LMFDB - Embedded newform 2001.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.467085$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.467085 q^{2} -1.00000 q^{3} -1.78183 q^{4} -0.0105419 q^{5} +0.467085 q^{6} -1.85912 q^{7} +1.76644 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.467085 q^{2} -1.00000 q^{3} -1.78183 q^{4} -0.0105419 q^{5} +0.467085 q^{6} -1.85912 q^{7} +1.76644 q^{8} +1.00000 q^{9} +0.00492395 q^{10} -1.01164 q^{11} +1.78183 q^{12} +2.69792 q^{13} +0.868368 q^{14} +0.0105419 q^{15} +2.73859 q^{16} -3.50932 q^{17} -0.467085 q^{18} -7.48241 q^{19} +0.0187838 q^{20} +1.85912 q^{21} +0.472521 q^{22} +1.00000 q^{23} -1.76644 q^{24} -4.99989 q^{25} -1.26016 q^{26} -1.00000 q^{27} +3.31264 q^{28} -1.00000 q^{29} -0.00492395 q^{30} +9.06687 q^{31} -4.81203 q^{32} +1.01164 q^{33} +1.63915 q^{34} +0.0195986 q^{35} -1.78183 q^{36} -3.80689 q^{37} +3.49493 q^{38} -2.69792 q^{39} -0.0186215 q^{40} +0.921766 q^{41} -0.868368 q^{42} +5.98292 q^{43} +1.80257 q^{44} -0.0105419 q^{45} -0.467085 q^{46} -8.75713 q^{47} -2.73859 q^{48} -3.54367 q^{49} +2.33537 q^{50} +3.50932 q^{51} -4.80723 q^{52} -9.78399 q^{53} +0.467085 q^{54} +0.0106645 q^{55} -3.28402 q^{56} +7.48241 q^{57} +0.467085 q^{58} +13.5157 q^{59} -0.0187838 q^{60} -1.50283 q^{61} -4.23500 q^{62} -1.85912 q^{63} -3.22954 q^{64} -0.0284411 q^{65} -0.472521 q^{66} -7.98178 q^{67} +6.25302 q^{68} -1.00000 q^{69} -0.00915421 q^{70} +3.19615 q^{71} +1.76644 q^{72} +12.3494 q^{73} +1.77814 q^{74} +4.99989 q^{75} +13.3324 q^{76} +1.88076 q^{77} +1.26016 q^{78} +9.57497 q^{79} -0.0288698 q^{80} +1.00000 q^{81} -0.430543 q^{82} +15.0096 q^{83} -3.31264 q^{84} +0.0369947 q^{85} -2.79453 q^{86} +1.00000 q^{87} -1.78699 q^{88} +9.07903 q^{89} +0.00492395 q^{90} -5.01575 q^{91} -1.78183 q^{92} -9.06687 q^{93} +4.09033 q^{94} +0.0788785 q^{95} +4.81203 q^{96} +1.28711 q^{97} +1.65520 q^{98} -1.01164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * 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 $

$2$	−0.467085	−0.330279	−0.165140	−	0.986270i	$-0.552807\pi$
$2$	−0.467085	−0.330279	−0.165140	+	0.986270i	$0.552807\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.78183	−0.890916
$5$	−0.0105419	−0.00471446	−0.00235723	−	0.999997i	$-0.500750\pi$
$5$	−0.0105419	−0.00471446	−0.00235723	+	0.999997i	$0.500750\pi$
$6$	0.467085	0.190687
$7$	−1.85912	−0.702682	−0.351341	−	0.936248i	$-0.614274\pi$
$7$	−1.85912	−0.702682	−0.351341	+	0.936248i	$0.614274\pi$
$8$	1.76644	0.624530
$9$	1.00000	0.333333
$10$	0.00492395	0.00155709
$11$	−1.01164	−0.305020	−0.152510	−	0.988302i	$-0.548736\pi$
$11$	−1.01164	−0.305020	−0.152510	+	0.988302i	$0.548736\pi$
$12$	1.78183	0.514370
$13$	2.69792	0.748268	0.374134	−	0.927375i	$-0.377940\pi$
$13$	2.69792	0.748268	0.374134	+	0.927375i	$0.377940\pi$
$14$	0.868368	0.232081
$15$	0.0105419	0.00272189
$16$	2.73859	0.684646
$17$	−3.50932	−0.851135	−0.425568	−	0.904927i	$-0.639926\pi$
$17$	−3.50932	−0.851135	−0.425568	+	0.904927i	$0.639926\pi$
$18$	−0.467085	−0.110093
$19$	−7.48241	−1.71658	−0.858292	−	0.513162i	$-0.828474\pi$
$19$	−7.48241	−1.71658	−0.858292	+	0.513162i	$0.828474\pi$
$20$	0.0187838	0.00420019
$21$	1.85912	0.405693
$22$	0.472521	0.100742
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.76644	−0.360573
$25$	−4.99989	−0.999978
$26$	−1.26016	−0.247137
$27$	−1.00000	−0.192450
$28$	3.31264	0.626030
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.00492395	−0.000898985 0
$31$	9.06687	1.62846	0.814229	−	0.580544i	$-0.197160\pi$
$31$	9.06687	1.62846	0.814229	+	0.580544i	$0.197160\pi$
$32$	−4.81203	−0.850655
$33$	1.01164	0.176103
$34$	1.63915	0.281112
$35$	0.0195986	0.00331276
$36$	−1.78183	−0.296972
$37$	−3.80689	−0.625850	−0.312925	−	0.949778i	$-0.601309\pi$
$37$	−3.80689	−0.625850	−0.312925	+	0.949778i	$0.601309\pi$
$38$	3.49493	0.566952
$39$	−2.69792	−0.432013
$40$	−0.0186215	−0.00294432
$41$	0.921766	0.143956	0.0719778	−	0.997406i	$-0.477069\pi$
$41$	0.921766	0.143956	0.0719778	+	0.997406i	$0.477069\pi$
$42$	−0.868368	−0.133992
$43$	5.98292	0.912386	0.456193	−	0.889881i	$-0.349213\pi$
$43$	5.98292	0.912386	0.456193	+	0.889881i	$0.349213\pi$
$44$	1.80257	0.271747
$45$	−0.0105419	−0.00157149
$46$	−0.467085	−0.0688680
$47$	−8.75713	−1.27736	−0.638679	−	0.769473i	$-0.720519\pi$
$47$	−8.75713	−1.27736	−0.638679	+	0.769473i	$0.720519\pi$
$48$	−2.73859	−0.395281
$49$	−3.54367	−0.506239
$50$	2.33537	0.330272
$51$	3.50932	0.491403
$52$	−4.80723	−0.666643
$53$	−9.78399	−1.34393	−0.671967	−	0.740581i	$-0.734551\pi$
$53$	−9.78399	−1.34393	−0.671967	+	0.740581i	$0.734551\pi$
$54$	0.467085	0.0635623
$55$	0.0106645	0.00143800
$56$	−3.28402	−0.438846
$57$	7.48241	0.991070
$58$	0.467085	0.0613313
$59$	13.5157	1.75960	0.879799	−	0.475346i	$-0.157677\pi$
$59$	13.5157	1.75960	0.879799	+	0.475346i	$0.157677\pi$
$60$	−0.0187838	−0.00242498
$61$	−1.50283	−0.192418	−0.0962088	−	0.995361i	$-0.530672\pi$
$61$	−1.50283	−0.192418	−0.0962088	+	0.995361i	$0.530672\pi$
$62$	−4.23500	−0.537846
$63$	−1.85912	−0.234227
$64$	−3.22954	−0.403693
$65$	−0.0284411	−0.00352768
$66$	−0.472521	−0.0581633
$67$	−7.98178	−0.975130	−0.487565	−	0.873087i	$-0.662115\pi$
$67$	−7.98178	−0.975130	−0.487565	+	0.873087i	$0.662115\pi$
$68$	6.25302	0.758290
$69$	−1.00000	−0.120386
$70$	−0.00915421	−0.00109414
$71$	3.19615	0.379313	0.189656	−	0.981851i	$-0.439263\pi$
$71$	3.19615	0.379313	0.189656	+	0.981851i	$0.439263\pi$
$72$	1.76644	0.208177
$73$	12.3494	1.44539	0.722694	−	0.691168i	$-0.242903\pi$
$73$	12.3494	1.44539	0.722694	+	0.691168i	$0.242903\pi$
$74$	1.77814	0.206705
$75$	4.99989	0.577337
$76$	13.3324	1.52933
