LMFDB - Embedded newform 6034.2.a.n.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.44853 q^{3} +1.00000 q^{4} -1.26403 q^{5} -1.44853 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.901751 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.44853 q^{3} +1.00000 q^{4} -1.26403 q^{5} -1.44853 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.901751 q^{9} +1.26403 q^{10} -3.22511 q^{11} +1.44853 q^{12} -2.31777 q^{13} +1.00000 q^{14} -1.83098 q^{15} +1.00000 q^{16} +3.60165 q^{17} +0.901751 q^{18} +5.33546 q^{19} -1.26403 q^{20} -1.44853 q^{21} +3.22511 q^{22} -7.66129 q^{23} -1.44853 q^{24} -3.40224 q^{25} +2.31777 q^{26} -5.65182 q^{27} -1.00000 q^{28} -0.214755 q^{29} +1.83098 q^{30} -5.47162 q^{31} -1.00000 q^{32} -4.67167 q^{33} -3.60165 q^{34} +1.26403 q^{35} -0.901751 q^{36} +0.154141 q^{37} -5.33546 q^{38} -3.35737 q^{39} +1.26403 q^{40} +3.69908 q^{41} +1.44853 q^{42} +7.50104 q^{43} -3.22511 q^{44} +1.13984 q^{45} +7.66129 q^{46} +0.101562 q^{47} +1.44853 q^{48} +1.00000 q^{49} +3.40224 q^{50} +5.21710 q^{51} -2.31777 q^{52} +9.39083 q^{53} +5.65182 q^{54} +4.07662 q^{55} +1.00000 q^{56} +7.72860 q^{57} +0.214755 q^{58} +11.8493 q^{59} -1.83098 q^{60} +5.95759 q^{61} +5.47162 q^{62} +0.901751 q^{63} +1.00000 q^{64} +2.92972 q^{65} +4.67167 q^{66} -2.95438 q^{67} +3.60165 q^{68} -11.0976 q^{69} -1.26403 q^{70} +10.7018 q^{71} +0.901751 q^{72} -15.7336 q^{73} -0.154141 q^{74} -4.92826 q^{75} +5.33546 q^{76} +3.22511 q^{77} +3.35737 q^{78} -13.6695 q^{79} -1.26403 q^{80} -5.48159 q^{81} -3.69908 q^{82} -1.96725 q^{83} -1.44853 q^{84} -4.55257 q^{85} -7.50104 q^{86} -0.311080 q^{87} +3.22511 q^{88} -0.350463 q^{89} -1.13984 q^{90} +2.31777 q^{91} -7.66129 q^{92} -7.92583 q^{93} -0.101562 q^{94} -6.74416 q^{95} -1.44853 q^{96} -17.6621 q^{97} -1.00000 q^{98} +2.90824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	1.44853	0.836311	0.418156	−	0.908375i	$-0.362677\pi$
$3$	1.44853	0.836311	0.418156	+	0.908375i	$0.362677\pi$
$4$	1.00000	0.500000
$5$	−1.26403	−0.565289	−0.282645	−	0.959225i	$-0.591212\pi$
$5$	−1.26403	−0.565289	−0.282645	+	0.959225i	$0.591212\pi$
$6$	−1.44853	−0.591361
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.901751	−0.300584
$10$	1.26403	0.399720
$11$	−3.22511	−0.972406	−0.486203	−	0.873846i	$-0.661618\pi$
$11$	−3.22511	−0.972406	−0.486203	+	0.873846i	$0.661618\pi$
$12$	1.44853	0.418156
$13$	−2.31777	−0.642835	−0.321417	−	0.946938i	$-0.604159\pi$
$13$	−2.31777	−0.642835	−0.321417	+	0.946938i	$0.604159\pi$
$14$	1.00000	0.267261
$15$	−1.83098	−0.472758
$16$	1.00000	0.250000
$17$	3.60165	0.873527	0.436764	−	0.899576i	$-0.356125\pi$
$17$	3.60165	0.873527	0.436764	+	0.899576i	$0.356125\pi$
$18$	0.901751	0.212545
$19$	5.33546	1.22404	0.612020	−	0.790843i	$-0.290357\pi$
$19$	5.33546	1.22404	0.612020	+	0.790843i	$0.290357\pi$
$20$	−1.26403	−0.282645
$21$	−1.44853	−0.316096
$22$	3.22511	0.687595
$23$	−7.66129	−1.59749	−0.798745	−	0.601670i	$-0.794502\pi$
$23$	−7.66129	−1.59749	−0.798745	+	0.601670i	$0.794502\pi$
$24$	−1.44853	−0.295681
$25$	−3.40224	−0.680448
$26$	2.31777	0.454553
$27$	−5.65182	−1.08769
$28$	−1.00000	−0.188982
$29$	−0.214755	−0.0398791	−0.0199395	−	0.999801i	$-0.506347\pi$
$29$	−0.214755	−0.0398791	−0.0199395	+	0.999801i	$0.506347\pi$
$30$	1.83098	0.334290
$31$	−5.47162	−0.982732	−0.491366	−	0.870953i	$-0.663502\pi$
$31$	−5.47162	−0.982732	−0.491366	+	0.870953i	$0.663502\pi$
$32$	−1.00000	−0.176777
$33$	−4.67167	−0.813234
$34$	−3.60165	−0.617677
$35$	1.26403	0.213659
$36$	−0.901751	−0.150292
$37$	0.154141	0.0253407	0.0126703	−	0.999920i	$-0.495967\pi$
$37$	0.154141	0.0253407	0.0126703	+	0.999920i	$0.495967\pi$
$38$	−5.33546	−0.865526
$39$	−3.35737	−0.537610
$40$	1.26403	0.199860
$41$	3.69908	0.577699	0.288850	−	0.957374i	$-0.406727\pi$
$41$	3.69908	0.577699	0.288850	+	0.957374i	$0.406727\pi$
$42$	1.44853	0.223514
$43$	7.50104	1.14390	0.571949	−	0.820289i	$-0.306188\pi$
$43$	7.50104	1.14390	0.571949	+	0.820289i	$0.306188\pi$
$44$	−3.22511	−0.486203
$45$	1.13984	0.169917
$46$	7.66129	1.12960
$47$	0.101562	0.0148144	0.00740720	−	0.999973i	$-0.497642\pi$
$47$	0.101562	0.0148144	0.00740720	+	0.999973i	$0.497642\pi$
$48$	1.44853	0.209078
$49$	1.00000	0.142857
$50$	3.40224	0.481149
$51$	5.21710	0.730541
$52$	−2.31777	−0.321417
$53$	9.39083	1.28993	0.644965	−	0.764212i	$-0.276872\pi$
$53$	9.39083	1.28993	0.644965	+	0.764212i	$0.276872\pi$
$54$	5.65182	0.769115
$55$	4.07662	0.549691
$56$	1.00000	0.133631
$57$	7.72860	1.02368
$58$	0.214755	0.0281988
$59$	11.8493	1.54264	0.771322	−	0.636445i	$-0.219596\pi$
$59$	11.8493	1.54264	0.771322	+	0.636445i	$0.219596\pi$
$60$	−1.83098	−0.236379
$61$	5.95759	0.762792	0.381396	−	0.924412i	$-0.375443\pi$
$61$	5.95759	0.762792	0.381396	+	0.924412i	$0.375443\pi$
$62$	5.47162	0.694897
$63$	0.901751	0.113610
$64$	1.00000	0.125000
$65$	2.92972	0.363388
$66$	4.67167	0.575043
$67$	−2.95438	−0.360935	−0.180467	−	0.983581i	$-0.557761\pi$
$67$	−2.95438	−0.360935	−0.180467	+	0.983581i	$0.557761\pi$
$68$	3.60165	0.436764
$69$	−11.0976	−1.33600
$70$	−1.26403	−0.151080
$71$	10.7018	1.27007	0.635035	−	0.772483i	$-0.280986\pi$
$71$	10.7018	1.27007	0.635035	+	0.772483i	$0.280986\pi$
$72$	0.901751	0.106272
$73$	−15.7336	−1.84148	−0.920739	−	0.390179i	$-0.872413\pi$
$73$	−15.7336	−1.84148	−0.920739	+	0.390179i	$0.872413\pi$
$74$	−0.154141	−0.0179186
$75$	−4.92826	−0.569066
$76$	5.33546	0.612020
$77$	3.22511	0.367535
$78$	3.35737	0.380147
$79$	−13.6695	−1.53794	−0.768970	−	0.639285i	$-0.779230\pi$
