LMFDB - Embedded newform 6038.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.34935 q^{3} +1.00000 q^{4} -0.768821 q^{5} -2.34935 q^{6} -1.35127 q^{7} +1.00000 q^{8} +2.51947 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.34935 q^{3} +1.00000 q^{4} -0.768821 q^{5} -2.34935 q^{6} -1.35127 q^{7} +1.00000 q^{8} +2.51947 q^{9} -0.768821 q^{10} +0.0447602 q^{11} -2.34935 q^{12} -1.53733 q^{13} -1.35127 q^{14} +1.80623 q^{15} +1.00000 q^{16} +1.98014 q^{17} +2.51947 q^{18} +7.85650 q^{19} -0.768821 q^{20} +3.17460 q^{21} +0.0447602 q^{22} +1.66674 q^{23} -2.34935 q^{24} -4.40891 q^{25} -1.53733 q^{26} +1.12894 q^{27} -1.35127 q^{28} +8.99740 q^{29} +1.80623 q^{30} -8.75848 q^{31} +1.00000 q^{32} -0.105158 q^{33} +1.98014 q^{34} +1.03888 q^{35} +2.51947 q^{36} -9.23625 q^{37} +7.85650 q^{38} +3.61173 q^{39} -0.768821 q^{40} -2.82468 q^{41} +3.17460 q^{42} -10.6789 q^{43} +0.0447602 q^{44} -1.93702 q^{45} +1.66674 q^{46} -6.05088 q^{47} -2.34935 q^{48} -5.17408 q^{49} -4.40891 q^{50} -4.65205 q^{51} -1.53733 q^{52} +9.24416 q^{53} +1.12894 q^{54} -0.0344126 q^{55} -1.35127 q^{56} -18.4577 q^{57} +8.99740 q^{58} +9.30314 q^{59} +1.80623 q^{60} -11.9284 q^{61} -8.75848 q^{62} -3.40447 q^{63} +1.00000 q^{64} +1.18193 q^{65} -0.105158 q^{66} -5.67951 q^{67} +1.98014 q^{68} -3.91577 q^{69} +1.03888 q^{70} -3.32562 q^{71} +2.51947 q^{72} +8.75485 q^{73} -9.23625 q^{74} +10.3581 q^{75} +7.85650 q^{76} -0.0604830 q^{77} +3.61173 q^{78} +4.32760 q^{79} -0.768821 q^{80} -10.2107 q^{81} -2.82468 q^{82} +12.3779 q^{83} +3.17460 q^{84} -1.52237 q^{85} -10.6789 q^{86} -21.1381 q^{87} +0.0447602 q^{88} +12.3881 q^{89} -1.93702 q^{90} +2.07734 q^{91} +1.66674 q^{92} +20.5768 q^{93} -6.05088 q^{94} -6.04024 q^{95} -2.34935 q^{96} +14.2906 q^{97} -5.17408 q^{98} +0.112772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * 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
$3$	−2.34935	−1.35640	−0.678200	−	0.734877i	$-0.737240\pi$
$3$	−2.34935	−1.35640	−0.678200	+	0.734877i	$0.737240\pi$
$4$	1.00000	0.500000
$5$	−0.768821	−0.343827	−0.171914	−	0.985112i	$-0.554995\pi$
$5$	−0.768821	−0.343827	−0.171914	+	0.985112i	$0.554995\pi$
$6$	−2.34935	−0.959120
$7$	−1.35127	−0.510731	−0.255365	−	0.966845i	$-0.582196\pi$
$7$	−1.35127	−0.510731	−0.255365	+	0.966845i	$0.582196\pi$
$8$	1.00000	0.353553
$9$	2.51947	0.839823
$10$	−0.768821	−0.243123
$11$	0.0447602	0.0134957	0.00674786	−	0.999977i	$-0.497852\pi$
$11$	0.0447602	0.0134957	0.00674786	+	0.999977i	$0.497852\pi$
$12$	−2.34935	−0.678200
$13$	−1.53733	−0.426379	−0.213189	−	0.977011i	$-0.568385\pi$
$13$	−1.53733	−0.426379	−0.213189	+	0.977011i	$0.568385\pi$
$14$	−1.35127	−0.361141
$15$	1.80623	0.466367
$16$	1.00000	0.250000
$17$	1.98014	0.480254	0.240127	−	0.970741i	$-0.422811\pi$
$17$	1.98014	0.480254	0.240127	+	0.970741i	$0.422811\pi$
$18$	2.51947	0.593844
$19$	7.85650	1.80241	0.901203	−	0.433398i	$-0.142686\pi$
$19$	7.85650	1.80241	0.901203	+	0.433398i	$0.142686\pi$
$20$	−0.768821	−0.171914
$21$	3.17460	0.692756
$22$	0.0447602	0.00954291
$23$	1.66674	0.347540	0.173770	−	0.984786i	$-0.444405\pi$
$23$	1.66674	0.347540	0.173770	+	0.984786i	$0.444405\pi$
$24$	−2.34935	−0.479560
$25$	−4.40891	−0.881783
$26$	−1.53733	−0.301495
$27$	1.12894	0.217265
$28$	−1.35127	−0.255365
$29$	8.99740	1.67078	0.835388	−	0.549661i	$-0.185243\pi$
$29$	8.99740	1.67078	0.835388	+	0.549661i	$0.185243\pi$
$30$	1.80623	0.329772
$31$	−8.75848	−1.57307	−0.786535	−	0.617546i	$-0.788127\pi$
$31$	−8.75848	−1.57307	−0.786535	+	0.617546i	$0.788127\pi$
$32$	1.00000	0.176777
$33$	−0.105158	−0.0183056
$34$	1.98014	0.339591
$35$	1.03888	0.175603
$36$	2.51947	0.419911
$37$	−9.23625	−1.51843	−0.759215	−	0.650840i	$-0.774417\pi$
$37$	−9.23625	−1.51843	−0.759215	+	0.650840i	$0.774417\pi$
$38$	7.85650	1.27449
$39$	3.61173	0.578340
$40$	−0.768821	−0.121561
$41$	−2.82468	−0.441141	−0.220571	−	0.975371i	$-0.570792\pi$
$41$	−2.82468	−0.441141	−0.220571	+	0.975371i	$0.570792\pi$
$42$	3.17460	0.489852
$43$	−10.6789	−1.62852	−0.814261	−	0.580499i	$-0.802858\pi$
$43$	−10.6789	−1.62852	−0.814261	+	0.580499i	$0.802858\pi$
$44$	0.0447602	0.00674786
$45$	−1.93702	−0.288754
$46$	1.66674	0.245748
$47$	−6.05088	−0.882612	−0.441306	−	0.897357i	$-0.645485\pi$
$47$	−6.05088	−0.882612	−0.441306	+	0.897357i	$0.645485\pi$
$48$	−2.34935	−0.339100
$49$	−5.17408	−0.739154
$50$	−4.40891	−0.623515
$51$	−4.65205	−0.651417
$52$	−1.53733	−0.213189
$53$	9.24416	1.26978	0.634892	−	0.772601i	$-0.281045\pi$
$53$	9.24416	1.26978	0.634892	+	0.772601i	$0.281045\pi$
$54$	1.12894	0.153629
$55$	−0.0344126	−0.00464019
$56$	−1.35127	−0.180571
$57$	−18.4577	−2.44478
$58$	8.99740	1.18142
$59$	9.30314	1.21117	0.605583	−	0.795782i	$-0.292940\pi$
$59$	9.30314	1.21117	0.605583	+	0.795782i	$0.292940\pi$
$60$	1.80623	0.233184
$61$	−11.9284	−1.52727	−0.763637	−	0.645646i	$-0.776588\pi$
$61$	−11.9284	−1.52727	−0.763637	+	0.645646i	$0.776588\pi$
$62$	−8.75848	−1.11233
$63$	−3.40447	−0.428923
$64$	1.00000	0.125000
$65$	1.18193	0.146601
$66$	−0.105158	−0.0129440
$67$	−5.67951	−0.693862	−0.346931	−	0.937891i	$-0.612776\pi$
$67$	−5.67951	−0.693862	−0.346931	+	0.937891i	$0.612776\pi$
$68$	1.98014	0.240127
$69$	−3.91577	−0.471403
$70$	1.03888	0.124170
$71$	−3.32562	−0.394679	−0.197339	−	0.980335i	$-0.563230\pi$
$71$	−3.32562	−0.394679	−0.197339	+	0.980335i	$0.563230\pi$
$72$	2.51947	0.296922
$73$	8.75485	1.02468	0.512339	−	0.858783i	$-0.328779\pi$
$73$	8.75485	1.02468	0.512339	+	0.858783i	$0.328779\pi$
$74$	−9.23625	−1.07369
$75$	10.3581	1.19605
