LMFDB - Embedded newform 6014.2.a.i.1.10

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			1.10
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.706567 q^{3} +1.00000 q^{4} +0.802206 q^{5} -0.706567 q^{6} +5.13557 q^{7} +1.00000 q^{8} -2.50076 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.706567 q^{3} +1.00000 q^{4} +0.802206 q^{5} -0.706567 q^{6} +5.13557 q^{7} +1.00000 q^{8} -2.50076 q^{9} +0.802206 q^{10} +2.39080 q^{11} -0.706567 q^{12} +6.35830 q^{13} +5.13557 q^{14} -0.566812 q^{15} +1.00000 q^{16} +0.473928 q^{17} -2.50076 q^{18} +4.23909 q^{19} +0.802206 q^{20} -3.62862 q^{21} +2.39080 q^{22} -4.74709 q^{23} -0.706567 q^{24} -4.35647 q^{25} +6.35830 q^{26} +3.88666 q^{27} +5.13557 q^{28} -5.70018 q^{29} -0.566812 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.68926 q^{33} +0.473928 q^{34} +4.11978 q^{35} -2.50076 q^{36} +3.31425 q^{37} +4.23909 q^{38} -4.49256 q^{39} +0.802206 q^{40} +10.6512 q^{41} -3.62862 q^{42} +11.2327 q^{43} +2.39080 q^{44} -2.00613 q^{45} -4.74709 q^{46} +2.95565 q^{47} -0.706567 q^{48} +19.3740 q^{49} -4.35647 q^{50} -0.334862 q^{51} +6.35830 q^{52} +2.40238 q^{53} +3.88666 q^{54} +1.91791 q^{55} +5.13557 q^{56} -2.99520 q^{57} -5.70018 q^{58} -12.8208 q^{59} -0.566812 q^{60} -3.15779 q^{61} -1.00000 q^{62} -12.8428 q^{63} +1.00000 q^{64} +5.10066 q^{65} -1.68926 q^{66} -13.9330 q^{67} +0.473928 q^{68} +3.35413 q^{69} +4.11978 q^{70} -0.918178 q^{71} -2.50076 q^{72} -13.8041 q^{73} +3.31425 q^{74} +3.07814 q^{75} +4.23909 q^{76} +12.2781 q^{77} -4.49256 q^{78} -0.425635 q^{79} +0.802206 q^{80} +4.75611 q^{81} +10.6512 q^{82} +2.70092 q^{83} -3.62862 q^{84} +0.380188 q^{85} +11.2327 q^{86} +4.02756 q^{87} +2.39080 q^{88} -8.81020 q^{89} -2.00613 q^{90} +32.6534 q^{91} -4.74709 q^{92} +0.706567 q^{93} +2.95565 q^{94} +3.40063 q^{95} -0.706567 q^{96} -1.00000 q^{97} +19.3740 q^{98} -5.97883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.706567	−0.407937	−0.203968	−	0.978977i	$-0.565384\pi$
$3$	−0.706567	−0.407937	−0.203968	+	0.978977i	$0.565384\pi$
$4$	1.00000	0.500000
$5$	0.802206	0.358757	0.179379	−	0.983780i	$-0.442591\pi$
$5$	0.802206	0.358757	0.179379	+	0.983780i	$0.442591\pi$
$6$	−0.706567	−0.288455
$7$	5.13557	1.94106	0.970531	−	0.240978i	$-0.0774682\pi$
$7$	5.13557	1.94106	0.970531	+	0.240978i	$0.0774682\pi$
$8$	1.00000	0.353553
$9$	−2.50076	−0.833588
$10$	0.802206	0.253680
$11$	2.39080	0.720854	0.360427	−	0.932787i	$-0.382631\pi$
$11$	2.39080	0.720854	0.360427	+	0.932787i	$0.382631\pi$
$12$	−0.706567	−0.203968
$13$	6.35830	1.76347	0.881737	−	0.471741i	$-0.156374\pi$
$13$	6.35830	1.76347	0.881737	+	0.471741i	$0.156374\pi$
$14$	5.13557	1.37254
$15$	−0.566812	−0.146350
$16$	1.00000	0.250000
$17$	0.473928	0.114944	0.0574722	−	0.998347i	$-0.481696\pi$
$17$	0.473928	0.114944	0.0574722	+	0.998347i	$0.481696\pi$
$18$	−2.50076	−0.589436
$19$	4.23909	0.972515	0.486258	−	0.873816i	$-0.338362\pi$
$19$	4.23909	0.972515	0.486258	+	0.873816i	$0.338362\pi$
$20$	0.802206	0.179379
$21$	−3.62862	−0.791830
$22$	2.39080	0.509721
$23$	−4.74709	−0.989836	−0.494918	−	0.868940i	$-0.664802\pi$
$23$	−4.74709	−0.989836	−0.494918	+	0.868940i	$0.664802\pi$
$24$	−0.706567	−0.144227
$25$	−4.35647	−0.871293
$26$	6.35830	1.24696
$27$	3.88666	0.747988
$28$	5.13557	0.970531
$29$	−5.70018	−1.05850	−0.529249	−	0.848467i	$-0.677526\pi$
$29$	−5.70018	−1.05850	−0.529249	+	0.848467i	$0.677526\pi$
$30$	−0.566812	−0.103485
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−1.68926	−0.294063
$34$	0.473928	0.0812780
$35$	4.11978	0.696370
$36$	−2.50076	−0.416794
$37$	3.31425	0.544859	0.272430	−	0.962176i	$-0.412173\pi$
$37$	3.31425	0.544859	0.272430	+	0.962176i	$0.412173\pi$
$38$	4.23909	0.687672
$39$	−4.49256	−0.719386
$40$	0.802206	0.126840
$41$	10.6512	1.66343	0.831716	−	0.555202i	$-0.187359\pi$
$41$	10.6512	1.66343	0.831716	+	0.555202i	$0.187359\pi$
$42$	−3.62862	−0.559908
$43$	11.2327	1.71297	0.856486	−	0.516170i	$-0.172643\pi$
$43$	11.2327	1.71297	0.856486	+	0.516170i	$0.172643\pi$
$44$	2.39080	0.360427
$45$	−2.00613	−0.299056
$46$	−4.74709	−0.699920
$47$	2.95565	0.431126	0.215563	−	0.976490i	$-0.430841\pi$
$47$	2.95565	0.431126	0.215563	+	0.976490i	$0.430841\pi$
$48$	−0.706567	−0.101984
$49$	19.3740	2.76772
$50$	−4.35647	−0.616097
$51$	−0.334862	−0.0468900
$52$	6.35830	0.881737
$53$	2.40238	0.329992	0.164996	−	0.986294i	$-0.447239\pi$
$53$	2.40238	0.329992	0.164996	+	0.986294i	$0.447239\pi$
$54$	3.88666	0.528907
$55$	1.91791	0.258612
$56$	5.13557	0.686269
$57$	−2.99520	−0.396725
$58$	−5.70018	−0.748471
$59$	−12.8208	−1.66913	−0.834564	−	0.550912i	$-0.814280\pi$
$59$	−12.8208	−1.66913	−0.834564	+	0.550912i	$0.814280\pi$
$60$	−0.566812	−0.0731751
$61$	−3.15779	−0.404313	−0.202157	−	0.979353i	$-0.564795\pi$
$61$	−3.15779	−0.404313	−0.202157	+	0.979353i	$0.564795\pi$
$62$	−1.00000	−0.127000
$63$	−12.8428	−1.61804
$64$	1.00000	0.125000
$65$	5.10066	0.632659
$66$	−1.68926	−0.207934
$67$	−13.9330	−1.70219	−0.851094	−	0.525014i	$-0.824060\pi$
$67$	−13.9330	−1.70219	−0.851094	+	0.525014i	$0.824060\pi$
$68$	0.473928	0.0574722
$69$	3.35413	0.403790
$70$	4.11978	0.492408
$71$	−0.918178	−0.108968	−0.0544838	−	0.998515i	$-0.517351\pi$
$71$	−0.918178	−0.108968	−0.0544838	+	0.998515i	$0.517351\pi$
$72$	−2.50076	−0.294718
$73$	−13.8041	−1.61565	−0.807825	−	0.589422i	$-0.799355\pi$
$73$	−13.8041	−1.61565	−0.807825	+	0.589422i	$0.799355\pi$
$74$	3.31425	0.385274
$75$	3.07814	0.355432
$76$	4.23909	0.486258
$77$	12.2781	1.39922
