LMFDB - Embedded newform 6014.2.a.i.1.7

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.45310 q^{3} +1.00000 q^{4} +1.69777 q^{5} -1.45310 q^{6} -3.88385 q^{7} +1.00000 q^{8} -0.888510 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.45310 q^{3} +1.00000 q^{4} +1.69777 q^{5} -1.45310 q^{6} -3.88385 q^{7} +1.00000 q^{8} -0.888510 q^{9} +1.69777 q^{10} -5.71208 q^{11} -1.45310 q^{12} -1.97572 q^{13} -3.88385 q^{14} -2.46703 q^{15} +1.00000 q^{16} +2.53313 q^{17} -0.888510 q^{18} +5.15974 q^{19} +1.69777 q^{20} +5.64360 q^{21} -5.71208 q^{22} +5.53750 q^{23} -1.45310 q^{24} -2.11757 q^{25} -1.97572 q^{26} +5.65038 q^{27} -3.88385 q^{28} -6.04027 q^{29} -2.46703 q^{30} -1.00000 q^{31} +1.00000 q^{32} +8.30021 q^{33} +2.53313 q^{34} -6.59389 q^{35} -0.888510 q^{36} -3.22276 q^{37} +5.15974 q^{38} +2.87091 q^{39} +1.69777 q^{40} -10.1706 q^{41} +5.64360 q^{42} +8.31484 q^{43} -5.71208 q^{44} -1.50849 q^{45} +5.53750 q^{46} +0.451730 q^{47} -1.45310 q^{48} +8.08426 q^{49} -2.11757 q^{50} -3.68088 q^{51} -1.97572 q^{52} -4.50352 q^{53} +5.65038 q^{54} -9.69782 q^{55} -3.88385 q^{56} -7.49759 q^{57} -6.04027 q^{58} +4.48387 q^{59} -2.46703 q^{60} -5.81132 q^{61} -1.00000 q^{62} +3.45084 q^{63} +1.00000 q^{64} -3.35433 q^{65} +8.30021 q^{66} +3.36267 q^{67} +2.53313 q^{68} -8.04652 q^{69} -6.59389 q^{70} -8.71457 q^{71} -0.888510 q^{72} +4.06115 q^{73} -3.22276 q^{74} +3.07703 q^{75} +5.15974 q^{76} +22.1848 q^{77} +2.87091 q^{78} +7.18202 q^{79} +1.69777 q^{80} -5.54502 q^{81} -10.1706 q^{82} -1.83249 q^{83} +5.64360 q^{84} +4.30067 q^{85} +8.31484 q^{86} +8.77709 q^{87} -5.71208 q^{88} +15.5366 q^{89} -1.50849 q^{90} +7.67340 q^{91} +5.53750 q^{92} +1.45310 q^{93} +0.451730 q^{94} +8.76006 q^{95} -1.45310 q^{96} -1.00000 q^{97} +8.08426 q^{98} +5.07524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	−1.45310	−0.838946	−0.419473	−	0.907768i	$-0.637785\pi$
$3$	−1.45310	−0.838946	−0.419473	+	0.907768i	$0.637785\pi$
$4$	1.00000	0.500000
$5$	1.69777	0.759267	0.379633	−	0.925137i	$-0.376050\pi$
$5$	1.69777	0.759267	0.379633	+	0.925137i	$0.376050\pi$
$6$	−1.45310	−0.593224
$7$	−3.88385	−1.46796	−0.733978	−	0.679173i	$-0.762338\pi$
$7$	−3.88385	−1.46796	−0.733978	+	0.679173i	$0.762338\pi$
$8$	1.00000	0.353553
$9$	−0.888510	−0.296170
$10$	1.69777	0.536883
$11$	−5.71208	−1.72226	−0.861129	−	0.508387i	$-0.830242\pi$
$11$	−5.71208	−1.72226	−0.861129	+	0.508387i	$0.830242\pi$
$12$	−1.45310	−0.419473
$13$	−1.97572	−0.547967	−0.273983	−	0.961734i	$-0.588341\pi$
$13$	−1.97572	−0.547967	−0.273983	+	0.961734i	$0.588341\pi$
$14$	−3.88385	−1.03800
$15$	−2.46703	−0.636984
$16$	1.00000	0.250000
$17$	2.53313	0.614374	0.307187	−	0.951649i	$-0.400612\pi$
$17$	2.53313	0.614374	0.307187	+	0.951649i	$0.400612\pi$
$18$	−0.888510	−0.209424
$19$	5.15974	1.18372	0.591862	−	0.806039i	$-0.298393\pi$
$19$	5.15974	1.18372	0.591862	+	0.806039i	$0.298393\pi$
$20$	1.69777	0.379633
$21$	5.64360	1.23154
$22$	−5.71208	−1.21782
$23$	5.53750	1.15465	0.577324	−	0.816515i	$-0.304097\pi$
$23$	5.53750	1.15465	0.577324	+	0.816515i	$0.304097\pi$
$24$	−1.45310	−0.296612
$25$	−2.11757	−0.423514
$26$	−1.97572	−0.387471
$27$	5.65038	1.08742
$28$	−3.88385	−0.733978
$29$	−6.04027	−1.12165	−0.560825	−	0.827935i	$-0.689516\pi$
$29$	−6.04027	−1.12165	−0.560825	+	0.827935i	$0.689516\pi$
$30$	−2.46703	−0.450416
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	8.30021	1.44488
$34$	2.53313	0.434428
$35$	−6.59389	−1.11457
$36$	−0.888510	−0.148085
$37$	−3.22276	−0.529819	−0.264909	−	0.964273i	$-0.585342\pi$
$37$	−3.22276	−0.529819	−0.264909	+	0.964273i	$0.585342\pi$
$38$	5.15974	0.837020
$39$	2.87091	0.459714
$40$	1.69777	0.268441
$41$	−10.1706	−1.58838	−0.794189	−	0.607671i	$-0.792104\pi$
$41$	−10.1706	−1.58838	−0.794189	+	0.607671i	$0.792104\pi$
$42$	5.64360	0.870827
$43$	8.31484	1.26800	0.634000	−	0.773333i	$-0.281412\pi$
$43$	8.31484	1.26800	0.634000	+	0.773333i	$0.281412\pi$
$44$	−5.71208	−0.861129
$45$	−1.50849	−0.224872
$46$	5.53750	0.816460
$47$	0.451730	0.0658916	0.0329458	−	0.999457i	$-0.489511\pi$
$47$	0.451730	0.0658916	0.0329458	+	0.999457i	$0.489511\pi$
$48$	−1.45310	−0.209736
$49$	8.08426	1.15489
$50$	−2.11757	−0.299469
$51$	−3.68088	−0.515426
$52$	−1.97572	−0.273983
$53$	−4.50352	−0.618606	−0.309303	−	0.950963i	$-0.600096\pi$
$53$	−4.50352	−0.618606	−0.309303	+	0.950963i	$0.600096\pi$
$54$	5.65038	0.768919
$55$	−9.69782	−1.30765
$56$	−3.88385	−0.519001
$57$	−7.49759	−0.993081
$58$	−6.04027	−0.793126
$59$	4.48387	0.583750	0.291875	−	0.956456i	$-0.405721\pi$
$59$	4.48387	0.583750	0.291875	+	0.956456i	$0.405721\pi$
$60$	−2.46703	−0.318492
$61$	−5.81132	−0.744063	−0.372032	−	0.928220i	$-0.621339\pi$
$61$	−5.81132	−0.744063	−0.372032	+	0.928220i	$0.621339\pi$
$62$	−1.00000	−0.127000
$63$	3.45084	0.434765
$64$	1.00000	0.125000
$65$	−3.35433	−0.416053
$66$	8.30021	1.02168
$67$	3.36267	0.410815	0.205408	−	0.978676i	$-0.434148\pi$
$67$	3.36267	0.410815	0.205408	+	0.978676i	$0.434148\pi$
$68$	2.53313	0.307187
$69$	−8.04652	−0.968688
$70$	−6.59389	−0.788120
$71$	−8.71457	−1.03423	−0.517114	−	0.855916i	$-0.672994\pi$
$71$	−8.71457	−1.03423	−0.517114	+	0.855916i	$0.672994\pi$
$72$	−0.888510	−0.104712
$73$	4.06115	0.475322	0.237661	−	0.971348i	$-0.423619\pi$
$73$	4.06115	0.475322	0.237661	+	0.971348i	$0.423619\pi$
$74$	−3.22276	−0.374638
$75$	3.07703	0.355305
$76$	5.15974	0.591862
$77$	22.1848	2.52820
$78$	2.87091	0.325067
$79$	7.18202	0.808041	0.404020	−	0.914750i	$-0.367612\pi$
