LMFDB - Embedded newform 6023.2.a.d.1.91

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.91
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05329 q^{2} -1.57639 q^{3} -0.890573 q^{4} -0.962486 q^{5} -1.66041 q^{6} -0.503253 q^{7} -3.04462 q^{8} -0.514982 q^{9} +O(q^{10})$	\(q+1.05329 q^{2} -1.57639 q^{3} -0.890573 q^{4} -0.962486 q^{5} -1.66041 q^{6} -0.503253 q^{7} -3.04462 q^{8} -0.514982 q^{9} -1.01378 q^{10} -2.69550 q^{11} +1.40389 q^{12} -1.88116 q^{13} -0.530073 q^{14} +1.51726 q^{15} -1.42573 q^{16} -1.38121 q^{17} -0.542427 q^{18} -1.00000 q^{19} +0.857164 q^{20} +0.793325 q^{21} -2.83915 q^{22} +0.314071 q^{23} +4.79952 q^{24} -4.07362 q^{25} -1.98141 q^{26} +5.54100 q^{27} +0.448184 q^{28} -7.01715 q^{29} +1.59812 q^{30} -4.95731 q^{31} +4.58753 q^{32} +4.24917 q^{33} -1.45482 q^{34} +0.484374 q^{35} +0.458629 q^{36} -5.82633 q^{37} -1.05329 q^{38} +2.96545 q^{39} +2.93040 q^{40} -7.57449 q^{41} +0.835604 q^{42} -7.77343 q^{43} +2.40054 q^{44} +0.495663 q^{45} +0.330809 q^{46} +2.82753 q^{47} +2.24752 q^{48} -6.74674 q^{49} -4.29072 q^{50} +2.17734 q^{51} +1.67531 q^{52} -11.1562 q^{53} +5.83629 q^{54} +2.59438 q^{55} +1.53222 q^{56} +1.57639 q^{57} -7.39112 q^{58} -9.47250 q^{59} -1.35123 q^{60} +3.42370 q^{61} -5.22151 q^{62} +0.259166 q^{63} +7.68348 q^{64} +1.81059 q^{65} +4.47563 q^{66} -8.12513 q^{67} +1.23007 q^{68} -0.495100 q^{69} +0.510188 q^{70} +1.93720 q^{71} +1.56793 q^{72} +4.60995 q^{73} -6.13683 q^{74} +6.42163 q^{75} +0.890573 q^{76} +1.35652 q^{77} +3.12349 q^{78} +13.0433 q^{79} +1.37225 q^{80} -7.18985 q^{81} -7.97816 q^{82} +1.81491 q^{83} -0.706514 q^{84} +1.32940 q^{85} -8.18770 q^{86} +11.0618 q^{87} +8.20678 q^{88} -9.64321 q^{89} +0.522078 q^{90} +0.946700 q^{91} -0.279704 q^{92} +7.81468 q^{93} +2.97822 q^{94} +0.962486 q^{95} -7.23175 q^{96} -14.3265 q^{97} -7.10629 q^{98} +1.38813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	1.05329	0.744791	0.372395	−	0.928074i	$-0.378537\pi$
$2$	1.05329	0.744791	0.372395	+	0.928074i	$0.378537\pi$
$3$	−1.57639	−0.910131	−0.455066	−	0.890458i	$-0.650384\pi$
$3$	−1.57639	−0.910131	−0.455066	+	0.890458i	$0.650384\pi$
$4$	−0.890573	−0.445287
$5$	−0.962486	−0.430437	−0.215218	−	0.976566i	$-0.569046\pi$
$5$	−0.962486	−0.430437	−0.215218	+	0.976566i	$0.569046\pi$
$6$	−1.66041	−0.677858
$7$	−0.503253	−0.190212	−0.0951059	−	0.995467i	$-0.530319\pi$
$7$	−0.503253	−0.190212	−0.0951059	+	0.995467i	$0.530319\pi$
$8$	−3.04462	−1.07644
$9$	−0.514982	−0.171661
$10$	−1.01378	−0.320585
$11$	−2.69550	−0.812724	−0.406362	−	0.913712i	$-0.633203\pi$
$11$	−2.69550	−0.812724	−0.406362	+	0.913712i	$0.633203\pi$
$12$	1.40389	0.405269
$13$	−1.88116	−0.521740	−0.260870	−	0.965374i	$-0.584009\pi$
$13$	−1.88116	−0.521740	−0.260870	+	0.965374i	$0.584009\pi$
$14$	−0.530073	−0.141668
$15$	1.51726	0.391754
$16$	−1.42573	−0.356433
$17$	−1.38121	−0.334994	−0.167497	−	0.985873i	$-0.553568\pi$
$17$	−1.38121	−0.334994	−0.167497	+	0.985873i	$0.553568\pi$
$18$	−0.542427	−0.127851
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.857164	0.191668
$21$	0.793325	0.173118
$22$	−2.83915	−0.605310
$23$	0.314071	0.0654884	0.0327442	−	0.999464i	$-0.489575\pi$
$23$	0.314071	0.0654884	0.0327442	+	0.999464i	$0.489575\pi$
$24$	4.79952	0.979699
$25$	−4.07362	−0.814724
$26$	−1.98141	−0.388587
$27$	5.54100	1.06637
$28$	0.448184	0.0846988
$29$	−7.01715	−1.30305	−0.651526	−	0.758626i	$-0.725871\pi$
$29$	−7.01715	−1.30305	−0.651526	+	0.758626i	$0.725871\pi$
$30$	1.59812	0.291775
$31$	−4.95731	−0.890360	−0.445180	−	0.895441i	$-0.646860\pi$
$31$	−4.95731	−0.890360	−0.445180	+	0.895441i	$0.646860\pi$
$32$	4.58753	0.810968
$33$	4.24917	0.739686
$34$	−1.45482	−0.249500
$35$	0.484374	0.0818742
$36$	0.458629	0.0764382
$37$	−5.82633	−0.957843	−0.478921	−	0.877858i	$-0.658972\pi$
$37$	−5.82633	−0.957843	−0.478921	+	0.877858i	$0.658972\pi$
$38$	−1.05329	−0.170867
$39$	2.96545	0.474852
$40$	2.93040	0.463338
$41$	−7.57449	−1.18294	−0.591469	−	0.806328i	$-0.701452\pi$
$41$	−7.57449	−1.18294	−0.591469	+	0.806328i	$0.701452\pi$
$42$	0.835604	0.128937
$43$	−7.77343	−1.18544	−0.592718	−	0.805410i	$-0.701945\pi$
$43$	−7.77343	−1.18544	−0.592718	+	0.805410i	$0.701945\pi$
$44$	2.40054	0.361895
$45$	0.495663	0.0738890
$46$	0.330809	0.0487752
$47$	2.82753	0.412437	0.206219	−	0.978506i	$-0.433884\pi$
$47$	2.82753	0.412437	0.206219	+	0.978506i	$0.433884\pi$
$48$	2.24752	0.324401
$49$	−6.74674	−0.963819
$50$	−4.29072	−0.606799
$51$	2.17734	0.304888
$52$	1.67531	0.232324
$53$	−11.1562	−1.53242	−0.766210	−	0.642590i	$-0.777860\pi$
$53$	−11.1562	−1.53242	−0.766210	+	0.642590i	$0.777860\pi$
$54$	5.83629	0.794219
$55$	2.59438	0.349826
$56$	1.53222	0.204751
$57$	1.57639	0.208798
$58$	−7.39112	−0.970501
$59$	−9.47250	−1.23322	−0.616608	−	0.787271i	$-0.711493\pi$
$59$	−9.47250	−1.23322	−0.616608	+	0.787271i	$0.711493\pi$
$60$	−1.35123	−0.174443
$61$	3.42370	0.438360	0.219180	−	0.975684i	$-0.429662\pi$
$61$	3.42370	0.438360	0.219180	+	0.975684i	$0.429662\pi$
$62$	−5.22151	−0.663132
$63$	0.259166	0.0326519
$64$	7.68348	0.960435
$65$	1.81059	0.224576
$66$	4.47563	0.550911
$67$	−8.12513	−0.992643	−0.496321	−	0.868139i	$-0.665316\pi$
$67$	−8.12513	−0.992643	−0.496321	+	0.868139i	$0.665316\pi$
$68$	1.23007	0.149168
$69$	−0.495100	−0.0596031
$70$	0.510188	0.0609791
$71$	1.93720	0.229904	0.114952	−	0.993371i	$-0.463329\pi$
$71$	1.93720	0.229904	0.114952	+	0.993371i	$0.463329\pi$
$72$	1.56793	0.184782
$73$	4.60995	0.539554	0.269777	−	0.962923i	$-0.413050\pi$
$73$	4.60995	0.539554	0.269777	+	0.962923i	$0.413050\pi$
