LMFDB - Embedded newform 6046.2.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, 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("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.76254 q^{3} +1.00000 q^{4} +2.17667 q^{5} +2.76254 q^{6} -4.35539 q^{7} -1.00000 q^{8} +4.63161 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.76254 q^{3} +1.00000 q^{4} +2.17667 q^{5} +2.76254 q^{6} -4.35539 q^{7} -1.00000 q^{8} +4.63161 q^{9} -2.17667 q^{10} -2.94338 q^{11} -2.76254 q^{12} -4.67137 q^{13} +4.35539 q^{14} -6.01313 q^{15} +1.00000 q^{16} +1.08580 q^{17} -4.63161 q^{18} -0.712194 q^{19} +2.17667 q^{20} +12.0319 q^{21} +2.94338 q^{22} -3.38085 q^{23} +2.76254 q^{24} -0.262104 q^{25} +4.67137 q^{26} -4.50738 q^{27} -4.35539 q^{28} -7.31965 q^{29} +6.01313 q^{30} -2.53572 q^{31} -1.00000 q^{32} +8.13120 q^{33} -1.08580 q^{34} -9.48024 q^{35} +4.63161 q^{36} +1.73589 q^{37} +0.712194 q^{38} +12.9048 q^{39} -2.17667 q^{40} -1.30940 q^{41} -12.0319 q^{42} -8.68277 q^{43} -2.94338 q^{44} +10.0815 q^{45} +3.38085 q^{46} -5.51611 q^{47} -2.76254 q^{48} +11.9694 q^{49} +0.262104 q^{50} -2.99956 q^{51} -4.67137 q^{52} -8.99994 q^{53} +4.50738 q^{54} -6.40677 q^{55} +4.35539 q^{56} +1.96746 q^{57} +7.31965 q^{58} -5.34184 q^{59} -6.01313 q^{60} -6.69659 q^{61} +2.53572 q^{62} -20.1724 q^{63} +1.00000 q^{64} -10.1680 q^{65} -8.13120 q^{66} -11.9162 q^{67} +1.08580 q^{68} +9.33973 q^{69} +9.48024 q^{70} +12.5763 q^{71} -4.63161 q^{72} -2.77790 q^{73} -1.73589 q^{74} +0.724073 q^{75} -0.712194 q^{76} +12.8196 q^{77} -12.9048 q^{78} -11.2369 q^{79} +2.17667 q^{80} -1.44303 q^{81} +1.30940 q^{82} +5.33052 q^{83} +12.0319 q^{84} +2.36343 q^{85} +8.68277 q^{86} +20.2208 q^{87} +2.94338 q^{88} +13.6017 q^{89} -10.0815 q^{90} +20.3456 q^{91} -3.38085 q^{92} +7.00503 q^{93} +5.51611 q^{94} -1.55021 q^{95} +2.76254 q^{96} +16.5193 q^{97} -11.9694 q^{98} -13.6326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * 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
$3$	−2.76254	−1.59495	−0.797476	−	0.603351i	$-0.793832\pi$
$3$	−2.76254	−1.59495	−0.797476	+	0.603351i	$0.793832\pi$
$4$	1.00000	0.500000
$5$	2.17667	0.973437	0.486718	−	0.873559i	$-0.338194\pi$
$5$	2.17667	0.973437	0.486718	+	0.873559i	$0.338194\pi$
$6$	2.76254	1.12780
$7$	−4.35539	−1.64618	−0.823090	−	0.567910i	$-0.807752\pi$
$7$	−4.35539	−1.64618	−0.823090	+	0.567910i	$0.807752\pi$
$8$	−1.00000	−0.353553
$9$	4.63161	1.54387
$10$	−2.17667	−0.688324
$11$	−2.94338	−0.887463	−0.443731	−	0.896160i	$-0.646346\pi$
$11$	−2.94338	−0.887463	−0.443731	+	0.896160i	$0.646346\pi$
$12$	−2.76254	−0.797476
$13$	−4.67137	−1.29561	−0.647803	−	0.761808i	$-0.724312\pi$
$13$	−4.67137	−1.29561	−0.647803	+	0.761808i	$0.724312\pi$
$14$	4.35539	1.16403
$15$	−6.01313	−1.55258
$16$	1.00000	0.250000
$17$	1.08580	0.263345	0.131673	−	0.991293i	$-0.457965\pi$
$17$	1.08580	0.263345	0.131673	+	0.991293i	$0.457965\pi$
$18$	−4.63161	−1.09168
$19$	−0.712194	−0.163389	−0.0816943	−	0.996657i	$-0.526033\pi$
$19$	−0.712194	−0.163389	−0.0816943	+	0.996657i	$0.526033\pi$
$20$	2.17667	0.486718
$21$	12.0319	2.62558
$22$	2.94338	0.627531
$23$	−3.38085	−0.704957	−0.352478	−	0.935820i	$-0.614661\pi$
$23$	−3.38085	−0.704957	−0.352478	+	0.935820i	$0.614661\pi$
$24$	2.76254	0.563900
$25$	−0.262104	−0.0524209
$26$	4.67137	0.916131
$27$	−4.50738	−0.867445
$28$	−4.35539	−0.823090
$29$	−7.31965	−1.35923	−0.679613	−	0.733571i	$-0.737852\pi$
$29$	−7.31965	−1.35923	−0.679613	+	0.733571i	$0.737852\pi$
$30$	6.01313	1.09784
$31$	−2.53572	−0.455429	−0.227715	−	0.973728i	$-0.573125\pi$
$31$	−2.53572	−0.455429	−0.227715	+	0.973728i	$0.573125\pi$
$32$	−1.00000	−0.176777
$33$	8.13120	1.41546
$34$	−1.08580	−0.186213
$35$	−9.48024	−1.60245
$36$	4.63161	0.771935
$37$	1.73589	0.285378	0.142689	−	0.989768i	$-0.454425\pi$
$37$	1.73589	0.285378	0.142689	+	0.989768i	$0.454425\pi$
$38$	0.712194	0.115533
$39$	12.9048	2.06643
$40$	−2.17667	−0.344162
$41$	−1.30940	−0.204495	−0.102247	−	0.994759i	$-0.532603\pi$
$41$	−1.30940	−0.204495	−0.102247	+	0.994759i	$0.532603\pi$
$42$	−12.0319	−1.85656
$43$	−8.68277	−1.32411	−0.662055	−	0.749455i	$-0.730316\pi$
$43$	−8.68277	−1.32411	−0.662055	+	0.749455i	$0.730316\pi$
$44$	−2.94338	−0.443731
$45$	10.0815	1.50286
$46$	3.38085	0.498480
$47$	−5.51611	−0.804608	−0.402304	−	0.915506i	$-0.631791\pi$
$47$	−5.51611	−0.804608	−0.402304	+	0.915506i	$0.631791\pi$
$48$	−2.76254	−0.398738
$49$	11.9694	1.70991
$50$	0.262104	0.0370672
$51$	−2.99956	−0.420023
$52$	−4.67137	−0.647803
$53$	−8.99994	−1.23624	−0.618118	−	0.786085i	$-0.712105\pi$
$53$	−8.99994	−1.23624	−0.618118	+	0.786085i	$0.712105\pi$
$54$	4.50738	0.613377
$55$	−6.40677	−0.863889
$56$	4.35539	0.582013
$57$	1.96746	0.260597
$58$	7.31965	0.961117
$59$	−5.34184	−0.695448	−0.347724	−	0.937597i	$-0.613045\pi$
$59$	−5.34184	−0.695448	−0.347724	+	0.937597i	$0.613045\pi$
$60$	−6.01313	−0.776292
$61$	−6.69659	−0.857411	−0.428705	−	0.903444i	$-0.641030\pi$
$61$	−6.69659	−0.857411	−0.428705	+	0.903444i	$0.641030\pi$
$62$	2.53572	0.322037
$63$	−20.1724	−2.54149
$64$	1.00000	0.125000
$65$	−10.1680	−1.26119
$66$	−8.13120	−1.00088
$67$	−11.9162	−1.45580	−0.727898	−	0.685686i	$-0.759502\pi$
$67$	−11.9162	−1.45580	−0.727898	+	0.685686i	$0.759502\pi$
$68$	1.08580	0.131673
$69$	9.33973	1.12437
$70$	9.48024	1.13311
$71$	12.5763	1.49253	0.746267	−	0.665647i	$-0.231844\pi$
$71$	12.5763	1.49253	0.746267	+	0.665647i	$0.231844\pi$
$72$	−4.63161	−0.545840
$73$	−2.77790	−0.325128	−0.162564	−	0.986698i	$-0.551976\pi$
