LMFDB - Embedded newform 8033.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77688 q^{2} -0.579971 q^{3} +5.71104 q^{4} -3.81454 q^{5} +1.61051 q^{6} -2.45600 q^{7} -10.3051 q^{8} -2.66363 q^{9} +O(q^{10})$	\(q-2.77688 q^{2} -0.579971 q^{3} +5.71104 q^{4} -3.81454 q^{5} +1.61051 q^{6} -2.45600 q^{7} -10.3051 q^{8} -2.66363 q^{9} +10.5925 q^{10} -0.0141696 q^{11} -3.31224 q^{12} +0.539691 q^{13} +6.82001 q^{14} +2.21232 q^{15} +17.1939 q^{16} +0.0793569 q^{17} +7.39658 q^{18} -1.33715 q^{19} -21.7850 q^{20} +1.42441 q^{21} +0.0393473 q^{22} +1.02562 q^{23} +5.97666 q^{24} +9.55074 q^{25} -1.49865 q^{26} +3.28474 q^{27} -14.0263 q^{28} -1.00000 q^{29} -6.14335 q^{30} -5.10423 q^{31} -27.1352 q^{32} +0.00821798 q^{33} -0.220364 q^{34} +9.36853 q^{35} -15.2121 q^{36} +3.51349 q^{37} +3.71310 q^{38} -0.313005 q^{39} +39.3093 q^{40} -5.17591 q^{41} -3.95541 q^{42} +3.12512 q^{43} -0.0809234 q^{44} +10.1605 q^{45} -2.84801 q^{46} -6.97805 q^{47} -9.97198 q^{48} -0.968056 q^{49} -26.5212 q^{50} -0.0460247 q^{51} +3.08220 q^{52} +3.63740 q^{53} -9.12133 q^{54} +0.0540507 q^{55} +25.3094 q^{56} +0.775508 q^{57} +2.77688 q^{58} -6.67196 q^{59} +12.6347 q^{60} -1.36668 q^{61} +14.1738 q^{62} +6.54189 q^{63} +40.9632 q^{64} -2.05867 q^{65} -0.0228203 q^{66} +9.30393 q^{67} +0.453211 q^{68} -0.594827 q^{69} -26.0152 q^{70} -9.91905 q^{71} +27.4490 q^{72} +2.85003 q^{73} -9.75652 q^{74} -5.53915 q^{75} -7.63652 q^{76} +0.0348006 q^{77} +0.869176 q^{78} -6.35916 q^{79} -65.5870 q^{80} +6.08585 q^{81} +14.3729 q^{82} -1.70852 q^{83} +8.13487 q^{84} -0.302710 q^{85} -8.67807 q^{86} +0.579971 q^{87} +0.146020 q^{88} -5.81746 q^{89} -28.2146 q^{90} -1.32548 q^{91} +5.85733 q^{92} +2.96030 q^{93} +19.3772 q^{94} +5.10061 q^{95} +15.7376 q^{96} -15.0122 q^{97} +2.68817 q^{98} +0.0377427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.77688	−1.96355	−0.981774	−	0.190052i	$-0.939134\pi$
$2$	−2.77688	−1.96355	−0.981774	+	0.190052i	$0.939134\pi$
$3$	−0.579971	−0.334846	−0.167423	−	0.985885i	$-0.553545\pi$
$3$	−0.579971	−0.334846	−0.167423	+	0.985885i	$0.553545\pi$
$4$	5.71104	2.85552
$5$	−3.81454	−1.70592	−0.852958	−	0.521980i	$-0.825194\pi$
$5$	−3.81454	−1.70592	−0.852958	+	0.521980i	$0.825194\pi$
$6$	1.61051	0.657487
$7$	−2.45600	−0.928281	−0.464141	−	0.885761i	$-0.653637\pi$
$7$	−2.45600	−0.928281	−0.464141	+	0.885761i	$0.653637\pi$
$8$	−10.3051	−3.64341
$9$	−2.66363	−0.887878
$10$	10.5925	3.34965
$11$	−0.0141696	−0.00427231	−0.00213615	−	0.999998i	$-0.500680\pi$
$11$	−0.0141696	−0.00427231	−0.00213615	+	0.999998i	$0.500680\pi$
$12$	−3.31224	−0.956161
$13$	0.539691	0.149683	0.0748416	−	0.997195i	$-0.476155\pi$
$13$	0.539691	0.149683	0.0748416	+	0.997195i	$0.476155\pi$
$14$	6.82001	1.82273
$15$	2.21232	0.571220
$16$	17.1939	4.29848
$17$	0.0793569	0.0192469	0.00962344	−	0.999954i	$-0.496937\pi$
$17$	0.0793569	0.0192469	0.00962344	+	0.999954i	$0.496937\pi$
$18$	7.39658	1.74339
$19$	−1.33715	−0.306763	−0.153382	−	0.988167i	$-0.549016\pi$
$19$	−1.33715	−0.306763	−0.153382	+	0.988167i	$0.549016\pi$
$20$	−21.7850	−4.87128
$21$	1.42441	0.310832
$22$	0.0393473	0.00838888
$23$	1.02562	0.213856	0.106928	−	0.994267i	$-0.465899\pi$
$23$	1.02562	0.213856	0.106928	+	0.994267i	$0.465899\pi$
$24$	5.97666	1.21998
$25$	9.55074	1.91015
$26$	−1.49865	−0.293910
$27$	3.28474	0.632149
$28$	−14.0263	−2.65073
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.14335	−1.12162
$31$	−5.10423	−0.916746	−0.458373	−	0.888760i	$-0.651568\pi$
$31$	−5.10423	−0.916746	−0.458373	+	0.888760i	$0.651568\pi$
$32$	−27.1352	−4.79687
$33$	0.00821798	0.00143057
$34$	−0.220364	−0.0377922
$35$	9.36853	1.58357
$36$	−15.2121	−2.53535
$37$	3.51349	0.577614	0.288807	−	0.957387i	$-0.406741\pi$
$37$	3.51349	0.577614	0.288807	+	0.957387i	$0.406741\pi$
$38$	3.71310	0.602344
$39$	−0.313005	−0.0501209
$40$	39.3093	6.21534
$41$	−5.17591	−0.808341	−0.404171	−	0.914684i	$-0.632440\pi$
$41$	−5.17591	−0.808341	−0.404171	+	0.914684i	$0.632440\pi$
$42$	−3.95541	−0.610333
$43$	3.12512	0.476576	0.238288	−	0.971194i	$-0.423414\pi$
$43$	3.12512	0.476576	0.238288	+	0.971194i	$0.423414\pi$
$44$	−0.0809234	−0.0121997
$45$	10.1605	1.51464
$46$	−2.84801	−0.419916
$47$	−6.97805	−1.01785	−0.508927	−	0.860810i	$-0.669958\pi$
$47$	−6.97805	−1.01785	−0.508927	+	0.860810i	$0.669958\pi$
$48$	−9.97198	−1.43933
$49$	−0.968056	−0.138294
$50$	−26.5212	−3.75067
$51$	−0.0460247	−0.00644475
$52$	3.08220	0.427424
$53$	3.63740	0.499635	0.249817	−	0.968293i	$-0.419629\pi$
$53$	3.63740	0.499635	0.249817	+	0.968293i	$0.419629\pi$
$54$	−9.12133	−1.24126
$55$	0.0540507	0.00728819
$56$	25.3094	3.38211
$57$	0.775508	0.102719
$58$	2.77688	0.364622
$59$	−6.67196	−0.868615	−0.434307	−	0.900765i	$-0.643007\pi$
$59$	−6.67196	−0.868615	−0.434307	+	0.900765i	$0.643007\pi$
$60$	12.6347	1.63113
$61$	−1.36668	−0.174986	−0.0874929	−	0.996165i	$-0.527885\pi$
$61$	−1.36668	−0.174986	−0.0874929	+	0.996165i	$0.527885\pi$
$62$	14.1738	1.80008
$63$	6.54189	0.824201
$64$	40.9632	5.12040
$65$	−2.05867	−0.255347
$66$	−0.0228203	−0.00280899
$67$	9.30393	1.13666	0.568328	−	0.822802i	$-0.307590\pi$
$67$	9.30393	1.13666	0.568328	+	0.822802i	$0.307590\pi$
$68$	0.453211	0.0549599
$69$	−0.594827	−0.0716088
$70$	−26.0152	−3.10942
$71$	−9.91905	−1.17717	−0.588587	−	0.808434i	$-0.700316\pi$
$71$	−9.91905	−1.17717	−0.588587	+	0.808434i	$0.700316\pi$
$72$	27.4490	3.23490
$73$	2.85003	0.333571	0.166785	−	0.985993i	$-0.446661\pi$
$73$	2.85003	0.333571	0.166785	+	0.985993i	$0.446661\pi$
$74$	−9.75652	−1.13417
$75$	−5.53915	−0.639606