$79$	−13.6695	−1.53794	−0.768970	+	0.639285i	$0.779230\pi$
$80$	−1.26403	−0.141322
$81$	−5.48159	−0.609066
$82$	−3.69908	−0.408495
$83$	−1.96725	−0.215934	−0.107967	−	0.994154i	$-0.534434\pi$
$83$	−1.96725	−0.215934	−0.107967	+	0.994154i	$0.534434\pi$
$84$	−1.44853	−0.158048
$85$	−4.55257	−0.493796
$86$	−7.50104	−0.808857
$87$	−0.311080	−0.0333513
$88$	3.22511	0.343797
$89$	−0.350463	−0.0371490	−0.0185745	−	0.999827i	$-0.505913\pi$
$89$	−0.350463	−0.0371490	−0.0185745	+	0.999827i	$0.505913\pi$
$90$	−1.13984	−0.120149
$91$	2.31777	0.242969
$92$	−7.66129	−0.798745
$93$	−7.92583	−0.821870
$94$	−0.101562	−0.0104754
$95$	−6.74416	−0.691936
$96$	−1.44853	−0.147840
$97$	−17.6621	−1.79332	−0.896659	−	0.442723i	$-0.854013\pi$
$97$	−17.6621	−1.79332	−0.896659	+	0.442723i	$0.854013\pi$
$98$	−1.00000	−0.101015
$99$	2.90824	0.292289
$100$	−3.40224	−0.340224
$101$	8.91473	0.887049	0.443524	−	0.896262i	$-0.353728\pi$
$101$	8.91473	0.887049	0.443524	+	0.896262i	$0.353728\pi$
$102$	−5.21710	−0.516570
$103$	9.46770	0.932880	0.466440	−	0.884553i	$-0.345536\pi$
$103$	9.46770	0.932880	0.466440	+	0.884553i	$0.345536\pi$
$104$	2.31777	0.227276
$105$	1.83098	0.178686
$106$	−9.39083	−0.912118
$107$	17.0234	1.64571	0.822856	−	0.568250i	$-0.192380\pi$
$107$	17.0234	1.64571	0.822856	+	0.568250i	$0.192380\pi$
$108$	−5.65182	−0.543846
$109$	19.5460	1.87217	0.936086	−	0.351773i	$-0.114421\pi$
$109$	19.5460	1.87217	0.936086	+	0.351773i	$0.114421\pi$
$110$	−4.07662	−0.388690
$111$	0.223279	0.0211927
$112$	−1.00000	−0.0944911
$113$	−14.8821	−1.39999	−0.699997	−	0.714146i	$-0.746815\pi$
$113$	−14.8821	−1.39999	−0.699997	+	0.714146i	$0.746815\pi$
$114$	−7.72860	−0.723849
$115$	9.68407	0.903044
$116$	−0.214755	−0.0199395
$117$	2.09005	0.193226
$118$	−11.8493	−1.09081
$119$	−3.60165	−0.330162
$120$	1.83098	0.167145
$121$	−0.598690	−0.0544264
$122$	−5.95759	−0.539375
$123$	5.35824	0.483136
$124$	−5.47162	−0.491366
$125$	10.6206	0.949939
$126$	−0.901751	−0.0803344
$127$	7.87038	0.698383	0.349191	−	0.937051i	$-0.386456\pi$
$127$	7.87038	0.698383	0.349191	+	0.937051i	$0.386456\pi$
$128$	−1.00000	−0.0883883
$129$	10.8655	0.956654
$130$	−2.92972	−0.256954
$131$	−0.0345986	−0.00302290	−0.00151145	−	0.999999i	$-0.500481\pi$
$131$	−0.0345986	−0.00302290	−0.00151145	+	0.999999i	$0.500481\pi$
$132$	−4.67167	−0.406617
$133$	−5.33546	−0.462643
$134$	2.95438	0.255219
$135$	7.14404	0.614861
$136$	−3.60165	−0.308839
$137$	−2.39977	−0.205026	−0.102513	−	0.994732i	$-0.532688\pi$
$137$	−2.39977	−0.205026	−0.102513	+	0.994732i	$0.532688\pi$
$138$	11.0976	0.944694
$139$	−13.1736	−1.11737	−0.558683	−	0.829381i	$-0.688693\pi$
$139$	−13.1736	−1.11737	−0.558683	+	0.829381i	$0.688693\pi$
$140$	1.26403	0.106830
$141$	0.147116	0.0123894
$142$	−10.7018	−0.898075
$143$	7.47506	0.625096
$144$	−0.901751	−0.0751459
$145$	0.271456	0.0225432
$146$	15.7336	1.30212
$147$	1.44853	0.119473
$148$	0.154141	0.0126703
$149$	14.8747	1.21859	0.609293	−	0.792945i	$-0.291453\pi$
$149$	14.8747	1.21859	0.609293	+	0.792945i	$0.291453\pi$
$150$	4.92826	0.402390
$151$	24.1404	1.96452	0.982259	−	0.187530i	$-0.0600480\pi$
$151$	24.1404	1.96452	0.982259	+	0.187530i	$0.0600480\pi$
$152$	−5.33546	−0.432763
$153$	−3.24779	−0.262568
$154$	−3.22511	−0.259886
$155$	6.91627	0.555528
$156$	−3.35737	−0.268805
$157$	6.06502	0.484041	0.242021	−	0.970271i	$-0.422190\pi$
$157$	6.06502	0.484041	0.242021	+	0.970271i	$0.422190\pi$
$158$	13.6695	1.08749
$159$	13.6029	1.07878
$160$	1.26403	0.0999300
$161$	7.66129	0.603794
$162$	5.48159	0.430674
$163$	10.5901	0.829477	0.414738	−	0.909941i	$-0.363873\pi$
$163$	10.5901	0.829477	0.414738	+	0.909941i	$0.363873\pi$
$164$	3.69908	0.288850
$165$	5.90512	0.459713
$166$	1.96725	0.152688
$167$	3.80166	0.294181	0.147091	−	0.989123i	$-0.453009\pi$
$167$	3.80166	0.294181	0.147091	+	0.989123i	$0.453009\pi$
$168$	1.44853	0.111757
$169$	−7.62793	−0.586764
$170$	4.55257	0.349166
$171$	−4.81126	−0.367926
$172$	7.50104	0.571949
$173$	16.4571	1.25121	0.625605	−	0.780140i	$-0.284852\pi$
$173$	16.4571	1.25121	0.625605	+	0.780140i	$0.284852\pi$
$174$	0.311080	0.0235829
$175$	3.40224	0.257185
$176$	−3.22511	−0.243102
$177$	17.1641	1.29013
$178$	0.350463	0.0262683
$179$	19.1032	1.42784	0.713921	−	0.700227i	$-0.246918\pi$
$179$	19.1032	1.42784	0.713921	+	0.700227i	$0.246918\pi$
$180$	1.13984	0.0849584
$181$	15.4524	1.14857	0.574285	−	0.818655i	$-0.305280\pi$
$181$	15.4524	1.14857	0.574285	+	0.818655i	$0.305280\pi$
$182$	−2.31777	−0.171805
$183$	8.62977	0.637931
$184$	7.66129	0.564798
$185$	−0.194839	−0.0143248
$186$	7.92583	0.581150
$187$	−11.6157	−0.849423
$188$	0.101562	0.00740720
$189$	5.65182	0.411109
$190$	6.74416	0.489273
$191$	4.74568	0.343385	0.171692	−	0.985151i	$-0.445076\pi$
$191$	4.74568	0.343385	0.171692	+	0.985151i	$0.445076\pi$
$192$	1.44853	0.104539
$193$	4.37571	0.314970	0.157485	−	0.987521i	$-0.449661\pi$
$193$	4.37571	0.314970	0.157485	+	0.987521i	$0.449661\pi$
$194$	17.6621	1.26807
$195$	4.24380	0.303905
$196$	1.00000	0.0714286
$197$	3.06798	0.218585	0.109292	−	0.994010i	$-0.465142\pi$
$197$	3.06798	0.218585	0.109292	+	0.994010i	$0.465142\pi$
$198$	−2.90824	−0.206680
$199$	−26.2836	−1.86320	−0.931599	−	0.363488i	$-0.881586\pi$
$199$	−26.2836	−1.86320	−0.931599	+	0.363488i	$0.881586\pi$
$200$	3.40224	0.240575
$201$	−4.27951	−0.301854
$202$	−8.91473	−0.627238
$203$	0.214755	0.0150729
$204$	5.21710	0.365270
$205$	−4.67573	−0.326567
$206$	−9.46770	−0.659646
$207$	6.90858	0.480179
$208$	−2.31777	−0.160709
$209$	−17.2074	−1.19026
