LMFDB - Embedded newform 6034.2.a.p.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.58330 q^{3} +1.00000 q^{4} -2.70248 q^{5} -1.58330 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.493160 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.58330 q^{3} +1.00000 q^{4} -2.70248 q^{5} -1.58330 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.493160 q^{9} +2.70248 q^{10} -3.32112 q^{11} +1.58330 q^{12} -0.521828 q^{13} -1.00000 q^{14} -4.27884 q^{15} +1.00000 q^{16} +5.72337 q^{17} +0.493160 q^{18} +1.35955 q^{19} -2.70248 q^{20} +1.58330 q^{21} +3.32112 q^{22} +0.952140 q^{23} -1.58330 q^{24} +2.30341 q^{25} +0.521828 q^{26} -5.53072 q^{27} +1.00000 q^{28} +1.32712 q^{29} +4.27884 q^{30} -5.57029 q^{31} -1.00000 q^{32} -5.25834 q^{33} -5.72337 q^{34} -2.70248 q^{35} -0.493160 q^{36} -0.895989 q^{37} -1.35955 q^{38} -0.826210 q^{39} +2.70248 q^{40} +8.53008 q^{41} -1.58330 q^{42} -5.56406 q^{43} -3.32112 q^{44} +1.33276 q^{45} -0.952140 q^{46} +11.8504 q^{47} +1.58330 q^{48} +1.00000 q^{49} -2.30341 q^{50} +9.06182 q^{51} -0.521828 q^{52} -9.76520 q^{53} +5.53072 q^{54} +8.97528 q^{55} -1.00000 q^{56} +2.15257 q^{57} -1.32712 q^{58} -0.914957 q^{59} -4.27884 q^{60} -2.32025 q^{61} +5.57029 q^{62} -0.493160 q^{63} +1.00000 q^{64} +1.41023 q^{65} +5.25834 q^{66} -4.33781 q^{67} +5.72337 q^{68} +1.50752 q^{69} +2.70248 q^{70} +5.95622 q^{71} +0.493160 q^{72} -5.02387 q^{73} +0.895989 q^{74} +3.64699 q^{75} +1.35955 q^{76} -3.32112 q^{77} +0.826210 q^{78} +0.371661 q^{79} -2.70248 q^{80} -7.27731 q^{81} -8.53008 q^{82} +6.44337 q^{83} +1.58330 q^{84} -15.4673 q^{85} +5.56406 q^{86} +2.10123 q^{87} +3.32112 q^{88} -12.2229 q^{89} -1.33276 q^{90} -0.521828 q^{91} +0.952140 q^{92} -8.81944 q^{93} -11.8504 q^{94} -3.67415 q^{95} -1.58330 q^{96} +7.32853 q^{97} -1.00000 q^{98} +1.63785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.58330	0.914119	0.457059	−	0.889436i	$-0.348903\pi$
$3$	1.58330	0.914119	0.457059	+	0.889436i	$0.348903\pi$
$4$	1.00000	0.500000
$5$	−2.70248	−1.20859	−0.604293	−	0.796762i	$-0.706544\pi$
$5$	−2.70248	−1.20859	−0.604293	+	0.796762i	$0.706544\pi$
$6$	−1.58330	−0.646380
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.493160	−0.164387
$10$	2.70248	0.854600
$11$	−3.32112	−1.00136	−0.500678	−	0.865634i	$-0.666916\pi$
$11$	−3.32112	−1.00136	−0.500678	+	0.865634i	$0.666916\pi$
$12$	1.58330	0.457059
$13$	−0.521828	−0.144729	−0.0723645	−	0.997378i	$-0.523054\pi$
$13$	−0.521828	−0.144729	−0.0723645	+	0.997378i	$0.523054\pi$
$14$	−1.00000	−0.267261
$15$	−4.27884	−1.10479
$16$	1.00000	0.250000
$17$	5.72337	1.38812	0.694061	−	0.719916i	$-0.255820\pi$
$17$	5.72337	1.38812	0.694061	+	0.719916i	$0.255820\pi$
$18$	0.493160	0.116239
$19$	1.35955	0.311901	0.155951	−	0.987765i	$-0.450156\pi$
$19$	1.35955	0.311901	0.155951	+	0.987765i	$0.450156\pi$
$20$	−2.70248	−0.604293
$21$	1.58330	0.345504
$22$	3.32112	0.708066
$23$	0.952140	0.198535	0.0992674	−	0.995061i	$-0.468350\pi$
$23$	0.952140	0.198535	0.0992674	+	0.995061i	$0.468350\pi$
$24$	−1.58330	−0.323190
$25$	2.30341	0.460682
$26$	0.521828	0.102339
$27$	−5.53072	−1.06439
$28$	1.00000	0.188982
$29$	1.32712	0.246440	0.123220	−	0.992379i	$-0.460678\pi$
$29$	1.32712	0.246440	0.123220	+	0.992379i	$0.460678\pi$
$30$	4.27884	0.781206
$31$	−5.57029	−1.00045	−0.500227	−	0.865894i	$-0.666750\pi$
$31$	−5.57029	−1.00045	−0.500227	+	0.865894i	$0.666750\pi$
$32$	−1.00000	−0.176777
$33$	−5.25834	−0.915359
$34$	−5.72337	−0.981551
$35$	−2.70248	−0.456803
$36$	−0.493160	−0.0821934
$37$	−0.895989	−0.147300	−0.0736498	−	0.997284i	$-0.523465\pi$
$37$	−0.895989	−0.147300	−0.0736498	+	0.997284i	$0.523465\pi$
$38$	−1.35955	−0.220548
$39$	−0.826210	−0.132300
$40$	2.70248	0.427300
$41$	8.53008	1.33217	0.666087	−	0.745874i	$-0.267968\pi$
$41$	8.53008	1.33217	0.666087	+	0.745874i	$0.267968\pi$
$42$	−1.58330	−0.244309
$43$	−5.56406	−0.848511	−0.424255	−	0.905543i	$-0.639464\pi$
$43$	−5.56406	−0.848511	−0.424255	+	0.905543i	$0.639464\pi$
$44$	−3.32112	−0.500678
$45$	1.33276	0.198676
$46$	−0.952140	−0.140385
$47$	11.8504	1.72857	0.864283	−	0.503006i	$-0.167773\pi$
$47$	11.8504	1.72857	0.864283	+	0.503006i	$0.167773\pi$
$48$	1.58330	0.228530
$49$	1.00000	0.142857
$50$	−2.30341	−0.325751
$51$	9.06182	1.26891
$52$	−0.521828	−0.0723645
$53$	−9.76520	−1.34135	−0.670677	−	0.741750i	$-0.733996\pi$
$53$	−9.76520	−1.34135	−0.670677	+	0.741750i	$0.733996\pi$
$54$	5.53072	0.752636
$55$	8.97528	1.21023
$56$	−1.00000	−0.133631
$57$	2.15257	0.285115
$58$	−1.32712	−0.174260
$59$	−0.914957	−0.119117	−0.0595586	−	0.998225i	$-0.518969\pi$
$59$	−0.914957	−0.119117	−0.0595586	+	0.998225i	$0.518969\pi$
$60$	−4.27884	−0.552396
$61$	−2.32025	−0.297078	−0.148539	−	0.988907i	$-0.547457\pi$
$61$	−2.32025	−0.297078	−0.148539	+	0.988907i	$0.547457\pi$
$62$	5.57029	0.707428
$63$	−0.493160	−0.0621323
$64$	1.00000	0.125000
$65$	1.41023	0.174918
$66$	5.25834	0.647256
$67$	−4.33781	−0.529948	−0.264974	−	0.964256i	$-0.585363\pi$
$67$	−4.33781	−0.529948	−0.264974	+	0.964256i	$0.585363\pi$
$68$	5.72337	0.694061
$69$	1.50752	0.181484
$70$	2.70248	0.323008
$71$	5.95622	0.706873	0.353437	−	0.935459i	$-0.385013\pi$
$71$	5.95622	0.706873	0.353437	+	0.935459i	$0.385013\pi$
$72$	0.493160	0.0581195
$73$	−5.02387	−0.587999	−0.294000	−	0.955806i	$-0.594986\pi$
$73$	−5.02387	−0.587999	−0.294000	+	0.955806i	$0.594986\pi$
$74$	0.895989	0.104157
$75$	3.64699	0.421118
$76$	1.35955	0.155951
$77$	−3.32112	−0.378477
$78$	0.826210	0.0935499
