LMFDB - Embedded newform 531.2.i.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

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:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	531.46
Dual form			531.2.i.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65338 - 1.94651i) q^{2} +(-0.731672 + 4.46300i) q^{4} +(-0.865278 + 1.63209i) q^{5} +(-2.96873 + 0.322869i) q^{7} +(5.52030 - 3.32145i) q^{8} +O(q^{10})$	\(q+(-1.65338 - 1.94651i) q^{2} +(-0.731672 + 4.46300i) q^{4} +(-0.865278 + 1.63209i) q^{5} +(-2.96873 + 0.322869i) q^{7} +(5.52030 - 3.32145i) q^{8} +(4.60751 - 1.01419i) q^{10} +(-1.34480 + 0.453117i) q^{11} +(0.0906890 + 0.326632i) q^{13} +(5.53691 + 5.24484i) q^{14} +(-7.02074 - 2.36556i) q^{16} +(5.48778 + 0.596832i) q^{17} +(-0.404228 - 7.45555i) q^{19} +(-6.65091 - 5.05589i) q^{20} +(3.10547 + 1.86850i) q^{22} +(-5.20536 - 2.40826i) q^{23} +(0.890931 + 1.31402i) q^{25} +(0.485850 - 0.716575i) q^{26} +(0.731172 - 13.4857i) q^{28} +(6.31204 - 7.43111i) q^{29} +(0.367396 - 6.77621i) q^{31} +(2.23414 + 5.60728i) q^{32} +(-7.91166 - 11.6688i) q^{34} +(2.04183 - 5.12460i) q^{35} +(0.851751 + 0.512481i) q^{37} +(-13.8440 + 13.1137i) q^{38} +(0.644310 + 11.8836i) q^{40} +(4.25981 - 1.97080i) q^{41} +(4.73498 + 1.59540i) q^{43} +(-1.03831 - 6.33339i) q^{44} +(3.91875 + 14.1141i) q^{46} +(-1.64649 - 3.10562i) q^{47} +(1.87277 - 0.412227i) q^{49} +(1.08472 - 3.90679i) q^{50} +(-1.52411 + 0.165757i) q^{52} +(-11.8048 - 2.59843i) q^{53} +(0.424102 - 2.58691i) q^{55} +(-15.3159 + 11.6428i) q^{56} -24.9010 q^{58} +(6.35981 + 4.30730i) q^{59} +(8.57456 + 10.0948i) q^{61} +(-13.7974 + 10.4885i) q^{62} +(0.280274 - 0.528653i) q^{64} +(-0.611563 - 0.134615i) q^{65} +(-2.15987 + 1.29955i) q^{67} +(-6.67892 + 24.0553i) q^{68} +(-13.3510 + 4.49848i) q^{70} +(3.67652 + 6.93466i) q^{71} +(-6.93951 - 6.57345i) q^{73} +(-0.410718 - 2.50527i) q^{74} +(33.5699 + 3.65094i) q^{76} +(3.84606 - 1.77938i) q^{77} +(-5.27421 - 4.00935i) q^{79} +(9.93570 - 9.41160i) q^{80} +(-10.8793 - 5.03329i) q^{82} +(4.15362 - 10.4248i) q^{83} +(-5.72254 + 8.44012i) q^{85} +(-4.72327 - 11.8545i) q^{86} +(-5.91871 + 6.96804i) q^{88} +(8.82969 - 10.3951i) q^{89} +(-0.374690 - 0.940402i) q^{91} +(14.5567 - 21.4695i) q^{92} +(-3.32284 + 8.33969i) q^{94} +(12.5179 + 5.79139i) q^{95} +(7.91972 - 7.50196i) q^{97} +(-3.89880 - 2.96379i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{8}{29}\right)$

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 $

$2$	−1.65338	−	1.94651i	−1.16912	−	1.37639i	−0.912091	−	0.409987i	$-0.865533\pi$
$2$	−1.65338	−	1.94651i	−1.16912	−	1.37639i	−0.257026	−	0.966404i	$-0.582743\pi$
$3$		0			0
$3$		0			0
$4$	−0.731672	+	4.46300i	−0.365836	+	2.23150i
$5$	−0.865278	+	1.63209i	−0.386964	+	0.729892i	−0.998099	−	0.0616348i	$-0.980369\pi$
$5$	−0.865278	+	1.63209i	−0.386964	+	0.729892i	0.611135	+	0.791527i	$0.290713\pi$
$6$		0			0
$7$	−2.96873	+	0.322869i	−1.12207	+	0.122033i	−0.650294	−	0.759683i	$-0.725354\pi$
$7$	−2.96873	+	0.322869i	−1.12207	+	0.122033i	−0.471781	+	0.881716i	$0.656389\pi$
$8$	5.52030	−	3.32145i	1.95172	−	1.17431i
$9$		0			0
$10$	4.60751	−	1.01419i	1.45702	−	0.320715i
$11$	−1.34480	+	0.453117i	−0.405473	+	0.136620i	−0.514646	−	0.857403i	$-0.672077\pi$
$11$	−1.34480	+	0.453117i	−0.405473	+	0.136620i	0.109172	+	0.994023i	$0.465180\pi$
$12$		0			0
$13$	0.0906890	+	0.326632i	0.0251526	+	0.0905914i	0.975061	−	0.221937i	$-0.0712379\pi$
$13$	0.0906890	+	0.326632i	0.0251526	+	0.0905914i	−0.949908	+	0.312528i	$0.898824\pi$
$14$	5.53691	+	5.24484i	1.47980	+	1.40174i
$15$		0			0
$16$	−7.02074	−	2.36556i	−1.75519	−	0.591391i
$17$	5.48778	+	0.596832i	1.33098	+	0.144753i	0.745812	−	0.666157i	$-0.232062\pi$
$17$	5.48778	+	0.596832i	1.33098	+	0.144753i	0.585171	+	0.810910i	$0.301027\pi$
$18$		0			0
$19$	−0.404228	−	7.45555i	−0.0927363	−	1.71042i	−0.561814	−	0.827263i	$-0.689896\pi$
$19$	−0.404228	−	7.45555i	−0.0927363	−	1.71042i	0.469078	−	0.883157i	$-0.344586\pi$
$20$	−6.65091	−	5.05589i	−1.48719	−	1.13053i
$21$		0			0
$22$	3.10547	+	1.86850i	0.662088	+	0.398365i
$23$	−5.20536	−	2.40826i	−1.08539	−	0.502156i	−0.206145	−	0.978521i	$-0.566092\pi$
$23$	−5.20536	−	2.40826i	−1.08539	−	0.502156i	−0.879247	+	0.476366i	$0.841954\pi$
$24$		0			0
$25$	0.890931	+	1.31402i	0.178186	+	0.262805i
$26$	0.485850	−	0.716575i	0.0952830	−	0.140532i
$27$		0			0
$28$	0.731172	−	13.4857i	0.138179	−	2.54855i
$29$	6.31204	−	7.43111i	1.17212	−	1.37992i	0.262261	−	0.964997i	$-0.415532\pi$
$29$	6.31204	−	7.43111i	1.17212	−	1.37992i	0.909855	−	0.414926i	$-0.136192\pi$
$30$		0			0
$31$	0.367396	−	6.77621i	0.0659862	−	1.21704i	−0.758695	−	0.651446i	$-0.774163\pi$
$31$	0.367396	−	6.77621i	0.0659862	−	1.21704i	0.824681	−	0.565598i	$-0.191355\pi$
$32$	2.23414	+	5.60728i	0.394944	+	0.991236i
$33$		0			0
$34$	−7.91166	−	11.6688i	−1.35684	−	2.00119i
$35$	2.04183	−	5.12460i	0.345132	−	0.866215i
$36$		0			0
$37$	0.851751	+	0.512481i	0.140027	+	0.0842514i	0.583843	−	0.811866i	$-0.301548\pi$
$37$	0.851751	+	0.512481i	0.140027	+	0.0842514i	−0.443816	+	0.896118i	$0.646376\pi$
$38$	−13.8440	+	13.1137i	−2.24579	+	2.12732i
$39$		0			0
$40$	0.644310	+	11.8836i	0.101874	+	1.87896i
$41$	4.25981	−	1.97080i	0.665271	−	0.307787i	−0.0580350	−	0.998315i	$-0.518484\pi$
$41$	4.25981	−	1.97080i	0.665271	−	0.307787i	0.723306	+	0.690527i	$0.242621\pi$
$42$		0			0
$43$	4.73498	+	1.59540i	0.722078	+	0.243296i	0.656260	−	0.754535i	$-0.272138\pi$
$43$	4.73498	+	1.59540i	0.722078	+	0.243296i	0.0658185	+	0.997832i	$0.479034\pi$
$44$	−1.03831	−	6.33339i	−0.156531	−	0.954794i
$45$		0			0
$46$	3.91875	+	14.1141i	0.577788	+	2.08100i
$47$	−1.64649	−	3.10562i	−0.240166	−	0.453001i	0.733903	−	0.679255i	$-0.237697\pi$
$47$	−1.64649	−	3.10562i	−0.240166	−	0.453001i	−0.974068	+	0.226254i	$0.927352\pi$
$48$		0			0
$49$	1.87277	−	0.412227i	0.267538	−	0.0588895i
$50$	1.08472	−	3.90679i	0.153402	−	0.552504i
$51$		0			0
$52$	−1.52411	+	0.165757i	−0.211357	+	0.0229864i
$53$	−11.8048	−	2.59843i	−1.62151	−	0.356921i	−0.690904	−	0.722946i	$-0.742787\pi$
$53$	−11.8048	−	2.59843i	−1.62151	−	0.356921i	−0.930605	+	0.366025i	$0.880718\pi$
$54$		0			0
$55$	0.424102	−	2.58691i	0.0571859	−	0.348819i
$56$	−15.3159	+	11.6428i	−2.04667	+	1.55584i
$57$		0			0
$58$	−24.9010			−3.26966
$59$	6.35981	+	4.30730i	0.827977	+	0.560762i
$59$	6.35981	+	4.30730i	0.827977	+	0.560762i
$60$		0			0
$61$	8.57456	+	10.0948i	1.09786	+	1.29250i	0.952974	+	0.303052i	$0.0980057\pi$
$61$	8.57456	+	10.0948i	1.09786	+	1.29250i	0.144886	+	0.989448i	$0.453718\pi$
$62$	−13.7974	+	10.4885i	−1.75227	+	1.33204i
$63$		0			0
$64$	0.280274	−	0.528653i	0.0350343	−	0.0660816i
$65$	−0.611563	−	0.134615i	−0.0758551	−	0.0166970i
$66$		0			0
$67$	−2.15987	+	1.29955i	−0.263870	+	0.158765i	−0.641341	−	0.767256i	$-0.721622\pi$
$67$	−2.15987	+	1.29955i	−0.263870	+	0.158765i	0.377471	+	0.926022i	$0.376794\pi$
$68$	−6.67892	+	24.0553i	−0.809938	+	2.91713i
$69$		0			0
$70$	−13.3510	+	4.49848i	−1.59575	+	0.537671i
$71$	3.67652	+	6.93466i	0.436323	+	0.822992i	0.999995	−	0.00300607i	$-0.000956863\pi$
$71$	3.67652	+	6.93466i	0.436323	+	0.822992i	−0.563673	+	0.825998i	$0.690612\pi$
$72$		0			0
$73$	−6.93951	−	6.57345i	−0.812208	−	0.769365i	0.163940	−	0.986470i	$-0.447580\pi$
$73$	−6.93951	−	6.57345i	−0.812208	−	0.769365i	−0.976148	+	0.217106i	$0.930338\pi$
$74$	−0.410718	−	2.50527i	−0.0477450	−	0.291232i
$75$		0			0
$76$	33.5699	+	3.65094i	3.85073	+	0.418792i
$77$	3.84606	−	1.77938i	0.438299	−	0.202779i
$78$		0			0
$79$	−5.27421	−	4.00935i	−0.593395	−	0.451087i	0.264877	−	0.964282i	$-0.414669\pi$