$210$	−1.83098	−0.126350
$211$	−8.94228	−0.615612	−0.307806	−	0.951449i	$-0.599595\pi$
$211$	−8.94228	−0.615612	−0.307806	+	0.951449i	$0.599595\pi$
$212$	9.39083	0.644965
$213$	15.5019	1.06217
$214$	−17.0234	−1.16369
$215$	−9.48150	−0.646633
$216$	5.65182	0.384557
$217$	5.47162	0.371438
$218$	−19.5460	−1.32382
$219$	−22.7906	−1.54005
$220$	4.07662	0.274845
$221$	−8.34780	−0.561534
$222$	−0.223279	−0.0149855
$223$	−27.0980	−1.81461	−0.907307	−	0.420470i	$-0.861865\pi$
$223$	−27.0980	−1.81461	−0.907307	+	0.420470i	$0.861865\pi$
$224$	1.00000	0.0668153
$225$	3.06797	0.204532
$226$	14.8821	0.989946
$227$	0.799865	0.0530889	0.0265444	−	0.999648i	$-0.491550\pi$
$227$	0.799865	0.0530889	0.0265444	+	0.999648i	$0.491550\pi$
$228$	7.72860	0.511839
$229$	−1.41408	−0.0934453	−0.0467227	−	0.998908i	$-0.514878\pi$
$229$	−1.41408	−0.0934453	−0.0467227	+	0.998908i	$0.514878\pi$
$230$	−9.68407	−0.638549
$231$	4.67167	0.307374
$232$	0.214755	0.0140994
$233$	2.30009	0.150684	0.0753419	−	0.997158i	$-0.475995\pi$
$233$	2.30009	0.150684	0.0753419	+	0.997158i	$0.475995\pi$
$234$	−2.09005	−0.136631
$235$	−0.128377	−0.00837442
$236$	11.8493	0.771322
$237$	−19.8007	−1.28620
$238$	3.60165	0.233460
$239$	9.46668	0.612349	0.306174	−	0.951975i	$-0.400951\pi$
$239$	9.46668	0.612349	0.306174	+	0.951975i	$0.400951\pi$
$240$	−1.83098	−0.118189
$241$	15.2642	0.983254	0.491627	−	0.870806i	$-0.336402\pi$
$241$	15.2642	0.983254	0.491627	+	0.870806i	$0.336402\pi$
$242$	0.598690	0.0384853
$243$	9.01518	0.578324
$244$	5.95759	0.381396
$245$	−1.26403	−0.0807556
$246$	−5.35824	−0.341629
$247$	−12.3664	−0.786855
$248$	5.47162	0.347448
$249$	−2.84963	−0.180588
$250$	−10.6206	−0.671709
$251$	1.32168	0.0834237	0.0417118	−	0.999130i	$-0.486719\pi$
$251$	1.32168	0.0834237	0.0417118	+	0.999130i	$0.486719\pi$
$252$	0.901751	0.0568050
$253$	24.7085	1.55341
$254$	−7.87038	−0.493831
$255$	−6.59455	−0.412967
$256$	1.00000	0.0625000
$257$	−9.58020	−0.597597	−0.298798	−	0.954316i	$-0.596586\pi$
$257$	−9.58020	−0.597597	−0.298798	+	0.954316i	$0.596586\pi$
$258$	−10.8655	−0.676456
$259$	−0.154141	−0.00957788
$260$	2.92972	0.181694
$261$	0.193656	0.0119870
$262$	0.0345986	0.00213751
$263$	26.9818	1.66377	0.831885	−	0.554947i	$-0.187262\pi$
$263$	26.9818	1.66377	0.831885	+	0.554947i	$0.187262\pi$
$264$	4.67167	0.287522
$265$	−11.8703	−0.729184
$266$	5.33546	0.327138
$267$	−0.507657	−0.0310681
$268$	−2.95438	−0.180467
$269$	−7.60283	−0.463553	−0.231776	−	0.972769i	$-0.574454\pi$
$269$	−7.60283	−0.463553	−0.231776	+	0.972769i	$0.574454\pi$
$270$	−7.14404	−0.434773
$271$	23.1724	1.40763	0.703813	−	0.710386i	$-0.251479\pi$
$271$	23.1724	1.40763	0.703813	+	0.710386i	$0.251479\pi$
$272$	3.60165	0.218382
$273$	3.35737	0.203197
$274$	2.39977	0.144976
$275$	10.9726	0.661672
$276$	−11.0976	−0.667999
$277$	21.5203	1.29303	0.646515	−	0.762902i	$-0.276226\pi$
$277$	21.5203	1.29303	0.646515	+	0.762902i	$0.276226\pi$
$278$	13.1736	0.790098
$279$	4.93404	0.295393
$280$	−1.26403	−0.0755400
$281$	−29.3424	−1.75042	−0.875210	−	0.483742i	$-0.839277\pi$
$281$	−29.3424	−1.75042	−0.875210	+	0.483742i	$0.839277\pi$
$282$	−0.147116	−0.00876066
$283$	−30.0854	−1.78839	−0.894197	−	0.447674i	$-0.852253\pi$
$283$	−30.0854	−1.78839	−0.894197	+	0.447674i	$0.852253\pi$
$284$	10.7018	0.635035
$285$	−9.76914	−0.578674
$286$	−7.47506	−0.442010
$287$	−3.69908	−0.218350
$288$	0.901751	0.0531362
$289$	−4.02815	−0.236950
$290$	−0.271456	−0.0159405
$291$	−25.5842	−1.49977
$292$	−15.7336	−0.920739
$293$	19.2131	1.12244	0.561221	−	0.827666i	$-0.310332\pi$
$293$	19.2131	1.12244	0.561221	+	0.827666i	$0.310332\pi$
$294$	−1.44853	−0.0844802
$295$	−14.9778	−0.872040
$296$	−0.154141	−0.00895929
$297$	18.2277	1.05768
$298$	−14.8747	−0.861671
$299$	17.7571	1.02692
$300$	−4.92826	−0.284533
$301$	−7.50104	−0.432352
$302$	−24.1404	−1.38912
$303$	12.9133	0.741849
$304$	5.33546	0.306010
$305$	−7.53055	−0.431198
$306$	3.24779	0.185664
$307$	−2.60073	−0.148431	−0.0742156	−	0.997242i	$-0.523645\pi$
$307$	−2.60073	−0.148431	−0.0742156	+	0.997242i	$0.523645\pi$
$308$	3.22511	0.183767
$309$	13.7143	0.780178
$310$	−6.91627	−0.392818
$311$	−10.9513	−0.620991	−0.310495	−	0.950575i	$-0.600495\pi$
$311$	−10.9513	−0.620991	−0.310495	+	0.950575i	$0.600495\pi$
$312$	3.35737	0.190074
$313$	21.0786	1.19143	0.595717	−	0.803195i	$-0.296868\pi$
$313$	21.0786	1.19143	0.595717	+	0.803195i	$0.296868\pi$
$314$	−6.06502	−0.342269
$315$	−1.13984	−0.0642225
$316$	−13.6695	−0.768970
$317$	−3.41278	−0.191681	−0.0958403	−	0.995397i	$-0.530554\pi$
$317$	−3.41278	−0.191681	−0.0958403	+	0.995397i	$0.530554\pi$
$318$	−13.6029	−0.762815
$319$	0.692609	0.0387787
$320$	−1.26403	−0.0706612
$321$	24.6589	1.37633
$322$	−7.66129	−0.426947
$323$	19.2164	1.06923
$324$	−5.48159	−0.304533
$325$	7.88562	0.437415
$326$	−10.5901	−0.586529
$327$	28.3131	1.56572
$328$	−3.69908	−0.204248
$329$	−0.101562	−0.00559931
$330$	−5.90512	−0.325066
$331$	1.05122	0.0577806	0.0288903	−	0.999583i	$-0.490803\pi$
$331$	1.05122	0.0577806	0.0288903	+	0.999583i	$0.490803\pi$
$332$	−1.96725	−0.107967
$333$	−0.138997	−0.00761700
$334$	−3.80166	−0.208018
$335$	3.73441	0.204033
$336$	−1.44853	−0.0790240
$337$	8.35437	0.455092	0.227546	−	0.973767i	$-0.426930\pi$
$337$	8.35437	0.455092	0.227546	+	0.973767i	$0.426930\pi$
$338$	7.62793	0.414905
$339$	−21.5573	−1.17083
$340$	−4.55257	−0.246898
$341$	17.6466	0.955615
$342$	4.81126	0.260163
$343$	−1.00000	−0.0539949
$344$	−7.50104	−0.404429
$345$	14.0277	0.755226
$346$	−16.4571	−0.884739