$73$	−2.77790	−0.325128	−0.162564	+	0.986698i	$0.551976\pi$
$74$	−1.73589	−0.201793
$75$	0.724073	0.0836087
$76$	−0.712194	−0.0816943
$77$	12.8196	1.46092
$78$	−12.9048	−1.46118
$79$	−11.2369	−1.26425	−0.632123	−	0.774868i	$-0.717816\pi$
$79$	−11.2369	−1.26425	−0.632123	+	0.774868i	$0.717816\pi$
$80$	2.17667	0.243359
$81$	−1.44303	−0.160336
$82$	1.30940	0.144600
$83$	5.33052	0.585100	0.292550	−	0.956250i	$-0.405496\pi$
$83$	5.33052	0.585100	0.292550	+	0.956250i	$0.405496\pi$
$84$	12.0319	1.31279
$85$	2.36343	0.256350
$86$	8.68277	0.936287
$87$	20.2208	2.16790
$88$	2.94338	0.313765
$89$	13.6017	1.44178	0.720890	−	0.693050i	$-0.243733\pi$
$89$	13.6017	1.44178	0.720890	+	0.693050i	$0.243733\pi$
$90$	−10.0815	−1.06268
$91$	20.3456	2.13280
$92$	−3.38085	−0.352478
$93$	7.00503	0.726387
$94$	5.51611	0.568944
$95$	−1.55021	−0.159048
$96$	2.76254	0.281950
$97$	16.5193	1.67729	0.838643	−	0.544682i	$-0.183350\pi$
$97$	16.5193	1.67729	0.838643	+	0.544682i	$0.183350\pi$
$98$	−11.9694	−1.20909
$99$	−13.6326	−1.37013
$100$	−0.262104	−0.0262104
$101$	−12.4822	−1.24203	−0.621013	−	0.783800i	$-0.713279\pi$
$101$	−12.4822	−1.24203	−0.621013	+	0.783800i	$0.713279\pi$
$102$	2.99956	0.297001
$103$	3.53836	0.348645	0.174323	−	0.984689i	$-0.444226\pi$
$103$	3.53836	0.348645	0.174323	+	0.984689i	$0.444226\pi$
$104$	4.67137	0.458066
$105$	26.1895	2.55583
$106$	8.99994	0.874151
$107$	−3.87517	−0.374627	−0.187313	−	0.982300i	$-0.559978\pi$
$107$	−3.87517	−0.374627	−0.187313	+	0.982300i	$0.559978\pi$
$108$	−4.50738	−0.433723
$109$	16.7997	1.60912	0.804558	−	0.593875i	$-0.202403\pi$
$109$	16.7997	1.60912	0.804558	+	0.593875i	$0.202403\pi$
$110$	6.40677	0.610862
$111$	−4.79545	−0.455164
$112$	−4.35539	−0.411545
$113$	−16.1824	−1.52232	−0.761158	−	0.648567i	$-0.775369\pi$
$113$	−16.1824	−1.52232	−0.761158	+	0.648567i	$0.775369\pi$
$114$	−1.96746	−0.184270
$115$	−7.35901	−0.686231
$116$	−7.31965	−0.679613
$117$	−21.6360	−2.00025
$118$	5.34184	0.491756
$119$	−4.72908	−0.433514
$120$	6.01313	0.548921
$121$	−2.33651	−0.212410
$122$	6.69659	0.606281
$123$	3.61728	0.326159
$124$	−2.53572	−0.227715
$125$	−11.4539	−1.02447
$126$	20.1724	1.79710
$127$	−5.94078	−0.527159	−0.263580	−	0.964638i	$-0.584903\pi$
$127$	−5.94078	−0.527159	−0.263580	+	0.964638i	$0.584903\pi$
$128$	−1.00000	−0.0883883
$129$	23.9865	2.11189
$130$	10.1680	0.891796
$131$	−17.2061	−1.50331	−0.751653	−	0.659558i	$-0.770743\pi$
$131$	−17.2061	−1.50331	−0.751653	+	0.659558i	$0.770743\pi$
$132$	8.13120	0.707730
$133$	3.10188	0.268967
$134$	11.9162	1.02940
$135$	−9.81108	−0.844403
$136$	−1.08580	−0.0931066
$137$	−2.96525	−0.253339	−0.126669	−	0.991945i	$-0.540429\pi$
$137$	−2.96525	−0.253339	−0.126669	+	0.991945i	$0.540429\pi$
$138$	−9.33973	−0.795051
$139$	2.43423	0.206468	0.103234	−	0.994657i	$-0.467081\pi$
$139$	2.43423	0.206468	0.103234	+	0.994657i	$0.467081\pi$
$140$	−9.48024	−0.801227
$141$	15.2385	1.28331
$142$	−12.5763	−1.05538
$143$	13.7496	1.14980
$144$	4.63161	0.385967
$145$	−15.9325	−1.32312
$146$	2.77790	0.229900
$147$	−33.0659	−2.72723
$148$	1.73589	0.142689
$149$	3.03900	0.248964	0.124482	−	0.992222i	$-0.460273\pi$
$149$	3.03900	0.248964	0.124482	+	0.992222i	$0.460273\pi$
$150$	−0.724073	−0.0591203
$151$	−23.1654	−1.88517	−0.942585	−	0.333966i	$-0.891613\pi$
$151$	−23.1654	−1.88517	−0.942585	+	0.333966i	$0.891613\pi$
$152$	0.712194	0.0577666
$153$	5.02900	0.406571
$154$	−12.8196	−1.03303
$155$	−5.51943	−0.443331
$156$	12.9048	1.03321
$157$	0.481829	0.0384542	0.0192271	−	0.999815i	$-0.493879\pi$
$157$	0.481829	0.0384542	0.0192271	+	0.999815i	$0.493879\pi$
$158$	11.2369	0.893956
$159$	24.8627	1.97174
$160$	−2.17667	−0.172081
$161$	14.7249	1.16049
$162$	1.44303	0.113375
$163$	−10.8373	−0.848839	−0.424420	−	0.905466i	$-0.639522\pi$
$163$	−10.8373	−0.848839	−0.424420	+	0.905466i	$0.639522\pi$
$164$	−1.30940	−0.102247
$165$	17.6989	1.37786
$166$	−5.33052	−0.413728
$167$	−11.0859	−0.857850	−0.428925	−	0.903340i	$-0.641107\pi$
$167$	−11.0859	−0.857850	−0.428925	+	0.903340i	$0.641107\pi$
$168$	−12.0319	−0.928282
$169$	8.82171	0.678593
$170$	−2.36343	−0.181267
$171$	−3.29860	−0.252251
$172$	−8.68277	−0.662055
$173$	−17.9249	−1.36281	−0.681404	−	0.731907i	$-0.738630\pi$
$173$	−17.9249	−1.36281	−0.681404	+	0.731907i	$0.738630\pi$
$174$	−20.2208	−1.53294
$175$	1.14157	0.0862942
$176$	−2.94338	−0.221866
$177$	14.7570	1.10921
$178$	−13.6017	−1.01949
$179$	−11.6062	−0.867492	−0.433746	−	0.901035i	$-0.642808\pi$
$179$	−11.6062	−0.867492	−0.433746	+	0.901035i	$0.642808\pi$
$180$	10.0815	0.751430
$181$	13.1615	0.978286	0.489143	−	0.872204i	$-0.337310\pi$
$181$	13.1615	0.978286	0.489143	+	0.872204i	$0.337310\pi$
$182$	−20.3456	−1.50812
$183$	18.4996	1.36753
$184$	3.38085	0.249240
$185$	3.77846	0.277798
$186$	−7.00503	−0.513633
$187$	−3.19592	−0.233709
$188$	−5.51611	−0.402304
$189$	19.6314	1.42797
$190$	1.55021	0.112464
$191$	10.6083	0.767590	0.383795	−	0.923418i	$-0.374617\pi$
$191$	10.6083	0.767590	0.383795	+	0.923418i	$0.374617\pi$
$192$	−2.76254	−0.199369
$193$	7.39717	0.532460	0.266230	−	0.963910i	$-0.414222\pi$
$193$	7.39717	0.532460	0.266230	+	0.963910i	$0.414222\pi$
$194$	−16.5193	−1.18602
$195$	28.0896	2.01154
$196$	11.9694	0.854956
$197$	−2.62899	−0.187308	−0.0936541	−	0.995605i	$-0.529855\pi$
$197$	−2.62899	−0.187308	−0.0936541	+	0.995605i	$0.529855\pi$
$198$	13.6326	0.968826
$199$	4.34367	0.307915	0.153957	−	0.988077i	$-0.450798\pi$
$199$	4.34367	0.307915	0.153957	+	0.988077i	$0.450798\pi$
$200$	0.262104	0.0185336