$79$	−5.27421	−	4.00935i	−0.593395	−	0.451087i	−0.858272	+	0.513195i	$0.828462\pi$
$80$	9.93570	−	9.41160i	1.11085	−	1.05225i
$81$		0			0
$82$	−10.8793	−	5.03329i	−1.20142	−	0.555834i
$83$	4.15362	−	10.4248i	0.455919	−	1.14427i	−0.503928	−	0.863746i	$-0.668112\pi$
$83$	4.15362	−	10.4248i	0.455919	−	1.14427i	0.959847	−	0.280525i	$-0.0905084\pi$
$84$		0			0
$85$	−5.72254	+	8.44012i	−0.620697	+	0.915459i
$86$	−4.72327	−	11.8545i	−0.509323	−	1.27830i
$87$		0			0
$88$	−5.91871	+	6.96804i	−0.630936	+	0.742796i
$89$	8.82969	−	10.3951i	0.935945	−	1.10188i	−0.0586736	−	0.998277i	$-0.518687\pi$
$89$	8.82969	−	10.3951i	0.935945	−	1.10188i	0.994619	−	0.103603i	$-0.0330370\pi$
$90$		0			0
$91$	−0.374690	−	0.940402i	−0.0392782	−	0.0985809i
$92$	14.5567	−	21.4695i	1.51764	−	2.23835i
$93$		0			0
$94$	−3.32284	+	8.33969i	−0.342724	+	0.860173i
$95$	12.5179	+	5.79139i	1.28431	+	0.594184i
$96$		0			0
$97$	7.91972	−	7.50196i	0.804126	−	0.761709i	−0.170546	−	0.985350i	$-0.554553\pi$
$97$	7.91972	−	7.50196i	0.804126	−	0.761709i	0.974672	+	0.223641i	$0.0717944\pi$
$98$	−3.89880	−	2.96379i	−0.393838	−	0.299388i
$99$		0			0
$100$	−6.51636	+	3.01479i	−0.651636	+	0.301479i
$101$	−2.96945	−	0.322947i	−0.295471	−	0.0321344i	−0.0408171	−	0.999167i	$-0.512996\pi$
$101$	−2.96945	−	0.322947i	−0.295471	−	0.0321344i	−0.254654	+	0.967032i	$0.581962\pi$
$102$		0			0
$103$	0.171841	+	1.04818i	0.0169320	+	0.103280i	0.993940	−	0.109920i	$-0.0350595\pi$
$103$	0.171841	+	1.04818i	0.0169320	+	0.103280i	−0.977008	+	0.213201i	$0.931611\pi$
$104$	1.58552	+	1.50189i	0.155473	+	0.147272i
$105$		0			0
$106$	14.4599	+	27.2743i	1.40447	+	2.64911i
$107$	−4.82184	+	1.62467i	−0.466145	+	0.157062i	−0.542566	−	0.840013i	$-0.682547\pi$
$107$	−4.82184	+	1.62467i	−0.466145	+	0.157062i	0.0764214	+	0.997076i	$0.475651\pi$
$108$		0			0
$109$	3.86799	−	13.9312i	0.370486	−	1.33437i	−0.509949	−	0.860204i	$-0.670336\pi$
$109$	3.86799	−	13.9312i	0.370486	−	1.33437i	0.880435	−	0.474166i	$-0.157250\pi$
$110$	−5.73665	+	3.45163i	−0.546968	+	0.329100i
$111$		0			0
$112$	21.6065	+	4.75594i	2.04162	+	0.449394i
$113$	0.0429307	−	0.0809758i	0.00403858	−	0.00761757i	−0.881485	−	0.472213i	$-0.843455\pi$
$113$	0.0429307	−	0.0809758i	0.00403858	−	0.00761757i	0.885523	+	0.464595i	$0.153800\pi$
$114$		0			0
$115$	8.43457	−	6.41179i	0.786527	−	0.597903i
$116$	28.5467	+	33.6078i	2.65049	+	3.12040i
$117$		0			0
$118$	−2.13099	−	19.5011i	−0.196174	−	1.79522i
$119$	−16.4844			−1.51113
$120$		0			0
$121$	−7.15384	+	5.43821i	−0.650349	+	0.494383i
$122$	5.47253	−	33.3810i	0.495460	−	3.02217i
$123$		0			0
$124$	29.9734	+	6.59765i	2.69169	+	0.592487i
$125$	−12.0977	+	1.31571i	−1.08205	+	0.117680i
$126$		0			0
$127$	1.99435	−	7.18298i	0.176970	−	0.637387i	−0.820835	−	0.571165i	$-0.806492\pi$
$127$	1.99435	−	7.18298i	0.176970	−	0.637387i	0.997805	−	0.0662219i	$-0.0210945\pi$
$128$	10.2973	−	2.26660i	0.910159	−	0.200341i
$129$		0			0
$130$	0.749118	+	1.41299i	0.0657020	+	0.123927i
$131$	1.01074	+	3.64035i	0.0883087	+	0.318059i	0.994490	−	0.104830i	$-0.0334298\pi$
$131$	1.01074	+	3.64035i	0.0883087	+	0.318059i	−0.906181	+	0.422889i	$0.861016\pi$
$132$		0			0
$133$	3.60721	+	22.0030i	0.312785	+	1.90790i
$134$	6.10068	+	2.05556i	0.527019	+	0.177573i
$135$		0			0
$136$	32.2766	−	14.9327i	2.76769	−	1.28047i
$137$	0.118260	+	2.18118i	0.0101037	+	0.186351i	0.999229	+	0.0392729i	$0.0125042\pi$
$137$	0.118260	+	2.18118i	0.0101037	+	0.186351i	−0.989125	+	0.147078i	$0.953013\pi$
$138$		0			0
$139$	−2.69453	+	2.55239i	−0.228547	+	0.216491i	−0.793400	−	0.608700i	$-0.791691\pi$
$139$	−2.69453	+	2.55239i	−0.228547	+	0.216491i	0.564854	+	0.825191i	$0.308933\pi$
$140$	21.3771	+	12.8622i	1.80670	+	1.08705i
$141$		0			0
$142$	7.41969	−	18.6220i	0.622647	−	1.56273i
$143$	−0.269961	−	0.398163i	−0.0225753	−	0.0332961i
$144$		0			0
$145$	6.66655	+	16.7318i	0.553627	+	1.38950i
$146$	−1.32164	+	24.3763i	−0.109380	+	2.01739i
$147$		0			0
$148$	−2.91041	+	3.42640i	−0.239234	+	0.281648i
$149$	0.288180	−	5.31516i	0.0236086	−	0.435435i	−0.962705	−	0.270554i	$-0.912793\pi$
$149$	0.288180	−	5.31516i	0.0236086	−	0.435435i	0.986313	−	0.164881i	$-0.0527241\pi$
$150$		0			0
$151$	10.4366	−	15.3929i	0.849320	−	1.25265i	−0.116436	−	0.993198i	$-0.537147\pi$
$151$	10.4366	−	15.3929i	0.849320	−	1.25265i	0.965755	−	0.259455i	$-0.0835428\pi$
$152$	−26.9947	−	39.8142i	−2.18956	−	3.22936i
$153$		0			0
$154$	−9.82258	−	4.54441i	−0.791526	−	0.366199i
$155$	10.7415	+	6.46293i	0.862776	+	0.519115i
$156$		0			0
$157$	0.393871	+	0.299413i	0.0314343	+	0.0238957i	0.620773	−	0.783990i	$-0.286819\pi$
$157$	0.393871	+	0.299413i	0.0314343	+	0.0238957i	−0.589339	+	0.807886i	$0.700612\pi$
$158$	0.916036	+	16.8953i	0.0728759	+	1.34412i
$159$		0			0
$160$	−11.0847	−	1.20554i	−0.876324	−	0.0953060i
$161$	16.2308	+	5.46881i	1.27917	+	0.431003i
$162$		0			0
$163$	0.853859	+	0.808818i	0.0668794	+	0.0633515i	0.720409	−	0.693549i	$-0.243954\pi$
$163$	0.853859	+	0.808818i	0.0668794	+	0.0633515i	−0.653530	+	0.756901i	$0.726713\pi$
$164$	5.67890	+	20.4535i	0.443447	+	1.59715i
$165$		0			0
$166$	−27.1595	+	9.15110i	−2.10799	+	0.710263i
$167$	−18.7016	+	4.11653i	−1.44717	+	0.318547i	−0.867962	−	0.496631i	$-0.834570\pi$
$167$	−18.7016	+	4.11653i	−1.44717	+	0.318547i	−0.579211	+	0.815178i	$0.696639\pi$
$168$		0			0
$169$	11.0407	−	6.64296i	0.849283	−	0.510997i
$170$	25.8903	−	2.81574i	1.98570	−	0.215958i
$171$		0			0
$172$	−10.5847	+	19.9649i	−0.807078	+	1.52231i
$173$	−0.132900	+	0.810656i	−0.0101042	+	0.0616330i	−0.991397	−	0.130887i	$-0.958218\pi$
$173$	−0.132900	+	0.810656i	−0.0101042	+	0.0616330i	0.981293	+	0.192520i	$0.0616659\pi$
$174$		0			0
$175$	−3.06919	−	3.61333i	−0.232009	−	0.273142i
$176$	10.5134			0.792477
$177$		0			0
$178$	−34.8331			−2.61085
$179$	1.75645	+	2.06786i	0.131283	+	0.154559i	0.823876	−	0.566770i	$-0.191807\pi$
$179$	1.75645	+	2.06786i	0.131283	+	0.154559i	−0.692592	+	0.721329i	$0.743531\pi$
$180$		0			0
$181$	3.00493	−	18.3293i	0.223355	−	1.36240i	−0.602318	−	0.798256i	$-0.705756\pi$
$181$	3.00493	−	18.3293i	0.223355	−	1.36240i	0.825673	−	0.564148i	$-0.190795\pi$
$182$	−1.21100	+	2.28418i	−0.0897650	+	0.169315i
$183$		0			0
$184$	−36.7341	+	3.99507i	−2.70807	+	0.294520i
$185$	−1.57342	+	0.946693i	−0.115680	+	0.0696023i
$186$		0			0
$187$	−7.65042	+	1.68398i	−0.559454	+	0.123145i
$188$	15.0651	−	5.07601i	1.09873	−	0.370206i
$189$		0			0
$190$	−9.42383	−	33.9416i	−0.683677	−	2.46238i
$191$	−10.1070	−	9.57389i	−0.731319	−	0.692743i	0.228443	−	0.973557i	$-0.426637\pi$
$191$	−10.1070	−	9.57389i	−0.731319	−	0.692743i	−0.959762	+	0.280815i	$0.909395\pi$
$192$		0			0
$193$	9.68535	+	3.26337i	0.697167	+	0.234903i	0.645498	−	0.763762i	$-0.276650\pi$
$193$	9.68535	+	3.26337i	0.697167	+	0.234903i	0.0516680	+	0.998664i	$0.483546\pi$
$194$	−27.6970	−	3.01223i	−1.98853	−	0.216265i
$195$		0			0
$196$	0.469519	+	8.65977i	0.0335371	+	0.618555i
$197$	−4.44499	−	3.37899i	−0.316692	−	0.240743i	0.434736	−	0.900558i	$-0.356842\pi$
$197$	−4.44499	−	3.37899i	−0.316692	−	0.240743i	−0.751428	+	0.659815i	$0.770635\pi$
$198$		0			0
$199$	16.3678	+	9.84820i	1.16028	+	0.698120i	0.959554	−	0.281526i	$-0.0908406\pi$
$199$	16.3678	+	9.84820i	1.16028	+	0.698120i	0.200731	+	0.979646i	$0.435668\pi$
$200$	9.28268	+	4.29463i	0.656385	+	0.303676i
$201$		0			0
$202$	4.28101	+	6.31402i	0.301211	+	0.444253i
$203$	−16.3395	+	24.0989i	−1.14681	+	1.69141i
$204$		0			0
$205$	−0.469406	+	8.65768i	−0.0327847	+	0.604679i
$206$	1.75618	−	2.06753i	0.122359	−	0.144052i
$207$		0			0
$208$	0.135965	−	2.50773i	0.00942749	−	0.173880i