$77$	1.88076	0.214332
$78$	1.26016	0.142685
$79$	9.57497	1.07727	0.538634	−	0.842540i	$-0.318941\pi$
$79$	9.57497	1.07727	0.538634	+	0.842540i	$0.318941\pi$
$80$	−0.0288698	−0.00322774
$81$	1.00000	0.111111
$82$	−0.430543	−0.0475455
$83$	15.0096	1.64752	0.823760	−	0.566939i	$-0.191872\pi$
$83$	15.0096	1.64752	0.823760	+	0.566939i	$0.191872\pi$
$84$	−3.31264	−0.361439
$85$	0.0369947	0.00401264
$86$	−2.79453	−0.301342
$87$	1.00000	0.107211
$88$	−1.78699	−0.190494
$89$	9.07903	0.962376	0.481188	−	0.876617i	$-0.340205\pi$
$89$	9.07903	0.962376	0.481188	+	0.876617i	$0.340205\pi$
$90$	0.00492395	0.000519029 0
$91$	−5.01575	−0.525794
$92$	−1.78183	−0.185769
$93$	−9.06687	−0.940191
$94$	4.09033	0.421885
$95$	0.0788785	0.00809276
$96$	4.81203	0.491126
$97$	1.28711	0.130686	0.0653432	−	0.997863i	$-0.479186\pi$
$97$	1.28711	0.130686	0.0653432	+	0.997863i	$0.479186\pi$
$98$	1.65520	0.167200
$99$	−1.01164	−0.101673
$100$	8.90896	0.890896
$101$	17.9301	1.78411	0.892054	−	0.451929i	$-0.149264\pi$
$101$	17.9301	1.78411	0.892054	+	0.451929i	$0.149264\pi$
$102$	−1.63915	−0.162300
$103$	16.4218	1.61809	0.809044	−	0.587748i	$-0.199985\pi$
$103$	16.4218	1.61809	0.809044	+	0.587748i	$0.199985\pi$
$104$	4.76570	0.467316
$105$	−0.0195986	−0.00191263
$106$	4.56996	0.443874
$107$	3.00179	0.290194	0.145097	−	0.989417i	$-0.453651\pi$
$107$	3.00179	0.290194	0.145097	+	0.989417i	$0.453651\pi$
$108$	1.78183	0.171457
$109$	−13.8887	−1.33030	−0.665150	−	0.746710i	$-0.731632\pi$
$109$	−13.8887	−1.33030	−0.665150	+	0.746710i	$0.731632\pi$
$110$	−0.00498125	−0.000474943 0
$111$	3.80689	0.361334
$112$	−5.09136	−0.481088
$113$	−2.10899	−0.198397	−0.0991984	−	0.995068i	$-0.531628\pi$
$113$	−2.10899	−0.198397	−0.0991984	+	0.995068i	$0.531628\pi$
$114$	−3.49493	−0.327330
$115$	−0.0105419	−0.000983033 0
$116$	1.78183	0.165439
$117$	2.69792	0.249423
$118$	−6.31300	−0.581159
$119$	6.52425	0.598077
$120$	0.0186215	0.00169991
$121$	−9.97659	−0.906963
$122$	0.701949	0.0635515
$123$	−0.921766	−0.0831128
$124$	−16.1556	−1.45082
$125$	0.105417	0.00942882
$126$	0.868368	0.0773604
$127$	17.6790	1.56876	0.784380	−	0.620281i	$-0.212981\pi$
$127$	17.6790	1.56876	0.784380	+	0.620281i	$0.212981\pi$
$128$	11.1325	0.983986
$129$	−5.98292	−0.526767
$130$	0.0132844	0.00116512
$131$	−4.77362	−0.417073	−0.208536	−	0.978015i	$-0.566870\pi$
$131$	−4.77362	−0.417073	−0.208536	+	0.978015i	$0.566870\pi$
$132$	−1.80257	−0.156893
$133$	13.9107	1.20621
$134$	3.72817	0.322065
$135$	0.0105419	0.000907298 0
$136$	−6.19900	−0.531560
$137$	3.89537	0.332804	0.166402	−	0.986058i	$-0.446785\pi$
$137$	3.89537	0.332804	0.166402	+	0.986058i	$0.446785\pi$
$138$	0.467085	0.0397609
$139$	3.17159	0.269011	0.134505	−	0.990913i	$-0.457055\pi$
$139$	3.17159	0.269011	0.134505	+	0.990913i	$0.457055\pi$
$140$	−0.0349214	−0.00295139
$141$	8.75713	0.737483
$142$	−1.49287	−0.125279
$143$	−2.72931	−0.228237
$144$	2.73859	0.228215
$145$	0.0105419	0.000875453 0
$146$	−5.76823	−0.477382
$147$	3.54367	0.292277
$148$	6.78324	0.557579
$149$	1.96821	0.161242	0.0806211	−	0.996745i	$-0.474310\pi$
$149$	1.96821	0.161242	0.0806211	+	0.996745i	$0.474310\pi$
$150$	−2.33537	−0.190683
$151$	−2.94743	−0.239859	−0.119929	−	0.992782i	$-0.538267\pi$
$151$	−2.94743	−0.239859	−0.119929	+	0.992782i	$0.538267\pi$
$152$	−13.2172	−1.07206
$153$	−3.50932	−0.283712
$154$	−0.878473	−0.0707894
$155$	−0.0955816	−0.00767730
$156$	4.80723	0.384887
$157$	−6.42396	−0.512688	−0.256344	−	0.966586i	$-0.582518\pi$
$157$	−6.42396	−0.512688	−0.256344	+	0.966586i	$0.582518\pi$
$158$	−4.47233	−0.355799
$159$	9.78399	0.775921
$160$	0.0507277	0.00401038
$161$	−1.85912	−0.146519
$162$	−0.467085	−0.0366977
$163$	12.2619	0.960425	0.480212	−	0.877152i	$-0.340560\pi$
$163$	12.2619	0.960425	0.480212	+	0.877152i	$0.340560\pi$
$164$	−1.64243	−0.128252
$165$	−0.0106645	−0.000830232 0
$166$	−7.01077	−0.544142
$167$	5.89625	0.456266	0.228133	−	0.973630i	$-0.426738\pi$
$167$	5.89625	0.456266	0.228133	+	0.973630i	$0.426738\pi$
$168$	3.28402	0.253368
$169$	−5.72124	−0.440095
$170$	−0.0172797	−0.00132529
$171$	−7.48241	−0.572194
$172$	−10.6605	−0.812859
$173$	−1.40065	−0.106490	−0.0532449	−	0.998581i	$-0.516956\pi$
$173$	−1.40065	−0.106490	−0.0532449	+	0.998581i	$0.516956\pi$
$174$	−0.467085	−0.0354097
$175$	9.29540	0.702666
$176$	−2.77045	−0.208831
$177$	−13.5157	−1.01590
$178$	−4.24068	−0.317853
$179$	17.5946	1.31508	0.657539	−	0.753420i	$-0.271597\pi$
$179$	17.5946	1.31508	0.657539	+	0.753420i	$0.271597\pi$
$180$	0.0187838	0.00140006
$181$	−21.6515	−1.60934	−0.804672	−	0.593719i	$-0.797659\pi$
$181$	−21.6515	−1.60934	−0.804672	+	0.593719i	$0.797659\pi$
$182$	2.34279	0.173659
$183$	1.50283	0.111092
$184$	1.76644	0.130224
$185$	0.0401317	0.00295054
$186$	4.23500	0.310525
$187$	3.55016	0.259613
$188$	15.6037	1.13802
$189$	1.85912	0.135231
$190$	−0.0368430	−0.00267287
$191$	9.02504	0.653029	0.326514	−	0.945192i	$-0.394126\pi$
$191$	9.02504	0.653029	0.326514	+	0.945192i	$0.394126\pi$
$192$	3.22954	0.233072
$193$	2.31723	0.166798	0.0833988	−	0.996516i	$-0.473422\pi$
$193$	2.31723	0.166798	0.0833988	+	0.996516i	$0.473422\pi$
$194$	−0.601191	−0.0431630
$195$	0.0284411	0.00203671
$196$	6.31422	0.451016
$197$	21.2889	1.51677	0.758384	−	0.651808i	$-0.225989\pi$
$197$	21.2889	1.51677	0.758384	+	0.651808i	$0.225989\pi$
$198$	0.472521	0.0335806
$199$	−5.92224	−0.419816	−0.209908	−	0.977721i	$-0.567317\pi$
$199$	−5.92224	−0.419816	−0.209908	+	0.977721i	$0.567317\pi$
$200$	−8.83199	−0.624516
$201$	7.98178	0.562992
$202$	−8.37487	−0.589254
$203$	1.85912	0.130485
$204$	−6.25302	−0.437799
$205$	−0.00971712	−0.000678673 0
$206$	−7.67039	−0.534421
$207$	1.00000	0.0695048
