LMFDB - Embedded newform 6038.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$1$
Dimension:	$57$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.79555 q^{3} +1.00000 q^{4} +3.22751 q^{5} +1.79555 q^{6} -1.51507 q^{7} -1.00000 q^{8} +0.223993 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.79555 q^{3} +1.00000 q^{4} +3.22751 q^{5} +1.79555 q^{6} -1.51507 q^{7} -1.00000 q^{8} +0.223993 q^{9} -3.22751 q^{10} -0.334044 q^{11} -1.79555 q^{12} -3.11595 q^{13} +1.51507 q^{14} -5.79514 q^{15} +1.00000 q^{16} -0.373017 q^{17} -0.223993 q^{18} +5.41572 q^{19} +3.22751 q^{20} +2.72038 q^{21} +0.334044 q^{22} -7.71658 q^{23} +1.79555 q^{24} +5.41680 q^{25} +3.11595 q^{26} +4.98445 q^{27} -1.51507 q^{28} -1.39739 q^{29} +5.79514 q^{30} +0.765930 q^{31} -1.00000 q^{32} +0.599792 q^{33} +0.373017 q^{34} -4.88990 q^{35} +0.223993 q^{36} -3.58127 q^{37} -5.41572 q^{38} +5.59483 q^{39} -3.22751 q^{40} +3.21312 q^{41} -2.72038 q^{42} +5.17046 q^{43} -0.334044 q^{44} +0.722937 q^{45} +7.71658 q^{46} +11.4314 q^{47} -1.79555 q^{48} -4.70456 q^{49} -5.41680 q^{50} +0.669770 q^{51} -3.11595 q^{52} +10.1849 q^{53} -4.98445 q^{54} -1.07813 q^{55} +1.51507 q^{56} -9.72418 q^{57} +1.39739 q^{58} +14.8169 q^{59} -5.79514 q^{60} -11.7310 q^{61} -0.765930 q^{62} -0.339365 q^{63} +1.00000 q^{64} -10.0567 q^{65} -0.599792 q^{66} +2.38148 q^{67} -0.373017 q^{68} +13.8555 q^{69} +4.88990 q^{70} -14.9770 q^{71} -0.223993 q^{72} +7.44897 q^{73} +3.58127 q^{74} -9.72613 q^{75} +5.41572 q^{76} +0.506101 q^{77} -5.59483 q^{78} +3.83842 q^{79} +3.22751 q^{80} -9.62180 q^{81} -3.21312 q^{82} -5.05547 q^{83} +2.72038 q^{84} -1.20392 q^{85} -5.17046 q^{86} +2.50908 q^{87} +0.334044 q^{88} -13.8973 q^{89} -0.722937 q^{90} +4.72088 q^{91} -7.71658 q^{92} -1.37526 q^{93} -11.4314 q^{94} +17.4793 q^{95} +1.79555 q^{96} -8.56170 q^{97} +4.70456 q^{98} -0.0748234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) $ 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.79555	−1.03666	−0.518330	−	0.855181i	$-0.673446\pi$
$3$	−1.79555	−1.03666	−0.518330	+	0.855181i	$0.673446\pi$
$4$	1.00000	0.500000
$5$	3.22751	1.44339	0.721693	−	0.692214i	$-0.243364\pi$
$5$	3.22751	1.44339	0.721693	+	0.692214i	$0.243364\pi$
$6$	1.79555	0.733029
$7$	−1.51507	−0.572643	−0.286322	−	0.958134i	$-0.592433\pi$
$7$	−1.51507	−0.572643	−0.286322	+	0.958134i	$0.592433\pi$
$8$	−1.00000	−0.353553
$9$	0.223993	0.0746642
$10$	−3.22751	−1.02063
$11$	−0.334044	−0.100718	−0.0503590	−	0.998731i	$-0.516037\pi$
$11$	−0.334044	−0.100718	−0.0503590	+	0.998731i	$0.516037\pi$
$12$	−1.79555	−0.518330
$13$	−3.11595	−0.864209	−0.432104	−	0.901824i	$-0.642229\pi$
$13$	−3.11595	−0.864209	−0.432104	+	0.901824i	$0.642229\pi$
$14$	1.51507	0.404920
$15$	−5.79514	−1.49630
$16$	1.00000	0.250000
$17$	−0.373017	−0.0904700	−0.0452350	−	0.998976i	$-0.514404\pi$
$17$	−0.373017	−0.0904700	−0.0452350	+	0.998976i	$0.514404\pi$
$18$	−0.223993	−0.0527955
$19$	5.41572	1.24245	0.621225	−	0.783632i	$-0.286635\pi$
$19$	5.41572	1.24245	0.621225	+	0.783632i	$0.286635\pi$
$20$	3.22751	0.721693
$21$	2.72038	0.593636
$22$	0.334044	0.0712185
$23$	−7.71658	−1.60902	−0.804509	−	0.593940i	$-0.797572\pi$
$23$	−7.71658	−1.60902	−0.804509	+	0.593940i	$0.797572\pi$
$24$	1.79555	0.366515
$25$	5.41680	1.08336
$26$	3.11595	0.611088
$27$	4.98445	0.959259
$28$	−1.51507	−0.286322
$29$	−1.39739	−0.259489	−0.129744	−	0.991547i	$-0.541416\pi$
$29$	−1.39739	−0.259489	−0.129744	+	0.991547i	$0.541416\pi$
$30$	5.79514	1.05804
$31$	0.765930	0.137565	0.0687825	−	0.997632i	$-0.478089\pi$
$31$	0.765930	0.137565	0.0687825	+	0.997632i	$0.478089\pi$
$32$	−1.00000	−0.176777
$33$	0.599792	0.104410
$34$	0.373017	0.0639719
$35$	−4.88990	−0.826544
$36$	0.223993	0.0373321
$37$	−3.58127	−0.588757	−0.294378	−	0.955689i	$-0.595113\pi$
$37$	−3.58127	−0.588757	−0.294378	+	0.955689i	$0.595113\pi$
$38$	−5.41572	−0.878545
$39$	5.59483	0.895891
$40$	−3.22751	−0.510314
$41$	3.21312	0.501805	0.250903	−	0.968012i	$-0.419273\pi$
$41$	3.21312	0.501805	0.250903	+	0.968012i	$0.419273\pi$
$42$	−2.72038	−0.419764
$43$	5.17046	0.788488	0.394244	−	0.919006i	$-0.371006\pi$
$43$	5.17046	0.788488	0.394244	+	0.919006i	$0.371006\pi$
$44$	−0.334044	−0.0503590
$45$	0.722937	0.107769
$46$	7.71658	1.13775
$47$	11.4314	1.66744	0.833720	−	0.552187i	$-0.186207\pi$
$47$	11.4314	1.66744	0.833720	+	0.552187i	$0.186207\pi$
$48$	−1.79555	−0.259165
$49$	−4.70456	−0.672080
$50$	−5.41680	−0.766052
$51$	0.669770	0.0937866
$52$	−3.11595	−0.432104
$53$	10.1849	1.39901	0.699504	−	0.714629i	$-0.253404\pi$
$53$	10.1849	1.39901	0.699504	+	0.714629i	$0.253404\pi$
$54$	−4.98445	−0.678298
$55$	−1.07813	−0.145375
$56$	1.51507	0.202460
$57$	−9.72418	−1.28800
$58$	1.39739	0.183486
$59$	14.8169	1.92899	0.964495	−	0.264100i	$-0.0850749\pi$
$59$	14.8169	1.92899	0.964495	+	0.264100i	$0.0850749\pi$
$60$	−5.79514	−0.748150
$61$	−11.7310	−1.50200	−0.751000	−	0.660302i	$-0.770428\pi$
$61$	−11.7310	−1.50200	−0.751000	+	0.660302i	$0.770428\pi$
$62$	−0.765930	−0.0972732
$63$	−0.339365	−0.0427559
$64$	1.00000	0.125000
$65$	−10.0567	−1.24739
$66$	−0.599792	−0.0738293
$67$	2.38148	0.290944	0.145472	−	0.989362i	$-0.453530\pi$
$67$	2.38148	0.290944	0.145472	+	0.989362i	$0.453530\pi$
$68$	−0.373017	−0.0452350
$69$	13.8555	1.66801
$70$	4.88990	0.584455
$71$	−14.9770	−1.77744	−0.888721	−	0.458448i	$-0.848406\pi$
$71$	−14.9770	−1.77744	−0.888721	+	0.458448i	$0.848406\pi$
$72$	−0.223993	−0.0263978
$73$	7.44897	0.871835	0.435918	−	0.899987i	$-0.356424\pi$
$73$	7.44897	0.871835	0.435918	+	0.899987i	$0.356424\pi$
