LMFDB - Embedded newform 667.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.28888$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28888 q^{2} +3.25447 q^{3} -0.338793 q^{4} +4.18846 q^{5} -4.19461 q^{6} -3.67888 q^{7} +3.01442 q^{8} +7.59155 q^{9} +O(q^{10})$	\(q-1.28888 q^{2} +3.25447 q^{3} -0.338793 q^{4} +4.18846 q^{5} -4.19461 q^{6} -3.67888 q^{7} +3.01442 q^{8} +7.59155 q^{9} -5.39841 q^{10} -5.13684 q^{11} -1.10259 q^{12} +4.32617 q^{13} +4.74163 q^{14} +13.6312 q^{15} -3.20763 q^{16} +0.381268 q^{17} -9.78458 q^{18} +1.30789 q^{19} -1.41902 q^{20} -11.9728 q^{21} +6.62076 q^{22} +1.00000 q^{23} +9.81033 q^{24} +12.5432 q^{25} -5.57590 q^{26} +14.9430 q^{27} +1.24638 q^{28} -1.00000 q^{29} -17.5690 q^{30} +5.12340 q^{31} -1.89459 q^{32} -16.7177 q^{33} -0.491408 q^{34} -15.4088 q^{35} -2.57197 q^{36} -6.52227 q^{37} -1.68572 q^{38} +14.0794 q^{39} +12.6258 q^{40} -5.19412 q^{41} +15.4315 q^{42} -3.41912 q^{43} +1.74033 q^{44} +31.7969 q^{45} -1.28888 q^{46} -4.78004 q^{47} -10.4391 q^{48} +6.53417 q^{49} -16.1667 q^{50} +1.24082 q^{51} -1.46568 q^{52} +1.50843 q^{53} -19.2598 q^{54} -21.5154 q^{55} -11.0897 q^{56} +4.25650 q^{57} +1.28888 q^{58} +5.31889 q^{59} -4.61816 q^{60} -7.01094 q^{61} -6.60344 q^{62} -27.9284 q^{63} +8.85716 q^{64} +18.1200 q^{65} +21.5470 q^{66} -8.40996 q^{67} -0.129171 q^{68} +3.25447 q^{69} +19.8601 q^{70} -2.40424 q^{71} +22.8841 q^{72} +1.76206 q^{73} +8.40641 q^{74} +40.8214 q^{75} -0.443106 q^{76} +18.8978 q^{77} -18.1466 q^{78} -6.13455 q^{79} -13.4350 q^{80} +25.8570 q^{81} +6.69459 q^{82} +3.80378 q^{83} +4.05630 q^{84} +1.59692 q^{85} +4.40683 q^{86} -3.25447 q^{87} -15.4846 q^{88} -1.90259 q^{89} -40.9823 q^{90} -15.9155 q^{91} -0.338793 q^{92} +16.6739 q^{93} +6.16089 q^{94} +5.47806 q^{95} -6.16588 q^{96} -5.23059 q^{97} -8.42175 q^{98} -38.9966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	−1.28888	−0.911374	−0.455687	−	0.890140i	$-0.650606\pi$
$2$	−1.28888	−0.911374	−0.455687	+	0.890140i	$0.650606\pi$
$3$	3.25447	1.87897	0.939483	−	0.342594i	$-0.111306\pi$
$3$	3.25447	1.87897	0.939483	+	0.342594i	$0.111306\pi$
$4$	−0.338793	−0.169397
$5$	4.18846	1.87314	0.936568	−	0.350486i	$-0.113983\pi$
$5$	4.18846	1.87314	0.936568	+	0.350486i	$0.113983\pi$
$6$	−4.19461	−1.71244
$7$	−3.67888	−1.39049	−0.695243	−	0.718774i	$-0.744703\pi$
$7$	−3.67888	−1.39049	−0.695243	+	0.718774i	$0.744703\pi$
$8$	3.01442	1.06576
$9$	7.59155	2.53052
$10$	−5.39841	−1.70713
$11$	−5.13684	−1.54881	−0.774407	−	0.632687i	$-0.781952\pi$
$11$	−5.13684	−1.54881	−0.774407	+	0.632687i	$0.781952\pi$
$12$	−1.10259	−0.318291
$13$	4.32617	1.19986	0.599932	−	0.800051i	$-0.295194\pi$
$13$	4.32617	1.19986	0.599932	+	0.800051i	$0.295194\pi$
$14$	4.74163	1.26725
$15$	13.6312	3.51956
$16$	−3.20763	−0.801908
$17$	0.381268	0.0924710	0.0462355	−	0.998931i	$-0.485278\pi$
$17$	0.381268	0.0924710	0.0462355	+	0.998931i	$0.485278\pi$
$18$	−9.78458	−2.30625
$19$	1.30789	0.300051	0.150026	−	0.988682i	$-0.452064\pi$
$19$	1.30789	0.300051	0.150026	+	0.988682i	$0.452064\pi$
$20$	−1.41902	−0.317303
$21$	−11.9728	−2.61268
$22$	6.62076	1.41155
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	9.81033	2.00252
$25$	12.5432	2.50864
$26$	−5.57590	−1.09352
$27$	14.9430	2.87579
$28$	1.24638	0.235544
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−17.5690	−3.20764
$31$	5.12340	0.920190	0.460095	−	0.887870i	$-0.347815\pi$
$31$	5.12340	0.920190	0.460095	+	0.887870i	$0.347815\pi$
$32$	−1.89459	−0.334920
$33$	−16.7177	−2.91017
$34$	−0.491408	−0.0842757
$35$	−15.4088	−2.60457
$36$	−2.57197	−0.428661
$37$	−6.52227	−1.07225	−0.536127	−	0.844137i	$-0.680113\pi$
$37$	−6.52227	−1.07225	−0.536127	+	0.844137i	$0.680113\pi$
$38$	−1.68572	−0.273459
$39$	14.0794	2.25450
$40$	12.6258	1.99631
$41$	−5.19412	−0.811186	−0.405593	−	0.914054i	$-0.632935\pi$
$41$	−5.19412	−0.811186	−0.405593	+	0.914054i	$0.632935\pi$
$42$	15.4315	2.38113
$43$	−3.41912	−0.521411	−0.260706	−	0.965418i	$-0.583955\pi$
$43$	−3.41912	−0.521411	−0.260706	+	0.965418i	$0.583955\pi$
$44$	1.74033	0.262364
$45$	31.7969	4.74000
$46$	−1.28888	−0.190035
$47$	−4.78004	−0.697240	−0.348620	−	0.937264i	$-0.613350\pi$
$47$	−4.78004	−0.697240	−0.348620	+	0.937264i	$0.613350\pi$
$48$	−10.4391	−1.50676
$49$	6.53417	0.933453
$50$	−16.1667	−2.28631
$51$	1.24082	0.173750
$52$	−1.46568	−0.203253
$53$	1.50843	0.207199	0.103599	−	0.994619i	$-0.466964\pi$
$53$	1.50843	0.207199	0.103599	+	0.994619i	$0.466964\pi$
$54$	−19.2598	−2.62092
$55$	−21.5154	−2.90114
$56$	−11.0897	−1.48192
$57$	4.25650	0.563787
$58$	1.28888	0.169238
$59$	5.31889	0.692460	0.346230	−	0.938150i	$-0.387462\pi$
$59$	5.31889	0.692460	0.346230	+	0.938150i	$0.387462\pi$
$60$	−4.61816	−0.596202
$61$	−7.01094	−0.897659	−0.448829	−	0.893618i	$-0.648159\pi$
$61$	−7.01094	−0.897659	−0.448829	+	0.893618i	$0.648159\pi$
$62$	−6.60344	−0.838638
$63$	−27.9284	−3.51865
$64$	8.85716	1.10715
$65$	18.1200	2.24751
$66$	21.5470	2.65226
$67$	−8.40996	−1.02744	−0.513720	−	0.857958i	$-0.671733\pi$
$67$	−8.40996	−1.02744	−0.513720	+	0.857958i	$0.671733\pi$
$68$	−0.129171	−0.0156643
$69$	3.25447	0.391792
$70$	19.8601	2.37374
$71$	−2.40424	−0.285330	−0.142665	−	0.989771i	$-0.545567\pi$
$71$	−2.40424	−0.285330	−0.142665	+	0.989771i	$0.545567\pi$
$72$	22.8841	2.69692
$73$	1.76206	0.206234	0.103117	−	0.994669i	$-0.467118\pi$
$73$	1.76206	0.206234	0.103117	+	0.994669i	$0.467118\pi$
$74$	8.40641	0.977225
$75$	40.8214	4.71365
$76$	−0.443106	−0.0508277
