LMFDB - Embedded newform 644.2.i.a.93.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 $ x^14 + 13x^12 - 8x^11 + 130x^10 - 78x^9 + 505x^8 - 519x^7 + 1508x^6 - 955x^5 + 1023x^4 + 156x^3 + 107x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.3
Root			$0.0453148 + 0.0784875i$ of defining polynomial
Character	$\chi$	$=$	644.93
Dual form			644.2.i.a.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03959 - 1.80062i) q^{3} +(0.832793 - 1.44244i) q^{5} +(-2.64459 + 0.0784875i) q^{7} +(-0.661478 + 1.14571i) q^{9} +O(q^{10})$	\(q+(-1.03959 - 1.80062i) q^{3} +(0.832793 - 1.44244i) q^{5} +(-2.64459 + 0.0784875i) q^{7} +(-0.661478 + 1.14571i) q^{9} +(-0.494262 - 0.856087i) q^{11} -2.84085 q^{13} -3.46304 q^{15} +(-1.02169 - 1.76962i) q^{17} +(-1.57247 + 2.72360i) q^{19} +(2.89060 + 4.68029i) q^{21} +(0.500000 - 0.866025i) q^{23} +(1.11291 + 1.92762i) q^{25} -3.48686 q^{27} +3.06771 q^{29} +(-3.31480 - 5.74140i) q^{31} +(-1.02766 + 1.77995i) q^{33} +(-2.08918 + 3.88002i) q^{35} +(-4.00232 + 6.93223i) q^{37} +(2.95331 + 5.11528i) q^{39} +1.47285 q^{41} -4.79477 q^{43} +(1.10175 + 1.90829i) q^{45} +(-5.26758 + 9.12372i) q^{47} +(6.98768 - 0.415134i) q^{49} +(-2.12427 + 3.67934i) q^{51} +(-1.05423 - 1.82598i) q^{53} -1.64647 q^{55} +6.53887 q^{57} +(-5.30091 - 9.18145i) q^{59} +(0.886494 - 1.53545i) q^{61} +(1.65941 - 3.08186i) q^{63} +(-2.36584 + 4.09776i) q^{65} +(-2.30965 - 4.00044i) q^{67} -2.07917 q^{69} +3.86351 q^{71} +(-5.12559 - 8.87778i) q^{73} +(2.31393 - 4.00785i) q^{75} +(1.37431 + 2.22520i) q^{77} +(-0.641961 + 1.11191i) q^{79} +(5.60933 + 9.71564i) q^{81} -8.51653 q^{83} -3.40343 q^{85} +(-3.18915 - 5.52378i) q^{87} +(4.35745 - 7.54733i) q^{89} +(7.51288 - 0.222971i) q^{91} +(-6.89204 + 11.9374i) q^{93} +(2.61909 + 4.53639i) q^{95} +10.2838 q^{97} +1.30778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.03959	−	1.80062i	−0.600205	−	1.03959i	−0.992790	−	0.119870i	$-0.961752\pi$
$3$	−1.03959	−	1.80062i	−0.600205	−	1.03959i	0.392584	−	0.919716i	$-0.371581\pi$
$4$		0			0
$5$	0.832793	−	1.44244i	0.372436	−	0.645079i	−0.617503	−	0.786568i	$-0.711856\pi$
$5$	0.832793	−	1.44244i	0.372436	−	0.645079i	0.989940	+	0.141490i	$0.0451892\pi$
$6$		0			0
$7$	−2.64459	+	0.0784875i	−0.999560	+	0.0296655i
$7$	−2.64459	+	0.0784875i	−0.999560	+	0.0296655i
$8$		0			0
$9$	−0.661478	+	1.14571i	−0.220493	+	0.381905i
$10$		0			0
$11$	−0.494262	−	0.856087i	−0.149026	−	0.258120i	0.781842	−	0.623477i	$-0.214280\pi$
$11$	−0.494262	−	0.856087i	−0.149026	−	0.258120i	−0.930868	+	0.365357i	$0.880947\pi$
$12$		0			0
$13$	−2.84085			−0.787911			−0.393955	−	0.919130i	$-0.628894\pi$
$13$	−2.84085			−0.787911			−0.393955	+	0.919130i	$0.628894\pi$
$14$		0			0
$15$	−3.46304			−0.894153
$16$		0			0
$17$	−1.02169	−	1.76962i	−0.247796	−	0.429196i	0.715118	−	0.699004i	$-0.246373\pi$
$17$	−1.02169	−	1.76962i	−0.247796	−	0.429196i	−0.962914	+	0.269808i	$0.913040\pi$
$18$		0			0
$19$	−1.57247	+	2.72360i	−0.360750	+	0.624836i	−0.988084	−	0.153913i	$-0.950812\pi$
$19$	−1.57247	+	2.72360i	−0.360750	+	0.624836i	0.627335	+	0.778750i	$0.284146\pi$
$20$		0			0
$21$	2.89060	+	4.68029i	0.630781	+	1.02132i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	1.11291	+	1.92762i	0.222582	+	0.385524i
$26$		0			0
$27$	−3.48686			−0.671047
$28$		0			0
$29$	3.06771			0.569660			0.284830	−	0.958578i	$-0.408063\pi$
$29$	3.06771			0.569660			0.284830	+	0.958578i	$0.408063\pi$
$30$		0			0
$31$	−3.31480	−	5.74140i	−0.595355	−	1.03119i	−0.993497	−	0.113862i	$-0.963678\pi$
$31$	−3.31480	−	5.74140i	−0.595355	−	1.03119i	0.398141	−	0.917324i	$-0.369655\pi$
$32$		0			0
$33$	−1.02766	+	1.77995i	−0.178892	+	0.309850i
$34$		0			0
$35$	−2.08918	+	3.88002i	−0.353136	+	0.655843i
$36$		0			0
$37$	−4.00232	+	6.93223i	−0.657978	+	1.13965i	0.323161	+	0.946344i	$0.395255\pi$
$37$	−4.00232	+	6.93223i	−0.657978	+	1.13965i	−0.981138	+	0.193307i	$0.938079\pi$
$38$		0			0
$39$	2.95331	+	5.11528i	0.472908	+	0.819101i
$40$		0			0
$41$	1.47285			0.230021			0.115010	−	0.993364i	$-0.463310\pi$
$41$	1.47285			0.230021			0.115010	+	0.993364i	$0.463310\pi$
$42$		0			0
$43$	−4.79477			−0.731196			−0.365598	−	0.930773i	$-0.619135\pi$
$43$	−4.79477			−0.731196			−0.365598	+	0.930773i	$0.619135\pi$
$44$		0			0
$45$	1.10175	+	1.90829i	0.164239	+	0.284470i
$46$		0			0
$47$	−5.26758	+	9.12372i	−0.768356	+	1.33083i	0.170098	+	0.985427i	$0.445591\pi$
$47$	−5.26758	+	9.12372i	−0.768356	+	1.33083i	−0.938454	+	0.345404i	$0.887742\pi$
$48$		0			0
$49$	6.98768	−	0.415134i	0.998240	−	0.0593048i
$50$		0			0
$51$	−2.12427	+	3.67934i	−0.297457	+	0.515211i
$52$		0			0
$53$	−1.05423	−	1.82598i	−0.144810	−	0.250818i	0.784492	−	0.620139i	$-0.212924\pi$
$53$	−1.05423	−	1.82598i	−0.144810	−	0.250818i	−0.929302	+	0.369321i	$0.879590\pi$
$54$		0			0
$55$	−1.64647			−0.222010
$56$		0			0
$57$	6.53887			0.866095
$58$		0			0
$59$	−5.30091	−	9.18145i	−0.690120	−	1.19532i	−0.971798	−	0.235814i	$-0.924224\pi$
$59$	−5.30091	−	9.18145i	−0.690120	−	1.19532i	0.281678	−	0.959509i	$-0.409109\pi$
$60$		0			0
$61$	0.886494	−	1.53545i	0.113504	−	0.196595i	−0.803677	−	0.595066i	$-0.797126\pi$
$61$	0.886494	−	1.53545i	0.113504	−	0.196595i	0.917181	+	0.398472i	$0.130459\pi$
$62$		0			0
$63$	1.65941	−	3.08186i	0.209066	−	0.388278i
$64$		0			0
$65$	−2.36584	+	4.09776i	−0.293447	+	0.508264i
$66$		0			0
$67$	−2.30965	−	4.00044i	−0.282169	−	0.488731i	0.689750	−	0.724048i	$-0.257721\pi$
$67$	−2.30965	−	4.00044i	−0.282169	−	0.488731i	−0.971919	+	0.235317i	$0.924387\pi$
$68$		0			0
$69$	−2.07917			−0.250303
$70$		0			0
$71$	3.86351			0.458514			0.229257	−	0.973366i	$-0.426370\pi$
$71$	3.86351			0.458514			0.229257	+	0.973366i	$0.426370\pi$
$72$		0			0
$73$	−5.12559	−	8.87778i	−0.599905	−	1.03907i	−0.992835	−	0.119497i	$-0.961872\pi$
$73$	−5.12559	−	8.87778i	−0.599905	−	1.03907i	0.392930	−	0.919569i	$-0.371462\pi$
$74$		0			0
$75$	2.31393	−	4.00785i	0.267190	−	0.462787i
$76$		0			0
$77$	1.37431	+	2.22520i	0.156617	+	0.253586i
$78$		0			0
$79$	−0.641961	+	1.11191i	−0.0722263	+	0.125100i	−0.899877	−	0.436144i	$-0.856344\pi$
$79$	−0.641961	+	1.11191i	−0.0722263	+	0.125100i	0.827650	+	0.561244i	$0.189677\pi$
$80$		0			0
$81$	5.60933	+	9.71564i	0.623259	+	1.07952i
$82$		0			0