$208$	7.38848	0.512299
$209$	7.56948	0.523592
$210$	0.00915421	0.000631701 0
$211$	7.72273	0.531655	0.265828	−	0.964021i	$-0.414355\pi$
$211$	7.72273	0.531655	0.265828	+	0.964021i	$0.414355\pi$
$212$	17.4334	1.19733
$213$	−3.19615	−0.218996
$214$	−1.40209	−0.0958452
$215$	−0.0630710	−0.00430141
$216$	−1.76644	−0.120191
$217$	−16.8564	−1.14429
$218$	6.48723	0.439371
$219$	−12.3494	−0.834495
$220$	−0.0190024	−0.00128114
$221$	−9.46786	−0.636877
$222$	−1.77814	−0.119341
$223$	−10.9381	−0.732469	−0.366234	−	0.930523i	$-0.619353\pi$
$223$	−10.9381	−0.732469	−0.366234	+	0.930523i	$0.619353\pi$
$224$	8.94614	0.597739
$225$	−4.99989	−0.333326
$226$	0.985077	0.0655263
$227$	21.4894	1.42630	0.713152	−	0.701010i	$-0.247267\pi$
$227$	21.4894	1.42630	0.713152	+	0.701010i	$0.247267\pi$
$228$	−13.3324	−0.882959
$229$	−10.3996	−0.687228	−0.343614	−	0.939111i	$-0.611651\pi$
$229$	−10.3996	−0.687228	−0.343614	+	0.939111i	$0.611651\pi$
$230$	0.00492395	0.000324675 0
$231$	−1.88076	−0.123745
$232$	−1.76644	−0.115972
$233$	9.36159	0.613298	0.306649	−	0.951823i	$-0.400792\pi$
$233$	9.36159	0.613298	0.306649	+	0.951823i	$0.400792\pi$
$234$	−1.26016	−0.0823791
$235$	0.0923164	0.00602206
$236$	−24.0827	−1.56765
$237$	−9.57497	−0.621961
$238$	−3.04738	−0.197532
$239$	12.7171	0.822603	0.411302	−	0.911499i	$-0.365074\pi$
$239$	12.7171	0.822603	0.411302	+	0.911499i	$0.365074\pi$
$240$	0.0288698	0.00186354
$241$	−1.69211	−0.108999	−0.0544993	−	0.998514i	$-0.517356\pi$
$241$	−1.69211	−0.108999	−0.0544993	+	0.998514i	$0.517356\pi$
$242$	4.65992	0.299551
$243$	−1.00000	−0.0641500
$244$	2.67779	0.171428
$245$	0.0373568	0.00238664
$246$	0.430543	0.0274504
$247$	−20.1869	−1.28446
$248$	16.0161	1.01702
$249$	−15.0096	−0.951196
$250$	−0.0492389	−0.00311414
$251$	8.84699	0.558417	0.279209	−	0.960230i	$-0.409928\pi$
$251$	8.84699	0.558417	0.279209	+	0.960230i	$0.409928\pi$
$252$	3.31264	0.208677
$253$	−1.01164	−0.0636011
$254$	−8.25761	−0.518129
$255$	−0.0369947	−0.00231670
$256$	1.25924	0.0787026
$257$	−4.57937	−0.285653	−0.142827	−	0.989748i	$-0.545619\pi$
$257$	−4.57937	−0.285653	−0.142827	+	0.989748i	$0.545619\pi$
$258$	2.79453	0.173980
$259$	7.07748	0.439773
$260$	0.0506772	0.00314286
$261$	−1.00000	−0.0618984
$262$	2.22969	0.137750
$263$	5.65466	0.348681	0.174341	−	0.984685i	$-0.444221\pi$
$263$	5.65466	0.348681	0.174341	+	0.984685i	$0.444221\pi$
$264$	1.78699	0.109982
$265$	0.103141	0.00633593
$266$	−6.49749	−0.398387
$267$	−9.07903	−0.555628
$268$	14.2222	0.868759
$269$	14.8896	0.907837	0.453919	−	0.891043i	$-0.350026\pi$
$269$	14.8896	0.907837	0.453919	+	0.891043i	$0.350026\pi$
$270$	−0.00492395	−0.000299662 0
$271$	11.4241	0.693965	0.346983	−	0.937872i	$-0.387206\pi$
$271$	11.4241	0.693965	0.346983	+	0.937872i	$0.387206\pi$
$272$	−9.61057	−0.582727
$273$	5.01575	0.303567
$274$	−1.81947	−0.109918
$275$	5.05807	0.305013
$276$	1.78183	0.107254
$277$	−4.30028	−0.258379	−0.129189	−	0.991620i	$-0.541238\pi$
$277$	−4.30028	−0.258379	−0.129189	+	0.991620i	$0.541238\pi$
$278$	−1.48140	−0.0888487
$279$	9.06687	0.542819
$280$	0.0346197	0.00206892
$281$	25.7614	1.53679	0.768397	−	0.639973i	$-0.221054\pi$
$281$	25.7614	1.53679	0.768397	+	0.639973i	$0.221054\pi$
$282$	−4.09033	−0.243575
$283$	−26.5143	−1.57611	−0.788056	−	0.615604i	$-0.788912\pi$
$283$	−26.5143	−1.57611	−0.788056	+	0.615604i	$0.788912\pi$
$284$	−5.69499	−0.337936
$285$	−0.0788785	−0.00467236
$286$	1.27482	0.0753818
$287$	−1.71367	−0.101155
$288$	−4.81203	−0.283552
$289$	−4.68467	−0.275569
$290$	−0.00492395	−0.000289144 0
$291$	−1.28711	−0.0754518
$292$	−22.0046	−1.28772
$293$	−9.65842	−0.564251	−0.282126	−	0.959377i	$-0.591039\pi$
$293$	−9.65842	−0.564251	−0.282126	+	0.959377i	$0.591039\pi$
$294$	−1.65520	−0.0965330
$295$	−0.142481	−0.00829555
$296$	−6.72464	−0.390862
$297$	1.01164	0.0587011
$298$	−0.919323	−0.0532550
$299$	2.69792	0.156025
$300$	−8.90896	−0.514359
$301$	−11.1230	−0.641117
$302$	1.37670	0.0792203
$303$	−17.9301	−1.03006
$304$	−20.4912	−1.17525
$305$	0.0158426	0.000907145 0
$306$	1.63915	0.0937041
$307$	−9.87759	−0.563744	−0.281872	−	0.959452i	$-0.590955\pi$
$307$	−9.87759	−0.563744	−0.281872	+	0.959452i	$0.590955\pi$
$308$	−3.35119	−0.190952
$309$	−16.4218	−0.934204
$310$	0.0446448	0.00253565
$311$	−24.0414	−1.36326	−0.681632	−	0.731695i	$-0.738730\pi$
$311$	−24.0414	−1.36326	−0.681632	+	0.731695i	$0.738730\pi$
$312$	−4.76570	−0.269805
$313$	−16.8236	−0.950924	−0.475462	−	0.879736i	$-0.657719\pi$
$313$	−16.8236	−0.950924	−0.475462	+	0.879736i	$0.657719\pi$
$314$	3.00054	0.169330
$315$	0.0195986	0.00110425
$316$	−17.0610	−0.959755
$317$	7.39291	0.415227	0.207614	−	0.978211i	$-0.433430\pi$
$317$	7.39291	0.415227	0.207614	+	0.978211i	$0.433430\pi$
$318$	−4.56996	−0.256271
$319$	1.01164	0.0566408
$320$	0.0340454	0.00190319
$321$	−3.00179	−0.167544
$322$	0.868368	0.0483923
$323$	26.2582	1.46104
$324$	−1.78183	−0.0989906
$325$	−13.4893	−0.748251
$326$	−5.72735	−0.317208
$327$	13.8887	0.768049
$328$	1.62824	0.0899046
$329$	16.2806	0.897577
$330$	0.00498125	0.000274209 0
$331$	6.93138	0.380983	0.190492	−	0.981689i	$-0.438992\pi$
$331$	6.93138	0.380983	0.190492	+	0.981689i	$0.438992\pi$
$332$	−26.7446	−1.46780
$333$	−3.80689	−0.208617
$334$	−2.75405	−0.150695
$335$	0.0841428	0.00459721
$336$	5.09136	0.277757
$337$	4.06977	0.221694	0.110847	−	0.993837i	$-0.464644\pi$
$337$	4.06977	0.221694	0.110847	+	0.993837i	$0.464644\pi$
$338$	2.67231	0.145354
$339$	2.10899	0.114544
$340$	−0.0659184	−0.00357493
$341$	−9.17238	−0.496712
$342$	3.49493	0.188984
$343$	19.6020	1.05841
$344$	10.5685	0.569813
$345$	0.0105419	0.000567554 0
$346$	0.654225	0.0351714