$74$	−6.13683	−0.713393
$75$	6.42163	0.741506
$76$	0.890573	0.102156
$77$	1.35652	0.154590
$78$	3.12349	0.353665
$79$	13.0433	1.46748	0.733742	−	0.679428i	$-0.237772\pi$
$79$	13.0433	1.46748	0.733742	+	0.679428i	$0.237772\pi$
$80$	1.37225	0.153422
$81$	−7.18985	−0.798872
$82$	−7.97816	−0.881041
$83$	1.81491	0.199212	0.0996061	−	0.995027i	$-0.468242\pi$
$83$	1.81491	0.199212	0.0996061	+	0.995027i	$0.468242\pi$
$84$	−0.706514	−0.0770870
$85$	1.32940	0.144194
$86$	−8.18770	−0.882902
$87$	11.0618	1.18595
$88$	8.20678	0.874846
$89$	−9.64321	−1.02218	−0.511089	−	0.859528i	$-0.670758\pi$
$89$	−9.64321	−1.02218	−0.511089	+	0.859528i	$0.670758\pi$
$90$	0.522078	0.0550319
$91$	0.946700	0.0992411
$92$	−0.279704	−0.0291611
$93$	7.81468	0.810345
$94$	2.97822	0.307180
$95$	0.962486	0.0987489
$96$	−7.23175	−0.738088
$97$	−14.3265	−1.45463	−0.727316	−	0.686303i	$-0.759232\pi$
$97$	−14.3265	−1.45463	−0.727316	+	0.686303i	$0.759232\pi$
$98$	−7.10629	−0.717844
$99$	1.38813	0.139513
$100$	3.62786	0.362786
$101$	15.2122	1.51367	0.756834	−	0.653607i	$-0.226745\pi$
$101$	15.2122	1.51367	0.756834	+	0.653607i	$0.226745\pi$
$102$	2.29337	0.227078
$103$	11.6547	1.14837	0.574186	−	0.818725i	$-0.305318\pi$
$103$	11.6547	1.14837	0.574186	+	0.818725i	$0.305318\pi$
$104$	5.72742	0.561620
$105$	−0.763564	−0.0745162
$106$	−11.7507	−1.14133
$107$	−4.63217	−0.447809	−0.223904	−	0.974611i	$-0.571880\pi$
$107$	−4.63217	−0.447809	−0.223904	+	0.974611i	$0.571880\pi$
$108$	−4.93466	−0.474838
$109$	4.70335	0.450499	0.225250	−	0.974301i	$-0.427680\pi$
$109$	4.70335	0.450499	0.225250	+	0.974301i	$0.427680\pi$
$110$	2.73265	0.260547
$111$	9.18459	0.871763
$112$	0.717505	0.0677978
$113$	15.5479	1.46262	0.731312	−	0.682043i	$-0.238908\pi$
$113$	15.5479	1.46262	0.731312	+	0.682043i	$0.238908\pi$
$114$	1.66041	0.155511
$115$	−0.302289	−0.0281886
$116$	6.24929	0.580232
$117$	0.968764	0.0895622
$118$	−9.97733	−0.918487
$119$	0.695100	0.0637198
$120$	−4.61947	−0.421698
$121$	−3.73427	−0.339479
$122$	3.60616	0.326486
$123$	11.9404	1.07663
$124$	4.41485	0.396465
$125$	8.73323	0.781124
$126$	0.272978	0.0243188
$127$	9.07571	0.805339	0.402670	−	0.915345i	$-0.368082\pi$
$127$	9.07571	0.805339	0.402670	+	0.915345i	$0.368082\pi$
$128$	−1.08210	−0.0956449
$129$	12.2540	1.07890
$130$	1.90708	0.167262
$131$	21.8042	1.90504	0.952522	−	0.304468i	$-0.0984787\pi$
$131$	21.8042	1.90504	0.952522	+	0.304468i	$0.0984787\pi$
$132$	−3.78420	−0.329372
$133$	0.503253	0.0436376
$134$	−8.55815	−0.739311
$135$	−5.33313	−0.459003
$136$	4.20527	0.360599
$137$	−8.74917	−0.747492	−0.373746	−	0.927531i	$-0.621927\pi$
$137$	−8.74917	−0.747492	−0.373746	+	0.927531i	$0.621927\pi$
$138$	−0.521486	−0.0443918
$139$	−20.5698	−1.74471	−0.872353	−	0.488877i	$-0.837407\pi$
$139$	−20.5698	−1.74471	−0.872353	+	0.488877i	$0.837407\pi$
$140$	−0.431370	−0.0364575
$141$	−4.45730	−0.375372
$142$	2.04044	0.171230
$143$	5.07067	0.424031
$144$	0.734227	0.0611856
$145$	6.75391	0.560881
$146$	4.85563	0.401855
$147$	10.6355	0.877202
$148$	5.18877	0.426515
$149$	−5.98050	−0.489941	−0.244971	−	0.969530i	$-0.578778\pi$
$149$	−5.98050	−0.489941	−0.244971	+	0.969530i	$0.578778\pi$
$150$	6.76386	0.552267
$151$	14.6008	1.18820	0.594099	−	0.804392i	$-0.297509\pi$
$151$	14.6008	1.18820	0.594099	+	0.804392i	$0.297509\pi$
$152$	3.04462	0.246951
$153$	0.711300	0.0575052
$154$	1.42881	0.115137
$155$	4.77134	0.383244
$156$	−2.64095	−0.211445
$157$	1.20426	0.0961101	0.0480550	−	0.998845i	$-0.484698\pi$
$157$	1.20426	0.0961101	0.0480550	+	0.998845i	$0.484698\pi$
$158$	13.7384	1.09297
$159$	17.5865	1.39470
$160$	−4.41543	−0.349070
$161$	−0.158057	−0.0124567
$162$	−7.57302	−0.594993
$163$	−14.1443	−1.10787	−0.553934	−	0.832560i	$-0.686874\pi$
$163$	−14.1443	−1.10787	−0.553934	+	0.832560i	$0.686874\pi$
$164$	6.74564	0.526746
$165$	−4.08977	−0.318388
$166$	1.91163	0.148371
$167$	−9.93269	−0.768615	−0.384307	−	0.923205i	$-0.625560\pi$
$167$	−9.93269	−0.768615	−0.384307	+	0.923205i	$0.625560\pi$
$168$	−2.41538	−0.186350
$169$	−9.46124	−0.727787
$170$	1.40025	0.107394
$171$	0.514982	0.0393817
$172$	6.92281	0.527859
$173$	0.762499	0.0579717	0.0289859	−	0.999580i	$-0.490772\pi$
$173$	0.762499	0.0579717	0.0289859	+	0.999580i	$0.490772\pi$
$174$	11.6513	0.883284
$175$	2.05006	0.154970
$176$	3.84307	0.289682
$177$	14.9324	1.12239
$178$	−10.1571	−0.761309
$179$	−24.3281	−1.81837	−0.909185	−	0.416392i	$-0.863294\pi$
$179$	−24.3281	−1.81837	−0.909185	+	0.416392i	$0.863294\pi$
$180$	−0.441424	−0.0329018
$181$	11.4685	0.852449	0.426224	−	0.904617i	$-0.359843\pi$
$181$	11.4685	0.852449	0.426224	+	0.904617i	$0.359843\pi$
$182$	0.997153	0.0739139
$183$	−5.39710	−0.398965
$184$	−0.956229	−0.0704941
$185$	5.60776	0.412291
$186$	8.23115	0.603537
$187$	3.72306	0.272257
$188$	−2.51812	−0.183653
$189$	−2.78852	−0.202835
$190$	1.01378	0.0735473
$191$	21.7663	1.57495	0.787477	−	0.616344i	$-0.211387\pi$
$191$	21.7663	1.57495	0.787477	+	0.616344i	$0.211387\pi$
$192$	−12.1122	−0.874122
$193$	−17.9619	−1.29293	−0.646463	−	0.762945i	$-0.723753\pi$
$193$	−17.9619	−1.29293	−0.646463	+	0.762945i	$0.723753\pi$
$194$	−15.0900	−1.08340
$195$	−2.85420	−0.204394
$196$	6.00846	0.429176
$197$	12.7224	0.906432	0.453216	−	0.891401i	$-0.350277\pi$
$197$	12.7224	0.906432	0.453216	+	0.891401i	$0.350277\pi$
$198$	1.46211	0.103908
$199$	−0.0704774	−0.00499601	−0.00249801	−	0.999997i	$-0.500795\pi$
$199$	−0.0704774	−0.00499601	−0.00249801	+	0.999997i	$0.500795\pi$
$200$	12.4026	0.876999
$201$	12.8084	0.903436
$202$	16.0229	1.12737