$347$	−7.54630	−0.405107	−0.202553	−	0.979271i	$-0.564924\pi$
$347$	−7.54630	−0.405107	−0.202553	+	0.979271i	$0.564924\pi$
$348$	−0.311080	−0.0166757
$349$	2.03679	0.109027	0.0545133	−	0.998513i	$-0.482639\pi$
$349$	2.03679	0.109027	0.0545133	+	0.998513i	$0.482639\pi$
$350$	−3.40224	−0.181857
$351$	13.0996	0.699206
$352$	3.22511	0.171899
$353$	−29.7876	−1.58544	−0.792718	−	0.609589i	$-0.791334\pi$
$353$	−29.7876	−1.58544	−0.792718	+	0.609589i	$0.791334\pi$
$354$	−17.1641	−0.912260
$355$	−13.5273	−0.717957
$356$	−0.350463	−0.0185745
$357$	−5.21710	−0.276118
$358$	−19.1032	−1.00964
$359$	11.9211	0.629173	0.314586	−	0.949229i	$-0.398134\pi$
$359$	11.9211	0.629173	0.314586	+	0.949229i	$0.398134\pi$
$360$	−1.13984	−0.0600747
$361$	9.46716	0.498272
$362$	−15.4524	−0.812162
$363$	−0.867223	−0.0455174
$364$	2.31777	0.121484
$365$	19.8877	1.04097
$366$	−8.62977	−0.451085
$367$	35.9106	1.87452	0.937260	−	0.348632i	$-0.113354\pi$
$367$	35.9106	1.87452	0.937260	+	0.348632i	$0.113354\pi$
$368$	−7.66129	−0.399372
$369$	−3.33565	−0.173647
$370$	0.194839	0.0101292
$371$	−9.39083	−0.487548
$372$	−7.92583	−0.410935
$373$	1.76229	0.0912480	0.0456240	−	0.998959i	$-0.485472\pi$
$373$	1.76229	0.0912480	0.0456240	+	0.998959i	$0.485472\pi$
$374$	11.6157	0.600633
$375$	15.3844	0.794445
$376$	−0.101562	−0.00523768
$377$	0.497754	0.0256356
$378$	−5.65182	−0.290698
$379$	−6.08120	−0.312370	−0.156185	−	0.987728i	$-0.549920\pi$
$379$	−6.08120	−0.312370	−0.156185	+	0.987728i	$0.549920\pi$
$380$	−6.74416	−0.345968
$381$	11.4005	0.584065
$382$	−4.74568	−0.242810
$383$	−10.3380	−0.528248	−0.264124	−	0.964489i	$-0.585083\pi$
$383$	−10.3380	−0.528248	−0.264124	+	0.964489i	$0.585083\pi$
$384$	−1.44853	−0.0739202
$385$	−4.07662	−0.207764
$386$	−4.37571	−0.222718
$387$	−6.76407	−0.343837
$388$	−17.6621	−0.896659
$389$	−29.5639	−1.49895	−0.749474	−	0.662033i	$-0.769694\pi$
$389$	−29.5639	−1.49895	−0.749474	+	0.662033i	$0.769694\pi$
$390$	−4.24380	−0.214893
$391$	−27.5933	−1.39545
$392$	−1.00000	−0.0505076
$393$	−0.0501173	−0.00252808
$394$	−3.06798	−0.154563
$395$	17.2786	0.869381
$396$	2.90824	0.146145
$397$	−2.23532	−0.112188	−0.0560938	−	0.998426i	$-0.517865\pi$
$397$	−2.23532	−0.112188	−0.0560938	+	0.998426i	$0.517865\pi$
$398$	26.2836	1.31748
$399$	−7.72860	−0.386914
$400$	−3.40224	−0.170112
$401$	11.2737	0.562979	0.281490	−	0.959564i	$-0.409171\pi$
$401$	11.2737	0.562979	0.281490	+	0.959564i	$0.409171\pi$
$402$	4.27951	0.213443
$403$	12.6820	0.631734
$404$	8.91473	0.443524
$405$	6.92887	0.344298
$406$	−0.214755	−0.0106581
$407$	−0.497123	−0.0246414
$408$	−5.21710	−0.258285
$409$	32.5916	1.61155	0.805777	−	0.592220i	$-0.201748\pi$
$409$	32.5916	1.61155	0.805777	+	0.592220i	$0.201748\pi$
$410$	4.67573	0.230918
$411$	−3.47615	−0.171466
$412$	9.46770	0.466440
$413$	−11.8493	−0.583065
$414$	−6.90858	−0.339538
$415$	2.48666	0.122065
$416$	2.31777	0.113638
$417$	−19.0823	−0.934466
$418$	17.2074	0.841643
$419$	16.8439	0.822880	0.411440	−	0.911437i	$-0.365026\pi$
$419$	16.8439	0.822880	0.411440	+	0.911437i	$0.365026\pi$
$420$	1.83098	0.0893428
$421$	−0.753904	−0.0367430	−0.0183715	−	0.999831i	$-0.505848\pi$
$421$	−0.753904	−0.0367430	−0.0183715	+	0.999831i	$0.505848\pi$
$422$	8.94228	0.435304
$423$	−0.0915840	−0.00445297
$424$	−9.39083	−0.456059
$425$	−12.2537	−0.594390
$426$	−15.5019	−0.751070
$427$	−5.95759	−0.288308
$428$	17.0234	0.822856
$429$	10.8279	0.522775
$430$	9.48150	0.457239
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.65182	−0.271923
$433$	−13.5708	−0.652171	−0.326086	−	0.945340i	$-0.605730\pi$
$433$	−13.5708	−0.652171	−0.326086	+	0.945340i	$0.605730\pi$
$434$	−5.47162	−0.262646
$435$	0.393213	0.0188531
$436$	19.5460	0.936086
$437$	−40.8765	−1.95539
$438$	22.7906	1.08898
$439$	−10.6671	−0.509114	−0.254557	−	0.967058i	$-0.581930\pi$
$439$	−10.6671	−0.509114	−0.254557	+	0.967058i	$0.581930\pi$
$440$	−4.07662	−0.194345
$441$	−0.901751	−0.0429405
$442$	8.34780	0.397064
$443$	10.5775	0.502553	0.251277	−	0.967915i	$-0.419150\pi$
$443$	10.5775	0.502553	0.251277	+	0.967915i	$0.419150\pi$
$444$	0.223279	0.0105964
$445$	0.442994	0.0209999
$446$	27.0980	1.28313
$447$	21.5466	1.01912
$448$	−1.00000	−0.0472456
$449$	−22.5821	−1.06572	−0.532859	−	0.846204i	$-0.678882\pi$
$449$	−22.5821	−1.06572	−0.532859	+	0.846204i	$0.678882\pi$
$450$	−3.06797	−0.144626
$451$	−11.9299	−0.561758
$452$	−14.8821	−0.699997
$453$	34.9682	1.64295
$454$	−0.799865	−0.0375395
$455$	−2.92972	−0.137348
$456$	−7.72860	−0.361925
$457$	−4.14872	−0.194069	−0.0970345	−	0.995281i	$-0.530936\pi$
$457$	−4.14872	−0.194069	−0.0970345	+	0.995281i	$0.530936\pi$
$458$	1.41408	0.0660758
$459$	−20.3558	−0.950129
$460$	9.68407	0.451522
$461$	25.6956	1.19676	0.598382	−	0.801211i	$-0.295811\pi$
$461$	25.6956	1.19676	0.598382	+	0.801211i	$0.295811\pi$
$462$	−4.67167	−0.217346
$463$	19.0380	0.884773	0.442386	−	0.896825i	$-0.354132\pi$
$463$	19.0380	0.884773	0.442386	+	0.896825i	$0.354132\pi$
$464$	−0.214755	−0.00996977
$465$	10.0184	0.464594
$466$	−2.30009	−0.106549
$467$	−2.34262	−0.108404	−0.0542018	−	0.998530i	$-0.517261\pi$
$467$	−2.34262	−0.108404	−0.0542018	+	0.998530i	$0.517261\pi$
$468$	2.09005	0.0966128
$469$	2.95438	0.136420
$470$	0.128377	0.00592161
$471$	8.78538	0.404809
$472$	−11.8493	−0.545407
$473$	−24.1916	−1.11233
$474$	19.8007	0.909478
$475$	−18.1525	−0.832895
$476$	−3.60165	−0.165081
$477$	−8.46819	−0.387732
$478$	−9.46668	−0.432996
$479$	6.41867	0.293277	0.146638	−	0.989190i	$-0.453155\pi$