$201$	32.9189	2.32192
$202$	12.4822	0.878245
$203$	31.8799	2.23753
$204$	−2.99956	−0.210011
$205$	−2.85014	−0.199063
$206$	−3.53836	−0.246529
$207$	−15.6588	−1.08836
$208$	−4.67137	−0.323901
$209$	2.09626	0.145001
$210$	−26.1895	−1.80725
$211$	−3.78824	−0.260793	−0.130397	−	0.991462i	$-0.541625\pi$
$211$	−3.78824	−0.260793	−0.130397	+	0.991462i	$0.541625\pi$
$212$	−8.99994	−0.618118
$213$	−34.7425	−2.38052
$214$	3.87517	0.264901
$215$	−18.8995	−1.28894
$216$	4.50738	0.306688
$217$	11.0440	0.749719
$218$	−16.7997	−1.13782
$219$	7.67404	0.518564
$220$	−6.40677	−0.431944
$221$	−5.07218	−0.341191
$222$	4.79545	0.321850
$223$	−7.70100	−0.515697	−0.257849	−	0.966185i	$-0.583014\pi$
$223$	−7.70100	−0.515697	−0.257849	+	0.966185i	$0.583014\pi$
$224$	4.35539	0.291006
$225$	−1.21396	−0.0809310
$226$	16.1824	1.07644
$227$	−26.2781	−1.74414	−0.872068	−	0.489385i	$-0.837221\pi$
$227$	−26.2781	−1.74414	−0.872068	+	0.489385i	$0.837221\pi$
$228$	1.96746	0.130298
$229$	4.66418	0.308218	0.154109	−	0.988054i	$-0.450749\pi$
$229$	4.66418	0.308218	0.154109	+	0.988054i	$0.450749\pi$
$230$	7.35901	0.485238
$231$	−35.4145	−2.33010
$232$	7.31965	0.480559
$233$	−18.5503	−1.21527	−0.607634	−	0.794217i	$-0.707881\pi$
$233$	−18.5503	−1.21527	−0.607634	+	0.794217i	$0.707881\pi$
$234$	21.6360	1.41439
$235$	−12.0068	−0.783235
$236$	−5.34184	−0.347724
$237$	31.0422	2.01641
$238$	4.72908	0.306541
$239$	18.9376	1.22497	0.612486	−	0.790481i	$-0.290169\pi$
$239$	18.9376	1.22497	0.612486	+	0.790481i	$0.290169\pi$
$240$	−6.01313	−0.388146
$241$	0.948007	0.0610665	0.0305332	−	0.999534i	$-0.490279\pi$
$241$	0.948007	0.0610665	0.0305332	+	0.999534i	$0.490279\pi$
$242$	2.33651	0.150196
$243$	17.5086	1.12317
$244$	−6.69659	−0.428705
$245$	26.0534	1.66449
$246$	−3.61728	−0.230629
$247$	3.32692	0.211687
$248$	2.53572	0.161019
$249$	−14.7257	−0.933206
$250$	11.4539	0.724406
$251$	15.9028	1.00378	0.501888	−	0.864932i	$-0.332639\pi$
$251$	15.9028	1.00378	0.501888	+	0.864932i	$0.332639\pi$
$252$	−20.1724	−1.27074
$253$	9.95114	0.625623
$254$	5.94078	0.372758
$255$	−6.52906	−0.408866
$256$	1.00000	0.0625000
$257$	−10.9975	−0.686003	−0.343002	−	0.939335i	$-0.611444\pi$
$257$	−10.9975	−0.686003	−0.343002	+	0.939335i	$0.611444\pi$
$258$	−23.9865	−1.49333
$259$	−7.56046	−0.469784
$260$	−10.1680	−0.630595
$261$	−33.9018	−2.09847
$262$	17.2061	1.06300
$263$	−12.6353	−0.779125	−0.389562	−	0.921000i	$-0.627374\pi$
$263$	−12.6353	−0.779125	−0.389562	+	0.921000i	$0.627374\pi$
$264$	−8.13120	−0.500441
$265$	−19.5899	−1.20340
$266$	−3.10188	−0.190188
$267$	−37.5752	−2.29957
$268$	−11.9162	−0.727898
$269$	−10.3269	−0.629641	−0.314820	−	0.949151i	$-0.601944\pi$
$269$	−10.3269	−0.629641	−0.314820	+	0.949151i	$0.601944\pi$
$270$	9.81108	0.597083
$271$	9.28733	0.564165	0.282083	−	0.959390i	$-0.408975\pi$
$271$	9.28733	0.564165	0.282083	+	0.959390i	$0.408975\pi$
$272$	1.08580	0.0658363
$273$	−56.2055	−3.40171
$274$	2.96525	0.179138
$275$	0.771473	0.0465216
$276$	9.33973	0.562186
$277$	12.6818	0.761975	0.380988	−	0.924580i	$-0.375584\pi$
$277$	12.6818	0.761975	0.380988	+	0.924580i	$0.375584\pi$
$278$	−2.43423	−0.145995
$279$	−11.7445	−0.703123
$280$	9.48024	0.566553
$281$	13.1532	0.784654	0.392327	−	0.919826i	$-0.371670\pi$
$281$	13.1532	0.784654	0.392327	+	0.919826i	$0.371670\pi$
$282$	−15.2385	−0.907438
$283$	−13.8351	−0.822413	−0.411206	−	0.911542i	$-0.634892\pi$
$283$	−13.8351	−0.822413	−0.411206	+	0.911542i	$0.634892\pi$
$284$	12.5763	0.746267
$285$	4.28252	0.253674
$286$	−13.7496	−0.813032
$287$	5.70296	0.336635
$288$	−4.63161	−0.272920
$289$	−15.8210	−0.930649
$290$	15.9325	0.935587
$291$	−45.6353	−2.67519
$292$	−2.77790	−0.162564
$293$	−31.2640	−1.82646	−0.913230	−	0.407444i	$-0.866420\pi$
$293$	−31.2640	−1.82646	−0.913230	+	0.407444i	$0.866420\pi$
$294$	33.0659	1.92844
$295$	−11.6274	−0.676975
$296$	−1.73589	−0.100896
$297$	13.2669	0.769826
$298$	−3.03900	−0.176044
$299$	15.7932	0.913346
$300$	0.724073	0.0418044
$301$	37.8168	2.17973
$302$	23.1654	1.33302
$303$	34.4826	1.98097
$304$	−0.712194	−0.0408471
$305$	−14.5763	−0.834635
$306$	−5.02900	−0.287489
$307$	23.7572	1.35589	0.677947	−	0.735111i	$-0.262870\pi$
$307$	23.7572	1.35589	0.677947	+	0.735111i	$0.262870\pi$
$308$	12.8196	0.730462
$309$	−9.77486	−0.556072
$310$	5.51943	0.313483
$311$	−8.10414	−0.459543	−0.229772	−	0.973245i	$-0.573798\pi$
$311$	−8.10414	−0.459543	−0.229772	+	0.973245i	$0.573798\pi$
$312$	−12.9048	−0.730592
$313$	21.0257	1.18844	0.594222	−	0.804301i	$-0.297460\pi$
$313$	21.0257	1.18844	0.594222	+	0.804301i	$0.297460\pi$
$314$	−0.481829	−0.0271912
$315$	−43.9088	−2.47398
$316$	−11.2369	−0.632123
$317$	22.8436	1.28302	0.641512	−	0.767113i	$-0.278307\pi$
$317$	22.8436	1.28302	0.641512	+	0.767113i	$0.278307\pi$
$318$	−24.8627	−1.39423
$319$	21.5445	1.20626
$320$	2.17667	0.121680
$321$	10.7053	0.597511
$322$	−14.7249	−0.820588
$323$	−0.773301	−0.0430276
$324$	−1.44303	−0.0801682
$325$	1.22439	0.0679168
$326$	10.8373	0.600220
$327$	−46.4097	−2.56646
$328$	1.30940	0.0722998
$329$	24.0248	1.32453
$330$	−17.6989	−0.974295
$331$	21.6177	1.18822	0.594109	−	0.804384i	$-0.297505\pi$
$331$	21.6177	1.18822	0.594109	+	0.804384i	$0.297505\pi$
$332$	5.33052	0.292550
$333$	8.03995	0.440587
$334$	11.0859	0.606591
$335$	−25.9376	−1.41712
$336$	12.0319	0.656395
$337$	−1.90747	−0.103906	−0.0519531	−	0.998650i	$-0.516545\pi$
$337$	−1.90747	−0.103906	−0.0519531	+	0.998650i	$0.516545\pi$
$338$	−8.82171	−0.479838
$339$	44.7046	2.42802
$340$	2.36343	0.128175