$77$	18.8978	2.15361
$78$	−18.1466	−2.05470
$79$	−6.13455	−0.690191	−0.345095	−	0.938568i	$-0.612153\pi$
$79$	−6.13455	−0.690191	−0.345095	+	0.938568i	$0.612153\pi$
$80$	−13.4350	−1.50208
$81$	25.8570	2.87300
$82$	6.69459	0.739294
$83$	3.80378	0.417519	0.208760	−	0.977967i	$-0.433057\pi$
$83$	3.80378	0.417519	0.208760	+	0.977967i	$0.433057\pi$
$84$	4.05630	0.442579
$85$	1.59692	0.173211
$86$	4.40683	0.475201
$87$	−3.25447	−0.348915
$88$	−15.4846	−1.65066
$89$	−1.90259	−0.201674	−0.100837	−	0.994903i	$-0.532152\pi$
$89$	−1.90259	−0.201674	−0.100837	+	0.994903i	$0.532152\pi$
$90$	−40.9823	−4.31992
$91$	−15.9155	−1.66839
$92$	−0.338793	−0.0353216
$93$	16.6739	1.72901
$94$	6.16089	0.635447
$95$	5.47806	0.562037
$96$	−6.16588	−0.629303
$97$	−5.23059	−0.531086	−0.265543	−	0.964099i	$-0.585551\pi$
$97$	−5.23059	−0.531086	−0.265543	+	0.964099i	$0.585551\pi$
$98$	−8.42175	−0.850725
$99$	−38.9966	−3.91930
$100$	−4.24955	−0.424955
$101$	18.5662	1.84741	0.923703	−	0.383110i	$-0.125147\pi$
$101$	18.5662	1.84741	0.923703	+	0.383110i	$0.125147\pi$
$102$	−1.59927	−0.158351
$103$	6.34875	0.625561	0.312780	−	0.949825i	$-0.398740\pi$
$103$	6.34875	0.625561	0.312780	+	0.949825i	$0.398740\pi$
$104$	13.0409	1.27876
$105$	−50.1476	−4.89390
$106$	−1.94418	−0.188835
$107$	4.81598	0.465579	0.232789	−	0.972527i	$-0.425215\pi$
$107$	4.81598	0.465579	0.232789	+	0.972527i	$0.425215\pi$
$108$	−5.06260	−0.487149
$109$	−3.37159	−0.322940	−0.161470	−	0.986878i	$-0.551624\pi$
$109$	−3.37159	−0.322940	−0.161470	+	0.986878i	$0.551624\pi$
$110$	27.7308	2.64403
$111$	−21.2265	−2.01473
$112$	11.8005	1.11504
$113$	−1.63180	−0.153507	−0.0767534	−	0.997050i	$-0.524455\pi$
$113$	−1.63180	−0.153507	−0.0767534	+	0.997050i	$0.524455\pi$
$114$	−5.48610	−0.513821
$115$	4.18846	0.390576
$116$	0.338793	0.0314562
$117$	32.8423	3.03627
$118$	−6.85540	−0.631091
$119$	−1.40264	−0.128580
$120$	41.0902	3.75100
$121$	15.3871	1.39883
$122$	9.03624	0.818103
$123$	−16.9041	−1.52419
$124$	−1.73577	−0.155877
$125$	31.5944	2.82589
$126$	35.9963	3.20681
$127$	−13.2651	−1.17709	−0.588545	−	0.808464i	$-0.700299\pi$
$127$	−13.2651	−1.17709	−0.588545	+	0.808464i	$0.700299\pi$
$128$	−7.62662	−0.674104
$129$	−11.1274	−0.979715
$130$	−23.3544	−2.04832
$131$	−9.78850	−0.855225	−0.427613	−	0.903962i	$-0.640645\pi$
$131$	−9.78850	−0.855225	−0.427613	+	0.903962i	$0.640645\pi$
$132$	5.66383	0.492973
$133$	−4.81159	−0.417217
$134$	10.8394	0.936382
$135$	62.5883	5.38675
$136$	1.14930	0.0985518
$137$	−13.0750	−1.11708	−0.558538	−	0.829479i	$-0.688637\pi$
$137$	−13.0750	−1.11708	−0.558538	+	0.829479i	$0.688637\pi$
$138$	−4.19461	−0.357069
$139$	−15.5582	−1.31963	−0.659813	−	0.751430i	$-0.729364\pi$
$139$	−15.5582	−1.31963	−0.659813	+	0.751430i	$0.729364\pi$
$140$	5.22041	0.441206
$141$	−15.5565	−1.31009
$142$	3.09877	0.260043
$143$	−22.2228	−1.85837
$144$	−24.3509	−2.02924
$145$	−4.18846	−0.347833
$146$	−2.27108	−0.187956
$147$	21.2652	1.75393
$148$	2.20970	0.181636
$149$	−1.57713	−0.129203	−0.0646016	−	0.997911i	$-0.520578\pi$
$149$	−1.57713	−0.129203	−0.0646016	+	0.997911i	$0.520578\pi$
$150$	−52.6138	−4.29590
$151$	−0.660885	−0.0537820	−0.0268910	−	0.999638i	$-0.508561\pi$
$151$	−0.660885	−0.0537820	−0.0268910	+	0.999638i	$0.508561\pi$
$152$	3.94254	0.319782
$153$	2.89441	0.233999
$154$	−24.3570	−1.96274
$155$	21.4592	1.72364
$156$	−4.77000	−0.381905
$157$	6.45683	0.515311	0.257656	−	0.966237i	$-0.417050\pi$
$157$	6.45683	0.515311	0.257656	+	0.966237i	$0.417050\pi$
$158$	7.90668	0.629022
$159$	4.90913	0.389319
$160$	−7.93542	−0.627350
$161$	−3.67888	−0.289936
$162$	−33.3265	−2.61838
$163$	7.40570	0.580059	0.290029	−	0.957018i	$-0.406335\pi$
$163$	7.40570	0.580059	0.290029	+	0.957018i	$0.406335\pi$
$164$	1.75973	0.137412
$165$	−70.0213	−5.45115
$166$	−4.90261	−0.380516
$167$	−12.5137	−0.968337	−0.484168	−	0.874975i	$-0.660878\pi$
$167$	−12.5137	−0.968337	−0.484168	+	0.874975i	$0.660878\pi$
$168$	−36.0910	−2.78448
$169$	5.71573	0.439672
$170$	−2.05824	−0.157860
$171$	9.92894	0.759285
$172$	1.15838	0.0883253
$173$	−1.51830	−0.115435	−0.0577173	−	0.998333i	$-0.518382\pi$
$173$	−1.51830	−0.115435	−0.0577173	+	0.998333i	$0.518382\pi$
$174$	4.19461	0.317993
$175$	−46.1449	−3.48823
$176$	16.4771	1.24201
$177$	17.3101	1.30111
$178$	2.45221	0.183801
$179$	−20.0342	−1.49742	−0.748712	−	0.662896i	$-0.769327\pi$
$179$	−20.0342	−1.49742	−0.748712	+	0.662896i	$0.769327\pi$
$180$	−10.7726	−0.802940
$181$	8.19072	0.608812	0.304406	−	0.952542i	$-0.401542\pi$
$181$	8.19072	0.608812	0.304406	+	0.952542i	$0.401542\pi$
$182$	20.5131	1.52053
$183$	−22.8169	−1.68667
$184$	3.01442	0.222226
$185$	−27.3183	−2.00848
$186$	−21.4907	−1.57577
$187$	−1.95851	−0.143220
$188$	1.61944	0.118110
$189$	−54.9737	−3.99875
$190$	−7.06055	−0.512226
$191$	−1.37096	−0.0991992	−0.0495996	−	0.998769i	$-0.515795\pi$
$191$	−1.37096	−0.0991992	−0.0495996	+	0.998769i	$0.515795\pi$
$192$	28.8253	2.08029
$193$	−18.5215	−1.33320	−0.666602	−	0.745414i	$-0.732252\pi$
$193$	−18.5215	−1.33320	−0.666602	+	0.745414i	$0.732252\pi$
$194$	6.74159	0.484018
$195$	58.9709	4.22299
$196$	−2.21373	−0.158124
$197$	−20.7478	−1.47822	−0.739111	−	0.673583i	$-0.764754\pi$
$197$	−20.7478	−1.47822	−0.739111	+	0.673583i	$0.764754\pi$
$198$	50.2618	3.57195
$199$	9.02496	0.639763	0.319881	−	0.947458i	$-0.396357\pi$
$199$	9.02496	0.639763	0.319881	+	0.947458i	$0.396357\pi$
$200$	37.8105	2.67360
$201$	−27.3699	−1.93053
$202$	−23.9296	−1.68368
$203$	3.67888	0.258207
$204$	−0.420383	−0.0294327