$79$	7.18202	0.808041	0.404020	+	0.914750i	$0.367612\pi$
$80$	1.69777	0.189817
$81$	−5.54502	−0.616113
$82$	−10.1706	−1.12315
$83$	−1.83249	−0.201142	−0.100571	−	0.994930i	$-0.532067\pi$
$83$	−1.83249	−0.201142	−0.100571	+	0.994930i	$0.532067\pi$
$84$	5.64360	0.615768
$85$	4.30067	0.466474
$86$	8.31484	0.896612
$87$	8.77709	0.941003
$88$	−5.71208	−0.608910
$89$	15.5366	1.64688	0.823439	−	0.567405i	$-0.192053\pi$
$89$	15.5366	1.64688	0.823439	+	0.567405i	$0.192053\pi$
$90$	−1.50849	−0.159009
$91$	7.67340	0.804391
$92$	5.53750	0.577324
$93$	1.45310	0.150679
$94$	0.451730	0.0465924
$95$	8.76006	0.898763
$96$	−1.45310	−0.148306
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	8.08426	0.816633
$99$	5.07524	0.510081
$100$	−2.11757	−0.211757
$101$	2.41664	0.240464	0.120232	−	0.992746i	$-0.461636\pi$
$101$	2.41664	0.240464	0.120232	+	0.992746i	$0.461636\pi$
$102$	−3.68088	−0.364461
$103$	5.09525	0.502050	0.251025	−	0.967981i	$-0.419232\pi$
$103$	5.09525	0.502050	0.251025	+	0.967981i	$0.419232\pi$
$104$	−1.97572	−0.193735
$105$	9.58155	0.935064
$106$	−4.50352	−0.437421
$107$	11.7790	1.13872	0.569358	−	0.822090i	$-0.307192\pi$
$107$	11.7790	1.13872	0.569358	+	0.822090i	$0.307192\pi$
$108$	5.65038	0.543708
$109$	20.4927	1.96284	0.981421	−	0.191865i	$-0.0614536\pi$
$109$	20.4927	1.96284	0.981421	+	0.191865i	$0.0614536\pi$
$110$	−9.69782	−0.924650
$111$	4.68298	0.444489
$112$	−3.88385	−0.366989
$113$	2.75934	0.259576	0.129788	−	0.991542i	$-0.458570\pi$
$113$	2.75934	0.259576	0.129788	+	0.991542i	$0.458570\pi$
$114$	−7.49759	−0.702214
$115$	9.40142	0.876687
$116$	−6.04027	−0.560825
$117$	1.75545	0.162291
$118$	4.48387	0.412774
$119$	−9.83828	−0.901873
$120$	−2.46703	−0.225208
$121$	21.6279	1.96617
$122$	−5.81132	−0.526132
$123$	14.7788	1.33256
$124$	−1.00000	−0.0898027
$125$	−12.0840	−1.08083
$126$	3.45084	0.307425
$127$	10.6550	0.945479	0.472740	−	0.881202i	$-0.343265\pi$
$127$	10.6550	0.945479	0.472740	+	0.881202i	$0.343265\pi$
$128$	1.00000	0.0883883
$129$	−12.0823	−1.06378
$130$	−3.35433	−0.294194
$131$	−10.0782	−0.880536	−0.440268	−	0.897867i	$-0.645116\pi$
$131$	−10.0782	−0.880536	−0.440268	+	0.897867i	$0.645116\pi$
$132$	8.30021	0.722440
$133$	−20.0396	−1.73766
$134$	3.36267	0.290490
$135$	9.59306	0.825639
$136$	2.53313	0.217214
$137$	8.96758	0.766152	0.383076	−	0.923717i	$-0.374865\pi$
$137$	8.96758	0.766152	0.383076	+	0.923717i	$0.374865\pi$
$138$	−8.04652	−0.684966
$139$	−1.68386	−0.142823	−0.0714117	−	0.997447i	$-0.522750\pi$
$139$	−1.68386	−0.142823	−0.0714117	+	0.997447i	$0.522750\pi$
$140$	−6.59389	−0.557285
$141$	−0.656408	−0.0552795
$142$	−8.71457	−0.731310
$143$	11.2855	0.943740
$144$	−0.888510	−0.0740425
$145$	−10.2550	−0.851631
$146$	4.06115	0.336103
$147$	−11.7472	−0.968893
$148$	−3.22276	−0.264909
$149$	15.5695	1.27550	0.637751	−	0.770243i	$-0.279865\pi$
$149$	15.5695	1.27550	0.637751	+	0.770243i	$0.279865\pi$
$150$	3.07703	0.251239
$151$	15.8987	1.29382	0.646909	−	0.762567i	$-0.276061\pi$
$151$	15.8987	1.29382	0.646909	+	0.762567i	$0.276061\pi$
$152$	5.15974	0.418510
$153$	−2.25071	−0.181959
$154$	22.1848	1.78771
$155$	−1.69777	−0.136368
$156$	2.87091	0.229857
$157$	−1.61899	−0.129210	−0.0646048	−	0.997911i	$-0.520579\pi$
$157$	−1.61899	−0.129210	−0.0646048	+	0.997911i	$0.520579\pi$
$158$	7.18202	0.571371
$159$	6.54405	0.518977
$160$	1.69777	0.134221
$161$	−21.5068	−1.69497
$162$	−5.54502	−0.435658
$163$	−11.7792	−0.922617	−0.461309	−	0.887240i	$-0.652620\pi$
$163$	−11.7792	−0.922617	−0.461309	+	0.887240i	$0.652620\pi$
$164$	−10.1706	−0.794189
$165$	14.0919	1.09705
$166$	−1.83249	−0.142229
$167$	13.6471	1.05605	0.528023	−	0.849230i	$-0.322934\pi$
$167$	13.6471	1.05605	0.528023	+	0.849230i	$0.322934\pi$
$168$	5.64360	0.435413
$169$	−9.09652	−0.699733
$170$	4.30067	0.329847
$171$	−4.58448	−0.350584
$172$	8.31484	0.634000
$173$	7.92021	0.602163	0.301081	−	0.953598i	$-0.402652\pi$
$173$	7.92021	0.602163	0.301081	+	0.953598i	$0.402652\pi$
$174$	8.77709	0.665390
$175$	8.22431	0.621699
$176$	−5.71208	−0.430564
$177$	−6.51550	−0.489735
$178$	15.5366	1.16452
$179$	9.03284	0.675146	0.337573	−	0.941299i	$-0.390394\pi$
$179$	9.03284	0.675146	0.337573	+	0.941299i	$0.390394\pi$
$180$	−1.50849	−0.112436
$181$	11.0730	0.823047	0.411524	−	0.911399i	$-0.364997\pi$
$181$	11.0730	0.823047	0.411524	+	0.911399i	$0.364997\pi$
$182$	7.67340	0.568790
$183$	8.44441	0.624229
$184$	5.53750	0.408230
$185$	−5.47151	−0.402274
$186$	1.45310	0.106546
$187$	−14.4694	−1.05811
$188$	0.451730	0.0329458
$189$	−21.9452	−1.59628
$190$	8.76006	0.635521
$191$	−0.293757	−0.0212555	−0.0106278	−	0.999944i	$-0.503383\pi$
$191$	−0.293757	−0.0212555	−0.0106278	+	0.999944i	$0.503383\pi$
$192$	−1.45310	−0.104868
$193$	2.80944	0.202228	0.101114	−	0.994875i	$-0.467759\pi$
$193$	2.80944	0.202228	0.101114	+	0.994875i	$0.467759\pi$
$194$	−1.00000	−0.0717958
$195$	4.87416	0.349046
$196$	8.08426	0.577447
$197$	5.53205	0.394142	0.197071	−	0.980389i	$-0.436857\pi$
$197$	5.53205	0.394142	0.197071	+	0.980389i	$0.436857\pi$
$198$	5.07524	0.360682
$199$	2.60813	0.184885	0.0924427	−	0.995718i	$-0.470533\pi$
$199$	2.60813	0.184885	0.0924427	+	0.995718i	$0.470533\pi$
$200$	−2.11757	−0.149735
$201$	−4.88628	−0.344652
$202$	2.41664	0.170034
$203$	23.4595	1.64653
$204$	−3.68088	−0.257713
$205$	−17.2673	−1.20600
$206$	5.09525	0.355003
$207$	−4.92013	−0.341972
$208$	−1.97572	−0.136992
$209$	−29.4728	−2.03868
$210$	9.58155	0.661190
