LMFDB - Embedded newform 2669.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2669,2,Mod(1,2669)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2669, 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("2669.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2669 = 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2669.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:	$21.3120722995$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2669.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29985 q^{2} -1.57945 q^{3} +3.28932 q^{4} -1.13990 q^{5} +3.63250 q^{6} -3.55948 q^{7} -2.96525 q^{8} -0.505346 q^{9} +O(q^{10})$	\(q-2.29985 q^{2} -1.57945 q^{3} +3.28932 q^{4} -1.13990 q^{5} +3.63250 q^{6} -3.55948 q^{7} -2.96525 q^{8} -0.505346 q^{9} +2.62159 q^{10} -5.74383 q^{11} -5.19531 q^{12} -1.21212 q^{13} +8.18627 q^{14} +1.80041 q^{15} +0.241000 q^{16} +1.00000 q^{17} +1.16222 q^{18} +3.93428 q^{19} -3.74949 q^{20} +5.62201 q^{21} +13.2100 q^{22} +4.61479 q^{23} +4.68346 q^{24} -3.70064 q^{25} +2.78771 q^{26} +5.53651 q^{27} -11.7083 q^{28} +3.49590 q^{29} -4.14067 q^{30} -0.651110 q^{31} +5.37624 q^{32} +9.07208 q^{33} -2.29985 q^{34} +4.05743 q^{35} -1.66224 q^{36} +2.04193 q^{37} -9.04825 q^{38} +1.91449 q^{39} +3.38008 q^{40} +3.98027 q^{41} -12.9298 q^{42} +2.24809 q^{43} -18.8933 q^{44} +0.576042 q^{45} -10.6133 q^{46} +6.71679 q^{47} -0.380647 q^{48} +5.66987 q^{49} +8.51092 q^{50} -1.57945 q^{51} -3.98707 q^{52} -4.75495 q^{53} -12.7332 q^{54} +6.54737 q^{55} +10.5547 q^{56} -6.21398 q^{57} -8.04006 q^{58} +5.74992 q^{59} +5.92212 q^{60} -5.86829 q^{61} +1.49746 q^{62} +1.79877 q^{63} -12.8466 q^{64} +1.38170 q^{65} -20.8644 q^{66} -10.7684 q^{67} +3.28932 q^{68} -7.28881 q^{69} -9.33150 q^{70} -1.31648 q^{71} +1.49848 q^{72} +10.9957 q^{73} -4.69615 q^{74} +5.84496 q^{75} +12.9411 q^{76} +20.4450 q^{77} -4.40304 q^{78} -16.9324 q^{79} -0.274715 q^{80} -7.22859 q^{81} -9.15405 q^{82} +1.14568 q^{83} +18.4926 q^{84} -1.13990 q^{85} -5.17029 q^{86} -5.52159 q^{87} +17.0319 q^{88} +12.5219 q^{89} -1.32481 q^{90} +4.31453 q^{91} +15.1795 q^{92} +1.02839 q^{93} -15.4476 q^{94} -4.48467 q^{95} -8.49149 q^{96} -0.981233 q^{97} -13.0399 q^{98} +2.90262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) $ 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * 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 $

$2$	−2.29985	−1.62624	−0.813121	−	0.582095i	$-0.802233\pi$
$2$	−2.29985	−1.62624	−0.813121	+	0.582095i	$0.802233\pi$
$3$	−1.57945	−0.911894	−0.455947	−	0.890007i	$-0.650699\pi$
$3$	−1.57945	−0.911894	−0.455947	+	0.890007i	$0.650699\pi$
$4$	3.28932	1.64466
$5$	−1.13990	−0.509777	−0.254889	−	0.966970i	$-0.582039\pi$
$5$	−1.13990	−0.509777	−0.254889	+	0.966970i	$0.582039\pi$
$6$	3.63250	1.48296
$7$	−3.55948	−1.34536	−0.672678	−	0.739936i	$-0.734856\pi$
$7$	−3.55948	−1.34536	−0.672678	+	0.739936i	$0.734856\pi$
$8$	−2.96525	−1.04838
$9$	−0.505346	−0.168449
$10$	2.62159	0.829021
$11$	−5.74383	−1.73183	−0.865915	−	0.500192i	$-0.833263\pi$
$11$	−5.74383	−1.73183	−0.865915	+	0.500192i	$0.833263\pi$
$12$	−5.19531	−1.49976
$13$	−1.21212	−0.336183	−0.168091	−	0.985771i	$-0.553760\pi$
$13$	−1.21212	−0.336183	−0.168091	+	0.985771i	$0.553760\pi$
$14$	8.18627	2.18787
$15$	1.80041	0.464863
$16$	0.241000	0.0602499
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.16222	0.273938
$19$	3.93428	0.902585	0.451292	−	0.892376i	$-0.350963\pi$
$19$	3.93428	0.902585	0.451292	+	0.892376i	$0.350963\pi$
$20$	−3.74949	−0.838411
$21$	5.62201	1.22682
$22$	13.2100	2.81637
$23$	4.61479	0.962249	0.481125	−	0.876652i	$-0.340228\pi$
$23$	4.61479	0.962249	0.481125	+	0.876652i	$0.340228\pi$
$24$	4.68346	0.956008
$25$	−3.70064	−0.740127
$26$	2.78771	0.546714
$27$	5.53651	1.06550
$28$	−11.7083	−2.21265
$29$	3.49590	0.649172	0.324586	−	0.945856i	$-0.394775\pi$
$29$	3.49590	0.649172	0.324586	+	0.945856i	$0.394775\pi$
$30$	−4.14067	−0.755979
$31$	−0.651110	−0.116943	−0.0584714	−	0.998289i	$-0.518623\pi$
$31$	−0.651110	−0.116943	−0.0584714	+	0.998289i	$0.518623\pi$
$32$	5.37624	0.950394
$33$	9.07208	1.57925
$34$	−2.29985	−0.394422
$35$	4.05743	0.685832
$36$	−1.66224	−0.277041
$37$	2.04193	0.335692	0.167846	−	0.985813i	$-0.446319\pi$
$37$	2.04193	0.335692	0.167846	+	0.985813i	$0.446319\pi$
$38$	−9.04825	−1.46782
$39$	1.91449	0.306563
$40$	3.38008	0.534438
$41$	3.98027	0.621614	0.310807	−	0.950473i	$-0.399401\pi$
$41$	3.98027	0.621614	0.310807	+	0.950473i	$0.399401\pi$
$42$	−12.9298	−1.99511
$43$	2.24809	0.342831	0.171416	−	0.985199i	$-0.445166\pi$
$43$	2.24809	0.342831	0.171416	+	0.985199i	$0.445166\pi$
$44$	−18.8933	−2.84827
$45$	0.576042	0.0858712
$46$	−10.6133	−1.56485
$47$	6.71679	0.979744	0.489872	−	0.871794i	$-0.337043\pi$
$47$	6.71679	0.979744	0.489872	+	0.871794i	$0.337043\pi$
$48$	−0.380647	−0.0549416
$49$	5.66987	0.809982
$50$	8.51092	1.20363
$51$	−1.57945	−0.221167
$52$	−3.98707	−0.552907
$53$	−4.75495	−0.653143	−0.326572	−	0.945172i	$-0.605893\pi$
$53$	−4.75495	−0.653143	−0.326572	+	0.945172i	$0.605893\pi$
$54$	−12.7332	−1.73276
$55$	6.54737	0.882847
$56$	10.5547	1.41044
$57$	−6.21398	−0.823062
$58$	−8.04006	−1.05571
$59$	5.74992	0.748576	0.374288	−	0.927312i	$-0.377887\pi$
$59$	5.74992	0.748576	0.374288	+	0.927312i	$0.377887\pi$
$60$	5.92212	0.764542
$61$	−5.86829	−0.751358	−0.375679	−	0.926750i	$-0.622590\pi$
$61$	−5.86829	−0.751358	−0.375679	+	0.926750i	$0.622590\pi$
$62$	1.49746	0.190177
$63$	1.79877	0.226623
$64$	−12.8466	−1.60582
$65$	1.38170	0.171378
$66$	−20.8644	−2.56823
$67$	−10.7684	−1.31556	−0.657782	−	0.753208i	$-0.728505\pi$
