LMFDB - Embedded newform 6014.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.761502 q^{3} +1.00000 q^{4} -0.855697 q^{5} +0.761502 q^{6} +0.402181 q^{7} +1.00000 q^{8} -2.42012 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.761502 q^{3} +1.00000 q^{4} -0.855697 q^{5} +0.761502 q^{6} +0.402181 q^{7} +1.00000 q^{8} -2.42012 q^{9} -0.855697 q^{10} +1.67879 q^{11} +0.761502 q^{12} -0.475182 q^{13} +0.402181 q^{14} -0.651615 q^{15} +1.00000 q^{16} -5.00852 q^{17} -2.42012 q^{18} -0.663790 q^{19} -0.855697 q^{20} +0.306261 q^{21} +1.67879 q^{22} -1.38725 q^{23} +0.761502 q^{24} -4.26778 q^{25} -0.475182 q^{26} -4.12743 q^{27} +0.402181 q^{28} +6.21922 q^{29} -0.651615 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.27840 q^{33} -5.00852 q^{34} -0.344145 q^{35} -2.42012 q^{36} +2.96029 q^{37} -0.663790 q^{38} -0.361852 q^{39} -0.855697 q^{40} -4.87391 q^{41} +0.306261 q^{42} -11.2652 q^{43} +1.67879 q^{44} +2.07089 q^{45} -1.38725 q^{46} +8.20984 q^{47} +0.761502 q^{48} -6.83825 q^{49} -4.26778 q^{50} -3.81400 q^{51} -0.475182 q^{52} -0.285144 q^{53} -4.12743 q^{54} -1.43654 q^{55} +0.402181 q^{56} -0.505477 q^{57} +6.21922 q^{58} +1.24347 q^{59} -0.651615 q^{60} -1.31892 q^{61} +1.00000 q^{62} -0.973324 q^{63} +1.00000 q^{64} +0.406612 q^{65} +1.27840 q^{66} -2.46651 q^{67} -5.00852 q^{68} -1.05639 q^{69} -0.344145 q^{70} -8.70802 q^{71} -2.42012 q^{72} -7.63765 q^{73} +2.96029 q^{74} -3.24992 q^{75} -0.663790 q^{76} +0.675179 q^{77} -0.361852 q^{78} -2.05826 q^{79} -0.855697 q^{80} +4.11730 q^{81} -4.87391 q^{82} -12.4074 q^{83} +0.306261 q^{84} +4.28578 q^{85} -11.2652 q^{86} +4.73594 q^{87} +1.67879 q^{88} -8.53492 q^{89} +2.07089 q^{90} -0.191109 q^{91} -1.38725 q^{92} +0.761502 q^{93} +8.20984 q^{94} +0.568003 q^{95} +0.761502 q^{96} -1.00000 q^{97} -6.83825 q^{98} -4.06288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * 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
$3$	0.761502	0.439653	0.219827	−	0.975539i	$-0.429451\pi$
$3$	0.761502	0.439653	0.219827	+	0.975539i	$0.429451\pi$
$4$	1.00000	0.500000
$5$	−0.855697	−0.382679	−0.191340	−	0.981524i	$-0.561283\pi$
$5$	−0.855697	−0.382679	−0.191340	+	0.981524i	$0.561283\pi$
$6$	0.761502	0.310882
$7$	0.402181	0.152010	0.0760051	−	0.997107i	$-0.475783\pi$
$7$	0.402181	0.152010	0.0760051	+	0.997107i	$0.475783\pi$
$8$	1.00000	0.353553
$9$	−2.42012	−0.806705
$10$	−0.855697	−0.270595
$11$	1.67879	0.506175	0.253088	−	0.967443i	$-0.418554\pi$
$11$	1.67879	0.506175	0.253088	+	0.967443i	$0.418554\pi$
$12$	0.761502	0.219827
$13$	−0.475182	−0.131792	−0.0658959	−	0.997827i	$-0.520991\pi$
$13$	−0.475182	−0.131792	−0.0658959	+	0.997827i	$0.520991\pi$
$14$	0.402181	0.107487
$15$	−0.651615	−0.168246
$16$	1.00000	0.250000
$17$	−5.00852	−1.21474	−0.607372	−	0.794417i	$-0.707776\pi$
$17$	−5.00852	−1.21474	−0.607372	+	0.794417i	$0.707776\pi$
$18$	−2.42012	−0.570427
$19$	−0.663790	−0.152284	−0.0761419	−	0.997097i	$-0.524260\pi$
$19$	−0.663790	−0.152284	−0.0761419	+	0.997097i	$0.524260\pi$
$20$	−0.855697	−0.191340
$21$	0.306261	0.0668317
$22$	1.67879	0.357920
$23$	−1.38725	−0.289261	−0.144631	−	0.989486i	$-0.546199\pi$
$23$	−1.38725	−0.289261	−0.144631	+	0.989486i	$0.546199\pi$
$24$	0.761502	0.155441
$25$	−4.26778	−0.853556
$26$	−0.475182	−0.0931909
$27$	−4.12743	−0.794324
$28$	0.402181	0.0760051
$29$	6.21922	1.15488	0.577440	−	0.816433i	$-0.304052\pi$
$29$	6.21922	1.15488	0.577440	+	0.816433i	$0.304052\pi$
$30$	−0.651615	−0.118968
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.27840	0.222542
$34$	−5.00852	−0.858954
$35$	−0.344145	−0.0581711
$36$	−2.42012	−0.403353
$37$	2.96029	0.486668	0.243334	−	0.969943i	$-0.421759\pi$
$37$	2.96029	0.486668	0.243334	+	0.969943i	$0.421759\pi$
$38$	−0.663790	−0.107681
$39$	−0.361852	−0.0579427
$40$	−0.855697	−0.135298
$41$	−4.87391	−0.761178	−0.380589	−	0.924744i	$-0.624279\pi$
$41$	−4.87391	−0.761178	−0.380589	+	0.924744i	$0.624279\pi$
$42$	0.306261	0.0472572
$43$	−11.2652	−1.71793	−0.858967	−	0.512031i	$-0.828893\pi$
$43$	−11.2652	−1.71793	−0.858967	+	0.512031i	$0.828893\pi$
$44$	1.67879	0.253088
$45$	2.07089	0.308709
$46$	−1.38725	−0.204539
$47$	8.20984	1.19753	0.598764	−	0.800925i	$-0.295659\pi$
$47$	8.20984	1.19753	0.598764	+	0.800925i	$0.295659\pi$
$48$	0.761502	0.109913
$49$	−6.83825	−0.976893
$50$	−4.26778	−0.603556
$51$	−3.81400	−0.534066
$52$	−0.475182	−0.0658959
$53$	−0.285144	−0.0391676	−0.0195838	−	0.999808i	$-0.506234\pi$
$53$	−0.285144	−0.0391676	−0.0195838	+	0.999808i	$0.506234\pi$
$54$	−4.12743	−0.561672
$55$	−1.43654	−0.193703
$56$	0.402181	0.0537437
$57$	−0.505477	−0.0669521
$58$	6.21922	0.816623
$59$	1.24347	0.161886	0.0809428	−	0.996719i	$-0.474207\pi$
$59$	1.24347	0.161886	0.0809428	+	0.996719i	$0.474207\pi$
$60$	−0.651615	−0.0841231
$61$	−1.31892	−0.168870	−0.0844350	−	0.996429i	$-0.526909\pi$
$61$	−1.31892	−0.168870	−0.0844350	+	0.996429i	$0.526909\pi$
$62$	1.00000	0.127000
$63$	−0.973324	−0.122627
$64$	1.00000	0.125000
$65$	0.406612	0.0504340
$66$	1.27840	0.157361
$67$	−2.46651	−0.301333	−0.150666	−	0.988585i	$-0.548142\pi$
$67$	−2.46651	−0.301333	−0.150666	+	0.988585i	$0.548142\pi$
$68$	−5.00852	−0.607372
$69$	−1.05639	−0.127175
$70$	−0.344145	−0.0411332
$71$	−8.70802	−1.03345	−0.516726	−	0.856151i	$-0.672849\pi$
$71$	−8.70802	−1.03345	−0.516726	+	0.856151i	$0.672849\pi$
$72$	−2.42012	−0.285213
$73$	−7.63765	−0.893920	−0.446960	−	0.894554i	$-0.647493\pi$
$73$	−7.63765	−0.893920	−0.446960	+	0.894554i	$0.647493\pi$
$74$	2.96029	0.344126
$75$	−3.24992	−0.375269
$76$	−0.663790	−0.0761419
$77$	0.675179	0.0769438