$479$	6.41867	0.293277	0.146638	+	0.989190i	$0.453155\pi$
$480$	1.83098	0.0835726
$481$	−0.357265	−0.0162899
$482$	−15.2642	−0.695266
$483$	11.0976	0.504960
$484$	−0.598690	−0.0272132
$485$	22.3254	1.01374
$486$	−9.01518	−0.408937
$487$	−0.883066	−0.0400155	−0.0200078	−	0.999800i	$-0.506369\pi$
$487$	−0.883066	−0.0400155	−0.0200078	+	0.999800i	$0.506369\pi$
$488$	−5.95759	−0.269688
$489$	15.3400	0.693701
$490$	1.26403	0.0571029
$491$	−22.4448	−1.01292	−0.506460	−	0.862263i	$-0.669046\pi$
$491$	−22.4448	−1.01292	−0.506460	+	0.862263i	$0.669046\pi$
$492$	5.35824	0.241568
$493$	−0.773473	−0.0348355
$494$	12.3664	0.556390
$495$	−3.67609	−0.165228
$496$	−5.47162	−0.245683
$497$	−10.7018	−0.480041
$498$	2.84963	0.127695
$499$	19.9212	0.891796	0.445898	−	0.895084i	$-0.352884\pi$
$499$	19.9212	0.891796	0.445898	+	0.895084i	$0.352884\pi$
$500$	10.6206	0.474970
$501$	5.50683	0.246027
$502$	−1.32168	−0.0589895
$503$	3.31834	0.147958	0.0739788	−	0.997260i	$-0.476430\pi$
$503$	3.31834	0.147958	0.0739788	+	0.997260i	$0.476430\pi$
$504$	−0.901751	−0.0401672
$505$	−11.2684	−0.501439
$506$	−24.7085	−1.09843
$507$	−11.0493	−0.490717
$508$	7.87038	0.349191
$509$	23.8167	1.05566	0.527829	−	0.849351i	$-0.323006\pi$
$509$	23.8167	1.05566	0.527829	+	0.849351i	$0.323006\pi$
$510$	6.59455	0.292012
$511$	15.7336	0.696013
$512$	−1.00000	−0.0441942
$513$	−30.1551	−1.33138
$514$	9.58020	0.422565
$515$	−11.9674	−0.527347
$516$	10.8655	0.478327
$517$	−0.327549	−0.0144056
$518$	0.154141	0.00677259
$519$	23.8386	1.04640
$520$	−2.92972	−0.128477
$521$	21.2943	0.932920	0.466460	−	0.884542i	$-0.345529\pi$
$521$	21.2943	0.932920	0.466460	+	0.884542i	$0.345529\pi$
$522$	−0.193656	−0.00847609
$523$	−0.989607	−0.0432725	−0.0216362	−	0.999766i	$-0.506888\pi$
$523$	−0.989607	−0.0432725	−0.0216362	+	0.999766i	$0.506888\pi$
$524$	−0.0345986	−0.00151145
$525$	4.92826	0.215087
$526$	−26.9818	−1.17646
$527$	−19.7068	−0.858443
$528$	−4.67167	−0.203309
$529$	35.6954	1.55197
$530$	11.8703	0.515611
$531$	−10.6851	−0.463694
$532$	−5.33546	−0.231322
$533$	−8.57363	−0.371365
$534$	0.507657	0.0219685
$535$	−21.5180	−0.930303
$536$	2.95438	0.127610
$537$	27.6716	1.19412
$538$	7.60283	0.327781
$539$	−3.22511	−0.138915
$540$	7.14404	0.307431
$541$	29.7230	1.27789	0.638947	−	0.769251i	$-0.279370\pi$
$541$	29.7230	1.27789	0.638947	+	0.769251i	$0.279370\pi$
$542$	−23.1724	−0.995341
$543$	22.3834	0.960563
$544$	−3.60165	−0.154419
$545$	−24.7067	−1.05832
$546$	−3.35737	−0.143682
$547$	−18.7571	−0.801997	−0.400998	−	0.916079i	$-0.631337\pi$
$547$	−18.7571	−0.801997	−0.400998	+	0.916079i	$0.631337\pi$
$548$	−2.39977	−0.102513
$549$	−5.37227	−0.229283
$550$	−10.9726	−0.467872
$551$	−1.14582	−0.0488135
$552$	11.0976	0.472347
$553$	13.6695	0.581287
$554$	−21.5203	−0.914310
$555$	−0.282230	−0.0119800
$556$	−13.1736	−0.558683
$557$	−3.12542	−0.132428	−0.0662142	−	0.997805i	$-0.521092\pi$
$557$	−3.12542	−0.132428	−0.0662142	+	0.997805i	$0.521092\pi$
$558$	−4.93404	−0.208875
$559$	−17.3857	−0.735337
$560$	1.26403	0.0534148
$561$	−16.8257	−0.710382
$562$	29.3424	1.23773
$563$	32.6668	1.37674	0.688371	−	0.725359i	$-0.258326\pi$
$563$	32.6668	1.37674	0.688371	+	0.725359i	$0.258326\pi$
$564$	0.147116	0.00619472
$565$	18.8114	0.791402
$566$	30.0854	1.26459
$567$	5.48159	0.230205
$568$	−10.7018	−0.449037
$569$	12.7210	0.533293	0.266647	−	0.963794i	$-0.414084\pi$
$569$	12.7210	0.533293	0.266647	+	0.963794i	$0.414084\pi$
$570$	9.76914	0.409184
$571$	−7.60141	−0.318109	−0.159055	−	0.987270i	$-0.550845\pi$
$571$	−7.60141	−0.318109	−0.159055	+	0.987270i	$0.550845\pi$
$572$	7.47506	0.312548
$573$	6.87427	0.287177
$574$	3.69908	0.154397
$575$	26.0655	1.08701
$576$	−0.901751	−0.0375730
$577$	13.7678	0.573159	0.286579	−	0.958056i	$-0.407482\pi$
$577$	13.7678	0.573159	0.286579	+	0.958056i	$0.407482\pi$
$578$	4.02815	0.167549
$579$	6.33836	0.263413
$580$	0.271456	0.0112716
$581$	1.96725	0.0816154
$582$	25.5842	1.06050
$583$	−30.2864	−1.25434
$584$	15.7336	0.651061
$585$	−2.64188	−0.109228
$586$	−19.2131	−0.793687
$587$	−20.6386	−0.851844	−0.425922	−	0.904760i	$-0.640050\pi$
$587$	−20.6386	−0.851844	−0.425922	+	0.904760i	$0.640050\pi$
$588$	1.44853	0.0597365
$589$	−29.1936	−1.20290
$590$	14.9778	0.616626
$591$	4.44408	0.182805
$592$	0.154141	0.00633517
$593$	39.6214	1.62706	0.813528	−	0.581525i	$-0.197544\pi$
$593$	39.6214	1.62706	0.813528	+	0.581525i	$0.197544\pi$
$594$	−18.2277	−0.747892
$595$	4.55257	0.186637
$596$	14.8747	0.609293
$597$	−38.0727	−1.55821
$598$	−17.7571	−0.726143
$599$	−12.5956	−0.514643	−0.257321	−	0.966326i	$-0.582840\pi$
$599$	−12.5956	−0.514643	−0.257321	+	0.966326i	$0.582840\pi$
$600$	4.92826	0.201195
$601$	−18.3882	−0.750072	−0.375036	−	0.927010i	$-0.622370\pi$
$601$	−18.3882	−0.750072	−0.375036	+	0.927010i	$0.622370\pi$
$602$	7.50104	0.305719
$603$	2.66411	0.108491
$604$	24.1404	0.982259
$605$	0.756760	0.0307667
$606$	−12.9133	−0.524566
$607$	−23.2820	−0.944988	−0.472494	−	0.881334i	$-0.656646\pi$
$607$	−23.2820	−0.944988	−0.472494	+	0.881334i	$0.656646\pi$
$608$	−5.33546	−0.216382
$609$	0.311080	0.0126056
$610$	7.53055	0.304903
$611$	−0.235398	−0.00952320
$612$	−3.24779	−0.131284
$613$	−27.5399	−1.11233	−0.556163	−	0.831073i	$-0.687727\pi$
$613$	−27.5399	−1.11233	−0.556163	+	0.831073i	$0.687727\pi$
$614$	2.60073	0.104957
$615$	−6.77295	−0.273112
$616$	−3.22511	−0.129943
$617$	−8.33362	−0.335499	−0.167749	−	0.985830i	$-0.553650\pi$
$617$	−8.33362	−0.335499	−0.167749	+	0.985830i	$0.553650\pi$
$618$	−13.7143	−0.551669