$67$	−10.7684	−1.31556	−0.657782	+	0.753208i	$0.728505\pi$
$68$	3.28932	0.398889
$69$	−7.28881	−0.877470
$70$	−9.33150	−1.11533
$71$	−1.31648	−0.156238	−0.0781188	−	0.996944i	$-0.524891\pi$
$71$	−1.31648	−0.156238	−0.0781188	+	0.996944i	$0.524891\pi$
$72$	1.49848	0.176597
$73$	10.9957	1.28695	0.643475	−	0.765467i	$-0.277492\pi$
$73$	10.9957	1.28695	0.643475	+	0.765467i	$0.277492\pi$
$74$	−4.69615	−0.545916
$75$	5.84496	0.674918
$76$	12.9411	1.48445
$77$	20.4450	2.32993
$78$	−4.40304	−0.498546
$79$	−16.9324	−1.90504	−0.952522	−	0.304470i	$-0.901521\pi$
$79$	−16.9324	−1.90504	−0.952522	+	0.304470i	$0.901521\pi$
$80$	−0.274715	−0.0307140
$81$	−7.22859	−0.803177
$82$	−9.15405	−1.01090
$83$	1.14568	0.125755	0.0628776	−	0.998021i	$-0.479972\pi$
$83$	1.14568	0.125755	0.0628776	+	0.998021i	$0.479972\pi$
$84$	18.4926	2.01771
$85$	−1.13990	−0.123639
$86$	−5.17029	−0.557526
$87$	−5.52159	−0.591977
$88$	17.0319	1.81561
$89$	12.5219	1.32731	0.663657	−	0.748037i	$-0.269003\pi$
$89$	12.5219	1.32731	0.663657	+	0.748037i	$0.269003\pi$
$90$	−1.32481	−0.139647
$91$	4.31453	0.452285
$92$	15.1795	1.58257
$93$	1.02839	0.106640
$94$	−15.4476	−1.59330
$95$	−4.48467	−0.460117
$96$	−8.49149	−0.866659
$97$	−0.981233	−0.0996291	−0.0498145	−	0.998758i	$-0.515863\pi$
$97$	−0.981233	−0.0996291	−0.0498145	+	0.998758i	$0.515863\pi$
$98$	−13.0399	−1.31723
$99$	2.90262	0.291724
$100$	−12.1726	−1.21726
$101$	−0.988512	−0.0983606	−0.0491803	−	0.998790i	$-0.515661\pi$
$101$	−0.988512	−0.0983606	−0.0491803	+	0.998790i	$0.515661\pi$
$102$	3.63250	0.359671
$103$	11.8029	1.16297	0.581485	−	0.813557i	$-0.302472\pi$
$103$	11.8029	1.16297	0.581485	+	0.813557i	$0.302472\pi$
$104$	3.59425	0.352446
$105$	−6.40850	−0.625406
$106$	10.9357	1.06217
$107$	10.3218	0.997843	0.498921	−	0.866647i	$-0.333730\pi$
$107$	10.3218	0.997843	0.498921	+	0.866647i	$0.333730\pi$
$108$	18.2114	1.75239
$109$	7.37784	0.706669	0.353334	−	0.935497i	$-0.385048\pi$
$109$	7.37784	0.706669	0.353334	+	0.935497i	$0.385048\pi$
$110$	−15.0580	−1.43572
$111$	−3.22513	−0.306116
$112$	−0.857833	−0.0810576
$113$	−4.87779	−0.458864	−0.229432	−	0.973325i	$-0.573687\pi$
$113$	−4.87779	−0.458864	−0.229432	+	0.973325i	$0.573687\pi$
$114$	14.2912	1.33850
$115$	−5.26038	−0.490533
$116$	11.4991	1.06767
$117$	0.612541	0.0566295
$118$	−13.2240	−1.21737
$119$	−3.55948	−0.326297
$120$	−5.33866	−0.487351
$121$	21.9916	1.99923
$122$	13.4962	1.22189
$123$	−6.28663	−0.566847
$124$	−2.14171	−0.192331
$125$	9.91782	0.887077
$126$	−4.13690	−0.368544
$127$	17.3580	1.54027	0.770137	−	0.637878i	$-0.220188\pi$
$127$	17.3580	1.54027	0.770137	+	0.637878i	$0.220188\pi$
$128$	18.7927	1.66106
$129$	−3.55075	−0.312626
$130$	−3.17770	−0.278702
$131$	−21.4752	−1.87630	−0.938148	−	0.346234i	$-0.887460\pi$
$131$	−21.4752	−1.87630	−0.938148	+	0.346234i	$0.887460\pi$
$132$	29.8410	2.59732
$133$	−14.0040	−1.21430
$134$	24.7656	2.13942
$135$	−6.31105	−0.543168
$136$	−2.96525	−0.254268
$137$	9.10336	0.777752	0.388876	−	0.921290i	$-0.372863\pi$
$137$	9.10336	0.777752	0.388876	+	0.921290i	$0.372863\pi$
$138$	16.7632	1.42698
$139$	−4.92372	−0.417625	−0.208812	−	0.977956i	$-0.566960\pi$
$139$	−4.92372	−0.417625	−0.208812	+	0.977956i	$0.566960\pi$
$140$	13.3462	1.12796
$141$	−10.6088	−0.893423
$142$	3.02771	0.254080
$143$	6.96223	0.582211
$144$	−0.121788	−0.0101490
$145$	−3.98496	−0.330933
$146$	−25.2885	−2.09289
$147$	−8.95527	−0.738618
$148$	6.71658	0.552099
$149$	−3.06868	−0.251396	−0.125698	−	0.992069i	$-0.540117\pi$
$149$	−3.06868	−0.251396	−0.125698	+	0.992069i	$0.540117\pi$
$150$	−13.4425	−1.09758
$151$	−10.5914	−0.861919	−0.430960	−	0.902371i	$-0.641825\pi$
$151$	−10.5914	−0.861919	−0.430960	+	0.902371i	$0.641825\pi$
$152$	−11.6661	−0.946247
$153$	−0.505346	−0.0408548
$154$	−47.0205	−3.78902
$155$	0.742198	0.0596148
$156$	6.29736	0.504193
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	38.9420	3.09806
$159$	7.51020	0.595598
$160$	−6.12836	−0.484489
$161$	−16.4262	−1.29457
$162$	16.6247	1.30616
$163$	−18.7383	−1.46770	−0.733848	−	0.679314i	$-0.762277\pi$
$163$	−18.7383	−1.46770	−0.733848	+	0.679314i	$0.762277\pi$
$164$	13.0924	1.02235
$165$	−10.3412	−0.805063
$166$	−2.63490	−0.204508
$167$	2.54604	0.197018	0.0985091	−	0.995136i	$-0.468593\pi$
$167$	2.54604	0.197018	0.0985091	+	0.995136i	$0.468593\pi$
$168$	−16.6707	−1.28617
$169$	−11.5308	−0.886981
$170$	2.62159	0.201067
$171$	−1.98817	−0.152039
$172$	7.39471	0.563841
$173$	10.9572	0.833057	0.416529	−	0.909123i	$-0.363247\pi$
$173$	10.9572	0.833057	0.416529	+	0.909123i	$0.363247\pi$
$174$	12.6988	0.962697
$175$	13.1723	0.995734
$176$	−1.38426	−0.104343
$177$	−9.08170	−0.682623
$178$	−28.7984	−2.15853
$179$	16.4178	1.22712	0.613562	−	0.789646i	$-0.289736\pi$
$179$	16.4178	1.22712	0.613562	+	0.789646i	$0.289736\pi$
$180$	1.89479	0.141229
$181$	16.0787	1.19512	0.597562	−	0.801823i	$-0.296136\pi$
$181$	16.0787	1.19512	0.597562	+	0.801823i	$0.296136\pi$
$182$	−9.92278	−0.735525
$183$	9.26866	0.685159
$184$	−13.6840	−1.00880
$185$	−2.32759	−0.171128
$186$	−2.36516	−0.173422
$187$	−5.74383	−0.420030
$188$	22.0937	1.61135
$189$	−19.7071	−1.43348
$190$	10.3141	0.748261
$191$	−19.2084	−1.38987	−0.694935	−	0.719073i	$-0.744567\pi$
$191$	−19.2084	−1.38987	−0.694935	+	0.719073i	$0.744567\pi$
$192$	20.2905	1.46434
$193$	−12.5991	−0.906906	−0.453453	−	0.891280i	$-0.649808\pi$
$193$	−12.5991	−0.906906	−0.453453	+	0.891280i	$0.649808\pi$
$194$	2.25669	0.162021
$195$	−2.18232	−0.156279
$196$	18.6500	1.33215