$78$	−0.361852	−0.0409717
$79$	−2.05826	−0.231572	−0.115786	−	0.993274i	$-0.536939\pi$
$79$	−2.05826	−0.231572	−0.115786	+	0.993274i	$0.536939\pi$
$80$	−0.855697	−0.0956698
$81$	4.11730	0.457478
$82$	−4.87391	−0.538234
$83$	−12.4074	−1.36188	−0.680942	−	0.732337i	$-0.738430\pi$
$83$	−12.4074	−1.36188	−0.680942	+	0.732337i	$0.738430\pi$
$84$	0.306261	0.0334159
$85$	4.28578	0.464858
$86$	−11.2652	−1.21476
$87$	4.73594	0.507746
$88$	1.67879	0.178960
$89$	−8.53492	−0.904699	−0.452350	−	0.891841i	$-0.649414\pi$
$89$	−8.53492	−0.904699	−0.452350	+	0.891841i	$0.649414\pi$
$90$	2.07089	0.218291
$91$	−0.191109	−0.0200337
$92$	−1.38725	−0.144631
$93$	0.761502	0.0789640
$94$	8.20984	0.846781
$95$	0.568003	0.0582759
$96$	0.761502	0.0777204
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−6.83825	−0.690768
$99$	−4.06288	−0.408334
$100$	−4.26778	−0.426778
$101$	−10.5871	−1.05345	−0.526725	−	0.850035i	$-0.676580\pi$
$101$	−10.5871	−1.05345	−0.526725	+	0.850035i	$0.676580\pi$
$102$	−3.81400	−0.377642
$103$	5.44614	0.536625	0.268312	−	0.963332i	$-0.413534\pi$
$103$	5.44614	0.536625	0.268312	+	0.963332i	$0.413534\pi$
$104$	−0.475182	−0.0465954
$105$	−0.262067	−0.0255751
$106$	−0.285144	−0.0276957
$107$	1.14211	0.110412	0.0552060	−	0.998475i	$-0.482418\pi$
$107$	1.14211	0.110412	0.0552060	+	0.998475i	$0.482418\pi$
$108$	−4.12743	−0.397162
$109$	19.1806	1.83717	0.918584	−	0.395226i	$-0.129334\pi$
$109$	19.1806	1.83717	0.918584	+	0.395226i	$0.129334\pi$
$110$	−1.43654	−0.136969
$111$	2.25426	0.213965
$112$	0.402181	0.0380025
$113$	−19.5827	−1.84219	−0.921093	−	0.389343i	$-0.872702\pi$
$113$	−19.5827	−1.84219	−0.921093	+	0.389343i	$0.872702\pi$
$114$	−0.505477	−0.0473423
$115$	1.18706	0.110694
$116$	6.21922	0.577440
$117$	1.15000	0.106317
$118$	1.24347	0.114470
$119$	−2.01433	−0.184653
$120$	−0.651615	−0.0594840
$121$	−8.18165	−0.743786
$122$	−1.31892	−0.119409
$123$	−3.71149	−0.334654
$124$	1.00000	0.0898027
$125$	7.93041	0.709318
$126$	−0.973324	−0.0867106
$127$	17.8498	1.58391	0.791957	−	0.610577i	$-0.209062\pi$
$127$	17.8498	1.58391	0.791957	+	0.610577i	$0.209062\pi$
$128$	1.00000	0.0883883
$129$	−8.57850	−0.755295
$130$	0.406612	0.0356622
$131$	−5.65587	−0.494155	−0.247078	−	0.968996i	$-0.579470\pi$
$131$	−5.65587	−0.494155	−0.247078	+	0.968996i	$0.579470\pi$
$132$	1.27840	0.111271
$133$	−0.266964	−0.0231487
$134$	−2.46651	−0.213074
$135$	3.53183	0.303971
$136$	−5.00852	−0.429477
$137$	−13.2170	−1.12920	−0.564602	−	0.825363i	$-0.690970\pi$
$137$	−13.2170	−1.12920	−0.564602	+	0.825363i	$0.690970\pi$
$138$	−1.05639	−0.0899260
$139$	8.68942	0.737027	0.368514	−	0.929622i	$-0.379867\pi$
$139$	8.68942	0.737027	0.368514	+	0.929622i	$0.379867\pi$
$140$	−0.344145	−0.0290856
$141$	6.25181	0.526497
$142$	−8.70802	−0.730761
$143$	−0.797733	−0.0667098
$144$	−2.42012	−0.201676
$145$	−5.32176	−0.441948
$146$	−7.63765	−0.632097
$147$	−5.20734	−0.429494
$148$	2.96029	0.243334
$149$	−14.0238	−1.14888	−0.574438	−	0.818548i	$-0.694779\pi$
$149$	−14.0238	−1.14888	−0.574438	+	0.818548i	$0.694779\pi$
$150$	−3.24992	−0.265355
$151$	−2.79629	−0.227558	−0.113779	−	0.993506i	$-0.536296\pi$
$151$	−2.79629	−0.227558	−0.113779	+	0.993506i	$0.536296\pi$
$152$	−0.663790	−0.0538405
$153$	12.1212	0.979941
$154$	0.675179	0.0544075
$155$	−0.855697	−0.0687312
$156$	−0.361852	−0.0289713
$157$	−8.50975	−0.679152	−0.339576	−	0.940579i	$-0.610284\pi$
$157$	−8.50975	−0.679152	−0.339576	+	0.940579i	$0.610284\pi$
$158$	−2.05826	−0.163746
$159$	−0.217138	−0.0172201
$160$	−0.855697	−0.0676488
$161$	−0.557925	−0.0439706
$162$	4.11730	0.323486
$163$	17.5470	1.37439	0.687195	−	0.726473i	$-0.258842\pi$
$163$	17.5470	1.37439	0.687195	+	0.726473i	$0.258842\pi$
$164$	−4.87391	−0.380589
$165$	−1.09393	−0.0851621
$166$	−12.4074	−0.962998
$167$	−0.0189001	−0.00146253	−0.000731266	−	1.00000i	$-0.500233\pi$
$167$	−0.0189001	−0.00146253	−0.000731266		1.00000i	$0.500233\pi$
$168$	0.306261	0.0236286
$169$	−12.7742	−0.982631
$170$	4.28578	0.328704
$171$	1.60645	0.122848
$172$	−11.2652	−0.858967
$173$	−2.34391	−0.178204	−0.0891020	−	0.996023i	$-0.528400\pi$
$173$	−2.34391	−0.178204	−0.0891020	+	0.996023i	$0.528400\pi$
$174$	4.73594	0.359031
$175$	−1.71642	−0.129749
$176$	1.67879	0.126544
$177$	0.946902	0.0711735
$178$	−8.53492	−0.639719
$179$	9.96668	0.744945	0.372472	−	0.928043i	$-0.378510\pi$
$179$	9.96668	0.744945	0.372472	+	0.928043i	$0.378510\pi$
$180$	2.07089	0.154355
$181$	4.20225	0.312351	0.156176	−	0.987729i	$-0.450083\pi$
$181$	4.20225	0.312351	0.156176	+	0.987729i	$0.450083\pi$
$182$	−0.191109	−0.0141660
$183$	−1.00436	−0.0742442
$184$	−1.38725	−0.102269
$185$	−2.53311	−0.186238
$186$	0.761502	0.0558360
$187$	−8.40828	−0.614874
$188$	8.20984	0.598764
$189$	−1.65997	−0.120745
$190$	0.568003	0.0412073
$191$	14.4894	1.04842	0.524210	−	0.851589i	$-0.324361\pi$
$191$	14.4894	1.04842	0.524210	+	0.851589i	$0.324361\pi$
$192$	0.761502	0.0549567
$193$	4.70178	0.338441	0.169221	−	0.985578i	$-0.445875\pi$
$193$	4.70178	0.338441	0.169221	+	0.985578i	$0.445875\pi$
$194$	−1.00000	−0.0717958
$195$	0.309636	0.0221735
$196$	−6.83825	−0.488446
$197$	25.1192	1.78967	0.894834	−	0.446400i	$-0.147294\pi$
$197$	25.1192	1.78967	0.894834	+	0.446400i	$0.147294\pi$
$198$	−4.06288	−0.288736
$199$	14.0088	0.993055	0.496527	−	0.868021i	$-0.334608\pi$
$199$	14.0088	0.993055	0.496527	+	0.868021i	$0.334608\pi$
$200$	−4.26778	−0.301778
$201$	−1.87825	−0.132482
$202$	−10.5871	−0.744902
$203$	2.50125	0.175553
$204$	−3.81400	−0.267033
$205$	4.17059	0.291287
$206$	5.44614	0.379451
$207$	3.35730	0.233348