$76$	−7.63652	−0.875969
$77$	0.0348006	0.00396590
$78$	0.869176	0.0984148
$79$	−6.35916	−0.715461	−0.357731	−	0.933825i	$-0.616449\pi$
$79$	−6.35916	−0.715461	−0.357731	+	0.933825i	$0.616449\pi$
$80$	−65.5870	−7.33285
$81$	6.08585	0.676205
$82$	14.3729	1.58722
$83$	−1.70852	−0.187535	−0.0937674	−	0.995594i	$-0.529891\pi$
$83$	−1.70852	−0.187535	−0.0937674	+	0.995594i	$0.529891\pi$
$84$	8.13487	0.887587
$85$	−0.302710	−0.0328335
$86$	−8.67807	−0.935781
$87$	0.579971	0.0621794
$88$	0.146020	0.0155657
$89$	−5.81746	−0.616650	−0.308325	−	0.951281i	$-0.599768\pi$
$89$	−5.81746	−0.616650	−0.308325	+	0.951281i	$0.599768\pi$
$90$	−28.2146	−2.97408
$91$	−1.32548	−0.138948
$92$	5.85733	0.610669
$93$	2.96030	0.306969
$94$	19.3772	1.99860
$95$	5.10061	0.523312
$96$	15.7376	1.60621
$97$	−15.0122	−1.52426	−0.762130	−	0.647424i	$-0.775846\pi$
$97$	−15.0122	−1.52426	−0.762130	+	0.647424i	$0.775846\pi$
$98$	2.68817	0.271546
$99$	0.0377427	0.00379329
$100$	54.5447	5.45447
$101$	−3.87487	−0.385564	−0.192782	−	0.981242i	$-0.561751\pi$
$101$	−3.87487	−0.385564	−0.192782	+	0.981242i	$0.561751\pi$
$102$	0.127805	0.0126546
$103$	−9.10744	−0.897383	−0.448692	−	0.893687i	$-0.648110\pi$
$103$	−9.10744	−0.897383	−0.448692	+	0.893687i	$0.648110\pi$
$104$	−5.56157	−0.545357
$105$	−5.43347	−0.530253
$106$	−10.1006	−0.981057
$107$	−5.98233	−0.578333	−0.289167	−	0.957279i	$-0.593378\pi$
$107$	−5.98233	−0.578333	−0.289167	+	0.957279i	$0.593378\pi$
$108$	18.7593	1.80512
$109$	−16.6143	−1.59136	−0.795681	−	0.605715i	$-0.792887\pi$
$109$	−16.6143	−1.59136	−0.795681	+	0.605715i	$0.792887\pi$
$110$	−0.150092	−0.0143107
$111$	−2.03772	−0.193412
$112$	−42.2283	−3.99020
$113$	−15.5696	−1.46466	−0.732332	−	0.680948i	$-0.761568\pi$
$113$	−15.5696	−1.46466	−0.732332	+	0.680948i	$0.761568\pi$
$114$	−2.15349	−0.201693
$115$	−3.91226	−0.364820
$116$	−5.71104	−0.530257
$117$	−1.43754	−0.132900
$118$	18.5272	1.70557
$119$	−0.194901	−0.0178665
$120$	−22.7982	−2.08119
$121$	−10.9998	−0.999982
$122$	3.79511	0.343593
$123$	3.00188	0.270670
$124$	−29.1505	−2.61779
$125$	−17.3590	−1.55264
$126$	−18.1660	−1.61836
$127$	0.332279	0.0294850	0.0147425	−	0.999891i	$-0.495307\pi$
$127$	0.332279	0.0294850	0.0147425	+	0.999891i	$0.495307\pi$
$128$	−59.4794	−5.25729
$129$	−1.81248	−0.159580
$130$	5.71668	0.501386
$131$	−2.29312	−0.200351	−0.100176	−	0.994970i	$-0.531940\pi$
$131$	−2.29312	−0.200351	−0.100176	+	0.994970i	$0.531940\pi$
$132$	0.0469332	0.00408501
$133$	3.28404	0.284762
$134$	−25.8359	−2.23188
$135$	−12.5298	−1.07839
$136$	−0.817781	−0.0701242
$137$	−3.37043	−0.287955	−0.143978	−	0.989581i	$-0.545989\pi$
$137$	−3.37043	−0.287955	−0.143978	+	0.989581i	$0.545989\pi$
$138$	1.65176	0.140607
$139$	9.79116	0.830475	0.415238	−	0.909713i	$-0.363698\pi$
$139$	9.79116	0.830475	0.415238	+	0.909713i	$0.363698\pi$
$140$	53.5041	4.52192
$141$	4.04707	0.340825
$142$	27.5440	2.31144
$143$	−0.00764722	−0.000639493 0
$144$	−45.7983	−3.81653
$145$	3.81454	0.316781
$146$	−7.91418	−0.654982
$147$	0.561444	0.0463071
$148$	20.0657	1.64939
$149$	−9.82818	−0.805156	−0.402578	−	0.915386i	$-0.631886\pi$
$149$	−9.82818	−0.805156	−0.402578	+	0.915386i	$0.631886\pi$
$150$	15.3815	1.25590
$151$	3.70296	0.301343	0.150671	−	0.988584i	$-0.451856\pi$
$151$	3.70296	0.301343	0.150671	+	0.988584i	$0.451856\pi$
$152$	13.7795	1.11766
$153$	−0.211378	−0.0170889
$154$	−0.0966371	−0.00778724
$155$	19.4703	1.56389
$156$	−1.78758	−0.143121
$157$	2.38587	0.190413	0.0952066	−	0.995458i	$-0.469649\pi$
$157$	2.38587	0.190413	0.0952066	+	0.995458i	$0.469649\pi$
$158$	17.6586	1.40484
$159$	−2.10958	−0.167301
$160$	103.508	8.18306
$161$	−2.51891	−0.198518
$162$	−16.8996	−1.32776
$163$	1.66718	0.130583	0.0652917	−	0.997866i	$-0.479202\pi$
$163$	1.66718	0.130583	0.0652917	+	0.997866i	$0.479202\pi$
$164$	−29.5598	−2.30824
$165$	−0.0313478	−0.00244043
$166$	4.74436	0.368233
$167$	−18.4517	−1.42784	−0.713919	−	0.700228i	$-0.753082\pi$
$167$	−18.4517	−1.42784	−0.713919	+	0.700228i	$0.753082\pi$
$168$	−14.6787	−1.13249
$169$	−12.7087	−0.977595
$170$	0.840589	0.0644703
$171$	3.56168	0.272368
$172$	17.8477	1.36087
$173$	4.22962	0.321572	0.160786	−	0.986989i	$-0.448597\pi$
$173$	4.22962	0.321572	0.160786	+	0.986989i	$0.448597\pi$
$174$	−1.61051	−0.122092
$175$	−23.4566	−1.77316
$176$	−0.243632	−0.0183644
$177$	3.86954	0.290852
$178$	16.1544	1.21082
$179$	−17.7841	−1.32925	−0.664625	−	0.747177i	$-0.731409\pi$
$179$	−17.7841	−1.32925	−0.664625	+	0.747177i	$0.731409\pi$
$180$	58.0273	4.32510
$181$	−4.19495	−0.311808	−0.155904	−	0.987772i	$-0.549829\pi$
$181$	−4.19495	−0.311808	−0.155904	+	0.987772i	$0.549829\pi$
$182$	3.68070	0.272831
$183$	0.792636	0.0585933
$184$	−10.5691	−0.779163
$185$	−13.4023	−0.985360
$186$	−8.22040	−0.602749
$187$	−0.00112446	−8.22285e−5 0
$188$	−39.8520	−2.90650
$189$	−8.06734	−0.586812
$190$	−14.1638	−1.02755
$191$	14.6063	1.05688	0.528438	−	0.848972i	$-0.322778\pi$
$191$	14.6063	1.05688	0.528438	+	0.848972i	$0.322778\pi$
$192$	−23.7575	−1.71455
$193$	−11.3854	−0.819537	−0.409768	−	0.912190i	$-0.634390\pi$
$193$	−11.3854	−0.819537	−0.409768	+	0.912190i	$0.634390\pi$
$194$	41.6871	2.99296
$195$	1.19397	0.0855020
$196$	−5.52861	−0.394901
$197$	−2.59869	−0.185149	−0.0925747	−	0.995706i	$-0.529510\pi$
$197$	−2.59869	−0.185149	−0.0925747	+	0.995706i	$0.529510\pi$
$198$	−0.104807	−0.00744830
$199$	−6.72039	−0.476396	−0.238198	−	0.971217i	$-0.576557\pi$
$199$	−6.72039	−0.476396	−0.238198	+	0.971217i	$0.576557\pi$
$200$	−98.4214	−6.95945
$201$	−5.39601	−0.380605
$202$	10.7600	0.757073