$211$	27.9500	1.92416	0.962079	−	0.272770i	$-0.0879397\pi$
$211$	27.9500	1.92416	0.962079	+	0.272770i	$0.0879397\pi$
$212$	−4.50352	−0.309303
$213$	12.6631	0.867662
$214$	11.7790	0.805194
$215$	14.1167	0.962751
$216$	5.65038	0.384460
$217$	3.88385	0.263653
$218$	20.4927	1.38794
$219$	−5.90125	−0.398769
$220$	−9.69782	−0.653827
$221$	−5.00476	−0.336656
$222$	4.68298	0.314301
$223$	1.72110	0.115254	0.0576268	−	0.998338i	$-0.481647\pi$
$223$	1.72110	0.115254	0.0576268	+	0.998338i	$0.481647\pi$
$224$	−3.88385	−0.259500
$225$	1.88148	0.125432
$226$	2.75934	0.183548
$227$	−7.07334	−0.469474	−0.234737	−	0.972059i	$-0.575423\pi$
$227$	−7.07334	−0.469474	−0.234737	+	0.972059i	$0.575423\pi$
$228$	−7.49759	−0.496540
$229$	12.7733	0.844081	0.422040	−	0.906577i	$-0.361314\pi$
$229$	12.7733	0.844081	0.422040	+	0.906577i	$0.361314\pi$
$230$	9.40142	0.619911
$231$	−32.2367	−2.12102
$232$	−6.04027	−0.396563
$233$	−21.9914	−1.44070	−0.720351	−	0.693610i	$-0.756019\pi$
$233$	−21.9914	−1.44070	−0.720351	+	0.693610i	$0.756019\pi$
$234$	1.75545	0.114757
$235$	0.766935	0.0500293
$236$	4.48387	0.291875
$237$	−10.4362	−0.677902
$238$	−9.83828	−0.637721
$239$	7.75498	0.501628	0.250814	−	0.968035i	$-0.419302\pi$
$239$	7.75498	0.501628	0.250814	+	0.968035i	$0.419302\pi$
$240$	−2.46703	−0.159246
$241$	2.04336	0.131625	0.0658123	−	0.997832i	$-0.479036\pi$
$241$	2.04336	0.131625	0.0658123	+	0.997832i	$0.479036\pi$
$242$	21.6279	1.39029
$243$	−8.89370	−0.570531
$244$	−5.81132	−0.372032
$245$	13.7252	0.876873
$246$	14.7788	0.942264
$247$	−10.1942	−0.648642
$248$	−1.00000	−0.0635001
$249$	2.66279	0.168747
$250$	−12.0840	−0.764260
$251$	−21.3681	−1.34874	−0.674370	−	0.738394i	$-0.735585\pi$
$251$	−21.3681	−1.34874	−0.674370	+	0.738394i	$0.735585\pi$
$252$	3.45084	0.217382
$253$	−31.6307	−1.98860
$254$	10.6550	0.668555
$255$	−6.24930	−0.391346
$256$	1.00000	0.0625000
$257$	25.4413	1.58698	0.793491	−	0.608582i	$-0.208261\pi$
$257$	25.4413	1.58698	0.793491	+	0.608582i	$0.208261\pi$
$258$	−12.0823	−0.752209
$259$	12.5167	0.777750
$260$	−3.35433	−0.208026
$261$	5.36684	0.332199
$262$	−10.0782	−0.622633
$263$	26.1890	1.61488	0.807440	−	0.589950i	$-0.200852\pi$
$263$	26.1890	1.61488	0.807440	+	0.589950i	$0.200852\pi$
$264$	8.30021	0.510842
$265$	−7.64596	−0.469687
$266$	−20.0396	−1.22871
$267$	−22.5762	−1.38164
$268$	3.36267	0.205408
$269$	−3.39683	−0.207109	−0.103554	−	0.994624i	$-0.533022\pi$
$269$	−3.39683	−0.207109	−0.103554	+	0.994624i	$0.533022\pi$
$270$	9.59306	0.583815
$271$	−4.63852	−0.281770	−0.140885	−	0.990026i	$-0.544995\pi$
$271$	−4.63852	−0.281770	−0.140885	+	0.990026i	$0.544995\pi$
$272$	2.53313	0.153593
$273$	−11.1502	−0.674840
$274$	8.96758	0.541752
$275$	12.0957	0.729400
$276$	−8.04652	−0.484344
$277$	−20.6630	−1.24152	−0.620760	−	0.784000i	$-0.713176\pi$
$277$	−20.6630	−1.24152	−0.620760	+	0.784000i	$0.713176\pi$
$278$	−1.68386	−0.100991
$279$	0.888510	0.0531937
$280$	−6.59389	−0.394060
$281$	−31.0173	−1.85034	−0.925170	−	0.379553i	$-0.876078\pi$
$281$	−31.0173	−1.85034	−0.925170	+	0.379553i	$0.876078\pi$
$282$	−0.656408	−0.0390885
$283$	22.9777	1.36588	0.682940	−	0.730475i	$-0.260701\pi$
$283$	22.9777	1.36588	0.682940	+	0.730475i	$0.260701\pi$
$284$	−8.71457	−0.517114
$285$	−12.7292	−0.754013
$286$	11.2855	0.667325
$287$	39.5010	2.33167
$288$	−0.888510	−0.0523560
$289$	−10.5833	−0.622545
$290$	−10.2550	−0.602194
$291$	1.45310	0.0851820
$292$	4.06115	0.237661
$293$	7.96954	0.465586	0.232793	−	0.972526i	$-0.425214\pi$
$293$	7.96954	0.465586	0.232793	+	0.972526i	$0.425214\pi$
$294$	−11.7472	−0.685111
$295$	7.61259	0.443222
$296$	−3.22276	−0.187319
$297$	−32.2754	−1.87281
$298$	15.5695	0.901916
$299$	−10.9406	−0.632709
$300$	3.07703	0.177653
$301$	−32.2935	−1.86137
$302$	15.8987	0.914868
$303$	−3.51161	−0.201737
$304$	5.15974	0.295931
$305$	−9.86630	−0.564943
$306$	−2.25071	−0.128665
$307$	−5.11328	−0.291830	−0.145915	−	0.989297i	$-0.546613\pi$
$307$	−5.11328	−0.291830	−0.145915	+	0.989297i	$0.546613\pi$
$308$	22.1848	1.26410
$309$	−7.40389	−0.421193
$310$	−1.69777	−0.0964270
$311$	−27.8403	−1.57868	−0.789338	−	0.613958i	$-0.789576\pi$
$311$	−27.8403	−1.57868	−0.789338	+	0.613958i	$0.789576\pi$
$312$	2.87091	0.162534
$313$	−20.5761	−1.16303	−0.581515	−	0.813535i	$-0.697540\pi$
$313$	−20.5761	−1.16303	−0.581515	+	0.813535i	$0.697540\pi$
$314$	−1.61899	−0.0913650
$315$	5.85874	0.330102
$316$	7.18202	0.404020
$317$	10.8124	0.607283	0.303642	−	0.952786i	$-0.401797\pi$
$317$	10.8124	0.607283	0.303642	+	0.952786i	$0.401797\pi$
$318$	6.54405	0.366972
$319$	34.5025	1.93177
$320$	1.69777	0.0949084
$321$	−17.1160	−0.955321
$322$	−21.5068	−1.19853
$323$	13.0703	0.727249
$324$	−5.54502	−0.308057
$325$	4.18373	0.232071
$326$	−11.7792	−0.652389
$327$	−29.7778	−1.64672
$328$	−10.1706	−0.561576
$329$	−1.75445	−0.0967260
$330$	14.0919	0.775732
$331$	−9.85331	−0.541587	−0.270793	−	0.962637i	$-0.587286\pi$
$331$	−9.85331	−0.541587	−0.270793	+	0.962637i	$0.587286\pi$
$332$	−1.83249	−0.100571
$333$	2.86346	0.156916
$334$	13.6471	0.746737
$335$	5.70905	0.311919
$336$	5.64360	0.307884
$337$	−5.92556	−0.322786	−0.161393	−	0.986890i	$-0.551599\pi$
$337$	−5.92556	−0.322786	−0.161393	+	0.986890i	$0.551599\pi$
$338$	−9.09652	−0.494786
$339$	−4.00958	−0.217771
$340$	4.30067	0.233237
$341$	5.71208	0.309327
$342$	−4.58448	−0.247900
$343$	−4.21108	−0.227377
$344$	8.31484	0.448306
$345$	−13.6612	−0.735493
$346$	7.92021	0.425793
$347$	17.5076	0.939859	0.469929	−	0.882704i	$-0.344279\pi$