$341$	7.46360	0.404176
$342$	3.29860	0.178368
$343$	−21.6436	−1.16864
$344$	8.68277	0.468144
$345$	20.3295	1.09450
$346$	17.9249	0.963651
$347$	4.55459	0.244503	0.122252	−	0.992499i	$-0.460988\pi$
$347$	4.55459	0.244503	0.122252	+	0.992499i	$0.460988\pi$
$348$	20.2208	1.08395
$349$	−4.50856	−0.241338	−0.120669	−	0.992693i	$-0.538504\pi$
$349$	−4.50856	−0.241338	−0.120669	+	0.992693i	$0.538504\pi$
$350$	−1.14157	−0.0610192
$351$	21.0556	1.12387
$352$	2.94338	0.156883
$353$	16.7564	0.891851	0.445925	−	0.895070i	$-0.352875\pi$
$353$	16.7564	0.891851	0.445925	+	0.895070i	$0.352875\pi$
$354$	−14.7570	−0.784327
$355$	27.3745	1.45289
$356$	13.6017	0.720890
$357$	13.0643	0.691433
$358$	11.6062	0.613409
$359$	23.9033	1.26157	0.630784	−	0.775958i	$-0.282733\pi$
$359$	23.9033	1.26157	0.630784	+	0.775958i	$0.282733\pi$
$360$	−10.0815	−0.531341
$361$	−18.4928	−0.973304
$362$	−13.1615	−0.691752
$363$	6.45469	0.338783
$364$	20.3456	1.06640
$365$	−6.04657	−0.316492
$366$	−18.4996	−0.966989
$367$	−23.1724	−1.20959	−0.604795	−	0.796381i	$-0.706745\pi$
$367$	−23.1724	−1.20959	−0.604795	+	0.796381i	$0.706745\pi$
$368$	−3.38085	−0.176239
$369$	−6.06465	−0.315713
$370$	−3.77846	−0.196433
$371$	39.1982	2.03507
$372$	7.00503	0.363194
$373$	−1.20424	−0.0623532	−0.0311766	−	0.999514i	$-0.509925\pi$
$373$	−1.20424	−0.0623532	−0.0311766	+	0.999514i	$0.509925\pi$
$374$	3.19592	0.165257
$375$	31.6417	1.63397
$376$	5.51611	0.284472
$377$	34.1928	1.76102
$378$	−19.6314	−1.00973
$379$	−7.13552	−0.366527	−0.183263	−	0.983064i	$-0.558666\pi$
$379$	−7.13552	−0.366527	−0.183263	+	0.983064i	$0.558666\pi$
$380$	−1.55021	−0.0795242
$381$	16.4116	0.840793
$382$	−10.6083	−0.542768
$383$	28.5284	1.45773	0.728866	−	0.684656i	$-0.240048\pi$
$383$	28.5284	1.45773	0.728866	+	0.684656i	$0.240048\pi$
$384$	2.76254	0.140975
$385$	27.9040	1.42212
$386$	−7.39717	−0.376506
$387$	−40.2152	−2.04425
$388$	16.5193	0.838643
$389$	−13.0611	−0.662224	−0.331112	−	0.943591i	$-0.607424\pi$
$389$	−13.0611	−0.662224	−0.331112	+	0.943591i	$0.607424\pi$
$390$	−28.0896	−1.42237
$391$	−3.67093	−0.185647
$392$	−11.9694	−0.604545
$393$	47.5326	2.39770
$394$	2.62899	0.132447
$395$	−24.4589	−1.23066
$396$	−13.6326	−0.685063
$397$	2.80146	0.140601	0.0703006	−	0.997526i	$-0.477604\pi$
$397$	2.80146	0.140601	0.0703006	+	0.997526i	$0.477604\pi$
$398$	−4.34367	−0.217729
$399$	−8.56906	−0.428989
$400$	−0.262104	−0.0131052
$401$	−1.21224	−0.0605363	−0.0302682	−	0.999542i	$-0.509636\pi$
$401$	−1.21224	−0.0605363	−0.0302682	+	0.999542i	$0.509636\pi$
$402$	−32.9189	−1.64185
$403$	11.8453	0.590056
$404$	−12.4822	−0.621013
$405$	−3.14099	−0.156077
$406$	−31.8799	−1.58217
$407$	−5.10938	−0.253262
$408$	2.99956	0.148500
$409$	−17.7634	−0.878344	−0.439172	−	0.898403i	$-0.644728\pi$
$409$	−17.7634	−0.878344	−0.439172	+	0.898403i	$0.644728\pi$
$410$	2.85014	0.140759
$411$	8.19162	0.404063
$412$	3.53836	0.174323
$413$	23.2658	1.14483
$414$	15.6588	0.769588
$415$	11.6028	0.569558
$416$	4.67137	0.229033
$417$	−6.72464	−0.329307
$418$	−2.09626	−0.102531
$419$	26.9492	1.31656	0.658278	−	0.752775i	$-0.271285\pi$
$419$	26.9492	1.31656	0.658278	+	0.752775i	$0.271285\pi$
$420$	26.1895	1.27792
$421$	30.0062	1.46241	0.731206	−	0.682157i	$-0.238958\pi$
$421$	30.0062	1.46241	0.731206	+	0.682157i	$0.238958\pi$
$422$	3.78824	0.184409
$423$	−25.5485	−1.24221
$424$	8.99994	0.437076
$425$	−0.284593	−0.0138048
$426$	34.7425	1.68328
$427$	29.1662	1.41145
$428$	−3.87517	−0.187313
$429$	−37.9838	−1.83388
$430$	18.8995	0.911417
$431$	−33.7381	−1.62511	−0.812554	−	0.582886i	$-0.801923\pi$
$431$	−33.7381	−1.62511	−0.812554	+	0.582886i	$0.801923\pi$
$432$	−4.50738	−0.216861
$433$	−25.0326	−1.20299	−0.601495	−	0.798877i	$-0.705428\pi$
$433$	−25.0326	−1.20299	−0.601495	+	0.798877i	$0.705428\pi$
$434$	−11.0440	−0.530131
$435$	44.0140	2.11031
$436$	16.7997	0.804558
$437$	2.40782	0.115182
$438$	−7.67404	−0.366680
$439$	22.6087	1.07905	0.539527	−	0.841968i	$-0.318603\pi$
$439$	22.6087	1.07905	0.539527	+	0.841968i	$0.318603\pi$
$440$	6.40677	0.305431
$441$	55.4375	2.63988
$442$	5.07218	0.241259
$443$	−38.3887	−1.82390	−0.911950	−	0.410301i	$-0.865424\pi$
$443$	−38.3887	−1.82390	−0.911950	+	0.410301i	$0.865424\pi$
$444$	−4.79545	−0.227582
$445$	29.6065	1.40348
$446$	7.70100	0.364653
$447$	−8.39535	−0.397086
$448$	−4.35539	−0.205773
$449$	26.1460	1.23390	0.616952	−	0.787000i	$-0.288367\pi$
$449$	26.1460	1.23390	0.616952	+	0.787000i	$0.288367\pi$
$450$	1.21396	0.0572269
$451$	3.85408	0.181481
$452$	−16.1824	−0.761158
$453$	63.9951	3.00675
$454$	26.2781	1.23329
$455$	44.2857	2.07615
$456$	−1.96746	−0.0921349
$457$	−12.2443	−0.572763	−0.286382	−	0.958116i	$-0.592453\pi$
$457$	−12.2443	−0.572763	−0.286382	+	0.958116i	$0.592453\pi$
$458$	−4.66418	−0.217943
$459$	−4.89411	−0.228438
$460$	−7.35901	−0.343115
$461$	10.2999	0.479713	0.239856	−	0.970808i	$-0.422900\pi$
$461$	10.2999	0.479713	0.239856	+	0.970808i	$0.422900\pi$
$462$	35.4145	1.64763
$463$	0.176309	0.00819376	0.00409688	−	0.999992i	$-0.498696\pi$
$463$	0.176309	0.00819376	0.00409688	+	0.999992i	$0.498696\pi$
$464$	−7.31965	−0.339806
$465$	15.2476	0.707092
$466$	18.5503	0.859324
$467$	11.0499	0.511329	0.255665	−	0.966766i	$-0.417706\pi$
$467$	11.0499	0.511329	0.255665	+	0.966766i	$0.417706\pi$
$468$	−21.6360	−1.00012
$469$	51.8996	2.39650
$470$	12.0068	0.553831
$471$	−1.33107	−0.0613325
$472$	5.34184	0.245878
$473$	25.5567	1.17510
$474$	−31.0422	−1.42582
$475$	0.186669	0.00856497
$476$	−4.72908	−0.216757
$477$	−41.6842	−1.90859