$203$	2.45600	0.172378
$204$	−0.262849	−0.0184031
$205$	19.7437	1.37896
$206$	25.2902	1.76205
$207$	−2.73186	−0.189878
$208$	9.27940	0.643411
$209$	0.0189469	0.00131059
$210$	15.0881	1.04118
$211$	−13.7996	−0.950001	−0.475000	−	0.879986i	$-0.657552\pi$
$211$	−13.7996	−0.950001	−0.475000	+	0.879986i	$0.657552\pi$
$212$	20.7733	1.42672
$213$	5.75276	0.394173
$214$	16.6122	1.13559
$215$	−11.9209	−0.812999
$216$	−33.8496	−2.30318
$217$	12.5360	0.850998
$218$	46.1359	3.12472
$219$	−1.65293	−0.111695
$220$	0.308686	0.0208116
$221$	0.0428282	0.00288093
$222$	5.65850	0.379774
$223$	−0.639122	−0.0427988	−0.0213994	−	0.999771i	$-0.506812\pi$
$223$	−0.639122	−0.0427988	−0.0213994	+	0.999771i	$0.506812\pi$
$224$	66.6441	4.45284
$225$	−25.4397	−1.69598
$226$	43.2348	2.87594
$227$	−3.31831	−0.220244	−0.110122	−	0.993918i	$-0.535124\pi$
$227$	−3.31831	−0.220244	−0.110122	+	0.993918i	$0.535124\pi$
$228$	4.42896	0.293315
$229$	4.69721	0.310401	0.155200	−	0.987883i	$-0.450398\pi$
$229$	4.69721	0.310401	0.155200	+	0.987883i	$0.450398\pi$
$230$	10.8638	0.716341
$231$	−0.0201834	−0.00132797
$232$	10.3051	0.676563
$233$	7.49670	0.491125	0.245562	−	0.969381i	$-0.421027\pi$
$233$	7.49670	0.491125	0.245562	+	0.969381i	$0.421027\pi$
$234$	3.99187	0.260956
$235$	26.6181	1.73637
$236$	−38.1038	−2.48035
$237$	3.68813	0.239570
$238$	0.541215	0.0350818
$239$	2.41358	0.156121	0.0780607	−	0.996949i	$-0.475127\pi$
$239$	2.41358	0.156121	0.0780607	+	0.996949i	$0.475127\pi$
$240$	38.0385	2.45538
$241$	0.627621	0.0404286	0.0202143	−	0.999796i	$-0.493565\pi$
$241$	0.627621	0.0404286	0.0202143	+	0.999796i	$0.493565\pi$
$242$	30.5451	1.96351
$243$	−13.3838	−0.858574
$244$	−7.80518	−0.499676
$245$	3.69269	0.235917
$246$	−8.33584	−0.531474
$247$	−0.721647	−0.0459173
$248$	52.5996	3.34008
$249$	0.990893	0.0627953
$250$	48.2038	3.04868
$251$	9.50427	0.599904	0.299952	−	0.953954i	$-0.403029\pi$
$251$	9.50427	0.599904	0.299952	+	0.953954i	$0.403029\pi$
$252$	37.3610	2.35352
$253$	−0.0145326	−0.000913657 0
$254$	−0.922698	−0.0578952
$255$	0.175563	0.0109942
$256$	83.2406	5.20254
$257$	−2.47466	−0.154365	−0.0771825	−	0.997017i	$-0.524592\pi$
$257$	−2.47466	−0.154365	−0.0771825	+	0.997017i	$0.524592\pi$
$258$	5.03303	0.313343
$259$	−8.62913	−0.536188
$260$	−11.7572	−0.729149
$261$	2.66363	0.164875
$262$	6.36772	0.393399
$263$	−13.1448	−0.810541	−0.405271	−	0.914197i	$-0.632823\pi$
$263$	−13.1448	−0.810541	−0.405271	+	0.914197i	$0.632823\pi$
$264$	−0.0846871	−0.00521213
$265$	−13.8750	−0.852335
$266$	−9.11938	−0.559145
$267$	3.37396	0.206483
$268$	53.1351	3.24575
$269$	8.35679	0.509522	0.254761	−	0.967004i	$-0.418003\pi$
$269$	8.35679	0.509522	0.254761	+	0.967004i	$0.418003\pi$
$270$	34.7937	2.11748
$271$	17.8653	1.08524	0.542620	−	0.839978i	$-0.317432\pi$
$271$	17.8653	1.08524	0.542620	+	0.839978i	$0.317432\pi$
$272$	1.36446	0.0827323
$273$	0.768741	0.0465263
$274$	9.35927	0.565414
$275$	−0.135331	−0.00816074
$276$	−3.39708	−0.204480
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−27.1888	−1.63068
$279$	13.5958	0.813959
$280$	−96.5437	−5.76959
$281$	−30.0557	−1.79298	−0.896488	−	0.443069i	$-0.853890\pi$
$281$	−30.0557	−1.79298	−0.896488	+	0.443069i	$0.853890\pi$
$282$	−11.2382	−0.669226
$283$	−20.8065	−1.23682	−0.618408	−	0.785857i	$-0.712222\pi$
$283$	−20.8065	−1.23682	−0.618408	+	0.785857i	$0.712222\pi$
$284$	−56.6481	−3.36145
$285$	−2.95821	−0.175229
$286$	0.0212354	0.00125567
$287$	12.7120	0.750368
$288$	72.2782	4.25903
$289$	−16.9937	−0.999630
$290$	−10.5925	−0.622014
$291$	8.70665	0.510393
$292$	16.2766	0.952518
$293$	18.3090	1.06963	0.534813	−	0.844971i	$-0.320382\pi$
$293$	18.3090	1.06963	0.534813	+	0.844971i	$0.320382\pi$
$294$	−1.55906	−0.0909263
$295$	25.4505	1.48178
$296$	−36.2069	−2.10448
$297$	−0.0465436	−0.00270073
$298$	27.2916	1.58096
$299$	0.553515	0.0320106
$300$	−31.6343	−1.82641
$301$	−7.67530	−0.442397
$302$	−10.2827	−0.591701
$303$	2.24731	0.129105
$304$	−22.9908	−1.31862
$305$	5.21327	0.298511
$306$	0.586970	0.0335548
$307$	12.3322	0.703838	0.351919	−	0.936031i	$-0.385529\pi$
$307$	12.3322	0.703838	0.351919	+	0.936031i	$0.385529\pi$
$308$	0.198748	0.0113247
$309$	5.28205	0.300486
$310$	−54.0666	−3.07078
$311$	12.5189	0.709882	0.354941	−	0.934889i	$-0.384501\pi$
$311$	12.5189	0.709882	0.354941	+	0.934889i	$0.384501\pi$
$312$	3.22555	0.182611
$313$	21.5512	1.21815	0.609073	−	0.793114i	$-0.291542\pi$
$313$	21.5512	1.21815	0.609073	+	0.793114i	$0.291542\pi$
$314$	−6.62527	−0.373886
$315$	−24.9543	−1.40602
$316$	−36.3174	−2.04301
$317$	5.53800	0.311045	0.155522	−	0.987832i	$-0.450294\pi$
$317$	5.53800	0.311045	0.155522	+	0.987832i	$0.450294\pi$
$318$	5.85806	0.328504
$319$	0.0141696	0.000793347 0
$320$	−156.256	−8.73498
$321$	3.46958	0.193653
$322$	6.99471	0.389800
$323$	−0.106112	−0.00590423
$324$	34.7565	1.93092
$325$	5.15445	0.285917
$326$	−4.62955	−0.256407
$327$	9.63582	0.532862
$328$	53.3383	2.94512
$329$	17.1381	0.944855
$330$	0.0870491	0.00479189
$331$	−20.9418	−1.15106	−0.575532	−	0.817779i	$-0.695205\pi$
$331$	−20.9418	−1.15106	−0.575532	+	0.817779i	$0.695205\pi$
$332$	−9.75744	−0.535509
$333$	−9.35864	−0.512850
$334$	51.2382	2.80363
$335$	−35.4902	−1.93904
$336$	24.4912	1.33610
$337$	−25.5864	−1.39378	−0.696889	−	0.717179i	$-0.745433\pi$
$337$	−25.5864	−1.39378	−0.696889	+	0.717179i	$0.745433\pi$
$338$	35.2906	1.91955
$339$	9.02991	0.490437
$340$	−1.72879	−0.0937569
$341$	0.0723250	0.00391662
$342$	−9.89033	−0.534808
$343$	19.5696	1.05666
$344$	−32.2047	−1.73636
$345$	2.26899	0.122159