$347$	7.42107	0.398384	0.199192	−	0.979960i	$-0.436168\pi$
$347$	7.42107	0.398384	0.199192	+	0.979960i	$0.436168\pi$
$348$	−1.78183	−0.0955162
$349$	24.6446	1.31919	0.659597	−	0.751619i	$-0.270727\pi$
$349$	24.6446	1.31919	0.659597	+	0.751619i	$0.270727\pi$
$350$	−4.34174	−0.232076
$351$	−2.69792	−0.144004
$352$	4.86803	0.259467
$353$	−21.7155	−1.15580	−0.577901	−	0.816107i	$-0.696128\pi$
$353$	−21.7155	−1.15580	−0.577901	+	0.816107i	$0.696128\pi$
$354$	6.31300	0.335532
$355$	−0.0336933	−0.00178826
$356$	−16.1773	−0.857396
$357$	−6.52425	−0.345300
$358$	−8.21816	−0.434343
$359$	−11.8532	−0.625587	−0.312794	−	0.949821i	$-0.601265\pi$
$359$	−11.8532	−0.625587	−0.312794	+	0.949821i	$0.601265\pi$
$360$	−0.0186215	−0.000981441 0
$361$	36.9865	1.94666
$362$	10.1131	0.531533
$363$	9.97659	0.523635
$364$	8.93723	0.468438
$365$	−0.130186	−0.00681423
$366$	−0.701949	−0.0366915
$367$	−11.8459	−0.618349	−0.309174	−	0.951005i	$-0.600053\pi$
$367$	−11.8459	−0.618349	−0.309174	+	0.951005i	$0.600053\pi$
$368$	2.73859	0.142759
$369$	0.921766	0.0479852
$370$	−0.0187449	−0.000974503 0
$371$	18.1896	0.944358
$372$	16.1556	0.837630
$373$	−34.5101	−1.78687	−0.893434	−	0.449195i	$-0.851711\pi$
$373$	−34.5101	−1.78687	−0.893434	+	0.449195i	$0.851711\pi$
$374$	−1.65823	−0.0857449
$375$	−0.105417	−0.00544373
$376$	−15.4689	−0.797749
$377$	−2.69792	−0.138950
$378$	−0.868368	−0.0446640
$379$	−3.08382	−0.158405	−0.0792027	−	0.996859i	$-0.525237\pi$
$379$	−3.08382	−0.158405	−0.0792027	+	0.996859i	$0.525237\pi$
$380$	−0.140548	−0.00720997
$381$	−17.6790	−0.905724
$382$	−4.21546	−0.215682
$383$	−24.4060	−1.24709	−0.623544	−	0.781788i	$-0.714308\pi$
$383$	−24.4060	−1.24709	−0.623544	+	0.781788i	$0.714308\pi$
$384$	−11.1325	−0.568105
$385$	−0.0198266	−0.00101046
$386$	−1.08234	−0.0550898
$387$	5.98292	0.304129
$388$	−2.29342	−0.116431
$389$	−0.324732	−0.0164645	−0.00823227	−	0.999966i	$-0.502620\pi$
$389$	−0.324732	−0.0164645	−0.00823227	+	0.999966i	$0.502620\pi$
$390$	−0.0132844	−0.000672682 0
$391$	−3.50932	−0.177474
$392$	−6.25967	−0.316161
$393$	4.77362	0.240797
$394$	−9.94371	−0.500957
$395$	−0.100938	−0.00507874
$396$	1.80257	0.0905824
$397$	6.99747	0.351193	0.175596	−	0.984462i	$-0.443815\pi$
$397$	6.99747	0.351193	0.175596	+	0.984462i	$0.443815\pi$
$398$	2.76619	0.138657
$399$	−13.9107	−0.696406
$400$	−13.6926	−0.684631
$401$	18.5106	0.924374	0.462187	−	0.886782i	$-0.347065\pi$
$401$	18.5106	0.924374	0.462187	+	0.886782i	$0.347065\pi$
$402$	−3.72817	−0.185944
$403$	24.4617	1.21852
$404$	−31.9483	−1.58949
$405$	−0.0105419	−0.000523829 0
$406$	−0.868368	−0.0430964
$407$	3.85119	0.190897
$408$	6.19900	0.306896
$409$	−10.9316	−0.540533	−0.270266	−	0.962786i	$-0.587112\pi$
$409$	−10.9316	−0.540533	−0.270266	+	0.962786i	$0.587112\pi$
$410$	0.00453872	0.000224152 0
$411$	−3.89537	−0.192145
$412$	−29.2609	−1.44158
$413$	−25.1274	−1.23644
$414$	−0.467085	−0.0229560
$415$	−0.158229	−0.00776717
$416$	−12.9825	−0.636517
$417$	−3.17159	−0.155313
$418$	−3.53560	−0.172932
$419$	25.7158	1.25630	0.628150	−	0.778092i	$-0.283812\pi$
$419$	25.7158	1.25630	0.628150	+	0.778092i	$0.283812\pi$
$420$	0.0349214	0.00170399
$421$	34.0277	1.65841	0.829204	−	0.558945i	$-0.188794\pi$
$421$	34.0277	1.65841	0.829204	+	0.558945i	$0.188794\pi$
$422$	−3.60718	−0.175595
$423$	−8.75713	−0.425786
$424$	−17.2828	−0.839328
$425$	17.5462	0.851116
$426$	1.49287	0.0723300
$427$	2.79394	0.135208
$428$	−5.34869	−0.258539
$429$	2.72931	0.131772
$430$	0.0294596	0.00142067
$431$	−34.2245	−1.64854	−0.824269	−	0.566199i	$-0.808413\pi$
$431$	−34.2245	−1.64854	−0.824269	+	0.566199i	$0.808413\pi$
$432$	−2.73859	−0.131760
$433$	9.01368	0.433170	0.216585	−	0.976264i	$-0.430508\pi$
$433$	9.01368	0.433170	0.216585	+	0.976264i	$0.430508\pi$
$434$	7.87338	0.377934
$435$	−0.0105419	−0.000505443 0
$436$	24.7474	1.18519
$437$	−7.48241	−0.357932
$438$	5.76823	0.275617
$439$	29.1400	1.39078	0.695389	−	0.718633i	$-0.255232\pi$
$439$	29.1400	1.39078	0.695389	+	0.718633i	$0.255232\pi$
$440$	0.0188382	0.000898077 0
$441$	−3.54367	−0.168746
$442$	4.42230	0.210347
$443$	−40.2151	−1.91068	−0.955338	−	0.295516i	$-0.904508\pi$
$443$	−40.2151	−1.91068	−0.955338	+	0.295516i	$0.904508\pi$
$444$	−6.78324	−0.321918
$445$	−0.0957099	−0.00453708
$446$	5.10902	0.241919
$447$	−1.96821	−0.0930933
$448$	6.00411	0.283667
$449$	5.94087	0.280367	0.140183	−	0.990126i	$-0.455231\pi$
$449$	5.94087	0.280367	0.140183	+	0.990126i	$0.455231\pi$
$450$	2.33537	0.110091
$451$	−0.932492	−0.0439093
$452$	3.75786	0.176755
$453$	2.94743	0.138482
$454$	−10.0374	−0.471078
$455$	0.0528754	0.00247883
$456$	13.2172	0.618953
$457$	9.12815	0.426997	0.213498	−	0.976943i	$-0.431514\pi$
$457$	9.12815	0.426997	0.213498	+	0.976943i	$0.431514\pi$
$458$	4.85752	0.226977
$459$	3.50932	0.163801
$460$	0.0187838	0.000875799 0
$461$	29.1021	1.35542	0.677709	−	0.735330i	$-0.262973\pi$
$461$	29.1021	1.35542	0.677709	+	0.735330i	$0.262973\pi$
$462$	0.878473	0.0408703
$463$	−19.7693	−0.918760	−0.459380	−	0.888240i	$-0.651928\pi$
$463$	−19.7693	−0.918760	−0.459380	+	0.888240i	$0.651928\pi$
$464$	−2.73859	−0.127136
$465$	0.0955816	0.00443249
$466$	−4.37266	−0.202560
$467$	17.0583	0.789366	0.394683	−	0.918817i	$-0.370854\pi$
$467$	17.0583	0.789366	0.394683	+	0.918817i	$0.370854\pi$
$468$	−4.80723	−0.222214
$469$	14.8391	0.685206
$470$	−0.0431196	−0.00198896
$471$	6.42396	0.296000
$472$	23.8747	1.09892
$473$	−6.05254	−0.278296
$474$	4.47233	0.205421
$475$	37.4112	1.71654
$476$	−11.6251	−0.532836
$477$	−9.78399	−0.447978
$478$	−5.93999	−0.271689
$479$	−17.3642	−0.793392	−0.396696	−	0.917950i	$-0.629843\pi$