$197$	6.72339	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$197$	6.72339	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$198$	−6.67559	−0.474414
$199$	−7.80495	−0.553278	−0.276639	−	0.960974i	$-0.589221\pi$
$199$	−7.80495	−0.553278	−0.276639	+	0.960974i	$0.589221\pi$
$200$	10.9733	0.775931
$201$	17.0081	1.19966
$202$	2.27343	0.159958
$203$	−12.4436	−0.873368
$204$	−5.19531	−0.363745
$205$	−4.53710	−0.316885
$206$	−27.1448	−1.89127
$207$	−2.33206	−0.162089
$208$	−0.292122	−0.0202550
$209$	−22.5978	−1.56312
$210$	14.7386	1.01706
$211$	−14.3659	−0.988991	−0.494496	−	0.869180i	$-0.664647\pi$
$211$	−14.3659	−0.988991	−0.494496	+	0.869180i	$0.664647\pi$
$212$	−15.6406	−1.07420
$213$	2.07931	0.142472
$214$	−23.7385	−1.62273
$215$	−2.56259	−0.174767
$216$	−16.4172	−1.11705
$217$	2.31761	0.157330
$218$	−16.9679	−1.14921
$219$	−17.3671	−1.17356
$220$	21.5364	1.45198
$221$	−1.21212	−0.0815363
$222$	7.41732	0.497818
$223$	3.77635	0.252883	0.126442	−	0.991974i	$-0.459644\pi$
$223$	3.77635	0.252883	0.126442	+	0.991974i	$0.459644\pi$
$224$	−19.1366	−1.27862
$225$	1.87010	0.124673
$226$	11.2182	0.746223
$227$	−8.44429	−0.560467	−0.280233	−	0.959932i	$-0.590412\pi$
$227$	−8.44429	−0.560467	−0.280233	+	0.959932i	$0.590412\pi$
$228$	−20.4398	−1.35366
$229$	24.2489	1.60241	0.801207	−	0.598387i	$-0.204192\pi$
$229$	24.2489	1.60241	0.801207	+	0.598387i	$0.204192\pi$
$230$	12.0981	0.797725
$231$	−32.2918	−2.12465
$232$	−10.3662	−0.680576
$233$	3.48174	0.228097	0.114048	−	0.993475i	$-0.463618\pi$
$233$	3.48174	0.228097	0.114048	+	0.993475i	$0.463618\pi$
$234$	−1.40876	−0.0920932
$235$	−7.65644	−0.499451
$236$	18.9134	1.23115
$237$	26.7438	1.73720
$238$	8.18627	0.530637
$239$	−23.1857	−1.49976	−0.749881	−	0.661573i	$-0.769889\pi$
$239$	−23.1857	−1.49976	−0.749881	+	0.661573i	$0.769889\pi$
$240$	0.433898	0.0280080
$241$	−1.18075	−0.0760590	−0.0380295	−	0.999277i	$-0.512108\pi$
$241$	−1.18075	−0.0760590	−0.0380295	+	0.999277i	$0.512108\pi$
$242$	−50.5774	−3.25124
$243$	−5.19235	−0.333089
$244$	−19.3027	−1.23573
$245$	−6.46307	−0.412910
$246$	14.4583	0.921830
$247$	−4.76883	−0.303433
$248$	1.93071	0.122600
$249$	−1.80955	−0.114675
$250$	−22.8095	−1.44260
$251$	−4.53993	−0.286558	−0.143279	−	0.989682i	$-0.545765\pi$
$251$	−4.53993	−0.286558	−0.143279	+	0.989682i	$0.545765\pi$
$252$	5.91672	0.372718
$253$	−26.5065	−1.66645
$254$	−39.9209	−2.50486
$255$	1.80041	0.112746
$256$	−17.5274	−1.09546
$257$	29.6886	1.85193	0.925963	−	0.377614i	$-0.123255\pi$
$257$	29.6886	1.85193	0.925963	+	0.377614i	$0.123255\pi$
$258$	8.16619	0.508405
$259$	−7.26821	−0.451625
$260$	4.54484	0.281859
$261$	−1.76664	−0.109352
$262$	49.3898	3.05131
$263$	−13.6733	−0.843131	−0.421566	−	0.906798i	$-0.638519\pi$
$263$	−13.6733	−0.843131	−0.421566	+	0.906798i	$0.638519\pi$
$264$	−26.9010	−1.65564
$265$	5.42016	0.332958
$266$	32.2070	1.97474
$267$	−19.7776	−1.21037
$268$	−35.4206	−2.16366
$269$	30.5057	1.85997	0.929983	−	0.367603i	$-0.119822\pi$
$269$	30.5057	1.85997	0.929983	+	0.367603i	$0.119822\pi$
$270$	14.5145	0.883323
$271$	−22.9815	−1.39603	−0.698014	−	0.716084i	$-0.745933\pi$
$271$	−22.9815	−1.39603	−0.698014	+	0.716084i	$0.745933\pi$
$272$	0.241000	0.0146128
$273$	−6.81457	−0.412436
$274$	−20.9364	−1.26481
$275$	21.2558	1.28177
$276$	−23.9753	−1.44314
$277$	−7.63415	−0.458692	−0.229346	−	0.973345i	$-0.573659\pi$
$277$	−7.63415	−0.458692	−0.229346	+	0.973345i	$0.573659\pi$
$278$	11.3238	0.679159
$279$	0.329036	0.0196989
$280$	−12.0313	−0.719009
$281$	27.0578	1.61414	0.807068	−	0.590459i	$-0.201053\pi$
$281$	27.0578	1.61414	0.807068	+	0.590459i	$0.201053\pi$
$282$	24.3987	1.45292
$283$	−16.8238	−1.00007	−0.500035	−	0.866005i	$-0.666680\pi$
$283$	−16.8238	−1.00007	−0.500035	+	0.866005i	$0.666680\pi$
$284$	−4.33033	−0.256958
$285$	7.08329	0.419578
$286$	−16.0121	−0.946816
$287$	−14.1677	−0.836292
$288$	−2.71686	−0.160093
$289$	1.00000	0.0588235
$290$	9.16483	0.538177
$291$	1.54981	0.0908512
$292$	36.1684	2.11660
$293$	−1.90107	−0.111062	−0.0555309	−	0.998457i	$-0.517685\pi$
$293$	−1.90107	−0.111062	−0.0555309	+	0.998457i	$0.517685\pi$
$294$	20.5958	1.20117
$295$	−6.55432	−0.381607
$296$	−6.05485	−0.351931
$297$	−31.8008	−1.84527
$298$	7.05752	0.408831
$299$	−5.59369	−0.323492
$300$	19.2260	1.11001
$301$	−8.00204	−0.461230
$302$	24.3588	1.40169
$303$	1.56130	0.0896945
$304$	0.948159	0.0543807
$305$	6.68925	0.383025
$306$	1.16222	0.0664397
$307$	33.8353	1.93108	0.965541	−	0.260252i	$-0.0838055\pi$
$307$	33.8353	1.93108	0.965541	+	0.260252i	$0.0838055\pi$
$308$	67.2503	3.83194
$309$	−18.6420	−1.06051
$310$	−1.70695	−0.0969481
$311$	−11.7092	−0.663967	−0.331983	−	0.943285i	$-0.607718\pi$
$311$	−11.7092	−0.663967	−0.331983	+	0.943285i	$0.607718\pi$
$312$	−5.67694	−0.321393
$313$	−13.2319	−0.747912	−0.373956	−	0.927446i	$-0.621999\pi$
$313$	−13.2319	−0.747912	−0.373956	+	0.927446i	$0.621999\pi$
$314$	−2.29985	−0.129788
$315$	−2.05041	−0.115527
$316$	−55.6961	−3.13315
$317$	−23.4531	−1.31726	−0.658630	−	0.752467i	$-0.728864\pi$
$317$	−23.4531	−1.31726	−0.658630	+	0.752467i	$0.728864\pi$
$318$	−17.2724	−0.968586
$319$	−20.0799	−1.12426
$320$	14.6438	0.818611
$321$	−16.3027	−0.909927
$322$	37.7779	2.10528
$323$	3.93428	0.218909
$324$	−23.7772	−1.32095
$325$	4.48563	0.248818
$326$	43.0953	2.38683
$327$	−11.6529	−0.644407
$328$	−11.8025	−0.651685
$329$	−23.9082	−1.31810
$330$	23.7833	1.30923
$331$	−20.9069	−1.14915	−0.574573	−	0.818453i	$-0.694832\pi$
$331$	−20.9069	−1.14915	−0.574573	+	0.818453i	$0.694832\pi$
$332$	3.76853	0.206825
$333$	−1.03188	−0.0565468
$334$	−5.85551	−0.320399
$335$	12.2748	0.670644
$336$	1.35490	0.0739160