$209$	3.92184	+	9.84308i	0.271279	+	0.680860i
$210$		0			0
$211$	−9.38922	−	13.8481i	−0.646381	−	0.953340i	−0.999840	−	0.0178903i	$-0.994305\pi$
$211$	−9.38922	−	13.8481i	−0.646381	−	0.953340i	0.353459	−	0.935450i	$-0.385005\pi$
$212$	20.2340	−	50.7835i	1.38968	−	3.48782i
$213$		0			0
$214$	11.1348	+	6.69957i	0.761157	+	0.457973i
$215$	−6.70091	+	6.34744i	−0.456998	+	0.432892i
$216$		0			0
$217$	1.09713	+	20.2354i	0.0744780	+	1.37367i
$218$	−33.5126	+	15.5046i	−2.26976	+	1.05010i
$219$		0			0
$220$	11.2351	+	3.78554i	0.757468	+	0.255221i
$221$	0.302737	+	1.84661i	0.0203643	+	0.124217i
$222$		0			0
$223$	−3.53921	−	12.7471i	−0.237003	−	0.853607i	−0.982369	−	0.186952i	$-0.940139\pi$
$223$	−3.53921	−	12.7471i	−0.237003	−	0.853607i	0.745366	−	0.666655i	$-0.232275\pi$
$224$	−8.44298	−	15.9251i	−0.564120	−	1.06404i
$225$		0			0
$226$	−0.228601	+	0.0503189i	−0.0152063	+	0.00334717i
$227$	−1.20854	+	4.35278i	−0.0802139	+	0.288904i	−0.992768	−	0.120053i	$-0.961694\pi$
$227$	−1.20854	+	4.35278i	−0.0802139	+	0.288904i	0.912554	+	0.408957i	$0.134107\pi$
$228$		0			0
$229$	−16.0028	+	1.74040i	−1.05749	+	0.115009i	−0.620304	−	0.784361i	$-0.712991\pi$
$229$	−16.0028	+	1.74040i	−1.05749	+	0.115009i	−0.437187	+	0.899370i	$0.644025\pi$
$230$	−26.4262	−	5.81684i	−1.74249	−	0.383551i
$231$		0			0
$232$	10.1623	−	61.9871i	0.667186	−	4.06965i
$233$	−15.4459	+	11.7417i	−1.01190	+	0.769224i	−0.973185	−	0.230026i	$-0.926119\pi$
$233$	−15.4459	+	11.7417i	−1.01190	+	0.769224i	−0.0387130	+	0.999250i	$0.512326\pi$
$234$		0			0
$235$	6.49331			0.423577
$236$	−23.8768	+	25.2323i	−1.55424	+	1.64248i
$237$		0			0
$238$	27.2551	+	32.0871i	1.76668	+	2.07990i
$239$	11.5094	−	8.74923i	0.744482	−	0.565941i	−0.162702	−	0.986675i	$-0.552021\pi$
$239$	11.5094	−	8.74923i	0.744482	−	0.565941i	0.907184	+	0.420735i	$0.138228\pi$
$240$		0			0
$241$	−10.1230	+	19.0940i	−0.652078	+	1.22995i	0.308311	+	0.951286i	$0.400236\pi$
$241$	−10.1230	+	19.0940i	−0.652078	+	1.22995i	−0.960389	+	0.278664i	$0.910108\pi$
$242$	22.4136	+	4.93360i	1.44080	+	0.317144i
$243$		0			0
$244$	−51.3266	+	30.8822i	−3.28585	+	1.97703i
$245$	−0.947673	+	3.41321i	−0.0605446	+	0.218062i
$246$		0			0
$247$	2.39856	−	0.808170i	0.152617	−	0.0514226i
$248$	−20.4788	−	38.6270i	−1.30040	−	2.45282i
$249$		0			0
$250$	22.5632	+	21.3730i	1.42702	+	1.35175i
$251$	1.10964	+	6.76852i	0.0700400	+	0.427225i	0.998449	+	0.0556663i	$0.0177283\pi$
$251$	1.10964	+	6.76852i	0.0700400	+	0.427225i	−0.928409	+	0.371559i	$0.878823\pi$
$252$		0			0
$253$	8.09140	+	0.879993i	0.508702	+	0.0553247i
$254$	−17.2792	+	7.99420i	−1.08419	+	0.501601i
$255$		0			0
$256$	−22.3900	−	17.0204i	−1.39937	−	1.06378i
$257$	5.45453	−	5.16680i	0.340244	−	0.322296i	−0.498430	−	0.866930i	$-0.666090\pi$
$257$	5.45453	−	5.16680i	0.340244	−	0.322296i	0.838674	+	0.544634i	$0.183331\pi$
$258$		0			0
$259$	−2.69408	−	1.24642i	−0.167402	−	0.0774485i
$260$	1.04825	−	2.63091i	0.0650098	−	0.163162i
$261$		0			0
$262$	5.41485	−	7.98631i	0.334531	−	0.493396i
$263$	2.52603	+	6.33987i	0.155762	+	0.390933i	0.986061	−	0.166385i	$-0.0532096\pi$
$263$	2.52603	+	6.33987i	0.155762	+	0.390933i	−0.830299	+	0.557318i	$0.811830\pi$
$264$		0			0
$265$	14.4553	−	17.0181i	0.887980	−	1.04541i
$266$	36.8650	−	43.4008i	2.26034	−	2.66107i
$267$		0			0
$268$	−4.21958	−	10.5903i	−0.257752	−	0.646908i
$269$	12.7357	−	18.7838i	0.776511	−	1.14527i	−0.209372	−	0.977836i	$-0.567142\pi$
$269$	12.7357	−	18.7838i	0.776511	−	1.14527i	0.985884	−	0.167432i	$-0.0535476\pi$
$270$		0			0
$271$	−6.54128	+	16.4174i	−0.397354	+	0.997284i	0.585130	+	0.810939i	$0.301043\pi$
$271$	−6.54128	+	16.4174i	−0.397354	+	0.997284i	−0.982484	+	0.186344i	$0.940336\pi$
$272$	−37.1165	−	17.1719i	−2.25052	−	1.04120i
$273$		0			0
$274$	4.05017	−	3.83653i	0.244680	−	0.231773i
$275$	−1.79353	−	1.36341i	−0.108154	−	0.0822166i
$276$		0			0
$277$	−30.0648	+	13.9094i	−1.80642	+	0.835737i	−0.862067	+	0.506794i	$0.830831\pi$
$277$	−30.0648	+	13.9094i	−1.80642	+	0.835737i	−0.944350	+	0.328944i	$0.893307\pi$
$278$	9.42334	+	1.02485i	0.565174	+	0.0614664i
$279$		0			0
$280$	−5.74962	−	35.0712i	−0.343606	−	2.09590i
$281$	15.4941	+	14.6768i	0.924303	+	0.875547i	0.992515	−	0.122124i	$-0.0389707\pi$
$281$	15.4941	+	14.6768i	0.924303	+	0.875547i	−0.0682115	+	0.997671i	$0.521729\pi$
$282$		0			0
$283$	−11.2838	−	21.2836i	−0.670754	−	1.26518i	−0.952163	−	0.305589i	$-0.901147\pi$
$283$	−11.2838	−	21.2836i	−0.670754	−	1.26518i	0.281409	−	0.959588i	$-0.409198\pi$
$284$	−33.6394	+	11.3344i	−1.99613	+	0.672574i
$285$		0			0
$286$	−0.328680	+	1.18380i	−0.0194353	+	0.0699994i
$287$	−12.0099	+	7.22613i	−0.708924	+	0.426545i
$288$		0			0
$289$	13.1570	+	2.89607i	0.773940	+	0.170357i
$290$	21.5463	−	40.6406i	1.26524	−	2.38650i
$291$		0			0
$292$	34.4148	−	26.1614i	2.01397	−	1.53098i
$293$	−5.45573	−	6.42298i	−0.318727	−	0.375234i	0.579345	−	0.815082i	$-0.303308\pi$
$293$	−5.45573	−	6.42298i	−0.318727	−	0.375234i	−0.898072	+	0.439848i	$0.855032\pi$
$294$		0			0
$295$	−12.5329	+	6.65276i	−0.729693	+	0.387339i
$296$	6.40411			0.372231
$297$		0			0
$298$	−10.8225	+	8.22705i	−0.626930	+	0.476580i
$299$	0.314545	−	1.91864i	0.0181906	−	0.110958i
$300$		0			0
$301$	−14.5720	−	3.20754i	−0.839915	−	0.184879i
$302$	−47.2181	+	5.13528i	−2.71710	+	0.295502i
$303$		0			0
$304$	−14.7986	+	53.2997i	−0.848758	+	3.05695i
$305$	−23.8949	+	5.25967i	−1.36822	+	0.301168i
$306$		0			0
$307$	4.03150	+	7.60422i	0.230090	+	0.433996i	0.971494	−	0.237063i	$-0.0761848\pi$
$307$	4.03150	+	7.60422i	0.230090	+	0.433996i	−0.741404	+	0.671058i	$0.765840\pi$
$308$	5.12730	+	18.4669i	0.292155	+	1.05225i
$309$		0			0
$310$	−5.17959	−	31.5941i	−0.294181	−	1.79442i
$311$	−1.37617	−	0.463686i	−0.0780356	−	0.0262932i	0.280013	−	0.959996i	$-0.409661\pi$
$311$	−1.37617	−	0.463686i	−0.0780356	−	0.0262932i	−0.358049	+	0.933703i	$0.616558\pi$
$312$		0			0
$313$	6.19424	−	2.86576i	0.350119	−	0.161982i	−0.236945	−	0.971523i	$-0.576146\pi$
$313$	6.19424	−	2.86576i	0.350119	−	0.161982i	0.587063	+	0.809541i	$0.300284\pi$
$314$	−0.0684084	−	1.26172i	−0.00386051	−	0.0712029i
$315$		0			0
$316$	21.7527	−	20.6053i	1.22369	−	1.15914i
$317$	5.01895	+	3.01980i	0.281892	+	0.169609i	0.649477	−	0.760381i	$-0.274988\pi$
$317$	5.01895	+	3.01980i	0.281892	+	0.169609i	−0.367585	+	0.929990i	$0.619815\pi$
$318$		0			0
$319$	−5.12129	+	12.8535i	−0.286737	+	0.719656i
$320$	0.620293	+	0.914864i	0.0346754	+	0.0511425i
$321$		0			0
$322$	−16.1907	−	40.6356i	−0.902272	−	2.26453i
$323$	2.23140	−	41.1557i	0.124158	−	2.28996i
$324$		0			0
$325$	−0.348405	+	0.410174i	−0.0193260	+	0.0227524i
$326$	0.162619	−	2.99933i	0.00900663	−	0.166118i
$327$		0			0
$328$	16.9695	−	25.0282i	0.936986	−	1.38195i
$329$	5.89070	+	8.68813i	0.324765	+	0.478992i
$330$		0			0
$331$	11.8913	+	5.50148i	0.653603	+	0.302389i	0.718525	−	0.695502i	$-0.244818\pi$
$331$	11.8913	+	5.50148i	0.653603	+	0.302389i	−0.0649219	+	0.997890i	$0.520680\pi$
$332$	43.4868	+	26.1651i	2.38665	+	1.43600i
$333$		0			0
$334$	38.9337	+	29.5967i	2.13036	+	1.61946i
$335$	−0.252092	−	4.64957i	−0.0137733	−	0.254033i
$336$		0			0
$337$	12.9442	+	1.40776i	0.705114	+	0.0766857i	0.453649	−	0.891181i	$-0.350122\pi$
$337$	12.9442	+	1.40776i	0.705114	+	0.0766857i	0.251465	+	0.967866i	$0.419088\pi$
$338$	−31.1850	−	10.5075i	−1.69624	−	0.571531i
$339$		0			0
$340$	−33.4812	−	31.7151i	−1.81577	−	1.71999i
$341$	2.57634	+	9.27914i	0.139517	+	0.502494i
$342$		0			0
$343$	14.3828	−	4.84612i	0.776596	−	0.261666i
$344$	31.4376	−	6.91993i	1.69500	−	0.373098i
$345$		0			0
$346$	1.79769	−	1.08163i	0.0966442	−	0.0581489i