$479$	−17.3642	−0.793392	−0.396696	+	0.917950i	$0.629843\pi$
$480$	−0.0507277	−0.00231539
$481$	−10.2707	−0.468303
$482$	0.790362	0.0360000
$483$	1.85912	0.0845929
$484$	17.7766	0.808027
$485$	−0.0135685	−0.000616116 0
$486$	0.467085	0.0211874
$487$	39.5581	1.79255	0.896274	−	0.443500i	$-0.146263\pi$
$487$	39.5581	1.79255	0.896274	+	0.443500i	$0.146263\pi$
$488$	−2.65465	−0.120171
$489$	−12.2619	−0.554502
$490$	−0.0174488	−0.000788258 0
$491$	8.63557	0.389718	0.194859	−	0.980831i	$-0.437575\pi$
$491$	8.63557	0.389718	0.194859	+	0.980831i	$0.437575\pi$
$492$	1.64243	0.0740465
$493$	3.50932	0.158052
$494$	9.42902	0.424232
$495$	0.0106645	0.000479335 0
$496$	24.8304	1.11492
$497$	−5.94202	−0.266536
$498$	7.01077	0.314160
$499$	−39.3668	−1.76230	−0.881150	−	0.472837i	$-0.843230\pi$
$499$	−39.3668	−1.76230	−0.881150	+	0.472837i	$0.843230\pi$
$500$	−0.187836	−0.00840028
$501$	−5.89625	−0.263425
$502$	−4.13230	−0.184434
$503$	−34.5468	−1.54037	−0.770183	−	0.637823i	$-0.779835\pi$
$503$	−34.5468	−1.54037	−0.770183	+	0.637823i	$0.779835\pi$
$504$	−3.28402	−0.146282
$505$	−0.189016	−0.00841111
$506$	0.472521	0.0210061
$507$	5.72124	0.254089
$508$	−31.5010	−1.39763
$509$	−4.87692	−0.216165	−0.108083	−	0.994142i	$-0.534471\pi$
$509$	−4.87692	−0.216165	−0.108083	+	0.994142i	$0.534471\pi$
$510$	0.0172797	0.000765158 0
$511$	−22.9590	−1.01565
$512$	−22.8532	−1.00998
$513$	7.48241	0.330357
$514$	2.13896	0.0943454
$515$	−0.173116	−0.00762841
$516$	10.6605	0.469305
$517$	8.85904	0.389620
$518$	−3.30579	−0.145248
$519$	1.40065	0.0614819
$520$	−0.0502394	−0.00220314
$521$	28.3250	1.24094	0.620470	−	0.784230i	$-0.286942\pi$
$521$	28.3250	1.24094	0.620470	+	0.784230i	$0.286942\pi$
$522$	0.467085	0.0204438
$523$	9.04905	0.395687	0.197844	−	0.980234i	$-0.436606\pi$
$523$	9.04905	0.395687	0.197844	+	0.980234i	$0.436606\pi$
$524$	8.50578	0.371577
$525$	−9.29540	−0.405684
$526$	−2.64121	−0.115162
$527$	−31.8185	−1.38604
$528$	2.77045	0.120569
$529$	1.00000	0.0434783
$530$	−0.0481759	−0.00209263
$531$	13.5157	0.586533
$532$	−24.7865	−1.07463
$533$	2.48685	0.107717
$534$	4.24068	0.183512
$535$	−0.0316445	−0.00136811
$536$	−14.0993	−0.608998
$537$	−17.5946	−0.759261
$538$	−6.95473	−0.299840
$539$	3.58491	0.154413
$540$	−0.0187838	−0.000808326 0
$541$	−42.1779	−1.81337	−0.906685	−	0.421808i	$-0.861396\pi$
$541$	−42.1779	−1.81337	−0.906685	+	0.421808i	$0.861396\pi$
$542$	−5.33604	−0.229202
$543$	21.6515	0.929155
$544$	16.8870	0.724022
$545$	0.146413	0.00627165
$546$	−2.34279	−0.100262
$547$	−31.3645	−1.34105	−0.670525	−	0.741887i	$-0.733931\pi$
$547$	−31.3645	−1.34105	−0.670525	+	0.741887i	$0.733931\pi$
$548$	−6.94089	−0.296500
$549$	−1.50283	−0.0641392
$550$	−2.36255	−0.100740
$551$	7.48241	0.318761
$552$	−1.76644	−0.0751846
$553$	−17.8010	−0.756977
$554$	2.00860	0.0853372
$555$	−0.0401317	−0.00170350
$556$	−5.65124	−0.239666
$557$	−39.1429	−1.65854	−0.829269	−	0.558850i	$-0.811243\pi$
$557$	−39.1429	−1.65854	−0.829269	+	0.558850i	$0.811243\pi$
$558$	−4.23500	−0.179282
$559$	16.1414	0.682709
$560$	0.0536724	0.00226807
$561$	−3.55016	−0.149888
$562$	−12.0328	−0.507571
$563$	18.0039	0.758775	0.379388	−	0.925238i	$-0.376135\pi$
$563$	18.0039	0.758775	0.379388	+	0.925238i	$0.376135\pi$
$564$	−15.6037	−0.657036
$565$	0.0222326	0.000935334 0
$566$	12.3844	0.520557
$567$	−1.85912	−0.0780757
$568$	5.64580	0.236892
$569$	41.1091	1.72338	0.861691	−	0.507433i	$-0.169406\pi$
$569$	41.1091	1.72338	0.861691	+	0.507433i	$0.169406\pi$
$570$	0.0368430	0.00154318
$571$	−32.4790	−1.35920	−0.679601	−	0.733582i	$-0.737847\pi$
$571$	−32.4790	−1.35920	−0.679601	+	0.733582i	$0.737847\pi$
$572$	4.86317	0.203340
$573$	−9.02504	−0.377026
$574$	0.800432	0.0334094
$575$	−4.99989	−0.208510
$576$	−3.22954	−0.134564
$577$	7.17376	0.298647	0.149324	−	0.988788i	$-0.452290\pi$
$577$	7.17376	0.298647	0.149324	+	0.988788i	$0.452290\pi$
$578$	2.18814	0.0910147
$579$	−2.31723	−0.0963007
$580$	−0.0187838	−0.000779955 0
$581$	−27.9047	−1.15768
$582$	0.601191	0.0249202
$583$	9.89785	0.409927
$584$	21.8145	0.902689
$585$	−0.0284411	−0.00117589
$586$	4.51131	0.186360
$587$	3.16686	0.130710	0.0653552	−	0.997862i	$-0.479182\pi$
$587$	3.16686	0.130710	0.0653552	+	0.997862i	$0.479182\pi$
$588$	−6.31422	−0.260394
$589$	−67.8421	−2.79538
$590$	0.0665507	0.00273985
$591$	−21.2889	−0.875706
$592$	−10.4255	−0.428486
$593$	1.38330	0.0568054	0.0284027	−	0.999597i	$-0.490958\pi$
$593$	1.38330	0.0568054	0.0284027	+	0.999597i	$0.490958\pi$
$594$	−0.472521	−0.0193878
$595$	−0.0687777	−0.00281961
$596$	−3.50702	−0.143653
$597$	5.92224	0.242381
$598$	−1.26016	−0.0515317
$599$	−0.353620	−0.0144485	−0.00722427	−	0.999974i	$-0.502300\pi$
$599$	−0.353620	−0.0144485	−0.00722427	+	0.999974i	$0.502300\pi$
$600$	8.83199	0.360565
$601$	−1.76477	−0.0719863	−0.0359931	−	0.999352i	$-0.511459\pi$
$601$	−1.76477	−0.0719863	−0.0359931	+	0.999352i	$0.511459\pi$
$602$	5.19537	0.211748
$603$	−7.98178	−0.325043
$604$	5.25183	0.213694
$605$	0.105172	0.00427584
$606$	8.37487	0.340206
$607$	−34.2574	−1.39047	−0.695233	−	0.718785i	$-0.744699\pi$
$607$	−34.2574	−1.39047	−0.695233	+	0.718785i	$0.744699\pi$
$608$	36.0056	1.46022
$609$	−1.85912	−0.0753354
$610$	−0.00739985	−0.000299611 0
$611$	−23.6260	−0.955806
$612$	6.25302	0.252763
$613$	10.3428	0.417743	0.208871	−	0.977943i	$-0.433021\pi$
$613$	10.3428	0.417743	0.208871	+	0.977943i	$0.433021\pi$
$614$	4.61368	0.186193
$615$	0.00971712	0.000391832 0
$616$	3.32224	0.133857
$617$	33.9967	1.36866	0.684328	−	0.729174i	$-0.260096\pi$
$617$	33.9967	1.36866	0.684328	+	0.729174i	$0.260096\pi$
$618$	7.67039	0.308548
$619$	22.6908	0.912022	0.456011	−	0.889974i	$-0.349278\pi$