$208$	−0.475182	−0.0329479
$209$	−1.11437	−0.0770824
$210$	−0.262067	−0.0180843
$211$	−19.7147	−1.35722	−0.678608	−	0.734501i	$-0.737416\pi$
$211$	−19.7147	−1.35722	−0.678608	+	0.734501i	$0.737416\pi$
$212$	−0.285144	−0.0195838
$213$	−6.63117	−0.454360
$214$	1.14211	0.0780730
$215$	9.63964	0.657418
$216$	−4.12743	−0.280836
$217$	0.402181	0.0273018
$218$	19.1806	1.29907
$219$	−5.81609	−0.393015
$220$	−1.43654	−0.0968515
$221$	2.37996	0.160093
$222$	2.25426	0.151296
$223$	−9.56673	−0.640636	−0.320318	−	0.947310i	$-0.603790\pi$
$223$	−9.56673	−0.640636	−0.320318	+	0.947310i	$0.603790\pi$
$224$	0.402181	0.0268718
$225$	10.3285	0.688568
$226$	−19.5827	−1.30262
$227$	−0.853649	−0.0566587	−0.0283293	−	0.999599i	$-0.509019\pi$
$227$	−0.853649	−0.0566587	−0.0283293	+	0.999599i	$0.509019\pi$
$228$	−0.505477	−0.0334760
$229$	−17.5682	−1.16094	−0.580468	−	0.814283i	$-0.697131\pi$
$229$	−17.5682	−1.16094	−0.580468	+	0.814283i	$0.697131\pi$
$230$	1.18706	0.0782727
$231$	0.514150	0.0338286
$232$	6.21922	0.408311
$233$	−17.4262	−1.14163	−0.570815	−	0.821079i	$-0.693373\pi$
$233$	−17.4262	−1.14163	−0.570815	+	0.821079i	$0.693373\pi$
$234$	1.15000	0.0751775
$235$	−7.02514	−0.458270
$236$	1.24347	0.0809428
$237$	−1.56737	−0.101812
$238$	−2.01433	−0.130570
$239$	15.7237	1.01708	0.508540	−	0.861038i	$-0.330185\pi$
$239$	15.7237	1.01708	0.508540	+	0.861038i	$0.330185\pi$
$240$	−0.651615	−0.0420616
$241$	−12.6288	−0.813493	−0.406746	−	0.913541i	$-0.633337\pi$
$241$	−12.6288	−0.813493	−0.406746	+	0.913541i	$0.633337\pi$
$242$	−8.18165	−0.525936
$243$	15.5176	0.995455
$244$	−1.31892	−0.0844350
$245$	5.85147	0.373837
$246$	−3.71149	−0.236636
$247$	0.315421	0.0200698
$248$	1.00000	0.0635001
$249$	−9.44823	−0.598757
$250$	7.93041	0.501563
$251$	10.6057	0.669425	0.334713	−	0.942320i	$-0.391361\pi$
$251$	10.6057	0.669425	0.334713	+	0.942320i	$0.391361\pi$
$252$	−0.973324	−0.0613137
$253$	−2.32890	−0.146417
$254$	17.8498	1.12000
$255$	3.26363	0.204376
$256$	1.00000	0.0625000
$257$	4.22101	0.263299	0.131650	−	0.991296i	$-0.457973\pi$
$257$	4.22101	0.263299	0.131650	+	0.991296i	$0.457973\pi$
$258$	−8.57850	−0.534074
$259$	1.19057	0.0739784
$260$	0.406612	0.0252170
$261$	−15.0512	−0.931647
$262$	−5.65587	−0.349421
$263$	−17.4091	−1.07349	−0.536745	−	0.843744i	$-0.680346\pi$
$263$	−17.4091	−1.07349	−0.536745	+	0.843744i	$0.680346\pi$
$264$	1.27840	0.0786804
$265$	0.243997	0.0149886
$266$	−0.266964	−0.0163686
$267$	−6.49935	−0.397754
$268$	−2.46651	−0.150666
$269$	−7.28569	−0.444216	−0.222108	−	0.975022i	$-0.571294\pi$
$269$	−7.28569	−0.444216	−0.222108	+	0.975022i	$0.571294\pi$
$270$	3.53183	0.214940
$271$	−8.39224	−0.509792	−0.254896	−	0.966968i	$-0.582041\pi$
$271$	−8.39224	−0.509792	−0.254896	+	0.966968i	$0.582041\pi$
$272$	−5.00852	−0.303686
$273$	−0.145530	−0.00880787
$274$	−13.2170	−0.798468
$275$	−7.16473	−0.432049
$276$	−1.05639	−0.0635873
$277$	−24.0529	−1.44520	−0.722599	−	0.691268i	$-0.757053\pi$
$277$	−24.0529	−1.44520	−0.722599	+	0.691268i	$0.757053\pi$
$278$	8.68942	0.521157
$279$	−2.42012	−0.144889
$280$	−0.344145	−0.0205666
$281$	21.1134	1.25952	0.629760	−	0.776790i	$-0.283153\pi$
$281$	21.1134	1.25952	0.629760	+	0.776790i	$0.283153\pi$
$282$	6.25181	0.372290
$283$	22.2750	1.32411	0.662057	−	0.749454i	$-0.269684\pi$
$283$	22.2750	1.32411	0.662057	+	0.749454i	$0.269684\pi$
$284$	−8.70802	−0.516726
$285$	0.432535	0.0256212
$286$	−0.797733	−0.0471709
$287$	−1.96020	−0.115707
$288$	−2.42012	−0.142607
$289$	8.08529	0.475605
$290$	−5.32176	−0.312505
$291$	−0.761502	−0.0446400
$292$	−7.63765	−0.446960
$293$	23.7321	1.38645	0.693223	−	0.720723i	$-0.256190\pi$
$293$	23.7321	1.38645	0.693223	+	0.720723i	$0.256190\pi$
$294$	−5.20734	−0.303698
$295$	−1.06403	−0.0619503
$296$	2.96029	0.172063
$297$	−6.92910	−0.402067
$298$	−14.0238	−0.812378
$299$	0.659195	0.0381222
$300$	−3.24992	−0.187634
$301$	−4.53067	−0.261143
$302$	−2.79629	−0.160908
$303$	−8.06206	−0.463153
$304$	−0.663790	−0.0380710
$305$	1.12859	0.0646230
$306$	12.1212	0.692923
$307$	−1.60928	−0.0918467	−0.0459233	−	0.998945i	$-0.514623\pi$
$307$	−1.60928	−0.0918467	−0.0459233	+	0.998945i	$0.514623\pi$
$308$	0.675179	0.0384719
$309$	4.14725	0.235929
$310$	−0.855697	−0.0486003
$311$	−30.0043	−1.70139	−0.850693	−	0.525662i	$-0.823818\pi$
$311$	−30.0043	−1.70139	−0.850693	+	0.525662i	$0.823818\pi$
$312$	−0.361852	−0.0204858
$313$	−20.0550	−1.13357	−0.566787	−	0.823864i	$-0.691814\pi$
$313$	−20.0550	−1.13357	−0.566787	+	0.823864i	$0.691814\pi$
$314$	−8.50975	−0.480233
$315$	0.832871	0.0469269
$316$	−2.05826	−0.115786
$317$	12.4439	0.698921	0.349461	−	0.936951i	$-0.386365\pi$
$317$	12.4439	0.698921	0.349461	+	0.936951i	$0.386365\pi$
$318$	−0.217138	−0.0121765
$319$	10.4408	0.584572
$320$	−0.855697	−0.0478349
$321$	0.869718	0.0485430
$322$	−0.557925	−0.0310919
$323$	3.32461	0.184986
$324$	4.11730	0.228739
$325$	2.02797	0.112492
$326$	17.5470	0.971840
$327$	14.6061	0.807717
$328$	−4.87391	−0.269117
$329$	3.30184	0.182036
$330$	−1.09393	−0.0602187
$331$	12.5608	0.690402	0.345201	−	0.938529i	$-0.387811\pi$
$331$	12.5608	0.690402	0.345201	+	0.938529i	$0.387811\pi$
$332$	−12.4074	−0.680942
$333$	−7.16423	−0.392597
$334$	−0.0189001	−0.00103417
$335$	2.11059	0.115314
$336$	0.306261	0.0167079
$337$	−31.1137	−1.69487	−0.847437	−	0.530897i	$-0.821855\pi$
$337$	−31.1137	−1.69487	−0.847437	+	0.530897i	$0.821855\pi$
$338$	−12.7742	−0.694825
$339$	−14.9123	−0.809923
$340$	4.28578	0.232429
$341$	1.67879	0.0909118
$342$	1.60645	0.0868668
$343$	−5.56548	−0.300508
$344$	−11.2652	−0.607381
$345$	0.903951	0.0486671