$347$	7.27599	−	0.791312i	0.390596	−	0.0424799i	0.0892857	−	0.996006i	$-0.471542\pi$
$347$	7.27599	−	0.791312i	0.390596	−	0.0424799i	0.301310	+	0.953526i	$0.402576\pi$
$348$		0			0
$349$	−5.14404	+	9.70269i	−0.275354	+	0.519373i	−0.982163	−	0.188032i	$-0.939789\pi$
$349$	−5.14404	+	9.70269i	−0.275354	+	0.519373i	0.706809	+	0.707405i	$0.250134\pi$
$350$	−1.95885	+	11.9484i	−0.104705	+	0.638670i
$351$		0			0
$352$	−5.54523	−	6.52835i	−0.295562	−	0.347962i
$353$	19.2272			1.02336			0.511680	−	0.859176i	$-0.329023\pi$
$353$	19.2272			1.02336			0.511680	+	0.859176i	$0.329023\pi$
$354$		0			0
$355$	−14.4992			−0.769537
$356$	39.9330	+	47.0127i	2.11644	+	2.49167i
$357$		0			0
$358$	1.12102	−	6.83791i	0.0592477	−	0.361395i
$359$	7.32611	−	13.8185i	0.386657	−	0.729313i	−0.611419	−	0.791307i	$-0.709401\pi$
$359$	7.32611	−	13.8185i	0.386657	−	0.729313i	0.998077	+	0.0619941i	$0.0197460\pi$
$360$		0			0
$361$	−36.5332	+	3.97322i	−1.92280	+	0.209117i
$362$	−40.6464	+	24.4562i	−2.13633	+	1.28539i
$363$		0			0
$364$	4.47116	−	0.984177i	0.234353	−	0.0515849i
$365$	16.7331	−	5.63803i	0.875849	−	0.295108i
$366$		0			0
$367$	4.42542	+	15.9389i	0.231005	+	0.832006i	0.984623	+	0.174693i	$0.0558932\pi$
$367$	4.42542	+	15.9389i	0.231005	+	0.832006i	−0.753618	+	0.657313i	$0.771693\pi$
$368$	30.8486	+	29.2213i	1.60809	+	1.52327i
$369$		0			0
$370$	4.44421	+	1.49743i	0.231043	+	0.0778476i
$371$	35.8841	+	3.90263i	1.86301	+	0.202615i
$372$		0			0
$373$	0.247390	+	4.56283i	0.0128093	+	0.236255i	0.997926	+	0.0643685i	$0.0205033\pi$
$373$	0.247390	+	4.56283i	0.0128093	+	0.236255i	−0.985117	+	0.171886i	$0.945014\pi$
$374$	15.9270	+	12.1074i	0.823563	+	0.626056i
$375$		0			0
$376$	−19.4043	−	11.6752i	−1.00070	−	0.602102i
$377$	2.99967	+	1.38780i	0.154491	+	0.0714751i
$378$		0			0
$379$	−3.91734	−	5.77765i	−0.201220	−	0.296778i	0.713668	−	0.700484i	$-0.247032\pi$
$379$	−3.91734	−	5.77765i	−0.201220	−	0.296778i	−0.914889	+	0.403706i	$0.867722\pi$
$380$	−35.0059	+	51.6299i	−1.79577	+	2.64856i
$381$		0			0
$382$	−1.92490	+	35.5028i	−0.0984866	+	1.81648i
$383$	−1.04789	+	1.23367i	−0.0535444	+	0.0630374i	−0.788282	−	0.615314i	$-0.789029\pi$
$383$	−1.04789	+	1.23367i	−0.0535444	+	0.0630374i	0.734738	+	0.678351i	$0.237305\pi$
$384$		0			0
$385$	−0.423812	+	7.81676i	−0.0215995	+	0.398379i
$386$	−9.66138	−	24.2482i	−0.491751	−	1.23420i
$387$		0			0
$388$	27.6866	+	40.8347i	1.40557	+	2.07307i
$389$	−6.79600	+	17.0567i	−0.344571	+	0.864808i	0.649922	+	0.760001i	$0.274802\pi$
$389$	−6.79600	+	17.0567i	−0.344571	+	0.864808i	−0.994493	+	0.104807i	$0.966578\pi$
$390$		0			0
$391$	−27.1285	−	16.3227i	−1.37195	−	0.825474i
$392$	8.96903	−	8.49592i	0.453005	−	0.429109i
$393$		0			0
$394$	0.772015	+	14.2390i	0.0388936	+	0.717349i
$395$	11.1073	−	5.13877i	0.558867	−	0.258560i
$396$		0			0
$397$	−24.2083	−	8.15671i	−1.21498	−	0.409374i	−0.362424	−	0.932013i	$-0.618051\pi$
$397$	−24.2083	−	8.15671i	−1.21498	−	0.409374i	−0.852554	+	0.522639i	$0.824947\pi$
$398$	−7.89264	−	48.1430i	−0.395623	−	2.41319i
$399$		0			0
$400$	−3.14659	−	11.3330i	−0.157329	−	0.566649i
$401$	7.13733	+	13.4624i	0.356421	+	0.672281i	0.995280	−	0.0970422i	$-0.0309382\pi$
$401$	7.13733	+	13.4624i	0.356421	+	0.672281i	−0.638859	+	0.769324i	$0.720593\pi$
$402$		0			0
$403$	2.24665	−	0.494525i	0.111913	−	0.0246340i
$404$	3.61397	−	13.0164i	0.179802	−	0.647588i
$405$		0			0
$406$	73.9242	−	8.03974i	3.66880	−	0.399006i
$407$	−1.37765	−	0.303244i	−0.0682876	−	0.0150312i
$408$		0			0
$409$	0.392437	−	2.39376i	0.0194048	−	0.118364i	−0.975348	−	0.220673i	$-0.929175\pi$
$409$	0.392437	−	2.39376i	0.0194048	−	0.118364i	0.994753	+	0.102309i	$0.0326230\pi$
$410$	17.6284	−	13.4008i	0.870604	−	0.661816i
$411$		0			0
$412$	−4.80376			−0.236664
$413$	−20.2712	−	10.7338i	−0.997483	−	0.528176i
$414$		0			0
$415$	13.4202	+	15.7994i	0.658769	+	0.775563i
$416$	−1.62890	+	1.23826i	−0.0798636	+	0.0607107i
$417$		0			0
$418$	12.6754	−	23.9083i	0.619972	−	1.16939i
$419$	−12.4290	−	2.73584i	−0.607198	−	0.133654i	−0.0992797	−	0.995060i	$-0.531654\pi$
$419$	−12.4290	−	2.73584i	−0.607198	−	0.133654i	−0.507919	+	0.861405i	$0.669585\pi$
$420$		0			0
$421$	5.28290	−	3.17862i	0.257473	−	0.154916i	−0.380965	−	0.924589i	$-0.624408\pi$
$421$	5.28290	−	3.17862i	0.257473	−	0.154916i	0.638438	+	0.769673i	$0.279581\pi$
$422$	−11.4315	+	41.1724i	−0.556474	+	2.00424i
$423$		0			0
$424$	−73.7964	+	24.8649i	−3.58387	+	1.20755i
$425$	4.10498	+	7.74282i	0.199121	+	0.375582i
$426$		0			0
$427$	−28.7148	−	27.2001i	−1.38961	−	1.31631i
$428$	−3.72288	−	22.7086i	−0.179952	−	1.09766i
$429$		0			0
$430$	23.4345	+	2.54866i	1.13011	+	0.122907i
$431$	23.9261	−	11.0694i	1.15248	−	0.533193i	0.251843	−	0.967768i	$-0.418963\pi$
$431$	23.9261	−	11.0694i	1.15248	−	0.533193i	0.900636	+	0.434575i	$0.143101\pi$
$432$		0			0
$433$	17.3210	+	13.1671i	0.832392	+	0.632768i	0.932081	−	0.362251i	$-0.117992\pi$
$433$	17.3210	+	13.1671i	0.832392	+	0.632768i	−0.0996885	+	0.995019i	$0.531785\pi$
$434$	37.5744	−	35.5924i	1.80363	−	1.70849i
$435$		0			0
$436$	59.3450	+	27.4559i	2.84211	+	1.31490i
$437$	−15.8507	+	39.7823i	−0.758242	+	1.90304i
$438$		0			0
$439$	−5.17436	+	7.63161i	−0.246959	+	0.364237i	−0.930884	−	0.365315i	$-0.880961\pi$
$439$	−5.17436	+	7.63161i	−0.246959	+	0.364237i	0.683925	+	0.729552i	$0.260272\pi$
$440$	−6.25113	−	15.6891i	−0.298011	−	0.747951i
$441$		0			0
$442$	3.09391	−	3.64243i	0.147162	−	0.173253i
$443$	4.57556	−	5.38677i	0.217392	−	0.255933i	−0.642647	−	0.766163i	$-0.722164\pi$
$443$	4.57556	−	5.38677i	0.217392	−	0.255933i	0.860038	+	0.510229i	$0.170440\pi$
$444$		0			0
$445$	9.32560	+	23.4055i	0.442076	+	1.10953i
$446$	−18.9607	+	27.9649i	−0.897813	+	1.32418i
$447$		0			0
$448$	−0.661373	+	1.65992i	−0.0312469	+	0.0784238i
$449$	−21.2870	−	9.84840i	−1.00459	−	0.464775i	−0.152579	−	0.988291i	$-0.548758\pi$
$449$	−21.2870	−	9.84840i	−1.00459	−	0.464775i	−0.852015	+	0.523517i	$0.824620\pi$
$450$		0			0
$451$	−4.83561	+	4.58053i	−0.227700	+	0.215689i
$452$	0.329984	+	0.250847i	0.0155211	+	0.0117989i
$453$		0			0
$454$	10.4709	−	4.84437i	0.491425	−	0.227357i
$455$	1.85903	+	0.202182i	0.0871526	+	0.00947842i
$456$		0			0
$457$	−3.97552	−	24.2496i	−0.185967	−	1.13435i	−0.900535	−	0.434783i	$-0.856825\pi$
$457$	−3.97552	−	24.2496i	−0.185967	−	1.13435i	0.714568	−	0.699566i	$-0.246623\pi$
$458$	29.8464	+	28.2720i	1.39463	+	1.32106i
$459$		0			0
$460$	22.4445	+	42.3348i	1.04648	+	1.97387i
$461$	−11.5945	+	3.90665i	−0.540011	+	0.181951i	−0.576072	−	0.817399i	$-0.695415\pi$
$461$	−11.5945	+	3.90665i	−0.540011	+	0.181951i	0.0360615	+	0.999350i	$0.488519\pi$
$462$		0			0
$463$	−9.34713	+	33.6653i	−0.434398	+	1.56456i	0.345355	+	0.938472i	$0.387758\pi$
$463$	−9.34713	+	33.6653i	−0.434398	+	1.56456i	−0.779753	+	0.626087i	$0.784655\pi$
$464$	−61.8940	+	37.2404i	−2.87336	+	1.72884i
$465$		0			0
$466$	48.3934	+	10.6522i	2.24178	+	0.493453i
$467$	10.1067	−	19.0633i	0.467684	−	0.882145i	−0.531696	−	0.846935i	$-0.678445\pi$
$467$	10.1067	−	19.0633i	0.467684	−	0.882145i	0.999380	−	0.0352098i	$-0.0112099\pi$
$468$		0			0
$469$	5.99249	−	4.55537i	0.276707	−	0.210347i
$470$	−10.7359	−	12.6393i	−0.495211	−	0.583008i
$471$		0			0
$472$	49.4146	+	2.65375i	2.27449	+	0.122149i
$473$	−7.09052			−0.326022
$474$		0			0
$475$	9.43664	−	7.17354i	0.432983	−	0.329145i
$476$	12.0612	−	73.5700i	0.552824	−	3.37208i
$477$		0			0
$478$	−36.0599	−	7.93739i	−1.64934	−	0.363048i
$479$	−17.6020	+	1.91433i	−0.804257	+	0.0874682i	−0.501007	−	0.865443i	$-0.667037\pi$
$479$	−17.6020	+	1.91433i	−0.804257	+	0.0874682i	−0.303249	+	0.952911i	$0.598072\pi$