$619$	22.6908	0.912022	0.456011	+	0.889974i	$0.349278\pi$
$620$	0.170310	0.00683983
$621$	−1.00000	−0.0401286
$622$	11.2294	0.450258
$623$	−16.8790	−0.676244
$624$	−7.38848	−0.295776
$625$	24.9983	0.999933
$626$	7.85804	0.314070
$627$	−7.56948	−0.302296
$628$	11.4464	0.456762
$629$	13.3596	0.532683
$630$	−0.00915421	−0.000364712 0
$631$	44.0926	1.75530	0.877649	−	0.479304i	$-0.159111\pi$
$631$	44.0926	1.75530	0.877649	+	0.479304i	$0.159111\pi$
$632$	16.9136	0.672786
$633$	−7.72273	−0.306951
$634$	−3.45312	−0.137141
$635$	−0.186370	−0.00739586
$636$	−17.4334	−0.691280
$637$	−9.56053	−0.378802
$638$	−0.472521	−0.0187073
$639$	3.19615	0.126438
$640$	−0.117358	−0.00463896
$641$	35.7799	1.41322	0.706611	−	0.707603i	$-0.250223\pi$
$641$	35.7799	1.41322	0.706611	+	0.707603i	$0.250223\pi$
$642$	1.40209	0.0553362
$643$	14.1099	0.556438	0.278219	−	0.960518i	$-0.410256\pi$
$643$	14.1099	0.556438	0.278219	+	0.960518i	$0.410256\pi$
$644$	3.31264	0.130536
$645$	0.0630710	0.00248342
$646$	−12.2648	−0.482553
$647$	31.5829	1.24165	0.620826	−	0.783948i	$-0.286797\pi$
$647$	31.5829	1.24165	0.620826	+	0.783948i	$0.286797\pi$
$648$	1.76644	0.0693922
$649$	−13.6730	−0.536713
$650$	6.30065	0.247132
$651$	16.8564	0.660655
$652$	−21.8486	−0.855657
$653$	40.0535	1.56742	0.783708	−	0.621130i	$-0.213326\pi$
$653$	40.0535	1.56742	0.783708	+	0.621130i	$0.213326\pi$
$654$	−6.48723	−0.253671
$655$	0.0503228	0.00196627
$656$	2.52433	0.0985587
$657$	12.3494	0.481796
$658$	−7.60441	−0.296451
$659$	2.01244	0.0783933	0.0391967	−	0.999232i	$-0.487520\pi$
$659$	2.01244	0.0783933	0.0391967	+	0.999232i	$0.487520\pi$
$660$	0.0190024	0.000739667 0
$661$	−22.8081	−0.887134	−0.443567	−	0.896241i	$-0.646287\pi$
$661$	−22.8081	−0.887134	−0.443567	+	0.896241i	$0.646287\pi$
$662$	−3.23755	−0.125831
$663$	9.46786	0.367701
$664$	26.5136	1.02893
$665$	−0.146645	−0.00568664
$666$	1.77814	0.0689017
$667$	−1.00000	−0.0387202
$668$	−10.5061	−0.406494
$669$	10.9381	0.422891
$670$	−0.0393019	−0.00151836
$671$	1.52032	0.0586912
$672$	−8.94614	−0.345105
$673$	5.35191	0.206301	0.103150	−	0.994666i	$-0.467108\pi$
$673$	5.35191	0.206301	0.103150	+	0.994666i	$0.467108\pi$
$674$	−1.90093	−0.0732211
$675$	4.99989	0.192446
$676$	10.1943	0.392088
$677$	−30.9706	−1.19030	−0.595149	−	0.803615i	$-0.702907\pi$
$677$	−30.9706	−1.19030	−0.595149	+	0.803615i	$0.702907\pi$
$678$	−0.985077	−0.0378316
$679$	−2.39290	−0.0918309
$680$	0.0653489	0.00250602
$681$	−21.4894	−0.823477
$682$	4.28428	0.164054
$683$	−48.6419	−1.86123	−0.930615	−	0.365999i	$-0.880727\pi$
$683$	−48.6419	−1.86123	−0.930615	+	0.365999i	$0.880727\pi$
$684$	13.3324	0.509777
$685$	−0.0410644	−0.00156899
$686$	−9.15579	−0.349570
$687$	10.3996	0.396771
$688$	16.3847	0.624662
$689$	−26.3964	−1.00562
$690$	−0.00492395	−0.000187451 0
$691$	49.3224	1.87631	0.938156	−	0.346213i	$-0.112532\pi$
$691$	49.3224	1.87631	0.938156	+	0.346213i	$0.112532\pi$
$692$	2.49573	0.0948734
$693$	1.88076	0.0714440
$694$	−3.46627	−0.131578
$695$	−0.0334344	−0.00126824
$696$	1.76644	0.0669567
$697$	−3.23477	−0.122526
$698$	−11.5111	−0.435703
$699$	−9.36159	−0.354088
$700$	−16.5628	−0.626016
$701$	24.7023	0.932993	0.466497	−	0.884523i	$-0.345516\pi$
$701$	24.7023	0.932993	0.466497	+	0.884523i	$0.345516\pi$
$702$	1.26016	0.0475616
$703$	28.4848	1.07432
$704$	3.26712	0.123134
$705$	−0.0923164	−0.00347684
$706$	10.1430	0.381737
$707$	−33.3342	−1.25366
$708$	24.0827	0.905085
$709$	21.9049	0.822655	0.411328	−	0.911488i	$-0.365065\pi$
$709$	21.9049	0.822655	0.411328	+	0.911488i	$0.365065\pi$
$710$	0.0157377	0.000590624 0
$711$	9.57497	0.359089
$712$	16.0376	0.601033
$713$	9.06687	0.339557
$714$	3.04738	0.114045
$715$	0.0287720	0.00107601
$716$	−31.3505	−1.17162
$717$	−12.7171	−0.474930
$718$	5.53645	0.206618
$719$	24.6474	0.919194	0.459597	−	0.888128i	$-0.347994\pi$
$719$	24.6474	0.919194	0.459597	+	0.888128i	$0.347994\pi$
$720$	−0.0288698	−0.00107591
$721$	−30.5301	−1.13700
$722$	−17.2758	−0.642941
$723$	1.69211	0.0629304
$724$	38.5793	1.43379
$725$	4.99989	0.185691
$726$	−4.65992	−0.172946
$727$	1.09130	0.0404741	0.0202370	−	0.999795i	$-0.493558\pi$
$727$	1.09130	0.0404741	0.0202370	+	0.999795i	$0.493558\pi$
$728$	−8.86002	−0.328374
$729$	1.00000	0.0370370
$730$	0.0608078	0.00225060
$731$	−20.9960	−0.776564
$732$	−2.67779	−0.0989739
$733$	−11.3513	−0.419271	−0.209635	−	0.977780i	$-0.567228\pi$
$733$	−11.3513	−0.419271	−0.209635	+	0.977780i	$0.567228\pi$
$734$	5.53303	0.204228
$735$	−0.0373568	−0.00137793
$736$	−4.81203	−0.177374
$737$	8.07467	0.297434
$738$	−0.430543	−0.0158485
$739$	37.8330	1.39171	0.695854	−	0.718183i	$-0.255026\pi$
$739$	37.8330	1.39171	0.695854	+	0.718183i	$0.255026\pi$
$740$	−0.0715080	−0.00262868
$741$	20.1869	0.741585
$742$	−8.49611	−0.311902
$743$	19.9697	0.732618	0.366309	−	0.930493i	$-0.380621\pi$
$743$	19.9697	0.732618	0.366309	+	0.930493i	$0.380621\pi$
$744$	−16.0161	−0.587177
$745$	−0.0207486	−0.000760170 0
$746$	16.1192	0.590165
$747$	15.0096	0.549173
$748$	−6.32578	−0.231294
$749$	−5.58070	−0.203914
$750$	0.0492389	0.00179795
$751$	−10.9630	−0.400046	−0.200023	−	0.979791i	$-0.564102\pi$
$751$	−10.9630	−0.400046	−0.200023	+	0.979791i	$0.564102\pi$
$752$	−23.9821	−0.874539
$753$	−8.84699	−0.322402
$754$	1.26016	0.0458922
$755$	0.0310714	0.00113080
$756$	−3.31264	−0.120480
$757$	30.3461	1.10295	0.551474	−	0.834192i	$-0.314066\pi$
$757$	30.3461	1.10295	0.551474	+	0.834192i	$0.314066\pi$
$758$	1.44041	0.0523180
$759$	1.01164	0.0367201
$760$	0.139334	0.00505417
$761$	−53.4315	−1.93689	−0.968446	−	0.249223i	$-0.919825\pi$
$761$	−53.4315	−1.93689	−0.968446	+	0.249223i	$0.919825\pi$
$762$	8.25761	0.299142