$74$	3.58127	0.416314
$75$	−9.72613	−1.12308
$76$	5.41572	0.621225
$77$	0.506101	0.0576755
$78$	−5.59483	−0.633490
$79$	3.83842	0.431856	0.215928	−	0.976409i	$-0.430722\pi$
$79$	3.83842	0.431856	0.215928	+	0.976409i	$0.430722\pi$
$80$	3.22751	0.360846
$81$	−9.62180	−1.06909
$82$	−3.21312	−0.354830
$83$	−5.05547	−0.554910	−0.277455	−	0.960739i	$-0.589491\pi$
$83$	−5.05547	−0.554910	−0.277455	+	0.960739i	$0.589491\pi$
$84$	2.72038	0.296818
$85$	−1.20392	−0.130583
$86$	−5.17046	−0.557546
$87$	2.50908	0.269002
$88$	0.334044	0.0356092
$89$	−13.8973	−1.47311	−0.736557	−	0.676376i	$-0.763550\pi$
$89$	−13.8973	−1.47311	−0.736557	+	0.676376i	$0.763550\pi$
$90$	−0.722937	−0.0762043
$91$	4.72088	0.494883
$92$	−7.71658	−0.804509
$93$	−1.37526	−0.142608
$94$	−11.4314	−1.17906
$95$	17.4793	1.79334
$96$	1.79555	0.183257
$97$	−8.56170	−0.869309	−0.434654	−	0.900597i	$-0.643130\pi$
$97$	−8.56170	−0.869309	−0.434654	+	0.900597i	$0.643130\pi$
$98$	4.70456	0.475232
$99$	−0.0748234	−0.00752003
$100$	5.41680	0.541680
$101$	−1.53878	−0.153115	−0.0765573	−	0.997065i	$-0.524393\pi$
$101$	−1.53878	−0.153115	−0.0765573	+	0.997065i	$0.524393\pi$
$102$	−0.669770	−0.0663172
$103$	−13.0599	−1.28683	−0.643416	−	0.765516i	$-0.722484\pi$
$103$	−13.0599	−1.28683	−0.643416	+	0.765516i	$0.722484\pi$
$104$	3.11595	0.305544
$105$	8.78005	0.856846
$106$	−10.1849	−0.989248
$107$	−5.71617	−0.552603	−0.276301	−	0.961071i	$-0.589109\pi$
$107$	−5.71617	−0.552603	−0.276301	+	0.961071i	$0.589109\pi$
$108$	4.98445	0.479629
$109$	13.4059	1.28406	0.642028	−	0.766681i	$-0.278093\pi$
$109$	13.4059	1.28406	0.642028	+	0.766681i	$0.278093\pi$
$110$	1.07813	0.102796
$111$	6.43034	0.610340
$112$	−1.51507	−0.143161
$113$	−12.2023	−1.14790	−0.573949	−	0.818891i	$-0.694589\pi$
$113$	−12.2023	−1.14790	−0.573949	+	0.818891i	$0.694589\pi$
$114$	9.72418	0.910753
$115$	−24.9053	−2.32243
$116$	−1.39739	−0.129744
$117$	−0.697949	−0.0645254
$118$	−14.8169	−1.36400
$119$	0.565148	0.0518070
$120$	5.79514	0.529022
$121$	−10.8884	−0.989856
$122$	11.7310	1.06207
$123$	−5.76931	−0.520201
$124$	0.765930	0.0687825
$125$	1.34524	0.120321
$126$	0.339365	0.0302330
$127$	−15.9462	−1.41500	−0.707499	−	0.706715i	$-0.750176\pi$
$127$	−15.9462	−1.41500	−0.707499	+	0.706715i	$0.750176\pi$
$128$	−1.00000	−0.0883883
$129$	−9.28382	−0.817394
$130$	10.0567	0.882035
$131$	12.2150	1.06723	0.533613	−	0.845729i	$-0.320834\pi$
$131$	12.2150	1.06723	0.533613	+	0.845729i	$0.320834\pi$
$132$	0.599792	0.0522052
$133$	−8.20520	−0.711481
$134$	−2.38148	−0.205729
$135$	16.0874	1.38458
$136$	0.373017	0.0319860
$137$	−6.10340	−0.521449	−0.260724	−	0.965413i	$-0.583961\pi$
$137$	−6.10340	−0.521449	−0.260724	+	0.965413i	$0.583961\pi$
$138$	−13.8555	−1.17946
$139$	20.4553	1.73499	0.867497	−	0.497442i	$-0.165727\pi$
$139$	20.4553	1.73499	0.867497	+	0.497442i	$0.165727\pi$
$140$	−4.88990	−0.413272
$141$	−20.5256	−1.72857
$142$	14.9770	1.25684
$143$	1.04086	0.0870414
$144$	0.223993	0.0186660
$145$	−4.51009	−0.374542
$146$	−7.44897	−0.616481
$147$	8.44726	0.696718
$148$	−3.58127	−0.294378
$149$	1.96177	0.160715	0.0803573	−	0.996766i	$-0.474394\pi$
$149$	1.96177	0.160715	0.0803573	+	0.996766i	$0.474394\pi$
$150$	9.72613	0.794135
$151$	−1.76024	−0.143247	−0.0716233	−	0.997432i	$-0.522818\pi$
$151$	−1.76024	−0.143247	−0.0716233	+	0.997432i	$0.522818\pi$
$152$	−5.41572	−0.439273
$153$	−0.0835531	−0.00675487
$154$	−0.506101	−0.0407827
$155$	2.47204	0.198559
$156$	5.59483	0.447945
$157$	−13.7698	−1.09895	−0.549475	−	0.835510i	$-0.685172\pi$
$157$	−13.7698	−1.09895	−0.549475	+	0.835510i	$0.685172\pi$
$158$	−3.83842	−0.305368
$159$	−18.2875	−1.45030
$160$	−3.22751	−0.255157
$161$	11.6912	0.921393
$162$	9.62180	0.755960
$163$	−0.992885	−0.0777688	−0.0388844	−	0.999244i	$-0.512380\pi$
$163$	−0.992885	−0.0777688	−0.0388844	+	0.999244i	$0.512380\pi$
$164$	3.21312	0.250903
$165$	1.93583	0.150704
$166$	5.05547	0.392380
$167$	−4.33513	−0.335463	−0.167731	−	0.985833i	$-0.553644\pi$
$167$	−4.33513	−0.335463	−0.167731	+	0.985833i	$0.553644\pi$
$168$	−2.72038	−0.209882
$169$	−3.29087	−0.253144
$170$	1.20392	0.0923361
$171$	1.21308	0.0927666
$172$	5.17046	0.394244
$173$	−15.8554	−1.20547	−0.602733	−	0.797943i	$-0.705922\pi$
$173$	−15.8554	−1.20547	−0.602733	+	0.797943i	$0.705922\pi$
$174$	−2.50908	−0.190213
$175$	−8.20684	−0.620379
$176$	−0.334044	−0.0251795
$177$	−26.6044	−1.99971
$178$	13.8973	1.04165
$179$	6.22917	0.465590	0.232795	−	0.972526i	$-0.425213\pi$
$179$	6.22917	0.465590	0.232795	+	0.972526i	$0.425213\pi$
$180$	0.722937	0.0538846
$181$	22.6373	1.68262	0.841308	−	0.540556i	$-0.181786\pi$
$181$	22.6373	1.68262	0.841308	+	0.540556i	$0.181786\pi$
$182$	−4.72088	−0.349935
$183$	21.0636	1.55706
$184$	7.71658	0.568874
$185$	−11.5586	−0.849802
$186$	1.37526	0.100839
$187$	0.124604	0.00911196
$188$	11.4314	0.833720
$189$	−7.55180	−0.549313
$190$	−17.4793	−1.26808
$191$	−5.10676	−0.369512	−0.184756	−	0.982784i	$-0.559149\pi$
$191$	−5.10676	−0.369512	−0.184756	+	0.982784i	$0.559149\pi$
$192$	−1.79555	−0.129583
$193$	20.8372	1.49989	0.749947	−	0.661498i	$-0.230079\pi$
$193$	20.8372	1.49989	0.749947	+	0.661498i	$0.230079\pi$
$194$	8.56170	0.614694
$195$	18.0574	1.29312
$196$	−4.70456	−0.336040
$197$	−27.2669	−1.94269	−0.971343	−	0.237682i	$-0.923612\pi$
$197$	−27.2669	−1.94269	−0.971343	+	0.237682i	$0.923612\pi$
$198$	0.0748234	0.00531747
$199$	26.1977	1.85711	0.928554	−	0.371196i	$-0.121052\pi$
$199$	26.1977	1.85711	0.928554	+	0.371196i	$0.121052\pi$
$200$	−5.41680	−0.383026
$201$	−4.27606	−0.301610
$202$	1.53878	0.108268