$337$	26.1907	1.42670	0.713350	−	0.700808i	$-0.247177\pi$
$337$	26.1907	1.42670	0.713350	+	0.700808i	$0.247177\pi$
$338$	26.5190	1.44245
$339$	7.70421	0.418435
$340$	−3.74949	−0.203344
$341$	3.73987	0.202525
$342$	4.57250	0.247252
$343$	4.73456	0.255642
$344$	−6.66617	−0.359416
$345$	8.30849	0.447314
$346$	−25.1999	−1.35475
$347$	−29.2663	−1.57110	−0.785549	−	0.618799i	$-0.787619\pi$
$347$	−29.2663	−1.57110	−0.785549	+	0.618799i	$0.787619\pi$
$348$	−18.1623	−0.973601
$349$	−29.5880	−1.58381	−0.791905	−	0.610644i	$-0.790910\pi$
$349$	−29.5880	−1.58381	−0.791905	+	0.610644i	$0.790910\pi$
$350$	−30.2944	−1.61930
$351$	−6.71094	−0.358203
$352$	−30.8802	−1.64592
$353$	−18.3131	−0.974706	−0.487353	−	0.873205i	$-0.662038\pi$
$353$	−18.3131	−0.974706	−0.487353	+	0.873205i	$0.662038\pi$
$354$	20.8866	1.11011
$355$	1.50065	0.0796464
$356$	41.1884	2.18298
$357$	5.62201	0.297548
$358$	−37.7585	−1.99560
$359$	20.2416	1.06831	0.534156	−	0.845386i	$-0.320630\pi$
$359$	20.2416	1.06831	0.534156	+	0.845386i	$0.320630\pi$
$360$	−1.70811	−0.0900252
$361$	−3.52148	−0.185341
$362$	−36.9788	−1.94356
$363$	−34.7345	−1.82309
$364$	14.1919	0.743856
$365$	−12.5340	−0.656058
$366$	−21.3166	−1.11423
$367$	1.40877	0.0735371	0.0367685	−	0.999324i	$-0.488294\pi$
$367$	1.40877	0.0735371	0.0367685	+	0.999324i	$0.488294\pi$
$368$	1.11216	0.0579755
$369$	−2.01141	−0.104710
$370$	5.35312	0.278295
$371$	16.9252	0.878710
$372$	3.38272	0.175386
$373$	8.09766	0.419281	0.209640	−	0.977779i	$-0.432771\pi$
$373$	8.09766	0.419281	0.209640	+	0.977779i	$0.432771\pi$
$374$	13.2100	0.683071
$375$	−15.6647	−0.808921
$376$	−19.9170	−1.02714
$377$	−4.23746	−0.218241
$378$	45.3234	2.33118
$379$	−29.1339	−1.49651	−0.748255	−	0.663411i	$-0.769108\pi$
$379$	−29.1339	−1.49651	−0.748255	+	0.663411i	$0.769108\pi$
$380$	−14.7515	−0.756737
$381$	−27.4161	−1.40457
$382$	44.1764	2.26026
$383$	25.0531	1.28015	0.640077	−	0.768310i	$-0.278902\pi$
$383$	25.0531	1.28015	0.640077	+	0.768310i	$0.278902\pi$
$384$	−29.6821	−1.51471
$385$	−23.3052	−1.18774
$386$	28.9762	1.47485
$387$	−1.13606	−0.0577494
$388$	−3.22759	−0.163856
$389$	5.51756	0.279751	0.139876	−	0.990169i	$-0.455330\pi$
$389$	5.51756	0.279751	0.139876	+	0.990169i	$0.455330\pi$
$390$	5.01900	0.254147
$391$	4.61479	0.233380
$392$	−16.8126	−0.849165
$393$	33.9189	1.71098
$394$	−15.4628	−0.779005
$395$	19.3012	0.971148
$396$	9.54765	0.479787
$397$	−0.745689	−0.0374251	−0.0187125	−	0.999825i	$-0.505957\pi$
$397$	−0.745689	−0.0374251	−0.0187125	+	0.999825i	$0.505957\pi$
$398$	17.9502	0.899764
$399$	22.1185	1.10731
$400$	−0.891853	−0.0445926
$401$	20.8279	1.04010	0.520048	−	0.854137i	$-0.325914\pi$
$401$	20.8279	1.04010	0.520048	+	0.854137i	$0.325914\pi$
$402$	−39.1160	−1.95093
$403$	0.789227	0.0393142
$404$	−3.25153	−0.161770
$405$	8.23984	0.409441
$406$	28.6184	1.42031
$407$	−11.7285	−0.581361
$408$	4.68346	0.231866
$409$	−17.4939	−0.865020	−0.432510	−	0.901629i	$-0.642372\pi$
$409$	−17.4939	−0.865020	−0.432510	+	0.901629i	$0.642372\pi$
$410$	10.4347	0.515331
$411$	−14.3783	−0.709228
$412$	38.8234	1.91269
$413$	−20.4667	−1.00710
$414$	5.36340	0.263597
$415$	−1.30596	−0.0641071
$416$	−6.51667	−0.319506
$417$	7.77676	0.380830
$418$	51.9716	2.54202
$419$	−13.7710	−0.672758	−0.336379	−	0.941727i	$-0.609202\pi$
$419$	−13.7710	−0.672758	−0.336379	+	0.941727i	$0.609202\pi$
$420$	−21.0796	−1.02858
$421$	4.45623	0.217184	0.108592	−	0.994086i	$-0.465366\pi$
$421$	4.45623	0.217184	0.108592	+	0.994086i	$0.465366\pi$
$422$	33.0395	1.60834
$423$	−3.39430	−0.165036
$424$	14.0996	0.684739
$425$	−3.70064	−0.179507
$426$	−4.78212	−0.231694
$427$	20.8881	1.01084
$428$	33.9516	1.64111
$429$	−10.9965	−0.530915
$430$	5.89359	0.284214
$431$	6.50932	0.313543	0.156771	−	0.987635i	$-0.449891\pi$
$431$	6.50932	0.313543	0.156771	+	0.987635i	$0.449891\pi$
$432$	1.33430	0.0641964
$433$	−12.3380	−0.592926	−0.296463	−	0.955044i	$-0.595807\pi$
$433$	−12.3380	−0.592926	−0.296463	+	0.955044i	$0.595807\pi$
$434$	−5.33017	−0.255856
$435$	6.29404	0.301776
$436$	24.2681	1.16223
$437$	18.1558	0.868511
$438$	39.9419	1.90850
$439$	−33.2830	−1.58851	−0.794255	−	0.607584i	$-0.792139\pi$
$439$	−33.2830	−1.58851	−0.794255	+	0.607584i	$0.792139\pi$
$440$	−19.4146	−0.925555
$441$	−2.86524	−0.136440
$442$	2.78771	0.132598
$443$	19.2798	0.916010	0.458005	−	0.888950i	$-0.348564\pi$
$443$	19.2798	0.916010	0.458005	+	0.888950i	$0.348564\pi$
$444$	−10.6085	−0.503456
$445$	−14.2736	−0.676634
$446$	−8.68505	−0.411249
$447$	4.84682	0.229247
$448$	45.7270	2.16040
$449$	−31.9281	−1.50678	−0.753390	−	0.657574i	$-0.771583\pi$
$449$	−31.9281	−1.50678	−0.753390	+	0.657574i	$0.771583\pi$
$450$	−4.30096	−0.202749
$451$	−22.8620	−1.07653
$452$	−16.0446	−0.754675
$453$	16.7286	0.785979
$454$	19.4206	0.911455
$455$	−4.91811	−0.230565
$456$	18.4260	0.862878
$457$	31.9571	1.49489	0.747444	−	0.664324i	$-0.231281\pi$
$457$	31.9571	1.49489	0.747444	+	0.664324i	$0.231281\pi$
$458$	−55.7690	−2.60591
$459$	5.53651	0.258422
$460$	−17.3031	−0.806760
$461$	18.9966	0.884758	0.442379	−	0.896828i	$-0.354135\pi$
$461$	18.9966	0.884758	0.442379	+	0.896828i	$0.354135\pi$
$462$	74.2665	3.45519
$463$	26.6538	1.23871	0.619353	−	0.785113i	$-0.287395\pi$
$463$	26.6538	1.23871	0.619353	+	0.785113i	$0.287395\pi$
$464$	0.842511	0.0391126
$465$	−1.17226	−0.0543624
$466$	−8.00750	−0.370940
$467$	−13.0327	−0.603080	−0.301540	−	0.953454i	$-0.597501\pi$
$467$	−13.0327	−0.603080	−0.301540	+	0.953454i	$0.597501\pi$
$468$	2.01485	0.0931363
$469$	38.3297	1.76990
$470$	17.6087	0.812228
$471$	−1.57945	−0.0727771
$472$	−17.0500	−0.784789