$76$	7.85650	0.901203
$77$	−0.0604830	−0.00689268
$78$	3.61173	0.408948
$79$	4.32760	0.486893	0.243446	−	0.969914i	$-0.421722\pi$
$79$	4.32760	0.486893	0.243446	+	0.969914i	$0.421722\pi$
$80$	−0.768821	−0.0859568
$81$	−10.2107	−1.13452
$82$	−2.82468	−0.311934
$83$	12.3779	1.35865	0.679323	−	0.733839i	$-0.262274\pi$
$83$	12.3779	1.35865	0.679323	+	0.733839i	$0.262274\pi$
$84$	3.17460	0.346378
$85$	−1.52237	−0.165124
$86$	−10.6789	−1.15154
$87$	−21.1381	−2.26624
$88$	0.0447602	0.00477146
$89$	12.3881	1.31314	0.656570	−	0.754265i	$-0.272007\pi$
$89$	12.3881	1.31314	0.656570	+	0.754265i	$0.272007\pi$
$90$	−1.93702	−0.204180
$91$	2.07734	0.217765
$92$	1.66674	0.173770
$93$	20.5768	2.13371
$94$	−6.05088	−0.624101
$95$	−6.04024	−0.619716
$96$	−2.34935	−0.239780
$97$	14.2906	1.45099	0.725494	−	0.688229i	$-0.241611\pi$
$97$	14.2906	1.45099	0.725494	+	0.688229i	$0.241611\pi$
$98$	−5.17408	−0.522661
$99$	0.112772	0.0113340
$100$	−4.40891	−0.440891
$101$	−11.7109	−1.16528	−0.582641	−	0.812730i	$-0.697980\pi$
$101$	−11.7109	−1.16528	−0.582641	+	0.812730i	$0.697980\pi$
$102$	−4.65205	−0.460621
$103$	6.59125	0.649455	0.324728	−	0.945808i	$-0.394727\pi$
$103$	6.59125	0.649455	0.324728	+	0.945808i	$0.394727\pi$
$104$	−1.53733	−0.150748
$105$	−2.44070	−0.238188
$106$	9.24416	0.897872
$107$	12.0930	1.16908	0.584538	−	0.811367i	$-0.301276\pi$
$107$	12.0930	1.16908	0.584538	+	0.811367i	$0.301276\pi$
$108$	1.12894	0.108632
$109$	2.07080	0.198346	0.0991732	−	0.995070i	$-0.468380\pi$
$109$	2.07080	0.198346	0.0991732	+	0.995070i	$0.468380\pi$
$110$	−0.0344126	−0.00328111
$111$	21.6992	2.05960
$112$	−1.35127	−0.127683
$113$	14.5372	1.36755	0.683773	−	0.729695i	$-0.260338\pi$
$113$	14.5372	1.36755	0.683773	+	0.729695i	$0.260338\pi$
$114$	−18.4577	−1.72872
$115$	−1.28143	−0.119494
$116$	8.99740	0.835388
$117$	−3.87325	−0.358083
$118$	9.30314	0.856423
$119$	−2.67569	−0.245280
$120$	1.80623	0.164886
$121$	−10.9980	−0.999818
$122$	−11.9284	−1.07995
$123$	6.63618	0.598364
$124$	−8.75848	−0.786535
$125$	7.23377	0.647008
$126$	−3.40447	−0.303295
$127$	2.42295	0.215002	0.107501	−	0.994205i	$-0.465715\pi$
$127$	2.42295	0.215002	0.107501	+	0.994205i	$0.465715\pi$
$128$	1.00000	0.0883883
$129$	25.0886	2.20893
$130$	1.18193	0.103662
$131$	18.3383	1.60222	0.801111	−	0.598516i	$-0.204243\pi$
$131$	18.3383	1.60222	0.801111	+	0.598516i	$0.204243\pi$
$132$	−0.105158	−0.00915280
$133$	−10.6162	−0.920544
$134$	−5.67951	−0.490635
$135$	−0.867953	−0.0747015
$136$	1.98014	0.169795
$137$	18.8437	1.60993	0.804965	−	0.593323i	$-0.202184\pi$
$137$	18.8437	1.60993	0.804965	+	0.593323i	$0.202184\pi$
$138$	−3.91577	−0.333332
$139$	−14.0119	−1.18848	−0.594238	−	0.804290i	$-0.702546\pi$
$139$	−14.0119	−1.18848	−0.594238	+	0.804290i	$0.702546\pi$
$140$	1.03888	0.0878016
$141$	14.2157	1.19718
$142$	−3.32562	−0.279080
$143$	−0.0688112	−0.00575429
$144$	2.51947	0.209956
$145$	−6.91739	−0.574458
$146$	8.75485	0.724557
$147$	12.1557	1.00259
$148$	−9.23625	−0.759215
$149$	−13.1079	−1.07384	−0.536919	−	0.843634i	$-0.680412\pi$
$149$	−13.1079	−1.07384	−0.536919	+	0.843634i	$0.680412\pi$
$150$	10.3581	0.845736
$151$	14.6152	1.18937	0.594684	−	0.803959i	$-0.297277\pi$
$151$	14.6152	1.18937	0.594684	+	0.803959i	$0.297277\pi$
$152$	7.85650	0.637247
$153$	4.98889	0.403328
$154$	−0.0604830	−0.00487386
$155$	6.73370	0.540864
$156$	3.61173	0.289170
$157$	3.42015	0.272958	0.136479	−	0.990643i	$-0.456421\pi$
$157$	3.42015	0.272958	0.136479	+	0.990643i	$0.456421\pi$
$158$	4.32760	0.344285
$159$	−21.7178	−1.72233
$160$	−0.768821	−0.0607806
$161$	−2.25221	−0.177499
$162$	−10.2107	−0.802227
$163$	22.8435	1.78924	0.894620	−	0.446827i	$-0.147446\pi$
$163$	22.8435	1.78924	0.894620	+	0.446827i	$0.147446\pi$
$164$	−2.82468	−0.220571
$165$	0.0808474	0.00629396
$166$	12.3779	0.960708
$167$	−9.99322	−0.773299	−0.386649	−	0.922227i	$-0.626368\pi$
$167$	−9.99322	−0.773299	−0.386649	+	0.922227i	$0.626368\pi$
$168$	3.17460	0.244926
$169$	−10.6366	−0.818201
$170$	−1.52237	−0.116761
$171$	19.7942	1.51370
$172$	−10.6789	−0.814261
$173$	2.97071	0.225859	0.112930	−	0.993603i	$-0.463977\pi$
$173$	2.97071	0.225859	0.112930	+	0.993603i	$0.463977\pi$
$174$	−21.1381	−1.60247
$175$	5.95762	0.450354
$176$	0.0447602	0.00337393
$177$	−21.8564	−1.64283
$178$	12.3881	0.928530
$179$	−7.20333	−0.538402	−0.269201	−	0.963084i	$-0.586760\pi$
$179$	−7.20333	−0.538402	−0.269201	+	0.963084i	$0.586760\pi$
$180$	−1.93702	−0.144377
$181$	−7.55812	−0.561790	−0.280895	−	0.959738i	$-0.590631\pi$
$181$	−7.55812	−0.561790	−0.280895	+	0.959738i	$0.590631\pi$
$182$	2.07734	0.153983
$183$	28.0240	2.07159
$184$	1.66674	0.122874
$185$	7.10102	0.522078
$186$	20.5768	1.50876
$187$	0.0886314	0.00648137
$188$	−6.05088	−0.441306
$189$	−1.52550	−0.110964
$190$	−6.04024	−0.438205
$191$	−7.28813	−0.527351	−0.263675	−	0.964611i	$-0.584935\pi$
$191$	−7.28813	−0.527351	−0.263675	+	0.964611i	$0.584935\pi$
$192$	−2.34935	−0.169550
$193$	12.8635	0.925932	0.462966	−	0.886376i	$-0.346785\pi$
$193$	12.8635	0.925932	0.462966	+	0.886376i	$0.346785\pi$
$194$	14.2906	1.02600
$195$	−2.77678	−0.198849
$196$	−5.17408	−0.369577
$197$	9.96075	0.709674	0.354837	−	0.934928i	$-0.384536\pi$
$197$	9.96075	0.709674	0.354837	+	0.934928i	$0.384536\pi$
$198$	0.112772	0.00801435
$199$	−8.38027	−0.594061	−0.297031	−	0.954868i	$-0.595996\pi$
$199$	−8.38027	−0.594061	−0.297031	+	0.954868i	$0.595996\pi$
$200$	−4.40891	−0.311757
$201$	13.3432	0.941155
$202$	−11.7109	−0.823978
$203$	−12.1579	−0.853317
$204$	−4.65205	−0.325708
$205$	2.17168	0.151676