$83$	−8.51653			−0.934811			−0.467405	−	0.884043i	$-0.654811\pi$
$83$	−8.51653			−0.934811			−0.467405	+	0.884043i	$0.654811\pi$
$84$		0			0
$85$	−3.40343			−0.369153
$86$		0			0
$87$	−3.18915	−	5.52378i	−0.341913	−	0.592211i
$88$		0			0
$89$	4.35745	−	7.54733i	0.461889	−	0.800015i	−0.537166	−	0.843477i	$-0.680505\pi$
$89$	4.35745	−	7.54733i	0.461889	−	0.800015i	0.999055	+	0.0434611i	$0.0138385\pi$
$90$		0			0
$91$	7.51288	−	0.222971i	0.787564	−	0.0233737i
$92$		0			0
$93$	−6.89204	+	11.9374i	−0.714671	+	1.23785i
$94$		0			0
$95$	2.61909	+	4.53639i	0.268712	+	0.465424i
$96$		0			0
$97$	10.2838			1.04416			0.522080	−	0.852896i	$-0.325156\pi$
$97$	10.2838			1.04416			0.522080	+	0.852896i	$0.325156\pi$
$98$		0			0
$99$	1.30778			0.131436
$100$		0			0
$101$	−6.74071	−	11.6753i	−0.670726	−	1.16173i	−0.977699	−	0.210013i	$-0.932649\pi$
$101$	−6.74071	−	11.6753i	−0.670726	−	1.16173i	0.306972	−	0.951718i	$-0.400684\pi$
$102$		0			0
$103$	3.35673	−	5.81403i	0.330748	−	0.572873i	−0.651910	−	0.758296i	$-0.726032\pi$
$103$	3.35673	−	5.81403i	0.330748	−	0.572873i	0.982659	+	0.185423i	$0.0593655\pi$
$104$		0			0
$105$	9.15831	−	0.271805i	0.893760	−	0.0265255i
$106$		0			0
$107$	−0.0996616	+	0.172619i	−0.00963466	+	0.0166877i	−0.870803	−	0.491633i	$-0.836400\pi$
$107$	−0.0996616	+	0.172619i	−0.00963466	+	0.0166877i	0.861168	+	0.508321i	$0.169734\pi$
$108$		0			0
$109$	−9.87314	−	17.1008i	−0.945676	−	1.63796i	−0.754393	−	0.656423i	$-0.772069\pi$
$109$	−9.87314	−	17.1008i	−0.945676	−	1.63796i	−0.191283	−	0.981535i	$-0.561265\pi$
$110$		0			0
$111$	16.6430			1.57969
$112$		0			0
$113$	3.53986			0.333002			0.166501	−	0.986041i	$-0.446753\pi$
$113$	3.53986			0.333002			0.166501	+	0.986041i	$0.446753\pi$
$114$		0			0
$115$	−0.832793	−	1.44244i	−0.0776583	−	0.134508i
$116$		0			0
$117$	1.87916	−	3.25481i	0.173729	−	0.300907i
$118$		0			0
$119$	2.84084	+	4.59972i	0.260420	+	0.421656i
$120$		0			0
$121$	5.01141	−	8.68002i	0.455583	−	0.789092i
$122$		0			0
$123$	−1.53116	−	2.65204i	−0.138060	−	0.239126i
$124$		0			0
$125$	12.0352			1.07646
$126$		0			0
$127$	1.50216			0.133295			0.0666475	−	0.997777i	$-0.478770\pi$
$127$	1.50216			0.133295			0.0666475	+	0.997777i	$0.478770\pi$
$128$		0			0
$129$	4.98458	+	8.63354i	0.438867	+	0.760141i
$130$		0			0
$131$	6.12937	−	10.6164i	0.535525	−	0.927557i	−0.463612	−	0.886038i	$-0.653447\pi$
$131$	6.12937	−	10.6164i	0.535525	−	0.927557i	0.999138	−	0.0415190i	$-0.0132197\pi$
$132$		0			0
$133$	3.94477	−	7.32621i	0.342055	−	0.635263i
$134$		0			0
$135$	−2.90383	+	5.02959i	−0.249922	+	0.432878i
$136$		0			0
$137$	3.62370	+	6.27642i	0.309593	+	0.536231i	0.978273	−	0.207319i	$-0.0664738\pi$
$137$	3.62370	+	6.27642i	0.309593	+	0.536231i	−0.668680	+	0.743550i	$0.733140\pi$
$138$		0			0
$139$	6.73017			0.570846			0.285423	−	0.958402i	$-0.407866\pi$
$139$	6.73017			0.570846			0.285423	+	0.958402i	$0.407866\pi$
$140$		0			0
$141$	21.9044			1.84468
$142$		0			0
$143$	1.40413	+	2.43202i	0.117419	+	0.203376i
$144$		0			0
$145$	2.55477	−	4.42499i	0.212162	−	0.367476i
$146$		0			0
$147$	−8.01179	−	12.1506i	−0.660801	−	1.00216i
$148$		0			0
$149$	−4.21743	+	7.30480i	−0.345505	+	0.598433i	−0.985445	−	0.169992i	$-0.945626\pi$
$149$	−4.21743	+	7.30480i	−0.345505	+	0.598433i	0.639940	+	0.768425i	$0.278959\pi$
$150$		0			0
$151$	−1.65419	−	2.86515i	−0.134616	−	0.233162i	0.790835	−	0.612030i	$-0.209647\pi$
$151$	−1.65419	−	2.86515i	−0.134616	−	0.233162i	−0.925451	+	0.378868i	$0.876314\pi$
$152$		0			0
$153$	2.70330			0.218549
$154$		0			0
$155$	−11.0422			−0.886928
$156$		0			0
$157$	−1.36542	−	2.36498i	−0.108972	−	0.188746i	0.806382	−	0.591395i	$-0.201423\pi$
$157$	−1.36542	−	2.36498i	−0.108972	−	0.188746i	−0.915354	+	0.402649i	$0.868089\pi$
$158$		0			0
$159$	−2.19192	+	3.79653i	−0.173831	+	0.301084i
$160$		0			0
$161$	−1.25432	+	2.32952i	−0.0988544	+	0.183592i
$162$		0			0
$163$	10.4458	−	18.0927i	0.818179	−	1.41713i	−0.0888439	−	0.996046i	$-0.528317\pi$
$163$	10.4458	−	18.0927i	0.818179	−	1.41713i	0.907023	−	0.421082i	$-0.138349\pi$
$164$		0			0
$165$	1.71165	+	2.96467i	0.133252	+	0.230799i
$166$		0			0
$167$	4.58070			0.354465			0.177233	−	0.984169i	$-0.443285\pi$
$167$	4.58070			0.354465			0.177233	+	0.984169i	$0.443285\pi$
$168$		0			0
$169$	−4.92955			−0.379197
$170$		0			0
$171$	−2.08031	−	3.60320i	−0.159085	−	0.275544i
$172$		0			0
$173$	−1.89064	+	3.27469i	−0.143743	+	0.248970i	−0.928903	−	0.370322i	$-0.879247\pi$
$173$	−1.89064	+	3.27469i	−0.143743	+	0.248970i	0.785160	+	0.619293i	$0.212581\pi$
$174$		0			0
$175$	−3.09449	−	5.01041i	−0.233921	−	0.378751i
$176$		0			0
$177$	−11.0215	+	19.0898i	−0.828427	+	1.43488i
$178$		0			0
$179$	11.3563	+	19.6696i	0.848806	+	1.47018i	0.882274	+	0.470736i	$0.156012\pi$
$179$	11.3563	+	19.6696i	0.848806	+	1.47018i	−0.0334679	+	0.999440i	$0.510655\pi$
$180$		0			0
$181$	−4.78760			−0.355859			−0.177930	−	0.984043i	$-0.556940\pi$
$181$	−4.78760			−0.355859			−0.177930	+	0.984043i	$0.556940\pi$
$182$		0			0
$183$	−3.68635			−0.272503
$184$		0			0
$185$	6.66621	+	11.5462i	0.490110	+	0.848895i
$186$		0			0
$187$	−1.00997	+	1.74931i	−0.0738561	+	0.127922i
$188$		0			0
$189$	9.22131	−	0.273675i	0.670752	−	0.0199069i
$190$		0			0
$191$	−1.82929	+	3.16843i	−0.132363	+	0.229259i	−0.924587	−	0.380971i	$-0.875590\pi$
$191$	−1.82929	+	3.16843i	−0.132363	+	0.229259i	0.792224	+	0.610230i	$0.208923\pi$
$192$		0			0
$193$	−9.28068	−	16.0746i	−0.668038	−	1.15708i	−0.978452	−	0.206474i	$-0.933801\pi$
$193$	−9.28068	−	16.0746i	−0.668038	−	1.15708i	0.310414	−	0.950601i	$-0.399532\pi$
$194$		0			0
$195$	9.83799			0.704513
$196$		0			0
$197$	−12.2158			−0.870341			−0.435170	−	0.900348i	$-0.643312\pi$
$197$	−12.2158			−0.870341			−0.435170	+	0.900348i	$0.643312\pi$
$198$		0			0
$199$	−10.1874	−	17.6451i	−0.722166	−	1.25083i	−0.960130	−	0.279554i	$-0.909813\pi$
$199$	−10.1874	−	17.6451i	−0.722166	−	1.25083i	0.237964	−	0.971274i	$-0.423520\pi$
$200$		0			0
$201$	−4.80217	+	8.31760i	−0.338719	+	0.586678i
$202$		0			0
$203$	−8.11284	+	0.240777i	−0.569410	+	0.0168992i
$204$		0			0
$205$	1.22658	−	2.12450i	0.0856681	−	0.148381i
$206$		0			0
$207$	0.661478	+	1.14571i	0.0459759	+	0.0796326i
$208$		0			0
$209$	3.10885			0.215044
$210$		0			0