$203$	2.11715	0.148594
$204$	0.669770	0.0468933
$205$	10.3704	0.724298
$206$	13.0599	0.909928
$207$	−1.72846	−0.120136
$208$	−3.11595	−0.216052
$209$	−1.80909	−0.125137
$210$	−8.78005	−0.605881
$211$	−17.3817	−1.19661	−0.598303	−	0.801270i	$-0.704158\pi$
$211$	−17.3817	−1.19661	−0.598303	+	0.801270i	$0.704158\pi$
$212$	10.1849	0.699504
$213$	26.8919	1.84260
$214$	5.71617	0.390749
$215$	16.6877	1.13809
$216$	−4.98445	−0.339149
$217$	−1.16044	−0.0787756
$218$	−13.4059	−0.907965
$219$	−13.3750	−0.903797
$220$	−1.07813	−0.0726875
$221$	1.16230	0.0781849
$222$	−6.43034	−0.431576
$223$	−6.77608	−0.453760	−0.226880	−	0.973923i	$-0.572853\pi$
$223$	−6.77608	−0.453760	−0.226880	+	0.973923i	$0.572853\pi$
$224$	1.51507	0.101230
$225$	1.21332	0.0808882
$226$	12.2023	0.811686
$227$	0.845167	0.0560957	0.0280479	−	0.999607i	$-0.491071\pi$
$227$	0.845167	0.0560957	0.0280479	+	0.999607i	$0.491071\pi$
$228$	−9.72418	−0.644000
$229$	−3.49449	−0.230922	−0.115461	−	0.993312i	$-0.536835\pi$
$229$	−3.49449	−0.230922	−0.115461	+	0.993312i	$0.536835\pi$
$230$	24.9053	1.64221
$231$	−0.908728	−0.0597899
$232$	1.39739	0.0917431
$233$	5.57411	0.365172	0.182586	−	0.983190i	$-0.441553\pi$
$233$	5.57411	0.365172	0.182586	+	0.983190i	$0.441553\pi$
$234$	0.697949	0.0456264
$235$	36.8949	2.40676
$236$	14.8169	0.964495
$237$	−6.89206	−0.447687
$238$	−0.565148	−0.0366331
$239$	−10.6176	−0.686793	−0.343396	−	0.939191i	$-0.611577\pi$
$239$	−10.6176	−0.686793	−0.343396	+	0.939191i	$0.611577\pi$
$240$	−5.79514	−0.374075
$241$	−10.1537	−0.654056	−0.327028	−	0.945015i	$-0.606047\pi$
$241$	−10.1537	−0.654056	−0.327028	+	0.945015i	$0.606047\pi$
$242$	10.8884	0.699934
$243$	2.32305	0.149024
$244$	−11.7310	−0.751000
$245$	−15.1840	−0.970070
$246$	5.76931	0.367838
$247$	−16.8751	−1.07374
$248$	−0.765930	−0.0486366
$249$	9.07733	0.575253
$250$	−1.34524	−0.0850801
$251$	25.0526	1.58131	0.790653	−	0.612265i	$-0.209741\pi$
$251$	25.0526	1.58131	0.790653	+	0.612265i	$0.209741\pi$
$252$	−0.339365	−0.0213780
$253$	2.57768	0.162057
$254$	15.9462	1.00055
$255$	2.16169	0.135370
$256$	1.00000	0.0625000
$257$	13.4927	0.841652	0.420826	−	0.907141i	$-0.361740\pi$
$257$	13.4927	0.841652	0.420826	+	0.907141i	$0.361740\pi$
$258$	9.28382	0.577985
$259$	5.42587	0.337147
$260$	−10.0567	−0.623693
$261$	−0.313005	−0.0193745
$262$	−12.2150	−0.754643
$263$	−15.4617	−0.953411	−0.476705	−	0.879063i	$-0.658169\pi$
$263$	−15.4617	−0.953411	−0.476705	+	0.879063i	$0.658169\pi$
$264$	−0.599792	−0.0369147
$265$	32.8719	2.01931
$266$	8.20520	0.503093
$267$	24.9533	1.52712
$268$	2.38148	0.145472
$269$	−4.05450	−0.247207	−0.123604	−	0.992332i	$-0.539445\pi$
$269$	−4.05450	−0.247207	−0.123604	+	0.992332i	$0.539445\pi$
$270$	−16.0874	−0.979046
$271$	27.3851	1.66353	0.831763	−	0.555131i	$-0.187332\pi$
$271$	27.3851	1.66353	0.831763	+	0.555131i	$0.187332\pi$
$272$	−0.373017	−0.0226175
$273$	−8.47657	−0.513025
$274$	6.10340	0.368720
$275$	−1.80945	−0.109114
$276$	13.8555	0.834003
$277$	−2.00032	−0.120188	−0.0600939	−	0.998193i	$-0.519140\pi$
$277$	−2.00032	−0.120188	−0.0600939	+	0.998193i	$0.519140\pi$
$278$	−20.4553	−1.22683
$279$	0.171562	0.0102712
$280$	4.88990	0.292228
$281$	8.13677	0.485399	0.242699	−	0.970102i	$-0.421967\pi$
$281$	8.13677	0.485399	0.242699	+	0.970102i	$0.421967\pi$
$282$	20.5256	1.22228
$283$	10.0343	0.596477	0.298238	−	0.954491i	$-0.403601\pi$
$283$	10.0343	0.596477	0.298238	+	0.954491i	$0.403601\pi$
$284$	−14.9770	−0.888721
$285$	−31.3849	−1.85908
$286$	−1.04086	−0.0615476
$287$	−4.86811	−0.287355
$288$	−0.223993	−0.0131989
$289$	−16.8609	−0.991815
$290$	4.51009	0.264841
$291$	15.3729	0.901178
$292$	7.44897	0.435918
$293$	−15.8332	−0.924987	−0.462494	−	0.886623i	$-0.653045\pi$
$293$	−15.8332	−0.924987	−0.462494	+	0.886623i	$0.653045\pi$
$294$	−8.44726	−0.492654
$295$	47.8215	2.78428
$296$	3.58127	0.208157
$297$	−1.66503	−0.0966147
$298$	−1.96177	−0.113642
$299$	24.0445	1.39053
$300$	−9.72613	−0.561538
$301$	−7.83362	−0.451522
$302$	1.76024	0.101291
$303$	2.76296	0.158728
$304$	5.41572	0.310613
$305$	−37.8619	−2.16796
$306$	0.0835531	0.00477641
$307$	−17.0561	−0.973445	−0.486722	−	0.873557i	$-0.661808\pi$
$307$	−17.0561	−0.973445	−0.486722	+	0.873557i	$0.661808\pi$
$308$	0.506101	0.0288378
$309$	23.4497	1.33401
$310$	−2.47204	−0.140403
$311$	−17.3925	−0.986237	−0.493119	−	0.869962i	$-0.664143\pi$
$311$	−17.3925	−0.986237	−0.493119	+	0.869962i	$0.664143\pi$
$312$	−5.59483	−0.316745
$313$	−2.64479	−0.149492	−0.0747460	−	0.997203i	$-0.523815\pi$
$313$	−2.64479	−0.149492	−0.0747460	+	0.997203i	$0.523815\pi$
$314$	13.7698	0.777076
$315$	−1.09530	−0.0617133
$316$	3.83842	0.215928
$317$	5.90314	0.331553	0.165777	−	0.986163i	$-0.446987\pi$
$317$	5.90314	0.331553	0.165777	+	0.986163i	$0.446987\pi$
$318$	18.2875	1.02551
$319$	0.466790	0.0261352
$320$	3.22751	0.180423
$321$	10.2637	0.572861
$322$	−11.6912	−0.651523
$323$	−2.02016	−0.112405
$324$	−9.62180	−0.534545
$325$	−16.8785	−0.936250
$326$	0.992885	0.0549908
$327$	−24.0710	−1.33113
$328$	−3.21312	−0.177415
$329$	−17.3194	−0.954848
$330$	−1.93583	−0.106564
$331$	1.81353	0.0996806	0.0498403	−	0.998757i	$-0.484129\pi$
$331$	1.81353	0.0996806	0.0498403	+	0.998757i	$0.484129\pi$
$332$	−5.05547	−0.277455
$333$	−0.802177	−0.0439590
$334$	4.33513	0.237208
$335$	7.68625	0.419945
$336$	2.72038	0.148409
$337$	−36.0891	−1.96590	−0.982950	−	0.183872i	$-0.941137\pi$
$337$	−36.0891	−1.96590	−0.982950	+	0.183872i	$0.941137\pi$
$338$	3.29087	0.178999
$339$	21.9098	1.18998
$340$	−1.20392	−0.0652915
$341$	−0.255854	−0.0138553