$78$	−4.49256	−0.508683
$79$	−0.425635	−0.0478877	−0.0239438	−	0.999713i	$-0.507622\pi$
$79$	−0.425635	−0.0478877	−0.0239438	+	0.999713i	$0.507622\pi$
$80$	0.802206	0.0896893
$81$	4.75611	0.528456
$82$	10.6512	1.17622
$83$	2.70092	0.296464	0.148232	−	0.988953i	$-0.452642\pi$
$83$	2.70092	0.296464	0.148232	+	0.988953i	$0.452642\pi$
$84$	−3.62862	−0.395915
$85$	0.380188	0.0412371
$86$	11.2327	1.21125
$87$	4.02756	0.431800
$88$	2.39080	0.254860
$89$	−8.81020	−0.933880	−0.466940	−	0.884289i	$-0.654644\pi$
$89$	−8.81020	−0.933880	−0.466940	+	0.884289i	$0.654644\pi$
$90$	−2.00613	−0.211464
$91$	32.6534	3.42301
$92$	−4.74709	−0.494918
$93$	0.706567	0.0732676
$94$	2.95565	0.304852
$95$	3.40063	0.348897
$96$	−0.706567	−0.0721137
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	19.3740	1.95707
$99$	−5.97883	−0.600895
$100$	−4.35647	−0.435647
$101$	−7.76907	−0.773051	−0.386526	−	0.922279i	$-0.626325\pi$
$101$	−7.76907	−0.773051	−0.386526	+	0.922279i	$0.626325\pi$
$102$	−0.334862	−0.0331563
$103$	−9.16346	−0.902903	−0.451451	−	0.892296i	$-0.649094\pi$
$103$	−9.16346	−0.902903	−0.451451	+	0.892296i	$0.649094\pi$
$104$	6.35830	0.623482
$105$	−2.91090	−0.284075
$106$	2.40238	0.233340
$107$	−9.35846	−0.904716	−0.452358	−	0.891836i	$-0.649417\pi$
$107$	−9.35846	−0.904716	−0.452358	+	0.891836i	$0.649417\pi$
$108$	3.88666	0.373994
$109$	3.28347	0.314499	0.157250	−	0.987559i	$-0.449737\pi$
$109$	3.28347	0.314499	0.157250	+	0.987559i	$0.449737\pi$
$110$	1.91791	0.182866
$111$	−2.34174	−0.222268
$112$	5.13557	0.485265
$113$	15.3571	1.44468	0.722338	−	0.691540i	$-0.243067\pi$
$113$	15.3571	1.44468	0.722338	+	0.691540i	$0.243067\pi$
$114$	−2.99520	−0.280527
$115$	−3.80814	−0.355111
$116$	−5.70018	−0.529249
$117$	−15.9006	−1.47001
$118$	−12.8208	−1.18025
$119$	2.43389	0.223114
$120$	−0.566812	−0.0517426
$121$	−5.28407	−0.480370
$122$	−3.15779	−0.285893
$123$	−7.52576	−0.678575
$124$	−1.00000	−0.0898027
$125$	−7.50581	−0.671340
$126$	−12.8428	−1.14413
$127$	6.55700	0.581840	0.290920	−	0.956747i	$-0.406039\pi$
$127$	6.55700	0.581840	0.290920	+	0.956747i	$0.406039\pi$
$128$	1.00000	0.0883883
$129$	−7.93667	−0.698784
$130$	5.10066	0.447358
$131$	−21.5293	−1.88103	−0.940513	−	0.339758i	$-0.889655\pi$
$131$	−21.5293	−1.88103	−0.940513	+	0.339758i	$0.889655\pi$
$132$	−1.68926	−0.147031
$133$	21.7701	1.88771
$134$	−13.9330	−1.20363
$135$	3.11790	0.268346
$136$	0.473928	0.0406390
$137$	0.217613	0.0185919	0.00929595	−	0.999957i	$-0.497041\pi$
$137$	0.217613	0.0185919	0.00929595	+	0.999957i	$0.497041\pi$
$138$	3.35413	0.285523
$139$	−18.5053	−1.56960	−0.784798	−	0.619752i	$-0.787233\pi$
$139$	−18.5053	−1.56960	−0.784798	+	0.619752i	$0.787233\pi$
$140$	4.11978	0.348185
$141$	−2.08837	−0.175872
$142$	−0.918178	−0.0770518
$143$	15.2014	1.27121
$144$	−2.50076	−0.208397
$145$	−4.57272	−0.379744
$146$	−13.8041	−1.14244
$147$	−13.6890	−1.12905
$148$	3.31425	0.272430
$149$	−18.8309	−1.54269	−0.771343	−	0.636419i	$-0.780415\pi$
$149$	−18.8309	−1.54269	−0.771343	+	0.636419i	$0.780415\pi$
$150$	3.07814	0.251329
$151$	12.3675	1.00645	0.503225	−	0.864155i	$-0.332147\pi$
$151$	12.3675	1.00645	0.503225	+	0.864155i	$0.332147\pi$
$152$	4.23909	0.343836
$153$	−1.18518	−0.0958163
$154$	12.2781	0.989399
$155$	−0.802206	−0.0644347
$156$	−4.49256	−0.359693
$157$	−8.65300	−0.690585	−0.345292	−	0.938495i	$-0.612220\pi$
$157$	−8.65300	−0.690585	−0.345292	+	0.938495i	$0.612220\pi$
$158$	−0.425635	−0.0338617
$159$	−1.69744	−0.134616
$160$	0.802206	0.0634199
$161$	−24.3790	−1.92133
$162$	4.75611	0.373675
$163$	11.0116	0.862496	0.431248	−	0.902233i	$-0.358073\pi$
$163$	11.0116	0.862496	0.431248	+	0.902233i	$0.358073\pi$
$164$	10.6512	0.831716
$165$	−1.35514	−0.105497
$166$	2.70092	0.209632
$167$	−1.38799	−0.107406	−0.0537030	−	0.998557i	$-0.517102\pi$
$167$	−1.38799	−0.107406	−0.0537030	+	0.998557i	$0.517102\pi$
$168$	−3.62862	−0.279954
$169$	27.4279	2.10984
$170$	0.380188	0.0291591
$171$	−10.6010	−0.810677
$172$	11.2327	0.856486
$173$	13.4919	1.02577	0.512884	−	0.858458i	$-0.328577\pi$
$173$	13.4919	1.02577	0.512884	+	0.858458i	$0.328577\pi$
$174$	4.02756	0.305329
$175$	−22.3729	−1.69123
$176$	2.39080	0.180213
$177$	9.05876	0.680898
$178$	−8.81020	−0.660353
$179$	−13.0702	−0.976915	−0.488457	−	0.872588i	$-0.662440\pi$
$179$	−13.0702	−0.976915	−0.488457	+	0.872588i	$0.662440\pi$
$180$	−2.00613	−0.149528
$181$	20.2958	1.50857	0.754286	−	0.656546i	$-0.227983\pi$
$181$	20.2958	1.50857	0.754286	+	0.656546i	$0.227983\pi$
$182$	32.6534	2.42043
$183$	2.23119	0.164934
$184$	−4.74709	−0.349960
$185$	2.65871	0.195472
$186$	0.706567	0.0518080
$187$	1.13307	0.0828581
$188$	2.95565	0.215563
$189$	19.9602	1.45189
$190$	3.40063	0.246707
$191$	15.5431	1.12466	0.562331	−	0.826913i	$-0.309905\pi$
$191$	15.5431	1.12466	0.562331	+	0.826913i	$0.309905\pi$
$192$	−0.706567	−0.0509921
$193$	0.775427	0.0558165	0.0279082	−	0.999610i	$-0.491115\pi$
$193$	0.775427	0.0558165	0.0279082	+	0.999610i	$0.491115\pi$
$194$	−1.00000	−0.0717958
$195$	−3.60396	−0.258085
$196$	19.3740	1.38386
$197$	21.4619	1.52910	0.764548	−	0.644567i	$-0.222962\pi$
$197$	21.4619	1.52910	0.764548	+	0.644567i	$0.222962\pi$
$198$	−5.97883	−0.424897
$199$	14.6991	1.04199	0.520995	−	0.853560i	$-0.325561\pi$
$199$	14.6991	1.04199	0.520995	+	0.853560i	$0.325561\pi$
$200$	−4.35647	−0.308049
$201$	9.84460	0.694385
$202$	−7.76907	−0.546630
$203$	−29.2737	−2.05461
$204$	−0.334862	−0.0234450
$205$	8.54442	0.596768
$206$	−9.16346	−0.638449
$207$	11.8713	0.825115
$208$	6.35830	0.440869