$480$		0			0
$481$	−0.0901485	+	0.324686i	−0.00411042	+	0.0148044i
$482$	53.9037	−	11.8651i	2.45525	−	0.540441i
$483$		0			0
$484$	−19.0365	−	35.9066i	−0.865294	−	1.63212i
$485$	5.39109	+	19.4170i	0.244797	+	0.881679i
$486$		0			0
$487$	−6.06916	−	37.0203i	−0.275020	−	1.67755i	−0.657399	−	0.753543i	$-0.728343\pi$
$487$	−6.06916	−	37.0203i	−0.275020	−	1.67755i	0.382379	−	0.924006i	$-0.375105\pi$
$488$	80.8634	+	27.2461i	3.66051	+	1.23337i
$489$		0			0
$490$	8.21071	−	3.79868i	0.370922	−	0.171607i
$491$	0.400094	+	7.37930i	0.0180560	+	0.333023i	0.993580	+	0.113131i	$0.0360879\pi$
$491$	0.400094	+	7.37930i	0.0180560	+	0.333023i	−0.975524	+	0.219893i	$0.929429\pi$
$492$		0			0
$493$	39.0742	−	37.0131i	1.75981	−	1.66699i
$494$	−5.53885	−	3.33262i	−0.249205	−	0.149941i
$495$		0			0
$496$	−18.6090	+	46.7050i	−0.835567	+	2.09711i
$497$	−13.1536	−	19.4001i	−0.590019	−	0.870213i
$498$		0			0
$499$	−9.22406	−	23.1507i	−0.412926	−	1.03637i	−0.977491	−	0.210977i	$-0.932335\pi$
$499$	−9.22406	−	23.1507i	−0.412926	−	1.03637i	0.564565	−	0.825388i	$-0.309044\pi$
$500$	2.97956	−	54.9548i	0.133250	−	2.45765i
$501$		0			0
$502$	11.3403	−	13.3509i	0.506144	−	0.595879i
$503$	0.396365	−	7.31053i	0.0176731	−	0.325960i	−0.976306	−	0.216393i	$-0.930571\pi$
$503$	0.396365	−	7.31053i	0.0176731	−	0.325960i	0.993979	−	0.109567i	$-0.0349465\pi$
$504$		0			0
$505$	3.09648	−	4.56696i	0.137791	−	0.203227i
$506$	−11.6653	−	17.2050i	−0.518584	−	0.764854i
$507$		0			0
$508$	30.5985	+	14.1564i	1.35759	+	0.628087i
$509$	−12.3014	−	7.40150i	−0.545250	−	0.328066i	0.216138	−	0.976363i	$-0.430654\pi$
$509$	−12.3014	−	7.40150i	−0.545250	−	0.328066i	−0.761387	+	0.648297i	$0.775481\pi$
$510$		0			0
$511$	22.7239	+	17.2743i	1.00525	+	0.764168i
$512$	2.74708	+	50.6670i	0.121405	+	2.23919i
$513$		0			0
$514$	−19.0757	−	2.07460i	−0.841391	−	0.0915068i
$515$	−1.85941	−	0.626509i	−0.0819356	−	0.0276073i
$516$		0			0
$517$	3.62142	+	3.43039i	0.159270	+	0.150868i
$518$	2.02818	+	7.30486i	0.0891133	+	0.320957i
$519$		0			0
$520$	−3.82313	+	1.28816i	−0.167655	+	0.0564897i
$521$	−13.0095	+	2.86361i	−0.569958	+	0.125457i	−0.490594	−	0.871388i	$-0.663220\pi$
$521$	−13.0095	+	2.86361i	−0.569958	+	0.125457i	−0.0793642	+	0.996846i	$0.525289\pi$
$522$		0			0
$523$	−34.9876	+	21.0513i	−1.52990	+	0.920510i	−0.532654	+	0.846333i	$0.678805\pi$
$523$	−34.9876	+	21.0513i	−1.52990	+	0.920510i	−0.997245	+	0.0741763i	$0.976367\pi$
$524$	−16.9864	+	1.84738i	−0.742055	+	0.0807034i
$525$		0			0
$526$	8.16413	−	15.3992i	0.355973	−	0.671436i
$527$	6.06045	−	36.9671i	0.263997	−	1.61031i
$528$		0			0
$529$	6.40617	+	7.54193i	0.278529	+	0.327910i
$530$	−57.0259			−2.47705
$531$		0			0
$532$	−100.839			−4.37191
$533$	1.03004	+	1.21266i	0.0446162	+	0.0525262i
$534$		0			0
$535$	1.52063	−	9.27545i	0.0657427	−	0.401013i
$536$	−7.60674	+	14.3478i	−0.328561	+	0.619732i
$537$		0			0
$538$	−57.6199	+	6.26654i	−2.48417	+	0.270170i
$539$	−2.33171	+	1.40294i	−0.100434	+	0.0604291i
$540$		0			0
$541$	−28.7334	+	6.32470i	−1.23535	+	0.271920i	−0.784188	−	0.620524i	$-0.786920\pi$
$541$	−28.7334	+	6.32470i	−1.23535	+	0.271920i	−0.451158	+	0.892444i	$0.648989\pi$
$542$	42.7718	−	14.4115i	1.83721	−	0.619027i
$543$		0			0
$544$	8.91389	+	32.1049i	0.382180	+	1.37649i
$545$	19.3901	+	18.3673i	0.830581	+	0.786768i
$546$		0			0
$547$	18.4062	+	6.20178i	0.786994	+	0.265169i	0.683970	−	0.729510i	$-0.260252\pi$
$547$	18.4062	+	6.20178i	0.786994	+	0.265169i	0.103023	+	0.994679i	$0.467148\pi$
$548$	−9.82116	−	1.06812i	−0.419539	−	0.0456276i
$549$		0			0
$550$	0.311505	+	5.74537i	0.0132826	+	0.244983i
$551$	−57.9545	−	44.0559i	−2.46895	−	1.87684i
$552$		0			0
$553$	16.9522	+	10.1998i	0.720880	+	0.433739i
$554$	76.7834	+	35.5238i	3.26222	+	1.50926i
$555$		0			0
$556$	−9.41981	−	13.8932i	−0.399489	−	0.589202i
$557$	8.46160	−	12.4799i	0.358529	−	0.528791i	−0.605059	−	0.796180i	$-0.706851\pi$
$557$	8.46160	−	12.4799i	0.358529	−	0.528791i	0.963589	+	0.267389i	$0.0861609\pi$
$558$		0			0
$559$	−0.0916987	+	1.69128i	−0.00387844	+	0.0715336i
$560$	−26.4577	+	31.1484i	−1.11804	+	1.31626i
$561$		0			0
$562$	2.95089	−	54.4259i	0.124476	−	2.29582i
$563$	8.53353	+	21.4176i	0.359646	+	0.902642i	0.991800	+	0.127800i	$0.0407915\pi$
$563$	8.53353	+	21.4176i	0.359646	+	0.902642i	−0.632154	+	0.774842i	$0.717829\pi$
$564$		0			0
$565$	0.0950127	+	0.140133i	0.00399722	+	0.00589545i
$566$	−22.7722	+	57.1540i	−0.957188	+	2.40236i
$567$		0			0
$568$	43.3287	+	26.0700i	1.81803	+	1.09387i
$569$	−0.202025	+	0.191368i	−0.00846932	+	0.00802257i	−0.691922	−	0.721972i	$-0.743236\pi$
$569$	−0.202025	+	0.191368i	−0.00846932	+	0.00802257i	0.683453	+	0.729994i	$0.260477\pi$
$570$		0			0
$571$	−1.57392	−	29.0292i	−0.0658663	−	1.21483i	−0.825470	−	0.564447i	$-0.809090\pi$
$571$	−1.57392	−	29.0292i	−0.0658663	−	1.21483i	0.759603	−	0.650387i	$-0.225393\pi$
$572$	1.97452	−	0.913512i	0.0825590	−	0.0381959i
$573$		0			0
$574$	33.9227	+	11.4299i	1.41591	+	0.477075i
$575$	−1.47311	−	8.98556i	−0.0614328	−	0.374724i
$576$		0			0
$577$	3.24906	+	11.7020i	0.135260	+	0.487163i	0.999884	−	0.0152576i	$-0.00485683\pi$
$577$	3.24906	+	11.7020i	0.135260	+	0.487163i	−0.864624	+	0.502420i	$0.832443\pi$
$578$	−16.1163	−	30.3985i	−0.670349	−	1.26441i
$579$		0			0
$580$	−79.5517	+	17.5107i	−3.30320	+	0.727090i
$581$	−8.96513	+	32.2895i	−0.371936	+	1.33959i
$582$		0			0
$583$	17.0525	−	1.85457i	0.706241	−	0.0768084i
$584$	−60.1416	−	13.2382i	−2.48868	−	0.547800i
$585$		0			0
$586$	−3.48200	+	21.2393i	−0.143840	+	0.877386i
$587$	−16.5987	+	12.6180i	−0.685104	+	0.520802i	−0.888837	−	0.458224i	$-0.848486\pi$
$587$	−16.5987	+	12.6180i	−0.685104	+	0.520802i	0.203733	+	0.979026i	$0.434693\pi$
$588$		0			0
$589$	−50.6689			−2.08778
$590$	33.6713	+	13.3959i	1.38623	+	0.551499i
$591$		0			0
$592$	−4.76762	−	5.61287i	−0.195948	−	0.230688i
$593$	5.81627	−	4.42142i	0.238846	−	0.181566i	−0.478903	−	0.877868i	$-0.658966\pi$
$593$	5.81627	−	4.42142i	0.238846	−	0.181566i	0.717749	+	0.696302i	$0.245172\pi$
$594$		0			0
$595$	14.2636	−	26.9040i	0.584752	−	1.10296i
$596$	23.5107	+	5.17510i	0.963036	+	0.211980i
$597$		0			0
$598$	−4.25472	+	2.55998i	−0.173988	+	0.104685i
$599$	5.41242	−	19.4938i	0.221146	−	0.796494i	−0.766826	−	0.641856i	$-0.778165\pi$
$599$	5.41242	−	19.4938i	0.221146	−	0.796494i	0.987971	−	0.154639i	$-0.0494213\pi$
$600$		0			0
$601$	23.4470	−	7.90020i	0.956421	−	0.322256i	0.202545	−	0.979273i	$-0.435079\pi$
$601$	23.4470	−	7.90020i	0.956421	−	0.322256i	0.753876	+	0.657017i	$0.228182\pi$
$602$	17.8495	+	33.6678i	0.727493	+	1.37220i
$603$		0			0
$604$	61.0621	+	57.8411i	2.48458	+	2.35352i
$605$	−2.68557	−	16.3813i	−0.109184	−	0.665993i
$606$		0			0
$607$	18.0992	+	1.96841i	0.734625	+	0.0798953i	0.467781	−	0.883844i	$-0.345054\pi$
$607$	18.0992	+	1.96841i	0.734625	+	0.0798953i	0.266844	+	0.963740i	$0.414019\pi$
$608$	40.9022	−	18.9234i	1.65880	−	0.767444i
$609$		0			0
$610$	49.7454	+	37.8155i	2.01413	+	1.53110i
$611$	0.865075	−	0.819443i	0.0349972	−	0.0331511i
$612$		0			0
$613$	25.8562	+	11.9624i	1.04432	+	0.483155i	0.865596	−	0.500743i	$-0.166940\pi$
$613$	25.8562	+	11.9624i	1.04432	+	0.483155i	0.178727	+	0.983899i	$0.442802\pi$
$614$	8.13608	−	20.4200i	0.328346	−	0.824085i
$615$		0			0
$616$	15.3213	−	22.5972i	0.617312	−	0.910467i
$617$	−5.17655	−	12.9922i	−0.208400	−	0.523044i	0.787206	−	0.616691i	$-0.211527\pi$
$617$	−5.17655	−	12.9922i	−0.208400	−	0.523044i	−0.995606	+	0.0936463i	$0.970148\pi$
$618$		0			0
$619$	12.6793	−	14.9272i	0.509624	−	0.599976i	−0.445829	−	0.895118i	$-0.647091\pi$