$206$	6.59125	0.459234
$207$	4.19930	0.291872
$208$	−1.53733	−0.106595
$209$	0.351659	0.0243247
$210$	−2.44070	−0.168424
$211$	15.9218	1.09610	0.548049	−	0.836446i	$-0.315371\pi$
$211$	15.9218	1.09610	0.548049	+	0.836446i	$0.315371\pi$
$212$	9.24416	0.634892
$213$	7.81306	0.535342
$214$	12.0930	0.826661
$215$	8.21019	0.559930
$216$	1.12894	0.0768147
$217$	11.8350	0.803415
$218$	2.07080	0.140252
$219$	−20.5683	−1.38987
$220$	−0.0344126	−0.00232010
$221$	−3.04413	−0.204770
$222$	21.6992	1.45636
$223$	12.4940	0.836660	0.418330	−	0.908295i	$-0.362616\pi$
$223$	12.4940	0.836660	0.418330	+	0.908295i	$0.362616\pi$
$224$	−1.35127	−0.0902853
$225$	−11.1081	−0.740541
$226$	14.5372	0.967000
$227$	16.6401	1.10444	0.552221	−	0.833698i	$-0.313781\pi$
$227$	16.6401	1.10444	0.552221	+	0.833698i	$0.313781\pi$
$228$	−18.4577	−1.22239
$229$	−1.41638	−0.0935973	−0.0467986	−	0.998904i	$-0.514902\pi$
$229$	−1.41638	−0.0935973	−0.0467986	+	0.998904i	$0.514902\pi$
$230$	−1.28143	−0.0844948
$231$	0.142096	0.00934923
$232$	8.99740	0.590708
$233$	−5.94220	−0.389286	−0.194643	−	0.980874i	$-0.562355\pi$
$233$	−5.94220	−0.389286	−0.194643	+	0.980874i	$0.562355\pi$
$234$	−3.87325	−0.253203
$235$	4.65205	0.303466
$236$	9.30314	0.605583
$237$	−10.1671	−0.660422
$238$	−2.67569	−0.173440
$239$	16.7186	1.08144	0.540720	−	0.841203i	$-0.318152\pi$
$239$	16.7186	1.08144	0.540720	+	0.841203i	$0.318152\pi$
$240$	1.80623	0.116592
$241$	0.228886	0.0147438	0.00737191	−	0.999973i	$-0.497653\pi$
$241$	0.228886	0.0147438	0.00737191	+	0.999973i	$0.497653\pi$
$242$	−10.9980	−0.706978
$243$	20.6017	1.32160
$244$	−11.9284	−0.763637
$245$	3.97794	0.254141
$246$	6.63618	0.423108
$247$	−12.0780	−0.768507
$248$	−8.75848	−0.556164
$249$	−29.0800	−1.84287
$250$	7.23377	0.457504
$251$	−14.9964	−0.946562	−0.473281	−	0.880911i	$-0.656931\pi$
$251$	−14.9964	−0.946562	−0.473281	+	0.880911i	$0.656931\pi$
$252$	−3.40447	−0.214462
$253$	0.0746038	0.00469030
$254$	2.42295	0.152029
$255$	3.57659	0.223975
$256$	1.00000	0.0625000
$257$	−2.46707	−0.153891	−0.0769457	−	0.997035i	$-0.524517\pi$
$257$	−2.46707	−0.153891	−0.0769457	+	0.997035i	$0.524517\pi$
$258$	25.0886	1.56195
$259$	12.4806	0.775509
$260$	1.18193	0.0733003
$261$	22.6687	1.40316
$262$	18.3383	1.13294
$263$	15.3877	0.948846	0.474423	−	0.880297i	$-0.342657\pi$
$263$	15.3877	0.948846	0.474423	+	0.880297i	$0.342657\pi$
$264$	−0.105158	−0.00647201
$265$	−7.10710	−0.436586
$266$	−10.6162	−0.650923
$267$	−29.1041	−1.78114
$268$	−5.67951	−0.346931
$269$	2.15678	0.131501	0.0657506	−	0.997836i	$-0.479056\pi$
$269$	2.15678	0.131501	0.0657506	+	0.997836i	$0.479056\pi$
$270$	−0.867953	−0.0528219
$271$	7.50708	0.456022	0.228011	−	0.973658i	$-0.426778\pi$
$271$	7.50708	0.456022	0.228011	+	0.973658i	$0.426778\pi$
$272$	1.98014	0.120064
$273$	−4.88042	−0.295376
$274$	18.8437	1.13839
$275$	−0.197344	−0.0119003
$276$	−3.91577	−0.235702
$277$	17.4754	1.04999	0.524997	−	0.851104i	$-0.324066\pi$
$277$	17.4754	1.04999	0.524997	+	0.851104i	$0.324066\pi$
$278$	−14.0119	−0.840379
$279$	−22.0667	−1.32110
$280$	1.03888	0.0620851
$281$	−15.0758	−0.899347	−0.449674	−	0.893193i	$-0.648460\pi$
$281$	−15.0758	−0.899347	−0.449674	+	0.893193i	$0.648460\pi$
$282$	14.2157	0.846531
$283$	25.7535	1.53088	0.765442	−	0.643504i	$-0.222520\pi$
$283$	25.7535	1.53088	0.765442	+	0.643504i	$0.222520\pi$
$284$	−3.32562	−0.197339
$285$	14.1907	0.840583
$286$	−0.0688112	−0.00406889
$287$	3.81690	0.225304
$288$	2.51947	0.148461
$289$	−13.0791	−0.769356
$290$	−6.91739	−0.406203
$291$	−33.5736	−1.96812
$292$	8.75485	0.512339
$293$	−4.49067	−0.262348	−0.131174	−	0.991359i	$-0.541875\pi$
$293$	−4.49067	−0.262348	−0.131174	+	0.991359i	$0.541875\pi$
$294$	12.1557	0.708938
$295$	−7.15245	−0.416432
$296$	−9.23625	−0.536846
$297$	0.0505316	0.00293214
$298$	−13.1079	−0.759318
$299$	−2.56233	−0.148184
$300$	10.3581	0.598025
$301$	14.4301	0.831736
$302$	14.6152	0.841011
$303$	27.5131	1.58059
$304$	7.85650	0.450601
$305$	9.17079	0.525118
$306$	4.98889	0.285196
$307$	24.4499	1.39543	0.697715	−	0.716375i	$-0.254200\pi$
$307$	24.4499	1.39543	0.697715	+	0.716375i	$0.254200\pi$
$308$	−0.0604830	−0.00344634
$309$	−15.4852	−0.880922
$310$	6.73370	0.382449
$311$	−4.83925	−0.274409	−0.137204	−	0.990543i	$-0.543812\pi$
$311$	−4.83925	−0.274409	−0.137204	+	0.990543i	$0.543812\pi$
$312$	3.61173	0.204474
$313$	−8.17725	−0.462205	−0.231103	−	0.972929i	$-0.574233\pi$
$313$	−8.17725	−0.462205	−0.231103	+	0.972929i	$0.574233\pi$
$314$	3.42015	0.193010
$315$	2.61743	0.147475
$316$	4.32760	0.243446
$317$	−15.3454	−0.861881	−0.430941	−	0.902380i	$-0.641818\pi$
$317$	−15.3454	−0.861881	−0.430941	+	0.902380i	$0.641818\pi$
$318$	−21.7178	−1.21787
$319$	0.402726	0.0225483
$320$	−0.768821	−0.0429784
$321$	−28.4108	−1.58573
$322$	−2.25221	−0.125511
$323$	15.5570	0.865612
$324$	−10.2107	−0.567260
$325$	6.77796	0.375973
$326$	22.8435	1.26518
$327$	−4.86504	−0.269037
$328$	−2.82468	−0.155967
$329$	8.17636	0.450777
$330$	0.0808474	0.00445050
$331$	−3.79084	−0.208363	−0.104182	−	0.994558i	$-0.533222\pi$
$331$	−3.79084	−0.208363	−0.104182	+	0.994558i	$0.533222\pi$
$332$	12.3779	0.679323
$333$	−23.2704	−1.27521
$334$	−9.99322	−0.546805
$335$	4.36653	0.238569
$336$	3.17460	0.173189
$337$	−22.4746	−1.22427	−0.612135	−	0.790753i	$-0.709689\pi$
$337$	−22.4746	−1.22427	−0.612135	+	0.790753i	$0.709689\pi$
$338$	−10.6366	−0.578556
$339$	−34.1531	−1.85494
$340$	−1.52237	−0.0825622
$341$	−0.392031	−0.0212297
$342$	19.7942	1.07035
$343$	16.4504	0.888239
$344$	−10.6789	−0.575770
$345$	3.01053	0.162081