$346$	−11.7451	−0.631422
$347$	6.47387	0.347536	0.173768	−	0.984787i	$-0.444406\pi$
$347$	6.47387	0.347536	0.173768	+	0.984787i	$0.444406\pi$
$348$	3.31224	0.177555
$349$	13.3317	0.713632	0.356816	−	0.934175i	$-0.383862\pi$
$349$	13.3317	0.713632	0.356816	+	0.934175i	$0.383862\pi$
$350$	65.1362	3.48168
$351$	1.77275	0.0946221
$352$	0.384496	0.0204937
$353$	17.0387	0.906878	0.453439	−	0.891287i	$-0.350197\pi$
$353$	17.0387	0.906878	0.453439	+	0.891287i	$0.350197\pi$
$354$	−10.7452	−0.571103
$355$	37.8366	2.00816
$356$	−33.2238	−1.76086
$357$	0.113037	0.00598254
$358$	49.3844	2.61005
$359$	−15.1661	−0.800438	−0.400219	−	0.916420i	$-0.631066\pi$
$359$	−15.1661	−0.800438	−0.400219	+	0.916420i	$0.631066\pi$
$360$	−104.706	−5.51847
$361$	−17.2120	−0.905896
$362$	11.6488	0.612250
$363$	6.37956	0.334840
$364$	−7.56988	−0.396769
$365$	−10.8716	−0.569043
$366$	−2.20105	−0.115051
$367$	0.497800	0.0259849	0.0129925	−	0.999916i	$-0.495864\pi$
$367$	0.497800	0.0259849	0.0129925	+	0.999916i	$0.495864\pi$
$368$	17.6344	0.919254
$369$	13.7867	0.717708
$370$	37.2167	1.93480
$371$	−8.93345	−0.463802
$372$	16.9064	0.876557
$373$	27.1584	1.40621	0.703104	−	0.711087i	$-0.251797\pi$
$373$	27.1584	1.40621	0.703104	+	0.711087i	$0.251797\pi$
$374$	0.00312248	0.000161460 0
$375$	10.0677	0.519895
$376$	71.9096	3.70845
$377$	−0.539691	−0.0277955
$378$	22.4020	1.15223
$379$	−20.4820	−1.05209	−0.526045	−	0.850456i	$-0.676326\pi$
$379$	−20.4820	−1.05209	−0.526045	+	0.850456i	$0.676326\pi$
$380$	29.1298	1.49433
$381$	−0.192712	−0.00987295
$382$	−40.5599	−2.07523
$383$	−1.46597	−0.0749076	−0.0374538	−	0.999298i	$-0.511925\pi$
$383$	−1.46597	−0.0749076	−0.0374538	+	0.999298i	$0.511925\pi$
$384$	34.4963	1.76038
$385$	−0.132749	−0.00676549
$386$	31.6158	1.60920
$387$	−8.32417	−0.423142
$388$	−85.7354	−4.35256
$389$	−26.0673	−1.32167	−0.660833	−	0.750533i	$-0.729797\pi$
$389$	−26.0673	−1.32167	−0.660833	+	0.750533i	$0.729797\pi$
$390$	−3.31551	−0.167887
$391$	0.0813897	0.00411605
$392$	9.97592	0.503860
$393$	1.32995	0.0670869
$394$	7.21625	0.363550
$395$	24.2573	1.22052
$396$	0.215550	0.0108318
$397$	20.3870	1.02320	0.511598	−	0.859225i	$-0.329054\pi$
$397$	20.3870	1.02320	0.511598	+	0.859225i	$0.329054\pi$
$398$	18.6617	0.935427
$399$	−1.90465	−0.0953517
$400$	164.215	8.21074
$401$	21.5313	1.07522	0.537612	−	0.843192i	$-0.319326\pi$
$401$	21.5313	1.07522	0.537612	+	0.843192i	$0.319326\pi$
$402$	14.9841	0.747337
$403$	−2.75470	−0.137222
$404$	−22.1295	−1.10099
$405$	−23.2147	−1.15355
$406$	−6.82001	−0.338472
$407$	−0.0497848	−0.00246774
$408$	0.474289	0.0234808
$409$	−30.4181	−1.50408	−0.752040	−	0.659117i	$-0.770930\pi$
$409$	−30.4181	−1.50408	−0.752040	+	0.659117i	$0.770930\pi$
$410$	−54.8259	−2.70766
$411$	1.95475	0.0964208
$412$	−52.0130	−2.56250
$413$	16.3863	0.806319
$414$	7.58605	0.372834
$415$	6.51723	0.319918
$416$	−14.6446	−0.718011
$417$	−5.67859	−0.278082
$418$	−0.0526132	−0.00257340
$419$	−14.4952	−0.708138	−0.354069	−	0.935219i	$-0.615202\pi$
$419$	−14.4952	−0.708138	−0.354069	+	0.935219i	$0.615202\pi$
$420$	−31.0308	−1.51415
$421$	−3.37993	−0.164728	−0.0823639	−	0.996602i	$-0.526247\pi$
$421$	−3.37993	−0.164728	−0.0823639	+	0.996602i	$0.526247\pi$
$422$	38.3197	1.86537
$423$	18.5870	0.903730
$424$	−37.4838	−1.82037
$425$	0.757917	0.0367644
$426$	−15.9747	−0.773977
$427$	3.35657	0.162436
$428$	−34.1653	−1.65144
$429$	0.00443517	0.000214132 0
$430$	33.1029	1.59636
$431$	−23.9700	−1.15460	−0.577298	−	0.816534i	$-0.695893\pi$
$431$	−23.9700	−1.15460	−0.577298	+	0.816534i	$0.695893\pi$
$432$	56.4776	2.71728
$433$	−20.3158	−0.976315	−0.488158	−	0.872756i	$-0.662331\pi$
$433$	−20.3158	−0.976315	−0.488158	+	0.872756i	$0.662331\pi$
$434$	−34.8109	−1.67098
$435$	−2.21232	−0.106073
$436$	−94.8851	−4.54417
$437$	−1.37140	−0.0656030
$438$	4.58999	0.219318
$439$	13.2477	0.632277	0.316139	−	0.948713i	$-0.397614\pi$
$439$	13.2477	0.632277	0.316139	+	0.948713i	$0.397614\pi$
$440$	−0.556998	−0.0265538
$441$	2.57855	0.122788
$442$	−0.118929	−0.00565685
$443$	−14.9966	−0.712510	−0.356255	−	0.934389i	$-0.615947\pi$
$443$	−14.9966	−0.712510	−0.356255	+	0.934389i	$0.615947\pi$
$444$	−11.6375	−0.552292
$445$	22.1910	1.05195
$446$	1.77476	0.0840375
$447$	5.70006	0.269604
$448$	−100.606	−4.75317
$449$	−26.5834	−1.25455	−0.627275	−	0.778798i	$-0.715830\pi$
$449$	−26.5834	−1.25455	−0.627275	+	0.778798i	$0.715830\pi$
$450$	70.6429	3.33014
$451$	0.0733407	0.00345348
$452$	−88.9186	−4.18238
$453$	−2.14761	−0.100904
$454$	9.21455	0.432460
$455$	5.05611	0.237034
$456$	−7.99169	−0.374245
$457$	21.0800	0.986079	0.493040	−	0.870007i	$-0.335886\pi$
$457$	21.0800	0.986079	0.493040	+	0.870007i	$0.335886\pi$
$458$	−13.0436	−0.609487
$459$	0.260667	0.0121669
$460$	−22.3431	−1.04175
$461$	−3.87515	−0.180484	−0.0902419	−	0.995920i	$-0.528764\pi$
$461$	−3.87515	−0.180484	−0.0902419	+	0.995920i	$0.528764\pi$
$462$	0.0560467	0.00260753
$463$	−31.5417	−1.46587	−0.732934	−	0.680300i	$-0.761850\pi$
$463$	−31.5417	−1.46587	−0.732934	+	0.680300i	$0.761850\pi$
$464$	−17.1939	−0.798208
$465$	−11.2922	−0.523664
$466$	−20.8174	−0.964347
$467$	−27.0140	−1.25006	−0.625028	−	0.780602i	$-0.714913\pi$
$467$	−27.0140	−1.25006	−0.625028	+	0.780602i	$0.714913\pi$
$468$	−8.20984	−0.379500
$469$	−22.8505	−1.05514
$470$	−73.9151	−3.40945
$471$	−1.38374	−0.0637592
$472$	68.7552	3.16472
$473$	−0.0442818	−0.00203608
$474$	−10.2415	−0.470406
$475$	−12.7708	−0.585963
$476$	−1.11309	−0.0510182
$477$	−9.68869	−0.443615
$478$	−6.70221	−0.306552
$479$	−18.9377	−0.865286	−0.432643	−	0.901565i	$-0.642419\pi$