$205$	−21.7554	−1.51946
$206$	−8.18276	−0.570120
$207$	7.59155	0.527649
$208$	−13.8768	−0.962180
$209$	−6.71844	−0.464724
$210$	64.6341	4.46018
$211$	11.9605	0.823396	0.411698	−	0.911320i	$-0.364936\pi$
$211$	11.9605	0.823396	0.411698	+	0.911320i	$0.364936\pi$
$212$	−0.511045	−0.0350987
$213$	−7.82450	−0.536126
$214$	−6.20722	−0.424317
$215$	−14.3209	−0.976674
$216$	45.0446	3.06490
$217$	−18.8484	−1.27951
$218$	4.34557	0.294319
$219$	5.73456	0.387506
$220$	7.28929	0.491444
$221$	1.64943	0.110953
$222$	27.3584	1.83617
$223$	−10.0296	−0.671632	−0.335816	−	0.941928i	$-0.609012\pi$
$223$	−10.0296	−0.671632	−0.335816	+	0.941928i	$0.609012\pi$
$224$	6.96998	0.465701
$225$	95.2223	6.34815
$226$	2.10319	0.139902
$227$	12.8144	0.850523	0.425261	−	0.905071i	$-0.360182\pi$
$227$	12.8144	0.850523	0.425261	+	0.905071i	$0.360182\pi$
$228$	−1.44207	−0.0955036
$229$	3.19732	0.211285	0.105642	−	0.994404i	$-0.466310\pi$
$229$	3.19732	0.211285	0.105642	+	0.994404i	$0.466310\pi$
$230$	−5.39841	−0.355961
$231$	61.5023	4.04655
$232$	−3.01442	−0.197906
$233$	−27.1798	−1.78061	−0.890305	−	0.455364i	$-0.849509\pi$
$233$	−27.1798	−1.78061	−0.890305	+	0.455364i	$0.849509\pi$
$234$	−42.3297	−2.76718
$235$	−20.0210	−1.30603
$236$	−1.80200	−0.117300
$237$	−19.9647	−1.29685
$238$	1.80783	0.117184
$239$	−4.34212	−0.280869	−0.140434	−	0.990090i	$-0.544850\pi$
$239$	−4.34212	−0.280869	−0.140434	+	0.990090i	$0.544850\pi$
$240$	−43.7239	−2.82236
$241$	11.6814	0.752466	0.376233	−	0.926525i	$-0.377219\pi$
$241$	11.6814	0.752466	0.376233	+	0.926525i	$0.377219\pi$
$242$	−19.8321	−1.27486
$243$	39.3215	2.52248
$244$	2.37526	0.152060
$245$	27.3681	1.74848
$246$	21.7873	1.38911
$247$	5.65817	0.360021
$248$	15.4441	0.980700
$249$	12.3793	0.784505
$250$	−40.7213	−2.57544
$251$	−3.07955	−0.194380	−0.0971898	−	0.995266i	$-0.530985\pi$
$251$	−3.07955	−0.194380	−0.0971898	+	0.995266i	$0.530985\pi$
$252$	9.46196	0.596047
$253$	−5.13684	−0.322950
$254$	17.0971	1.07277
$255$	5.19714	0.325457
$256$	−7.88454	−0.492784
$257$	29.1604	1.81898	0.909489	−	0.415729i	$-0.136473\pi$
$257$	29.1604	1.81898	0.909489	+	0.415729i	$0.136473\pi$
$258$	14.3419	0.892887
$259$	23.9947	1.49096
$260$	−6.13893	−0.380720
$261$	−7.59155	−0.469905
$262$	12.6162	0.779430
$263$	22.1485	1.36574	0.682868	−	0.730542i	$-0.260732\pi$
$263$	22.1485	1.36574	0.682868	+	0.730542i	$0.260732\pi$
$264$	−50.3940	−3.10154
$265$	6.31799	0.388111
$266$	6.20155	0.380241
$267$	−6.19191	−0.378939
$268$	2.84924	0.174045
$269$	13.7724	0.839718	0.419859	−	0.907589i	$-0.362079\pi$
$269$	13.7724	0.839718	0.419859	+	0.907589i	$0.362079\pi$
$270$	−80.6687	−4.90934
$271$	6.71784	0.408080	0.204040	−	0.978963i	$-0.434593\pi$
$271$	6.71784	0.408080	0.204040	+	0.978963i	$0.434593\pi$
$272$	−1.22297	−0.0741533
$273$	−51.7963	−3.13486
$274$	16.8521	1.01807
$275$	−64.4324	−3.88542
$276$	−1.10259	−0.0663682
$277$	−3.89335	−0.233929	−0.116964	−	0.993136i	$-0.537316\pi$
$277$	−3.89335	−0.233929	−0.116964	+	0.993136i	$0.537316\pi$
$278$	20.0526	1.20267
$279$	38.8946	2.32856
$280$	−46.4487	−2.77584
$281$	−1.01407	−0.0604942	−0.0302471	−	0.999542i	$-0.509629\pi$
$281$	−1.01407	−0.0604942	−0.0302471	+	0.999542i	$0.509629\pi$
$282$	20.0504	1.19398
$283$	−4.16457	−0.247558	−0.123779	−	0.992310i	$-0.539501\pi$
$283$	−4.16457	−0.247558	−0.123779	+	0.992310i	$0.539501\pi$
$284$	0.814539	0.0483340
$285$	17.8282	1.05605
$286$	28.6425	1.69367
$287$	19.1086	1.12794
$288$	−14.3829	−0.847520
$289$	−16.8546	−0.991449
$290$	5.39841	0.317006
$291$	−17.0228	−0.997893
$292$	−0.596974	−0.0349353
$293$	32.2403	1.88350	0.941750	−	0.336313i	$-0.109180\pi$
$293$	32.2403	1.88350	0.941750	+	0.336313i	$0.109180\pi$
$294$	−27.4083	−1.59848
$295$	22.2779	1.29707
$296$	−19.6609	−1.14276
$297$	−76.7600	−4.45407
$298$	2.03272	0.117752
$299$	4.32617	0.250189
$300$	−13.8300	−0.798476
$301$	12.5785	0.725015
$302$	0.851800	0.0490156
$303$	60.4230	3.47121
$304$	−4.19524	−0.240614
$305$	−29.3650	−1.68144
$306$	−3.73055	−0.213261
$307$	−30.7765	−1.75651	−0.878255	−	0.478193i	$-0.841292\pi$
$307$	−30.7765	−1.75651	−0.878255	+	0.478193i	$0.841292\pi$
$308$	−6.40245	−0.364814
$309$	20.6618	1.17541
$310$	−27.6583	−1.57088
$311$	22.4954	1.27560	0.637799	−	0.770203i	$-0.279845\pi$
$311$	22.4954	1.27560	0.637799	+	0.770203i	$0.279845\pi$
$312$	42.4411	2.40276
$313$	26.6925	1.50875	0.754375	−	0.656444i	$-0.227940\pi$
$313$	26.6925	1.50875	0.754375	+	0.656444i	$0.227940\pi$
$314$	−8.32207	−0.469642
$315$	−116.977	−6.59091
$316$	2.07834	0.116916
$317$	25.5022	1.43235	0.716173	−	0.697923i	$-0.245892\pi$
$317$	25.5022	1.43235	0.716173	+	0.697923i	$0.245892\pi$
$318$	−6.32727	−0.354815
$319$	5.13684	0.287608
$320$	37.0979	2.07383
$321$	15.6735	0.874807
$322$	4.74163	0.264241
$323$	0.498658	0.0277461
$324$	−8.76017	−0.486676
$325$	54.2640	3.01002
$326$	−9.54504	−0.528651
$327$	−10.9727	−0.606794
$328$	−15.6573	−0.864528
$329$	17.5852	0.969503
$330$	90.2489	4.96804
$331$	4.67948	0.257208	0.128604	−	0.991696i	$-0.458950\pi$
$331$	4.67948	0.257208	0.128604	+	0.991696i	$0.458950\pi$
$332$	−1.28870	−0.0707263
$333$	−49.5141	−2.71336
$334$	16.1286	0.882517
$335$	−35.2248	−1.92453
$336$	38.4043	2.09513
$337$	−24.1609	−1.31613	−0.658065	−	0.752962i	$-0.728625\pi$
$337$	−24.1609	−1.31613	−0.658065	+	0.752962i	$0.728625\pi$
$338$	−7.36688	−0.400706
$339$	−5.31063	−0.288434
$340$	−0.541027	−0.0293413
$341$	−26.3181	−1.42520
$342$	−12.7972	−0.691993
$343$	1.71373	0.0925329
$344$	−10.3067	−0.555698
