LMFDB - Embedded newform 6014.2.a.i.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.13670 q^{3} +1.00000 q^{4} -0.941618 q^{5} -3.13670 q^{6} -2.29539 q^{7} +1.00000 q^{8} +6.83889 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.13670 q^{3} +1.00000 q^{4} -0.941618 q^{5} -3.13670 q^{6} -2.29539 q^{7} +1.00000 q^{8} +6.83889 q^{9} -0.941618 q^{10} +4.48900 q^{11} -3.13670 q^{12} +4.81251 q^{13} -2.29539 q^{14} +2.95357 q^{15} +1.00000 q^{16} +3.75274 q^{17} +6.83889 q^{18} +5.13373 q^{19} -0.941618 q^{20} +7.19996 q^{21} +4.48900 q^{22} +4.35532 q^{23} -3.13670 q^{24} -4.11336 q^{25} +4.81251 q^{26} -12.0415 q^{27} -2.29539 q^{28} +2.83758 q^{29} +2.95357 q^{30} -1.00000 q^{31} +1.00000 q^{32} -14.0806 q^{33} +3.75274 q^{34} +2.16138 q^{35} +6.83889 q^{36} -8.29176 q^{37} +5.13373 q^{38} -15.0954 q^{39} -0.941618 q^{40} +9.50778 q^{41} +7.19996 q^{42} +3.66241 q^{43} +4.48900 q^{44} -6.43962 q^{45} +4.35532 q^{46} +3.82340 q^{47} -3.13670 q^{48} -1.73118 q^{49} -4.11336 q^{50} -11.7712 q^{51} +4.81251 q^{52} -3.40587 q^{53} -12.0415 q^{54} -4.22692 q^{55} -2.29539 q^{56} -16.1030 q^{57} +2.83758 q^{58} +13.3578 q^{59} +2.95357 q^{60} -14.2134 q^{61} -1.00000 q^{62} -15.6979 q^{63} +1.00000 q^{64} -4.53154 q^{65} -14.0806 q^{66} +0.506352 q^{67} +3.75274 q^{68} -13.6613 q^{69} +2.16138 q^{70} +3.18159 q^{71} +6.83889 q^{72} -10.0252 q^{73} -8.29176 q^{74} +12.9024 q^{75} +5.13373 q^{76} -10.3040 q^{77} -15.0954 q^{78} +2.49532 q^{79} -0.941618 q^{80} +17.2538 q^{81} +9.50778 q^{82} -2.16106 q^{83} +7.19996 q^{84} -3.53365 q^{85} +3.66241 q^{86} -8.90065 q^{87} +4.48900 q^{88} +1.44102 q^{89} -6.43962 q^{90} -11.0466 q^{91} +4.35532 q^{92} +3.13670 q^{93} +3.82340 q^{94} -4.83402 q^{95} -3.13670 q^{96} -1.00000 q^{97} -1.73118 q^{98} +30.6998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.13670	−1.81097	−0.905487	−	0.424373i	$-0.860495\pi$
$3$	−3.13670	−1.81097	−0.905487	+	0.424373i	$0.860495\pi$
$4$	1.00000	0.500000
$5$	−0.941618	−0.421104	−0.210552	−	0.977583i	$-0.567526\pi$
$5$	−0.941618	−0.421104	−0.210552	+	0.977583i	$0.567526\pi$
$6$	−3.13670	−1.28055
$7$	−2.29539	−0.867576	−0.433788	−	0.901015i	$-0.642823\pi$
$7$	−2.29539	−0.867576	−0.433788	+	0.901015i	$0.642823\pi$
$8$	1.00000	0.353553
$9$	6.83889	2.27963
$10$	−0.941618	−0.297766
$11$	4.48900	1.35348	0.676742	−	0.736220i	$-0.263391\pi$
$11$	4.48900	1.35348	0.676742	+	0.736220i	$0.263391\pi$
$12$	−3.13670	−0.905487
$13$	4.81251	1.33475	0.667375	−	0.744722i	$-0.267418\pi$
$13$	4.81251	1.33475	0.667375	+	0.744722i	$0.267418\pi$
$14$	−2.29539	−0.613469
$15$	2.95357	0.762610
$16$	1.00000	0.250000
$17$	3.75274	0.910174	0.455087	−	0.890447i	$-0.349608\pi$
$17$	3.75274	0.910174	0.455087	+	0.890447i	$0.349608\pi$
$18$	6.83889	1.61194
$19$	5.13373	1.17776	0.588879	−	0.808221i	$-0.299569\pi$
$19$	5.13373	1.17776	0.588879	+	0.808221i	$0.299569\pi$
$20$	−0.941618	−0.210552
$21$	7.19996	1.57116
$22$	4.48900	0.957058
$23$	4.35532	0.908148	0.454074	−	0.890964i	$-0.349970\pi$
$23$	4.35532	0.908148	0.454074	+	0.890964i	$0.349970\pi$
$24$	−3.13670	−0.640276
$25$	−4.11336	−0.822671
$26$	4.81251	0.943810
$27$	−12.0415	−2.31738
$28$	−2.29539	−0.433788
$29$	2.83758	0.526926	0.263463	−	0.964670i	$-0.415135\pi$
$29$	2.83758	0.526926	0.263463	+	0.964670i	$0.415135\pi$
$30$	2.95357	0.539246
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−14.0806	−2.45113
$34$	3.75274	0.643590
$35$	2.16138	0.365340
$36$	6.83889	1.13982
$37$	−8.29176	−1.36316	−0.681578	−	0.731745i	$-0.738706\pi$
$37$	−8.29176	−1.36316	−0.681578	+	0.731745i	$0.738706\pi$
$38$	5.13373	0.832801
$39$	−15.0954	−2.41720
$40$	−0.941618	−0.148883
$41$	9.50778	1.48487	0.742433	−	0.669920i	$-0.233672\pi$
$41$	9.50778	1.48487	0.742433	+	0.669920i	$0.233672\pi$
$42$	7.19996	1.11098
$43$	3.66241	0.558513	0.279256	−	0.960217i	$-0.409912\pi$
$43$	3.66241	0.558513	0.279256	+	0.960217i	$0.409912\pi$
$44$	4.48900	0.676742
$45$	−6.43962	−0.959962
$46$	4.35532	0.642158
$47$	3.82340	0.557701	0.278850	−	0.960335i	$-0.410047\pi$
$47$	3.82340	0.557701	0.278850	+	0.960335i	$0.410047\pi$
$48$	−3.13670	−0.452744
$49$	−1.73118	−0.247311
$50$	−4.11336	−0.581716
$51$	−11.7712	−1.64830
$52$	4.81251	0.667375
$53$	−3.40587	−0.467832	−0.233916	−	0.972257i	$-0.575154\pi$
$53$	−3.40587	−0.467832	−0.233916	+	0.972257i	$0.575154\pi$
$54$	−12.0415	−1.63863
$55$	−4.22692	−0.569958
$56$	−2.29539	−0.306735
$57$	−16.1030	−2.13289
$58$	2.83758	0.372593
$59$	13.3578	1.73904	0.869521	−	0.493896i	$-0.164428\pi$
$59$	13.3578	1.73904	0.869521	+	0.493896i	$0.164428\pi$
$60$	2.95357	0.381305
$61$	−14.2134	−1.81985	−0.909923	−	0.414778i	$-0.863859\pi$
$61$	−14.2134	−1.81985	−0.909923	+	0.414778i	$0.863859\pi$
$62$	−1.00000	−0.127000
$63$	−15.6979	−1.97775
$64$	1.00000	0.125000
$65$	−4.53154	−0.562069
$66$	−14.0806	−1.73321
$67$	0.506352	0.0618607	0.0309304	−	0.999522i	$-0.490153\pi$
$67$	0.506352	0.0618607	0.0309304	+	0.999522i	$0.490153\pi$
$68$	3.75274	0.455087
$69$	−13.6613	−1.64463
$70$	2.16138	0.258335
$71$	3.18159	0.377585	0.188793	−	0.982017i	$-0.439543\pi$
$71$	3.18159	0.377585	0.188793	+	0.982017i	$0.439543\pi$
$72$	6.83889	0.805971
$73$	−10.0252	−1.17336	−0.586678	−	0.809820i	$-0.699564\pi$
$73$	−10.0252	−1.17336	−0.586678	+	0.809820i	$0.699564\pi$
$74$	−8.29176	−0.963897
$75$	12.9024	1.48984
$76$	5.13373	0.588879
$77$	−10.3040	−1.17425
$78$	−15.0954	−1.70922
$79$	2.49532	0.280746	0.140373	−	0.990099i	$-0.455170\pi$