$346$	−2.34391	−0.126009
$347$	−2.91874	−0.156686	−0.0783431	−	0.996926i	$-0.524963\pi$
$347$	−2.91874	−0.156686	−0.0783431	+	0.996926i	$0.524963\pi$
$348$	4.73594	0.253873
$349$	−1.25576	−0.0672191	−0.0336096	−	0.999435i	$-0.510700\pi$
$349$	−1.25576	−0.0672191	−0.0336096	+	0.999435i	$0.510700\pi$
$350$	−1.71642	−0.0917465
$351$	1.96128	0.104685
$352$	1.67879	0.0894800
$353$	30.9773	1.64876	0.824378	−	0.566040i	$-0.191525\pi$
$353$	30.9773	1.64876	0.824378	+	0.566040i	$0.191525\pi$
$354$	0.946902	0.0503273
$355$	7.45143	0.395481
$356$	−8.53492	−0.452350
$357$	−1.53392	−0.0811835
$358$	9.96668	0.526756
$359$	−27.5206	−1.45248	−0.726240	−	0.687441i	$-0.758734\pi$
$359$	−27.5206	−1.45248	−0.726240	+	0.687441i	$0.758734\pi$
$360$	2.07089	0.109145
$361$	−18.5594	−0.976810
$362$	4.20225	0.220866
$363$	−6.23034	−0.327008
$364$	−0.191109	−0.0100168
$365$	6.53552	0.342085
$366$	−1.00436	−0.0524986
$367$	−9.71262	−0.506994	−0.253497	−	0.967336i	$-0.581581\pi$
$367$	−9.71262	−0.506994	−0.253497	+	0.967336i	$0.581581\pi$
$368$	−1.38725	−0.0723153
$369$	11.7954	0.614046
$370$	−2.53311	−0.131690
$371$	−0.114680	−0.00595387
$372$	0.761502	0.0394820
$373$	25.4451	1.31750	0.658750	−	0.752362i	$-0.271086\pi$
$373$	25.4451	1.31750	0.658750	+	0.752362i	$0.271086\pi$
$374$	−8.40828	−0.434782
$375$	6.03902	0.311854
$376$	8.20984	0.423390
$377$	−2.95526	−0.152204
$378$	−1.65997	−0.0853798
$379$	16.4348	0.844201	0.422100	−	0.906549i	$-0.361293\pi$
$379$	16.4348	0.844201	0.422100	+	0.906549i	$0.361293\pi$
$380$	0.568003	0.0291379
$381$	13.5927	0.696373
$382$	14.4894	0.741344
$383$	10.2652	0.524525	0.262263	−	0.964997i	$-0.415531\pi$
$383$	10.2652	0.524525	0.262263	+	0.964997i	$0.415531\pi$
$384$	0.761502	0.0388602
$385$	−0.577749	−0.0294448
$386$	4.70178	0.239314
$387$	27.2632	1.38587
$388$	−1.00000	−0.0507673
$389$	−8.45990	−0.428934	−0.214467	−	0.976731i	$-0.568801\pi$
$389$	−8.45990	−0.428934	−0.214467	+	0.976731i	$0.568801\pi$
$390$	0.309636	0.0156790
$391$	6.94806	0.351379
$392$	−6.83825	−0.345384
$393$	−4.30695	−0.217257
$394$	25.1192	1.26549
$395$	1.76125	0.0886180
$396$	−4.06288	−0.204167
$397$	−21.5099	−1.07955	−0.539776	−	0.841809i	$-0.681491\pi$
$397$	−21.5099	−1.07955	−0.539776	+	0.841809i	$0.681491\pi$
$398$	14.0088	0.702196
$399$	−0.203293	−0.0101774
$400$	−4.26778	−0.213389
$401$	−5.63121	−0.281209	−0.140605	−	0.990066i	$-0.544905\pi$
$401$	−5.63121	−0.281209	−0.140605	+	0.990066i	$0.544905\pi$
$402$	−1.87825	−0.0936788
$403$	−0.475182	−0.0236705
$404$	−10.5871	−0.526725
$405$	−3.52316	−0.175067
$406$	2.50125	0.124135
$407$	4.96971	0.246339
$408$	−3.81400	−0.188821
$409$	−3.42002	−0.169109	−0.0845545	−	0.996419i	$-0.526947\pi$
$409$	−3.42002	−0.169109	−0.0845545	+	0.996419i	$0.526947\pi$
$410$	4.17059	0.205971
$411$	−10.0648	−0.496458
$412$	5.44614	0.268312
$413$	0.500098	0.0246082
$414$	3.35730	0.165002
$415$	10.6169	0.521165
$416$	−0.475182	−0.0232977
$417$	6.61701	0.324036
$418$	−1.11437	−0.0545055
$419$	4.26006	0.208117	0.104059	−	0.994571i	$-0.466817\pi$
$419$	4.26006	0.208117	0.104059	+	0.994571i	$0.466817\pi$
$420$	−0.262067	−0.0127876
$421$	9.08516	0.442783	0.221392	−	0.975185i	$-0.428940\pi$
$421$	9.08516	0.442783	0.221392	+	0.975185i	$0.428940\pi$
$422$	−19.7147	−0.959696
$423$	−19.8688	−0.966052
$424$	−0.285144	−0.0138478
$425$	21.3753	1.03685
$426$	−6.63117	−0.321281
$427$	−0.530443	−0.0256699
$428$	1.14211	0.0552060
$429$	−0.607475	−0.0293292
$430$	9.63964	0.464865
$431$	25.1014	1.20909	0.604547	−	0.796570i	$-0.293354\pi$
$431$	25.1014	1.20909	0.604547	+	0.796570i	$0.293354\pi$
$432$	−4.12743	−0.198581
$433$	−1.93529	−0.0930043	−0.0465021	−	0.998918i	$-0.514807\pi$
$433$	−1.93529	−0.0930043	−0.0465021	+	0.998918i	$0.514807\pi$
$434$	0.402181	0.0193053
$435$	−4.05253	−0.194304
$436$	19.1806	0.918584
$437$	0.920841	0.0440498
$438$	−5.81609	−0.277903
$439$	−36.5717	−1.74547	−0.872736	−	0.488193i	$-0.837656\pi$
$439$	−36.5717	−1.74547	−0.872736	+	0.488193i	$0.837656\pi$
$440$	−1.43654	−0.0684843
$441$	16.5494	0.788064
$442$	2.37996	0.113203
$443$	34.2472	1.62713	0.813567	−	0.581471i	$-0.197523\pi$
$443$	34.2472	1.62713	0.813567	+	0.581471i	$0.197523\pi$
$444$	2.25426	0.106983
$445$	7.30330	0.346210
$446$	−9.56673	−0.452998
$447$	−10.6792	−0.505107
$448$	0.402181	0.0190013
$449$	−13.5355	−0.638779	−0.319389	−	0.947624i	$-0.603478\pi$
$449$	−13.5355	−0.638779	−0.319389	+	0.947624i	$0.603478\pi$
$450$	10.3285	0.486891
$451$	−8.18230	−0.385289
$452$	−19.5827	−0.921093
$453$	−2.12938	−0.100047
$454$	−0.853649	−0.0400637
$455$	0.163532	0.00766648
$456$	−0.505477	−0.0236711
$457$	38.0897	1.78176	0.890880	−	0.454238i	$-0.150089\pi$
$457$	38.0897	1.78176	0.890880	+	0.454238i	$0.150089\pi$
$458$	−17.5682	−0.820906
$459$	20.6723	0.964901
$460$	1.18706	0.0553471
$461$	7.83058	0.364707	0.182353	−	0.983233i	$-0.441629\pi$
$461$	7.83058	0.364707	0.182353	+	0.983233i	$0.441629\pi$
$462$	0.514150	0.0239204
$463$	27.2539	1.26660	0.633299	−	0.773907i	$-0.281700\pi$
$463$	27.2539	1.26660	0.633299	+	0.773907i	$0.281700\pi$
$464$	6.21922	0.288720
$465$	−0.651615	−0.0302179
$466$	−17.4262	−0.807254
$467$	−14.2518	−0.659495	−0.329747	−	0.944069i	$-0.606964\pi$
$467$	−14.2518	−0.659495	−0.329747	+	0.944069i	$0.606964\pi$
$468$	1.15000	0.0531585
$469$	−0.991985	−0.0458056
$470$	−7.02514	−0.324045
$471$	−6.48019	−0.298591
$472$	1.24347	0.0572352
$473$	−18.9120	−0.869576
$474$	−1.56737	−0.0719916
$475$	2.83291	0.129983
$476$	−2.01433	−0.0923267
$477$	0.690082	0.0315967
$478$	15.7237	0.719184
$479$	19.7923	0.904335	0.452168	−	0.891933i	$-0.350651\pi$