$478$	−18.9376	−0.866187
$479$	−31.2532	−1.42800	−0.713998	−	0.700147i	$-0.753118\pi$
$479$	−31.2532	−1.42800	−0.713998	+	0.700147i	$0.753118\pi$
$480$	6.01313	0.274461
$481$	−8.10897	−0.369737
$482$	−0.948007	−0.0431805
$483$	−40.6781	−1.85092
$484$	−2.33651	−0.106205
$485$	35.9572	1.63273
$486$	−17.5086	−0.794204
$487$	−8.98541	−0.407168	−0.203584	−	0.979057i	$-0.565259\pi$
$487$	−8.98541	−0.407168	−0.203584	+	0.979057i	$0.565259\pi$
$488$	6.69659	0.303140
$489$	29.9383	1.35386
$490$	−26.0534	−1.17697
$491$	−0.355763	−0.0160554	−0.00802769	−	0.999968i	$-0.502555\pi$
$491$	−0.355763	−0.0160554	−0.00802769	+	0.999968i	$0.502555\pi$
$492$	3.61728	0.163080
$493$	−7.94768	−0.357945
$494$	−3.32692	−0.149685
$495$	−29.6737	−1.33373
$496$	−2.53572	−0.113857
$497$	−54.7747	−2.45698
$498$	14.7257	0.659877
$499$	13.8667	0.620757	0.310379	−	0.950613i	$-0.399544\pi$
$499$	13.8667	0.620757	0.310379	+	0.950613i	$0.399544\pi$
$500$	−11.4539	−0.512233
$501$	30.6251	1.36823
$502$	−15.9028	−0.709777
$503$	25.4268	1.13372	0.566862	−	0.823813i	$-0.308157\pi$
$503$	25.4268	1.13372	0.566862	+	0.823813i	$0.308157\pi$
$504$	20.1724	0.898552
$505$	−27.1697	−1.20903
$506$	−9.95114	−0.442382
$507$	−24.3703	−1.08232
$508$	−5.94078	−0.263580
$509$	−24.5463	−1.08799	−0.543997	−	0.839087i	$-0.683090\pi$
$509$	−24.5463	−1.08799	−0.543997	+	0.839087i	$0.683090\pi$
$510$	6.52906	0.289112
$511$	12.0988	0.535220
$512$	−1.00000	−0.0441942
$513$	3.21013	0.141731
$514$	10.9975	0.485078
$515$	7.70185	0.339384
$516$	23.9865	1.05595
$517$	16.2360	0.714060
$518$	7.56046	0.332187
$519$	49.5183	2.17361
$520$	10.1680	0.445898
$521$	21.8354	0.956628	0.478314	−	0.878189i	$-0.341248\pi$
$521$	21.8354	0.956628	0.478314	+	0.878189i	$0.341248\pi$
$522$	33.9018	1.48384
$523$	34.1760	1.49441	0.747206	−	0.664592i	$-0.231395\pi$
$523$	34.1760	1.49441	0.747206	+	0.664592i	$0.231395\pi$
$524$	−17.2061	−0.751653
$525$	−3.15362	−0.137635
$526$	12.6353	0.550924
$527$	−2.75329	−0.119935
$528$	8.13120	0.353865
$529$	−11.5698	−0.503036
$530$	19.5899	0.850931
$531$	−24.7413	−1.07368
$532$	3.10188	0.134484
$533$	6.11671	0.264944
$534$	37.5752	1.62604
$535$	−8.43497	−0.364675
$536$	11.9162	0.514701
$537$	32.0627	1.38361
$538$	10.3269	0.445223
$539$	−35.2304	−1.51748
$540$	−9.81108	−0.422202
$541$	−1.01831	−0.0437808	−0.0218904	−	0.999760i	$-0.506968\pi$
$541$	−1.01831	−0.0437808	−0.0218904	+	0.999760i	$0.506968\pi$
$542$	−9.28733	−0.398925
$543$	−36.3591	−1.56032
$544$	−1.08580	−0.0465533
$545$	36.5673	1.56637
$546$	56.2055	2.40537
$547$	−34.2495	−1.46440	−0.732201	−	0.681088i	$-0.761507\pi$
$547$	−34.2495	−1.46440	−0.732201	+	0.681088i	$0.761507\pi$
$548$	−2.96525	−0.126669
$549$	−31.0160	−1.32373
$550$	−0.771473	−0.0328957
$551$	5.21301	0.222082
$552$	−9.33973	−0.397525
$553$	48.9408	2.08118
$554$	−12.6818	−0.538798
$555$	−10.4381	−0.443074
$556$	2.43423	0.103234
$557$	12.6643	0.536605	0.268302	−	0.963335i	$-0.413537\pi$
$557$	12.6643	0.536605	0.268302	+	0.963335i	$0.413537\pi$
$558$	11.7445	0.497183
$559$	40.5604	1.71552
$560$	−9.48024	−0.400613
$561$	8.82886	0.372755
$562$	−13.1532	−0.554834
$563$	12.4150	0.523231	0.261616	−	0.965172i	$-0.415745\pi$
$563$	12.4150	0.523231	0.261616	+	0.965172i	$0.415745\pi$
$564$	15.2385	0.641655
$565$	−35.2238	−1.48188
$566$	13.8351	0.581534
$567$	6.28494	0.263943
$568$	−12.5763	−0.527690
$569$	23.4326	0.982348	0.491174	−	0.871062i	$-0.336568\pi$
$569$	23.4326	0.982348	0.491174	+	0.871062i	$0.336568\pi$
$570$	−4.28252	−0.179375
$571$	−6.46113	−0.270390	−0.135195	−	0.990819i	$-0.543166\pi$
$571$	−6.46113	−0.270390	−0.135195	+	0.990819i	$0.543166\pi$
$572$	13.7496	0.574901
$573$	−29.3058	−1.22427
$574$	−5.70296	−0.238037
$575$	0.886137	0.0369544
$576$	4.63161	0.192984
$577$	43.8863	1.82701	0.913505	−	0.406827i	$-0.133365\pi$
$577$	43.8863	1.82701	0.913505	+	0.406827i	$0.133365\pi$
$578$	15.8210	0.658068
$579$	−20.4350	−0.849248
$580$	−15.9325	−0.661560
$581$	−23.2165	−0.963181
$582$	45.6353	1.89164
$583$	26.4902	1.09711
$584$	2.77790	0.114950
$585$	−47.0944	−1.94711
$586$	31.2640	1.29150
$587$	3.64943	0.150628	0.0753141	−	0.997160i	$-0.476004\pi$
$587$	3.64943	0.150628	0.0753141	+	0.997160i	$0.476004\pi$
$588$	−33.0659	−1.36361
$589$	1.80593	0.0744119
$590$	11.6274	0.478693
$591$	7.26269	0.298747
$592$	1.73589	0.0713445
$593$	3.21840	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$593$	3.21840	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$594$	−13.2669	−0.544349
$595$	−10.2936	−0.421998
$596$	3.03900	0.124482
$597$	−11.9996	−0.491109
$598$	−15.7932	−0.645833
$599$	16.7206	0.683187	0.341593	−	0.939848i	$-0.389033\pi$
$599$	16.7206	0.683187	0.341593	+	0.939848i	$0.389033\pi$
$600$	−0.724073	−0.0295602
$601$	30.2773	1.23504	0.617518	−	0.786557i	$-0.288138\pi$
$601$	30.2773	1.23504	0.617518	+	0.786557i	$0.288138\pi$
$602$	−37.8168	−1.54130
$603$	−55.1912	−2.24756
$604$	−23.1654	−0.942585
$605$	−5.08581	−0.206768
$606$	−34.4826	−1.40076
$607$	−28.4726	−1.15567	−0.577834	−	0.816154i	$-0.696102\pi$
$607$	−28.4726	−1.15567	−0.577834	+	0.816154i	$0.696102\pi$
$608$	0.712194	0.0288833
$609$	−88.0694	−3.56875
$610$	14.5763	0.590176
$611$	25.7678	1.04245
$612$	5.02900	0.203285
$613$	−11.3588	−0.458777	−0.229388	−	0.973335i	$-0.573673\pi$
$613$	−11.3588	−0.458777	−0.229388	+	0.973335i	$0.573673\pi$
$614$	−23.7572	−0.958762
$615$	7.87362	0.317495
$616$	−12.8196	−0.516515
$617$	7.81646	0.314679	0.157339	−	0.987545i	$-0.449708\pi$
$617$	7.81646	0.314679	0.157339	+	0.987545i	$0.449708\pi$