$79$	0.371661	0.0418151	0.0209076	−	0.999781i	$-0.493344\pi$
$79$	0.371661	0.0418151	0.0209076	+	0.999781i	$0.493344\pi$
$80$	−2.70248	−0.302147
$81$	−7.27731	−0.808590
$82$	−8.53008	−0.941990
$83$	6.44337	0.707252	0.353626	−	0.935387i	$-0.384949\pi$
$83$	6.44337	0.707252	0.353626	+	0.935387i	$0.384949\pi$
$84$	1.58330	0.172752
$85$	−15.4673	−1.67767
$86$	5.56406	0.599988
$87$	2.10123	0.225276
$88$	3.32112	0.354033
$89$	−12.2229	−1.29563	−0.647813	−	0.761799i	$-0.724316\pi$
$89$	−12.2229	−1.29563	−0.647813	+	0.761799i	$0.724316\pi$
$90$	−1.33276	−0.140485
$91$	−0.521828	−0.0547024
$92$	0.952140	0.0992674
$93$	−8.81944	−0.914534
$94$	−11.8504	−1.22228
$95$	−3.67415	−0.376960
$96$	−1.58330	−0.161595
$97$	7.32853	0.744099	0.372050	−	0.928213i	$-0.378655\pi$
$97$	7.32853	0.744099	0.372050	+	0.928213i	$0.378655\pi$
$98$	−1.00000	−0.101015
$99$	1.63785	0.164610
$100$	2.30341	0.230341
$101$	15.0787	1.50039	0.750194	−	0.661218i	$-0.229960\pi$
$101$	15.0787	1.50039	0.750194	+	0.661218i	$0.229960\pi$
$102$	−9.06182	−0.897254
$103$	−5.18408	−0.510803	−0.255401	−	0.966835i	$-0.582208\pi$
$103$	−5.18408	−0.510803	−0.255401	+	0.966835i	$0.582208\pi$
$104$	0.521828	0.0511694
$105$	−4.27884	−0.417572
$106$	9.76520	0.948480
$107$	−1.58530	−0.153257	−0.0766284	−	0.997060i	$-0.524416\pi$
$107$	−1.58530	−0.153257	−0.0766284	+	0.997060i	$0.524416\pi$
$108$	−5.53072	−0.532194
$109$	−12.0692	−1.15602	−0.578009	−	0.816030i	$-0.696170\pi$
$109$	−12.0692	−1.15602	−0.578009	+	0.816030i	$0.696170\pi$
$110$	−8.97528	−0.855759
$111$	−1.41862	−0.134649
$112$	1.00000	0.0944911
$113$	13.0248	1.22527	0.612635	−	0.790366i	$-0.290109\pi$
$113$	13.0248	1.22527	0.612635	+	0.790366i	$0.290109\pi$
$114$	−2.15257	−0.201607
$115$	−2.57314	−0.239947
$116$	1.32712	0.123220
$117$	0.257345	0.0237915
$118$	0.914957	0.0842286
$119$	5.72337	0.524661
$120$	4.27884	0.390603
$121$	0.0298592	0.00271448
$122$	2.32025	0.210066
$123$	13.5057	1.21777
$124$	−5.57029	−0.500227
$125$	7.28749	0.651813
$126$	0.493160	0.0439342
$127$	16.2744	1.44412	0.722061	−	0.691830i	$-0.243195\pi$
$127$	16.2744	1.44412	0.722061	+	0.691830i	$0.243195\pi$
$128$	−1.00000	−0.0883883
$129$	−8.80957	−0.775640
$130$	−1.41023	−0.123685
$131$	15.4489	1.34978	0.674889	−	0.737919i	$-0.264191\pi$
$131$	15.4489	1.34978	0.674889	+	0.737919i	$0.264191\pi$
$132$	−5.25834	−0.457679
$133$	1.35955	0.117888
$134$	4.33781	0.374730
$135$	14.9467	1.28641
$136$	−5.72337	−0.490775
$137$	0.317867	0.0271572	0.0135786	−	0.999908i	$-0.495678\pi$
$137$	0.317867	0.0271572	0.0135786	+	0.999908i	$0.495678\pi$
$138$	−1.50752	−0.128329
$139$	17.7683	1.50709	0.753543	−	0.657399i	$-0.228343\pi$
$139$	17.7683	1.50709	0.753543	+	0.657399i	$0.228343\pi$
$140$	−2.70248	−0.228401
$141$	18.7628	1.58011
$142$	−5.95622	−0.499835
$143$	1.73305	0.144925
$144$	−0.493160	−0.0410967
$145$	−3.58652	−0.297845
$146$	5.02387	0.415778
$147$	1.58330	0.130588
$148$	−0.895989	−0.0736498
$149$	16.2555	1.33170	0.665852	−	0.746084i	$-0.268068\pi$
$149$	16.2555	1.33170	0.665852	+	0.746084i	$0.268068\pi$
$150$	−3.64699	−0.297775
$151$	1.93556	0.157514	0.0787570	−	0.996894i	$-0.474905\pi$
$151$	1.93556	0.157514	0.0787570	+	0.996894i	$0.474905\pi$
$152$	−1.35955	−0.110274
$153$	−2.82254	−0.228189
$154$	3.32112	0.267624
$155$	15.0536	1.20914
$156$	−0.826210	−0.0661498
$157$	16.3063	1.30139	0.650693	−	0.759341i	$-0.274479\pi$
$157$	16.3063	1.30139	0.650693	+	0.759341i	$0.274479\pi$
$158$	−0.371661	−0.0295677
$159$	−15.4612	−1.22616
$160$	2.70248	0.213650
$161$	0.952140	0.0750391
$162$	7.27731	0.571760
$163$	4.71664	0.369436	0.184718	−	0.982792i	$-0.440863\pi$
$163$	4.71664	0.369436	0.184718	+	0.982792i	$0.440863\pi$
$164$	8.53008	0.666087
$165$	14.2106	1.10629
$166$	−6.44337	−0.500103
$167$	2.84265	0.219971	0.109985	−	0.993933i	$-0.464920\pi$
$167$	2.84265	0.219971	0.109985	+	0.993933i	$0.464920\pi$
$168$	−1.58330	−0.122154
$169$	−12.7277	−0.979054
$170$	15.4673	1.18629
$171$	−0.670474	−0.0512724
$172$	−5.56406	−0.424255
$173$	−25.4969	−1.93850	−0.969248	−	0.246086i	$-0.920855\pi$
$173$	−25.4969	−1.93850	−0.969248	+	0.246086i	$0.920855\pi$
$174$	−2.10123	−0.159294
$175$	2.30341	0.174121
$176$	−3.32112	−0.250339
$177$	−1.44865	−0.108887
$178$	12.2229	0.916146
$179$	−6.07909	−0.454373	−0.227186	−	0.973851i	$-0.572953\pi$
$179$	−6.07909	−0.454373	−0.227186	+	0.973851i	$0.572953\pi$
$180$	1.33276	0.0993378
$181$	−3.12539	−0.232309	−0.116154	−	0.993231i	$-0.537057\pi$
$181$	−3.12539	−0.232309	−0.116154	+	0.993231i	$0.537057\pi$
$182$	0.521828	0.0386805
$183$	−3.67365	−0.271564
$184$	−0.952140	−0.0701927
$185$	2.42139	0.178024
$186$	8.81944	0.646673
$187$	−19.0080	−1.39000
$188$	11.8504	0.864283
$189$	−5.53072	−0.402301
$190$	3.67415	0.266551
$191$	21.3995	1.54842	0.774208	−	0.632931i	$-0.218148\pi$
$191$	21.3995	1.54842	0.774208	+	0.632931i	$0.218148\pi$
$192$	1.58330	0.114265
$193$	16.5247	1.18947	0.594735	−	0.803921i	$-0.297257\pi$
$193$	16.5247	1.18947	0.594735	+	0.803921i	$0.297257\pi$
$194$	−7.32853	−0.526158
$195$	2.23282	0.159895
$196$	1.00000	0.0714286
$197$	26.3841	1.87979	0.939893	−	0.341469i	$-0.110924\pi$
$197$	26.3841	1.87979	0.939893	+	0.341469i	$0.110924\pi$
$198$	−1.63785	−0.116397
$199$	6.01640	0.426492	0.213246	−	0.976999i	$-0.431597\pi$
$199$	6.01640	0.426492	0.213246	+	0.976999i	$0.431597\pi$
$200$	−2.30341	−0.162876
$201$	−6.86806	−0.484435
$202$	−15.0787	−1.06093
$203$	1.32712	0.0931457
$204$	9.06182	0.634454
$205$	−23.0524	−1.61005
$206$	5.18408	0.361192
$207$	−0.469557	−0.0326365
$208$	−0.521828	−0.0361823