$347$	17.5076	0.939859	0.469929	+	0.882704i	$0.344279\pi$
$348$	8.77709	0.470501
$349$	−13.0417	−0.698107	−0.349054	−	0.937103i	$-0.613497\pi$
$349$	−13.0417	−0.698107	−0.349054	+	0.937103i	$0.613497\pi$
$350$	8.22431	0.439608
$351$	−11.1636	−0.595868
$352$	−5.71208	−0.304455
$353$	−12.5574	−0.668365	−0.334182	−	0.942508i	$-0.608460\pi$
$353$	−12.5574	−0.668365	−0.334182	+	0.942508i	$0.608460\pi$
$354$	−6.51550	−0.346295
$355$	−14.7954	−0.785256
$356$	15.5366	0.823439
$357$	14.2960	0.756623
$358$	9.03284	0.477401
$359$	3.29025	0.173653	0.0868263	−	0.996223i	$-0.472327\pi$
$359$	3.29025	0.173653	0.0868263	+	0.996223i	$0.472327\pi$
$360$	−1.50849	−0.0795043
$361$	7.62287	0.401204
$362$	11.0730	0.581982
$363$	−31.4274	−1.64951
$364$	7.67340	0.402195
$365$	6.89491	0.360896
$366$	8.44441	0.441396
$367$	−4.51343	−0.235599	−0.117800	−	0.993037i	$-0.537584\pi$
$367$	−4.51343	−0.235599	−0.117800	+	0.993037i	$0.537584\pi$
$368$	5.53750	0.288662
$369$	9.03667	0.470430
$370$	−5.47151	−0.284450
$371$	17.4910	0.908087
$372$	1.45310	0.0753395
$373$	−36.1459	−1.87156	−0.935781	−	0.352582i	$-0.885304\pi$
$373$	−36.1459	−1.87156	−0.935781	+	0.352582i	$0.885304\pi$
$374$	−14.4694	−0.748197
$375$	17.5592	0.906755
$376$	0.451730	0.0232962
$377$	11.9339	0.614626
$378$	−21.9452	−1.12874
$379$	21.1460	1.08620	0.543100	−	0.839668i	$-0.317251\pi$
$379$	21.1460	1.08620	0.543100	+	0.839668i	$0.317251\pi$
$380$	8.76006	0.449381
$381$	−15.4828	−0.793206
$382$	−0.293757	−0.0150299
$383$	13.9958	0.715151	0.357575	−	0.933884i	$-0.383604\pi$
$383$	13.9958	0.715151	0.357575	+	0.933884i	$0.383604\pi$
$384$	−1.45310	−0.0741530
$385$	37.6648	1.91958
$386$	2.80944	0.142997
$387$	−7.38782	−0.375544
$388$	−1.00000	−0.0507673
$389$	13.6819	0.693700	0.346850	−	0.937921i	$-0.387251\pi$
$389$	13.6819	0.693700	0.346850	+	0.937921i	$0.387251\pi$
$390$	4.87416	0.246813
$391$	14.0272	0.709386
$392$	8.08426	0.408317
$393$	14.6446	0.738722
$394$	5.53205	0.278700
$395$	12.1934	0.613519
$396$	5.07524	0.255041
$397$	12.7572	0.640267	0.320133	−	0.947373i	$-0.396272\pi$
$397$	12.7572	0.640267	0.320133	+	0.947373i	$0.396272\pi$
$398$	2.60813	0.130734
$399$	29.1195	1.45780
$400$	−2.11757	−0.105878
$401$	−5.22836	−0.261092	−0.130546	−	0.991442i	$-0.541673\pi$
$401$	−5.22836	−0.261092	−0.130546	+	0.991442i	$0.541673\pi$
$402$	−4.88628	−0.243706
$403$	1.97572	0.0984177
$404$	2.41664	0.120232
$405$	−9.41418	−0.467794
$406$	23.4595	1.16427
$407$	18.4087	0.912484
$408$	−3.68088	−0.182231
$409$	20.0462	0.991223	0.495612	−	0.868544i	$-0.334944\pi$
$409$	20.0462	0.991223	0.495612	+	0.868544i	$0.334944\pi$
$410$	−17.2673	−0.852773
$411$	−13.0308	−0.642760
$412$	5.09525	0.251025
$413$	−17.4147	−0.856919
$414$	−4.92013	−0.241811
$415$	−3.11115	−0.152720
$416$	−1.97572	−0.0968677
$417$	2.44682	0.119821
$418$	−29.4728	−1.44156
$419$	−27.4074	−1.33894	−0.669469	−	0.742840i	$-0.733478\pi$
$419$	−27.4074	−1.33894	−0.669469	+	0.742840i	$0.733478\pi$
$420$	9.58155	0.467532
$421$	−27.7528	−1.35259	−0.676294	−	0.736632i	$-0.736415\pi$
$421$	−27.7528	−1.35259	−0.676294	+	0.736632i	$0.736415\pi$
$422$	27.9500	1.36059
$423$	−0.401367	−0.0195151
$424$	−4.50352	−0.218710
$425$	−5.36407	−0.260196
$426$	12.6631	0.613530
$427$	22.5703	1.09225
$428$	11.7790	0.569358
$429$	−16.3989	−0.791746
$430$	14.1167	0.680768
$431$	15.1555	0.730014	0.365007	−	0.931005i	$-0.381067\pi$
$431$	15.1555	0.730014	0.365007	+	0.931005i	$0.381067\pi$
$432$	5.65038	0.271854
$433$	14.8990	0.716001	0.358000	−	0.933721i	$-0.383459\pi$
$433$	14.8990	0.716001	0.358000	+	0.933721i	$0.383459\pi$
$434$	3.88385	0.186431
$435$	14.9015	0.714472
$436$	20.4927	0.981421
$437$	28.5720	1.36679
$438$	−5.90125	−0.281972
$439$	−30.1347	−1.43825	−0.719124	−	0.694881i	$-0.755457\pi$
$439$	−30.1347	−1.43825	−0.719124	+	0.694881i	$0.755457\pi$
$440$	−9.69782	−0.462325
$441$	−7.18294	−0.342045
$442$	−5.00476	−0.238052
$443$	11.2577	0.534871	0.267435	−	0.963576i	$-0.413824\pi$
$443$	11.2577	0.534871	0.267435	+	0.963576i	$0.413824\pi$
$444$	4.68298	0.222244
$445$	26.3776	1.25042
$446$	1.72110	0.0814966
$447$	−22.6240	−1.07008
$448$	−3.88385	−0.183494
$449$	−0.277528	−0.0130973	−0.00654867	−	0.999979i	$-0.502085\pi$
$449$	−0.277528	−0.0130973	−0.00654867	+	0.999979i	$0.502085\pi$
$450$	1.88148	0.0886939
$451$	58.0952	2.73560
$452$	2.75934	0.129788
$453$	−23.1024	−1.08544
$454$	−7.07334	−0.331968
$455$	13.0277	0.610747
$456$	−7.49759	−0.351107
$457$	22.5419	1.05446	0.527232	−	0.849721i	$-0.323230\pi$
$457$	22.5419	1.05446	0.527232	+	0.849721i	$0.323230\pi$
$458$	12.7733	0.596855
$459$	14.3131	0.668080
$460$	9.40142	0.438343
$461$	9.18099	0.427601	0.213801	−	0.976877i	$-0.431416\pi$
$461$	9.18099	0.427601	0.213801	+	0.976877i	$0.431416\pi$
$462$	−32.2367	−1.49979
$463$	−19.8916	−0.924441	−0.462221	−	0.886765i	$-0.652947\pi$
$463$	−19.8916	−0.924441	−0.462221	+	0.886765i	$0.652947\pi$
$464$	−6.04027	−0.280412
$465$	2.46703	0.114406
$466$	−21.9914	−1.01873
$467$	−6.71226	−0.310606	−0.155303	−	0.987867i	$-0.549635\pi$
$467$	−6.71226	−0.310606	−0.155303	+	0.987867i	$0.549635\pi$
$468$	1.75545	0.0811457
$469$	−13.0601	−0.603059
$470$	0.766935	0.0353761
$471$	2.35255	0.108400
$472$	4.48387	0.206387
$473$	−47.4950	−2.18382
$474$	−10.4362	−0.479349
$475$	−10.9261	−0.501324
$476$	−9.83828	−0.450937
$477$	4.00143	0.183213
$478$	7.75498	0.354705
$479$	4.17051	0.190556	0.0952778	−	0.995451i	$-0.469626\pi$
$479$	4.17051	0.190556	0.0952778	+	0.995451i	$0.469626\pi$