$479$	19.7923	0.904335	0.452168	+	0.891933i	$0.350651\pi$
$480$	−0.651615	−0.0297420
$481$	−1.40667	−0.0641388
$482$	−12.6288	−0.575226
$483$	−0.424861	−0.0193318
$484$	−8.18165	−0.371893
$485$	0.855697	0.0388552
$486$	15.5176	0.703893
$487$	5.87908	0.266406	0.133203	−	0.991089i	$-0.457474\pi$
$487$	5.87908	0.266406	0.133203	+	0.991089i	$0.457474\pi$
$488$	−1.31892	−0.0597045
$489$	13.3621	0.604255
$490$	5.85147	0.264343
$491$	−21.8037	−0.983985	−0.491993	−	0.870599i	$-0.663731\pi$
$491$	−21.8037	−0.983985	−0.491993	+	0.870599i	$0.663731\pi$
$492$	−3.71149	−0.167327
$493$	−31.1491	−1.40288
$494$	0.315421	0.0141915
$495$	3.47659	0.156261
$496$	1.00000	0.0449013
$497$	−3.50220	−0.157095
$498$	−9.44823	−0.423385
$499$	−0.931010	−0.0416777	−0.0208389	−	0.999783i	$-0.506634\pi$
$499$	−0.931010	−0.0416777	−0.0208389	+	0.999783i	$0.506634\pi$
$500$	7.93041	0.354659
$501$	−0.0143924	−0.000643007 0
$502$	10.6057	0.473355
$503$	35.2536	1.57188	0.785939	−	0.618304i	$-0.212180\pi$
$503$	35.2536	1.57188	0.785939	+	0.618304i	$0.212180\pi$
$504$	−0.973324	−0.0433553
$505$	9.05931	0.403134
$506$	−2.32890	−0.103532
$507$	−9.72758	−0.432017
$508$	17.8498	0.791957
$509$	6.68178	0.296165	0.148082	−	0.988975i	$-0.452690\pi$
$509$	6.68178	0.296165	0.148082	+	0.988975i	$0.452690\pi$
$510$	3.26363	0.144516
$511$	−3.07172	−0.135885
$512$	1.00000	0.0441942
$513$	2.73974	0.120963
$514$	4.22101	0.186181
$515$	−4.66025	−0.205355
$516$	−8.57850	−0.377648
$517$	13.7826	0.606160
$518$	1.19057	0.0523107
$519$	−1.78489	−0.0783480
$520$	0.406612	0.0178311
$521$	9.16912	0.401706	0.200853	−	0.979621i	$-0.435629\pi$
$521$	9.16912	0.401706	0.200853	+	0.979621i	$0.435629\pi$
$522$	−15.0512	−0.658774
$523$	2.42001	0.105819	0.0529097	−	0.998599i	$-0.483150\pi$
$523$	2.42001	0.105819	0.0529097	+	0.998599i	$0.483150\pi$
$524$	−5.65587	−0.247078
$525$	−1.30706	−0.0570447
$526$	−17.4091	−0.759073
$527$	−5.00852	−0.218175
$528$	1.27840	0.0556354
$529$	−21.0755	−0.916328
$530$	0.243997	0.0105986
$531$	−3.00933	−0.130594
$532$	−0.266964	−0.0115743
$533$	2.31600	0.100317
$534$	−6.49935	−0.281254
$535$	−0.977300	−0.0422524
$536$	−2.46651	−0.106537
$537$	7.58965	0.327517
$538$	−7.28569	−0.314108
$539$	−11.4800	−0.494479
$540$	3.53183	0.151986
$541$	1.71129	0.0735740	0.0367870	−	0.999323i	$-0.488288\pi$
$541$	1.71129	0.0735740	0.0367870	+	0.999323i	$0.488288\pi$
$542$	−8.39224	−0.360477
$543$	3.20002	0.137326
$544$	−5.00852	−0.214739
$545$	−16.4128	−0.703046
$546$	−0.145530	−0.00622811
$547$	−13.7681	−0.588680	−0.294340	−	0.955701i	$-0.595100\pi$
$547$	−13.7681	−0.588680	−0.294340	+	0.955701i	$0.595100\pi$
$548$	−13.2170	−0.564602
$549$	3.19193	0.136228
$550$	−7.16473	−0.305505
$551$	−4.12825	−0.175869
$552$	−1.05639	−0.0449630
$553$	−0.827793	−0.0352013
$554$	−24.0529	−1.02191
$555$	−1.92897	−0.0818800
$556$	8.68942	0.368514
$557$	−13.7784	−0.583809	−0.291904	−	0.956447i	$-0.594289\pi$
$557$	−13.7784	−0.583809	−0.291904	+	0.956447i	$0.594289\pi$
$558$	−2.42012	−0.102452
$559$	5.35304	0.226410
$560$	−0.344145	−0.0145428
$561$	−6.40292	−0.270331
$562$	21.1134	0.890615
$563$	41.5904	1.75283	0.876413	−	0.481561i	$-0.159930\pi$
$563$	41.5904	1.75283	0.876413	+	0.481561i	$0.159930\pi$
$564$	6.25181	0.263249
$565$	16.7569	0.704967
$566$	22.2750	0.936290
$567$	1.65590	0.0695413
$568$	−8.70802	−0.365380
$569$	−0.439817	−0.0184381	−0.00921904	−	0.999958i	$-0.502935\pi$
$569$	−0.439817	−0.0184381	−0.00921904	+	0.999958i	$0.502935\pi$
$570$	0.432535	0.0181169
$571$	35.5997	1.48980	0.744900	−	0.667176i	$-0.232497\pi$
$571$	35.5997	1.48980	0.744900	+	0.667176i	$0.232497\pi$
$572$	−0.797733	−0.0333549
$573$	11.0337	0.460941
$574$	−1.96020	−0.0818170
$575$	5.92047	0.246901
$576$	−2.42012	−0.100838
$577$	−4.25062	−0.176956	−0.0884778	−	0.996078i	$-0.528200\pi$
$577$	−4.25062	−0.176956	−0.0884778	+	0.996078i	$0.528200\pi$
$578$	8.08529	0.336304
$579$	3.58041	0.148797
$580$	−5.32176	−0.220974
$581$	−4.99000	−0.207020
$582$	−0.761502	−0.0315653
$583$	−0.478698	−0.0198257
$584$	−7.63765	−0.316048
$585$	−0.984048	−0.0406854
$586$	23.7321	0.980366
$587$	−15.0848	−0.622616	−0.311308	−	0.950309i	$-0.600767\pi$
$587$	−15.0848	−0.622616	−0.311308	+	0.950309i	$0.600767\pi$
$588$	−5.20734	−0.214747
$589$	−0.663790	−0.0273510
$590$	−1.06403	−0.0438054
$591$	19.1283	0.786833
$592$	2.96029	0.121667
$593$	43.2625	1.77658	0.888290	−	0.459284i	$-0.151894\pi$
$593$	43.2625	1.77658	0.888290	+	0.459284i	$0.151894\pi$
$594$	−6.92910	−0.284304
$595$	1.72366	0.0706631
$596$	−14.0238	−0.574438
$597$	10.6677	0.436600
$598$	0.659195	0.0269565
$599$	39.5867	1.61747	0.808735	−	0.588174i	$-0.200153\pi$
$599$	39.5867	1.61747	0.808735	+	0.588174i	$0.200153\pi$
$600$	−3.24992	−0.132678
$601$	−16.2493	−0.662822	−0.331411	−	0.943486i	$-0.607525\pi$
$601$	−16.2493	−0.662822	−0.331411	+	0.943486i	$0.607525\pi$
$602$	−4.53067	−0.184656
$603$	5.96925	0.243087
$604$	−2.79629	−0.113779
$605$	7.00101	0.284632
$606$	−8.06206	−0.327499
$607$	−20.4621	−0.830530	−0.415265	−	0.909700i	$-0.636311\pi$
$607$	−20.4621	−0.830530	−0.415265	+	0.909700i	$0.636311\pi$
$608$	−0.663790	−0.0269202
$609$	1.90471	0.0771826
$610$	1.12859	0.0456954
$611$	−3.90117	−0.157824
$612$	12.1212	0.489970
$613$	−16.5117	−0.666902	−0.333451	−	0.942767i	$-0.608213\pi$
$613$	−16.5117	−0.666902	−0.333451	+	0.942767i	$0.608213\pi$
$614$	−1.60928	−0.0649454
$615$	3.17591	0.128065
$616$	0.675179	0.0272037
$617$	17.2653	0.695077	0.347538	−	0.937666i	$-0.387018\pi$
$617$	17.2653	0.695077	0.347538	+	0.937666i	$0.387018\pi$
$618$	4.14725	0.166827