$79$	2.49532	0.280746	0.140373	+	0.990099i	$0.455170\pi$
$80$	−0.941618	−0.105276
$81$	17.2538	1.91708
$82$	9.50778	1.04996
$83$	−2.16106	−0.237207	−0.118603	−	0.992942i	$-0.537842\pi$
$83$	−2.16106	−0.237207	−0.118603	+	0.992942i	$0.537842\pi$
$84$	7.19996	0.785580
$85$	−3.53365	−0.383278
$86$	3.66241	0.394928
$87$	−8.90065	−0.954250
$88$	4.48900	0.478529
$89$	1.44102	0.152748	0.0763739	−	0.997079i	$-0.475666\pi$
$89$	1.44102	0.152748	0.0763739	+	0.997079i	$0.475666\pi$
$90$	−6.43962	−0.678796
$91$	−11.0466	−1.15800
$92$	4.35532	0.454074
$93$	3.13670	0.325261
$94$	3.82340	0.394354
$95$	−4.83402	−0.495960
$96$	−3.13670	−0.320138
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−1.73118	−0.174875
$99$	30.6998	3.08544
$100$	−4.11336	−0.411336
$101$	0.538527	0.0535854	0.0267927	−	0.999641i	$-0.491471\pi$
$101$	0.538527	0.0535854	0.0267927	+	0.999641i	$0.491471\pi$
$102$	−11.7712	−1.16553
$103$	6.19731	0.610639	0.305320	−	0.952250i	$-0.401237\pi$
$103$	6.19731	0.610639	0.305320	+	0.952250i	$0.401237\pi$
$104$	4.81251	0.471905
$105$	−6.77961	−0.661622
$106$	−3.40587	−0.330807
$107$	−0.160248	−0.0154917	−0.00774587	−	0.999970i	$-0.502466\pi$
$107$	−0.160248	−0.0154917	−0.00774587	+	0.999970i	$0.502466\pi$
$108$	−12.0415	−1.15869
$109$	−1.97899	−0.189553	−0.0947765	−	0.995499i	$-0.530214\pi$
$109$	−1.97899	−0.189553	−0.0947765	+	0.995499i	$0.530214\pi$
$110$	−4.22692	−0.403021
$111$	26.0088	2.46864
$112$	−2.29539	−0.216894
$113$	0.0743457	0.00699385	0.00349693	−	0.999994i	$-0.498887\pi$
$113$	0.0743457	0.00699385	0.00349693	+	0.999994i	$0.498887\pi$
$114$	−16.1030	−1.50818
$115$	−4.10105	−0.382425
$116$	2.83758	0.263463
$117$	32.9122	3.04273
$118$	13.3578	1.22969
$119$	−8.61402	−0.789646
$120$	2.95357	0.269623
$121$	9.15110	0.831919
$122$	−14.2134	−1.28683
$123$	−29.8231	−2.68906
$124$	−1.00000	−0.0898027
$125$	8.58130	0.767535
$126$	−15.6979	−1.39848
$127$	11.9878	1.06374	0.531871	−	0.846825i	$-0.321489\pi$
$127$	11.9878	1.06374	0.531871	+	0.846825i	$0.321489\pi$
$128$	1.00000	0.0883883
$129$	−11.4879	−1.01145
$130$	−4.53154	−0.397443
$131$	8.89234	0.776927	0.388464	−	0.921464i	$-0.373006\pi$
$131$	8.89234	0.776927	0.388464	+	0.921464i	$0.373006\pi$
$132$	−14.0806	−1.22556
$133$	−11.7839	−1.02180
$134$	0.506352	0.0437421
$135$	11.3384	0.975858
$136$	3.75274	0.321795
$137$	12.6451	1.08034	0.540172	−	0.841555i	$-0.318359\pi$
$137$	12.6451	1.08034	0.540172	+	0.841555i	$0.318359\pi$
$138$	−13.6613	−1.16293
$139$	−19.6201	−1.66416	−0.832078	−	0.554658i	$-0.812849\pi$
$139$	−19.6201	−1.66416	−0.832078	+	0.554658i	$0.812849\pi$
$140$	2.16138	0.182670
$141$	−11.9929	−1.00998
$142$	3.18159	0.266993
$143$	21.6033	1.80656
$144$	6.83889	0.569908
$145$	−2.67192	−0.221891
$146$	−10.0252	−0.829688
$147$	5.43019	0.447874
$148$	−8.29176	−0.681578
$149$	−19.6317	−1.60829	−0.804144	−	0.594434i	$-0.797376\pi$
$149$	−19.6317	−1.60829	−0.804144	+	0.594434i	$0.797376\pi$
$150$	12.9024	1.05347
$151$	−2.70805	−0.220378	−0.110189	−	0.993911i	$-0.535146\pi$
$151$	−2.70805	−0.220378	−0.110189	+	0.993911i	$0.535146\pi$
$152$	5.13373	0.416401
$153$	25.6646	2.07486
$154$	−10.3040	−0.830321
$155$	0.941618	0.0756326
$156$	−15.0954	−1.20860
$157$	14.1846	1.13206	0.566028	−	0.824386i	$-0.308479\pi$
$157$	14.1846	1.13206	0.566028	+	0.824386i	$0.308479\pi$
$158$	2.49532	0.198517
$159$	10.6832	0.847232
$160$	−0.941618	−0.0744415
$161$	−9.99717	−0.787888
$162$	17.2538	1.35558
$163$	−12.3768	−0.969425	−0.484713	−	0.874673i	$-0.661076\pi$
$163$	−12.3768	−0.969425	−0.484713	+	0.874673i	$0.661076\pi$
$164$	9.50778	0.742433
$165$	13.2586	1.03218
$166$	−2.16106	−0.167730
$167$	12.6284	0.977211	0.488606	−	0.872505i	$-0.337506\pi$
$167$	12.6284	0.977211	0.488606	+	0.872505i	$0.337506\pi$
$168$	7.19996	0.555489
$169$	10.1602	0.781555
$170$	−3.53365	−0.271019
$171$	35.1090	2.68485
$172$	3.66241	0.279256
$173$	11.0290	0.838520	0.419260	−	0.907866i	$-0.362290\pi$
$173$	11.0290	0.838520	0.419260	+	0.907866i	$0.362290\pi$
$174$	−8.90065	−0.674756
$175$	9.44176	0.713730
$176$	4.48900	0.338371
$177$	−41.8995	−3.14936
$178$	1.44102	0.108009
$179$	13.4630	1.00627	0.503135	−	0.864208i	$-0.332180\pi$
$179$	13.4630	1.00627	0.503135	+	0.864208i	$0.332180\pi$
$180$	−6.43962	−0.479981
$181$	7.16751	0.532757	0.266378	−	0.963869i	$-0.414173\pi$
$181$	7.16751	0.532757	0.266378	+	0.963869i	$0.414173\pi$
$182$	−11.0466	−0.818827
$183$	44.5833	3.29569
$184$	4.35532	0.321079
$185$	7.80767	0.574031
$186$	3.13670	0.229994
$187$	16.8461	1.23191
$188$	3.82340	0.278850
$189$	27.6398	2.01050
$190$	−4.83402	−0.350696
$191$	0.868376	0.0628335	0.0314167	−	0.999506i	$-0.489998\pi$
$191$	0.868376	0.0628335	0.0314167	+	0.999506i	$0.489998\pi$
$192$	−3.13670	−0.226372
$193$	−24.5080	−1.76413	−0.882063	−	0.471132i	$-0.843846\pi$
$193$	−24.5080	−1.76413	−0.882063	+	0.471132i	$0.843846\pi$
$194$	−1.00000	−0.0717958
$195$	14.2141	1.01789
$196$	−1.73118	−0.123656
$197$	−5.22238	−0.372079	−0.186039	−	0.982542i	$-0.559565\pi$
$197$	−5.22238	−0.372079	−0.186039	+	0.982542i	$0.559565\pi$
$198$	30.6998	2.18174
$199$	18.2702	1.29514	0.647569	−	0.762006i	$-0.275786\pi$
$199$	18.2702	1.29514	0.647569	+	0.762006i	$0.275786\pi$
$200$	−4.11336	−0.290858
$201$	−1.58827	−0.112028
$202$	0.538527	0.0378906
$203$	−6.51336	−0.457148
$204$	−11.7712	−0.824151
$205$	−8.95270	−0.625284
$206$	6.19731	0.431787
$207$	29.7856	2.07024
$208$	4.81251	0.333687
$209$	23.0453	1.59408
$210$	−6.77961	−0.467837