$479$	−18.9377	−0.865286	−0.432643	+	0.901565i	$0.642419\pi$
$480$	−60.0319	−2.74007
$481$	1.89620	0.0864591
$482$	−1.74283	−0.0793835
$483$	1.46090	0.0664731
$484$	−62.8203	−2.85547
$485$	57.2647	2.60026
$486$	37.1653	1.68585
$487$	−20.7132	−0.938604	−0.469302	−	0.883038i	$-0.655494\pi$
$487$	−20.7132	−0.938604	−0.469302	+	0.883038i	$0.655494\pi$
$488$	14.0838	0.637544
$489$	−0.966915	−0.0437254
$490$	−10.2541	−0.463235
$491$	−39.4337	−1.77962	−0.889809	−	0.456333i	$-0.849163\pi$
$491$	−39.4337	−1.77962	−0.889809	+	0.456333i	$0.849163\pi$
$492$	17.1439	0.772904
$493$	−0.0793569	−0.00357405
$494$	2.00392	0.0901608
$495$	−0.143971	−0.00647103
$496$	−87.7617	−3.94062
$497$	24.3612	1.09275
$498$	−2.75159	−0.123302
$499$	−3.82642	−0.171294	−0.0856470	−	0.996326i	$-0.527296\pi$
$499$	−3.82642	−0.171294	−0.0856470	+	0.996326i	$0.527296\pi$
$500$	−99.1381	−4.43359
$501$	10.7015	0.478106
$502$	−26.3922	−1.17794
$503$	23.8211	1.06213	0.531064	−	0.847331i	$-0.321792\pi$
$503$	23.8211	1.06213	0.531064	+	0.847331i	$0.321792\pi$
$504$	−67.4149	−3.00290
$505$	14.7809	0.657739
$506$	0.0403552	0.00179401
$507$	7.37070	0.327344
$508$	1.89766	0.0841951
$509$	−3.60036	−0.159583	−0.0797916	−	0.996812i	$-0.525425\pi$
$509$	−3.60036	−0.159583	−0.0797916	+	0.996812i	$0.525425\pi$
$510$	−0.487517	−0.0215876
$511$	−6.99968	−0.309647
$512$	−112.190	−4.95814
$513$	−4.39219	−0.193920
$514$	6.87182	0.303103
$515$	34.7407	1.53086
$516$	−10.3511	−0.455684
$517$	0.0988765	0.00434858
$518$	23.9620	1.05283
$519$	−2.45306	−0.107677
$520$	21.2149	0.930333
$521$	−14.5773	−0.638643	−0.319321	−	0.947646i	$-0.603455\pi$
$521$	−14.5773	−0.638643	−0.319321	+	0.947646i	$0.603455\pi$
$522$	−7.39658	−0.323740
$523$	16.3324	0.714167	0.357083	−	0.934072i	$-0.383771\pi$
$523$	16.3324	0.714167	0.357083	+	0.934072i	$0.383771\pi$
$524$	−13.0961	−0.572107
$525$	13.6042	0.593735
$526$	36.5014	1.59154
$527$	−0.405056	−0.0176445
$528$	0.141299	0.00614926
$529$	−21.9481	−0.954266
$530$	38.5292	1.67360
$531$	17.7716	0.771224
$532$	18.7553	0.813145
$533$	−2.79339	−0.120995
$534$	−9.36907	−0.405439
$535$	22.8198	0.986588
$536$	−95.8780	−4.14130
$537$	10.3143	0.445095
$538$	−23.2058	−1.00047
$539$	0.0137170	0.000590833 0
$540$	−71.5582	−3.07937
$541$	−20.1427	−0.866004	−0.433002	−	0.901393i	$-0.642546\pi$
$541$	−20.1427	−0.866004	−0.433002	+	0.901393i	$0.642546\pi$
$542$	−49.6097	−2.13092
$543$	2.43295	0.104408
$544$	−2.15336	−0.0923247
$545$	63.3760	2.71473
$546$	−2.13470	−0.0913566
$547$	−10.7151	−0.458144	−0.229072	−	0.973410i	$-0.573569\pi$
$547$	−10.7151	−0.458144	−0.229072	+	0.973410i	$0.573569\pi$
$548$	−19.2487	−0.822262
$549$	3.64034	0.155366
$550$	0.375796	0.0160240
$551$	1.33715	0.0569645
$552$	6.12976	0.260900
$553$	15.6181	0.664149
$554$	−2.77688	−0.117978
$555$	7.77297	0.329944
$556$	55.9177	2.37144
$557$	3.04650	0.129084	0.0645421	−	0.997915i	$-0.479441\pi$
$557$	3.04650	0.129084	0.0645421	+	0.997915i	$0.479441\pi$
$558$	−37.7538	−1.59825
$559$	1.68660	0.0713355
$560$	161.082	6.80695
$561$	0.000652153 0	2.75339e−5 0
$562$	83.4611	3.52059
$563$	−7.56691	−0.318907	−0.159454	−	0.987205i	$-0.550973\pi$
$563$	−7.56691	−0.318907	−0.159454	+	0.987205i	$0.550973\pi$
$564$	23.1130	0.973232
$565$	59.3909	2.49859
$566$	57.7770	2.42855
$567$	−14.9468	−0.627709
$568$	102.217	4.28892
$569$	30.5895	1.28238	0.641189	−	0.767383i	$-0.278441\pi$
$569$	30.5895	1.28238	0.641189	+	0.767383i	$0.278441\pi$
$570$	8.21458	0.344071
$571$	20.9635	0.877295	0.438648	−	0.898659i	$-0.355458\pi$
$571$	20.9635	0.877295	0.438648	+	0.898659i	$0.355458\pi$
$572$	−0.0436736	−0.00182608
$573$	−8.47123	−0.353891
$574$	−35.2998	−1.47338
$575$	9.79539	0.408496
$576$	−109.111	−4.54629
$577$	47.0388	1.95825	0.979126	−	0.203252i	$-0.0651511\pi$
$577$	47.0388	1.95825	0.979126	+	0.203252i	$0.0651511\pi$
$578$	47.1894	1.96282
$579$	6.60318	0.274419
$580$	21.7850	0.904574
$581$	4.19613	0.174085
$582$	−24.1773	−1.00218
$583$	−0.0515406	−0.00213459
$584$	−29.3699	−1.21533
$585$	5.48355	0.226717
$586$	−50.8419	−2.10026
$587$	−31.5170	−1.30085	−0.650423	−	0.759572i	$-0.725408\pi$
$587$	−31.5170	−1.30085	−0.650423	+	0.759572i	$0.725408\pi$
$588$	3.20643	0.132231
$589$	6.82511	0.281224
$590$	−70.6728	−2.90955
$591$	1.50717	0.0619966
$592$	60.4106	2.48286
$593$	27.3767	1.12423	0.562114	−	0.827060i	$-0.309988\pi$
$593$	27.3767	1.12423	0.562114	+	0.827060i	$0.309988\pi$
$594$	0.129246	0.00530302
$595$	0.743457	0.0304788
$596$	−56.1292	−2.29914
$597$	3.89763	0.159520
$598$	−1.53704	−0.0628544
$599$	8.81439	0.360146	0.180073	−	0.983653i	$-0.442367\pi$
$599$	8.81439	0.360146	0.180073	+	0.983653i	$0.442367\pi$
$600$	57.0816	2.33035
$601$	8.90945	0.363424	0.181712	−	0.983352i	$-0.441836\pi$
$601$	8.90945	0.363424	0.181712	+	0.983352i	$0.441836\pi$
$602$	21.3134	0.868668
$603$	−24.7823	−1.00921
$604$	21.1478	0.860491
$605$	41.9592	1.70588
$606$	−6.24051	−0.253503
$607$	0.450187	0.0182725	0.00913626	−	0.999958i	$-0.497092\pi$
$607$	0.450187	0.0182725	0.00913626	+	0.999958i	$0.497092\pi$
$608$	36.2838	1.47150
$609$	−1.42441	−0.0577200
$610$	−14.4766	−0.586141
$611$	−3.76599	−0.152356
$612$	−1.20719	−0.0487976
$613$	−39.4540	−1.59353	−0.796766	−	0.604288i	$-0.793458\pi$
$613$	−39.4540	−1.59353	−0.796766	+	0.604288i	$0.793458\pi$
$614$	−34.2451	−1.38202
$615$	−11.4508	−0.461741
$616$	−0.358624	−0.0144494
$617$	−21.8101	−0.878042	−0.439021	−	0.898477i	$-0.644675\pi$
$617$	−21.8101	−0.878042	−0.439021	+	0.898477i	$0.644675\pi$
$618$	−14.6676	−0.590018
$619$	−2.88319	−0.115885	−0.0579426	−	0.998320i	$-0.518454\pi$
