17 + 60 * q^18 + 33 * q^19 + 23 * q^20 + 30 * q^21 + 78 * q^22 + 31 * q^23 + 36 * q^24 + 280 * q^25 - 7 * q^26 + 52 * q^27 + 165 * q^28 + 34 * q^29 + 17 * q^30 + 30 * q^31 + 65 * q^32 + 86 * q^33 + 37 * q^34 + 12 * q^35 + 210 * q^36 + 138 * q^37 + 15 * q^38 + 37 * q^39 + 27 * q^40 + 57 * q^41 + 2 * q^42 + 92 * q^43 + 37 * q^44 + 50 * q^45 + 62 * q^46 + 26 * q^47 + 79 * q^48 + 266 * q^49 + 19 * q^50 + 28 * q^51 + 139 * q^52 + 44 * q^53 + 33 * q^54 + 36 * q^55 - 2 * q^56 + 207 * q^57 + 150 * q^58 + 13 * q^59 - 15 * q^60 + 87 * q^61 + 22 * q^62 + 161 * q^63 + 254 * q^64 + 137 * q^65 - 25 * q^66 + 87 * q^67 + 68 * q^68 - 16 * q^69 + 28 * q^70 + 32 * q^71 + 120 * q^72 + 329 * q^73 + 29 * q^74 + 37 * q^75 + 42 * q^76 + 45 * q^77 + 63 * q^79 - 17 * q^80 + 269 * q^81 + 29 * q^82 + 51 * q^83 + 6 * q^84 + 224 * q^85 - 20 * q^86 + 34 * q^87 + 199 * q^88 + 24 * q^89 - 103 * q^90 + 46 * q^91 + 22 * q^92 + 119 * q^93 + 18 * q^94 + 13 * q^95 - 6 * q^96 + 204 * q^97 - 22 * q^98 + 43 * q^99

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