$345$	13.6312	0.733879
$346$	1.95691	0.105204
$347$	21.5069	1.15455	0.577277	−	0.816549i	$-0.304115\pi$
$347$	21.5069	1.15455	0.577277	+	0.816549i	$0.304115\pi$
$348$	1.10259	0.0591051
$349$	−26.7629	−1.43259	−0.716293	−	0.697799i	$-0.754163\pi$
$349$	−26.7629	−1.43259	−0.716293	+	0.697799i	$0.754163\pi$
$350$	59.4752	3.17908
$351$	64.6461	3.45055
$352$	9.73221	0.518728
$353$	31.2917	1.66549	0.832744	−	0.553659i	$-0.186769\pi$
$353$	31.2917	1.66549	0.832744	+	0.553659i	$0.186769\pi$
$354$	−22.3107	−1.18580
$355$	−10.0700	−0.534462
$356$	0.644584	0.0341629
$357$	−4.56484	−0.241597
$358$	25.8216	1.36471
$359$	24.0817	1.27098	0.635492	−	0.772108i	$-0.280798\pi$
$359$	24.0817	1.27098	0.635492	+	0.772108i	$0.280798\pi$
$360$	95.8492	5.05170
$361$	−17.2894	−0.909969
$362$	−10.5568	−0.554855
$363$	50.0768	2.62835
$364$	5.39205	0.282620
$365$	7.38032	0.386303
$366$	29.4081	1.53719
$367$	−34.2762	−1.78920	−0.894601	−	0.446866i	$-0.852540\pi$
$367$	−34.2762	−1.78920	−0.894601	+	0.446866i	$0.852540\pi$
$368$	−3.20763	−0.167209
$369$	−39.4314	−2.05272
$370$	35.2099	1.83048
$371$	−5.54933	−0.288107
$372$	−5.64902	−0.292888
$373$	27.2701	1.41199	0.705996	−	0.708215i	$-0.250499\pi$
$373$	27.2701	1.41199	0.705996	+	0.708215i	$0.250499\pi$
$374$	2.52428	0.130527
$375$	102.823	5.30975
$376$	−14.4090	−0.743090
$377$	−4.32617	−0.222809
$378$	70.8544	3.64436
$379$	−20.0842	−1.03165	−0.515827	−	0.856693i	$-0.672515\pi$
$379$	−20.0842	−1.03165	−0.515827	+	0.856693i	$0.672515\pi$
$380$	−1.85593	−0.0952072
$381$	−43.1709	−2.21171
$382$	1.76700	0.0904076
$383$	1.34037	0.0684897	0.0342448	−	0.999413i	$-0.489097\pi$
$383$	1.34037	0.0684897	0.0342448	+	0.999413i	$0.489097\pi$
$384$	−24.8206	−1.26662
$385$	79.1527	4.03400
$386$	23.8719	1.21505
$387$	−25.9564	−1.31944
$388$	1.77209	0.0899642
$389$	30.1105	1.52666	0.763330	−	0.646008i	$-0.223563\pi$
$389$	30.1105	1.52666	0.763330	+	0.646008i	$0.223563\pi$
$390$	−76.0063	−3.84873
$391$	0.381268	0.0192815
$392$	19.6967	0.994835
$393$	−31.8563	−1.60694
$394$	26.7414	1.34721
$395$	−25.6943	−1.29282
$396$	13.2118	0.663916
$397$	−21.1262	−1.06030	−0.530148	−	0.847905i	$-0.677864\pi$
$397$	−21.1262	−1.06030	−0.530148	+	0.847905i	$0.677864\pi$
$398$	−11.6321	−0.583063
$399$	−15.6591	−0.783938
$400$	−40.2340	−2.01170
$401$	−29.6567	−1.48099	−0.740493	−	0.672064i	$-0.765408\pi$
$401$	−29.6567	−1.48099	−0.740493	+	0.672064i	$0.765408\pi$
$402$	35.2765	1.75943
$403$	22.1647	1.10410
$404$	−6.29010	−0.312944
$405$	108.301	5.38151
$406$	−4.74163	−0.235323
$407$	33.5038	1.66072
$408$	3.74036	0.185175
$409$	15.8519	0.783826	0.391913	−	0.920002i	$-0.371813\pi$
$409$	15.8519	0.783826	0.391913	+	0.920002i	$0.371813\pi$
$410$	28.0400	1.38480
$411$	−42.5523	−2.09895
$412$	−2.15091	−0.105968
$413$	−19.5676	−0.962857
$414$	−9.78458	−0.480886
$415$	15.9320	0.782070
$416$	−8.19632	−0.401858
$417$	−50.6335	−2.47953
$418$	8.65925	0.423538
$419$	8.95208	0.437338	0.218669	−	0.975799i	$-0.429829\pi$
$419$	8.95208	0.437338	0.218669	+	0.975799i	$0.429829\pi$
$420$	16.9897	0.829011
$421$	−37.9501	−1.84958	−0.924788	−	0.380484i	$-0.875757\pi$
$421$	−37.9501	−1.84958	−0.924788	+	0.380484i	$0.875757\pi$
$422$	−15.4156	−0.750422
$423$	−36.2879	−1.76438
$424$	4.54703	0.220824
$425$	4.78232	0.231976
$426$	10.0848	0.488612
$427$	25.7924	1.24818
$428$	−1.63162	−0.0788675
$429$	−72.3234	−3.49181
$430$	18.4578	0.890116
$431$	35.4309	1.70665	0.853324	−	0.521380i	$-0.174583\pi$
$431$	35.4309	1.70665	0.853324	+	0.521380i	$0.174583\pi$
$432$	−47.9318	−2.30612
$433$	−10.6178	−0.510261	−0.255131	−	0.966907i	$-0.582118\pi$
$433$	−10.6178	−0.510261	−0.255131	+	0.966907i	$0.582118\pi$
$434$	24.2933	1.16611
$435$	−13.6312	−0.653566
$436$	1.14227	0.0547050
$437$	1.30789	0.0625650
$438$	−7.39115	−0.353163
$439$	11.6557	0.556295	0.278147	−	0.960538i	$-0.410280\pi$
$439$	11.6557	0.556295	0.278147	+	0.960538i	$0.410280\pi$
$440$	−64.8566	−3.09191
$441$	49.6045	2.36212
$442$	−2.12591	−0.101119
$443$	−23.0692	−1.09605	−0.548026	−	0.836461i	$-0.684621\pi$
$443$	−23.0692	−1.09605	−0.548026	+	0.836461i	$0.684621\pi$
$444$	7.19140	0.341289
$445$	−7.96892	−0.377763
$446$	12.9269	0.612108
$447$	−5.13270	−0.242769
$448$	−32.5845	−1.53947
$449$	21.0609	0.993926	0.496963	−	0.867772i	$-0.334448\pi$
$449$	21.0609	0.993926	0.496963	+	0.867772i	$0.334448\pi$
$450$	−122.730	−5.78554
$451$	26.6814	1.25638
$452$	0.552842	0.0260035
$453$	−2.15083	−0.101055
$454$	−16.5162	−0.775145
$455$	−66.6613	−3.12513
$456$	12.8309	0.600860
$457$	21.3393	0.998209	0.499105	−	0.866542i	$-0.333662\pi$
$457$	21.3393	0.998209	0.499105	+	0.866542i	$0.333662\pi$
$458$	−4.12095	−0.192559
$459$	5.69730	0.265927
$460$	−1.41902	−0.0661622
$461$	−4.11175	−0.191503	−0.0957517	−	0.995405i	$-0.530525\pi$
$461$	−4.11175	−0.191503	−0.0957517	+	0.995405i	$0.530525\pi$
$462$	−79.2690	−3.68793
$463$	−13.9335	−0.647543	−0.323771	−	0.946135i	$-0.604951\pi$
$463$	−13.9335	−0.647543	−0.323771	+	0.946135i	$0.604951\pi$
$464$	3.20763	0.148911
$465$	69.8381	3.23867
$466$	35.0315	1.62280
$467$	−32.6447	−1.51062	−0.755308	−	0.655370i	$-0.772513\pi$
$467$	−32.6447	−1.51062	−0.755308	+	0.655370i	$0.772513\pi$
$468$	−11.1268	−0.514335
$469$	30.9392	1.42864
$470$	25.8046	1.19028
$471$	21.0135	0.968253
$472$	16.0334	0.737995
$473$	17.5635	0.807569
$474$	25.7320	1.18191
$475$	16.4052	0.752721
$476$	0.475205	0.0217810
$477$	11.4513	0.524319
$478$	5.59647	0.255976
$479$	−11.8247	−0.540285	−0.270143	−	0.962820i	$-0.587071\pi$