$619$	−19.1897	−0.771301	−0.385651	−	0.922645i	$-0.626023\pi$
$619$	−19.1897	−0.771301	−0.385651	+	0.922645i	$0.626023\pi$
$620$	−0.855697	−0.0343656
$621$	5.72576	0.229767
$622$	−30.0043	−1.20306
$623$	−3.43258	−0.137523
$624$	−0.361852	−0.0144857
$625$	14.5529	0.582115
$626$	−20.0550	−0.801558
$627$	−0.848592	−0.0338895
$628$	−8.50975	−0.339576
$629$	−14.8267	−0.591177
$630$	0.832871	0.0331824
$631$	−44.4047	−1.76772	−0.883862	−	0.467748i	$-0.845066\pi$
$631$	−44.4047	−1.76772	−0.883862	+	0.467748i	$0.845066\pi$
$632$	−2.05826	−0.0818732
$633$	−15.0128	−0.596704
$634$	12.4439	0.494212
$635$	−15.2740	−0.606131
$636$	−0.217138	−0.00861007
$637$	3.24941	0.128746
$638$	10.4408	0.413355
$639$	21.0744	0.833691
$640$	−0.855697	−0.0338244
$641$	−4.63350	−0.183012	−0.0915061	−	0.995805i	$-0.529168\pi$
$641$	−4.63350	−0.183012	−0.0915061	+	0.995805i	$0.529168\pi$
$642$	0.869718	0.0343251
$643$	44.7698	1.76555	0.882774	−	0.469798i	$-0.155673\pi$
$643$	44.7698	1.76555	0.882774	+	0.469798i	$0.155673\pi$
$644$	−0.557925	−0.0219853
$645$	7.34060	0.289036
$646$	3.32461	0.130805
$647$	−15.3866	−0.604908	−0.302454	−	0.953164i	$-0.597806\pi$
$647$	−15.3866	−0.604908	−0.302454	+	0.953164i	$0.597806\pi$
$648$	4.11730	0.161743
$649$	2.08752	0.0819425
$650$	2.02797	0.0795437
$651$	0.306261	0.0120033
$652$	17.5470	0.687195
$653$	39.0536	1.52829	0.764143	−	0.645047i	$-0.223162\pi$
$653$	39.0536	1.52829	0.764143	+	0.645047i	$0.223162\pi$
$654$	14.6061	0.571142
$655$	4.83971	0.189103
$656$	−4.87391	−0.190294
$657$	18.4840	0.721130
$658$	3.30184	0.128719
$659$	17.6445	0.687331	0.343666	−	0.939092i	$-0.388331\pi$
$659$	17.6445	0.687331	0.343666	+	0.939092i	$0.388331\pi$
$660$	−1.09393	−0.0425811
$661$	17.9787	0.699291	0.349646	−	0.936882i	$-0.386302\pi$
$661$	17.9787	0.699291	0.349646	+	0.936882i	$0.386302\pi$
$662$	12.5608	0.488188
$663$	1.81234	0.0703856
$664$	−12.4074	−0.481499
$665$	0.228440	0.00885852
$666$	−7.16423	−0.277608
$667$	−8.62759	−0.334062
$668$	−0.0189001	−0.000731266 0
$669$	−7.28508	−0.281658
$670$	2.11059	0.0815392
$671$	−2.21419	−0.0854778
$672$	0.306261	0.0118143
$673$	−22.5244	−0.868253	−0.434126	−	0.900852i	$-0.642943\pi$
$673$	−22.5244	−0.868253	−0.434126	+	0.900852i	$0.642943\pi$
$674$	−31.1137	−1.19846
$675$	17.6150	0.678000
$676$	−12.7742	−0.491315
$677$	−15.0062	−0.576734	−0.288367	−	0.957520i	$-0.593112\pi$
$677$	−15.0062	−0.576734	−0.288367	+	0.957520i	$0.593112\pi$
$678$	−14.9123	−0.572702
$679$	−0.402181	−0.0154343
$680$	4.28578	0.164352
$681$	−0.650055	−0.0249102
$682$	1.67879	0.0642843
$683$	−32.6671	−1.24997	−0.624986	−	0.780636i	$-0.714895\pi$
$683$	−32.6671	−1.24997	−0.624986	+	0.780636i	$0.714895\pi$
$684$	1.60645	0.0614241
$685$	11.3097	0.432123
$686$	−5.56548	−0.212491
$687$	−13.3782	−0.510410
$688$	−11.2652	−0.429483
$689$	0.135495	0.00516196
$690$	0.903951	0.0344128
$691$	−40.5374	−1.54212	−0.771058	−	0.636765i	$-0.780272\pi$
$691$	−40.5374	−1.54212	−0.771058	+	0.636765i	$0.780272\pi$
$692$	−2.34391	−0.0891020
$693$	−1.63401	−0.0620709
$694$	−2.91874	−0.110794
$695$	−7.43551	−0.282045
$696$	4.73594	0.179515
$697$	24.4111	0.924637
$698$	−1.25576	−0.0475311
$699$	−13.2701	−0.501921
$700$	−1.71642	−0.0648746
$701$	−15.8409	−0.598303	−0.299151	−	0.954206i	$-0.596704\pi$
$701$	−15.8409	−0.598303	−0.299151	+	0.954206i	$0.596704\pi$
$702$	1.96128	0.0740237
$703$	−1.96501	−0.0741117
$704$	1.67879	0.0632719
$705$	−5.34965	−0.201480
$706$	30.9773	1.16585
$707$	−4.25791	−0.160135
$708$	0.946902	0.0355867
$709$	37.6339	1.41337	0.706685	−	0.707528i	$-0.250190\pi$
$709$	37.6339	1.41337	0.706685	+	0.707528i	$0.250190\pi$
$710$	7.45143	0.279647
$711$	4.98123	0.186811
$712$	−8.53492	−0.319859
$713$	−1.38725	−0.0519528
$714$	−1.53392	−0.0574054
$715$	0.682618	0.0255285
$716$	9.96668	0.372472
$717$	11.9736	0.447163
$718$	−27.5206	−1.02706
$719$	−43.1781	−1.61027	−0.805135	−	0.593091i	$-0.797907\pi$
$719$	−43.1781	−1.61027	−0.805135	+	0.593091i	$0.797907\pi$
$720$	2.07089	0.0771773
$721$	2.19034	0.0815723
$722$	−18.5594	−0.690709
$723$	−9.61685	−0.357655
$724$	4.20225	0.156176
$725$	−26.5423	−0.985755
$726$	−6.23034	−0.231230
$727$	9.22427	0.342109	0.171055	−	0.985262i	$-0.445283\pi$
$727$	9.22427	0.342109	0.171055	+	0.985262i	$0.445283\pi$
$728$	−0.191109	−0.00708298
$729$	−0.535220	−0.0198230
$730$	6.53552	0.241890
$731$	56.4222	2.08685
$732$	−1.00436	−0.0371221
$733$	25.5923	0.945275	0.472637	−	0.881257i	$-0.343302\pi$
$733$	25.5923	0.945275	0.472637	+	0.881257i	$0.343302\pi$
$734$	−9.71262	−0.358499
$735$	4.45591	0.164359
$736$	−1.38725	−0.0511346
$737$	−4.14077	−0.152527
$738$	11.7954	0.434196
$739$	6.36490	0.234137	0.117068	−	0.993124i	$-0.462650\pi$
$739$	6.36490	0.234137	0.117068	+	0.993124i	$0.462650\pi$
$740$	−2.53311	−0.0931189
$741$	0.240194	0.00882373
$742$	−0.114680	−0.00421002
$743$	2.70565	0.0992605	0.0496303	−	0.998768i	$-0.484196\pi$
$743$	2.70565	0.0992605	0.0496303	+	0.998768i	$0.484196\pi$
$744$	0.761502	0.0279180
$745$	12.0001	0.439651
$746$	25.4451	0.931613
$747$	30.0272	1.09864
$748$	−8.40828	−0.307437
$749$	0.459335	0.0167837
$750$	6.03902	0.220514
$751$	−43.9500	−1.60376	−0.801879	−	0.597486i	$-0.796166\pi$
$751$	−43.9500	−1.60376	−0.801879	+	0.597486i	$0.796166\pi$
$752$	8.20984	0.299382
$753$	8.07625	0.294315
$754$	−2.95526	−0.107624
$755$	2.39277	0.0870819
$756$	−1.65997	−0.0603726
$757$	−8.62635	−0.313530	−0.156765	−	0.987636i	$-0.550107\pi$
$757$	−8.62635	−0.313530	−0.156765	+	0.987636i	$0.550107\pi$
$758$	16.4348	0.596940
$759$	−1.77346	−0.0643727
$760$	0.568003	0.0206036
$761$	−37.5297	−1.36045	−0.680225	−	0.733004i	$-0.738118\pi$
