LMFDB - Embedded newform 671.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.04858$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04858 q^{2} -3.34590 q^{3} -0.900472 q^{4} -4.37157 q^{5} -3.50846 q^{6} -3.70774 q^{7} -3.04139 q^{8} +8.19507 q^{9} +O(q^{10})$	\(q+1.04858 q^{2} -3.34590 q^{3} -0.900472 q^{4} -4.37157 q^{5} -3.50846 q^{6} -3.70774 q^{7} -3.04139 q^{8} +8.19507 q^{9} -4.58396 q^{10} +1.00000 q^{11} +3.01289 q^{12} -2.73457 q^{13} -3.88788 q^{14} +14.6269 q^{15} -1.38821 q^{16} -3.57396 q^{17} +8.59322 q^{18} -3.41697 q^{19} +3.93648 q^{20} +12.4058 q^{21} +1.04858 q^{22} -3.58464 q^{23} +10.1762 q^{24} +14.1107 q^{25} -2.86742 q^{26} -17.3822 q^{27} +3.33872 q^{28} -1.76305 q^{29} +15.3375 q^{30} +0.137590 q^{31} +4.62712 q^{32} -3.34590 q^{33} -3.74760 q^{34} +16.2087 q^{35} -7.37943 q^{36} -3.66060 q^{37} -3.58298 q^{38} +9.14960 q^{39} +13.2957 q^{40} +1.23012 q^{41} +13.0085 q^{42} -5.20323 q^{43} -0.900472 q^{44} -35.8253 q^{45} -3.75880 q^{46} +1.30362 q^{47} +4.64481 q^{48} +6.74736 q^{49} +14.7962 q^{50} +11.9581 q^{51} +2.46240 q^{52} -6.66269 q^{53} -18.2267 q^{54} -4.37157 q^{55} +11.2767 q^{56} +11.4329 q^{57} -1.84871 q^{58} -8.84884 q^{59} -13.1711 q^{60} -1.00000 q^{61} +0.144275 q^{62} -30.3852 q^{63} +7.62834 q^{64} +11.9544 q^{65} -3.50846 q^{66} +0.443376 q^{67} +3.21825 q^{68} +11.9939 q^{69} +16.9962 q^{70} -13.9796 q^{71} -24.9244 q^{72} -6.52034 q^{73} -3.83845 q^{74} -47.2129 q^{75} +3.07689 q^{76} -3.70774 q^{77} +9.59412 q^{78} -10.2318 q^{79} +6.06865 q^{80} +33.5739 q^{81} +1.28989 q^{82} +4.85996 q^{83} -11.1710 q^{84} +15.6238 q^{85} -5.45603 q^{86} +5.89900 q^{87} -3.04139 q^{88} +6.77646 q^{89} -37.5659 q^{90} +10.1391 q^{91} +3.22787 q^{92} -0.460364 q^{93} +1.36696 q^{94} +14.9375 q^{95} -15.4819 q^{96} +10.0223 q^{97} +7.07518 q^{98} +8.19507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	1.04858	0.741461	0.370730	−	0.928741i	$-0.379107\pi$
$2$	1.04858	0.741461	0.370730	+	0.928741i	$0.379107\pi$
$3$	−3.34590	−1.93176	−0.965879	−	0.258994i	$-0.916609\pi$
$3$	−3.34590	−1.93176	−0.965879	+	0.258994i	$0.916609\pi$
$4$	−0.900472	−0.450236
$5$	−4.37157	−1.95503	−0.977514	−	0.210871i	$-0.932370\pi$
$5$	−4.37157	−1.95503	−0.977514	+	0.210871i	$0.932370\pi$
$6$	−3.50846	−1.43232
$7$	−3.70774	−1.40140	−0.700698	−	0.713458i	$-0.747128\pi$
$7$	−3.70774	−1.40140	−0.700698	+	0.713458i	$0.747128\pi$
$8$	−3.04139	−1.07529
$9$	8.19507	2.73169
$10$	−4.58396	−1.44958
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.01289	0.869747
$13$	−2.73457	−0.758433	−0.379216	−	0.925308i	$-0.623806\pi$
$13$	−2.73457	−0.758433	−0.379216	+	0.925308i	$0.623806\pi$
$14$	−3.88788	−1.03908
$15$	14.6269	3.77664
$16$	−1.38821	−0.347052
$17$	−3.57396	−0.866813	−0.433407	−	0.901199i	$-0.642689\pi$
$17$	−3.57396	−0.866813	−0.433407	+	0.901199i	$0.642689\pi$
$18$	8.59322	2.02544
$19$	−3.41697	−0.783907	−0.391953	−	0.919985i	$-0.628201\pi$
$19$	−3.41697	−0.783907	−0.391953	+	0.919985i	$0.628201\pi$
$20$	3.93648	0.880223
$21$	12.4058	2.70716
$22$	1.04858	0.223559
$23$	−3.58464	−0.747450	−0.373725	−	0.927540i	$-0.621920\pi$
$23$	−3.58464	−0.747450	−0.373725	+	0.927540i	$0.621920\pi$
$24$	10.1762	2.07721
$25$	14.1107	2.82213
$26$	−2.86742	−0.562348
$27$	−17.3822	−3.34520
$28$	3.33872	0.630958
$29$	−1.76305	−0.327391	−0.163695	−	0.986511i	$-0.552341\pi$
$29$	−1.76305	−0.327391	−0.163695	+	0.986511i	$0.552341\pi$
$30$	15.3375	2.80023
$31$	0.137590	0.0247120	0.0123560	−	0.999924i	$-0.496067\pi$
$31$	0.137590	0.0247120	0.0123560	+	0.999924i	$0.496067\pi$
$32$	4.62712	0.817968
$33$	−3.34590	−0.582447
$34$	−3.74760	−0.642708
$35$	16.2087	2.73977
$36$	−7.37943	−1.22990
$37$	−3.66060	−0.601800	−0.300900	−	0.953656i	$-0.597287\pi$
$37$	−3.66060	−0.601800	−0.300900	+	0.953656i	$0.597287\pi$
$38$	−3.58298	−0.581236
$39$	9.14960	1.46511
$40$	13.2957	2.10223
$41$	1.23012	0.192113	0.0960563	−	0.995376i	$-0.469377\pi$
$41$	1.23012	0.192113	0.0960563	+	0.995376i	$0.469377\pi$
$42$	13.0085	2.00725
$43$	−5.20323	−0.793486	−0.396743	−	0.917930i	$-0.629860\pi$
$43$	−5.20323	−0.793486	−0.396743	+	0.917930i	$0.629860\pi$
$44$	−0.900472	−0.135751
$45$	−35.8253	−5.34053
$46$	−3.75880	−0.554205
$47$	1.30362	0.190153	0.0950764	−	0.995470i	$-0.469690\pi$
$47$	1.30362	0.190153	0.0950764	+	0.995470i	$0.469690\pi$
$48$	4.64481	0.670420
$49$	6.74736	0.963909
$50$	14.7962	2.09250
$51$	11.9581	1.67447
$52$	2.46240	0.341474
$53$	−6.66269	−0.915190	−0.457595	−	0.889161i	$-0.651289\pi$
$53$	−6.66269	−0.915190	−0.457595	+	0.889161i	$0.651289\pi$
$54$	−18.2267	−2.48034
$55$	−4.37157	−0.589463
$56$	11.2767	1.50691
$57$	11.4329	1.51432
$58$	−1.84871	−0.242747
$59$	−8.84884	−1.15202	−0.576010	−	0.817443i	$-0.695391\pi$
$59$	−8.84884	−1.15202	−0.576010	+	0.817443i	$0.695391\pi$
$60$	−13.1711	−1.70038
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.144275	0.0183230
$63$	−30.3852	−3.82818
$64$	7.62834	0.953543
$65$	11.9544	1.48276
$66$	−3.50846	−0.431862
$67$	0.443376	0.0541670	0.0270835	−	0.999633i	$-0.491378\pi$
$67$	0.443376	0.0541670	0.0270835	+	0.999633i	$0.491378\pi$
$68$	3.21825	0.390270
$69$	11.9939	1.44389
$70$	16.9962	2.03143
$71$	−13.9796	−1.65908	−0.829539	−	0.558448i	$-0.811397\pi$
$71$	−13.9796	−1.65908	−0.829539	+	0.558448i	$0.811397\pi$
$72$	−24.9244	−2.93737
$73$	−6.52034	−0.763149	−0.381574	−	0.924338i	$-0.624618\pi$
$73$	−6.52034	−0.763149	−0.381574	+	0.924338i	$0.624618\pi$
$74$	−3.83845	−0.446211
$75$	−47.2129	−5.45168
$76$	3.07689	0.352943