$211$	1.40257	0.0965568	0.0482784	−	0.998834i	$-0.484627\pi$
$211$	1.40257	0.0965568	0.0482784	+	0.998834i	$0.484627\pi$
$212$	−3.40587	−0.233916
$213$	−9.97970	−0.683798
$214$	−0.160248	−0.0109543
$215$	−3.44860	−0.235192
$216$	−12.0415	−0.819317
$217$	2.29539	0.155821
$218$	−1.97899	−0.134034
$219$	31.4459	2.12492
$220$	−4.22692	−0.284979
$221$	18.0601	1.21485
$222$	26.0088	1.74559
$223$	14.5891	0.976960	0.488480	−	0.872575i	$-0.337552\pi$
$223$	14.5891	0.976960	0.488480	+	0.872575i	$0.337552\pi$
$224$	−2.29539	−0.153367
$225$	−28.1308	−1.87539
$226$	0.0743457	0.00494540
$227$	−3.75780	−0.249414	−0.124707	−	0.992194i	$-0.539799\pi$
$227$	−3.75780	−0.249414	−0.124707	+	0.992194i	$0.539799\pi$
$228$	−16.1030	−1.06645
$229$	17.2074	1.13710	0.568549	−	0.822650i	$-0.307505\pi$
$229$	17.2074	1.13710	0.568549	+	0.822650i	$0.307505\pi$
$230$	−4.10105	−0.270415
$231$	32.3206	2.12654
$232$	2.83758	0.186296
$233$	−26.6071	−1.74309	−0.871544	−	0.490317i	$-0.836881\pi$
$233$	−26.6071	−1.74309	−0.871544	+	0.490317i	$0.836881\pi$
$234$	32.9122	2.15154
$235$	−3.60019	−0.234850
$236$	13.3578	0.869521
$237$	−7.82708	−0.508424
$238$	−8.61402	−0.558364
$239$	−1.05494	−0.0682387	−0.0341193	−	0.999418i	$-0.510863\pi$
$239$	−1.05494	−0.0682387	−0.0341193	+	0.999418i	$0.510863\pi$
$240$	2.95357	0.190652
$241$	10.5829	0.681707	0.340854	−	0.940116i	$-0.389284\pi$
$241$	10.5829	0.681707	0.340854	+	0.940116i	$0.389284\pi$
$242$	9.15110	0.588255
$243$	−17.9955	−1.15441
$244$	−14.2134	−0.909923
$245$	1.63011	0.104144
$246$	−29.8231	−1.90145
$247$	24.7061	1.57201
$248$	−1.00000	−0.0635001
$249$	6.77858	0.429575
$250$	8.58130	0.542729
$251$	25.5090	1.61012	0.805058	−	0.593196i	$-0.202134\pi$
$251$	25.5090	1.61012	0.805058	+	0.593196i	$0.202134\pi$
$252$	−15.6979	−0.988877
$253$	19.5510	1.22916
$254$	11.9878	0.752179
$255$	11.0840	0.694108
$256$	1.00000	0.0625000
$257$	−17.6678	−1.10209	−0.551043	−	0.834477i	$-0.685770\pi$
$257$	−17.6678	−1.10209	−0.551043	+	0.834477i	$0.685770\pi$
$258$	−11.4879	−0.715205
$259$	19.0328	1.18264
$260$	−4.53154	−0.281034
$261$	19.4059	1.20120
$262$	8.89234	0.549371
$263$	−23.0783	−1.42307	−0.711536	−	0.702650i	$-0.752000\pi$
$263$	−23.0783	−1.42307	−0.711536	+	0.702650i	$0.752000\pi$
$264$	−14.0806	−0.866604
$265$	3.20703	0.197006
$266$	−11.7839	−0.722519
$267$	−4.52005	−0.276623
$268$	0.506352	0.0309304
$269$	−0.785630	−0.0479007	−0.0239504	−	0.999713i	$-0.507624\pi$
$269$	−0.785630	−0.0479007	−0.0239504	+	0.999713i	$0.507624\pi$
$270$	11.3384	0.690036
$271$	−4.15512	−0.252405	−0.126203	−	0.992004i	$-0.540279\pi$
$271$	−4.15512	−0.252405	−0.126203	+	0.992004i	$0.540279\pi$
$272$	3.75274	0.227544
$273$	34.6498	2.09710
$274$	12.6451	0.763918
$275$	−18.4648	−1.11347
$276$	−13.6613	−0.822317
$277$	5.87005	0.352697	0.176349	−	0.984328i	$-0.443571\pi$
$277$	5.87005	0.352697	0.176349	+	0.984328i	$0.443571\pi$
$278$	−19.6201	−1.17674
$279$	−6.83889	−0.409434
$280$	2.16138	0.129167
$281$	−2.31717	−0.138231	−0.0691154	−	0.997609i	$-0.522018\pi$
$281$	−2.31717	−0.138231	−0.0691154	+	0.997609i	$0.522018\pi$
$282$	−11.9929	−0.714165
$283$	−13.8308	−0.822153	−0.411076	−	0.911601i	$-0.634847\pi$
$283$	−13.8308	−0.822153	−0.411076	+	0.911601i	$0.634847\pi$
$284$	3.18159	0.188793
$285$	15.1629	0.898170
$286$	21.6033	1.27743
$287$	−21.8241	−1.28823
$288$	6.83889	0.402985
$289$	−2.91691	−0.171583
$290$	−2.67192	−0.156901
$291$	3.13670	0.183877
$292$	−10.0252	−0.586678
$293$	6.54342	0.382271	0.191135	−	0.981564i	$-0.438783\pi$
$293$	6.54342	0.382271	0.191135	+	0.981564i	$0.438783\pi$
$294$	5.43019	0.316695
$295$	−12.5780	−0.732318
$296$	−8.29176	−0.481948
$297$	−54.0540	−3.13653
$298$	−19.6317	−1.13723
$299$	20.9600	1.21215
$300$	12.9024	0.744918
$301$	−8.40667	−0.484553
$302$	−2.70805	−0.155831
$303$	−1.68920	−0.0970419
$304$	5.13373	0.294440
$305$	13.3836	0.766345
$306$	25.6646	1.46715
$307$	−22.0324	−1.25746	−0.628728	−	0.777625i	$-0.716424\pi$
$307$	−22.0324	−1.25746	−0.628728	+	0.777625i	$0.716424\pi$
$308$	−10.3040	−0.587125
$309$	−19.4391	−1.10585
$310$	0.941618	0.0534803
$311$	18.0798	1.02521	0.512605	−	0.858625i	$-0.328681\pi$
$311$	18.0798	1.02521	0.512605	+	0.858625i	$0.328681\pi$
$312$	−15.0954	−0.854608
$313$	−6.25481	−0.353543	−0.176771	−	0.984252i	$-0.556565\pi$
$313$	−6.25481	−0.353543	−0.176771	+	0.984252i	$0.556565\pi$
$314$	14.1846	0.800485
$315$	14.7815	0.832841
$316$	2.49532	0.140373
$317$	−28.4942	−1.60039	−0.800197	−	0.599737i	$-0.795272\pi$
$317$	−28.4942	−1.60039	−0.800197	+	0.599737i	$0.795272\pi$
$318$	10.6832	0.599084
$319$	12.7379	0.713186
$320$	−0.941618	−0.0526381
$321$	0.502649	0.0280551
$322$	−9.99717	−0.557121
$323$	19.2656	1.07197
$324$	17.2538	0.958542
$325$	−19.7955	−1.09806
$326$	−12.3768	−0.685487
$327$	6.20750	0.343276
$328$	9.50778	0.524980
$329$	−8.77621	−0.483848
$330$	13.2586	0.729861
$331$	−22.6293	−1.24382	−0.621909	−	0.783089i	$-0.713643\pi$
$331$	−22.6293	−1.24382	−0.621909	+	0.783089i	$0.713643\pi$
$332$	−2.16106	−0.118603
$333$	−56.7064	−3.10749
$334$	12.6284	0.690993
$335$	−0.476790	−0.0260498
$336$	7.19996	0.392790
$337$	2.14203	0.116684	0.0583419	−	0.998297i	$-0.481419\pi$
$337$	2.14203	0.116684	0.0583419	+	0.998297i	$0.481419\pi$
$338$	10.1602	0.552643
$339$	−0.233200	−0.0126657
$340$	−3.53365	−0.191639
$341$	−4.48900	−0.243093
$342$	35.1090	1.89848
$343$	20.0415	1.08214
$344$	3.66241	0.197464
$345$	12.8638	0.692562
$346$	11.0290	0.592923
$347$	−7.96052	−0.427343	−0.213672	−	0.976906i	$-0.568542\pi$