$479$	−11.8247	−0.540285	−0.270143	+	0.962820i	$0.587071\pi$
$480$	−25.8256	−1.17877
$481$	−28.2164	−1.28656
$482$	−15.0559	−0.685778
$483$	−11.9728	−0.544781
$484$	−5.21305	−0.236957
$485$	−21.9081	−0.994796
$486$	−50.6806	−2.29892
$487$	33.8627	1.53447	0.767233	−	0.641369i	$-0.221633\pi$
$487$	33.8627	1.53447	0.767233	+	0.641369i	$0.221633\pi$
$488$	−21.1339	−0.956687
$489$	24.1016	1.08991
$490$	−35.2742	−1.59352
$491$	−7.01774	−0.316706	−0.158353	−	0.987383i	$-0.550618\pi$
$491$	−7.01774	−0.316706	−0.158353	+	0.987383i	$0.550618\pi$
$492$	5.72700	0.258193
$493$	−0.381268	−0.0171714
$494$	−7.29269	−0.328114
$495$	−163.335	−7.34138
$496$	−16.4340	−0.737908
$497$	8.84490	0.396748
$498$	−15.9554	−0.714977
$499$	−17.8635	−0.799681	−0.399841	−	0.916585i	$-0.630935\pi$
$499$	−17.8635	−0.799681	−0.399841	+	0.916585i	$0.630935\pi$
$500$	−10.7040	−0.478696
$501$	−40.7253	−1.81947
$502$	3.96917	0.177153
$503$	21.7670	0.970544	0.485272	−	0.874363i	$-0.338721\pi$
$503$	21.7670	0.970544	0.485272	+	0.874363i	$0.338721\pi$
$504$	−84.1879	−3.75003
$505$	77.7638	3.46044
$506$	6.62076	0.294329
$507$	18.6017	0.826129
$508$	4.49414	0.199395
$509$	−21.6851	−0.961175	−0.480587	−	0.876947i	$-0.659576\pi$
$509$	−21.6851	−0.961175	−0.480587	+	0.876947i	$0.659576\pi$
$510$	−6.69848	−0.296614
$511$	−6.48241	−0.286765
$512$	25.4155	1.12321
$513$	19.5439	0.862885
$514$	−37.5842	−1.65777
$515$	26.5915	1.17176
$516$	3.76989	0.165960
$517$	24.5543	1.07990
$518$	−30.9262	−1.35882
$519$	−4.94127	−0.216898
$520$	54.6212	2.39530
$521$	−23.2799	−1.01991	−0.509955	−	0.860201i	$-0.670338\pi$
$521$	−23.2799	−1.01991	−0.509955	+	0.860201i	$0.670338\pi$
$522$	9.78458	0.428259
$523$	5.23245	0.228799	0.114400	−	0.993435i	$-0.463506\pi$
$523$	5.23245	0.228799	0.114400	+	0.993435i	$0.463506\pi$
$524$	3.31628	0.144872
$525$	−150.177	−6.55427
$526$	−28.5467	−1.24470
$527$	1.95339	0.0850910
$528$	53.6241	2.33369
$529$	1.00000	0.0434783
$530$	−8.14312	−0.353714
$531$	40.3786	1.75228
$532$	1.63013	0.0706752
$533$	−22.4707	−0.973312
$534$	7.98062	0.345355
$535$	20.1716	0.872093
$536$	−25.3511	−1.09500
$537$	−65.2005	−2.81361
$538$	−17.7509	−0.765298
$539$	−33.5650	−1.44575
$540$	−21.2045	−0.912497
$541$	42.6054	1.83175	0.915875	−	0.401465i	$-0.131499\pi$
$541$	42.6054	1.83175	0.915875	+	0.401465i	$0.131499\pi$
$542$	−8.65848	−0.371913
$543$	26.6564	1.14394
$544$	−0.722347	−0.0309704
$545$	−14.1218	−0.604911
$546$	66.7592	2.85703
$547$	9.76176	0.417383	0.208691	−	0.977982i	$-0.433080\pi$
$547$	9.76176	0.417383	0.208691	+	0.977982i	$0.433080\pi$
$548$	4.42974	0.189229
$549$	−53.2239	−2.27154
$550$	83.0455	3.54107
$551$	−1.30789	−0.0557181
$552$	9.81033	0.417555
$553$	22.5683	0.959701
$554$	5.01806	0.213197
$555$	−88.9064	−3.77386
$556$	5.27100	0.223540
$557$	22.0226	0.933126	0.466563	−	0.884488i	$-0.345492\pi$
$557$	22.0226	0.933126	0.466563	+	0.884488i	$0.345492\pi$
$558$	−50.1304	−2.12219
$559$	−14.7917	−0.625622
$560$	49.4259	2.08863
$561$	−6.37391	−0.269107
$562$	1.30701	0.0551329
$563$	1.66816	0.0703045	0.0351523	−	0.999382i	$-0.488808\pi$
$563$	1.66816	0.0703045	0.0351523	+	0.999382i	$0.488808\pi$
$564$	5.27043	0.221925
$565$	−6.83472	−0.287539
$566$	5.36762	0.225618
$567$	−95.1247	−3.99486
$568$	−7.24737	−0.304093
$569$	−7.92623	−0.332285	−0.166142	−	0.986102i	$-0.553131\pi$
$569$	−7.92623	−0.332285	−0.166142	+	0.986102i	$0.553131\pi$
$570$	−22.9783	−0.962456
$571$	22.2556	0.931370	0.465685	−	0.884951i	$-0.345808\pi$
$571$	22.2556	0.931370	0.465685	+	0.884951i	$0.345808\pi$
$572$	7.52894	0.314801
$573$	−4.46174	−0.186392
$574$	−24.6286	−1.02798
$575$	12.5432	0.523087
$576$	67.2396	2.80165
$577$	1.76754	0.0735835	0.0367918	−	0.999323i	$-0.488286\pi$
$577$	1.76754	0.0735835	0.0367918	+	0.999323i	$0.488286\pi$
$578$	21.7236	0.903581
$579$	−60.2775	−2.50505
$580$	1.41902	0.0589217
$581$	−13.9937	−0.580555
$582$	21.9403	0.909454
$583$	−7.74855	−0.320912
$584$	5.31159	0.219795
$585$	137.559	5.68735
$586$	−41.5539	−1.71657
$587$	31.6969	1.30827	0.654135	−	0.756377i	$-0.273033\pi$
$587$	31.6969	1.30827	0.654135	+	0.756377i	$0.273033\pi$
$588$	−7.20452	−0.297109
$589$	6.70087	0.276104
$590$	−28.7136	−1.18212
$591$	−67.5232	−2.77753
$592$	20.9210	0.859850
$593$	11.5949	0.476146	0.238073	−	0.971247i	$-0.423484\pi$
$593$	11.5949	0.476146	0.238073	+	0.971247i	$0.423484\pi$
$594$	98.9342	4.05932
$595$	−5.87490	−0.240847
$596$	0.534320	0.0218866
$597$	29.3714	1.20209
$598$	−5.57590	−0.228016
$599$	44.2328	1.80730	0.903652	−	0.428268i	$-0.140876\pi$
$599$	44.2328	1.80730	0.903652	+	0.428268i	$0.140876\pi$
$600$	123.053	5.02361
$601$	−17.7972	−0.725964	−0.362982	−	0.931796i	$-0.618241\pi$
$601$	−17.7972	−0.725964	−0.362982	+	0.931796i	$0.618241\pi$
$602$	−16.2122	−0.660760
$603$	−63.8446	−2.59995
$604$	0.223903	0.00911050
$605$	64.4482	2.62019
$606$	−77.8779	−3.16358
$607$	16.6439	0.675556	0.337778	−	0.941226i	$-0.390325\pi$
$607$	16.6439	0.675556	0.337778	+	0.941226i	$0.390325\pi$
$608$	−2.47792	−0.100493
$609$	11.9728	0.485162
$610$	37.8479	1.53242
$611$	−20.6793	−0.836593
$612$	−0.980608	−0.0396387
$613$	47.0438	1.90008	0.950040	−	0.312129i	$-0.101042\pi$
$613$	47.0438	1.90008	0.950040	+	0.312129i	$0.101042\pi$
$614$	39.6672	1.60084
$615$	−70.8021	−2.85502
$616$	56.9659	2.29522
$617$	2.14822	0.0864842	0.0432421	−	0.999065i	$-0.486231\pi$
$617$	2.14822	0.0864842	0.0432421	+	0.999065i	$0.486231\pi$
$618$	−26.6305	−1.07124
$619$	−42.3549	−1.70239	−0.851193	−	0.524853i	$-0.824120\pi$