$209$	−4.51522	−0.312324
$210$	4.27884	0.295268
$211$	−23.6512	−1.62822	−0.814110	−	0.580711i	$-0.802774\pi$
$211$	−23.6512	−1.62822	−0.814110	+	0.580711i	$0.802774\pi$
$212$	−9.76520	−0.670677
$213$	9.43048	0.646166
$214$	1.58530	0.108369
$215$	15.0368	1.02550
$216$	5.53072	0.376318
$217$	−5.57029	−0.378136
$218$	12.0692	0.817429
$219$	−7.95429	−0.537501
$220$	8.97528	0.605113
$221$	−2.98662	−0.200902
$222$	1.41862	0.0952115
$223$	23.7565	1.59085	0.795426	−	0.606051i	$-0.207247\pi$
$223$	23.7565	1.59085	0.795426	+	0.606051i	$0.207247\pi$
$224$	−1.00000	−0.0668153
$225$	−1.13595	−0.0757300
$226$	−13.0248	−0.866397
$227$	19.4279	1.28948	0.644738	−	0.764403i	$-0.276966\pi$
$227$	19.4279	1.28948	0.644738	+	0.764403i	$0.276966\pi$
$228$	2.15257	0.142557
$229$	19.3121	1.27618	0.638090	−	0.769962i	$-0.279725\pi$
$229$	19.3121	1.27618	0.638090	+	0.769962i	$0.279725\pi$
$230$	2.57314	0.169668
$231$	−5.25834	−0.345973
$232$	−1.32712	−0.0871298
$233$	14.6923	0.962527	0.481263	−	0.876576i	$-0.340178\pi$
$233$	14.6923	0.962527	0.481263	+	0.876576i	$0.340178\pi$
$234$	−0.257345	−0.0168232
$235$	−32.0256	−2.08912
$236$	−0.914957	−0.0595586
$237$	0.588451	0.0382240
$238$	−5.72337	−0.370991
$239$	−5.56574	−0.360018	−0.180009	−	0.983665i	$-0.557613\pi$
$239$	−5.56574	−0.360018	−0.180009	+	0.983665i	$0.557613\pi$
$240$	−4.27884	−0.276198
$241$	10.9440	0.704965	0.352482	−	0.935818i	$-0.385338\pi$
$241$	10.9440	0.704965	0.352482	+	0.935818i	$0.385338\pi$
$242$	−0.0298592	−0.00191942
$243$	5.06999	0.325240
$244$	−2.32025	−0.148539
$245$	−2.70248	−0.172655
$246$	−13.5057	−0.861090
$247$	−0.709449	−0.0451412
$248$	5.57029	0.353714
$249$	10.2018	0.646512
$250$	−7.28749	−0.460901
$251$	−21.1219	−1.33321	−0.666603	−	0.745413i	$-0.732252\pi$
$251$	−21.1219	−1.33321	−0.666603	+	0.745413i	$0.732252\pi$
$252$	−0.493160	−0.0310662
$253$	−3.16217	−0.198804
$254$	−16.2744	−1.02115
$255$	−24.4894	−1.53359
$256$	1.00000	0.0625000
$257$	14.4326	0.900281	0.450140	−	0.892958i	$-0.351374\pi$
$257$	14.4326	0.900281	0.450140	+	0.892958i	$0.351374\pi$
$258$	8.80957	0.548460
$259$	−0.895989	−0.0556740
$260$	1.41023	0.0874588
$261$	−0.654484	−0.0405115
$262$	−15.4489	−0.954438
$263$	15.6750	0.966563	0.483281	−	0.875465i	$-0.339445\pi$
$263$	15.6750	0.966563	0.483281	+	0.875465i	$0.339445\pi$
$264$	5.25834	0.323628
$265$	26.3903	1.62114
$266$	−1.35955	−0.0833591
$267$	−19.3525	−1.18436
$268$	−4.33781	−0.264974
$269$	−0.431597	−0.0263149	−0.0131575	−	0.999913i	$-0.504188\pi$
$269$	−0.431597	−0.0263149	−0.0131575	+	0.999913i	$0.504188\pi$
$270$	−14.9467	−0.909626
$271$	18.4044	1.11798	0.558992	−	0.829173i	$-0.311188\pi$
$271$	18.4044	1.11798	0.558992	+	0.829173i	$0.311188\pi$
$272$	5.72337	0.347031
$273$	−0.826210	−0.0500045
$274$	−0.317867	−0.0192031
$275$	−7.64991	−0.461307
$276$	1.50752	0.0907422
$277$	−25.5082	−1.53264	−0.766320	−	0.642459i	$-0.777914\pi$
$277$	−25.5082	−1.53264	−0.766320	+	0.642459i	$0.777914\pi$
$278$	−17.7683	−1.06567
$279$	2.74705	0.164461
$280$	2.70248	0.161504
$281$	27.1737	1.62104	0.810522	−	0.585708i	$-0.199183\pi$
$281$	27.1737	1.62104	0.810522	+	0.585708i	$0.199183\pi$
$282$	−18.7628	−1.11731
$283$	−9.10806	−0.541418	−0.270709	−	0.962661i	$-0.587258\pi$
$283$	−9.10806	−0.541418	−0.270709	+	0.962661i	$0.587258\pi$
$284$	5.95622	0.353437
$285$	−5.81728	−0.344586
$286$	−1.73305	−0.102478
$287$	8.53008	0.503515
$288$	0.493160	0.0290597
$289$	15.7570	0.926883
$290$	3.58652	0.210608
$291$	11.6033	0.680195
$292$	−5.02387	−0.294000
$293$	11.2588	0.657746	0.328873	−	0.944374i	$-0.393331\pi$
$293$	11.2588	0.657746	0.328873	+	0.944374i	$0.393331\pi$
$294$	−1.58330	−0.0923399
$295$	2.47265	0.143963
$296$	0.895989	0.0520783
$297$	18.3682	1.06583
$298$	−16.2555	−0.941657
$299$	−0.496853	−0.0287338
$300$	3.64699	0.210559
$301$	−5.56406	−0.320707
$302$	−1.93556	−0.111379
$303$	23.8741	1.37153
$304$	1.35955	0.0779753
$305$	6.27044	0.359044
$306$	2.82254	0.161354
$307$	18.3338	1.04637	0.523183	−	0.852221i	$-0.324745\pi$
$307$	18.3338	1.04637	0.523183	+	0.852221i	$0.324745\pi$
$308$	−3.32112	−0.189239
$309$	−8.20796	−0.466935
$310$	−15.0536	−0.854988
$311$	−3.61896	−0.205212	−0.102606	−	0.994722i	$-0.532718\pi$
$311$	−3.61896	−0.205212	−0.102606	+	0.994722i	$0.532718\pi$
$312$	0.826210	0.0467749
$313$	−28.2909	−1.59910	−0.799549	−	0.600600i	$-0.794928\pi$
$313$	−28.2909	−1.59910	−0.799549	+	0.600600i	$0.794928\pi$
$314$	−16.3063	−0.920218
$315$	1.33276	0.0750923
$316$	0.371661	0.0209076
$317$	−20.5920	−1.15656	−0.578281	−	0.815838i	$-0.696276\pi$
$317$	−20.5920	−1.15656	−0.578281	+	0.815838i	$0.696276\pi$
$318$	15.4612	0.867024
$319$	−4.40754	−0.246775
$320$	−2.70248	−0.151073
$321$	−2.51001	−0.140095
$322$	−0.952140	−0.0530607
$323$	7.78119	0.432957
$324$	−7.27731	−0.404295
$325$	−1.20198	−0.0666740
$326$	−4.71664	−0.261231
$327$	−19.1092	−1.05674
$328$	−8.53008	−0.470995
$329$	11.8504	0.653336
$330$	−14.2106	−0.782265
$331$	−19.4355	−1.06827	−0.534137	−	0.845398i	$-0.679363\pi$
$331$	−19.4355	−1.06827	−0.534137	+	0.845398i	$0.679363\pi$
$332$	6.44337	0.353626
$333$	0.441866	0.0242141
$334$	−2.84265	−0.155543
$335$	11.7229	0.640488
$336$	1.58330	0.0863761
$337$	27.0421	1.47308	0.736539	−	0.676395i	$-0.236459\pi$
$337$	27.0421	1.47308	0.736539	+	0.676395i	$0.236459\pi$
$338$	12.7277	0.692295
$339$	20.6222	1.12004
$340$	−15.4673	−0.838833
$341$	18.4996	1.00181
$342$	0.670474	0.0362551
$343$	1.00000	0.0539949
$344$	5.56406	0.299994
$345$	−4.07405	−0.219340
$346$	25.4969	1.37072