$211$	2.76436			0.190306			0.0951532	−	0.995463i	$-0.469666\pi$
$211$	2.76436			0.190306			0.0951532	+	0.995463i	$0.469666\pi$
$212$		0			0
$213$	−4.01645	−	6.95669i	−0.275202	−	0.476664i
$214$		0			0
$215$	−3.99305	+	6.91617i	−0.272324	+	0.471679i
$216$		0			0
$217$	9.21690	+	14.9235i	0.625684	+	1.01307i
$218$		0			0
$219$	−10.6570	+	18.4584i	−0.720132	+	1.24731i
$220$		0			0
$221$	2.90247	+	5.02723i	0.195241	+	0.338168i
$222$		0			0
$223$	14.7299			0.986389			0.493194	−	0.869919i	$-0.335829\pi$
$223$	14.7299			0.986389			0.493194	+	0.869919i	$0.335829\pi$
$224$		0			0
$225$	−2.94467			−0.196311
$226$		0			0
$227$	−12.2577	−	21.2309i	−0.813570	−	1.40914i	−0.910350	−	0.413839i	$-0.864188\pi$
$227$	−12.2577	−	21.2309i	−0.813570	−	1.40914i	0.0967799	−	0.995306i	$-0.469146\pi$
$228$		0			0
$229$	−11.8456	+	20.5172i	−0.782781	+	1.35582i	0.147535	+	0.989057i	$0.452866\pi$
$229$	−11.8456	+	20.5172i	−0.782781	+	1.35582i	−0.930316	+	0.366759i	$0.880467\pi$
$230$		0			0
$231$	2.57802	−	4.78790i	0.169621	−	0.315021i
$232$		0			0
$233$	−5.24516	+	9.08488i	−0.343622	+	0.595170i	−0.985102	−	0.171969i	$-0.944987\pi$
$233$	−5.24516	+	9.08488i	−0.343622	+	0.595170i	0.641481	+	0.767139i	$0.278320\pi$
$234$		0			0
$235$	8.77361	+	15.1963i	0.572327	+	0.991300i
$236$		0			0
$237$	2.66949			0.173402
$238$		0			0
$239$	−18.4871			−1.19583			−0.597916	−	0.801559i	$-0.704004\pi$
$239$	−18.4871			−1.19583			−0.597916	+	0.801559i	$0.704004\pi$
$240$		0			0
$241$	5.94815	+	10.3025i	0.383154	+	0.663642i	0.991511	−	0.130021i	$-0.0415045\pi$
$241$	5.94815	+	10.3025i	0.383154	+	0.663642i	−0.608357	+	0.793663i	$0.708171\pi$
$242$		0			0
$243$	6.43247	−	11.1414i	0.412643	−	0.714718i
$244$		0			0
$245$	5.22048	−	10.4250i	0.333525	−	0.666031i
$246$		0			0
$247$	4.46716	−	7.73734i	0.284238	−	0.492315i
$248$		0			0
$249$	8.85367	+	15.3350i	0.561078	+	0.971816i
$250$		0			0
$251$	16.3755			1.03361			0.516805	−	0.856103i	$-0.327121\pi$
$251$	16.3755			1.03361			0.516805	+	0.856103i	$0.327121\pi$
$252$		0			0
$253$	−0.988525			−0.0621480
$254$		0			0
$255$	3.53816	+	6.12826i	0.221568	+	0.383767i
$256$		0			0
$257$	−4.59191	+	7.95343i	−0.286436	+	0.496121i	−0.972956	−	0.230989i	$-0.925804\pi$
$257$	−4.59191	+	7.95343i	−0.286436	+	0.496121i	0.686521	+	0.727110i	$0.259137\pi$
$258$		0			0
$259$	10.0404	−	18.6470i	0.623880	−	1.15867i
$260$		0			0
$261$	−2.02923	+	3.51472i	−0.125606	+	0.217556i
$262$		0			0
$263$	4.01599	+	6.95591i	0.247637	+	0.428920i	0.962870	−	0.269967i	$-0.0870127\pi$
$263$	4.01599	+	6.95591i	0.247637	+	0.428920i	−0.715233	+	0.698886i	$0.753679\pi$
$264$		0			0
$265$	−3.51182			−0.215729
$266$		0			0
$267$	−18.1198			−1.10891
$268$		0			0
$269$	4.19305	+	7.26258i	0.255655	+	0.442808i	0.965073	−	0.261980i	$-0.0843755\pi$
$269$	4.19305	+	7.26258i	0.255655	+	0.442808i	−0.709418	+	0.704788i	$0.751042\pi$
$270$		0			0
$271$	2.85582	−	4.94642i	0.173479	−	0.300474i	−0.766155	−	0.642656i	$-0.777833\pi$
$271$	2.85582	−	4.94642i	0.173479	−	0.300474i	0.939634	+	0.342182i	$0.111166\pi$
$272$		0			0
$273$	−8.21177	−	13.2960i	−0.496999	−	0.804712i
$274$		0			0
$275$	1.10014	−	1.90550i	0.0663410	−	0.114906i
$276$		0			0
$277$	−8.29343	−	14.3646i	−0.498304	−	0.863088i	0.501694	−	0.865045i	$-0.332710\pi$
$277$	−8.29343	−	14.3646i	−0.498304	−	0.863088i	−0.999998	+	0.00195715i	$0.999377\pi$
$278$		0			0
$279$	8.77067			0.525086
$280$		0			0
$281$	−12.8040			−0.763824			−0.381912	−	0.924199i	$-0.624734\pi$
$281$	−12.8040			−0.763824			−0.381912	+	0.924199i	$0.624734\pi$
$282$		0			0
$283$	−6.24196	−	10.8114i	−0.371046	−	0.642671i	0.618681	−	0.785643i	$-0.287668\pi$
$283$	−6.24196	−	10.8114i	−0.371046	−	0.642671i	−0.989727	+	0.142972i	$0.954334\pi$
$284$		0			0
$285$	5.44553	−	9.43193i	0.322565	−	0.558699i
$286$		0			0
$287$	−3.89508	+	0.115600i	−0.229920	+	0.00682368i
$288$		0			0
$289$	6.41230	−	11.1064i	0.377194	−	0.653319i
$290$		0			0
$291$	−10.6909	−	18.5172i	−0.626711	−	1.08549i
$292$		0			0
$293$	−18.3771			−1.07360			−0.536800	−	0.843710i	$-0.680367\pi$
$293$	−18.3771			−1.07360			−0.536800	+	0.843710i	$0.680367\pi$
$294$		0			0
$295$	−17.6583			−1.02810
$296$		0			0
$297$	1.72342	+	2.98506i	0.100003	+	0.173211i
$298$		0			0
$299$	−1.42043	+	2.46025i	−0.0821454	+	0.142280i
$300$		0			0
$301$	12.6802	−	0.376329i	0.730874	−	0.0216913i
$302$		0			0
$303$	−14.0151	+	24.2749i	−0.805147	+	1.39456i
$304$		0			0
$305$	−1.47653	−	2.55743i	−0.0845459	−	0.146438i
$306$		0			0
$307$	20.5832			1.17474			0.587371	−	0.809318i	$-0.300163\pi$
$307$	20.5832			1.17474			0.587371	+	0.809318i	$0.300163\pi$
$308$		0			0
$309$	−13.9584			−0.794068
$310$		0			0
$311$	13.0743	+	22.6454i	0.741377	+	1.28410i	0.951869	+	0.306507i	$0.0991601\pi$
$311$	13.0743	+	22.6454i	0.741377	+	1.28410i	−0.210492	+	0.977596i	$0.567507\pi$
$312$		0			0
$313$	−6.40691	+	11.0971i	−0.362140	+	0.627245i	−0.988313	−	0.152439i	$-0.951287\pi$
$313$	−6.40691	+	11.0971i	−0.362140	+	0.627245i	0.626173	+	0.779684i	$0.284620\pi$
$314$		0			0
$315$	−3.06345	−	4.96015i	−0.172606	−	0.279473i
$316$		0			0
$317$	0.213486	−	0.369769i	0.0119906	−	0.0207683i	−0.859968	−	0.510348i	$-0.829517\pi$
$317$	0.213486	−	0.369769i	0.0119906	−	0.0207683i	0.871958	+	0.489580i	$0.162850\pi$
$318$		0			0
$319$	−1.51626	−	2.62623i	−0.0848940	−	0.147041i
$320$		0			0
$321$	0.414427			0.0231311
$322$		0			0
$323$	6.42631			0.357570
$324$		0			0
$325$	−3.16162	−	5.47608i	−0.175375	−	0.303758i
$326$		0			0
$327$	−20.5280	+	35.5555i	−1.13520	+	1.96622i
$328$		0			0
$329$	13.2145	−	24.5419i	0.728538	−	1.35304i
$330$		0			0
$331$	14.3241	−	24.8101i	0.787324	−	1.36368i	−0.140277	−	0.990112i	$-0.544799\pi$
$331$	14.3241	−	24.8101i	0.787324	−	1.36368i	0.927601	−	0.373573i	$-0.121867\pi$
$332$		0			0
$333$	−5.29490	−	9.17103i	−0.290159	−	0.502570i
$334$		0			0
$335$	−7.69385			−0.420360
$336$		0			0
$337$	−3.28857			−0.179140			−0.0895698	−	0.995981i	$-0.528549\pi$
$337$	−3.28857			−0.179140			−0.0895698	+	0.995981i	$0.528549\pi$
$338$		0			0
$339$	−3.67999	−	6.37392i	−0.199869	−	0.346184i
$340$		0			0
$341$	−3.27676	+	5.67552i	−0.177447	+	0.307346i
$342$		0			0
$343$	−18.4469	+	1.64630i	−0.996041	+	0.0888920i
$344$		0			0
$345$	−1.73152	+	2.99908i	−0.0932219	+	0.161465i
$346$		0			0