$209$	10.1348	0.701041
$210$	−2.91090	−0.200871
$211$	13.9954	0.963483	0.481742	−	0.876313i	$-0.340004\pi$
$211$	13.9954	0.963483	0.481742	+	0.876313i	$0.340004\pi$
$212$	2.40238	0.164996
$213$	0.648754	0.0444519
$214$	−9.35846	−0.639731
$215$	9.01095	0.614542
$216$	3.88666	0.264454
$217$	−5.13557	−0.348625
$218$	3.28347	0.222385
$219$	9.75354	0.659083
$220$	1.91791	0.129306
$221$	3.01337	0.202702
$222$	−2.34174	−0.157167
$223$	3.59412	0.240680	0.120340	−	0.992733i	$-0.461601\pi$
$223$	3.59412	0.240680	0.120340	+	0.992733i	$0.461601\pi$
$224$	5.13557	0.343134
$225$	10.8945	0.726299
$226$	15.3571	1.02154
$227$	5.87565	0.389981	0.194990	−	0.980805i	$-0.437532\pi$
$227$	5.87565	0.389981	0.194990	+	0.980805i	$0.437532\pi$
$228$	−2.99520	−0.198362
$229$	13.7414	0.908058	0.454029	−	0.890987i	$-0.349986\pi$
$229$	13.7414	0.908058	0.454029	+	0.890987i	$0.349986\pi$
$230$	−3.80814	−0.251101
$231$	−8.67531	−0.570794
$232$	−5.70018	−0.374235
$233$	4.77922	0.313097	0.156549	−	0.987670i	$-0.449963\pi$
$233$	4.77922	0.313097	0.156549	+	0.987670i	$0.449963\pi$
$234$	−15.9006	−1.03945
$235$	2.37104	0.154670
$236$	−12.8208	−0.834564
$237$	0.300740	0.0195351
$238$	2.43389	0.157766
$239$	8.60051	0.556321	0.278160	−	0.960535i	$-0.410275\pi$
$239$	8.60051	0.556321	0.278160	+	0.960535i	$0.410275\pi$
$240$	−0.566812	−0.0365876
$241$	23.6282	1.52203	0.761014	−	0.648735i	$-0.224702\pi$
$241$	23.6282	1.52203	0.761014	+	0.648735i	$0.224702\pi$
$242$	−5.28407	−0.339673
$243$	−15.0205	−0.963564
$244$	−3.15779	−0.202157
$245$	15.5420	0.992939
$246$	−7.52576	−0.479825
$247$	26.9534	1.71501
$248$	−1.00000	−0.0635001
$249$	−1.90838	−0.120939
$250$	−7.50581	−0.474709
$251$	−9.33470	−0.589201	−0.294600	−	0.955621i	$-0.595187\pi$
$251$	−9.33470	−0.589201	−0.294600	+	0.955621i	$0.595187\pi$
$252$	−12.8428	−0.809022
$253$	−11.3493	−0.713527
$254$	6.55700	0.411423
$255$	−0.268628	−0.0168221
$256$	1.00000	0.0625000
$257$	−27.3826	−1.70808	−0.854039	−	0.520209i	$-0.825854\pi$
$257$	−27.3826	−1.70808	−0.854039	+	0.520209i	$0.825854\pi$
$258$	−7.93667	−0.494115
$259$	17.0205	1.05761
$260$	5.10066	0.316330
$261$	14.2548	0.882350
$262$	−21.5293	−1.33009
$263$	−6.22349	−0.383757	−0.191878	−	0.981419i	$-0.561458\pi$
$263$	−6.22349	−0.383757	−0.191878	+	0.981419i	$0.561458\pi$
$264$	−1.68926	−0.103967
$265$	1.92720	0.118387
$266$	21.7701	1.33481
$267$	6.22500	0.380964
$268$	−13.9330	−0.851094
$269$	−0.253301	−0.0154440	−0.00772201	−	0.999970i	$-0.502458\pi$
$269$	−0.253301	−0.0154440	−0.00772201	+	0.999970i	$0.502458\pi$
$270$	3.11790	0.189749
$271$	−31.3021	−1.90147	−0.950735	−	0.310005i	$-0.899669\pi$
$271$	−31.3021	−1.90147	−0.950735	+	0.310005i	$0.899669\pi$
$272$	0.473928	0.0287361
$273$	−23.0718	−1.39637
$274$	0.217613	0.0131465
$275$	−10.4154	−0.628075
$276$	3.35413	0.201895
$277$	−20.0825	−1.20664	−0.603320	−	0.797499i	$-0.706156\pi$
$277$	−20.0825	−1.20664	−0.603320	+	0.797499i	$0.706156\pi$
$278$	−18.5053	−1.10987
$279$	2.50076	0.149717
$280$	4.11978	0.246204
$281$	4.74828	0.283258	0.141629	−	0.989920i	$-0.454766\pi$
$281$	4.74828	0.283258	0.141629	+	0.989920i	$0.454766\pi$
$282$	−2.08837	−0.124360
$283$	20.4056	1.21299	0.606493	−	0.795089i	$-0.292576\pi$
$283$	20.4056	1.21299	0.606493	+	0.795089i	$0.292576\pi$
$284$	−0.918178	−0.0544838
$285$	−2.40277	−0.142328
$286$	15.2014	0.898879
$287$	54.6997	3.22882
$288$	−2.50076	−0.147359
$289$	−16.7754	−0.986788
$290$	−4.57272	−0.268519
$291$	0.706567	0.0414197
$292$	−13.8041	−0.807825
$293$	23.2609	1.35892	0.679459	−	0.733713i	$-0.262214\pi$
$293$	23.2609	1.35892	0.679459	+	0.733713i	$0.262214\pi$
$294$	−13.6890	−0.798362
$295$	−10.2849	−0.598812
$296$	3.31425	0.192637
$297$	9.29223	0.539190
$298$	−18.8309	−1.09084
$299$	−30.1834	−1.74555
$300$	3.07814	0.177716
$301$	57.6863	3.32499
$302$	12.3675	0.711668
$303$	5.48937	0.315356
$304$	4.23909	0.243129
$305$	−2.53319	−0.145050
$306$	−1.18518	−0.0677523
$307$	5.72268	0.326611	0.163305	−	0.986576i	$-0.447784\pi$
$307$	5.72268	0.326611	0.163305	+	0.986576i	$0.447784\pi$
$308$	12.2781	0.699611
$309$	6.47460	0.368327
$310$	−0.802206	−0.0455622
$311$	−14.8572	−0.842475	−0.421237	−	0.906950i	$-0.638404\pi$
$311$	−14.8572	−0.842475	−0.421237	+	0.906950i	$0.638404\pi$
$312$	−4.49256	−0.254341
$313$	−1.46213	−0.0826447	−0.0413223	−	0.999146i	$-0.513157\pi$
$313$	−1.46213	−0.0826447	−0.0413223	+	0.999146i	$0.513157\pi$
$314$	−8.65300	−0.488317
$315$	−10.3026	−0.580485
$316$	−0.425635	−0.0239438
$317$	−11.2367	−0.631115	−0.315558	−	0.948906i	$-0.602192\pi$
$317$	−11.2367	−0.631115	−0.315558	+	0.948906i	$0.602192\pi$
$318$	−1.69744	−0.0951877
$319$	−13.6280	−0.763022
$320$	0.802206	0.0448447
$321$	6.61238	0.369067
$322$	−24.3790	−1.35859
$323$	2.00903	0.111785
$324$	4.75611	0.264228
$325$	−27.6997	−1.53650
$326$	11.0116	0.609877
$327$	−2.31999	−0.128296
$328$	10.6512	0.588112
$329$	15.1789	0.836842
$330$	−1.35514	−0.0745977
$331$	15.0377	0.826545	0.413273	−	0.910607i	$-0.364386\pi$
$331$	15.0377	0.826545	0.413273	+	0.910607i	$0.364386\pi$
$332$	2.70092	0.148232
$333$	−8.28815	−0.454188
$334$	−1.38799	−0.0759475
$335$	−11.1771	−0.610672
$336$	−3.62862	−0.197957
$337$	−9.41523	−0.512880	−0.256440	−	0.966560i	$-0.582550\pi$
$337$	−9.41523	−0.512880	−0.256440	+	0.966560i	$0.582550\pi$
$338$	27.4279	1.49188
$339$	−10.8508	−0.589337
$340$	0.380188	0.0206186
$341$	−2.39080	−0.129469
$342$	−10.6010	−0.573235
$343$	63.5476	3.43125
$344$	11.2327	0.605627
$345$	2.69071	0.144863
$346$	13.4919	0.725328