$77$	−3.70774	−0.422537
$78$	9.59412	1.08632
$79$	−10.2318	−1.15116	−0.575582	−	0.817744i	$-0.695225\pi$
$79$	−10.2318	−1.15116	−0.575582	+	0.817744i	$0.695225\pi$
$80$	6.06865	0.678496
$81$	33.5739	3.73044
$82$	1.28989	0.142444
$83$	4.85996	0.533450	0.266725	−	0.963773i	$-0.414058\pi$
$83$	4.85996	0.533450	0.266725	+	0.963773i	$0.414058\pi$
$84$	−11.1710	−1.21886
$85$	15.6238	1.69464
$86$	−5.45603	−0.588339
$87$	5.89900	0.632439
$88$	−3.04139	−0.324213
$89$	6.77646	0.718303	0.359152	−	0.933279i	$-0.383066\pi$
$89$	6.77646	0.718303	0.359152	+	0.933279i	$0.383066\pi$
$90$	−37.5659	−3.95979
$91$	10.1391	1.06286
$92$	3.22787	0.336529
$93$	−0.460364	−0.0477376
$94$	1.36696	0.140991
$95$	14.9375	1.53256
$96$	−15.4819	−1.58012
$97$	10.0223	1.01761	0.508807	−	0.860881i	$-0.330087\pi$
$97$	10.0223	1.01761	0.508807	+	0.860881i	$0.330087\pi$
$98$	7.07518	0.714701
$99$	8.19507	0.823635
$100$	−12.7063	−1.27063
$101$	3.74654	0.372795	0.186398	−	0.982474i	$-0.440319\pi$
$101$	3.74654	0.372795	0.186398	+	0.982474i	$0.440319\pi$
$102$	12.5391	1.24156
$103$	−2.80382	−0.276268	−0.138134	−	0.990414i	$-0.544111\pi$
$103$	−2.80382	−0.276268	−0.138134	+	0.990414i	$0.544111\pi$
$104$	8.31688	0.815537
$105$	−54.2327	−5.29257
$106$	−6.98639	−0.678578
$107$	−2.77807	−0.268566	−0.134283	−	0.990943i	$-0.542873\pi$
$107$	−2.77807	−0.268566	−0.134283	+	0.990943i	$0.542873\pi$
$108$	15.6522	1.50613
$109$	17.2902	1.65610	0.828051	−	0.560653i	$-0.189450\pi$
$109$	17.2902	1.65610	0.828051	+	0.560653i	$0.189450\pi$
$110$	−4.58396	−0.437064
$111$	12.2480	1.16253
$112$	5.14712	0.486357
$113$	0.779327	0.0733129	0.0366565	−	0.999328i	$-0.488329\pi$
$113$	0.779327	0.0733129	0.0366565	+	0.999328i	$0.488329\pi$
$114$	11.9883	1.12281
$115$	15.6705	1.46128
$116$	1.58758	0.147403
$117$	−22.4100	−2.07180
$118$	−9.27875	−0.854178
$119$	13.2513	1.21475
$120$	−44.4860	−4.06100
$121$	1.00000	0.0909091
$122$	−1.04858	−0.0949343
$123$	−4.11587	−0.371115
$124$	−0.123896	−0.0111262
$125$	−39.8280	−3.56232
$126$	−31.8614	−2.83844
$127$	14.6452	1.29955	0.649775	−	0.760127i	$-0.274863\pi$
$127$	14.6452	1.29955	0.649775	+	0.760127i	$0.274863\pi$
$128$	−1.25529	−0.110953
$129$	17.4095	1.53282
$130$	12.5352	1.09941
$131$	−19.4616	−1.70037	−0.850184	−	0.526485i	$-0.823510\pi$
$131$	−19.4616	−1.70037	−0.850184	+	0.526485i	$0.823510\pi$
$132$	3.01289	0.262238
$133$	12.6693	1.09856
$134$	0.464917	0.0401627
$135$	75.9875	6.53997
$136$	10.8698	0.932078
$137$	−3.49132	−0.298284	−0.149142	−	0.988816i	$-0.547651\pi$
$137$	−3.49132	−0.298284	−0.149142	+	0.988816i	$0.547651\pi$
$138$	12.5766	1.07059
$139$	16.4285	1.39345	0.696723	−	0.717341i	$-0.254641\pi$
$139$	16.4285	1.39345	0.696723	+	0.717341i	$0.254641\pi$
$140$	−14.5955	−1.23354
$141$	−4.36179	−0.367329
$142$	−14.6588	−1.23014
$143$	−2.73457	−0.228676
$144$	−11.3765	−0.948038
$145$	7.70731	0.640058
$146$	−6.83713	−0.565845
$147$	−22.5760	−1.86204
$148$	3.29627	0.270952
$149$	−0.249187	−0.0204142	−0.0102071	−	0.999948i	$-0.503249\pi$
$149$	−0.249187	−0.0204142	−0.0102071	+	0.999948i	$0.503249\pi$
$150$	−49.5067	−4.04221
$151$	1.97551	0.160765	0.0803824	−	0.996764i	$-0.474386\pi$
$151$	1.97551	0.160765	0.0803824	+	0.996764i	$0.474386\pi$
$152$	10.3923	0.842930
$153$	−29.2889	−2.36786
$154$	−3.88788	−0.313294
$155$	−0.601487	−0.0483126
$156$	−8.23895	−0.659644
$157$	12.3079	0.982273	0.491137	−	0.871083i	$-0.336582\pi$
$157$	12.3079	0.982273	0.491137	+	0.871083i	$0.336582\pi$
$158$	−10.7289	−0.853544
$159$	22.2927	1.76793
$160$	−20.2278	−1.59915
$161$	13.2909	1.04747
$162$	35.2051	2.76597
$163$	−20.7896	−1.62837	−0.814183	−	0.580609i	$-0.802815\pi$
$163$	−20.7896	−1.62837	−0.814183	+	0.580609i	$0.802815\pi$
$164$	−1.10769	−0.0864960
$165$	14.6269	1.13870
$166$	5.09608	0.395532
$167$	15.6872	1.21391	0.606956	−	0.794735i	$-0.292390\pi$
$167$	15.6872	1.21391	0.606956	+	0.794735i	$0.292390\pi$
$168$	−37.7307	−2.91099
$169$	−5.52214	−0.424780
$170$	16.3829	1.25651
$171$	−28.0023	−2.14139
$172$	4.68536	0.357256
$173$	−17.6768	−1.34394	−0.671970	−	0.740578i	$-0.734552\pi$
$173$	−17.6768	−1.34394	−0.671970	+	0.740578i	$0.734552\pi$
$174$	6.18560	0.468929
$175$	−52.3187	−3.95492
$176$	−1.38821	−0.104640
$177$	29.6073	2.22542
$178$	7.10569	0.532594
$179$	−4.13876	−0.309345	−0.154673	−	0.987966i	$-0.549432\pi$
$179$	−4.13876	−0.309345	−0.154673	+	0.987966i	$0.549432\pi$
$180$	32.2597	2.40450
$181$	−19.0239	−1.41404	−0.707018	−	0.707195i	$-0.749960\pi$
$181$	−19.0239	−1.41404	−0.707018	+	0.707195i	$0.749960\pi$
$182$	10.6317	0.788072
$183$	3.34590	0.247336
$184$	10.9023	0.803728
$185$	16.0026	1.17653
$186$	−0.482731	−0.0353955
$187$	−3.57396	−0.261354
$188$	−1.17388	−0.0856136
$189$	64.4487	4.68795
$190$	15.6633	1.13633
$191$	−11.8258	−0.855688	−0.427844	−	0.903853i	$-0.640727\pi$
$191$	−11.8258	−0.855688	−0.427844	+	0.903853i	$0.640727\pi$
$192$	−25.5237	−1.84201
$193$	11.4767	0.826111	0.413055	−	0.910706i	$-0.364462\pi$
$193$	11.4767	0.826111	0.413055	+	0.910706i	$0.364462\pi$
$194$	10.5093	0.754521
$195$	−39.9982	−2.86433
$196$	−6.07581	−0.433986
$197$	8.29185	0.590770	0.295385	−	0.955378i	$-0.404552\pi$
$197$	8.29185	0.590770	0.295385	+	0.955378i	$0.404552\pi$
$198$	8.59322	0.610693
$199$	−14.5450	−1.03106	−0.515532	−	0.856870i	$-0.672406\pi$
$199$	−14.5450	−1.03106	−0.515532	+	0.856870i	$0.672406\pi$
$200$	−42.9160	−3.03462
$201$	−1.48349	−0.104637
$202$	3.92857	0.276413
$203$	6.53695	0.458804
$204$	−10.7680	−0.753908
$205$	−5.37757	−0.375586
$206$	−2.94004	−0.204842