$480$	−2.46703	−0.112604
$481$	6.36728	0.290323
$482$	2.04336	0.0930726
$483$	31.2515	1.42199
$484$	21.6279	0.983085
$485$	−1.69777	−0.0770919
$486$	−8.89370	−0.403426
$487$	10.8411	0.491256	0.245628	−	0.969364i	$-0.421006\pi$
$487$	10.8411	0.491256	0.245628	+	0.969364i	$0.421006\pi$
$488$	−5.81132	−0.263066
$489$	17.1163	0.774026
$490$	13.7252	0.620043
$491$	19.0393	0.859232	0.429616	−	0.903012i	$-0.358649\pi$
$491$	19.0393	0.859232	0.429616	+	0.903012i	$0.358649\pi$
$492$	14.7788	0.666281
$493$	−15.3008	−0.689112
$494$	−10.1942	−0.458659
$495$	8.61661	0.387288
$496$	−1.00000	−0.0449013
$497$	33.8460	1.51820
$498$	2.66279	0.119322
$499$	−37.2081	−1.66567	−0.832833	−	0.553525i	$-0.813282\pi$
$499$	−37.2081	−1.66567	−0.832833	+	0.553525i	$0.813282\pi$
$500$	−12.0840	−0.540413
$501$	−19.8306	−0.885965
$502$	−21.3681	−0.953703
$503$	13.1024	0.584208	0.292104	−	0.956387i	$-0.405645\pi$
$503$	13.1024	0.584208	0.292104	+	0.956387i	$0.405645\pi$
$504$	3.45084	0.153712
$505$	4.10290	0.182577
$506$	−31.6307	−1.40615
$507$	13.2181	0.587038
$508$	10.6550	0.472740
$509$	31.8227	1.41051	0.705257	−	0.708951i	$-0.250831\pi$
$509$	31.8227	1.41051	0.705257	+	0.708951i	$0.250831\pi$
$510$	−6.24930	−0.276723
$511$	−15.7729	−0.697751
$512$	1.00000	0.0441942
$513$	29.1545	1.28720
$514$	25.4413	1.12217
$515$	8.65058	0.381190
$516$	−12.0823	−0.531892
$517$	−2.58032	−0.113482
$518$	12.5167	0.549952
$519$	−11.5088	−0.505182
$520$	−3.35433	−0.147097
$521$	−1.45864	−0.0639040	−0.0319520	−	0.999489i	$-0.510172\pi$
$521$	−1.45864	−0.0639040	−0.0319520	+	0.999489i	$0.510172\pi$
$522$	5.36684	0.234900
$523$	25.1226	1.09854	0.549268	−	0.835647i	$-0.314907\pi$
$523$	25.1226	1.09854	0.549268	+	0.835647i	$0.314907\pi$
$524$	−10.0782	−0.440268
$525$	−11.9507	−0.521572
$526$	26.1890	1.14189
$527$	−2.53313	−0.110345
$528$	8.30021	0.361220
$529$	7.66392	0.333214
$530$	−7.64596	−0.332119
$531$	−3.98397	−0.172889
$532$	−20.0396	−0.868828
$533$	20.0942	0.870378
$534$	−22.5762	−0.976968
$535$	19.9980	0.864590
$536$	3.36267	0.145245
$537$	−13.1256	−0.566411
$538$	−3.39683	−0.146448
$539$	−46.1779	−1.98902
$540$	9.59306	0.412820
$541$	1.30985	0.0563150	0.0281575	−	0.999603i	$-0.491036\pi$
$541$	1.30985	0.0563150	0.0281575	+	0.999603i	$0.491036\pi$
$542$	−4.63852	−0.199242
$543$	−16.0901	−0.690492
$544$	2.53313	0.108607
$545$	34.7919	1.49032
$546$	−11.1502	−0.477184
$547$	25.9387	1.10906	0.554530	−	0.832164i	$-0.312898\pi$
$547$	25.9387	1.10906	0.554530	+	0.832164i	$0.312898\pi$
$548$	8.96758	0.383076
$549$	5.16342	0.220369
$550$	12.0957	0.515763
$551$	−31.1662	−1.32772
$552$	−8.04652	−0.342483
$553$	−27.8939	−1.18617
$554$	−20.6630	−0.877888
$555$	7.95064	0.337486
$556$	−1.68386	−0.0714117
$557$	−46.9128	−1.98776	−0.993879	−	0.110477i	$-0.964762\pi$
$557$	−46.9128	−1.98776	−0.993879	+	0.110477i	$0.964762\pi$
$558$	0.888510	0.0376136
$559$	−16.4278	−0.694822
$560$	−6.59389	−0.278643
$561$	21.0255	0.887697
$562$	−31.0173	−1.30839
$563$	−20.3756	−0.858731	−0.429365	−	0.903131i	$-0.641263\pi$
$563$	−20.3756	−0.858731	−0.429365	+	0.903131i	$0.641263\pi$
$564$	−0.656408	−0.0276397
$565$	4.68472	0.197088
$566$	22.9777	0.965823
$567$	21.5360	0.904427
$568$	−8.71457	−0.365655
$569$	26.1645	1.09687	0.548436	−	0.836192i	$-0.315223\pi$
$569$	26.1645	1.09687	0.548436	+	0.836192i	$0.315223\pi$
$570$	−12.7292	−0.533168
$571$	24.6279	1.03065	0.515323	−	0.856996i	$-0.327672\pi$
$571$	24.6279	1.03065	0.515323	+	0.856996i	$0.327672\pi$
$572$	11.2855	0.471870
$573$	0.426858	0.0178322
$574$	39.5010	1.64874
$575$	−11.7260	−0.489010
$576$	−0.888510	−0.0370213
$577$	−18.6491	−0.776372	−0.388186	−	0.921581i	$-0.626898\pi$
$577$	−18.6491	−0.776372	−0.388186	+	0.921581i	$0.626898\pi$
$578$	−10.5833	−0.440206
$579$	−4.08239	−0.169658
$580$	−10.2550	−0.425816
$581$	7.11711	0.295267
$582$	1.45310	0.0602328
$583$	25.7245	1.06540
$584$	4.06115	0.168052
$585$	2.98035	0.123222
$586$	7.96954	0.329219
$587$	−22.3889	−0.924089	−0.462045	−	0.886857i	$-0.652884\pi$
$587$	−22.3889	−0.924089	−0.462045	+	0.886857i	$0.652884\pi$
$588$	−11.7472	−0.484447
$589$	−5.15974	−0.212603
$590$	7.61259	0.313405
$591$	−8.03860	−0.330664
$592$	−3.22276	−0.132455
$593$	−37.4656	−1.53853	−0.769263	−	0.638932i	$-0.779376\pi$
$593$	−37.4656	−1.53853	−0.769263	+	0.638932i	$0.779376\pi$
$594$	−32.2754	−1.32428
$595$	−16.7032	−0.684763
$596$	15.5695	0.637751
$597$	−3.78986	−0.155109
$598$	−10.9406	−0.447393
$599$	14.8939	0.608550	0.304275	−	0.952584i	$-0.401586\pi$
$599$	14.8939	0.608550	0.304275	+	0.952584i	$0.401586\pi$
$600$	3.07703	0.125619
$601$	−18.6763	−0.761822	−0.380911	−	0.924612i	$-0.624390\pi$
$601$	−18.6763	−0.761822	−0.380911	+	0.924612i	$0.624390\pi$
$602$	−32.2935	−1.31619
$603$	−2.98777	−0.121671
$604$	15.8987	0.646909
$605$	36.7192	1.49285
$606$	−3.51161	−0.142649
$607$	27.5758	1.11927	0.559633	−	0.828740i	$-0.310942\pi$
$607$	27.5758	1.11927	0.559633	+	0.828740i	$0.310942\pi$
$608$	5.15974	0.209255
$609$	−34.0889	−1.38135
$610$	−9.86630	−0.399475
$611$	−0.892493	−0.0361064
$612$	−2.25071	−0.0909796
$613$	30.4578	1.23018	0.615089	−	0.788458i	$-0.289120\pi$
$613$	30.4578	1.23018	0.615089	+	0.788458i	$0.289120\pi$
$614$	−5.11328	−0.206355
$615$	25.0911	1.01177
$616$	22.1848	0.893853
$617$	11.5634	0.465524	0.232762	−	0.972534i	$-0.425224\pi$
$617$	11.5634	0.465524	0.232762	+	0.972534i	$0.425224\pi$
$618$	−7.40389	−0.297828
$619$	1.72314	0.0692589	0.0346295	−	0.999400i	$-0.488975\pi$
$619$	1.72314	0.0692589	0.0346295	+	0.999400i	$0.488975\pi$