$619$	47.6877	1.91673	0.958366	−	0.285542i	$-0.0921737\pi$
$619$	47.6877	1.91673	0.958366	+	0.285542i	$0.0921737\pi$
$620$	6.91627	0.277764
$621$	43.3002	1.73758
$622$	10.9513	0.439107
$623$	0.350463	0.0140410
$624$	−3.35737	−0.134402
$625$	3.58643	0.143457
$626$	−21.0786	−0.842471
$627$	−24.9255	−0.995430
$628$	6.06502	0.242021
$629$	0.555163	0.0221358
$630$	1.13984	0.0454122
$631$	9.06920	0.361039	0.180520	−	0.983571i	$-0.442222\pi$
$631$	9.06920	0.361039	0.180520	+	0.983571i	$0.442222\pi$
$632$	13.6695	0.543744
$633$	−12.9532	−0.514843
$634$	3.41278	0.135539
$635$	−9.94836	−0.394789
$636$	13.6029	0.539391
$637$	−2.31777	−0.0918335
$638$	−0.692609	−0.0274206
$639$	−9.65036	−0.381762
$640$	1.26403	0.0499650
$641$	−8.20148	−0.323939	−0.161969	−	0.986796i	$-0.551785\pi$
$641$	−8.20148	−0.323939	−0.161969	+	0.986796i	$0.551785\pi$
$642$	−24.6589	−0.973210
$643$	38.6839	1.52554	0.762772	−	0.646667i	$-0.223838\pi$
$643$	38.6839	1.52554	0.762772	+	0.646667i	$0.223838\pi$
$644$	7.66129	0.301897
$645$	−13.7343	−0.540786
$646$	−19.2164	−0.756061
$647$	14.5250	0.571038	0.285519	−	0.958373i	$-0.407834\pi$
$647$	14.5250	0.571038	0.285519	+	0.958373i	$0.407834\pi$
$648$	5.48159	0.215337
$649$	−38.2152	−1.50008
$650$	−7.88562	−0.309299
$651$	7.92583	0.310638
$652$	10.5901	0.414738
$653$	33.1727	1.29815	0.649074	−	0.760725i	$-0.275157\pi$
$653$	33.1727	1.29815	0.649074	+	0.760725i	$0.275157\pi$
$654$	−28.3131	−1.10713
$655$	0.0437336	0.00170881
$656$	3.69908	0.144425
$657$	14.1878	0.553518
$658$	0.101562	0.00395931
$659$	2.38108	0.0927539	0.0463769	−	0.998924i	$-0.485232\pi$
$659$	2.38108	0.0927539	0.0463769	+	0.998924i	$0.485232\pi$
$660$	5.90512	0.229856
$661$	−35.0387	−1.36285	−0.681423	−	0.731890i	$-0.738639\pi$
$661$	−35.0387	−1.36285	−0.681423	+	0.731890i	$0.738639\pi$
$662$	−1.05122	−0.0408570
$663$	−12.0921	−0.469617
$664$	1.96725	0.0763442
$665$	6.74416	0.261527
$666$	0.138997	0.00538603
$667$	1.64530	0.0637064
$668$	3.80166	0.147091
$669$	−39.2523	−1.51758
$670$	−3.73441	−0.144273
$671$	−19.2139	−0.741743
$672$	1.44853	0.0558784
$673$	−23.1260	−0.891440	−0.445720	−	0.895172i	$-0.647052\pi$
$673$	−23.1260	−0.891440	−0.445720	+	0.895172i	$0.647052\pi$
$674$	−8.35437	−0.321798
$675$	19.2288	0.740118
$676$	−7.62793	−0.293382
$677$	−1.52519	−0.0586177	−0.0293089	−	0.999570i	$-0.509331\pi$
$677$	−1.52519	−0.0586177	−0.0293089	+	0.999570i	$0.509331\pi$
$678$	21.5573	0.827903
$679$	17.6621	0.677810
$680$	4.55257	0.174583
$681$	1.15863	0.0443988
$682$	−17.6466	−0.675722
$683$	−29.1688	−1.11611	−0.558057	−	0.829803i	$-0.688453\pi$
$683$	−29.1688	−1.11611	−0.558057	+	0.829803i	$0.688453\pi$
$684$	−4.81126	−0.183963
$685$	3.03337	0.115899
$686$	1.00000	0.0381802
$687$	−2.04835	−0.0781494
$688$	7.50104	0.285974
$689$	−21.7658	−0.829211
$690$	−14.0277	−0.534025
$691$	−30.5639	−1.16271	−0.581353	−	0.813652i	$-0.697476\pi$
$691$	−30.5639	−1.16271	−0.581353	+	0.813652i	$0.697476\pi$
$692$	16.4571	0.625605
$693$	−2.90824	−0.110475
$694$	7.54630	0.286454
$695$	16.6517	0.631636
$696$	0.311080	0.0117915
$697$	13.3228	0.504636
$698$	−2.03679	−0.0770935
$699$	3.33175	0.126018
$700$	3.40224	0.128593
$701$	35.7765	1.35126	0.675629	−	0.737242i	$-0.263872\pi$
$701$	35.7765	1.35126	0.675629	+	0.737242i	$0.263872\pi$
$702$	−13.0996	−0.494414
$703$	0.822416	0.0310180
$704$	−3.22511	−0.121551
$705$	−0.185959	−0.00700362
$706$	29.7876	1.12107
$707$	−8.91473	−0.335273
$708$	17.1641	0.645065
$709$	−46.5856	−1.74956	−0.874779	−	0.484523i	$-0.838993\pi$
$709$	−46.5856	−1.74956	−0.874779	+	0.484523i	$0.838993\pi$
$710$	13.5273	0.507672
$711$	12.3265	0.462280
$712$	0.350463	0.0131342
$713$	41.9197	1.56990
$714$	5.21710	0.195245
$715$	−9.44867	−0.353360
$716$	19.1032	0.713921
$717$	13.7128	0.512114
$718$	−11.9211	−0.444892
$719$	22.9733	0.856760	0.428380	−	0.903599i	$-0.359084\pi$
$719$	22.9733	0.856760	0.428380	+	0.903599i	$0.359084\pi$
$720$	1.13984	0.0424792
$721$	−9.46770	−0.352596
$722$	−9.46716	−0.352331
$723$	22.1107	0.822306
$724$	15.4524	0.574285
$725$	0.730649	0.0271356
$726$	0.867223	0.0321856
$727$	−45.7342	−1.69619	−0.848094	−	0.529846i	$-0.822250\pi$
$727$	−45.7342	−1.69619	−0.848094	+	0.529846i	$0.822250\pi$
$728$	−2.31777	−0.0859024
$729$	29.5036	1.09272
$730$	−19.8877	−0.736076
$731$	27.0161	0.999225
$732$	8.62977	0.318966
$733$	16.4772	0.608599	0.304299	−	0.952576i	$-0.401578\pi$
$733$	16.4772	0.608599	0.304299	+	0.952576i	$0.401578\pi$
$734$	−35.9106	−1.32549
$735$	−1.83098	−0.0675368
$736$	7.66129	0.282399
$737$	9.52818	0.350975
$738$	3.33565	0.122787
$739$	7.07809	0.260372	0.130186	−	0.991490i	$-0.458443\pi$
$739$	7.07809	0.260372	0.130186	+	0.991490i	$0.458443\pi$
$740$	−0.194839	−0.00716241
$741$	−17.9131	−0.658055
$742$	9.39083	0.344748
$743$	37.7294	1.38416	0.692078	−	0.721823i	$-0.256695\pi$
$743$	37.7294	1.38416	0.692078	+	0.721823i	$0.256695\pi$
$744$	7.92583	0.290575
$745$	−18.8021	−0.688854
$746$	−1.76229	−0.0645221
$747$	1.77397	0.0649063
$748$	−11.6157	−0.424712
$749$	−17.0234	−0.622020
$750$	−15.3844	−0.561757
$751$	−22.3861	−0.816879	−0.408439	−	0.912785i	$-0.633927\pi$
$751$	−22.3861	−0.816879	−0.408439	+	0.912785i	$0.633927\pi$
$752$	0.101562	0.00370360
$753$	1.91450	0.0697682
$754$	−0.497754	−0.0181271
$755$	−30.5141	−1.11052
$756$	5.65182	0.205555
$757$	−39.3845	−1.43146	−0.715728	−	0.698379i	$-0.753905\pi$
$757$	−39.3845	−1.43146	−0.715728	+	0.698379i	$0.753905\pi$
$758$	6.08120	0.220879
$759$	35.7911	1.29913
$760$	6.74416	0.244636
$761$	−4.36983	−0.158406	−0.0792031	−	0.996858i	$-0.525238\pi$