$619$	12.6793	−	14.9272i	0.509624	−	0.599976i	0.955453	+	0.295142i	$0.0953669\pi$
$620$	−36.7033	+	43.2105i	−1.47404	+	1.73537i
$621$		0			0
$622$	1.37277	+	3.44539i	0.0550429	+	0.138147i
$623$	−22.8567	+	33.7111i	−0.915734	+	1.35061i
$624$		0			0
$625$	5.38243	−	13.5089i	0.215297	−	0.540355i
$626$	−15.8197	−	7.31896i	−0.632281	−	0.292524i
$627$		0			0
$628$	−1.62446	+	1.53877i	−0.0648232	+	0.0614038i
$629$	4.36836	+	3.32074i	0.174178	+	0.132407i
$630$		0			0
$631$	−5.21081	+	2.41078i	−0.207439	+	0.0959716i	−0.520858	−	0.853644i	$-0.674388\pi$
$631$	−5.21081	+	2.41078i	−0.207439	+	0.0959716i	0.313419	+	0.949615i	$0.398526\pi$
$632$	−42.4321	−	4.61477i	−1.68786	−	0.183566i
$633$		0			0
$634$	−2.42016	−	14.7623i	−0.0961169	−	0.586287i
$635$	9.99760	+	9.47023i	0.396743	+	0.375814i
$636$		0			0
$637$	0.304486	+	0.574321i	0.0120642	+	0.0227554i
$638$	33.4869	−	11.2830i	1.32576	−	0.446700i
$639$		0			0
$640$	−5.21072	+	18.7673i	−0.205972	+	0.741843i
$641$	14.9280	−	8.98185i	0.589619	−	0.354762i	−0.189269	−	0.981925i	$-0.560612\pi$
$641$	14.9280	−	8.98185i	0.589619	−	0.354762i	0.778888	+	0.627164i	$0.215784\pi$
$642$		0			0
$643$	−30.2263	−	6.65330i	−1.19201	−	0.262381i	−0.425706	−	0.904862i	$-0.639974\pi$
$643$	−30.2263	−	6.65330i	−1.19201	−	0.262381i	−0.766301	+	0.642481i	$0.777905\pi$
$644$	−36.2830	+	68.4369i	−1.42975	+	2.69679i
$645$		0			0
$646$	−83.7993	+	63.7026i	−3.29704	+	2.50635i
$647$	−18.2820	−	21.5232i	−0.718738	−	0.846163i	0.274581	−	0.961564i	$-0.411461\pi$
$647$	−18.2820	−	21.5232i	−0.718738	−	0.846163i	−0.993319	+	0.115400i	$0.963185\pi$
$648$		0			0
$649$	−10.5044	−	2.91073i	−0.412334	−	0.114256i
$650$	1.37446			0.0539106
$651$		0			0
$652$	−4.23450	+	3.21898i	−0.165836	+	0.126065i
$653$	−0.623213	+	3.80143i	−0.0243882	+	0.148761i	−0.996213	−	0.0869411i	$-0.972291\pi$
$653$	−0.623213	+	3.80143i	−0.0243882	+	0.148761i	0.971825	+	0.235702i	$0.0757391\pi$
$654$		0			0
$655$	−6.81595	−	1.50030i	−0.266321	−	0.0586217i
$656$	−34.5691	+	3.75962i	−1.34970	+	0.146788i
$657$		0			0
$658$	7.17197	−	25.8311i	0.279593	−	1.00700i
$659$	22.6401	−	4.98347i	0.881934	−	0.194128i	0.249158	−	0.968463i	$-0.419846\pi$
$659$	22.6401	−	4.98347i	0.881934	−	0.194128i	0.632777	+	0.774334i	$0.281915\pi$
$660$		0			0
$661$	−3.78004	−	7.12991i	−0.147027	−	0.277322i	0.799050	−	0.601265i	$-0.205336\pi$
$661$	−3.78004	−	7.12991i	−0.147027	−	0.277322i	−0.946077	+	0.323943i	$0.894991\pi$
$662$	−8.95209	−	32.2425i	−0.347933	−	1.25314i
$663$		0			0
$664$	−11.6963	−	71.3441i	−0.453903	−	2.76869i
$665$	−39.0321	−	13.1514i	−1.51360	−	0.509991i
$666$		0			0
$667$	−50.7524	+	23.4806i	−1.96514	+	0.909172i
$668$	−4.68865	−	86.4771i	−0.181409	−	3.34590i
$669$		0			0
$670$	−8.63364	+	8.17822i	−0.333547	+	0.315952i
$671$	−16.1052	−	9.69017i	−0.621734	−	0.374085i
$672$		0			0
$673$	−6.65748	+	16.7090i	−0.256627	+	0.644085i	−0.999684	−	0.0251432i	$-0.991996\pi$
$673$	−6.65748	+	16.7090i	−0.256627	+	0.644085i	0.743057	+	0.669228i	$0.233375\pi$
$674$	−18.6614	−	27.5235i	−0.718811	−	1.06017i
$675$		0			0
$676$	21.5694	+	54.1350i	0.829591	+	2.08212i
$677$	0.369901	−	6.82243i	0.0142165	−	0.262207i	−0.982781	−	0.184774i	$-0.940845\pi$
$677$	0.369901	−	6.82243i	0.0142165	−	0.262207i	0.996998	−	0.0774334i	$-0.0246725\pi$
$678$		0			0
$679$	−21.0894	+	24.8283i	−0.809335	+	0.952823i
$680$	−3.55668	+	65.5991i	−0.136393	+	2.51561i
$681$		0			0
$682$	13.8023	−	20.3568i	0.528517	−	0.779504i
$683$	−24.3739	−	35.9488i	−0.932642	−	1.37554i	−0.926798	−	0.375561i	$-0.877450\pi$
$683$	−24.3739	−	35.9488i	−0.932642	−	1.37554i	−0.00584404	−	0.999983i	$-0.501860\pi$
$684$		0			0
$685$	−3.66221	−	1.69432i	−0.139926	−	0.0647367i
$686$	−33.2132	−	19.9837i	−1.26809	−	0.762983i
$687$		0			0
$688$	−29.4691	−	22.4018i	−1.12350	−	0.854061i
$689$	−0.221833	−	4.09146i	−0.00845115	−	0.155872i
$690$		0			0
$691$	−40.1008	−	4.36122i	−1.52551	−	0.165909i	−0.693411	−	0.720542i	$-0.743893\pi$
$691$	−40.1008	−	4.36122i	−1.52551	−	0.165909i	−0.832095	+	0.554634i	$0.812858\pi$
$692$	−3.52072	−	1.18627i	−0.133838	−	0.0450951i
$693$		0			0
$694$	−13.5703	−	12.8545i	−0.515121	−	0.487949i
$695$	−1.83421	−	6.60623i	−0.0695756	−	0.250589i
$696$		0			0
$697$	24.5532	−	8.27293i	0.930018	−	0.313359i
$698$	27.3915	−	6.02932i	1.03678	−	0.228213i
$699$		0			0
$700$	18.3719	−	11.0540i	0.694394	−	0.417803i
$701$	29.2765	−	3.18401i	1.10576	−	0.120259i	0.463023	−	0.886346i	$-0.346765\pi$
$701$	29.2765	−	3.18401i	1.10576	−	0.120259i	0.642736	+	0.766088i	$0.277799\pi$
$702$		0			0
$703$	3.47653	−	6.55743i	0.131120	−	0.247318i
$704$	−0.137372	+	0.837931i	−0.00517740	+	0.0315807i
$705$		0			0
$706$	−31.7899	−	37.4260i	−1.19643	−	1.40854i
$707$	8.91976			0.335462
$708$		0			0
$709$	43.8261			1.64592			0.822962	−	0.568096i	$-0.192320\pi$
$709$	43.8261			1.64592			0.822962	+	0.568096i	$0.192320\pi$
$710$	23.9727	+	28.2228i	0.899679	+	1.05918i
$711$		0			0
$712$	14.2156	−	86.7116i	0.532754	−	3.24965i
$713$	−18.2313	+	34.3878i	−0.682767	+	1.28783i
$714$		0			0
$715$	0.883429	−	0.0960786i	0.0330384	−	0.00359314i
$716$	−10.5140	+	6.32606i	−0.392926	+	0.236416i
$717$		0			0
$718$	−39.0107	+	8.58691i	−1.45587	+	0.320461i
$719$	22.4416	−	7.56145i	0.836930	−	0.281995i	0.131981	−	0.991252i	$-0.457866\pi$
$719$	22.4416	−	7.56145i	0.836930	−	0.281995i	0.704949	+	0.709258i	$0.250970\pi$
$720$		0			0
$721$	−0.848573	−	3.05628i	−0.0316025	−	0.113822i
$722$	68.1372	+	64.5430i	2.53580	+	2.40204i
$723$		0			0
$724$	79.6049	+	26.8220i	2.95849	+	0.996833i
$725$	15.3883	+	1.67357i	0.571505	+	0.0621550i
$726$		0			0
$727$	1.25212	+	23.0940i	0.0464385	+	0.856508i	0.925254	+	0.379347i	$0.123851\pi$
$727$	1.25212	+	23.0940i	0.0464385	+	0.856508i	−0.878816	+	0.477161i	$0.841666\pi$
$728$	−5.19190	−	3.94678i	−0.192425	−	0.146278i
$729$		0			0
$730$	−38.6406	−	23.2493i	−1.43015	−	0.860495i
$731$	25.0324	+	11.5812i	0.925855	+	0.428346i
$732$		0			0
$733$	5.29941	+	7.81605i	0.195738	+	0.288692i	0.912874	−	0.408241i	$-0.133858\pi$
$733$	5.29941	+	7.81605i	0.195738	+	0.288692i	−0.717136	+	0.696933i	$0.754547\pi$
$734$	23.7084	−	34.9673i	0.875093	−	1.29067i
$735$		0			0
$736$	1.87424	−	34.5683i	0.0690853	−	1.27420i
$737$	2.31575	−	2.72631i	0.0853018	−	0.100425i
$738$		0			0
$739$	0.963920	−	17.7785i	0.0354584	−	0.653991i	−0.925745	−	0.378149i	$-0.876561\pi$
$739$	0.963920	−	17.7785i	0.0354584	−	0.653991i	0.961203	−	0.275842i	$-0.0889567\pi$
$740$	−3.07387	−	7.71483i	−0.112998	−	0.283603i
$741$		0			0
$742$	−51.7336	−	76.3014i	−1.89920	−	2.80111i
$743$	−17.9077	+	44.9450i	−0.656971	+	1.64887i	0.0996535	+	0.995022i	$0.468227\pi$
$743$	−17.9077	+	44.9450i	−0.656971	+	1.64887i	−0.756624	+	0.653850i	$0.773153\pi$
$744$		0			0
$745$	8.42545	+	5.06943i	0.308685	+	0.185729i
$746$	8.47258	−	8.02565i	0.310203	−	0.293840i
$747$		0			0
$748$	−1.91803	−	35.3759i	−0.0701300	−	1.29347i
$749$	13.7902	−	6.38001i	0.503882	−	0.233121i
$750$		0			0
$751$	20.1042	+	6.77391i	0.733614	+	0.247183i	0.661219	−	0.750193i	$-0.270039\pi$
$751$	20.1042	+	6.77391i	0.733614	+	0.247183i	0.0723948	+	0.997376i	$0.476936\pi$
$752$	4.21308	+	25.6986i	0.153635	+	0.937132i
$753$		0			0
$754$	−2.25824	−	8.13345i	−0.0822403	−	0.296203i
$755$	16.0919	+	30.3526i	0.585645	+	1.10464i
$756$		0			0
$757$	23.8648	−	5.25305i	0.867382	−	0.190925i	0.241080	−	0.970505i	$-0.422498\pi$
$757$	23.8648	−	5.25305i	0.867382	−	0.190925i	0.626303	+	0.779580i	$0.284567\pi$
$758$	−4.76940	+	17.1778i	−0.173232	+	0.623926i
$759$		0			0
$760$	88.3383	−	9.60737i	3.20437	−	0.348496i
$761$	15.1184	+	3.32782i	0.548043	+	0.120633i	0.480357	−	0.877073i	$-0.340507\pi$