$620$	−1.69777	−0.0681842
$621$	31.2890	1.25558
$622$	−27.8403	−1.11629
$623$	−60.3418	−2.41754
$624$	2.87091	0.114929
$625$	−9.92806	−0.397122
$626$	−20.5761	−0.822387
$627$	42.8269	1.71034
$628$	−1.61899	−0.0646048
$629$	−8.16366	−0.325507
$630$	5.85874	0.233418
$631$	25.9096	1.03144	0.515722	−	0.856756i	$-0.327524\pi$
$631$	25.9096	1.03144	0.515722	+	0.856756i	$0.327524\pi$
$632$	7.18202	0.285686
$633$	−40.6141	−1.61426
$634$	10.8124	0.429414
$635$	18.0898	0.717871
$636$	6.54405	0.259489
$637$	−15.9722	−0.632843
$638$	34.5025	1.36597
$639$	7.74298	0.306308
$640$	1.69777	0.0671103
$641$	−22.4882	−0.888231	−0.444115	−	0.895970i	$-0.646482\pi$
$641$	−22.4882	−0.888231	−0.444115	+	0.895970i	$0.646482\pi$
$642$	−17.1160	−0.675514
$643$	12.0051	0.473434	0.236717	−	0.971579i	$-0.423929\pi$
$643$	12.0051	0.473434	0.236717	+	0.971579i	$0.423929\pi$
$644$	−21.5068	−0.847487
$645$	−20.5129	−0.807696
$646$	13.0703	0.514243
$647$	6.06205	0.238324	0.119162	−	0.992875i	$-0.461979\pi$
$647$	6.06205	0.238324	0.119162	+	0.992875i	$0.461979\pi$
$648$	−5.54502	−0.217829
$649$	−25.6122	−1.00537
$650$	4.18373	0.164099
$651$	−5.64360	−0.221190
$652$	−11.7792	−0.461309
$653$	−19.0294	−0.744680	−0.372340	−	0.928096i	$-0.621444\pi$
$653$	−19.0294	−0.744680	−0.372340	+	0.928096i	$0.621444\pi$
$654$	−29.7778	−1.16441
$655$	−17.1105	−0.668562
$656$	−10.1706	−0.397094
$657$	−3.60838	−0.140776
$658$	−1.75445	−0.0683956
$659$	23.4274	0.912604	0.456302	−	0.889825i	$-0.349174\pi$
$659$	23.4274	0.912604	0.456302	+	0.889825i	$0.349174\pi$
$660$	14.0919	0.548525
$661$	−4.21309	−0.163870	−0.0819351	−	0.996638i	$-0.526110\pi$
$661$	−4.21309	−0.163870	−0.0819351	+	0.996638i	$0.526110\pi$
$662$	−9.85331	−0.382960
$663$	7.27239	0.282436
$664$	−1.83249	−0.0711144
$665$	−34.0227	−1.31934
$666$	2.86346	0.110957
$667$	−33.4480	−1.29511
$668$	13.6471	0.528023
$669$	−2.50093	−0.0966915
$670$	5.70905	0.220560
$671$	33.1947	1.28147
$672$	5.64360	0.217707
$673$	−3.83359	−0.147774	−0.0738870	−	0.997267i	$-0.523540\pi$
$673$	−3.83359	−0.147774	−0.0738870	+	0.997267i	$0.523540\pi$
$674$	−5.92556	−0.228244
$675$	−11.9651	−0.460536
$676$	−9.09652	−0.349866
$677$	−36.2455	−1.39303	−0.696514	−	0.717543i	$-0.745267\pi$
$677$	−36.2455	−1.39303	−0.696514	+	0.717543i	$0.745267\pi$
$678$	−4.00958	−0.153987
$679$	3.88385	0.149048
$680$	4.30067	0.164923
$681$	10.2782	0.393863
$682$	5.71208	0.218727
$683$	9.86350	0.377416	0.188708	−	0.982033i	$-0.439570\pi$
$683$	9.86350	0.377416	0.188708	+	0.982033i	$0.439570\pi$
$684$	−4.58448	−0.175292
$685$	15.2249	0.581714
$686$	−4.21108	−0.160780
$687$	−18.5608	−0.708138
$688$	8.31484	0.317000
$689$	8.89771	0.338976
$690$	−13.6612	−0.520072
$691$	23.9406	0.910742	0.455371	−	0.890302i	$-0.349507\pi$
$691$	23.9406	0.910742	0.455371	+	0.890302i	$0.349507\pi$
$692$	7.92021	0.301081
$693$	−19.7115	−0.748777
$694$	17.5076	0.664580
$695$	−2.85882	−0.108441
$696$	8.77709	0.332695
$697$	−25.7634	−0.975858
$698$	−13.0417	−0.493637
$699$	31.9556	1.20867
$700$	8.22431	0.310850
$701$	−0.851797	−0.0321719	−0.0160860	−	0.999871i	$-0.505121\pi$
$701$	−0.851797	−0.0321719	−0.0160860	+	0.999871i	$0.505121\pi$
$702$	−11.1636	−0.421342
$703$	−16.6286	−0.627159
$704$	−5.71208	−0.215282
$705$	−1.11443	−0.0419719
$706$	−12.5574	−0.472605
$707$	−9.38584	−0.352991
$708$	−6.51550	−0.244867
$709$	43.4949	1.63348	0.816742	−	0.577003i	$-0.195778\pi$
$709$	43.4949	1.63348	0.816742	+	0.577003i	$0.195778\pi$
$710$	−14.7954	−0.555260
$711$	−6.38130	−0.239318
$712$	15.5366	0.582259
$713$	−5.53750	−0.207381
$714$	14.2960	0.535013
$715$	19.1602	0.716550
$716$	9.03284	0.337573
$717$	−11.2687	−0.420839
$718$	3.29025	0.122791
$719$	−23.5729	−0.879122	−0.439561	−	0.898213i	$-0.644866\pi$
$719$	−23.5729	−0.879122	−0.439561	+	0.898213i	$0.644866\pi$
$720$	−1.50849	−0.0562180
$721$	−19.7892	−0.736987
$722$	7.62287	0.283694
$723$	−2.96920	−0.110426
$724$	11.0730	0.411524
$725$	12.7907	0.475034
$726$	−31.4274	−1.16638
$727$	−15.0553	−0.558369	−0.279184	−	0.960238i	$-0.590064\pi$
$727$	−15.0553	−0.558369	−0.279184	+	0.960238i	$0.590064\pi$
$728$	7.67340	0.284395
$729$	29.5585	1.09476
$730$	6.89491	0.255192
$731$	21.0625	0.779026
$732$	8.44441	0.312114
$733$	1.75320	0.0647559	0.0323780	−	0.999476i	$-0.489692\pi$
$733$	1.75320	0.0647559	0.0323780	+	0.999476i	$0.489692\pi$
$734$	−4.51343	−0.166594
$735$	−19.9441	−0.735649
$736$	5.53750	0.204115
$737$	−19.2078	−0.707530
$738$	9.03667	0.332644
$739$	−33.3406	−1.22645	−0.613226	−	0.789907i	$-0.710129\pi$
$739$	−33.3406	−1.22645	−0.613226	+	0.789907i	$0.710129\pi$
$740$	−5.47151	−0.201137
$741$	14.8132	0.544175
$742$	17.4910	0.642114
$743$	−22.2526	−0.816370	−0.408185	−	0.912899i	$-0.633838\pi$
$743$	−22.2526	−0.816370	−0.408185	+	0.912899i	$0.633838\pi$
$744$	1.45310	0.0532731
$745$	26.4334	0.968446
$746$	−36.1459	−1.32339
$747$	1.62819	0.0595722
$748$	−14.4694	−0.529055
$749$	−45.7477	−1.67159
$750$	17.5592	0.641173
$751$	−46.6432	−1.70203	−0.851017	−	0.525138i	$-0.824014\pi$
$751$	−46.6432	−1.70203	−0.851017	+	0.525138i	$0.824014\pi$
$752$	0.451730	0.0164729
$753$	31.0499	1.13152
$754$	11.9339	0.434607
$755$	26.9924	0.982354
$756$	−21.9452	−0.798139
$757$	0.0559114	0.00203213	0.00101607	−	0.999999i	$-0.499677\pi$
$757$	0.0559114	0.00203213	0.00101607	+	0.999999i	$0.499677\pi$
$758$	21.1460	0.768059
$759$	45.9624	1.66833
$760$	8.76006	0.317761
$761$	3.38638	0.122756	0.0613782	−	0.998115i	$-0.480450\pi$