$618$	9.77486	0.393202
$619$	−13.2221	−0.531441	−0.265721	−	0.964050i	$-0.585610\pi$
$619$	−13.2221	−0.531441	−0.265721	+	0.964050i	$0.585610\pi$
$620$	−5.51943	−0.221666
$621$	15.2388	0.611512
$622$	8.10414	0.324946
$623$	−59.2407	−2.37343
$624$	12.9048	0.516607
$625$	−23.6208	−0.944831
$626$	−21.0257	−0.840356
$627$	−5.79099	−0.231270
$628$	0.481829	0.0192271
$629$	1.88483	0.0751530
$630$	43.9088	1.74937
$631$	9.24006	0.367841	0.183920	−	0.982941i	$-0.441121\pi$
$631$	9.24006	0.367841	0.183920	+	0.982941i	$0.441121\pi$
$632$	11.2369	0.446978
$633$	10.4652	0.415953
$634$	−22.8436	−0.907235
$635$	−12.9311	−0.513156
$636$	24.8627	0.985869
$637$	−55.9134	−2.21537
$638$	−21.5445	−0.852956
$639$	58.2485	2.30428
$640$	−2.17667	−0.0860405
$641$	−11.1288	−0.439561	−0.219780	−	0.975549i	$-0.570534\pi$
$641$	−11.1288	−0.439561	−0.219780	+	0.975549i	$0.570534\pi$
$642$	−10.7053	−0.422504
$643$	27.3126	1.07710	0.538552	−	0.842592i	$-0.318971\pi$
$643$	27.3126	1.07710	0.538552	+	0.842592i	$0.318971\pi$
$644$	14.7249	0.580243
$645$	52.2107	2.05579
$646$	0.773301	0.0304251
$647$	39.6652	1.55940	0.779701	−	0.626153i	$-0.215371\pi$
$647$	39.6652	1.55940	0.779701	+	0.626153i	$0.215371\pi$
$648$	1.44303	0.0566874
$649$	15.7231	0.617184
$650$	−1.22439	−0.0480244
$651$	−30.5096	−1.19576
$652$	−10.8373	−0.424420
$653$	31.2086	1.22129	0.610644	−	0.791905i	$-0.290910\pi$
$653$	31.2086	1.22129	0.610644	+	0.791905i	$0.290910\pi$
$654$	46.4097	1.81476
$655$	−37.4521	−1.46337
$656$	−1.30940	−0.0511237
$657$	−12.8661	−0.501956
$658$	−24.0248	−0.936584
$659$	38.4660	1.49842	0.749211	−	0.662331i	$-0.230433\pi$
$659$	38.4660	1.49842	0.749211	+	0.662331i	$0.230433\pi$
$660$	17.6989	0.688930
$661$	−44.0276	−1.71247	−0.856237	−	0.516584i	$-0.827204\pi$
$661$	−44.0276	−1.71247	−0.856237	+	0.516584i	$0.827204\pi$
$662$	−21.6177	−0.840197
$663$	14.0121	0.544184
$664$	−5.33052	−0.206864
$665$	6.75177	0.261822
$666$	−8.03995	−0.311542
$667$	24.7467	0.958195
$668$	−11.0859	−0.428925
$669$	21.2743	0.822512
$670$	25.9376	1.00206
$671$	19.7106	0.760920
$672$	−12.0319	−0.464141
$673$	−17.8490	−0.688030	−0.344015	−	0.938964i	$-0.611787\pi$
$673$	−17.8490	−0.688030	−0.344015	+	0.938964i	$0.611787\pi$
$674$	1.90747	0.0734728
$675$	1.18140	0.0454723
$676$	8.82171	0.339296
$677$	20.3105	0.780595	0.390298	−	0.920689i	$-0.372372\pi$
$677$	20.3105	0.780595	0.390298	+	0.920689i	$0.372372\pi$
$678$	−44.7046	−1.71687
$679$	−71.9481	−2.76112
$680$	−2.36343	−0.0906334
$681$	72.5941	2.78181
$682$	−7.46360	−0.285796
$683$	24.2018	0.926057	0.463028	−	0.886344i	$-0.346763\pi$
$683$	24.2018	0.926057	0.463028	+	0.886344i	$0.346763\pi$
$684$	−3.29860	−0.126125
$685$	−6.45438	−0.246609
$686$	21.6436	0.826355
$687$	−12.8850	−0.491592
$688$	−8.68277	−0.331028
$689$	42.0420	1.60167
$690$	−20.3295	−0.773932
$691$	1.11439	0.0423932	0.0211966	−	0.999775i	$-0.493252\pi$
$691$	1.11439	0.0423932	0.0211966	+	0.999775i	$0.493252\pi$
$692$	−17.9249	−0.681404
$693$	59.3752	2.25548
$694$	−4.55459	−0.172890
$695$	5.29851	0.200984
$696$	−20.2208	−0.766468
$697$	−1.42175	−0.0538527
$698$	4.50856	0.170652
$699$	51.2458	1.93829
$700$	1.14157	0.0431471
$701$	25.0059	0.944459	0.472229	−	0.881476i	$-0.343449\pi$
$701$	25.0059	0.944459	0.472229	+	0.881476i	$0.343449\pi$
$702$	−21.0556	−0.794694
$703$	−1.23629	−0.0466275
$704$	−2.94338	−0.110933
$705$	33.1691	1.24922
$706$	−16.7564	−0.630634
$707$	54.3648	2.04460
$708$	14.7570	0.554603
$709$	0.771447	0.0289723	0.0144861	−	0.999895i	$-0.495389\pi$
$709$	0.771447	0.0289723	0.0144861	+	0.999895i	$0.495389\pi$
$710$	−27.3745	−1.02735
$711$	−52.0447	−1.95183
$712$	−13.6017	−0.509746
$713$	8.57291	0.321058
$714$	−13.0643	−0.488917
$715$	29.9284	1.11926
$716$	−11.6062	−0.433746
$717$	−52.3159	−1.95377
$718$	−23.9033	−0.892064
$719$	23.6881	0.883416	0.441708	−	0.897159i	$-0.354373\pi$
$719$	23.6881	0.883416	0.441708	+	0.897159i	$0.354373\pi$
$720$	10.0815	0.375715
$721$	−15.4109	−0.573933
$722$	18.4928	0.688230
$723$	−2.61890	−0.0973980
$724$	13.1615	0.489143
$725$	1.91851	0.0712518
$726$	−6.45469	−0.239556
$727$	3.78304	0.140305	0.0701526	−	0.997536i	$-0.477651\pi$
$727$	3.78304	0.140305	0.0701526	+	0.997536i	$0.477651\pi$
$728$	−20.3456	−0.754059
$729$	−44.0389	−1.63107
$730$	6.04657	0.223794
$731$	−9.42776	−0.348698
$732$	18.4996	0.683764
$733$	−37.8543	−1.39818	−0.699090	−	0.715034i	$-0.746411\pi$
$733$	−37.8543	−1.39818	−0.699090	+	0.715034i	$0.746411\pi$
$734$	23.1724	0.855309
$735$	−71.9735	−2.65478
$736$	3.38085	0.124620
$737$	35.0739	1.29196
$738$	6.06465	0.223243
$739$	−20.8785	−0.768027	−0.384014	−	0.923327i	$-0.625458\pi$
$739$	−20.8785	−0.768027	−0.384014	+	0.923327i	$0.625458\pi$
$740$	3.77846	0.138899
$741$	−9.19075	−0.337631
$742$	−39.1982	−1.43901
$743$	−17.7427	−0.650916	−0.325458	−	0.945556i	$-0.605519\pi$
$743$	−17.7427	−0.650916	−0.325458	+	0.945556i	$0.605519\pi$
$744$	−7.00503	−0.256817
$745$	6.61490	0.242351
$746$	1.20424	0.0440904
$747$	24.6889	0.903318
$748$	−3.19592	−0.116855
$749$	16.8779	0.616703
$750$	−31.6417	−1.15539
$751$	−32.1636	−1.17366	−0.586832	−	0.809708i	$-0.699625\pi$
$751$	−32.1636	−1.17366	−0.586832	+	0.809708i	$0.699625\pi$
$752$	−5.51611	−0.201152
$753$	−43.9321	−1.60098
$754$	−34.1928	−1.24523
$755$	−50.4234	−1.83509
$756$	19.6314	0.713986
$757$	15.9337	0.579120	0.289560	−	0.957160i	$-0.406491\pi$
$757$	15.9337	0.579120	0.289560	+	0.957160i	$0.406491\pi$
$758$	7.13552	0.259174
$759$	−27.4904	−0.997838
$760$	1.55021	0.0562321
$761$	−25.0815	−0.909203	−0.454602	−	0.890695i	$-0.650218\pi$