$619$	−42.3549	−1.70239	−0.851193	+	0.524853i	$0.824120\pi$
$620$	−7.27022	−0.291979
$621$	14.9430	0.599644
$622$	−28.9939	−1.16255
$623$	6.99940	0.280425
$624$	−45.1614	−1.80790
$625$	69.6158	2.78463
$626$	−34.4034	−1.37504
$627$	−21.8649	−0.873201
$628$	−2.18753	−0.0872920
$629$	−2.48673	−0.0991525
$630$	150.769	6.00679
$631$	−24.6603	−0.981711	−0.490855	−	0.871241i	$-0.663316\pi$
$631$	−24.6603	−0.981711	−0.490855	+	0.871241i	$0.663316\pi$
$632$	−18.4921	−0.735576
$633$	38.9251	1.54713
$634$	−32.8692	−1.30540
$635$	−55.5605	−2.20485
$636$	−1.66318	−0.0659494
$637$	28.2679	1.12002
$638$	−6.62076	−0.262118
$639$	−18.2519	−0.722033
$640$	−31.9438	−1.26269
$641$	16.0011	0.632004	0.316002	−	0.948759i	$-0.397659\pi$
$641$	16.0011	0.632004	0.316002	+	0.948759i	$0.397659\pi$
$642$	−20.2012	−0.797277
$643$	37.7703	1.48952	0.744759	−	0.667334i	$-0.232565\pi$
$643$	37.7703	1.48952	0.744759	+	0.667334i	$0.232565\pi$
$644$	1.24638	0.0491143
$645$	−46.6067	−1.83514
$646$	−0.642709	−0.0252871
$647$	34.5123	1.35682	0.678408	−	0.734685i	$-0.262670\pi$
$647$	34.5123	1.35682	0.678408	+	0.734685i	$0.262670\pi$
$648$	77.9438	3.06192
$649$	−27.3223	−1.07249
$650$	−69.9397	−2.74326
$651$	−61.3415	−2.40416
$652$	−2.50900	−0.0982600
$653$	−9.67983	−0.378801	−0.189400	−	0.981900i	$-0.560654\pi$
$653$	−9.67983	−0.378801	−0.189400	+	0.981900i	$0.560654\pi$
$654$	14.1425	0.553016
$655$	−40.9987	−1.60195
$656$	16.6608	0.650497
$657$	13.3768	0.521877
$658$	−22.6652	−0.883580
$659$	−43.3472	−1.68857	−0.844283	−	0.535897i	$-0.819974\pi$
$659$	−43.3472	−1.68857	−0.844283	+	0.535897i	$0.819974\pi$
$660$	23.7227	0.923406
$661$	−0.814945	−0.0316977	−0.0158489	−	0.999874i	$-0.505045\pi$
$661$	−0.814945	−0.0316977	−0.0158489	+	0.999874i	$0.505045\pi$
$662$	−6.03128	−0.234412
$663$	5.36801	0.208476
$664$	11.4662	0.444974
$665$	−20.1531	−0.781505
$666$	63.8177	2.47288
$667$	−1.00000	−0.0387202
$668$	4.23955	0.164033
$669$	−32.6410	−1.26197
$670$	45.4004	1.75397
$671$	36.0140	1.39031
$672$	22.6836	0.875037
$673$	42.2226	1.62756	0.813781	−	0.581172i	$-0.197406\pi$
$673$	42.2226	1.62756	0.813781	+	0.581172i	$0.197406\pi$
$674$	31.1405	1.19949
$675$	187.433	7.21432
$676$	−1.93645	−0.0744789
$677$	40.8174	1.56874	0.784370	−	0.620293i	$-0.212986\pi$
$677$	40.8174	1.56874	0.784370	+	0.620293i	$0.212986\pi$
$678$	6.84476	0.262871
$679$	19.2427	0.738468
$680$	4.81380	0.184601
$681$	41.7041	1.59810
$682$	33.9208	1.29889
$683$	32.0002	1.22445	0.612227	−	0.790682i	$-0.290274\pi$
$683$	32.0002	1.22445	0.612227	+	0.790682i	$0.290274\pi$
$684$	−3.36386	−0.128620
$685$	−54.7643	−2.09244
$686$	−2.20879	−0.0843321
$687$	10.4056	0.396997
$688$	10.9673	0.418124
$689$	6.52571	0.248610
$690$	−17.5690	−0.668839
$691$	−17.0658	−0.649215	−0.324607	−	0.945849i	$-0.605232\pi$
$691$	−17.0658	−0.649215	−0.324607	+	0.945849i	$0.605232\pi$
$692$	0.514391	0.0195542
$693$	143.464	5.44974
$694$	−27.7198	−1.05223
$695$	−65.1647	−2.47184
$696$	−9.81033	−0.371859
$697$	−1.98035	−0.0750112
$698$	34.4942	1.30562
$699$	−88.4559	−3.34571
$700$	15.6336	0.590894
$701$	−8.92226	−0.336989	−0.168495	−	0.985703i	$-0.553891\pi$
$701$	−8.92226	−0.336989	−0.168495	+	0.985703i	$0.553891\pi$
$702$	−83.3210	−3.14475
$703$	−8.53043	−0.321731
$704$	−45.4978	−1.71476
$705$	−65.1577	−2.45398
$706$	−40.3311	−1.51788
$707$	−68.3028	−2.56879
$708$	−5.86456	−0.220404
$709$	−0.494674	−0.0185779	−0.00928894	−	0.999957i	$-0.502957\pi$
$709$	−0.494674	−0.0185779	−0.00928894	+	0.999957i	$0.502957\pi$
$710$	12.9791	0.487095
$711$	−46.5707	−1.74654
$712$	−5.73520	−0.214936
$713$	5.12340	0.191873
$714$	5.88352	0.220185
$715$	−93.0794	−3.48097
$716$	6.78744	0.253658
$717$	−14.1313	−0.527743
$718$	−31.0384	−1.15834
$719$	−3.19568	−0.119179	−0.0595895	−	0.998223i	$-0.518979\pi$
$719$	−3.19568	−0.119179	−0.0595895	+	0.998223i	$0.518979\pi$
$720$	−101.993	−3.80105
$721$	−23.3563	−0.869834
$722$	22.2839	0.829323
$723$	38.0167	1.41386
$724$	−2.77496	−0.103131
$725$	−12.5432	−0.465843
$726$	−64.5429	−2.39541
$727$	5.82605	0.216076	0.108038	−	0.994147i	$-0.465543\pi$
$727$	5.82605	0.216076	0.108038	+	0.994147i	$0.465543\pi$
$728$	−47.9759	−1.77810
$729$	50.3996	1.86665
$730$	−9.51233	−0.352067
$731$	−1.30360	−0.0482154
$732$	7.73020	0.285716
$733$	−37.5460	−1.38679	−0.693396	−	0.720557i	$-0.743886\pi$
$733$	−37.5460	−1.38679	−0.693396	+	0.720557i	$0.743886\pi$
$734$	44.1778	1.63063
$735$	89.0686	3.28534
$736$	−1.89459	−0.0698356
$737$	43.2006	1.59131
$738$	50.8223	1.87080
$739$	21.9698	0.808173	0.404086	−	0.914721i	$-0.367590\pi$
$739$	21.9698	0.808173	0.404086	+	0.914721i	$0.367590\pi$
$740$	9.25524	0.340230
$741$	18.4143	0.676467
$742$	7.15241	0.262573
$743$	28.5154	1.04613	0.523065	−	0.852293i	$-0.324789\pi$
$743$	28.5154	1.04613	0.523065	+	0.852293i	$0.324789\pi$
$744$	50.2623	1.84270
$745$	−6.60573	−0.242015
$746$	−35.1478	−1.28685
$747$	28.8766	1.05654
$748$	0.663530	0.0242611
$749$	−17.7174	−0.647381
$750$	−132.526	−4.83917
$751$	44.0311	1.60672	0.803359	−	0.595495i	$-0.203044\pi$
$751$	44.0311	1.60672	0.803359	+	0.595495i	$0.203044\pi$
$752$	15.3326	0.559123
$753$	−10.0223	−0.365233
$754$	5.57590	0.203062
$755$	−2.76809	−0.100741
$756$	18.6247	0.677374
$757$	42.9767	1.56202	0.781008	−	0.624521i	$-0.214706\pi$
$757$	42.9767	1.56202	0.781008	+	0.624521i	$0.214706\pi$
$758$	25.8860	0.940223
$759$	−16.7177	−0.606813
$760$	16.5132	0.598996
$761$	42.3746	1.53608	0.768039	−	0.640403i	$-0.221233\pi$
$761$	42.3746	1.53608	0.768039	+	0.640403i	$0.221233\pi$