$761$	3.38638	0.122756	0.0613782	+	0.998115i	$0.480450\pi$
$762$	−15.4828	−0.560881
$763$	−79.5904	−2.88137
$764$	−0.293757	−0.0106278
$765$	−3.82119	−0.138156
$766$	13.9958	0.505688
$767$	−8.85888	−0.319876
$768$	−1.45310	−0.0524341
$769$	−6.94061	−0.250285	−0.125142	−	0.992139i	$-0.539939\pi$
$769$	−6.94061	−0.250285	−0.125142	+	0.992139i	$0.539939\pi$
$770$	37.6648	1.35735
$771$	−36.9686	−1.33139
$772$	2.80944	0.101114
$773$	33.1212	1.19129	0.595644	−	0.803249i	$-0.296897\pi$
$773$	33.1212	1.19129	0.595644	+	0.803249i	$0.296897\pi$
$774$	−7.38782	−0.265550
$775$	2.11757	0.0760653
$776$	−1.00000	−0.0358979
$777$	−18.1880	−0.652490
$778$	13.6819	0.490520
$779$	−52.4775	−1.88020
$780$	4.87416	0.174523
$781$	49.7783	1.78121
$782$	14.0272	0.501612
$783$	−34.1298	−1.21970
$784$	8.08426	0.288723
$785$	−2.74868	−0.0981046
$786$	14.6446	0.522355
$787$	11.8566	0.422643	0.211321	−	0.977417i	$-0.432223\pi$
$787$	11.8566	0.422643	0.211321	+	0.977417i	$0.432223\pi$
$788$	5.53205	0.197071
$789$	−38.0551	−1.35480
$790$	12.1934	0.433823
$791$	−10.7168	−0.381047
$792$	5.07524	0.180341
$793$	11.4816	0.407722
$794$	12.7572	0.452737
$795$	11.1103	0.394042
$796$	2.60813	0.0924427
$797$	−10.7044	−0.379170	−0.189585	−	0.981864i	$-0.560714\pi$
$797$	−10.7044	−0.379170	−0.189585	+	0.981864i	$0.560714\pi$
$798$	29.1195	1.03082
$799$	1.14429	0.0404821
$800$	−2.11757	−0.0748674
$801$	−13.8044	−0.487756
$802$	−5.22836	−0.184620
$803$	−23.1976	−0.818627
$804$	−4.88628	−0.172326
$805$	−36.5137	−1.28694
$806$	1.97572	0.0695918
$807$	4.93593	0.173753
$808$	2.41664	0.0850170
$809$	18.1943	0.639676	0.319838	−	0.947472i	$-0.396372\pi$
$809$	18.1943	0.639676	0.319838	+	0.947472i	$0.396372\pi$
$810$	−9.41418	−0.330781
$811$	−1.97432	−0.0693276	−0.0346638	−	0.999399i	$-0.511036\pi$
$811$	−1.97432	−0.0693276	−0.0346638	+	0.999399i	$0.511036\pi$
$812$	23.4595	0.823266
$813$	6.74022	0.236390
$814$	18.4087	0.645224
$815$	−19.9984	−0.700513
$816$	−3.68088	−0.128857
$817$	42.9024	1.50096
$818$	20.0462	0.700901
$819$	−6.81789	−0.238236
$820$	−17.2673	−0.603001
$821$	−4.82790	−0.168495	−0.0842474	−	0.996445i	$-0.526849\pi$
$821$	−4.82790	−0.168495	−0.0842474	+	0.996445i	$0.526849\pi$
$822$	−13.0308	−0.454500
$823$	−23.8356	−0.830856	−0.415428	−	0.909626i	$-0.636368\pi$
$823$	−23.8356	−0.830856	−0.415428	+	0.909626i	$0.636368\pi$
$824$	5.09525	0.177502
$825$	−17.5763	−0.611927
$826$	−17.4147	−0.605934
$827$	−11.1054	−0.386171	−0.193086	−	0.981182i	$-0.561849\pi$
$827$	−11.1054	−0.386171	−0.193086	+	0.981182i	$0.561849\pi$
$828$	−4.92013	−0.170986
$829$	14.6812	0.509898	0.254949	−	0.966955i	$-0.417941\pi$
$829$	14.6812	0.509898	0.254949	+	0.966955i	$0.417941\pi$
$830$	−3.11115	−0.107990
$831$	30.0254	1.04157
$832$	−1.97572	−0.0684958
$833$	20.4785	0.709536
$834$	2.44682	0.0847263
$835$	23.1697	0.801820
$836$	−29.4728	−1.01934
$837$	−5.65038	−0.195306
$838$	−27.4074	−0.946772
$839$	26.7220	0.922547	0.461274	−	0.887258i	$-0.347393\pi$
$839$	26.7220	0.922547	0.461274	+	0.887258i	$0.347393\pi$
$840$	9.58155	0.330595
$841$	7.48482	0.258097
$842$	−27.7528	−0.956424
$843$	45.0712	1.55233
$844$	27.9500	0.962079
$845$	−15.4438	−0.531284
$846$	−0.401367	−0.0137993
$847$	−83.9993	−2.88625
$848$	−4.50352	−0.154652
$849$	−33.3887	−1.14590
$850$	−5.36407	−0.183986
$851$	−17.8460	−0.611754
$852$	12.6631	0.433831
$853$	28.8460	0.987668	0.493834	−	0.869556i	$-0.335595\pi$
$853$	28.8460	0.987668	0.493834	+	0.869556i	$0.335595\pi$
$854$	22.5703	0.772339
$855$	−7.78340	−0.266187
$856$	11.7790	0.402597
$857$	−41.6074	−1.42128	−0.710641	−	0.703555i	$-0.751595\pi$
$857$	−41.6074	−1.42128	−0.710641	+	0.703555i	$0.751595\pi$
$858$	−16.3989	−0.559849
$859$	−30.1784	−1.02967	−0.514837	−	0.857288i	$-0.672147\pi$
$859$	−30.1784	−1.02967	−0.514837	+	0.857288i	$0.672147\pi$
$860$	14.1167	0.481375
$861$	−57.3987	−1.95614
$862$	15.1555	0.516198
$863$	28.5384	0.971459	0.485729	−	0.874109i	$-0.338554\pi$
$863$	28.5384	0.971459	0.485729	+	0.874109i	$0.338554\pi$
$864$	5.65038	0.192230
$865$	13.4467	0.457202
$866$	14.8990	0.506289
$867$	15.3785	0.522281
$868$	3.88385	0.131826
$869$	−41.0243	−1.39165
$870$	14.9015	0.505208
$871$	−6.64370	−0.225113
$872$	20.4927	0.693970
$873$	0.888510	0.0300715
$874$	28.5720	0.966464
$875$	46.9324	1.58661
$876$	−5.90125	−0.199385
$877$	−52.6385	−1.77748	−0.888738	−	0.458416i	$-0.848417\pi$
$877$	−52.6385	−1.77748	−0.888738	+	0.458416i	$0.848417\pi$
$878$	−30.1347	−1.01700
$879$	−11.5805	−0.390601
$880$	−9.69782	−0.326913
$881$	21.2107	0.714608	0.357304	−	0.933988i	$-0.383696\pi$
$881$	21.2107	0.714608	0.357304	+	0.933988i	$0.383696\pi$
$882$	−7.18294	−0.241862
$883$	−14.5008	−0.487992	−0.243996	−	0.969776i	$-0.578458\pi$
$883$	−14.5008	−0.487992	−0.243996	+	0.969776i	$0.578458\pi$
$884$	−5.00476	−0.168328
$885$	−11.0618	−0.371839
$886$	11.2577	0.378211
$887$	2.87471	0.0965234	0.0482617	−	0.998835i	$-0.484632\pi$
$887$	2.87471	0.0965234	0.0482617	+	0.998835i	$0.484632\pi$
$888$	4.68298	0.157151
$889$	−41.3824	−1.38792
$890$	26.3776	0.884180
$891$	31.6736	1.06111
$892$	1.72110	0.0576268
$893$	2.33081	0.0779975
$894$	−22.6240	−0.756658
$895$	15.3357	0.512616
$896$	−3.88385	−0.129750
$897$	15.8977	0.530809
$898$	−0.277528	−0.00926121
$899$	6.04027	0.201454
$900$	1.88148	0.0627161
$901$	−11.4080	−0.380056
$902$	58.0952	1.93436
$903$	46.9256	1.56159
$904$	2.75934	0.0917741
$905$	18.7994	0.624913
$906$	−23.1024	−0.767524
$907$	48.8045	1.62053	0.810263	−	0.586067i	$-0.199324\pi$