$761$	−25.0815	−0.909203	−0.454602	+	0.890695i	$0.650218\pi$
$762$	−16.4116	−0.594530
$763$	−73.1690	−2.64889
$764$	10.6083	0.383795
$765$	10.9465	0.395771
$766$	−28.5284	−1.03077
$767$	24.9537	0.901026
$768$	−2.76254	−0.0996845
$769$	−8.94973	−0.322735	−0.161368	−	0.986894i	$-0.551590\pi$
$769$	−8.94973	−0.322735	−0.161368	+	0.986894i	$0.551590\pi$
$770$	−27.9040	−1.00559
$771$	30.3809	1.09414
$772$	7.39717	0.266230
$773$	−13.4536	−0.483893	−0.241946	−	0.970290i	$-0.577786\pi$
$773$	−13.4536	−0.483893	−0.241946	+	0.970290i	$0.577786\pi$
$774$	40.2152	1.44551
$775$	0.664624	0.0238740
$776$	−16.5193	−0.593010
$777$	20.8860	0.749283
$778$	13.0611	0.468263
$779$	0.932550	0.0334121
$780$	28.0896	1.00577
$781$	−37.0169	−1.32457
$782$	3.67093	0.131272
$783$	32.9924	1.17905
$784$	11.9694	0.427478
$785$	1.04878	0.0374327
$786$	−47.5326	−1.69543
$787$	6.05189	0.215726	0.107863	−	0.994166i	$-0.465599\pi$
$787$	6.05189	0.215726	0.107863	+	0.994166i	$0.465599\pi$
$788$	−2.62899	−0.0936541
$789$	34.9054	1.24267
$790$	24.4589	0.870210
$791$	70.4807	2.50601
$792$	13.6326	0.484413
$793$	31.2823	1.11087
$794$	−2.80146	−0.0994200
$795$	54.1178	1.91936
$796$	4.34367	0.153957
$797$	−18.0974	−0.641041	−0.320521	−	0.947242i	$-0.603858\pi$
$797$	−18.0974	−0.641041	−0.320521	+	0.947242i	$0.603858\pi$
$798$	8.56906	0.303341
$799$	−5.98940	−0.211890
$800$	0.262104	0.00926679
$801$	62.9978	2.22592
$802$	1.21224	0.0428056
$803$	8.17641	0.288539
$804$	32.9189	1.16096
$805$	32.0513	1.12966
$806$	−11.8453	−0.417233
$807$	28.5284	1.00425
$808$	12.4822	0.439123
$809$	12.0412	0.423347	0.211674	−	0.977340i	$-0.432109\pi$
$809$	12.0412	0.423347	0.211674	+	0.977340i	$0.432109\pi$
$810$	3.14099	0.110363
$811$	1.41692	0.0497549	0.0248774	−	0.999691i	$-0.492080\pi$
$811$	1.41692	0.0497549	0.0248774	+	0.999691i	$0.492080\pi$
$812$	31.8799	1.11877
$813$	−25.6566	−0.899816
$814$	5.10938	0.179084
$815$	−23.5891	−0.826291
$816$	−2.99956	−0.105006
$817$	6.18382	0.216344
$818$	17.7634	0.621083
$819$	94.2330	3.29277
$820$	−2.85014	−0.0995313
$821$	35.5837	1.24188	0.620940	−	0.783858i	$-0.286751\pi$
$821$	35.5837	1.24188	0.620940	+	0.783858i	$0.286751\pi$
$822$	−8.19162	−0.285716
$823$	−8.99176	−0.313433	−0.156716	−	0.987644i	$-0.550091\pi$
$823$	−8.99176	−0.313433	−0.156716	+	0.987644i	$0.550091\pi$
$824$	−3.53836	−0.123265
$825$	−2.13122	−0.0741996
$826$	−23.2658	−0.809519
$827$	22.9623	0.798477	0.399238	−	0.916847i	$-0.369275\pi$
$827$	22.9623	0.798477	0.399238	+	0.916847i	$0.369275\pi$
$828$	−15.6588	−0.544181
$829$	−41.3381	−1.43573	−0.717866	−	0.696181i	$-0.754881\pi$
$829$	−41.3381	−1.43573	−0.717866	+	0.696181i	$0.754881\pi$
$830$	−11.6028	−0.402738
$831$	−35.0339	−1.21531
$832$	−4.67137	−0.161951
$833$	12.9964	0.450297
$834$	6.72464	0.232855
$835$	−24.1303	−0.835062
$836$	2.09626	0.0725006
$837$	11.4295	0.395060
$838$	−26.9492	−0.930945
$839$	31.3212	1.08133	0.540663	−	0.841239i	$-0.318173\pi$
$839$	31.3212	1.08133	0.540663	+	0.841239i	$0.318173\pi$
$840$	−26.1895	−0.903624
$841$	24.5773	0.847493
$842$	−30.0062	−1.03408
$843$	−36.3362	−1.25148
$844$	−3.78824	−0.130397
$845$	19.2020	0.660567
$846$	25.5485	0.878375
$847$	10.1764	0.349665
$848$	−8.99994	−0.309059
$849$	38.2200	1.31171
$850$	0.284593	0.00976146
$851$	−5.86878	−0.201179
$852$	−34.7425	−1.19026
$853$	−39.8615	−1.36483	−0.682416	−	0.730964i	$-0.739071\pi$
$853$	−39.8615	−1.36483	−0.682416	+	0.730964i	$0.739071\pi$
$854$	−29.1662	−0.998048
$855$	−7.17998	−0.245550
$856$	3.87517	0.132451
$857$	47.9880	1.63924	0.819619	−	0.572909i	$-0.194185\pi$
$857$	47.9880	1.63924	0.819619	+	0.572909i	$0.194185\pi$
$858$	37.9838	1.29675
$859$	−44.9383	−1.53327	−0.766637	−	0.642081i	$-0.778071\pi$
$859$	−44.9383	−1.53327	−0.766637	+	0.642081i	$0.778071\pi$
$860$	−18.8995	−0.644469
$861$	−15.7546	−0.536917
$862$	33.7381	1.14912
$863$	55.4925	1.88899	0.944493	−	0.328532i	$-0.106554\pi$
$863$	55.4925	1.88899	0.944493	+	0.328532i	$0.106554\pi$
$864$	4.50738	0.153344
$865$	−39.0167	−1.32661
$866$	25.0326	0.850642
$867$	43.7062	1.48434
$868$	11.0440	0.374859
$869$	33.0743	1.12197
$870$	−44.0140	−1.49222
$871$	55.6650	1.88614
$872$	−16.7997	−0.568908
$873$	76.5111	2.58951
$874$	−2.40782	−0.0814459
$875$	49.8860	1.68646
$876$	7.67404	0.259282
$877$	−16.4843	−0.556636	−0.278318	−	0.960489i	$-0.589777\pi$
$877$	−16.4843	−0.556636	−0.278318	+	0.960489i	$0.589777\pi$
$878$	−22.6087	−0.763006
$879$	86.3678	2.91311
$880$	−6.40677	−0.215972
$881$	−16.7953	−0.565848	−0.282924	−	0.959142i	$-0.591304\pi$
$881$	−16.7953	−0.565848	−0.282924	+	0.959142i	$0.591304\pi$
$882$	−55.4375	−1.86668
$883$	−8.70711	−0.293018	−0.146509	−	0.989209i	$-0.546804\pi$
$883$	−8.70711	−0.293018	−0.146509	+	0.989209i	$0.546804\pi$
$884$	−5.07218	−0.170596
$885$	32.1212	1.07974
$886$	38.3887	1.28969
$887$	8.52410	0.286211	0.143106	−	0.989707i	$-0.454291\pi$
$887$	8.52410	0.286211	0.143106	+	0.989707i	$0.454291\pi$
$888$	4.79545	0.160925
$889$	25.8744	0.867799
$890$	−29.6065	−0.992411
$891$	4.24738	0.142293
$892$	−7.70100	−0.257849
$893$	3.92854	0.131464
$894$	8.39535	0.280782
$895$	−25.2630	−0.844448
$896$	4.35539	0.145503
$897$	−43.6294	−1.45674
$898$	−26.1460	−0.872502
$899$	18.5606	0.619031
$900$	−1.21396	−0.0404655
$901$	−9.77213	−0.325557
$902$	−3.85408	−0.128327
$903$	−104.470	−3.47656
$904$	16.1824	0.538220
$905$	28.6482	0.952299
$906$	−63.9951	−2.12610
$907$	29.5728	0.981949	0.490974	−	0.871174i	$-0.336641\pi$
$907$	29.5728	0.981949	0.490974	+	0.871174i	$0.336641\pi$