$207$	−29.3764	−2.04180
$208$	3.79615	0.263216
$209$	−3.41697	−0.236357
$210$	−56.8675	−3.92423
$211$	0.541157	0.0372548	0.0186274	−	0.999826i	$-0.494070\pi$
$211$	0.541157	0.0372548	0.0186274	+	0.999826i	$0.494070\pi$
$212$	5.99956	0.412052
$213$	46.7745	3.20494
$214$	−2.91304	−0.199131
$215$	22.7463	1.55129
$216$	52.8660	3.59708
$217$	−0.510150	−0.0346313
$218$	18.1302	1.22793
$219$	21.8164	1.47422
$220$	3.93648	0.265397
$221$	9.77324	0.657419
$222$	12.8431	0.861971
$223$	2.10788	0.141154	0.0705769	−	0.997506i	$-0.477516\pi$
$223$	2.10788	0.141154	0.0705769	+	0.997506i	$0.477516\pi$
$224$	−17.1562	−1.14630
$225$	115.638	7.70919
$226$	0.817190	0.0543587
$227$	15.7091	1.04265	0.521326	−	0.853358i	$-0.325438\pi$
$227$	15.7091	1.04265	0.521326	+	0.853358i	$0.325438\pi$
$228$	−10.2950	−0.681800
$229$	28.1097	1.85754	0.928769	−	0.370658i	$-0.120868\pi$
$229$	28.1097	1.85754	0.928769	+	0.370658i	$0.120868\pi$
$230$	16.4319	1.08349
$231$	12.4058	0.816238
$232$	5.36213	0.352041
$233$	−8.97992	−0.588294	−0.294147	−	0.955760i	$-0.595036\pi$
$233$	−8.97992	−0.588294	−0.294147	+	0.955760i	$0.595036\pi$
$234$	−23.4987	−1.53616
$235$	−5.69888	−0.371754
$236$	7.96813	0.518681
$237$	34.2345	2.22377
$238$	13.8951	0.900688
$239$	−21.2846	−1.37679	−0.688393	−	0.725338i	$-0.741684\pi$
$239$	−21.2846	−1.37679	−0.688393	+	0.725338i	$0.741684\pi$
$240$	−20.3051	−1.31069
$241$	6.87287	0.442721	0.221360	−	0.975192i	$-0.428950\pi$
$241$	6.87287	0.442721	0.221360	+	0.975192i	$0.428950\pi$
$242$	1.04858	0.0674055
$243$	−60.1885	−3.86110
$244$	0.900472	0.0576468
$245$	−29.4966	−1.88447
$246$	−4.31583	−0.275167
$247$	9.34394	0.594541
$248$	−0.418466	−0.0265726
$249$	−16.2610	−1.03050
$250$	−41.7630	−2.64132
$251$	14.0231	0.885127	0.442564	−	0.896737i	$-0.354069\pi$
$251$	14.0231	0.885127	0.442564	+	0.896737i	$0.354069\pi$
$252$	27.3610	1.72358
$253$	−3.58464	−0.225365
$254$	15.3567	0.963565
$255$	−52.2759	−3.27364
$256$	−16.5730	−1.03581
$257$	−16.1968	−1.01033	−0.505164	−	0.863024i	$-0.668568\pi$
$257$	−16.1968	−1.01033	−0.505164	+	0.863024i	$0.668568\pi$
$258$	18.2553	1.13653
$259$	13.5726	0.843359
$260$	−10.7646	−0.667590
$261$	−14.4483	−0.894329
$262$	−20.4071	−1.26076
$263$	−6.48123	−0.399650	−0.199825	−	0.979832i	$-0.564037\pi$
$263$	−6.48123	−0.399650	−0.199825	+	0.979832i	$0.564037\pi$
$264$	10.1762	0.626301
$265$	29.1264	1.78922
$266$	13.2848	0.814542
$267$	−22.6734	−1.38759
$268$	−0.399247	−0.0243879
$269$	−5.22267	−0.318432	−0.159216	−	0.987244i	$-0.550897\pi$
$269$	−5.22267	−0.318432	−0.159216	+	0.987244i	$0.550897\pi$
$270$	79.6793	4.84913
$271$	−29.4857	−1.79113	−0.895564	−	0.444932i	$-0.853228\pi$
$271$	−29.4857	−1.79113	−0.895564	+	0.444932i	$0.853228\pi$
$272$	4.96140	0.300829
$273$	−33.9244	−2.05320
$274$	−3.66095	−0.221166
$275$	14.1107	0.850905
$276$	−10.8001	−0.650092
$277$	−5.94054	−0.356932	−0.178466	−	0.983946i	$-0.557114\pi$
$277$	−5.94054	−0.356932	−0.178466	+	0.983946i	$0.557114\pi$
$278$	17.2266	1.03319
$279$	1.12756	0.0675055
$280$	−49.2969	−2.94605
$281$	19.4281	1.15898	0.579490	−	0.814979i	$-0.303252\pi$
$281$	19.4281	1.15898	0.579490	+	0.814979i	$0.303252\pi$
$282$	−4.57371	−0.272360
$283$	0.615702	0.0365997	0.0182998	−	0.999833i	$-0.494175\pi$
$283$	0.615702	0.0365997	0.0182998	+	0.999833i	$0.494175\pi$
$284$	12.5883	0.746977
$285$	−49.9796	−2.96053
$286$	−2.86742	−0.169554
$287$	−4.56097	−0.269226
$288$	37.9196	2.23443
$289$	−4.22680	−0.248635
$290$	8.08177	0.474578
$291$	−33.5338	−1.96578
$292$	5.87139	0.343597
$293$	−26.6793	−1.55862	−0.779311	−	0.626638i	$-0.784431\pi$
$293$	−26.6793	−1.55862	−0.779311	+	0.626638i	$0.784431\pi$
$294$	−23.6729	−1.38063
$295$	38.6833	2.25223
$296$	11.1333	0.647111
$297$	−17.3822	−1.00862
$298$	−0.261293	−0.0151363
$299$	9.80245	0.566890
$300$	42.5139	2.45454
$301$	19.2923	1.11199
$302$	2.07149	0.119201
$303$	−12.5356	−0.720150
$304$	4.74347	0.272056
$305$	4.37157	0.250316
$306$	−30.7118	−1.75568
$307$	−2.87745	−0.164225	−0.0821123	−	0.996623i	$-0.526167\pi$
$307$	−2.87745	−0.164225	−0.0821123	+	0.996623i	$0.526167\pi$
$308$	3.33872	0.190241
$309$	9.38131	0.533684
$310$	−0.630710	−0.0358219
$311$	11.1447	0.631960	0.315980	−	0.948766i	$-0.397667\pi$
$311$	11.1447	0.631960	0.315980	+	0.948766i	$0.397667\pi$
$312$	−27.8275	−1.57542
$313$	16.4685	0.930856	0.465428	−	0.885086i	$-0.345900\pi$
$313$	16.4685	0.930856	0.465428	+	0.885086i	$0.345900\pi$
$314$	12.9058	0.728317
$315$	132.831	7.48419
$316$	9.21343	0.518296
$317$	−23.3937	−1.31392	−0.656959	−	0.753926i	$-0.728158\pi$
$317$	−23.3937	−1.31392	−0.656959	+	0.753926i	$0.728158\pi$
$318$	23.3758	1.31085
$319$	−1.76305	−0.0987120
$320$	−33.3479	−1.86420
$321$	9.29516	0.518805
$322$	13.9367	0.776660
$323$	12.2121	0.679501
$324$	−30.2324	−1.67958
$325$	−38.5866	−2.14040
$326$	−21.7996	−1.20737
$327$	−57.8513	−3.19919
$328$	−3.74128	−0.206577
$329$	−4.83350	−0.266479
$330$	15.3375	0.844301
$331$	−34.5833	−1.90087	−0.950435	−	0.310922i	$-0.899362\pi$
$331$	−34.5833	−1.90087	−0.950435	+	0.310922i	$0.899362\pi$
$332$	−4.37626	−0.240178
$333$	−29.9989	−1.64393
$334$	16.4494	0.900069
$335$	−1.93825	−0.105898
$336$	−17.2218	−0.939524
$337$	26.3764	1.43681	0.718406	−	0.695624i	$-0.244872\pi$
$337$	26.3764	1.43681	0.718406	+	0.695624i	$0.244872\pi$
$338$	−5.79043	−0.314958
$339$	−2.60755	−0.141623
$340$	−14.0688	−0.762989
$341$	0.137590	0.00745094
$342$	−29.3628	−1.58776
$343$	0.936717	0.0505780
$344$	15.8251	0.853230
$345$	−52.4321	−2.82285
$346$	−18.5356	−0.996479