$473$	−12.9127	−0.593725
$474$	−61.5069	−2.82510
$475$	−14.5593	−0.668028
$476$	−11.7083	−0.536648
$477$	2.40290	0.110021
$478$	53.3238	2.43897
$479$	15.4290	0.704968	0.352484	−	0.935818i	$-0.385337\pi$
$479$	15.4290	0.704968	0.352484	+	0.935818i	$0.385337\pi$
$480$	9.67942	0.441803
$481$	−2.47508	−0.112854
$482$	2.71556	0.123690
$483$	25.9444	1.18051
$484$	72.3374	3.28806
$485$	1.11850	0.0507886
$486$	11.9416	0.541684
$487$	−23.3165	−1.05657	−0.528285	−	0.849067i	$-0.677165\pi$
$487$	−23.3165	−1.05657	−0.528285	+	0.849067i	$0.677165\pi$
$488$	17.4010	0.787705
$489$	29.5961	1.33838
$490$	14.8641	0.671492
$491$	13.2409	0.597554	0.298777	−	0.954323i	$-0.403421\pi$
$491$	13.2409	0.597554	0.298777	+	0.954323i	$0.403421\pi$
$492$	−20.6788	−0.932271
$493$	3.49590	0.157447
$494$	10.9676	0.493456
$495$	−3.30868	−0.148714
$496$	−0.156917	−0.00704580
$497$	4.68599	0.210195
$498$	4.16169	0.186490
$499$	9.57676	0.428715	0.214357	−	0.976755i	$-0.431234\pi$
$499$	9.57676	0.428715	0.214357	+	0.976755i	$0.431234\pi$
$500$	32.6229	1.45894
$501$	−4.02133	−0.179660
$502$	10.4412	0.466012
$503$	−17.2462	−0.768971	−0.384485	−	0.923131i	$-0.625621\pi$
$503$	−17.2462	−0.768971	−0.384485	+	0.923131i	$0.625621\pi$
$504$	−5.33380	−0.237586
$505$	1.12680	0.0501420
$506$	60.9611	2.71005
$507$	18.2122	0.808833
$508$	57.0961	2.53323
$509$	8.86221	0.392811	0.196405	−	0.980523i	$-0.437073\pi$
$509$	8.86221	0.392811	0.196405	+	0.980523i	$0.437073\pi$
$510$	−4.14067	−0.183352
$511$	−39.1390	−1.73141
$512$	2.72492	0.120426
$513$	21.7822	0.961705
$514$	−68.2795	−3.01168
$515$	−13.4540	−0.592855
$516$	−11.6796	−0.514164
$517$	−38.5801	−1.69675
$518$	16.7158	0.734451
$519$	−17.3063	−0.759661
$520$	−4.09708	−0.179669
$521$	10.5885	0.463893	0.231946	−	0.972729i	$-0.425491\pi$
$521$	10.5885	0.463893	0.231946	+	0.972729i	$0.425491\pi$
$522$	4.06301	0.177833
$523$	11.3587	0.496681	0.248340	−	0.968673i	$-0.420115\pi$
$523$	11.3587	0.496681	0.248340	+	0.968673i	$0.420115\pi$
$524$	−70.6388	−3.08587
$525$	−20.8050	−0.908005
$526$	31.4466	1.37114
$527$	−0.651110	−0.0283628
$528$	2.18637	0.0951495
$529$	−1.70376	−0.0740764
$530$	−12.4656	−0.541469
$531$	−2.90570	−0.126097
$532$	−46.0635	−1.99711
$533$	−4.82459	−0.208976
$534$	45.4856	1.96835
$535$	−11.7657	−0.508677
$536$	31.9309	1.37920
$537$	−25.9311	−1.11901
$538$	−70.1586	−3.02475
$539$	−32.5668	−1.40275
$540$	−20.7591	−0.893328
$541$	15.2606	0.656106	0.328053	−	0.944659i	$-0.393608\pi$
$541$	15.2606	0.656106	0.328053	+	0.944659i	$0.393608\pi$
$542$	52.8541	2.27028
$543$	−25.3955	−1.08983
$544$	5.37624	0.230504
$545$	−8.40997	−0.360244
$546$	15.6725	0.670721
$547$	1.83471	0.0784465	0.0392233	−	0.999230i	$-0.487512\pi$
$547$	1.83471	0.0784465	0.0392233	+	0.999230i	$0.487512\pi$
$548$	29.9439	1.27914
$549$	2.96552	0.126565
$550$	−48.8853	−2.08447
$551$	13.7538	0.585933
$552$	21.6132	0.919918
$553$	60.2705	2.56296
$554$	17.5574	0.745944
$555$	3.67631	0.156051
$556$	−16.1957	−0.686851
$557$	−6.16899	−0.261389	−0.130694	−	0.991423i	$-0.541721\pi$
$557$	−6.16899	−0.261389	−0.130694	+	0.991423i	$0.541721\pi$
$558$	−0.756734	−0.0320351
$559$	−2.72497	−0.115254
$560$	0.977841	0.0413213
$561$	9.07208	0.383023
$562$	−62.2290	−2.62497
$563$	11.9205	0.502389	0.251195	−	0.967937i	$-0.419177\pi$
$563$	11.9205	0.502389	0.251195	+	0.967937i	$0.419177\pi$
$564$	−34.8958	−1.46938
$565$	5.56017	0.233918
$566$	38.6922	1.62636
$567$	25.7300	1.08056
$568$	3.90370	0.163796
$569$	32.6884	1.37037	0.685184	−	0.728370i	$-0.259722\pi$
$569$	32.6884	1.37037	0.685184	+	0.728370i	$0.259722\pi$
$570$	−16.2905	−0.682335
$571$	−6.54466	−0.273885	−0.136943	−	0.990579i	$-0.543728\pi$
$571$	−6.54466	−0.273885	−0.136943	+	0.990579i	$0.543728\pi$
$572$	22.9010	0.957540
$573$	30.3386	1.26741
$574$	32.5836	1.36001
$575$	−17.0776	−0.712187
$576$	6.49195	0.270498
$577$	17.1954	0.715852	0.357926	−	0.933750i	$-0.383484\pi$
$577$	17.1954	0.715852	0.357926	+	0.933750i	$0.383484\pi$
$578$	−2.29985	−0.0956613
$579$	19.8997	0.827003
$580$	−13.1078	−0.544273
$581$	−4.07804	−0.169185
$582$	−3.56433	−0.147746
$583$	27.3116	1.13113
$584$	−32.6051	−1.34921
$585$	−0.698234	−0.0288684
$586$	4.37219	0.180613
$587$	−13.2029	−0.544941	−0.272470	−	0.962164i	$-0.587841\pi$
$587$	−13.2029	−0.544941	−0.272470	+	0.962164i	$0.587841\pi$
$588$	−29.4568	−1.21478
$589$	−2.56165	−0.105551
$590$	15.0740	0.620585
$591$	−10.6192	−0.436817
$592$	0.492106	0.0202254
$593$	44.0616	1.80939	0.904696	−	0.426058i	$-0.140098\pi$
$593$	44.0616	1.80939	0.904696	+	0.426058i	$0.140098\pi$
$594$	73.1371	3.00085
$595$	4.05743	0.166339
$596$	−10.0939	−0.413462
$597$	12.3275	0.504531
$598$	12.8647	0.526075
$599$	−43.1078	−1.76134	−0.880668	−	0.473734i	$-0.842906\pi$
$599$	−43.1078	−1.76134	−0.880668	+	0.473734i	$0.842906\pi$
$600$	−17.3318	−0.707567
$601$	12.4897	0.509465	0.254733	−	0.967012i	$-0.418013\pi$
$601$	12.4897	0.509465	0.254733	+	0.967012i	$0.418013\pi$
$602$	18.4035	0.750071
$603$	5.44174	0.221605
$604$	−34.8387	−1.41757
$605$	−25.0681	−1.01916
$606$	−3.59077	−0.145865
$607$	30.0719	1.22058	0.610290	−	0.792178i	$-0.291053\pi$
$607$	30.0719	1.22058	0.610290	+	0.792178i	$0.291053\pi$
$608$	21.1516	0.857811
$609$	19.6540	0.796419
$610$	−15.3843	−0.622891
$611$	−8.14158	−0.329373
$612$	−1.66224	−0.0671923
$613$	−43.5320	−1.75824	−0.879121	−	0.476599i	$-0.841869\pi$
$613$	−43.5320	−1.75824	−0.879121	+	0.476599i	$0.841869\pi$
$614$	−77.8162	−3.14041
$615$	7.16611	0.288966
$616$	−60.6247	−2.44264
$617$	−33.2861	−1.34005	−0.670025	−	0.742339i	$-0.733716\pi$