$203$	3.53140	0.247856
$204$	−1.93908	−0.135763
$205$	7.29034	0.509180
$206$	12.2758	0.855298
$207$	−0.161741	−0.0112418
$208$	2.68203	0.185965
$209$	2.69550	0.186452
$210$	−0.804257	−0.0554990
$211$	−28.8130	−1.98357	−0.991785	−	0.127913i	$-0.959172\pi$
$211$	−28.8130	−1.98357	−0.991785	+	0.127913i	$0.959172\pi$
$212$	9.93540	0.682366
$213$	−3.05380	−0.209243
$214$	−4.87903	−0.333524
$215$	7.48181	0.510255
$216$	−16.8702	−1.14787
$217$	2.49478	0.169357
$218$	4.95401	0.335528
$219$	−7.26710	−0.491065
$220$	−2.31049	−0.155773
$221$	2.59828	0.174780
$222$	9.67407	0.649281
$223$	3.59594	0.240802	0.120401	−	0.992725i	$-0.461582\pi$
$223$	3.59594	0.240802	0.120401	+	0.992725i	$0.461582\pi$
$224$	−2.30869	−0.154256
$225$	2.09784	0.139856
$226$	16.3765	1.08935
$227$	−21.9721	−1.45834	−0.729168	−	0.684334i	$-0.760093\pi$
$227$	−21.9721	−1.45834	−0.729168	+	0.684334i	$0.760093\pi$
$228$	−1.40389	−0.0929752
$229$	24.6860	1.63130	0.815649	−	0.578546i	$-0.196380\pi$
$229$	24.6860	1.63130	0.815649	+	0.578546i	$0.196380\pi$
$230$	−0.318399	−0.0209946
$231$	−2.13841	−0.140697
$232$	21.3646	1.40265
$233$	9.81522	0.643016	0.321508	−	0.946907i	$-0.395810\pi$
$233$	9.81522	0.643016	0.321508	+	0.946907i	$0.395810\pi$
$234$	1.02039	0.0667051
$235$	−2.72145	−0.177528
$236$	8.43596	0.549134
$237$	−20.5614	−1.33560
$238$	0.732145	0.0474579
$239$	−2.38412	−0.154216	−0.0771079	−	0.997023i	$-0.524569\pi$
$239$	−2.38412	−0.154216	−0.0771079	+	0.997023i	$0.524569\pi$
$240$	−2.16320	−0.139634
$241$	10.1014	0.650687	0.325344	−	0.945596i	$-0.394520\pi$
$241$	10.1014	0.650687	0.325344	+	0.945596i	$0.394520\pi$
$242$	−3.93328	−0.252841
$243$	−5.28896	−0.339287
$244$	−3.04906	−0.195196
$245$	6.49364	0.414863
$246$	12.5767	0.801863
$247$	1.88116	0.119695
$248$	15.0931	0.958416
$249$	−2.86101	−0.181309
$250$	9.19865	0.581774
$251$	−1.74088	−0.109883	−0.0549415	−	0.998490i	$-0.517497\pi$
$251$	−1.74088	−0.109883	−0.0549415	+	0.998490i	$0.517497\pi$
$252$	−0.230807	−0.0145394
$253$	−0.846580	−0.0532240
$254$	9.55939	0.599809
$255$	−2.09566	−0.131235
$256$	−16.5067	−1.03167
$257$	5.35468	0.334016	0.167008	−	0.985956i	$-0.446589\pi$
$257$	5.35468	0.334016	0.167008	+	0.985956i	$0.446589\pi$
$258$	12.9070	0.803557
$259$	2.93212	0.182193
$260$	−1.61246	−0.100001
$261$	3.61371	0.223683
$262$	22.9663	1.41886
$263$	−8.30925	−0.512370	−0.256185	−	0.966628i	$-0.582466\pi$
$263$	−8.30925	−0.512370	−0.256185	+	0.966628i	$0.582466\pi$
$264$	−12.9371	−0.796225
$265$	10.7377	0.659610
$266$	0.530073	0.0325009
$267$	15.2015	0.930316
$268$	7.23603	0.442011
$269$	−6.04279	−0.368435	−0.184218	−	0.982885i	$-0.558975\pi$
$269$	−6.04279	−0.368435	−0.184218	+	0.982885i	$0.558975\pi$
$270$	−5.61735	−0.341861
$271$	12.9023	0.783757	0.391878	−	0.920017i	$-0.371825\pi$
$271$	12.9023	0.783757	0.391878	+	0.920017i	$0.371825\pi$
$272$	1.96924	0.119403
$273$	−1.49237	−0.0903225
$274$	−9.21544	−0.556725
$275$	10.9805	0.662146
$276$	0.440923	0.0265404
$277$	−3.67630	−0.220887	−0.110444	−	0.993882i	$-0.535227\pi$
$277$	−3.67630	−0.220887	−0.110444	+	0.993882i	$0.535227\pi$
$278$	−21.6660	−1.29944
$279$	2.55293	0.152840
$280$	−1.47474	−0.0881323
$281$	18.2279	1.08739	0.543694	−	0.839284i	$-0.317025\pi$
$281$	18.2279	1.08739	0.543694	+	0.839284i	$0.317025\pi$
$282$	−4.69484	−0.279574
$283$	−11.6645	−0.693385	−0.346693	−	0.937979i	$-0.612695\pi$
$283$	−11.6645	−0.693385	−0.346693	+	0.937979i	$0.612695\pi$
$284$	−1.72522	−0.102373
$285$	−1.51726	−0.0898745
$286$	5.34090	0.315814
$287$	3.81189	0.225009
$288$	−2.36249	−0.139211
$289$	−15.0922	−0.887779
$290$	7.11384	0.417739
$291$	22.5841	1.32391
$292$	−4.10550	−0.240256
$293$	−27.4401	−1.60307	−0.801535	−	0.597948i	$-0.795983\pi$
$293$	−27.4401	−1.60307	−0.801535	+	0.597948i	$0.795983\pi$
$294$	11.2023	0.653332
$295$	9.11715	0.530821
$296$	17.7390	1.03106
$297$	−14.9358	−0.866661
$298$	−6.29922	−0.364904
$299$	−0.590819	−0.0341679
$300$	−5.71893	−0.330183
$301$	3.91200	0.225484
$302$	15.3790	0.884959
$303$	−23.9804	−1.37764
$304$	1.42573	0.0817714
$305$	−3.29526	−0.188686
$306$	0.749208	0.0428294
$307$	32.5430	1.85733	0.928663	−	0.370925i	$-0.120959\pi$
$307$	32.5430	1.85733	0.928663	+	0.370925i	$0.120959\pi$
$308$	−1.20808	−0.0688368
$309$	−18.3724	−1.04517
$310$	5.02562	0.285436
$311$	−16.4446	−0.932489	−0.466245	−	0.884656i	$-0.654393\pi$
$311$	−16.4446	−0.932489	−0.466245	+	0.884656i	$0.654393\pi$
$312$	−9.02867	−0.511148
$313$	11.8342	0.668910	0.334455	−	0.942412i	$-0.391448\pi$
$313$	11.8342	0.668910	0.334455	+	0.942412i	$0.391448\pi$
$314$	1.26843	0.0715819
$315$	−0.249444	−0.0140546
$316$	−11.6160	−0.653451
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	18.5238	1.03876
$319$	18.9147	1.05902
$320$	−7.39524	−0.413406
$321$	7.30212	0.407565
$322$	−0.166481	−0.00927762
$323$	1.38121	0.0768528
$324$	6.40309	0.355727
$325$	7.66313	0.425074
$326$	−14.8981	−0.825130
$327$	−7.41433	−0.410013
$328$	23.0615	1.27336
$329$	−1.42296	−0.0784505
$330$	−4.30773	−0.237132
$331$	−14.2207	−0.781638	−0.390819	−	0.920468i	$-0.627808\pi$
$331$	−14.2207	−0.781638	−0.390819	+	0.920468i	$0.627808\pi$
$332$	−1.61631	−0.0887065
$333$	3.00045	0.164424
$334$	−10.4620	−0.572457
$335$	7.82032	0.427270
$336$	−1.13107	−0.0617049
$337$	10.7460	0.585369	0.292685	−	0.956209i	$-0.405451\pi$
$337$	10.7460	0.585369	0.292685	+	0.956209i	$0.405451\pi$
$338$	−9.96546	−0.542049
$339$	−24.5096	−1.33118
$340$	−1.18393	−0.0642074
$341$	13.3625	0.723617
$342$	0.542427	0.0293311
$343$	6.91809	0.373542
$344$	23.6671	1.27605
$345$	0.476527	0.0256553