$347$	16.1179	+	27.9171i	0.865257	+	1.49867i	0.866792	+	0.498670i	$0.166178\pi$
$347$	16.1179	+	27.9171i	0.865257	+	1.49867i	−0.00153529	+	0.999999i	$0.500489\pi$
$348$		0			0
$349$	−18.7933			−1.00598			−0.502992	−	0.864291i	$-0.667767\pi$
$349$	−18.7933			−1.00598			−0.502992	+	0.864291i	$0.667767\pi$
$350$		0			0
$351$	9.90566			0.528725
$352$		0			0
$353$	−13.1794	−	22.8274i	−0.701470	−	1.21498i	−0.967950	−	0.251142i	$-0.919194\pi$
$353$	−13.1794	−	22.8274i	−0.701470	−	1.21498i	0.266480	−	0.963840i	$-0.414139\pi$
$354$		0			0
$355$	3.21750	−	5.57287i	0.170767	−	0.295777i
$356$		0			0
$357$	5.32904	−	9.89707i	0.282042	−	0.523809i
$358$		0			0
$359$	−8.18487	+	14.1766i	−0.431981	+	0.748212i	−0.997044	−	0.0768352i	$-0.975518\pi$
$359$	−8.18487	+	14.1766i	−0.431981	+	0.748212i	0.565063	+	0.825048i	$0.308852\pi$
$360$		0			0
$361$	4.55467	+	7.88892i	0.239720	+	0.415207i
$362$		0			0
$363$	−20.8392			−1.09377
$364$		0			0
$365$	−17.0742			−0.893706
$366$		0			0
$367$	6.98291	+	12.0948i	0.364505	+	0.631341i	0.988697	−	0.149930i	$-0.0479049\pi$
$367$	6.98291	+	12.0948i	0.364505	+	0.631341i	−0.624192	+	0.781271i	$0.714572\pi$
$368$		0			0
$369$	−0.974259	+	1.68747i	−0.0507179	+	0.0878460i
$370$		0			0
$371$	2.93132	+	4.74622i	0.152186	+	0.246411i
$372$		0			0
$373$	−2.21829	+	3.84219i	−0.114859	+	0.198941i	−0.917723	−	0.397220i	$-0.869975\pi$
$373$	−2.21829	+	3.84219i	−0.114859	+	0.198941i	0.802865	+	0.596161i	$0.203308\pi$
$374$		0			0
$375$	−12.5117	−	21.6708i	−0.646099	−	1.11908i
$376$		0			0
$377$	−8.71493			−0.448842
$378$		0			0
$379$	3.47569			0.178534			0.0892670	−	0.996008i	$-0.471548\pi$
$379$	3.47569			0.178534			0.0892670	+	0.996008i	$0.471548\pi$
$380$		0			0
$381$	−1.56162	−	2.70481i	−0.0800044	−	0.138572i
$382$		0			0
$383$	−7.31187	+	12.6645i	−0.373619	+	0.647127i	−0.990119	−	0.140228i	$-0.955217\pi$
$383$	−7.31187	+	12.6645i	−0.373619	+	0.647127i	0.616500	+	0.787355i	$0.288550\pi$
$384$		0			0
$385$	4.35424	−	0.129227i	0.221913	−	0.00658604i
$386$		0			0
$387$	3.17164	−	5.49344i	0.161223	−	0.279247i
$388$		0			0
$389$	−8.20978	−	14.2198i	−0.416252	−	0.720970i	0.579307	−	0.815110i	$-0.303323\pi$
$389$	−8.20978	−	14.2198i	−0.416252	−	0.720970i	−0.995559	+	0.0941396i	$0.969990\pi$
$390$		0			0
$391$	−2.04338			−0.103338
$392$		0			0
$393$	−25.4880			−1.28570
$394$		0			0
$395$	1.06924	+	1.85198i	0.0537994	+	0.0931832i
$396$		0			0
$397$	1.10084	−	1.90671i	0.0552497	−	0.0956953i	−0.837078	−	0.547084i	$-0.815738\pi$
$397$	1.10084	−	1.90671i	0.0552497	−	0.0956953i	0.892327	+	0.451389i	$0.149071\pi$
$398$		0			0
$399$	−17.2926	+	0.513220i	−0.865714	+	0.0256931i
$400$		0			0
$401$	4.42622	−	7.66643i	0.221035	−	0.382843i	−0.734088	−	0.679055i	$-0.762390\pi$
$401$	4.42622	−	7.66643i	0.221035	−	0.382843i	0.955122	+	0.296211i	$0.0957233\pi$
$402$		0			0
$403$	9.41686	+	16.3105i	0.469087	+	0.812483i
$404$		0			0
$405$	18.6856			0.928497
$406$		0			0
$407$	7.91279			0.392222
$408$		0			0
$409$	1.83363	+	3.17595i	0.0906673	+	0.157040i	0.907792	−	0.419420i	$-0.137767\pi$
$409$	1.83363	+	3.17595i	0.0906673	+	0.157040i	−0.817125	+	0.576461i	$0.804433\pi$
$410$		0			0
$411$	7.53429	−	13.0498i	0.371639	−	0.643698i
$412$		0			0
$413$	14.7394	+	23.8651i	0.725276	+	1.17432i
$414$		0			0
$415$	−7.09251	+	12.2846i	−0.348157	+	0.603026i
$416$		0			0
$417$	−6.99659	−	12.1185i	−0.342625	−	0.593443i
$418$		0			0
$419$	−32.0724			−1.56684			−0.783420	−	0.621493i	$-0.786526\pi$
$419$	−32.0724			−1.56684			−0.783420	+	0.621493i	$0.786526\pi$
$420$		0			0
$421$	−10.5009			−0.511781			−0.255891	−	0.966706i	$-0.582369\pi$
$421$	−10.5009			−0.511781			−0.255891	+	0.966706i	$0.582369\pi$
$422$		0			0
$423$	−6.96878	−	12.0703i	−0.338834	−	0.586877i
$424$		0			0
$425$	2.27410	−	3.93886i	0.110310	−	0.191063i
$426$		0			0
$427$	−2.22390	+	4.13022i	−0.107622	+	0.199875i
$428$		0			0
$429$	2.91942	−	5.05659i	0.140951	−	0.244134i
$430$		0			0
$431$	18.8228	+	32.6021i	0.906663	+	1.57039i	0.818669	+	0.574265i	$0.194712\pi$
$431$	18.8228	+	32.6021i	0.906663	+	1.57039i	0.0879936	+	0.996121i	$0.471954\pi$
$432$		0			0
$433$	9.15378			0.439903			0.219951	−	0.975511i	$-0.429410\pi$
$433$	9.15378			0.439903			0.219951	+	0.975511i	$0.429410\pi$
$434$		0			0
$435$	−10.6236			−0.509364
$436$		0			0
$437$	1.57247	+	2.72360i	0.0752215	+	0.130287i
$438$		0			0
$439$	−9.59019	+	16.6107i	−0.457715	+	0.792785i	−0.998840	−	0.0481571i	$-0.984665\pi$
$439$	−9.59019	+	16.6107i	−0.457715	+	0.792785i	0.541125	+	0.840942i	$0.317999\pi$
$440$		0			0
$441$	−4.14657	+	8.28048i	−0.197456	+	0.394309i
$442$		0			0
$443$	−0.351260	+	0.608399i	−0.0166888	+	0.0289059i	−0.874249	−	0.485477i	$-0.838646\pi$
$443$	−0.351260	+	0.608399i	−0.0166888	+	0.0289059i	0.857560	+	0.514383i	$0.171979\pi$
$444$		0			0
$445$	−7.25771	−	12.5707i	−0.344049	−	0.595910i
$446$		0			0
$447$	17.5375			0.829496
$448$		0			0
$449$	28.3683			1.33878			0.669392	−	0.742910i	$-0.266555\pi$
$449$	28.3683			1.33878			0.669392	+	0.742910i	$0.266555\pi$
$450$		0			0
$451$	−0.727975	−	1.26089i	−0.0342790	−	0.0593730i
$452$		0			0
$453$	−3.43935	+	5.95713i	−0.161595	+	0.279890i
$454$		0			0
$455$	5.93505	−	11.0226i	0.278240	−	0.516746i
$456$		0			0
$457$	−2.49028	+	4.31329i	−0.116490	+	0.201767i	−0.918375	−	0.395712i	$-0.870498\pi$
$457$	−2.49028	+	4.31329i	−0.116490	+	0.201767i	0.801884	+	0.597480i	$0.203831\pi$
$458$		0			0
$459$	3.56249	+	6.17042i	0.166283	+	0.288011i
$460$		0			0
$461$	33.4498			1.55791			0.778956	−	0.627078i	$-0.215749\pi$
$461$	33.4498			1.55791			0.778956	+	0.627078i	$0.215749\pi$
$462$		0			0
$463$	−8.58397			−0.398931			−0.199465	−	0.979905i	$-0.563921\pi$
$463$	−8.58397			−0.398931			−0.199465	+	0.979905i	$0.563921\pi$
$464$		0			0
$465$	11.4793	+	19.8827i	0.532339	+	0.922038i
$466$		0			0
$467$	6.68463	−	11.5781i	0.309328	−	0.535772i	−0.668888	−	0.743364i	$-0.733229\pi$
$467$	6.68463	−	11.5781i	0.309328	−	0.535772i	0.978216	+	0.207592i	$0.0665626\pi$
$468$		0			0
$469$	6.42206	+	10.3982i	0.296543	+	0.480145i
$470$		0			0
$471$	−2.83895	+	4.91720i	−0.130812	+	0.226572i
$472$		0			0
$473$	2.36987	+	4.10474i	0.108967	+	0.188736i
$474$		0			0
$475$	−7.00008			−0.321186
$476$		0			0
$477$	2.78940			0.127718
$478$		0			0