$347$	−8.06413	−0.432905	−0.216453	−	0.976293i	$-0.569449\pi$
$347$	−8.06413	−0.432905	−0.216453	+	0.976293i	$0.569449\pi$
$348$	2.10123	0.112638
$349$	15.4270	0.825790	0.412895	−	0.910779i	$-0.364518\pi$
$349$	15.4270	0.825790	0.412895	+	0.910779i	$0.364518\pi$
$350$	−2.30341	−0.123122
$351$	2.88608	0.154048
$352$	3.32112	0.177016
$353$	−9.77202	−0.520112	−0.260056	−	0.965594i	$-0.583741\pi$
$353$	−9.77202	−0.520112	−0.260056	+	0.965594i	$0.583741\pi$
$354$	1.44865	0.0769949
$355$	−16.0966	−0.854317
$356$	−12.2229	−0.647813
$357$	9.06182	0.479602
$358$	6.07909	0.321290
$359$	14.0136	0.739609	0.369804	−	0.929110i	$-0.379425\pi$
$359$	14.0136	0.739609	0.369804	+	0.929110i	$0.379425\pi$
$360$	−1.33276	−0.0702424
$361$	−17.1516	−0.902718
$362$	3.12539	0.164267
$363$	0.0472761	0.00248135
$364$	−0.521828	−0.0273512
$365$	13.5769	0.710648
$366$	3.67365	0.192025
$367$	−19.9866	−1.04329	−0.521645	−	0.853162i	$-0.674682\pi$
$367$	−19.9866	−1.04329	−0.521645	+	0.853162i	$0.674682\pi$
$368$	0.952140	0.0496337
$369$	−4.20670	−0.218992
$370$	−2.42139	−0.125882
$371$	−9.76520	−0.506984
$372$	−8.81944	−0.457267
$373$	6.06090	0.313821	0.156911	−	0.987613i	$-0.449847\pi$
$373$	6.06090	0.313821	0.156911	+	0.987613i	$0.449847\pi$
$374$	19.0080	0.982882
$375$	11.5383	0.595834
$376$	−11.8504	−0.611140
$377$	−0.692529	−0.0356671
$378$	5.53072	0.284470
$379$	2.55501	0.131242	0.0656210	−	0.997845i	$-0.479097\pi$
$379$	2.55501	0.131242	0.0656210	+	0.997845i	$0.479097\pi$
$380$	−3.67415	−0.188480
$381$	25.7673	1.32010
$382$	−21.3995	−1.09490
$383$	20.9547	1.07074	0.535369	−	0.844618i	$-0.320173\pi$
$383$	20.9547	1.07074	0.535369	+	0.844618i	$0.320173\pi$
$384$	−1.58330	−0.0807975
$385$	8.97528	0.457422
$386$	−16.5247	−0.841083
$387$	2.74397	0.139484
$388$	7.32853	0.372050
$389$	11.2040	0.568064	0.284032	−	0.958815i	$-0.408328\pi$
$389$	11.2040	0.568064	0.284032	+	0.958815i	$0.408328\pi$
$390$	−2.23282	−0.113063
$391$	5.44945	0.275591
$392$	−1.00000	−0.0505076
$393$	24.4603	1.23386
$394$	−26.3841	−1.32921
$395$	−1.00441	−0.0505372
$396$	1.63785	0.0823048
$397$	14.1512	0.710227	0.355113	−	0.934823i	$-0.384442\pi$
$397$	14.1512	0.710227	0.355113	+	0.934823i	$0.384442\pi$
$398$	−6.01640	−0.301575
$399$	2.15257	0.107763
$400$	2.30341	0.115170
$401$	−18.7652	−0.937091	−0.468545	−	0.883439i	$-0.655222\pi$
$401$	−18.7652	−0.937091	−0.468545	+	0.883439i	$0.655222\pi$
$402$	6.86806	0.342548
$403$	2.90673	0.144795
$404$	15.0787	0.750194
$405$	19.6668	0.977251
$406$	−1.32712	−0.0658640
$407$	2.97569	0.147499
$408$	−9.06182	−0.448627
$409$	28.5304	1.41074	0.705369	−	0.708840i	$-0.250781\pi$
$409$	28.5304	1.41074	0.705369	+	0.708840i	$0.250781\pi$
$410$	23.0524	1.13848
$411$	0.503279	0.0248249
$412$	−5.18408	−0.255401
$413$	−0.914957	−0.0450221
$414$	0.469557	0.0230775
$415$	−17.4131	−0.854775
$416$	0.521828	0.0255847
$417$	28.1325	1.37766
$418$	4.51522	0.220847
$419$	−39.0302	−1.90675	−0.953375	−	0.301788i	$-0.902417\pi$
$419$	−39.0302	−1.90675	−0.953375	+	0.301788i	$0.902417\pi$
$420$	−4.27884	−0.208786
$421$	−12.3623	−0.602500	−0.301250	−	0.953545i	$-0.597404\pi$
$421$	−12.3623	−0.602500	−0.301250	+	0.953545i	$0.597404\pi$
$422$	23.6512	1.15132
$423$	−5.84417	−0.284153
$424$	9.76520	0.474240
$425$	13.1833	0.639483
$426$	−9.43048	−0.456908
$427$	−2.32025	−0.112285
$428$	−1.58530	−0.0766284
$429$	2.74395	0.132479
$430$	−15.0368	−0.725137
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−5.53072	−0.266097
$433$	3.21796	0.154646	0.0773228	−	0.997006i	$-0.475363\pi$
$433$	3.21796	0.154646	0.0773228	+	0.997006i	$0.475363\pi$
$434$	5.57029	0.267383
$435$	−5.67854	−0.272265
$436$	−12.0692	−0.578009
$437$	1.29448	0.0619233
$438$	7.95429	0.380071
$439$	−9.56516	−0.456520	−0.228260	−	0.973600i	$-0.573304\pi$
$439$	−9.56516	−0.456520	−0.228260	+	0.973600i	$0.573304\pi$
$440$	−8.97528	−0.427879
$441$	−0.493160	−0.0234838
$442$	2.98662	0.142059
$443$	16.4443	0.781294	0.390647	−	0.920541i	$-0.372251\pi$
$443$	16.4443	0.781294	0.390647	+	0.920541i	$0.372251\pi$
$444$	−1.41862	−0.0673247
$445$	33.0322	1.56588
$446$	−23.7565	−1.12490
$447$	25.7374	1.21734
$448$	1.00000	0.0472456
$449$	−15.7456	−0.743081	−0.371540	−	0.928417i	$-0.621170\pi$
$449$	−15.7456	−0.743081	−0.371540	+	0.928417i	$0.621170\pi$
$450$	1.13595	0.0535492
$451$	−28.3294	−1.33398
$452$	13.0248	0.612635
$453$	3.06458	0.143987
$454$	−19.4279	−0.911798
$455$	1.41023	0.0661126
$456$	−2.15257	−0.100803
$457$	30.5014	1.42680	0.713398	−	0.700759i	$-0.247155\pi$
$457$	30.5014	1.42680	0.713398	+	0.700759i	$0.247155\pi$
$458$	−19.3121	−0.902396
$459$	−31.6544	−1.47750
$460$	−2.57314	−0.119973
$461$	12.2428	0.570206	0.285103	−	0.958497i	$-0.407972\pi$
$461$	12.2428	0.570206	0.285103	+	0.958497i	$0.407972\pi$
$462$	5.25834	0.244640
$463$	−30.2608	−1.40634	−0.703170	−	0.711022i	$-0.748233\pi$
$463$	−30.2608	−1.40634	−0.703170	+	0.711022i	$0.748233\pi$
$464$	1.32712	0.0616101
$465$	23.8344	1.10529
$466$	−14.6923	−0.680609
$467$	−0.0167118	−0.000773328 0	−0.000386664	−	1.00000i	$-0.500123\pi$
$467$	−0.0167118	−0.000773328 0	−0.000386664		1.00000i	$0.500123\pi$
$468$	0.257345	0.0118958
$469$	−4.33781	−0.200301
$470$	32.0256	1.47723
$471$	25.8178	1.18962
$472$	0.914957	0.0421143
$473$	18.4789	0.849661
$474$	−0.588451	−0.0270284
$475$	3.13159	0.143687
$476$	5.72337	0.262330
$477$	4.81581	0.220501
$478$	5.56574	0.254571
$479$	−12.5820	−0.574885	−0.287442	−	0.957798i	$-0.592805\pi$
$479$	−12.5820	−0.574885	−0.287442	+	0.957798i	$0.592805\pi$
$480$	4.27884	0.195301
$481$	0.467552	0.0213185