$346$	0.803135	0.0431768
$347$	−20.4068	−1.09549	−0.547747	−	0.836644i	$-0.684514\pi$
$347$	−20.4068	−1.09549	−0.547747	+	0.836644i	$0.684514\pi$
$348$	−9.85134	−0.528087
$349$	18.9198	1.01276	0.506378	−	0.862312i	$-0.330984\pi$
$349$	18.9198	1.01276	0.506378	+	0.862312i	$0.330984\pi$
$350$	2.15932	0.115420
$351$	−10.4235	−0.556365
$352$	−12.3657	−0.659094
$353$	−10.5709	−0.562634	−0.281317	−	0.959615i	$-0.590771\pi$
$353$	−10.5709	−0.562634	−0.281317	+	0.959615i	$0.590771\pi$
$354$	15.7282	0.835944
$355$	−1.86453	−0.0989590
$356$	8.58798	0.455162
$357$	−1.09575	−0.0579934
$358$	−25.6247	−1.35431
$359$	8.80926	0.464935	0.232467	−	0.972604i	$-0.425320\pi$
$359$	8.80926	0.464935	0.232467	+	0.972604i	$0.425320\pi$
$360$	−1.50911	−0.0795368
$361$	1.00000	0.0526316
$362$	12.0797	0.634896
$363$	5.88668	0.308971
$364$	−0.843106	−0.0441907
$365$	−4.43701	−0.232244
$366$	−5.68473	−0.297146
$367$	−1.78215	−0.0930276	−0.0465138	−	0.998918i	$-0.514811\pi$
$367$	−1.78215	−0.0930276	−0.0465138	+	0.998918i	$0.514811\pi$
$368$	−0.447782	−0.0233423
$369$	3.90073	0.203064
$370$	5.90661	0.307070
$371$	5.61439	0.291484
$372$	−6.95955	−0.360836
$373$	30.9015	1.60002	0.800011	−	0.599986i	$-0.204827\pi$
$373$	30.9015	1.60002	0.800011	+	0.599986i	$0.204827\pi$
$374$	3.92148	0.202775
$375$	−13.7670	−0.710925
$376$	−8.60875	−0.443963
$377$	13.2004	0.679854
$378$	−2.93713	−0.151070
$379$	8.76460	0.450207	0.225104	−	0.974335i	$-0.427728\pi$
$379$	8.76460	0.450207	0.225104	+	0.974335i	$0.427728\pi$
$380$	−0.857164	−0.0439716
$381$	−14.3069	−0.732965
$382$	22.9263	1.17301
$383$	−18.4966	−0.945133	−0.472567	−	0.881295i	$-0.656672\pi$
$383$	−18.4966	−0.945133	−0.472567	+	0.881295i	$0.656672\pi$
$384$	1.70581	0.0870495
$385$	−1.30563	−0.0665411
$386$	−18.9192	−0.962960
$387$	4.00318	0.203493
$388$	12.7588	0.647728
$389$	4.28581	0.217299	0.108650	−	0.994080i	$-0.465347\pi$
$389$	4.28581	0.217299	0.108650	+	0.994080i	$0.465347\pi$
$390$	−3.00631	−0.152231
$391$	−0.433800	−0.0219382
$392$	20.5413	1.03749
$393$	−34.3721	−1.73384
$394$	13.4004	0.675102
$395$	−12.5540	−0.631659
$396$	−1.23624	−0.0621232
$397$	4.05260	0.203394	0.101697	−	0.994815i	$-0.467573\pi$
$397$	4.05260	0.203394	0.101697	+	0.994815i	$0.467573\pi$
$398$	−0.0742334	−0.00372099
$399$	−0.793325	−0.0397159
$400$	5.80790	0.290395
$401$	−27.1044	−1.35353	−0.676764	−	0.736200i	$-0.736618\pi$
$401$	−27.1044	−1.35353	−0.676764	+	0.736200i	$0.736618\pi$
$402$	13.4910	0.672871
$403$	9.32550	0.464536
$404$	−13.5476	−0.674016
$405$	6.92012	0.343864
$406$	3.71960	0.184601
$407$	15.7049	0.778462
$408$	−6.62917	−0.328193
$409$	27.4222	1.35594	0.677971	−	0.735089i	$-0.262860\pi$
$409$	27.4222	1.35594	0.677971	+	0.735089i	$0.262860\pi$
$410$	7.67887	0.379232
$411$	13.7921	0.680316
$412$	−10.3794	−0.511355
$413$	4.76707	0.234572
$414$	−0.170361	−0.00837278
$415$	−1.74682	−0.0857482
$416$	−8.62988	−0.423114
$417$	32.4261	1.58791
$418$	2.83915	0.138868
$419$	31.5808	1.54282	0.771410	−	0.636338i	$-0.219552\pi$
$419$	31.5808	1.54282	0.771410	+	0.636338i	$0.219552\pi$
$420$	0.680010	0.0331811
$421$	3.24970	0.158381	0.0791903	−	0.996860i	$-0.474767\pi$
$421$	3.24970	0.158381	0.0791903	+	0.996860i	$0.474767\pi$
$422$	−30.3486	−1.47735
$423$	−1.45613	−0.0707993
$424$	33.9664	1.64955
$425$	5.62654	0.272927
$426$	−3.21654	−0.155842
$427$	−1.72299	−0.0833812
$428$	4.12528	0.199403
$429$	−7.99338	−0.385924
$430$	7.88054	0.380034
$431$	16.1157	0.776264	0.388132	−	0.921604i	$-0.373120\pi$
$431$	16.1157	0.776264	0.388132	+	0.921604i	$0.373120\pi$
$432$	−7.89998	−0.380088
$433$	−19.8304	−0.952986	−0.476493	−	0.879178i	$-0.658092\pi$
$433$	−19.8304	−0.952986	−0.476493	+	0.879178i	$0.658092\pi$
$434$	2.62774	0.126136
$435$	−10.6468	−0.510476
$436$	−4.18868	−0.200601
$437$	−0.314071	−0.0150241
$438$	−7.65439	−0.365741
$439$	−7.36504	−0.351514	−0.175757	−	0.984434i	$-0.556237\pi$
$439$	−7.36504	−0.351514	−0.175757	+	0.984434i	$0.556237\pi$
$440$	−7.89891	−0.376566
$441$	3.47445	0.165450
$442$	2.73676	0.130174
$443$	−20.0266	−0.951492	−0.475746	−	0.879583i	$-0.657822\pi$
$443$	−20.0266	−0.951492	−0.475746	+	0.879583i	$0.657822\pi$
$444$	−8.17955	−0.388184
$445$	9.28145	0.439983
$446$	3.78758	0.179347
$447$	9.42762	0.445911
$448$	−3.86674	−0.182686
$449$	−32.9045	−1.55286	−0.776429	−	0.630204i	$-0.782971\pi$
$449$	−32.9045	−1.55286	−0.776429	+	0.630204i	$0.782971\pi$
$450$	2.20964	0.104164
$451$	20.4171	0.961402
$452$	−13.8465	−0.651287
$453$	−23.0167	−1.08142
$454$	−23.1430	−1.08616
$455$	−0.911185	−0.0427170
$456$	−4.79952	−0.224758
$457$	−7.08501	−0.331423	−0.165712	−	0.986174i	$-0.552992\pi$
$457$	−7.08501	−0.331423	−0.165712	+	0.986174i	$0.552992\pi$
$458$	26.0016	1.21498
$459$	−7.65330	−0.357226
$460$	0.269211	0.0125520
$461$	−14.7068	−0.684963	−0.342481	−	0.939525i	$-0.611267\pi$
$461$	−14.7068	−0.684963	−0.342481	+	0.939525i	$0.611267\pi$
$462$	−2.25237	−0.104790
$463$	−31.6800	−1.47229	−0.736147	−	0.676822i	$-0.763357\pi$
$463$	−31.6800	−1.47229	−0.736147	+	0.676822i	$0.763357\pi$
$464$	10.0046	0.464451
$465$	−7.52152	−0.348802
$466$	10.3383	0.478913
$467$	−6.92304	−0.320360	−0.160180	−	0.987088i	$-0.551207\pi$
$467$	−6.92304	−0.320360	−0.160180	+	0.987088i	$0.551207\pi$
$468$	−0.862755	−0.0398809
$469$	4.08900	0.188812
$470$	−2.86649	−0.132221
$471$	−1.89838	−0.0874728
$472$	28.8402	1.32748
$473$	20.9533	0.963433
$474$	−21.6571	−0.994746
$475$	4.07362	0.186911
$476$	−0.619038	−0.0283736
$477$	5.74523	0.263056
$478$	−2.51118	−0.114859
$479$	−40.3410	−1.84323	−0.921613	−	0.388111i	$-0.873128\pi$