$907$	48.8045	1.62053	0.810263	+	0.586067i	$0.199324\pi$
$908$	−7.07334	−0.234737
$909$	−2.14721	−0.0712183
$910$	13.0277	0.431864
$911$	53.1891	1.76223	0.881117	−	0.472898i	$-0.156792\pi$
$911$	53.1891	1.76223	0.881117	+	0.472898i	$0.156792\pi$
$912$	−7.49759	−0.248270
$913$	10.4673	0.346418
$914$	22.5419	0.745619
$915$	14.3367	0.473956
$916$	12.7733	0.422040
$917$	39.1421	1.29259
$918$	14.3131	0.472404
$919$	−4.95813	−0.163554	−0.0817768	−	0.996651i	$-0.526059\pi$
$919$	−4.95813	−0.163554	−0.0817768	+	0.996651i	$0.526059\pi$
$920$	9.40142	0.309956
$921$	7.43009	0.244830
$922$	9.18099	0.302360
$923$	17.2176	0.566723
$924$	−32.2367	−1.06051
$925$	6.82442	0.224385
$926$	−19.8916	−0.653679
$927$	−4.52718	−0.148692
$928$	−6.04027	−0.198281
$929$	60.7791	1.99410	0.997048	−	0.0767751i	$-0.0244623\pi$
$929$	60.7791	1.99410	0.997048	+	0.0767751i	$0.0244623\pi$
$930$	2.46703	0.0808970
$931$	41.7126	1.36708
$932$	−21.9914	−0.720351
$933$	40.4546	1.32442
$934$	−6.71226	−0.219632
$935$	−24.5658	−0.803388
$936$	1.75545	0.0573787
$937$	49.8032	1.62700	0.813500	−	0.581565i	$-0.197560\pi$
$937$	49.8032	1.62700	0.813500	+	0.581565i	$0.197560\pi$
$938$	−13.0601	−0.426427
$939$	29.8991	0.975720
$940$	0.766935	0.0250147
$941$	−4.23102	−0.137927	−0.0689636	−	0.997619i	$-0.521969\pi$
$941$	−4.23102	−0.137927	−0.0689636	+	0.997619i	$0.521969\pi$
$942$	2.35255	0.0766503
$943$	−56.3196	−1.83402
$944$	4.48387	0.145938
$945$	−37.2580	−1.21200
$946$	−47.4950	−1.54420
$947$	−31.6365	−1.02805	−0.514024	−	0.857776i	$-0.671846\pi$
$947$	−31.6365	−1.02805	−0.514024	+	0.857776i	$0.671846\pi$
$948$	−10.4362	−0.338951
$949$	−8.02371	−0.260461
$950$	−10.9261	−0.354489
$951$	−15.7114	−0.509478
$952$	−9.83828	−0.318860
$953$	−2.52818	−0.0818958	−0.0409479	−	0.999161i	$-0.513038\pi$
$953$	−2.52818	−0.0818958	−0.0409479	+	0.999161i	$0.513038\pi$
$954$	4.00143	0.129551
$955$	−0.498733	−0.0161386
$956$	7.75498	0.250814
$957$	−50.1355	−1.62065
$958$	4.17051	0.134743
$959$	−34.8287	−1.12468
$960$	−2.46703	−0.0796230
$961$	1.00000	0.0322581
$962$	6.36728	0.205289
$963$	−10.4657	−0.337254
$964$	2.04336	0.0658123
$965$	4.76979	0.153545
$966$	31.2515	1.00550
$967$	32.4116	1.04229	0.521143	−	0.853469i	$-0.325506\pi$
$967$	32.4116	1.04229	0.521143	+	0.853469i	$0.325506\pi$
$968$	21.6279	0.695146
$969$	−18.9924	−0.610123
$970$	−1.69777	−0.0545122
$971$	45.3733	1.45610	0.728050	−	0.685524i	$-0.240427\pi$
$971$	45.3733	1.45610	0.728050	+	0.685524i	$0.240427\pi$
$972$	−8.89370	−0.285265
$973$	6.53987	0.209659
$974$	10.8411	0.347371
$975$	−6.07936	−0.194695
$976$	−5.81132	−0.186016
$977$	1.28013	0.0409550	0.0204775	−	0.999790i	$-0.493481\pi$
$977$	1.28013	0.0409550	0.0204775	+	0.999790i	$0.493481\pi$
$978$	17.1163	0.547319
$979$	−88.7464	−2.83635
$980$	13.7252	0.438436
$981$	−18.2080	−0.581335
$982$	19.0393	0.607569
$983$	−2.98270	−0.0951333	−0.0475666	−	0.998868i	$-0.515147\pi$
$983$	−2.98270	−0.0951333	−0.0475666	+	0.998868i	$0.515147\pi$
$984$	14.7788	0.471132
$985$	9.39216	0.299259
$986$	−15.3008	−0.487276
$987$	2.54939	0.0811478
$988$	−10.1942	−0.324321
$989$	46.0434	1.46410
$990$	8.61661	0.273854
$991$	23.1288	0.734711	0.367356	−	0.930081i	$-0.380263\pi$
$991$	23.1288	0.734711	0.367356	+	0.930081i	$0.380263\pi$
$992$	−1.00000	−0.0317500
$993$	14.3178	0.454362
$994$	33.8460	1.07353
$995$	4.42801	0.140377
$996$	2.66279	0.0843736
$997$	−44.1591	−1.39853	−0.699266	−	0.714862i	$-0.746490\pi$
$997$	−44.1591	−1.39853	−0.699266	+	0.714862i	$0.746490\pi$
$998$	−37.2081	−1.17780
$999$	−18.2098	−0.576133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.7	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.45310 q^{3} +1.00000 q^{4} +1.69777 q^{5} -1.45310 q^{6} -3.88385 q^{7} +1.00000 q^{8} -0.888510 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.45310 q^{3} +1.00000 q^{4} +1.69777 q^{5} -1.45310 q^{6} -3.88385 q^{7} +1.00000 q^{8} -0.888510 q^{9} +1.69777 q^{10} -5.71208 q^{11} -1.45310 q^{12} -1.97572 q^{13} -3.88385 q^{14} -2.46703 q^{15} +1.00000 q^{16} +2.53313 q^{17} -0.888510 q^{18} +5.15974 q^{19} +1.69777 q^{20} +5.64360 q^{21} -5.71208 q^{22} +5.53750 q^{23} -1.45310 q^{24} -2.11757 q^{25} -1.97572 q^{26} +5.65038 q^{27} -3.88385 q^{28} -6.04027 q^{29} -2.46703 q^{30} -1.00000 q^{31} +1.00000 q^{32} +8.30021 q^{33} +2.53313 q^{34} -6.59389 q^{35} -0.888510 q^{36} -3.22276 q^{37} +5.15974 q^{38} +2.87091 q^{39} +1.69777 q^{40} -10.1706 q^{41} +5.64360 q^{42} +8.31484 q^{43} -5.71208 q^{44} -1.50849 q^{45} +5.53750 q^{46} +0.451730 q^{47} -1.45310 q^{48} +8.08426 q^{49} -2.11757 q^{50} -3.68088 q^{51} -1.97572 q^{52} -4.50352 q^{53} +5.65038 q^{54} -9.69782 q^{55} -3.88385 q^{56} -7.49759 q^{57} -6.04027 q^{58} +4.48387 q^{59} -2.46703 q^{60} -5.81132 q^{61} -1.00000 q^{62} +3.45084 q^{63} +1.00000 q^{64} -3.35433 q^{65} +8.30021 q^{66} +3.36267 q^{67} +2.53313 q^{68} -8.04652 q^{69} -6.59389 q^{70} -8.71457 q^{71} -0.888510 q^{72} +4.06115 q^{73} -3.22276 q^{74} +3.07703 q^{75} +5.15974 q^{76} +22.1848 q^{77} +2.87091 q^{78} +7.18202 q^{79} +1.69777 q^{80} -5.54502 q^{81} -10.1706 q^{82} -1.83249 q^{83} +5.64360 q^{84} +4.30067 q^{85} +8.31484 q^{86} +8.77709 q^{87} -5.71208 q^{88} +15.5366 q^{89} -1.50849 q^{90} +7.67340 q^{91} +5.53750 q^{92} +1.45310 q^{93} +0.451730 q^{94} +8.76006 q^{95} -1.45310 q^{96} -1.00000 q^{97} +8.08426 q^{98} +5.07524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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