$347$	−7.96052	−0.427343	−0.213672	+	0.976906i	$0.568542\pi$
$348$	−8.90065	−0.477125
$349$	36.1026	1.93253	0.966264	−	0.257554i	$-0.0829165\pi$
$349$	36.1026	1.93253	0.966264	+	0.257554i	$0.0829165\pi$
$350$	9.44176	0.504683
$351$	−57.9496	−3.09312
$352$	4.48900	0.239264
$353$	−26.3994	−1.40510	−0.702550	−	0.711634i	$-0.747955\pi$
$353$	−26.3994	−1.40510	−0.702550	+	0.711634i	$0.747955\pi$
$354$	−41.8995	−2.22693
$355$	−2.99584	−0.159003
$356$	1.44102	0.0763739
$357$	27.0196	1.43003
$358$	13.4630	0.711540
$359$	−11.0859	−0.585091	−0.292545	−	0.956252i	$-0.594502\pi$
$359$	−11.0859	−0.585091	−0.292545	+	0.956252i	$0.594502\pi$
$360$	−6.43962	−0.339398
$361$	7.35520	0.387116
$362$	7.16751	0.376716
$363$	−28.7043	−1.50658
$364$	−11.0466	−0.578998
$365$	9.43987	0.494105
$366$	44.5833	2.33041
$367$	21.5701	1.12595	0.562975	−	0.826474i	$-0.309657\pi$
$367$	21.5701	1.12595	0.562975	+	0.826474i	$0.309657\pi$
$368$	4.35532	0.227037
$369$	65.0227	3.38495
$370$	7.80767	0.405901
$371$	7.81780	0.405880
$372$	3.13670	0.162630
$373$	20.7444	1.07410	0.537051	−	0.843550i	$-0.319538\pi$
$373$	20.7444	1.07410	0.537051	+	0.843550i	$0.319538\pi$
$374$	16.8461	0.871089
$375$	−26.9170	−1.38999
$376$	3.82340	0.197177
$377$	13.6559	0.703314
$378$	27.6398	1.42164
$379$	−4.31693	−0.221746	−0.110873	−	0.993835i	$-0.535365\pi$
$379$	−4.31693	−0.221746	−0.110873	+	0.993835i	$0.535365\pi$
$380$	−4.83402	−0.247980
$381$	−37.6020	−1.92641
$382$	0.868376	0.0444300
$383$	−16.0610	−0.820678	−0.410339	−	0.911933i	$-0.634590\pi$
$383$	−16.0610	−0.820678	−0.410339	+	0.911933i	$0.634590\pi$
$384$	−3.13670	−0.160069
$385$	9.70244	0.494482
$386$	−24.5080	−1.24743
$387$	25.0468	1.27320
$388$	−1.00000	−0.0507673
$389$	20.1797	1.02315	0.511576	−	0.859238i	$-0.329062\pi$
$389$	20.1797	1.02315	0.511576	+	0.859238i	$0.329062\pi$
$390$	14.2141	0.719759
$391$	16.3444	0.826573
$392$	−1.73118	−0.0874377
$393$	−27.8926	−1.40700
$394$	−5.22238	−0.263099
$395$	−2.34964	−0.118223
$396$	30.6998	1.54272
$397$	8.60858	0.432052	0.216026	−	0.976388i	$-0.430690\pi$
$397$	8.60858	0.432052	0.216026	+	0.976388i	$0.430690\pi$
$398$	18.2702	0.915801
$399$	36.9626	1.85045
$400$	−4.11336	−0.205668
$401$	33.1300	1.65443	0.827215	−	0.561885i	$-0.189924\pi$
$401$	33.1300	1.65443	0.827215	+	0.561885i	$0.189924\pi$
$402$	−1.58827	−0.0792159
$403$	−4.81251	−0.239728
$404$	0.538527	0.0267927
$405$	−16.2464	−0.807293
$406$	−6.51336	−0.323253
$407$	−37.2217	−1.84501
$408$	−11.7712	−0.582763
$409$	37.2470	1.84175	0.920873	−	0.389863i	$-0.127478\pi$
$409$	37.2470	1.84175	0.920873	+	0.389863i	$0.127478\pi$
$410$	−8.95270	−0.442142
$411$	−39.6639	−1.95648
$412$	6.19731	0.305320
$413$	−30.6615	−1.50875
$414$	29.7856	1.46388
$415$	2.03489	0.0998888
$416$	4.81251	0.235953
$417$	61.5424	3.01375
$418$	23.0453	1.12718
$419$	−9.87647	−0.482497	−0.241249	−	0.970463i	$-0.577557\pi$
$419$	−9.87647	−0.482497	−0.241249	+	0.970463i	$0.577557\pi$
$420$	−6.77961	−0.330811
$421$	1.90405	0.0927977	0.0463989	−	0.998923i	$-0.485225\pi$
$421$	1.90405	0.0927977	0.0463989	+	0.998923i	$0.485225\pi$
$422$	1.40257	0.0682759
$423$	26.1478	1.27135
$424$	−3.40587	−0.165404
$425$	−15.4364	−0.748774
$426$	−9.97970	−0.483518
$427$	32.6254	1.57886
$428$	−0.160248	−0.00774587
$429$	−67.7632	−3.27164
$430$	−3.44860	−0.166306
$431$	28.4697	1.37134	0.685669	−	0.727914i	$-0.259510\pi$
$431$	28.4697	1.37134	0.685669	+	0.727914i	$0.259510\pi$
$432$	−12.0415	−0.579345
$433$	−34.9553	−1.67984	−0.839921	−	0.542708i	$-0.817399\pi$
$433$	−34.9553	−1.67984	−0.839921	+	0.542708i	$0.817399\pi$
$434$	2.29539	0.110182
$435$	8.38101	0.401839
$436$	−1.97899	−0.0947765
$437$	22.3591	1.06958
$438$	31.4459	1.50254
$439$	−34.2515	−1.63473	−0.817366	−	0.576118i	$-0.804567\pi$
$439$	−34.2515	−1.63473	−0.817366	+	0.576118i	$0.804567\pi$
$440$	−4.22692	−0.201511
$441$	−11.8393	−0.563778
$442$	18.0601	0.859032
$443$	14.8825	0.707087	0.353543	−	0.935418i	$-0.384977\pi$
$443$	14.8825	0.707087	0.353543	+	0.935418i	$0.384977\pi$
$444$	26.0088	1.23432
$445$	−1.35689	−0.0643228
$446$	14.5891	0.690815
$447$	61.5787	2.91257
$448$	−2.29539	−0.108447
$449$	31.3017	1.47722	0.738608	−	0.674135i	$-0.235483\pi$
$449$	31.3017	1.47722	0.738608	+	0.674135i	$0.235483\pi$
$450$	−28.1308	−1.32610
$451$	42.6804	2.00974
$452$	0.0743457	0.00349693
$453$	8.49433	0.399099
$454$	−3.75780	−0.176362
$455$	10.4017	0.487638
$456$	−16.1030	−0.754091
$457$	−18.7270	−0.876011	−0.438006	−	0.898972i	$-0.644315\pi$
$457$	−18.7270	−0.876011	−0.438006	+	0.898972i	$0.644315\pi$
$458$	17.2074	0.804049
$459$	−45.1885	−2.10922
$460$	−4.10105	−0.191213
$461$	−31.1408	−1.45037	−0.725187	−	0.688552i	$-0.758247\pi$
$461$	−31.1408	−1.45037	−0.725187	+	0.688552i	$0.758247\pi$
$462$	32.3206	1.50369
$463$	−15.1702	−0.705017	−0.352509	−	0.935809i	$-0.614671\pi$
$463$	−15.1702	−0.705017	−0.352509	+	0.935809i	$0.614671\pi$
$464$	2.83758	0.131731
$465$	−2.95357	−0.136969
$466$	−26.6071	−1.23255
$467$	0.662805	0.0306709	0.0153355	−	0.999882i	$-0.495118\pi$
$467$	0.662805	0.0306709	0.0153355	+	0.999882i	$0.495118\pi$
$468$	32.9122	1.52137
$469$	−1.16228	−0.0536689
$470$	−3.60019	−0.166064
$471$	−44.4929	−2.05013
$472$	13.3578	0.614844
$473$	16.4406	0.755938
$474$	−7.82708	−0.359510
$475$	−21.1169	−0.968908
$476$	−8.61402	−0.394823
$477$	−23.2924	−1.06648
$478$	−1.05494	−0.0482520
$479$	−35.8312	−1.63717	−0.818584	−	0.574387i	$-0.805240\pi$
$479$	−35.8312	−1.63717	−0.818584	+	0.574387i	$0.805240\pi$