$342$	−1.21308	−0.0655959
$343$	17.7332	0.957505
$344$	−5.17046	−0.278773
$345$	44.7187	2.40757
$346$	15.8554	0.852394
$347$	0.0389920	0.00209320	0.00104660	−	0.999999i	$-0.499667\pi$
$347$	0.0389920	0.00209320	0.00104660	+	0.999999i	$0.499667\pi$
$348$	2.50908	0.134501
$349$	−20.8660	−1.11693	−0.558466	−	0.829528i	$-0.688610\pi$
$349$	−20.8660	−1.11693	−0.558466	+	0.829528i	$0.688610\pi$
$350$	8.20684	0.438674
$351$	−15.5313	−0.829000
$352$	0.334044	0.0178046
$353$	9.26208	0.492971	0.246485	−	0.969147i	$-0.420724\pi$
$353$	9.26208	0.492971	0.246485	+	0.969147i	$0.420724\pi$
$354$	26.6044	1.41401
$355$	−48.3384	−2.56553
$356$	−13.8973	−0.736557
$357$	−1.01475	−0.0537063
$358$	−6.22917	−0.329222
$359$	−33.2513	−1.75494	−0.877468	−	0.479636i	$-0.840769\pi$
$359$	−33.2513	−1.75494	−0.877468	+	0.479636i	$0.840769\pi$
$360$	−0.722937	−0.0381021
$361$	10.3300	0.543684
$362$	−22.6373	−1.18979
$363$	19.5507	1.02614
$364$	4.72088	0.247442
$365$	24.0416	1.25839
$366$	−21.0636	−1.10101
$367$	−23.5350	−1.22852	−0.614259	−	0.789105i	$-0.710545\pi$
$367$	−23.5350	−1.22852	−0.614259	+	0.789105i	$0.710545\pi$
$368$	−7.71658	−0.402255
$369$	0.719715	0.0374669
$370$	11.5586	0.600901
$371$	−15.4309	−0.801132
$372$	−1.37526	−0.0713041
$373$	−27.3080	−1.41395	−0.706977	−	0.707236i	$-0.749942\pi$
$373$	−27.3080	−1.41395	−0.706977	+	0.707236i	$0.749942\pi$
$374$	−0.124604	−0.00644313
$375$	−2.41543	−0.124732
$376$	−11.4314	−0.589529
$377$	4.35420	0.224252
$378$	7.55180	0.388423
$379$	−1.02566	−0.0526847	−0.0263423	−	0.999653i	$-0.508386\pi$
$379$	−1.02566	−0.0526847	−0.0263423	+	0.999653i	$0.508386\pi$
$380$	17.4793	0.896668
$381$	28.6322	1.46687
$382$	5.10676	0.261284
$383$	1.99014	0.101691	0.0508457	−	0.998707i	$-0.483808\pi$
$383$	1.99014	0.101691	0.0508457	+	0.998707i	$0.483808\pi$
$384$	1.79555	0.0916287
$385$	1.63344	0.0832480
$386$	−20.8372	−1.06058
$387$	1.15815	0.0588718
$388$	−8.56170	−0.434654
$389$	−30.0810	−1.52517	−0.762585	−	0.646888i	$-0.776070\pi$
$389$	−30.0810	−1.52517	−0.762585	+	0.646888i	$0.776070\pi$
$390$	−18.0574	−0.914370
$391$	2.87842	0.145568
$392$	4.70456	0.237616
$393$	−21.9326	−1.10635
$394$	27.2669	1.37369
$395$	12.3885	0.623334
$396$	−0.0748234	−0.00376002
$397$	14.1628	0.710810	0.355405	−	0.934712i	$-0.384343\pi$
$397$	14.1628	0.710810	0.355405	+	0.934712i	$0.384343\pi$
$398$	−26.1977	−1.31317
$399$	14.7328	0.737564
$400$	5.41680	0.270840
$401$	19.1414	0.955878	0.477939	−	0.878393i	$-0.341384\pi$
$401$	19.1414	0.955878	0.477939	+	0.878393i	$0.341384\pi$
$402$	4.27606	0.213271
$403$	−2.38660	−0.118885
$404$	−1.53878	−0.0765573
$405$	−31.0544	−1.54311
$406$	−2.11715	−0.105072
$407$	1.19630	0.0592984
$408$	−0.669770	−0.0331586
$409$	−36.6969	−1.81455	−0.907274	−	0.420541i	$-0.861840\pi$
$409$	−36.6969	−1.81455	−0.907274	+	0.420541i	$0.861840\pi$
$410$	−10.3704	−0.512156
$411$	10.9589	0.540565
$412$	−13.0599	−0.643416
$413$	−22.4486	−1.10462
$414$	1.72846	0.0849490
$415$	−16.3166	−0.800948
$416$	3.11595	0.152772
$417$	−36.7284	−1.79860
$418$	1.80909	0.0884854
$419$	−38.1489	−1.86370	−0.931848	−	0.362850i	$-0.881804\pi$
$419$	−38.1489	−1.86370	−0.931848	+	0.362850i	$0.881804\pi$
$420$	8.78005	0.428423
$421$	12.4503	0.606791	0.303395	−	0.952865i	$-0.401880\pi$
$421$	12.4503	0.606791	0.303395	+	0.952865i	$0.401880\pi$
$422$	17.3817	0.846128
$423$	2.56055	0.124498
$424$	−10.1849	−0.494624
$425$	−2.02056	−0.0980116
$426$	−26.8919	−1.30292
$427$	17.7733	0.860110
$428$	−5.71617	−0.276301
$429$	−1.86892	−0.0902324
$430$	−16.6877	−0.804753
$431$	−24.9546	−1.20202	−0.601010	−	0.799241i	$-0.705235\pi$
$431$	−24.9546	−1.20202	−0.601010	+	0.799241i	$0.705235\pi$
$432$	4.98445	0.239815
$433$	−9.97520	−0.479377	−0.239689	−	0.970850i	$-0.577045\pi$
$433$	−9.97520	−0.479377	−0.239689	+	0.970850i	$0.577045\pi$
$434$	1.16044	0.0557028
$435$	8.09808	0.388273
$436$	13.4059	0.642028
$437$	−41.7908	−1.99913
$438$	13.3750	0.639081
$439$	−5.47847	−0.261473	−0.130737	−	0.991417i	$-0.541734\pi$
$439$	−5.47847	−0.261473	−0.130737	+	0.991417i	$0.541734\pi$
$440$	1.07813	0.0513978
$441$	−1.05379	−0.0501803
$442$	−1.16230	−0.0552851
$443$	−11.3086	−0.537288	−0.268644	−	0.963240i	$-0.586576\pi$
$443$	−11.3086	−0.537288	−0.268644	+	0.963240i	$0.586576\pi$
$444$	6.43034	0.305170
$445$	−44.8537	−2.12627
$446$	6.77608	0.320857
$447$	−3.52245	−0.166606
$448$	−1.51507	−0.0715804
$449$	32.5124	1.53436	0.767178	−	0.641435i	$-0.221660\pi$
$449$	32.5124	1.53436	0.767178	+	0.641435i	$0.221660\pi$
$450$	−1.21332	−0.0571966
$451$	−1.07332	−0.0505409
$452$	−12.2023	−0.573949
$453$	3.16060	0.148498
$454$	−0.845167	−0.0396657
$455$	15.2367	0.714307
$456$	9.72418	0.455377
$457$	−17.4396	−0.815791	−0.407895	−	0.913029i	$-0.633737\pi$
$457$	−17.4396	−0.815791	−0.407895	+	0.913029i	$0.633737\pi$
$458$	3.49449	0.163287
$459$	−1.85929	−0.0867841
$460$	−24.9053	−1.16122
$461$	41.3549	1.92609	0.963046	−	0.269337i	$-0.0868046\pi$
$461$	41.3549	1.92609	0.963046	+	0.269337i	$0.0868046\pi$
$462$	0.908728	0.0422778
$463$	−7.85555	−0.365079	−0.182539	−	0.983199i	$-0.558432\pi$
$463$	−7.85555	−0.365079	−0.182539	+	0.983199i	$0.558432\pi$
$464$	−1.39739	−0.0648722
$465$	−4.43867	−0.205839
$466$	−5.57411	−0.258216
$467$	11.9750	0.554135	0.277068	−	0.960850i	$-0.410637\pi$
$467$	11.9750	0.554135	0.277068	+	0.960850i	$0.410637\pi$
$468$	−0.697949	−0.0322627
$469$	−3.60811	−0.166607
$470$	−36.8949	−1.70184
$471$	24.7244	1.13924
$472$	−14.8169	−0.682001
$473$	−1.72716	−0.0794151
$474$	6.89206	0.316563
$475$	29.3359	1.34602
$476$	0.565148	0.0259035
$477$	2.28135	0.104456