$617$	−33.2861	−1.34005	−0.670025	+	0.742339i	$0.733716\pi$
$618$	42.8738	1.72464
$619$	−3.86936	−0.155523	−0.0777613	−	0.996972i	$-0.524777\pi$
$619$	−3.86936	−0.155523	−0.0777613	+	0.996972i	$0.524777\pi$
$620$	2.44133	0.0980462
$621$	25.5498	1.02528
$622$	26.9294	1.07977
$623$	−44.5712	−1.78571
$624$	0.461391	0.0184704
$625$	7.19789	0.287916
$626$	30.4315	1.21629
$627$	35.6920	1.42540
$628$	3.28932	0.131258
$629$	2.04193	0.0814172
$630$	4.71563	0.187875
$631$	38.1808	1.51995	0.759976	−	0.649951i	$-0.225211\pi$
$631$	38.1808	1.51995	0.759976	+	0.649951i	$0.225211\pi$
$632$	50.2089	1.99720
$633$	22.6902	0.901856
$634$	53.9388	2.14218
$635$	−19.7863	−0.785197
$636$	24.7035	0.979557
$637$	−6.87259	−0.272302
$638$	46.1807	1.82831
$639$	0.665278	0.0263180
$640$	−21.4218	−0.846769
$641$	1.13469	0.0448177	0.0224088	−	0.999749i	$-0.492866\pi$
$641$	1.13469	0.0448177	0.0224088	+	0.999749i	$0.492866\pi$
$642$	37.4938	1.47976
$643$	9.51365	0.375182	0.187591	−	0.982247i	$-0.439932\pi$
$643$	9.51365	0.375182	0.187591	+	0.982247i	$0.439932\pi$
$644$	−54.0311	−2.12913
$645$	4.04748	0.159369
$646$	−9.04825	−0.355999
$647$	3.75155	0.147489	0.0737443	−	0.997277i	$-0.476505\pi$
$647$	3.75155	0.147489	0.0737443	+	0.997277i	$0.476505\pi$
$648$	21.4346	0.842030
$649$	−33.0266	−1.29641
$650$	−10.3163	−0.404638
$651$	−3.66055	−0.143468
$652$	−61.6362	−2.41386
$653$	−21.7275	−0.850263	−0.425131	−	0.905132i	$-0.639772\pi$
$653$	−21.7275	−0.850263	−0.425131	+	0.905132i	$0.639772\pi$
$654$	26.8000	1.04796
$655$	24.4795	0.956493
$656$	0.959245	0.0374522
$657$	−5.55663	−0.216785
$658$	54.9854	2.14356
$659$	44.7145	1.74183	0.870915	−	0.491434i	$-0.163527\pi$
$659$	44.7145	1.74183	0.870915	+	0.491434i	$0.163527\pi$
$660$	−34.0156	−1.32406
$661$	26.4252	1.02782	0.513911	−	0.857844i	$-0.328196\pi$
$661$	26.4252	1.02782	0.513911	+	0.857844i	$0.328196\pi$
$662$	48.0828	1.86879
$663$	1.91449	0.0743525
$664$	−3.39724	−0.131839
$665$	15.9631	0.619021
$666$	2.37318	0.0919587
$667$	16.1328	0.624666
$668$	8.37473	0.324028
$669$	−5.96455	−0.230603
$670$	−28.2303	−1.09063
$671$	33.7065	1.30122
$672$	30.2253	1.16596
$673$	13.1273	0.506020	0.253010	−	0.967464i	$-0.418580\pi$
$673$	13.1273	0.506020	0.253010	+	0.967464i	$0.418580\pi$
$674$	−60.2348	−2.32016
$675$	−20.4886	−0.788607
$676$	−37.9284	−1.45878
$677$	−8.63096	−0.331715	−0.165857	−	0.986150i	$-0.553039\pi$
$677$	−8.63096	−0.331715	−0.165857	+	0.986150i	$0.553039\pi$
$678$	−17.7185	−0.680477
$679$	3.49268	0.134037
$680$	3.38008	0.129620
$681$	13.3373	0.511087
$682$	−8.60114	−0.329355
$683$	34.1339	1.30610	0.653048	−	0.757316i	$-0.273490\pi$
$683$	34.1339	1.30610	0.653048	+	0.757316i	$0.273490\pi$
$684$	−6.53973	−0.250053
$685$	−10.3769	−0.396480
$686$	−10.8888	−0.415736
$687$	−38.2999	−1.46123
$688$	0.541790	0.0206556
$689$	5.76359	0.219575
$690$	−19.1083	−0.727441
$691$	−3.51090	−0.133561	−0.0667805	−	0.997768i	$-0.521273\pi$
$691$	−3.51090	−0.133561	−0.0667805	+	0.997768i	$0.521273\pi$
$692$	36.0416	1.37010
$693$	−10.3318	−0.392473
$694$	67.3082	2.55498
$695$	5.61253	0.212896
$696$	16.3729	0.620614
$697$	3.98027	0.150764
$698$	68.0481	2.57566
$699$	−5.49923	−0.208000
$700$	43.3280	1.63765
$701$	−24.9837	−0.943623	−0.471811	−	0.881700i	$-0.656400\pi$
$701$	−24.9837	−0.943623	−0.471811	+	0.881700i	$0.656400\pi$
$702$	15.4342	0.582525
$703$	8.03353	0.302990
$704$	73.7885	2.78101
$705$	12.0929	0.455447
$706$	42.1174	1.58511
$707$	3.51858	0.132330
$708$	−29.8727	−1.12268
$709$	24.9168	0.935770	0.467885	−	0.883789i	$-0.345016\pi$
$709$	24.9168	0.935770	0.467885	+	0.883789i	$0.345016\pi$
$710$	−3.45128	−0.129524
$711$	8.55671	0.320902
$712$	−37.1305	−1.39152
$713$	−3.00474	−0.112528
$714$	−12.9298	−0.483885
$715$	−7.93622	−0.296798
$716$	54.0035	2.01820
$717$	36.6207	1.36762
$718$	−46.5527	−1.73733
$719$	9.61138	0.358444	0.179222	−	0.983809i	$-0.442642\pi$
$719$	9.61138	0.358444	0.179222	+	0.983809i	$0.442642\pi$
$720$	0.138826	0.00517374
$721$	−42.0120	−1.56461
$722$	8.09888	0.301409
$723$	1.86494	0.0693578
$724$	52.8882	1.96557
$725$	−12.9371	−0.480470
$726$	79.8843	2.96478
$727$	−5.02660	−0.186426	−0.0932131	−	0.995646i	$-0.529714\pi$
$727$	−5.02660	−0.186426	−0.0932131	+	0.995646i	$0.529714\pi$
$728$	−12.7937	−0.474165
$729$	29.8868	1.10692
$730$	28.8263	1.06691
$731$	2.24809	0.0831488
$732$	30.4876	1.12686
$733$	0.236838	0.00874780	0.00437390	−	0.999990i	$-0.498608\pi$
$733$	0.236838	0.00874780	0.00437390	+	0.999990i	$0.498608\pi$
$734$	−3.23996	−0.119589
$735$	10.2081	0.376531
$736$	24.8102	0.914516
$737$	61.8516	2.27833
$738$	4.62596	0.170284
$739$	−33.5855	−1.23546	−0.617732	−	0.786389i	$-0.711948\pi$
$739$	−33.5855	−1.23546	−0.617732	+	0.786389i	$0.711948\pi$
$740$	−7.65620	−0.281448
$741$	7.53212	0.276699
$742$	−38.9254	−1.42899
$743$	−15.3693	−0.563844	−0.281922	−	0.959437i	$-0.590972\pi$
$743$	−15.3693	−0.563844	−0.281922	+	0.959437i	$0.590972\pi$
$744$	−3.04945	−0.111798
$745$	3.49798	0.128156
$746$	−18.6234	−0.681852
$747$	−0.578966	−0.0211833
$748$	−18.8933	−0.690808
$749$	−36.7401	−1.34245
$750$	36.0265	1.31550
$751$	14.3018	0.521881	0.260941	−	0.965355i	$-0.415967\pi$
$751$	14.3018	0.521881	0.260941	+	0.965355i	$0.415967\pi$
$752$	1.61874	0.0590295
$753$	7.17058	0.261310
$754$	9.74554	0.354912
$755$	12.0731	0.439387
$756$	−64.8229	−2.35759
$757$	−53.2518	−1.93547	−0.967735	−	0.251970i	$-0.918921\pi$
$757$	−53.2518	−1.93547	−0.967735	+	0.251970i	$0.918921\pi$
$758$	67.0038	2.43369
$759$	41.8657	1.51963
$760$	13.2982	0.482375
$761$	−9.56984	−0.346907	−0.173453	−	0.984842i	$-0.555493\pi$