$482$	−10.9440	−0.498485
$483$	1.50752	0.0685947
$484$	0.0298592	0.00135724
$485$	−19.8052	−0.899309
$486$	−5.06999	−0.229980
$487$	1.95798	0.0887244	0.0443622	−	0.999016i	$-0.485874\pi$
$487$	1.95798	0.0887244	0.0443622	+	0.999016i	$0.485874\pi$
$488$	2.32025	0.105033
$489$	7.46786	0.337708
$490$	2.70248	0.122086
$491$	−14.0568	−0.634376	−0.317188	−	0.948363i	$-0.602739\pi$
$491$	−14.0568	−0.634376	−0.317188	+	0.948363i	$0.602739\pi$
$492$	13.5057	0.608883
$493$	7.59562	0.342089
$494$	0.709449	0.0319196
$495$	−4.42625	−0.198945
$496$	−5.57029	−0.250113
$497$	5.95622	0.267173
$498$	−10.2018	−0.457153
$499$	−30.3090	−1.35682	−0.678409	−	0.734684i	$-0.737330\pi$
$499$	−30.3090	−1.35682	−0.678409	+	0.734684i	$0.737330\pi$
$500$	7.28749	0.325906
$501$	4.50077	0.201079
$502$	21.1219	0.942718
$503$	2.39815	0.106928	0.0534642	−	0.998570i	$-0.482974\pi$
$503$	2.39815	0.106928	0.0534642	+	0.998570i	$0.482974\pi$
$504$	0.493160	0.0219671
$505$	−40.7499	−1.81335
$506$	3.16217	0.140576
$507$	−20.1518	−0.894971
$508$	16.2744	0.722061
$509$	−29.2221	−1.29525	−0.647623	−	0.761961i	$-0.724237\pi$
$509$	−29.2221	−1.29525	−0.647623	+	0.761961i	$0.724237\pi$
$510$	24.4894	1.08441
$511$	−5.02387	−0.222243
$512$	−1.00000	−0.0441942
$513$	−7.51927	−0.331984
$514$	−14.4326	−0.636595
$515$	14.0099	0.617350
$516$	−8.80957	−0.387820
$517$	−39.3568	−1.73091
$518$	0.895989	0.0393675
$519$	−40.3693	−1.77202
$520$	−1.41023	−0.0618427
$521$	2.82227	0.123646	0.0618230	−	0.998087i	$-0.480309\pi$
$521$	2.82227	0.123646	0.0618230	+	0.998087i	$0.480309\pi$
$522$	0.654484	0.0286460
$523$	23.7303	1.03765	0.518826	−	0.854880i	$-0.326369\pi$
$523$	23.7303	1.03765	0.518826	+	0.854880i	$0.326369\pi$
$524$	15.4489	0.674889
$525$	3.64699	0.159168
$526$	−15.6750	−0.683463
$527$	−31.8809	−1.38875
$528$	−5.25834	−0.228840
$529$	−22.0934	−0.960584
$530$	−26.3903	−1.14632
$531$	0.451220	0.0195813
$532$	1.35955	0.0589438
$533$	−4.45123	−0.192804
$534$	19.3525	0.837467
$535$	4.28425	0.185224
$536$	4.33781	0.187365
$537$	−9.62503	−0.415351
$538$	0.431597	0.0186075
$539$	−3.32112	−0.143051
$540$	14.9467	0.643203
$541$	−28.9663	−1.24536	−0.622680	−	0.782477i	$-0.713956\pi$
$541$	−28.9663	−1.24536	−0.622680	+	0.782477i	$0.713956\pi$
$542$	−18.4044	−0.790535
$543$	−4.94844	−0.212358
$544$	−5.72337	−0.245388
$545$	32.6168	1.39715
$546$	0.826210	0.0353585
$547$	5.48548	0.234542	0.117271	−	0.993100i	$-0.462585\pi$
$547$	5.48548	0.234542	0.117271	+	0.993100i	$0.462585\pi$
$548$	0.317867	0.0135786
$549$	1.14426	0.0488356
$550$	7.64991	0.326193
$551$	1.80428	0.0768651
$552$	−1.50752	−0.0641644
$553$	0.371661	0.0158046
$554$	25.5082	1.08374
$555$	3.83379	0.162735
$556$	17.7683	0.753543
$557$	−6.54215	−0.277200	−0.138600	−	0.990348i	$-0.544260\pi$
$557$	−6.54215	−0.277200	−0.138600	+	0.990348i	$0.544260\pi$
$558$	−2.74705	−0.116292
$559$	2.90348	0.122804
$560$	−2.70248	−0.114201
$561$	−30.0954	−1.27063
$562$	−27.1737	−1.14625
$563$	1.86183	0.0784668	0.0392334	−	0.999230i	$-0.487508\pi$
$563$	1.86183	0.0784668	0.0392334	+	0.999230i	$0.487508\pi$
$564$	18.7628	0.790057
$565$	−35.1993	−1.48085
$566$	9.10806	0.382840
$567$	−7.27731	−0.305618
$568$	−5.95622	−0.249917
$569$	20.0258	0.839523	0.419762	−	0.907634i	$-0.362114\pi$
$569$	20.0258	0.839523	0.419762	+	0.907634i	$0.362114\pi$
$570$	5.81728	0.243659
$571$	13.7563	0.575685	0.287842	−	0.957678i	$-0.407062\pi$
$571$	13.7563	0.575685	0.287842	+	0.957678i	$0.407062\pi$
$572$	1.73305	0.0724627
$573$	33.8819	1.41544
$574$	−8.53008	−0.356039
$575$	2.19317	0.0914614
$576$	−0.493160	−0.0205483
$577$	−9.21998	−0.383833	−0.191916	−	0.981411i	$-0.561470\pi$
$577$	−9.21998	−0.383833	−0.191916	+	0.981411i	$0.561470\pi$
$578$	−15.7570	−0.655405
$579$	26.1635	1.08732
$580$	−3.58652	−0.148922
$581$	6.44337	0.267316
$582$	−11.6033	−0.480971
$583$	32.4314	1.34317
$584$	5.02387	0.207889
$585$	−0.695470	−0.0287541
$586$	−11.2588	−0.465097
$587$	33.4621	1.38113	0.690564	−	0.723272i	$-0.257363\pi$
$587$	33.4621	1.38113	0.690564	+	0.723272i	$0.257363\pi$
$588$	1.58330	0.0652942
$589$	−7.57307	−0.312043
$590$	−2.47265	−0.101798
$591$	41.7739	1.71835
$592$	−0.895989	−0.0368249
$593$	−31.7523	−1.30391	−0.651956	−	0.758257i	$-0.726051\pi$
$593$	−31.7523	−1.30391	−0.651956	+	0.758257i	$0.726051\pi$
$594$	−18.3682	−0.753657
$595$	−15.4673	−0.634098
$596$	16.2555	0.665852
$597$	9.52577	0.389864
$598$	0.496853	0.0203178
$599$	−2.30728	−0.0942730	−0.0471365	−	0.998888i	$-0.515010\pi$
$599$	−2.30728	−0.0942730	−0.0471365	+	0.998888i	$0.515010\pi$
$600$	−3.64699	−0.148888
$601$	−27.5665	−1.12446	−0.562231	−	0.826980i	$-0.690057\pi$
$601$	−27.5665	−1.12446	−0.562231	+	0.826980i	$0.690057\pi$
$602$	5.56406	0.226774
$603$	2.13924	0.0871164
$604$	1.93556	0.0787570
$605$	−0.0806941	−0.00328068
$606$	−23.8741	−0.969820
$607$	−30.9130	−1.25472	−0.627361	−	0.778729i	$-0.715865\pi$
$607$	−30.9130	−1.25472	−0.627361	+	0.778729i	$0.715865\pi$
$608$	−1.35955	−0.0551369
$609$	2.10123	0.0851463
$610$	−6.27044	−0.253882
$611$	−6.18389	−0.250174
$612$	−2.82254	−0.114094
$613$	34.7721	1.40443	0.702216	−	0.711964i	$-0.252194\pi$
$613$	34.7721	1.40443	0.702216	+	0.711964i	$0.252194\pi$
$614$	−18.3338	−0.739892
$615$	−36.4988	−1.47178
$616$	3.32112	0.133812
$617$	17.8570	0.718895	0.359447	−	0.933165i	$-0.382965\pi$
$617$	17.8570	0.718895	0.359447	+	0.933165i	$0.382965\pi$
$618$	8.20796	0.330173
$619$	−16.6362	−0.668666	−0.334333	−	0.942455i	$-0.608511\pi$
$619$	−16.6362	−0.668666	−0.334333	+	0.942455i	$0.608511\pi$