$347$	23.3321	1.25253	0.626267	−	0.779609i	$-0.284582\pi$
$347$	23.3321	1.25253	0.626267	+	0.779609i	$0.284582\pi$
$348$	4.02756	0.215900
$349$	−20.2424	−1.08355	−0.541775	−	0.840523i	$-0.682248\pi$
$349$	−20.2424	−1.08355	−0.541775	+	0.840523i	$0.682248\pi$
$350$	−22.3729	−1.19588
$351$	24.7125	1.31906
$352$	2.39080	0.127430
$353$	33.9925	1.80924	0.904618	−	0.426223i	$-0.140156\pi$
$353$	33.9925	1.80924	0.904618	+	0.426223i	$0.140156\pi$
$354$	9.05876	0.481468
$355$	−0.736568	−0.0390930
$356$	−8.81020	−0.466940
$357$	−1.71970	−0.0910164
$358$	−13.0702	−0.690783
$359$	−12.2624	−0.647185	−0.323593	−	0.946197i	$-0.604891\pi$
$359$	−12.2624	−0.647185	−0.323593	+	0.946197i	$0.604891\pi$
$360$	−2.00613	−0.105732
$361$	−1.03007	−0.0542144
$362$	20.2958	1.06672
$363$	3.73355	0.195960
$364$	32.6534	1.71151
$365$	−11.0737	−0.579626
$366$	2.23119	0.116626
$367$	−21.9660	−1.14662	−0.573309	−	0.819340i	$-0.694340\pi$
$367$	−21.9660	−1.14662	−0.573309	+	0.819340i	$0.694340\pi$
$368$	−4.74709	−0.247459
$369$	−26.6360	−1.38662
$370$	2.65871	0.138220
$371$	12.3376	0.640534
$372$	0.706567	0.0366338
$373$	13.9045	0.719950	0.359975	−	0.932962i	$-0.382785\pi$
$373$	13.9045	0.719950	0.359975	+	0.932962i	$0.382785\pi$
$374$	1.13307	0.0585895
$375$	5.30336	0.273864
$376$	2.95565	0.152426
$377$	−36.2435	−1.86663
$378$	19.9602	1.02664
$379$	12.8514	0.660134	0.330067	−	0.943958i	$-0.392929\pi$
$379$	12.8514	0.660134	0.330067	+	0.943958i	$0.392929\pi$
$380$	3.40063	0.174448
$381$	−4.63296	−0.237354
$382$	15.5431	0.795256
$383$	23.2679	1.18893	0.594467	−	0.804120i	$-0.297363\pi$
$383$	23.2679	1.18893	0.594467	+	0.804120i	$0.297363\pi$
$384$	−0.706567	−0.0360568
$385$	9.84957	0.501981
$386$	0.775427	0.0394682
$387$	−28.0904	−1.42791
$388$	−1.00000	−0.0507673
$389$	−18.7014	−0.948201	−0.474100	−	0.880471i	$-0.657227\pi$
$389$	−18.7014	−0.948201	−0.474100	+	0.880471i	$0.657227\pi$
$390$	−3.60396	−0.182494
$391$	−2.24978	−0.113776
$392$	19.3740	0.978536
$393$	15.2119	0.767339
$394$	21.4619	1.08123
$395$	−0.341447	−0.0171801
$396$	−5.97883	−0.300447
$397$	−36.3561	−1.82466	−0.912331	−	0.409454i	$-0.865719\pi$
$397$	−36.3561	−1.82466	−0.912331	+	0.409454i	$0.865719\pi$
$398$	14.6991	0.736798
$399$	−15.3821	−0.770067
$400$	−4.35647	−0.217823
$401$	−9.83088	−0.490931	−0.245465	−	0.969405i	$-0.578941\pi$
$401$	−9.83088	−0.490931	−0.245465	+	0.969405i	$0.578941\pi$
$402$	9.84460	0.491004
$403$	−6.35830	−0.316729
$404$	−7.76907	−0.386526
$405$	3.81537	0.189587
$406$	−29.2737	−1.45283
$407$	7.92371	0.392764
$408$	−0.334862	−0.0165781
$409$	1.17322	0.0580121	0.0290061	−	0.999579i	$-0.490766\pi$
$409$	1.17322	0.0580121	0.0290061	+	0.999579i	$0.490766\pi$
$410$	8.54442	0.421979
$411$	−0.153758	−0.00758432
$412$	−9.16346	−0.451451
$413$	−65.8421	−3.23988
$414$	11.8713	0.583444
$415$	2.16669	0.106359
$416$	6.35830	0.311741
$417$	13.0752	0.640296
$418$	10.1348	0.495711
$419$	−6.97394	−0.340699	−0.170350	−	0.985384i	$-0.554490\pi$
$419$	−6.97394	−0.340699	−0.170350	+	0.985384i	$0.554490\pi$
$420$	−2.91090	−0.142037
$421$	15.9430	0.777015	0.388507	−	0.921446i	$-0.372991\pi$
$421$	15.9430	0.777015	0.388507	+	0.921446i	$0.372991\pi$
$422$	13.9954	0.681286
$423$	−7.39138	−0.359381
$424$	2.40238	0.116670
$425$	−2.06465	−0.100150
$426$	0.648754	0.0314323
$427$	−16.2170	−0.784796
$428$	−9.35846	−0.452358
$429$	−10.7408	−0.518572
$430$	9.01095	0.434546
$431$	−36.6968	−1.76762	−0.883810	−	0.467845i	$-0.845030\pi$
$431$	−36.6968	−1.76762	−0.883810	+	0.467845i	$0.845030\pi$
$432$	3.88666	0.186997
$433$	15.2798	0.734300	0.367150	−	0.930162i	$-0.380334\pi$
$433$	15.2798	0.734300	0.367150	+	0.930162i	$0.380334\pi$
$434$	−5.13557	−0.246515
$435$	3.23093	0.154911
$436$	3.28347	0.157250
$437$	−20.1233	−0.962630
$438$	9.75354	0.466042
$439$	27.9198	1.33254	0.666271	−	0.745710i	$-0.267890\pi$
$439$	27.9198	1.33254	0.666271	+	0.745710i	$0.267890\pi$
$440$	1.91791	0.0914330
$441$	−48.4499	−2.30714
$442$	3.01337	0.143332
$443$	−6.16531	−0.292923	−0.146461	−	0.989216i	$-0.546788\pi$
$443$	−6.16531	−0.292923	−0.146461	+	0.989216i	$0.546788\pi$
$444$	−2.34174	−0.111134
$445$	−7.06760	−0.335036
$446$	3.59412	0.170187
$447$	13.3053	0.629318
$448$	5.13557	0.242633
$449$	10.4024	0.490920	0.245460	−	0.969407i	$-0.421061\pi$
$449$	10.4024	0.490920	0.245460	+	0.969407i	$0.421061\pi$
$450$	10.8945	0.513571
$451$	25.4648	1.19909
$452$	15.3571	0.722338
$453$	−8.73845	−0.410568
$454$	5.87565	0.275758
$455$	26.1948	1.22803
$456$	−2.99520	−0.140263
$457$	0.415939	0.0194568	0.00972840	−	0.999953i	$-0.496903\pi$
$457$	0.415939	0.0194568	0.00972840	+	0.999953i	$0.496903\pi$
$458$	13.7414	0.642094
$459$	1.84200	0.0859770
$460$	−3.80814	−0.177555
$461$	−18.4630	−0.859909	−0.429955	−	0.902850i	$-0.641470\pi$
$461$	−18.4630	−0.859909	−0.429955	+	0.902850i	$0.641470\pi$
$462$	−8.67531	−0.403612
$463$	13.5540	0.629907	0.314954	−	0.949107i	$-0.398011\pi$
$463$	13.5540	0.629907	0.314954	+	0.949107i	$0.398011\pi$
$464$	−5.70018	−0.264624
$465$	0.566812	0.0262853
$466$	4.77922	0.221393
$467$	−5.44205	−0.251828	−0.125914	−	0.992041i	$-0.540186\pi$
$467$	−5.44205	−0.251828	−0.125914	+	0.992041i	$0.540186\pi$
$468$	−15.9006	−0.735005
$469$	−71.5538	−3.30405
$470$	2.37104	0.109368
$471$	6.11393	0.281715
$472$	−12.8208	−0.590126
$473$	26.8552	1.23480
$474$	0.300740	0.0138134
$475$	−18.4675	−0.847346
$476$	2.43389	0.111557
$477$	−6.00778	−0.275077
$478$	8.60051	0.393378
$479$	−23.5879	−1.07776	−0.538880	−	0.842383i	$-0.681152\pi$
$479$	−23.5879	−1.07776	−0.538880	+	0.842383i	$0.681152\pi$