$479$	−40.3410	−1.84323	−0.921613	+	0.388111i	$0.873128\pi$
$480$	6.96046	0.317700
$481$	10.9603	0.499745
$482$	10.6397	0.484626
$483$	0.249161	0.0113372
$484$	3.32564	0.151165
$485$	13.7890	0.626127
$486$	−5.57082	−0.252698
$487$	0.923414	0.0418439	0.0209219	−	0.999781i	$-0.493340\pi$
$487$	0.923414	0.0418439	0.0209219	+	0.999781i	$0.493340\pi$
$488$	−10.4239	−0.471866
$489$	22.2970	1.00831
$490$	6.83970	0.308986
$491$	29.6594	1.33851	0.669255	−	0.743033i	$-0.266614\pi$
$491$	29.6594	1.33851	0.669255	+	0.743033i	$0.266614\pi$
$492$	−10.6338	−0.479408
$493$	9.69219	0.436514
$494$	1.98141	0.0891480
$495$	−1.33606	−0.0600514
$496$	7.06781	0.317354
$497$	−0.974904	−0.0437304
$498$	−3.01348	−0.135037
$499$	−37.0206	−1.65727	−0.828636	−	0.559788i	$-0.810882\pi$
$499$	−37.0206	−1.65727	−0.828636	+	0.559788i	$0.810882\pi$
$500$	−7.77758	−0.347824
$501$	15.6578	0.699540
$502$	−1.83365	−0.0818399
$503$	−15.0565	−0.671336	−0.335668	−	0.941980i	$-0.608962\pi$
$503$	−15.0565	−0.671336	−0.335668	+	0.941980i	$0.608962\pi$
$504$	−0.789063	−0.0351477
$505$	−14.6415	−0.651539
$506$	−0.891697	−0.0396408
$507$	14.9146	0.662382
$508$	−8.08259	−0.358607
$509$	−20.2363	−0.896960	−0.448480	−	0.893793i	$-0.648034\pi$
$509$	−20.2363	−0.896960	−0.448480	+	0.893793i	$0.648034\pi$
$510$	−2.20734	−0.0977427
$511$	−2.31997	−0.102630
$512$	−15.2222	−0.672734
$513$	−5.54100	−0.244641
$514$	5.64005	0.248772
$515$	−11.2175	−0.494302
$516$	−10.9131	−0.480421
$517$	−7.62161	−0.335198
$518$	3.08838	0.135696
$519$	−1.20200	−0.0527619
$520$	−5.51256	−0.241742
$521$	−1.29998	−0.0569533	−0.0284766	−	0.999594i	$-0.509066\pi$
$521$	−1.29998	−0.0569533	−0.0284766	+	0.999594i	$0.509066\pi$
$522$	3.80629	0.166597
$523$	42.5340	1.85988	0.929940	−	0.367711i	$-0.119858\pi$
$523$	42.5340	1.85988	0.929940	+	0.367711i	$0.119858\pi$
$524$	−19.4183	−0.848291
$525$	−3.23171	−0.141043
$526$	−8.75208	−0.381609
$527$	6.84711	0.298265
$528$	−6.05819	−0.263649
$529$	−22.9014	−0.995711
$530$	11.3099	0.491271
$531$	4.87817	0.211695
$532$	−0.448184	−0.0194312
$533$	14.2488	0.617186
$534$	16.0116	0.692891
$535$	4.45839	0.192753
$536$	24.7380	1.06852
$537$	38.3507	1.65496
$538$	−6.36483	−0.274407
$539$	18.1858	0.783320
$540$	4.74954	0.204388
$541$	−12.1895	−0.524068	−0.262034	−	0.965059i	$-0.584393\pi$
$541$	−12.1895	−0.524068	−0.262034	+	0.965059i	$0.584393\pi$
$542$	13.5899	0.583735
$543$	−18.0789	−0.775841
$544$	−6.33636	−0.271669
$545$	−4.52690	−0.193911
$546$	−1.57191	−0.0672714
$547$	−26.1808	−1.11941	−0.559706	−	0.828692i	$-0.689086\pi$
$547$	−26.1808	−1.11941	−0.559706	+	0.828692i	$0.689086\pi$
$548$	7.79177	0.332848
$549$	−1.76314	−0.0752491
$550$	11.5656	0.493161
$551$	7.01715	0.298941
$552$	1.50739	0.0641589
$553$	−6.56408	−0.279133
$554$	−3.87222	−0.164515
$555$	−8.84004	−0.375239
$556$	18.3189	0.776894
$557$	0.00118472	5.01982e−5 0	2.50991e−5	−	1.00000i	$-0.499992\pi$
$557$	0.00118472	5.01982e−5 0	2.50991e−5		1.00000i	$0.499992\pi$
$558$	2.68898	0.113834
$559$	14.6231	0.618490
$560$	−0.690588	−0.0291827
$561$	−5.86902	−0.247790
$562$	19.1994	0.809877
$563$	5.42230	0.228523	0.114261	−	0.993451i	$-0.463550\pi$
$563$	5.42230	0.228523	0.114261	+	0.993451i	$0.463550\pi$
$564$	3.96955	0.167148
$565$	−14.9646	−0.629567
$566$	−12.2862	−0.516427
$567$	3.61831	0.151955
$568$	−5.89805	−0.247477
$569$	29.8960	1.25331	0.626653	−	0.779298i	$-0.284424\pi$
$569$	29.8960	1.25331	0.626653	+	0.779298i	$0.284424\pi$
$570$	−1.59812	−0.0669377
$571$	18.8873	0.790409	0.395204	−	0.918593i	$-0.370674\pi$
$571$	18.8873	0.790409	0.395204	+	0.918593i	$0.370674\pi$
$572$	−4.51580	−0.188815
$573$	−34.3122	−1.43341
$574$	4.01504	0.167584
$575$	−1.27941	−0.0533550
$576$	−3.95685	−0.164869
$577$	−8.36216	−0.348121	−0.174061	−	0.984735i	$-0.555689\pi$
$577$	−8.36216	−0.348121	−0.174061	+	0.984735i	$0.555689\pi$
$578$	−15.8966	−0.661210
$579$	28.3150	1.17673
$580$	−6.01485	−0.249753
$581$	−0.913359	−0.0378925
$582$	23.7877	0.986033
$583$	30.0715	1.24544
$584$	−14.0356	−0.580796
$585$	−0.932421	−0.0385509
$586$	−28.9025	−1.19395
$587$	−1.15152	−0.0475281	−0.0237641	−	0.999718i	$-0.507565\pi$
$587$	−1.15152	−0.0475281	−0.0237641	+	0.999718i	$0.507565\pi$
$588$	−9.47170	−0.390606
$589$	4.95731	0.204263
$590$	9.60303	0.395351
$591$	−20.0555	−0.824972
$592$	8.30679	0.341407
$593$	−21.9293	−0.900528	−0.450264	−	0.892895i	$-0.648670\pi$
$593$	−21.9293	−0.900528	−0.450264	+	0.892895i	$0.648670\pi$
$594$	−15.7317	−0.645481
$595$	−0.669024	−0.0274273
$596$	5.32607	0.218164
$597$	0.111100	0.00454703
$598$	−0.622305	−0.0254480
$599$	9.61645	0.392917	0.196459	−	0.980512i	$-0.437056\pi$
$599$	9.61645	0.392917	0.196459	+	0.980512i	$0.437056\pi$
$600$	−19.5514	−0.798184
$601$	22.1939	0.905308	0.452654	−	0.891686i	$-0.350477\pi$
$601$	22.1939	0.905308	0.452654	+	0.891686i	$0.350477\pi$
$602$	4.12049	0.167939
$603$	4.18430	0.170398
$604$	−13.0031	−0.529089
$605$	3.59418	0.146124
$606$	−25.2584	−1.02605
$607$	−41.2594	−1.67467	−0.837333	−	0.546693i	$-0.815886\pi$
$607$	−41.2594	−1.67467	−0.837333	+	0.546693i	$0.815886\pi$
$608$	−4.58753	−0.186049
$609$	−5.56688	−0.225581
$610$	−3.47088	−0.140532
$611$	−5.31903	−0.215185
$612$	−0.633465	−0.0256063
$613$	16.9917	0.686286	0.343143	−	0.939283i	$-0.388508\pi$
$613$	16.9917	0.686286	0.343143	+	0.939283i	$0.388508\pi$
$614$	34.2773	1.38332
$615$	−11.4925	−0.463420
$616$	−4.13009	−0.166406
$617$	−48.9378	−1.97016	−0.985080	−	0.172097i	$-0.944946\pi$
$617$	−48.9378	−1.97016	−0.985080	+	0.172097i	$0.944946\pi$
$618$	−19.3515	−0.778433