$479$	9.98362	+	17.2921i	0.456163	+	0.790098i	0.998754	−	0.0498991i	$-0.0158900\pi$
$479$	9.98362	+	17.2921i	0.456163	+	0.790098i	−0.542591	+	0.839997i	$0.682557\pi$
$480$		0			0
$481$	11.3700	−	19.6934i	0.518428	−	0.897943i
$482$		0			0
$483$	5.49855	−	0.163189i	0.250193	−	0.00742535i
$484$		0			0
$485$	8.56427	−	14.8337i	0.388883	−	0.673566i
$486$		0			0
$487$	17.6255	+	30.5283i	0.798689	+	1.38337i	0.920470	+	0.390813i	$0.127806\pi$
$487$	17.6255	+	30.5283i	0.798689	+	1.38337i	−0.121781	+	0.992557i	$0.538861\pi$
$488$		0			0
$489$	−43.4373			−1.96430
$490$		0			0
$491$	10.6733			0.481680			0.240840	−	0.970565i	$-0.422577\pi$
$491$	10.6733			0.481680			0.240840	+	0.970565i	$0.422577\pi$
$492$		0			0
$493$	−3.13426	−	5.42869i	−0.141160	−	0.244496i
$494$		0			0
$495$	1.08911	−	1.88639i	0.0489517	−	0.0847868i
$496$		0			0
$497$	−10.2174	+	0.303237i	−0.458312	+	0.0136020i
$498$		0			0
$499$	20.0916	−	34.7997i	0.899424	−	1.55785i	0.0711930	−	0.997463i	$-0.477319\pi$
$499$	20.0916	−	34.7997i	0.899424	−	1.55785i	0.828231	−	0.560386i	$-0.189347\pi$
$500$		0			0
$501$	−4.76204	−	8.24809i	−0.212752	−	0.368497i
$502$		0			0
$503$	9.89782			0.441322			0.220661	−	0.975351i	$-0.429179\pi$
$503$	9.89782			0.441322			0.220661	+	0.975351i	$0.429179\pi$
$504$		0			0
$505$	−22.4545			−0.999211
$506$		0			0
$507$	5.12470	+	8.87623i	0.227596	+	0.394207i
$508$		0			0
$509$	6.02205	−	10.4305i	0.266923	−	0.462324i	−0.701143	−	0.713021i	$-0.747326\pi$
$509$	6.02205	−	10.4305i	0.266923	−	0.462324i	0.968066	+	0.250697i	$0.0806598\pi$
$510$		0			0
$511$	14.2519	+	23.0758i	0.630465	+	1.02081i
$512$		0			0
$513$	5.48299	−	9.49681i	0.242080	−	0.419295i
$514$		0			0
$515$	−5.59092	−	9.68376i	−0.246366	−	0.426718i
$516$		0			0
$517$	10.4143			0.458019
$518$		0			0
$519$	7.86195			0.345101
$520$		0			0
$521$	19.8928	+	34.4553i	0.871518	+	1.50951i	0.860426	+	0.509576i	$0.170198\pi$
$521$	19.8928	+	34.4553i	0.871518	+	1.50951i	0.0110927	+	0.999938i	$0.496469\pi$
$522$		0			0
$523$	−17.1822	+	29.7605i	−0.751327	+	1.30134i	0.195853	+	0.980633i	$0.437252\pi$
$523$	−17.1822	+	29.7605i	−0.751327	+	1.30134i	−0.947180	+	0.320703i	$0.896081\pi$
$524$		0			0
$525$	−5.80484	+	10.7807i	−0.253344	+	0.470510i
$526$		0			0
$527$	−6.77340	+	11.7319i	−0.295054	+	0.511048i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	14.0258			0.608666
$532$		0			0
$533$	−4.18415			−0.181236
$534$		0			0
$535$	0.165995	+	0.287512i	0.00717659	+	0.0124302i
$536$		0			0
$537$	23.6116	−	40.8965i	1.01892	−	1.76481i
$538$		0			0
$539$	−3.80914	−	5.77688i	−0.164071	−	0.248828i
$540$		0			0
$541$	−1.68562	+	2.91959i	−0.0724706	+	0.125523i	−0.899984	−	0.435924i	$-0.856422\pi$
$541$	−1.68562	+	2.91959i	−0.0724706	+	0.125523i	0.827513	+	0.561447i	$0.189755\pi$
$542$		0			0
$543$	4.97712	+	8.62062i	0.213589	+	0.369946i
$544$		0			0
$545$	−32.8891			−1.40882
$546$		0			0
$547$	11.9057			0.509050			0.254525	−	0.967066i	$-0.418081\pi$
$547$	11.9057			0.509050			0.254525	+	0.967066i	$0.418081\pi$
$548$		0			0
$549$	1.17279	+	2.03134i	0.0500536	+	0.0866953i
$550$		0			0
$551$	−4.82389	+	8.35522i	−0.205505	+	0.355945i
$552$		0			0
$553$	1.61045	−	2.99093i	0.0684833	−	0.127187i
$554$		0			0
$555$	13.8602	−	24.0066i	0.588333	−	1.01902i
$556$		0			0
$557$	17.7090	+	30.6729i	0.750355	+	1.29965i	0.947651	+	0.319309i	$0.103451\pi$
$557$	17.7090	+	30.6729i	0.750355	+	1.29965i	−0.197295	+	0.980344i	$0.563216\pi$
$558$		0			0
$559$	13.6212			0.576117
$560$		0			0
$561$	4.19979			0.177315
$562$		0			0
$563$	−20.0435	−	34.7164i	−0.844733	−	1.46312i	−0.885853	−	0.463966i	$-0.846426\pi$
$563$	−20.0435	−	34.7164i	−0.844733	−	1.46312i	0.0411201	−	0.999154i	$-0.486907\pi$
$564$		0			0
$565$	2.94797	−	5.10603i	0.124022	−	0.214812i
$566$		0			0
$567$	−15.5969	−	25.2536i	−0.655009	−	1.06055i
$568$		0			0
$569$	20.6226	−	35.7194i	0.864544	−	1.49743i	−0.00295553	−	0.999996i	$-0.500941\pi$
$569$	20.6226	−	35.7194i	0.864544	−	1.49743i	0.867499	−	0.497438i	$-0.165726\pi$
$570$		0			0
$571$	10.2410	+	17.7379i	0.428571	+	0.742307i	0.996746	−	0.0806007i	$-0.0256838\pi$
$571$	10.2410	+	17.7379i	0.428571	+	0.742307i	−0.568175	+	0.822907i	$0.692351\pi$
$572$		0			0
$573$	7.60683			0.317780
$574$		0			0
$575$	2.22582			0.0928233
$576$		0			0
$577$	−14.0890	−	24.4029i	−0.586534	−	1.01591i	−0.994682	−	0.102991i	$-0.967159\pi$
$577$	−14.0890	−	24.4029i	−0.586534	−	1.01591i	0.408148	−	0.912916i	$-0.366175\pi$
$578$		0			0
$579$	−19.2961	+	33.4219i	−0.801920	+	1.38897i
$580$		0			0
$581$	22.5227	−	0.668441i	0.934399	−	0.0277316i
$582$		0			0
$583$	−1.04213	+	1.80503i	−0.0431607	+	0.0747565i
$584$		0			0
$585$	−3.12991	−	5.42116i	−0.129406	−	0.224137i
$586$		0			0
$587$	−28.7008			−1.18461			−0.592304	−	0.805715i	$-0.701781\pi$
$587$	−28.7008			−1.18461			−0.592304	+	0.805715i	$0.701781\pi$
$588$		0			0
$589$	20.8497			0.859097
$590$		0			0
$591$	12.6994	+	21.9960i	0.522383	+	0.904794i
$592$		0			0
$593$	20.8741	−	36.1551i	0.857198	−	1.48471i	−0.0173926	−	0.999849i	$-0.505537\pi$
$593$	20.8741	−	36.1551i	0.857198	−	1.48471i	0.874591	−	0.484862i	$-0.161130\pi$
$594$		0			0
$595$	9.00066	−	0.267126i	0.368991	−	0.0109511i
$596$		0			0
$597$	−21.1814	+	36.6872i	−0.866896	+	1.50151i
$598$		0			0
$599$	−10.1173	−	17.5237i	−0.413381	−	0.715997i	0.581876	−	0.813278i	$-0.302319\pi$
$599$	−10.1173	−	17.5237i	−0.413381	−	0.715997i	−0.995257	+	0.0972803i	$0.968986\pi$
$600$		0			0
$601$	−5.85589			−0.238867			−0.119433	−	0.992842i	$-0.538108\pi$
$601$	−5.85589			−0.238867			−0.119433	+	0.992842i	$0.538108\pi$
$602$		0			0
$603$	6.11114			0.248865
$604$		0			0
$605$	−8.34693	−	14.4573i	−0.339351	−	0.587773i
$606$		0			0
$607$	22.1393	−	38.3464i	0.898606	−	1.55643i	0.0693298	−	0.997594i	$-0.477914\pi$
$607$	22.1393	−	38.3464i	0.898606	−	1.55643i	0.829277	−	0.558838i	$-0.188753\pi$
$608$		0			0
$609$	8.86754	+	14.3578i	0.359331	+	0.581807i
$610$		0			0
$611$	14.9644	−	25.9191i	0.605396	−	1.04858i
$612$		0			0
$613$	−20.8218	−	36.0645i	−0.840986	−	1.45663i	−0.889062	−	0.457787i	$-0.848642\pi$
$613$	−20.8218	−	36.0645i	−0.840986	−	1.45663i	0.0480763	−	0.998844i	$-0.484691\pi$
$614$		0			0
$615$	−5.10054			−0.205674
$616$		0			0
$617$	−29.3910			−1.18324			−0.591619	−	0.806217i	$-0.701511\pi$