$620$	15.0536	0.604568
$621$	−5.26602	−0.211318
$622$	3.61896	0.145107
$623$	−12.2229	−0.489701
$624$	−0.826210	−0.0330749
$625$	−31.2114	−1.24845
$626$	28.2909	1.13073
$627$	−7.14895	−0.285502
$628$	16.3063	0.650693
$629$	−5.12808	−0.204470
$630$	−1.33276	−0.0530983
$631$	36.8662	1.46762	0.733811	−	0.679354i	$-0.237740\pi$
$631$	36.8662	1.46762	0.733811	+	0.679354i	$0.237740\pi$
$632$	−0.371661	−0.0147839
$633$	−37.4470	−1.48839
$634$	20.5920	0.817813
$635$	−43.9813	−1.74535
$636$	−15.4612	−0.613078
$637$	−0.521828	−0.0206756
$638$	4.40754	0.174496
$639$	−2.93737	−0.116201
$640$	2.70248	0.106825
$641$	11.1723	0.441278	0.220639	−	0.975356i	$-0.429186\pi$
$641$	11.1723	0.441278	0.220639	+	0.975356i	$0.429186\pi$
$642$	2.51001	0.0990621
$643$	23.8337	0.939909	0.469955	−	0.882691i	$-0.344270\pi$
$643$	23.8337	0.939909	0.469955	+	0.882691i	$0.344270\pi$
$644$	0.952140	0.0375196
$645$	23.8077	0.937428
$646$	−7.78119	−0.306147
$647$	−16.7531	−0.658633	−0.329317	−	0.944220i	$-0.606818\pi$
$647$	−16.7531	−0.658633	−0.329317	+	0.944220i	$0.606818\pi$
$648$	7.27731	0.285880
$649$	3.03868	0.119279
$650$	1.20198	0.0471457
$651$	−8.81944	−0.345661
$652$	4.71664	0.184718
$653$	33.4373	1.30850	0.654252	−	0.756276i	$-0.272984\pi$
$653$	33.4373	1.30850	0.654252	+	0.756276i	$0.272984\pi$
$654$	19.1092	0.747227
$655$	−41.7504	−1.63132
$656$	8.53008	0.333044
$657$	2.47757	0.0966592
$658$	−11.8504	−0.461979
$659$	2.26026	0.0880472	0.0440236	−	0.999030i	$-0.485982\pi$
$659$	2.26026	0.0880472	0.0440236	+	0.999030i	$0.485982\pi$
$660$	14.2106	0.553145
$661$	25.8608	1.00587	0.502935	−	0.864324i	$-0.332253\pi$
$661$	25.8608	1.00587	0.502935	+	0.864324i	$0.332253\pi$
$662$	19.4355	0.755383
$663$	−4.72871	−0.183648
$664$	−6.44337	−0.250051
$665$	−3.67415	−0.142477
$666$	−0.441866	−0.0171220
$667$	1.26361	0.0489270
$668$	2.84265	0.109985
$669$	37.6136	1.45423
$670$	−11.7229	−0.452893
$671$	7.70584	0.297481
$672$	−1.58330	−0.0610771
$673$	22.6696	0.873850	0.436925	−	0.899498i	$-0.356068\pi$
$673$	22.6696	0.873850	0.436925	+	0.899498i	$0.356068\pi$
$674$	−27.0421	−1.04162
$675$	−12.7395	−0.490344
$676$	−12.7277	−0.489527
$677$	−24.6894	−0.948890	−0.474445	−	0.880285i	$-0.657351\pi$
$677$	−24.6894	−0.948890	−0.474445	+	0.880285i	$0.657351\pi$
$678$	−20.6222	−0.791990
$679$	7.32853	0.281243
$680$	15.4673	0.593144
$681$	30.7602	1.17874
$682$	−18.4996	−0.708387
$683$	25.1404	0.961970	0.480985	−	0.876729i	$-0.340279\pi$
$683$	25.1404	0.961970	0.480985	+	0.876729i	$0.340279\pi$
$684$	−0.670474	−0.0256362
$685$	−0.859031	−0.0328219
$686$	−1.00000	−0.0381802
$687$	30.5769	1.16658
$688$	−5.56406	−0.212128
$689$	5.09575	0.194133
$690$	4.07405	0.155097
$691$	−11.0999	−0.422259	−0.211129	−	0.977458i	$-0.567714\pi$
$691$	−11.0999	−0.422259	−0.211129	+	0.977458i	$0.567714\pi$
$692$	−25.4969	−0.969248
$693$	1.63785	0.0622166
$694$	8.06413	0.306110
$695$	−48.0185	−1.82144
$696$	−2.10123	−0.0796470
$697$	48.8208	1.84922
$698$	−15.4270	−0.583921
$699$	23.2624	0.879864
$700$	2.30341	0.0870607
$701$	51.6678	1.95147	0.975734	−	0.218960i	$-0.0702665\pi$
$701$	51.6678	1.95147	0.975734	+	0.218960i	$0.0702665\pi$
$702$	−2.88608	−0.108928
$703$	−1.21814	−0.0459429
$704$	−3.32112	−0.125170
$705$	−50.7062	−1.90971
$706$	9.77202	0.367775
$707$	15.0787	0.567093
$708$	−1.44865	−0.0544436
$709$	−23.6152	−0.886886	−0.443443	−	0.896303i	$-0.646243\pi$
$709$	−23.6152	−0.886886	−0.443443	+	0.896303i	$0.646243\pi$
$710$	16.0966	0.604094
$711$	−0.183288	−0.00687385
$712$	12.2229	0.458073
$713$	−5.30369	−0.198625
$714$	−9.06182	−0.339130
$715$	−4.68355	−0.175155
$716$	−6.07909	−0.227186
$717$	−8.81223	−0.329099
$718$	−14.0136	−0.522982
$719$	29.8266	1.11235	0.556173	−	0.831067i	$-0.312269\pi$
$719$	29.8266	1.11235	0.556173	+	0.831067i	$0.312269\pi$
$720$	1.33276	0.0496689
$721$	−5.18408	−0.193065
$722$	17.1516	0.638318
$723$	17.3276	0.644421
$724$	−3.12539	−0.116154
$725$	3.05691	0.113531
$726$	−0.0472761	−0.00175458
$727$	−15.9288	−0.590765	−0.295383	−	0.955379i	$-0.595447\pi$
$727$	−15.9288	−0.590765	−0.295383	+	0.955379i	$0.595447\pi$
$728$	0.521828	0.0193402
$729$	29.8593	1.10590
$730$	−13.5769	−0.502504
$731$	−31.8452	−1.17784
$732$	−3.67365	−0.135782
$733$	−39.5955	−1.46249	−0.731246	−	0.682114i	$-0.761061\pi$
$733$	−39.5955	−1.46249	−0.731246	+	0.682114i	$0.761061\pi$
$734$	19.9866	0.737718
$735$	−4.27884	−0.157827
$736$	−0.952140	−0.0350963
$737$	14.4064	0.530667
$738$	4.20670	0.154851
$739$	25.3114	0.931093	0.465547	−	0.885023i	$-0.345858\pi$
$739$	25.3114	0.931093	0.465547	+	0.885023i	$0.345858\pi$
$740$	2.42139	0.0890122
$741$	−1.12327	−0.0412644
$742$	9.76520	0.358492
$743$	−49.0323	−1.79882	−0.899411	−	0.437105i	$-0.856004\pi$
$743$	−49.0323	−1.79882	−0.899411	+	0.437105i	$0.856004\pi$
$744$	8.81944	0.323336
$745$	−43.9302	−1.60948
$746$	−6.06090	−0.221905
$747$	−3.17761	−0.116263
$748$	−19.0080	−0.695002
$749$	−1.58530	−0.0579256
$750$	−11.5383	−0.421319
$751$	46.5286	1.69785	0.848926	−	0.528511i	$-0.177250\pi$
$751$	46.5286	1.69785	0.848926	+	0.528511i	$0.177250\pi$
$752$	11.8504	0.432141
$753$	−33.4424	−1.21871
$754$	0.692529	0.0252204
$755$	−5.23083	−0.190369
$756$	−5.53072	−0.201150
$757$	16.7343	0.608218	0.304109	−	0.952637i	$-0.401641\pi$
$757$	16.7343	0.608218	0.304109	+	0.952637i	$0.401641\pi$
$758$	−2.55501	−0.0928021
$759$	−5.00667	−0.181731
$760$	3.67415	0.133275
$761$	−43.0444	−1.56036	−0.780180	−	0.625555i	$-0.784872\pi$
$761$	−43.0444	−1.56036	−0.780180	+	0.625555i	$0.784872\pi$
$762$	−25.7673	−0.933450