$478$	10.6176	0.485636
$479$	−9.19535	−0.420146	−0.210073	−	0.977686i	$-0.567370\pi$
$479$	−9.19535	−0.420146	−0.210073	+	0.977686i	$0.567370\pi$
$480$	5.79514	0.264511
$481$	11.1590	0.508808
$482$	10.1537	0.462488
$483$	−20.9921	−0.955172
$484$	−10.8884	−0.494928
$485$	−27.6330	−1.25475
$486$	−2.32305	−0.105376
$487$	−36.4613	−1.65222	−0.826111	−	0.563508i	$-0.809451\pi$
$487$	−36.4613	−1.65222	−0.826111	+	0.563508i	$0.809451\pi$
$488$	11.7310	0.531037
$489$	1.78277	0.0806198
$490$	15.1840	0.685943
$491$	−30.8186	−1.39082	−0.695412	−	0.718611i	$-0.744778\pi$
$491$	−30.8186	−1.39082	−0.695412	+	0.718611i	$0.744778\pi$
$492$	−5.76931	−0.260101
$493$	0.521251	0.0234759
$494$	16.8751	0.759247
$495$	−0.241493	−0.0108543
$496$	0.765930	0.0343913
$497$	22.6912	1.01784
$498$	−9.07733	−0.406765
$499$	32.6780	1.46287	0.731435	−	0.681912i	$-0.238851\pi$
$499$	32.6780	1.46287	0.731435	+	0.681912i	$0.238851\pi$
$500$	1.34524	0.0601607
$501$	7.78394	0.347761
$502$	−25.0526	−1.11815
$503$	−33.3624	−1.48756	−0.743779	−	0.668426i	$-0.766968\pi$
$503$	−33.3624	−1.48756	−0.743779	+	0.668426i	$0.766968\pi$
$504$	0.339365	0.0151165
$505$	−4.96643	−0.221003
$506$	−2.57768	−0.114592
$507$	5.90891	0.262424
$508$	−15.9462	−0.707499
$509$	34.6506	1.53586	0.767930	−	0.640534i	$-0.221287\pi$
$509$	34.6506	1.53586	0.767930	+	0.640534i	$0.221287\pi$
$510$	−2.16169	−0.0957212
$511$	−11.2857	−0.499250
$512$	−1.00000	−0.0441942
$513$	26.9944	1.19183
$514$	−13.4927	−0.595138
$515$	−42.1510	−1.85740
$516$	−9.28382	−0.408697
$517$	−3.81859	−0.167941
$518$	−5.42587	−0.238399
$519$	28.4692	1.24966
$520$	10.0567	0.441017
$521$	38.9893	1.70815	0.854076	−	0.520148i	$-0.174123\pi$
$521$	38.9893	1.70815	0.854076	+	0.520148i	$0.174123\pi$
$522$	0.313005	0.0136999
$523$	30.5147	1.33432	0.667158	−	0.744916i	$-0.267510\pi$
$523$	30.5147	1.33432	0.667158	+	0.744916i	$0.267510\pi$
$524$	12.2150	0.533613
$525$	14.7358	0.643122
$526$	15.4617	0.674163
$527$	−0.285705	−0.0124455
$528$	0.599792	0.0261026
$529$	36.5456	1.58894
$530$	−32.8719	−1.42787
$531$	3.31887	0.144026
$532$	−8.20520	−0.355740
$533$	−10.0119	−0.433664
$534$	−24.9533	−1.07984
$535$	−18.4490	−0.797619
$536$	−2.38148	−0.102864
$537$	−11.1848	−0.482659
$538$	4.05450	0.174802
$539$	1.57153	0.0676906
$540$	16.0874	0.692290
$541$	−16.1342	−0.693664	−0.346832	−	0.937927i	$-0.612743\pi$
$541$	−16.1342	−0.693664	−0.346832	+	0.937927i	$0.612743\pi$
$542$	−27.3851	−1.17629
$543$	−40.6463	−1.74430
$544$	0.373017	0.0159930
$545$	43.2678	1.85339
$546$	8.47657	0.362764
$547$	10.2444	0.438021	0.219010	−	0.975723i	$-0.429717\pi$
$547$	10.2444	0.438021	0.219010	+	0.975723i	$0.429717\pi$
$548$	−6.10340	−0.260724
$549$	−2.62765	−0.112146
$550$	1.80945	0.0771553
$551$	−7.56787	−0.322402
$552$	−13.8555	−0.589729
$553$	−5.81547	−0.247299
$554$	2.00032	0.0849856
$555$	20.7540	0.880956
$556$	20.4553	0.867497
$557$	−35.1127	−1.48777	−0.743887	−	0.668305i	$-0.767020\pi$
$557$	−35.1127	−1.48777	−0.743887	+	0.668305i	$0.767020\pi$
$558$	−0.171562	−0.00726282
$559$	−16.1109	−0.681418
$560$	−4.88990	−0.206636
$561$	−0.223733	−0.00944601
$562$	−8.13677	−0.343229
$563$	10.9723	0.462429	0.231215	−	0.972903i	$-0.425730\pi$
$563$	10.9723	0.462429	0.231215	+	0.972903i	$0.425730\pi$
$564$	−20.5256	−0.864284
$565$	−39.3831	−1.65686
$566$	−10.0343	−0.421773
$567$	14.5777	0.612207
$568$	14.9770	0.628421
$569$	12.9597	0.543298	0.271649	−	0.962396i	$-0.412431\pi$
$569$	12.9597	0.543298	0.271649	+	0.962396i	$0.412431\pi$
$570$	31.3849	1.31457
$571$	7.59243	0.317733	0.158867	−	0.987300i	$-0.449216\pi$
$571$	7.59243	0.317733	0.158867	+	0.987300i	$0.449216\pi$
$572$	1.04086	0.0435207
$573$	9.16942	0.383058
$574$	4.86811	0.203191
$575$	−41.7992	−1.74315
$576$	0.223993	0.00933302
$577$	−42.5345	−1.77073	−0.885367	−	0.464893i	$-0.846093\pi$
$577$	−42.5345	−1.77073	−0.885367	+	0.464893i	$0.846093\pi$
$578$	16.8609	0.701319
$579$	−37.4142	−1.55488
$580$	−4.51009	−0.187271
$581$	7.65939	0.317765
$582$	−15.3729	−0.637229
$583$	−3.40222	−0.140905
$584$	−7.44897	−0.308240
$585$	−2.25264	−0.0931350
$586$	15.8332	0.654065
$587$	34.4233	1.42080	0.710402	−	0.703797i	$-0.248513\pi$
$587$	34.4233	1.42080	0.710402	+	0.703797i	$0.248513\pi$
$588$	8.44726	0.348359
$589$	4.14806	0.170918
$590$	−47.8215	−1.96878
$591$	48.9590	2.01391
$592$	−3.58127	−0.147189
$593$	11.7173	0.481172	0.240586	−	0.970628i	$-0.422660\pi$
$593$	11.7173	0.481172	0.240586	+	0.970628i	$0.422660\pi$
$594$	1.66503	0.0683169
$595$	1.82402	0.0747775
$596$	1.96177	0.0803573
$597$	−47.0393	−1.92519
$598$	−24.0445	−0.983252
$599$	−31.8350	−1.30074	−0.650371	−	0.759617i	$-0.725387\pi$
$599$	−31.8350	−1.30074	−0.650371	+	0.759617i	$0.725387\pi$
$600$	9.72613	0.397068
$601$	−20.6962	−0.844215	−0.422108	−	0.906546i	$-0.638710\pi$
$601$	−20.6962	−0.844215	−0.422108	+	0.906546i	$0.638710\pi$
$602$	7.83362	0.319275
$603$	0.533434	0.0217231
$604$	−1.76024	−0.0716233
$605$	−35.1424	−1.42874
$606$	−2.76296	−0.112238
$607$	−16.8718	−0.684806	−0.342403	−	0.939553i	$-0.611241\pi$
$607$	−16.8718	−0.684806	−0.342403	+	0.939553i	$0.611241\pi$
$608$	−5.41572	−0.219636
$609$	−3.80144	−0.154042
$610$	37.8619	1.53298
$611$	−35.6196	−1.44102
$612$	−0.0835531	−0.00337743
$613$	−11.7054	−0.472777	−0.236389	−	0.971659i	$-0.575964\pi$
$613$	−11.7054	−0.472777	−0.236389	+	0.971659i	$0.575964\pi$
$614$	17.0561	0.688330
$615$	−18.6205	−0.750851
$616$	−0.506101	−0.0203914
$617$	−41.6385	−1.67630	−0.838151	−	0.545439i	$-0.816363\pi$
$617$	−41.6385	−1.67630	−0.838151	+	0.545439i	$0.816363\pi$