$761$	15.1184	+	3.32782i	0.548043	+	0.120633i	0.0676864	+	0.997707i	$0.478438\pi$
$762$		0			0
$763$	−6.98505	+	42.6069i	−0.252876	+	1.54247i
$764$	50.1233	−	38.1028i	1.81340	−	1.37851i
$765$		0			0
$766$	4.13390			0.149364
$767$	−0.830137	+	2.46794i	−0.0299745	+	0.0891122i
$768$		0			0
$769$	8.39257	+	9.88050i	0.302644	+	0.356300i	0.892371	−	0.451303i	$-0.149041\pi$
$769$	8.39257	+	9.88050i	0.302644	+	0.356300i	−0.589727	+	0.807603i	$0.700765\pi$
$770$	15.9161	−	12.0991i	0.573578	−	0.436022i
$771$		0			0
$772$	−21.6509	+	40.8380i	−0.779234	+	1.46979i
$773$	−22.1414	−	4.87369i	−0.796370	−	0.175294i	−0.201894	−	0.979407i	$-0.564710\pi$
$773$	−22.1414	−	4.87369i	−0.796370	−	0.175294i	−0.594476	+	0.804113i	$0.702641\pi$
$774$		0			0
$775$	9.23144	−	5.55437i	0.331603	−	0.199519i
$776$	18.8018	−	67.7181i	0.674946	−	2.43094i
$777$		0			0
$778$	44.4374	−	14.9727i	1.59316	−	0.536797i
$779$	−16.4153	−	30.9626i	−0.588140	−	1.10935i
$780$		0			0
$781$	−8.08640	−	7.65985i	−0.289354	−	0.274091i
$782$	13.0815	+	79.7937i	0.467794	+	2.85342i
$783$		0			0
$784$	−14.1234	−	1.53601i	−0.504405	−	0.0548574i
$785$	−0.829476	+	0.383756i	−0.0296053	+	0.0136969i
$786$		0			0
$787$	20.5331	+	15.6089i	0.731928	+	0.556397i	0.903404	−	0.428791i	$-0.141060\pi$
$787$	20.5331	+	15.6089i	0.731928	+	0.556397i	−0.171476	+	0.985188i	$0.554854\pi$
$788$	18.3327	−	17.3657i	0.653076	−	0.618626i
$789$		0			0
$790$	−28.3672	−	13.1241i	−1.00926	−	0.466934i
$791$	−0.101305	+	0.254256i	−0.00360199	+	0.00904031i
$792$		0			0
$793$	−2.51965	+	3.71621i	−0.0894755	+	0.131966i
$794$	24.1484	+	60.6078i	0.856993	+	2.15089i
$795$		0			0
$796$	−55.9284	+	65.8440i	−1.98233	+	2.33378i
$797$	30.7370	−	36.1864i	1.08876	−	1.28179i	0.131892	−	0.991264i	$-0.457895\pi$
$797$	30.7370	−	36.1864i	1.08876	−	1.28179i	0.956868	−	0.290523i	$-0.0938293\pi$
$798$		0			0
$799$	−7.18207	−	18.0256i	−0.254083	−	0.637701i
$800$	−5.37763	+	7.93141i	−0.190128	+	0.280418i
$801$		0			0
$802$	14.4040	−	36.1514i	0.508624	−	1.27655i
$803$	12.3108	+	5.69559i	0.434439	+	0.200993i
$804$		0			0
$805$	−22.9698	+	21.7581i	−0.809578	+	0.766873i
$806$	−4.67716	−	3.55549i	−0.164746	−	0.125237i
$807$		0			0
$808$	−17.4649	+	8.08013i	−0.614413	+	0.284258i
$809$	55.5555	+	6.04202i	1.95323	+	0.212426i	0.996825	−	0.0796294i	$-0.0253737\pi$
$809$	55.5555	+	6.04202i	1.95323	+	0.212426i	0.956401	+	0.292055i	$0.0943392\pi$
$810$		0			0
$811$	7.79356	+	47.5386i	0.273669	+	1.66931i	0.663313	+	0.748342i	$0.269150\pi$
$811$	7.79356	+	47.5386i	0.273669	+	1.66931i	−0.389644	+	0.920966i	$0.627402\pi$
$812$	−95.5983	−	90.5556i	−3.35484	−	3.17788i
$813$		0			0
$814$	1.68751	+	3.18299i	0.0591474	+	0.111564i
$815$	−2.05889	+	0.693720i	−0.0721197	+	0.0243000i
$816$		0			0
$817$	9.98058	−	35.9468i	0.349176	−	1.25762i
$818$	−5.30833	+	3.19391i	−0.185601	+	0.111673i
$819$		0			0
$820$	−38.2958	−	8.42954i	−1.33735	−	0.294372i
$821$	−14.4449	+	27.2459i	−0.504130	+	0.950889i	0.492614	+	0.870248i	$0.336042\pi$
$821$	−14.4449	+	27.2459i	−0.504130	+	0.950889i	−0.996743	+	0.0806411i	$0.974303\pi$
$822$		0			0
$823$	36.1068	−	27.4477i	1.25860	−	0.956766i	0.258647	−	0.965972i	$-0.416723\pi$
$823$	36.1068	−	27.4477i	1.25860	−	0.956766i	0.999958	+	0.00920566i	$0.00293029\pi$
$824$	4.43010	+	5.21551i	0.154330	+	0.181691i
$825$		0			0
$826$	12.6226	+	57.2053i	0.439197	+	1.99043i
$827$	−7.91166			−0.275116			−0.137558	−	0.990494i	$-0.543925\pi$
$827$	−7.91166			−0.275116			−0.137558	+	0.990494i	$0.543925\pi$
$828$		0			0
$829$	−3.24197	+	2.46449i	−0.112598	+	0.0855951i	−0.659958	−	0.751302i	$-0.729426\pi$
$829$	−3.24197	+	2.46449i	−0.112598	+	0.0855951i	0.547360	+	0.836897i	$0.315633\pi$
$830$	8.56513	−	52.2450i	0.297300	−	1.81345i
$831$		0			0
$832$	0.198093	+	0.0436035i	0.00686763	+	0.00151168i
$833$	10.5234	−	1.14448i	0.364613	−	0.0396540i
$834$		0			0
$835$	9.46354	−	34.0846i	0.327499	−	1.17955i
$836$	−46.7992	+	10.3013i	−1.61858	+	0.356277i
$837$		0			0
$838$	15.2246	+	28.7167i	0.525925	+	0.992000i
$839$	5.44915	+	19.6261i	0.188126	+	0.677567i	0.996091	+	0.0883367i	$0.0281551\pi$
$839$	5.44915	+	19.6261i	0.188126	+	0.677567i	−0.807965	+	0.589230i	$0.799431\pi$
$840$		0			0
$841$	−10.6878	−	65.1930i	−0.368546	−	2.24803i
$842$	−14.9219	−	5.02776i	−0.514242	−	0.173268i
$843$		0			0
$844$	68.6738	−	31.7719i	2.36385	−	1.09363i
$845$	1.28863	+	23.7674i	0.0443302	+	0.817622i
$846$		0			0
$847$	19.4820	−	18.4543i	0.669409	−	0.634098i
$848$	76.7315	+	46.1678i	2.63497	+	1.58541i
$849$		0			0
$850$	8.28438	−	20.7922i	0.284152	−	0.713167i
$851$	−3.19948	−	4.71888i	−0.109677	−	0.161761i
$852$		0			0
$853$	10.8326	+	27.1877i	0.370900	+	0.930890i	0.989415	+	0.145116i	$0.0463556\pi$
$853$	10.8326	+	27.1877i	0.370900	+	0.930890i	−0.618514	+	0.785774i	$0.712265\pi$
$854$	−5.46879	+	100.866i	−0.187138	+	3.45156i
$855$		0			0
$856$	−21.2217	+	24.9842i	−0.725344	+	0.853941i
$857$	1.67600	−	30.9121i	0.0572512	−	1.05594i	−0.818911	−	0.573920i	$-0.805422\pi$
$857$	1.67600	−	30.9121i	0.0572512	−	1.05594i	0.876163	−	0.482016i	$-0.160095\pi$
$858$		0			0
$859$	−6.05352	+	8.92828i	−0.206544	+	0.304629i	−0.916825	−	0.399289i	$-0.869257\pi$
$859$	−6.05352	+	8.92828i	−0.206544	+	0.304629i	0.710282	+	0.703917i	$0.248568\pi$
$860$	−23.4258	−	34.5504i	−0.798812	−	1.17816i
$861$		0			0
$862$	−61.1056	−	28.2705i	−2.08127	−	0.962896i
$863$	3.18295	+	1.91512i	0.108349	+	0.0651915i	0.568697	−	0.822547i	$-0.307448\pi$
$863$	3.18295	+	1.91512i	0.108349	+	0.0651915i	−0.460348	+	0.887739i	$0.652275\pi$
$864$		0			0
$865$	−1.20807	−	0.918348i	−0.0410755	−	0.0312248i
$866$	−3.00834	−	55.4856i	−0.102228	−	1.88548i
$867$		0			0
$868$	−91.1132	−	9.90916i	−3.09258	−	0.336339i
$869$	8.90947	+	3.00195i	0.302233	+	0.101834i
$870$		0			0
$871$	−0.620351	−	0.587628i	−0.0210198	−	0.0199110i
$872$	−24.9195	−	89.7520i	−0.843881	−	3.03939i
$873$		0			0
$874$	103.644	−	34.9217i	3.50581	−	1.18124i
$875$	35.4901	−	7.81196i	1.19978	−	0.264092i
$876$		0			0
$877$	−34.9051	+	21.0017i	−1.17866	+	0.709176i	−0.963580	−	0.267420i	$-0.913829\pi$
$877$	−34.9051	+	21.0017i	−1.17866	+	0.709176i	−0.215080	+	0.976596i	$0.569001\pi$
$878$	23.4102	−	2.54601i	0.790057	−	0.0859238i
$879$		0			0
$880$	−9.09701	+	17.1588i	−0.306660	+	0.578422i
$881$	−6.19665	+	37.7979i	−0.208771	+	1.27344i	0.649546	+	0.760323i	$0.274959\pi$
$881$	−6.19665	+	37.7979i	−0.208771	+	1.27344i	−0.858316	+	0.513121i	$0.828489\pi$
$882$		0			0
$883$	20.8198	+	24.5109i	0.700641	+	0.824858i	0.991252	−	0.131983i	$-0.0421345\pi$
$883$	20.8198	+	24.5109i	0.700641	+	0.824858i	−0.290611	+	0.956841i	$0.593859\pi$
$884$	−8.46293			−0.284639
$885$		0			0
$886$	−18.0506			−0.606421
$887$	−5.31794	−	6.26076i	−0.178559	−	0.210216i	0.665600	−	0.746308i	$-0.268176\pi$
$887$	−5.31794	−	6.26076i	−0.178559	−	0.210216i	−0.844159	+	0.536093i	$0.819900\pi$
$888$		0			0
$889$	−3.60151	+	21.9682i	−0.120791	+	0.736791i
$890$	30.1403	−	56.8506i	1.01030	−	1.90564i
$891$		0			0
$892$	59.4797	−	6.46881i	1.99153	−	0.216592i
$893$	−22.4885	+	13.5309i	−0.752549	+	0.452794i
$894$		0			0
$895$	−4.89474	+	1.07741i	−0.163613	+	0.0360140i
$896$	−29.8380	+	10.0536i	−0.996818	+	0.335867i
$897$		0			0
$898$	16.0255	+	57.7185i	0.534777	+	1.92609i
$899$	−48.0358	−	45.5019i	−1.60208	−	1.51757i
$900$		0			0
$901$	−63.2311	−	21.3051i	−2.10653	−	0.709774i
$902$	16.9112	+	1.83920i	0.563080	+	0.0612387i
$903$		0			0
$904$	−0.0319674	−	0.589603i	−0.00106322	−	0.0196099i
$905$	27.3149	+	20.7642i	0.907978	+	0.690227i
$906$		0			0
$907$	20.9619	+	12.6124i	0.696029	+	0.418787i	0.819130	−	0.573608i	$-0.194457\pi$