$762$	55.6421	2.01570
$763$	12.4037	0.449044
$764$	0.464472	0.0168040
$765$	12.1231	0.438313
$766$	−1.72757	−0.0624197
$767$	23.0104	0.830858
$768$	−25.6600	−0.925925
$769$	−44.7656	−1.61429	−0.807145	−	0.590354i	$-0.798988\pi$
$769$	−44.7656	−1.61429	−0.807145	+	0.590354i	$0.798988\pi$
$770$	−102.018	−3.67648
$771$	94.9016	3.41780
$772$	6.27495	0.225840
$773$	27.3930	0.985257	0.492628	−	0.870240i	$-0.336036\pi$
$773$	27.3930	0.985257	0.492628	+	0.870240i	$0.336036\pi$
$774$	33.4547	1.20250
$775$	64.2639	2.30843
$776$	−15.7672	−0.566009
$777$	78.0898	2.80146
$778$	−38.8087	−1.39136
$779$	−6.79336	−0.243397
$780$	−19.9789	−0.715361
$781$	12.3502	0.441924
$782$	−0.491408	−0.0175727
$783$	−14.9430	−0.534021
$784$	−20.9592	−0.748543
$785$	27.0442	0.965248
$786$	41.0589	1.46452
$787$	−20.4857	−0.730237	−0.365118	−	0.930961i	$-0.618971\pi$
$787$	−20.4857	−0.730237	−0.365118	+	0.930961i	$0.618971\pi$
$788$	7.02923	0.250406
$789$	72.0816	2.56617
$790$	33.1168	1.17824
$791$	6.00319	0.213449
$792$	−117.552	−4.17703
$793$	−30.3305	−1.07707
$794$	27.2292	0.966327
$795$	20.5617	0.729248
$796$	−3.05760	−0.108374
$797$	25.8146	0.914402	0.457201	−	0.889364i	$-0.348852\pi$
$797$	25.8146	0.914402	0.457201	+	0.889364i	$0.348852\pi$
$798$	20.1827	0.714461
$799$	−1.82247	−0.0644745
$800$	−23.7642	−0.840192
$801$	−14.4436	−0.510339
$802$	38.2239	1.34973
$803$	−9.05142	−0.319418
$804$	9.27275	0.327025
$805$	−15.4088	−0.543091
$806$	−28.5676	−1.00625
$807$	44.8218	1.57780
$808$	55.9663	1.96889
$809$	−47.5765	−1.67270	−0.836351	−	0.548195i	$-0.815315\pi$
$809$	−47.5765	−1.67270	−0.836351	+	0.548195i	$0.815315\pi$
$810$	−139.587	−4.90457
$811$	20.6697	0.725810	0.362905	−	0.931826i	$-0.381785\pi$
$811$	20.6697	0.725810	0.362905	+	0.931826i	$0.381785\pi$
$812$	−1.24638	−0.0437394
$813$	21.8630	0.766768
$814$	−43.1824	−1.51354
$815$	31.0185	1.08653
$816$	−3.98010	−0.139332
$817$	−4.47185	−0.156450
$818$	−20.4312	−0.714359
$819$	−120.823	−4.22190
$820$	7.37058	0.257392
$821$	−5.38616	−0.187978	−0.0939892	−	0.995573i	$-0.529962\pi$
$821$	−5.38616	−0.187978	−0.0939892	+	0.995573i	$0.529962\pi$
$822$	54.8447	1.91293
$823$	−26.6246	−0.928075	−0.464038	−	0.885816i	$-0.653600\pi$
$823$	−26.6246	−0.928075	−0.464038	+	0.885816i	$0.653600\pi$
$824$	19.1378	0.666696
$825$	−209.693	−7.30057
$826$	25.2202	0.877523
$827$	23.3930	0.813455	0.406728	−	0.913549i	$-0.366670\pi$
$827$	23.3930	0.813455	0.406728	+	0.913549i	$0.366670\pi$
$828$	−2.57197	−0.0893820
$829$	−29.7744	−1.03411	−0.517054	−	0.855953i	$-0.672971\pi$
$829$	−29.7744	−1.03411	−0.517054	+	0.855953i	$0.672971\pi$
$830$	−20.5344	−0.712759
$831$	−12.6708	−0.439545
$832$	38.3176	1.32842
$833$	2.49127	0.0863173
$834$	65.2604	2.25978
$835$	−52.4130	−1.81383
$836$	2.27616	0.0787227
$837$	76.5592	2.64627
$838$	−11.5381	−0.398578
$839$	−38.4282	−1.32669	−0.663344	−	0.748314i	$-0.730863\pi$
$839$	−38.4282	−1.32669	−0.663344	+	0.748314i	$0.730863\pi$
$840$	−151.166	−5.21572
$841$	1.00000	0.0344828
$842$	48.9131	1.68566
$843$	−3.30025	−0.113667
$844$	−4.05214	−0.139480
$845$	23.9401	0.823565
$846$	46.7707	1.60801
$847$	−56.6073	−1.94505
$848$	−4.83848	−0.166154
$849$	−13.5534	−0.465153
$850$	−6.16382	−0.211417
$851$	−6.52227	−0.223580
$852$	2.65089	0.0908180
$853$	−46.2140	−1.58234	−0.791169	−	0.611597i	$-0.790527\pi$
$853$	−46.2140	−1.58234	−0.791169	+	0.611597i	$0.790527\pi$
$854$	−33.2433	−1.13756
$855$	41.5870	1.42224
$856$	14.5174	0.496194
$857$	−10.4809	−0.358019	−0.179010	−	0.983847i	$-0.557289\pi$
$857$	−10.4809	−0.358019	−0.179010	+	0.983847i	$0.557289\pi$
$858$	93.2161	3.18234
$859$	7.73093	0.263776	0.131888	−	0.991265i	$-0.457896\pi$
$859$	7.73093	0.263776	0.131888	+	0.991265i	$0.457896\pi$
$860$	4.85181	0.165445
$861$	62.1882	2.11937
$862$	−45.6662	−1.55540
$863$	−30.3638	−1.03360	−0.516798	−	0.856107i	$-0.672876\pi$
$863$	−30.3638	−1.03360	−0.516798	+	0.856107i	$0.672876\pi$
$864$	−28.3110	−0.963158
$865$	−6.35936	−0.216225
$866$	13.6851	0.465039
$867$	−54.8528	−1.86290
$868$	6.38571	0.216745
$869$	31.5122	1.06898
$870$	17.5690	0.595643
$871$	−36.3829	−1.23279
$872$	−10.1634	−0.344176
$873$	−39.7083	−1.34392
$874$	−1.68572	−0.0570202
$875$	−116.232	−3.92936
$876$	−1.94283	−0.0656422
$877$	−28.6725	−0.968202	−0.484101	−	0.875012i	$-0.660853\pi$
$877$	−28.6725	−0.968202	−0.484101	+	0.875012i	$0.660853\pi$
$878$	−15.0227	−0.506993
$879$	104.925	3.53903
$880$	69.0136	2.32645
$881$	−27.1297	−0.914024	−0.457012	−	0.889461i	$-0.651080\pi$
$881$	−27.1297	−0.914024	−0.457012	+	0.889461i	$0.651080\pi$
$882$	−63.9341	−2.15277
$883$	26.2496	0.883368	0.441684	−	0.897171i	$-0.354381\pi$
$883$	26.2496	0.883368	0.441684	+	0.897171i	$0.354381\pi$
$884$	−0.558815	−0.0187950
$885$	72.5028	2.43716
$886$	29.7334	0.998914
$887$	38.2089	1.28293	0.641465	−	0.767153i	$-0.278327\pi$
$887$	38.2089	1.28293	0.641465	+	0.767153i	$0.278327\pi$
$888$	−63.9856	−2.14722
$889$	48.8009	1.63673
$890$	10.2710	0.344283
$891$	−132.823	−4.44974
$892$	3.39796	0.113772
$893$	−6.25178	−0.209208
$894$	6.61543	0.221253
$895$	−83.9123	−2.80488
$896$	28.0574	0.937333
$897$	14.0794	0.470096
$898$	−27.1450	−0.905839
$899$	−5.12340	−0.170875
$900$	−32.2607	−1.07536
$901$	0.575115	0.0191599
$902$	−34.3890	−1.14503
$903$	40.9365	1.36228
$904$	−4.91893	−0.163601
$905$	34.3065	1.14039
$906$	2.77215	0.0920986
$907$	2.94859	0.0979063	0.0489531	−	0.998801i	$-0.484412\pi$
$907$	2.94859	0.0979063	0.0489531	+	0.998801i	$0.484412\pi$
$908$	−4.34144	−0.144076