$480$	2.95357	0.134812
$481$	−39.9041	−1.81947
$482$	10.5829	0.482040
$483$	31.3581	1.42684
$484$	9.15110	0.415959
$485$	0.941618	0.0427567
$486$	−17.9955	−0.816293
$487$	19.0203	0.861893	0.430947	−	0.902377i	$-0.358180\pi$
$487$	19.0203	0.861893	0.430947	+	0.902377i	$0.358180\pi$
$488$	−14.2134	−0.643413
$489$	38.8223	1.75561
$490$	1.63011	0.0736408
$491$	−5.01281	−0.226225	−0.113112	−	0.993582i	$-0.536082\pi$
$491$	−5.01281	−0.226225	−0.113112	+	0.993582i	$0.536082\pi$
$492$	−29.8231	−1.34453
$493$	10.6487	0.479594
$494$	24.7061	1.11158
$495$	−28.9075	−1.29929
$496$	−1.00000	−0.0449013
$497$	−7.30299	−0.327584
$498$	6.77858	0.303756
$499$	17.8097	0.797270	0.398635	−	0.917110i	$-0.369484\pi$
$499$	17.8097	0.797270	0.398635	+	0.917110i	$0.369484\pi$
$500$	8.58130	0.383767
$501$	−39.6114	−1.76971
$502$	25.5090	1.13852
$503$	14.7890	0.659410	0.329705	−	0.944084i	$-0.393051\pi$
$503$	14.7890	0.659410	0.329705	+	0.944084i	$0.393051\pi$
$504$	−15.6979	−0.699241
$505$	−0.507087	−0.0225651
$506$	19.5510	0.869150
$507$	−31.8696	−1.41538
$508$	11.9878	0.531871
$509$	22.8839	1.01431	0.507157	−	0.861854i	$-0.330697\pi$
$509$	22.8839	1.01431	0.507157	+	0.861854i	$0.330697\pi$
$510$	11.0840	0.490808
$511$	23.0117	1.01798
$512$	1.00000	0.0441942
$513$	−61.8176	−2.72931
$514$	−17.6678	−0.779292
$515$	−5.83550	−0.257143
$516$	−11.4879	−0.505726
$517$	17.1633	0.754839
$518$	19.0328	0.836254
$519$	−34.5947	−1.51854
$520$	−4.53154	−0.198721
$521$	44.1321	1.93346	0.966730	−	0.255797i	$-0.0823380\pi$
$521$	44.1321	1.93346	0.966730	+	0.255797i	$0.0823380\pi$
$522$	19.4059	0.849374
$523$	18.8438	0.823981	0.411991	−	0.911188i	$-0.364834\pi$
$523$	18.8438	0.823981	0.411991	+	0.911188i	$0.364834\pi$
$524$	8.89234	0.388464
$525$	−29.6160	−1.29255
$526$	−23.0783	−1.00626
$527$	−3.75274	−0.163472
$528$	−14.0806	−0.612781
$529$	−4.03115	−0.175267
$530$	3.20703	0.139304
$531$	91.3528	3.96437
$532$	−11.7839	−0.510898
$533$	45.7563	1.98192
$534$	−4.52005	−0.195602
$535$	0.150892	0.00652364
$536$	0.506352	0.0218711
$537$	−42.2293	−1.82233
$538$	−0.785630	−0.0338709
$539$	−7.77126	−0.334732
$540$	11.3384	0.487929
$541$	9.71884	0.417846	0.208923	−	0.977932i	$-0.433004\pi$
$541$	9.71884	0.417846	0.208923	+	0.977932i	$0.433004\pi$
$542$	−4.15512	−0.178478
$543$	−22.4823	−0.964809
$544$	3.75274	0.160898
$545$	1.86345	0.0798216
$546$	34.6498	1.48288
$547$	−26.2584	−1.12273	−0.561364	−	0.827569i	$-0.689723\pi$
$547$	−26.2584	−1.12273	−0.561364	+	0.827569i	$0.689723\pi$
$548$	12.6451	0.540172
$549$	−97.2042	−4.14858
$550$	−18.4648	−0.787344
$551$	14.5674	0.620592
$552$	−13.6613	−0.581466
$553$	−5.72775	−0.243569
$554$	5.87005	0.249394
$555$	−24.4903	−1.03956
$556$	−19.6201	−0.832078
$557$	29.2732	1.24035	0.620173	−	0.784465i	$-0.287062\pi$
$557$	29.2732	1.24035	0.620173	+	0.784465i	$0.287062\pi$
$558$	−6.83889	−0.289513
$559$	17.6254	0.745475
$560$	2.16138	0.0913351
$561$	−52.8411	−2.23095
$562$	−2.31717	−0.0977439
$563$	15.5399	0.654929	0.327465	−	0.944863i	$-0.393806\pi$
$563$	15.5399	0.654929	0.327465	+	0.944863i	$0.393806\pi$
$564$	−11.9929	−0.504991
$565$	−0.0700052	−0.00294514
$566$	−13.8308	−0.581350
$567$	−39.6041	−1.66322
$568$	3.18159	0.133497
$569$	−32.5446	−1.36434	−0.682170	−	0.731193i	$-0.738964\pi$
$569$	−32.5446	−1.36434	−0.682170	+	0.731193i	$0.738964\pi$
$570$	15.1629	0.635102
$571$	−7.91983	−0.331435	−0.165717	−	0.986173i	$-0.552994\pi$
$571$	−7.91983	−0.331435	−0.165717	+	0.986173i	$0.552994\pi$
$572$	21.6033	0.903281
$573$	−2.72383	−0.113790
$574$	−21.8241	−0.910920
$575$	−17.9150	−0.747107
$576$	6.83889	0.284954
$577$	0.689268	0.0286946	0.0143473	−	0.999897i	$-0.495433\pi$
$577$	0.689268	0.0286946	0.0143473	+	0.999897i	$0.495433\pi$
$578$	−2.91691	−0.121327
$579$	76.8743	3.19479
$580$	−2.67192	−0.110945
$581$	4.96047	0.205795
$582$	3.13670	0.130020
$583$	−15.2889	−0.633203
$584$	−10.0252	−0.414844
$585$	−30.9907	−1.28131
$586$	6.54342	0.270306
$587$	19.3050	0.796801	0.398401	−	0.917211i	$-0.369565\pi$
$587$	19.3050	0.796801	0.398401	+	0.917211i	$0.369565\pi$
$588$	5.43019	0.223937
$589$	−5.13373	−0.211532
$590$	−12.5780	−0.517827
$591$	16.3810	0.673825
$592$	−8.29176	−0.340789
$593$	−21.1610	−0.868977	−0.434489	−	0.900677i	$-0.643071\pi$
$593$	−21.1610	−0.868977	−0.434489	+	0.900677i	$0.643071\pi$
$594$	−54.0540	−2.21786
$595$	8.11112	0.332523
$596$	−19.6317	−0.804144
$597$	−57.3081	−2.34546
$598$	20.9600	0.857119
$599$	44.2548	1.80820	0.904102	−	0.427317i	$-0.140541\pi$
$599$	44.2548	1.80820	0.904102	+	0.427317i	$0.140541\pi$
$600$	12.9024	0.526737
$601$	13.8582	0.565286	0.282643	−	0.959225i	$-0.408789\pi$
$601$	13.8582	0.565286	0.282643	+	0.959225i	$0.408789\pi$
$602$	−8.40667	−0.342630
$603$	3.46288	0.141020
$604$	−2.70805	−0.110189
$605$	−8.61685	−0.350325
$606$	−1.68920	−0.0686190
$607$	−23.4270	−0.950872	−0.475436	−	0.879750i	$-0.657710\pi$
$607$	−23.4270	−0.950872	−0.475436	+	0.879750i	$0.657710\pi$
$608$	5.13373	0.208200
$609$	20.4305	0.827884
$610$	13.3836	0.541888
$611$	18.4002	0.744391
$612$	25.6646	1.03743
$613$	4.02416	0.162534	0.0812672	−	0.996692i	$-0.474103\pi$
$613$	4.02416	0.162534	0.0812672	+	0.996692i	$0.474103\pi$
$614$	−22.0324	−0.889156
$615$	28.0819	1.13237
$616$	−10.3040	−0.415160
$617$	−6.79494	−0.273554	−0.136777	−	0.990602i	$-0.543674\pi$
$617$	−6.79494	−0.273554	−0.136777	+	0.990602i	$0.543674\pi$
$618$	−19.4391	−0.781956
$619$	13.2390	0.532121	0.266060	−	0.963956i	$-0.414278\pi$