$346$	2.97071	0.159707
$347$	−33.6061	−1.80407	−0.902035	−	0.431662i	$-0.857927\pi$
$347$	−33.6061	−1.80407	−0.902035	+	0.431662i	$0.857927\pi$
$348$	−21.1381	−1.13312
$349$	−10.3310	−0.553008	−0.276504	−	0.961013i	$-0.589176\pi$
$349$	−10.3310	−0.553008	−0.276504	+	0.961013i	$0.589176\pi$
$350$	5.95762	0.318448
$351$	−1.73555	−0.0926370
$352$	0.0447602	0.00238573
$353$	−3.22610	−0.171708	−0.0858539	−	0.996308i	$-0.527362\pi$
$353$	−3.22610	−0.171708	−0.0858539	+	0.996308i	$0.527362\pi$
$354$	−21.8564	−1.16165
$355$	2.55681	0.135701
$356$	12.3881	0.656570
$357$	6.28616	0.332699
$358$	−7.20333	−0.380708
$359$	17.8972	0.944579	0.472289	−	0.881444i	$-0.343428\pi$
$359$	17.8972	0.944579	0.472289	+	0.881444i	$0.343428\pi$
$360$	−1.93702	−0.102090
$361$	42.7246	2.24866
$362$	−7.55812	−0.397246
$363$	25.8382	1.35615
$364$	2.07734	0.108882
$365$	−6.73092	−0.352312
$366$	28.0240	1.46484
$367$	35.9259	1.87532	0.937660	−	0.347555i	$-0.112988\pi$
$367$	35.9259	1.87532	0.937660	+	0.347555i	$0.112988\pi$
$368$	1.66674	0.0868850
$369$	−7.11670	−0.370481
$370$	7.10102	0.369165
$371$	−12.4913	−0.648517
$372$	20.5768	1.06686
$373$	16.3077	0.844382	0.422191	−	0.906507i	$-0.361261\pi$
$373$	16.3077	0.844382	0.422191	+	0.906507i	$0.361261\pi$
$374$	0.0886314	0.00458302
$375$	−16.9947	−0.877602
$376$	−6.05088	−0.312050
$377$	−13.8320	−0.712383
$378$	−1.52550	−0.0784632
$379$	26.4949	1.36095	0.680477	−	0.732769i	$-0.261773\pi$
$379$	26.4949	1.36095	0.680477	+	0.732769i	$0.261773\pi$
$380$	−6.04024	−0.309858
$381$	−5.69236	−0.291628
$382$	−7.28813	−0.372893
$383$	−4.67800	−0.239035	−0.119517	−	0.992832i	$-0.538135\pi$
$383$	−4.67800	−0.239035	−0.119517	+	0.992832i	$0.538135\pi$
$384$	−2.34935	−0.119890
$385$	0.0465006	0.00236989
$386$	12.8635	0.654732
$387$	−26.9052	−1.36767
$388$	14.2906	0.725494
$389$	14.7148	0.746071	0.373036	−	0.927817i	$-0.378317\pi$
$389$	14.7148	0.746071	0.373036	+	0.927817i	$0.378317\pi$
$390$	−2.77678	−0.140608
$391$	3.30038	0.166907
$392$	−5.17408	−0.261330
$393$	−43.0831	−2.17325
$394$	9.96075	0.501815
$395$	−3.32715	−0.167407
$396$	0.112772	0.00566700
$397$	32.5853	1.63541	0.817704	−	0.575639i	$-0.195247\pi$
$397$	32.5853	1.63541	0.817704	+	0.575639i	$0.195247\pi$
$398$	−8.38027	−0.420065
$399$	24.9413	1.24863
$400$	−4.40891	−0.220446
$401$	−9.24205	−0.461526	−0.230763	−	0.973010i	$-0.574122\pi$
$401$	−9.24205	−0.461526	−0.230763	+	0.973010i	$0.574122\pi$
$402$	13.3432	0.665497
$403$	13.4647	0.670723
$404$	−11.7109	−0.582641
$405$	7.85019	0.390079
$406$	−12.1579	−0.603386
$407$	−0.413417	−0.0204923
$408$	−4.65205	−0.230311
$409$	9.51333	0.470404	0.235202	−	0.971947i	$-0.424425\pi$
$409$	9.51333	0.470404	0.235202	+	0.971947i	$0.424425\pi$
$410$	2.17168	0.107251
$411$	−44.2706	−2.18371
$412$	6.59125	0.324728
$413$	−12.5710	−0.618579
$414$	4.19930	0.206385
$415$	−9.51635	−0.467139
$416$	−1.53733	−0.0753738
$417$	32.9190	1.61205
$418$	0.351659	0.0172002
$419$	−6.76150	−0.330321	−0.165161	−	0.986267i	$-0.552814\pi$
$419$	−6.76150	−0.330321	−0.165161	+	0.986267i	$0.552814\pi$
$420$	−2.44070	−0.119094
$421$	−13.3451	−0.650398	−0.325199	−	0.945646i	$-0.605431\pi$
$421$	−13.3451	−0.650398	−0.325199	+	0.945646i	$0.605431\pi$
$422$	15.9218	0.775059
$423$	−15.2450	−0.741238
$424$	9.24416	0.448936
$425$	−8.73026	−0.423480
$426$	7.81306	0.378544
$427$	16.1184	0.780025
$428$	12.0930	0.584538
$429$	0.161662	0.00780512
$430$	8.21019	0.395930
$431$	−13.8130	−0.665350	−0.332675	−	0.943042i	$-0.607951\pi$
$431$	−13.8130	−0.665350	−0.332675	+	0.943042i	$0.607951\pi$
$432$	1.12894	0.0543162
$433$	26.7663	1.28631	0.643154	−	0.765737i	$-0.277626\pi$
$433$	26.7663	1.28631	0.643154	+	0.765737i	$0.277626\pi$
$434$	11.8350	0.568100
$435$	16.2514	0.779195
$436$	2.07080	0.0991732
$437$	13.0948	0.626408
$438$	−20.5683	−0.982789
$439$	24.9386	1.19026	0.595128	−	0.803631i	$-0.297101\pi$
$439$	24.9386	1.19026	0.595128	+	0.803631i	$0.297101\pi$
$440$	−0.0344126	−0.00164056
$441$	−13.0359	−0.620758
$442$	−3.04413	−0.144794
$443$	34.9417	1.66013	0.830065	−	0.557667i	$-0.188304\pi$
$443$	34.9417	1.66013	0.830065	+	0.557667i	$0.188304\pi$
$444$	21.6992	1.02980
$445$	−9.52425	−0.451493
$446$	12.4940	0.591608
$447$	30.7950	1.45655
$448$	−1.35127	−0.0638413
$449$	22.4630	1.06009	0.530046	−	0.847969i	$-0.322174\pi$
$449$	22.4630	1.06009	0.530046	+	0.847969i	$0.322174\pi$
$450$	−11.1081	−0.523642
$451$	−0.126433	−0.00595352
$452$	14.5372	0.683773
$453$	−34.3363	−1.61326
$454$	16.6401	0.780958
$455$	−1.59711	−0.0748734
$456$	−18.4577	−0.864362
$457$	9.16708	0.428818	0.214409	−	0.976744i	$-0.431217\pi$
$457$	9.16708	0.428818	0.214409	+	0.976744i	$0.431217\pi$
$458$	−1.41638	−0.0661833
$459$	2.23546	0.104342
$460$	−1.28143	−0.0597468
$461$	−8.47980	−0.394944	−0.197472	−	0.980309i	$-0.563273\pi$
$461$	−8.47980	−0.394944	−0.197472	+	0.980309i	$0.563273\pi$
$462$	0.142096	0.00661090
$463$	−20.8807	−0.970407	−0.485204	−	0.874401i	$-0.661255\pi$
$463$	−20.8807	−0.970407	−0.485204	+	0.874401i	$0.661255\pi$
$464$	8.99740	0.417694
$465$	−15.8199	−0.733628
$466$	−5.94220	−0.275267
$467$	21.9925	1.01769	0.508846	−	0.860857i	$-0.330072\pi$
$467$	21.9925	1.01769	0.508846	+	0.860857i	$0.330072\pi$
$468$	−3.87325	−0.179041
$469$	7.67453	0.354377
$470$	4.65205	0.214583
$471$	−8.03515	−0.370240
$472$	9.30314	0.428212
$473$	−0.477991	−0.0219781
$474$	−10.1671	−0.466989
$475$	−34.6386	−1.58933
$476$	−2.67569	−0.122640
$477$	23.2904	1.06639
$478$	16.7186	0.764693
$479$	13.6676	0.624490	0.312245	−	0.950002i	$-0.398919\pi$