$347$	1.69236	0.0908505	0.0454252	−	0.998968i	$-0.485536\pi$
$347$	1.69236	0.0908505	0.0454252	+	0.998968i	$0.485536\pi$
$348$	−5.31188	−0.284747
$349$	6.03472	0.323031	0.161515	−	0.986870i	$-0.448362\pi$
$349$	6.03472	0.323031	0.161515	+	0.986870i	$0.448362\pi$
$350$	−54.8606	−2.93242
$351$	47.5328	2.53711
$352$	4.62712	0.246627
$353$	−26.2075	−1.39488	−0.697442	−	0.716641i	$-0.745679\pi$
$353$	−26.2075	−1.39488	−0.697442	+	0.716641i	$0.745679\pi$
$354$	31.0458	1.65007
$355$	61.1131	3.24355
$356$	−6.10201	−0.323406
$357$	−44.3377	−2.34660
$358$	−4.33984	−0.229368
$359$	−34.8559	−1.83962	−0.919811	−	0.392361i	$-0.871658\pi$
$359$	−34.8559	−1.83962	−0.919811	+	0.392361i	$0.871658\pi$
$360$	108.959	5.74263
$361$	−7.32431	−0.385490
$362$	−19.9482	−1.04845
$363$	−3.34590	−0.175614
$364$	−9.12995	−0.478539
$365$	28.5042	1.49198
$366$	3.50846	0.183390
$367$	−6.14546	−0.320791	−0.160395	−	0.987053i	$-0.551277\pi$
$367$	−6.14546	−0.320791	−0.160395	+	0.987053i	$0.551277\pi$
$368$	4.97623	0.259404
$369$	10.0809	0.524792
$370$	16.7801	0.872354
$371$	24.7035	1.28254
$372$	0.414545	0.0214932
$373$	−10.2796	−0.532260	−0.266130	−	0.963937i	$-0.585745\pi$
$373$	−10.2796	−0.532260	−0.266130	+	0.963937i	$0.585745\pi$
$374$	−3.74760	−0.193784
$375$	133.260	6.88154
$376$	−3.96482	−0.204470
$377$	4.82119	0.248304
$378$	67.5799	3.47593
$379$	4.37974	0.224972	0.112486	−	0.993653i	$-0.464119\pi$
$379$	4.37974	0.224972	0.112486	+	0.993653i	$0.464119\pi$
$380$	−13.4508	−0.690013
$381$	−49.0013	−2.51041
$382$	−12.4004	−0.634459
$383$	12.0420	0.615318	0.307659	−	0.951497i	$-0.400454\pi$
$383$	12.0420	0.615318	0.307659	+	0.951497i	$0.400454\pi$
$384$	4.20007	0.214334
$385$	16.2087	0.826071
$386$	12.0343	0.612529
$387$	−42.6409	−2.16756
$388$	−9.02483	−0.458166
$389$	0.343493	0.0174158	0.00870790	−	0.999962i	$-0.497228\pi$
$389$	0.343493	0.0174158	0.00870790	+	0.999962i	$0.497228\pi$
$390$	−41.9414	−2.12379
$391$	12.8114	0.647899
$392$	−20.5213	−1.03648
$393$	65.1167	3.28470
$394$	8.69470	0.438033
$395$	44.7290	2.25056
$396$	−7.37943	−0.370830
$397$	9.80951	0.492325	0.246163	−	0.969229i	$-0.420830\pi$
$397$	9.80951	0.492325	0.246163	+	0.969229i	$0.420830\pi$
$398$	−15.2516	−0.764494
$399$	−42.3901	−2.12216
$400$	−19.5885	−0.979427
$401$	17.3536	0.866597	0.433298	−	0.901251i	$-0.357350\pi$
$401$	17.3536	0.866597	0.433298	+	0.901251i	$0.357350\pi$
$402$	−1.55557	−0.0775846
$403$	−0.376251	−0.0187424
$404$	−3.37366	−0.167846
$405$	−146.771	−7.29311
$406$	6.85454	0.340185
$407$	−3.66060	−0.181449
$408$	−36.3693	−1.80055
$409$	24.6177	1.21727	0.608634	−	0.793451i	$-0.291718\pi$
$409$	24.6177	1.21727	0.608634	+	0.793451i	$0.291718\pi$
$410$	−5.63883	−0.278482
$411$	11.6816	0.576212
$412$	2.52476	0.124386
$413$	32.8092	1.61444
$414$	−30.8036	−1.51392
$415$	−21.2457	−1.04291
$416$	−12.6532	−0.620373
$417$	−54.9681	−2.69180
$418$	−3.58298	−0.175249
$419$	−32.2609	−1.57605	−0.788025	−	0.615644i	$-0.788896\pi$
$419$	−32.2609	−1.57605	−0.788025	+	0.615644i	$0.788896\pi$
$420$	48.8350	2.38290
$421$	6.54360	0.318916	0.159458	−	0.987205i	$-0.449025\pi$
$421$	6.54360	0.318916	0.159458	+	0.987205i	$0.449025\pi$
$422$	0.567448	0.0276229
$423$	10.6833	0.519439
$424$	20.2638	0.984098
$425$	−50.4310	−2.44626
$426$	49.0470	2.37634
$427$	3.70774	0.179430
$428$	2.50157	0.120918
$429$	9.14960	0.441747
$430$	23.8514	1.15022
$431$	−13.0726	−0.629686	−0.314843	−	0.949144i	$-0.601952\pi$
$431$	−13.0726	−0.629686	−0.314843	+	0.949144i	$0.601952\pi$
$432$	24.1301	1.16096
$433$	25.1025	1.20635	0.603176	−	0.797608i	$-0.293902\pi$
$433$	25.1025	1.20635	0.603176	+	0.797608i	$0.293902\pi$
$434$	−0.534935	−0.0256777
$435$	−25.7879	−1.23644
$436$	−15.5693	−0.745636
$437$	12.2486	0.585931
$438$	22.8764	1.09308
$439$	17.1476	0.818412	0.409206	−	0.912442i	$-0.365806\pi$
$439$	17.1476	0.818412	0.409206	+	0.912442i	$0.365806\pi$
$440$	13.2957	0.633846
$441$	55.2951	2.63310
$442$	10.2481	0.487451
$443$	7.63044	0.362533	0.181267	−	0.983434i	$-0.441980\pi$
$443$	7.63044	0.362533	0.181267	+	0.983434i	$0.441980\pi$
$444$	−11.0290	−0.523413
$445$	−29.6238	−1.40430
$446$	2.21028	0.104660
$447$	0.833755	0.0394353
$448$	−28.2839	−1.33629
$449$	−5.37178	−0.253510	−0.126755	−	0.991934i	$-0.540456\pi$
$449$	−5.37178	−0.253510	−0.126755	+	0.991934i	$0.540456\pi$
$450$	121.256	5.71606
$451$	1.23012	0.0579241
$452$	−0.701762	−0.0330081
$453$	−6.60986	−0.310559
$454$	16.4723	0.773085
$455$	−44.3237	−2.07793
$456$	−34.7717	−1.62834
$457$	33.7367	1.57814	0.789068	−	0.614306i	$-0.210564\pi$
$457$	33.7367	1.57814	0.789068	+	0.614306i	$0.210564\pi$
$458$	29.4753	1.37729
$459$	62.1233	2.89967
$460$	−14.1109	−0.657923
$461$	−5.88384	−0.274038	−0.137019	−	0.990568i	$-0.543752\pi$
$461$	−5.88384	−0.274038	−0.137019	+	0.990568i	$0.543752\pi$
$462$	13.0085	0.605209
$463$	22.3323	1.03787	0.518935	−	0.854814i	$-0.326329\pi$
$463$	22.3323	1.03787	0.518935	+	0.854814i	$0.326329\pi$
$464$	2.44748	0.113622
$465$	2.01252	0.0933283
$466$	−9.41620	−0.436197
$467$	19.1127	0.884431	0.442216	−	0.896909i	$-0.354193\pi$
$467$	19.1127	0.884431	0.442216	+	0.896909i	$0.354193\pi$
$468$	20.1795	0.932800
$469$	−1.64392	−0.0759093
$470$	−5.97576	−0.275641
$471$	−41.1809	−1.89751
$472$	26.9127	1.23876
$473$	−5.20323	−0.239245
$474$	35.8978	1.64884
$475$	−48.2157	−2.21229
$476$	−11.9325	−0.546923
$477$	−54.6012	−2.50002
$478$	−22.3187	−1.02083
$479$	−15.5456	−0.710296	−0.355148	−	0.934810i	$-0.615570\pi$
$479$	−15.5456	−0.710296	−0.355148	+	0.934810i	$0.615570\pi$