$761$	−9.56984	−0.346907	−0.173453	+	0.984842i	$0.555493\pi$
$762$	63.0529	2.28417
$763$	−26.2612	−0.950721
$764$	−63.1826	−2.28586
$765$	0.576042	0.0208268
$766$	−57.6185	−2.08184
$767$	−6.96962	−0.251658
$768$	27.6836	0.998945
$769$	9.16640	0.330549	0.165274	−	0.986248i	$-0.447149\pi$
$769$	9.16640	0.330549	0.165274	+	0.986248i	$0.447149\pi$
$770$	53.5985	1.93156
$771$	−46.8917	−1.68876
$772$	−41.4426	−1.49155
$773$	15.0732	0.542145	0.271072	−	0.962559i	$-0.412622\pi$
$773$	15.0732	0.542145	0.271072	+	0.962559i	$0.412622\pi$
$774$	2.61278	0.0939145
$775$	2.40952	0.0865526
$776$	2.90960	0.104449
$777$	11.4798	0.411834
$778$	−12.6896	−0.454943
$779$	15.6595	0.561060
$780$	−7.17834	−0.257026
$781$	7.56164	0.270577
$782$	−10.6133	−0.379532
$783$	19.3551	0.691694
$784$	1.36644	0.0488014
$785$	−1.13990	−0.0406846
$786$	−78.0086	−2.78247
$787$	−35.7869	−1.27566	−0.637832	−	0.770175i	$-0.720169\pi$
$787$	−35.7869	−1.27566	−0.637832	+	0.770175i	$0.720169\pi$
$788$	22.1154	0.787829
$789$	21.5962	0.768847
$790$	−44.3899	−1.57932
$791$	17.3624	0.617335
$792$	−8.60700	−0.305836
$793$	7.11310	0.252594
$794$	1.71497	0.0608622
$795$	−8.56085	−0.303622
$796$	−25.6730	−0.909955
$797$	−19.2030	−0.680206	−0.340103	−	0.940388i	$-0.610462\pi$
$797$	−19.2030	−0.680206	−0.340103	+	0.940388i	$0.610462\pi$
$798$	−50.8693	−1.80076
$799$	6.71679	0.237623
$800$	−19.8955	−0.703413
$801$	−6.32786	−0.223584
$802$	−47.9011	−1.69145
$803$	−63.1575	−2.22878
$804$	55.9450	1.97303
$805$	18.7242	0.659941
$806$	−1.81511	−0.0639343
$807$	−48.1822	−1.69609
$808$	2.93119	0.103119
$809$	−42.0325	−1.47778	−0.738891	−	0.673825i	$-0.764650\pi$
$809$	−42.0325	−1.47778	−0.738891	+	0.673825i	$0.764650\pi$
$810$	−18.9504	−0.665850
$811$	−10.8741	−0.381842	−0.190921	−	0.981605i	$-0.561147\pi$
$811$	−10.8741	−0.381842	−0.190921	+	0.981605i	$0.561147\pi$
$812$	−40.9309	−1.43639
$813$	36.2981	1.27303
$814$	26.9739	0.945433
$815$	21.3597	0.748197
$816$	−0.380647	−0.0133253
$817$	8.84462	0.309434
$818$	40.2335	1.40673
$819$	−2.18033	−0.0761868
$820$	−14.9240	−0.521168
$821$	−17.8887	−0.624322	−0.312161	−	0.950029i	$-0.601053\pi$
$821$	−17.8887	−0.624322	−0.312161	+	0.950029i	$0.601053\pi$
$822$	33.0679	1.15338
$823$	−13.2497	−0.461855	−0.230928	−	0.972971i	$-0.574176\pi$
$823$	−13.2497	−0.461855	−0.230928	+	0.972971i	$0.574176\pi$
$824$	−34.9984	−1.21923
$825$	−33.5725	−1.16884
$826$	47.0704	1.63779
$827$	12.1471	0.422397	0.211198	−	0.977443i	$-0.432263\pi$
$827$	12.1471	0.422397	0.211198	+	0.977443i	$0.432263\pi$
$828$	−7.67090	−0.266582
$829$	−50.0635	−1.73878	−0.869389	−	0.494128i	$-0.835487\pi$
$829$	−50.0635	−1.73878	−0.869389	+	0.494128i	$0.835487\pi$
$830$	3.00352	0.104254
$831$	12.0577	0.418279
$832$	15.5716	0.539849
$833$	5.66987	0.196449
$834$	−17.8854	−0.619321
$835$	−2.90222	−0.100435
$836$	−74.3315	−2.57081
$837$	−3.60488	−0.124603
$838$	31.6713	1.09407
$839$	−20.7019	−0.714710	−0.357355	−	0.933969i	$-0.616321\pi$
$839$	−20.7019	−0.714710	−0.357355	+	0.933969i	$0.616321\pi$
$840$	19.0028	0.655660
$841$	−16.7787	−0.578575
$842$	−10.2487	−0.353193
$843$	−42.7364	−1.47192
$844$	−47.2542	−1.62656
$845$	13.1439	0.452163
$846$	7.80639	0.268389
$847$	−78.2785	−2.68968
$848$	−1.14594	−0.0393518
$849$	26.5723	0.911958
$850$	8.51092	0.291922
$851$	9.42309	0.323019
$852$	6.83953	0.234319
$853$	−30.1406	−1.03199	−0.515997	−	0.856590i	$-0.672579\pi$
$853$	−30.1406	−1.03199	−0.515997	+	0.856590i	$0.672579\pi$
$854$	−48.0395	−1.64388
$855$	2.26631	0.0775060
$856$	−30.6067	−1.04611
$857$	13.5241	0.461973	0.230987	−	0.972957i	$-0.425805\pi$
$857$	13.5241	0.461973	0.230987	+	0.972957i	$0.425805\pi$
$858$	25.2903	0.863396
$859$	−32.3698	−1.10444	−0.552222	−	0.833697i	$-0.686220\pi$
$859$	−32.3698	−1.10444	−0.552222	+	0.833697i	$0.686220\pi$
$860$	−8.42920	−0.287433
$861$	22.3771	0.762610
$862$	−14.9705	−0.509896
$863$	22.0521	0.750662	0.375331	−	0.926891i	$-0.377529\pi$
$863$	22.0521	0.750662	0.375331	+	0.926891i	$0.377529\pi$
$864$	29.7656	1.01265
$865$	−12.4900	−0.424674
$866$	28.3756	0.964242
$867$	−1.57945	−0.0536408
$868$	7.62338	0.258754
$869$	97.2568	3.29921
$870$	−14.4754	−0.490761
$871$	13.0526	0.442270
$872$	−21.8772	−0.740854
$873$	0.495862	0.0167824
$874$	−41.7557	−1.41241
$875$	−35.3023	−1.19343
$876$	−57.1261	−1.93011
$877$	25.1709	0.849959	0.424980	−	0.905203i	$-0.360281\pi$
$877$	25.1709	0.849959	0.424980	+	0.905203i	$0.360281\pi$
$878$	76.5460	2.58330
$879$	3.00265	0.101277
$880$	1.57791	0.0531915
$881$	−23.7581	−0.800431	−0.400216	−	0.916421i	$-0.631065\pi$
$881$	−23.7581	−0.800431	−0.400216	+	0.916421i	$0.631065\pi$
$882$	6.58964	0.221885
$883$	28.3346	0.953534	0.476767	−	0.879030i	$-0.341808\pi$
$883$	28.3346	0.953534	0.476767	+	0.879030i	$0.341808\pi$
$884$	−3.98707	−0.134100
$885$	10.3522	0.347985
$886$	−44.3406	−1.48965
$887$	17.5656	0.589795	0.294897	−	0.955529i	$-0.404715\pi$
$887$	17.5656	0.589795	0.294897	+	0.955529i	$0.404715\pi$
$888$	9.56332	0.320924
$889$	−61.7855	−2.07222
$890$	32.8272	1.10037
$891$	41.5198	1.39096
$892$	12.4216	0.415907
$893$	26.4257	0.884302
$894$	−11.1470	−0.372811
$895$	−18.7146	−0.625560
$896$	−66.8923	−2.23471
$897$	8.83494	0.294990
$898$	73.4299	2.45039
$899$	−2.27622	−0.0759161
$900$	6.15136	0.205045
$901$	−4.75495	−0.158411
$902$	52.5793	1.75070
$903$	12.6388	0.420593
$904$	14.4639	0.481061
$905$	−18.3281	−0.609247
$906$	−38.4734	−1.27819
$907$	27.6114	0.916822	0.458411	−	0.888740i	$-0.348419\pi$
$907$	27.6114	0.916822	0.458411	+	0.888740i	$0.348419\pi$
$908$	−27.7760	−0.921778
$909$	0.499540	0.0165687
$910$	11.3109	0.374954