$763$	−12.0692	−0.436934
$764$	21.3995	0.774208
$765$	7.62786	0.275786
$766$	−20.9547	−0.757126
$767$	0.477450	0.0172397
$768$	1.58330	0.0571324
$769$	19.9637	0.719910	0.359955	−	0.932970i	$-0.382792\pi$
$769$	19.9637	0.719910	0.359955	+	0.932970i	$0.382792\pi$
$770$	−8.97528	−0.323446
$771$	22.8511	0.822964
$772$	16.5247	0.594735
$773$	−17.6655	−0.635383	−0.317692	−	0.948194i	$-0.602908\pi$
$773$	−17.6655	−0.635383	−0.317692	+	0.948194i	$0.602908\pi$
$774$	−2.74397	−0.0986300
$775$	−12.8307	−0.460891
$776$	−7.32853	−0.263079
$777$	−1.41862	−0.0508927
$778$	−11.2040	−0.401682
$779$	11.5970	0.415507
$780$	2.23282	0.0799477
$781$	−19.7813	−0.707832
$782$	−5.44945	−0.194872
$783$	−7.33994	−0.262308
$784$	1.00000	0.0357143
$785$	−44.0675	−1.57284
$786$	−24.4603	−0.872469
$787$	31.9157	1.13767	0.568835	−	0.822451i	$-0.307394\pi$
$787$	31.9157	1.13767	0.568835	+	0.822451i	$0.307394\pi$
$788$	26.3841	0.939893
$789$	24.8183	0.883553
$790$	1.00441	0.0357352
$791$	13.0248	0.463109
$792$	−1.63785	−0.0581983
$793$	1.21077	0.0429957
$794$	−14.1512	−0.502206
$795$	41.7837	1.48192
$796$	6.01640	0.213246
$797$	−3.06021	−0.108398	−0.0541991	−	0.998530i	$-0.517261\pi$
$797$	−3.06021	−0.108398	−0.0541991	+	0.998530i	$0.517261\pi$
$798$	−2.15257	−0.0762002
$799$	67.8246	2.39946
$800$	−2.30341	−0.0814378
$801$	6.02786	0.212984
$802$	18.7652	0.662623
$803$	16.6849	0.588797
$804$	−6.86806	−0.242218
$805$	−2.57314	−0.0906913
$806$	−2.90673	−0.102385
$807$	−0.683347	−0.0240550
$808$	−15.0787	−0.530467
$809$	17.9069	0.629572	0.314786	−	0.949163i	$-0.398067\pi$
$809$	17.9069	0.629572	0.314786	+	0.949163i	$0.398067\pi$
$810$	−19.6668	−0.691021
$811$	1.10383	0.0387607	0.0193803	−	0.999812i	$-0.493831\pi$
$811$	1.10383	0.0387607	0.0193803	+	0.999812i	$0.493831\pi$
$812$	1.32712	0.0465729
$813$	29.1396	1.02197
$814$	−2.97569	−0.104298
$815$	−12.7466	−0.446495
$816$	9.06182	0.317227
$817$	−7.56459	−0.264652
$818$	−28.5304	−0.997542
$819$	0.257345	0.00899235
$820$	−23.0524	−0.805024
$821$	−18.2434	−0.636699	−0.318350	−	0.947973i	$-0.603129\pi$
$821$	−18.2434	−0.636699	−0.318350	+	0.947973i	$0.603129\pi$
$822$	−0.503279	−0.0175539
$823$	−42.7449	−1.48999	−0.744997	−	0.667068i	$-0.767549\pi$
$823$	−42.7449	−1.48999	−0.744997	+	0.667068i	$0.767549\pi$
$824$	5.18408	0.180596
$825$	−12.1121	−0.421689
$826$	0.914957	0.0318354
$827$	2.35535	0.0819034	0.0409517	−	0.999161i	$-0.486961\pi$
$827$	2.35535	0.0819034	0.0409517	+	0.999161i	$0.486961\pi$
$828$	−0.469557	−0.0163182
$829$	29.9334	1.03963	0.519814	−	0.854279i	$-0.326001\pi$
$829$	29.9334	1.03963	0.519814	+	0.854279i	$0.326001\pi$
$830$	17.4131	0.604417
$831$	−40.3872	−1.40102
$832$	−0.521828	−0.0180911
$833$	5.72337	0.198303
$834$	−28.1325	−0.974150
$835$	−7.68221	−0.265854
$836$	−4.51522	−0.156162
$837$	30.8077	1.06487
$838$	39.0302	1.34828
$839$	10.2303	0.353190	0.176595	−	0.984284i	$-0.443492\pi$
$839$	10.2303	0.353190	0.176595	+	0.984284i	$0.443492\pi$
$840$	4.27884	0.147634
$841$	−27.2387	−0.939267
$842$	12.3623	0.426032
$843$	43.0241	1.48183
$844$	−23.6512	−0.814110
$845$	34.3964	1.18327
$846$	5.84417	0.200927
$847$	0.0298592	0.00102598
$848$	−9.76520	−0.335338
$849$	−14.4208	−0.494920
$850$	−13.1833	−0.452182
$851$	−0.853106	−0.0292441
$852$	9.43048	0.323083
$853$	55.3261	1.89433	0.947165	−	0.320746i	$-0.103933\pi$
$853$	55.3261	1.89433	0.947165	+	0.320746i	$0.103933\pi$
$854$	2.32025	0.0793973
$855$	1.81194	0.0619672
$856$	1.58530	0.0541845
$857$	−32.2053	−1.10011	−0.550055	−	0.835128i	$-0.685393\pi$
$857$	−32.2053	−1.10011	−0.550055	+	0.835128i	$0.685393\pi$
$858$	−2.74395	−0.0936768
$859$	−43.3378	−1.47867	−0.739334	−	0.673339i	$-0.764860\pi$
$859$	−43.3378	−1.47867	−0.739334	+	0.673339i	$0.764860\pi$
$860$	15.0368	0.512749
$861$	13.5057	0.460272
$862$	1.00000	0.0340601
$863$	−9.57366	−0.325891	−0.162946	−	0.986635i	$-0.552099\pi$
$863$	−9.57366	−0.325891	−0.162946	+	0.986635i	$0.552099\pi$
$864$	5.53072	0.188159
$865$	68.9050	2.34284
$866$	−3.21796	−0.109351
$867$	24.9481	0.847281
$868$	−5.57029	−0.189068
$869$	−1.23433	−0.0418718
$870$	5.67854	0.192521
$871$	2.26359	0.0766988
$872$	12.0692	0.408714
$873$	−3.61414	−0.122320
$874$	−1.29448	−0.0437864
$875$	7.28749	0.246362
$876$	−7.95429	−0.268750
$877$	41.4848	1.40084	0.700421	−	0.713730i	$-0.252996\pi$
$877$	41.4848	1.40084	0.700421	+	0.713730i	$0.252996\pi$
$878$	9.56516	0.322809
$879$	17.8261	0.601258
$880$	8.97528	0.302556
$881$	2.19818	0.0740585	0.0370293	−	0.999314i	$-0.488211\pi$
$881$	2.19818	0.0740585	0.0370293	+	0.999314i	$0.488211\pi$
$882$	0.493160	0.0166056
$883$	−6.51889	−0.219378	−0.109689	−	0.993966i	$-0.534985\pi$
$883$	−6.51889	−0.219378	−0.109689	+	0.993966i	$0.534985\pi$
$884$	−2.98662	−0.100451
$885$	3.91495	0.131600
$886$	−16.4443	−0.552458
$887$	43.5597	1.46259	0.731296	−	0.682060i	$-0.238916\pi$
$887$	43.5597	1.46259	0.731296	+	0.682060i	$0.238916\pi$
$888$	1.41862	0.0476057
$889$	16.2744	0.545826
$890$	−33.0322	−1.10724
$891$	24.1689	0.809687
$892$	23.7565	0.795426
$893$	16.1112	0.539142
$894$	−25.7374	−0.860786
$895$	16.4286	0.549149
$896$	−1.00000	−0.0334077
$897$	−0.786668	−0.0262661
$898$	15.7456	0.525438
$899$	−7.39246	−0.246552
$900$	−1.13595	−0.0378650
$901$	−55.8899	−1.86196
$902$	28.3294	0.943267
$903$	−8.80957	−0.293164
$904$	−13.0248	−0.433199
$905$	8.44632	0.280765
$906$	−3.06458	−0.101814
$907$	−41.2553	−1.36986	−0.684930	−	0.728609i	$-0.740167\pi$
$907$	−41.2553	−1.36986	−0.684930	+	0.728609i	$0.740167\pi$
$908$	19.4279	0.644738
$909$	−7.43622	−0.246644