$480$	67.6803	3.08917
$481$	10.0102	0.456424
$482$	7.20679	0.328260
$483$	−44.4702	−2.02346
$484$	−0.900472	−0.0409305
$485$	−43.8134	−1.98946
$486$	−63.1127	−2.86285
$487$	−20.0391	−0.908058	−0.454029	−	0.890987i	$-0.650014\pi$
$487$	−20.0391	−0.908058	−0.454029	+	0.890987i	$0.650014\pi$
$488$	3.04139	0.137677
$489$	69.5599	3.14561
$490$	−30.9297	−1.39726
$491$	−29.3234	−1.32335	−0.661674	−	0.749792i	$-0.730154\pi$
$491$	−29.3234	−1.32335	−0.661674	+	0.749792i	$0.730154\pi$
$492$	3.70622	0.167089
$493$	6.30108	0.283786
$494$	9.79791	0.440829
$495$	−35.8253	−1.61023
$496$	−0.191004	−0.00857634
$497$	51.8329	2.32503
$498$	−17.0510	−0.764073
$499$	20.0561	0.897833	0.448917	−	0.893574i	$-0.351810\pi$
$499$	20.0561	0.897833	0.448917	+	0.893574i	$0.351810\pi$
$500$	35.8639	1.60388
$501$	−52.4879	−2.34499
$502$	14.7043	0.656287
$503$	39.4207	1.75768	0.878840	−	0.477116i	$-0.158318\pi$
$503$	39.4207	1.75768	0.878840	+	0.477116i	$0.158318\pi$
$504$	92.4132	4.11641
$505$	−16.3783	−0.728825
$506$	−3.75880	−0.167099
$507$	18.4765	0.820572
$508$	−13.1876	−0.585104
$509$	−21.0880	−0.934710	−0.467355	−	0.884070i	$-0.654793\pi$
$509$	−21.0880	−0.934710	−0.467355	+	0.884070i	$0.654793\pi$
$510$	−54.8156	−2.42728
$511$	24.1758	1.06947
$512$	−14.8676	−0.657060
$513$	59.3944	2.62233
$514$	−16.9837	−0.749118
$515$	12.2571	0.540113
$516$	−15.6768	−0.690132
$517$	1.30362	0.0573333
$518$	14.2320	0.625318
$519$	59.1448	2.59617
$520$	−36.3579	−1.59440
$521$	−7.08472	−0.310387	−0.155194	−	0.987884i	$-0.549600\pi$
$521$	−7.08472	−0.310387	−0.155194	+	0.987884i	$0.549600\pi$
$522$	−15.1503	−0.663110
$523$	4.12511	0.180378	0.0901892	−	0.995925i	$-0.471253\pi$
$523$	4.12511	0.180378	0.0901892	+	0.995925i	$0.471253\pi$
$524$	17.5246	0.765567
$525$	175.053	7.63996
$526$	−6.79612	−0.296325
$527$	−0.491743	−0.0214207
$528$	4.64481	0.202139
$529$	−10.1503	−0.441319
$530$	30.5415	1.32664
$531$	−72.5168	−3.14696
$532$	−11.4083	−0.494613
$533$	−3.36385	−0.145705
$534$	−23.7749	−1.02884
$535$	12.1445	0.525054
$536$	−1.34848	−0.0582453
$537$	13.8479	0.597581
$538$	−5.47641	−0.236105
$539$	6.74736	0.290629
$540$	−68.4246	−2.94453
$541$	−7.15144	−0.307464	−0.153732	−	0.988113i	$-0.549129\pi$
$541$	−7.15144	−0.307464	−0.153732	+	0.988113i	$0.549129\pi$
$542$	−30.9182	−1.32805
$543$	63.6522	2.73158
$544$	−16.5372	−0.709025
$545$	−75.5854	−3.23772
$546$	−35.5725	−1.52236
$547$	17.1457	0.733098	0.366549	−	0.930399i	$-0.380539\pi$
$547$	17.1457	0.733098	0.366549	+	0.930399i	$0.380539\pi$
$548$	3.14384	0.134298
$549$	−8.19507	−0.349757
$550$	14.7962	0.630913
$551$	6.02430	0.256644
$552$	−36.4780	−1.55261
$553$	37.9368	1.61324
$554$	−6.22915	−0.264651
$555$	−53.5432	−2.27278
$556$	−14.7934	−0.627379
$557$	−4.19354	−0.177686	−0.0888429	−	0.996046i	$-0.528317\pi$
$557$	−4.19354	−0.177686	−0.0888429	+	0.996046i	$0.528317\pi$
$558$	1.18234	0.0500527
$559$	14.2286	0.601806
$560$	−22.5010	−0.950841
$561$	11.9581	0.504873
$562$	20.3719	0.859339
$563$	47.3440	1.99531	0.997655	−	0.0684397i	$-0.0218021\pi$
$563$	47.3440	1.99531	0.997655	+	0.0684397i	$0.0218021\pi$
$564$	3.92767	0.165385
$565$	−3.40689	−0.143329
$566$	0.645615	0.0271372
$567$	−124.484	−5.22782
$568$	42.5175	1.78400
$569$	3.47622	0.145731	0.0728653	−	0.997342i	$-0.476786\pi$
$569$	3.47622	0.145731	0.0728653	+	0.997342i	$0.476786\pi$
$570$	−52.4078	−2.19512
$571$	36.7702	1.53879	0.769393	−	0.638776i	$-0.220559\pi$
$571$	36.7702	1.53879	0.769393	+	0.638776i	$0.220559\pi$
$572$	2.46240	0.102958
$573$	39.5681	1.65298
$574$	−4.78256	−0.199620
$575$	−50.5817	−2.10940
$576$	62.5148	2.60478
$577$	9.99462	0.416082	0.208041	−	0.978120i	$-0.433291\pi$
$577$	9.99462	0.416082	0.208041	+	0.978120i	$0.433291\pi$
$578$	−4.43215	−0.184353
$579$	−38.3999	−1.59585
$580$	−6.94022	−0.288177
$581$	−18.0195	−0.747575
$582$	−35.1630	−1.45755
$583$	−6.66269	−0.275940
$584$	19.8309	0.820608
$585$	97.9668	4.05043
$586$	−27.9755	−1.15566
$587$	6.57054	0.271195	0.135598	−	0.990764i	$-0.456705\pi$
$587$	6.57054	0.271195	0.135598	+	0.990764i	$0.456705\pi$
$588$	20.3291	0.838356
$589$	−0.470143	−0.0193719
$590$	40.5627	1.66994
$591$	−27.7437	−1.14122
$592$	5.08168	0.208856
$593$	−6.26491	−0.257269	−0.128635	−	0.991692i	$-0.541059\pi$
$593$	−6.26491	−0.257269	−0.128635	+	0.991692i	$0.541059\pi$
$594$	−18.2267	−0.747850
$595$	−57.9292	−2.37487
$596$	0.224386	0.00919120
$597$	48.6660	1.99177
$598$	10.2787	0.420327
$599$	−15.7524	−0.643624	−0.321812	−	0.946804i	$-0.604292\pi$
$599$	−15.7524	−0.643624	−0.321812	+	0.946804i	$0.604292\pi$
$600$	143.593	5.86215
$601$	−39.6549	−1.61756	−0.808778	−	0.588114i	$-0.799871\pi$
$601$	−39.6549	−1.61756	−0.808778	+	0.588114i	$0.799871\pi$
$602$	20.2296	0.824495
$603$	3.63349	0.147967
$604$	−1.77889	−0.0723820
$605$	−4.37157	−0.177730
$606$	−13.1446	−0.533963
$607$	−41.6334	−1.68985	−0.844923	−	0.534888i	$-0.820354\pi$
$607$	−41.6334	−1.68985	−0.844923	+	0.534888i	$0.820354\pi$
$608$	−15.8107	−0.641210
$609$	−21.8720	−0.886298
$610$	4.58396	0.185599
$611$	−3.56484	−0.144218
$612$	26.3738	1.06610
$613$	1.39979	0.0565368	0.0282684	−	0.999600i	$-0.491001\pi$
$613$	1.39979	0.0565368	0.0282684	+	0.999600i	$0.491001\pi$
$614$	−3.01725	−0.121766
$615$	17.9928	0.725540
$616$	11.2767	0.454351
$617$	−20.4608	−0.823720	−0.411860	−	0.911247i	$-0.635121\pi$
$617$	−20.4608	−0.823720	−0.411860	+	0.911247i	$0.635121\pi$
$618$	9.83709	0.395706
$619$	−10.8266	−0.435156	−0.217578	−	0.976043i	$-0.569816\pi$