$761$	−4.36983	−0.158406	−0.0792031	+	0.996858i	$0.525238\pi$
$762$	−11.4005	−0.412997
$763$	−19.5460	−0.707614
$764$	4.74568	0.171692
$765$	4.10529	0.148427
$766$	10.3380	0.373527
$767$	−27.4639	−0.991665
$768$	1.44853	0.0522694
$769$	1.36858	0.0493524	0.0246762	−	0.999695i	$-0.492145\pi$
$769$	1.36858	0.0493524	0.0246762	+	0.999695i	$0.492145\pi$
$770$	4.07662	0.146911
$771$	−13.8772	−0.499777
$772$	4.37571	0.157485
$773$	−33.0732	−1.18956	−0.594781	−	0.803888i	$-0.702761\pi$
$773$	−33.0732	−1.18956	−0.594781	+	0.803888i	$0.702761\pi$
$774$	6.76407	0.243129
$775$	18.6158	0.668698
$776$	17.6621	0.634033
$777$	−0.223279	−0.00801009
$778$	29.5639	1.05992
$779$	19.7363	0.707126
$780$	4.24380	0.151953
$781$	−34.5144	−1.23502
$782$	27.5933	0.986733
$783$	1.21376	0.0433762
$784$	1.00000	0.0357143
$785$	−7.66634	−0.273623
$786$	0.0501173	0.00178762
$787$	−16.8755	−0.601547	−0.300773	−	0.953696i	$-0.597245\pi$
$787$	−16.8755	−0.601547	−0.300773	+	0.953696i	$0.597245\pi$
$788$	3.06798	0.109292
$789$	39.0841	1.39143
$790$	−17.2786	−0.614745
$791$	14.8821	0.529148
$792$	−2.90824	−0.103340
$793$	−13.8083	−0.490349
$794$	2.23532	0.0793286
$795$	−17.1945	−0.609824
$796$	−26.2836	−0.931599
$797$	−22.6911	−0.803761	−0.401881	−	0.915692i	$-0.631643\pi$
$797$	−22.6911	−0.803761	−0.401881	+	0.915692i	$0.631643\pi$
$798$	7.72860	0.273589
$799$	0.365792	0.0129408
$800$	3.40224	0.120287
$801$	0.316030	0.0111664
$802$	−11.2737	−0.398087
$803$	50.7425	1.79066
$804$	−4.27951	−0.150927
$805$	−9.68407	−0.341319
$806$	−12.6820	−0.446704
$807$	−11.0130	−0.387674
$808$	−8.91473	−0.313619
$809$	18.2557	0.641835	0.320917	−	0.947107i	$-0.396009\pi$
$809$	18.2557	0.641835	0.320917	+	0.947107i	$0.396009\pi$
$810$	−6.92887	−0.243456
$811$	10.7230	0.376535	0.188267	−	0.982118i	$-0.439713\pi$
$811$	10.7230	0.376535	0.188267	+	0.982118i	$0.439713\pi$
$812$	0.214755	0.00753644
$813$	33.5660	1.17721
$814$	0.497123	0.0174241
$815$	−13.3861	−0.468895
$816$	5.21710	0.182635
$817$	40.0215	1.40017
$818$	−32.5916	−1.13954
$819$	−2.09005	−0.0730324
$820$	−4.67573	−0.163284
$821$	25.1558	0.877942	0.438971	−	0.898501i	$-0.355343\pi$
$821$	25.1558	0.877942	0.438971	+	0.898501i	$0.355343\pi$
$822$	3.47615	0.121245
$823$	−22.6642	−0.790025	−0.395012	−	0.918676i	$-0.629260\pi$
$823$	−22.6642	−0.790025	−0.395012	+	0.918676i	$0.629260\pi$
$824$	−9.46770	−0.329823
$825$	15.8942	0.553363
$826$	11.8493	0.412289
$827$	−46.7646	−1.62617	−0.813083	−	0.582148i	$-0.802212\pi$
$827$	−46.7646	−1.62617	−0.813083	+	0.582148i	$0.802212\pi$
$828$	6.90858	0.240090
$829$	−3.07344	−0.106745	−0.0533725	−	0.998575i	$-0.516997\pi$
$829$	−3.07344	−0.106745	−0.0533725	+	0.998575i	$0.516997\pi$
$830$	−2.48666	−0.0863132
$831$	31.1729	1.08137
$832$	−2.31777	−0.0803543
$833$	3.60165	0.124790
$834$	19.0823	0.660768
$835$	−4.80540	−0.166298
$836$	−17.2074	−0.595132
$837$	30.9246	1.06891
$838$	−16.8439	−0.581864
$839$	20.3451	0.702391	0.351196	−	0.936302i	$-0.385775\pi$
$839$	20.3451	0.702391	0.351196	+	0.936302i	$0.385775\pi$
$840$	−1.83098	−0.0631749
$841$	−28.9539	−0.998410
$842$	0.753904	0.0259812
$843$	−42.5034	−1.46390
$844$	−8.94228	−0.307806
$845$	9.64190	0.331691
$846$	0.0915840	0.00314872
$847$	0.598690	0.0205712
$848$	9.39083	0.322482
$849$	−43.5798	−1.49565
$850$	12.2537	0.420297
$851$	−1.18092	−0.0404815
$852$	15.5019	0.531087
$853$	6.13553	0.210076	0.105038	−	0.994468i	$-0.466504\pi$
$853$	6.13553	0.210076	0.105038	+	0.994468i	$0.466504\pi$
$854$	5.95759	0.203865
$855$	6.08156	0.207985
$856$	−17.0234	−0.581847
$857$	32.3955	1.10661	0.553305	−	0.832979i	$-0.313366\pi$
$857$	32.3955	1.10661	0.553305	+	0.832979i	$0.313366\pi$
$858$	−10.8279	−0.369658
$859$	21.0123	0.716929	0.358465	−	0.933543i	$-0.383300\pi$
$859$	21.0123	0.716929	0.358465	+	0.933543i	$0.383300\pi$
$860$	−9.48150	−0.323317
$861$	−5.35824	−0.182608
$862$	−1.00000	−0.0340601
$863$	8.12612	0.276616	0.138308	−	0.990389i	$-0.455834\pi$
$863$	8.12612	0.276616	0.138308	+	0.990389i	$0.455834\pi$
$864$	5.65182	0.192279
$865$	−20.8022	−0.707296
$866$	13.5708	0.461155
$867$	−5.83491	−0.198164
$868$	5.47162	0.185719
$869$	44.0856	1.49550
$870$	−0.393213	−0.0133312
$871$	6.84758	0.232021
$872$	−19.5460	−0.661912
$873$	15.9268	0.539042
$874$	40.8765	1.38267
$875$	−10.6206	−0.359043
$876$	−22.7906	−0.770024
$877$	39.3833	1.32988	0.664940	−	0.746896i	$-0.268457\pi$
$877$	39.3833	1.32988	0.664940	+	0.746896i	$0.268457\pi$
$878$	10.6671	0.359998
$879$	27.8308	0.938711
$880$	4.07662	0.137423
$881$	−13.7834	−0.464375	−0.232187	−	0.972671i	$-0.574588\pi$
$881$	−13.7834	−0.464375	−0.232187	+	0.972671i	$0.574588\pi$
$882$	0.901751	0.0303635
$883$	42.7783	1.43960	0.719802	−	0.694179i	$-0.244232\pi$
$883$	42.7783	1.43960	0.719802	+	0.694179i	$0.244232\pi$
$884$	−8.34780	−0.280767
$885$	−21.6958	−0.729297
$886$	−10.5775	−0.355359
$887$	19.9689	0.670489	0.335244	−	0.942131i	$-0.391181\pi$
$887$	19.9689	0.670489	0.335244	+	0.942131i	$0.391181\pi$
$888$	−0.223279	−0.00749275
$889$	−7.87038	−0.263964
$890$	−0.442994	−0.0148492
$891$	17.6787	0.592259
$892$	−27.0980	−0.907307
$893$	0.541882	0.0181334
$894$	−21.5466	−0.720625
$895$	−24.1470	−0.807144
$896$	1.00000	0.0334077
$897$	25.7218	0.858826
$898$	22.5821	0.753576
$899$	1.17506	0.0391904
$900$	3.06797	0.102266
$901$	33.8224	1.12679
$902$	11.9299	0.397223
$903$	−10.8655	−0.361581
$904$	14.8821	0.494973
$905$	−19.5323	−0.649275
$906$	−34.9682	−1.16174
$907$	−29.8320	−0.990554	−0.495277	−	0.868735i	$-0.664933\pi$