$480$	−0.566812	−0.0258713
$481$	21.0730	0.960845
$482$	23.6282	1.07624
$483$	17.2254	0.783782
$484$	−5.28407	−0.240185
$485$	−0.802206	−0.0364263
$486$	−15.0205	−0.681343
$487$	25.3706	1.14965	0.574825	−	0.818277i	$-0.305070\pi$
$487$	25.3706	1.14965	0.574825	+	0.818277i	$0.305070\pi$
$488$	−3.15779	−0.142946
$489$	−7.78044	−0.351844
$490$	15.5420	0.702114
$491$	−23.7647	−1.07249	−0.536243	−	0.844064i	$-0.680157\pi$
$491$	−23.7647	−1.07249	−0.536243	+	0.844064i	$0.680157\pi$
$492$	−7.52576	−0.339287
$493$	−2.70148	−0.121668
$494$	26.9534	1.21269
$495$	−4.79625	−0.215575
$496$	−1.00000	−0.0449013
$497$	−4.71536	−0.211513
$498$	−1.90838	−0.0855165
$499$	6.00473	0.268808	0.134404	−	0.990927i	$-0.457088\pi$
$499$	6.00473	0.268808	0.134404	+	0.990927i	$0.457088\pi$
$500$	−7.50581	−0.335670
$501$	0.980709	0.0438148
$502$	−9.33470	−0.416628
$503$	25.1892	1.12313	0.561565	−	0.827433i	$-0.310199\pi$
$503$	25.1892	1.12313	0.561565	+	0.827433i	$0.310199\pi$
$504$	−12.8428	−0.572065
$505$	−6.23239	−0.277338
$506$	−11.3493	−0.504540
$507$	−19.3797	−0.860682
$508$	6.55700	0.290920
$509$	−14.1571	−0.627501	−0.313750	−	0.949506i	$-0.601586\pi$
$509$	−14.1571	−0.627501	−0.313750	+	0.949506i	$0.601586\pi$
$510$	−0.268628	−0.0118951
$511$	−70.8920	−3.13608
$512$	1.00000	0.0441942
$513$	16.4759	0.727429
$514$	−27.3826	−1.20779
$515$	−7.35098	−0.323923
$516$	−7.93667	−0.349392
$517$	7.06637	0.310779
$518$	17.0205	0.747840
$519$	−9.53291	−0.418448
$520$	5.10066	0.223679
$521$	−0.547255	−0.0239757	−0.0119878	−	0.999928i	$-0.503816\pi$
$521$	−0.547255	−0.0239757	−0.0119878	+	0.999928i	$0.503816\pi$
$522$	14.2548	0.623916
$523$	22.9328	1.00278	0.501391	−	0.865221i	$-0.332822\pi$
$523$	22.9328	1.00278	0.501391	+	0.865221i	$0.332822\pi$
$524$	−21.5293	−0.940513
$525$	15.8080	0.689916
$526$	−6.22349	−0.271357
$527$	−0.473928	−0.0206446
$528$	−1.68926	−0.0735157
$529$	−0.465178	−0.0202251
$530$	1.92720	0.0837123
$531$	32.0618	1.39136
$532$	21.7701	0.943856
$533$	67.7232	2.93342
$534$	6.22500	0.269382
$535$	−7.50741	−0.324574
$536$	−13.9330	−0.601814
$537$	9.23499	0.398519
$538$	−0.253301	−0.0109206
$539$	46.3195	1.99512
$540$	3.11790	0.134173
$541$	−28.0826	−1.20737	−0.603683	−	0.797225i	$-0.706301\pi$
$541$	−28.0826	−1.20737	−0.603683	+	0.797225i	$0.706301\pi$
$542$	−31.3021	−1.34454
$543$	−14.3403	−0.615402
$544$	0.473928	0.0203195
$545$	2.63402	0.112829
$546$	−23.0718	−0.987384
$547$	14.3533	0.613704	0.306852	−	0.951757i	$-0.400724\pi$
$547$	14.3533	0.613704	0.306852	+	0.951757i	$0.400724\pi$
$548$	0.217613	0.00929595
$549$	7.89688	0.337030
$550$	−10.4154	−0.444116
$551$	−24.1636	−1.02940
$552$	3.35413	0.142761
$553$	−2.18588	−0.0929529
$554$	−20.0825	−0.853223
$555$	−1.87856	−0.0797403
$556$	−18.5053	−0.784798
$557$	6.43917	0.272837	0.136418	−	0.990651i	$-0.456441\pi$
$557$	6.43917	0.272837	0.136418	+	0.990651i	$0.456441\pi$
$558$	2.50076	0.105866
$559$	71.4209	3.02078
$560$	4.11978	0.174092
$561$	−0.800588	−0.0338009
$562$	4.74828	0.200294
$563$	−28.2881	−1.19220	−0.596101	−	0.802910i	$-0.703284\pi$
$563$	−28.2881	−1.19220	−0.596101	+	0.802910i	$0.703284\pi$
$564$	−2.08837	−0.0879361
$565$	12.3196	0.518288
$566$	20.4056	0.857711
$567$	24.4253	1.02577
$568$	−0.918178	−0.0385259
$569$	−1.63319	−0.0684667	−0.0342334	−	0.999414i	$-0.510899\pi$
$569$	−1.63319	−0.0684667	−0.0342334	+	0.999414i	$0.510899\pi$
$570$	−2.40277	−0.100641
$571$	5.86557	0.245467	0.122733	−	0.992440i	$-0.460834\pi$
$571$	5.86557	0.245467	0.122733	+	0.992440i	$0.460834\pi$
$572$	15.2014	0.635603
$573$	−10.9823	−0.458791
$574$	54.6997	2.28312
$575$	20.6805	0.862437
$576$	−2.50076	−0.104198
$577$	39.2681	1.63475	0.817376	−	0.576105i	$-0.195428\pi$
$577$	39.2681	1.63475	0.817376	+	0.576105i	$0.195428\pi$
$578$	−16.7754	−0.697764
$579$	−0.547891	−0.0227696
$580$	−4.57272	−0.189872
$581$	13.8707	0.575455
$582$	0.706567	0.0292881
$583$	5.74361	0.237876
$584$	−13.8041	−0.571219
$585$	−12.7555	−0.527377
$586$	23.2609	0.960901
$587$	40.3412	1.66506	0.832530	−	0.553980i	$-0.186892\pi$
$587$	40.3412	1.66506	0.832530	+	0.553980i	$0.186892\pi$
$588$	−13.6890	−0.564527
$589$	−4.23909	−0.174669
$590$	−10.2849	−0.423424
$591$	−15.1642	−0.623774
$592$	3.31425	0.136215
$593$	3.75290	0.154113	0.0770565	−	0.997027i	$-0.475448\pi$
$593$	3.75290	0.154113	0.0770565	+	0.997027i	$0.475448\pi$
$594$	9.29223	0.381265
$595$	1.95248	0.0800438
$596$	−18.8309	−0.771343
$597$	−10.3859	−0.425066
$598$	−30.1834	−1.23429
$599$	−10.1190	−0.413453	−0.206727	−	0.978399i	$-0.566281\pi$
$599$	−10.1190	−0.413453	−0.206727	+	0.978399i	$0.566281\pi$
$600$	3.07814	0.125664
$601$	−47.6737	−1.94465	−0.972326	−	0.233630i	$-0.924939\pi$
$601$	−47.6737	−1.94465	−0.972326	+	0.233630i	$0.924939\pi$
$602$	57.6863	2.35112
$603$	34.8431	1.41892
$604$	12.3675	0.503225
$605$	−4.23891	−0.172336
$606$	5.48937	0.222990
$607$	−36.0399	−1.46281	−0.731407	−	0.681942i	$-0.761136\pi$
$607$	−36.0399	−1.46281	−0.731407	+	0.681942i	$0.761136\pi$
$608$	4.23909	0.171918
$609$	20.6838	0.838150
$610$	−2.53319	−0.102566
$611$	18.7929	0.760280
$612$	−1.18518	−0.0479081
$613$	20.7083	0.836399	0.418200	−	0.908355i	$-0.362661\pi$
$613$	20.7083	0.836399	0.418200	+	0.908355i	$0.362661\pi$
$614$	5.72268	0.230949
$615$	−6.03720	−0.243444
$616$	12.2781	0.494699
$617$	−33.1003	−1.33257	−0.666284	−	0.745698i	$-0.732116\pi$
$617$	−33.1003	−1.33257	−0.666284	+	0.745698i	$0.732116\pi$
$618$	6.47460	0.260447
$619$	28.6441	1.15130	0.575651	−	0.817695i	$-0.304749\pi$