$618$	−23.4497	−0.943286
$619$	38.1834	1.53472	0.767361	−	0.641216i	$-0.221570\pi$
$619$	38.1834	1.53472	0.767361	+	0.641216i	$0.221570\pi$
$620$	2.47204	0.0992797
$621$	−38.4630	−1.54347
$622$	17.3925	0.697375
$623$	21.0554	0.843568
$624$	5.59483	0.223973
$625$	−22.7423	−0.909690
$626$	2.64479	0.105707
$627$	3.24831	0.129725
$628$	−13.7698	−0.549475
$629$	1.33587	0.0532648
$630$	1.09530	0.0436379
$631$	−39.4519	−1.57056	−0.785278	−	0.619143i	$-0.787480\pi$
$631$	−39.4519	−1.57056	−0.785278	+	0.619143i	$0.787480\pi$
$632$	−3.83842	−0.152684
$633$	31.2097	1.24047
$634$	−5.90314	−0.234443
$635$	−51.4665	−2.04239
$636$	−18.2875	−0.725148
$637$	14.6592	0.580817
$638$	−0.466790	−0.0184804
$639$	−3.35474	−0.132711
$640$	−3.22751	−0.127578
$641$	−23.3697	−0.923047	−0.461524	−	0.887128i	$-0.652697\pi$
$641$	−23.3697	−0.923047	−0.461524	+	0.887128i	$0.652697\pi$
$642$	−10.2637	−0.405074
$643$	30.3149	1.19550	0.597752	−	0.801681i	$-0.296061\pi$
$643$	30.3149	1.19550	0.597752	+	0.801681i	$0.296061\pi$
$644$	11.6912	0.460697
$645$	−29.9636	−1.17982
$646$	2.02016	0.0794820
$647$	−17.7209	−0.696681	−0.348341	−	0.937368i	$-0.613255\pi$
$647$	−17.7209	−0.696681	−0.348341	+	0.937368i	$0.613255\pi$
$648$	9.62180	0.377980
$649$	−4.94948	−0.194284
$650$	16.8785	0.662028
$651$	2.08362	0.0816636
$652$	−0.992885	−0.0388844
$653$	−3.82384	−0.149638	−0.0748192	−	0.997197i	$-0.523838\pi$
$653$	−3.82384	−0.149638	−0.0748192	+	0.997197i	$0.523838\pi$
$654$	24.0710	0.941251
$655$	39.4239	1.54042
$656$	3.21312	0.125451
$657$	1.66851	0.0650949
$658$	17.3194	0.675180
$659$	13.5996	0.529763	0.264882	−	0.964281i	$-0.414667\pi$
$659$	13.5996	0.529763	0.264882	+	0.964281i	$0.414667\pi$
$660$	1.93583	0.0753522
$661$	15.3168	0.595755	0.297877	−	0.954604i	$-0.403721\pi$
$661$	15.3168	0.595755	0.297877	+	0.954604i	$0.403721\pi$
$662$	−1.81353	−0.0704848
$663$	−2.08697	−0.0810512
$664$	5.05547	0.196190
$665$	−26.4823	−1.02694
$666$	0.802177	0.0310837
$667$	10.7831	0.417522
$668$	−4.33513	−0.167731
$669$	12.1668	0.470395
$670$	−7.68625	−0.296946
$671$	3.91867	0.151279
$672$	−2.72038	−0.104941
$673$	−25.7927	−0.994235	−0.497118	−	0.867683i	$-0.665608\pi$
$673$	−25.7927	−0.994235	−0.497118	+	0.867683i	$0.665608\pi$
$674$	36.0891	1.39010
$675$	26.9998	1.03922
$676$	−3.29087	−0.126572
$677$	5.92034	0.227537	0.113769	−	0.993507i	$-0.463708\pi$
$677$	5.92034	0.227537	0.113769	+	0.993507i	$0.463708\pi$
$678$	−21.9098	−0.841442
$679$	12.9716	0.497804
$680$	1.20392	0.0461681
$681$	−1.51754	−0.0581522
$682$	0.255854	0.00979717
$683$	−28.1587	−1.07746	−0.538731	−	0.842478i	$-0.681096\pi$
$683$	−28.1587	−1.07746	−0.538731	+	0.842478i	$0.681096\pi$
$684$	1.21308	0.0463833
$685$	−19.6988	−0.752651
$686$	−17.7332	−0.677058
$687$	6.27452	0.239388
$688$	5.17046	0.197122
$689$	−31.7357	−1.20903
$690$	−44.7187	−1.70241
$691$	−20.7077	−0.787759	−0.393879	−	0.919162i	$-0.628867\pi$
$691$	−20.7077	−0.787759	−0.393879	+	0.919162i	$0.628867\pi$
$692$	−15.8554	−0.602733
$693$	0.113363	0.00430629
$694$	−0.0389920	−0.00148012
$695$	66.0196	2.50427
$696$	−2.50908	−0.0951065
$697$	−1.19855	−0.0453983
$698$	20.8660	0.789790
$699$	−10.0086	−0.378559
$700$	−8.20684	−0.310189
$701$	−31.2409	−1.17995	−0.589976	−	0.807421i	$-0.700863\pi$
$701$	−31.2409	−1.17995	−0.589976	+	0.807421i	$0.700863\pi$
$702$	15.5313	0.586191
$703$	−19.3951	−0.731501
$704$	−0.334044	−0.0125898
$705$	−66.2466	−2.49499
$706$	−9.26208	−0.348583
$707$	2.33137	0.0876801
$708$	−26.6044	−0.999854
$709$	−31.9284	−1.19909	−0.599547	−	0.800339i	$-0.704653\pi$
$709$	−31.9284	−1.19909	−0.599547	+	0.800339i	$0.704653\pi$
$710$	48.3384	1.81411
$711$	0.859776	0.0322441
$712$	13.8973	0.520824
$713$	−5.91036	−0.221345
$714$	1.01475	0.0379761
$715$	3.35940	0.125634
$716$	6.22917	0.232795
$717$	19.0643	0.711971
$718$	33.2513	1.24093
$719$	−3.59316	−0.134002	−0.0670011	−	0.997753i	$-0.521343\pi$
$719$	−3.59316	−0.134002	−0.0670011	+	0.997753i	$0.521343\pi$
$720$	0.722937	0.0269423
$721$	19.7867	0.736896
$722$	−10.3300	−0.384443
$723$	18.2314	0.678034
$724$	22.6373	0.841308
$725$	−7.56939	−0.281120
$726$	−19.5507	−0.725593
$727$	22.3087	0.827385	0.413692	−	0.910417i	$-0.364239\pi$
$727$	22.3087	0.827385	0.413692	+	0.910417i	$0.364239\pi$
$728$	−4.72088	−0.174968
$729$	24.6943	0.914603
$730$	−24.0416	−0.889819
$731$	−1.92867	−0.0713345
$732$	21.0636	0.778532
$733$	19.9007	0.735050	0.367525	−	0.930014i	$-0.380205\pi$
$733$	19.9007	0.735050	0.367525	+	0.930014i	$0.380205\pi$
$734$	23.5350	0.868693
$735$	27.2636	1.00563
$736$	7.71658	0.284437
$737$	−0.795520	−0.0293034
$738$	−0.719715	−0.0264931
$739$	42.6554	1.56910	0.784552	−	0.620063i	$-0.212893\pi$
$739$	42.6554	1.56910	0.784552	+	0.620063i	$0.212893\pi$
$740$	−11.5586	−0.424901
$741$	30.3000	1.11310
$742$	15.4309	0.566486
$743$	47.6806	1.74923	0.874615	−	0.484818i	$-0.161114\pi$
$743$	47.6806	1.74923	0.874615	+	0.484818i	$0.161114\pi$
$744$	1.37526	0.0504196
$745$	6.33163	0.231973
$746$	27.3080	0.999817
$747$	−1.13239	−0.0414319
$748$	0.124604	0.00455598
$749$	8.66040	0.316444
$750$	2.41543	0.0881992
$751$	20.1382	0.734853	0.367427	−	0.930052i	$-0.380239\pi$
$751$	20.1382	0.734853	0.367427	+	0.930052i	$0.380239\pi$
$752$	11.4314	0.416860
$753$	−44.9831	−1.63928
$754$	−4.35420	−0.158570
$755$	−5.68120	−0.206760
$756$	−7.55180	−0.274656
$757$	−1.86406	−0.0677506	−0.0338753	−	0.999426i	$-0.510785\pi$
$757$	−1.86406	−0.0677506	−0.0338753	+	0.999426i	$0.510785\pi$
$758$	1.02566	0.0372537
$759$	−4.62835	−0.167998
$760$	−17.4793	−0.634040
$761$	36.4568	1.32156	0.660779	−	0.750581i	$-0.270226\pi$