$619$	13.2390	0.532121	0.266060	+	0.963956i	$0.414278\pi$
$620$	0.941618	0.0378163
$621$	−52.4444	−2.10452
$622$	18.0798	0.724932
$623$	−3.30771	−0.132520
$624$	−15.0954	−0.604299
$625$	12.4865	0.499459
$626$	−6.25481	−0.249992
$627$	−72.2862	−2.88683
$628$	14.1846	0.566028
$629$	−31.1168	−1.24071
$630$	14.7815	0.588907
$631$	−0.366596	−0.0145940	−0.00729699	−	0.999973i	$-0.502323\pi$
$631$	−0.366596	−0.0145940	−0.00729699	+	0.999973i	$0.502323\pi$
$632$	2.49532	0.0992587
$633$	−4.39944	−0.174862
$634$	−28.4942	−1.13165
$635$	−11.2879	−0.447946
$636$	10.6832	0.423616
$637$	−8.33131	−0.330098
$638$	12.7379	0.504298
$639$	21.7585	0.860755
$640$	−0.941618	−0.0372207
$641$	−19.6955	−0.777925	−0.388963	−	0.921253i	$-0.627167\pi$
$641$	−19.6955	−0.777925	−0.388963	+	0.921253i	$0.627167\pi$
$642$	0.502649	0.0198380
$643$	0.512586	0.0202144	0.0101072	−	0.999949i	$-0.496783\pi$
$643$	0.512586	0.0202144	0.0101072	+	0.999949i	$0.496783\pi$
$644$	−9.99717	−0.393944
$645$	10.8172	0.425927
$646$	19.2656	0.757994
$647$	−1.03975	−0.0408770	−0.0204385	−	0.999791i	$-0.506506\pi$
$647$	−1.03975	−0.0408770	−0.0204385	+	0.999791i	$0.506506\pi$
$648$	17.2538	0.677791
$649$	59.9633	2.35377
$650$	−19.7955	−0.776445
$651$	−7.19996	−0.282189
$652$	−12.3768	−0.484713
$653$	8.45935	0.331040	0.165520	−	0.986206i	$-0.447070\pi$
$653$	8.45935	0.331040	0.165520	+	0.986206i	$0.447070\pi$
$654$	6.20750	0.242733
$655$	−8.37319	−0.327168
$656$	9.50778	0.371217
$657$	−68.5609	−2.67482
$658$	−8.77621	−0.342132
$659$	−43.1042	−1.67910	−0.839550	−	0.543282i	$-0.817181\pi$
$659$	−43.1042	−1.67910	−0.839550	+	0.543282i	$0.817181\pi$
$660$	13.2586	0.516090
$661$	17.0452	0.662980	0.331490	−	0.943459i	$-0.392449\pi$
$661$	17.0452	0.662980	0.331490	+	0.943459i	$0.392449\pi$
$662$	−22.6293	−0.879513
$663$	−56.6491	−2.20007
$664$	−2.16106	−0.0838652
$665$	11.0960	0.430283
$666$	−56.7064	−2.19733
$667$	12.3586	0.478527
$668$	12.6284	0.488606
$669$	−45.7617	−1.76925
$670$	−0.476790	−0.0184200
$671$	−63.8041	−2.46313
$672$	7.19996	0.277744
$673$	−31.0731	−1.19778	−0.598890	−	0.800831i	$-0.704392\pi$
$673$	−31.0731	−1.19778	−0.598890	+	0.800831i	$0.704392\pi$
$674$	2.14203	0.0825079
$675$	49.5308	1.90644
$676$	10.1602	0.390778
$677$	36.4764	1.40190	0.700951	−	0.713209i	$-0.252759\pi$
$677$	36.4764	1.40190	0.700951	+	0.713209i	$0.252759\pi$
$678$	−0.233200	−0.00895599
$679$	2.29539	0.0880890
$680$	−3.53365	−0.135509
$681$	11.7871	0.451682
$682$	−4.48900	−0.171893
$683$	12.8080	0.490083	0.245042	−	0.969513i	$-0.421198\pi$
$683$	12.8080	0.490083	0.245042	+	0.969513i	$0.421198\pi$
$684$	35.1090	1.34243
$685$	−11.9069	−0.454938
$686$	20.0415	0.765187
$687$	−53.9745	−2.05925
$688$	3.66241	0.139628
$689$	−16.3908	−0.624438
$690$	12.8638	0.489716
$691$	11.2502	0.427978	0.213989	−	0.976836i	$-0.431354\pi$
$691$	11.2502	0.427978	0.213989	+	0.976836i	$0.431354\pi$
$692$	11.0290	0.419260
$693$	−70.4680	−2.67686
$694$	−7.96052	−0.302177
$695$	18.4747	0.700784
$696$	−8.90065	−0.337378
$697$	35.6803	1.35149
$698$	36.1026	1.36650
$699$	83.4585	3.15669
$700$	9.44176	0.356865
$701$	45.9074	1.73390	0.866949	−	0.498397i	$-0.166078\pi$
$701$	45.9074	1.73390	0.866949	+	0.498397i	$0.166078\pi$
$702$	−57.9496	−2.18717
$703$	−42.5676	−1.60547
$704$	4.48900	0.169185
$705$	11.2927	0.425308
$706$	−26.3994	−0.993556
$707$	−1.23613	−0.0464895
$708$	−41.8995	−1.57468
$709$	18.2103	0.683903	0.341951	−	0.939718i	$-0.388912\pi$
$709$	18.2103	0.683903	0.341951	+	0.939718i	$0.388912\pi$
$710$	−2.99584	−0.112432
$711$	17.0652	0.639997
$712$	1.44102	0.0540045
$713$	−4.35532	−0.163108
$714$	27.0196	1.01118
$715$	−20.3421	−0.760751
$716$	13.4630	0.503135
$717$	3.30905	0.123579
$718$	−11.0859	−0.413722
$719$	−19.7726	−0.737395	−0.368697	−	0.929549i	$-0.620196\pi$
$719$	−19.7726	−0.737395	−0.368697	+	0.929549i	$0.620196\pi$
$720$	−6.43962	−0.239991
$721$	−14.2253	−0.529776
$722$	7.35520	0.273732
$723$	−33.1955	−1.23455
$724$	7.16751	0.266378
$725$	−11.6720	−0.433487
$726$	−28.7043	−1.06532
$727$	−40.6714	−1.50842	−0.754210	−	0.656633i	$-0.771980\pi$
$727$	−40.6714	−1.50842	−0.754210	+	0.656633i	$0.771980\pi$
$728$	−11.0466	−0.409414
$729$	4.68526	0.173528
$730$	9.43987	0.349385
$731$	13.7441	0.508344
$732$	44.5833	1.64785
$733$	49.9604	1.84533	0.922665	−	0.385601i	$-0.126006\pi$
$733$	49.9604	1.84533	0.922665	+	0.385601i	$0.126006\pi$
$734$	21.5701	0.796167
$735$	−5.11316	−0.188602
$736$	4.35532	0.160539
$737$	2.27301	0.0837275
$738$	65.0227	2.39352
$739$	21.9914	0.808965	0.404482	−	0.914546i	$-0.367452\pi$
$739$	21.9914	0.808965	0.404482	+	0.914546i	$0.367452\pi$
$740$	7.80767	0.287016
$741$	−77.4957	−2.84688
$742$	7.81780	0.287001
$743$	−42.6877	−1.56606	−0.783030	−	0.621984i	$-0.786327\pi$
$743$	−42.6877	−1.56606	−0.783030	+	0.621984i	$0.786327\pi$
$744$	3.13670	0.114997
$745$	18.4855	0.677258
$746$	20.7444	0.759505
$747$	−14.7792	−0.540743
$748$	16.8461	0.615953
$749$	0.367831	0.0134403
$750$	−26.9170	−0.982869
$751$	43.8860	1.60142	0.800712	−	0.599049i	$-0.204455\pi$
$751$	43.8860	1.60142	0.800712	+	0.599049i	$0.204455\pi$
$752$	3.82340	0.139425
$753$	−80.0142	−2.91588
$754$	13.6559	0.497318
$755$	2.54995	0.0928021
$756$	27.6398	1.00525
$757$	21.0469	0.764962	0.382481	−	0.923963i	$-0.375070\pi$
$757$	21.0469	0.764962	0.382481	+	0.923963i	$0.375070\pi$
$758$	−4.31693	−0.156798
$759$	−61.3258	−2.22598
$760$	−4.83402	−0.175348
$761$	−5.74909	−0.208404	−0.104202	−	0.994556i	$-0.533229\pi$