$619$	28.6441	1.15130	0.575651	+	0.817695i	$0.304749\pi$
$620$	−0.802206	−0.0322174
$621$	−18.4503	−0.740385
$622$	−14.8572	−0.595719
$623$	−45.2454	−1.81272
$624$	−4.49256	−0.179846
$625$	15.7611	0.630445
$626$	−1.46213	−0.0584386
$627$	−7.16094	−0.285980
$628$	−8.65300	−0.345292
$629$	1.57072	0.0626285
$630$	−10.3026	−0.410465
$631$	−2.88050	−0.114671	−0.0573355	−	0.998355i	$-0.518260\pi$
$631$	−2.88050	−0.114671	−0.0573355	+	0.998355i	$0.518260\pi$
$632$	−0.425635	−0.0169309
$633$	−9.88869	−0.393040
$634$	−11.2367	−0.446266
$635$	5.26007	0.208739
$636$	−1.69744	−0.0673079
$637$	123.186	4.88080
$638$	−13.6280	−0.539538
$639$	2.29615	0.0908341
$640$	0.802206	0.0317100
$641$	−8.47161	−0.334608	−0.167304	−	0.985905i	$-0.553506\pi$
$641$	−8.47161	−0.334608	−0.167304	+	0.985905i	$0.553506\pi$
$642$	6.61238	0.260970
$643$	−29.1075	−1.14789	−0.573944	−	0.818895i	$-0.694587\pi$
$643$	−29.1075	−1.14789	−0.573944	+	0.818895i	$0.694587\pi$
$644$	−24.3790	−0.960666
$645$	−6.36684	−0.250694
$646$	2.00903	0.0790441
$647$	−7.35684	−0.289227	−0.144614	−	0.989488i	$-0.546194\pi$
$647$	−7.35684	−0.289227	−0.144614	+	0.989488i	$0.546194\pi$
$648$	4.75611	0.186837
$649$	−30.6520	−1.20320
$650$	−27.6997	−1.08647
$651$	3.62862	0.142217
$652$	11.0116	0.431248
$653$	26.2049	1.02548	0.512739	−	0.858544i	$-0.328631\pi$
$653$	26.2049	1.02548	0.512739	+	0.858544i	$0.328631\pi$
$654$	−2.31999	−0.0907188
$655$	−17.2709	−0.674832
$656$	10.6512	0.415858
$657$	34.5208	1.34679
$658$	15.1789	0.591737
$659$	0.734593	0.0286157	0.0143078	−	0.999898i	$-0.495446\pi$
$659$	0.734593	0.0286157	0.0143078	+	0.999898i	$0.495446\pi$
$660$	−1.35514	−0.0527486
$661$	−1.63065	−0.0634248	−0.0317124	−	0.999497i	$-0.510096\pi$
$661$	−1.63065	−0.0634248	−0.0317124	+	0.999497i	$0.510096\pi$
$662$	15.0377	0.584456
$663$	−2.12915	−0.0826894
$664$	2.70092	0.104816
$665$	17.4641	0.677230
$666$	−8.28815	−0.321159
$667$	27.0593	1.04774
$668$	−1.38799	−0.0537030
$669$	−2.53949	−0.0981823
$670$	−11.1771	−0.431810
$671$	−7.54964	−0.291451
$672$	−3.62862	−0.139977
$673$	−20.2958	−0.782345	−0.391173	−	0.920317i	$-0.627930\pi$
$673$	−20.2958	−0.782345	−0.391173	+	0.920317i	$0.627930\pi$
$674$	−9.41523	−0.362661
$675$	−16.9321	−0.651717
$676$	27.4279	1.05492
$677$	−39.2221	−1.50743	−0.753714	−	0.657202i	$-0.771740\pi$
$677$	−39.2221	−1.50743	−0.753714	+	0.657202i	$0.771740\pi$
$678$	−10.8508	−0.416724
$679$	−5.13557	−0.197085
$680$	0.380188	0.0145795
$681$	−4.15154	−0.159087
$682$	−2.39080	−0.0915485
$683$	−13.0692	−0.500077	−0.250039	−	0.968236i	$-0.580443\pi$
$683$	−13.0692	−0.500077	−0.250039	+	0.968236i	$0.580443\pi$
$684$	−10.6010	−0.405338
$685$	0.174570	0.00666998
$686$	63.5476	2.42626
$687$	−9.70923	−0.370430
$688$	11.2327	0.428243
$689$	15.2750	0.581932
$690$	2.69071	0.102433
$691$	13.7591	0.523421	0.261710	−	0.965146i	$-0.415713\pi$
$691$	13.7591	0.523421	0.261710	+	0.965146i	$0.415713\pi$
$692$	13.4919	0.512884
$693$	−30.7047	−1.16637
$694$	23.3321	0.885675
$695$	−14.8450	−0.563104
$696$	4.02756	0.152664
$697$	5.04788	0.191202
$698$	−20.2424	−0.766186
$699$	−3.37684	−0.127724
$700$	−22.3729	−0.845617
$701$	−9.19880	−0.347434	−0.173717	−	0.984796i	$-0.555578\pi$
$701$	−9.19880	−0.347434	−0.173717	+	0.984796i	$0.555578\pi$
$702$	24.7125	0.932714
$703$	14.0494	0.529884
$704$	2.39080	0.0901067
$705$	−1.67530	−0.0630954
$706$	33.9925	1.27932
$707$	−39.8986	−1.50054
$708$	9.05876	0.340449
$709$	−19.0044	−0.713726	−0.356863	−	0.934157i	$-0.616154\pi$
$709$	−19.0044	−0.713726	−0.356863	+	0.934157i	$0.616154\pi$
$710$	−0.736568	−0.0276429
$711$	1.06441	0.0399186
$712$	−8.81020	−0.330176
$713$	4.74709	0.177780
$714$	−1.71970	−0.0643583
$715$	12.1947	0.456055
$716$	−13.0702	−0.488457
$717$	−6.07683	−0.226944
$718$	−12.2624	−0.457629
$719$	4.32714	0.161375	0.0806875	−	0.996739i	$-0.474288\pi$
$719$	4.32714	0.161375	0.0806875	+	0.996739i	$0.474288\pi$
$720$	−2.00613	−0.0747639
$721$	−47.0595	−1.75259
$722$	−1.03007	−0.0383354
$723$	−16.6949	−0.620891
$724$	20.2958	0.754286
$725$	24.8327	0.922262
$726$	3.73355	0.138565
$727$	19.7194	0.731353	0.365676	−	0.930742i	$-0.380838\pi$
$727$	19.7194	0.731353	0.365676	+	0.930742i	$0.380838\pi$
$728$	32.6534	1.21022
$729$	−3.65534	−0.135383
$730$	−11.0737	−0.409858
$731$	5.32350	0.196897
$732$	2.23119	0.0824671
$733$	−2.60878	−0.0963575	−0.0481788	−	0.998839i	$-0.515342\pi$
$733$	−2.60878	−0.0963575	−0.0481788	+	0.998839i	$0.515342\pi$
$734$	−21.9660	−0.810781
$735$	−10.9814	−0.405056
$736$	−4.74709	−0.174980
$737$	−33.3110	−1.22703
$738$	−26.6360	−0.980485
$739$	−19.7462	−0.726375	−0.363187	−	0.931716i	$-0.618312\pi$
$739$	−19.7462	−0.726375	−0.363187	+	0.931716i	$0.618312\pi$
$740$	2.65871	0.0977361
$741$	−19.0444	−0.699613
$742$	12.3376	0.452926
$743$	23.3501	0.856631	0.428316	−	0.903629i	$-0.359107\pi$
$743$	23.3501	0.856631	0.428316	+	0.903629i	$0.359107\pi$
$744$	0.706567	0.0259040
$745$	−15.1062	−0.553450
$746$	13.9045	0.509081
$747$	−6.75435	−0.247129
$748$	1.13307	0.0414291
$749$	−48.0610	−1.75611
$750$	5.30336	0.193651
$751$	−50.0686	−1.82703	−0.913515	−	0.406805i	$-0.866643\pi$
$751$	−50.0686	−1.82703	−0.913515	+	0.406805i	$0.866643\pi$
$752$	2.95565	0.107782
$753$	6.59559	0.240357
$754$	−36.2435	−1.31991
$755$	9.92126	0.361071
$756$	19.9602	0.725945
$757$	17.5949	0.639498	0.319749	−	0.947502i	$-0.396401\pi$
$757$	17.5949	0.639498	0.319749	+	0.947502i	$0.396401\pi$
$758$	12.8514	0.466785
$759$	8.01907	0.291074
$760$	3.40063	0.123354
$761$	37.7003	1.36663	0.683317	−	0.730122i	$-0.260537\pi$