$761$	−37.5297	−1.36045	−0.680225	+	0.733004i	$0.738118\pi$
$762$	13.5927	0.492410
$763$	7.71407	0.279268
$764$	14.4894	0.524210
$765$	−10.3721	−0.375003
$766$	10.2652	0.370895
$767$	−0.590873	−0.0213352
$768$	0.761502	0.0274783
$769$	36.8315	1.32818	0.664089	−	0.747654i	$-0.268820\pi$
$769$	36.8315	1.32818	0.664089	+	0.747654i	$0.268820\pi$
$770$	−0.577749	−0.0208206
$771$	3.21430	0.115760
$772$	4.70178	0.169221
$773$	42.1637	1.51652	0.758261	−	0.651951i	$-0.226049\pi$
$773$	42.1637	1.51652	0.758261	+	0.651951i	$0.226049\pi$
$774$	27.2632	0.979955
$775$	−4.26778	−0.153303
$776$	−1.00000	−0.0358979
$777$	0.906621	0.0325249
$778$	−8.45990	−0.303302
$779$	3.23526	0.115915
$780$	0.309636	0.0110867
$781$	−14.6190	−0.523108
$782$	6.94806	0.248462
$783$	−25.6694	−0.917348
$784$	−6.83825	−0.244223
$785$	7.28177	0.259897
$786$	−4.30695	−0.153624
$787$	−38.6845	−1.37895	−0.689477	−	0.724308i	$-0.742159\pi$
$787$	−38.6845	−1.37895	−0.689477	+	0.724308i	$0.742159\pi$
$788$	25.1192	0.894834
$789$	−13.2571	−0.471964
$790$	1.76125	0.0626624
$791$	−7.87579	−0.280031
$792$	−4.06288	−0.144368
$793$	0.626725	0.0222557
$794$	−21.5099	−0.763358
$795$	0.185804	0.00658980
$796$	14.0088	0.496527
$797$	34.7814	1.23202	0.616010	−	0.787738i	$-0.288748\pi$
$797$	34.7814	1.23202	0.616010	+	0.787738i	$0.288748\pi$
$798$	−0.203293	−0.00719650
$799$	−41.1192	−1.45469
$800$	−4.26778	−0.150889
$801$	20.6555	0.729825
$802$	−5.63121	−0.198845
$803$	−12.8220	−0.452480
$804$	−1.87825	−0.0662409
$805$	0.477414	0.0168266
$806$	−0.475182	−0.0167376
$807$	−5.54806	−0.195301
$808$	−10.5871	−0.372451
$809$	−40.3446	−1.41844	−0.709220	−	0.704987i	$-0.750953\pi$
$809$	−40.3446	−1.41844	−0.709220	+	0.704987i	$0.750953\pi$
$810$	−3.52316	−0.123791
$811$	−45.8375	−1.60957	−0.804786	−	0.593565i	$-0.797720\pi$
$811$	−45.8375	−1.60957	−0.804786	+	0.593565i	$0.797720\pi$
$812$	2.50125	0.0877767
$813$	−6.39070	−0.224132
$814$	4.96971	0.174188
$815$	−15.0149	−0.525950
$816$	−3.81400	−0.133517
$817$	7.47776	0.261614
$818$	−3.42002	−0.119578
$819$	0.462506	0.0161613
$820$	4.17059	0.145643
$821$	46.8154	1.63387	0.816934	−	0.576731i	$-0.195672\pi$
$821$	46.8154	1.63387	0.816934	+	0.576731i	$0.195672\pi$
$822$	−10.0648	−0.351049
$823$	13.4031	0.467204	0.233602	−	0.972332i	$-0.424949\pi$
$823$	13.4031	0.467204	0.233602	+	0.972332i	$0.424949\pi$
$824$	5.44614	0.189725
$825$	−5.45595	−0.189952
$826$	0.500098	0.0174007
$827$	37.3277	1.29801	0.649005	−	0.760784i	$-0.275185\pi$
$827$	37.3277	1.29801	0.649005	+	0.760784i	$0.275185\pi$
$828$	3.35730	0.116674
$829$	11.4200	0.396633	0.198316	−	0.980138i	$-0.436453\pi$
$829$	11.4200	0.396633	0.198316	+	0.980138i	$0.436453\pi$
$830$	10.6169	0.368520
$831$	−18.3163	−0.635386
$832$	−0.475182	−0.0164740
$833$	34.2495	1.18668
$834$	6.61701	0.229128
$835$	0.0161727	0.000559681 0
$836$	−1.11437	−0.0385412
$837$	−4.12743	−0.142665
$838$	4.26006	0.147161
$839$	−43.9108	−1.51597	−0.757984	−	0.652273i	$-0.773816\pi$
$839$	−43.9108	−1.51597	−0.757984	+	0.652273i	$0.773816\pi$
$840$	−0.262067	−0.00904217
$841$	9.67864	0.333746
$842$	9.08516	0.313095
$843$	16.0779	0.553752
$844$	−19.7147	−0.678608
$845$	10.9308	0.376033
$846$	−19.8688	−0.683102
$847$	−3.29050	−0.113063
$848$	−0.285144	−0.00979189
$849$	16.9625	0.582151
$850$	21.3753	0.733166
$851$	−4.10665	−0.140774
$852$	−6.63117	−0.227180
$853$	17.8752	0.612034	0.306017	−	0.952026i	$-0.401003\pi$
$853$	17.8752	0.612034	0.306017	+	0.952026i	$0.401003\pi$
$854$	−0.530443	−0.0181514
$855$	−1.37463	−0.0470115
$856$	1.14211	0.0390365
$857$	−21.9065	−0.748311	−0.374156	−	0.927366i	$-0.622067\pi$
$857$	−21.9065	−0.748311	−0.374156	+	0.927366i	$0.622067\pi$
$858$	−0.607475	−0.0207388
$859$	31.5914	1.07789	0.538943	−	0.842342i	$-0.318824\pi$
$859$	31.5914	1.07789	0.538943	+	0.842342i	$0.318824\pi$
$860$	9.63964	0.328709
$861$	−1.49269	−0.0508708
$862$	25.1014	0.854958
$863$	−9.15724	−0.311716	−0.155858	−	0.987779i	$-0.549814\pi$
$863$	−9.15724	−0.311716	−0.155858	+	0.987779i	$0.549814\pi$
$864$	−4.12743	−0.140418
$865$	2.00568	0.0681950
$866$	−1.93529	−0.0657640
$867$	6.15696	0.209101
$868$	0.402181	0.0136509
$869$	−3.45539	−0.117216
$870$	−4.05253	−0.137394
$871$	1.17204	0.0397132
$872$	19.1806	0.649537
$873$	2.42012	0.0819085
$874$	0.920841	0.0311479
$875$	3.18946	0.107823
$876$	−5.81609	−0.196507
$877$	−1.63849	−0.0553278	−0.0276639	−	0.999617i	$-0.508807\pi$
$877$	−1.63849	−0.0553278	−0.0276639	+	0.999617i	$0.508807\pi$
$878$	−36.5717	−1.23423
$879$	18.0721	0.609556
$880$	−1.43654	−0.0484257
$881$	−18.1053	−0.609983	−0.304992	−	0.952355i	$-0.598654\pi$
$881$	−18.1053	−0.609983	−0.304992	+	0.952355i	$0.598654\pi$
$882$	16.5494	0.557246
$883$	20.5087	0.690173	0.345087	−	0.938571i	$-0.387850\pi$
$883$	20.5087	0.690173	0.345087	+	0.938571i	$0.387850\pi$
$884$	2.37996	0.0800467
$885$	−0.810261	−0.0272366
$886$	34.2472	1.15056
$887$	−15.2985	−0.513673	−0.256837	−	0.966455i	$-0.582680\pi$
$887$	−15.2985	−0.513673	−0.256837	+	0.966455i	$0.582680\pi$
$888$	2.25426	0.0756481
$889$	7.17885	0.240771
$890$	7.30330	0.244807
$891$	6.91210	0.231564
$892$	−9.56673	−0.320318
$893$	−5.44961	−0.182364
$894$	−10.6792	−0.357165
$895$	−8.52846	−0.285075
$896$	0.402181	0.0134359
$897$	0.501978	0.0167606
$898$	−13.5355	−0.451685
$899$	6.21922	0.207422
$900$	10.3285	0.344284
$901$	1.42815	0.0475786
$902$	−8.18230	−0.272441
$903$	−3.45011	−0.114812
$904$	−19.5827	−0.651311
$905$	−3.59586	−0.119530
$906$	−2.12938	−0.0707438
$907$	30.4415	1.01079	0.505397	−	0.862887i	$-0.331346\pi$