$479$	13.6676	0.624490	0.312245	+	0.950002i	$0.398919\pi$
$480$	1.80623	0.0824429
$481$	14.1992	0.647426
$482$	0.228886	0.0104255
$483$	5.29125	0.240760
$484$	−10.9980	−0.499909
$485$	−10.9869	−0.498889
$486$	20.6017	0.934512
$487$	−34.9706	−1.58467	−0.792335	−	0.610086i	$-0.791135\pi$
$487$	−34.9706	−1.58467	−0.792335	+	0.610086i	$0.791135\pi$
$488$	−11.9284	−0.539973
$489$	−53.6675	−2.42693
$490$	3.97794	0.179705
$491$	−35.1153	−1.58473	−0.792366	−	0.610046i	$-0.791151\pi$
$491$	−35.1153	−1.58473	−0.792366	+	0.610046i	$0.791151\pi$
$492$	6.63618	0.299182
$493$	17.8161	0.802397
$494$	−12.0780	−0.543417
$495$	−0.0867014	−0.00389694
$496$	−8.75848	−0.393267
$497$	4.49380	0.201574
$498$	−29.0800	−1.30310
$499$	18.7341	0.838653	0.419326	−	0.907836i	$-0.362266\pi$
$499$	18.7341	0.838653	0.419326	+	0.907836i	$0.362266\pi$
$500$	7.23377	0.323504
$501$	23.4776	1.04890
$502$	−14.9964	−0.669321
$503$	−4.08332	−0.182066	−0.0910331	−	0.995848i	$-0.529017\pi$
$503$	−4.08332	−0.182066	−0.0910331	+	0.995848i	$0.529017\pi$
$504$	−3.40447	−0.151647
$505$	9.00361	0.400655
$506$	0.0746038	0.00331654
$507$	24.9892	1.10981
$508$	2.42295	0.107501
$509$	18.5263	0.821162	0.410581	−	0.911824i	$-0.365326\pi$
$509$	18.5263	0.821162	0.410581	+	0.911824i	$0.365326\pi$
$510$	3.57659	0.158374
$511$	−11.8301	−0.523335
$512$	1.00000	0.0441942
$513$	8.86952	0.391599
$514$	−2.46707	−0.108818
$515$	−5.06749	−0.223300
$516$	25.0886	1.10446
$517$	−0.270839	−0.0119115
$518$	12.4806	0.548368
$519$	−6.97926	−0.306356
$520$	1.18193	0.0518311
$521$	21.7623	0.953423	0.476712	−	0.879060i	$-0.341829\pi$
$521$	21.7623	0.953423	0.476712	+	0.879060i	$0.341829\pi$
$522$	22.6687	0.992181
$523$	32.8445	1.43619	0.718095	−	0.695945i	$-0.245014\pi$
$523$	32.8445	1.43619	0.718095	+	0.695945i	$0.245014\pi$
$524$	18.3383	0.801111
$525$	−13.9966	−0.610860
$526$	15.3877	0.670936
$527$	−17.3430	−0.755473
$528$	−0.105158	−0.00457640
$529$	−20.2220	−0.879216
$530$	−7.10710	−0.308713
$531$	23.4390	1.01716
$532$	−10.6162	−0.460272
$533$	4.34247	0.188093
$534$	−29.1041	−1.25946
$535$	−9.29736	−0.401960
$536$	−5.67951	−0.245317
$537$	16.9232	0.730289
$538$	2.15678	0.0929854
$539$	−0.231593	−0.00997541
$540$	−0.867953	−0.0373508
$541$	−38.8947	−1.67221	−0.836107	−	0.548566i	$-0.815174\pi$
$541$	−38.8947	−1.67221	−0.836107	+	0.548566i	$0.815174\pi$
$542$	7.50708	0.322457
$543$	17.7567	0.762013
$544$	1.98014	0.0848977
$545$	−1.59207	−0.0681969
$546$	−4.88042	−0.208863
$547$	36.0234	1.54025	0.770126	−	0.637892i	$-0.220194\pi$
$547$	36.0234	1.54025	0.770126	+	0.637892i	$0.220194\pi$
$548$	18.8437	0.804965
$549$	−30.0532	−1.28264
$550$	−0.197344	−0.00841478
$551$	70.6881	3.01141
$552$	−3.91577	−0.166666
$553$	−5.84774	−0.248671
$554$	17.4754	0.742458
$555$	−16.6828	−0.708146
$556$	−14.0119	−0.594238
$557$	−38.5411	−1.63304	−0.816519	−	0.577318i	$-0.804099\pi$
$557$	−38.5411	−1.63304	−0.816519	+	0.577318i	$0.804099\pi$
$558$	−22.0667	−0.934158
$559$	16.4171	0.694367
$560$	1.03888	0.0439008
$561$	−0.208227	−0.00879134
$562$	−15.0758	−0.635935
$563$	23.4315	0.987519	0.493759	−	0.869599i	$-0.335622\pi$
$563$	23.4315	0.987519	0.493759	+	0.869599i	$0.335622\pi$
$564$	14.2157	0.598588
$565$	−11.1765	−0.470199
$566$	25.7535	1.08250
$567$	13.7974	0.579435
$568$	−3.32562	−0.139540
$569$	−11.4515	−0.480074	−0.240037	−	0.970764i	$-0.577159\pi$
$569$	−11.4515	−0.480074	−0.240037	+	0.970764i	$0.577159\pi$
$570$	14.1907	0.594382
$571$	−11.2854	−0.472278	−0.236139	−	0.971719i	$-0.575882\pi$
$571$	−11.2854	−0.472278	−0.236139	+	0.971719i	$0.575882\pi$
$572$	−0.0688112	−0.00287714
$573$	17.1224	0.715299
$574$	3.81690	0.159314
$575$	−7.34853	−0.306455
$576$	2.51947	0.104978
$577$	−14.6182	−0.608563	−0.304282	−	0.952582i	$-0.598416\pi$
$577$	−14.6182	−0.608563	−0.304282	+	0.952582i	$0.598416\pi$
$578$	−13.0791	−0.544017
$579$	−30.2208	−1.25593
$580$	−6.91739	−0.287229
$581$	−16.7258	−0.693902
$582$	−33.5736	−1.39167
$583$	0.413771	0.0171366
$584$	8.75485	0.362278
$585$	2.97784	0.123119
$586$	−4.49067	−0.185508
$587$	−2.02754	−0.0836857	−0.0418429	−	0.999124i	$-0.513323\pi$
$587$	−2.02754	−0.0836857	−0.0418429	+	0.999124i	$0.513323\pi$
$588$	12.1557	0.501295
$589$	−68.8110	−2.83531
$590$	−7.15245	−0.294462
$591$	−23.4013	−0.962602
$592$	−9.23625	−0.379608
$593$	−17.9978	−0.739082	−0.369541	−	0.929214i	$-0.620485\pi$
$593$	−17.9978	−0.739082	−0.369541	+	0.929214i	$0.620485\pi$
$594$	0.0505316	0.00207334
$595$	2.05713	0.0843341
$596$	−13.1079	−0.536919
$597$	19.6882	0.805785
$598$	−2.56233	−0.104782
$599$	17.5014	0.715089	0.357544	−	0.933896i	$-0.383614\pi$
$599$	17.5014	0.715089	0.357544	+	0.933896i	$0.383614\pi$
$600$	10.3581	0.422868
$601$	21.4558	0.875198	0.437599	−	0.899170i	$-0.355829\pi$
$601$	21.4558	0.875198	0.437599	+	0.899170i	$0.355829\pi$
$602$	14.4301	0.588126
$603$	−14.3093	−0.582721
$604$	14.6152	0.594684
$605$	8.45549	0.343765
$606$	27.5131	1.11764
$607$	36.8577	1.49601	0.748004	−	0.663694i	$-0.231012\pi$
$607$	36.8577	1.49601	0.748004	+	0.663694i	$0.231012\pi$
$608$	7.85650	0.318623
$609$	28.5632	1.15744
$610$	9.17079	0.371315
$611$	9.30221	0.376327
$612$	4.98889	0.201664
$613$	3.49985	0.141358	0.0706788	−	0.997499i	$-0.477483\pi$
$613$	3.49985	0.141358	0.0706788	+	0.997499i	$0.477483\pi$
$614$	24.4499	0.986718
$615$	−5.10204	−0.205734
$616$	−0.0604830	−0.00243693
$617$	−35.9756	−1.44832	−0.724162	−	0.689630i	$-0.757773\pi$
$617$	−35.9756	−1.44832	−0.724162	+	0.689630i	$0.757773\pi$
$618$	−15.4852	−0.622906
$619$	−20.9894	−0.843634	−0.421817	−	0.906681i	$-0.638607\pi$