$761$	37.7003	1.36663	0.683317	+	0.730122i	$0.260537\pi$
$762$	−4.63296	−0.167835
$763$	16.8625	0.610462
$764$	15.5431	0.562331
$765$	−0.950759	−0.0343748
$766$	23.2679	0.840703
$767$	−81.5185	−2.94346
$768$	−0.706567	−0.0254960
$769$	−42.7474	−1.54151	−0.770755	−	0.637132i	$-0.780121\pi$
$769$	−42.7474	−1.54151	−0.770755	+	0.637132i	$0.780121\pi$
$770$	9.84957	0.354954
$771$	19.3476	0.696788
$772$	0.775427	0.0279082
$773$	38.4333	1.38235	0.691174	−	0.722688i	$-0.257094\pi$
$773$	38.4333	1.38235	0.691174	+	0.722688i	$0.257094\pi$
$774$	−28.0904	−1.00969
$775$	4.35647	0.156489
$776$	−1.00000	−0.0358979
$777$	−12.0262	−0.431436
$778$	−18.7014	−0.670479
$779$	45.1513	1.61771
$780$	−3.60396	−0.129042
$781$	−2.19518	−0.0785498
$782$	−2.24978	−0.0804518
$783$	−22.1547	−0.791743
$784$	19.3740	0.691930
$785$	−6.94149	−0.247752
$786$	15.2119	0.542591
$787$	31.4934	1.12262	0.561310	−	0.827606i	$-0.310298\pi$
$787$	31.4934	1.12262	0.561310	+	0.827606i	$0.310298\pi$
$788$	21.4619	0.764548
$789$	4.39731	0.156549
$790$	−0.341447	−0.0121481
$791$	78.8675	2.80421
$792$	−5.97883	−0.212448
$793$	−20.0781	−0.712996
$794$	−36.3561	−1.29023
$795$	−1.36170	−0.0482944
$796$	14.6991	0.520995
$797$	−50.3480	−1.78342	−0.891709	−	0.452609i	$-0.850493\pi$
$797$	−50.3480	−1.78342	−0.891709	+	0.452609i	$0.850493\pi$
$798$	−15.3821	−0.544519
$799$	1.40077	0.0495555
$800$	−4.35647	−0.154024
$801$	22.0322	0.778471
$802$	−9.83088	−0.347140
$803$	−33.0029	−1.16465
$804$	9.84460	0.347192
$805$	−19.5569	−0.689292
$806$	−6.35830	−0.223961
$807$	0.178974	0.00630018
$808$	−7.76907	−0.273315
$809$	14.4412	0.507727	0.253863	−	0.967240i	$-0.418299\pi$
$809$	14.4412	0.507727	0.253863	+	0.967240i	$0.418299\pi$
$810$	3.81537	0.134059
$811$	−11.1404	−0.391191	−0.195596	−	0.980685i	$-0.562664\pi$
$811$	−11.1404	−0.391191	−0.195596	+	0.980685i	$0.562664\pi$
$812$	−29.2737	−1.02730
$813$	22.1171	0.775679
$814$	7.92371	0.277726
$815$	8.83358	0.309427
$816$	−0.334862	−0.0117225
$817$	47.6165	1.66589
$818$	1.17322	0.0410208
$819$	−81.6585	−2.85338
$820$	8.54442	0.298384
$821$	−38.8100	−1.35448	−0.677239	−	0.735763i	$-0.736824\pi$
$821$	−38.8100	−1.35448	−0.677239	+	0.735763i	$0.736824\pi$
$822$	−0.153758	−0.00536292
$823$	−8.52196	−0.297057	−0.148528	−	0.988908i	$-0.547454\pi$
$823$	−8.52196	−0.297057	−0.148528	+	0.988908i	$0.547454\pi$
$824$	−9.16346	−0.319224
$825$	7.35921	0.256215
$826$	−65.8421	−2.29094
$827$	19.1540	0.666049	0.333025	−	0.942918i	$-0.391931\pi$
$827$	19.1540	0.666049	0.333025	+	0.942918i	$0.391931\pi$
$828$	11.8713	0.412557
$829$	−1.79769	−0.0624365	−0.0312182	−	0.999513i	$-0.509939\pi$
$829$	−1.79769	−0.0624365	−0.0312182	+	0.999513i	$0.509939\pi$
$830$	2.16669	0.0752069
$831$	14.1896	0.492233
$832$	6.35830	0.220434
$833$	9.18189	0.318134
$834$	13.0752	0.452757
$835$	−1.11345	−0.0385327
$836$	10.1348	0.350521
$837$	−3.88666	−0.134343
$838$	−6.97394	−0.240911
$839$	−14.2438	−0.491752	−0.245876	−	0.969301i	$-0.579076\pi$
$839$	−14.2438	−0.491752	−0.245876	+	0.969301i	$0.579076\pi$
$840$	−2.91090	−0.100436
$841$	3.49208	0.120417
$842$	15.9430	0.549432
$843$	−3.35498	−0.115552
$844$	13.9954	0.481742
$845$	22.0028	0.756921
$846$	−7.39138	−0.254121
$847$	−27.1367	−0.932427
$848$	2.40238	0.0824980
$849$	−14.4179	−0.494821
$850$	−2.06465	−0.0708169
$851$	−15.7330	−0.539321
$852$	0.648754	0.0222260
$853$	−25.9139	−0.887277	−0.443638	−	0.896206i	$-0.646312\pi$
$853$	−25.9139	−0.887277	−0.443638	+	0.896206i	$0.646312\pi$
$854$	−16.2170	−0.554935
$855$	−8.50416	−0.290836
$856$	−9.35846	−0.319866
$857$	−45.6023	−1.55775	−0.778873	−	0.627182i	$-0.784208\pi$
$857$	−45.6023	−1.55775	−0.778873	+	0.627182i	$0.784208\pi$
$858$	−10.7408	−0.366686
$859$	32.6543	1.11415	0.557075	−	0.830462i	$-0.311924\pi$
$859$	32.6543	1.11415	0.557075	+	0.830462i	$0.311924\pi$
$860$	9.01095	0.307271
$861$	−38.6490	−1.31715
$862$	−36.6968	−1.24990
$863$	−13.2078	−0.449598	−0.224799	−	0.974405i	$-0.572173\pi$
$863$	−13.2078	−0.449598	−0.224799	+	0.974405i	$0.572173\pi$
$864$	3.88666	0.132227
$865$	10.8233	0.368002
$866$	15.2798	0.519229
$867$	11.8529	0.402547
$868$	−5.13557	−0.174312
$869$	−1.01761	−0.0345200
$870$	3.23093	0.109539
$871$	−88.5902	−3.00176
$872$	3.28347	0.111192
$873$	2.50076	0.0846380
$874$	−20.1233	−0.680682
$875$	−38.5466	−1.30311
$876$	9.75354	0.329541
$877$	28.7001	0.969133	0.484566	−	0.874754i	$-0.338977\pi$
$877$	28.7001	0.969133	0.484566	+	0.874754i	$0.338977\pi$
$878$	27.9198	0.942249
$879$	−16.4354	−0.554353
$880$	1.91791	0.0646529
$881$	50.4576	1.69996	0.849980	−	0.526815i	$-0.176614\pi$
$881$	50.4576	1.69996	0.849980	+	0.526815i	$0.176614\pi$
$882$	−48.4499	−1.63139
$883$	−38.6937	−1.30215	−0.651074	−	0.759014i	$-0.725681\pi$
$883$	−38.6937	−1.30215	−0.651074	+	0.759014i	$0.725681\pi$
$884$	3.01337	0.101351
$885$	7.26699	0.244277
$886$	−6.16531	−0.207128
$887$	−5.57792	−0.187288	−0.0936441	−	0.995606i	$-0.529852\pi$
$887$	−5.57792	−0.187288	−0.0936441	+	0.995606i	$0.529852\pi$
$888$	−2.34174	−0.0785836
$889$	33.6739	1.12939
$890$	−7.06760	−0.236906
$891$	11.3709	0.380940
$892$	3.59412	0.120340
$893$	12.5293	0.419277
$894$	13.3053	0.444995
$895$	−10.4850	−0.350475
$896$	5.13557	0.171567
$897$	21.3266	0.712074
$898$	10.4024	0.347133
$899$	5.70018	0.190112
$900$	10.8945	0.363150
$901$	1.13855	0.0379307
$902$	25.4648	0.847885
$903$	−40.7593	−1.35638
$904$	15.3571	0.510770
$905$	16.2814	0.541211
$906$	−8.73845	−0.290315
$907$	−18.7105	−0.621273	−0.310636	−	0.950529i	$-0.600542\pi$