$619$	−2.88319	−0.115885	−0.0579426	+	0.998320i	$0.518454\pi$
$620$	111.196	4.46573
$621$	3.36888	0.135189
$622$	−34.7635	−1.39389
$623$	14.2877	0.572425
$624$	−5.38178	−0.215444
$625$	18.4630	0.738519
$626$	−59.8450	−2.39189
$627$	−0.0109887	−0.000438845 0
$628$	13.6258	0.543729
$629$	0.278819	0.0111173
$630$	69.2951	2.76078
$631$	27.8292	1.10786	0.553931	−	0.832563i	$-0.313127\pi$
$631$	27.8292	1.10786	0.553931	+	0.832563i	$0.313127\pi$
$632$	65.5318	2.60671
$633$	8.00334	0.318104
$634$	−15.3783	−0.610751
$635$	−1.26749	−0.0502989
$636$	−12.0479	−0.477732
$637$	−0.522451	−0.0207002
$638$	−0.0393473	−0.00155778
$639$	26.4207	1.04519
$640$	226.887	8.96849
$641$	3.74769	0.148025	0.0740124	−	0.997257i	$-0.476420\pi$
$641$	3.74769	0.148025	0.0740124	+	0.997257i	$0.476420\pi$
$642$	−9.63458	−0.380247
$643$	37.1968	1.46690	0.733449	−	0.679744i	$-0.237909\pi$
$643$	37.1968	1.46690	0.733449	+	0.679744i	$0.237909\pi$
$644$	−14.3856	−0.566873
$645$	6.91378	0.272230
$646$	0.294660	0.0115932
$647$	35.0638	1.37850	0.689250	−	0.724523i	$-0.257940\pi$
$647$	35.0638	1.37850	0.689250	+	0.724523i	$0.257940\pi$
$648$	−62.7153	−2.46369
$649$	0.0945392	0.00371099
$650$	−14.3133	−0.561412
$651$	−7.27051	−0.284954
$652$	9.52132	0.372884
$653$	28.9524	1.13299	0.566497	−	0.824064i	$-0.308298\pi$
$653$	28.9524	1.13299	0.566497	+	0.824064i	$0.308298\pi$
$654$	−26.7575	−1.04630
$655$	8.74722	0.341782
$656$	−88.9942	−3.47464
$657$	−7.59143	−0.296170
$658$	−47.5904	−1.85527
$659$	−16.0208	−0.624082	−0.312041	−	0.950069i	$-0.601013\pi$
$659$	−16.0208	−0.624082	−0.312041	+	0.950069i	$0.601013\pi$
$660$	−0.179029	−0.00696869
$661$	9.03118	0.351272	0.175636	−	0.984455i	$-0.443802\pi$
$661$	9.03118	0.351272	0.175636	+	0.984455i	$0.443802\pi$
$662$	58.1528	2.26017
$663$	−0.0248391	−0.000964671 0
$664$	17.6065	0.683265
$665$	−12.5271	−0.485781
$666$	25.9878	1.00701
$667$	−1.02562	−0.0397120
$668$	−105.379	−4.07722
$669$	0.370672	0.0143310
$670$	98.5520	3.80740
$671$	0.0193654	0.000747592 0
$672$	−38.6516	−1.49102
$673$	−18.7086	−0.721163	−0.360582	−	0.932728i	$-0.617422\pi$
$673$	−18.7086	−0.721163	−0.360582	+	0.932728i	$0.617422\pi$
$674$	71.0502	2.73675
$675$	31.3717	1.20750
$676$	−72.5801	−2.79154
$677$	41.6821	1.60197	0.800987	−	0.598681i	$-0.204308\pi$
$677$	41.6821	1.60197	0.800987	+	0.598681i	$0.204308\pi$
$678$	−25.0749	−0.962997
$679$	36.8700	1.41494
$680$	3.11946	0.119626
$681$	1.92453	0.0737480
$682$	−0.200838	−0.00769047
$683$	−0.488780	−0.0187026	−0.00935132	−	0.999956i	$-0.502977\pi$
$683$	−0.488780	−0.0187026	−0.00935132	+	0.999956i	$0.502977\pi$
$684$	20.3409	0.777753
$685$	12.8567	0.491227
$686$	−54.3422	−2.07480
$687$	−2.72425	−0.103937
$688$	53.7331	2.04855
$689$	1.96307	0.0747870
$690$	−6.30072	−0.239864
$691$	−18.3324	−0.697397	−0.348698	−	0.937235i	$-0.613376\pi$
$691$	−18.3324	−0.697397	−0.348698	+	0.937235i	$0.613376\pi$
$692$	24.1555	0.918256
$693$	−0.0926962	−0.00352124
$694$	−17.9771	−0.682403
$695$	−37.3488	−1.41672
$696$	−5.97666	−0.226545
$697$	−0.410744	−0.0155580
$698$	−37.0206	−1.40125
$699$	−4.34787	−0.164451
$700$	−133.962	−5.06328
$701$	−0.591886	−0.0223552	−0.0111776	−	0.999938i	$-0.503558\pi$
$701$	−0.591886	−0.0223552	−0.0111776	+	0.999938i	$0.503558\pi$
$702$	−4.92269	−0.185795
$703$	−4.69806	−0.177191
$704$	−0.580434	−0.0218759
$705$	−15.4377	−0.581418
$706$	−47.3144	−1.78070
$707$	9.51668	0.357912
$708$	22.0991	0.830536
$709$	−40.1102	−1.50637	−0.753185	−	0.657809i	$-0.771484\pi$
$709$	−40.1102	−1.50637	−0.753185	+	0.657809i	$0.771484\pi$
$710$	−105.068	−3.94312
$711$	16.9385	0.635242
$712$	59.9496	2.24671
$713$	−5.23497	−0.196051
$714$	−0.313889	−0.0117470
$715$	0.0291707	0.00109092
$716$	−101.566	−3.79570
$717$	−1.39981	−0.0522767
$718$	42.1145	1.57170
$719$	15.2876	0.570130	0.285065	−	0.958508i	$-0.407985\pi$
$719$	15.2876	0.570130	0.285065	+	0.958508i	$0.407985\pi$
$720$	174.700	6.51067
$721$	22.3679	0.833024
$722$	47.7957	1.77877
$723$	−0.364002	−0.0135374
$724$	−23.9575	−0.890374
$725$	−9.55074	−0.354706
$726$	−17.7153	−0.657475
$727$	21.0303	0.779971	0.389986	−	0.920821i	$-0.372480\pi$
$727$	21.0303	0.779971	0.389986	+	0.920821i	$0.372480\pi$
$728$	13.6592	0.506245
$729$	−10.4953	−0.388715
$730$	30.1890	1.11734
$731$	0.248000	0.00917260
$732$	4.52678	0.167315
$733$	−33.8263	−1.24940	−0.624701	−	0.780864i	$-0.714779\pi$
$733$	−33.8263	−1.24940	−0.624701	+	0.780864i	$0.714779\pi$
$734$	−1.38233	−0.0510227
$735$	−2.14165	−0.0789961
$736$	−27.8303	−1.02584
$737$	−0.131833	−0.00485614
$738$	−38.2840	−1.40925
$739$	21.6003	0.794580	0.397290	−	0.917693i	$-0.369951\pi$
$739$	21.6003	0.794580	0.397290	+	0.917693i	$0.369951\pi$
$740$	−76.5414	−2.81372
$741$	0.418534	0.0153752
$742$	24.8071	0.910697
$743$	−33.8548	−1.24201	−0.621007	−	0.783805i	$-0.713276\pi$
$743$	−33.8548	−1.24201	−0.621007	+	0.783805i	$0.713276\pi$
$744$	−30.5062	−1.11841
$745$	37.4900	1.37353
$746$	−75.4155	−2.76116
$747$	4.55088	0.166508
$748$	−0.00642183	−0.000234805 0
$749$	14.6926	0.536856
$750$	−27.9568	−1.02084
$751$	−33.1667	−1.21027	−0.605135	−	0.796123i	$-0.706881\pi$
$751$	−33.1667	−1.21027	−0.605135	+	0.796123i	$0.706881\pi$
$752$	−119.980	−4.37522
$753$	−5.51220	−0.200876
$754$	1.49865	0.0545778
$755$	−14.1251	−0.514065
$756$	−46.0729	−1.67566
$757$	33.7806	1.22778	0.613888	−	0.789393i	$-0.289605\pi$
$757$	33.7806	1.22778	0.613888	+	0.789393i	$0.289605\pi$
$758$	56.8760	2.06583
$759$	0.00842849	0.000305935 0
$760$	−52.5624	−1.90664