$761$	36.4568	1.32156	0.660779	+	0.750581i	$0.270226\pi$
$762$	−28.6322	−1.03723
$763$	−20.3109	−0.735306
$764$	−5.10676	−0.184756
$765$	−0.269668	−0.00974987
$766$	−1.99014	−0.0719067
$767$	−46.1686	−1.66705
$768$	−1.79555	−0.0647913
$769$	−40.5421	−1.46198	−0.730992	−	0.682386i	$-0.760942\pi$
$769$	−40.5421	−1.46198	−0.730992	+	0.682386i	$0.760942\pi$
$770$	−1.63344	−0.0588652
$771$	−24.2268	−0.872507
$772$	20.8372	0.749947
$773$	7.64166	0.274851	0.137426	−	0.990512i	$-0.456117\pi$
$773$	7.64166	0.274851	0.137426	+	0.990512i	$0.456117\pi$
$774$	−1.15815	−0.0416287
$775$	4.14889	0.149033
$776$	8.56170	0.307347
$777$	−9.74242	−0.349507
$778$	30.0810	1.07846
$779$	17.4014	0.623468
$780$	18.0574	0.646558
$781$	5.00298	0.179021
$782$	−2.87842	−0.102932
$783$	−6.96523	−0.248917
$784$	−4.70456	−0.168020
$785$	−44.4422	−1.58621
$786$	21.9326	0.782308
$787$	−17.0287	−0.607007	−0.303503	−	0.952830i	$-0.598156\pi$
$787$	−17.0287	−0.607007	−0.303503	+	0.952830i	$0.598156\pi$
$788$	−27.2669	−0.971343
$789$	27.7623	0.988363
$790$	−12.3885	−0.440764
$791$	18.4874	0.657335
$792$	0.0748234	0.00265873
$793$	36.5532	1.29804
$794$	−14.1628	−0.502619
$795$	−59.0232	−2.09334
$796$	26.1977	0.928554
$797$	14.9015	0.527839	0.263920	−	0.964545i	$-0.414985\pi$
$797$	14.9015	0.527839	0.263920	+	0.964545i	$0.414985\pi$
$798$	−14.7328	−0.521536
$799$	−4.26411	−0.150853
$800$	−5.41680	−0.191513
$801$	−3.11290	−0.109989
$802$	−19.1414	−0.675908
$803$	−2.48828	−0.0878096
$804$	−4.27606	−0.150805
$805$	37.7333	1.32993
$806$	2.38660	0.0840643
$807$	7.28005	0.256270
$808$	1.53878	0.0541342
$809$	39.7631	1.39800	0.698999	−	0.715123i	$-0.253629\pi$
$809$	39.7631	1.39800	0.698999	+	0.715123i	$0.253629\pi$
$810$	31.0544	1.09114
$811$	11.9839	0.420813	0.210406	−	0.977614i	$-0.432521\pi$
$811$	11.9839	0.420813	0.210406	+	0.977614i	$0.432521\pi$
$812$	2.11715	0.0742972
$813$	−49.1712	−1.72451
$814$	−1.19630	−0.0419303
$815$	−3.20455	−0.112250
$816$	0.669770	0.0234467
$817$	28.0018	0.979658
$818$	36.6969	1.28308
$819$	1.05744	0.0369500
$820$	10.3704	0.362149
$821$	39.7106	1.38591	0.692955	−	0.720981i	$-0.256309\pi$
$821$	39.7106	1.38591	0.692955	+	0.720981i	$0.256309\pi$
$822$	−10.9589	−0.382237
$823$	−52.5528	−1.83187	−0.915937	−	0.401322i	$-0.868551\pi$
$823$	−52.5528	−1.83187	−0.915937	+	0.401322i	$0.868551\pi$
$824$	13.0599	0.454964
$825$	3.24896	0.113114
$826$	22.4486	0.781086
$827$	−8.03071	−0.279255	−0.139628	−	0.990204i	$-0.544591\pi$
$827$	−8.03071	−0.279255	−0.139628	+	0.990204i	$0.544591\pi$
$828$	−1.72846	−0.0600680
$829$	−8.90328	−0.309224	−0.154612	−	0.987975i	$-0.549413\pi$
$829$	−8.90328	−0.309224	−0.154612	+	0.987975i	$0.549413\pi$
$830$	16.3166	0.566356
$831$	3.59168	0.124594
$832$	−3.11595	−0.108026
$833$	1.75488	0.0608031
$834$	36.7284	1.27180
$835$	−13.9917	−0.484202
$836$	−1.80909	−0.0625686
$837$	3.81774	0.131960
$838$	38.1489	1.31783
$839$	40.6315	1.40276	0.701378	−	0.712789i	$-0.252568\pi$
$839$	40.6315	1.40276	0.701378	+	0.712789i	$0.252568\pi$
$840$	−8.78005	−0.302941
$841$	−27.0473	−0.932666
$842$	−12.4503	−0.429066
$843$	−14.6100	−0.503194
$844$	−17.3817	−0.598303
$845$	−10.6213	−0.365384
$846$	−2.56055	−0.0880334
$847$	16.4967	0.566834
$848$	10.1849	0.349752
$849$	−18.0171	−0.618344
$850$	2.02056	0.0693047
$851$	27.6351	0.947320
$852$	26.8919	0.921302
$853$	−42.1555	−1.44338	−0.721688	−	0.692218i	$-0.756634\pi$
$853$	−42.1555	−1.44338	−0.721688	+	0.692218i	$0.756634\pi$
$854$	−17.7733	−0.608189
$855$	3.91523	0.133898
$856$	5.71617	0.195375
$857$	−7.24551	−0.247502	−0.123751	−	0.992313i	$-0.539492\pi$
$857$	−7.24551	−0.247502	−0.123751	+	0.992313i	$0.539492\pi$
$858$	1.86892	0.0638039
$859$	−8.31387	−0.283666	−0.141833	−	0.989891i	$-0.545300\pi$
$859$	−8.31387	−0.283666	−0.141833	+	0.989891i	$0.545300\pi$
$860$	16.6877	0.569046
$861$	8.74092	0.297890
$862$	24.9546	0.849957
$863$	−12.2729	−0.417775	−0.208887	−	0.977940i	$-0.566984\pi$
$863$	−12.2729	−0.417775	−0.208887	+	0.977940i	$0.566984\pi$
$864$	−4.98445	−0.169575
$865$	−51.1735	−1.73995
$866$	9.97520	0.338971
$867$	30.2745	1.02818
$868$	−1.16044	−0.0393878
$869$	−1.28220	−0.0434957
$870$	−8.09808	−0.274550
$871$	−7.42057	−0.251437
$872$	−13.4059	−0.453982
$873$	−1.91776	−0.0649062
$874$	41.7908	1.41360
$875$	−2.03813	−0.0689013
$876$	−13.3750	−0.451899
$877$	−6.43997	−0.217462	−0.108731	−	0.994071i	$-0.534679\pi$
$877$	−6.43997	−0.217462	−0.108731	+	0.994071i	$0.534679\pi$
$878$	5.47847	0.184889
$879$	28.4293	0.958897
$880$	−1.07813	−0.0363438
$881$	5.80169	0.195464	0.0977319	−	0.995213i	$-0.468841\pi$
$881$	5.80169	0.195464	0.0977319	+	0.995213i	$0.468841\pi$
$882$	1.05379	0.0354828
$883$	−38.6766	−1.30157	−0.650785	−	0.759262i	$-0.725560\pi$
$883$	−38.6766	−1.30157	−0.650785	+	0.759262i	$0.725560\pi$
$884$	1.16230	0.0390925
$885$	−85.8658	−2.88635
$886$	11.3086	0.379920
$887$	−0.252983	−0.00849435	−0.00424717	−	0.999991i	$-0.501352\pi$
$887$	−0.252983	−0.00849435	−0.00424717	+	0.999991i	$0.501352\pi$
$888$	−6.43034	−0.215788
$889$	24.1596	0.810288
$890$	44.8537	1.50350
$891$	3.21411	0.107677
$892$	−6.77608	−0.226880
$893$	61.9092	2.07171
$894$	3.52245	0.117808
$895$	20.1047	0.672026
$896$	1.51507	0.0506150
$897$	−43.1730	−1.44150
$898$	−32.5124	−1.08495
$899$	−1.07030	−0.0356966
$900$	1.21332	0.0404441
$901$	−3.79916	−0.126568
$902$	1.07332	0.0357378
$903$	14.0656	0.468075
$904$	12.2023	0.405843
$905$	73.0620	2.42866
$906$	−3.16060	−0.105004
$907$	−34.3808	−1.14159	−0.570797	−	0.821091i	$-0.693366\pi$
$907$	−34.3808	−1.14159	−0.570797	+	0.821091i	$0.693366\pi$