$907$	20.9619	+	12.6124i	0.696029	+	0.418787i	−0.123102	+	0.992394i	$0.539284\pi$
$908$	−18.5422	−	8.57854i	−0.615345	−	0.284689i
$909$		0			0
$910$	−2.68014	−	3.95291i	−0.0888457	−	0.131038i
$911$	11.0452	−	16.2905i	0.365945	−	0.539728i	−0.599487	−	0.800385i	$-0.704629\pi$
$911$	11.0452	−	16.2905i	0.365945	−	0.539728i	0.965432	+	0.260657i	$0.0839390\pi$
$912$		0			0
$913$	−0.862147	+	15.9014i	−0.0285329	+	0.526259i
$914$	−40.6291	+	47.8323i	−1.34389	+	1.58215i
$915$		0			0
$916$	3.94134	−	72.6937i	0.130225	−	2.40187i
$917$	−4.17597	−	10.4809i	−0.137903	−	0.346109i
$918$		0			0
$919$	17.2302	+	25.4126i	0.568371	+	0.838285i	0.997900	−	0.0647681i	$-0.0206308\pi$
$919$	17.2302	+	25.4126i	0.568371	+	0.838285i	−0.429529	+	0.903053i	$0.641320\pi$
$920$	25.2649	−	63.4100i	0.832958	−	2.09057i
$921$		0			0
$922$	26.7745	+	16.1097i	0.881772	+	0.530544i
$923$	−1.93166	+	1.82977i	−0.0635814	+	0.0602275i
$924$		0			0
$925$	0.0854378	+	1.57581i	0.00280918	+	0.0518122i
$926$	80.9843	−	37.4673i	2.66131	−	1.23125i
$927$		0			0
$928$	55.7703	+	18.7912i	1.83075	+	0.616851i
$929$	−9.21167	−	56.1887i	−0.302225	−	1.84349i	−0.503548	−	0.863967i	$-0.667972\pi$
$929$	−9.21167	−	56.1887i	−0.302225	−	1.84349i	0.201323	−	0.979525i	$-0.435476\pi$
$930$		0			0
$931$	−3.83040	−	13.7959i	−0.125536	−	0.452141i
$932$	−41.1019	−	77.5263i	−1.34634	−	2.53946i
$933$		0			0
$934$	−53.8172	+	11.8461i	−1.76095	+	0.387615i
$935$	3.87133	−	13.9433i	0.126606	−	0.455994i
$936$		0			0
$937$	13.7752	−	1.49814i	0.450016	−	0.0489422i	0.119695	−	0.992811i	$-0.461808\pi$
$937$	13.7752	−	1.49814i	0.450016	−	0.0489422i	0.330321	+	0.943869i	$0.392843\pi$
$938$	−18.7749	−	4.13268i	−0.613024	−	0.134937i
$939$		0			0
$940$	−4.75097	+	28.9797i	−0.154960	+	0.945212i
$941$	−26.3386	+	20.0221i	−0.858615	+	0.652702i	−0.938945	−	0.344066i	$-0.888196\pi$
$941$	−26.3386	+	20.0221i	−0.858615	+	0.652702i	0.0803304	+	0.996768i	$0.474402\pi$
$942$		0			0
$943$	−26.9201			−0.876637
$944$	−34.4614	−	45.2850i	−1.12162	−	1.47390i
$945$		0			0
$946$	11.7233	+	13.8018i	0.381159	+	0.448735i
$947$	−3.56666	+	2.71131i	−0.115901	+	0.0881056i	−0.661519	−	0.749928i	$-0.730088\pi$
$947$	−3.56666	+	2.71131i	−0.115901	+	0.0881056i	0.545618	+	0.838034i	$0.316295\pi$
$948$		0			0
$949$	1.51776	−	2.86281i	0.0492687	−	0.0929306i
$950$	−29.5657	−	6.50791i	−0.959239	−	0.211145i
$951$		0			0
$952$	−90.9990	+	54.7523i	−2.94930	+	1.77453i
$953$	−2.32432	+	8.37144i	−0.0752920	+	0.271177i	−0.991608	−	0.129278i	$-0.958734\pi$
$953$	−2.32432	+	8.37144i	−0.0752920	+	0.271177i	0.916316	+	0.400455i	$0.131148\pi$
$954$		0			0
$955$	24.3708	−	8.21149i	0.788622	−	0.265718i
$956$	30.6267	+	57.7681i	0.990538	+	1.86835i
$957$		0			0
$958$	32.8291	+	31.0974i	1.06066	+	1.00471i
$959$	−1.05532	−	6.43716i	−0.0340780	−	0.207867i
$960$		0			0
$961$	−14.9638	−	1.62741i	−0.482704	−	0.0524972i
$962$	0.781054	−	0.361354i	0.0251822	−	0.0116505i
$963$		0			0
$964$	−77.8096	−	59.1493i	−2.50608	−	1.90507i
$965$	−13.7066	+	12.9836i	−0.441232	+	0.417957i
$966$		0			0
$967$	13.4175	+	6.20760i	0.431478	+	0.199623i	0.623593	−	0.781750i	$-0.285672\pi$
$967$	13.4175	+	6.20760i	0.431478	+	0.199623i	−0.192115	+	0.981372i	$0.561535\pi$
$968$	−21.4286	+	53.7817i	−0.688741	+	1.72861i
$969$		0			0
$970$	28.8818	−	42.5975i	0.927339	−	1.36772i
$971$	15.4853	+	38.8651i	0.496945	+	1.24724i	0.937019	+	0.349277i	$0.113573\pi$
$971$	15.4853	+	38.8651i	0.496945	+	1.24724i	−0.440074	+	0.897962i	$0.645048\pi$
$972$		0			0
$973$	7.17523	−	8.44734i	0.230027	−	0.270809i
$974$	−62.0257	+	73.0223i	−1.98743	+	2.33979i
$975$		0			0
$976$	−36.3200	−	91.1563i	−1.16257	−	2.91784i
$977$	13.0736	−	19.2822i	0.418263	−	0.616891i	−0.558938	−	0.829209i	$-0.688791\pi$
$977$	13.0736	−	19.2822i	0.418263	−	0.616891i	0.977201	+	0.212318i	$0.0681014\pi$
$978$		0			0
$979$	−7.16399	+	17.9803i	−0.228962	+	0.574651i
$980$	−14.5398	−	6.72681i	−0.464456	−	0.214880i
$981$		0			0
$982$	13.7024	−	12.9796i	0.437261	−	0.414195i
$983$	23.4601	+	17.8339i	0.748261	+	0.568813i	0.908311	−	0.418296i	$-0.137372\pi$
$983$	23.4601	+	17.8339i	0.748261	+	0.568813i	−0.160050	+	0.987109i	$0.551166\pi$
$984$		0			0
$985$	9.36096	−	4.33084i	0.298265	−	0.137992i
$986$	−136.651	−	14.8617i	−4.35185	−	0.473293i
$987$		0			0
$988$	1.85190	+	11.2961i	0.0589168	+	0.359377i
$989$	−20.8051	−	19.7077i	−0.661565	−	0.626668i
$990$		0			0
$991$	−9.07465	−	17.1166i	−0.288266	−	0.543727i	0.696512	−	0.717545i	$-0.254734\pi$
$991$	−9.07465	−	17.1166i	−0.288266	−	0.543727i	−0.984778	+	0.173818i	$0.944390\pi$
$992$	38.8169	−	13.0789i	1.23244	−	0.415257i
$993$		0			0
$994$	−16.0146	+	57.6793i	−0.507952	+	1.82948i
$995$	−30.2359	+	18.1923i	−0.958541	+	0.576735i
$996$		0			0
$997$	−1.54922	−	0.341010i	−0.0490644	−	0.0107999i	0.190370	−	0.981712i	$-0.439031\pi$
$997$	−1.54922	−	0.341010i	−0.0490644	−	0.0107999i	−0.239435	+	0.970912i	$0.576962\pi$
$998$	−29.8121	+	56.2316i	−0.943686	+	1.77998i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.46.1		140
3.2	odd	2		177.2.e.a.46.5	✓	140
59.9	even	29	inner	531.2.i.c.127.1		140
177.68	odd	58		177.2.e.a.127.5	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.46.5	✓	140	3.2	odd	2
177.2.e.a.127.5	yes	140	177.68	odd	58
531.2.i.c.46.1		140	1.1	even	1	trivial
531.2.i.c.127.1		140	59.9	even	29	inner

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65338 - 1.94651i) q^{2} +(-0.731672 + 4.46300i) q^{4} +(-0.865278 + 1.63209i) q^{5} +(-2.96873 + 0.322869i) q^{7} +(5.52030 - 3.32145i) q^{8} +O(q^{10})\)	\(q+(-1.65338 - 1.94651i) q^{2} +(-0.731672 + 4.46300i) q^{4} +(-0.865278 + 1.63209i) q^{5} +(-2.96873 + 0.322869i) q^{7} +(5.52030 - 3.32145i) q^{8} +(4.60751 - 1.01419i) q^{10} +(-1.34480 + 0.453117i) q^{11} +(0.0906890 + 0.326632i) q^{13} +(5.53691 + 5.24484i) q^{14} +(-7.02074 - 2.36556i) q^{16} +(5.48778 + 0.596832i) q^{17} +(-0.404228 - 7.45555i) q^{19} +(-6.65091 - 5.05589i) q^{20} +(3.10547 + 1.86850i) q^{22} +(-5.20536 - 2.40826i) q^{23} +(0.890931 + 1.31402i) q^{25} +(0.485850 - 0.716575i) q^{26} +(0.731172 - 13.4857i) q^{28} +(6.31204 - 7.43111i) q^{29} +(0.367396 - 6.77621i) q^{31} +(2.23414 + 5.60728i) q^{32} +(-7.91166 - 11.6688i) q^{34} +(2.04183 - 5.12460i) q^{35} +(0.851751 + 0.512481i) q^{37} +(-13.8440 + 13.1137i) q^{38} +(0.644310 + 11.8836i) q^{40} +(4.25981 - 1.97080i) q^{41} +(4.73498 + 1.59540i) q^{43} +(-1.03831 - 6.33339i) q^{44} +(3.91875 + 14.1141i) q^{46} +(-1.64649 - 3.10562i) q^{47} +(1.87277 - 0.412227i) q^{49} +(1.08472 - 3.90679i) q^{50} +(-1.52411 + 0.165757i) q^{52} +(-11.8048 - 2.59843i) q^{53} +(0.424102 - 2.58691i) q^{55} +(-15.3159 + 11.6428i) q^{56} -24.9010 q^{58} +(6.35981 + 4.30730i) q^{59} +(8.57456 + 10.0948i) q^{61} +(-13.7974 + 10.4885i) q^{62} +(0.280274 - 0.528653i) q^{64} +(-0.611563 - 0.134615i) q^{65} +(-2.15987 + 1.29955i) q^{67} +(-6.67892 + 24.0553i) q^{68} +(-13.3510 + 4.49848i) q^{70} +(3.67652 + 6.93466i) q^{71} +(-6.93951 - 6.57345i) q^{73} +(-0.410718 - 2.50527i) q^{74} +(33.5699 + 3.65094i) q^{76} +(3.84606 - 1.77938i) q^{77} +(-5.27421 - 4.00935i) q^{79} +(9.93570 - 9.41160i) q^{80} +(-10.8793 - 5.03329i) q^{82} +(4.15362 - 10.4248i) q^{83} +(-5.72254 + 8.44012i) q^{85} +(-4.72327 - 11.8545i) q^{86} +(-5.91871 + 6.96804i) q^{88} +(8.82969 - 10.3951i) q^{89} +(-0.374690 - 0.940402i) q^{91} +(14.5567 - 21.4695i) q^{92} +(-3.32284 + 8.33969i) q^{94} +(12.5179 + 5.79139i) q^{95} +(7.91972 - 7.50196i) q^{97} +(-3.89880 - 2.96379i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

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