$619$	−10.8266	−0.435156	−0.217578	+	0.976043i	$0.569816\pi$
$620$	0.541622	0.0217521
$621$	62.3090	2.50037
$622$	11.6862	0.468573
$623$	−25.1254	−1.00663
$624$	−12.7015	−0.508469
$625$	103.558	4.14230
$626$	17.2686	0.690194
$627$	11.4329	0.456584
$628$	−11.0829	−0.442255
$629$	13.0829	0.521648
$630$	139.285	5.54923
$631$	24.7224	0.984182	0.492091	−	0.870544i	$-0.336233\pi$
$631$	24.7224	0.984182	0.492091	+	0.870544i	$0.336233\pi$
$632$	31.1188	1.23784
$633$	−1.81066	−0.0719672
$634$	−24.5302	−0.974219
$635$	−64.0225	−2.54065
$636$	−20.0739	−0.795984
$637$	−18.4511	−0.731060
$638$	−1.84871	−0.0731911
$639$	−114.564	−4.53209
$640$	5.48759	0.216916
$641$	−26.1321	−1.03216	−0.516078	−	0.856542i	$-0.672608\pi$
$641$	−26.1321	−1.03216	−0.516078	+	0.856542i	$0.672608\pi$
$642$	9.74675	0.384674
$643$	−33.7092	−1.32936	−0.664680	−	0.747128i	$-0.731432\pi$
$643$	−33.7092	−1.32936	−0.664680	+	0.747128i	$0.731432\pi$
$644$	−11.9681	−0.471610
$645$	−76.1070	−2.99671
$646$	12.8054	0.503823
$647$	−45.0479	−1.77101	−0.885507	−	0.464626i	$-0.846189\pi$
$647$	−45.0479	−1.77101	−0.885507	+	0.464626i	$0.846189\pi$
$648$	−102.111	−4.01131
$649$	−8.84884	−0.347347
$650$	−40.4613	−1.58702
$651$	1.70691	0.0668992
$652$	18.7204	0.733148
$653$	−17.0953	−0.668989	−0.334495	−	0.942398i	$-0.608566\pi$
$653$	−17.0953	−0.668989	−0.334495	+	0.942398i	$0.608566\pi$
$654$	−60.6620	−2.37207
$655$	85.0779	3.32427
$656$	−1.70766	−0.0666731
$657$	−53.4347	−2.08468
$658$	−5.06833	−0.197584
$659$	5.01554	0.195378	0.0976888	−	0.995217i	$-0.468855\pi$
$659$	5.01554	0.195378	0.0976888	+	0.995217i	$0.468855\pi$
$660$	−13.1711	−0.512683
$661$	−6.01241	−0.233856	−0.116928	−	0.993140i	$-0.537305\pi$
$661$	−6.01241	−0.233856	−0.116928	+	0.993140i	$0.537305\pi$
$662$	−36.2635	−1.40942
$663$	−32.7003	−1.26998
$664$	−14.7810	−0.573615
$665$	−55.3846	−2.14772
$666$	−31.4564	−1.21891
$667$	6.31991	0.244708
$668$	−14.1259	−0.546547
$669$	−7.05275	−0.272675
$670$	−2.03242	−0.0785191
$671$	−1.00000	−0.0386046
$672$	57.4029	2.21437
$673$	−17.5451	−0.676312	−0.338156	−	0.941090i	$-0.609803\pi$
$673$	−17.5451	−0.676312	−0.338156	+	0.941090i	$0.609803\pi$
$674$	27.6578	1.06534
$675$	−245.274	−9.44061
$676$	4.97253	0.191251
$677$	−17.5776	−0.675562	−0.337781	−	0.941225i	$-0.609676\pi$
$677$	−17.5776	−0.675562	−0.337781	+	0.941225i	$0.609676\pi$
$678$	−2.73424	−0.105008
$679$	−37.1602	−1.42608
$680$	−47.5182	−1.82224
$681$	−52.5612	−2.01415
$682$	0.144275	0.00552458
$683$	7.30031	0.279338	0.139669	−	0.990198i	$-0.455396\pi$
$683$	7.30031	0.279338	0.139669	+	0.990198i	$0.455396\pi$
$684$	25.2153	0.964130
$685$	15.2626	0.583153
$686$	0.982226	0.0375016
$687$	−94.0522	−3.58832
$688$	7.22317	0.275381
$689$	18.2196	0.694110
$690$	−54.9795	−2.09303
$691$	43.1838	1.64279	0.821394	−	0.570361i	$-0.193197\pi$
$691$	43.1838	1.64279	0.821394	+	0.570361i	$0.193197\pi$
$692$	15.9174	0.605090
$693$	−30.3852	−1.15424
$694$	1.77458	0.0673621
$695$	−71.8183	−2.72422
$696$	−17.9412	−0.680058
$697$	−4.39641	−0.166526
$698$	6.32791	0.239515
$699$	30.0459	1.13644
$700$	47.1115	1.78065
$701$	37.3223	1.40964	0.704822	−	0.709384i	$-0.251027\pi$
$701$	37.3223	1.40964	0.704822	+	0.709384i	$0.251027\pi$
$702$	49.8421	1.88117
$703$	12.5082	0.471755
$704$	7.62834	0.287504
$705$	19.0679	0.718139
$706$	−27.4808	−1.03425
$707$	−13.8912	−0.522433
$708$	−26.6606	−1.00197
$709$	11.0716	0.415803	0.207902	−	0.978150i	$-0.433337\pi$
$709$	11.0716	0.415803	0.207902	+	0.978150i	$0.433337\pi$
$710$	64.0822	2.40496
$711$	−83.8501	−3.14462
$712$	−20.6098	−0.772386
$713$	−0.493213	−0.0184710
$714$	−46.4918	−1.73991
$715$	11.9544	0.447068
$716$	3.72684	0.139278
$717$	71.2162	2.65962
$718$	−36.5493	−1.36401
$719$	−13.2672	−0.494782	−0.247391	−	0.968916i	$-0.579573\pi$
$719$	−13.2672	−0.494782	−0.247391	+	0.968916i	$0.579573\pi$
$720$	49.7330	1.85344
$721$	10.3958	0.387161
$722$	−7.68015	−0.285826
$723$	−22.9960	−0.855229
$724$	17.1305	0.636650
$725$	−24.8778	−0.923940
$726$	−3.50846	−0.130211
$727$	35.1613	1.30406	0.652031	−	0.758192i	$-0.273917\pi$
$727$	35.1613	1.30406	0.652031	+	0.758192i	$0.273917\pi$
$728$	−30.8369	−1.14289
$729$	100.663	3.72827
$730$	29.8890	1.10624
$731$	18.5962	0.687804
$732$	−3.01289	−0.111360
$733$	−36.4561	−1.34654	−0.673269	−	0.739397i	$-0.735110\pi$
$733$	−36.4561	−1.34654	−0.673269	+	0.739397i	$0.735110\pi$
$734$	−6.44404	−0.237854
$735$	98.6928	3.64034
$736$	−16.5866	−0.611390
$737$	0.443376	0.0163320
$738$	10.5707	0.389113
$739$	34.9363	1.28515	0.642577	−	0.766221i	$-0.277865\pi$
$739$	34.9363	1.28515	0.642577	+	0.766221i	$0.277865\pi$
$740$	−14.4099	−0.529718
$741$	−31.2639	−1.14851
$742$	25.9037	0.950956
$743$	−8.92310	−0.327357	−0.163678	−	0.986514i	$-0.552336\pi$
$743$	−8.92310	−0.327357	−0.163678	+	0.986514i	$0.552336\pi$
$744$	1.40015	0.0513319
$745$	1.08934	0.0399103
$746$	−10.7791	−0.394650
$747$	39.8277	1.45722
$748$	3.21825	0.117671
$749$	10.3004	0.376368
$750$	139.735	5.10239
$751$	2.86645	0.104598	0.0522991	−	0.998631i	$-0.483345\pi$
$751$	2.86645	0.104598	0.0522991	+	0.998631i	$0.483345\pi$
$752$	−1.80970	−0.0659929
$753$	−46.9198	−1.70985
$754$	5.05542	0.184107
$755$	−8.63609	−0.314299
$756$	−58.0342	−2.11068
$757$	−6.53429	−0.237493	−0.118746	−	0.992925i	$-0.537888\pi$
$757$	−6.53429	−0.237493	−0.118746	+	0.992925i	$0.537888\pi$
$758$	4.59253	0.166808
$759$	11.9939	0.435350
$760$	−45.4309	−1.64795
$761$	−6.03040	−0.218602	−0.109301	−	0.994009i	$-0.534861\pi$
$761$	−6.03040	−0.218602	−0.109301	+	0.994009i	$0.534861\pi$