$619$	−20.9894	−0.843634	−0.421817	+	0.906681i	$0.638607\pi$
$620$	6.73370	0.270432
$621$	1.88165	0.0755081
$622$	−4.83925	−0.194036
$623$	−16.7397	−0.670661
$624$	3.61173	0.144585
$625$	16.4831	0.659324
$626$	−8.17725	−0.326828
$627$	−0.826171	−0.0329941
$628$	3.42015	0.136479
$629$	−18.2891	−0.729232
$630$	2.61743	0.104281
$631$	−25.0839	−0.998575	−0.499288	−	0.866436i	$-0.666405\pi$
$631$	−25.0839	−0.998575	−0.499288	+	0.866436i	$0.666405\pi$
$632$	4.32760	0.172143
$633$	−37.4058	−1.48675
$634$	−15.3454	−0.609442
$635$	−1.86281	−0.0739234
$636$	−21.7178	−0.861167
$637$	7.95427	0.315160
$638$	0.402726	0.0159441
$639$	−8.37879	−0.331460
$640$	−0.768821	−0.0303903
$641$	30.6051	1.20883	0.604415	−	0.796670i	$-0.293407\pi$
$641$	30.6051	1.20883	0.604415	+	0.796670i	$0.293407\pi$
$642$	−28.4108	−1.12128
$643$	−27.9838	−1.10357	−0.551787	−	0.833985i	$-0.686054\pi$
$643$	−27.9838	−1.10357	−0.551787	+	0.833985i	$0.686054\pi$
$644$	−2.25221	−0.0887496
$645$	−19.2886	−0.759490
$646$	15.5570	0.612080
$647$	8.30677	0.326573	0.163286	−	0.986579i	$-0.447791\pi$
$647$	8.30677	0.326573	0.163286	+	0.986579i	$0.447791\pi$
$648$	−10.2107	−0.401114
$649$	0.416410	0.0163455
$650$	6.77796	0.265853
$651$	−27.8047	−1.08975
$652$	22.8435	0.894620
$653$	−17.8657	−0.699137	−0.349569	−	0.936911i	$-0.613672\pi$
$653$	−17.8657	−0.699137	−0.349569	+	0.936911i	$0.613672\pi$
$654$	−4.86504	−0.190238
$655$	−14.0988	−0.550887
$656$	−2.82468	−0.110285
$657$	22.0576	0.860548
$658$	8.17636	0.318748
$659$	−3.24604	−0.126448	−0.0632239	−	0.997999i	$-0.520138\pi$
$659$	−3.24604	−0.126448	−0.0632239	+	0.997999i	$0.520138\pi$
$660$	0.0808474	0.00314698
$661$	−33.0689	−1.28623	−0.643115	−	0.765769i	$-0.722358\pi$
$661$	−33.0689	−1.28623	−0.643115	+	0.765769i	$0.722358\pi$
$662$	−3.79084	−0.147335
$663$	7.15173	0.277750
$664$	12.3779	0.480354
$665$	8.16198	0.316508
$666$	−23.2704	−0.901711
$667$	14.9964	0.580661
$668$	−9.99322	−0.386649
$669$	−29.3528	−1.13485
$670$	4.36653	0.168694
$671$	−0.533917	−0.0206116
$672$	3.17460	0.122463
$673$	−37.0499	−1.42817	−0.714083	−	0.700061i	$-0.753156\pi$
$673$	−37.0499	−1.42817	−0.714083	+	0.700061i	$0.753156\pi$
$674$	−22.4746	−0.865690
$675$	−4.97740	−0.191580
$676$	−10.6366	−0.409101
$677$	24.6857	0.948748	0.474374	−	0.880323i	$-0.342675\pi$
$677$	24.6857	0.948748	0.474374	+	0.880323i	$0.342675\pi$
$678$	−34.1531	−1.31164
$679$	−19.3104	−0.741064
$680$	−1.52237	−0.0583803
$681$	−39.0935	−1.49807
$682$	−0.392031	−0.0150117
$683$	−22.9871	−0.879577	−0.439789	−	0.898101i	$-0.644947\pi$
$683$	−22.9871	−0.879577	−0.439789	+	0.898101i	$0.644947\pi$
$684$	19.7942	0.756850
$685$	−14.4875	−0.553538
$686$	16.4504	0.628080
$687$	3.32759	0.126955
$688$	−10.6789	−0.407131
$689$	−14.2113	−0.541409
$690$	3.01053	0.114609
$691$	21.9127	0.833598	0.416799	−	0.908999i	$-0.363152\pi$
$691$	21.9127	0.833598	0.416799	+	0.908999i	$0.363152\pi$
$692$	2.97071	0.112930
$693$	−0.152385	−0.00578863
$694$	−33.6061	−1.27567
$695$	10.7727	0.408630
$696$	−21.1381	−0.801237
$697$	−5.59326	−0.211860
$698$	−10.3310	−0.391036
$699$	13.9603	0.528028
$700$	5.95762	0.225177
$701$	−47.4196	−1.79101	−0.895507	−	0.445048i	$-0.853187\pi$
$701$	−47.4196	−1.79101	−0.895507	+	0.445048i	$0.853187\pi$
$702$	−1.73555	−0.0655043
$703$	−72.5646	−2.73683
$704$	0.0447602	0.00168696
$705$	−10.9293	−0.411621
$706$	−3.22610	−0.121416
$707$	15.8246	0.595145
$708$	−21.8564	−0.821413
$709$	4.43915	0.166716	0.0833578	−	0.996520i	$-0.473436\pi$
$709$	4.43915	0.166716	0.0833578	+	0.996520i	$0.473436\pi$
$710$	2.55681	0.0959553
$711$	10.9032	0.408904
$712$	12.3881	0.464265
$713$	−14.5981	−0.546704
$714$	6.28616	0.235253
$715$	0.0529035	0.00197848
$716$	−7.20333	−0.269201
$717$	−39.2780	−1.46686
$718$	17.8972	0.667918
$719$	19.0812	0.711610	0.355805	−	0.934560i	$-0.384207\pi$
$719$	19.0812	0.711610	0.355805	+	0.934560i	$0.384207\pi$
$720$	−1.93702	−0.0721885
$721$	−8.90654	−0.331697
$722$	42.7246	1.59005
$723$	−0.537734	−0.0199985
$724$	−7.55812	−0.280895
$725$	−39.6688	−1.47326
$726$	25.8382	0.958945
$727$	0.576473	0.0213802	0.0106901	−	0.999943i	$-0.496597\pi$
$727$	0.576473	0.0213802	0.0106901	+	0.999943i	$0.496597\pi$
$728$	2.07734	0.0769915
$729$	−17.7686	−0.658098
$730$	−6.73092	−0.249122
$731$	−21.1458	−0.782104
$732$	28.0240	1.03580
$733$	−32.2953	−1.19285	−0.596427	−	0.802667i	$-0.703414\pi$
$733$	−32.2953	−1.19285	−0.596427	+	0.802667i	$0.703414\pi$
$734$	35.9259	1.32605
$735$	−9.34559	−0.344717
$736$	1.66674	0.0614369
$737$	−0.254216	−0.00936417
$738$	−7.11670	−0.261969
$739$	36.1043	1.32812	0.664060	−	0.747680i	$-0.268832\pi$
$739$	36.1043	1.32812	0.664060	+	0.747680i	$0.268832\pi$
$740$	7.10102	0.261039
$741$	28.3756	1.04240
$742$	−12.4913	−0.458571
$743$	−2.28177	−0.0837099	−0.0418550	−	0.999124i	$-0.513327\pi$
$743$	−2.28177	−0.0837099	−0.0418550	+	0.999124i	$0.513327\pi$
$744$	20.5768	0.754381
$745$	10.0776	0.369215
$746$	16.3077	0.597068
$747$	31.1856	1.14102
$748$	0.0886314	0.00324069
$749$	−16.3409	−0.597083
$750$	−16.9947	−0.620558
$751$	2.69880	0.0984808	0.0492404	−	0.998787i	$-0.484320\pi$
$751$	2.69880	0.0984808	0.0492404	+	0.998787i	$0.484320\pi$
$752$	−6.05088	−0.220653
$753$	35.2318	1.28392
$754$	−13.8320	−0.503731
$755$	−11.2365	−0.408937
$756$	−1.52550	−0.0554819
$757$	−47.5315	−1.72756	−0.863781	−	0.503867i	$-0.831910\pi$
$757$	−47.5315	−1.72756	−0.863781	+	0.503867i	$0.831910\pi$
$758$	26.4949	0.962340
$759$	−0.175271	−0.00636192
$760$	−6.04024	−0.219103
$761$	17.8832	0.648266	0.324133	−	0.946012i	$-0.394928\pi$