$909$	140.946	4.67489
$910$	85.9183	2.84816
$911$	42.3040	1.40159	0.700797	−	0.713361i	$-0.252828\pi$
$911$	42.3040	1.40159	0.700797	+	0.713361i	$0.252828\pi$
$912$	−13.6533	−0.452105
$913$	−19.5394	−0.646660
$914$	−27.5037	−0.909742
$915$	−95.5675	−3.15936
$916$	−1.08323	−0.0357909
$917$	36.0107	1.18918
$918$	−7.34313	−0.242359
$919$	−21.7786	−0.718411	−0.359205	−	0.933258i	$-0.616952\pi$
$919$	−21.7786	−0.718411	−0.359205	+	0.933258i	$0.616952\pi$
$920$	12.6258	0.416259
$921$	−100.161	−3.30042
$922$	5.29955	0.174531
$923$	−10.4011	−0.342357
$924$	−20.8366	−0.685473
$925$	−81.8101	−2.68990
$926$	17.9585	0.590154
$927$	48.1968	1.58299
$928$	1.89459	0.0621930
$929$	−12.7455	−0.418168	−0.209084	−	0.977898i	$-0.567048\pi$
$929$	−12.7455	−0.418168	−0.209084	+	0.977898i	$0.567048\pi$
$930$	−90.0128	−2.95164
$931$	8.54600	0.280084
$932$	9.20835	0.301630
$933$	73.2106	2.39681
$934$	42.0750	1.37674
$935$	−8.20314	−0.268271
$936$	99.0005	3.23593
$937$	−7.64509	−0.249754	−0.124877	−	0.992172i	$-0.539854\pi$
$937$	−7.64509	−0.249754	−0.124877	+	0.992172i	$0.539854\pi$
$938$	−39.8769	−1.30203
$939$	86.8699	2.83489
$940$	6.78298	0.221236
$941$	15.7444	0.513254	0.256627	−	0.966511i	$-0.417389\pi$
$941$	15.7444	0.513254	0.256627	+	0.966511i	$0.417389\pi$
$942$	−27.0839	−0.882441
$943$	−5.19412	−0.169144
$944$	−17.0610	−0.555289
$945$	−230.255	−7.49020
$946$	−22.6372	−0.735998
$947$	−11.3219	−0.367911	−0.183956	−	0.982935i	$-0.558890\pi$
$947$	−11.3219	−0.367911	−0.183956	+	0.982935i	$0.558890\pi$
$948$	6.76390	0.219681
$949$	7.62297	0.247452
$950$	−21.1443	−0.686010
$951$	82.9960	2.69133
$952$	−4.22814	−0.137035
$953$	43.7432	1.41698	0.708491	−	0.705720i	$-0.249376\pi$
$953$	43.7432	1.41698	0.708491	+	0.705720i	$0.249376\pi$
$954$	−14.7593	−0.477851
$955$	−5.74221	−0.185814
$956$	1.47108	0.0475782
$957$	16.7177	0.540405
$958$	15.2406	0.492402
$959$	48.1015	1.55328
$960$	120.734	3.89667
$961$	−4.75074	−0.153250
$962$	36.3675	1.17254
$963$	36.5608	1.17815
$964$	−3.95758	−0.127465
$965$	−77.5764	−2.49727
$966$	15.4315	0.496500
$967$	27.7940	0.893794	0.446897	−	0.894586i	$-0.352529\pi$
$967$	27.7940	0.893794	0.446897	+	0.894586i	$0.352529\pi$
$968$	46.3832	1.49081
$969$	1.62286	0.0521339
$970$	28.2369	0.906632
$971$	14.8469	0.476460	0.238230	−	0.971209i	$-0.423433\pi$
$971$	14.8469	0.476460	0.238230	+	0.971209i	$0.423433\pi$
$972$	−13.3219	−0.427299
$973$	57.2366	1.83492
$974$	−43.6449	−1.39847
$975$	176.600	5.65574
$976$	22.4885	0.719840
$977$	−11.2742	−0.360693	−0.180346	−	0.983603i	$-0.557722\pi$
$977$	−11.2742	−0.360693	−0.180346	+	0.983603i	$0.557722\pi$
$978$	−31.0640	−0.993317
$979$	9.77329	0.312356
$980$	−9.27213	−0.296187
$981$	−25.5956	−0.817205
$982$	9.04502	0.288638
$983$	−7.29224	−0.232586	−0.116293	−	0.993215i	$-0.537101\pi$
$983$	−7.29224	−0.232586	−0.116293	+	0.993215i	$0.537101\pi$
$984$	−50.9560	−1.62442
$985$	−86.9015	−2.76891
$986$	0.491408	0.0156496
$987$	57.2304	1.82166
$988$	−1.91695	−0.0609863
$989$	−3.41912	−0.108722
$990$	210.520	6.69075
$991$	49.5478	1.57394	0.786969	−	0.616993i	$-0.211649\pi$
$991$	49.5478	1.57394	0.786969	+	0.616993i	$0.211649\pi$
$992$	−9.70676	−0.308190
$993$	15.2292	0.483285
$994$	−11.4000	−0.361586
$995$	37.8007	1.19836
$996$	−4.19402	−0.132892
$997$	24.4536	0.774454	0.387227	−	0.921985i	$-0.373433\pi$
$997$	24.4536	0.774454	0.387227	+	0.921985i	$0.373433\pi$
$998$	23.0239	0.728809
$999$	−97.4625	−3.08358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.5	✓	16
3.2	odd	2		6003.2.a.q.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.5	✓	16	1.1	even	1	trivial
6003.2.a.q.1.12		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28888 q^{2} +3.25447 q^{3} -0.338793 q^{4} +4.18846 q^{5} -4.19461 q^{6} -3.67888 q^{7} +3.01442 q^{8} +7.59155 q^{9} +O(q^{10})\)	\(q-1.28888 q^{2} +3.25447 q^{3} -0.338793 q^{4} +4.18846 q^{5} -4.19461 q^{6} -3.67888 q^{7} +3.01442 q^{8} +7.59155 q^{9} -5.39841 q^{10} -5.13684 q^{11} -1.10259 q^{12} +4.32617 q^{13} +4.74163 q^{14} +13.6312 q^{15} -3.20763 q^{16} +0.381268 q^{17} -9.78458 q^{18} +1.30789 q^{19} -1.41902 q^{20} -11.9728 q^{21} +6.62076 q^{22} +1.00000 q^{23} +9.81033 q^{24} +12.5432 q^{25} -5.57590 q^{26} +14.9430 q^{27} +1.24638 q^{28} -1.00000 q^{29} -17.5690 q^{30} +5.12340 q^{31} -1.89459 q^{32} -16.7177 q^{33} -0.491408 q^{34} -15.4088 q^{35} -2.57197 q^{36} -6.52227 q^{37} -1.68572 q^{38} +14.0794 q^{39} +12.6258 q^{40} -5.19412 q^{41} +15.4315 q^{42} -3.41912 q^{43} +1.74033 q^{44} +31.7969 q^{45} -1.28888 q^{46} -4.78004 q^{47} -10.4391 q^{48} +6.53417 q^{49} -16.1667 q^{50} +1.24082 q^{51} -1.46568 q^{52} +1.50843 q^{53} -19.2598 q^{54} -21.5154 q^{55} -11.0897 q^{56} +4.25650 q^{57} +1.28888 q^{58} +5.31889 q^{59} -4.61816 q^{60} -7.01094 q^{61} -6.60344 q^{62} -27.9284 q^{63} +8.85716 q^{64} +18.1200 q^{65} +21.5470 q^{66} -8.40996 q^{67} -0.129171 q^{68} +3.25447 q^{69} +19.8601 q^{70} -2.40424 q^{71} +22.8841 q^{72} +1.76206 q^{73} +8.40641 q^{74} +40.8214 q^{75} -0.443106 q^{76} +18.8978 q^{77} -18.1466 q^{78} -6.13455 q^{79} -13.4350 q^{80} +25.8570 q^{81} +6.69459 q^{82} +3.80378 q^{83} +4.05630 q^{84} +1.59692 q^{85} +4.40683 q^{86} -3.25447 q^{87} -15.4846 q^{88} -1.90259 q^{89} -40.9823 q^{90} -15.9155 q^{91} -0.338793 q^{92} +16.6739 q^{93} +6.16089 q^{94} +5.47806 q^{95} -6.16588 q^{96} -5.23059 q^{97} -8.42175 q^{98} -38.9966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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