$762$	−51.3820	−1.86137
$763$	−64.1076	−2.32085
$764$	10.6488	0.385261
$765$	128.038	4.62924
$766$	12.6271	0.456234
$767$	24.1977	0.873730
$768$	55.4515	2.00093
$769$	17.5588	0.633188	0.316594	−	0.948561i	$-0.397461\pi$
$769$	17.5588	0.633188	0.316594	+	0.948561i	$0.397461\pi$
$770$	16.9962	0.612499
$771$	54.1928	1.95171
$772$	−10.3344	−0.371945
$773$	15.6869	0.564219	0.282110	−	0.959382i	$-0.408966\pi$
$773$	15.6869	0.564219	0.282110	+	0.959382i	$0.408966\pi$
$774$	−44.7125	−1.60716
$775$	1.94149	0.0697405
$776$	−30.4818	−1.09423
$777$	−45.4125	−1.62917
$778$	0.360181	0.0129131
$779$	−4.20329	−0.150598
$780$	36.0172	1.28962
$781$	−13.9796	−0.500231
$782$	13.4338	0.480392
$783$	30.6457	1.09519
$784$	−9.36674	−0.334526
$785$	−53.8047	−1.92037
$786$	68.2803	2.43548
$787$	12.3130	0.438913	0.219456	−	0.975622i	$-0.429572\pi$
$787$	12.3130	0.438913	0.219456	+	0.975622i	$0.429572\pi$
$788$	−7.46658	−0.265986
$789$	21.6856	0.772027
$790$	46.9021	1.66870
$791$	−2.88954	−0.102740
$792$	−24.9244	−0.885649
$793$	2.73457	0.0971074
$794$	10.2861	0.365040
$795$	−97.4542	−3.45635
$796$	13.0973	0.464222
$797$	30.2884	1.07287	0.536435	−	0.843941i	$-0.319771\pi$
$797$	30.2884	1.07287	0.536435	+	0.843941i	$0.319771\pi$
$798$	−44.4496	−1.57350
$799$	−4.65910	−0.164827
$800$	65.2918	2.30841
$801$	55.5335	1.96218
$802$	18.1967	0.642548
$803$	−6.52034	−0.230098
$804$	1.33584	0.0471115
$805$	−58.1023	−2.04784
$806$	−0.394530	−0.0138967
$807$	17.4745	0.615133
$808$	−11.3947	−0.400864
$809$	16.9083	0.594464	0.297232	−	0.954805i	$-0.403937\pi$
$809$	16.9083	0.594464	0.297232	+	0.954805i	$0.403937\pi$
$810$	−153.902	−5.40755
$811$	7.91179	0.277820	0.138910	−	0.990305i	$-0.455640\pi$
$811$	7.91179	0.277820	0.138910	+	0.990305i	$0.455640\pi$
$812$	−5.88633	−0.206570
$813$	98.6563	3.46003
$814$	−3.83845	−0.134538
$815$	90.8832	3.18350
$816$	−16.6004	−0.581129
$817$	17.7793	0.622019
$818$	25.8137	0.902556
$819$	83.0904	2.90341
$820$	4.84235	0.169102
$821$	11.4856	0.400849	0.200424	−	0.979709i	$-0.435768\pi$
$821$	11.4856	0.400849	0.200424	+	0.979709i	$0.435768\pi$
$822$	12.2492	0.427239
$823$	49.6509	1.73072	0.865360	−	0.501150i	$-0.167090\pi$
$823$	49.6509	1.73072	0.865360	+	0.501150i	$0.167090\pi$
$824$	8.52750	0.297070
$825$	−47.2129	−1.64374
$826$	34.4032	1.19704
$827$	−28.8091	−1.00179	−0.500895	−	0.865508i	$-0.666996\pi$
$827$	−28.8091	−1.00179	−0.500895	+	0.865508i	$0.666996\pi$
$828$	26.4526	0.919292
$829$	17.6759	0.613910	0.306955	−	0.951724i	$-0.400690\pi$
$829$	17.6759	0.613910	0.306955	+	0.951724i	$0.400690\pi$
$830$	−22.2779	−0.773277
$831$	19.8765	0.689507
$832$	−20.8602	−0.723198
$833$	−24.1148	−0.835529
$834$	−57.6387	−1.99586
$835$	−68.5778	−2.37323
$836$	3.07689	0.106416
$837$	−2.39162	−0.0826666
$838$	−33.8283	−1.16858
$839$	47.1348	1.62727	0.813637	−	0.581373i	$-0.197484\pi$
$839$	47.1348	1.62727	0.813637	+	0.581373i	$0.197484\pi$
$840$	164.943	5.69106
$841$	−25.8916	−0.892815
$842$	6.86152	0.236464
$843$	−65.0044	−2.23887
$844$	−0.487296	−0.0167734
$845$	24.1404	0.830456
$846$	11.2023	0.385143
$847$	−3.70774	−0.127400
$848$	9.24919	0.317619
$849$	−2.06008	−0.0707017
$850$	−52.8811	−1.81381
$851$	13.1220	0.449815
$852$	−42.1191	−1.44298
$853$	−31.2622	−1.07040	−0.535198	−	0.844726i	$-0.679763\pi$
$853$	−31.2622	−1.07040	−0.535198	+	0.844726i	$0.679763\pi$
$854$	3.88788	0.133041
$855$	122.414	4.18648
$856$	8.44919	0.288787
$857$	−34.5940	−1.18171	−0.590854	−	0.806778i	$-0.701209\pi$
$857$	−34.5940	−1.18171	−0.590854	+	0.806778i	$0.701209\pi$
$858$	9.59412	0.327538
$859$	−44.4954	−1.51816	−0.759082	−	0.650996i	$-0.774352\pi$
$859$	−44.4954	−1.51816	−0.759082	+	0.650996i	$0.774352\pi$
$860$	−20.4824	−0.698445
$861$	15.2606	0.520079
$862$	−13.7077	−0.466888
$863$	−10.5376	−0.358704	−0.179352	−	0.983785i	$-0.557400\pi$
$863$	−10.5376	−0.358704	−0.179352	+	0.983785i	$0.557400\pi$
$864$	−80.4296	−2.73627
$865$	77.2753	2.62744
$866$	26.3221	0.894462
$867$	14.1424	0.480303
$868$	0.459376	0.0155922
$869$	−10.2318	−0.347089
$870$	−27.0408	−0.916769
$871$	−1.21244	−0.0410820
$872$	−52.5862	−1.78079
$873$	82.1337	2.77980
$874$	12.8437	0.434445
$875$	147.672	4.99222
$876$	−19.6451	−0.663746
$877$	9.28499	0.313532	0.156766	−	0.987636i	$-0.449893\pi$
$877$	9.28499	0.313532	0.156766	+	0.987636i	$0.449893\pi$
$878$	17.9807	0.606820
$879$	89.2664	3.01088
$880$	6.06865	0.204574
$881$	18.7212	0.630733	0.315367	−	0.948970i	$-0.397872\pi$
$881$	18.7212	0.630733	0.315367	+	0.948970i	$0.397872\pi$
$882$	57.9815	1.95234
$883$	18.6366	0.627171	0.313585	−	0.949560i	$-0.398470\pi$
$883$	18.6366	0.627171	0.313585	+	0.949560i	$0.398470\pi$
$884$	−8.80053	−0.295994
$885$	−129.431	−4.35077
$886$	8.00116	0.268804
$887$	51.4140	1.72631	0.863157	−	0.504936i	$-0.168484\pi$
$887$	51.4140	1.72631	0.863157	+	0.504936i	$0.168484\pi$
$888$	−37.2510	−1.25006
$889$	−54.3006	−1.82118
$890$	−31.0630	−1.04124
$891$	33.5739	1.12477
$892$	−1.89808	−0.0635525
$893$	−4.45444	−0.149062
$894$	0.874263	0.0292397
$895$	18.0929	0.604779
$896$	4.65429	0.155489
$897$	−32.7980	−1.09509
$898$	−5.63276	−0.187968
$899$	−0.242579	−0.00809047
$900$	−104.129	−3.47095
$901$	23.8122	0.793299
$902$	1.28989	0.0429485
$903$	−64.5500	−2.14809
$904$	−2.37024	−0.0788329
$905$	83.1645	2.76448
$906$	−6.93100	−0.230267
$907$	2.02951	0.0673888	0.0336944	−	0.999432i	$-0.489273\pi$
$907$	2.02951	0.0673888	0.0336944	+	0.999432i	$0.489273\pi$
$908$	−14.1456	−0.469439
$909$	30.7032	1.01836
$910$	−46.4772	−1.54070