$761$	17.8832	0.648266	0.324133	+	0.946012i	$0.394928\pi$
$762$	−5.69236	−0.206212
$763$	−2.79820	−0.101302
$764$	−7.28813	−0.263675
$765$	−3.83557	−0.138675
$766$	−4.67800	−0.169023
$767$	−14.3020	−0.516415
$768$	−2.34935	−0.0847750
$769$	−6.88781	−0.248381	−0.124190	−	0.992258i	$-0.539633\pi$
$769$	−6.88781	−0.248381	−0.124190	+	0.992258i	$0.539633\pi$
$770$	0.0465006	0.00167576
$771$	5.79602	0.208738
$772$	12.8635	0.462966
$773$	−4.84956	−0.174427	−0.0872133	−	0.996190i	$-0.527796\pi$
$773$	−4.84956	−0.174427	−0.0872133	+	0.996190i	$0.527796\pi$
$774$	−26.9052	−0.967089
$775$	38.6154	1.38711
$776$	14.2906	0.513002
$777$	−29.3214	−1.05190
$778$	14.7148	0.527552
$779$	−22.1921	−0.795116
$780$	−2.77678	−0.0994246
$781$	−0.148856	−0.00532647
$782$	3.30038	0.118021
$783$	10.1575	0.363001
$784$	−5.17408	−0.184789
$785$	−2.62949	−0.0938503
$786$	−43.0831	−1.53672
$787$	7.01578	0.250086	0.125043	−	0.992151i	$-0.460093\pi$
$787$	7.01578	0.250086	0.125043	+	0.992151i	$0.460093\pi$
$788$	9.96075	0.354837
$789$	−36.1512	−1.28702
$790$	−3.32715	−0.118375
$791$	−19.6436	−0.698447
$792$	0.112772	0.00400718
$793$	18.3379	0.651197
$794$	32.5853	1.15641
$795$	16.6971	0.592185
$796$	−8.38027	−0.297031
$797$	−15.4501	−0.547270	−0.273635	−	0.961834i	$-0.588226\pi$
$797$	−15.4501	−0.547270	−0.273635	+	0.961834i	$0.588226\pi$
$798$	24.9413	0.882912
$799$	−11.9816	−0.423878
$800$	−4.40891	−0.155879
$801$	31.2115	1.10280
$802$	−9.24205	−0.326348
$803$	0.391869	0.0138288
$804$	13.3432	0.470578
$805$	1.73155	0.0610291
$806$	13.4647	0.474273
$807$	−5.06704	−0.178368
$808$	−11.7109	−0.411989
$809$	36.4737	1.28235	0.641173	−	0.767397i	$-0.278448\pi$
$809$	36.4737	1.28235	0.641173	+	0.767397i	$0.278448\pi$
$810$	7.85019	0.275828
$811$	14.5740	0.511764	0.255882	−	0.966708i	$-0.417634\pi$
$811$	14.5740	0.511764	0.255882	+	0.966708i	$0.417634\pi$
$812$	−12.1579	−0.426658
$813$	−17.6368	−0.618549
$814$	−0.413417	−0.0144902
$815$	−17.5626	−0.615190
$816$	−4.65205	−0.162854
$817$	−83.8991	−2.93526
$818$	9.51333	0.332626
$819$	5.23380	0.182884
$820$	2.17168	0.0758382
$821$	21.7711	0.759817	0.379908	−	0.925024i	$-0.375956\pi$
$821$	21.7711	0.759817	0.379908	+	0.925024i	$0.375956\pi$
$822$	−44.2706	−1.54412
$823$	50.1040	1.74652	0.873258	−	0.487257i	$-0.162003\pi$
$823$	50.1040	1.74652	0.873258	+	0.487257i	$0.162003\pi$
$824$	6.59125	0.229617
$825$	0.463631	0.0161416
$826$	−12.5710	−0.437402
$827$	−20.0097	−0.695807	−0.347903	−	0.937530i	$-0.613106\pi$
$827$	−20.0097	−0.695807	−0.347903	+	0.937530i	$0.613106\pi$
$828$	4.19930	0.145936
$829$	−5.86948	−0.203856	−0.101928	−	0.994792i	$-0.532501\pi$
$829$	−5.86948	−0.203856	−0.101928	+	0.994792i	$0.532501\pi$
$830$	−9.51635	−0.330317
$831$	−41.0559	−1.42421
$832$	−1.53733	−0.0532973
$833$	−10.2454	−0.354982
$834$	32.9190	1.13989
$835$	7.68300	0.265881
$836$	0.351659	0.0121624
$837$	−9.88780	−0.341772
$838$	−6.76150	−0.233572
$839$	16.6508	0.574850	0.287425	−	0.957803i	$-0.407201\pi$
$839$	16.6508	0.574850	0.287425	+	0.957803i	$0.407201\pi$
$840$	−2.44070	−0.0842122
$841$	51.9533	1.79149
$842$	−13.3451	−0.459901
$843$	35.4184	1.21988
$844$	15.9218	0.548049
$845$	8.17765	0.281320
$846$	−15.2450	−0.524134
$847$	14.8612	0.510638
$848$	9.24416	0.317446
$849$	−60.5040	−2.07649
$850$	−8.73026	−0.299445
$851$	−15.3945	−0.527715
$852$	7.81306	0.267671
$853$	−29.0029	−0.993040	−0.496520	−	0.868025i	$-0.665389\pi$
$853$	−29.0029	−0.993040	−0.496520	+	0.868025i	$0.665389\pi$
$854$	16.1184	0.551561
$855$	−15.2182	−0.520451
$856$	12.0930	0.413331
$857$	37.1818	1.27011	0.635054	−	0.772468i	$-0.280978\pi$
$857$	37.1818	1.27011	0.635054	+	0.772468i	$0.280978\pi$
$858$	0.161662	0.00551905
$859$	10.6671	0.363956	0.181978	−	0.983303i	$-0.441750\pi$
$859$	10.6671	0.363956	0.181978	+	0.983303i	$0.441750\pi$
$860$	8.21019	0.279965
$861$	−8.96725	−0.305603
$862$	−13.8130	−0.470473
$863$	16.3180	0.555472	0.277736	−	0.960657i	$-0.410416\pi$
$863$	16.3180	0.555472	0.277736	+	0.960657i	$0.410416\pi$
$864$	1.12894	0.0384073
$865$	−2.28395	−0.0776565
$866$	26.7663	0.909557
$867$	30.7273	1.04356
$868$	11.8350	0.401707
$869$	0.193704	0.00657097
$870$	16.2514	0.550974
$871$	8.73128	0.295848
$872$	2.07080	0.0701260
$873$	36.0046	1.21857
$874$	13.0948	0.442937
$875$	−9.77475	−0.330447
$876$	−20.5683	−0.694937
$877$	−26.2240	−0.885520	−0.442760	−	0.896640i	$-0.646001\pi$
$877$	−26.2240	−0.885520	−0.442760	+	0.896640i	$0.646001\pi$
$878$	24.9386	0.841638
$879$	10.5502	0.355849
$880$	−0.0344126	−0.00116005
$881$	45.3611	1.52826	0.764128	−	0.645065i	$-0.223170\pi$
$881$	45.3611	1.52826	0.764128	+	0.645065i	$0.223170\pi$
$882$	−13.0359	−0.438942
$883$	−5.07429	−0.170763	−0.0853817	−	0.996348i	$-0.527211\pi$
$883$	−5.07429	−0.170763	−0.0853817	+	0.996348i	$0.527211\pi$
$884$	−3.04413	−0.102385
$885$	16.8036	0.564848
$886$	34.9417	1.17389
$887$	26.3530	0.884848	0.442424	−	0.896806i	$-0.354119\pi$
$887$	26.3530	0.884848	0.442424	+	0.896806i	$0.354119\pi$
$888$	21.6992	0.728178
$889$	−3.27405	−0.109808
$890$	−9.52425	−0.319254
$891$	−0.457033	−0.0153112
$892$	12.4940	0.418330
$893$	−47.5388	−1.59082
$894$	30.7950	1.02994
$895$	5.53807	0.185117
$896$	−1.35127	−0.0451426
$897$	6.01983	0.200996
$898$	22.4630	0.749599
$899$	−78.8035	−2.62825
$900$	−11.1081	−0.370271
$901$	18.3047	0.609818
$902$	−0.126433	−0.00420977
$903$	−33.9014	−1.12817
$904$	14.5372	0.483500
$905$	5.81084	0.193159
$906$	−34.3363	−1.14075
$907$	−12.9152	−0.428841	−0.214421	−	0.976741i	$-0.568786\pi$
$907$	−12.9152	−0.428841	−0.214421	+	0.976741i	$0.568786\pi$