$907$	−18.7105	−0.621273	−0.310636	+	0.950529i	$0.600542\pi$
$908$	5.87565	0.194990
$909$	19.4286	0.644406
$910$	26.1948	0.868348
$911$	−12.1761	−0.403412	−0.201706	−	0.979446i	$-0.564649\pi$
$911$	−12.1761	−0.403412	−0.201706	+	0.979446i	$0.564649\pi$
$912$	−2.99520	−0.0991811
$913$	6.45735	0.213707
$914$	0.415939	0.0137580
$915$	1.78987	0.0591713
$916$	13.7414	0.454029
$917$	−110.565	−3.65119
$918$	1.84200	0.0607949
$919$	−28.6089	−0.943720	−0.471860	−	0.881673i	$-0.656417\pi$
$919$	−28.6089	−0.943720	−0.471860	+	0.881673i	$0.656417\pi$
$920$	−3.80814	−0.125551
$921$	−4.04346	−0.133236
$922$	−18.4630	−0.608048
$923$	−5.83805	−0.192162
$924$	−8.67531	−0.285397
$925$	−14.4384	−0.474732
$926$	13.5540	0.445412
$927$	22.9156	0.752648
$928$	−5.70018	−0.187118
$929$	14.0094	0.459634	0.229817	−	0.973234i	$-0.426187\pi$
$929$	14.0094	0.459634	0.229817	+	0.973234i	$0.426187\pi$
$930$	0.566812	0.0185865
$931$	82.1283	2.69165
$932$	4.77922	0.156549
$933$	10.4976	0.343676
$934$	−5.44205	−0.178069
$935$	0.908953	0.0297260
$936$	−15.9006	−0.519727
$937$	20.5505	0.671355	0.335678	−	0.941977i	$-0.391035\pi$
$937$	20.5505	0.671355	0.335678	+	0.941977i	$0.391035\pi$
$938$	−71.5538	−2.33632
$939$	1.03310	0.0337138
$940$	2.37104	0.0773348
$941$	−7.80368	−0.254393	−0.127196	−	0.991878i	$-0.540598\pi$
$941$	−7.80368	−0.254393	−0.127196	+	0.991878i	$0.540598\pi$
$942$	6.11393	0.199202
$943$	−50.5620	−1.64652
$944$	−12.8208	−0.417282
$945$	16.0122	0.520876
$946$	26.8552	0.873137
$947$	−22.2363	−0.722583	−0.361292	−	0.932453i	$-0.617664\pi$
$947$	−22.2363	−0.722583	−0.361292	+	0.932453i	$0.617664\pi$
$948$	0.300740	0.00976757
$949$	−87.7707	−2.84916
$950$	−18.4675	−0.599164
$951$	7.93947	0.257455
$952$	2.43389	0.0788828
$953$	25.5283	0.826943	0.413471	−	0.910517i	$-0.364316\pi$
$953$	25.5283	0.826943	0.413471	+	0.910517i	$0.364316\pi$
$954$	−6.00778	−0.194509
$955$	12.4688	0.403480
$956$	8.60051	0.278160
$957$	9.62910	0.311265
$958$	−23.5879	−0.762091
$959$	1.11756	0.0360880
$960$	−0.566812	−0.0182938
$961$	1.00000	0.0322581
$962$	21.0730	0.679420
$963$	23.4033	0.754160
$964$	23.6282	0.761014
$965$	0.622052	0.0200246
$966$	17.2254	0.554217
$967$	11.0116	0.354108	0.177054	−	0.984201i	$-0.443343\pi$
$967$	11.0116	0.354108	0.177054	+	0.984201i	$0.443343\pi$
$968$	−5.28407	−0.169836
$969$	−1.41951	−0.0456013
$970$	−0.802206	−0.0257573
$971$	−53.9538	−1.73146	−0.865730	−	0.500511i	$-0.833146\pi$
$971$	−53.9538	−1.73146	−0.865730	+	0.500511i	$0.833146\pi$
$972$	−15.0205	−0.481782
$973$	−95.0350	−3.04668
$974$	25.3706	0.812925
$975$	19.5717	0.626796
$976$	−3.15779	−0.101078
$977$	−50.7714	−1.62432	−0.812161	−	0.583434i	$-0.801709\pi$
$977$	−50.7714	−1.62432	−0.812161	+	0.583434i	$0.801709\pi$
$978$	−7.78044	−0.248791
$979$	−21.0634	−0.673191
$980$	15.5420	0.496470
$981$	−8.21118	−0.262163
$982$	−23.7647	−0.758362
$983$	17.5925	0.561114	0.280557	−	0.959837i	$-0.409481\pi$
$983$	17.5925	0.561114	0.280557	+	0.959837i	$0.409481\pi$
$984$	−7.52576	−0.239912
$985$	17.2168	0.548574
$986$	−2.70148	−0.0860325
$987$	−10.7249	−0.341379
$988$	26.9534	0.857503
$989$	−53.3227	−1.69556
$990$	−4.79625	−0.152435
$991$	−29.8230	−0.947359	−0.473680	−	0.880697i	$-0.657075\pi$
$991$	−29.8230	−0.947359	−0.473680	+	0.880697i	$0.657075\pi$
$992$	−1.00000	−0.0317500
$993$	−10.6251	−0.337178
$994$	−4.71536	−0.149562
$995$	11.7917	0.373821
$996$	−1.90838	−0.0604693
$997$	35.4035	1.12124	0.560620	−	0.828074i	$-0.310563\pi$
$997$	35.4035	1.12124	0.560620	+	0.828074i	$0.310563\pi$
$998$	6.00473	0.190076
$999$	12.8814	0.407548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.706567 q^{3} +1.00000 q^{4} +0.802206 q^{5} -0.706567 q^{6} +5.13557 q^{7} +1.00000 q^{8} -2.50076 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.706567 q^{3} +1.00000 q^{4} +0.802206 q^{5} -0.706567 q^{6} +5.13557 q^{7} +1.00000 q^{8} -2.50076 q^{9} +0.802206 q^{10} +2.39080 q^{11} -0.706567 q^{12} +6.35830 q^{13} +5.13557 q^{14} -0.566812 q^{15} +1.00000 q^{16} +0.473928 q^{17} -2.50076 q^{18} +4.23909 q^{19} +0.802206 q^{20} -3.62862 q^{21} +2.39080 q^{22} -4.74709 q^{23} -0.706567 q^{24} -4.35647 q^{25} +6.35830 q^{26} +3.88666 q^{27} +5.13557 q^{28} -5.70018 q^{29} -0.566812 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.68926 q^{33} +0.473928 q^{34} +4.11978 q^{35} -2.50076 q^{36} +3.31425 q^{37} +4.23909 q^{38} -4.49256 q^{39} +0.802206 q^{40} +10.6512 q^{41} -3.62862 q^{42} +11.2327 q^{43} +2.39080 q^{44} -2.00613 q^{45} -4.74709 q^{46} +2.95565 q^{47} -0.706567 q^{48} +19.3740 q^{49} -4.35647 q^{50} -0.334862 q^{51} +6.35830 q^{52} +2.40238 q^{53} +3.88666 q^{54} +1.91791 q^{55} +5.13557 q^{56} -2.99520 q^{57} -5.70018 q^{58} -12.8208 q^{59} -0.566812 q^{60} -3.15779 q^{61} -1.00000 q^{62} -12.8428 q^{63} +1.00000 q^{64} +5.10066 q^{65} -1.68926 q^{66} -13.9330 q^{67} +0.473928 q^{68} +3.35413 q^{69} +4.11978 q^{70} -0.918178 q^{71} -2.50076 q^{72} -13.8041 q^{73} +3.31425 q^{74} +3.07814 q^{75} +4.23909 q^{76} +12.2781 q^{77} -4.49256 q^{78} -0.425635 q^{79} +0.802206 q^{80} +4.75611 q^{81} +10.6512 q^{82} +2.70092 q^{83} -3.62862 q^{84} +0.380188 q^{85} +11.2327 q^{86} +4.02756 q^{87} +2.39080 q^{88} -8.81020 q^{89} -2.00613 q^{90} +32.6534 q^{91} -4.74709 q^{92} +0.706567 q^{93} +2.95565 q^{94} +3.40063 q^{95} -0.706567 q^{96} -1.00000 q^{97} +19.3740 q^{98} -5.97883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 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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