$911$	−7.53273	−0.249570	−0.124785	−	0.992184i	$-0.539824\pi$
$911$	−7.53273	−0.249570	−0.124785	+	0.992184i	$0.539824\pi$
$912$	−15.8712	−0.525547
$913$	4.85996	0.160841
$914$	35.3758	1.17013
$915$	−14.6269	−0.483549
$916$	−25.3120	−0.836330
$917$	72.1587	2.38289
$918$	65.1415	2.14999
$919$	13.5098	0.445647	0.222823	−	0.974859i	$-0.428473\pi$
$919$	13.5098	0.445647	0.222823	+	0.974859i	$0.428473\pi$
$920$	−47.6602	−1.57131
$921$	9.62767	0.317242
$922$	−6.16970	−0.203188
$923$	38.2283	1.25830
$924$	−11.1710	−0.367500
$925$	−51.6536	−1.69836
$926$	23.4173	0.769540
$927$	−22.9775	−0.754680
$928$	−8.15786	−0.267795
$929$	−26.0074	−0.853276	−0.426638	−	0.904423i	$-0.640302\pi$
$929$	−26.0074	−0.853276	−0.426638	+	0.904423i	$0.640302\pi$
$930$	2.11029	0.0691993
$931$	−23.0555	−0.755615
$932$	8.08616	0.264871
$933$	−37.2892	−1.22079
$934$	20.0413	0.655771
$935$	15.6238	0.510954
$936$	68.1574	2.22779
$937$	−18.6188	−0.608249	−0.304125	−	0.952632i	$-0.598364\pi$
$937$	−18.6188	−0.608249	−0.304125	+	0.952632i	$0.598364\pi$
$938$	−1.72379	−0.0562838
$939$	−55.1021	−1.79819
$940$	5.13168	0.167377
$941$	−17.2886	−0.563593	−0.281797	−	0.959474i	$-0.590930\pi$
$941$	−17.2886	−0.563593	−0.281797	+	0.959474i	$0.590930\pi$
$942$	−43.1816	−1.40693
$943$	−4.40955	−0.143595
$944$	12.2840	0.399811
$945$	−281.742	−9.16508
$946$	−5.45603	−0.177391
$947$	26.2804	0.853997	0.426998	−	0.904252i	$-0.359571\pi$
$947$	26.2804	0.853997	0.426998	+	0.904252i	$0.359571\pi$
$948$	−30.8272	−1.00122
$949$	17.8303	0.578797
$950$	−50.5582	−1.64033
$951$	78.2729	2.53817
$952$	−40.3025	−1.30621
$953$	−1.47920	−0.0479161	−0.0239580	−	0.999713i	$-0.507627\pi$
$953$	−1.47920	−0.0479161	−0.0239580	+	0.999713i	$0.507627\pi$
$954$	−57.2539	−1.85366
$955$	51.6975	1.67289
$956$	19.1662	0.619878
$957$	5.89900	0.190688
$958$	−16.3009	−0.526657
$959$	12.9449	0.418014
$960$	111.579	3.60119
$961$	−30.9811	−0.999389
$962$	10.4965	0.338421
$963$	−22.7665	−0.733640
$964$	−6.18883	−0.199329
$965$	−50.1713	−1.61507
$966$	−46.6307	−1.50032
$967$	−19.5515	−0.628735	−0.314368	−	0.949301i	$-0.601792\pi$
$967$	−19.5515	−0.628735	−0.314368	+	0.949301i	$0.601792\pi$
$968$	−3.04139	−0.0977539
$969$	−40.8606	−1.31263
$970$	−45.9420	−1.47511
$971$	−45.5452	−1.46161	−0.730807	−	0.682584i	$-0.760856\pi$
$971$	−45.5452	−1.46161	−0.730807	+	0.682584i	$0.760856\pi$
$972$	54.1981	1.73840
$973$	−60.9126	−1.95277
$974$	−21.0127	−0.673289
$975$	129.107	4.13473
$976$	1.38821	0.0444354
$977$	28.3536	0.907112	0.453556	−	0.891228i	$-0.350155\pi$
$977$	28.3536	0.907112	0.453556	+	0.891228i	$0.350155\pi$
$978$	72.9394	2.33235
$979$	6.77646	0.216577
$980$	26.5608	0.848455
$981$	141.694	4.52395
$982$	−30.7481	−0.981211
$983$	29.9924	0.956609	0.478304	−	0.878194i	$-0.341252\pi$
$983$	29.9924	0.956609	0.478304	+	0.878194i	$0.341252\pi$
$984$	12.5179	0.399058
$985$	−36.2484	−1.15497
$986$	6.60721	0.210417
$987$	16.1724	0.514774
$988$	−8.41395	−0.267683
$989$	18.6517	0.593091
$990$	−37.5659	−1.19392
$991$	23.7764	0.755281	0.377640	−	0.925952i	$-0.376736\pi$
$991$	23.7764	0.755281	0.377640	+	0.925952i	$0.376736\pi$
$992$	0.636648	0.0202136
$993$	115.712	3.67202
$994$	54.3512	1.72392
$995$	63.5844	2.01576
$996$	14.6425	0.463967
$997$	−38.0358	−1.20460	−0.602302	−	0.798268i	$-0.705750\pi$
$997$	−38.0358	−1.20460	−0.602302	+	0.798268i	$0.705750\pi$
$998$	21.0305	0.665708
$999$	63.6293	2.01314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.12	✓	19
3.2	odd	2		6039.2.a.k.1.8		19
11.10	odd	2		7381.2.a.i.1.8		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.12	✓	19	1.1	even	1	trivial
6039.2.a.k.1.8		19	3.2	odd	2
7381.2.a.i.1.8		19	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+1.04858 q^{2} -3.34590 q^{3} -0.900472 q^{4} -4.37157 q^{5} -3.50846 q^{6} -3.70774 q^{7} -3.04139 q^{8} +8.19507 q^{9} +O(q^{10})\)	\(q+1.04858 q^{2} -3.34590 q^{3} -0.900472 q^{4} -4.37157 q^{5} -3.50846 q^{6} -3.70774 q^{7} -3.04139 q^{8} +8.19507 q^{9} -4.58396 q^{10} +1.00000 q^{11} +3.01289 q^{12} -2.73457 q^{13} -3.88788 q^{14} +14.6269 q^{15} -1.38821 q^{16} -3.57396 q^{17} +8.59322 q^{18} -3.41697 q^{19} +3.93648 q^{20} +12.4058 q^{21} +1.04858 q^{22} -3.58464 q^{23} +10.1762 q^{24} +14.1107 q^{25} -2.86742 q^{26} -17.3822 q^{27} +3.33872 q^{28} -1.76305 q^{29} +15.3375 q^{30} +0.137590 q^{31} +4.62712 q^{32} -3.34590 q^{33} -3.74760 q^{34} +16.2087 q^{35} -7.37943 q^{36} -3.66060 q^{37} -3.58298 q^{38} +9.14960 q^{39} +13.2957 q^{40} +1.23012 q^{41} +13.0085 q^{42} -5.20323 q^{43} -0.900472 q^{44} -35.8253 q^{45} -3.75880 q^{46} +1.30362 q^{47} +4.64481 q^{48} +6.74736 q^{49} +14.7962 q^{50} +11.9581 q^{51} +2.46240 q^{52} -6.66269 q^{53} -18.2267 q^{54} -4.37157 q^{55} +11.2767 q^{56} +11.4329 q^{57} -1.84871 q^{58} -8.84884 q^{59} -13.1711 q^{60} -1.00000 q^{61} +0.144275 q^{62} -30.3852 q^{63} +7.62834 q^{64} +11.9544 q^{65} -3.50846 q^{66} +0.443376 q^{67} +3.21825 q^{68} +11.9939 q^{69} +16.9962 q^{70} -13.9796 q^{71} -24.9244 q^{72} -6.52034 q^{73} -3.83845 q^{74} -47.2129 q^{75} +3.07689 q^{76} -3.70774 q^{77} +9.59412 q^{78} -10.2318 q^{79} +6.06865 q^{80} +33.5739 q^{81} +1.28989 q^{82} +4.85996 q^{83} -11.1710 q^{84} +15.6238 q^{85} -5.45603 q^{86} +5.89900 q^{87} -3.04139 q^{88} +6.77646 q^{89} -37.5659 q^{90} +10.1391 q^{91} +3.22787 q^{92} -0.460364 q^{93} +1.36696 q^{94} +14.9375 q^{95} -15.4819 q^{96} +10.0223 q^{97} +7.07518 q^{98} +8.19507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

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