$761$	−5.74909	−0.208404	−0.104202	+	0.994556i	$0.533229\pi$
$762$	−37.6020	−1.36218
$763$	4.54256	0.164452
$764$	0.868376	0.0314167
$765$	−24.1663	−0.873733
$766$	−16.0610	−0.580307
$767$	64.2847	2.32118
$768$	−3.13670	−0.113186
$769$	−32.8704	−1.18534	−0.592668	−	0.805447i	$-0.701925\pi$
$769$	−32.8704	−1.18534	−0.592668	+	0.805447i	$0.701925\pi$
$770$	9.70244	0.349652
$771$	55.4185	1.99585
$772$	−24.5080	−0.882063
$773$	8.98312	0.323100	0.161550	−	0.986864i	$-0.448351\pi$
$773$	8.98312	0.323100	0.161550	+	0.986864i	$0.448351\pi$
$774$	25.0468	0.900290
$775$	4.11336	0.147756
$776$	−1.00000	−0.0358979
$777$	−59.7003	−2.14174
$778$	20.1797	0.723477
$779$	48.8104	1.74881
$780$	14.2141	0.508946
$781$	14.2822	0.511056
$782$	16.3444	0.584475
$783$	−34.1686	−1.22109
$784$	−1.73118	−0.0618278
$785$	−13.3565	−0.476714
$786$	−27.8926	−0.994896
$787$	−42.8095	−1.52599	−0.762996	−	0.646403i	$-0.776273\pi$
$787$	−42.8095	−1.52599	−0.762996	+	0.646403i	$0.776273\pi$
$788$	−5.22238	−0.186039
$789$	72.3898	2.57715
$790$	−2.34964	−0.0835965
$791$	−0.170652	−0.00606770
$792$	30.6998	1.09087
$793$	−68.4023	−2.42904
$794$	8.60858	0.305507
$795$	−10.0595	−0.356773
$796$	18.2702	0.647569
$797$	−12.9086	−0.457246	−0.228623	−	0.973515i	$-0.573422\pi$
$797$	−12.9086	−0.457246	−0.228623	+	0.973515i	$0.573422\pi$
$798$	36.9626	1.30846
$799$	14.3483	0.507605
$800$	−4.11336	−0.145429
$801$	9.85498	0.348209
$802$	33.1300	1.16986
$803$	−45.0029	−1.58812
$804$	−1.58827	−0.0560141
$805$	9.41352	0.331783
$806$	−4.81251	−0.169513
$807$	2.46429	0.0867470
$808$	0.538527	0.0189453
$809$	−6.87311	−0.241646	−0.120823	−	0.992674i	$-0.538553\pi$
$809$	−6.87311	−0.241646	−0.120823	+	0.992674i	$0.538553\pi$
$810$	−16.2464	−0.570842
$811$	−28.8667	−1.01365	−0.506824	−	0.862050i	$-0.669181\pi$
$811$	−28.8667	−1.01365	−0.506824	+	0.862050i	$0.669181\pi$
$812$	−6.51336	−0.228574
$813$	13.0334	0.457100
$814$	−37.2217	−1.30462
$815$	11.6542	0.408229
$816$	−11.7712	−0.412076
$817$	18.8019	0.657793
$818$	37.2470	1.30231
$819$	−75.5464	−2.63980
$820$	−8.95270	−0.312642
$821$	−26.9867	−0.941841	−0.470920	−	0.882176i	$-0.656078\pi$
$821$	−26.9867	−0.941841	−0.470920	+	0.882176i	$0.656078\pi$
$822$	−39.6639	−1.38344
$823$	40.5909	1.41491	0.707455	−	0.706759i	$-0.249843\pi$
$823$	40.5909	1.41491	0.707455	+	0.706759i	$0.249843\pi$
$824$	6.19731	0.215894
$825$	57.9187	2.01647
$826$	−30.6615	−1.06685
$827$	41.6808	1.44938	0.724692	−	0.689073i	$-0.241982\pi$
$827$	41.6808	1.44938	0.724692	+	0.689073i	$0.241982\pi$
$828$	29.7856	1.03512
$829$	−6.86472	−0.238422	−0.119211	−	0.992869i	$-0.538036\pi$
$829$	−6.86472	−0.238422	−0.119211	+	0.992869i	$0.538036\pi$
$830$	2.03489	0.0706320
$831$	−18.4126	−0.638725
$832$	4.81251	0.166844
$833$	−6.49667	−0.225096
$834$	61.5424	2.13104
$835$	−11.8911	−0.411508
$836$	23.0453	0.797039
$837$	12.0415	0.416213
$838$	−9.87647	−0.341177
$839$	−17.9514	−0.619751	−0.309875	−	0.950777i	$-0.600287\pi$
$839$	−17.9514	−0.619751	−0.309875	+	0.950777i	$0.600287\pi$
$840$	−6.77961	−0.233919
$841$	−20.9481	−0.722349
$842$	1.90405	0.0656179
$843$	7.26827	0.250332
$844$	1.40257	0.0482784
$845$	−9.56704	−0.329116
$846$	26.1478	0.898981
$847$	−21.0054	−0.721753
$848$	−3.40587	−0.116958
$849$	43.3829	1.48890
$850$	−15.4364	−0.529463
$851$	−36.1133	−1.23795
$852$	−9.97970	−0.341899
$853$	29.8240	1.02115	0.510576	−	0.859832i	$-0.329432\pi$
$853$	29.8240	1.02115	0.510576	+	0.859832i	$0.329432\pi$
$854$	32.6254	1.11642
$855$	−33.0593	−1.13060
$856$	−0.160248	−0.00547716
$857$	−31.6639	−1.08162	−0.540810	−	0.841145i	$-0.681882\pi$
$857$	−31.6639	−1.08162	−0.540810	+	0.841145i	$0.681882\pi$
$858$	−67.7632	−2.31340
$859$	8.89678	0.303554	0.151777	−	0.988415i	$-0.451500\pi$
$859$	8.89678	0.303554	0.151777	+	0.988415i	$0.451500\pi$
$860$	−3.44860	−0.117596
$861$	68.4556	2.33296
$862$	28.4697	0.969682
$863$	40.4669	1.37751	0.688754	−	0.724995i	$-0.258158\pi$
$863$	40.4669	1.37751	0.688754	+	0.724995i	$0.258158\pi$
$864$	−12.0415	−0.409658
$865$	−10.3851	−0.353104
$866$	−34.9553	−1.18783
$867$	9.14947	0.310732
$868$	2.29539	0.0779107
$869$	11.2015	0.379985
$870$	8.38101	0.284143
$871$	2.43682	0.0825685
$872$	−1.97899	−0.0670171
$873$	−6.83889	−0.231461
$874$	22.3591	0.756307
$875$	−19.6974	−0.665895
$876$	31.4459	1.06246
$877$	−29.0342	−0.980415	−0.490207	−	0.871606i	$-0.663079\pi$
$877$	−29.0342	−0.980415	−0.490207	+	0.871606i	$0.663079\pi$
$878$	−34.2515	−1.15593
$879$	−20.5248	−0.692283
$880$	−4.22692	−0.142490
$881$	−48.7200	−1.64142	−0.820709	−	0.571347i	$-0.806421\pi$
$881$	−48.7200	−1.64142	−0.820709	+	0.571347i	$0.806421\pi$
$882$	−11.8393	−0.398651
$883$	−40.6812	−1.36903	−0.684515	−	0.728999i	$-0.739986\pi$
$883$	−40.6812	−1.36903	−0.684515	+	0.728999i	$0.739986\pi$
$884$	18.0601	0.607427
$885$	39.4534	1.32621
$886$	14.8825	0.499986
$887$	−19.7996	−0.664804	−0.332402	−	0.943138i	$-0.607859\pi$
$887$	−19.7996	−0.664804	−0.332402	+	0.943138i	$0.607859\pi$
$888$	26.0088	0.872797
$889$	−27.5166	−0.922877
$890$	−1.35689	−0.0454831
$891$	77.4521	2.59474
$892$	14.5891	0.488480
$893$	19.6283	0.656837
$894$	61.5787	2.05950
$895$	−12.6770	−0.423745
$896$	−2.29539	−0.0766836
$897$	−65.7453	−2.19517
$898$	31.3017	1.04455
$899$	−2.83758	−0.0946387
$900$	−28.1308	−0.937693
$901$	−12.7814	−0.425809
$902$	42.6804	1.42110
$903$	26.3692	0.877513
$904$	0.0743457	0.00247270
$905$	−6.74906	−0.224346
$906$	8.49433	0.282205
$907$	37.0798	1.23121	0.615607	−	0.788053i	$-0.288911\pi$