$908$	−26.2781	−0.872068
$909$	−57.8127	−1.91753
$910$	−44.2857	−1.46806
$911$	−26.7462	−0.886142	−0.443071	−	0.896487i	$-0.646111\pi$
$911$	−26.7462	−0.886142	−0.443071	+	0.896487i	$0.646111\pi$
$912$	1.96746	0.0651492
$913$	−15.6897	−0.519255
$914$	12.2443	0.405005
$915$	40.2675	1.33120
$916$	4.66418	0.154109
$917$	74.9393	2.47471
$918$	4.89411	0.161530
$919$	−19.5884	−0.646163	−0.323082	−	0.946371i	$-0.604719\pi$
$919$	−19.5884	−0.646163	−0.323082	+	0.946371i	$0.604719\pi$
$920$	7.35901	0.242619
$921$	−65.6301	−2.16259
$922$	−10.2999	−0.339208
$923$	−58.7486	−1.93373
$924$	−35.4145	−1.16505
$925$	−0.454984	−0.0149598
$926$	−0.176309	−0.00579386
$927$	16.3883	0.538263
$928$	7.31965	0.240279
$929$	−35.9911	−1.18083	−0.590414	−	0.807100i	$-0.701036\pi$
$929$	−35.9911	−1.18083	−0.590414	+	0.807100i	$0.701036\pi$
$930$	−15.2476	−0.499990
$931$	−8.52452	−0.279380
$932$	−18.5503	−0.607634
$933$	22.3880	0.732949
$934$	−11.0499	−0.361564
$935$	−6.95647	−0.227501
$936$	21.6360	0.707194
$937$	15.3530	0.501560	0.250780	−	0.968044i	$-0.419313\pi$
$937$	15.3530	0.501560	0.250780	+	0.968044i	$0.419313\pi$
$938$	−51.8996	−1.69458
$939$	−58.0843	−1.89551
$940$	−12.0068	−0.391617
$941$	−57.3331	−1.86901	−0.934503	−	0.355954i	$-0.884156\pi$
$941$	−57.3331	−1.86901	−0.934503	+	0.355954i	$0.884156\pi$
$942$	1.33107	0.0433686
$943$	4.42691	0.144160
$944$	−5.34184	−0.173862
$945$	42.7310	1.39004
$946$	−25.5567	−0.830920
$947$	−0.788129	−0.0256108	−0.0128054	−	0.999918i	$-0.504076\pi$
$947$	−0.788129	−0.0256108	−0.0128054	+	0.999918i	$0.504076\pi$
$948$	31.0422	1.00820
$949$	12.9766	0.421238
$950$	−0.186669	−0.00605635
$951$	−63.1063	−2.04636
$952$	4.72908	0.153270
$953$	27.3265	0.885191	0.442596	−	0.896721i	$-0.354058\pi$
$953$	27.3265	0.885191	0.442596	+	0.896721i	$0.354058\pi$
$954$	41.6842	1.34958
$955$	23.0908	0.747200
$956$	18.9376	0.612486
$957$	−59.5175	−1.92393
$958$	31.2532	1.00975
$959$	12.9148	0.417041
$960$	−6.01313	−0.194073
$961$	−24.5701	−0.792584
$962$	8.10897	0.261444
$963$	−17.9483	−0.578375
$964$	0.948007	0.0305332
$965$	16.1012	0.518316
$966$	40.6781	1.30880
$967$	10.5154	0.338154	0.169077	−	0.985603i	$-0.445921\pi$
$967$	10.5154	0.338154	0.169077	+	0.985603i	$0.445921\pi$
$968$	2.33651	0.0750982
$969$	2.13627	0.0686269
$970$	−35.9572	−1.15452
$971$	−12.6001	−0.404356	−0.202178	−	0.979349i	$-0.564802\pi$
$971$	−12.6001	−0.404356	−0.202178	+	0.979349i	$0.564802\pi$
$972$	17.5086	0.561587
$973$	−10.6020	−0.339884
$974$	8.98541	0.287911
$975$	−3.38241	−0.108324
$976$	−6.69659	−0.214353
$977$	−34.0580	−1.08961	−0.544805	−	0.838563i	$-0.683396\pi$
$977$	−34.0580	−1.08961	−0.544805	+	0.838563i	$0.683396\pi$
$978$	−29.9383	−0.957322
$979$	−40.0350	−1.27953
$980$	26.0534	0.832245
$981$	77.8094	2.48426
$982$	0.355763	0.0113529
$983$	33.5308	1.06947	0.534734	−	0.845021i	$-0.320412\pi$
$983$	33.5308	1.06947	0.534734	+	0.845021i	$0.320412\pi$
$984$	−3.61728	−0.115315
$985$	−5.72246	−0.182333
$986$	7.94768	0.253106
$987$	−66.3694	−2.11256
$988$	3.32692	0.105844
$989$	29.3552	0.933440
$990$	29.6737	0.943091
$991$	−46.8233	−1.48739	−0.743695	−	0.668519i	$-0.766928\pi$
$991$	−46.8233	−1.48739	−0.743695	+	0.668519i	$0.766928\pi$
$992$	2.53572	0.0805093
$993$	−59.7198	−1.89515
$994$	54.7747	1.73735
$995$	9.45475	0.299736
$996$	−14.7257	−0.466603
$997$	−12.6372	−0.400225	−0.200112	−	0.979773i	$-0.564131\pi$
$997$	−12.6372	−0.400225	−0.200112	+	0.979773i	$0.564131\pi$
$998$	−13.8667	−0.438942
$999$	−7.82430	−0.247550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.g.1.8	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.g.1.8	✓	69	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.76254 q^{3} +1.00000 q^{4} +2.17667 q^{5} +2.76254 q^{6} -4.35539 q^{7} -1.00000 q^{8} +4.63161 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.76254 q^{3} +1.00000 q^{4} +2.17667 q^{5} +2.76254 q^{6} -4.35539 q^{7} -1.00000 q^{8} +4.63161 q^{9} -2.17667 q^{10} -2.94338 q^{11} -2.76254 q^{12} -4.67137 q^{13} +4.35539 q^{14} -6.01313 q^{15} +1.00000 q^{16} +1.08580 q^{17} -4.63161 q^{18} -0.712194 q^{19} +2.17667 q^{20} +12.0319 q^{21} +2.94338 q^{22} -3.38085 q^{23} +2.76254 q^{24} -0.262104 q^{25} +4.67137 q^{26} -4.50738 q^{27} -4.35539 q^{28} -7.31965 q^{29} +6.01313 q^{30} -2.53572 q^{31} -1.00000 q^{32} +8.13120 q^{33} -1.08580 q^{34} -9.48024 q^{35} +4.63161 q^{36} +1.73589 q^{37} +0.712194 q^{38} +12.9048 q^{39} -2.17667 q^{40} -1.30940 q^{41} -12.0319 q^{42} -8.68277 q^{43} -2.94338 q^{44} +10.0815 q^{45} +3.38085 q^{46} -5.51611 q^{47} -2.76254 q^{48} +11.9694 q^{49} +0.262104 q^{50} -2.99956 q^{51} -4.67137 q^{52} -8.99994 q^{53} +4.50738 q^{54} -6.40677 q^{55} +4.35539 q^{56} +1.96746 q^{57} +7.31965 q^{58} -5.34184 q^{59} -6.01313 q^{60} -6.69659 q^{61} +2.53572 q^{62} -20.1724 q^{63} +1.00000 q^{64} -10.1680 q^{65} -8.13120 q^{66} -11.9162 q^{67} +1.08580 q^{68} +9.33973 q^{69} +9.48024 q^{70} +12.5763 q^{71} -4.63161 q^{72} -2.77790 q^{73} -1.73589 q^{74} +0.724073 q^{75} -0.712194 q^{76} +12.8196 q^{77} -12.9048 q^{78} -11.2369 q^{79} +2.17667 q^{80} -1.44303 q^{81} +1.30940 q^{82} +5.33052 q^{83} +12.0319 q^{84} +2.36343 q^{85} +8.68277 q^{86} +20.2208 q^{87} +2.94338 q^{88} +13.6017 q^{89} -10.0815 q^{90} +20.3456 q^{91} -3.38085 q^{92} +7.00503 q^{93} +5.51611 q^{94} -1.55021 q^{95} +2.76254 q^{96} +16.5193 q^{97} -11.9694 q^{98} -13.6326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * q^99

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