$617$	−29.3910			−1.18324			−0.591619	+	0.806217i	$0.701511\pi$
$618$		0			0
$619$	−5.28116	−	9.14724i	−0.212268	−	0.367659i	0.740156	−	0.672435i	$-0.234752\pi$
$619$	−5.28116	−	9.14724i	−0.212268	−	0.367659i	−0.952424	+	0.304777i	$0.901418\pi$
$620$		0			0
$621$	−1.74343	+	3.01971i	−0.0699615	+	0.121177i
$622$		0			0
$623$	−10.9313	+	20.3016i	−0.437953	+	0.813366i
$624$		0			0
$625$	4.45830	−	7.72200i	0.178332	−	0.308880i
$626$		0			0
$627$	−3.23192	−	5.59785i	−0.129070	−	0.223557i
$628$		0			0
$629$	16.3565			0.652178
$630$		0			0
$631$	46.5742			1.85409			0.927045	−	0.374950i	$-0.122340\pi$
$631$	46.5742			1.85409			0.927045	+	0.374950i	$0.122340\pi$
$632$		0			0
$633$	−2.87379	−	4.97755i	−0.114223	−	0.197840i
$634$		0			0
$635$	1.25099	−	2.16677i	0.0496439	−	0.0859858i
$636$		0			0
$637$	−19.8510	+	1.17933i	−0.786524	+	0.0467269i
$638$		0			0
$639$	−2.55562	+	4.42647i	−0.101099	+	0.175109i
$640$		0			0
$641$	−3.53229	−	6.11811i	−0.139517	−	0.241651i	0.787797	−	0.615935i	$-0.211222\pi$
$641$	−3.53229	−	6.11811i	−0.139517	−	0.241651i	−0.927314	+	0.374284i	$0.877888\pi$
$642$		0			0
$643$	14.6500			0.577741			0.288870	−	0.957368i	$-0.406720\pi$
$643$	14.6500			0.577741			0.288870	+	0.957368i	$0.406720\pi$
$644$		0			0
$645$	16.6045			0.653801
$646$		0			0
$647$	−1.61862	−	2.80354i	−0.0636347	−	0.110219i	0.832453	−	0.554096i	$-0.186936\pi$
$647$	−1.61862	−	2.80354i	−0.0636347	−	0.110219i	−0.896088	+	0.443877i	$0.853603\pi$
$648$		0			0
$649$	−5.24008	+	9.07609i	−0.205691	+	0.356268i
$650$		0			0
$651$	17.2897	−	32.1103i	0.677635	−	1.25850i
$652$		0			0
$653$	22.9334	−	39.7217i	0.897451	−	1.55443i	0.0667105	−	0.997772i	$-0.478750\pi$
$653$	22.9334	−	39.7217i	0.897451	−	1.55443i	0.830741	−	0.556659i	$-0.187917\pi$
$654$		0			0
$655$	−10.2090	−	17.6825i	−0.398898	−	0.690912i
$656$		0			0
$657$	13.5619			0.529099
$658$		0			0
$659$	33.3690			1.29987			0.649937	−	0.759988i	$-0.274795\pi$
$659$	33.3690			1.29987			0.649937	+	0.759988i	$0.274795\pi$
$660$		0			0
$661$	−5.54098	−	9.59726i	−0.215519	−	0.373290i	0.737914	−	0.674895i	$-0.235811\pi$
$661$	−5.54098	−	9.59726i	−0.215519	−	0.373290i	−0.953433	+	0.301605i	$0.902478\pi$
$662$		0			0
$663$	6.03474	−	10.4525i	0.234370	−	0.405941i
$664$		0			0
$665$	−7.28245	−	11.7913i	−0.282401	−	0.457247i
$666$		0			0
$667$	1.53386	−	2.65672i	0.0593912	−	0.102869i
$668$		0			0
$669$	−15.3130	−	26.5229i	−0.592036	−	1.02544i
$670$		0			0
$671$	−1.75264			−0.0676600
$672$		0			0
$673$	4.48730			0.172973			0.0864863	−	0.996253i	$-0.472436\pi$
$673$	4.48730			0.172973			0.0864863	+	0.996253i	$0.472436\pi$
$674$		0			0
$675$	−3.88057	−	6.72134i	−0.149363	−	0.258705i
$676$		0			0
$677$	−2.99559	+	5.18852i	−0.115130	+	0.199411i	−0.917832	−	0.396970i	$-0.870062\pi$
$677$	−2.99559	+	5.18852i	−0.115130	+	0.199411i	0.802702	+	0.596381i	$0.203395\pi$
$678$		0			0
$679$	−27.1964	+	0.807149i	−1.04370	+	0.0309755i
$680$		0			0
$681$	−25.4858	+	44.1427i	−0.976618	+	1.69155i
$682$		0			0
$683$	−2.51795	−	4.36121i	−0.0963466	−	0.166877i	0.813823	−	0.581112i	$-0.197382\pi$
$683$	−2.51795	−	4.36121i	−0.0963466	−	0.166877i	−0.910170	+	0.414235i	$0.864049\pi$
$684$		0			0
$685$	12.0712			0.461215
$686$		0			0
$687$	49.2582			1.87932
$688$		0			0
$689$	2.99491	+	5.18734i	0.114097	+	0.197622i
$690$		0			0
$691$	−9.03556	+	15.6500i	−0.343729	+	0.595356i	−0.985122	−	0.171857i	$-0.945023\pi$
$691$	−9.03556	+	15.6500i	−0.343729	+	0.595356i	0.641393	+	0.767212i	$0.278357\pi$
$692$		0			0
$693$	−3.45853	+	0.102644i	−0.131379	+	0.00389912i
$694$		0			0
$695$	5.60484	−	9.70787i	0.212604	−	0.368240i
$696$		0			0
$697$	−1.50480	−	2.60639i	−0.0569983	−	0.0987240i
$698$		0			0
$699$	21.8112			0.824974
$700$		0			0
$701$	−21.4949			−0.811851			−0.405926	−	0.913906i	$-0.633051\pi$
$701$	−21.4949			−0.811851			−0.405926	+	0.913906i	$0.633051\pi$
$702$		0			0
$703$	−12.5871	−	21.8014i	−0.474730	−	0.822257i
$704$		0			0
$705$	18.2418	−	31.5958i	0.687028	−	1.18997i
$706$		0			0
$707$	18.7428	+	30.3472i	0.704894	+	1.14132i
$708$		0			0
$709$	−13.1340	+	22.7488i	−0.493259	+	0.854349i	−0.999970	−	0.00776668i	$-0.997528\pi$
$709$	−13.1340	+	22.7488i	−0.493259	+	0.854349i	0.506711	+	0.862116i	$0.330861\pi$
$710$		0			0
$711$	−0.849286	−	1.47101i	−0.0318507	−	0.0551671i
$712$		0			0
$713$	−6.62960			−0.248280
$714$		0			0
$715$	4.67739			0.174924
$716$		0			0
$717$	19.2189	+	33.2882i	0.717745	+	1.24317i
$718$		0			0
$719$	6.10584	−	10.5756i	0.227709	−	0.394404i	−0.729420	−	0.684067i	$-0.760210\pi$
$719$	6.10584	−	10.5756i	0.227709	−	0.394404i	0.957129	+	0.289663i	$0.0935431\pi$
$720$		0			0
$721$	−8.42084	+	15.6392i	−0.313608	+	0.582433i
$722$		0			0
$723$	12.3672	−	21.4207i	0.459942	−	0.796643i
$724$		0			0
$725$	3.41410	+	5.91339i	0.126796	+	0.219618i
$726$		0			0
$727$	31.7476			1.17745			0.588726	−	0.808333i	$-0.299630\pi$
$727$	31.7476			1.17745			0.588726	+	0.808333i	$0.299630\pi$
$728$		0			0
$729$	6.90756			0.255836
$730$		0			0
$731$	4.89877	+	8.48492i	0.181188	+	0.313826i
$732$		0			0
$733$	−11.4666	+	19.8607i	−0.423528	+	0.733572i	−0.996282	−	0.0861555i	$-0.972542\pi$
$733$	−11.4666	+	19.8607i	−0.423528	+	0.733572i	0.572754	+	0.819728i	$0.305875\pi$
$734$		0			0
$735$	−24.1986	+	1.43763i	−0.892579	+	0.0530276i
$736$		0			0
$737$	−2.28315	+	3.95453i	−0.0841009	+	0.145667i
$738$		0			0
$739$	−18.2469	−	31.6046i	−0.671225	−	1.16260i	−0.977557	−	0.210671i	$-0.932435\pi$
$739$	−18.2469	−	31.6046i	−0.671225	−	1.16260i	0.306332	−	0.951925i	$-0.400898\pi$
$740$		0			0
$741$	−18.5760			−0.682406
$742$		0			0
$743$	43.3428			1.59009			0.795046	−	0.606549i	$-0.207446\pi$
$743$	43.3428			1.59009			0.795046	+	0.606549i	$0.207446\pi$
$744$		0			0
$745$	7.02449	+	12.1668i	0.257357	+	0.445756i
$746$		0			0
$747$	5.63350	−	9.75751i	0.206119	−	0.357009i
$748$		0			0
$749$	0.250015	−	0.464328i	0.00913537	−	0.0169662i
$750$		0			0
$751$	−26.1136	+	45.2302i	−0.952901	+	1.65047i	−0.213800	+	0.976878i	$0.568584\pi$
$751$	−26.1136	+	45.2302i	−0.952901	+	1.65047i	−0.739101	+	0.673595i	$0.764749\pi$
$752$		0			0
$753$	−17.0237	−	29.4859i	−0.620379	−	1.07453i
$754$		0			0
$755$	−5.51040			−0.200544
$756$		0			0
$757$	8.29338			0.301428			0.150714	−	0.988577i	$-0.451843\pi$
$757$	8.29338			0.301428			0.150714	+	0.988577i	$0.451843\pi$