$908$	0.845167	0.0280479
$909$	−0.344676	−0.0114322
$910$	−15.2367	−0.505091
$911$	−22.8819	−0.758111	−0.379056	−	0.925374i	$-0.623751\pi$
$911$	−22.8819	−0.758111	−0.379056	+	0.925374i	$0.623751\pi$
$912$	−9.72418	−0.322000
$913$	1.68875	0.0558894
$914$	17.4396	0.576851
$915$	67.9828	2.24744
$916$	−3.49449	−0.115461
$917$	−18.5065	−0.611140
$918$	1.85929	0.0613656
$919$	−25.8700	−0.853374	−0.426687	−	0.904399i	$-0.640319\pi$
$919$	−25.8700	−0.853374	−0.426687	+	0.904399i	$0.640319\pi$
$920$	24.9053	0.821104
$921$	30.6251	1.00913
$922$	−41.3549	−1.36195
$923$	46.6675	1.53608
$924$	−0.908728	−0.0298950
$925$	−19.3990	−0.637836
$926$	7.85555	0.258150
$927$	−2.92533	−0.0960803
$928$	1.39739	0.0458716
$929$	−25.6563	−0.841755	−0.420877	−	0.907118i	$-0.638278\pi$
$929$	−25.6563	−0.841755	−0.420877	+	0.907118i	$0.638278\pi$
$930$	4.43867	0.145550
$931$	−25.4786	−0.835026
$932$	5.57411	0.182586
$933$	31.2290	1.02239
$934$	−11.9750	−0.391833
$935$	0.402161	0.0131521
$936$	0.697949	0.0228132
$937$	−11.1480	−0.364189	−0.182095	−	0.983281i	$-0.558288\pi$
$937$	−11.1480	−0.364189	−0.182095	+	0.983281i	$0.558288\pi$
$938$	3.60811	0.117809
$939$	4.74884	0.154972
$940$	36.8949	1.20338
$941$	30.3948	0.990842	0.495421	−	0.868653i	$-0.335014\pi$
$941$	30.3948	0.990842	0.495421	+	0.868653i	$0.335014\pi$
$942$	−24.7244	−0.805563
$943$	−24.7943	−0.807414
$944$	14.8169	0.482248
$945$	−24.3735	−0.792870
$946$	1.72716	0.0561549
$947$	29.6878	0.964725	0.482363	−	0.875972i	$-0.339779\pi$
$947$	29.6878	0.964725	0.482363	+	0.875972i	$0.339779\pi$
$948$	−6.89206	−0.223844
$949$	−23.2106	−0.753448
$950$	−29.3359	−0.951782
$951$	−10.5994	−0.343708
$952$	−0.565148	−0.0183165
$953$	57.3859	1.85891	0.929456	−	0.368934i	$-0.120277\pi$
$953$	57.3859	1.85891	0.929456	+	0.368934i	$0.120277\pi$
$954$	−2.28135	−0.0738614
$955$	−16.4821	−0.533348
$956$	−10.6176	−0.343396
$957$	−0.838144	−0.0270933
$958$	9.19535	0.297088
$959$	9.24708	0.298604
$960$	−5.79514	−0.187037
$961$	−30.4134	−0.981076
$962$	−11.1590	−0.359782
$963$	−1.28038	−0.0412596
$964$	−10.1537	−0.327028
$965$	67.2521	2.16492
$966$	20.9921	0.675408
$967$	24.7251	0.795106	0.397553	−	0.917579i	$-0.369859\pi$
$967$	24.7251	0.795106	0.397553	+	0.917579i	$0.369859\pi$
$968$	10.8884	0.349967
$969$	3.62729	0.116525
$970$	27.6330	0.887241
$971$	24.5136	0.786679	0.393340	−	0.919393i	$-0.371320\pi$
$971$	24.5136	0.786679	0.393340	+	0.919393i	$0.371320\pi$
$972$	2.32305	0.0745118
$973$	−30.9912	−0.993533
$974$	36.4613	1.16830
$975$	30.3061	0.970573
$976$	−11.7310	−0.375500
$977$	−18.0822	−0.578501	−0.289251	−	0.957253i	$-0.593406\pi$
$977$	−18.0822	−0.578501	−0.289251	+	0.957253i	$0.593406\pi$
$978$	−1.78277	−0.0570068
$979$	4.64232	0.148369
$980$	−15.1840	−0.485035
$981$	3.00283	0.0958730
$982$	30.8186	0.983461
$983$	47.0288	1.49999	0.749993	−	0.661446i	$-0.230057\pi$
$983$	47.0288	1.49999	0.749993	+	0.661446i	$0.230057\pi$
$984$	5.76931	0.183919
$985$	−88.0041	−2.80404
$986$	−0.521251	−0.0166000
$987$	31.0978	0.989853
$988$	−16.8751	−0.536868
$989$	−39.8983	−1.26869
$990$	0.241493	0.00767515
$991$	−58.4489	−1.85669	−0.928345	−	0.371720i	$-0.878768\pi$
$991$	−58.4489	−1.85669	−0.928345	+	0.371720i	$0.878768\pi$
$992$	−0.765930	−0.0243183
$993$	−3.25628	−0.103335
$994$	−22.6912	−0.719722
$995$	84.5534	2.68052
$996$	9.07733	0.287626
$997$	20.2545	0.641468	0.320734	−	0.947169i	$-0.396070\pi$
$997$	20.2545	0.641468	0.320734	+	0.947169i	$0.396070\pi$
$998$	−32.6780	−1.03440
$999$	−17.8507	−0.564770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.c.1.14	✓	57

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.c.1.14	✓	57	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.79555 q^{3} +1.00000 q^{4} +3.22751 q^{5} +1.79555 q^{6} -1.51507 q^{7} -1.00000 q^{8} +0.223993 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.79555 q^{3} +1.00000 q^{4} +3.22751 q^{5} +1.79555 q^{6} -1.51507 q^{7} -1.00000 q^{8} +0.223993 q^{9} -3.22751 q^{10} -0.334044 q^{11} -1.79555 q^{12} -3.11595 q^{13} +1.51507 q^{14} -5.79514 q^{15} +1.00000 q^{16} -0.373017 q^{17} -0.223993 q^{18} +5.41572 q^{19} +3.22751 q^{20} +2.72038 q^{21} +0.334044 q^{22} -7.71658 q^{23} +1.79555 q^{24} +5.41680 q^{25} +3.11595 q^{26} +4.98445 q^{27} -1.51507 q^{28} -1.39739 q^{29} +5.79514 q^{30} +0.765930 q^{31} -1.00000 q^{32} +0.599792 q^{33} +0.373017 q^{34} -4.88990 q^{35} +0.223993 q^{36} -3.58127 q^{37} -5.41572 q^{38} +5.59483 q^{39} -3.22751 q^{40} +3.21312 q^{41} -2.72038 q^{42} +5.17046 q^{43} -0.334044 q^{44} +0.722937 q^{45} +7.71658 q^{46} +11.4314 q^{47} -1.79555 q^{48} -4.70456 q^{49} -5.41680 q^{50} +0.669770 q^{51} -3.11595 q^{52} +10.1849 q^{53} -4.98445 q^{54} -1.07813 q^{55} +1.51507 q^{56} -9.72418 q^{57} +1.39739 q^{58} +14.8169 q^{59} -5.79514 q^{60} -11.7310 q^{61} -0.765930 q^{62} -0.339365 q^{63} +1.00000 q^{64} -10.0567 q^{65} -0.599792 q^{66} +2.38148 q^{67} -0.373017 q^{68} +13.8555 q^{69} +4.88990 q^{70} -14.9770 q^{71} -0.223993 q^{72} +7.44897 q^{73} +3.58127 q^{74} -9.72613 q^{75} +5.41572 q^{76} +0.506101 q^{77} -5.59483 q^{78} +3.83842 q^{79} +3.22751 q^{80} -9.62180 q^{81} -3.21312 q^{82} -5.05547 q^{83} +2.72038 q^{84} -1.20392 q^{85} -5.17046 q^{86} +2.50908 q^{87} +0.334044 q^{88} -13.8973 q^{89} -0.722937 q^{90} +4.72088 q^{91} -7.71658 q^{92} -1.37526 q^{93} -11.4314 q^{94} +17.4793 q^{95} +1.79555 q^{96} -8.56170 q^{97} +4.70456 q^{98} -0.0748234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * q^99

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