$761$	29.7072	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$761$	29.7072	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$762$	0.535138	0.0193860
$763$	40.8048	1.47723
$764$	83.4172	3.01793
$765$	0.806309	0.0291522
$766$	4.07082	0.147085
$767$	−3.60079	−0.130017
$768$	−48.2771	−1.74205
$769$	37.0849	1.33732	0.668658	−	0.743570i	$-0.266869\pi$
$769$	37.0849	1.33732	0.668658	+	0.743570i	$0.266869\pi$
$770$	0.368626	0.0132844
$771$	1.43523	0.0516886
$772$	−65.0223	−2.34020
$773$	−2.41679	−0.0869259	−0.0434630	−	0.999055i	$-0.513839\pi$
$773$	−2.41679	−0.0869259	−0.0434630	+	0.999055i	$0.513839\pi$
$774$	23.1152	0.830859
$775$	−48.7492	−1.75112
$776$	154.702	5.55350
$777$	5.00464	0.179541
$778$	72.3857	2.59515
$779$	6.92096	0.247969
$780$	6.81882	0.244153
$781$	0.140549	0.00502925
$782$	−0.226009	−0.00808207
$783$	−3.28474	−0.117387
$784$	−16.6447	−0.594453
$785$	−9.10101	−0.324829
$786$	−3.69309	−0.131728
$787$	36.0198	1.28397	0.641984	−	0.766718i	$-0.278112\pi$
$787$	36.0198	1.28397	0.641984	+	0.766718i	$0.278112\pi$
$788$	−14.8413	−0.528698
$789$	7.62359	0.271407
$790$	−67.3595	−2.39654
$791$	38.2389	1.35962
$792$	−0.388943	−0.0138205
$793$	−0.737586	−0.0261924
$794$	−56.6122	−2.00909
$795$	8.04710	0.285401
$796$	−38.3805	−1.36036
$797$	−2.47493	−0.0876666	−0.0438333	−	0.999039i	$-0.513957\pi$
$797$	−2.47493	−0.0876666	−0.0438333	+	0.999039i	$0.513957\pi$
$798$	5.28897	0.187228
$799$	−0.553757	−0.0195905
$800$	−259.161	−9.16273
$801$	15.4956	0.547510
$802$	−59.7899	−2.11125
$803$	−0.0403839	−0.00142512
$804$	−30.8168	−1.08683
$805$	9.60851	0.338655
$806$	7.64947	0.269441
$807$	−4.84669	−0.170612
$808$	39.9309	1.40477
$809$	−17.5044	−0.615423	−0.307711	−	0.951480i	$-0.599563\pi$
$809$	−17.5044	−0.615423	−0.307711	+	0.951480i	$0.599563\pi$
$810$	64.4644	2.26505
$811$	−22.0166	−0.773108	−0.386554	−	0.922267i	$-0.626335\pi$
$811$	−22.0166	−0.773108	−0.386554	+	0.922267i	$0.626335\pi$
$812$	14.0263	0.492228
$813$	−10.3614	−0.363389
$814$	0.138246	0.00484553
$815$	−6.35952	−0.222764
$816$	−0.791345	−0.0277026
$817$	−4.17875	−0.146196
$818$	84.4674	2.95333
$819$	3.53060	0.123369
$820$	112.757	3.93766
$821$	51.3248	1.79125	0.895623	−	0.444813i	$-0.146730\pi$
$821$	51.3248	1.79125	0.895623	+	0.444813i	$0.146730\pi$
$822$	−5.42810	−0.189327
$823$	−6.12741	−0.213588	−0.106794	−	0.994281i	$-0.534059\pi$
$823$	−6.12741	−0.213588	−0.106794	+	0.994281i	$0.534059\pi$
$824$	93.8532	3.26953
$825$	0.0784878	0.00273259
$826$	−45.5028	−1.58325
$827$	−33.7956	−1.17519	−0.587594	−	0.809156i	$-0.699925\pi$
$827$	−33.7956	−1.17519	−0.587594	+	0.809156i	$0.699925\pi$
$828$	−15.6018	−0.542200
$829$	0.125209	0.00434868	0.00217434	−	0.999998i	$-0.499308\pi$
$829$	0.125209	0.00434868	0.00217434	+	0.999998i	$0.499308\pi$
$830$	−18.0976	−0.628175
$831$	−0.579971	−0.0201190
$832$	22.1075	0.766439
$833$	−0.0768219	−0.00266172
$834$	15.7687	0.546027
$835$	70.3849	2.43577
$836$	0.108207	0.00374241
$837$	−16.7661	−0.579520
$838$	40.2514	1.39046
$839$	22.2344	0.767616	0.383808	−	0.923413i	$-0.374612\pi$
$839$	22.2344	0.767616	0.383808	+	0.923413i	$0.374612\pi$
$840$	55.9925	1.93193
$841$	1.00000	0.0344828
$842$	9.38565	0.323451
$843$	17.4315	0.600371
$844$	−78.8099	−2.71275
$845$	48.4780	1.66769
$846$	−51.6137	−1.77452
$847$	27.0155	0.928264
$848$	62.5411	2.14767
$849$	12.0671	0.414143
$850$	−2.10464	−0.0721887
$851$	3.60349	0.123526
$852$	32.8543	1.12557
$853$	−43.1292	−1.47672	−0.738359	−	0.674408i	$-0.764399\pi$
$853$	−43.1292	−1.47672	−0.738359	+	0.674408i	$0.764399\pi$
$854$	−9.32079	−0.318951
$855$	−13.5862	−0.464637
$856$	61.6485	2.10710
$857$	16.3392	0.558136	0.279068	−	0.960271i	$-0.409975\pi$
$857$	16.3392	0.558136	0.279068	+	0.960271i	$0.409975\pi$
$858$	−0.0123159	−0.000420458 0
$859$	1.94886	0.0664942	0.0332471	−	0.999447i	$-0.489415\pi$
$859$	1.94886	0.0664942	0.0332471	+	0.999447i	$0.489415\pi$
$860$	−68.0808	−2.32154
$861$	−7.37262	−0.251258
$862$	66.5618	2.26710
$863$	50.7725	1.72832	0.864158	−	0.503221i	$-0.167852\pi$
$863$	50.7725	1.72832	0.864158	+	0.503221i	$0.167852\pi$
$864$	−89.1321	−3.03234
$865$	−16.1341	−0.548575
$866$	56.4145	1.91704
$867$	9.85585	0.334722
$868$	71.5936	2.43004
$869$	0.0901069	0.00305667
$870$	6.14335	0.208279
$871$	5.02124	0.170138
$872$	171.212	5.79798
$873$	39.9870	1.35336
$874$	3.80821	0.128815
$875$	42.6338	1.44128
$876$	−9.43998	−0.318947
$877$	−34.8816	−1.17787	−0.588934	−	0.808181i	$-0.700452\pi$
$877$	−34.8816	−1.17787	−0.588934	+	0.808181i	$0.700452\pi$
$878$	−36.7872	−1.24151
$879$	−10.6187	−0.358160
$880$	0.929343	0.0313282
$881$	−33.7728	−1.13783	−0.568917	−	0.822395i	$-0.692638\pi$
$881$	−33.7728	−1.13783	−0.568917	+	0.822395i	$0.692638\pi$
$882$	−7.16030	−0.241100
$883$	−46.2650	−1.55694	−0.778471	−	0.627681i	$-0.784004\pi$
$883$	−46.2650	−1.55694	−0.778471	+	0.627681i	$0.784004\pi$
$884$	0.244594	0.00822657
$885$	−14.7605	−0.496170
$886$	41.6437	1.39905
$887$	24.3122	0.816324	0.408162	−	0.912909i	$-0.366170\pi$
$887$	24.3122	0.816324	0.408162	+	0.912909i	$0.366170\pi$
$888$	20.9989	0.704678
$889$	−0.816078	−0.0273704
$890$	−61.6216	−2.06556
$891$	−0.0862342	−0.00288895
$892$	−3.65005	−0.122213
$893$	9.33070	0.312240
$894$	−15.8284	−0.529380
$895$	67.8384	2.26759
$896$	146.082	4.88024
$897$	−0.321023	−0.0107186
$898$	73.8189	2.46337
$899$	5.10423	0.170235
$900$	−145.287	−4.84290
$901$	0.288653	0.00961641
$902$	−0.203658	−0.00678108
$903$	4.45145	0.148135
$904$	160.446	5.33636
$905$	16.0018	0.531918
$906$	5.96365	0.198129
$907$	−37.9664	−1.26065	−0.630326	−	0.776330i	$-0.717079\pi$