$907$	30.4415	1.01079	0.505397	+	0.862887i	$0.331346\pi$
$908$	−0.853649	−0.0283293
$909$	25.6219	0.849824
$910$	0.163532	0.00542102
$911$	0.355786	0.0117877	0.00589386	−	0.999983i	$-0.498124\pi$
$911$	0.355786	0.0117877	0.00589386	+	0.999983i	$0.498124\pi$
$912$	−0.505477	−0.0167380
$913$	−20.8294	−0.689353
$914$	38.0897	1.25989
$915$	0.859425	0.0284117
$916$	−17.5682	−0.580468
$917$	−2.27468	−0.0751166
$918$	20.6723	0.682288
$919$	25.9320	0.855417	0.427708	−	0.903917i	$-0.359321\pi$
$919$	25.9320	0.855417	0.427708	+	0.903917i	$0.359321\pi$
$920$	1.18706	0.0391363
$921$	−1.22547	−0.0403807
$922$	7.83058	0.257887
$923$	4.13789	0.136200
$924$	0.514150	0.0169143
$925$	−12.6339	−0.415399
$926$	27.2539	0.895620
$927$	−13.1803	−0.432898
$928$	6.21922	0.204156
$929$	49.5359	1.62522	0.812610	−	0.582808i	$-0.198046\pi$
$929$	49.5359	1.62522	0.812610	+	0.582808i	$0.198046\pi$
$930$	−0.651615	−0.0213673
$931$	4.53916	0.148765
$932$	−17.4262	−0.570815
$933$	−22.8483	−0.748020
$934$	−14.2518	−0.466333
$935$	7.19494	0.235300
$936$	1.15000	0.0375888
$937$	−44.4540	−1.45225	−0.726125	−	0.687563i	$-0.758681\pi$
$937$	−44.4540	−1.45225	−0.726125	+	0.687563i	$0.758681\pi$
$938$	−0.991985	−0.0323895
$939$	−15.2719	−0.498380
$940$	−7.02514	−0.229135
$941$	24.7319	0.806238	0.403119	−	0.915148i	$-0.367926\pi$
$941$	24.7319	0.806238	0.403119	+	0.915148i	$0.367926\pi$
$942$	−6.48019	−0.211136
$943$	6.76133	0.220179
$944$	1.24347	0.0404714
$945$	1.42043	0.0462067
$946$	−18.9120	−0.614883
$947$	−41.7967	−1.35821	−0.679106	−	0.734040i	$-0.737632\pi$
$947$	−41.7967	−1.35821	−0.679106	+	0.734040i	$0.737632\pi$
$948$	−1.56737	−0.0509058
$949$	3.62928	0.117811
$950$	2.83291	0.0919118
$951$	9.47608	0.307283
$952$	−2.01433	−0.0652849
$953$	6.54099	0.211884	0.105942	−	0.994372i	$-0.466214\pi$
$953$	6.54099	0.211884	0.105942	+	0.994372i	$0.466214\pi$
$954$	0.690082	0.0223422
$955$	−12.3986	−0.401208
$956$	15.7237	0.508540
$957$	7.95067	0.257009
$958$	19.7923	0.639462
$959$	−5.31562	−0.171650
$960$	−0.651615	−0.0210308
$961$	1.00000	0.0322581
$962$	−1.40667	−0.0453530
$963$	−2.76404	−0.0890698
$964$	−12.6288	−0.406746
$965$	−4.02330	−0.129515
$966$	−0.424861	−0.0136697
$967$	30.0940	0.967758	0.483879	−	0.875135i	$-0.339227\pi$
$967$	30.0940	0.967758	0.483879	+	0.875135i	$0.339227\pi$
$968$	−8.18165	−0.262968
$969$	2.53169	0.0813297
$970$	0.855697	0.0274748
$971$	−35.7032	−1.14577	−0.572886	−	0.819635i	$-0.694176\pi$
$971$	−35.7032	−1.14577	−0.572886	+	0.819635i	$0.694176\pi$
$972$	15.5176	0.497728
$973$	3.49472	0.112036
$974$	5.87908	0.188378
$975$	1.54431	0.0494573
$976$	−1.31892	−0.0422175
$977$	32.0108	1.02411	0.512057	−	0.858951i	$-0.328884\pi$
$977$	32.0108	1.02411	0.512057	+	0.858951i	$0.328884\pi$
$978$	13.3621	0.427273
$979$	−14.3284	−0.457937
$980$	5.85147	0.186918
$981$	−46.4192	−1.48205
$982$	−21.8037	−0.695783
$983$	−7.83069	−0.249760	−0.124880	−	0.992172i	$-0.539855\pi$
$983$	−7.83069	−0.249760	−0.124880	+	0.992172i	$0.539855\pi$
$984$	−3.71149	−0.118318
$985$	−21.4944	−0.684869
$986$	−31.1491	−0.991989
$987$	2.51436	0.0800329
$988$	0.315421	0.0100349
$989$	15.6277	0.496931
$990$	3.47659	0.110493
$991$	31.9621	1.01531	0.507655	−	0.861560i	$-0.330512\pi$
$991$	31.9621	1.01531	0.507655	+	0.861560i	$0.330512\pi$
$992$	1.00000	0.0317500
$993$	9.56504	0.303537
$994$	−3.50220	−0.111083
$995$	−11.9873	−0.380022
$996$	−9.44823	−0.299379
$997$	13.9337	0.441286	0.220643	−	0.975355i	$-0.429184\pi$
$997$	13.9337	0.441286	0.220643	+	0.975355i	$0.429184\pi$
$998$	−0.931010	−0.0294706
$999$	−12.2184	−0.386572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.15	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.15	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.761502 q^{3} +1.00000 q^{4} -0.855697 q^{5} +0.761502 q^{6} +0.402181 q^{7} +1.00000 q^{8} -2.42012 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.761502 q^{3} +1.00000 q^{4} -0.855697 q^{5} +0.761502 q^{6} +0.402181 q^{7} +1.00000 q^{8} -2.42012 q^{9} -0.855697 q^{10} +1.67879 q^{11} +0.761502 q^{12} -0.475182 q^{13} +0.402181 q^{14} -0.651615 q^{15} +1.00000 q^{16} -5.00852 q^{17} -2.42012 q^{18} -0.663790 q^{19} -0.855697 q^{20} +0.306261 q^{21} +1.67879 q^{22} -1.38725 q^{23} +0.761502 q^{24} -4.26778 q^{25} -0.475182 q^{26} -4.12743 q^{27} +0.402181 q^{28} +6.21922 q^{29} -0.651615 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.27840 q^{33} -5.00852 q^{34} -0.344145 q^{35} -2.42012 q^{36} +2.96029 q^{37} -0.663790 q^{38} -0.361852 q^{39} -0.855697 q^{40} -4.87391 q^{41} +0.306261 q^{42} -11.2652 q^{43} +1.67879 q^{44} +2.07089 q^{45} -1.38725 q^{46} +8.20984 q^{47} +0.761502 q^{48} -6.83825 q^{49} -4.26778 q^{50} -3.81400 q^{51} -0.475182 q^{52} -0.285144 q^{53} -4.12743 q^{54} -1.43654 q^{55} +0.402181 q^{56} -0.505477 q^{57} +6.21922 q^{58} +1.24347 q^{59} -0.651615 q^{60} -1.31892 q^{61} +1.00000 q^{62} -0.973324 q^{63} +1.00000 q^{64} +0.406612 q^{65} +1.27840 q^{66} -2.46651 q^{67} -5.00852 q^{68} -1.05639 q^{69} -0.344145 q^{70} -8.70802 q^{71} -2.42012 q^{72} -7.63765 q^{73} +2.96029 q^{74} -3.24992 q^{75} -0.663790 q^{76} +0.675179 q^{77} -0.361852 q^{78} -2.05826 q^{79} -0.855697 q^{80} +4.11730 q^{81} -4.87391 q^{82} -12.4074 q^{83} +0.306261 q^{84} +4.28578 q^{85} -11.2652 q^{86} +4.73594 q^{87} +1.67879 q^{88} -8.53492 q^{89} +2.07089 q^{90} -0.191109 q^{91} -1.38725 q^{92} +0.761502 q^{93} +8.20984 q^{94} +0.568003 q^{95} +0.761502 q^{96} -1.00000 q^{97} -6.83825 q^{98} -4.06288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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