$907$	−29.8320	−0.990554	−0.495277	+	0.868735i	$0.664933\pi$
$908$	0.799865	0.0265444
$909$	−8.03887	−0.266632
$910$	2.92972	0.0971194
$911$	13.0430	0.432134	0.216067	−	0.976379i	$-0.430677\pi$
$911$	13.0430	0.432134	0.216067	+	0.976379i	$0.430677\pi$
$912$	7.72860	0.255919
$913$	6.34460	0.209976
$914$	4.14872	0.137228
$915$	−10.9083	−0.360616
$916$	−1.41408	−0.0467227
$917$	0.0345986	0.00114255
$918$	20.3558	0.671843
$919$	−51.8241	−1.70952	−0.854760	−	0.519024i	$-0.826295\pi$
$919$	−51.8241	−1.70952	−0.854760	+	0.519024i	$0.826295\pi$
$920$	−9.68407	−0.319274
$921$	−3.76724	−0.124135
$922$	−25.6956	−0.846240
$923$	−24.8043	−0.816445
$924$	4.67167	0.153687
$925$	−0.524426	−0.0172430
$926$	−19.0380	−0.625629
$927$	−8.53751	−0.280409
$928$	0.214755	0.00704969
$929$	20.6123	0.676266	0.338133	−	0.941098i	$-0.390205\pi$
$929$	20.6123	0.676266	0.338133	+	0.941098i	$0.390205\pi$
$930$	−10.0184	−0.328518
$931$	5.33546	0.174863
$932$	2.30009	0.0753419
$933$	−15.8633	−0.519341
$934$	2.34262	0.0766529
$935$	14.6825	0.480170
$936$	−2.09005	−0.0683156
$937$	−10.7696	−0.351829	−0.175914	−	0.984405i	$-0.556288\pi$
$937$	−10.7696	−0.351829	−0.175914	+	0.984405i	$0.556288\pi$
$938$	−2.95438	−0.0964638
$939$	30.5331	0.996409
$940$	−0.128377	−0.00418721
$941$	−31.6617	−1.03214	−0.516070	−	0.856546i	$-0.672606\pi$
$941$	−31.6617	−1.03214	−0.516070	+	0.856546i	$0.672606\pi$
$942$	−8.78538	−0.286243
$943$	−28.3397	−0.922869
$944$	11.8493	0.385661
$945$	−7.14404	−0.232396
$946$	24.1916	0.786538
$947$	−29.7484	−0.966693	−0.483346	−	0.875429i	$-0.660579\pi$
$947$	−29.7484	−0.966693	−0.483346	+	0.875429i	$0.660579\pi$
$948$	−19.8007	−0.643098
$949$	36.4669	1.18377
$950$	18.1525	0.588946
$951$	−4.94352	−0.160305
$952$	3.60165	0.116730
$953$	−14.4958	−0.469565	−0.234783	−	0.972048i	$-0.575438\pi$
$953$	−14.4958	−0.469565	−0.234783	+	0.972048i	$0.575438\pi$
$954$	8.46819	0.274168
$955$	−5.99866	−0.194112
$956$	9.46668	0.306174
$957$	1.00327	0.0324310
$958$	−6.41867	−0.207378
$959$	2.39977	0.0774927
$960$	−1.83098	−0.0590947
$961$	−1.06136	−0.0342376
$962$	0.357265	0.0115187
$963$	−15.3508	−0.494674
$964$	15.2642	0.491627
$965$	−5.53101	−0.178049
$966$	−11.0976	−0.357061
$967$	19.6733	0.632649	0.316325	−	0.948651i	$-0.397551\pi$
$967$	19.6733	0.632649	0.316325	+	0.948651i	$0.397551\pi$
$968$	0.598690	0.0192426
$969$	27.8357	0.894210
$970$	−22.3254	−0.716825
$971$	50.1679	1.60996	0.804982	−	0.593299i	$-0.202175\pi$
$971$	50.1679	1.60996	0.804982	+	0.593299i	$0.202175\pi$
$972$	9.01518	0.289162
$973$	13.1736	0.422325
$974$	0.883066	0.0282952
$975$	11.4226	0.365815
$976$	5.95759	0.190698
$977$	46.9127	1.50087	0.750435	−	0.660944i	$-0.229844\pi$
$977$	46.9127	1.50087	0.750435	+	0.660944i	$0.229844\pi$
$978$	−15.3400	−0.490521
$979$	1.13028	0.0361239
$980$	−1.26403	−0.0403778
$981$	−17.6257	−0.562744
$982$	22.4448	0.716243
$983$	34.9309	1.11412	0.557062	−	0.830471i	$-0.311929\pi$
$983$	34.9309	1.11412	0.557062	+	0.830471i	$0.311929\pi$
$984$	−5.35824	−0.170814
$985$	−3.87801	−0.123564
$986$	0.773473	0.0246324
$987$	−0.147116	−0.00468277
$988$	−12.3664	−0.393427
$989$	−57.4676	−1.82736
$990$	3.67609	0.116834
$991$	32.8605	1.04385	0.521924	−	0.852992i	$-0.325214\pi$
$991$	32.8605	1.04385	0.521924	+	0.852992i	$0.325214\pi$
$992$	5.47162	0.173724
$993$	1.52273	0.0483225
$994$	10.7018	0.339440
$995$	33.2232	1.05325
$996$	−2.84963	−0.0902941
$997$	31.3910	0.994163	0.497081	−	0.867704i	$-0.334405\pi$
$997$	31.3910	0.994163	0.497081	+	0.867704i	$0.334405\pi$
$998$	−19.9212	−0.630595
$999$	−0.871179	−0.0275629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.16	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.44853 q^{3} +1.00000 q^{4} -1.26403 q^{5} -1.44853 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.901751 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.44853 q^{3} +1.00000 q^{4} -1.26403 q^{5} -1.44853 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.901751 q^{9} +1.26403 q^{10} -3.22511 q^{11} +1.44853 q^{12} -2.31777 q^{13} +1.00000 q^{14} -1.83098 q^{15} +1.00000 q^{16} +3.60165 q^{17} +0.901751 q^{18} +5.33546 q^{19} -1.26403 q^{20} -1.44853 q^{21} +3.22511 q^{22} -7.66129 q^{23} -1.44853 q^{24} -3.40224 q^{25} +2.31777 q^{26} -5.65182 q^{27} -1.00000 q^{28} -0.214755 q^{29} +1.83098 q^{30} -5.47162 q^{31} -1.00000 q^{32} -4.67167 q^{33} -3.60165 q^{34} +1.26403 q^{35} -0.901751 q^{36} +0.154141 q^{37} -5.33546 q^{38} -3.35737 q^{39} +1.26403 q^{40} +3.69908 q^{41} +1.44853 q^{42} +7.50104 q^{43} -3.22511 q^{44} +1.13984 q^{45} +7.66129 q^{46} +0.101562 q^{47} +1.44853 q^{48} +1.00000 q^{49} +3.40224 q^{50} +5.21710 q^{51} -2.31777 q^{52} +9.39083 q^{53} +5.65182 q^{54} +4.07662 q^{55} +1.00000 q^{56} +7.72860 q^{57} +0.214755 q^{58} +11.8493 q^{59} -1.83098 q^{60} +5.95759 q^{61} +5.47162 q^{62} +0.901751 q^{63} +1.00000 q^{64} +2.92972 q^{65} +4.67167 q^{66} -2.95438 q^{67} +3.60165 q^{68} -11.0976 q^{69} -1.26403 q^{70} +10.7018 q^{71} +0.901751 q^{72} -15.7336 q^{73} -0.154141 q^{74} -4.92826 q^{75} +5.33546 q^{76} +3.22511 q^{77} +3.35737 q^{78} -13.6695 q^{79} -1.26403 q^{80} -5.48159 q^{81} -3.69908 q^{82} -1.96725 q^{83} -1.44853 q^{84} -4.55257 q^{85} -7.50104 q^{86} -0.311080 q^{87} +3.22511 q^{88} -0.350463 q^{89} -1.13984 q^{90} +2.31777 q^{91} -7.66129 q^{92} -7.92583 q^{93} -0.101562 q^{94} -6.74416 q^{95} -1.44853 q^{96} -17.6621 q^{97} -1.00000 q^{98} +2.90824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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