$907$	−37.9664	−1.26065	−0.630326	+	0.776330i	$0.717079\pi$
$908$	−18.9510	−0.628912
$909$	10.3212	0.342334
$910$	−14.0402	−0.465427
$911$	−1.26322	−0.0418523	−0.0209262	−	0.999781i	$-0.506661\pi$
$911$	−1.26322	−0.0418523	−0.0209262	+	0.999781i	$0.506661\pi$
$912$	13.3340	0.441534
$913$	0.0242091	0.000801206 0
$914$	−58.5365	−1.93621
$915$	−3.02354	−0.0999553
$916$	26.8260	0.886356
$917$	5.63192	0.185982
$918$	−0.723840	−0.0238903
$919$	−3.84499	−0.126834	−0.0634172	−	0.997987i	$-0.520200\pi$
$919$	−3.84499	−0.126834	−0.0634172	+	0.997987i	$0.520200\pi$
$920$	40.3162	1.32919
$921$	−7.15234	−0.235677
$922$	10.7608	0.354388
$923$	−5.35322	−0.176203
$924$	−0.115268	−0.00379204
$925$	33.5564	1.10333
$926$	87.5875	2.87830
$927$	24.2589	0.796767
$928$	27.1352	0.890756
$929$	−29.0391	−0.952742	−0.476371	−	0.879244i	$-0.658048\pi$
$929$	−29.0391	−0.952742	−0.476371	+	0.879244i	$0.658048\pi$
$930$	31.3571	1.02824
$931$	1.29443	0.0424234
$932$	42.8139	1.40242
$933$	−7.26060	−0.237701
$934$	75.0144	2.45455
$935$	0.00428929	0.000140275 0
$936$	14.8140	0.484210
$937$	−37.0185	−1.20934	−0.604671	−	0.796475i	$-0.706696\pi$
$937$	−37.0185	−1.20934	−0.604671	+	0.796475i	$0.706696\pi$
$938$	63.4529	2.07181
$939$	−12.4991	−0.407892
$940$	152.017	4.95825
$941$	24.0246	0.783178	0.391589	−	0.920140i	$-0.371925\pi$
$941$	24.0246	0.783178	0.391589	+	0.920140i	$0.371925\pi$
$942$	3.84247	0.125194
$943$	−5.30849	−0.172868
$944$	−114.717	−3.73372
$945$	30.7732	1.00105
$946$	0.122965	0.00399794
$947$	26.6230	0.865131	0.432566	−	0.901602i	$-0.357608\pi$
$947$	26.6230	0.865131	0.432566	+	0.901602i	$0.357608\pi$
$948$	21.0630	0.684096
$949$	1.53813	0.0499299
$950$	35.4628	1.15057
$951$	−3.21188	−0.104152
$952$	2.00847	0.0650950
$953$	38.5440	1.24856	0.624281	−	0.781200i	$-0.285392\pi$
$953$	38.5440	1.24856	0.624281	+	0.781200i	$0.285392\pi$
$954$	26.9043	0.871059
$955$	−55.7164	−1.80294
$956$	13.7840	0.445808
$957$	−0.00821798	−0.000265649 0
$958$	52.5877	1.69903
$959$	8.27778	0.267304
$960$	90.6239	2.92488
$961$	−4.94688	−0.159577
$962$	−5.26550	−0.169767
$963$	15.9347	0.513489
$964$	3.58437	0.115445
$965$	43.4300	1.39806
$966$	−4.05673	−0.130523
$967$	−23.6778	−0.761426	−0.380713	−	0.924693i	$-0.624321\pi$
$967$	−23.6778	−0.761426	−0.380713	+	0.924693i	$0.624321\pi$
$968$	113.354	3.64334
$969$	0.0615419	0.00197701
$970$	−159.017	−5.10573
$971$	21.9696	0.705036	0.352518	−	0.935805i	$-0.385325\pi$
$971$	21.9696	0.705036	0.352518	+	0.935805i	$0.385325\pi$
$972$	−76.4357	−2.45168
$973$	−24.0471	−0.770915
$974$	57.5180	1.84299
$975$	−2.98943	−0.0957384
$976$	−23.4986	−0.752173
$977$	−41.6113	−1.33126	−0.665632	−	0.746280i	$-0.731838\pi$
$977$	−41.6113	−1.33126	−0.665632	+	0.746280i	$0.731838\pi$
$978$	2.68500	0.0858569
$979$	0.0824313	0.00263452
$980$	21.0891	0.673667
$981$	44.2544	1.41294
$982$	109.503	3.49437
$983$	−49.5585	−1.58067	−0.790336	−	0.612674i	$-0.790094\pi$
$983$	−49.5585	−1.58067	−0.790336	+	0.612674i	$0.790094\pi$
$984$	−30.9347	−0.986161
$985$	9.91283	0.315849
$986$	0.220364	0.00701783
$987$	−9.93961	−0.316381
$988$	−4.12136	−0.131118
$989$	3.20517	0.101919
$990$	0.399790	0.0127062
$991$	22.9806	0.730002	0.365001	−	0.931007i	$-0.381069\pi$
$991$	22.9806	0.730002	0.365001	+	0.931007i	$0.381069\pi$
$992$	138.504	4.39751
$993$	12.1456	0.385430
$994$	−67.6480	−2.14567
$995$	25.6352	0.812692
$996$	5.65904	0.179313
$997$	27.1977	0.861360	0.430680	−	0.902505i	$-0.358274\pi$
$997$	27.1977	0.861360	0.430680	+	0.902505i	$0.358274\pi$
$998$	10.6255	0.336344
$999$	11.5409	0.365138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.3	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.3	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77688 q^{2} -0.579971 q^{3} +5.71104 q^{4} -3.81454 q^{5} +1.61051 q^{6} -2.45600 q^{7} -10.3051 q^{8} -2.66363 q^{9} +O(q^{10})\)	\(q-2.77688 q^{2} -0.579971 q^{3} +5.71104 q^{4} -3.81454 q^{5} +1.61051 q^{6} -2.45600 q^{7} -10.3051 q^{8} -2.66363 q^{9} +10.5925 q^{10} -0.0141696 q^{11} -3.31224 q^{12} +0.539691 q^{13} +6.82001 q^{14} +2.21232 q^{15} +17.1939 q^{16} +0.0793569 q^{17} +7.39658 q^{18} -1.33715 q^{19} -21.7850 q^{20} +1.42441 q^{21} +0.0393473 q^{22} +1.02562 q^{23} +5.97666 q^{24} +9.55074 q^{25} -1.49865 q^{26} +3.28474 q^{27} -14.0263 q^{28} -1.00000 q^{29} -6.14335 q^{30} -5.10423 q^{31} -27.1352 q^{32} +0.00821798 q^{33} -0.220364 q^{34} +9.36853 q^{35} -15.2121 q^{36} +3.51349 q^{37} +3.71310 q^{38} -0.313005 q^{39} +39.3093 q^{40} -5.17591 q^{41} -3.95541 q^{42} +3.12512 q^{43} -0.0809234 q^{44} +10.1605 q^{45} -2.84801 q^{46} -6.97805 q^{47} -9.97198 q^{48} -0.968056 q^{49} -26.5212 q^{50} -0.0460247 q^{51} +3.08220 q^{52} +3.63740 q^{53} -9.12133 q^{54} +0.0540507 q^{55} +25.3094 q^{56} +0.775508 q^{57} +2.77688 q^{58} -6.67196 q^{59} +12.6347 q^{60} -1.36668 q^{61} +14.1738 q^{62} +6.54189 q^{63} +40.9632 q^{64} -2.05867 q^{65} -0.0228203 q^{66} +9.30393 q^{67} +0.453211 q^{68} -0.594827 q^{69} -26.0152 q^{70} -9.91905 q^{71} +27.4490 q^{72} +2.85003 q^{73} -9.75652 q^{74} -5.53915 q^{75} -7.63652 q^{76} +0.0348006 q^{77} +0.869176 q^{78} -6.35916 q^{79} -65.5870 q^{80} +6.08585 q^{81} +14.3729 q^{82} -1.70852 q^{83} +8.13487 q^{84} -0.302710 q^{85} -8.67807 q^{86} +0.579971 q^{87} +0.146020 q^{88} -5.81746 q^{89} -28.2146 q^{90} -1.32548 q^{91} +5.85733 q^{92} +2.96030 q^{93} +19.3772 q^{94} +5.10061 q^{95} +15.7376 q^{96} -15.0122 q^{97} +2.68817 q^{98} +0.0377427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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