$910$	−1.41023	−0.0467487
$911$	−20.2279	−0.670179	−0.335089	−	0.942186i	$-0.608766\pi$
$911$	−20.2279	−0.670179	−0.335089	+	0.942186i	$0.608766\pi$
$912$	2.15257	0.0712787
$913$	−21.3992	−0.708211
$914$	−30.5014	−1.00890
$915$	9.92798	0.328209
$916$	19.3121	0.638090
$917$	15.4489	0.510168
$918$	31.6544	1.04475
$919$	59.6675	1.96825	0.984124	−	0.177482i	$-0.0567952\pi$
$919$	59.6675	1.96825	0.984124	+	0.177482i	$0.0567952\pi$
$920$	2.57314	0.0848339
$921$	29.0279	0.956502
$922$	−12.2428	−0.403196
$923$	−3.10812	−0.102305
$924$	−5.25834	−0.172987
$925$	−2.06383	−0.0678582
$926$	30.2608	0.994433
$927$	2.55658	0.0839692
$928$	−1.32712	−0.0435649
$929$	−37.1253	−1.21804	−0.609021	−	0.793154i	$-0.708437\pi$
$929$	−37.1253	−1.21804	−0.609021	+	0.793154i	$0.708437\pi$
$930$	−23.8344	−0.781560
$931$	1.35955	0.0445573
$932$	14.6923	0.481263
$933$	−5.72990	−0.187589
$934$	0.0167118	0.000546826 0
$935$	51.3689	1.67994
$936$	−0.257345	−0.00841158
$937$	−0.945044	−0.0308732	−0.0154366	−	0.999881i	$-0.504914\pi$
$937$	−0.945044	−0.0308732	−0.0154366	+	0.999881i	$0.504914\pi$
$938$	4.33781	0.141635
$939$	−44.7931	−1.46177
$940$	−32.0256	−1.04456
$941$	16.4887	0.537516	0.268758	−	0.963208i	$-0.413387\pi$
$941$	16.4887	0.537516	0.268758	+	0.963208i	$0.413387\pi$
$942$	−25.8178	−0.841189
$943$	8.12183	0.264483
$944$	−0.914957	−0.0297793
$945$	14.9467	0.486215
$946$	−18.4789	−0.600801
$947$	11.3799	0.369798	0.184899	−	0.982758i	$-0.440804\pi$
$947$	11.3799	0.369798	0.184899	+	0.982758i	$0.440804\pi$
$948$	0.588451	0.0191120
$949$	2.62159	0.0851005
$950$	−3.13159	−0.101602
$951$	−32.6033	−1.05723
$952$	−5.72337	−0.185496
$953$	42.1916	1.36672	0.683360	−	0.730081i	$-0.260518\pi$
$953$	42.1916	1.36672	0.683360	+	0.730081i	$0.260518\pi$
$954$	−4.81581	−0.155918
$955$	−57.8319	−1.87139
$956$	−5.56574	−0.180009
$957$	−6.97845	−0.225581
$958$	12.5820	0.406505
$959$	0.317867	0.0102645
$960$	−4.27884	−0.138099
$961$	0.0281364	0.000907626 0
$962$	−0.467552	−0.0150745
$963$	0.781807	0.0251934
$964$	10.9440	0.352482
$965$	−44.6576	−1.43758
$966$	−1.50752	−0.0485038
$967$	−12.2276	−0.393213	−0.196607	−	0.980482i	$-0.562992\pi$
$967$	−12.2276	−0.393213	−0.196607	+	0.980482i	$0.562992\pi$
$968$	−0.0298592	−0.000959712 0
$969$	12.3200	0.395774
$970$	19.8052	0.635907
$971$	−13.0815	−0.419804	−0.209902	−	0.977722i	$-0.567314\pi$
$971$	−13.0815	−0.419804	−0.209902	+	0.977722i	$0.567314\pi$
$972$	5.06999	0.162620
$973$	17.7683	0.569625
$974$	−1.95798	−0.0627377
$975$	−1.90310	−0.0609480
$976$	−2.32025	−0.0742694
$977$	−48.8306	−1.56223	−0.781114	−	0.624388i	$-0.785348\pi$
$977$	−48.8306	−1.56223	−0.781114	+	0.624388i	$0.785348\pi$
$978$	−7.46786	−0.238796
$979$	40.5938	1.29738
$980$	−2.70248	−0.0863276
$981$	5.95204	0.190034
$982$	14.0568	0.448572
$983$	54.7451	1.74610	0.873049	−	0.487632i	$-0.162139\pi$
$983$	54.7451	1.74610	0.873049	+	0.487632i	$0.162139\pi$
$984$	−13.5057	−0.430545
$985$	−71.3024	−2.27188
$986$	−7.59562	−0.241894
$987$	18.7628	0.597227
$988$	−0.709449	−0.0225706
$989$	−5.29776	−0.168459
$990$	4.42625	0.140675
$991$	41.2538	1.31047	0.655236	−	0.755424i	$-0.272569\pi$
$991$	41.2538	1.31047	0.655236	+	0.755424i	$0.272569\pi$
$992$	5.57029	0.176857
$993$	−30.7723	−0.976529
$994$	−5.95622	−0.188920
$995$	−16.2592	−0.515452
$996$	10.2018	0.323256
$997$	−40.5668	−1.28476	−0.642381	−	0.766385i	$-0.722053\pi$
$997$	−40.5668	−1.28476	−0.642381	+	0.766385i	$0.722053\pi$
$998$	30.3090	0.959416
$999$	4.95546	0.156784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.18	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.18	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.58330 q^{3} +1.00000 q^{4} -2.70248 q^{5} -1.58330 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.493160 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.58330 q^{3} +1.00000 q^{4} -2.70248 q^{5} -1.58330 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.493160 q^{9} +2.70248 q^{10} -3.32112 q^{11} +1.58330 q^{12} -0.521828 q^{13} -1.00000 q^{14} -4.27884 q^{15} +1.00000 q^{16} +5.72337 q^{17} +0.493160 q^{18} +1.35955 q^{19} -2.70248 q^{20} +1.58330 q^{21} +3.32112 q^{22} +0.952140 q^{23} -1.58330 q^{24} +2.30341 q^{25} +0.521828 q^{26} -5.53072 q^{27} +1.00000 q^{28} +1.32712 q^{29} +4.27884 q^{30} -5.57029 q^{31} -1.00000 q^{32} -5.25834 q^{33} -5.72337 q^{34} -2.70248 q^{35} -0.493160 q^{36} -0.895989 q^{37} -1.35955 q^{38} -0.826210 q^{39} +2.70248 q^{40} +8.53008 q^{41} -1.58330 q^{42} -5.56406 q^{43} -3.32112 q^{44} +1.33276 q^{45} -0.952140 q^{46} +11.8504 q^{47} +1.58330 q^{48} +1.00000 q^{49} -2.30341 q^{50} +9.06182 q^{51} -0.521828 q^{52} -9.76520 q^{53} +5.53072 q^{54} +8.97528 q^{55} -1.00000 q^{56} +2.15257 q^{57} -1.32712 q^{58} -0.914957 q^{59} -4.27884 q^{60} -2.32025 q^{61} +5.57029 q^{62} -0.493160 q^{63} +1.00000 q^{64} +1.41023 q^{65} +5.25834 q^{66} -4.33781 q^{67} +5.72337 q^{68} +1.50752 q^{69} +2.70248 q^{70} +5.95622 q^{71} +0.493160 q^{72} -5.02387 q^{73} +0.895989 q^{74} +3.64699 q^{75} +1.35955 q^{76} -3.32112 q^{77} +0.826210 q^{78} +0.371661 q^{79} -2.70248 q^{80} -7.27731 q^{81} -8.53008 q^{82} +6.44337 q^{83} +1.58330 q^{84} -15.4673 q^{85} +5.56406 q^{86} +2.10123 q^{87} +3.32112 q^{88} -12.2229 q^{89} -1.33276 q^{90} -0.521828 q^{91} +0.952140 q^{92} -8.81944 q^{93} -11.8504 q^{94} -3.67415 q^{95} -1.58330 q^{96} +7.32853 q^{97} -1.00000 q^{98} +1.63785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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