$619$	11.9052	0.478511	0.239256	−	0.970957i	$-0.423097\pi$
$619$	11.9052	0.478511	0.239256	+	0.970957i	$0.423097\pi$
$620$	−4.24923	−0.170653
$621$	1.74027	0.0698346
$622$	−17.3210	−0.694510
$623$	4.85297	0.194430
$624$	−4.22794	−0.169253
$625$	11.9625	0.478500
$626$	12.4649	0.498198
$627$	−4.24917	−0.169696
$628$	−1.07248	−0.0427965
$629$	8.04741	0.320871
$630$	−0.262738	−0.0104677
$631$	−2.40523	−0.0957507	−0.0478754	−	0.998853i	$-0.515245\pi$
$631$	−2.40523	−0.0957507	−0.0478754	+	0.998853i	$0.515245\pi$
$632$	−39.7119	−1.57965
$633$	45.4207	1.80531
$634$	1.05329	0.0418316
$635$	−8.73524	−0.346648
$636$	−15.6621	−0.621043
$637$	12.6917	0.502863
$638$	19.9228	0.788750
$639$	−0.997625	−0.0394654
$640$	1.04150	0.0411691
$641$	38.2601	1.51118	0.755592	−	0.655043i	$-0.227349\pi$
$641$	38.2601	1.51118	0.755592	+	0.655043i	$0.227349\pi$
$642$	7.69127	0.303550
$643$	2.63190	0.103792	0.0518960	−	0.998652i	$-0.483474\pi$
$643$	2.63190	0.103792	0.0518960	+	0.998652i	$0.483474\pi$
$644$	0.140762	0.00554679
$645$	−11.7943	−0.464400
$646$	1.45482	0.0572393
$647$	−10.8463	−0.426410	−0.213205	−	0.977007i	$-0.568390\pi$
$647$	−10.8463	−0.426410	−0.213205	+	0.977007i	$0.568390\pi$
$648$	21.8904	0.859935
$649$	25.5332	1.00226
$650$	8.07153	0.316591
$651$	−3.93276	−0.154137
$652$	12.5966	0.493319
$653$	29.3592	1.14891	0.574457	−	0.818535i	$-0.305213\pi$
$653$	29.3592	1.14891	0.574457	+	0.818535i	$0.305213\pi$
$654$	−7.80946	−0.305374
$655$	−20.9863	−0.820001
$656$	10.7992	0.421638
$657$	−2.37404	−0.0926203
$658$	−1.49880	−0.0584292
$659$	−39.3278	−1.53199	−0.765997	−	0.642844i	$-0.777754\pi$
$659$	−39.3278	−1.53199	−0.765997	+	0.642844i	$0.777754\pi$
$660$	3.64224	0.141774
$661$	1.14634	0.0445875	0.0222937	−	0.999751i	$-0.492903\pi$
$661$	1.14634	0.0445875	0.0222937	+	0.999751i	$0.492903\pi$
$662$	−14.9785	−0.582157
$663$	−4.09592	−0.159072
$664$	−5.52571	−0.214439
$665$	−0.484374	−0.0187832
$666$	3.16036	0.122461
$667$	−2.20389	−0.0853348
$668$	8.84579	0.342254
$669$	−5.66862	−0.219162
$670$	8.23709	0.318227
$671$	−9.22859	−0.356266
$672$	3.63940	0.140393
$673$	3.58713	0.138274	0.0691369	−	0.997607i	$-0.477975\pi$
$673$	3.58713	0.138274	0.0691369	+	0.997607i	$0.477975\pi$
$674$	11.3186	0.435978
$675$	−22.5719	−0.868794
$676$	8.42592	0.324074
$677$	−10.9958	−0.422604	−0.211302	−	0.977421i	$-0.567770\pi$
$677$	−10.9958	−0.422604	−0.211302	+	0.977421i	$0.567770\pi$
$678$	−25.8158	−0.991451
$679$	7.20984	0.276688
$680$	−4.04752	−0.155215
$681$	34.6366	1.32728
$682$	14.0746	0.538944
$683$	−17.4766	−0.668725	−0.334363	−	0.942445i	$-0.608521\pi$
$683$	−17.4766	−0.668725	−0.334363	+	0.942445i	$0.608521\pi$
$684$	−0.458629	−0.0175361
$685$	8.42095	0.321748
$686$	7.28678	0.278210
$687$	−38.9149	−1.48470
$688$	11.0828	0.422529
$689$	20.9866	0.799525
$690$	0.501923	0.0191079
$691$	−30.3172	−1.15332	−0.576660	−	0.816984i	$-0.695644\pi$
$691$	−30.3172	−1.15332	−0.576660	+	0.816984i	$0.695644\pi$
$692$	−0.679061	−0.0258140
$693$	−0.698583	−0.0265370
$694$	−21.4943	−0.815914
$695$	19.7981	0.750985
$696$	−33.6790	−1.27660
$697$	10.4620	0.396276
$698$	19.9281	0.754291
$699$	−15.4726	−0.585229
$700$	−1.82573	−0.0690062
$701$	21.6537	0.817850	0.408925	−	0.912568i	$-0.365904\pi$
$701$	21.6537	0.817850	0.408925	+	0.912568i	$0.365904\pi$
$702$	−10.9790	−0.414376
$703$	5.82633	0.219744
$704$	−20.7108	−0.780569
$705$	4.29009	0.161574
$706$	−11.1343	−0.419045
$707$	−7.65558	−0.287918
$708$	−13.2984	−0.499784
$709$	−26.0832	−0.979575	−0.489787	−	0.871842i	$-0.662926\pi$
$709$	−26.0832	−0.979575	−0.489787	+	0.871842i	$0.662926\pi$
$710$	−1.96390	−0.0737038
$711$	−6.71706	−0.251909
$712$	29.3599	1.10031
$713$	−1.55695	−0.0583083
$714$	−1.15415	−0.0431929
$715$	−4.88045	−0.182518
$716$	21.6660	0.809696
$717$	3.75831	0.140357
$718$	9.27873	0.346279
$719$	−28.6774	−1.06949	−0.534744	−	0.845014i	$-0.679592\pi$
$719$	−28.6774	−1.06949	−0.534744	+	0.845014i	$0.679592\pi$
$720$	−0.706683	−0.0263365
$721$	−5.86527	−0.218434
$722$	1.05329	0.0391995
$723$	−15.9238	−0.592211
$724$	−10.2136	−0.379584
$725$	28.5852	1.06163
$726$	6.20040	0.230118
$727$	10.8996	0.404244	0.202122	−	0.979360i	$-0.435216\pi$
$727$	10.8996	0.404244	0.202122	+	0.979360i	$0.435216\pi$
$728$	−2.88234	−0.106827
$729$	29.9070	1.10767
$730$	−4.67348	−0.172973
$731$	10.7368	0.397114
$732$	4.80651	0.177654
$733$	−15.1370	−0.559097	−0.279548	−	0.960132i	$-0.590185\pi$
$733$	−15.1370	−0.559097	−0.279548	+	0.960132i	$0.590185\pi$
$734$	−1.87713	−0.0692861
$735$	−10.2365	−0.377580
$736$	1.44081	0.0531090
$737$	21.9013	0.806745
$738$	4.10861	0.151240
$739$	−45.5758	−1.67653	−0.838267	−	0.545260i	$-0.816431\pi$
$739$	−45.5758	−1.67653	−0.838267	+	0.545260i	$0.816431\pi$
$740$	−4.99412	−0.183587
$741$	−2.96545	−0.108939
$742$	5.91360	0.217095
$743$	47.8450	1.75526	0.877632	−	0.479335i	$-0.159122\pi$
$743$	47.8450	1.75526	0.877632	+	0.479335i	$0.159122\pi$
$744$	−23.7927	−0.872284
$745$	5.75614	0.210889
$746$	32.5484	1.19168
$747$	−0.934645	−0.0341969
$748$	−3.31566	−0.121233
$749$	2.33115	0.0851785
$750$	−14.5007	−0.529491
$751$	−33.6249	−1.22699	−0.613495	−	0.789699i	$-0.710237\pi$
$751$	−33.6249	−1.22699	−0.613495	+	0.789699i	$0.710237\pi$
$752$	−4.03130	−0.147006
$753$	2.74431	0.100008
$754$	13.9039	0.506349
$755$	−14.0531	−0.511444
$756$	2.48339	0.0903198
$757$	−50.8130	−1.84683	−0.923415	−	0.383804i	$-0.874614\pi$
$757$	−50.8130	−1.84683	−0.923415	+	0.383804i	$0.874614\pi$
$758$	9.23170	0.335310
$759$	1.33454	0.0484409
$760$	−2.93040	−0.106297
$761$	−32.6552	−1.18375	−0.591875	−	0.806029i	$-0.701612\pi$