$907$	37.0798	1.23121	0.615607	+	0.788053i	$0.288911\pi$
$908$	−3.75780	−0.124707
$909$	3.68293	0.122155
$910$	10.4017	0.344812
$911$	47.3975	1.57035	0.785175	−	0.619273i	$-0.212573\pi$
$911$	47.3975	1.57035	0.785175	+	0.619273i	$0.212573\pi$
$912$	−16.1030	−0.533223
$913$	−9.70097	−0.321055
$914$	−18.7270	−0.619434
$915$	−41.9805	−1.38783
$916$	17.2074	0.568549
$917$	−20.4114	−0.674044
$918$	−45.1885	−1.49144
$919$	−5.04463	−0.166407	−0.0832035	−	0.996533i	$-0.526515\pi$
$919$	−5.04463	−0.166407	−0.0832035	+	0.996533i	$0.526515\pi$
$920$	−4.10105	−0.135208
$921$	69.1091	2.27722
$922$	−31.1408	−1.02557
$923$	15.3114	0.503982
$924$	32.3206	1.06327
$925$	34.1069	1.12143
$926$	−15.1702	−0.498522
$927$	42.3827	1.39203
$928$	2.83758	0.0931482
$929$	22.2416	0.729723	0.364862	−	0.931062i	$-0.381116\pi$
$929$	22.2416	0.729723	0.364862	+	0.931062i	$0.381116\pi$
$930$	−2.95357	−0.0968515
$931$	−8.88741	−0.291273
$932$	−26.6071	−0.871544
$933$	−56.7108	−1.85663
$934$	0.662805	0.0216876
$935$	−15.8626	−0.518761
$936$	32.9122	1.07577
$937$	−2.72283	−0.0889511	−0.0444755	−	0.999010i	$-0.514162\pi$
$937$	−2.72283	−0.0889511	−0.0444755	+	0.999010i	$0.514162\pi$
$938$	−1.16228	−0.0379496
$939$	19.6195	0.640257
$940$	−3.60019	−0.117425
$941$	22.1672	0.722631	0.361315	−	0.932444i	$-0.382328\pi$
$941$	22.1672	0.722631	0.361315	+	0.932444i	$0.382328\pi$
$942$	−44.4929	−1.44966
$943$	41.4095	1.34848
$944$	13.3578	0.434760
$945$	−26.0262	−0.846632
$946$	16.4406	0.534529
$947$	7.80788	0.253722	0.126861	−	0.991921i	$-0.459510\pi$
$947$	7.80788	0.253722	0.126861	+	0.991921i	$0.459510\pi$
$948$	−7.82708	−0.254212
$949$	−48.2461	−1.56614
$950$	−21.1169	−0.685121
$951$	89.3778	2.89827
$952$	−8.61402	−0.279182
$953$	27.2865	0.883897	0.441949	−	0.897040i	$-0.354287\pi$
$953$	27.2865	0.883897	0.441949	+	0.897040i	$0.354287\pi$
$954$	−23.2924	−0.754118
$955$	−0.817678	−0.0264594
$956$	−1.05494	−0.0341193
$957$	−39.9550	−1.29156
$958$	−35.8312	−1.15765
$959$	−29.0254	−0.937281
$960$	2.95357	0.0953262
$961$	1.00000	0.0322581
$962$	−39.9041	−1.28656
$963$	−1.09592	−0.0353154
$964$	10.5829	0.340854
$965$	23.0772	0.742881
$966$	31.3581	1.00893
$967$	−26.3563	−0.847562	−0.423781	−	0.905765i	$-0.639297\pi$
$967$	−26.3563	−0.847562	−0.423781	+	0.905765i	$0.639297\pi$
$968$	9.15110	0.294128
$969$	−60.4304	−1.94130
$970$	0.941618	0.0302335
$971$	6.43375	0.206469	0.103234	−	0.994657i	$-0.467081\pi$
$971$	6.43375	0.206469	0.103234	+	0.994657i	$0.467081\pi$
$972$	−17.9955	−0.577206
$973$	45.0358	1.44378
$974$	19.0203	0.609451
$975$	62.0927	1.98856
$976$	−14.2134	−0.454961
$977$	−14.1364	−0.452265	−0.226132	−	0.974097i	$-0.572608\pi$
$977$	−14.1364	−0.452265	−0.226132	+	0.974097i	$0.572608\pi$
$978$	38.8223	1.24140
$979$	6.46874	0.206742
$980$	1.63011	0.0520719
$981$	−13.5341	−0.432111
$982$	−5.01281	−0.159965
$983$	56.4890	1.80172	0.900859	−	0.434111i	$-0.142938\pi$
$983$	56.4890	1.80172	0.900859	+	0.434111i	$0.142938\pi$
$984$	−29.8231	−0.950725
$985$	4.91748	0.156684
$986$	10.6487	0.339124
$987$	27.5283	0.876237
$988$	24.7061	0.786006
$989$	15.9510	0.507212
$990$	−28.9075	−0.918739
$991$	−27.3453	−0.868651	−0.434326	−	0.900756i	$-0.643013\pi$
$991$	−27.3453	−0.868651	−0.434326	+	0.900756i	$0.643013\pi$
$992$	−1.00000	−0.0317500
$993$	70.9813	2.25252
$994$	−7.30299	−0.231637
$995$	−17.2035	−0.545389
$996$	6.77858	0.214788
$997$	−2.10897	−0.0667918	−0.0333959	−	0.999442i	$-0.510632\pi$
$997$	−2.10897	−0.0667918	−0.0333959	+	0.999442i	$0.510632\pi$
$998$	17.8097	0.563755
$999$	99.8448	3.15895

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.13670 q^{3} +1.00000 q^{4} -0.941618 q^{5} -3.13670 q^{6} -2.29539 q^{7} +1.00000 q^{8} +6.83889 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.13670 q^{3} +1.00000 q^{4} -0.941618 q^{5} -3.13670 q^{6} -2.29539 q^{7} +1.00000 q^{8} +6.83889 q^{9} -0.941618 q^{10} +4.48900 q^{11} -3.13670 q^{12} +4.81251 q^{13} -2.29539 q^{14} +2.95357 q^{15} +1.00000 q^{16} +3.75274 q^{17} +6.83889 q^{18} +5.13373 q^{19} -0.941618 q^{20} +7.19996 q^{21} +4.48900 q^{22} +4.35532 q^{23} -3.13670 q^{24} -4.11336 q^{25} +4.81251 q^{26} -12.0415 q^{27} -2.29539 q^{28} +2.83758 q^{29} +2.95357 q^{30} -1.00000 q^{31} +1.00000 q^{32} -14.0806 q^{33} +3.75274 q^{34} +2.16138 q^{35} +6.83889 q^{36} -8.29176 q^{37} +5.13373 q^{38} -15.0954 q^{39} -0.941618 q^{40} +9.50778 q^{41} +7.19996 q^{42} +3.66241 q^{43} +4.48900 q^{44} -6.43962 q^{45} +4.35532 q^{46} +3.82340 q^{47} -3.13670 q^{48} -1.73118 q^{49} -4.11336 q^{50} -11.7712 q^{51} +4.81251 q^{52} -3.40587 q^{53} -12.0415 q^{54} -4.22692 q^{55} -2.29539 q^{56} -16.1030 q^{57} +2.83758 q^{58} +13.3578 q^{59} +2.95357 q^{60} -14.2134 q^{61} -1.00000 q^{62} -15.6979 q^{63} +1.00000 q^{64} -4.53154 q^{65} -14.0806 q^{66} +0.506352 q^{67} +3.75274 q^{68} -13.6613 q^{69} +2.16138 q^{70} +3.18159 q^{71} +6.83889 q^{72} -10.0252 q^{73} -8.29176 q^{74} +12.9024 q^{75} +5.13373 q^{76} -10.3040 q^{77} -15.0954 q^{78} +2.49532 q^{79} -0.941618 q^{80} +17.2538 q^{81} +9.50778 q^{82} -2.16106 q^{83} +7.19996 q^{84} -3.53365 q^{85} +3.66241 q^{86} -8.90065 q^{87} +4.48900 q^{88} +1.44102 q^{89} -6.43962 q^{90} -11.0466 q^{91} +4.35532 q^{92} +3.13670 q^{93} +3.82340 q^{94} -4.83402 q^{95} -3.13670 q^{96} -1.00000 q^{97} -1.73118 q^{98} +30.6998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 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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