$758$		0			0
$759$	1.02766	+	1.77995i	0.0373016	+	0.0646082i
$760$		0			0
$761$	1.72204	−	2.98266i	0.0624239	−	0.108121i	−0.833124	−	0.553086i	$-0.813450\pi$
$761$	1.72204	−	2.98266i	0.0624239	−	0.108121i	0.895548	+	0.444964i	$0.146784\pi$
$762$		0			0
$763$	27.4526	+	44.4496i	0.993850	+	1.60918i
$764$		0			0
$765$	2.25129	−	3.89935i	0.0813957	−	0.140981i
$766$		0			0
$767$	15.0591	+	26.0831i	0.543753	+	0.941808i
$768$		0			0
$769$	−36.2297			−1.30648			−0.653239	−	0.757152i	$-0.726590\pi$
$769$	−36.2297			−1.30648			−0.653239	+	0.757152i	$0.726590\pi$
$770$		0			0
$771$	19.0948			0.687681
$772$		0			0
$773$	19.5220	+	33.8131i	0.702157	+	1.21617i	0.967708	+	0.252075i	$0.0811130\pi$
$773$	19.5220	+	33.8131i	0.702157	+	1.21617i	−0.265550	+	0.964097i	$0.585554\pi$
$774$		0			0
$775$	7.37816	−	12.7793i	0.265031	−	0.459048i
$776$		0			0
$777$	−44.0139	+	1.30627i	−1.57899	+	0.0468622i
$778$		0			0
$779$	−2.31602	+	4.01146i	−0.0829799	+	0.143725i
$780$		0			0
$781$	−1.90959	−	3.30750i	−0.0683303	−	0.118352i
$782$		0			0
$783$	−10.6967			−0.382269
$784$		0			0
$785$	−4.54845			−0.162341
$786$		0			0
$787$	−1.22694	−	2.12512i	−0.0437357	−	0.0757525i	0.843329	−	0.537398i	$-0.180593\pi$
$787$	−1.22694	−	2.12512i	−0.0437357	−	0.0757525i	−0.887065	+	0.461645i	$0.847259\pi$
$788$		0			0
$789$	8.34994	−	14.4625i	0.297266	−	0.514880i
$790$		0			0
$791$	−9.36146	+	0.277834i	−0.332855	+	0.00987866i
$792$		0			0
$793$	−2.51840	+	4.36199i	−0.0894309	+	0.154899i
$794$		0			0
$795$	3.65084	+	6.32344i	0.129482	+	0.224269i
$796$		0			0
$797$	−5.36871			−0.190170			−0.0950848	−	0.995469i	$-0.530312\pi$
$797$	−5.36871			−0.190170			−0.0950848	+	0.995469i	$0.530312\pi$
$798$		0			0
$799$	21.5274			0.761583
$800$		0			0
$801$	5.76472	+	9.98479i	0.203686	+	0.352795i
$802$		0			0
$803$	−5.06677	+	8.77591i	−0.178802	+	0.309695i
$804$		0			0
$805$	2.31561	+	3.74929i	0.0816144	+	0.132145i
$806$		0			0
$807$	8.71808	−	15.1002i	0.306891	−	0.531551i
$808$		0			0
$809$	16.9603	+	29.3762i	0.596294	+	1.03281i	0.993363	+	0.115023i	$0.0366941\pi$
$809$	16.9603	+	29.3762i	0.596294	+	1.03281i	−0.397069	+	0.917789i	$0.629973\pi$
$810$		0			0
$811$	−33.2078			−1.16608			−0.583042	−	0.812442i	$-0.698138\pi$
$811$	−33.2078			−1.16608			−0.583042	+	0.812442i	$0.698138\pi$
$812$		0			0
$813$	−11.8755			−0.416491
$814$		0			0
$815$	−17.3984	−	30.1349i	−0.609439	−	1.05558i
$816$		0			0
$817$	7.53963	−	13.0590i	0.263778	−	0.456878i
$818$		0			0
$819$	−4.71415	+	8.75511i	−0.164726	+	0.305928i
$820$		0			0
$821$	−21.5519	+	37.3290i	−0.752167	+	1.30279i	0.194604	+	0.980882i	$0.437658\pi$
$821$	−21.5519	+	37.3290i	−0.752167	+	1.30279i	−0.946770	+	0.321909i	$0.895675\pi$
$822$		0			0
$823$	−14.7391	−	25.5289i	−0.513773	−	0.889882i	−0.999872	−	0.0159778i	$-0.994914\pi$
$823$	−14.7391	−	25.5289i	−0.513773	−	0.889882i	0.486099	−	0.873904i	$-0.338419\pi$
$824$		0			0
$825$	−4.57476			−0.159273
$826$		0			0
$827$	29.2293			1.01640			0.508202	−	0.861238i	$-0.330310\pi$
$827$	29.2293			1.01640			0.508202	+	0.861238i	$0.330310\pi$
$828$		0			0
$829$	15.3456	+	26.5793i	0.532974	+	0.923138i	0.999258	+	0.0385033i	$0.0122590\pi$
$829$	15.3456	+	26.5793i	0.532974	+	0.923138i	−0.466284	+	0.884635i	$0.654408\pi$
$830$		0			0
$831$	−17.2435	+	29.8666i	−0.598170	+	1.03606i
$832$		0			0
$833$	−7.87388	−	11.9414i	−0.272814	−	0.413745i
$834$		0			0
$835$	3.81478	−	6.60739i	0.132016	−	0.228658i
$836$		0			0
$837$	11.5582	+	20.0195i	0.399511	+	0.691974i
$838$		0			0
$839$	−47.3773			−1.63565			−0.817823	−	0.575470i	$-0.804819\pi$
$839$	−47.3773			−1.63565			−0.817823	+	0.575470i	$0.804819\pi$
$840$		0			0
$841$	−19.5891			−0.675487
$842$		0			0
$843$	13.3109	+	23.0551i	0.458451	+	0.794061i
$844$		0			0
$845$	−4.10530	+	7.11059i	−0.141227	+	0.244612i
$846$		0			0
$847$	−12.5718	+	23.3484i	−0.431973	+	0.802260i
$848$		0			0
$849$	−12.9781	+	22.4788i	−0.445408	+	0.771469i
$850$		0			0
$851$	4.00232	+	6.93223i	0.137198	+	0.237634i
$852$		0			0
$853$	−42.0607			−1.44013			−0.720065	−	0.693907i	$-0.755888\pi$
$853$	−42.0607			−1.44013			−0.720065	+	0.693907i	$0.755888\pi$
$854$		0			0
$855$	−6.92987			−0.236997
$856$		0			0
$857$	−25.1953	−	43.6395i	−0.860654	−	1.49070i	−0.871299	−	0.490753i	$-0.836722\pi$
$857$	−25.1953	−	43.6395i	−0.860654	−	1.49070i	0.0106449	−	0.999943i	$-0.496612\pi$
$858$		0			0
$859$	−16.0150	+	27.7387i	−0.546423	+	0.946433i	0.452093	+	0.891971i	$0.350678\pi$
$859$	−16.0150	+	27.7387i	−0.546423	+	0.946433i	−0.998516	+	0.0544616i	$0.982656\pi$
$860$		0			0
$861$	4.25743	+	6.89337i	0.145093	+	0.234926i
$862$		0			0
$863$	−17.8475	+	30.9128i	−0.607536	+	1.05228i	0.384109	+	0.923288i	$0.374509\pi$
$863$	−17.8475	+	30.9128i	−0.607536	+	1.05228i	−0.991645	+	0.128995i	$0.958825\pi$
$864$		0			0
$865$	3.14903	+	5.45428i	0.107070	+	0.185451i
$866$		0			0
$867$	−26.6645			−0.905575
$868$		0			0
$869$	1.26919			0.0430543
$870$		0			0
$871$	6.56138	+	11.3647i	0.222324	+	0.385076i
$872$		0			0
$873$	−6.80250	+	11.7823i	−0.230230	+	0.398770i
$874$		0			0
$875$	−31.8282	+	0.944615i	−1.07599	+	0.0319338i
$876$		0			0
$877$	19.9051	−	34.4767i	0.672148	−	1.16419i	−0.305145	−	0.952306i	$-0.598705\pi$
$877$	19.9051	−	34.4767i	0.672148	−	1.16419i	0.977294	−	0.211889i	$-0.0679616\pi$
$878$		0			0
$879$	19.1045	+	33.0900i	0.644380	+	1.11610i
$880$		0			0
$881$	−14.3634			−0.483915			−0.241957	−	0.970287i	$-0.577789\pi$
$881$	−14.3634			−0.483915			−0.241957	+	0.970287i	$0.577789\pi$
$882$		0			0
$883$	25.5239			0.858949			0.429474	−	0.903079i	$-0.358699\pi$
$883$	25.5239			0.858949			0.429474	+	0.903079i	$0.358699\pi$
$884$		0			0
$885$	18.3573	+	31.7957i	0.617073	+	1.06880i
$886$		0			0
$887$	5.01897	−	8.69311i	0.168520	−	0.291886i	−0.769379	−	0.638792i	$-0.779434\pi$
$887$	5.01897	−	8.69311i	0.168520	−	0.291886i	0.937900	+	0.346906i	$0.112768\pi$
$888$		0			0
$889$	−3.97259	+	0.117901i	−0.133236	+	0.00395426i
$890$		0			0
$891$	5.54496	−	9.60415i	0.185763	−	0.321751i
$892$		0			0
$893$	−16.5662	−	28.6936i	−0.554368	−	0.960193i
$894$		0			0
$895$	37.8296			1.26451
$896$		0			0
$897$	5.90662			0.197216
$898$		0			0
$899$	−10.1689	−	17.6130i	−0.339150	−	0.587426i
$900$		0			0
$901$	−2.15419	+	3.73117i	−0.0717666	+	0.124303i