$761$	−32.6552	−1.18375	−0.591875	+	0.806029i	$0.701612\pi$
$762$	−15.0694	−0.545905
$763$	−2.36698	−0.0856903
$764$	−19.3845	−0.701306
$765$	−0.684616	−0.0247524
$766$	−19.4824	−0.703926
$767$	17.8193	0.643418
$768$	26.0211	0.938956
$769$	−15.4007	−0.555364	−0.277682	−	0.960673i	$-0.589566\pi$
$769$	−15.4007	−0.555364	−0.277682	+	0.960673i	$0.589566\pi$
$770$	−1.37521	−0.0495592
$771$	−8.44108	−0.303998
$772$	15.9964	0.575723
$773$	−14.0832	−0.506537	−0.253268	−	0.967396i	$-0.581506\pi$
$773$	−14.0832	−0.506537	−0.253268	+	0.967396i	$0.581506\pi$
$774$	4.21652	0.151560
$775$	20.1942	0.725398
$776$	43.6187	1.56582
$777$	−4.62218	−0.165820
$778$	4.51421	0.161842
$779$	7.57449	0.271384
$780$	2.54188	0.0910138
$781$	−5.22174	−0.186848
$782$	−0.456918	−0.0163394
$783$	−38.8820	−1.38953
$784$	9.61904	0.343537
$785$	−1.15908	−0.0413693
$786$	−36.2039	−1.29135
$787$	9.17379	0.327010	0.163505	−	0.986542i	$-0.447720\pi$
$787$	9.17379	0.327010	0.163505	+	0.986542i	$0.447720\pi$
$788$	−11.3302	−0.403622
$789$	13.0987	0.466324
$790$	−13.2230	−0.470454
$791$	−7.82453	−0.278208
$792$	−4.22635	−0.150177
$793$	−6.44053	−0.228710
$794$	4.26858	0.151486
$795$	−16.9268	−0.600332
$796$	0.0627653	0.00222466
$797$	−9.67361	−0.342657	−0.171328	−	0.985214i	$-0.554806\pi$
$797$	−9.67361	−0.342657	−0.171328	+	0.985214i	$0.554806\pi$
$798$	−0.835604	−0.0295801
$799$	−3.90542	−0.138164
$800$	−18.6879	−0.660715
$801$	4.96608	0.175468
$802$	−28.5489	−1.00810
$803$	−12.4261	−0.438509
$804$	−11.4068	−0.402288
$805$	0.152128	0.00536181
$806$	9.82249	0.345982
$807$	9.52581	0.335324
$808$	−46.3153	−1.62937
$809$	46.6742	1.64098	0.820489	−	0.571663i	$-0.193701\pi$
$809$	46.6742	1.64098	0.820489	+	0.571663i	$0.193701\pi$
$810$	7.28892	0.256107
$811$	−23.6887	−0.831823	−0.415912	−	0.909405i	$-0.636537\pi$
$811$	−23.6887	−0.831823	−0.415912	+	0.909405i	$0.636537\pi$
$812$	−3.14497	−0.110367
$813$	−20.3391	−0.713322
$814$	16.5418	0.579792
$815$	13.6137	0.476867
$816$	−3.10430	−0.108672
$817$	7.77343	0.271958
$818$	28.8836	1.00989
$819$	−0.487533	−0.0170358
$820$	−6.49258	−0.226731
$821$	−22.6680	−0.791117	−0.395559	−	0.918441i	$-0.629449\pi$
$821$	−22.6680	−0.791117	−0.395559	+	0.918441i	$0.629449\pi$
$822$	14.5272	0.506693
$823$	39.0048	1.35962	0.679810	−	0.733388i	$-0.262062\pi$
$823$	39.0048	1.35962	0.679810	+	0.733388i	$0.262062\pi$
$824$	−35.4842	−1.23615
$825$	−17.3095	−0.602640
$826$	5.02112	0.174707
$827$	8.13528	0.282892	0.141446	−	0.989946i	$-0.454825\pi$
$827$	8.13528	0.282892	0.141446	+	0.989946i	$0.454825\pi$
$828$	0.144042	0.00500582
$829$	−46.0216	−1.59840	−0.799198	−	0.601068i	$-0.794742\pi$
$829$	−46.0216	−1.59840	−0.799198	+	0.601068i	$0.794742\pi$
$830$	−1.83992	−0.0638645
$831$	5.79529	0.201036
$832$	−14.4539	−0.501097
$833$	9.31869	0.322873
$834$	34.1542	1.18266
$835$	9.56007	0.330840
$836$	−2.40054	−0.0830245
$837$	−27.4685	−0.949449
$838$	33.2638	1.14908
$839$	−27.2851	−0.941985	−0.470992	−	0.882137i	$-0.656104\pi$
$839$	−27.2851	−0.941985	−0.470992	+	0.882137i	$0.656104\pi$
$840$	2.32476	0.0802120
$841$	20.2404	0.697945
$842$	3.42288	0.117960
$843$	−28.7344	−0.989666
$844$	25.6601	0.883257
$845$	9.10630	0.313266
$846$	−1.53373	−0.0527306
$847$	1.87928	0.0645729
$848$	15.9057	0.546205
$849$	18.3879	0.631072
$850$	5.92640	0.203274
$851$	−1.82988	−0.0627276
$852$	2.71963	0.0931730
$853$	44.5899	1.52673	0.763364	−	0.645969i	$-0.223546\pi$
$853$	44.5899	1.52673	0.763364	+	0.645969i	$0.223546\pi$
$854$	−1.81481	−0.0621016
$855$	−0.495663	−0.0169513
$856$	14.1032	0.482037
$857$	17.5103	0.598140	0.299070	−	0.954231i	$-0.403324\pi$
$857$	17.5103	0.598140	0.299070	+	0.954231i	$0.403324\pi$
$858$	−8.41937	−0.287433
$859$	−13.8986	−0.474213	−0.237106	−	0.971484i	$-0.576199\pi$
$859$	−13.8986	−0.474213	−0.237106	+	0.971484i	$0.576199\pi$
$860$	−6.66310	−0.227210
$861$	−6.00904	−0.204787
$862$	16.9745	0.578154
$863$	−4.56684	−0.155457	−0.0777285	−	0.996975i	$-0.524767\pi$
$863$	−4.56684	−0.155457	−0.0777285	+	0.996975i	$0.524767\pi$
$864$	25.4195	0.864788
$865$	−0.733894	−0.0249532
$866$	−20.8872	−0.709775
$867$	23.7913	0.807996
$868$	−2.22179	−0.0754124
$869$	−35.1582	−1.19266
$870$	−11.2142	−0.380198
$871$	15.2847	0.517902
$872$	−14.3199	−0.484934
$873$	7.37787	0.249703
$874$	−0.330809	−0.0111898
$875$	−4.39503	−0.148579
$876$	6.47189	0.218665
$877$	33.5984	1.13454	0.567268	−	0.823533i	$-0.308000\pi$
$877$	33.5984	1.13454	0.567268	+	0.823533i	$0.308000\pi$
$878$	−7.75755	−0.261804
$879$	43.2565	1.45900
$880$	−3.69890	−0.124690
$881$	16.5631	0.558023	0.279012	−	0.960288i	$-0.409993\pi$
$881$	16.5631	0.558023	0.279012	+	0.960288i	$0.409993\pi$
$882$	3.65961	0.123226
$883$	−42.5696	−1.43258	−0.716291	−	0.697802i	$-0.754162\pi$
$883$	−42.5696	−1.43258	−0.716291	+	0.697802i	$0.754162\pi$
$884$	−2.31396	−0.0778270
$885$	−14.3722	−0.483117
$886$	−21.0939	−0.708663
$887$	−12.9142	−0.433617	−0.216808	−	0.976214i	$-0.569565\pi$
$887$	−12.9142	−0.433617	−0.216808	+	0.976214i	$0.569565\pi$
$888$	−27.9636	−0.938397
$889$	−4.56738	−0.153185
$890$	9.77609	0.327695
$891$	19.3802	0.649263
$892$	−3.20245	−0.107226
$893$	−2.82753	−0.0946196
$894$	9.93005	0.332110
$895$	23.4155	0.782693
$896$	0.544570	0.0181928
$897$	0.931363	0.0310973
$898$	−34.6581	−1.15656
$899$	34.7862	1.16019
$900$	−1.86828	−0.0622760
$901$	15.4091	0.513351
$902$	21.5052	0.716043
$903$	−6.16686	−0.205220
$904$	−47.3375	−1.57442
$905$	−11.0383	−0.366925
$906$	−24.2433	−0.805429
$907$	−17.3641	−0.576566	−0.288283	−	0.957545i	$-0.593084\pi$
$907$	−17.3641	−0.576566	−0.288283	+	0.957545i	$0.593084\pi$