$763$	25.8208	0.934777
$764$	−16.0811	−0.581793
$765$	0.0369947	0.00133755
$766$	11.3997	0.411887
$767$	36.4643	1.31665
$768$	−1.25924	−0.0454390
$769$	40.3898	1.45649	0.728246	−	0.685315i	$-0.240336\pi$
$769$	40.3898	1.45649	0.728246	+	0.685315i	$0.240336\pi$
$770$	0.00926074	0.000333734 0
$771$	4.57937	0.164922
$772$	−4.12891	−0.148603
$773$	21.5543	0.775255	0.387627	−	0.921816i	$-0.373295\pi$
$773$	21.5543	0.775255	0.387627	+	0.921816i	$0.373295\pi$
$774$	−2.79453	−0.100447
$775$	−45.3333	−1.62842
$776$	2.27360	0.0816176
$777$	−7.07748	−0.253903
$778$	0.151677	0.00543790
$779$	−6.89703	−0.247112
$780$	−0.0506772	−0.00181453
$781$	−3.23334	−0.115698
$782$	1.63915	0.0586160
$783$	1.00000	0.0357371
$784$	−9.70464	−0.346594
$785$	0.0677205	0.00241705
$786$	−2.22969	−0.0795303
$787$	−28.6203	−1.02020	−0.510101	−	0.860114i	$-0.670392\pi$
$787$	−28.6203	−1.02020	−0.510101	+	0.860114i	$0.670392\pi$
$788$	−37.9331	−1.35131
$789$	−5.65466	−0.201311
$790$	0.0471466	0.00167740
$791$	3.92086	0.139410
$792$	−1.78699	−0.0634981
$793$	−4.05451	−0.143980
$794$	−3.26841	−0.115992
$795$	−0.103141	−0.00365805
$796$	10.5524	0.374021
$797$	−41.4204	−1.46719	−0.733593	−	0.679589i	$-0.762158\pi$
$797$	−41.4204	−1.46719	−0.733593	+	0.679589i	$0.762158\pi$
$798$	6.49749	0.230009
$799$	30.7316	1.08721
$800$	24.0596	0.850636
$801$	9.07903	0.320792
$802$	−8.64602	−0.305302
$803$	−12.4931	−0.440872
$804$	−14.2222	−0.501578
$805$	0.0195986	0.000690759 0
$806$	−11.4257	−0.402453
$807$	−14.8896	−0.524140
$808$	31.6723	1.11423
$809$	16.4746	0.579215	0.289608	−	0.957145i	$-0.406475\pi$
$809$	16.4746	0.579215	0.289608	+	0.957145i	$0.406475\pi$
$810$	0.00492395	0.000173010 0
$811$	−20.4990	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$811$	−20.4990	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$812$	−3.31264	−0.116251
$813$	−11.4241	−0.400661
$814$	−1.79884	−0.0630492
$815$	−0.129263	−0.00452788
$816$	9.61057	0.336437
$817$	−44.7667	−1.56619
$818$	5.10599	0.178527
$819$	−5.01575	−0.175265
$820$	0.0173143	0.000604640 0
$821$	13.5365	0.472427	0.236213	−	0.971701i	$-0.424094\pi$
$821$	13.5365	0.472427	0.236213	+	0.971701i	$0.424094\pi$
$822$	1.81947	0.0634613
$823$	5.32001	0.185444	0.0927219	−	0.995692i	$-0.470443\pi$
$823$	5.32001	0.185444	0.0927219	+	0.995692i	$0.470443\pi$
$824$	29.0081	1.01055
$825$	−5.05807	−0.176099
$826$	11.7366	0.408370
$827$	2.86383	0.0995851	0.0497926	−	0.998760i	$-0.484144\pi$
$827$	2.86383	0.0995851	0.0497926	+	0.998760i	$0.484144\pi$
$828$	−1.78183	−0.0619229
$829$	−50.6084	−1.75770	−0.878852	−	0.477095i	$-0.841690\pi$
$829$	−50.6084	−1.75770	−0.878852	+	0.477095i	$0.841690\pi$
$830$	0.0739066	0.00256533
$831$	4.30028	0.149175
$832$	−8.71304	−0.302070
$833$	12.4359	0.430877
$834$	1.48140	0.0512968
$835$	−0.0621574	−0.00215105
$836$	−13.4875	−0.466476
$837$	−9.06687	−0.313397
$838$	−12.0115	−0.414930
$839$	−19.9598	−0.689089	−0.344545	−	0.938770i	$-0.611967\pi$
$839$	−19.9598	−0.689089	−0.344545	+	0.938770i	$0.611967\pi$
$840$	−0.0346197	−0.00119449
$841$	1.00000	0.0344828
$842$	−15.8938	−0.547738
$843$	−25.7614	−0.887269
$844$	−13.7606	−0.473660
$845$	0.0603125	0.00207481
$846$	4.09033	0.140628
$847$	18.5477	0.637306
$848$	−26.7943	−0.920120
$849$	26.5143	0.909968
$850$	−8.19558	−0.281106
$851$	−3.80689	−0.130499
$852$	5.69499	0.195107
$853$	2.93688	0.100557	0.0502784	−	0.998735i	$-0.483989\pi$
$853$	2.93688	0.100557	0.0502784	+	0.998735i	$0.483989\pi$
$854$	−1.30501	−0.0446565
$855$	0.0788785	0.00269759
$856$	5.30248	0.181235
$857$	−36.5423	−1.24826	−0.624131	−	0.781320i	$-0.714547\pi$
$857$	−36.5423	−1.24826	−0.624131	+	0.781320i	$0.714547\pi$
$858$	−1.27482	−0.0435217
$859$	15.2091	0.518929	0.259464	−	0.965753i	$-0.416454\pi$
$859$	15.2091	0.518929	0.259464	+	0.965753i	$0.416454\pi$
$860$	0.112382	0.00383219
$861$	1.71367	0.0584018
$862$	15.9858	0.544478
$863$	−11.0986	−0.377802	−0.188901	−	0.981996i	$-0.560493\pi$
$863$	−11.0986	−0.377802	−0.188901	+	0.981996i	$0.560493\pi$
$864$	4.81203	0.163709
$865$	0.0147655	0.000502042 0
$866$	−4.21016	−0.143067
$867$	4.68467	0.159100
$868$	30.0353	1.01946
$869$	−9.68639	−0.328588
$870$	0.00492395	0.000166937 0
$871$	−21.5342	−0.729658
$872$	−24.5336	−0.830813
$873$	1.28711	0.0435621
$874$	3.49493	0.118218
$875$	−0.195984	−0.00662546
$876$	22.0046	0.743465
$877$	−23.3671	−0.789051	−0.394526	−	0.918885i	$-0.629091\pi$
$877$	−23.3671	−0.789051	−0.394526	+	0.918885i	$0.629091\pi$
$878$	−13.6109	−0.459345
$879$	9.65842	0.325771
$880$	0.0292057	0.000984525 0
$881$	45.1791	1.52212	0.761061	−	0.648680i	$-0.224679\pi$
$881$	45.1791	1.52212	0.761061	+	0.648680i	$0.224679\pi$
$882$	1.65520	0.0557334
$883$	25.5241	0.858955	0.429478	−	0.903077i	$-0.358698\pi$
$883$	25.5241	0.858955	0.429478	+	0.903077i	$0.358698\pi$
$884$	16.8701	0.567404
$885$	0.142481	0.00478944
$886$	18.7839	0.631056
$887$	15.3894	0.516725	0.258362	−	0.966048i	$-0.416817\pi$
$887$	15.3894	0.516725	0.258362	+	0.966048i	$0.416817\pi$
$888$	6.72464	0.225664
$889$	−32.8674	−1.10234
$890$	0.0447047	0.00149850
$891$	−1.01164	−0.0338911
$892$	19.4898	0.652568
$893$	65.5245	2.19269
$894$	0.919323	0.0307468
$895$	−0.185479	−0.00619989
$896$	−20.6967	−0.691429
$897$	−2.69792	−0.0900808
$898$	−2.77489	−0.0925994
$899$	−9.06687	−0.302397
$900$	8.90896	0.296965
$901$	34.3352	1.14387
$902$	0.435553	0.0145023
$903$	11.1230	0.370149
$904$	−3.72539	−0.123905
$905$	0.228247	0.00758719
$906$	−1.37670	−0.0457379
$907$	−15.7921	−0.524368	−0.262184	−	0.965018i	$-0.584443\pi$
$907$	−15.7921	−0.524368	−0.262184	+	0.965018i	$0.584443\pi$
$908$	−38.2905	−1.27072
$909$	17.9301	0.594703
$910$	−0.0246973	−0.000818708 0