$911$	−13.0681	−0.432966	−0.216483	−	0.976286i	$-0.569459\pi$
$911$	−13.0681	−0.432966	−0.216483	+	0.976286i	$0.569459\pi$
$912$	−1.49757	−0.0495894
$913$	−6.58061	−0.217787
$914$	−73.4966	−2.43105
$915$	−10.5653	−0.349279
$916$	79.7625	2.63543
$917$	76.4404	2.52429
$918$	−12.7332	−0.420257
$919$	−25.0992	−0.827945	−0.413973	−	0.910289i	$-0.635859\pi$
$919$	−25.0992	−0.827945	−0.413973	+	0.910289i	$0.635859\pi$
$920$	15.5983	0.514262
$921$	−53.4411	−1.76094
$922$	−43.6893	−1.43883
$923$	1.59574	0.0525244
$924$	−106.218	−3.49433
$925$	−7.55645	−0.248455
$926$	−61.2997	−2.01443
$927$	−5.96452	−0.195901
$928$	18.7948	0.616970
$929$	28.1118	0.922317	0.461158	−	0.887318i	$-0.347434\pi$
$929$	28.1118	0.922317	0.461158	+	0.887318i	$0.347434\pi$
$930$	2.69603	0.0884064
$931$	22.3068	0.731077
$932$	11.4526	0.375142
$933$	18.4940	0.605468
$934$	29.9732	0.980754
$935$	6.54737	0.214122
$936$	−1.81634	−0.0593689
$937$	−42.9970	−1.40465	−0.702325	−	0.711856i	$-0.747855\pi$
$937$	−42.9970	−1.40465	−0.702325	+	0.711856i	$0.747855\pi$
$938$	−88.1527	−2.87829
$939$	20.8991	0.682017
$940$	−25.1845	−0.821428
$941$	−8.51209	−0.277486	−0.138743	−	0.990328i	$-0.544306\pi$
$941$	−8.51209	−0.277486	−0.138743	+	0.990328i	$0.544306\pi$
$942$	3.63250	0.118353
$943$	18.3681	0.598148
$944$	1.38573	0.0451017
$945$	22.4640	0.730755
$946$	29.6972	0.965540
$947$	−44.0696	−1.43207	−0.716035	−	0.698064i	$-0.754045\pi$
$947$	−44.0696	−1.43207	−0.716035	+	0.698064i	$0.754045\pi$
$948$	87.9691	2.85710
$949$	−13.3282	−0.432650
$950$	33.4843	1.08637
$951$	37.0430	1.20120
$952$	10.5547	0.342081
$953$	4.14862	0.134387	0.0671934	−	0.997740i	$-0.478596\pi$
$953$	4.14862	0.134387	0.0671934	+	0.997740i	$0.478596\pi$
$954$	−5.52631	−0.178921
$955$	21.8956	0.708524
$956$	−76.2654	−2.46660
$957$	31.7151	1.02520
$958$	−35.4844	−1.14645
$959$	−32.4032	−1.04635
$960$	−23.1290	−0.746487
$961$	−30.5761	−0.986324
$962$	5.69231	0.183527
$963$	−5.21606	−0.168085
$964$	−3.88388	−0.125091
$965$	14.3617	0.462320
$966$	−59.6682	−1.91979
$967$	7.22868	0.232459	0.116229	−	0.993222i	$-0.462919\pi$
$967$	7.22868	0.232459	0.116229	+	0.993222i	$0.462919\pi$
$968$	−65.2106	−2.09595
$969$	−6.21398	−0.199622
$970$	−2.57239	−0.0825946
$971$	20.9987	0.673881	0.336940	−	0.941526i	$-0.390608\pi$
$971$	20.9987	0.673881	0.336940	+	0.941526i	$0.390608\pi$
$972$	−17.0793	−0.547819
$973$	17.5259	0.561854
$974$	53.6244	1.71824
$975$	−7.08482	−0.226896
$976$	−1.41426	−0.0452693
$977$	−0.0919647	−0.00294221	−0.00147111	−	0.999999i	$-0.500468\pi$
$977$	−0.0919647	−0.00294221	−0.00147111	+	0.999999i	$0.500468\pi$
$978$	−68.0667	−2.17653
$979$	−71.9234	−2.29868
$980$	−21.2591	−0.679098
$981$	−3.72836	−0.119037
$982$	−30.4522	−0.971767
$983$	−16.7608	−0.534586	−0.267293	−	0.963615i	$-0.586129\pi$
$983$	−16.7608	−0.534586	−0.267293	+	0.963615i	$0.586129\pi$
$984$	18.6415	0.594268
$985$	−7.66397	−0.244194
$986$	−8.04006	−0.256048
$987$	37.7618	1.20197
$988$	−15.6862	−0.499045
$989$	10.3745	0.329889
$990$	7.60949	0.241845
$991$	−34.5350	−1.09704	−0.548520	−	0.836137i	$-0.684809\pi$
$991$	−34.5350	−1.09704	−0.548520	+	0.836137i	$0.684809\pi$
$992$	−3.50053	−0.111142
$993$	33.0213	1.04790
$994$	−10.7771	−0.341828
$995$	8.89683	0.282049
$996$	−5.95219	−0.188602
$997$	−31.0480	−0.983299	−0.491649	−	0.870793i	$-0.663606\pi$
$997$	−31.0480	−0.983299	−0.491649	+	0.870793i	$0.663606\pi$
$998$	−22.0251	−0.697194
$999$	11.3052	0.357680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2669.2.a.b.1.6	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2669.2.a.b.1.6	✓	45	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:	\( N \)	\(=\)	\( 2669 = 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2669.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29985 q^{2} -1.57945 q^{3} +3.28932 q^{4} -1.13990 q^{5} +3.63250 q^{6} -3.55948 q^{7} -2.96525 q^{8} -0.505346 q^{9} +O(q^{10})\)	\(q-2.29985 q^{2} -1.57945 q^{3} +3.28932 q^{4} -1.13990 q^{5} +3.63250 q^{6} -3.55948 q^{7} -2.96525 q^{8} -0.505346 q^{9} +2.62159 q^{10} -5.74383 q^{11} -5.19531 q^{12} -1.21212 q^{13} +8.18627 q^{14} +1.80041 q^{15} +0.241000 q^{16} +1.00000 q^{17} +1.16222 q^{18} +3.93428 q^{19} -3.74949 q^{20} +5.62201 q^{21} +13.2100 q^{22} +4.61479 q^{23} +4.68346 q^{24} -3.70064 q^{25} +2.78771 q^{26} +5.53651 q^{27} -11.7083 q^{28} +3.49590 q^{29} -4.14067 q^{30} -0.651110 q^{31} +5.37624 q^{32} +9.07208 q^{33} -2.29985 q^{34} +4.05743 q^{35} -1.66224 q^{36} +2.04193 q^{37} -9.04825 q^{38} +1.91449 q^{39} +3.38008 q^{40} +3.98027 q^{41} -12.9298 q^{42} +2.24809 q^{43} -18.8933 q^{44} +0.576042 q^{45} -10.6133 q^{46} +6.71679 q^{47} -0.380647 q^{48} +5.66987 q^{49} +8.51092 q^{50} -1.57945 q^{51} -3.98707 q^{52} -4.75495 q^{53} -12.7332 q^{54} +6.54737 q^{55} +10.5547 q^{56} -6.21398 q^{57} -8.04006 q^{58} +5.74992 q^{59} +5.92212 q^{60} -5.86829 q^{61} +1.49746 q^{62} +1.79877 q^{63} -12.8466 q^{64} +1.38170 q^{65} -20.8644 q^{66} -10.7684 q^{67} +3.28932 q^{68} -7.28881 q^{69} -9.33150 q^{70} -1.31648 q^{71} +1.49848 q^{72} +10.9957 q^{73} -4.69615 q^{74} +5.84496 q^{75} +12.9411 q^{76} +20.4450 q^{77} -4.40304 q^{78} -16.9324 q^{79} -0.274715 q^{80} -7.22859 q^{81} -9.15405 q^{82} +1.14568 q^{83} +18.4926 q^{84} -1.13990 q^{85} -5.17029 q^{86} -5.52159 q^{87} +17.0319 q^{88} +12.5219 q^{89} -1.32481 q^{90} +4.31453 q^{91} +15.1795 q^{92} +1.02839 q^{93} -15.4476 q^{94} -4.48467 q^{95} -8.49149 q^{96} -0.981233 q^{97} -13.0399 q^{98} +2.90262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * q^99

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