$908$	19.5677	0.649378
$909$	−7.83400	−0.259837
$910$	−0.959745	−0.0318152
$911$	−20.2821	−0.671977	−0.335988	−	0.941866i	$-0.609070\pi$
$911$	−20.2821	−0.671977	−0.335988	+	0.941866i	$0.609070\pi$
$912$	−2.24752	−0.0744227
$913$	−4.89209	−0.161905
$914$	−7.46260	−0.246841
$915$	5.19463	0.171729
$916$	−21.9847	−0.726396
$917$	−10.9731	−0.362362
$918$	−8.06117	−0.266058
$919$	26.6233	0.878220	0.439110	−	0.898433i	$-0.355294\pi$
$919$	26.6233	0.878220	0.439110	+	0.898433i	$0.355294\pi$
$920$	0.920356	0.0303432
$921$	−51.3005	−1.69041
$922$	−15.4905	−0.510154
$923$	−3.64419	−0.119950
$924$	1.90441	0.0626505
$925$	23.7343	0.780378
$926$	−33.3683	−1.09655
$927$	−6.00197	−0.197130
$928$	−32.1914	−1.05673
$929$	25.8704	0.848779	0.424390	−	0.905480i	$-0.360489\pi$
$929$	25.8704	0.848779	0.424390	+	0.905480i	$0.360489\pi$
$930$	−7.92236	−0.259785
$931$	6.74674	0.221115
$932$	−8.74117	−0.286327
$933$	25.9232	0.848688
$934$	−7.29199	−0.238601
$935$	−3.58340	−0.117190
$936$	−2.94952	−0.0964080
$937$	23.2948	0.761008	0.380504	−	0.924779i	$-0.375750\pi$
$937$	23.2948	0.761008	0.380504	+	0.924779i	$0.375750\pi$
$938$	4.30692	0.140626
$939$	−18.6554	−0.608796
$940$	2.42365	0.0790509
$941$	−35.4177	−1.15458	−0.577291	−	0.816538i	$-0.695890\pi$
$941$	−35.4177	−1.15458	−0.577291	+	0.816538i	$0.695890\pi$
$942$	−1.99955	−0.0651489
$943$	−2.37893	−0.0774687
$944$	13.5053	0.439559
$945$	2.68391	0.0873078
$946$	22.0700	0.717556
$947$	−20.0870	−0.652739	−0.326370	−	0.945242i	$-0.605825\pi$
$947$	−20.0870	−0.652739	−0.326370	+	0.945242i	$0.605825\pi$
$948$	18.3114	0.594727
$949$	−8.67206	−0.281507
$950$	4.29072	0.139209
$951$	−1.57639	−0.0511181
$952$	−2.11632	−0.0685902
$953$	−26.1168	−0.846006	−0.423003	−	0.906128i	$-0.639024\pi$
$953$	−26.1168	−0.846006	−0.423003	+	0.906128i	$0.639024\pi$
$954$	6.05142	0.195922
$955$	−20.9497	−0.677918
$956$	2.12323	0.0686702
$957$	−29.8171	−0.963849
$958$	−42.4909	−1.37282
$959$	4.40305	0.142182
$960$	11.6578	0.376254
$961$	−6.42503	−0.207259
$962$	11.5444	0.372205
$963$	2.38548	0.0768711
$964$	−8.99602	−0.289742
$965$	17.2881	0.556523
$966$	0.262439	0.00844385
$967$	37.8897	1.21845	0.609225	−	0.792998i	$-0.291481\pi$
$967$	37.8897	1.21845	0.609225	+	0.792998i	$0.291481\pi$
$968$	11.3694	0.365428
$969$	−2.17734	−0.0699462
$970$	14.5239	0.466334
$971$	46.7458	1.50014	0.750072	−	0.661356i	$-0.230019\pi$
$971$	46.7458	1.50014	0.750072	+	0.661356i	$0.230019\pi$
$972$	4.71020	0.151080
$973$	10.3518	0.331864
$974$	0.972625	0.0311649
$975$	−12.0801	−0.386873
$976$	−4.88128	−0.156246
$977$	−33.5785	−1.07427	−0.537136	−	0.843496i	$-0.680494\pi$
$977$	−33.5785	−1.07427	−0.537136	+	0.843496i	$0.680494\pi$
$978$	23.4853	0.750977
$979$	25.9933	0.830749
$980$	−5.78306	−0.184733
$981$	−2.42214	−0.0773330
$982$	31.2400	0.996909
$983$	−58.7664	−1.87436	−0.937178	−	0.348851i	$-0.886572\pi$
$983$	−58.7664	−1.87436	−0.937178	+	0.348851i	$0.886572\pi$
$984$	−36.3540	−1.15892
$985$	−12.2451	−0.390161
$986$	10.2087	0.325112
$987$	2.24315	0.0714002
$988$	−1.67531	−0.0532987
$989$	−2.44141	−0.0776324
$990$	−1.40726	−0.0447258
$991$	−37.8485	−1.20230	−0.601148	−	0.799138i	$-0.705290\pi$
$991$	−37.8485	−1.20230	−0.601148	+	0.799138i	$0.705290\pi$
$992$	−22.7418	−0.722053
$993$	22.4174	0.711393
$994$	−1.02686	−0.0325700
$995$	0.0678335	0.00215047
$996$	2.54794	0.0807346
$997$	21.5018	0.680968	0.340484	−	0.940250i	$-0.389409\pi$
$997$	21.5018	0.680968	0.340484	+	0.940250i	$0.389409\pi$
$998$	−38.9936	−1.23432
$999$	−32.2837	−1.02141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.91	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.91	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05329 q^{2} -1.57639 q^{3} -0.890573 q^{4} -0.962486 q^{5} -1.66041 q^{6} -0.503253 q^{7} -3.04462 q^{8} -0.514982 q^{9} +O(q^{10})\)	\(q+1.05329 q^{2} -1.57639 q^{3} -0.890573 q^{4} -0.962486 q^{5} -1.66041 q^{6} -0.503253 q^{7} -3.04462 q^{8} -0.514982 q^{9} -1.01378 q^{10} -2.69550 q^{11} +1.40389 q^{12} -1.88116 q^{13} -0.530073 q^{14} +1.51726 q^{15} -1.42573 q^{16} -1.38121 q^{17} -0.542427 q^{18} -1.00000 q^{19} +0.857164 q^{20} +0.793325 q^{21} -2.83915 q^{22} +0.314071 q^{23} +4.79952 q^{24} -4.07362 q^{25} -1.98141 q^{26} +5.54100 q^{27} +0.448184 q^{28} -7.01715 q^{29} +1.59812 q^{30} -4.95731 q^{31} +4.58753 q^{32} +4.24917 q^{33} -1.45482 q^{34} +0.484374 q^{35} +0.458629 q^{36} -5.82633 q^{37} -1.05329 q^{38} +2.96545 q^{39} +2.93040 q^{40} -7.57449 q^{41} +0.835604 q^{42} -7.77343 q^{43} +2.40054 q^{44} +0.495663 q^{45} +0.330809 q^{46} +2.82753 q^{47} +2.24752 q^{48} -6.74674 q^{49} -4.29072 q^{50} +2.17734 q^{51} +1.67531 q^{52} -11.1562 q^{53} +5.83629 q^{54} +2.59438 q^{55} +1.53222 q^{56} +1.57639 q^{57} -7.39112 q^{58} -9.47250 q^{59} -1.35123 q^{60} +3.42370 q^{61} -5.22151 q^{62} +0.259166 q^{63} +7.68348 q^{64} +1.81059 q^{65} +4.47563 q^{66} -8.12513 q^{67} +1.23007 q^{68} -0.495100 q^{69} +0.510188 q^{70} +1.93720 q^{71} +1.56793 q^{72} +4.60995 q^{73} -6.13683 q^{74} +6.42163 q^{75} +0.890573 q^{76} +1.35652 q^{77} +3.12349 q^{78} +13.0433 q^{79} +1.37225 q^{80} -7.18985 q^{81} -7.97816 q^{82} +1.81491 q^{83} -0.706514 q^{84} +1.32940 q^{85} -8.18770 q^{86} +11.0618 q^{87} +8.20678 q^{88} -9.64321 q^{89} +0.522078 q^{90} +0.946700 q^{91} -0.279704 q^{92} +7.81468 q^{93} +2.97822 q^{94} +0.962486 q^{95} -7.23175 q^{96} -14.3265 q^{97} -7.10629 q^{98} +1.38813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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