$902$		0			0
$903$	−13.8598	−	22.4409i	−0.461224	−	0.746787i
$904$		0			0
$905$	−3.98708	+	6.90582i	−0.132535	+	0.229557i
$906$		0			0
$907$	−11.9224	−	20.6502i	−0.395878	−	0.685680i	0.597335	−	0.801992i	$-0.296226\pi$
$907$	−11.9224	−	20.6502i	−0.395878	−	0.685680i	−0.993213	+	0.116312i	$0.962893\pi$
$908$		0			0
$909$	17.8353			0.591561
$910$		0			0
$911$	−12.6212			−0.418159			−0.209080	−	0.977899i	$-0.567047\pi$
$911$	−12.6212			−0.418159			−0.209080	+	0.977899i	$0.567047\pi$
$912$		0			0
$913$	4.20940	+	7.29090i	0.139311	+	0.241293i
$914$		0			0
$915$	−3.06996	+	5.31733i	−0.101490	+	0.175786i
$916$		0			0
$917$	−15.3764	+	28.5570i	−0.507773	+	0.943036i
$918$		0			0
$919$	8.89196	−	15.4013i	0.293319	−	0.508043i	−0.681274	−	0.732029i	$-0.738574\pi$
$919$	8.89196	−	15.4013i	0.293319	−	0.508043i	0.974592	+	0.223986i	$0.0719070\pi$
$920$		0			0
$921$	−21.3980	−	37.0624i	−0.705087	−	1.22125i
$922$		0			0
$923$	−10.9756			−0.361268
$924$		0			0
$925$	−17.8169			−0.585817
$926$		0			0
$927$	4.44081	+	7.69171i	0.145855	+	0.252629i
$928$		0			0
$929$	14.7301	−	25.5132i	0.483278	−	0.837063i	−0.516537	−	0.856265i	$-0.672779\pi$
$929$	14.7301	−	25.5132i	0.483278	−	0.837063i	0.999816	+	0.0192021i	$0.00611260\pi$
$930$		0			0
$931$	−9.85726	+	19.6844i	−0.323059	+	0.645131i
$932$		0			0
$933$	27.1838	−	47.0837i	0.889956	−	1.54145i
$934$		0			0
$935$	1.68219	+	2.91363i	0.0550134	+	0.0952859i
$936$		0			0
$937$	10.6168			0.346837			0.173418	−	0.984848i	$-0.444519\pi$
$937$	10.6168			0.346837			0.173418	+	0.984848i	$0.444519\pi$
$938$		0			0
$939$	26.6421			0.869433
$940$		0			0
$941$	26.0935	+	45.1952i	0.850622	+	1.47332i	0.880647	+	0.473772i	$0.157108\pi$
$941$	26.0935	+	45.1952i	0.850622	+	1.47332i	−0.0300249	+	0.999549i	$0.509559\pi$
$942$		0			0
$943$	0.736426	−	1.27553i	0.0239813	−	0.0415369i
$944$		0			0
$945$	7.28468	−	13.5291i	0.236971	−	0.440102i
$946$		0			0
$947$	20.1715	−	34.9381i	0.655487	−	1.13534i	−0.326284	−	0.945272i	$-0.605797\pi$
$947$	20.1715	−	34.9381i	0.655487	−	1.13534i	0.981771	−	0.190065i	$-0.0608700\pi$
$948$		0			0
$949$	14.5610	+	25.2205i	0.472672	+	0.818691i
$950$		0			0
$951$	−0.887750			−0.0287873
$952$		0			0
$953$	−38.5027			−1.24722			−0.623612	−	0.781734i	$-0.714335\pi$
$953$	−38.5027			−1.24722			−0.623612	+	0.781734i	$0.714335\pi$
$954$		0			0
$955$	3.04685	+	5.27729i	0.0985936	+	0.170769i
$956$		0			0
$957$	−3.15256	+	5.46039i	−0.101908	+	0.176509i
$958$		0			0
$959$	−10.0758	−	16.3141i	−0.325364	−	0.526811i
$960$		0			0
$961$	−6.47578	+	11.2164i	−0.208896	+	0.361819i
$962$		0			0
$963$	−0.131848	−	0.228367i	−0.00424874	−	0.00735904i
$964$		0			0
$965$	−30.9155			−0.995206
$966$		0			0
$967$	−11.0101			−0.354061			−0.177030	−	0.984205i	$-0.556649\pi$
$967$	−11.0101			−0.354061			−0.177030	+	0.984205i	$0.556649\pi$
$968$		0			0
$969$	−6.68071	−	11.5713i	−0.214615	−	0.371724i
$970$		0			0
$971$	5.93481	−	10.2794i	0.190457	−	0.329881i	−0.754945	−	0.655788i	$-0.772336\pi$
$971$	5.93481	−	10.2794i	0.190457	−	0.329881i	0.945402	+	0.325907i	$0.105670\pi$
$972$		0			0
$973$	−17.7985	+	0.528234i	−0.570594	+	0.0169344i
$974$		0			0
$975$	−6.57355	+	11.3857i	−0.210522	+	0.364635i
$976$		0			0
$977$	13.2511	+	22.9517i	0.423942	+	0.734289i	0.996321	−	0.0857003i	$-0.0273128\pi$
$977$	13.2511	+	22.9517i	0.423942	+	0.734289i	−0.572379	+	0.819989i	$0.693979\pi$
$978$		0			0
$979$	−8.61490			−0.275333
$980$		0			0
$981$	26.1235			0.834059
$982$		0			0
$983$	14.3654	+	24.8816i	0.458185	+	0.793600i	0.998865	−	0.0476287i	$-0.0151664\pi$
$983$	14.3654	+	24.8816i	0.458185	+	0.793600i	−0.540680	+	0.841228i	$0.681833\pi$
$984$		0			0
$985$	−10.1732	+	17.6206i	−0.324146	+	0.561438i
$986$		0			0
$987$	−57.9281	+	1.71922i	−1.84387	+	0.0547235i
$988$		0			0
$989$	−2.39738	+	4.15239i	−0.0762324	+	0.132038i
$990$		0			0
$991$	−23.6344	−	40.9359i	−0.750770	−	1.30037i	−0.947450	−	0.319905i	$-0.896349\pi$
$991$	−23.6344	−	40.9359i	−0.750770	−	1.30037i	0.196679	−	0.980468i	$-0.436984\pi$
$992$		0			0
$993$	−59.5645			−1.89022
$994$		0			0
$995$	−33.9360			−1.07584
$996$		0			0
$997$	9.58911	+	16.6088i	0.303690	+	0.526007i	0.976969	−	0.213382i	$-0.0684479\pi$
$997$	9.58911	+	16.6088i	0.303690	+	0.526007i	−0.673279	+	0.739389i	$0.735115\pi$
$998$		0			0
$999$	13.9555	−	24.1717i	0.441534	−	0.764759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.i.a.93.3	✓	14
7.2	even	3		4508.2.a.m.1.5		7
7.4	even	3	inner	644.2.i.a.277.3	yes	14
7.5	odd	6		4508.2.a.l.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.i.a.93.3	✓	14	1.1	even	1	trivial
644.2.i.a.277.3	yes	14	7.4	even	3	inner
4508.2.a.l.1.3		7	7.5	odd	6
4508.2.a.m.1.5		7	7.2	even	3

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03959 - 1.80062i) q^{3} +(0.832793 - 1.44244i) q^{5} +(-2.64459 + 0.0784875i) q^{7} +(-0.661478 + 1.14571i) q^{9} +O(q^{10})\)	\(q+(-1.03959 - 1.80062i) q^{3} +(0.832793 - 1.44244i) q^{5} +(-2.64459 + 0.0784875i) q^{7} +(-0.661478 + 1.14571i) q^{9} +(-0.494262 - 0.856087i) q^{11} -2.84085 q^{13} -3.46304 q^{15} +(-1.02169 - 1.76962i) q^{17} +(-1.57247 + 2.72360i) q^{19} +(2.89060 + 4.68029i) q^{21} +(0.500000 - 0.866025i) q^{23} +(1.11291 + 1.92762i) q^{25} -3.48686 q^{27} +3.06771 q^{29} +(-3.31480 - 5.74140i) q^{31} +(-1.02766 + 1.77995i) q^{33} +(-2.08918 + 3.88002i) q^{35} +(-4.00232 + 6.93223i) q^{37} +(2.95331 + 5.11528i) q^{39} +1.47285 q^{41} -4.79477 q^{43} +(1.10175 + 1.90829i) q^{45} +(-5.26758 + 9.12372i) q^{47} +(6.98768 - 0.415134i) q^{49} +(-2.12427 + 3.67934i) q^{51} +(-1.05423 - 1.82598i) q^{53} -1.64647 q^{55} +6.53887 q^{57} +(-5.30091 - 9.18145i) q^{59} +(0.886494 - 1.53545i) q^{61} +(1.65941 - 3.08186i) q^{63} +(-2.36584 + 4.09776i) q^{65} +(-2.30965 - 4.00044i) q^{67} -2.07917 q^{69} +3.86351 q^{71} +(-5.12559 - 8.87778i) q^{73} +(2.31393 - 4.00785i) q^{75} +(1.37431 + 2.22520i) q^{77} +(-0.641961 + 1.11191i) q^{79} +(5.60933 + 9.71564i) q^{81} -8.51653 q^{83} -3.40343 q^{85} +(-3.18915 - 5.52378i) q^{87} +(4.35745 - 7.54733i) q^{89} +(7.51288 - 0.222971i) q^{91} +(-6.89204 + 11.9374i) q^{93} +(2.61909 + 4.53639i) q^{95} +10.2838 q^{97} +1.30778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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