$911$	2.70731	0.0896972	0.0448486	−	0.998994i	$-0.485719\pi$
$911$	2.70731	0.0896972	0.0448486	+	0.998994i	$0.485719\pi$
$912$	20.4912	0.678532
$913$	−15.1843	−0.502526
$914$	−4.26363	−0.141028
$915$	−0.0158426	−0.000523740 0
$916$	18.5304	0.612262
$917$	8.87473	0.293069
$918$	−1.63915	−0.0541001
$919$	23.0679	0.760940	0.380470	−	0.924793i	$-0.375762\pi$
$919$	23.0679	0.760940	0.380470	+	0.924793i	$0.375762\pi$
$920$	−0.0186215	−0.000613934 0
$921$	9.87759	0.325478
$922$	−13.5932	−0.447667
$923$	8.62294	0.283828
$924$	3.35119	0.110246
$925$	19.0340	0.625836
$926$	9.23397	0.303447
$927$	16.4218	0.539363
$928$	4.81203	0.157963
$929$	−27.9038	−0.915494	−0.457747	−	0.889083i	$-0.651343\pi$
$929$	−27.9038	−0.915494	−0.457747	+	0.889083i	$0.651343\pi$
$930$	−0.0446448	−0.00146396
$931$	26.5152	0.869000
$932$	−16.6808	−0.546397
$933$	24.0414	0.787081
$934$	−7.96770	−0.260711
$935$	−0.0374252	−0.00122394
$936$	4.76570	0.155772
$937$	−50.2667	−1.64214	−0.821070	−	0.570827i	$-0.806623\pi$
$937$	−50.2667	−1.64214	−0.821070	+	0.570827i	$0.806623\pi$
$938$	−6.93113	−0.226309
$939$	16.8236	0.549016
$940$	−0.164492	−0.00536515
$941$	−0.205558	−0.00670099	−0.00335050	−	0.999994i	$-0.501066\pi$
$941$	−0.205558	−0.00670099	−0.00335050	+	0.999994i	$0.501066\pi$
$942$	−3.00054	−0.0977628
$943$	0.921766	0.0300168
$944$	37.0140	1.20470
$945$	−0.0195986	−0.000637542 0
$946$	2.82705	0.0919154
$947$	12.3180	0.400283	0.200141	−	0.979767i	$-0.435860\pi$
$947$	12.3180	0.400283	0.200141	+	0.979767i	$0.435860\pi$
$948$	17.0610	0.554115
$949$	33.3177	1.08154
$950$	−17.4742	−0.566939
$951$	−7.39291	−0.239731
$952$	11.5247	0.373517
$953$	−12.5356	−0.406068	−0.203034	−	0.979172i	$-0.565080\pi$
$953$	−12.5356	−0.406068	−0.203034	+	0.979172i	$0.565080\pi$
$954$	4.56996	0.147958
$955$	−0.0951406	−0.00307868
$956$	−22.6598	−0.732870
$957$	−1.01164	−0.0327016
$958$	8.11057	0.262041
$959$	−7.24197	−0.233855
$960$	−0.0340454	−0.00109881
$961$	51.2081	1.65188
$962$	4.79729	0.154671
$963$	3.00179	0.0967315
$964$	3.01506	0.0971086
$965$	−0.0244279	−0.000786361 0
$966$	−0.868368	−0.0279393
$967$	−33.5440	−1.07870	−0.539351	−	0.842081i	$-0.681330\pi$
$967$	−33.5440	−1.07870	−0.539351	+	0.842081i	$0.681330\pi$
$968$	−17.6230	−0.566426
$969$	−26.2582	−0.843534
$970$	0.00633767	0.000203490 0
$971$	−22.4426	−0.720216	−0.360108	−	0.932911i	$-0.617260\pi$
$971$	−22.4426	−0.720216	−0.360108	+	0.932911i	$0.617260\pi$
$972$	1.78183	0.0571523
$973$	−5.89637	−0.189029
$974$	−18.4770	−0.592042
$975$	13.4893	0.432003
$976$	−4.11563	−0.131738
$977$	−7.78408	−0.249035	−0.124517	−	0.992217i	$-0.539738\pi$
$977$	−7.78408	−0.249035	−0.124517	+	0.992217i	$0.539738\pi$
$978$	5.72735	0.183140
$979$	−9.18469	−0.293544
$980$	−0.0665636	−0.00212630
$981$	−13.8887	−0.443433
$982$	−4.03355	−0.128716
$983$	33.4760	1.06772	0.533859	−	0.845574i	$-0.320741\pi$
$983$	33.4760	1.06772	0.533859	+	0.845574i	$0.320741\pi$
$984$	−1.62824	−0.0519065
$985$	−0.224424	−0.00715074
$986$	−1.63915	−0.0522012
$987$	−16.2806	−0.518216
$988$	35.9697	1.14435
$989$	5.98292	0.190246
$990$	−0.00498125	−0.000158314 0
$991$	2.35201	0.0747140	0.0373570	−	0.999302i	$-0.488106\pi$
$991$	2.35201	0.0747140	0.0373570	+	0.999302i	$0.488106\pi$
$992$	−43.6300	−1.38526
$993$	−6.93138	−0.219961
$994$	2.77543	0.0880314
$995$	0.0624314	0.00197921
$996$	26.7446	0.847435
$997$	28.4195	0.900055	0.450028	−	0.893015i	$-0.351414\pi$
$997$	28.4195	0.900055	0.450028	+	0.893015i	$0.351414\pi$
$998$	18.3876	0.582051
$999$	3.80689	0.120445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.6	✓	11
3.2	odd	2		6003.2.a.m.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.6	✓	11	1.1	even	1	trivial
6003.2.a.m.1.6		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-0.467085 q^{2} -1.00000 q^{3} -1.78183 q^{4} -0.0105419 q^{5} +0.467085 q^{6} -1.85912 q^{7} +1.76644 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.467085 q^{2} -1.00000 q^{3} -1.78183 q^{4} -0.0105419 q^{5} +0.467085 q^{6} -1.85912 q^{7} +1.76644 q^{8} +1.00000 q^{9} +0.00492395 q^{10} -1.01164 q^{11} +1.78183 q^{12} +2.69792 q^{13} +0.868368 q^{14} +0.0105419 q^{15} +2.73859 q^{16} -3.50932 q^{17} -0.467085 q^{18} -7.48241 q^{19} +0.0187838 q^{20} +1.85912 q^{21} +0.472521 q^{22} +1.00000 q^{23} -1.76644 q^{24} -4.99989 q^{25} -1.26016 q^{26} -1.00000 q^{27} +3.31264 q^{28} -1.00000 q^{29} -0.00492395 q^{30} +9.06687 q^{31} -4.81203 q^{32} +1.01164 q^{33} +1.63915 q^{34} +0.0195986 q^{35} -1.78183 q^{36} -3.80689 q^{37} +3.49493 q^{38} -2.69792 q^{39} -0.0186215 q^{40} +0.921766 q^{41} -0.868368 q^{42} +5.98292 q^{43} +1.80257 q^{44} -0.0105419 q^{45} -0.467085 q^{46} -8.75713 q^{47} -2.73859 q^{48} -3.54367 q^{49} +2.33537 q^{50} +3.50932 q^{51} -4.80723 q^{52} -9.78399 q^{53} +0.467085 q^{54} +0.0106645 q^{55} -3.28402 q^{56} +7.48241 q^{57} +0.467085 q^{58} +13.5157 q^{59} -0.0187838 q^{60} -1.50283 q^{61} -4.23500 q^{62} -1.85912 q^{63} -3.22954 q^{64} -0.0284411 q^{65} -0.472521 q^{66} -7.98178 q^{67} +6.25302 q^{68} -1.00000 q^{69} -0.00915421 q^{70} +3.19615 q^{71} +1.76644 q^{72} +12.3494 q^{73} +1.77814 q^{74} +4.99989 q^{75} +13.3324 q^{76} +1.88076 q^{77} +1.26016 q^{78} +9.57497 q^{79} -0.0288698 q^{80} +1.00000 q^{81} -0.430543 q^{82} +15.0096 q^{83} -3.31264 q^{84} +0.0369947 q^{85} -2.79453 q^{86} +1.00000 q^{87} -1.78699 q^{88} +9.07903 q^{89} +0.00492395 q^{90} -5.01575 q^{91} -1.78183 q^{92} -9.06687 q^{93} +4.09033 q^{94} +0.0788785 q^{95} +4.81203 q^{96} +1.28711 q^{97} +1.65520 q^{98} -1.01164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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