$908$	16.6401	0.552221
$909$	−29.5053	−0.978630
$910$	−1.59711	−0.0529435
$911$	9.83084	0.325710	0.162855	−	0.986650i	$-0.447930\pi$
$911$	9.83084	0.325710	0.162855	+	0.986650i	$0.447930\pi$
$912$	−18.4577	−0.611196
$913$	0.554035	0.0183359
$914$	9.16708	0.303220
$915$	−21.5454	−0.712271
$916$	−1.41638	−0.0467986
$917$	−24.7799	−0.818304
$918$	2.23546	0.0737811
$919$	20.9317	0.690473	0.345236	−	0.938516i	$-0.387799\pi$
$919$	20.9317	0.690473	0.345236	+	0.938516i	$0.387799\pi$
$920$	−1.28143	−0.0422474
$921$	−57.4415	−1.89276
$922$	−8.47980	−0.279267
$923$	5.11258	0.168283
$924$	0.142096	0.00467462
$925$	40.7218	1.33893
$926$	−20.8807	−0.686182
$927$	16.6064	0.545427
$928$	8.99740	0.295354
$929$	−11.5576	−0.379194	−0.189597	−	0.981862i	$-0.560718\pi$
$929$	−11.5576	−0.379194	−0.189597	+	0.981862i	$0.560718\pi$
$930$	−15.8199	−0.518753
$931$	−40.6502	−1.33226
$932$	−5.94220	−0.194643
$933$	11.3691	0.372208
$934$	21.9925	0.719618
$935$	−0.0681417	−0.00222847
$936$	−3.87325	−0.126601
$937$	47.3496	1.54684	0.773421	−	0.633892i	$-0.218544\pi$
$937$	47.3496	1.54684	0.773421	+	0.633892i	$0.218544\pi$
$938$	7.67453	0.250582
$939$	19.2113	0.626936
$940$	4.65205	0.151733
$941$	49.6694	1.61918	0.809589	−	0.586998i	$-0.199690\pi$
$941$	49.6694	1.61918	0.809589	+	0.586998i	$0.199690\pi$
$942$	−8.03515	−0.261799
$943$	−4.70802	−0.153314
$944$	9.30314	0.302791
$945$	1.17284	0.0381524
$946$	−0.477991	−0.0155408
$947$	−16.2881	−0.529293	−0.264646	−	0.964346i	$-0.585255\pi$
$947$	−16.2881	−0.529293	−0.264646	+	0.964346i	$0.585255\pi$
$948$	−10.1671	−0.330211
$949$	−13.4591	−0.436901
$950$	−34.6386	−1.12383
$951$	36.0517	1.16906
$952$	−2.67569	−0.0867198
$953$	−20.2901	−0.657259	−0.328630	−	0.944459i	$-0.606587\pi$
$953$	−20.2901	−0.657259	−0.328630	+	0.944459i	$0.606587\pi$
$954$	23.2904	0.754053
$955$	5.60327	0.181318
$956$	16.7186	0.540720
$957$	−0.946146	−0.0305845
$958$	13.6676	0.441581
$959$	−25.4629	−0.822241
$960$	1.80623	0.0582959
$961$	45.7109	1.47455
$962$	14.1992	0.457800
$963$	30.4679	0.981816
$964$	0.228886	0.00737191
$965$	−9.88969	−0.318360
$966$	5.29125	0.170243
$967$	−43.3175	−1.39300	−0.696498	−	0.717559i	$-0.745259\pi$
$967$	−43.3175	−1.39300	−0.696498	+	0.717559i	$0.745259\pi$
$968$	−10.9980	−0.353489
$969$	−36.5488	−1.17412
$970$	−10.9869	−0.352768
$971$	−15.5441	−0.498834	−0.249417	−	0.968396i	$-0.580239\pi$
$971$	−15.5441	−0.498834	−0.249417	+	0.968396i	$0.580239\pi$
$972$	20.6017	0.660800
$973$	18.9338	0.606991
$974$	−34.9706	−1.12053
$975$	−15.9238	−0.509971
$976$	−11.9284	−0.381818
$977$	−54.0391	−1.72886	−0.864431	−	0.502751i	$-0.832321\pi$
$977$	−54.0391	−1.72886	−0.864431	+	0.502751i	$0.832321\pi$
$978$	−53.6675	−1.71610
$979$	0.554495	0.0177218
$980$	3.97794	0.127071
$981$	5.21731	0.166576
$982$	−35.1153	−1.12057
$983$	−5.08277	−0.162115	−0.0810576	−	0.996709i	$-0.525830\pi$
$983$	−5.08277	−0.162115	−0.0810576	+	0.996709i	$0.525830\pi$
$984$	6.63618	0.211554
$985$	−7.65803	−0.244005
$986$	17.8161	0.567380
$987$	−19.2092	−0.611434
$988$	−12.0780	−0.384254
$989$	−17.7990	−0.565976
$990$	−0.0867014	−0.00275555
$991$	−0.144098	−0.00457743	−0.00228872	−	0.999997i	$-0.500729\pi$
$991$	−0.144098	−0.00457743	−0.00228872	+	0.999997i	$0.500729\pi$
$992$	−8.75848	−0.278082
$993$	8.90602	0.282624
$994$	4.49380	0.142535
$995$	6.44293	0.204254
$996$	−29.0800	−0.921434
$997$	−37.1102	−1.17529	−0.587646	−	0.809118i	$-0.699945\pi$
$997$	−37.1102	−1.17529	−0.587646	+	0.809118i	$0.699945\pi$
$998$	18.7341	0.593017
$999$	−10.4272	−0.329901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.10	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.10	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.34935 q^{3} +1.00000 q^{4} -0.768821 q^{5} -2.34935 q^{6} -1.35127 q^{7} +1.00000 q^{8} +2.51947 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.34935 q^{3} +1.00000 q^{4} -0.768821 q^{5} -2.34935 q^{6} -1.35127 q^{7} +1.00000 q^{8} +2.51947 q^{9} -0.768821 q^{10} +0.0447602 q^{11} -2.34935 q^{12} -1.53733 q^{13} -1.35127 q^{14} +1.80623 q^{15} +1.00000 q^{16} +1.98014 q^{17} +2.51947 q^{18} +7.85650 q^{19} -0.768821 q^{20} +3.17460 q^{21} +0.0447602 q^{22} +1.66674 q^{23} -2.34935 q^{24} -4.40891 q^{25} -1.53733 q^{26} +1.12894 q^{27} -1.35127 q^{28} +8.99740 q^{29} +1.80623 q^{30} -8.75848 q^{31} +1.00000 q^{32} -0.105158 q^{33} +1.98014 q^{34} +1.03888 q^{35} +2.51947 q^{36} -9.23625 q^{37} +7.85650 q^{38} +3.61173 q^{39} -0.768821 q^{40} -2.82468 q^{41} +3.17460 q^{42} -10.6789 q^{43} +0.0447602 q^{44} -1.93702 q^{45} +1.66674 q^{46} -6.05088 q^{47} -2.34935 q^{48} -5.17408 q^{49} -4.40891 q^{50} -4.65205 q^{51} -1.53733 q^{52} +9.24416 q^{53} +1.12894 q^{54} -0.0344126 q^{55} -1.35127 q^{56} -18.4577 q^{57} +8.99740 q^{58} +9.30314 q^{59} +1.80623 q^{60} -11.9284 q^{61} -8.75848 q^{62} -3.40447 q^{63} +1.00000 q^{64} +1.18193 q^{65} -0.105158 q^{66} -5.67951 q^{67} +1.98014 q^{68} -3.91577 q^{69} +1.03888 q^{70} -3.32562 q^{71} +2.51947 q^{72} +8.75485 q^{73} -9.23625 q^{74} +10.3581 q^{75} +7.85650 q^{76} -0.0604830 q^{77} +3.61173 q^{78} +4.32760 q^{79} -0.768821 q^{80} -10.2107 q^{81} -2.82468 q^{82} +12.3779 q^{83} +3.17460 q^{84} -1.52237 q^{85} -10.6789 q^{86} -21.1381 q^{87} +0.0447602 q^{88} +12.3881 q^{89} -1.93702 q^{90} +2.07734 q^{91} +1.66674 q^{92} +20.5768 q^{93} -6.05088 q^{94} -6.04024 q^{95} -2.34935 q^{96} +14.2906 q^{97} -5.17408 q^{98} +0.112772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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